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 = 130 MPa, σᵧ = −10 MPa and τₓᵧ = 60 MPa (tension positive). Find the largest principal stress σ₁.

σ_x = 130 MPaσ_y = −10 MPaτ_xy = 60 MPa

σ₁ = MPa

2.Easy

A point in a loaded part has σₓ = 140 MPa, σᵧ = −20 MPa and τₓᵧ = −30 MPa (tension positive). Find the smallest principal stress σ₂.

σ_x = 140 MPaσ_y = −20 MPaτ_xy = −30 MPa

σ₂ = MPa

3.Medium

A point in a loaded part has σₓ = 30 MPa, σᵧ = 20 MPa and τₓᵧ = 20 MPa (tension positive). Find the angle θ_p from the x-axis to the direction of the largest principal stress, between −90° and 90°.

σ_x = 30 MPaσ_y = 20 MPaτ_xy = 20 MPa

θ_p = °

4.Medium

A point in a loaded part has σₓ = 140 MPa, σᵧ = 0 MPa and τₓᵧ = 60 MPa (tension positive). Find the maximum in-plane shear stress τ_max.

σ_x = 140 MPaσ_y = 0 MPaτ_xy = 60 MPa

τ_max = MPa

5.Hard

A point in a loaded part has σₓ = 110 MPa, σᵧ = 80 MPa and τₓᵧ = −40 MPa (tension positive). Find the shear stress τ_θ on a plane whose normal is rotated 25° counter-clockwise from the x-axis (positive in the same sense as τₓᵧ).

σ_x = 110 MPaσ_y = 80 MPaτ_xy = −40 MPaθ = 25°

τ_θ = MPa

6.Hard

A solid shaft of diameter 25 mm carries an axial tensile force of 80 kN together with a torque of 100 N·m. At the surface of the shaft, find the maximum in-plane shear stress τ_max.

d = 25 mmF = 80 kNT = 100 N·m

τ_max = MPa

Answer key

1. σ₁ = 152.2 MPa
2. σ₂ = −25.44 MPa
3. θ_p = 37.98 °
4. τ_max = 92.2 MPa
5. τ_θ = −37.2 MPa
6. τ_max = 87.76 MPa

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