The collapse design of edge supported rectangular slabs under uniformly distributed load, based on energetically conform yield line schemes

摘要

The yield line theory of slabs is the basis for a structural computation which is only adequate to the dimensioning of cross sections in her ultimate state. It knows only the difficulty to determine the real fracture scheme; this is the purpose of a cumbrous optimization of the slabs energetic balance. For the sake of simplicity we take usually a logical approximate scheme; for the (very frequent) edgesupported rectangular slab under uniformly distributed load this is the "envelope-form" according to the 45 degrees-assumption. This is, in the authors opinion, the main reason for the common scepticism regarding the ultimate state examination of slabs. The essay takes the exact ("energetically conform") fracture scheme as basis for a computation algorithm. Its conversion in a computer program allows a more accurate ultimate state calculation of the "general rectangular slab" under uniformly distributed load. In three examples, the results are compared with those of the customary yield line theory (which usually commits small, but always wrong mistakes) as well as those of the elastic theory. The negative results for the slab with free rotable edges are attributed to the neglected torsional stresses by the state of failure. On the contrary, using the yield line theory even slight fixing degrees of the edges are leading to rather high steel savings.