Investigation of optimal layout of ties in STM developed by topology optimization

Strut-and-tie models (STMs) have been wildly used for the design of disturbed regions in structural concrete members. The STM developed based on the load path method or with the aid of stress trajectories is not unique and varies with the designer's intuition and past experience. As a result, topology optimization methods have been adopted to generate STMs in reinforced concrete structures. However, such models are just a preliminary configuration and the detailed layout of ties in an STM cannot be determined by the optimal topology. This is because reinforced concrete is assumed to be a uniform elastic continuum. Therefore, the effect of the steel reinforcement on the load transmission cannot be considered in the optimization process. Recently, the criterion of minimum strain energy has been proposed to determine the optimal layout of STMs obtained by the modified optimization method. However, the strain energy criterion does not work when the minimum strain energy in ties is zero when evaluated by mathematical equations. To address this issue, the maximum stiffness criterion is proposed to discover the optimal layout of ties in STMs by evaluating the stiffnesses of strut ties.