Question

The stresses on two mutually perpendicular planes are 40N/mm² (Tensile) and 20N/mm² (Tensile). The shear stress across these planes is 10N/mm². Determine by Mohr’s circle method the magnitude and direction of resultant stress on a plane making an angle 30º with the plane of first stress.

Answer 1

For the given stress system, the mohr’s circle has been drawn and this depicts as shown in fig.

OA = σx = 40N/mm² 

OB = σy = 20N/mm² 

AE = BF = τ = 10N/mm² 

2θ = 120º 

Scale 1cm = 5N/mm² 

From Measurement: 

σ_n = OQ = 27N/mm² 

σ_t = PQ = 13.5N/mm² 

σ_r = OP = 30N/mm² 

And ϕ = 27º