Random vibration of hysteretic systems under bi‐directional ground motions

Abstract

SUMMARYA random vibration method is developed for the response analysis of hysteretic structural systems under stochastic twodimensional earthquake excitations. The biaxial hysteretic restoring force is modelled by coupled non-linear differential equations; the response statistics are obtained using the equivalent linearization technique. The validity of the proposed model is appraised using available biaxial loading tests of reinforced concrete columns. A parametric study was performed to examine the significance of theeffects of biaxial interaction under earthquake excitations. A practical method to evaluate the extreme response statistics is also presented.

Evaluation of Damage in Reinforced Concrete Columns Under Biaxial Loading

“…However, the quadrangular and circular paths present higher levels of damping when compared to that obtained for similar demands in the uniaxial tests. For example, for ductility factor of 6 in the columns tested under uniaxial load conditions an equivalent damping of around 20% was reached, while for the quadrangular load path it was reached an equivalent damping of approximately 30% [5]. …”

“…Consequently, current knowledge on the inelastic response of RC columns under biaxial cyclic moments is still very much behind the present understanding of the 1D cyclic bending behavior with compressive axial load [1,[3][4][5].…”

Reduced-order coupled bidirectional modeling of the Roll-N-Cage isolator with application to the updated bridge benchmark

“…The reduced model of RNC devices introduced in this work adopts the coupled bi-directional formulation [12] initially proposed, in a different framework, by Park et al as an expansion of the Bouc-Wen [13] mono-directional hysteretic model. The Park et al model can be seen, as it can the Bouc-Wen one, as a black-box semi-physical model which can match an hysteretic behavior of a device by properly tuning its parameters.…”

“…Following the formulation in [12], the restoring force vector in a hysteretic system may be expressed as: (1) in which u is the displacement vector with orthogonal components u x and u y , in x and y directions respectively; q the restoring force vector with components q x and q y ; K is the initial stiffness matrix; α is the post-yielding stiffness ratio; Z represents the hysteretic displacement vector.…”

“…It can also be summarized as it follows: (9) The vectors defining the lower and upper bounds of the parameters to identify have been set taking into account what is reported in [12,13].…”