In a previous post Bob Morrison says...
BTW, I will post the "trick" part of the question later today.



Okay gang here's the question I posed the other day:

Now for a really interesting problem, let's say you want to take out a
post and increase the span of the 3-2x12 from 13 feet to 18 feet, but
you must leave the 3-2x12 in place. "Flitch" beams are allowed. Do you
compute combined section properties of wood and steel or do you simply
let the steel carry all the load and the wood becomes "filler"? This
problem has a trick in it that I will not divulge.


The "trick" in the question is that nearly all wood beams are split over
posts making them simple spans. If you want to move the post to
increase the span then you must take in account that there is no moment
transfer at the existing post location. The easiest way to do this is
to ignore the contribution from the wood for section modulus and moment
of inertia UNLESS you want to get into a complex shear transfer analysis
for those parts of the beam located away from the existing support. In
most residential projects this is simply not feasible (and I doubt in
most commercial jobs either).

So, the short answer is to design the "flitch" beam in such a way that
the steel carries all the load for bending and deflection and the wood
is simply "filler". It is a different matter when one gets to the
supports. The wood may be used as long as allowable shear and bearing
stresses are not exceeded.

Here's another way of looking at it: If the wood has an E of 1.8x10^6
and you do a section transform to steel for your "composite" beam, then
a 6x (5-1/2" wide) will have a transformed width of 0.34". In other
words your 6x suddenly becomes a very small part of the beam and can
safely be ignored.



--
Bob Morrison, PE, SE
R L Morrison Engineering Co
Structural & Civil Engineering
Poulsbo WA