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
100 kN100 kNθ = 50°A = 500 mm²

A bar with cross-sectional area 500 mm² carries an axial tensile force of 100 kN. Find the magnitude of the shear stress |τθ| on a section whose normal makes an angle of 50° with the bar axis.

P = 100 kNA = 500 mm²θ = 50°
|τθ| = MPa
2.Easy
30 kN30 kNθ = 35°A = 800 mm²

A bar with cross-sectional area 800 mm² carries an axial compressive force of 30 kN. Find the normal stress σθ on a section whose normal makes an angle of 35° with the bar axis (tension positive).

P = −30 kNA = 800 mm²θ = 35°
σθ = MPa
3.Medium
σx​ = −10σy​ = −10τxy​ = −40MPa

A point in a loaded part has σₓ = −10 MPa, σᵧ = −10 MPa and τₓᵧ = −40 MPa (tension positive). Find the angle θp from the x-axis to the direction of the largest principal stress, between −90° and 90°.

σx = −10 MPaσy = −10 MPaτxy = −40 MPa
θp = °
4.Medium
σx​ = 140σy​ = 50τxy​ = 10MPa

A point in a loaded part has σₓ = 140 MPa, σᵧ = 50 MPa and τₓᵧ = 10 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = 140 MPaσy = 50 MPaτxy = 10 MPa
τmax = MPa
5.Hard
50°D = 400 mm, t = 10 mm, p = 2 MPap

A thin-walled cylindrical tank of inner diameter 400 mm and wall thickness 10 mm holds gas at a gauge pressure of 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 = 400 mmt = 10 mmp = 2 MPaα = 50°
σn = MPa
6.Hard
40°D = 1500 mm, t = 8 mm, p = 1 MPap

A thin-walled cylindrical tank of inner diameter 1500 mm and wall thickness 8 mm holds gas at a gauge pressure of 1 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 = 1500 mmt = 8 mmp = 1 MPaα = 40°
σn = MPa

Answer key

  1. 1. |τθ| = 98.48 MPa
  2. 2. σθ = −25.16 MPa
  3. 3. θp = −45 °
  4. 4. τmax = 46.1 MPa
  5. 5. σn = 28.26 MPa
  6. 6. σn = 74.38 MPa

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