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load distribution to members with unequal moments of interia

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wallerdf

wallerdf

Structural
Aug 4, 2009
33
I am working on a design to transform an existing office building (60 psf) to an laboratory (120 psf by owner request). There are existing floor joists at 4 ft o.c. and the existing slab is good for about 300 psf @ 4' span. My solution was to come up between each joist with a new steel beam. It was more cost effective then stiffening the existing joists. I'm going to have them shim and weld the beam to the underside of the deck to ensure a tight fit.

In my design the joists have an I=171 in^4 and the new steel beams have an I=88.6 in^4. I distributed the floor load based on stiffness. 66% went to the joist and 34% went to the beams.

A fellow engineer disagreed with my approach. He said the slab was so stiff that essentially the entire load will be transfered to the joists and the beam would just be taken for a ride. His suggestion would be to make the beams moment of inertia as close to that of the joist. This would add approx. $30K to the job.

I feel the distibution of load is valid. For the beam to deflect it needs to take load, right. Any thoughts would be helpful.
 
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If you do not shore up the existing joists, they will take 100% of the dead load and 66% of the live load.

If you shore up the existing joists, your approach is valid.

DaveAtkins
 
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If your slab were perfectly rigid, the beam and joist would deflect the same and the load would distribute by stiffness, as you say. If your slab were perfectly flexible, deflection wouldn't matter and the beam and joist would share the load by tributary area. Since your slab is neither perfectly rigid or flexible, the solution is somewhere in between. Short of doing a flexibility analysis, I would assume the joist takes the load by the stiffness proportion (171/260), and the beam by tributary area (1/2).
 
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I essentially agree with Dave Atkins. If you do not relieve dead load on the joists by jacking, they will take 100% of dead load and a portion of the live load.

Why not create a little computer model with spring constants for joist and beam and model the slab as a beam element? This will give you the distribution to each but it should be close to what Dave described.
 
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I sort of agree with MIECZ. Well, I agree with him in theory, but would just do it a little differently.

I would say (if you're not relieving the DL stress by jacking) that the joists take all the DL and the their trib width of the LL. I would assign the trib width LL to the steel beams. That is assuming the slab is simple between joists. Ah, now thinking about it, if it's simple between joists, it could be continuous over the intermittent beams. Maybe the steel beams get 0.625*4 of the LL, and the joists get 0.375*4 of the LL.

I also agree with Dave about jacking and the validity of your load distribution.
 
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Yes, Dave is correct that, for unshored construction, the existing joists will carry the dead load.
 
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wallerdf:

Listen to the guidance of your fellow engineer! I think that he is steering you in the right direction! If you add steel beams of insufficient stiffness, the joists will still be overstressed. The trick is to choose a beam that is not only strong enough but stiff enough to take away enough load from the joist so that both the beam and the joist are within allowables.

If you are doubling the live load and the joist is carrying the full dead load, the joist will still be overstressed if it is carrying 100% DL + 66% LL. Conclusion: you need a stiffer beam. In fact, the beam will need to be at least equal to or close in stiffness to the joist even if you jack up the joist to distribute the dead load.
 
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I agree that the joists will continue to support the load in them at the time the new beams were installed and then the old and new members will support added loads in proportion to their stiffness.

It isn't always easy to support a jack from the middle of an elevated floor. On one job that I heard of, they cambered the beam to get a reverse deflection into it and them jacket the ends up close to the girder and columns until it was at the right elevation. They couldn't use a normal camber, it would have been too great, they had it done by a heat straightening expert, he was able to put about the right amount of camber into the beams.

Michael.
Timing has a lot to do with the outcome of a rain dance.
 
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Since I'm not jacking the joists the 100% DL + 66% LL makes sense. The existing joists were chosen by taking the span and finding the joist size that would give them the maximum load allowed. For example on a 24' span, they chose a 24K4 even though a 18K5 or 20K4 would work just fine. Some joists were close to taking the entire load but fell about 15-20% short. I checked using the 100% DL + 66% LL and the joists do work. My whole point is that for the beam to deflect it has to take load.
 
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Have you checked to see if there is room to place the new beams? Usually there are mechanical and electrical items in place which would make the addition of beams difficult to accomplish in practice.

Assuming that the beams can be placed, the deflection of a joist will be slightly greater than a beam of equal moment of inertia due to shear deflection which is greater in a trussed member than a beam with solid web.

BA
 
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They are gutting the interior down to the structure.
 
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Have you checked the effect of point loads on these design assumptions?
 
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For the joists, then, use 100% DL + 66% LL.
For the beams, w/o further analysis, I would use 50% LL, and would design the beams for some of the DL as well, just to be safe.

 
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My whole point is that for the beam to deflect it has to take load.
Click to expand...

Yes you are correct....it's called Hooke's Law.

 
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"There are existing floor joists at 4 ft o.c. and the existing slab is good for about 300 psf @ 4' span"

You're looking for 120psf and what's your new spacing with joists and new beams?

 
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Placing new beams will entail removal of existing bridging. I would think that after "gutting the original down to the structure" it would be more cost effective to repair the joists in place than to introduce new beams.

BA
 
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