Classical and Timoshenko-Like beam models

  1. saeid Khadem Moshir

    Dear Prof. Yu,
    There is a question regarding the VAM. 
    One can obtain the 3D strain and stress fields (because of finding 3D warping fields) of a composite beam using the Classical beam model of VAM (first approximation of the beam strain energy) with high accuracy for the case of straight beams. If this work can be done, why is it needed to go through the Timoshenko-Like beam model and consequently transforming the strain energy to generalized Timoshenko-Like beam model? In other meaning, is it possible to say that the Classical beam model can capture the transverse shear effects implicitly? 
    The Classical beam model (4*4 matrix) is asymptotically correct, so that it one can say that it can capture the transverse shear effect implicitly, so that is it necessary to go through the Timoshenko-Like (6*6 matrix) beam model? 
    In terms of 1D solution, it is observed that the Classical beam model (4*4) is not adequate for short wavelength beam problems and one needs to go through the Timoshenko-Like beam model.
    Thank you very much

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    1. Wenbin Yu

      If the transverse shear strains/stresses are generated by extension, torsion, and two bendings, then the classical beam model is sufficient. Otherwise, the transverse shear strains/stresses obtained by the Timoshenko model will be better. For example, for a cantilever beam subject to a tip transverse shear force, the classical beam model cannot obtain any stresses at the tip due to zero moment. However the Timoshenko should be able to obtain transverse shear stress distribution over the cross-section. 

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