# Analysing beam structure

1. Nov 13, 2013

### 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?

2. Nov 13, 2013

### SteamKing

Staff Emeritus
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.

3. Nov 13, 2013

### aerograce

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.

#### Attached Files:

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4. Nov 13, 2013

### SteamKing

Staff Emeritus
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.

5. Nov 13, 2013

### aerograce

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

6. Nov 13, 2013

### SteamKing

Staff Emeritus
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.