1. Purpose of Mohr’s Circle
Visual tool used to determine the stresses that exist at a given point in relation to the angle of orientation of the stress element.
There are 4 possible variations in Mohr’s Circle depending on the positive directions are defined.

2. Sample Problem A particular point on the part Some Part y x
sy = -2 ksi
Some Part
sx = 6 ksi
txy = 3 ksi
x & y  orientation

3. Mohr’s Circle t (CW) sy = -2 ksi x-axis y-axis (6 ksi, 3 ksi) 6 3
sx = 6 ksi
(-2 ksi, -3 ksi) 2 3
txy = 3 ksi s
Center of Mohr’s Circle

4. Mohr’s Circle (savg, tmax) t (CW) sy = -2 ksi x-face sx = 6 ksi
(6 ksi, 3ksi)
txy = 3 ksi s s2 s1
savg = 2 ksi
(-2 ksi, -3ksi)
y-face
(savg, tmin)

5. Mohr’s Circle (savg, tmax) t (CW) (2 ksi, 5 ksi) sy = -2 ksi x-face
sx = 6 ksi
(6 ksi, 3ksi) R
3 ksi
txy = 3 ksi s s2 s1
4 ksi
y-face
s1 = savg + R = 7 ksi
s2 = savg – R = -3 ksi
(savg, tmin)
(2 ksi, -5 ksi)

6. Mohr’s Circle (savg, tmax) t (CW) (2 ksi, 5 ksi) sy = -2 ksi x-face
sx = 6 ksi
(6 ksi, 3ksi)
3 ksi 2q
txy = 3 ksi s s2 s1
4 ksi
y-face
(savg, tmin)
(2 ksi, -5 ksi)

7. Principle Stress Element
(savg, tmax)
(2 ksi, 5 ksi)
t (CW)
s2 = -3 ksi
x-face
(6 ksi, 3ksi)
q = °
3 ksi
s1 = 7 ksi 2q s
Principle Stress Element s2 s1
4 ksi
Rotation on element is half of the rotation from the circle in same direction from x-axis
(savg, tmin)
(2 ksi, -5 ksi)

8. Maximum Shear Stress Element
(savg, tmax)
(2 ksi, 5 ksi)
t (CW)
x-face
savg = 2 ksi
f = °
(6 ksi, 3ksi) 2f
tmax = 5 ksi
3 ksi 2q s
savg = 2 ksi s2 s1
Maximum Shear Stress Element
4 ksi
y-face
(savg, tmin)
(2 ksi, -5 ksi)

9. Relationship Between Elements
savg = 2 ksi
tmax = 5 ksi
sy = -2 ksi
savg = 2 ksi
f = °
sx = 6 ksi
q = °
s2 = -3 ksi
txy = 3 ksi
s1 = 7 ksi
q + f = ° ° = 45 °

10. What’s the stress at angle of 15° CCW from the x-axis?y
A particular point on the part V x
s = ? ksi
Some Part
s = ? ksi U
15° x
t = ? ksi
U & V  new 15° from x-axis

11. Rotation on Mohr’s Circle
(savg, tmax)
Rotation on Mohr’s Circle
t (CW)
(sU, tU)
x-face
30° s s2 s1
savg = 2 ksi
y-face
15° on part and element is 30° on Mohr’s Circle
(sV, tV)
(savg, tmin)

12. Rotation on Mohr’s Circle
(savg, tmax)
t (CW)
Rotation on Mohr’s Circle
(sU, tU)
x-face R
sU = savg + R*cos(66.869°)
sU = 3.96 ksi
sV = savg – R*cos(66.869°)
sV = ksi
tUV = R*sin(66.869°)
tUV = 4.60 ksi
66.869° s s2 s1
savg = 2 ksi
y-face
(sV, tV)
(savg, tmin)

13. What’s the stress at angle of 15° CCW from the x-axis?y
A particular point on the part V x
sV = .036 ksi
sU = 3.96 ksi
Some Part U
15° x
t = 4.60 ksi