Chapter 6, Problem 6.33P

Interpretation Introduction

Interpretation:

Diameter of cylindrical bar of steel is 10 mm. A load is applied along the bar of axis results in elastic deformation. Load applied on bar is to be determined which causes elastic reduction of 0.003 mm in diameter. Poison's ratio and modulus of elasticity of this bar is 0.30 and 207GPa respectively.

Concept introduction:

Applied force is calculated by using the following formula-

Radial strain −

${\epsilon }_r=\frac{\Delta d}{d}$

Here,

e_r = radial strain

Δd= change in diameter

d= diameter

Axial strain-

${\epsilon }_l=\frac{{\epsilon }_r}{v}$

Here,

e_r = radial strain

e_l = axial strain

$v=\text{Poisson’s ratio}$

Hooke's law-

$\sigma \propto \epsilon$

Stress-

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

Here,

$\sigma (stress)=\frac{F}{A}$

E = modulus of elasticity

e = strain or it can be axial strain