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 = 30 MPa, σᵧ = 30 MPa and τₓᵧ = 40 MPa (tension positive). Find the smallest principal stress σ₂.

σ_x = 30 MPaσ_y = 30 MPaτ_xy = 40 MPa

σ₂ = MPa

2.Easy

A point in a loaded part has σₓ = 10 MPa, σᵧ = −40 MPa and τₓᵧ = 50 MPa (tension positive). Find the smallest principal stress σ₂.

σ_x = 10 MPaσ_y = −40 MPaτ_xy = 50 MPa

σ₂ = MPa

3.Medium

A point in a loaded part has σₓ = 100 MPa, σᵧ = 110 MPa and τₓᵧ = −10 MPa (tension positive). Find the maximum in-plane shear stress τ_max.

σ_x = 100 MPaσ_y = 110 MPaτ_xy = −10 MPa

τ_max = MPa

4.Medium

A point in a loaded part has σₓ = −50 MPa, σᵧ = −30 MPa and τₓᵧ = 30 MPa (tension positive). Find the angle θ_p from the x-axis to the direction of the largest principal stress, between −90° and 90°.

σ_x = −50 MPaσ_y = −30 MPaτ_xy = 30 MPa

θ_p = °

5.Hard

A point in a loaded part has σₓ = 150 MPa, σᵧ = 20 MPa and τₓᵧ = −10 MPa (tension positive). Find the shear stress τ_θ on a plane whose normal is rotated 30° counter-clockwise from the x-axis (positive in the same sense as τₓᵧ).

σ_x = 150 MPaσ_y = 20 MPaτ_xy = −10 MPaθ = 30°

τ_θ = MPa

6.Hard

A point in a thin plate is in plane stress: σₓ = 140 MPa, σᵧ = −60 MPa and τₓᵧ = 40 MPa (σ_z = 0). Find the von Mises equivalent stress σ_vM.

σ_x = 140 MPaσ_y = −60 MPaτ_xy = 40 MPa

σ_vM = MPa

Answer key

1. σ₂ = −10 MPa
2. σ₂ = −70.9 MPa
3. τ_max = 11.18 MPa
4. θ_p = 54.22 °
5. τ_θ = −61.29 MPa
6. σ_vM = 190.8 MPa

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