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​ = 140σy​ = 40τxy​ = −60MPa

A point in a loaded part has σₓ = 140 MPa, σᵧ = 40 MPa and τₓᵧ = −60 MPa (tension positive). Find the smallest principal stress σ2.

σx = 140 MPaσy = 40 MPaτxy = −60 MPa
σ2 = MPa
2.Easy
σx​ = −70σy​ = 120τxy​ = −20MPa

A point in a loaded part has σₓ = −70 MPa, σᵧ = 120 MPa and τₓᵧ = −20 MPa (tension positive). Find the largest principal stress σ1.

σx = −70 MPaσy = 120 MPaτxy = −20 MPa
σ1 = MPa
3.Medium
σx​ = −30σy​ = 50τxy​ = 40MPa

A point in a loaded part has σₓ = −30 MPa, σᵧ = 50 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 = −30 MPaσy = 50 MPaτxy = 40 MPa
θp = °
4.Medium
σx​ = −10σy​ = 80τxy​ = 10MPa

A point in a loaded part has σₓ = −10 MPa, σᵧ = 80 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 = −10 MPaσy = 80 MPaτxy = 10 MPa
θp = °
5.Hard
σx​ = 160σy​ = −80τxy​ = −60MPa

A point in a thin plate is in plane stress: σₓ = 160 MPa, σᵧ = −80 MPa and τₓᵧ = −60 MPa (σz = 0). The material has a yield strength of 350 MPa. Find the factor of safety n against yielding by the von Mises (distortion energy) criterion.

σx = 160 MPaσy = −80 MPaτxy = −60 MPaσY = 350 MPa
n =
6.Hard
σx​ = −60σy​ = −40τxy​ = 40MPa

A point in a loaded part has σₓ = −60 MPa, σᵧ = −40 MPa and τₓᵧ = 40 MPa (tension positive). Find the shear stress τθ on a plane whose normal is rotated 35° counter-clockwise from the x-axis (positive in the same sense as τₓᵧ).

σx = −60 MPaσy = −40 MPaτxy = 40 MPaθ = 35°
τθ = MPa

Answer key

  1. 1. σ2 = 11.9 MPa
  2. 2. σ1 = 122.1 MPa
  3. 3. θp = 67.5 °
  4. 4. θp = 83.74 °
  5. 5. n = 1.484
  6. 6. τθ = 23.08 MPa

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