Non-linear behaviour of composite columns under varying load history

Slender composite concrete-steel and reinforced concrete (RC) columns may be subject to instability and their failure is strongly related to their previous load histories. Viscosity, plasticity, and cracking, in fact, provide a nonlinear, history dependent behavior that plays a fundamental role in the system progress in time and increases deformation, reducing reliability with respect to stability. A formulation of the problem, involving the nonlinear behavior of the materials, is presented in this paper with the aim of furnishing a tool for evaluating the consequences of varying load histories on structural stability in time. The numerical solution of the integro-differential equations governing the problem cannot be performed by standard methods and it was necessary to develop a solving method suitable for this particular problem. The results furnished by the approximate solution were tested by comparison with available experimental data concerning slender columns under sustained and varying loads. Some applications are also presented to demonstrate the importance of the entire previous load history in the failure that occurs in time.