1.Easy
A bar with cross-sectional area 800 mm² carries an axial tensile force of 70 kN. Find the normal stress σθ on a section whose normal makes an angle of 35° with the bar axis (tension positive).
P = 70 kNA = 800 mm²θ = 35°
σθ = MPa
Mohr’s circle & stress transformation worksheet with answers
2.Easy
A point in a loaded part has σₓ = −50 MPa, σᵧ = 110 MPa and τₓᵧ = −60 MPa (tension positive). Find the smallest principal stress σ2.
σx = −50 MPaσy = 110 MPaτxy = −60 MPa
σ2 = MPa
3.Medium
A point in a loaded part has σₓ = 110 MPa, σᵧ = 40 MPa and τₓᵧ = 50 MPa (tension positive). Find the maximum in-plane shear stress τmax.
σx = 110 MPaσy = 40 MPaτxy = 50 MPa
τmax = MPa
4.Medium
A point in a loaded part has σₓ = 160 MPa, σᵧ = 100 MPa and τₓᵧ = 30 MPa (tension positive). Find the angle θp from the x-axis to the direction of the largest principal stress, between −90° and 90°.
σx = 160 MPaσy = 100 MPaτxy = 30 MPa
θp = °
5.Hard
A point in a loaded part has σₓ = 10 MPa, σᵧ = 110 MPa and τₓᵧ = 10 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 60° counter-clockwise from the x-axis.
σx = 10 MPaσy = 110 MPaτxy = 10 MPaθ = 60°
σθ = MPa
6.Hard
A solid shaft of diameter 25 mm carries an axial tensile force of 150 kN together with a torque of 400 N·m. At the surface of the shaft, find the largest principal stress σ1.
d = 25 mmF = 150 kNT = 400 N·m
σ1 = MPa
Answer key
- 1. σθ = 58.71 MPa
- 2. σ2 = −70 MPa
- 3. τmax = 61.03 MPa
- 4. θp = 22.5 °
- 5. σθ = 93.66 MPa
- 6. σ1 = 353.6 MPa
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