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​ = 90σy​ = −70τxy​ = 10MPa

A point in a loaded part has σₓ = 90 MPa, σᵧ = −70 MPa and τₓᵧ = 10 MPa (tension positive). Find the smallest principal stress σ2.

σx = 90 MPaσy = −70 MPaτxy = 10 MPa
σ2 = MPa
2.Easy
σx​ = 160σy​ = −80τxy​ = −30MPa

A point in a loaded part has σₓ = 160 MPa, σᵧ = −80 MPa and τₓᵧ = −30 MPa (tension positive). Find the largest principal stress σ1.

σx = 160 MPaσy = −80 MPaτxy = −30 MPa
σ1 = MPa
3.Medium
σx​ = 80σy​ = 120τxy​ = 60MPa

A point in a thin plate is in plane stress: σₓ = 80 MPa, σᵧ = 120 MPa and τₓᵧ = 60 MPa, with σz = 0. Find the absolute maximum shear stress τabs at the point (considering all planes in three dimensions).

σx = 80 MPaσy = 120 MPaτxy = 60 MPaσz = 0
τabs = MPa
4.Medium
σx​ = 70σy​ = −50τxy​ = −10MPa

A point in a loaded part has σₓ = 70 MPa, σᵧ = −50 MPa and τₓᵧ = −10 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 = −50 MPaτxy = −10 MPa
θp = °
5.Hard
σx​ = 60σy​ = −70τxy​ = −30MPa

A point in a loaded part has σₓ = 60 MPa, σᵧ = −70 MPa and τₓᵧ = −30 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 45° clockwise from the x-axis.

σx = 60 MPaσy = −70 MPaτxy = −30 MPaθ = -45°
σθ = MPa
6.Hard
σx​ = 10σy​ = 10τxy​ = 10MPa

A point in a thin plate is in plane stress: σₓ = 10 MPa, σᵧ = 10 MPa and τₓᵧ = 10 MPa (σz = 0). The material has a yield strength of 275 MPa. Find the factor of safety n against yielding by the Tresca (maximum shear stress) criterion.

σx = 10 MPaσy = 10 MPaτxy = 10 MPaσY = 275 MPa
n =

Answer key

  1. 1. σ2 = −70.62 MPa
  2. 2. σ1 = 163.7 MPa
  3. 3. τabs = 81.62 MPa
  4. 4. θp = −4.731 °
  5. 5. σθ = 25 MPa
  6. 6. n = 13.75

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