Rectangular Plates of a Trapezoidal Cross-Section Subjected to Thermal Load

Abstract

The method to calculate rectangular tanks as a system of bi-directionally bent plates with the use of separated plates methodology is a widely known and currently most often used approach to verify numerical calculations obtained from computer software supporting the design process, in which spatial operation of tanks is taken into account. In these calculations, due to their static scheme, it is possible to distinguish supported plates, plates fixed on four edges and plates with one edge free and three fixed. The subject literature contains publications on plates or tanks with walls of a constant thickness, however, there are very few references on plates or tanks with walls of linearly variable thickness. The wall plate of a tank is subject to hydrostatic load or soil pressure and might be exposed to thermal load in the case of, i.e. filling it with hot liquid or during climate action. The article presents the results of static calculations for rectangular plates with a linearly variable thickness, a trapezoidal cross-section, three fixed edges and one edge free, subjected to permanent and thermal loads. Trapezoidal cross-section walls are optimal when used in structures where load distribution is triangular in shape (hydrostatic load). For tanks recessed in the ground, the load on walls increases along with the depth of foundations and obtains the highest value in the bottom part of the wall. Trapezoidal or triangular load distribution causes that the highest values of bending moments in the vertical cross-section occur at the point where a wall connects to the bottom, while the upper free edge of the tank takes zero value. The above statements lead to the conclusion that structural and economic considerations should determine the choice of walls with a thickness increasing along with the tank depth, since it is more economical in terms of material usage. The impact of thermal load is often neglected in the design process, which may cause operational problems and even pose a threat to the safety of use. In addition to the numerical analysis, the article presents the results of model tests for a plate with a linearly variable thickness made of resin, subjected to thermal load. The convergence of the obtained results proves the correctness of calculations and tests performed. This also contributes to the recognition of statics in rectangular plates of a trapezoidal cross-section.