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 = 0 MPa, σᵧ = −30 MPa and τₓᵧ = −30 MPa (tension positive). Find the largest principal stress σ₁.

σ_x = 0 MPaσ_y = −30 MPaτ_xy = −30 MPa

σ₁ = MPa

2.Easy

A point in a loaded part has σₓ = 160 MPa, σᵧ = 20 MPa and τₓᵧ = 30 MPa (tension positive). Find the largest principal stress σ₁.

σ_x = 160 MPaσ_y = 20 MPaτ_xy = 30 MPa

σ₁ = MPa

3.Medium

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

σ_x = 60 MPaσ_y = 20 MPaτ_xy = 20 MPa

τ_max = MPa

4.Medium

A point has σₓ = 130 MPa, σᵧ = −40 MPa and τₓᵧ = 20 MPa (tension positive). The element is rotated 30° clockwise. Find the normal stress σ_y′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.

σ_x = 130 MPaσ_y = −40 MPaτ_xy = 20 MPaθ = -30°

σ_y′ = MPa

5.Hard

A point in a thin plate is in plane stress: σₓ = −70 MPa, σᵧ = −50 MPa and τₓᵧ = 20 MPa (σ_z = 0). Find the von Mises equivalent stress σ_vM.

σ_x = −70 MPaσ_y = −50 MPaτ_xy = 20 MPa

σ_vM = MPa

6.Hard

A point in a loaded part has σₓ = 30 MPa, σᵧ = 110 MPa and τₓᵧ = −60 MPa (tension positive). Find the normal stress σ_θ on a plane whose normal is rotated 40° counter-clockwise from the x-axis.

σ_x = 30 MPaσ_y = 110 MPaτ_xy = −60 MPaθ = 40°

σ_θ = MPa

Answer key

1. σ₁ = 18.54 MPa
2. σ₁ = 166.2 MPa
3. τ_max = 28.28 MPa
4. σ_y′ = 19.82 MPa
5. σ_vM = 71.41 MPa
6. σ_θ = 3.966 MPa

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