Question

The equilibrium equation in polar coordinates is given by _____________

(a) \(\frac{1}{r}  \frac{∂τ_{rθ}}{∂θ}+\frac{σ_r-σ_θ}{r}=0\)

(b) \(\frac{∂σ_r}{∂r}+\frac{∂τ_{rθ}}{∂θ}+\frac{σ_r-σ_θ}{r}=0\)

(c) \(\frac{∂σ_r}{∂r}+\frac{1}{r}  \frac{∂τ_{rθ}}{∂θ}+\frac{σ_r-σ_θ}{r}=0\)

(d) \(\frac{∂σ_r}{∂r}+\frac{1}{r}  \frac{∂τ_{rθ}}{∂θ}=0\)

The question was asked during an interview.

Enquiry is from Stress Distribution in division Stress Distribution of Geotechnical Engineering I

Answer 1

The correct answer is (c) \(\frac{∂σ_r}{∂r}+\frac{1}{r}  \frac{∂τ_{rθ}}{∂θ}+\frac{σ_r-σ_θ}{r}=0\)

Explanation: The equilibrium equations in polar coordinates are given by,

 1. \(\frac{∂σ_r}{∂r}+\frac{1}{r}  \frac{∂τ_{rθ}}{∂θ}+\frac{σ_r-σ_θ}{r}=0 \)

 2. \(\frac{1}{r}\frac{∂σ_θ}{∂θ}+\frac{∂τ_{rθ}}{∂r}+\frac{2τ_{rθ}}{r}=0.\)