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​ = 110σy​ = 100τxy​ = 40MPa

A point in a loaded part has σₓ = 110 MPa, σᵧ = 100 MPa and τₓᵧ = 40 MPa (tension positive). Find the largest principal stress σ1.

σx = 110 MPaσy = 100 MPaτxy = 40 MPa
σ1 = MPa
2.Easy
160 kN160 kNθ = 30°A = 400 mm²

A bar with cross-sectional area 400 mm² carries an axial tensile force of 160 kN. Find the magnitude of the shear stress |τθ| on a section whose normal makes an angle of 30° with the bar axis.

P = 160 kNA = 400 mm²θ = 30°
|τθ| = MPa
3.Medium
σx​ = 70σy​ = −20τxy​ = −50MPa

A point has σₓ = 70 MPa, σᵧ = −20 MPa and τₓᵧ = −50 MPa (tension positive). The element is rotated 25° counter-clockwise. Find the normal stress σy′ on the faces of the rotated element that are perpendicular to the rotated y′-axis.

σx = 70 MPaσy = −20 MPaτxy = −50 MPaθ = 25°
σy′ = MPa
4.Medium
σx​ = 40σy​ = −10τxy​ = −60MPa

A point has σₓ = 40 MPa, σᵧ = −10 MPa and τₓᵧ = −60 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 = 40 MPaσy = −10 MPaτxy = −60 MPa
θs = °
5.Hard
σx​ = 70σy​ = 100τxy​ = 60MPa

A point in a loaded part has σₓ = 70 MPa, σᵧ = 100 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 = 70 MPaσy = 100 MPaτxy = 60 MPaθ = -20°
σθ = MPa
6.Hard
σx​ = 90σy​ = −10τxy​ = −60MPa

A point in a loaded part has σₓ = 90 MPa, σᵧ = −10 MPa and τₓᵧ = −60 MPa (tension positive). Find the normal stress σθ on a plane whose normal is rotated 25° counter-clockwise from the x-axis.

σx = 90 MPaσy = −10 MPaτxy = −60 MPaθ = 25°
σθ = MPa

Answer key

  1. 1. σ1 = 145.3 MPa
  2. 2. |τθ| = 173.2 MPa
  3. 3. σy′ = 34.38 MPa
  4. 4. θs = −78.69 °
  5. 5. σθ = 34.94 MPa
  6. 6. σθ = 26.18 MPa

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