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to my fellow mechanical engineers, please help me with some basic machine design problems. a certain drive shaft rotating at 500 rpm transmits 200 hp to an 8 inch diameter gear. Design a suitable solid shaft for this application. the shaft is ductile. Design stresses are to be limited to Smax= 134 ksi and SHEAR max = 40 ksi

Engineering
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The highest grade of aluminum would be it best bet maybe air plane grade?
The best I can do is say to use \[\tau=F/Ao\] \[\tau=G * \gamma\] where tau is shear, and G is shear modulus (a constant for each metal) and \[\sigma=\epsilon*E\] where E is modulus of elasticity (constant for each metal), sigma is stress, and epsilon is strain. For stress, you sub yield strength or tensile strength (given for each metal). If this is a real application use yield strength because that says when it will deform where tensile strength says where it will break. We don't want any deformity in a real application. \[Ao = (do/2)^{2} \pi\] This is all from a materials science POV, so please disregard if you are in a higher level than that.

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