250+ TOP MCQs on Stress Distribution – Vertical Pressure – 1 and Answers

Soil Mechanics Multiple Choice Questions on “Stress Distribution – Vertical Pressure – 1”.

1. The maximum vertical stress is _______ when a concentrated load of 20 kN acts at a radial distance of 2m.
a) 0.444 kN/m²
b) 0.555 kN/m²
c) 0.666 kN/m²
d) 0.777 kN/m²
Answer: a
Clarification: Given,
radial distance r=2m
load Q=20 kN
The maximum vertical stress is given by,
((σ_z)_{max}=frac{0.0888Q}{r^2} )
∴ ((σ_z){max}=frac{0.0888*20}{2^2} )
∴ ()(σ_z)_max=0.444 kN/m².

2. When the maximum vertical stress is 0.111 kN/m² at a radial distance of 4m from the point load is __________ kN.
a) 0
b) 10
c) 20
d) 30
Answer: c
Clarification: Given,
(σ_z)_max=0.111 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{0.111*4^2}{0.0888} )
Q=20 kN.

3. What will be the intensity of vertical stress at a depth of 4m directly below the concentrated load of 20 kN?
a) 0.4356 kN/m²
b) 0.244 kN/m²
c) 0.652 kN/m²
d) 0.597 kN/m²
Answer: d
Clarification: Given,
Z=4m
Q=20 kN
r=0
The Boussinesq’s vertical stress σ_z is given by,
(σ_z=frac{3Q}{2πz^2}left[frac{1}{1+(frac{r}{z})^2}right]^{frac{5}{2}})
∴ (σ_z=frac{3*20}{2π4^2})
∴ σ_z=0.597 kN/m².

4. If r/z ratio is 0.5 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) 0.597 kN/m²
Answer: c
Clarification: Given,
r/z=0.5
Q=20 kN
Z=6m
(σ_z=frac{0.2733Q}{z^2} )
(σ_z=frac{0.2733*20}{6^2} )
σ_z=0.1518 kN/m².

5. If a load of 30 kN is acting on a point on the ground surface, then the intensity of vertical stress directly below the point on its axis of loading at a depth of 2m is given by __________
a) 4.356 kN/m²
b) 2.44 kN/m²
c) 3.58kN/m²
d) 5.97 kN/m²
Answer: c
Clarification: Given,
Z=2m
Q=30 kN
(σ_z=frac{0.4775Q}{z^2} )
(σ_z=frac{0.4775*30}{2^2} )
∴ σ_z=3.58kN/m².

6. The Boussinesq influence factor for r/z ratio equal to 0.3 is given by ____________
a) 0.3840
b) 0.5465
c) 0.9873
d) 0.2312
Answer: a
Clarification: Given,
r/z=0.3
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+(0.3)}^2right]^{frac{5}{2}} )
K_B=0.3840.

7. When the ratio of r/z equals to 0.5, the Boussinesq influence factor is ________ of the maximum.
a) 23%
b) 57%
c) 17.7%
d) 1.8%
Answer: b
Clarification: Given,
r/z=0.5
The maximum K_B is given by,
r/z=0, therefore K_B=0.4775
for r/z=0.5, K_B=0.2733
∴ the Boussinesq influence factor is 0.2733/0.4775*100=57% of the maximum.

8. When the maximum vertical stress ((σ_z)_{max}=frac{0.0888Q}{r^2}) at a point, the shear stress at that point is ____________
a) (τ_{rz}=frac{0.0888Q}{r^2} )
b) (τ_{rz}=frac{0.0725Q}{r^2} )
c) (τ_{rz}=frac{0.234Q}{r^2} )
d) (τ_{rz}=frac{0.328Q}{r^2} )
Answer: b
Clarification: Since the shear stress is given by the relation,
(τ_{rz}=frac{(σ_z)_{max} r}{z})
For maximum vertical stress,
r/z=0.817
∴ (τ_{rz}=frac{0.0888Q}{r^2}*0.817)
∴ (τ_{rz}=frac{0.0725Q}{r^2}. )

9. For maximum vertical stress, the shear stress is _________ if the load is 20 kN and r=2m.
a) 0.4356 kN/m²
b) 0.244 kN/m²
c) 0.1518 kN/m²
d) 0.3625 kN/m²
Answer: d
Clarification: Given,
r=2m
Q=20 kN
(τ_{rz}=frac{0.0725Q}{r^2} )
(τ_{rz}=frac{0.0725*20}{2^2} )
∴ τ_rz=0.3625 kN/m².

10. When the ratio of r/z equals to 1, the Boussinesq influence factor is ________ of the maximum.
a) 23%
b) 57%
c) 17.7%
d) 1.8%
Answer: c
Clarification: Given,
r/z=1
The maximum K_B is given by,
r/z=0, therefore K_B=0.4775
for r/z=0.5, KB=0.0844
∴ the Boussinesq influence factor is 0.0844/0.4775*100=17.7% of the maximum.

11. When the ratio of r/z equals to 2, the Boussinesq influence factor is ________ of the maximum.
a) 23%
b) 57%
c) 17.7%
d) 1.8%
Answer: d
Clarification: Given,
r/z=2
The maximum K_B is given by,
r/z=0, therefore K_B=0.4775
for r/z=0.5, K_B=0.0085
∴ the Boussinesq influence factor is 0.0085/0.4775*100=1.8% of the maximum.