An Improved Model For The Analysis Of Plates Stiffened By Parallel Beams With Deformable Connection

摘要

In this paper a general solution for the analysis of plates stiffened by arbitrarily placed parallel beams of arbitrary doubly symmetric cross section with deformable connection subjected to an arbitrary loading is presented. According to the proposed model, the stiffening beams are isolated from the plate by sections in the lower outer surface of the plate, making the hypothesis that the plate and the beams can slip in all directions of the connection without separation (i.e. uplift neglected) and 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 taking into account their relation with the interface slip through the shear connector stiffness. Any distribution of connectors in each direction of the interfaces can be handled. 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 describing better in this way the actual response of the plate-beams system. The analysis of both the plate and the beams is accomplished on their deformed shape taking into account the arising inplane forces of the plate as well as the axial and transverse forces of the beams. 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. Three additional finite element models using beam, shell or solid finite elements are also employed for the verification of the accuracy of the results of the proposed model.