Development of Strut-and-Tie Models in Deep Beams with Web Openings

Abstract

The strut-and-tie models of a total of fourteen (14) concrete deep beams with varying size and location of web openings are developed herein using a topology optimisation approach. By systematically eliminating inefficient materials from an over-designed discretized domain, the load transfer mechanism in deep beams is progressively characterised by the residual part of the structure. Both von Mises stress and displacement sensitivity number are used as deletion criteria with the aim of maximising the material efficiency and overall stiffness of the structural beam. The performance indices in terms of von Mises stress and nodal displacement are evaluated to monitor the optimisation process and to determine the optimal topology which is transformed to the strut-and-tie model. The relationship between the strut-and-tie models and the ultimate load-carrying capacity of the beams are discussed in some detail. A series of comparisons offer insight into the varying characteristics of the strut-and-tie models influenced by the size and location of web openings. To demonstrate the effectiveness of the resulting strut-and-tie model in aiding the design of deep beams, a worked design example of a representative beam is also presented where the practical layout of main steel reinforcement is determined.