Shear deformation effect in plates stiffened by parallel beams

Abstract

In this paper a general solution for the analysis of shear deformable stiffened plates subjected to arbitrary loading is presented. According to the proposed model, the arbitrarily placed parallel stiffening beams of arbitrary doubly symmetric cross section are isolated from the plate by sections in the lower outer surface of the plate, taking into account the arising tractions in all directions at the fictitious interfaces. These tractions are integrated with respect to each half of the interface width resulting two interface lines, along which the loading of the beams as well as the additional loading of the plate is defined. Their unknown distribution is established by applying continuity conditions in all directions at the interfaces. The utilization of two interface lines for each beam enables the nonuniform distribution of the interface transverse shear forces and the nonuniform torsional response of the beams to be taken into account. The analysis of both the plate and the beams is accomplished on their deformed shape taking into account second-order effects. The analysis of the plate is based on Reissner's theory, which may be considered as the standard thick plate theory with which all others are compared, while the analysis of the beams is performed employing the linearized second order theory taking into account shear deformation effect. Six boundary value problems are formulated and solved using the analog equation method (AEM), a BEM based method. The solution of the aforementioned plate and beam problems, which are nonlinearly coupled, is achieved using iterative numerical methods. The adopted model permits the evaluation of the shear forces at the interfaces in both directions, the knowledge of which is very important in the design of prefabricated ribbed plates. The effectiveness, the range of applications of the proposed method and the influence of shear deformation effect are illustrated by working out numerical examples with great practical interest.Keywords Elastic stiffened plate · Reinforced plate with beams · Bending · Nonuniform torsion · Warping · Ribbed plate · Boundary element method · Slab-and-beam structure · Shear deformation · Reissner's theory IntroductionStructural plate systems stiffened by beams are widely used in buildings, bridges, ships, aircrafts and machines. Stiffening of the plate is used to increase its load carrying capacity and to prevent buckling especially in case of in-plane loading. Moreover, for cases wherein the plate or the beams are not very "thin" or the stiffeners are closely spaced, the error incurred from the ignorance of the effect of shear deformation may be substantial, E. J. Sapountzakis (B) · V. G. Mokos