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​ = 10σy​ = 120τxy​ = −40MPa

A point in a loaded part has σₓ = 10 MPa, σᵧ = 120 MPa and τₓᵧ = −40 MPa (tension positive). Find the smallest principal stress σ2.

σx = 10 MPaσy = 120 MPaτxy = −40 MPa
σ2 = MPa
2.Easy
σx​ = 100σy​ = 80τxy​MPa

A point has σₓ = 100 MPa and σᵧ = 80 MPa, plus some shear stress. On an element rotated by 60° the normal stress in the rotated x′ direction is 67.7 MPa. Find the normal stress σy′ in the rotated y′ direction.

σx = 100 MPaσy = 80 MPaσx′ = 67.7 MPaθ = 60°
σy′ = MPa
3.Medium
σx​ = −50σy​ = −70τxy​ = 60MPa

A point in a loaded part has σₓ = −50 MPa, σᵧ = −70 MPa and τₓᵧ = 60 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = −50 MPaσy = −70 MPaτxy = 60 MPa
τmax = MPa
4.Medium
σx​ = 150σy​ = −50τxy​ = −10MPa

A point in a loaded part has σₓ = 150 MPa, σᵧ = −50 MPa and τₓᵧ = −10 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = 150 MPaσy = −50 MPaτxy = −10 MPa
τmax = MPa
5.Hard
σx​ = −20σy​ = 110τxy​ = 30MPa

A point in a loaded part has σₓ = −20 MPa, σᵧ = 110 MPa and τₓᵧ = 30 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 60° counter-clockwise from the x-axis.

σx = −20 MPaσy = 110 MPaτxy = 30 MPaθ = 60°
σθ = MPa
6.Hard
σx​τxy​top surface of the shaft

A solid shaft of diameter 50 mm carries a bending moment of 1000 N·m together with a torque of 750 N·m. At the top surface, where the bending stress is tensile and largest, find the maximum in-plane shear stress τmax.

d = 50 mmM = 1000 N·mT = 750 N·m
τmax = MPa

Answer key

  1. 1. σ2 = −3.007 MPa
  2. 2. σy′ = 112.3 MPa
  3. 3. τmax = 60.83 MPa
  4. 4. τmax = 100.5 MPa
  5. 5. σθ = 103.5 MPa
  6. 6. τmax = 50.93 MPa

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