Early-Stage Design of Concrete Girder Bridges Using Set-Based Design Parametric Exploration of Design Alternatives Consider- ing CO2 Emissions, Cost, and Buildability Master’s thesis in Structural Engineering and Building Technology ALICE BEISCHER KARIN FURUHJELM DEPARTMENT OF ARCHITECTURE AND CIVIL ENGINEERING DEVISION OF STRUCTURAL ENGINEERING CHALMERS UNIVERSITY OF TECHNOLOGY Master’s thesis ACEX30 Gothenburg, Sweden 2025 MASTER’S THESIS ACEX30 Early-Stage Design of Concrete Girder Bridges Using Set-Based Design Parametric Exploration of Design Alternatives Considering CO2 Emissions, Cost, and Buildability Master’s Thesis in the Master’s Programme Structural Engineering and Building Technology ALICE BEISCHER KARIN FURUHJELM Department of Architecture and Civil Engineering Division of Structural Engineering CHALMERS UNIVERSITY OF TECHNOLOGY Gothenburg, Sweden 2025 Early-Stage Design of Concrete Girder Bridges Using Set-Based Design Parametric Exploration of Design Alternatives Considering CO2 Emissions, Cost, and Buildability Master’s Thesis in the Master’s Programme Structural Engineering and Building Technology ALICE BEISCHER KARIN FURUHJELM © ALICE BEISCHER & KARIN FURUHJELM, 2025. Supervisor: Alexander Kjellgren, Skanska Examiner: Rasmus Rempling, Department of Structural Engineering Examensarbete ACEX30 Institutionen för Arkitektur och Samhällsbyggnadsteknik Chalmers Tekniska Högskola, 2025 Department of Architecture and Civil Engineering Division of Structural Engineering Chalmers University of Technology SE-412 96 Gothenburg Sweden Telephone +46 31 772 1000 Cover: A normalized probability density distribution representing the buildability cost criterion for design solutions brought forward with the developed set-based design algorithm, to- gether with a sketch of a two girder reinforced concrete bridge. Department of Architecture and Civil Engineering Gothenburg, Sweden, 2025 I Early-Stage Design of Concrete Girder Bridges Using Set-Based Design Parametric Exploration of Design Alternatives Considering CO2 Emissions, Cost, and Buildability Master’s thesis in the Master’s Programme Structural Engineering and Building Technology ALICE BEISCHER KARIN FURUHJELM Department of Architecture and Civil Engineering Division of Structural Engineering Chalmers University of Technology ABSTRACT This thesis investigates the application of parametric multi-criteria optimization in the early-stage design of reinforced concrete girder bridges using a set-based design (SBD) approach. As the construction industry faces increasing pressure to reduce greenhouse gas emissions in line with Sweden’s 2045 net-zero targets, methods that allow sustain- able solutions in the initial stages of a project are encouraged. However, minimizing the use of carbon-intensive materials, such as concrete, can present challenges for buildabil- ity, particularly when more geometrically complex structures are introduced. To address this situation, the study incorporates both environmental impact and buildability into the optimization criteria, enabling identification of solutions that balance these potentially conflicting objectives. A developed parametric Python algorithm was used to generate a wide design space based on geometry parameters from a reference project. The study focused on cross-sections with two main girders—either of rectangular or I-shaped pro- files. Each alternative was structurally verified by the algorithm through finite element analysis using BRIGADE/Plus, and subsequently evaluated in terms of investment cost, CO2 emissions, and buildability. The analysis of over 100,000 cross-section alternatives revealed groups of material-efficient solutions that reduced both emissions and cost, al- though some with buildability that was negatively impacted due to increased production complexity. The results underscore the trade-offs between key criteria and demonstrate the ability of the SBD method to identify solutions that meet multiple performance tar- gets. Overall, the study highlights the value of SBD in supporting early-stage decision- making, enabling more informed trade-offs, and reducing risk in tendering processes aimed at sustainable infrastructure development. Key words: set-based design, parametric modeling, multi-criteria optimization, girder bridge, reinforced concrete, buildability, environmental impact I Set-baserad design i tidiga skeden av betongbalkbroars utformning Parametrisk utforskning av designalternativ med hänsyn till CO2-utsläpp, kostnad och byggbarhet ALICE BEISCHER KARIN FURUHJELM Institutionen för arkitektur och samhällsbyggnadsteknik Avdelningen för Konstruktionsteknik Chalmers tekniska högskola SAMMANFATTNING Det här examensarbetet undersöker tillämpningen av parametrisk flerkriterieoptimer- ing i tidiga skeden av projektering av balkbroar i armerad betong, med hjälp av set- baserad design (SBD). Byggbranschen står inför ett ökande tryck att minska växthus- gasutsläppen i enlighet med Sveriges mål om nettonollupsläpp till 2045, vilket skapar ett behov av metoder som möjliggör hållbara lösningar redan i projektets inledande faser, där potentialen för effektiva implementeringar är stor. Att minimera användnin- gen av koldioxidintensiva material, såsom betong, kan dock innebära utmaningar för byggbarheten, särskilt när mer geometriskt komplexa strukturer införs. För att hantera detta inkluderar studien både klimatpåverkan och byggbarhet som optimeringskriterier, vilket möjliggör identifiering av lösningar som balanserar dessa potentiellt motstridiga mål. En parametrisk algoritm, utvecklad i Python, användes för att generera en bred lös- ningsrymd baserat på geometriparametrar från ett referensprojekt. Studien fokuserade på tvärsnitt med två huvudbalkar där både rektangulära och I-balksprofiler undersöktes. Varje broalternativ verifierades strukturellt av algoritmen genom finita elementanalys i programmet BRIGADE/Plus, och utvärderades därefter med avseende på invester- ingskostnad, CO2-utsläpp och byggbarhet. Analysen av över 100 000 tvärsnittsalter- nativ visade grupper av materialeffektiva lösningar som minskade både utsläpp och kostnader, även om byggbarheten i vissa fall påverkades negativt till följd av ökad produktionskomplexitet. Resultaten tydliggör avvägningarna mellan olika kriterier och demonstrerar SBD-metodens förmåga att identifiera lösningar som presterar väl i flera kategorier. Sammanfattningsvis tyder arbetet på att set-baserad design kan stödja beslutsfat- tande i tidiga skeden genom att tydliggöra kompromisser, ge bättre beslutsunderlag och minska osäkerhet i upphandlingsskedet vid utveckling av hållbar infrastruktur. Nyckelord: set-baserad design, parametrisk modellering, flerkriterieoptimering, balk- bro, armerad betong, byggbarhet, materialanvändning, CO2-utsläpp II Contents ABSTRACT I SAMMANFATTNING II CONTENTS IV PREFACE VI NOMENCLATURE IX 1 INTRODUCTION 1 1.1 Background 1 1.2 Aim and objectives 2 1.3 Limitations 3 1.4 Methodology 3 2 THEORETICAL FRAMEWORK 4 2.1 Planning and design process of infrastructure projects 4 2.1.1 Importance of early-stage design optimization 5 2.2 Concrete bridge types 6 2.2.1 Slab bridges 6 2.2.2 Slab frame bridges 6 2.2.3 Girder bridges 7 2.2.4 Box girder bridges 8 2.3 Climate impact of reinforced concrete structures 8 2.3.1 Carbon dioxide emission of reinforced concrete 9 2.3.2 The potential to reduce material consumption 10 2.4 Design methods 11 2.4.1 Point-based design 11 2.4.2 Set-based design 12 2.4.3 Parametric modeling 13 2.5 Multi-objective optimization 13 2.5.1 Optimization criteria for environmental impact 14 2.5.2 Optimization criteria for buildability 15 2.6 Traffic load models 18 2.6.1 Traffic load models in Eurocode 18 2.6.2 National vehicle model 19 3 REFERENCE PROJECT 20 3.1 Östrand road bridge 20 3.2 Modeling the reference bridge 21 3.3 Modifications 22 4 APPLYING THE SET-BASED DESIGN ALGORITHM 23 4.1 Generation of design set 24 4.1.1 Rebar layout generation 25 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 III 4.2 Resistance verification 27 4.2.1 Load categories 28 4.2.2 Load combinations 29 4.2.3 Structural verification in ULS and SLS 29 4.3 Multi-criteria evaluation 30 5 RESULTS 33 5.1 Mapping of design spaces 33 5.2 Relationship between criteria 36 5.3 Comparison of sets within Design Space C 40 5.3.1 Evaluation based on girder shape 40 5.3.2 Evaluation based on concrete class 42 5.3.3 Evaluation based on rebar diamater 43 5.4 Exploration of Design Space D 43 6 DISCUSSION 47 6.1 Method discussion 47 6.1.1 Implications of excluding pre-stressing in the FE model 48 6.1.2 Buildability considerations for I-shaped girders 48 6.1.3 Assumptions and limitations in cost and buildability factors 49 6.2 Discussion of results 50 6.3 Possible further studies 51 7 CONCLUSION 53 A SOFTWARE I A.1 BRIGADE/Plus and Abaqus I B VERIFICATION OF FE MODEL II B.1 Self-weight II B.2 Traffic load III C LOADS IV C.1 Permanent loads IV C.2 Variable loads IV D VERIFICATION OF RESISTANCE VI D.1 Serviceability limit state VI D.2 Ultimate limit state VI D.2.1 Bending moment resistance VI D.2.2 Shear resistance VIII E CRITERIA CALCULATION IX E.1 Environmental impact cost IX E.2 Investment cost X E.3 Buildability cost XI IV CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 Preface This study was conducted at the Department of Architecture and Civil Engineering at Chalmers University of Technology during the spring of 2025, as our master’s thesis at the end of the Civil Engineer and the Architecture and Engineering programs. The project was carried out with the support of the Department of Bridge and Infrastructure at Skanska in Gothenburg, Sweden. We would especially like to thank our supervisor at Skanska, Alexander Kjellgren, for supporting us throughout this process while still allowing us to take full ownership of the project. We are also grateful to the entire Department of Bridge and Infrastructure at Skanska for welcoming us and for taking the time to discuss challenges and ideas. We are also equally grateful to our supervisor and examiner at Chalmers, Rasmus Rem- pling, for his experience and guidance. Our opponents, Erik and Alex, also deserve the thanks for providing valuable feedback and offering a fresh perspective throughout the entire process. Special thanks to Pontus Nyberg for generously sharing his knowledge of BRIGADE/Plus and for helping us resolve countless error messages. Finally, we are very grateful to our families, friends, and partners for their support throughout our entire studies at Chalmers. Gothenburg, June 2025 Alice Beischer Karin Furuhjelm VI CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 Nomenclature This nomenclature list presents the acronyms, design parameters, constraints, and the definitions of the design spaces used in this report. Acronyms CO2 Carbon Dioxide FE Finite Element FEM Finite Element Method FLS Fatigue Limit State LCA Life Cycle Assessment LM Load Model PBD Point-Based Design SBD Set-Based Design SLS Serviceability Limit State ULS Ultimate Limit state Design parameters & constraints W Width of bridge deck L Span length of bridge MBh Height of main beam MBb Width of main beam Webt Web thickness of I-profile Flt Thickness of bottom flange of I-profile EBh Height of edge beam EBb Width of edge beam ϕ, ϕrebar Diameter of tensile reinforcement fck Characteristic compression strength of concrete nlayers Number of layers of tensile reinforcement nbars Number of bars in one layer As Required reinforcement amount δmax Maximum vertical deflection in the span CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 VII Design Spaces Design Space A Set of design solutions, regardless of input parameters or fea- sibility Design Space B Set of design solutions for specified input parameters, regard- less of feasibility Design Space C Set of feasible design solutions for specified input parameters Design Space D Set of the 10% best performing design solutions in each opti- mization criteria VIII CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 IX X CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 1 Introduction This chapter introduces the background, aim and objectives of the thesis project, as well as covers its limitations and methodology. 1.1 Background The construction industry is a significant contributor to global CO2 emissions, and re- ducing these emissions is a crucial goal to meet climate targets. The construction sector was responsible for 22% of Sweden’s greenhouse gas emissions in 2021, where new construction represents roughly 20% of those emissions (Fossilfritt Sverige, 2024). The roadmap for fossil-free competitiveness in the construction sector outlines strategies aimed at reducing the industry’s carbon footprint and promoting sustainability prac- tices, with the ultimate goal of reaching net zero greenhouse gas emissions by 2045. Thus, a key aspect of this strategy is the early integration of life-cycle consideration in the design, where consultants are encouraged to propose effective, sustainable solutions in the initial stages of a project. There are considerable possibilities to affect a project’s total climate impact in the plan- ning and design stages. This can be achieved by implementing materials with a low carbon footprint or designs with optimized material and energy demand (Fossilfritt Sverige, 2024). For civil projects, most of the impact of the construction phase on the climate comes from materials, where asphalt, concrete, and steel contribute up to 80%. Thus, a design of optimized material use contributes to strategies to reach net zero greenhouse gas emissions. Buildability is also a critical factor in the construction sector. It is defined by the Con- struction Industry Research and Information Association (CIRIA) in the UK as “the extent to which the design of a building facilitates ease of construction, subject to the overall requirements for the completed building” (Wimalaratne et al., 2021). Buildabil- ity involves integrating construction knowledge and experience throughout the project delivery process to achieve overall project objectives, such as cost, quality, productiv- ity, safety, and timely completion. It can also be defined as a process that promotes design that facilitates building construction. Although it is recommended to incorpo- rate the aspect of buildability throughout all phases of a construction project, the design phase is considered critical to implement buildability. Thus, structural designers have a significant responsibility to include buildability in the project. In practice, aiming for environmental sustainability in a construction project must be balanced with buildability. When these two objectives are successfully incorporated, design solutions with a reduced climate impact and a high level of buildability could possibly be found. One promising approach to achieving this balance is set-based de- CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 1 sign (SBD). SBD is an approach that maintains a wide range of design options as long as possible during the design process (Nahm and Ishikawa, 2005). Instead of narrowing down to a single solution early in the process, SBD allows simultaneous exploration of multiple alternatives and criteria, such as buildability and material reduction. This approach is particularly beneficial in structural engineering, where it allows the con- sideration of various design criteria and input from stakeholders before finalizing the optimal solution (Rempling et al., 2019). Finding solutions that have a high degree of buildability and sustainability is a priority for contractors who often work with design- build contracts. Recent research has explored the application of set-based design in bridge engineer- ing to balance sustainability and buildability. For instance, Bergenram and Ulander (2023) implemented a parametric multi-criteria optimization approach for slab frame bridges, considering investment cost, environmental impact, and buildability. Their findings indicated that while environmental impact could be reduced by up to 13.7%, this often came with a slight increase in costs due to buildability considerations. Simi- larly, Mathern et al. (2018) proposed a conceptual framework integrating sustainability, buildability, and performance in structural design, emphasizing the importance of in- formed decision-making in early design stages. These studies highlight the potential of SBD in optimizing bridge designs but also reveal limitations. Notably, much of the existing research focuses on slab frame bridges, leaving a gap in the application of SBD to other bridge types, such as concrete girder bridges. Furthermore, while buildability is acknowledged as a critical factor, there is a lack of comprehensive methods to quan- titatively assess it within automated design processes. This study aims to address these gaps by exploring the implementation of SBD with parametric calculation models in the early design of concrete girder bridges, evaluating design solutions based on both buildability and CO2 equivalents. 1.2 Aim and objectives The purpose of the study was to explore the possibility of implementing set-based de- sign with parametric calculation models in the early design of concrete girder bridges, evaluating the generated design solutions based on buildability and CO2 equivalents. Thus, the objectives of the project were to: • Explore the potential of digital and automated design workflow in early-stage bridge design, • Implement multi-objective optimization on the cross-section of a reinforced con- crete girder bridge, to explore trade-offs between climate impact, buildability, and investment cost, • Investigate how buildability aspects can be incorporated into the automated de- sign process for girder bridges, and to • Assess whether the proposed method can generate design solutions with reduced climate impact. 2 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 1.3 Limitations The study was limited to reinforced concrete girder bridges. The environmental impact considered was limited to the impact of the material since the differentiating factors be- tween the different designs were the cross-sectional area and thus the amount of mate- rial. Quantitative measurements of buildability were investigated and based on previous studies. To evaluate the climate impact of bridge designs, the impact has been limited to only the amount of concrete and reinforcement steel in the bridges. This included only the superstructure, excluding abutments and details such as guardrails. Several bridge life cycle assessment (LCA) studies show that the dominant materials in climate impact are concrete, reinforcement steel, and construction steel (Uppenberg et al., 2017). In addi- tion, asphalt can also have notable climate impact in the total life-cycle (Hammervold et al., 2013). However, the amount of asphalt used for each bridge design is assumed to not differ significantly, making it a less interesting aspect to include. In conclusion, the environmental impact calculations in the study were limited to the impact of the reinforced concrete material of the superstructure. Also, any required foundation work was excluded from this study. It is a variable that varies for every situation, making it a complex problem with the work load becoming a study of its own (Uppenberg et al., 2017). Thus, although foundation work, like piling, are common and can also contribute to a significant part of the total environmental impact in bridge construction, it was excluded from the study. Since the method was intended to facilitate in the early design process, full dimension checks were not included in the structural verification. Some limitations were made to reduce the computational work. The designs were verified for bending moment and shear in ULS and deflection in SLS to be considered feasible solutions. 1.4 Methodology In the initial stage of the project, a literature study was carried out exploring relevant fields of research and obtaining knowledge on nearby topics, such as parametric design and bridge types. The main part of the project work was to develop a set-based multi-criteria optimiza- tion algorithm for bridge design, focusing on generating, verifying and evaluating de- sign alternatives. The process involved finite element modeling (FEM) for structural verification, and the optimization criteria were centered on environmental impact and buildability. A reference project was chosen to guide the process. Digital tools were integral to the methodology, with Python employed for algorithm development and data handling. The finite element analysis was conducted using BRIGADE/Plus, enabling precise structural assessments of the generated design alternatives. The approach pri- oritized the systematic generation of extensive design datasets, which allowed for the exploration of complex cross-sectional geometries and efficient handling of large data sets. This, in turn, provided supported for informed decision-making in the design pro- cess. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 3 2 Theoretical Framework In this chapter, theoretical background is provided on topics covered in the thesis. Ini- tially, information about the the design processes related to infrastructure projects is included. Followed by information on bridge types and the climate impact of construct- ing civil projects. Further, the load categories that apply are described, as well as an exploration of different design methods. Lastly, the multi-objective optimization and its criteria are explained. 2.1 Planning and design process of infrastructure projects The Swedish Transport Administration has determined a project process for large in- frastructure projects, where both climate calculations and economic calculations are required in multiple steps of the process (Miliutenko, 2022). The planning and design process of infrastructure projects, such as bridges, is comprehensive and involves mul- tiple stages and stakeholders, see Figure 2.1. Preliminary design Detailed design & Approval Construction Documentation Operation Conceptual Phase Construction Phase Figure 2.1: The Swedish Transport Administration’s process for developing infrastruc- ture, with the studied phase highlighted. The process can be divided into the following phases: Conceptual design: The process begins with identifying the need for the infrastructure project by considering factors such as traffic demand, urban development, safety, and environmental impact (Eriksson, 2013). A feasibility study is conducted to assess the technical, economic, and environmental viability of the project, including initial climate calculations using the tool Klimatkalkyl for projects with a total cost of ≥ 50 million SEK (Miliutenko, 2022). Often in this initial phase, different alternatives with respect to location, routing, and design are explored and presented on a conceptual level. Roughly estimated calculations are used to analyze how different choices affect the project’s climate performance and economic cost. The stakeholders involved provide input for evaluating the risks and concerns with the specific project going forward. Preliminary Design: In this phase, the project design is further refined. More detailed design plans that include technical specifications are part of the consultation materials produced in this stage, along with Environmental Impact Assessments (EIA). EIA are 4 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 developed to determine the significant environmental impact of the project (Trafikver- ket, 2022). Conducting more detailed financial evaluations to assess the project’s eco- nomic feasibility is also part of this phase, in a cost-benefit analysis. Detailed design and Approval: The final engineering designs feature comprehensive and detailed design plans, including all technical specifications and construction details (Trafikverket, 2022). Another climate calculation is included in the decision-making materials for approval. Obtaining all necessary permits and approvals to proceed with construction is also part of this phase. Construction Documentation: This phase involves preparing detailed plans for the con- struction process, including timelines and resource allocation, as well as other docu- ments for the procurement of contractors and suppliers (Eriksson, 2013). The climate calculation is aligned with the latest economic data which serves as the basis for the tendering process. Construction and Operation: In the final phases, along with constructing and operating the project itself, compiling a climate declaration is part of the project’s final report (Miliutenko, 2022). This declaration includes the actual climate impact of the project and is used to monitor and improve climate efficiency in future projects. This approach ensures transparency in the planning and design of infrastructure while considering environmental impacts. The use of the Klimatkalkyl tool throughout the process helps maintain consistency and allows for ongoing refinement of the climate calculations as the project progresses. The iteration in performing climate calculations can be aided by using an automated design flow, such as set-based design (Hansson & Tacking, 2024). With the design and calculated climate impact automatically adjusting when a parameter is changed, signifi- cant time can be saved. The uncertainty involved in decision making in the preliminary phase is also managed through the use of set-based design. 2.1.1 Importance of early-stage design optimization In early project phases, the potential for optimization is greater while the cost of making changes are lower (Bragança et al., 2014). The possibility of influencing cost and en- vironmental impact is high in the early design phase, while the cumulated impacts and costs are still low, see Figure 2.2. This relationship changes throughout the construc- tion’s life time, and late changes will cost more both economically and environmentally. Thus, optimization of a design is most effective in the early stages of a project and is substantial in creating solutions with low environmental impact and achieving climate goals. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 5 Cost of design changes Ability to impact project Preliminary design Detailed design Construction documentation Construction Operation Figure 2.2: How the ability to change the design correlates with the cost according to the Macleamy curve. 2.2 Concrete bridge types Different types of bridges offer specific advantages, making them more suitable for certain applications (Kettil, 2023). This section provides an overview of the most com- monly constructed concrete bridges in Sweden with short to medium spans, including the cross-section types evaluated in this study. 2.2.1 Slab bridges Slab bridges consist of a solid reinforced concrete slab that spans between supports (Concrete Bridge Development Group, n.d.). The construction of slab bridges is typ- ically straightforward and cost-effective. The slab distributes loads uniformly in all directions, making it suitable for small to medium-sized bridges. Figure 2.3: A slab bridge’s typical shape of the bridge deck. 2.2.2 Slab frame bridges Slab frame bridges are an extension of slab bridges, incorporating a frame structure to provide additional support and stability (Yavari, 2017). These bridges are often used in 6 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 urban areas where space is limited and complex load conditions are present. The frame structure, including frame legs and wing walls, allows for better distribution of loads. This bridge type is very common in Sweden and has been a subject for set-based design in previous studies (Bergenram & Ulander, 2023) Figure 2.4: Typical appearance of a slab frame bridge. 2.2.3 Girder bridges Girder bridges are among the simplest and most common bridge types, using beams, also called girders, to support the bridge deck (Concrete Bridge Development Group, n.d.). These girders can be made from either steel or concrete with various cross-section shapes, such as I-girders or rectangular cross-sections. The straightforward design of girder bridges allows for rapid construction and cost-effectiveness, especially for short to medium spans. Concrete girder bridges with span lengths over 30 meters are typically pre-stressed (Kettil, 2023). Figure 2.5: Girder bridge with I-shaped girders. I-shaped girders are considered more material-efficient than rectangular cross-sections, as they require approximately 20% less concrete per square meter of bridge deck to achieve the same structural capacity (Kettil, 2023). This efficiency makes them a favor- able option in terms of material consumption and environmental impact. However, their more complex geometry introduces challenges in the form of intricate reinforcement detailing and more demanding formwork. As a result, I-girders are most commonly CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 7 used in prefabricated beams, where minimizing the weight of structural elements is es- sential for transportation and lifting. In some cases, these prefabricated I-beams may also be applied in girder bridges, depending on project-specific constraints and logistic considerations. The production techniques used in prefabricated I-girders can also be adapted for in-situ construction, particularly in medium-span bridges (Kettil, 2023). In such cases, rein- forcement must be completed before the formwork is assembled around the girder, and the top surface of the bottom flange should be sufficiently inclined to prevent air pock- ets from forming during casting. Although feasible, this process adds complexity to construction and generally requires more labor time compared to bridges using rectan- gular girders. If the girder geometry can be standardized to allow for reusable formwork across multiple spans or projects, it may help reduce formwork costs and material use. Ultimately, while I-girder bridges can offer material and environmental benefits, these advantages must be carefully weighed against increased construction complexity, labor effort, and associated costs. 2.2.4 Box girder bridges Box girder bridges are characterized by their hollow box-shaped cross-sections, typ- ically constructed from prestressed concrete (Concrete Bridge Development Group, n.d.). The void ensures that the material is used where it is most effective. Multiple shape variations exist for the box cross-section, such as trapezoidal or square boxes. It is also possible for the box girder depth to vary along the span. This advanced cross-sectional design provides high torsional stiffness and strength, making box girder bridges particularly suitable for spans longer than 45 meters, curved alignments, and complex load conditions. The enclosed structure also offers better protection against environmental factors, reducing maintenance needs. However, the complexity of their design and construction can lead to higher costs compared to simpler bridge types. Figure 2.6: Box bridge with a trapezoidal box shape. 2.3 Climate impact of reinforced concrete structures Reinforced concrete has many applications and is the most widely used construction material in the world (Lea & Mason, 2025). However, the production of concrete and steel used in bridges accounts for a substantial share of total emissions from infrastruc- ture construction (Uppenberg et al., 2017). These emissions are commonly referred to as embodied carbon, which encompasses the total greenhouse gas emissions arising from the extraction, processing, transportation, and manufacturing of construction ma- terials. Understanding the sources and magnitudes of these emissions is beneficial in 8 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 evaluating the climate impact of concrete structures and identifying opportunities for improvement. This section provides an overview of the carbon dioxide emissions as- sociated with reinforced concrete, followed by an exploration of strategies to reduce its environmental footprint through material efficiency and design optimization. 2.3.1 Carbon dioxide emission of reinforced concrete Cement is a key ingredient in concrete, but is also an enormous contributor to its CO2 emission (Lea & Mason, 2025). Figure 2.7 shows an example of how the components of a typical concrete mix contribute to its carbon footprint. The manufacture of cement is a significant contributor to global warming, as 4–8% of the world’s carbon dioxide emissions are estimated to come from its production. The step in the production process of burning raw materials in a kiln to produce cement clinker, and the carbon dioxide directly emitted from this chemical reaction, called calcination, is more than half of the total emission of cement production. Possible actions to reduce the emissions of cement production could be the introduction of renewable energy to replace fossil fuels in the manufacturing process, increasing the energy efficiency of cement plants, carbon capture and storage, and reducing the amount of portland cement needed by adding supplementary cementious material (SCM) such as blast furnace slag or fly ash. From another perspective, reducing the material consumption of concrete itself by increasing structural efficiency could also be a possible action to reduce the CO2 emissions of concrete in the building industry. Concrete Composition Concrete Carbon Footprint Figure 2.7: Components of a concrete mix and their corresponding share of the mate- rial’s carbon footprint. Redrawn from (Niveditha et al., 2020). In addition to cement, reinforcing steel is a significant contributor to the climate impact of reinforced concrete structures due to its high embodied carbon. Among construction materials, reinforcing steel emits the most CO2 per unit weight (Kwon et al., 2021), about 9.2 times that of concrete class C25/30, for example. On a global scale, the steel CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 9 sector is responsible for an estimated 6–7% of total greenhouse gas emissions (Sheng et al., 2024). A major source of these emissions is the energy-intensive blast furnace- basic oxygen furnace (BF-BOF) production route used in manufacturing virgin steel. The process involves iron ore and coal at high temperatures and generally burns natu- ral gas as energy that also emits significant amounts of CO2. Although reinforcement bars are typically made of 90-100% recycled steel, the recycling process of steel still has a significant environmental burden, although it is lower than virgin steel (Purnell, 2013). This underlines the importance of including reinforcing steel in environmental assessments of concrete structures, especially when moving from material-level data to evaluating the total embodied carbon of entire structural systems Estimating the embodied carbon of reinforced concrete is complex (Purnell, 2013). Ce- ment and reinforcing steel have the biggest contributions out of the components in re- inforced concrete, while aggregate, water, and admixtures have minimal influence. De- pending on the design requirements and the structural component studied, the propor- tions of these five components can be altered to obtain different structural properties. A study by Purnell (2012) has shown that structural design and loading are the main influences on the embodied carbon of reinforced concrete (Purnell, 2013). For compar- ison, the embodied carbon of plain concrete is instead strongly dependent on the mix design and its compressive strength. Thus, both concrete and reinforcing steel are pa- rameters where optimization enables the possibility to reduce the total CO2 emissions of reinforced concrete structures. 2.3.2 The potential to reduce material consumption In a study funded by SBUF (Development Fund of the Swedish Construction Indus- try), the goal was to establish construction solutions with "optimized" geometries that result in significant material savings and thus reductions of CO2 emission, compared to the standard cross-section designs. These solutions were also required to meet the functional requirements and be compatible with production methods that ensure rea- sonable time frames and costs. The report, "Climate-optimized Concrete Bridges – Geometry and Material" (Kettil, 2023), shows that concrete volumes, can be signifi- cantly reduced, by approximately 30%, while still meeting functional requirements. In some cases, deviations from the bridge standard may be necessary, but this can still be accepted by demonstrating that the alternative solution meets the required function. In addition, combining the material-efficient geometries of the study with so-called "green concrete", concrete containing SCM and less cement, could lead to CO2 reductions up to 50%. A proposed reason for why this approach is not currently implemented is that the increased production cost is considered to outweigh the material savings. This point again highlights the need to find solutions with low climate impact without compromis- ing on buildability factors. A recent study by Björnsson et al. (2025) found that the material consumption of con- crete bridges in Sweden has increased in the last 50 years and investigated the reason for this increase. Although investigations indicate that different factors contribute, a general conclusion was that the development of design codes and engineering practices has had a significant impact on increased material consumption. For example, traffic loads have increased, while durability requirements have become stricter. Also, how engineers analyze structures has developed over time, with increased use of 3D FEM over analytical calculations. The study also aimed to investigate whether these devel- 10 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 opments are justified. However, drawing a definitive conclusion on whether an increase in material consumption leads to better performance or is a waste of material proved to be difficult. Some mitigating measures suggested by Björnsson et al. (2025) to reduce the trend of increasing material consumption are to challenge and clarify code provisions and to encourage both conceptual thinking among engineers and the courage to question design codes when justified. Björnsson et al. (2025) further specifies that, although the transition to greener material alternatives reduces the environmental impact of a structure, it is not enough to focus solely on that. To further reduce the environmental footprint, it is necessary to focus on how to systematically reduce material consump- tion. In addition, Björnsson et al. (2025) mention that the choices made in the early design process have a big impact on the material consumption of the structure, meaning that early choices could, for example, "lock in" geometries and other structural bound- ary conditions which limits the possibility of saving on material in later design stages. This problem could SBD help with, through its possibility of exploring multiple design alternatives in the early design process before finalizing the chosen solution, enabling comparison between design alternatives of different material consumptions. 2.4 Design methods This section introduces the traditional and most commonly used design method in the field of structural engineering today, point-based design, as well as the more recently developed methods of set-based design and parametric design, which are both used in combination in the thesis work. 2.4.1 Point-based design The traditional design method used in structural engineering is often called point-based design (PBD), as it is based on a single design option selected early in the process (Par- rish et al., 2007). The chosen design is then refined in more detail as new information arises throughout the project, see Figure 2.8. Taking into account the multiple stake- holders that place demands on the outcome, this method requires an iterative rework of the chosen design (Parrish et al., 2007; Mathern et al., 2018). The decision-making process in structural engineering, and thus in point-based design, is typically driven by the judgment, based on experience, of the engineers involved (Fernández and Ramos, 2014). However, the perspectives of other stakeholders are generally not considered, which can result in solutions that, while technically feasible, are suboptimal in other terms, such as cost, environmental impact, or buildability. The additional work due to the need for rework as well as the inability to cater to multiple criteria simultaneously are reasons why the point-based design method is deemed ineffective. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 11 Figure 2.8: Schematic figure of the point-based design process. Arrows represent de- sign decisions made and small circles the new design. The star represents the final design. 2.4.2 Set-based design Improving the buildability and performance of structures while simultaneously reducing their economic and environmental impact has become a topic of greater interest in recent years (Mathern et al., 2021). Set-based design (SBD) allows the exploration of many design solutions and the evaluation of them against the objectives of the project, thus giving the possibility to find the most appropriate designs. Set-based design considers a set of design options from the beginning, instead of pre- ferring a single solution as in PBD (Parrish et al., 2007). This approach allows main- taining a broad design space as long as possible and allows decisions to be postponed, thus minimizing the need for rework. A valued benefit and incentive for the develop- ment of the method is the economic precaution to avoid a complete redesign late in the process. In comparison, there is a risk with point-based design, where significant new learning points that arise later in the timeline require a complete redesign to meet updated demands. However, in SBD, the design space is narrowed down as new cri- teria are introduced during the process. There is also the possibility to revisit previous choices since all design options within the sets remain available, allowing for an ongo- ing comparison of alternatives. A crucial aspect of SBD is that the criteria that eliminate options from the design set are well defined and documented (Parrish et al., 2007). The idea behind this is to keep all stakeholders informed about decisions made and to easily reacquire design sets that are disregarded in case of elimination criteria shifting. A study by Bergenram et al. (2024), on multi-criteria optimization of slab frame bridges, structured the SBD algorithm into four design spaces, labeled A through D. A similar approach to design spaces was used in this study, as illustrated in Figure 2.9. Design Space A was the initial and largest design space, covering all possible bridge cross- section designs, regardless of feasibility. Design Space B refers to the set of designs within Design Space A that defined by the established governing geometry input pa- rameters for the structure. Of this set, a check of technical feasibility is made through ULS and SLS verification. Thus, Design Space C only includes the designs that meet these constraints. What separates Design Space D from the previous is the filtering 12 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 through multiple criteria such as cost, environmental impact, and buildability. The final Design Space D consists of the designs optimized according to selected criteria. This structure is one of several possible approaches to implementing SBD, and the specific formulation of design spaces can be adapted to suit the objectives and context of a given study. Figure 2.9: A visual representation of the set-based design method. 2.4.3 Parametric modeling Parametric modeling is a common design practice within computer-aided design (CAD), which is used in a variety of design fields such as architecture, structural engineering and product design. The demand for flexible design tools within these fields is what drove the inclusion of parametric modeling in various design software (Hernandez, 2006). Parametric modeling easily allows for variations when working on a design, without the need to erase or rework. This flexibility is possible due to the ability for users to define adjustable parameters and rules with respect to different attributes of the design. Changing a parameter subsequently reconfigures all linked design functions performed in the software and gives the user immediate visual feedback on the change of input. One prominent area of use for parametric modeling is to generate multiple design op- tions (Lee and Ostwald, 2020). This process can be automated and controlled through the algorithmic functions of parametric design tools, such as Grasshopper. Creating a large number of design solutions with this method can hence be utilized as a design set used in set-based design to further automatize that process. 2.5 Multi-objective optimization Multi-objective optimization aids in maximizing the utility values of various potentially conflicting objectives (Mathern et al., 2021). It is common in engineering problems that CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 13 different objectives will, to some degree, contradict each other, resulting in no single correct solution which satisfies all objectives. Multi-objective optimization aids in the compromising between objectives. An optimization problem can mathematically be expressed by the general formulation in equation (2.1) (Yavari et al., 2016; Khouri Chalouhi, 2019). Objective functions fi(x), constraint functions gj(x) and hk(x), and design variables x are used to define an optimization model to find the optimal solution. minimize fi(x), i = 1, 2, . . . , M subject to gj(x) ≤ 0, j = 1, 2, . . . , J hk(x) = 0, k = 1, 2, . . . , K where x = [x1, x2, . . . , xn] ∈ Rn (2.1) The objective functions describe the objectives and intentions of the project. Relevant objectives for a building or civil engineering project are related to the economy, the performance of the structure, the environmental impact and the buildability (Mathern et al., 2021). Examples of objectives are to reduce the construction cost, minimize the deflection of structural elements, and reduce the construction time and CO2 emission of a project. In addition to objective functions, constraints and design variables are needed to construct an optimization model. Objective functions can be understood as mathematical formulations of the optimization criteria, serving as tools to evaluate and compare design alternatives in relation to defined goals. Constraint functions and design variables limit and define the design problem (Mathern et al., 2021). Structural norms and standards establish the constraints in structural de- sign with the intention of the construction to be structurally sound. The design effects of loads are determined by appropriate structural and load models, that should be within the limit of the associated design constraint. The design variables, also called design parameters, and their possible values define the design problem and generate a design space of possible configurations. Concrete class, element dimensions, and diameter of reinforcement bars are examples of design variables in the context of this study. With the objectives, constraints, and design variables defined, an optimization model can be defined for a set-based design process. 2.5.1 Optimization criteria for environmental impact The objective function for an optimization criterion of the environmental impact can be described by the environmental impact of each relevant material (Yavari et al., 2017). As described in Sections 1.3 and 2.3.1, concrete and reinforcing steel dominate the total CO2 emissions of reinforced concrete bridges and where the possibility of optimization is the highest. The environmental impact of a bridge can then be simplified to include only the effect of these two materials in the preliminary design phase. In a study by Yavari et al. (2017), the environmental cost of reinforced concrete was assessed using a detailed life cycle assessment with the ReCiPe midpoint method and two monetary weighting systems to convert environmental impact to monetary cost. The ReCiPe midpoint method is the most comprehensive LCA methodology currently available and includes 11 types of impact categories. The study by Yavari et al. (2017) chose to include six of these impact categories due to the "limited availability of mon- 14 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 etary values in practice", and only impact categories with indicators available in both investigated weighing methods. These impact categories in the LCA covered not only green house gas emissions, but also parameters related to ecosystem quality, resources and human health. Through a cradle-to-grave LCA, the study by Yavari et al. (2017) produced character- ized values of the environmental impacts of three common concrete strength classes and reinforcement, using the Ecoinvent version 3 database. The two monetary weight- ing systems investigated and compared by Yavari et al. (2017) were Ecovalue12 and Exotax02. The Ecovalue weighting system is derived from the reduction in benefits re- sulting from environmental deterioration, with a focus on Swedish conditions (Finnve- den et al., 2013). The Ecotax set is "based on environmental taxed and fees" (Yavari et al., 2017). However, the results of the study show that both weighting systems yield the same optimized results in total. Finally, the objective function for the environmental optimization criterion was defined as in equation (2.2) (Yavari et al., 2017). f(x) = EnvCostconcrete + αreb × EnvCostreinforcement (2.2a) EnvCost = n∑ i=1 impacti × monetaryi (2.2b) where EnvCost is the total associated environmental cost of the n number of impact categories, impacti is the impact based on the characterized environmental impacts for the i’th impact category and monetaryi is the associated environmental cost of impacti based on the Ecovalue or Ecotax monetary weighting factors. To consider additional re- inforcement needed in design details and anchorage length, αreb was introduced, based on practical experience in design, set equal to 1.4. This method of defining environmental optimization criteria presented by Yavari et al. (2017) was able to be efficiently applied to the design process of slab frame bridges. This work was also supported by another study by Bergenram and Ulander (2023) who implemented the same method with confirmed results. 2.5.2 Optimization criteria for buildability Buildability has several positive impacts on the outcome of construction projects. A high degree of buildability results in benefits not only for the outcome of the project, but also for the client and the construction organization (Osuizugbo et al., 2023). Build- ability is shown to be economically, safety and quality beneficial, see Figure 2.10. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 15 Project - Improved quality and performance - Faster project completion - Enhanced safety - Easier maintenance Client - Reduced project and maintenance costs - Lower bidding costs - Increased goodwill and recognition - Greater job satisfaction Organisation - Increased efficiency and productivity - Cost-effectiveness in construction and labor - Reduced waste and rework - Smoother project delivery and planning - Effective problem and risk management - Improved communication and teamwork - Better design and construction methods - Valuable feedback for future projects Impact of Buildability Figure 2.10: Possible impact of buildability according to (Osuizugbo et al., 2023). The concept of buildability needs to be discretized into measurable quantities to enable its implementation into an optimization model. Buildability is a complex concept with numerous aspects concerning what is feasible and efficient during construction (Os- uizugbo et al., 2023). A study by Yavari et al. (2016) investigated the possibility of optimizing the investment cost when building slab frame bridges, where the investment cost included the cost of material, the procurement cost and the production cost. When both labor and material costs are considered, there is the possibility of also quantifying and implementing aspects of buildability in an optimization model (Bergenram & Ulan- der, 2023). Yavari et al. (2016) defined an objective function based on the material and labor costs of concrete, formwork, and reinforcement, see equation (2.3), and presented unit prices for different construction processes. f(x) = Costconcrete + Costformwork + αreb × Costreinforcement (2.3) The factor αreb accounts for the additional cost associated with increased reinforcement amounts due to anchorage lengths and detailing, and was set equal to 1.4. The study by Yavari et al. (2016) implemented three aspects of buildability into the objective function for their cost optimization: • The thickness of the structural members was assumed to affect the buildability, 16 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 as a thinner concrete section involves larger amounts and more dense reinforce- ment, resulting in more labor hours and longer construction time. This was im- plemented by a factor that increased the labor cost of the reinforcement. • Varying thickness of the structural members was assumed to increase both the cost of the formwork and the reinforcement work, increasing labor costs com- pared to members of constant thickness. This aspect was implemented by a factor that increased the cost of formwork and reinforcement labor. • A concrete mix of a higher strength class was assumed to increase the labor time due to its less workable properties. This was implemented by adding an additional cost per volume for concrete class C50/60 and higher. Based on the study by Yavari et al. (2016), Bergenram and Ulander (2023) further de- veloped a definition of measurable buildability criteria, since both studies focused on the implementation of an optimization algorithm on slab frame bridges. Bergenram and Ulander (2023) interviewed a structural engineer specialist and a calculation engineer at Skanska to further study the possible interpretations of the buildability criteria. In real- ity, buildability is assessed by capacities related to different tasks, "ultimately adjusting the number of labor hours needed to finish certain production procedures" (Bergenram & Ulander, 2023, p. 31). The labor hours differ from different construction processes; what type of structural element is being casted, the properties of the reinforcement, the transporting conditions, the climate on site, and factors of the surroundings. However, some of these aspects do not correlate with the design of the bridge and cannot be taken into account when optimizing the design solution (Khouri Chalouhi et al., 2019). The relevant factor is the time required to build an element, which is related to the amount of material and the complexity of the element. The time to erect an element can vary sig- nificantly depending on the shape and function of it. Consequently, buildability criteria suitable for integration into optimization frameworks should be limited to quantifiable design-related parameters that influence the duration and complexity of the production. From the recommendation of experienced professionals working at Skanska, Bergen- ram and Ulander (2023) implemented two additional buildability aspects in their ob- jective function in comparison to the study by Yavari et al. (2016). In interviews, they found that the addition and anchorage of shear reinforcement increases labor costs. In addition, smaller diameters of reinforcement bars correspond to more hours of place- ment due to the increased number of bars needed to reach the same unit volume as larger diameters. Both of these buildability aspects were implemented, respectively, by a fac- tor that increased the labor cost of the reinforcement. Bergenram and Ulander (2023) ultimately defined the buildability cost for a bridge design as: costbuild = costbuild,var + costbuild,sl + costbuild,conc,class+ αreb × (costbuild,ϕ + costbuild,stirrup) (2.4) In addition to the buildability aspects mentioned above, Khouri Chalouhi (2019) de- scribes that the type of cross-section affect the buildability. Different shapes of the elements has a consequence on the labor cost for the same amount of material, because the reinforcement work difficulty increases, and thus takes longer. Figure 2.11 displays an example of three different cross-section types with increasing reinforcement labor hours for every cross-section type presented. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 17 Figure 2.11: Examples of different cross-section types with varying buildability due to their shape, illustration inspired by (Khouri Chalouhi, 2019). 2.6 Traffic load models In Sweden, the design of road bridges must comply with the European Standard, Eu- rocode SS-EN 1991-2 (Swedish Institute for Standards, 2011), and the regulations set forth by the Swedish Transport Agency (Transportstyrelsen, 2018). In this section, the focus is on the traffic loads that affect the superstructure. This includes four Load Mod- els (LM) according to Eurocode and a National Vehicle model according to the Swedish Transport Agency. 2.6.1 Traffic load models in Eurocode According to SS-EN 1991-2 (Swedish Institute for Standards, 2011), traffic loads from cars, lorries, and special vehicles produce static and dynamic forces. Simplified load models are applied to represent real load situations. Traffic actions can include ver- tical loading, horizontal acceleration and braking forces, and centrifugal forces from asymmetrical loading across the bridge deck. The load models for vertical loads presented in Eurocode are as follows: • Load Model 1 (LM1): Concentrated and uniformly distributed loads, which cover most of the effects of the traffic of lorries and cars. This model should be used for general and local verifications. • Load Model 2 (LM2): A single axle load applied on specific tire contact ar- eas which covers the dynamic effects of normal traffic on structural members of length 3 m to 7 m. • Load Model 3 (LM3): A set of assemblies of axle loads representing special 18 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 vehicles (e.g. for industrial transport) which can travel on routes permitted for abnormal loads. It is intended for general and local verifications. • Load Model 4 (LM4): A crowd loading, intended only for general verifications. 2.6.2 National vehicle model In the national vehicle model, several load cases (A-O) are involved, as outlined by the Swedish Transport Agency (Transportstyrelsen, 2018). These cases should be tested individually, with the vehicle placed in the most unfavorable position. The vehicle can occupy a maximum of two load fields with loading factors of 1.0 and 0.8, respectively. Additional load fields, if present, are subjected to a uniform load of 0 or 5 kN/m. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 19 3 Reference Project A reference project was chosen from Skanska’s archive and acted as a base for the gen- eration of the design set, where the geometry of the bridge was used as a base point from which to proceed with optimization. The study was also limited to the analysis of the superstructure, excluding the supports and foundation. First, an FE model was created based on the superstructure of the reference project. Secondly, support reactions, de- flection, bending moment, and shear forces were compared with the calculation report of the reference project to verify the FE model. In addition, analytical calculations also supported the verified model. Verifications are expanded on in Appendix B. In addition, during the production of the FE model, a macro recorded the modeling. The macro script was then parameterized in preparation for the SBD algorithm. This chapter describes the reference project, how the FE model was made, and the modifications made from the reference project to the model. 3.1 Östrand road bridge The selected reference bridge was the Östrand road bridge – a two-lane road bridge spanning four railway tracks on the Swedish east coast, close to Sundsvall. It is a simply supported girder bridge on traditional concrete abutments, see Figure 3.1. The bridge has a span of 35.5 meters and a deck width of 9.0 meters. The superstructure was constructed by in-situ casted reinforced concrete and consists of a bridge deck with edge beams and two prestressed main beams, as illustrated in Figure 3.2. The concrete used in the superstructure is of strength class C32/40. The reinforcement bars are of type B500B. In addition, three cross beams in reinforced concrete stabilize the superstructure. Figure 3.1: Elevation of Östrand road bridge, originally produced by Skanska. 20 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 1200 9000 400 17 00 42 0 3450 30 0 Figure 3.2: Cross-section of Östrand road bridge, with measurements in mm. 3.2 Modeling the reference bridge The geometry of the reference bridge was modeled in the FE program BRIGADE/Plus to verify the structural behavior of the model to the original calculation report by Skan- ska, where fem3dyn was used as the FE solver. BRIGADE/Plus is further described in Appendix A. Total reactions, cross-sectional forces, and deflection were compared with the original results, both with self-weight and traffic loads applied to the bridge model, for verification, see Appendix B. The system model in BRIGADE/Plus consists of beam and shell elements. The main beams, cross beams, and edge beams were modeled as wire elements with beam sec- tions. To simulate the main beams’ capacity to support the bridge in ULS, the bridge deck slab was modeled as a planar shell element with limited stiffness in the longitu- dinal direction, adjusted through the material property. However, to obtain the value of the deflection in SLS, the shell element of the bridge deck was modeled with an isotropic material. These assumptions were also made in the original calculations of the reference project. The slabs and beams were connected by ties and couplings to represent "stiff-beam connections" or casted concrete connections. Couplings were used in node-node con- nections between the cross beam end nodes and the main beams. Ties connected the main beams to the slab surfaces above the beams. A view of the FE model is presented in Figure 3.3 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 21 Printed using Abaqus/CAE on: Tue May 27 08:44:41 Västeuropa, sommartid 2025 Figure 3.3: Sketch of structural model in BRIGADE/Plus, with distributed load and boundary conditions. The original design of the Östrand bridge was made according to the regulations Bro 2004 from the Swedish Transport Administration (Vägverket, 2004). To verify the FE model, traffic loads were applied to the bridge according to the same regulations. When continuing with the optimization algorithm, the traffic load was applied according to current standards and codes; see Section 4.2. 3.3 Modifications Several modifications were made when modeling the reference project to simplify the process and minimize computational time. These adjustments include modeling the bridge straight, instead of curved with a radius of 100 m, and without inclination in any direction. The six point loads, placed in longitudinal and transversal directions on the bridge deck to simulate axial loading from traffic, according to Bro 2004 (Vägverket, 2004), were simplified by an equivalent transverse line load. In addition, the prestress- ing of the main beams was excluded from the model. Comparison with the results of the reference project verified all mentioned modifications; see Appendix B. 22 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 4 Applying the Set-Based Design Algorithm The set-based design algorithm used in the study was coded in Python and consisted of three main parts: generations of design set, resistance verification, and multi-criteria evaluation. Figure 4.1 illustrates an overview of the algorithm layout, while Sections 4.1-4.3 give an in-depth description of each part. Generation of design set Combine parameters into bridge cross section alternatives Start of Algorithm Resistance verification of Design space B Define parameter ranges and increments Multi-criteria evaluation of Design space C Define objective function Bridge alternative fulfills objective function? No Bridge alternative disregarded Bridge alternatives make up Design space B Generate rebar layouts for every alternative Bridge alternatives make up Design space D Bridge alternatives make up Design space C Calculate cross- sectional forces & deflection in FEM Calculate cross- sectional resistance SLS checks ULS checks Yes No Bridge alternative disregarded Calculate environment cost & buildability cost Yes Structural demands fullfilled? Figure 4.1: Layout of the SBD algorithm. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 23 4.1 Generation of design set The geometry of the bridge of the reference project acted as a basis for the generation of the design set. Some aspects of the bridge were chosen as fixed parameters, such as the span length, width and thickness of the bridge deck, thus making the girders the main focus in the cross-section variations. These parameters were considered to be the established governing geometry and, as a result, narrow down the Design Space A to Design Space B. The fixed parameters and their values are presented in Table 4.1. Table 4.1: Fixed design parameters of girder bridge. Fixed design parameter Value [m] Span length 35.5 Thickness of bridge deck 0.3 Width of bridge deck 9.0 Geometry of edge beams 0.4 × 0.42 The generation of Design Space B focused on two types of cross-sections, one with rectangular girders and one with I-profile girders. The intervals of the variable parame- ters were derived from the existing geometry of the reference bridge girders, including the design of the reference project within the selected ranges. The studied design pa- rameters and their ranges for rectangular beam cross-sections are presented in Table 4.2. Table 4.2: Parameter ranges and values for girder bridge cross-sections with rectangu- lar main beams. Studied design parameter Values Concrete strength class C32/40, C35/45, C50/60 Reinforcement diameter ϕ16, ϕ20, ϕ25 [mm] Height of main beam 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 2.0, 2.1, 2.2, 2.3, 2.4 [m] Width of main beam 0.8, 0.9, 1.0, 1.1,1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8 [m] For I-profile beam sections, additional parameters studied were bottom flange thickness and web thickness. The width of the main beam of the rectangular girder was used for the width of both the top and bottom flange of the I-profile. The top flange was consid- ered part of the slab and therefore had fixed geometry in terms of thickness. The bottom flange thickness and web thickness parameters were implemented in relationship with the beam height and beam width, respectively, as a ratio. This implementation was made to avoid the absurd randomized combinations that would otherwise occur with independent ranges. The chosen ratio intervals of the parameters of the I-profile are presented in Table 4.3. All parameters are also visualized in Figure 4.2. 24 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 Table 4.3: Additional parameter ranges for I-girder cross-sections. Studied design parameter Ratio range [m/m] Web thickness [0.30, 0.40, 0.50, 0.60, 0.70] Bottom flange thickness [0.30, 0.40, 0.50, 0.60, 0.70] Figure 4.2: Bridge geometry width parameters illustrated. Fixed parameters are marked in grey and variable in black. 4.1.1 Rebar layout generation For each concrete cross-section geometry, multiple tensile reinforcement layouts were generated for the beams, as part of a sub-algorithm in the script. The rebar layouts were created based on input from the beam geometry parameters, such as the necessary concrete cover, the width of the rectangular girder and the width of the I-girder flange, combined with a calculated required reinforcement amount As [mm2/m]. To account for the curtailment of the reinforcing bars, the required reinforcement was determined at seven positions along the length of the bridge. These seven positions were also used when assessing the need and spacing for shear reinforcement. This level of detail was assumed sufficient for the calculation. If the same method were applied to a bridge with a shorter span, fewer evaluation points might be necessary, and vice versa. Figure 4.3 illustrates the sections in which the need for reinforcement was calculated. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 25 Figure 4.3: Assessment positions along the bridge, with example spacing of shear re- inforcement. At each position along the span, the algorithm assigned the required number of rebars to a layout according to common practice rules. The rules applied for longitudinal rebar placement were as follows: • The bottom rebar layer is filled with the maximum number of bars possible before filling any additional layers. • Rebar positions are stacked vertically to accommodate casting. • The flange of I-section girders are filled with bars before placing bars in the web • The uppermost layer of reinforcement always has an even number of bars for simplification. The sub-algorithm takes concrete cover, rebar diameter and minimum spacing between bars, both vertically and horizontally, into account. Figure 4.4 presents the parameters incorporated in the algorithm, of which ϕrebar and fck were variable parameters from the input. fck was the characteristic strength in compression, dependent on the concrete class parameter. nlayers and nbars refer to the number of layers of tensile reinforcement and the number of bars in each layer. These parameters were not part of the input but rather an output produced by the sub-algorithm, used in later steps to verify the capacity of each solution. A new rebar layout was created for each size of rebar diameter. Some variation in required reinforcement amount As was also introduced, to further widen the design space of possible reinforced concrete cross-sections. Relevant data from each rebar layout generated in this step was extracted to be used in the succeeding parts of the algorithm, namely the cross-section resistance verification in Section 4.2, and the multi-criteria evaluation in Section 4.3. 26 CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 Figure 4.4: Parameters related to tensile reinforcement layout. 4.2 Resistance verification The second part of the set-based design algorithm was the verification of the structural resistance of Design Space B. This includes the use of FEM to analyze the load effects on the structure, with the applied loads and load combinations presented in Sections 4.2.1-4.2.2. The structural verification in ULS and SLS is described in more detail in Section 4.2.3. Figure 4.5 shows an overview of the structural verification process, narrowing down Design Space B to a smaller Design Space C, which contains only feasible solutions. CHALMERS Architecture and Civil Engineering, Master’s Thesis ACEX30 27 DESIGN SET B Parameters Bridge Alternative Disregarded FE-Analysis Rebar Layout Generation Extract Sectional Forces & Deflection Values Cross-Section Resistance Calculation MEd < MRd VEd