Rotation-free finite element ‘yield line’ analysis of non-isotropic slabs

Abstract

A new, non-incremental advance in the lower bound finite element (FE) method for non-isotropic slab analysis is presented as a development of earlier work by the authors that was applicable only to isotropic slabs. The method provides a faster and simpler alternative to the full non-linear FE method in the non-linear analysis of slabs. Reinforced concrete was modelled as elastic perfectly plastic material, with rotation-free (RF) plate elements used to model slabs. They were modified to allow plastic yield lines to pass through elements satisfying non-isotropic yield conditions. Satisfying yield conditions and finding yield line directions differ significantly in their sophistication from their isotropic counterparts, as slab moment capacity is direction-dependent and yield line direction does not coincide with principal moment direction. Yield line effects were projected to element sides then used in curvature calculations. Analysis was performed incrementally, with the slab considered to behave linearly within each load increment. As a result, no iterations were required to reduce the unbalanced forces, as the behaviour within each load increment was in equilibrium. Accuracy was assessed against benchmark examples, and generally was within 2.5% of yield line collapse loads.