Properties-of-Areas

Properties-of-Areas - Properties of Areas and Lines Areas y...

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Unformatted text preview: Properties of Areas and Lines Areas y The coordinates of the centroid of the area A are is» /x (M (M A A l' , ~ — ~ i x: , y: . «V /dA i l A A x The moment of inertia about the x axis Ix, the moment of inertia about the y axis 1y, and the product of inertia IX}, are 1x : /y2dA, I), : /x2dA, In, 2 /xydA. A A ' . .t The polar moment of inertia about 0 is J0 : frsz 2 /(x2 + fldA : 1x + 1).. A A Triangular area 1 ' l r 1 » = e I = -~-~ 3 ,, _- _ 3 Area 2 bh x 12 bh , ll 36 bh ( x Area : bh l l , 1 7 1 2—1713, 1,,=~hb5. Ir,=~b2h‘ ,t 3 1 3 . M 4 Cneular area I . ' 3 , 1 i I: I E W: 1r = 13% a 1w = 0 Area = 7R- 1", = ly- = 1 77R“, 1”, = 0 y r“ %h T , fl 1 ,1 w; x _ 14 t l -r / mtji ‘ ‘ 3 b 7- Triangular area 4R “.1 “3; Area = 7 bh Semicircular area 1 l l A ' 1 A l 4 M Ix=e~blf 1 =~hb3 1 =—b~h~ Area=e7rR I =I,=—wR L —0 “sq Quzmcr—circuiar arm; g 377 Area = (xk‘z 1 Itzi—R“ ' 4 1:0 (a ; \ R / \ /,, // \ 2‘1 V (KT? ‘ \ . \ 2R 51g ‘ fizz "‘ Circular sector 1 . “ 1 4 fl—sm2a , 1‘.=*R ” 4 y L 1 ; Area 3 7m}? = A R‘ W 1 I 1" I I V I 79“ 2 W Ha)". = 7* 7T: ’1 “7 ~(z‘ “ x V 6 1 .V . \_\ (n + 1,3611%" / 471+ 2 I X Tfmelfly J L “ii.__‘ ‘ Spandrel Cbrz-‘rl 1 ‘\ Area = V J”; a *- ~sin20z , ’l 2 ‘ ’V — (,Ebln'H I ‘ Cbn~.> W (:Lqu—FZ 911+3’ “V n-i-27 W 4n+4 Lines The coordinates of the centroid of the line L are / x dL / dL - L L x = 2 u a / clL L i: ...
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This note was uploaded on 12/01/2011 for the course PHY 108 taught by Professor Iashvili during the Fall '08 term at SUNY Buffalo.

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Properties-of-Areas - Properties of Areas and Lines Areas y...

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