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
τxy​ = −90MPapure shear

A point on the surface of a shaft in torsion is in pure shear with τₓᵧ = −90 MPa (σₓ = σᵧ = 0). Find the normal stress σθ on a plane whose normal is rotated 45° clockwise from the x-axis.

τxy = −90 MPaθ = -45°
σθ = MPa
2.Easy
σx​ = −60σy​ = 90τxy​ = −20MPa

A point in a loaded part has σₓ = −60 MPa, σᵧ = 90 MPa and τₓᵧ = −20 MPa (tension positive). Find the smallest principal stress σ2.

σx = −60 MPaσy = 90 MPaτxy = −20 MPa
σ2 = MPa
3.Medium
σx​ = −30σy​ = −30τxy​ = 30MPa

A point has σₓ = −30 MPa, σᵧ = −30 MPa and τₓᵧ = 30 MPa (tension positive). The element is rotated 20° clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.

σx = −30 MPaσy = −30 MPaτxy = 30 MPaθ = -20°
σy′ = MPa
4.Medium
σx​ = −60σy​ = 30τxy​ = −60MPa

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

σx = −60 MPaσy = 30 MPaτxy = −60 MPaθ = -30°
σy′ = MPa
5.Hard
55°D = 1000 mm, t = 6 mm, p = 2 MPap

A thin-walled cylindrical tank of inner diameter 1000 mm and wall thickness 6 mm holds gas at a gauge pressure of 2 MPa. It is made from plate welded along a helical seam at 55° to the axis of the cylinder. Find the normal stress σn acting across the weld seam.

D = 1000 mmt = 6 mmp = 2 MPaα = 55°
σn = MPa
6.Hard
σx​ = −70σy​ = 20τxy​ = 30MPa

A point in a loaded part has σₓ = −70 MPa, σᵧ = 20 MPa and τₓᵧ = 30 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 30° clockwise from the x-axis.

σx = −70 MPaσy = 20 MPaτxy = 30 MPaθ = -30°
σθ = MPa

Answer key

  1. 1. σθ = 90 MPa
  2. 2. σ2 = −62.62 MPa
  3. 3. σy′ = −10.72 MPa
  4. 4. σy′ = −44.46 MPa
  5. 5. σn = 110.7 MPa
  6. 6. σθ = −73.48 MPa

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