Seismic response of building frames with flexible base optimized for reverse rocking response

•Topology optimization of flexible base for seismic response reduction.•Utilize rocking deformation of base in opposite direction to drift of frame.•Roof displacement is reduced by the dominant second mode.•Responses can be further reduced by installing viscous dampers at support.

A reverse rocking response is investigated for a steel frame that has flexible base. The mechanism of response reduction is first investigated using a simple flexible base model consisting of truss elements. It is demonstrated that the roof displacement is reduced by the dominant second mode, in which the base rotates in the opposite direction to the upper frame. Seismic responses of the frame can be further reduced by installing viscous dampers at the support. A topology optimization approach is next presented for design of flexible base structure consisting of frame elements. It is shown that the cross-sectional properties and nodal locations are successfully optimized using a nonlinear programming approach to generate a flexible base.