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​ = −30τxy​ = 10MPa

A point in a loaded part has σₓ = −60 MPa, σᵧ = −30 MPa and τₓᵧ = 10 MPa (tension positive). Find the smallest principal stress σ2.

σx = −60 MPaσy = −30 MPaτxy = 10 MPa
σ2 = MPa
2.Easy
σx​ = 160σy​ = 10τxy​ = −20MPa

A point in a loaded part has σₓ = 160 MPa, σᵧ = 10 MPa and τₓᵧ = −20 MPa (tension positive). Find the largest principal stress σ1.

σx = 160 MPaσy = 10 MPaτxy = −20 MPa
σ1 = MPa
3.Medium
σx​ = 140σy​ = 20τxy​ = 30MPa

A point in a thin plate is in plane stress: σₓ = 140 MPa, σᵧ = 20 MPa and τₓᵧ = 30 MPa, with σz = 0. Find the absolute maximum shear stress τabs at the point (considering all planes in three dimensions).

σx = 140 MPaσy = 20 MPaτxy = 30 MPaσz = 0
τabs = MPa
4.Medium
σx​ = 150σy​ = 90τxy​ = −40MPa

A point in a loaded part has σₓ = 150 MPa, σᵧ = 90 MPa and τₓᵧ = −40 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = 150 MPaσy = 90 MPaτxy = −40 MPa
τmax = MPa
5.Hard
σx​ = 100σy​ = −60τxy​ = 30MPa

A point in a loaded part has σₓ = 100 MPa, σᵧ = −60 MPa and τₓᵧ = 30 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 35° counter-clockwise from the x-axis.

σx = 100 MPaσy = −60 MPaτxy = 30 MPaθ = 35°
σθ = MPa
6.Hard
50°D = 1000 mm, t = 5 mm, p = 1.2 MPap

A thin-walled cylindrical tank of inner diameter 1000 mm and wall thickness 5 mm holds gas at a gauge pressure of 1.2 MPa. It is made from plate welded along a helical seam at 50° to the axis of the cylinder. Find the normal stress σn acting across the weld seam.

D = 1000 mmt = 5 mmp = 1.2 MPaα = 50°
σn = MPa

Answer key

  1. 1. σ2 = −63.03 MPa
  2. 2. σ1 = 162.6 MPa
  3. 3. τabs = 73.54 MPa
  4. 4. τmax = 50 MPa
  5. 5. σθ = 75.55 MPa
  6. 6. σn = 84.79 MPa

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