Stress Analysis of Beams in Bending

A viscoelastic bar in pure bending can be analyzed in a similar manner as the axial bar in tension or compression and the circular cylindrical bar in torsion. Assume a time dependent bending moment is applied to a bar (with a vertical axis of symmetry) as shown in Fig. 8.4, 

For a viscoelastic bar in the transform domain, the solution is found by replacing all variables in the elastic solution by their Laplace transform (and all moduli by s times their Laplace transform) such that. 

Inversion of the Eq. 8.33 will give the solution for axial stress in the time domain, 

---