Continuos RC beams on beam supports in a 3D model, how valid? 4

[IJR]

I have an old habit of designing continuous RC beams resting on other beams (not on columns) by hand or spreadsheet and assuming the supports to be non-rotating and vertically non deflecting. If necessary I would then utilize redistribution to modify moments as most codes suggest.

But in 3D elastic wire frame, with strength design in mind, modelling a continuous beam resting on beam, wont that rely on elastic deformations? Is that proper analysis?

regs
IJR

 

[dik]

It likely will. With hard supports adjacent to a beam support, the negative moment over the hard support will likely increase (depends on the flexibility of the beam support). Always found it to be a pain to accommodate deflections, this is one of the real advantages of 3D frame software.

Some codes allow for a redistibution of flexural reinforcing to reflect 'plastic' redistribution of moments.

On a positive side... lower strength concrete tends to behave less elastically than high strength stuff and for small percentages of reinforcing, the concrete strength has little effect on flexural strength <G>, but it does affect shear strength.

For quick 'knock-offs', I usually calculate the deflection of the other beam, 'guess' the deflection at the point of support and use 3/4 of this value (assuming beams help support each other) to determine the increase in negative reinf (I leave the positive reinf. unchanged).

Can also have an impact on shear reinf, also.

 

[JAE]

Good response dik.

Also....IJR: I always know you've been around 'cause I see stars everywhere. Your encouragements are encouraging!

 

[IJR]

JAE, thanx, and congrats for mastering the week. As for stars, if I submit them it is because pals here really deserve my show of respect.Most of you guys are simply great.

Dik: You seem to be telling me that the elastic deformation at beam-supports of my continuous beam are OK, and with a little adjustment on negative moment I can go ahead. Did I get you right?

regs
IJR

 

[dik]

Not sure... don't follow your reply.

In a simple case, if you have a beam support, then it can increase the negative moment by providing a greater deflection (rotation at fixed support). I usually increase the negative moment (to reduce cracking) and leave the positive moment the same (safety). If I have several of the same type (replicated on many floors) then I will be more refined in the analysis. The negative moment will increase as the flexibility of the supporting beam increases.

A 3D program will give the increase directly, else, calculations require a solution of simultaneous equations (have to iterate, too) and re-calc using a deflection (messy and time consuming).

Also, if things are non-symmetrical, depending on the geometry... can introduce some torsional moments and increase shear.

 

[IJR]

dik:

Now I see where we differ

My point is the deflection as calculated by 3D elastic analysis using gross section and factored load is not real.
Should I rely on it anyway?

If you want to discuss further, please do

respects
IJR

 

[fida]

What is plinth beam and purpose

 

[dik]

I'm not sure what a plinth beam is, but the plinth is the lower course(s) of masonry or more recently decorative band just above grade/slab in a building. It's purpose, originally, was to deflect rainwater sheeting down the face of the building and preventing erosion of the soil adjacent to the building.

A plinth beam may be a grade beam that is elevated above grade and may project beyond the face of the building. Just a WAG...

 

[StructuralDzine]

Ho! Big question. Or rather several.
First the result of your 3d analysis will be only as good as the data you start with. If the steel beams are much stiffer than the concrete then differences in the concrete moment of inertia will make little difference. Otherwise you will need to calculate average moments of inertia for the cracked sections at maximum working stress and adjust those values in the analysis. If necessary divide the concrete beams into sections. Remember that some moment redistribution is possible and that the results will be only approximate at best.

Grid structures often end up with substantial torsional moments in the concrete beams. Depending on actual fixity this may be unrealistic. Adjust the torsional moment of inertia of the concrete beams, eg divide by 100, to ensure you don't get significant torsion (but do not use zero). Provide minimum torsional reinforcement in the beams to cope with compatability torsion. You will find deflections increase as more of the load gets carried by flexural moment.

The computer analysis at servicability load will give you deflections but while the steel beams will not creep the concrete will deflect further with time due to creep and shrinkage. You cannot simply factor the load to allow for this because that would affect the steel deflections as well. It is probably easiest to manually adjust the concrete component of the deflection. If however the deflections from the analysis are much less than allowable deflections then detailed calculations would be unnecessary.

You will have to do separate analyses for the strength limit state and the servicability limit state.

You will be lucky if your best analysis comes within 10% of true values so don't overanalyse, but keep a little on the conservative side.

 

[capper]

If I could add my bit.....

I have recently designed a grid of ground beams, supported by piles & I did use a 3d analysis model, though the beams were in a planar arrangement. As I know that these beams will be poured monolithically I did not reduce the torsional constant section property of the rectangles I was using to represent my beams. Yes the analysis did give some peaks of torsional effects & I designed for these.

I would not agree with the recommendations saying that you should reduce the section property so as to avoid big torsional effects, above. I do not think though that it is a dangerous thing to do, just that reasonable torsional cracks could develop & these would in turn ensure that the TM's are re-distributed into ordinary BM's in the beams. This is the case that the above recommendations design for.

Maybe it just comes down to the engineers choice of extra links for torsion or to put up with cracking (which won't be seen in ground beams).

Excellent discussion.......

 

[StructuralDzine]

Capper, in your case with monolithic construction I agree with designing for torsion, but if the connections between the steel and concrete beams are not rigid I doubt significant torsional moments would develop. That's why I suggested reducing the torsional rigidity AND provide minimum torsional reinforcement to ensure that some compatability torsion could be handled. It is a case of how well the computer model represents the actual construction.

 

[capper]

Thanks, StructuralDzine, I seem to have missed the bit about it resting on steel beams - in that case we are all in agreement!! Group Hug!! I am not used to the situation of a mixed (steel & RC) floor support system? It wouldn't seem economic to mix - is it a US thing or elsewhere??#

Oh, the torsional &quot;carryover&quot; would then depend on the connection detail between the beams wouldn't it??

Thanks

 

[IJR]

Capper/StructuralDzine

I have been following your discussion with interest, and I find your comments very useful.

However if you would like to, go on discussing my original question: A continouous RC beam resting on an RC beam. This question is still unanswered.

My doubt was: In doing the statics of the continuous beam , a general purpose software will take into account displacement of the main beam in calculating moments of the continuous beam. But I know that deflections of an RC beam are not easy to determine and do depend on a lot of factors.
Am I overconcerned?

regs and thanx for extending the discussion this far

IJR

 

[dik]

Sorry... thought it had been answered.

If the supporting beam is not stiff, then software that treats it as rigid support will be in error and the negative moment over the rigid support should be increased as well as the positive reinforcing.

How much depends on the stiffness of the supporting beam. A really flexible beam will act as 'no' support and a really stiff beam will act as a 'rigid' support and the solution will be somewhere between. The problem is complicated with concrete because the long term deflection of the supporting beam is a guess at best (I can calculate deflections, but based on years of experience, I do not have a high confidence in the outcome). You are not being overly concerned...

 

[IJR]

Respects Dik

IJR

 

[JAE]

IJR - not to discount the other comments which were good...For years our firm and a previous firm I was with designed a multitude of cast-in-place concrete floors and roofs with no allowance for the flexibility of the supporting girders (i.e. - assumed that they were perfectly rigid). This was essentially the method used for many years by thousands of engineers before the advent of computers.

In many cases, for example, we would analyze a continuous run of a concrete pan joist supported by numerous supporting concrete girders. While I haven't done an exhaustive check considering the flexibility of the supporting girder and its effect on the moments and shears of the supported continuous joist, I would think it is a minimal effect, or, an effect that is more than accounted for by the load factors included in your design.

We have a lot of floors out there that have performed very well using this procedure.

As far as torsional effects go, the ACI code allows the designer to neglect torsional effects, or provide for a minimum torsional moment, if the system is not dependent upon the torsional restraint for safety. In other words, if you design you joist to be simply supported at the perimeter beam, then the perimeter beam doesn't need to torsionally resist the negative moment of the joist that it supports (see ACI 11.6.2.2)

 

[IJR]

respects JAE

regs
IJr

 

[StructuralDzine]

Sorry, don't know where I got the steel beams from. The discussion still applies. i.e. what happens depends on the connection between the two sets of beams and their relative stiffness. As JAE says a lot of designs using simplistic assumptions are still performing well. If you use simple design methods allow an extra factor of safety to compensate.

 

[capper]

Sorry gentlemen been away form the machine for a while, glad to see this one is turning out a real little gem.

Grillage Analysis:
Ok, are the beams to be cast at the same time ?:
Yes: do take load patterning into account on the CBeam
and just qualitatively asess the torsion that occurs
Lots of Torsion: Hmm - design for it
Not so much: Yea load factors etc. etc. Nominal links
No: I would still check qualitatively but in this case it
would depend on the surface at the junction of the two
beams: it might be scabbled or separated

1D Beam Analysis:
Dik, above was spot on, the ratios of stiffnesses is critical. However, if the C-Beam is resting across transverse beams of equal stiffness then rigid pin supports can be used in the analysis as there is no relative displacements of one support of the C-beam to another support. I think in this case the small extra deflections that load patterning might produce could be ignored (anyone??).
Oh, Dik said:
&quot;If the supporting beam is not stiff, then software that treats it as rigid support will be in error and the negative moment over the rigid support should be increased as well as the positive reinforcing.&quot;

I think this should read:
&quot;If the supporting beam is not stiff, then software that treats it as rigid support will be in error and the negative moment over the rigid support should be DEcreased and the positive reinforcment increased.&quot; (anyone??)

One more thing on the point of calulating the actual deflections of an RC beam - Yes it is difficult & non-linear but software is around that will give a moment rotaion curve for a section and this can be integrated over the length of the beam etc. etc. but in my opinion once we use the same method for all beams the relative deflections will be equal and this is the thing we are interested in. Codes at this point in time are built upon years of experience and once adhered to actual deflection problems shouldn't arise.

Difference in stiffnesses of supports:
Something I haven't addressed yet - how to deal with this situation with a standard 1D continuous beam analysis program:
1. Analyse the supporting beam for 100kN (maybe kips in US??). Get a deflection from it.
2. Divide one by the other & get a linear load-deflection constant.
3. Analyse the C-beam with rigid supports.
4. Calculate the deflection of the supporting beam from the reaction results of the C-beam.
5. If the program can handle fixed displacements do a separate analysis of this displacement alone (if not use moment distribution - easy enough for this bit - no load patterning or anything just 6EI/L stuff)
6. Superimpose these results onto the original C-beam & get another BMD & reactions.
7. (This bit is the killer!!!) Repeat the above until the differences in the reactions is acceptable.

If people are interested I did the above on a cable stay footbridge as part of my undergrad thesis - I could put it on the web.

This one is good - keep it going!

 

[dik]

Capper...
both the positive and negative moment will have to be increased for a flexible support... The negative moment is increased because of the greater curvature and the positive moment increased because the equivalent span is increased also. Assuming equal spans, without the intermediate support (ie, very flexible) the span is doubled and the +ve moment is fourpled <G> (illustrative, not gospel).