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​ = −30MPapure shear

A point on the surface of a shaft in torsion is in pure shear with τₓᵧ = −30 MPa (σₓ = σᵧ = 0). Find the normal stress σθ on a plane whose normal is rotated 30° counter-clockwise from the x-axis.

τxy = −30 MPaθ = 30°
σθ = MPa
2.Easy
σx​ = 30σy​ = 80τxy​MPa

A point has σₓ = 30 MPa and σᵧ = 80 MPa, plus some shear stress. On an element rotated by 50° the normal stress in the rotated x′ direction is 19.9 MPa. Find the normal stress σy′ in the rotated y′ direction.

σx = 30 MPaσy = 80 MPaσx′ = 19.9 MPaθ = 50°
σy′ = MPa
3.Medium
σx​ = −80σy​ = −20τxy​ = 40MPa

A point in a loaded part has σₓ = −80 MPa, σᵧ = −20 MPa and τₓᵧ = 40 MPa (tension positive). Find the angle θp from the x-axis to the direction of the largest principal stress, between −90° and 90°.

σx = −80 MPaσy = −20 MPaτxy = 40 MPa
θp = °
4.Medium
σx​ = −60σy​ = 120τxy​ = −20MPa

A point has σₓ = −60 MPa, σᵧ = 120 MPa and τₓᵧ = −20 MPa (tension positive). The element is rotated 35° counter-clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.

σx = −60 MPaσy = 120 MPaτxy = −20 MPaθ = 35°
σy′ = MPa
5.Hard
σx​ = −70τxy​ = 40MPa

A point in a thin plate is in plane stress: σₓ = −70 MPa, σᵧ = 0 MPa and τₓᵧ = 40 MPa (σz = 0). Find the von Mises equivalent stress σvM.

σx = −70 MPaσy = 0 MPaτxy = 40 MPa
σvM = MPa
6.Hard
σx​ = −50σy​ = −60τxy​ = −20MPa

A point in a loaded part has σₓ = −50 MPa, σᵧ = −60 MPa and τₓᵧ = −20 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 45° clockwise from the x-axis.

σx = −50 MPaσy = −60 MPaτxy = −20 MPaθ = -45°
σθ = MPa

Answer key

  1. 1. σθ = −25.98 MPa
  2. 2. σy′ = 90.1 MPa
  3. 3. θp = 63.43 °
  4. 4. σy′ = 79.58 MPa
  5. 5. σvM = 98.49 MPa
  6. 6. σθ = −35 MPa

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