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​ = 80σy​ = −30τxy​ = −20MPa

A point in a loaded part has σₓ = 80 MPa, σᵧ = −30 MPa and τₓᵧ = −20 MPa (tension positive). Find the smallest principal stress σ2.

σx = 80 MPaσy = −30 MPaτxy = −20 MPa
σ2 = MPa
2.Easy
σx​ = 20σy​ = 90τxy​ = 40MPa

A point in a loaded part has σₓ = 20 MPa, σᵧ = 90 MPa and τₓᵧ = 40 MPa (tension positive). Find the largest principal stress σ1.

σx = 20 MPaσy = 90 MPaτxy = 40 MPa
σ1 = MPa
3.Medium
σx​ = 110σy​ = 60τxy​ = 30MPa

A point has σₓ = 110 MPa, σᵧ = 60 MPa and τₓᵧ = 30 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 = 110 MPaσy = 60 MPaτxy = 30 MPa
θs = °
4.Medium
σx​ = 120σy​ = 110τxy​ = 40MPa

A point has σₓ = 120 MPa, σᵧ = 110 MPa and τₓᵧ = 40 MPa (tension positive). The element is rotated 20° clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.

σx = 120 MPaσy = 110 MPaτxy = 40 MPaθ = -20°
σy′ = MPa
5.Hard
σx​ = 80σy​ = 110τxy​ = 30MPa

A point in a loaded part has σₓ = 80 MPa, σᵧ = 110 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 = 110 MPaτxy = 30 MPaθ = -20°
σθ = MPa
6.Hard
σx​ = 60σy​ = −70τxy​ = 20MPa

A point in a loaded part has σₓ = 60 MPa, σᵧ = −70 MPa and τₓᵧ = 20 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 60° counter-clockwise from the x-axis.

σx = 60 MPaσy = −70 MPaτxy = 20 MPaθ = 60°
σθ = MPa

Answer key

  1. 1. σ2 = −33.52 MPa
  2. 2. σ1 = 108.2 MPa
  3. 3. θs = −19.9 °
  4. 4. σy′ = 136.9 MPa
  5. 5. σθ = 64.23 MPa
  6. 6. σθ = −20.18 MPa

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