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297Chap4

# 297Chap4 - Equilibrium of a rigid body A body is said to be...

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Equilibrium of a rigid body A body is said to be in equilibrium when the external forces acting on it form a system of forces equivalent to zero. R = Σ F = 0 M R A = Σ M = Σ ( r × F ) = 0 where A is an arbitrary point. In component form, Σ F x = 0 Σ F y = 0 Σ F z = 0 Σ M Ax = 0 Σ M Ay = 0 Σ M Az = 0

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CE 297 2 Free body diagrams 1. Choose the free body to be used and sketch it. 2. Indicate all external forces including those applied by the removed bodies (reactions). Place weights at the center of gravity. Clearly mark magnitudes and assumed directions. 3. Choose a coordinate system and indicate dimensions.
Reactions at supports and connections

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CE 297 4 Equilibrium of a rigid body in two-dimensions Choose x and y axes in the plane of the structure and for each of the forces applied to the structure F z = 0 M x = M y = 0 The three-dimensional equations of equilib- rium reduce to Σ F x = 0 Σ F y = 0 Σ M A = 0 where A is an arbitrary point.
CE 297 5 Equilibrium of a rigid body in two-dimensions (cont.) We can also sum the moments about another point B Σ M B = 0 But this is not an independent equation. To see this, Σ M B = Σ ( r B × F ) = Σ [( r A + r B / A ) × F ] = Σ ( r A × F ) + r B / A × Σ F = Σ M A + r B / A × Σ F = 0

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297Chap4 - Equilibrium of a rigid body A body is said to be...

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