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CE30-Lecture4

CE30-Lecture4 - Lecture 4 Equilibrium of Rigid Bodies...

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Lecture 4 Equilibrium of Rigid Bodies

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Introduction The necessary and sufficient condition for the static equilibrium of a body are that the resultant force and couple from all external forces form a system equivalent to zero, ( ) ∑∑ = × = = 0 0 F r M F O r r r r = = = = = = 0 0 0 0 0 0 z y x z y x M M M F F F Resolving each force and moment into its rectangular components leads to 6 scalar equations which also express the conditions for static equilibrium, For a rigid body in static equilibrium, the external forces and moments are balanced and will impart no translational or rotational motion to the body.
Free-Body Diagram First step in the static equilibrium analysis of a rigid body is identification of all forces acting on the body with a free-body diagram. Select the extent of the free-body and detach it from the ground and all other bodies. Include the dimensions necessary to compute the moments of the forces. Indicate point of application and assumed direction of unknown applied forces. These usually consist of reactions through which the ground and other bodies oppose the possible motion of the rigid body. Indicate point of application, magnitude, and direction of external forces, including the rigid body weight.

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Reactions at Supports and Connections for a 2D Structure Reactions equivalent to a force with known line of action.
What is REACTION (force) ? Reaction is a type of passive external forces , and it usually arises due to the enforcement of a displacement constraint.

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Reactions at Supports and Connections for a 2D Structure Reactions equivalent to a force of unknown direction and magnitude. Reactions equivalent to a force of unknown direction and magnitude and a couple.of unknown magnitude
Equilibrium of a Rigid Body in Two Dimensions For all forces and moments acting on a two- dimensional structure, O z y x z M M M M F = = = = 0 0 Equations of equilibrium become = = = 0 0 0 A y x M F F where A is any point in the plane of the structure. The 3 equations can be solved for no more than 3 unknowns. The 3 equations can not be augmented with additional equations, but they can be replaced = = = 0 0 0 B A x M M F

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Statically Indeterminate Reactions More unknowns than equations Fewer unknowns than equations, partially constrained Equal number unknowns and equations but improperly constrained
Sample Problem 4.1 A fixed crane has a mass of 1000 kg and is used to lift a 2400 kg crate.

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CE30-Lecture4 - Lecture 4 Equilibrium of Rigid Bodies...

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