What is the comparative strength (for equal deflection??) of a 2X4 wood
beam compared to an "I" beam constructed with three 2X4s? (two for
flanges and one for web).  Maybe the web should be 1X4 or 1X6 or 1X8
but 2X4s are easiest to buy here in Nicaragua.
If span matters use 14 feet
"Simple approximation" calculation is fine.
Thanks!

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Clarification of Question by jpsjps-ga on 03 Oct 2006 17:16 PDT

Subject: Re: Strength *ESTIMATE* of 2X4 Wood Beam vs I beam made from three 2X4s 
From: barneca-ga on 03 Oct 2006 06:19 PDT

Thank You cab - Your answer below is exactly what I wanted!
Please post that as an answer so you get paid the peanuts offer I made!

"the stress and deflection under the same load for (3)2x4's in an
i-beam vs. a single 2x4?"
"(3)2x4's properly nailed together are roughly 13-14 times as stiff as
a single 2x4, i.e. the i-beam deflects about 93% less than a single
2x4."

Thanks again,  John

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Clarification of Question by jpsjps-ga on 05 Oct 2006 10:32 PDT

cab - THANKS again!!
Is it simple to "guesstimate" how much the span can be increased for
the "I" beam compared to the single 2X4 for the same deflection (or
same bending stress if that is what matters)?
Two different types of loads:
1)  Identical Single load in center of beams.
2)  Distributed load that increases directly with span (Roof Rafters).

Ignore this additional question if it is not a simple quick
calculation.  I obviously don't know enough to even construct
meaningful questions.

I spent a couple of hours on Google but learned that this subject is
not simple enough for me to learn in a couple of hours.  I am a
retired EE but this looks tougher to learn than EE.

Please at least post an answer to the original question to claim the offer.
THANKS AGAIN!!!!
John

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Clarification of Question by jpsjps-ga on 07 Oct 2006 12:09 PDT

cal - THANKS!!

"first off, it looks like this is your first time asking a question on
google answers"
YEP

"i?m not a google researcher, just a commenter and member of the
peanut gallery. i can?t get paid for the answer, only researchers can
do that.
comments are free, but worth what you pay for them; you can?t really
have the same level of confidence in a comment as in an answer.
it?s hard to beat free."
YEP & NO - You obviously know this subject.

Hey - You gave me the answer I asked for.  I found those equations
while doing research and they did not sound right so I needed
verification from an expert.  Yes I know that the 2X4s have to be
connected so they will not "slip" and that has been done!

No further answers needed!!

THANKS AGAIN!!!

John

"comparative strength (for equal deflection??)" doesn't really make
sense, at least not to me.  you might get more action on your question
if you clarified what you would like compared.

the stress and deflection under the same load for (3)2x4's in an
i-beam vs. a single 2x4?

the stress and deflection under the same load for (3)2x4's in an
i-beam vs. (3)2x4's side by side?

the stress under a particular load for (3)2x4's in an i-beam vs. the
stress under a *much* smaller load, which causes the same deflection
in a single 2x4?

(3)2x4's properly nailed together are roughly 13-14 times as stiff as
a single 2x4, i.e. the i-beam deflects about 93% less than a single
2x4.

-cab

that wasn?t an answer, just a free comment.  if that answered your
question, the good news is i saved you $5, the bad news is some google
researcher?s kids are going to bed hungry tonight.  i wonder if the
good karma and the bad karma cancel each other out?  :)

for a given span and a given type of wood, a (3)2x4 i-beam can
theoretically carry 13-14 times the load to get the same deflection as
a single 2x4;  7-8 times the load to have the same maximum bending
stress;  but only about double the load to get the same shear stress. 
luckily, shear stress is only a concern for short spans, and wouldn?t
control for a 14 ft span.

keep in mind these increases assume a perfect connection between the
2x4?s.  depending on the actual load, species of wood, span of the
beam, etc.,  you might not be able to nail them frequently enough to
get the entire increase.  the nailing can?t be determined without this
additional info, so if you need it you could repost the question and
maybe feed a researcher?s kids after all.

if you don?t need that info, then glad to be of help.

-cab

hi john,

first off, it looks like this is your first time asking a question on
google answers, so i should have explained better before.  i?m not a
google researcher, just a commenter and member of the peanut gallery. 
i can?t get paid for the answer, only researchers can do that. 
comments are free, but worth what you pay for them; you can?t really
have the same level of confidence in a comment as in an answer.

on the other hand, it?s hard to beat free.

since i?ve already waded into this, i?ll finish it up for you.  if
we?re making guestimates, we can throw out complications like shear
(which hardly ever controls) and nailing (which i don?t have enough
information to consider).  leaving these issues aside, it?s not that
hard.

i?ll give you the equations, then the answers, and you can figure out
the steps in between if you want to.

I = moment of inertia = stiffness of shape for deflection
E = modulus of elasticity = stiffness of material for deflection
S = section modulus = resistance of shape to bending

P = point load
L = span of beam
w = distributed load

I-beam:   I=72.95in^4,   S=22.45in^3
2x4:   I=5.36in^4,   S=3.06in^3

Point load:
Deflection = PL^3/(48EI)
Bending stress = PL/(4S)

Distributed load:
Deflection = 5wL^4/(384EI)
Bending stress = wL^2/(8S)

E, P, w, and L are the same for all cases.  I and S vary.  so we can
just set deflections or bending stresses equal to each other, and we
can solve for how much longer the i-beam can be for the same
deflection or bending stress.

Point load:
Deflection: I-beam can be 2.39 times as long as 2x4 for same
deflection under same P.
Bending stress: I-beam can be 7.34 times as long as 2x4 for same bending stress.

Distributed load:
Deflection: I-beam can be 1.92 times as long as 2x4 for same
deflection under same w.
Bending stress: I-beam can be 2.71 times as long as 2x4 for same bending stress.

just remember nailing limitations haven?t been considered, and could
bring some of these numbers down quite a bit.

enjoy.

-cab

CAB,
I really don't understand anything you have posted, so perhaps I
shouldn't comment, but wouldn't it add to the strength if the 2x4s are
glued as well as being nailed (screwed?) together?  I recognize that
gluing may be beyond DIY capability.

Just a thought, Myoarin

good point myoarin, when i say "nailed", you should interpret that as
"nailed, screwed, glued, or some combination of those".  my point was
that to get them to act compositely with each other, you need to think
about their connection, not just the shape.

-cab

glad i could help.

-cab