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​ = −70σy​ = −50τxy​ = −60MPa

A point in a loaded part has σₓ = −70 MPa, σᵧ = −50 MPa and τₓᵧ = −60 MPa (tension positive). Find the largest principal stress σ1.

σx = −70 MPaσy = −50 MPaτxy = −60 MPa
σ1 = MPa
2.Easy
σx​ = 90σy​ = −60τxy​ = −40MPa

A point in a loaded part has σₓ = 90 MPa, σᵧ = −60 MPa and τₓᵧ = −40 MPa (tension positive). Find the largest principal stress σ1.

σx = 90 MPaσy = −60 MPaτxy = −40 MPa
σ1 = MPa
3.Medium
σx​ = −60σy​ = −70τxy​ = −40MPa

A point has σₓ = −60 MPa, σᵧ = −70 MPa and τₓᵧ = −40 MPa (tension positive). The element is rotated 15° counter-clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.

σx = −60 MPaσy = −70 MPaτxy = −40 MPaθ = 15°
σy′ = MPa
4.Medium
σx​ = −40σy​ = −30τxy​ = −40MPa

A point has σₓ = −40 MPa, σᵧ = −30 MPa and τₓᵧ = −40 MPa (tension positive). The element is rotated 50° counter-clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.

σx = −40 MPaσy = −30 MPaτxy = −40 MPaθ = 50°
σy′ = MPa
5.Hard
50°D = 500 mm, t = 15 mm, p = 1.5 MPap

A thin-walled cylindrical tank of inner diameter 500 mm and wall thickness 15 mm holds gas at a gauge pressure of 1.5 MPa. It is made from plate welded along a helical seam at 50° to the axis of the cylinder. Find the normal stress σn acting across the weld seam.

D = 500 mmt = 15 mmp = 1.5 MPaα = 50°
σn = MPa
6.Hard
σx​ = 110σy​ = 110τxy​ = 50MPa

A point in a thin plate is in plane stress: σₓ = 110 MPa, σᵧ = 110 MPa and τₓᵧ = 50 MPa (σz = 0). The material has a yield strength of 275 MPa. Find the factor of safety n against yielding by the Tresca (maximum shear stress) criterion.

σx = 110 MPaσy = 110 MPaτxy = 50 MPaσY = 275 MPa
n =

Answer key

  1. 1. σ1 = 0.8276 MPa
  2. 2. σ1 = 100 MPa
  3. 3. σy′ = −49.33 MPa
  4. 4. σy′ = 3.524 MPa
  5. 5. σn = 17.66 MPa
  6. 6. n = 1.719

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