Study of stress-strain state of a free girdle of a beam with break of a web

Abstract

Purpose. In the article the ground of energy method of investigation of stress state of metal beam with abrupt change of web height and girdle is presented to get if possible simple dependencies for effective width of free girdle at inclined region in place of transition of smaller web height to larger one and for optimal design of such beam on the whole, for these dependencies to be applied in simple formulae of strength of materials at engineering calculations using simplified beam and rod models. Method. There is presented on the simple example of plane problem of the theory of elasticity for rectangular plate at action of self-balanced shear external loads on it applied to mutual opposite edges the application of energy method and classic approach for definition of effective width of plate in its middle part, comparison of these methodologies between itself, the discussion and analyzing of findings. Investigations of stress-strain state of plate were provided by finite element method and using analytical solution. Results. There is shown high similarity of dependencies of full elastic energy of plate and effective width of plate on real width, despite these dependencies have different physical nature and units of measure. The particularity of inclined part of free girdle of observed beam is that the plane stress state is not realized completely there, because there is warping of free girdle and as the result complex stress-strain state and that's why classic idea of effective width don't work completely. The circumstance is complicated by the fact that the stress state on upper and lower surfaces of girdle of inclined zone is different, but stress concentration in the place of transition from smaller web height to inclined zone input its correctives into stress state of this field. This circumstance made to look for alternate ways of taking into account of work of girdle on the inclined part. Scientific novelty. It is offered applying of energy method meaning using an elastic energy dependency of a free girdle (or its part) on its geometrical parameters for development of relations of effective width and for optimal design, because elastic energy consider all parts of stress-strain state. Practical importance. The possibility of application of energy method both as auxiliary to classic one and as independent for development of mentioned above relations is shown.