Increased Traffic Loads on Swedish Highway Bridges: A Case study of the bridge at highway interchange Värö

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Increased Traffic Loads on Swedish Highway Bridges

A Case study of the bridge at highway interchange Värö

Fredrik Forsberg

Civil Engineering, masters level 2017

Luleå University of Technology

Department of Civil, Environmental and Natural Resources Engineering

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Preface

This Master Thesis, written for the consulting engineering group Ramböll at their bridge department in Stockholm, is the final part of my Master of Science in Civil Engineering at Luleå University of Technology. The thesis was initiated by Dr. Ali Farhang, head of the bridge department at Ramböll Sweden, with the aim to investigate the effects of the planned traffic load increase on Swedish road bridges.

I would like to thank Ali, along with his colleague Murtazah Khalil at the Ramböll bridge department in Stockholm, who acted as supervisors during the work, for all the support they provided throughout the Master Thesis work and for letting me perform my work at their Stockholm office.

I would also like to thank my supervisor Professor Lennart Elfgren at the Division of Structural Engineering at Luleå University of Technology for introducing me to the bridge subject as well as all the support he offered me in the process of finalizing this Master thesis.

Stockholm, January 2017 Fredrik Forsberg

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Abstract

The Swedish government is planning to increase the maximum vehicle gross load regulations on parts of the national roads from the present 60 t, for the load carrying capacity class BK1, to 74 t, for the proposed new load carrying capacity class BK4. The initial implementation of the new load carrying capacity class for 74 t vehicles will only regard major highways and important roads, however, at a later stage the plan is to implement the new BK4 class on the full current BK1 road network. The biggest obstacle which arises when implementing these increased traffic loads is insufficient load carrying capacity for the bridges on the road network.

Thus, the objective of this thesis is to examine and analyze the effects of the increased traffic loads on Swedish road bridges. In order to identify the structural effects of the load increase, and draw general conclusions regarding the effects on the bridge network as a whole, a case study with load carrying capacity calculations is carried out on a two-span concrete slab fram bridge at a highway interchange in Värö in western Sweden. The bridge is classified as critical by Trafikverket. The load carrying capacity calculation is carried out using the Swedish standards, in which maximum load values for the axle load, A, and the bogie load, B, are calculated.

The load effects acting on the bridge are calculated using the finite element software BRIGADE/Standard, with input traffic A and B loads amounting to 12 t and 21 t respectively for the new BK4 class and to 12 t and 18 t respectively for class BK1. In addition to the load carrying capacity calculations with BK4 traffic loads, a comparison is carried out between the results obtained when using the axle- and bogie loads from the BK1 versus the BK4 load carrying capacity class in the load carrying capacity calculations.

The load carrying capacity calculations performed on the studied bridge shows that the capacity of the bridge, both in regards to moment and shear force, is insufficient to meet the new, increased, BK4 A/B – requirements. The critical A/B – values for the whole bridge are 17 t and 18 t respectively, to be compared with the required 12- and 21 t limit for the new BK4 load carrying capacity class, thus, making the load carrying capacity of the bridge inadequate. The critical A/B – values appear for the longitudinal shear force load case at the point where the shear force reinforcement over the column support ends. Moreover, the difference between the results obtained when using the BK1 versus the BK4 traffic loads in the calculations were found to be negligible.

Due to the differing properties and characteristics of each individual bridge on the Swedish road network it is difficult to make general statements regarding the effects of the increased traffic loads on the bridge network as a whole. Specific load carrying capacity calculations will need to be performed on each individual bridge in order to evaluate its capability to withstand

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the new increased BK4 traffic load. However, capacity calculations regarding the BK1 load carrying capacity class can, with sufficient accuracy, be used to evaluate the capability of a bridge to withstand the increased traffic loads in the BK4 load carrying capacity class, thus, making it easier to evaluate the strengthening needs for the bridge network as a whole.

Keywords: BRIGADE/Standard, Concrete slab frame bridge, FEM, Load carrying capacity calculation, Load carrying capacity class

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Sammanfattning

Sveriges regering planerar en utökning av den maximalt tillåtna bruttovikten för fordon på delar av det allmänna vägnätet från den nuvarande begränsningen på 60 t, för bärighetsklass BK1, till 74 t, för den nya föreslagna bärighetsklassen BK4. I det första skedet kommer den nya bärighetsklassen, för fordon med bruttovikt upp till 74 t, bara att implementeras på stora motorvägar och andra ur transportsynpunkt viktiga vägar, men, i ett senare skede finns också planer på att implementera den nya bärighetsklassen, BK4, på hela det nuvarande BK1 vägnätet. Det största problemet som förväntas uppkomma under införandet av de nya, ökade, trafiklasterna är otillräcklig bärighet på vägnätets broar.

Således är målet med denna uppsats att undersöka och analysera effekterna av dessa ökade trafiklaster för broar på det Svenska vägnätet. För att identifiera effekterna, och dra generella slutsatser, gällande denna ökade trafiklast för broarna på det Svenska vägnätet i sin helhet kommer en fallstudie med bärighetsberäkningar utföras på en plattrambro vid trafikplats Värö - en bro som Trafikverket bedömer som kritisk. Bärighetsberäkningen utförs enligt svenska standarder, där maximala tillåtna värden på axellasten, A, och bogielasten, B, beräknas.

Lasteffekterna som verkar på bron beräknas med hjälp finita element programvaran BRIGADE/Standard med trafiklaster, A och B, som uppgår till 12 respektive 21 t för den nya BK4 bärighetsklassen och 12 respektive 18 t för bärighetsklass BK1. Som tillägg till bärighetsberäkningarna med BK4 laster utförs också en jämförelse av resultaten som uppkommer när axel- och bogielasterna från BK1 respektive BK4 används i beräkningarna.

Bärighetsberäkningarna på den studerade bron visar att brons kapacitet, både gällande moment och tvärkraft, är otillräcklig när den belastas med de ökade BK4 trafiklasterna. De kritiska A- och B- värdena för bron är 17 respektive 18 t, värden som skall jämföras med kraven på 12 respektive 21 t för den nya bärighetsklassen BK4 – därmed är brons bärighet otillräcklig. De kritiska A- och B-värdena för bron uppkommer för lastfallet med longitudinell tvärkraft vid punkten där tvärkraftsarmeringen över mittstödet slutar verka. Jämförelsen mellan beräkningsresultaten som uppkom med trafiklaster enligt BK1 respektive BK4 visade att skillnaden mellan beräkningsresultaten var försumbar.

På grund av de varierande egenskaperna hos varje enskild bro på det Svenska vägnätet är det svårt att dra generella slutsatser gällande effekterna av lastökningen för vägnätet som helhet.

Specifika bärighetsberäkningar måste utföras på varje individuell bro för att kunna utvärdera dess kapacitet att klara av de nya, ökade, BK4 trafiklasterna. Emellertid kan bärighetsberäkningar som beträffar bärighetsklassen BK1, med tillräcklig tillförlitlighet, användas för att bedöma en bros möjlighet att motstå de ökade trafiklasterna i den nya bärighetsklassen BK4, vilket förenklar utvärderingen av vilka broar som kräver förstärkning.

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Nyckelord: BRIGADE/Standard, Bärighetsberäkningar, Plattrambro, FEM, Bärighetsklasser

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List of Figures

Figure 1 - Gross loads for different load carrying capacity classes (Trafikverket, 2014a). ... 7

Figure 2 - Type load model c (Trafikverket, 2016a)... 11

Figure 3 - Sketch of type load model c. ... 11

Figure 4 - Result section - moment (Pacoste, Plos & Johansson, 2012). ... 16

Figure 5 - Result section - shear force (Pacoste, Plos & Johansson, 2012). ... 17

Figure 6 - BRIGADE/Standard structure lines (Scanscot Technology AB, 2015a). ... 18

Figure 7 - A BRIGADE/Standard four-node shell element with one integration point (Scanscot Technology AB, 2015a). ... 18

Figure 8 - BRIGADE/Standard coordinate system for shell elements (Scanscot Technology AB, 2015a)... 18

Figure 9 - BRIGADE/Standard directions for the shell element moments (Scanscot Technology AB, 2015a). ... 19

Figure 10 - BRIGADE/Standard directions for the shell element shear forces (Scanscot Technology AB, 2015a). ... 19

Figure 11 - BRIGADE/Standard traffic lanes (Scanscot Technology AB, 2015a). ... 19

Figure 12 - Self- and pavement weight acting on the bridge (Scanscot Technology AB, 2015a). ... 20

Figure 13 - Bridge carriageway division. ... 23

Figure 14 - Type vehicles passing the bridge on their own lanes. ... 23

Figure 15 - Type vehicles in the middle of the carriageway, alone on the bridge – eccentricity cases. ... 24

Figure 16 - Superstructure cross-section, concrete slab frame bridge. ... 26

Figure 17 - Principal sketch of a concrete slab frame bridge... 26

Figure 18 - Bridge location (Värö bridge). ... 27

Figure 19 - Värö bridge from the west. ... 28

Figure 20 - Overview drawing of Värö bridge (Trafikverket, 2016c). ... 28

Figure 21 - Bridge cross-section - Värö Bridge (Trafikverket, 2016c). ... 28

Figure 22 - System drawing. ... 29

Figure 23 - Shear force reinforcement distribution (Trafikverket, 2016c). ... 32

Figure 24 - Reinforcement - connection between abutment and slab (Trafikverket, 2016c). . 32

Figure 25 - BRIGADE/Standard bridge geometry. ... 34

Figure 26 - Support lines and mesh generation sections. ... 35

Figure 27 - Convergence test. ... 35

Figure 28 - Finite element mesh on the bridge. ... 36

Figure 29 - Material manager - BRIGADE/Standard model. ... 37

Figure 30 - Traffic lanes for traffic passing the bridge on its own lane. ... 39

Figure 31 - Traffic lanes for traffic passing the bridge in the middle of the carriageway, alone on the bridge... 40

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Figure 32 - Result lines - Traffic passing the bridge on its own lane. ... 41

Figure 33 - Result lines - Traffic passing the bridge in the middle of the carriageway, alone on the bridge. ... 42

Figure 34 - Result sections - longitudinal shear force. ... 42

Figure 35 - Deformed bridge model - dead weight load case. ... 43

Figure 36 - BRIGADE/Standard dead weight moment. ... 43

Figure 37 - FRAME ANALYSIS dead weight moment. ... 44

Figure 38 - BRIGADE/Standard dead weight shear force. ... 45

Figure 39 - FRAME ANALYSIS dead weight shear force. ... 45

Figure 40 - Critical section and critical point – moment. ... 46

Figure 41 - Critical point and critical result section line - shear force. ... 50

Figure 42 – Load carrying capacity: Bogie load - Result line 1. ... 58

Figure 43 – Load carrying capacity calculation: Bogie load - Result line 2. ... 59

Figure 44 – Load carrying capacity calculation: Bogie load - Result line 3. ... 60

Figure 45 - Transversal shear force: Bogie load – load carrying capacity calculation - Result line 5. ... 62

Figure 46 - Longitudinal shear force: Bogie load – load carrying capacity calculation - Result line 6. ... 63

Figure 47 - Magnified longitudinal shear force diagram: Bogie load - load carrying capacity calculation - Result line 6 ... 63

Figure 48 - Principle sketch - widening of column top. ... 65

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List of Tables

Table 1 - Eccentricity of type vehicles (Trafikverket, 2016a). ... 23

Table 2 - Material parameters concrete class K40 (Trafikverket, 2016a). ... 30

Table 3 - Design concrete material parameters. ... 31

Table 4 - Characteristic reinforcement material parameters (Trafikverket, 2016c). ... 31

Table 5 - Reinforcement design parameters. ... 31

Table 6 - Transversal and longitudinal reinforcement quantities (Trafikverket, 2016c). ... 32

Table 7 - Finite element mesh model 4. ... 36

Table 8 - Material parameters - Earth pressure (Trafikverket, 2016a). ... 38

Table 9 - Result verification – moment. ... 44

Table 10 - Result verification - shear force. ... 45

Table 11 - Geometry and material input. ... 47

Table 12 - Geometry and material input - connection between slab and abutments. ... 48

Table 13 - Moment resistance - connection between the slab and the abutments. ... 49

Table 14 - Geometry and material input - shear force calculation. ... 50

Table 15 - Shear resistance. ... 52

Table 16 - Load carrying capacity calculation results - Traffic on own lane. ... 57

Table 17 - Load carrying capacity calculation results - Traffic in the middle of the carriageway. ... 57

Table 18 - Comparison BK1/BK4. ... 64

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Notations

Roman upper case letters

As Reinforcement area [mm²]

D Dynamic contribution factor [%]

Eck Characteristic value of modulus of elasticity of concrete [GPa]

Ecd Design value of modulus of elasticity of concrete [GPa]

Esk Design value of modulus of elasticity for reinforcing steel [MPa]

Esd Design value of modulus of elasticity for reinforcing steel [MPa]

G Shear modulus [MPa]

L Length [m]

MRd Moment resistance [kNm]

MEd Moment load effect [kNm]

Mperm Moment stemming from permanent actions [kNm]

Mtraffic Moment stemming from traffic load [kNm]

VRd Shear force resistance [kN]

VEd Shear force [kN]

Vperm Shear force stemming from permanent load [kN]

Vtraffic Shear force stemming from traffic load [kN]

Vaz Transversal shear force [kN]

Vsz Longitudinal shear force [kN]

xL Length from reference point [m]

Q Point load [kN]

Roman lower case letters

a Equivalent width circular column [mm]

al Moment curve shift distance [mm]

b Width [mm]

c Concrete cover thickness [mm]

d CG reinforcement to cross-section outer edge [mm]

fck Characteristic compressive strength of concrete [MPa]

fck,adjusted Adjusted characteristic compressive strength of concrete [MPa]

fcd Design compressive strength of concrete [MPa]

fctk Characteristic tensile strength of concrete [MPa]

fctd Design tensile strength of concrete [MPa]

fsv Design yield strength shear reinforcement [MPa]

fv Concrete formal shear resistance [MPa]

fvR Positive shear resistance contribution [MPa]

fyk Characteristic steel yield strength [MPa]

f Design steel yield strength [MPa]

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h Height [mm]

k Proportionality factor for increasing/decreasing traffic point loads [-]

v Velocity [km/h]

x The height of the concrete cross-section compression zone [mm]

Greek letters

ν Poisson’s ratio [-]

ρ Weight [kN/m³]

ψ Factor [-]

η Factor [-]

γ Partial factor [-]

γn Partial factor [-]

γm Partial factor [-]

εs Reinforcement strain [-]

εsγ Reinforcement yield strength strain [-]

εcu Ultimate compressive strain in the concrete [-]

Other notations

∅ Diameter [mm]

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Abbreviations

A Axle load

B Bogie load

BK1 Load carrying capacity class for vehicles with a gross load not exceeding 60 t.

BK2 Load carrying capacity class for vehicles with a gross load not exceeding 51,4 t.

BK3 Load carrying capacity class for vehicles with a gross load not exceeding 37 t.

BK4 Proposed load carrying capacity class for vehicles with a gross load not exceeding 74 t.

EN Eurocode

EU European Union

FEA Finite Element Analysis FEM Finite Element Method SLS Serviceability Limit State ULS Ultimate Limit State

t Ton (1000 kg)

2-D Two-dimensional 3-D Three-dimensional

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1 Introduction

In this chapter, the background of the problem as well as the reason for its importance is summarized and presented. The goals and objectives of the thesis are stated as well as the limitations on the work.

1.1 Background

The Swedish government is planning to increase the maximum allowed vehicle gross load on parts of the public roads from the present 60 t to 74 t, which, according to Trafikverket (2015), will mean that, at the initial stage, approximately 66 bridges will require strengthening.

Following this planned load increase Trafikverket (2014a) proposes the implementation of a new load carrying capacity class called BK4 for 74 t vehicles with a maximum length of 25.5 m. The roads affected, in the initial stage, by this new load carrying capacity class are major highways and important roads, namely E-roads: E4, E6, E10, E18, E20 and parts of the national roads 40, 50, 55, and 56 on which 2/3 of the total road freight volume is transported, see appendix A for a map of the proposed changes. At a later stage, the Swedish government is planning to allow for 74 t vehicles on the whole BK1 road network, consisting of a total of 15 442 bridges. Approximately 1000 of these bridges will require strengthening according to Trafikverket (2015), strengthening works that is expected to cost roughly 9,6 billion Swedish Crowns.

According to Transportstyrelsen (2014), the change is supposed to streamline the Swedish road- transport sector as an increased load on each truck will decrease the total number of trucks and thereby create significant economic, environmental and safety related benefits. The socioeconomic benefit for the initial changes, in which only the major highways are affected, is, according to Trafikverket (2014a), approximated to be between 2,6 and 5,6 billion Swedish crowns over the next 40 years.

Comparatively the EU has a general limit of 40 t on their roads and bridges, which, with the planned changes makes the Swedish road infrastructure very internationally competitive (Transportstyrelsen, 2014). The only other country within the EU to have significantly increased the loads on their roads and bridges are Finland, who increased their maximum traffic load to 76 t in 2013 (Kommunikationsministeriet, 2013).

The biggest obstacle which arises when implementing the new load carrying capacity class BK4 is insufficient load carrying capacity for the bridges on the proposed road network. In order to identify the bridges that require strengthening a load carrying capacity calculation ais carried out, in which maximum load values for the axle load, A, and the bogie load, B, is calculated.

These load values, A and B, is the common capacity representation for bridges in Sweden.

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The Swedish road network presently consists of three load carrying capacity classes with a fourth, the BK4, at the planning stage, all of which has their own A and B values as load carrying capacity representation (Trafikverket, 2016a). The new load carrying capacity class will require an uptick in the maximum A/B – values, from a respective 12 and 18 t limit for the BK1 load carrying capacity class, to, according to Trafikverket (2015), a respective 12 and 21 t limit for the new load carrying capacity class BK4.

With the big variation of applicable bridge types, especially when implementing the increased load on the whole BK1 road network, the decision is made to focus the calculation and analysis on the most common bridge type in Sweden, the concrete slab frame bridge - which makes up approximately 50 % of the Swedish bridge stock (Trafikverket, 2014b).

1.2 Goal and objectives

The goal of this thesis is to examine the effects of the increased traffic load on Swedish road bridges, or, more specifically, on a Swedish concrete slab frame bridge and try to draw general conclusions regarding the effects of the increased traffic loads on the Swedish bridge network as a whole.

1.3 Limitations

Calculations and analysis will be performed on a concrete slab bridge, where a suitable bridge will be assessed and studied on a case basis. The assumption is made that non-prestressed concrete slab bridges will be more critical and thereby the thesis will focus on non-prestressed bridges and disregard prestressed bridges.

The calculations will be performed in ultimate limit state; thus it follows that the effects of the increased load in regards to fatigue is disregarded. Furthermore, the superstructure is deemed to be the most critical part of the bridge in regards to the ultimate limit state capacity, thereby, only the superstructure will be taken into account in this thesis.

Using the Swedish standards for load carrying capacity calculations on bridges, as well as the calculation methodology used by Ramböll, the bridges are assessed with the assumption that they are undamaged. In traditional load carrying capacity calculations on Swedish bridges the capacity to withhold the load of military vehicles are calculated, however, as this thesis focuses on the effect of the increased traffic load, calculations regarding military vehicles will not be carried out. Furthermore, the effects of snow and wind are deemed insignificant in comparison to other actions and are thereby disregarded.

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1.4 Disposition

This thesis consists of nine chapters, all of which are briefly summarized in the following sections.

1 - Introduction

In this chapter, the background of the problem as well as the reason for its importance is summarized and presented. The goals and objectives of the thesis are stated as well as the limitations on the work.

2 - Methodology

This chapter describes the methods and approaches used in this master thesis as well as the research validity, reliability and generalization.

3 - Literature review

In this chapter, general research regarding load carrying capacity calculations on highway bridges are presented. Furthermore, the theory behind the Swedish load carrying capacity classes for road bridges is presented and described as well as some general theory regarding actions on road bridges. The theory behind, and the methods used, when performing load carrying capacity calculations on Swedish road bridges are thoroughly examined. Some background on the usage of FEM, both generally and using the software BRIGADE/Standard, is also presented in this chapter. Finally, some general theory regarding concrete slab frame bridges is also described in this paragraph.

4 - Case study – Bridge at highway interchange Värö

The studied concrete slab frame bridge, the bridge at highway interchange Värö is thoroughly described. The bridge material properties and reinforcement design is also presented.

5 - BRIGADE/Standard model

The BRIGADE/Standard model used to calculate the load effects on the bridge is described.

Descriptions of the modelling of the bridge geometry, boundary conditions and material properties is presented and in addition to this the model verification process is presented.

6 - Resistance calculations

Resistance calculations, regarding both moment and shear forces, for the critical points in the bridge are performed and presented.

7 – Load carrying capacity calculations

Load carrying capacity calculations, in which A/B load limits are calculated, in regards to both moment and shear forces are presented and carried out for all critical parts of the bridge.

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8 - Results and analysis

The results of the load carrying capacity calculations are presented and analyzed for both moment and shear force cases and a comparison between load carrying capacity calculations using the BK1 input A/B – values and BK4 input values is performed.

9 - Discussion and conclusions

In this paragraph, the results of the load carrying capacity calculations performed on the bridge at highway interchange Värö will be discussed and conclusions will be made, both in regards to the specific bridge studied in this thesis, but also in regards to bridges on the Swedish road network in general.

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2 Methodology

This chapter describes the methods and approaches used in this master thesis as well as the research validity, reliability and generalization.

2.1 Literature review

In order to identify research and gain knowledge of the subject a literature review, in which books, articles and research papers are studied, is performed. Studies regarding, both the old load carrying capacity classes and the proposed new load carrying capacity class, for Swedish roads and bridges were conducted, studies in which a representative from Trafikverket were consulted when relevant questions emerged. Loads and actions on road bridges, both according to the Swedish standards and Eurocode, are studied. The load carrying capacity calculation process for bridges, both in general and with a focus on Swedish rules and regulations, is studied in order to be able to analyze the bridge and its capacity to withstand the new, increased, traffic loads. Drawings of relevant bridges, bridges assessed to be at risk when BK4 is implemented, are obtained using the, by Trafikverket supplied, database BaTMan. Furthermore, studies of the FE-software BRIGADE/Standard, as well as the finite element analysis method in general, were also required to get an understanding of the software and its applications for concrete bridges and load carrying capacity calculations.

2.2 Case study

A case study with load carrying capacity calculations is performed on the bridge at highway interchange Värö in order to analyze the structural effects of the increased load and identify critical elements in the bridge. In order to calculate the design load effects on different significant parts of the bridge, the bridge is modelled in the finite element software BRIGADE/Standard - a software specifically designed to model bridges and bridge-like structures. In order to make sure that the software produces reliable results the load effects produced by the BRIGADE/Standard model are verified and controlled using the 2-D frame analysis software, FRAME Analysis.

The resistance in regards to moment and shear force is calculated using hand-calculations for all critical sections on the bridge. Calculations carried out using the relevant Swedish codes and regulations for load carrying capacity calculations on concrete bridges as well as rules and regulations for regular concrete structures. Using the calculated capacities and the load effects produced by the BRIGADE/Standard software the design load carrying capacity, expressed by the A/B – values, is calculated for all critical parts of the bridge and for all relevant load cases.

Using these calculated load carrying capacities the design load carrying capacity for the whole bridge is determined. A thorough evaluation and analysis of the results are then carried out in order to draw conclusions of the effects of the increased traffic loads, both in regards to the specific bridge studied- and in regards to bridges on the Swedish road network in general. In addition to this analysis, suggestions regarding future studies will be presented and discussed.

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2.3 Validity, reliability and generalization

It is important to design and plan the research structure in such a way that it links the case study and data collection with the literature and initial goal and objective of the study, see paragraph 1.2, which should make sure that there is a clear view of what is to be achieved (Rowley, 2002).

In this case, a combined literature- and case study is conducted in order to examine the problem.

The motivation for this approach is the fact that each individual bridge, and bridge type, has its own characteristics and flaws, thereby making a broader study hard to conduct.

It is important that the study is as generalizable as possible - that you can claim that the results of your study can be applied to theory and that the results are applicable to other comparable situations (Rowley, 2002). In this case, the generalization of the study is quite limited as each individual bridge varies considerably in its characteristics. The results will be weaker if the bridge types or loading conditions differ significantly from the case studied in this thesis.

The validity of a research refers to how well the study measures what it is supposed to measure - how well the goals and objectives of the study is met and achieved (Rowley, 2002). It is important to seek to reduce subjectivity in the study as much as possible. Furthermore, it is important from a validity standpoint to make the study as transparent as possible. This will be achieved by complete result transparency; full results will be presented in appendices and clear explanations on every step of the calculation process will be presented.

Another issue with close ties to the validity and generalizability of a study is the reliability, which is the degree of which it can be demonstrated that the study can be repeated with the same result; that the assessment produces stable and consistent results (Rowley, 2002).

Reliability within the study will be achieved through thorough demonstrations and documentations of studies and calculation procedures, thereby ensuring that the study could be repeated with similar results. However, the reliability of the study faces the same difficulty as the generalization; the result reliability will decrease significantly if the loading conditions or considered bridge type is altered.

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3 Literature review

In this chapter, general research regarding load carrying capacity calculations on highway bridges are presented. Furthermore, the theory behind the Swedish load carrying capacity classes for road bridges is presented and described as well as some general theory regarding actions on road bridges. The theory behind, and the methods used, when performing load carrying capacity calculations on Swedish road bridges are thoroughly examined. Some background on the usage of FEM, both generally and using the software BRIGADE/Standard, is also presented in this chapter. Finally, some general theory regarding concrete slab frame bridges is also described in this paragraph.

3.1 Load carrying capacity classes

Different load carrying capacity classes control the load capacity regulations of the Swedish road- and bridge network. These load carrying capacity classes are in turn used to regulate the traffic on each national road. Presently there are three different load carrying capacity classes, BK1, BK2 and BK3 with a fourth, BK4, being proposed. The maximum gross load for each load carrying capacity class depends on the length of the vehicle, counted as the distance between the first- and last axle. As the length of the vehicle increases, so does the acceptable gross load for each load carrying capacity class, see Figure 1. As seen in Figure 1 the maximum gross load for BK1 is 60 t, BK2 is 51,4 t, BK3 is 37 t and the new proposed load carrying capacity class BK4 has a maximum gross load of 74 t (Trafikverket, 2014a). Trafikverket also proposes that the maximum gross load for class BK1 is increased to 64 t in conjuncture with the suggested new load carrying capacity class BK4. The total length of the vehicle is also regulated within the load carrying capacity classes, with a maximum length of 25,5 m for classes BK1 and BK4 (Trafikverket, 2014a).

Figure 1 - Gross loads for different load carrying capacity classes (Trafikverket, 2014a).

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The maximum vehicle load of each load carrying capacity class is denominated by the maximum axle load, bogie load, maximum length and gross load. Values for a triple axel load are also included in the different load carrying capacity classes. Trafikverket (2014a) defines the applicable load and vehicle variables that apply to load carrying capacity classes as follows:

 The axle load is the total static load that the wheels on a wheel axle transfer to the road.

 A bogie is two wheel axles with a distance between them that are below 2 meters.

 The bogie load is the total static load that the wheels of a bogie transfer to the road.

 A triple axel is three wheel axles with a distance between the first-and last axle that are below 5 m.

 The triple axel load is the total static load that the wheels on a triple axel transfer to the road.

 The gross load of a vehicle is the combined total static load that all the wheels of a vehicle transfer to the road at any given moment, i.e. the sum of the axle, bogie and triple axel loads of a vehicle.

The gross load curve for vehicles of different load carrying capacity classes on the Swedish road network, viewed in Figure 1, is determined using different “type vehicles”, taken forth in collaboration with truck and vehicle manufacturers. The proposed new load carrying capacity class, BK4, for vehicles with a gross load up to 74 t will have the same maximum length as the vehicles in class BK1, 25,5 m. The new BK4 capacity curve were determined using the same vehicle limits in regards to axle, bogie and triple axel load as in BK1, see Appendix B, but the increased gross load limit ensures that the capacity curve moves “upwards” for vehicles with a distance between the axles that exceeds 4,4 meters, see Figure 1. In a practical sense, the vehicles need nine axles in order to achieve the maximum BK4 load, 74t (Trafikverket, 2014a).

Load carrying capacity calculations for Swedish road bridges are carried out using the Swedish type vehicle model, further explained in paragraph 3.2, where 14 different type cases are used to, as accurately as possible, simulate traffic loads on bridges. These type cases are, when the correct loads for each load carrying capacity class is used, creating a similar curve as in Figure 1. Depending on the load carrying capacity class assigned to the bridge, different loads - axle load, A, and bogie load, B, are used as point loads in the type cases. load carrying capacity class BK1 has, for example, an A of 120 kN and a B of 180 kN. In order to allow 74 t-vehicles, with the same length restrictions as in BK1, the B-value for the proposed load carrying capacity class BK4 will be 210 kN (Trafikverket, 2015).

3.2 Actions on bridges

An action can, according to SS-EN 1990 (2002), be divided into direct and indirect actions, where direct actions are defined as a set of forces or loads which are applied to the structure and indirect actions refers to a set of imposed deformations or accelerations caused, for example, by temperature changes, moisture variation, uneven settlement or earthquakes. This

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thesis will largely focus on the direct actions on bridges, which are the most important ones when conducting a load carrying capacity calculation (COST, 2004).

Furthermore, the actions can be classified by their variation in time, where the following, perhaps more common, classifications are used (SS-EN 1990, 2002):

 Permanent actions: Self-weight of structures, fixed equipment and road surfacing, and indirect actions caused by shrinkage and uneven settlements.

 Variable actions: Imposed loads, wind actions or snow loads.

 Accidental actions: explosions, or impact from vehicles crashing into the structure.

These actions, and how they specifically are used in bridge load carrying capacity calculations in Sweden, will be further explained in the following paragraphs.

3.2.1 Permanent actions

One of the main components when calculating the permanent actions on a structure is the self- weight which, in the case of a road bridge, consists of the load-carrying part of the structure (Trafikverket, 2016a). When calculating the self-weight according to Trafikverket (2016a), reinforced concrete is assumed to have a specific weight of 24 kN/m³.

The specific weight of the pavement, 22 kN/m³ for asphalt pavement and 23 kN/m³ for concrete pavement, also needs to be added to the permanent load. According to Trafikverket (2016a) the shrinkage of the concrete is only considered for composite and prestressed concrete bridges and thereby won’t have to be considered in this thesis. Furthermore, the earth pressure will have to be considered using factors and coefficients according to Trafikverket (2016a).

3.2.2 Variable actions 3.2.2.1 Snow loads

Snow loads are, according to Trafikverket (2016a), only taken into account when the bridge in question have a roof structure, thus, snow loads aren’t considered on the bridges in this thesis.

3.2.2.2 Wind loads

Using the same reasoning as with the snow loads, the wind loads on the structure is not considered in this thesis.

3.2.2.3 Traffic loads

Traffic loads on road bridges in Sweden is primarily simulated and calculated using two different load models, the Eurocode load model, where load model 1 is decisive for most bridges, and the Swedish load model, defined by Trafikverket, called the type vehicle model.

These two load models are based on real traffic measurements on bridges and is designed to simulate those traffic effects as accurately as possible (SS-EN 1991-2, 2003), (Trafikverket, 2016a).

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The Eurocode load model 1 for bridges, see SS-EN 1991-2 (2003), is based on uniformly distributed loads acting in combination with bogie loads on the, by lane, divided bridge surface.

The traffic loads on each lane are assigned a predetermined load value and adjustment factor, depending on the specific, predisposed, lane placement on the bridge. However, for load carrying capacity calculations regarding existing road bridges the Eurocode load model is disregarded and the type vehicle model, defined by Trafikverket (Trafikverket, 2016a), is applied on the bridge.

The type vehicle load model is using different type cases to represent real heavy vehicles and traffic situations. The model consists of 14 different vertical loading scenarios, represented by the letters a-n, where each scenario denotes a, by extensive tests and experiments formed (Carlsson, 2006), load case, see Appendix C. The point loads, A and B, in each load model are representing the axle -and bogie loads of real heavy vehicles and the uniformly distributed load, q, are meant to represent lighter traffic in-between the heavier vehicles (Trafikverket, 2016a).

The capacity of road bridges is represented by a maximum traffic load, denoted by the maximum axle load, A, and bogie load, B. The uniformly distributed load, q, which is evenly distributed over the width of the loading field, is set as 5 kN/m in unfavorable loading conditions and 0 kN/m in favorable loading conditions. When conducting a load carrying capacity calculation, the result of the calculations are capacity values for the point loads A and B. These calculated A and B values are then compared to the limits and requirements of each load carrying capacity class. Load carrying capacity class BK1 has, for example, an A requirement of 12 t and a B requirement of 18 t and the new, proposed, load carrying capacity class BK4 has an A requirement of 12 t and a B requirement of 21 t (Trafikverket, 2015).

The type vehicle models, always centrally placed, are acting on notional load lanes with a width of 3 m. The number and placement of the notional load lanes should always represent the most unfavorable possible influence on the bridge, where the number of notional load lanes depends on how many that fits on the carriageway. However, the maximum number of load lanes is four.

The number of notional load lanes on which type vehicles are placed are a maximum of two lanes where the type vehicles on one notional lane are multiplied with a factor of 1,0 and the other with a factor of 0,8. The remaining lanes are only affected by the uniformly distributed load, q, see (Trafikverket, 2016a).

The transverse distance between the wheels are, according to Trafikverket (2016a), spanning between 1,7 m to 2,3 m and the wheels themselves have a distribution of 0,3 m in the transverse direction and 0,2 m in the longitudinal direction. As an example, consider type load model c;

see Figure 2. The bogie point load, B, is divided onto four wheels, and thereby four point loads,

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a sketch of this can be seen in Figure 3 along with a sketch of the distances between the axles and the dimensions of the wheels.

Figure 2 - Type load model c (Trafikverket, 2016a).

Figure 3 - Sketch of type load model c.

For every point load in the type load model, a dynamic contribution for the vertical loads should to be added. This is achieved by adding a dynamic contribution factor, D, to the point loads, calculated using equation 3.1

𝐷 = 180+8(𝑣−10)

20+𝐿 [%] (3.1)

Where v is 80 km/h and L is calculated using paragraph 10.5 in Trafikverket (2016a).

3.2.2.4 Surcharge

Surcharge is the load acting on the bridge when a temporary load, usually traffic load, is placed on the part of the road which is connecting the road to the bridge, see Trafikverket (2016a).

3.2.2.5 Braking force

The load created when the type vehicles are braking or accelerating is called braking force and are said to equate to a horizontal force on the bridge, see Trafikverket (2016a).

3.2.3 Load combinations

When combining the loads and actions presented in the previous paragraphs it is integral that the loads are added together in the most unfavorable way possible. According to Trafikverket (2016a) the applicable load combination, there are plenty of other possible combinations, are

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load combination A which is the primary load combination for bridge capacity calculations in the ultimate limit state, ULS. Trafikverket (2016a) states that the amount of variable loads considered is limited at a maximum of four loads, where the ones considered, as one would suspect, are the most unfavorable ones. The most unfavorable of the variable loads are given the higher load coefficient value, ψγ. Coefficients, both the higher- and lower ones, are presented in Appendix D.

3.3 FEM

The finite element method (FEM) or finite element analysis (FEA) is an approximate numerical method used for solving complex differential equations regarding a wide range of physical problems, including complex structural engineering problems. Broo, Lundgren and Plos (2008) suggests that the finite element method can be especially effective and helpful when assessing existing structures, such as bridges, because of their complexity in a geometrical sense and the complexity of the actions on the structures. When using FEM to evaluate existing structures, higher capacities are often reached compared to the results achieved from more traditional forms of calculation. Broo, Lundgren and Plos (2008) suggests that the reason for the higher estimated capacities primarily is a more favorable load distribution as the structure in most FEM software products is analyzed in three dimensions.

When using the finite element method for structural problems, the complex structures are subdivided into a finite number of elements. Elements, interconnected by nodes, whose relation between their nodal displacements and nodal reactions can be specified by a limited number of functions and parameters, called shape, or form, functions. The displacements, strains and stresses of an element is calculated by assembling all of the elements into vectors or matrices and solving the general system, see equation 3.2 (Rombach, 2004).

[𝐊] ∗ {𝐮} = {𝐅} (3.2)

The stiffness of all the elements are represented by the global stiffness matrix [K], the loads on the structure are represented by the vector {F} and the nodal displacements, the typical result of a FEM calculation, are denoted by the vector {u}. In order to find the form or shape functions that, as closely as possible, approximates the behavior of the structure different methods can be used. For simple problems, basic equilibrium relations can be used to find the relation between the nodal forces and their displacements. However, as the complexity of the structure increases so does the complexity of the methods used - leading to the usage of virtual work- and virtual displacement principles (Rombach, 2004).

The first step of conducting a finite element analysis of a structure in a more practical sense is, according to Samuelsson & Wiberg (1998), to simplify the structure in regards to various parameters such as boundary conditions, geometry, material parameters and loads. A material

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next step is to divide the structure into finite elements, a process where it is important to consider both the element type and size, as this greatly can influence the future calculations and results. The stiffness matrix, an integral part of the finite element method, is calculated for each element and then put together to form a global stiffness matrix for the whole structure.

Geometry- and boundary conditions are then assigned to the model in order to solve the equation system for the whole structure and create relevant results.

Perhaps the most important step, when conducting a finite element analysis, is to perform extensive result verification in order to make sure that the results of the FEM calculations are reasonable and correct. Almost no software is, as Rombach (2004) puts it “free from errors”

which makes a critical distrust, leading to post processing checks of the FEM results integral when using FEA on structural problems. The errors can sometimes stem from simple software glitches but it should always be kept in mind that the finite element method is a numerical method based on lots of assumptions and simplifications, the result of any calculation can only be as accurate as the underlying assumptions and the underlying numerical model.

These boundary, support, element and load assumptions and simplifications can greatly affect the results, for example, Pacoste, Plos, and Johansson (2012) states that the support conditions in a finite element model of a structure often have a decisive influence on the analysis results.

Davidson (2003) supports this statement and states that the modeling of the supports for slabs, regular or bridge slabs, significantly can affect the moment load effect over that support.

It is especially important to be cautious when modelling point loads, for example tires of passing vehicles, as point loads can create discontinuity zones on which singularities, infinite stresses and internal forces, can occur. Rombach (2004) clarifies that these stresses only occur in the numerical model, and not in the real structure, and are caused by the simplifications and assumptions regarding the element behavior. These discontinuity zone behaviors are not always as drastic as the creation of infinite stresses, they can be subtler and harder to recognize, creating local stress surges that significantly changes the result of the calculation, a phenomenon that underlines the importance of proper result interpretation and analysis. To avoid and, at least partially, limit this problem, point loads are often modelled as uniformly distributed loads, for example, the point loads from the wheels of vehicles passing a bridge is evenly distributed over the whole wheel-area.

Both closely knitted to- and significantly affecting this problem is the process and decisions involved when dividing the structure into finite elements, a process called discretization. The size and shape of the elements can significantly affect the result and Rambach (2004) stresses that the discretization phase is where most of the mistakes when performing FEM calculations occurs. To emphasize this, Davidson (2003) states that the size of the finite elements, also called the mesh size, significantly affects the moment and shear forces that are calculated in certain

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points of the structure, making the discretization face essential in order to achieve reliable results from the FEM calculation. One method to limit the risk and probability of mistakes in the discretization and element mesh generation phase is to perform a convergence study. A process in which the element mesh size in the model is continuously reduced until the results, for example the moment curve for the dead weight load case, converges. This process makes sure that the element mesh sizes, in a global perspective, is properly modelled and that the element mesh is dense enough.

Another important aspect to consider is which material analysis model is used in the FEM calculations. Typically, in order to simplify the analysis and to be able to use the superposition principle when evaluating the effects of load combinations, linear analysis is adopted, even though concrete slabs usually, due to cracking and reinforcement distribution, display clear non-linear response. This is, at least in ultimate limit state, reasonable since concrete slabs typically have good plastic deformability. Since the design is based on a moment (and force) distribution that satisfies equilibrium, the load carrying capacity will be adequate if the structure has sufficient plastic deformation capacity (Pacoste, Plos & Johansson, 2012).

There are multiple different types of elements that can be used to divide the structure, Broo, Lundgren and Plos (2008) states that in order to model an entire structure, like a whole bridge, structural finite elements are used, such as, beam, shell and truss elements. Typically, when performing FEM calculations on concrete slabs and slab bridges the elements are specified as shell elements. Davidson (2003) adds that using 3D shell elements, sometimes in combination with beam elements, is the most common and effective method when modelling concrete bridges using FEM.

3.3.1 Modeling orthotropic slabs using FEM

When modelling concrete bridges using FEA an important aspect to consider - and choice to make - is whether the slab is considered to have an isotropic or orthotropic behavior. Usually when performing FEA the assumption is made that the slab, or structure, has an isotropic behavior. However, when considering the reinforcement and cracks in the concrete, which usually disrupts the isotropic behavior, concrete slabs doesn’t have an isotropic behavior and thereby the model might produce more accurate results when modelled in a, at least partially, orthotropic way (Rombach, 2004).

Bridges and slabs are generally not equally reinforced in both the longitudinal and transversal direction. Thereby, the concrete will behave differently in different directions, and the relative stiffness due to reinforcement orientation- and quantity will produce a stress distribution with significant differences from the stress distribution produced by an analysis assuming isotropic conditions. Old bridge slabs were generally designed using a two-dimensional, and thereby partially orthotropic, stress distribution, creating significantly higher stresses in the longitudinal

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longitudinal direction compared to the reinforcement amounts in the transversal direction is often significantly higher in old concrete bridges.

This creates a problem when analyzing these older bridges with modern numerical methods such as FEM. The FEM software, which as mentioned earlier usually is using an assumption of isotropic material behavior, will thereby produce significantly larger stresses in the transversal direction compared to the stresses obtained from the two-dimensional model used in the original design calculations. Thus, the older bridges, which have been operational for decades, will, when making load carrying capacity calculations using modern methods, often be deemed unsafe (COST, 2004).

One solution to this problem is to scale the material properties in accordance with the amount of reinforcement in transversal and longitudinal direction, creating a scaled orthotropic material model or, also called, a transversally orthotropic model. Two of the three directions are said to be equally stiff, creating a model that has different stiffness’s in the longitudinal and transversal directions. Kwak & Filippou (1990) clarifies that the usage of orthotropic finite element material models is especially efficient and accurate for FEM using shell elements, which is the usual element model used when modeling concrete bridges in finite element software.

Unlike isotropic material models, which are parametrized by a single Young’s modulus of elasticity, the transversally orthotropic material model has two different Young’s moduli – Ea

and Es (Li & Barbic, 2014). These different modules of elasticity can be scaled in different ways in the finite element material model. One suitable solution, which is used in the load carrying capacity calculation performed in this thesis, is to scale the modulus of elasticity in accordance to the relation between the amount of longitudinal and transversal reinforcement.

When assigning the material shear modulus to the transversally orthotropic finite element model, Huber (1923) proposes that the shear modulus in the longitudinal direction is calculated using the classical formula, see equation 3.3 and that, the shear modulus in the transversal direction is calculated using the geometrical mean of the two different modules of elasticity, see equation 3.4. The poisson ratio, 𝜐, defined as the ratio between the lateral strain and the axial strain, is, according to Rombach (2004), said to be 0,2 when modelling concrete slabs using finite element analysis.

𝐺 = _2(1+𝜐)^𝐸 (3.3)

𝐺 = _2(1+𝜐)^√𝐸^𝑎^𝐸^𝑠 (3.4)

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3.3.2 FEM result sections

Another important aspect to consider when post-processing and acquiring results from the FEM calculations is that unrealistic cross-sectional moments and shear forces can occur in the finite element model due to simplifications in the modeling (Pacoste, Plos & Johansson, 2012).

These unrealistic moments and shear forces usually occurs over the supports, making the modeling and choice of result sections over and around the supports crucial in order to obtain accurate and reasonable results from the finite element model.

Pacoste, Plos & Johansson (2012) states that if the slab is monolithically connected with its supports, columns or walls, it can be shown that the maximum stresses appears at the border of the connection and not inside the connection region, see Figure 4. This stems from the fact that the cross-sectional moments and forces in the slab is defined as integrals of the stresses over the cross-section and, thereby do not have a clear interpretation inside a connection region (Pacoste, Plos & Johansson, 2012). These support areas must, according to Pacoste, Plos &

Johansson (2012), be seen as disturbed regions, where beam or slab theory and its applications are not valid. Pacoste, Plos & Johansson (2012) states that a critical bending crack will form no closer to the theoretical support point than along the surface of the column or wall. Thus, this is also where the tensile reinforcement will start to yield. Thereby, as previously stated, the critical cross-section for bending failure is along the surface of the column or wall.

Figure 4 - Result section - moment (Pacoste, Plos & Johansson, 2012).

For circular columns, the width a, see Figure 4, is calculated using equation 3.5, where ∅ is the diameter of the column.

𝑎 =^√𝜋∅₂ (3.5)

Regarding the failure section for shear forces, Pacoste, Plos & Johansson (2012) states that the critical shear cracks will occur where it transfers the largest possible shear force across the inclined shear crack. Thus, a critical shear crack will develop no closer to a support than with its lower end at the support edge, see Figure 5.

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This phenomenon stems from the fact that if the shear crack is moved towards the center of the support, a portion of the load would be directly transferred down to the support without passing the shear crack. Thus, the shear force transferred over the shear crack would be reduced.

Figure 5 - Result section - shear force (Pacoste, Plos & Johansson, 2012).

Thereby, Pacoste, Plos & Johansson (2012) makes the conclusion that the critical result in a slab, with emphasis on shear forces, are not located closer to the support edge than the distance z cot θ – independent of the slab-support connection and stiffness of the slab. For slabs without shear reinforcement Pacoste, Plos & Johansson (2012) concludes that the shear crack inclination is not steeper than 45 degrees, making the simplification in equation 3.6 viable.

𝑧 cot 𝜃 = 𝑧 ≈ 𝑑 (3.6)

To further simplify the equations presented in Figure 5 Pacoste, Plos & Johansson states that, particularly for cases where moving loads such as traffic is involved, cot θ can be said to be equal to 1.5, leading to the simplifications, for result sections regarding cross-sections with shear reinforcement, that are presented in equation 3.7.

𝑧 cot 𝜃 = 1.5𝑧 ≈ 1,5𝑑 (3.7)

To clarify, the distance from the center of the support to the critical shear section for cross- sections without shear reinforcement is presented in equation 3.8 and the distance for cross- sections with shear reinforcement are presented in equation 3.9.

𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑤𝑖𝑡ℎ𝑜𝑢𝑡 𝑠ℎ𝑒𝑎𝑟 𝑟𝑒𝑖𝑛𝑓𝑜𝑟𝑐𝑒𝑚𝑒𝑛𝑡: ^𝑎₂+ 𝑑 (3.8)

𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑤𝑖𝑡ℎ 𝑠ℎ𝑒𝑎𝑟 𝑟𝑒𝑖𝑛𝑓𝑜𝑟𝑐𝑒𝑚𝑒𝑛𝑡: ^𝑎₂+ 1,5𝑑 (3.9)

3.3.3 BRIGADE/Standard

The FEM software used in this thesis is BRIGADE/Standard, a finite element program used when analyzing and designing bridge structures, which provides a three-dimensional analysis

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concept and a graphical user interface for pre- and post-processing (Scanscot Technology AB, 2015b).

So-called structure lines describe the geometry of the bridge. Lines that usually consists of a stake out line in the center of the bridge, which describes the direction of the bridge, and two borderlines that describes the width and banking of the bridge, see Figure 6. The rest of the bridge geometry, such as the bridge deck geometry, is modelled using these structure lines, along with transversal support lines added to indicate support locations as basis points (Scanscot Technology AB, 2015a).

Figure 6 - BRIGADE/Standard structure lines (Scanscot Technology AB, 2015a).

BRIGADE/Standard uses 4-node shell elements with one integration point, see Figure 7, to model the deck of the structure. Elements that can be used for both thick and thin shell structures, as they are able to handle transverse shear forces. The results of the FEM calculation are interpolated between the integration point and the nodes.

Figure 7 - A BRIGADE/Standard four-node shell element with one integration point (Scanscot Technology AB, 2015a).

The result sections for stresses and section forces in the BRIGADE/Standard shell elements are denominated using a local s, a and z coordinate system, visualized in Figure 8.

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More specifically, the moment and shear force shell element section forces for the bridge deck is described using the directions presented in Figure 9 and Figure 10 below.

Figure 9 - BRIGADE/Standard directions for the shell element moments (Scanscot Technology AB, 2015a).

Figure 10 - BRIGADE/Standard directions for the shell element shear forces (Scanscot Technology AB, 2015a).

BRIGADE/Standard will calculate the traffic loads acting on the bridge using the type vehicle model, described in paragraph 3.2.2, where the type vehicles are acting on user specified traffic lanes. Each lane symbolizes the centerline of the type vehicle configuration moving along the bridge, see Figure 11, and BRIGADE/Standard will, for each node and result component, find the most critical traffic load position and/or positions (Scanscot Technology AB, 2015a).

Figure 11 - BRIGADE/Standard traffic lanes (Scanscot Technology AB, 2015a).

Furthermore, BRIGADE/Standard will calculate the actions due to the self-weight and pavement weight acting upon the bridge, see Figure 12.

Increased Traffic Loads on Swedish Highway Bridges: A Case study of the bridge at highway interchange Värö