Mohr’s Circle

Mohr’s Circle

The graphical method solution of complex stress

problems using Mohr's circle is a very powerful

technique, since all the information relating to any

plane within the stressed elements are contained in

the single construction

It provides the convenient and quick solution which

is less prone to arithmetical errors and is highly

recommended.

Mohr’s Circle

What is Stress

The force of resistance offered by a body against

the deformation is called the stress.

The external force acting on the body is called the

load. The load is applied on the body while the

stress is induced in the material of the body

Mohr’s Circle

Type of stress

•

Normal stress

•

Shear stress

•

Bending stress

Mohr’s Circle

Principal Stress

Any structural member is subjected to different types of

stresses such as normal or shear stresses

simultaneously. Hence it is necessary to find out the

region where the effect of these stresses will be critical

from the design point of view

When such stresses act at a point in a stressed

material, there always exist three principal planes, and

the normal stresses acting on them are called

principal

stresses

One of these principal stresses is the greatest

normal stress and one of them is the least normal

stress

Mohr’s Circle

Principal Stress

Mohr’s Circle

Mohr’s Circle

Mohr’s circle is a graphical construction making it

possible to determine the stresses in a cross

section if the principal stresses are known

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Mohr’s Circle

Mohr circle for like forces

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Mohr’s Circle

Mohr circle for unlike forces

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Mohr’s Circle

Unequal Like Principal Stress

•

Let P

1

and P

2

be

two unequal like principal

stresses.

Let it be required to find the resultant

stress on a plane inclined at an angle θ with the

major principal plane.

•

An axis OX set off OA = P

1

and OB =P

2

Click to view Image

Mohr’s Circle

Principal Stress and Stress transformation

using Mohr’s Circle

Consider a rectangular block ABCD whose thickness

perpendicular to the plane of the paper is unity. Here

the block be subjected to principal stresses p1 and p2.

Consider any oblique sectional plane BE at an angle θ

with the principal plane BA

Mohr’s Circle

Principal Stress and Stress transformation

using Mohr’s Circle

Click to view Image

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