Analysis of Axially Loaded Bars

Consider an elastic and a viscoelastic bar in uniaxial tension as shown in Fig. 8.1 where the axial load may be time dependent. 

As noted for an elastic bar in Chapter 2, the average or engineering stress, the average or engineering strain and Hooke s law are given by, 

the deformation varies with time only because the load varies with time. Note the cross sectional area used is still the original area and is constant. If tme stress were used, the cross section would change but for many polymers under practical loads the variation would be small and can be neglected. 

For a viscoelastic bar, a solution for stresses, strains and displacements can be obtained using the correspondence principle by replacing all variables in Eq. 8,7 by their Laplace transforms and the moduli by s times their Laplace transform. 

Comparing Eq. 8.11 with the first Eq. in 8.7 it is seen that the stress is exactly the same as in an elastic beam with a time dependent axial load. 

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