Understanding How to Add Moments Together: Explained and Clarified

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In summary, when calculating bending moments of beams, you must add moments if they are in the same plane.
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deufo
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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
 
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bump? :redface:
 
  • #3
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.
 
  • #4
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?
 
  • #5
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.
 
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What is the concept of adding moments together?

Adding moments together is the process of combining two or more individual moments to determine the overall moment of a system. Moments are physical quantities that represent the tendency of an object to rotate around an axis.

Why is it important to add moments together?

Adding moments together is important because it allows scientists and engineers to analyze the rotational behavior of a system. By combining individual moments, we can determine the overall stability and strength of a structure and make informed decisions in design and construction.

What is the formula for adding moments together?

The formula for adding moments together is M = F * d, where M is the moment, F is the force applied, and d is the distance from the point of rotation to the line of action of the force. This formula is also known as the cross product formula.

Can moments be added together if they have different axes of rotation?

Yes, moments can be added together even if they have different axes of rotation. This is because moments are vector quantities and can be added using vector addition. The resulting moment will have a direction and magnitude that reflects the combined effect of the individual moments.

Is there a limit to the number of moments that can be added together?

No, there is no limit to the number of moments that can be added together. As long as the individual moments are defined and have a common reference point, they can be added together using the cross product formula. However, in real-world applications, there may be practical limitations based on the available resources and structural integrity.

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