727_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

727_Mechanics SolutionInstructors_Sol.Manual-Mechanics_Materials_7e.book_Gere_light.1

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Unformatted text preview: 09Ch09.qxd 9/27/08 1:31 PM Page 721 SECTION 9.3 Deflections by Integration of the Bending-Moment Equation 19 PL 24 EI – M(x) EI ¿ 19 PLx 24 EI Px + PL 3 P x2 PL x + + C3 2 3 P x3 PL x2 + + C3 x + C4 6 6 19 P L x2 48 L 21 b 22 B.C. B.C. B.C. 19 PL 24 Px + PL 3 P ax L M(x) 19 PL 24 Px + PL 3 Px P x2 + 2L 2 19 PL x 24 P x2 PL x + 2 3 EI B.C. M(x) EI ¿ B.C. EI – EI – For 19 P L x2 48 PL x2 P x3 + 6 6 L …x…L 2 (L) 0 L ¿R a b 3 L b 3 Ra L ¿L a b 2 L(a) 19 PL L2 48 0 L ¿L a b 3 La L2 Pa b 3 0 L b 3 + C3 3565 3 PL 10368 C3 3 L3 Pa b 3 + 6 L3 Pa b 2 PLL2 + C5 L + C6 16 L + C3 a b + C4 3 L2 Pa b 2 L PL a b 2 4 8 L4 Pa b 2 L3 Pa b 2 L2 PL a b 2 12 16 + + 24 L (1) (2) 6L L + C4 2 PL x2 + C5 x + C6 16 + C3 L2 PL a b 3 6 C3 R(a) L PL a b 3 PL x + C5 8 P x4 Px3 + 24 L 12 PL4 PL3 + 24 L 12 2 C2 L ¿R a b 2 PL3 PLL2 + 6 6 Px2 P x3 + 6L 4 PL 8 (3) (4) + C5 L + C5 a b + C6 2 (5) From (1)–(5) C2 12 PL 18 C4 389 P L3 1152 C5 5 P L2 144 C6 ; L 3 (x) PL ( 10368 EI For L L …x… 3 2 (x) P ( 1152 EI 648 L x2 + 192 x3 + 64 L2 x + 389 L3) For L …x…L 2 (x) P ( 144EIL 72 L2 x2 + 12 x3L + 6 x4 + 5L3 x + 49 L4) For 0 … x … dA (0) 721 3565PL3 10368 EI ; 4104 x2 + 3565 L2) dC L ab 3 3109PL3 10368 EI 49 P L3 144 ; ; ; ...
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