Chapter 6, Problem 6.34P

Interpretation Introduction

(a)

Interpretation:

The length and the diameter of the given bar should be determined

A 500-lb load is applied on the bar, after this length and the diameter of the bar are to be determined where the Poisson's ratio is 0.30.

Concept Introduction:

Following formulas will be used for the calculation of new length and the diameter of titanium bar-

$\delta l=\frac{PL}{AE}$

Stress formula-

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

Poisson's ratio-

$\gamma =-\frac{e_{lateral}}{e_{longitudnal}}$

P= applied force

L= initial length

A= area

E= modulus of elasticity

δl= Change in length

P= applied force

A = area

Interpretation Introduction

(b)

Interpretation:

The applied load should be determined for the given copper bar.

Concept Introduction:

Applied load is calculated by using the following formulas-

Relation between rigidity modulus, modulus of elasticity and Poisson's ratio is-

$G=\frac{E}{2(1+v)}$

Where,

G = modulus of rigidity

E = modulus of elasticity

$v$ = Poisson's ratio

Hooke's law for shear stress (t) and strain (τ) is −

$\tau =G\gamma$

Shear stress is −

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

Shear strain is-

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

Where,

τ = shear stress

γ = shear strain

G = proportional constant, modulus of rigidity

τ = shear stress

F= applied force

A= area

τ = shear strain

ΔA= deformed area or change in area