Understanding How to Add Moments Together: Explained and Clarified

[deufo]

Hi people,

I'm a bit confused as to when we can and cannot add 2 moments together. From what I understand, we CAN add them together if they are both about the same origin but CANNOT if they are about different origins.

But when drawing and calculating bending moment diagrams, you have to find the bending moment at each point/section of the structure but doing so seems to require you to add external moments and internal moments together even though they do not rotate about the same point.

Could someone please clarify this for me?

Thanks

 

[tiny-tim]

bump?

 

[Bob S]

A torque is the vector cross product of a lever arm and a force. If the force had a component parallel to the lever arm, that part would not be a torque. So the vector cross product is the right equation. Thus said, having two moments about the same origin is insufficient. They must be on the same axis (defined by the vector cross product).

If you are calculating the torque about a roof overhang, a weight at the end of the overhang puts twice as much torque at the roof support as it does half way out. Thus a 10 Newton weight at the end of a 10 meter overhang produces 100 Newton-meters of torque at the roof support, but only 5 N-m half way out. Another 10 Newton weight half way out produces an additional 5 N-m at the roof support, but none half way out. So here we have 15 N-m at the roof support, and only 5 N-m half way out.

 

[Mapes]

Hi deufo, welcome to PF. If an external moment is specified to be applied to the structure (e.g., 5 N-m at a point), it is added to the bending moment and applies to the whole structure. Note the difference between this scenario and that of an internal force that acts via a lever arm, producing a different moment in different parts of the structure. Does this answer your question?

 

[nasar]

Hi..
To clarify your doubt
1.Understand while finding Bending moment on beams at different locations,you are actually finding out bending moment at that point because of remote load.
You should add moments on beam if it is already experiencing a moment component throughout.
Ex:
Bending moment because of remote load =P*L
Uniform bending moment on beam =M
Total moment =M+/-PL
Where M is uniform bending moment on beam
2.You can add moments if they are in the same plane only.