Concrete Plates Designed with FEM - Prosjektering av betongplater med FEM

Abstract

Most engineering companies design plates by use of finite element programs that are entirely automated. The program decides the element type, the meshing, and performs all the calculations. Often, the automatic procedure is hidden for the user, and it's difficult for the engineer to verify that the analysis is done correctly. Therefore, the goal of this thesis is to describe how concrete plates should be modelled in commercial design software, and how a selection of design programs perform the automatic design procedure. The focus has been on plates subjected primarily to bending in both the Ultimate Limit State (ULS) and in the Serviceability Limit State (SLS). When modelling a plate, the element type and mesh are often defined automatically by the software while the boundary conditions need to be specifed by the user. It is normally recommended to use pinned support at the centre of columns or walls, because it avoids unintended rotational restraint. It is, however, also possible to model more realistically, with spring supports, if: The stress distribution over the support is of interest The rotational restraint from the support is of importance for the stresses in the plate. The theory background and manuals for a chosen set of design programs were examined to figure out how the automatic design procedure for concrete plates can be carried out. The main problem of plate design is that, in contrast to simple beam theory, plates also contain twisting moments. This causes the reinforcement and the principal moments to be in different directions. The main steps of the design procedure in ULS are to rotate the stress resultants to the directions of the reinforcement, and then calculate either the design moments, or imaginary in-plane forces. These forces are then used to find the required reinforcement for the upper and lower layer of the plate. An essential difference between the programs is the assumptions for the stress distribution in the cross section, and the internal lever arm. The programs are also separated by the way they define the crack angle. Normally, the crack angle is assumed to be 45 degrees in order to achieve a minimum amount of reinforcement. If, however, only one reinforcement direction is needed, the optimal crack angle is no longer 45 degrees. In that case, some of the programs, like "FEM design", calculates a new optimal crack angle. In SLS, the programs differ in the way the stiffness reduction due to cracks is accounted for. One alternative is to reduce the stiffness locally in elements where the concrete is cracked. Another alternative is to give the whole plate a reduced stiffness to achieve a smooth deformation pattern. The crack width is controlled by either of the following two approaches: Direct calculation of the crack width, and comparing this with the maximum allowed width Indirect calculation where the diameter and spacing of the reinforcement bars are controlled against tabulated maximum values