Question 8.70: The 3/4 -in. -diameter shaft is subjected to the loading sho...

The \frac{3}{4} -in . -diameter shaft is subjected to the loading shown. Determine the stress components at point A. Sketch the results on a volume element located at this point. The journal bearing at C can exert only force components  C_{y}  \text{and}   C_{z} on the shaft, and the thrust bearing at D can exert force components D_{x}, D_{y},   \text{and} D_{z} on the shaft.

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A=\frac{\pi}{4}\left(0.75^{2}\right)=0.44179 \mathrm{in}^{2}

 

I=\frac{\pi}{4}\left(0.375^{4}\right)=0.015531 \mathrm{in}^{4}

 

Q_{A}=0

 

\tau_{A}=0

 

\sigma_{A}=\frac{M_{y} c}{I}=\frac{-1250(0.375)}{0.015531}=-30.2 \mathrm{ksi}=30.2 \mathrm{ksi}(C)
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