# Inelastic stress analysis of curved beams with bending and shear coupling

Yen-Po Wang, Chien Liang Lee, Shih Chiao Huang

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

3 Scopus citations

## Abstract

The inelastic stress analysis of curved beams under pure bending has been extensively studied in the past few years. Nevertheless, the analysis for those under end shear, or moment and shear coupling, are not yet available. In this paper, the analytical model for inelastic stress analysis of symmetrical curved beams with bending and shear coupling is derived. This problem arises from the investigation of the inelastic behaviour of an in-plane flexural damper consisting of a circular arch with two straight arms. In-plane lateral forces applying to the end of the arm makes the arch a circular cantilever subjected to moment and shear simultaneously. Extended from the classical theory of elasticity, the proposed computational model adopts the generalized Hook's law in plane stress with consideration of the plastic strains defined by the total deformation theory. The swift-type nonlinear hardening law is considered for the inelastic constitutive relations of the material with its behaviour governed by von Mises' yield criterion. With the introduction of a certain form of Airy stress function that satisfies the compatibility equation in polar coordinates, the strain-compatibility equation with the corresponding boundary conditions can be simplified as a second-order ordinary differential equation of a properly defined generalized stress function dependent on radius of the wide curved beam. Solution of this ODE equation becomes a boundary-valued problem that can be solved numerically in both elastic and inelastic stages. To validate the proposed model, a preliminary numerical study of the stress analysis in the elastic stage has been conducted. Encouragingly, the numerical solution agrees perfectly with its analytical counterpart given by classical theory of elasticity.

Original language English Proceedings of the World Congress on Civil, Structural, and Environmental Engineering, CSEE 2016 Avestia Publishing 9781927877180 https://doi.org/10.11159/icsenm16.107 Published - 1 Jan 2016 Proceedings of the World Congress on Civil, Structural, and Environmental Engineering, CSEE 2016 - Prague, Czech RepublicDuration: 30 Mar 2016 → 31 Mar 2016

### Publication series

Name World Congress on Civil, Structural, and Environmental Engineering 2371-5294

### Conference

Conference Proceedings of the World Congress on Civil, Structural, and Environmental Engineering, CSEE 2016 Czech Republic Prague 30/03/16 → 31/03/16

## Keywords

• Boundary-valued problem
• Curved beam
• Elasticity
• Inelastic stress analysis
• Strain-compatibility
• Total deformation theory