From the Rolls-Royce experimental archive: a quarter of a million communications from Rolls-Royce, 1906 to 1960's. Documents from the Sir Henry Royce Memorial Foundation (SHRMF).
Mathematical analysis and calculations for torsional stress in a rod.
| Identifier | ExFiles\Box 170\3\ img006 | |
| Date | 4th December 1935 guessed | |
| (Sheet 4) T = ∫₀ʳ¹ f m r₁ x 2πrδr x r plus ∫ᵣ₁ʳ² f m x 2πrδr x r = f m x π/2 x r₁³ + f.m. x 2π/3 { r₂³ - r₁³ } T = f m { 2π/3 r₂³ - π/6 r₁³ } Where r₁ = (f m / f o) r₂ And f o = (G r₂ θ) / l l being length of rod. θ being angle of twist. (8) how if one takes the case of say a 20" rod 1" dia with an elastic limit of 100,000#/in² Angular rate of rod T/θ = 56,500 lbs ins/rad. If the rod is initially wound up through 1/2 rad. and successively wound up to .8 radian, the theoretical chart looks something like attached. In other words without any assumption of cold working changing the elastic limit we have improved the shaft so that from an initial elastic capacity of 19630 lbs ins. at 20° angle it now has a capacity of 25600 lbs ins at 26° angle. The max stress of 100,000 runs about .300" below the surface of the shaft when wound up, and there is 30,000 lbs/in² negative (reversed) skin stress in the shaft when released. | ||