Design Project _ UQAC Sports Arena by Othmane Laraki

DESIGNPROJECT UQAC SPORTS ARENA Winter 2013

Caroline CHAN Arnaud DUSSER Othmane LARAKI Randy(Chao) WANG

DEPARTMENT OF CIVIL ENGINEERING

CIVE 418 DESIGN PROJECT ACE ENGINEERING CONSULTANTS Université du Québec à Chicoutimi Arena CHAN Caroline (260378165) DUSSER Arnaud (260375070) LARAKI Othmane (260363959) WANG Randy (260349967) Advisor: Louis‐Philippe Poirier DATE OF SUBMISSION: April 16th, 2013

Statement of Authorship

We, ACE Engineering Consultants, certify that this technical document, Structural

Design of the UQAC Arena in Chicoutimi, is the original work of: CHAN Caroline DUSSER Arnaud LARAKI Othmane WANG Randy

_____________________________________ Date : _______________________

Acknowledgments ACE Engineering Consultants would like to extend its appreciation to professors D. Lignos, W. E. Taylor, and G. McClure for their assistance and support in providing the resources needed to reach the many milestones of this project. ACE would also like to thank Mr. Louisâ&#x20AC;?Philippe Poirier (SNC Lavalin), for his continuous feedback and guidance throughout the analysis and design phases of this project. His advices and mentoring have contributed to the success of the project.

Table of ContentsÂ Â Statement of Authorship .......................................................................................................................................... i Acknowledgments ..................................................................................................................................................... ii Table of Contents ..................................................................................................................................................... iii Table of Figures .......................................................................................................................................................... v Table of Tables ......................................................................................................................................................... vii 1. Introduction .................................................................................................................................................... 1 2. Project Objectives ......................................................................................................................................... 2 1)

Design brief ............................................................................................................................................ 2

Requirements ........................................................................................................................................ 4

Constraints and challenges.............................................................................................................. 4

Design criteria ....................................................................................................................................... 5

3. Tasks and responsibilities ........................................................................................................................ 6 1)

Task delegation .................................................................................................................................... 6

Time frame (Gantt chart) ................................................................................................................. 7

4. Data ..................................................................................................................................................................... 8 1)

Codes and regulation standards used in the design process ............................................ 8

Data initially received ........................................................................................................................ 9

Data collected ........................................................................................................................................ 9

5. Materials ........................................................................................................................................................ 12 1)

Exposure class and minimum specified compressive strength .................................... 12

Concrete Composition .................................................................................................................... 12

6. Loading Analysis ........................................................................................................................................ 17 1)

Dead loads ........................................................................................................................................... 17

Live loads ............................................................................................................................................. 19

Snow loads ........................................................................................................................................... 20

Wind loads ........................................................................................................................................... 22

Seismic loads ...................................................................................................................................... 27

7. Design Summary ........................................................................................................................................ 29 1)

Design Process ................................................................................................................................... 29

Contacts ................................................................................................................................................ 29

Software used ..................................................................................................................................... 29

Design .................................................................................................................................................... 31 iii

LEED Certification and environmental concerns ............................................................... 53

8. Conclusions .................................................................................................................................................. 57 References .................................................................................................................................................................. 59 Appendix ..................................................................................................................................................................... 60

Table of Figures Figure 1 ‐ View of the mechanical room and the main building of the UQAC arena in the summer time (Les Architectes Associés, 2009) ............................................................................................ 3 Figure 2 ‐ Perspective view of the arena UQAC in the winter time (S. Groleau, 2009) ............... 3 Figure 3 ‐ Interior view of the UQAC Arena (Les Architectes Associés, 2009) ............................... 4 Figure 4 ‐ ACE Gantt Chart ..................................................................................................................................... 7 Figure 5 ‐ Cross section of a green roof (CIRIA green roofs: An Introduction & overview benefits, 2008) ......................................................................................................................................................... 11 Figure 6 ‐ Travelling distance between BPDL International (point B) and UQAC Arena (point A) (Source: Google, 2013) ................................................................................................................................... 13 Figure 7 ‐ Travelling distance between Philippe Trépanier inc. (point B) and UQAC Arena (point A) (Source: Google, 2013) ..................................................................................................................... 16 Figure 8: Snow loading for arched roofs, from NBCC 2005 .................................................................. 20 Figure 9: Snow loading for curved arena roof, Case 1 and Case 3 ..................................................... 21 Figure 10: Snow loading on lower adjacent roofs .................................................................................... 22 Figure 11: Wind loading on walls .................................................................................................................... 23 Figure 12: Wind loading on curved roof ....................................................................................................... 24 Figure 13 ‐ Wind loading perpendicular to the ridge of the main building with minimization of zones 2 and 2E (After NBCC 2005) ............................................................................................................ 25 Figure 14 ‐ Wind loading parallel to the ridge of the main building with minimization of zones 2 an 2E (After NBCC 2005) .................................................................................................................... 25 Figure 15 ‐ Winds perpendicular to the ridge of the main building with minimization of zones 3 and 3E (After NBCC 2005) ................................................................................................................. 26 Figure 16 ‐ Winds parallel to the ridge of the main building with minimization of zones 3 and 3E (After NBCC 2005) .................................................................................................................................. 26 Figure 17 ‐ Simplified top view of Structure ............................................................................................... 27 Figure 18 ‐ Front View of Structure ................................................................................................................ 28 Figure 19 ‐ General view of Building's roof steel structure .................................................................. 31 Figure 20 ‐ Rendered Side View of Main Roof Truss System ............................................................... 32 Figure 21 ‐ Side view of main building with overlaping SAP2000 Model ...................................... 33 Figure 22: Floor plan showing layout of all columns .............................................................................. 34 Figure 23: Location of critical columns, part of braced bay system ................................................. 35 Figure 24: SAP2000 analysis of column 4 .................................................................................................... 35 Figure 25: Deflection pattern of column under seismic consideration and lateral loading from the mechanical building ............................................................................................................................ 37 Figure 26 ‐ Column designation for the side buildings .......................................................................... 39 Figure 27 ‐ Girt designation for the lockers room .................................................................................... 40 Figure 28 ‐ Girt designation for the mechanical room ............................................................................ 40 Figure 29: Cross section of ice rink slab on grade .................................................................................... 41 Figure 30 ‐ Spread footing detailed dimensions and reinforcement specifications in 2D view ......................................................................................................................................................................................... 43 Figure 31 ‐ Spread footing detailed dimensions and reinforcement specifications in 3D view ......................................................................................................................................................................................... 44 Figure 32 ‐ Diagram of final Basement Wall dimensions ...................................................................... 45 Figure 33 ‐ Diagram of final Retaining Wall dimensions ....................................................................... 46 v

Figure 34: Fastener support pattern .............................................................................................................. 47 Figure 35: Shear diagrams of roof and floor systems ............................................................................. 48 Figure 36: Flow of forces through diaphragm, joists, beams and columns ................................... 49 Figure 37 ‐ Schokbeton Design Diagram ...................................................................................................... 51 Figure 38 ‐ Cross‐sectional view of Schokbeton's prefabricated concrete slabs ........................ 52 Figure 39 ‐ Bleacher Dimensions ..................................................................................................................... 53 Figure 40: Green roof on adjacent buildings ............................................................................................... 55 Figure 41 ‐ Interior view of Arena ................................................................................................................... 56 Figure 42 ‐ 3D Rendered View .......................................................................................................................... 58

Table of Tables Table 1: Dead load of extensive green roof (After CIBSE KS:11, 2007) .......................................... 11 Table 2: Concrete mixtures design summary (After CSA A23.1 and CSA A23.3) ........................ 15 Table 3 ‐ Applicable dead loads (Source: 10th edition of the Handbook of Steel Construction, NBCC 2005, CIBSE KS: 11, CANAM Joists catalogue) ............................................................................... 18 Table 4 ‐ Specified Live loads on Structure ................................................................................................. 20 Table 5: Snow loading for all three roofs ...................................................................................................... 21 Table 6: Wind loading on wall ........................................................................................................................... 23 Table 7: Wind loading on lower adjacent roofs ......................................................................................... 24 Table 8: Summary of column factored loads, sections and special considerations ................... 36

vii

1. Introduction The university of Québec in Chicoutimi (Université du Québec à Chicoutimi, UQAC) is a branch of the University of Québec (Université de Québec) founded in 1969 and based in the Chicoutimi borough of Saguenay, at the following address : 555, boulevard Université, Chicoutimi, QC, G7H2B1 (UQAC, 2013). It is currently enrolling about 6500 students, and approximately 200 professors work for the university (UQAC, 2013) ; these numbers rank the UQAC as the third largest university from the University of Québec branches, hence the need to provide remarkable facilities to sustain its prestige and accommodate the needs of its students and staff. In order to enhance the UQAC’s ability to provide various services to its students, the need emerged to provide a sport facility with an arena to the ever growing student body. ACE Engineering Consultants has been given the responsibility to carry on the structural design of this 24000 ft2 arena facing the football field with synthetic surface in January 2013 (3070m2 with the outdoor football field). This project consists of the adaptation of previously established architectural plans provided by a consortium formed of les Architectes Associés (Leblond, Tremblay, Boulay, Fradette, Boudreault) and Lemay & Associés that were followed and respected all along the project. ACE Engineering Consultants designed the building by following specific guidelines reflective of its long experience in the field of structural design. The architectural plans provided the initial dimensions and the structure layout. These plans also allowed the ACE engineering team to visualize the possible problems that could occur with the choice of certain structural solutions. Serviceability was the main objective of this project, as it was important that the constructed arena could be fully used, without issue, after its construction. The main goal of this project was to design the arena by using a steel structure, but also to incorporate an environmental‐friendly facet consisting of green roofs and design towards a LEED certification.

2. Project Objectives 1) Design brief The project was born from the need of the UQAC to provide its new hockey team with the appropriate infrastructure and services (new bleachers, locker rooms, polyvalent rooms...) in order to serve academic and municipal users. The building houses a hockey rink with locker‐rooms, press gallery and stands (figure 3). The roof’s rounded shape gives this building a unique look; it is supported by main truss systems that support the rest of the building’s roof. The building is partly embedded in the ground as it follows the previous Sports Center design and the client’s will to integrate the building in its environment by these means, which was further enhanced by the windows design aiming to improve savings in energy consumption. The sports rooms of the building are mostly located in the basement of the structure, while the ground floor houses the spaces allocated to the public. The building is also composed of a mezzanine that hosts classrooms and lodges. The floor slab used for the mezzanine shall be designed as either a flat plate of a flat slab with drop panels (one way slab). The lower roofs have been designed as green roofs in an environmental‐friendly perspective aiming at reducing the cost associated with energy consumption on the long term, among others. Also, geotechnical data availability has not been made possible, borehole records have not been provided, hence the inability to derive the soil properties. Information on the soil bearing capacity was provided however, (as will be seen in the “Data” section), and important values such as the unit weight of soil have been assumed. Also, as can be seen from the architectural plans, shallow foundations are privileged, although no specification has been made clear as to the type of foundation that is to be used in this project.

Figure 1 ‐ View of the mechanical room and the main building of the UQAC arena in the summer time (Les Architectes Associés, 2009)

Figure 2 ‐ Perspective view of the arena UQAC in the winter time (S. Groleau, 2009)

2) Requirements The design of the arena was to be conducted in compliance with all federal, provincial and local regulations while meeting the owner’s specifications. Furthermore, ACE Engineering Consultants decided to introduce an environmental‐friendly feature to the project by ensuring that the flat roof’s placed around the higher curved roof were designed as green roofs.

Figure 3 ‐ Interior view of the UQAC Arena (Les Architectes Associés, 2009)

3) Constraints and challenges The general constraint consisted in ensuring that all designs were conducted in accordance with the codes prescribed by the legal authorities, which are to be subsequently elaborated upon. The main building was embedded in the soil, due to the client’s and developers’ will to incorporate the structure to its direct environment. The limited bearing capacity of the site on which the arena was to be constructed represented a challenge as foundations were to be designed in order to address this constraint, which eventually resulted in a cost increase. The structure consisted of a single story building with a basement; its roof (supported by tension‐beams) has a curved shape, which confers a certain difficulty to the 4

design of wind and snow loads. Also, the two lower flat roofs on either side of the main structure were to be designed as green roofs in an environmental‐friendly perspective. The arena houses an ice rink, hence a concrete slab was designed by considering an incorporated cooling system allowing it to keep the overlaying ice rink frozen. The presence of a refrigerating system in the main building was also accounted for in the design by adding additional weights. Chicoutimi is a zone in which considerable seismic activity is present. Seismic analysis was therefore completed and the building was designed in consequence. Eventually, cost‐efficiency was sought after by examining the different options available for structural elements, favoring lighter ones and the one’s using the less material possible.

4) Design criteria The evaluation and selection process upon which the structure’s design was based upon was carried out on the grounds of structural, architectural, economical and constructional factors.

3. Tasks and responsibilities 1) Task delegation Tasks were assigned according to each member’s strengths and weaknesses. While each member had specific tasks, a system of constant review was put in place, where the work done by one was peer reviewed at every step to ensure that no errors were present, avoiding the need to redo further calculations as a result. The following diagram illustrates the member’s specialties, showing the very divers and technical strength of the ACE team.

Caroline CHAN

Arnaud DUSSER

Othmane LARAKI

Randy WANG

Column Design

Steel Truss Design

Column Design

3D Modeling

Team Management

Lateral Bracing System

Girts Design

Slab Design

Base Plate Connection Design

Seismic Design

Foundations and Footings

Diaphragm Design

Global Analysis

Foundations and Footings

Global Analysis

Interior Floor Design

Slab Design

Roof Diaphragm Design

Loading Patterns

Lower Roofs Design

2) Time frame (Gantt chart) From Day 1, a very specific schedule was set up, where the team first commenced by tackling analysis, before starting design. This approach ensures that all the necessary load values were obtained before engaging in design. The 3D modeling and rendering also started from the very start of the project and followed through all the way to the final weeks before the presentation. Figure 4 shows the Gantt chart used and followed by the team.

Figure 4 ‐ ACE Gantt Chart

4. Data In January of 2013, ACE Engineering Consultants was provided with architectural plans relative to the design of a wood and steel hybrid structure provided by Les Architectes Associés (Leblond, Tremblay, Boulay, Fradette, Boudreault) and Lemay & Associés. The plans were not complete as the bracing system was only preliminary and the main roof structure was yet to be designed. The structure as it was detailed by the architectural plans was reviewed and several aspects were changed: the bleachers facing the football stadium was converted into a flat roof of height 3.93m, and the trapezoidal design of the main building as provided on the architectural plans was straightened to a rectangular shape. Furthermore, in order to proceed with the design and analysis of the structure, ACE Engineering Consultants had to carry out research in several fields of the engineering profession, ranging from structural analysis to geotechnical analysis of the location of the structure. The data used in order to support this analysis is consigned in this section.

1) Codes and regulation standards used in the design process The compliance of the design with the relevant standards and regulations applicable to the project location was ensured through the consultation of the followings documents: ‐National Building Code of Canada, Volume 1, Twelfth Edition, 2005 ‐Handbook of Steel Construction, 10th Edition, CISC‐ICCA ‐CIBSE Knowledge series KS: 11 (Green Roofs) ‐CANAM Joist Catalogue, 42nd Edition ‐Concrete Design Handbook by CAC, 3rd edition, 2006 (CSA A23.3‐04) ‐Concrete materials and methods of concrete construction/Test methods and standard practices for concrete, Eleventh Edition, 2009 (CSA A23.1‐09 /A23.2‐09)

‐Canadian Foundation Engineering Manual, 4th Edition, Canadian geotechnical society, 2006 ‐Design Floor Slabs on Grade, 2nd edition, Boyd C. Ringo and Robert B. Anderson, 1996

2) Data initially received i.

Design values

The following data has been provided by Louis‐Philippe Poirier, our advisor in SNC Lavalin’s Structures Department: ‐Soil bearing capacity = 200 kPa. ‐Class C site in an open location. ii.

Structural and architectural drawings

An exhaustive list of architectural plans and drawings were provided to ACE Engineering Consultants, hence allowing an advanced understanding of the use of space, as well as providing ACE with relevant details, allowing the design to be conducted efficiently. The plans have been useful in providing ACE with guidelines in the initial phase of the design which consisted in determining the dimensions to be used, as well as the shapes to be considered for design. In effect, as it has been evoked in the design brief of this section, several modifications have been made to the design originally suggested by the architectural plans in order to provide the design team with a sense of initiative and creativity emphasizing the control of the project. The architectural plans provided by Architectes Associés (Leblond, Tremblay, Boulay, Fradette, Boudreault) and Lemay & Associés have been included in the appendix.

3) Data collected The site of interest in our project is located in Chicoutimi (Québec), which is a seismically active zone according to NBCC 2005 Structural Commentary (Division B, part 4), hence the need to consider seismic analysis in the design of the area. Other relevant parameters have been addressed by use of data provided by the codes previously evoked.

Climatic data (Gravity loads data)

The snow loads with a return period of 50 years have been provided in the NBCC 2005 Structural Commentary (Division B, Appendix C) as being Ss=2.5kPa and Sr=0.4kPa. Similarly, the hourly wind pressure for a return period of 50 years has been provided as being q=0.36kPa. ii.

Seismic data

From the NBCC 2005 Structural Commentary (Division B, Appendix C), the seismic data was given as being : Sa(0.2)=0.62; Sa(0.5)=0.30; Sa(1.0)=0.14; Sa(2.0)=0.047; PGA=0.39. iii.

Material data

The design of the UQAC arena was carried out using structural steel (for the structural components and members), and reinforced concrete for numerous parts of the structure (slabs for the interior floor, ice rink slab, concrete bleachers,...). More details as to the mixtures chosen for concrete casting and steel members specifications was provided at the end of this section. a. Green roofs The UQAC arena aims at presenting an environmental friendly design, using as many alternatives which include the design of green roofs for the side buildings. In effect, the side buildings were to be designed as assembly areas where people can stand when the weather is favorable. Green roofs are purposely fitted with vegetation and soil media, and can affect storm water runoff, energy savings and thermal insulation for the structure. Although green roofs can be intensive (planted with an abundant vegetation that might include trees and shrubs), extensive green roofs (planted with plants allowed to seed naturally) have been privileged for our structure because of the difference in price and availability. The fact that the roof was aimed at welcoming people created the need to provide as much space as possible on the roof.

An extensive green roof provides a wide diversity of plants, good insulation properties, very good aesthetics, a good energy efficiency and presents an enhanced accessibility with respect to an intensive green roof. (which makes it very suitable for recreational purposes)

Figure 5 ‐ Cross section of a green roof (CIRIA green roofs: An Introduction & overview benefits, 2008)

The substrate shall provide the mechanical strength, based on considerations ranging from grain size, pore structure, water retention properties, air volume, weight and nutrient reserves. The drainage layer is composed of granular material which protects the root proof layer from being mechanically damaged. It retains water for times of droughts and also provides the overlaying layer with a balanced supply of water and air. Eventually, the root membrane usually composed of a copper or heavy grade polythene‐based material further prevents the plants from damaging the waterproofing (Willmot Dixon, 2010). Table 1: Dead load of extensive green roof (After CIBSE KS:11, 2007)

Thickness (mm) 50 (overall thickness for growing medium and drainage layer)

Dead Load (kN/m2) Rainfall Retention 0.7

50%

b. Concrete elements Many concrete elements had to be designed in the UQAC arena, ranging from the foundations (spread footings, retaining walls, basement walls) to the concrete bleachers allowing the crowd to view games on the ice rink.

5. Materials 1) Exposure class and minimum specified compressive strength The use of concrete mixtures in order to support the casting of the concrete elements of the structure was to be done considering the differences in conditions and exposures, hence the necessity to consider different concrete mixtures, respectively applicable to the elements exposed to freeze and thaw, and to those which are not. The exposure classes were determined using CSA A23.1. The concrete elements which were not dramatically affected by freeze thaw had an N exposure class (all interior members and spread footing foundations fall under this category). Due to the non‐provision of geotechnical data for the soil at the location of the arena (hence no indication as to the chloride concentration in this zone), the foundation walls was considered as having a C‐1 exposure class for conservative purposes (i.e. assume it was exposed to chlorides and undergoing freeze and thaw). The exterior walls were also considered to be subjected to freeze thaw, hence they were a C‐1 exposure class as well. Furthermore, all the concrete used in the UQAC arena presenting a C‐1 class of exposure was considered to require a 28‐day minimum specified compressive strength of 35MPa (CSA A23.1‐00, table 2), this value was therefore used for the design of all concrete materials in the structure in order to ensure an early start of the project (the 28‐day strength was defined as the average compressive strength of two companion test specimens and copies of the test report were forwarded to the City Engineer and concrete supplier within thirty‐five days of concrete placement). Concrete was mixed, placed, and cured in accordance with CSA A23.1 or CSA A23.4.

2) Concrete Composition i.

Cement

The concrete design of the structure was addressed using General Use (GU) Hydraulic Portland Cement which complied with CSA A23.1. This general‐purpose cement

was suitable for the casting of the concrete elements required in this structure as long as no special requirements were needed.

Figure 6 ‐ Travelling distance between BPDL International (point B) and UQAC Arena (point A) (Source: Google, 2013)

Another alternative would have been to use precast concrete provided by BPDL International, a manufacturer and construction company located at 1035 Rue des Pins, Alma, QC G8B 7V7, which is a one hour‐drive from the location of the arena. ii.

Aggregates

Aggregates were chosen in compliance with CSA standard A23.1.5. A blend of washed aggregates whose maximum size is 20mm was used in all concrete mixtures. The coarse aggregates consist of well‐graded round gravel with an oven‐dry relative density of 2.68, an oven‐dry ridded bulk density of 1600 kg/m3 and an absorption rate of 0.5%, whereas the fine aggregates consist of natural sand with an oven‐dry relative density of 2.64, a fineness modulus of 2.80, and an absorption rate of 0.7%.

iii.

Slump

To ensure the consistency of concrete, slump was specified within specific limits based on CSA. Although a maximum slump of 100mm could have been used for columns in order to increase the workability of concrete for these elements, both mixtures use a slump of 75mm ± 20mm. iv.

Admixtures

The concrete elements exposed to freeze and thaw are made out of air‐entrained concrete: air bubbles should be introduced into the concrete by adding a surfactant whose prime purpose is to increase the durability of hardened concrete in freeze‐thaw conditions and the resistance to the scaling caused by de‐icing salts, for instance (during freezing, the air bubbles provide room for the expansion of moisture, which allows the dissipation of pressure, hence preventing surface scaling). Such members include the exterior walls, the foundations walls. Other concrete elements which are not directly affected by the attrition cycles due to freeze and thaw are cast from non‐air‐entrained concrete. These elements include the basement slab, the interior floors slabs, the interior walls, the foundation piles and the bleachers. Air‐entraining admixtures are conform to the requirements of ASTM C494. Furthermore, in an environmental‐friendly perspective aiming at qualifying this project for a LEED specification, blast furnace slag is used so as to comply with the LEED Canada Rating System for New Construction and Major Renovations (2009). The use of this fine‐grained recycled material (by‐product of iron and steel manufacturing) further allows an increase in workability of fresh concrete. v.

Concrete mixture

In order to accommodate these two types of exposure conditions, two mixtures were created based on CSA 23.1 (Table).

Table 2: Concrete mixtures design summary (After CSA A23.1 and CSA A23.3)

AIR‐ENTRAINED MIXTURE

USE

Exterior walls

walls,

retaining

CEMENT TYPE

General Use (GU) Hydraulic Portland Cement EXPOSURE TYPE C‐1 28‐DAYS STRENGTH (fc’) 35 MPa MAX. AGGREGATE SIZE 20mm AIR CONTENT 5% to 8% ADMIXTURES Air‐entrainers + water reducers + blast furnace slag SLUMP 75mm WATER‐TO‐CEMENT RATIO 0.40 vi.

NON AIR‐ENTRAINED MIXTURE All interior members (slab, columns, interior walls) and spread footings General Use (GU) Hydraulic Portland Cement N 35 MPa 20mm 0% Water reducers + blast furnace slag 75mm 0.50

Air content

The mixture aimed at air‐entrained concrete casted elements of the structure exhibit an air content ranging from 5% to 8% consisting of the air bubbles introduced in the concrete in order to increase resistance to freeze thaw cycles (these values are specified for a 20mm blend of aggregates in table A3). A value of 8% for the air‐entrained concrete mixture is used in order to increase the freeze thaw resistance. The non‐air‐entrained concrete mixture is exhibited a 0% air content, since it presents no enhanced resistance to freeze and thaw. vii.

Water content

Compliance with the limiting values provided by CSA A23.1 for various exposure classes have been respected (table A2 provides limiting values for the water to cement ratio, table A4 provides the minimum amount of cement required), in order to prevent variations in the specified compressive strength of concrete. Furthermore, it is ensured that mixing water with concrete shall be clear and free from injurious amounts of oil, acid, alkali, organic matter, sediment, or any other deleterious substance.

viii.

Steel Reinforcement

All the reinforcing steel used in the structure is grade 300W steel, that shall be provided by Philippe Trépanier inc., located in Jonquière, Québec, Canada, which represents a 25 minutes’ drive from the arena.

Figure 7 ‐ Travelling distance between Philippe Trépanier inc. (point B) and UQAC Arena (point A) (Source: Google, 2013)

6. Loading Analysis The UQAC arena has been designed by accounting for dead, live, wind and snow loads, as well as by considering seismic activity (since Chicoutimi is considered to be a seismically active zone). The load calculations were carried out using the NBCC 2005, the tenth edition Handbook of Steel Construction, the 42nd edition of the CANAM joist catalogue, as well as the 2007 CIBSE KS: 11. The specified loads have been factored based on the ULS combinations provided in NBCC 2005 (Structural Commentary, part 4, division B, table 4.1.3.2).

1) Dead loads The dead loads have been taken from the CANAM Joists catalogue (42nd edition) for the

interior

floors

(Table

4.1.5.3,

Part

4.1.5.3,

Division

B).

For the roofs, the dead load values have been provided by the tenth edition of the Handbook of Steel Construction (Table p 7‐56,7‐57;CISC‐ICCA) and have been complemented with values inherent to green roof design provided by the CIBSE design guidelines for green (Knowledge series KS: 11, 2007).

Table 3 ‐ Applicable dead loads (Source: 10th edition of the Handbook of Steel Construction, NBCC 2005, CIBSE KS: 11, CANAM Joists catalogue)

INTERIOR FLOOR LOADS Design Dead Load Reference (kPa)

Materials

38mm deck with 90mm N.D. 2,55 cover

Handbook of Steel Construction, 10th Edition, CISC ‐ ICCA

Joists

CANAM Joist Catalogue, 42nd Edition

0,19

Ducts/Pipes/Wiring Allowance 0,25

Handbook of Steel Construction, 10th Edition, CISC ‐ ICCA

Sprayed fire protection

0,07

Handbook of Steel Construction, 10th Edition, CISC ‐ ICCA

Suspended Ceiling

0,48

CANAM Joist Catalogue, 42nd Edition

3,54

CURVED ROOF LOADS Materials

Design Dead Load (kPa)

Reference

Corrugated Steel Deck

0,1

Handbook of Steel Construction, 10th Edition, CISC ‐ ICCA

Plywood (19mm)

0,11

Handbook of Steel Construction, 10th Edition, CISC ‐ ICCA

Insulation ‐ Rigid Foam 0,06 (200mm)

Handbook of Steel Construction, 10th Edition, CISC ‐ ICCA

Plywood (19mm)

0,11

Handbook of Steel Construction, 10th Edition, CISC ‐ ICCA

Steel Deck

0,15

Handbook of Steel Construction, 10th Edition, CISC ‐ ICCA

Ducts/Pipes/Wiring Allowance

0,25

Handbook of Steel Construction, 10th Edition, CISC ‐ ICCA

0,78

LOWER ROOF LOADS Materials

Design Dead Load (kPa)

Reference

Earth/Soil Media

‐

CIBSE (2007) Green Roofs – CIBSE Knowledge series KS: 11

Drainage/Aeration/Water Storage and Root Barrier

‐

CIBSE (2007) Green Roofs – CIBSE Knowledge series KS: 11

Insulation

‐

CIBSE (2007) Green Roofs – CIBSE Knowledge series KS: 11

Membrane Protection and ‐ Root Barrier

CIBSE (2007) Green Roofs – CIBSE Knowledge series KS: 11

Roofing Membrane

0,7

CIBSE (2007) Green Roofs – CIBSE Knowledge series KS: 11

Corrugated Steel Deck

0,1

Handbook of Steel Construction, 10th Edition, CISC ‐ ICCA

Plywood (19mm)

0,11

Handbook of Steel Construction, 10th Edition, CISC ‐ ICCA

0,06

Handbook of Steel Construction, 10th Edition, CISC ‐ ICCA

Plywood (19mm)

0,11

Handbook of Steel Construction, 10th Edition, CISC ‐ ICCA

Steel Deck

0,15

Handbook of Steel Construction, 10th Edition, CISC ‐ ICCA

Ducts/Pipes/Wiring Allowance 0,25

Handbook of Steel Construction, 10th Edition, CISC ‐ ICCA

Joists

0,19

CANAM Joists Catalogue (42nd Edition)

1,69

Insulation (200mm)

‐

Rigid

Foam

2) Live loads The specified concentrated live loads on areas of floor or roof were provided in the NBCC 2005 (Table 4.1.5.10, part 4.1.5.11, Division B), as seen in table 4.

Table 4 ‐ Specified Live loads on Structure CURVED ROOF LOADS Use of Area of Floor or Roof Roofs INTERIOR FLOOR LOADS Location Main Building Mechanical Room Lockers Room LOWER ROOF LOADS Use of Area of Floor or Roof Roofs

Minimum Specified Live Load (kPa) Reference 1 National Building Code of Canada, Volume 1, Table 4.1.5.3, 2005 or 2 kPa if not designed for future expansion Minimum Specified Live Load (kPa) 4.8 3.6 4.8

Reference National Building Code of Canada, Volume 1, Table 4.1.5.3, 2005 National Building Code of Canada, Volume 1, Table 4.1.5.3, 2005 National Building Code of Canada, Volume 1, Table 4.1.5.3, 2005

Minimum Specified Live Load (kPa) 4.8

Reference National Building Code of Canada, Volume 1, Table 4.1.5.3, 2005

3) Snow loads i.

Curved

The snow distribution and loading patterns for the curved roof was determined using Figure G‐3 provided in the NBCC 2005 Structural Commentary (Figure 8). The approach considered in the commentary considers a fully arched roof, while that of the arena is a monoslope arched shape. In order to account for this difference in shape, dimensions such as the building width (denoted as ‘b’) was doubled.

Figure 8: Snow loading for arched roofs, from NBCC 2005

Three loading cases were defined, as displayed in Table 5, and displayed in Figure 9. Case 1: Uniform loading 2.4 kPa Case 3: 2.5 kPa at lower end

Figure 9: Snow loading for curved arena roof, Case 1 and Case 3

ii.

Lower Roofs: Mechanical and Locker Room

Snow distribution and loading patterns for the lower adjacent roofs were defined using Figure G‐5 from the NBCC 2005 Structural Commentary. There was significant snow drift along the ridge of the lower roofs and the main building, as illustrated in Figure 10. A summary of the snow loading is found in the table 5 below.

Table 5: Snow loading for all three roofs

Curved Roof Figure G‐3 Is Ss Cb Cw Cs Ca Sr Smax S S (kPa) NB Case 1 1 2.5 0.8 0.75 1 1 0.4 2.40 2.40 Uniform load Case 2 1 2.5 0.8 0.75 1 0.84 0.4 3.4 1.66 1.66 Case 3 (edge) 1 2.5 0.8 0.75 1 1.40 0.4 5.4 2.50 2.50 Mechanical Figure G‐5 Roof x 0 1 2.5 0.8 1 1 5.0671 0.4 10.5342 at edge xd=10.17 1 2.5 0.8 1 1 1 0.4 2.4 3.54 Locker Roof Figure G‐5 x 0 1 2.5 0.8 1 1 5.0671 0.4 10.5342 at edge xd=10.17 1 2.5 0.8 1 1 1 0.4 2.4 5.37 * xd (10.17m) is greater than the width (8.75m and 6.46m) of the lower buildings, therefore must interpolate

10.53kPa 10.53kPa 5.4 kPa

3.5 kPa

Figure 10: Snow loading on lower adjacent roofs

4) Wind loads The hourly wind pressure value was provided by NBCC 2005 as being q=0.36kPa for a return period of 50 years (Table C‐2, Appendix C, division B, Structural Commentary, Part 4, NBCC 2005). The structure was assumed to be located in an open terrain, due to the small number of surrounding buildings. Since the height of the building and its height to width ratio are less than 60m and 4, respectively, the static procedure can be used to conduct the wind pressure analysis. The methodology used for the determination of the wind loads was derived from the NBCC 2005 Structural Commentary. Three types of wind loading patterns have been analyzed, in order to alternatively design the braces, walls and roof(s) of the building based on NBCC 2005’s Commentary I. i.

Walls/Cladding

The wind loading distribution on the main and lower adjacent building walls was determined using Figure 1‐8 in the NBCC 2005 Structural Commentary. Details on the calculations can be found in the Appendix. Wind loading patterns are shown in Figure 11 and Table 6. 22

e4 e1

e5 w5

Figure 11: Wind loading on walls

Table 6: Wind loading on wall

Zone e1 e2 e3 e4 w1 w2 w3 e5 w4 w5 e6 w6 w7

Pressure Suction 0.63 ‐0.79 0.66 ‐0.82 0.66 ‐0.79 0.66 ‐0.82 0.58 ‐0.73 0.58 ‐0.73 0.58 ‐0.73 0.66 ‐0.85 0.60 ‐0.76 0.58 ‐0.73 0.69 ‐0.88 0.60 ‐0.76 0.58 ‐0.73

ii.

Roof

The wind loading distribution on the curved and lower adjacent roofs was determined in compliance with NBCC 2005 Structural Commentary, using Figure I‐27and Figure I‐9 respectively. Details on the calculations can be found in the Appendix. Wind loading patterns are shown in Figure 12 and Table 7.

‐0.47 ‐0.41

‐0.47

‐0.53

‐0.41

‐0.23

Figure 12: Wind loading on curved roof

Table 7: Wind loading on lower adjacent roofs

Zone c s1 s2 r

z or w 1.00 1.00 1.00 3.96

L 1.00 3.96 59.19 59.19

Area 1.00 3.96 59.19 234.39

CpCg 1.60 ‐1.90 1.40 ‐1.60 1.30 ‐1.50 1.30 ‐1.50

P(kPa) 0.42 ‐0.49 0.36 ‐0.42 0.34 ‐0.39 0.34 ‐0.39

Given the large openings in the building such as the side windows and Zamboni doors, the building is classified to be in Category 2 when considering Cpi values when analysing internal suction. However, because the gravity loads applied to the structure is much more significant compared to the suction possible within, suction was not considered in the design process.

iii.

Bracings

On the basis of figure I‐7 from NBCC 2005, four loading cases have been evaluated. For each scenario (winds perpendicular or parallel to the ridge of the building), end zones have either been maximized or minimized, hence accounting for the slope of the curved roof (all following scenarios have been addressed for an end zone width of y=6.0m). Details on the calculations can be found in the appendix.

Figure 13 ‐ Wind loading perpendicular to the ridge of the main building with minimization of zones 2 and 2E (After NBCC 2005)

Figure 14 ‐ Wind loading parallel to the ridge of the main building with minimization of zones 2 an 2E (After NBCC 2005)

Figure 15 â&#x20AC;? Winds perpendicular to the ridge of the main building with minimization of zones 3 and 3E (After NBCC 2005)

Figure 16 â&#x20AC;? Winds parallel to the ridge of the main building with minimization of zones 3 and 3E (After NBCC 2005)

5) Seismic loads

Figure 17 ‐ Simplified top view of Structure

Using the NBCC Division B, Appendix C, the seismic values of the city of Chicoutimi were determined. Given the high seismic activity of Chicoutimi, the resultant base shear was found to be higher than that of the Wind. The Seismic loading, was therefore the control for our brace design. The wall weights were determined from typical wall sections given by VicWest, a company specialized in industrial panels. This wall weight was estimated at 1.5 kPa, from the steel Handbook, assuming a metal curtain wall all around the building. From these values, the weights of each building were determined, in the North‐ South direction and the East‐West Direction. These directions are not based on the absolute north, but set up for simplicity when organizing loading in each direction. The code requires 100% loading in each direction; therefore, 100% seismic loading was considered in both the North‐South direction and the East‐West direction. No higher mode effects were considered, despite the multiple floors in our building for the sake of simplicity. Given our building’s complexity, doing a simpler Equivalent Static Force Procedure, proves to be more conservative and allowed an easier general seismic analysis. The arena’s period, Ta, was also determined is a more conservative, simpler way, by assuming it to be 5% of the out of ground building’s height. Using Conventional 27

Construction coefficients for bracing ductility (Rd= 1.5, Ro= 1.3), it was found that 13.74% of the weight of the building should be considered as lateral static force in each direction of seismic loading. Notional loads were also calculated for each building element, using a value of 0.5% of the gravity loads (1.0 D + 0.25 S + 0.5 L). Bracing was considered to be tension‐ only, allowing us to use double L sections in all brace bays. Since the arena’s side buildings did not possess their own lateral system, their stability was reliant on the main building. Depending on the direction of the loading, it was necessary to consider 100% of that building’s lateral load to be going into a single wall of the main arena. In the other cases, an off‐set of 10% of the building’s width was considered in order to account for torsional effects and conservatism. Because of the structures impossibility to transfer the loads of the main structure (the locker’s room building and interior building) to the South Braces in the East‐West direction, 100% of their load was also considered on that bracing group. Also, given the lack of shear capacity of the composite steel decks in the upper part of the building, additional bracing was required to ensure stability in the N‐S direction.

Figure 18 ‐ Front View of Structure

7. Design Summary 1) Design Process The design process was carried out through investigations led by Ace Engineering Consultants, which were further corroborated by the feedback and advice of the contacts listed below. The main milestones were determined in the early stage of the project, and design considerations were addressed in parallel manner by each member of Ace Engineering Consultants and were allocated on the grounds of the specific skills and talents of each. Calculations were checked and verified in order to ensure the consistency and accuracy of results.

2) Contacts i.

External advisor

Ace Engineering Consultants had the opportunity to extensively interact with M. Louis‐Philippe Poirier, chief of services in the Structures department of SNC Lavalin (Transport, Infrastructure and building division). ii.

McGill University professors

Ace Engineering Consultants was provided feedback and advice by the following professors in McGill University: ‐Professor Ghislaine McClure ‐Professor Dimitrios Lignos ‐Professor William Taylor

3) Software used 

Autodesk REVIT Architecture 2013 This building information modeling software was used to design the building and its components in 3D. It was further used for the overall modeling of the structure. 29



Autodesk AutoCAD 2013 This computer‐aided design and drafting software was used for structure layout, plans visioning, detailing of certain structural elements and connections, among others.



Trimble Sketchup Pro 8.0 This 3D Communication software was used for the dimensional detailing of certain portions of the building, such as the spread footings.



SAP2000 This integrated software for structural analysis and design was used for the design analysis of the structure under inputted loads.



Microsoft Office o Excel was used for design calculations; o PowerPoint was used for the preparation of presentations; o Word was used for the redaction of reports.

4) Design i.

Curved roof design

Figure 19 ‐ General view of Building's roof steel structure

The main roof represents the biggest weight of the entire structure. It spans clear 36 m in order to free the main ice rink of obstructing columns. A CANAM P‐3606 type 22 deck was used to cover the entire roof and help transfer shear forces. CANAM joists, spaced at intervals of 1.5 m individually spanned 6m to transfer gravitational loads to main girder beams spanning 10.75 m on the outer spans and 9.2 m on the inner spans. These Girder beams were designed for flexure and W610x101 beams were used. The main roof system can be seen in figure 19. These loads were then transferred to the main roof elements: curved truss systems. These trusses were composed of one main W beam section at the top, spanning the entire length and smaller HSS members for the rest. The top member was required to be designed for flexure and compression, while the bottom truss elements were designed only for tension; since their pin connected nature removed all moments from their spans. This truss structure can be viewed in figure 20. The dimensions of the truss were first determined by 31

following a curve symmetrical to that of the roof. This did not respect however the required clearance of 20’ from the ice rink’s surface. It was therefore necessary to up curve the bottom truss until the clearance was given. The truss was modeled into SAP2000 to perform the indeterminate analysis. These calculations were then redone by hand to ensure their accuracy (considering a determinate structure).

Figure 20 ‐ Rendered Side View of Main Roof Truss System

Given the different snow loads, it was determined that having a uniform snow load on the entire structure created the worst compression and tension loads. Using the second snow loading case, with snow drifting to the bottom of the roof on the other hand created the worst moments and shear in the top W member. The entire truss was therefore designed in order to respect all of these max loadings. Lateral stability was also ensured to the truss by using several L sections on either side of the truss. These were designed for the maximum tension load that could occur in them, assumed to be 2% of the load in the interior compression members. On either side of the arena, beams were also designed, spanning from column to column and designed for flexure. ii.

Bracings design

All the braces of the main building’s structure were considered to be tension‐only. The use of Double‐L sections ensured this, since their slenderness in compression far exceeded the normal limit, meaning that it is safe to assume that the braces possessed no compression force. Depending on the location of each bracing bay, the loads were applied at the different heights by which the loads enter the bays. In the North‐South direction, a particularity of the structure was that the bracing bays were of different height, as seen in figure 21. This difference in height induced a 32

difference in rigidity between the different bays. Therefore, the smaller bay, being more rigid would take up more of the lateral load than its higher counter‐part. To determine this rigidity, it was first assumed that half the total load was taken by each bay. This enabled a preliminary design of the various members of the individual bays. These bays were then inputted into SAP2000 as an equal load was applied at the highest point of each bay. The resultant lateral deflection of each bay was then divided by the height of the bay, which showed us that 64% of the lateral was taken by the smaller bay, while 36% was taken by the taller one. The loads were then recalculated and the braces were redesigned to resist the tension loads. P∆ effects were also calculated and factored to the final forces. The chosen braces were doubled checked and all satisfied the applied load.

Figure 21 ‐ Side view of main building with overlaping SAP2000 Model

The beams spanning the bays were designed for compression, taking only their self‐ weight as lateral loading. This process was repeated for each bracing segments, using the calculated lateral loads determined from the seismic analysis. Refer to the appendix for more detail on the design. 33

iii.

Columns for main building

The main structure of the arena housing the skating rink is held up by a total of 34 columns, all spanning from the slab to the curved roof. The tallest columns span 11 meters while the shortest measure 6.5 meters. The floorplan, shown in Figure *, lays out the locations of the columns. It can be noted that all columns were oriented with the strong axis resisting the wind loading.

Figure 22: Floor plan showing layout of all columns

Four different columns were designed, as indicated in Figure 22, a different design for each side of the building. The four critical columns chosen were those which were part of the brace bay, since they were subject to additional compression and tension forces. The columns were modeled on SAP2000 in order to analyse the critical loading patterns, deflection shape and compression forces and bending forces applied, as shown in Figure 23 below. The results are found in the Appendix.

Figure 23: Location of critical columns, part of braced bay system

Figure 24: SAP2000 analysis of column 4

Â 35

A summary of the analysis of loadings can be found in Table 8.

Table 8: Summary of column factored loads, sections and special considerations

Column

Special Considerations Shortest column/total L=Lu/carrying half of roof truss load 7.14m exposed to wind loading/supporting larger braced bay Carrying dead‐live loads from Main+Lockers building/part of 2 braced bays Carrying dead‐live loads from Main+Mechanical building/bending induced by lateral movement of weight of Mechanical roof and floor in east‐west direction

1 2 3

Lu (m)

Cf Mf Vf (kN) (kNm) (kN)

6.5

745

11.5

14.8

W200x52

1011

55.79

23.61

W200x59

1634

4.48

13.3

W200x86

1199

800

1130 W310x179

Section

Special considerations were noted for Column 4. During seismic activity in the East‐ West direction, the movement of weights of the roof and floor of the Mechanical building will induce lateral forces onto the 11m columns, as shown in Figure 25 The W310x179 section has a moment resistance of 950 kNm, which exceeds the factored moment applied of 800 kN.m.

Figure 25: Deflection pattern of column under seismic consideration and lateral loading from the mechanical building

Class 1 sections were chosen for all four designed columns in order to better accommodate for seismic influence. All columns were made of grade 350W steel. The cross‐section strength, overall in‐plane member strength and lateral torsional buckling stability of each section chose had to be adequate under the combined action of compressive and bending forces, based on the guidelines provided by S16 standards. The allowable deflection L/240 = 11/240m= 0.46m. The smallest cross‐sectional area was minimized in order to leave adequate area around the rink. The calculations are found in the Appendix. In order to account for Pδ effect (a second order elastic analysis required), amplification factors U1x and U1y were incorporated in the combined action requirements to simulate a second order analysis.

iv.

Exterior and column design for adjacent buildings (mechanical room and lockers room)

Specific columns had to be designed with respect for geometric considerations (such as the specificity of the tributary width with respect to the member considered) and for every specific loading pattern. In effect, the columns were to support vertical gravity loads previously developed for the lower roofs and uniformly distributed wind loads while meeting serviceability deflection limits. The cross‐section strength, overall in‐plane member strength, flexural or lateral torsional stability and shear resistance have been checked based on the guidelines provided by S16 standards. In order to account for the portion of gravity loads and wind loads taken by a specific column, the tributary width (and area) of each member had to be determined (the values are of the latter are provided in the appendix of this report). Both framing building presented specifications that led us to design for 5 different types of columns. Although some columns present different tributary areas, the variances were so small that a conservative approach was adopted in order to design a single column for a group of members presenting the same tributary width and loading. In this perspective, columns A‐4, A‐5, A‐6 and A‐7(in the lockers room) have been designed similarly, and so were columns D‐0, E‐0, E5‐0 and F‐0 in the mechanical room (figure26). Exceptionally, columns A‐2 and A‐9 presented a tributary width that was significantly different from the one of the other exterior columns of the lockers room; they have therefore been designed separately. The two corner columns of each building have been designed separately insofar as they were subjected to different wind loads for the same contact surface. Such considerations coupled with the guidelines provided by S16 for column design allowed the determination of the section used for each column, as can be seen in figure 26.

Figure 26 ‐ Column designation for the side buildings

Girts design

C‐section girts were designed to provide lateral support to the columns and resist

wind loads. The girt system had to be designed such as to be competent and adequately stiff to provide the required stabilizing resistance in addition to its role as a column support. The girts bracing the entire structure (main, mechanical and locker room) were designed considering to be uniformly loaded simply supported beams under wind loads and according to the guidelines provided by S16. In order to determine the loading on each girt, the wind load being transferred from the cladding had to be considered first. As to the lower roofs, two girts have been initially assumed to be spanning the entire height of the buildings, which eventually allowed us to derive a tributary width aiming at the determination of the wind loading in kN/m. Girts are cold‐formed using high‐strength steel to minimize weight while maximizing capacity.

Figure 27 â&#x20AC;? Girt designation for the lockers room

Figure 28 â&#x20AC;? Girt designation for the mechanical room

vi.

Ice Rink slab design

CIMCO was contacted for their expertise in the design of refrigerated slab on grade systems. Figures 29 below, courtesy of CIMCO, illustrate a typical cross section. Special features embedded in the slab include cooling pipes (denoted in blue) to keep the ice rink frozen and heating pipes to ensure that the underlying soil and building foundations do not freeze and heave.

~5 inches Rebar mesh (10M) Cooling pipes Pipe stand Insulation

Heating pipes

Figure 29: Cross section of ice rink slab on grade

The only significant loading that must be considered is that of the moving Zamboni (load of 5148 kg transferred through the wheels). The applied stress and moment were compared to the critical stress and moments, which were determined using modulus of rupture, section modulus and required safety factor of 1.7. The reinforcement mesh is place at the center of the concrete slab as to prevent bending in both positive and negative bending. Refer to the appendix for more detail on the design. vii.

Foundation design

a. Spread footings After the structure’s design was completed, the ability of foundations to adequately carry

the

loads

down

the

soil

media

was

checked.

No extensive data was initially provided about the soil’s characteristics, such as the bulk unit weight, cohesion, and water content. Relevant values have been acquired through investigation or request to our contact in SNC Lavalin; if some values could not be obtained by such means, they were conservatively assumed. This foundation system (comprising a steel base plated anchored to a concrete pedestal incorporated to the spread footing) was designed on the basis of the procedures provided by the Concrete Design Handbook by CAC (3rd edition, 2006, CSA A23.3‐04), the Handbook of Steel Construction (10th Edition, CISC‐ICCA, S16), and the Canadian Foundation Engineering Manual (4th Edition, Canadian geotechnical society, 2006). The spread footing has been designed in order to account for the worst case loading scenario on the interior columns (corresponding to beam columns B‐2, B‐4, B‐5, B‐6, B‐7, B‐ 9) while the base plate was designed in order to accommodate the largest section used for the interior columns in the main building, i.e. a W310x79 section. The base plate was designed as a 360mmx360mmx17mm plate, based on the guidelines provided by the Handbook of Steel Construction. It was to be placed between the column and a supporting pedestal that was to transfer the load from the column to the footing itself. The pedestal has been designed such as to have a 385mmx385mm cross 42

section. It was reinforced by use of four 35M compression bars which were to develop yield stress in compression, four 20M dowels and 10M ties with 400 mm spacing. The column would carry the load to the pedestal (thanks to the connection established by the base plate anchored to the pedestal by means of four anchor rods), which would eventually transmit it to the spread footing that would transfer it to the soil. For the spread footing, the two‐way shear requirements governed the design over the one‐way shear requirements; it has been designed accordingly. The spread footing was eventually designed to be a 3.5mx3.5mx0.5m footing reinforced with nine 25M bars in each direction. The figures provided below show 3D as well as a 2D detailing of the spread footing design under the basement of the structure. Design calculations can be found in the appendix.

Figure 30 ‐ Spread footing detailed dimensions and reinforcement specifications in 2D view

Figure 31 ‐ Spread footing detailed dimensions and reinforcement specifications in 3D view

b. Basement walls Given the underground nature of our structure, walls needed to be designed in order to resist the lateral pressure of the surrounding soil, but also, in the case of the walls surrounding the side buildings, to support the main steel columns and joists. In the case of these side buildings, the retaining walls were designed as basement walls, were a pin connection was assumed at the top and a fixed connection at the bottom. With this set up, the wall was able to be designed as a one‐way slab with a triangular distributed load from the soil and a uniform load from the live surcharge load of 12 kPa considered all around the structure to account for a possible fire‐truck coming up‐close to the structure. Reinforcement was therefore specified at a spacing of 300 mm o/c with 25M bars. Since the wall was supported both at the top and the bottom, it was much smaller and requiring less concrete than its cantilever counter‐part, as seen in figure 32. 44

Figure 32 â&#x20AC;? Diagram of final Basement Wall dimensions

Once designed, the bearing capacity of the wall was checked, ensuring that it resisted both the point load from the columns (transferred through baseplates) and that of the joists spaced out at 1 m o/c. The load from the joists was also transferred by the median of baseplates. c. RetainingÂ wallsÂ

Throughout the rest of the building, mainly around the main ice rink, basement walls

could not be used since there was no support available at the upper part of the wall. As a result, columns could not rest on top of the walls and spanned all the way to the bottom floor, incorporating a standard footing and using larger dimensions at those localized areas. The retaining walls were designed to resist, like the basement walls, soil pressures, and live load surcharges. They were also designed to resist overturning and sliding. The final design 45

pressure was compared to the bearing capacity of the soil, ensuring a pressure lower than the capacity of 200 kPa. Rebar was placed at 500 mm o/c in the wall and 350 mm o/c in the base. Bar cut‐offs were also calculated in order to limit steel use. The final dimensions of this wall can be seen in figure 33.

Figure 33 ‐ Diagram of final Retaining Wall dimensions

viii.

Interior floor and roof (diaphragm) slab design

Diaphragm is another structural component that has to be designed to transfer shear flows from the roof into braces. With steel decks being applied throughout the roofs and floors of the structure, the diaphragm designs follow the in‐depth guidelines of CANAM Steel Deck Diaphragms Catalogue. The design of steel decks is also referred to CANAM Steel Deck Catalogue. Steel decks P‐3615 and P‐3606 are found to hold up the same load capacities. However, P‐3606 is chosen because screws are used instead of button punch as side‐lap fastening, and would be more economical and practical for installation. As shown in the diagram below (FIG.1), the 46

shear diagram shows an uneven distribution of lateral loads from seismic across the roof, with a maximum of 500 kN on each end, and a different shear force is also to be consider from the side of the building. However, the Nâ&#x20AC;?S loads will be more critical given a shorter shear length. With accordance to the CANAM Catalogue, a fastener pattern of 36/4 and side lap spacing of 900mm o/c is designed as shown in Figure 34.

Only Minimum Fasteners Required 36/4 at Support 900 mm o/c Lapâ&#x20AC;? Spacing

Figure 34: Fastener support pattern

For locations where only the peak shear forces at the end exceeds the resistance with minimum fasteners, a smaller spacing for fasteners is assigned starting from 3/4 points away from zero shears for economic considerations. Therefore, the decks in between would only require minimum fasteners, and would be much cost saving for a building of almost 70 meters long. We have also checked the shear from the other side and made sure the resistance at the ends will satisfy. The same procedures are applied to every roofs and floors. 47

Then a challenge is faced. A high shear force is found to be exerted at the upper floor and main floor of the building, due to shorter shear lengths. With the same thickness of deck, even the closest fastener spacing possible will not satisfy the required resistance. Instead of increasing the thickness of the deck across two floors, which will be very costly, the team has decided to put in two extra braces to increase the rigidity of the building. Now, as shown in the Figure 35, the roof and floor systems function react like a continuous beam with simply supported at four locations. The modification also results in a change in shear diagrams, with a much smaller shear force distributed at four different locations. With a much lower shear force, only a minimum number of fasteners are needed. An exception is that the forces at the center supports reach exactly the resistance capacity of the lowest fastener pattern. To be more conservative, the final design has decreased the sideâ&#x20AC;?spacing to 600 mm o/c for two decks from supports towards the midâ&#x20AC;?point.

Figure 35: Shear diagrams of roof and floor systems

The first step of the design of roof and floor systems is to understand the flow of forces. All the gravity loads are directly taken up by the steel decks, and then passing on to underlying joists as distributed loads. Consequently, the forces flow through two ends of the joists and pass on as point loads on to beams. Eventually, the forces leave the system through the beams and onto columns. The flow is demonstrated in Figure***.The design

process follows the same order, also because the spacing of joists depends on the decks, and the depth of the joists set a limit for the choice of a beam section. First off, for the design of steel deck, all possible loads have been taken into consideration. And it is obvious that the trapezoidal distributed snow loads controls the design, which range from less than 4 kPa to over 10 kPa. So as advised by the catalogue, we have considered the 10 kPa snow load all over the roof for the design of decks to keep it at the same thickness, and ended up requiring Type 18 of P‐3606 steel deck. For the floors, composite steel decks are used and only Type 22 is required since only a 4.8kPa live load dominates. All steel decks are triple‐spanned since we have such a big area to cover, and one benefit is that overlapping of decks decrease deflection and increases their load capacities.

Figure 36: Flow of forces through diaphragm, joists, beams and columns

The spacing of 1 meter is used to avoid further increase in requirement of thickness, and also to avoid an unreasonable depth of joist. What’s also done to avoid such situation for the roof joists is instead of using 10 kPa of snow all overs the deck, we applied theory of superposition and cut the trapezoidal distribution into a triangular and rectangular distribution, finding the maximum shear at one side as requirement for shear capacity by 49

adding up the end shear, and write down balancing equations to find value and location of the maximum moment. However, the Canadian CANAM Catalogue only provides resistance that accounts for evenly distributed loads. To achieve being both economical and conservative, we have referred to the Imperial version, which has more detailed codes, regulations, and design procedures. KCS‐ Series is chosen because it’s designed specifically to account for special loadings as such. Sections are listed by their shear and moment capacities instead uniformly distributed resistance. Through calculations and references, 28KCS3 has a depth of 700 mm and is sufficient to carry to the shear loads despite the span requirement of more than 6m. One other benefit of using KCS‐series is that it allows different designs of beams at two ends. The exterior beams, at the roof of the locker room, which take the smaller half of the trapezoidal loads on top, are, therefore, designed differently from the interior ones, which carry half of both the interior floors and the exterior roof. However, a maximum span of over 10 meters is required. And with joists fully supporting the beam to prevent lateral buckling, deflection controls the design. In order to avoid heavy and costly class 1 sections such as a W360x314 for the interior beam, a more economical design is to instead increasing the depth of the beam and chose class 3 sections such as W530x150. The only restraint of its depth is to be 100 mm less than the depth of the joists. It’s a serviceability criterion for the convenience of HVAC installation. However, the section used as an example failed to meet such requirement since the joists of the interior floors requires only a depth of 550 mm according to the Canadian Catalogue. Nevertheless, it is increased to its maximum depth of 600 mm with a self‐weight increase of only less than 0.5kg/m per joist. At the same time, the size of beams is decreased down to W460x177 to meet the requirement, and still remain cost saving.

ix.

Bleachers design

Figure 37 ‐ Schokbeton Design Diagram

The bleachers are put in place to allow the visitors of the UQAC arena to view the hockey games and the action going on, on the ice. They are positioned as part of the main interior building and are set above the ice‐rink floor in order to allow the best visibility when viewing the ice. 9.2 meters separates each column. At first, casting the concrete structure in its final position was considered, however, after analysis, it was determined that prefabricated concrete slabs, would be easier and quicker to install, due to the lack of required form‐work and reinforcement placement. Several local companies exist, however, it was determined that the local Quebecer company Schokbeton offered the best product for our design, as pictured in figure 38. Their prefabricated, pre‐stressed concrete elements proved to be perfect for our design. From their design table, seen in figure 37, it was determined that a 10” (254 mm) slab was required. 4‐32 mm tubes are present in this one‐ way 965 mm wide slab. Through these tubes, 4‐15mm steel strands are pulled and tensioned as necessary to resist the vibrational loads from the spectators.

Figure 38 â&#x20AC;? Crossâ&#x20AC;?sectional view of Schokbeton's prefabricated concrete slabs

A live load of 4.8 kPa was considered for this design and the resultant dead weight from the slab is 3.34 kPa. A steel structure was then needed to be designed to hold up these slabs. A bent beam was used in order to hold the concrete slabs in offset of 460 mm. A full weld is required at this bend. Given the load, the beam was in tension and flexion. Given an allowable deflection of L/360= 8.04 mm, a W310x45 was used. The supporting column, under simple compression was determined to be a W200x27. A transfer plate was also designed in order to transfer the load from the concrete slabs to the inclined beam. Two shear stiffeners were also designed to avoid crumpling of the thin steel sheet.

Figure 39 ‐ Bleacher Dimensions

5) LEED Certification and environmental concerns In addition to the structural aspects of the arena design, ACE Engineering Consultants is also part of the integrative project team aiming to achieve a Leadership in Energy and Environmental Design (LEED) Gold certification under LEED for New Construction. The goal is to promote the green building movement and help creating a more sustainable, while providing students, institutional staff, and other users in the community with a healthier and more comfortable ambience. Following the guideline provided by the U.S. Green Building Council (USGBC), the strategies proposed by the team are also divided into seven different categories: Sustainable Sites Water Efficiency Energy and Atmosphere Materials and Resources 53

Indoor Environmental Quality Innovation and Design Regional Priority Innovation and Design The first credits in the category were earned by the team of ACE Engineering Consultants, by having a LEED Certified AP leading the integrated project team. Within an integrated team, all stakeholders, including but not limiting to the owner, the architects, civil engineers, structural engineers, mechanical engineers, future facility users, etc., can be involved in the process of design and decision making. Another structural related aspect of the design, with potential of earning more credits in category, is also proposed by the team of ACE Engineering Consultant. The team has agreed to incorporate high levels of fly ash in concrete to divert waste water materials from landfills. Sustainable Sites With green roofs, green fields and pervious pavers, our project will significantly improve water infiltration, as shown in Figure 1. In addition, rainwater will be harvested from the main roof and converging into the plumbing system to provide water to flush toilets. The main roof of the building is composed of high reflective steel decks and will reflect sun lights during summer days to minimize greenhouse effect. Also, priority parking is also provided to facility users with low emission and fuel efficient vehicles. Another transportation criterion addressed is the proximity of the site of project and nearby transportations. Buses stations are few blocks away and biking racks will be also provided near the entrance of the building. Water Efficiency With two green roofs incorporated into our design, landscape engineers have proposed drip irrigation to improve water efficiency on landscaping. Submeters will also be 54

installed to help identifying leaking problems or maintenance issues in process water systems.

Figure 40: Green roof on adjacent buildings

Energy and Atmosphere In addition to highâ&#x20AC;?performance mechanical systems, all appliances to be used in the building are required to have Energy Star labelled. Facility staffs are also required to be trained for efficient operation and maintenance of the system. Material and Resources ACE engineering consultants has also participated in the choice of construction materials. Structural components such as steel members and concrete materials are to be purchased from local providers. In detail, steel members will be purchased from Philippe TrĂŠpanier inc., which is less than 20km away from the project site, and concrete materials from BPDL International 50km away. Certain parts of the materials are recyclable and marked down for reuse during demolition.

Indoor Environmental Quality Since indoor quality would be critical for the comfort and health of the facility users, various strategies will be strictly enforced. First of all, smoking within the building is prohibited and outdoor smoking is restricted to designated areas. Indoor materials are to be measured with low VOC. High‐efficient ventilation system will cooperate with large windows and some operable windows to further enhance the user experience within the building.

Figure 41 ‐ Interior view of Arena

8. Conclusions Lessons learnt: ‐An efficient communication is the prime factor of success in such a project as many disciplines were concerned. In effect, due to the many different considerations that were to be accounted for, an error in one design calculation that would not have been made public within short notice could have led to important changes in design. Such matters would have been addressed with great difficulty, since it is hard to retrace the sequence of calculations that led to a fault in the design. Hence, an effective communication allowed the prevention of such chained mistakes. Furthermore, many alternatives were considered in order to optimize the communication between team members, ranging from the social media Facebook, to the online sharing platforms Dropbox and GoogleDocs. ‐We have been faced with certain realities in engineering design, such the fact that many uncertainties arise during the design progress. An important number of points were made relevant as the design was performed, in order to account for uncertainties, high seismicity in the area, a specific geometry,… Many standards that were not familiar to many of the Ace Engineering Consultants team members had to be considered for some particular designs (ice rink slab, foundations, diaphragms,…). In effect, throughout this project, the impossibility to establish a final schedule right from the start was made clear, yet it provided us with the opportunity to learn from new codes and standards, and discover new concepts in engineering. ‐The main purpose of the design process was to be able to obtain an optimal compromise accounting for as much for a conservative design as for reasonable assumptions. In effect, an important amount of our data had to be assumed in order to carry on with the design, as the major source of initial data we were provided with were preliminary architectural plans. This provided us with the opportunity to refine the design of the structure itself and address certain points with a freedom that was yet to account for certain considerations (such as cost‐effectiveness, structural criteria…).

‐The use of software widened as the project went on as the increasing complexity of the design was to be accounted for by different means; this allowed us to develop our design skills by use of rightly adapted software. ‐The design of the UQAC arena consisted of a complex project whose complexity required the extensive investment of all team members. In effect, as the project went on and the complexity increased, a unity built up within the team. Every member was willing to help his peers in order to contribute more actively to an efficient design, and tasks assignments were often fused or reviewed such as to accommodate the preferences of each member. Often the team’s needs have been favored over personal plans, which led to an important amount of time working together. These frequent interactions between team members and this sense of solidarity reinforced interpersonal bonds, and enhanced the efficiency of the project.

Figure 42 ‐ 3D Rendered View

References ‐ Schokbeton Concrete Slab Design Manual ‐ CANAM Catalogs ‐ National Building Code of Canada, Volume 1, Twelfth Edition, 2005 ‐ Handbook of Steel Construction, 10th Edition, CISC‐ICCA ‐ CIBSE Knowledge series KS: 11 (Green Roofs) ‐ CANAM Joist Catalogue, 42nd Edition ‐ Concrete Design Handbook by CAC, 3rd edition, 2006 (CSA A23.3‐04) ‐ Concrete materials and methods of concrete construction/Test methods and standard practices for concrete, Eleventh Edition, 2009 (CSA A23.1‐09 /A23.2‐09) ‐ Canadian Foundation Engineering Manual, 4th Edition, Canadian geotechnical society, 2006 ‐ Design Floor Slabs on Grade, 2nd edition, Boyd C. Ringo and Robert B. Anderson, 1996

APPENDIX UQAC SPORTS ARENA Winter 2013

Caroline CHAN Arnaud DUSSER Othmane LARAKI Randy(Chao) WANG

Project Title: Project Detail: Design Detail: Comments:

UQAC Arena Tributary Area

March 13thth, 2013 Caroline Chan Othmane Laraki Randy Wang

DATE: DESIGNED BY: VERIFIED BY: CHECKED BY:

Tributary Area

Coordinate Member

Trib Width (m)

Length (m)

Area (m^2)

9.144

32.203 36.783

336.34

Roof Purlin

2.286

36.783

84.09

Roof Beam Beam 1 Beam 2 Beam

3.86 4.544 6.039

9.144 9.144 9.144

35.30 41.55 55.22

9.144 9.144 9.144 5.3625 5.3625 2.335 2.5 2.335 2.5

16.1015 2.335 16.1015 6.039 6.039 5.3625 5.3625 5.3625 5.3625

147.23 21.35 147.23 32.38 32.38 12.52 13.41 12.52 3.00

9.144 9.144 6.039 / 7.6975 7.8625 / 7.8625

H/2 1.245 3.569 3.569 / 3.569 1.245 / 1.245

11.38 32.63 21.55 / 27.47 9.79 / 9.79

(according to simplified drawing)

Notes

Source

Main Building Gravity Loads Roof Truss

Exterior Column Column H Column B Column C Column 10 Column 1 Column B10 Column H10 Column B1 Column H1

All 6

H:2,4 5,6,7,9 B:2,4,5,6,7,9 C:2,4,5,6,7,9 10:C,D,E,E.5,F,G 1:C,D,E,E.5,F,G B10 H10 B1 H1

Half distance between A1, Skeleton two trusses Length is half of building width, width is 1/4 of dist btwn truss. Edge purlins A2, Skeleton will be the same design (even though there is smaller T.A. b/c there more purlins in span)

A2, Skeleton

Length dist btwn truss, will probably design a A2, Skeleton typical beam and use A2, Skeleton same design for all roof beams

A2, Skeleton A2, Skeleton

corner columns

A2, Skeleton A2, Skeleton A2, Skeleton A2, Skeleton A2, Skeleton A2, Skeleton

Interior Floor Truss Randy Interior Columns Randy Interior Beams Randy

Lateral Loads Girt

Othmane

Exterior Column Column 1 Column 2 Column 3 Column 4 Column 5 Column 6 Column 7 Column 8

H:2,4 5,6,7,9 B:2,4,5,6,7,9 10:C,D,E,E.5,F,G 1:C,D,E,E.5,F,G B10 H10 B1 H1

A8, A2, Skeleton Assume all Col 3&4 A8, A2, Skeleton design the same, even A8, A2, Skeleton Col C,D,1,10 Assume no lateral load dA8, A2, Skeleton

A8, A2, Skeleton A8, A2, Skeleton Assume no lateral load dA8, A2, Skeleton Same as Col 6 A8, A2, Skeleton

Project Title: Project Detail: Design Detail: Comments:

Mechanical Building Column Column 0 Column B0 Column G0 Column 1

0:D,E,E.5,F,G B0 G0 1:B,C,D,E,E.5,F,G

Roof Truss

Randy

Beam

Randy

Bleachers Building

UQAC Arena Tributary Area

March 13thth, 2013 Caroline Chan Othmane Laraki Randy Wang

DATE: DESIGNED BY: VERIFIED BY: CHECKED BY:

Height: 4.25m

6.039 3.86 3.019 6.039

4.374 4.374 4.374 4.374

26.41 16.88 13.21 26.41

9.144 5.3625 9.9345 9.144

3.23 3.23 3.23 3.23

29.54 17.32 32.09 29.54

*Are the cols connecting mechanical and main carrying A2, Simplified gravity loads here too? A2, Simplified

A2, Simplified Must be added to A2, Simplified Main Building Gravity columns

Height: 3.93m

Column Column A4,A5,A6,A7A:4,5,6,7 Column A1, A10 A1, 10 Column A2, A9 A2,9 Column B B:2,4,5,6,7,9

Roof Truss

Randy

Beam

Randy

Typical columns Corner Different TA Must be added to Main Building Gravity columns

Project Title:

UQAC Arena

DATE:

March 13thth, 2013 Caroline Chan

Project Detail:

Tributary Area

Design Detail:

Interior floor loads

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Randy Wang

Comments:

Interior floor slab loading onto gravity columns Int floor slab given by Randy

227.34 kPa

(factored)

D for interior slab

3.54 kPa

4.8 kPa

1.25D+1.5L

11.625 kPa

Columns B2,B4,B5,B6,B7,B9 TA

LOAD (kN)

Upper Floor

9.9345

2.335

23.1970575

269.6657934 kN

Ground Floor

9.93

5.565

55.2854925

642.6938503 kN

Total

912.3596438 kN

Columns C2,C4,C5,C6,C7,C9 TA

LOAD (kN)

Upper Floor

9.9345

2.335

23.1970575

269.6657934 kN

Ground Floor

9.93

2.335

23.1970575

269.6657934 kN

Total

539.3315869 kN

Columns 1D,1E,1E.5,1F,1G TA Upper Floor Ground Floor

6.04

4.374

LOAD (kN) 0

0 kN

26.414586

307.0695623 kN

Total

307.0695623 kN

Columns B1, C1 TA

LOAD (kN)

Upper Floor

5.3625

2.335

12.5214375

145.5617109 kN

Ground Floor

5.36

5.565

29.8423125

346.9168828 kN

Total

492.4785938 kN

Project Title:

January 26th, 2013

UQAC Arena

DATE:

Project Detail:

Load Calculations

Design Detail:

Dead and Live Loads

VERIFIED BY:

Caroline Chan

Comments:

Curved roof, Lower roofs, interior floors

CHECKED BY:

Randy (Chao) Wang

Othmane Laraki

The following has been established on the basis of values provided by the NBCC 2005, the Handbook of Steel Construction, 10th edition (CISCͲICCA), the 42nd edition of the CANAM Joists Catalogue and the CIBSE knowledge series KS:11 Handbook. DEAD LOADS

Main building

Materials

Design Dead Load (kPa)

Reference

Corrugated Steel Deck

0.1

Handbook of Steel Construction, 10th Edition, CISC Ͳ ICCA

Plywood (19mm)

0.11

Handbook of Steel Construction, 10th Edition, CISC Ͳ ICCA

Insulation Ͳ Rigd Foam (200mm)

0.06

Handbook of Steel Construction, 10th Edition, CISC Ͳ ICCA

Plywood (19mm)

0.11

Handbook of Steel Construction, 10th Edition, CISC Ͳ ICCA

Steel Deck

0.15

Handbook of Steel Construction, 10th Edition, CISC Ͳ ICCA

Ducts/Pipes/Wiring Allowance

0.25

Handbook of Steel Construction, 10th Edition, CISC Ͳ ICCA

є = 0.78 kPa

Interior floors

Materials

Design Dead Load (kPa)

Reference

38mm deck with 90mm N.D. cover

2.55

Handbook of Steel Construction, 10th Edition, CISC Ͳ ICCA

Joists

0.19

CANAM Joist Catalogue, 42nd Edition

Ducts/Pipes/Wiring Allowance

0.25

Handbook of Steel Construction, 10th Edition, CISC Ͳ ICCA

Sprayed fire protection

0.07

Handbook of Steel Construction, 10th Edition, CISC Ͳ ICCA

Suspended Ceiling

0.48

CANAM Joist Catalogue, 42nd Edition

є = 3.54

Side buildings (Mechanical room and lockers room)

Materials

Design Dead Load (kPa)

Earth/Soil Media Drainage/Aeration/Water Storage Insulation

є = 0.7

Membrane Protection, Root Barrier

Reference

CIBSE (2007) Green Roofs – CIBSE Knowledge series KS:11

Roofing Membrane

Corrugated Steel Deck

0.1

Handbook of Steel Construction, 10th Edition, CISC Ͳ ICCA

CIBSE (2007) Green Roofs – CIBSE Knowledge series KS:11

Plywood (19mm)

0.11

Handbook of Steel Construction, 10th Edition, CISC Ͳ ICCA

Insulation Ͳ Rigd Foam (200mm)

0.06

Handbook of Steel Construction, 10th Edition, CISC Ͳ ICCA

Plywood (19mm)

0.11

Handbook of Steel Construction, 10th Edition, CISC Ͳ ICCA

Steel Deck

0.15

Handbook of Steel Construction, 10th Edition, CISC Ͳ ICCA

Ducts/Pipes/Wiring Allowance

0.25

Handbook of Steel Construction, 10th Edition, CISC Ͳ ICCA

Joists

0.19

CANAM Joists Catalogue (42nd Edition)

є = 1.69

Project Title:

January 26th, 2013

UQAC Arena

DATE:

Project Detail:

Load Calculations

Design Detail:

Dead and Live Loads

VERIFIED BY:

Caroline Chan

Comments:

Curved roof, Lower roofs, interior floors

CHECKED BY:

Randy (Chao) Wang

Othmane Laraki

LIVE LOADS

Main building

Use of Area

Minimum Specified Live Load (kPa)

Reference

Roofs

National Building Code of Canada, Volume 1, Table 4.1.5.3, 2005

Interior floors

Location

Use of area

Minimum Specified Live Load (kPa)

Reference

Main Building

Office area

4.8

NBCC, Volume 1, Table 4.1.5.3, 2005

Mechanical Room

Machine room

3.6

NBCC, Volume 1, Table 4.1.5.3, 2005

Lockers Room

Storage area

4.8

NBCC, Volume 1, Table 4.1.5.3, 2005

Side buildings (Mechanical room and lockers room)

Use of Area

Minimum Specified Live Load (kPa)

Reference

Roofs

4.8

National Building Code of Canada, Volume 1, Table 4.1.5.3, 2005

February 4th, 2013 Caroline Chan

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Snow load analysis

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Randy Wang

Comments: Higher Curved Roof

S=Is(Ss(Cb*Cw*Cs*Ca)+Sr)

Caluculations, Tables below Cw=0.75

For load Case I, Cw=1.0

NBCC 2010, 4.1.6.2. (4)

Cb:

NBCC 2010, 4.1.6.2. (2)

Cb shall be 0.8 except for large roofs: 1) Cb=1.0Ͳ(30/Lc)^2

Cw=1

where Lc is >70

2) Cb=1.3Ͳ(140/Lc)^2

Cw=0.75

where Lc is >200

36.795 m

69.154 m

54.01236132 m

Lc=2wͲ(w^2)/L

Cb = 0.8

Ca:

Figure GͲ3, Commentaries p. GͲ8

Case 1

Case 2

0.840467455 3*A/(SsCb)

Case 3

Ca=2xA/(CbX)

4.948

vertical dim of roof

73.59

*multiply the actual dim by 2 because monoslope

0.560311637

A=(h/b)/0.12

A<1

20.596

x is dim from center to mid

36.795

where X is dim from center to edge (which is the entire width of the building)

Ca at midpoint: Ca at edge:

0.784086049 1.400779091

Justification

References

Is= 1

NBCC 2010, 4.1.6.2.

Ss= 2.5

Table cͲ2 App C

Cb= 0.8

small roof, calculations above

NBCC 2010, 4.1.6.2. (2)

Cw= 0.75

below treeline, open terrain no obstruction

NBCC 2010, 4.1.6.2. (4)

Cs= 1 Ca= varies

slope less than 30

NBCC 2010, 4.1.6.2. (5) Figure GͲ3, Commentaries p. GͲ8

Sr= 0.4

Table cͲ2 App C

Curved Roof Figure GͲ3

S (kPa)

Case 1

2.5

0.8

0.4

2.40

Case 2

2.5

0.8

0.75

0.840467455

0.4

1.66

Case 3 (mid)

2.5

0.8

0.75

0.784086049

0.4

1.58

Case 3 (edge)

2.5

0.8

0.75

1.400779091

0.4

2.50

February 4th, 2013 Caroline Chan

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Snow load analysis

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Randy Wang

Comments: Lower adjacent roofs Mechanical lower green roof S=Is[Ss(CbCwCsCa)+Sr] Justification Is= 1

References

normal

NBCC 2010, 4.1.6.2.

Ss= 2.5

Table cͲ2 App C

Cb= 0.8

small roof

NBCC 2010, 4.1.6.2. (2)

Cw= 1

drifting

NBCC 2010, 4.1.6.2. (4)

Cs= 1

slope 0

NBCC 2010, 4.1.6.2. (5)

Ca= 5.06709794

Figure GͲ5, Commentaries p. GͲ11

Sr= 0.4

Table cͲ2 App C xd

location

10.16774485

Ca= 5.06709794 S=

10.53419588

Figure GͲ5, Commentaries p. GͲ11

2.4

32.673 m

8.745 m

Lc (upper)=

54.01236132 m

ɶ=

Lc of upper curve roof

4 kN/m^3

hp (lower)=

0.406 m

hp (upper)=

2.885

0.8Ss/ɶ=

0.5

h'= hͲCbCwSs/ɶ

density of snow parapet on mechanical roof no parapet on curved roof height of mechanical: 4.25

yes, drifting

2.385

F= 2, or

(0.35(ɶlc/Ss Ͳ 6*(ɶhp/Ss)^2)^0.5)+Cb

xd =

height of main: 7.138

5(hͲCbSs/ɶ) 5(Ss/ɶ)(FͲCb)

max=

4.053678352

11.925 10.16774485

Ca= (ɶh)/(CbSs) F/Cb

5.77 5.06709794

min=

10.16774485

min=

5.06709794

4.053678352

10.53 kPa at the edge of high roof and low roof 2.4 kPa at xd, which is 10.167 meters away from edge

10.53

5.37

6.46

February 4th, 2013 Caroline Chan

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Snow load analysis

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Randy Wang

Comments: Bleacher's Roof S=Is[Ss(CbCwCsCa)+Sr] Justification Is= 1

References

normal

NBCC 2010, 4.1.6.2.

Ss= 2.5

Table cͲ2 App C

Cb= 0.8

small roof

NBCC 2010, 4.1.6.2. (2)

Cw= 1

drifting

NBCC 2010, 4.1.6.2. (4)

Cs= 1

slope 0

NBCC 2010, 4.1.6.2. (5)

Sr= 0.4

Table cͲ2 App C xd

dge of main building

10.16774485

Ca= 5.06709794 S=

10.53419588

Figure GͲ5, Commentaries p. GͲ11

2.4

61.189 m

7.153 m

Lc (upper)=

54.01236132 m

ɶ=

Lc of upper curve roof

4 kN/m^3

density of snow

hp (lower)=

parapet on lower roof

hp (upper)=

no parapet on curved roof

3.208

0.8Ss/ɶ=

0.5

h'= hͲCbCwSs/ɶ

height of bleachers: 3.93

yes, drifting

2.708

F= 2, or

(0.35(ɶlc/Ss Ͳ 6(ɶhp/Ss)^2)^0.5)+Cb

xd =

5(hͲCbSs/ɶ) 5(Ss/ɶ)(FͲCb)

Ca(0)= (ɶh)/(CbSs) F/Cb

height of main: 7.138

4.053678352

15.04 10.16774485 6.416 5.06709794

min=

10.16774485

min=

5.06709794

max=

4.053678352

10.53 3.54

8.748

0 10.53

8.748 3.54

10.17 2.4

10.53 kPa at the edge of high roof and low roof 2.4 kPa at xd, which is 10.167 meters away from edge

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Wind load analysis

Comments:

February 4th, 2013 Caroline Chan

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Randy Wang

WIND LOADS Main building

Open Terrain Dimensions Width w

36.80

Length L

69.15

10% w

3.68

40% H

2.86

Height

curved

roof 2 7.14

min=

2.86

>4% w

1.47

roof 1 4.25

3.93

Walls Pext Fig IͲ8

Dim CpCg

Walls

z or w

Area

2.86

2.88

8.22

1.50

Ͳ1.70

2.86

3.26

9.31

1.60

Ͳ1.80

2.86

2.49

7.11

1.60

Ͳ1.70

2.86

3.21

9.16

1.60

Ͳ1.80

31.08

3.14

97.54

1.30

Ͳ1.50

63.44

4.25

269.64

1.30

Ͳ1.50

63.44

3.14

199.09

1.30

Ͳ1.50

Pint Pint = IwqCeCpCg Justification

References

Iw= 1

NBCC 2010, 4.1.7.1.

q= 0.36

Table cͲ2 App C

Ce= 0.813784305

<0.9 not ok use 0.9

Cp= varies

significant openings, Cat 2

NBCC 2010, 4.1.7.1. (5) Commentary para IͲ31

Cg= 2

Commentary para IͲ22 Cat 2

1.00

0.36

0.90

2.00

Pint (kPa)

Cp 0.30

Ͳ0.45

Pressure

Suction

0.19

Ͳ0.29

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Wind load analysis

Comments:

Figure IͲ8, Commentaries CpCg

1.00

0.36

0.81

1.50

1.00

0.36

0.81

1.00

0.36

1.00

February 4th, 2013 Caroline Chan

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Randy Wang

Pext (kPa) Pressure

Suction

Ͳ1.70

0.44

Ͳ0.50

1.60

Ͳ1.80

0.47

Ͳ0.53

0.81

1.60

Ͳ1.70

0.47

Ͳ0.50

0.36

0.81

1.60

Ͳ1.80

0.47

Ͳ0.53

1.00

0.36

0.81

1.30

Ͳ1.50

0.38

Ͳ0.44

1.00

0.36

0.81

1.30

Ͳ1.50

0.38

Ͳ0.44

1.00

0.36

0.81

1.30

Ͳ1.50

0.38

Ͳ0.44

Combining Pext and Pint Net (kPa) Walls

Pressure

Suction

0.63

Ͳ0.79

0.66

Ͳ0.82

0.66

Ͳ0.79

0.66

Ͳ0.82

0.58

Ͳ0.73

0.58

Ͳ0.73

0.58

Ͳ0.73

Roof Fig IͲ27 Cg

2.00

0.00

30.00

90.00

0.00

30.00

0.70

0.60

Ͳ0.30

0.41

0.35

Ͳ0.18

Ͳ0.20

Ͳ0.30

Ͳ0.12

Ͳ0.18

Pext (kPa) 90.00

Ͳ0.30

0.20

0.90

Ͳ0.18

0.12

0.53

Ͳ0.30

Ͳ0.40

Ͳ0.30

Ͳ0.18

Ͳ0.23

Ͳ0.18

Ͳ0.10

Ͳ0.80

Ͳ0.06

Ͳ0.47

Ͳ0.50

Ͳ0.40

Ͳ0.70

Ͳ0.29

Ͳ0.23

Ͳ0.41

Ͳ0.80

Ͳ0.70

Ͳ0.50

Ͳ0.47

Ͳ0.41

Ͳ0.29

Ͳ0.80

Ͳ0.90

Ͳ0.30

Ͳ0.47

Ͳ0.53

Ͳ0.18

Ͳ0.40

Ͳ0.70

Ͳ0.10

Ͳ0.23

Ͳ0.41

Ͳ0.06

Ͳ0.10

Ͳ0.40

Ͳ0.10

Ͳ0.06

Ͳ0.23

Ͳ0.06

Ͳ0.80

Ͳ0.47

Ͳ0.70

Ͳ0.41

Ͳ0.50

Ͳ0.29

Ͳ0.10

Ͳ0.06

Ͳ0.10

Ͳ0.06

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Wind load analysis

Comments:

February 4th, 2013 Caroline Chan

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Randy Wang

Bleachers Building

Walls Pext Fig IͲ8 Dimensions Width w

5.96

Length L

61.19

z 10% w

0.60

40% H

2.86

Height

curved

roof 2 7.14

min=

0.60

>4% w

>1m

0.24

USE 1

roof 1 4.25

3.93

Dim CpCg

Walls

z or w

Area

1.00

3.93

1.60

Ͳ1.90

5.36

3.93

21.08

1.40

Ͳ1.60

60.00

3.93

235.79

1.30

Ͳ1.50

Pint Pint = IwqCeCpCg Justification

References

Iw= 1

NBCC 2010, 4.1.7.1.

q= 0.36

Table cͲ2 App C

Ce= 0.722224989

<0.9 not ok use 0.9

Cp= varies

significant openings, Cat 2

Commentary para IͲ8 Commentary para IͲ31

Cg= 2

Commentary para IͲ22 Cat 2

Pint (kPa)

1.00

0.36

0.90

2.00

1.00

0.36

0.81

1.60

Ͳ1.90

0.47

Ͳ0.56

1.00

0.36

0.81

1.40

Ͳ1.60

0.41

Ͳ0.47

1.00

0.36

0.81

1.30

Ͳ1.50

0.38

Ͳ0.44

Cp 0.30

Ͳ0.45

Figure IͲ8, Commentaries CpCg

Pressure

Suction

0.19

Ͳ0.29

Pext (kPa) Pressure

Suction

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Wind load analysis

Comments:

February 4th, 2013 Caroline Chan

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Randy Wang

Combining Pext and Pint Net (kPa) Walls

Pressure

Suction

0.66

Ͳ0.85

0.60

Ͳ0.76

0.58

Ͳ0.73

Roof Fig IͲ10 For stepped roofs (adjacent roofs) Conditions and dimensions H=

7.14

h1= h2=

3.93

43.95

W1=

36.80

W2=

7.15

b= 4.81

h1>3

h1 >0.3H 2.14

3.21

W1, W2

both conditions met

3.21

>0.25W=

10.99

<0.75W=

32.96

not met

Must carry out with Fig IͲ9 (below)

1.5(h1) but <30m

**************** Fig IͲ9 no overhang Dim CpCg

Section

z or w

Area

1.00

1.60

1.00

3.96

1.40

Ͳ1.60

1.00

59.19

1.30

Ͳ1.50

3.96

59.19

234.39

1.30

Ͳ1.50

min=

0.87

Ͳ1.90

Mechanical Building

Walls Pext Fig IͲ8 Dimensions Width w

8.75

Length L

31.87

Height H

z 10% w

0.87

40% H

2.86 curved

roof 2 7.14

>4% w 0.35

>1m NO

USE 1

roof 1 4.25

3.93

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Wind load analysis

Comments:

February 4th, 2013 Caroline Chan

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Randy Wang

Dim CpCg

Walls

z or w

Area

1.00

4.25

1.70

Ͳ2.00

7.00

4.25

29.73

1.40

Ͳ1.60

30.13

4.25

128.03

1.30

Ͳ1.50

1.00

0.36

0.81

1.70

1.00

0.36

0.81

1.00

0.36

0.81

Figure IͲ8, Commentaries

Pext (kPa)

CpCg

Pressure

Suction

Ͳ2.00

0.50

Ͳ0.59

1.40

Ͳ1.60

0.41

Ͳ0.47

1.30

Ͳ1.50

0.38

Ͳ0.44

Combining Pext and Pint Net (kPa) Walls

Pressure

Suction

0.69

Ͳ0.88

0.60

Ͳ0.76

0.58

Ͳ0.73

Pint Pint = IwqCeCpCg Justification

References

Iw= 1

NBCC 2010, 4.1.7.1.

q= 0.36

Table cͲ2 App C

Ce= 0.733621055

<0.9 not ok use 0.9

Cp= varies

significant openings, Cat 2

Commentary para IͲ8 Commentary para IͲ31

Cg= 2

Commentary para IͲ22 Cat 2

1.00

0.36

0.90

2.00

Pint (kPa)

Cp 0.30

Ͳ0.45

Pressure

Suction

0.19

Ͳ0.29

DATE:

February 2nd, 2013

Project Title:

UQAC Arena

Project Detail:

Wind loading

Design Detail:

Primary structural actions arising from wind loads

VERIFIED BY:

Caroline Chan

Comments:

acting simultaneously on all surfaces

CHECKED BY:

Randy (Chao) Wang

Othmane Laraki

The hourly wind pressure value was provided by NBCC 2005 as being q=0.36kPa for a return period of 50 years (Table CͲ2, Appendix C, division B, Structural Commentary, Part 4, NBCC 2005). The structure was assumed to be located in an open terrain, due to the small number of surrounding buildings. Since the height of the building and its height to width ratio are less than 60m and 4, respectively, the static procedure can be used to conduct the wind pressure analysis. The methodology used for the determination of the wind loads was derived from the NBCC 2005 Structural Commentary. On the basis of the data provided by figure IͲ7, in the National Building Code of Canada (2005, Commentary I), the following have been established: The building must be designed for all wind direction. Each corner must be considered in turn as the windward corner shown in the sketches. For all roof slopes, Load Cases 1,4 and load cases 2,3 are required as two separate loading conditions to generate the wind actions, including torsion, to be resisted by the structural system. Certain CpCg coefficients might be interpolated linearly (here, between 5° and 20°). Positive coefficients denote forces toward the surface, whereas negative coefficients denote forces away from the surface. The endͲzone width z is the lesser of 10% of the least horizontal dimension or 40% of height H but not less than 4% of the least horizontal dimension, or 1m. Hence, z= min (0.10x32.673;0.4x2.49) > max(0.04x32.673;1) = 1m The end zone width y should be the greater of 6m or 2z.

y=max(6;2x1)=6m

On the basis of the data provided by figure IͲ7, in the National Building Code of Canada (2005, Commentary I), the following have been established: Considering our location as an open terrain (exposed location), and the building as a normal importance building, Ce=(h/10)2=(2.49/10)2=0.76<0.9 so we shall use Ce=0.9

P=IwͼqͼCeͼCpͼCg On the basis of this data, the following holds true: ͵ Ǧ

ͳ Ǧ with minimization of zones 2 and 2E (After NBCC 2005)

with minimization of zones 3 and 3E (After NBCC 2005)

ʹ Ǧ with minimization of zones 2 an 2E (After NBCC 2005)

with minimization of zones 3 and 3E (After NBCC 2005)

Ͷ Ǧ

Project Title:

February 4th, 2013

UQAC Arena

DATE:

Project Detail:

Seismic Analysis

Design Detail:

Design of Lateral Stabilizing System

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments:

Arnaud Dusser

Design Summary: Bracing Group No

2 5

2 5 3

Bracing group 1, 3 Larger brace bay: Member 1: Cf =

217.42

6100

W200x52

Member 2: Tf =

4500

Member 3: Tf =

271.46

7580.24

Cf =

161.08

4500

Cf =

430.72

6100

Tf =

161.08

4250

L89x89x6.4

Member 4:

Member 5: W200x52

Member 6:

Member 7: Tf =

523.05

7434.55

Cf =

458.05

4250

Cf =

644.05

6100

Tf =

458.05

3850

L127x127x7.9

Member 8:

Member 9: W200x52

Member 10:

Member 11: Tf =

770.55

7213.36

Cf =

868.55

3850

L127x127x7.9

Member 12:

Project Title:

February 4th, 2013

UQAC Arena

DATE:

Project Detail:

Seismic Analysis

Design Detail:

Design of Lateral Stabilizing System

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments:

Arnaud Dusser

Smaller Brace Bay: Member 1: Cf =

766.45

6100

W200x59

Member 2: Tf =

4450

Tf =

949.23

7550.66

Cf =

556.7

4450

Cf =

1147.12

6100

Tf =

556.7

3850

Tf =

1363.10

7213.36

Cf =

1285.23

3850

Cf =

303.54

9200

Member 3: L152x152x9.5

Member 4:

Member 5: W250x73

Member 6:

Member 7: L152x152x13

Member 8:

Bracing group 2: Member 1: W250x73

Member 2: Tf =

4500

Member 3: Tf =

340.30

10241.58

Cf =

149.79

4500

Cf =

682.63

9200

L89x89x6.4

Member 4:

Member 5: W250x73

Member 6:

8 Tf =

149.79

4250

Tf =

747.11

10134.22

Cf =

461.38

4250

Cf =

1058.28

9200

Tf =

461.38

3850

Member 7: L127x127x7.9

Member 8:

Member 9: W250x131

Member 10:

Project Title:

February 4th, 2013

UQAC Arena

DATE:

Project Detail:

Seismic Analysis

Design Detail:

Design of Lateral Stabilizing System

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments:

Arnaud Dusser

Member 11: Tf =

1156.52

9973.09

Cf =

907.71

3850

Cf =

368.2

9200

L152x152x13

Member 12:

Bracing group 4: Member 1: W250x73

Member 2: Tf =

6050

Tf =

440.68

11011.02

Cf =

242.13

6050

Cf =

185.98

4700

Tf =

4250

Tf =

250.35

10134.22

Cf =

167.92

4250

Cf =

377.33

4700

Tf =

167.92

3850

Member 3: L152x152x9.5

Member 4:

Bracing group 5: Member 1: W200x42

Member 2:

Member 3: L89x89x6.4

Member 4:

Member 5: W200x42

Member 6:

Member 7: Tf =

489.47

9973.09

Cf =

477.49

3850

L127x127x7.9

Member 8:

Project Title:

February 4th, 2013

UQAC Arena

DATE:

Project Detail:

Seismic Analysis

Design Detail:

Design of Lateral Stabilizing System

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments:

Arnaud Dusser

Dimensions and Areas 1 hn= Main Roof EͲW=

67.2

Main Roof NͲS=

Main Roof: A=

2486.4

2 hn=

4.25

Building 2 Roof EͲW=

67.2

Building 2 Roof NͲS=

Building 2 Roof: A=

403.2

hn=

4.25

Building 3 Roof EͲW=

8.8

Building 3 Roof NͲS=

31.9

Building 3 Roof: A=

280.72

Dead Loads

Main roof =

0.78

kPa

Green roof =

1.7

kPa

Interior Floor =

3.54

kPa

Snow Loads Main roof =

2.4

kPa

Building 2 =

7.95

kPa

Building 3 =

7.04

kPa

Live Loads Main Roof =

kPa

Floors =

4.8

kPa

Floor Building 3 =

3.6

kPa

Wall caldding =

1.5

kPa

Walls Considering a metal curtain wall (Steel HB)

Earthquake Loads 1.0 D + 1.0 E + 0.5L + 0.25 S Weights NͲS direction 1.0 D + 0.25 S + Wwalls Main Roof W1NS =

4640.83

Building 2 Roof W2NS =

1701.00

Building 3 Roof W3NS =

1027.39

Main Roof W1EW =

4097.23

Building 2 Roof W2EW =

1525.05

Building 3 Roof W3EW =

1072.97

Interior floor (Top) W4 =

1118.07

Building 2 floor + botom floor W5 =

2545.40

Building 3 floor W6 =

993.75

Bleacher weight W7 =

372.60

EͲW direction

Interior Floors:

Mv =

No higher mode effects in singleͲstorey building

Ie =

Normal Importance building

Rd =

1.5

Ro =

1.3

Project Title:

February 4th, 2013

UQAC Arena

DATE:

Project Detail:

Seismic Analysis

Design Detail:

Design of Lateral Stabilizing System

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments: Sa(0.2) =

0.62

Sa(0.5) =

0.3

Sa(1.0) =

0.14

Sa(2.0) =

0.047

Sa(0.2) = 0.75 g, Fa =

Sa(0.2) = 0.50 g, Fa =

By interpolating, Fa =

Sa (1.0) < 0.1, Fv =

Sa (1.0) = 0.2, Fv =

By interpolating, Fv =

Class C, table 4.1.8.4.C.

0.62

FvSa(0.5s) =

0.3

FaSa(0.2s) =

0.62

FvSa(1.0s) =

0.14

FvSa(2.0s) =

0.047

FvSa(4.0s)=FvSa(2.0s)/2 =

0.0235

Ta = 0.025*hn =

0.189

0.6

0.268

S(Ta) = S(0.6s) =

Table CͲ2 NBCC

Class C, table 4.1.8.4.B.

FaSa(0.2s) =

Max Ta = 0.05*hn =

Arnaud Dusser

Check whether ESFP can be used: 1) IeFaSa(0.2s)=1.0*1.0*0.62= 0.62 g > 0.35 g Not OK 2) Regular Structure, less than 60m in height and has a funadamental period of vibration in the two orthogonal lateral directions of less than 2s. OK OK to use ESFP V(CC) > S(2.0s) Mv Ie / (RdRo) =

2.41

V(CC) = S(Ta) Mv Ie / (RdRo) =

13.74

V(CC) < (2/3) S(0.2s) Mv Ie / (RdRo) =

21.20

Main Roof C1NS =

3431.73

Building 2 Roof C2NS =

1489.20

Building 3 Roof C3NS =

973.69

Main Roof C1EW =

3431.73

Building 2 Roof C2EW =

1489.20

Building 3 Roof C3EW =

973.69

Interior floor (Top) C4 =

1120.47

Building 2 floor + botom floor C5 =

2547.80

Building 3 floor C6 =

995.55

Bleacher weight C7 =

375.00

єCf :

1.0 D + 0.25 S + 0.5 L NͲS direction

EͲW direction

Interior Floors:

Project Title:

DATE:

Project Detail:

Seismic Analysis

Design Detail:

Design of Lateral Stabilizing System

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments: Notional Loads:

February 4th, 2013

UQAC Arena

Arnaud Dusser

0.5 % of єCf NͲS direction Main Roof N1NS =

17.16

Building 2 Roof N2NS =

7.45

Building 3 Roof N3NS =

4.87

Main Roof N1EW =

17.16

Building 2 Roof N2EW =

7.45

Building 3 Roof N3EW =

4.87

EͲW direction

Interior Floors: Interior floor (Top) N4 =

5.60

Building 2 floor + botom floor N5 =

12.74

Building 3 floor N6 =

4.98

Bleacher weight N7 =

1.88

NͲS Direction Loads Applied on each (1/2 of total load) brace with notional loads: Bracing group 1 Larger:

Smaller:

Top point =

299.40

Middle point =

293.85

Bottom point =

297.02

Top point =

593.25

Bottom point =

297.02

Bracing group 3 Larger:

Smaller:

Top point =

299.40

Middle point =

182.53

Bottom point =

189.21

Top point =

481.93

Bottom point =

189.21

Fu =

0.450

GPa

Top Brace Tf =

372.06

Middle Brace Tf =

723.81

Bottom Brace Tf =

1053.52

Design for group 1, apply same design to bracing group 3

Bracing group 1 Larger

Smaller

Larger

Smaller

Top Brace Tf =

734.33

Bottom Brace Tf =

1052.76

Top Brace Ag =

1837.33

mm2

Small Brace

double angles ( 8 mm spacing)

L89x89x6.4

2180

mm2

Middle Brace Ag =

3574.37

L127x127x7.9

3910

mm2

Bottom Brace Ag =

5202.57

mm2

L152x152x9.5

5610

mm2

Top Brace Ag =

3626.32

mm2

L127x127x7.9

3910

mm2

Bottom Brace Ag =

5198.81

mm2

L152x152x9.5

5610

mm2

Bay Height

Ratio

Horizontal Deflection: Tall Brace

Preliminary:

Fraction of force taken by Bay

7.89

12600

0.00062619

0.36

3.4

9650

0.000352332

0.64

Project Title:

February 4th, 2013

UQAC Arena

DATE:

Project Detail:

Seismic Analysis

Design Detail:

Design of Lateral Stabilizing System

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments:

Arnaud Dusser

Reviewed forces in each bay after rigidity factoring: Bracing group 1

єCf

Larger:

with Pѐ effects:

Top point =

215.61

617.82

216.81

Middle point =

212.07

820.42

213.81

Bottom point =

213.89

884.66

216.75

Smaller:

Top point =

759.28

2556.15

766.03

Bottom point =

380.14

1572.29

384.90

Fu=

0.450

Gpa

Bracing group 1 Larger

Smaller

Larger

Smaller

Top Brace Tf =

269.96

Middle Brace Tf =

518.79

Bottom Brace Tf =

760.39

Top Brace Tf =

940.86

Bottom Brace Tf =

1346.27

Top Brace Ag =

1333.14

mm2

Middle Brace Ag =

2561.93

Bottom Brace Ag =

double angles ( 8 mm spacing)

L89x89x6.4

2180

mm2

L127x127x7.9

3910

mm2

3755.01

mm2

L127x127x7.9

3910

mm2

Top Brace Ag =

4646.22

mm2

L152x152x9.5

5610

mm2

Bottom Brace Ag =

6648.25

mm2

L152x152x13

7400

mm2

6100

200

Gpa

Top Brace L =

7580.24

4500

Middle Brace L =

7434.55

4250

Bottom Brace L =

7213.36

3850

Pѐ effects of bracing group 1

h Larger

Smaller

Larger

Smaller

Larger

Smaller

Top Brace L =

7550.66

4450

Bottom Brace L =

7213.36

3850

Top Brace ѐf =

5.83

Middle Brace ѐf =

6.01

Bottom Brace ѐf =

8.29

Top Brace ѐf =

7.84

Bottom Brace ѐf =

7.76

Top Brace U2 =

1.006

Middle Brace U2 =

1.008

Bottom Brace U2 =

1.013

Top Brace U2 =

1.009

Bottom Brace U2 =

1.013

Project Title:

February 4th, 2013

UQAC Arena

DATE:

Project Detail:

Seismic Analysis

Design Detail:

Design of Lateral Stabilizing System

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments:

Arnaud Dusser

Reviewed forces after consideration of Pѐ effects: Bracing group 1 Top Brace Tf =

271.46

Middle Brace Tf =

523.05

Bottom Brace Tf =

770.55

Larger

Top Brace Tf =

949.23

Bottom Brace Tf =

1363.10

Top Brace Ag =

1340.56

mm2

Smaller

Larger

L89x89x6.4

2180

mm2

Middle Brace Ag =

2582.95

L127x127x7.9

3910

mm2

Bottom Brace Ag =

3805.20

mm2

L127x127x7.9

3910

mm2

Top Brace Ag =

4687.55

mm2

L152x152x9.5

5610

mm2

Bottom Brace Ag =

6731.37

mm2

L152x152x13

7400

mm2

Smaller

Slenderness Check:

double angles ( 8 mm spacing)

A (mm2)

Top Brace: L89x89x6.4

2180

27.7

136.827

< 300 OK

Middle Brace: L127x127x7.9

3910

39.8

93.399

< 300 OK

Bottom Brace Ag: L127x127x7.9

3910

39.8

90.620

< 300 OK

double angles ( 8 mm spacing) Larger

Smaller

L/rx

Top Brace Ag: L152x152x9.5

5610

47.6

79.314

< 300 OK

Bottom Brace Ag: L152x152x13

7400

47.1

76.575

< 300 OK

Bay Compression Beams: Axial Forces: W200x59

Class 1

A =

7560

mm2

b =

205

t =

14.2

h =

186.8

w =

9.1

k =

L =

6100

ry =

Fy =

0.35

GPa

E =

200

GPa

ʄ = K L/r SQRT(Fy/(ʋ2 E)) =

1.562

Cr = 0.9 A Fy (1+ʄx2 x 1.34)-1/1.34 Slenderness check:

801.23

> Cf

kL/r =

117.31

< 200

bel/t =

7.22

< 200/SQRT(Fy) =

10.69

h/w =

20.53

< 670/SQRT(Fy) =

35.81

Project Title:

February 4th, 2013

UQAC Arena

DATE:

Project Detail:

Seismic Analysis

Design Detail:

Design of Lateral Stabilizing System

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments: W200x52

Class 1 6650

mm2

b =

206

t =

12.6

h =

190.2

w =

7.9

A =

Arnaud Dusser

k =

L =

6100

ry =

51.8

Fy =

0.35

GPa

E =

200

GPa

ʄ = K L/r SQRT(Fy/(ʋ2 E)) =

1.57

Cr = 0.9 A Fy (1+ʄx2 x 1.34)-1/1.34 Slenderness check:

700.62

> Cf

kL/r =

117.76

< 200

bel/t =

8.17

< 200/SQRT(Fy) =

10.69

h/w =

24.08

< 670/SQRT(Fy) =

35.81

W250x73

Class 2

A =

9280

mm2

b =

254

mm mm

t =

14.2

h =

236.8

w =

8.6

k =

L =

6100

ry =

64.6

Fy =

0.35

Gpa

E =

200

GPa

ʄ = K L/r SQRT(Fy/(ʋ2 E)) =

1.26

Cr = 0.9 A Fy (1+ʄx2 x 1.34)-1/1.34 kN

> Cf

94.43

< 200

bel/t =

8.94

< 200/SQRT(Fy) =

10.69

h/w =

27.53

< 670/SQRT(Fy) =

35.81

= Slenderness check:

kL/r =

Smaller

wih Pѐ

Bracing group 1 Larger

1338.79

Top Beam Cf =

217.42

W200x52

Middle Beam Cf =

430.72

W200x52

Bottom Beam Cf =

644.05

W200x52

Top Beam Cf =

766.45

W200x59

Bottom Beam Cf =

1147.12

W250x73

Project Title:

February 4th, 2013

UQAC Arena

DATE:

Project Detail:

Seismic Analysis

Design Detail:

Design of Lateral Stabilizing System

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments: Bracing group 5

єCf

Arnaud Dusser

with Pѐ effects:

Top point =

182.53

652.42

185.37 kN

Bottom point =

189.21

730.70

192.91 kN

Fu=

0.450

GPa

Bracing group 5 Top Brace Tf =

246.51

Bottom Brace Tf =

480.09

Top Brace Ag =

1217.33

mm2

2370.81

double angles

Bracing group 5 Bottom Brace Ag =

L89x89x6.4

2180

mm2

L127x127x7.9

3910

mm2

Pѐ effects of bracing group 5 a =

4700

E =

200

Gpa

Top Brace L =

10134.22

4250

Bottom Brace L =

9973.09

3850

Bracing group 5

Bracing group 5 Top Brace ѐf =

12.35

Bottom Brace ѐf =

12.99

Top Brace U2 =

1.016

Bottom Brace U2 =

1.020

Bracing group 5

Reviewed forces after consideration of Pѐ effects Bracing group 5 Top Brace Tf =

250.35

Bottom Brace Tf =

489.47

Top Brace Ag =

1236.31

mm2

Bottom Brace Ag =

2417.16

double angles

Bracing group 5 mm

L89x89x6.4

2180

mm2

L127x127x7.9

3910

mm2

double angles ( 8 mm spacing)

L/rx

Top Brace: L89x89x6.4

2180

27.7

182.93

< 300 OK

Bottom Brace: L127x127x7.9

3910

39.8

125.29

< 300 OK

Beams: Axial Forces: W200x42

Class 1

A =

5310

mm2

b =

166

t =

11.8

h =

151.6

w =

7.2

k =

L =

4700

ry =

41.2

Fy =

0.35

GPa

E =

200

GPa

ʄ = K L/r SQRT(Fy/(ʋ2 E)) =

1.52

Cr = 0.9 A Fy (1+ʄx2 x 1.34)-1/1.34 Slenderness check:

587.20

> Cf

kL/r =

114.08

< 200

bel/t =

7.03

< 200/SQRT(Fy) =

10.69

h/w =

21.06

< 670/SQRT(Fy) =

35.81

Project Title:

DATE:

Project Detail:

Seismic Analysis

Design Detail:

Design of Lateral Stabilizing System

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments: Bracing group 5 Larger

February 4th, 2013

UQAC Arena

Arnaud Dusser

with Pѐ effects Top Beam Cf =

185.98

W200x42

Bottom Beam Cf =

377.33

W200x42

EͲW Direction Loads Applied on each (1/2 of total load) brace with notional loads: єCf

Bracing group 2

with Pѐ effects:

Top point =

299.40

857.93

301.92

Middle point =

371.85

1548.26

377.59

Bottom point =

381.00

1710.29

386.55

Top point =

365.95

1230.23

368.20

Fu=

0.450

GPa

Bracing group 4

Bracing group 2 Top Brace Tf =

337.46

Middle Brace Tf =

735.75

Bottom Brace Tf =

1139.92

Top Brace Tf =

437.99

Top Brace Ag =

1666.47

mm2

L89x89x6.4

2180

Middle Brace Ag =

3633.33

mm2

L127x127x7.9

3910

Bottom Brace Ag =

5629.23

mm2

L152x152x13

7400

Top Brace Ag =

2162.91

mm2

L127x127x7.9

3910

9200

200

GPa

Top Brace L =

10241.58

4500

Middle Brace L =

10134.22

4250

Bottom Brace L =

9973.09

3850

Top Brace L =

11011.02

6050

Bracing group 4

double angles

Bracing group 2

Bracing group 4

Pѐ effects of bracing group 1

Bracing group 2

Bracing group 4

Bracing group 2 Top Brace ѐf =

8.82

Middle Brace ѐf =

10.50

Bottom Brace ѐf =

8.33

Top Brace ѐf =

7.38

Bracing group 4 Bracing group 2 Top Brace U2 =

1.008

Middle Brace U2 =

1.015

Bottom Brace U2 =

1.015

Top Brace U2 =

1.006

Bracing group 4

Project Title:

February 4th, 2013

UQAC Arena

DATE:

Project Detail:

Seismic Analysis

Design Detail:

Design of Lateral Stabilizing System

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments:

Arnaud Dusser

Reviewed forces after consideration of Pѐ effects Bracing group 2 Top Brace Tf =

340.30

Middle Brace Tf =

747.11

Bottom Brace Tf =

1156.52

Top Brace Tf =

440.68

Top Brace Ag =

1680.52

mm2

L89x89x6.4

2180

Middle Brace Ag =

3689.41

mm2

L127x127x7.9

3910

Bottom Brace Ag =

5711.21

mm2

L152x152x13

7400

Top Brace Ag =

2176.22

mm2

L152x152x9.5

5610

Bracing group 4 double angles ( 8 mm spacing)

Bracing group 2

Bracing group 4

Bracing group 2

double angles ( 8 mm spacing) Top Brace:

L/rx

L89x89x6.4

2180

27.7

184.87

< 300 OK

Middle Brace:

L127x127x7.9

3910

39.8

127.31

< 300 OK

Bottom Brace:

L152x152x13

7400

47.1

105.87

< 300 OK

Top Brace:

L152x152x9.5

5610

47.6

115.66

< 300 OK

W250x131

Class 1

A =

16700

mm2

b =

261

t =

25.1

h =

230.2

w =

15.4

Bracing group 4

Beams: Axial Forces:

k =

L =

9200

ry =

66.8

Fy =

0.35

GPa

E =

200

GPa

ʄ = K L/r SQRT(Fy/(ʋ2 E)) =

1.83

Cr = 0.9 A Fy (1+ʄx2 x 1.34)-1/1.34 Slenderness check:

1367.81

> Cf

k L/r =

137.72

< 200

bel/t =

5.20

< 200/SQRT(Fy) =

10.69

h/w =

14.95

< 670/SQRT(Fy) =

35.81

W250x73

Class 2 9280

mm2

b =

254

t =

14.2

h =

236.8

w =

8.6

A =

k =

L =

9200

ry =

64.6

Fy =

0.35

GPa

E =

200

GPa

ʄ = K L/r SQRT(Fy/(ʋ2 E)) =

1.90

Project Title:

February 4th, 2013

UQAC Arena

DATE:

Project Detail:

Seismic Analysis

Design Detail:

Design of Lateral Stabilizing System

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments:

Arnaud Dusser

Cr = 0.9 A Fy (1+Ê&#x201E;x2 x 1.34)-1/1.34 Slenderness check:

718.42

> Cf

k L/r =

142.41

< 200

bel/t =

8.94

< 200/SQRT(Fy) =

10.69

h/w =

27.53

< 670/SQRT(Fy) =

35.81

Bracing group 1 Larger

Smaller

Top Beam Cf =

303.54

W250x73

Middle Beam Cf =

682.63

W250x73

Bottom Beam Cf =

1058.28

W250x131

Top Beam Cf =

368.20

W250x73

Project Title:

UQAC Arena

DATE:

March 4th, 2013

Project Detail:

Braces

Design Detail:

Beams

VERIFIED BY:

Caroline Chan

CHECKED BY:

Arnaud Dusser

Comments:

Randy Wang

Section W530x74: BottomÍ˛Beam of the 3 Story Bracing Properties: Factored Compressive Load

Cf =

431

Max. Factored Moment, x-axis

Mfx =

544

kN-m

Load case, x-direction

caseX =

Member class

class =

Member shape

shape =

Gross Area

Ag =

63400

Effective Length Factor

mm^2

Unsupported length wrt x-axis.

L =

800

Depth of section

d =

529

Clear depth of web bet. flange

h =

529

Flange width

b =

166

Flange thickness

13.6

Web thickness

web =

Moment of inertia, x-axis

Ix =

9.7

Elastic section modulus, x-axis

Sx =

1550000

mm^3

Plastic section modulus, x-axis

Zx =

1810000

mm^3 mm^4

4.11E+08

mm mm^4

Moment of inertia, y-axis

Iy =

10400000

Elastic section modulus, y-axis

Sy =

125000

mm^3

Plastic section modulus, y-axis

Zy =

200000

mm^3

Distance between web stiffeners

a =

5000

Load resistance factor

phi =

0.9

Elastic modulus

Est =

200000

Yield strength

Fy =

350

Mpa

Ultimate strength

Fu =

450

Mpa Mpa

Mpa

Shear modulus

77000

St. venant torsion constant

4.80E+05

mm^4

Warping torsional constant

Cw =

6.92E+11

mm^6

Web area

Aw =

d*web 5131.30

Capacity Check: = Flange area

2*b*t

= kv =

IF(a/h<1,4+5.34/(a/h)^2,5.34+4/(a/h)^2)

= KF = Fs_case

= FsCase = =

Inelastic buckling strength

mm^2

Af =

Fcri = =

4515.20

mm^2

5.38 sqrt(kv/Fy) 0.12 IF(h/web<=439*KF,1,IF(h/web<=502*KF,2,IF(h/web<=621*KF,3,4))) 2.00 290*sqrt(Fy*kv)/(h/web) 230.85 Mpa

Project Title:

UQAC Arena

DATE:

March 4th, 2013

Project Detail:

Braces

Design Detail:

Beams

VERIFIED BY:

Caroline Chan

CHECKED BY:

Arnaud Dusser

Comments: Inelastic postͲbuckling strength Elastic buckling strength Elastic postͲbuckling strength

Ultimate shear stress Elastic shear resistance, yͲdir. Elastic shear resistance, xͲdir. Plastic shear resistance, yͲdir. Plastic shear resistance, xͲdir. Effective width Effective section modulus, xͲaxis

Plastic moment, xͲaxis Yield moment, yͲaxis Plastic moment, xͲaxis Yield moment, yͲaxis

Lat. Supported Mrx, Class 1 Lat. Supported Mrx, Class 2 Lat. Supported Mrx, Class 3 Lat. Supported Mrx, Class 4 Laterally supported bending, x

Fti = = Fcre = = Fte = = Fs1 = = Fs2 = = Fs3 = = Fs4 = = Fs = = Vrey = = Vrex = = Vrpy = = Vrpx = = beff = = Sex = =

0.66*Fy 231.00

Mpa

Fcri 230.85

Mpa

Fcri+Fti 228.23

Mpa

Fcre+Fte 314.61

Mpa

index(Fs1:Fs4,FsCase,1) 230.85 Mpa phi*Aw*Fs/1e3 1066.11

phi*Af*Fs/1e3 938.10

0.55*phi*web*d*Fy/1e3 889.00 kN 0.55*phi*Af*Fy/1e3 782.26 kN 200*t/sqrt(Fy) 145.39

1/(6*d)*(beff*d^3Ͳ(beffͲweb)*(dͲ2*t)^3) 1379284.39 mm^3

kNͲm kNͲm

Zy*Fy/1e6 70.00

kNͲm

Sy*Fy/1e6 43.75

kNͲm

sMrx1 = = sMrx2 = = sMrx3 = = sMrx4 = = sMrx =

phi*Mpx 570.15

kNͲm

phi*Mpx 570.15

kNͲm

phi*Myx 488.25

kNͲm

phi*Sex*Fy/1e6 434.47 570.15

kNͲm kNͲm

sMry1 = = sMry2 = = sMry3 = = sMry4 = =

Lat. Supported Mry, Class 4

(0.5*FyͲ0.866*Fcre)*(1/sqrt(1+(a/h)^2)) Ͳ11.28 Mpa

Sx*Fy/1e6 542.50

Lat. Supported Mry, Class 1

Lat. Supported Mry, Class 3

180000*kv/(h/web)^2 325.89 Mpa

Zx*Fy/1e6 633.50

Sey = =

Lat. Supported Mry, Class 2

(0.5*FyͲ0.866*Fcri)*(1/sqrt(1+(a/h)^2)) Ͳ2.62 Mpa

Mpx = = Myx = = Mpy = = Myy = =

Effective section modulus, yͲaxis

Randy Wang

1/(6*beff)*(2*t*beff^3+(dͲ2*t)*web^3) 96351.90 mm^3 phi*Mpy 63.00

kNͲm

phi*Mpy 63.00

kNͲm

phi*Myy 39.38

kNͲm

phi*Sey*Fy/1e6 30.35

kNͲm

Project Title:

UQAC Arena

DATE:

March 4th, 2013

Project Detail:

Braces

Design Detail:

Beams

VERIFIED BY:

Caroline Chan

CHECKED BY:

Arnaud Dusser

Comments: Laterally supported bending, y

sMry =

Compressive Resistance, l=0

n= Cr0 = =

ry = =

Lambda

lam = =

Compressive Resistance

Cr = =

w1x = w1y = Euler buckling strength, xͲaxis

Cex = =

Euler buckling strength, yͲaxis

Cey = =

U1x = U1x_ = U1y = Modifier for Class 1 IͲshapes Modifier for Class 1 IͲshapes

I1 = I2 =

CrossͲsectional strength

cross = =

Overall member strength

overall = =

Lat. torsional buckling strength

lateral = =

63.00 1.34 phi*Ag*Fy/1000 19971.00

Randy Wang

kNͲm

sqrt(Iy/Ag) 12.81 mm K*L/ry*sqrt(Fy/(PI()^2*Est)) 0.83 phi*Ag*Fy*(1+lam^(2*n))^(Ͳ1/n)/1000 13995.41 kN 1.00 1.00 PI()^2*Est*Ix/L^2/1000 1267627.32 kN PI()^2*Est*Iy/L^2/1000 32076.21 kN 1.00 1.00 1.02 1.00 1.00 Cf/Cr0+I1*Mfx/sMrx+I2*Mfy/sMry 98% OK Cf/Cr+I1*U1x*Mfx/sMrx+I2*U1y*Mfy/sMry 99% OK Cf/Cr+I1*U1x_*Mfx/uMrx+I2*U1y*Mfy/sMry 99% OK

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Roof Design

Design Detail:

Structural Steel Design

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments:

February 27th, 2013 Arnaud Dusser

Roof Area 2476.61 723.69

m2 m2

0.72 1.48

kPa kPa

2.40

kPa

Main Roof= Floors=

1.00 2.40

kPa kPa

1.25D + 1.5S + 0.5L D=

0.10

KPa

4.23

kPa

Use CANAM

5.00 3.40

kPa kPa

Use CANAM PÍ²3606 type 22 (triple span 1800 mm max) Diaphragm Check OK

5.00

kPa

3.62

kPa

Main Roof: A= Smaller Building Roof: A= Dead Loads

Main roof = Green roof =

Snow Loads Live Loads

Top Steel Deck:

Total Factored Load: wf= Bottom Steel Deck: 1.25D + 1.5S + 0.5L Total Factored Load= Total Unfactored Load= Steel Joists: 1.25D + 1.5S + 0.5L Total Factored Load= 1.0D + 1.0S + 0.5L SLS= Joist Spacing = Factored Load= Service Load= Max Span=

1500.00 7.50 5.43 6039.00

mm kN/m kN/m mm

Using CANAM Joist Depth selection table(Span=6m, FL= 9.0, SL=6.0) : ideal joist depth is 450mm with a 10.5 kg/m type joist From CANAM catalog: 1 bridge line required L 1 1/4 x 1 1/4 x 0.090 Horizontal Bridging angle size Roof Truss Design Case 1: 1.25 D + 1.5 S + 0.5L (Case 1 snow load) Point T.A.: 1 T.W. (mm) 2 9125 3 T.W. around Truss 4 1625 5 6 7

Applied uniform load: 3860 4544 6039 6039 6039 5519 2500

mm mm mm mm mm mm mm

8.125 kN/m 35.2 41.5 55.1 55.1 55.1 50.4 22.8

m2 m2 m2 m2 m2 m2 m2

Point Loads: 176.11 207.32 275.53 275.53 275.53 251.80 114.06

kN kN kN kN kN kN kN

Case 1 : 1.25D + 1.5S + 0.5L

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Roof Design

Design Detail:

Structural Steel Design

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments:

February 27th, 2013 Arnaud Dusser

Case 2: 1.25 D + 1.5 S + 0.5L (Case 3 snow load with varying Live Load) S= 0.0571x+0.4 Point 1 2 3 4 4.5 5 6 7

T.A.: T.W. (mm) 9125 T.W. about Truss 1625

T.L. (mm) 3860 4544 6039 3020 3020 6039 5519 2500

x (mm) 2335 6195 10739 16778 19798 22818 28857 34376 36876

T.A. (m2) 35.2 41.5 55.1 27.6 27.6 55.1 50.4 22.8

S @ x (kPa) 0.53 0.75 1.01 1.36 1.53 1.70 2.05 2.36 2.51

F. L. (kN/m)

Point Loads (kN)

3.03 3.62 4.35 4.98 6.22 6.85 7.65 8.21

65.70 92.27 147.60 189.91 232.16 237.10 115.23

Case 2: 1.25D + 1.5S + 0.5L

From SAP2000 analysis : Summary: Case 1: Case 2:

Joint Reactions (kN) FyR FyL 869.12 970.67 719.18 548.39

Top Compression Member: Mf+ (kN.m) MfͲ (kN.m) 99.32 Ͳ43.18 334.01 Ͳ312.400

Cf1 (kN) Ͳ2227.7 Ͳ1602.81

Vf (kN) 47.06 Ͳ101.65

Web members: Cf2 (kN) Ͳ205.19 Ͳ145.83

Tension Members: Tf (kN) 2282.04 1621.92

Girder Design: Mf+ =

440.670

kN.m

Vf = P =

145.760 4.070

kN kN

Try W610x101

Class 1

Flexure: L= Fy =

1625

350

MPa

Zx =

2900000

mm3

Mr =

0.9 Fy Zx

913.5

kN.m

Fs = d = t = w = h = Aw =

231 603 14.9 10.5 573.2

MPa mm mm mm mm

6331.5

< Lu=2890 mm

> Mf

Shear:

mm2

Vr =

0.9 Fs Aw

1316.32

> Vf

29.79 26.53

mm mm

Deflection: ѐmax = ѐ =

Use W610x101

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Roof Design

Design Detail:

Structural Steel Design

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments:

February 27th, 2013 Arnaud Dusser

Main Roof Truss: Top Compression member: W310x129 Cf =

2227.70

Mfx =

334.01

kN.m

Vf =

101.65

Try W310x129 L = Fy =

Class 1 6039 350

mm MPa

A = Zx =

16500

mm2

2160000

mm3

Ix = E =

308000000 200000

mm4 MPa

Cr = =

5197.50

Full Lateral Support

CrossͲsecton strength:

Mrx = =

0.9 A Fy

0.9 Zx Fy

680.40

w1 =

1.00

Ce =

16670.57

kN.m

U1x =

1.15

Cf/Cr + 0.85 x U1x x Mfx/Mrx =

0.91

< 1 OK

Mfx/Mrx =

0.49

< 1 OK

Overall inͲplane member strength: rx = 137.00 mm k = 1.00 K x L/r = 44.08 ʄx = K L/r SQRT(Fy/(ʋ2 E)) = 0.59 Cr = 0.9 A Fy (1+ʄx2 x 1.34)-1/1.34 = 4427.15 kN Cf/Cr + 0.85 U1x Mfx/Mrx =

0.98

< 1

h = d = w = Aw =

276.80 318 13.10

mm mm mm

4165.80

Shear Check:

Vr =

dxw

mm2

Aw 0.9 0.66 Fy

866.07

Check: h/w =

21.13

< 439 SQRT(kv/Fy)=

> Vf

OK 54.23

Use W310x129

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Roof Design

Design Detail:

Structural Steel Design

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments:

February 27th, 2013 Arnaud Dusser

Compression Web Members: HSS 102x102x4.8 Cf =

205.19

1 3180 39.20 81.12

mm mm < 200

Try HSS 102x102x4.8 K = L = r = K x L/r =

A = 1790 mm2 E = 200000 MPa Fy = 350 Mpa ʄ = K L/r SQRT(Fy/(ʋ2 E)) = 1.08 Cr = 0.9 A Fy (1+ʄx2 x 1.34)-1/1.34 =

380.53

> Cf

> Tf

< 300

Use HSS 102x102x4.8 Tension Members: HSS 254x254x13 Tf =

2282.04

Fu =

450 Tf/(0.75 0.6 Fu)

MPa

11269.33

mm2

11800 97.60 6100

mm2 mm2 mm2

Estimated A = =

Try HSS 254x254x13 A = r = L = Tr = = L/r =

0.75 0.6 A Fu

2389.5 62.5

Use HSS 254x254x13 Lateral Stability Braces (Tension Only): L19x19x3.2 Tfx =

4.10

Tfy =

8.03

Tf = =

SQRT(Tfy2 + Tfx2)

Fu =

9.02

450

MPa

Estimated A =

44.54

mm2

Try L19x19x3.2 A = r = L =

111 5.72 1501.63

mm2 mm2 mm

Tr =

0.75 0.6 A Fu

22.48

> Tf

L/r =

262.52

< 300

Use L19x19x3.2

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Roof Design

Design Detail:

Structural Steel Design

VERIFIED BY:

Randy (Chao) Wang

CHECKED BY:

Caroline Chan

Comments:

February 27th, 2013 Arnaud Dusser

End Beam element: W310x24 L = w = Vf =

4700 8.13 19.09

mm kN/m kN

Mf =

89.74

kN.m

ѐmax =

13.06

Try W310x24 Flexure: Fy =

Considered fully braced because of steel deck 350 Mpa mm3 kN.m

Zx =

328000

Mr =

103.32

Fs = =

0.66 Fy

231

MPa

d = t = w = h = Aw =

305 6.7 5.6 291.6

mm mm mm mm

1708

> Mf

> Vf

< ѐmax

> Mf

> Vf

< ѐmax

Shear:

Vr = =

mm2

0.9 Aw Fs

355.09

Deflection: E = 200000 I = 42700000 ѐ = 5 w L4/(384 E I) = 6.04

MPa mm4 mm

Use W310x24 Side Beam Element: W250x45 L = w = Vf =

6100 6.87 20.94

mm kN/m kN

Mf =

127.73

kN.m

ѐmax =

16.94

Try W250x45 Flexure: Considered fully braced because of steel deck Fy =

350

Mpa

Zx =

602000

mm3

Mr =

0.9 Fy Zx

189.63

kN.m

231 266 13 7.6 240

Mpa mm mm mm mm

Shear: Fs = d = t = w = h = Aw = = Vr = =

2021.6

mm2

0.9 Aw Fs

420.29

Deflection: E = I = ѐ = =

200000 71100000

MPa mm4

5 w L4/(384 E I)

8.70

Use W250x45

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Building Columns

Design Detail:

Column B

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Arnaud Dusser

Comments:

March 23rd, 2013 Caroline Chan

D Beam Column B2, B4, B5, B6, B7, B9

Total height:

321.13

540.12

312

1.25

0.5

1.5

10.988 m

Above ground

7.138 m

Axial load:

Wind load: strong axis

5.3 kN/m

weak axis

none

kN/m

Axial

Moment

Only along top 3.208m Only along top 7.15m

Loading Cases Shear

1634

2 1.25D+1.4W+0.5L

1166

3 1.25D+1.4W+0.5S

864

4 1.0E+1.0D+0.25S

1552

183.65

in compression

1 1.25D+1.5S+0.5L

4.481 at 3.208

13.298

at 3.209

13.298

3930

Column

Member chosen:

w200x86

Ag=

11000 mm2

rx=

92.6 mm

20.6 mm 13 mm

ry=

53.3 mm

Fy=

350 MPa

222 mm

Fu=

450 MPa

209 mm

Mass=

350 kg/m

ࢥ=

0.9

KL effective length

4000 mm

Elastic Local Buckling limits

(page 1-126 of Steel Handbook)

(b/2)/t=

5.072815534

<200/((Fy)^0.5)=

10.69044968 Therefore OK

(d-2t)/w=

13.90769231

<670/((Fy)^0.5)=

35.81300642 Therefore OK

Slenderness

k = 1.0

pin ended

WHY 200? Lx (strong)=

3930 mm

(kLx)/rx=

42.44060475 <200

Ly (weak)=

3930 mm

(kLy)/ry=

73.73358349 <200

CLASS?

controls

Determine Ȝ

Ȝ=(kL/r)((Fy/Eʌ^2)^0.5)

Ȝ=

200000 MPa

0.565419705

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Building Columns

Design Detail:

Column B

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Arnaud Dusser

Comments:

March 23rd, 2013 Caroline Chan

Determine Cr

1.34

W-shape

Cr=ࢥAFy(1+Ȝ^(2n))^(-1/n) Cr =

2992.730474 kN

1634.00

Therefore OK

Beam Column

Member chosen:

w200x86

222

209

mm mm

20.6

11000

mm2

Ix =

9.47E+07

mm4

45.4

Iy =

3.14E+07

mm4

15.3

92.6

Rx = Ry =

53.3

Zx =

9.81E+05

mm3

495

Zy =

4.58E+05

mm3

229

1.39E+06 mm4

220

Cw =

3.18E+11 mm6

69.6

Lu =

3.93 m

77000 MPa

3930 mm

Cross-section strength

(Cf/Cr) + U1x(Mfx/Mrx) + Uy1(Mfy/Mry) <= 1.0 Class 1 Section

(from Steel Handbook pg. 4-7 - Flange and Web both Class 1)

ࢥ= Cf =

0.9 1634.00 kN

Mfx =

4.481 kNm

Mfy =

0 kNm

Cr = 0.9*A*345 =

3465.00 kN

Mrx = 0.9*Zx*345 =

304.60 kN.m

Mry = 0.9*Zy*345 =

142.21 kN.m

200000 MPa

Lx =

3930 mm

Ly =

3930 mm

Cex = ʌ^2*EIx / Lx^2 =

12090.78 kN

Cey = ʌ^2*EIy / Ly^2 =

4008.98 kN

w1x = 0.6-0.4(kx) =

1 since it is subjected to distrubted load

w1y = 0.6-0.4(ky) =

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Building Columns

Design Detail:

Column B

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Arnaud Dusser

Comments: U1x = w1 / (1- Cf/Cex)

1.16

U1y = w1 / (1- Cf/Cey)

1.69

March 23rd, 2013 Caroline Chan

Checks: (Cf/Cr) + 0.85*U1x(Mfx0.4860

< 1.0, Therefore OKAY

Mfx/Mrx + Mfy/Mry =

< 1.0, Therefore OKAY

0.0147

Overall In-Plane Member Strength

KL/Rx = 1.0*7000/Rx =

42.441 < 200, therefore OKAY

KL/Ry = 1.0*7000/Ry =

73.734 < 200, therefore OKAY

KL/Ry controls

Ȝ = kL/R*SQRT(Fy/(ʌ^2*E)) =141.414*SQRT(345/(ʌ^2*200000)) = Ȝ=

0.9748

Cr =

ࢥAFy(1+Ȝ^(2n))^(-1/n)

Cr =

0.9*8450*345*(1+Ȝ^(2*1.34))^(-1/1.34)

Cr =

2087.879 kN Check (Cf/Cr) + 0.85U1x(Mfx/Mrx) + ȕUy1(Mfy/Mry) <= 1.0 & Mry>Mfy

Checks: (Cf/Cr) + U1x(Mfx/Mrx) 0.7971

< 1.0, Therefore OKAY

From Before: Mfx/Mrx 0.0147

< 1.0, Therefore OKAY

Flexural or Lateral Torsional Stability

Mry =

142.21

Cr =

2087.879

L > Lu ?

3.93

w2 =

1.00

Mu =

No need to determine Lateral-Torsional Buckling (Cl. 13.8.2)

w2*ʌ/L*SQRT(E*Iy*J*G + (ʌE/L)^2*Iy*Cw)

Mu =

389.1253 kN.m

Mp = Zx*Fy =

338445.00 kN.m

0.67Mp = Mu < 0.67Mp ?

>4.11 NO

226758.15 kN.m YES

Mrx' = ࢥMu =

350.213 kN.m

(Cf/Cr) + U1x(Mfx/Mrx) 0.7952

< 1.0, Therefore OKAY

Mfx/Mrx + Mfy/Mry =

< 1.0, Therefore OKAY

0.0128

Shear Check

Vfx =

13.298

Vfy =

0.000 ???

h/w <= 439*SQRT(kv/Fy) ?

h/w = (d - 2*t)/w =

13.908

439 * sqrt(kv/Fy) =

54.617 where kv = 5.34 for shear an unstiffened web) pg 1-19 of notes

Vrx = 0.9*d*w*0.66*Fy

591.428 kN

Vry = 0.9*2*b*t*0.66*34

1764.611 kN

Vrx > Vfx ?

OKAY

Vry > Vfy ?

OKAY

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Building Columns

Design Detail:

Column B

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Arnaud Dusser

Comments:

March 23rd, 2013 Caroline Chan

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Building Columns

Design Detail:

Column 10

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Arnaud Dusser

Comments:

March 23rd, 2013 Caroline Chan

Beam Column 10

Total height:

10.988 m

Above ground

7.138 m

Axial load:

Wind load: strong axis

5.3 kN/m

weak axis

none

kN/m

Axial

Moment

Only along top 3.208m Only along top 7.15m

Loading Cases Shear

1 1.25D+1.5S+0.5L

361

2 1.25D+1.4W+0.5L

245

55.79 at 5.49

23.61

3 1.25D+1.4W+0.5S

193

55.79 at 5.49

23.61

4 1.0E+1.0D+0.25S

1011

315

in tension

Column

1011.00 kN

Cf Member chosen:

w200x59

Ag=

7560 mm2

rx=

89.9 mm

14.2 mm 9.1 mm

ry=

52 mm

Fy=

350 MPa 450 MPa

210 mm

Fu=

205 mm

Mass=

59 kg/m

ࢥ=

0.9

KL effective length

4000 mm

Elastic Local Buckling limits

(page 1-126 of Steel Handbook)

(b/2)/t=

7.218309859

<200/((Fy)^0.5)=

10.69044968 Therefore OK

(d-2t)/w=

19.95604396

<670/((Fy)^0.5)=

35.81300642 Therefore OK

Slenderness

k = 1.0

pin ended

WHY 200? Lx (strong)=

3930 mm

(kLx)/rx=

43.71523915 <200

Ly (weak)=

3930 mm

(kLy)/ry=

75.57692308 <200

CLASS?

controls

Determine Ȝ

Ȝ=(kL/r)((Fy/Eʌ^2)^0.5)

Ȝ=

200000 MPa

0.582401165

Determine Cr

100

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Building Columns

Design Detail:

Column 10

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Arnaud Dusser

Comments: n=

1.34

March 23rd, 2013 Caroline Chan

W-shape

Cr=ࢥAFy(1+Ȝ^(2n))^(-1/n) Cr =

2034.524039 kN

1011.00

Therefore OK

Beam Column

Member chosen:

w200x59

210

205

mm mm

14.2

9.1

7560

mm2

Ix =

6.11E+07

mm4

45.4

Iy =

2.04E+07

mm4

15.3

89.9

Rx = Ry =

Zx =

6.53E+05

mm3

495

Zy =

3.03E+05

mm3

229

4.63E+05 mm4

220

Cw =

1.96E+11 mm6

69.6

Lu =

3.93 m

77000 MPa

3930 mm

Cross-section strength

(Cf/Cr) + U1x(Mfx/Mrx) + Uy1(Mfy/Mry) <= 1.0 Class 1 Section

(from Steel Handbook pg. 4-7 - Flange and Web both Class 1)

ࢥ=

0.9

Cf =

671.00 kN

Mfx =

7.39 kNm

Mfy =

0 kNm

Cr = 0.9*A*345 =

2347.38 kN

Mrx = 0.9*Zx*345 =

202.76 kN.m

Mry = 0.9*Zy*345 =

94.08 kN.m

CHECK CLASS!!!!

200000 MPa

Lx =

3930 mm

Ly =

3930 mm

Cex = ʌ^2*EIx / Lx^2 =

7800.91 kN

Cey = ʌ^2*EIy / Ly^2 =

2604.56 kN

w1x = 0.6-0.4(kx) =

1 since it is subjected to distrubted load

w1y = 0.6-0.4(ky) =

U1x = w1 / (1- Cf/Cex)

1.09

U1y = w1 / (1- Cf/Cey)

1.35

101

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Building Columns

Design Detail:

Column 10

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Arnaud Dusser

Comments:

March 23rd, 2013 Caroline Chan

Checks: (Cf/Cr) + 0.85*U1x(Mfx0.3197

< 1.0, Therefore OKAY

Mfx/Mrx + Mfy/Mry =

< 1.0, Therefore OKAY

0.0364

Overall In-Plane Member Strength

KL/Rx = 1.0*7000/Rx =

43.715 < 200, therefore OKAY

KL/Ry = 1.0*7000/Ry =

75.577 < 200, therefore OKAY

KL/Ry controls

Ȝ = kL/R*SQRT(Fy/(ʌ^2*E)) =141.414*SQRT(345/(ʌ^2*200000)) = Ȝ=

0.9992

Cr =

ࢥAFy(1+Ȝ^(2n))^(-1/n)

Cr =

0.9*8450*345*(1+Ȝ^(2*1.34))^(-1/1.34)

Cr =

1420.853 kN Check (Cf/Cr) + 0.85U1x(Mfx/Mrx) + ȕUy1(Mfy/Mry) <= 1.0 & Mry>Mfy

Checks: (Cf/Cr) + U1x(Mfx/Mrx)0.5061

< 1.0, Therefore OKAY

From Before: Mfx/Mrx 0.0364

< 1.0, Therefore OKAY

Flexural or Lateral Torsional Stability

Mry =

94.08

Cr =

1420.853

L > Lu ?

3.93

w2 =

1.00

Mu =

Therefore determine Lateral-Torsional Buckling (Cl. 13.8.2)

w2*ʌ/L*SQRT(E*Iy*J*G + (ʌE/L)^2*Iy*Cw)

Mu =

189.0599 kN.m

Mp = Zx*Fy =

225285.00 kN.m

0.67Mp = Mu < 0.67Mp ?

>4 NO

150940.95 kN.m YES

Mrx' = ࢥMu =

170.154 kN.m

(Cf/Cr) + U1x(Mfx/Mrx)0.5126

< 1.0, Therefore OKAY

Mfx/Mrx + Mfy/Mry =

< 1.0, Therefore OKAY

0.0434

Shear Check

Vfx =

23.610

Vfy =

0.000 ???

h/w <= 439*SQRT(kv/Fy) ?

h/w = (d - 2*t)/w =

19.956

439 * sqrt(kv/Fy) =

54.617 where kv = 5.34 for shear an unstiffened web) pg 1-19 of notes

Vrx = 0.9*d*w*0.66*Fy

391.621 kN

Vry = 0.9*2*b*t*0.66*3

1193.102 kN

Vrx > Vfx ?

OKAY

Vry > Vfy ?

OKAY

102

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Building Columns

Design Detail:

Column 10

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Arnaud Dusser

Comments:

March 23rd, 2013 Caroline Chan

103

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Building Columns

Design Detail:

Column H

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Arnaud Dusser

Comments:

March 23rd, 2013 Caroline Chan

D Beam Column H

Total height:

321.13

540.12

312

1.25

0.5

1.5

10.988 m

Above ground

7.138 m

Axial load:

Wind load: strong axis

5.3 kN/m

weak axis

none

kN/m

Axial

Moment

Only along top 3.208m Only along top 7.15m

Loading Cases Shear

1 1.25D+1.5S+0.5L

745

2 1.25D+1.4W+0.5L

216

11.5 at 3.17

14.792

3 1.25D+1.4W+0.5S

319

11.5 at 3.18

14.792

4 1.0E+1.0D+0.25S

444

Tension

Column

1139.68 kN

Cf Member chosen:

w200x52

Ag=

7560 mm2

rx=

89.9 mm

14.2 mm 9.1 mm

ry=

52 mm

Fy=

350 MPa 450 MPa

210 mm

Fu=

205 mm

Mass=

59 kg/m

ࢥ=

0.9

KL effective length

4000 mm

Elastic Local Buckling limits

(page 1-126 of Steel Handbook)

(b/2)/t=

7.218309859

<200/((Fy)^0.5)=

10.69044968 Therefore OK

(d-2t)/w=

19.95604396

<670/((Fy)^0.5)=

35.81300642 Therefore OK

Slenderness

k = 1.0

pin ended

WHY 200? Lx (strong)=

3930 mm

(kLx)/rx=

43.71523915 <200

Ly (weak)=

3930 mm

(kLy)/ry=

75.57692308 <200

CLASS?

controls

Determine Ȝ

Ȝ=(kL/r)((Fy/Eʌ^2)^0.5)

Ȝ=

200000 MPa

0.582401165

104

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Building Columns

Design Detail:

Column H

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Arnaud Dusser

Comments:

March 23rd, 2013 Caroline Chan

Determine Cr

1.34

W-shape

Cr=ࢥAFy(1+Ȝ^(2n))^(-1/n) Cr =

2034.524039 kN

1139.68

Therefore OK

Beam Column

Member chosen:

w200x52

210

205

mm mm

14.2

9.1

7560

mm2

Ix =

6.11E+07

mm4

45.4

Iy =

2.04E+07

mm4

15.3

89.9

Rx = Ry =

Zx =

6.53E+05

mm3

495

Zy =

3.03E+05

mm3

229

4.63E+05 mm4

220

Cw =

1.96E+11 mm6

69.6

Lu =

3.93 m

77000 MPa

3930 mm

Cross-section strength

(Cf/Cr) + U1x(Mfx/Mrx) + Uy1(Mfy/Mry) <= 1.0 Class 1 Section

(from Steel Handbook pg. 4-7 - Flange and Web both Class 1)

ࢥ=

0.9

Cf =

745.00 kN

Mfx =

11.5 kNm

Mfy =

0 kNm

Cr = 0.9*A*345 =

2347.38 kN

Mrx = 0.9*Zx*345 =

202.76 kN.m

Mry = 0.9*Zy*345 =

94.08 kN.m

CHECK CLASS!!!!

200000 MPa

Lx =

3930 mm

Ly =

3930 mm

Cex = ʌ^2*EIx / Lx^2 =

7800.91 kN

Cey = ʌ^2*EIy / Ly^2 =

2604.56 kN

w1x = 0.6-0.4(kx) =

1 since it is subjected to distrubted load

w1y = 0.6-0.4(ky) =

105

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Building Columns

Design Detail:

Column H

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Arnaud Dusser

Comments: U1x = w1 / (1- Cf/Cex)

1.11

U1y = w1 / (1- Cf/Cey)

1.40

March 23rd, 2013 Caroline Chan

Checks: (Cf/Cr) + 0.85*U1x(Mfx0.3707

< 1.0, Therefore OKAY

Mfx/Mrx + Mfy/Mry =

< 1.0, Therefore OKAY

0.0567

Overall In-Plane Member Strength

KL/Rx = 1.0*7000/Rx =

43.715 < 200, therefore OKAY

KL/Ry = 1.0*7000/Ry =

75.577 < 200, therefore OKAY

KL/Ry controls

Ȝ = kL/R*SQRT(Fy/(ʌ^2*E)) =141.414*SQRT(345/(ʌ^2*200000)) = Ȝ=

0.9992

Cr =

ࢥAFy(1+Ȝ^(2n))^(-1/n)

Cr =

0.9*8450*345*(1+Ȝ^(2*1.34))^(-1/1.34)

Cr =

1420.853 kN Check (Cf/Cr) + 0.85U1x(Mfx/Mrx) + ȕUy1(Mfy/Mry) <= 1.0 & Mry>Mfy

Checks: (Cf/Cr) + U1x(Mfx/Mrx) 0.5776

< 1.0, Therefore OKAY

From Before: Mfx/Mrx 0.0567

< 1.0, Therefore OKAY

Flexural or Lateral Torsional Stability

Mry =

94.08

Cr =

1420.853

L > Lu ?

3.93

w2 =

1.00

Mu =

Therefore determine Lateral-Torsional Buckling (Cl. 13.8.2)

w2*ʌ/L*SQRT(E*Iy*J*G + (ʌE/L)^2*Iy*Cw)

Mu =

189.0599 kN.m

Mp = Zx*Fy =

225285.00 kN.m

0.67Mp = Mu < 0.67Mp ?

>3.43 YES

150940.95 kN.m YES

Mrx' = ࢥMu =

170.154 kN.m

(Cf/Cr) + U1x(Mfx/Mrx) 0.5878

< 1.0, Therefore OKAY

Mfx/Mrx + Mfy/Mry =

< 1.0, Therefore OKAY

0.0676

Shear Check

Vfx =

14.792

Vfy =

0.000 ???

h/w <= 439*SQRT(kv/Fy) ?

h/w = (d - 2*t)/w =

19.956

439 * sqrt(kv/Fy) =

54.617 where kv = 5.34 for shear an unstiffened web) pg 1-19 of notes

Vrx = 0.9*d*w*0.66*Fy

391.621 kN

Vry = 0.9*2*b*t*0.66*34

1193.102 kN

Vrx > Vfx ?

OKAY

Vry > Vfy ?

OKAY

106

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Building Columns

Design Detail:

Column H

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Arnaud Dusser

Comments:

March 23rd, 2013 Caroline Chan

107

Project Title:

UQAC Arena

DATE:

Project Detail:

Main Building Columns

Design Detail:

Column 1

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Arnaud Dusser

Comments:

Beam Column 1

Total height:

10.988 m

Above ground

March 23rd, 2013 Caroline Chan

241.00

404.00

356

1.25

0.5

1.5

7.138 m

Axial load:

Wind load: strong axis

5.3 kN/m

weak axis

none

kN/m

Axial

Moment

Only along top 3.208m Only along top 7.15m

Loading Cases Shear

1038

2 1.25D+1.4W+0.5L

504.48

14.5 at 3.208

3 1.25D+1.4W+0.5S

480

14.5 at 3.209

12.3

4 1.0E+1.0D+0.25S

1199

800 at 7.138

1130

127

800 at 7.139

1130

in tension

1 1.25D+1.5S+0.5L

4000

12.3

Column

Member chosen:

w310x179

Ag=

7560 mm2

rx=

89.9 mm

14.2 mm 9.1 mm

ry=

52 mm

Fy=

350 MPa 450 MPa

210 mm

Fu=

205 mm

Mass=

59 kg/m

ࢥ=

0.9

KL effective length

4000 mm

Elastic Local Buckling limits

(page 1-126 of Steel Handbook)

(b/2)/t=

7.218309859

<200/((Fy)^0.5)=

10.69044968 Therefore OK

(d-2t)/w=

19.95604396

<670/((Fy)^0.5)=

35.81300642 Therefore OK

Slenderness

k = 1.0

pin ended

WHY 200? Lx (strong)=

3930 mm

(kLx)/rx=

43.71523915 <200

Ly (weak)=

3930 mm

(kLy)/ry=

75.57692308 <200

CLASS?

controls

Determine Ȝ

Ȝ=(kL/r)((Fy/Eʌ^2)^0.5)

Ȝ=

200000 MPa

0.582401165

108

Determine Cr

1.34

W-shape

Cr=ࢥAFy(1+Ȝ^(2n))^(-1/n) Cr =

2034.524039 kN

0.00

Therefore OK

Beam Column

Member chosen:

w310x179

333

313

mm mm

28.1

22800

mm2

Ix =

4.45E+08

mm4

45.4

Iy =

1.44E+08

mm4

15.3

140

Rx = Ry =

79.5

Zx =

3.05E+06

mm3

495

Zy =

1.40E+06

mm3

229

5.38E+06 mm4

220

Cw =

3.34E+12 mm6

69.6

Lu =

3.93 m

77000 MPa

3930 mm

Cross-section strength

(Cf/Cr) + U1x(Mfx/Mrx) + Uy1(Mfy/Mry) <= 1.0 Class 1 Section

(from Steel Handbook pg. 4-7 - Flange and Web both Class 1)

ࢥ= Cf =

0.9

Mfx =

800 kNm

Mfy =

0 kNm

Cr = 0.9*A*345 =

CHECK CLASS!!!!

1199.00 kN

7079.40 kN

Mrx = 0.9*Zx*345 =

947.03 kN.m

Mry = 0.9*Zy*345 =

434.70 kN.m

200000 MPa

Lx =

3930 mm

Ly =

3930 mm

Cex = ʌ^2*EIx / Lx^2 =

56815.16 kN

Cey = ʌ^2*EIy / Ly^2 =

18385.13 kN

w1x = 0.6-0.4(kx) =

1 since it is subjected to distrubted load

w1y = 0.6-0.4(ky) =

U1x = w1 / (1- Cf/Cex)

1.02

U1y = w1 / (1- Cf/Cey)

1.07

109

Checks: (Cf/Cr) + 0.85*U1x(Mfx

0.902882514 < 1.0, Therefore OKAY

Mfx/Mrx + Mfy/Mry =

0.8448 < 1.0, Therefore OKAY

Overall In-Plane Member Strength

KL/Rx = 1.0*7000/Rx =

28.071 < 200, therefore OKAY

KL/Ry = 1.0*7000/Ry =

49.434 < 200, therefore OKAY

KL/Ry controls

Ȝ = kL/R*SQRT(Fy/(ʌ^2*E)) =141.414*SQRT(345/(ʌ^2*200000)) = Ȝ=

0.6535

Cr =

ࢥAFy(1+Ȝ^(2n))^(-1/n)

Cr =

0.9*8450*345*(1+Ȝ^(2*1.34))^(-1/1.34)

Cr =

5838.560 kN Check (Cf/Cr) + 0.85U1x(Mfx/Mrx) + ȕUy1(Mfy/Mry) <= 1.0 & Mry>Mfy

Checks: (Cf/Cr) + U1x(Mfx/Mrx) 0.9389

< 1.0, Therefore OKAY

From Before: Mfx/Mrx 0.8448

< 1.0, Therefore OKAY

Flexural or Lateral Torsional Stability

Mry =

434.70

Cr =

5838.560

L > Lu ?

3.93

w2 =

1.00

Mu =

Therefore determine Lateral-Torsional Buckling (Cl. 13.8.2)

w2*ʌ/L*SQRT(E*Iy*J*G + (ʌE/L)^2*Iy*Cw)

Mu =

1783.1359 kN.m

Mp = Zx*Fy =

1052250.00 kN.m

0.67Mp = Mu < 0.67Mp ?

>3.43 YES

705007.5 kN.m YES

Mrx' = ࢥMu =

1604.822 kN.m

(Cf/Cr) + U1x(Mfx/Mrx) 0.6382

< 1.0, Therefore OKAY

Mfx/Mrx + Mfy/Mry =

< 1.0, Therefore OKAY

0.4985

Shear Check

Vfx =

1130.000

Vfy =

0.000 ???

h/w <= 439*SQRT(kv/Fy) ?

h/w = (d - 2*t)/w =

15.378

439 * sqrt(kv/Fy) =

54.617 where kv = 5.34 for shear an unstiffened web) pg 1-19 of notes

Vrx = 0.9*d*w*0.66*Fy

1228.350 kN

Vry = 0.9*2*b*t*0.66*34

3604.842 kN

Vrx > Vfx ?

OKAY

Vry > Vfy ?

OKAY

110

111

Project Title:

UQAC Arena

DATE:

March 26th, 2013

Project Detail:

Lockers Room roof

Design Detail:

Design of exterior and corner columns

VERIFIED BY:

Randy (Chao) Wang

Othmane Laraki

Comments:

CHECKED BY:

Arnaud Dusser

The following calculations have been performand on the basis of the guidelines provided by the Handbook of Steel Construction, 10th edition (CISCͲICCA), as well as the NBCC 2005 (Commentary I) For the distributed wind loads, we consider the load combination : wf=1.4W (NBCC 2005) in the direction perpendicular to the lockers room's largest dimension, Columns

A-2, A-9

A-1, A-10

Wind Loads (kN/m)

8.0668

A-4, A-5, A-6, A-7

4.35435

7.4249

in the direction perpendicular to the lockers room's shortest dimension, Columns

A-2, A-9

A-1, A-10

Wind Loads (kN/m)

9.17948

A-4, A-5, A-6, A-7

4.95495

8.44906

For the gravity loads, we consider the load combination : wf=1.25D+1.5S+0.5L (NBCC 2005) wf= [(1.25x1.70kPa+1.5x5.37kPa+0.5x4.8kPa)x6.46m/2]+[1.5(10.53-5.37)kPax6.46m/6) = 48.97 kN/m Multiplying by the tributary width corresponding to each column: Column

AͲ2, AͲ9

Gravity Load (kN)

AͲ1, AͲ10 486.492465

A-4, A-5, A-6, A-7

262.601625

447.78168

The unbraced length is L=3.93m, and the girts is assumed to be a simply supported beam with pinͲpin connection, ie. K=1.0 Design of columns AͲ1 and AͲ10 based on the beam selection tables provided by the Handbook of Steel Construction, 10th edition, CISCͲICCA (page 6Ͳ54), and Cf, we shall try :

W150x22 (grade 350W steel)

d =

152 mm

b =

152 mm

t =

6.6 mm

w =

5.8 mm

A =

2850 mm2

Ix =

12100000 mm4

Iy =

3870000 mm4

Rx = Ry =

65.1 mm 36.9 mm

Zx =

176000 mm3

Zy =

͹͹͸ͲͲ mm3

J = Cw =

42000 mm4 20400000000 mm6

Lu =

2.47 m

G =

77000 MPa

Strong Axis M = 102*0.228 =

0.00

kN.m

єM @ A = 0 R1 =

8.55629775 kN

is Vf

єF in horizontal direcƟon = 0 = R2 + 9.8 Ͳ 3.75*7 R2 =

8.55629775 kN x = R2/4.25 = M @ x =

2.177175 8.308549973

m kN.m

is Mfx

Weak Axis M =

0 kN.m єM @ A = 0 =

R1 = R2 = x = 8.25/3.75 = M @ x =

9.73647675

9.74

kN 1.965 m

9.566088407 kN.m

is Mfy

112

Project Title:

UQAC Arena

DATE:

March 26th, 2013

Project Detail:

Lockers Room roof

Design Detail:

Design of exterior and corner columns

VERIFIED BY:

Randy (Chao) Wang

Othmane Laraki

Comments:

CHECKED BY:

Arnaud Dusser

CrossͲSection strength from Steel Handbook pg. 4Ͳ6 Ͳ Flange is class 1 and Web is class 3, hence the section is class 3 Interaction equation :

(Cf/Cr) + U1x(Mfx/Mrx) + Uy1(Mfy/Mry) ч 1.0

੮ =

0.9

Cf =

262.601625

Mfx =

Mfy =

Cr = 0.9ͼAͼ345 =

884.93

Mrx = 0.9ͼZxͼ345 =

54.648

kN.m

Mry = 0.9ͼZyͼ345 =

24.0948

kN.m

E =

200000

MPa

Lx =

3930

Ly =

3930

Cex = ʋ2ͼEͼIx / Lx2 =

1546.42909

Cey = ʋ2ͼEͼIy / Ly2 =

494.6017007

w1x = 0.6Ͳ0.4(kx) =

1.00

w1y = 0.6Ͳ0.4(ky) =

1.00

U1x = w1 / (1Ͳ Cf/Cex) =

1.204545885

U1y = w1 / (1Ͳ Cf/Cey) =

2.131903187

since it is subjected to distrubted load

Checks: (Cf/Cr) + U1x(Mfx/Mrx) 0.2968

< 1.0, Therefore OK

Mfx/Mrx + Mfy/Mry =

< 1.0, Therefore OK

0.0000

Overall InͲPlane Member Strength KL/Rx = 1.0ͼ7000/Rx =

60.36866359

< 200, therefore OK

KL/Ry = 1.0ͼ7000/Ry =

106.50

< 200, therefore OK

KL/Ry controls

ʄ = (kL/Ry)ͼsqrt(Fy/(ʋ2*E)) =141.414ͼsqrt(345/(ʋ2ͼ200000)) ʄ =

1.408026606

Cr = ੮AFy(1+ʄ2n)Ͳ1/n

with n=1.34

Cr = 0.9ͼ2850ͼ345ͼ(1+1.86962x1.34)Ͳ1/1.34 Cr = Check the following :

347.3008334

Mry>Mfy (Cf/Cr) + U1x(Mfx/Mrx) + Uy1(Mfy/Mry) ч 1.0

(Cf/Cr) + U1x(Mfx/Mrx) + Uy1(Mfy/Mry) =

0.76

< 1.0, Therefore OK

From Before : Mfx/Mrx + Mfy/Mry =

0.00

< 1.0, Therefore OK

Mry > Mfy

Therefore OK

113

Project Title:

UQAC Arena

DATE:

March 26th, 2013

Project Detail:

Lockers Room roof

Design Detail:

Design of exterior and corner columns

VERIFIED BY:

Randy (Chao) Wang

Othmane Laraki

Comments:

CHECKED BY:

Arnaud Dusser

Flexural or Lateral Torsional Stability Mry =

24.09

Cr =

347.3008334

L > Lu ?

YES

w2 =

kNͼm kN Therefore determine LateralͲTorsional Buckling (Cl. 13.8.2) (Conservative approach)

Mu = (w2ͼʋ/L)ͼsqrt(EͼIyͼJͼG + (ʋͼE/L)2ͼIyͼCw) Mu = Mp = ZxͼFy = 0.67Mp = Mu < 0.67Mp ?

53.7500588

kN.m

362.25

kN.m

242.7075

kN.m

YES

Mrx' = ੮Mu =

48.37505292

kN.m

(Cf/Cr) + U1x(Mfx/Mrx) + Uy1(Mfy/Mry) = 0.756121494 Mfx/Mrx + Mfy/Mry = 0

< 1.0, Therefore OKAY < 1.0, Therefore OKAY

Shear Check Vfx =

8.55629775

Vfy =

9.73647675

h/w ч 439ͼSQRT(kv/Fy) ? h/w = (d Ͳ 2ͼt)/w =

23.93103448

439ͼsqrt(kv/Fy) =

54.61671826

Vrx = 0.9ͼdͼwͼ0.66ͼFy =

180.666288

411.17

Vry = 0.9ͼ2ͼbͼtͼ0.66ͼ345 = Vrx > Vfx ?

Vry > Vfy ?

where kv = 5.34 for shear in an unstiffened web (S16)

114

Project Title:

UQAC Arena

DATE:

March 26th, 2013

Project Detail:

Lockers Room roof

Design Detail:

Design of exterior and corner columns

VERIFIED BY:

Randy (Chao) Wang

Othmane Laraki

Comments:

CHECKED BY:

Arnaud Dusser

Design of columns AͲ2 and AͲ9 based on the beam selection tables provided by the Handbook of Steel Construction, 10th edition, CISCͲICCA (page 6Ͳ54), and Cf, we shall try :

W150x37 (grade 350W steel)

d =

162 mm

b =

154 mm

t =

11.6 mm

w =

8.1 mm

A =

4730 mm2

Ix =

22200000 mm4

Iy =

7070000 mm4

Rx =

68.5 mm

Ry =

38.6 mm

Zx =

310000 mm3

Zy =

140000 mm3 193000 mm4

J =

40000000000 mm6

Cw = Lu =

2.64 m

G =

77000 MPa

Strong Axis єM @ A = 0 R1 =

15.85

is Vf

єF in horizontal direcƟon = 0 R2 =

15.851262 kN

x = R2/4.25 =

4.0334 m

M @ x =

Ͳ1.68

kN.m

18.04

is Mfx

Weak Axis єM @ A = 0 R1 = єF in horizontal direcƟon = 0 R2 = x = 8.25/3.75 = M @ x =

18.0376782 kN 1.965 m 17.72201883

kN.m

is Mfy

CrossͲSection Strength from Steel Handbook pg. 4Ͳ6 Ͳ Flange is class 1 and Web is class 1, hence the section is class 1 Interaction equation : ɴ= ੮ = Cf =

(Cf/Cr) + 0.85ͼU1x(Mfx/Mrx) + ɴͼUy1(Mfy/Mry) ч 1.0 1.138406029

Mfy =

0 1468.665

Mrx = 0.9ͼZxͼ345 =

96.255

kN.m

Mry = 0.9ͼZyͼ345 =

43.47

kN.m

E =

0.85

486.492465 kN

Mfx =

Cr = 0.9ͼAͼ345 =

>0.85 hence ɴ=

0.9

200000

MPa

Lx =

3930

Ly =

3930

Cex = ʋ2ͼEͼIx / Lx2 =

2837.250066

Cey = ʋ2ͼEͼIy / Ly2 =

903.5746831

w1x = 0.6Ͳ0.4(kx) =

1 since it is subjected to a uniformly distributed load

w1y = 0.6Ͳ0.4(ky) =

U1x = w1 / (1Ͳ Cf/Cex) =

1.206951353

U1y = w1 / (1Ͳ Cf/Cey) =

2.166418619

115

Project Title:

UQAC Arena

DATE:

March 26th, 2013

Project Detail:

Lockers Room roof

Design Detail:

Design of exterior and corner columns

VERIFIED BY:

Randy (Chao) Wang

Othmane Laraki

Comments:

CHECKED BY:

Arnaud Dusser

Checks: (Cf/Cr) + 0.85ͼU1x(Mfx/Mrx) + ɴͼUy1(Mfy/Mry) =

0.331248082

< 1.0, Therefore OKAY

Mfx/Mrx + Mfy/Mry = Overall InͲPlane Member Strength

KL/Rx = 1.0ͼ7000/Rx =

57.37226277

< 200, therefore OK

KL/Ry = 1.0ͼ7000/Ry =

101.81

< 200, therefore OK

KL/Ry controls

ʄ = (kL/Ry)ͼsqrt(Fy/(ʋ2*E)) =141.414ͼsqrt(345/(ʋ2ͼ200000)) ʄ =

1.346015071

Cr = ੮AFy(1+ʄ2n)Ͳ1/n

with n=1.34

Cr = 0.9ͼ4730ͼ345ͼ(1+1.86962x1.34)Ͳ1/1.34 Cr =

614.0201356

Mry>Mfy

Check the following :

(Cf/Cr) + 0.85ͼU1x(Mfx/Mrx) + ɴͼUy1(Mfy/Mry) ч 1.0 (Cf/Cr) + 0.85ͼU1x(Mfx/Mrx) + ɴͼUy1(Mfy/Mry)

0.79

< 1.0, Therefore OK

From Before : Mfx/Mrx + Mfy/Mry =

0.00

< 1.0, Therefore OK

Mry > Mfy

Therefore OK

Flexural or Lateral Torsional Stability Mry = Cr = L > Lu ? w2 =

43.47 614.0201356 YES 1

kNͼm kN Therefore determine LateralͲTorsional Buckling (Cl. 13.8.2) (Conservative approach)

Mu = (w2ͼʋ/L)ͼsqrt(EͼIyͼJͼG + (ʋͼE/L)2ͼIyͼCw) 134.3400304

kN.m

Mp = ZxͼFy =

Mu =

106.95

kN.m

0.67Mp =

71.6565

kN.m

Mu < 0.67Mp ?

YES

Mrx' = ੮Mu =

120.9060274

kN.m

(Cf/Cr) + 0.85ͼU1x(Mfx/Mrx) + ɴͼUy1(Mfy/Mry) = 0.792307022 Mfx/Mrx + Mfy/Mry = 0

< 1.0, Therefore OKAY < 1.0, Therefore OKAY

Shear Check Vfx =

15.851262

Vfy =

18.0376782

h/w ч 439ͼSQRT(kv/Fy) ? h/w = (d Ͳ 2ͼt)/w =

17.13580247

439ͼsqrt(kv/Fy) =

54.61671826

Vrx = 0.9ͼdͼwͼ0.66ͼFy =

268.909146

732.17

Vry = 0.9ͼ2ͼbͼtͼ0.66ͼ345 = Vrx > Vfx ?

Vry > Vfy ?

where kv = 5.34 for shear in an unstiffened web (S16)

116

Project Title:

UQAC Arena

DATE:

March 26th, 2013

Project Detail:

Lockers Room roof

Design Detail:

Design of exterior and corner columns

VERIFIED BY:

Randy (Chao) Wang

Othmane Laraki

Comments:

CHECKED BY:

Arnaud Dusser

Design of Columns AͲ4, AͲ5, AͲ6, AͲ7 based on the beam selection tables provided by the Handbook of Steel Construction, 10th edition, CISCͲICCA (page 6Ͳ54), and Cf, we shall try :

W150x30 (grade 350W steel)

d =

157 mm

b =

153 mm

t =

9.3 mm

w =

6.6 mm

A =

3790 mm2

Ix =

17200000 mm4

Iy =

5560000 mm4

Rx =

67.3 mm

Ry =

38.3 mm

Zx =

244000 mm3

Zy =

111000 mm3 101000 mm4

J =

30300000000 mm6

Cw = Lu =

2.44 m

G =

77000 MPa

Strong Axis єM @ A = 0 R1 =

14.59

is Vf

єF in horizontal direcƟon = 0 R2 =

14.5899285 kN

x = R2/4.25 =

3.71245 m

M @ x =

3.00

kN.m

0.00

is Mfx

Weak Axis єM @ A = 0 R1 = єF in horizontal direcƟon = 0 R2 =

0 kN

CrossͲSection Strength from Steel Handbook pg. 4Ͳ6 Ͳ Flange is class 1 and Web is class 2, hence the section is class 2 Interaction equation : ɴ= ੮ = Cf = Mfx =

Cr = 0.9ͼAͼ345 =

(Cf/Cr) + 0.85ͼU1x(Mfx/Mrx) + ɴͼUy1(Mfy/Mry) ч 1.0 1.142623308

>0.85 hence ɴ=

0.85

0.9 447.78168 kN 0

1176.795

Mrx = 0.9ͼZxͼ345 =

75.762

kN.m

Mry = 0.9ͼZyͼ345 =

34.4655

kN.m

E =

200000

MPa

Lx =

3930

Ly =

3930

Cex = ʋ2ͼEͼIx / Lx2 =

2198.229781

Cey = ʋ2ͼEͼIy / Ly2 =

710.590557

w1x = 0.6Ͳ0.4(kx) =

1 since it is subjected to a uniformly distributed load

w1y = 0.6Ͳ0.4(ky) =

U1x = w1 / (1Ͳ Cf/Cex) =

1.255809744

U1y = w1 / (1Ͳ Cf/Cey) =

2.703830118

117

Project Title:

UQAC Arena

DATE:

March 26th, 2013

Project Detail:

Lockers Room roof

Design Detail:

Design of exterior and corner columns

VERIFIED BY:

Randy (Chao) Wang

Othmane Laraki

Comments:

CHECKED BY:

Arnaud Dusser

Checks: (Cf/Cr) + 0.85ͼU1x(Mfx/Mrx) + ɴͼUy1(Mfy/Mry) =

0.380509503

< 1.0, Therefore OKAY

Mfx/Mrx + Mfy/Mry = Overall InͲPlane Member Strength

KL/Rx = 1.0ͼ7000/Rx =

58.39524517

< 200, therefore OK

KL/Ry = 1.0ͼ7000/Ry =

102.61

< 200, therefore OK

KL/Ry controls

ʄ = (kL/Ry)ͼsqrt(Fy/(ʋ2*E)) =141.414ͼsqrt(345/(ʋ2ͼ200000)) ʄ =

1.35655827

Cr = ੮AFy(1+ʄ2n)Ͳ1/n

with n=1.34

Cr = 0.9ͼ3790ͼ345ͼ(1+1.86962x1.34)Ͳ1/1.34 Cr =

486.7151103

Mry>Mfy

Check the following :

(Cf/Cr) + 0.85ͼU1x(Mfx/Mrx) + ɴͼUy1(Mfy/Mry) ч 1.0 (Cf/Cr) + 0.85ͼU1x(Mfx/Mrx) + ɴͼUy1(Mfy/Mry)

0.92

< 1.0, Therefore OK

From Before : Mfx/Mrx + Mfy/Mry =

0.00

< 1.0, Therefore OK

Mry > Mfy

Therefore OK

Flexural or Lateral Torsional Stability Mry = Cr = L > Lu ? w2 =

34.47 486.7151103 YES 1

kNͼm kN Therefore determine LateralͲTorsional Buckling (Cl. 13.8.2) (Conservative approach)

Mu = (w2ͼʋ/L)ͼsqrt(EͼIyͼJͼG + (ʋͼE/L)2ͼIyͼCw) Mu = Mp = ZxͼFy = 0.67Mp = Mu < 0.67Mp ?

90.98350593

kN.m

84.18

kN.m

56.4006

kN.m

YES

Mrx' = ੮Mu =

81.88515533

kN.m

(Cf/Cr) + 0.85ͼU1x(Mfx/Mrx) + ɴͼUy1(Mfy/Mry) = 0.920007763 Mfx/Mrx + Mfy/Mry = 0

< 1.0, Therefore OKAY < 1.0, Therefore OKAY

Shear Check Vfx =

14.5899285

Vfy =

h/w ч 439ͼSQRT(kv/Fy) ? h/w = (d Ͳ 2ͼt)/w =

20.96969697

439ͼsqrt(kv/Fy) =

54.61671826

Vrx = 0.9ͼdͼwͼ0.66ͼFy =

212.348466

583.19

Vry = 0.9ͼ2ͼbͼtͼ0.66ͼ345 = Vrx > Vfx ?

Vry > Vfy ?

where kv = 5.34 for shear in an unstiffened web (S16)

118

Project Title:

UQAC Arena

DATE:

March 26th, 2013

Project Detail:

Mechanical Room

Design Detail:

Design of exterior and corner columns

VERIFIED BY:

Randy (Chao) Wang

Othmane Laraki

Comments:

CHECKED BY:

Caroline Chan

B-0

G-0

Wind Loads (kN/m)

3.1343

D-0, E-0, E5-0, F-0

2.4514

4.903668

in the direction perpendicular to the lockers room's shortest dimension, Columns

B-0

G-0

Wind Loads (kN/m)

3.56664

D-0, E-0, E5-0, F-0

2.789556

5.58

For the gravity loads, we consider the load combination : wf=1.25D+1.5S+0.5L (NBCC 2005) wf= [1.25x1.69kPa+1.5x3.54kPa+0.5x4.8kPa]+[1.5(10.53-3.54)kPax8.75m/6) = 58.27 kN/m Multiplying by the tributary width corresponding to each column: Column

B-0

G-0

Gravity Load (kN)

224.9222

D-0, E-0, E5-0, F-0

175.9754

351.9508

The unbraced length is L=4.25m, and the girts is assumed to be a simply supported beam with pinͲpin connection, ie. K=1.0 Design of columns BͲ0 based on the beam selection tables provided by the Handbook of Steel Construction, 10th edition, CISCͲICCA (page 6Ͳ54), and Cf, we shall try :

W150x22 (grade 350W steel)

d =

152 mm

b =

152 mm

t =

6.6 mm

w =

5.8 mm

A =

2850 mm2

Ix =

12100000 mm4

Iy =

3870000 mm4

Rx = Ry =

65.1 mm 36.9 mm

Zx =

176000 mm3

Zy =

͹͹͸ͲͲ mm3

J = Cw =

42000 mm4 20400000000 mm6

Lu =

2.47 m

G =

77000 MPa

Strong Axis єM @ A = 0 R1 =

6.6603875 kN

is Vf

єF in horizontal direcƟon = 0 R2 =

9.4046125 kN x = R2/4.25 = M @ x =

2.21285

7.064567047

kN.m

is Mfx

Weak Axis M =

0 kN.m єM @ A = 0 =

R1 =

7.57911 R2 =

x = 8.25/3.75 = M @ x =

7.58

kN kN 2.125 m

8.052804375 kN.m

is Mfy

119

Project Title:

UQAC Arena

DATE:

March 26th, 2013

Project Detail:

Mechanical Room

Design Detail:

Design of exterior and corner columns

VERIFIED BY:

Randy (Chao) Wang

Othmane Laraki

Comments:

CHECKED BY:

Caroline Chan

CrossͲSection strength from Steel Handbook pg. 4Ͳ6 Ͳ Flange is class 1 and Web is class 3, hence the section is class 3 Interaction equation :

(Cf/Cr) + U1x(Mfx/Mrx) + Uy1(Mfy/Mry) ч 1.0

੮ =

0.9

Cf =

224.9222

Mfx =

Mfy =

Cr = 0.9ͼAͼ345 =

884.93

Mrx = 0.9ͼZxͼ345 =

54.648

kN.m

Mry = 0.9ͼZyͼ345 =

24.0948

kN.m

E =

200000

MPa

Lx =

4250

Ly =

4250

Cex = ʋ2ͼEͼIx / Lx2 =

1322.322084

Cey = ʋ2ͼEͼIy / Ly2 =

422.9245014

w1x = 0.6Ͳ0.4(kx) =

1.00

w1y = 0.6Ͳ0.4(ky) =

1.00

U1x = w1 / (1Ͳ Cf/Cex) =

1.204959198

U1y = w1 / (1Ͳ Cf/Cey) =

2.135957504

since it is subjected to distrubted load

Checks: (Cf/Cr) + U1x(Mfx/Mrx) 0.2968

< 1.0, Therefore OK

Mfx/Mrx + Mfy/Mry =

< 1.0, Therefore OK

0.0000

Overall InͲPlane Member Strength KL/Rx = 1.0ͼ4250/Rx =

65.28417819

< 200, therefore OK

KL/Ry = 1.0ͼ4250/Ry =

115.18

< 200, therefore OK

KL/Ry controls

ʄ = (kL/Ry)ͼsqrt(Fy/(ʋ2*E)) =115.18ͼsqrt(345/(ʋ2ͼ200000)) ʄ =

1.522675083

Cr = ੮AFy(1+ʄ2n)Ͳ1/n

with n=1.34

Cr = 0.9ͼ2850ͼ345ͼ(1+1.86962x1.34)Ͳ1/1.34 Cr = Check the following :

309.5411963

Mry>Mfy (Cf/Cr) + U1x(Mfx/Mrx) + Uy1(Mfy/Mry) ч 1.0

(Cf/Cr) + U1x(Mfx/Mrx) + Uy1(Mfy/Mry) =

0.73

< 1.0, Therefore OK

From Before : Mfx/Mrx + Mfy/Mry =

0.00

< 1.0, Therefore OK

Mry > Mfy

Therefore OK

120

Project Title:

UQAC Arena

DATE:

March 26th, 2013

Project Detail:

Mechanical Room

Design Detail:

Design of exterior and corner columns

VERIFIED BY:

Randy (Chao) Wang

Othmane Laraki

Comments:

CHECKED BY:

Caroline Chan

Flexural or Lateral Torsional Stability Mry =

24.09

Cr =

309.5411963

L > Lu ?

YES

w2 =

kNͼm kN Therefore determine LateralͲTorsional Buckling (Cl. 13.8.2) (Conservative approach)

Mu = (w2ͼʋ/L)ͼsqrt(EͼIyͼJͼG + (ʋͼE/L)2ͼIyͼCw) Mu = Mp = ZxͼFy = 0.67Mp = Mu < 0.67Mp ?

25.14550399

kN.m

362.25

kN.m

242.7075

kN.m

YES

Mrx' = ੮Mu =

22.63095359

kN.m

(Cf/Cr) + U1x(Mfx/Mrx) + Uy1(Mfy/Mry) = 0.726630906 Mfx/Mrx + Mfy/Mry = 0

< 1.0, Therefore OKAY < 1.0, Therefore OKAY

Shear Check Vfx =

9.4046125

Vfy =

7.57911

h/w ч 439ͼSQRT(kv/Fy) ? h/w = (d Ͳ 2ͼt)/w =

23.93103448

439ͼsqrt(kv/Fy) =

54.61671826

Vrx = 0.9ͼdͼwͼ0.66ͼFy =

180.666288

411.17

Vry = 0.9ͼ2ͼbͼtͼ0.66ͼ345 = Vrx > Vfx ?

Vry > Vfy ?

where kv = 5.34 for shear in an unstiffened web (S16)

121

Project Title:

UQAC Arena

DATE:

March 26th, 2013

Project Detail:

Mechanical Room

Design Detail:

Design of exterior and corner columns

VERIFIED BY:

Randy (Chao) Wang

Othmane Laraki

Comments:

CHECKED BY:

Caroline Chan

Design of columnsGͲ0 based on the beam selection tables provided by the Handbook of Steel Construction, 10th edition, CISCͲICCA (page 6Ͳ53), and Cf, we shall try :

W150x22 (grade 350W steel)

d =

152 mm

b =

152 mm

t =

6.6 mm

w =

5.8 mm

A =

2850 mm2

Ix =

12100000 mm4

Iy =

3870000 mm4

Rx =

65.1 mm

Ry =

36.9 mm

Zx =

176000 mm3

Zy =

77600 mm3 42000 mm4

J =

20400000000 mm6

Cw = Lu =

2.47 m

G =

77000 MPa

Strong Axis єM @ A = 0 R1 =

5.21

is Vf

єF in horizontal direcƟon = 0 R2 =

5.209225 kN

x = R2/4.25 =

1.2257 m

M @ x =

4.54

kN.m

5.93

is Mfx

Weak Axis єM @ A = 0 R1 = єF in horizontal direcƟon = 0 R2 = x = 8.25/3.75 = M @ x =

5.9278065 kN 2.125 m 6.298294406

kN.m

is Mfy

CrossͲSection Strength from Steel Handbook pg. 4Ͳ6 Ͳ Flange is class 1 and Web is class 3, hence the section is class 3 Interaction equation : ੮ = Cf =

(Cf/Cr) + U1x(Mfx/Mrx) +Uy1(Mfy/Mry) ч 1.0 0.9 175.9754 kN

Mfx =

Mfy =

0 884.925

Mrx = 0.9ͼZxͼ345 =

Cr = 0.9ͼAͼ345 =

54.648

kN.m

Mry = 0.9ͼZyͼ345 =

24.0948

kN.m

E =

200000

MPa

Lx =

4250

Ly =

4250

Cex = ʋ2ͼEͼIx / Lx2 =

1322.322084

Cey = ʋ2ͼEͼIy / Ly2 =

422.9245014

w1x = 0.6Ͳ0.4(kx) =

1 since it is subjected to a uniformly distributed load

w1y = 0.6Ͳ0.4(ky) =

U1x = w1 / (1Ͳ Cf/Cex) =

1.153509756

U1y = w1 / (1Ͳ Cf/Cey) =

1.712597855

122

Project Title:

UQAC Arena

DATE:

March 26th, 2013

Project Detail:

Mechanical Room

Design Detail:

Design of exterior and corner columns

VERIFIED BY:

Randy (Chao) Wang

Othmane Laraki

Comments:

CHECKED BY:

Caroline Chan

Checks: (Cf/Cr) + U1x(Mfx/Mrx) + Uy1(Mfy/Mry) =

0.198859112

< 1.0, Therefore OKAY

Mfx/Mrx + Mfy/Mry = Overall InͲPlane Member Strength

KL/Rx = 1.0ͼ4250/Rx =

65.28417819

< 200, therefore OK

KL/Ry = 1.0ͼ4250/Ry =

115.18

< 200, therefore OK

KL/Ry controls

ʄ = (kL/Ry)ͼsqrt(Fy/(ʋ2*E)) =115.18ͼsqrt(345/(ʋ2ͼ200000)) ʄ =

1.522675083

Cr = ੮AFy(1+ʄ2n)Ͳ1/n

with n=1.34

Cr = 0.9ͼ2850ͼ345ͼ(1+1.522672x1.34)Ͳ1/1.34 Cr =

309.5411963

Mry>Mfy

Check the following :

(Cf/Cr) + U1x(Mfx/Mrx) +Uy1(Mfy/Mry) ч 1.0 (Cf/Cr) + U1x(Mfx/Mrx) + Uy1(Mfy/Mry)

0.57

< 1.0, Therefore OK

From Before : Mfx/Mrx + Mfy/Mry =

0.00

< 1.0, Therefore OK

Mry > Mfy

Therefore OK

Flexural or Lateral Torsional Stability Mry =

24.09

Cr =

309.5411963

L > Lu ?

YES

w2 =

kNͼm kN Therefore determine LateralͲTorsional Buckling (Cl. 13.8.2) (Conservative approach)

Mu = (w2ͼʋ/L)ͼsqrt(EͼIyͼJͼG + (ʋͼE/L)2ͼIyͼCw) Mu = Mp = ZxͼFy = 0.67Mp = Mu < 0.67Mp ?

25.14550399

kN.m

362.25

kN.m

242.7075

kN.m

YES

Mrx' = ੮Mu =

22.63095359

kN.m

(Cf/Cr) + U1x(Mfx/Mrx) + Uy1(Mfy/Mry) = 0.568503973 Mfx/Mrx + Mfy/Mry = 0

< 1.0, Therefore OKAY < 1.0, Therefore OKAY

Shear Check Vfx =

5.209225

Vfy =

5.9278065

h/w ч 439ͼSQRT(kv/Fy) ? h/w = (d Ͳ 2ͼt)/w =

23.93103448

439ͼsqrt(kv/Fy) =

54.61671826

Vrx = 0.9ͼdͼwͼ0.66ͼFy =

180.666288

411.17

Vry = 0.9ͼ2ͼbͼtͼ0.66ͼ345 = Vrx > Vfx ?

Vry > Vfy ?

where kv = 5.34 for shear in an unstiffened web (S16)

123

Project Title:

UQAC Arena

DATE:

March 26th, 2013

Project Detail:

Mechanical Room

Design Detail:

Design of exterior and corner columns

VERIFIED BY:

Randy (Chao) Wang

Othmane Laraki

Comments:

CHECKED BY:

Caroline Chan

Design of Columns DͲ0, EͲ0, E5Ͳ0, FͲ0 based on the beam selection tables provided by the Handbook of Steel Construction, 10th edition, CISCͲICCA (page 6Ͳ54), and Cf, we shall try :

W150x37 (grade 350W steel)

d =

162 mm

b =

154 mm

t =

11.6 mm

w =

8.1 mm

A =

4730 mm2

Ix =

22200000 mm4

Iy =

7070000 mm4

Rx =

68.5 mm

Ry =

38.6 mm

Zx =

310000 mm3

Zy =

140000 mm3 193000 mm4

J =

40000000000 mm6

Cw = Lu =

2.64 m

G =

77000 MPa

Strong Axis єM @ A = 0 R1 =

10.42

is Vf

єF in horizontal direcƟon = 0 R2 =

10.4202945 kN

x = R2/4.25 =

2.451834 m

M @ x =

10.81

kN.m

0.00

is Mfx

Weak Axis єM @ A = 0 R1 = єF in horizontal direcƟon = 0 R2 =

0 kN

CrossͲSection Strength from Steel Handbook pg. 4Ͳ6 Ͳ Flange is class 1 and Web is class 2, hence the section is class 2 Interaction equation : ɴ= ੮ = Cf = Mfx =

Cr = 0.9ͼAͼ345 =

(Cf/Cr) + 0.85ͼU1x(Mfx/Mrx) + ɴͼUy1(Mfy/Mry) ч 1.0 1.182245705

>0.85 hence ɴ=

351.9508 kN 0

1468.665

Mrx = 0.9ͼZxͼ345 =

96.255

kN.m

Mry = 0.9ͼZyͼ345 =

43.47

kN.m

E =

0.85

0.9

200000

MPa

Lx =

4250

Ly =

4250

Cex = ʋ2ͼEͼIx / Lx2 =

2426.078535

Cey = ʋ2ͼEͼIy / Ly2 =

772.6295155

w1x = 0.6Ͳ0.4(kx) =

1 since it is subjected to a uniformly distributed load

w1y = 0.6Ͳ0.4(ky) =

U1x = w1 / (1Ͳ Cf/Cex) =

1.169686174

U1y = w1 / (1Ͳ Cf/Cey) =

1.836626116

124

Project Title:

UQAC Arena

DATE:

March 26th, 2013

Project Detail:

Mechanical Room

Design Detail:

Design of exterior and corner columns

VERIFIED BY:

Randy (Chao) Wang

Othmane Laraki

Comments:

CHECKED BY:

Caroline Chan

Checks: (Cf/Cr) + 0.85ͼU1x(Mfx/Mrx) + ɴͼUy1(Mfy/Mry) =

0.239639945

< 1.0, Therefore OKAY

Mfx/Mrx + Mfy/Mry = Overall InͲPlane Member Strength

KL/Rx = 1.0ͼ4250/Rx =

62.04379562

< 200, therefore OK

KL/Ry = 1.0ͼ4250/Ry =

110.10

< 200, therefore OK

KL/Ry controls

ʄ = (kL/Ry)ͼsqrt(Fy/(ʋ2*E)) =110.10ͼsqrt(345/(ʋ2ͼ200000)) ʄ =

1.455614263

Cr = ੮AFy(1+ʄ2n)Ͳ1/n

with n=1.34

Cr = 0.9ͼ4730ͼ345ͼ(1+1.45562x1.34)Ͳ1/1.34 Cr =

549.3340376

Mry>Mfy

Check the following :

(Cf/Cr) + 0.85ͼU1x(Mfx/Mrx) + ɴͼUy1(Mfy/Mry) ч 1.0 (Cf/Cr) + 0.85ͼU1x(Mfx/Mrx) + ɴͼUy1(Mfy/Mry)

0.64

< 1.0, Therefore OK

From Before : Mfx/Mrx + Mfy/Mry =

0.00

< 1.0, Therefore OK

Mry > Mfy

Therefore OK

Flexural or Lateral Torsional Stability Mry = Cr = L > Lu ? w2 =

43.47 549.3340376 YES 1

kNͼm kN Therefore determine LateralͲTorsional Buckling (Cl. 13.8.2) (Conservative approach)

Mu = (w2ͼʋ/L)ͼsqrt(EͼIyͼJͼG + (ʋͼE/L)2ͼIyͼCw) Mu = Mp = ZxͼFy = 0.67Mp = Mu < 0.67Mp ?

68.49431118

kN.m

362.25

kN.m

242.7075

kN.m

YES

Mrx' = ੮Mu =

61.64488006

kN.m

(Cf/Cr) + 0.85ͼU1x(Mfx/Mrx) + ɴͼUy1(Mfy/Mry) = 0.640686315 Mfx/Mrx + Mfy/Mry = 0

< 1.0, Therefore OKAY < 1.0, Therefore OKAY

Shear Check Vfx =

10.4202945

Vfy =

h/w ч 439ͼSQRT(kv/Fy) ? h/w = (d Ͳ 2ͼt)/w =

17.13580247

439ͼsqrt(kv/Fy) =

54.61671826

Vrx = 0.9ͼdͼwͼ0.66ͼFy =

268.909146

732.17

Vry = 0.9ͼ2ͼbͼtͼ0.66ͼ345 = Vrx > Vfx ?

Vry > Vfy ?

where kv = 5.34 for shear in an unstiffened web (S16)

125

Project Title:

UQAC Arena

DATE:

April 1st, 2013

Project Detail:

Side buildings

Design Detail:

Girts Design

VERIFIED BY:

Othmane Laraki Caroline Chan

Comments:

Mechanical room, Lockers room

CHECKED BY:

Randy Wang

The following calculations have been completed with support of CSA S16Ͳ2009, CISCͲIBBC 10th edition, and NBCC 2005 Assume :

G=77000 Mpa E=200000 Mpa

Fy=345Mpa

axial forces are negligible

Fu=450Mpa

Mechanical Room Single span of a girt L=

6.04 m along the largest side of the building 8.75 m along shortest side of the building

Height of the building = 4.25m Load Combination with respect to NBCC 2005: maximize wind loads using wf=1.4W Assume 2 bleachers spanning the height of the building,hence o/c spacing = 4.25/3= 1.417m wf=1.4W=1.4x0.58kPax1.417m =

1.2173 kN/m

along largest side

wf=1.4W=1.4x0.66kPax1.417m =

1.3094 kN/m

along shortest side

assume neglegible compression and neglegible shear transfer from roof diaphragm. Largest Side

Shortest Side

Maximum Shear = wfͼL/2 = Vf (kN)

3.676246

5.728625

Maximum Bending Moment =wfͼL2/8 = Mf (kNͼm)

5.55113146

12.53136719

Largest Side Preliminary sizing made according to CSA SͲ16 2009, CISCͲIBBC 10th edition Try Section C180x22

Fy =

345 Mpa

Sx =

127000 mm3

Zx = Non applicable d =

mm3 178 mm

w =

10.6 mm

Cw =

3470000000 mm6

J =

110000 mm4

Fu =

450 Mpa

Ix =

568000 mm4

Iy =

11300000 mm4

b =

58 mm

t =

9.3 mm

Check moment resistance Beam class bel/t=

3.11827957

ч 200 /sqrt(Fy)

Flange is class 1

h/w=(dͲ2t)/w=

15.03773585

ч 1100/sqrt(Fy)

Web is class 1 Overall, beam is class 1

L=6.039m>Lu hence we shall use Mr' My=SxͼFy=

43.815

kNͼm

Mu= w2ͼ(ѓ/L)ͼsqrt(EͼIyͼGͼJ+(ѓͼE/L)2ͼIyͼCw)

use w2=1

= 10.70358296

kNͼm

so Mr' = 9.633224664

kNͼm

> Mf hence OK for flexural resistance

29.35605

Check Shear Resistance h/w=

15.03773585

Vr =ɌͼAwͼFs = 0.9ͼ(dͼw)ͼ(0.66ͼFy)=

ч439ͼsqrt(Kv/Fy)= 54.61671826 386.661924

steel wont yield upon buckling

>Vf hence OK for shear resistance

Check Deflection Lateral allowed deflection according to Table D1 (CSA S16Ͳ2009) is L/300= ѐmax= 5ͼwfͼL4/(384ͼEͼI) =

9.334170237

15.1

< allowed deflection therefore OK

Use C180x22 for Mechanical Room's largest side

126

Project Title:

UQAC Arena

DATE:

April 1st, 2013

Project Detail:

Side buildings

Design Detail:

Girts Design

VERIFIED BY:

Othmane Laraki Caroline Chan

Comments:

Mechanical room, Lockers room

CHECKED BY:

Randy Wang

Shortest Side Preliminary sizing made according to CSA SͲ16 2009, CISCͲIBBC 10th edition Try Section C250x30

Fy =

345 Mpa

Sx =

257000 mm3

Zx = Non applicable d =

mm3 254 mm

w =

9.6 mm

Cw =

15000000000 mm6

J =

153000 mm4

Fu =

450 Mpa

Ix =

32700000 mm4

Iy =

1160000 mm4

b =

69 mm

t =

11.1 mm

Check moment resistance Beam class bel/t=

3.108108108

ч 200 /sqrt(Fy)

Flange is class 1

h/w=(dͲ2t)/w=

24.14583333

ч 1100/sqrt(Fy)

Web is class 1 Overall, beam is class 1

L=8.75m>Lu hence we shall use Mr' My=SxͼFy=

88.665

kNͼm

Mu= w2ͼ(ѓ/L)ͼsqrt(EͼIyͼGͼJ+(ѓͼE/L)2ͼIyͼCw) = 18.038454 so Mr' = 16.2346086

use w2=1

kNͼm

> Mf hence OK for flexural resistance

59.40555

Check Shear Resistance h/w=

24.14583333

Vr =ɌͼAwͼFs = 0.9ͼ(dͼw)ͼ(0.66ͼFy)=

ч439ͼsqrt(Kv/Fy)= 54.61671826 499.701312

steel wont yield upon buckling

>Vf hence OK for shear resistance

Check Deflection Lateral allowed deflection according to Table D1 (CSA S16Ͳ2009) is L/300= ѐmax= 5ͼwfͼL4/(384ͼEͼI) =

15.28148573

21.875

< allowed deflection therefore OK

Use C250x30 for Mechanical Room's shortest side

127

Project Title:

UQAC Arena

DATE:

April 1st, 2013

Project Detail:

Side buildings

Design Detail:

Girts Design

VERIFIED BY:

Othmane Laraki Caroline Chan

Comments:

Mechanical room, Lockers room

CHECKED BY:

Randy Wang

Lockers Room Single span of a girt L=

10.725 m along the largest side of the building 6.46 m along shortest side of the building

Height of the building = 3.93m Load Combination with respect to NBCC 2005: maximize wind loads using wf=1.4W Assume 2 bleachers spanning the height of the building,hence o/c spacing = 3.93/3= 1.31m wf=1.4W=1.4x0.58kPax1.31m =

1.0637 kN/m

along largest side

wf=1.4W=1.4x0.66kPax1.31m =

1.2104 kN/m

along shortest side

assume neglegible compression and neglegible shear transfer from roof diaphragm. Largest Side

Shortest Side

Maximum Shear = wfͼL/2 = Vf (kN)

5.70409125

3.909592

Maximum Bending Moment =wfͼL2/8 = Mf (kNͼm)

15.29409466

6.31399108

Largest Side Preliminary sizing made according to CSA SͲ16 2009, CISCͲIBBC 10th edition Try Section C310x31

Fy =

345 Mpa

Sx =

351000 mm3

Zx = Non applicable d =

mm3 305 mm

w =

7.2 mm

Cw =

29300000000 mm6

J =

152000 mm4

Fu =

450 Mpa

Ix =

53500000 mm4

Iy =

1590000 mm4

b =

74 mm

t =

12.7 mm

Check moment resistance Beam class bel/t=

2.913385827

ч 200 /sqrt(Fy)

Flange is class 1

h/w=(dͲ2t)/w=

38.83333333

ч 1100/sqrt(Fy)

Web is class 1 Overall, beam is class 1

L=9.14m>Lu hence we shall use Mr' My=SxͼFy=

121.095

kNͼm

Mu= w2ͼ(ѓ/L)ͼsqrt(EͼIyͼGͼJ+(ѓͼE/L)2ͼIyͼCw)

use w2=1

= 21.46398968

kNͼm

so Mr' = 19.31759072

kNͼm

> Mf hence OK for flexural resistance

81.13365

Check Shear Resistance h/w=

38.83333333

Vr =ɌͼAwͼFs = 0.9ͼ(dͼw)ͼ(0.66ͼFy)=

ч439ͼsqrt(Kv/Fy)= 54.61671826 450.02628

steel wont yield upon buckling

>Vf hence OK for shear resistance

Check Deflection Lateral allowed deflection according to Table D1 (CSA S16Ͳ2009) is L/300= ѐmax= 5ͼwfͼL4/(384ͼEͼI) =

17.12629281

26.8125

< allowed deflection therefore OK

Use C310x31 for Locker Room's largest side

128

Project Title:

UQAC Arena

DATE:

April 1st, 2013

Project Detail:

Side buildings

Design Detail:

Girts Design

VERIFIED BY:

Othmane Laraki Caroline Chan

Comments:

Mechanical room, Lockers room

CHECKED BY:

Randy Wang

Shortest Side Preliminary sizing made according to CSA SͲ16 2009, CISCͲIBBC 10th edition Try Section C180x22

Fy =

345 Mpa

Sx =

127000 mm3

Zx = Non applicable d =

mm3 178 mm

w =

10.6 mm

Cw =

3470000000 mm6

J =

110000 mm4

Fu =

450 Mpa

Ix =

568000 mm4

Iy =

11300000 mm4

b =

58 mm

t =

9.3 mm

Check moment resistance Beam class bel/t=

3.11827957

ч 200 /sqrt(Fy)

Flange is class 1

h/w=(dͲ2t)/w=

15.03773585

ч 1100/sqrt(Fy)

Web is class 1 Overall, beam is class 1

L=9.14m>Lu hence we shall use Mr' My=SxͼFy=

43.815

kNͼm

Mu= w2ͼ(ѓ/L)ͼsqrt(EͼIyͼGͼJ+(ѓͼE/L)2ͼIyͼCw) = 9.357060378 so Mr' = 8.42135434

use w2=1

kNͼm

> Mf hence OK for flexural resistance

29.35605

Check Shear Resistance h/w=

15.03773585

Vr =ɌͼAwͼFs = 0.9ͼ(dͼw)ͼ(0.66ͼFy)=

ч439ͼsqrt(Kv/Fy)= 54.61671826 386.661924

steel wont yield upon buckling

>Vf hence OK for shear resistance

Check Deflection Lateral allowed deflection according to Table D1 (CSA S16Ͳ2009) is L/300= ѐmax= 5ͼwfͼL4/(384ͼEͼI) =

12.14477093

16.15

< allowed deflection therefore OK

Use C180x22 for Locker Room's shortest side

129

Project Title:

UQAC Arena

DATE:

Project Detail:

Ice Rink Slab on grad

February 20th, 2012

Design Detail:

VERIFIED BY:

Comments:

CHECKED BY:

Randy Wang Caroline Chan

SECTION DETAILS Composition of the Slab:

INPUT

Reference/ Notes

Concrete Slab Modulus of Rupture MOR

Slab Thickness

130 [mm]

Width

1000 [mm]

Safety Factor

1.7

1.1

S.F. for Slab Thickne SFt

604*6.895

4165 [kPa]

Vehicle Weight

Contact Area

Load Factor

Capacity Reduction Fju

0.9

400 [MPa]

gning Floor Slabs on Grade

5148 [kg] 20.6*0.00645

2 0.13287 [m ]

Steel Reinforcement Yielding Strength

Cover

d_c

20 [mm]

Size of Rebar

d_b

11.3 [mm]

Number of Rebars n

CrossͲSectional AreaA

Use 10M Rebars

4 100 [mm2]

DESIGN (CALCULATIONS)

Reference/ Notes

Initial Applied Stress Fb

250*6.895

Designed Section MoSM

b*t^2/6/10^9

Applied Moment

SM*Fb

Allowable Stress

MOR/SFt

Required Section MoSM_req

Mf/Fr

Required Thickness t_req

SQRT(SM_req*10^9 =

Resulted Safety Fact SF_r

MOR/Fb

1724 [kPa]

Fig.29 Ͳ PCA Charts

0.002817 [m3] 4.86 [kNm] 3785.98 [kPa] 0.001282 [m3] 87.72 [mm] 2.4

Design Moment

Mf_d

Mf*a

Depth of Rebars

tͲd_cͲd_b

Required Steel Reinf As

Mf_d*10^6/(0.9*40 =

Spacing

1000/n

250 [mm]

Check Efficiency

eff_0

As/(A*n)

76%

9.71 [kNm] 99 [mm] 2

303.7 [mm ]

130

April 2nd, 2013

Project Title:

UQAC Arena

DATE:

Project Detail:

Foundations

Design Detail:

Spread footings design

VERIFIED BY:

Arnaud Dusser

CHECKED BY:

Caroline Chan

Comments:

Othmane Laraki

The spread footing system is designed for columns BͲ2, BͲ4, BͲ5, BͲ6, BͲ7, BͲ9 on the basis of the procedures and assumptions suggested by: Concrete Design Handbook by CAC, 3rd edition, 2006 (CSA A23.3Ͳ04) Canadian Foundation Engineering Manual, 4th Edition, Canadian geotechnical society, 2006 Handbook of Steel Construction, 10th Edition, CISCͲICCA The spread footing design relies on the most critical column (B2), which exhibits a loading of fc’ for footing = 35MPa

Pf = 1634 kN in compression

assuming concrete of normal density with maximum size of aggregate being 20mm

qall = 200kPa assume ɶ = 19 kN/m3 Let's first determine the footing plan dimensions Assuming a depth of 2.5m of the footing, and making an initial estimate of 600mm for the footing thickness, we have: qall, net = qallͲ (ɶc*hc + ɶs*hs) =

149.7736 kPa 10.90979986 m2

A > Pservice/qall, net=

Therefore, let's try a footing of size

3.5m by 3.5m 12.25 m2

Hence, A= We shall now determine the factored soil pressure: qf =

Pf/A =

133.3877551 kPa

The design of a base plate is to be considered, in order to transmit the total load by bearing on the concrete contact area alone. We shall now determine the design of the base plate From the guidelines provided by the tenth edition of the Handbook of Steel Construction, Largest of columns BͲ2, BͲ4, BͲ5, BͲ6, BͲ7, BͲ9 is a W310x79 section W310x79

22800 mm2

A= d=

PLATE

333 mm

313 mm

28.10 mm

18 mm

The bearing stress is : Br = 0.85ͼɌcͼfc'=

fc’= 35 Mpa Fy= 300 Mpa grade 350W steel

19.3375 MPa

Bearing area required is = Cf/Bearing Stress = 84499.0303813833 mm2 Let's try a 360mm square base plate B= 360mm

129600 mm2

C= 360mm

Actual bearing stress=

Cf / A=

12.60802469

kPa

m= (CͲ0.95d)/2= 21.825 n=(BͲ0.80b)/2= 54.8 Mf = 18931.20123 Mr= ɌͼZͼFy =

N.mm/mm width

0.9ͼ(t2/4)ͼ300 N.mm/mm width

MrшMf ў t=16.747mm Check deflection: t>m/5= 4.365

therefore OK

t>n/5= 10.96

therefore OK Hence the base plate is of dimensions:

360mmx360mmx16.75mm

131

April 2nd, 2013

Project Title:

UQAC Arena

DATE:

Project Detail:

Foundations

Design Detail:

Spread footings design

VERIFIED BY:

Arnaud Dusser

CHECKED BY:

Caroline Chan

Comments:

Othmane Laraki

Now, we shall determine the required footing thickness based on the twoͲway shear requirements Based on the procedures specified by CSA A23.1, the following holds true Vf, 2Ͳway у Pf =

1634 kN (factored shear force)

Vc=vcͼb0ͼd=

1461.271706 ͼb0ͼd kN (factored shear resistance) vc,1 = (1+2/ɴc)ͼ0.19ͼʄͼɌcͼsqrt(fc’) = 2.19190756

Mpa

ɲ=4.0

for an interior column

vc,2 = (ɲͼd/b0+0.19)ͼʄͼɌcͼsqrt(fc’) = 2.701527564

Mpa

ɴc=(b2/b1)=

vc,3 = (0.38)ͼʄͼɌcͼsqrt(fc’) = 1.461271706

Mpa

d=effective depth= 0.3785m b0=perimeter of critical section = ʄ=1

Vc=Vf ў vcͼb0ͼd=Vc=Vf ў

b0ͼd = 1.11820409087158

2.954m

(normal density concrete)

The column transmits its total loading to the footings through a base plate of size BxC

with B= 360

for a square column,

and C= 360

b0ͼd= 4(t+d)ͼd ў

Vc/Vf=4ͼd2+4ͼdͼt

with t=thickness of column=width of footing

Therefore, d=

0.3785 m

Consequently, b0=4*(t+d)=

2.954 m

we shall now verify that

vc,3 < vc,2 and vc,3<vc,1 vc,3 Ͳ vc,2 =

Ͳ1.240255858

Hence ok

vc,3 Ͳ vc,1 =

Ͳ0.730635853

Hence ok

We shall now determine the footing thickness, h, assuming 25MͲbars h> d+cover+25mm+25/2mm=

491

hence thickness h=

490 mm

from cl. 13.3.4.1, if d>300mm from the 2Ͳway shear calculations, the value of vc obtained shall be multiplied by 1300/(1000+d) Furthermore, as we use a base plate and a pedestal, the size effect factor from cl. 13.4.4.4 need not apply.

The pedestal shall have a cleareance of 25mm in each direction. Hence, the dimensions of the pedestal shall be:

385mmx385mm

It should further exhibit a 50mm clearance at each end and in every direction, with respect to the ties and dowels used for its reinforcement. The pedestal is assumed to exhibit the same concrete compressive strength as the footing, ie. fc’= 30Mpa

Final Check for twoͲway shear requirements Vr = vcͼb0ͼd =

2123.177744 kN

Vf,2Ͳway = qfͼ(Footing areaͲ(t+d)2) =

kN 1556.243976

hence the footing design complies with twoͲway shear requirements

Vr > Vf,2Ͳway

132

April 2nd, 2013

Project Title:

UQAC Arena

DATE:

Project Detail:

Foundations

Design Detail:

Spread footings design

VERIFIED BY:

Arnaud Dusser

CHECKED BY:

Caroline Chan

Comments:

Othmane Laraki

We shall now check the oneͲway shear resistance of the footing The critical section for one way shear is taken at a distance d from the face of the column (hence of the base plate) The factored shear force for oneͲway shear is determined from the equilibrium of the freeͲbody diagram of an overhang on oneͲside of the critical section Vf, 1Ͳway = qfͼbwͼ[((LͲt)/2)Ͳd] =

550.4245714 kN

Vc=ʄͼɌcͼɴͼsqrt(fc’)ͼbwͼdv=

1091.738544 kN

With ʄ=

1 (normal density concrete)

bw=footing width= dv=shear depth= ɴ= 230/ (1000+dv)= Vc>Vf

3.5 m 0.3528 m 0.229918885 since maximum aggregate size is 20mm

Hence, no shear reinforcement is needed

We shall use a footing of size 3.5m x 3.5m, thickness h=510mm, effective depth d=398mm, and a base plate of dimensions 360mm x 360mm.

Flexural Design we shall use the lower of the two effective depths: Using 75mm reinforcement,

d = 377.5

d = 0.3528 m mm

Distance from point of zero shear to the column face is =

1.5575 m

Mf=qfͼ0.5ͼfooting widthͼ(Distance from point of zero shear to column face)2=

566.2524875 kN.m

Mr = ɌsͼAsͼfyͼ(dͲ0.5a) with a= (ɌsͼAsͼfy) /( ɲ1ͼ Ɍcͼfc’ͼb) ў Mr = Ɍs*As*fy*(dͲ(Ɍs*As*fy) /( 2*ɲ1* Ɍc*fc’*b)) As > [ͲB + sqrt(B2Ͳ4ͼAͼC)]/(2ͼA)

with

0.907378336

Ͳ128690

566252487.5

As >

4545.831729 mm2

Take As=

4500 mm2

Check minimum reinforcement requirement As,min=0.002ͼAs =

3430 mm2< As therefore OK

a= (ɌsͼAsͼfy) /( ɲ1ͼɌcͼfc’ͼb) = 24.0188383 Mr = ɌsͼAsͼfyͼ(dͲ0.5a)= 560.7305887

mm kNͼm > Mf therefore OK for flexural resistance

We will therefore use 9 bars of 25.2mm diameter in each direction

Check minimum spacing requirement Smax =

500 mm

The footing is of width :

3500 mm

Assuming 100mm end spacing, s=

412.5 mm < Smax, therefore OK

133

April 2nd, 2013

Project Title:

UQAC Arena

DATE:

Project Detail:

Foundations

Design Detail:

Spread footings design

VERIFIED BY:

Arnaud Dusser

CHECKED BY:

Caroline Chan

Comments:

Othmane Laraki

Check development for the flexural reinforcement The clear spacing between the bars is: 2ͼdbarͲspacing=

412.5 mm

Ͳ362.1 <0

hence ld= 0.45ͼk1ͼk2ͼk3ͼk4ͼfyͼdbar/sqrt(fc') = ld provided is =

766.7239399 mm

1457.5 mm which is bigger than

766.7239399 mm

therefore, it is OK

While referring to cl. 2.2 (CSA A23.3), and since h/b=(2.5Ͳ0.6)/3.5 < 3, the member can be qualified as a pedestal (in which case reinforcement is not required in the footing) However, according to the CSA requirements for column design, it is good practice to provide longitudinal reinforcement (minimum 4Ͳ15M corner bars) and ties (10M ties). The total load is transmitted by bearing on the concrete area alone. The design bearing strength of the footing is Br = sqrt (A2/A1)ͼ0.85ͼfc’ͼA1 =

7711.2 kN > Pf

with A1=base plate area, and A2=supporting area=4ͼA1

Hence, no need to provide additional bearing strength by providing dowels. CSA still requires us to provide at least minimum dowels (cl. 15.9.2.1)

648 mm2

Minimum dowels area : Ad,min= We shall use 4Ͳ20M bars as dowels (of diameter 19.5mm) Ldb,dowels= L1 provided is =

343.2 mm 376 mm > Ldb, dowels assume the pedestal has 4Ͳ35M compression bars We shall provide distance L2 such that 35M bars develop yield stress in compression L2 = max (0.073ͼ400ͼdb ; 300 ; ldb, dowels)=

1022 mm

We shall therefore use L2=1000mm Assume we use 10M ties with a maximum spacing of : Smax= 542.4mm We shall also check bearing strength of the pedestal Br=0.85ͼɌcͼfc’ͼAc + AdͼɌsͼfy=

2762.829375 kN > Pf

134

April 2nd, 2013

Project Title:

UQAC Arena

DATE:

Project Detail:

Foundations

Design Detail:

Spread footings design

VERIFIED BY:

Arnaud Dusser

CHECKED BY:

Caroline Chan

Comments:

Othmane Laraki

135

Project Title: UQAC Arena

DATE:

February 20th, 2012

Project Detail: Buildings 2 and 3

Design Detail: Foundation Design

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Caroline Chan

Comments:

Arnaud Dusser

Base plate design: f'c= Bearing Stress =

MPa

19.338

MPa

350 W Grade Bearing Plate: Fy = Factored Bearing Reaction =

350 486.49

MPa kN

25157.85

mm2

d =

162

b =

154

B =

200

C =

200

Try plate of 200x200: A =

40000

mm2

Actual Bearing Stress =

12.162

MPa

m =

23.05

n =

38.40

Mf =

8966.98

Mr =

78.75

therefore t =

10.67

Bearing Area Required = W150x37

Solve for Cantilever Lengths:

use t =

Nmm/mm width

check deflections: t > m/5 =

4.61

t >n/5 =

7.68

use 200x200x12mm base plate Joist Base plate: f'c=

MPa

19.3

MPa

Fy =

350

MPa

Factored Bearing Reaction =

48.7

Bearing Stress = 350 W Grade Bearing Plate:

Bearing Area Required =

2519.9

kN mm2

Wall Width =

400

Useable Wall Width =

375

assume 100 mm wide joists try 125x100: 125 100 A = assume k = Bending length n = Mf = t= use t = Check Deflection: t >

12500

mm2

42.5 17464.2 14.9

mm Nmm/mm width mm

12.5

use 125x100x16mm base plate

136

Project Title: UQAC Arena

DATE:

February 20th, 2012

Project Detail: Buildings 2 and 3

Design Detail: Foundation Design

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Caroline Chan

Comments:

Arnaud Dusser

Basement Wall Design: dimensions: 1 =

400

2 =

4450

3 =

300

4 =

300

5 =

450

6 =

1000

7 =

450

Wall Height = 8 =

4000

concrete density =

2400

kg/m3

fc' =

MPa

Fy =

400

MPa

Height of Wall =

Live load Surcharge =

Soil Density =

1900

Angle of Internal Friction, ɲ =

Base Friction Coefficient =

m kN/m

kg/m3

5 6

0.45

Allowable Soil Pressure =

200

Ca =

MPa

0.333

Uniform Pressure Caused by Surcharge =

Horizontal Pressure Caused by Surcharge =

kN/m2 kN/m of wall

Maximum Lateral Pressure due to Retained Soil =

24.85

kN/m2

Horizontal Force, P2, Caused by Retained Soil =

49.70

kN/m of wall

ɲ1 =

0.798

>0.67

ɴ1 =

0.883

>0.67

Factored Moment at Base of Wall: Mf = w l2/8 =

197.11

kN.m

Assume amount of Steel such as c/d = a/ (ɴ1 d) =

0.330

b =

1000

Assuming Mr = Mf : d =

200.78

Vf =

246.39

d =

320.37

Total thickness required = d + cover + bars =

380.37

400

Consider Pin Support at Top and Fixed at Bottom:

Shear strength: Setting Vr = Vf :

Choose Thickness =

137

Project Title: UQAC Arena

DATE:

February 20th, 2012

Project Detail: Buildings 2 and 3

Design Detail: Foundation Design

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Caroline Chan

Comments:

Arnaud Dusser

Overturning: Forces:

Arm (m)

Moment (kN.m)

W1 =

41.91

0.500

20.95

W2 =

10.59

0.500

5.30

W3 =

24.88

0.850

21.15

W4 =

2.52

0.150

0.38

Surcharge =

3.60

0.850

3.06

Soil Pressure on Top Height (Surcharge) =

71.20

2.675

190.46

Soil Pressure on Top Height (Soil) =

110.59

1.933

213.81

Resistance of Top Floor (No Surchage) =

82.94

4.900

406.42

Resistance of Top Floor (Full Surchage) =

109.64

4.900

537.25

Passive Pressure Resistance:

22.65

0.300

6.79

Distance from Toe to Resultant Vertical Forces on Brace: No Surcharge:

0.642

Surcharge beyond point:

0.541

Full Surcharge:

0.427

OK all in middle tier Safety against overturning: No Surcharge: SF =

3.192

> 2

Surcharge beyond point: SF =

2.564

> 2

Full Surcharge: SF =

2.483

> 2

With Full surcharge, the direct pressure is :

83.50

kN/m2

Moment about center of footing :

6.10

pressure from moment =

36.57

kN/m2

Maximum soil pressure =

120.08

kN/m2

Maximum Soil Pressure:

< 200 MPa max soil pressure

Safety against sliding: Ę&#x2026; =

0.450

Frictional resistance =

35.96

Passive earth pressure =

22.65

Support resistance =

82.94

Total sliding resistance =

141.55

SF =

0.78

Design of reinforcement: Solving for As, (quadratic): a =

Í˛1

b =

400

c =

21630143.29

As =

4455.12

mm2

a =

81.20

mm2

therefore, Mr =

423.77

kN.m

Min As =

800

mm2

Smax =

600

mm2

138

Project Title: UQAC Arena

DATE:

February 20th, 2012

Project Detail: Buildings 2 and 3

Design Detail: Foundation Design

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Caroline Chan

Comments: Use No. 25 @ 250 mm (As =

2000

mm2/m)

36.45

Arnaud Dusser

Check Capacity : a = c/d =

0.124

< 0.636

Mr =

205.46

kN.m

d =

392.5

As,min =

900

mm2

Use No 25 @ 350 Ͳ> As =

1250

mm2/m

Reinforcement in heel:

Since d> 300 mm Check Vr =

260.14

> Vf

Bearing Wall: Pr = 2/3 ɲ1 ʔc f'c Ag (1Ͳ(k hn/(32 t))2) =

4535.78

Column:

Br = 0.85 ʔc f'c Ab =

773.50

Joists:

Br = 0.85 ʔc f'c Ab =

290.06

139

Project Title: UQAC Arena

DATE:

February 20th, 2012

Project Detail: Buildings 2 and 3

Design Detail: Foundation Design

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Caroline Chan

Comments:

Arnaud Dusser

Retaining Wall Design (No support): Dimensions:

1 =

600

2 =

4450

3 =

3700

4 =

1000

5 =

500

6 =

5300

7 =

450

Wall Height = 8 =

4000

Concrete Density =

2400

kg/m3

fc' =

MPa

Fy =

400

MPa

height of wall = Live load surcharge = Soil Density = angle of internal friction, ɲ =

m 2

kN/m

1900

kN/m2

base friction coefficient =

allowable soil pressure =

200

Ca =

3 5 6

o MPa

0.333 kN/m2

Uniform pressure caused by surcharge =

4.0

horizontal pressure caused by surcharge =

16.0

kN/m of wall

maximum lateral pressure due to retained soil =

24.9

kN/m2

horizontal force, P2, caused by retained soil =

49.7

kN/m of wall

ɲ1 =

0.798

>0.67

ɴ1 =

0.883

>0.67

factored moment at base of wall: Mf = w*l^2/8 =

788.4

kN.m

assume amount of steel such as c/d = a/ (ɴ1*d) =

0.330

b =

1000

assuming Mr=Mf: d=

401.6

Vf =

394.2

d =

512.6

Total thickness required = d + cover + bars =

572.6

choose thickness =

600.0

consider pin support at top and fixed at bottom:

Shear strength: Setting Vr=Vf:

140

Project Title: UQAC Arena

DATE:

February 20th, 2012

Project Detail: Buildings 2 and 3

Design Detail: Foundation Design

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Caroline Chan

Comments:

Arnaud Dusser

Overturning: Forces:

arm (m)

W1 =

62.862

1.300

81.721

W2 =

62.392

2.650

165.338

W3 =

306.891

3.450

1058.774

W4 =

8.388

0.500

4.194

Surcharge =

44.4

3.450

153.180

Soil Pressure on Top Height (Surcharge) =

Moment (kN.m)

71.2

2.725

194.020

Soil Pressure on Top Height (Soil) =

110.591

1.983

219.340

Passive Pressure Resistance:

25.233

0.317

7.990

Distance from toe to resultant vertical forces on brace: No Surcharge:

2.494

Surcharge beyond point:

2.054

Full Surcharge:

2.181

OK all in middle tier Safety against overturning: No Surcharge: SF =

4.973

> 2

Surcharge beyond point: SF =

2.169

> 2

Full Surcharge: SF =

2.540

> 2

With Full surcharge, the direct pressure is :

91.497

kN/m2

Moment about center of footing :

227.234

pressure from moment =

48.537

kN/m2

Maximum soil pressure =

140.034

kN/m2

Maximum Soil Pressure:

< 200 MPa max soil pressure

Safety against sliding: Ę&#x2026; =

0.450

Frictional resistance =

198.240

Passive earth pressure =

25.233

Total sliding resistance =

223.472

SF =

1.229

Design of reinforcement: Solving for As, (quadratic): a =

Í˛1.000

b =

600.000

c =

86520573.176

As =

9006.480

mm2

a =

164.149

mm2

therefore, Mr =

1318.310

kN.m

Min As =

800.000

mm2

Smax =

600.000

mm2

Use No. 25 @ 250 mm at base of wall (As =

2000.000

mm2/m)

Stem at Base:

Check Capacity : a =

36.451

141

Project Title: UQAC Arena

DATE:

February 20th, 2012

Project Detail: Buildings 2 and 3

Design Detail: Foundation Design

VERIFIED BY:

Othmane Laraki

CHECKED BY:

Caroline Chan

Comments: c/d =

0.077

< 0.636

Mr =

336.164

kN.m

Use No. 25 @ 500 mm at base of wall (As =

1000.000

mm2/m)

Arnaud Dusser

Stem at Top:

Check Capacity : a =

18.226

c/d =

0.039

< 0.636

Mr =

171.180

kN.m

ld =

760.639

300.000

d =

442.500

As,min =

1000.000

mm2

Use No 25 @ 350 Ͳ> As =

1250.000

mm2/m

283.111

Bar cutͲoffs:

from Cl. 12.10.4: steel must be carried at least 12 db = Reinforcement in heel:

Since d> 300 mm Check Vr =

> Vf

Reinforcement in toe: Use No 25 bars @ 350 mm spacing Shear OK

142

Project Title:

UQAC Arena

DATE:

Project Detail:

February 27th, 2013

Design Detail:

Locker Room Roof Design

VERIFIED BY:

Comments:

Designed with CANAM steel decks and open web joists.

CHECKED BY:

Randy Wang

Design Summary: Ref:

Steel Deck:

CANAM Steel Deck

PͲ3606 Type 18 Ͳ Triple Span

Joist :

Ref:

Open Web Steel Joist

Code of Standard Practice* Cl.6.1

KCSͲ Series: 28KCS3

*Note: American codes and standards for steel joist design are referred and applied to account for special loading cases ( nonͲuniformly distributed snow loads)

Beam: West Side

W460x177

East Side

W530x123

Loading Condition:

Loading Conditions Dead Load Live Load Snow Load

Factored Load

for joist:

w_Di = w_L =

1.67

kPa

4.8

kPa

w_S = w_Smin =

10.53

kPa

5.37

kPa

W_S = =

(w_SͲw_Smin)*1.5*sp/2*s_j/1000

w_fi = =

(w_Di*1.25+w_Smin*1.5+w_L*0.5)*s_j/1000

w_fji = =

(w_Di*1.2+w_Smin*1.6)*s_j/1000

W_Sj = =

(w_SͲw_Smin)*1.6*sp*s_j/1000/2

x_max = Mf_ji =

25000.2

12.5425 10.596

kN/m kN/m

26666.88

3.38

w_fji*x_max/2*(sp/1000Ͳx_max) +W_Sj/1000*x_max/3*(1Ͳx_max^2/(sp/1000)^2) 76.97398191 kNm

Vf_ji =

(w_fji*sp/2+2*W_S/3)/1000 50.89188

Steel Deck Design Thickness

t_sd = d_sd =

1.217 37.8

13.26

kg/m2

Section Modulus

wt_sd = M+ =

15813

mm3

15994

mm3

Moment of Inertia

MͲ = I_sd =

363493

mm4

Span per Deck

l_sd =

1000

Overall Depth Weight

143

Project Title:

UQAC Arena

DATE:

Project Detail:

Resistance for Factored Load

Design Detail:

Locker Room Roof Design

Comments:

Designed with CANAM steel decks and open web joists.

February 27th, 2013 Randy Wang

VERIFIED BY:

Resistance for Service Load

wr_sd = wur_sd =

21.59

kPa

25.8

kPa

Shape Designation

Desj =

Spacing

s_j =

1000

Span

sp =

6460

Design Length

dl = =

Load Capacity:

Mr_j = =

1269*0.11298

Vr_j = =

12000*0.004482

CHECKED BY:

Joist 28KCS3

spͲ102 6358 143.37162 53.784

mm kN/m kN/m

Depth

d_j = =

28*25.4

SelfͲweight

w_j = =

12.5*1.488*9.81/1000

711.2 0.182466

mm kN/m

Beam Suggested Depth Limitation

d_lim = =

d_jͲ100 611.2

Shape Designation

Des1 =

SelfͲweight

w_b = =

Type of Shape

shape = ls =

rolled

Lo = Lu =

10725

1000

Type of Lateral Support Overall Length Laterally Unsupported Length Boundary Condition at

W460x177 150*9.81/1000/(sp/1000) 0.227786378 kPa sup

Web Stiffener

ends = ws =

none

Web Stiffener Distance

a_w =

7300

Shape of Moment Distribution

moment = load =

Bending About XͲAxis Loading Applied Relative to Shear Centre Linear Distributed Mom, Max Linear Distributed Mom, Min

Mfmax = Mfmin =

Maximum shear load

Vspec =

Max. Moment about YͲaxis

Mfmay =

linear top 1199.969679 kNm 0

kNm

445.5053428 kN Bending about YͲAxis 0

KNm

Section Properties Yield Strength Elastic Modulus of Steel Shear Modulus of Steel Resistance Factor Resis. Factor Interior Bearing Resist. Factor Bearing End

Fy = E= Gs = ˇ= ˇi = ˇe =

Member designation = Area Radius of gyration about X Radius of gyration about Y Elastic section modulus about the XͲAxis

A= rx = ry = Sx =

350

Mpa

200000

Mpa

77000

Mpa

0.9 0.8 0.75 W460x177 22600

mm2

201

68.2

3780000

mm3

144

Project Title:

UQAC Arena

DATE:

Project Detail: Design Detail: Comments: Elastic section modulus about the YͲAxis Plastic section modulus about the XͲAxis Plastic section modulus about the YͲAxis St.Venant torsion constant Warping torsional constant

Zy = J=

735000

mm3

4280000

mm3

1130000

mm3

4410000

mm4

Cw = tw =

5.44E+12

mm6

16.6

tf = d=

26.9

482

286

Moment of inertia about X

bb = Ix =

910000000

mm4

Moment of inertia about Y

Iy =

105000000

mm4

Adjusted Dead Load

w_D = =

Adjusted Total Load

w_f = =

(w_D*1.25+w_Smin*1.5+w_L*0.5)*s_j/1000

for joists:

w_fj = =

(w_D*1.2+w_Smin*1.6)*s_j/1000

for deck:

w_sd = =

Web thickness Flange thickness Depth Width

Randy Wang

VERIFIED BY:

Designed with CANAM steel decks and open web joists. Sy = Zx =

February 27th, 2013

CHECKED BY:

Check Steel Deck

Check Capacity

w_DiͲ0.19Ͳ0.15+wt_sd*9.81/1000+w_j/s_j*1000+w_b 1.870332978 kPa 12.79291622 kN/m 10.83639957 kN/m 1.25*w_D+1.5*w_S+0.5*w_L 20.53291622 IF(wr_sd>w_sd, "OK", "FAIL")

= Efficiency

eff_sd = =

Check Deflection

OK w_sd/wr_sd 0.951038269 IF(wur_sd>w_L, "OK", "FAIL")

OK Check Joist Design

Adjusted Factored Loads

Mf_j = =

w_fj*x_max/2*(sp/1000Ͳx_max) +W_Sj/1000*x_max/3*(1Ͳx_max^2/(sp/1000)^2)

Vf_j = =

(w_fj*sp/2+2*W_S/3)/1000

Check Moment Capacity Efficiency

78.22530977 kNm 51.66837062 kN IF(Mf_j<Mr_j, "OK", "FAIL")

eff_j0 = =

Mf_j/Mr_j

Check Shear Capacity

0.545612233 IF(Vf_j<Vr_j, "OK", "FAIL")

= Efficiency

eff_j1 = =

Check Spacing

OK Vf_j/Vr_j 0.960664336 IF(s_j>152,"OK","FAIL")

= Check Span

OK IF(sp<24*d_j, "OK", "FAIL")

OK Check Beams Design

Adjusted Factored Loads

Mf_0 = =

w_f*x_max/2*(sp/1000Ͳx_max) +W_S/1000*x_max/3*(1Ͳx_max^2/(sp/1000)^2)

(loading case for beam desing)

Vf_0 = =

(w_f*sp/2+2*W_S/3)/1000

Applied Loads

P= =

Number of Joist Supported

Nj = =

Total Applied Forces

P_t = =

P*(Lo/s_j)

where reaction:

R_y = =

P_t/2

87.04564006 kNm 57.9879194

Vf_0+25.09 83.0779194

roundup( Lo/s_j, 0) 11 891.0106855 kN 445.5053428 kN

145

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Locker Room Roof Design

VERIFIED BY:

Comments:

Designed with CANAM steel decks and open web joists.

CHECKED BY:

Spacing (end load and support)

s_end = =

(Lo Ͳ(NjͲ1)*s_j )/2

Spacing (quarter pt and pt load)

s_qt = =

Lo/4Ͳs_endͲs_j*2

362.5 318.75

February 27th, 2013 Randy Wang

kN kN

Coefficient to account for Increase of Resistance if Moment Gradient exists Maximum Moment

Mmax = =

(R_y*s_end+P*s_j*(5/2+(1+4)*(4)/2))/1000

OneͲquarter Point

Ma = =

(R_y*Lo/4ͲP*((1+2)*2/2)*s_j+3*s_qt)/1000

Midpoint

Mb = =

(R_y*s_end+P*s_j*(5/2+(1+4)*(4)/2))/1000

ThreeͲquarter Point

Mc = =

(R_y*Lo/4ͲP*((1+2)*2/2)*s_j+3*s_qt)/1000

Max. Shear Load

Vf = =

w2 for Curved Bending Moment Distribution

w2_c = =

1199.969679 kNm 946.2336921 kNm 1199.969679 kNm 946.2336921 kNm R_y 445.5053428 kN 4*Mmax/sqrt(Mmax^2+4*Ma^2+7*Mb^2+4*Mc^2) 1.110491619 For linear bending moment distribution

Moment ratio for w2_l

kp = =

Mfmin/Mfmax

Equivalent moment factor

w2_l = =

1.75+1.05*kp+0.3*kp^2

which w2?

w2_b = =

if(moment="linear",w2_l,w2_c)

Set w2 limit to 2.5

w2c = =

0 1.75

1.75 if(w2_b>2.5,2.5,w2_b) 1.75

Considering Location of Application of Loads and Effect on w2 for laterally unsupported case Resulting coefficient

w2 = =

if(load="top",1.0,w2c) 1

Considering Beam End Conditions and Effect on Lu for laterally unsupported case Effective Length

Le = =

Resulting Length

L= =

if(ends="pin",Lu*1.2,Lu*1.4) 1200

if(load="top",Le,Lu) 1200

Local Buckling Width to Thickness Ratio

d_t = =

(bb/2)/tf

Check

chk0 = =

if(d_t<200/sqrt(Fy),"OK","NOT OK")

Efficiency

eff0 = =

d_t/(200/sqrt(Fy))

5.31598513 OK 0.497264876 Check Section Class

Flange b/t

fl = =

(bb/2)/tf

Class 1:

c1 = =

145 / (Fy)^0.5

Class 2:

c2 = =

170 / (Fy)^ 0.5

Class 3:

c3 = =

200 / (Fy)^0.5

Flange is Class:

class_F = =

5.31598513 7.750576015 9.086882225 10.69044968 if(fl<=c1,1,if(fl<=c2,2,if(fl<=c3,3,4))) 1

146

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Locker Room Roof Design

VERIFIED BY:

Comments:

Designed with CANAM steel decks and open web joists.

CHECKED BY:

February 27th, 2013 Randy Wang

Web h/w

wl = =

(d Ͳ 2*tf) / tw

Class 1:

C1 = =

1100 / (Fy)^ 0.5

Class 2:

C2 = =

1700 / (Fy)^ 0.5

Class 3:

C3 = =

1900 / (Fy) ^0.5

Web is Class:

class_W = =

Section is Class:

class = =

25.79518072 58.79747322 90.86882225 101.5592719 if(wl<=C1,1,if(wl<=C2,2,if(wl<=C3,3,4))) 1 MAX(class_F,class_W) 1 Shear in YͲdirection for Unstiffened Webs

Web height

hw = =

dͲ2*tf

Cross section rolled shapes

Awr = =

d*tw

Cross section welded shapes

Aww = =

Cross section

Aw = =

if(shape="rolled",Awr,Aww)

Stress limit (i)

Fsai = =

0.66*Fy

Stress limit (ii)

Fsaii = =

670*sqrt(Fy)/(hw/tw)

Stress limit (iii)

Fsaiii = =

961200/(hw/tw)^2

For slr < = 1014/sqrt(Fy)

Vrai = =

ˇ*Aw*Fsai/1000

For 1014/sqrt(Fy) < slr < 1435/sqrt(Fy)

Vraii = =

ˇ*Aw*Fsaii/1000

For slr > 1435/sqrt(Fy)

Vraiii = =

ˇ*Aw*Fsaiii/1000

Vraiv = =

if((hw/tw)/sqrt(Fy)>1014,Vraii,Vrai)

Shear Resistance

V_ar = =

if((hw/tw)/sqrt(Fy)>1435,Vraiii,Vraiv)

Check

chk1 = =

if(ws="stif","NA",if(V_ar>Vf,"OK","NOT OK"))

Efficiency

eff1 = =

Vf/V_ar

428.2

8001.2

mm2

hw*tw 7108.12 8001.2 231

mm2 mm2 Mpa

485.9261263 Mpa 1444.563417 Mpa 1663.44948 3499.19291

kN kN

10402.41673 kN 1663.44948 1663.44948

kN kN

OK 0.267820182 Shear in YͲdirection for stiffened webs

Critical Stress

Fcri = =

290*sqrt(Fy*kv)/(hw/tw)

Euler Stress

Fcre = =

180000*kv/(hw/tw)^2

Stress Limit (i)

Fsbi = =

0.66*Fy

Stress Limit (ii)

Fsbii = =

Fcri

Stress Limit (iii)

Fsbiii = =

Fcri+ka*(0.5*FyͲ0.866*Fcri)

Stress Limit (iii)

Fsbiv = =

Fcre+ka*(0.5*FyͲ0.866*Fcre)

Aspect Ratio of Stiffened Web Surface

a_h = =

486.6570386 Mpa 1448.286502 Mpa 231

Mpa

486.6570386 Mpa 472.225988

Mpa

1385.090971 Mpa a_w/hw 17.04810836

147

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Locker Room Roof Design

VERIFIED BY:

Comments:

Designed with CANAM steel decks and open web joists.

CHECKED BY:

Shear Buckling Coefficient

kv1 = =

4+5.34/(a_h)^2

Shear Buckling Coefficient

kv2 = =

5.34+4/(a_h)^2

Resulting shear buckling coefficient

kv = =

Parameter

kvFy = =

Aspect Coefficient

ka = =

slr < = 439/sqrt(kv/Fy)

Vrbi = =

ˇ*Aw*Fsbi/1000

For 439/sqrt(kv/Fy) < slr < 502/sqrt(kv/Fy)

Vrbii = =

ˇ*Aw*Fsbii/1000

For 502/sqrt(kv/Fy) < slr < 621/sqrt(kv/Fy)

Vrbiii = =

ˇ*Aw*Fsbiii/1000

For 621/sqrt(kv/Fy) < slr

Vrbiv = =

ˇ*Aw*Fsbiv/1000

Vrbv = =

if((hw/tw)>439/kvFy,Vrbii,Vrbi)

Vrbvi = =

if((hw/tw)>502/kvFy,Vrbiii,Vrbv)

Shear Resistance

Vbr = =

if((hw/tw)>621/kvFy,Vrbv,Vrbvi)

Check

chk7 = =

if(ws="none","NA",if(Vbr>Vf,"OK","NOT OK"))

Efficiency

eff7 = =

Vf/Vbr

February 27th, 2013 Randy Wang

4.018373372 5.353762825 if(a_h<1,kv1,kv2) 5.353762825 sqrt(kv/Fy) 0.123678879 1/(sqrt(1+(a_h)^2)) 0.058556882 1663.44948

3504.456268 kN 3400.537118 kN 9974.150891 kN 1663.44948 1663.44948 1663.44948

kN kN kN

NA 0.267820182 Laterally supported

Yielding reaching Mp

Mp = =

Zx*Fy/1000^2

Yielding reaching My

My = =

Sx*Fy/1000^2

Resulting moment, supported

Mrs = =

IF(class<3,ˇ*Mp,ˇ*My)

Check

chk6 = =

if(ls="uns","NA",if(Mrs>Mfm,"OK","NOT OK"))

Efficiency

eff6 = =

Mfm/Mrs

1498 1323 1348.2

kNm kNm kNm

OK 0.890053167

Laterally unsupported, for doubly symmetric Class 1 and 2 sections Elastic lateralͲtorsional buckling

Mu = =

(w2*pi()/L)*sqrt(E*Iy*Gs*J+((pi()*E/L)^2)*Iy*Cw)/1000^2 33498.93687 kNm when Mu > 0.67 Mp (intermediate)

(a)(i)

Mra_i = =

1.15*ˇ*Mp*(1Ͳ(0.28*Mp/Mu))

Limit resistance to yielding

Mrai = =

if(Mra_i>(ˇ*Mp),ˇ*Mp,Mra_i)

1531.017075 kNm 1348.2

kNm

when Mu <= 0.67 Mp (slender) (a)(ii)

Mra_ii = =

Limit resistance to yielding

Mraii = =

Intermediate or slender beam?

type_a = = Mr12 = =

ˇ*Mu 30149.04318 kNm if(Mra_ii>(ˇ*Mp),ˇ*Mp,Mra_ii) 1348.2

kNm

if(Mu>0.67*Mp,"inter","slender") inter if(type_a="inter",Mrai,Mraii) 1348.2

kNm

148

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Locker Room Roof Design

VERIFIED BY:

Comments:

Designed with CANAM steel decks and open web joists.

CHECKED BY:

February 27th, 2013 Randy Wang

Laterally unsupported, for doubly symmetric Class 3 when Mu > 0.67 My (intermediate) (a)(i)

Mrb_i = =

1.15*ˇ*My*(1Ͳ(0.28*My/Mu))

Limit resistance to yielding

Mrbi = =

if(Mrb_i>(ˇ*My),ˇ*My,Mra_i)

1354.162867 kNm 1190.7

kNm

when Mu <= 0.67 My (slender) (a)(ii)

Mrb_ii = =

Limit resistance to yielding

Mrbii = =

Intermediate or slender beam?

type_b = =

Resulting resistance, unsupported

ˇ*Mu 30149.04318 kNm if(Mrb_ii>(ˇ*My),ˇ*My,Mrb_ii) 1190.7

kNm

if(Mu>0.67*My,"inter","slender") inter

Mr3 = =

if(type_b="inter",Mrai,Mrbii)

Mrx = =

IF(class<3,Mr12,Mr3)

1348.2 1348.2

kNm kNm

Applied maximum factored moment

Mfm = =

if(moment="linear",Mfmax,Mmax)

Check

chk2 = =

if(ls="sup","NA",if(Mrx>Mfm,"OK","NOT OK"))

Efficiency

eff2 = =

Mfm/Mrx

1199.969679 kNm NA 0.890053167 Bending Resistance about YͲAxis

Bending resistance

Mry12 = =

ˇ*Zy*Fy/1000^2

Mry3 = =

ˇ*Sy*Fy/1000^2

355.95 231.525

kNm kNm

Mry = =

if(class<3,Mry12,Mry3)

Check

chk3 = =

if(Mry>Mfmay,"OK","NOT OK")

Efficiency

eff3 = =

Mfmay/Mry

355.95

kNm

OK 0 Biaxial Bending Resistance

Interaction sum

iS = =

Mfm/Mrx+Mfmay/Mry

Check

chk4 = =

if(iS<1.0,"OK","NOT OK")

Efficiency

eff4 = =

0.890053167 OK 0.890053167

Deflections for Simple Beam with Uniformly Distributed Loading Limit for floors under live load

ldelta = =

Lo/300

Specified live load deflection

delta1 = =

5*w_L*sp/1000*Lo^4/(384*E*Ix)

Deflection at centre

delta = =

5*w_D*sp/1000*Lo^4/(384*E*Ix)

Check

chk5 = =

if(ldelta>delta1,"OK","NOT OK")

Efficiency

eff5 = =

delta1/ldelta

35.75

29.35150339 mm 11.43689265 mm OK 0.821021074

149

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Locker Room Roof Design

VERIFIED BY:

Comments:

Designed with CANAM steel decks and open web joists.

CHECKED BY:

February 27th, 2013 Randy Wang

Webs Check Slenderness

chk8 = =

if(hw/tw<83000/Fy,"OK","NOT OK")

Efficiency

eff8 = =

(hw/tw)/(83000/Fy)

OK 0.108774858

Check Beams Design Adjusted Factored Loads

Mf_0 = =

w_f*x_max/2*(sp/1000Ͳx_max) +W_S/1000*x_max/3*(1Ͳx_max^2/(sp/1000)^2)

(loading case for beam desing)

Vf_0 = =

(w_f*sp/2+W_S/3)/1000

Applied Loads

P= =

Number of Joist Supported

Nj = =

Total Applied Forces

P_t = =

P*(Lo/s_j)

where reaction:

R_y = =

P_t/2

Spacing (end load and support)

s_end = =

(Lo Ͳ(NjͲ1)*s_j )/2

Spacing (quarter pt and pt load)

s_qt = =

Lo/4Ͳs_endͲs_j*2

87.76890099 kNm 50.1033269

Vf_0 50.1033269

roundup( Lo/s_j, 0) 11 537.358181

268.6790905 kN 362.5 318.75

kN kN

Coefficient to account for Increase of Resistance if Moment Gradient exists Maximum Moment

Mmax = =

(R_y*s_end+P*s_j*(5/2+(1+4)*(4)/2))/1000

OneͲquarter Point

Ma = =

(R_y*Lo/4ͲP*((1+2)*2/2)*s_j+3*s_qt)/1000

Midpoint

Mb = =

(R_y*s_end+P*s_j*(5/2+(1+4)*(4)/2))/1000

ThreeͲquarter Point

Mc = =

(R_y*Lo/4ͲP*((1+2)*2/2)*s_j+3*s_qt)/1000

Max. Shear Load

Vf = =

w2 for Curved Bending Moment Distribution

w2_c = =

723.6877565 kNm 571.0420807 kNm 723.6877565 kNm 571.0420807 kNm R_y 268.6790905 kN 4*Mmax/sqrt(Mmax^2+4*Ma^2+7*Mb^2+4*Mc^2) 1.110208456 For linear bending moment distribution

Moment ratio for w2_l

kp = =

Mfmin/Mfmax

Equivalent moment factor

w2_l = =

1.75+1.05*kp+0.3*kp^2

which w2?

w2_b = =

if(moment="linear",w2_l,w2_c)

Set w2 limit to 2.5

w2c = =

0 1.75

1.75 if(w2_b>2.5,2.5,w2_b) 1.75

Considering Location of Application of Loads and Effect on w2 for laterally unsupported case Resulting coefficient

w2 = =

if(load="top",1.0,w2c) 1

Considering Beam End Conditions and Effect on Lu for laterally unsupported case Effective Length

Le = =

Resulting Length

L= =

if(ends="pin",Lu*1.2,Lu*1.4) 1200

if(load="top",Le,Lu) 1200

150

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Locker Room Roof Design

VERIFIED BY:

Comments:

Designed with CANAM steel decks and open web joists.

CHECKED BY:

February 27th, 2013 Randy Wang

Local Buckling Width to Thickness Ratio

d_t = =

(bb/2)/tf

Check

chk0 = =

if(d_t<200/sqrt(Fy),"OK","NOT OK")

Efficiency

eff0 = =

d_t/(200/sqrt(Fy))

5 OK 0.467707173

Check Section Class Flange b/t

fl = =

(bb/2)/tf

Class 1:

c1 = =

145 / (Fy)^0.5

Class 2:

c2 = =

170 / (Fy)^ 0.5

Class 3:

c3 = =

200 / (Fy)^0.5

Flange is Class:

class_F = =

5 7.750576015 9.086882225 10.69044968 if(fl<=c1,1,if(fl<=c2,2,if(fl<=c3,3,4))) 1 Web

h/w

wl = =

(d Ͳ 2*tf) / tw

Class 1:

C1 = =

1100 / (Fy)^ 0.5

Class 2:

C2 = =

1700 / (Fy)^ 0.5

Class 3:

C3 = =

1900 / (Fy) ^0.5

Web is Class:

class_W = =

Section is Class:

class = =

38.29007634 58.79747322 90.86882225 101.5592719 if(wl<=C1,1,if(wl<=C2,2,if(wl<=C3,3,4))) 1 MAX(class_F,class_W) 1 Shear in YͲdirection for Unstiffened Webs

Web height

hw = =

dͲ2*tf

Cross section rolled shapes

Awr = =

d*tw

Cross section welded shapes

Aww = =

Cross section

Aw = =

if(shape="rolled",Awr,Aww)

Stress limit (i)

Fsai = =

0.66*Fy

Stress limit (ii)

Fsaii = =

670*sqrt(Fy)/(hw/tw)

Stress limit (iii)

Fsaiii = =

961200/(hw/tw)^2

For slr < = 1014/sqrt(Fy)

Vrai = =

ˇ*Aw*Fsai/1000

For 1014/sqrt(Fy) < slr < 1435/sqrt(Fy)

Vraii = =

ˇ*Aw*Fsaii/1000

For slr > 1435/sqrt(Fy)

Vraiii = =

ˇ*Aw*Fsaiii/1000

Vraiv = =

if((hw/tw)/sqrt(Fy)>1014,Vraii,Vrai)

Shear Resistance

V_ar = =

if((hw/tw)/sqrt(Fy)>1435,Vraiii,Vraiv)

Check

chk1 =

if(ws="stif","NA",if(V_ar>Vf,"OK","NOT OK"))

501.6

7126.4

mm2

hw*tw 6570.96 7126.4 231

mm2 mm2 Mpa

327.3577241 Mpa 655.6035519 Mpa 1481.57856

2099.593877 kN 4204.883837 kN 1481.57856 1481.57856

kN kN

151

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Locker Room Roof Design

VERIFIED BY:

Comments:

Designed with CANAM steel decks and open web joists.

CHECKED BY:

= Efficiency

eff1 = =

February 27th, 2013 Randy Wang

OK Vf/V_ar 0.181346503 Shear in YͲdirection for stiffened webs

Critical Stress

Fcri = =

290*sqrt(Fy*kv)/(hw/tw)

Euler Stress

Fcre = =

180000*kv/(hw/tw)^2

Stress Limit (i)

Fsbi = =

0.66*Fy

Stress Limit (ii)

Fsbii = =

Fcri

Stress Limit (iii)

Fsbiii = =

Fcri+ka*(0.5*FyͲ0.866*Fcri)

Stress Limit (iii)

Fsbiv = =

Fcre+ka*(0.5*FyͲ0.866*Fcre)

Aspect Ratio of Stiffened Web Surface

a_h = =

a_w/hw

Shear Buckling Coefficient

kv1 = =

4+5.34/(a_h)^2

Shear Buckling Coefficient

kv2 = =

5.34+4/(a_h)^2

Resulting shear buckling coefficient

kv = =

Parameter

kvFy = =

Aspect Coefficient

ka = =

slr < = 439/sqrt(kv/Fy)

Vrbi = =

ˇ*Aw*Fsbi/1000

For 439/sqrt(kv/Fy) < slr < 502/sqrt(kv/Fy)

Vrbii = =

ˇ*Aw*Fsbii/1000

For 502/sqrt(kv/Fy) < slr < 621/sqrt(kv/Fy)

Vrbiii = =

ˇ*Aw*Fsbiii/1000

For 621/sqrt(kv/Fy) < slr

Vrbiv = =

ˇ*Aw*Fsbiv/1000

Vrbv = =

if((hw/tw)>439/kvFy,Vrbii,Vrbi)

Vrbvi = =

if((hw/tw)>502/kvFy,Vrbiii,Vrbv)

Shear Resistance

Vbr = =

if((hw/tw)>621/kvFy,Vrbv,Vrbvi)

Check

chk7 = =

if(ws="none","NA",if(Vbr>Vf,"OK","NOT OK"))

Efficiency

eff7 = =

Vf/Vbr

328.0069367 Mpa 657.9221708 Mpa 231

Mpa

328.0069367 Mpa 320.531209

Mpa

630.8610584 Mpa 14.55342903 4.025212191 5.358885536 if(a_h<1,kv1,kv2) 5.358885536 sqrt(kv/Fy) 0.123738036 1/(sqrt(1+(a_h)^2)) 0.068550692 1481.57856 2103.75777

kN kN

2055.810247 kN 4046.191422 kN 1481.57856 1481.57856 1481.57856

kN kN kN

NA 0.181346503 Bending Resistance about XͲAxis Laterally supported

Yielding reaching Mp

Mp = =

Zx*Fy/1000^2

Yielding reaching My

My = =

Sx*Fy/1000^2

Resulting moment, supported

Mrs = =

IF(class<3,ˇ*Mp,ˇ*My)

Check

chk6 = =

if(ls="uns","NA",if(Mrs>Mfm,"OK","NOT OK"))

Efficiency

eff6 =

Mfm/Mrs

1123.5 980 1011.15

kNm kNm kNm

152

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Locker Room Roof Design

VERIFIED BY:

Comments:

Designed with CANAM steel decks and open web joists.

CHECKED BY:

February 27th, 2013 Randy Wang

0.715707617

Laterally unsupported, for doubly symmetric Class 1 and 2 sections Elastic lateralͲtorsional buckling

Mu = =

(w2*pi()/L)*sqrt(E*Iy*Gs*J+((pi()*E/L)^2)*Iy*Cw)/1000^2 12374.68494 kNm

when Mu > 0.67 Mp (intermediate) (a)(i)

Mra_i = =

1.15*ˇ*Mp*(1Ͳ(0.28*Mp/Mu))

Limit resistance to yielding

Mrai = =

if(Mra_i>(ˇ*Mp),ˇ*Mp,Mra_i)

1133.262095 kNm 1011.15

kNm

when Mu <= 0.67 Mp (slender) (a)(ii)

Mra_ii = =

Limit resistance to yielding

Mraii = =

Intermediate or slender beam?

type_a = = Mr12 = =

ˇ*Mu 11137.21644 kNm if(Mra_ii>(ˇ*Mp),ˇ*Mp,Mra_ii) 1011.15

kNm

if(Mu>0.67*Mp,"inter","slender") inter if(type_a="inter",Mrai,Mraii) 1011.15

kNm

Laterally unsupported, for doubly symmetric Class 3 when Mu > 0.67 My (intermediate) (a)(i)

Mrb_i = =

1.15*ˇ*My*(1Ͳ(0.28*My/Mu))

Limit resistance to yielding

Mrbi = =

if(Mrb_i>(ˇ*My),ˇ*My,Mra_i)

991.8086056 kNm 882

kNm

when Mu <= 0.67 My (slender) (a)(ii)

Mrb_ii = =

Limit resistance to yielding

Mrbii = =

Intermediate or slender beam?

type_b = =

ˇ*Mu 11137.21644 kNm if(Mrb_ii>(ˇ*My),ˇ*My,Mrb_ii) 882

kNm

if(Mu>0.67*My,"inter","slender") inter

Mr3 = =

if(type_b="inter",Mrai,Mrbii)

Resulting resistance, unsupported

Mrx = =

IF(class<3,Mr12,Mr3)

Applied maximum factored moment

Mfm = =

if(moment="linear",Mfmax,Mmax)

Check

chk2 = =

if(ls="sup","NA",if(Mrx>Mfm,"OK","NOT OK"))

Efficiency

eff2 = =

Mfm/Mrx

1011.15 1011.15

kNm kNm

723.6877565 kNm NA 0.715707617 Bending Resistance about YͲAxis

Bending resistance

Mry12 = =

ˇ*Zy*Fy/1000^2

Mry3 = =

ˇ*Sy*Fy/1000^2

157.185 100.485

kNm kNm

Mry = =

if(class<3,Mry12,Mry3)

Check

chk3 = =

if(Mry>Mfmay,"OK","NOT OK")

Efficiency

eff3 =

Mfmay/Mry

157.185

kNm

153

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Locker Room Roof Design

VERIFIED BY:

Comments:

Designed with CANAM steel decks and open web joists.

CHECKED BY:

February 27th, 2013 Randy Wang

0 Biaxial Bending Resistance

Interaction sum

iS = =

Mfm/Mrx+Mfmay/Mry

Check

chk4 = =

if(iS<1.0,"OK","NOT OK")

Efficiency

eff4 = =

0.715707617 OK 0.715707617

Deflections for Simple Beam with Uniformly Distributed Loading Limit for floors under live load

ldelta = =

Lo/300

Specified live load deflection

delta1 = =

5*w_L*sp/1000*Lo^4/(384*E*Ix)

Deflection at centre

delta = =

5*w_D*sp/1000*Lo^4/(384*E*Ix)

Check

chk5 = =

if(ldelta>delta1,"OK","NOT OK")

Efficiency

eff5 = =

delta1/ldelta

Check Slenderness

chk8 = =

if(hw/tw<83000/Fy,"OK","NOT OK")

Efficiency

eff8 = =

(hw/tw)/(83000/Fy)

35.75

35.09838119 mm 14.48899732 mm OK 0.9817729 Webs OK 0.161464177

154

Project Title:

UQAC Arena

DATE:

Project Detail:

February 27th, 2013

Design Detail:

Mechanical Room Floor Design

VERIFIED BY:

Comments:

Designed with CANAM steel decks and open web joists.

CHECKED BY:

Randy Wang

Design Summary: Composite Steel Deck:

Ref:

PͲ3606 Composite

CANAM Steel Deck

Type 22 Ͳ Triple Span

Code of Standard Practice*

Joist Girder: Open Web Steel Joist Span 9m/ Depth 750mm

Cl.6.1

*Note: American codes and standards for steel joist design are referred and applied to account for special loading cases ( nonͲuniformly distributed snow loads)

Beam: W530x74 Loading Condition: Dead Load

w_Di =

3.54

kPa

Live Load

w_L =

4.8

kPa

Factored Load

w_fi = =

for joist:

w_fji = =

(w_Di*1.25+w_L*1.5)*s_j/1000 kN/m 13.95 (w_Di*1.2+w_L*1.6)*s_j/1000 14.31

kN/m

Properties: Steel Deck Design Thickness

t_sd =

0.762

Overall Depth

d_sd =

37.4

Weight

wt_sd =

8.5

kg/m2

Section Modulus

M+ =

9529

mm3

MͲ =

10081

mm3

Steel Area

A_sd =

1016

mm2

Moment of Inertia

I_sd =

202228

mm4

Center of Gravity

cg_sd =

22.5

Thickness of Concrete Slab

t_c =

100

Span per Deck

l_sd =

1000

Self Weight

w_comp =

1.85

Comp. Mom.of Inertia

Mcomp =

5360000

kPa

Factored Resistance

wr_sd =

20.00

Spacing

s_j =

1200

Span

sp =

8748

Design Length

dl =

8646

Load Capacity

L_T =

15.0

kN/m

service load:

L_L =

10.0

Depth

d_j =

SelfͲweight

w_j =

mm4 kPa

Joist

750 19.4*9.81/1000 0.19

kN/m mm kN/m

Beam Suggested Depth Limitation

d_lim =

Shape Designation

Des1 =

Type of Shape

shape =

W530x74 rolled

Type of Lateral Support

ls =

supported

d_jͲ100 650

155

Project Title:

UQAC Arena

DATE:

Project Detail:

February 27th, 2013

Design Detail:

Mechanical Room Floor Design

Comments:

Designed with CANAM steel decks and open web joists.

Randy Wang

VERIFIED BY: CHECKED BY:

Overall Length

Lo =

7720.00

Laterally Unsupported Length

Lu =

1200

Boundary Condition at

ends =

Web Stiffener

ws =

none

Web Stiffener Distance

a_w =

7300

Shape of Moment Distribution

moment =

Loading Applied Relative to Shear Centre

load =

top

Linear Distributed Mom, Max

Mfmax =

358

kNm

Linear Distributed Mom, Min

Mfmin =

kNm

Maximum shear load

Vspec =

199

Max. Moment about YͲaxis

Mfmay =

Yield Strength

Fy =

350

Mpa

Elastic Modulus of Steel

200000.00

Mpa

Shear Modulus of Steel

Gs = ˇ=

77000.00 1

Mpa

Resistance Factor

pin mm

Bending About XͲAxis linear

Bending about YͲAxis 0

KNm

Section Properties

Resis. Factor Interior Bearing

ˇi =

Resist. Factor Bearing End

ˇe =

Member designation =

W530x74

Area

9520.00

mm2

Radius of gyration about X

rx =

208.00

mm mm

Radius of gyration about Y

ry =

33.1

Elastic section modulus about the XͲAxis

Sx =

1550000

mm3

Elastic section modulus about the YͲAxis

Sy =

125000

mm3

Plastic section modulus about the XͲAxis

Zx =

1810000

mm3

Plastic section modulus about the YͲAxis

Zy =

200000

mm3

St.Venant torsion constant

Warping torsional constant

Cw =

480000

mm4

692000000000

Web thickness

tw =

mm6 mm

Flange thickness

tf =

13.6

Depth

Width

bb =

529 166

Moment of inertia about X

Ix =

411000000

mm mm4

Moment of inertia about Y

Iy =

10400000

mm4

Adjusted Dead Load

w_D =

Adjusted Total Load

w_f =

for joist:

w_fj =

for deck:

w_sd =

Design Detail: Check Steel Deck = = = = Check Capacity

w_DiͲ0.19Ͳ2.55+w_comp+ wt_sd*9.81/1000+w_j/s_j*1000+w_b 2.89198

kPa

w_D*1.25+w_L*1.5 10.814975

kPa

w_D*1.2+w_L*1.6 11.150376

kPa

1.25*w_D+1.5*w_L 10.814975

kN/m

IF(wr_sd>w_sd, "OK", "FAIL") =

Deck only varies in span, a lower dead load will not alter design

Check Joist Design Applied Load

L_j = =

Check Capacity

w_fj*s_j/1000 13.3804512

kN/m

IF(L_j<L_T, IF(w_L*s_j/1000<L_L, "OK", "FAIL"), "FAIL")

156

Project Title:

UQAC Arena

DATE:

Project Detail:

February 27th, 2013

Design Detail:

Mechanical Room Floor Design

Comments:

Designed with CANAM steel decks and open web joists. =

Check Spacing

Randy Wang

VERIFIED BY: CHECKED BY:

OK IF(s_j>152,"OK","FAIL")

= Check Span

OK IF(sp<24*d_j, "OK", "FAIL")

Ref:

Code of Standard Practice* Cl.2.2 Cl.2.2

Check Beams Design Applied Loads

Number of Joist Supported

Nj =

Total Applied Forces

P_t =

where reaction:

R_y =

Spacing (end load and support)

s_end =

Spacing (quarter pt and pt load)

s_qt =

(w_f*s_j/1000)*sp/1000/2 56.76564078

= = =

roundup( Lo/s_j, 0) 7 P*Nj 397.3594855

Each beam supports half a bay

P_t/2 198.6797427

Symetric Loading Pattern

(Lo Ͳ(NjͲ1)*s_j )/2

260

Lo/4Ͳs_endͲs_j*2

470

Coefficient to account for Increase of Resistance if Moment Gradient exists Maximum Moment

Mmax = =

OneͲquarter Point

Ma =

Midpoint

Mb =

ThreeͲquarter Point

Mc =

Max. Shear Load

Vf =

w2 for Curved Bending Moment Distribution

w2_c =

= = = = =

(R_y*s_end+P*s_j*(3/2+(1+2)*(2)/2))/1000 358.1911933

kNm

(R_y*Lo/4ͲP*(((1+1)*1/2)*s_j+1*s_qt))/1000 288.6532834

kNm

(R_y*s_end+P*s_j*(3/2+(1+2)*(2)/2))/1000 358.1911933

kNm

(R_y*Lo/4ͲP*(((1+1)*1/2)*s_j+1*s_qt))/1000 261.9734322

kNm

R_y 198.6797427

4*Mmax/sqrt(Mmax^2+4*Ma^2+7*Mb^2+4*Mc^2) 1.120781307

Cl.13.6(a)(ii)

For linear bending moment distribution Moment ratio for w2_l

kp =

Mfmin/Mfmax

= Equivalent moment factor

w2_l = =

which w2?

w2_b = =

Set w2 limit to 2.5

w2c = =

Moment Gradient exists, non

0 1.75+1.05*kp+0.3*kp^2 1.75

linear distribution

if(moment="linear",w2_l,w2_c) 1.75 if(w2_b>2.5,2.5,w2_b) 1.75

Considering Location of Application of Loads and Effect on w2 for laterally unsupported case Resulting coefficient

w2 =

if(load="top",1.0,w2c)

Considering Beam End Conditions and Effect on Lu for laterally unsupported case Effective Length

Le = =

Resulting Length

L= =

if(ends="pin",Lu*1.2,Lu*1.4) 1440

if(load="top",Le,Lu) 1440

Local Buckling Width to Thickness Ratio

d_t =

Check

chk0 =

= =

(bb/2)/tf 6.102941176

Ref:

Handbook of Steel Construction Table 1

if(d_t<200/sqrt(Fy),"OK","NOT OK") OK

157

Project Title:

UQAC Arena

DATE:

Project Detail:

February 27th, 2013

Design Detail:

Mechanical Room Floor Design

Comments:

Designed with CANAM steel decks and open web joists.

Efficiency

eff0 = =

Randy Wang

VERIFIED BY: CHECKED BY:

d_t/(200/sqrt(Fy)) 0.570877873 Check Section Class Flange Table 2

b/t

fl =

Class 1:

c1 =

Class 2:

c2 =

Class 3:

c3 =

Flange is Class:

class_F =

= = = =

(bb/2)/tf 6.102941176 145 / (Fy)^0.5 7.750576015 170 / (Fy)^ 0.5 9.086882225 200 / (Fy)^0.5 10.69044968 if(fl<=c1,1,if(fl<=c2,2,if(fl<=c3,3,4)))

1 Web

h/w

wl = =

51.73195876

Class 1:

C1 =

1100 / (Fy)^ 0.5

58.79747322

Class 2:

C2 =

1700 / (Fy)^ 0.5

90.86882225

Class 3:

C3 =

1900 / (Fy) ^0.5

Web is Class:

class_W =

Section is Class:

class =

(d Ͳ 2*tf) / tw

101.5592719 if(wl<=C1,1,if(wl<=C2,2,if(wl<=C3,3,4)))

1 MAX(class_F,class_W)

1 Shear in YͲdirection for Unstiffened Webs

Web height

hw =

dͲ2*tf

Cl.13.4.1.1

= Cross section rolled shapes

Awr = =

501.8

5131.3

mm2

d*tw

Cross section welded shapes

Aww =

Cross section

Aw =

Stress limit (i)

Fsai =

Stress limit (ii)

Fsaii =

Stress limit (iii)

Fsaiii = =

359.1665778

For slr < = 1014/sqrt(Fy)

Vrai =

ˇ*Aw*Fsai/1000

For 1014/sqrt(Fy) < slr < 1435/sqrt(Fy)

Vraii =

For slr > 1435/sqrt(Fy)

Vraiii =

= =

hw*tw 4867.46 5131.3

= = = Vraiv = = Shear Resistance

V_ar =

Check

chk1 =

Efficiency

eff1 =

231

Mpa

Cl.13.4.1.1(a)(i)

670*sqrt(Fy)/(hw/tw) 242.2980406

Mpa

Cl.13.4.1.1(a)(ii)

Mpa

Cl.13.4.1.1(a)(iii)

Cl.13.4.1.1(a)(i)

Cl.13.4.1.1(a)(ii)

Cl.13.4.1.1(a)(iii)

961200/(hw/tw)^2

1066.79727 ˇ*Aw*Fsaii/1000 1118.973542 ˇ*Aw*Fsaiii/1000 1658.692315

if((hw/tw)/sqrt(Fy)>1014,Vraii,Vrai) 1066.79727

if((hw/tw)/sqrt(Fy)>1435,Vraiii,Vraiv) 1066.79727

if(ws="stif","NA",if(V_ar>Vf,"OK","NOT OK"))

= =

mm2

0.66*Fy

= =

mm2

if(shape="rolled",Awr,Aww)

OK Vf/V_ar 0.186239456

158

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Mechanical Room Floor Design

VERIFIED BY:

Comments:

Designed with CANAM steel decks and open web joists.

CHECKED BY:

February 27th, 2013 Randy Wang

Shear in YͲdirection for stiffened webs Critical Stress

Fcri = =

Euler Stress

Fcre = =

290*sqrt(Fy*kv)/(hw/tw) 242.7789049

180000*kv/(hw/tw)^2 360.4378257

Stress Limit (i)

Fsbi =

Stress Limit (ii)

Fsbii =

Stress Limit (iii)

Fsbiii =

Stress Limit (iii)

Fsbiv =

Aspect Ratio of Stiffened Web Surface

a_h =

Shear Buckling Coefficient

kv1 =

Shear Buckling Coefficient

kv2 =

Resulting shear buckling coefficient

kv =

Parameter

kvFy =

Aspect Coefficient

ka = =

0.068577897

slr < = 439/sqrt(kv/Fy)

Vrbi =

ˇ*Aw*Fsbi/1000

For 439/sqrt(kv/Fy) < slr < 502/sqrt(kv/Fy)

Vrbii =

For 502/sqrt(kv/Fy) < slr < 621/sqrt(kv/Fy)

Vrbiii =

For 621/sqrt(kv/Fy) < slr

Vrbiv =

= = = = = = =

= = = = Vrbv = = Vrbvi = = Shear Resistance

Vbr =

Check

chk7 =

Efficiency

eff7 =

231

Mpa

Cl.13.4.1.1(b)(i)

242.7789049

Mpa

Cl.13.4.1.1(b)(ii)

Fcri Fcri+ka*(0.5*FyͲ0.866*Fcri) 240.3617719

Mpa

Cl.13.4.1.1(b)(iii)

Fcre+ka*(0.5*FyͲ0.866*Fcre) 351.0331108

Mpa

Cl.13.4.1.1(b)(iv)

Cl.13.4.1.1(b)(i)

Cl.13.4.1.1(b)(ii)

Cl.13.4.1.1(b)(iii)

Cl.13.4.1.1(b)(iv)

a_w/hw 14.54762854 4+5.34/(a_h)^2 4.025232301 5.34+4/(a_h)^2 5.3589006 if(a_h<1,kv1,kv2) 5.3589006 sqrt(kv/Fy) 0.12373821 1/(sqrt(1+(a_h)^2))

1066.79727 ˇ*Aw*Fsbii/1000 1121.194255 ˇ*Aw*Fsbiii/1000 1110.031524 ˇ*Aw*Fsbiv/1000 1621.130581

if((hw/tw)>439/kvFy,Vrbii,Vrbi) 1066.79727

if((hw/tw)>502/kvFy,Vrbiii,Vrbv) 1066.79727

if((hw/tw)>621/kvFy,Vrbv,Vrbvi) 1066.79727

if(ws="none","NA",if(Vbr>Vf,"OK","NOT OK"))

= =

Mpa

0.66*Fy

= =

Cl.13.4.1.1

Mpa

NA Vf/Vbr 0.186239456 Bending Resistance about XͲAxis Laterally supported

Yielding reaching Mp

Mp =

Yielding reaching My

My =

Resulting moment, supported

Mrs =

Check

chk6 =

Efficiency

eff6 =

= = = = =

Zx*Fy/1000^2 633.5

kNm

Sx*Fy/1000^2 542.5

kNm

Cl.13.6(a), Class 1 and 2

Cl.13.6(a), Class 3

IF(class<3,ˇ*Mp,ˇ*My) 570.15

kNm

if(ls="uns","NA",if(Mrs>Mfm,"OK","NOT OK")) NA Mfm/Mrs 0.628240276

159

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Mechanical Room Floor Design

VERIFIED BY:

Comments:

Designed with CANAM steel decks and open web joists.

CHECKED BY:

February 27th, 2013 Randy Wang

Laterally unsupported, for doubly symmetric Class 1 and 2 sections Elastic lateralͲtorsional buckling

Mu = =

(w2*pi()/L)*sqrt(E*Iy*Gs*J+((pi()*E/L)^2)*Iy*Cw)/1000^2 2624.391015

kNm

Cl.13.6(a)

when Mu > 0.67 Mp (intermediate) (a)(i) Limit resistance to yielding

Mra_i =

1.15*ˇ*Mp*(1Ͳ(0.28*Mp/Mu))

1133.262095

Mrai =

611.3562425

1011.15

when Mu <= 0.67 Mp (slender) (a)(ii)

kNm kNm

570.15 Mra_ii = =

Limit resistance to yielding

Mraii =

Intermediate or slender beam?

type_a =

ˇ*Mu 11137.21644 2361.951914

kNm

if(Mu>0.67*Mp,"inter","slender")

= Mr12 =

kNm

if(Mra_ii>(ˇ*Mp),ˇ*Mp,Mra_ii)

570.15 if(type_a="inter",Mrai,Mraii)

inter

kNm

570.15 when Mu > 0.67 My (intermediate) (a)(i)

Mrb_i = =

Limit resistance to yielding

Mrbi = =

Cl.13.6(b)

1.15*ˇ*My*(1Ͳ(0.28*My/Mu)) 991.8086056

kNm

if(Mrb_i>(ˇ*My),ˇ*My,Mra_i) 528.9885504

kNm

488.25 (a)(ii)

Mrb_ii =

ˇ*Mu

11137.21644

Limit resistance to yielding

Mrbii =

2361.951914

Intermediate or slender beam?

type_b =

= = Mr3 = Resulting resistance, unsupported

882

kNm kNm

488.25 inter inter

1011.15

Mrx =

570.15

1011.15

kNm kNm

570.15 Applied maximum factored moment

Mfm =

if(moment="linear",Mfmax,Mmax)

883.8273494

Check

chk2 =

358.1911933

Efficiency

eff2 =

= =

kNm

OK Mfm/Mrx 0.628240276 Bending Resistance about YͲAxis

Bending resistance

Mry12 = = Mry3 = = Mry = =

ˇ*Zy*Fy/1000^2 63

Cl.13.5(a)

39.375

kNm

Cl.13.5(b)

if(class<3,Mry12,Mry3) 63

Check

chk3 = =

Efficiency

eff3 =

Mfmay/Mry

kNm

ˇ*Sy*Fy/1000^2

kNm

if(Mry>Mfmay,"OK","NOT OK")

160

Project Title:

UQAC Arena

DATE:

Project Detail:

Design Detail:

Mechanical Room Floor Design

VERIFIED BY:

Comments:

Designed with CANAM steel decks and open web joists.

CHECKED BY:

Biaxial Bending Resistance Interaction sum

iS =

Check

chk4 =

Efficiency

eff4 =

Mfm/Mrx+Mfmay/Mry

0.628240276

Randy Wang

If laterally unsupported

Cl.13.6(f)

if(iS<1.0,"OK","NOT OK")

= =

February 27th, 2013

OK iS 0.628240276

Deflections for Simple Beam with Uniformly Distributed Loading Limit for floors under live load

ldelta = =

Specified live load deflection

delta1 =

Deflection at centre

delta =

Check

chk5 =

Efficiency

eff5 =

= = = =

Lo/300 25.73333333

Table 1 Appendix D

5*w_L*sp/1000*Lo^4/(384*E*Ix) 23.62578109

5*w_D*sp/1000*Lo^4/(384*E*Ix) 14.23443466

if(ldelta>delta1,"OK","NOT OK") OK

Approaximate as uniformly distributed load (Conservative) Cl.14.3.1

delta1/ldelta 0.918100301

Webs Check Slenderness

chk8 = =

Efficiency

eff8 = =

if(hw/tw<83000/Fy,"OK","NOT OK") OK (hw/tw)/(83000/Fy) 0.218146814

161

Project Title:

UQAC Arena

DATE:

February 30th, 2013

Project Detail:

Roof and Floors

Randy (Chao) Wang

Design Detail:

Diaphram Design for Floors and Roofs

VERIFIED BY:

Arnaud Dusser

Comments:

Groud Floor Ͳ Long Shear Length

CHECKED BY:

Othmane Laraki

Design Summary: Ref:

Steel Deck Designation:

CANAM Steel Deck Diaphram

PͲ3606 Composite Type 22 Ͳ Triple Span

Forces Applied: Horizontal axial load

F_h =

(553+81)/2

Ref:

317

Shear length

L_Q =

67.2

Linear shear force

Qf =

CANAM Steel Deck Diaphram

F_h/L_Q

4.717261905

kN/m

Connections: Joist spacing

s_j =

1000

Support fasteners

SideͲlap fasteners

# 10

Shear at Maximum

Qf_1 =

Puddle weld

Shear Flow = Shear at 3/4 Point

25.2

Qf_2 =

Qf/L_Q*d_2 1.768973214

d_3 =

16.8

Qf_3 =

Qf/L_Q*d_3

= Shear at 1/4 Point

4.717261905

d_2 =

= Shear at 1/2 Point

1.179315476

d_4 =

8.4

Qf_4 =

Qf/L_Q*d_4

0.589657738

kN/m m

* Only mininum fastening is needed

kN/m

Shear Resistance Finalized Design

Resistance at 1/4 Point

Qr_4 =

Check Capacity Resistance at 1/2 Point

Check Capacity

7 7 7

kN/m

IF(Qr_2>Qf_2,"OK", "NOT OK") Qr_1 =

kN/m

IF(Qr_3>Qf_3,"OK", "NOT OK") Qr_2 =

Check Capacity Resistance at Maximum

kN/m

IF(Qr_4>Qf_4,"OK", "NOT OK") Qr_3 =

Check Capacity Resistance at 3/4 Point

Support Pattern @ 36/4

kN/m

IF(Qr_1>Qf_1,"OK", "NOT OK")

162

Project Title:

UQAC Arena

DATE:

Project Detail:

Design of Interior Bleachers

Design Detail:

Design of Supporting Steel Structure

VERIFIED BY:

Caroline Chan

CHECKED BY:

Othmane Laraki

Comments: Live Load: L = Span =

4.800 9.2

February 20th, 2013 Arnaud Dusser

kPa m

From SCHOKBETON Charte of Design: use 10" (254 mm) prefab element From SCHOKBETON Table of Allowable live loads: use 4Ͳ15 mm strands for post tensionning 965 Weight: D = Total Factored Load: wL = = T.W. =

3.340

mm wide (4 Tubes) kPa

1.25 D + 1.5 L 11.375 9.2

kPa m

Distributed Load =

wL T.W.

104.650

kN/m

Mf =

106.5

kN.m

Vf =

Ͳ158.8

Cf =

Ͳ24.85

Tf =

71.5

RL (South side) =

158.74

RR (North Side) =

166

From SAP2000 Model: Supporting Beam:

Beam Design: (Tension + Bending) Estimate A (using Ag) = = Estimate A (using Ane) = =

Tf / (0.9 Fy) 226.98 Tf / (0.75 Fu) 211.85

Estimate Z =

Mf / (0.9 Fy)

338095.24

Try W310x45

mm2

mm3

(Class 1)

d =

313

t =

11.20

h =

290.60

w =

6.600

From Steel HB 6Ͳ52

Flexural resistance: Ag =

5690

Ane =

5690

Fy =

0.350

GPa

Fu =

0.450

GPa

Tr =

0.75 Ane Fu

1493.63

Zx =

708000

mm3

163

Project Title:

UQAC Arena

DATE:

Project Detail:

Design of Interior Bleachers

Design Detail:

Design of Supporting Steel Structure

VERIFIED BY:

Caroline Chan

CHECKED BY:

Othmane Laraki

Comments: Mr =

0.9 Fy Zx

223.02

February 20th, 2013 Arnaud Dusser

kN.m

Tf/Tr + Mf/Mr =

0.525

Mf/Mr Ͳ (Tf x Z)/(Mr x A)

0.438

Full Lateral Stability Shear Resistance: Fs =

0.66 Fy

0.231

GPa

Aw =

2065.80

mm2

Vr =

0.9 Fs Aw

429.48

kN >Vf

h/w =

44.03

< 439 x SQRT(kv/Fy)=

From SAP Model: ѐ =

5.59

ѐ Allowable =

8.04

mm =

RL (South side) =

160

RR (North Side) =

167

Cf =

100.99

Br =

100.99

OK 54.225

965 x 3/360

> Cf.

> Bf

use W310x45 with Full Moment resistant connection at angle With Beam Dead Load :

Connection Design:

Fy = 200/SQRT(Fy) =

350

choose t =

min bel =

200/SQRT(Fy) t

= b = choose w = K x L = E =

MPa

10.69

53.45

mm mm

125

345

200000

MPa

Ix = b t3/3 + w ((12 w)3Ͳ t3)/12 = A = = rx = =

95156.25

mm3

t b +(12 w Ͳ t) w 900

mm2

SQRT(Ix/A) 10.282

ʄ = K L/rx SQRT(Fy/(ʋ2 E)) =

0.447

Cr = 0.9 A Fy (1+ʄ2 x 1.34) Ͳ1/1.34 = Br = =

261.309 1.5 0.9 Fy A 425.250

164

Project Title:

UQAC Arena

DATE:

Project Detail:

Design of Interior Bleachers

Design Detail:

Design of Supporting Steel Structure

VERIFIED BY:

Caroline Chan

CHECKED BY:

Othmane Laraki

Comments:

February 20th, 2013 Arnaud Dusser

Column Design: Cf = Try W200x27

160

Class 2

A =

3390

mm2

b =

133

mm mm

t =

8.4

h =

190.2

w =

5.8

k =

L =

3000

ry =

31.2

Fy =

0.350

Gpa

E =

200

GPa

From Steel HB 6Ͳ54

ʄ = k L/ry SQRT(Fy/(ʋ2 E)) =

1.28

Cr = 0.9 x A x Fy x (1+ʄ2 x 1.34) Ͳ1/1.34 kN

> Cf

477.603

Slenderness check: kL/r =

96.154

< 200

bel/t =

7.917

< 200/SQRT(Fy) =

10.690

h/w =

32.793

< 670/SQRT(Fy) =

35.813

Use W200x27

165

Project Title:

UQAC Arena

DATE:

Design Detail:

February 20th, 2012

Project Detail:

Anchor Bolts

Randy Wang

VERIFIED BY:

Caroline Chan

CHECKED BY:

Comments:

INPUT

Reference/ Notes

Concrete Aspects

Concrete Design Handbo

Concrete Strength

Number of Bolts

R_ss

0.8

29 [mm]

30 [Mpa]

Anchor Properties

Diameter

Assume Ductile Steel

Head Diameter

d_head

148.1 [mm]

Embedment Depth

h_ef

625 [mm]

400 [MPa]

Fut

517 [MPa]

Resistance Mod. FactoR

Calibration Factor

Ɍs

0.85

Ɍc

0.65

Cl.D.5.4 Condition B in Tension Cl.D.6.2.2

1.25

Cl.D.6.2.6

W_cp

1.00

Cast-in Anchor

W_ec

1.00

Concentric Tension

W_c_p

1.40

Modifictation Factors W_c

c_min

Projected Area

A_N

Applied Force

A_se

PI()*d^2/4

#NAME?

N_sr

ĭs*n*A_se*Fut*R_ss/ =

#NAME?

A_No

9*h_ef^2

chk_0

IF(A_N/A_No>n,"OK:,"=

N_br

k*ĭc*SQRT(Fc)*h_ef^ =

IF(c_min>=1.5*h_ef,1, =

N_cbgr

A_N/A_No*(W_ed*W_=

#NAME?

A_bh

PI()*(d_head^2-d^2)/4 =

#NAME? #NAME?

50.0 [mm] (75+150+(1.5*h_ef))*((=

2354063

A_No if distant from edge

315.0 [kN]

DESIGN (CALCULATIONS)

Reference/ Notes

Modifictation Factors W_ed

3515625 Cl.D.6.2.1

#NAME?

N_pr

0.9*ĭc*Fc*(4.5*d)*d*R=

W_c_p*N_pr

MIN(N_sr,N_cbgr,N_c =

#NAME?

eff

Tf/N

#NAME?

[kN]

0.72

N_cpr

[kN]

Cl.D.6.2.2

Cl.D.6.2.5

[kN]

Cl.D.6.3.5

#NAME? [kN]

[kN]

166

167

168

169

170

171

172

173

174

175

176

177

178

179