Long Term Deflection Estimates 1

[Trenno]

Hi all,

I know full well the ins and outs of long term deflection - creep, shrinkage, cracking, f'c, mix design, restraint, P/A, compression reo and the list goes on...

But what I'm asking here are people's 'back of the envelope' deflection estimates.

For example, I've seen people get a quick figure by factoring up the elastic uncracked deflections - 3G + 1.5Q. This can be back calculated from various code equations.

I've also seen a RAM Concept file with the load combo - 3.35G + 1.64Q (note the creep factor being set to 3.35).

Anyone have any reference material that quotes some of these elastic uncracked deflection multipliers, purely just to get ballpark figures?

Or do people more opt for span/depth ratios to give them a feel for a particular design?

 

[Retrograde]

Some info here:

https://spiral.imperial.ac.uk/bitstream/10044/1/19337/2/Magazine of Concrete Research_55_2003.pdf

 

[KootK]

My favorite deflection check is just reinforcement ratio. Anything less than 1/2_rho_b and I sleep easy.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[Retrograde]

SLABS by Inducta uses 2.4G + 1.26Q by default. This is based on 50% compression reinforcement ratio.

 

[IDS]

A reasonable estimate would be to calculate deflections using short term cracked section properties, including tension stiffening, and multiply by 3.

Anything more precise than that, without taking account of reinforcement ratio, concrete tensile strength, loss of tension stiffening, etc is just fooling yourself, and to use factors to 3 significant figures is just ridiculous.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[rapt]

I would agree with IDS, for RC members 3 times cracked short term deflection, or if you want to be lazier still, 6 times uncracked short term deflection.

Reductions for compression reinforcement such as those in SLABS are grossly un-conservative in most cases.

I have never found a relationship to reinforcement ratio like Kootk's to have any relevance!

 

[Retrograde]

SLABS by Inducta uses 2.4G + 1.26Q by default. This is based on 50% compression reinforcement ratio.

To clarify these are used with cracked section properties by Inducta.

The paper I linked to in my earlier post agrees with RAPT's 6 times uncracked short term deflection suggestion.

 

[KootK]

I have never found a relationship to reinforcement ratio like Kootk's to have any relevance!

I'm surprised to hear this rapt. I first saw the method proposed by David Fanella (snippet below). I thought that it was an interesting proposition and began checking 0.5 rho_b along side my normal deflection calcs. Low and behold, I found it to be a very reliable rule of thumb deflection check.

Conceptually, I'm sure that we can agree that any concrete bending member proportioned such that it can be lightly reinforced is likely to be in pretty good shape from a deflection standpoint. It's never the singly and lightly reinforced members that have deflection problems. Rather, it's the member with four layers of tension steel and some compression reinforcing thrown in to boot that cause headaches.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[rapt]

I only have your snippet to read, but for the reinforcement % he does not say < , he says = . Not knowing what type of deflection checks you compare it to I cannot comment further.

Re your conceptual thinking,

- with 4 layers of tension steel and extra compression steel, I would assume it is a transfer beam, and if dimensioned properly for shear and flexure I would normally not expect deflection problems in that type of beam. They are normally relatively low span/depth ratios and are approaching deep beams and I find that shear normally controls, not deflection.
And with an RC beam requiring that much reinforcing I would use bonded PT anyway!

- I find that relatively lightly loaded slabs and beams are more likely to have deflection problems according to my long term deflection calculations!

 

[IDS]

I can't comment on building structures, but in the area where I do most of my work (buried arches) the main deflection problems occur with structures where the maximum serviceability bending moment is about the nominal cracking moment, i.e. lightly reinforced slabs.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[Trenno]

My favorite deflection check is just reinforcement ratio. Anything less than 1/2_rho_b and I sleep easy.

What's this 1/2_rho_b business? Please elaborate. Many thanks!

 

[KootK]

@Trenno: 1/2_rho_b = a reinforcing ratio of half of the balanced reinforcing ratio.

@rapt/IDS:

Consider two mildly reinforced beams where the following is true:

1) All parameters are identical except the reinforcing ratio and beam depth.

2) Beam #1 has a reinforcement ratio of 0.25 times the balanced reinforcement ratio and the depth is made as small as possible.

3) Beam #2 has a reinforcement ratio of 0.75 times the balanced reinforcement ratio and the depth is made as small as possible.

Do you guys really have any doubt at all that:

1) Beam #1 will be deeper than beam #2 and;

2) Beam #1 will deflect less than beam #2?




I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[IDS]

KootK - If the required depth is controlled by the deflection limits, and the calculation is done using typical code simplified methods, then I have no doubt that Beam 1 will exceed the expected deflection by considerably more than Beam 2.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[hokie66]

I agree with KootK. As he posed the question, the deeper Beam #1 will deflect less.

 

[IDS]

I agree with KootK. As he posed the question, the deeper Beam #1 will deflect less.

With the question as posed, if the design is controlled by deflection, then immediately after removal of formwork they will both deflect the same. Within a few days under most circumstances the lightly reinforced beam will deflect more, because the factors that the code simplified methods do not deal with adequately affect lightly loaded beams more than heavily loaded beams.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[IDS]

affect lightly loaded beams more than heavily loaded beams

That should read lightly reinforced and heavily reinforced, since in this example the loading is the same.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[hokie66]

No, the loading is greater on Beam 1, because it is deeper. And because it is deeper, it will deflect less. I think your language varies from the question posed by KootK.

 

[IDS]

I assumed the beam self weight was negligible, but it's irrelevant. All KootK has said is that the beam depth is made as small as possible (presumably satisfying all code requirements). If the depth of both beams is controlled by reinforcement stress, and if the code requirements are such that both beams have the same limiting stress, then yes the deeper beam will deflect less. But deflection control is also a code requirement, and this requirement often controls the design, and since this is a thread about deflections it seems quite reasonable to assume that the beam depths will be controlled by deflection.

In that case, as I said, although they start off with the same deflection, it is probable that the more lightly reinforced beam will deflect more than the more heavily reinforced one over time.

The point is that in my experience lightly reinforced beams and slabs often have deflections greatly exceeding what would be expected from a simplistic analysis.

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/

 

[KootK]

@IDS/Hokie: an assumption not explicitly stated in the mental experiment that I posed above is this: longitudinal reinforcement was to be selected based on bending capacity. As the 0.5 rho_b algorithm is itself meant to be a rudimentary deflection check, the experiment loses all meaning if one assumes that a more detailed deflection assessment has already influenced the beam proportions.

I like to debate structural engineering theory -- a lot. If I challenge you on something, know that I'm doing so because I respect your opinion enough to either change it or adopt it.

 

[rapt]

Beam 1 will deflect less if I achieve the increased steel ratio in beam 2 by reducing the depth by 40% or more for the example you have suggested. If I had changed the width rather than depth, there would be a much reduced increase in deflections in Beam 2.

But for less extreme changes in steel ratio, the effect will depend on whether you effect the change in steel ratio by changing the beam depth or beam width.

What it gets down to is there are too many variables involved to base it on a simplistic rule like this.

Why not just calculate expected long term deflections based on a rational and proven model and get rid of the guesses.

I still stand by my statement that I have seen a lot of designs where long term deflections were a problem for lightly reinforced slabs and beams which indicates that the % reinforcement rule does not actually work for all cases.