Chapter 6, Problem 6.32P

Interpretation Introduction

Interpretation:

The diameter of the cylindrical metal bar is 0.505 in. on which 4000 lbs force is applied. This applied load causes a reduction in the size of the diameter of 0.0003 in. This deformation which occurs in the bar is purely elastic. Poisson's ratio of the material is to be determined when the modulus of elasticity is $15\times {10}^6\text{psi}$.

Concept introduction:

Poisson's ratio is calculated by using the following formulas-

Hooke's law equation is as follows:

$\tau \propto \gamma$

Here,

t = shear stress

γ = shear strain

Shear stress can be calculated as follow:

$\tau =\frac{F}{A}$

Here,

t = shear stress

F = applied force

A = area

Shear strain can be calculated as follows:

$\gamma =\frac{\Delta A}{A}$

The relation between modulus of rigidity and Poisson's ratio-

$E=2G(1+v)$