Hello pizlou, I believe that I have a good understanding of your
problem. First, here is a very good place to find information for wood
beams:
http://www.awc.org/technical/spantables/tutorial.htm
You say your beam is pine and it looks like the numbers we need would be:
Fb (allowable bending stress) = 1105 psi
E (modulus of elasticity) = 1,400,00 psi
You will also notice that the deflection should be limited to L/240 or
in your case:
D = (25 x 12) / 240 = 1.25 in
We also need to know what I (moment of inertia) and S (section
modulus) are for your 6 x 16 beam.
I = bd^3/12 = (6 x 16^3)/12 = 2048 in^4
S = bd^2/6 = (6 x 16^2)/6 = 256 in^3
Keeping this as simple as possible the load on the beam is:
(Using a live load of 20 psf and a dead load of 16 psf)
w = 10 x 36 psf = 360 lb per ft
The beam formulas for this loading are:
M (maximum bending moment) = wl^2/8
D (deflection @ center of span) = 5wl^4/384 EI
l (beam span) = 25 ft
Solving for M:
M = 360 x 25^2 / 8 = 28,125 ft lb = 337,500 in lb
The section modulus of the required beam (S) = M/Fb = 337,500/1105
= 305 in^3
Now we must calculate the required I (moment of inertia):
Solving for I in the above formula for deflection we get:
I = 5wl^4/384 ED = (5 x 360 x 25^4 / 384 x 1,400,000 x 1.25) x 1728
NOTE: 1728 is a conversion factor to get the proper units for I
I = 1808 in^4
Here are the numbers we need to compare:
S (for your beam) = 256
S (required) = 305
I (for your beam) = 2048
I (required) = 1808
Your 6 x16 pine beam is probably adequate. It lacks a little in
allowable yield strength (Fb), but what we have used might not be the
actual value for your beam. If you look at the chart, you will see
that if your beam is a better grade with Fb = 1580 psi the required S
would then be:
S = M/Fb = 337,500/1580 = 213 in^3 which looks good (213 less than 256).
The fact that your beam is more than strong enough to satisfy the
deflection criteria is most important.
If you can get a more accurate value for the Fb of your actual beam,
we can possibly make you feel a little more safe.
Please ask for a clarification if there is anything you don't understand.
Redhoss |