lectures 21-26

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

This preview shows pages 1–13. Sign up to view the full content.

450 ft-lb 300 lb 40 plf 4 ft 3 ft 8 ft V (lb) 0 M (lb-ft) 0

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
75 ft-lb 50 lb 10 ft 10 ft V (lb) 0 M (lb-ft) 0 50 plf
Centroid – The geometric center of an object. 2L/3 x x y y

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
x y L x 3 2 = L y 3 1 = In general… Centroid only depends on geometry, not density
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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
12’ 6” 4” 15” 6” 4” 18” 24” ? ? = = ξ ψ

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
3” 4” 4” 1” Find the location of the centroid.
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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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.
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.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 46

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

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online