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
10 kN10 kNθ = 20°A = 250 mm²

A bar with cross-sectional area 250 mm² carries an axial tensile force of 10 kN. Find the magnitude of the shear stress |τθ| on a section whose normal makes an angle of 20° with the bar axis.

P = 10 kNA = 250 mm²θ = 20°
|τθ| = MPa
2.Easy
σx​ = 80σy​ = −70τxy​ = 50MPa

A point in a loaded part has σₓ = 80 MPa, σᵧ = −70 MPa and τₓᵧ = 50 MPa (tension positive). Find the smallest principal stress σ2.

σx = 80 MPaσy = −70 MPaτxy = 50 MPa
σ2 = MPa
3.Medium
σx​ = 70σy​ = 0τxy​ = 60MPa

A point in a loaded part has σₓ = 70 MPa, σᵧ = 0 MPa and τₓᵧ = 60 MPa (tension positive). Find the angle θp from the x-axis to the direction of the largest principal stress, between −90° and 90°.

σx = 70 MPaσy = 0 MPaτxy = 60 MPa
θp = °
4.Medium
σx​ = 110σy​ = 110τxy​ = 30MPa

A point in a loaded part has σₓ = 110 MPa, σᵧ = 110 MPa and τₓᵧ = 30 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = 110 MPaσy = 110 MPaτxy = 30 MPa
τmax = MPa
5.Hard
σx​ = 130σy​ = −60τxy​ = 40MPa

A point in a loaded part has σₓ = 130 MPa, σᵧ = −60 MPa and τₓᵧ = 40 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 30° counter-clockwise from the x-axis.

σx = 130 MPaσy = −60 MPaτxy = 40 MPaθ = 30°
σθ = MPa
6.Hard
σx​ = 80σy​ = −80τxy​ = 30MPa

A point in a loaded part has σₓ = 80 MPa, σᵧ = −80 MPa and τₓᵧ = 30 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 20° clockwise from the x-axis.

σx = 80 MPaσy = −80 MPaτxy = 30 MPaθ = -20°
σθ = MPa

Answer key

  1. 1. |τθ| = 12.86 MPa
  2. 2. σ2 = −85.14 MPa
  3. 3. θp = 29.87 °
  4. 4. τmax = 30 MPa
  5. 5. σθ = 117.1 MPa
  6. 6. σθ = 42 MPa

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