A multicriterion design of steel frames with shakedown constraints

The minimum volume design of elastic perfectly plastic steel frames subjected to fixed and cyclic loads is searched in such a way that the structure remains in elastic field in serviceability conditions, while it is subjected to alternating plasticity under very strong cyclic actions, incremental and instantaneous collapse being prevented. The problem is faced on the grounds of a statical and a kinematical approach. The Kuhn–Tucker conditions of the two problems prove that they are each one the dual of the other and provide useful pieces of information about the structural behaviour. Numerical applications confirm the theoretical expectations: optimal designs turn out to be quite light, with stiffness and resistance suitable to completely preserve the structure integrity in serviceability conditions, and suitable to avoid collapse and to allow a great amount of plastic dissipation production under the action of very strong cyclic loads, plastic deformations being null in the cycle.