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​ = −20σy​ = 120τxy​ = −60MPa

A point in a loaded part has σₓ = −20 MPa, σᵧ = 120 MPa and τₓᵧ = −60 MPa (tension positive). Find the largest principal stress σ1.

σx = −20 MPaσy = 120 MPaτxy = −60 MPa
σ1 = MPa
2.Easy
σx​ = −70σy​ = 50τxy​ = −10MPa

A point in a loaded part has σₓ = −70 MPa, σᵧ = 50 MPa and τₓᵧ = −10 MPa (tension positive). Find the smallest principal stress σ2.

σx = −70 MPaσy = 50 MPaτxy = −10 MPa
σ2 = MPa
3.Medium
σx​ = 130σy​ = 10τxy​ = −10MPa

A point has σₓ = 130 MPa, σᵧ = 10 MPa and τₓᵧ = −10 MPa (tension positive). Find the angle θs, between −90° and 90°, from the x-axis to the normal of the plane on which the shear stress has its maximum positive value +R (shear positive in the same sense as τₓᵧ).

σx = 130 MPaσy = 10 MPaτxy = −10 MPa
θs = °
4.Medium
σx​ = −40MPaτxy​ = ?

A point has σₓ = −40 MPa and σᵧ = 0 MPa. How large can the shear stress τxy (magnitude) become before the largest principal stress reaches 20 MPa?

σx = −40 MPaσy = 0 MPaσ1 = 20 MPa
τxy = MPa
5.Hard
σx​ = 0σy​ = 90τxy​ = −60MPa

A point in a loaded part has σₓ = 0 MPa, σᵧ = 90 MPa and τₓᵧ = −60 MPa (tension positive). Find the shear stress τθ on a plane whose normal is rotated 45° counter-clockwise from the x-axis (positive in the same sense as τₓᵧ).

σx = 0 MPaσy = 90 MPaτxy = −60 MPaθ = 45°
τθ = MPa
6.Hard
σx​τxy​surface of the shaft

A solid shaft of diameter 50 mm carries an axial compressive force of 20 kN together with a torque of 1000 N·m. At the surface of the shaft, find the largest principal stress σ1.

d = 50 mmF = −20 kNT = 1000 N·m
σ1 = MPa

Answer key

  1. 1. σ1 = 142.2 MPa
  2. 2. σ2 = −70.83 MPa
  3. 3. θs = −49.73 °
  4. 4. τxy = 34.64 MPa
  5. 5. τθ = 45 MPa
  6. 6. σ1 = 35.97 MPa

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