Question

In a plane strain situation in xy plane, the displacements at a point are given as:

$u=(-2x+8y)\times {10}^{-6}unit$

$v=(-3x+5y)\times {10}^{-6}unit$

What is the shearing strain?

• A. $9\times {10}^{-6}$
• B. $7\times {10}^{-6}$
• C. $5\times {10}^{-6}$
• D. $3\times {10}^{-6}$

Answer 1

The correct option is C $5\times {10}^{-6}$

The shearing strain in xy plane is given by

${\varphi }_{xy}=\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x}$

$u=(-2x+8y)\times {10}^{-6}$

$\Rightarrow \frac{\partial u}{\partial y}=8\times {10}^{-6}$

$v=(-3x+5y)\times {10}^{-6}$

$\Rightarrow \frac{\partial v}{\partial x}=-3\times {10}^{-6}$

$\therefore {\varphi }_{xy}=8\times {10}^{-6}-3\times {10}^{-6}$

$=5\times {10}^{-6}$