1. Mohr Circle Pole Method FAMU-FSU College of Engineering Department of Civil Engineering Soil Mechanics CEG 3011 By Kamal Tawfiq, Ph.D., P.E. Fall 2007

2. (+F x, + J xy ) FxFx FnFn FyFy (+F y, - J xy ) +J+J Center A B O -J xy +J xy F1F1 F2F2 -J-J FyFy FxFx J xy FyFy FxFx (+) (-) Sign of Shear Stress is based on the rotation of the shear I. Draw Mohr Circle 1- Locate Points A & B 2- Connect Points A & B with a stright line 3- Line A B intersects axis F n at the center of the circle (o) 4- Usin your Compass, draw a circle with a radius = OA. 5- Mohr circle will intersects F n axis at pints F 1 and F 2. 6- F 1 and F 2 represent the major and minor principal stresses. 7- Determine the magnitudes of F 1 and F 2. FxFx FyFy

3. FxFx Pole FnFn F1F1 F2F2 -J-J FyFy +J+J (+F y, - J xy ) (+F x, + J xy ) FyFy J xy FyFy FxFx FxFx II. Establishing the Pole on the Circle 7- Determine the orintation of the plane at which + F y and - J xy are acting (Horizontal) 8- Draw a line from point (+F y, - J xy ) on Mohr Circle parallel to the plane ( // ) 9- Determine the orintation of the plane at which + F y and + J xy are acting (Vertical) 10- Draw a line from point (+F y, - J xy ) on Mohr Circle parallel to the plane (/// ) 11- Extend the two lines (//) and (///) so that they intersect on the circumference of Mohr Circle. 12- This intersection represents the POLE

4. F x, J xy FyFy FxFx J xy FyFy FxFx FxFx Pole F2F2 FnFn F1F1 F2F2 2 -J-J FyFy F y, J xy F1F1 +J+J III. Establishing the Directions of the Principal Stresses (2) 13- From the Pole extend two lines. One through F 1 and another through F 2. 14- The directions of these two lines represents 2.

5. F x, J xy FxFx Pole F2F2 FnFn F1F1 F2F2 2 -J-J FyFy F y, J xy F1F1 +J+J 2 FyFy FxFx J xy FyFy FxFx F2F2 F1F1 F1F1 F2F2

6. B FyFy FxFx FyFy FxFx (+F n, + J n ) FxFx FnFn FyFy (+F y, - J xy ) +J+J Center A O -J xy +J xy F1F1 F2F2 -J-J B 2 J xy Pole X (+F x, + J xy ) FnFn JnJn Plane where F 1 is acting Plane where F 2 is acting M o h r C i r c l e Pole Method