A theory has been carried out on the shear stress , assuming that the shear force can generate both warping displacement and rigid vertical translation of the structural section. Relations have been obtained for the normal and tangential stresses , based on the Vlasov hypotheses about the thinwalled beams, and developed in orthogonal curvilinear coordinates, what allows to account for the influence of the branches curvature. A numerical method has been also developed , which modifies the stationary method elaborated by Hughes, assuming a cubic law for the warping function , according to the verified Poisson equation , and utilizing the expressions obtained for the displacement and the stress fields. In order to verify the influence of the shear deflection, a procedure has been adopted, which is a numerical translation of the Neumann problem, and substitutes the condition of absence of rigid warping components , for the assumption of zero values of the warping function on the neutral axis, assumed by Hughes , as a numerical translation of the mixed Dirichlet-Neumann problem. The application to a simplified structure considered by Hughes, shows the negligible influence of the shear deflection , and allows to change the Hughes method for the only order of the warping function.

A numerical method for the shear stress determination

PISCOPO, VINCENZO;
2007

Abstract

A theory has been carried out on the shear stress , assuming that the shear force can generate both warping displacement and rigid vertical translation of the structural section. Relations have been obtained for the normal and tangential stresses , based on the Vlasov hypotheses about the thinwalled beams, and developed in orthogonal curvilinear coordinates, what allows to account for the influence of the branches curvature. A numerical method has been also developed , which modifies the stationary method elaborated by Hughes, assuming a cubic law for the warping function , according to the verified Poisson equation , and utilizing the expressions obtained for the displacement and the stress fields. In order to verify the influence of the shear deflection, a procedure has been adopted, which is a numerical translation of the Neumann problem, and substitutes the condition of absence of rigid warping components , for the assumption of zero values of the warping function on the neutral axis, assumed by Hughes , as a numerical translation of the mixed Dirichlet-Neumann problem. The application to a simplified structure considered by Hughes, shows the negligible influence of the shear deflection , and allows to change the Hughes method for the only order of the warping function.
9788890117435
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11367/36903
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