Shear Strength - II

Consider a mass of soil acted upon by several forces:

 

Figure 1

Assumptions:
1. Forces act in 2-dimensional plane
2. Resolve forces into components on a small element, say at point O above, and on a plane passing through O at an angle alpha to the horizontal.
3. Sign convention: Use the following

 

Fig. 2: Sign convention

Resolution of forces of first figure into components on a small element at point O:

Fig. 3: Resolution of forces in Fig. 1 into components on a small element at point O.

Length CA = 1; Depth into the screen = 1; Length AB = cos(alpha); CB = sin(alpha)

4. Equilibrium and development of Mohr's circle:
   I've provided this because I believe it is essential to understand the practicality of an issue from theoretical point of view as well.

Please do let me know if you I have missed anything in my attempt to dissect shear strength. You'll observe that the discussions and problems in shear strength will become interesting as we move along.