Are Moments Treated Differently than Forces in Beam Analysis?

[aerograce]

I am always wondering, when we are analysing beam structure where many externally applied moments are added on, why we can sum up all the externally applied moments and write equilibrium equations according to that. Because these moments are actually along different axes. Is it because in analysing process, we treat all moments as couples? If that is the case, then in real life, is our analysing method inaccurate?

 

[SteamKing]

Well, moments have qualities of a vector like forces do. When you say, '... sum up all the externally applied moments ...', you must pay attention to their point of application and their direction. You don't just add up their magnitudes.

 

[aerograce]

Well, moments have qualities of a vector like forces do. When you say, '... sum up all the externally applied moments ...', you must pay attention to their point of application and their direction. You don't just add up their magnitudes.

Its better to explain my point with one typical example in analysing a beam. You can view the attached file.

In the equation Mc(left)=0, it actually sums up the moments though they are along different axis.

 

[SteamKing]

I don't see your confusion. The reacting moment Ma and the applied couple at B are both acting about an axis coming out of the paper, even though they are applied at different points along the beam. Therefore, they can be combined by adding their magnitudes.

 

[aerograce]

I don't see your confusion. The reacting moment Ma and the applied couple at B are both acting about an axis coming out of the paper, even though they are applied at different points along the beam. Therefore, they can be combined by adding their magnitudes.

But their axes are actually not the same right? They are just parallel to each other. And also, why the moments applied won't affect the force equilibrium equations? Because if we don't assume moments as a couple, they will affect the net force on the system

 

[SteamKing]

I think the point you are missing about moments is that, unlike forces, they can translate without affecting the equilibrium of the beam. Moments, or couples, are known as 'free vectors' because of this property.

http://en.wikipedia.org/wiki/Couple_(mechanics)

This is a subtle, but important, characteristic which should be covered in any intro. mechanics or statics course.