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Question 11.45:  The bearings at A and D exert only  y and z components of f...

The bearings at A and D exert only  y and z components of force on the shaft. If \tau_{\text {allow }}=60  \mathrm{MPa}, determine to the nearest millimeter the smallest-diameter shaft that will support the loading. Use the maximum-shear stress theory of failure.

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Critical moment is at point B :

M=\sqrt{(473.7)^{2}+(147.4)^{2}}=496.1  \mathrm{~N} \cdot \mathrm{m}

 

T=150  \mathrm{~N} \cdot \mathrm{m}

 

c=\left(\frac{2}{\pi \tau_{\text {allow }}} \sqrt{M^{2}+T^{2}}\right)^{1 / 3}=\left(\frac{2}{\pi(60)\left(10^{6}\right)} \sqrt{496.1^{2}+150^{2}}\right)^{1 / 3}=0.0176

 

c=0.0176  \mathrm{~m}=17.6  \mathrm{~mm}

 

d=2 c=35.3  \mathrm{~mm}

 

Use  d=36  \mathrm{~mm}

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