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

Modal superposition techniques such as the response-spectrum 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 non-linear 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 first-order 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.