1.Easy
A point in a loaded part has σₓ = 150 MPa, σᵧ = 110 MPa and τₓᵧ = −20 MPa (tension positive). Find the largest principal stress σ1.
σx = 150 MPaσy = 110 MPaτxy = −20 MPa
σ1 = MPa
Mohr’s circle & stress transformation worksheet with answers
2.Easy
At a point in a loaded part the in-plane principal stresses are σ₁ = 60 MPa and σ₂ = 0 MPa (tension positive). Find the normal stress σavg that acts on the planes of maximum in-plane shear stress.
σ1 = 60 MPaσ2 = 0 MPa
σavg = MPa
3.Medium
A point has σₓ = 160 MPa, σᵧ = 20 MPa and τₓᵧ = 30 MPa (tension positive). The element is rotated 35° counter-clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.
σx = 160 MPaσy = 20 MPaτxy = 30 MPaθ = 35°
σy′ = MPa
4.Medium
A point has σₓ = 50 MPa and σᵧ = 60 MPa. How large can the shear stress τxy (magnitude) become before the largest principal stress reaches 100 MPa?
σx = 50 MPaσy = 60 MPaσ1 = 100 MPa
τxy = MPa
5.Hard
A point in a loaded part has σₓ = 140 MPa, σᵧ = 0 MPa and τₓᵧ = −60 MPa (tension positive). Find the shear stress τθ on a plane whose normal is rotated 50° counter-clockwise from the x-axis (positive in the same sense as τₓᵧ).
σx = 140 MPaσy = 0 MPaτxy = −60 MPaθ = 50°
τθ = MPa
6.Hard
A solid shaft of diameter 20 mm carries an axial tensile force of 40 kN together with a torque of 400 N·m. At the surface of the shaft, find the maximum in-plane shear stress τmax.
d = 20 mmF = 40 kNT = 400 N·m
τmax = MPa
Answer key
- 1. σ1 = 158.3 MPa
- 2. σavg = 30 MPa
- 3. σy′ = 37.87 MPa
- 4. τxy = 44.72 MPa
- 5. τθ = −58.52 MPa
- 6. τmax = 262.5 MPa
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