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​ = 90σy​ = −70τxy​ = 30MPa

A point in a loaded part has σₓ = 90 MPa, σᵧ = −70 MPa and τₓᵧ = 30 MPa (tension positive). Find the smallest principal stress σ2.

σx = 90 MPaσy = −70 MPaτxy = 30 MPa
σ2 = MPa
2.Easy
σx​ = −30σy​ = 20τxy​ = 30MPa

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

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

A point in a loaded part has σₓ = 20 MPa, σᵧ = 90 MPa and τₓᵧ = −50 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = 20 MPaσy = 90 MPaτxy = −50 MPa
τmax = MPa
4.Medium
σx​ = 70σy​ = 30τxy​ = −60MPa

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

σx = 70 MPaσy = 30 MPaτxy = −60 MPaθ = 40°
σy′ = MPa
5.Hard
σx​ = 130σy​ = −60τxy​ = −50MPa

A point in a loaded part has σₓ = 130 MPa, σᵧ = −60 MPa and τₓᵧ = −50 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 30° counter-clockwise from the x-axis.

σx = 130 MPaσy = −60 MPaτxy = −50 MPaθ = 30°
σθ = MPa
6.Hard
25°D = 500 mm, t = 15 mm, p = 2 MPap

A thin-walled cylindrical tank of inner diameter 500 mm and wall thickness 15 mm holds gas at a gauge pressure of 2 MPa. It is made from plate welded along a helical seam at 25° to the axis of the cylinder. Find the normal stress σn acting across the weld seam.

D = 500 mmt = 15 mmp = 2 MPaα = 25°
σn = MPa

Answer key

  1. 1. σ2 = −75.44 MPa
  2. 2. σ1 = 34.05 MPa
  3. 3. τmax = 61.03 MPa
  4. 4. σy′ = 105.6 MPa
  5. 5. σθ = 39.2 MPa
  6. 6. σn = 30.36 MPa

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