Question

Q2. (20 points) The gate shown below is 5 ft wide. It is hinged at point B and it rests against a smooth wall at A. The gate is rectangular. There is seawater acting on the gate with specific weight Yseawater = 64 lb/ft i. Draw a diagram for this question and show all forces acting on the gate with their locations ii. Find the force acting on the gate iii. Find the location of this force h iv. Find the horizontal force Pexerted by the wall at point A V. Find B vi. Find B Wale Seawater 64 16 CY 204 Cate A=bh' Icg vect. 12 b.h q ft

Answer 1

page-(4) lovestiom isolution → trivem that hate i Hold between smooth wall and Hinge 3, to support sea-water. free surface wall Searwater ($95.64 101 fet3 FA 2oft n b ht ldet h L COP (Folx ght (FBy ha 692 + (972 fig-i 36 + 81 h = 110.81 ft

cil Draw a page- (2) diagram for this ovestion and show all forces acting on the gente with their docation, F. B.D of hate 'Y O= family FA А Fy=FILO (33.6919 G ☺ Con eft X Fx = F8170 (FB), Bx gfut (FB) y = By figna lill find the force acting on the gate t = distance of centre of gravity of Plate from free suoface. (20-6) + (AG) simo 14+ 3 = (17) ft

page- (3) it = (17) ft -> area of Gate= Gate= A= ban 5 * 10,81 А (54,05) ft? Force acting on the gate = F F = [(-399 ata] 64 x 54.05 x 17 (58806.49.16 ans (ii) find the location of this force h* h* distance of centre of poesson from free water surface.

Page - (4) (In) Sim²o + A 2 2 12 t hogy xxxt Ch'ü x x [sim (33.6077 (2x h t. 2 0.815 x gim² 133.69] +17 12 X 17 0.176 t 17 h* (1701767 ft A : Location of acting of Force For at this point

10 page-(5) find the Northair horizontal force P (Fal exerted by the wall at point Ai FA=P T R Fa (58806-454 119 6 PE 0 = 33.69 Hinge B g PL AB= h' (10.81 oft x= n* 17.176-14 hy - (23-6) 26= (3.176 ) fat AP gimo a x 3.176 AP x Simo) sim (83069) AP= (5.725) fall

Page (6) AP = (10.81- BP = AB - 5.725.964 BP = (5.085) ft EMB 11 o FX (BP FAX-6 FX siogs = (FA) x 6 FA = [158806.47% 5.0859 elt - (49838.424) Ib las NI find Bx Bx Horizontal Reaction at Hinge B. FA Froso = Fy AY Ex=Fsimo (Foly B =Bx (FBly = By

Ex page-A) Horizontal campament of Hydrostatic force (F) Esimo 17 = (58806,4) Sim (33.69) Fx = (32619.86) Fy a vertical component of Hy disostatic force (Fy] (F cosol (33.697 (58806,47 tersey 1980.16785786) = (48929:92) dit Fy Since Plate is in static equilibrium EFN=0 Bx + Fx.= FA By = FA > F

Bx pagi-(8) 32619.86) = (49838.424 Bx = (17218.564) It (vi) find By Since, E Fw=0 By Fy =0 -> Bay - Fy = F.coso By =(48929-92) dinle p