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​ = 60MPa

A point in a loaded part has σₓ = 90 MPa, σᵧ = 70 MPa and τₓᵧ = 60 MPa (tension positive). Find the smallest principal stress σ2.

σx = 90 MPaσy = 70 MPaτxy = 60 MPa
σ2 = MPa
2.Easy
σx​ = 160σy​ = 80τxy​ = −30MPa

A point in a loaded part has σₓ = 160 MPa, σᵧ = 80 MPa and τₓᵧ = −30 MPa (tension positive). Find the largest principal stress σ1.

σx = 160 MPaσy = 80 MPaτxy = −30 MPa
σ1 = MPa
3.Medium
σx​ = −60σy​ = −20τxy​ = −10MPa

A point has σₓ = −60 MPa, σᵧ = −20 MPa and τₓᵧ = −10 MPa (tension positive). The element is rotated 45° clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.

σx = −60 MPaσy = −20 MPaτxy = −10 MPaθ = -45°
σy′ = MPa
4.Medium
σx​ = 10σy​ = −30τxy​ = 50MPa

A point has σₓ = 10 MPa, σᵧ = −30 MPa and τₓᵧ = 50 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 = 10 MPaσy = −30 MPaτxy = 50 MPa
θs = °
5.Hard
σx​ = −10σy​ = −50τxy​ = −30MPa

A point in a thin plate is in plane stress: σₓ = −10 MPa, σᵧ = −50 MPa and τₓᵧ = −30 MPa (σz = 0). The material has a yield strength of 275 MPa. Find the factor of safety n against yielding by the von Mises (distortion energy) criterion.

σx = −10 MPaσy = −50 MPaτxy = −30 MPaσY = 275 MPa
n =
6.Hard
σx​ = 90σy​ = 120τxy​ = 10MPa

A point in a thin plate is in plane stress: σₓ = 90 MPa, σᵧ = 120 MPa and τₓᵧ = 10 MPa (σz = 0). The material has a yield strength of 420 MPa. Find the factor of safety n against yielding by the Tresca (maximum shear stress) criterion.

σx = 90 MPaσy = 120 MPaτxy = 10 MPaσY = 420 MPa
n =

Answer key

  1. 1. σ2 = 19.17 MPa
  2. 2. σ1 = 170 MPa
  3. 3. σy′ = −50 MPa
  4. 4. θs = −10.9 °
  5. 5. n = 3.969
  6. 6. n = 3.414

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