Question

well explained please

The dam has water of depth 4 ft on one side. The width of the dam (the dimension into the page) is 8 ft. The weight density of the water is y = 62.4 lb/ft?, and atmospheric pressure Patm = 2120 lb/ft?. If you neglect the weight of the dam, what are the reactions at A and B? B T 2 ft 2 it 2 ft

Answer 1

M House 2ff 26+ 2ft BC and CA and their locations see that Giver weight dernity of water, ſ= 624 (6/p13. let devide the ACB section in two sections Ac and BO. section 'Bc is vertical and section nach makes 0-45°. Griven Paton = 212016/472 let calculate thydrostatic fores acting on 2 we tano O= 45° 2 Sections section BC: we know that for a vertically submerged sumbace, Total Pressure will be the Presiune acting at the depth of Centroid.

Total Precure or a Average presure, P = Pation + aug rhal for section Be heG § - lift 2 .. 2120 + 62.4 x 1 Pary 2182-4 lblet Pang Net Force acting FACE Pong on section BC is Area gel Given width of dam 8 ff. . Area BC 2x 8 = 16 eth For = 2182-44 16 = 34918.4 lbs. FC = 34918. 4 (bs. This force will out at the Centre of Precure, (COP) which can be vertical subbrerged surface as given for LG + hoi COP = dBehen where can Moment of Inertia about centroid 8x(2) of section c = bd 12 12

8x1213 Copa i2 + 1 164 (1) COP 1.33 H. FBC 34918.4 lbs acts at 133 off depth from water surface. Section di R for section dc, A) projected vertical Fone Hi above the surface Ac. K21 Ful fu weight of water A projected, [volume of water] + Pater. (Apajected). r [Area x width]t (2120 x(2x8)). r [faren of triangle Ace + dren of restonghe cpar) x width 7437920 [Cx2x1) +(*2))x 8 3+ 35920 62.4 Fv 36915.2 (65. Horizontal fone, FH = Pang & A Projected.

we have Patm+ rher Paug - for section de centroid will be als 2 nco 2+ = 3ft. 21204 62.443 Pary Paugh 2307.2 16/4 Projected Area, ad projected - 2x 8 = 16 ft" Fi 2307.2 x 16 36915. 2 (6s. Net Force force arting section Ac is FACT i FACT (36915:25+ (369152) FAC= 52265.976 (bs. This FAC will act at Centre A Preelne which can be given for incliened sarbre as Ich sino Cop f исс, Aachen

Ica Moment of Inertia of Ac section be 8x (262) about centroid, 12 12 V22) Ich = 15.085 It' 2 190° 2 A and o = 45° :. Сое 15.0854 sin uso 46 8x252) x3 + 3 : COP 3.11 ft. FAC acts at 3.1 ff depth from water sumbone- free body diagram of ACR' is shown below: B RB I L 1.33ff aff FBC 3.ll.ft. aff RAY ht 1.89 st 45 RAX K eft and In the equilibrium, EFx=0 efy-o. RB+ RAM = BC + FH.

. RATRAK 34918.4+ 36915.2 RB+ RAK- 71833.6 (bs ③ and RAY fy 36915.2 lbs RAY Also, EMA Roth Focl.4-1.33) + 4 (0.89) + F(0.8a). 4R8 349918-4 (2-67) + 369152(2x 0-89). RB = 39735.296 (65. from Eg. O, RAR - 32098.304 lbs. " RAF RA= Saurray (32098-30417 66915.2) RAF 48918 638 16s. Reaction at support, A, RA-48918.638 165 Reaction at support B, RB-39735.296 (65.