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​ = 100σy​ = −70τxy​ = 40MPa

A point in a loaded part has σₓ = 100 MPa, σᵧ = −70 MPa and τₓᵧ = 40 MPa (tension positive). Find the smallest principal stress σ2.

σx = 100 MPaσy = −70 MPaτxy = 40 MPa
σ2 = MPa
2.Easy
σx​ = −60σy​ = 30τxy​ = 20MPa

A point in a loaded part has σₓ = −60 MPa, σᵧ = 30 MPa and τₓᵧ = 20 MPa (tension positive). Find the smallest principal stress σ2.

σx = −60 MPaσy = 30 MPaτxy = 20 MPa
σ2 = MPa
3.Medium
σx​ = −40σy​ = 20τxy​ = −60MPa

A point in a loaded part has σₓ = −40 MPa, σᵧ = 20 MPa and τₓᵧ = −60 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = −40 MPaσy = 20 MPaτxy = −60 MPa
τmax = MPa
4.Medium
σx​ = 100σy​ = −60τxy​ = −60MPa

A point in a loaded part has σₓ = 100 MPa, σᵧ = −60 MPa and τₓᵧ = −60 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = 100 MPaσy = −60 MPaτxy = −60 MPa
τmax = MPa
5.Hard
σx​ = 90σy​ = 30τxy​ = −50MPa

A point in a thin plate is in plane stress: σₓ = 90 MPa, σᵧ = 30 MPa and τₓᵧ = −50 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 = 90 MPaσy = 30 MPaτxy = −50 MPaσY = 275 MPa
n =
6.Hard
σx​ = 30τxy​ = −60MPa

A point in a thin plate is in plane stress: σₓ = 30 MPa, σᵧ = 0 MPa and τₓᵧ = −60 MPa (σz = 0). The material has a yield strength of 250 MPa. Find the factor of safety n against yielding by the von Mises (distortion energy) criterion.

σx = 30 MPaσy = 0 MPaτxy = −60 MPaσY = 250 MPa
n =

Answer key

  1. 1. σ2 = −78.94 MPa
  2. 2. σ2 = −64.24 MPa
  3. 3. τmax = 67.08 MPa
  4. 4. τmax = 100 MPa
  5. 5. n = 2.341
  6. 6. n = 2.311

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