A guide to non-linear finite element modelling of shear and torsion in concrete bridges
Non-linear finite element (FE) analysis has become an important tool for structural design and assessment of reinforced concrete structures. When shear and torsion are limiting the capacity of a structure, three dimensional non-linear finite element methods often show higher load-carrying capacity compared to conventional analyses; therefore there is much to gain by using these methods, especially at assessment of existing structures. The reason for the higher capacities evaluated are mainly a more favourable load distribution when the structure is analysed in three dimensions and that the fracture energy associated with concrete cracking is included. In order to be able to use these higher capacities in reality, it is important that the modelling method is verified and to be aware of possible limitations. Recommendations are given concerning analysis methods and how a verification can be done, both concerning the capability of the program and concerning the actual FE model.
Most important comments and recommendations are:
• It is important to note that in FE programs commercially available today, beam elements cannot describe shear cracking and shear failure or reduced torsional stiffness due to cracking. The same applies for the out-of-plane shear in shell elements.
• Most often in analysis of bridges, it is enough to assume full interaction between the reinforcement and the concrete. One exception is if the slip is important for the global response or the final failure, as if a shear failure takes place in a region where prestressing is anchored. Then the modelling should include slip between the steel and the concrete.
• It is recommended that only the fracture energy of plain concrete is taken into account when defining the softening response of concrete, i.e. when the stress-strain relationship of the concrete is defined. This will yield results on the safe side; i.e. underestimation of the capacity and overestimation of deformations and crack widths.
• It is often more stable to perform analyses using deformation control than load control. A method to enable deformation-controlled loading for several point loads by using a separate statically determined arrangement of stiff beams is described.
Comments and recommendations are also given concerning how to model important details such as supports and connections, how different loading types can be considered, how to perform the analyses, how to evaluate the results through post-processing, and how to use the results in a safety format context.
finite element modelling