The basic rule of thumb, going back to the original Matrix system, is
that the center-to-center hole spacing is equal to whatever the square
thickness of the beam. Hole positions start at half the thickness from
the end of a beam. The original stock was 2"x 2" -one half 2"x 4"
dimensional lumber. Where things started getting wonky was when
American lumber companies started screwing around with base dimensions
for lumber (who notices what goes on behind the drywall...) leading
the 2x4 of the 1950s (when Ken Isaacs invented the system) shrinking
today to 1.5"x 3.5". Further complicating matters, when Matrix became
Box Beam in the 70s, the desire to use it with increasingly strong
materials and a poor availability of aluminum tubing led people to
look for what was off-the-shelf; steel tubing made by Telestrut (now
marketed as part of the Unistrut line - http://www.unistrut.com/about/index.php?P=po_ts)
as used in municipal road signs. Telestrut is 1 7/8" inches square
with 1 7/8" hole spacing. But it includes a nesting inner beam of 1
5/8" square with 1 7/8" hole spacing.
With Grid Beam today the base size is 1.5" square using wood or
aluminum (for some reason, steel in this dimension has never been easy
to find) with all other dimensions based on half-inch multiples from
1" and up (topping off at 4") to allow holes to line-up at some
interval. Larger dimension stock (2" and up) may double-up the hole
spacing, again sticking to the half-inch multiples. There are no fixed
standards for holes and bolts but the usual base hole sizes are 5/16"
using 1/4" bolts for wood 1 1/2" square stock and up, 21/64" and
11/32" holes for 5/16" bolts and 7/16" for 3/8" bolts for alloy from
1" to 2" stock.
A basic kit-of-parts uses beam lengths in 3" to 9 " and then whole
foot multiples from 1' to 8'. Panel sizes all derive from 4x8 sheet
stock in 1/2' multiples to 4' square.
Eric Hunting