Limit Analysis and Plastic Design of Grid Systems

Abstract

Limit analysis and plastic design are techniques developed to represent more realistic behavior of indeterminate steel structures. They take advantage of the fact these structures have a greater load-carrying capacity than indicated by the elastic analysis and the allowable stress design concept. Furthermore, the theoretical and experimental research of the last 40 years or so has led to the realization that the assumption of perfectly elastic behavior of structures is by far too simple. The actual performance of structures often departs considerably from pure theory of elasticity. In many instances, the calculated local stresses will be exceeded due to residual stresses from rolling, welding and cold-forming. Additional stresses can also be a product of erection and differential settlement of foundation. When highly stressed sections of a continuous structure yield, they merely transfer additional moments to less stressed areas and readjust themselves to carry the load more efficiently. In fact, there is not a valid reason to insist the calculated service stresses in a steel structure should be below yield stress, as long as there is no danger of low cycle-fatigue or brittle failure. This paper presents the upper bound approach to the analysis of orthogonal grid systems applying the kinematic or mechanism method. The corresponding virtual work equations are formally written and solved for the value of the ultimate load. The load obtained in this way is the correct limit load only if the corresponding bending moments nowhere exceed the maximum plastic moments (the plasticity condition).