. The strength of materials; a text-book for engineers and architects. 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. Fig. 144. piece of sector; the volume of pyramid therefore re-jDresents t
. The strength of materials; a text-book for engineers and architects. 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. Fig. 144. piece of sector; the volume of pyramid therefore re-jDresents the whole load acting on the sector, and to find themoment about the point o of the force on the sector weregard the volume of the pjTamid as acting at the centre of gravity of the p^Tamid which is at distance --. - from o. Now the volume of a pyramid = J area of base x height ab = g Ra A D X O A1 R 5aR2 TORSION AND TWISTING OF SHAFTS 323 3R Moment about o = Volume x 4 3 4 5 a R^ 2Now in the whole section there will be — of these sectors, a • because the whole circumference subtends an angle 2 tt at thecentre. .*. Total moment about o of all the forces on the 5aR3 2 7r section = —-.— X — 4 a ~ 2 ~ 16 But this total moment must be equal to the torque T . rp _ SttW 16 This agrees with our previous result (equation (7)). Horse-Power Transmitted by Shafting. We have seen on p. 312 that ^ X 33,000 X 12 . „T = ^^ m. lbs. X 33,000 X 12 . ^= —c.—TVT— cti^at. m. tons. 2 TT N X 2,240 . •, putti
Size: 2050px × 1219px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1910, bookpublishernewyorkdvannostran
