Bounds on transient phase plastic deformations in optimal design of steel frames subjected to cyclic loads

A minimum volume multicriterion design of elastic perfectly plastic steel frames subjected to a combination of quasi-static fixed and cyclic loads, bounding the transient phase plastic deformations, is proposed. The problem is formulated according to a plastic shakedown criterion, so that incremental and instantaneous collapse are certainly prevented when the frame is subjected to very strongly amplified cyclic loads. The further condition that the structure must also behave elastically in serviceability conditions is imposed. Since the steady-state loading history is known it is possible to directly bound the steady-state plastic deformations. By applying a suitable own bounding theorem, it is also possible to indirectly bound the transient plastic deformations, whichever the unknown transient real loading history is. A numerical application confirms the fundamental role played by the transient phase plastic deformations both on the design as well as on the structural behaviour and the great performance of the proposed formulation.