I'm bulding a barn 50' x 120' the 120 section have an opening of 30'
for an 30' x 30' adition. Roof trusses sits on 2' on center. Reaction
on the trusses is 3300 lbs. Can you help me with sizing an I-beam for
this opening?

---

Request for Question Clarification by redhoss-ga on 14 Sep 2005 16:36 PDT

I can help you, but I need to know something first. The 3,300 lb.
number sounds a little high if it is per end. What is your live load
and dead load. Could the 3,300 lbs. be a total number, say 1,650 lbs.
per end. Are you in a heavy snow area. You would have to be in a 60
PSF area to get 3,300 lbs. per side. Once we get past this, the rest
is easy.

---

Clarification of Question by hankconti-ga on 15 Sep 2005 04:32 PDT

Loading (psf)
TCLL 30.0
TCDL 15.0
BCLL  0.0
BCDL 10.0

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
to
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