1.Easy
A point in a loaded part has σₓ = 60 MPa, σᵧ = 50 MPa and τₓᵧ = −50 MPa (tension positive). Find the largest principal stress σ1.
σx = 60 MPaσy = 50 MPaτxy = −50 MPa
σ1 = MPa
Mohr’s circle & stress transformation worksheet with answers
2.Easy
A point on the surface of a shaft in torsion is in pure shear with τₓᵧ = 30 MPa (σₓ = σᵧ = 0). Find the normal stress σθ on a plane whose normal is rotated 30° counter-clockwise from the x-axis.
τxy = 30 MPaθ = 30°
σθ = MPa
3.Medium
A point in a thin plate is in plane stress: σₓ = 100 MPa, σᵧ = 60 MPa and τₓᵧ = 30 MPa, with σz = 0. Find the absolute maximum shear stress τabs at the point (considering all planes in three dimensions).
σx = 100 MPaσy = 60 MPaτxy = 30 MPaσz = 0
τabs = MPa
4.Medium
A point has σₓ = 80 MPa, σᵧ = 20 MPa and τₓᵧ = −30 MPa (tension positive). Find the angle θs, between −90° and 90°, from the x-axis to the normal of the plane on which the shear stress has its maximum positive value +R (shear positive in the same sense as τₓᵧ).
σx = 80 MPaσy = 20 MPaτxy = −30 MPa
θs = °
5.Hard
A point in a loaded part has σₓ = 120 MPa, σᵧ = 40 MPa and τₓᵧ = 50 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 15° counter-clockwise from the x-axis.
σx = 120 MPaσy = 40 MPaτxy = 50 MPaθ = 15°
σθ = MPa
6.Hard
A solid shaft of diameter 20 mm carries an axial compressive force of 50 kN together with a torque of 500 N·m. At the surface of the shaft, find the maximum in-plane shear stress τmax.
d = 20 mmF = −50 kNT = 500 N·m
τmax = MPa
Answer key
- 1. σ1 = 105.2 MPa
- 2. σθ = 25.98 MPa
- 3. τabs = 58.03 MPa
- 4. θs = −67.5 °
- 5. σθ = 139.6 MPa
- 6. τmax = 328.1 MPa
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