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 = 180 MPa and σ₂ = −30 MPa (tension positive). Find the maximum in-plane shear stress τ_max.

σ₁ = 180 MPaσ₂ = −30 MPa

τ_max = MPa

2.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

3.Medium

A point in a loaded part has σₓ = 160 MPa, σᵧ = 60 MPa and τₓᵧ = 50 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 = 160 MPaσ_y = 60 MPaτ_xy = 50 MPa

θ_p = °

4.Medium

A point has σₓ = 120 MPa and σᵧ = 50 MPa. How large can the shear stress τ_xy (magnitude) become before the largest principal stress reaches 175 MPa?

σ_x = 120 MPaσ_y = 50 MPaσ₁ = 175 MPa

τ_xy = MPa

5.Hard

A point in a loaded part has σₓ = 110 MPa, σᵧ = 60 MPa and τₓᵧ = −50 MPa (tension positive). Find the shear stress τ_θ on a plane whose normal is rotated 50° counter-clockwise from the x-axis (positive in the same sense as τₓᵧ).

σ_x = 110 MPaσ_y = 60 MPaτ_xy = −50 MPaθ = 50°

τ_θ = MPa

6.Hard

A point in a thin plate is in plane stress: σₓ = 110 MPa, σᵧ = 70 MPa and τₓᵧ = 20 MPa (σ_z = 0). Find the von Mises equivalent stress σ_vM.

σ_x = 110 MPaσ_y = 70 MPaτ_xy = 20 MPa

σ_vM = MPa

Answer key

1. τ_max = 105 MPa
2. σ₂ = −95.62 MPa
3. θ_p = 22.5 °
4. τ_xy = 82.92 MPa
5. τ_θ = −15.94 MPa
6. σ_vM = 102.5 MPa

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