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Unformatted text preview: ble to calculate the centroids of such distributions. If a load is considered to be concentrated at the centroid of the distributed load, it will generate the same reactions as the distributed load. Example Consider a beam that carries a UDL. 4‐7 Example Consider the beam shown below. q( x ) 2 x 2 4‐8 4.3 Area Moments of Inertia 4.3.1 Definition Area moments of inertia are used extensively in beam analysis and in dynamics. y
z
dA x
O y
x The most widely‐used of these moments are I x y 2 dA A I y x 2 dA A where the x‐y origin is assumed to be located at the centroid of the section. 4‐9 Example Calculate Ix and Iy for a rectangular cross section shown below. y dy y h x b 4‐10 Below, is a table of moment of inertiavalues for some commons shapes Ix Shape Iy 4‐11 4.3.2 Parallelaxis Theorem The moment of inertia of an area about an axis that does not pass through its centroid can be calculated using the parallel axis theorem. It takes the form 2
I x I x ' Ad y I y I y ' Ad x2 The theorem is often used for calculating the moment of inertia of a composite area. Example 4‐12 4.4 Problems 4‐13...
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 Winter '13
 Polak

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