$23.$ The shaft in Figure P$12-2$ rotates at $200$ rpm $.$ Pulley $\backslash ($ A $\backslash )$ receives $10$ hp from below. Gear $\backslash ($ C $\backslash )$ delivers $6$ hp to the mating gear below it$.$ Chain sprocket $\backslash ($ D $\backslash )$ delivers $4$ hp to a shaft above. Use SAE $1117$ cold$-$drawn steel.

Comprehensive Shaft Design Problems

For each of the following Problems $22$ through $30,$ it will be necessary to do the following:

$($a$)$ Determine the magnitude of the torque in the shaft at all points.

$($b$)$ Compute the forces acting on the shaft at all powertransmitting elements.

$($c$)$ Compute the reactions at the bearings.

$($d$)$ Draw the complete load, shear, and bending moment diagrams.

Neglect the weight of the elements on the shafts, unless otherwise noted.

The objective of any problem, at the discretion of the instructor, could be any of the following:

$-$ Design the complete shaft, including the specification of the overall geometry and the consideration of stress concentration factors. The analysis would show the minimum acceptable diameter at each point on the shaft to be safe from the standpoint of strength.

rigure r$12-$L $(1$rtodiems $\backslash (\backslash$angle$,1\backslash$angle$,13\backslash ),$ and $\backslash (\backslash$angle $3)\backslash )$

$-$ Given a suggested geometry of one part of the shaft, specify the minimum acceptable diameter for the shaft at that point.

$-$ Specify the required geometry at any selected element on the shaft: a gear, sheave, bearing, or other.

$-$ Make a working drawing of the design for the shaft, following the appropriate stress analysis, and specify the final dimensions.

$-$ Suggest how the given shaft can be redesigned by moving or reorienting the elements on the shaft to improve the design to produce lower stresses, smaller shaft size, more convenient assembly, and so on$.$

$-$ Incorporate the given shaft into a more comprehensive machine, and complete the design of the entire machine. In most problems, the type of machine for which the shaft is being designed is suggested.