1.Easy
A bar with cross-sectional area 500 mm² carries an axial tensile force of 140 kN. Find the normal stress σθ on a section whose normal makes an angle of 25° with the bar axis (tension positive).
P = 140 kNA = 500 mm²θ = 25°
σθ = 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 = 80 MPa (σₓ = σᵧ = 0). Find the normal stress σθ on a plane whose normal is rotated 45° clockwise from the x-axis.
τxy = 80 MPaθ = -45°
σθ = MPa
3.Medium
A point has σₓ = 120 MPa and σᵧ = 60 MPa. How large can the shear stress τxy (magnitude) become before the largest principal stress reaches 180 MPa?
σx = 120 MPaσy = 60 MPaσ1 = 180 MPa
τxy = MPa
4.Medium
A point has σₓ = 110 MPa, σᵧ = 110 MPa and τₓᵧ = 40 MPa (tension positive). The element is rotated 40° counter-clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.
σx = 110 MPaσy = 110 MPaτxy = 40 MPaθ = 40°
σy′ = MPa
5.Hard
A point in a loaded part has σₓ = 160 MPa, σᵧ = 80 MPa and τₓᵧ = −50 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 45° clockwise from the x-axis.
σx = 160 MPaσy = 80 MPaτxy = −50 MPaθ = -45°
σθ = MPa
6.Hard
A point in a loaded part has σₓ = −60 MPa, σᵧ = −30 MPa and τₓᵧ = −50 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 50° counter-clockwise from the x-axis.
σx = −60 MPaσy = −30 MPaτxy = −50 MPaθ = 50°
σθ = MPa
Answer key
- 1. σθ = 230 MPa
- 2. σθ = −80 MPa
- 3. τxy = 84.85 MPa
- 4. σy′ = 70.61 MPa
- 5. σθ = 170 MPa
- 6. σθ = −91.64 MPa
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