Moment along a rebar lap splice 2

[JSA2]

A cantilevered retaining wall that I am designing has vertical bars, lapped with vertical footing dowels. The wall height from top of footing is 8-feet. There are footing dowels (#4 @ 9") which extend from the footing, 3-feet into the wall. They are lapped with vertical wall reinforcing (#4 @ 18") which is 8-feet long; therefore, the lap is 3 feet at the bottom of the wall.

The footing dowels are designed for the moment at the top of the footing. The vertical reinforcing bars are designed for the moment at the top of footing dowels - at the 3-foot height. But the moment changes pretty rapidly along the length of the lap, because it is a cantilevered retaining wall.

How do I know that I don't have a development deficiency at any particular cross section along the lap?

 

[msquared48]

I can see that you are trying tosave steel here, but atwhat cost - your confidence in your design? Why not just design both bars to the moment at the top of the footing and be done with it? Peace of mind is a good thing.

Mike McCann
MMC Engineering

 

[DaveAtkins]

I agree with Mike--however, to answer your question, unless the moment diagram is convex (which it isn't on a cantilever), the bar will always be "more" developed than the moment in the wall.

DaveAtkins

 

[JSA2]

Dave, but the loading is triangular for a cantilevered retaining wall, so the moment is indeed "convex," isn't it? That was actually the source of my concern, as I imagine a critical section at various positions along the lap, I wondered if moment could increase faster than the gradual development (starting from zero) of the footing bar side of the lap.

Thank you both for your input.

 

[DaveAtkins]

No, a convex moment diagram bulges outward, like the moment diagram for a simple span beam. Since the moment diagram for a retaining wall is linear, and development occurs in a linear fashion, your bars will always be developed at least as much as the moment in the wall.

DaveAtkins

 

[JSA2]

Sorry Dave, I think I meant concave. The momenent diagram for a linearly-varying load is parabolic, not linear, right?

 

[kslee1000]

JSA2:

Randomly check required reinforcing at two locations, say 1' and 2' above the footing. For each location, calculate the reinforcing required and make sure the reinforcing ratio is maintained wthin the range of one development length above this specific location/plane. Done.

 

[swivel63]

i agree with mike. some extra bars doesn't hurt anyone.

 

[DaveAtkins]

Yes, the moment diagram will be parabolic, and concave. My mistake.

But, in any event this is better than a linear moment diagram, in terms of development of reinforcing.

DaveAtkins

 

[miecz]

The moment diagram for a linearly varying load is concave (cubic, I think). For a uniform load due to surcharge, it's also concave (parabolic, I think). So if you have the required reinforcing developed at both ends of the splice, you'll have enough developed in between. The problem with adding reinforcing when it's not necessary is that, after a while, people start to think that it is necessary. Besides which, somebody has to pay for that extra reinforcing.

 

[JSA2]

Kslee, this was my thought too. I haven't done that yet, but I suspect when I do, I will concur with Miecz too. Thank you all for your input.

 

[csd72]

assume your strees varies linearly from zero at the end of the bar to full strength at the end of the required lap length.

Now you can create a reinforcing force diagram and compare

 

[Tomfh]

You don't need to explicitly check the forces between the ends of the lap. As Dave and miecz point out, the anchorage builds up faster than the moment.

 

[kslee1000]

JSA2:

Experience can be gained either by open discussion, or self persuasion, depending on the nature of the topic in concern. For this case, I think a quick calculation may provide better understanding and strengthen your conviction for other matters that share the similarities. Have fun.

 

[msquared48]

That's fine, but do it on your nickel, not the client's.

Mike McCann
MMC Engineering

 

[kslee1000]

I think an engineer shall find time to settle his curious mind, trivial or not. None of my clients argues how I spent my time, as long as I deliver the products that fitting their's interests within agreed time frame and budget. Fact of matter is, I would not hesitate to apply the cook book solutions only if there is no doubt. Otherwise, find time and ways to settle it.

 

[ChipB]

Man, you guys are confusing me. And I thought I had a good grasp on retaining walls.

JSA2, I think you need to carefully consider your design.

In cantilever retaining wall design, the dowels coming out of your footing, serve one purpose and one purpose only. That purpose is to transfer the moment from your wall, to your footing. The wall itself, basically creates a vertical force couple. Tension in the steel pulling out of the footing, compression in the concrete pushing into the footing. Never the less, it should transfer the moment into the footing. Most of us turn the bend of the dowel into the toe of the footing. These dowels should have a Class B lap splice (1.3ld) into the wall, and be fully developed in your footing.

The primary reinforcing in your footing should be in the top portion of your footing on the heel side. If reinforcing is needed on the toe side, it should be in the bottom portion of your footing (which is why most of us turn our dowels that way).

If a key is required, the vertical reinforcing should be placed towards the toe of the wall.

I say all of this because your original post doesn't make sense. Hopefully, your footing is thicker than your wall. I can't figure out why you would need reinforcing @ 9" in your footing, and @ 18" in your wall. It doesn't add up. As others have stated, don't make it by such a gnat's behind. There are very few times where I have spaced reinforcing greater than 12".

 

[JSA2]

Chip, My question which started this ONLY refers to the vertical lap splice between the wall dowels and the footing dowels.

The lap is 3-feet and it is at the bottom of the wall. The dowels are designed for the wall moment at the top of footing. The wall verts are designed for the moment at the top of the lap (3-feet above top of footing). The footing dowels are a greater area of steel, say per lineal foot of wall than the the verts.

As you imagine the moment increasing below the top of the lap, the bars which are there to resist this increasing moment (the footing dowels) are not yet developed. But the moment is increasing in what has been described here as a concave cubic shape. My inquiry was for the purpose of understanding whether I only had to check the reinf quantity at the top and bottom of the lap, or if there could be a critical, governing section somewhere along the lap.

 

[Dinosaur]

Well, I may be a dinosaur, but this is a very straight forward question. To terminate a bar in a beam (every other bar in your example is terminated), you need to check three things.

The bar termination has always been the tough part of solving this problem in my experience.

In my copy of ACI 318 (don't ask what year) it appears you should check article 12.10.

Good Luck

 

[ChipB]

Nope. Therein lies your problem. The way you have described your design, the wall verts should be designed for your maximum moment, at the bottom of the wall.

I understand what you are trying to do, but, I think you are going around it from not quite the right angle. I'll try to explain but as you already know, it can get confusing.

You're trying to treat it as a stepped wall, w/ your step being three feet from top of footing. When you do this, you have to lap the reinforcing at the step. If the wall was being formed in two pours, the first of which is 3 feet from the footing, and your design shows that at this location, you need #4@18, then every other one of your #4@9 dowels have to extend out from the top of that 3' pour, whatever length is required (I think around 30" for f'c=4000).

Does that make sense?