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GPSC AE CE 2018 Official Paper (Part B - Civil)

Option 3 : P/2S^{2}

CT 3: Building Materials

3014

10 Questions
20 Marks
12 Mins

__Given__**: -**

__Solution__**: - **

We know,

Normal Stress at any oblique plane is given by –

\({\sigma _{x'/y'}} = \frac{{{\sigma _x} + {\sigma _y}}}{2} \pm \frac{{{\sigma _x} - {\sigma _y}}}{2}cos2θ \)

Here,

θ – is the angle with the major stress = 90° - 45°= 45°

Hence,

\({\sigma _{x'/y'}} = \frac{P}{{2{S^2}}} \pm \frac{P}{{2{S^2}}}cos90^\circ = \frac{P}{{2{S^2}}}\)