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 = 120 MPa and σ₂ = 80 MPa (tension positive). Find the maximum in-plane shear stress τ_max.

σ₁ = 120 MPaσ₂ = 80 MPa

τ_max = MPa

2.Easy

A point in a loaded part has σₓ = 40 MPa, σᵧ = 110 MPa and τₓᵧ = 10 MPa (tension positive). Find the smallest principal stress σ₂.

σ_x = 40 MPaσ_y = 110 MPaτ_xy = 10 MPa

σ₂ = MPa

3.Medium

A point in a loaded part has σₓ = 10 MPa, σᵧ = −30 MPa and τₓᵧ = −10 MPa (tension positive). Find the maximum in-plane shear stress τ_max.

σ_x = 10 MPaσ_y = −30 MPaτ_xy = −10 MPa

τ_max = MPa

4.Medium

A point has σₓ = 130 MPa and σᵧ = 30 MPa. How large can the shear stress τ_xy (magnitude) become before the largest principal stress reaches 170 MPa?

σ_x = 130 MPaσ_y = 30 MPaσ₁ = 170 MPa

τ_xy = MPa

5.Hard

A point in a thin plate is in plane stress: σₓ = 160 MPa, σᵧ = 20 MPa and τₓᵧ = −40 MPa (σ_z = 0). The material has a yield strength of 355 MPa. Find the factor of safety n against yielding by the Tresca (maximum shear stress) criterion.

σ_x = 160 MPaσ_y = 20 MPaτ_xy = −40 MPaσ_Y = 355 MPa

n =

6.Hard

A point in a loaded part has σₓ = 40 MPa, σᵧ = 120 MPa and τₓᵧ = 30 MPa (tension positive). Find the normal stress σ_θ on a plane whose normal is rotated 30° counter-clockwise from the x-axis.

σ_x = 40 MPaσ_y = 120 MPaτ_xy = 30 MPaθ = 30°

σ_θ = MPa

Answer key

1. τ_max = 20 MPa
2. σ₂ = 38.6 MPa
3. τ_max = 22.36 MPa
4. τ_xy = 74.83 MPa
5. n = 2.081
6. σ_θ = 85.98 MPa

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