An Analytical Method to Visualize Higher Mode Effects on Yielding Cantilever Walls

Abstract

A nonlinear flexural plastic hinge developing at the base of the cantilever wall changes its dynamic properties. In such systems, contribution of higher modes to the total shear force response after yielding may be underestimated when they are assumed to prone same or some nonlinearity as the first mode. In order to calculate the modal properties of a cantilever walls developing a plastic hinge at the base after yielding, the fundamental analytical beam formulation is revisited, and by applying special boundary condition reflecting the nonlinear deformation at the fixed base, that is, plastic hinge rotation, a novel formulation that is able to track changes in the modal properties of yielding cantilever shear wall is derived. The modal properties are effectively calculated depending on the level of nonlinear plastic rotation demand. Derived formulation can be very useful in the analysis of higher mode effects on shear wall systems, where the essential understanding of dynamic shear force amplification in cantilever wall system lays in the variation of the systems dynamic modal properties extending from linear to nonlinear range. A mode superposition method using equivalent nonlinear modal single-degree-of-freedom (SDOF) systems is presented for the estimation of maximum shear force.