Soil Mechanics Questions and Answers – Stress Distribution – Vertical Pressure – 1

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This set of Soil Mechanics Multiple Choice Questions & Answers (MCQs) focuses 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

Explanation: Given,
The maximum vertical stress is given by,
$$(σ_z)_{max}=\frac{0.0888Q}{r^2}$$
∴ $$(σ_z){max}=\frac{0.0888*20}{2^2}$$
∴ (σz)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

Explanation: Given,
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

Explanation: Given,
Z=4m
Q=20 kN
r=0
The Boussinesq’s vertical stress σz is given by,
$$σ_z=\frac{3Q}{2πz^2}\left[\frac{1}{1+(\frac{r}{z})^2}\right]^{\frac{5}{2}}$$
∴ $$σ_z=\frac{3*20}{2π4^2}$$
∴ σz=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

Explanation: Given,
r/z=0.5
Q=20 kN
Z=6m
$$σ_z=\frac{0.2733Q}{z^2}$$
$$σ_z=\frac{0.2733*20}{6^2}$$
σz=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

Explanation: Given,
Z=2m
Q=30 kN
$$σ_z=\frac{0.4775Q}{z^2}$$
$$σ_z=\frac{0.4775*30}{2^2}$$
∴ σz=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

Explanation: Given,
r/z=0.3
The Boussinesq influence factor is given by,
$$K_B=\frac{3}{2π}\left[\frac{1}{1+(\frac{r}{z})^2}\right]^{\frac{5}{2}}$$
$$K_B=\frac{3}{2π}\left[\frac{1}{1+(0.3)}^2\right]^{\frac{5}{2}}$$
KB=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%

Explanation: Given,
r/z=0.5
The maximum KB is given by,
r/z=0, therefore KB=0.4775
for r/z=0.5, KB=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) $$τ_{rz}=\frac{0.328Q}{r^2}$$

Explanation: 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

Explanation: Given,
r=2m
Q=20 kN
$$τ_{rz}=\frac{0.0725Q}{r^2}$$
$$τ_{rz}=\frac{0.0725*20}{2^2}$$
∴ τrz=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%

Explanation: Given,
r/z=1
The maximum KB is given by,
r/z=0, therefore KB=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%

Explanation: Given,
r/z=2
The maximum KB is given by,
r/z=0, therefore KB=0.4775
for r/z=0.5, KB=0.0085
∴ the Boussinesq influence factor is 0.0085/0.4775*100=1.8% of the maximum.

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