Statics of Non-Concurrent Force Systems

Definition of a Load  |  Free-Body Diagram of a Rigid Body


Supporting a Rigid Body:A rigid body is usually supported at one or more locations. These supports help keep the body in a stationary position. At a support location, the body exerts a load (action) on to the support and the support exerts an equal and opposite load (reaction) on the body.

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In order to identify the type of reaction exerted by the support, we consider the movement that the support helps to restrain. For example, if a support prevents the translation of the body along a particular direction, then there is a reaction force in the same direction at the point of support. Similarly, if the support prevents the rotation of the body, then the reaction load is in the form of a moment. As described below, it is also possible for a support to restrain the body in more than one direction.

As a general rule, we must remeber the following fact: Movement Prevented = Reaction Created

In the following discussion, a rigid body is represented by a trapezoid. The coordinate system shown helps to identify the directions of designated reaction forces.

 


Support Reactions in Two-Dimensional Force Systems: Some examples of typical supports and the reactions they exert on the body are shown below.

Roller: Body is free to move in the direction parallel to the support line, and is free to rotate, but it is restrained against translation in the perpendicular or normal direction. Hence, the reaction force has a known direction and an unknown magnitude, Rn.

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A roller support may also be represented in alternative forms as shown below.

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Pin or Hinge: Body is free to rotate about the hinge point, but is restrained against translation in any arbitrary direction. Therefore, the direction of the reaction force is not known. As a result, it is represented in terms of its two rectangular components. Hence, the reaction force is represented by two rectangular components of assumed direction and unknown magnitude, Rx and Ry.

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Weightless Link: Sometimes a body is connected to a rigid support via a weightless link. Since the force in the link is always along its axis, the direction of the reaction force is known, but its magnitude is not. Hence, the reaction force has a known direction and an unknown magnitude, R.

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Fixed or Clamped: Body is restrained against translation in all directions as well as rotation about the support point. As a result, there is a reaction force (represented in terms of its rectangular components of assumed direction and unknown magnitude Rx and Ry), and a reaction moment of assumed direction and unknown magnitude, M.

Notice that the last two representations of reaction forces are equivalent because the resultant reaction force can be expressed in terms of either Rx and Ry or Rx' and Ry' components.


 
 
 

Definition of a Load  |  Free-Body Diagram of a Rigid Body