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​ = 30τxy​ = 40MPa

A point in a loaded part has σₓ = −40 MPa, σᵧ = 30 MPa and τₓᵧ = 40 MPa (tension positive). Find the smallest principal stress σ2.

σx = −40 MPaσy = 30 MPaτxy = 40 MPa
σ2 = MPa
2.Easy
σx​ = 70σy​ = −80τxy​ = 60MPa

A point in a loaded part has σₓ = 70 MPa, σᵧ = −80 MPa and τₓᵧ = 60 MPa (tension positive). Find the largest principal stress σ1.

σx = 70 MPaσy = −80 MPaτxy = 60 MPa
σ1 = MPa
3.Medium
σx​ = 50σy​ = 100τxy​ = 40MPa

A point has σₓ = 50 MPa, σᵧ = 100 MPa and τₓᵧ = 40 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 = 50 MPaσy = 100 MPaτxy = 40 MPa
θs = °
4.Medium
σx​ = 60σy​ = −60τxy​ = 30MPa

A point has σₓ = 60 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 = 60 MPaσy = −60 MPaτxy = 30 MPa
θs = °
5.Hard
σx​ = 30σy​ = 100τxy​ = 30MPa

A point in a loaded part has σₓ = 30 MPa, σᵧ = 100 MPa and τₓᵧ = 30 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 30° clockwise from the x-axis.

σx = 30 MPaσy = 100 MPaτxy = 30 MPaθ = -30°
σθ = MPa
6.Hard
σx​ = 100σy​ = 30τxy​ = 20MPa

A point in a loaded part has σₓ = 100 MPa, σᵧ = 30 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 = 100 MPaσy = 30 MPaτxy = 20 MPaθ = 40°
σθ = MPa

Answer key

  1. 1. σ2 = −58.15 MPa
  2. 2. σ1 = 91.05 MPa
  3. 3. θs = 16 °
  4. 4. θs = −31.72 °
  5. 5. σθ = 21.52 MPa
  6. 6. σθ = 90.77 MPa

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