دانلود رایگان مقاله مقاومت پلاستیک کامل لوله ها تحت خمش و نیروی محوری

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.

7. Conclusions

This short paper has presented the formal analysis of the state of full plasticity under bending and axial force in a circular tube or cylinder of any thickness. The two limiting cases of a thin tube (cylindrical shell) and a circular solid section have been shown as special cases. The chief goal of the paper has been to find approximate but simple formulas that can accurately capture the outcome of the general equations, since these are too complicated for use in design calculations. Two different approximate formulas have been presented that are suitable for adoption into design guides and standards. The precision of each has been demonstrated. These expressions also allow easy identi- fication of the orientation of the plastic strain vector on the yield surface, making it easier to formulate plastic collapse analyses of redundant structures in which axial and bending stress resultants strongly interact, such as arches and axially restrained beams. The accurate representation of the full plastic state in I, H, C and RHS sections involves a simple calculation that is part of the standard training of structural engineers. By contrast, the same analysis for circular tubular sections is not trivial, so it would be appropriate to include accurate expressions in guides and standards for design. The results of this study should be particularly useful for the design of tension members subject to small bending actions.