The use of modal-combination rules with cable-stayed bridges

Abstract

Modal superposition techniques such as the responsespectrum method (RSM) can be used to quickly estimate the peak response of a structure to earthquake-induced vibration and, as such, are widely used in preliminary design. Modal-combination rules for use with the RSM are typically founded on assumptions of linear structural behaviour, well-separated natural modes, classical damping and stationary excitation. By contrast, the response of cable-stayed bridges is known to be nonlinear with three-dimensional orthogonal mode shapes that can be coupled and closely spaced. Furthermore, it is widely known that the use of stationary stochastic processes for modelling earthquake excitation is a firstorder approximation and there is thus sufficient reason to doubt the validity of the RSM for estimating the response of cable-stayed bridges. This paper critiques the historical development and theoretical consistency of popular modal-combination rules with a view to assessing their suitability for estimating the response of cable-stayed bridges and their relative performance is investigated using an example finite-element model. In many cases, the more sophisticated modal-combination rules can be reliably employed; however, numerous scenarios are envisaged where such rules are likely to be inaccurate and caution is advised against their use under these circumstances.

Structural behaviour and design criteria of under‐deck cable‐stayed bridges subjected to seismic action

“…Consequently, there are many detailed references covering their behaviour and design (e.g. [1][2][3]), including papers specifically about their seismic behaviour (e.g., [4,5]). …”