Evaluation of triangular plate elements in rigid-plastic finite element analysis of reinforced concrete Original Research Article

The performance of three triangular plate elements for rigid-plastic finite element analysis of reinforced concrete is evaluated. The element types considered are 2 variants of the constant stress triangle, the first one with no prescribed stress continuity at all and the second one with prescribed stress continuity in inter-element normal stresses. The third element type is an element with linearly varying stresses with complete inter-element continuity. The yield surface for reinforced concrete plates is linearised, whereby the rigid-plastic analysis is formulated as a linearly constrained optimisation problem, which is solved by a very effective internal point method. The elements are evaluated for simple stress configurations for which analytical results are available. It is shown that prescribed inter-element continuity may result in rather inaccurate results for concentrated loading and small reinforcing degrees. Bending and shear of reinforced concrete beams have received particular attention. The main result of this evaluation, when using the elements with inter-element continuity, is that only a course mesh density corresponding to two elements in the depth of the beam is required to obtain very accurate results. The constant stress triangle with no prescribed stress continuity requires considerably more elements. A more complex problem with a tapered concrete wall, having a large circular opening, is hereafter considered, the results of which are interpreted and explained in terms of the performance observed for the simple problems. To demonstrate the practical applicability of the rigid-plastic analysis, a very large, real-life structural system comprising more than 4000 elements is analysed. Finally, an example with individual reinforcing bars represented as stringer elements is presented.