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Q: SIZING AN I BEAM TO SPAN 14 FEET ( Answered 5 out of 5 stars,   0 Comments )
Category: Science > Physics
Asked by: goose1027-ga
List Price: $50.00
Posted: 17 May 2006 12:45 PDT
Expires: 16 Jun 2006 12:45 PDT
Question ID: 729814
I am making an addition to my kitchen which will result in a 14 foot
load bear- ing wall being removed.  This wall supports a second story.
 Using info from another website I have calculated the weight on this
beam to be 1200 pounds per linear foot.  What size I beam do I need to
support this load?  I would like to limit the depth to 12 inches or
Thank you,
J. R.
Answered By: redhoss-ga on 18 May 2006 05:49 PDT
Rated:5 out of 5 stars
Hello J. R., you have done the hardest part of the calculations by
providing the load applied to the beam. I can help you with the rest.

The beam formulas for this loading are:

M (maximum bending moment) = wl^2/8
D (deflection @ center of span) = 5wl^4/384 EI
NOTE: Maximum deflection is limited to D = l/360 = 14 x 12 / 360 = 0.46 in
w (load per foot) = 1200 lb per ft
l (beam span) = 14 ft
Where E is a constant for steel = 30,000,000 psi
And I is the moment of inertia

Solving for M:

M = 1200 x 14^2 / 8 = 29,400 ft lb = 352,800 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 = 352,800/19,800 
                                             = 17.8 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 1200 x 14^4 / 384 x 30,000,000 x 0.46) x 1728
NOTE: 1728 is a conversion factor to get the proper units for I

I =  75.2 in^4

Now we can look for a beam with these minimum properties and a maximum
depth of 12 inches.

A good choice would be a 10.25 inch deep Wide Flange beam weighing 19 #
per ft (W10x19)
S = 18.8 in^3
I = 96.3 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 kitchen project, Redhoss

Request for Answer Clarification by goose1027-ga on 19 May 2006 16:32 PDT
Thanks for your prompt reply Redhoss.  To satisfy my curiosity, what
is the flange width, flange thickness, and web thickness of the W10x19

Thank you,
J. R.

Clarification of Answer by redhoss-ga on 20 May 2006 06:21 PDT
Thanks for the tip. Here is what you need:

Flange width: 4.020"
Flange thickness: 0.394"
Web thickness: 0.25"

If you have another beam you would rather use, I will be glad to check
it out for you.

Request for Answer Clarification by goose1027-ga on 25 May 2006 18:05 PDT
Thanks for the clarification, Redhoss.  I do have another question.  I
had planned to support this beam on each end with a 6x6 wooden post. 
Since the beam is only 4 inches wide, I thought of using two metal
posts.  What size metal posts would I need to support this load?  I
can use either round or square.  Since this isn't a clarification of
the original question, do I need to go through the process and ask as
a new question?

J. R.

Clarification of Answer by redhoss-ga on 26 May 2006 06:05 PDT
The reaction at each end of the beam is:

14 x 1200/2 = 8400#

The bearing area on the 6x6 is:

A = 4 x 6 = 24 sq in

So, the pressure in the wood would be:

p = 8400/24 = 350 psi (this is much less than allowable compressive strength)

I see no problem in using the 6x6 wood columns that you planned to
use. It will certainly make nailing much easier. However, if you want
to use steel, how about a 4 inch square light gauge tube. If you can
get 14 ga., it would work just fine.
goose1027-ga rated this answer:5 out of 5 stars and gave an additional tip of: $10.00
Very prompt and professional reply.  I requested the same info from
another website 2 months ago and still haven't heard from them.
J. R.

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