Creep effect combined with cracked section to check slab vertical deflection ?? 3

I use Ian Gilbert's braking factor and effective stiffness. See sections 4.2 and 4.3 here:

Thanks Steveh49.
That's as per AS code. I'm looking for ACI guideline regarding this.

Of course you should consider creep. When done according to some standard (e.g., ACI), the procedure is straightforward, and yet, the deflection is probably under- or overestimated by quite a large margin, as is typical for RC structures.

To calculate plate cracked stiffness by some analytical method (and then implement the reduction in software), I would reduce the stiffness by first calculating the transformed section in two orthogonal directions, and then take the ratio of uncracked 2nd moment of area to average (in the two directions) cracked 2nd moment of area and apply that ratio as a reduction to the elastic modulus. Keep the poisson´s ratio to simulate the effect of torsional rigidity, which is always present to some degree also in cracked slabs.

If you wish to get very scientific about this, there are publications (both European and American) that address this, including "FIB 2010 model code" and "FIB bulletin 45, Practitioner´s guide to finite element modelling of reinforced concrete structures (2008)".

If I remember correctly, creep is a long-term phenomenon due to the "sustained" load. It usually does not possess a problem for the typical slabs, except for the slab that carries a significant deadweight such as heavy equipment. This article has a few leads that might interest you.

The Gilbert method didn't make it into the Australian code. Its validity for design is based on the code allowing 'refined calculation' by other recognised methods. It's based on fundamental concrete behaviour so equally valid if designing to ACI's 'more comprehensive analysis' provisions.

le99,

Self-weight is usually a significant portion of the weight of a slab, particularly if it is not prestressed. Concrete creep is also not strongly dependent on the load level; minor loads can cause significant creep in the life-span of an RC slab. Creep will creep (no pun intended) into the slab, in time, with the same certainty that the sun rises and sets each day.

NewbieInSE:

You shall review the ACI provision below.

ACI318-11 9.5.2.5 — Unless values are obtained by a more comprehensive analysis, additional long-term deflection resulting from creep and shrinkage of flexural members (normalweight or lightweight concrete) shall be determined by multiplying the immediate deflection caused by the sustained load considered, by the factor λΔ

(9-11)

Gilbert's books and papers on Long term effects cover general theory as well as ACI, Eurocode and Australian codes. The code part of it is really only material properties. Deflections do not work differently in ACI code countries!

You need to worry about more than creep. Depending on the design, shrinkage can have a much larger effect than creep.

If you are not going to calculate it properly and just use fudge factors, use the ACI code multiplier for long term effects, ingoring the compression reinforcement reduction unless you have a relatively deep heavily reinforced section, multiplied by the cracking effect you are suggesting.

Result will be 5 - 6 times the short term uncracked deflection for RC members.

but the best idea to account for all effects is to do the real calculations properly.

Thanks all, sorry for being late.
I got the gist.

rapt said:

wouldn't u consider the effect of top reinforcement in calculating the vertical deflection of a 6" slab? The thumbrule multiplier which you mentioned to be 5-6, is it 2.5*2? 2.5 for cracking (40%) and 2 for creep (not considering top reinf.)?

Click to expand...

I thought a "quote" was to quote what I said!

Top reinforcement will only have an effect on both creep and shrinkage warping deflection if it is in the compression zone. It is doubtful if that would be the case in a 6" slab. And to be fully effective it has to be in a fairly highly compressed zone, so much closer to the compression face than the neutral axis, not near the neutral axis.

So, no never in a shallow member or a lightly reinforced member.

Where are you getting a creep factor of 2 from. There is a creep and shrinkage multiplier of 2, resulting in a deflection multiplier of 3. This is not the creep factor for the concrete. A creep factor of 2 will not necessarily result in an increase in deflection of 2 times. The long term deflection multiplier of 2 is not the concrete creep factor. It is an estimate of the combined effect on long term deflection of creep and shrinkage.

6 comes from cracking with tension stiffening of about 2 and creep and shrinkage multiplier of about 3 to give 6 times for the total long term deflection.

The top reinforcement will affect shrinkage warping even if the compressive stress zone stops above the reinforcement. Top reinforcement doesn't reduce the compressive creep if below the compression though.

Thanks rapt and steveh.
I understood.

Steveh49,

The effect of reinforcement on shrinkage warping is based on the distance of the each reinforcement layer from the neutral axis.

So unless the section is uncracked, the compression face reinforcement will not exactly balance out the tension face reinforcement. For T-beams it is even worse.

If the compression face reinforcement is below the neutral axis, it is tension reinforcement and causes added shrinkage warping.

It's different if cracked compared with uncracked, but the top reinforcement still reduces shrinkage warping compared with no top reinforcement.

Steve49,

Only if it is in the compression zone. That will probably not be the case in a 6" slab mentioned above.