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​ = 150σy​ = 20τxy​ = −50MPa

A point in a loaded part has σₓ = 150 MPa, σᵧ = 20 MPa and τₓᵧ = −50 MPa (tension positive). Find the smallest principal stress σ2.

σx = 150 MPaσy = 20 MPaτxy = −50 MPa
σ2 = MPa
2.Easy
σx​ = −10σy​ = 20τxy​ = 30MPa

A point in a loaded part has σₓ = −10 MPa, σᵧ = 20 MPa and τₓᵧ = 30 MPa (tension positive). Find the largest principal stress σ1.

σx = −10 MPaσy = 20 MPaτxy = 30 MPa
σ1 = MPa
3.Medium
σx​ = 40σy​ = 40τxy​ = −50MPa

A point in a loaded part has σₓ = 40 MPa, σᵧ = 40 MPa and τₓᵧ = −50 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = 40 MPaσy = 40 MPaτxy = −50 MPa
τmax = MPa
4.Medium
σx​ = 150σy​ = 60τxy​ = −10MPa

A point in a loaded part has σₓ = 150 MPa, σᵧ = 60 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 = 150 MPaσy = 60 MPaτxy = −10 MPa
θp = °
5.Hard
σx​ = 90σy​ = −80τxy​ = −40MPa

A point in a loaded part has σₓ = 90 MPa, σᵧ = −80 MPa and τₓᵧ = −40 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 45° clockwise from the x-axis.

σx = 90 MPaσy = −80 MPaτxy = −40 MPaθ = -45°
σθ = MPa
6.Hard
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 shear stress τθ on a plane whose normal is rotated 20° counter-clockwise from the x-axis (positive in the same sense as τₓᵧ).

σx = −10 MPaσy = 120 MPaτxy = 40 MPaθ = 20°
τθ = MPa

Answer key

  1. 1. σ2 = 2.994 MPa
  2. 2. σ1 = 38.54 MPa
  3. 3. τmax = 50 MPa
  4. 4. θp = −6.264 °
  5. 5. σθ = 45 MPa
  6. 6. τθ = 72.42 MPa

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