30_ch 04 Mechanical Design budynas_SM_ch04

30_ch 04 Mechanical Design budynas_SM_ch04 -...

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Chapter 4 99 R B = w ( l a ) 3 [3 ( L 4 a 4 ) 4 a ( l 3 a 3 ) ] = w 8 ( l a ) ( 3 l 2 + 2 al + a 2 ) Ans. R C = w l R B = w 8 ( l a ) ( 5 l 2 10 a 2 ) Ans. M C = w l 2 2 R B ( l a ) = w 8 ( l 2 2 a 2 ) Ans. 4-61 A = π 4 (0 . 012 2 ) = 1 . 131(10 4 )m 2 (1) R A + F BE + F DF = 20 kN ( a ) ± M A = 3 F 2(20) + F = 0 F + 3 F = 40 kN ( b ) (2) M = R A x + F ± x 0 . 5 ² 1 20(10 3 ) ± x 1 ² 1 EI dy dx = R A x 2 2 + F 2 ± x 0 . 5 ² 2 10(10 3 ) ± x 1 ² 2 + C 1 EIy = R A x 3 6 + F 6 ± x 0 . 5 ² 3 10 3 (10 3 ) ± x 1 ² 3 + C 1 x + C 2 (3) y = 0 at x = 0 ± C 2 = 0 y B =− ² Fl AE ³ F (1) 1 . 131(10 4 )209(10 9 ) 4 . 2305(10 8 ) F Substituting and evaluating at x = 0 . 5m B = 209(10 9 )(8)(10 7 )( 4 . 2305)(10 8 ) F = R A 0 . 5 3 6 + C 1 . 5) 2 . 0833(10 2 ) R A + 7 . 0734(10 3 ) F + 0 . 5 C 1 = 0 ( c ) y D ² ³ F 1 . 131(10 4 )(209)(10 9 ) 4 . 2305(10 8 ) F Substituting and evaluating at x = 1 . D 7 . 0734(10 3 ) F = R A 1 . 5 3 6 + F 6 (1 . 5 0 . 5) 3 10 3 3 )(1 . 5 1) 3 + 1 . 5 C 1 0 . 5625 R A + 0 . 166 67 F + 7 . 0734(10 3 ) F + 1 . 5 C 1 = 416 . 67 ( d ) 111 0 013 0 2 . 0833(10 2 )7 . 0734(10 3 )00 . 5 0 . 5625 0 . 166 67 7 . 0734(10
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