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QUESTION: 1

‘p_{1}’ and ‘p_{2}’ are two equal tensile principal stresses. On the plane AB inclined at 45° to the plane of ‘p_{1}’ as shown in the figure below,

Solution:

The plane AB is principal plane, and at the principal plane shear stress is zero.

QUESTION: 2

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

Solution:

QUESTION: 3

For a general two dimensional stress system, what are the coordinates of the centre of Mohr’s circle?

Solution:

From the above figure coordinates of the centre are

QUESTION: 4

A Mohr’s circle reduces to a point when the body is subjected to

Solution:

When the normal stresses on the two mutually perpendicular planes are equal and alike then radius of Mohr’s circle will be zero.

i.e.

Hence Mohr’s circle reduces to a point.

QUESTION: 5

If a body carries two unlike principal stresses, what is the maximum shear stress?

Solution:

The principal stress given are unlike i.e if one is tensile and other is compressive. Let σ_{1} be tensile and σ_{2} be compressive, then

QUESTION: 6

Maximum shear stress in a Mohr’s circle

Solution:

Radius of the Mohr’s Circle

Maximum shear stress,

∴ Radius of Mohr’s circle is equal to maximum shear stress

QUESTION: 7

In a two dimensional problem, the state of pure shear at a point is characterized by

Solution:

QUESTION: 8

In a plane stress problem there are normal tensile stresses σ_{x} and σ_{y} accompanied by shear stres τ_{xy} at a point along orthogonal Cartesian co-ordinates x and y respectively. If it is observed that the minimum principal stress on a certain plane is zero then,

Solution:

Principal stresses,

Since minimum principal stress is zero, so

QUESTION: 9

State of stress at a point in a strained body is shown in figure.

Which one of the figure given below represents correctly the Mohr's circle for the state of stress?

Solution:

Mohr’s circle for pure shear stress

Since neither tensile nor compressive stress exists, the Mohr’s diagram is simply a circle of radius τ_{xy} and centre at the intersection of the two axes. It can also be verified by transformation of plane formula.

QUESTION: 10

The equivalent bending moment under combined action of bending moment M and torque T is

Solution:

Maximum principal stress,

### Stress & Strain- 2

Video | 03:26 min

### Chapter - Stress, Strain, Stress-Strain

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