Beam: W caculation for reinforcement of joists with W6 Question
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Posted by: smegal

02/07/2006, 21:51:17

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I want to reinforce 2 x 10 joists with a W6 I-beam. I am trying to find the correct calculation for a 10 ft i-beam length under the joists where the uniform load is 8000#. I am restricted to W^ because of surrounding structures.

Ituitively it does not seem that the I-beam would have to support all of W. Please check the drawing which shows a ledger board support on one end and the foundation on the other end.

Thank you in advance for any help you can provide.


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Re: Beam: W caculation for reinforcement of joists with W6
Re: Beam: W caculation for reinforcement of joists with W6 -- smegal Post Reply Top of thread Forum
Posted by: swearingen

02/08/2006, 13:15:39

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There are a few other pieces of information needed to answer your question definitively, but I'll work with what you've given so far.

Some assumptions:

1. The 8000# is distributed evenly over the joists.
2. The joists are 10' long from ledger to foundation.
3. The ledger is continuously supported and has the same deflection characteristics as the other end.

The key here is the relative stiffness of the joists versus the W6. I would calculate the stiffness of the joists and the W6 as a function of distributed load per inch of deflection. I would then ratio the total load using this stiffness comparison. For example, if you put 100 lb/ft on the W6 and you calculate a deflection of 0.32", then the stiffness is 312.5 lb/ft /in. If you're joists come in at 75 lb/ft /in, that means that approximately (312.5 / (312.5 + 75)) = 81% of the load will go to the W6.

To understand how this works, think about it in the extreme: if the joists were rubber bands, the W6 would take practically all of the load. If the joists were W36 steel beams, the W6 would see next to nothing.

Now, if my assumption that the ledger is not fully supported, and is a wooden beam parallel to the W6, then things get worse for the W6.

Note that if properly supported, a W6x16 or larger will hold 8000# as a POINT LOAD in the center of a 10' span, which is way worse than what you have. You may be OK as is with the assumptions I've made.








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Re: Beam: W caculation for reinforcement of joists with W6
Re: Re: Beam: W caculation for reinforcement of joists with W6 -- swearingen Post Reply Top of thread Forum
Posted by: smegal

02/08/2006, 23:28:33

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I should have said that I am not an ME but should have been in light of my current situation (unemployed).

Max span for 2x10 is around 14ft and that is what I have. The ledger is somewhat over supported as you can see below. I found the following facts and I apoligize if you already know this but the Module of Elasticity for these joists on 16 in centers is 1.2 based on 1.E06 lb/sf. The bending value for this joist is 1036 lb/sq inch. The table also has L/360 deflection maximum at .5 in.

I hope this helps in addition to my post. I may end up using 3 2x6 fastened together unless a W6x? can be used. Thanks again.



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Re: Beam: W caculation for reinforcement of joists with W6
Re: Re: Beam: W caculation for reinforcement of joists with W6 -- smegal Post Reply Top of thread Forum
Posted by: swearingen

02/09/2006, 08:02:51

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Let's do the calcs here:

At 16" centers with an allowable bending value of 1036psi and a simple span of 14', the allowable load for that member would be about 60#/sf of floor. Checking allowable deflection for that load shows about 0.53" which is close enough.*

If you took these 14' joists at 16" on center and put a 10' span W6x15 under them at their center, things change drastically. The W6 is much stiffer than the joists. If we make the assumption that the load is uniform (which is slightly unconservative in this case - the joists provide discrete loading points to the W6), the loading on the W6 would be 60 x 7' = 420#/LF of beam. The moment on the W6 would be 5.25 ft-k, which is fine, and the resulting deflection would be about .11". Considering that I'm ignoring any help from the joists (which won't be much anyway), you can see that a W6 would work fine in this case.


* Please note that there are many design factors for wood based on moisture content, load duration, load distribution, load sharing, etc. These factors may increase or decrease your wood's design strength considerably. For joists that will spend their lives inside a climate controlled environment and are properly installed, these numbers should be close.








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Re: Beam: W caculation for reinforcement of joists with W6
Re: Re: Beam: W caculation for reinforcement of joists with W6 -- swearingen Post Reply Top of thread Forum
Posted by: smegal

02/20/2006, 16:06:48

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Many thanks to all who contributed to this problem resolution. I appreciate your taking time out to deal with this. Continued good luck to you both.







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Re: Beam: W caculation for reinforcement of joists with W6
Re: Re: Beam: W caculation for reinforcement of joists with W6 -- swearingen Post Reply Top of thread Forum
Posted by: zekeman

02/08/2006, 14:49:58

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To get a little fancier and with the use of compute power, and along the same lines, I would distribute the load into n equal point loads on each of the contact points and write the equality the deflections so that
k1Q1=c11P1+c12P2+.....c1nPn
.
.
.
k1Qn=cn1P1+............cnnPn
where the cij are the influence coefficients by Castigliano.
and since the total load is F then
Q1+P1=F/n
.
.
Qn+Pn=F/n
we have 2n linear eq in 2n variables and by computer you can get a very good conservative solution.







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