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MCQs

Total Questions : 189 | Page 14 of 19 pages
Question 131. For both plane stress as well as plain strain case the equilibrium equation in x-direction is _______
  1.    \(\frac{∂σ_x}{∂x}+\frac{∂τ_{yx}}{∂y}=0\)
  2.    \(\frac{∂σ_x}{∂x}+\frac{∂τ_{yx}}{∂y}+\frac{∂τ_{zx}}{∂z}+X=1\)
  3.    \(\frac{∂σ_x}{∂x}+\frac{∂τ_{yx}}{∂y}+X=0\)
  4.    \(\frac{∂σ_x}{∂x}+\frac{∂τ_{zx}}{∂z}=0\)
 Discuss Question
Answer: Option D. -> \(\frac{∂σ_x}{∂x}+\frac{∂τ_{zx}}{∂z}=0\)
Answer: (d).\(\frac{∂σ_x}{∂x}+\frac{∂τ_{zx}}{∂z}=0\)
Question 132. For both plane stress as well as plain strain case the equilibrium equation in z-direction is _______
  1.    \(\frac{∂τ_{xz}}{∂x}+\frac{∂σ_z}{∂z}+γ=0\)
  2.    \(\frac{∂σ_x}{∂x}+\frac{∂τ_{zx}}{∂z}+γ=1\)
  3.    \(\frac{∂σ_x}{∂x}+\frac{∂τ_{yx}}{∂y}+γ=0\)
  4.    \(\frac{∂σ_x}{∂x}+\frac{∂τ_{zx}}{∂z}=0\)
 Discuss Question
Answer: Option A. -> \(\frac{∂τ_{xz}}{∂x}+\frac{∂σ_z}{∂z}+γ=0\)
Answer: (a).\(\frac{∂τ_{xz}}{∂x}+\frac{∂σ_z}{∂z}+γ=0\)
Question 133. The compatibility equation in terms of plane stress case is given by ________
  1.    \((\frac{∂^2}{∂x^2} +\frac{∂^2}{∂z^2})=0\)
  2.    \((\frac{∂^2}{∂y^2} +\frac{∂^2}{∂z^2})(σ_y+σ_z )=0\)
  3.    \((\frac{∂^2}{∂x^2} +\frac{∂^2}{∂y^2})(σ_x+σ_y )=0\)
  4.    \((\frac{∂^2}{∂x^2} +\frac{∂^2}{∂z^2})(σ_x+σ_z )=0\)
 Discuss Question
Answer: Option D. -> \((\frac{∂^2}{∂x^2} +\frac{∂^2}{∂z^2})(σ_x+σ_z )=0\)
Answer: (d).\((\frac{∂^2}{∂x^2} +\frac{∂^2}{∂z^2})(σ_x+σ_z )=0\)
Question 134. For two dimensional case, for both plane stress as well as plain strain case the compatibility equation is _______
  1.    \(\frac{∂^2 ε_x}{∂z^2} +\frac{∂^2 ε_z}{∂x^2} =\frac{∂^2 Γ_{xz}}{∂x∂z}\)
  2.    \(\frac{∂^2 ε_z}{∂z^2} +\frac{∂^2 ε_y}{∂x^2} =\frac{∂^2 Γ_{zy}}{∂z∂y}\)
  3.    \(\frac{∂^2 ε_x}{∂y^2} +\frac{∂^2 ε_y}{∂x^2} =\frac{∂^2 Γ_{xy}}{∂x∂y}\)
  4.    \(\frac{∂^2 ε_z}{∂z^2} +\frac{∂^2 ε_y}{∂x^2} =0\)
 Discuss Question
Answer: Option A. -> \(\frac{∂^2 ε_x}{∂z^2} +\frac{∂^2 ε_z}{∂x^2} =\frac{∂^2 Γ_{xz}}{∂x∂z}\)
Answer: (a).\(\frac{∂^2 ε_x}{∂z^2} +\frac{∂^2 ε_z}{∂x^2} =\frac{∂^2 Γ_{xz}}{∂x∂z}\)
Question 135. The Boussinesq equation representing the vertical stress is ___________
  1.    \(σ_z=\frac{3}{2π} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{5/2}\)
  2.    \(σ_z=\frac{3Q}{2π} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^5\)
  3.    \(σ_z=\frac{3Q}{2πz^2}\left[\frac{1}{1+(\frac{r}{z})^2} \right]^{\frac{5}{2}}\)
  4.    \(σ_z=\frac{3Q}{2π} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^2\)
 Discuss Question
Answer: Option C. -> \(σ_z=\frac{3Q}{2πz^2}\left[\frac{1}{1+(\frac{r}{z})^2} \right]^{\frac{5}{2}}\)
Answer: (c).\(σ_z=\frac{3Q}{2πz^2}\left[\frac{1}{1+(\frac{r}{z})^2} \right]^{\frac{5}{2}}\)
Question 136. The Boussinesq equation representing the tangential stress is ___________
  1.    \(τ_{rz}=\frac{3}{2πz^3} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{5/2}\)
  2.    \(τ_{rz}=\frac{3Qr}{2π} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^5\)
  3.    \(τ_{rz}=\frac{3Qr}{2πz^3} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{\frac{5}{2}}\)
  4.    \(τ_{rz}=\frac{3Q}{2πz^3} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^2\)
 Discuss Question
Answer: Option C. -> \(τ_{rz}=\frac{3Qr}{2πz^3} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{\frac{5}{2}}\)
Answer: (c).\(τ_{rz}=\frac{3Qr}{2πz^3} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{\frac{5}{2}}\)
Question 137. The Boussinesq influence factor is given by ____________
  1.    \(K_B=\frac{3Q}{2πz} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{5/2}\)
  2.    \(K_B=\frac{3Q}{2π} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{\frac{5}{2}}\)
  3.    \(K_B=\frac{3}{2π} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{\frac{5}{2}}\)
  4.    \(K_B=\frac{3}{2πz} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{\frac{5}{2}}\)
 Discuss Question
Answer: Option C. -> \(K_B=\frac{3}{2π} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{\frac{5}{2}}\)
Answer: (c).\(K_B=\frac{3}{2π} \left[\frac{1}{1+(\frac{r}{z})^2} \right]^{\frac{5}{2}}\)
Question 138. ____________ is not the vertical pressure distribution diagram, which can be prepared by Boussinesq’s theory.
  1.    stress isobars
  2.    vertical pressure distribution on a horizontal plane
  3.    horizontal pressure distribution on a horizontal plane
  4.    vertical pressure distribution on a vertical plane
 Discuss Question
Answer: Option C. -> horizontal pressure distribution on a horizontal plane
Answer: (c).horizontal pressure distribution on a horizontal plane
Question 139. The intensities of pressure below a point load where r=0 on axis of loading is ____________
  1.    \(σ_z=\frac{0.4775Q}{z^2} \)
  2.    \(σ_z=\frac{0.7Q}{z^2} \)
  3.    \(σ_z=\frac{0.4775Q}{z^3} \)
  4.    \(σ_z=\frac{0.8Q}{z}\)
 Discuss Question
Answer: Option A. -> \(σ_z=\frac{0.4775Q}{z^2} \)
Answer: (a).\(σ_z=\frac{0.4775Q}{z^2} \)
Question 140. An isobar is a curve connecting all points of _______ below the ground.
  1.    equal vertical pressure
  2.    unequal vertical pressure
  3.    equal horizontal pressure
  4.    unequal horizontal pressure
 Discuss Question
Answer: Option A. -> equal vertical pressure
Answer: (a).equal vertical pressure

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