Assessing Dynamic Response of Slender Structures: A Novel Framework Using Dimensional Analysis

Abstract

This study develops two parallel seismic design frameworks—spectrum based iterative design (SBID) and spectrum based direct design (SBDD)—for free-standing slender systems subjected to base excitation, founded on the principles of dimensional analysis. The formulation establishes an intrinsic relationship between the two approaches, demonstrating that they are fundamentally interlinked through consistent non-dimensional parameters governing rocking response. Within the SBID framework, design is achieved through the combined and iterative use of stability coefficient spectra (SCS) and rocking spectra (RS), which together capture acceleration demand and rotational response. In contrast, the SBDD approach employs constant rotation spectra (CRS) to directly relate excitation intensity to a prescribed permissible rotation (implicitly ensuring stability). As such, SBDD obviates the need for iterations and enhances computational efficiency. The spectra are constructed for both idealized pulse-type and recorded seismic excitations, illustrating their applicability across a range of loading scenarios. The methodology is further extended to bidirectional excitations, where coupled rotations about orthogonal axes are considered. It is shown that the proposed methodology can explicitly incorporate the effects of base flexibility and incidence angles of loading. Overall, the study provides a unified and efficient framework, especially for preliminary assessment and design of rocking systems.