1. Compound Normal & Shear Stresses
Lecture # 25
Compound Normal & Shear Stresses
Problem…
Find the state of stress at point A, B and C, which are
contained in a plane 100in from the free end,
Show stress over an element. y
40N C
30N A B z
12mm x
Free End
100mm
6mm

2. Internal forces and moments
Solution…
Internal forces and moments x y z
40N
30N 30
4000 60 40
3000 y
Summary:
N = 0
Mz = 4000
My = 3000
Vz = 30
Vy = 40
T = 60

3. Compound Normal Stress…

4. Compound Shear Stress…

5. 2 3  x-plane 4 5 6  y-plane 7 8 9  z-plane y 69.4 0.833 0.625 z
41.6
0.269
0.625
0.833 2 1 3 6 4 5 9 7 8
 x-plane
 y-plane
 z-plane

6. Stress Transformation
Objective:
To be able to find the maximum stress and the
maximum shear stress and their orientation.

7. Plane, Stress Transformation
+ Fx’ = 0;
+ Fy’ = 0;

9. Principal Normal Stress

10. Maximum Shear Stress

11. Mohr's Circle

12. R = distance between A and C max = C + R min = C – R max =  R min
A (x, xy) R
2P
2S
R = distance between A and C
max = C + R
min = C – R
max =  R
min
2S + 2P = 90o

13. The enD