The Earthquake Engineering Online Archive

A beam element for seismic damage analysis

Spacone, Enrico; Ciampi, Vincenzo; Filippou, Filip C.

UCB/EERC-92/07, Earthquake Engineering Research Center, University of California, Berkeley, 1992-08, 118 pages (555.1/S62/1995)

This study proposes a beam finite element model with distributed inelasticity and two nonlinear end rotational springs for the nonlinear dynamic analysis of frame structures under earthquake excitations. The beam element is based on the assumption that deformations are small and shear deformations are neglected. The axial behavior is assumed linear elastic and is uncoupled from the flexural behavior. The element is derived with the mixed method of finite element theory. The force distribution within the element is based on interpolation functions that satisfy equilibrium. The relation between element forces and corresponding deformations is derived from the weighted integral of the constitutive force-deformation relation. While the element can also be derived with the virtual force principle, the mixed method approach has the advantage of pointing the way to the consistent numerical implementation of the element state determination. A special nonlinear algorithm for the state determination is proposed that yields the stiffness matrix and the resisting forces of the flexibility-based beam element. The study concludes with a demonstration of the ability of the proposed model to trace the softening response of a cantilever beam without numerical difficulties and with correlation studies of the response of the model with the experimental behavior of two reinforced concrete cantilever beams that highlight the flexibility of the constitutive law in the description of the hysteretic behavior of structural members.

Available online: http://nisee.berkeley.edu/documents/EERC/EERC-92-07.pdf (8 MB)