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.

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1.Easy
σx​ = −60σy​ = 60τxy​ = −20MPa

A point in a loaded part has σₓ = −60 MPa, σᵧ = 60 MPa and τₓᵧ = −20 MPa (tension positive). Find the largest principal stress σ1.

σx = −60 MPaσy = 60 MPaτxy = −20 MPa
σ1 = MPa
2.Easy
σx​ = 100σy​ = −20τxy​ = −60MPa

A point in a loaded part has σₓ = 100 MPa, σᵧ = −20 MPa and τₓᵧ = −60 MPa (tension positive). Find the smallest principal stress σ2.

σx = 100 MPaσy = −20 MPaτxy = −60 MPa
σ2 = MPa
3.Medium
σx​ = −10σy​ = −20τxy​ = −60MPa

A point in a loaded part has σₓ = −10 MPa, σᵧ = −20 MPa and τₓᵧ = −60 MPa (tension positive). Find the angle θp from the x-axis to the direction of the largest principal stress, between −90° and 90°.

σx = −10 MPaσy = −20 MPaτxy = −60 MPa
θp = °
4.Medium
σx​ = 10σy​ = −30τxy​ = 30MPa

A point in a loaded part has σₓ = 10 MPa, σᵧ = −30 MPa and τₓᵧ = 30 MPa (tension positive). Find the angle θp from the x-axis to the direction of the largest principal stress, between −90° and 90°.

σx = 10 MPaσy = −30 MPaτxy = 30 MPa
θp = °
5.Hard
σx​ = −20σy​ = 90τxy​ = 30MPa

A point in a loaded part has σₓ = −20 MPa, σᵧ = 90 MPa and τₓᵧ = 30 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 35° counter-clockwise from the x-axis.

σx = −20 MPaσy = 90 MPaτxy = 30 MPaθ = 35°
σθ = MPa
6.Hard
σx​ = −80σy​ = 50τxy​ = −20MPa

A point in a thin plate is in plane stress: σₓ = −80 MPa, σᵧ = 50 MPa and τₓᵧ = −20 MPa (σz = 0). The material has a yield strength of 300 MPa. Find the factor of safety n against yielding by the von Mises (distortion energy) criterion.

σx = −80 MPaσy = 50 MPaτxy = −20 MPaσY = 300 MPa
n =

Answer key

  1. 1. σ1 = 63.25 MPa
  2. 2. σ2 = −44.85 MPa
  3. 3. θp = −42.62 °
  4. 4. θp = 28.15 °
  5. 5. σθ = 44.38 MPa
  6. 6. n = 2.526

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