ECS221L25

# ECS221L25 - 2 d k k = 2 2 A d J J 2 = C r x y dA C d r’...

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The Parallel Axis Theorem The parallel axis theorem is used with the method of composite parts. x y y x If I x is known for centroidal axis how to get it for any other parallel axis? x y

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Theorem: Proof: I WRT lower axis WRT centroidal axis 2 Ad I I + = C y’ d y dA I = dA y I 2 + = dA d) y ( 2 + + = dA d dA y 2d dA y 2 2 + + = dA d dA y 2d dA y 2 2 y = y’+d
…more I + + = dA d dA y 2d dA y 2 2 C y’ d y dA = dA y A y axis centroidal from C locates y 0 = A d I I 2 + = possible! smallest the is I

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Other Parallel Axis Theorems Radius of gyration: Polar moment of inertia:

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Unformatted text preview: 2 d k k + = 2 2 A d J J 2 + = C r x y dA C d r’ The Rectangle Given I x , I y . Compute Recall: I x = bh 3 /3 I y =b 3 h/3 . y x I , I y x h b y’ x’ 3 12 1 2 2 h 3 3 1 2 y x x bh (bh) ) ( bh A d I I =-=-= 3 12 1 y hb I = Composite Parts Area composed of simple shapes. x y 1 3 2 ∫ ∫ ∫ ∫ + + = = A 3 A 2 2 A 2 1 A 2 2 x dA y dA y dA y dA y I...
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ECS221L25 - 2 d k k = 2 2 A d J J 2 = C r x y dA C d r’...

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