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 worksheetPractise 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
σx​ = 0σy​ = 10τxy​ = 10MPa

A point in a loaded part has σₓ = 0 MPa, σᵧ = 10 MPa and τₓᵧ = 10 MPa (tension positive). Find the smallest principal stress σ2.

σx = 0 MPaσy = 10 MPaτxy = 10 MPa
σ2 = MPa
2.Easy
σx​ = 0σy​ = −80τxy​ = 40MPa

A point in a loaded part has σₓ = 0 MPa, σᵧ = −80 MPa and τₓᵧ = 40 MPa (tension positive). Find the largest principal stress σ1.

σx = 0 MPaσy = −80 MPaτxy = 40 MPa
σ1 = MPa
3.Medium
σx​ = −70σy​ = 30τxy​ = −40MPa

A point in a loaded part has σₓ = −70 MPa, σᵧ = 30 MPa and τₓᵧ = −40 MPa (tension positive). Find the angle θp from the x-axis to the direction of the largest principal stress, between −90° and 90°.

σx = −70 MPaσy = 30 MPaτxy = −40 MPa
θp = °
4.Medium
σx​ = 90σy​ = 110τxy​ = 30MPa

A point in a loaded part has σₓ = 90 MPa, σᵧ = 110 MPa and τₓᵧ = 30 MPa (tension positive). Find the angle θp from the x-axis to the direction of the largest principal stress, between −90° and 90°.

σx = 90 MPaσy = 110 MPaτxy = 30 MPa
θp = °
5.Hard
σx​ = −50σy​ = −30τxy​ = 30MPa

A point in a thin plate is in plane stress: σₓ = −50 MPa, σᵧ = −30 MPa and τₓᵧ = 30 MPa (σz = 0). The material has a yield strength of 420 MPa. Find the factor of safety n against yielding by the Tresca (maximum shear stress) criterion.

σx = −50 MPaσy = −30 MPaτxy = 30 MPaσY = 420 MPa
n =
6.Hard
σx​τxy​top surface of the shaft

A solid shaft of diameter 30 mm carries a bending moment of 500 N·m together with a torque of 250 N·m. At the top surface, where the bending stress is tensile and largest, find the largest principal stress σ1.

d = 30 mmM = 500 N·mT = 250 N·m
σ1 = MPa

Answer key

  1. 1. σ2 = −6.18 MPa
  2. 2. σ1 = 16.57 MPa
  3. 3. θp = −70.67 °
  4. 4. θp = 54.22 °
  5. 5. n = 5.864
  6. 6. σ1 = 199.8 MPa

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