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A linear elastic structure under plane stress condition is subjected to two sets of loading, $\text{I}$ and $\text{II}$. The resulting states of stress at a point corresponding to these two loadings are as shown in the figure below. If these two sets of loading are applied simultaneously, then the net normal component of stress $\sigma _{xx}$ is __________________.

  1. $3\sigma /2$
  2. $\sigma \left ( 1+1/\sqrt{2} \right )$
  3. $\sigma /2$
  4. $\sigma \left ( 1-1/\sqrt{2} \right )$
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Sigma cos^2 0+ sigma cos^2 45= net sigmaxx
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