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​ = 50σy​ = −20τxy​ = −20MPa

A point in a loaded part has σₓ = 50 MPa, σᵧ = −20 MPa and τₓᵧ = −20 MPa (tension positive). Find the smallest principal stress σ2.

σx = 50 MPaσy = −20 MPaτxy = −20 MPa
σ2 = MPa
2.Easy
σx​ = 50σy​ = −30τxy​ = 20MPa

A point in a loaded part has σₓ = 50 MPa, σᵧ = −30 MPa and τₓᵧ = 20 MPa (tension positive). Find the largest principal stress σ1.

σx = 50 MPaσy = −30 MPaτxy = 20 MPa
σ1 = MPa
3.Medium
σx​ = 90σy​ = 110τxy​ = 10MPa

A point in a thin plate is in plane stress: σₓ = 90 MPa, σᵧ = 110 MPa and τₓᵧ = 10 MPa, with σz = 0. Find the absolute maximum shear stress τabs at the point (considering all planes in three dimensions).

σx = 90 MPaσy = 110 MPaτxy = 10 MPaσz = 0
τabs = MPa
4.Medium
σx​ = 100σy​ = −30MPaτxy​ = ?

A point has σₓ = 100 MPa and σᵧ = −30 MPa. How large can the shear stress τxy (magnitude) become before the largest principal stress reaches 145 MPa?

σx = 100 MPaσy = −30 MPaσ1 = 145 MPa
τxy = MPa
5.Hard
σx​ = −10σy​ = 100τxy​ = 60MPa

A point in a loaded part has σₓ = −10 MPa, σᵧ = 100 MPa and τₓᵧ = 60 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 60° counter-clockwise from the x-axis.

σx = −10 MPaσy = 100 MPaτxy = 60 MPaθ = 60°
σθ = MPa
6.Hard
σx​ = −60σy​ = 120τxy​ = −30MPa

A point in a thin plate is in plane stress: σₓ = −60 MPa, σᵧ = 120 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 von Mises (distortion energy) criterion.

σx = −60 MPaσy = 120 MPaτxy = −30 MPaσY = 420 MPa
n =

Answer key

  1. 1. σ2 = −25.31 MPa
  2. 2. σ1 = 54.72 MPa
  3. 3. τabs = 57.07 MPa
  4. 4. τxy = 88.74 MPa
  5. 5. σθ = 124.5 MPa
  6. 6. n = 2.514

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