ME 221Lecture 231 ME 221 Statics Lecture #23 Section 5.5

ME 221Lecture 232 Homework #8 Chapter 9 problems: –42, 43, 50 & 55 Chapter 5 problems: –11, 13, 16, 20, 24 & 25 –See Blackboard for additional information Due Wednesday, October 30

ME 221Lecture 233 Quiz #5 Wednesday, October 30

ME 221Lecture 234 Last Lecture Equilibrium equations Free body diagrams Modeling supports

ME 221Lecture 235 Equilibrium Equations When the force system is replaced by a resultant force and moment that are zero, the rigid body is in equilibrium. The equilibrium conditions may be expressed as:

ME 221Lecture 236 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. 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.

ME 221Lecture 237 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. 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.

ME 221Lecture 238 Special Cases Equilibrium of Rigid Bodies - 2D & 3D Two- and Three-Force Members Special Supports

ME 221Lecture 239 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)

ME 221Lecture 2310 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 

ME 221Lecture 2311 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.

ME 221Lecture 2312 Chapter 5 Equilibrium Examples