6161103 5.5 equilibrium in three dimensions (fbd)

5.5 Equilibrium in Three Dimensions (FBD)


� Consider types of reaction that can occur at the supports

Support Reactions

� Important to recognize the symbols used to � Important to recognize the symbols used to represent each of these supports and to clearly understand how the forces and couple moments are developed by each support

� As in 2D, a force that is developed by a support that restricts the translation of the attached member



Support Reactions� A couple moment is developed when rotation

of the attached member is preventedExample

The ball and socket joint prevents any � The ball and socket joint prevents any translation of connecting member; therefore, a force must act on the member at the point of connection

� This force have unknown magnitude Fx, Fyand Fz

� Magnitude of the force is given by

222zyx FFFF ++=



Support Reactions

� The force’s orientation is defined by the coordinate angles α, β and γ

Since connecting member is allow to rotate � Since connecting member is allow to rotate freely about any axis, no couple moment is resisted by a ball and socket joint

� Single bearing supports, single pin and single hinge are shown to support both force and couple moment components



Support Reactions

� However, if these supports are used with other bearings, pins or hinges to hold a rigid body in equilibrium and the supports are body in equilibrium and the supports are properly aligned when connected to the body, the force reactions at these supports alone may be adequate for supporting the body

� Couple moments become redundant and not shown on the FBD



� Ball and socket joint provides a connection for the housing of an earth housing of an earth grader to its frame

� Journal bearing supports the end of the shaft



� Thrust bearing is used to support the drive shaft on the machinemachine

� Pin is used to support the end of the strut used on a tractor



Example 5.14

Several examples of objects along with their

associated free-body diagrams are shown. In

all cases, the x, y and z axes are established 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.



Solution

6161103 5.5 equilibrium in three dimensions (fbd)

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