Question

A rectangular region in a solid is in a state of plane strain. The (x, y) coordinates of the corners of the undeformed rectangle are given by P(0, 0), Q(4, 0), R(4, 3), S(0, 3). The rectangle is subjected to uniform strain ${\epsilon }_{xx}=0.001,{\epsilon }_{yy}=0.002,{\gamma }_{xy=0.003}$. The deformed length of the elongated diagonal, upto three decimal places, is _______
units.

• A. 5.014

Answer 1

The correct option is A 5.014


${\epsilon }_x=0.001$
${\epsilon }_y=0.002$
${\gamma }_{xy}=0.003$

$\theta ={\tan }^{-1}\left(\frac{3}{4}\right)={36.87}^{\circ }$

${\epsilon }_{\theta }=\frac{({\epsilon }_x+{\epsilon }_y)}{2}+\frac{({\epsilon }_x-{\epsilon }_y)}{2}\cos 2\theta +\frac{{\gamma }_{xy}}{2}\left(\sin 2\theta \right)$

${\epsilon }_{\theta }=2.8\times {10}^{-3}$

$\frac{\Delta L_{\text{diagonal(PR)}}}{L_{diagonal\left(PR\right)}}=2.8\times {10}^{-3}$

$\Delta L_{\text{diagonal(PR)}}=0.014$ units
So, $L_{\text{diagonal (PR)}}^{\prime }=L_{\text{diagonal (PR)}}+\Delta L_{\text{diagonal(PR)}}$

$=5+0.014$

$=5.014$ units