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​ = 60σy​ = 50τxy​ = 30MPa

A point in a loaded part has σₓ = 60 MPa, σᵧ = 50 MPa and τₓᵧ = 30 MPa (tension positive). Find the smallest principal stress σ2.

σx = 60 MPaσy = 50 MPaτxy = 30 MPa
σ2 = MPa
2.Easy
σx​ = 80σy​ = 80τxy​ = 20MPa

A point in a loaded part has σₓ = 80 MPa, σᵧ = 80 MPa and τₓᵧ = 20 MPa (tension positive). Find the largest principal stress σ1.

σx = 80 MPaσy = 80 MPaτxy = 20 MPa
σ1 = MPa
3.Medium
σx​ = 150σy​ = 100τxy​ = 20MPa

A point in a thin plate is in plane stress: σₓ = 150 MPa, σᵧ = 100 MPa and τₓᵧ = 20 MPa, with σz = 0. Find the absolute maximum shear stress τabs at the point (considering all planes in three dimensions).

σx = 150 MPaσy = 100 MPaτxy = 20 MPaσz = 0
τabs = MPa
4.Medium
σx​ = 90σy​ = 120τxy​ = −60MPa

A point has σₓ = 90 MPa, σᵧ = 120 MPa and τₓᵧ = −60 MPa (tension positive). The element is rotated 50° counter-clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.

σx = 90 MPaσy = 120 MPaτxy = −60 MPaθ = 50°
σy′ = MPa
5.Hard
σx​ = 120σy​ = 70τxy​ = −30MPa

A point in a loaded part has σₓ = 120 MPa, σᵧ = 70 MPa and τₓᵧ = −30 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 30° counter-clockwise from the x-axis.

σx = 120 MPaσy = 70 MPaτxy = −30 MPaθ = 30°
σθ = MPa
6.Hard
40°D = 800 mm, t = 6 mm, p = 1.2 MPap

A thin-walled cylindrical tank of inner diameter 800 mm and wall thickness 6 mm holds gas at a gauge pressure of 1.2 MPa. It is made from plate welded along a helical seam at 40° to the axis of the cylinder. Find the normal stress σn acting across the weld seam.

D = 800 mmt = 6 mmp = 1.2 MPaα = 40°
σn = MPa

Answer key

  1. 1. σ2 = 24.59 MPa
  2. 2. σ1 = 100 MPa
  3. 3. τabs = 78.51 MPa
  4. 4. σy′ = 161.5 MPa
  5. 5. σθ = 81.52 MPa
  6. 6. σn = 63.47 MPa

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