Analysis of Circular Cylinder Bars in Torsion

A viscoelastic bar in torsion can be analyzed in a similar manner as the axial bar in tension or compression. Assume a time dependent end torque is applied to a circular cylindrical bar as shown in Fig. 8.2, 

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

Inversion of the equation for the transform of shear stress will give the solution for shear stress in the time domain. 

As for the uniaxial tension case, while the elastic solution for angular displacement is constant in time for a constant torque input, the viscoelastic bar exhibits increasing displacement from creep over time. Note again that the expression Eq. 8.31 is quite simple in the step input case and analogous in form to the elastic solution Eq. 8.26. For time varying loading, the integration of Eq. 8.29 is nontrivial and results in a more complex form. 

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