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​ = −80τxy​ = 50MPa

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

σx = −50 MPaσy = −80 MPaτxy = 50 MPa
σ1 = MPa
2.Easy
σx​ = −40σy​ = 10τxy​ = −30MPa

A point in a loaded part has σₓ = −40 MPa, σᵧ = 10 MPa and τₓᵧ = −30 MPa (tension positive). Find the smallest principal stress σ2.

σx = −40 MPaσy = 10 MPaτxy = −30 MPa
σ2 = MPa
3.Medium
σx​ = 80σy​ = 50τxy​ = −10MPa

A point has σₓ = 80 MPa, σᵧ = 50 MPa and τₓᵧ = −10 MPa (tension positive). The element is rotated 30° counter-clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.

σx = 80 MPaσy = 50 MPaτxy = −10 MPaθ = 30°
σy′ = MPa
4.Medium
σx​ = 80σy​ = −80τxy​ = −10MPa

A point in a loaded part has σₓ = 80 MPa, σᵧ = −80 MPa and τₓᵧ = −10 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = 80 MPaσy = −80 MPaτxy = −10 MPa
τmax = MPa
5.Hard
25°D = 1000 mm, t = 15 mm, p = 2.5 MPap

A thin-walled cylindrical tank of inner diameter 1000 mm and wall thickness 15 mm holds gas at a gauge pressure of 2.5 MPa. It is made from plate welded along a helical seam at 25° to the axis of the cylinder. Find the magnitude of the shear stress |τn| acting along the weld seam.

D = 1000 mmt = 15 mmp = 2.5 MPaα = 25°
|τn| = MPa
6.Hard
σx​ = 0σy​ = −40τxy​ = 30MPa

A point in a loaded part has σₓ = 0 MPa, σᵧ = −40 MPa and τₓᵧ = 30 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 45° clockwise from the x-axis.

σx = 0 MPaσy = −40 MPaτxy = 30 MPaθ = -45°
σθ = MPa

Answer key

  1. 1. σ1 = −12.8 MPa
  2. 2. σ2 = −54.05 MPa
  3. 3. σy′ = 66.16 MPa
  4. 4. τmax = 80.62 MPa
  5. 5. |τn| = 15.96 MPa
  6. 6. σθ = −50 MPa

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