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​ = −50σy​ = 30τxy​ = −30MPa

A point in a loaded part has σₓ = −50 MPa, σᵧ = 30 MPa and τₓᵧ = −30 MPa (tension positive). Find the smallest principal stress σ2.

σx = −50 MPaσy = 30 MPaτxy = −30 MPa
σ2 = MPa
2.Easy
σx​ = 150σy​ = −70τxy​ = −20MPa

A point in a loaded part has σₓ = 150 MPa, σᵧ = −70 MPa and τₓᵧ = −20 MPa (tension positive). Find the smallest principal stress σ2.

σx = 150 MPaσy = −70 MPaτxy = −20 MPa
σ2 = MPa
3.Medium
σx​ = −60σy​ = −80τxy​ = 30MPa

A point in a loaded part has σₓ = −60 MPa, σᵧ = −80 MPa and τₓᵧ = 30 MPa (tension positive). Find the angle θp from the x-axis to the direction of the largest principal stress, between −90° and 90°.

σx = −60 MPaσy = −80 MPaτxy = 30 MPa
θp = °
4.Medium
σx​ = 40σy​ = 50MPaτxy​ = ?

A point has σₓ = 40 MPa and σᵧ = 50 MPa. How large can the shear stress τxy (magnitude) become before the largest principal stress reaches 85 MPa?

σx = 40 MPaσy = 50 MPaσ1 = 85 MPa
τxy = MPa
5.Hard
σx​ = 140σy​ = −60τxy​ = −30MPa

A point in a thin plate is in plane stress: σₓ = 140 MPa, σᵧ = −60 MPa and τₓᵧ = −30 MPa (σz = 0). The material has a yield strength of 300 MPa. Find the factor of safety n against yielding by the von Mises (distortion energy) criterion.

σx = 140 MPaσy = −60 MPaτxy = −30 MPaσY = 300 MPa
n =
6.Hard
σx​ = 40σy​ = 90τxy​ = −50MPa

A point in a loaded part has σₓ = 40 MPa, σᵧ = 90 MPa and τₓᵧ = −50 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 30° clockwise from the x-axis.

σx = 40 MPaσy = 90 MPaτxy = −50 MPaθ = -30°
σθ = MPa

Answer key

  1. 1. σ2 = −60 MPa
  2. 2. σ2 = −71.8 MPa
  3. 3. θp = 35.78 °
  4. 4. τxy = 39.69 MPa
  5. 5. n = 1.62
  6. 6. σθ = 95.8 MPa

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