Assessment of Effects of Reductions of Lateral Stiffness along Height on Buildings Modeled as Elastic Cantilever Shear Beams

摘要

A simplified model useful for assessing economic losses due to moderate seismicity events in urban areas has been developed by studying the behavior of buildings before yielding their structural system, allowing for nonuniform stiffness along their height. In particular, buildings are modeled as cantilever shear beams with uniform mass and parabolic reduction of lateral stiffness. This particular stiffness distribution is relevant, as it could be expected to occur in buildings where earthquake action is a critical structural design criterion. The equation of motion governing the dynamic behavior of the proposed model is solved analytically, finding mode shapes in terms of first and second zero-order Legendre functions. The solution is verified by comparing it with results obtained from fine mesh finite element models. The effect of reducing the lateral stiffness is then studied in the first five modes of vibration. Results include modal periods, mode shapes, modal participation factors, and derivatives of mode shapes. In general, it is found that effects of reduction of lateral stiffness in mode shapes are moderate when the lateral stiffness in the free end is smaller than about seventy percent of the lateral stiffness at the fixed end, but become significant for larger reductions. Effects are particularly important for the derivative of the mode shapes, which could play a significant role in estimating interstory drift demands in buildings. Model usefulness is showcased by analyzing a test case where both acceleration and drift demands are assessed by considering uniform beams and beams with parabolic stiffness variation, finding notable improvements by considering the latter.