Equilibrium of Rigid Bodies
Equilibrium of Rigid Bodies
ContentsIntroduction（绪论）Free-BodyDiagram（受力简图）Reactions at Supports and Connections for a Two-DimensionalStructure（支撑与连接处的作用力与反作用力）Equilibrium of a Rigid Body in Two Dimensions（两维刚体的平衡条件）EquilibriumofaTwo-ForceBody（二力构件的平衡）·EquilibriumofaThree-ForceBody（三力构件的平衡）2
Contents • Introduction（绪论） • Free-Body Diagram（受力简图） • Reactions at Supports and Connections for a Two-Dimensional Structure（支撑与连接处的作用力与反作用力） • Equilibrium of a Rigid Body in Two Dimensions（两维刚体的 平衡条件） • Equilibrium of a Two-Force Body（二力构件的平衡） • Equilibrium of a Three-Force Body（三力构件的平衡） 2
Introduction. For a rigid body in static equilibrium, the external forces andmoments are balanced and will impart no translational or rotationalmotion to the body.. The necessary and sufficient condition for the static equilibrium of abody are that the resultant force and couple from all external forcesform a system equivalent to zero,ZF=0 ZMo=Z(r×F)=0: Resolving each force and moment into its rectangular componentsleads to 6 scalar equations which also express the conditions for staticequilibrium,ZF, =0ZFx=0ZF,=0ZM=0ZM=0ZM, =03
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, F 0 MO r F 0 0 0 0 0 0 0 x y z x y z 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. 3
Free-Body DiagramFirst step in the static equilibrium analysis of arigidbody is identification of all forces acting on thebody with a free-body diagram.A2400 kgGKSelecttheextentofthefree-bodyanddetachit1.5m土from the ground and all other bodies.B. Indicate point of application, magnitude, and4mdirection of external forces, including the rigid+2m-bodyweight..Indicate point of application and assumeddirection of unknown applied forces. These23.5kNusually consist of reactions through which theground and other bodies oppose the possible1.5mmotion of the rigid body.B9.81kNB:Includethedimensions necessaryto compute4m←2m→the moments of theforces.4
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. 4
Reactions at Supports and ConnectionsReactionsequivalenttoaforcewithknownlineofaction.ForcewithknownFrictionlessRockerRollersline of actionsurfaceShort cableShort linkForce withknownlineofaction900CollaronForce with knownFrictionlesspininslotfrictionless rodlineofaction5
Reactions at Supports and Connections • Reactions equivalent to a force with known line of action. 5