Forum A+P Vol.14 by POLIS University

Përmbajtja Editorial Projecting the "Third Tirana" of the 21-st Century Building Tirana's Green Future

Prof .Dr.Besnik Aliaj .............................................................................................................................................8

Artikuj Shkencorë Tirana between Historicism & Avangardism The third Tirana

Doc. Sotir Dhamo.................................................................................................................................................12

Tirana Nor then Corridor International Competition Competition Brief.............................................................................................................................................34 GRIMSHAW ARCHITECTS/ BuildingTirana’sGreenFuture......................................................................................40 DAR / Dar’s Tirana North...............................................................................................................................54 WEST 8 / Let Tirana Breathe.................................................................................................................................66 KCAP/Axis of Gentle Heroism...............................................................................................................................80 GMP/ Tirana Green and Smart City......................................................................................................................92 CinoZucchiArchitetti/A Flowing Boulevard, an Urban River..............................................................................98 AS&P / A Green Boulevard for the 21st Century.................................................................................................110 Korça City CenterInternational Competition BOLLES+WILSON / MasterplanKorçaCityCentre.................................................................................................122 DOMUS/ ReconnectingKorça..........................................................................................................................132 JOUBERT ARCHITECTURE/ Korça Mozaique...........................................................................................................144 51N4E/ KorçaCityCenter MasterPlan...................................................................................................................154 Artikuj Shkencorë Kondensimi në sistemet e fasadave të avancuara. Diagrami Glaser

Ark.Endrit Tuzi .................................................................................................................................................156

Mbi Propocionet dhe Format Racionale të Strukturave Inxhinierike

Feti Selmani, Niko Pojani, Musa Stavileci.............................................................................................................166

Mjeshtër i arkitekturës së shekullit të njëzetë

Doc. Dr. Arben Shtylla........................................................................................................................................176

Për Surrealizmin Socialist të Qendros

Besim Tula................................................................................................................................................188

AUA- Unioni Shqiptar i Arkitekteve,Urbanisteve dhe Planifikuesve Deklarata Publike - A ka nevojë për të patur një Urdhër?.........................................................................192

PhD Program at U_ POLIS Architecture & Urban Planning The Notice for admission to the International Doctorate in Architecture and Urban Planning (I.D.A.U.P.) for the academic year 2014/2015 (30rd Cycle) at the University of Ferrara and Polis University of Tirana (Albania) is now available. Starting from August 1, 2014 you can sign up for the competition. The program is the result of an international agreement between the Università degli Studi di Ferrara (Italy) Polis University of Tirana (Albania); in addition, the University of Malta participates in several training and researching activities of the PhD program. The research topics are available on the webpage of the PhD program. Selection application forms, along with all documents listed below must be submitted electronically using the online procedure available on the web page: https:// studiare.unife.it/Start.do. Iinstructions for completing the online application form are available on the following web link: How to register online for the Ph.D. selection. The choice made shall be binding and determine the allocation of available places, which shall be awarded according to the order of the final classification. The Commission shall evaluate the candidates’ qualifications and interviews. For the acceptance of the admission application, each candidate must also have at least 2 recommendation letters written and signed by teachers, experts, researchers or professionals, qualified for the courses’ topics. The interview will be conducted via conference call on the Internet (interviews will be held on October 20th , 2014 at 9.00 a.m. - italian time). After the proceedings approval, the list shall be published on this webpage and on the reserved area.

SPACE FOR THINKING DA

EDITORIAL

Projecting the “Third Tirana” of the 21-st Century Building Tirana’s Green Future Prof. Dr. Besnik Aliaj

The city of Tirana is recognized for its

Tirana entered a new development

own remarkable surrounding landscape

paradigm in the very early 90s: the

and its “organic” origin dating back to the

introduction of the market economy and

Ottoman Empire, although signs of an earlier

freedom of movement shook the temporarily

human settlement existed a long time before.

sleeping entrepreneurial spirit of Albanians.

This is considered the “first” Tirana. Events

Crowds of people and families relocated

of considerable magnitude have occurred in

from the rural and remote locations towards

this territory which has considerably evolved

Tirana and other bigger cities, mostly located

through history.

in the western coastal plain (s) of the country.

The first phase of political and urban

Initially this was totally out of any order or

reforms in Tirana was undertaken from the

logic of formal planning perspective, and

date of its establishment as the capital of

this situation still exists. But despite the

Albania in 1920 up to the fall of the “Berlin

fact that this huge extra-legal energy faced

Wall” at the brink of the ‘90s. These were

the “vacuum” of reactions-measures from

the transformations undertaken under the

the public authorities and institutions, in

regimes of the “Monarchy” and “Centralized

Tirana, during the last 15 years, there exist

Economy”. Thanks to such interventions,

at least two political projects that have been

free from any political and ideological

impacting the present-day trends, and will

prejudices, the city was transformed from a

continue to impact the future. The first

small town (almost a village), to an “ordered”

has been the project of the former mayor

small city: this was a kind of pre-urbanization

of Tirana, Edi Rama (2000-2011) and the

process. This could be considered the era of

second is the project of the actual mayor,

the “new” Tirana, or the “second” Tirana.

Lulzim Basha (2011 – ongoing).

Cv: The former mayor is well-known for

the city’s surrounding area. Such a city

initiating a projects-based process of city

needs a solid vision and long-term effective

beautification

solutions.

and

modernization

(the

coloring facades projects), upgrading parts

The present mayor Lulzim Basha is

of the city (widening streets, bringing back

recognized for applying another strategy

green-space,

informal

which at first looks more modest in terms

settlements), encouraging the cultural and

of public relations, but is based instead on

artistic life of the city (Tirana International Art

a more holistic and systematic approach

Biannual), and branding it internationally,

(drafting and approving a regulatory plan

etc. This was done in a charismatic top-down

of the city, the first since the collapse of

approach and in a situation where citizens

centralized economy); starting a process of

had almost lost confidence and hope in

formalizing extralegal assets, introducing

positive developments. I have written about

low taxes, encouraging self-employment

the successes and failures of such a practice

and an easy-doing-business atmosphere;

in a previous issue of the Forum A+P Journal

opening up strategic infrastructure projects,

(issue nr. 10).

with the objective of integrating the whole

and

demolishing

Currently, one must keep in mind that

city structure in one living organism

Tirana has reached a development typology

(extending the main city boulevard

of a mid-size city in a European-global

towards the northern informal settlements;

perspective. Its population has reached the

planning an alternative northern green

number of 700,000 inhabitants within the

park; introducing an integrated public

administrative borders, and more than a

transport of rail and bus services,

million residents when taking into account

developing a multimodal transport station,

Besnik Aliaj - Co-founder, and Rector of POLIS University. Graduated as Architect-Urban Planner (Polytechnic University of Tirana). Postgraduate studies in real estate (UPT). Diploma “Master in Urban Management” (Urban Management Center, IHS / Erasmus University, Rotterdam, Netherlands). Doctor of Science in Urban Planning (UPT). Professional trainings and scientific research near IPC College Denmark (1994), University of Oslo (1995), University of Florence, Tempus Program (1998), etc. Work experience at local governments 1990-92. 16 years as lecturer at the Faculty of Civil Engineering (UPT). Guest lecturer at the Academy of Fine Arts of Tirana (1994-2005). Co-founder and Executive Director of CoPLAN, Institute for Habitat Development (1997-2005). Work experiences with local/ regional/central government institutions, and with international organizations: World Bank, UN, UNDP, UN Habitat, FAO, OSCE, SOROS, GTZ, ATZ, IHS Rotterdam, ILDPeru, and with governmental institutions of the Netherlands, USA, Austria, Kosovo, etc. Adviser of Albanian Prime-minister on territorial, tourism and property issues (2005-2007). Co-founder of architecture bureau ‘Metro_POLIS’ ltd. Participant in many international conferences, events and networks, including ENHR, AESOP, AEEA, Balkanology network, etc. Author of several publications, scientific articles and local forums, including the Albanian periodical on architecture and urban planning: “Forum A+ P”. Co-founder of TAW - Tirana Bienale of Architecture.

EDITORIAL initiating a new city ring and widening 2

the 1st prize. Meanwhile, 2 others projects

other main entry access roads, etc.).

were considered as innovative and awarded

Such

strategy

was

already

‘innovation’ awards.

structured before the elections thanks

Despite a highly divided city in terms

to the establishment of a distinguished

of political positioning, the competition

citizens and expertise committees, which

served indeed as a good public-professional

helped the actual mayor to develop a good

“educational” event; and a democratic

understanding of the city situation, and

exercise in terms of final decision making.

formulate a political vision and an electoral

The two final concept designs and the two

program, now under implementation. In

innovation awards set different standards

addition, after the elections he continued to

and visions in terms of practice. The first

be consulted by free brainstorming groups

one was focused on maximizing a real-

for feedbacks. This was also followed by a

estate and infrastructure leverage approach,

process of public meetings and discussions,

while the second one was more concerned

as well as intellectual reflections and events

with doing this by restoring public space

over city problems/issues (including Tirana

and maximizing community feelings as

Art Days, Tirana Architecture Weeks, Tirana

instruments against the existing extreme

Design Weeks, etc.) in order to adapt his

individualistic behaviors and the fragmented-

interventions during the current mandate

distorted reality. It is a fact already that the

and include free public opinions.

final winning project (Grimshaw Architects)

This issue of the Forum A+P Journal

somehow mediates among approaches,

focuses most of its attention on the

trying to integrate concerns coming from

experience of the International Competition

people, businesses, professional circles, and

for the Urban Design of the Northern

politicians; although that somehow losses

Extension of the Tirana’s Boulevard and the

the historic chance to do it in a ‘state of art’

Environmental Rehabilitation of the Tirana

standard.

River, by 2012. The competition and its

Of course, what is more important

following city debate drew the attention of

is that the implementation of such a

many well-known international architectural-

project has already started and the core

engineering studios and urban-landscape

financing luckily is already there. But its

design companies. The presence of local

implementation

studios had improved but was still not

burdened by the extreme politicizations of

fully integrated on equal terms. However,

public life in Albania, especially after the

the jury was formed with a balanced set of

political change of the central government

local and international expertise. The final

during the parliamentary elections 2013.

remains

unfortunately

decision surprisingly appointed two winners

The first signs of such central-local

and decided to let the public decide on

political ‘clash’ are already there: including:

the conflict for the improvement of

events that happen once in the life of a city.

Skanderbeg square; the conflict with the

They have the size of magnitude and impact

Prefect over the compensation price for

similar to the strong operations undertaken

the land and housing owners along the

by the former King Zog in a heroic phase

new northern boulevard; the debate with

of the city and nation’s development during

environmentalists over the new ring-road;

which a modern Tirana, the real European

the intervention of central government over

capital of Albanians, was established.

the approved new urban regulatory plan,

This is already a mental jump for

and so on… This practically reduces the

the rational and good governance of

speed of positive changes in the city thanks

our cities in Albania: it is a change of

to such injections of public investment.

thinking and practices despite the nitty-

And this is not good at all for any “side”

gritty fights. Therefore under such existing

involved into this fake conflict under the

circumstances, and imperfect, more than

circumstances of a global recession.

the success of mayor Basha during the next

Nevertheless,

paradoxically

still

election, the important fact is that he has

happens in a very irrational way; ironically,

seriously contributed in the establishment

as the former mayor, also the actual one,

of such qualitative change! One can say that

happens to have become the leader of the

Rama created important precedents, while

opposition. This means that the city project

Basha established a tradition of practices.

and vision of mayor Basha might face

For architecture and city professionals

serious political blocking during further

this is an important lesson to learn, an

implementation. Nevertheless, despite that,

important conclusion to draw. Personally,

it is very important to underline that Mr.

I learned that the struggle for a better

Basha, like his predecessor, has already

city is not just the result of nice and great

set a standard in somehow projecting the

“pictorial” visions designed by architects

“third” Tirana, or the “new Tirana of the

and planners and is also not just the result

21st century” with a broader vision and a

of participatory processes. Of course, it

metropolitan flavor. Indeed, their projects

must be embedded in the “blood” of the

are also somehow complementing each

community and policymakers. But above all

other, and neutralizing differences of

one can say: politicians, who indeed have

respective strategies and approaches.

not the best reputation among professionals,

From the other side, the urban

are instead, not ‘enemies’ but our ‘partners’

regeneration of public space a long

in the battle for a better balance of interests,

Lana River, or the tram and multimodal

for a better city and fair society. Of course

station project, or the competition and

there are no global recipes for this, but any

implementation of the project of the new

actor must find his/her own model in his/

northern boulevard of Tirana, are indeed

her own city!

EDITORIAL

Tirana Public Transport Terminal Project by the Consortium between Italferr SpA (the authorised signatory for its Consortium partners), CMS Adonnino Ascoli & Casavola Scamoni Sh.P.K and A&B Business Consulting SH.P.K. (the â&#x20AC;&#x153;Consultantâ&#x20AC;?)

SCIENTIFIC ARTICLE

Tirana between Historicism & Avant-gardism The Third Tirana Sotir Dhamo The article is reviewed by: Dr. Vera Bushati ; PhD. Antonino Di Raimo

Introduction

Cv:

The motivation for this article is generated in Tirana was directly related to political

Sotir Dhamo is an architect and urban planner with a great deal of experience in the fi elds of design and urban planning. He is also the author of several research studies conducted by the Institute of Architecture and Urban Planning, the Ministry of Public Work and Territory Regulation, Co-Plan, the Institute for Habitat Developemnt, etc. Sotir is one of the founders of POLIS University, the International School of Architecture and Urban Developemnt Policies in Tirana. In addition, he has earned a Marster’s degree in public Administration from the Syracuse University of New York (USA) a course with a particular focus on space transformation and development at an urban and territorial level.

from observing a recent tendency in the and economic powers. architectural expression of Tirana to go back to a pseudo-historic language. Regarding

Tirana can be characterized as a

this concern, the paper focuses on the city not easily shaped through plans: following question: will the architecture of a

blurred

fragmented

situation

Tirana continue to be influenced by the created by the continuous interaction most avant-garde international trends, or between spontaneous developments and will it fall in the black hole of Balkan’s local planning decisions is typical in Tirana. nationalisms? The existence of both trends While the authoritarian power design is in Tirana is evident and, not only during the unambiguously legible in many parts of two last decades, but much further back in the city, or at different scales of the city’s history. This dialectic between historicism hierarchies, traces of recording over from and avant-gardism, a continuous stream peoples who have invaded the city in in the history of architecture, is true for different phases of its life are also visible. Albania too. Most importantly, trying to The same is true at an architectonic scale: answer the question above is crucial in Tirana is also characterized by a wide the framework of projects with an epochal variety of architectonic languages due not impact on the city; such is the project for only to a conscious design process but the extension of Tirana’s North Boulevard. also to many “architectures” built without In order to answer the question, first I try architects. As part of this dynamic context, to analyze the variety and coexistence of many people question the future of Tirana. architectonic expressions starting from In this respect the project for the extension the beginning of the 1920’s to the present of the 3 km northern boulevard is the days; to some extent, I also explore how first important test which will show the this architectonic expression was affected dominating trends in urban design and by external and internal influences; and, in architecture in Tirana. Considering the particular, how architectonic representation fact that the area impacted by this project

SCIENTIFIC ARTICLE covers a fifth of the overall area of the city,

approach to building survived in the second

we may conclude that this project is the

half of the 20-th century. Among other

second most important urban intervention

things, he says that the modernist tendency

in Tirana’s history, the first being those

to reduce all form to abstraction was

undertaken by King Zog in the early ‘20s

unsatisfactory in representing the power and

with the aim of transforming the city into a

ideology of the state (Frampton, 2007, p.p.

European capital.

210)1. Will this – as he calls “iconographic

Recently the manifestation of “a new”

inadequacy” or “the failure of abstract form

decorating fashion and “historicist” language

to communicate” with people – present

is becoming evident in Tirana again. This

a problem again for the representation of

“new trend” is gradually enveloping the

architecture in the present symptomatic

facades of many new apartment buildings,

nationalistically ill-Balkans? Despite the

hotels, residencies, etc. with plagiarized

fact that these concerns were written for

pieces of history, such as pilasters, capitals,

another context, they sound quite actual for

statues, floral motives, etc. The same

what is happening in the framework of the

tendency has also explicitly manifested

nationalist ideologies in the Balkans and

itself in some other Balkan capitals such

the risks Tirana is exposed to.

as Prishtina and, most obviously, Skopje. raised: Will Tirana be emancipated enough

Variety and coexisting of architectonic expressions in Tirana

to push away the nationalistic clouds that

As mentioned above, there is clear evidence

nourish precisely the aforementioned kind of

that recently in Tirana a growing number of

backward provincial current in architecture?

“architects” have attempted to use a pseudo-

Will Albanian politicians be smart enough

historic language (I will try to avoid the

and free from nationalistic complexes not to

phrase historicist style as much as possible).

repeat the same megalomania displayed in

This kind of language is more evident in

project Skopje 2014?

private initiatives such as hotels, residential

At this point some other concerns may be

The detailed design of many important

buildings etc. but not yet typical in

projects already in Tirana’s waiting list, and

important public buildings, except religious

most importantly, further developments on

institutions (the Orthodox Church and the

the site of the new boulevard, will provide

project for the New Mosque). The most

the answers to these questions.

typical example in Tirana which explicitly

But how has this historicist approach

illustrated the preference for historicist

survived in the beginning of the new

language was the international competition

millennium? To explore this question let us

for the New Mosque. This competition

take some arguments from the History of

drew entries from some of the most avant-

Modern Architecture written by Frampton1

garde contemporary studios. The winning

in another context. In the chapter on architecture and the state, ideology and representation, he argues why the historicist 14

1 Frampton K. (2007) – Modern Architecture, a critical History , fourth edition, Thames & Hudson world of art

project designed by BIG architects was canceled and considered “non-appropriate” for a traditional mosque in Tirana. Some months later a “typical traditional mosque”

was copy-pasted from medieval Istanbul and

World War. During the communist regime, it

parachuted on the building site. In many

was a clear strategy to gradually sever ties with

other cases the creation of this false image

everything from the compromised historic

is forcefully demanded by the clients and is

past, including the architectonic language.

fatefully combined with the poor education

On an urban scale this was reflected in the

and /or pragmatism of architects and

preference for erasing the old neighborhoods

politicians.

rather than enhancing them, and on an

This kind of historic language, as

architectonic scale it was reflected in the

an imported phenomenon, appeared for

dry, stripped, impoverished but, at the same

the first time in Tirana in the project for

time, archaic expression, applied to the main

the neoclassic ceremonial complex of

public buildings.

the Ministry square (1929-1931), during

We may conclude that by the end

the monarchy period. This tendency was

of the Second World War three basic

intensified even more during the Second

architectonic

World War, in the construction programs

Tirana: first, the historicist neoclassic style

implemented during the Italian Fascist

manifested as a very late reminiscence of the

occupation of Albania. The most important

European Beaux arts tradition; second, the

public buildings in Tirana belonging to

Italian “Stile Littorio” imported from fascist

this period, such as “la Casa Del Fascio”

Italy, or as Frampton calls this consciously

(today the University headquarters), the

“modernized” but conservative and stripped

“Dopolavoro complex” (The University of

historicist style, “The New tradition”2, and

Arts), the Stadium, etc. were designed and

third, elements of modern architecture

built according to the official preference

which referred to the European Modern

of the Italian fascist architecture, “Stile

Movement mostly imported in Albania

Littorio”. Despite this fact, it is important

from Albanian architects who studied in

to mention that, during the same period

European countries and also from Italian

in Tirana, elements of modern architecture

architects who were using this style in Italy

mostly applied to residential typologies, also

despite Fascism’s official preference for the

appeared for the first time. More details

“Stile Littorio”. Let us analyze each of them

about each of them will be presented in the

in the Albanian context and how these

following paragraphs.

approaches were affected by the external

However, this short period that lasted

approaches

coexisted

and internal influences.

from the beginning of the ‘20s till the end of the Second World War could not give Tirana

the aspect of a “European historic city”. The

The neoclassic style in Tirana is mainly

only history which was intimately embodied

represented in the buildings of the ministry

in Tirana was that of the “organic town of

square and in many residential villas built

the origin” and the objects related to it

in the period that starts from the beginning

such as the old bazaar, the old mosques, the

of the 20’s till the end of the Second World

hamam. etc, that were demolished without any hesitation after the end of the Second

2 This term was originally coined after Henry-Russell Hitchcock in 1929; in Frampton K. (2007) – Modern Architecture, a critical History , fourth edition, Thames & Hudson world of art

SCIENTIFIC ARTICLE War. In order to better understand the

the Ministry Square, designed some years

architectonic developments in Tirana during

later by Florestano De Fausto in the neo-

that period it is important to see them in

classic style, represented the most imposing

the context of the main architecture trends

complex in Tirana with their decorations

in a wider international context. While

and

the historicist tendency was degrading

sculptures, and pompous entrances. Despite

and dying in other European countries,

the fact that this language was outdated in

in a context of cultural, territorial and

comparison with many other European

technical transformations which created the

countries and it was like an alien in the

conditions for the emergence of the modern

spontaneous, organic and quasi-vernacular

movement or other forms of interpretations

Tirana, this architecture fulfilled the political

of historic language, it survived in the

goal and left one of the most important

project for the ministry square in Tirana. As

traces in the city. What the establishment of

Frampton argues in his history of modern

the new Albanian state needed at that time

architecture, the main line of European

was this: institutions that embodied a “new”

Classicism, the Beaux Arts, reached a

typology of architectonic representation

dead end in the Paris Exhibition of 1900,

and a new image of Albania no longer as a

“the generic style of the establishment,

part of the Ottoman Empire but as part of

the late 19th century public mode which

Europe.

decorative

cornices,

oscillated constantly between Neo-Gothic

A similar language extended to the

and Neo-Baroque … degenerated into an

architecture of the urban villas for the

eclectic elaboration” … not convincing for

bourgeoisie of this time and to some other

architectural expression (2007, p.p. 210) .

public buildings appearing along the new

The first design concept of the main axe

opened or stretched avenues such as Rruga

of the boulevard was designed by Armando

Nana Mbretneshë (Rruga e Durrësit),

Brasini4 in 1925 (Aliaj et al. 2003, p.p. 30,

Mussolini Boulevard (Rruga e Kavajës),

31). It was a majestic design and redundant

Zogu i Parë Boulevard, etc.

with excessive historic language. This kind

architecture appeared also in other Albanian

of “ideal city” rooted in the central axe of

Balkan cities such as Shkodra, Vlora,

the boulevard, next to the spontaneous

Manastir, Prizren, Kostur, etc. (Bushati5,

/ organic Tirana, was a typical political

2012, p.p. 8). According to Bushati (2012),

diagram where architecture and urban

there is a wide range of stylistic variety in

design were exploited by the state so as to

the architectonic expression of these villas,

demonstrate its power as a newly created

starting from traditional ones built without

nation. As part of the main axe project,

architects (master builders) and the ones

3 Frampton K. (2007) – Modern Architecture, a critical History , fourth edition, Thames & Hudson world of art 4 Aliaj, B. Lulo, K. Myftiu, G. (2003) - Tirana the Challenge of Urban Development, Cetis, Tirane, 16

ornaments,

A similar

built with architects which are characterized 5 Bushati, V. (2012) Vilat e Tiranës – gjysma e parë e shekullit XX, POLIS_Press, Tiranë

by neoclassical, or eclectic style, and finally

/ spontaneous one. If we explore this new

a more rationalist one similar to what was

housing system within the larger urban

built in Europe (Bushati p.p. 9). The owners

system of that time we can notice that there is

of these villas were politicians, intellectuals,

a binary relationship between the typology of

government clerks, traders and very well-

the urban villas and the urban morphology:

known families in Tirana. So, owning a villa

in some cases they were adapted in the

immersed in the garden was an indicator of

existing organic structure and in other cases

social status in the Tirana of the 20’s and

the new parts of the city are the direct result

‘40s.

of the aggregation of this new typology.

The architectural lexicon of these villas

Not only could they follow the historic

is quite rich. It includes capitals and pilasters;

traces mediating between two different

decoration represented by a complex geometry

typological and spatial conceptions, but they

which originates from very different sources

also demonstrated founding properties. In

and makes difficult their precise architectonic

the later periods of Tirana’s development,

classification (often the decorum is totally

especially during the communist regime,

unrelated to the structure); window cornice

we do not see any sort of attempt to set the

embellished with stylized geometric or floral

problem of housing within the larger urban

motives inspired from nature; balusters with

system, or to explore the binary relationship

different shapes which enrich the staircases,

between the housing typology and urban

balconies and terraces with their alternated

morphology. Contrarily, the housing system

rhythms; decorated colonnades or pilasters

detached from the historic traces of the

normally at the entrance of the villas with

districts was consciously used to create the

classical orders or their composites that vary

disjunction from the past.

from neo-doric, neo-ionic, etc.; decorated fences and balconies which vary from the

traditional ones to neoclassic, art nouveau,

The Italian “Stile Littorio” in Tirana is

art deco, and modern art. The same can be

represented in the main public buildings,

said for the decoration of the floor and the

such as the National Bank, Hotel Dajti,

roofs in the interior of the villas (Bushati ,

“La casa del Fascio”, the “dopolavoro

2012, p.p. 13, 20-21)

complex” etc., which were designed and

From the urban point of view, if we

built during the Italian Fascist Occupation

refer to Rossi’s statement6 that the house

of Albania. To have more complete view

represents the manifestation of a culture

of the emergence of such a style and the

(Rossi, 1984, p.p.77-82), it is clear that the

manifestation of a wide range of varieties

urban villas built during this period created

within it, it is first worth seeing the larger

a new culture in Tirana aside the organic

international context and, more specifically,

6 Rossi, A. (1984) The Architecture of the City. The MIT Press Cambridge, Massachusetts and London, England

the Italian one. As

mentioned

the

previous 17

SCIENTIFIC ARTICLE paragraphs, despite the degradation of the

for this official style, typical, according to

historicist style based on the Beaux-arts

some scholars, of the Italy of this period is

tradition, a specific line of thought oriented

the existence of a variety of ways in which the

towards the historicist approach survived

Italian architects confronted the ideological

in Europe. As Frampton argues (2007),

issue (Doordan. Denis P, 1983, p.p. 121)7.

this conservative trend that persisted with

It is important to understand the Italian

tradition but had a new face was emerging

architecture of that period from this point

as the ruling taste in the ‘30s wherever

of view as well because it directly reflects

the power wished to represent itself in a

on Albania. Two clear and very different

progressive light. The re-emergence of this

fractions coexisted in Italy: one linked

historicist language, coined as the New

with the historic tradition and the spirit of

Tradition, reappeared in many different

ancient Rome represented by architects such

contexts and developed to represent the

as Marcello Piacentini, Armando Brasini,

official architectures of power not only in

and the alternative represented by the Italian

totalitarian countries such as the Third

Movement of Rationalist Architects (MIAR)

Reich, Germany (1929-1941), Fascist Italy

related to the European Modern Movement

(1922 -1942), colonial India, New Delhi

and CIAM represented by architects such as

(1912-1931), Soviet Union (1931-1938),

Adalberto Libera, Giuseppe Terragni, etc. As

but also in countries such as USA, France

Zevi8 argues, there is an attempt of progressive

etc. gradually distinguishing itself from the

architects in the Italy of that time to integrate

neoclassicism of the beaux-arts. In Europe

political and architectural ideologies (Zevi,

the New Tradition consciously broke with

Storia

the public style of the Neo-Baroque to

Doordan. Denis P. p.p. 121). In fact, many

return in spirit, form, solemnity and clarity

architects of that period were assuming that

to that of ancient Rome. Typical examples

modernism in the arts and fascism in politics

are the Stuttgart’s Railway Station, designed

were supposed to be related to aspects of the

by Paul Bonatz built in 1913-27, and Edwin

modernization of Italian culture (Doordan.

Lutyens’s New Delhi commissioned in 1912

Denis P, 1983, p.p. 128). Both fractions were

but realized in 1931. It is worth remembering

equally committed to the reinterpretation of

here that the New Tradition was developed

the classical tradition but in very different

in parallel with the modern movement

ways. This duality representing modernity

but was isolated and far away from the

and tradition that was embodied in the

progressive aspirations of this Movement

Italian architecture of this period was

(Frampton, 2007, p.p. 211, 218, 210-222).

expressed in Albania too.

The architecture of this period in Albania, specifically in Tirana, was strongly influenced by the Italian current of the New Tradition “Stile Littorio”. Despite the preference that Mussolini Regime showed 20

dell’Architettura

Moderna,

The main public buildings built in 7 Doordan, Denis, P. (1983), The political Content in Ital-

ian Architecture during the Fascist Era, Art Journal (p.p. 121-131), summer 1983

8 Zevi,B. (1950), storia dell’Architettura Moderna, 5th edition 1975, Turin, in Doordan, Denis, P. (1983), The political Content in Italian Architecture during the Fascist Era, Art Journal (p.p. 121-131), summer 1983

Tirana during the Italian occupation, as part

the same period; a typical example is villa

of the “oltre mare project” were designed

Nepravishta, etc.

according to the official “Stile Litorio”. This

The architecture and the urban traces

architecture was conservative compared

left in Tirana during this period played an

to the avant-garde modern architecture of

important role in the consolidation of a new

the same period in Italy. The “oltre mare”

urban structure and shape of the city (more

project was part of the Fascist colonial

details about this in the next paragraphs,

project in which, in addition to Albania,

the 1942 plan). This new architecture

other Italian colonies in North Africa were

created a new urban scale for Tirana as a

also included.

capital city, and most importantly brought

The most typical expression of the New

a new typology of the public space. These

Tradition in Tirana is the new complex in

buildings still play a very important role

the southern part of the city which included

in the city structure, and are successfully

“La casa del Fascio” in the center, the “dopo

adapted to new functions and further social

lavoro complex”, the stadium, the gym, etc.

and physical transformations of the city.

Here we can clearly see the typical program for these kind of complexes and also the main

elements typical for the lexicon of the “Stile

In Albania the first elements of modern

Littorio,” such as the stripped and simplified

architecture appeared in the period between

classicism, lithic solidity, the marble and

the two World Wars. The most important

travertine covering, the repetition of simple

Albanian modern architects who worked

elements, the use of “basso-relievo”, the

during this period were Qemal Butka,

decoration of the square with statues, etc.

Anton Lufi, Skeneder Kristo Luarasi,

The original design included the proposal

Gjovalin Kroqi, Kristo Sotir, etc. As

for a number of statues which could never

Luarasi9 argues (2013, p.p. 175) modern

be completed, in order to emphasize the

architecture in Albania is represented in

main axes in the buildings surrounding the

the built and non-built projects of the

quadratic square. From the urban point of

Albanian architects who worked in the

view this complex also embodies the same

period between the 20’s and 30’s. This

official principles of the Fascist Architecture

period also coincides with the emergence,

in Italy; on a different scale we can assume

development, and consolidation of modern

that the foundation of this new complex

architecture in Europe. He also argues that

outside the existing city was the parallel

the Albanian modern architecture of this

of EUR in Rome. It was a utopia and

period is related to the European modern

monumentality separated from the social

architecture not only in terms of formal and

reality of Tirana. While the public buildings

syntactic features but also in the social and

were designed according to the official style, a more rationalist approach was especially expressed in some urban villas built during

9. Luarasi, S. (2013) Duke empatizuar Sizifin – Drejt reklamimit dhe rehabilitimit te arkitektures modern shqiptare, nje moment nga vepra arkitektonike e Skender Kristo Luarasit, Forum A+P 13, POLIS_Press 21

SCIENTIFIC ARTICLE political aspects. The main characteristic

of 15-20 years Tirana was transformed

of modern architecture (including the

because of this progressive move. Since the

Albanian one) is the avant-garde value

early ’30s several urban villas and/or other

in all aspects of the architectonic design:

objects were designed and built under the

conceptualization of form and space, the

influence of such a trend and in contrast

relationship between internal and external

to the “historic” conservative tendencies

space, the minimalist and pure design. The

represented in the monumental neoclassical

architecture of this period demonstrates

or in the eclectic style mentioned in the

a variety of styles and conceptualizations

previous paragraphs. However, in many

as well as the hybridization with the local

cases architectural expression was subject to

and regional typologies. These topics need

the individual tastes and the background of

further research in order to be supported

their owners. Often, the architecture of this

by specific examples that are focused in the

period successfully hybridized the abstract

Albanian context.

and poetic aspects of the local Albanian

The urban villa was the typology in

architecture such as the use of roofs and

which this architecture was most present.

roof eaves, the use of stone, the modern

Most of them were located in the southern

treatment of balconies and terraces, etc.

part of Tirana, on both sides of the new

(Luarasi10 2013, p.p. 176)10. The modern

boulevard stretching from Elbasani Road to

character of some urban villas is also

Sami Frasheri Road. Some exemplars can

expressed in the fact that many of them put

still be seen in the former “blloku area”,

more value on the purity of the materials

Jul Varoboba street, Asim Zeneli Street,

rather than on the decorations11. That is

Papa Gjon Pali II street, etc. Typical in this

why we see the beauty of the marble, the use

area are some villas designed by Skender

of massive wood, or squared stones, bricks,

K. Luarasi, including his house, known as

and terracotta, etc. without any make-up or

the Luarasi villa, etc. and Simonidhi’s villa.

stylization. (Bushati, 2012, p.p. 21)

The investors of these villas represented a

Albanian modern architecture is related

specific social stratum of Tirana: the middle

to the European modern architecture as a

/ small “bourgeoisie”. Most of them were

result of a group of Albanian architects who

educated abroad and prone to want to

studied in Europe and worked in Albania and

change the feudal and oriental image of

also because of the influence of the Italian

the country. Their will towards progress,

rationalist architecture during the Italian

reinforced by the European orientation of

occupation. Unfortunately, the exemplars

the abovementioned Albanian architects

of this architecture nowadays are a species

working during this period, triggered

10 Luarasi, S. (2013) Duke empatizuar Sizifin – Drejt reklamimit dhe rehabilitimit te arkitektures modern shqiptare, nje moment nga vepra arkitektonike e Skender Kristo Luarasit, Forum A+P 13, POLIS_Press 11 Bushati, V. (2012), Vilat e Tiranës – gjysma e parë e shekullit XX, POLIS_Press, Tiranë

the avant-garde trend that we find in the architecture of that period. In the course 22

in extinction. They are not considered as

exchanges and relationships that continued

protected heritage. A lot of these urban

up to ’60 with the Soviet Union (SU) and

villas

demolished

up to ’64 with the rest of the communist

under the pressure of urbanization and

bloc; secondly, the considerable number of

redevelopment of real estate, or have already

students who graduated in the SU and in

lost their identity because of incompetent

the rest of the block (Bulgaria, Romania,

interventions. What was avant-garde at the

Czechoslovakia, Poland, DDR, etc.). After

time in which they were built in many cases

that Albania had its own contingent of

has been erased by ridiculous decorations.

architects and engineers educated with a

Their new face represents the falsity, fast

“new ideology” but in the former Eastern

enrichment and the need, on the part of

Bloc countries; and thirdly, the assistance

their new owners, for a “new” identity and

given during the same period to Albania by

social status.

architects and urban planners from these

have

already

been

countries. Along with Albanian architects

4. After the Second World War

and engineers, they designed and assisted in

This was a period of self-isolation. Albania

important projects of this period such as the

gradually separated from the rest of the world

Palace of Culture in Tirana, the Park in the

and from the international discourse in all

periphery of Tirana, some residential blocs,

fields, including architecture. Architecture

etc.

ideological

Despite the isolation that followed in

instruments in demonstrating the state’s

the next period, in terms of architecture and

power and in the support of the “revolution”

urban development Albania followed the

and transformations in the country. They

same track as the Eastern Bloc, but badly

were part of a social experiment used to

equipped with a very poor local economy,

influence the creation of a new physical

poor technological and theoretical know-

and social reality. The construction activity

how, and most importantly, with a

in general and, architecture and urbanism

high degree of limitations derived from

in particular, were considered important

ideological interpretations. This is also

components of “social progress” and the

reflected in many models copied from the

“construction of socialism” in Albania.

Eastern bloc countries and adapted to the

and

urbanism

became

After 1978, when Albania broke with

Albanian reality.

However, the “spirit”

China, the country had become totally

of the proletarian culture that flourished

self isolated, but before that some strong

in the SU during this phase is what most

influences from the Eastern bloc countries

influenced Albania not only when both

are visible in the country’s architecture

countries were closely connected, but also

and urbanism. Some are the reasons of

after the relationships were broken. The

such an influence: firstly, the intensive

inertia of people educated there, as well 23

SCIENTIFIC ARTICLE

SCIENTIFIC ARTICLE as the nostalgia of love with the SU was

1933, about the party pronouncements on

stronger than anyone could imagine.

what was believed to be the new tasks of

Let us see first how this official

Soviet realism as they were meant to apply

language originally emerged in the SU.

to architecture. This “critical assimilation

As Frampton

argues, the emergence of

of previous architectural heritage” was

a new language in the SU was due to the

supposed to be achieved through “historical

challenge made by VOPRA (group of

research” because this would create the

Young Proletarian Architects) against the

“clarity of meaning” easy to read for the

constructivist intellectuals pretending that

“mass perception”. As he argues, this was

only the proletariat could create a proletarian

an old-fashioned argument for populism,

culture; in addition, it was due to the pre-war

the antithesis of progressive historical

academics who remained unsympathetic to

transformation. In fact, what happened

constructivism; and most importantly to

was a fallacy of critical assimilation of

the Party itself that sensed that people were

heritage because it was not driven by a

incapable of responding to the abstract

rational concept of history. What we see

aesthetic of modern architecture. The

is a mechanical penetration of classical

monumental Socio-Realist line was officially

principles (Charley, 1996, p.p. 27).

adopted by the Central Committee of the

Different from the SU, where there is

Party in 1932. In the apologia for Social

a visible penetration of classical principles

Realism written by Anatole Lunacharsky,

that attributed to architecture an aspect

he insisted that Hellenic culture, a “cradle

between the neo-classical and highly

of civilization and art,” could still serve

eclectic, idiosyncratic and a mixture of

as a model for architecture in the SU

historical symbols and meanings from

(Frampton, 2007, p.p. 214). However, as

the orthodox church to classical antiquity

Charley (1996) argues, this was supposed

(Charley, 1996, p.p. 29)15, in Albania this

to be the “critical assimilation of previous

flavor of neoclassicism never pervaded

architectural heritage” . This was not to be

architecture during the communist regime

achieved through any kind of “bourgeois

in such a way. This (lack of neoclassic flavor)

eclecticism”

“profound

was also a result of the absence of pre-war

assimilation of the workings of the previous

academicians with a beaux-arts background.

architectural compositional methods and

However, the same neoclassic “flavor” is

principles for the expression of the new

visible in buildings designed by Russian

socialist content” . This is what Charley

architects or under the influence of such

(1996, p.p. 27) extracts from the editorial

a style, such as the Kinostudio building,

columns of the Arkhitektura CCCR in July

The Palace of Culture, Shallvare and Agimi

but

the

12 Frampton K. (2007) – Modern Architecture, a critical History , fourth edition, Thames & Hudson world of art 13 Arkhitektura CCCR (July 1933), p.1; in Charley, Jonathan. (1996) The dialectic of the built environment: The making of an imperial city, The Journal of Architecture, 1: 1, 19-37 14 Arkhitektura CCCR (July 1933), p.2; in Charley, Jonathan. (1996) The dialectic of the built environment: The making of an imperial city, The Journal of Architecture, 1: 1, 19-37

housing blocs, etc. A central theoretical concept that 15 Charley, Jonathan. (1996) The dialectic of the built environment: The making of an imperial city, The Journal of Architecture, 1: 1, 19-37

Albania copied from the soviet project was

which different typologies and categories in

what Charley 16 (1996) described in the case

architecture have been treated from center

of the SU as the search for an ideal unity

to periphery, from city to city, etc. From this

of form and content that was celebrated

point of view, first, we can distinguish the

in the synthesis of “national form” and

a/stylistic 4-5 stories standardized low-cost

“socialist content” (Charley, 1996, p.p.

residential blocs, supposed to support the

28). This union was exactly what Albanian

“new” collective life and be the incubators

architecture was pretending to achieve too.

for a new model. With few exceptions, they

Despite this fact it was a very superficial and

were very poor freestanding apartment

vague understanding of these theoretical

blocks detached from any historic traces.

notions.

imprecise

The only exception, were some blocks in the

concepts were translated into archaic

central areas built according to special design

symbols plagiarized from the Albanian folk

(the apartment bloc behind the National

and historic culture, often also mixed with

Bank, or behind the National Museum,

the revolutionary symbols. In the total lack

Barrikadat towers, etc). In addition, we

of understanding of the original theoretical

can distinguish the standardized public

concept, in many cases, the use of these

buildings such as schools, kinder-gardens,

superficial symbols was the only criteria to

commercial services, cultural centers, etc.

classify if the architecture was following the

Also in this case there are huge differences

party line. As a result, in many cases, we see

from the center to periphery, from Tirana to

socio-proletarian symbols (the star, pickaxe,

other smaller centers. In most of the cases,

shovel, rifle, wheat ears, hammer and

it is difficult to speak about architectonic

sickle), quite often as part of the work of

expression because the pragmatic approach

artists engraved in basso-relievo, or the use

and the fulfillment of the functional

of traditional materials (such as stone) quite

program requirements were considered

artificially used in facades. In general we can

most important; and lastly, special or

say that there is no real fusion and intimate

unique buildings, such as government

relationship between the elements that

buildings, museums, hotels, train stations,

create the lexicon of architectonic language

etc. These buildings are some of the most

and the building itself which adds a sense of

distinguished architectures of this period,

archaic sterility to these architectures. An issue to be discussed within the framework of this period is the huge difference and contrast in architectonic treatment based on typological discrimination and the category of the city. Despite the claims for an equal society, there are huge differences in the way in

such as the Museum of the dictator (the

practice

these

“pyramid”), the Central Comity of the Communist Party, Hotel Tirana, the National Museum, the National Gallery of Arts, etc. These cases demonstrate the maximum effort to reach the best architectural expression within the official line of this time. There are some common

16 Charley, Jonathan. (1996) The dialectic of the built environment: The making of an imperial city, The Journal of Architecture, 1: 1, 19-37

characteristics of these buildings; they are 27

SCIENTIFIC ARTICLE massive in scale and often organized around

architecture and urbanism, more than ever,

a central axis in a symmetric layout (typical

allied with the power.

is the pyramid, the national museum, etc.); they stay on pedestals and can only be

Languages along the main axes of the Boulevard

approached through a series of triumphal

The ceremonial axe or the main

stairways; in many cases they are adorned

boulevard where the new city and the new

with stylized folkloric or revolutionary

architecture started almost one century ago is

motifs, which even in this cases have mostly

the most representative space in Tirana. The

been plagiarized, without being assimilated

discussions about its further development

as part of the architectural expression. This

are the focus of the current debates. With

treatment attributes to these structures quite

this concern in mind, it is worth analyzing

an archaic character and also reinforces the

the urban structure and meaning of the

iconic aspects of this architecture.

most representative space in Tirana in order

From 1944 to 1991, under the centralized economy, significant changes happened in

in terms of architecture and city scale.

the city structure. Regulatory urban plans

Tirana started the tradition of opening

based on zoning as the main regulation

and stretching of the new avenues quite late

criteria, were the main instruments for large

in comparison with other capitals in the

scale urban transformations. This instrument

region. At the beginning of the last century

was used as an “ideological instrument”

Tirana was a small organic town / village,

to link the territorial development policy

until it was declared the capital of Albania

with the ideological objectives generated at

in 1920. The first attempts to move from

the national scale. The city was considered

spontaneous to organized urban planning

almost a mechanic collection the pieces of

were initiated under the monarchy period:

which could be removed according to the

the opening of several main avenues such

needs for space and services. Tirana was

as Rruga e Durresit, Rruga e Kavajes;

becoming an “excellent” example of a city

Zogu i Parë Boulevard, are some of them. Without any doubt, the most significant project was the ceremonial complex of the government buildings and the central axe of the boulevard first designed by Armando Brasini17 as part of the King Zog’s projects for Tirana. The boulevard was included in the first regulatory plan (formulated by G. Bossio and F. Poggi in 1942), as the symmetric axe and the central element of Tirana. This axial scheme can be analyzed in relation to the topography, and in relation

designed by demolition, where the alienated space of oppression was gradually becoming dominant. All this was done in the name of social progress which in reality conditioned not only architecture and territory but the entire social life. Despite all these efforts, at the beginning of the ‘90s, with the collapse of the regime, it became clear that the dream projected towards a city and a society where there were no rich and poor, gradually was shrunken and reflected in the desolation of the poor housing blocs where everybody was poor. The dream ultimately came to an end. 28

to understand its future generative capacity

In Albania, like in all totalitarian regimes,

to the political power, as a structure representing a political diagram. In terms 17 Aliaj, B. Lulo, K. Myftiu, G. (2003) - Tirana the Challenge of Urban Development, Cetis, Tirane, 2003, p.p. 31

of the first element, topography, the

of the road, the number and index of the

boulevard alignment is fixed by the specific

house type. In a similar way, this is also true

location: parallel to the direction of the

for that part of Tirana that was built as a

Dajti Mountains, almost in the north-south

political power diagram. If we refer to the

direction (slightly inclined to the west)

first design options, the King’s palace was

gradually descending through sequential

in the dominant hill at the south end of

river necklaces (Lana, Tirana, Terkuza river,

the axe (later substituted with “la casa del

etc.); The chosen location and the direction

Fascio”) and the land along the axe was

of the boulevard was a perfect interpretation

distributed to the higher rank clerks. As we

of Tirana’s valley topographic features; not

mentioned in the previous paragraphs this

only because it became the generator axe for

area became the ground for the modern

the future development of the city, but also

expression in architecture. The area still is

because of the reinforcement effects on the

perceived as one of the most “privileged”

identity and orientation of the entire city.

areas in Tirana and the land prices are the

Related to the axe as a Governmental

highest in the city.

linear system or as a political diagram, as

It is important to extend this analysis

Kostov argues in the book City Shaping18

to the catalytic role this axe played in the

(2003, p.p. 174), it (the boulevard) celebrates

future development of the city. After the

monocentric domination. Axial alignment

boulevard was included in the 1942 plan

is commonly used in association with an

as the main centrality of the city, later

overall urban diagram that upholds its

developments reconfirmed the importance

premises and highlights its effects. Kostov

of such a decision. There are several reasons

uses the scheme of New Delhi designed by

why this boulevard was so successful and

the British E Lutyens, commissioned in

went far beyond merely being a ceremonial

1912 but built during the ‘20s, to illustrate

or a political diagram: firstly, this axe

this scheme (2003 p.p. 176-178). He

reconciled the initial organic city with the

describes some details that may be worth

founded city (“Tirana e re”). In this respect

using for analyzing that part of Tirana

it represented the “meeting place” between

which was designed and built during the

the spontaneous city and the designed

same period under King Zog’s project.

one, between the everyday city and the

Among other things, he argues about an

ideal one. Because of this, aside from the

elaborate hierarchic spatial structure based

organic pattern, a consciously designed one,

on occupational rank and socio-economic

substantially different from the previous

status, such as: the hierarchical housing that

one, was laying down in a very natural way.

fanned out from the axes along avenues; the

Secondly, it was the visualization at the city

rank was precisely indicated by the altitude

scale of two important geographic features:

and size of the compound and its proximity

the Tirana valley gradually distending

to the government palace, the size of the

towards the sea, and the mountain range in

dwelling, the width of the road, the name

its background. This way, the boulevard was

18 Kostof, S. (2003) The City Shaped – Urban Patterns and Meanings through History. Fourth printing , Bulfinch Press AOL Time Warner Book Group, Boston, New York, London

mediating a dialog between the geographic scale and the human scale. Finally, at the

SCIENTIFIC ARTICLE

end of this period two different Tirana/

pyramid, the apartment bloc towers in the

s with legible architectonic and urban

same area, Rogner Hotel, etc. In 2004 a new

features were created: one rooted in the

era started: international competitions. The

organic radials and the other one rooted in

central axe and the “Skanderbeg Square”

the re-foundation axis of the boulevard.

as well as the buildings proposed along this

It is no accident that during the

axe, became the arena of the most important

communist regime, along the same axe,

international competitions. After more

the communist government imposed their

than five decades a new language appeared

own hierarchic structure. The headquarters

in Tirana. An important mental shift was

of the Communist Party was built during

about to happen.

this axe in a neoclassic style, following the

The first international competition that

Russian line of socio realism in architecture

was dedicated to the central axe of Tirana

as described in the previous paragraphs.

was won by the French group “Architecture

Ironically, under an ideology that was

Studio”. Some of the most important

propagating the idea for an egalitarian

proposals of this plan included a new design

society the most important people of

for the “Skanderbeg Square” and the “Mother

the state hierarchy / nomenclature were

Teresa Square”; the pedestrianization of some

living in the same area and the same

sectors along the central axes; the creation of

villas designated for the bourgeois of the

“Tirana Central Park”, a new train terminal;

previous monarchic structure. This area

etc. One of the central ideas of their proposal

was even closed during this period and was

was to increase the presence and visibility

symbolically called “the bloc(k)”. There are

of the central axe. Related to this, the plan

no substantial interventions during this

proposed one of the most debated themes: a

period along the axe except in the main

series of towers along the main axe (only two of

square (“Skanderbeg square”) that totally

which are under construction). The design of

changed its aspect, increasingly becoming

these towers also went through international

bigger. I have discussed these interventions

competitions which were supposed to bring

and the related erasing operations in other

an avant-garde and extravagant architectonic

issues of Forum A+P (number 5 and 8). As

language along the axe, which would be

a conclusion, the development of the axe

very different from the neoclassic one. The

of the boulevard was stopped at the train

following years questioned many of this

station.

plan’s proposals, starting from the idea of

During the first decade after the ‘90s

pedestrianization; the lack of investments

most of the developments along the axe

needed to solve the traffic problems at a

contributed to deform the original concept:

larger scale (city and metropolitan) and the

typical are the generic / faceless architectures

lack of public parking near the central area

such as the “twin towers” in front of the

made the further implementation of this

plan impossible. In a similar way doubts were

Parliament won by Wolf Prix of Coop

raised about whether there was a need to

himmelb(l)au (the project cancelled, the

build all the towers proposed by the plan, etc.

building site changed); The New Mosque

Only a few years later, another

won by BIG Architects (the project

international competition was organized

cancelled, the building site changed); and

for one of the most important parts

many other competitions.

already proposed by the previous plan:

During the last two years the attention

Tirana’s “Skanderbeg Square”. Important

has been mainly focused on the project

international

for the extension of the Northern Tirana

this competition; among others Daniel

Boulevard that is supposed to give a new

Libeskind Architects (New York, USA);

dimension to the city. The idea to further

MVRDV (Rotterdam, The Netherlands);

extend this axe was included since in the

Architecture

France);

1989 plan. According to this plan the axe

Atena Studio (Rome, Italy), Josep Lluis

was considered as a new access from the

Mateo – MAP Arquitectos (Barcelona,

North, mainly conceived as a shortcut to

Sapain), etc. The competition was won

the international airport. In 2012 this idea

by the young Belgian studio 51N4E bvba

reemerged again and became the focus

(Brussels, Belgium). The implementation

of another international competition. It

of works on site, started some months

drew entries from important international

after the competition, was suspended for

studios, among others: KCAP, Holland;

financial and political reasons. What was

Grimshaw Architects, UK; West8, Holland;

implemented had nothing to do with any

Cino Zucchi Architetti, Italy; Albert Speer

one of the dozens of projects presented for

and Partners, Germany; DAR Group,

Skanderbeg Square. It showed the failure of

Turkey/UK,

politics and administration in guaranteeing

competition

the continuity of the important urban

Architects. The project area, impacted by

projects.

the extension of the 3 km boulevard and the

studios

Studio

participated

(Paris,

Some other important international

etc. was

The won

international by

Grimshaw

organization of a 7 km river side park, covers

the

a fifth of the overall area of the city. The

abovementioned towers in the center: the

design of the winning project was based on

first one was won by the Belgian studio

the analysis of the existing informal urban

51N4E (under construction); The second

settlement and patterns of land ownership.

tower was won by the Italian Archea Studio

It proposes the creation of sequences of

(under construction); Other competitions

public spaces threaded along the boulevard

were organized for the Urban Complex

and urban living rooms which reflect Tirana’s

won by Winy Maas of MVRDV Holland

Mediterranean outdoor culture.

competitions

were

organized

for

(under construction); The New Albanian

The avant-garde language would seem an

SCIENTIFIC ARTICLE

unlikely language for the continuation of a

the ground. Despite this fact and perhaps

power diagram like the one of Tirana. Despite

most importantly their impact goes beyond

the prejudice for monumentality, this is one

being merely competitions: in their totality

of the reasons that made the government axes

they represented an important educational

of Brasilia iconoclastic as a product of the

process for local architects and planners.

‘60s. The (neoclassic) Mall in Washington

If the opening of the boulevard during

DC can be considered another reference

the monarchy period generated the “second

for this kind of formal model. However, as

Tirana” (Tirana e re) made of a different

you will see in the proposals presented in

pattern, different urban fabric, and a different

this A+P issue, the design proposals for the

architectonic expression, what will be generated

extension of the Tirana Boulevard are far

by the tides of the Northern Boulevard? Will

beyond the monumentality of the neoclassic

it play the same catalytic role for the areas

and modernist axes.

under its gravity? How will its architectonic expression be materialized? Will it impose the

Conclusive remarks

continuation of the avant-garde language that

So far, Tirana has demonstrated one of the

so many international competitions brought

best examples of openness to architectonic and

to Tirana, or will it go backward to the well-

urban experiments. The period after 2004,

known historic or nationalist language? Most

full of new ideas and inspirations relating to

importantly, it is vital that Tirana in the future

the city and its architecture, is a second revival

will demonstrate to be a nationalistic complex-

after King Zog’s “grand traveaux” and “Stile

free area to be open to architectonic and urban

Littorio” operations. Many projects remain

innovations oriented towards the future.

from this phase but few concrete actions on

Building Tirana's GREEN Future

Tirana Northern Boulevard & River COMPETITION BRIEF Times of Transition & Urban Challenge After centuries of isolation and suppression

million inhabitants which is four times

communist

the size it used to be 20 years ago and

dictatorships, Albania has made great efforts

amounts to more than one quarter of the

in opening up towards modernization and

country’s entire population. The moment

freedom during the past 20 years.

for building Tirana’s GREEN Future is

Tirana, Albania’s young but dynamic capital

now!The competition design task is the

city is the center of the Albanian speaking

production of a comprehensive vision and

region and situated in the middle of a

urban design ideas for the development of

major European transit corridor connecting

Tirana’s two main ecological corridors:

one

the

harshest

Southern Europe to the Near East. The city of Tirana, closely connected geographically

Tirana’s urban landmark:

and economically to the nearby harbor city

The Central Boulevard

of Durres, is the main driver of the country’s

The design of a new lively downtown area along

economic

the Northern extension of the city’s central

and

cultural

development,

continuously growing into a superregional metropolis.

boulevard: The extension of the city’s central North/

After a massive rural exodus in the early

South axis (Boulevard Deshmoret e Kombit

1990s the city of Tirana was confronted

- Zogu I Pare) from the old train station to

with the phenomenon of massive informal

Paskuqan Lake in the North (zone 2+3) shall

building activity resulting in huge areas of

result in a generous green boulevard or park

uncontrolled urban sprawl which placed

running through the city center between the

at a great risk the quality of urban life for

two main parks, the existing “Parku i Liqenit” in

the whole city. The process of informal

the South and the future “Parku i Paskuqanit”

development

slowed

in the North (zone 5). The area of the new

down: land ownership is in the process of

boulevard shall form a new public and cultural

clarification; buildings and property have

center for a series of main functions to be newly

become either legalized or clearly labeled

founded or in urgent need of modernization

as not permitted, planning and urban

(National Library, Concert Hall, Modern Art

management instruments are ready to be

Galleria, Convention Center, Palace of Justice

used to turn projects into reality.

and New City Hall plus other supporting

Tirana has a population of nearly one

functions).

has

considerably

Competition organizing authority: Municipality of Tirana (MoT) Competition development, brief & management: The Mayor of Tirana/ Mr. Lulzim Basha Arch. Ulrike Bega/Advisor to the Mayor for Urban Development & Project Coordination, MoT, assisted by SymbioticA Competition committee: Eng. Henrik Hysenbegasi, General Director of the Department of Strategic Projects and Foreign Investments, MoT Arch. Gjergj Bakallbashi, Director of the Urban Planning Department, MoT Special thanks to: Arch. Urim Hoxha, Director for Strategic Projects, MoT and all staff of his department. All staff of the Urban Planning Department, MoT A great number of institutions, authorities and individuals helped preparing this international competition by providing information and collecting materials for this competition brief. We would like to express our special thanks to all and each of them for their kind co-operation and willingness to help.

Building Tirana's GREEN Future

Map of Competition Area

Zone 5

PASKUQANI LAKE

Zone 3-b Zone 3 Zone 3-a

TIRAN

Zone 4 A RIV

Zone 2

Zone 2-b

Zone 2-a

LANA

RIVE

D EVAR E KOMBIT BOUL T MORE DESH

D EVAR BOUL I ZOGU

RINGROAD CRO

Zone 1

7 TIRANA LAKE

Tirana’s new landscape landmark:

Competition Area

The Tirana River The

The urban area impacted by this urban

project comprises 14 km² (which is 1/4 of

development & recreational areas along the

the size of the city) expected to generate

Tirana River, the regeneration of the river

huge potentials for urban restructuring,

itself:

new urban developments and the urgently

The

structuring

environmental

the

regeneration

and clean-up of the Tirana River shall be

needed new recreational space (please also refer to “Map of Competition Area”).

accompanied by the development of a new green and urban river front (zone 4) between

Levels of Intervention

Kamza and Tufine framed by dense mixed-

The competition assignment will be split

use developments on both river sides and

into the following levels of intervention:

well integrated with the natural context.

• Strategic Development Area: 1400 ha

The

refined

design

and

the

Master Plan Area (boulevard + river): 585 ha

implementation of interventions in both

• Implementation Area Boulevard: 18 - 36 ha

areas shall result in the hugely increased

• Strategic Development Area (zones 1-5)

potential of urban recreational space and

The Master Plan zones have to follow an

the functional rezoning will compensate

overall strategic plan to be developed for all

the inner city’s problems of congestion and

five zones in regards of:

pollution. At the same time it will catalyze

• The strategic urban development and

the social integration and urban upgrading

landscaping (land use and building

of the adjacent underdeveloped areas.

activity, the program, environmental assets, etc.),

Creating a Vision for the Future: The design teams are asked to provide the

most

innovative

and

• The city-wide integration with the Master Plan areas,

sustainable

• The integrated solution of traffic and

solutions for structuring the described

public transport means for both corridors,

corridors and regenerating these areas

• The strategic concept for upgrading and

through urban, landscape, ecological and

potentials for future developments in the

infrastructure design proposals.

adjacent areas (zone 2a+b+c, 3a+b)

Building Tirana's GREEN Future Master Plan Area (zones 2+3 &4):The

landscape, ecological and infrastructure

areas of the Northern Boulevard and the

design proposals.

Tirana River have to be elaborated at a

Sustainability

conceptual Master Plan level. The winning

All design proposals must reflect the

team will be contracted for the production

principles

of the Detailed Urban and Infrastructure

through the following actions:

Master Plans for these areas.

• Reinforce the ecological potentials of

Implementation Project Area (in

sustainability

planning

both corridors

zone 2): The first part of the boulevard

• Respect the model of the compact city

is subject for implementation within the

(densification vs further urban sprawl)

year 2012. Participants have to prepare

• Provide multifunctional mixed urban

a Detailed Master Plan for the so-called

areas (residential + small / medium

implementation area, a special area directly

business, small-scale industry and craft

connected to the existing boulevard.

activities), reinforce the local daily activity

The winning team will be contracted to

avoiding regular long distance travel

develop a detailed design project for the

within the city

assigned implementation area. Please note

• Apply site-specific planning and design

that precise adjustments can be made to

ideas regarding climate, economy and

the boundaries of the assigned area in

construction heritage

accordance with the proposed idea.

• Provide feasible solutions based on a good understanding of local restrictions

Design Objectives

and limitations regarding legislation,

Creating a Vision for the Future:

operation of maintenance, know-how

The design teams are asked to provide the

and the level of experience, ownership

most innovative and sustainable solutions

conflicts, etc.,

for structuring the described corridors and

• Reserve areas for flexible development

regenerating these areas through urban,

• Integrate innovative ideas about renewable

energy resources (e.g. solar, wind, hydro, geo-thermal power usage, etc.)

Good Planning A

fully-integrated

design

process

urban planning, architectural design, and technical considerations is expected to be the foundation of this project: • Create a clear identity for both corridors • Respect the heritage and properties of the existing urban design and architecture but enhance the overall qualities • Improve urban connections, car flow, structuring of landscape and green areas

Scope of Work: For the Master Plan level the following items have to be integrated in the design: • Pedestrian access • Effective system for car traffic and public transport • Road and streetscape design • Access for service and emergency vehicles • Adequate parking spaces • Bicycle routes and circulation • Provision of sufficient public infrastructure • Landscaping and park design • Water and shading elements • Exterior lighting • Waste collection and recycling • Street furniture • Space for accommodation of public events After launching the competition brief many international studios were approached. In the following chapters only the seven studios selected to participate in the competition are presented.

Building Tirana's GREEN Future

Grimshaw Architects Office: Founded in 1980 by Sir Nicholas Grimshaw, the firm was one of the pioneers of hightech architecture.The practice became a Partnership in 2007 and operates worldwide with offices in New York, London, Melbourne and Sydney employing over 250 staff. Grimshaw’s international portfolio covers all major sectors, and has been honored with over 150 international design awards including the prestigious Lubetkin Prize. The practice is dedicated to the deepest level of involvement in the design of their buildings in order to deliver projects which meet the highest possible standards of excellence. The company’s work is characterized by strong conceptual legibility, innovation and a rigorous approach to detailing, all underpinned by the principles of humane, enduring and sustainable design.

GRIMSHAW ARCHITECTS Building Tirana’s Green Future The people of Tirana are the focus, energy,

which lie in a bowl defined by surrounding

and inspiration of the Grimshaw master plan.

mountain ranges. Our proposals aim to

Giving consideration to the future of Tirana

strengthen this key identity and to formalize

requires a balance between grand gestures

the informal spread of settlements giving

befitting a capital and humanity befitting its

clarity and improving legibility and character.

inhabitants. The Mediterranean climate, the

Our strategy is backed up by a network of

Albanian love for the outdoors together with

robust but high quality urban landscapes. We

their sense of community requires beautiful

call these “Urban Living Rooms”. There is a

and safe places to meet, discuss, eat, drink

space with a retail character, one embracing

and play. The starting point for our master

the world of justice, another world of civic

plan is therefore a structure of walkable

governance, and the largest addressing the

neighborhoods where basic amenities such

world of culture.

Main Works: International Terminal Waterloo, London; Paddington Station: Phase I Redevelopment, London, UK; Stansted Airport - Generation 2 Masterplan, London, UK; The Eden Project, Cornwall, UK; Heathrow Aiport Pier 4A, Terminal A2 Concourse B; London, UK.

as a local shop, a doctor, a dentist, a primary

Our design strives to formalize the Informal

school, a bus or tram stop are all available

character of the existing. By inserting a new

within walking distance of residential areas.

hierarchy to the existing street network we can

URL: http://grimshaw-architects.com

A city is a complex system of many different

transform the current layout of the informal

layers. A progressive and contemporary capital

settlements into a structured part of the city.

city should aim to provide an integrated

We believe that MORE PEOPLE with MORE

balance between a global and a local outlook.

GREEN will create A SUSTAINABLE

Tirana is a city with two rivers and two lakes

GREEN CITY. It is therefore vital that the

process of densification provides momentum

the river park. We propose the application

GRIMSHAW ARCHITECTS LONDON

for Tirana to progress towards its green future.

of a Transit Oriented Development model

Master-planning & Architecture

A process of ‘urban acupuncture’ aims to

upon Tirana, as a sustainable measure

instigate positive change within a pre-existing

of development. We have formulated an

environment through physical intervention.

acceptable walking distance of 600 metres

This method will allow us to implement the

as a basis for Epicentres of Humanity, which

masterplan principles within the existing

will for the heart of the new neighborhoods.

grain.

identified

Focusing on the opportunities presented by

available sites/locations where regeneration

the city has formed the basis for the strategy

can be implanted by means of a private public

of densification. We have defined these as the

partnership projects thereby enabling positive

base texture upon which we can develop a new

and far reaching change in the areas that need

density more in line with planning aspiration

it the most.

and the idea of an Eco Compact City.

have

analytically

Our vision is a real city which is served by a range of high quality transport choices

The Boulevard

where economic growth is stimulated by a

The Boulevard is the main organising line

sustainable means of travel into, out of and

that runs through the city. We have organised

around the city. We have developed a series

the various functions along the boulevard as

of city wide strategies in support of our

‘urban living rooms’. Each of these serves as

detailed proposals for the boulevard and

a quarter characterised by its predominant

NevenSidor/ Design partner, Paolo Vimercati/ Project leader Specialist Design Review Panel, Nicolas Grimshaw/ Chairman, Kirsten Lees/ Partner master planning and urban realm, Nell MC Clements/ Associate director transport and infrastructure Transport & Infrastructure Lead/ Ronan Friel Urban Design Lead/Adina Bisek Architectural Lead/ Eric Osborne GRONTMIJ/ Landscape Design Transport Engineers ARUP / Consultant Engineers Structural Electrical Services, Specialist Engineers Geotechnical, Hydrology, Waste Management, Economic and Planning-Consultant, Environmental Consultant

Building Tirana's GREEN Future

The River Park function. We have designed these quarters

The underlying theme for the River Park

to exude distinct characteristics that are in

is:

keeping with their function and status.

TRANSFORM

RECONNECT,

AND

the

The Tirana River has become a neglected

boulevard strictly retains the north-south

area and is, in some places, abused. It will

axis. We have located the trams centrally

become a destination and place of celebration

along a grassy corridor, so as to consolidate

and has the opportunity to become the

the tram stops going north and south. The

symbol of new life in Tirana and a natural

Tirana River has become a neglected area and

part of the city.

The

RESTORE,

movement

corridor

along

is, in some places, abused. It will become a

The masterplan seeks to restore the

destination and place of celebration and has

river to its original character and quality.

the opportunity to become the symbol of new

The debris and rubbish will be removed to

life in Tirana and a natural part of the city.

create an amenity experience for everyone

The masterplan will reconnect the river. A

in Tirana and improve the cityâ&#x20AC;&#x2122;s biodiversity.

new City Pavillion at the top of the Boulevard

The restored river will encourage social

on the Pasquchan hill will be the symbolic

interaction, attract visitors and create many

place of the masterplan. A symbol of the

opportunities to introduce a programme of

aspiration of the project and a place to watch

activities and interventions along its length.

the City of Tirana grows into its future.

The river restoration provides the opportunity

to introduce different river types such as pools

Një Qytetar, Një Pemë. This woodland will

and backwaters.

descend to the edge of the lake and when complete will extend to a newly defined level

Regeneration Masterplan

edge where a simple path will allow people to

The masterplanwill reconnect the River.

walk all around the lake.

New artist-designed bridges across the river

Located at even distances apart, pavilions

will become a feature and celebration of the

representing each region of Albania will

new improved river corridor. They will sit

create resting areas. At each Pavilion a clearing

comfortably within the structure of the park

in the woodland will be designed with the

and seamlessly connect people with the river

characteristics of the landscape of the region.

and the natural environment. A network of

When the lake is full, all the pavilions will be

paths, cycle routes and bridle ways bring easy

linked by the water in harmony to symbolize

access for everyone.

a new peaceful and united. Albania with

The masterplan will transform the river

Tirana at its core. The park will provide

into a new sustainable and accessible

a place of belonging for people who have

environment that is a real asset for the city

moved to Tirana and will be a peaceful and

of Tirana, providing a cherished natural

beautiful tourist attraction to demonstrate

place where people can escape from the

the Albanian landscape and natural beauty.

urban environment. The design approach is to reinvigorate the corridor through the

Impact Assessment of the Proposed Design

development of a clear spatial landscape

Our proposals aim for Tirana to become a

narrative reflecting the demands of both

truly sustainable city and a place for people.

passive and active recreation. A showcase

We want our designs to have a far greater

where natural life can be celebrated, whether

impact than the creation of an axial boulevard

in the form of varied and rich indigenous

and a river park, instead to provide holistic

planting, demonstrations of natural crafts or

solutions to create a city that people can enjoy

walking, cycling and horse riding.

living in. For this purpose, we have created the Charter for Urban Living as a process to

The Paskuqan Park

achieve long term prosperity and vision.

The new park symbolises hope for everyone. The northern park will be a new green space

Environment Impact

for all the citizens of Tirana. The expansion

We have considered solutions that work

of the city is fuelled by immigration from all

on a large-scale framework to address issues

over Albania. These are people who come to

of connectivity, infrastructure, transport,

Tirana with hope for their future.

mobility, amenity, housing and density. These

This park will become a symbol of that future to welcome its new citizens. A total of

are presented as varying strategies at the citywide scale.

750,000 trees will create new urban woodland.

Strategy for densification addresses

Each inhabitant will plant a tree in the park,

the issue of informal settlements and

following the municipality‘s own project:

infill land. This would result in better 43

Building Tirana's GREEN Future use of land resources whilst providing for

sustainable and compact urban form which is

improved housing with improved access

the way forward for a 21st century future city.

to basic amenities. We propose to define a

We also propose a waste from energy

clear boundary for Tirana to ensure clarity

system and an intuitive strategy for the

between its urban areas and the surrounding

collection of refuse which would ensure

mountain landscape thereby improving the

a cleaner city. As the river park is created,

image of the city and preventing sprawl. This

it will be maintained, thereby creating a

would have an immense impact on Albania’s

cleaner environment for the river and its

natural resources ensuring these are protected

surroundings. There is no ‘one-size-fits all’

thereby adding to its increased tourist appeal.

solution to the issue of informal settlements.

A densification strategy also provides

We propose a pattern which would need

for a greater critical mass within a set urban

to consider the specific socio-economic

area to ensure that these can support and

context. The pattern would need to be

sustain basic amenities and public transport.

further developed to understand the nature

This is overlaid with a network of walkable

of deprivation and pursue an integrated,

neighbourhoods each with its own centre

people-focused and place-based approach.

located within a five minutes’ walk of each

Our pattern proposes to be a system of land-

residence. The key environmental impact of

management committed to providing people

this strategy would be a reduction in car usage

access to a good level of amenities and open

and an increase in walking and cycling and

space. We have described our methodology in

an overriding reduction in sprawl with its

previous chapters.

negative environmental effects. Our proposal provides for an appropriate

Traffic Impact

built mass resulting in defined urban spaces

Through a clear hierarchy of streets, traffic flow

and streets. We propose an improvement

and management would be smoother thus

in the public transport provision with the

creating less congestion zones. This would be

introduction of buses initially leading onto

further enhanced by a reduction in private car

the tramway system. Our strategy proposes

usage due to the increase in public transport.

a major interchange at the rail station with

We propose that all roads should be designed

trams and buses connecting onto the city

as streets thereby providing greater priority

centre and with the key areas within the

to pedestrians and cyclists. This is a more

boulevard. The impact of this proposal would

sustainable approach to road design. Greater

lead to a reduction in car usage thereby

emphasis on walking and cycling would

reducing pollution. It would also create a

reduce the overall impact on the environment.

Smoother traffic flow along with a clear

for the citizens of Tirana. Designed and

parking strategy would ensure reduced clutter

maintained green open spaces and corridors

and congestion on the streets as cars would

would lead to healthier lives as people

be parked off street in parking garages or

would be encouraged to be outdoors and

in underground car parks. This would also

have a greater relation with their natural

reduce the occurrence of traffic collisions

surroundings. Less stress will be created

with increased safety on the roads. Greater

with more the streamlined and efficient

provision of cycle lanes on new roads and

travel options. A good quality of life would

wider existing roads would also provide safer

also lead to a longer life expectancy and

cycling and encourage more people to cycle.

facilitate a greater work output

Service access provided at the back of

Good public and communal spaces

buildings would help to reduce congestion

encourage people to gather and interact

and conflict along main movement corridors

thereby improving community spirit and

particularly in the boulevard, reducing

general morale.

congestion along the main carriageway.

with the creation of clear landmarks and

This can be achieved

We propose a hydrogen bus service which

interesting nodal spaces with good quality

is sustainable and will reduce pollution. Streets

outdoor spaces, which would instil greater

with clear lanes for buses would help these

pride in the people of Tirana. Creating a

services to move more smoothly rendering

safer city with a clear hierarchy of streets

them easier and more attractive to use.

will encourage a sense of inclusiveness and also improve active frontages onto streets to

Impact on the Quality of Life

provide greater natural surveillance.

Our designs and city wide strategies propose

We will strive to make Tirana a more

to improve Tirana as a better place for its

accessible city for all ages. This will include

people to live in and ensure that it is a more

providing access for all, for young children

attractive city for tourists to visit. It is hoped

in the form of play areas, improved schools

that our proposals will attract expat Albanians

and crĂ¨ches, to the supplying the youth

back to their city and ultimately increase the

with improved sports facilities, a river park,

overall investment in the country. Improved

major cycling and walking areas as well as

housing stock would provide every resident

public open spaces where they can gather.

with a good place to live and good access to

In addition to this, the elderly will be a key

facilities and amenities.

concern and the design will create areas

Similarly, an increase in walking and cycling would result in improved health

where they can meet, while allowing for suitable transport options.

Dar Al-Handasah (Shair and Partners) Office: Dar Al-Handasah (Shair and Partners) has been a pioneering force in the planning, design and implementation of development projects in the Middle East, Africa and Asia since its beginnings in 1956. Today we are a global consultancy with 43 offices throughout 30 countries, known for our problem identification, tailor madedesigns, quality, on-time deliverables and multidisciplinary expertise. Main Works: Oqyana (Australiasia Segment of The World), Dubai, UAE; Bonny Master Plan, Nigeria; Sharm El-Sheikh Airport, Egypt; URL: http://www.dargroup.com

DAR Darâ&#x20AC;&#x2122;s Tirana North Tirana North, a city for a new economy,

Importantly, the linear park will provide

will deliver 16,000 new homes and 20,000

connectivity between Lake Park to the

new jobs creating a sustainable mixed

south, the cultural heart of Tirana and the

use development in the heart of Tirana.

developing Lake Paskuqan area to the north.

Regeneration of the River Tirana and existing

The River Tirana enterprise zone, linked to a

communities is the key to building a modern

research park on the new university campus,

boulevard development with new cultural

will introduce innovative new businesses

and civic institutions including a state-of-the-

to the area, recycling redundant industrial

art university campus.

land with new technology parks and spin-off research and development activities.

Tirana Park is the new linear park within

New sports and leisure facilities,

the boulevard which will become the focal

including a world class golf course and

point for a range of civic and recreational

the planting of 10,000 trees around Lake

activities including shopping, going to the

Paskuqan, will provide open space and

library, relaxing in the gardens and eating

recreation for all including young people,

and drinking in one of the numerous cafes

families and the older generation.

and restaurants which activate the park. 54

Darâ&#x20AC;&#x2122;s approach to the Northern

DAR Master-planning & Architecture

David Abdo/ graphic designer, Anna Anastasiou/ urban designer, MehrnoushEsfahani/ graphic designer, Vicki Gibbs/ environmentalist, Steven Hancock/ graphic & urban designer, Richard Hodgetts/ landscape architect Daniel Horner/ urban designer, Quake Hsu/ urban designer, Peter Igoe/ landscape architect, Vytautas Jackevicius, architect, Peter Lutman/ public transport specialist, John Mc Cawley/ environmentalist, Edouard Moreau/ urban designer, Phongsak Norkaewmongkhon/ graphic designer Maria Paschalidou/ urban planner James Richford/ landscape architect Amir Sadafi/ architect, Saeed Shohani/ transport planner, Celine Serhal/ economist, MulhamSleiman/ economist, James Stewart/ graphic designer, Tava Walton/ project manager, Min Zhang/ graphic designer ArX Solutions, Miami Crystal CG, London Glowfrog Studios, London Pipers Architectural Model makers, London

River and Boulevard Project is to deliver

zone for the city accessed by the proposed

an integrated land use and transport plan

northern ring road and LRT system

which opens up the northern part of the city

• In addition to modern business parks

for development and enables regeneration

along the river creating new high density

of existing housing and employment areas

residential areas along a cleaned up and

within the city. The key land use moves

managed river corridor which is home to

within the strategic plan are defined below:

a series of smaller and connected riverside

• The expansion of the city centre – proposing

parks

major new civic, retail and leisure uses along

• Strengthening the green spine from the

the boulevard extension into the northern

Big Park Lake to Lake Paskuqan along a

development area

new linear park connecting the existing

• Bringing together existing university uses

boulevard to the river Tirana

within Tirana into a new consolidated

• Creating new sports and leisure uses at Lake

campus at the northern end of the boulevard

Paskuqan – extending the boulevard across

extension

the river and providing a direct green link to

• Creating a series of employment hubs along the River Tirana creating a new enterprise

the renovated park • The key transport moves within the 55

Building Tirana's GREEN Future strategic plan are set out in more detail in

LRT and buses and robust waste and

the transport section of this report and are

water management to clean up existing

summarised below:

parks, waterways and open spaces. Finally

• To deliver the northern ring road extension

new renewable energy opportunities will

on the south side of the river to access

help to stabilize energy supply, reduce the

new development areas and minimise

carbon footprint of the city in the future,

expropriation

and provide a new direction for small-scale

• To provide an LRT system connection from the site of the old railway station to the site

industry in a country already recognized for its renewable energy credentials.

of the proposed new multi modal station to the west along the existing railway line –

The Recreation Park

again to minimise expropriation

The western end of the river corridor

• To upgrade the existing road to the north

comprises

the

recreational

part

of the river and provide new river crossings

the proposals. On the northern bank

to improve accessibility from the northern

surrounded by new residential development

expansion areas

will be the canoe and water park surrounded

• To utilise the new and improved roads along

by semi natural woodland planting. On

the river to provide utilities infrastructure in

the southern bank will be an area edged

the form of trunk sewer interceptors to assist

by formal stepped terraces and a walk way

in the clean-up of the River Tirana

comprising football pitches and a cricket

• To provide new bus routes, bus rapid transit (BRT) and park and ride bus facilities to

pitch. The whole area will be accessed by sinuous paths and woodland planting.

enable a sustainable transport network

Beyond the recreational area the river

to be developed in Tirana Sustainable

corridor will revert back to an ecological

environmental and transport solutions are

diverse country park with sinuous pathways

central to Tirana North including active

and indigenous woodland and under-storey

management of the River Tirana to create

planting. An activity keep fit trail would be

ecological pools and reed beds, walking

located along the paths. More formal grids

and cycling tracks beyond the city limits,

of trees will be designed creating the feel of

a new public transport network including

an arboretum.

Tirana Research & Development Park

and traffic calmed environments for

The River Tirana Enterprise Zone will

children to play. Children’s’ play space will

accommodate new research & development

also be a requirement of each residential

parks (R&D parks) to the east of the

development.

boulevard. The R&D parks will be located on formerly industrial land and will benefit

Enterprise Zone

from close proximity to the proposed

The River Tirana Enterprise Zone will be

university campus adjacent to the River

poised to become the premier research

Tirana. Located close to the proposed

and innovation centre within the Balkan

Outer Ring Road the R&D parks will

Region and look to set a new standard for

enjoy excellent road access and will share

the formation of research environments

resources, investment and ideas with the

in which knowledge-based businesses can

educational facilities at the university. The

flourish to the benefit of the local, regional

R&D parks are also located close to proposed

and international economy.

new housing developments to encourage

The object of the River Tirana

sustainable live – work arrangements and

Enterprise Zone is to utilise Tirana’s young

travel patterns.

educated population to advance science and technology through collaborative research

Tirana Riverside Communities

and innovation. Enterprise zones which

The Tirana riverside communities will

embody and integrate education, science,

encompass high density living for mixed

technology and business into holistic living

and

environments can act as major catalyst for

balanced

communities

including

starter homes for young people, larger units

regeneration and economic growth.

for families and accessible ground floor

The location and design of the

units for the elderly and mobility impaired.

River Tirana Enterprise Zone along the

Each community will enjoy private open

Tirana River incorporates a total ‘living

space in the form of balconies, communal

environment’ in which the community

open space in the form of courtyards and

lives, work and play in harmony with their

public open space in the riverside parks.

environment through healthy sites and

Shared streets will provide good access

buildings. Only in such an environment

Building Tirana's GREEN Future will Tirana North realize its vision to propel

facilities, including an 18 hole golf course,

the next generation of innovation, discovery

and playing fields.

and entrepreneurship.

Environment and Sustainability The Boulevard

The Environment and Sustainability Policy

An analysis of built form, character, heritage

Framework is a high-level overview and

and public realm has been undertaken

analysis of the environmental, social and

in order to inform the continuity of the

economic issues influencing the success of

existing boulevard character to the northern

the master plan. It is a holistic tool to ensure

extension.

that all environmental and sustainability issues are identified and responded to and

The Paskuqan Park

is included as Appendix A of the Delivery

Zone 5 will be developed as a leisure and

Report.

recreation area serving the entire city of Tirana, and beyond. Central to this will be

Regulatory Influences

the redeveloped Lake Paskuqan Park. Over

The

10,000 new trees will be planted, reflecting

Programme (UNDP) has been assisting

Albaniaâ&#x20AC;&#x2122;s

Albania with accelerating environmentally

native

woodlands.

Walking

United

Nations

development.

Development

trails and running paths will run between

sustainable

starting

woodland areas of Oak, Hornbeam, Linden

point was to review the existing Strategic

and many other native species.

Environmental Assessment (SEA) and

A brand new resort with a hotel, Casino

Environmental Impact Assessment (EIA)

and country club will also be developed

legislation, and ensure its appropriateness

here, with state of the art sports and leisure

in relation to the EU standard. The Tirana Northern Boulevard and River Project, as a planning instrument will, upon completion, require an SEA to be conducted on it.

Individual projects within the master plan

(PV) generating electricity. Solar thermal

may be subject to separate EIAs.

should form part of all new developments with hot water requirements. Solar PV can

The Ecological Potential of the River Tirana Corridor

supply power needs, particularly to new

The River Tirana originates to the east in

is a Solar PV farm in Zone 5 and PV street

the mountains of the Mali iDajtit Protected

lighting.

Area, a park of rich biodiversity. Following

Heat Pumps - Heat pumps extract heat from

solid waste and waste water management

water, the ground or the air and compress

interventions to clean the river, the corridor

this to higher temperatures for water and

will be redesigned to form a linear park

space heating (e.g. new-build under-floor

accommodating development, recreation

heating). Heat pumps can also extract heat

and

paths

from buildings and return the heat to the

connecting the entire length. The urban

water body, ground or air, during the warmer

river is relatively steep and a fast flowing

months. Lake Paskuqan may be suitable to

river results during periods of high rainfall,

supply space heating via a Lake Source Heat

which when loaded with coarse sand

Pump.

and cobbles, becomes a destructive force.

Hydropower - The dam proposed on the River

Reflecting this, the redesign has considered

Tirana to balance river flow, can also generate

the existing natural movement of the river.

hydropower.

Distinct management units along the river

Energy from Waste (EfW) and Biogas - An

are defined. Weirs are included to develop

Energy from Waste (EfW) Combined Heat

broader, gentler areas of water. In addition,

and Power plant can provide energy from

a dam is proposed in the mountains, to

a proportion of the waste generated by the

regulate river flow â&#x20AC;&#x201C; increase flow in the dry

city. By siting the EfW plant alongside the

summers and decrease flow in the winter.

Kashar WWTP, a further source of bio-energy,

The dam is also considered for hydropower

methane (biogas) from the WWTP, could also

generation.

be combusted in the CHP plant.

ecology,

with

foot/cycle

energy-efficient buildings. Also recommended

Landfill Biogas - The Sharra Landfill site

Utilities & Renewable Resources Renewable Energy

currently receives most of Tiranaâ&#x20AC;&#x2122;s waste. The

Approximately 85% of Albaniaâ&#x20AC;&#x2122;s power

this site and combusted for heat and power,

generation is hydro-electric. Albania is well

e.g for the new Kombinat development.

positioned to further develop the renewable

Electrical Power Demand Management - It is

energy industry, providing a driver for light

important to reduce power demand, and this

industrial development in the city.

is particularly cost-effective with new-build.

Solar Power - Solar power provides renewable

All new buildings and their contents should

energy for Tirana in two forms: solar thermal

be designed to sustainability codes that reduce

providing hot water and solar photovoltaic

power demand.

methane (biogas) should be extracted from

Building Tirana's GREEN Future

Water Supply Fresh water is sourced from Lake Bovilles,

The existing combined waste water and

supplemented by springs and aquifer wells

storm water drainage network flows into the

in and around the city. An additional

R. Tirana and R. Lana, and heavily pollutes

reservoir has been proposed in the Erzen

both. The recommended development of

Valley (south-east of Tirana). A sustainable

separate storm water and sewage waste water

approach to water resources involves

networks and the construction of a Waste

improved demand management and the

Water Treatment Plant (WWTP) at Kashar

collection of water revenues that match

are necessary precursors to city development.

costs of supply. Recommendations for improvements have been made in the

Solid Waste

‘Water Supply and Sewerage Master Plan

Solid waste is sent to the Sharra landfill site, 6km

for Albania’ and the ‘National Water Supply

to the south-west of Tirana. An overall Integrated

and Sewerage Services Strategy 2011-2017’.

Waste Management Strategy (IWMS) requires

These recommendations must be enacted in

development that would, in sequential order,

order that there is connectivity throughout

consider waste avoidance, reduction, recycling,

the municipality to a clean water supply,

energy recovery, treatment and finally disposal.

under adequate pressure.

The construction of Energy from Waste (EfW) plant can provide an important contribution

Waste Water

to this strategy. Also required would be Waste

Improved waste water management is a key

Segregation / Transfer Stations as part of the

issue to be resolved ahead of re-development.

overall strategy.

Building Tirana's GREEN Future

WEST 8 Let Tirana Breathe Tirana’s ambition to extend the boulevard

The Central Boulevard and it’s extension a

demands an approach for the boulevard as

world class public space, the axe should be

a whole. Team West 8 sees the boulevard

approached from the open space, the public

in three ways:

domain and not by the architecture. In the

• The representation of the nation in the

opinion of West 8 the Central Boulevard

capital. The gravity line of the country with

needs to be:

major governmental buildings, symbols

• Greener, more trees that can grow big,

and monuments of the history of Albania

provide shade and give the city a lush

• The green lung that connects the city with the landscape: Parku I Madh to the new Park on Lake Paskuqan • The public space where people gather: an esplanade, golden mile, ramblas

character • More space for the pedestrians. At the moment the boulevard of the national heroes is the smallest highway from Europe • Introduce a new highway for cyclist: a royal

Even the most undemocratic regimes from

cycle path (6m wide) that runs from the

the past have been unable to realize the axe

Plaza Mother Teresa to the Skanderbeg

as one coherent composition and with the

Square to the Trana River. It continues

fluctuations in the world economy it will

along the new river Park and is connected

even be more unlikely that this will happen.

to new urban forest around lake Pasqukan

Once in a while there will be an outstanding

• Along the boulevard runs a tram that

piece of architecture: may be a public

becomes a light train towards the airport.

building as a new town hall or a library or a commercial building. But the majority of

West 8 proposes to connect the axis mentally

the architecture will be realized in a very

between two new landmarks:

common Albanian way. The development

• The flag view tower on the Skanderbeg

of the Central Boulevard and it’s extension

square: a monument for the 25 anniversary

requires a strategy, good ideas and flexibility.

of the democracy. The monument is

It requires not a blue print in order to make

designed as a sixty meter high flag from

West 8 Office: West 8 is an award-winning international office for urban design and landscape architecture, founded in 1987. Over the last 20 years West 8 has established itself as a leading practice with an international team of 70 architects, urban designers, landscape architects and industrial engineers. West 8's main office is based at the port of Rotterdam, and has three branch offices in Belgium, New York and Toronto. West 8 has extensive experience in largescale urban master planning and design, landscape interventions, waterfront projects, parks, squares and gardens. West8 also develops concepts and visions for large-scale planning issues that address global warming, urbanization and infrastructure. Main Works: Schouwburgplein in Rotterdam (NL), Borneo Sporenburg in Amsterdam (NL), Chiswick Park in London (UK); Governors Island, New York, USA; Toronto Waterfront Project, (CA); Playa de Palma in Mallorca (ES) and Miami Lincoln Park (USA). URL: http://www.west8.nl

TIRANA NORTHEN CORRIDOR

coated steel with a platform on top and the

live and to look back to the city. Thanks to

eagle as a void. Like the Eifel tower the flag

new highway for bicycle it takes 20 minutes

is open to the public

to be in the heart of the city.

• On the other side of the Axe on the sloops from Paskuqan Lake to the hills stands the

The Boulevard

tower of Hospitality a table from 40 by 40

The boulevard is a chain of public green

that serves as a well as a panorama deck.

spaces which facilitate the connection between the heart of the city with the surrounding

The Physical extension of the central

landscape. Lush green public spaces, set against

Boulevard is limited to the new Tirana river

the silhouette of the mountainous backdrop,

park. It is the boulevard form the democratic

aid the surrounding landscape to manifest

period: It is curved and eloquent. It creates

itself deep into the city. The green axis forms

equality instead of hierarchy. It widens

the natural counterpart to the dense urban

so that there are places for activities. It

centre and the chaos of the city.

combines the quality a boulevard and a park

The green axis consists of a chain of

or esplanade. It is a place to be or to live or

landscapes and urban spaces, including South

work on. It is enriched with activities like a

Lake Park, Mother Teresa Square, Lana River,

generous fountain, a super call skate park,

Boulevard of the National Heroes, Skanderbeg

esplanadegardens,and custom made design

Square, Boulevard, The new Park Lane in

for furniture.

the North, The Tirana River Park and the

West 8 calls it the Boulevard of Europe.

Paskuqan Lake and Park.

Along the Boulevard of Europe one finds

The surrounding landscape is accessible

the new Town hall, andconvention center,

by means of a highway for cyclists. This makes

the library, the new Palace of Justice.

it possible to travel from the Tirana River to

Unique about the design of the River

the Skandabeq Square in just 10 minutes and

park is that it is the cleaning operation is

from the University to Paskuqan Lake in 30

used to the new topography on site. The

minutes.

river keeps a natural look and condition the

The Central Boulevard is the gathering

vegetation is related to the river bed. The

space for society. Its central position in the

ring road is designed as an urban boulevard

urban tissue and its public buildings and

that makes it possible to develop new real

attractive open spaces provide an incentive for

estate along the new river parkway.

the city’s inhabitants to congregate in this area.

The Pasqukan Lake is integrated in

Here, vehicular traffic is not dominating,

the Paskuqan Park. The Park, forested, is

and the spaces are easily accessible for cyclists,

the pace for riding horse, searching for

pedestrians and public transportation. In

mushrooms picknicks, canoeing and lunch

summer, the day comes to a close with a

on the lake. The PaskuqanPark is connected

walk along the promenades. Lovers meet

with the Tirana River Park with tree green

near the fountains. Political debates take

lanes that run down the hill toward the river

place underneath the trees, and if there may

and the ring road. Along the lanes arise

be a cause to fight for, public protest rallies

villas in big gardens. There is the place to

march along the boulevard. It is where the

WEST 8 Urban Design & Landscape Architecture b.v

Adriaan Geuze/ urban designer -director, Edzo Bindels/urban designer - director, Martin Biewenga/ urban designer-partner, Christian Dobrick/landscape architect-project manager, Christoph Elsässer/ urban designer-project manager Design Team Sima Agisheva, Rikus Beekman, Karsten Buchholz, Maria Castrillo, Ela Chojecka, Fernando Diez, Kenya Endo, Juan Figueroa, Rob Koningen, Perry Maas, Jan Nijs, AttilioRanieri David Santamaria, Eva Recio, Harrie Van Oorschot, JorisWeijts, Bruno Wober WITT EVEEN +BOS RAADGEVENDE INGENIEURS B.V. Marten van der Wijk/ specialist waste management, Niels J. Monster/ specialist hydraulics, Tom Willems/specialist sustainable development MIC MOBILITY IN CHAIN Frederico Parolotto/ senior partner Francesca Arcuri/ consultant VGG b.v. Jan Winsemius/ Director

Building Tirana's GREEN Future Christmas markets trade and the street theatre and buskers perform. The elderly, students, street traders and trendy youths populate the area and give the boulevard its colour. The Central Boulevard is not exclusive; instead it is a melting pot. A six meter wide track that provides convenient access to the city and surrounding landscape dominates the street profile of the Central Boulevard zone. The bicycle as a modern means of urban transport reclaims its dominant position in the public realm and is deliberately used to solve future mobility demands. Cycling is healthy, cheap, sustainable and hip. Also, as an extension of the Central Boulevard, the Bike track will be continued to the north. This Highway for Cyclists is linked to a trail leading along the banks of the Tirana River. The track traverses north of the river to Lake Paskuqan. The bike is of essential importance to recreational users, commuters and students. The experience of the landscape whilst cycling, adds to the feeling of freedom and enjoyment of living in the city.

The River Tirana River will be freed from waste and will be transformed into a continuous ecological biotope all along zone 4. The waste will be safely stored on site. The natural riverbed will be kept and its surroundings transformed into a landscape park. The microorganisms in the wetlands natural contitions will help to degrade the waste. Alongside the Tirana River Park an infrastructure for motorized traffic will be added, which is essential to deal with the expected growth of the cityâ&#x20AC;&#x2122;s traffic. The infrastructure is situated on both sides of the Riverbed Park and guarantees the openness of landscape in between. The 70

soft and naturally landscaped River park

Recycling and Green Rehabilitation

areas present the driver with a friendly

Strategies

and green welcome in Tirana. The road wonâ&#x20AC;&#x2122;t resemble a highway but bears the expression of a Parkway instead. A Parkway which connects previous disconnected areas. Concurrently, the beauty of the River landscape will grow into an attractive area

The waste dumped in the tirana river has all kind of different origins and varies from household to debris. For each waste category there are different solutions feasible. the key to a cost-effective solution is to recycle as

to reside. In the riverbed the highway for

much as possible and to integrate the waste

cyclists is situated. Both the Parkway and

storage with eco-dynamic designs into spatial

the River Park will increase land value

planning of the (new) riverbed. For optimal

of adjacent areas and stimulate further

management of the waste the following

development.

strategies are suitable (top â&#x20AC;&#x201C; down): 71

The Paskuqan Park

the Paskuqan Lake. Currently the lake area

The Paskuqan Hills are situated north

is almost disconnected from the city tissue

of the Tirana River, in the central axis

of Tirana; therefore, we propose to realize

extension zone. This area is mainly used

three wide green corridors for cyclists, cars

for housing. The Hills, sloping upwards to

and hikers from the Tirana River to the

the sun, offer beautiful vistas over the city

lake park. These corridors will be situated

center and its future proximity to the Tirana

in low settled areas and will contribute to

parkway offer the area outstanding potential

excellent additional development qualities.

for development and densification. Its

Densification of these areas may be

northern boundary is naturally created by

developed.

According

to the market driven

be transformed into a city park as "Parku

principle, the high quality public space

i Madh", with pathways, bicycle tracks,

corridors will provide an identity to the

playgrounds, kiosks and sporting facilities.

adjacent developments. The three lanes

An iconic tower for recreational purpose

end at the half moon shaped road at the

will be positioned in the straight axis and

Southside of Pakuqan Park. Alongside this

will highlight the contra post of the central

road, a series of existing sculptural buildings

axis. The tower will be a highlight in the axis.

face the park. These buildings should be

It contributes to the city structure and offers

regarded as the first address of Paskuqan

stunning views to the Albanian mountains

Hills. Step by step, this basic landscape will

on the one side and the capital on the other. 73

ment frameworks, ningful along the ation and harmomes crucial for the

Building Tirana's GREEN Future

KCAP Axis of Gentle Heroism KCAP Architects & Planners

Office: KCAP Architects & Planners is a Dutch office based in Rotterdam (NL), Zurich (CH) and Shanghai (CN) for architecture, urban design and urban planning, founded by Kees Christiaanse in 1989. During the last 20 years KCAP has established itself as one of the leading international practices in the fields of architecture and urbanism. With a multi-disciplinary approach to ill depend on how ll as the new city design issues, KCAP has gained extensive complex and the city on a experience in large-scale urban design and l have a profound ana. Thismaster impact planning, waterfront redevelopments, al peripheries and remain, itcampus will be design and public transportation hubs.

es. These centers on infrastructures polycentric urban e scale, reach and

Main Works: Hafencity in Hamburg (DE); Perm 2020 Strategic Masterplan (RS); vision for Schiphol Airport Amsterdam; Strategic Vision for Bruxelles 2040; South of Olympic Park, Beijing, China, 2009; Legacy Masterplan Framework, London, England. URL: http://www.kcap.eu

Every society needs a clear direction for its

include and integrate them as constituting

future development. People who had critical

part of the genuine Albanian cultural

roles in history are the cornerstones defining

milieu. The axis incorporates connections

the path. Two most unique national heroes,

with Kamza and the airport and as such

Mother Theresa and Skanderbeg stand

generates a framework unlocking a network

on their respective squares which define

of centralities.

the main urban axis cutting through and

Tirana’s Northern Boulevard City

spatially articulating the whole city. Hardly

(TNBC) will be a new city in the city as it

anywhere else can one find such a unique

also will be an engine for the city. It will offer

mix between subtle, genuine and persistent

a new world, literally a new horizon and

humanity and decisive statesmanship and

define a new idea for Tirana and Albania.

bravery as with the two key historical figures

Tradition and innovation, side-by-side in a

of Albania.

landscape of great buildings, international

Their importance is already recognized

cultural attractions and vibrant open spaces:

in the urban space of the existing city. We are

Tirana Northern Boulevard City will offer

inspired by both of them and try to combine

all of this and much more. It will be the

their strengths to outline a new urban era for

crowning glory of Tirana’s northward shift,

Tirana as an ‘Open City’ based on ‘Designed

establishing a new hub for business, leisure

Coexistence’. We envision a city that is

and life.

diverse, lively and socially sustainable, where

It will unlock an urban economy based

people can productively relate to each other

on service industry and tourism, with

culturally, socially, as well as economically.

knowledge centers, services, leisure retail,

Tirana’s Northern Boulevard City will

creative manufacturing. The scale of the site,

become a glocalcentre of international

coupled with the critical fact that the majority

distinction, a thriving new city district in

of the site is under public ownership, make

Tirana, and an anchor in the social and

possible this unique form of development,

economic regeneration of Northern Tirana.

land management, long-term value creation

When imagining the continuation of

KCAP Kees Christiaanse/ urban planner Ruurd Gietema/ urban planner, Olaf Gerson/ project lead and management, Petar Zaklanovic /project design lead and urban planning, Michiel van Driesche/ landscape architect, Alexandra Merkulova/ architect, Bouke Veurman/ architect, Koen Klok/ 3D rendering, Chris Gasior/ assistant designer, Sebastiaan Dobiets/ assistant designer Systematica Traffic design and strategic transport modelling Luca Guala/ traffic engineer Metro_POLIS Architecture and Planning Local partner/ local specific input, communication, implementation and general feedback, Besnik Aliaj/ urban planner, Sotir Dhamo/ urban planner, Elvan Dajko/architect, Endrit Marku/architect, Ledian Bregasi/ architect, Andonino Di Raimo/ architect

and exemplary design aspiration.

the monumental Boulevard and building

TNBC will define the next generation

on its prestige and profile, we explore its

of living and working in Tirana. It will

wider potential to unlock an urban future of

be a place where global attractions co-

Tirana. A stronger, more visible axis reaches

exist with emerging new Northern Tirana

out towards the northern city extensions,

neighborhoods, combining the best of

Building Tirana's GREEN Future city living in one district. It will be a place

children will have now a better future and

unlike any other in Tirana, offering the best

access to what their parents were missing.

in knowledge, service, leisure and cultural amenities and urban parks, and at the

The Boulevard

same time creating places to live that are

The existing sequence of squares along

rooted in the ethos and fabric of Northern

the boulevard will be enriched with 3 new

Tirana’s diverse and vital communities. It

places, enriching the axis with particular and

is organized as a ‘connected urban mosaic’

outspoken centers. Firstly we add a urban

with development of various districts within

balcony at the end of the existing boulevard.

a framework of infrastructure, public spaces,

The height difference makes the balcony a

landscape en water. Connecting to Tirana

place in the city from which a clear view to

vibrant centers/places and linking to Greater

both, north and south of the axis can be cast.

Tirana and beyond. A city organized in such

At the place where the Tirana River used

way it offers qualitative daily urban systems.

to cut the city from its rapidly developing

It will cater for Tirana citizens who want

north-east extensions, we envision a land

to live and work without a long commute

bridge, with a high quality park on and

and raise a family or start a business in a

diverse uses around it. Topography allows

stable urban community. It will be a place

for wide open views on both boulevard and

where the Boulevard, the river and the

the Tirana river.

lake provides the impetus for a healthy and

Eventually the sequence ends with a

sustainable lifestyle, anchored by sports and

new Skanderbeg visitor’s center, positioned

active living. Over the next 25 years, TNBC

at the tip of the highest hill in the proposed

is expected to deliver 8.000 new homes and

recreational zone around the lake. The

7,000 –8,000 new jobs along with education,

center is designed so that it opens the views

health, and community facilities, making a

to the north, towards Kruja, Skanderbeg’s

significant contribution to Tirana’s housing,

place of birth. As such, the axis becomes

employment and community needs.

a visual, symbolic corridor and eventually

Above all the axis of gentle heroism refers to the normal people. As such it is a

combined by (public) transport it will turn into a functional trans- urban direction.

kind of tribute to them and all the people

As a grand development project the

that suffered during the difficult years of

Boulevard stiches four disconnected parts of

the communism and that they had to leave

Tirana into a coherent and synergetic whole.

everything, making a shift in their live and

Stretching across the Tirana River, the plan

invest all what they gained for a better future

is the unique chance to secure and articulate

for them and most of all for their children.

the connection between the old southern

This could be a kind of pay back where they

and fast growing northern parts of the

be a place where global attractions co-exist with emerging new making a shift in their live and invest all what they gained for a better on its prestige and we explore its wider potential to It will axis building that connects some ofprofile, the major tokens of the Albanian nationNorthern TiranaThe neighborhoods, combining best of city living in one unlock an urban future of Tirana. A stronger, more visible axis reaches via future for them and most of all for their children. This could be a kind of dentity. Stretching from Petrela, cutting through Tirana Mother competition sitetheepitomizes both of the development frameworks, out towards the northern city extensions, include and integrate them district. It will be a place unlike any other in Tirana, offering the best pay back where they children will have now a better future and access to resa asand Skenderbeg squares, all thecultural way to theThe historic of service, organic along the Tirana river and parks, symbolic along the knowledge, leisure and cultural amenities and urban constituting part of the genuine Albanian milieu. axis intown whatand their meaningful parents were missing. ja, the axis spatially determine the region. historical axis cutting straight through the site. Utilization and harmonization of these two development frameworks becomes crucial for the success of any proposal. Northern Boulevard versus the valley of progress

Building Tirana's GREEN Future

DURRES

RES

Tirana is seated in a natural amphitheater. Combined with two important investments occurring at the moment, The Tirana-Elbasani new Highway and the Tirana-Dibra Highway this creates the “valley of easy progress”. It results in a logical but questionable organic spatial develPETRELA opment as Tirana expands towardsPETRELA the north-west, stretching in the diPETRELA rection of Durres and the Adriatic Sea. Messy urban development and a loss of the specific character of the urja-Tirana-Petrela North.axis Boulevard: Cultural axis Kruja-Tirana-Petrela ard: Cultural Kruja-Tirana-Petrela ban ambient dominate the sight. KRUJA

In this context we stress the importance of The Northern Boulevard. Not only it is an important element in the framework of the major development of the infrastructure of the region. The boulevard lies along the axis that connects some of the major tokens of the Albanian national identity. Stretching from Petrela, cutting through Tirana via Mother Theresa and Skenderbeg squares, all the way to the historic town of Kruja, the axis spatially determine the region.

As such, the axis becomes the ultimate driver for more than only the spatial development of the city. It enables Tirana to reinvent itself by reinforcing and rediscovering its hidden meanings. The competition site epitomizes both of the development frameworks, organic along the Tirana river and symbolic and meaningful along the historical axis cutting straight through the site. Utilization and harmonization of these two development frameworks becomes crucial for the success of any proposal.

KRUJA

Two directions of Tirana’s spatial development

city. The areas east and west of the railway

KRUJA

line will be linked together extending the DURRES

RES

adjacent streets into the new park, towards carefully envisioned destinations, built in

DURRES

PETRELA

and along the park. Public buildings in and

na-Durres Two engines for development... Valley of Progress: Metropolis Tirana-Durres Two engines for development... ...combined on the site. ...combined on the site. ress: Metropolis Tirana-Durres Two engines for development... ...combined on the site. PETRELA

along the park and the park itself act as the

North. Boulevard: Cultural axis Kruja-Tirana-Petrela

destinations for both new development and

KRUJA

Framework for qualities k forAqualities

the existing surrounding urban context.

robust torobust surrounding communities transforming sitetransforming the catalysts of site thetransforming new of Tirana, willofdepend how will depend cture ensure that Awill convergence of TNBC transport infrastructure willwill ensure that connections TNBC will connections tothe surrounding communities the site the catalysts the new polycentric vision ofon Tirana, torobust surrounding communities the thepolycentric catalysts ofvision the new polycentric vision ofon Tirana, how will depend on how f transport infrastructure willwill ensure that connections TNBC fromin anTirana. informal backyard into a shared and welcoming place. Networks the and different neighborhoods and districts, as well as the new city Tirana. Theofplaces extended boulevard, be one the best-connected The extended boulevard, from an informal backyard into awell shared welcoming place. Networks well the different neighborhoods districts, as well as the new city from an informal backyard into a shared and welcoming place. Networks well the different neighborhoods and districts, as well and as the new city t-connected in Tirana. The places extended boulevard, paths and connect site through and bothand with their direct neighbors and the city onwith a their d airport, and new proposed the territories link to the theand northern territories and andbridges thestreets, newwill proposed of streets, andacross bridges willcenters connect theintegrate siteitsthrough across its centers willtheir integrate both and the city on a of paths andthe bridges willpaths connect the siteitsthrough andwill across centers will integrate both with direct neighbors and direct the cityneighbors on a orthern airport, and of thestreets, new airport, proposed edges, providing a clear and legible movement pattern, both east-west wider scale. structural network which offers a east-west ring road add up to an infrastructural network which offers a edges, providing a clear and legible movement pattern, both east-west wider scale. ad add up to an infrastructural network which offers a edges, providing a clear and legible movement pattern, both east-west wider scale. and north-south. The development of the framework will have a profound regional and international access. and north-south. Theinfrastructural development of the infrastructural and north-south. Theinfrastructural development of the framework will have aframework profound will have a profound lcess. andcitywide, international access. The dynamic, young, The diverse and creative ofand TNB park will bringofand impact the shape and dynamics of northern Tirana. This impact The dynamic, young, diverse creative energy of TNB park will bring impact on the shape and dynamics of northern dynamic, young,energy diverse creative energy TNB parkon will bring impact on the shape and dynamics of northern Tirana. This impact Tirana. This impact life into surrounding communities. Residents willsurrounding enjoyResidents strong will felt Residents atstrong the historic urban center, onwill agricultural peripheries and artly along the existing Arunning ‘T’ shaped tramline connection, partly running along thethe existing life into the communities. willbe enjoy strong be felt at the historic urban center, on agricultural peripheries and life into surrounding communities. willbe enjoy will felt at the historic urban center, on agricultural peripheries and mline connection, partly running along thethe existing physical, economic and social links with their longtime neighbors. Vital the areas between. While the recognizable city will remain, it will nl serve between the historic city center, railway track, will serve as athe connection between the historic city center, and physical, economic and social linksneighbors. with theirVital longtime Vital While the areas between. While the citybe will remain, it will be physical, economic social links with their longtime theneighbors. areas between. the recognizable citybe willrecognizable remain, it will as a connection between historic city center, connections will open up opportunities for shared amenities including supplemented with multiple centers, hubs and nodes. These centers tation. This means TNBC will be the airport and the relocated railway station. This means TNBC will be connections will open up opportunities for shared amenities including supplemented with multiple centers, hubs and nodes. These centers he relocated railway station. This means TNBC will be connections will open up opportunities for shared amenities including supplemented with multiple centers, hubs and nodes. These centers schools, enterprise, and training, andjobs collaborations inand thejobs arts andtraining, will in beand drawn together a the network of communication station and the city center less than a historic few minutes away from the station and thejobs historic city center schools, enterprise, and collaborations arts together and will drawn infrastructures together in a network of communication infrastructures schools, enterprise, and training, collaborations the arts and willinin be drawn inbe a network of communication infrastructures nutes away from the station and the historic city center entertainment. (rail, road, air, and internet) and will form a complex polycentric urban rport. and less than 20 minutes to Tirana Airport. entertainment. (rail, road, internet) andpolycentric will form aurban complex polycentric urban entertainment. (rail, road, air, and internet) andair, willand form a complex minutes to Tirana Airport. Theaims success of and theaTNBC as aofnew ofThe North andTNBC as oneasofaTirana system that into theand once hinterlands. Therural scale, reach and ms toIn create a network anda network addition to aims this,ofthe Masterplan create network safe and success the new piece of extend North as rural one of system that extend into the once hinterlands. The success ofpiece the TNBC as aTirana newofpiece of North and as one of Tirana system that extend into the once hinterlands. Therural scale, reach and The scale, reach and s, the Masterplan tosafe create oftosafe

Being a large urban development by any

standard, and definitely in Tirana’s context,

DURRES

the plan has a responsibility for igniting a

PETRELA

Valley of Progress: Metropolis Tirana-Durres

process of regeneration of its immediate

Two engines for development...

...combined on the site.

context. We propose improvement of the

Blue and green strategy n strategy

wo engines for development...

New Urban Quarters New & Urban Mosaic Transportation Modes Urban Quarters & Urban Mosaic Transportation Modes Urban Quarters New & Urban Mosaic Transportation Modes Kruja Castle

Kruja Castle Preza Castle

Albanopolis

Tirana Albanopolis International Airport

ko - Sh na Tira way High

Tirana International Airport

ko - Sh na Tira way High

Preza Castle

public space at the edges of the site, towards

...combined on the site.

Albanopolis

Tirana International Airport

Albanopolis Preza Castle

Albanopolis

Kruja Castle

Preza Castle

ko - Sh na Tira way High

A Framework for qualities

Kruja Castle

the existing urban structures. By widening

dra

- Dibra Tirana y Highwa

Farka Lake

Paskuqani Lake

urban plazas, old and new development will

jti Da a- r an Tir bleca Ca

Farka Lake Kombinati

Kombinati OUTER CONNECTIONS

aan Tir bleca Ca

come together. Allowing for a productive

Farka Lake

NEW TRAM LINE

jti

Da r

jti Da a- r an Tir bleca Ca

Tirana Big Park

Kombinati

OUTER CONNECTIONS

Dajti Mountain and Castle

Economic centrality

Tirana Big Park

Farka Lake

Paskuqani Lake

Dajti Mountain and Castle

Economic centrality

Tirana Big Park

Dajti Mountain and Castle

Economic centrality

e ay urr hw - D Hig ana Tir

Paskuqani Lake

Dajti Mountain and Castle

- Dibra Tirana y Highwa

of the street profiles or the creation of

Paskuqani Lake

e ay urr hw - D Hig ana Tir

Dajti Mountain and Castle

Kamza

Paskuqani Lake

e ay urr hw - D Hig ana Tir

Kamza

Dajti Mountain and Castle

dra

robust connections to surrounding communities transforming the site the catalysts of the new polycentric vision of Tirana, will depend on how from an informal backyard into a shared and welcoming place. Networks well the different neighborhoods and districts, as well as the new city of streets, paths and bridges will connect the site through and across its centers will integrate both with their direct neighbors and the city on a edges, providing a clear and legible movement pattern, both east-west wider scale. and north-south. The development of the infrastructural framework will have a profound The dynamic, young, diverse and creative energy of TNB park will bring impact on the shape and dynamics of northern Tirana. This impact A ‘T’ shaped tramline connection, partly running along the existing life into the surrounding communities. Residents will enjoy strong will be felt at the historic urban center, on agricultural peripheries and railway track, will serve as a connection between the historic city center, physical, economic and social links with their longtime neighbors. Vital the areas between. While the recognizable city will remain, it will be the airport and the relocated railway station. This means TNBC will be connections will open up opportunities for shared amenities including supplemented with multiple centers, hubs and nodes. These centers ust connections to surrounding communities transforming the site thejobs catalysts of the new polycentric vision depend on how enterprise, and training, and collaborations in the arts and of willTirana, be drawnwill together in a network of communication infrastructures less than a few minutes away from the station and the historic city center schools, entertainment. well the different neighborhoods and districts, (rail, road, and as internet) and will form a complex polycentric urban and less thanbackyard 20 minutes into to Tirana Airport. and welcoming place. Networks m an informal a shared asair, well the new city The success of the TNBC as a new piece of North Tirana and as one of system that extend into the once rural The scale, reach and In addition to this, the Masterplan aims to create a network of safe and Farka Lake Farka Lake treets, paths and bridges will connect the site through and across its centers will integrate both with their direct neighbors and the city on hinterlands. a A convergence of transport infrastructure will ensure that TNBC will be one of the best-connected places in Tirana. The extended boulevard, the link to the northern territories and airport, and the new proposed east-west ring road add up to an infrastructural network which offers a citywide, regional and international access.

coexistence and driving the existing, low

es, providing a clear and legible movement pattern, both east-west wider scale. north-south. The development of the infrastructural framework will have a profound dynamic, young, bring impact on the shape and dynamics of northern Tirana. This impact Blue and green diverse strategy and creative energy of TNB park will New Urban Quarters & Urban Mosaic Transportation Modes into the surrounding communities. Residents will enjoy strong will be felt at the historic urban center, on agricultural peripheries and sical, economic and social links with their longtime neighbors. Vital the areas between. While the recognizable city will remain, it will be nections will open up opportunities for shared amenities including supplemented with multiple centers, hubs and nodes. These centers ools, enterprise, jobs and training, and collaborations in the arts and will be drawn together in a network of communication infrastructures ertainment. (rail, road, air, and internet) and will form a complex polycentric urban success of the TNBC as a new piece of North Tirana and as one of system that extend into the once rural hinterlands. The scale, reach and RIVERS

INNER CONNECTIONS

OUTER CONNECTIONS

PEDESTRIAN NATURALISTIC PATH

INNER CONNECTIONS

ECONOMICAL CENTRALITIES

PEDESTRIAN NATURALISTIC PATH

GREATER TIRANA RING ROAD

PEDESTRIAN NATURALISTIC PATH

NATURAL CENTRALITIES

Economic centrality

OUTER CONNECTIONS

ECONOMICAL CENTRALITIES

NATURAL CENTRALITIES

LAKES

NEW TRAM LINE

TRAIN LINE WEB

INNER CONNECTIONS

PEDESTRIAN NATURALISTIC PATH

Economic centrality

NATURAL CENTRALITIES

INNER CONNECTIONS

Kavaja Tirana Highway Economic centrality

TRAIN LINE WEB

GREATER TIRANA RING ROAD OUTER CONNECTIONS

GREATER TIRANA RING ROAD

Kavaja Tirana Highway

OUTER CONNECTIONS

lb -E a y an a Tir ighw H

Kruja Castle

Preza Castle

Shko aTiran way High

Albanopolis

Tirana International Airport

dra

Dajti Mountain and Castle

in an organic way, beyond the immediacy

Economic centrality

Tirana Big Park

Farka Lake

Transportation Modes Farka Lake

Kombinati

OUTER CONNECTIONS

RIVERS

INNER CONNECTIONS

PEDESTRIAN NATURALISTIC PATH

NEW TRAM LINE TRAIN LINE WEB GREATER TIRANA RING ROAD

PEDESTRIAN NATURALISTIC PATH

NATURAL CENTRALITIES

ajti -D na r Tira leca Cab

of any design dogma, resulting in a variety,

Tirana Big Park

New Urban Quarters & Urban Mosaic

- Dibra Tirana Highway

Paskuqani Lake

Dajti Mountain and Castle

densification and improvement, a gradual process of gentrification will manifest itself

e ay urr hw - D Hig ana Tir

Kamza

Paskuqani Lake

quality built structure into a gradual as

Petrela Castle

Kruja Castle

lb -E a y an a Tir ighw H

Petrela Castle

Kavaja Tirana Highway

INNER CONNECTIONS

lb -E a y an a Tir ighw H

a Castle

Economic centrality

ECONOMICAL CENTRALITIES

LAKES NATURAL CENTRALITIES

OUTER CONNECTIONS

Kavaja Tirana Highway

INNER CONNECTIONS

richness of urban ambient and overall

Kruja Castle Albanopolis

inclusion and interaction of old and new n

Petrela Castle

a as

Tirana International Airport

lb -E a y an a Tir ighw H

- Shk na Tira ay hw Hig

za Castle

NEW TRAM LINE

Petrela Castle

odra

communities.

- Dibra Tirana ay Highw

Dajti Mountain and Castle

Paskuqani Lake

e ay urr hw - D Hig ana Tir

Kamza

jti

The River

Da r

aan a Tir blec Ca

Economic centrality

We propose to combine two necessary

Tirana Big Park

Kombinati

interventions in a proposal for a River

Farka Lake NEW TRAM LINE

TIONS

TRAIN LINE WEB

TIONS

GREATER TIRANA RING ROAD

TURALISTIC PATH

Economic centrality

ENTRALITIES

RALITIES

OUTER CONNECTIONS

Kavaja Tirana Highway

Park. Enabling sufficient size for the river

INNER CONNECTIONS

lb -E a y an a Tir ighw H

Petrela Castle

and the development of a strategic east west transport connection alongside the river, whilst simultaneously reveal the latent qualities of the ambient. The result provides

true added value. The proposed river park

opportunity for equalizing the quality of

offers a safe and appealing environment for

urban space between the old part of Tirana

present and future residents and provides

and its fast growing north-east extensions. A

new opportunities for strategic urban

higher level of harmonization of the cityâ&#x20AC;&#x2122;s

projects.

living and working conditions from both

The river, industrial structures and

sides of the Tirana river is achieved.

promenades inherited from the past will

Immediately visible qualities of the

be upgraded by being integrated into a new

space around the lake are articulated

section enhanced by tree planting, islands,

through a number of leisure and catering

lawns and pavilions to create a spectacular

uses. New City Zoo park, recreational and

urban water park. Along the river we

sport activities and clusters of new residential

identified various abandoned industrial

areas around the lake are added. Skanderbeg

complexes, which we propose to reuse

visitorâ&#x20AC;&#x2122;s centre is proposed on the trajectory

as new breeding grounds and incubator

of the main city axis, at the tip of the highest

environments for startup businesses and

hill in the park. It opens the views towards

creative manufacturing. This action will

historic city of Kruja. Intensive forestation

not only help to have a better mix used

is envisioned in order to arrive at a variety

environment, but will also secure more job

of intimate spatial conditions, where the

opportunities for the inhabitants of the

proposed uses could optimally develop their

poorer areas.

best qualities.

Parts of the river park are used for water

Well accessible from proposed road

purification as well as containment areas,

and tram line traced around the lake, a

thus improving both quality and safety.

genuine multipurpose public ambient is

The variation of the water influx of the

formulated. Not only will this provide new

river throughout the seasons will create a

spaces for the city of Tirana, but also by

dynamic park setting. The low water levels

reallocating the zoo and other facilities

in summer will reveal one continuous big

in the future, it can free up inner parts

park, as opposed to various smaller parks in

of Tirana which gradually have been

the winter period, when water levels are up.

occupied and built upon in the last years. In this way additional necessary public

The Paskuqan Park

and green spaces within the existing city

Distinct green and recreational zone is

can be provided for.

proposed for the northern end of the

The Paskuqan Park will become a new

boulevard. The recreational park area from

attractive city destination and will trigger

the south of the city, the only one in Tirana,

urban regeneration and improvement of

is mirrored to the north. We seize another

quality of life on a wider city scale.

Building Tirana's GREEN Future AS&P - Albert Speer & Partners Office: Albert Speer & Partner GmbH, based in Frankfurt am Main, Germany and Shanghai, China combines innovative approaches in architecture, urban and transport planning with over 40 years of international planning and building experience. The projects range from structural design, urban planning and urban and regional development to recreation and tourism planning, conceptual transport planning and project management as well as planning-specific preparation of major events and expert opinions for policy advising. Main Works: Master plan “North Bund”, Shanghai, China; Master Plan A101 Western Quadrant, Moscow, Russia; Urban Master Plan Downtown Cologne, Germany. URL: http://www.as-p.de

AS&P A Green Boulevard for the 21st Century The existing monumental boulevard is the spatial spine of Tirana’s present urban fabric. As a classical international boulevard – spatially characterized by alignment an

• The classical representative Grand Park (Parku i Madh) • The new Sports and Leisure Park in the hilly north (ParkuPaskuqan).

symmetry - it follows an urban design

While the southern part of the Boulevard

language of the last century. The grammar

represents straight design principles of the

of a broad variety of road profiles and a

last century, the northern extension opens

hierarchy of public urban spaces and squares

a new urban design chapter for Tirana and

characterize this language.

follows a more playful and greener attitude.

Like a ''gallery of nations history''

A transformation of geometrical pattern

cultural, political and worldly monuments

into curved lines and an organically shaped

are assembled along this axis and give the city

landscape corridor is the overall design

core it´s face and identity. It connects and

theme of the new boulevard.

distributes metropolitan mobility by ring-

For future visitors of Albania, the New

and radial roads and it concentrates primary

Central Boulevard should be the gateway to

urban facilities and addresses.

the country and and it´s attractions. It should

The new boulevard will stretch between two important and green aiming poles:

give an impression about its cultural and economic abilities. For the citizens of Tirana

AS&P Albert Speer an Partners GmbH, Architects/ Planners Albert Speer/ managing partner Michael Denkel/ urban planner, member of the board

themselves the boulevard should promote as

Apartments in highrise buildings close to the

a space of integration, communication and

New Urban Park or living in the green water

leisure activities in the future.

featured axis of Tirana River Space.

The meandering new urban river space is crossing the boulevard at the turning point

Tirana River Regeneration & Development

of townscape and landscape and completes

Master Plan Area is located along the Tirana

the new cross shaped footprint on Tirana´s

River bed running from “Kamza Bridge” in

map. Albania´s national memory – the New

the West to “Tufina Bridge” in the East of the

National Library and Mediathek – will define

Tirana. This zone encompasses a total surface

this intersection and define a prominent

of ca. 350 ha. The Tirana River is currently

counterpart to the prominent addresses at

in a critical environmental condition and

Mother-Theresa-Square in the south.

therefore subject to a major regeneration

The competition area should develop

project in combination with the new Outer

as a vital mixed urban space and carefully

Ring Road construction. At the same time

complete the strong existing local peculiarities.

the river is one of the few remaining potential

A broad variety of residential areas with

recreational assets for the metropolitan area of

different standards and characters of urban

Tirana - not to be lost but to be developed with

housing are offered in the new town spaces.

the maximum care.

Team and design coordination: Michael Heller/ architect-urban planner Design Team: Chrstian Baumgarten/ landscape architect, Axel Brechenser/ student of urban planning, Robert Hagen/ architect/urban designer, Mathias Dilger/ landscape architect, Michael Dinter/ transportation planner, Erik Dressler/ urban planner, Stephan Kaczmarek/urban designer business economist, VeronikaValek/ transportation planner, Michael Vogt/ urban planner/ management Renderings & Architectural Design: ChristophTillmann/ architect AG, Engineering Consultants Hubert Bruch/ managing partner gbm-modellbaugmbh Anselm Gronau/ architect, Stefan Möller/ architect PLANPOOL.EU.SARL Oliver H. Leichte.K.

Building Tirana's GREEN Future

A series of mid-scale industrial areas had

• Assessing and defining of how to treat

been established on the South side of the

potential risk and flood areas and the

Tirana River during communist time. Most

required infrastructural measures foreseen

of the former industrial plots are either not

(in correspondence with design proposal);

re-used yet or transformed into warehouse

• Designing the river landscape, river shores

or storage functions. In view of the recent

and related infrastructure interventions,

urbanization along the Tirana River and due

incorporating the placement of water

to changed requirements and standards these

features and areas for e.g. sailing and other

development are mainly obsolete or subject

recreational purposes;

to moving into the light industry corridor

• Identifying the layout of the Outer Ring Road, in order to guarantee the most smart

between Tirana and Durres. The North side of the Tirana River is

/ un-harmful integration in coordination

much less developed and defined by recent

with the overall strategic concept and

residential urban sprawl.The main goals of

solution of new urban plan;

this project were as follows: • Defining the former industrial plots

The River Space

which are either not re-used yet neither

As a special feature, the „artificial

transformed into warehouse or storage

“element of the Boulevard is crossed by

functions

These

a meandering meadow river space at its

zones cover nearly 25% of the river side

northern pole which defines the border

development with a total area of nearly

between suburban and urban space. Water

86ha. With the implementation of this

- as subject for urban developments - is a

project these zones are seen as a potential

worldwide successful theme. While Tirana

for sustainable development and an

turned its back towards the river in the past,

economical potential since they will employ

the River Space should be defined by a new

a considerable amount of people.

urban waterfront and be opened for a broad

for

redevelopment.

• Providing a projection of a dense urban

number of new residential neighborhoods

development, in a zone of 225 ha,

in the future. The green watercourse is

covering 75% of the development area,

subdivided by a series of smaller green

along the Tirana River. Definition of

north-south corridors which are designated

kind of development on each river bank,

to open up new green resources for the city

proposals of how these developments

and it´s neighborhoods in the northern

profit from the new urban qualities,

space of Tirana. Bridges and bridge heads are

definition of functional program and land

indicated within the urban space by buildings

use distribution are also provided in this

with a moderate height.

project.

Public and other supporting functions

• Defining the use of available water

are located close to the bridge heads and

resources, providing clear measures for

generate urban life with the new river space.

the river’s regeneration and provision of

Mixed use developments define the western

concept of improving the water quality;

and eastern poles of the Urban River Space.

Building Tirana's GREEN Future

Cino Zucchi Architetti “A Flowing Boulevard, an Urban River”

The center of Tirana is marked by a

environment capable of hosting all the

clear urban layout, but its recent growth

activities and needs of a fast-growing

filled up a large area around it without

capital and to constitute a vital and loved

any order, structure, adequate services or

backdrop for the daily lives of its citizens.

meaningful public spaces. In our proposal, the voids rather

The River Corridor

than the buildings become the catalysts of

The river park is defined by the

new urban regeneration, attracting public

proposed alignment of the ring road

and private functions around a sequence

running south of the river. This is a

of green spaces of high environmental

wide urban road connecting west to east

quality. The extension of the boulevard

and giving great accessibility to the new

into a lively green promenade progressively

development while giving continuity to

opens up to the beautiful landscape of the

the existing western ring road. The south

hills across the Tirana river.

urban edge is punctuated with district

A set of new public buildings

centers and special destinations as well as

articulate its central portion, creating a

the facing of the superblocks capturing the

new grand esplanade at the junction of

opportunity to face the park and the hills

the new proposed tram lines and a series

to the other side. Some special destinations

of smaller squares in relationship with the

and residential towers are located between

existing urban fabric on the two sides of

the ring road and the river park to take

the new boulevard. At the end of the axis,

advantage of the beautiful location.

a green terrace overlooks the river, the new

The ring road carries great capacity

artificial lake and the leisure areas climbing

to deal with the expected flows but keeps

their way to the new Paskuqan lake park.

a strong urban character, avoiding any

If the previous extension of the

separation between infrastructure and

main axis aimed to extend the growing

urban fabric. The location of the future

city structure outwards, the new portion

railway station as well as the driving forces

of the boulevard brings the landscape

pulling the urban development to the west

which surrounds Tirana into the heart

suggested the proposed alignment of the

of the city fabric, generating a new urban

northern ring road and the extension of

CinoZucchiArchitettis CinoZucchi/ architect, Andrea Vigan/ architect, Sarah Zezza/ architect, Andrea Balestrieri/ architect, NicolBolletta/ architect, Anne Sophie Buyck/ architect Iris Bergamaschi/ architect, Giorgio Marzullo/ architect Graphic design /Diego Martinelli/ architect Render view/ MatteoVecchi/ architect Engram studio/ Stefano Goffi Model scale 1:2000, Model scale 1:500 One Works (consultant) Leonardo Cavalli/ architect, Norma Beatriz Stivaletta/ architect, Davide Aprea/ architect, Camilo Pelaez/architect, Antoine Verhoeven/ architect, Michele Pugliese/ architect, Alessia Mapelli/ architect, Francesca Sirtori/engineer Gustafson Porter(consultant) Neil Porter/ architect, Lot Locher/ architect, Katya Larina/ architect, Yiota Goutsou/ architect, Jeg Dudley/ architect, Jennifer Mui/ landscape architect, Nina Kolbeck/ landscape architect, Harry Bix/ landscape architect TiborVarga/ landscape architect BuroHappold London (consultant) Paolo Cresci/engineer Giammichele Melis/ engineer, Bernardo Vasques/engineer, Bob Tong/ engineer, John De camposCruiz/architect Andrew Dannatt/engineer, Adam Crozier/ architect Antonello Stella Architects (consultant) Antonello Stella, architect Claudia Awad, architect

Building Tirana's GREEN Future the existing western ring road to join as

address public spaces and parks. It is a

close as possible to the railway station.

rare resource in an urban area. The two

The northern edge of the river park

apparently conflicting options lead to the

suggests a different approach to the

design of a boulevard flanked by a linear

transformation of the urban pattern.

park following a sinuous contour, running

Lower density is applied to take advantage

from the existing city center to the future

of the potentials of the hillsides and

Paskuqan Park to the north of the town.

housing estates run gently down toward

The higher density to the east of the axis

the riverbanks. Community services such

is balanced by the generous open spaces to

as schools and sports centers may also take

the west.

the opportunity of a closer relationship with the river park.

The main boulevard is supported by other, more contained public spaces serving specific needs and uses. A long

The Boulevard

retail courtyard flanks the boulevard

The asymmetrical boulevard runs from the

to the east and acts as main anchor for

existing train station to the River and opens

the commercial activities in this new

up to the hills reaching the northern park.

part of town. Further north a new plaza

This space is the main catalyst for all main

surrounded by public offices opens onto

urban destinations of a city capital and

the boulevard and the new town hall. A

defines the formal character of the city. The

second plaza to the west of the boulevard

City hall, the Museums, the philharmonic

gives access to the Library and mediateque.

complex, the library, the new ministry of

Both plazas are the main focus for the two

Justice, all face or are strongly linked to the

green esplanades running east and west

boulevard together with other ancillary

from the boulevard.

buildings. The boulevard leans over to the

river park and opens up onto a hillside

River Park

area hosting a new stadium (or other large

The development of the North Ring Road

sport facility) and an amusement park.

provides Tirana with its biggest Green

Most of the development takes

opportunity. The natural elevation of the

advantage of land availability to provide

Paskuquani foot hills contains the river to

a quick opportunity for the town to

the north, whilst the north Ring Road can

address its future. On the other hand,

provide an ideal flood barrier to the low

land availability is an opportunity to

lying plain to the south.

seamless

an emphasis has been placed on sports

relationship between an engineered road

activities serving the densely populated city

solution and the natural and organic bends

to the south. Small car parks serve club

and curves of the river, requires a light

houses, and links to slip ways for canoes

touch!

and kayaks. On the north bank facing south

However

create

We have used the detailed topographical

the emphasis is on providing orchards and

survey to define a widenedriver flood plain

allotments for city dwellers on the former

of wet woodland and reed beds. On either

fields that still occupy some of the un-

side, a series of earth banks and gabion

planned settlements.

walls define elevated terraces that step up to

At the cross axis between the Boulevard

the new roads and urban development that

Park and River Park the landscape of

will exist to either side. The terraces form

retained terraces gives way to walls of rock

the new park landscapes of dry woodland,

strata that provide a ramped link between

meadows, sports fields and agricultural

both parks, screen the Ring Road and

plots that will provide Tirana’s growing

provide terraces for cafes and restaurants

population with much needed recreation

looking north across the lake to a large

space.

Urban Beach. The Lake will be topped

As detailed data on the river’s flood

up by a water channel from the river and

potential is limited, the new terrace

cleaned by reed beds to the east, with an

topography should be seen as a strategy

overflow channel to the west.

for development of the River Park. Lines retaining walls emphasise the rivers organic

River Park – Restoration and Natural Habitats

forms and provide much needed shade for

Tirana River is polluted by quarry acitivities

cyclists, joggers and walkers.

upstream, rainwater run-off from the

of trees placed on the earth and gabion

Views along the river towards the cities

city, black water discharge into the river,

old and new landmarks and the mountains

and rubbish dumped along its banks.We

will open up and close down as one takes

propose a restoration strategy to include

each bend. The road bridges linking the

• wetlands with reedbeds upstream of city

north and south banks of the river will pass

to filter out silts and discharge from the

overhead and smaller pedestrian bridges

quarries

will link communities across the river. On the Tirana Rivers south bank

• cessation of black-water discharge into river, re-directing them to sewage treatment plants

Building Tirana's GREEN Future • cleaning and remodeling river banks to slow down river flow, create additional

has shaped the design. • Natural

rainwater

run-off

simulation

seasonal water storage, create space for

forms the basis of the river park design by

recreational activities, such as walking,

identifying areas that are prone to flooding. • Rainwater management shapes the public

cycling and team sports. by

spaces, creating a ‘water chain’, linking

reedbed

the various public squares and parks into

filtration) at points of entry into river

a network with one other, the Boulevard

zone.

Park and the River Park.

• cleaning

rainwater

phytoremediation

run-off (e.g.

Success will be contingent upon the

Stormwater management provides

interception of existing waste water inlets,

opportunities for recreation:Temporary

policing and prevention of fly tipping,

storage of water in Paskuqan Lake reservoir

control of agricultural and industrial

provides opportunities for water recreation

waste discharges and strict Governmental

requested in the Brief.

control of future development.

• Pasqukan Park: We propose to extend lake to historic dimensions by re-

Sustainable Water Strategy

establishing water feeds up to mountains,

Environmentally sustainable cities integrate

to create an open water body of 9.3Ha

ecological and recreational principles in a

with opportunities for boating, rowing

holistic approach to water management. For

boats, peddle boats and small sailing

Tirana, four different strategies are required:

boats (dinghies) with a club house, boat

• SUDS: Sustainable Urban Drainage Systems

storage and quai on the ward shore of the

slow down rainwater run-off to avoid

lake (shore on the side of the main wind

overflowing drainage systems during flash

direction) and small beaches.

floods. • Rainwater and sewerage systems are assumed

river is provided for canoes; small natural

to be separate. These systems also support the

weir-type structures create on-line lakes for

biodiversity of the city.

fishing.

• Rainwater harvesting: irrigation requirements are met through seasonal storage, natural water capture and native planting along natural rain paths.

102

• River Park: At suitable locations, access to

• Stormwater channels link pedestrian paths through the city. Energy, Water and Waste Strategies: We intend to use macro-level planning

• Flood risk mitigation: Temporal flood

to understand how the Tirana Northern

plains, reed beds and other methods slow

Boulevard and River Project will interact

down the flow of side steam prior to

with its resources and find the optimum

discharge into the river.

strategy to achieve your long term

• Pollution removal: filtration of polluted

vision for the area. In order to produce

river water and pollution carried by the

guidelines for a sustainable energy

rainwater run-off across hard surfaces of the

strategy, a review will be carried on the

city. The combination of these strategies

following key areas:

Reduce demand for energy.Passive Design; low-energy appliances.

distances; leak prevention • Alternative sources of water rainwater

• Efficient use and distribution of energy

harvesting; treating waste water for non-

• Small

potable reuse; groundwater

distribution

distances;

district

heating • Efficient generation

Waste Production Reduction Strategy

• Combined Heat and Power

From a sustainability perspective, the

• Renewable energy

principle hierarchy which should be

• Wind, Solar thermal, PV, Geothermal,

considered when designing waste treatment

Biomass

and disposal strategies is as follows:

Water consumption reduction strategy: Water supply and treatment in Albania have historically been poor but service is

Prevent and Reduce • avoid packaging; efficient manufacturing; change patterns of use

improving, water supply is intermittent

• Reuse and Recycle salvage used products

and waste water is not generally treated.

and components; reclaim materials for

In order to help improve the situation,

reuse; composting

the

approach

sustainable

water

Recover energy/ energy from waste

management across the Masterplan will

• Dispose to landfill

focus on three areas:

• the last resort – to be avoided

• Reduce demand for water low water use

• These options will be explored in

appliances; educate users • Efficient use and distribution short

more detail in the impact assessment report. 103

GMP “Tirana Green and Smart City” The planning of the urban expansion of Tirana as a „Smart & Green City“ is a

• To develop Tirana as a tourist attraction

project of important social dimension in

in the southern Mediterranean area.

Albania. A new generation is growing up

• To develop a city of short distances.

and these citizens long for a capital, with

• To organize a city with an intelligent

which they can identify with and which offers them a new future with a wider range of perspectives. The citizens of Tirana are willing to participate in the development of this monumental project, to give their capital a distinctive recognition and to fill Tirana with new refreshing life. The objectives of

110

based on the genius loci.

mobility system • A city that emancipates itself from individual motorized traffic. • A city which produces its energy from renewable sources. • Creation of urban foundations for future economic properity. Tirana faces a crucial moment in its

urban planning:

development in which it has the unique

• Tirana, the green city capital of Albania.

opportunity to implement a new town

• Building a green city.

planning for its future and to become a

• A city with a strong identity with a design

model for other Green & Smart Cities.

Landscape and Urban Space Merge The Green Corridors

allow recognizing historically developed

The newly created city lies between the

areas can be recognized as a separate layer

town center and the adjoining countryside

of time. While whole buildings can be

to the north. While this transition is today

kept in the green corridors north of Tirana

a seemingly arbitrary dissolution of urban

River, in the southern green corridors

structure into the landscapes, the new

one can find elements of the former city

design provides a different approach. The

structure. Former plot parcels remain

very dense urban structure develops over

recognizable or isolated country lanes and

the river into the landscape, at the same

roads, which represent future connections

time the green park extends itself into the

within the park. A new layer of trees and

city center. These four green corridors

new pathways is superimposed to create a

form not only neighborhoods but create

complex green carpet.

ARGUS Urban and Transport Planning Konrad Rothfuchs/transport planner engineer

neighborhood parks and are also important

The Boulevard

fresh air suppliers and green links.

The continuity of the central boulevard

Transsloar Energietechnik GmbH Matthias Schuler/ climate engineer

urban structures. Paths and former built

retreats, meeting places, playgrounds,

These gaps in the new city structure

to the north is an important element for

GMP Architektenvon Gerkan/ Margund Partner, Meinhard von Gerkan- partner Nikolaus Goetze/ceo, Hinrich Muller/ project manager Design Team: TanjaGutena/architect, Kai Siebke/architect, Alexander Montero Herberth/architect, Gudmundur Jonsson/architect Breimann a Bruun Landscape Architects MAA Bertel Kehlet Bruun/ landscape architect

111

Building Tirana's GREEN Future the entire city. The boulevard is not only a

residents. The wide walkways invite one

street, but it also serves as a link between

to stroll; the resident of Tirana enjoys the

two important open spaces surrounding

open spaces in the city’s center and will

Tirana:

seek his inspiration and relaxation there.

• The southern city ParkuiMadh with its spacious artificial lake • The newly created north park with its large water reservoir.

The creation of the green corridors is the result of successive thinning out of the existing building structure. The demolition of the existing urban fabric

The boulevard is not like the Champs

is done in parallel with the creation of

Elysee an ever-constant street, but it is

new districts. This creates high quality

an open space, diverse, adap-table and

spaces for the city, with a high value as

responsive to its environment. At some

a recreational green lung. Their edges

points the boulevards is a park, a plaza, an

will be preserved for residential housing.

avenue, or open public space. In any case,

Nestled in the green corridors are schools,

it is always a public place for the residents

kindergartens, sports facilities and many

to communicate, stroll and being seen.

other institutions of social life.

The boulevard will be a place of urban

At the beginning of the new northern

life. In addition to offices, shops and

boulevard and at the crossing point of the

markets can be found here, as well as stages

new outer ring road lie two plazas as a

for events and concerts, playing areas for

business center with impressive high-rise

children and pergolas under which the

landmark buildings. Here, companies will

people of Tirana sit protected from the

locate inter-national headquarters and

sun. Throughout the year, the boulevard

financial services. The Cultural Plaza with

will be like a public living room offering

Tirana’s new philharmonic hall, theater and

the population and visitors of Tirana a

National Museum, will be the cultural je-wel

wide range of different activities. The

of the city. The cultural center is located by

center of the city will concentrate the main

the large bridge crossing the River Tirana.

attractions of Tirana. To achieve this, the

The situation at the crossing point between

dimensions of the boulevard must match

the boulevard is unique and it creates an

the surroundings. The Boulevard unites

distinguish image of the city of Tirana. The

the city and should not be perceived as

river gains back its original natural quality.

green barrier that separates two sides of

It is, as well as the mountain silhouettes, a

the city.

central element of the city.

Its width of 100 m provides sufficient

112

space for pedestrians, motorized traffic,

The River Park -A Natural Idyll

a future-oriented tram („light train“) and

While the green corridors, the North

for non-motorized traffic, visitors and

Park and the Boulevard are specifically

designed for the city inhabitants, the

The Paskuqan Park

Tirana River Park forms a natural inner-

At the northern end of the new northern

city landscape. The river is renatured, so

Boulevard lies the prospective Eco Centre

that a natural meadow will develop around

of Albania. To the west the view opens up

it. Only narrow, winding paths allow the

wide into a vast and generous landscape

experience of this natural landscape,

park - the Paskuqani Lake Park. The tree

otherwise visitors only linger in the green

edges frame a view of the water reservoir

spaces along the edges of the river. Special

and the city behind it, wide meadows give

points are created where the river meets

the recreation area its identity.

other public landscaped spaces. The feen

A loop walk, like a path of experience,

corridors push themselves as bastions of

takes visitors through the park. Starting at

flat grass into the river landscape.

the Eco Center, the visitor passes along the

They are the link between the northern

forest edge. From a small hill the visitor

and southern shores, and represent the

can overlook the entire park and the city

jumping of the city across the river. At

behind it. Children fly kites while their

high tide, when the whole countryside

parents lie in the sun on the edge of the lake.

is flooded with water, only the bastions

The trail continues down the hill towards

lawns stay dry. From here the visitor can

the water. The dense reeds obstruct briefly

experience the river and the vigor of the

to view from a wooden footbridge running

water. At the crossing point of the river and

over the water. Suddenly, you reach the

the Boulevard two contrasting landscapes

edge of the reed and you find yourself in

converge. The Boulevard widens at the

the middle of the lake which reflects the

Cultural Plaza and opens up to the river

city on its surface seeming to merge with it.

park. It provides a stage for this special

Between the lake and the western suburbs

moment. Generous outdoor stairways

lies a sloping ridge.

connect the upper level and the urban river

The balcony by the water reservoir

landscape. At this very unique intersection

provides a spectacular view over the city,

the Cultural landmark buildings of Tirana

a perfect place for a rest. The Loop Walk

are situated overlooking the river park.

continues into the green corridors. Further

Other public buildings are found along

down the hills lies the city, views from the

the floodplains. These landmark buildings

park target important elements such as

lie along the river like stones washed on the

the Tirana Cultural Center or the Tirana

shore by the water. Recreational features

Town Hall, which will be visible from the

such as sports halls and swimming pools,

hillside park. Ultimately the trail leads the

cultural buildings such as museums and

visitor back along the forest edge to the

libraries will benefit from the prominent

Eco-center and either into the city or to

location in the urban fabric.

the countryside.

113

118

119

STAGE II

KORÇA MASTERPLAN COMPETITION The Municipality of Korça on 2009 launced the announce of the International Competition for the Master Plan of the City Center. All the applications were thoroughly reviewed and commented by the Evaluation Committee. The Evaluation Committee rated the 12 applications on the basis of the Competition Brief principal evaluation criteria. By the end of this process, the Evaluation Committee came out with 5 (five) short-listed finalists.

• • • • •

51N4E BVBA BOLLES+WILSON STUDIO DANIEL LIBESKIND JA - JOUBERT ARCHITECTURE 5-DOMUS CONCEPT

Composed of public spaces, parks, living apartments, commercial and administrative facilities, cultural heritage monuments, the City Center Area has a significant potential for becoming a premier public space, a leading tourist attraction for the City as well as a modern area of living and commercial premises. Through the City Center Master Plan we aim to foster the transformation, aesthetical improvement, functional attributes, and the city’s regeneration respecting also those values that distinguish Korça from other cities.

KORÇA MASTERPLAN COMPETION

BOLLES+WILSON Masterplan Korça City Centre [Winning Project]

Surrounded by dramatic mountains and

Resurrection’ anchors, at the other end a

a wide arcadian valley Korça focuses a

Commercial Anchor is added. These are

region of 360,000 inhabitants. Its urbane

connected by the Boulevard Shën Gjergji

morphology

and

– a ‘Cultural Promenade’. Reduction in

ambitions of returning emigrants. Many

expansive communist road widths allows

Novecento and Art Nouveau villas are

an extension of the Cathedral Square.

now restored. The aim of the competition

This square is planned three steps above

was to find a concept which integrates a

the street and framed by café pergolas.

traffic and pedestrian rational with the

A large stage left of the cathedral and a

qualitative and development needs of the

smaller stage to the right facilitate events.

city – a commercial strategy providing

Curved paving stripes echo the Cathedral

administrative facilities and a framework for

geometry and serve to discipline market

residential development. The competition

stands.

reflects

the

wealth

brief also emphasised that the scale of

New figure on the Korça skyline and

the new Korça should be respectful and

counterpoint to the Cathedral, a ‘Vertical

appropriate to the historic scale.

Mall’ occupies and marshals the paradeground scaled Theatre Square. A new

122

In this proposition are identified five

commercial strip extends from here to the

zones for the revitalisation of the 197,000

Bazaar via new shopping/housing blocks

sqm city centre. Each zone possessing its

and a new Bus Station Roof – a Farmers-

own unique character, together they add up

market platform. This – the second of the

to a network of urbane public spaces. At one

five zones – creates a new commercial hub

end of the centre the Cathedral of ‘Christ’s

in downtown Korça.

The third zone is rescripted as a

of public land for private development

‘Cultural promenade’, a semi-pedestrian

finances the upgrading of the park itself.

connection

and

An ‘Active Edge’ mediates between park

downtown Mall. Here a number of

and surrounding city – Prismic Pavilions

significant buildings such as the ‘Education

on wooden decks attracting cafes and

Museum’ are extended out into the tree-

individual user groups such as Youth Club,

lined, shady and café-filled Promenade

Kindergarten, Kadare Literature Club etc.

as a carpet-like patterned paving, a

This extensive spectrum of solutions

choreographed sequence of Urban Living

filled out in visual vignettes and disciplined

Rooms.

by precise plan geometries was chosen by

The

between

fourth

Cathedral

zone

revitalises

the jury as the template for Korças future.

dilapidated villa zone with carefully placed new development. In order not to overwhelm the delicate historic scale of Korça a ‘Patchwork Strategy’ is invented – new buildings are paired with restored existing villas to form ‘Development Islands’ (shared economic benefit) and thereby create a network of active blockinternal passages. The final zone of the Masterplan is the Central Park (‘green heart’). Here a new triangular-block frames the park edge and by the sale 123

124

125

126

127

128

129

130

131

KORÇA MASTERPLAN COMPETION

DOMUS RECONNECTING Korça LANDSCAPE URBAN PARK

Master plan aims to achieve a healthy and

What dreams do Korça inhabitants have

sustainable spatial and social environment

for the future and prosperity of their city?

for the city centre of Korça and his citizens

What does the city need as a living entity?

and visitors. A new public Landscape Park

What transformations must take place in

is proposed for the city centre emphasizing

the city centre so that those goals become

the relationship between the city and the

a sustainable and balanced reality?

constant presence of the surrounding

The master plan proposal will also

132

mountains of Korça.

address these issues and present a phased

The Landscape Urban Park spreads out

design strategy so that those aspirations can

from the centralpart of the site reinforcing

be planned and achieved. Korça citizens

its connection to the city. The public park

are proud of their cultural traditions and

is the conceptual foundation of the master

architectural heritage. The city and its

plan proposal. This new park also links

inhabitants give us a sense of glamour

the Cathedral, the Theatre and the town

and an aspiration and will for Korça to

Hall Squares. An interaction between the

take an increasingly important role within

park and the city blocks brings to this area

this region, aspiring to a more European

new activities, thus promoting healthy

and cosmopolitan way of living. The

lifestyles, the use of bicycle, outdoor life

in general and safe and comfortable spaces

neighbourhoods. The strategy for the

for children and seniors; a vibrating and

master plan city blocks is based in a

dynamic place, alive 24 hours a day, 7 days

re-interpretation of the square inside

a week, 365 days a year.

the old bazaar city block and of the topography of the surrounding mountains

NETWORK PATH

of Korça. This public space, where people

The site area with nearly 200.000 m2 is

can also gather and enjoy city life, is linked

located where different and disconnected

to the street through a public passageway.

urban fabrics come together. Some of

The proposal aims at integrating the new

the existing streets seem to be suddenly

and the existing city blocks, through the

interrupted once they come closer to the

connection of the open city blocks with

site area.

the network of the proposed passageways

The proposal aims at linking these

through the park.

diverse areas through a matrix of urban

These new city blocks will constitute

pathways interconnected to each other

a modern architectural archetype adapted

through the landscape urban park. This

to the urban scale of the city of Korça. The

new public landscape urban park, network

new city bocks proposed by the master

of streets and the permeable open city

plan will be opened and permeable public

blocks will enhance the sense of continuity

spaces. Through the unique architectural

with the nearby neighbourhoods. Korça

heritage

new city centre will thus be able to promote

concept is presented for the open city

greater civic and public involvement in a

blocks, reinforcing their role in the city

democratic society.

and therefore they become a key part of

Korça,

contemporary

the public realm. This will contribute

OPEN CITY BLOCKS

to establish a 21st century sustainable

Korça cultural and architectural heritage

quality of life, connecting architectural

have been able to present its citizens a

contemporary values to the existing

sense of glamour and pride in their city.

landscape, preserving the pride in Korça

This is linked to the quality of public life

cultural heritage and offering its citizens a

in the streets in the historical city centre

European standard of living.

133

KORÇA MASTERPLAN COMPETION LANDSCAPE URBAN PARK [CONCEPTS]

This material will be a base to accommodate

The public realm represents the identity of

the urban art work, urban signage,

a society, its desires and goals. Public spaces

furniture,

are also constantly adapting themselves to

collectors, public lighting, seating areas,

the dynamic of permanence and change of

and water elements.

infrastructures,

recycling

values of a given community. In general, current day public spaces located in the

ART INTERVENTION IN THE PROPOSAL

master plan area are mainly composed by

The project strategy for the entire site

different and disconnected parts.

connects art, landscape and architecture.

These different areas need to be

Elements such as the white stone and water

better interconnected through a clear

are a base for artistic interventions. It is

design strategy, spatial configuration and

proposed that several artists could be invited

definition of rather more user friendly

and each artist could be responsible to give

materials and textures. This will contribute

an identity to different areas of the site.

for Korça citizens and visitors to fully enjoy

The stone elements could be associated to

the new city centre open spaces.

sculpture, painting and photography and

The Master Plan will attempt to

the water could be associated with music,

integrate principles of local memory and

light and movement. It is also possible

identity of Korça and its citizens. The

that some elements could have a more

proposal intends to clarify and re-invent

definitive imprint on the site and more

the geometry of the city centre new

ephemeral ones could be associated to a

landscape urban park, urban pathways,

particular festival or event.

streets and squares.

The urban park and Cathedral

This will also emphasize the visual and

Square are places where other form of

tactile qualities of the new public spaces

art and culture could take place: outdoor

through their multi layered materiality.

concerts, film festivals, theatre, fashion

The urban park is mostly composed by a

shows or events like street fairs, parades,

permeable material base, largely vegetation

etc. Example for artist interventions:

and namely grass. The matrix of urban

artistic

component

this

pathways that intersect and connect the

proposal can be based on the following

whole project are mainly built in local

phrases, such as:“When words turn into

traditional dark cobblestone that is

art, shapes become alive”; “Verb created the

juxtaposed to the vegetation.

world... Writing is a tool of our indelible

These

134

The

pathways

continue

the

memory”. The proposal will select some

pavement of the streets at the north of the

key sentences with a relevant meaning to

Boulevard and merge into the site. The

Albanese people. Those Writings would

most relevant public places and spaces for

use a process of artistic transformation

gathering are characterized by a layer of a

of the alphabet, explainable by gestalt

contrasting solid and abstract white stone.

concepts, working with the observer’s

perception and character’s configurations,

SHËN GJERGJI BOULEVARD

creating new and harmonic shapes.

The renewal of Boulevard Shën Gjergji is

This artistic intervention can be

a key element in the process of renovation

adapted to diverse expressions and it can

of the city of Korça into a glamorous

be used both vertically and horizontally.

and cosmopolitan European city. The

This concept can even evolve, for instance,

Boulevard will be like a magnet, a place for

in three dimensions and be merged with

pedestrian access and stroll and a variety of

other artistic forms such as sculpture or

outdoor public events, defining generous

poetry. It can be easily accomplished and

spaces around the existing public Historical

appealing to emotions for both inhabitants

Buildings such as the Public Library.

and visitors.

Traffic will be limited to emergencies and

These interventions will be mainly

local loading and unloading services only

located in the white stone layer that unites

with a local governmental preestablished

public spaces, on pavements or even urban

schedule. The existing traffic will be mainly

furnishings like sitting places or water

redirected to Shëtitore Fan Noli Avenue.

elements’ structures. The Squares and

The boulevard renewal in local

the centre of the Landscape Park are also

traditional dark cobblestone pavement

privileged places to explore this concept,

will evoke local memory as it continues

and might contain words by several poets,

and incorporates the network of pathways

national or not, contemporary or not,

that link the city and the quarters to the

around themes like Park and Nature, Spirit

new urban park.

and Faith, Reality and Fiction. This would

The

cultural

and

architectural

allow the artistic intervention to become

heritage buildings, as identified in the

even more global and an integral part of

brief to be kept, will be maintained and/

quotidian life.

or refurbished into public buildings,

Artistic concept in the city blocks The

emphasizing the role of the boulevard as a

art projects applied into the new block

cultural, architectural and tourism entity.

contain the following phrase: ”A wave

The public space around them will be

of energy generated by human hands in

developed to emphasize their relevance.

harmony with the mother of all: the earth.”

A layer of a contrasting solid and abstract

The underlined words are the grounds

white stone will define those spaces around

to artistic concepts associated with each

these buildings and hold events,

new block almost as a logo and a tool to

urban art work, public lighting and seating

animate its interior public space. The intention is to subtly enhance the notion of movement that comes from the blocks’

areas. Existing trees in the boulevard will be preserved as much as possible. New mixed use and public buildings are proposed for the south side of the

shapes, a tension coming from the depths

boulevard. The existing and new buildings

of the earth until it reaches the sky.

will strengthen the identity of the boulevard 135

KORร A MASTERPLAN COMPETION and the connection with the landscape

throughout the whole year to promote

urban park. Both the Cathedral and the

Korรงa economy and tourism. The space

Theatre Squares will reinforce the essential

around the Cathedral is redesign in a

role that the boulevard will have in the city

series of platforms with different scales

centre to reconnect Korรงa different urban

and heights to resolve the difference

realities.

of levels of the topography around the Cathedral. Those different levels can

136

CATHEDRAL SQUARE

accommodate different kinds of activities

Presently, the Cathedral Square is one

such as esplanades, spaces with shading

of the most important public places

architectural devices, water features and

for the city life and identity of Korรงa.

children playground areas. These different

The Cathedral and the Square strong

platforms will also contribute to establish

identity enable this space to hold many

a better connection between the Square

different events, festivals and regional fairs

and the east part of the city and to some

of its museums.The new Cathedral Square

and white platform areas creating a pause

will be able to continue to accommodate

moment for pedestrians walking thought

a great multiplicity of events with greater

Republika Boulevard.These two squares

fl exibility in a more spatial organised way

are interconnected through the pavement

and with better suited infrastructure.

materials and platforms in a contrast

The Republika Boulevard was slightly

between the local traditional cobblestone

relocated and car parking removed to

and the white abstract and clear stone

provide for more space for the Square in

surfaces.

front of the Cathedral. This will increase the Square ability to hold all sorts of

THEATRE SQUARE

events. The Square redesign also intends to

It is essential to redefine traffic, car

reinforce the pedestrian connection to the

parking and pedestrian pathways. The two

Shën Gjergji Boulevard and to the public

existing avenues will meet at the North

buildings located there. The materials of the

part of the Theatre Square. This will allow

platforms will also be based on a contrast

for a much simpler intersection as traffic

between local traditional cobblestone and

is directed to the Shëtitore Fan Noli on

the abstract and white stone where most of

the Southern part of our intervention

the events will tae place.

area. The pedestrian character of the Shën

Public lighting of the Square will highlight both the architectural heritage

Gjergji Boulevard will be extended to the Theatre Square.

of the city and the urban pathways. A

This will allow a better integration

cybernetic fountain is proposed on the

with the Theatre, providing a generous

side of the Cathedral

public space where people can gather and enjoy themselves in front of the building.

CINEMA SQUARE

This space will be mainly built in an

Nearby the Cathedral Square is the

abstract white stone platform that crosses

Cinema Square that will enhance the value

the street, emphasizing the proximity of

of culture and entertainment within the

the Theatre to the boulevard.

city. Traffic was removed from the centre

Different kinds of events will be

of the square allowing for better shading

more related to the city quotidian and

137

every day life, where the theatre, hotels,

parking

and

traffic

were

redefined,

new esplanades areas will develop into a

allowing for a more dignifying relocation

social life nucleus.Abundant shading will

of the Unknown Soldier Monument that

be available, as new trees will beadded to

will connect this square to the urban

the existing ones that will be preserved as

landscape park.

much as possible.

LANDSCAPE URBAN PARK TOWN HALL SQUARE

The current park has a tremendous

To complete the network a public spaces in

potential that is not fully developed and

the city centre, the master plan intervention

that will to be taken into consideration

also defines another important public

in the master plan proposal. The space

space: the Town Hall Square. This new

occupied today by the Vangjush Mio Park

Square will enhance the importance of

will become a much wider space: an urban

municipal government and local identity.

landscape park. The landscape urban park is one of the central and key elements of

THEATRE SQUARE

138

the Master plan proposal. It is through the

A better definition of the space

park that the matrix of pathways and bicycle

in front of the town hall building will

ways are able to connect the different parts

be implemented through the renewal

of the project and the diverse areas of the

andreshape of the existing garden. Car

city. Tree planting strategy will establish

a symbiotic relation with public spaces

Contamination

and adapt to the extreme (hot and cold)

become one of the unifying cores of the

weather conditions found here.

proposal. The new park will be able to host

The

network

matrix

Trees

and

vegetation

proposed,

a great variety of events. The urban park

deconstructs itself on several places,

will become a continuous entity that binds

generating clear and open areas in the Park.

together all the site interventions. The

Wherever shading requirements increase,

Avenue Shetitore Fan Noli was redesigned:

trees density will increase too. Different

the traffic was changed to the opposite side

vegetation density will help defining the

of the park. The existing trees were kept

diverse uses of space.

and the pedestrian areas concentrated

The black cobblestone pavement

on the park side. This change allows for

coming from the North slowly fades

the possibilities of different events in the

through the park. The existing school

Avenue and the visual extension of the

can at first be integrated in the renewed

park.

park; however, if relocated in the future, the park can expand or accommodate

OPEN CITY BLOCKS

a new exceptional public building. The

The existing blocks nearby the cathedral

park interacts as well with the city blocks,

are mostly composed by current buildings

also bringing the natural landscape to

with a character and scale that do not seem

the interiors of these spaces. Green

to be the best suited for Korรงa new city

139

KORÇA MASTERPLAN COMPETION centre. These buildings present themselves

Theatre blocks

as an obstruction and do not allow for a

The existing city blocks will be redefined

strong connection between the Cathedral

by new buildings, rehabilitating some of

Square, the Boulevard and the landscape

the existing one and bringing new public

urban park.

spaces into their interior, according to

The

proposed

blocks,

mainly

composed by new buildings, will promote

140

the overall master plan urban strategy and proposal for the city centre of Korça.

greater permeability and a continuity of

The proposal for these blocks is

public space within the city centre at the

to incorporate the existing buildings,

ground level. A series of passageways that

redefining,

interconnect the whole site, intersect

ground floors and façades, with the

these blocks and link the different streets

purpose to further develop public space.

surrounding Korça city centre and the new

The urban strategy for some of the larger

landscape urban park. The buildings will

buildings to be kept in this area will be

mostly have retail and restaurant areas

phased over time, including, if possible,

and public services on the ground floor.

the hotels facing the Theatre Square and

The interiors of these blocks are open to

the Democracy Block, allowing for the

the city and are places, bringing life to the

municipality, residents, property owners

inner part of the blocks and connecting

and investors to work together to reinforce

them to the natural landscape of the park.

the dynamic of the master plan. The existing

These new blocks will have underground

buildings facing the Boulevard, particularly

car parking for residents, visitors and the

the building where the independency of

general public.

the region was declared, the Hotel Palas

whenever

possible,

their

The upper floors will be mixed use,

and the Bomboneria housing complex

composed mainly with residential, office

will be rehabilitated as public open to the

areas and hotels to promote tourism and

public, reinforcing and promoting tourism

reinforcing life 24h a day, 7 days a week,

in Korça. The proposal for the existing

within these city blocks. The buildings will

buildings consists in upgrading them to

always be lower than the cathedral. These

a rather more contemporary architecture

new buildings will have different heights

and thus contributing to a greater degree

and densities according to their proximity

to the new identity of Korça city centre.

to existing buildings. The Themistokli

The new buildings will mainly be of mixed

Villa

Building

use. The interiors of these blocks will also

will be maintained as part of the city

be public with small natural landscape

cultural architectural heritage and will be

areas, so that their inhabitants can also

rehabilitated to reinforce the relationship

gather and enjoy the outside spaces using

between the new city blocks and the Shën

new underground car parking areas with

Gjergji Boulevard.

access through a secondary street.

and

the

Rumanian

141

142

143

KORร A MASTERPLAN COMPETION

JOUBERT ARCHITECTURE Korรงa MOZAIQUE

144

How can the assets of Korça, a compact city

act with ambition to develop an attractive

with a great ladscape, be used to increase

and sustainable future for the city, as can

the recognisability and attraction of the

be seen in the projects for underground

city? The city suffers from low investment

infrastructure, the Republic blvd and the

and high emigration, taking away skills

market area. But which aspects should

and the means to improve them. But

be given priority and which ultimate goal

maybe this seeming ‘problem’ can actually

should be aimed for? The natural and

become an advantage? Can Korça avoid

geographical surroundings of the city

the pitfalls of too rapid and unstructured

are a clear asset. The position between

development, which can be seen in other

Macedonia, Greece and Tirana has the

parts of the region? And use the time this

potential to be used more extensively for

gives to reflect on the future it wants? Even

trade and economic development. To

develop into a hub for services and tourism

achieve this some steps have been made in

in the region? The Geneva or Vancouver of

infrastructural development inside the city

southeastern Europe? The city of Korça has

as well as in transport connection to other

some great moments of potential as well

regions, such as better road connections to

as some areas which need to be seriously

Macedonia, Greece and Tirana. A possible

(re) developed. The city has decided to

ring road will avoid traffic congestion in the centre in the future and a future airport, avoiding through traffic in the city. The surrounding landscape is a great scenic backdrop for the city, which is an asset for (eco)-tourism as well as for leisure opportunities for its citizens. The position of the city as well as its surprisingly compact development give it the opportunity for a lively center, due to its accessibility and proximity of functions, which is very closely connected to its surroundings. A more pedestrian and less car-oriented center will add to this attraction

PROCESS The city development can be divided in clear steps: • Analyze the traffic system of the city, to be able to focus the development on increasing the green structure and improving pedestrian traffic. • (Re)evaluate

the

green

spaces

and

increase their size, usability. Working

145

with local trees and flowers a specific and recognizable green structure will be developed.

INVESTMENT Through a clearly managed and structured investment str tegy a development during

• Position new functions in such a way that

the next years can be planned and

all functions are mixed. No residential

managed. Going beyond a mere fulfilment

area, or business area, but only mixed-

of current needs, to a vision for the next

use in all parts of the center. Creating a

decades of what kind of town Korça wants

surrounding that is used during the day

to become. This is possible through an

and into the evening.

investment process involving the city as well

• Redevelop the existing structures around

as national, local and private investors and

the area, ranging from the Borova Hotel,

owners, where possibilities of investment

the Majestik Theater, the area around the

are coupled to public uses. Investments

church etc.

public projects are linked to an investor

Then we would insert new functions in

on the edge of it. Each project should be

a clear and rec gnizable fashion. Filling

clearly defined, have its own identity and

in gaps and creating a common identity

character.

for each area through architecture and

146

art. Given the new developments around

REUSE

the city center and the goals of the

There are some remarkable buildings

municipality it is advisable to focus the

around the central area, which should

city on its current citizens and its future,

be upgraded one by one and possibly

sustainable development.

adjust their functions. This reappraisal

of the history of Korça is the first step

Air-conditioning needs 10x the energy

in the process of development. The Villa

for 1 deg temperature difference than

of Seferis could become a theater, the

heating. So the main focus should be to

location of the former cathedral a place

reduce this need. Again thicker walls

of contemplation, the Themistokli Villa

help, but also recessed windows to reduce

a museum etc. These projects will add

direct sunlight, and introduction of water

character to their surroundings, while

and planting into buildings. Evaporative

linking the city to its history.

airconditioning

CLIMATE

systems

would

help,

without raising costs. On an urban scale we also introduce

The climate of Korça, hot dry summers and

water and more green, which due to natural

cold winters, bring with it the framework

evaporation reduces the ‘heat-island’ effect

for the development of architecture and

in the city and provides shade. To avoid

urban ensembles. Climate aspects should

too rapid evaporation we would collect

be clearly addressed in future development

run off (rain)water from the whole area.

in Korça: Higher isolation values should

Also we should implement an easy system

be implemented to reduce heating costs.

of grey water collection from all new

This can be done in several ways, such as

structures. By collecting and filtering it in

double glazing, more isolating materials

a central location, we can make it usable

and thicker walls.

for irrigation. Even making possible usage

The second, more important factor, is the reduction of air-conditioning usage.

by the public for swimming in a natural pool and in a water square.

147

KORÇA MASTERPLAN COMPETION MATERIALS All these developments should be executed in a recognizable fashion. Using a local material, a local stone, which can be found in the mountains in the region, avoiding transport costs, creating local jobs and a long lasting and flexible finish, rough and

‘Rolling Rock’ indicating development. The essential first step in improving the city is making a more efficient traffic system, giving space occupied by cars back to the public. Allowing for more green space, squares etc. Roads consisting of wide asphalt surfaces such

rocky but also smooth and shiny. A rough

as the Cathedral square, Theater Square

rocky finish has the added advantage of

and Cinema square can be turned into

shading the façade, making the façade

efficient roads with parking on the sides.

itself less hot and allowing for vegetation

This allows for the creation of green spaces

and humidity, reducing the need for

and shaded squares. The investment

further cooling.

already agreed for the republic boulevard

Korça?

148

new developments in the city, a kind of

and the pedestrianisation of Themistokli Germenji Boulevard will allow for a large

By developing clear identities for each of

public space in the center of town. Theater

the proposed projects, keeping them to a

square could be turned into a square with

scale fitting to Korça, we will develop a scala

major public functions, like the theater

of neighbourhoods and qualities for the

and the Hotel. This could be the first step

city: With a phased approach, each project

in the redevelopment of the city center.

can be developed separately, which would

By redeveloping the two corners across

pave the way to an attractive center of

from the cathedral, a multifunctional

recognizable and diverse neighbourhoods

square for the city becomespossible. By

which is flexible in time and investment

keeping the existing café, turning the

needs:

Themistokli Germenji villa into a theater,

Mobile information pavillion (route

redeveloping the entrance to the education

= phasing)The first step in the process of

museum and positioning new buildings on

phasing the various projects would be to

its edge the square will have clear facades.

provide information, allowing the citizens

Adding a multifunctional auditorium

of Korça to know what initiatives are taken

which can double as a stage more public

in their city and allowing them to give their

events are possible.

opinion. By positioning the pavilion in the

By widening Themistokli Germenji

hotspot locations of development a direct

Boulevard the buildings along it will

link between each project and the city is

be placed on the boulevard, allowing

made. The pavillion would also be the first

the areas in-between and towards the

structure made of natural stone as part of

historic neighborhood to become high

quality public spaces. Thereby making

panoramic bar or restaurant on the roof,

the heritage area part of the city center,

creating a new quality neighbourhood.

reconnecting the old neighborhoods. The

Cinema square: By making a more

library has a special position, as it is an

efficient street in front of the Cinema it

appreciated public building, that replaced

becomes possible to make a shaded square

the destroyed St. Georgeâ&#x20AC;&#x2122;s Cathedral. A

with trees for people to meet before seeing

new plaze around the library, allowing

a movie. It would even become imaginable

for easier accessibility to the library,

to extend the cinema with a new hall on

could contain a pool in the location of

the roof, which would light up Cinema Sq.

the former cathedral. The boulevard will

creating a festive entrance to the Cinema

be developed between 2 squares. Theater

and more space for visitors.

square in the north and Cathedral square

Cathedral Park and Sedat Babani Street Park : this area could become a

in the south. Misto Mame area: Along the newly

quiet forested area. The infrastructure

pedestrianised boulevard there will be

adjustments allow for a widening of

an additional attention to commercial

Cathedral sq. giving more space to the

development.

private

Cathedral, allowing for a drop-off area.

developments within a clear framework

By introducing more green on the square,

for the Misto Mame Street Area this could

shaded areas around the cathedral are

turn into a dense and lively area with

created. Ringing the Cathedral in green

rooftop restaurants, shopping courtyards,

improves the neighbourhood to the

boutiques and cafes towards the park.

southeast , connecting it directly to the

In time the whole area should become

square. Lanes of Flagstones lead through

pedestrian and could turn into a high

the park and to the entrance of the

quality urban space through individual

Cathedral.

allowing

projects. The boulevard neighborhood

The area around Ligor Rembeci Street

could turn into a dense city fabric by

was said to be a point of possibly total

allowing private owners to develop their

redevelopment. But how can a city such as

properties on an individual scale. Gap fill

KorĂ§a tear down buildings? Isnâ&#x20AC;&#x2122;t it possible

ins, courtyard projects and roof extensions

to keep existing buildings, fill in the in-

all executed in the same material would

between spaces with commercial space

allow for a future oriented, but highly

on the ground +1st floor and allowing for

flexible development opportunity. With

housing above? Thus creating a phaseable

clear surroundings, the boulevard on one

and privately developed shopping area. By

side, the park on the other, the edges will

adding patios to the new structure we allow

be highly attractive points for boutique

light to come into the shopping area as

shops, galleries, cafes, restaurants, with a

well as the new housing, while the existing

149

KORĂ&#x2021;A MASTERPLAN COMPETION houses would become public circulation

smaller in summer and larger in winter,

space. We would add the needed parking

changing with the seasons. Developing

for an inner city development while the

150

partnerships

with

roof would be used as private gardens

developments on its edges, financially

with a view. The roof would also collect

as well as commercially, would provide

rainwater for irrigation. By adding a water

the

buffer in the shopping area two goals

redevelopment. We could imagine for

can be achieved: natural air-conditiong

example a part of the park used for the

through evaporation for the shopping area

great local production of fruits and

and a cleaning system for grey water for the

vegetables, which could be used in a local

housing which can be used in the park for

restaurant on the edge of the park. You see

underground irrigation. Each inhabitant

what you eat!

can irrigate 20-30 m2 of park. By adding a

How

incentives

can

and

the

Themistokli

means

for

Germenji

reed bed / natural water treatment this can

School change from a border to the park to

even be turned into a feature of the park

an element in the park? The school should

with a beach and paddle pool.

remain in the park as an educational

Vangjush Mio Park: Reducing the

facility. Especially in an education-oriented

roads going through Vangjush Mio Park

city such as KorĂ§a it is appopriate to be

further improves the pedestrian quality

in the center of town. But where will the

and allows for development along its

school have its outdoor activities? Would

edges. We would keep all the existing

it be possible to develop the large roof of

trees, making the trunks visible for views

the school for sports? Becoming a symbol

through the park. By adding Pinus Pinaes

for an educational facility in the center of

trees, low maintenance, evergreen trees

town while allowing the park to extend

and a careful selection of plants, shade for

around the school, providing space in the

picknicks and resting is created. Clearings

park for after school activities.

allow for larger events, a beach, sports,

The bus station is in urgent need

gatherings. By surrounding the clearings

of redevelopment. We should avoid the

with deciduous trees, the clearings will be

ugly developments seen around so many

bus stations in the region. We could add

facing south and west.

housing program to this gateway to the

As Korça grows and develops the

city. In conjunction with the new social

opportunity would arise to develop Hotel

housing development this would help in

Behar Koçi Belli / Hotel Palace into one

the redevelopment of the housing across

project, the way it was originally conceived.

the street. Forming the building in such

A new drop-off on Theater Square would

a way that noise and pollution from the

add a new entrance to the hotel and

buses is absorbed and doesn’t disturb the

an atrium addition would allow for an

housing above can be achieved through

increase in the amount or rooms available.

smart shaping of the volume.

Allowing for rooftop views over the city

Redevelopment of Edit Durham st.

and a new coherence to the unregulated

housing project + parking + extension of

development of the hotel in the last years.

park: At a later stage in the development

New Andon Zako Cajupi Theatre.

of Korça it might become feasible to

The theater is a very attractive building,

redevelop the housing project in the center.

but slightly small for the city and in need

Providing a phased approach of building

of improvement in the future, while it

and replacement we would provide more

has the potential to become a landmark

apartments than the existing situation and

on Theater square. We could add to it,

allow for covered parking on grade. By

replacing the roof with a lifted hall, allowing

allowing for trees and green between the

for a new foyer in between. A festive venue

new housing projects we would extend the

for Korça with a view over the city to the

park, making a connection to the bazaar

mountains. Through such a development

area, offer a substantial amount of parking

in a step-by step approach, where each

and a diverse range of housing typologies.

step brings a clear benefit and quality in

The housing blocks will be developed

itself, this central neighborhood could

independently, with different heights and

become a model city for the region and

apartment types. By tilting the facades

even beyond…. While most importantly

outwards and making recessed windows

adding to the quality of life of the citizens

more shade is provided in the apartments

of Korça……

151

KORÃ&#x2021;A MASTERPLAN COMPETION

152

Library and stage

JA 4

auditorium arrangement

+ 8.

equipment room

Urban furniture

+ 8.00 auditorium arrangement + 1.80 cafe

+ 8.00

kitchen

storage

+ 8.

cafe

stage arrangement + 1.80 cafe

+ 0.00 - 1.20 3 7

4 7

+ 0.00 - 1.20

equipment room

stage arrangement

Plans ground ďŹ&#x201A;oor & Stage (performance & auditorium 1:500

Cross & long sections 1:500

3 7 1

stone paving tile 3,6m x 3,6m boulevard; cinema square

flagstone paving cathedral square; park

stone bench 3,6m x 0,45m x 0,45m boulevard; cinema square; theatre square

stone cube bench 1,2m x 1,2m x 0,45m boulevard

dustbin 0,8m x 0,8m x 0,8m boulevard; cinema square; theatre square

tree lights boulevard; cinema square; theatre square; cathedral square; park

urban furniture light fixture boulevard; cinema square; theatre square

light fixture in stone paving 3,6m x 0,2m Korca square; theatre square

light fixture d.0,1m cathedral square; park

St George water

+ 12.00 library plaza

10 light fixture for routing indication

+ 0.85 + 0.00

Urban furniture 1:100

Plan Library plaza 1:500

Section Library plaza 1:500 0

3. Misto Mame Area

30 m

50 m

historical and comtemplation courtyard

lecture room

shop

cafe fashion store

Existing

Adding Program

fashion store

fashion store secret courtyard

health center local products

cafe

fashion store bar / cafe

y liver d de an ncy erge em ss acce

r/ ba

fe ca

store

+ 36.30 new hotel extension + 33.00 roof panoramic restaurant

+ 30.00

restaurant restaurant internal courtyard

fashion store bar

gallery

local products

health center

private courtyard

parc

fashion store

cafe

fashion store

passage

grand and green courtyard

cafe

snack snack

bar

+ 09.00 boulevard historical courtyard

independence house

+ 03.00 + 00.00

club

Section existing buildings with additions 1:500 0

4. Majestik Cinema & Square

Plan existing buildings with additions 1:500

30 m

50 m

30 m

50 m

screen room foyer

Majestik Cinema

New Hall

Canopy and light

Plan New hall 1:500

Existing situation + 22.27

+ 18.40

screen room foyer

Enlarge square in front of Cathedral & new Square

Connect Cathedral square to residential area

+ 16.50 + 13.50

existing screen room

+ 00.00

Section 1:500

5. Cathedral square

Cathedral Square

foyer

screening room

153 Plan 1:500 0

30 m

KORÇA MASTERPLAN COMPETION

51N4E KORÇA City Center Master Plan Korça City Center Following the principles of the compact city Korça's unstructured and partly vacant city centre offers a high development potential and shall become a well integrated and representative focus point in the city with a vibrant mixture of different scale functions on 2 levels of urban intervention: Project-A: Network of public spaces and squares, restoration and activation of the existing borders & boundaries: Korça City • Theatre Square (music pavilion, open theatre foyer, pedestrianized square) • Boulevard (public terraces, library winter-garden, wider sidewalks) • Cathedral Park (new trees, soft scape, public bldg., hotel, pedestrianized area) • Cinema Square (Open air cinema, pedestrianized area) Project-B: Development of a new Centre Block, creation of new space formations for enabling new mix-use programs Strategy on compacting the city: Kor�a is undergoing the continued process of a

This phenomenon can also be witnessed in many areas throughout the city

especially in the big former industrial plots which are currently run down or d shrinking population. Identifying a clear

serted but also offer a big potential for city regeneration within the city bounda (the outer ring road).

city boundary, preventing further sprawl

outside and densifying the city fabric within, is suggested to be the base urban planning intervention

154

51N4E

KORCA City Center Master Plan

ARTIKULL SHKENCOR "Kondensimi në sistemet e fasadave të avancuara. Diagrami Glaser”. Endrit Tuzi Artikulli u recensua nga: Dr Arben Shtylla

Abstract:

Qëllimi i punimit

Kjo është e qartë, kur ne konsiderojmë

Qëllimi i punimit, është sensibilizimi

që puna e ndërtesës është reduktuar

i masës së njerëzve për përdorimin

në minimum ne ato zona

e teknologjive te reja te fasadave.

e jashtme klimatike, takojnë kushtet

Climate change and greenhouse gases are pressing issues that can not be ignored any longer, even though scientists still need to work on various uncertainties lacking sufficient verified knowledge and consensus for a better climate. According to official EU data, buildings use more than one third of the worldwide energy consumption, for constructing, operating, renovating to provide the living and working space with the desired day- today comfort. Simultaneously, the corresponding costs and the saving potential are huge over a life span of 40 - 50 years. This means that architects and investors have a major responsibility towards society and future generations.

Objektivat e këtij artikulli kanë të bëjnë

e ambjentit qëne njerëzit gjejme të

me analizimin e shembujve shqipëtar

përshtatshme. Megjithatë, sa më e madhe

në drejtim të aplikimit te fasadave

të jetë diferenca e kushteve të jashtme

me teknologji te avancuar.Paraqitja e

me ato të brendëshme, aq më e madhe

rasteve në përballjen me fenomenin e

do të jetë ndërmarrja teknike e kërkuar

kondensimit, referuar grakikut- Glaser.

për të realizuar kushtet e nevojëshme për

Evidentimi i veçorive pozitive të rasteve

okupimin e interierit.

Building envelopes featuring the latest low-energy technology are one environmental, cost-cutting path. For instance, the ventilated façade systems, so far mostly used in European countries with long and severe winters, have proven their cost and energy-efficiency for over 30 years. Built with the appropriate high thermal insulation and high quality, durable skin materials, ventilated façade systems tremendously reduce the energy bill for heating and cooling services, while at the same time providing comfortable and cosy indoor conditions. They keep a building structurallysound and effective over many years without heavy

Ndertesat “zarf”, siç sigurojnë mbrojtje

Si mënyrë është krijimi shtreave të

ndaj kohes dhe mundësojne magainim

jashtme me materiale të ndryshme, të cilët

të nxehtësisë, paraqesin arsyen më

kanë koeficintë termikë dhe trashësi të

të rëndë sishme e primare për një

ndryshme.

“ Water Condensation in Advanced facades systems. Glasser diagram”.

156

ku kushtet

konkrete.Gjetja e vendosjes më të mirë

Problemi është të përcaktohet se

e shtresëzimit për të evituar proçesin e

cila formë është më e përshtatshme

kondensimit të brendshëm.

përshtatshme

Hyrje

për

të

realizuar

një

termoizolim më të mirë për ndërtesat e banimit dhe administrative.

ndëtesë. Në me strukturën e veprave

Objektivi i realizimit të një fasade

të tilla si urat, kullat, digat apo vinçat,

të avancuar të një ndërtesë të rehatëshme

ndërtesat përmbajnë dhoma realizimi i

me një harxhim minimal të energjisë, dhe

të cilave duhet të vlerësohet si element

investime kapitale të reduktuara, brenda

të brendshëm të qytetërimit njerëzor,

një të ardhmeje të afërt , do të vazhdojë të

lidhur ngushtë me nevojat e detyruara

jetë një sfidë ne arkitekture and teknologji.

nga kushtet klimatike.

Kemi një sërë arsyesh për të patur një

vlerësim ndaj fasadave me teknologji të

të ndërtesave, me qëllim që të arrijë

avancuar, që janë:

efiçencën më të mire ambientale.

Të thellojë kuptimin e kombinimeve

Analizë e situatës së kondensimit

të projektimit ambiental dhe struktures

për dy objekte në Tiranë të realizuar me

së ndërtesës.Të përcaktojë format më të

fasadë të ventiluar dhe veshje “kapotë”.

mira të fasadave për tipologji të ndryshme

1. Prerja tërthore e murit të një pallati me fasadë të tipit “kapotë”

Cv: Endrit Tuzi, ka mbaruar Universitetin Politeknik të Tiranës, Fakulteti i Inxhinierisë së Ndërtimit, Dega e Arkitekturë, në vitet 1990-1995. 1994-1995 Ka mbaruar kursin e “Urban Planning”, të drejtuar nga përfaqësuesi i Konsullatës së Britanisë së Madhe, Mr.David Allen. 2004 Ka mbaruar kursin për Rehabilitim dhe Konservim të Ndërtimeve historike, organizuar nga Universiti i Bolonjës. 2009 - 2010 Ka punuar si ekspert urban (Team Leader), në Projektin për Planin e Përgjithshëm Rregullues të qytetit të Shkodrës. 1995 – 2008 Ka punuar në disa studio Projektimi në Tiranë, si dhe ka realizuar disa projekte të tija në qytetin e Tiranës dhe Shkodrës.

2. Ndërtesë me (9+2)kate tek rruga: “Bogdani”, Tiranë, sipërfaqe totale 10400 m2. Investitor: Pandi Cerapuli, Kompania: “Classic Construction” Ltd., ndërtuar në vitet 2009-2011

është pedagog efektiv pranë Fakultetit të Arkitekturës dhe Urbanistikës, që nga viti shkollor 2001.Që në fillim ka qënë angazhuar në mësimdhënie në seksionin e Teknologjisë së Arkitekturës, në lëndët “ Teknologji Arkitekture 1” e ‘Teknologji Arkitekture 2” (seminare), për studentët e kursit II - Arkitekturë & Urbanistikë; në lëndën “ Elementë të ndërtesës” (seminare) për studentët e kursit I- Arkitekturë, si dhe në 157

ARTIKULL SHKENCOR maintenance. The worlds of architecture and construction have exciting challenges ahead. The method of creating layers with materials which have different thermal coefficients and thickness provides very optimal possibilities for dwelling conditions. The objective of realizing advanced façades for environmentally-built buildings with minimal energy consumption and reduced investment of capital within the near future will continue to be a challenge in architecture and technology. This paper evaluates the problem of water condensation in the inner wall surfaces, specifically for ventilated facades. At the same time, we have dwelling buildings with ventilated façades, such as a the 9-story building near the Academy of Fine Arts, at the “Martirs of 4 February” Street, object of 9+2 stories, at the “Bogdani” Street, Tirana. The best way is to determine our result for the risk of condensation referring to the Glaser diagram.

3. Prerja tërthore e murit të pallatit 9k, pas Akademisë së Arteve, Tiranë

3.Ndërtesë me 9 kate, tek rruga: “Dëshmorët e 4 Shkurtit”; Investitor: “Archimed. International” Ltd., Tirana, Ark. Ermal Bleta. Ark. Doriana Bleta, Ark. Roland Lika, ndërtuar në vitet 2008- 2012. Të shohim se si ndryshon shpërndarja e temperaturave për situatën e një fasade të ventiluar ( ndërtesa tek rruga Bogdani), kur konsiderojmë si temperaturë të brendshme 20° C, dhe temperaturë të jashtme -1° C. Rezistenca e përgjithshme është :

Rp =

R = Rb + R1 + R2 + R3 + R4 + R5 + R6 + Rj, ku

Rbrendshme = 0.13 m2k/w

[4]

R1 (suva e brendëshme) = 0.022 m2k/w; R2 (tullë me bira 25cm) = 0.481 m2k/w; R3 (avull. izolues) = 0.01 m2k/w; R4 (pambuk mineral) = 2.558 m2k/w; R5 (hapësirë ajri) = = 0.35 m2k/w; R6 (qeramikë) = 3.125 m2k/w; Rjashtme = 0.4 m2k/w. dhe përfundimisht Rp = 0.13 + 0.022 + 0.481 + 0.01 + 2.558 + 0.35 + 3.125 + 0.4 = 7.106 m2k/w Përcaktojmë temperaturat e sipërfaqeve të shtresave, duke filluar nga brenda-jashtë: temperatura e sipërfaqes së brendëshme: Në sipërfaqen e kontaktit të ajrit të brendshëm me suvanë, kemi: Rp =

R = Rb + R1 + R2 + R3 + R4 + R5 + R6 + Rj, ku

1. tb-suva =

Rb = 20º -

( 1 )

7.106

0.13 = 19.616

Në sipërfaqen e kontaktit të suvasë me murin e tullës, kemi:

2. tsuva-mur =

(Rb+R1) = 20º -

( 1 )

7.106

(0.13+0.022) = 19.551

Në sipërfaqen e kontaktit të murit të tullës me avull. izoluesin, kemi:

3. tmur-p-av.izol = 158

(Rb+R1+R2) = 20º -

[4] (Ngrohja, ventilimi dhe klimatizimi i ndërtesave, Prof.Luan Voshtina, Dr. Gjergj Simaku 2004 pp.238-239).

( 1 )

7.106

(0.13+0.022+0.481) = 18.13

Në sipërfaqen e kontaktit të avull. izol. me pambukun mineral kemi:

4. t av.izol - p.mineral =

(Rb+R1+R2+R3) = 20º -

(0.13+0.022+0.481+0.01) = 18.1

( 1 )

7.106

Në sipërfaqen e kontaktit të pambukut mineral me korridorin e ajrit kemi:

5. t p.mineral - ajër =

(Rb+R1+R2+R3+R4) = 20º -

(0.13+0.022+0.481+0.01+2.588 ) = 10.45

( 1 )

7.106

Në sipërfaqen e kontaktit të ajrit me qeramikën kemi:

6. tajër - qeramikë = 20º -

( 1 )

7.106

(Rb+R1+R2+R3+R4+R5) =

(0.13+0.022+0.481+0.01+2.588+0.35) = 9.5

Në sipërfaqen e kontaktit të ajrit me qeramikën kemi:

7. t- qeramikë - ajër = = 20º -

( 1 )

7.106

(Rb+R1+R2+R3+R4+R5+ R6) =

(0.13+0.022+0.481+0.01+2.588+0.35+3.125) = 0.184

lëndën: “Arkitekturë Teknike” (seminare) për studentët e Ndërtimit, kursi II. Në vitin shkollor 2006-2007 ka filluar dhënien e ciklit të Leksioneve në lëndën “Arkitekturë Teknike” - kursi II-Ndërtim, e më pas, nga viti shkollor 2008-2009 e në vazhdim jep Leksione në lëndën “ Teknologji Arkitekture 1” për kursin II të Arkitekturës dhe Urbanistikës. Gjatë viteve 2004-2006 ka kryer Shkollën pasuniversitare (Master i Nivelit të Dytë) për 2vjet, pranë F.I.N. në “Rilevim dhe dokumentim Arkitektonik, Restaurimi Arkitektonik”, organizuar nga Universiteti “La Sapienza” në Romë, dhe Universiteti Politeknik i Valencias, pjesë e Programit TEMPUS. është duke kryer doktoraturën pranë degës së Arkitekturës në Fakultetin e Arkitekturës & Urbanistikes më temën: “Vështrim kritik mbi teknologjinë e fasadave tek ne, dhe mundësitë e aplikimit të teknologjive të avancuara sot”.

Për të realizuar diagramën presion- trashësi, gjejmë me anë të interpolimit, vlerat e presioneve përkatës për temperaturat e gjetura: Tab.1 Vetitë fizike te ajrit te lagesht ne preseion barometrik B=1 daN/Cm2

[4] (Ngrohja, ventilimi dhe klimatizimi i ndërtesave, Prof.Luan Voshtina, Dr. Gjergj Simaku 2004 pp 306).

[4]

159

ARTIKULL SHKENCOR 1. pĂŤr KĂŤshtu, pĂŤr temperaturĂŤn 19.616Âş, interpolim,nga tabela fizike tĂŤ ajrit, 1. KĂŤshtu, temperaturĂŤn 19.616Âş, meme interpolim,nga tabelae vetive e vetive fizike tĂŤ ajrit, kemi pĂŤr presioni 219.7, pĂŤrtabela 20Âş presioni-233.7 1. KĂŤshtu, pĂŤrtemperaturĂŤn temperaturĂŤn19Âş 19.616Âş, meĂŤshtĂŤ interpolim,nga e vetive fizikedaNcm2 tĂŤ ajrit, dhe

kemi pĂŤr temperaturĂŤn 19Âş presioni ĂŤshtĂŤ 219.7, 20Âşpresioni-233.7 presioni-233.7 daNcm2 kemi pĂŤr temperaturĂŤn 19Âş presioni ĂŤshtĂŤ 219.7,pĂŤr pĂŤr 20Âş daNcm2 dhe dhe gjejmĂŤ: gjejmĂŤ: gjejmĂŤ: đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 = â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0â&#x2C6;&#x2019;â&#x2C6;&#x2019;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 = đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 20 â&#x2C6;&#x2019; 19 233.7 â&#x2C6;&#x2019; 219.7 20 â&#x2C6;&#x2019; 19â&#x2C6;&#x2019; 19 =233.7 19.616 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; â&#x2C6;&#x2019; 219.7 219.7 = 19.616 â&#x2C6;&#x2019; 19 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 219.7

Y0 = 219.7+ (0.616 x 14) = 228.324daN/cm2 Y0 = 219.7+ (0.616 x 14) = 228.324daN/cm2

2. PĂŤr temperaturĂŤn 19.551Âş, me interpolim,nga tabelaee vetive vetive fizike gjejmĂŤ: 2. PĂŤr temperaturĂŤn 19.551Âş, me interpolim,nga tabela fiziketĂŤtĂŤajrit, ajrit, gjejmĂŤ: 2.

PĂŤr temperaturĂŤn 19.551Âş, me interpolim,nga e vetive fizike tĂŤ ajrit, gjejmĂŤ: đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 tabela đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 =đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1= đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 20 â&#x2C6;&#x2019; 19 233.7 â&#x2C6;&#x2019; 219.7 =233.7 â&#x2C6;&#x2019; 219.7 20 â&#x2C6;&#x2019; 19 19.551 â&#x2C6;&#x2019; 19= đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 219.7 19.551ENDRIT â&#x2C6;&#x2019; 19 TUZI đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 219.7

ENDRIT TUZI Y0 = 219.7+ (0.551 x 14) = 227.414daN/cm2 ENDRIT TUZI Y0 = 219.7+ (0.551 x 14) = 227.414daN/cm2 3. PĂŤr temperaturĂŤn 18.13Âş, ENDRIT me interpolim,nga tabela e vetive fizike tĂŤ ajrit nĂŤ presion TUZI 3. PĂŤr 3. temperaturĂŤn 18.13Âş, me interpolim,nga tabela vetive fizike ajrit presion barik B = daNcm2, pĂŤr temperaturĂŤn 19Âş presioni 219.7, pĂŤr 18Âş presioni ĂŤshtĂŤ6 PĂŤr temperaturĂŤn 18.13Âş, me interpolim,nga tabela eeĂŤshtĂŤ vetive fizike tĂŤtĂŤ ajrit nĂŤ nĂŤ presion 3. PĂŤr temperaturĂŤn 18.13Âş, me interpolim,nga tabela e vetive fizike tĂŤ ajrit nĂŤ presion6 206.4 dhepĂŤr gjejmĂŤ. barik BBdaNcm2, ==daNcm2, temperaturĂŤn 19Âş presioni ĂŤshtĂŤ219.7, 219.7, pĂŤr 18Âş presioni ĂŤshtĂŤ barik B daNcm2, pĂŤr18.13Âş, temperaturĂŤn 19Âş presioni 18Âş presioni ĂŤshtĂŤ 3. =PĂŤr temperaturĂŤn me interpolim,nga eĂŤshtĂŤ vetive fizike tĂŤpĂŤr ajrit18Âş nĂŤpresioni presion barik daNcm2, pĂŤr temperaturĂŤn 19Âştabela presioni ĂŤshtĂŤ 219.7, pĂŤr ĂŤshtĂŤ 206.4 daNcm2, dhe gjejmĂŤ. barik B =daNcm2, daNcm2, pĂŤrgjejmĂŤ. temperaturĂŤn 19Âş presioni ĂŤshtĂŤ 219.7, pĂŤr 18Âş presioni ĂŤshtĂŤ 206.4 dhe đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 206.4 daNcm2, dhe gjejmĂŤ. = 206.4 daNcm2, dhe gjejmĂŤ. đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0â&#x2C6;&#x2019; â&#x2C6;&#x2019;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0â&#x2C6;&#x2019; â&#x2C6;&#x2019;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 = = đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 19đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019;â&#x2C6;&#x2019; 18 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2219.7 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019;â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1206.4 == đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 18.13 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019;â&#x2C6;&#x2019; 19 206.4 19â&#x2C6;&#x2019;â&#x2C6;&#x2019;18 1818 219.7 219.7 â&#x2C6;&#x2019;206.4 206.4 = = 19 â&#x2C6;&#x2019; 18 219.7 â&#x2C6;&#x2019; 206.4 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 206.4 18.13 â&#x2C6;&#x2019; 18 18.13 â&#x2C6;&#x2019; 18 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 206.4 Y0 = 206.4+ (0.13 x 13.3) = 208.29daN/cm2 =

18.13 â&#x2C6;&#x2019; 18

đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 206.4

Y0Y0= = 206.4+ (0.13 == 208.29daN/cm2 206.4+ (0.13xx13.3) 13.3) 208.29daN/cm2 4. PĂŤr temperaturĂŤn 18.1, me interpolim,nga tabela e vetive fizike tĂŤ ajrit, kemi qĂŤ nĂŤ 206.4+ (0.13 x18.1, 13.3)me = interpolim,nga 208.29daN/cm2 tabela e vetive fizike tĂŤ ajrit, kemi qĂŤ nĂŤ 18Âş 4. Y0 PĂŤr =temperaturĂŤn 18Âş presioni ĂŤshtĂŤ 206.4 e pĂŤr 19Âş ĂŤshtĂŤ 219.7 dan/cm2, gjejmĂŤ: 4.4.PĂŤr vetive fizike fizike tĂŤtĂŤajrit, ajrit,kemi kemiqĂŤ qĂŤnĂŤnĂŤ PĂŤrtemperaturĂŤn temperaturĂŤn18.1, 18.1,me meinterpolim,nga interpolim,nga tabela e vetive

4. ĂŤshtĂŤ PĂŤr temperaturĂŤn 18.1, meĂŤshtĂŤ interpolim,nga tabela vetive tĂŤ ajrit, kemi qĂŤ nĂŤ presioni 206.4 eĂŤshtĂŤ pĂŤr 19Âş dan/cm2, gjejmĂŤ: 2fizike ,, gjejmĂŤ: 18Âş presioniĂŤshtĂŤ 206.4 pĂŤr219.7 19Âş ĂŤshtĂŤ ĂŤshtĂŤ 219.7edan/cm 18Âş presioni 206.4 eepĂŤr 19Âş 219.7 gjejmĂŤ:

đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 18Âş presioni ĂŤshtĂŤ 206.4 e pĂŤr 19Âş ĂŤshtĂŤ 219.7 = dan/cm2, gjejmĂŤ: đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0â&#x2C6;&#x2019; â&#x2C6;&#x2019;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0â&#x2C6;&#x2019; â&#x2C6;&#x2019;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 = â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 = đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; â&#x2C6;&#x2019;â&#x2C6;&#x2019;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 19đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019;â&#x2C6;&#x2019; 18 206.4 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 = 219.7 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 =đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 18.1 18 219.7 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019;â&#x2C6;&#x2019;206.4 19â&#x2C6;&#x2019;â&#x2C6;&#x2019;â&#x2C6;&#x2019; 18 206.4 19 18 219.7 â&#x2C6;&#x2019; 206.4 = 1918.1 â&#x2C6;&#x2019; 18 219.7 â&#x2C6;&#x2019; 206.4 = 18 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; â&#x2C6;&#x2019; 206.4 206.4 = đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 18.1 â&#x2C6;&#x2019;â&#x2C6;&#x2019;18 Y0 = 206.4+ (0.1 x 13.3) = 207.73daN/cm2 18.1 â&#x2C6;&#x2019; 18 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 206.4

= 206.4+ (0.1xx13.3) 13.3)== 207.73daN/cm2 207.73daN/cm2 Y0Y0== 206.4+ 206.4+ (0.1 5. PĂŤr temperaturĂŤn me interpolim,nga tabela e vetive fizike tĂŤ ajrit,kemi qĂŤ nĂŤ Y0 (0.1 x 13.3) =10.45Âş, 207.73daN/cm2 2, gjejmĂŤ: 10Â° presioni ĂŤshtĂŤ 122.8 e pĂŤr 11Âş ĂŤshtĂŤ 131.2 dan/cm 5.PĂŤr PĂŤrtemperaturĂŤn temperaturĂŤn 10.45Âş, me interpolim,nga tabela fizike qĂŤ nĂŤ 5. PĂŤr 5. temperaturĂŤn 10.45Âş, me me interpolim,nga tabela eee vetive vetive fiziketĂŤtĂŤtĂŤajrit,kemi ajrit,kemi qĂŤ nĂŤ 10.45Âş, interpolim,nga tabela vetive fizike ajrit,kemi 5. PĂŤr temperaturĂŤn 10.45Âş, me interpolim,nga tabela e vetive fizike tĂŤ ajrit,kemi qĂŤ nĂŤqĂŤ nĂŤ 2, gjejmĂŤ: 10Â° presioni ĂŤshtĂŤ 122.8 e pĂŤr 11Âş ĂŤshtĂŤ 131.2 dan/cm đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;211Âş â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 10Â°presioni presioni ĂŤshtĂŤ122.8 e pĂŤr ĂŤshtĂŤ 131.2 dan/cm 2, gjejmĂŤ: 10Â° presioni ĂŤshtĂŤ 122.8 e122.8 pĂŤr e11Âş ĂŤshtĂŤ 131.2 dan/cm2, 10Â° ĂŤshtĂŤ pĂŤr 11Âş ĂŤshtĂŤ 131.2 dan/cm 2, gjejmĂŤ: gjejmĂŤ: = đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; â&#x2C6;&#x2019;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 = đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019;â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 = â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019;â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 = 131.2 11đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; 10 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1122.8 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019;â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1=đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 10.45 â&#x2C6;&#x2019; 10 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 11 â&#x2C6;&#x2019; 10 131.2 â&#x2C6;&#x2019;122.8 122.8 â&#x2C6;&#x2019; 122.8 1111 â&#x2C6;&#x2019;â&#x2C6;&#x2019; 1010 131.2 â&#x2C6;&#x2019; 122.8 = 131.2 10.45 â&#x2C6;&#x2019; 10 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 122.8 == Y0 = 122.8+ (0.45 x 8.4) =10.45 126.58daN/cm2 â&#x2C6;&#x2019;â&#x2C6;&#x2019; 1010 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 122.8 10.45 â&#x2C6;&#x2019; 122.8

Y0 = 122.8+ (0.45 x 8.4) = 126.58daN/cm2 6 122.8+ PĂŤr temperaturĂŤn 9.5, me interpolim,nga tabela e vetive fizike tĂŤ ajrit, kemi qĂŤ nĂŤ 9Â° Y0 (0.45 = =126.58daN/cm2 Y0 == 122.8+ (0.45xx8.4) 8.4) 126.58daN/cm2 presioni ĂŤshtĂŤ 114.7 e pĂŤr 10Âş ĂŤshtĂŤ 122.8 dan/cm 2, gjejmĂŤ: 6 PĂŤr temperaturĂŤn 9.5, me interpolim,nga tabela e vetive fizike tĂŤ ajrit, kemi qĂŤ nĂŤ 9Â° 66 PĂŤr temperaturĂŤn 9.5, me interpolim,nga tabela e vetive fizike tĂŤ ajrit, kemikemi nĂŤqĂŤ9Â°nĂŤ 9Â° PĂŤr temperaturĂŤn 9.5, me interpolim,nga tabela e vetive fizike tĂŤ tĂŤ ajrit, 6. PĂŤr temperaturĂŤn 9.5, me interpolim,nga tabela e vetive fizike ajrit,qĂŤkemi qĂŤ nĂŤ 9Â° presioni ĂŤshtĂŤ 114.7 e pĂŤr 10Âşđ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 ĂŤshtĂŤ 122.8 dan/cm 2, gjejmĂŤ: â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 2, gjejmĂŤ: presioni ĂŤshtĂŤ 114.7 e pĂŤr 10Âş ĂŤshtĂŤ 122.8 dan/cm 2, gjejmĂŤ: presioni ĂŤshtĂŤ 114.7 e pĂŤr 10Âş ĂŤshtĂŤ 122.8 dan/cm =

presioni ĂŤshtĂŤ 114.7 e pĂŤr 10Âş ĂŤshtĂŤđ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 122.8 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1dan/cm2, đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; â&#x2C6;&#x2019;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 gjejmĂŤ: â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019;â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 = đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; = 122.8 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 10 â&#x2C6;&#x2019; 9 = đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 = đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 114.7 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 9.5â&#x2C6;&#x2019; â&#x2C6;&#x2019;99 122.8 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019;â&#x2C6;&#x2019;114.7 10 114.7 10 â&#x2C6;&#x2019; 9 122.8 â&#x2C6;&#x2019; 114.7 = 122.8 10 â&#x2C6;&#x2019; 9 114.7 9.5 â&#x2C6;&#x2019;=9 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019;â&#x2C6;&#x2019;114.7 9.5 â&#x2C6;&#x2019; 9 =đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 114.7

9.5 â&#x2C6;&#x2019; 9

160

đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 114.7

Y0 = 114.7 + (0.5 x 8.1) = 118.75daN/cm2 = 114.7 + (0.5 x 8.1) = 118.75daN/cm2 Y0Y0=6 114.7 + (0.5 x 8.1) = 118.75daN/cm2 PĂŤr temperaturĂŤn 0.18, me interpolim,nga tabela e vetive fizike tĂŤ ajrit, kemi qĂŤ nĂŤ 0Â° Y0 = 114.7 + (0.5 x 8.1) = 118.75daN/cm2 presioni ĂŤshtĂŤ 61.1 e pĂŤr 1Âş ĂŤshtĂŤ 65.7tabela dan/cm 2,e vetive gjejmĂŤ: 6 PĂŤr temperaturĂŤn 0.18, me interpolim,nga tabela fizike tĂŤ ajrit, kemi qĂŤ0Â° nĂŤ 0Â° 6 PĂŤr temperaturĂŤn 0.18, me interpolim,nga e vetive fizike tĂŤ ajrit, kemi qĂŤ nĂŤ presioni ĂŤshtĂŤ 61.1 e me pĂŤr 1Âş ĂŤshtĂŤ 65.7 dan/cm 6 presioni PĂŤr temperaturĂŤn 0.18, interpolim,nga tabela e gjejmĂŤ: vetive fizike tĂŤ ajrit, kemi qĂŤ nĂŤ 0Â° 2, 2, gjejmĂŤ: ĂŤshtĂŤ 61.1 e pĂŤr 1Âş ĂŤshtĂŤ 65.7 dan/cm presioni ĂŤshtĂŤ 61.1 e pĂŤr 1Âş ĂŤshtĂŤ 65.7 dan/cm2, gjejmĂŤ:

7. PĂŤr temperaturĂŤn 0.18, me interpolim,nga tabela e vetive fizike tĂŤ ajrit, kemi qĂŤ nĂŤ 0Â° KONDENSIMI NĂ&#x2039; FASADAT E AVANCUARA . DIAGRAMI GLASER

presioni ĂŤshtĂŤ 61.1 e pĂŤr 1Âş ĂŤshtĂŤ 65.7 dan/cm2, gjejmĂŤ:

KONDENSIMI NĂ&#x2039; FASADAT E AVANCUARA . DIAGRAMI GLASER

1â&#x2C6;&#x2019;0 65.7 â&#x2C6;&#x2019; 61.1 = 0.18 â&#x2C6;&#x2019;0 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 61.1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1

Y0 = 61.1 + (0.18 1x â&#x2C6;&#x2019; 4.6) KĂŤto janĂŤ vlerat qĂŤ na duhen pĂŤr 0 = 61.928daN/cm2. 65.7 â&#x2C6;&#x2019; 61.1 = realizimin e grafikut presion-trashĂŤsi pĂŤrpresion-trashĂŤsi rastin tonĂŤ.PĂŤrpĂŤr tĂŤ ndĂŤrtuar diagramĂŤn Glaser, KĂŤto janĂŤ vlerat qĂŤ na duhen pĂŤr0.18 realizimin eđ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 grafikut rastin tonĂŤ. â&#x2C6;&#x2019;0 â&#x2C6;&#x2019; 61.1 marrim dhe vlerat e presioneve nĂŤ dy ekstremitetet, jashtĂŤ dhe brenda, dhe i marrim nĂŤ PĂŤr tĂŤ ndĂŤrtuar diagramĂŤn Glaser, marrim dhe vlerat e presioneve nĂŤ dy ekstremitetet, vlerat pĂŤrkatĂŤse pĂŤr 20Â° dhe W= 75% marrim temperaturĂŤn e pikĂŤs sĂŤ vesĂŤs 15.4Â° C e Y0 = + (0.18 x 4.6) = 61.928daN/cm2. KĂŤto janĂŤ qĂŤ naW= duhen jashtĂŤ dhe61.1 brenda, dhe i marrim nĂŤ vlerat pĂŤrkatĂŤse pĂŤrvlerat 20Â° dhe 75%pĂŤrmarrim me interpolim tĂŤ vlerave 170.5 daN/cm2, e 181.7 pĂŤr 16Â°C, gjejmĂŤ realizimin e grafikut presion-trashĂŤsi pĂŤr rastin tonĂŤ.PĂŤr tĂŤ ndĂŤrtuar diagramĂŤn temperaturĂŤn e pikĂŤs sĂŤ vesĂŤs 15.4Â° C e me interpolim tĂŤ vlerave 170.5 daN/cm2, e Glaser, 181.7 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 16 â&#x2C6;&#x2019; 15brenda, 181.7 marrim dhe vlerat e presioneve nĂŤ đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 dy ekstremitetet, jashtĂŤ dhe dheâ&#x2C6;&#x2019; i170.5 marrim nĂŤ = = pĂŤr 16Â°C, gjejmĂŤ: đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019;marrim đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 15.4 â&#x2C6;&#x2019;e15 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0vesĂŤs â&#x2C6;&#x2019; 170.5 vlerat pĂŤrkatĂŤse pĂŤr 20Â° dhe W= 75% temperaturĂŤn pikĂŤs sĂŤ 15.4Â° C e me interpolim tĂŤ vlerave 170.5 daN/cm2, e 181.7 pĂŤr 16Â°C, gjejmĂŤ Y0 = 170.5 + 0.4đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 x 11.2 174.98daN/cm2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 =16 181.7 â&#x2C6;&#x2019; 170.5 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 â&#x2C6;&#x2019; 15 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1

= đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 15.4 â&#x2C6;&#x2019; 15 Tab.2 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 170.5

(Temperatura e pikĂŤs sĂŤ vesĂŤs nĂŤ funksin tĂŤ temperaturĂŤs sĂŤ ajrit dhe tĂŤ lagĂŤshtisĂŤ relative), [4]

dhe klimatizimi i ndĂŤrtesave, Prof.Luan Voshtina, Dr. Gjergj Simaku Y0 = 170.5 + (Ngrohja, 0.4 x 11.2ventilimi = 174.98daN/cm2 2004 pp 306). Tab.2

Rel.nĂŤ funksin tb=16Â°C tb=18Â°C tb=20Â°C Tab.2 Temperatura eNr pikĂŤs sĂŤLag. vesĂŤs tĂŤ temperaturĂŤs sĂŤ tĂŤ ajrit dhe tĂŤrelative), lagĂŤshtisĂŤ (Temperatura e pikĂŤs sĂŤ vesĂŤs nĂŤ funksin tĂŤtb=12Â°C temperaturĂŤs sĂŤ ajrit dhe lagĂŤshtisĂŤ [4]

tb=22Â°C 1 100 +12 +16 +18 +20 +22 [5] (Ngrohja, ventilimi dhe klimatizimi i ndĂŤrtesave, Prof.Luan Voshtina, Dr. Gjergj Simaku relative 2 95 +11.2 +15.2 +17.2 +19.2 +21.2 2004 pp 306). +10.4 +14.35 +16.3 +18.3 20.3 Nr Lag. Rel. 3 tb=12Â°C 90 tb=16Â°C tb=18Â°C tb=20Â°C tb=22Â°C 4 85 +9.6 +13.5 +15.45 +17.4 +19.4 Lag. Rel. tb=12Â°C tb=16Â°C tb=18Â°C +20 tb=20Â°C tb=22Â°C 1 Nr 100 +12 +16 +18 +22 5 +8.7 +12.55 +16.4 +18.4 +1280 +16 +18 +20+14.5 +22 2 1 95100 +11.2 +15.2 +17.2 +19.2 +21.2 6 75 +7.7 +11.6 +13.5 +15.4 +17.4 +11.2 +15.2 +17.2 +19.2 +21.2 3 2 90 95 +10.4 +14.35 +16.3 +18.3 20.3 7 70 +6.7 +10.5 +12.45 +14.4 +16.3 3 +10.4 +14.35 +16.3 +18.3 20.3 85 90 +9.6 +13.5 +15.45 +17.4 +19.4 8 65 +5.6 +9.4 +11.3 +13.2 +15.1 4 +9.6 +13.5 +15.45 +17.4 +19.4 80 85 +8.7 +12.55 +14.5 +16.4 +18.4 9 60 +4.5 +8.2 +10.1 +12.0 +13.9 +8.7 +12.55 +14.5 +16.4 +18.4 6 5 75 80 +7.7 +11.6 +13.5 +15.4 +17.4 10 55 +3.3 +7 +8.8 +10.7 +12.55 6 +7.7 +11.6 +13.5 +15.4 +17.4 70 75 11 +6.7 +10.5 +12.45 +14.4 +16.3 +1.9 +5.6 +7.45 +9.3 +11.1 +6.750 +10.5 +12.45 +14.4 +16.3 8 7 65 70 12 +5.6 +9.4 +11.3 +13.2 +15.1 45 +0.45 +4.1 +5.9 +7.7 +9.2 8 +5.6 +9.4 +11.3 +13.2 +15.1 60 65 13 +4.5 +8.2 +10.1 +12.0 +13.9 40 -1.05 +2.4 +4.2 +6.0 +7.4 +4.5 +10.1 +12.0 +13.9 10 9 55 60 14 +3.3 +7+8.2 +8.8 +10.7 +12.55 35 -2.6 +0.6 +2.3 +4.1 +5.85 +3.3 +8.8 +10.7 +12.55 11 10 50 55 15 +1.9 +5.6+7 +7.45 +9.3 +11.1 30 -4.5 +1.4 +0.2 +1.9 +3.65 11 50 +1.9 +5.6 +7.45 +9.3 +11.1 12 45 +0.45 25 +4.1-6.55 +5.9-3.5 +7.7 -2.0 +9.2 16 -0.55 +1.10 +0.45 +4.1 +5.9 +7.7 13 12 40 45 1.05 +2.4 +4.2 +6.0 +7.4+9.2 -1.05 +2.4 +4.2 +6.0 +7.4 1 13 35 40 2.6 +0.6 +2.3 +4.1 +5.85 14 35 -2.6 +0.6 +2.3 +4.1 +5.85 1 30pĂŤr kontaktin 4.5 brenda me +1.4 +0.2 vlerĂŤn 174.98 +1.9 daN/cm2 +3.65 murin tĂŤ kemi dhe 15 30 -4.5 +1.4 +0.2 +1.9 +3.65jashtĂŤ, direkt nga 16 25 6.55 3.5 2.0 0.55 +1.10 tabela 56.2 daN/cm2. 16 25 -6.55 -3.5 -2.0 -0.55 +1.10

SiĂ§brenda shohim ndĂŤrpriten, gjĂŤ qĂŤdaN/cm2 nĂŤnkuptondhe mosjashtĂŤ, krijimdirekt tĂŤ kondensimit. pĂŤr kontaktin megrafikĂŤt murin nuk tĂŤ kemi vlerĂŤn 174.98 pĂŤr kontaktin brenda me murin tĂŤ kemi vlerĂŤn 174.98 daN/cm2 dhe jashtĂŤ, direkt nga nga tabela 56.2 daN/cm2. tabela 56.2 daN/cm2.

SiĂ§ shohim grafikĂŤt nuk ndĂŤrpriten, gjĂŤ qĂŤ nĂŤnkupton mos krijim tĂŤ kondensimit. 8 [5] Termoteknika, ngrohja dhe ajri i kondicionuar (Fizika teknike), Prof.Luan Voshtina, Prof.Dr.Angjelin Shtjefni, Dr.Ramadan Alushaj TiramĂŤ 2009.(pp.248,249)

161

ARTIKULL SHKENCOR

ENDRIT TUZI

diagrama e presion-trashësi DIAGRAMA E PRESION-TRASHËSI P(an/cm2) 250

228.324

225 200 175 150 118.75 125 100 75 61.928 50 56.2 25 0 0

207.73

208.129

227.414 174.98

126.58

S (cm)

Fig.4 (Grafiku presion-trashësi e fasadës së ventiluar) Fig.4 (Grafiku presion-trashësi e fasadës së ventiluar)

DIAGRAMA E TEMPERATURË-TRASHËSI ENDRIT TUZI

e presion-trashësi diagrama 20

19.551

DIAGRAMA 17.5 E PRESION-TRASHËSI18.518.13

19.616

P(an/cm2)15 12.5 250 10 225

T °C

9.5

7.5 200 1755 150 2.5 118.75 125 0 100 0.184 0 5 75 61.928

228.324

10.45

207.73

208.129

227.414 174.98

126.58 10

S (cm)

50 56.2 25Fig.5 (Grafiku temperaturë-trashësi e fasadës së ventiluar) 0 0

•

S (cm)

Të shohim se si ndryshon shpërndarja e temperaturave për situatën e një fasad Fig.4 (Grafiku presion-trashësi e fasadëstësëbrendëshme ventiluar) 20° C, dhe temper “kapotë”, kur konsiderojmë si temperaturë Fig.4 (Grafiku presion-trashësi e fasadës së ventiluar) jashtme -1° C. Rezistenca e përgjithshme është :

+ R1 + R2 + R3 + R4 + Rj, [5] Termoteknika, ngrohja dhe ajri i ko Rp = Σ R =ERb DIAGRAMA TEMPERATURË-TRASHËSI

(Fizika teknike), Prof.Luan Voshtina, Prof. Dr.Angjelin Shtjefni, Dr.Ramadan Alush 20 2009.(pp.248,249) 19.551 17.5

162

15 12.5

18.13 18.5

19.616

SiĂ§ shohim grafikĂŤt nuk ndĂŤrpriten, gjĂŤ qĂŤ nĂŤnkupton mos krijim tĂŤ kondensimit. TĂŤ shohim se si ndryshon shpĂŤrndarja e temperaturave pĂŤr situatĂŤn e njĂŤ fasade tĂŤ tipit

Rp =

R = Rb + R1 + R2 + R3 + R4 + Rj,

[5] ku

KONDENSIMI NĂ&#x2039; FASADAT E AVANCUARA . DIAGRAMI GLASER KONDENSIMI NĂ&#x2039; FASADAT E AVANCUARA . DIAGRAMI GLASER

â&#x20AC;&#x153;kapotĂŤâ&#x20AC;?, kur konsiderojmĂŤ si temperaturĂŤ tĂŤ brendĂŤshme 20Â° C, dhe temperaturĂŤ tĂŤ KONDENSIMI NĂ&#x2039; FASADAT E AVANCUARA . DIAGRAMI GLASER KONDENSIMI NĂ&#x2039; FASADAT E AVANCUARA . DIAGRAMI GLASER DIAGRAMI GLASER

KONDENSIMI E AVANCUARA jashtme -1Â° C. RezistencaNĂ&#x2039;e FASADAT pĂŤrgjithshme ĂŤshtĂŤ : .

ku ku = =0.13 R1(suva (suvae brendĂŤshme) e brendĂŤshme) = 0.022 ku ku RbrendĂŤshme RbrendĂŤshme 0.13m2k/w, m k/w, R1 = 0.022 m k/wm2k/w RbrendĂŤshme = 0.13 m22k/w, R1 (suva e brendĂŤshme) = 0.022 m22k/w ku R2 (tullĂŤ me bira 25cm) = 0.481 m2k/w, R3 (polisterol) = 0.769 m2k/w RbrendĂŤshme ==0.13 m R1 eebrendĂŤshme) ==0.022 m RbrendĂŤshme 0.13 m2k/w, k/w, R1(suva (suva brendĂŤshme) 0.022 m2k/w k/w R2 (tullĂŤ me bira 25cm) = 0.481 m k/w, R3 (polisterol) = 0.769 m k/w R2 (tullĂŤ me bira 25cm)2 = 0.481 m22k/w, R3 (polisterol) = 0.769 2m22k/w RbrendĂŤshme = 0.13 m=2k/w, R1m2k/w, (suva e brendĂŤshme) m2k/w R4 (suva e jashtme) 0.033 Rjashtme == 0.022 0.4 m2k/w R2 bira ==0.481 m R3 0.769 R2 (tullĂŤ me bira25cm) 25cm) 0.481 m22k/w, k/w, R3(polisterol) (polisterol) 0.769m m22k/w k/w R4(tullĂŤ (suvame e jashtme) = 0.033 m k/w, Rjashtme = 0.4 m == k/w R4 (suva e jashtme) = 0.033 m22k/w, Rjashtme = 0.4 m2 k/w R2 (tullĂŤ me bira 25cm) = 0.481 m2k/w, R3 (polisterol)2= 0.769 m2k/w R4 ==0.033 Rjashtme R4(suva (suvaeejashtme) jashtme) 0.033m m2k/w, k/w, Rjashtme 0.4m m22k/w Dhe pĂŤrfundimisht Rp = 0.13 0.481 + 0.769 =+=0.4 +k/w 0.4 = 1.835 m2k/w. pĂŤrfundimisht Rp +=+ 0.022 0.13 +2++0.022 0.481++0.033 0.769 + 0.033 + 0.4 = 1.835 m2k/w. DheDhe pĂŤrfundimisht Rp = 0.13 0.022 0.481 ++ 0.769 0.033 + 0.4 = 1.835 m2k/w. R4 (suva e jashtme) = 0.033 m2k/w, Rjashtme = 0.4 m2k/w Dhe pĂŤrfundimisht Rp = 0.13 + 0.022 + 0.481 + 0.769 + 0.033 + 0.4 = 1.835 m k/w. Dhe pĂŤrfundimisht Rp = 0.13 + 0.022 + 0.481 + 0.769 + 0.033 +duke 0.4 1.835 nga m22k/w. PĂŤrcaktojmĂŤ temperaturat e sipĂŤrfaqeve tĂŤ shtresave, duke filluar nga =brenda-jashtĂŤ: PĂŤrcaktojmĂŤ temperaturat e sipĂŤrfaqeve tĂŤ shtresave, filluar brenda-jashtĂŤ: PĂŤrcaktojmĂŤ temperaturat e sipĂŤrfaqeve tĂŤ shtresave, duke filluar nga brenda-jashtĂŤ: Dhe pĂŤrfundimisht Rp = 0.13 + 0.022 + 0.481 + 0.769 + 0.033 + 0.4 = 1.835 m2k/w. PĂŤrcaktojmĂŤ eesipĂŤrfaqeve PĂŤrcaktojmĂŤ sipĂŤrfaqevetĂŤtĂŤshtresave, shtresave,duke dukefilluar filluarnga ngabrenda-jashtĂŤ: brenda-jashtĂŤ: temperatura temperaturat etemperaturat sipĂŤrfaqes sĂŤ brendĂŤshme: temperatura e sipĂŤrfaqes sĂŤ brendĂŤshme: temperatura e sipĂŤrfaqes sĂŤ brendĂŤshme: PĂŤrcaktojmĂŤ temperaturat e sipĂŤrfaqeve tĂŤ shtresave, duke filluar nga brenda-jashtĂŤ: temperatura eesipĂŤrfaqes sĂŤ temperatura sipĂŤrfaqes sĂŤtĂŤbrendĂŤshme: brendĂŤshme: NĂŤ NĂŤ sipĂŤrfaqen e kontaktit ajrit tĂŤ me suvanĂŤ,me kemi: sipĂŤrfaqen e kontaktit tĂŤ brendshĂŤm ajrit tĂŤ brendshĂŤm suvanĂŤ, kemi: NĂŤ sipĂŤrfaqen e kontaktit tĂŤ ajrit tĂŤ brendshĂŤm me suvanĂŤ, kemi: temperatura e sipĂŤrfaqes sĂŤ brendĂŤshme: NĂŤ me NĂŤsipĂŤrfaqen sipĂŤrfaqeneekontaktit kontaktit ajrittĂŤtĂŤbrendshĂŤm brendshĂŤm mesuvanĂŤ, suvanĂŤ,kemi: kemi: đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą tĂŤtĂŤajrit 20â ° â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą Rb 20â ° â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) 1. t b-suva = = 20ÂştĂŤ -brendshĂŤm 0.13 = kemi: 18.51â ° NĂŤ sipĂŤrfaqen e kontaktit tĂŤ ajrit me suvanĂŤ, 1. tb-suva = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąâ&#x2C6;&#x2018;â&#x2C6;&#x2018;â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą Rb = 20Âş - 20â ° 1.835 0.13 = 18.51â ° â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą 20â °1.835 â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) 1. Rb = 20Âş 0.13 1. ttb-suva b-suva== đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąâ&#x2C6;&#x2018; 20Âş -- 20â ° 0.13 == 18.51â ° 18.51â ° đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąâ&#x2C6;&#x2018;â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą RbtĂŤ=suvasĂŤ â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026; 1.835 đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;kontaktit NĂŤNĂŤ sipĂŤrfaqen e kontaktit me1.835 murin emurin tullĂŤs, sipĂŤrfaqen e tĂŤ suvasĂŤ me e=tullĂŤs, 1. t b-suva = Rb = 20Âş 0.13 kemi: 18.51â °kemi: NĂŤ sipĂŤrfaqen e kontaktit tĂŤ suvasĂŤ me murin e tullĂŤs, kemi: â&#x2C6;&#x2018; đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026; 1.835 NĂŤ eetullĂŤs, kemi: NĂŤsipĂŤrfaqen sipĂŤrfaqeneekontaktit kontaktit suvasĂŤme memurin murin20â ° tullĂŤs, kemi: đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą tĂŤtĂŤsuvasĂŤ â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą tĂŤ â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) t suva-mure = (Rb+R1) = 20Âş - 20â ° (0.13+0.022) = 18.26â ° NĂŤ2. sipĂŤrfaqen kontaktit suvasĂŤ me murin e tullĂŤs, kemi: 2. tsuva-mur = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąâ&#x2C6;&#x2018;â&#x2C6;&#x2018;â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą (Rb+R1) = 20Âş - 20â ° 1.835 (0.13+0.022) = 18.26â ° â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą 20â °1.835 â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) 2. t suva-mur = (Rb+R1) = 20Âş (0.13+0.022) ==18.26â ° 2. tsuva-mur = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąâ&#x2C6;&#x2018;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąâ&#x2C6;&#x2018;â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą = 20Âş - 20â ° 18.26â ° â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) (0.13+0.022) 1.835 đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026; đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą (Rb+R1) 1.835 NĂŤ2.sipĂŤrfaqen e kontaktit tĂŤ murit tĂŤ tullĂŤs me polisterolin, kemi: tsuva-mure=kontaktit (Rb+R1) =tullĂŤs 20Âş - me polisterolin, (0.13+0.022) = 18.26â ° NĂŤ sipĂŤrfaqen tĂŤ murit tĂŤ kemi: â&#x2C6;&#x2018; đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026; 1.835 NĂŤ sipĂŤrfaqen e kontaktit tĂŤ tĂŤmurit tullĂŤs me polisterolin, kemi: NĂŤ sipĂŤrfaqen eekontaktit polisterolin, kemi: NĂŤ sipĂŤrfaqen kontaktit murit tĂŤtullĂŤs tullĂŤstĂŤme me polisterolin, kemi: đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;ĄtĂŤtĂŤ đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą murit 20â ° â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą (Rb+R1+R2) t mur-p-plost. = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;ĄtĂŤ = me 20Âş polisterolin, - 20â ° â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) (0.13+0.022+0.481) = NĂŤ3. sipĂŤrfaqen e kontaktit murit tĂŤ tullĂŤs kemi: 3. tmur-p-plost. = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąâ&#x2C6;&#x2018;â&#x2C6;&#x2018;â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą (Rb+R1+R2) = 20Âş - 20â ° 1.835 (0.13+0.022+0.481) = â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą 20â °1.835 â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) 3. t mur-p-plost. = (Rb+R1+R2) = 20Âş (0.13+0.022+0.481) = 12.75â ° 3. tmur-p-plost. = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąâ&#x2C6;&#x2018;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąâ&#x2C6;&#x2018;â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) (0.13+0.022+0.481) = 1.835 đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026; đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą (Rb+R1+R2) = 20Âş - 20â ° 12.75â ° 1.835 3. tmur-p-plost. = â&#x2C6;&#x2018; (Rb+R1+R2) = 20Âş (0.13+0.022+0.481) = 1.835 kemi: 12.75â ° 12.75â ° NĂŤ sipĂŤrfaqen e kontaktitđ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026; tĂŤ polisterolit. me suvanĂŤ e jashtme NĂŤ12.75â ° sipĂŤrfaqen e kontaktit tĂŤ polisterolit. me suvanĂŤ e jashtme kemi: NĂŤ sipĂŤrfaqen eekontaktit me jashtme NĂŤ sipĂŤrfaqen e kontaktit tĂŤ polisterolit. meeesuvanĂŤ ekemi: jashtme kemi: NĂŤ sipĂŤrfaqen kontaktit polisterolit. mesuvanĂŤ suvanĂŤ jashtme kemi: đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;ĄtĂŤtĂŤ đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą polisterolit. 20â ° â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą (Rb+R1+R2+R3) 20â ° â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) t polis. - suva = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;ĄtĂŤ = 20Âşe -jashtme NĂŤ4. sipĂŤrfaqen e kontaktit polisterolit. me suvanĂŤ kemi: 4. t polis. - suva = đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąâ&#x2C6;&#x2018;â&#x2C6;&#x2018;â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą (Rb+R1+R2+R3) = 20Âş - 20â ° 1.835 â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą 20â °1.835 â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) 4. ttpolis. (Rb+R1+R2+R3) ==20Âş -(0.13+0.022+0.481+0.769) = 3.955â ° 4. polis.--suva suva== đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąâ&#x2C6;&#x2018; (Rb+R1+R2+R3) 20Âş đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą 20â ° â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) 1.835 đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026; (0.13+0.022+0.481+0.769) = 3.955â ° â&#x2C6;&#x2018; 1.835 4. t polis. - suva = â&#x2C6;&#x2018; (Rb+R1+R2+R3) = 20Âş 1.835 đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026; == 3.955â ° (0.13+0.022+0.481+0.769) (0.13+0.022+0.481+0.769) 3.955â ° (0.13+0.022+0.481+0.769) = 3.955â ° NĂŤ sipĂŤrfaqen e kontaktit tĂŤ suvasĂŤ sĂŤ me ajrin jashtĂŤ kemi: NĂŤ sipĂŤrfaqen e kontaktit tĂŤ suvasĂŤ sĂŤ me ajrin jashtĂŤ kemi: NĂŤ eekontaktit me kemi: NĂŤsipĂŤrfaqen sipĂŤrfaqen kontaktit suvasĂŤ sĂŤ meajrin ajrin jashtĂŤ kemi: đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;ĄtĂŤtĂŤ đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą suvasĂŤ â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą tĂŤsĂŤ â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) NĂŤ sipĂŤrfaqen e kontaktit suvasĂŤ sĂŤ jashtĂŤ me ajrin jashtĂŤ20â ° kemi: đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą 5. t p.mineral ajĂŤr = (Rb+R1+R2+R3+R4) = 20Âş - 20â ° â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) NĂŤ 5. sipĂŤrfaqen e kontaktit suvasĂŤ sĂŤ me ajrin jashtĂŤ kemi: t p.mineral - ajĂŤr = tĂŤ (Rb+R1+R2+R3+R4) = 20Âş 1.835 đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąâ&#x2C6;&#x2018; â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą 20â ° â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) â&#x2C6;&#x2018; đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą 20â °1.835 â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) 5. ttp.mineral (Rb+R1+R2+R3+R4) ==20Âş -(0.13+0.022+0.481+0.769+0.4 ) = 0.622â ° 5. p.mineral--ajĂŤr ajĂŤr== đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąâ&#x2C6;&#x2018; (Rb+R1+R2+R3+R4) 20Âş đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą â&#x2C6;&#x2019;đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą 20â ° â&#x2C6;&#x2019;(â&#x2C6;&#x2019;1â °) 1.835 đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026; (0.13+0.022+0.481+0.769+0.4 ) = 0.622â ° de tĂŤ tipit 5. t p.mineral - ajĂŤr = â&#x2C6;&#x2018; đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026; (Rb+R1+R2+R3+R4) = 20Âş - 1.835 â&#x2C6;&#x2018; 1.835 đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026;đ?&#x2018;&#x2026; (0.13+0.022+0.481+0.769+0.4 ) = 0.622â ° ) = -trashĂŤsi, 0.622â ° gjejmĂŤ me anĂŤ tĂŤ interpolimit, vlerat e presioneve PĂŤr tĂŤ realizuar diagramĂŤn presionraturĂŤ tĂŤ (0.13+0.022+0.481+0.769+0.4 PĂŤr tĂŤ realizuar diagramĂŤn presiontrashĂŤsi, gjejmĂŤ me anĂŤ tĂŤ interpolimit, vlerat e presioneve (0.13+0.022+0.481+0.769+0.4 ) = pĂŤrkatĂŤs pĂŤr temperaturat e gjetura: 0.622â ° PĂŤr tĂŤtĂŤrealizuar diagramĂŤn pĂŤrkatĂŤs pĂŤr temperaturat epresiongjetura:trashĂŤsi, PĂŤr realizuar diagramĂŤnpresiontrashĂŤsi,gjejmĂŤ gjejmĂŤme meanĂŤ anĂŤtĂŤtĂŤinterpolimit, interpolimit,vlerat vlerateepresioneve presioneve pĂŤrkatĂŤs pĂŤr temperaturat e gjetura: PĂŤr tĂŤ realizuar diagramĂŤn presiontrashĂŤsi, gjejmĂŤ me anĂŤ tĂŤ interpolimit, vlerat e presioneve pĂŤrkatĂŤs pĂŤr temperaturat e gjetura: 10 pĂŤrkatĂŤs pĂŤr temperaturat e gjetura: 10

ondicionuar haj TiramĂŤ 9

10 10 10

163

ARTIKULL SHKENCOR

ENDRIT TUZI ENDRIT TUZI

1. KĂŤshtu, pĂŤr temperaturĂŤn 18.51, me interpolim,nga tabela e vetive fizike tĂŤ ajrit, ENDRIT TUZI PĂŤr19ÂştĂŤpresioni realizuar diagramĂŤn trashĂŤsi, gjejmĂŤ dhe me tabela anĂŤ tĂŤe vetive interpolimit, vlerat e kemi pĂŤr temperaturĂŤn ĂŤshtĂŤ 219.7, pĂŤr presion18Âş presioni 206.4 daNcm2 ENDRIT TUZI 1. KĂŤshtu, pĂŤr temperaturĂŤn 18.51, me interpolim,nga fizike tĂŤ ajrit, gjejmĂŤ: pĂŤr temperaturĂŤn 19Âş presioni ĂŤshtĂŤ 219.7, pĂŤr 18Âş presioni 206.4 daNcm2 dhe presionevekemi pĂŤrkatĂŤs pĂŤr temperaturat e gjetura: 1.1. KĂŤshtu, pĂŤr temperaturĂŤn 18.51, me interpolim,nga tabela eevetive fizike tĂŤtĂŤajrit, gjejmĂŤ: KĂŤshtu, pĂŤrâ&#x2C6;&#x2019; temperaturĂŤn me interpolim,nga tabela vetive fizike ajrit, đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1temperaturĂŤn đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 18.51,18.51, 1. KĂŤshtu, pĂŤr me interpolim,nga tabela e vetive fizike tĂŤ ajrit, kemi kemi pĂŤr temperaturĂŤn 19Âş presioni ĂŤshtĂŤ 219.7, pĂŤr 18Âş presioni 206.4 daNcm2 dhe = kemi pĂŤr temperaturĂŤn 19Âş presioni ĂŤshtĂŤ 219.7, pĂŤr 18Âş presioni 206.4 daNcm2 dhe đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019;presioni đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 pĂŤr temperaturĂŤn 19Âş ĂŤshtĂŤ 219.7, pĂŤr 18Âş presioni 206.4 daNcm2 dhe gjejmĂŤ: gjejmĂŤ: = gjejmĂŤ: đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 19 â&#x2C6;&#x2019; 18 219.7 â&#x2C6;&#x2019; 206.4 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019;â&#x2C6;&#x2019;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 = đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2â&#x2C6;&#x2019;â&#x2C6;&#x2019;â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1=219.7 18.51 â&#x2C6;&#x2019; 18 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 219.7 19 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; 18 206.4 = đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 = đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 18.51 â&#x2C6;&#x2019; 18 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 219.7 Y0 = 206.4+ (0.51 x 13.3) = 213.183daN/cm2 19 â&#x2C6;&#x2019; 18 219.7 206.4 19 â&#x2C6;&#x2019; 18 = 219.7â&#x2C6;&#x2019;â&#x2C6;&#x2019;206.4 Y0 = 206.4+ (0.51 x 13.3) =18.51 213.183daN/cm2 â&#x2C6;&#x2019;â&#x2C6;&#x2019;18 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019;â&#x2C6;&#x2019;219.7 2. PĂŤr temperaturĂŤn 18.26Âş, me interpolim,nga tabela e vetive fizike tĂŤ = ajrit, đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0gjejmĂŤ. 219.7 18.51 18 2. PĂŤr temperaturĂŤn 18.26Âş, me interpolim,nga tabela e vetive fizike tĂŤ ajrit, gjejmĂŤ. Y0 Y0 ==206.4+ 206.4+(0.51 (0.51xx13.3) 13.3)== 213.183daN/cm2 213.183daN/cm2 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1

đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1

2.2. PĂŤr temperaturĂŤn me interpolim,nga tabela eevetive tĂŤtĂŤajrit, gjejmĂŤ. = 18.26Âş, 18.26Âş, 18.26Âş, međ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 interpolim,nga vetive fizike ajrit, gjejmĂŤ. 2.PĂŤr temperaturĂŤn interpolim,nga eđ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 vetive fizikefizike tĂŤ ajrit, gjejmĂŤ. đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019;PĂŤr đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1temperaturĂŤn đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 me â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 tabela đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019;tabela 19 â&#x2C6;&#x2019; 18 219.7 â&#x2C6;&#x2019; 206.4 = 18.26 â&#x2C6;&#x2019; 18 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 206.4

= đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019;â&#x2C6;&#x2019;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2â&#x2C6;&#x2019;â&#x2C6;&#x2019;â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 19 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; 18 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1==219.7 206.4 â&#x2C6;&#x2019;â&#x2C6;&#x2019;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019;â&#x2C6;&#x2019;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 = đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 18.26 â&#x2C6;&#x2019; 18 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 206.4 219.7 19 â&#x2C6;&#x2019; 18 19 â&#x2C6;&#x2019; 18 = 219.7â&#x2C6;&#x2019;â&#x2C6;&#x2019;206.4 206.4 = đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 206.4 18.26 â&#x2C6;&#x2019; 18 18.26 â&#x2C6;&#x2019; 18 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 206.4

Y0 = 206.4+ (0.26 x 13.3) = 209.858 daN/cm2 Y0 = 206.4+ (0.26 x 13.3) = 209.858 daN/cm2

3. PĂŤr temperaturĂŤn 12.75Âş, me interpolim,nga tabela e vetive fizike tĂŤ ajrit, gjejmĂŤ. 3. PĂŤr temperaturĂŤn 12.75Âş, me interpolim,nga tabela e vetive fizike tĂŤ ajrit, gjejmĂŤ. (0.26 xx13.3) KĂŤshtu, kemi pĂŤr temperaturĂŤnY0 13Âş =presioni ĂŤshtĂŤ 149.8, pĂŤr =12Âş presionidaN/cm2 140.2. daNcm2 dhe Y0 =206.4+ 206.4+ (0.26 13.3) = 209.858 209.858 daN/cm2 gjejmĂŤ: kemi pĂŤr 12.75Âş, temperaturĂŤn 13Âş interpolim,nga presioni ĂŤshtĂŤ 149.8, pĂŤr 12Âş presioni 140.2. daNcm2 dhe 3. PĂŤrKĂŤshtu, temperaturĂŤn me interpolim,nga tabela e vetive fizike tĂŤ ajrit, gjejmĂŤ. 3.3. PĂŤr PĂŤrtemperaturĂŤn temperaturĂŤn12.75Âş, 12.75Âş,me me interpolim,ngatabela tabelaeevetive vetivefizike fiziketĂŤtĂŤajrit, ajrit, gjejmĂŤ. gjejmĂŤ. gjejmĂŤ: KĂŤshtu, kemi pĂŤr temperaturĂŤn 13Âş presioni ĂŤshtĂŤ 149.8, pĂŤr 12Âş presioni 140.2. daNcm2 KĂŤshtu, kemi pĂŤr temperaturĂŤn 13Âş KĂŤshtu, 13Âşpresioni presioniĂŤshtĂŤ ĂŤshtĂŤ149.8, 149.8,pĂŤr pĂŤr12Âş 12Âşpresioni presioni140.2. 140.2.daNcm2 daNcm2dhe dhe đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019;kemi đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 pĂŤr đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2temperaturĂŤn â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 dhegjejmĂŤ: gjejmĂŤ: = gjejmĂŤ: đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 = đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 13 â&#x2C6;&#x2019; 12 149.8 â&#x2C6;&#x2019; 140.2 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019;â&#x2C6;&#x2019;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 = đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2â&#x2C6;&#x2019;â&#x2C6;&#x2019;â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 12.75 â&#x2C6;&#x2019; 12 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 140.2 140.2 13 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; 12 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1==149.8 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 = đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 140.2 12.75 â&#x2C6;&#x2019; 12 13 â&#x2C6;&#x2019; 12 149.8 13 â&#x2C6;&#x2019; 12 = 149.8â&#x2C6;&#x2019;â&#x2C6;&#x2019;140.2 140.2 = đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 140.2 12.75 Y0 = 140.2+ (0.75 x 9.6) = 147.4 daN/cm2 12.75â&#x2C6;&#x2019;â&#x2C6;&#x2019;12 12 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 140.2

Y0 = 140.2+ (0.75 x 9.6) = 147.4 daN/cm2

4.PĂŤr temperaturĂŤn 3.955Âş, me interpolim,nga tabela e vetive fizike tĂŤ ajrit, gjejmĂŤ. 4.PĂŤr 4.PĂŤr temperaturĂŤn 3.955Âş, me interpolim,nga tabela fizike tĂŤ tĂŤ ajrit, ajrit, gjejmĂŤ. gjejmĂŤ. temperaturĂŤn interpolim,nga tabela ee vetive vetive fizike ==140.2+ (0.75 xx3.955Âş, 9.6) ==me 147.4 daN/cm2 KĂŤshtu, kemi pĂŤr temperaturĂŤnY0 3Âş presioni ĂŤshtĂŤ 75.9, pĂŤr 4Âş presioni 81.3 daNcm2 dhe Y0 140.2+ (0.75 9.6) 147.4 daN/cm2 KONDENSIMI NĂ&#x2039; FASADAT E AVANCUARA . DIAGRAMI GLASER KĂŤshtu, kemi pĂŤr temperaturĂŤn 3Âş presioni ĂŤshtĂŤ 75.9, pĂŤr 4Âş presioni 81.3 daNcm2 dhe gjejmĂŤ: KĂŤshtu, kemi pĂŤr temperaturĂŤn 3Âş presioni ĂŤshtĂŤ 75.9,e .vetive pĂŤr 4Âş presioni 81.3 daNcm2 dhe KONDENSIMI NĂ&#x2039; me FASADAT E AVANCUARA DIAGRAMI GLASER 4.PĂŤr temperaturĂŤn 3.955Âş, interpolim,nga tabela fizike tĂŤ ajrit, gjejmĂŤ. 4.PĂŤr temperaturĂŤn 3.955Âş, me interpolim,nga tabela e vetive fizike tĂŤ ajrit, gjejmĂŤ. gjejmĂŤ: gjejmĂŤ: 4 â&#x2C6;&#x2019; 3 ĂŤshtĂŤ 81.3 â&#x2C6;&#x2019; 75.9 KĂŤshtu, kemi pĂŤr temperaturĂŤn 3Âş3Âşpresioni pĂŤr =81.375.9, KĂŤshtu, 75.9, pĂŤr4Âş4Âşpresioni presioni81.3 81.3daNcm2 daNcm2dhe dhe 4presioni â&#x2C6;&#x2019; 3â&#x2C6;&#x2019; 3 ĂŤshtĂŤ đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019;kemi đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 pĂŤr đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2temperaturĂŤn â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 3.955 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; â&#x2C6;&#x2019; 75.9 75.9 gjejmĂŤ: = = gjejmĂŤ: 3.955 â&#x2C6;&#x2019; 75.9 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2â&#x2C6;&#x2019;â&#x2C6;&#x2019;3 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 = đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 11 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019;â&#x2C6;&#x2019;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 Y0 = 75.9+ (0.955 x 5.4) = 81.057 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2daN/cm2 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1= đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2â&#x2C6;&#x2019;â&#x2C6;&#x2019;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 Y0 = 75.9+ (0.955 x 5.4) = 81.057đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 daN/cm2=đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 11 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0â&#x2C6;&#x2019;â&#x2C6;&#x2019;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 5.PĂŤr temperaturĂŤn -0.622, me interpolim,nga tabela e vetive fizike tĂŤ ajrit, gjejmĂŤ. temperaturĂŤn -0.622,me meinterpolim,nga interpolim,nga tabela fizike tĂŤ ajrit, gjejmĂŤ. 5.PĂŤr5.PĂŤr temperaturĂŤn -0.622, tabelae vetive e vetive fizike tĂŤ ajrit, gjejmĂŤ. 11 11 KĂŤshtu, kemi pĂŤr temperaturĂŤn 0Âş presioni ĂŤshtĂŤ 61.1, pĂŤr -1Âş presioni 56.2 daNcm2 dhe KĂŤshtu, pĂŤr temperaturĂŤn 0Âş presioni ĂŤshtĂŤ 61.1, presioni 56.2 daNcm2 dhe KĂŤshtu, kemikemi pĂŤr temperaturĂŤn 0Âş presioni ĂŤshtĂŤ 61.1, pĂŤrpĂŤr -1Âş-1Âş presioni 56.2 daNcm2 dhe gjejmĂŤ: gjejmĂŤ: gjejmĂŤ: đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 = â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;2 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0â&#x2C6;&#x2019;â&#x2C6;&#x2019;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1= đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;2 đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;0 â&#x2C6;&#x2019; đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;đ?&#x2018;&#x2039;1 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;1 61.1 â&#x2C6;&#x2019; 56.2 0 â&#x2C6;&#x2019; â&#x2C6;&#x2019;1 0 â&#x2C6;&#x2019; â&#x2C6;&#x2019;1â&#x2C6;&#x2019; 0 =61.1 â&#x2C6;&#x2019; 56.2 0.622 = đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 56.2 0.622 â&#x2C6;&#x2019; 0 đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;đ?&#x2018;&#x152;0 â&#x2C6;&#x2019; 56.2

164

Y0 = 56.2+ (0.622 x 4.9) = 59.24 daN/cm2 Y0 = 56.2+ (0.622 x 4.9) = 59.24 daN/cm2 daN/cm2

Y0 = 56.2+ (0.622 x 4.9) = 59.24 daN/cm2 diagrama e presion-trashësi daN/cm2 225 200 175 147.4 150 125 100 81.057 75 59.24 50 56.2 25 0 0

209.859 213.183 174.98

10 15 20 25 30 35 40 45 50

Fig.6 (Grafiku presion-trashësi e fasadës “kapotë”)

S (cm)

ENDRIT TUZI “kapotë”) Fig.6 (Grafiku presion-trashësi e fasadës

diagrama e presion-trashësi 20

18.26 18.51

17.5 15 12.5 10

12.75

7.5 5 2.5 0 -2.5 0

3.955 -0.622 5 10

40 S (cm)

T °C

Fig.7 (Grafiku temperaturë-trashësi e fasadës “kapotë”)

Konkluzionet Është provuar që si për fasadën e ventiluar, ashtu dhe për fasadën me veshje-“kapotë”,nuk

Konkluzionet: kemi moment të kondensimit të ujërave. Prandaj dalim me konkluzionin final, që mbështetur në diagramin Glaser, grafiku i presioneve të pjesshëm qëndron më lart se ai

Është si përnuk fasadën ashtu i vlerave për pikën provuar e vesës, për që rrjedhojë ka rrezik e të ventiluar, kondensimit të ujit.

dhe për fasadën me veshje-“kapotë” 165 kemi moment të kondensimit të ujërave. Prandaj dalim me konkluzionin final, që mbë në diagramin Glaser, grafiku i presioneve të pjesshëm qëndron më lart se ai i vlerave p

ARTIKULL SHKENCOR

MBI PROPORCIONET DHE FORMAT RACIONALE TË STRUKTURAVE INXHINIERIKE Feti Selmani, Niko Pojani, Musa Stavileci Artikulli u recensua nga: Prof.Asc. Dr Diana Haxhiusheni, Ing. Merita Guri

Abstract:

HYRJE

numri të veçantë, i shënuar zakonisht me.

Frequently, in discussions, papers and some books, attempts have been made, in order to make attributions - at times deserved and at times not, to some numbers, such as the so-called “golden ratio” or in some cases “golden section” and even “divine proportion”. Some of the “structures” created by Nature are beautiful and, since, at the very heart of theirs, lies the number, there is no doubt that, some of them possess some hidden “magic” within. They manifest themselves mainly, through proportions between physical patterns or objects, created either by the Nature or by the man. In this paper, two of these numbers and their implication with civil engineering structures are discussed: Euler’s number and the number - often called “golden ratio” or “golden section”.

Shumë herë, nga autorë të ndryshëm,

Thelbi dhe origjina e këtij numri gjenden

tentohet që disa numrave tu vishen

te gjeometria e matematikanit të madh

cilësime nganjëherë “të merituara”

të lashtësisë, Euklidit (rreth 300 vjet p.e.s

[1]

, dhe më konkretisht në konceptin e

por ndonjëherë edhe të glorifikohen [2],

[3]

duke u dhënë vlerësime jo-realiste. Në

proporcioneve. Në kontekstin e definimit

këtë artikull, në kontekstin e teorisë së

të proporcionit, numri shpreh pikërisht

strukturave ndërtimore do të referohen

një proporcion, por disi të veçantë.

dhe diskutohen dy numra të tillë; numri

Në librin e gjashtë mbi gjeometrinë

ϕ, i cili lidhet me të ashtuquajturën

të Euklidit

“prerja e artë” apo “relacioni i artë” dhe,

së cilës për të gjetur “prerjen e artë” të një

numri i Eulerit apo siç quhet nganjëherë

segmenti me gjatësi a+b, ku a>b (Fig.1),

edhe numri i Neperit “e”.

është e nevojshme që “pjesa e vogël, d.m.th.

[4],

gjendet një teoremë sipas

b-ja, të qëndrojë në relacion me pjesën më të madhe, d.m.th. a-në, sikurse pjesa

166

“RELACIONI I ARTË” NË STRUKTURAT INXHINIERIKE

e madhe a rri me gjatësinë e segmentit të

Numri ϕ : Nga Euklidi te Fibonaçi

shprehet përmes barazimit vijues:

plotë, d.m.th. a+b. Kjo, ndryshe mund të

Kur në arkitekturë flitet për harmoninë

b/a=a/((a+b))

dhe proporcionet, shpesh i referohemi

prej ku shkruhet:

të ashtuquajturës “prerje e artë”, që

b(a+b)=a^2 marrë

kështu

(1) (2)

matematikisht shprehet përmes një

duke

përfundimisht

[1] Leonhardt, 1982 [2] Bukhary, S. M. N., 2007, ‘The influence of varying maxillary lateral incisor dimensions on perceived smile aesthetic’, British Dental Journal, no. 203, pp. 687 – 693.

[3] www.mathword.com [4] Hawking, S., 2007, God Created the Integers – the mathematical breakthroughs that changed history, Running Press Book Publishers, Philadelphia, Pennsylvania.

+ đ??šđ??šđ??šđ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;â&#x2C6;&#x2019;2 đ??šđ??šđ??šđ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; = đ??šđ??šđ??šđ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;â&#x2C6;&#x2019;1 marrĂŤdhĂŤniet:

(4)

interesante midis termave fqinjĂŤ tĂŤ serisĂŤ

a=1.618b; e serisĂŤ b=1/a=0.618a orma e zhvilluar (4) ĂŤshtĂŤ:

(3)

sĂŤ FibonaĂ§it: me largimin nga origjina,

PikĂŤrisht numri 1.618 ĂŤshtĂŤ definuar si

d.m.th. nga anĂŤtari i parĂŤ (1-shi) raporti

, 1, 2, 3,numri 5, 8, apo 13,ndryshe 21, 34, 55, 89, 144, 233, â&#x20AC;&#x153;relacioni i artĂŤâ&#x20AC;?.KohĂŤ nĂŤ mes tĂŤ termit F

(n+1)

(5)

dhe atij Fn i afrohet

NĂŤ TabelĂŤn 1, pas jepen raportet mĂŤ vonĂŤ Euklidit, teorinĂŤinteresante mbi numrat midis gjithnjĂŤtermave e mĂŤ tepĂŤr fqinjĂŤ numrit tĂŤ. serisĂŤ sĂŤ FibonaĂ§it: me largimin nga rigjina,e d.m.th. nga shumĂŤ anĂŤtarimatematikanĂŤ, i parĂŤ (1-shi) raporti nĂŤ mes tĂŤ termit đ??šđ??šđ??šđ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;+1 dhe atij đ??šđ??šđ??šđ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; i afrohet gjithnjĂŤ e kanĂŤ zhvilluar e mĂŤ tepĂŤrnjĂŤnumrit â&#x2C6;&#x2026;.qenĂŤ matematikani i shquar Tabela 1 - Raportet midis termave fqinjĂŤ tĂŤ serisĂŤ sĂŤ FibonaĂ§it ndĂŤr ta ka italian Leonardo Pisano Bigollo, i njohur

Po kĂŤshtu mund tĂŤ konstatohet se

CV:

Tabela 1 - Raportet midis termave fqinjĂŤ tĂŤ serisĂŤ sĂŤ FibonaĂ§it Feti Selmani ka lindur mĂŤ 15 maj 1964 nĂŤ TupallĂŤ, komuna e MedvegjĂŤs. Studimet / +1 kryesisht pĂŤr librin e tij â&#x20AC;&#x153;Libri i llogaritjeveâ&#x20AC;? universitare i ka kryer nĂŤ PrishtinĂŤ, ndĂŤrsa đ??šđ??šđ??šđ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; đ??šđ??šđ??šđ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;+1 /đ??šđ??šđ??šđ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; 1 studimet e thelluara pasuniversitare dhe (â&#x20AC;&#x153;Liber Abaciâ&#x20AC;?) . NĂŤ kĂŤtĂŤ libĂŤr jepet dhe mĂŤ shumĂŤ me emrin FibonaĂ§i [5]. -Ai njihet [4]

njĂŤ seri numerike e famshme e tij, termi i pĂŤrgjithshĂŤm i sĂŤ cilĂŤs ĂŤshtĂŤ:

Fig.1 Ndarja e njĂŤ segmenti sipas â&#x20AC;&#x153;prerjes sĂŤ artĂŤâ&#x20AC;?(nga Euklidi, Libri 6, aksioma 32)

Fn=F(n-1)+F(n-2)

(4)

Forma e zhvilluar e serisĂŤ (4) ĂŤshtĂŤ:

1,1,2,3,5,8,13,21,34,55,89,144,233,

1 1 2 3 5 8 13 ... 144 233

1 2 3 5 8 13 ... 144 233

edhe seria

(5)

1 1 2 2 1.5 1.5 1.667 1.667 1.600 1.600 1.625 1.625 ... ... 1.617 1.617 1.618 1.618 â&#x2030;&#x2026; â&#x2C6;&#x2026;

o kĂŤshtu NĂŤ mundTabelĂŤn tĂŤ konstatohet edhe seria đ??šđ??šđ??šđ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; = 1 + â&#x2C6;&#x2018;â&#x2C6;&#x17E; đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;=1 1, jepen se raportet

asi lim[5]đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;â&#x2020;&#x2019;â&#x2C6;&#x17E; đ??šđ??šđ??šđ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; = đ?&#x153;&#x2122;đ?&#x153;&#x2122;đ?&#x153;&#x2122;đ?&#x153;&#x2122;. www.vitruvius.be

2.2 Nga Vitruvi te Palladio dhe KorbyziĂŠ

(â&#x2C6;&#x2019;1)đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; +1 đ??šđ??šđ??šđ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; â&#x2C6;&#x2122;đ??šđ??šđ??šđ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; +1

doktoratĂŤn nĂŤ TiranĂŤ. Feti Selmani ĂŤshtĂŤ projektues i strukturave inxhinierike duke filluar nga urat, urat pĂŤr kĂŤmbĂŤsorĂŤ e deri tek objektet e ndĂŤrtimit tĂŤ lartĂŤ - rrokaqiejt. Ai ka jetuar dhe punuar pĂŤr mĂŤ tepĂŤr se njĂŤ dekadĂŤ nĂŤ ZvicĂŤr ndĂŤrkaq ĂŤshtĂŤ kthyer nĂŤ PrishtinĂŤ pas mbarimit tĂŤ luftĂŤs nĂŤ KosovĂŤ dhe ĂŤshtĂŤ pronar i ndĂŤrmarrjes PAN Engineering nga Prishtina. LĂŤmi i ngushtĂŤ i interesit tĂŤ tij janĂŤ biostrukturat, dinamika e strukturave, kontrolli pasiv i strukturave dhe strukturat inteligjente. Ă&#x2039;shtĂŤ botues i dhjetĂŤra artikujve brenda dhe jashtĂŤ vendit si dhe pjesĂŤmarrĂŤs i seminareve dhe konferencave pĂŤr vlerĂŤndĂŤrkombĂŤtare. kufitare Aktualisht numrin ĂŤshtĂŤ nĂŤ pĂŤrgatitje tĂŤ njĂŤ libri. 167

â&#x2C6;&#x2026;,

13 ... 144 233

ARTIKULL SHKENCOR

1.625 ... 1.617 1.618 â&#x2030;&#x2026; â&#x2C6;&#x2026;

d.m.th. masĂŤ), term ky qĂŤ pĂŤrdorej pĂŤr tĂŤđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; +1 (â&#x2C6;&#x2019;1)

ka pĂŤr vlerĂŤ kufitare numrin , pasi

â&#x2C6;&#x2018;â&#x2C6;&#x17E; Po kĂŤshtu mund tĂŤ konstatohet se edhe seria đ??šđ??šđ??šđ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; = 1 +gjeometrike đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;=1 standardizuar proporcionet nĂŤ

đ??šđ??šđ??šđ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; â&#x2C6;&#x2122;đ??šđ??šđ??šđ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; +1

pasi limđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;â&#x2020;&#x2019;â&#x2C6;&#x17E; đ??šđ??šđ??šđ??šđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; = đ?&#x153;&#x2122;đ?&#x153;&#x2122;đ?&#x153;&#x2122;đ?&#x153;&#x2122;.

konstruksione tĂŤ ndryshme, veĂ§anĂŤrisht nĂŤ

ato tĂŤ tempujve, ku si modul â&#x20AC;&#x153;referencĂŤâ&#x20AC;?

2.2 Nga Vitruvi KorbyziĂŠ diametri Nga Vitruvi te Palladio dheteLePalladio CorbusiĂŠ dhepĂŤrdorej

i njĂŤ kolone. Sipas

parimit â&#x20AC;&#x153;ordinatio Vitruvianâ&#x20AC;? duhej Koncepti i proporcioneve dhe i numrit â&#x2C6;&#x2026; ka qenĂŤ objekt studimi jo vetĂŤm qĂŤ: largĂŤsia kolonave nĂŤ tempuj ka qenĂŤ objekt studimi jo vetĂŤm i shumĂŤ dijetarĂŤve dhe hulumtuesve nga fushamidis tĂŤ ndryshme, midis tyre edhe

Koncepti i proporcioneve dhe i numrit Ď&#x2022;

matematikanĂŤve,

por

dhe

shumĂŤ

tĂŤ ishte 2 1â &#x201E;4 module

[7]

, me pĂŤrjashtim

NĂŤ veprĂŤn â&#x20AC;&#x153;DhjetĂŤ libra mbi ArkitekturĂŤnâ&#x20AC;? (www.vitruviusbe), (lat. â&#x20AC;&#x153;D dijetarĂŤve dhe hulumtuesve nga fusha tĂŤ tĂŤ hapĂŤsirĂŤs qendrore qĂŤ duhet tĂŤ ishte arkitekti i shquar roman Vitruvio (Marcus Vitruvius Pollio) qĂŤ ka jetuar n ndryshme, midis tyre edhe tĂŤ ArkitekturĂŤs. 3 module; kolonat tĂŤ kishin njĂŤ lartĂŤsi (rreth viteve 85 p.e.r., vdiq nĂŤ vitin 20 p.e.r) merret gjerĂŤsisht me kĂŤtĂŤ 1â &#x201E;2 modulesh; trashĂŤsia e bazĂŤs sĂŤ NĂŤ veprĂŤn â&#x20AC;&#x153;DhjetĂŤ libra mbi tĂŤprej themel tĂŤ triadĂŤs sĂŤ famshme tij:9 â&#x20AC;&#x153;qĂŤndrueshmĂŤri, shfrytĂŤzueshmĂŤri tĂŤ ishte gjysĂŤm kĂŤshtu me ArkitekturĂŤnâ&#x20AC;? â&#x20AC;&#x153;De kĂŤto architectura venustasâ&#x20AC;?), -(lat. parime qĂŤ do tĂŤtyre pĂŤrcillnin ndĂŤr moduli, shekuj eveprimtarinĂŤ nje radhĂŤ. VlerĂŤsohet se aplikimi i kĂŤtyre libri decemâ&#x20AC;?) arkitekti i shquar romane strukturave bĂŤjĂŤ me arkitekturĂŤn dhe artin inxhinierike. [6]

â&#x20AC;&#x153;rigjideâ&#x20AC;? empirike, kanĂŤ siguruar Vitruvi, u bĂŤ i njohur sidomos merregullave tĂŤ ashtuquajturin â&#x20AC;&#x153;ordinatio i Vitruvit mbijetesĂŤn e tempujve jetuar nĂŤ kohĂŤn e perandorit August (rreth qĂŤ tĂŤ dyjat rrjedhin nga fjala greke metron, qĂŤ d.m.th. antikĂŤ masĂŤ),pĂŤrgjatĂŤ term ky qĂŤ kohĂŤrave deri nĂŤ ditĂŤt e sotĂŤm. viteve 85 p.e.r., vdiq nĂŤ vitin 20 p.e.r) proporcionet gjeometrike nĂŤ konstruksione tĂŤ ndryshme, veĂ§anĂŤrisht nĂŤ Triada Sipas dhe â&#x20AC;&#x153;ordinatoâ&#x20AC;?-ja e Vitruvios Vitruv merret gjerĂŤsisht me kĂŤtĂŤ numĂŤr, duke ie njĂŤ kolone. â&#x20AC;&#x153;referencĂŤâ&#x20AC;? pĂŤrdorej diametri parimit â&#x20AC;&#x153;ordinatio konkretizuar nĂŤ pĂŤrjashtim realizimin e shumĂŤ vendosur nĂŤ themel tĂŤ triadĂŤstĂŤsĂŤishte famshme kolonave nĂŤ tempuj 2 1ďż˝4janĂŤ module [1], me tĂŤ hapĂŤsirĂŤ arkitektonike qĂŤ tĂŤ tij: â&#x20AC;&#x153;qĂŤndrueshmĂŤri, shfrytĂŤzueshmĂŤri, veprave tĂŤ spikatura module; kolonat tĂŤ kishin njĂŤ lartĂŤsi prej 9 1ďż˝2 modulesh; trashĂŤsia e b hijeshiâ&#x20AC;? (â&#x20AC;&#x153;firmitas, utilitas, venustasâ&#x20AC;?) tĂŤ mahnitin dhe emocionojnĂŤ me moduli, e kĂŤshtu me radhĂŤ. VlerĂŤsohet se aplikimi i kĂŤtyre rregullave â&#x20AC;&#x153;rig - parime kĂŤto qĂŤ do tĂŤ pĂŤrcillnin ndĂŤr madhĂŤshtinĂŤ, bukurinĂŤ artistike dhe mbijetesĂŤn e tempujve antikĂŤ pĂŤrgjatĂŤ kohĂŤrave deri nĂŤ ditĂŤt e sotĂŤm. proporcionet tĂŤ tyre.nĂŤ Rregullat shekuj Triada veprimtarinĂŤ vis-Ă -vis asaj dhe njerĂŤzore â&#x20AC;&#x153;ordinatoâ&#x20AC;?-ja e Vitruvios janĂŤe kĂŤndshme konkretizuar realizimin tĂŤ proporcioneve, gjenden bukurinĂŤ tĂŤ qĂŤ arkitektonike ka tĂŤ bĂŤjĂŤ me arkitekturĂŤn dhe artindhe e Vitruviane qĂŤ tĂŤ mahnitin emocionojnĂŤ me madhĂŤshtinĂŤ, kĂŤndshme tĂŤ tyre. Rregullat Vitruviane tĂŤ proporcioneve, gjenden zbatuara deri dhe nĂŤ ndĂŤrtesat gotike tĂŤ tĂŤ zb strukturave inxhinierike. gotikeu tĂŤ gjersa me shumĂŤ arkitekturore tĂŤ Rilindjes u frymĂŤz MesjetĂŤs, gjersa shumĂŤ teori arkitekturore Vitruvi, bĂŤ MesjetĂŤs, i njohur sidomos tĂŤ teori konceptet e tij mbi raportet arkitekturore harmonike. ashtuquajturin â&#x20AC;&#x153;ordinatio i Vitruvitâ&#x20AC;? tĂŤ Rilindjes u frymĂŤzuan nga vepra e NjĂŤri prej dishepujve mĂŤ besnikĂŤ tĂŤ kĂŤsaj fryme tĂŤ krijimtarisĂŤ ka qe (commoditas dhe modica â&#x20AC;&#x201C; qĂŤ tĂŤ dyjat Vitruvit dhe konceptet e tij mbi raportet periudhĂŤs sĂŤ Rilindjes italiane, Andrea di Pietro da Padova, i njohur harmonike. rrjedhin nga (1508Ăˇ1580). fjala greke metron, qĂŤ arkitekturore Palladio NĂŤ vitin 1570 Palladio boton katĂŤr libra mbi Vitruvio (Marcus Vitruvius Pollio) qĂŤ ka

[6] www.vitruvius.be Fig.2.Vila Emo, nĂŤ provincĂŤn e Trevizos, Itali, vepĂŤr e Andrea Palladios â&#x20AC;&#x201C; njĂŤ dishepull i neoklasicizmit

168

[7] Fritz, L., 1982, BrĂźcken: Ă&#x201E;esthetik und Gestaltung=Bridges: Asthetic and Design, Deutsche Verlags-Anstalt, Stuttgart.

Njëri prej dishepujve më besnikë të

Mbi “guackën e Nautilius-it”

kësaj fryme të krijimtarisë ka qenë arkitekti

“Estetika” e numrit (Fig.2 evidentohet në

dhe inxhinieri i periudhës së Rilindjes

shumë raste, sikurse është p.sh. “guacka e

italiane, Andrea di Pietro da Padova, i

Nautiliusit”, e treguar në (Fig.3a) pranë një

njohur më tepër me emrin Andrea Palladio

spiraleje të ngjashme logaritmike (Fig.3b),

(1508÷1580). Në vitin 1570 Palladio boton

apo asaj të simuluar[8] me programin

katër libra mbi arkitekturën (“I quattro libri

Matlab (Fig.3c), gjeometria e së cilës është

dell’Architettura”) , me të cilat ai e ngriti në

lidhur me raportet midis termave fqinjë të

një nivel të lartë konceptin e proporcioneve

serisë së Fibonaçit. Këto dy figura, njëra

harmonike. Shembull i aplikimit virtuoz të

“natyrale” dhe tjetra “virtuale”, shërbejnë

tyre është vepra e tij Villa Emo, në provincën

shpesh si ilustrime të ligjeve të estetikës, të

e Trevizos - Itali (Fig.2). Karakteristikë

cilat sipas Leonhardt-it (Leonhardt 1982)

e dukshme aty, është fakti që forma e

shprehin tendencë të fortë që të lidhen me

strukturës është në pajtueshmëri të plotë me

numrat, e në këtë rast me numrin ϕ.

[6]

fluksin e rrjedhjes së forcave, aq sa shkalla dhe masat e elementeve konstruktive nxisin

Matematikisht, tri figurat e mësipërme i lidh marrëdhënia (Apsen 1990)

një ndjenjë të lartë sigurie tek vrojtuesi i saj.

u(t)=reθ

(6)

Si veçori bazë e rregullsisë dhe harmonisë

që

aty evidentohet simetria dhe përsëritja.

ekuacionin e rritjes së “guackës së Nautilusit”

Ndërkaq, ndër arkitektët modernë që

sipas

(Thompson

D’Arcy 1961).

Thompson Në

këtë

Musa Stavileci është lindur më 15 janar 1948 në Gjakovë. I diplomuar pranë Fakultetit Teknik, Universiteti Prishtinës. I magjistruar pranë Fakultetit të Ndërtimtarisë në Zagreb, Kroaci. I specializuar në Institutin e Ndërtimtarisë, pranë Katedrës Teoria Mekanike dhe Aplikative, Moskë. I doktoruar pranë Fakultetit të Ndërtimtarisë dhe Arkitekturës, Universiteti Prishtinës. Ka avancim permanent në punën profesionale, shkencore dhe pedagogjike. Është autor i katër teksteve universitare dhe autor apo bashkëautor i disa punimeve shkencore, të botuara në Kosovë dhe jashtë.Që nga viti 1974 është i punësuar pranë Universitetit të Prishtinës. I angazhuar si profesor vizitor pranë Fakultetit të Shkencave të Zbatuara, Universiteti Shtetëror i Tetovës dhe Kolegjit Universitar UBT, Prishtinë.Ka diplomuar dhe magjistruar me dhjetëra studentë. Udhëheqës dhe bashkëudhëheqës në punimet e doktoraturës. Anëtar Komisioni për vlerësimin e tezave të disertacionit.Ka marrë mirënjohje për avancimin dhe zhvillimin e proceseve mësimore shkencore.

shpreh shprehje

kanë trajtuar konceptin e proporcioneve

matematike dhe formën që ajo mishëron,

ka qenë arkitekti i shquar zvicerano-francez

përmbahen disa nga komponentet themelore

i shek XX (Le Corbuisier, pseudonim i

të së bukurës: rregulli, përsëritja dhe

Charles-Éduard-Jeanneret-Gris, 1887-1965).

ngjashmëria e vazhdueshme që për rezultatin

Në traditën më të mirë të Vitruvios, Korbyzié-

final ka pikërisht atë të “prerjes së artë” –

ja i zhvilloi parimet e proporcioneve të

numri ϕ. E rëndësishme është të ceket edhe

harmonishme në Modulor-in e tij, të bazuar

prezenca e numrit të Euler-it apo siç quhet

kryesisht në numrin ϕ.

nganjëherë edhe numri i Neperit "e".

[8] Selmani, F., 2006, ‘Biologjia e strukturave’, revista arkline, no. 2.

Prof.Dr. Niko Pojani është lektor i Statikes dhe i Dinamikes së strukturave, si dhe Inxhinierisë sizmike në Fakultetin e NdertimitUPT. Ka kryer disa specializime (France, Itali, Angli, SHBA,Gjermani, Greqi, Maqedoni etj). Pjesëmarrëses aktiv në këshilla e forume inxhiniërike, akademike e shkencore të vendit, ai ka kontribuar edhe në një sere projektesh shkencore e inxhinierike kombëtare e ndërkombëtare. Në fushat e mësipërme është autor ose bashkautor në shume artikuj shkencore, brenda e jashtë vendit, si dhe rreth 15 librave. Interes të gjere ka patur veçanërisht libri i tij "Inxhinieria Sizmike'.

-20

-40

-60

-80

-100

-50

100

Fig.3. Guacka e Nautilusit (a), spiralja logaritmike (b) e ndërtuar duke iu referuar vetisë së serisë së Fibo150naçit dhe simulimi me Matlab (c)

169

ARTIKULL SHKENCOR Ilustrime nga strukturat e ramave strukturat e ramave tip-ramĂŤ me rigela tĂŤ ngurtĂŤ Le tĂŤ kalojmĂŤ tani2.3 nĂŤIlustrime fushĂŤn e nga lĂŤkundjeve tĂŤ strukturave 2.3 Ilustrime nga strukturat e ramave kalojmĂŤ taniramave nĂŤ fushĂŤn e lĂŤkundjeve tĂŤ jepen strukturave tip-ramĂŤ me rigela (shear frame), dukeLeiutĂŤreferuar katĂŤr plane dykatĂŤshe qĂŤ nĂŤ 2.3 Ilustrime nga strukturat e ramave Le tĂŤ kalojmĂŤ tani nĂŤ fushĂŤn e lĂŤkundjeve tĂŤ strukturave tip-ramĂŤ meB,rigela duke iu referuar katĂŤr ramave plane dykatĂŤshe qĂŤ jepen nĂŤ đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š đ??šđ??šđ??šđ??š. 4 - A, C, D Fig.4 - A, B, C, D duke iu referuar katĂŤr ramave plane dykatĂŤshe qĂŤ jepen nĂŤ đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š. 4 - A, B, C, D Le tĂŤ kalojmĂŤ tani nĂŤ fushĂŤn e lĂŤkundjeve tĂŤ strukturave tip-ramĂŤ me rigela duke iu referuar katĂŤr ramave plane dykatĂŤshe qĂŤ jepen nĂŤ đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š. 4 - A, B, C, D

Fig.4 KatĂŤr rama dykatĂŤshe me masa dhe ngurtĂŤsi dhe konfiguracione tĂŤ ndryshme (A, B, C, D)

Sikurse dihet, referuar zhvendosjeve un (t) dhe nxitimeve un (t) tĂŤdhe kateve 1 dhe đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š. 4 KatĂŤr rama dykatĂŤshe me masa dhe ngurtĂŤsi konfiguracione tĂŤ nd n đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š đ??šđ??šđ??šđ??š . 4 KatĂŤr rama dykatĂŤshe me masa dhe ngurtĂŤsi dhe konfiguracione tĂŤ nd 2 (n=1, 2), si dhe Sikurse ngurtĂŤsive kn referuar dhe masave mn tĂŤ tyre,đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘shkruar formĂŤn matricore nxitimeve đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘Ě&#x2C6;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) tĂŤ kateve 1 dihet, zhvendosjeve đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) dhenĂŤ đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š. 4dihet, KatĂŤr rama dykatĂŤshe masa dhe dhe ngurtĂŤsi dhe matricore konfiguracione tĂŤ nd nxitimeve đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘Ě&#x2C6; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) tĂŤ kateve 1 Sikurse referuar zhvendosjeve đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘shkruar masave đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; tĂŤme tyre, formĂŤn ngurtĂŤsive đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; dhe đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;(đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) ekuacioni diferencial i lĂŤkundjeve tĂŤ lira pa shuarje tĂŤ secilĂŤs prej nĂŤ ramave tĂŤ Fig4 đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;ĂŤshtĂŤ:ekuacioni dhe masave đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; tĂŤ tyre, shkruar nĂŤ formĂŤn matricore ekuacioni ngurtĂŤsive đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tĂŤ lira (Chopra 2007) pazhvendosjeve shuarje prejdhe ramave tĂŤ đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘ . 4Ě&#x2C6; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) ĂŤshtĂŤ: đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; referuar đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; tĂŤ secilĂŤs nxitimeve tĂŤ kateve 1 Sikurse dihet, đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; tĂŤ lira (Chopra 2007) pa shuarje tĂŤ secilĂŤs prej ramave tĂŤ đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š đ??šđ??šđ??šđ??š . 4 ĂŤshtĂŤ: masave đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; tĂŤâ&#x2C6;&#x2019;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; tyre, shkruar nĂŤ formĂŤn matricore ekuacioni ngurtĂŤsive đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; + đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;1 0 đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;Ě&#x2C6; 1 dhe đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘ 1 (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) 0 1 2 2 ďż˝ ďż˝đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘Ě&#x2C6; Ě&#x2C6; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) ďż˝ ďż˝ ďż˝ ďż˝ ďż˝ ďż˝tĂŤđ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;lira (Chopra + = ďż˝ ďż˝ 2007) pa shuarje tĂŤ secilĂŤs prej ramave tĂŤ đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š đ??šđ??šđ??šđ??š . 4 ĂŤshtĂŤ: 0 đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; 0 + đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; â&#x2C6;&#x2019;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘ (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) 1 đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;222ďż˝ ďż˝đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘121(đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) 00 11â&#x2C6;&#x2019;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;2 22 2 ďż˝ ďż˝đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘Ě&#x2C6; 121(đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) ďż˝ 001 đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘Ě&#x2C6; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą)ďż˝ + ďż˝ â&#x2C6;&#x2019;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą)ďż˝ = ďż˝00ďż˝ đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;22 đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘22(đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) 2 2 đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; 022 đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘Ě&#x2C6;Ě&#x2C6; 212(đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) + đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; â&#x2C6;&#x2019;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;1 đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; 2 i mĂŤposhtĂŤm 2 ku fitohet lehtĂŤ algjebrik tĂŤ lira harmo ďż˝ ďż˝đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘Ě&#x2C6; (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) ďż˝i mĂŤposhtĂŤm ďż˝ 1 ďż˝ ďż˝đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘ 1 (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) ďż˝ = ďż˝00ďż˝ tĂŤi lĂŤkundjeve ďż˝lehtĂŤ +ekuacioni prej ku fitohetprej lira harmonike (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) 2 (đ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ąđ?&#x2018;Ą) 0 kuekuacioni đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;fitohet â&#x2C6;&#x2019;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;2 algjebrik đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;2 đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘đ?&#x2018;˘i2lĂŤkundjeve 2 prej lehtĂŤ ekuacioni i mĂŤposhtĂŤm algjebrik i lĂŤkundjeve tĂŤ lira harmo 2 â&#x;Śđ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;â&#x;§ { ) â&#x2C6;&#x2026;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; } = {0} (â&#x;Śđ??žđ??žđ??žđ??žâ&#x;§ â&#x2C6;&#x2019; đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; â&#x2C6;&#x2122; tĂŤ tyre: prej lehtĂŤ i mĂŤposhtĂŤm algjebrik i lĂŤkundjeve tĂŤ lira harmo ){â&#x2C6;&#x2026;ekuacioni (â&#x;Śđ??žđ??žđ??žđ??žâ&#x;§ku â&#x2C6;&#x2019; fitohet đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;2đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;2 â&#x2C6;&#x2122; â&#x;Śđ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;â&#x;§ đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;} = {0} ku đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; dhe â&#x2C6;&#x2026;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; janĂŤ pĂŤrkatĂŤsisht frekuenca dhe forma kryesore e â&#x20AC;&#x153;nâ&#x20AC;?-tĂŤ e lĂŤkund 2 â&#x;Śđ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;đ?&#x2018;&#x20AC;â&#x;§ { ) â&#x2C6;&#x2026;pĂŤrkatĂŤsisht (â&#x;Śđ??žđ??žđ??žđ??žâ&#x;§ đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; â&#x2C6;&#x2026;â&#x2C6;&#x2122; đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; janĂŤ ku đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;â&#x2C6;&#x2019;dhe đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; } = {0} frekuenca dhe forma kryesore e â&#x20AC;&#x153;nâ&#x20AC;?-tĂŤ e lĂŤkund đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;2 e â&#x20AC;&#x153;nâ&#x20AC;?-tĂŤ e lĂŤkundjeve. đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; ku Ď&#x2030;n dhe Ď&#x2022;n janĂŤ pĂŤrkatĂŤsisht frekuenca forma ďż˝đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;1frekuenca ďż˝ , nga kryesore dhe đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ kryesore = dhe barazimi (8) meret NĂŤse đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;ź = 2dhe ku đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;zĂŤvendĂŤsohen dhe â&#x2C6;&#x2026;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; janĂŤ pĂŤrkatĂŤsisht â&#x20AC;&#x153;nâ&#x20AC;?-tĂŤ e lĂŤkund đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;22ďż˝đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;forma đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; 2 1 , nga barazimie(8) 2ďż˝ dhe đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ = meret NĂŤse zĂŤvendĂŤsohen đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;ź = đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; 1 NĂŤse zĂŤvendĂŤsohen Îą=m2 â &#x201E;m1 dhe Î˛=k â &#x201E;k , nga barazimi (8) meret 1 đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; 1 1 đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ â&#x2C6;&#x2122; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;1 â&#x2C6;&#x2019; đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;2 â&#x2C6;&#x2122;đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;=1 2đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;21ďż˝ â&#x2C6;&#x2019;đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ â&#x2C6;&#x2122;đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;1= đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;2ďż˝ , ngaâ&#x2C6;&#x2026;1đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;1 + 0 barazimi NĂŤse zĂŤvendĂŤsohen đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;1 dhe ďż˝ďż˝ ďż˝ = ďż˝ ďż˝(8) meret 22 â&#x2C6;&#x2122; đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;ďż˝ďż˝ â&#x2C6;&#x2122; ďż˝â&#x2C6;&#x2026; â&#x2C6;&#x2026;1đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; â&#x2C6;&#x2122; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;11â&#x2C6;&#x2122; â&#x2C6;&#x2019; đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D; â&#x2C6;&#x2019;đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;11 + đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝â&#x2C6;&#x2019;đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ 0 đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; 1 đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ â&#x2C6;&#x2122; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; â&#x2C6;&#x2019; đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;â&#x2C6;&#x2122;2đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;â&#x2C6;&#x2122;11đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;ź â&#x2C6;&#x2122; đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; 1 1đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; 1 đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; 1 1 đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; 1 ďż˝ďż˝ â&#x2C6;&#x2122; ďż˝ 2đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; ďż˝ = ďż˝ ďż˝ ďż˝ďż˝ 22 2 â&#x2C6;&#x2026; 0 â&#x2C6;&#x2019;đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ â&#x2C6;&#x2122; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ â&#x2C6;&#x2122; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; â&#x2C6;&#x2019; đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D; â&#x2C6;&#x2122; đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;ź â&#x2C6;&#x2122; đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; 2đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; 2đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; â&#x2C6;&#x2026; + đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ â&#x2C6;&#x2122; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;1 â&#x2C6;&#x2019; 11đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;ekuacioni đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;1ku 11 â&#x2C6;&#x2019;đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ â&#x2C6;&#x2122;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;1 11 0 đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; â&#x2C6;&#x2122; đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;1 prej rezultoni i mĂŤposhtĂŤm i frekuencave: ďż˝ďż˝ ďż˝ďż˝ â&#x2C6;&#x2122; ďż˝ 1đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; ďż˝ = ďż˝ ďż˝ 2 â&#x2C6;&#x2026; 0 â&#x2C6;&#x2019;đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ â&#x2C6;&#x2122; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ â&#x2C6;&#x2122; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; â&#x2C6;&#x2019; đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D; â&#x2C6;&#x2122; đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;ź â&#x2C6;&#x2122; đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; prej ku rezultoni ekuacioni i mĂŤposhtĂŤm i frekuencave: 2đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; 1 1 2 đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; 2 1 2 4 prej ku rezultoni i mĂŤposhtĂŤm i frekuencave: đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;ekuacioni 12đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;1 đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;1 ( đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ + đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;ź + đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝)đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; + đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;12đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ = 0 2 i frekuencave: 22 prej mĂŤposhtĂŤm đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;121ku đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;4đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;4rezultoni â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;11đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;11(ekuacioni đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ + đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;ź +i đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝)đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D; đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; + đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;11 đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ = 0 đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;12 đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;4 â&#x2C6;&#x2019; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;1 đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;1 ( đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ + đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;ź + đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝)đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;2 + đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;12 đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ = 0

170

Rasti A PĂŤr rastin ď&#x201A; Rasti A e shtangĂŤsive dhe masave tĂŤ njĂŤjta pĂŤr tĂŤ dy katet, si nĂŤ fig Fig.4 A, d.m.th. kur ď&#x201A; Rasti A PĂŤr rastin e shtangĂŤsive dhe masave tĂŤ njĂŤjta pĂŤr tĂŤ dy katet, si nĂŤ fig đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š. 4đ??´đ??´đ??´đ??´, d.m.th. kur ď&#x201A; đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;2Rasti Ađ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;ďż˝ tĂŤ=dy ď&#x201A; Rasti A PĂŤr rastin e shtangĂŤsive dhe pĂŤr ďż˝đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;1 = â &#x201E;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; = 1 1 katet, si nĂŤ fig đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š. 4đ??´đ??´đ??´đ??´, d.m.th. kur đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;ź = dhe masave đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ = tĂŤ2ďż˝njĂŤjta đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;tĂŤ dy đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;1 = pĂŤr PĂŤr rastin e shtangĂŤsive dhe masave tĂŤ njĂŤjta katet, si nĂŤ fig đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š. 4đ??´đ??´đ??´đ??´, d.m.th. kur đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;ďż˝dy= đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;â &#x201E;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; =nĂŤ1dhe 2ďż˝ ethjeshtohet 2ďż˝ pĂŤr PĂŤr shtangĂŤsive masave katet, 1 si nĂŤ fig đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š. 4đ??´đ??´đ??´đ??´, d.m.th. kur = tĂŤ đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;ź =rastin dhe đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝tĂŤ=njĂŤjta ekuacioni formĂŤn: đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; = đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;(10) đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; 1 đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; 2 2 đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;ź = đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;22ďż˝đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;11 = đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;â &#x201E;â &#x201E;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; = 1 dhe đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ = đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;22ďż˝đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;1 = đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;ďż˝đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; = 1 ďż˝đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;(10) đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;ź4 = đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ = ďż˝đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;11 = ďż˝đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; = 1 ekuacioni thjeshtohet formĂŤn: đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; = 1 nĂŤ dhe 12 = 1 đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;2 đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;ekuacioni đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; 2 = 0 nĂŤ formĂŤn: (11) đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; â&#x2C6;&#x2019; 3đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D; đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; +thjeshtohet (10) ekuacioni (10) thjeshtohet nĂŤ formĂŤn: 2 4 2 2 đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; â&#x2C6;&#x2019; 3đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; + đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; = 0 (11) 22 44 fitohen22vlerat22 vijuese tĂŤ frekuencave rrethore tĂŤ lĂŤkundjeve: Nga đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; zgjidhja đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D; â&#x2C6;&#x2019; 3đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D; + đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; = 0 (11) 2 2 4 2 đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; NĂŤ dyđ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;vlerat e mĂŤsipĂŤrme prezenca e numrave tĂŤ â&#x20AC;&#x153;prerjes sĂŤ artĂŤâ&#x20AC;?. đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; â&#x2C6;&#x2019; 3đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; + đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;konstatohet =0 (11) Nga zgjidhja fitohen vlerat vijuese tĂŤ frekuencave rrethore tĂŤ lĂŤkundjeve: đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; ďż˝ ďż˝ ďż˝ ďż˝ đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;1 =Nga 0.618 dhe vijuese đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;2 = (12) đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; rrethore tĂŤ lĂŤkundjeve: zgjidhjađ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;fitohen vlerat tĂŤ 1.618 frekuencave Nga=zgjidhja fitohen vlerat vijuese tĂŤ frekuencave rrethore tĂŤ lĂŤkundjeve: đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; ďż˝ ďż˝ ďż˝ ďż˝ đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D; 0.618 dhe đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D; = 1.618 (12) NĂŤ dy 1vlerat e mĂŤsipĂŤrme konstatohet prezenca e numrave tĂŤ â&#x20AC;&#x153;prerjes sĂŤ artĂŤâ&#x20AC;?. 2 đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;ďż˝đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;ďż˝đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; ďż˝ ďż˝ đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D; = 0.618 dhe đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D; = 1.618 (12) 1 = {â&#x2C6;&#x2026;sĂŤ } tĂŤartĂŤâ&#x20AC;?. đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;ďż˝đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;tĂŤ lĂŤkundjeve VleraNĂŤ tilla dalin edhe nĂŤ shprehjet e formave kryesore kĂŤsaj rame. Konkretisht ďż˝ ďż˝đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;1tĂŤ dhe đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;222prezenca = 1.618 (12) vlerat e đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;mĂŤsipĂŤrme konstatohet eďż˝numrave tĂŤ â&#x20AC;&#x153;prerjes 1 dy 0.618 đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; Vlera tĂŤ tilla dalin edhe nĂŤ shprehjet e formave kryesore tĂŤ lĂŤkundjeve {ďż˝} tĂŤ kĂŤsaj rame. marim: NĂŤ dy tĂŤ vlerat edalin mĂŤsipĂŤrme konstatohet prezenca ekryesore numravetĂŤtĂŤlĂŤkundjeve â&#x20AC;&#x153;prerjes sĂŤ {artĂŤâ&#x20AC;?. } Vlera tilla edhe nĂŤ shprehjet e formave â&#x2C6;&#x2026; tĂŤ kĂŤsaj rame. Konkretisht NĂŤ dy vlerat e mĂŤsipĂŤrme konstatohet prezenca e numrave tĂŤ â&#x20AC;&#x153;prerjes sĂŤ artĂŤâ&#x20AC;?. tĂŤmarim: tilla dalin edhe nĂŤ shprehjet e formave kryesore tĂŤ lĂŤkundjeve {{â&#x2C6;&#x2026;}} tĂŤ kĂŤsaj rame. Konkretisht marim: Konkretisht {â&#x2C6;&#x2026;}1đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;Vlera = {1.00 (13) Vlera tĂŤ tilla 1.618} dalin edhe nĂŤ shprehjet e formave kryesore tĂŤ lĂŤkundjeve â&#x2C6;&#x2026; tĂŤ kĂŤsaj rame. Konkretisht marim: {â&#x2C6;&#x2026;}đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;2{marim: =}1đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;{1.00 â&#x2C6;&#x2019; 0.618} (14) (13) = {1.00 1.618} â&#x2C6;&#x2026; {{â&#x2C6;&#x2026; }đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021; = {1.00 1.618} (13) (14) {â&#x2C6;&#x2026; = {1.00 {1.00 â&#x2C6;&#x2019; 0.618} 1.618} (13) â&#x2C6;&#x2026;}}12đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;11đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021; = { } â&#x2C6;&#x2026; = {1.00 â&#x2C6;&#x2019; 0.618} (14) ď&#x201A; Rasti {â&#x2C6;&#x2026;}2đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;đ?&#x2018;&#x2021;22B= {1.00 â&#x2C6;&#x2019; 0.618} (14) Rastiď&#x201A; B Rasti B Nga ď&#x201A; đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šRasti . 4 â&#x2C6;&#x2019;B đ??ľđ??ľđ??ľđ??ľ, nĂŤ rastin B, kemi ď&#x201A; đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; RastinĂŤBrastin B, kemi đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; Nga Fig.4-B, 1ďż˝ dhe 2ďż˝đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š . 4đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; đ??ľđ??ľđ??ľđ??ľ, nĂŤ rastin B, kemi đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;ź = Nga đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ = 2ďż˝đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; = đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;ďż˝2đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; = 1ďż˝2 đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;1 = â&#x2C6;&#x2019;ďż˝2đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; = 2 1 Nga đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š đ??šđ??šđ??šđ??š. 4 â&#x2C6;&#x2019; đ??ľđ??ľđ??ľđ??ľ,đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;nĂŤ rastin1B, kemi đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; Nga đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š2đ??šđ??šđ??šđ??šďż˝.đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; 4 â&#x2C6;&#x2019;=đ??ľđ??ľđ??ľđ??ľ, ďż˝ nĂŤ rastin ďż˝B, dhe kemi đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ = đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;2ďż˝ = đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;ďż˝ = 1ďż˝ đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;ź = đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; 2đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; = 2 1 2 đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; 1ďż˝2 Prandaj tani kemi ekuacionin: 1 đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;ź = đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;22ďż˝đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;11 = đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;ďż˝2đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; = 1ďż˝2 dhe đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ = đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;222ďż˝đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;1 = đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;ďż˝2đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; 1ďż˝2 2đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; = ďż˝ ďż˝ ďż˝ ďż˝ = = đ?&#x203A;źđ?&#x203A;źđ?&#x203A;źđ?&#x203A;ź = dhe đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝đ?&#x203A;˝ = 1 ďż˝ 1 đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; = 2 = 2 2 2đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; 2 2đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;1 tani1 kemi ekuacionin: 2đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;2Prandaj đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;4 â&#x2C6;&#x2019; 5đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D; + 2đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; = 0 (15) đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; Prandaj tani kemi ekuacionin: Prandaj tani kemi ekuacionin: 2 2 4 2 Prandaj tani kemiđ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; ekuacionin: đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; â&#x2C6;&#x2019; + 2đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; 0 (15) Nga 2đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; zgjidhja e 5đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D; ekuacionit (15) = marrim frekuencat: 2đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;222 đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;4đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;44 â&#x2C6;&#x2019; 5đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;2đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;22 + 2đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;222 = 0 (15) 2đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; zgjidhja đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; â&#x2C6;&#x2019;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;5đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D; + 2đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; (15) = 0 marrim đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;frekuencat: (15) Nga e ekuacionit đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A;đ?&#x2018;&#x203A; ďż˝ ďż˝đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; ďż˝ ďż˝đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; 0.707 dhe(15)đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;marrim (16) đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;1 = 2 = 1.414 Nga zgjidhja e ekuacionit (15) marrim frekuencat: Nga zgjidhja e ekuacionit frekuencat: Nga zgjidhjaďż˝eđ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;ďż˝ ekuacionit (15) marrim frekuencat: ďż˝đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;ďż˝đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; dhe đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;2 = tĂŤ 1.414 (16) Taniđ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;konstatohet e numrave â&#x20AC;&#x153;prerjes sĂŤ artĂŤâ&#x20AC;? nĂŤ tĂŤ dy vlerat. 1 = 0.707 â&#x20AC;&#x153;zhdukjaâ&#x20AC;? đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;ďż˝đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; ďż˝đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;ďż˝đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; dhe đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D; = 1.414 (16) đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;11 = 0.707ďż˝ 2 đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC;đ?&#x2018;&#x2DC; 2 đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; ďż˝ ďż˝đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; ďż˝đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161;đ?&#x2018;&#x161; sĂŤ artĂŤâ&#x20AC;? nĂŤ tĂŤ dy vlerat. dhe (16) đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;1 =konstatohet Tani â&#x20AC;&#x153;zhdukjaâ&#x20AC;? tĂŤ â&#x20AC;&#x153;prerjes 2 = 1.414 ď&#x201A; Rastet C0.707 dhe ďż˝ D (ramat me dyeđ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;đ?&#x153;&#x201D;numrave hapĂŤsira dritĂŤ) Tani konstatohet â&#x20AC;&#x153;zhdukjaâ&#x20AC;? e numrave tĂŤ â&#x20AC;&#x153;prerjes sĂŤ artĂŤâ&#x20AC;? nĂŤ tĂŤ dy vlerat. konstatohet e unumrave tĂŤ â&#x20AC;&#x153;prerjes sĂŤramat artĂŤâ&#x20AC;? nĂŤ tĂŤ dyB,vlerat. Canaloge dhe Dâ&#x20AC;&#x153;zhdukjaâ&#x20AC;? (ramat me dy hapĂŤsira dritĂŤ) Nga ď&#x201A; Tani njĂŤRastet analizĂŤ si ajo qĂŤ paraqit mĂŤ sipĂŤr pĂŤr A dhe duke patur parasysh tĂŤ dhĂŤnat Tani konstatohet â&#x20AC;&#x153;zhdukjaâ&#x20AC;? e numrave tĂŤ â&#x20AC;&#x153;prerjes sĂŤ artĂŤâ&#x20AC;? nĂŤ tĂŤ dy vlerat. ď&#x201A; Rastet C dhe D (ramat me dy hapĂŤsira dritĂŤ) e figNga 4-c dhe d mund tĂŤ konstatohet se pĂŤr ramĂŤn e rastit C, dalin pĂŤrsĂŤri e â&#x20AC;&#x153;prerjes sĂŤ artĂŤâ&#x20AC;? ď&#x201A; Rastet C dheanaloge D (ramat me qĂŤ dyuhapĂŤsira dritĂŤ) njĂŤ analizĂŤ si ajo paraqit mĂŤ sipĂŤr pĂŤr ramat A dhe B,numrat duke patur parasysh tĂŤ dhĂŤnat (Pojani et al. 2002) PĂŤrkundrazi, nĂŤ ramĂŤn D, qĂŤ e ka kolonĂŤn e mesit e katit tĂŤ parĂŤ tĂŤ lidhur Nga analizĂŤ analoge sikonstatohet ajo qĂŤ u paraqit mĂŤ sipĂŤrepĂŤr ramat A dhepĂŤrsĂŤri B, duke patur parasysh tĂŤme dhĂŤnat d mund tĂŤ se pĂŤr ramĂŤn rastit C, dalin numrat e â&#x20AC;&#x153;prerjes artĂŤâ&#x20AC;? eNga fig njĂŤ 4-c dhe njĂŤrigelin analizĂŤata analoge siâ&#x20AC;&#x153;zhduken. ajo qĂŤ u paraqit mĂŤ sipĂŤr pĂŤr ramat A dhe B, duke patur parasysh tĂŤsĂŤdhĂŤnat Ă§ernierĂŤ me numra e d mund tĂŤ konstatohet se pĂŤr ramĂŤn rastit C, dalin pĂŤrsĂŤri numrat e â&#x20AC;&#x153;prerjes sĂŤ artĂŤâ&#x20AC;? e fig 4-c dhe (Pojani et al. 2002) PĂŤrkundrazi, nĂŤ ramĂŤn D, qĂŤ e ka kolonĂŤn e mesit e katit tĂŤ parĂŤ tĂŤ lidhur me Rastete C (ramat me dy dritĂŤ) figdhe 4-cDdhe d mund tĂŤ hapĂŤsira konstatohet se pĂŤr ramĂŤn e rastit C, dalin pĂŤrsĂŤri numrat e â&#x20AC;&#x153;prerjes sĂŤ artĂŤâ&#x20AC;? (Pojani et al. 2002) PĂŤrkundrazi, nĂŤ ramĂŤn D, qĂŤ e ka kolonĂŤn e mesit e katit tĂŤ parĂŤ tĂŤ lidhur me Ă§ernierĂŤ me rigelin ata numra â&#x20AC;&#x153;zhduken. Konstatim (Pojanii pĂŤrgjithshĂŤm: et al. 2002) PĂŤrkundrazi, nĂŤ ramĂŤn D, qĂŤ e ka kolonĂŤn e mesit e katit tĂŤ parĂŤ tĂŤ lidhur me Ă§ernierĂŤ me rigelin ata numra â&#x20AC;&#x153;zhduken. â&#x20AC;&#x153;Prerja e artĂŤâ&#x20AC;?meĂŤshtĂŤ pranishme nĂŤâ&#x20AC;&#x153;zhduken. rastet kur struktura karakterizohet nga rregullsia nĂŤ shpĂŤrndarjen e Ă§ernierĂŤ rigelin ata numra Konstatim i pĂŤrgjithshĂŤm: shtangĂŤsive (ngurtĂŤsive) dhe masave e njĂŤpĂŤr rame dykatĂŤshe. NĂŤ rastin kur nĂŤ kjoshpĂŤrndarjen rregullsi e Nga njĂŤ analizĂŤ analoge si ajo qĂŤ u nĂŤpĂŤr paraqit mĂŤstruktura sipĂŤr ramat A dhe B,nga duke patur Konstatim i pĂŤrgjithshĂŤm: â&#x20AC;&#x153;Prerja e artĂŤâ&#x20AC;? ĂŤshtĂŤ pranishme nĂŤ rastet katet kur karakterizohet rregullsia Konstatim i kur pĂŤrgjithshĂŤm: mungon, d.m.th nĂŤpĂŤr kate kemi ndryshim shtangĂŤsish, ndryshim tĂŤ shpĂŤrndarjes e masave tĂŤ e â&#x20AC;&#x153;Prerja e artĂŤâ&#x20AC;? ĂŤshtĂŤ pranishme nĂŤ rastet kur struktura karakterizohet nga rregullsia nĂŤ shpĂŤrndarjen shtangĂŤsive (ngurtĂŤsive) dhed mund masave nĂŤpĂŤr katet e senjĂŤkarakterizohet dykatĂŤshe. NĂŤdalin rastin nĂŤ kurshpĂŤrndarjen kjoose rregullsi parasysh tĂŤ dhĂŤnat eĂŤshtĂŤ fig 4-c dhe tĂŤartĂŤâ&#x20AC;? konstatohet pĂŤrrame ramĂŤn e rastit C, â&#x20AC;&#x153;Prerja eatĂŤherĂŤ artĂŤâ&#x20AC;? pranishme nĂŤ rastet kurzhduken struktura nga tĂŤ rregullsia e dyja shtangĂŤsive bashkĂŤ, numrat e â&#x20AC;&#x153;prerjes sĂŤ nga vlerat pĂŤrkatĂŤse frekuencave rrethore (ngurtĂŤsive) dhe masave nĂŤpĂŤr katet e njĂŤ rame dykatĂŤshe. NĂŤ rastin kur kjo rregullsi mungon, d.m.th kur nĂŤpĂŤrdhe kate kemi ndryshim shtangĂŤsish, ndryshim tĂŤ shpĂŤrndarjes e masave ose tĂŤ shtangĂŤsive (ngurtĂŤsive) masave nĂŤpĂŤr katet e njĂŤ rame dykatĂŤshe. NĂŤ rastin kur kjo rregullsi [7] dhe formave kryesore tĂŤ lĂŤkundjeve. pĂŤrsĂŤri numrat e â&#x20AC;&#x153;prerjes sĂŤ artĂŤâ&#x20AC;?kate nĂŤ ramĂŤn D, qĂŤ e ka kolonĂŤn e mesit e e masave mungon, d.m.th kur nĂŤpĂŤr kemi ndryshim shtangĂŤsish, tĂŤ shpĂŤrndarjes ose tĂŤ dyja bashkĂŤ, atĂŤherĂŤ numrat e PĂŤrkundrazi, â&#x20AC;&#x153;prerjes sĂŤ artĂŤâ&#x20AC;? zhduken ngandryshim vlerat pĂŤrkatĂŤse tĂŤ frekuencave rrethore mungon, d.m.th kur nĂŤpĂŤr kate kemi ndryshim shtangĂŤsish, ndryshim tĂŤ shpĂŤrndarjes e masave ose tĂŤ dyja bashkĂŤ, atĂŤherĂŤ numrat e â&#x20AC;&#x153;prerjes sĂŤ artĂŤâ&#x20AC;? zhduken nga vlerat pĂŤrkatĂŤse tĂŤ frekuencave rrethore dhe formave kryesore tĂŤ lĂŤkundjeve. katit3.tĂŤ parĂŤ tĂŤ lidhur me Ă§ernierĂŤ me rigelin ata numra â&#x20AC;&#x153;zhduken. dyja bashkĂŤ, atĂŤherĂŤ numrat e â&#x20AC;&#x153;prerjes sĂŤ artĂŤâ&#x20AC;? zhduken nga vlerat pĂŤrkatĂŤse tĂŤ frekuencave rrethore â&#x20AC;&#x153;STRUKTURATâ&#x20AC;? dhe formave kryesoreEtĂŤKRIJUARA lĂŤkundjeve. NGA NATYRA dhe formave kryesore tĂŤ lĂŤkundjeve. Konstatim i pĂŤrgjithshĂŤm: 3.- â&#x20AC;&#x153;STRUKTURATâ&#x20AC;? E KRIJUARA NGA NATYRA 3.1 Sfidimi natyror dhe inxhinierik i forcave gravitacionale 3.- â&#x20AC;&#x153;STRUKTURATâ&#x20AC;? E KRIJUARA NGA NATYRA â&#x20AC;&#x153;Prerja artĂŤâ&#x20AC;? ĂŤshtĂŤ pranishme nĂŤ rastet kur struktura karakterizohet nga rregullsia 3.- eâ&#x20AC;&#x153;STRUKTURATâ&#x20AC;? E KRIJUARA NGA NATYRA Sfidimi natyror inxhinierik i forcave gravitacionale Dihet se3.1 fenomenet natyroredhe zhvillohen sipas ligjshmĂŤrive tĂŤ caktuara. Por, a krijon natyra nĂŤ mĂŤnyrĂŤ nĂŤ e shtangĂŤsive (ngurtĂŤsive) dhe masavedhe nĂŤpĂŤr katet e njĂŤâ&#x20AC;&#x201C; rame dykatĂŤshe. 3.1 Sfidimi natyror dhe inxhinierik ikaotike forcave gravitacionale tĂŤ shpĂŤrndarjen disiplinuar dhe tĂŤ rregullt apo nĂŤ mĂŤnyrĂŤ tĂŤ parregullt kjo ĂŤshtĂŤ pyetje e vjetĂŤr po 3.1seSfidimi natyror dhe inxhinierik forcave gravitacionale Dihet fenomenet natyrore zhvillohen isipas ligjshmĂŤrive tĂŤ caktuara. Por, anjĂŤ krijon natyra nĂŤ mĂŤnyrĂŤ aq rastin saDihet edhe vetĂŤ historia njerĂŤzore dhe gjetja e sĂŤ vĂŤrtetĂŤs mbetet njĂŤra nga detyrat mĂŤ tĂŤ vĂŤshtira pĂŤr NĂŤ kur kjo rregullsi mungon, d.m.th kur nĂŤpĂŤr kate kemi ndryshim shtangĂŤsish, se fenomenet zhvillohen sipaskaotike ligjshmĂŤrive tĂŤ caktuara. Por,ĂŤshtĂŤ a krijon natyra enĂŤvjetĂŤr mĂŤnyrĂŤ tĂŤ disiplinuar dhe tĂŤ natyrore rregullt apo nĂŤ mĂŤnyrĂŤ dhe tĂŤ parregullt â&#x20AC;&#x201C; kjo njĂŤ pyetje po Dihet seveprĂŤn fenomenet natyrore zhvillohen sipas(â&#x20AC;&#x153;On ligjshmĂŤrive tĂŤ caktuara. Por,Dâ&#x20AC;&#x2122;Arcy a krijon natyra nĂŤ mĂŤnyrĂŤ njeriun. NĂŤedhe e historia tijtĂŤâ&#x20AC;&#x153;PĂŤr rritjen dhe formĂŤnâ&#x20AC;? Growth and Formâ&#x20AC;?) [5], W. Thompson tĂŤ disiplinuar dhe rregullt apo nĂŤ mĂŤnyrĂŤ kaotike dhe tĂŤ parregullt â&#x20AC;&#x201C; kjo ĂŤshtĂŤ njĂŤ pyetje e vjetĂŤr po aq sa vetĂŤ njerĂŤzore dhe gjetja e sĂŤ vĂŤrtetĂŤs mbetet njĂŤra nga detyrat mĂŤ tĂŤ vĂŤshtira pĂŤr ndryshim tĂŤmĂŤsojmĂŤ shpĂŤrndarjes masaveapo ose tĂŤkurrĂŤ dyja bashkĂŤ, atĂŤherĂŤ e â&#x20AC;&#x153;prerjes artĂŤâ&#x20AC;? tĂŤ â&#x20AC;&#x153;ne disiplinuar dhe tĂŤ emĂŤsojmĂŤ, rregullt nĂŤ mĂŤnyrĂŤ dhe tĂŤnumrat parregullt â&#x20AC;&#x201C; kjo sĂŤ ĂŤshtĂŤ njĂŤ pyetje emĂŤ vjetĂŤr po thotĂŤ: dhe por nukkaotike tĂŤ njohim tĂŤ tĂŤrĂŤn, qoftĂŤ edhe mbi tĂŤ pĂŤr aq sa edhe vetĂŤ historia njerĂŤzore dhe gjetja edo sĂŤ(â&#x20AC;&#x153;On vĂŤrtetĂŤs mbetet njĂŤra nga[5], detyrat mĂŤgjĂŤnĂŤ tĂŤ vĂŤshtira njeriun. NĂŤ veprĂŤn e tij â&#x20AC;&#x153;PĂŤr rritjen dhe formĂŤnâ&#x20AC;? Growth and Formâ&#x20AC;?) Dâ&#x20AC;&#x2122;Arcy W. Thompson aq sa edhe vetĂŤ historia njerĂŤzore dhe gjetja e sĂŤ vĂŤrtetĂŤs mbetet njĂŤra nga detyrat mĂŤ tĂŤ vĂŤshtira pĂŤr vogĂŤlnjeriun. dhe tĂŤ veprĂŤn thjeshtĂŤ...â&#x20AC;? (â&#x20AC;&#x153;We learn and learn,nuk but never know it all,tĂŤrĂŤn, about the smallest, humblest zhduken ngamĂŤ vlerat pĂŤrkatĂŤse frekuencave dhe formave kryesore tĂŤ lĂŤkundjeve. NĂŤ e tij tĂŤ â&#x20AC;&#x153;PĂŤr rritjen dherrethore formĂŤnâ&#x20AC;? (â&#x20AC;&#x153;On and Formâ&#x20AC;?) [5], Dâ&#x20AC;&#x2122;Arcy W. Thompson thotĂŤ: â&#x20AC;&#x153;ne mĂŤsojmĂŤ, do tĂŤGrowth njohim tĂŤ mbi mĂŤ tĂŤ njeriun. NĂŤmĂŤsojmĂŤ veprĂŤn edhe tij â&#x20AC;&#x153;PĂŤr rritjen por dhe kurrĂŤ formĂŤnâ&#x20AC;? (â&#x20AC;&#x153;On Growth and Formâ&#x20AC;?)qoftĂŤ [5], edhe Dâ&#x20AC;&#x2122;Arcy W.gjĂŤnĂŤ Thompson thing...â&#x20AC;?). thotĂŤ: â&#x20AC;&#x153;ne mĂŤ mĂŤsojmĂŤ dhe mĂŤsojmĂŤ, por kurrĂŤ nuk do tĂŤnever njohim tĂŤ tĂŤrĂŤn, qoftĂŤ edhe mbi gjĂŤnĂŤ mĂŤ tĂŤ vogĂŤl dhe tĂŤ thjeshtĂŤ...â&#x20AC;? (â&#x20AC;&#x153;We learn and learn, but know it all, about the smallest, humblest thotĂŤ:iuâ&#x20AC;&#x153;ne mĂŤsojmĂŤ mĂŤsojmĂŤ, por kurrĂŤ nuk do tĂŤ njohim tĂŤ tĂŤrĂŤn, qoftĂŤ edhe mbi gjĂŤnĂŤ mĂŤ tĂŤ Duke tanidhe InxhinierisĂŤ, mund thuhet njĂŤraknow nga e pĂŤrhershme mbetet vogĂŤl dhereferuar mĂŤ tĂŤ thjeshtĂŤ...â&#x20AC;? (â&#x20AC;&#x153;We learn andtĂŤlearn, butsenever itsfidat all, about the smallest, humblest thing...â&#x20AC;?). vogĂŤl dhe mĂŤ tĂŤ thjeshtĂŤ...â&#x20AC;? (â&#x20AC;&#x153;We learn and learn, but never know it all, about the smallest, humblest pasqyrimi dhe iu â&#x20AC;&#x153;imitimiâ&#x20AC;? i natyrĂŤs, i ligjeve pĂŤrmes tĂŤ modeleve thing...â&#x20AC;?). se krijimit njĂŤra nga Duke referuari saktĂŤ tani InxhinierisĂŤ, mundtĂŤtĂŤsaj,thuhet sfidat e matematike pĂŤrhershme dhe mbetet thing...â&#x20AC;?). [7] Pojani, N.,Duke Lako, N.,iuTeoria e strukturave Dinamika e strukreferuar tanii saktĂŤ InxhinierisĂŤ, mund tĂŤ tĂŤ thuhet se njĂŤra nga sfidat e pĂŤrhershme mbetet pasqyrimi dhe â&#x20AC;&#x153;imitimiâ&#x20AC;? i natyrĂŤs, i ligjeve saj, pĂŤrmes krijimit tĂŤ modeleve matematike dhe turave, SHBLU, pp 249-251, TiranĂŤ. Duke iu referuar tani InxhinierisĂŤ, mund tĂŤ thuhet se njĂŤra nga sfidat e pĂŤrhershme mbetet pasqyrimi dhe â&#x20AC;&#x153;imitimiâ&#x20AC;? i saktĂŤ i natyrĂŤs, i ligjeve tĂŤ saj, pĂŤrmes krijimit tĂŤ modeleve matematike dhe pasqyrimi dhe â&#x20AC;&#x153;imitimiâ&#x20AC;? i saktĂŤ i natyrĂŤs, i ligjeve tĂŤ saj, pĂŤrmes krijimit tĂŤ modeleve matematike dhe

171

ARTIKULL SHKENCOR “STRUKTURAT” Të KRIJUARA NGA NATYRA"

e përhershme mbetet pasqyrimi dhe

Sfidimi natyror dhe inxhinierik i forcave

përmes krijimit të modeleve matematike

gravitacionale, dihet se fenomenet natyrore

dhe fizike e deri te realizimi i strukturave

zhvillohen sipas ligjshmërive të caktuara.

konkrete inxhinierike. Natyrisht, do të

Por, a krijon natyra në mënyrë të disiplinuar

themi se sfida është fituar dhe e “vërteta”

dhe të rregullt apo në mënyrë kaotike dhe

e synuar është arritur, kur rezultatet e

të parregullt – kjo është një pyetje e vjetër

eksperimenteve në shkallë të reduktuar

po aq sa edhe vetë historia njerëzore dhe

apo reale përafrojnë mirë me ato të fituara

gjetja e së vërtetës mbetet njëra nga detyrat

përmes simulimeve teorike.

“imitimi” i saktë i natyrës, i ligjeve të saj,

më të vështira për njeriun. Në veprën e tij

Njëri prej fenomeneve natyrore i

“Për rritjen dhe formën” (“On Growth and

cili dikton jetën në planetin tonë është

Form”)

, D’Arcy W. Thompson thotë:

gravitacioni. Ky faktor i përhershëm nuk

“ne mësojmë dhe mësojmë, por kurrë

mund të harrohet kurrsesi nga inxhinieri

nuk do të njohim të tërën, qoftë edhe mbi

strukturist, dhe nga arkitekti po ashtu,

gjënë më të vogël dhe më të thjeshtë...”

gjatë procesit të “krijimit” të një strukture.

(“We learn and learn, but never know it

Nga pikëpamja strukturore mund të

all, about the smallest, humblest thing...”).

thuhet se ajo projektohet pikërisht si

Duke iu referuar tani Inxhinierisë,

“sfidim” i forcave-peshë, krahas dhe

mund të thuhet se njëra nga sfidat

veprimeve të tjera eventuale si p.sh era e

[8]

tërmeti (në fakt, edhe madhësia e forcave sizmike është shumë e varur nga forcat peshë, është një përqindje e caktuar e tyre). [8] Thompson, D’. W., 1961, On Growth and Form, Cambridge University Press, Cambridge.

172

Aktualisht, gati kudo në botë vërehen

Fig.7: Litar i përkulshëm nën veprimin e ngarkesës p(s) përgjatë aksit të tij

tendenca për struktura “spektakolare” për

Owachomo-s mund të interpretohet p.sh.

nga forma e tyre në plan dhe lartësi. Por,

ura Salginatobel (Sälginatobel brücke) në

pa vënë kufizime të ngurta për shprehjet

Schiers – Zvicër (Fig.5b), e projektuar nga

dhe stilet estetike, duhet patur parasysh

inxhinieri i shquar zvicerian Robert Majaar

se përvoja ka treguar që, sidomos për

(Robert Maillart, 1872-1940).

rajonet sizmike, zgjidhjet e mira njëherësh arkitekturore dhe strukturore arrihen kur

Bio-strukturat

harmonizohen kërkesat e tyre përkatëse,

Le të shohim tani se ç’kanë të

duke u dhënë prioritet këtyre parimeve:

përbashkët, vija e zinxhirit apo e litarit

thjeshtësi, rregullsi, simetri, përsëritje

(“vargorja”), ura e varur dhe rrjeta e

dhe ngjashmëri përmes variacioneve të

merimangës. Për këtë po i referohemi së

formave. Në thelb, pikërisht këto janë

pari një litari (kavo) me hapësirë , shigjetë

evidente dhe në shumë “struktura” të

dhe me mbështetje që ndodhen në të njëjtin

çuditshme ku, me “bëmat” e saj, natyra

nivel horizontal () Nga Teoria e strukturave

ka lënë vulën e saj “inxhinierike”. Të tilla

dihet që një litar me fleksibilitet të lartë

mund të përmenden disa “ura natyrore”

nuk ka aftësi të punojë as në përkulje, as

në Owachomo, Utah, USA. Në

është

në shtypje, as në prerje e as në përdredhje,

paraqitur njëra prej tyre, me hapësirë–

por vetëm në tërheqje. Në duket se litari

dritë dhe lartësi (shigjetë) h=32m.

i nënshtrohetr ngarkesës së shpërndarë e

Duke iu përmbajtur parimeve të

cila mund të jetë ngarkesë e jashtme apo

mësipërme, në fushën e ndërtimit janë

edhe vetë pesha vetjake e tij. Ndërkaq, me

realizuar shumë vepra të bukura arti, jo

p(s) aty është shënuar po e njëjta ngarkesë,

vetëm ndërtesa por dhe struktura të tjera

por referuar tani vijës “s” të vetë litarit.

inxhinierike. Si imitim i “urave natyrore” të

Fig.8 Vargorja (vija e ndërprerë) vs parabola (vija e plotët)

Litar i përkulshëm nën veprimin e

173

ARTIKULL SHKENCOR a) ngarkesĂŤs pĂŤrgjatĂŤ aksit tĂŤ tij.Nga đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??škushtet . 7: e ekuilibrit tĂŤ njĂŤ elementi p.m.v.

tĂŤ

ĂŤshtĂŤ shprehjanĂŤn matematike e vijĂŤs LitarKjo i pĂŤrkulshĂŤm veprimin e ngark apo formĂŤs gjeometrike qĂŤ merr njĂŤ litar,

a) ekuacioni kushtet e ekuilibrit tĂŤ njĂŤ elementie varur p.m.v. tĂŤ b)litarit zinxhir ose strukturĂŤ me đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; shkallĂŤ litarit (shih fig. Nga 7-b), meret lehtĂŤ (đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; ) p đ??šđ??šđ??šđ??š. 7:i uljeve i pĂŤrkulshĂŤm nĂŤn veprimin etĂŤngarkesĂŤs diferencial linear i Litar shkallĂŤs sĂŤ dytĂŤ i uljeve litarit, tĂŤ lartĂŤ fleksibiliteti (paâ&#x20AC;&#x153;yâ&#x20AC;? ngurtĂŤsi ndaj siđ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?vijo diferencial linear i shkallĂŤs sĂŤđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š dytĂŤ â&#x20AC;&#x153;yâ&#x20AC;? tĂŤ litarit, si

đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;(đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ)ďż˝ pĂŤrkuljes), qĂŤ i nĂŤnshtrohet peshĂŤs sĂŤ saj = đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śâ&#x20AC;˛â&#x20AC;˛ Nga kushtet eđ??ťđ??ťđ??ťđ??ť ekuilibrit tĂŤ njĂŤ elementi p.m.v. đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; tĂŤ litarit (shih fig

katenoidĂŤ (nga diferencial linear i shkallĂŤs vetjake. sĂŤ dytĂŤShpesh i uljeveajo â&#x20AC;&#x153;yâ&#x20AC;?quhet tĂŤ litarit, si vijon italishtja: catena â&#x20AC;&#x201C; zinxhir), nĂŤ shqip (ku): H ĂŤshtĂŤ komponentja horizontale e ku:=đ??ťđ??ťđ??ťđ??ťđ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;(đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ) ĂŤshtĂŤ horizontale e tĂŤrheqjes sĂŤ mund litarit. ďż˝đ??ťđ??ťđ??ťđ??ť komponentja đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śâ&#x20AC;˛â&#x20AC;˛

tĂŤ quhet â&#x20AC;&#x153;vargoreâ&#x20AC;?. NĂŤ mĂŤkonstante poshtĂŤ, ĂŤshtĂŤ Nga zgjidhja e kĂŤtij ekuacioni, pĂŤr ngarkesĂŤ đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;(đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ ) = 2 bĂŤrĂŤ njĂŤ krahasim i simuluar (me Matlab) Nga zgjidhja pĂŤr horizontale ku: eđ??ťđ??ťđ??ťđ??ťkĂŤtij komponentja e tĂŤrheqjes sĂŤ litarit. ) (ĂŤshtĂŤ đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;0 đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľekuacioni, ďż˝ đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Ś = nĂŤ mes lakores sĂŤ vargores đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;dhe (đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ )asaj ngarkesĂŤ konstante pĂŤr uljet merret )ekuacioni, Nga zgjidhja e (kĂŤtij pĂŤr tĂŤ ngarkesĂŤ konstante = đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;tĂŤ0 pĂŤr ulje 2đ??ťđ??ťđ??ťđ??ť 2 (đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E; đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ ) a) parabolĂŤs, ku mund tĂŤ shihet dallimi fare shprehja: đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Ś = 0 ďż˝(2đ??ťđ??ťđ??ťđ??ť ) e cila paraqet formĂŤn racionale litaritnĂŤdhe ĂŤshtĂŤ nĂŤ fakt njĂŤ i vogĂŤl i cili tĂŤ ekziston mes tyre, pĂŤrderisa đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š đ??šđ??šđ??šđ??š . 7: Litar i pĂŤrkulshĂŤm nĂŤn veprimin e ngar forma racionale parabolike ĂŤshtĂŤ edhe vlefshme pĂŤr fazĂŤn kur lit nĂŤ ( nĂŤ paraqitet rrjetanĂŤe merimangĂŤs cila paraqet formĂŤn racionale tĂŤmes) litarit ĂŤshtĂŤ fakt njĂŤ parabolĂŤ e e cila paraqet eformĂŤn racionale tĂŤ litarit varur racionale â&#x20AC;&#x153;e pĂŤrfaqĂŤsuarâ&#x20AC;? nga kĂŤto vija) pĂŤr gjendet nĂŤ shfrytĂŤzim, forma ĂŤshtĂŤ e( vlefshme fazĂŤn litari (kavoja dhe nĂŤ djathtas) ipet njĂŤ foto kur e njĂŤ ure tĂŤ dhe ĂŤshtĂŤ nĂŤ fakt njĂŤ kushtet parabolĂŤ eeparabolike shkallĂŤs Nga ekuilibrit tĂŤ njĂŤ elementi p.m.v. đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018;&#x2018;đ?&#x2018; đ?&#x2018; đ?&#x2018; đ?&#x2018; litak (variable actions, sipas Eurokodit EN-1990 (EN1990 2002)) varur â&#x20AC;&#x153;e pĂŤrfaqĂŤsuarâ&#x20AC;? nga kĂŤto vija) gjendet nĂŤ shfrytĂŤzim, d.m.th tĂŤ varur (PĂšnt Suransuns, Tiers, CH, si vi sĂŤ dytĂŤ. Praktikisht, formalinear racionale diferencial i shkallĂŤs sĂŤEN-1990 dytĂŤdai uljeve â&#x20AC;&#x153;yâ&#x20AC;?2002)) tĂŤ litarit, (variable sipas Eurokodit (EN1990 janĂŤ domi tĂŤ litarit.actions, projektues: JĂźrg Conzett, www.flickriver. parabolike ĂŤshtĂŤtĂŤelitarit. vlefshme pĂŤr fazĂŤn kur đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;(đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ) Por, nĂŤďż˝rastin kur pesha vetjake ĂŤshtĂŤ dominante, d.m.th. đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śâ&#x20AC;˛â&#x20AC;˛ Por, = đ??ťđ??ťđ??ťđ??ť nĂŤ rastin kurose pesha vetjake dominante, d.m.th. kurnĂŤjemi com) e meĂŤshtĂŤ qĂŤllim tĂŤ krahasimit tĂŤ formĂŤs litari (kavoja, zinxhiri, apo njĂŤ strukturĂŤ e strukturĂŤs gjegjĂŤsisht kavos sĂŤ varur, apo kur edhe faz gjegjĂŤsisht kavos ose strukturĂŤs sĂŤe varur, apostrukturĂŤ kur edhe nĂŤ fazĂŤn e pĂŤrhe tĂŤ cilĂŤn merr njĂŤ e krijuar nga varur â&#x20AC;&#x153;e pĂŤrfaqĂŤsuarâ&#x20AC;? nga kĂŤto vija) gjendet veĂ§uar (kyrasti rasti mĂŤ i shpeshtĂŤ pĂŤr â&#x20AC;&#x153;strukturatâ&#x20AC;? e krijuara nga veĂ§uar mĂŤ i shpeshtĂŤ horizontale pĂŤr â&#x20AC;&#x153;strukturatâ&#x20AC;? e krijuara nga natyra), ng ku: đ??ťđ??ťđ??ťđ??ť (ky ĂŤshtĂŤ komponentja e tĂŤrheqjes sĂŤ litarit. njeriu (ura atĂŤherĂŤ e varur) dhe njĂŤ strukturĂŤ e nĂŤ shfrytĂŤzim, shpĂŤrndarĂŤ d.m.th kur ngarkesat e tĂŤ sipas aksit kavos, e cila pĂŤrshkru shpĂŤrndarĂŤ sipas aksit tĂŤ kavos, atĂŤherĂŤ lakorjalakorja e cila pĂŤrshkruan formĂŤn Nga zgjidhja e kĂŤtij ekuacioni, pĂŤr ngarkesĂŤ konstante ndryshueshme shprehet (variablesi:si: actions, sipas krijuar nga natyra (rrjeta e merimangĂŤs) đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E; (đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľ ) shprehet 2) [9] 0 đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľdominuese đ??ťđ??ťđ??ťđ??ť( đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? 0 đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? 0 Eurokodit EN-1990 )đ??ťđ??ťđ??ťđ??ťđ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E;đ?&#x2018;&#x17E; janĂŤ vis- (Fig.10 a,b) si dhe shprehja matematikore ďż˝ đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Ś = đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľďż˝ đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Ś = ďż˝cosh =đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?0 ďż˝cosh 2đ??ťđ??ťđ??ťđ??ťđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľďż˝) đ??ťđ??ťđ??ťđ??ť(đ??ťđ??ťđ??ťđ??ť đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?

tĂŤrheqjes sĂŤ litarit.

0 Ă -vis peshĂŤs vetjake tĂŤ litarit.

(19) e cila i pĂŤrkufizon edhe njĂŤrĂŤn edhe

Kjo ĂŤshtĂŤ shprehja matematike e vijĂŤs apo formĂŤs gjeometrike qĂŤ merr n Kjokur matematike tjetrĂŤn. e vijĂŤs apo formĂŤs gjeometrike Por, nĂŤ rastin peshashprehja vetjake ĂŤshtĂŤ evarur cilaĂŤshtĂŤ paraqet litarit dhe ndaj ĂŤshtĂŤpĂŤrkuljes), nĂŤ fakt nqĂŤ me shkallĂŤformĂŤn tĂŤ lartĂŤ racionale fleksibilitetitĂŤ(pa ngurtĂŤsi varur me shkallĂŤ tĂŤ lartĂŤ fleksibiliteti (pa ngurtĂŤsi ndaj pĂŤr Vargorja (vija e ndĂŤrprerĂŤ) vs parabola dominante, d.m.th. kur jemi nĂŤ fazĂŤn e italishtja:pĂŤr catena â&#x20AC;&#x201C; zinxhi vetjake. racionale Shpesh ajoparabolike quhet katenoidĂŤ forma ĂŤshtĂŤ (nga e vlefshme fazĂŤn kur l vetjake. Shpesh ajo quhet katenoidĂŤ (vija e plotĂŤt) si ĂŤshtĂŤ dhe (nga analogjitĂŤ saj shfrytĂŤzim me catena montimit tĂŤ litarit, gjegjĂŤsisht ose â&#x20AC;&#x153;vargoreâ&#x20AC;?. NĂŤ kavos đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š. 8 majtas mĂŤ poshtĂŤ, bĂŤrĂŤ italishtja: njĂŤ enĂŤ krahasim i sim varur â&#x20AC;&#x153;e pĂŤrfaqĂŤsuarâ&#x20AC;? nga kĂŤto vija) gjendet â&#x20AC;&#x153;vargoreâ&#x20AC;?. NĂŤ đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š đ??šđ??šđ??šđ??š . 8 majtas mĂŤ poshtĂŤ, ĂŤshtĂŤ bĂŤrĂŤ njĂŤ krah lakores sĂŤ vargores dhe asaj tĂŤ parabolĂŤs, ku mund tĂŤ shihet dallimi fare e merimangĂŤs) dhe 2002) strukturĂŤs sĂŤ varur, apo kur edhe nĂŤ fazĂŤnsipas e biostrukturat (variable actions, Eurokodit(rrjeta EN-1990 (EN1990 tyre, pĂŤrderisa nĂŤ (đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š. dhe 8 nĂŤ asaj mes) tĂŤ paraqitet rrjeta ku e merimangĂŤs dhe nĂŤ d( lakores sĂŤ vargores parabolĂŤs, mund tĂŤ shihet pĂŤrhershme kavoja funksionon si e veĂ§uar urĂŤn e varur (PĂšnt da Suransuns Fig.11) tĂŤ litarit. njĂŤ ure tĂŤ varur (PĂšnt da Suransuns, Tiers, CH, projektues: JĂźrg Conzett tyre, pĂŤrderisa nĂŤ (đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š. 8 nĂŤ mes) paraqitet rrjeta e merimangĂŤ Si karakteristikĂŤ themelore qoftĂŤ e (ky rasti mĂŤ i shpeshtĂŤ pĂŤr â&#x20AC;&#x153;strukturatâ&#x20AC;? e Por, nĂŤ rastin kur pesha vetjake ĂŤshtĂŤ dominante, d.m.th formĂŤs e merr njĂŤda strukturĂŤ e krijuar nga CH, njeriuprojektues: (ura e varur) njĂŤ uretĂŤtĂŤcilĂŤn varur (PĂšnt Suransuns, Tiers, JĂźd strukturĂŤs sĂŤ sĂŤ krijuar nga apo natyra qoftĂŤ e e nĂŤ natyrangarkesa (rrjeta kavos evertikale merimangĂŤs) si dhe shprehja matematikore (19) cila i krijuara nga natyra), e strukturĂŤs gjegjĂŤsisht ose varur, kur edhe formĂŤs tĂŤ cilĂŤn e merr njĂŤ strukturĂŤ e krijuar nga njeriu (urafa tjetrĂŤn. asaj tĂŤ krijuar njeriu ĂŤshtĂŤ eforma e shpĂŤrndarĂŤ sipas aksit tĂŤ kavos, veĂ§uar (ky rastiatĂŤherĂŤ mĂŤ i shpeshtĂŤ pĂŤrnga â&#x20AC;&#x153;strukturatâ&#x20AC;? krijuara ng

natyra (rrjeta e merimangĂŤs) si dhe shprehja matematikore (1

shpĂŤrndarĂŤ sipas aksit â&#x20AC;&#x153;vargoresâ&#x20AC;? tĂŤ kavos, (katenoidĂŤs), atĂŤherĂŤ lakorja e cila pĂŤrshk matematikisht lakorja e cila pĂŤrshkruan e litarit tjetrĂŤn. formĂŤn shprehet [10] mund tĂŤ shprehet si: si: đ??ťđ??ťđ??ťđ??ť đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? đ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Śđ?&#x2018;Ś = ďż˝cosh 0 đ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľđ?&#x2018;Ľďż˝ đ?&#x2018;?đ?&#x2018;?đ?&#x2018;?đ?&#x2018;? 0 đ??ťđ??ťđ??ťđ??ť

grafikisht e paraqitur nĂŤ

majtas ĂŤshtĂŤ

prezenca e numrit (numri i Euler-it apo

Kjo ĂŤshtĂŤ shprehja matematike e vijĂŤs apo formĂŤs gjeometrik siĂ§ quhet nganjĂŤherĂŤ numri i Neper-it). varur me shkallĂŤ tĂŤ lartĂŤ fleksibiliteti (pa nĂŤngurtĂŤsi PĂŤrderisa faktori ĂŤprmban veten e tijndaj p vetjake. Shpesh ajo quhet katenoidĂŤ (nga italishtja: cate â&#x20AC;&#x153;vargoreâ&#x20AC;?. NĂŤ đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š. 8 majtas mĂŤ poshtĂŤ, ĂŤshtĂŤ bĂŤrĂŤ njĂŤ kra lakores sĂŤ vargores dhe asaj tĂŤ parabolĂŤs, ku mund tĂŤ shihet tyre, pĂŤrderisa nĂŤ (đ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??šđ??š. 8 nĂŤ mes) paraqitet rrjeta e meriman

[9] CEN, B-1050, ÂŠ 2002, EN 1990: Eurocode â&#x20AC;&#x201C; Basis of structural design, CEN, Brussels.

174

tĂŤ pĂŤrshkruar nga ekuacioni (19) dhe

aspektin mekanik të strukturës së varur, numri kushtëzon formën e vargores dhe është aty pranishëm që t’u “tregojë” rrugën këtyre formave. Në këtë kuptim mund të flitet për të ashtuquajturat “bio-struktura”. Fizikisht, edhe kavoja, litari, zinxhiri apo ura e varur, si edhe fija e merimangës tentojnë kah një gjendje e natyrshme, racionale. Sikurse dihet, edhe shprehjet analitike të formave racionale të harqeve e përmbajnë këtë numur irracional.

Fig.10. (a)

PËRMBLEDHJE & PËRFUNDIME Teknologjitë e sotshme moderne kanë bërë që, shpeshherë, inxhinieri strukturist të “humbas” kontaktin me realitetin fizik të problemit dhe “rrëshqas” në rrafshin e besimit të parezervë ndaj rezultateve të makinës – kompjuterit. Ky artikull, larg nga tendenca për të parashtruar teori të reja

Fig.10. (b)

nga ato ekzistuese, ka për qëllim themelor thirrjen për “kthim në origjinë” të kohë pas kohëshmë.Duke pasur parasysh që numri qëndron në “shpirtin” e secilit problem inxhinierik, dy nga këta numra (numri dhe numri ) janë vizituar me theks të veçantë në “anatominë” e tyre si dhe ndërlidhjet të cilat i kanë me disa nga strukturat elementare inxhinierike. Një theks i veçantë i artikullit

Fig.11

bjen mbi rolin të cilin këta numra luajnë në estetikë. Por për këtë dhe disa veçori tjera, mbase do të flasim në një të ardhme të afërt. Fig.10. Biostrukturat (a-rrjeta e merimangës) dhe ura e varur b (Pùnt da Suransuns (www.flickriver.com)). Fig.11-12.“Ura natyrore” në Owachomo, Utah, ShBA dhe “Sälginatobel brücke”, në Schiers – Zvicër, vepër e Robert Maillart Fig.12 175

ARTIKULL SHKENCOR

Mjeshtër i arkitekturës së shekullit të njëzetë Doc. Dr. Arben Shtylla

Ne studio ditën e 100 vjetorit.

Nga fotot e fundit, me “mikun” e tij, duhanin.

Ky artikull eshtë shkruar nga Doc.Dr. Arben Shtylla. Arben Shtylla eshtë arkitekt dhe pedagog në Universitetin Polis. Autor i nje serë veprash arkitektonike në Shqiperi eshtë specializuar në fushen e teknologjisë së arkitekturës në objektet bashkohore. Doktoruar në Itali. Mbas ka fituar titullin ''Doc'' pranë Universitetit Polis dhe njohur nga Ministria e Arsimit. Pjesëmarrës në konferenca ndërkombetare në lidhje me arkitekturen, teknologjite e ndryshme të aplikimit të saj si dhe mbi eficencen energjetike në shërbim të saj.

Artikulli në vijim është një homazh me rastin e

Niemeyer, Njëqind qirinj për arkitektin

ndarjes nga jeta të arkitektit të shquar Brazialin

e famshëm”. Mbushte njëqind vjeç, më

Oscar Niemeyer dhe është një përmbledhje

15 dhjetor 2007, një nga arkitektët më të

biografike e veprave, principeve dhe botëkuptimit

mëdhenj të arkitekturës moderne që ende

të tij profesional. Artikulli bazohet në ekstrakte

ishte gjallë. Festimet u zhvilluan jo vetëm

të vlerësimeve dhe analizave të shkruara për

në Brazil, por edhe në vendet ku janë

arkitektin e shquar, të cilat janë nxjerrë nga

ndërtuar veprat e tij, që janë më shumë se

autori i këtij shkrimi nga koleksionet e mediave

600 (Fig. 1). Kur po mendoja se është koha

të shkuara, intervistat me arkitektin përpara se

për të përgatitur një tjetër artikull, këtë

të ndahej nga jeta, periodikët e arkitekturës dhe

radhë për njëqind e pesë vjetorin, erdhi

mediat elektronike.

lajmi i vdekjes së Oskar Niemeyerit. Më 5 dhjetor 2012, mbylli sytë, O. Niemeyeri, në

176

Rreth pesë vjet më parë, në nëntor të Panoramic view of the castle of Berat, Albania.

Rio de Zhaneiro, në qytetin e tij të lindjes,

vitit 2007, pata shkruar artikullin “Oskar

ku jetoi dhe punoi deri në ditët e fundit

Sekretariati i Kombeve te Bashkuara. New York (1947-1952).

të jetës, me përjashtim të emigrimit të

Le Corbusier

detyruar jashtë1 (siti i Fondacionit Oskar

Në vitin 1936 ai takon të famshmin Le

Niemeyer) (Fig. 2).

Corbusier, të cilin e kishin thirrur në

Emri i plotë, Oscar Ribeiro de

Brazil për të projektuar një sërë godinash

Almeida Niemeyer Soares Filho, tregon

publike. Takimi me autorin e «Vers une

qartë origjinën e tij mikse: Ribeiro e Soares

architecture” (Drejt një arkitekture) përbën

janë emra portugezë, Almeida është arab,

një pikë nisje për karrierën profesionale

ndërsa Niemeyer gjerman; këtyre duhet t’i

dhe për drejtimin modernist të arkitekturës

shtojmë edhe diçka nga traditat afrikane

së Niemeyerit.

dhe indiane, që janë të pranishme në

Më

vonë,

më

1947

të

çdo familje braziliane, krijohet padashur

bashkëpunojë me Le Corbusier-in, edhe

një “ndërkombëtarizim”, i cili i parapriu

për projektin e selisë së Sekretariatit të

veprës së mjeshtrit.

Kombeve të Bashkuara, i famshmi «Pallati

Edhe formimi i Niemeyer-it lidhet me

i xhamtë», në New York (1947-1952).

qytetin e lindjes, në Shkollën Kombëtare

Kritikët e arkitekturës do të theksonin, se

të arteve të bukura, ku regjistrohet në vitin

në këtë vepër, idetë e Niemeyer-it, kanë

1929. Këtu ai u diplomua si inxhinier

qenë më të pranishme se ato të mjeshtrit

arkitekt, “engenheiro arquiteto”, dhe filloi

francez. Ideja e Niemeyer-it, ose ‘skema

praktikën në studiot e arkitektit të dëgjuar

32’ u pranua nga komiteti për aprovimin

Lucio Costa, me të cilin ka bashkëpunuar

e projektit, The Board of Design, por kjo

për një kohë të gjatë. Duke treguar fillimet

ndryshoi në sajë të presionit që ushtroi Le

e tij, mjeshtri thotë: « Në të kundërt me

Corbusier-i, i cili kishte propozuar idenë

pjesën më të madhe të shokëve, nuk doja të

23/32 (të hartuar së bashku me Bodiansky-

përshtatesha me një arkitekturë komerciale,

in dhe Weissmann- in), duke pranuar një

që e shihnim kudo. Edhe pse nuk kisha

skemë, e cila përfshinte idetë e të dyve, por

para, pranova të punoja gratis në studion e

kryesisht bazohej tek skema e projektuar

Kostës, ku gjeja përgjigjen e shumë pyetjeve

nga Niemeyer-i. Në gjysmën e dytë të viteve ‹50, ndodh një shkëputje e qartë nga «sacro catechismo” i Le Corbusier-it, duke përpunuar një gjuhë tjetër në arkitekturën moderne:

dhe dyshimeve që kisha si student i ri»(siti i Fondacionit Oskar Niemeyer)1. 1 Materialet për jetën dhe veprën e Oskar Niemeyerit janë informacione të marra nga siti i Fondacionit Oskar Niemeyer: niemeyer. org.br

177

Selia e Grupit Mondadori ne Milano, 1975

Le Corbusier-i ka qenë një përkrahës

vendosjes së diktaturës ushtarake, siç

i këndit të drejtë, ndërsa unë preferoj

pohohet në sitin e Fondacionit Oskar

vijat e lakuara (siti i Fondacionit Oskar

Niemeyer, ai shkoi në Paris, ku qëndroi deri

Niemeyer). Pikërisht linjat e lakuara, do

në mesin e viteve ‹80. Në fillim të karrierës

të përbënin një nga veçoritë, karakteristike

Niemeyer-in e ftuan për të dhënë mësim

të arkitekturës së mjeshtrit brazilian, së

në Yale University, por nuk iu dha viza për

cilave i qëndroi konsekuent deri në fund

të udhëtuar drejt Shteteve të Bashkuara

të veprës së tij.

të Amerikës. Megjithatë në vitin 1950, fama e tij u bë e njohur nëpërmjet botimit

Botëkuptimi I njohur për idetë e tij të majta, ai bëhet anëtar i Partisë Komuniste, «Partido Comunista Brasileiro” më 1945. Nga miqtë e tij të vjetër ishte edhe Fidel Castro i cili sikurse shkruan gazeta “the guardian”, duke qeshur thoshte se unë dhe Niemeyeri jemi komunistët e fundit të këtij planeti2 (Glancey J. 2007). Më 1964, pas grushtit të shtetit dhe 2 Glancey J, 2007, The Guardian, 1 August 2007: http://www. guardian.co.uk/artanddesign/2007/aug/01/architecture/print

178

të librit të parë me punimet e arkitektit, ndërsa më 1953, Niemeyer-i u zgjodh në postin e Rektorit të Universitetit të njohur, Harvard Graduate School of Design, por në sajë të prirjeve të tij politike, për të dytën herë ju refuzua viza e hyrjes për në SH.B.A. Në vitin 1963 ai zgjidhet anëtar nderi i American Institute of Architects, një nga institucionet më të nderuara në Shtetet e Bashkuara. Sipas Santin-it, duket se fama e arkitektit të madh doli më e fortë

Kisha e San Franceskos se Asizit, Belo Horizonte, 1940.

se rregullat e ngurta të “luftës së ftohtë”, që

botës, por konsekuent në bindjet e tija,

zhvillohej në ato vite. Gjatë azilit në Paris,

vazhdoi të merrej me godinat publike. Ai

ku hapi një studio, mjeshtri projektoi

theksonte se: «jeta është më e rëndësishme

selinë e Partisë Komuniste Franceze (1965),

se arkitektura dhe se drejtësia shoqërore

Pallatin Mondadori në Milano (1968), etj,

është i vetmi qëllim, për të cilin duhet të

(Santini 2012)3.

punojmë» (Cotroneo 2012)4. Kur u kthye

Botëkuptimi i Niemeyer-it, duket

në atdhe, ju besuan një sërë projektesh me

qartë edhe në projektin më të rëndësishëm

interes shoqëror, ku mund të përmenden

të jetës së tij, Brazilias, ku parimi i barazisë,

Memoriali i Amerikës Latine (1987),

nisur nga një ideologji socialiste, duket se

Parlamenti për Vendet e Amerikës Latine

është përdorur qartë si në arkitekturë edhe

(1991), Muzeu i Artit Modern - MAC

në urbanistikë. Kështu, lagjet e qytetit

(1991), Auditoriumi i Ibirapueras (1999),

janë ndarë sipas funksionit, por godinat

Caminho

e banimit janë të gjitha të një tipi, me

dhjetëvjeçarin e fundit Oskar Niemeyer-i

pak mundësi ndryshimesh në interier.

ka qenë shumë aktiv, edhe pse në moshë

Banesat e këtij qyteti janë të gjitha pronë

të kaluar. Nga punimet më të fundit mund

e qeverisë e cila i jep me qira punonjësve.

të përmendim Auditoriumin e Ravelos

Vetë qyteti nuk ka zona të “privilegjuara”,

në Itali (2000), projektin e Qendrës

ministrat dhe punëtorët e thjeshtë banojnë

Administrative të Shtetit të Minas Gerais

në të njëjtin pallat. Parime këto shumë

(2003), Pavijonin e Serpentine Gallery në

të propaganduara edhe për zhvillimet

Londër (2003) dhe projektin për Portin e

në Shqipëri deri në prag të viteve ’90.

Muzikës në Argjentinë, (2008).

Niemeyer-it

(1997).

Në

Natyrisht idetë e Niemeyer-it, nuk mundën të realizoheshin të gjitha pasi shumë nga

Brazilia

ato u lanë mënjanë, ose u ndryshuan nga

Në vitin 1940 Niemeyer-i takohet me

presidentet e mëvonshëm.

Juscelino Kubitschek de Oliveira, që në

Pas famës së madhe që mori pas viteve

atë kohë ishte kryetar i bashkisë së Belo

’60, Niemeyer-i mund të projektonte

Horizonte, kryeqyteti i shtetit të Minas

godina shumë luksoze në çdo vend të

Gerais. Kryetari i bashkisë, së bashku

3 Santini, F. 2012, Addio a Oscar Niemeyer, erede degli antichi Maestri d’Opera, ERASMO. Anno XIII - Numero 21-22

4 Cotroneo Rocco, 2012, Addio a Niemeyer, maestro del Novecento. Corriere della sera. 12 dicembre 2012

179

ARTIKULL SHKENCOR me guvernatorin i kërkuan Niemeyer-it

hartoheshin edhe një sërë projektesh për

projektimin e disa godinave në zonën e

godina të institucioneve të rëndësishme

Pampulhas, projekte që njihen tashmë

dhe Niemeyer-i projektoi ato më kryesoret

si «Kompleksi i Pampulhas”. Projekti i

si Palacio da Alvorada selia e qeverisë,

Kishës së Shën Franceskos së Asizit (Fig.

rezidencën e Presidentit të Republikës,

5) do të bëhej një nga veprat e para të

Dhomën

arkitekturës moderne për të gjithë Brazilin

Kombëtar, Katedralen, si dhe disa godina

(pritzkerprize, 1998)5.

të ministrive dhe shumë godina për banesa

Deputeteve,

Kongresin

Bashkëpunimi me Juscelino Kubitschek-

të cilat janë konceptuar sipas parimit “për

un u bë shumë i rëndësishëm në shtator

një të ardhme më të barabartë”7, (Fig.

të vitit 1956, pak kohë pasi ai u zgjodh

7). Edhe tek vetë katedralja, Niemeyer-i,

president i Brazilit. Sipas dëshmisë së vetë

mbetet besnik i ideve të tij, si një komunist

mjeshtrit, presidenti i paraqiti dëshirën për

dhe ateist i njohur, duke krijuar një imazh

të realizuar një ide ambicioze: «Po mendoj

tepër simbolik, ku godina shëmbëllen me

të krijoj një kryeqytet të ri për vendin

dy duar të bashkuara dhe të ngritura lart

dhe dua që ti të më ndihmosh ... Oskar,

drejt qiellit (Fig. 10).

këtë radhë do të ndërtojmë kryeqytetin e

Projekti i Brazilias kishte formën

Brazilit»6. Në grupin e projektimit për planin

e një aeroplani, simboli i zhvillimit të

urbanistik të udhëhequr nga Lucio Costa

teknologjisë dhe parashikonte një popullsi

për kryeqytetin e ri që u quajt Brazilia,

prej 200.000 banorësh. I ndërtuar nga

mori pjesë edhe Oskar Niemeyer-i (Fig.

hiçi, shumë shpejt, brenda katër vitesh,

6). Krahas këtij plani, kërkohej që të

ky qytet u kthye në një enciklopedi të

5 Biografia e Oscar Niemeyer nga pritzkerprize.com 1998:

7 Decoist, architecture and interior design, 2012. The Stunning Architecture of Oscar Niemeyer. www.decoist.com/2012-12-12/

http://www.pritzkerprize.com/1988-niemeyer/bio, 1988

6 The New York Times, 2012 “A Legendary Modernist” –

Fotot nga nytimes.com

180

Plani urbanistik i Brazilias

arkitekturës moderne, nëpërmjet stilit

është projektuar, por edhe konceptuar si

plastik të Niemeyer-it që krijoi një bashkësi

një valle; secila nga pjesët që e formojnë

të linjave të kurbëzuara të elementëve

është vendosur në mënyrë fluide dhe ashtu

ndërtimorë elegantë që duken sikur

si një balerinë duket sikur qëndrojnë mbi

qëndrojnë rastësisht në këmbë.

majat e gishtave, si të ngrira në një çast në

Ndërtimet e Brazilias janë akoma në

një ekuilibër perfekt»8 (Basulto, 2012 )(Fig.

“mode”. Brazilia ka mbetur monument

12).

i një ideje të veçantë të krijuesit kryesor

Linjat e kurbëta të Niemeyer-it

të saj Oscar Niemeyer-it. Pavarësisht nga opinionet, jo gjithmonë të njëjta, nuk ka qytetet tjetër në botë, që të ketë pasur këtë interes në nivel botëror. Niemeyer-i ka frymëzuar dhe mësuar në dekada

Karakteristikën kryesore të veprave të tij mjeshtri e përmblidhte në pak fjalë: “Nuk është këndi i drejtë ai që më tërheq, as edhe vija e drejtë, e ngurtë, e pandryshuar

arkitektët e gjithë botës, duke përbërë një

që krijohet nga njeriu. Ajo që më pëlqen

rast shumë të veçantë të jetëgjatësisë së

është vija e lakuar, e lirë dhe sensuale; vijat

vlerave arkitektonike dhe urbanistike të

e kurbëta që i gjej në malet e vendit tim,

arkitekturës moderne. Mund të duket e

në rrjedhën e lumenjve të tij, në dallgët

pabesueshme, por është fakt se me gjithë

e oqeanit, në retë e qiellit dhe në trupin

punën e madhe për projektet e Brazilias,

e femrës së dashuruar”9 (Niemeyer 2000,

ai ka përfituar vetëm një rrogë modeste,

p. 70). Kjo shprehet qartë në godinën

si një nëpunës i shtetit. Ser Norman

Copan, e cila ka 38 kate dhe është 140

Foster në dedikimin e tij për Niemeyer-in pas vdekjes, thekson se “Brazilia jo vetëm

Pamje ajrore ne ditët e sotme. Brazilia.

8 Basulto, David. 2012. “Tribute to Oscar Niemeyer by Norman Foster”. ArchDaily. www.archdaily.com/303636 9 Niemeyer, O. 2000, The Curves of Time: The Memoirs

of Oscar Niemeyer, London: Phaidon, p. 70.

181

ARTIKULL SHKENCOR metra e gjatë. Ky ka qenë për shumë kohë

Ministrisë se Edukimit dhe Shëndetësisë,

edhe kompleksi i banimit më i madh në

një nga veprat e para të Niemeyer-it, duket

botë10 (Fig. 16).

sikur është një projekt i ditëve të sotme.

Bashkë me Le Corbusier-in, Perret-in

Trajtimi i fasadës jugore me elemente të

e pak të tjerë, ai ka studiuar dhe përdorur

mbrojtjes nga dielli, brisolei, është një

në ndërtimet e godinave, cilësitë dhe

element i pranishëm në projektet e viteve të

mundësitë e vërteta të betonit të armuar,

fundit, kur arkitektët po vlerësojnë gjithnjë

duke rizbuluar një material që fillimet i

e më shumë projektimin ambiental. E

kishte në Romën antike ku u përdor vetëm

veçanta është se mjeshtri Niemeyer, e ka

për fortifikime. Në veprën e Niemeyer-it

realizuar këtë ide kaq novatore, rreth 70

gjejmë një përputhje të pazakontë midis

vjet më parë (Fig. 17).

frymëzimit formal e estetik të arkitektit

E gjithë vepra e Oskar Niemeyer-

dhe logjikës së statikës së inxhinierit. Si

it dëshmon një fakt të rëndësishëm,

një mjeshtër i rrallë i ndërtimeve, ai u

se fatmirësisht akoma, arkitektura nuk

frymëzua nga parimet e ekuilibrit dhe u

është vetëm një mall komercial, që shitet

udhëhoq nga llogaritjet e inxhinierisë,

e blihet dhe aq më pak produkt vetëm i

duke na dhënë mesazhe të ligjeve të

të ashtuquajturve “ArchiStar”, por shpesh

harmonisë universale11. “Arkitektura është hobi im – përsëriste shpesh – është një nga kënaqësitë e mia: të krijosh forma të reja, që të mundëson betoni i armuar, ta gdhendësh, ta shumëfishosh, duke përdorur teknika sa më të avancuara; Kjo është për mua spektakli i krijimit të arkitekturës”12. Projekti për godinën e

është thjesht krijim i ndjerë që një njeri

10 The New York Times, 2012 “A Legendary Modernist”

– Fotot nga nytimes.com.

arkitektët që u përgatitën me parimet e

ning Architecture of Oscar Niemeyer. www.decoist.com.

Arkitekturës Moderne ka qenë ngulitur

Oscar Niemeyer: “I miei 100 anni” http://www.architettiroma.it/archweb/notizie/9951.aspx

mirë në kokë ajo që ishte pranuar nga të

11 Decoist, architecture and interior design, 2012. The Stun12 Achille Bonito Oliva, 2007 La Repubblica del 15.12.07

182

Pallati Alvorada, selia e Qeverise ne Brazilia, 1958-60.

e dëshmon me lapsin e tij në një fletë vizatimi. Oscar Niemeyer-i, mund të konsiderohet si i fundmi i arkitektëve të mëdhenj të shekullit të kaluar, si një personazh i famshëm, pothuaj historik i arkitekturës moderne. Përsëri N. Foster-i thotë se, për

gjithë se “forma ndjek funksionin”, ndërsa Niemeyer-i arriti të provojë se “kur një formë krijon bukuri, pra është e bukur, ajo bëhet funksionale, pra realizon atë që është thelbësore në arkitekturë” ... dhe Foster-i vazhdon: ajo që më pëlqen më shumë në punët e tij është se edhe një godinë e vetme, është e projektuar për shfrytëzimin nga një publik i gjerë, pra ka përmasa publike13.

Kryevepra Në vitin 1996, në moshën 89 vjeçare Niemeyer-i krijoi atë që shumë kritikë të

Katedralja e Brazilias (Catedral Metropolitana Nossa Senhora Aparecida). 1958-1970.

arkitekturës e quajnë veprën e tij më të mirë: Muzeun e artit modern në Niterói. Godina është vendosur mbi një shkëmb dhe përara saj hapet një panoramë e mrekullueshme e gjirit të Guanabaras dhe e vetë qytetit të Rio de Zhaneiros14 (Fig. 19). Inaugurimi i muzeut, shkaktoi një admirim të përgjithshëm, të ngjashëm me atë të Guggenheim Museum në Bilbao të Frank Gehry-it, që u inaugurua një vit më pas. Këto dy projekte janë shumë të ndryshëm nga njëri-tjetri për nga elementet e përdorura. Atje ku Gehry

Godina e Ministrisë se Jashtme.

përdori veshjet me pllaka prej titani dhe krijoi projektin e tij me ndihmën e një seri kompjuterësh,

Nemeyer-i përdori

materiale shumë më pak të kushtueshëm, betonin e bardhë dhe u besoi skicave të tij me dorë të lirë, që janë bërë të famshme për thjeshtësinë dhe saktësinë e shprehjes së formës dhe volumit. Duke përdorur një material bazë të ndërtimit, Niemeyer-i e ka 13 Basulto, David. 2012. “Tribute to Oscar Niemeyer by

Norman Foster”. ArchDaily. www. archdaily.com/303636

14 Niemeyer, O. 2000, The Curves of Time: The Memoirs of Oscar Niemeyer, London: Phaidon. Web site i muzeumit, http://www.macniteroi.com. br/?page_id=148

Pallati Planalto, selia e Presidentit te Brazilit.

183

Linjat e kurbeta te Niemeyerit.

Harku i Apoteozit, ne Sambodrome, Brazil, 1983. Godina COPPANA e ndertuar ne SAN PAOLO. 1957-1966.

Godinen e Ministrise se Edukimit dhe Shendetesise. 1936.

kthyer betonin e armuar të lyer me ngjyrë

një ashensor, për të plotësuar kërkesën e

të bardhë në një kryevepër të shprehjes

vetme që i shkaktoi mosha, për të eliminuar

(Fig. 20, 21).

rampat e shkallëve. Edhe në vitet e fundit

Kjo vepër qëndron me dinjitet krahas

studioja buçiste nga projektet që tashmë

veprave të famshme, që përfaqësojnë një

janë në dorën e nipërve dhe stërnipërve

arkitekturë pa kohë, sikurse vila Falling

të mjeshtrit që kanë zgjedhur të vazhdojnë

water e Frank Lloyd Wright-it, kapela në

rrugën e tij (Fig. 27).

Ronchamp e Le Corbusier-it apo shtëpia

Me rastin e 100 vjetorit të lindjes

e Farnworth-it e Mies van der Rohes.

në një intervistë të gjatë dhënë revistës

Studiuesit e kësaj vepre kanë theksuar se

Espresso (Bortolan 2007)19, Niemeyer-i jep

kjo godinë është aq e veçantë dhe e bukur,

një panoramë pothuajse të plotë të kredos

sa e tërheq vëmendjen e vizitorit më

së tij jo vetëm si arkitekt dhe intelektual

shumë se veprat e artit që ekspozohen aty16

i shquar, por edhe si një njeri me mision

(pritzkerprize, 1988) (Fig. 22).

social dhe i përkushtuar në zhvillimet e

Ai u shqua si një profesionist aktiv

vendit të tij dhe të gjithë botës. Më poshtë

i jetës dhe zhvillimeve të Brazilit, por

po japim disa nga pjesët e kësaj interviste,

veçanërisht të qytetit të tij Rio de Janeiro,

që mund ta quajmë edhe testamentin

deri në fund të jetës. Krahas aktivitetit

intelektual që mjeshtri i madh ka lënë. Në

si arkitekt, Niemeyer-i, na ka lënë edhe

këtë intervistë Niemeyer-i flet për botën

disa vepra në dy fusha pak të njohura nga

e arkitekturës dhe aktorët e mëdhenj të

publiku, në skulpturë, kryesisht në atë

saj. Ai thotë «Çështja është gjithmonë se

monumentale dhe në dizajn, jo vetëm me

arkitektura duhet të suprimojë, të çudisë

karriget dhe poltronat që kanë qenë objekti

.. Po shpjegohem, moda sot udhëheq

klasik i shumë arkitektëve të mëdhenj, por

çdo gjë, mënyrën e të ngrënit, veshjen,

edhe me produkte të dizajnit modern si

madje edhe hapësirat arkitektonike në

këpucët sportive Converse

të cilat nuk gjen vend aspekti praktik,

(Delaqua,

2012) (Fig. 23-26).

funksional. Po jap vetëm një shembull

Edhe pse kishte kaluar një shekull të

përse nuk më pëlqen të kritikojë kolegët,

jetës, ai çdo mëngjes ishte i përpiktë kur

si veprat e spanjollit Santiago Calatrava,

hynte në studion e tij në Copacabana

të cilat paraqiten shumë komplekse,

(Cotroneo 2012)18. Në studion gjithë

sikur duan që të provokojnë shikuesin.

dritë, ku ai shpiku edhe Sambodromin,

Në shumë vepra Duket se i vetmi qëllim

stadiumin ku mund të organizoheshin

është dukja, pamja. Po e përsëris, gabimet

sfilatat e karnavaleve të famshme, me

vijnë, sepse merret në konsideratë vetëm

kalimin e viteve, nuk kanë ndryshuar

aspekti estetik, jo ai praktik, funksional».

shumë gjëra. Në vitet e fundit është shtuar

Kur atij i drejtohet pyetja në se sipas tij

15. Decoist, architecture and interior design, 2012. The Stunning Architecture of Oscar Niemeyer. www.decoist.com.

gjatë këtyre viteve filozofia e arkitekturës

16.

http://www.pritzkerprize.com/1988-niemeyer/bio, 1988. Biografia e Oscar Niemeyer nga pritzkerprize.com 17. Delaqua Victor, 2012. http://www.archdaily.com.br/br/0177424/converse-lanca-colecao-oscar-niemeyer/ 18. Cotroneo Rocco, 2012, Addio a Niemeyer, maestro del Novecento. Corriere della sera. 12 dicembre 2012.

ka ndryshuar, ai përgjigjet ... «sigurisht. Nuk ekziston arkitekturë e vjetër, antike, 19. Bortolan Jerry, 2007. L’intervista concessa a L’Espresso nel 2007.spresso.repubblica.it/dettaglio/niemeyer-architetto-del-vivere/2196094.

Këpucët sportive, Converse.

ARTIKULL SHKENCOR

Muzeun e artit modern ne Niterรณi

186

ose e re, moderne, por vetëm e bukur ose

arkitekturën antike, për shembull, nuk

e shëmtuar. Po jap një shembull, duke u

mund të bëjë kupola më të mëdha se 40

nisur nga një fakt: sot kemi beton arme, që

metra: nuk ishte e mundur teknikisht ta

të afron mundësi të pafundme. Prandaj,

kalojë këtë hapësirë. Kupola e Brazilias, që

kur punoj për një projekt, para së gjithash

kam projektuar dhe ndërtuar është me një

heq gjysmën e kolonave të strukturës. Kjo

hapësirë prej 80 metrash. Mund të bësh

e bën arkitekturën më të lehtë, mbulesën

atë që të lejon periudha ku jeton».

më të madhe. Pra, objektivi është të

Në takimin e tij me mjeshtrin N. Foster

tentojmë gjithmonë për një arkitekturë

ai kujton: “Më tha se arkitektura është e

të ndryshme, që të suprimojë, të çudisë».

rëndësishme, por jeta është akoma më

Më tej gazetari i kujton se sapo ka thënë

rëndësishme. Edhe pse në fund të fundit,

se arkitektet shohin vetëm anën e jashtme

arkitektura e tij është trashëgimia që ai na

dhe nuk mendojnë për funksionin ... Ai

la pas. Ai vetë si një njeri, përjetësisht i ri,

përgjigjet ... «Forma që i japim një godine

na la një burim gëzimi dhe frymëzimi për

duhet t’i shkaktojë kënaqësi estetike

shumë gjenerata që do të vijnë”20.Dhe një

shikuesit, por duhet të ketë edhe një aspekt

njeriu të tillë nuk mund t’i thuash vetëm

funksional. I respektoj të gjithë kolegët.

se faleminderit 21 (Micheli 2012).

Por gjithashtu mendoj se mund të krijohen forma akoma më të lira, duke shfrytëzuar cilësitë e mrekullueshme të beton armesë, me të cilën mund të bëjmë çdo gjë. Në

20 Basulto, David. “Tribute to Oscar Niemeyer by Norman Foster”. 06 Dec 2012. ArchDaily. www.archdaily. com/303636. 21 Micheli, Simone. Attratto dalla linea libera. 2012. www.archilovers.com/s1919/attratto-dalla-linea-libera.

Fig. 25. Rio Chaise. 1978. 187

Gëzim Qëndro

KRITIK LIBRI

Gëzim Qëndro

Le surréalisme socialiste

Série RETINA

Collection Eidos

Le surréalisme socialiste

L’autopsie de l’utopie

Këto ditë doli në Francë libri i estetit

je në një qytet jashtë shtetit dhe vetëm

Gëzim Qendro "Le surrealisme socialiste"

emri është i joni, pjesa tjetër ka një pamje

(L'autopsie

nga

ndryshe. Dhe në ketë rast autori matet në

shtëpia botuese "L'Harmattan". Studimi

një arenë tjetër dhe në kushte të tjera ku

u përzgjodh si pjesë e Collection Eidos,

i nënshtrohet të tjera rregullave, por që

serie "Retina" e udhëhequr nga Michel

kryesorja, autori i librit është përsëri i joni.

Costantini dhe François Soulages. Kjo

Ka diçka nga ajo ndjesia që na linte në

kolanë ka brenda saj filozofë, estetë, analistë

kohën e diktaturës interesimi dhe botimi

arti të shquar të cilët kanë sjellë në studimet

i studimeve të prof.Ramadan Sokoli në

e tyre mendime të vlefshme për skenën

Perëndim, ku ai shihej pastaj nga ne si

artistike, të para nga një kënd i ri dhe i

njeri magjik, apo kur prof. Eqrem Çabej

mirëargumentuar. Botimi i këtij libri është

në konferencat për gjuhën që mbaheshin

një ngjarje për kulturën dhe veçanërisht

jashtë shtetit ishte si në shtëpinë e tij për

për artet pamore, pasi të përzgjidhesh nga

nga niveli i dijes.

Préface de Gilles Rouet de

l'utopie),

botuar

një shtëpi botuese franceze është një rast

Komiteti shkencor ndërkombëtar i

i rrallë për mendimin tonë estetik, në një

lekturës i sh.b. "Harmattan" është i përbërë

seri ku janë 10 autorë gjithsejt.

nga mjaft emra të njohur të studiuesve nga vende të ndryshme të botës. Kur niset një

188

Kur e shikon librin ke një përshtypje

kolanë, shtëpia botuese garanton që emrat

të veçantë. Të krijohet ajo ndjesia, që kur

e pjesëmarrësve për botim janë figura të

Për Surrealizmin Socialist të Qendros Autor : Piktor Besim Tula

njohura dhe me vlerë në arritjet e tyre. Kjo

Hyrja e librit është bërë nga Gilles

përzgjedhje nga ana e saj është një nder

Rouet Professeur des Universites Chaire

i madh për të gjithë kritikën e artit tonë,

Jean Monnet, ku ju paraqet lexuesve

kur ajo të kërkon të jesh pjesëmarrës. Kemi

francezë

fituar jashtë shtetit gara sporti, baleti,

historike dhe politike.

Shqipërinë,

artin,

kushtet

instrumenti etj por në fushën e estetikës

Ky libër lexohet si një roman, shkruan

është tjetër gjë, ku krahas punës duhet

në parathënie autori, dhe tematika e

dhe një njohje e gjerë e mendimit estetik

zgjedhur, që nuk është kronologjike,

të të gjitha kohërave dhe është një tjetër

lejon të artikulohen një numër i madh

dimension konkurrimi.

veprash

arti,

të

evidentojë

atributet

Ky studim shërben si referim për

dhe mitet si karakterististikë që bëjnë

studiues të huaj dhe të brendshëm, për të

lexuesin të kuptoje logjikën krahasuese

vendosur në vendin e caktuara atë periudhë

të

gjysmë shekullore të krijimtarisë artistike

dhe fesë, ndërrmarje që konsiderohet

pamore, e cila arriti t'i nxjerrë thinjat

si më e përshtatëshme e një analize të

njeriut të saj të ri 46 vjeçar. Të gjesh lidhjet

ndryshimeve. Ngjasojnë kështu Heroi me

e artistit me burimin e frymëzimit dhe

Lajmësin e së Mirës, Parti, Parajsë…

ngjashmërive

midis

komunizmit

gjithë rregullat dhe ritet që duheshin për

Gëzim Qëndro na fton ne të kalojmë

të arritur deri tek pranimi dhe ekspozimi

antagonizmin klasik midis marksizmit dhe

i veprës.

fesë dhe lexuesi lehtësisht mund të ndjekë

189

KRITIK LIBRI ketë pistë në saj të përshtatshmërisë së

kush e ka trajtuar këtë temë para tij. Për

analizave të shfaqjes konkrete të regjimit,

disa faqe tekset që shkruhen, një studiuesi

që nuk është tjetër por sundim mbi të

i duhet të shfletojë pafundësisht libra.

vërtetën e asaj që nuk është...

Kjo është njëra prej vetive që Gëzimi e ka

Dhe e mbyll parathënien me "Ne nuk

me shumicë. Ky seriozitet dhe vërtetësi e

kemi arritur ta njohim mirë Shqipërinë…

argumentit e bëri që të mos lakmonte titull

aq më shumë shqiptarët! Falënderoj Gezim

në vendin tonë. Kjo ndërmarrje serioze u

Qëndron për ketë mundësi që na krijoi."

kurorëzua dhe u çmua në Francë. Ne tani

Studimi fillon me një thënie të

kemi një studim të botuar prej tyre.

përfaqëson

Libri ka një gjuhë të rrjedhshme,

qartësisht thelbin e ndërtesës ideore,

të saktë, pa ngarkese dhe me shembuj

artistike, estetike, ideologjike të Realizmit

të argumentuar, ku rezultatet e këtyre

socialist që u përdor për të krijuar një botë

veprave artistike nuk ishin rastësi, por një

ku do të jetohej, ëndërrohej dhe do të

domosdoshmëri e metodës së Realizmit

bëhej art. Thënia është kjo " Ngjarja më

Socialist, se nuk kishte rrugë tjetër.

Hannah

Arendt,

cila

e madhe e doktrinës totalitare nuk është fitorja e komunizmit, por krijimi i njeriut që nuk arrin të dalloje realitetin nga sajimi dhe të vërtetën nga gënjeshtra".

190

Koha dhe intelektuali Një

intelektual

përkushtuar

seriozisht realizon. Këtë e ilustron më

Me një gjuhë të qartë, me fakte të

së miri Gëzim Qëndro. Në karrierën

bollshme autori i bën kësaj periudhe

e tij mund të shquajmë veprimtari të

autopsinë duke e parë atë në shumë

shumta dhe të gjithanshme. Po cilësojmë

pika, ku pjesë të jetës ishin të ndaluara

disa të këtyre kohëve: Ai është pionieri i

të trajtoheshin si shiu, vdekja, gjumi

organizimit të ekspozitave të arteve pamore

etj. Heroi nuk kishte probleme të jetës

në Universitet. Universitetin Polis, e ktheu

familjare dhe ishte kurdoherë në të njëjtën

në seleksionuesin e artistëve cilësore, punë

gjendje emocionale pozitive. Të gjitha

që duhej ta bënte GKA. Është formuluesi

argumentet janë të ilustruara me thënie

i tekstit të parë për shkollat e larta të

filozofësh, sociologësh apo estetësh të

artit "Gjuha Pamore", që sot zhvillohet

kohëve të ndryshme të cilët trajtojnë kete

në këtë universitet. Solli në shqip kohet

problem, por sipas konceptit të tyre. Për

e fundit librin "Fuqia e imazheve" si dhe

një që merret me trajtimin filozofik apo

"5 fytyrat e modernitetit" etj. etj. Puna

estetik të një problemi e ka të qartë se çfarë

këmbëngulëse për të pajisur me historinë

pune pret të njohë ato çfarë janë thënë dhe

e vërtetë kryeveprën tonë "Motra Tonë",

është pjesë e ambicies së tij. Komenti rreth kompozimit "Çeta e Shahin Matrakut" e Spiro Xegës, si tabloja e parë realiste shqiptare, e cila është një vlerë në historinë e artit tonë. Shpjegimi i domethënies si dhe cilësitë kompozicionale të figurave të kësaj vepre, ku artisti me besnikëri na paraqet të vërtetën e subjektit. Çfarë e bën Gëzimin të ecë përpara? Me sa duket është drita. Ajo që të bën të ndjehesh si jashtë gravitetit të tokës, duke të hequr peshën e problemeve dhe nevojën e shpagimit. Një intelektual i tillë me cilësi të provuara sjell përparim në ketë kohë me huqe, që siç shihet ende nuk ka nevojë për seriozitet. Kjo dritë është pronë e njerëzve që duan të realizojnë. Kjo dritë ka udhëhequr në kohët e diktaturës Naxhi Bakallin kur konstruktonte me virtuozitet dhe elegancë figurat e tij, i betuar, vetëm me një vijë. Kjo dritë nxiste Llambi Blidon të rrinte orë e orë të tëra mbi tavaloce, duke provuar bashkëveprimin e ngjyrave si një organizëm i gjallë dhe delikat pastaj duke u rebeluar në akorde koloristike të papara në artin tonë. Çdo periudhë shtetërisht jo serioze, provokon nga ana tjetër individë që bëjnë punë shumë serioze. Design-i i librit është i nivelit të lartë dhe ritmi kompozicional i përkryer. Në kopertinë është zgjedhur pjesë nga tabloja e piktorit të ri Enkelejd Zonja "Në damarët tonë" një nga zërat më sugjestivë të artistëve të rinj.

191

AUA - DEKLARATë PëR SHTYP Unionit Shqiptar të Arkitektëve, Urbanistëve dhe Planifikuesve i është dërguar për mendim, prej drejtorisë së përgjithshme të Zhvillimit Urban të Ministrisë së Zhvillimit Urban dhe Turizmit, projektligji dhe rregullorja e Urdhërit Profesional të Inxhinierëve dhe Arkitektëve. Duke vlerësuar qasjen gjithëpërfshirëse të ministrisë, anëtarët e Unionit Shqiptar të Arkitektëve, Urbanistëve dhe Planifikuesve u mblodhën në datë 3 Prill 2014 për të diskutuar projektligjin e propozuar. Komentet e anëtarëve mund të grupohen si më poshtë në tre tematika kryesore 1. A ka nevojë për të patur një Urdhër?, 2. Procedura e anëtarësimit në urdhër, 3. Përfaqësimi në urdhër.

1. A ka nevojë për të patur një Urdhër? Unioni Shqiptar i Arkitektëve, Urbanistëve dhe Planifikuesve ka dyshime të thella mbi nevojën praktike për të patur një urdhër. Këto dyshime lindin për disa arsye historike dhe praktike. Në ato vende perëndimore, ku egziston urdhëri dhe eksperienca me Urdhërat e Arkitektëve është më e gjatë dhe e shtresëzuar, po vihet gjithmonë e më shumë në pikëpyetje egzistenca e tyre pasi shpesh urdhëri kthehet në një mekanizëm burokratik që jo vetëm nuk garanton cilësinë e të vepruarit por shndërohet në pengesë të tregut të lirë. Për të marr një rast konkret, në Italinë fqinje, urdhëri i arkitektëve është krijuar gjatë kohës së diktaturës fashiste të Mussolinit, me qëllimin e vetëm për të krijuar monopole në treg duke patur nën kontroll veprimin e arkitekëve. Krijimi i urdherit dhe provimi i shtetit për arkitektët është në kundërshtim me politikat e "acquis communautaire" sepse krijon monopol, duke shkuar në drejtim krejtësisht të kundert me politikën dhe ekonomine e tregut te Bashkimit Evropian. Ky rrezik është akoma më i dukshëm në vende si i yni, ku tregu nuk është akoma i konsoliduar dhe ku prania e një autoriteti me kompetenca jo të qarta mund të kthehet në një hallkë burokratike të ndjeshme ndaj korrupsionit. Për më tepër, veprimi i arkitektëve është i kontrolluar nëpërmjet një numri të konsiderueshëm hallkash, që fillojnë që nga mekanizmi i lejeve të ndertimit e deri tek kolaudimi i ndërtesave. Fakti që deri më sot është abuzuar me ndërtimet nuk vjen nga mungesa e organeve kontrolluese por nga mosveprimi dhe korruptimi i tyre. Nëse arsyesja e krijimit të urdhërit është e lidhur me rritjen e kontrollit mbi aktivitetin e ndërtimit, ju kujtojmë se egzistojnë tashmë të gjitha ligjet, rregulloret dhe organet që kanë pikërisht për detyrë kontrollin e këtij aktiviteti. Urdhëri do ishte vetem një taksë e shtyar, për më tepër, vetë makina burokratike e stërmadhe që parashikon krijimi i urdhërit nuk është ekonomikisht e qëndrueshme dhe për këtë arsye arkitektët dhe inxhinierët e të gjitha fushave detyrohen të ndajnë të njëjtin urdhër, për të ndarë shpenzimet e tij. Mendojmë se e vetmja

192

arësye për të patur një urdhër të përbashkët, praktikë e pahasur deri më sot në praktikën perëndimore, mund të jetë e lidhur me papërballueshmërinë e kostove të veprimtarisë së urdhërit. Gjithashtu mbeteten të paqarta shërbimet që urdhëri do t'u japë anëtarëve të tij. Të paqartë mbeten edhe iniciatorëet e krijimit të urdhërit. Rreziku është që grupime që deri më sotë kanë patur nën kontroll kualifikimet e mëtejshme të arkitektëve, duke bllokuar programet e doktoraturës në Fakultetin e Arkitekturës dhe Urbanistikës të UPTsë, të kenë tashmë nën kontroll edhe aktivitetin e tregut të lirë. Ky rrezik vihet re në disa nene të ligjit ku përmendet shprehimisht UPT duke diskriminuar institucione e institute publike apo private të akredituara, me rezultate tëdukshme nëfushat e interesit. 2. Procedura e anëtaësimit në Urdhër Për mendimin tonë edhe procedura e anëtarësimit në Urdhër paraqet gjithashtu një numër problematikash. Projektligji përmend organizimin e provimit të shtetit, një praktikë shumë komplekse, delikate dhe e kompromentueshme. Problemi i provimit të shtetit është sa moral, edhe teknik. Çështja morale lidhet me autoritetin që instutucioni i provimit të shtetit merr mbi institucionin e universitetit duke testuar profesionistë që duhet të kenë kryer tashmë të gjithë procesin e arsimimit të lartë. Pra krijohet një entitet me autoritet të paqartë akademik, që duhet të gjykojë punën e më shumë se 30 pedagogëve që kanë çertifikuar aftësitë e arkitektëve. Problemet teknike të provimit të shtetit lidhen me burokratizimin e tepruar të një procedure që duhet të jetë thjeshtë administrative duke shtuar përsëri hallka të korruptueshme. E paqartë akoma mbetet arsyeja e të paturit nga ana e urdhërit të një rregjistri të studiove pranë të cilave mund të kryhet praktika e parashikuar përpara rregjiistrimit në urdhër. Përsëri, shtohet një hallkë e panevojshme burokratike me rrezik të lartë korruptimi. Me çfarë kriteri do të dalloheshin në këtë pike sudiot e denja për të pritur praktikantë, nga ato

të padenjat? Ndërhohe që çdo studio në territorin e vendit tone vepron sipas ligjesh e rregulloresh të mirëpërcaktuara. 3. Përfaqësimi në Urdhër Na duhet të pranojmë se përfaqësimi i profesionistëve në organet drejtuese të urdhërit paraqet një numër problemesh e kontradiktash. Në relacionin e projektligjit përmendet fakti se deri më sot ka patur shumë raste të shkeljes së etikës profesionale gjë që ka krijuar anomali në marrëdhënien brenda profesionit. Pa qenë shumë diplomatik mund të thuhet edhe se sjellja e shumë arkitektëve që kanë vepruar 20 vitet e fundit ka pjesërisht shkatëruar qytetet tona. Në këtë projektligj parashikohet që garantët e etikës së profesionit të zgjidhen persona që kanë të paktën 20 ose 15 vite eksperiencë pune duke e kufizuar mundësinë për t’u përfaqësuar në organet drejtuese të urdhërit vetëm për një grup që ka vepruar në njërën nga perjudhat jo më të lavdishme të histories tonë të arkitekturës. Duke përdorur një diskriminat kaq të fortë moshe, jo vetëm përjashtohen disa breza të tërë profesionistësh me arsmimim dhe eksperiencë nga më të larmishmet por krijohet mundësina që në organet drejtuese të urdhërit të gjejmë disa nga përgjegjësit e situates aktuale. Akoma më problematike duket situata e pëfaqësimit në komisionet e provit të shtetit. Ky komision, duke u drejtuar drejtëpërdrejtë nga organet drejtuese të urdhërit është shumë i brishtë ndaj presioneve korruptuese. Përgjegjësit e situates aktuale, jo vetëm që mund të gjenden të legjitimuar nga vetë urdhëri por mund të kenë nën kontroll edhe të ardhmen e profesionit tone duke vendosur mbi ata që munden apo nuk munden të ushtrojë profesionin. E njëjta situatë vërehet edhe kur projektligji përmend gradat shkencore. Njihet rëndom fakti që arkitektët me grada shkencore numërohen me gishtat e duarve, pikërisht për arsye të bllokimit sistematik që istitucionet e detyruara nga ligji për të garantuar kërkimin shkencor, kanë kryen ndaj procesit të dhënies së gradave shkencore. Nuk do të donim që ky projektligj, në emër të kthimit të rregullit në qytetet tona, të

përdorej prej lobeve bllokuese, retrograde dhe monopolizuese për të futur nën kontroll aktivitetin e kategorive më të brishta të tregut tone që janë të arkitektëtve e rinj e premtues. Duke patur parasysh të gjitha problemet e mësipërme, Unioni Shqiptar i Arkitektëve, Urbanistëve dhe Planifikuesve shprehet kundër krijimit të Urdhërit të Arkitektit dhe kundër krijimit të provimit të shtetit, pasi egzistojnë tashmë të gjithë mekanizmat që adresojnë të gjitha nevojat. Le të vëmë ne punë këto mekanizma! Propozojmë që kushtet për marrjen e licensës të jenë dy. Përfundimi i studimeve të larta në përputhje me profesionin e arkitektit dhe kryerja e praktikës profesionale pranë studiove të licensuara. Vërtetimi i kryerjes së praktikës profesionale të bëhet nëpërmjet vërtetimeve të zyrës së tatim taksave, ku praktikanti duhet të rregjistrohet nga punëdhënësi duke shmangur një nga plagët më të rënda për arkitektët e rinj shqiptar që është punësimi pa pagesë e në të zezë. Me plotësimin e këtyre kushteve arkitektit duhet t’i garantohet e drejta e ushtrimit të profesionit e pa kontrolluar nga konkurentë të tij por e rregulluar nga ligjet e Republikës së Shqipërisë. Autoriteti përgjegjës për kontrollin administrativ të aplikimeve për liçencë propozojmë të jetë një zyrë e posatshme pranë Ministrisë së Zhvillimit Urban dhe Turizmit e cila do të ketë edhe të drejtën e ngritjes së komisioneve gjykuese në raste të shkeljes së etikës profesionale. Për këtë ekzistonbaza ligjore Me shpresën që komentet tona të konsiderohen si konstruktive, shpresojmë që institucioni shtetëror, në përputhje me misionin që qeveria ka marrë përsipër të dobësojë monopolet e të forcojë konkurencën e lire, nga të paktat garanci të rritjes së cilësisë në fushën tonë. Me respekt Kryetari i Unionit Shqiptar të Arkitektëve Urbanistëve dhe Planifikuesve Ark. Ledian Bregasi

193

CTU

TIRANA

POLIS UNIVERSITY

AR CH ITE

OF TIRANA

MUNICIPALITY