lecture9 - 0 Centroids of Composite Areas.i-ABLE 551...

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Unformatted text preview: 0 Centroids of Composite Areas .i-ABLE 551 CENT-ROI!)- IL-f—‘Zffi- ‘_-‘ "- r Bing f-fic“: -. Sémicircular are “i=7” 'LijGATIQNS 150R A FEW COMMON LINE SEGMENTS AND AREAS _ Circular sector LA=LT2ir .. 2r sin or 36" 3a . 'ycr—O Quadranf of a circ'Ié Semicircular area «m? Affi— xc=_r Ar ””37? Quadfgnt of an ellipse mb A — ”2:" x z .341 C 317 yd_ 5-3"; Paraboiic sp'andre} bk ' A 5 ~57 3b 7‘6. f“ T -271 5":- 10 Quadrant ofia parabola - _ 217k "* T It: 2 £22. '8 -_.£’£_ 3C " 5 Locate the centroid of the shaded 211% shown in the,figure. o L "t J/ ,3" 5/ , _ 80mm 801mm 80mm 1mm 80 mm 80 rmn (80)(<go)': (p/LFOOQMM)L waw) 2 (2900 W31 ZAL' 1; AV: EA'SQ V O O 0 Locate the centroid of the shaded area shown in the figure. X 1‘ 1 ‘ 50111111450 mm 1 . r I; t i 1 5011me50mm3 7500K = S‘C375‘o)—r75(‘25003+000350) 25 mm»! .— A Xi EZQA @3003 Y: 75CA H— <27 5(A131—15—{A35 __ ~ 9» (7506sz ’75 (375cfi) + 97.501506) +131 \Q So) \7 = (NC/750101 Distributed Loads Resultant Force 4% w(x) (Load Distribution Lb/ ft) IIIIIIIIIIIIIIIIIIIIIIIII-I-IIIIIIIIIIIIIIIIIIIIIIII... \flfl 51b 1 ‘ w(x) = 5 lb/ft 94w x=20 ft w(x) (Load Distribution Lb/ ft) “Recall” What is the resultant of this force system? A) Will be the force that has the same force components in all directions as the original system K & B) The force will be located at a point that will create the same moment, about any fioint, as the original force system Same here w(x) =\5 lb/ft . i o ' w(x) =2 2:2 lb/ft Ion [OS-T- ’2. (as: S “JUDGE-7‘: C‘D‘Z’. d1 0 j‘ 0 _ 3 /0 ._ -123 :0 ~— ééé QGAES\ «f CGQLWMD at M 1044' xx.- [05-1— 2. gag YA:- g «meflxolxfi ”23234; $313 ' \ b ‘_ L1 )0 0696‘.er ‘cl 1%.. [:0 —— é 000L435 9-:- I" .. /' if“ w(x)=101b/ft mm=QWfi "45—0 +l01-JOj R =150nglfl/ — E547” IOH 25" V' R“: Xf‘ f llwc'vflof’k: :2 0‘1 +- {W’WJI Q 0 1/ \_ 615: E c, 1- mg L; — — 2 I50 hwgicroo) TLgigg-zflys] S: RSRT‘CQOOO "(OOXAEQ‘QSO YA"- Isrorr'r- / DoZmflDZfl $23.1 E L a a. _.H..... 0:u .h xE f0? I: 48mg 70:? >>c3m 4. 7 .1 a10m<.n.o..woc 57.493 (f figflu fez” n 72.8 :grdnds To? d mm: W Lg [(f" 2““IL- 1",) wfldk TC’F’ ...
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