Mohr’s circle & stress transformation worksheet with answers

Free printable Mohr’s circle & stress transformation worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A point in a loaded part has σₓ = 20 MPa, σᵧ = 0 MPa and τₓᵧ = 10 MPa (tension positive). Find the largest principal stress σ₁.

σ_x = 20 MPaσ_y = 0 MPaτ_xy = 10 MPa

σ₁ = MPa

2.Easy

A point in a loaded part has σₓ = 140 MPa, σᵧ = −30 MPa and τₓᵧ = −40 MPa (tension positive). Find the smallest principal stress σ₂.

σ_x = 140 MPaσ_y = −30 MPaτ_xy = −40 MPa

σ₂ = MPa

3.Medium

A point in a loaded part has σₓ = 90 MPa, σᵧ = 60 MPa and τₓᵧ = 60 MPa (tension positive). Find the maximum in-plane shear stress τ_max.

σ_x = 90 MPaσ_y = 60 MPaτ_xy = 60 MPa

τ_max = MPa

4.Medium

A point has σₓ = −80 MPa, σᵧ = −10 MPa and τₓᵧ = 40 MPa (tension positive). The element is rotated 20° clockwise. Find the normal stress σ_y′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.

σ_x = −80 MPaσ_y = −10 MPaτ_xy = 40 MPaθ = -20°

σ_y′ = MPa

5.Hard

A solid shaft of diameter 50 mm carries an axial tensile force of 60 kN together with a torque of 750 N·m. At the surface of the shaft, find the largest principal stress σ₁.

d = 50 mmF = 60 kNT = 750 N·m

σ₁ = MPa

6.Hard

A point in a loaded part has σₓ = 160 MPa, σᵧ = 0 MPa and τₓᵧ = −30 MPa (tension positive). Find the normal stress σ_θ on a plane whose normal is rotated 20° counter-clockwise from the x-axis.

σ_x = 160 MPaσ_y = 0 MPaτ_xy = −30 MPaθ = 20°

σ_θ = MPa

Answer key

1. σ₁ = 24.14 MPa
2. σ₂ = −38.94 MPa
3. τ_max = 61.85 MPa
4. σ_y′ = 7.523 MPa
5. σ₁ = 49.44 MPa
6. σ_θ = 122 MPa

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