DEFLECTION ANALYSIS OF A 12 METRE CONCRETE BEAM 8

[azh]

I was doing a deflection check on a 12 metre reinforced concrete simply supported beam.In the code it says compliance with the span/ effective depth ratio (20 for simply supported) will generally limit total deflections to span/250.
When I checked the actual span depth ratio for a 1 metre deep beam, the result was simply 13.3 ( ie 12000/900 ), hence this means this is well below the allowable basic span depth ratio of 20.
However, when I used the formula 5 wLxLxL/(384EI), the max deflection came out to be 54.6 mm, whereas, as mentioned above, the allowable limit is span/250 = 48 mm.

Do I have to increase the beam depth ?

 

[whymrg]

If you have complied with depth/span ratio you do not need to check deflection, unless you have other requirements.
I had the same results before. I looks like this ratio established based on tests, not on elastic behavior (Code is not based on elastic behavior of concrete).

 

[emil]

Deflection check of a 12m beam is not very simple. You cannot rely only on span-depth ratio. I would suggest to consider post-tensioning. The span is too large for reliable calculation of deflection in ordinary reinforced concrete.

 

[Taro]

emil,

I disagree. 12 meters is well within the bounds of common practice for which standard span/depth ratios have performed well for many decades.

Now for the disclaimers...

Of course, this is assuming typical values for concrete weight, reinforcement strength and loading. And you would not rely solely on span/depth ratios if you have brittle finishes, partitions, or equipment attached to the slab that are sensitive to displacements. If any of these conditions apply, deflections should be calculated, and the effects of cracking and creep should be included.

Post-tensioning will allow greater span/depth members to be used, but it might not be practical to PT this beam if there is no other PT on the job. If depth is not a concern, make the beam a bit deeper and add some compression reinforcing to reduce creep.

 

[JAE]

azh,
What did you use for the "I" of the beam? Did you include an integral cast slab? Did you use the ACI effective moment of inertia, Ie? (are you using ACI or some other code?). Are your deflections total load or dead load?

If you are under ACI, whymrg is right in that you really don't need to check deflections if you meet the general criteria given.

 

[azh]

Dear JAE and others,
The CODE I am using is BS8110 (British standard).
I=bdxdxd/12 where b stands for the rectangular width of the beam, in this case b=350mm and d is the effective depth of the beam =900mm in this case.The deflection I calculated was based on the ultimate (factored)load of the dead and imposed load (i.e total load).

Am I doing the right thing? For your information I am not familiar with the ACI ( is it an American code)

Actually, I did analysed a 1100mm deep beam and the deflection was within the allowable limit.But the architect may not be in favour of this. TARO was right, in saying that Post tensioning is not practical.

Helpful and ethusiastic engineers, please reply!

 

[IJR]

Here is how I can be of help: not on the subject but on where the subject gets talked of.

If you are using BS8110, then that code does have very simplified deflection checks. Check out for example T.J.MacGinley and B.S.Choo Reinf. concrete design Theory and practice if you are having trouble following the "law" kind of prose in codes(joke intended).

If you are in U.K, the visit RCC website, they even have free spreadsheets for offer within UK(never abroad though), written specifically for BS8110.

ACI318 is a strong US code worth your time to check on. Not really different from BS in principle but material quality differences and perhaps more emphasis on lateral resistance of structures is placed in US than is in UK.

Good luck.
IJR

 

[dik]

I've used regular reinforced 16" x 36" deep conc beams for spans as great as 58' for parking structures. A portion of the moment is taken by the columns.

Deflection calculations are fairly involved to accommodate long term effects and account for T-shape (due to slab), percent of steel and concrete strength. Reinforcing is often in several layers.

Crack widths also checked.

Long term deflection not an issue since there are no partitions.

 

[azh]

Thanks dik ! 58 ft seems very long.What is the spacing of these beams ?

 

[LPPE]

The ACI is the American Concrete Institute. ACI provides the modulus of elasticity (Ec) for concrete, and an effective moment of inertia (Ie) for computing deflections. Ie is a combination of Icr (moment of inertia of cracked section transformed to concrete), Mcr (cracking moment), Ma (maximum moment), Ig (moment of inertia of gross concrete section neglecting reinforcement). Ie should be less than Ig. The formula for Ie is too long to type into words. Its found in ACI 9.5.2.3 (ACI 318-95).

Just 2 things to check for your deflection analysis.

 

[IJR]

Azh

Excuse me if I am wrong, but I think your problem is not in the analysis for deflection but rather you seem intrigued by the span of your beam. You are not sure it will work and you are sharing the typical set of worries we all experience.

And none of us can really tell you much since we dont have sufficient input.

However, with my assumptions stated above, let me tell you this: 12m is not a big deal. I know a stadium wing with RC frames spaced 9m apart and one span of a beam in this wing crossing over some 15m, the beam is 1.4m deep, 60-70cm wide and is stuffed with high strength steel reinforcement in double layers, like dik mentioned.

Another one is a coach(bus) terminal with roof supported by RC beams again spaced some 6-7m apart and crossing real distance. This one is about 1.2m deep and some 0.40m wide and supports roof slab.

Both seem perfectly well.

As for the architect- With such a span to cross and whatever loading conditions you have, he is supposed to co-operate or change the design.

Well, I just thought without numbers I can help.

regs
IJR

 

[phuduhudu]

There are a few things to bear in mind. IF you are using BS 8110 you can use the span/depth ratio but there are a number of adjustments to be made to the ratio of 20 in this case. The first is for spans over 10m which is applicable in your case. The other is for the tension reinforcement quantity, then for the compression reinforcement quantity. This generally means that you can get a higher span/depth ratio by including additional tension or compression reinforcement. I haven't got the code to hand now but I think there may be a factor for the concrete grade as well.

BS8110 part 2 gives guidance on deflection and creep deflections which you can use if deflections are critical. However, deflections with concrete beams are not very easy to calculate and the best you can get is a range of possible deflections. There are several ways to calculate the EI value. The simplest and least accurate is the simple section modulus you used. The next best is a transformed section modulus which uses the transformed section taking into account the steel as well. The most accurate is the transformed section modulus which takes into account the cracked concrete section however the amount of cracking varies along the section with the bending moment so you need to do an analysis of a varying EI along the section. Then the E value varies with time too so as you can see the whole process can get pretty complex and at the end of it you still aren't guaranteed very accurate results. I guess that's why the simplified rules were developed.

One other comment I would make is that the difference between the allowable deflection of 48mm and the calculated of 55mm is not that significant with the inaccuracies we are talking about. Carl Bauer

http://www.bauerconsultbotswana.com

 

[dik]

Picking up about 15' of 5-1/2 to 6" of concrete slab and 50 psf LL. Typical parking garage construction

 

[chandr]

azh

Be careful. You wrote that you used Factored load to compute defl. The load factor must be 1 in this case. But the inertia must also be the effective I, not the gross one you said you used.

 

[azh]

Chandr

Isn't factored load make it more conservative?

Thanx everyone. I think dik's experience tells a lot.

 

[phuduhudu]

Yes the factored load makes it more conservative but with a deflection check you are looking for a realistic value of deflection and not a value which is statistically unlikely to be exceeded. The reason being that the results of the deflection being exceeded should not be disastrous as failure of the section would be. Carl Bauer

http://www.bauerconsultbotswana.com

 

[Taro]

Factored loads should not be used for deflection checks. Use the service loads, because deflection is a serviceability criterion. I would even propose that using factored loads for deflection checks could be UNCONSERVATIVE. You would like the beam to be proportioned so that a ductile failure occurs if the beam is overloaded. In this way, large deflections will be a warning to the structure occupants that a failure is imminent. If you make the beam so stiff that it doesn't deflect much even when the ultimate strength of the beam is reached, you are likely to experience a catastrophic brittle failure.

 

[dik]

Just to clarify... by the statement that 'long term deflections are not an issue', I meant that they wouldn't cause problems, not that they weren't calculated. Deflections, moreover, are determined by service loads, not factored loads.

On a personal side, I feel uncomfortable with the comment that 'Dik's experience tells a lot'. The comments in response to your question are sound engineering opinions, from some pretty talented fellows...

 

[azh]

I am so sorry Dik. I did not mean to make you uncomfortable but it's just that your expert opinions and comments are very helpful.Thanks again.

 

[IJR]

Azh

You seem to be an interested new engineer and every word told will be useful to you, because you are interested. Just like Taro was and dik was, and currently I am.

Your comment that using factored loads for deflection is on the safe side can not pass without a warning.

Reinforced concrete design is a strength design(loads factored up and section strength factored down). Deflection, vibrations, crack limitations etc are designed for serviceability(loads and section/material factored by 1). The term "safe side" can only be used when you know what it means.It should not be used blindly. I have personally come across such a blind use of the term and there have been cases where it was the contrary.

I recommend you immediately learn the difference between the two and the situations where they interact. A typical example: Code min requirements in RC design are often specified to save you from carrying out serviceability checks, eg min slab thickness and min beam reinforcement. So you go on carrying out strength design, but dont be surprised when someone mentions unfactored loads in RC design.

If my assumption that you are new to RC design are correct, then let me suggest that whatever design you carry out, spend time to master the concepts and behavior pretty well. You will be rewarded later.

Just like me, use this forum to learn different aspects of structural engineering.I underline: DIFFERENT ASPECTS.

Good luck
Ijr