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​ = 120σy​ = −60τxy​ = 10MPa

A point in a loaded part has σₓ = 120 MPa, σᵧ = −60 MPa and τₓᵧ = 10 MPa (tension positive). Find the largest principal stress σ1.

σx = 120 MPaσy = −60 MPaτxy = 10 MPa
σ1 = MPa
2.Easy
σx​ = −10σy​ = −20τxy​ = −50MPa

A point in a loaded part has σₓ = −10 MPa, σᵧ = −20 MPa and τₓᵧ = −50 MPa (tension positive). Find the smallest principal stress σ2.

σx = −10 MPaσy = −20 MPaτxy = −50 MPa
σ2 = MPa
3.Medium
σx​ = 80σy​ = −60MPaτxy​ = ?

A point has σₓ = 80 MPa and σᵧ = −60 MPa. How large can the shear stress τxy (magnitude) become before the largest principal stress reaches 135 MPa?

σx = 80 MPaσy = −60 MPaσ1 = 135 MPa
τxy = MPa
4.Medium
σx​ = 30σy​ = −80τxy​ = −10MPa

A point in a loaded part has σₓ = 30 MPa, σᵧ = −80 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 = 30 MPaσy = −80 MPaτxy = −10 MPa
θp = °
5.Hard
60°D = 500 mm, t = 8 mm, p = 3 MPap

A thin-walled cylindrical tank of inner diameter 500 mm and wall thickness 8 mm holds gas at a gauge pressure of 3 MPa. It is made from plate welded along a helical seam at 60° to the axis of the cylinder. Find the magnitude of the shear stress |τn| acting along the weld seam.

D = 500 mmt = 8 mmp = 3 MPaα = 60°
|τn| = MPa
6.Hard
σx​ = −70σy​ = 60τxy​ = 40MPa

A point in a loaded part has σₓ = −70 MPa, σᵧ = 60 MPa and τₓᵧ = 40 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 20° counter-clockwise from the x-axis.

σx = −70 MPaσy = 60 MPaτxy = 40 MPaθ = 20°
σθ = MPa

Answer key

  1. 1. σ1 = 120.6 MPa
  2. 2. σ2 = −65.25 MPa
  3. 3. τxy = 103.6 MPa
  4. 4. θp = −5.152 °
  5. 5. |τn| = 20.3 MPa
  6. 6. σθ = −29.08 MPa

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