Calculation of RC Flat Slabs and Flat Foundations Punching Using Mini-Max Principle

The punching problem of reinforced concrete flat slabs and flat foundations has two main aspects, related to load carrying capacity of these structures under shear forces. The first is obtaining the shear force value, and the second–finding the control area (failure zone dimensions). Generally, the punching shear force is taken, based on experimental data, and the control perimeter is assigned according to existing design codes. At the same time, the assigned control perimeter is different for flat slabs and flat foundations. The available experimental and finite element analysis data, used for assigning this area, has a wide scatter and differs by 40-50% from the values, given in modern design provisions. The present study is focused on the above-mentioned second aspect and deals with exact evaluation of the control perimeter under shear punching in flat slabs and flat foundations. This study emphasizes the difference between punching shear due to concentrated load and support reaction force to distributed one. These both cases are investigated using mini-max principle: the internal shear forces are maximized and the control perimeter dimension leads to minimal external load. Efficiency of the proposed method is demonstrated by numerical examples and comparison with available data, based on results of experiments and finite element analyzes. The obtained results can be used as a basis for refinement of existing punching shear models and further development of modern design provisions in this field.