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 = 160 MPa and σ₂ = −110 MPa (tension positive). Find the normal stress σ_avg that acts on the planes of maximum in-plane shear stress.

σ₁ = 160 MPaσ₂ = −110 MPa

σ_avg = MPa

2.Easy

A point in a loaded part has σₓ = −10 MPa, σᵧ = −80 MPa and τₓᵧ = −40 MPa (tension positive). Find the largest principal stress σ₁.

σ_x = −10 MPaσ_y = −80 MPaτ_xy = −40 MPa

σ₁ = MPa

3.Medium

A point has σₓ = 20 MPa and σᵧ = 100 MPa. How large can the shear stress τ_xy (magnitude) become before the largest principal stress reaches 155 MPa?

σ_x = 20 MPaσ_y = 100 MPaσ₁ = 155 MPa

τ_xy = MPa

4.Medium

A point in a loaded part has σₓ = 140 MPa, σᵧ = −80 MPa and τₓᵧ = −50 MPa (tension positive). Find the maximum in-plane shear stress τ_max.

σ_x = 140 MPaσ_y = −80 MPaτ_xy = −50 MPa

τ_max = MPa

5.Hard

A solid shaft of diameter 25 mm carries an axial tensile force of 190 kN together with a torque of 250 N·m. At the surface of the shaft, find the largest principal stress σ₁.

d = 25 mmF = 190 kNT = 250 N·m

σ₁ = MPa

6.Hard

A point in a thin plate is in plane stress: σₓ = 10 MPa, σᵧ = 110 MPa and τₓᵧ = 10 MPa (σ_z = 0). Find the von Mises equivalent stress σ_vM.

σ_x = 10 MPaσ_y = 110 MPaτ_xy = 10 MPa

σ_vM = MPa

Answer key

1. σ_avg = 25 MPa
2. σ₁ = 8.151 MPa
3. τ_xy = 86.17 MPa
4. τ_max = 120.8 MPa
5. σ₁ = 403.5 MPa
6. σ_vM = 106.8 MPa

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