Obliczanie Współrzędnych Środka Ścinania Dowolnego Przekroju Asymetrycznego o Brzegu Jednospójnym

Abstract

The paper is concerned with a computation method of the fluxural centre and the torsional rigidity. The mathematical model is based on the fundamental equations of the theory of elasticity and its solution is reduced to the determination of the distribution of the shear stress flexural over the surface. To do this a stress function is introduced, for which Poisson's equation is obtained together with appropriate boundary conditions. The problem is solved by means of the variational calculus, by seeking for the extremum value of the relevant functional by means of the Ritz method.
For profiles, the edge of which is described in a non-analytic manner solutions are given in a numerical form. The accuracy of the method is determined for elliptic and circular sections.