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Originally Posted by Andrew Lawrence
I should have gone into more detail - my apologies - Yes, as Akash said, you shouldn't have a problem with cantilevered shafts if you use the right grade material in the correct manner. For a live axle setup, 7075 aluminum in 1/2" hex should work perfectly. I've yet to have problems with it.
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You're still missing way too much detail to speak in general here. The point of interest is more than just the shaft sizing; how the load is applied and supported also matters. Essentially you want the cantilevered load as close to the support as possible and each of the support bearings a reasonable distance apart. In a drivetrain it's fairly easy to get those supports far enough apart, so unless you're doing something really strange like half-inch tubing, the main area of attention should be getting the load as close to the support as possible. Don't space out wheels or use excessive spacing between sprockets.
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If you're doing anything smaller or dead axle, I'd go with a steel alloy (I hear 4140 is good), though I find it better to stick with live axle and use 7075 al.
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You're saying that for an equal size shaft and load, you need steel for a dead axle but can use aluminum for a live axle? I don't follow; the bending loads on the shaft should be identical. If anything the lack of torsional loads on the axle would slightly reduce the stresses involved on a dead axle.
OP: If you're deviating from the tried and true 1/2" shafting west coast type setup, you should probably do some math to be sure. Very simple statics, just draw a free body diagram and look at the forces and moments at play. If you need help with this I can walk you through the math; I'm a bit busy at the moment though.