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​ = 80σy​ = −40τxy​ = 60MPa

A point in a loaded part has σₓ = 80 MPa, σᵧ = −40 MPa and τₓᵧ = 60 MPa (tension positive). Find the largest principal stress σ1.

σx = 80 MPaσy = −40 MPaτxy = 60 MPa
σ1 = MPa
2.Easy
σx​ = 90σy​ = −10MPaprincipal element

At a point in a loaded part the in-plane principal stresses are σ₁ = 90 MPa and σ₂ = −10 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σ1 = 90 MPaσ2 = −10 MPa
τmax = MPa
3.Medium
σx​ = 10σy​ = −50MPaτxy​ = ?

A point has σₓ = 10 MPa and σᵧ = −50 MPa. How large can the shear stress τxy (magnitude) become before the largest principal stress reaches 40 MPa?

σx = 10 MPaσy = −50 MPaσ1 = 40 MPa
τxy = MPa
4.Medium
σx​ = 90σy​ = 70τxy​ = −20MPa

A point in a loaded part has σₓ = 90 MPa, σᵧ = 70 MPa and τₓᵧ = −20 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = 90 MPaσy = 70 MPaτxy = −20 MPa
τmax = MPa
5.Hard
σx​ = 120σy​ = 50τxy​ = 40MPa

A point in a loaded part has σₓ = 120 MPa, σᵧ = 50 MPa and τₓᵧ = 40 MPa (tension positive). Find the shear stress τθ on a plane whose normal is rotated 45° clockwise from the x-axis (positive in the same sense as τₓᵧ).

σx = 120 MPaσy = 50 MPaτxy = 40 MPaθ = -45°
τθ = MPa
6.Hard
55°D = 600 mm, t = 5 mm, p = 0.8 MPap

A thin-walled cylindrical tank of inner diameter 600 mm and wall thickness 5 mm holds gas at a gauge pressure of 0.8 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 = 600 mmt = 5 mmp = 0.8 MPaα = 55°
σn = MPa

Answer key

  1. 1. σ1 = 104.9 MPa
  2. 2. τmax = 50 MPa
  3. 3. τxy = 51.96 MPa
  4. 4. τmax = 22.36 MPa
  5. 5. τθ = 35 MPa
  6. 6. σn = 31.9 MPa

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