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
50 kN50 kNθ = 60°A = 400 mm²

A bar with cross-sectional area 400 mm² carries an axial tensile force of 50 kN. Find the normal stress σθ on a section whose normal makes an angle of 60° with the bar axis (tension positive).

P = 50 kNA = 400 mm²θ = 60°
σθ = MPa
2.Easy
σx​ = 160σy​ = 20τxy​ = −10MPa

A point in a loaded part has σₓ = 160 MPa, σᵧ = 20 MPa and τₓᵧ = −10 MPa (tension positive). Find the smallest principal stress σ2.

σx = 160 MPaσy = 20 MPaτxy = −10 MPa
σ2 = MPa
3.Medium
σx​ = 0σy​ = −70τxy​ = −60MPa

A point in a loaded part has σₓ = 0 MPa, σᵧ = −70 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 = 0 MPaσy = −70 MPaτxy = −60 MPa
θp = °
4.Medium
σx​ = −40σy​ = 100τxy​ = 30MPa

A point in a loaded part has σₓ = −40 MPa, σᵧ = 100 MPa and τₓᵧ = 30 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = −40 MPaσy = 100 MPaτxy = 30 MPa
τmax = MPa
5.Hard
σx​ = 160σy​ = −50τxy​ = 20MPa

A point in a loaded part has σₓ = 160 MPa, σᵧ = −50 MPa and τₓᵧ = 20 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 45° counter-clockwise from the x-axis.

σx = 160 MPaσy = −50 MPaτxy = 20 MPaθ = 45°
σθ = MPa
6.Hard
σx​ = −50σy​ = 0τxy​ = 50MPa

A point in a loaded part has σₓ = −50 MPa, σᵧ = 0 MPa and τₓᵧ = 50 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 20° clockwise from the x-axis.

σx = −50 MPaσy = 0 MPaτxy = 50 MPaθ = -20°
σθ = MPa

Answer key

  1. 1. σθ = 31.25 MPa
  2. 2. σ2 = 19.29 MPa
  3. 3. θp = −29.87 °
  4. 4. τmax = 76.16 MPa
  5. 5. σθ = 75 MPa
  6. 6. σθ = −76.29 MPa

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