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# Steel design - Gerber system

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• To: seaint(--nospam--at)seaint.org
• Subject: Steel design - Gerber system
• From: Kevin Below <kevinbelow(--nospam--at)videotron.ca>
• Date: Thu, 09 Feb 2006 22:26:57 -0500

Title: Message
Using the Gerber system (suspended spans between cantilevered beams) in a steel roof system makes for an economical design.

But it sure is time-consuming to design, unless you just guess at economical cantilever lengths.  So I wrote a spreadsheet to design all the beams along a grid line, then total up the total weight of steel.  Adjusting (playing with) the cantilever lengths allows optimisation pretty easily.  But it took me several hours to put together the sheet (like a whole weekend) for one particular grid line - choosing the beams to satisfy moment at the unbraced length between joists, shear, and inertia.  I added a chart to plot the moment and shear diagrams, to identify the negative moment zones under pattern live load cases (to be sure to brace the bottom flange where required), so it's pretty sexy.

Small changes in the cantilever lengths reduced my initial guessed design by 4 or 5 % total steel weight.

The layout was something like :

o-----------------------o------------o----------------------------------o-------------o--------------------------------o---------------------o
^                          ^                     ^                          ^                    ^                            ^
o = node
^ = support

Another 3 hours for a second grid line.

o----------o--------------------------------o----------o-------------------------------o--------------o---------------------------o------------o
^                  ^                   ^                      ^                      ^                        ^                ^                   ^

2 hours for the third.  (I am getting better at it).  I tried 3 different arrangements on one grid line, to see if there were any major differences in optimal weight.  There weren't.  All three were within 1 or 2 percent once optimised.

But we need a tool that addresses Gerber system in a more user-friendly fashion.  Software like Etabs, Staad, VisualDesign, etc., can be used, but it takes a lot of clicks to adjust the cantilever by a few cm and get to the total steel weight each time.

Anyone know of any tools to do this for a general case, say 10 spans, where you can place a cantilever in the spans of your choosing ?

o-----------------o----o----o----------------------o----o----o------------------------------o----o----o--------------------------------o----o----o--------------------------o----o----o--------- etc.
^                       ^                                  ^                                          ^                                            ^                                      ^

If you could specify which of the above nodes are rigid joints and which are pinned, you could cover any arrangement of cantilevers and suspended spans.
I can't see a way to do this with Excel, without getting into stiffness matrices, which I haven't used since uni many years ago.

Any ideas ?  I would be willing to contribute my spreadsheet if anyone is interested in developing the tool with me.

Kevin Below

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