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Re: Rigid frame deflections (again)

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Monte Griffiths asks:
> It seems we have hit upon the age old question when trying to size the lighest
> frame for a given load. Make the columns deeper and/or heavier, or upsize the
> beam....? If the beam span is short then it has a large effect on the frame
> stiffness, if the beam span is long, relative to the columns; the columns
> provide more of the frame stiffness. I just play with the structural analysis
> program for a given condition and usually converge on the best solution
> quickly. I would imagine there is an optimization method to do this, anyone
> know of one? A computer isn't always handy. Thanks in advance.

Very often, drift controls the frame selection.  My comments below 
speak to drift optimization (not strength optimization).

 In the optimum frame, the amount of drift that occurs per unit 
volume is equal for all of the elements of the frame.  If you 
calculate the amount of drift that occurs due to column deformation 
(shear and flexural), beam deformation (shear and flexural), and 
panel zone deformation (shear and flexural) and then divide each of 
these by the volume of each of these elements you will find out how 
close you are to the optimum solution.

Usually this type of work is done with a computer (to reduce the 
calculation time).  However, if you want to do a quick frame 
optimization by hand (perhaps even ignoring panel zone deformations, 
which can be significant), just keep the column and beam 
contributions to drift separate and divide these numbers by the 
volume (or weight) of the column and beam, respectively.  You should 
be able to quickly converge on a similar deflection per unit volume 
for the frame members.  Optimization curves are quite flat near the 
"best" answer and typical steel sections are selected from tables, so 
just try to get CLOSE to the same drift per unit volume.

-Mike Valley

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Michael Valley                                   E-mail: mtv(--nospam--at)skilling.com
Skilling Ward Magnusson Barkshire Inc.                  Tel:(206)292-1200
1301 Fifth Ave, #3200,  Seattle  WA 98101-2699          Fax:        -1201