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# Theories Of Failure

## 10 Questions MCQ Test Mock Test Series for Civil Engineering (CE) GATE 2020 | Theories Of Failure

Description
This mock test of Theories Of Failure for Civil Engineering (CE) helps you for every Civil Engineering (CE) entrance exam. This contains 10 Multiple Choice Questions for Civil Engineering (CE) Theories Of Failure (mcq) to study with solutions a complete question bank. The solved questions answers in this Theories Of Failure quiz give you a good mix of easy questions and tough questions. Civil Engineering (CE) students definitely take this Theories Of Failure exercise for a better result in the exam. You can find other Theories Of Failure extra questions, long questions & short questions for Civil Engineering (CE) on EduRev as well by searching above.
QUESTION: 1

### A certain steel has proportionality limit of 300 N/mm2 in simple tension. It is subjected to principal stress of 120 N/mm2 (tensile), 60 N/mm2 (tensile) and 30 N/mm2 (compressive). The factor of safety according to maximum shear stress theory is

Solution:

Proportionality limit shear stress
= 300/2 = 150N/mm2
Maximum shear stress ∴ Factor of safety = 150/75 = 2.0

QUESTION: 2

### All the theories of failure, will give nearly the same result when

Solution:

When one of the principal stresses at a point is large in comparison to the other, the situation resembles uniaxial tension test. Therefore all theories give nearly the same results.

QUESTION: 3

### The principal stresses developed at a point are +60, -60, 0 MPa. Using shear strain energy theory, factor of safety obtained is √3.  What is yield stress of the material?

Solution: QUESTION: 4

For ductile material the suitable theory of failure is

Solution:

For ductile material the most suitable theory is maximum shear stress theory.
Other theories for ductile material, Maximum Strain Energy Theory and Maximum Shear Stress Theory (Most Conservative Theory)
For brittle material the most suitable theory is Maximum Principal Stress Theory.
Other theories for brittle material, Maximum Principal Stress Theory.

QUESTION: 5

Which of the following theories of failure is most appropriate for a brittle material?

Solution:

Maximum principal stress theory (Rankine theory) is suitable for brittle materials.

QUESTION: 6

In a structural member, there are perpendicular tensile stresses of 100 N/mm2 and 50 N/mm2. What is the equivalent stress in simple tension, according to the maximum principal strain theory? (Poisson’s ratio = 0.25)

Solution:

Equivalent stress
= σ1 - μσ2
= 100 - 0.25 x 50 = 87.5 N/mm2

QUESTION: 7

Permissible bending moment in a circular shaft under pure bending is M, according to maximum principal stress theory of failure. According to maximum shear theory of failure, the permissible bending moment in the shaft is

Solution:

According to maximum principal stress theory,
σ1 = σy
According to maximum shear stress theory,
σ1 - σ2 = σy
Under pure bending, Therefore, in both the cases, permissible bending moment is M,

QUESTION: 8

A shaft subjected to pure torsion is to be designed which of the following theories gives the largest diameter of shaft?

Solution:

It is clear from the relation T/J = (Shear Stress)/ (Radial Distance) that a shaft subjected to pure torsion is to be designed for maximum shear stress theory.

QUESTION: 9

If maximum principal stress σ1 = 60 N/mm2, σ2 and σ3 of value zero act on a cube of unit dimensions, then the maximum shear stress energy stored in it would be

Solution:

Shear strain energy QUESTION: 10

In a 2D stress system, the two principal stress are p1 = 180 N/mm2 (tensile) and p2 (compressive). For the materials, yield stress in simple tension and compression is 240 N/mm2 and Poisson’s ratio is 0.25. According to maximum normal strain theory for what value of p2 shall yielding commence?

Solution:

Yielding may occur either in tension or compression.
For yielding in tension,
According to normal strain theory, For yielding in compression, 