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

To improve the structural performance of D-Regions, the iterative and tedious tasks are required, which include selecting shapes of strut-and-tie model (STM), constructing STM models, proportioning the D-Regions, and performing nonlinear analysis of the D-Regions. The selection of STM shape for D-Regions with complex geometry, loading and boundary conditions is not simple and the inappropriate STM shape can result in poor structural performance of the D-Regions. In addition, the application of nonlinear finite element analysis (FEA) is currently unpractical and limited due to the modelling difficulty, accuracy and reliability of the existing formulation, and insufficient model calibration.

To eliminate the deficiency and impracticability of the current design and analysis techniques, a new design and analysis technique is thus proposed and developed. The topology optimization scheme entitled "performance based topology optimization" (PBO) proposed by Liang et al. [1] is adopted to select the optimal STM shape. The optimal STM shape is subsequently used to construct a STM model by using the computer-aided strut-and-tie (CAST) developed by Tjhin [2]. The amount of reinforcement is determined to satisfy the requirements of the STM code provisions. To assess the structural performance and capacity of the designed D-Regions, the newly proposed nonlinear FEA is adopted. The proposed FEA is to overcome the difficulty in modelling the complex reinforcement by developing a new embedded reinforcement including bond stress-slip formulation, and to overcome the shortcomings in current state-of-the-art behaviour models by developing a new model specialized for D-Regions that considers: (i) the tensile responses of cracked concrete between and at crack locations [3], (ii) the impact of difference between the direction of principal strain and stress [4], (iii) the impact of differences between the direction of principal stress and crack orientation [5], and (iv) the effect of dowel action.

From the example, by using the proposed technique, the effective structural performance of D-Regions is achieved; for examples, exceptionally high cracking load, less crack development and propagation, high post-cracking stiffness, more uniform stress distribution in the reinforcement, and a higher capacity. In addition, the economical design implied by the higher ratio of the structural capacity to the reinforcement volume is also obtained.

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

Tjhin, "Analysis and Design Tools for Structural Concrete Using Strut-And-Tie Models", PhD Thesis, University of Illinois at Urbana-Champaign, USA, 2004.

3

F.J. Vecchio, M.P. Collins, "The Modified Compression Field Theory for Reinforced Concrete Elements Subjected to Shear", ACI Journal, Proceedings, 83(2), 219-231, 1986.

4

F.J. Vecchio, "Disturbed Stress Field Model for Reinforced Concrete: Formulation", Journal of Structural Engineering, ASCE, 126(9), 1070-1077, 2000. doi:10.1061/(ASCE)0733-9445(2000)126:9(1070)

5

T.J. Nagle, D.A. Kuchma, "Shear Transfer Resistance in High-Strength Concrete Girders", Magazine of Concrete Research, 59(8), 611-620, 2007. doi:10.1680/macr.2007.59.8.611

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