Question

State of stress on two perpendicular planes AC and BC is given in Fig. 3.16. Draw Mohr’* stress circle, taking BC on reference plane, determine

(i) Principal Stresses

(ii) Principal angles

(iii) Maximum shear stress

(iv) Normal and shear stresses on inclined plane AB, with θ = 30°.

Answer 1

Draw x–y coordinates ox and oy (Fig. 3.17)

To some suitable scale,

Say, 20 MPa = 10 mm

Take

OA = 100 MPa

AB = 40 MPa

(the shear stress on reference plane is positive)

OC = -40 MPa

CD = −40 MPa

Join B and D points and the line BD intersects abscissa at E, that is, the centre of Mohr’* stress circle. With E as centre and radius of the circle equal to EB or ED, draw a circle, intersecting x-axis at H and I. Draw a vertical line from E, that is, LEN.

OH = p1 (maximum principal stress) = 110 MPa

OI = p2 (minimum principal stress) = −52 MPa

Take angle BEK = 2q3 = 2 × 30 = 60°, the coordinates of point K (OM, MK) give the normal and shear stresses on inclined plane