1. Mohr's Circle - Application
Example:
The axial loading P produces the state of stress in
the material. Draw Mohr’s circle for this case.  P

2. Solution: D F C E  
A(, 0) y' x' x
45o

3. Example: The torsional loading T produces the state of stress
in the shaft. Draw Mohr’s circle for this case.  T

4. Solution: D C B  
A(0, -) x' x
45o

5. Example:
Due to the applied loading, the element at point A on the solid cylinder is subject to the state of stress shown. Determine the principal stresses acting at this point. M
6MPa
12MPa T P A

6. Solution: A D B (MPa) C 2.49 MPa x' 14.5 MPa (MPa) 22.5o x 12 R=8.496
R=8.49 A x' x
22.5o
2.49 MPa
14.5 MPa

7. Example:
The state of plane stress at a point is shown on the element. Determine the maximum in-plane shear stresses and the orientation of the element upon which they act.
90 MPa
60 MPa
20 MPa

8. Solution:

9. Example:
The state of plane stress at a point is shown on the element. Represent this state of stress on an element oriented 30o counterclockwise from the position shown.
8 MPa
12 MPa
6 MPa

10. Solution:

11. Example:
The beam is subjected to the distributed loading of w = 120 kN/m. Determine the principal stresses in the beam at point P, which lies at the top of the web. Neglect the size of the fillets and stress concentrations at this point. I = 67.4 (10-6) m4.

12. Solution:
45.4 MPa
35.2 MPa

13. The enD