> I have to admit that I have done this a time or two in the past, for
> "complex" geometries, only to find that simple hand methods are about as
> accurate--AS LONG AS you can provide sufficient boundary elements. If you
> have a weird situation where you don't have nice, rectangular tributary
> areas, you might have to think about it.
But this is the same thing. The issue you describe is not the analysis of
the flexible diaphragm, but if you have a diaphragm at all. If you have a
highly irregular shape the layout and detailing of the boundaries is where
the engineering comes in, not the method of analysis. Diaphhragm boundaries
do not have to be at the extreme edges of the roof shape. If you have
irregular flexible shapes, define your diaphragm where you can develop
proper boundaries and drag the forces from the irregular attachments back
into the designated diaphragm. Now the tricky irregular diaphragms have been
reduced to imposed loads, not resisting elements.
> The converse of your argument is then "why use some gross simplifying
> assumptions that might leave you out of the ballpark, when it's so easy to
> throw together a computer model to handle a situation you're not really
If the system is so complex that you cannot model the behavior properly,
either actual or envelope, then how can you be sure about the computer
model? Computer modeling should be a tool for analysis, not a means of
analyzing something we do not understand. A 6 bay frame is a tedious hand
analysis, but it is still frame behavior. Computer results must be viewed
from an overall perspective with a critical eye for results that do not fit
the expected behavior. If you simply model a jumble of incoherent elements
without a planned system and behavior, the results are pretty meaningless
unless you proceed to detail all the same pinned / fixed / continuous /
discontinuous and element assumptions you built into the computer model into
the actual structure.
The methods of analysis we use are not gross simplifications, just
simplifications. You still need to provide a detailed structure where the
simplifications are accounted for and conservative. If the structure or
element does not fit one of our usual tools of analysis, use an envelope
approach to capture upper and lower bounds for design. If the system is too
indeterminate, detail some of the indeterminacy out of the system, and
simplify the structure to predictable modes of behavior.
Even finite element has specific rules and assumptions of behavior built
into the underlying theories upon which the software code was written.
Improper modeling will produce equally erroneous results for rigid elements.
Most computer FEA programs are still just matrix stiffness methods. General
FEA is highly dependent on the placement and density of the nodal pattern
and the material properties assumed for the various elements. Concrete is
not a linear elastic material, but most FEA analysis assumes classical
linear elastic behavior, only on an elemental basis. Is the mesh dense
enough for the results to have real meaning? The model does not
redistribute forces automatically to account for changes in flexibility due
to cracking or anisotropic behavior. FEA is intended to be an iterative
process, with the mesh and element structure modified in response to the
results of each iteration.
So just because you modeled something in the computer does not make it more
accurate. And whether you model something by hand or in the computer you
are still making simplifying assumptions. Whether the time to model
something properly in the computer is worth the savings is up to you.
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