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 = 70 MPa, σᵧ = 80 MPa and τₓᵧ = −20 MPa (tension positive). Find the smallest principal stress σ₂.

σ_x = 70 MPaσ_y = 80 MPaτ_xy = −20 MPa

σ₂ = MPa

2.Easy

A point in a loaded part has σₓ = −50 MPa, σᵧ = 110 MPa and τₓᵧ = 50 MPa (tension positive). Find the smallest principal stress σ₂.

σ_x = −50 MPaσ_y = 110 MPaτ_xy = 50 MPa

σ₂ = MPa

3.Medium

A point in a loaded part has σₓ = 80 MPa, σᵧ = 30 MPa and τₓᵧ = 20 MPa (tension positive). Find the maximum in-plane shear stress τ_max.

σ_x = 80 MPaσ_y = 30 MPaτ_xy = 20 MPa

τ_max = MPa

4.Medium

A point in a loaded part has σₓ = 20 MPa, σᵧ = 60 MPa and τₓᵧ = −30 MPa (tension positive). Find the maximum in-plane shear stress τ_max.

σ_x = 20 MPaσ_y = 60 MPaτ_xy = −30 MPa

τ_max = MPa

5.Hard

A point in a thin plate is in plane stress: σₓ = −20 MPa, σᵧ = −10 MPa and τₓᵧ = −40 MPa (σ_z = 0). Find the von Mises equivalent stress σ_vM.

σ_x = −20 MPaσ_y = −10 MPaτ_xy = −40 MPa

σ_vM = MPa

6.Hard

A point in a loaded part has σₓ = 100 MPa, σᵧ = −10 MPa and τₓᵧ = −20 MPa (tension positive). Find the shear stress τ_θ on a plane whose normal is rotated 45° counter-clockwise from the x-axis (positive in the same sense as τₓᵧ).

σ_x = 100 MPaσ_y = −10 MPaτ_xy = −20 MPaθ = 45°

τ_θ = MPa

Answer key

1. σ₂ = 54.38 MPa
2. σ₂ = −64.34 MPa
3. τ_max = 32.02 MPa
4. τ_max = 36.06 MPa
5. σ_vM = 71.41 MPa
6. τ_θ = −55 MPa

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