GATE 2017 ME (ME1) – Question 52
A rectangular region in plane strain has undeformed corners P(0,0), Q(4,0), R(4,3), S(0,3). Uniform strains are $\epsilon_{xx}=0.001$, $\epsilon_{yy}=0.002$, $\gamma_{xy}=0.003$. Find the deformed length of the elongated diagonal, to three decimal places.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 5.013 to 5.015
Explanation
The original diagonal PR has vector $(4,3)$ and length 5. Its normal strain is $\epsilon_n=[\epsilon_{xx}(4^2)+\epsilon_{yy}(3^2)+\gamma_{xy}(4)(3)]/25=(0.016+0.018+0.036)/25=0.0028$. The first-order deformed length is $5(1+0.0028)=5.014$. The shear contribution has the opposite sign for the other diagonal, so PR is the more elongated one.