Remaining capacity in RC beam once steel has yielded

[PAK_ENG]

Hi all. I have a reinforced concrete beam that has developed a significant crack on the bottom (almost 1/16").

With the size of the crack, the assumption is that the reinforcing steel in the bottom of the beam has yielded.

How would I calculate the remaining capacity of the beam? Is there a corresponding loss in cross sectional area of the steel once it has yielded? I'm using AASHTO LRFD code. Thanks!

 

[EngDM]

When you calculate the capacity of an RC beam you are already assuming the steel has yielded, and you limit concrete compressive strain. It's not like the beam has "used up" it's capacity and has X amount of capacity left. As long as you aren't exceeding the design loads, and the designer did it correctly prior to stamping, the crack is likely superficial for strength since the RC beam calculation assumes no strength is gained from concrete in tension anyways. I'd be worried about corrosion of the bars since you said you are using AASHTO.

Do you know the reinforcing in the beam? Aside from a serviceability aspect or corrosion aspect (since you are using AASHTO)

 

[ANE91]

If you know the rebar layout and beam dimensions, then you can use strain compatibility to determine where along the M-phi curve the cracked section of beam is at. Same applies if any prestressing is present; the math is just a bit more involved.

Don’t have rebar layout? Ask for as-builts or test with GPR. (My preference is to do both.) Otherwise, do a load test.

 

[Tomfh]

Without continuity elsewhere the remaining capacity is zero if the steel has yielded.

Are you sure it’s yielding? Do you have other information?

 

[canwesteng]

If the steel truly has begun yielding, the crack on any normally sized beam is going to be a lot bigger than that. Did you test a beam to failure in undergrad?

 

[HTURKAK]

Hi all. I have a reinforced concrete beam that has developed a significant crack on the bottom (almost 1/16").

Is this one crack along the beam? Can you post a picture ?
If the steel yielded , the remaining capacity of the beam would be negligible.

 

[ANE91]

Why are multiple engineers saying that yielded tensile reinforcement = failure? That makes no sense to me. We take advantage of post-yield strength all the time, particularly in seismic areas.

Failure by design is when the concrete crushes in the compression zone. We make sure that the steel (tensile or compressive, or both) yields well in advance of that, to give occupants/users warning. Steel yield doesn’t mean the beam can no longer carry any load.

In the real world, our elasto-plastic idealizations are conservative.

 

[phamENG]

If the steel has yielded, then more load will result in more deflection and higher concrete compressive stress, but the steel will not continue to elongate just because it has yielded. We simplify the stress/strain curve of steel to a linear elastic zone and a horizontal plastic zone that would imply infinite strain at yield, but that's not the case in reality.

When the load reduces such that the tension in the bars is something below yield, the steel will rebound most but not all of the strain. So the crack won't close entirely. But that doesn't mean the bar is still at yield.