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​ = 90σy​ = −70τxy​ = −60MPa

A point in a loaded part has σₓ = 90 MPa, σᵧ = −70 MPa and τₓᵧ = −60 MPa (tension positive). Find the largest principal stress σ1.

σx = 90 MPaσy = −70 MPaτxy = −60 MPa
σ1 = MPa
2.Easy
σx​ = −80σy​ = 10τxy​ = 30MPa

A point in a loaded part has σₓ = −80 MPa, σᵧ = 10 MPa and τₓᵧ = 30 MPa (tension positive). Find the smallest principal stress σ2.

σx = −80 MPaσy = 10 MPaτxy = 30 MPa
σ2 = MPa
3.Medium
σx​ = 10σy​ = −10τxy​ = 50MPa

A point in a loaded part has σₓ = 10 MPa, σᵧ = −10 MPa and τₓᵧ = 50 MPa (tension positive). Find the angle θp from the x-axis to the direction of the largest principal stress, between −90° and 90°.

σx = 10 MPaσy = −10 MPaτxy = 50 MPa
θp = °
4.Medium
σx​ = 130σy​ = 120τxy​ = −30MPa

A point in a loaded part has σₓ = 130 MPa, σᵧ = 120 MPa and τₓᵧ = −30 MPa (tension positive). Find the angle θp from the x-axis to the direction of the largest principal stress, between −90° and 90°.

σx = 130 MPaσy = 120 MPaτxy = −30 MPa
θp = °
5.Hard
σx​ = 60σy​ = −30τxy​ = −10MPa

A point in a thin plate is in plane stress: σₓ = 60 MPa, σᵧ = −30 MPa and τₓᵧ = −10 MPa (σz = 0). The material has a yield strength of 250 MPa. Find the factor of safety n against yielding by the Tresca (maximum shear stress) criterion.

σx = 60 MPaσy = −30 MPaτxy = −10 MPaσY = 250 MPa
n =
6.Hard
σx​ = −20σy​ = 10τxy​ = 40MPa

A point in a loaded part has σₓ = −20 MPa, σᵧ = 10 MPa and τₓᵧ = 40 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 35° counter-clockwise from the x-axis.

σx = −20 MPaσy = 10 MPaτxy = 40 MPaθ = 35°
σθ = MPa

Answer key

  1. 1. σ1 = 110 MPa
  2. 2. σ2 = −89.08 MPa
  3. 3. θp = 39.35 °
  4. 4. θp = −40.27 °
  5. 5. n = 2.712
  6. 6. σθ = 27.46 MPa

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