Force-Based Versus Displacement-Based Formulations in the Cyclic Nonlinear Analysis of RC Frames

Abstract eng:
The current work deals with the comparison between the numerical results of two different frame element formulations, namely the classical displacement-based element versus the force-based approach. In the former an approximation is made for the displacement field throughout the frame element length, from which strains, stresses and stress resultants are computed. The fact that this displaced shape is only approximate is responsible for most of the problems that these elements present when inelastic behaviour is expected. On the other hand, force-based elements satisfy exactly the equilibrium conditions by using an exact description for the stress resultants’ field throughout the frame element length. It implies a somewhat more complex iterative procedure to solve nonlinear problems. Nevertheless, this increase in complexity is clearly justified by the overwhelming benefit that the force-based solution holds for any material response. From the earthquake engineering analysis viewpoint, where large inelastic demands are expected, such characteristic plays a major role on behalf of the flexibility approach, as will be subsequently observed. To validate and evaluate both formulations, numerical and experimental results of cyclic tests on bridge piers are compared, including strain localization phenomena. The superiority of force-based formulations in comparable conditions is established.

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