### Mohr Circle

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
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 P1 and P2 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 = P1 and OB =P2
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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