Retaining Wall - Flexural Reinforcement from Stem Into Footing 21

[CWEngineer]

I am trying to get some clarification regarding the flexural reinforcement of the stem of a retaining wall into the footing.

Does the flexural reinforcement in the stem of a wall, need to be developed into the toe, such as show in Figure 1 of the attached document. Or is providing a standard hook (12db), sufficient, such as that show on Figure 2 of the attached document? If providing a standard hook is sufficient, can the hook be turned towards the heel?

Thanks in advance

 

[KootK]

Thanks for the sketches Tom -- definitely food for thought.

yes in most occasions these perpendicular splitting forces do not interact critically with the concrete tension forces (e.g. your go to example above)

I'm curious to know where we stand with that example Tom. Consider it as presented, in isolation from the retaining wall business. Is it your opinion that, in that example, the bars would still develop to yield without initiating a concrete breakout failure?

Your rod-snapping and frustrum-pull-out examples do not have global tension forces aligned with the bar perpendicular splitting forces...cheating

1) As I understand it now, having bar splitting forces aligned with global tension forces, makes things worse, right?

2) So if my example doesn't have those aligned tension forces, would that not make my example more optimistic with regard to capacity?

3) If my example is more optimistic with regard to capacity, and still indicates a serious lack of capacity, is there still not a problem?

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.

 

[Tomfh]

Consider it as presented, in isolation from the retaining wall business. Is it your opinion that, in that example, the bars would still develop to yield without initiating a concrete breakout failure?

If the breakout cones are inadequate to resist the tensile uplift then not I don't believe the bars would yield. However I suspect your case would actually yield bars, despite your loading it up with bars. You have 1000 times the area of concrete than you do steel - that equals bar snap not concrete snap. But for the sake of argument yes lets say it will fail in frustrum pullout.

1) As I understand it now, having bar splitting forces aligned with global tension forces, makes things worse, right?

That's my understanding of it. It will break even easier.

2) So if my example doesn't have those aligned tension forces, would that not make my example more optimistic with regard to capacity?

Yes yours is more optimistic than the bad cases and is still failing.

3) If my example is more optimistic with regard to capacity, and still indicates a serious lack of capacity, is there still not a problem?

Your example in plain unstressed concrete. In abominable retaining wall footing we have top steel. We also have the C force at the front face of the wall strutting against the hook, making it harder to pull out.

If you believe your example is a suitable analogy, do you think adding a little bit of extra hook length is going to improve capacity?

This is where I'm at (not arguing, just trying to clarify my own understanding):

-Your examples WON'T break the bars. Cone break-out will occur if going by the numbers (although in reality the bars probably yield).
-135 hook into the bottom of an unstressed reinforced beam WILL BREAK the bar. (Wheeler)
-A 90 degree hook into the opening side (detail (a), U74 )is really bad and WON'T BREAK the bar. This is the one I would call ABOMINABLE
-A 90 degree hook into the toe (your abominable detail) is much better and may break the bar.
-We haven't completely established the difference between a 90 degree standard hook going into the toe (abominable detail #1) vs a hook with full code development length into the toe (your detail #5), That being said, Nilsson series U74, U75, U76, U70 show the range of toe lengths and hook length achieving 94%+ capacity, with marginal increase in capacity as the toe (and hook length) increases.
-Adding a diagonal bar is ideal, but a hassle for a small wall.

 

[KootK]

You have 1000 times the area of concrete than you do steel - that equals bar snap not concrete snap. But for the sake of argument yes lets say it will fail in frustrum pullout.

For the sake of argument, why don't we both just stick to what we actually belive. I believe that the appendix D method that I proposed above accounts generously for the amount of concrete that surrounds the rebar.

our example in plain unstressed concrete. In abominable retaining wall footing we have top steel. We also have the C force at the front face of the wall strutting against the hook, making it harder to pull out.

Agreed. There are somewhat accepted anchorage design methods to account for these things. The footing top steel bumps your phi factor up from 0.70 to 0.75. In Eligehausen's book on anchorage, he cites a method by Zhao for accounting for the influence of the compression force. I've included the method and an updated calc below. That'll get you to within about 20% of what is needed with the normal load factors included.

If you believe your example is a suitable analogy, do you think adding a little bit of extra hook length is going to improve capacity?

I really do. While I know that you and CEL don't like the pulley analogy, I really think that it's the key to this. That mechanism allows the tension in the rebar to be turned (or developed depending on your perspective) without relying much on the bond stress form of anchorage. Somewhere between most and all of the rebar tension can be resisted through bearing against the monster strut coming into the rebar bend. The corner condition is kind of a unique animal. In most other STM joints, the bar force goes to zero as it crosses the restraining/developing strut. In the corner condition, the bar tension not only does not drop to zero, it may not drop at all (d_stem = d_footing).

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.

 

[Tomfh]

For the sake of argument, why don't we both just stick to what we actually belive. I believe that the appendix D method that I proposed above accounts generously for the amount of concrete that surrounds the rebar.

I'm not too familiar with appendix D specifics sorry. I don't doubt your numbers, I'm just not sure they accurately reflect the true cone failure strength. Cone failure numbers are usually rather conservative.

In Eligehausen's book on anchorage, he cites a method by Zhao for accounting for the influence of the compression force. I've included the method and an updated calc below.

Good to see someone quantifying this effect!

I really do. While I know that you and CEL don't like the pulley analogy,

I was referring to your cone pullout example. Is that what you referring to?. I was asking if you thought lengthening the hooks will improve the frustrum pullout strength. I don't think it would, and I don't see how pulley analogys work there?

Somewhere between most and all of the rebar tension can be resisted through bearing against the monster strut coming into the rebar bend.

I agree with this very much. The curve can bear onto those solid struts, as opposed to a hook turning outwards which has only unconfined concrete in tension to bear upon.

Where we seem to differ is your belief that we still need the full tension force at the exit of the bend, i.e. the pulley analogy, where we have full bar force occuring at the exit of the bend/pulley. I don't understand this at all. If there is development/bearing occuring along the curve, and most of the bar load is strutting directly off the curved portion, why this need to start all over again at the end of the curve? Why reset the development counter to zero if most of the load is already gone? It doesn't hurt to extend the bar, and personally I extend the bar all the way just for good measure. However I don't really understand why it needs it.

Consider Nilson's U76, which has a very short hook, around 200mm, and it's achieving 94% efficiency, exactly the same efficiency as U78, which has a hook around twice as long.

 

[TehMightyEngineer]

Just out of curiosity, what would be needed to actually test some joints?

If I made a case to my boss I might be able to donate some precast joints cast to simulate a retaining wall joint that could be tested. Heck, maybe even the University of Maine next to one of our plants might be interested and I know they have the equipment for this sort of testing. If not them, and if my boss approves, we could ship them cheap to someone willing to test them. I'd love to see this happen.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries

http://www.americanconcrete.com

 

[CELinOttawa]

That is an awesome idea! Sounds like a good basis of a Master's project too...

To me a full scale test is easy and simple:

- Built using small bars and thickness, say 10M and 200mm thick.
- Bars are instrumented with strin gauges before and after the bend.
- Probable cmpression strut is instrumented.
- Wall is placed and blocked in position.
- Compacted granular is placed behind the wall and an actuated UDL is placed onto the fill pushing down until we achieve failure.
- Record all data on the bars and see what is actually going on...

 

[KootK]

Just out of curiosity, what would be needed to actually test some joints?

I'd do it as a T-Joint test like Nilsson's but with the standard, inward hook detailing. In the photos below, you can see the expected crack pattern starting to form up.

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.

 

[KootK]

I was referring to your cone pullout example. Is that what you referring to?. I was asking if you thought lengthening the hooks will improve the frustrum pullout strength. I don't think it would, and I don't see how pulley analogys work there?

No, I was referring to the retaining wall case where the pulley mechanism would come into play. I agree that the hook extensions would make little to no difference in the straight frustum pullout scenario. In my opinion, there is a significant difference between a development case and a corner joint case. With the frustum pullout being just a straight up development case, the extension would have no benefit.

Where we seem to differ is your belief that we still need the full tension force at the exit of the bend, i.e. the pulley analogy, where we have full bar force occuring at the exit of the bend/pulley. I don't understand this at all. If there is development/bearing occuring along the curve, and most of the bar load is strutting directly off the curved portion, why this need to start all over again at the end of the curve? Why reset the development counter to zero if most of the load is already gone?

Yeah. For now, let's say that we're dealing with what is a "normal" retaining wall detailing configuration in my market. The stem bars turn the corner and become the toe flexural reinforcing. Here's how I see it:

1) The stem creates a moment demand (Ms) at the joint.

2) The heel contributes some of the joint moment (Mh) resisting Ms.

3) The toe contributes some of the joint moment (Mt) resisting Ms.

4) Mh + Mt = Ms

5) The existence of Ms means that there is some flexural tension in the rebar at point "A" in the diagram below. This is just M/jd stuff.

6) The existence of Mt means that there is some flexural tension in the rebar at point "B" in the diagram below. This, again is just M/jd stuff.

7) Taken together, #5 and #6 mean that there is tension on both the vertical and horizontal legs of the corner bar. It's only the imbalance that needs to be dealt with as bond stress style development. Just like the sketch that I posted before but with unequal vertical and horizontal tension in the general case.

If you disagree with any of that, please let me know which parts.

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.

 

[Tomfh]

No, I was referring to the retaining wall case where the pulley mechanism would come into play. I agree that the hook extensions would make little to no difference in the straight frustum pullout scenario.

Noted.

If you disagree with any of that, please let me know which parts.

Agree there is flexural bending stress and hence reinforcement stress at point A and point B.

And yes if most of the moment is resisted by toe and if you using the same bar for toe and stem then OF COURSE you get the same load AsFy in both of them. It more or less resembles your pulley diagram immediately above.

However only a residual portion of the applied load at A remains in the bar at B, and vice versa. If using a hook to resist A and a straight bottom bar to resist B then you no longer need the full load at the hook tail, because the straight bar is now carrying most of that tension. I believe you are double counting in assuming you need full tension load at the exit of the pulley. The load from A doesn't get gobbled up around the hook by the struts and then reappear fully intact at the exist of the hook.

 

[KootK]

OF COURSE you get the same load AsFy in both of them.

I believe you are double counting in assuming you need full tension load at the exit of the pulley

The thing that I'm about to clarify may already be crystal clear to you as I've already clarified it several times above. Probably just semantics now. That said, I'm going to clarify it one more time because it's critical to this discussion:

1) WHAT I HAVE SAID: in general there will be some level of tension on both the vertical and horizontal legs of the corner bars. That level of tension may be the same but, in general, need not be.

2) WHAT I HAVE NOT SAID: the level of tension will be AsFy for both the vertical and horizontal legs of the corner bars.

Moving along... I think that we're very close to isolating the core issue now.

Please let me know what you think of these statements which I believe to be true:

1) 100% of the moment in the toe must get transferred to/from the stem.

2) #1 is true even when using standard hooked stem bars and full length footing bottom bars.



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.

 

[Tomfh]

wHAT I HAVE NOT SAID: the level of tension will be AsFy for both the vertical and horizontal legs of the corner bars.

But that's what your pulley diagram clearly shows? AsFy in both. Isn't that the whole reason you call a regular hook an abomination? Because you say it doesn't give full development length along the base of the footing, and thus doesn't resolve the stem load?



1)


and 2) YES

 

[KootK]

But that's what your pulley diagram clearly shows? AsFy in both

But now, given all that follows, it is clear that I do not expect it to be AsFy tension at both the horizontal and vertical legs, right?

The tension on the vertical leg could potentially take on any value from zero to As x fy. Same goes for the tension on the horizontal leg.

Who says they're the same? Certainly not me...Because, in the general case, you're not taking it all out at the exit bar.

I don't know what to say Tom. I've already clarified, repeatedly and at length, my opinion that 2X is the upper limit and that there is no need for symmetry.

7) Taken together, #5 and #6 mean that there is tension on both the vertical and horizontal legs of the corner bar. It's only the imbalance that needs to be dealt with as bond stress style development.

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.

 

[Tomfh]

it is clear that I do not expect it to be AsFy tension at both the horizontal and vertical legs, right?

I thought you did expect it. Hence you saying you need the full Ld + ??? lap on the horizontal.

If in fact you do not expect AsFy tension horizontally, why then is a shorter hook an abomination? Why the need for full development length on the horizontal if you agree there's a lesser tensile force on the horizontal leg?

 

[KootK]

I thought you did expect it. Hence you saying you need the full Ld + ??? lap on the horizontal.

Nope. Absolutely not. I expect there to be some significant tension coming in through the horizontal leg. And we can calculate that easily as (M_toe / jd_toe). For walls with heels and toes, it will usually be less than As x fy because:

1) M_toe = M_stem - M_heel and;
2) jd_toe >= jd stem

I believe that we're now in agreement regarding the joint mechanics when the stem bars become the footing bars. In what follows, I'll assume that we're talking about the condition where the stem bars terminate in a hook and there is a separate mat of bottom reinforcing.

Why the need for full development length on the horizontal if you agree there's a lesser tensile force on the horizontal leg?

Because, fundamentally, I don't believe that it is a matter of rebar development. The bottom mat of toe reinforcing must transfer 100% of it's tension around the corner and into the stem bars. As such, I see the primary function of the horizontal legs of the corner bars as being to lap splice the footing bars with the stem bars. Technically, the bars do not need to be spliced for As x Fy. They only need to be spliced for the tension in the footing bars at the splice location. Of course, most designers are just going to splice for As x fy anyhow to keep things simple.

The splice that I'm talking about is shown in the bottom right of the sketch below (diagonal struts between green and red in plan). In forcing the rebar tension to "turn the corner" so to speak, most of the job will get done via bearing of the corner bar on the concrete strut coming into the corner. What cannot be statically resolved that way will manifest itself as some magnitude of bond stress around the bend. My sketches, and the clips from the curved bar node article above show just that.

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.

 

[TehMightyEngineer]

Technically, the bars do not need to be spliced for As x Fy. They only need to be spliced for the tension in the footing bars at the splice location.

I just want to highlight this because it seems like the key to getting both of the arguments to find a common ground that I've seen so far. Though I will fully admit I'm now having trouble following each of the arguments completely.

Professional Engineer (ME, NH, MA) Structural Engineer (IL)
American Concrete Industries

http://www.americanconcrete.com

 

[Tomfh]

Because, fundamentally, I don't believe that it is a matter of rebar development. The bottom mat of toe reinforcing must transfer 100% of it's tension around the corner and into the stem bars. As such, I see the primary function of the horizontal legs of the corner bars as being to lap splice the footing bars with the stem bars. Technically, the bars do not need to be spliced for As x Fy. They only need to be spliced for the tension in the footing bars at the splice location. Of course, most designers are just going to splice for As x fy anyhow to keep things simple.

Ok, to clarify, you want the increased hook length not to anchor the hook, but to give the bottom bars something to grab onto?

 

[KootK]

Precisely. I suppose that, in some very low demand situations, a standard hook might suffice as a splice.

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.

 

[Tomfh]

Precisely. I suppose that, in some very low demand situations, a standard hook might suffice as a splice.

I think we should assume the bars are working hard!

You posted nilsson's image T13 and T16 above, which appear to show a hairpin detail, and a pair of L-bars detail. (it's a bit hard to see exactly)

Could you please post the reinforcing details of these, and the joints capacities. I'd be interested to see the test results of how the horizontal bar's degree of continuity with the vertical bar affects the capacity.

 

[KootK]

Here you go Tom.

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.

 

[Tomfh]

Great. Thank you.

You have a point that a single unbroken bar or a full tension lap provides a stronger joint than a short lap (or no lap), hence T13 having lower capacity than T2, T12b, T16. The horizontal bar force can get into the joint more directly with a continuous bar or longer lap bar.

However the T13 hairpin doesn't perform that much worse, and it has no lap whatsoever between the horizontal bar and the hairpin! So I disagree you need to provide AsFy worth of lap between the horizontal and vertical bars. It's not a simple lap case where we have to provide Ld. Even cases T2, T12b, T16 don't necessarily loo like full tension laps.

Our case with a short hook lapping with the horizontal bars presumably does better than the hairpin with virtually no lap, but not quite as good as a single unbroken bar or a fully lapping bar.