Shear Reinforcement when phiVc meets Vu in ACI 318 08

[ishvaaag]

You determine phiVc per 11.11.2.1 of 11.11.2.2 and find your Vu is less than that. Let's call this phiVc1. Then, if you meet the geometrical conditions therein stated, as per 11.11.3 you are "permitted" to reinforce in shear by a method that only acknowledges a lower design shear stress, i.e., a lower phiVc, let's call it phiVc2, that may not meet your Vu above; in fact a design shear stress that when designing reinforcement for punching shear determines where such reinforcement becomes already unnecesary.

It is your interpretation of the code that whenever the lower phiVc2 does not meet your Vu -but is still met by phiVc1- the code makes mandatory to reinforce for punching shear by the stated method? Note that if so it might be making void the use of phiVc1 to determine a thickness without shear reinforcement, for anywhere the plate is not meeting through the corresponding phiVc2 the standing Vu you would be being asked to reinforce in shear, i.e., asked reinforcement, and it would be the scheme for shear reinforcement with the limit reaction what would be determining how to proceed.

Also, by other codes one-way shear checks were (or are still) ASKED AS WELL when the slab is in two way action. Think for example in a slender footing in ACI 318 08. Is it your understanding that by the present ACI 318 08 such checks for one-way shear have been entirely forfeited when in a two-way behaviour of the slab or footing?

 

[ishvaaag]

The previous question is not moot in that it puts into question the rationality of specs within the code. One sees that punching tests may end throwint the cone at 2d or 2h from the face, and still ACI makes a point of having the critical section at d/2 from the face; of course a fragile kind of failure and, again, we have been bombarded over the years with for fragile, say, joints, safety factors must go bigger to deliver common reliability with less unreliable parts. OK. So we go safe. But then we go to design a two-way slab and find that apparently we are able to let it to go unreinforced in shear at twice the shear stress we are "permitted" to practice punching shear reinforcement. And not allowing so might wipe out of the market some significant fraction of postensioning slabs when unreinforced in shear.

This is a reasonable quigmare, but from the technical standpoint I am far more concerned that two tiers of safety are exposed, for, at least, the two are deemed to deliver the asked for reliability in shear at the joint.

And this is quite puzzling from the technical standpoint, for it is asserted that the model code specifications on limit strength are based on statistical reliability, that will give an assesment of when shear reinforcement becomes necessary, be one, or the other. So what comes to the mind in the question is that the touted consistence with statistical reliability is biased by some peer voting, fortunately by expert seniors.

 

[rapt]

Ishvaaag,

There is nothing illogical in it. The concrete contribution to capacity reduces once you are relying on shear reinforcement to take some of the stress.

If you study the latest EC2 for beam shear, a similar effect occurs. If the applied shear is greater than the allowed capacity, Vuc is reduced to zero and the full capacity is carried by the reinforcement!

ACI code requires checks on Beam shear and Punching shear for 2way slabs. See clause 11.1 in the 08 code.

 

[ishvaaag]

Thanks, rapt. I try always to understand the whys of the things, and even seeing that it may produce safer joints, I still see something inconvenient, namely: indefinition.

I mean ... you are "permitted" to reinforce. But, hey, if you don't reinforce you are still within the limit capacity, so some will not reinforce, and will go along with their more fragile joints, and others will reinforce.
I don't see this a particularly good feature of the code when thinking in the cases in which it is considered something mandatory to comply, and if it puzzles me somewhat it may puzzle more those who are to decide legally on the issue with less technical basis. You may do it better, says the code, but we should always we able to do better, safer, no need to permit.

The EC thing from the classical derivation (Mörsch analogy) makes scarce sense, and only rigidity in field action (making the cracks narrower when appear) explains the thing ... in some kind of comeback, there were times when making to work steel beyond 1200 kgf/cm2 was not recommended if you wanted good serviceability; and maybe it was simpler.

Respect 11.11 it is clear that a one-way slab is to be checked such way, and it may be understood that also for two-way, but then again indefinition appears for both the solicitations and the resisting surfaces in shear, that only in the context of direct design or equivalent frame might have an agreeable definition; but what to do with FEM analysis giving vx or vy, and solicitations at joints, etc?

 

[rapt]

I do not see the problem. You do not have to reinforce if the concrete capacity as per 11.11.2.1 of 11.11.2.2 is greater than the applied shear.

If the applied shear is greater than the capacity calculated above, then you have to reinforce and you can allow for a certain contribution towards the joint capacity from the concrete and the rest is supplied by the shear reinforcement. To mobilize the ligatures in punching shear, the concrete becomes less effective.

The more "fragile joint" is deemed acceptable by the code.

If you want to make the joint less fragile, forget ties, add some continuous bottom reinforcement. This will make it much more ductile and it is not mentioned in ACI at all.

 

[ishvaaag]

Thanks again, rapt.

Sometimes insisting in simple common sense issues may be positive; I had -for a brief time- a senior partner that said that to think always pays. And I see that WHEN stirrups are mobilized one may consider the concrete contribution to stand shear to be less. But the question is that we would be using one or the other scheme (reinforced or not) for the SAME solicitation, that will have the bulk of material inserts in the cohesive matrix in quite akin state, particularly when not cracked. I mean, you need the reinforcement because concrete "has" cracked, or you don't need, because "it has not". The real situation for the particular range of solicitations relative to Vc "should" be closer to "has not" cracked. And this "has not" relates the solicitation with state, that then "could" be assumed for both treatments of the structural situation (to reinforce or not). See, since children we are taught that 2+2=4 but here the code leads us to accept 2=4; what only would be acceptable in what in spanish would be called "el teorema del punto gordo" ("the gross point theorem"), your tolerance or allowance for one and the same situation allows to take twice the other value by your chosen decision. The point is that we are talking of one solicitation and state, and not one with concrete more degraded -"cracked"- than the other, except notionally, of course.

The issue is not entirely dissimilar respect minimum steel for ductility in flexure when the design moment is hugely exceeded by the first cracking moment. I mean, you may be asked to add "a lot" of steel on the minimum steel for ductility to ensure ductile behaviour, but for a solicitation never, by the code loadings, to be present.

And in fact once one OCT (the third party supervisors in Spain for insurance for dwelling construction) through its "by the -its interpretation- letter" asked us to so provide "anywhere" -in more than rheological minimum rebar- in a foundation mat, that we managed to reduce to max positive and negative zones, where the mechanical requirement was more than enough to cover it.

And the designer then may rightly ask: but does the cracking moment covers the design moment or not? Or is it that the design moment is to grow magically over its rational calculation only to ruin the design and cause a fragile failure? If the intent of the code is to meet such magically grown solicitation, state it by proper aggrandizement of the solicitation, from loadings. If not, it is not to occur, and every rational scheme to stand the solicitations be deemed acceptable, what, your point (and mine's), is precisely what ACI is doing for the unreinforced sections in shear when permitted.

Even if in some past thread EITengineer made clear point that minimum steel for ductile flexural behaviour is also a requirement for foundations, it is not so the case for punching shear, see 11.4.6.1 (a).

And the minimum requirement in ACI itself for minimum flexural steel is not the same when the cracking moment vastly exceeds the design moment, see 10.5.3 (use the traditional 4/3 of design moment). For footings and slabs ACI goes further by dismissing entirely the minimum flexural steel on mechanical behaviour by relegating the minimum to be used to the one to be provided for rheological effects, see 10.5.4

 

[rapt]

Regarding your last point allowing 4/3 of the cracking moment, I agree with you. It has been in the ACI code and I think it is wrong when you look at design of cross-section from first principles basis and look at strains in the reinforcement etc. But that is the problem in many codes.

Interestingly, BS8110 does not require minimum reinforcement to provide a minimum of the cracking moment in RC design either. And its minumum for slabs of any concrete strength is .13%, far lower than the cracking moment for normal concrete strengths.

Unfortunately some of the older codes like ACI and BS have old rules that have not moved with the materials now being used and new understanding of design.