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Deflection of Beam Supporting a Concrete Slab..... 3

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DMWWEngr

DMWWEngr

Structural
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I'm looking for a "rule-of-thumb" for steel beam deflections. I have looked in LRFD and found the L/360 for Live Load (LL) deflections but I can't seem to find anything for Total Load (TL) deflections. I've also searched the archives and nothing came up that applied to what I'm looking for.

I have a 20 ft span and I'm getting a (service) TL deflection of about 0.8 inches.

I'm trying to determine if this amount of deflection will crack the concrete floor that is supported by the steel beam?? If it will crack, to what extent will it crack (severly or just hairline cracks)??

I have no feel for acceptable deflections so I, again, must turn to you guys for advice. Any comments appreciated. ---
Andrew
 
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Wouldn't the dead load deflection be taken out from the pre-cambering of the beam?
 
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No, there is a dead load being added to the beam that increases the deflection of the beam. Furthermore, I can't find anything in the construction plans that states the beams are cambered. They could be cambered but I'm figuring it as if they are not.

Thanks for the reply. ---
Andrew
 
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As per the steel spanish code, at 6 m length, the total deflection (service level under live, dead and superimposed dead loads) must not exceed L/400 if not supporting masonry partitions and L/500 if supporting masonry partitions or bearing walls. Roofs have less stringent limits.

You at L/300 are not meeting these limits, so it would be out of the spanish code compliance and some problems it warns off could develop.
 
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DMWWEngr,

The purpose to limit the deflection of steel beams is to avoid damage to other items supported on or from the beam, as concrete slabs, plastered ceilings, etc.

I would limit the deflection of the beam under the live load plus any superimposed dead load added after the concrete slab is poured to the 1/360 limit given by AISC.

AEF
 
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For a given slab section, you can find the moment that will cause the rupture stress (fr)of the concrete, then calculate the deflection of the slab at rupture. Limit your steel beam deflection by this value to avoid cracks. See ACI 318 for fr.
 
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Accrding to IBC 2000 the live load deflection should not be more than L/360 and total load deflection L/240. 0.8 in deflection you have shown looks like ok and may not give much probles(this is said, assuming your floor is of concrete metal deck). But in practice we normally make sure the total deflection not to exceed L/360.
 
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I would say span/250. The span/depth ratio in BS8110 for slabs are based on limiting the slab deflection to below L/250, whereby deflection calculations are not necessary. Otherwise additional reinforcement is provided to reduce the deflection.
The deflection of the steel beam can be therefore be limited to span/250, unless brittle finishes appear above the beam (on floor or wall) where span/360 would be adviseable.
The pre-cambering of the beam is generally only done for "large" spans, due to the associated costs.

 
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l/360 is the one.
Also, if your TL deflection is .8, I would assume your DL deflection is about .4? Its tough to camber a 20' beam so little. It probably has/had a natural camber of that when it rolled off the mill.

 
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To: haynewp,

Using the procedure you suggested (in ACI 9.5.2.3) I'm getting a ridiculouly low moment and allowable deflection. This seems like a great idea but it's not working in this case (or I've made, yet another, calculation error :-)). I'm getting such a low moment that the slab would be cracked in its currently loaded state...which it is not. Have you used this procedure sucessfully before with steel construction??

To: pylko,
There is not an even split in DL to LL deflection. The DL deflection makes up most of the deflection. The deflection due to the LL is around 0.20". FYI.

Thanks to everyone for the great responses. ---
Andrew
 
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The deflection of the steel beam only needs to be limited to l/360 if there are brittle finishes which may crack. (ie:plaster etc) i would normally limit the delfection of a steel beam carrying a concrete floor to l/360 for imposed loads only and l/250 for dead + imposed.
A quick way to size the beam would be to let the Moment of Inertia =18ML where M=Moment and L=span if you are working with ultimate moments just divide by 1.5
 
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Yes, it is a small moment that would cause the slab to crack, but remember you have a steel beam you are counting on to take your moment, not your slab. It's the deflection of the steel beam that you are worried about, which would then allow the slab to take enough of the moment to cause it to crack.
 
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If cracks in the slab are critical, I would also check the slab spanning perpendicular to the beams as well.
 
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As for cambering, there is a minimum amount that AISC indicates for various beam depths - See the AISC LRFD Manual, page 1-185 (Table 1-10 on page 1-186)

When the beam deflects there is a curvature that the slab will experience (post-conc. hardening loads plus live load).

With this deflection and the moment of inertia of the slab itself (rather small) you can back-calculate the load, w, that would create that deflection in the slab over that span (delta = (5wL^4/(384EI)). This w will be very small as the slab is very flexible. The load w, creates a moment (wl^2/8) that can then be applied to the cross section of the slab and compared to the cracking moment of the slab, Mcr = frI/y where

fr = 7.5(sqrt(f'c))
I = gross moment of inertia of your slab
y = half your slab depth

You probably will see that your w, and thus your M, is so small that you don't exceed Mcr and thus the slab does not crack.

All this above to simply make the point that dlew made above that the deflection limits are usually concerned with brittle attachments and not necessarily for the concrete slab it supports.

I agree with the other comments above - we usually limit live load deflections to L/360 and total load deflections to L/240.
 
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Dont forget the quality of the curing of the concrete it self.
I've seen real desasters resulting of uncontrolled addition of water or poor curing methods.
 
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Agree with above that the limits are for easily damaged attachments since under service load due to the displacement compatibility of slabs and steel beams and the low stiffness of slab, the deflection induced tensile stress in slab should be very low, and in the case of composite construction the slab is even in compresson. Just want to add a ref. here:

AISC: Steel Design Guide Series#3: Serviceability Design Considerations for Low-Rise Buildings:

Considering beams supporting:
ceilings: DL.defl <= L/360 <= 1&quot;
partions: 0.5LL.defl <= L/360 <= 3/8&quot; to 1&quot;
 
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Thanks to everyone for the great responses!! ---
Andrew
 
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Andrew,
Here's my 2 cents worth. Good discussion.
First, your dead load deflection will not cause cracks. When the concrete is poured (and most of the dl is added) the beam will deflect. The concrete is at its heaviest prior to curing, so when it hardens it will be lighter but since the beam has already deflected no new cracks will develop.

Second, concrete will crack, there is nothing we can do about it accept try to control the size, frequency and regularity of the cracks.

Third, if you are checking a slab section for cracking under design live load, stop. I would look at a realistic expectation of live load. For instance in the commentary in the back of ASCE it says the average live load for an office building is around 11 psf. Yet we design for 50 psf (a worst case scenario load). So what I might do is take twice what the expected live load is and check the slab for that.

Fourth, if the floor is going to be covered with carpet like in a standard office building, don't worry about small cracks, they will be hidden by the covering.

Fifth, what I think is much more of a factor in building performance is are you asking them to pour a level floor or a consistant thickness of slab. This can make a helluva difference when the spans get longer. Doors can scrape floors or have huge gaps under one end. On the other hand you have to add in a surcharge of dead load if you want a flat floor. For our office we spec a flat floor and add 3-4 psf into the dl to account.

There you go. This is what we use.

Ps. We use L/270 < 1 1/2&quot; for composite floor total load deflections. L/360 for live load deflections. We use 90% dl camber with a 3/4&quot; minimum.
 
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