Question

5. The following state of strain has been measured by strain gages at a point on the surface of a crane hook: where strain gages (d. b, c) have θαー30°; θb--30°.0c-900. Determine the strain tensor components

Answer 1

$\left ( \epsilon _{n} \right )_{\theta }=\frac{\epsilon _{x}+\epsilon _{y}}{2}+\frac{\epsilon _{x}-\epsilon _{y}}{2}cos2\theta +\frac{\gamma _{xy}}{2}sin2\theta$

when $\left ( \epsilon _{n} \right )_{\theta }=1000\mu$ $\theta _{a}=30^{o}$   

  $\left ( \epsilon _{n} \right )_{\theta }=-250\mu$$\theta _{b}=-30^{o}$   

  $\left ( \epsilon _{n} \right )_{\theta }=200\mu$   $\theta _{c}=90^{o}$

using three equation three unknown we can find strain tensor component $\epsilon _{x},\epsilon _{y}$ and $\gamma _{xy}$

given data &ニ2001イ a= 30 de have to And We know that Ex4 Sx-C o2 Si220 when Sa 30 coo 叉 hlher %--30.

subshkete the valeee at Ex and Ey we ger lxy 3 2000L 3 hy x Singo, 12.50 Component o nooma stsain 8x-1300,U-433.334 (Ana) .. . Component at Shem Stou nt ay- 1443-37%n('n