Evaluate the normal and tangential stresses:
Q. 20: At the point in stressed body, the principal stresses are σ_{x }= 80 kN/m^{2} and σ_{y} = 40 kN/m^{2}. 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/m^{2}
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/m^{2}
and τ = 52kN/m^{2} .......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/m^{2 } and P′ Q′-52 kN/m^{2} .......ANS