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QUESTION: 1

When two mutually perpendicular principal stresses are unequal but like, the maximum shear stress is represented by

Solution:

QUESTION: 2

Assertion (A): A plane state of stress does not necessarily result into a plane state of strain as well.

Reason (R): Normal stresses acting along X and Y directions will also result into normal strain along the Z-direction.

Solution:

QUESTION: 3

Principal strains at a point are 100 x 10^{-6} and -200 x 10^{-6} . What is the maximum shear strain at the point?

Solution:

don' t confusewithMaximumShear stress

QUESTION: 4

The number of strain readings (using strain gauges) needed on a plane surface to determine the principal strains and their directions is:

Solution:

Three strain gauges are needed on a plane surface to determine the principal strains and their directions.

QUESTION: 5

Assertion (A): Mohr's construction is possible for stresses, strains and area moment of inertia.

Reason (R): Mohr's circle represents the transformation of second-order tensor.

Solution:

QUESTION: 6

On a plane, resultant stress is inclined at an angle of 45^{o} to the plane. If the normal stress is 100 N /mm^{2}, the shear stress on the plane is:

Solution:

QUESTION: 7

The complementary shear stresses of intensity τ are induced at a point in the material, as shown in the figure. Which one of the following is the correct set of orientations of principal planes with respect to AB?

Solution:

It is a case of pure shear so principal planes will be along the diagonal.

QUESTION: 8

A body is subjected to a pure tensile stress of 100 units. What is the maximum shear produced in the body at some oblique plane due to the above?

Solution:

QUESTION: 9

A material element subjected to a plane state of stress such that the maximum shear stress is equal to the maximum tensile stress, would correspond to

Solution:

QUESTION: 10

A solid circular shaft of diameter 100 mm is subjected to an axial stress of 50 MPa. It is further subjected to a torque of 10 kNm. The maximum principal stress experienced on the shaft is closest to

Solution:

Shear Stress

Maximum principal Stress

QUESTION: 11

The maximum principle stress for the stress state shown in the figure is

Solution:

QUESTION: 12

In a Mohr's circle, the radius of the circle is taken as:

Where, σ_{x} and σ_{y} are normal stresses along x and y directions respectively and τ_{xy} is the shear stress.

Solution:

QUESTION: 13

The Mohr's circle of plane stress for a point in a body is shown. The design is to be done on the basis of the maximum shear stress theory for yielding. Then, yielding will just begin if the designer chooses a ductile material whose yield strength is:

Solution:

According to maximum shear stress theory for yielding, for like stresses, we have

σ_{y} = 100 MPa

**Note**: For unlike stresses we have

QUESTION: 14

Determine the directions of maximum and minimum principal stresses at the point “P” from the Mohr's circle

Solution:

From the Mohr‟s circle it will give all directions

QUESTION: 15

Which one of the following Mohr‟s circles represents the state of pure shear?

Solution:

QUESTION: 16

Assertion (A): If the state at a point is pure shear, then the principal planes through that point making an angle of 45° with plane of shearing stress carries principal stresses whose magnitude is equal to that of shearing stress.

Reason (R): Complementary shear stresses are equal in magnitude, but opposite in direction.

Solution:

QUESTION: 17

When a component is subjected to axial stress the normal stress σ_{n} is maximum, if cos θ is _______ . (σ_{n}=σ_{x}Cos^{2}θ)

1. maximum

2. minimum

3. always one

4. always zero

Solution:

QUESTION: 18

An elastic material of Young‟s modulus E and Poisson‟s ratio ν is subjected to a compressive stress of σ1 in the longitudinal direction. Suitable lateral compressive stress σ 2 are also applied along the other two each of the lateral directions to half of the magnitude that would be under σ1 acting alone. The magnitude of σ2 is

Solution:

QUESTION: 19

If the principal stresses and maximum shearing stresses are of equal numerical value at a point in a stressed body, the state of stress can be termed as

Solution:

QUESTION: 20

A piece of material is subjected, to two perpendicular tensile stresses of 70 MPa and 10 MPa. The magnitude of the resultant stress on a plane in which the maximum shear stress occurs is

Solution:

QUESTION: 21

Principal stresses at a point in plane stressed element are σ_{x} = σ_{y }= 500 kg/cm2 . Normal stress on the plane inclined at 45^{o} to x-axis will be:

Solution:

When stresses are alike, then normal stress σn on plane inclined at angle 45° is

QUESTION: 22

At a point in two-dimensional stress system σx = 100 N/mm^{2}, σy = τxy = 40 N/mm^{2}. What is the radius of the Mohr circle for stress drawn with a scale of: 1 cm = 10 N/mm^{2}?

Solution:

Radius of the Mohr circle

QUESTION: 23

Assertion (A): Mohr's circle of stress can be related to Mohr's circle of strain by some constant of proportionality

Reason (R): The relationship is a function of yield stress of the material.

Solution:

QUESTION: 24

The principal strains at a point in a body, under biaxial state of stress, are 1000 ×10^{–6} and –600 × 10^{–6}. What is the maximum shear strain at that point?

Solution:

QUESTION: 25

Which of the following stresses can be determined using Mohr's circle method?

Solution:

QUESTION: 26

Normal stresses of equal magnitude p, but of opposite signs, act at a point of a strained material in perpendicular direction. What is the magnitude of the resultant normal stress on a plane inclined at 45° to the applied stresses?

Solution:

QUESTION: 27

A point in two-dimensional stress state, is subjected to biaxial stress as shown in the above figure. The shear stress acting on the plane AB is

Solution:

QUESTION: 28

What are the normal and shear stresses on the 45o planes shown?

Solution:

QUESTION: 29

If a body is subjected to stresses in xy plane with stresses of 60N/mm² and 80N/mm² acting along x and y axes respectively. Also the shear stress acting is 20N/mm²Find the maximum amount of shear stress to which the body is subjected.

Solution:

τ(max) = √( [σ(x) - σ(y) ]²/2² + τ²).

QUESTION: 30

State of stress in a plane element is shown in figure I. Which one of the following figures -II is the correct sketch of Mohr's circle of the state of stress?

Solution:

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