The strength reserve due to restrained bending in brittle-matrix structures

Purely flexural (i.e., in the absence of membrane forces) response of structures with no-tension or quasi-brittle matrix is rarely possible. When in-plane displacements at slab supports are restrained, important compressive membrane forces occur from the very beginning of the deformation process. They strengthen seriously the structure (the “dome effect”) but make its response extremely unstable. Therefore, the analysis aiming at evaluation of the ultimate strength for such structures, even when based on a simple elastic–plastic model, appears to be cumbersome and frustrating potential users. The corresponding geometrically non-linear procedures, especially if commercial finite element codes are used, become slow and capricious. The direct FEM approach to restrained bending is still of limited utility for practical purposes and simplified methods are needed, especially for rapid diagnostic of massive concrete slabs.Here a mixed method for elastic–plastic structures is proposed using an analytical approach with its parameters calibrated with the incremental FEM analysis performed in benchmark cases. It is based on an old authors’ proposition and consists in applying the classical post-yield approach (PYA) combined with elastic “spring model”. The method furnishes analytical description of the load-deflection response of regular shape reinforced slabs and simple formulae for the ultimate-peak loads. It needs no more knowledge than the elementary limit analysis (plastic hinges, yield lines). Basic ideas of the approach are recalled and applied to slabs in one- and two-way bending, as well as to pressurized cylinders. The importance of the strength reserve due to the dome effect and the pertinence of the method are verified compared to the finite element simulation and to some tests on reinforced concrete models.The restrained bending response is very sensitive to “secondary effects” (e.g., shape and support imperfections) that may strongly reduce the structure strength. The approximate method permits easily to account for initial deflections, imperfect contact and compliant supports.