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properties of areas and lines

# properties of areas and lines - Properties of Areas and...

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Unformatted text preview: Properties of Areas and Lines Areas The coordinates of the centroid of the area A are The moment of inertia about the x axis IX. the moment Of inertia _\= about the y axis and the product of inertia [0‘ are 1‘ = ji‘sz. I» = fxgdA, In = fxydA. A .4 A The polar moment of inertia about 0 is Jo : /r2dA : /(x2 + ﬂan : 1*. + 1).. Oik%(a+b)w+ A A ' k, g; .. Triangular area l l , Area=—bh I=—b:'", I-=—bh3 2 * 12 1 ‘ 36 y. R . A" Area : bk 1 a l 1 1 2 1 I [I = E b}?! 1v = a M7! 1r} 3 1b 11‘ Circuinrareu I—Lbh3 I—LHﬁ 1 —0 i 1 4 _ 12 _ 12 L ‘ ‘ Area : TW 1,.7- : 1v : 4 ER, : o .x’ I i r y; Area = 1M2 Semicireulurareu 1— 1—H? [—1113 1 —l!3i2 Are'1=l:rR2 I=I=lnR4 [ =0 x—127, _\—41), M78): ( 2 ‘ ‘ 8 E U 1 l I it 8 :i 3 '27 ‘ ....=—22 Irr:-rtR‘, 1.»: 777R“. 1,“:0 I: bh, A I?!) I4» h , 8 ~, 9n) . A i R | 1' A. ‘1‘ 45 4_ 3n ‘ Quarter Circuliu‘ alga Quartcrielliptical area - - ( 1 l w 1 l A i I; Area = HR“- 1, : 1‘ = — 1:164. 1H : R4 ma 4 m’ 4 - 16 s \ a (n + 1 Mb” 4n + 2 ‘ v f L” _(n + H!) x n + 2 m. I) I Circular sector Spandrel Arsa : 0R2 F _ (,bml 1 1R4 1-2 1. 1R4 +l-r) Arcdin+l .27 a——51na, “:7 0: —smga, A 4 2 ‘ 4 2 I 7 £317}: 1 — cbn+3 I i (linii—Z In : U ‘ 9n + 3‘ ' n + 3‘ " 4:1 + 4 LInes y The coordinates; of the centroid of the line L are fde /ydL fad], L L 1, ;- = . 3: = E = —— . / dL [LIL / dL , L . l. . 1 J: V x —.r 2R _ R sin 0; f (x Semicircular arc Queu'ter’circulzlr arc Circular arc ...
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properties of areas and lines - Properties of Areas and...

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