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​ = −70σy​ = 30τxy​ = −50MPa

A point in a loaded part has σₓ = −70 MPa, σᵧ = 30 MPa and τₓᵧ = −50 MPa (tension positive). Find the largest principal stress σ1.

σx = −70 MPaσy = 30 MPaτxy = −50 MPa
σ1 = MPa
2.Easy
σx​ = 130σy​ = −60τxy​ = 20MPa

A point in a loaded part has σₓ = 130 MPa, σᵧ = −60 MPa and τₓᵧ = 20 MPa (tension positive). Find the smallest principal stress σ2.

σx = 130 MPaσy = −60 MPaτxy = 20 MPa
σ2 = MPa
3.Medium
σx​ = 0σy​ = 30τxy​ = −30MPa

A point in a loaded part has σₓ = 0 MPa, σᵧ = 30 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 = 0 MPaσy = 30 MPaτxy = −30 MPa
θp = °
4.Medium
σx​ = −50σy​ = 60τxy​ = 20MPa

A point has σₓ = −50 MPa, σᵧ = 60 MPa and τₓᵧ = 20 MPa (tension positive). The element is rotated 20° clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.

σx = −50 MPaσy = 60 MPaτxy = 20 MPaθ = -20°
σy′ = MPa
5.Hard
σx​ = 0σy​ = −10τxy​ = 10MPa

A point in a loaded part has σₓ = 0 MPa, σᵧ = −10 MPa and τₓᵧ = 10 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 50° counter-clockwise from the x-axis.

σx = 0 MPaσy = −10 MPaτxy = 10 MPaθ = 50°
σθ = MPa
6.Hard
60°D = 1200 mm, t = 8 mm, p = 0.5 MPap

A thin-walled cylindrical tank of inner diameter 1200 mm and wall thickness 8 mm holds gas at a gauge pressure of 0.5 MPa. It is made from plate welded along a helical seam at 60° to the axis of the cylinder. Find the magnitude of the shear stress |τn| acting along the weld seam.

D = 1200 mmt = 8 mmp = 0.5 MPaα = 60°
|τn| = MPa

Answer key

  1. 1. σ1 = 50.71 MPa
  2. 2. σ2 = −62.08 MPa
  3. 3. θp = −58.28 °
  4. 4. σy′ = 59.99 MPa
  5. 5. σθ = 3.98 MPa
  6. 6. |τn| = 8.119 MPa

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