Publication Details

This article was originally published as Liang, QQ, Uy, B and Steven, GP, Performance-Based Optimization for Strut-Tie Modeling of Structural Concrete, Journal of Structural Engineering, 128(6), June 2002, 815-823. Copyright American Society of Civil Engineers. Original journal available here.


Conventional trial-and-error methods are not efficient in developing appropriate strut-and-tie models in complex structural concrete members. This paper describes a performance-based optimization (PBO) technique for automatically producing optimal strut-and-tie models for the design and detailing of structural concrete. The PBO algorithm utilizes the finite element method as a modeling and analytical tool. Developing strut-and-tie models in structural concrete is treated as an optimal topology design problem of continuum structures. The optimal strut-and-tie model that idealizes the load transfer mechanism in cracked structural concrete is generated by gradually removing regions that are ineffective in carrying loads from a structural concrete member based on overall stiffness performance criteria. A performance index is derived for evaluating the performance of strut-and-tie systems in an optimization process. Fundamental concepts underlying the development of strut-and-tie models are introduced. Design examples of a low-rise concrete shearwall with openings and a bridge pier are presented to demonstrate the validity and effectiveness of the PBO technique as a rational and reliable design tool for structural concrete.

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