1. The vertical compressive stress at a point in a soil is 100kN/m2 while the horizontal compressive stress at the same point is 57kN/m2. Both stresses are principal stress.
(a) Draw the Mohr circle that describes the 2D stress state at the point.
(b) Find the maximum shear stress that acts at the point.
(c) Determine the angle of the plane on which the maximum shear stress acts.
2. On a failure plane in a cohesion-less soil mass, the shear and normal stresses at failure are 4.2kPa and 15.5kPa, accordingly. Use the Mohr circle to determine the principal stresses at failure, the friction angle of the soil and the angle of inclination of the failure plane to the horizontal. Assume a 2D stress state and the major principal stress acts on the horizontal plane (i.e., σ1 = σv ).
3. A mass of cohesion-less sand is in plane stress condition. The following stress state is measured. (1) Normal stress on horizontal plane = 296kPa. (2) Normal stress on vertical plane = 160kPa. Shear stress on horizontal and vertical planes = 64kPa. Draw the Mohr circle based on this information, and find the magnitude and direction of the principal stresses.
4. The state of the plane stress in a body is described by the following stresses:
the major principal stress = 8,500kPa in compression, and the minor principal stress = 1,500kPa in tension. Determine by the means of Mohr circle the normal and shear stresses on a plane inclined at 20 degree to the plane on which the minor principal stress acts. Check the results you obtained from the Mohr circle with analytical solution available in the textbook.