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​ = 140σy​ = 100τxy​ = −60MPa

A point in a loaded part has σₓ = 140 MPa, σᵧ = 100 MPa and τₓᵧ = −60 MPa (tension positive). Find the smallest principal stress σ2.

σx = 140 MPaσy = 100 MPaτxy = −60 MPa
σ2 = MPa
2.Easy
σx​ = −80σy​ = 70τxy​ = 10MPa

A point in a loaded part has σₓ = −80 MPa, σᵧ = 70 MPa and τₓᵧ = 10 MPa (tension positive). Find the largest principal stress σ1.

σx = −80 MPaσy = 70 MPaτxy = 10 MPa
σ1 = MPa
3.Medium
σx​ = 10σy​ = −30MPaτxy​ = ?

A point has σₓ = 10 MPa and σᵧ = −30 MPa. How large can the shear stress τxy (magnitude) become before the largest principal stress reaches 25 MPa?

σx = 10 MPaσy = −30 MPaσ1 = 25 MPa
τxy = MPa
4.Medium
σx​ = 40σy​ = −70τxy​ = 30MPa

A point has σₓ = 40 MPa, σᵧ = −70 MPa and τₓᵧ = 30 MPa (tension positive). The element is rotated 60° counter-clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.

σx = 40 MPaσy = −70 MPaτxy = 30 MPaθ = 60°
σy′ = MPa
5.Hard
50°D = 400 mm, t = 10 mm, p = 1.5 MPap

A thin-walled cylindrical tank of inner diameter 400 mm and wall thickness 10 mm holds gas at a gauge pressure of 1.5 MPa. It is made from plate welded along a helical seam at 50° to the axis of the cylinder. Find the normal stress σn acting across the weld seam.

D = 400 mmt = 10 mmp = 1.5 MPaα = 50°
σn = MPa
6.Hard
σx​ = 80σy​ = 30τxy​ = −30MPa

A point in a thin plate is in plane stress: σₓ = 80 MPa, σᵧ = 30 MPa and τₓᵧ = −30 MPa (σz = 0). The material has a yield strength of 350 MPa. Find the factor of safety n against yielding by the von Mises (distortion energy) criterion.

σx = 80 MPaσy = 30 MPaτxy = −30 MPaσY = 350 MPa
n =

Answer key

  1. 1. σ2 = 56.75 MPa
  2. 2. σ1 = 70.66 MPa
  3. 3. τxy = 28.72 MPa
  4. 4. σy′ = −13.48 MPa
  5. 5. σn = 21.2 MPa
  6. 6. n = 4.015

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