Optimal design of elastic plastic frames accounting for seismic protection devices

The optimal design of elastic perfectly plastic steel frames with or without suitable protection devices and subjected to static as well as seismic loadings is studied. Two minimum volume problem formulations are proposed, on the grounds of the so-called statical approach, accounting for three different resistance limits: the purely elastic limit, the (elastic) shakedown limit and the instantaneous collapse limit. The adopted load combinations are characterized by the presence of fixed loads, of quasi-static perfect cyclic loads and dynamic (seismic) loads. The linear elastic effects of the dynamic actions are studied by utilizing a modal technique. The proposed treatment is referred to the most recent Italian code related to the structural analysis and design. The solution of the optimization problem is reached by using an appropriate linearization iterative technique specialized to the proposed formulations. Flexural frames and cross-braced frames are studied, and the related minimum volume structures are reached for assigned features of the base isolation device. The Bree diagrams of the obtained optimal designs are also determined in order to characterize their structural behaviour.