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​ = 0σy​ = −50τxy​ = −40MPa

A point in a loaded part has σₓ = 0 MPa, σᵧ = −50 MPa and τₓᵧ = −40 MPa (tension positive). Find the smallest principal stress σ2.

σx = 0 MPaσy = −50 MPaτxy = −40 MPa
σ2 = MPa
2.Easy
σx​ = 50σy​ = 60τxy​ = −10MPa

A point in a loaded part has σₓ = 50 MPa, σᵧ = 60 MPa and τₓᵧ = −10 MPa (tension positive). Find the smallest principal stress σ2.

σx = 50 MPaσy = 60 MPaτxy = −10 MPa
σ2 = MPa
3.Medium
σx​ = 110σy​ = 50τxy​ = −40MPa

A point has σₓ = 110 MPa, σᵧ = 50 MPa and τₓᵧ = −40 MPa (tension positive). Find the angle θs, between −90° and 90°, from the x-axis to the normal of the plane on which the shear stress has its maximum positive value +R (shear positive in the same sense as τₓᵧ).

σx = 110 MPaσy = 50 MPaτxy = −40 MPa
θs = °
4.Medium
σx​ = −70σy​ = 70τxy​ = 50MPa

A point in a loaded part has σₓ = −70 MPa, σᵧ = 70 MPa and τₓᵧ = 50 MPa (tension positive). Find the angle θp from the x-axis to the direction of the largest principal stress, between −90° and 90°.

σx = −70 MPaσy = 70 MPaτxy = 50 MPa
θp = °
5.Hard
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 normal stress σθ on a plane whose normal is rotated 45° clockwise from the x-axis.

σx = 80 MPaσy = −20 MPaτxy = −40 MPaθ = -45°
σθ = MPa
6.Hard
σx​τxy​surface of the shaft

A solid shaft of diameter 50 mm carries an axial compressive force of 30 kN together with a torque of 400 N·m. At the surface of the shaft, find the largest principal stress σ1.

d = 50 mmF = −30 kNT = 400 N·m
σ1 = MPa

Answer key

  1. 1. σ2 = −72.17 MPa
  2. 2. σ2 = 43.82 MPa
  3. 3. θs = −71.57 °
  4. 4. θp = 72.23 °
  5. 5. σθ = 70 MPa
  6. 6. σ1 = 10.36 MPa

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