A generalized beam theory with shear deformation

A new formulation of the Generalized Beam Theory (GBT) that coherently accounts for shear deformation is presented in this paper. In particular, a modified formulation of the kinematics early proposed by Silvestre and Camotim for shear deformable GBT is devised. The new formulation, which preserves the general format of the original GBT for flexural modes, introduces the shear deformation along the wall thickness direction besides that along the wall midline, so guaranteeing a coherent matching between bending and shear strain components of the beam. According to the new kinematics, a reviewed form of the cross-section analysis procedure is devised, based on a unique modal decomposition for both flexural and shear modes. Much attention is posed on the mechanical interpretation of the deformation parameters in the modal space. It is shown that, in the modal space, it is possible to clearly distinguish bending deflections from deflections due to shearing strains, and to recover classical beam degrees of freedom and standard beam theories as special cases. The effectiveness of the proposed approach is illustrated on two typical benchmark problems.