Problem_15_04 - σ u 150 MPa ⋅:= M 7.5 kN ⋅ m ⋅:= d...

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Problem 15.4 Given: A circular shaft is made of gray cast iron, which may be considered to be linearly elastic up to its ultimate strength σ u = 150 MPa. The shaft has a diameter of 125 mm and is subjected to a bending moment M = 7.5 kN-m. Find: the maximum value for torque T that can be applied to the shaft if it has been designed with a factor of safety of 3.0 for both M and T. Solution:
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Unformatted text preview: σ u 150 MPa ⋅ := M 7.5 kN ⋅ m ⋅ := d 125 mm ⋅ := SF 3. := r d 2 := I π d 4 ⋅ 64 := J 2 I ⋅ := σ M r ⋅ I 39.114 MPa = := τ T r ⋅ J = σ 1 σ xx σ yy + 2 σ xx σ yy − 2 ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 2 σ xy 2 + + = σ u SF σ 2 σ 2 4 τ 2 + + = τ σ u SF σ 2 − ⎛ ⎜ ⎝ ⎞ ⎟ ⎠ 2 σ 2 4 − 23.33MPa = := T τ J ⋅ r 8.947 kN m ⋅ = :=...
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