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297Chap9

# 297Chap9 - Moment of inertia of an area For...

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Moment of inertia of an area Forlinearly-varying distributed loads, Resultant force R = A ky dA = k A ydA = kQ x The first moment of the area about the x -axis Q x = A The first moment of the area about the y -axis Q y = A xdA

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CE 297 2 Moment of inertia of an area (cont.) Forlinearly-varying distributed loads, Resultant moment about the x -axis M = A ky 2 dA = k A y 2 dA = kI x The second moment of the area about the x - axis. I x = A y 2 dA
CE 297 3 Moment of inertia of an area (cont.) The second moment, or moment of inertia ,ofanarea about the x -axis. I x = A y 2 dA The moment of inertia of the area about the y -axis. I y = A x 2 dA

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CE 297 4 Moment of inertia of an area (cont.) Direct integration I x = A y 2 dA I y = A x 2 dA I x = dI x = y y 2 ( a - x ) dy I y = dI y = x x 2 ydx
CE 297 5 Moment of inertia of an area (cont.) Moment of inertia of a rectangular section I x = A y 2 dA = h 0 y 2 bdy I x = 1 3 bh 3 = 1 3 h 3 b I y = 1 3 hb 3 = 1 3 b 3 h

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CE 297 6 Moment of inertia of an area (cont.) Computing I
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297Chap9 - Moment of inertia of an area For...

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