Question

At a point in a stressed body, the principal stresses are σ_x = 80 kN/m² (tensile) and σ_y = 40 kN/m² (Compressive). Determine normal and tangential stresses on planes whose normal are at 30° arid 120° with x-axis using Mohr’s stress circle Method.

Answer 1

Steps: 

1. Taking origin at O draw the axes. 

2. Cut off OA = σ_x = 80 kN/m² and OB = – σ_y = – 40 kN/m². Let us choose a suitable scale, say 1 mm = 2 kN/m² 

3. Bisect AB at C.

4. With C as centre and CA as radius, draw a circle, which is Mohr’s circle. 

5. At C draw a straight line CP making an angle 2θ = 60º with CX. 

6. From P draw perpendicular to OX to intersect at Q. 

7. Then OQ = σ and PQ = τ 

It is found σ = 50 kN/m² and τ = 52kN/m²

Similarly, at C draw a straight line, CP making an angle 2θ = 240° with CX. From P′ draw perpendicular to OX to intersect at Q′. Then 

OQ′ = σ = –10kN/m² and P′Q′= –52 kN/m²