If p₁ and p₂ are mutually perpendicular principal stresses acting on a soil mass, the normal stress on any plane inclined at angle $${\theta ^ \circ }$$ to the principal plane carrying the principal stress p₁, is:

A) $$\frac{{{{\text{p}}_1} - {{\text{p}}_2}}}{2} + \frac{{{{\text{p}}_1} + {{\text{p}}_2}}}{2}\sin \,2\theta $$ B) $$\frac{{{{\text{p}}_1} - {{\text{p}}_2}}}{2} + \frac{{{{\text{p}}_1} + {{\text{p}}_2}}}{2}\cos\,2\theta $$ C) $$\frac{{{{\text{p}}_1} + {{\text{p}}_2}}}{2} + \frac{{{{\text{p}}_1} - {{\text{p}}_2}}}{2}\cos\,2\theta $$ D) $$\frac{{{{\text{p}}_1} + {{\text{p}}_2}}}{2} + \frac{{{{\text{p}}_1} - {{\text{p}}_2}}}{2}\sin \,2\theta $$

Answer & Solution

Correct Answer: Option C

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If p1 and p2 are mutually perpendicular principal stresses acting on...

If p1 and p2 are mutually perpendicular principal stresses acting on a soil mass, the normal stress on any plane inclined at angle $${\theta ^ \circ }$$ to the principal plane carrying the principal stress p1, is:

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If p₁ and p₂ are mutually perpendicular principal stresses acting on a soil mass, the normal stress on any plane inclined at angle $${\theta ^ \circ }$$ to the principal plane carrying the principal stress p₁, is: