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
120 kN120 kNθ = 25°A = 1000 mm²

A bar with cross-sectional area 1000 mm² carries an axial tensile force of 120 kN. Find the normal stress σθ on a section whose normal makes an angle of 25° with the bar axis (tension positive).

P = 120 kNA = 1000 mm²θ = 25°
σθ = MPa
2.Easy
50 kN50 kNθ = 20°A = 500 mm²

A bar with cross-sectional area 500 mm² carries an axial tensile force of 50 kN. Find the magnitude of the shear stress |τθ| on a section whose normal makes an angle of 20° with the bar axis.

P = 50 kNA = 500 mm²θ = 20°
|τθ| = MPa
3.Medium
σx​ = 80σy​ = 60τxy​ = −60MPa

A point in a loaded part has σₓ = 80 MPa, σᵧ = 60 MPa and τₓᵧ = −60 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = 80 MPaσy = 60 MPaτxy = −60 MPa
τmax = MPa
4.Medium
σx​ = 30σy​ = 10τxy​ = 60MPa

A point in a loaded part has σₓ = 30 MPa, σᵧ = 10 MPa and τₓᵧ = 60 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = 30 MPaσy = 10 MPaτxy = 60 MPa
τmax = MPa
5.Hard
σx​ = 130σy​ = 0τxy​ = 30MPa

A point in a loaded part has σₓ = 130 MPa, σᵧ = 0 MPa and τₓᵧ = 30 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 60° counter-clockwise from the x-axis.

σx = 130 MPaσy = 0 MPaτxy = 30 MPaθ = 60°
σθ = MPa
6.Hard
σx​ = 10σy​ = −10τxy​ = 50MPa

A point in a loaded part has σₓ = 10 MPa, σᵧ = −10 MPa and τₓᵧ = 50 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 35° counter-clockwise from the x-axis.

σx = 10 MPaσy = −10 MPaτxy = 50 MPaθ = 35°
σθ = MPa

Answer key

  1. 1. σθ = 98.57 MPa
  2. 2. |τθ| = 32.14 MPa
  3. 3. τmax = 60.83 MPa
  4. 4. τmax = 60.83 MPa
  5. 5. σθ = 58.48 MPa
  6. 6. σθ = 50.4 MPa

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