Theoretical Foundation Engineering
Featuring an easy-to-understand format where detailed mathematical treatment is kept to a minimum, this in-depth book provides numerous charts, drawings, and illustrations to illuminate the problems and theory.
TABLE OF CONTENTS Theoretical Foundation Engineering
Appendix A: The Pole Method for Finding Stresses from Mohr's Circle
In geotechnical engineering, Mohr's circle is an extremely useful tool for determination of stresses on a given plane in a soil mass. The principles of Mohr's circle will be demonstrated in this appendix.
Let ABCD be a soil element as shown in Fig. A.I. The stresses on the horizontal faces ( AB and CD) of the element are:
| Normal stress | + ? x |
| Shear stress | + ? |
Figure A.1: The pole method for finding stresses along a plane.
Figure A.1: (Continued).
Similarly, the stresses on the vertical faces ( AD and BC) are:
| Normal stress | + ? y |
| Shear stress | ?? |
The sign conventions used for the stresses stated above are:
| Normal stress | + ve for compression |
| Shear stress | + ve if they act on opposite in such as way as to create terclockwise rotation faces counterclockwise rotation |
The above-mentioned stresses on the vertical and horizontal planes of the soil element are presented in a graphical form as points M and N, respectively, in Fig. A.lb. In this figure
If a circle is drawn with X as the center and XM as the radius it will be referred to as the Mohr's circle. Point M represents the stresses on the horizontal plane. So, if a line is drawn from this point which is parallel to the plane on which the corresponding stresses act (in this case, horizontal plane), it will intersect the Mohr's circle at point P,...
Copyright Braja M. Das 2007 under license agreement with Books24x7
