Engineering Questions with Answers - Multiple Choice Questions

# Stress Distribution – Vertical Pressure – 1

1 - Question

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,
(σz)max=0.0888Qr2
∴ (σz)max=0.08882022
∴ z)max=0.444 kN/m2.

2 - Question

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
(σz)max=0.0888Qr2
∴ Q=(σz)maxr20.0888
∴ Q=0.111420.0888
Q=20 kN.

3 - Question

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,
σz=3Q2πz2[11+(rz)2]52
∴ σz=3202π42
∴ σz=0.597 kN/m2.

4 - Question

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
σz=0.2733Qz2
σz=0.27332062
σz=0.1518 kN/m2.

5 - Question

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
σz=0.4775Qz2
σz=0.47753022
∴ σz=3.58kN/m2.

6 - Question

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,
KB=32π[11+(rz)2]52
KB=32π[11+(0.3)2]52
KB=0.3840.

7 - Question

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 - Question

When the maximum vertical stress (σz)max=0.0888Qr2 at a point, the shear stress at that point is ____________
a) τrz=0.0888Qr2
b) τrz=0.0725Qr2
c) τrz=0.234Qr2
d) τrz=0.328Qr2

Explanation: Since the shear stress is given by the relation,
τrz=(σz)maxrz
For maximum vertical stress,
r/z=0.817
∴ τrz=0.0888Qr20.817
∴ τrz=0.0725Qr2.

9 - Question

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
τrz=0.0725Qr2
τrz=0.07252022
∴ τrz=0.3625 kN/m2.

10 - Question

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 - Question

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%