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Backcalculating Loads

Backcalculating Loads

Backcalculating Loads

(OP)
Assuming I have a stiff beam, supported on multiple supports and I know the reactions on these supports. (the support are shear walls and their reactions are wall shears)
Is there a smart way to backcalculate what distributed load can cause the said reactions.

I am trying to set up a spreadsheet to do diaphragm design based on wall shears calculated by an analysis program.

RE: Backcalculating Loads

If I understand the question right, there is not a unique solution. For example, with a simply-supported span, any symmetrical load distribution can produce the same end reactionss.

RE: Backcalculating Loads

Trial and error! I have to back into loadings fairly often. It is, at best, a guessing game; however, you can be reasonably accurate. As for doing a spreadsheet to compute....each application is different.

RE: Backcalculating Loads

The deep beam is the slab with horizontal loading, the reactions being the shear in the shearwalls?

There are tables/diagrams with coefficients for various numbers of spans, but they are for equal spans and, I think, pinned at the end walls. If this is your case, "The Steel Designer's Manual" has them. It's on Scribd, but it looks like you have now to become a member there.

Michael.
Timing has a lot to do with the outcome of a rain dance.

RE: Backcalculating Loads

(OP)
Yes, it's a slab with horizontal loading and reactions are wall shears. I think my loading could nd up being trapezoidal and like JStephen says, there may not be a unique solution.

RE: Backcalculating Loads

Without thinking it over too deeply, You might be able to set up something by loading each span separately with a uniform load and combining with simultaneous equations, much like sidesway in moment distribution solutions. You could look at the differences of UDL after combining and make a good estimate of a trapezoidal diagram.

It's an interesting problem.

Michael.
Timing has a lot to do with the outcome of a rain dance.

RE: Backcalculating Loads

For a uniform load over all of the spans, it is easy. The loading is equal to the Σreaction / Σspan length. The slope (a straight line) on the diaphragm's shear diagram is equal to the loading. I don't think you can determine the loading when all you know is the span and the reactions. There would be an infinite number of solutions. When the loading is not uniform, I have estimated (hand calculated) the lateral loads, drawn the shear diagram, and compared the results with the analysis software's reactions.

RE: Backcalculating Loads

My last sentance is not entirely correct. The software analysis results used depends on the lateral system. For instance, with moment frames, I have compared the hand calculations for diaphragm shear with the change in column shear at each frame line of the story in question. (The column shear results can also be used in the collector calculations)

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