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EAS207-Exam-problems-from-Ch-9&10

EAS207-Exam-problems-from-Ch-9&10 - m EMMM Fflwmy...

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Unformatted text preview: m EMMM Fflwmy 20;) (J Prohiem #2: Water is heid back by the submerged rectanguiar gate 6 as shown in figure 2. Find the resuitant force on the gate (and its point of action) due to hydrostatic pressure. Also find the support reaction at the gate’s hinge support. (30 points) , hi: QCEE‘EZ ‘ m: 40 Utevz‘ii ' “2: 20 [I], Ymgz 62rd: L19/32,? RF Jzts‘ostziniz-A'SMZO) 30/ ,3 FW: ijgzgstctssmi324xi0‘si‘vs NA 9mm now 52, Mme WW“? mg: SBTKSX§QX®I W; + [42 (40‘turi0‘tveXis) @1623 (it? \w/ :3 ,_ (424$) SEQ) ($2.43»- 2§~4§):0 3. (SQ-pts.) A bracket is made of brass (y = 0.300 lb/in.3) and aluminum (7 = 0.100 lb/in.3) plates as shown below. a. Locate the centroid of the bracket. b. Locate the center of gravity of the bracket. W2 A“; xc=£ 377 ‘4r W"; Brass 3 in. dia. hole 4. (30 pts.) Determine the maximum and minimum moments of inertia with respect to centroidal axes through C for the composite of the four square areas shown. Find the angle 0t measured from the x-axis to the axis of maximum moment of inertia. at we: Asia tcgaamgaéw 9"“ F33? égafiféeéwsm‘ Vflx E K .3 s n . ,. . «E 5% My aging aw Ea?me V. iii a \ , 23E; 2%“? % W\R%M\k KKK Ekafi n. Xmfiw ffi%%% am». a .EE 6:52.142.“ W.“ K% 5&5 , . _ n a k @ AM; a gig ax E gmmmq a fix; “56 \nv MI \ §% MHWV M, 5% ayaswmwx $3; % w wflwm u w. 31% m Mk \Nx, wafim m x8 x\m§, «gawk , $qu w RKQNWQ, xawmefiv. xfiwxww m gawk? «$5; $wa9 khxge kmfiwe \mxmmfi 3&3. wmgw xii kwwmw fiafi g , m A x a . A \V %% km “Swgk , » ‘Exizsgv 5E2 EaEfifnSEfféL raettrasit it§ti§rii it; "IE/til :29 at? “swimmnm‘nwwwwwm Q2 (30 pts) A bracket is made of steel (y = 0.284 lb/in.3) and aluminum (y = 0.100 lb/in.3) plates as shown below. a. Locate the centggéd of the bracket b. Locate the center of gravity of the bracket Aluminum Q3 (30 pts) For the composite area shown below with the x-y axes through the centroid: a) Determine the normal moments of inertia IX and L, and the product of inertia Ixy b) Use Mohrs circle or the transformation eq’ns, to determine 1max and 1mm and their orientation to the X—y axes. Show the principal axes on a sketch of the composite area. \ , J a/ (5M 0/ ‘ . / 7o / j] 2? ’L’E‘L‘“4575m NF Alummum fl. : 4530 : (37f/n f 240 ~— 42v:- Sin‘ flSteeI 34'284 ’ /?&&_, fin. f 9 :2 ' 27:5 " 74M: 1"“\ ‘ I5} ' ' Aluminum :2253'3 r ,/6//‘) 2; ~ 2’4 X66 44-24 é’m’ . \%'§<\g" Jé I _.: ;: 7 ,9 g 5/49 3 1m. fit”; £34“ 256 {My ' In. /AM W flé yzw mitts: Aw 5w 14v @XVMWMW _ / 5:0 3 1.5j A0" 5 40 800(400 4 j 30 4:9 2 //0 3/24 {5‘15 5' 605 0’65“ 5‘50 x2713 /7/.8 #212, I ~ 3 50 5 @5325 3 5 525 xzs 250 Q 5%} A215 25 Z ‘24ol¢4«.24 1/; 70 /530 /Z<:70> 122533 12643 2mg #2 meda/Kénazg 6.. 373: 5’) (547‘ (at/5,5792; 5) AW; x8: 3% "272.22% .=— MM 0/. 325 l “gm 22' go. 3255» 4’ :41”. x /¥* 325 45;”. : 2675 #4 HAM/5 ' : ‘/‘§= r--/4——°{ 2% 22m -? 7 . 55,3 :35‘6?’ W/ AM: EAS 207 - STATICS — Fall 2004 Second Exam ' Total Points: 100 Notes: 1. Closed Book; 2. Do all problems, 3. Draw free—body diagrams and reference axes Q1. (3) Using method of sections, determine the forces in members EF, KF and KL in the truss shown in Fig.1. Assume A is a pin support and G is a roller support. (b) Guess the forces in members BC, BI, and HL mg l‘ Fig.1 — Truss Q2. (3) Find the second moments of area Ixx & Iyy, and Ixy for the composite area shown in Fig.2. ' (b) Find the major andwr principal axes, and draw 6 axes in Fig.2. 7. r; t g, zy—«iA-xc y 7 g ,. 83 ("1-59; (3 Z “1733 + (2% “5f 3 CITY ‘39 {’2' 1 ’2... L ’2. ?’ 1‘2. 8 m. t1 + ‘5”: .Wn’i +82LX‘A?C3>+ v: VCLD Tyt “- : 924.491 + {@592 + (MW + WWW 23mm in“ A r“ Arc i3“, ‘1 5; Lx‘y( 4" 3' yfi Q. 2) Determine the x— and y-coordinates of the centroid of the shaded :. 5: F? r ' area“ \fige S‘V‘VXQV"‘W§§E\€3W« (33 pants) . ‘ XCQ M W (:54: ‘ M f X: 9“ " 56; fl ca%§fi ~23 , M “’7 - at; '" “\g ’c , if r mav- v , ‘4', ’ ’W M ' L3!” ' a 6:?” W ‘ v- * W 0.3 ) Determine mass moment of Fig.3 with respect to the x- and y— 490 pounds per cubic feet. (density w, May; "’ :2. Mbkoak m WW2: filflflg was .1 \/ inertia of the composite body shown in axes. The unit weight of the matertai is = unit weight / 9, where g=32.2+’c/sx3) (34points) I + X—Owfi {A Mac K /7é-;-s I V‘ k :1. f S 3 S 8 r ’ h ’\/ \ :(«j»—O\XV)> O I A. V Cycmlh)” I ,7 "£333: " , / 1W353 5; 7)“? K \4 ~ $M3’54 m 245;) X “ ,, + “‘"5 ‘ M fl ~ 144 . y > _\ M M ‘” “A? K“ ~\\’\ 2’: xi?“ Ck ., 1" 5* ’“ W31)” 3 M 1 7(~0\\<;}3 :2 W! I X 3 E5 MN. z: :3 ,/ L3 M W _ , M ~ N “$161M (\6*O\X{I)§ ‘ W "as: : Rig-*0“ {A} (Tax-‘MQQM AV [Iv/QXMBEQODK > M: (pg—9+ Maw (XMW L ‘ 1, '1r j? MkkcfiK (61;,4”) J;— Mgocx (3&2) (l. ‘ ,‘ 33 Nut”, QQJ'NQ'S') “V Myfl>a¥<<wz {7/3 “AWL; . ‘ M4 ‘ "4W SAwg ~ g WW m (-5? m r...— W WM 2:932 0.4) a) Determine Ix, By and lxy for the area shown in Fig. 4 (15 poénts) b) Determine the principal moments of area and its orientations with respect to x-axis. ‘ (10 points) “V i 24. ,- W 1: :— 44902 a? 0“ Z— V (g g0 zs .: 1mm 3 2,, ’ M I Q. 2) A composite body consists of a rectanguiar brass (mass density = 8.75 Mg/m ) biock attached to a steei (mass density = 7.87Mg/m ) cyiinder as shown in Fig.2 . Determine mass moment of inertia of the composite body with respect to the x-axis shown in Fig.2 (33points) ,,,,,,,,,,,,,,,,,,,, """" g7 tn + ( {3' 03$ (“37' g) "’7 WWW?" “Arm @006) C - ., Km ' ""72? A/ l E (873x103) / 'k A; I 5 39 56 kcmw % 5791"" 9 1 v ,i €2,734 + 6573962 " rs. ' 2-,: 2; 20652 672% IQWW’S’“ Lfixfia‘flzfifl j ’j ("KEN 0.3) Determine the Moments of Inertia of area (second moments of area) I): and Iy of the bounded area shown in Fig. 3 (34- points) ...
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