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.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.Easy

A point in a loaded part has σₓ = 30 MPa, σᵧ = −50 MPa and τₓᵧ = 20 MPa (tension positive). Find the largest principal stress σ₁.

σ_x = 30 MPaσ_y = −50 MPaτ_xy = 20 MPa

σ₁ = MPa

2.Easy

A point in a loaded part has σₓ = 10 MPa, σᵧ = 110 MPa and τₓᵧ = 60 MPa (tension positive). Find the smallest principal stress σ₂.

σ_x = 10 MPaσ_y = 110 MPaτ_xy = 60 MPa

σ₂ = MPa

3.Medium

A point in a thin plate is in plane stress: σₓ = 70 MPa, σᵧ = 50 MPa and τₓᵧ = 30 MPa, with σ_z = 0. Find the absolute maximum shear stress τ_abs at the point (considering all planes in three dimensions).

σ_x = 70 MPaσ_y = 50 MPaτ_xy = 30 MPaσ_z = 0

τ_abs = MPa

4.Medium

A point in a loaded part has σₓ = 20 MPa, σᵧ = 120 MPa and τₓᵧ = −60 MPa (tension positive). Find the maximum in-plane shear stress τ_max.

σ_x = 20 MPaσ_y = 120 MPaτ_xy = −60 MPa

τ_max = MPa

5.Hard

A point in a loaded part has σₓ = 100 MPa, σᵧ = 50 MPa and τₓᵧ = 40 MPa (tension positive). Find the shear stress τ_θ on a plane whose normal is rotated 15° counter-clockwise from the x-axis (positive in the same sense as τₓᵧ).

σ_x = 100 MPaσ_y = 50 MPaτ_xy = 40 MPaθ = 15°

τ_θ = MPa

6.Hard

A point in a loaded part has σₓ = −80 MPa, σᵧ = 60 MPa and τₓᵧ = 30 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 = −80 MPaσ_y = 60 MPaτ_xy = 30 MPaθ = 40°

σ_θ = MPa

Answer key

1. σ₁ = 34.72 MPa
2. σ₂ = −18.1 MPa
3. τ_abs = 45.81 MPa
4. τ_max = 78.1 MPa
5. τ_θ = 22.14 MPa
6. σ_θ = 7.389 MPa

Full step-by-step solutions: practise this topic on examproblems.com.