lectures 21-26 - 4 ft 40 plf 3 ft 8 ft 450 ft-lb 300 lb V...

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450 ft-lb 300 lb 40 plf 4 ft 3 ft 8 ft V (lb) 0 M (lb-ft) 0
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75 ft-lb 50 lb 10 ft 10 ft V (lb) 0 M (lb-ft) 0 50 plf
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Centroid – The geometric center of an object. 2L/3 x x y y
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x y L x 3 2 = L y 3 1 = In general… Centroid only depends on geometry, not density
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Coordinates of the centroid , or average position, of an area is… = = A A A A dA ydA y dA xdA x 2 x y y = x 2 –x + 1 Determine the x-component of the centroid of the area.
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In discrete form, or when dealing with a combination of simple shapes… = = A A A A dA ydA y dA xdA x = = i i i i i i i i i i A A y y A A x x Sum of individual centroids times area Sum of areas Centroids of Composite Areas 1 2 x y
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12’ 6” 4” 15” 6” 4” 18” 24” ? ? = = ξ ψ
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3” 4” 4” 1” Find the location of the centroid.
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Center of gravity vs. Center of mass The point at which the resultant weight of a system of particles acts. Since c.g. depends on the acceleration of gravity, center of mass is a better term to use. Center of gravity of the solar system??? Center of mass is independent of gravity.
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c.g. = = = W zW z W yW y W xW x Center of mass = = = m zm z m ym y m xm x 100 lb 300 lb 100 lb (4,8)ft (10,6)ft (5,3)ft Find the center of gravity.
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Moments of Inertia Area Moment of Inertia Mass Moment of Inertia - used in Dynamics to calculate the rotational motions of objects. - used to calculate stresses and deflections in beams. Can be thought of as a measure of the cross-sectional area’s resistance to bending. F F Much easier to bend the board in this orientation… …than this one.
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v.s. b h x y 3 12 1 bh I x = 4 3 95 . 1 ) 5 . 2 )( 5 . 1 ( 12 1 in I x = = We are taking the larger dimension to the third power, therefore we get a larger moment of inertia about the centroidal x-axis. b
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This note was uploaded on 08/29/2010 for the course EGN 3311 taught by Professor Nohra during the Spring '08 term at University of South Florida.

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lectures 21-26 - 4 ft 40 plf 3 ft 8 ft 450 ft-lb 300 lb V...

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