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​ = −80MPaprincipal element

At a point in a loaded part the in-plane principal stresses are σ₁ = 40 MPa and σ₂ = −80 MPa (tension positive). Find the normal stress σavg that acts on the planes of maximum in-plane shear stress.

σ1 = 40 MPaσ2 = −80 MPa
σavg = MPa
2.Easy
σx​ = 50σy​ = −80τxy​ = 60MPa

A point in a loaded part has σₓ = 50 MPa, σᵧ = −80 MPa and τₓᵧ = 60 MPa (tension positive). Find the largest principal stress σ1.

σx = 50 MPaσy = −80 MPaτxy = 60 MPa
σ1 = MPa
3.Medium
σx​ = 60σy​ = −30MPaτxy​ = ?

A point has σₓ = 60 MPa and σᵧ = −30 MPa. How large can the shear stress τxy (magnitude) become before the largest principal stress reaches 90 MPa?

σx = 60 MPaσy = −30 MPaσ1 = 90 MPa
τxy = MPa
4.Medium
σx​ = 50σy​ = 60τxy​ = 40MPa

A point in a thin plate is in plane stress: σₓ = 50 MPa, σᵧ = 60 MPa and τₓᵧ = 40 MPa, with σz = 0. Find the absolute maximum shear stress τabs at the point (considering all planes in three dimensions).

σx = 50 MPaσy = 60 MPaτxy = 40 MPaσz = 0
τabs = MPa
5.Hard
σx​ = 140σy​ = −50τxy​ = −50MPa

A point in a loaded part has σₓ = 140 MPa, σᵧ = −50 MPa and τₓᵧ = −50 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 20° counter-clockwise from the x-axis.

σx = 140 MPaσy = −50 MPaτxy = −50 MPaθ = 20°
σθ = MPa
6.Hard
σx​ = 0σy​ = 30τxy​ = −60MPa

A point in a loaded part has σₓ = 0 MPa, σᵧ = 30 MPa and τₓᵧ = −60 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 30° clockwise from the x-axis.

σx = 0 MPaσy = 30 MPaτxy = −60 MPaθ = -30°
σθ = MPa

Answer key

  1. 1. σavg = −20 MPa
  2. 2. σ1 = 73.46 MPa
  3. 3. τxy = 60 MPa
  4. 4. τabs = 47.66 MPa
  5. 5. σθ = 85.63 MPa
  6. 6. σθ = 59.46 MPa

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