1.Easy
A bar with cross-sectional area 400 mm² carries an axial tensile force of 50 kN. Find the magnitude of the shear stress |τθ| on a section whose normal makes an angle of 40° with the bar axis.
P = 50 kNA = 400 mm²θ = 40°
|τθ| = MPa
Mohr’s circle & stress transformation worksheet with answers
2.Easy
A point in a loaded part has σₓ = 80 MPa, σᵧ = 110 MPa and τₓᵧ = 30 MPa (tension positive). Find the smallest principal stress σ2.
σx = 80 MPaσy = 110 MPaτxy = 30 MPa
σ2 = MPa
3.Medium
A point has σₓ = 140 MPa, σᵧ = 100 MPa and τₓᵧ = −10 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 = 140 MPaσy = 100 MPaτxy = −10 MPa
θs = °
4.Medium
A point has σₓ = 130 MPa, σᵧ = 10 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 = 130 MPaσy = 10 MPaτxy = −30 MPa
θs = °
5.Hard
A point in a thin plate is in plane stress: σₓ = −40 MPa, σᵧ = −60 MPa and τₓᵧ = 10 MPa (σz = 0). Find the von Mises equivalent stress σvM.
σx = −40 MPaσy = −60 MPaτxy = 10 MPa
σvM = MPa
6.Hard
A solid shaft of diameter 30 mm carries an axial tensile force of 110 kN together with a torque of 400 N·m. At the surface of the shaft, find the largest principal stress σ1.
d = 30 mmF = 110 kNT = 400 N·m
σ1 = MPa
Answer key
- 1. |τθ| = 61.55 MPa
- 2. σ2 = 61.46 MPa
- 3. θs = −58.28 °
- 4. θs = −58.28 °
- 5. σvM = 55.68 MPa
- 6. σ1 = 186.2 MPa
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