Question

In a material under a state of plane strain, a $10\times 10$ mm square centred at a point gets deformed as shown in the figure.

If the shear strain ${\gamma }_{xy}$ at this point is expressed as $0.001k$ (in rad.) the value of $k$ is

• A. $0.50$
• B. $0.25$
• C. $-0.25$
• D. $-0.50$

Answer 1

The correct option is D $-0.50$

Shear strain in an element is positive when the angle between two positive faces (or two negative faces) is reduced.
The strain is negative when the angle between two positive (or two negative) faces increase.


$\mathrm{Face}2\&3\mathrm{are}+\mathrm{ve}\mathrm{face}.\mathrm{Face}1\&4\mathrm{are}-\mathrm{ve}\mathrm{face}.\mathrm{Angle}\mathrm{between}1\&4\mathrm{is}\mathrm{increased}\mathrm{by}0.0005\mathrm{rad}.$
$\therefore {\gamma }_{xy}=-0.0005=0.001K$
$\therefore K=-0.5$