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​ = 20σy​ = −70τxy​ = −30MPa

A point in a loaded part has σₓ = 20 MPa, σᵧ = −70 MPa and τₓᵧ = −30 MPa (tension positive). Find the largest principal stress σ1.

σx = 20 MPaσy = −70 MPaτxy = −30 MPa
σ1 = MPa
2.Easy
σx​ = −50σy​ = 120τxy​ = 60MPa

A point in a loaded part has σₓ = −50 MPa, σᵧ = 120 MPa and τₓᵧ = 60 MPa (tension positive). Find the largest principal stress σ1.

σx = −50 MPaσy = 120 MPaτxy = 60 MPa
σ1 = MPa
3.Medium
σx​ = 100σy​ = 110τxy​ = 60MPa

A point in a loaded part has σₓ = 100 MPa, σᵧ = 110 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 = 100 MPaσy = 110 MPaτxy = 60 MPa
θp = °
4.Medium
σx​ = 10σy​ = 60τxy​ = −30MPa

A point has σₓ = 10 MPa, σᵧ = 60 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 = 10 MPaσy = 60 MPaτxy = −30 MPaθ = 20°
σy′ = MPa
5.Hard
σx​ = 30σy​ = −80τxy​ = −50MPa

A point in a thin plate is in plane stress: σₓ = 30 MPa, σᵧ = −80 MPa and τₓᵧ = −50 MPa (σz = 0). The material has a yield strength of 460 MPa. Find the factor of safety n against yielding by the von Mises (distortion energy) criterion.

σx = 30 MPaσy = −80 MPaτxy = −50 MPaσY = 460 MPa
n =
6.Hard
σx​ = −10σy​ = 90τxy​ = 40MPa

A point in a loaded part has σₓ = −10 MPa, σᵧ = 90 MPa and τₓᵧ = 40 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 20° clockwise from the x-axis.

σx = −10 MPaσy = 90 MPaτxy = 40 MPaθ = -20°
σθ = MPa

Answer key

  1. 1. σ1 = 29.08 MPa
  2. 2. σ1 = 139 MPa
  3. 3. θp = 47.38 °
  4. 4. σy′ = 73.43 MPa
  5. 5. n = 3.507
  6. 6. σθ = −24.01 MPa

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