Answer:
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.
[tex]A_0 = \pi r ^2[/tex]
[tex]r = \sqrt{\dfrac{A_o}{\pi}}[/tex]
[tex]r = \sqrt{\dfrac{\bigg (\dfrac{F}{\sigma} \bigg )}{\pi}}[/tex]
[tex]r = \sqrt{\dfrac{F}{ \sigma \pi}}[/tex]
To estimate the tensile stress:
We need to first determine the strain relating to elongation at 5.20 mm
[tex]Strain \ \ \varepsilon= \dfrac{\Delta l}{l_o}[/tex]
[tex]Strain \ \ \varepsilon= \dfrac{5.20}{104}[/tex]
Strain ε = 0.05
Using the stress-strain plot; let assume that under the circumstances; [tex]\sigma[/tex] = 340 MPa for stress corresponding to 0.05 strain
Thus;
The cylindrical brass alloy radius [tex]r = \sqrt{\dfrac{F}{ \sigma \pi}}[/tex]
[tex]r =\sqrt{ \dfrac{101000}{(340\times 10^{6})\pi}[/tex]
r = 0.009724 m
r = 9.724 mm
