Shakedown optimum design of reinforced concrete framed structures

Structures subjected to variable repeated loads can undergo the shakedown or adaptation phenomenon, which prevents them from collapse but may cause lack of serviceability, for the plastic deformations developed, although finite, as shakedown occurrence postulates, may exceed some maximum values imposed by external ductility criteria. This paper is devoted to the optimal design of reinforced concrete structures, subjected to variable and repeated loads. For such structures the knowledge of the actual values taken by the plastic deformations, at shakedown occurrence, is a crucial issue. An approximate assessment of such plastic deformations is needed, which is herein provided in the shape of quadratic constraints, by the so-called perturbation method. By suitable finite element discretization, the optimal shakedown problem is formulated as a convex nonlinear mathematical programming one. The M-N (bending moment-axial force) interaction is accounted for in the aim to provide the optimal shakedown design. The computational PLP strategy adopted has shown effectiveness, and it provides the optimal design reinforcement percentages, which turns out to be a safe design but not strictly optimal. The proposed approach also removes the usual approximations of bending moment-curvature or moment-rotation assumptions in optimal design, by incorporation of the average M̧-Ņ yield domain, so accounting for the combined internal forces áincorporation of the average