ME221Lecture 115 Chapter 5 Equilibrium of Rigid Bodies
ME221Lecture 116 Equilibrium of Rigid Bodies Equilibrium equations Free body diagrams Modeling supports
ME221Lecture 117 Newton’s second law states that if there is a net force acting on a body, then this will cause motion of the rigid body. If there is no motion, then the object is said to be in equilibrium. Equilibrium of Rigid Bodies
ME221Lecture 118 Equilibrium Equations When the force system is replaced by a resultant force and moment that are zero, the rigid body is in equilibrium. The moment equation is new and differentiates particle from rigid body equilibrium.
ME221Lecture 119 Examples of supports: rollers smooth surfaces rockers clamps slots collars cables links fixed Supports for Rigid Bodies If a rigid object is subjected to some set of forces but does not move, then its motion could be restrained by a normal force exerted by the ground, a wall or from fixing the object with some support.
ME221Lecture 1110 Support Reactions If the support prevents translation in a given direction, then a force is developed on the member in that direction. Likewise, if a rotation is prevented, then a couple moment is exerted on the member. See Figures 5.3, 5.9 and 5.10 (supports for rigid bodies subjected to 2-D and 3-D force systems)
ME221Lecture 1111 Free Body Diagram Draw the body separate from all other bodies (including ground). Draw the magnitudes and directions of all external forces acting on the body. –No need to scale arrow size Include necessary dimensions of the body –Dimensions are needed for summing moments Draw the positive sense of the coordinate system used to write out equilibrium equations –Include: applied loads, reactions due to supports, and the weight of the object.
ME221Lecture 1112 Importance of FBD The FBD is at least half of an equilibrium problem.
ME221Lecture 1113 Special Cases Equilibrium of Rigid Bodies - 2D & 3D Two- and Three-Force Members Special Supports
ME221Lecture 1114 Two- and Three-Force Members When the member is not subjected to a couple and the forces are applied only at two points, the member is said to be two-force member. F3F3 A B F1F1 F2F2 F6F6 F5F5 F4F4 Two-Force Members Let: and A B FAFA FBFB These forces will maintain equilibrium if: (F A and F B must be collinear)
ME221Lecture 1115 Two- and Three-Force Members If the member is subjected to three coplanar forces, then it is necessary that the forces are either concurrent or parallel if the member is to be in equilibrium. Three-Force Members F3F3 O F1F1 F2F2 F3F3 F2F2 F1F1
ME221Lecture 1116 Note: It should be noted that single bearing, single pin and single hinge supports can support both forces and couples. Most often, however, these supports are used in conjunction with other bearings, pins or hinges to hold the body in equilibrium. In this case, the force reaction at the support may be adequate.