Ultimate Equilibrium of RC Structures Using Mini-Max Principle

This monograph analyses experimental and theoretical investigations in the field of reinforced concrete structures and elements from the viewpoint of a new mini-max principle and application of this principle for calculation of forces, strengths and critical buckling loads in RC shells, columns, plates, etc. The basis of the mini-max principle was developed during solving a problem of finding an RC shell load bearing capacity via a kinematic method. Forming the internal forces'' fields at the plastic stage of the structure leads to a problem, related to interaction between the normal forces and bending moments, but at this stage the compressed shell section has an unknown eccentricity. Therefore an additional equation should be found for separating the above-mentioned forces. The following idea was proposed: the section compressed zone depth (static parameter) should be selected so that the maximum load bearing capacity of the structure is realized simultaneously with minimizing the external load the failure zone dimension (kinematic parameter). Development of this idea resulted in formulating the mini-max principle. The essence of this principle is that real load bearing capacity of the structure is calculated (without under- and over-estimation). With this aim it is proposed to use in the same calculation both extreme features of failure load. At the same time just one method is used (static or kinematic). Thus, the mini-max principle became a way for realizing the unity theorem of the limit equilibrium method, which joints the static and kinematic approaches. The mini-max principle enabled to solve some problems in load bearing capacity of structures that had no solutions or were solved approximately. Additionally, the principle was used for solving some new problems in calculation of RC shells.