Question 3 The vertical compressive stress at a point in a soil is 100 kN/m2 while the horizontal compressive stress at the same point is 57 kN/m2. Both stresses are principle 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 and obtain the normal stress on that plane (Use the pole method). (d) Confirm the maximum shear stress and the normal stress from (c) using the stress transformation equations (consider sign conventions!).

Consider a point in a structural member that is subjected to plane stress. Normal and shear stress magnitudes acting on horizontal and vertical planes at the point are Sx = 72 MPa, Sy = 12 MPa, and Sxy = 39 MPa. (a) Draw Mohr's circle for this state of stress. (b) Determine the principal stresses and the maximum in-plane shear stress acting at the point. (c) Show these stresses on an appropriate sketch (e.g., see Fig. 12.15 or Fig. 12.16). (d) Determine the absolute maximum shear stress at the point. Sxy S Answer: (a) Draw Mohr's Circle for this state of stress. (b) Op1 = i MPa Op2 = i MPa Tmax in-plane i MPa (c) Show these stresses on an appropriate sketch (e.g., see Fig. 12.15 or Fig. 12.16) (d) Tabs max i MPa

Explain the auger method and the wash boring method.

2