The sectorial co-ordinate of non-linearly elastic beams of three thin-walled open cross-sections

Abstract

A beam lamina of thin-walled open cross-section is considered. The sectional forces are a bimoment B and a Vlasov torsional moment M w . The material is assumed to be non-linearly elastic with the constitutive equation ϵ = K|σ| n sgn σ in uniaxial tension. A slight redefinition of the generalized sectorial moment of inertia I (n) ω is given. The sectorial co-ordinate as a function of n is determined for three commonly used cross-sections.