A unified approach to verify the reinforcement in two dimensional reinforced concrete membrane and shell structures

The paper is divided in the following parts. First, the problem of design/verification of reinforcement in concrete membrane, p1ate and shell structures is reviewed. Methods of analysis are classified , and the elastic-plastic approach is described and used in the development of an unified approach to verify the reinforcement in two dimensional reinforced concrete structures. Then, the developed methodology is applied to structures type membrane plate and membrane shell (applicable also to concrete walls) and to pure bending, as in the case of plates. Its application to the general case of folded plate and shell structures subjected to bending and axial stress resultants is shown. The methodology applied in this work is based on the standard elasticity equations,namely, equilibrium, compatibility und constitutive equations. Non linear constitutive equations of concrete and steel are considered. Namely, the tension strength concrete is not considered and a parabolic-rectangle diagram with a descendent branch is used. For the steel an elastic-plastic behavior is assumed, that is represented by a bilinear stress-strain diagram and in this way hardening effects can be simulated. At each section of the structure two or more reinforcement families are considered and they can be placed in plan along arbitrary directions. In this way many practical design situations, that are not contemplated in the majority of the Concrete Codes and Recommendations and are different to typical cases of orthogonal two steel bar families,are envisaged. An example of these cases are zones of high stress concentration where extra reinforcement families are demanded. Based on the presented methodology a computer program has been written. The main re sult is the set of curves representing the paths of the strains and stresses of each reinforcement family and the principal stresses in the concrete as function of the amplification factor. In this way the safety level at the point under study of the reinforced concrete structure can be obtained.