Hello bad67deuce, you did a very good job describing your problem.
Here is the info we need to do the calculations:
Live Load = 40 psf
Deflection limitation = L/360 = (25 x 12)/360 = 0.83 inch
2 x 12 weight = 4.1 # per ft
3/4 plywood = 2.13 # per sq ft
3/4 hardwood flooring = 3 3 per sq ft
Dead load calculation:
Quantity of 2 x 12 = (25 x 12)/16 (minus 1) = 18
Tributary area (area which beam supports) = 13/2 + 19/2= 16 ft x 25 ft
Weight of 2 x 12 = (18 x 4.1 x 16)/25 = 47.2 #/ft
Weight of flooring & plywood = (2.13 + 3) x 16 = 82.1 # per ft
Total dead load = 47.2 + 82.1 = 129.3 # per ft
Live load = 40 psf x 16 = 640 # per ft
Total load (w) = 129.3 + 640 = 769.3 # 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
Where E is a constant for steel + 30,000,000 psi
And I is the moment of inertia
Solving for M:
M = 769.3 x 25^2 / 8 = 60,102 ft lb = 721,224 in lb
The allowable bending stress for structural steel (s) = 0.55 x 36,000 psi
= 19,800 psi
The section modulus of the required beam (S) = M/s = 721,224/19,800
= 36.42 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 769.3 x 25^4 / 384 x 30,000,000 x 0.83) x 1728
NOTE: 1728 is a conversion factor to get the proper units for I
I = 272 in^4
Now we can look for a beam with these minimum properties.
A good choice would be a 16 inch deep Wide Flange beam weighing 26 #
per ft (W16x26)
S = 38.3 in^3
I = 300 in^4
Of course, you can use a heavier beam if there is one more available.
Please ask for a clarification if there is anything you don't
understand and I will try to explain.
Good luck with your project, Redhoss
Clarification of Answer by
03 Apr 2006 16:37 PDT
There are many beam that would satisfy the I and S minimum values we
calculated. I selected what would be the best choice for price. When
it comes to structural members pounds per foot determines how many
dollars you will spend. The W16x26 which I chose has these dimensions:
Depth = 15.65"
Flange width = 5.5"
Flange thickness = 0.345"
Web thickness = 0.250"
If you drop down to a 14 inch depth beam, you would need a W14x30,
going on down to a 12 inch requires a W12x36, 10 inch requires a
W10x54, and so on. You can see that after 12 inches the weight goes up
drastically. So, if you want to spend a few more dollars to gain
headroom the W12x36 might be the best bet. And yes, I do think that a
steel beam is the best material choice.