Simple Deflection Question 1

[Brobocop]

The code deflection limit charts for Floor Members simply states:

Live load = l/360
Nothing for Wind
D+L = l/240.

So am I only checking the Live Load deflection and the Load combination (D+L) deflection?

Does my Load combination of D+0.75L+0.75(0.6W)+0.75Lr not need to meet l/240? Or is 0.75L+0.75(0.6W)+0.75Lr considered the "L" in D+L = l/240

 

[hardbutmild]

What is Lr? How do you have wind load on a floor? Is it a top floor (flat roof) plate?

I'd say it depends. If winds duration is not long, I'd say that you don't need to include it in the check, but if at the location high winds are common I'd check with it. But again, it depends also on the specific structure since those limits are usually made because of aesthetic reasons or usage and are relatively arbitrary. I'd say it depends on specific project.

 

[Brobocop]

Interior floor beams that will be receiving load as a result of Live Roof loads and Wind loads, as they support a portion of the roof structure.

 

[r13]

You should point to another thread you've posted, so new readers wouldn't be confused.

For your case, I would suggest to include the wind, in hope to make the beam stiff enough, so occupants won't feel bumpy during wind event.

 

[rapt]

Wind would normally be involved for a gravity load member (beam or slab) deflection if it was a transfer member, so the wind load effect becomes a vertical load on the member.

One thing that is very unclear to me on ACI limit of LL deflection to L / 360 is what deflection are you actually talking about. Wnen you are looking at deflections for an elastic material like structural steel, it does not matter. But for RC and PT concrete, applying the LL to a member increases the DL deflection due to increased cracking under the combined loads. Then there are creep and shrinkage effects on deflection to consider. There is really no deflection called "LL deflection" for concrete members. ACI318 really needs to sort this out and stop copying Structural Steel deflection limit logic.

 

[JAE]

A few comments on this:
1. Brobocop - you really should indicate which code you are talking about - this is an international forum so your country and codes do affect the answers.
2. There definitely is a LL deflection for concrete inherent in ACI's (318) effective moment of inertia (Ie) equations. A few years ago I posted the following:

[blue]Ie for DL only will be different than Ie for D+L.

Thus, the most accurate dead load deflection would be calculated based on M(dead) with an Ie based on only dead.
Then you would calculate an Ie based on M(D+L) and calculate a total D+L deflection.

The live load deflection would be the net difference.

Now having said this above, I would also point out that in my opinion, the Ie formula in ACI seems very general and approximate and my guess is that a LOT of engineers simply use the Ie based on total load for everything and this is probably acceptable.[/blue]

 

[r13]

rapt,

For reinforced concrete, the deflection should be based on I[sub]e[/sub] or I[sub]cr[/sub], if Ma > M[sub]cr[/sub]. An approximate method with reasonable results. Note Ma is the maximum service load moment at the stage the deflection is checked.

 

[rapt]

JAE, I would be interested to know how many designers actually follow that approach!

And how do you account for Long Term effects due to shrinkage and creep on this?

 

[msquared48]

1.5x

Mike McCann, PE, SE (WA, HI)

 

[hardbutmild]

I wouldn't agree that Ie should be used based on the moment. If you check for dead load only, it needs to be satisfied at any point in time. At later stages of structures life, it'll be fully cracked. We can expect that D+L happened at least once. Now, if you remove live load after that, Ie stays the same, in other words, cracks don't fill up, they still exist. Creep usually reduces E by 3-4 times. I usually calculate elastic deflection of uncracked section and multiply it by 6,5 or 8. This is just a first step check.

 

[phamENG]

I know we've wandered into concrete deflections here, but based on the OP's other thread about an LVL in which he specifically asked if the member in question should be considered a floor member or a roof member, I'm going to assume that we're talking about deflection in that LVL.

Brobocop: I don't think I'd use that load combination. Look at what it includes - full dead load, most of the floor live load, a 10-year storm (so pretty bad), and most of the roof live load. How often are you going to have a room nearly full of people and furniture, roofers replacing the roof, and the storm of the decade all at the same time? It's possible, so we make sure it's strong enough for it, but so remote that I see very little reason to design for a serviceability condition around it.

Check it as a floor member and as a roof member with brittle ceiling finishes. Don't try to apply it to the strength combinations.

 

[JAE]

rapt - probably none....but me myself and I.

I'm not sure it is even the correct approach as you stated - ACI is a bit vague on this.
I can certainly see the use of Ie based on the maximum service load (whatever combination that is), which would give you the smallest value of Ie, which would then give you the largest deflections...a conservative approach.

 

[rapt]

JAE
And RAPT in its incremental deflection calculation but it also includes curvatures and deflections caused by long term effects!

msquared48
1.5 * what. LL deflection, Total deflection? It used to be 2 * total cracked deflection added to the initial cracked deflection. And total deflection includes DL and SDL deflection.

The point I am trying to make is that it is not "LL" deflection that ACI should be limiting as it is not defined as anything special, so many designers will unknowingly simply use the deflection calculated from LL only either using Ie or, if completely incompetent, Ig (don't laugh, I have seen it often), and not include any long term effects, most of which are caused by DL + SDL (+ permanent LL)(creep) and by shrinkage which is close to load independent (except for load effect on neutral axis depth).

My reading of the code is that they took the logic from the Steel code, where LL deflection is a logical number, no cracking, no increase in DL deflection caused by LL and no long term effects, so LL deflection is the deflection caused by LL in that case!

 

[Settingsun]

Is the ACI limit for live load deflection (L/360 as stated above) fundamentally different to the AS3600 limit of L/800? Aside from AS being more stringent of course. I've never heard it suggested that it be anything other than instantaneous deflection due to live load. Shooting from the hip, increased dead load deflection only an issue the first time the uncracked-cracked line is crossed on RC structures.

Edit: Are we discussing ACI 318R-14 Table 24.2.2? It says "Immediate deflection due to L".

 

[rapt]

Steveh,

Just as well someone can read English.

This is for floors not supporting or attached to other structural elements that will be damaged by deflections. And it is the only deflection limit defined for this case.

Looking at a simple case, for ease of calculation, assume L = 10.8m (about 35'), so maximum instantaneous LL deflection = 10800 / 360 = 30mm.

If we assume DL = LL (normally LL is less than DL)
and sustained load = .4LL (Australian permanent load for all but storage buildings)

Total Long Term deflection = (DL + .4LL) * 3 + .6LL = 4.8 * LL

So total long term deflection allowed in this case = 30 * 4.8 = 144mm = L / 75.

Hope no one is using the rule! This could be a floor slab in an office building, with 144mm deflection and a deflection ratio of L / 75.

Buildings in Australia have been demolished due to deflection problems with less deflection than that.

 

[Settingsun]

Clause 24.2.1 would cover total deflection except it's undone by the loose deemed-to-comply span/depth ratios. Ie they have no dependence on loading, concrete properties, reinforcement or deflection limit (which may vary depending on use of the floor).

Maybe US engineers can enlighten me on whether deflection of concrete floors is a chronic problem.

 

[rapt]

24.2.1 does not require the L/D method to be used. (see 7.3.1.1).

There was a calculation error in my previous post which I have fixed.

However that is not the worst case scenario. DL could easily be 1.5 to 2 * LL, eg office building.

For DL = 2 * LL the multiplier is (2LL + .4LL) * 3 + .6 = 7.8

So TLT deflection = 234 and L / deflection = 46

 

[r13]

The estimate of deflection, through calculation, of reinforced concrete structure is, to the best, an approximation; inaccurate at the worst due to the difficulties in catching all factors affecting its property and performance. Most engineers as I knew, were/are stuck to ACI tables for L/D ratio, and thickness by construction, that were proven to yield satisfactory results, as in no time the deflection has been a prevalent problem in most of concrete structures in the North America. However, for pedestal type structures that supporting heavy machinery, both instantaneous and long term deflections/shortening need to be investigated, due to the substantial sustained dead load involved.

The method for calculation of deflection of reinforced concrete structure is still unsettled. An interesting graph of strain vs time is provided below for the curios minds.

 

[rapt]

Retired13

Not sure how that diagram helps anyone. Yes, there is partial creep recovery when load is removed. That is why creep and shrinkage effects are calculated for permanent load, not maximum load in most cases.

We keep hearing how deflections cannot be calculated, so why try. Normally from Americans. If they design PT structures, they have to try as L/D ratios do not work. But this rule applies to all concrete members.

While most ACI318 designers may still use very approximate L/D ratios and have no idea of the possible level of deflections in their structure, the code allows them to use another supposedly more accurate method which, in the case I have indicated the limit defined is grossly un-conservative and illogical.

The limit, I think, comes from the American Steel code. In steel design, DL is usually lower than LL, and there are no long term effects.

In steel design, if DL = .5LL, then TLT deflection in the case above would be 45mm and L / deflection would be 240. This is a normally acceptable level of total long deflection. Most codes would use L / 250 as an overall limit. Even with DL = LL, the deflection would be 60 and L / deflection = 180, which is getting a little worrying but not too bad.

 

[r13]

I really don't want to stay on this topic much longer, as we have hijacked the question of OP (deflection of a wood beam subjects to both roof load and floor load). But I couldn't set aside my curiosity, if ACI deflection criteria L/XXX is not reasonable, then what you suggest? Euro code, or AS code? If I am remember correctly, for deflection sensitive structures, the ACI total deflection is limited to L/480 (Euro L/500). L/360 is instantaneous live load (a short duration load) deflection only.

I suggest to open a thread at ACI code issue forum to draw more participants then.