• question_answer   The state of plane stress at a point is described by ${{\sigma }_{x}}={{\sigma }_{y}}$ and ${{\tau }_{xy}}=0.$ The normal stress on the plane inclined at $45{}^\circ$ to the x-plane will be        A) $\sigma$                                 B) $\sqrt{2\sigma }$C) $\sqrt{3\sigma }$                      D) $2\sigma$

${{\sigma }_{1}}=\frac{1}{2}({{\sigma }_{x}}+{{\sigma }_{y}})+\frac{1}{2}({{\sigma }_{x}}-{{\sigma }_{y}})\,cos2\theta$ At $\theta =45{}^\circ$ ${{\sigma }_{1}}=\frac{1}{2}(\sigma +\sigma )+\frac{1}{2}(\sigma -\sigma )=\sigma$