Development of flexural reinforcement in footings and pile caps

[TomNally]

Hi, Friends:

Say that we have a 6'x6' isolated footing, 24" deep, with a single layer of rebars on the bottom. Is there any code requirement that the rebar at the edges of the footing be developed by hooks?

Followup and related question:

Say that we have a 6'x6' concrete pile cap, 24" deep, supported by 4 piles. Is there any code requirement that the rebar at the edges of the pile cap be developed by hooks?

To me, a plain reading of 12.10.3 suggests not, but there may be provisions which override that.

Thanks! I appreciate it.

---Tom Nally

 

[ishvaaag]

Omitting consideration of any code:

With the usual practices here (relatively deep footings) they are quite rigid and it may be the case that not only the actual capacity in flexural-tension exceeds that allowed by the added reinforcement, but the one when considering just the flexural strength allowed by the code also is of bigger capacity than that of the added steel, i.e., once the footing cracks in flexural tension the capacity of steel present (even if one meeting code requirements) is unable to prevent crack failure.

I understand the rebar working with the concrete whilst uncracked and then suddenly both attaining a state that cause the collapse of both. So for these cases rebar is just waste.

I once produced a worksheet to design footings of minimum volume for a set of loads that at service level would respect cracking strenght, then reinforced for factored loads and other requirements and found some were in the case above.

One footing of such design should NEVER crack for the LOADS never SHOULD attain the service level. Again, many cover requirements could be relaxed on that standing.

Respect your question, for strut and tie footings, i.e., rigid ones, it is a rationale of the same that the compressive strut must be contained and hence beyond point of lower support hook development able to anchor the force is required. But, curiously, being thick footings, you may be in one of the cases above, even generous rebar may be unable to enhance capacity above that of first cracking, given the stupendous flexural capacity of a tall footing section. Then the rebar would be, again, waste, and given this, its need of having hooks, forfeited. Yes, the section at the rebar, with just the strut and tie mechanism would ensure safety at the factored level, but you may find the flexural requirement stays under the flexural capacity of just the concrete.

For slender footings, the general requirement applies. But anchoring some rebar force just requires that at both sides of the point, enough length of rebar (with the required safety factors and mandatory minimums) be provided to anchor the load in bond. Omitting the minimums, at the end of a bar in some footing, the stress in the rebar is near nil, hence the theoretical requirement of development there is also nil (conservatively forfeited by any mandatory minimum development lengths). Towards the center of the footing, the required development length can be both bigger than the distance of the point to the end of the bar or more than enough; that would dictate the need of development beyond the end in plan out of the state at that point.

Not to forget that has been accepted practice (here) to use welded meshes that anchor the forces by the transverse rebar (one to the other), so it must be quite general the typical situations of uniform meshes having reserve of strength in general to provide the anchoring forces in shear-friction or confinement ways, or, if you want, as proceeds from the stresses actually resulting from 3D solid analyses.

 

[MaddEngineer]

My understanding of it is as follows:

For a typical centrically loaded spread footing the tension induced from bending will be balanced from the opposing ends. Essentially the tension in the rebar will be zero at the tip of the footing and increase as you approach the face of the pier/column being supported and then goes back to zero as you reach the other tip of the footing.

For an eccentrically loaded spread footing the rebar may have to be hooked at the short end, but depending on detailing could be resolved by the upturned footing dowels. If you can't upturn bars for instance you have a steel column and you don't want to hook the bottom bars I think you could probably analyze the imposed net tension and the National Concrete Masonry Association from what I understand states 200psi/inch (Service Load)for bonding strength in concrete, I don't know if ACI has a number but the NCMA value is probably based on some ACI publication.

So a #4 rebar would have a bonding strength of approx. 300lbs/inch, so a 24" runout would give you about 7,200lbs of anchoring force. Check this against your net tension and if the bonding with the concrete is sufficient you probably don't need to hook the bar at the short end. You could also somehow prorate the (full)tension development length based on ACI equations using your net tension as your force to be developed.

Now as ishvaaag stated for the deep footing arrangements that you have noted load transfer may actually be provided by shear (i.e., diagonal tension) or the plain strength of the concrete in bending anyway.

 

[Lion06]

The rebar needs to be developed enough to provide adequate moment capacity at each section. Typically, if it is fully developed at the critical section, then you're good.

ishvaag-
The code has minimum steel requirements to prevent the type of failure you're talking about.

 

[ishvaaag]

Certainly, there are minimum rebar requirements for bending, but not always has been in foundation (footings) be set as high as to prevent fragile cracking failure. In fact till recently the codes and technical books were reticent to state minimum steel requirement for foundations. This mainly because the massive sections of concrete would be producing sizeable amounts over the standing factored stresses or 4/3 of them.

Also, there was a time (maybe here that was so the case till 2005) where foundations without rebar were permitted. It could be argued that mass foundations still be viable technically even now if out of the EHE code (a derivated of CTE ruling reinforced and prestressed concrete).

I was mainly pointing that historically at some times the rationale for laying the mandated quantities of steel in footings have not been as rational as it may seem.

I also find somewhat curious that strut and tie action is in some way the recommended procedure of stating the capacities or required steel in rigid footings (as some simplification of more exact determination) where in rigid footings the likelihood of tensile strength cracking the concrete is the lesser, and so a "cable" "tie" behaviour less likely.

 

[TomNally]

Thanks to everyone.

The reason I ask is because I see example details where the longitudinal tensile rebars are hooked at the cantilever end of a beam. (In 318-08, see Figure R12.5.4 which shows hooked tensile steel at the end of a cantilver.) Yet, there seems to be no ambiguity in this:

12.10.3 -- Reinforcement shall extend beyond the point at which it is no longer required to resist flexure for a distance equal to d or 12db, whichever is greater, except at supports of simple spans and at the free end of cantilevers.

Any additional thoughts regarding Figure R12.5.4 or section 12.10.3?

Thanks again.

---Tom Nally

 

[Lion06]

ishvaag-

That may have been true in the past, but as of right now there are minimum steel requirements to prevent that type of failure.

 

[DaveAtkins]

As has been stated above, reinforcing needs to be developed at every section. A bar which is not properly developed could pull out of a cantilever if it is not hooked at the tip of the cantilever.

But most of the time this is not a problem--the straight development length is adequate--and this is why you don't see a hook at the edge of a footing very often.

For pile caps, I follow the CRSI standard details, which do have hooks at the end.

DaveAtkins

 

[hokie66]

Interesting that, in my experience at least, most footings in the US have only straight bars, while it is standard practice in Australia to use cogs (90 degree bends).

As to Tom's question about the ACI provisions, I think R12.5.4 gives guidance on how to develop a bar if it needs to be developed. But I don't know what 12.10.3 means. It says d and 12db don't apply to cantilever ends and simple supports, but does not say what does apply.

 

[DaveAtkins]

At the tip of a cantilever, moment is typically zero, so the bar does not need to be developed at all. And since you can't physically extend the bar beyond the tip of the cantilever, the Code says you don't need to (obviously).

At an interior point of inflection, moment is also zero, so the bar does not need to be developed at all. However, the location of an interior point of inflection is always a guess, so the Code makes you extend the bar past the location you assume for the point of inflection.

DaveAtkins

 

[hokie66]

Dave,
If that is typical for cantilevers, then what is R12.5.4 all about? The statement in 12.10.3 that d and 12db don't apply to cantilever ends doesn't mean to me that the bars can just stop.

 

[dik]

There is a direct correlation between shear and flexure. There is also a direct correlation between shear and bond force on the rebar. With larger diameter bars, added bond length is required to develop the larger bar, hence hooks are required to develop the bars.

Strut and tie can be used quite effectively for this type of problem and there is a good correlation with test results.

Dik

 

[hokie66]

I agree with the use of strut and tie analysis in these situations. But using strut and tie (or truss analogy), the ties need to be anchored at the nodes. To me, this argues that the ends of bars at cantilevers (such as spread footings) should be developed.

 

[MaddEngineer]

I think the original post was pertaining to footings, where it is understood that high thermal and shear forces should not be an issue.

Just looking at it from a purely logic standpoint if you have a cantilever with a large concentrated load at the end (i.e. high shear) it would probably make sense to hook the bar to reduced chances of diagonal cracking at the tip. Additionally if you have a beam exposed to high thermal forces then it may also make sense to hook the bar at the tip also. But if you don't want to bother analyzing these forces then take the easy road and just hook it, which is probably what happens more often than not even if the hook is not required.

 

[dik]

I've often seen spread footings without a hooked bottom bar. Because of the relative stiffness and due to the uniform loading I don't usually get concerned unless they are large bars because the shear starts from 0 (bond stress similar) to a maximum in a more or less uniform manner (just like the bond stress).

Dik

 

[DaveAtkins]

The bars MUST stop. They can't stick out of the end of the cantilever.

DaveAtkins

 

[Teguci]

First, the code is not a replacement for sound judgement it is a tool to help standardize our sound judgement.

12.10.3 does not exclude hooks from the ends of cantilevers, it tells us that we don't need to extend our development point beyond where it is theoretically needed. This provision has been placed in the code because in the past, concrete bents were detailed without this extension and failed. A shear crack formed at the end of the flexural reinforcement and split the top layer of reinforcement horizontally from the beam causing a failure mechanism.

ACI had a publication listing the history of concrete failures that impacted the code. I suggest that you good engineers out there find a copy of it and read it.

 

[dik]

DaveAtkins... so that's what I've been doing wrong... I figgured once they are buried... no one would notice <G>.

 

[JAE]

Yes, the stress in bottom footing bars at the ends is zero. But just inward from the end of the bar there is progressively higher stress to a maximum at the face of the pedestal (theoretically).

According to ACI, all bars should be developed. So theoretically, 1" in from the end of the bar you have to develop the bar - and it has a little bit of stress there. ACI chapter 12 provides for As(req'd)/As(provided) as a help. It also offers a minimum development length - 12" perhaps - can't remember and I'm away from the office.

So technically, you violate the intention of the code without the exception to the cantilever exclusion, which I think lets you off the hook. No pun intended.

We rarely, if ever, use hooks at the ends of spread footing bottom bars.

 

[hokie66]

The example given by the OP was a 6' x 6' footing, 2' deep. This is not really a flexural element. For a footing of that size to require 24" depth, the bearing capacity must be high, say weathered rock. So it really should be designed like the pile cap of the same size which he talks about, strut and tie, and thus the ends of the bars should be anchored.