Question

Normal and shear stresses on two planes at a point are shown in Fig. 3.36. Draw a Mohr’s stress circle at the point and determine the angle between the planes. What are the principal stresses at the point?

Answer 1

On two planes shear stresses are not equal and opposite, so θ ≠ 90°. Choose an x–y coordinate system. To some suitable scale take OA = 100 MPa. 

AB = +40 MPa 

OC = +40 MPa 

OD = +30 MPa 

Two points B and D lie on Mohr’s stress circle at the point (Fig. 3.37). Join B and D and draw perpendicular bisector of line BD, meeting the x-axis at E. Join BE and ED. With E as centre, draw a circle of radius EB or ED, which intersects x-axis at H and I.

Angle between the planes ∠BED = 2θ

 1/2 ∠ BED = 40° 

Principal stresses, p₁ = OH = 122 MPa, p₂ = OI = 29 MPa.