formula_sheet - x= xi Ai Ai y= yi Ai Ai I = ( I c + d 2 A)...

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1. Rectangle 6. Circle 2. Right Triangle 7. Hollow Circle 3. Triangle 8. Parabola 4. Trapezoid 9. Parabolic Spandrel 5. Semicircle 10. General Spandrel C b h x x x y y y b h C x x x y y y b h C x x x y y y a b h C x y a C x x y, y y r d C x y r d D C r x y R Zero slope h C x b x x - y y y - b h y - C x x x - y y Zero slope b h y - C x x x - y y Zero slope Ab h y h I bh x b I hb I bh I hb x y xy = == ′′ 21 2 2 33 3 3 A bh y h I bh x b I hb I bh I hb x y = 2 6 6 12 12 3 3 A bh y h I bh x ab I bh aa bb I b x y x = = + =− + () = 2 6 6 3 22 h 3 12 A h y h I h b b x = + = + + = + ++ 2 1 3 2 36 4 3 A r y r Ir II r x = π π π π π 2 4 4 2 4 38 8 9 8 Ar d rd == = π π ππ 2 2 44 4 46 4 AR r D d R r Dd == − π π π π 2 2 4 4 64 ′ = = y h b x A bh x b y h 2 2 2 3 3 8 3 5 ′ = = y h b x A bh x b y h 2 2 3 3 4 3 10 ′ = = + = + + = + + y h b x A bh n x n n by n n h n n 1 1 2 1 42 696 Table A.1 Properties of Plane Figures x xA A y yA A ii i i Σ Σ Σ Σ d A c =+ Σ 2
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Beam Slope
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This note was uploaded on 10/25/2010 for the course MECHINCAL 2010 taught by Professor علاءحجازي during the Spring '10 term at Hashemite University.

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formula_sheet - x= xi Ai Ai y= yi Ai Ai I = ( I c + d 2 A)...

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