Hello hankconti, sorry it took so long to get back with you. We will
use your truss reaction of 3,300 lbs. First we will calculate the
maximum bending moment:
Using the formula for a simple beam-uniformly distributed load from
the AISC (American Institute of Steel Construction):
M = (w x L^2)/8
Where "w" in your case is the total load on the beam divided by the
length or w = 3,300 lb x 14 (trusses on beam)/30 ft = 1540 lb/ft
M = (1540 x 30^2)/8 = 173,250 ft-lb
Section modulus = M / allowable stress
For a standard structural beam (yield stress = 36 ksi) the allowable
stress is usually taken as 0.6 x 36 ksi of 22,000 psi
Section modulus = 173,250/22,000 = 7.85 in.^3
This was an interesting exercise, but in your case the beam design is
controlled by deflection. The amount of deflection should be limited
D = L/360 or (30 ft x 12 in/ft)/360 = 1 in.
The formula for maximum deflection is:
D = 5wL^4/384 EI
Where E (Modulus of Elasticity) is a constant for steel = 30,000,000 psi
and I is the "Moment of Inertia" required.
Solving the above equation for I we get:
I = 5wL^4/384 ED
I = ((5 x 1540 x 30^4)/(384 x 30,000,000 x 1)) x 1728 in^3/Ft^3
Note: the 1728 factor is required to get the units correct
I = 935.55 in^4
In a wide flange beam a good choice would be a W21x49 with I = 971 in^4.
This is a beam that is 21 inches deep and weighs 49 lb. per ft.
I hope you have been able to follow this and I will be glad to answer
any questions you might have. Please ask for a clarification if you
need additional help.
Good luck with your project, Redhoss