1.Easy
A point on the surface of a shaft in torsion is in pure shear with τₓᵧ = −100 MPa (σₓ = σᵧ = 0). Find the normal stress σθ on a plane whose normal is rotated 20° counter-clockwise from the x-axis.
τxy = −100 MPaθ = 20°
σθ = MPa
Mohr’s circle & stress transformation worksheet with answers
2.Easy
A point in a loaded part has σₓ = 110 MPa, σᵧ = 80 MPa and τₓᵧ = 40 MPa (tension positive). Find the largest principal stress σ1.
σx = 110 MPaσy = 80 MPaτxy = 40 MPa
σ1 = MPa
3.Medium
A point in a thin plate is in plane stress: σₓ = 70 MPa, σᵧ = 0 MPa and τₓᵧ = 60 MPa, with σz = 0. Find the absolute maximum shear stress τabs at the point (considering all planes in three dimensions).
σx = 70 MPaσy = 0 MPaτxy = 60 MPaσz = 0
τabs = MPa
4.Medium
A point has σₓ = −40 MPa, σᵧ = 110 MPa and τₓᵧ = −20 MPa (tension positive). The element is rotated 25° counter-clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.
σx = −40 MPaσy = 110 MPaτxy = −20 MPaθ = 25°
σy′ = MPa
5.Hard
A point in a loaded part has σₓ = 10 MPa, σᵧ = 20 MPa and τₓᵧ = 20 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 45° clockwise from the x-axis.
σx = 10 MPaσy = 20 MPaτxy = 20 MPaθ = -45°
σθ = MPa
6.Hard
A point in a loaded part has σₓ = 100 MPa, σᵧ = 60 MPa and τₓᵧ = −50 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 60° counter-clockwise from the x-axis.
σx = 100 MPaσy = 60 MPaτxy = −50 MPaθ = 60°
σθ = MPa
Answer key
- 1. σθ = −64.28 MPa
- 2. σ1 = 137.7 MPa
- 3. τabs = 69.46 MPa
- 4. σy′ = 98.53 MPa
- 5. σθ = −5 MPa
- 6. σθ = 26.7 MPa
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