A cylindrical specimen of a brass alloy having a length of 104 mm (4.094 in.) must elongate only 5.20 mm (0.2047 in.) when a tensile load of 101000 N (22710 lbf) is applied. Under these circumstances what must be the radius of the specimen? Consider this brass alloy to have the stress–strain behavior

The radius of the specimen is assumed to be 9.724 mm

Explanation:

Given that:

For a cylindrical specimen of a brass alloy;

The length = 104 mm, Elongation = 5.20 mm and the tensile load = 101000 N

Let's first determine the radius of the cylindrical brass alloy from the knowledge of the cross-sectional area of a cylinder.

To estimate the tensile stress:

We need to first determine the strain relating to elongation at 5.20 mm

Strain ε = 0.05

Using the stress-strain plot; let assume that under the circumstances; = 340 MPa for stress corresponding to 0.05 strain

Thus;

The cylindrical brass alloy radius

r = 0.009724 m

r = 9.724 mm