Simplification and re-dimensioning of a concrete flat-slab pedestrian bridge according to Eurocode

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(1)l�. University of Stavanger. Faculty of Science and Technology. BACHELOR'S THESIS Study program/Specialization:. Fall semester, 2019. Civil Engineering/Structural Engineering Writers: Danilo Orbolato Moreira da Silva Glenn Andre Ulven. Open / Restricted access. P..�,.��..9t:h?�.-�.............. .�..��.. �.�� .............. . (Writer's signature). Faculty supervisor: Samindi Mudiyansele Samarakoon (University of Stavanger) Extemal supervisor: Håkon Emil Helland Sæstad (Statens Vegvesen) Thesis title:. Simplification and re-dimensioning of a concrete flat-slab pedestrian bridge according to Eurocode. Credits (ECTS): 20 STP Keywords:. -Bridge design - Reinforced concrete - Deflection calculations - Pedestrian bridge - Flat-slab - Eurocode. Pages: 137 + Supplemental material: 169 Stavanger, 07/12/2019 (Date/year).

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(3) Acknowledgements We would like to express our sincere gratitude to all involved in this project, making it possible for us to successfully conclude it using all the tools acquired through our time at the Department of Structural Engineering and Material Sciences at the University of Stavanger. For us, this Thesis represents the culmination of all the Structural Engineering know-how to a project. To our supervisor, Associate Professor Samindi Mudiyansele Samarakoon from Det teknisk- naturvitenskapelige fakultet, for which we will carry positive memories of her lectures and insights, and Bridge Engineer Håkon Emil Helland Sæstad from Statens Vegvesen we are most thankful for all the support and insight provided throughout this work that has been largely enriching for us.. i.

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(5) Objective This bachelor thesis is focused on optimisation of Myrdal Bru II, using Eurocodes and software analysis as the means to compare it with the existing design for maximization when changes are made to its dimensions and properties. A list of the codes and handbooks are listed in chapter 1.3. The first analysis was to simplify the design and compare it to the Standard Model (Original) to verify if significant changes would occur in its design loads due to self-weight and capacity of the structure to bear these loads. This attempt was made to conclude if the simplified model would, to some extent, be easier to build while satisfying the preset conditions in the codes. A further analysis was also carried out with emphasis on the bridge deck. Five different changes were done to the thickness of the bridge, to determine if significant changes would also occur in the reinforcement and if the deflections due to those changes would be too great. Tables with these results are found in chapter 4 and 5.. ii.

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(7) Contents Page Acknowledgments. 1 1.1 1.2 1.3 2 2.1. 2.2. 2.3. 2.4. i. Objective. ii. Figures. xi. Tables. xii. Chapter - Introduction Description of the Bridge . . . . . . . . . . . . . . CSI Bridge Software . . . . . . . . . . . . . . . . . Standards . . . . . . . . . . . . . . . . . . . . . . . Chapter - Load Analysis Design . . . . . . . . . . . . . . . 2.1.1 Limit State Design . . . . . . . 2.1.2 Ultimate Limit State . . . . . . 2.1.3 Serviceability Limit State . . . Characteristic Load Calculations . . 2.2.1 Self-Weight . . . . . . . . . . 2.2.2 Traffic Loads . . . . . . . . . Design Load Calculations . . . . . . 2.3.1 Vertical Design Load: . . . . . 2.3.2 Service Vehicle: . . . . . . . . 2.3.3 Horizontal Load: . . . . . . . . 2.3.4 Design Load FBD Diagrams . . . . 2.3.5 Load Model Combinations . . . . Temperature Load . . . . . . . . . . 2.4.1 Evenly Distributed Temperature . 2.4.2 Variable Temperature Difference iii. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . .. 1 1 3 4 5 5 5 6 6 7 7 8 9 9 9 9 10 11 15 15 17.

(8) 2.4.3 2.4.4 2.5 CSI 2.5.1 2.5.2 2.5.3 3. Linear Variable Temperature Difference . . Non-Linear Variable Temperature Difference Bridge Modelling Process . . . . . . . . . Graphics Modeling . . . . . . . . . . . . Defining the Loads . . . . . . . . . . . . Load Combinations . . . . . . . . . . . .. Chapter - Design of Reinforced Concrete Bridge 3.1 Material Properties . . . . . . . . . . . . 3.1.1 Concrete Compressive Strength. . . . . . 3.1.2 Steel Yield Strength . . . . . . . . . . 3.1.3 Partial Safety Factors . . . . . . . . . 3.1.4 Concrete Design Compressive Strength . . 3.1.5 Steel Tensile Strength . . . . . . . . . 3.2 Bending Reinforcement Over Column . . . . . 3.2.1 Introduction . . . . . . . . . . . . . . 3.2.2 Cover to the reinforcement . . . . . . . 3.2.3 Effective Depth . . . . . . . . . . . . 3.2.4 Design for flexure along Y-Axis . . . . 3.2.5 Lever Arm . . . . . . . . . . . . . . . 3.2.6 Required Steel Area . . . . . . . . . . 3.2.7 Spacing . . . . . . . . . . . . . . . . 3.2.8 Maximum Spacing Check . . . . . . . . . 3.2.9 Steel Reinforcement Provided . . . . . . 3.2.10 Minimum Reinforcement Area . . . . . . . 3.2.11 Maximum Reinforcement Area: . . . . . . 3.2.12 Transverse Reinforcement Over Column . . 3.2.13 Transversal Lever Arm . . . . . . . . . 3.2.14 Required Steel Area . . . . . . . . . . 3.2.15 Transversal Reinforcement Spacing . . . 3.2.16 Maximum Spacing . . . . . . . . . . . . 3.2.17 Steel Reinforcement Provided . . . . . .. iv. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . .. 17 18 19 19 20 21. . . . . . . . . . . . . . . . . . . . . . . . .. 22 22 22 22 23 23 24 25 25 26 27 28 28 29 29 29 30 30 31 32 32 32 33 33 33.

(9) 3.3. 3.4. 3.5. 3.6. 3.7. Bending Reinforcement at the Mid-Span . . . . . . . 3.3.1 Introduction . . . . . . . . . . . . . . . . . . 3.3.2 Design For Flexure . . . . . . . . . . . . . . . 3.3.3 Lever Arm . . . . . . . . . . . . . . . . . . . 3.3.4 Required Steel Area . . . . . . . . . . . . . . 3.3.5 Spacing . . . . . . . . . . . . . . . . . . . . 3.3.6 Maximum Spacing . . . . . . . . . . . . . . . . 3.3.7 Steel Reinforcement Provided . . . . . . . . . . 3.3.8 Minimum Reinforcement Area . . . . . . . . . . . 3.3.9 Maximum Reinforcement Area . . . . . . . . . . . 3.3.10 Transversal Reinforcement Mid-Span . . . . . . . 3.3.11 Lever Arm . . . . . . . . . . . . . . . . . . . 3.3.12 Required Steel Area . . . . . . . . . . . . . . 3.3.13 Spacing . . . . . . . . . . . . . . . . . . . . 3.3.14 Maximum Spacing . . . . . . . . . . . . . . . . 3.3.15 Steel Reinforcement Provided . . . . . . . . . . Shear Reinforcement . . . . . . . . . . . . . . . . 3.4.1 Introduction . . . . . . . . . . . . . . . . . . 3.4.2 Section ThatDO NOT Require Reinforcement . . . . 3.4.3 Section that DO Require Shear Reinforcement . . 3.4.4 Spacing Between Shear Reinforcement . . . . . . Punching Shear Reinforcement . . . . . . . . . . . . 3.5.1 Introduction . . . . . . . . . . . . . . . . . . 3.5.2 Punching shear resistance WITHOUT reinforcement Torsion Reinforcement . . . . . . . . . . . . . . . 3.6.1 Introduction . . . . . . . . . . . . . . . . . . 3.6.2 Deck Torsional Cross Section . . . . . . . . . 3.6.3 St Venant’s Torsional Constant, K . . . . . . . 3.6.4 St.Venant’s Constant for sections 1, 2 and 3 . . 3.6.5 Torsion Calculations . . . . . . . . . . . . . . 3.6.6 Combined Effect (Torsion + Shear) . . . . . . . Reinforcement Of Column . . . . . . . . . . . . . .. v. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 34 34 35 35 35 36 36 36 37 37 38 38 38 39 39 39 40 40 40 42 43 44 44 45 49 49 50 50 54 56 57 58.

(10) 3.7.1 Introduction . . . . . . . . . . . . . . . . . . 3.7.2 Dimensions . . . . . . . . . . . . . . . . . . . 3.7.3 Eccentricity, e, of The Load . . . . . . . . . . 3.7.4 Minimum Reinforcement . . . . . . . . . . . . . 3.7.5 Slenderness Ratio . . . . . . . . . . . . . . . 3.7.6 Normalized slenderness ratio . . . . . . . . . . 3.7.7 Equations for Determining the Creep Coefficient 3.7.8 Limit of normalized slenderness ratio . . . . . 3.7.9 Column Reinforcement . . . . . . . . . . . . . . 3.7.10 Bi-axial Bending Check . . . . . . . . . . . . . 3.8 Reinforcement of Foundation Pad . . . . . . . . . . 3.8.1 Introduction . . . . . . . . . . . . . . . . . . 3.8.2 Important Details Regarding Pad Design . . . . . 3.8.3 Bearing Capacity of Soil Under Foundation Pad . 3.8.4 Introduction . . . . . . . . . . . . . . . . . . 3.8.5 Maximum Design Vertical Pressure . . . . . . . . 3.8.6 Bending Reinforcement of Foundation Pad . . . . 3.8.7 Lever Arm . . . . . . . . . . . . . . . . . . . 3.8.8 Steel Required Area . . . . . . . . . . . . . . 3.8.9 Spacing . . . . . . . . . . . . . . . . . . . . 3.8.10 Number of Bars . . . . . . . . . . . . . . . . . 3.8.11 Punching Shear on Foundation Pad . . . . . . . . 3.8.12 Introduction . . . . . . . . . . . . . . . . . . 3.8.13 Effective Pad Depth, def f ;pad . . . . . . . . . . 3.8.14 Basic Control Perimeter . . . . . . . . . . . . 3.8.15 Punching shear stress at control perimeter . . . 3.8.16 Punching shear stress at column perimeter . . . 3.9 Reinforcements Of Abutment West . . . . . . . . . . 3.9.1 Introduction . . . . . . . . . . . . . . . . . . 3.9.2 Dimensions . . . . . . . . . . . . . . . . . . . 3.9.3 Strut-and-Tie Method . . . . . . . . . . . . . . 3.9.4 Design Of Deep-Beam . . . . . . . . . . . . . .. vi. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 58 59 59 60 61 61 62 65 66 68 70 70 71 72 72 74 75 76 76 76 77 78 78 79 79 81 83 84 84 85 86 87.

(11) 3.9.5 Forces on Abutment . . . . . . . . . . . . . . . 3.9.6 Control of Design Stresses in Concrete Struts . 3.9.7 Earth Pressure on Abutment West . . . . . . . . 3.9.8 Vertical pressure on terrain . . . . . . . . . . 3.9.9 Effective vertical pressure on terrain . . . . . 3.9.10 Horizontal Effective Active Pressure . . . . . . 3.9.11 Horizontal Active Pressure . . . . . . . . . . . 3.9.12 Horizontal Effective Passive Pressure . . . . . 3.9.13 Horizontal passive pressure . . . . . . . . . . 3.9.14 Moment Due To Horizontal Pressures From Terrain 3.9.15 Vertical Reinforcement . . . . . . . . . . . . . 3.9.16 Horizontal Tension Reinforcement at 0.1h . . . . 3.9.17 Horizontal Reinforcement . . . . . . . . . . . . 3.9.18 Bearing Capacity of Pad . . . . . . . . . . . . 3.9.19 Bending Reinforcement of West Abutment Pad . . . 3.9.20 Steel Area Required . . . . . . . . . . . . . . 3.9.21 Spacing . . . . . . . . . . . . . . . . . . . . 3.9.22 Number of Bars Needed . . . . . . . . . . . . . 3.10 Reinforcement Of Abutment East . . . . . . . . . . . 3.10.1 Dimensions . . . . . . . . . . . . . . . . . . . 3.10.2 Design of deep beam . . . . . . . . . . . . . . 3.10.3 Forces on Abutment . . . . . . . . . . . . . . . 3.10.4 Control of Stresses . . . . . . . . . . . . . . 3.10.5 Earth Pressure On Abutment . . . . . . . . . . . 3.10.6 Vertical Pressure . . . . . . . . . . . . . . . 3.10.7 Effective Vertical Pressure . . . . . . . . . . 3.10.8 Effective Horizontal Active Pressure . . . . . . 3.10.9 Horizontal Active Pressure . . . . . . . . . . . 3.10.10 Effective horizontal passive pressure . . . . . 3.10.11 Horizontal Passive Pressure . . . . . . . . . . 3.10.12 Moment Due to Horizontal Pressures . . . . . . . 3.10.13 Vertical Reinforcement . . . . . . . . . . . . .. vii. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 87 88 89 89 90 90 90 91 91 91 92 94 95 96 97 98 98 99 100 100 100 101 101 103 103 104 104 104 105 105 105 106.

(12) 3.10.14 Horizontal Reinforcement at 0.1h . 3.10.15 Horizontal Reinforcement . . . . . 3.10.16 East Abutment Pad Bearing capacity 3.10.17 Bending Reinforcement of pad . . . 3.10.18 Lever Arm . . . . . . . . . . . . 3.10.19 Steel Area Required . . . . . . . 3.10.20 Spacing . . . . . . . . . . . . . 3.10.21 Number of Bars Needed . . . . . . 3.11 Summary . . . . . . . . . . . . . . . .. . . . . . . . . .. 108 109 110 111 112 113 113 114 115. Chapter - Standard vs Simplified Model Comparison Introduction . . . . . . . . . . . . . . . . . . . . . Diagram Results . . . . . . . . . . . . . . . . . . .. 116 116 116. Chapter - Deck Resize Analysis 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . 5.1.1 Forces on the Deck . . . . . . . . . . . . . . . . 5.1.2 Deck Reinforcement, Spacing and No.of Bars . . . .. 126 126 126 128. 4 4.1 4.2 5. 6. Chapter - Conclusion. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. 132. Appendices. 138. A. Load Calculations. 139. B. CSI Bridge Detailed Modelling Procedure. 151. C. Analysis Diagrams. 178. D. Analysis Table Values. 184. E. Actions On Abutment Pads. 187. F. Deflection Calculation. 192. viii.

(13) G. Analysis Results Deck Reduction. 200. H. Reinforcement suggestion. 213. I. Myrdal Bru II - Detailed Drawings. 225. J. Beregningsdokument. 248. ix.

(14) List of Figures 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30. Bridge Vertical Section . . . . . . . . . Bridge Vertical Plan . . . . . . . . . . . Free Body Diagram . . . . . . . . . . . . Shear Force Diagram . . . . . . . . . . . Bending Moment Diagram . . . . . . . . . . Table NA.A2.4(B) . . . . . . . . . . . . . Table NA.6.2(C) . . . . . . . . . . . . . Modelling Process Diagram . . . . . . . . Loading Process Diagram . . . . . . . . . Load Combination Process Diagram . . . . . Partial Safety factors . . . . . . . . . . Parabola Rectangle Diagram . . . . . . . . Stress-Strain Diagram . . . . . . . . . . Simplified Deck Cross-Section Over Column Effective-Depth Stress-Strain Diagram . . Simplified Deck Cross-Section Mid-Span . . Shear Force Action . . . . . . . . . . . . Punching Shear Failure Diagram . . . . . . Torsion Action . . . . . . . . . . . . . . Torsion Action . . . . . . . . . . . . . . Simplified Cross Section . . . . . . . . . St. Venant’s Torsional Constant K . . . . Simplified Column Cross-Section . . . . . MN-Diagram for circular column . . . . . . Foundation Pad Diagram . . . . . . . . . . Soil Bearing Capacity Diagram . . . . . . Punching Shear on Pad . . . . . . . . . . Control Perimeter on Pad . . . . . . . . . Abutment West Cross-Section . . . . . . . Abutment West Strut-and-Tie . . . . . . .. x. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 2 2 10 10 10 13 18 19 20 21 23 23 24 25 27 34 40 44 49 49 50 50 58 69 70 72 78 78 84 86.

(15) 31 32 33 34 35 36 37 38 39. Abutment West Strut-and-Tie Cross-Section. Horizontal Earth Pressure . . . . . . . . Graph Bending Moment . . . . . . . . . . . Graph Shear Force . . . . . . . . . . . . Graph Torsion . . . . . . . . . . . . . . . Graph Longitudinal Reinforcement . . . . . Graph Transversal Reinforcement . . . . . Graph Shear Reinforcement . . . . . . . . Graph Vertical Displacement . . . . . . .. xi. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. . . . . . . . . .. 86 91 127 127 128 129 129 130 130.

(16) List of Tables 1 2 3 4 5 6. Designs Comparison . . . . . . Forces on Deck . . . . . . . . Deck Reinforcement Spacing and Forces on Abutments . . . . . Abutment Reinforcement Spacing Simplified Model Variations .. xii. . . . . . . . . . . Bars . . . . . . . and Bars . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. 116 126 128 131 131 132.

(17) 1 1.1. Chapter - Introduction Description of the Bridge. Myrdal Bru II is a pedestrian bridge completed in 2014 by the Norwegian Public Road Administration. It is located along FV-183 Totlandsvegen in the Hordaland municipality south-east of Bergen. The bridge was originally built as a temporary car bridge, used while the old Myrdal Bru was demolished and rebuilt in 2014. Therefore, it was designed to carry car loads. After the new car bridge, Myrdal Bru I, was completed, Myrdal Bru II was used as a pedestrian bridge. The bridge consists of a two span slack reinforced flat slab of 1000mm thickness, with abutments on each side and a column on its center. The abutments are connected to the deck via one pin and three rollers (two supports on each abutment). The column has a diameter of 800mm and is connected to the deck with a roller support. Both the abutments and the column is placed on solid rock. The bridge has two equal spans of 15.647m each, with the same width throughout its entire length of 31.294m. The bridge deck has a slope of 0.062, an incline of 3% and it has a slight curvature of radius 148.75m. The vertical sections of the bridge may be found at figure 1 and 2.. 1.

(18) Figure 1:. Figure 2:. Bridge Vertical Section. Bridge Vertical Plan. 2.

(19) 1.2. CSI Bridge Software. CSI Bridge is an engineering tool developed by Computers & Structures Incorporated (CSI) that specializes in bridge design and bridge analysis. It is a great software when doing bridge designs and analyzes, with lots of different options and parameters which can be modified to create the preferred bridge model. The computer software allows the user to easily model simple steel and concrete bridge designs, as well as complex bridge structures. The parametric modeller allows the user to make changes efficiently when needed, while maintaining total control over the modeled bridge design and the modeling process. Lanes and vehicles can be defined quickly and include width effects. When defining the vehicle loads it is possible to either create a user defined load pattern, select and use an existing load pattern, or modify the existing load patterns. We did the first option for our bridge, since there is no pre-defined pedestrian loads in the software. The computer software is very user-friendly, due to its understandable terminology and straightforward layout. Bridge models are easily created or edited in the Bridge-Wizard in the Home tab, or by following the tabs directly. When starting a new project, CSI Bridge gives the user the option to either start with and edit an existing bridge model, or start a new project where the user have to create the complete model from the beginning. After the model is created, the CSI Bridge allows the user to run the analysis of the bridge, where actions and deflections on the bridge, as well as support reactions are calculated by the software. Simple and practical charts are also available, to simulate modelling of construction sequences and scheduling.. 3.

(20) 1.3. Standards. Eurocodes: • Grunnlag for prosjektering av konstruksjoner NS-EN 1990:2002+NA:2008 • Laster på konstruksjoner - Del 1-1: og nyttelaster i bygninger NS-EN 1991-1-1:2002+NA:2008. Allmenne laster - Tetthet, egenvekt. • Laster på konstruksjoner - Del 1-5: NS-EN 1991-1-5:2003+NA:2008. Allmenne laster - Termiske påvirkninger. • Laster på konstruksjoner - Del 2: NS-EN 19912:2003+NA:2010. Trafikklast på bruer. • Prosjektering av betongkonstruksjoner - Del 1-1: og regler for bygninger NS-EN 1992-1-1:2004+NA:2008 • Geoteknisk Prosjektering - Del 1: NS-EN 1997-1:2004+NA:2008. Allmenne regler. Allmenne Regler. Handbooks from Statens Vegvesen: • Bruklassifisering Håndbok R412 • Bruprosjektering Håndbok N400 • Forankring med Bergbolter ved Fundamentering av Støttemurer og Landkar på Berg Intern Rapport Nr.2374 • Geoteknikk i vegbygging Håndbok 016 • Plassproduserte platebruer Håndbok 4. 4.

(21) 2. Chapter - Load Analysis. Any design process involves a number of assumptions. The loads to which a structure will be subjected must be estimated, sizes of members to check must be chosen and design criteria must be selected. All engineering design criteria have a common goal: That of ensuring a safe structure and ensuring the functionality of the structure. A bridge is no different than that and, like any other structure, should be able to withstand all the forces that may be applied to it. The nature of these forces varies from live loads, such as pedestrian and traffic load, to natural forces, such as wind, snow, temperature and seismic loads. In the analysis part, we do not consider the effect of wind, snow and seismic loads on the structure. In other words, only self-weight (including bridge deck, hand railings, edge beams and asphalt cover), pedestrian load, service vehicle load and temperature effect will be considered. Different combinations of these loads will, in turn, give different values for shear, moment and torsion forces which are later on used for further calculations.. 2.1 2.1.1. Design Limit State Design. A limit state is a condition of a structure beyond which it no longer fulfills the relevant design criteria. The condition may refer to a degree of loading or other actions on the structure, while the criteria refer to structural integrity, fitness for use, durability or other design requirements. A structure designed by LSD is proportioned to sustain all actions likely to occur during its design life, and to remain fit for use, with an appropriate level of reliability for each limit state. Building codes based on LSD implicitly define the appropriate levels of reliability by their prescriptions.. 5.

(22) 2.1.2. Ultimate Limit State. The ultimate limit state is the design for the safety of a structure and its users by limiting the stress that materials experience. In order to comply with engineering demands for strength and stability under design loads, ULS must be fulfilled as an established condition. ULS require that the structure must be able to withstand, with an adequate factor of safety against collapse or failure, the loads for which it is designed to ensure the safety of the building occupants and/or the safety of the structure itself. The possibility of buckling or overturning must also be taken into account, as must the possibility of accidental damages caused by vehicles and alike.. 2.1.3. Serviceability Limit State. Serviceability refers to the conditions under which a structure is still considered useful, apart from the material strength of the structure. These conditions are based on functionality, comfort and durability, which are essentials for the appearance of the structure. Should this limit state be exceeded, a structure that may still be structurally sound would nevertheless be considered unfit. Serviceability limit state design of structures includes factors such as durability, overall stability, fire resistance, deflection, cracking and excessive vibration. Deflection: The appearance or efficiency of any part of the structure must not be clearly affected by deflections nor the comforts of the ones who use it. Cracking: Local damage due to cracking and spalling must not affect the appearance, efficiency or durability of the structure.. 6.

(23) 2.2 2.2.1. Characteristic Load Calculations Self-Weight. Concrete Density: γc,B45 ≈ 25kN/m3. Self-weight of the deck: 78.9kN/m. Self-weight of the edge-beams: 2 ∗ 4.321kN/m = 8.643kN/m. Asphalt Cover: 2.5kN/m2 ∗ 3m = 7.5kN/m. Hand Railings: 2 ∗ 0.5kN/m = 1.0kN/m. Total Self-weight: 98.857kN/m. 7.

(24) 2.2.2. Traffic Loads. Distributed Pedestrian Load: qf k = 5.0kN/m2 Concentrated Pedestrian Load: Qf wk = 10kN Service Vehicle: Axle 1:. Qk.sv1 = 80kN. Axle 2:. Qk.sv2 = 40kN. (Axle 1 + Axle 2):. Qk.sv = 120kN. According to NS-EN 1991-2, NA.5.4(2), the bridge is subjected to a characteristic horizontal load from the service vehicle, Qf lk , along the bridge length. This load is equal to the highest of the two following values: • 10% of the total uniformly distributed load: 0.10 ∗ 15kN/m ∗ 31.294m = 46.941kN. • 60% percent of the total service vehicle load: 0.60 ∗ 120kN = 72.0kN. Qf lk = M ax[46.941kN ; 72.0kN ] = 72.0kN. 8.

(25) 2.3. Design Load Calculations. Detailed Calculation may be found on Appendix A. According to NS-EN 1990:2002+A1:2005+NA:2016, Table NA.A2.2, the value for ψ0 = 0.7 for pedestrian bridges.. 2.3.1. Vertical Design Load: Gd = γg ∗ Gk = 1.35 ∗ 97.9kN/m = 132.165kN/m qf d = γq ∗ qf k = 1.35 ∗ 0.7 ∗ 5.0kN/m2 = 4.725kN/m2 qf d ∗ b = 4.725kN/m2 ∗ 3m = 14.175kN/m. 2.3.2. Service Vehicle: Qd,sv1 = 1.35 ∗ 0.7 ∗ 80kN = 75.6kN. Qd,sv2 = 1.35 ∗ 0.7 ∗ 40kN = 37.8kN. 2.3.3. Horizontal Load: Qf ld = γq ∗ Qf lk = 1.35 ∗ 0.7 ∗ 72.0kN = 68.04kN. 9.

(26) 2.3.4. Design Load FBD Diagrams. Free Body Diagram. Figure 3:. Free Body Diagram. Shear Diagram. Figure 4:. Shear Force Diagram. Moment Diagram. Figure 5:. Bending Moment Diagram. 10.

(27) 2.3.5. Load Model Combinations. Equations 6.10(a) and 6.10(b) from Table NA.A2.4(B) - Dimensjonerende verdier for laster (STR/GEO) (Sett B) NS-EN 1990:2002+A1:2005+NA:2016 • Load Model 1 (Dead Load + Distributed pedestrian load). qf k = 5.0. kN m2. SectionN A.5.3.2.1(1)N S − EN 1991 − 2 : 2003 + N A : 2010. • Load Model 2 (Dead Load + Concentrated pedestrian load). Qf wk = 10kN. SectionN A.5.3.2.2(1)N S − EN 1991 − 2 : 2003 + N A : 2010. 11.

(28) • Load Model 3 ((Dead Load + Service vehicle) Qk.sv1 = 80kN Characteristic force of Service Vehicle on Axle 1: Qk.sv2 = 40kN Characteristic force of Service Vehicle on Axle 2: Qk.sv = Qk.sv1 + Qk.sv2 = 120kN. • Maximum Load. 12.

(29) Figure 6:. Table NA.A2.4(B). 13.

(30) 14.

(31) 2.4. Temperature Load. Thermal stress is stress created by any change in temperature to a material. These stresses can lead to fracture or plastic deformations depending on the other variables of heating, which include material types and constraints. Temperature gradients, thermal expansion or contraction and thermal shocks are factors that can lead to thermal stress. This type of stress is highly dependent on the thermal expansion coefficient which varies from material to material. In general the larger the temperature change, the higher the level of stress that can occur. 2.4.1. Evenly Distributed Temperature. The uniformly distributed temperature will depend on the lowest and highest expected temperature that occur on the location of the bridge. To calculate the evenly distributed temperature, the maximum and minimum air temperature is considered with a return period of 50 years. According to the isotherm map given in NS-EN 1991-1-5 these temperatures are: Tmin = −35◦ C Tmax = 36◦ C The values of Tmin and Tmax however, must be adjusted due to height effects. The minimum value is corrected by subtracting 0.3o C for each 100m over sea level and the maximum is subtracted 0.65o C for each 100m over sea level. The bottom of the bridge deck is located at 66.642m over sea level, and by adding 1.0m for the thickness of the deck that gives contour 67.642m above sea level. This gives:. Tmin = −35◦ C + (0.3◦ C ∗. 15. 67.642m ) = −34.797◦ C 100m.

(32) Tmax = 36◦ C − (0.65◦ C ∗. 67.642m ) = 35.560◦ C 100m. The bridge is of category type 3 (concrete). distributed temperature becomes:. Therefore, the uniformly. Te,max = Tmax − 3◦ C = 32.560◦ C Te,min = Tmin + 8◦ C = −26.797◦ C The initial temperature during construction is set to be: T0 = 10◦ C This gives a maximum characteristic value interval for contraction and expansion for the evenly distributed temperature: ∆TN ;contraction = −(T0 − Te,min ) = −36.797◦ C ∆TN ;expansion = (Te,max − T0 ) = 22.560◦ C. 16.

(33) 2.4.2. Variable Temperature Difference. If the temperature of the top and the bottom of the bridge deck are unequal, this means that there is a temperature difference throughout the deck section. This difference will, in turn, give a temperature effect (either positive or negative) with stress along the height of the cross-section. The temperature difference can be found by two different methods; one method for linear differences and one for non-linear.. 2.4.3. Linear Variable Temperature Difference. When calculating the linear variable temperature difference, the limiting values ∆TM.heat and ∆TM.cool are chosen from Table NA.6.1 in NS-EN 1991-1-5:2003. Due to the wearing surface, the temperature limits need to be modified by a factor ksur . Since the bridge deck has an asphalt cover of 50mm according to the drawings in Appendix I, ksur = 1.0, both if the deck top is warmer than the bottom, or if the bottom is the warmest. ∆TM.heat = 15.0◦ C ∗ ksur = 15.0◦ C ∆TM.cool = 8.0◦ C ∗ ksur = 8.0◦ C. 17.

(34) 2.4.4. Non-Linear Variable Temperature Difference. When calculating the non-linear variable temperature difference, the values from Table NA.6.2(C) in NS-EN 1991-1-5:2003 are used. In CSI Bridge, there is a method to apply temperature effect to the model due to these table values (see the detailed modelling procedure in Appendix B, pg....).. Figure 7:. Table NA.6.2(C). 18.

(35) 2.5 2.5.1. CSI Bridge Modelling Process Graphics Modeling. The modelling process on CSI Bridge often times follow a "path" from left to right on the tabs. Starting at Home, to Layout, and all the way to the Advanced tab. The procedure below describes some of these steps. A detailed procedure may be found in Appendix B.. Figure 8:. Modelling Process Diagram. 19.

(36) 2.5.2. Defining the Loads. In this chart, steps about how to add and modify different loads to the model is described. Detailed procedure may be found in Appendix B.. Figure 9:. Loading Process Diagram. 20.

(37) 2.5.3. Load Combinations. This simplified chart shows how the load combinations are added in CSI Bridge and how to obtain the values needed for design purposes. Detailed procedure may be found in Appendix B.. Figure 10:. Load Combination Process Diagram. 21.

(38) 3. Chapter - Design of Reinforced Concrete Bridge. 3.1. Material Properties. Both B45 concrete and B500NC steel will be used in the reinforcement design of the deck, abutments and the column.. 3.1.1. Concrete Compressive Strength.. Concrete elements must be capable of carrying forces caused by their self-weight and externally imposed loads. The load capacity of concrete structures is affected by the cracking behavior of concrete. Since the tensile strength of concrete is much lower than its compressive strength (approximately 10 times), concrete belongs to the group of brittle materials, but it is not perfectly brittle. According to the handbook N400, B45 concrete is the most common concrete type for bridge designs in Norway. Therefore, as one can read from the Design Drawings in Appendix I, B45 will be used. The compressive strength, fck , of B45 concrete is: fck = 45M P a 3.1.2. Steel Yield Strength. Structural members made of concrete are usually reinforced by steel bars. Steel reinforcement is used to resist tension, to distribute cracks and to limit cracks’ width. But the first aim of reinforcement is to protect against brittle failure in tensiled zones. The most common steel reinforcement, used for concrete structures in Norway, is B500NC. The yield strength, fyk , of B500NC is: fyk = 500M P a. 22.

(39) 3.1.3. Partial Safety Factors. For fatigue verification the partial factors for persistent design is given by table 2.2 from clause 2.4.2.4. Figure 11 shows the partial factors for materials for ultimate limit state.. Figure 11:. 3.1.4. Partial Safety factors. Concrete Design Compressive Strength. The design compressive strength, fcd , of the B45 concrete is calculated by the formula from clause 3.1.6 in NS-EN 1992-1-1:2004:. αcc = 0.85. γc = 1.5. fcd =. Figure 12:. αcc fck = 25.5M P a γc. Parabola Rectangle Diagram. 23. (1).

(40) 3.1.5. Steel Tensile Strength. Tensile Strength is the capacity of a material or structure to withstand actions tending to elongate, as opposed to compressive strength, which withstands actions tending to reduce size. In other words, tensile strength resists tension (being pulled apart), whereas compressive strength resists compression (being pushed together). Ultimate tensile strength is measured by the maximum stress that a material can withstand while being stretched or pulled before breaking. The tensile strength, fyd , of the reinforcing steel B500NC, shown in Figure 13, is calculated according to clause 3.2.7 in NS-EN 1992-1-1:2004. γs = 1.15 fyd =. Figure 13:. fyk = 434.783M P a γs. Stress-Strain Diagram. 24.

(41) 3.2 3.2.1. Bending Reinforcement Over Column Introduction. Bending moment is the measure of the bending effect that can occur when an external force is applied to a structural element. This concept is important in structural engineering as it can be used to calculate where, and how much bending may occur when forces are applied to the structure. The most common structural element that is subject to bending moments is the beam, which may bend when loaded at any point along its length. Failure can occur due to bending when the tensile stress exerted by a force is equivalent to or greater than the ultimate strength (or yield stress) of the element, thus requiring reinforcements for bending where the fibres are in tension.. Figure 14:. Simplified Deck Cross-Section Over Column. 25.

(42) 3.2.2. Cover to the reinforcement. The concrete cover is the distance between the surface of the reinforcement closest to the nearest concrete surface (including links and stirrups (i.e. reinforcement for shear) and surface reinforcement where relevant). It is crucial to have a minimum concrete cover to the reinforcement to ensure proper bonding of the reinforcement and the concrete, as well to provide fire resistance and durability to the structure. The nominal cover is calculated according to clause 4.4.1.1 in NS-EN 1992-1-1. Nominal cover: Cnom = Cmin + ∆Cdev Minimum cover due to environment conditions: Cmin,dur = 60mm - XD3:100 years is used. Allowance in design for deviation: ∆Cdev = 15mm. 26.

(43) 3.2.3. Effective Depth. Effective depth is the distance between extreme compression fiber to the centroid of tension reinforcement in a section under flexure.. Figure 15:. Effective-Depth Stress-Strain Diagram. 27.

(44) 3.2.4. Design for flexure along Y-Axis. 3.2.5. Lever Arm. 28.

(45) 3.2.6. Required Steel Area. 3.2.7. Spacing. 3.2.8. Maximum Spacing Check. 29.

(46) 3.2.9. Steel Reinforcement Provided. 3.2.10. Minimum Reinforcement Area. Minimum reinforcement is provided in concrete in order to improve their behaviour towards cracking and ductility at failure.. 30.

(47) 3.2.11. Maximum Reinforcement Area:. 31.

(48) 3.2.12. Transverse Reinforcement Over Column. The diameter of the transverse reinforcement (links, loops or helical spiral reinforcement) should not be less than 6mm or 25% of the maximum longitudinal bars, whichever is greater.. 3.2.13. Transversal Lever Arm. 3.2.14. Required Steel Area. 32.

(49) 3.2.15. Transversal Reinforcement Spacing. 3.2.16. Maximum Spacing. 3.2.17. Steel Reinforcement Provided. 33.

(50) 3.3 3.3.1. Bending Reinforcement at the Mid-Span Introduction. The maximum bending moments applied on each of the two spans are located at the center of the spans (between the abutment and the column). The bending moments decreases as they approaches the supports. Although they are decreasing, bending reinforcement is necessary along the bridge spans due to the forces acting on the bridge deck, causing the mid-span to "sag". The tensile reinforcement is calculated based on the maximum bending moment at one of the Mid-Spans obtained from the CSI Bridge Model.. Figure 16:. Simplified Deck Cross-Section Mid-Span. 34.

(51) 3.3.2. Design For Flexure. 3.3.3. Lever Arm. 3.3.4. Required Steel Area. 35.

(52) 3.3.5. Spacing. 3.3.6. Maximum Spacing. 3.3.7. Steel Reinforcement Provided. 36.

(53) 3.3.8. Minimum Reinforcement Area. 3.3.9. Maximum Reinforcement Area. 37.

(54) 3.3.10. Transversal Reinforcement Mid-Span. 3.3.11. Lever Arm. 3.3.12. Required Steel Area. 38.

(55) 3.3.13. Spacing. 3.3.14. Maximum Spacing. 3.3.15. Steel Reinforcement Provided. 39.

(56) 3.4 3.4.1. Shear Reinforcement Introduction. A shear force is a force applied perpendicular to a surface, in opposition to an offset force acting in the opposite direction. When a structural member experiences failure by shear, two parts of it are pushed in different directions, for example, when a piece of paper is cut by scissors.. Figure 17:. 3.4.2. Shear Force Action. Section ThatDO NOT Require Reinforcement. The concrete sections that do not require shear reinforcements are mainly lightly loaded floor slabs and pad foundations. Beams and decks are generally more heavily loaded, and therefore, they nearly always do require shear reinforcements. Maximum shear value Ved,z is obtained from computations on CSI Bridge program.. 40.

(57) 41.

(58) 3.4.3. Section that DO Require Shear Reinforcement. 42.

(59) 3.4.4. Spacing Between Shear Reinforcement. Spacing between shear reinforcement according to EC2 (Clause 9.2.2 and NA 9.2.2.4(5).. 43.

(60) 3.5 3.5.1. Punching Shear Reinforcement Introduction. Punching shear is one of the most difficult problems in design of concrete structures. Much experimental and theoretical work has been carried out to develop mechanical models, analyses methods and code regulations to find the shear resistance for punching. Among the factors which influences the punching shear resistance in the concrete deck, some of the most important ones are concrete quality, amount of longitudinal reinforcement and the bar sizes. Punching Shear:. Figure 18:. Punching Shear Failure Diagram. 44.

(61) 3.5.2. Punching shear resistance WITHOUT reinforcement. 45.

(62) 46.

(63) 47.

(64) 48.

(65) 3.6 3.6.1. Torsion Reinforcement Introduction. Torsional moments on an element will produce shear stresses within the element which will try to cause diagonal cracking, and may require reinforcement additional to that required for bending and shear. Diagonal cracking occurs when these tensile stresses exceed the tensile strength of the concrete.. Figure 19:. Torsion Action. Figure 20:. Torsion Action. 49.

(66) 3.6.2. Deck Torsional Cross Section. Our bridge deck cross-section was divided into three rectangular sections, each designed separately to carry a proportion of the torque Ted,deck .. Figure 21:. 3.6.3. Simplified Cross Section. St Venant’s Torsional Constant, K. Figure 22:. St.. Venant’s Torsional Constant K. 50.

(67) The torsion carried by each rectangle Ti (According to Reinforced Concrete Design To EuroCode 2 Pg:127) can be determined elastically by calculating the torsional stiffness of each part according to its St. Venant’s torsional stiffness from the expression:. Ti =. Ted,deck ∗ Ki ∗ (hmin3 ∗ hmax )i P (K ∗ hmin3 ∗ hmax ). Where hmin and hmax are the minimum and the maximum dimensions of each section. K is the St.Venant’s Torsional Constant that varies according to the ratio: hmax hmin typically values of each are shown in figure 22. The subdivision of a shape into its component rectangles should be done in order to maximize the stiffness expression: X. (Khmin3 hmax ). 51.

(68) 52.

(69) 53.

(70) 3.6.4. St.Venant’s Constant for sections 1, 2 and 3. 54.

(71) 55.

(72) 3.6.5. Torsion Calculations. 56.

(73) 3.6.6. Combined Effect (Torsion + Shear). 57.

(74) 3.7 3.7.1. Reinforcement Of Column Introduction. The column is a structure that carry the loads from the deck, beam or a slab down to the foundations, and therefore they are primarily compression members. Slenderness, and the risk of lateral deflections leading to buckling, is an important consideration in determining failure modes for columns. Therefore, it is important to check whether the column is a short column or a slender column before doing the reinforcement calculations. If it is slender, special requirements will apply for the design and the calculations, to prevent buckling. Design of the column is governed by ULS; deflection and cracking are usually not a problem, but nevertheless correct detailing of the reinforcement and adequate cover are important. Since the column has a circular cross-section, the bending reinforcement is symmetrical on both sides of the axis. Therefore, there is no need to calculate moment resistance about y- and z-axis separately.. Figure 23:. Simplified Column Cross-Section. 58.

(75) 3.7.2. Dimensions. 3.7.3. Eccentricity, e, of The Load. The distance between the center of the column cross-section and the eccentric load is referred as eccentricity, symbolized by e. Increase in the eccentric load increases the axial load and the moment acting on the column. This makes the column to bend additional increasing the bending of the column. For a cross-section with symmetrical reinforcement, loaded by the compression h force, it is necessary to assume the minimum eccentricity e0 = but 30 no less than 20mm. Here, h is the depth of the section in mm. ey along y-axis and ez along z-axis will also be evaluated.. 59.

(76) 3.7.4. Minimum Reinforcement. 60.

(77) 3.7.5. Slenderness Ratio. 3.7.6. Normalized slenderness ratio. 61.

(78) 3.7.7. Equations for Determining the Creep Coefficient. The creep coefficient ϕ(t, to ) may be calculated from Eurocode 2, Annex [B]. ϕ(t, to ) = ϕ0 βc (t, t0 ). Where: The notional creep coefficient ϕ0 may be estimated from ϕ0 = ϕRH β(fcm )β(t0 ). 62.

(79) The factor that allows for the effect of relative humidity ϕRH on the notional creep coefficient:. The factor β(fcm ) that allows for the effect of concrete strength on the notional creep coefficient:. The factor β(t0 ) to allow for the effect of concrete age at loading on the notional creep coefficient:. 63.

(80) 64.

(81) 3.7.8. Limit of normalized slenderness ratio. 65.

(82) 3.7.9. Column Reinforcement. 66.

(83) 67.

(84) 3.7.10. Bi-axial Bending Check. Since the column has a circular cross-section, the bending reinforcement is symmetrical on both sides of the axis. Therefore, there is no need to calculate moment resistance about y- and z-axis separately.. 68.

(85) Figure 24:. MN-Diagram for circular column. 69.

(86) 3.8 3.8.1. Reinforcement of Foundation Pad Introduction. Pad foundations are a form of spread foundations formed by rectangular, square, or sometimes circular concrete ‘pads’ that support localized single-point loads such as structural columns, groups of columns or framed structures. These loads are then spread by the pads to the bearing layer of soil or rock below. Pad foundations can also be used to support ground beams. A pad foundation should be designed to effectively spread a concentrated force into a bearing stratum. They are popular design solutions as they are generally cost-effective and relatively easy to design and construct. Moreover, pad foundations are suitable for most sub-soils except loose sands, loose gravels and filled areas.. Figure 25:. Foundation Pad Diagram. 70.

(87) In order for pad foundations to spread the load into the soil, the pad must be either sufficiently deep (allowing the force of the load to spread out at a pre-defined angle), or be constructed with adequate reinforcement. The bearing capacity of the soil, as well as the concrete strength, are factors that define the angle of the spreading of the load. There are a few considerations when designing a foundation pad. Due to the forces acting on the pad, the loss of overall stability, bearing failure and failure by sliding are among some concerns that must be examined. • Combined failure in the ground and in the structure. • Structural failure due to foundation movement. • Excessive settlements. • Excessive heave due to swelling, frost and other causes. 3.8.2. Important Details Regarding Pad Design. In this project however, it is important to notice that both the center column and the abutments are all placed on rock and not on soil. Appendix E (detailed Drawings in page K-203) shows this conditions. Therefore, bearing capacity of soil does not apply in the "traditional" sense, since the soil bearing capacity is set to 18000kN/m2 . This value is obtained from Intern Rapport Nr.2374 - Forankring Med Bergbolter Ved Fundamentering AV Støttemurer og Landkar på Berg.. 71.

(88) 3.8.3. Bearing Capacity of Soil Under Foundation Pad. 3.8.4. Introduction. Bearing capacity, σcm , is the capacity of soil to support the loads applied to the ground. The bearing capacity of soil is the maximum average contact pressure between the foundation and the soil which should not produce shear failure in the soil.. Figure 26:. Soil Bearing Capacity Diagram. 72.

(89) 73.

(90) 3.8.5. Maximum Design Vertical Pressure. σcm = 18000kN/m2 is obtained from Intern Rapport Nr.2374, Forankring Med Bergbolter Ved Fundamentering AV Støttemurer og Landkar på Berg.. 74.

(91) 3.8.6. Bending Reinforcement of Foundation Pad. 75.

(92) 3.8.7. Lever Arm. 3.8.8. Steel Required Area. 3.8.9. Spacing. 76.

(93) 3.8.10. Number of Bars. 77.

(94) 3.8.11. Punching Shear on Foundation Pad. 3.8.12. Introduction. Punching Shear occurs when an area is subjected to a concentrated state of stress relative to its immediate surroundings. Failure can occur either by pure punching or by bending induced punching, where the initial tension cracks will grow tangentially to form the punching surface. The cracked profile of the punched area indicates the mode of failure.. Figure 27:. Punching Shear on Pad. • Basic Control Perimeter. Figure 28:. Control Perimeter on Pad. 78.

(95) 3.8.13. Effective Pad Depth, def f ;pad. 3.8.14. Basic Control Perimeter. 79.

(96) 80.

(97) 3.8.15. Punching shear stress at control perimeter. (Clause 6.4.5). 81.

(98) 82.

(99) 3.8.16. Punching shear stress at column perimeter. 83.

(100) 3.9 3.9.1. Reinforcements Of Abutment West Introduction. Abutment refers to the substructure at the ends of a bridge span whereon the structure’s superstructure rests or contacts. Single-span bridges have abutments at each end which provide vertical and lateral support for the bridge, as well as acting as retaining walls to resist lateral movement of the earthen fill of the bridge approach. Multi-span bridges require piers to support ends of spans unsupported by abutments.. Figure 29:. Abutment West Cross-Section. 84.

(101) 3.9.2. Dimensions. Since. the abutment is considered as a deep-beam. Therefore, we need to apply the strut-and-tie method when calculating the reinforcements for the abutments.. 85.

(102) 3.9.3. Strut-and-Tie Method. The strut-and-tie modeling technique is a simple and effective method which can be used as a quick tool for analysis of discontinuous regions (D-regions) in reinforced and pre-stressed concrete structures. It serves practicing engineers to grasp load transfer characteristics in order to provide good details of reinforcement and to determine load carrying capacity of the members in a very effective way. Since the method is based on lower bound theorem of plasticity, it can be assured to deliver safe designed structure. In the analysis of both abutments, west and east, the strut-and-tie method is used for further computations.. Figure 30: Abutment West Strut-and-Tie. Figure 31: Abutment West Strut-and-Tie Cross-Section.. 86.

(103) 3.9.4. Design Of Deep-Beam. 3.9.5. Forces on Abutment. 87.

(104) 3.9.6. Control of Design Stresses in Concrete Struts. (Clause 6.5.4(4), Figure 6.27 in EC2). 88.

(105) 3.9.7. Earth Pressure on Abutment West. 3.9.8. Vertical pressure on terrain. 89.

(106) 3.9.9. Effective vertical pressure on terrain. 3.9.10. Horizontal Effective Active Pressure. 3.9.11. Horizontal Active Pressure. 90.

(107) 3.9.12. Horizontal Effective Passive Pressure. 3.9.13. Horizontal passive pressure. 3.9.14. Moment Due To Horizontal Pressures From Terrain. Figure 32:. Horizontal Earth Pressure. 91.

(108) 3.9.15. Vertical Reinforcement. 92.

(109) 93.

(110) 3.9.16. Horizontal Tension Reinforcement at 0.1h. 94.

(111) 3.9.17. Horizontal Reinforcement. 95.

(112) 3.9.18. Bearing Capacity of Pad. 96.

(113) 3.9.19. Bending Reinforcement of West Abutment Pad. 97.

(114) 3.9.20. Steel Area Required. 3.9.21. Spacing. 98.

(115) 3.9.22. Number of Bars Needed. 99.

(116) 3.10. Reinforcement Of Abutment East. 3.10.1. Dimensions. 3.10.2. Design of deep beam. 100.

(117) 3.10.3. Forces on Abutment. 3.10.4. Control of Stresses. 101.

(118) 102.

(119) 3.10.5. Earth Pressure On Abutment. 3.10.6. Vertical Pressure. 103.

(120) 3.10.7. Effective Vertical Pressure. 3.10.8. Effective Horizontal Active Pressure. 3.10.9. Horizontal Active Pressure. 104.

(121) 3.10.10. Effective horizontal passive pressure. 3.10.11. Horizontal Passive Pressure. 3.10.12. Moment Due to Horizontal Pressures. 105.

(122) 3.10.13. Vertical Reinforcement. 106.

(123) 107.

(124) 3.10.14. Horizontal Reinforcement at 0.1h. 108.

(125) 3.10.15. Horizontal Reinforcement. 109.

(126) 3.10.16. East Abutment Pad Bearing capacity. 110.

(127) 3.10.17. Bending Reinforcement of pad. 111.

(128) 3.10.18. Lever Arm. 112.

(129) 3.10.19. Steel Area Required. 3.10.20. Spacing. 113.

(130) 3.10.21. Number of Bars Needed. 114.

(131) 3.11. Summary. The analysis undertaken in chapter 2 and 3 are a complete analysis of loads and reinforcements, given the conditions to which the bridge was projected. In order to comply with engineering demands for strength and stability under design loads, ULS must be fulfilled as an established condition, which it was. Load Calculations were performed in Chapter 2 and Reinforcement of all the bridge components were performed in Chapter 3.. 115.

(132) 4 4.1. Chapter - Standard vs Simplified Model Comparison Introduction. In this chapter, a comparison between the Standard Model and Simplified Model will be carried out. No changes will be made for its dimensions, i.e., the length of the bridge along with the deck width and thickness will remain the same. However, changes will be made on the bridge’s slope, incline of the deck and the curvature (radius) of the bridge. The dimensions of the column and abutments will also be unchanged in both models.. Measurements Deck Length Total Length Span 1 Length Span 2 Width Thickness Slope Incline Radius. Designs Comparison Standard Simplified Model Model 31.294m 31.294m 15.647m 15.647m 15.647m 15.647m 3702mm 3702mm 1000mm 1000mm 0.062 0 3% 0% 148.75m 0m. Table 1:. 4.2. Designs Comparison. Diagram Results. 116.

(133) Standard model:. Axial Force Diagrams. Simplified model:. 117.

(134) Bending moment diagrams (about y-axis). Standard model:. Simplified model:. 118.

(135) Bending Moment Diagrams (about z-axis). Standard model:. Simplified model:. 119.

(136) Shear Force Diagrams (Horizontal). Standard model:. Simplified model:. 120.

(137) Shear Force Diagrams (Vertical). Standard model:. Simplified model:. 121.

(138) Standard model:. Torsion Diagrams. Simplified model:. 122.

(139) Standard model:. Displacement Diagrams. Simplified model:. 123.

(140) 124.

(141) 125.

(142) 5. Chapter - Deck Resize Analysis. 5.1. Introduction. In this analysis we came to consider the deck section of the bridge. Changing its dimensions may lead to serious consequences to its ability to satisfy the preset requirements. The deflection of the deck, due to the loads imposed onto it, should occur if the height is changed. Five different analyses were carried out to test these outcomes. 5.1.1. Forces on the Deck. Height Area Gk Med,y,B Med,z,B Med,y,AB Med,z,AB Ved,z Ned,column Medy,column Ted,deck. 1000mm 3, 269m2 98, 86kN/m 3954, 85kN m 262, 15kN m 2351, 31kN m 195, 69kN m 1292, 23kN 2627, 2kN 64, 75kN m 197, 71kN m Table 2:. Deck 900mm 2, 965m2 91, 27kN/m 3665, 75kN m 254, 14kN m 2179, 64kN m 191, 61kN m 1195, 76kN 2432, 4kN 53, 2kN m 199, 20kN m. 700mm 2, 363m2 76, 22kN/m 3068, 63kN m 237, 0kN m 1820, 31kN m 183, 1kN m 998, 2kN 2038, 9kN 32, 57kN m 202, 0kN m. Forces on Deck. 126. 500mm 1, 755m2 61, 0kN/m 2450, 77kN m 221, 36kN m 1462, 96kN m 174, 85kN m 797, 81kN 1639, 4kN 16, 57kN m 205, 35kN m.

(143) Figure 33:. Figure 34:. Graph Bending Moment. Graph Shear Force. 127.

(144) Figure 35: 5.1.2. Size SBy Barsl SBz Barst SABy SABz S Barsy Barsz. Graph Torsion. Deck Reinforcement, Spacing and No.of Bars Deck Reinforcement Spacing and Bars 1000mm 900mm 700mm 280mm 270mm 240mm 15 14 14 430mm 390mm 310mm 3/m 3/m 4/m 250mm 240mm 220mm 610mm 550mm 420mm 150mm 140mm 130mm 18 16 14 11 11 11 Table 3:. Deck Reinforcement Spacing and Bars. 128. 500mm 190mm 14 220mm 5/m 170mm 290mm 110mm 13 11.

(145) Figure 36:. Graph Longitudinal Reinforcement. Figure 37:. Graph Transversal Reinforcement. 129.

(146) Figure 38:. Figure 39:. Graph Shear Reinforcement. Graph Vertical Displacement. 130.

(147) Size Gk Fa.w Medy.w FA.e Med,y,e. Forces on Abutments 1000mm 900mm 700mm 98, 857kN/m 91, 27kN/m 76, 22kN/m 523, 26kN 497, 0kN 439, 0kN 220, 12kN m 195, 85kN m 195, 85kN m 522, 65kN 495, 4kN 436, 9kN 0kN m 0kN m 0kN m Table 4:. Size Sv.w Spad.w Barsl.pad.w Barst.pad.w Sve Spad.e Barsl.pad.e Barst.pad.e. Forces on Abutments. Abutment Reinforcement, Spacing and Bars 1000mm 900mm 700mm 869, 5mm 1000mm 1200mm 120mm 130mm 140mm 34 31 29 31 29 27 900mm 1000mm 1100mm 310mm 320mm 320mm 11 11 11 16 16 16 Table 5:. 500mm 61, 02kN/m 380, 80kN 195, 85kN m 378, 3kN 0kN m. Abutment Reinforcement Spacing and Bars. 131. 500mm 1500mm 150mm 27 25 1300mm 320mm 11 16.

(148) 6. Chapter - Conclusion. In this bachelor thesis the structural analysis of a concrete bridge was carried out. CSI Bridge software was used to create the model which was then used to perform various load combinations and arrangements to see how these changes would influence the bearing capacity of the structure. This analysis was divided in two separate sections in an attempt to compare the results to the original design. In the first part, a simplified model was developed in the software, where the bridge’s slope, angle and curvature were all set to 0 while the dimensions of the bridge deck, column and abutments were kept the same. The purpose of this simplification was to verify, given the same load combinations and conditions, that the criteria set by the Standards and codes in ULS and SLS would still be fulfilled. Another purpose was to figure out how significant the changes we obtained in the forces were, due to the simplification of the bridge model. A more detailed comparison was done in Chapter 4 - Standard Model vs Simplified Model.. Simplified Model Variations Forces Increase Reduction Axial Force 45.25% Moment Y-Axis 4.67% − Moment Z-Axis 28.3% Shear Horizontal 67.54% Shear Vertical 4.84% Torsion 62% Displacement 4.48% Table 6:. Simplified Model Variations. 132.

(149) As it can be observed, the results demonstrate that by simplifying the geometry of the structure some significant changes in forces on the structure may occur. Those changes implies that reinforcements would also have to be calculated in accordance with these changes. These simplifications however, were not done on the original design due to the topographical properties of the location of where it was being built. The second analysis carried out in this thesis was the re-dimensioning of the deck thickness. It was originally designed with a thickness of 1000mm and 5 subsequent reductions of 100mm each were made in order to verify its behaviour while fulfilling all the requirements. As expected, due to the bridge’s deck self-weight, all the forces subjected to the structure were being reduced except torsion, which went up by 3.66%. Data was collected and checks were made in order to see if any structural failure would occur. Since the self-weight of the deck was the primary reason for the forces we were obtaining, for each time we reduced its dimensions, these forces also changed. Because of that, no structural failure due to moment, shear or punching shear occurred. When the reinforcement calculations were done for each thickness reduction, we could verify that the number of bars and the spacing between the bars were also reduced in each analysis part.. Size SBy Barsl SBz Barst SABy SABz S Barsy Barsz. Deck Reinforcement Spacing and Bars 1000mm 900mm 700mm 280mm 270mm 240mm 15 14 14 430mm 390mm 310mm 3/m 3/m 4/m 250mm 240mm 220mm 610mm 550mm 420mm 150mm 140mm 130mm 18 16 14 11 11 11. 133. 500mm 190mm 14 220mm 5/m 170mm 290mm 110mm 13 11.

(150) When observing these changes, and that no failures occurred, we wondered if the deflection requirement would still be fulfilled. Deflection is the degree to which a structural element is displaced under a load. Therefore, deflection calculations were considered in this analysis as well. For deflection control, we selected the maximum allowable deflection limit (Span/350) that were appropriate to the structure and its intended use. The calculated deflection could not exceed this limit. Codes give a general guidance for both the selection of the allowable deflection limit and the calculation of the maximum deflection of the structure. However, the simplified procedures for calculating deflection in most codes were developed from tests on simply- supported reinforced concrete beams and often produce inaccurate predictions when applied to more complex structures, which were not the case here. These deflection limits were exceeded at a deck thickness of 500mm as shown in figure 39.. 134.

(151) The drastic change observed in the graph above is due to the cracked section that had not occurred on the structure in the previous thickness reductions. The design for serviceability was possibly one of the most important aspects of the design. Service load behaviour depends primarily on the properties of the concrete and these are often not known reliably at the design stage. Moreover, concrete behaves in a non-linear and inelastic manner at service loads. The non-linear behaviours that complicates serviceability calculations is due to cracking, tension stiffening, creep, and shrinkage. Out of these, shrinkage is the most problematic aspect of these calculations. Restraint to shrinkage causes time-dependent cracking and gradually reduces the beneficial effects of tension stiffening. It results in a gradual widening of existing cracks and, in flexural members, a significant increase in deflections with time, which is what occurred when the deck were reduced to 500mm. These restraint to shrinkage is probably the most common cause of unsightly cracking in concrete structures. In many cases, these problems arise because shrinkage has not been adequately considered in the design and the effects of shrinkage are not adequately modelled in the design procedures specified in codes of practice for crack control and deflection calculation. Appendix F (Deflection Calculation) shows the complete deflection calculation for the Standard Model.. 135.

(152) References • A. Aalberg, A.H. Clausen & P.K. Larsen, "Stålkonstruksjoner - Profiler og Formler", 3. utgave. Trondheim: Fagbokforlaget, 2014 • B. Mosley, J. Bungey & R. Hulse, "Reinforced Concrete Design: to Eurocode 2", 7th edition. Hampshire: Palgrave Macmillan, 2012. •. Eurokode: Grunnlag for prosjektering av konstruksjoner, NS-EN 1990:2002+NA:2008, Standard Norge.. • Eurokode 1: Laster på konstruksjoner - Del 1-1: Allmenne laster - Tetthet, egenvekt og nyttelaster i bygninger, NS-EN 1991-1-1:2002+NA:2008, Standard Norge. • Eurokode 1: Laster på konstruksjoner - Del 1-5: Allmenne laster - Termiske påvirkninger, NS-EN 1991-1-5:2003+NA:2008, Standard Norge. • Eurokode 1: Laster på konstruksjoner - Del 2: NS-EN 19912:2003+NA:2010, Standard Norge.. Trafikklast på bruer,. • Eurokode 2: Prosjektering av betongkonstruksjoner - Del 1-1: Allmenne regler og regler for bygninger, NS-EN 1992-1-1:2004+NA:2008, Standard Norge. • Eurokode 7: Geoteknisk Prosjektering - Del 1: NS-EN 1997-1:2004+NA:2008, Standard Norge.. Allmenne Regler,. • J.A. Øverli & S.I. Sørensen, "Concrete Structures 3 - Compendium", Norges Teknisk-Naturvitenskapelige Universitet: Department of Structural Engineering, 2011. • Statens vegvesen, "Bruklassifisering", Håndbok R412, 2014. • Statens vegvesen, "Bruprosjektering", Håndbok N400, 2015.. 136.

(153) • Statens vegvesen, "Forankring med Bergbolter ved Fundamentering av Støttemurer og Landkar på Berg", Intern Rapport Nr.2374, 2004. • Statens vegvesen, "Geoteknikk i vegbygging", Håndbok 016, 2010. • Statens vegvesen, "Plassproduserte platebruer", Håndbok 4, 2000.. 137.

(154) Appendices. 138.

(155) A. Load Calculations. 139.

(156) Load Calculations L ≔ 31.294 m. (Bridge length). bdeck ≔ 3702 mm. (Deck width). blane ≔ 3.0 m. (Lane width). hdeck ≔ 1000 mm. (Deck height). Section 1: hdeck.1 ≔ 350 mm Ad.1 ≔ bdeck ⋅ hdeck.1 = 1.296 m. 2. Section 2: hdeck.2 ≔ 430 mm bdeck.2 ≔ bdeck − 408 mm − 434 mm = 2.86 m ⎛ bdeck + bdeck.2 ⎞ 2 Ad.2 ≔ ⎜―――― ⎟ ⋅ hdeck.2 = 1.411 m 2 ⎝ ⎠ Section 3: hdeck.3 ≔ 220 mm bdeck.4 ≔ 430 mm bdeck.3 ≔ bdeck.2 − 2 ⋅ bdeck.4 = 2 m Ad.3 ≔ bdeck.3 ⋅ hdeck.3 = 0.44 m. 140. 2. Non-Commercial Use Only.

(157) Section 4: Ad.4 ≔ 61015.9884 mm. 2. Total area of the concrete deck: Adeck ≔ Ad.1 + Ad.2 + Ad.3 + 2 ⋅ Ad.4 = 3.269 m. 2. Area of edge beams. 141. Non-Commercial Use Only.

(158) hEB ≔ 700 mm. bEB.top ≔ 500 mm. Section 1:. bEB.bottom ≔ 150 mm. Section 2:. hEB.1 ≔ 220 mm. hEB.2 ≔ hEB − hEB.1 = 480 mm. Ab.1 ≔ bEB.top ⋅ hEB.1 = 0.11 m. 2. Ab.2 ≔ bEB.bottom ⋅ hEB.2 = 72000 mm. Section 3:. Section 4:. bEB.3 ≔ 70 mm. hEB.3 ≔ 70 mm. hEB.4 ≔ 20 mm. bEB.3 ⋅ hEB.3 2 = 2450 mm Ab.3 ≔ ―――― 2. bEB.top ⋅ hEB.4 2 = 5000 mm Ab.4 ≔ ――――― 2. Section 5:. Section 6:. hEB.5 ≔ 20 mm. bEB.5 ≔ 20 mm. hEB.6 ≔ 20 mm bEB.6 ≔ bEB.bottom − bEB.5 = 130 mm. bEB.5 ⋅ hEB.5 2 = 200 mm Ab.5 ≔ ―――― 2. hEB.6 ⋅ bEB.6 2 = 1300 mm Ab.6 ≔ ―――― 2. Area of each concrete Edge Beam: AEB ≔ Ab.1 + Ab.2 − Ab.3 − Ab.4 − 2 ⋅ Ab.5 − Ab.6 = 0.173 m. 142. Non-Commercial Use Only. 2. 2.

(159) Selfweight of concrete kN γconcrete ≔ 25 ―― 3 m. Density of reinforced concrete. kN Gk.concrete ≔ γconcrete ⋅ ⎛⎝Adeck + 2 ⋅ AEB⎞⎠ = 90.357 ―― m. Selfweight of concrete (deck +borders). kN kN Gk.hand.railings ≔ 2 ⋅ 0.5 ⋅ ―― = 1 ―― m m. Selfweight of hand railings on concrete borders. kN kN Gk.asphalt ≔ 2.5 ―― ⋅ blane = 7.5 ―― 2 m m. Selfweight of asphalt cover. kN Gk ≔ Gk.concrete + Gk.hand.railings + Gk.asphalt = 98.857 ―― Selfweight of bridge deck m. 143. Non-Commercial Use Only.

(160) Load Combinations Partial safety factors (from Tabell NA.A2.4(B) NS-EN 1990:2002+A1:2005+NA:2016) γG ≔ 1.35. γQ ≔ 1.35. Equations 6.10(a) and 6.10(b) from Tabell NA.A2.4(B) - Dimensjonerende verdier for laster (STR/GEO) (Sett B) NS-EN 1990:2002+A1:2005+NA:2016. ξ ≔ 0.89. ψ0 ≔ 0.7. Tabell NA.A2.2 - Verdier av ψ-faktorer for gangbruer NS-EN 1990:2002+A1:2005+NA:2016. Load Model 1 (Dead Load + Pedestrian distributed load): kN qfk ≔ 5.0 ―― 2 m. Section NA.5.3.2.1(1) NS-EN 1991-2:2003+NA:2010. Eq. 6.10(a). Load1.a ≔ γG ⋅ Gk ⋅ L + γQ ⋅ ψ0 ⋅ qfk ⋅ blane ⋅ L = 4619.975 kN Eq. 6.10(b) Load1.b ≔ γG ⋅ ξ ⋅ Gk ⋅ L + γQ ⋅ qfk ⋅ blane ⋅ L = 4350.684 kN. Load Model 2 (Dead Load + Pedestrian concentrated load): Qfwk ≔ 10 kN. Section NA.5.3.2.2(1) NS-EN 1991-2:2003+NA:2010. Eq. 6.10(a) Load2.a ≔ γG ⋅ Gk ⋅ L + γQ ⋅ ψ0 ⋅ Qfwk = 4185.833 kN Eq. 6.10(b) Load2.b ≔ γG ⋅ ξ ⋅ Gk ⋅ L + γQ ⋅ Qfwk = 3730.481 kN. 144. Non-Commercial Use Only.

(161) Load Model 3 (Dead Load + Service vehicle): Qk.sv1 ≔ 80 kN. Characteristic force of Service Vehicle on Axel 1:. Qk.sv2 ≔ 40 kN. . Characteristic force of Service Vehicle on Axel 2:. Qk.sv ≔ Qk.sv1 + Qk.sv2 = 120 kN. Section NA.5.6.3(1) NS-EN 1991-2:2003+NA:2010. Eq. 6.10(a) Load3.a ≔ γG ⋅ Gk ⋅ L + γQ ⋅ ψ0 ⋅ Qk.sv = 4289.783 kN Eq. 6.10(b) Load3.b ≔ γG ⋅ ξ ⋅ Gk ⋅ L + γQ ⋅ Qk.sv = 3878.981 kN. Max.Load ≔ max ⎛⎝Load1.a , Load1.b , Load2.a , Load2.b , Load3.a , Load3.b⎞⎠ = 4619.975 kN. 145. Non-Commercial Use Only.

(162) Design loads kN Gd ≔ γG ⋅ Gk = 133.456 ―― m. Design load of selfweight. kN qfd ≔ γQ ⋅ ψ0 ⋅ qfk = 4.725 ―― 2 m kN Qd ≔ qfd ⋅ blane = 14.175 ―― m. Design load of pedestrians. Qd.sv1 ≔ γQ ⋅ ψ0 ⋅ Qk.sv1 = 75.6 kN. . Design force of Service Vehicle on Axel 1. Qd.sv2 ≔ γQ ⋅ ψ0 ⋅ Qk.sv2 = 37.8 kN. . Design force of Service Vehicle on Axel 2. Qd.sv ≔ Qd.sv1 + Qd.sv2 = 113.4 kN. Design force of Service Vehicle. Horizontal forces Along the bridge length: Qflk.1 ≔ 10% ⋅ qfk ⋅ blane ⋅ L = 46.941 kN Qflk.2 ≔ 60% ⋅ Qk.sv = 72 kN Qflk ≔ max ⎛⎝Qflk.1 , Qflk.2⎞⎠ = 72 kN. Horizontal characteristic load along the bridge length. Qfld ≔ γQ ⋅ ψ0 ⋅ Qflk = 68.04 kN. Horizontal design load along the bridge length. Transverse of bridge length: Qftk ≔ 25% ⋅ Qflk = 18 kN . Horizontal characteristic load transverse of the bridge length. . Horizontal design load transverse of the bridge length. Qftd ≔ γQ ⋅ ψ0 ⋅ Qftk = 17.01 kN. 146. Non-Commercial Use Only.

(163) Calculation of support reactions EI ≔ 1 L ≔ 15.647 ⋅ m. 4. To find : ΔB. 5 ⋅ ⎛⎝Gd + Qd⎞⎠ ⋅ L ΔB ≔ ―――――― 24 ⋅ EI. 147. Non-Commercial Use Only.

(164) 2. x M (x) ≔ ⎛⎝Gd + Qd⎞⎠ ⋅ L ⋅ x − ⎛⎝Qd + Gd⎞⎠ ⋅ ― 2 x m1 (x) ≔ ― 2. x m2 (x) ≔ L − ― 2. 2⋅L ⎛L ⎞ 1 ⌠ (x) ⋅ m2 (x) d x⎟ ⋅ ⎜⌡ M (x) ⋅ m1 (x) d x + ⌠ ΔB ≔ ―― M ⌡ EI ⎜⎝0 ⎟⎠ L. 2⋅L ⎛L ⎞ ⌠ ⎛⎛ 2 ⎞ 2 ⎞ ⎞ ⎜⌠ ⎛ ⎟ ⎛x⎞ ⎛ x x x⎞ ⎮ ⎜⎜⎛⎝Gd + Qd⎞⎠ ⋅ L ⋅ x − ⎛⎝Qd + Gd⎞⎠ ⋅ ―⎟ ⋅ L − ―⎟ d x⎟ ΔB ≔ ⎜⎮ ⎜⎛⎝Gd + Qd⎞⎠ ⋅ L ⋅ x − ⎛⎝Qd + Gd⎞⎠ ⋅ ―⎟ ⋅ ⎜― x d + 2 ⎟⎠⎠ 2 ⎠ ⎝ 2 ⎟⎠ 2 ⎠ ⎜⎝ ⎮ ⌡⎝ ⌡ ⎝⎝ ⎜⎝⎮ ⎟⎠ 0 0. 4. 5 ⋅ ⎛⎝Gd + Qd⎞⎠ ⋅ L ΔB ≔ ―――――― 24 ⋅ EI. 148. Non-Commercial Use Only.

(165) To Find: δB 2⋅L ⎛L ⎞ ⌠ ⌠ 2 2 1 ⎜ ⎟ ( ) δB ≔ ―― ⎮ ⎛⎝m1 (x)⎞⎠ d x + ⎮ ⌡ m2 x d x⎟ EI ⎜⎝0⌡ ⎠ L. 2⋅L ⎛L ⎞ ⌠ 2 2 ⎜⌠ ⎟ ⎛ x⎞ ⎞ 1 x ⎮ ⎛― x δB ≔ ―― d x + − d L ⎜⎮ ⎜−― ⎟ ⎟ ⎜ ⎟⎠ ⎮ EI ⎜⎮ ⎟ ⌡⎝ 2 ⎠ ⌡⎝ 2 ⎝0 ⎠ L. 3. L δB ≔ ―― 6 ⋅ EI. ΔB By ≔ ―― δB. 149. Non-Commercial Use Only.

(166) Reactions. Ax ≔ −Qfld = −68.04 kN. 3 Ay ≔ ―⋅ ⎛⎝Gd + Qd⎞⎠ ⋅ L = 866.245 kN 8. 5 ⋅ ⎛⎝Gd + Qd⎞⎠ ⋅ L = 2887.485 kN By ≔ ――――― 4 3 Cy ≔ ―⋅ ⎛⎝Gd + Qd⎞⎠ ⋅ L = 866.245 kN 8. 150. Non-Commercial Use Only.

(167) B. CSI Bridge Detailed Modelling Procedure. 151.

(168) This section will show the complete design procedure of “Myrdal Bru II” in CSI Bridge.. The first thing to do is to create a layout line. The layout line will act as the reference line for the bridge. By clicking on the tab “Layout” → “Layout Line” → “New”, a window will show up where the length of the bridge is defined. For “Myrdal Bru II”, the length is set to 31.294 m, with a slope of 3.548°.. Under the label “Horizontal Layout Data” the horizontal curvature of the bridge is defined. First, by using the “Quick Start”-button, the shape of the layout line is chosen. “Myrdal Bru II” curves slightly to the left. Therefore, “Straight - Bent Left - Bent Left” is chosen as shown in the figure below.. 152.

(169) When clicking on «Define Horizontal Layout Data» and then “Edit Segment”, the selected segments from the chosen “Quick Start”-shape are adjusted to circular curves with radius of 148.75 m. The segments curve left to new bearing at station, as shown in the figure below.. When all the layout line segments are adjusted like above, the “Horizontal Layout Data”window looks like this:. 153.

(170) The next step of the procedure is to define the lane for pedestrians and the service vehicle. By clicking on the tab “Layout” → “Lanes” → “New”, the “Bridge Lane Data”window appears. The starting point of the lane is set to be at 0 m, and the end is at 31.294 m. Since “Myrdal Bru II” has a loading width of 3 m, the bridge has only one lane. Therefore, the centerline of the lane is placed along the layout line such that it curves along the bridge deck, without needing to define an additional radius.. After the lane is defined, only the center line appears in the 3-D model. To make the lane visible, click on the “Home” tab → “Display” → “More” → “Show Lanes” → “Show Lane Width” → “OK”.. 154.

(171) When defining the concrete class for the model, we went to the “Components” tab → “Properties” → “Type” → “Material Properties” → “New”. For “Myrdal Bru II”, the concrete B45 was used (C45/55 in CSI Bridge).. After the concrete class is defined, the next step is to design the bridge deck section. In the “Components” tab, we went to “Superstructure” → “Item” → “Deck Sections” → “New” and chose a flat slab concrete section. The dimensions of the section are set to the inserted values below:. 155.

(172) To modify the deck cross section such that the bottom edges become curved, as shown in the drawings of the bridge (Appendix C, p. K207), the section had to be converted to a user bridge section. Therefore, by clicking on the button “Convert To User Bridge Section”, the window below appears. There were applied a radius of 0.71 m on the two bottom points (Point 4 and 5 in the model) and the “Reference Point” was moved from (0, 0) to (1.851, 1) which is the center of the bridge deck.. 156.

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