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
150 kN150 kNθ = 60°A = 800 mm²

A bar with cross-sectional area 800 mm² carries an axial tensile force of 150 kN. Find the normal stress σθ on a section whose normal makes an angle of 60° with the bar axis (tension positive).

P = 150 kNA = 800 mm²θ = 60°
σθ = MPa
2.Easy
σx​ = 30σy​ = −70τxy​MPa

A point has σₓ = 30 MPa and σᵧ = −70 MPa, plus some shear stress. On an element rotated by 40° the normal stress in the rotated x′ direction is 18.2 MPa. Find the normal stress σy′ in the rotated y′ direction.

σx = 30 MPaσy = −70 MPaσx′ = 18.2 MPaθ = 40°
σy′ = MPa
3.Medium
σx​ = 150σy​ = 120τxy​ = −50MPa

A point in a thin plate is in plane stress: σₓ = 150 MPa, σᵧ = 120 MPa and τₓᵧ = −50 MPa, with σz = 0. Find the absolute maximum shear stress τabs at the point (considering all planes in three dimensions).

σx = 150 MPaσy = 120 MPaτxy = −50 MPaσz = 0
τabs = MPa
4.Medium
σx​ = 30σy​ = 60τxy​ = 20MPa

A point in a thin plate is in plane stress: σₓ = 30 MPa, σᵧ = 60 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 = 30 MPaσy = 60 MPaτxy = 20 MPaσz = 0
τabs = MPa
5.Hard
25°D = 800 mm, t = 5 mm, p = 0.8 MPap

A thin-walled cylindrical tank of inner diameter 800 mm and wall thickness 5 mm holds gas at a gauge pressure of 0.8 MPa. It is made from plate welded along a helical seam at 25° to the axis of the cylinder. Find the normal stress σn acting across the weld seam.

D = 800 mmt = 5 mmp = 0.8 MPaα = 25°
σn = MPa
6.Hard
20°D = 500 mm, t = 8 mm, p = 3 MPap

A thin-walled cylindrical tank of inner diameter 500 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 20° to the axis of the cylinder. Find the magnitude of the shear stress |τn| acting along the weld seam.

D = 500 mmt = 8 mmp = 3 MPaα = 20°
|τn| = MPa

Answer key

  1. 1. σθ = 46.88 MPa
  2. 2. σy′ = −58.2 MPa
  3. 3. τabs = 93.6 MPa
  4. 4. τabs = 35 MPa
  5. 5. σn = 58.28 MPa
  6. 6. |τn| = 15.07 MPa

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