Chapter 11, Problem 11.1P

To determine

(a)

By calculating the axial strain in the bar.

Answer to Problem 11.1P

   $\epsilon =0.004$

Explanation of Solution

Given:

The diameter of the steel rod, $d=2in\text{.}$

The original length of the rod, $l=10ft.$

The elongation of the rod under applied load, $\delta =0.48in.$

Concept Used:

Axial (Longitudinal) Strain, $\epsilon =\frac{elongation}{originallength}=\frac{\delta }{l}$

Calculation:

   $\epsilon =\frac{elongation}{originallength}=\frac{\delta }{l}=\frac{0.48}{10\times 12}=0.004$

Conclusion:

Axial (Longitudinal) Strain, $\epsilon =0.004$

To determine

(b)

The poison's ratio of the rod.

Answer to Problem 11.1P

   $\mu =0.3$

Explanation of Solution

Given:

The diameter of the steel rod, $d=2in\text{.}$

The original length of the rod, $l=10ft.$

The elongation of the rod under applied load, $\delta =0.48in.$

The transverse deformation of the rod, $=0.0024in.$

Concept Used:

Poisson's ratio is given by, $\mu =\frac{\text{tranverse strain}}{\text{axial strain}}$

Calculation:

The transverse strain of the rod = $\frac{\text{change in diameter}}{\text{original diameter}}=\frac{0.0024}{2}=0.0012$

Poisson's ratio of the rod, $\mu =\frac{\text{tranverse strain}}{\text{axial strain}}=\frac{0.0012}{0.004}=0.3$

Conclusion:

Poisson's ratio of the rod, $\mu =0.3$