Question

Assertion (A): A plane stress system consists of two principal stresses ${\sigma }_{1}and{\sigma }_2$ and a plane strain system consists of two principal strains ${\epsilon }_1={\sigma }_1/Eand{\epsilon }_2={\sigma }_2/E$. Both the systems are identical.
Reason (R): Stress is proportional to strain.

• A. both A and R are true and R is the correct explanation of A
• B. both A and R are true but R is not a correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Answer 1

The correct option is D A is false but R is true

Plane strain system is not identical with plane stress system, because
${\sigma }_3=0$ in plane stress system

${\epsilon }_3=0$ in plane stress system
In general,

${\epsilon }_3=\frac{1}{E}[{\sigma }_3-\mu ({\sigma }_1+{\sigma }_2\left)\right]$
Thus for plane strain ${\sigma }_3$ may be non-zero. However in the given problem the strain is given as ${\sigma }_1/E$ and effect of stress in lateral dimension is neglected.