University:
Michigan State University
Course:
ERG 160 | Success in Science, Technology, Engineering, and Mathematics
Academic year:

2024
Views:

88

Pages:

2
Author:

Madelyn Bradshaw

COSMOS: Complete Online Solutions Manual Organization System Chapter 9, Solution 62. Using equations developed on page 491 of text: yP = Now Ix I = ss′ yA yA R = γ yA yA = Σ yA 1  = ( h + 17 in.)  × 120 in. × 51 in.  2  1  + ( h + 34 in.)  × 84 in. × 51 in.  2   d = ( h + 79 in.) = ( 5202h + 124848 ) in 3 = ( 36.125h + 72.25 ) ft 3 Then, ( ) R = γ yA = 62.4 lb/ft 3 ( 36.125h + 72.75 ) ft 3 = 2254.2 ( h + 2 ) lb Also, I ss′ = ( I ss′ )1 + ( I ss′ )2 2  1  120  51 3  1  120  51    17  2  =  ft  ft  +   ft  ft    h +  ft  12   2  12  12     36  12  12   2  1  84  51 3  1  84  51    34  2  +  ft  ft  +   ft  ft    h +  ft  12   2  12  12     36  12  12    34 289  1156   4   2 68 =  21.324 + 21.25  h 2 + h+ h+  + 14.9266 + 14.875  h +   ft 12 144  12 144      ( ) = 36.125h 2 + 144.5h + 198.311 ft 4 continued COSMOS: Complete Online Solutions Manual Organization System ( Then = FBD of Gate: ) 36.125h 2 + 144.5h + 198.311 ft 4 I ss′ yP = = yA ( 36.125h + 72.25 ) ft 3 h 2 + 4h + 5.4896 ft h+2 For gate to open: ΣM AB = 0: − M open + ( yP − h ) R = 0  h 2 + 4h + 5.4896   2 ( 8000 lb ⋅ ft ) −  − h  ft   2254.2 ( h + 2 ) lb  = 0 h+2    or Thus 2h − 1.60826 = 0 d =h+ h = 0.80413 ft 79 79   ft =  0.80413 +  ft 12 12   = 7.3875 ft or d = 7.39 ft