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​ = 110σy​ = 70MPaprincipal element

At a point in a loaded part the in-plane principal stresses are σ₁ = 110 MPa and σ₂ = 70 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σ1 = 110 MPaσ2 = 70 MPa
τmax = MPa
2.Easy
σx​ = 30σy​ = 90τxy​ = 50MPa

A point in a loaded part has σₓ = 30 MPa, σᵧ = 90 MPa and τₓᵧ = 50 MPa (tension positive). Find the largest principal stress σ1.

σx = 30 MPaσy = 90 MPaτxy = 50 MPa
σ1 = MPa
3.Medium
σx​ = 90σy​ = 70τxy​ = −40MPa

A point has σₓ = 90 MPa, σᵧ = 70 MPa and τₓᵧ = −40 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 = 90 MPaσy = 70 MPaτxy = −40 MPaθ = -20°
σy′ = MPa
4.Medium
σx​ = 70MPaτxy​ = ?

A point has σₓ = 70 MPa and σᵧ = 0 MPa. How large can the shear stress τxy (magnitude) become before the largest principal stress reaches 120 MPa?

σx = 70 MPaσy = 0 MPaσ1 = 120 MPa
τxy = MPa
5.Hard
σx​ = −40σy​ = 40τxy​ = −30MPa

A point in a loaded part has σₓ = −40 MPa, σᵧ = 40 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 = −40 MPaσy = 40 MPaτxy = −30 MPaθ = 35°
σθ = MPa
6.Hard
40°D = 600 mm, t = 5 mm, p = 1.5 MPap

A thin-walled cylindrical tank of inner diameter 600 mm and wall thickness 5 mm holds gas at a gauge pressure of 1.5 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 = 600 mmt = 5 mmp = 1.5 MPaα = 40°
σn = MPa

Answer key

  1. 1. τmax = 20 MPa
  2. 2. σ1 = 118.3 MPa
  3. 3. σy′ = 46.63 MPa
  4. 4. τxy = 77.46 MPa
  5. 5. σθ = −41.87 MPa
  6. 6. σn = 71.41 MPa

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