Link zur deutschen Version: Querschnittsoptimierung von CFK-vorgespannten und mit nichtrostendem Stahl bewehrten Brückenträgern
As part of a research project on the development of a bridge system made of carbon fibre-reinforced polymers (CFRP)-prestressed concrete with stainless steel reinforcement, particular emphasis is placed on the durability of this material combination. However, this material combination also entails increased CO₂ emissions during production, reducing its environmental sustainability.
To what extent does this increase the CO₂ footprint (= Global Warming Potential, GWP) associated with the construction of the bridge compared to a conventional system?
This question was investigated by Näsbom et al. [1], showing that the proposed system can generate up to twice as much CO₂ during the production phase as a conventional alternative.
How much can this value be reduced?
This blog post addresses this question using structural optimisation. By means of computational algorithms, structural optimisation identifies a combination of design variables that minimises a defined objective function—in this case, the CO₂ footprint, while satisfying structural verifications. The present post is based on Merz et al. [2], which is submitted to the fib Congress in Lisbon in summer 2026.
As a first step, the cross-sectional geometry is parameterised. The reference cross-section shown in Figure 1(a) is simplified and described using variables representing the cross-section geometry, the reinforcement layout, and the level of prestressing (see Figure 1(b)). Based on the resulting material quantities of CFRP, steel, and concrete, the objective function is calculated using the CO₂ emission factors shown in Figure 1(c).
In addition to geometric constraints directly linked to the design variables, the girder must also satisfy a series of structural verification checks. These are illustrated in Figure 2. Figure 2(a) schematically shows the calculation of the cross-section’s bending resistance, which can be governed by either concrete crushing or CFRP rupture. Rupture of the steel reinforcement does not become governing due to its high ultimate strain (εsu ≈ 180 mε compared to εpu ≈ 16 mε). Figure 2(b) presents the applied ductility criterion. Stainless steel bars are provided to prevent brittle failure due to the material properties of CFRP. A minimum ratio of steel to CFRP area of 2 is specified, and all steel layers are required to yield upon reaching the bending resistance. For the fatigue check in Figure 2(c), the stress amplitude of the most highly loaded steel layer is compared to its long-term strength. Finally, a deformation check is carried out, with deformations determined from a moment–curvature relationship (see Figure 2(d)).
The following video illustrates an example optimisation process. The optimisation is carried out for different girder lengths. In the upper part of the video, the cross-sectional geometries for the various spans are shown. In the lower section, the development of the objective function values are steadily decreasing over the number of iterations.
The optimisation results are shown in Figure 3. Looking at the cross-sectional geometries in Figure 3(a), it is immediately noticeable that the height of the sections increases with span length. This is intuitive, as a greater structural height for longer spans allows a more efficient utilisation of the reinforcement. For the presented results, a maximum height of 
with a minimum value of 400 mm has been set. Another interesting finding is the wide variety of reinforcement layouts, which largely determine the web width 
. For spans longer than 7 m, the steel reinforcement is entirely placed below the CFRP prestressing. This arrangement is dictated by the ductility requirement, which specifies a minimum strain in the top steel layer, achieved in the results by positioning the steel as low as possible in the cross-section.
Examining the development of GWPtot along the length in Figure 3(b) shows a monotonic increase in the contributions from CFRP and steel, while the concrete contribution exhibits irregular jumps. These are due to the fact that the web area is significantly influenced by the reinforcement layout.
From the utilisation of the verification checks in Figure 3(c), it is evident that the fatigue checks and the minimum ductility strain govern all spans. Additionally, the width is chosen precisely to accommodate the selected reinforcement layout.
A key insight from the cross-sectional optimisation was the impact of the ductility criterion, which led to a not anticipated upwards shift of the CFRP reinforcement and which will be adapted in future studies. Nevertheless, the study (i) demonstrates the usefulness of structural optimisation to reduce the environmental impact of structures (ii) provides insight into the shares of the global warming potential of different materials in an optimised cross-section and (iii) shows that the fatigue requirement and web width have a significant impact on the GWP of a bridge girder. In the next step, the optimisation will be extended from the single main girder to the entire system, including transverse girders and the deck slab, enabling a holistic view of the GWP of single-span CFRP-prestressed stainless steel-reinforced bridges.
Paul Merz
Referenzen
- Näsbom, A., Thoma, K., Kaufmann, W. (2024). Construction and Testing of a CFRP-prestressed Railway Bridge Prototype. IABSE Symposium Manchester 2024: Construction’s Role for a World in Emergency, 90–98.
- Merz, P., Carstensen, J., Näsbom, A., Thoma, K., Kaufmann, W. (2026). Structural Optimisation of CFRP-Prestressed Stainless Steel-Reinforced Concrete T-Cross-Sections for Railway Bridges. Fib Congress Lisbon 2026, submitted manuscript.