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
τxy​ = −100MPapure shear

A point on the surface of a shaft in torsion is in pure shear with τₓᵧ = −100 MPa (σₓ = σᵧ = 0). Find the normal stress σθ on a plane whose normal is rotated 35° counter-clockwise from the x-axis.

τxy = −100 MPaθ = 35°
σθ = MPa
2.Easy
σx​ = 50σy​ = −80τxy​ = 30MPa

A point in a loaded part has σₓ = 50 MPa, σᵧ = −80 MPa and τₓᵧ = 30 MPa (tension positive). Find the largest principal stress σ1.

σx = 50 MPaσy = −80 MPaτxy = 30 MPa
σ1 = MPa
3.Medium
σx​ = 90σy​ = −30τxy​ = −50MPa

A point in a loaded part has σₓ = 90 MPa, σᵧ = −30 MPa and τₓᵧ = −50 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = 90 MPaσy = −30 MPaτxy = −50 MPa
τmax = MPa
4.Medium
σx​ = 110σy​ = 0τxy​ = −10MPa

A point in a loaded part has σₓ = 110 MPa, σᵧ = 0 MPa and τₓᵧ = −10 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = 110 MPaσy = 0 MPaτxy = −10 MPa
τmax = MPa
5.Hard
σx​ = −60σy​ = 120τxy​ = −30MPa

A point in a loaded part has σₓ = −60 MPa, σᵧ = 120 MPa and τₓᵧ = −30 MPa (tension positive). Find the shear stress τθ on a plane whose normal is rotated 30° clockwise from the x-axis (positive in the same sense as τₓᵧ).

σx = −60 MPaσy = 120 MPaτxy = −30 MPaθ = -30°
τθ = MPa
6.Hard
σx​ = −50σy​ = −60τxy​ = 40MPa

A point in a thin plate is in plane stress: σₓ = −50 MPa, σᵧ = −60 MPa and τₓᵧ = 40 MPa (σz = 0). The material has a yield strength of 355 MPa. Find the factor of safety n against yielding by the Tresca (maximum shear stress) criterion.

σx = −50 MPaσy = −60 MPaτxy = 40 MPaσY = 355 MPa
n =

Answer key

  1. 1. σθ = −93.97 MPa
  2. 2. σ1 = 56.59 MPa
  3. 3. τmax = 78.1 MPa
  4. 4. τmax = 55.9 MPa
  5. 5. τθ = −92.94 MPa
  6. 6. n = 3.725

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