Recent Advances in the Dynamic Analysis of Stiffened Plates - Application to Concrete or to Composite Steel-Concrete Structures

Evangelos   J.   Sapountzakis

Abstract

In this paper, an improved model for the dynamic analysis of reinforced concrete plates stiffened by arbitrarily placed parallel reinforced concrete or steel beams with deformable connection taking into account the influence of creep and shrinkage effects relative with the time of the casting and the time of the loading of the plate and the beams 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. 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 second-order effects. 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. Both free and forced damped or undamped transverse vibrations are considered and numerical examples with great practical interest with patent discussion are presented.

Keywords: Elastic stiffened plate, reinforced plate with beams, bending, deformable connection, nonuniform torsion, warping, ribbed plate, boundary element method, slab-and-beam structure, creep