Engineering Questions with Answers - Multiple Choice Questions

# Generalised Hooke’s Law

1 - Question

Hooke’s law states that within elastic limit, ______
a) stress is directly proportional to strain
b) stress is inversely proportional to strain
c) stress does not depend on strain
d) stress is equal to strain

Explanation: In the simplest form, the Hooke’s law states that within the elastic limit, stress is directly proportional to strain.
∴ Stress ∝ Strain.

2 - Question

The generalised Hooke’s law equation connecting the strain to stress contains ___________ elastic constants.
a) 40
b) 36
c) 39
d) 38

Explanation: The generalised Hooke’s law equation connecting the strain to stress contains 36 elastic constants. These elastic constants are independent of the stress components at a point.

3 - Question

An elastic body is said to be homogeneous if there are ______ elastic constants.
a) 36
b) 20
c) 26
d) 30

Explanation: The generalised Hooke’s law equation connecting the strain to stress contains 36 elastic constants. When there are only 36 constants, then the elastic body is said to be homogeneous.

4 - Question

An elastic body is said to be isotropic if the elastic constants are ______
a) same only in y- direction
b) same only in x- direction
c) different in al direction
d) same in all direction

Explanation: When the elastic constants are same in all the direction at a point in a soil body, then the soil body is said to be isotropic. By considering the homogeneity and the isotropy, the number of elastic constants reduces to only two.

5 - Question

The number of independent elastic constant is ______
a) 2
b) 5
c) 0
d) 6

Explanation: Harr in 1966 showed that by a series of rotations of axes, the number of independent constants for a homogeneous and isotropic body is only two.

6 - Question

In the generalised Hook’s law equation, εX=C11σx+ C12 (σYZ), the constant C11 is __________
a) E
b) 1/E
c) 0
d) μ

Explanation: Let us consider the case of uniaxial stress,
σYZ=0
∴ εX=C11σx
∴ C11= εXx=1/E.

7 - Question

In the generalised Hook’s law equation, εX=C11σx+ C12 (σYZ), the constant C12 is __________
a) E
b) 1/E
c) –μ/E
d) μ

Explanation: Let us consider the case of uniaxial stress,
σYZ=0
∴ εX=C11σx
∴ C11= εXx=1/E and let, εY= εZ= C12σx
C12σx=E εX
∴ C12=(1/E)*( εY/ εX)
∴ C12=–μ/E.

8 - Question

The modulus of elasticity in MPa for very soft clay is __________
a) 2-15
b) 15-60
c) 50-81
d) 100-200

Explanation: The modulus of elasticity in MPa for very soft clay is 2-15 MPa. For loess it is 15-60 MPa. For dense sand it is 50-81 MPa. And for sand and gravel it is 100-200 MPa.

9 - Question

The range of Poisson’s ratio μ for loess is _________
a) 0.1-0.3
b) 0.4-0.5
c) 0.3-0.35
d) 0.9-1