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​ = 40σy​ = −10τxy​ = 60MPa

A point in a loaded part has σₓ = 40 MPa, σᵧ = −10 MPa and τₓᵧ = 60 MPa (tension positive). Find the smallest principal stress σ2.

σx = 40 MPaσy = −10 MPaτxy = 60 MPa
σ2 = MPa
2.Easy
σx​ = 70σy​ = −60MPaprincipal element

At a point in a loaded part the in-plane principal stresses are σ₁ = 70 MPa and σ₂ = −60 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σ1 = 70 MPaσ2 = −60 MPa
τmax = MPa
3.Medium
σy​ = 50τxy​ = 30MPa

A point has σₓ = 0 MPa, σᵧ = 50 MPa and τₓᵧ = 30 MPa (tension positive). The element is rotated 20° counter-clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.

σx = 0 MPaσy = 50 MPaτxy = 30 MPaθ = 20°
σy′ = MPa
4.Medium
σx​ = 100σy​ = 30τxy​ = −60MPa

A point in a loaded part has σₓ = 100 MPa, σᵧ = 30 MPa and τₓᵧ = −60 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = 100 MPaσy = 30 MPaτxy = −60 MPa
τmax = MPa
5.Hard
σx​ = −30σy​ = −80τxy​ = −60MPa

A point in a thin plate is in plane stress: σₓ = −30 MPa, σᵧ = −80 MPa and τₓᵧ = −60 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 = −30 MPaσy = −80 MPaτxy = −60 MPaσY = 275 MPa
n =
6.Hard
σx​τxy​top surface of the shaft

A solid shaft of diameter 50 mm carries a bending moment of 750 N·m together with a torque of 1500 N·m. At the top surface, where the bending stress is tensile and largest, find the maximum in-plane shear stress τmax.

d = 50 mmM = 750 N·mT = 1500 N·m
τmax = MPa

Answer key

  1. 1. σ2 = −50 MPa
  2. 2. τmax = 65 MPa
  3. 3. σy′ = 24.87 MPa
  4. 4. τmax = 69.46 MPa
  5. 5. n = 2.195
  6. 6. τmax = 68.33 MPa

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