250+ TOP MCQs on Stress Distribution – Vertical Pressure – 2 and Answers

Soil Mechanics Multiple Choice Questions on “Stress Distribution – Vertical Pressure – 2”.

1. For maximum vertical stress, the shear stress is _________ if the load is 30 kN and r=4m.
a) 0.4356 kN/m²
b) 0.1359 kN/m²
c) 0.1518 kN/m²
d) 0.3625 kN/m²
Answer: b
Clarification: Given,
r=4m
Q=30 kN
(τ_{rz}=frac{0.0725Q}{r^2} )
(τ_{rz}=frac{0.0725*30}{4^2} )
∴ τ_rz=0.1359kN/m².

2. What will be the intensity of shear stress at a depth of 4m and at a radial distance of 1m from concentrated load of 20 kN?
a) 0.4356 kN/m²
b) 0.244 kN/m²
c) 0.652 kN/m²
d) 0.128 kN/m²
Answer: d
Clarification: Given,
Z=4m
Q=20 kN
r=1
The Boussinesq’s shear stress τ_rz is given by,
(τ_{rz}=frac{3Qr}{2πz^3}left[frac{1}{1+(frac{r}{z})^2}right]^{frac{5}{2}} )
∴ (τ_{rz}=frac{3*20*1}{2π4^3}left[frac{1}{1+(frac{1}{4})^2}right]^{frac{5}{2}} )
∴ τ_rz=0.128 kN/m².

3. If r/z ratio is 2 and load of 20 kN is acting at a point, then the vertical pressure at a depth 6m is ____________
a) 0.4356 kN/m²
b) 0.244 kN/m²
c) 0.1518 kN/m²
d) 4.72*10^-3 kN/m²
Answer: d
Clarification: Given,
r/z=2
Q=20 kN
Z=6m
(σ_z=frac{0.0085Q}{z^2} )
(σ_z=frac{0.0085*20}{6^2} )
σ_z=4.72*10^-3 kN/m².

4. The Boussinesq influence factor for r/z ratio equal to 1 is given by ____________
a) 0.3840
b) 0.5465
c) 0.0844
d) 0.2312
Answer: c
Clarification: Given,
r/z=1
The Boussinesq influence factor is given by,
(K_B=frac{3}{2π} left[frac{1}{1+(frac{r}{z})^2}right]^{frac{5}{2}} )
(K_B=frac{3}{2π} left[frac{1}{1+1^2}right]^{frac{5}{2}} )
K_B=0.0844.

5. When the maximum vertical stress is 0.235 kN/m² at a radial distance of 4m from the point load is __________ kN.
a) 42.34
b) 10.56
c) 20.76
d) 30.65
Answer: a
Clarification: Given,
(σ_z)_max=0.235 kN/m²
r=4m
since the maximum vertical stress is
((σ_z)_{max}=frac{0.0888Q}{r^2} )
∴ (Q=frac{(σ_z)_{max}r^2}{0.0888} )
∴ (Q=frac{0.235*4^2}{0.0888} )
Q=42.34 kN.

6. The Boussinesq’s vertical pressure σ_z under a uniformly loaded circular area is given by ________
a) (σ_z=qleft[1-left[frac{1}{1+(frac{a}{z})^2}right]^{frac{3}{2}}right] )
b) (σ_z=qleft[1+left[frac{1}{1+(frac{a}{z})^2}right]^{frac{3}{2}}right] )
c) (σ_z=qleft[frac{1}{1+(frac{a}{z})^2}right]^{frac{3}{2}} )
d) (σ_z=qleft[1-left[frac{1}{1+(frac{a}{z})^2}right]^{frac{5}{2}}right] )
Answer: a
Clarification: The Boussinesq’s vertical pressure σ_z under a uniformly loaded circular area is given by,
(σ_z=qleft[1-left[frac{1}{1+(frac{a}{z})^2}right]^{frac{3}{2}}right] )

where, q=load intensity per unit area
a=radius of circle
z= depth of point.

7. The Boussinesq influence factor for uniformly distributed circular area is given by ____________
a) (K_B= left[1-left[frac{1}{1+(frac{a}{z})^2}right]^{frac{3}{2}}right] )
b) (K_B= left[1+left[frac{1}{1+(frac{a}{z})^2}right]^{frac{3}{2}}right] )
c) (K_B= left[frac{1}{1+(frac{a}{z})^2}right]^{frac{3}{2}} )
d) (K_B= qleft[1-left[frac{1}{1+(frac{a}{z})^2}right]^{frac{5}{2}}right] )
Answer: a
Clarification: The Boussinesq influence factor for uniformly distributed circular area is given by,
(K_B= left[1-left[frac{1}{1+(frac{a}{z})^2}right]^{frac{3}{2}}right] )
where the K_B= Boussinesq influence factor which is a function of r/z ratio which is a dimensionless factor.

8. If θ is the apex angle which the line joining the apex makes with the outer edge of the loading of a circular area, then the Boussinesq’s vertical pressure σ_z under a uniformly loaded circular area is given by ______________
a) σ_z=q[1-sin³θ]
b) σ_z=q[1-cos³θ]
c) σ_z=q[1-tan³θ]
d) σ_z=q[1-cos²θ]
Answer: b
Clarification: The Boussinesq’s vertical pressure σ_z under a uniformly loaded circular area is given by,
(σ_z=qleft[1-left[frac{1}{1+(frac{a}{z})^2}right]^{frac{3}{2}}right]. ) If θ is the apex angle which the line joining the apex makes with the outer edge of the loading of a circular area, then the term,
(left[frac{1}{1+(frac{a}{z})^2}right]^{frac{3}{2}} = cos^3 θ)
∴ σ_z=q[1-cos³θ].

9. The Boussinesq’s vertical pressure σ_z due to line load is given by ________
a) (σ_z=frac{5q’}{πz}frac{1}{[1+frac{x}{z}^2 ]^2} )
b) (σ_z=frac{3q’}{πz}frac{1}{[1+(frac{x}{z})^2 ]^2} )
c) (σ_z=frac{2q’}{πz}frac{1}{[1+(frac{x}{z})^2 ]^2} )
d) (σ_z=frac{2q’}{z}frac{1}{[1+⌊frac{x}{z}⌋^2 ]^2} )
Answer: c
Clarification: The Boussinesq’s vertical pressure σ_z due to line load is given by,
(σ_z=frac{2q’}{πz}frac{1}{[1+(frac{x}{z})^2 ]^2} )
Where q’=line load intensity per unit length
X=horizontal distance from line load
Z= depth of point.

10. The Boussinesq’s vertical pressure σ_z due to line load at a point situated vertically below the line load is given by ________
a) (σ_z=frac{2q’}{πz})
b) (σ_z=frac{3q’}{πz})
c) (σ_z=frac{2q’}{πz}frac{1}{[1+(z)^2 ]^2} )
d) (σ_z=frac{2q’}{z})
Answer: a
Clarification: The Boussinesq’s vertical pressure σ_z due to line load is given by,
(σ_z=frac{2q’}{πz}frac{1}{[1+(frac{x}{z})^2 ]^2} ) at a point situated vertically below the line load implies x=0
∴ (σ_z=frac{2q’}{πz}frac{1}{[1+(frac{0}{z})^2 ]^2} )
∴ (σ_z=frac{2q’}{πz}.)

11. If θ is the angle subtended by the edges of the strip load, then the Boussinesq’s vertical pressure σ_z due to strip load is given by ________
a) (σ_z=frac{q}{π}(θ+sinθ))
b) (σ_z=frac{q}{π}(θ-sinθ))
c) (σ_z=frac{q}{π}(sinθ))
d) (σ_z=frac{q}{π} θ)
Answer: a
Clarification:

The vertical pressure due to elementary line load is given by,
(∆σ_z=frac{2q’}{πz}frac{1}{[1+(frac{0}{z})^2 ]^2} )
When θ is the angle subtended by the edges of the strip load, the Boussinesq’s vertical pressure σ_z due to strip load is given by (σ_z=frac{q}{π}(θ+sinθ).)