Question

By application of tensile force, the cross-sectional area of bar P is first reduced by 30% and then by an additional 20%. Another bar Q of the same material is reduced in the cross-sectional area by 50% in a single step by applying tensile force. After deformation, the true strain in bar P and bar Q will, respectively be

• A. 0.5 and 0.5
• B. 0.58 and 0.69
• C. 0.69 and 0.69
• D. 0.78 and 1.00

Answer 1

The correct option is B 0.58 and 0.69

For bar P,

Initial area $A_0=A$

$A_1=0.70A$

After second reduction

$A_2=0.80\times 0.70A$

$=0.56A$

True strain :
${ϵ}_T=ln\left(\frac{A_0}{A_2}\right)=ln\left(\frac{A}{0.56A}\right)$

$=0.5798=0.58$

For bar Q

Initial area $A_0=A$

After first reduction $A_1=0.50A$
True strain :
${ϵ}_T=ln\left(\frac{A_0}{A_1}\right)=ln\left(\frac{A}{0.5A}\right)$

$=0.693$