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

At a point in a loaded part the in-plane principal stresses are σ₁ = 150 MPa and σ₂ = −60 MPa (tension positive). Find the normal stress σ_avg that acts on the planes of maximum in-plane shear stress.

σ₁ = 150 MPaσ₂ = −60 MPa

σ_avg = MPa

2.Easy

A point in a loaded part has σₓ = 90 MPa, σᵧ = 70 MPa and τₓᵧ = 20 MPa (tension positive). Find the smallest principal stress σ₂.

σ_x = 90 MPaσ_y = 70 MPaτ_xy = 20 MPa

σ₂ = MPa

3.Medium

A point in a loaded part has σₓ = 0 MPa, σᵧ = 110 MPa and τₓᵧ = 50 MPa (tension positive). Find the maximum in-plane shear stress τ_max.

σ_x = 0 MPaσ_y = 110 MPaτ_xy = 50 MPa

τ_max = MPa

4.Medium

A point in a loaded part has σₓ = 0 MPa, σᵧ = 50 MPa and τₓᵧ = 30 MPa (tension positive). Find the maximum in-plane shear stress τ_max.

σ_x = 0 MPaσ_y = 50 MPaτ_xy = 30 MPa

τ_max = MPa

5.Hard

A point in a thin plate is in plane stress: σₓ = 0 MPa, σᵧ = 50 MPa and τₓᵧ = −30 MPa (σ_z = 0). Find the von Mises equivalent stress σ_vM.

σ_x = 0 MPaσ_y = 50 MPaτ_xy = −30 MPa

σ_vM = MPa

6.Hard

A thin-walled cylindrical tank of inner diameter 600 mm and wall thickness 12 mm holds gas at a gauge pressure of 1.2 MPa. It is made from plate welded along a helical seam at 20° to the axis of the cylinder. Find the normal stress σ_n acting across the weld seam.

D = 600 mmt = 12 mmp = 1.2 MPaα = 20°

σ_n = MPa

Answer key

1. σ_avg = 45 MPa
2. σ₂ = 57.64 MPa
3. τ_max = 74.33 MPa
4. τ_max = 39.05 MPa
5. σ_vM = 72.11 MPa
6. σ_n = 28.25 MPa

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