Reinforced concrete beam (fixed end changed to pinned end)

[deereman]

I need to increase the moment capacity of a few reinforced concrete joists by adding carbon fiber reinforcement to the bottom side only. The joists, originally built in 1958 appear to be designed with fixed ends. When I analyze them with the new loads and fixed ends, the moment is too high in the top. If I analyze them with pinned ends I can install enough reinforcement in the bottom to get them to work. If I do this, will a crack form perpendicular to the joist over the girder and then become a pinned connection? The joists were poured monolithically with the girders.

 

[hokie66]

I assume that rather than fixed, you mean the joists are continuous. Flexural cracking could occur, but that wouldn't form a pin. The amount of overstress would have to be assessed.

Have you checked the shear capacity of the joists? This is often a controlling factor in one way ribbed floors.

 

[deereman]

Yes, the joists are continuous with negative reinforcing at the girder. Under original loads, the joists do not work if you consider the ends pinned with a moment of wl^2/8 at midspan but it does work if you consider a fixed connection with a moment of wl^2/12 at the ends. This is why I assumed they orignaly designed it as a fixed connection. Maybe this isn't correct and it should actually be designed as a pinned connection because depending on the stiffness of the girder it will be able to rotate.

shear reinforcement is o.k.

 

[JAE]

deereman,
What hokie is getting at (I think) is if you allow the end-of-joist top bars to yield, then a vertical crack can occur near the support, essentially negating your Vc capacity.

This means that your Vs capacity from stirrups only must take 100% of the Vu shear (i.e. phi x Vc = 0) (correct me if that's not what you meant, hokie).

What will generally happen is the top end bars will go plastic and you end up with a higher positive moment. You still have a negative moment that has a fixed value based on the plastic condition of the top bars.

 

[hokie66]

You should stop using the term "fixed". Analyze it as a continuous beam.

 

[hokie66]

JAE's post crossed with mine. However, I don't agree that flexural cracking necessarily negates the concrete's contribution to shear capacity. Design codes for beams typically add the concrete and steel contributions to arrive at a shear capacity, but the codes are just a set of rules simplified for our design purposes, not the way beams actually behave. Shear strength after cracking is carried by some combination of tension of the stirrups, shear of the uncracked part of the section, dowel action, and aggregate interlock. Another way of looking at it is to apply a truss analogy, where the stirrups are the tension members, and the concrete between the cracks serves as the diagonal struts. In joists without stirrups (and it was not common in 1958 to use stirrups in ribs), the joists still have shear capacity after cracking due to compression stiffening, similar to what is called shear-friction today.

Perhaps if you can give us a sketch of your actual problem, we could offer better advice. One thing comes to mind...how will you fire rate the carbon fibre?

 

[deereman]

Attached is a detail. Yes, sorry about that, I should be saying continuous not fixed. There aren't any stirrups. I will need to add reinforcement to the web to increase the shear strength. Based on the top bars going plastic, can I then be conservative and design the beam as a simple span and provide bottom reinforcement to withstand the simple beam moment and not provide any additional top reinforcement?

Can we fireproof over the carbon fiber?

 

[hokie66]

One step at a time. How wide are the joists? No tapered ends? Concrete strength?

 

[hokie66]

Another one...are the moments and shears factored? In 1958, working stress design would have been used, but I am guessing that you have factored the loads.

 

[JAE]

hokie66,
Yes, I presume you are correct about still having some concrete shear strength remaining after the top flexural steel is yielded.

But if the top is significantly over stressed in neg. moment bending at the support, I get a little nervous.

It seems that you would have to use either shear friction or the traditional shear design with Vs+Vc.

For shear friction, the top steel is already spoken for by the negative moment. So the only "usable" shear friction steel is the bottom steel - presuming it is fully developed into the support, which usually it is not.

For the traditional shear design - with a crack near the support due to yielding of the top bars, how would I quantify the value of Vc remaining? That's what gets me nervous....so I assume Vc = 0.

 

[msquared48]

With the end condition I see, I would not consider the end fixed either, but that does not mean that reinforcing the end to develop such a moment should not be done, at least nominally to somewhat limit cracking.

Chances are here that any rotation in the beam will be due to rotation at the end joint, possibly inducing torsion into any transverse beam, or moment into a supporting column, which would tend to relieve any moment causing cracking. If you over-reinforce the end of the beam, you will force the cracking to develop, but it is a self-limiting situation, the reinforcing limiting the cracking too.

Mike McCann
MMC Engineering

http://mmcengineering.tripod.com

 

[hokie66]

JAE,
I have never used "shear friction" in my designs, but what I was pointing out is that the bending creates a big compressive force in the uncracked part of the web, similar to the clamping force assumed in the shear friction concept.

deereman,
I agree that designing the joists with simple span moments of wl^/8 is conservative. I would design the fibre reinforcement to take that full moment, as I don't know how the external fibre would interract with the bars. As to how that is done or fire rated, I haven't done it, so can't give advice.

If your ribs require shear reinforcement, how do you intend to do that?

 

[deereman]

Joists are 5" wide at the bottom and taper out to 12" wide at the top. There is no taper at the ends of the span. Loads are factored.

I haven't gotten to the shear reinforcement yet, but I was planning on using carbon fiber there also. Is there a better way? A cheaper way?

 

[hokie66]

Strange. Standard one way pans have/had a 1/12 taper, which would make 12" deep, 5" wide, ribs 7" wide at the slab soffit.

Carbon fibre may be your only option for shear augmentation, but I don't know enough about it to advise. The existing trussed bars would be effective shear reinforcement where they exist.

Just a few more comments: 1. Does your analysis use the clear span between beams? 2. You have 2-#6 bottom and 3-#6 top according to the joist elevation you posted. Is there additional reinforcement in the slab which could be effective as top bars? 3. In 1958, the bars would have been Grade 40, assuming you are in the US.

 

[JAE]

deereman,
According to your sketch, you have the following:

Left end: 1 #6 top
Middle bottom: 2 #6 bottom
First interior support/girder: 3 #6 top (one loose bar and two from the trussed bars from each side).

Is this the area of steel you are using? Just checking.

Agree with the fy = 40 psi.

You refer to wL^2/12. Are you using the standard ACI moment equations or analyzing the spans directly? The ACI equations are conservative (or are supposed to be).

If you analyze directly - be sure you alternate live loads per code (odd spans only, even spans only, three sets of adjacent span loadings, and load on all spans - six combinations altogether).

Also - a few tricks allowed by code not to forget (you may know this already - just in case):

1. Negative moment for design can be taken at the face of support (vs. centerline of support)
2. Negative moment can be reduced up to 10% by code if conditions are right (with an associated increase in positive moment).
3. Shear for design is the shear located a distance "d" from the support - not the shear at theoretical centerline of support.
4. "b" width for shear in tapered joists - typically we used the average width of the joists vs. the 5" you have at the bottom.
5. The diagonal bar portion from the truss bar can be used as shear reinforcement - at least in its short stretch of length. (see ACI inclined bar provisions in the shear chapter 11).
6. Joist shear capacity [φ]Vc is calculated at 1.10 x Vc (see chapter 7 or 8 in the joist definition section)
7. Per hokie - slab reinforcement can be utilized in some cases for negative reinforcement.