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# Mohr – Coulomb Failure Theory

The curve obtained by plotting the normal and shear stress is called as ___________

a) Mohr’s envelope

b) Coulomb envelope

c) Strength envelope

d) Stress envelope

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Answer: c

Explanation: If the normal and shear stress corresponding to failure are plotted, then a curve is obtained. The plot or curve is called the strength envelope.

Which of the following is coulomb’s strength equation?

a) S = c + tan φ

b) C = s + c tan φ

c) S = c + σ tan φ

d) S = tan φ

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Answer: c

Explanation: Coulomb defined the function F (σ) as a linear function of σ and gave the following strength equation:

S = c + σ tan φ.

The critical shear stress causing failure of material depends upon ____________

a) Properties of the material and normal stress on the plane

b) Intermediate principal stress

c) None of the mentioned

d) All of the mentioned

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Answer: a

Explanation: According to Mohr’s strength theory, the critical shear stress causing failure depends upon the properties of the materials as well as on normal stress on the failure plane.

Theory of failure, was first proposed by ____________

a) Coulomb

b) Mohr

c) Casagrande

d) Darcy

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Answer: a

Explanation: The theory of failures was first expressed by coulomb in 1776 and later generalized by Mohr.

The Mohr-Coulomb theory can be expressed algebraically by, which of the following equation.

a) S = c + σ tan φ

b) τf = s = F(σ)

c) s = F(σ)

d) τf = F(σ)

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Answer: b

Explanation: The Mohr-Coulomb failure theory can be expressed algebraically by the equation:τf = s = F (σ)

Where, τf = s=shear stress on failure plane, at failure=shear resistance of material

F (σ) = function of normal stress.

According to Coulomb, the relationship between shear strength and normal stress could be represented by _________

a) Linear curve

b) Parabolic curve

c) Straight line

d) None of the mentioned

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Answer: b

Explanation: Coulomb considered that the relationship between shear strength and normal stress could be adequately represented by the straight line.

Mohr envelope can be considered to be straight if the angle of internal friction φ is assumed to be __________

a) 90°

b) >90°

c) <90°

d) None of the mentioned

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Answer: d

Explanation: Mohr envelope can be considered straight if the angle of internal friction φ is assumed to be a constant.

Which of the following stresses does not have any influence on strength of a material?

a) Major principal stress

b) Minor principal stress

c) Intermediate principal stress

d) Shearing stress

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Answer: c

Explanation: When a material is subjected to three dimensional stresses, the intermediate principal stress does not have any influence on the strength of material.

The parameter φ in coulomb’s equation “S = c + σ tan φ”, represents ___________

a) Shearing resistance and Angle of internal friction

b) Angle of slope

c) None of the mentioned

d) All of the mentioned

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Answer: a

Explanation: The empirical constant φ in coulomb’s equation represents angle of internal friction or shearing resistance respectively.