Hibbeler — Statics and Mechanics of Materials
Torsion — the paddle wheel drive shaft
Every chapter so far has been a load pushing or pulling straight through a member — this is a twisting load, the first MM build in the guide that actually spins.
Concepts pulled in
- Torsion (τ = Tc/J)
- Polar moment of inertia
Every chapter so far has been about a load pushing or pulling straight through a member. Torsion is different: a twisting load, and it shows up the moment there's a rotating shaft — which is exactly the paddle wheel boat's drive shaft, the first MM build in this guide that actually spins.
The formula, for a solid round shaft: τ = Tc/J, where T is the applied torque, c is the shaft radius, and J is the polar moment of inertia (J = πd⁴/32 for a solid round shaft — note this is a different moment of inertia than the I used for bending, because torsion twists around the shaft's axis instead of bending it sideways).
Why it matters here specifically
The paddle wheel's drive shaft has to transmit the motor's torque to the paddle without twisting so much it flexes visibly or fails — and unlike the wood-beam chapters, this is a metal-shaft problem, so it pulls in the study shelf's materials/metallurgy text (Callister) for allowable shear stress on whatever shaft material ends up used (mild steel round stock is the likely starting point — see the Callister guide's own Chapter 1 for the actual number).
Open items for a later pass
This chapter is placeholder-shaped until the paddle wheel project has a confirmed motor torque rating and shaft diameter — right now it's queued as the anchor, not yet worked.
Modern Monticello · Technical Library · Worked calculation
Torsion — the paddle wheel drive shaft
Hibbeler — Statics and Mechanics of Materials · Chapter 16
Project or part: (not named)
Try your own numbers
This chapter has no worked answer yet, because it's waiting on the paddle wheel's real motor torque and shaft diameter, so those start empty. Enter the torque to get the smallest solid round shaft that holds it, or a diameter to get the most torque it can carry. Enter both to check a shaft you already have. Static torque only: keyways, shoulders, bending from the wheel's weight and fatigue are not included.
- Allowable shear: 0.5 × 54,000 psi ÷ 2 = 13,500 psi
Enter a torque (or motor horsepower and rpm) or a shaft diameter.
Allowable shear here is a standard design shortcut, not a Callister formula. The shaft also has to survive the keyway or set screw that connects it, bending from the paddle wheel, and repeated loading, so size up from these numbers rather than to them.
Worked example from the Modern Monticello Technical Library, using published design values and simplified checks. Not a stamped engineering design: your site, materials and loads will differ, and anything that could hurt someone if it fails deserves a licensed engineer's review. Provisional or example values are placeholders, not measurements of your material. Sources for every number: modernmonticellobuild.com/technical-library/paddle-wheel-drive-shaft-torsion
Print this calculation
Prints just the calculator above, with your numbers and the working, on a clean white page headed with this chapter and today's date. Add a name if you want it on the sheet, for a build file or a plan set.