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 = 100 MPa and τₓᵧ = −50 MPa (tension positive). Find the smallest principal stress σ₂.

σ_x = 60 MPaσ_y = 100 MPaτ_xy = −50 MPa

σ₂ = MPa

2.Easy

A point has σₓ = 80 MPa and σᵧ = 80 MPa, plus some shear stress. On an element rotated by 35° the normal stress in the rotated x′ direction is 89.4 MPa. Find the normal stress σ_y′ in the rotated y′ direction.

σ_x = 80 MPaσ_y = 80 MPaσ_x′ = 89.4 MPaθ = 35°

σ_y′ = MPa

3.Medium

A point has σₓ = −10 MPa and σᵧ = −20 MPa. How large can the shear stress τ_xy (magnitude) become before the largest principal stress reaches 50 MPa?

σ_x = −10 MPaσ_y = −20 MPaσ₁ = 50 MPa

τ_xy = MPa

4.Medium

A point has σₓ = 120 MPa and σᵧ = −10 MPa. How large can the shear stress τ_xy (magnitude) become before the largest principal stress reaches 140 MPa?

σ_x = 120 MPaσ_y = −10 MPaσ₁ = 140 MPa

τ_xy = MPa

5.Hard

A point in a thin plate is in plane stress: σₓ = 130 MPa, σᵧ = 40 MPa and τₓᵧ = −20 MPa (σ_z = 0). The material has a yield strength of 460 MPa. Find the factor of safety n against yielding by the von Mises (distortion energy) criterion.

σ_x = 130 MPaσ_y = 40 MPaτ_xy = −20 MPaσ_Y = 460 MPa

n =

6.Hard

A point in a loaded part has σₓ = −50 MPa, σᵧ = 110 MPa and τₓᵧ = 20 MPa (tension positive). Find the normal stress σ_θ on a plane whose normal is rotated 15° counter-clockwise from the x-axis.

σ_x = −50 MPaσ_y = 110 MPaτ_xy = 20 MPaθ = 15°

σ_θ = MPa

Answer key

1. σ₂ = 26.15 MPa
2. σ_y′ = 70.6 MPa
3. τ_xy = 64.81 MPa
4. τ_xy = 54.77 MPa
5. n = 3.82
6. σ_θ = −29.28 MPa

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