• # question_answer Principal stresses at a point in plane stressed element are ${{\sigma }_{x}}={{\sigma }_{y}}=500k\text{g/c}{{\text{m}}^{\text{2}}}.$ Normal stress on the plane inclined at $45{}^\circ$ to x-axis will be: A) 0                                 B) $500\,k\text{g/c}{{\text{m}}^{\text{2}}}$C) $707\,k\text{g/c}{{\text{m}}^{\text{2}}}$                   D) $1000\,k\text{g/c}{{\text{m}}^{\text{2}}}$

${{\sigma }_{n}}=\frac{1}{2}({{\sigma }_{x}}+{{\sigma }_{y}})+\frac{1}{2}({{\sigma }_{x}}-{{\sigma }_{y}})\,cos\theta$ For $\theta =45{}^\circ$ ${{\sigma }_{n}}=\frac{1}{2}({{\sigma }_{x}}+{{\sigma }_{y}})+\frac{1}{2}(500+500)=500\,\text{kg/c}{{\text{m}}^{\text{2}}}$