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 has σₓ = 40 MPa and σᵧ = 120 MPa, plus some shear stress. On an element rotated by 25° the normal stress in the rotated x′ direction is 31.3 MPa. Find the normal stress σ_y′ in the rotated y′ direction.

σ_x = 40 MPaσ_y = 120 MPaσ_x′ = 31.3 MPaθ = 25°

σ_y′ = MPa

2.Easy

A point in a loaded part has σₓ = 50 MPa, σᵧ = 20 MPa and τₓᵧ = 20 MPa (tension positive). Find the largest principal stress σ₁.

σ_x = 50 MPaσ_y = 20 MPaτ_xy = 20 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 150 MPa?

σ_x = −20 MPaσ_y = 100 MPaσ₁ = 150 MPa

τ_xy = MPa

4.Medium

A point in a loaded part has σₓ = −40 MPa, σᵧ = 80 MPa and τₓᵧ = −20 MPa (tension positive). Find the maximum in-plane shear stress τ_max.

σ_x = −40 MPaσ_y = 80 MPaτ_xy = −20 MPa

τ_max = MPa

5.Hard

A point in a loaded part has σₓ = −30 MPa, σᵧ = −30 MPa and τₓᵧ = 10 MPa (tension positive). Find the normal stress σ_θ on a plane whose normal is rotated 20° clockwise from the x-axis.

σ_x = −30 MPaσ_y = −30 MPaτ_xy = 10 MPaθ = -20°

σ_θ = MPa

6.Hard

A point in a thin plate is in plane stress: σₓ = 0 MPa, σᵧ = −80 MPa and τₓᵧ = 60 MPa (σ_z = 0). Find the von Mises equivalent stress σ_vM.

σ_x = 0 MPaσ_y = −80 MPaτ_xy = 60 MPa

σ_vM = MPa

Answer key

1. σ_y′ = 128.7 MPa
2. σ₁ = 60 MPa
3. τ_xy = 92.2 MPa
4. τ_max = 63.25 MPa
5. σ_θ = −36.43 MPa
6. σ_vM = 131.1 MPa

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