Mohr Circle - Globarena

nothingstockingsMechanics

Oct 30, 2013 (3 years and 9 months ago)

85 views

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

Click to view Image

Mohr’s Circle

Mohr circle for like forces

Click to view Image

Mohr’s Circle

Mohr circle for unlike forces

Click to view Image

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