Engineering Questions with Answers - Multiple Choice Questions

# Stress Distribution – Boussinesq Equations

1 - Question

The problems due to stress distribution in soils due to a concentrated load was studied by _____________
a) G.B Airy
b) Terzaghi
c) Darcy
d) Boussinesq

Explanation: Boussinesq in 1885 studied and solved the problems of stress distribution in soils due to a concentrated loads acting at the ground surface. Darcy gave the law of flow of water through soils. The stress function was introduced by G.B Airy in 1862.

2 - Question

The assumption made by Boussinesq in the solutions is by the ____________
a) theory of plasticity
b) theory of elasticity
c) yield point
d) failure point

Explanation: Boussinesq in 1885 studied and solved the problems of stress distribution in soils due to a concentrated loads acting at the ground surface, by assuming a suitable stress function. The assumptions made are based on theory of elasticity.

3 - Question

The assumption of Boussinesq equation is that the soil is ______________
a) elastic
b) semi-elastic
c) plastic
d) semi-plastic

Explanation: Boussinesq solved the problems of stress distribution in soils due to a concentrated loads acting at the ground surface. The assumptions made are based on theory of elasticity. Therefore, the soil is considered to be elastic.

4 - Question

The assumption of Boussinesq equation is that the soil is ______________
a) non-homogeneous
b) homogeneous
c) plastic
d) semi-plastic

Explanation: Boussinesq solved the problems of stress distribution in soils due to a concentrated loads acting at the ground surface. The assumptions made are based on theory of elasticity. Therefore, the soil is considered to be elastic and of homogeneous nature.

5 - Question

The assumption of Boussinesq equation is that the soil is ______________
a) semi-infinite
b) infinite
c) finite
d) semi- finite

Explanation: Semi-infinite condition is when one of the dimension extends to infinity. If XY pane is considered to be ground surface and the z-axis as depth, then this condition is known as semi-infinite.

6 - Question

The Boussinesq equation representing the polar radial stress is ___________
a) σR=3Q2cosβR2
b) σR=3Q2πcosβR2
c) σR=3Q2πcosβR
d) σR=3Q2πcosβR3

Explanation: Boussinesq showed that the polar radial stress is given by,
σR=3Q2πcosβR2 where σR is the polar radial stress
cosβ=zR
R is the polar radial coordinate=√(r2+z2).

7 - Question

The Boussinesq equation representing the vertical stress is ___________
a) σz=32π[11+(rz)2]5/2
b) σz=3Q2π[11+(rz)2]5
c) σz=3Q2πz2[11+(rz)2]52
d) σz=3Q2π[11+(rz)2]2

Explanation: Boussinesq showed that the polar radial stress is given by,
σR=3Q2πcosβR2
Boussinesq’s vertical stress σz is given by,
σzRcos2 β
∴ σz=3Q2πz2[11+(rz)2]52 where, σz is the vertical stress
Q is the point load acting at the ground surface
r is the radial horizontal distance
z is the vertical distance.

8 - Question

The Boussinesq equation representing the tangential stress is ___________
a) τrz=32πz3[11+(rz)2]5/2
b) τrz=3Qr2π[11+(rz)2]5
c) τrz=3Qr2πz3[11+(rz)2]52
d) τrz=3Q2πz3[11+(rz)2]2

Explanation: Boussinesq showed that the polar radial stress is given by,
σR=3Q2πcosβR2
Boussinesq’s tangential stress σz is given by,
τrz=12σRsin2β
∴ τrz=3Qr2πz3[11+(rz)2]5/2 where, τrz is the tangential stress
Q is the point load acting at the ground surface
r is the radial horizontal distance
z is the vertical distance.

9 - Question

The Boussinesq influence factor is given by ____________
a) KB=3Q2πz[11+(rz)2]5/2
b) KB=3Q2π[11+(rz)2]52
c) KB=32π[11+(rz)2]52
d) KB=32πz[11+(rz)2]52

Explanation: The Boussinesq influence factor is given by,
KB=32π[11+(rz)2]52 where the KB= Boussinesq influence factor which is a function of r/z ratio which is a dimensionless factor.

10 - Question

a) σz=0.4775Qz2
b) σz=0.7Qz2
c) σz=0.4775Qz3
d) σz=0.8Qz