Journal of Applied Engineering Science 10(2012)1 by JAES

CONTENTS

Dr Radomir Mijailoviü METHODOLOGY FOR ESTIMATING THE DEPENDENCE BETWEEN FORCE AND DEPLACEMENT - A VEHICLE CRASH CASE

1-8

Mr Aleksandar Manojloviü, Mr Olivera Medar, Jelena Trifunoviü, Dr Katarina Vukadinoviü COST OF ACTIVITIES IN PUBLIC UTILITY FLEETS

9 - 14

GNP 2012 CONFERENCE PAPERS Dr Biljana Šüepanoviü, Dr Miloš Kneževiü, Dr Duško Luþiü AN EXAMPLE OF ANN MODELING APLLICATION IN PATCH LOADING PROBLEMS OF STEEL STRUCTURES

15 - 20

MSc Igor Peško, Dr Jasmina Dražiü, MSc Vladimir Muþenski, Dr Milan Trivuniü PREPARING A DATA BASE FOR ESTIMATING SEISMIC DAMAGE ON BUILDINGS APPLYING ANN

21 - 26

MSc Marijana Lazarevska, Dr Ana Trombeva-Gavriloska, Dr Miloš Kneževiü, Dr Todorka Samardžioska, Dr Meri Cvetkovska NEURAL NETWORK PROGNOSTIC MODEL FOR RC BEAMS STRENGHTENED WITH CFRP STRIPS

27 - 30

Dr Marina ûetkoviü, Dr Ĉorÿe Vuksanoviü INFLUENCE OF BOUNDARY CONDITIONS ON NONLINEAR RESPONSE OF LAMINATED COMPOSITE PLATES

31 - 36

Dr Marina Rakoþeviü APPROXIMATE PROCEDURE FOR CALCULATION OF SHEAR STRESSES

37 - 42

Dr Predrag Petronijeviü, Dr Nenad Ivaniševiü, Dr Marina Rakoþeviü, Dr Dragan Arizanoviü METHODS OF CALCULATING DEPRECIATION EXPENSES OF CONSTRUCTION MACHINERY

43 - 48

MSc Nenad Fric, MSc Boris Gligiü, MSc Jelena Dobriü, Dr Zlatko Markoviü WIND TOWERS - DESIGN OF FRICTION CONNECTIONS FOR ASEMBLING SECTIONS OF TUBULAR STEEL TOWERS

49 - 52

Dr Todorka Samardžioska, Dr Ana Trombeva-Gavriloska, Dr Petar Cvetanovski, Mr Denis Popovski, Mr Mile Partikov STRENGTHENING AND OVERBUILDING OF CAR SERVICE ”AUTOMAKEDONIJA” IN SKOPJE, MACEDONIA

53 - 58

EVENTS REVIEW

ANNOUNCEMENT OF EVENTS

BOOK RECOMMENDATION

65 - 71

Journal of Applied Engineering Science 10(2012)1

IMPRESSUM Journal of Applied Engineering Science The journal publishes original and review articles covering the concept of technical science, energy and environment, industrial engineering, quality management and other related sciences. The Journal follows new trends and progress proven practice in listed ﬁelds, thus creating a unique forum for interdisciplinary or multidisciplinary dialogue. All published articles are indexed by international abstract base Elsevier Bibliographic Databases through service SCOPUS since 2006 and through service SCImago Journal Rank since 2011. Serbian Ministry of Education and Science admitted the Journal of Applied Engineering Science in a list of reference journals. Same Ministry ﬁnancially supports journal’s publication. Publisher Institute for Research and Design in Commerce and Industry www.iipp.rs For publisher: Prof. dr Branko Vasiü

Assistant Editor Dr Predrag Uskokoviü Institute for Research and Design in Commerce and Industry, Belgrade;

International Editorial Board Prof. dr Vukan Vuþiü, University of Pennsylvania, USA; Prof. dr Robert Bjekoviü, Hochschule Ravensburg-Weingarten, Germany; Prof. dr Jozef Aronov, Research Institute for Certiﬁcation JSC, Russia; Prof. dr Jezdimir Kneževiü, MIRCE Akademy, England; Dr Nebojša Kovaþeviü, Geotechnical consulting group, England; Adam Zielinski, Solaris Bus & Coach, Poland; Prof. dr Miloš Kneževiü, Faculty for Civil Engineering, Montenegro; MSc Siniša Vidoviü, Energy Testing & Balance Inc, USA; Dr Zdravko Milovanoviü, Faculty of Mechanical Engineering, Banja Luka.

Editorial Board Prof. dr Gradimir Danon, Faculty of Forestry, Belgrade; Doc. dr Dušan Milutinoviü, Institute for Transport and Trafﬁc CIP, Belgrade; Mr Ĉorÿe Milosavljeviü, CPI - Process Engineering Center, Belgrade; Prof. dr Miodrag Zec, Faculty of Philosophy, Belgrade; Prof. dr Nenad Ĉajiü, Mining and Geology Faculty, Belgrade; Prof. dr Vlastimir Dedoviü, Faculty of Transport and Trafﬁc Engeneering, Belgrade; Prof. dr Mirko Vujoševiü, Faculty of organizational sciences, Belgrade; Doc. dr Vladimir Popoviü, Faculty of Mechanical Engineering, Belgrade; Doc. dr Vesna Spasojeviü Brkiü, Faculty of Mechanical Engineering, Belgrade.

Publishing Council Prof. dr Milorad Milovanþeviü, Faculty of Mechanical Engineering, Belgrade; Milutin Ignjatoviü, Institute for Transport and Trafﬁc CIP, Belgrade; Dragan Beliü, Transport Company “Lasta”, Belgrade; Dr Deda Ĉeloviü, Port of Bar, Bar; Dr Drago Šeroviü, Adriatic Shipyard, Bijela; Cvijo Babiü, Belgrade Waterworks and Sewerage, Belgrade; Nenad Jankov, Power Plant Kostolac B, Kostolac; Miroslav Vukoviü, Mercator Business System, Belgrade; Dušan Ĉuraševiü, Euro Sumar, Belgrade.

Copublisher Faculty of Transport and Trafﬁc Engineering – Belgrade University www.sf.bg.ac.rs For copublisher: Prof. dr Slobodan Gvozdenoviü Editor in Chief Prof. dr Jovan Todoroviü Faculty of Mechanical Engineering, Belgrade;

ISSN 1451-4117 UDC 33 Papers are indexed by SCOPUS Journal of Applied Engineeering Science is also available on www.engineeringscience.rs and http://scindeks-eur.ceon.rs/index.php/jaes Designed and prepress: IIPP

Editorial Ofﬁce Nada Stanojeviü, Miloš Vasiü, Darko Stanojeviü, Miloš Dimitrijeviü, Mirjana Solunac, Ivana Spasojeviü, Andrija Ĉuraševiü, Institute IIPP, Belgrade; Bojan Manþiü, Faculty of Mechanical Engineering, Belgrade. Printed by: Beograﬁka, Beograd Journal of Applied Engineering Science 10(2012)1

EDITORIAL

CONSTRUCTION IS UNIVERSAL LANGUAGE OF MANKIND Prof dr. Miloš Kneževiü Dean of the Civil Engineering Faculty in Podgorica President of the GNP 2012 organisation committee

Conference of Civil Engineering, science and practice GNP2012 is traditionally held in Žabljak for the fourth time. Once again we are trying to share accomplishments in science and practice – the ones that were accomplished and ones that are waiting for better times. Horizons of conference GNP are expanded with increasing number of papers that were reviewed and among them 331 were chosen, that were signed by 596 authors from 16 countries. From Conference, eight papers were chosen for publishing. We give thanks to the members of scientiﬁc committee and authors, especially to our sponsors and friends, representatives of foreign and country institutions that provided help to us in organization of this conference. Without their help GNP2012 couldn’t be realised. Žabljak, February 2012. GNP 2012 Scientiﬁc Board Prof.dr Dragan Aranÿeloviü, FCEA, Niš Prof.dr Stanko Brþiü, CEF, Belgrade Prof.dr Meri Cvetkovska, CEF, Skoplje Prof.dr Aleksandra Deluka-Tibljaš, CEF, Rijeka Prof.dr Nebojša Ĉuranoviü, CEF, Podgorica Prof.dr Petar Ĉuranoviü, CEF, Podgorica Prof.dr Mihail Garevski, IZIIS, Skoplje Prof.dr Branislav Glavatoviü, CEF, Podgorica Doc.dr Armin Hadroviü, CEF, Mostar Doc.dr Tomaš Hanak, CEF, Brno Prof.dr Alen Harapin, FCEAG, Split Prof.dr Mustafa Hrasnica, CEF, Sarajevo Prof.dr Nenad Ivaniševiü, CEF, Belgrade Prof.dr Milorad Jovanovski, CEF, Skoplje Prof.dr Jelisava Kaleziü, CEF, Podgorica Prof.dr Miloš Kneževiü, CEF, Podgorica Prof.dr Ĉorÿe Laÿinoviü, FTS, Novi Sad Doc.dr Ivan Lovriü, CEF, Mostar Prof.dr Duško Luþiü, CEF, Podgorica Prof.dr Damir Markulak, CEF, Osijek Prof.dr Matjaž Mikoš, FCGE, Ljubljana

Prof.dr Dragan Milašinoviü, CEF, Subotica Prof.dr Zvonko Pavliþiü, FTS, Kosovska Mitrovica Prof.dr Radenko Pejoviü, CEF, Podgorica Prof.dr Zdenka Popoviü, CEF, Belgrade Prof.dr Živojin Prašþeviü, CEF, Belgrade Prof.dr Miroslav Premrov, CEF, Maribor Prof.dr Vlastimir Radonjanin, FTS, Novi Sad Prof.dr Miüko Raduloviü, CEF, Podgorica Doc.dr Marina Rakoþeviü, CEF, Podgorica Doc.dr Snežana Rutešiü, CEF, Podgorica Doc.dr Todorka Samardžioska, CEF, Skoplje Prof.dr Goran Sekuliü, CEF, Podgorica Prof.dr Milenko Stankoviü, FCEA, Banja Luka Prof.dr Boško Stevanoviü, CEF, Belgrade Doc.dr Biljana Šüepanoviü, CEF, Podgorica Doc.dr Ivana Štimac-Grandiü, CEF, Rijeka Prof.dr Zvonko Tomanoviü, CEF, Podgorica Prof.dr Milan Trivuniü, FTS, Novi Sad Prof.dr Mladen Uliüeviü, CEF, Podgorica Prof.dr Arsenije Vujoviü, CEF, Podgorica Prof.dr Ĉorÿe Vuksanoviü, CEF, Belgrade

CEF - Civil Engineering Faculty FTS - Faculty of Technical Science FCGE - Faculty of Civil and Geodetic Engineering FCEA - Faculty of Civil Engineering and Architecture FCEAG - Faculty of Civil Engineering, Architecture and Geodesy Institute for research and design in commerce & industry, Belgrade. All rights reserved.

Journal of Applied Engineering Science 10(2012)1

Golden sponsor INŽINJERSKA KOMORA CRNE GORE, Podgorica, Montenegro ATLAS GRUPA, Podgorica, Montenegro Sponsors CRNAGORAPUT, Podgorica, Montenegro DIREKCIJA ZA SAOBRAûAJ, Podgorica, Montenegro HI POLIEX, Berane, Montenegro KEMA, Puconci, Slovenia NOVKOL, Beograd, Serbia PERI OPLATE, Beograd, Serbia SIKA, Beograd, Serbia UNIVERZITET “SV. KIRIL I METODIJ”, Graÿevinski fakultet, Skoplje, FYR of Macedonia Donors GEOPROJEKT, Podgorica, Montenegro MINISTARSTVO ODRŽIVOG RAZVOJA I TURIZMA, Montenegro SODRA, Podgorica, Montenegro RZUP, Podgorica, Montenegro

Conference Friends ADING, Skoplje, FYR of Macedonia BEMAX, Podgorica, Montenegro CEMEX, Podgorica, Montenegro GEOBRUGG, Romanshorn, Switzerland GRALING, Nikšiü, Montenegro KINGSPAN, Beograd, Serbia KIPS, Podgorica, Montenegro MINISTARSTVO PROSVJETE I SPORTA, Montenegro SINTEK, Skoplje, FYR of Macedonia Organisational Board Civil engineering Faculty Podgorica Prof.dr Miloš Kneževiü, dipl.inž.graÿ. Mr Biljana Šüepanoviü, dipl.inž.graÿ. Mr Strahinja Pavloviü, dipl.inž.graÿ. Mr Mladen Gogiü, dipl.inž.graÿ. Goran Pavloviü, dipl.inž.el. Marija Jevriü, spec.sci.graÿ. Maja Lauševiü, spec.sci.graÿ. Mladen Muhadinoviü, spec.sci.graÿ. Miodrag Bujišiü, spec.sci.graÿ. Journal of Applied Engineering Science 10(2012)1

doi:10.5937/jaes10-1471

Paper number: 10(2012)1, 213, 1- 8

METHODOLOGY FOR ESTIMATING THE DEPENDENCE BETWEEN FORCE AND DEPLACEMENT - A VEHICLE CRASH CASE Dr Radomir Mijailoviü * University of Belgrade, Faculty of Transport and Traffic Engineering, Belgrade, Serbia Accident reconstruction software analyzed impact of vehicles considers usage of coefficient of restitution as a known quantity. In practice it is common that numerical value of coefficient of restitution is determined on basis of experience. Presence of error in its evaluation causes an essential error in output results. Thus, it is of exceptional importance to determine more precisely its numerical value. Improved solution of vehicle accident reconstruction software is presented in this paper. To archive that, in this paper was developed methodology which provides such analysis of impact process in which the coefficient of restitution becomes the result, and not input data. We have suggested new methodology for mathematical modeling of function dependence between force and displacement in a collision of vehicles. The compression process was approximated with piecewise linear function. The restitution process was approximated with linear curves. During process of restitution stiffness depends on maximum value of displacements during process of compression. The quality of the coherence between experimental data and mathematical function is quantified by residual sum of squares. Numerical examples are performed by usage of the obtained methodology. Keywords: methodology, reconstruction, vehicle, coefficient of restitution, error INTRODUCTION Coefficient of restitution represents a variable which substantially affects the output values which are obtained by analysis of collisions of bodies. Usually mechanical-mathematical models presume cognition of numeric values of coefficient of restitution. In practice, it is common that numerical value of coefficient of restitution is determined on basis of experience. This practice is particularly used in the case of inhomogeneous bodies of complex shape. One of the practical examples is the analysis of impact of vehicles. There are a few approaches in literature for defining the coefficient of restitution. The usual way is trough usage of characteristic velocities during the impact. In case of direct central collision of two bodies, coefficient of restitution is defined as ratio of absolute values of velocities at the end and the beginning of collision [21]. The coefficient of restitution can be defined using the graph of dependence between force and time. Coefficient of restitution is in this way defined as a ratio of impulse of restitution and impulse of compressive force [8, 15].

The coefficient of restitution is a function of velocity immediately prior to the collision. This connection is confirmed by experimental investigations of Zhang and Vu-Quoc [26]. By analysis of experimental results it may be concluded that during the displacement rise time, the influence of impact velocity on function dependence between force and displacement may be neglected. During the period of displacement decrease, the impact velocity has a non-negligible influence on dependence between force and displacement i.e. that curve dependence between force and displacement for a different value of impact velocity can not be obtained only by simple translation of curve graph. That is to say, the increase of impact velocity increases the slope of forcedisplacement curve. Ambrosio [1] suggests that it is necessary to include the relation between impact forces and displacements in the crash analysis of vehicles. Several software packages are available for the reconstruction of real vehicle accidents. The PC-Crash software is a common commercial tool for reconstructing road accidents [4].

* Faculty of Transport and Trafﬁc engineering, Vojvode Stepe 305, 11000 Belgrade, Serbia; radomirm@sf.bg.ac.rs

Dr Radomir Mijailoviü - Methodology for estimating the dependence between force and deformation - a vehicle crash case

It uses a number of important parameters for vehicle model. Most of them are given by default, within the software, and the results of the accident reconstruction are very sensible to their variations. The coefficient of restitution is one of them, used as the input data, and usually taken arbitrary. Based on currently published papers a necessity may be noticed for upgrade of old and defining new impact models. This is also one of directions of development in dynamics of multibody systems [20]. To that aim, a methodology is developed in this paper which provides such analysis of impact process in which the coefficient of restitution becomes the result, and not input data. We suggest that accident reconstruction software must have database with vehicles functions of dependence between force and displacement. The incomplete information about vehicle characteristics can cause incapability of accident reconstruction. Determining the adequate functions dependence between force and displacement of vehicles must to represent one of the major tasks in the analysis of impact of vehicles [6]. Their determination influence importantly on reduction of error in the output result of the analysis of impact process. There are a few approaches in literature for defining the functions dependence between force and displacement of collisions vehicles. Usually mechanical-mathematical model presume that the curve dependence between force and displacement can be described with two linear curves (one curve for compression process and one curve for restitution process) [16]. In this case force can be described in form of multiplication of displacement and appropriate stiffness. The difficulty lays in determining the stiffness during the processes of compression and restitution of vehicles. The approximate expression for the processes of compression may be found in the literature [8, 14]: (1) where mv – vehicle mass, v0 – impact velocity, max – maximal displacement of vehicle. To my knowledge the analytical expression for

exact determination of stiffness during the restitution processes is not yet available. Usually in practical defining the previous stiffness was calculated using coefficient of restitution. What is the problem? Usually mechanical-mathematical models presume cognition of numeric values of coefficient of restitution. In practice, it is common that numerical value of coefficient of restitution is determined is based on experience. The error present in determination of the value of coefficient of restitution has a considerable influence on the outcome results of the collision analysis and determination of stiffness during the processes of restitution. Does the stiffness during the processes of compression have significant correlation with the vehicle mass? The Insurance Institute for Highway Safety has evaluated the crashworthiness of more than 120 new vehicle models. The data indicate that there were no significant correlation between mass, front-end length, and stiffness to structural performance in the offset test [13]. The force displacement curves for the vehicle models can also be approximated as piecewise linear with three regions: before buckling has started, after buckling has started and when the occupant compartment starts to deform [24]. Elmarakbi and Zu [5] presume that the curve dependence between compression force and displacement can be described using piecewise linear functions but with two regions. Usually authors presume that the force has zero value at the moment when the appropriate displacement has zero value. However, there are other approaches to determining the functions dependence between force and displacement of vehicles. McCoy and Lankarani [12] presume that the force have value greater than zero at the initial moment of vehicle’s crash when the displacement has zero value. Macmillan [11] stated that what is needed is an analytical expression for the force upon displacement curves that satisfy the following criteria: • it must be simple enough to be manipulated; • it must satisfy the boundary conditions found in curves from impact tests; • it must correlate well with known test cases and hence justify its use to predict the outcome over a range of unknown examples; • it must be capable of representing the behavior of vehicles with different crush charJournal of Applied Engineering Science 10(2012)1, 213

Dr Radomir Mijailoviü - Methodology for estimating the dependence between force and deformation - a vehicle crash case

acteristics with changes to a small number of variables. Stiffness is different for different surfaces of vehicles. One such example is a frontal underride collision [2]. The experimental data for the crash tests may be found in literature. Most of the tests were made at about 60 km/h [7, 27]. It also can be found papers [9, 22, 25] which presented the experimental data for the same vehicle at different impact velocity. In literature great attention has been dedicate to dynamic behavior of vehicles [3, 17, 18]. Based on currently published papers I have concluded that there is necessity for deﬁning new functions dependence between force and displacement of vehicles. This paper’s objective is to suggest new methodology for mathematical modeling of function dependence between force and displacement in a collision of vehicles. This methodology and function dependence between force and displacement should be simple enough for practical implementation. The purpose of the methodology is reduction of error in the output results of the analysis of vehicle impact process too. The advantage of this methodology is also its easy and fast applicability. From the economic point of view this means lower implementation costs. Analyzing literature it can be noticed that the case of described previous function with two linear curves is often used. Analyzing experimental data, we have concluded that the linear approximation does not describe graph of dependence between force and displacement on satisfactory way. Therefore, we have approximated the compression process with piecewise linear functions. The restitution process was approximated with linear curves. During process of restitution stiffness (coefﬁcients of proportionality) depends on maximum value of displacements during

process of compression. The quality of the coherence between experimental data and mathematical function is quantiﬁed by residual sum of squares. METHODOLOGY FOR ESTIMATING THE DEPENDENCE BETWEEN FORCE AND DISPLACEMENT The function force–displacement The function dependence between force and displacement is determined by the following expression: (2) where Fk – the function dependence between compression force and displacement, Fr – the function dependence between restitution force and displacement, – displacement of vehicle. In this paper the function dependence between compression force and displacement of vehicles is analyzed for piecewise linear functions with one and more than one regions (n regions) (Figure 1).

Figure 1. Dependence between force and displacement

Function of dependence between compression force and displacement is given by expression:

(3)

where (i=1,...,n-1) – maximum value of displacements during process of compression for region ‘’i’’ (experimental data), ci, (i=1,...,n) – coefﬁcients of proportionality A,i,

Journal of Applied Engineering Science 10(2012)1 213

during process of compression for region ‘’i’’. Coefﬁcient of proportionality (c1 for i=1) in literature is known as the coefﬁcients of stiffness. Therefore, in the following text we will use notion stiffness for ci.

Dr Radomir Mijailoviü - Methodology for estimating the dependence between force and deformation - a vehicle crash case

It is necessary to define following unknown parameters ci and . A,i Experiment data are necessary to obtain the function dependence between force and displacement. In that sense experiment consists of impact of vehicles into an absolutely rigid barrier. To gain better results experiment must be repeated for different values of impact velocity [9, 10, 22, 23, 24, 25]. The experiment may be realized through crash test or by finite element method based computer program. The advantage of this methodology is also its easy and fast applicability. From the economic point of view this means lower implementation costs. Respecting legal terms, all new car models must pass crash tests before they are sold. But legislation provides a minimum statutory standard of safety for new vehicles, it is the aim of Euro NCAP to encourage manufacturers to exceed these minimum requirements [28]. Crash tests must be realized for all vehicles. Addition economic investment is necessary for process of crash test results. Vehicle manufacturer develop finite element models for their vehicles. Their addition assignment should be utilization of the vehicle finite element model using computer program. Minimum addition economic investment is also requested. The residual sum of squares The quality of the coherence between experimental curves and mathematical functions is quantified by residual sum of squares. Why was chosen just residual sum of squares? The function of dependence between compression force and displacement done by the minimization of a residual sum of squares also has minimum error using it in determination work during compression process. A minimal error in determining the work also results in a minimal error in determining coefficient of restitution. Residual sum of squares (RSS) measures the deviations of experimental from their predicted values: (4) where Fk,exp,i is the ith experimental value of the variable to be predicted, and Fk,i is the predicted value of Fk,exp,i, nk - represents number of experimental values.

The determination of unknown parameters The determination of unknown parameters was performed by the minimization of a residual sum of squares. We concluded that the analytical solution of minimization of the function (4) can’t be determined for n 1 (3) by application of some optimization methods [17]. Therefore, the unknown parameters (ci, A,i) should be numerically determined. The restitution process is significantly shorter than compression process. Using more complex functions error would not be significantly reduced. On the other hand they would be more complicated for practical implementation. Therefore, the restitution process was approximated with linear curve (Figure 1). Slopes of restitution lines are a function of maximum value of displacement during process of compression ( ). Bm Functions of dependence between restitution forces and displacement are given by expression: (5) where – maximum value of displacements during Bm process of compression, bm – coefficients of proportionality (stiffness) during process of restitution for Bm. The coefficients of proportionality during process of restitution (bm) depend of maximum values of displacements during process of compression ( Bm). Therefore, we have defined the coefficients of proportionality bm as function dependence of maximum value of displacements during process of compression ( Bm). The coefficients of proportionality during process of restitution (bm) can be determined from the conditions: during restitution process work determined by experimental data (Ar,m,exp) is equal to work determines using approximate functions (5) (Ar,m,approx): (6) Numerical value of work Ar,m,exp can be determined by using experimental data for the same vehicle characteristics and for different values of impact velocities. The analysis output data are two numerical values: Bm and Ar,m,exp. Journal of Applied Engineering Science 10(2012)1, 213

Dr Radomir Mijailoviü - Methodology for estimating the dependence between force and deformation - a vehicle crash case

Numerical value of work Ar,m,approx is given in following form:

• •

(7) • Displacement of vehicle in the instant of separation ( Cm) may be determined from the condition: (8) The displacement can be determined by Cm substitution of (5) into (8): (9) Finally, stiffness bm can be determined by applying equations (5), (6), (7) and (9): (10) The stiffness bm depends on the displacement (10) Bm . The next step of the analysis should be finding the equation that will approximate the dependence between bm and Bm on the best way. Previous equation should be determined using some software for curve fitting analysis. The curve fitting analysis is necessary because the experimental data have results for the different (but not all) values of impact velocity. For example, we may be having experimental data for impact velocities: 10, 20, 30, 50, 70 and 100 km/h. Accident reconstruction software may be needed the stiffness bm that should be calculated using experimental data for example for impact velocity of 57 km/h. Finally, the methodology for mathematical modeling of function dependence between force and displacement is given in following form: • collecting experimental data for different values of impact velocity; • the determination of unknown parameters (ci, ) by the minimization of a residual A,i sum of squares; • to determine number of regions (n) for piecewise linear function of dependence between compression force and displacement; • to write function of dependence between compression force and displacement (3); • the determination of works Ar,m,exp for different values of Bm; Journal of Applied Engineering Science 10(2012)1 213

•

the determination of stiffness bm for different values of Bm; to determine equation that approximate dependence between bm and Bm on the best way; to write function of dependence between restitution force and displacement (5); ﬁnally, we can write the function dependence between force and displacement (2).

Vehicle doesn’t have the same functions dependence between force and displacement (2) for different point of collisions vehicles. For example, frontal, rear and side vehicle area does not have the same values of stiffness. That is why NCAP is performing different crash tests. Therefore, suggested methodology must be applied for different vehicle’s areas. RESULTS ANALYSIS The ﬁrst key question that arises is: does linear approximation describe dependence between compression force and displacement better than piecewise linear function? The determination of unknown parameters was performed using experimental data given in papers [9, 10, 22, 23, 24, 25]. The experimental data from previous papers was derived using the case of direct central impact of vehicles into an absolutely rigid barrier. Quality comparison between two piecewise linear functions with subsequent number of regions (i.e. n and n+1) may be presented by comparing their RSS relative discrepancy: (11) The same calculation was used for comparing two functions with n=1 where stiffness obtained using equations (1) and (4):

(12) The relative discrepancy of the compression force for different values of regions was determined based on the experimental data obtained from 14 vehicles (Table 1). Results of the analysis show that the minimal relative discrepancies are appeared between piecewise linear functions dependence of compression force upon displacement with three and four regions.

Dr Radomir Mijailoviü - Methodology for estimating the dependence between force and deformation - a vehicle crash case

The relative discrepancy RSSn=3 n=4, for the most vehicles, tend to zero. The other relative discrepancies have bigger values. Looking at obtained results it may be noticed that the rela-

tive discrepancy RSSn=2 n=3 is between 1.5 and 28%. The relative discrepancy RSSn=1 n=2 is between 21.6 and 200.4%. The relative discrepancies for n 4 tend to zero.

Table 1. Relative discrepancy ( RSS) of the compression force for different values of regions and for various vehicle models RSSn=1(Eq.1 Eq.4)

RSSn=1 n=2

Chrysler Neon [24]

5.7

42.4

Dodge Caravan [24]

51.2

Ford Escort [9]

82.8

Ford Escort [22]

11.4

Vehicle

RSSn=2 n=3

RSSn=3 n=4

Ford Explorer [24]

23.3

1.1

21.6

0.2

166.1

14.9

122.1

3.7

0.1

169.9

1.5

2.7

Ford Taurus [24]

25.1

446.8

Geo Metro [24]

1.2

11.9

Honda Accord [24]

94.5

200.4

23.4

Vehicle 1 [23]

3.1

87.2

18.6

Vehicle 2 [23]

0.7

104.6

8.9

Vehicle 3 [23]

9.4

90.2

6.8

Vehicle 4 [23]

8.4

142.9

4.2

Vehicle 5 [23]

0.1

102.8

6.7

492.1

175.9

4.5

Yugo [10]

The approximate expression for the compression stiffness (1) is often used in practice. By analysis of RSSn=1(Eq.1 Eq.4) (Table 1) it can be concluded that this expression doesn’t have satisfactory results. Therefore, we propose to use piecewise linear functions dependence between compression force and displacement with three regions. In the following text we will present results of usage of methodology that we have proposed. We have used experimental data obtained for Ford Escort [22]. Compression stiffness (ci) and displacement ) for linear functions dependence between ( A,i compression force and displacement with three regions are:

The stiffness bm using equation (10) have following values:

(14)

The stiffness bm for Ford Escort were approximated using the results (14) by curve ﬁtting analysis: (15) By applying expressions (3), (5), (13) and (15) the function dependence between force and displacement (2) for Ford Escort obtains its ﬁnal form:

(13)

(16)

Journal of Applied Engineering Science 10(2012)1, 213

Dr Radomir Mijailoviü - Methodology for estimating the dependence between force and deformation - a vehicle crash case

where is the maximum value of displaceB ments during process of compression.

Figure 2. Dependence between coefﬁcient of restitution and impact velocities for Ford Escort

Consider an accident where Ford Escort has crashed into an absolutely rigid barrier. The software packages for the reconstruction of real vehicle accidents require usage coefficient of restitution as the input data. The purpose of the model presented in this paper is reduction of error in the output results of analysis of vehicle impact process. The next key question that arises is: how big is the error that is made using the model presented in this paper? Therefore, coefficient of restitution (kapprox) of impact of Ford Escort into an absolutely rigid barrier is calculated using the methodology for mathematical modeling of function dependence between force and displacement presented in this paper. The results were presented on the Figure 2. The coefficient of restitution calculated using appropriate experimental data (kexp) was also presented on the Figure 2. By analyzing Figure 2 it can be concluded that the errors have minimal values. The absolute error of coefficient of restitution has value in the range from 0.003 to 0.018. CONCLUSIONS The model developed in this paper which provides such analysis of impact process in which the coefficient of restitution becomes the result, and not input data. In this paper was developed methodology that can be used in analysis of impact process in which the coefficient of restitution becomes the result, and not input data. In this paper is suggested new methodology for mathematical modeling of function dependence between force and displacement in a collision of vehicles. This methodology and function dependence between force and displacement should Journal of Applied Engineering Science 10(2012)1 213

be simple enough for practical implementation. The purpose of the methodology is reduction of error in the output results of the analysis of vehicle impact process too. The advantage of this methodology is also its easy and fast applicability. From the economic point of view this means lower implementation costs. Further investigations may be directed towards establishing an analytical model for analysis of three dimensional vehicles collisions with the coefﬁcient of restitution as the end result. Since the three dimensional collision produces complex motion, future model should take into account the friction. Such analysis of collision processes would contribute to the analysis of trafﬁc accidents. ACKNOWLEDGEMENT The research work was supported by the Ministry of Science and Technological Development of the Republic of Serbia (Grant No. 36010). REFERENCES 1) Ambrosio, J. (2005). Crash analysis and dynamical behaviour of light road and rail vehicles. Vehicle System Dynamics, Vol. 43, No. 6–7, pp. 385–411 2) Boggessa, B.M., Morrb, D.B., Petermanb, E.K., Wiechel, J.F. (2010). Experimental evaluation of underride analysis techniques and empirical validation of a new analytical technique. Accident Analysis and Prevention, No. 42, pp. 140-152 3) Demiü, M. (2005). A contribution to design of semiactive vehicle suspension system. Journal of Applied Engineering Science (Istraživanja i projektovanja za privredu), 9, pp. 7-16 4) Depriester, J.P., Perrin, C., Serre, T., Chalandon, S. (2006). Comparision of several methods for real pedestrian accident. (available on-line: www.mathlab.mtu.edu) 5) Elmarakbi, A., Zu, J. (2007). Mathematical modelling of a vehicle crash with emphasis on the dynamic response analysis of extendable cubic nonlinear dampers using the incremental harmonic balance method. Proc. IMechE Part D: J. Automobile Engineering, Vol. 221, pp. 143 – 156 6) Harmati, I.A., Rovid, A., Varlaki, P. (2010). Application of LPV Type Force Model in Vehicle Crash Dynamics. Proceedings of the

Dr Radomir Mijailoviü - Methodology for estimating the dependence between force and deformation - a vehicle crash case

9th WSEAS International Conference on Applications of computer engineering 7) Huibers, J., de Beer, E. (2001). Curent front stiffness of European vehicles with regard to compatibility. International Technical Conference on the Enhanced Safety of Vehicles (ESV), Amsterdam, The Netherlands 8) Jankoviü, A., Simiü, D. (1996). Vehicle safety, monograph. DSP-mecatronic, Kragujevac 9) Kerkhoff, J.F., Husher, S.E., Varat, M.S., Busenga, A.M., Hamilton, K. (1993). An investigation into vehicle frontal impact stiffness, BEV and repeated testing for reconstruction. Society of Automotive Engineers International Congress, Detroit, Michigan, SAE Paper 930899 10) Kostiü, S., Bogiüeviü, D., Laliü, Z. (2007). Improving of methods for determination collision speed of vehicles based on their deformations. XXI International JUMV Automotive Conference Science and Motor Vehicles, Paper NMV0720S 11) Macmillan, R.H. (1983). Dynamics of vehicle collisions, Interscience Enterprises Ltd 12) McCoy, M.L., Lankarani, H.M. (2006). Determination of the crush stiffness coefﬁcients of a typical aftermarket frontal protective guard used in light trucks and vans with comparisons between guard stiffness and frontal vehicle crush coefﬁcients. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, Vol. 220, pp. 1073 – 1084 13) Nolan, J.M., Lund, A.K. (2001). Frontal offset deformable barrier crash testing and its effect on vehicle stiffness. International Technical Conference on the Enhanced Safety of Vehicles (ESV), Amsterdam, The Netherlands 14) Nusholtz, G.S., Xu, L., Shi, Y., Domenico, L.D. (2005). Vehicle mass, stiffness and their relationship. 19th ESV, Paper number 050413 15) Oztas, A.G. (1999). Application of Impulse Momentum Theory to Vehicle Collisions. Turkish Journal of Engineering and Environmental Science, 23, pp. 455–464 16) Pawlus, W., Karimi, H.R., Robbersmyr, K.G. (2011). Mathematical modeling of a vehicle crash test based on elasto-plastic unloading scenarios of spring-mass models. The International Journal of Advanced Manufacturing Technology, 55, pp.:369–378

17) Radisavljeviü, M., Demiü, M. (2004). A contribution to car body design of a passanger motor vehicle through improved vibro-acoustic parameters. Journal of Applied Engineering Science (Istraživanja i projektovanja za privredu), 6, pp. 25-34 18) Sekuliü, D., Dedoviü, V. (2008). Simulation of the oscillatory behavior of buses equipped with a classic and active suspension system. Journal of Applied Engineering Science (Istraživanja i projektovanja za privredu), 20, pp. 23-32 19) Šelmiü, R., Cvetkoviü, R., Mijailoviü, R. (2006). Optimization of cross-section in structures. monograph, The Faculty of Transport and Trafﬁc Engineering, Belgrade 20) Schiehlen, W. (2007). Research trends in multibody system dynamics. Multibody System Dynamic, 18: 3–13 21) Stronge, W.J. (2004). Impact mechanics. Cambridge University Press 22) Steffan, H., Geigl, B.C., Moser, A., Hoschopf, H. (1998). Comparison of 10 to 100 km/h rigid barrier impacts. Paper No. 98-S3-P-12, (www-nrd.nhtsa.dot.go) 23) Subramaniam, K., Verma, M., Nagappala, R., Tedesco, R., Carlin, L. (2007). Evaluation of stiffness matching concepts for vehicle safety improvement, Enhanced Safety of Vehicles Conference, Lyon, France, Paper Number 07-0112 24) Van der Zweep, C.D., Jenefeldt, F., Thomson, R. (2002). Improvement of vehicle crash compatibility through the development of crash test procedure. Project number – GRD2-2001-50083, 1998-2002 25) Varat, M.S., Husher, S.E. (2000). Vehicle impact response analysis through the use of acceleration data. SAE Tech. Paper 200001-0850 26) Zhang, X., Vu-Quoc. L. (2002). Modeling the dependence of the coefﬁcient of restitution on the impact velocity in elasto-plastic collisions, International Journal of Impact Engineering, 27, pp. 317–341. 27) www.nhtsa.dot.gov 28) www.euroncap.com Paper sent to revision: 17.02.2012. Paper ready for publication: 23.03.2012.

Journal of Applied Engineering Science 10(2012)1, 213

doi:10.5937/jaes10-1523

Paper number: 10(2012)1, 214, 9 - 14

COST OF ACTIVITIES IN PUBLIC UTILITY FLEETS Mr Aleksandar Manojloviü* University of Belgrade, Faculty of Transport and Traffic Engineering, Belgrade, Serbia Mr Olivera Medar University of Belgrade, Faculty of Transport and Traffic Engineering, Belgrade, Serbia Jelena Trifunoviü University of Belgrade, Faculty of Transport and Traffic Engineering, Belgrade, Serbia Dr Katarina Vukadinoviü University of Belgrade, Faculty of Transport and Traffic Engineering, Belgrade, Serbia With each day more present tendencies in business systems to focus on core processes, the position of the transport activity and the vehicle fleet within is imperatively examined: is it an activity creating an added value to the core system or a mere unavoidable cost-maker. A decisive role is attributed to the manner of defining the vehicle utilisation and the way of realisation of fleet related activities. Therefore, a link between activity based costing and the transport department (subsystem) has been presented in this paper. This link is especially important in public utility fleets. The legislation adopted in this respect announces changes in the corporate environment and conditions of public utility companies. As large fleets represent an integral part of the public utility systems, new conditions will cause a need for fleet cost allocation improvement, and therefore activity based costing. Will this engender the need for the creation of city fleets? Keywords: fleet management, cost efficiency, fleet activities, activity based costing INTRODUCTION Road transport fleets except in their core activity - public transport, are present in majority of other activities as well. In different forms of ownership, they are owned by companies, state authorities and institutions, complex public systems and other organisations. Total number of vehicles in such fleets is largely greater than in public transport fleets. Besides state authority and commercial fleets an important place is given to complex public systems’ fleets, i.e. large public companies [9]. They denote public utilities, activities of electricity, thermal power and gas production and distribution. In larger and more developed countries those fleets are composed of several thousands of vehicles while in our country they consist of few dozens to several hundreds, and very few of more than thousand vehicles. Those systems’ fleets are extremely heterogeneous by structure - composed mainly from passenger cars, light and heavy goods vehicles, as well as special vehicles, of different makes and different construction-operational characteristics. The worth of vehicles in fleets of certain public companies is very important.

Fleet Department has the task to assure the transport needs of an organisation on certain territory. In complex public systems the task of the transport department is to effectively support the core processes, which means to assure the transport needs consistent with requested volumes and quality, cost efficient usage of vehicles, vehicle availability, vehicle maintenance as well as to minimize their negative environmental impact. The fleet-transport department organisation depends on the organisation of the parent entity, which incorporates it, and on the fleet size.In this paper the link between Activity Based Costing and the transport department has been demonstrated. That link is especially important in Public Utility Fleets. The legislation adopted in this respect announces changes in the corporate environment and conditions of public utility companies. As large fleets represent an integral part of the public utility systems, new conditions will cause a need for fleet cost allocation improvement, and therefore activity based costing.

* Faculty of Transport and Trafﬁc engineering, Vojvode Stepe 305, 11000 Belgrade, Serbia; a.manojlovic@sf.bg.ac.rs

Mr Aleksandar Manojloviü etc. - Cost of activities in public utility ﬂeets

REASONS TO USE ACTIVITY BASED COSTING In practice there are three reason to use the system of cost accounting: • •

•

the obligation to deliver the ﬁnancial reports, management needs information for the cost assessment of activities’, services’ and users’, management requires information on process efﬁciency.

Although those requests have always existed, only recently it has been observed a significant growth of interest for the implementation of Activity based costing [3,4]. Direct costs are rather straightforward to understand and compensate. Overhead and/or indirect costs are significantly more difficult to define and allocate. Those costs show a growing trend in current business conditions. Therefore it is indispensable to implement a more complex cost accounting system. Activity based costing system allows to determine more precisely the state of a business system by better cost monitoring and allocation. As such, it

could be implemented as an additional tool for strategic decision-making as well as a business process state indicator, permitting more efficient resource allocation and, therefore, cost reduction.Essentially, a suitably defined Activity based costing system represents a financial plan of the entity defining activity costs upon products, services and users. The need for such systems appears in organisation systems of complex structures. In an organisation system owning a homogeneous fleet where vehicles approximately travel the same annual mileage, where the users’ attitude toward vehicle usage and technical condition is nearly at the same level, and where all vehicles have similar costs this method is pointless. The overhead of each service and for each user would, in such case, be identical and cost allocation would be straightforward. Since in reality fleets are mostly heterogeneous, as well as vehicle miles travelled, their operation time varies, and users differently take care of the vehicle condition - it will certainly mean that some vehicles and specific vehicle groups will have different costs.

Figure1 :Example of one Public Utility Company organisation

In such cases, the need for activity based costing in terms of allocation of actual costs that should be charged to different users and for different services offered by the transport organisational unit (transport department) is obvious. The organisation of a Public utility company and the position of the Transport department within this organisation chart are shown in Figure 1. 10

In accounting, the costs are displayed by categories of costs, such as Salaries, costs of Assets, Utility costs and so on, and not upon activities or functions, which certainly reveal the practicality of such cost breakdown method. Cost categories could be allocated to speciﬁc activities (Table 1), which represents a substantial difference in cost breakdown method. Journal of Applied Engineering Science 10(2012)1, 214

Mr Aleksandar Manojloviü and etc. - Cost of activities in public utility ﬂeets

Table 1: Difference in cost breakdown methods Accounting cost breakown

Activity based costing cost breakdown

Salaries

610.000€ Fleet Management

410.000€

Costs of Assets

230.000€ Fuel Management

25.000€

Utility costs

160.000€ Fleet Maintenance Management Driver Training

Total

The advantages of Activity based costing implementation could be really emphasised especially when the entity is engaged in giving complex and varied services, such as in most of Transport department activities, so as to deﬁne four phases [1,8] of this system implementation: • • • •

90.000€

1.000.000€

ACTIVITY BASED COSTING IN FLEET MANAGEMENT

identiﬁcation of activities, determination of each activity’s cost, determination of service users and types of services offered by Transport department, selection of activity cost drivers that associate activity costs to services and users.

Identiﬁcation of activities Activity based costing is focused on the question why are entities spending the funds. They spend their funds in order to accomplish key activities [2]. The ﬁrst step in this system development is

475.000€ 1.000.000€

determination of all those activities that must be accomplished and with what resources. Definition of activities, being the first step in the development of the system, equally representing the system foundation, should be realised with particular caution. From the point of Transport department, as an illustration of the problem, following activities could be potentially selected (Table 2): • fleet management, • fuel management, • fleet maintenance management, • driver training, etc. Depending on the fleet operation complexity, the activities defined in this way may not be sufficiently accurate, so they could be additionally subdivided. In this phase, two problems are noticed. The first being too general definition of activities, in opposite to the second - too detailed definition, which indicates the complexity of this step.

Table 2: Fleet Department Activities Fleet Management

Fuel Management

Fleet Maintenance Management

Driver Training programme realisation

Vehicle operation planning and monitoring

Fuel supplying

Maintenance interventions planning

Driver operation monitoring and control

Vehicle procurement

Fuelling station maintenance

Preventive maintenance programme monitoring and control

Driver training realisation

Planning of transport demand accomplishment

Bills payment

Billing for repair

Driver stimulation monitoring and control etc.

Used vehicles’ write-offs and sales etc.

Dealing with fuel cards etc.

monitoring and control of warranty period etc.

Determination of activity’s cost This phase involves determination of spending of funds for salaries, assets, utilities and others, as well as linking these costs to the activities identiﬁed in the previous phase by way of cost Journal of Applied Engineering Science 10(2012)1,214

drivers. This is a complicated process and it must be done throughout the entire organisation system, and may be simpliﬁed by: •

interviewing employees in order to determine the share of employees’ working time dedi-

Mr Aleksandar Manojloviü etc. - Cost of activities in public utility ﬂeets

cated to specific activity or share of resources spent on a particular purpose, • using existing information, if possible (e.g. if a sophisticated employees working time recording system is in place, particular activities that the employees have been engaged on could be established), • assessing, if no other data is available, provided that the assessment should be adjusted if the exact data become available further on. For example, existing data on consumed fuel could be used for assessing indirect costs that burden each user. Cost determination process can be very complex, therefore in complex organisation structures this process automation is indispensable. Determination of service users and types of services In this phase, the reason why organisation systems are linked to activities is determined. In terms of this section’s issues, first the types of services offered by the Transport department and their users are defined. Subsequently, the share of particular service types and users is assessed in total amount of performed activities. Transport department may provide services to internal or external users. Internal users may be individual employees or organisational units of the parent entity, meanwhile external users may be all other legal or natural persons. Services provided to internal users are fleet operation management, fuel supply, vehicle maintenance, driver training, carriage, etc. External users may require carriage services and certain services specific to specialised vehicle superstructure (waste materials removal, cargo lifting and so on). Selection of activity cost drivers The final phase combines all previous, and within the selection of activity cost drivers is performed, which will link activity costs to services and to users that generate those costs. For example, “fleet maintenance management” activity cost driver may be employees’ working hours or utilisation time of specialised equipment used for maintenance interventions on certain vehicles and for particular users. Recorded time may be associated with the activity “fleet maintenance management”. By using this cost driver, the activity “fleet maintenance management” is linked to particular services or users through employees’ or equipment’s working hour price. Equally, “fuel

management” activity cost causer/driver may be number of invoices for refuelling on external fuelling station or number of fuel consumption report. However, a special care should be given to the implementation of this phase because along with increasing the accuracy increase also the costs of calculations. Determination of the optimum ratio of accuracy costs and calculation costs is one of the most important elements for this system implementation. The Activity based costing system employs a process that allowing resource cost allocation to activities and their linking by means of activity drivers to the cost objects. Information obtained from this system may be used for performance measurement over activities and business process. Performance data may be used for better decision-making related to the process improvement [5]. Entire information may be applied to the cost planning process (budgeting). Regarding fleets, complexity and variety of activities is resulting from different vehicle operation practices, in other words different services for internal and external users. Future research trends in this field could consist in improving the method for services’ cost determination, related to determining activities’ unit costs for supplied services. ACTIVITY BASED INDIRECT COST ALLOCATION METHOD Organisational units for transport in our public companies can be considered as small entities with a limited number of employees. Therefore, the proposed method represents a modified method suitable for small production companies with three products in the production programme [10]. Since Transport department provides services, the modification was absolutely necessary. The proposed method for indirect cost allocation onto vehicles, services and fleet users consists of six steps [7]: 1st step - Identifying Main Activities In this step, essential activities of the Transport department are researched and determined as well as cost objects (vehicle groups, users, types of services). 2nd step - Determining Costs Categories This step consist of determining categories, i.e. types of costs that should be allocated to vehicle groups, users and types of services. Journal of Applied Engineering Science 10(2012)1, 214

Mr Aleksandar Manojloviü and etc. - Cost of activities in public utility ﬂeets

3rd step - Determining Dependence of Costs and Activities In this step the activities causing particular cost categories are to be identiﬁed. If dependence is determined, it should be indicated within the matrix of costs’ and activities’ dependence. Matrix columns represent cost categories, while activities determined in the 2nd step are shown in rows. If the activity i causes costs from category j, it should be referred in the cell i, j. 4th step - Identifying Expenditures on Resources In case of challenging data collection (or if they are impossible to collect), the share of resources spent on certain activity may be determined by expert assessment or by survey (interview). In the matrix of costs’ and activities’ dependence are input the percentages referring to the degree of resources spent by each activity. 5th step - Determining Activities Costs Once determined the percentage (share) of activities in resources’ “expenditures”, the following step is to calculate costs of activities, which can be expressed as follows: where: TA (i) – total costs of activity i

M – total number of cost categories Cost category (j) – amount of costs of category j ZAT (i,j) – value from the matrix of costs’ and activities’ dependence. 6th step - Cost Assignment to Cost Objects In this step are determined the activity cost drivers, followed by cost assignment to activities by means of those drivers, in other words using fees for activities’ “expenditures”. The described method is shown on Figure 2, and may be implemented by means of standard software applications for operations with tables. The proposed method, incorporating direct costs, will provide the actual vehicle unit costs (€/km) that designate the vehicle utilisation rate. According to the determined cost structure is obtained a foundation for: •

• •

management of fleet cost efficiency, involving also tax management and environmental protection [6], more efficient vehicle utilisation by users, decision-making regarding activities that

Journal of Applied Engineering Science 10(2012)1,214

should be performed by the Transport department. This method may be used as an analytical tool for selection of ﬂeet activities that should be subcontracted and those that should be kept.

Figure 2: Procedure for transport indirect allocation

CITY FLEET Determined activities of public utility companies’ fleets indicate a need to analyse the possibility for integrating those activities on the territory of cities and municipalities. Such activities initiate the creation of an organisational unit named City fleet, integrating fleets of all public utility companies and authorities on the territory of the city or of the municipality. In the Republic of Serbia and surrounding countries, those fleets would consist from several dozens to several hundreds of vehicles, while in the largest cities even several thousands of vehicles. It is obvious that formation of such a separate organisational unit would increase fleet cost efficiency, which will positively reflect the budget of municipalities and cities. Activity based costing is a convenient tool for decision-making upon City fleet creation. City fleet, organisational unit incorporating fleets’

Mr Aleksandar Manojloviü etc. - Cost of activities in public utility ﬂeets

activities of all companies and authorities financed from the local government budget, provides a good basis for improved vehicle utilisation in cities and municipalities. CONCLUSIONS Costs of activities provide powerful insight on fleet resources utilisation effectiveness and on the extent of contribution of important activities within costs of services. Such information is a key for decision-making on potential restructuring of the Transport department (organisational unit) or outsourcing certain activities from Transport’s domain. Since existing cost accounting systems do not provide adequate basis for cost management, it is indispensable to introduce a new costing system involving certain financial investments and time-consuming effort. Activity based costing require organisation changes, wide acceptance by employees, investments in software and computer equipment, ata collection equipment and so on. Despite the fact that activity based costing was “successfully” implemented in many large companies in developed countries, there are no guarantees that the investments will be returned soon. Using the proposed method for cost assessment, the risk of transition from the traditional cost accounting system to the new activity based costing may be significantly reduced. Since it does not require substantial investments in sophisticated data collection systems and serious organisational changes, the proposed method can be considered suitable for implementation in large fleets of our public companies, as an intermediate step for the gradual implementation of the activity based costing system, whereas the assessed data will be replaced by actual data. ACKNOWLEDGEMENT This paper is based on the project “Development of the Model for Managing the Vehicle Technical Condition in order to Increase its Energy Efficiency and Reduce Exhaust Emissions”, which is supported by the Ministry of Education and Science of the Republic of Serbia.

REFERENCES 1) Blocher J., Chen H., Lin W. (2005) Cost Management: A Strategic Emphasis, Second Edition, McGraw-Hill, New York, USA. 2) Cooper R., Kaplan R. (1998) How Cost Accounting Distorts Product Costs, Management Accounting, 20-27 3) Johnson H. (1987) The Decline of Cost Management: A Reinterpretation of 20th-Century Cost Accounting History, Journal of Cost Management, 128 (1), 5-12 4) Johnson H. (1991) Activity-Based Management: Past, Present, and Future, The Engineering Economist, 36 (2), 219-238 5) Kaplan R., Cooper R. (1998) Cost and Effect: Using Integrated Cost Systems to Drive Profitability and Performance, Harvard Business School Press, Boston 6) Kaplanoviü S., Ivkoviü I., Petroviü J. (2007). Tax on motor fuels in transportation sector: Instrument for environment protection, Istraživanja i projektovanja za privredu, 5 (16), pp 39-46 7) Manojloviü A. , (2006) Contribution to the Development of the Methodology for Fleet Cost Efficiency Management, Mr. Thesis, Faculty of Transport and Traffic Enginering, Belgrade, 2006. In Serbian 8) Miliüeviü V. (2005) Strategic accounting (in Serbian), Faculty of Economics, Belgrade, 2005. 9) NAFA (National Association of Fleet Administrators) (2002), NAFA´s Reference Book, New Jersey, USA 10) Roztocki, N., Valenzuela J., Porter J., Monk R., Needy K. (1999) A Procedure for Smooth Implementation of Activity Based Costing in Small Companies, Proceedings from the 1999 ASEM National Conference, American Society for Engineering Management. Paper sent to revision: 22.02.2012. Paper ready for publication: 22.03.2012.

Journal of Applied Engineering Science 10(2012)1, 214

doi:10.5937/jaes10-1659

Paper number: 10(2012)1, 215, 15 - 20

AN EXAMPLE OF ANN MODELLING APPLICATION IN PATCH LOADING PROBLEMS OF STEEL STRUCTURES Dr Biljana Šüepanoviü* University of Montenegro, Faculty of Civil Engineering, Podgorica, Montenegro Dr Miloš Kneževiü University of Montenegro, Faculty of Civil engineering, Podgorica, Montenegro Dr Duško Luþiü University of Montenegro, Faculty of Civil Engineering, Podgorica, Montenegro Three different collapse modes are observed in experimentally tested eccentrically patch loaded steel I-girders: eccentric, centric and mixed collapse mode. The most important difference between collapse modes is in collapse load. Numerous mutually dependant and related parameters, as well as their combinations influence the behaviour, collapse mode and collapse load of eccentrically patch loaded steel I-girders. Dealing with such a big number of correlated influential parameters, makes determination of collapse mode and calculation of collapse load difficult tasks. One approach that was analysed and assessed as successful method is application of Artificial Neural Networks (ANN). Keywords: patch load, eccentricity, steel I-girder, collapse mode/load, ANN modelling, forecast model

INTRODUCTION A series of experimental researches analysing patch loading problems was organised at the University of Montenegro, since 1998 [1-6]. Among the other issues, particular attention was paid to the problem of eccentric patch loading, having in mind that a certain eccentricity of load, regarding the web plane, is unavoidable in real structures. Fig. 1 shows tested girder with characteristic dimensions. Girder span, a, and web

depth, hw, as well as flange width, bf, are same in all tested girders (a = hw = 700 mm, bf = 150 mm). Web thickness, tw, flange thickness, tf, as well as load eccentricity, e, are variables (tw = 3 ÷ 10 mm, tf = 3 ÷ 15 mm, e = 0 ÷ 30 mm), making also variable influential parameters as e/bf, bf /tf, tf /tw, hw /tw. For the analysis of eccentric patch loading, 144 tests were done in the experiments from 1998 [1, 2], 2001 [3, 4] and 2007 [5, 6]. Girders are

Figure 1. Experimentally tested I-girder under eccentric patch loading * Faculty of Civil Engineering, Cetinjski put bb, 81000 Podgorica, Montenegro; biljazs@t-com.me

Dr Biljana Šüepanoviü and etc. - An example of ANN modeling application in patch loading problems of steel structures

grouped in series, by the dimensions. Six girders of same geometry make one series where load eccentricity varies in range from e = 0 to e = bf /6 = 25 mm. A few girders were also tested with eccentricity e = 30 mm. Most girders were loaded over the length c = 50 mm, while several samples had load length c = 150 mm. It was shown that the collapse mode of most (but not all!) girders subjected to eccentric patch loading was quite different from the collapse mode of centrically loaded girders. Three different collapse modes are observed in experimentally tested eccentrically patch loaded steel I-girders: eccentric [1-6], centric [1-6] and mixed [5, 6] collapse mode. Mixed collapse mode, having characte¬ristics of both, centric and eccentric collapse modes, may appear in two variants: as centric-mixed or as eccentric-mixed collapse mode, depending on dominant collapse mode characteristics [6]. Concerning engineering practice, the most important difference between collapse modes is in ultimate load. The reduction in ultimate load with an increase in load eccentricity is obvious in girders with eccentric collapse mode. For a certain girder geometry, even the smallest load eccentricity (e = 5 mm, i.e. e/bf = 1/30) reduced ultimate load over 40%. In case of centric collapse mode in eccentrically loaded girders, ultimate load does not change significantly with an increase in load eccentricity. Even for highest load eccentricity (e = 25 mm, i.e. e/bf = 1/6), girders of certain geometry behaved as if there is no eccentricity. Hence, in order to estimate ultimate load, the first step is to determine collapse mode of eccentrically loaded I-girder. Influential parameters are numerous, mutually dependant and related: girder geometry (all dimensions of girder and their ratios), load eccentricity and its relations with girder dimensions, as well as load application manner. Dealing with such a big number of correlated influential parameters, makes determination of collapse mode and calculation of collapse load difficult tasks. One approach that was analysed is application of Artificial Neural Networks (ANN). ANN modelling method is based on the analogy with the human nervous system [6, 7]. Artificial neuron imitates biological neuron. Artificial Neural Network, consisted of artificial neurons, is

computational simulation of human neural network, consisted of biological neurons. Humans use their mind to make conclusions and decisions in certain situations based on the previous (similar) experience. ANN does not have human mind and experience that should be used to process input data and make appropriate conclusions/decisions, i.e. output. In ANN modelling method human mind is replaced by mathematical functions (as much as such replacement is possible) and human experience is replaced by existing data base which is used for ANN training. By training ANN on some data base, forecast models are created in order to estimate output parameter(s) for certain set of input parameters that is not present in the data base, but that is in the range of data base. ANN MODELLING OF EXPERIMENTALLY TESTED GIRDERS Although the problems of collapse mode determination and collapse load calculation are mutually connected, collapse mode qualifying the level of collapse load, for the beginning these two issues are considered independently from each other. At first, Artificial Neural Network modelling was implemented in estimation of collapse load, without considering collapse mode. Latter on, the same networks, that gave good results in estimation of collapse load, were slightly modified, adapted and used to forecast collapse mode. FORECAST MODELS FOR COLLAPSE LOAD The basic idea was to estimate the collapse load, Pu, as the only output parameter, depending on numerous input parameters (material characteristics, girder geometry and load eccentricity), as well as to asses applicability of ANN modelling method for collapse load determination in engineering practice. Several types of forecast models were made using experimental data from 1998, 2001 and 2007: with dimensional (e.g. e, tf, tw) and dimensionless (e.g. e/bf, e/tf, e/tw, bf /tf, tf /tw, hw /tw) geometry inputs. Several types of network architecture were constructed: with one or two hidden levels of neurons; with different number of neurons (1 to 20) in each level, depending on inputs number and number of training data. Later on, comparison of different forecast models was done in order to evaluate which models provide the best forecast of collapse load. Afterwards, these best Journal of Applied Engineering Science 10(2012)1, 215

Dr Biljana Šüepanoviü and etc. - An example of ANN modeling application in patch loading problems of steel structures

models were used for assessing applicability of ANN modelling method in engineering practice, as a tool for determination of collapse load in eccentrically patch loaded steel I-girders. Only one computer software [6, 7] was used for training of all created Artiﬁcial Neural Networks, so that the following characteristics were the same for all networks, i.e. for all ANN forecast models: •

•

The training of feed-forward neural networks was done by means of improved back-propagation algorithm that assumes iterative training process. The number of training cycles in one iteration was 500. Iterative process of network training, i.e. model ﬁtting was stopped when error of validation data set showed intention to grow after lessening trend. The error of training data set constantly decreased.

ANN models were made separately for girders with different load lengths (c = 50 or 150 mm). Herein only load length of c = 50 mm and models with ﬁve dimensional inputs (e, tw, tf, ı0.2, w – web yielding stress, ı0.2, f – ﬂange yielding stress) and one output (Pu) will be considered. The com-

plete experimental data set for girders with load length c = 50 mm consists of 120 tested girders. 19 testes were exempted from the network training process and used as a comparison data set, i.e. as data for the evaluation of forecast models. The rest of 101 tests were divided in training data set (71 tests) and validation data set (30 tests). The best evaluated models show high level of match with experimental data and prove to be acceptable for engineering practice. Particularly good results are obtained from network with two hidden levels, each with ten neurons (“c50 – load – 2 – 10”) [6]. Examples of collapse load forecast models of this network are presented in Figure 2. Figure 2. illustrates estimation of collapse load and its relation with the load eccentricity Pu,ann(e) for tw = 5 mm and different values of tf = 5 ÷ 15 mm, all at fixed c = 50 mm, ı0.2, w = 28 kN/cm2 and ı0.2, f = 28 kN/cm2. Some of these values of tf have been tested experimentally (tf = 6, 8, 10 and 12 mm). However, ANN models fill in the gaps for values that were not present in the experiment and also widen domain of tf values. Appropriate graphical presentation of Pu,ann(e) for fixed value of tf and different values of tw

Figure 2. Estimation of collapse load Pu,ann (e) for tw = 5 mm and tf = 5 ÷ 15 mm, at c = 50 mm, ı0.2, w = 28 kN/cm2 and ı0.2, f = 28 kN/cm2, by means of Artiﬁcial Neural Network “c50 – load – 2 – 10”

might also be created, assuming ﬁxed values of c, ı0.2, w and ı0.2, f . Similar estimations of collapse load and its relations with the web thickness or dimensionless parameter tf /tw, i.e. Pu,ann(tw) or Pu,ann(tf /tw), might be made, as well. Such diagrams proved to be interesting, leading to various and important conclusions. Journal of Applied Engineering Science 10(2012)1 215

FORECAST MODELS FOR COLLAPSE MODE Initial intention was to train again all networks used for collapse load estimation, but with the new output. However, some networks, showing obvious and persistent non-adequate behaviour

Dr Biljana Šüepanoviü and etc. - An example of ANN modeling application in patch loading problems of steel structures

from the early stages of iterative training, were abandoned during the training process. Instead of them, some new networks were constructed. Still some networks created for collapse load estimation, after appropriate adaptation, were successfully used for the collapse mode forecast. Input parameters and network architecture were kept the same. Only output parameter was changed. Collapse mode was introduced instead of collapse load and the same iterative network training process was done again, with the new output. Comparison, training and validation data sets were the same as for collapse load models. In order to use available software [6, 7] for network training, it was necessary to transform collapse mode, being alpha-numerical, descriptive parameter, in the form of numerical parameter. Each type of collapse mode was assigned a numerical value from the interval [-1, 1]: centric col-

lapse mode = 1; centric-mixed = 0.3; eccentricmixed = -0.3; eccentric = -1. Among created networks, the best results are obtained from the following two [6]: network with one hidden level, with 6 neurons (“c50 – mode – 1 – 6”), and network with two hidden levels, each with 19 neurons (“c50 – mode – 2 – 19”). Examples of collapse mode forecast models of these networks are presented in Fig. 3 and Fig. 4. Four characteristic girder geometry types, i.e. four experimental series having representative sample in comparison data set were chosen for this presentation and comparison of ANN modelling of collapse mode with experimental results. Graphical presentation of results is chosen as the most suitable, having in mind character of output parameter – collapse mode. In this manner, visual evaluation of forecast models and assessment of ANN modelling application is enabled.

Fig. 3. Examples of collapse mode forecast models in experimental series EB VI and EB VII, for networks “c50 – mode – 1 – 6” and “c50 – mode – 2 – 19”

Journal of Applied Engineering Science 10(2012)1, 215

Dr Biljana Šüepanoviü and etc. - An example of ANN modeling application in patch loading problems of steel structures

In Figure 3 and Figure 4, lines present ANN forecast models for collapse mode, while dots present experimental results. X-dot (×) is sample from comparison data set. Square-dots ( ) are samples of same geometry as that one, but with different load eccentricity. Each of four diagrams presents one complete experimental series, i.e. girders with the same dimensions, differing only in load eccentricity: ﬁve girders presented with square-dots ( ) + one girder presented with X-dot (×) = 6 girders of one experimental series. Load length in all presented series was c = 50 mm. Generally speaking, presented ANN forecast models match experimental data well, what makes them applicable in practice. Noticeable discrepancy is observed only in case of centric collapse at high eccentricity of load, Fig. 4. It happens in girders with high ratio tf /tw. Only collapse mode for highest eccentricity (e = 25

mm) is not well forecasted, while ANN models provide good forecast of collapse mode for other eccentricities (e 20 mm) even in these girders. In case of series with “more expectable”, “more common” behaviour – centric behaviour of eccentrically loaded girders only up to the certain level of load eccentricity – ANN forecast modes have excellent match with experimental data, as shown in Figure 3. CONCLUSION WITH REMARKS Presented example of ANN modelling proves possibility of successful and useful application of this method both, in engineering practice for the purpose of determination of collapse load and collapse mode in eccentrically patch loaded steel I-girders, as well as in scientiﬁc research, in order to better understand the character and level of inﬂuence of certain parameters on collapse load and collapse mode.

Figure 4. Examples of collapse mode forecast models in experimental series EB XI and EB I, for networks “c50 – mode – 1 – 6” and “c50 – mode – 2 – 19” Journal of Applied Engineering Science 10(2012)1 215

Dr Biljana Šüepanoviü and etc. - An example of ANN modeling application in patch loading problems of steel structures

Not only that ANN models might be used to forecast collapse load of particular girders. Graphical presentation of such models as in Fig. 2 might help in establishing relations between collapse load and certain influential parameters. It may also be useful in making conclusions about correlation and interaction among influential parameters. Not only that ANN models might be used to forecast collapse mode of particular girders. They might also help in establishing general criteria for collapse mode identification in eccentrically patch loaded girders. One set of such criteria is formulated [6], based on existing experimental database. It means that proposed criteria are valid for the domain of experimental data. The question is what about girders with the dimensions out of experimental data domain. Graphical presentation of ANN models as in Fig. 3 and Fig. 4 might help answering this question. Diagrams in these Figures clearly imply separation of collapse mode types in girder of certain geometry, depending on load eccentricity. Zones of centric, mixed and eccentric collapse modes might be identified. By means of such diagrams, adequate ANN forecast models might provide new criteria for collapse mode identification, as well as their validation out of the experimental domain. Only one example is presented here, aiming picturing successful application of ANN modelling method in subject problem solving. However, further work in this domain should be welcomed. Even available experimental database used for network training in this example might provide different and better results. Improvement is possible through: another choice of numerical values for collapse mode types; another choice of data for comparison, training and validation sets; another choice of Artificial Neural Network type, i.e. type of its architecture and training process; use of another computer software. Any future experimental or numerical (e.g. finite element method) modelling will provide extension of database, enabling creation of ANN models with better results. Still, the fact that ANN modelling method belongs to the domain of artificial intelligence, should be kept in mind, since such methods should be strongly controlled by human intelligence in order to give results that comply with the reality.

REFERENCES 1) D. Luþiü: “A contribution to the analysis of thin-walled girders”, PhD thesis, Faculty of Civil Engineering, University of Belgrade, Belgrade, 1999. 2) D. Luþiü: “Experimental Investigation on Igirders Under Eccentric Patch Loading”, The 2nd European Conference on Steel Structures (EUROSTEEL 1999), Vol. 1, pp. 47-50, Prague, 1999. 3) D. Luþiü, B. Šüepanoviü: “Experimental Investigation on Locally Pressed I-beams Subjected to Eccentric Patch Loading”, The 3rd European Conference on Steel Structures (EUROSTEEL 2002), Vol. 1, pp. 473482, Coimbra, 2002; Journal of Construction Steel Research, Vol. 60, Nos. 3-5, pp. 525534, 2004. 4) B. Šüepanoviü: “I-girders under eccentric local loading – experimental-theoretical analysis”, MSc thesis, Faculty of Civil Engineering, University of Belgrade, Belgrade, 2002. 5) B. Šüepanoviü, D. Luþiü, S. Aleksiü: “An Experimental Research Ekscentro 2007 – Experimental Testing of Eccentrically Patch Loaded Steel I-Girders”, The 5th European Conference on Steel and Composite Structures (EUROSTEEL 2008), Vol. B, pp. 11491154, Graz, 2008. 6) B. Šüepanoviü: “Analysis of eccentrically locally loaded steel I-girders”, PhD thesis, Faculty of Civil Engineering, University of Montenegro, Podgorica and Faculty of Civil Engineering, University of Granada, Granada, 2010. 7) M. Kneževiü: “Risk management during realisation of the civil engineering projects”, PhD thesis, Faculty of Civil Engineering, University of Belgrade, Belgrade, 2004. Paper sent to revision: 07.03.2012. Paper ready for publication: 28.03.2012.

Journal of Applied Engineering Science 10(2012)1, 215

doi:10.5937/jaes10-1660

Paper number: 10(2012)1, 216, 21 - 26

PREPARING A DATA BASE FOR ESTIMATING SEISMIC DAMAGE ON BUILDINGS BY APPLYING ANN MSc Igor Peško* University of Novi Sad, Faculty of Tehnical Science, Novi Sad, Serbia Dr Jasmina Dražiü University of Novi Sad, Faculty of Tehnical Science, Novi Sad, Serbia MSc Vladimir Muþenski University of Novi Sad, Faculty of Tehnical Science, Novi Sad, Serbia Dr Milan Trivuniü University of Novi Sad, Faculty of Tehnical Science, Novi Sad, Serbia Seismic risk in urban areas increases over time, so the research projects on all the aspects of seismic safety carried out currently are numerous. In order to plan preventive measures, the estimation of possible damages on buildings plays a significant role. This paper describes preparation of a data base for predicting seismic damage category by applying artificial neural networks (ANN). The base will be defined relying upon the available data from the reports after the earthquake in Kraljevo (03/11/2010). Keywords: earthquake, damage, data base, artificial neural networks INTRODUCTION Earthquakes present a natural hazard (geologic hazard), with consequences such as the loss of human lives as well as economic losses caused by damages on buildings (material destruction). Defining damage caused on buildings is significant in all the phases of an earthquake. During the pre-quake phase, possible damages are defined with the aim of planning of preventive measures as well as the basis for estimation of certain area’s potential risks. Later on, immediately following the earthquake, it is done in order to rescue and shelter the victims, and in the phase after the earthquake, with the aim of undertaking measures to eliminate, reduce, and repair damages. This paper describes a data base preparation with the aim of future estimation of damages on buildings caused by earthquakes, by applying artificial neural networks (ANN). The origins of development of neuro-computing are related to an article by McCulloch and Pitts:’ A logical calculus of the ideas immanent in nervous activity’ [1]. There is still no uniformed definition which completely explains neural networks. One of the definitions offered in scientific-

technical books , from the engineer point of view, is ’a computational mechanism able to acquire, represent and compute mapping from one multivariate space of information to another, given a set of data representing that mapping.’ [2] Artificial neural networks imitate the functioning of biological neural networks, by using adequate mathematical models (of structures, functions and modes of processing). Mathematical model of an ANN consists of three basic segments: mathematical model of a neuron itself, network architecture (models of synaptic connections and structure of neurons within a network) and rules of network training. An artificial neural network is connected with its environment in two ways: by inputs through which the environment influences the artificial neural network, and by outputs, through which a neural network reciprocally influences its environment. SEISMIC ACTIVITY IN SERBIA According to a seismic map (for the period going 500 years backwards), over 90% of the territory of Serbia belongs to the VIII degree of MSK-64 scale, about 7% belongs to IX and only about 2-3% to VII degree of this scale, i.e. the whole

* Faculty of Tehcnical Science, Trg Dositeja Obradoviüa 6, Novi Sad, Serbia; igorbp@uns.ac.rs

MSc Igor Peško and etc. - Preparing a data base for estimating seismic damage on buildings by applying ANN

territory of Serbia, according to this scale, is seismically active. Serbia is located in a seismically active zone, in its border part, the so called Mediterranean-trans Asiatic seismic zone, or more precisely, Mediterranean belt. Owing to its position on the very edge of the plate, earthquakes in Serbia, according to estimations of seismologists, cannot exceed 6.2 to 6.3 units of the Richter magnitude scale. The most severe earthquake which hit Serbia in the last 100 years occurred in the year 1922 in Lazarevac, with the 5.9 Richter scale magnitude. Earthquakes of 5.7 degrees hit Vitina in 1921, Rudnik in 1927, Kopaonik in 1980 and Mionica in 1998. Regarding their energy, these earthquakes can be destructive, too. Earthquake prone areas in Serbia are the following: the regions of Kopaonik, Rudnik, Krupaj, Maljen, Lazarevac, Svilajnac, Golubac, Urosevac-Gnjilane, Vranje and Kraljevo.

The last earthquake of a stronger intensity on the territory of Serbia occurred on November 3, 2010, at 1:56 am. Its magnitude was 5.4 degrees on the Richter scale. The time of the earthquake beginning in its focus was 00:56:54.76 GMT, with the focal depth of 13km. The epicenter coordinates are 43.762N latitude and 20.713 E longitude, with the epicenter located 121km south from Belgrade, or 4km north from Kraljevo. Figure 1 shows the location of the main quake’s epicenter, on the outskirts of Sirca village. [3] After the main earthquake, a series of following tremors were registered in the area. Their magnitudes ranged from 1.0 to 4.4 degrees of the Richter scale. Those quakes of 2 degrees and below were only detected by instruments and could not be felt. During the interval of time until 1pm on November 9, 2010, the cluster of 258 earthquakes in total were registered. [3]

Figure 1. Epicenter of the main quake (Kraljevo, 03.11.2010)

CREATING A DATA BASES In areas struck by earthquakes, seismic risk management and decisions that are to be made after they occur can play a vital role for the people residing in those areas. In order to calculate seismic risk, it is necessary to develop a correlation between a quake and the amount of damage for the buildings on the observed locality, i.e. to deﬁne buildings’ vulnerability for the earthquake impact. Basic and the most important pre-condition for a high-quality functioning of a neural network is creation of an adequate data base for its training, i.e. deﬁning input and output data. Creating a data base for seismic damage estimation is fully based upon reports made immediately after the earthquake which occurred on November 3, 2010, near Kraljevo. When creating a data base, it is necessary to pay attention to the future use of the ANN.

It is necessary for the input and output data to be available in the same form in the future as well. Such approach will completely provide later application of neural networks for the needs of predicting damages as consequences of future earthquakes impact. In order to make a rough estimation of damages caused by the earthquake in Karaljevo, damages on buildings were identified. The data about the buildings for which the damage category was defined, in accordance with the enclosed classification, are given in table 1. Damages were divided into five categories (from 1 to 5). Category (0) belongs to buildings which suffered no damage, and the sixth category consists of totally destroyed buildings, as well as those which are not completely destroyed, but the amount of damage exceeds the level for which the reparation would be financially justiJournal of Applied Engineering Science 10(2012)1, 216

MSc Igor Peško and etc. - Preparing a data base for estimating seismic damage on buildings by applying ANN

Table 1. General data about the building from a report No.

Data about the building from the report

Building address

Year of construction, or the estimated age

Building purpose (residential or business)

Total number of ﬂats

Total number of business units

Total number of above-ground storeys

Total number of storeys (including underground storeys)

Total gross area of a building Type of construction:

•

AB skeletal or panel

•

Massive construction systems with horizontal and vertical ring beams and stiff inter-storey construction

•

Massive construction system with horizontal ring beams and stiff inter-storey construction

•

Massive construction system with wooden inter-storey construction

fied. The categories, as well as the description of damage for each of them, were taken from the Instructions for determining category and damage level on earthquake-hit residential buildings, of the Serbian Chamber of Engineers [4]. As the basis for these instructions, the following documents were used: • Regulations on technical normative for building construction in earthquake-prone areas (Official Gazette SFRJ 31/81, 48/82, 29/83, 21/88, 52/90); • Regulations on technical normative for reparation, reinforcement and reconstruction of buildings damaged by earthquakes and for reconstruction and revitalization of building constructions. (Official Gazette SFRJ 52/85); • Instructions for the common methodology for estimating damage caused by natural hazards (Official Gazette SFRJ 27/87). Categories and descriptions of damages are shown in table 2. Seismic resistance of a building is influenced by its architectural and construction features. Project solution and acquired configuration classify favorable and unfavorable forms of buildings in the base and cross section, whereas construction features based on its bearing capacity, ductility and stiffness of construction elements (interstorey construction, walls, pillars) are related to the type and materialization of the construction system [5]. Journal of Applied Engineering Science 10(2012)1 216

Data presented in table 1, building purpose (residential-business), year of construc-tion, building height (number of floors and construction system type, provide direct connection between them (ANN inputs) and damage category (ANN outputs) Within the data, the type of construction system comprises skeletal and panel constructions of reinforced cement and massive construction systems, with variants of reinforcement (horizontal or horizontal and vertical ring beams) and variants of inter-storey construction (stiff interstorey construction or wooden inter-storey construction). Taking the structure of all the input data into consideration, it was realized that there is a possibility of obtaining derived input data. Based on the building address from the report, it is possible, by linking it to the geodetic map of the town of Kraljevo, to locate a building, identify its shape and base dimensions, define its distance from the main earthquake epicenter, as well as the earthquake’s direction of propagation. The mentioned data are of great importance for defining the connection between the position of a building, earthquake location (distance between the building and the main quake epicenter (L)), and the caused damages. As an illustration of the derived input data for artificial neural network training, figure 2 shows three buildings, different in position and distance related to the earthquake epicenter.

MSc Igor Peško and etc. - Preparing a data base for estimating seismic damage on buildings by applying ANN

Direction of propagation is deﬁned by ĳ angle (an angle that covers the direction of propagation related to the longitudinal axis of a building). After deﬁning the ĳ angle, it is possible to decompose seismic propagation on the longitudinal direction (X) and transversal direction (Y) of a building,

and calculate the propagation distribution: • •

DX - % of earthquake propagation in the longitudinal direction of a building DY - % of earthquake propagation in the transversal direction of a building.

Table 2.Damage category Damage category

Data from the report

Without damage

Minor damage – damages on the smaller areas of rooﬁng, occurrence of minor cracks on plastered areas – mortar partially missing, partially cracked glass areas and damaged chimneys.

Medium damage – larger areas of rooﬁng, fascia, glass, demolition of chimneys, larger areas of mortal fallen off walls and ceilings, smaller cracks in supporting walls, and numerous in separating ones.

III

Larger damage – damage on the supporting elements of a roof construction, smaller cracks in construction elements, (foundations, walls and AB ring beams), bigger cracks or demolition of gable and separating walls

Massive damage – demolition of certain parts of roof construction or obvious deformation, numerous cracks on pillars, foundations, supporting walls and ﬁlled walls, demolition or obvious deformation of separating walls, occurrence of damages from the former category, disabled installations. Disabled installations are those which do not function due to the damage caused by the earthquake.

Massive damage and construction deformation– damages or deformation (dislocation) of certain construction elements – diagonal cracks in supporting pillars and walls, cracks in construction joints, i.e. disconnections on supporting walls joints or supporting and ﬁlled walls joints, on certain parts of a building, with occurrence of damage from the former category and other damages which could be repaired, along with installations which are out of order. Occurrence of damages mentioned above also relates to vertical communications (staircases and elevators. )

Figure 2. Position of three typical buildings in relation to the epicenter of the earthquake

Figure 2 emphasizes three typical positions of buildings: • Building 1 – direction of propagation matches the longitudinal axis of a building • Building 2 – direction of propagation matches the transversal axis of a building and

•

Building 3 – a building covers an angle related to the direction of propagation, so according to the angle ĳ=28° the propagation can be distributed, into longitudinal and transversal direction of a building. In this way, it is possible to analyze the impact of building position and its distance from the epiJournal of Applied Engineering Science 10(2012)1, 216

MSc Dragan Stamenkoviü and etc. - Combination free replacement and pro-rata warranty policy optimization model

center on the damage category for all the buildings included in the report. By analyzing the output data, the basic model for neural network training was deﬁned: INPUT: • YOC - Year of construction or the estimated age of a building • POB - Purpose of a building (residential or business) • TNAGS - Total number of the above-ground storeys • TNS - Total number of storeys (including underground storeys) • TGAB - Total gross area of a building • CT - Construction type • DFE - Distance from the epicenter of the earthquake

•

DX - % of earthquake propagation in the longitudinal direction of a building • DY - % of earthquake propagation in the transversal direction of a building. OUTPUT: • CBD - Category of the building damage caused by the earthquakeFigure 3 shows the structure of the model. After forming an appropriate ANN and its training, it is necessary to carry out the analysis of its sensitivity, based on which it is possible to deﬁne the inﬂuence of every individual input data on its quality. In this way, an opportunity arises to reduce the ANN model, i.e. to eliminate less important input data, which contributes to a more optimal structure.

Figure 3 Structure of the ANN model

The data base shortcoming is reﬂected in the fact that it is formed only upon the propagation of the November 3 2010 earthquake, of 5.4 degrees of Richter magnitude scale. If an estimation of some future’ projected’ seismic damages is to be carried out based upon the mentioned data base and the formed ANN, the ANN outputs will not be providing entirely correct results. Creating a data base upon the reports on the damages caused by November 3 2010 earthquake, only presents the initial phase in forming a more comprehensive base. While preparing the data base, the features of the earthquake itself were not taken into consi-deration, although they play a highly signiﬁcant role on the quality of the ANN output data. In order to be able to get precise predictions about potential seismic damages on buildings Journal of Applied Engineering Science 10(2012)1 216

by applying a neural network, one must take into consideration the features of the earthquake itself, such as its magnitude, focus depth, etc. This would only be possible through a more comprehensive collecting of data, which requires a prolonged collecting and expanding of the data base, relying upon some future earthquakes. CONCLUSION High-quality functioning of an artificial neural network (ANN) involves creating an adequate data base for its training along with defining input and output data. This paper presented the preparation of a data base for prediction of seismic damage category, by applying artificial neural networks. Forming a data base for damage estimation is based upon reports made immediately after the earthquake in Kraljevo (November 3,

MSc Igor Peško and etc. - Preparing a data base for estimating seismic damage on buildings by applying ANN

2010). Data contained in these reports provided a possibility to make connections between building features (ANN input) and the damage category (ANN output). After creating the adequate ANN and its training, it is possible to analyze the network sensitivity, the inﬂuence of every individual input data on its quality, reduce the ANN model, i.e. eliminate less important input data and obtain a more optimal structure. ANNs, in other words, present a powerful and adequate tool for prediction of possible damages on buildings, as the grounds for assessment of buildings’ vulnerability, with the aim of planning preventive measures of seismic safety. ACKNOWLEDGEMENTS The work reported in this paper is a part of the research within the research project TR 36043 “Development and application of a comprehensive approach to the design of new and safety assessment of existing structures for seismic risk reduction in Serbia”, supported by the Ministry for Science and Technology, Republic of Serbia. This support is gratefully acknowledged.

REFERENCES 1) W.S. McCulloch, W.A. Pitts: „A logical calculus of the ideas immanent in nervous activity“, Bulletin of Mathematical Biophysics ,Vol.5, 1943, p.115-133 2) J.H. Garret: „Where and why artiﬁcial neural networks are applicable in civil engineering“, ASCE, Journal of Computing in Civil Engineering [special issue], Vol.8, 1994; 129130 3) http://www.seismo.gov.rs/Vesti/Izvestaj.pdf (Report on results and activities of the Seismological survey of Serbia after the earthquake near Kraljevo on 03.11.2010 at 01:56 ) 4) http://www.ingkomora.org.rs/vesti/?id=1611-2010-001 (Instructions for determining catego¬ry and damage level on earthquakehit residential buildings, Serbian Chamber of Engineers) 5) J. Dražiü: “The Analysis of Interaction of Functional and Structural Building Properties in Aseismic Designing”, Doctoral dissertation, University of Novi Sad, Faculty of Technical Sciences, Novi Sad, 2005. (in Serbian) Paper sent to revision: 07.03.2012. Paper ready for publication: 29.03.2012.

Journal of Applied Engineering Science 10(2012)1, 216

doi:10.5937/jaes10-1661

Paper number: 10(2012)1, 217, 27 - 30

NEURAL NETWORK PROGNOSTIC MODEL FOR RC BEAMS STRENGTHENED WITH CFRP STRIPS MSc Marijana Lazarevska* University of Skopje, Faculty of Civil Engineering, Skopje, Macedonia Dr Ana Trombeva-Gavriloska University of Skopje, Faculty of Architecture, Skopje, Macedonia Dr Miloš Kneževiü University of Podgorica, Faculty of Civil Engineering, Podgorica, Montenegro Dr Todorka Samardžioska University of Skopje, Faculty of Civil Engineering, Skopje, Macedonia Dr Meri Cvetkovska University of Skopje, Faculty of Civil Engineering, Skopje, Macedonia Improper execution of bonding of FRP plates to the RC beam can result into appearance of zones where the bond is substantially weaker, and air pockets are present. This paper presents an attempt to model the weak bond zone and its influence on the global response of the externally CFRP strengthened RC beam. A numerical displacement-based fibber model was used for the prediction of the response of RC beams externally strengthened with CFRP. Also, using the concepts of artificial neural networks and the results of the performed numerical analyses, another prediction model has been made. Both models generated excellent results and some of them will be presented further below in this paper. Keywords: CFRP, neural network, RC beam, strengthening, discontinuous bond INTRODUCTION Performance of the materials used in the contemporary structures can significantly change as a result of change in the environmental conditions and the increasing of the loads, which were not taken into account in the design process. All these factors may decrease the bearing capacity or structural safety of the construction during their service life. The non adequate performance of the constructions imposes the need for repairing and strengthen¬ing. Increase of the load capacity and structural safety of the flexural loaded structural members is often carried out by external bonding of additional reinforcement. In the recent years, typical retrofitting technique involves the use of external bonded lighter, stronger and more durable FRP (fibre reinforced polymer) strips. In order to achieve successful external strengthening of the reinforced concrete structures by FRP strips, a thorough understanding of the effects that this type of FRP reinforcement has on beam failure mode, is required. Key role in the failure of the externally strengthened construc-

tion has the bond layer between concrete surface and FRP strip. Experimental researches show that the most often type of failure of the strengthened construction, caused from the maximal shear stresses, is followed by peeling of the FRP strip initiated at the end of the plate, where concrete is uncracked. Local shear failure is driven by a biaxial tension state composed by the interfacial stresses and the normal tension induced on concrete by the flexure [4]. From the theory proposed by Taljsten [5], it can be concluded that for the cases of sufficiently thin strengthening plates, the influence of the peeling stresses on the principal stresses is minute and therefore it can be neglected. For a proper determination of the bearing capacity of the RC structure strengthened with externally added FRP reinforcement, a model has to be used, which can accurately describe the stresses in the bond layer [3]. Artificial neural networks are a typical example of one modern interdisciplinary field which gives the basic knowledge principles that can be used for solving of many different and com-

* Faculty of Civil Engineering, Bulevar Partizanski odredi 54, PF 560 Skopje, Macedonia; marijana@gf.ukim.edu.mk

MSc Marijana Lazarevska and etc. - Neural network prognostic modelf for RC BEAMS strengthened with CFRP strips

plex engineering problems which could not be solved otherwise (using the traditional modeling and statistical methods). Neural networks are capable of collecting, memorizing, analyzing and processing large number of data gained from some experiments or numerical analyses. They have an excellent success in data prediction and they can be used for creating prognostic models that could solve various engineering problems and tasks. Their operation is reasonably simple and easy, yet correct and precise. These positive effects completely justify their application, as prognostic models, in many engineering researches [1, 2]. The bond between reinforced concrete beam and CFRP plate in this paper is modelled by a numerical displacement-based fibber model. Discontinuous bond zone is modelled by modification in the constitutive law for description of the bond between the reinforced concrete beam and CFRP plate. A simple approach for the weak zone in the bond description is proposed and the implemented modification is analysed by the distribution of the tensile force in the CFRP sheet along the externally strengthened reinforced concrete beam. Besides the numerical modeling, another objective of the research presented in this paper, was to build a prognostic model

which could generate accurate outputs for the response of RC beams externally strengthened with CFRP. For this purpose artiﬁcial neural networks were implemented in the prognostic modeling of the given engineering problem. The results obtained by the neural network’s model for the analyzed case applied on the numerically generated data from the proposed modeling of the weak zone show excellent accuracy. ANALYZED CASE The analyses were conducted for a reinforced concrete beam that is externally strengthened with CFRP strip. A 3200 mm beam element, presented in Figure 1, which has 2900 mm span and cross b/h=800/120 mm section is strengthened with CFRP strip with 100 mm width. Width of the external CFRP reinforcement is 100 mm. A weak bond layer with length of 504 mm, which starts at 200 mm and ends at 704 mm from the supports, is analysed. The adopted values of the Young’s modulus and the yielding strength of the CFRP strip are 150 GPa and 2400 MPa, and the corresponding values for the reinforced steel are 210 GPa and 460 MPa, respectively. The strengthened beam is subjected to four-point bending. Because of the case’s symmetry, only half of the beam has been analyzed.

Figure 1. Beam element strengthened with CFRP strip: ɚ) geometry of half beam; b) cross section of the strengthened beam

FORMULATION OF THE PROBLEM Numerical formulation of the bond layer Beam models that are based on the concept of discretization of the cross section into ﬁbbers layers are often used because the ﬁber model takes

into account both, axial and flexural influence. With appropriate modifications fibber model can be used for the analysis of the RC elements strengthened with externally added FRP plates with discontinuous zone in the bond layer.

Journal of Applied Engineering Science 10(2012)1, 217

MSc Marijana Lazarevska and etc. - Neural network prognostic model for RC BEAMS strenghened with CFRP strips

Figure 2. Comparison between the original and modiﬁed bond law

Figure 3. Neural network model used for the analyses of RC beams externally strengthened with CFRP

eter u used in the modeling process of the bond layer. The output parameter of the neural network model is the tensile force in CFRP plate expressed in KN. A multilayered non-recurrent neural network, with one input layer, two hidden layers and one output layer, was chosen for training of the network, Figure 3. Each hidden layer has 8 neurons inside. For network training 230 groups of input data were used, out of which 25 belonged to the validation data group (around 10%). The training process was conducted in specialized computer software that works under MS Excel.

In order to model the weak zone in the bond layer, a modification of the original constitutive bond law was introduced. Maximal shear stress, Ĳ1, remains unchanged, while the displacement at slip is significantly increased, Figure 2. This modification gives a much more flexible bond, compared to the perfectly bond area. The perfect bond is described by values u1,cont=0,0013 mm and Ĳ1=3,1 MPa. Detailed analyses of the implemented modification in the constitutive bond law could be found in [6]. NEURAL NETWORK’S PROGNOSTIC MODEL

RESULTS AND DISCUSSION

In order to build a neural network’s prognostic model which could generate accurate outputs for the response of RC beams externally strengthened with CFRP, the results from the numerical analyses carried out in [6] were used as input data. The ﬁrst step of the modeling procedure was to set up the mathematical model (deﬁne the architecture of the neural network) using the given input data, followed by the training process of the network. For this engineering problem the following input parameters are used: the length of the beam and selected values of the param-

Analysis of the tensile force distribution in CFRP strip along the beam for selected values of the parameter u1,disc used in the modeling process of the weak bond zone were carried out and the results are presented in Figure 4a). From the Figure 4a) it can be observed that in the section of the weak bond, the tensile force rate is smaller when a larger value of u1,disc is employed in the analysis. This is in accordance with the introduced bond modiﬁcation.

Figure 4. Results for the tensile force distribution in CFRP strip obtained by: a) Numerical analyses, b) Neural network Journal of Applied Engineering Science 10(2012)1, 217

MSc Marijana Lazarevska and etc. - Neural network prognostic modelf for RC BEAMS strengthened with CFRP strips

In order to check the network quality and accuracy, controlling tests were performed. The network was tested by using 30 different data groups, data which weren’t used for the learning and training process, Figure 4b.

The values of the tensile force obtained by numerical analyses and the results generated from the trained neural network were compared, Figure 5.

Figure 5. Comparison diagram of the results obtained from neural networks’ prognostic model (NN) and numerical method (NM)

From the Figure 5 could be seen that the corresponding curves constructed on the basis of the numerically achieved results and on the basis of the results from the neural networks approach are similar and give close results. After the comparison of both methods it could be concluded that neural networks present an excellent tool for prognostic modeling and can be used for determination of the tensile force in CRFP plates used for straightening of RC beams, especially in those cases when there are no (or very few) numerical results. CONCLUSIONS This paper presents an attempt for verification of the modified numerical model used for modeling the bond law between RC beam and CFRP strip. A simple approach that consists of a bond constitutive model modification which can be easily incorporated into the existing numerical model is proposed for modeling the weak zones. The application of neural networks for building a prognostic model which can be used for prediction of the response of RC beams externally strengthened with CFRP is of huge importance for the design process in civil engineering. Researches show that most of the experimental models for determination of the response of RC beams are extremely expensive, and analytical models are quiet complicated and time consumed. That is why a modern type of analyses, such as modeling through neural networks, can help a lot, especially in those cases when some prior analyses were already made.

REFERENCES 1) Kneževiü M.: “Risk management of civil engineering projects“, Doctoral dissertation, Civil Engineering Faculty of University in Belgrade, Serbia, 2005 2) Kneževiü M. and Radomir Z.: “Neural networks – application for usage of prognostic model of the experimental research for thin reinforced-concrete columns”, scientiﬁc research work, Materials and constructions, 2008 3) Monti, G. and Spacone, E., “Reinforced concrete ﬁbber beam element with bond- slip”, Journal of Structural Engineering, 126, 6, 2000, pp 654-661 4) Spacone, E., Limkatanyu, S. 2000. “Responses of Reinforced Concrete Members Including Bond-Slip Effects”, ACI Structural Journal, 97, 6, pp 831-839 5) Täljsten, B., “Strengthening of Beams by Plate Bonding”, Journal of Materials in Civil Engineering, 9, 4, 1997, pp 206-212 6) Trombeva A., Modeling of CFRP external strengthening of reinforced concrete structures with the weak zones in the bond layer, master thesis, University in Ljubljana, Faculty of Civil and Geodetic Engineering, 2004. Paper sent to revision: 07.03.2012. Paper ready for publication: 29.03.2012.

Journal of Applied Engineering Science 10(2012)1, 217

doi:10.5937/jaes10-1662

Paper number: 10(2012)1, 218, 31 - 36

INFLUENCE OF BOUNDARY CONDITIONS ON NONLINEAR RESPONSE OF LAMINATED COMPOSITE PLATES Dr Marina ûetkoviü* University of Belgrade, Faculty of Civil Engineering, Belgrade, Serbia Dr Ĉorÿe Vuksanoviü University of Belgrade, Faculty of Civil Engineering, Belgrade, Serbia In this paper the influence of different boundary conditions on geometrically nonlinear response of laminated composite plates is analyzed. Mathematical model, based on layer-wise displacement field of Reddy [1], is formulated using the von Karman, small strain large deflection theory. The principle if virtual displacements (PVD) is used to obtain the weak form of the problem. The weak form is discretized utilizing isoparametric finite element approximation. The originally coded MATLAB program is used to investigate the influence of different boundary conditions on geometrically nonlinear response of laminate composite plates. The accuracy of the numerical model is verified by comparison with the available results from the literature. Keywords: geometrical nonlinearity, boundary conditions, composite plates, finite element INTRODUCTION The low mass density and high tensile strength made composite materials lighter and stronger compared to most traditional materials and increased their use in almost all engineering applications. Due to high specific strength design thickness of composite materials is often small [2], the reason why they are usually produced in the form of laminated panels or plates, applied to reduce overall weight of structures. However, during their service life, under specific loading and boundary conditions, these panels may undergo large deflections. Large deflections imply that geometry of structure is continually changing during deformation and geometrical nonlinear analysis should be adopted. Usual mechanisms of plate geometrically nonlinear response to a transverse load assumes that, when deflection of plate reaches approximately value of plate thickness, coupling between inplane and out-of plane deformation is activated, giving plate extra stiffness in resisting external loading. However, amount of this extra stiffness to be activated is influenced not only by level of loading, but also by types of boundary conditions. Namely, it is straight forward to assume that restrained edges compare to free edges, would more constrain free deflection of plate,

thus giving response which less deviates from linear one. Even more, influence of boundary conditions on geometrically nonlinear response is much pronounced for laminated composite materials, due to their complex anisotropic material behaviour. Unlike in isotropic materials, where the boundary conditions depends only on the type of mechanical loading (bending, buckling, vibrations etc.), which may require natural or geometric, homogeneous or no homogeneous boundary conditions, nature of boundary conditions in composite laminates depend also on level of analysis (linear, nonlinear), as well as on lamination scheme. Depending on lamination scheme different bending-stretching coupling for antisymmetric cross-ply and antisymmetric angle-ply laminates is observed, demanding appropriate simply-supported boundary conditions. Regarding level of analysis, it is noticed that quarter plate symmetry boundary conditions for antisymmetric angle-ply laminates hold for linear analysis, but does not hold for geometrically nonlinear analysis [6]. In order to mathematically describe complex anisotropic nature of composite laminates and find most computationally efficient solution, different approaches are reported in literature. Most of them are restricted to simply supported boundary conditions, specific lamination schemes and

* Faculty of Civil Engineering, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia; cetkovicm@grf.bg.ac.rs

Dr Marina ûetkoviü and etc. - Inﬂuence of boundary conditions of nonlinear response of laminated composite plates

linear mechanical problem, which enable use of analytical methods in finding appropriate solution [3]. However, when solution of nonlinear mathematical model for different lamination schemes and different boundary conditions is needed, approximate methods should be used. Indeed, literature lacks relevant studies for three dimensional analyses involving boundary conditions which are different from simply supported ones along with multilayered architecture [8]. More ever it is worth to mentioning that a simply supported boundary condition is afar from an easy realization in laboratory. The real model often needs an identification of true boundary conditions which are usually in the middle of the other classical boundary conditions, such as simply supported, clamped, free or their combination [8]. The aim of this paper is to present the influence of different boundary conditions on geometrically nonlinear response of laminated composite plates. Mathematical model, based on layer-wise displacement field of Reddy [1], is formulated using von Karman, small strain large deflection theory, to include geometrically nonlinearity. Principle if virtual displacements (PVD) is used to obtain the weak form of the problem. The weak form or nonlinear integral equilibrium equations are discretized using isoparametric finite element approximation. The nonlinear algebric equations are then solved using direct iteration procedure. The originally coded MATLAB program is used to investigate the influence of different boundary condition on geometrically nonlinear response of cross ply and angle ply laminates [4]. The accuracy of the numerical model is verified by comparison with the available results from the literature. THEORETICAL FORMULATION Displacement field In the LW theory of Reddy [1] or Generalized Layerwise Plate Theory (GLPT), in-plane displacements components (U,V) are interpolated through the thickness using 1D linear Lagrangian interpolation function , while transverse displacement component w is assumed to be constant through the plate thickness.

(1) STRAIN-DISPLACEMENT RELATIONS The Green Lagrange strain tensor associated with the displacement ﬁeld Eq.(1) is computed using von Karman strain-displacement relation to include geometric nonlinearities as follows [7]:

(2) Constitutive equations For Hook’s elastic material, the stress-strain relations for k-th orthotropic lamina have the following form: (3) Where and are stress and strain component srespectively,and are transformed elastic coefﬁcients, of k-th lamina in global coordinates [4]. EQUILIBRIUM EQUATIONS Equilibrium equations may be obtained from the Principle of Virtual Displacements (PVD), in which sum of external virtual work done on the body and internal virtual work stored in the body should be equal zero [11]:

(4)

Journal of Applied Engineering Science 10(2012)1, 218

Dr Marina ûetkoviü and etc. - Inﬂuence of boundary conditionson nonlinear response of laminated composite plates

where

is distributed load in directions, while internal forces are:

(5) I

where A, B, B , D matrices are given in [5]. FINITE ELEMENT MODEL The GLPT ﬁnite element consists of middle surface plane and N+1 planes through the plate thickness Figure 1. The element requires only the C0 continuity of major unknowns, thus in each node only displacement components are adopted, that are (u,v,w)) in the middle surface element nodes and (UI, VI) in the I-th plane element nodes. The generalized displacements over element can be expressed as:

(6) where are displacement vectors, in the middle plane and I-th plane, respectively, are interpolation functions, while , are interpolation function matrix for the j-th node of the element , given in [4].

Figure 1. Plate ﬁnite element with n layers and m nodes

Substituting element displacement ﬁeld Eq.(6) in to weak form Eq.(4), the nonlinear laminated ﬁnite element is obtained:

where secant stiffness matrix is:

Journal of Applied Engineering Science 10(2012)1, 218

(7)

Dr Marina ûetkoviü and etc. - Inﬂuence of boundary conditions of nonlinear response of laminated composite plates

and external force vectors

are:

(9) EXAMPLE A nonlinear bending of square cross ply 0/90 plate, with a=b=1 and h=0.1, with three different boundary conditions (SS, HH and CC, Eqs. 13, 14, 15), made of material [9]: (10) subjected to uniform transverse pressure is:

are analyzed. The incre-mental load vector

(11) The displacements and stresses are shown on Figures 2, 3 and are given in following nondimensional form:

(12) Following boundary conditions are analyzed: Simply supported (SS):

(13) Simply supported-hinged (HH):

(14) Clamped (CC): (15)

Journal of Applied Engineering Science 10(2012)1, 218

Dr Marina ûetkoviü and etc. - Inﬂuence of boundary conditionson nonlinear response of laminated composite plates

Figure 2. Nonlinear bending of square cross ply 0/90 plate with different boundary conditions and a/h=10; central displacement versus load parameter

Figure 3. Nonlinear bending of square cross ply 0/90 plate with different boundary conditions and a/h=10; normal stresses versus load parameter

CONCLUSION In this paper laminated layerwise finite element model for geometrically nonlinear small strain large deflection analysis of laminated composite plates is derived using the PVD. The PVD is utilized to formulate isoparametric finite element model. Finite element solution is incorporated into a original MATLAB computer program. The accuracy of numerical model is verified calculating nonlinear response of plates with different Journal of Applied Engineering Science 10(2012)1, 218

boundary conditions and different load direction (unloading/loading). The analysis has shown that the discrepancy of nonlinear from linear response is greater for flexible plates, such as plates with SS compared to hinged (HH) and clamped (CC) boundary conditions. It is verified that the change of load direction (unloading/loading) has no influence on displacement field, while stress field is load direction dependent. Finally, a close agreement with results from literature is achived.

Dr Marina ûetkoviü and etc. - Inﬂuence of boundary conditions of nonlinear response of laminated composite plates

REFERENCES 1) Reddy J.N, Barbero E.J, Teply J.L, A plate bending element based on a generalized laminated plate theory, International Journal for Numerical Methods in Engineering, 1989, Vol. 28, pp. 2275-2292 2) Tahani M., A. Andakhshideh ,Interlaminar stresses in thick rectangular laminated plates with arbitrary laminations and boundary conditions under transverse loads, Composite Structures, 2011, doi, 10.1016/ j.compstruct.2011.12.027 3) Vuksanoviü Ĉ., Linear analysis of laminated composite plates using single layer higherorder discrete models, Composite Structures, 2000, Vol.48, pp. 205-211. 4) ûetkoviü M, Vuksanoviü Ĉ, Bending, Free Vibrations and Buckling of Laminated Composite and Sandwich Plates Using a Layerwise Displacement Model, Composite Structures, 2009, Vol. 88(2), pp. 219-227 5) ûetkoviü, M., Application of ﬁnite element method on generalized laminated plate theory, Master Thesis, in serbian, Faculty of Civil Engineering in Belgrade, Serbia, 2005

6) ûetkoviü, M., Nonlinear behaviour of laminated composite plates, PhD Thesis, in serbian, Faculty of Civil Engineering in Belgrade, Serbia, 2011 7) ûetkoviü, M., Vuksanoviü Ĉ., Large deflection analysis of laminated composite plates using layerwise displacement model, Structural Engineering and Mechanics, 2011,Vol. 40, No. 2, pp 257-277 8) Messina A., Influence of the edge-boundary conditions on three-dimensional free vibrations of isotropic and cross-ply multilayered rectangular plates, Composite Structures, 2011, Vol.93, pp 2135–2151 9) Thankam V.S. and Singh, G. and Rao, G.V. and Rath, A.K., Shear flexible element based on coupled displacement field for large deflection analysis of laminated plates, Computers and Structures, 2003, Vol. 81, pp 309320. Paper sent to revision: 07.03.2012. Paper ready for publication: 30.03.2012.

Journal of Applied Engineering Science 10(2012)1, 218

doi:10.5937/jaes10-1663

Paper number: 10(2012)1, 219, 37 - 42

APPROXIMATE PROCEDURE FOR CALCULATION OF SHEAR STRESSES ıxz AND ıyz Dr Marina Rakoþeviü* University of Montenegro, Faculty of Civil Engineering, Podgorica, Montenegro For thick and moderately thick plates which have middle plane parallel to plane (x,y) state of the stress in cross section, which is described with component of the stress in plane (x,y), doesn’t give a realistic presentation of state of the stress. In order to define state of the stress more „real“ it is necessary to define shear stresses in planes (x,z) and (y,z). This paper shows one approximate procedure that can be used to calculate components of shear stresses ıxz and ıyz. Procedure is applied to example for calculation of shear stresses for laminated composite plates. Theoretical bases are based on Layerwise theory, and solutions of theory equations are determined in closed form. At the end of paper there are the results of procedure application for plates with geometrical and material characteristics which are given graphically, using charts. Keywords: shear stresses, composite plate, layerwise theory GENERAL Layered composite plates consist of orthotropic layers with arbitrary angle of orientation of fibbers. Fibber and basic mass of each layer can have different physical and mechanical characteristics. By combining layers of different characteristics we can get plates of significantly higher bending stiffness, as well as higher axial and shear stiffness. In order to solve the problem of layered composite plates single-layer ESCT theories are available as well as Layer-wise theories (GLPT). It is proved that the accuracy of the calculation impact of these plates, using single-theory, decreases with increasing of the thickness. Due to this, classical 2D slab models cannot provide “real” state of stress and deformations of thick and moderately thick plates, especially of plates with highly anisotropic characteristics, such as layered composite plates and plate with delamination. In recent decades, the Layer-wise theory is developed based on the assumption that the components of displacement through the thickness of the plate can be shown by one-dimensional interpolation functions. Combining 2D plate model, in the plane (x, y), and 1D model, perpendicular to the plane of the plate, we get a model that can be used in resolving thick and moderately thick plates as well as plates with various forms of geometric and material nonlinearities.

The above theory allows the introduction of geometric imperfections by expanding the Layerwise theory, i.e., by simply upgrading or adding new members. Layer-wise theory is based on an analysis of the layer as a part of composite plate. For each of the composite layers, single-layer theory or ESC theory is applied, and then the layers are connected by introducing the assumed interpolation function through the thickness of the plate. Depending on the selected interpolation functions solutions with more or less accuracy are obtained. The assumption that each layer has a different change of shifts allows the obtaining of more “realistic” effects in arbitrary cross-section [1], [2]. LAYER-WISE THEORY The mathematical model of linear Layer-wise theory is based on the foundations of the Layerwise theory which neglects the deformation perpendicular to the plane of the plate İzz=0, while the shear components İxy, İxz, İyz differ from the zero [3]. Deformation tensor obtains the following form:

* Faculty of Civil Engineering, Cetinjski put bb, 81000 Podgorica, Montenegro; marinara@cg.ac.me

(1)

Dr Marina Rakoþeviü -Approximate procedure for calculation of shear stresses ıxz and ıyz

which, because of the symmetry properties can be shown as a vector:

If, along the two adjacent layers, a linear interpolation function is adopted, then the number of nodes along the thickness of the plate - N is for one higher than the number of layers – n. Relations of the stresses and deformations are deﬁned for each viewed layer j:

(2)

(6) Relation of components of deformation tensor and components of displacement vector are deﬁned with:

(3)

where is the transformed material stiffness of j orthotropic layer. It is necessary to make the transformation of material characteristics because each of the layers may have fibbers that carry in different directions, i.e., the fibbers can cover arbitrary angle in the plane (x,y). After defining the variable , the stiffness of the composite is determined, as a system of layers, taking into account the impact of one layer to another, [4]. ANALYTICAL SOLUTION

Having in mind the above assumption it is concluded that component of displacement, perpendicular to the plane of the plate, is constant along the thickness of the plate, i.e., w(x,y,z)=w(x,y). In that case, displacement of arbitrary point of the plate can be shown as the sum of displacement of the point of middle plane of the plate U(x,y), V(x, y) and W(x,y) as well as additional displacement along the thickness of the plate U(x,y,z) and V(x,y,z):

For simply supported rectangular laminated composite plate, which contains n orthotropic layers, displacements are shown in the following form:

(7) (4) where: Additional displacements are displayed in the form of the sum as a product of appropriate componential displacement of j-point along the thickness and interpolation function :

The equations of equilibrium are obtained in the following form:

(8)

(5)

Qmn - coefﬁcients of the load.

Journal of Applied Engineering Science 10(2012)1, 219

Dr Marina Rakoþeviþ - Approximate procedure for calculation of shear stresses ıxz and ıyz

Coefficient matrix contains sub-matrixes K whose parts are the function of material stiffness of layered composite plate and the coefficients of Į and ȕ. The solutions of the system of equations (8) are unknown coefficients Xmn, Ymn, Wmn, RmnJ i SmnJ in the same number as the number of equations (3+2N). Once determined the solutions, using relations (7) the values of componential displacement are defined, and then the components of deformation tensor (3). Stress components are calculated using relation of (6) [3], [5]. APPROXIMATE PROCEDURE FOR CALCULATION OF SHEAR STRESSES ıXZ AND ıYZ Shearing stresses in the planes (x, z) and (y, z) are inter-layers stresses that are important for the analysis of thick and moderately thick plates as well as plates that contain some form of delamination. The shown procedure is approximate procedure that can be applied in the process of solving numerical equations of the problems [3], [5], [6]. From the constitutive equations (6), using solutions of equations (8) and relations (7), (4) and (3), along each layer j, constant values of shear stresses for an arbitrary point in the plane (x, y) are obtained:

)

Assuming parabolic shear stress change along each layer j:

(10) where z is coordinate of the local coordinate system of j layer of observed plate. The coefﬁcients represent the shear stresses and at the ends and in the middle of observed layer, while N1(z), N2(z) and N3(z) are single-dimensional rectangular interpolation functions deﬁned by the following expression:

(11) where hj is thickness of the layer j. It is obvious that for n layers there will be per 3n of unknown coefficients for the stress ıXZ and 3n of unknown coefficients for stresses ıXZ. To determine the unknown it is necessary to write 3n equations for the required stresses ıXZ and 3n for stresses ıYZ . Display of approximate procedure is given for the shear stresses in the plane (x,z) with unknown coefficients To determine the 3n of unknown coefficients we set the following conditions: 1) The shear stresses at the top and bottom fibers of the plate are zero. Applying this condition only two equations can be written: (12) ıXZ n= 0 za z=hn ıXZ1 = 0 za z=0 (13) 2) In the connections of layers shear stresses have equal values. This condition gives the (n-1) equation: ıxzj (z=0) = ıxz j-1(z=hj-1) za j=2,3,...,n (14) 3) Along each layer j shear stresses have constant values defined by the relation (9). From this condition n equation is obtained. Journal of Applied Engineering Science 10(2012)1 219

Dr Marina Rakoþeviü -Approximate procedure for calculation of shear stresses ıxz and ıyz

4) Change of derivative of shear stresses ıxz,z in the connections of layers defines (n-1) equation It is concluded that in total (2+(n-1)+n+(n-1)=3n equations can be written, i.e., as many as the number of unknown coefficients For the adopted parabolic change (10) and (11) from the first condition (12) it is obtained that:

(15) From the second group of equations (14) (n-1) equation forms are obtained: (16) The third group of equations are the constitutive relations (9) which are j=1,...,n. From the fourth group of equations it is obtained: (17) where and are the ﬁrst derivatives of the shear stresses obtained from constitutive equations. For the analytical solution difference between ﬁrst derivatives has the following form:

(18)

for j=2,n. After determination of solutions from the above system of equations , j=1,n, using the expression (10) and (11) values of the stresses can be calculated ıxzj per the thickness of the plate. Shear stresses in the plane (y, z) are obtained applying the same procedure with unknown coefﬁcients

NUMERICAL EXAMPLES Applying the approximate procedure in Figures 1 to 4, for the adopted number of layers and adopted characteristics of layers, the change in shear stress is given ıyz and ıxz in dimensionless form:

Figure 1: Distribution of stress and along the thickness of the plate with layers 0o/90o/0o

Journal of Applied Engineering Science 10(2012)1, 219

Dr Marina Rakoþeviþ - Approximate procedure for calculation of shear stresses ıxz and ıyz

A square plate of symmetrical and anti-symmetrical arrangement of layers is considered. Layers of the plate contain ﬁbbers that with the x axis form the angles 00 and 900. The load is

Figure 2: Distribution of stress

and

evenly distributed, and the material characteristics of layers are: E1/E2=25, E2=1, G12=G23=0.5, G23=0.2, V12=V13=0.25.

along the thickness 0o/90o/0o/90o

Figure 3: Distribution of stress and thickness 0o/90o/0o/90o/0o

Figure 4: Distribution of stress

and

CONCLUSION Using the constitutive relations, deﬁned for the j layer of composite plate, constant values of shear stresses ıxzj and ıyzj are obtained along the thickness. In this case, in the connection points of two adjacent layers there are different stress Journal of Applied Engineering Science 10(2012)1, 219

along the

along the thickness 0o/90o/0o/90o/0o/90o

values, while in the top and bottom ﬁbbers of the plate the shear stresses are different from zero. It is concluded that using constitutive relations of the stresses and deformations a real change of the stress ıxz and ıyz are not obtained along the thickness of laminated composite plates. It is possible, by shown approximate procedure

Dr Marina Rakoþeviü -Approximate procedure for calculation of shear stresses ıxz and ıyz

to obtain parabolic change of shear stresses along the thickness of each layer of laminated composite plate. Numerical examples given in this paper were obtained using tailor made program prepared by the author. The stresses along each layer are deﬁned in three points, two at the ends and one in the middle of each layer. Deﬁning realistic distribution of shear stresses ıxz and ıyz is especially important for thick and moderately thick plates, as well as for plates containing some of the forms of delamination.

REFERENCES 1) J.N.Reddy, D.H.Robbins Jr:”Theories and computational models for composite laminates”, American Society of Mechanical Engineers, 1994. 2) J.N.Reddy: “Mechanics of Laminated Composite Plates - Theory and Analysis”, Department of Mechanical Engineering Texas A&M University College Station,Texas,1997. 3) M.Rakoþeviü: “Statiþka analiza slojevitih kompozitnih ploþa primjenom metode konaþnih elemenata”, doktorska disertacija, Graÿevinski fakultet Univerziteta Crna Gora, Podgorica, 2005. 4) M.Rakoþeviü: “Proraþun krutosti slojevitih kompozitnih ploþa”,Zbornik radova GNP- Internacinalni nauþno-struþni skup graÿevinarstvo-nauka i praksa,Žabljak,Knjiga 1.,st.67-72.,20-24.februar 2006.g. 5) M.Rakoþeviü: “ Proraþun sastavljenih slojevitih ploþa “, Graÿevinar 63 (2011) 9/10, 819-825, 6) R.A.Chaudhuri, P.Seide: An approximate semi-analytical method for prediction of interlaminar shear stresses in an arbitrarily laminated thick plate, Computers and Structures, Vol.25, No.4, pp.627-636, 1987. Paper sent to revision: 07.03.2012. Paper ready for publication: 30.03.2012.

Journal of Applied Engineering Science 10(2012)1, 219

Dr ýaslav Mitroviü and etc. - From idea to implementation in protection of electronic editions (book)

Paper number: 10(2012)1, 220, 43 - 48

doi:10.5937/jaes10-1664

METHODS OF CALCULATING DEPRECIATION EXPENSES OF CONSTRUCTION MACHINERY Dr Predrag Petronijeviü* University of Belgrade, Faculty of Civil Engineering, Belgrade, Serbia Dr Nenad Ivaniševiü University of Belgrade, Faculty of Civil Engineering, Belgrade, Serbia Dr Marina Rakoþeviü University of Montenegro, Faculty of Civil Engineering, Podgorica, Montenegro Dr Dragan Arizanoviü University of Belgrade, Faculty of Civil Engineering, Belgrade, Serbia Depreciation expenses represent a signiﬁcant part of total expenses of construction machinery. Precise calculation of depreciation expenses is often difﬁcult or impossible. Straight line method of depreciation, which is commonly used in the calculation of ownership costs of construction machinery, does not give accurate results. This paper analyzes methods of depreciation expenses calculation, as well as their impact on the overall expanses of construction machinery and the impact on the cost per unit of material processed. Keywords: depreciation, construction equipment, expenses INTRODUCTION In order to achieve successful management of a construction company and each of the construction projects it is essential to have an adequate approach to estimating and control of the expenses related to construction machinery. The revenue received must exceed the expenses incurred for work of a machine. A precise review of all the expenses has a key importance in the process of construction machinery selection [1]. Expenses of work hour increase during the lifetime of construction machinery. This process continues until the moment it is economically more viable to sell than to continue using the machine. This moment is considered as the end of the economic life time of the machine which

can be much shorter than the physically possible life time i.e. the period in which a machine can perform its duties. This period can be increased by appropriate and regular maintenance and service. CALCULATION OF DEPRECIATION EXPENCES When calculating ownership expenses, the purchase value is a known amount, cost of capital can be accurately determined and so can insurance costs. The uncertainty lies in the calculation of depreciation expenses. The problem is even more signiﬁcant having in mind that these depreciation expenses constitute 10% to 25% of the total expenses of machine work (ﬁgure 1).

Figure 1 – Structure of expenses for hauler Volvo 25E (left) and excavator Caterpillar 320 * Faculty of Civil Engineering, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia; pecap@grf.rs

Dr Predrag Petronijeviü and etc. - Methods of calculating depreciation expenses of construction machinery

Depreciation represents the reduction of market value of a construction machine through time. The main causes of depreciation are: •

physical damages and wear and tear during work, and • lowering of value due to elapsed time and functional outdate. Depreciation value represents the difference between the market value of a construction machine at the time it was purchased and the market value when it is sold or destroyed. Period of depreciation is the length of time which elapsed between the time a machine was purchased and the time it is sold or destroyed. Depreciation expenses are calculated by dividing depreciation value (DEPvalue) with the period of depreciation (DEPperiod).

When calculating depreciation expenses, some factors are explicitly given and precise while others are a result of estimating. There is always a signiﬁcant degree of uncertainty when depreciated value of a machine in a

particular moment in time is defined, i.e. in the residual value which is defined as “the amount of money for which a machine can be sold in a particular moment in time”. When calculating the depreciation expenses residual value is the future value on the end date of the period of ownership of a construction machine, so this value has to be estimated. Usually residual value has the biggest fall in the first years of the machine’s work life, while this decrease is smaller as the machine gets older. Estimation of the residual value of a machine in some future moment is made based on assumptions about the market conditions, the state of the machine, degree of its maintenance, needs of the owner, marketing activities and a whole number of different parameters which very often cannot be precisely described. Gunnar L. [2] has developed a model for approximation of the residual value of machines based on statistical data obtained from successfully finalized sales on the construction machine market. His central hypothesis was that it is possible, based on the data collected from the previous generation (G1), to predict the residual value of the current generation (G) of machines (figure 2).

Figure 2 – Changes in the residual value

The model, based on the purchase price of the previous generation LPG-1, its residual value RVG-1 and the purchase price of the current generation LPG, predicts the residual value of the current generation RVG not only at present, but also in some future moment in time. The goal of the research was to deﬁne, based on the previously mentioned input data, a regres-

sion formula which would give an estimated residual value of a current generation construction machine. Formula should calculate the expected percentage of residual value RVP (Residual Value Percent) of the current generation (the ratio between the expected auction value and the recommended retail price). In total 11 regression formulas were analyzed, with the main requirement for the model that it can easily ﬁt into the Journal of Applied Engineering Science 10(2012)1, 220

Dr Predrag Petronijeviüa and etc. - Methods of calculating depreciation expenses of construction machinery

existing data, easily be interpreted, conﬁrmed and used. Based on previous analysis three regression models were proposed, with different complexity and level of accuracy. The conclusion was that RVP can successfully be predicted with a model based on a second degree polynomial. Also an important result of the research was that the most important factors which inﬂuence the residual value have been recognized.

The deficiency of such an approach lies in the fact that it is based on a large number of data on actually achieved auction prices on a narrowly defined second hand market. Also there are a significant number of variables which have to be linked to small territories and short periods of time. Another problem lays in the need to define a separate formula with different parameters for each type of construction machines.

Figure 3 - Graph of RVP values compared to data gained from auctions

The approach given in paper [2] shows that, based on statistical data, it is possible to predict the sale price of a construction machine but it is not realistically achievable in practice due to insufﬁciency of historic data and the market structure. For this reason calculation of depreciation is usually done by applying other models, primarily based on the purchase price of a machine and its assumed life time. In literature there are mainly three ways for calculating depreciation: • • •

Straight Line Method Sum-of-the-Years Method Declining Balance Method

where N is the planned number of years the machine is going to be used (work life). The annual depreciation amount (D) is calculated according to the formula:

where P (Purchase Price) represents the price which was paid at the time t when the company bought the machine (new or used) and F represents the Salvage Value (market value of the machine when it is sold N years after it was bought).

STRAIGHT LINE METHOD (UNIFORM LOWERING METHOD) Straight Line Method assumes uniform lowering of value during time. In general, annual depreciation rate (R) is calculated using the following formula: Figure 4 - The change of value during time applying linear (uniform) depreciation Journal of Applied Engineering Science 10(2012)1, 220

Dr Predrag Petronijeviü and etc. - Methods of calculating depreciation expenses of construction machinery

Due to the simplicity of calculations, this method is the most common method used in the calculation of expenses of construction machine’s work hour. When using this method new and very old machines have the same annual depreciation. SUM-OF-THE-YEARS METHOD On the contrary to the linear depreciation used by the Straight Line Method, Sum-of-the-Years Method has a different depreciation amount for each year. When using the Sum-of-the-Years Method annual depreciation rate (Rm) is calculated according to formula:

DECLINING BALANCE METHOD Declining-Balance Method is often used when calculating depreciation of machinery for companies’ accounting purposes. This method enables changes in the rate of depreciation of a machine thorough the whole period of its usage, up to the end of its work life, when it reaches the Salvage Value which represents the bottom line of the machines depreciated value. According to this method, annual depreciation rate depends on the remaining value of the machine in the accounting books. Machines which have a lower remaining accounting value will have a lower annual depreciation rate. The calculations are done according to formula:

where N is the number of years the company is the owner of the machine, m is a particular year for which the depreciation amount is calculated and SOY (Sum of the Years) is the sum of years the company owns the machine:

Annual depreciation amount is calculated using the following formula:

This method is closer to the realistic changes in the value of the machine. The value of the annual depreciation rate linearly changes, so the depreciation rate used for new machines is higher than the rate for older machines. So a bigger drop in its value a machine has when it is new, then when it is older.

where N represents the planned number of years the machine is going to be used (work life), X is a value between 1,25 and 2,0 depending on the required speed of depreciation. Annual depreciation amount (Dm) is calculated by multiplying the depreciation rate with the accounting book value of the machine for the previous year. Accounting book value of a machine for a particular year (BVm) is the accounting value of this machine for the previous year (BVm-1) lowered for the annual depreciation value (Dm) of the machine.

Figure 5 – Comparative graph for reduction of value through time

Journal of Applied Engineering Science 10(2012)1, 220

Dr Predrag Petronijeviüa and etc. - Methods of calculating depreciation expenses of construction machinery

Table 1 – Depreciation during 8 years for the three methods of calculation

Str Line

Declining Balance

SOY

Str Line

Declining Balance

Str. line

SOY

Decl. Balance (X=2)

Decl. Balance (X=1,25)

Value of the machine [%]

SOY

Annual depreciation amoun [%]

Year

Rate of depreciation

0,22

0,13

0.25

20,00

11,25

25,00

100,00

0,19

0,13

0.25

17,50

11,25

18,75

80,00

88,75

75,00

84,38

0,17

0,13

0.25

15,00

11,25

14,06

62,50

77,50

56,25

71,19

0,14

0,13

0.25

12,50

11,25

10,55

47,50

66,25

42,19

60,07

0,11

0,13

0.25

10,00

11,25

7,91

35,00

55,00

31,64

50,68

0,08

0,13

0.25

7,50

11,25

5,93

25,00

43,75

23,73

42,76

0,06

0,13

0.25

5,00

11,25

4,45

17,50

32,50

17,80

36,08

0,03

0,13

0.25

2,50

11,25

3,34

12,50

21,25

13,35

30,44

INFLUENCE OF THE METHOD OF CALCULATING DEPRECIATION EXPENCES ON THE TOTAL EXPENCES OF THE MACHINE WORK HOUR In order to analyze the inﬂuence of the method of calculating depreciation expenses on the total expenses of the machine work hour, testing was performed using calculations of the total expenses of the work hour and output of two machines. The ﬁrst machine was excavator Caterpillar 320, engine power 140kW with bucket size 0,9m3. The second machine was hauler Volvo 25E engine power 140kW and capacity 15m3. Data on the purchase price, available work hours and usage of fuel and lubricants have been taken from document [3]. When comparing the three methods for calculating depreciation, it is clear that the uniform depreciation (St. Line) method is the easiest for calculating, but the results have the biggest variance from real values. The diagram given by I. Gunar et al. [2] can be treated as a realistic diagram of depreciation. Newer the less this method of uniform depreciation is the method most frequently used in practice. Sum-of-the-Years Method gives results close to real depreciation values. The calculations are simple, and the calculations of the depreciation rates do not depend on the type of machine or location where the machine will be sold. Declining-Balance Method gives results close to the results of the SOY method, but the rate of depreciation can be changed. This method is very practical for accounting purposes. Journal of Applied Engineering Science 10(2012)1, 220

According to the calculated values, the nearest to real values of depreciation is the Sum-of-theYears Method. As shown in Fig.1, depreciation expenses constitute around 21% of the total expenses of the work hour of hauler Volvo 25E and around 26% of the total expenses of the work hour of excavator Caterpillar 320. These values are calculated using the uniform depreciation method. When using the SOY method (method which sufﬁciently well describes the changes of the residual value during time, the participation of the depreciation expenses drastically changes with the age of the machine. In the performed calculations, assumptions were that the work life of a machine is 8 years, the residual value at the end of work life is 10% of the purchase price and that the annual number of work hours is 1.500. The depreciation expenses were calculated by dividing the annual depreciation calculated by using the Sum-of-the-Years Method and the Straight Line Method (uniform lowering method) with the annual number of work hours.

Figure 6 – depreciation expenses using SOY and Str. Line methods for excavator CAT 320

Dr Predrag Petronijeviü and etc. - Methods of calculating depreciation expenses of construction machinery

In the first year, the depreciation expenses calculated using SOY method are almost twice the expenses calculated using uniform depreciation (Straight Line). When using the straight line method, total expenses of the work hour and the cost per unit of material processed are the same during the entire work life of a machine and the amounts are: Cjm = 0,67€/m3 Kh= 58,30 €/h, If the calculation of depreciation is done using SOY method, expenses of work hour and cost per unit of material processed, in the first year of work of the machine, are: Cjm = 0,86€/m3 Kh= 74,86 €/h, Using the same method, in the eight year the situation is opposite. The lowering of value of the machine is much smaller than in the first year, so the depreciation expenses are smaller than if Straight Line method was used: Kh= 41,74 €/h, Cjm = 0,48€/m3 In the middle of the work life of a machine there is no significant differences between depreciation expenses calculated by the two methods, although at that moment there is the biggest difference between the residual value calculated using SOY and Straight Line methods. The difference is 21% of the purchase price of the machine.

CONCLUSION Previous data shows that calculations of depreciation according to the uniform method (Straight Line), although widely used, give results which are not in line with real life values. In the ﬁrst half of the work life, depreciation expenses are lower than real, while in the second half of the work life depreciation expenses calculated by using this method are higher than real. If the machine does not change its owner during its entire work life, this difference will not have signiﬁcant importance. In case a company bought a new machine, used it half of its work life and then sold it, the expenses which the company has calculated through depreciation expenses will be much lower than the difference between the purchase price and its residual (auction) value in the middle of its work life. Sum-of-the-Years Method gives results close to real depreciation values. The calculations are simple, and the calculations of the depreciation rates do not depend on the type of machine or location where the machine will be sold. If the depreciation is calculated as the lowering of the residual value in the unit of time, in the middle of the work life of the machine, values calculated according to the uniform method (StraightLine) and SOY method are practically equal. REFERENCE 1) P. Petronijeviü, “Optimizacija izbora graÿevinskih mašina”, PhD thesis, Belgrade, 2011.. 2) Gunnar L. Christine M. Anderson, Michael Vorster, “Statistical Considerations for Predicting Residual Value of Heavy Equipment”, Journal of Construction Engineering and Management, ASCE, July 2006 page 723 – 732 3) USACE, “Construction Equipment Ownership and Operating Expense Schedule”, 2007. Paper sent to revision: 07.03.2012. Paper ready for publication: 02.04.2012.

Journal of Applied Engineering Science 10(2012)1, 220

MSc Nenad Fric and etc. - Wind towers - design of friction connections for asembling sections of tubular steel towers

Paper number: 10(2012)1, 221, 49 - 52

doi:10.5937/jaes10-1670

WIND TOWERS – DESIGN OF FRICTION CONNECTIONS FOR ASEMBLING SECTIONS OF TUBULAR STEEL TOWERS MSc Nenad Fric* University of Belgrade, Faculty of Civil Engineering, Belgrade, Serbia MSc Boris Gligić University of Belgrade, Faculty of Civil Engineering, Belgrade, Serbia MSc Jelena Dobrić University of Belgrade, Faculty of Civil Engineering, Belgrade, Serbia Dr Zlatko Marković University of Belgrade, Faculty of Civil Engineering, Belgrade, Serbia The towers represent about 15 to 20% of the total installation costs and optimized design may therefore lead to substantial savings with regard to costs and use of materials. Some of the most interesting design and manufacturing details are connections used to assemble sections of tubular steel towers supporting wind turbines. There is traditional flange ring connection and on the other side, as a new proposal, friction connection. In this paper theoretic basis of design of friction connection of wind towers is given. Keywords: wind tower, friction connection, tension controlled bolts, friction surfaces GENERAL Currently, assembling sections of tubular steel towers with bolted ring flange connections is more often used than the friction connections. Bolted flange ring connection consists of steel rings which are welded at both tube ends and of high strength bolts which connect these rings. Friction connections constitute an innovative solution (in alternative to the flange connections) for assembling joints in tubular towers for wind turbines.

Figure 1. Bolted L-flange ring connection

Concerning the conception of the new configuration: • it uses tension control bolts (TCB), tightened by rotation of the nut (inside of the tower), • the bolts are preinstalled in normal holes on the upper segment of the tower, • or easy assembly it is used long open slotted holes on the lower segment of the tower.

Figure 2. Main concept of the friction connection in tubular tower for wind

* Faculty of Civil Engineering, Bulevar Kralja Aleksandra 73, 11000 Belgrade, Serbia; fric@imk.grf.bg.ac.rs

MSc Nenad Fric and etc. - Wind towers - design of frictions connections for asembling sections of tubular steel towers

Figure 3. Main concept of the friction connection in tubular tower for wind turbines

Tension Control Bolts (TCBs) are a special type of high strength fasteners initially developed in Japan (Figure 4). This type of fasteners was chosen because it was available on the market and for its simple installation. The producer claims that tightening procedure can be up to two times quicker and require four times less man hours than compared to normal bolts. It might also be advantageous to rely on electrical power rather than pneumatic or hydraulic power which are more difficult to provide during assembly of a wind tower. The mechanical properties are equivalent to those of High Strength Bolts. Grade S10T may be considered as bolt grade 10.9.

DESIGN OF FRICTION CONNECTIONS Friction connection is a connection where the resistance and the stiffness are achieved by the friction action between the joint plates. The global behaviour depends mainly of two key parameters: 1. Preload force in the bolts (high strength bolts) 2. Slip factor μ between contact surfaces (surface roughness and surface treatment).

Figure 6. Load transfer mechanism – friction connection Figure 4. Tension control bolts, Grade S10T (prior to pretendioning) tensioning, thightening

Their tightening is carried out entirely at the nut end (See Figure 5) with a special electric wrench. The spline is held by the inner socket while the outer socket rotates and turns the nut (a). An increasing tightening torque develops between inner and outer socket. When the resistance of the calibrated break-neck is reached it shears off, allowing the inner socket to rotate (b).

DESIGN OF FRICTION CONNECTIONS ACCORDING TO EUROCODES In Europe, the analysis and design of friction connections are predicted in Eurocode 3: Design of Steel Structures, Part 1.8: Design of joints. The execution specifications are covered by EN 1090: Execution of steel structures and aluminium structures, Part 2: Technical requirements for steel structures. In friction connections of Category C (slip-resistant at ultimate limit states) the failure modes are: 1. Slip resistance – Fs,Rd (in general the governing mode): 1)

Figure 5. Tension control bolts – tightening procedure

Journal of Applied Engineering Science 10(2012)1, 221

MSc Nenad Fric and etc. - Wind towers - design of friction connections for asembling sections of tubular steel towers

μ – slip factor (Table 18 of EN 1090-2), n – number of contact surfaces, ks – parameter (ks=1.0 for normalized holes;

ks=0.63 for slotted long holes), γM3 – partial safety factor taken as γM3=1.25

Table 1. Categories of bolted connections Category

Criteria

Remarks

Shear connections Fv,Ed ≤ Fv,Rd

A bearing type

Fv,Ed ≤ Fb,Rd

B Slip-resistant at serviceability

No preloading required. Bolt classes from 4.6 to 10.9 may be used.

Fv,Ed,ser ≤ Fs,Rd,ser

Preloaded 8.8 or 10.9 bolts should be used.For slip resistance at serviceability see 3.9.

Fv,Ed ≤ Fv,Rd Fv,Ed ≤ Fb,Rd

C Slip-resistant at ultimate

Fv,Ed ≤ Fs,Rd Fv,Ed ≤ Fb,Rd Fv,Ed ≤ Nnet,Rd

2. Bearing of the bolts or the joined plates due to contact pressure – Fb,Rd: 3)

Preloaded 8.8 or 10.9 bolts should be used.For slip resistance at ultimate see 3.9.Nnet,Rd see 3.4.1(1) c).

ns – number of bolts in rows, μ – slip factor, ks – reduced factor for long slotted holes (ks=0.63), γM3 – partial safety factor taken as γM3=1.25. 2. Bearing resistance does not develop because the holes are slotted. 3. Elastic resistance (instead ultimate resistance) of the net cross section of shell:

DESIGN OF FRICTION CONNECTIONS PROPOSED TO USE IN WIND TOWERS In the configuration of friction connection proposed to use in wind towers, there are some differences, when compared with normal friction connections. The ultimate resistance can be determined according to the following failure modes: 1. Ultimate slip design resistance Zs,Rd of one bolt row of the friction joint (segment model): 5)

c – segment width (distance between two bolt rows), d0 – diametar of the hole, s – shell tickness, fy,shell – characteristic yield strength of shell material, γM0 – partial safety factor taken as γM0=1.00 The friction surfaces and corresponding slip factor values predicted in EN 1090, Part 2 are described in the following table.

Table 2. Classification that may be assumed for friction surfaces Class

Slip factor μ

Surfaces blasted with shot or grit with loose rust removed, not pitted.

Surface treatment

0,50

Surfaces blasted with shot or grit: a) spray-metallized with a aluminium or zinc based product, b) with alkali-zinc silicate paint with a thickness of 50 μm to 80 μm

0,40

Surfaces cleaned by wire-brushing or flame cleaning, with loose rust remover

0,30

Surfaces as rolled

0,20

Journal of Applied Engineering Science 10(2012)1, 221

MSc Nenad Fric and etc. - Wind towers - design of frictions connections for asembling sections of tubular steel towers

In wind towers in general the surfaces are blasted and zinc coated (μ=0,40 to 0,50). For other surface treatment – the slip factor may be obtained through experimental tests, in accordance with the normalized procedure described in Annex G of EN 1090, Part 2.

At this moment, bolted ring flange connection is most often used assembling detail for wind towers. Table 4 illustrate material costs for this type of connection (defined by the radius and type of bolts) and it is very obvious that friction connections are much less expensive.

CONCLUSION

REFERENCE

Advantages (compared with actual flange connections) of the new configuration (friction connection) for use in wind towers are: 1. simpler to fabrication, 2. less expensive, 3. easy to assembly in situ – open slotted holes allowed the angular alignment while the upper segment is slide down to the final position, 4. slot weaken the lower section providing less sensitivity to the assembling tolerance (lower parts between slotted holes may bent), 5. the shell bending stiffness is stiffened by the overlapping connection and 6. better fatigue resistance. 7. Following table illustrate material costs for friction connections (defined by type and number of bolts).

1) EN 1993-1-8 (2005). “Eurocode 3 - Design of steel structures - Part 1-8: Design of joints”, CEN, Brussels, Belgium. 2) EN 1090-2 (2008). “Execution of steel structures and aluminium structures – Part 2: Technical requirements for steel structures.” 3) EN 1993-1-9 (2005). “Eurocode 3 - Design of steel structures - Part 1-9: Fatigue”, CEN, Brussels, Belgium. 4) Husson W. 2008. Friction connections with slotted holes for wind towers. Luleå University of Technology. 2008:45. 5) Heistermann C. 2011. Behaviour of Pretensioned Bolts in Friction Connections. Luleå University of Technology. 2011. 6) Training Course Wind towers: Design by FEM and Technological Features, Coimbra, Portugal, 2011. 7) N. Fric, M. Pavlović, Z. Marković, D. Buđevac: “ WIND TOWERS – DESIGN OF FLANGE RING CONNECTION”, 14th International Symposium MASE, Struga, Macedonia, 2011., p.259-264

Table 3. Prices of friction connections Component

Unite price [€]

Amount

Total price [€]

Connection 1 Bolt (M30x110 S10T)

5,45

588

3205

Total:

3205

Connection 2 Bolt (M30x110 S10T)

5,45

351

Paper sent to revision: 09.03.2012. Paper ready for publication: 02.04.2012.

1913

Table 4. Prices of bolted flange ring connections Component

Unite price [€]

Amount

Total price [€]

Connection 1 Flange (da=3917mm)

6762

13524

Bolt (M42x245 10.9)

20,32

124

2520

Total:

16044

Connection 1 Flange (da=3448mm)

4395

8790

Bolt (M36x205 10.9)

11,40

116

1322

Journal of Applied Engineering Science 10(2012)1, 221

doi:10.5937/jaes10-1665

Paper number: 10(2012)1, 222, 53 - 58

STRENGTHENING AND OVERBUILDING OF CAR SERVICE „AUTOMAKEDONIJA“ IN SKOPJE, MACEDONIA Dr Todorka Samardžioska* University of Skopje, Faculty of Civil Engineering, Skopje, Macedonia Dr Ana Trombeva-Gavriloska University of Skopje, Faculty of Civil Engineering, Skopje, Macedonia Dr Petar Cvetanovski University of Skopje, Faculty of Civil Engineering, Skopje, Macedonia Mr Denis Popovski University of Skopje, Faculty of Civil Engineering, Skopje, Macedonia Mr Mile Partikov University of Skopje, Faculty of Civil Engineering, Skopje, Macedonia Repair of the existing buildings has always been a great challenge for the building companies and for the civil engineering scientists, as well. When there is no available design documentation, a chain of activities precede to the main design for repair: measuring, in situ geotechnical investigations, determination of the quality and quantity of the built-in materials with various methods, etc. An example for repair and strengthening of the existing structure of a car service in Skopje, Republic of Macedonia, is presented in this paper, as well as a new steel structure for overbuilding. Keywords: strengthening, mechanical properties, reinforced concrete structure, steel structure INTRODUCTION The building of the car service “Automakedonija”, located in Avtokomanda in the city of Skopje in Republic of Macedonia, consists of two parts: the first one built in 1968, and the second one in 2006. The first one is used as a car service, and the second one has been adopted for offices and showroom. The new part of the building is physically separated with an expansion joint and it works independently of the old building. There is no design documentation for the structure of the old building from the construction period. Therefore, for the aims of the new building, geotechnical exploration of the soil has been performed during 2005 for the aims of the new building foundation. Last year, the Investor required an expert opinion about the bearing capacity of the existing structure, which is single storey reinforced concrete frame structure. Five frames in x-direction and four frames in ydirection were originally roofed with a reinforced concrete slab. A layer of low quality concrete with single slope and hydro-insulation were placed over the flat concrete roof slab for drainage and Journal of Applied Engineering Science 10(2012)1

protection of the atmospheric water and snow inﬂuence. Few years ago, when the new part of the building was constructed, the old building was roofed with metal sheeting, installed over a light steel structure. In that way, the reinforced concrete roof slab was completely protected of outside inﬂuences. An expert team from the Faculty of Civil Engineering in Skopje performed measuring and survey of the old building, as well as estimation of the quality and the quantity of the built-in materials and static analysis of the bearing capacity of the existing old building. The obtained reinforcement for the external columns in the building envelopes was greater than the existing built-in one, therefore there was a necessity of additional reinforcement. This problem was solved with another strengthening solution, reinforced concrete walls at the corners of the building. This solution gives an opportunity of re-distribution of the structural loads and of the bending moments, therefore the columns in the building envelope will be affected by loads with lower intensity. The resulting expert elaborate, see [2], states

Dr Todorka Samardžioska and etc. - Strengthening and overbuilding of car service “Automakedonija” in Skopje, Macedonia

that: „For the aims of overbuilding of administrative-business space onto the existing reinforced concrete slab, completion of Main Design for overbuilding is recommended. The new design should give a solution not only for the new storey, but also for the strengthening of the existing ground ﬂoor structure with stiffening of the building for satisfying the complete static and dynamic requirements”. The Main Design, see [1], consists of strengthening of the reinforced concrete structure and new steel structure for overbuilding.

ing of the lower part of the slab and the beams was not possible. Ten measures have been performed for each of the mentioned elements, and the average values are represented in the following Table 1: Table 1. Concrete class measured with Schmidt hammer element

QUALITY OF THE BUILT-IN MATERIALS

concrete class [MPa]

external column

36.7

internal column

36.5

slab – upper side

20.4

Building geometry The orthogonal frames of the old building structure consist of reinforced concrete columns and beams. The dimensions of all columns are 40/40cm, while the beams are with rectangular cross sections of two different sizes: the internal beams in x-direction are 50/45cm, while all the others are with dimensions of 40/45cm, see Figure1.

These results were not sufﬁcient; therefore kerns had been taken out as another method for conﬁrmation of the concrete class for all structural elements. One cylindrical sample was taken from the slab and two from the beams, see Figure 2.

Figure 1. a) Layout of the building; b) 3D model of the building In order to determine the thickness of the rooﬁng reinforced concrete slab, few holes were drilled in it. Slab thickness dp=15cm has been determined, and over it a layer of low quality concrete was placed with obviously smaller granulation and strength, with thickness of 5-15cm that enabled a slope for drainage of the atmospheric water.

Figure 2. Three sample cylinders taken from the slab and the beams

The obtained results for the samples are presented in the Table 2: Table 2.Concrete class obtained with sample kerns h [mm]

label

G [gr]

ҏ [kN/m3]

Fc [MPa]

24.35

31.1

slab I

94 103.4 717.2 1746.4

slab II

93.6

649.2 1528.9

23.55

27.6

Quality of the concrete

G-1 beam 94

93.1

645.7 1527.6

23.66

23.2

The quality of the built-in concrete was determined with in-situ testing, using the method of Schmidt hammer. The testing has been performed on two columns – one external and one internal and on the upper layer of the reinforced concrete slab. The measuring with the Schmidt hammer requires large, ﬂat and clean surface for obtaining reliable results, therefore the measur-

• Quality of the reinforcement With opening of the structural elements, i.e. removing the mortar layer and the protective concrete layer, the reinforcement in the elements was determined, see Fig. 3. All of them have been reinforced with smooth reinforcement GA 240/360, typical for the period of the building construction.

Journal of Applied Engineering Science 10(2012)1, 222

Dr Todorka Samardžioska and etc. - Strengthening and overbuilding of car service “Automakedonija” in Skopje, Macedonia

Figure 3. Reinforcement in the structural elements: a) slab, b) beam

• Foundation of the building Due to the fact of non-existing design documentation, individual foundations with dimensions of 80x80cm were assumed at foundation depth of 0.8m. The choice of the soil for the static analysis was inﬂuenced also by the results in the Elaborate for the performed terrain investigations and laboratory testing for the site location, which was completed before the construction of the new building, see [3]. STRENGTHENING OF THE RC STRUCTURE The strengthening of the existing reinforced concrete structure has been performed by adding reinforced concrete walls that contribute to the horizontal stiffness of the structure, as well as to its seismic eligibility. Four reinforced concrete walls are designed to be placed, two in each orthogonal direction. The walls in x-direction are placed along the axes RX1 and RX4, while in y-direction along RY1 and RY3 axes. The position of the reinforced concrete walls is given in the Figure 1b. The walls have dimensions: length 1.5m and width of 40cm. They are designed of concrete MB 30, while the reinforcement is RA 400/500-2. The reinforced concrete walls are founded over foundation band at level -0.50 m, according the drawings of the existing foundations. If necessary, during the foundation works, the foundation can be modiﬁed depending on the existing foundations. In order to provide complete connection

between the column and the reinforced concrete wall, the protective concrete layer of the column should be removed. Afterwards, reinforcing of the wall follows. The protective concrete layer should be renovated during the concreting of the wall. The reinforced concrete wall is designed to terminate 5 cm below the beams with placement of expanded polystyrene, in order not to introduce an additional load to the beams of the existing structure. The integral calculation of the existing strengthened and overbuilt structure is performed with three dimensional model, using the sophisticated software package TOWER6. The analysis of the loads comprises: permanent loads, imposed loads, loads of the overbuilt steel structure and seismic loads. The maximal period obtained due to seismic action is 0.338 sec in x-direction, and 0.3079 sec in y-direction. The appropriate maximal displacements at a level of the existing structure are 4.94 mm and 4.1. mm. The control of the bearing capacity of the structural elements has been performed using the characteristic loads envelope, according to the Rulebook for concrete and reinforced concrete – PBAB 87. Detailed representations of the load cases, geometry of the structure, bending moments envelopes and necessary reinforcement were given in the Main design of the overbuilding, see [1]. Typical examples ɚre presented in the Figures 4 and 5.

Figure 4. Maximal bending moments in one of the frames in y-direction Journal of Applied Engineering Science 10(2012)1, 222

Dr Todorka Samardžioska and etc. - Strengthening and overbuilding of car service “Automakedonija” in Skopje, Macedonia

Figure 5. Maximal bending moments in one of the frames in x-direction

STEEL STRUCTURE FOR OVERBUILDING The overbuilding is designed of light steel structure with tubular square and rectangular cross sectioned proﬁles. Before the construction of the steel structure, the layer of low quality concrete with single slope and the hydro-insulation with average thickness of 10cm should be removed from the reinforced concrete slab, which represents a load of 2.4 kN/m2. The columns are designed as SHS150.6 placed over the existing

reinforced concrete columns. The connection of the steel columns with the existing structure is performed using 8 anchors of 16 for each column, sealed in the perforated holes ( 25) in the concrete. The part of the overbuilding between the rows B and D and the lines 2 and 4 is elevated with a ridge in the middle (line 3). The edge parts are lower, with drainage towards the building sides, see Fig. 6.

Figure 6.Three-dimensional model of the steel structure for overbuilding

Span structure consists of truss girders framed in the columns. The trusses are placed in the rows B, C and D with span of 7m each, except the truss between the lines 2 and 4 which span is 14m, i.e. there is a lack of a column at position ɋ-3. Sliding trusses are designed between the columns Ⱥ-1 and ȼ-2, as well as between the Ⱥ-5 and ȼ-4. The truss girders at the lower part (RN1, RN2 and RN3) have been designed with ﬂanges of SHS100.5 and diagonals and verticals of SHS60.4. The truss girders in the upper part in

the rows B and D (RN4) have been designed with ﬂanges of SHS80.4 and diagonals of SHS50.3, see Fig.9. The truss in the row C (lines 2 and 4), with a span of 14m has been designed with ﬂanges of SHS100.5 and vertical and diagonal elements of SHS80.4 and SHS60.4. The connection along the lines 1 and 5 and row A, at the lower part, is realized with Vierendeel girders, as well as for the connection along the lines 2 and 4, at the upper part, see Figure 10. Joints of the structural elements have been performed with welding. The whole steel structure is made of steel with quality ɋ0361 (Ȱ235). Journal of Applied Engineering Science 10(2012)1, 222

Dr Todorka Samardžioska and etc. - Strengthening and overbuilding of car service “Automakedonija” in Skopje, Macedonia

Figure 7. Section along B-axis

Figure 8. Section along axis 3

Figure 9.Truss girder RN4

Figure 10. Vierendeel girders

Journal of Applied Engineering Science 10(2012)1, 222

Dr Todorka Samardžioska and etc. - Strengthening and overbuilding of car service “Automakedonija” in Skopje, Macedonia

The static analysis of the steel structure has been performed with the software package SAP2000. The model of the structure is special, consisted of frame elements. The inﬂuences of the permanent loads, snow, wind and seismic loads have been taken into account for the calculation. Control of the stresses and stability of the structural elements has been performed, as well.

REFERENCE 1) Main Design of overbuilding of the car service “Automakedonija” in Avtokomanda – Skopje, phase statics and dynamics, Faculty of Civil Engineering, 2011 2) Expert elaborate for the bearing capacity of the old building of the car service “Automakedonija” in Avtokomanda – Skopje, Faculty of Civil Engineering, 2011. 3) Elaborate for the performed terrain investigations and laboratory testing for the site location “Automakedonija” – Skopje, ADG Geotehnika, 2005. Paper sent to revision: 09.03.2012. Paper ready for publication: 02.04.2012.

Journal of Applied Engineering Science 10(2012)1, 222

Journal of Applied Engineering Science 10(2012)1

EVENTS REVIEW

CIVIL ENGINEERING - SCIENCE AND PRACTICE 4th INTERNATIONAL CONFERENCE ŽABLJAK, 03-07 MARCH 2012 Faculty of Civil Engineering, University of Montenegro, organized five-day International Conference “Civil Engineering – Science and Practice”, GNP 2012, at Žabljak, Montenegro, 03-07 March 2012. The aim of the Conference was to present and share recent achievements and latest developments in the broad fields of civil engineering science and practice. The Conference was great opportunity to meet colleagues and to exchange experiences in the wide domain of civil engineering and related disciplines, as well as to enjoy the most beautiful ski-resort of Montenegro. Started from 2006, GNP conferences were traditionally held every second year in the famous skicenter Žabljak on 1456 meters of altitude. Number of scientific papers, authors, participants, as well as number of represented countries continuously grows. Papers for GNP2012 were received from 16 different countries. Scientific Board, which includes 43 professors from 18 different Faculties for Civil Engineering, made a review of 400 received papers. In the Conference Proceedings GNP 2012 published 331 positively evaluated papers at approximately 2500 pages. Published papers were signed by 596 authors and co-authors grouped in 18 different topics. This year the event was attended by about 350 participants from universities, institutes and from industry. Participants were from the former Yugoslavia, as well as from the other countries. Besides the presentation of scientific papers, published in the Proceedings of the Conference, during GNP 2012 were held presentations of the leading construction companies and institutions both from Montenegro and wider European area. Engineering Chamber of Montenegro held four round tables with the following topics: • Act of engineering chamber, • Current problems of construction, • Application of FIDIC conditions of contract and • Conditions for the realization of international finance project in Montenegro. The GNP 2012 Organizing Committee had nine members, employees of Civil Engineering Faculty in Podgorica. Seven students from final year of Civil Engineering Faculty in Podgorica, authors of scientific papers, were also engaged in the organization of the conference. Credit for the successful realization of GNP 2012, belongs to the sponsors and friends of the Conference, representatives of foreign and domestic institutions, which are pointed out in the GNP 2012 Proceedings. Besides contributing to the science and profession, GNP are conceptually organized in such a way that leaves to the participants a considerable space of time for socializing, skiing, walking and other ways of enjoying nature and the beauty of Durmitor national park. Parallel working sessions in three halls were held in the morning, simultaneously with the poster sessions, from 8.30 to 11.00, in afternoon from 16.30h to 20.30h. Rest of the time was devoted to the enjoyment in the snow and the evening program content. This year the Youth Theatre from Podgorica bought further good mood to the Conference participants with special performance “Canary Soup!” Visit the web site www.gnp.ac.me and feel the atmosphere of the GNP 2012. Come to socialize at GNP 2014!

Journal of Applied Engineering Science 10(2012)1

ANNOUNCEMENT OF EVENTS

APPLICATION OF ISO 9004:2009 TOOLS WITH PURPOSE TO IMPROVE EFFECTIVENESS OF ISO 9001:2008 QUALITY MANAGEMENT SYSTEM Budva, Hotel Aleksandar, 25th-28th June, 2012 You have implemented QMS, but you don’t have expected beneﬁts or you think that you don’t use its full potentional? For you it seems that Quality Management System is inert? You think that problem is in people? Is it so? Where is the problem? How to achieve business success by applying Quality Management System? Answer: PRACTICAL INSTRUCTIONS FOR APPLYING QUALITY MANAGEMENT SYSTEM! Where: TRAINING “APPLICATION OF ISO 9004:2009 TOOLS WITH PURPOSE TO IMPROVE EFFECTIVENESS OF ISO 9001:2008 QUALITY MANAGEMENT SYSTEM” PROGRAMME: 1st Day •

Registration of participants, distribution of working material, determination of the speciﬁc company which will be used for practical exercise

2nd Day • •

Presentation 1: Introduction in training- Objective and content of training; Presentation 2: Reminder – Interpretation of requirements ISO 9001:2008 standard, in regard to the most often practical problems;

3rd Day •

• • •

Presentation 3: ISO 9004: 2009 - Interpretation of requirements ISO 9004:2009 standard with recommendations for performance improvement of implemented ISO 9001:2008 QMS; Presentation 4: Business risk and methods for evaluation of risks Presentation 5: Decision making based on evaluation risk Presentation 6: Implementation of recommendations for improving and evaluation of implemented solutions performance

4th Day Workshop 1: Discover the company X Workshop 2: Identify problems in company X Workshop 3: Apply the recommendations for improvments in company X Workshop 4: Evaluate the effect of implemented solutions Cost of the training is 49.000,00 RSD. For registration and payment until 1st June discount is 10%. Payment to the account 290-825-93, Universal bank Belgrade, with reference number PE1. Price includes participation, extensive work material, certiﬁcate and refreshments during the breaks.

The price does not include transport and accommodation costs that should be covered by the participants. Reservation of accommodation as well as dinar payments for hotel Aleksandar and Slovenska plaža are possible with the Kolubara turs agency at telephone: 011 8123 323

Institute for research and design in commerce and indistry Jurija Gagarina 12b, 11070, New Belgrade, Serbia Tel: +38111/ 6300 750; www.iipp.rs

Journal of Applied Engineering Science 10(2012)1

BOOK RECOMMENDATION Recommended by: Doc. dr Vesna Spasojeviü - Brkiü FROM ENVIRONMENTALLY RESPONSIBLE BUSINESS TO PROFIT: Practical guide for small and micro-enterprises Author: Dr Maja S. Todoroviü This practical guide has emerged as a result of years in consulting and research experience. It represents concise information on how small and micro-enterprises with currently available resources and opportunities in Serbia can apply a number of simple improvements in order to operate environmentally responsible while at the same time achieving cost savings and profit. Although small and micro-enterprises represent the majority of companies in Serbia, there is relatively small amount of information on how these types of companies by applying simple principles can operate environmentally responsible. Most medium and large companies already possess some knowledge and experience in conducting environmentally responsible business. Also, they have enough resources to organize department which will only deal with environmental issues of the company. On the other hand, small and microenterprises usually do not have enough information and/or resources and responsibility for environmental issues is often assigned to employees that already have a number of other work commitments. As such, guide is intended for business owners and company managers who don’t have much time to devote to this subject. Taking that into consideration, guide has been clearly defined and consists of: • Strategic approaches and tools for development of environmentally responsible business; • Questionnaires and checklists for the assessment and evaluation of environmental impacts of the operational processes in the following categories: ż energy consumption; ż water consumption; ż supply chain; ż transport; ż environmental suitability of the production/product; ż waste management; • Seven step action plan for continual improvements. The guide is written in easily understandable language and terminology. For efficient use of the proposed methodology, it has been further enriched with case studies, and analysis of the benefits of green marketing for small business competitiveness. Effective implementation of certain instruments is given for example of small business in service industry. In the end, highlighted features of the guide are useful sources of information on terms of legal regulations, programs, businesses, institutions and financing opportunities. A Practical Guide: “From environmentally responsible business to profit” is a true guideline for small and micro enterprises in their effort to reconcile business success with environmental responsibility. Format B5, 144 pages. ISBN: 978-86-7466-4162-2 Publisher: Academic Mind

Reviewer: Prof. dr Maja Levi-Jaksiü

Journal of Applied Engineering Science 10(2012)1

INSTRUCTIONS FOR AUTHORS The benefits of publishing in Journal for Applied Engineering Science are: • No page charges • World wide exposure of your work • Accelerate publication times • Online author service • Automatic transfer of metacontent in SCOPUS, SJR, SCIndeks and other bases supporting international protocols for data transfer • Assignment of numerical identifiers DOI • Fair, constructive and able to follow reviewing process • Dedicated team to manage the publication process and to deal with your needs Submission of the papers has to be done online, trough journal e-service at http://scindeks-eur.ceon.rs/index.php/jaes. For assistance during the process of submission and publication, please contact graphical editor Mr. Darko Stanojevic at dstanojevic@iipp.rs or +381 116300750 Every manuscript submitted to JAES will be considered only if the results contained in the paper were not already published, that are not currently in the process of publishing and not to be published in another journal. Each paper is sent to a review by two independent experts and the authors are obligated to adopt the observations and comments of the reviewers. Articles presented at conferences may also be submitted, provided these articles do not appear in substantially the same form in published conference proceedings. All articles are treated as confidential until they are published. Manuscripts must be in English free of typing errors. The maximum length of contributions is 10 pages. THE FORMAT OF THE MANUSCRIPT The manuscript should be written in the following format: • A Title, which adequately describes the content of the manuscript. • An Abstract should not exceed 250 words. The Abstract should state the principal objectives and the scope of the investigation, as well as the methodology employed. It should summarize the results and state the principal conclusions. • Not more than 10 significant key words should follow the abstract to aid indexing. • An Introduction, which should provide a review of recent literature and sufficient background information to allow the results of the article to be understood and evaluated. • A Theory or experimental methods used. • An Experimental section, which should provide details of the experimental set-up and the methods used for obtaining the results. • A Results section, which should clearly and concisely present the data using figures and tables where appropriate. • A Discussion section, which should describe the relationships and generalizations shown by the results and discuss the significance of the results making comparisons with previously published work. (It may be appropriate to combine the Results and Discussion sections into a single section to improve the clarity). • Conclusions, which should present one or more conclusions that have been drawn from the results and subsequent discussion and do not duplicate the Abstract. • References, which must be cited consecutively in the text using brackets [1] and collected together in a reference list at the end of the manuscript and in alphabetic order.

Journal of Applied Engineering Science 10(2012)1

INSTRUCTIONS FOR AUTHORS Units - standard SI symbols and abbreviations should be used. Abbreviations should be spelt out in full on ﬁrst appearance, e.g., variable time geometry (VTG). Meaning of symbols and units belonging to symbols should be explained in each case or quoted in a special table at the end of the manuscript before References. Figures must be cited in a consecutive numerical order in the text and referred to in both the text and the caption as Fig. 1, Fig. 2, etc. Figures should be prepared without borders and on white grounding and should be sent separately in their original formats. Pictures may be saved in resolution good enough for printing in any common format, e.g. BMP, GIF or JPG. Tables should carry separate titles and must be numbered in consecutive numerical order in the text and referred to in both the text and the caption as Table 1, Table 2, etc. The tables should each have a heading. Tables should not duplicate data found elsewhere in the manuscript. Acknowledgement of collaboration or preparation assistance may be included before References. Please note the source of funding for the research. REFERENCES must be written in alphabetical order and in the following form: Journal: /Number/ (must match number in the text), Last name, Initial of the authors name, (Year of publication). Article title: secondary title. Title of the Journal (italic), volume number (number of the journal), page number. /ң/ Petroviü, G., Petroviü, N., Marinkoviü, Z. (2008). Primena teorije Markova u mrežnim sistemima masovnog opsluživanja. FACTA UNIVERSITATIS Series Mechanical Engineering, 6 (1), 45 – 56. Book: /Number/ (must match number in the text), Last name, Initial of the authors name, (Year of publication) Book title: secondary title, Place of publishing: Publisher. /2/ Vasiü, B., Popoviü, V. (2007) Inženjerske metode menadžmenta, Beograd: Institut za istraživanja i projektovanja u privredi. Book chapter: /Number/ (must match number in the text), Last name, Initial of the authors name, (Year of publication) Chapter title: secondary title, Book title: secondary title, Place of publishing: Publisher, page numbers. /3/ Vasiü, B. (2004) Model Hardverskog resursa, Menadžment i inženjering u održavanju, Beograd: Institut za istraživanja i projektovanja u privredi, 95 – 97. Internet source: /Number/ (must match number in the text), link to the page from which the text is taken, retrieved on (state the date) /4/ http://www.autogume.net/veleprodaje/kelena/, retrieved on November 7th, 2010

Journal of Applied Engineering Science 10(2012)1

SADRŽAJ

OD UREĈIVAýKOG ODBORA Prof. dr Miloš Kneževiü UVODNIK

REZIMEI RADOVA Dr Radomir Mijailoviü METODOLOGIJA ZA ODREĈIVANJE ZAVISNOSTI IZMEĈU SILE I DEFORMACIJE TRANSPORTNIH SREDSTAVA

Mr Aleksandar Manojloviü, Mr Olivera Medar, Jelena Trifunoviü, Dr Katarina Vukadinoviü TROŠKOVI AKTIVNOSTI U VOZNIM PARKOVIMA JAVNIH PREDUZEûA

RADOVI SA GNP2012 KONFERENCIJE Dr Biljana Šüepanoviü, Dr Miloš Kneževiü, Dr Duško Luþiü PRIMER PRIMENE VEŠTAýKIH NEURONSKIH MREŽA U PATCH LOADING PROBLEMIMA ýELIýNIH KONSTRUKICJA

MSc Igor Peško, Dr Jasmina Dražiü, MSc Vladimir Muþenski, Dr Milan Trivuniü PRIPREMA BAZE PODATAKA ZA PROCENU OŠTEûENJA OBJEKATA OD DEJSTVA ZEMLJOTRESA PRIMENOM ANN

MSc Marijana Lazarevska, Dr Ana Trombeva-Gavriloska, Dr Miloš Kneževiü, Dr Todorka Samardžioska, Dr Meri Cvetkovska PROGNOZNI MODEL NEURONSKIH MREŽA ZA AB GREDE OJAýANJE CFRP TRAKAMA

Dr Marina ûetkoviü, Dr Ĉorÿe Vuksanoviü UTICAJ GRANIýNIH USLOVA NA NELINEARAN ODGOVOR LAMINATNIH KOMPOZITNIH PLOýA

Dr Marina Rakoþeviü APROKSIMATIVAN POSTUPAK ZA PRORAýUN NAPONA SMICANJA

Dr Predrag Petronijeviü, Dr Nenad Ivaniševiü, Dr Marina Rakoþeviü, Dr Dragan Arizanoviü METODE PRORAýUNA TROŠKOVA DEPRESIJACIJA GRAĈEVINSKIH MAŠINA

MSc Nenad Fric, MSc Boris Gligiü, MSc Jelena Dobriü, Dr Zlatko Markoviü VETROGENERATORI - PRORAýUN TARNOG SPOJA KAO MONTAŽNOG NASTAVKA CILINDRIýNOG ýELIýNOG TORNJA

Dr Todorka Samardžioska, Dr Ana Trombeva-Gavriloska, Dr Petar Cvetanovski, Mr Denis Popovski, Mr Mile Partikov OJAýANJE I NADGRADNJA OBJEKTA “AUTOMAKEDONIJA”

Journal of Applied Engineering Science 10(2012)1

OD UREĈIVAýKOG ODBORA

GRADITELJSTVO JE ZAJEDNIýKI JEZIK ýOVEýANSTVA Prof dr. Miloš Kneževiü Dekan graÿevinskog fakulteta u Podgorici Pedsednik organizacionog odbora GNP 2012

ýetvrti put na Žabljaku održava se Nauþno-struþni skup GNP 2012, tradicionalno, sa željom da svoja nauþna i struþna dostignuüa razmijenimo – i ona koja smo materijalizovali u prostoru, kao i ona koja þekaju blja vremena. Horizonti skupa GNP proširuju se kroz sve veüi broj radova, ovog puta recenziranih i odabranih za publikovanje njih 331, koje potpisuje 596 autora iz þak 16 zemalja. Sa konferencije odabrano je osam radova za publikovanje. Zahvaljujemo se þlanovima Nauþnog odbora i autorima, a posebno sponzorima i prijateljima, predstavnicima inostranih i domaüih institucija koji su nas podržali u organizaciji i pomogli održavanje Skupa GNP 2012. Bez njihove pomoüi, ovo se nebi moglo realizovati. Žabljak, Februar 2012.

GNP 2012 NAUýNI ODBOR Prof.dr Dragan Aranÿeloviü, FCEA, Niš Prof.dr Stanko Brþiü, CEF, Beograd Prof.dr Meri Cvetkovska, CEF, Skoplje Prof.dr Aleksandra Deluka-Tibljaš, CEF, Rijeka Prof.dr Nebojša Ĉuranoviü, CEF, Podgorica Prof.dr Petar Ĉuranoviü, CEF, Podgorica Prof.dr Mihail Garevski, IZIIS, Skoplje Prof.dr Branislav Glavatoviü, CEF, Podgorica Doc.dr Armin Hadroviü, CEF, Mostar Doc.dr Tomaš Hanak, CEF, Brno Prof.dr Alen Harapin, FCEAG, Split Prof.dr Mustafa Hrasnica, CEF, Sarajevo Prof.dr Nenad Ivaniševiü, CEF, Beograd Prof.dr Milorad Jovanovski, CEF, Skoplje Prof.dr Jelisava Kaleziü, CEF, Podgorica Prof.dr Miloš Kneževiü, CEF, Podgorica Prof.dr Ĉorÿe Laÿinoviü, FTS, Novi Sad Doc.dr Ivan Lovriü, CEF, Mostar Prof.dr Duško Luþiü, CEF, Podgorica Prof.dr Damir Markulak, CEF, Osijek Prof.dr Matjaž Mikoš, FCGE, Ljubljana

Prof.dr Dragan Milašinoviü, CEF, Subotica Prof.dr Zvonko Pavliþiü, FTS, Kosovska Mitrovica Prof.dr Radenko Pejoviü, CEF, Podgorica Prof.dr Zdenka Popoviü, CEF, Beograd Prof.dr Živojin Prašþeviü, CEF, Beograd Prof.dr Miroslav Premrov, CEF, Maribor Prof.dr Vlastimir Radonjanin, FTS, Novi Sad Prof.dr Miüko Raduloviü, CEF, Podgorica Doc.dr Marina Rakoþeviü, CEF, Podgorica Doc.dr Snežana Rutešiü, CEF, Podgorica Doc.dr Todorka Samardžioska, CEF, Skoplje Prof.dr Goran Sekuliü, CEF, Podgorica Prof.dr Milenko Stankoviü, FCEA, Banja Luka Prof.dr Boško Stevanoviü, CEF, Beograd Doc.dr Biljana Šüepanoviü, CEF, Podgorica Doc.dr Ivana Štimac-Grandiü, CEF, Rijeka Prof.dr Zvonko Tomanoviü, CEF, Podgorica Prof.dr Milan Trivuniü, FTS, Novi Sad Prof.dr Mladen Uliüeviü, CEF, Podgorica Prof.dr Arsenije Vujoviü, CEF, Podgorica Prof.dr Ĉorÿe Vuksanoviü, CEF, Beograd

Journal of Applied Engineering Science 10(2012)1

REZIMEI RADOVA Broj rada: 10(2012)1, 213

doi:10.5937/jaes10-1471

METODOLOGIJA ZA ODREĐIVANJE ZAVISNOSTI IZMEĐU SILE I DEFORMACIJE TRANSPORTNIH SREDSTAVA

Dr Radomir Mijailović Univerzitet u Beogradu, Saobraćajni fakultet, Beograd, Srbija Softveri za analizu saobraćajnih nezgoda svoj rad baziraju na unapred poznatoj vrednosti koeficijenta restitucije. U praksi je uobičajeno da se numerička vrednost koeficijenta restitucije određuje na osnovu iskustva. Greška u njegovoj proceni uslovljava i nužnu pojavu grešaka u izlaznim rezultatima. Stoga je od izuzetne važnosti što preciznije odrediti njegovu numeričku vrednost. U tom cilju je u radu razvijena metodologija kojom se obezbeđuje analiza procesa sudara u kojoj koeficijent restitucije postaje rezultat, a ne kao što je uobičajeno ulazni podatak. U radu je predložena metodologija za matematičko modeliranje funkcije zavisnosti između sile i deformacije transportnih sredstava koja učestvuju u saobraćajnoj nezgodi. Proces kompresije je modeliran sa više, a proces restitucije sa jednom linearnom funkcijom. Krutost koja odgovara procesu restitucije je definisana u funkciji od maksimalne deformacije koja se javlja tokom procesa kompresije. Kvalitet dobijene funkcije je kvantifikovan preko sume kvadrata greške. Predložena metodologija je na kraju rada i praktično primenjena. Ključne reči: metodologija, rekonstrukcija, vozila, koeficijent restitucije, greška. doi:10.5937/jaes10-1523

Broj rada: 10(2012)1, 214 TROŠKOVI AKTIVNOSTI U VOZNIM PARKOVIMA JAVNIH PREDUZEĆA

Mr Aleksandar Manojlović Univerzitet u Beogradu, Saobraćajni fakultet, Beograd, Srbija Mr Olivera Medar Univerzitet u Beogradu, Saobraćajni fakultet, Beograd, Srbija Jelena Trifunović Univerzitet u Beogradu, Saobraćajni fakultet, Beograd, Srbija Dr Katarina Vukadinović Univerzitet u Beogradu, Saobraćajni fakultet, Beograd, Srbija Sa sve prisutnijim tendencijama da se poslovni sistemi koncentrišu na svoje glavne delatnosti, neminovno se postavlja pitanje položaja koji treba da zauzme delatnost transporta i u okviru toga rad voznih parkova: kao delatnost koja stvara novu vrednost osnovnom sistemu ili kao trošak koji se ne može izbeći. Značajnu ulogu u tome ima način na koji je definisano korišćenje vozila i način odvijanja aktivnosti vezanih za vozni park. U ovom radu prikazana je veza obračuna troškova na bazi aktivnosti i podsistema transporta. Ta veza je posebno značajna u voznim parkovima javnih komunalnih preduzeća. Propisi usvojeni u prethodnom periodu najavljuju promene uslova poslovanja komunalnih privrednih društava (preduzeća). Kako su veliki vozni parkovi sastavni deo komunalnih sistema, novi uslovi će izazvati potrebu za poboljšanjem sistema određivanja troškova voznih parkova, a time i za određivanjem troškova aktivnosti. Da li će se javiti potreba za formiranjem gradskih voznih parkova? Kjučne reči: javno preduzeće, aktivnosti, troškovi, vozni park

Journal of Applied Engineering Science 10(2012)1

REZIMEI RADOVA doi:10.5937/jaes10-1659

Broj rada: 10(2012)1, 215

PRIMER PRIMENE VEŠTAČKIH NEURONSKIH MREŽA U PATCH LOADING PROBLEMIMA ČELIČNIH KONSTRUKCIJA Dr Biljana Šćepanović Univerzitet u Crnoj Gori, Građevinski fakultet, Podgorica, Crna Gora Dr Miloš Knežević Univerzitet u Crnoj Gori, Građevinski fakultet, Podgorica, Crna Gora Dr Duško Lučić Univerzitet u Crnoj Gori, Građevinski fakultet, Podgorica, Crna Gora Tri sasvim različita oblika loma su uočena kod eksperimentalno testiranih ekscentrično lokalno opterećenih čeličnih I-nosača: ekscentričan, centričan i mešoviti lom. Osnovna razlika, suštinska za inženjersku praksu, je u sili loma. Na ponašanje, oblik i silu loma ekscentrično lokalno opterećenih čeličnih I-nosača utiču brojni međusobno zavisni parametri, kao i njihove kombinacije. U takvim uslovima, veoma je teško unapred utvrditi oblik loma i odrediti silu loma. Jedan od analiziranih postupaka, koji je ocenjen kao uspesan metod z a rešavanje ovog zadatka, je modeliranje primenom veštačkih neuronskih mreža. Ključne reči: lokalno opterećenje, ekscentricitet, čelični I-nosač, oblik/sila loma, veštačka neuronska mreža, prognozni model

doi:10.5937/jaes10-1660

Broj rada: 10(2012)1, 216

PRIPREMA BAZE PODATAKA ZA PROCENU OŠTEĆENJA OBJEKATA OD DEJSTVA ZEMLJOTRESA PRIMENOM ANN MSc Igor Peško Univerzitet u Novom Sadu, Fakultet Tehničkih Nauka, Novi Sad, Srbija Dr Jasmina Dražić Univerzitet u Novom Sadu, Fakultet Tehničkih Nauka, Novi Sad, Srbija MSc Vladimir Mučenski Univerzitet u Novom Sadu, Fakultet Tehničkih Nauka, Novi Sad, Srbija Dr Milan Trivunić Univerzitet u Novom Sadu, Fakultet Tehničkih Nauka, Novi Sad, Srbija Seizmički rizik se u urbanim sredinama tokom vremena povećava, pa su aktuelna istraživanja svih aspekata seizmičke zaštite. U cilju planiranja preventivnih mera, značajna je procena mogućih oštećenja na objektima. U radu je opisana priprema baze podataka za predikciju kategorije oštećenja od dejstva zemljotresa, primenom veštačkih neuronskih mreža (ANN). Baza će biti definisana na osnovu raspoloživih podataka iz zapisnika koji su urađeni nakon zemljotresa u Kraljevu (03.11.2010.). Ključne reči: zemljotres, oštećenja, baza podataka, veštačke neuronske mreže.

Journal of Applied Engineering Science 10(2012)1

REZIMEI RADOVA doi:10.5937/jaes10-1661

Broj rada: 10(2012)1, 217

PROGNOZNI MODEL NEURONSKIH MREŽA ZA AB GREDE OJAČANJE CFRP TRAKAMA MSc Marijana Lazarevska Univerzitet u Skoplju, Građevinski fakultet, Skoplje, Makedonija Dr Ana Trombeva-Gavriloska Univerzitet u Skoplju, Građevinski fakultet, Skoplje, Makedonija Dr Miloš Knežević Univerzitet u Crnoj Gori, Građevinski fakultet, Podgorica, Crna Gora Dr Todorka Samardžioska Univerzitet u Skoplju, Građevinski fakultet, Skoplje, Makedonija Dr Meri Cvetkovska Univerzitet u Skoplju, Građevinski fakultet, Skoplje, Makedonija U slučaj slabo izvedene veze između FRP ploča i AB grede moguća je pojava slabih zona sa vazdusnim đepovima. U radu je, primenom numerickog modela, analiziran uticaj slabih zona na ponašanje AB nosača ojačanim FRP pločama. Isto tako, primenom koncepta veštačkih neuronskih mreža definisan je model za prognozu ponašanja AB greda ojačanim FRP pločama. Oba modela daju odlične rezultate i dio tih rezultata biće prezentiran u ovom radu. Ključne reči: CFRP, neuronske mreže, AB grede, ojačavanje, diskontinuirana veza.

doi:10.5937/jaes10-1662

Broj rada: 10(2012)1, 218

UTICAJ GRANIČNIH USLOVA NA NELINEARAN ODGOVOR LAMINATNIH KOMPOZITNIH PLOČA Dr Marina Ćetković Univerzitet u Beogradu, Građevinski fakultet, Beograd, Srbija Dr Đorđe Vuksanović Univerzitet u Beogradu, Građevinski fakultet, Beograd, Srbija U ovom radu analiziran je uticaj različitih graničnih uslova na geometrijski nelinearan odgovor laminatnih kompozitnih ploča. Matematički model, zasnovan na slojevitom polju pomeranja koje je predložio Reddy [1], formulisan je koristeći von Karman’ovu teoriju velikih pomeranja i malih deformacija. Princip virtulanih pomeranja je primenjen za dobijanje slabe forme problema. Slaba forma je diskretizovana koristeći izoparametarsku aproksimaciju konačnim elementom. Originalan MATLAB računski program je korišćen za analizu uticaja razlicitih graničnih uslova na nelinearna odgovor laminatnih kompozitnih ploča. Tačnost numeričkog modela je potvrđena poređenjem sa rešenjima iz literature. Ključne reči: geometrijska nelinearnost, granični uslovi, kompozitna ploča, konačni element

Journal of Applied Engineering Science 10(2012)1

REZIMEI RADOVA doi:10.5937/jaes10-1663

Broj rada: 10(2012)1, 219 APROKSIMATIVAN POSTUPAK ZA PRORAČUN NAPONA SMICANJA

Dr Marina Rakočević Univerzitet u Crnoj Gori, Građevinski fakultet, Podgorica, Crna Gora Za debele i umereno debele ploče čija je srednja ravan paralelna ravni (x,y) stanje napona u preseku, koje se opisuje sa komponentama napona u ravni (x,y), ne daju realnu sliku naponskog stanja. Za definisanje „realnijeg“ stanja napona potrebno je definisati smičuće napone u ravnima (x,z) i (y,z). U ovom radu prikazuje se jedan aproksimatrivan postupak koji se može koristiti za određivanje komponeti smičućih napona σxz i σyz. Postupak je primenjen na primeru proračuna smičućih napona za slojevite kompozitne ploče. Teorijske osnove su zasnovane na Teoriji slojeva, a rešenja jednačina teorije su određivana u zatvorenom obliku. Na kraju rada su grafički, pomoću dijagrama, prikazani rezultati primene postupka za ploče sa usvojenim geometrijskim i materijalnim karakteristikama. Ključne reči: smičući naponi, kompozitna ploča, teorija slojeva

doi:10.5937/jaes10-1664

Broj rada: 10(2012)1, 220

METODE PRORAČUNA TROŠKOVA DEPRESIJACIJA GRAĐEVINSKIH MAŠINA Dr Predrag Petronijević Univerzitet u Beogradu, Građevinski fakultet, Beograd, Srbija Dr Nenad Ivanišević Univerzitet u Beogradu, Građevinski fakultet, Beograd, Srbija Dr Marina Rakočević Univerzitet u Crnoj Gori, Građevinski fakultet, Podgorica, Podgorica Dr Dragan Arizanović Univerzitet u Beogradu, Građevinski fakultet, Beograd, Srbija Troškovi depresijacije predstavljaju značajani deo ukupnih troškova rada građevinskih mašina. Ipak, precizan proračun troškova depresijacije često je težak ili nemoguć. Metoda ravnomerne depresijacije, koja se najčešće koristi prilikom proračuna troškova rada građevinskih mašina, ne daje dovoljno tačne rezultate. U radu je analizirano više metoda proračuna troškova depresijacije, kao i njihov uticaj na ukupne tršokove rada građevinskih mašina i uticaj na troškove po jedinici mere obrađenog materijala. Ključne reči: depresijacija, građevinske mašine, troškovi

Journal of Applied Engineering Science 10(2012)1

REZIMEI RADOVA Broj rada: 10(2012)1, 221

doi:10.5937/jaes10-1670

VETROGENERATORI - PRORAČUN TARNOG SPOJA KAO MONTAŽNOG NASTAVKA CILINDRIČNOG ČELIČNOG TORNJA MSc Nenad Fric Univerzitet u Beogradu, Građevinski fakultet, Beograd, Srbija MSc Boris Gligić Univerzitet u Beogradu, Građevinski fakultet, Beograd, Srbija MSc Jelena Dobrić Univerzitet u Beogradu, Građevinski fakultet, Beograd, Srbija Dr Zlatko Marković Univerzitet u Beogradu, Građevinski fakultet, Beograd, Srbija Tornjevi predstavljaju 15 do 20% ukupne cene vetrogeneratora pa se optimizacijom u projektovanju može doći do značajne uštede u materijalu. Među najinteresantnijim projektantskim i izvođačkim detaljima je montažni nastavak tornja vetrogeneratora. Postoje tradicionalni nastavci sa čeonim pločama i sa druge strane, kao novi predlog, tarni spoj. U ovom radu date su teorijske osnove projektovanja tarnih spojeva kao montažnih nastavaka tornjeva vetrogeneratora. Ključne reči: vetrogeneratori, tarni spoj, zavrnjevi sa kontrolisanom silom pritezanja, tarna površina

Broj rada: 10(2012)1, 226

doi:10.5937/jaes10-1665

OJAČANJE I NADGRADNJA OBJEKTA “AUTOMAKEDONIJA” Dr Todorka Samardžioska* Univerzitet u Skoplju, Građevinski fakultet, Skoplje, Makedonija Dr Ana Trombeva-Gavriloska Univerzitet u Skoplju, Građevinski fakultet, Skoplje, Makedonija Dr Petar Cvetanovski Univerzitet u Skoplju, Građevinski fakultet, Skoplje, Makedonija Dr Denis Popovski Univerzitet u Skoplju, Građevinski fakultet, Skoplje, Makedonija Mr Mile Partikov Univerzitet u Skoplju, Građevinski fakultet, Skoplje, Makedonija Sanacija postojećih objekata je oduvjek bila veliki izazov za gradjevinsku praksu i za istraživače. U slučajevima kada nije dostupna projektna dokumentacija, glavnom projektu predhodi niz aktivnosti: snimanje, mjerenje, geotehnička istraživanja, utvrđivanje kvaliteta i količine ugrađenih materijala korišćenjem različitih metoda, itd. U ovom radu je prikazan primer za sanaciju i ukrućenje postojeće konstrukcije automobilskog servisa u Skoplju, kao i nova čelična konstrukcija za nadgradnju. Ključne reči: ojačanje, mehaničke karakteristike, ab konstrukcija, čelična konstrukcija.

Journal of Applied Engineering Science 10(2012)1

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CIP - Katalogizacija u publikaciji Narodna biblioteka Srbije, Beograd 33 Istraživanja i projektovanja za privredu = Journal of Applied Engineering Science: nauþno-struþni þasopis / glavni urednik Jovan Todoroviü; odgovorni urednik Predrag Uskokoviü. - God. 1, br. 1 (2003) Beograd (Vatroslava Lisinskog 12a): Institut za istraživanja i projektovanja u privredi, 2003 - (Beograd: Beograﬁka). - 29 cm Tromeseþno Drugo izdanje na drugom medijumu: Istraživanja i projektovanja za privredu (Online) = ISSN 1821-3197 ISSN 1451-4117 = Istraživanja i projektovanja za privredu COBISS.SR-ID 108368396 Journal of Applied Engineering Science 10(2012)1