Shape effects in doubly clamped bridge structures at large deflections

The shape of a doubly clamped bridge structure depends on its deflection. At large deflections, where the system exhibits nonlinear behaviour, the shape effect becomes significant. We present a general method, based on variational analysis, for computing corrections to the nominal linear regime shape function. The method is used to compute the first non-trivial correction and quantify the corresponding improvement in the large deflection regime. The model obtained is also validated using FEM simulations.