Numerical Limit Analysis of Precast Concrete Structures

Design and analysis of precast concrete structures in the ultimate limit state is largely done by simple analytical calculations and linear elastic finite element analysis, which necessarily leads to suboptimal designs. Numerical limit analysis provides a framework well suited for this task; the framework is based on the theory of rigid-plasticity, and the resulting mathematical optimisation problem can be solved efficiently using modern algorithms. This paper gives a brief introduction to convex optimisation and numerical limit analysis. The mathematical formulation of lower bound load optimisation as well as material optimisation is given and a four-storey shear wall is analysed using load optimisation. The analysis yields a capacity more than three times larger than the design load for the critical load case, and the collapse mode and stress distribution are analysed. Finally, numerical limit analysis of three-dimensional precast structures is discussed.