Equilibrium of a Rigid Body 5 Engineering Mechanics: Statics in SI Units, 12e Copyright © 2010 Pearson Education South Asia Pte Ltd
EQUILIBRIUM IN THREE DIMENSIONS Copyright © 2010 Pearson Education South Asia Pte Ltd
5.5 Free-Body Diagrams Support Reactions As in the two-dimensional case: A force is developed by a support that restricts the translation of its attached member A couple moment is developed when rotation of the attached member is prevented
Copyright © 2010 Pearson Education South Asia Pte Ltd 5.5 Free-Body Diagrams
Copyright © 2010 Pearson Education South Asia Pte Ltd 5.5 Free-Body Diagrams
Copyright © 2010 Pearson Education South Asia Pte Ltd 5.5 Free-Body Diagrams
Copyright © 2010 Pearson Education South Asia Pte Ltd 5.5 Free-Body Diagrams
Copyright © 2010 Pearson Education South Asia Pte Ltd Example 5.14 In all cases, the x, y and z axes are established and the unknown reaction components are indicated in the positive sense. The weight of the objects is neglected.
Copyright © 2010 Pearson Education South Asia Pte Ltd 5.6 Equations of Equilibrium Vector Equations of Equilibrium For two conditions for equilibrium of a rigid body in vector form, ∑F = 0 ∑M O = 0
Copyright © 2010 Pearson Education South Asia Pte Ltd 5.6 Equations of Equilibrium Scalar Equations of Equilibrium ∑F = ∑F x i + ∑F y j + ∑F z k = 0 ∑M O = ∑M x i + ∑M y j + ∑M z k = 0 ∑ F x = 0∑M x = 0 ∑ F y = 0∑M y = 0 ∑ F z = 0∑M z = 0
Copyright © 2010 Pearson Education South Asia Pte Ltd Example 5.15 The homogenous plate has a mass of 100kg and is subjected to a force and couple moment along its edges. If it is supported in the horizontal plane by means of a roller at A, a ball-and-socket joint at B, and a cord at C, determine the components of reactions at the supports.
Example 5.16 Determine the components of reaction that the ball-and- socket joint at A, the smooth journal bearing at B, and the roller support at C exert on the rod assembly in the figure. Copyright © 2010 Pearson Education South Asia Pte Ltd
Example 5.18 Rod AB is subjected to the 200-N force. Determine the reactions at the ball-and-socket joint A and the tension in the cables BD and BE. Copyright © 2010 Pearson Education South Asia Pte Ltd
5.7 Constraints for a Rigid Body Redundant Constraints More support than needed for equilibrium Statically indeterminate: more unknown loadings than equations of equilibrium
Copyright © 2010 Pearson Education South Asia Pte Ltd 5.7 Constraints for a Rigid Body Improper Constraints Instability caused by the improper constraining by the supports When all reactive forces are concurrent at this point, the body is improperly constrained