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 = −60 MPa, σᵧ = 10 MPa and τₓᵧ = 20 MPa (tension positive). Find the smallest principal stress σ₂.

σ_x = −60 MPaσ_y = 10 MPaτ_xy = 20 MPa

σ₂ = MPa

2.Easy

A point in a loaded part has σₓ = 20 MPa, σᵧ = 10 MPa and τₓᵧ = 10 MPa (tension positive). Find the largest principal stress σ₁.

σ_x = 20 MPaσ_y = 10 MPaτ_xy = 10 MPa

σ₁ = MPa

3.Medium

A point in a loaded part has σₓ = 0 MPa, σᵧ = 50 MPa and τₓᵧ = 50 MPa (tension positive). Find the maximum in-plane shear stress τ_max.

σ_x = 0 MPaσ_y = 50 MPaτ_xy = 50 MPa

τ_max = MPa

4.Medium

A point in a loaded part has σₓ = −80 MPa, σᵧ = 110 MPa and τₓᵧ = −20 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 = −80 MPaσ_y = 110 MPaτ_xy = −20 MPa

θ_p = °

5.Hard

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

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

σ_vM = MPa

6.Hard

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

σ_θ = MPa

Answer key

1. σ₂ = −65.31 MPa
2. σ₁ = 26.18 MPa
3. τ_max = 55.9 MPa
4. θ_p = −84.06 °
5. σ_vM = 71.41 MPa
6. σ_θ = 73.52 MPa

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