Solving the contact problem when strengthening the slab with a beam using discontinuous functions

Abstract

Problems of contact interaction of structures and their parts have a wide range of applications in construction. In particular, this problem arises during the reconstruction of existing buildings, when strengthen of floor slabs is required to increase their bearing capacity. In this case, the contact of the slab with the strengthening beams occurs along a continuous line of a given shape with a contact zone unknown in advance. In this paper, with the aim of constructing high-accuracy numerical-analytical solutions for the contact problem while keeping some series members, the mathematical apparatus of the theory of generalized functions is widely used. To solve the structurally nonlinear problem of strengthening the floor slab with an elastic beam, a step-by-step loading method is used. At each step, the deflection functions, the length of the contact segment, the value of the reaction along the contact segment are determined and the working scheme of the plate-beam reinforcement system is specified from the minimum functional condition of the potential energy of the contacting elastic elements. Using the proposed numerical-analytical approach, we obtained and analyzed solutions to the problem of one-sided support of a slab to an elastic gain beam. Due to the twodimensional approximation of the function of a slab deflection by discontinuous functions, the proposed approach shows satisfactory convergence, stability and accuracy of the solution while keeping some terms of the series.