When is strain to high when analyzing existing concrete beam?

[StructureMan44]

When analyzing an in use concrete beam for moment capacity that has greater compression reinforcement than tension reinforcement (under-reinforced), is there an upper limit for strain in the tension steel?

 

[rapt]

StructureMan44,

There should be but most codes do not specifically define one. Normally if ductile reinforcement is used and the amount of tension reinforcement is at least the minimum requirement (based on cracking moment) codes seem to assume that strain is not a problem.

But there are a few assumptions in there that are not always satisfied in design. The most significant is the ductility of the reinforcement.

Eurocode sets a limit if doing plastic design (assuming steel stress is not limited to yield).

 

[canwesteng]

0.2%, at which point the beam is assumed to fail when the steel yields. Do you mean under service loads?

 

[PicoStruc]

I disagree with canwesteng.

At 0.2%, the rebar yield but the beam is NOT considered failing.

Note that the ultimate moment resistance is located on a ductile plateau in the moment-curvature curve. (strain >>>>> 0.2%)

 

[Jerehmy]

fail =/= collapse. If a reinforced concrete beam tension steel is yielding, I'd consider that it has failed but has not collapsed.

From what I can gather, he needs a relatively high strain on the tension reinforcement before the beam reaches its maximum moment. I think he's wondering what is the limit on tension reinforcement strain.

I don't see how you'd get anywhere near the steel FRACTURE limit before the concrete would crush. I'm not sure there is a limit on tension steel strain. Yielding is good, let's use know there is an issue before failure.

 

[KootK]

I'm with PicoStruc on this one. Under-reinforced beams require rebar strains in excess of the yield strain in order to develop the design moment capacities that we attribute to them. In code: ((e_s >= e_y) =/= fail) AND ((e_s >= e_y) =/= collapse). I dig that notation for "not equal".

Check this out: Link. The usable rebar strain is obviously a function of the rebar material, bar size, and application. It seems that the value is likely to be at least an order of magnitude larger than the yield strain.

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.

 

[StructureMan44]

Thanks guys. I have a situation where we are looking to add a large tank to a 19in deep continuous slab on grade centered between grade beams on piles. The reinforcement is #11@12in on top and #10@12in on the bottom. I suspect the #11@12in were needed for negative moment at the grade beams and they decided to extend them the full length of the slab. I plan to initially conservatively assume the slab is unsupported from below. I haven’t dug deep into this yet but considering positive moment at the center of the slab it looks like the tension steel at the bottom will develop a lot of strain before the extreme compression concrete at the top reaches ecu=0.003in/in. This is why I was wondering if there is an upper limit to the strain in the tension steel.

 

[KootK]

I haven't quite sorted it out for myself yet, but I know that some engineers will insist that compression steel be tied laterally similar to column bars. That may be missing from your existing grade beams.

My feeling is that, if all else failed, you could say to hell with the crushed concrete and just assume that your beam is all rebar for the sake of flexure. Your moment capacity would then be approximated as phi x As_bottom x fy x (d - d') with phi = 0.9 (ACI). Your neutral axis would be fairly low on the section at yield and your bottom steel strain wouldn't be so bad.

Assuming normal cover, it takes a pretty steep strain diagram to have 0.003 in the concrete while, right next door, having less than 0.002 in the compression steel, which must be true. In short, my gut tells me that a moment capacity value very near to your ultimate moment capacity will be achieved when the top steel and compression concrete are still in a fairly elastic state.

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.

 

[canwesteng]

My line of thinking is the same as Jeremy. If you see a concrete beam with the steel yielded, replace or repair it, as at that point it will have large cracks that the steel will not force shut.
There is no limit on strain for ultimate load cases associated with collapse for the steel that I know of.
For the OP, consider an ultimate load case with appropriate factors to make sure the slab is appropriately sized for strength, then use appropriate factors for service loads and check deflections (using cracked moment of inertia, and simplifying conservative assumptions when needed). That should basically cover it.

 

[rapt]

A beam is not assumed to fail when the steel strain reaches yield in tension. It is assumed to have reached its maximum capacity.

This is a conservative assumption as the stress strain curve continues to increase after yield to a peak that could be at a strain of 1.5% (very low ductility steel) to 10-15% for Earthquake class steel. Plastic design normally will include for this increase. Normal designers forgo the increase for simplicity of calculation.

Eurocode suggests that the limit is .9 of the peak Strain, not the yield strain if this increase is allowed for.

Just make sure that ductile reinforcement (> 5% peak strain) has been used.

 

[IDS]

Under-reinforced sections are defined as those where the tension steel yields before the concrete crushes, which is a desirable condition. It is not related to the ratio of compression steel to tension steel.

For under-reinforced sections the proportion of compression steel makes little difference to the behaviour. If the steel is in the compression zone then it will slightly reduce the depth of the compression block, which will increase the strain in the tension steel at the design ULS condition, but increasing the strength of the concrete would have a greater effect.

Also note that for an under-reinforced section, because the compression zone is shallow, the section will be close to its ultimate capacity as soon as the tension steel reaches its yield strain, at 0.2%.

Most codes do indirectly limit steel strain through SLS requirements for steel stress limits or crack width limits. ACI 318 no longer has these requirements, but still indirectly limits strain, for typical span/depth ratios, with deflection limits.

Not directly related to the question, but I found the article linked below to be interesting background on the ACI approach to stress and crack width limits.

http://http-server.carleton.ca/~tedsherw/Sherwood6.pdf

Doug Jenkins
Interactive Design Services

http://newtonexcelbach.wordpress.com/