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​ = −40σy​ = 0τxy​ = 50MPa

A point in a loaded part has σₓ = −40 MPa, σᵧ = 0 MPa and τₓᵧ = 50 MPa (tension positive). Find the smallest principal stress σ2.

σx = −40 MPaσy = 0 MPaτxy = 50 MPa
σ2 = MPa
2.Easy
150 kN150 kNθ = 40°A = 800 mm²

A bar with cross-sectional area 800 mm² carries an axial tensile force of 150 kN. Find the magnitude of the shear stress |τθ| on a section whose normal makes an angle of 40° with the bar axis.

P = 150 kNA = 800 mm²θ = 40°
|τθ| = MPa
3.Medium
σx​ = 160σy​ = 40τxy​ = −10MPa

A point in a loaded part has σₓ = 160 MPa, σᵧ = 40 MPa and τₓᵧ = −10 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = 160 MPaσy = 40 MPaτxy = −10 MPa
τmax = MPa
4.Medium
σx​ = 50σy​ = 30τxy​ = 60MPa

A point in a loaded part has σₓ = 50 MPa, σᵧ = 30 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 = 50 MPaσy = 30 MPaτxy = 60 MPa
θp = °
5.Hard
σx​ = 140σy​ = 40τxy​ = −50MPa

A point in a loaded part has σₓ = 140 MPa, σᵧ = 40 MPa and τₓᵧ = −50 MPa (tension positive). Find the shear stress τθ on a plane whose normal is rotated 50° counter-clockwise from the x-axis (positive in the same sense as τₓᵧ).

σx = 140 MPaσy = 40 MPaτxy = −50 MPaθ = 50°
τθ = MPa
6.Hard
σx​ = 90σy​ = −50τxy​ = −20MPa

A point in a loaded part has σₓ = 90 MPa, σᵧ = −50 MPa and τₓᵧ = −20 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 40° counter-clockwise from the x-axis.

σx = 90 MPaσy = −50 MPaτxy = −20 MPaθ = 40°
σθ = MPa

Answer key

  1. 1. σ2 = −73.85 MPa
  2. 2. |τθ| = 92.33 MPa
  3. 3. τmax = 60.83 MPa
  4. 4. θp = 40.27 °
  5. 5. τθ = −40.56 MPa
  6. 6. σθ = 12.46 MPa

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