Plastyczne Wyczerpanie Nośności Ustrojów Płytowo-Żebrowych. Cz. 1. Rozwiązania Kinematyczne

In practical computations of bent structures composed of plates and beams it is customary to seperate mentally elements. After the loads and the boundary conditions for those elements are determined, interior forces and profile dimensions are found. Such an artificial division of the structure into elements results in the fact that the real safety factor of the structure as a whole differs considerably from the expected one. A correct estimate of the safety can be obtained on the basis of the limit analysis of the structure as a whole, assuming the limit load is attained simultaneously in all the elements.
The present paper is devoted to problems of limit load of ribbed plates, which are in most common use in building. The limit load is determined from the analysis of kinematically admissible fields of strain increment and statically admissible fields of section force (moments), The rigid-plastic deformation type is assumed. Plastic strain is assumed to be small. For R.C. structures plastic orthotropy and layered structure are assumed as well as non-homogeneity due to the ribs.
With the kinematic approach, which is the main object of this paper, an equation for the upper limit of the limit load is obtained for any polygonal plate supported in any manner and uniformly loaded over the entire surface. This equation enables us to compute the load without the necessity of determining the work increment, geometrical quantities and other quantities connected with the properties of the structure being the only involved.
Ribbed plates of 10 types are discussed. Solutions are given for ultimate loads. The paper presents also some criteria of simultaneous plastic exhaustion of the load carrying capacity of component
elements and the corresponding graphs.
The application of the limit analysis enables us to avoid two inconsistencies of the usual design procedure of R.C. structures in which a) The internal forces are determined for an elastic, isotropic and homogeneous structure while orthotropy and layered structure is introduced first for the determination of the dimensions of the ε1 m nt. b) The section forces are determined by the elastic method while the dimensioning of the sections is done by the plastic method. A separate paper which will appear in the next number will be devoted to the problem of deter- mining the lower (static) limit load for ribbed plates of which a kinematic analysis is the object of the present paper.