Suppose that a homogeneous steel bar with a constant cross-sectional area A is subjected to tension under axial load P (Fig. 3.10a). A gage length L is selected away from the ends of
the bar, to avoid disturbances by the end attachments that apply the load. The load P is increased in increments, and the corresponding elongation of the original gage length is measured. Figure 3.10b shows the plot of a typical load-deformation relationship resulting from this type of test.
Assuming that the load is applied concentrically, the strain at any point along the gage length will be
, and the stress at any point in the cross section of the bar will be Æ’ = P/A. Under these conditions, it is convenient to plot the relation between stress and strain.
Figure 3.11 shows the resulting plot of a typical stress-stain relationship resulting from this test.