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

A point in a loaded part has σₓ = −50 MPa, σᵧ = 30 MPa and τₓᵧ = 40 MPa (tension positive). Find the smallest principal stress σ₂.

σ_x = −50 MPaσ_y = 30 MPaτ_xy = 40 MPa

σ₂ = MPa

2.Easy

A point in a loaded part has σₓ = −80 MPa, σᵧ = 20 MPa and τₓᵧ = −40 MPa (tension positive). Find the largest principal stress σ₁.

σ_x = −80 MPaσ_y = 20 MPaτ_xy = −40 MPa

σ₁ = MPa

3.Medium

A point has σₓ = 110 MPa and σᵧ = −30 MPa. How large can the shear stress τ_xy (magnitude) become before the largest principal stress reaches 120 MPa?

σ_x = 110 MPaσ_y = −30 MPaσ₁ = 120 MPa

τ_xy = MPa

4.Medium

A point in a thin plate is in plane stress: σₓ = 160 MPa, σᵧ = 90 MPa and τₓᵧ = 30 MPa, with σ_z = 0. Find the absolute maximum shear stress τ_abs at the point (considering all planes in three dimensions).

σ_x = 160 MPaσ_y = 90 MPaτ_xy = 30 MPaσ_z = 0

τ_abs = MPa

5.Hard

A point in a loaded part has σₓ = 80 MPa, σᵧ = 40 MPa and τₓᵧ = 30 MPa (tension positive). Find the normal stress σ_θ on a plane whose normal is rotated 35° counter-clockwise from the x-axis.

σ_x = 80 MPaσ_y = 40 MPaτ_xy = 30 MPaθ = 35°

σ_θ = MPa

6.Hard

A solid shaft of diameter 60 mm carries an axial tensile force of 170 kN together with a torque of 750 N·m. At the surface of the shaft, find the maximum in-plane shear stress τ_max.

d = 60 mmF = 170 kNT = 750 N·m

τ_max = MPa

Answer key

1. σ₂ = −66.57 MPa
2. σ₁ = 34.03 MPa
3. τ_xy = 38.73 MPa
4. τ_abs = 85.55 MPa
5. σ_θ = 95.03 MPa
6. τ_max = 34.88 MPa

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