. Theory of structures and strength of materials. Fig. 299. - = AF = FC{2R - FC) = 2RD - D 2RD. Hence, Also, since/= I / = %DEyr The deflection at a distance x from F ~ D — — 2R Ex. 3. A timber beam of 20 ft. span, is 12 in. deep and 6in. wide: what uniformly distributed load {W) will deflect thebeam i in., E being 1,200,000 By Ex. 2, SR .-. R = 7200 in. Also, ^^^.20 12 =|/ 1200000 dd-12 7200 12 7200 W = 4800 lbs. 1200000 DEFLECTION OF GIRDERS. 387 Ex. 4. Let s,, f^, d^, and s^, f^, d^, respectively, be thelength, unit stress, and distance from the neutral axis of thestretched
. Theory of structures and strength of materials. Fig. 299. - = AF = FC{2R - FC) = 2RD - D 2RD. Hence, Also, since/= I / = %DEyr The deflection at a distance x from F ~ D — — 2R Ex. 3. A timber beam of 20 ft. span, is 12 in. deep and 6in. wide: what uniformly distributed load {W) will deflect thebeam i in., E being 1,200,000 By Ex. 2, SR .-. R = 7200 in. Also, ^^^.20 12 =|/ 1200000 dd-12 7200 12 7200 W = 4800 lbs. 1200000 DEFLECTION OF GIRDERS. 387 Ex. 4. Let s,, f^, d^, and s^, f^, d^, respectively, be thelength, unit stress, and distance from the neutral axis of thestretched and compressed outside fibres in Examples (i) and (2). Let d^-\- d.^=^ d =^ the total depth of the , from similar figures. s, R + d, ^ s, R-d,. X -R ^^ E-^-J-^R- . /.+/. :.S,-^, _ d^ _ d_ E I R R Ex. 5. A truss of span 120 ft. and 15 ft. deep is strainedso that the flange tensile and compressive unit stresses are ^10,000 and 8000 lbs., respectively. Find the deflection, anddifference of length between the extreme fibres. 10000+8000 ^1—^2 1530000000 ~ 120 ~ R .. s^ — s, = .864 in., and R = 25,000 ft= (120) Hence also D = -~ = .864 in. 8 X 25000 10. Camber.—Owing to the play at the joints, a bridge-truss, when first erected, will deflect to a much greater extent , ? A \ 388 THEORY OF STRUCTURES. than is indicated by theory, and the material of the truss willreceive a permanent set, which, however, will not prove detri-mental to the stability of the structure, unless it is increasedby subsequent loads. If the chords were made straight, they would curve down-wards, and, although it does not necessarily follow that thestrength of the truss would be sensibly impaired, the appear-ance would not be pleasing. In practice it
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