An Asymptotic Analysis on the Form of Naghdi Type Arch Model

We consider a one-dimensional model of generally curved elastic arches whose crosssections are rectangular. The model is of Naghdi’s type which is a generalization of the Timoshenko beam model, which allows bending, membrane and transverse shearing deformations. Its form is basically determined in the literature, except for the value of a shear correction factor. With this factor being set to 1, we prove that the modelling error in the interior relative energy norm is proportional to the arch thickness. This result holds for the full range of arch shapes and very general loads. Lower modelling accuracy is proven to hold up to the arch ends. Any shear correction factor other than 1 makes the model diverge from the elasticity theory when a significant shear is involved in the deformation.