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​ = 150σy​ = −20τxy​ = 20MPa

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

σx = 150 MPaσy = −20 MPaτxy = 20 MPa
σ2 = MPa
2.Easy
σx​ = 170σy​ = −100MPaprincipal element

At a point in a loaded part the in-plane principal stresses are σ₁ = 170 MPa and σ₂ = −100 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σ1 = 170 MPaσ2 = −100 MPa
τmax = MPa
3.Medium
σy​ = 60MPaτxy​ = ?

A point has σₓ = 0 MPa and σᵧ = 60 MPa. How large can the shear stress τxy (magnitude) become before the largest principal stress reaches 105 MPa?

σx = 0 MPaσy = 60 MPaσ1 = 105 MPa
τxy = MPa
4.Medium
σx​ = 70σy​ = 110τxy​ = 10MPa

A point in a loaded part has σₓ = 70 MPa, σᵧ = 110 MPa and τₓᵧ = 10 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = 70 MPaσy = 110 MPaτxy = 10 MPa
τmax = MPa
5.Hard
50°D = 400 mm, t = 8 mm, p = 3 MPap

A thin-walled cylindrical tank of inner diameter 400 mm and wall thickness 8 mm holds gas at a gauge pressure of 3 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 = 400 mmt = 8 mmp = 3 MPaα = 50°
σn = MPa
6.Hard
σx​ = 70σy​ = −80τxy​ = −30MPa

A point in a loaded part has σₓ = 70 MPa, σᵧ = −80 MPa and τₓᵧ = −30 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 50° counter-clockwise from the x-axis.

σx = 70 MPaσy = −80 MPaτxy = −30 MPaθ = 50°
σθ = MPa

Answer key

  1. 1. σ2 = −22.32 MPa
  2. 2. τmax = 135 MPa
  3. 3. τxy = 68.74 MPa
  4. 4. τmax = 22.36 MPa
  5. 5. σn = 52.99 MPa
  6. 6. σθ = −47.57 MPa

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