Full Plastic Resistance of Tubes Under Bending and Axial Force: Exact Treatment and Approximations. (May 2017) - Rotter, J. Michael; Sadowski, Adam J.
Abstract: The full plastic resistance under a combination of bending and axial force of tubes of all possible wall thicknesses, from thin cylinders to circular solid sections, does not ever seem to have been thoroughly studied, despite the fact that this is a relatively simple analysis. The first part of this paper presents a formal analysis of the state of full plasticity under longitudinal stresses in a right circular tube of any thickness free of cross-section distortions. The derivation leads to relatively complicated algebraic expressions which are unsuitable for design guides and standards, so the chief purpose of this paper is to devise suitably accurate but simple empirical descriptions that give quite precise values for the state of full plasticity whilst avoiding the complexity of a formal exact analysis. The accuracy of each approximation is demonstrated. The two limiting cases of a thin tube (cylindrical shell) and circular solid section are shown to be simple special cases. The approximate expressions are particularly useful for the definition of the full plastic condition in tension members subject to small bending actions, but also applicable to all structural members and steel building structures standards, as well as to standards on thin shells where they provide the full plastic reference resistance. These expressions are also useful because they give simple definitions of the orientation of the plastic strain vector, which can assist in the development of analyses of the plastic collapse of arches and axially restrained members under bending.