Evaluate the normal and tangential stresses:

Q. 20: At the point in stressed body, the principal stresses are σ_x = 80 kN/m² and σ_y = 40 kN/m². Determine the normal and tangential stresses on planes whose normal are at 30° arid 120° with  x axis by using Mohr's stress circle Method.

Sol.:

Steps:

1. Taking origin at the O draw 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 that is Mohr's circle.

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

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

7. Then OQ = σ and PQ =  τ

It is found σ = 50 kN/m² 

and  τ = 52kN/m² .......ANS

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

OQ′ = σ = -10kN/m²    and P′ Q′-52 kN/m² .......ANS