Solving Multiple Couples in Structural Engineering Analysis

[stinlin]

I didn't know where to post this since these forums are missing the best field of engineering (Civil/Structural).

Anywho, I got to thinking about this situation - a simply supported beam (or indeterminate to the nth degree even), or even a cantilever, with multiple concentrated moments. How would one go about drawing a moment or curvature diagram for this? I drew up this hypothetical idea (see attached I guess).

You'd think on my third year of this stuff, I'd have a good idea on what to do with a situation like this, but I just seem to get very confused. I don't really know where a situation would come up like this in practice, but it's more the theory of the situation that I'm interested in.

For a concentrated moment (one), I know you can usually just say clockwise or counter-clockwise positive, but even then, drawing the moment diagram gets me. Can anyone give some insight on the best way to approach this situation?

I want to throw this in - this is NOT a homework problem, extra credit problem, etc. This is simply my own interest (and because my Structural Analysis professor is kind of mean and likes to demoralize students, so I hate asking him questions). :) Thanks!

 

[FredGarvin]

Assuming you stay within linear boundaries, simply solve three individual problems, i.e. the beam with one couple at three different locations, and superimpose the results to arrive at the final.

 

[ravenprp]

As a structural engineer, I can definitely understand your confusion and frustration with solving multiple couples in structural analysis. It can be a challenging concept to grasp, but with some practice and understanding of the theory, it becomes easier to handle.

Firstly, it is important to understand the basic principles of couples in structural analysis. A couple is a pair of equal and opposite forces acting on a body, but not along the same line of action. When we have multiple couples acting on a beam or structure, we need to consider the net effect of all these forces on the structure.

To solve for multiple couples in structural analysis, it is best to break down the problem into smaller, more manageable parts. For example, in your hypothetical situation, you could first consider the effects of each individual couple on the beam. This means drawing separate moment diagrams for each couple, taking into account their direction and magnitude.

Once you have the moment diagrams for each individual couple, you can then superimpose them to get the overall moment diagram for the beam. This means adding the moments at each point along the beam, taking into account the direction of the moments. This will give you a more accurate representation of the actual moment distribution in the beam.

It is also helpful to remember the sign convention for moments in structural analysis. Clockwise moments are considered positive, while counterclockwise moments are considered negative. This will help you correctly draw the moment diagram for the beam.

In terms of practical applications, situations like this can arise in real-life scenarios where a beam or structure is subjected to multiple external forces or loads. By understanding how to solve for multiple couples, you will be better equipped to analyze and design structures that can withstand these forces.

I hope this helps in your understanding of solving multiple couples in structural analysis. Remember, practice makes perfect, and don't hesitate to ask for help from your professors or colleagues in the field. Good luck!