Estimation of the stress-strain state of the revolving long cylinder

Subject of a study is a difficult stress state of long hollow cylinder which is being bended by its own weight and rotated by turning moment. The stressed state over the cylinder section and the curvature of its longitudinal axis are investigated. The basic assumptions taken in the attention to solve the problem in question are usual common for the mechanics of materials and engineering approximations the hypothesis about the linearity of the physical relationships between the stresses and strains (linear theory of elasticity) and assumption about the small strains. Solution of problem is built on the basis of the differential equation of the elastic flexure of the central axis of cylinder and fundamental relationships between the curvature of this axis, applied loads, strains and stresses in the region of cylinder section. Boundary-value problem for the ordinary differential equation of the fourth order with the appropriate boundary conditions is solved using the method of variations of the arbitrary constants. This made it possible to obtain the exact solution of the task of the long cylinder bending which rotates around the longitudinal axis. This, as a result, made possible to determine the dependence of the curvature of cylinder central axis on the longitudinal coordinate and to find the stress distribution in the of cylinder section. The estimation of the contribution from each of the factors, which act on the subject of study, to the stressed state is executed. Solution of the presented problem made it possible to define equivalent stress in the outlying layers of cylinder as the result of the action of all power factors examined.