Partially Developed Reinforcement 1

[cam_b]

In all the engineering offices i have worked. When looking at an R.C. cross-section with partially developed reinforcement, the general approach has been to reduce the bar area by multiplying the area of the bar by the percentage of the bar development. However, the phi factor is not usually changed. So it is treated as a smaller but still ductile reinforcing bar. But if the bar can never reach its yield strength because its not fully developed, then i don't see how that bar could fail in a ductile manner. I'm just wondering how others handle the situation of partially developed reinforcement?

 

[KootK]

Prorating the anchorage length is common but assuming that represents a smaller, ductile bar is not. If you need yielded bars for seismic fuse development etc, then you need to be considering the properties of the real, physical bars.

 

[cam_b]

KootK, thanks for the response. I generally agree with you. To give you more context, i am writing some reinforced concrete design software and I'm trying to figure out how to handle situations where reinforcement is partially developed. For example, a few common situations i need to consider are:

1) For a beam or slab where there is additional top steel over an internal column. How do i calculate the moment capacity near the terminated ends of the additional top steel. Because those bars cannot reach their yield stress, so i don't think simply reducing the area based on the development is the correct answer. But it is certainly a common approach, at least where i live.

2) For a beam or slab above a corner or edge column. If that column has any fixity, then there will be significant moment near the edge of the slab, but the slab steel is unlikely to be fully developed (at least not according to the Australian concrete code, I'm not sure about others.)

My thought is to do two calculations, one where the partially developed bars are included, but a reduced phi factor is used (similar to an over-reinforced section, or low ductility steel) and another where any partially developed bars are ignored, but the normal phi factor is adopted. Then adopt the larger of these two capacities. It would be great to hear any thoughts you have on this if you don't mind.

 

[KootK]

My thought is to do two calculations, one where the partially developed bars are included, but a reduced phi factor is used (similar to an over-reinforced section, or low ductility steel) and another where any partially developed bars are ignored, but the normal phi factor is adopted.

I don't love the reduced phi factor method. To me, this issue feel binary. Either the bar pulls out of the concrete or it doesn't.

But it is certainly a common approach, at least where i live.

Agreed. That's how I see it in software, textbooks, and practice. Basically the sketch below where you construct a flexural demand to capacity graph that acknowledges the available tension picking up as bars come on line.

Is your question really whether or not the above is appropriate? Frankly, I question that myself. Once one commits to a flexural capacity calc that assumes that the concrete and rebar hit plastic strain levels (0.003 / 0.002 ish), it seems to me that that all bars on either side of the study section need to be fully developed. The best I can tell, we must implicitly assume that the new bars coming online accrue stress slowly and probably are not fully in adherence with the plane sections remaining plane assumption.

I feel that it is accurate to say that new bars coming online represent a local, disturbed region rather than a Bernoulli region.

 

[rapt]

There is a phi factor built into in the bond calculation for reduced capacity of the reinforcement. In Eurocode, which actually provides the basic calculation , converting material factors to equivalent phi, that comes to about 1.15 / 1.5 = .75. This is built into the Australian code development length formula. I assume it is in others also.

As long as you are not relying on reduced development within a plastic hinge zone, I would not think it is a problem to assume a reduced available stress in the bar. Though you are not reaching yield, of the bar, you are not relying on it for plastic rotation away from plastic hinge zones.

 

[cam_b]

KootK,

Not adhering to the plane sections remaining plane assumption certainly makes sense.

Rapt,

I can see how you could apply this approach to development of reinforcement at internal spans. But what about edge or corner columns where fixity between the column and slab attract a negative moment in the slab. Because it may not be possible to develop the top bars in accordance with the relevant code at the point of maximum moment. Would that not potentially result in a plastic hinge being assumed in a non-ductile area? or am i misunderstanding your comment.

 

[rapt]

If you limit the bar size, you could ensure the bar can develop yield at the critical section for bending near the inside face of the column. So the maximum bar size would be dependent on the support length.

In ASS3600, you would get 50% development from the cog, plus the length to the critical section. It is no use asking this of ACI designers as it says you get 100% development from the cog at the end!

 

[cam_b]

rapt,

Fair enough, that makes sense. Thanks for the response, that has really clarified how to approach partially developed reinforcement.