Questions and answers for exam Preparation

MCQs

Total Questions : 189 | Page 19 of 19 pages

Question 181. The relation between the stress component in x-direction on a horizontal plane in Cartesian coordinates and polar coordinates for vertical line load is ___________

σₓ=σᵣ tan²⁡θ
σₓ=σᵣ cosec²⁡θ
σₓ=σᵣ cos⁡θ
σₓ=σᵣ sin²⁡θ

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Answer: Option D. -> σₓ=σᵣ sin²⁡θ
Answer: (d).σₓ=σᵣ sin²⁡θ

Question 182. If the footing is flexible, then the distribution pressure is uniform.

True
False
May be True or False
Can't say

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Answer: Option A. -> True
Answer: (a).True

Question 183. The compatibility equation in terms of stress components in polar coordinates are given by ____________

\((\frac{∂^2}{∂r^2} +\frac{1}{r} \frac{∂}{∂r}+\frac{1}{r^2} \frac{∂^2}{∂θ^2} )(σ_r+σ_θ )=0\)
\((\frac{∂^2}{∂r^2} +\frac{1}{r} \frac{∂}{∂r}+\frac{1}{r^2} \frac{∂^2}{∂θ^2} )(σ_θ )=0\)
\((\frac{∂^2}{∂r^2} +\frac{1}{r} \frac{∂}{∂r}+\frac{1}{r^2} \frac{∂^2}{∂θ^2} )(σ_r )=0\)
\((\frac{∂^2}{∂r^2} +\frac{1}{r} \frac{∂}{∂r}+\frac{1}{r^2} \frac{∂^2}{∂θ^2} )(σ_r+σ_θ )=1\)

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Answer: Option A. -> \((\frac{∂^2}{∂r^2} +\frac{1}{r} \frac{∂}{∂r}+\frac{1}{r^2} \frac{∂^2}{∂θ^2} )(σ_r+σ_θ )=0\)
Answer: (a).\((\frac{∂^2}{∂r^2} +\frac{1}{r} \frac{∂}{∂r}+\frac{1}{r^2} \frac{∂^2}{∂θ^2} )(σ_r+σ_θ )=0\)

Question 184. The equilibrium equation in polar coordinates is given by _____________

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

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Answer: Option C. -> \(\frac{∂σ_r}{∂r}+\frac{1}{r} \frac{∂τ_{rθ}}{∂θ}+\frac{σ_r-σ_θ}{r}=0\)
Answer: (c).\(\frac{∂σ_r}{∂r}+\frac{1}{r} \frac{∂τ_{rθ}}{∂θ}+\frac{σ_r-σ_θ}{r}=0\)

Question 185. At a point there are ______ shear stresses.

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Answer: Option C. -> 6
Answer: (c).6

Question 186. There are _______ independent shearing stresses.

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Answer: Option B. -> 3
Answer: (b).3

Question 187. The equilibrium equation obtained by summing all forces on y-direction is ________

\(\frac{∂σ_x}{∂x} + \frac{∂τ_{yx}}{∂y} + \frac{∂τ_{zx}}{∂z} +X=0\)
\(\frac{∂τ_{xy}}{∂x} + \frac{∂σ_y}{∂y} +\frac{∂τ_{zy}}{∂z}+Y=0\)
\(\frac{∂τ_{xz}}{∂x} +\frac{∂τ_{yz}}{∂y} +\frac{∂σ_z}{∂z} +Z=0\)
\(\frac{∂σ_x}{∂x}+\frac{∂τ_{yx}}{∂y} +\frac{∂τ_{zx}}{∂z} = 0\)

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Answer: Option B. -> \(\frac{∂τ_{xy}}{∂x} + \frac{∂σ_y}{∂y} +\frac{∂τ_{zy}}{∂z}+Y=0\)
Answer: (b).\(\frac{∂τ_{xy}}{∂x} + \frac{∂σ_y}{∂y} +\frac{∂τ_{zy}}{∂z}+Y=0\)

Question 188. The equilibrium equation obtained by summing all forces on x-direction is ________

\(\frac{∂σ_x}{∂x} + \frac{∂τ_{yx}}{∂y} + \frac{∂τ_{zx}}{∂z} +X=0\)
\(\frac{∂τ_{xy}}{∂x} + \frac{∂σ_y}{∂y} +\frac{∂τ_{zy}}{∂z}+Y=0\)
\(\frac{∂τ_{xz}}{∂x} +\frac{∂τ_{yz}}{∂y} +\frac{∂σ_z}{∂z} +Z=0\)
\(\frac{∂σ_x}{∂x}+\frac{∂τ_{yx}}{∂y} +\frac{∂τ_{zx}}{∂z} = 0\)

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Answer: Option A. -> \(\frac{∂σ_x}{∂x} + \frac{∂τ_{yx}}{∂y} + \frac{∂τ_{zx}}{∂z} +X=0\)
Answer: (a).\(\frac{∂σ_x}{∂x} + \frac{∂τ_{yx}}{∂y} + \frac{∂τ_{zx}}{∂z} +X=0\)

Question 189. The total independent stresses at a point are _________

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Answer: Option B. -> 6
Answer: (b).6