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Now I have seen many times both in my physics book and other books when drawing a free body diagram the moment is not included but the forces are. For example in 2d when a beam is fixed to a wall there should be a moment at the point where the beam is fixed to the wall if we draw a free body diagram, right? Same things with hinges.

In a book im reading "engineering mechanics Statics and dynamics" by Hibbeler it says

"The couple moments are generally not applied if the body is supported elsewhere."

I'm a bit rusty but it says couple moment and that can be replaced by to opposite direction forces so is the moment replaced by the forces when drawing a free body diagram?

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    $\begingroup$ Page 237 - It should be noted that the single bearing supports in items (5) and (7). the single pin (8), and the single hinge (9) are shown to resist both force and couple-moment components. If, however, these supports are used in conjunction with other bearings, pins, or hinges to hold a rigid body in equilibrium and the supports are properly aligned when connected to the body, then the force reactions at these supports alone are adequate for supporting the body. $\endgroup$
    – Farcher
    Commented Jun 15 at 10:21
  • $\begingroup$ Page 237 cont'd - In other words, the couple moments become redundant and are not shown on the free-body diagram. The reason for this should become clear after studying the examples which follow. $\endgroup$
    – Farcher
    Commented Jun 15 at 10:21
  • $\begingroup$ @Farcher when do the couple moments become redundant? I don't understand even after seeing the examples. $\endgroup$
    – per persson
    Commented Jun 15 at 19:27
  • $\begingroup$ I think that what the author is trying to tell you is that if you can show all the forces on the diagram there is no need to show anything else. $\endgroup$
    – Farcher
    Commented Jun 15 at 21:28

2 Answers 2

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If a connection can sustain a moment—that is, if it can prevent conceivable rotation—then the moment should be drawn in the associated free-body diagram.

A fixed connection of a cantilever beam to a wall prevents rotation; thus, moments should appear in the free-body diagram for all planes being considered (e.g., in the x–y plane, a moment should appear around z):

Idealized pin supports, rollers, and hinges allow rotation and thus cannot sustain a moment:

enter image description here

I believe Hibbeler's quote is in the context of bearings. A bearing generally prevents rotation in two planes, and so moments are appropriate in the free-body diagram:

However, if the rod is fixed somewhere else to not undergo these rotations, then no moment can arise at the bearing (for a rigid rod), and so these moments can be left off—but only if it's assured that they can't arise because of constraints elsewhere. An idealized example would be if the rod passes through one or more additional bearings somewhere else.

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  • $\begingroup$ So the last part I have a bit difficulty understanding it. Consider a door that is fixed to the wall by two hinges. Suppose the door is open and we draw a free body diagram of it then there should be moments at the hinges in FBD right? I $\endgroup$
    – per persson
    Commented Jun 16 at 19:17
  • $\begingroup$ Here I have a picture of a door that in the FBD there are no moments at the hinges physicsforums.com/threads/… The picture is in the end I can't upload it here. What constraints are there which elimnates the moments at the hinges in the FBD. $\endgroup$
    – per persson
    Commented Jun 16 at 19:20
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    $\begingroup$ The forces at Hinge O already prevent rotation around the x and z axes at Hinge A—and vice versa—so neither hinge needs to apply a moment around these axes for the door to be fixed in place. Put another way, you could replace the hinges with pin connections (which can't apply a moment) and nothing would change. $\endgroup$
    – Chemomechanics
    Commented Jun 16 at 20:37
  • $\begingroup$ Ah, so the other hinge is the constraint that prevent rotation. But it's pretty difficult to tell when thats the case when drawing fbd. $\endgroup$
    – per persson
    Commented Jun 16 at 21:37
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The moment is not always included in a free-body diagram because its presence depends on the type of support or connection involved. If a support restricts rotation (such as a fixed support), then a reaction moment must be included to account for this constraint. However, for supports that allow free rotation (like pins or rollers), the reaction moment is not present, making it unnecessary to include in the diagram.

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