. The strength of materials; a text-book for engineers and architects. Fig. 143. I^ = I D* _ (D _ ^j4 j and if t is so smaU that squares and higher powers of jt may be neglected we may -^Tite (D - ^)4 = D* - 4D3^_ - BH I^, - D2 f *• e- Z,, = J) 2 5 7rD2i (9) Alternative Derivation of Formula for Solid Shaft.— The formulae (7) can also be derived as follows, and althoughwe recommend the previous method as the more satisfactory 322 THE STRENGTH OF MATERIALS we find by experience that some students find the alternativemethod more easy to follow. It is similar to the method wliichwe have ahead} us
. The strength of materials; a text-book for engineers and architects. Fig. 143. I^ = I D* _ (D _ ^j4 j and if t is so smaU that squares and higher powers of jt may be neglected we may -^Tite (D - ^)4 = D* - 4D3^_ - BH I^, - D2 f *• e- Z,, = J) 2 5 7rD2i (9) Alternative Derivation of Formula for Solid Shaft.— The formulae (7) can also be derived as follows, and althoughwe recommend the previous method as the more satisfactory 322 THE STRENGTH OF MATERIALS we find by experience that some students find the alternativemethod more easy to follow. It is similar to the method wliichwe have ahead} used for beams in some cases (see pp. 220-222).Consider a very small sector a o b, Fig. 144, of the circle, sosmall that we may consider a o b as being practically a verynarrow triangle. Set up a D, B c, to represent the maximumshear stress s and complete the pjTamid a b c d o as sho\^ if this pyramid be considered as di\ided up intoa number of slices as indicated, the volume of each shce= area of piece of sector x stress on it = load on each
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