In this paper a boundary element method is developed for the nonuniform torsion of simply or multiply connected prismatic bars of arbitrary cross section. The bar is subjected to an arbitrarily distributed twisting moment, while its edges are restrained by the most general linear torsional boundary conditions. Since warping is prevented, beside the Saint-Venant torsional shear stresses, the warping normal and shear stresses are also computed. Three boundary value problems with respect to the variable along the beam angle of twist and to the primary and secondary warping functions are formulated and solved employing a BEM approach. Both the warping and the torsion constants using only boundary discretization together with the torsional shear stresses and the warping normal and shear stresses are computed. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The magnitude of the warping shear stresses due to restrained warping is investigated by numerical examples with great practical interest.
In this paper a solution to the problem of plates reinforced with beams is presented. The adopted model takes into account the resulting inplane forces and deformations of the plate as well as the axial forces and deformations of the beam, due to combined response of the system. The analysis consists in isolating the beams from the plate by sections parallel to the lower outer surface of the plate. The forces at the interface, which produce lateral de¯ection and inplane deformation to the plate and lateral de¯ection and axial deformation to the beam, are established using continuity conditions at the interface. The solution of the arising plate and beam problems which are nonlinearly coupled, is achieved using the analog equation method (AEM). The adopted model describes better the actual response of the plate±beams system and permits the evaluation of the shear forces at the interface, the knowledge of which is very important in the design of composite or prefabricated ribbed plates. The resulting de¯ections are considerably smaller than those obtained by other models.
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