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MSU ME 221 - Old Lecture 23 sect 5.5

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PowerPoint PresentationHomework #8Quiz #5Last LectureEquilibrium EquationsSlide 6Free Body DiagramSlide 8Slide 9Slide 10Slide 11Chapter 5 Equilibrium ExamplesME 221 Lecture 23 1ME 221 StaticsLecture #23Section 5.5ME 221 Lecture 23 2Homework #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 30ME 221 Lecture 23 3Quiz #5Wednesday, October 30ME 221 Lecture 23 4Last Lecture•Equilibrium equations•Free body diagrams•Modeling supportsME 221 Lecture 23 5Equilibrium EquationsWhen the force system is replaced by a resultant force and moment that are zero, the rigid body is in equilibrium.~ ~0 and 0F M  The equilibrium conditions may be expressed as:0 00 00 0x xy yz zF MF MF M      ME 221 Lecture 23 6 Supports for Rigid BodiesIf 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 221 Lecture 23 7Free 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 221 Lecture 23 8Special Cases•Equilibrium of Rigid Bodies- 2D & 3DTwo- and Three-Force MembersSpecial SupportsME 221 Lecture 23 9Two- and Three-Force MembersWhen 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.F3ABF1F2F6F5F4Two-Force MembersLet: 321FFFFA654FFFFBandABFAFBThese forces will maintain equilibrium if: BAFF(FA and FB must be collinear)ME 221 Lecture 23 10Two- and Three-Force MembersIf 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 MembersF3OF1F2F3F2F1ME 221 Lecture 23 11Note:• 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 221 Lecture 23 12Chapter 5 Equilibrium


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