297Chap5

297Chap5 - Center of gravity of a two-dimensional body...

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Center of gravity of a two-dimensional body Gravitational attraction of the earth on a rigid body ,adistributed force, can be represented by a single equivalent force W applied at the center of gravity.
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CE 297 2 Center of gravity of a two-dimensional body (cont.) Foraflat horizontal plate Σ F z : Σ M y : Σ M x : W =∆ W 1 +∆ W 2 + ... xW = x 1 W 1 + x 2 W 2 + yW = y 1 W 1 + y 2 W 2 + W = dW = xdW = ydW
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CE 297 3 Center of gravity of a two-dimensional body (cont.) Forawire lying in the xy plane Σ F z : Σ M y : Σ M x : W =∆ W 1 +∆ W 2 + ... xW = x 1 W 1 + x 2 W 2 + yW = y 1 W 1 + y 2 W 2 + W = dW = xdW = ydW
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CE 297 4 Center of gravity of a two-dimensional body (cont.) Σ F z : Σ M y : Σ M x : W =∆ W 1 +∆ W 2 + ... xW = x 1 W 1 + x 2 W 2 + yW = y 1 W 1 + y 2 W 2 + W = dW = xdW = ydW The center of gravity is located at x = W y = W Note: For a wire lying in the xy plane, the center of gravity may not be located on the wire.
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CE 297 5 Centroids of areas and lines Forahomogeneous flat horizontal plate of uniform thickness W = γ t A W = tA where =specific weight t =thickess of the plate Σ F z : Σ M y : Σ M x : W =∆ W 1 +∆ W 2 + ... xW = x 1 W 1 + x 2 W 2 + yW = y 1 W 1 + y 2 W 2 + W = dW = xdW = ydW
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CE 297 6 Centroids of areas and lines (cont.) Σ F z : Σ M y : Σ M x : A =∆ A 1 +∆ A 2 + ... xA = x 1 A 1 + x 2 A 2 + yA = y 1 A 1 + y 2 A 2 + A = dA = xdA = ydA The centroid of an area is located at x = A y = A The centroid is a geometric prop- erty.
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CE 297 7 Centroids of areas and lines Forahomogeneous wire of uniform cross section W = γ a L W = aL where =specific weight a =c ross sectional area of the wire Σ F z : Σ M y : Σ M x : W =∆ W 1 +∆ W 2 + ... xW = x 1 W 1 + x 2 W 2 + yW = y 1 W 1 + y 2 W 2 + W = dW = xdW = ydW
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CE 297 8 Centroids of areas and lines (cont.) Σ F z : Σ M y : Σ M x : L =∆ L 1 +∆ L 2 + ... xL = x 1 L 1 + x 2 L 2 + yL = y 1 L 1 + y 2 L 2 + L = dL = xdL = ydL The centroid of the line L is located at x = L y = L The centroid is a geometric prop- erty.
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CE 297 9 First moments of areas and lines Forareas Q y = xdA = xA First moment of A with respect to y -axis Q x = ydA = yA First moment of A with respect to x -axis Forlines Q y = xdL = xL First moment of L
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This note was uploaded on 01/20/2012 for the course CE 297 taught by Professor Pujol during the Fall '08 term at Purdue.

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297Chap5 - Center of gravity of a two-dimensional body...

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