Presentation on theme: "EQUILIBRIUM OF RIGID BODIES"— Presentation transcript:
1 EQUILIBRIUM OF RIGID BODIES ME13A: CHAPTER FOUREQUILIBRIUM OF RIGID BODIES
2 4.1 INTRODUCTIONEquilibrium of a rigid body requires both a balance of forces, to prevent the body from translating with accelerated motion, and a balance of moments, to prevent the body from rotating.For equilibrium: F = 0 andMo = (r x F) = 0In three dimensions: Fx = 0 Fy = Fz = 0Mx = 0 My = Mz = 0
3 4.2 SOLUTION OF REAL PROBLEMS IN TWO DIMENSIONS Step 1: Examine the space diagram and select the significant body - the free body diagram. Detach this body from the space diagram and sketch its contoursStep 2: Identify and indicate all external forces acting on the body. The external forces consist of the externally applied forces, the weight and reactions of the body at the point of contact with other external bodies.Step 3: All the important dimensions must be included in the free body diagram.
6 Support ReactionsIf a support prevents the translation of a body in a given direction, then a force is developed on the body in that direction.Likewise, if rotation is prevented, a couple moment is exerted on the body.
7 4. 4 STATICALLY DETERMINATE AND INDETERMINATE REACTIONS 4.4 STATICALLY DETERMINATE AND INDETERMINATE REACTIONS. TYPES OF CONSTRAINTS IN TRUSSES
12 Difference Between Improper and Partial Constraints In improper constrained case, one equation of equilibrium has been discarded but in the partial case, there are only two unknowns so the two equations were used to determine them.
14 ExampleA truck mounted crane is used to lift a 3 kN compressor. The weights of the boom AB and of the truck are as shown, and the angle the boom forms with the horizontal is = 40o. Determine the reaction at each of the two (a) rear wheels (b) front wheels D
16 4.5 TWO AND THREE-FORCE MEMBERS The solution of some equilibrium problems are simplified if one is able to recognise members that are subjected to only two or three forces.4.5.1 Two-Force Members: When a member is subject to no couple moments and forces are applied at only two points on a member, the member is called a two-force member.
17 Two-Force MembersConsider a two-force member below in (a). The forces in the two points are first resolved to get their resultants, FA and FB. For translational or force equilibrium:
18 Two-Force Members Contd. ( F = 0) to be maintained, FA must be of equal magnitude and opposite direction to FB.For rotational or moment equilibrium:( Mo = 0) to be satisfied, FA must be collinear with FB.See other two force members in (c) below.
23 4.6 EQUILIBRIUM IN THREE DIMENSIONS 4.6.1 Reactions at Supports: See Fig of text book for possible supports and connections for a three dimensional structure.4.6.2 Equilbrium of a Rigid Body in Three DimensionsSix scalar equations are useable (see section 4.1)
24 Equilbrium of a Rigid Body in Three Dimensions Contd. Problems will better be solved if the vector form of the equilbrium equations is used i.e.F = Mo = (r x F) = 0Express the forces, F and position vectors, r in terms of scalar components and unit vectors. Compute all vector products either by direct calculation or by means of determinants.