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22_ch 04 Mechanical Design budynas_SM_ch04

22_ch 04 Mechanical Design budynas_SM_ch04 -...

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Chapter 4 91 When the second load is added, U becomes U = 1 2 P 1 ( P 1 δ 11 ) + 1 2 P 2 ( P 2 δ 22 ) + P 1 ( P 2 δ 12 ) For loading in the reverse order U ± = 1 2 P 2 ( P 2 δ 22 ) + 1 2 P 1 ( P 1 δ 11 ) + P 2 ( P 1 δ 21 ) Since the order of loading is immaterial U = U ± and P 1 P 2 δ 12 = P 2 P 1 δ 21 when P 1 = P 2 12 = δ 21 which states that the deﬂection at station 1 due to a unit load at station 2 is the same as the deﬂection at station 2 due to a unit load at 1. δ is sometimes called an inﬂuence coefﬁcient. 4-44 (a) From Table A-9-10 y AB = Fcx ( l 2 x 2 ) 6 EIl δ 12 = y F ± ± ± x = a = ca ( l 2 a 2 ) 6 y 2 = F δ 21 = F δ 12 = Fca ( l 2 a 2 ) 6 Substituting I = π d 4 64 y 2 = 400(7)(9)(23 2 9 2 )(64) 6(30)(10 6 )( π )(2) 4 (23) = 0 . 00347 in Ans. (b) The slope of the shaft at left bearing at
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