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​ = −70σy​ = 10τxy​ = −60MPa

A point in a loaded part has σₓ = −70 MPa, σᵧ = 10 MPa and τₓᵧ = −60 MPa (tension positive). Find the smallest principal stress σ2.

σx = −70 MPaσy = 10 MPaτxy = −60 MPa
σ2 = MPa
2.Easy
σx​ = 160σy​ = 50τxy​ = 50MPa

A point in a loaded part has σₓ = 160 MPa, σᵧ = 50 MPa and τₓᵧ = 50 MPa (tension positive). Find the largest principal stress σ1.

σx = 160 MPaσy = 50 MPaτxy = 50 MPa
σ1 = MPa
3.Medium
σx​ = 50σy​ = −40τxy​ = 30MPa

A point in a thin plate is in plane stress: σₓ = 50 MPa, σᵧ = −40 MPa and τₓᵧ = 30 MPa, with σz = 0. Find the absolute maximum shear stress τabs at the point (considering all planes in three dimensions).

σx = 50 MPaσy = −40 MPaτxy = 30 MPaσz = 0
τabs = MPa
4.Medium
σx​ = −40σy​ = −50τxy​ = 30MPa

A point has σₓ = −40 MPa, σᵧ = −50 MPa and τₓᵧ = 30 MPa (tension positive). Find the angle θs, between −90° and 90°, from the x-axis to the normal of the plane on which the shear stress has its maximum positive value +R (shear positive in the same sense as τₓᵧ).

σx = −40 MPaσy = −50 MPaτxy = 30 MPa
θs = °
5.Hard
σx​ = 100σy​ = −50τxy​ = 40MPa

A point in a thin plate is in plane stress: σₓ = 100 MPa, σᵧ = −50 MPa and τₓᵧ = 40 MPa (σz = 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.

σx = 100 MPaσy = −50 MPaτxy = 40 MPaσY = 460 MPa
n =
6.Hard
σy​ = −60τxy​ = −50MPa

A point in a thin plate is in plane stress: σₓ = 0 MPa, σᵧ = −60 MPa and τₓᵧ = −50 MPa (σz = 0). The material has a yield strength of 355 MPa. Find the factor of safety n against yielding by the Tresca (maximum shear stress) criterion.

σx = 0 MPaσy = −60 MPaτxy = −50 MPaσY = 355 MPa
n =

Answer key

  1. 1. σ2 = −102.1 MPa
  2. 2. σ1 = 179.3 MPa
  3. 3. τabs = 54.08 MPa
  4. 4. θs = −4.731 °
  5. 5. n = 3.08
  6. 6. n = 3.044

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