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​ = 190σy​ = −30MPaprincipal element

At a point in a loaded part the in-plane principal stresses are σ₁ = 190 MPa and σ₂ = −30 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σ1 = 190 MPaσ2 = −30 MPa
τmax = MPa
2.Easy
σx​ = 150MPaprincipal element

At a point in a loaded part the in-plane principal stresses are σ₁ = 150 MPa and σ₂ = 0 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σ1 = 150 MPaσ2 = 0 MPa
τmax = MPa
3.Medium
σx​ = 0σy​ = −20τxy​ = 50MPa

A point in a loaded part has σₓ = 0 MPa, σᵧ = −20 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 = 0 MPaσy = −20 MPaτxy = 50 MPa
θp = °
4.Medium
σx​ = −60σy​ = −50τxy​ = 50MPa

A point in a loaded part has σₓ = −60 MPa, σᵧ = −50 MPa and τₓᵧ = 50 MPa (tension positive). Find the maximum in-plane shear stress τmax.

σx = −60 MPaσy = −50 MPaτxy = 50 MPa
τmax = MPa
5.Hard
σx​ = −40σy​ = 80τxy​ = −60MPa

A point in a loaded part has σₓ = −40 MPa, σᵧ = 80 MPa and τₓᵧ = −60 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 20° clockwise from the x-axis.

σx = −40 MPaσy = 80 MPaτxy = −60 MPaθ = -20°
σθ = MPa
6.Hard
40°D = 400 mm, t = 8 mm, p = 2.5 MPap

A thin-walled cylindrical tank of inner diameter 400 mm and wall thickness 8 mm holds gas at a gauge pressure of 2.5 MPa. It is made from plate welded along a helical seam at 40° to the axis of the cylinder. Find the normal stress σn acting across the weld seam.

D = 400 mmt = 8 mmp = 2.5 MPaα = 40°
σn = MPa

Answer key

  1. 1. τmax = 110 MPa
  2. 2. τmax = 75 MPa
  3. 3. θp = 39.35 °
  4. 4. τmax = 50.25 MPa
  5. 5. σθ = 12.6 MPa
  6. 6. σn = 49.59 MPa

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