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# Generalised Hooke’s Law

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

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Answer: a

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

∴ Stress ∝ Strain.

The generalised Hooke’s law equation connecting the strain to stress contains ___________ elastic constants.

a) 40

b) 36

c) 39

d) 38

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Answer: b

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.

An elastic body is said to be homogeneous if there are ______ elastic constants.

a) 36

b) 20

c) 26

d) 30

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Answer: a

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.

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

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Answer: d

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.

The number of independent elastic constant is ______

a) 2

b) 5

c) 0

d) 6

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Answer: a

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.

In the generalised Hook’s law equation, ε_{X}=C_{11}σ_{x}+ C_{12} (σ_{Y}+σ_{Z}), the constant C_{11} is __________

a) E

b) 1/E

c) 0

d) μ

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Answer: b

Explanation: Let us consider the case of uniaxial stress,

σ_{Y}=σ_{Z}=0

∴ ε_{X}=C_{11}σ_{x}

∴ C_{11}= ε_{X}/σ_{x}=1/E.

In the generalised Hook’s law equation, ε_{X}=C_{11}σ_{x}+ C_{12} (σ_{Y}+σ_{Z}), the constant C_{12} is __________

a) E

b) 1/E

c) –μ/E

d) μ

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Answer: c

Explanation: Let us consider the case of uniaxial stress,

σ_{Y}=σ_{Z}=0

∴ ε_{X}=C_{11}σ_{x}

∴ C_{11}= ε_{X}/σ_{x}=1/E and let, ε_{Y}= ε_{Z}= C_{12}σ_{x}

C_{12}σ_{x}=E ε_{X}

∴ C_{12}=(1/E)*( ε_{Y}/ ε_{X})

∴ C_{12}=–μ/E.

The modulus of elasticity in MPa for very soft clay is __________

a) 2-15

b) 15-60

c) 50-81

d) 100-200

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Answer: a

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.

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

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Answer: a

Explanation: The range of Poisson’s ratio μ for loess is 0.1-0.3. The range of Poisson’s ratio μ for unsaturated clay is also 0.1-0.3. For saturated clay it is 0.4-0.5. For silt it is 0.3-0.35.