Keywords: strut-and-tie, topology optimization, finite element analysis, performance based design, validation, design standards.

The topology optimization technique has been well-known in its powerful tool for solving the material redistribution problem within a fixed design domain. One of the applications of topology optimization in civil engineering is to obtain the optimal shape of strut-and-tie models (STM) which are adopted in the design of D-Regions in reinforced concrete structures. While several research papers, for example Liang et al. [1], successfully demonstrated the application of topology optimization in obtaining the shape of a STM in simple types of D-Regions such as deep beams, shear walls, and corbels, no research work has applied topology optimization to obtain STM shapes in very complex D-Regions where several possible shapes of STMs composed of multiple STM members are possible. In addition, no experimental validation of the D-Regions designed using the optimal STM has been conducted and reported.

In this paper, the more extensive application of topology optimization in obtaining the shape of STMs for the design of complex D-Regions is demonstrated by using the in-house computational tool developed by using MATLAB to perform the topology optimization. The evolutionary topology optimization proposed by Xie and Steven [2] is adopted. The performance index (PI) proposed by Liang et al. [1] is used to monitor when the global optimum of the STM shape has been achieved. The D-Region designed using the optimal STM was then fabricated, instrumented, and tested to failure to assess the structural performance. To validate the topology optimization, the comparison of the measured structural responses and performance between the optimal and other STM shapes from the experimental programs reported by Kuchma et al. [3] and Yindeesuk and Kuchma [4] is undertaken. It was found that D-Regions designed by using the optimal shape of the STM have the highest cracking load, pre-and post-cracking stiffness, and capacity. In addition, the ratio of the observed capacity to the reinforcement volume of the specimen is also highest. This thus confirms the validity and effectiveness of the topology optimization technique in generating the shapes of the STM in the design of complex D-Regions.

1

Q.Q. Liang, Y.M. Xie, G.P. Steven, "Topology Optimization of Strut-and-Tie Models in Reinforced Concrete Structures Using an Evolutionary Procedure", ACI Structural Journal, 97(2), 322-330, 2000.

2

Y.M. Xie, G.P. Steven, "A Simple Evolutionary Procedure for Structural Optimization", Computers and Structures, 49(5), 885-896, 1993. doi:10.1016/0045-7949(93)90035-C

3

D.A. Kuchma, S. Yindeesuk, T.J. Nagle, J. Hart, H.H. Lee, "Experimental Validation of Strut-and-Tie Method for Complex Regions", ACI Structural Journal, 105(5), 578-589, 2008.

4

S. Yindeesuk, D.A. Kuchma, "Shape of Strut-and-Tie Model for Effective Structural Performance Design of Complex Regions" (submitted to ACI Structural Journal).

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