Short Notes: Mohr's Circle For Plane Stress and Plane Strain | Short Notes for Civil Engineering - Civil Engineering (CE) PDF Download

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Mohr's Circle For Plane Stress and Plane Strain 
Mohr's circle is the locus of points representing magnitude of normal and shear 
stress at various plane in a given stress element.Graphically, variation of normal 
stress and shear stress are studied with the help of Mohr's circle.
(Tl , £ 7 -
are Principal Stress then normal and shear stress on lane which is inclined at 
angle '0’ from major principal plane, then
D ifferent stress diagram
Normal stress:
Page 2


Mohr's Circle For Plane Stress and Plane Strain 
Mohr's circle is the locus of points representing magnitude of normal and shear 
stress at various plane in a given stress element.Graphically, variation of normal 
stress and shear stress are studied with the help of Mohr's circle.
(Tl , £ 7 -
are Principal Stress then normal and shear stress on lane which is inclined at 
angle '0’ from major principal plane, then
D ifferent stress diagram
Normal stress:
cr, + cr. cr, - cr
^-cos2d
Shear stress:
c r , + c r .
-=-sin 2 6 r = -
General State of Stress at an Element:
If
ax,oy
are normal stress on vertical and horizontal plane respectively and this plane is 
accompanied by shear stress then normal stress and shear stress on plane, which 
Is Inclined at an angle 6 from plane of
M ohr-s circle approach as slate ot stress 
then,
ag = ^ cos20 + rxy sin26
T0 ~ ~ {^ X 2 ~ ) s' n20 - Txy COS20
Let
< J X ,C T y
be two normal stresses(both tensile) and
T xy
be shear stress then,
• Maximum and Minimum Principal Stresses are:
• Radius of Mohr’s circle:
Page 3


Mohr's Circle For Plane Stress and Plane Strain 
Mohr's circle is the locus of points representing magnitude of normal and shear 
stress at various plane in a given stress element.Graphically, variation of normal 
stress and shear stress are studied with the help of Mohr's circle.
(Tl , £ 7 -
are Principal Stress then normal and shear stress on lane which is inclined at 
angle '0’ from major principal plane, then
D ifferent stress diagram
Normal stress:
cr, + cr. cr, - cr
^-cos2d
Shear stress:
c r , + c r .
-=-sin 2 6 r = -
General State of Stress at an Element:
If
ax,oy
are normal stress on vertical and horizontal plane respectively and this plane is 
accompanied by shear stress then normal stress and shear stress on plane, which 
Is Inclined at an angle 6 from plane of
M ohr-s circle approach as slate ot stress 
then,
ag = ^ cos20 + rxy sin26
T0 ~ ~ {^ X 2 ~ ) s' n20 - Txy COS20
Let
< J X ,C T y
be two normal stresses(both tensile) and
T xy
be shear stress then,
• Maximum and Minimum Principal Stresses are:
• Radius of Mohr’s circle:
t (— v© y
(°y ~ t*y) P(°a» • ^ m ax)
0
- d;
T(+ve) ,
SA
K V )
M ohr s circle for plane stressed
Strength of Materials
Observations from Mohr's Circle
The following are the observations of Mohr's circle as
* At point M on circle on is maximum and shear stress is zero. 
Maximum principal stress = coordinate of M
* At point N on circle on is minimum and shear stress t is zero, 
minimum principal stress = coordinate of N
* At point P on Circle t is maximum.
Maximum shear stress = ordinate of P(i.e. radius of circle) 
Also, normal stress on plane of maximum shear stress
Where, on = Average stress
* Mohr's circle becomes zero at a point if radius of circle has the following 
consideration.
Radius of circle
* If ax = oy, then radius of Mohr's circle is zero and rxy = 0
• The sum of normal stresses acting on perpendicular faces of a plane stress 
elements is constant and independent of the angle 0 .
a i + a 2 - a i + a 2