Beams with compression reinforcement
Beams with compression reinforcement
(OP)
In beams analysis, if the compression reinforcement does not yield, does the beam then get analyzed as if it has tension reinforcement only?
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Beams with compression reinforcement
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Beams with compression reinforcementBeams with compression reinforcement(OP)
In beams analysis, if the compression reinforcement does not yield, does the beam then get analyzed as if it has tension reinforcement only?
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RE: Beams with compression reinforcement
I will say yes.
I use computor aided softwere for a long time now, so I might be wrong, but in first principle you use the compression strength of the concrete only unless the beam is overstressed.
cheers
RE: Beams with compression reinforcement
RE: Beams with compression reinforcement
RE: Beams with compression reinforcement
If you want to account for it, use strain compatibility and sum moments about neutral axis.
RE: Beams with compression reinforcement
For compression reinforcement to be considered it must be tied. Check ACI 2005 7.11.
For your slab condition you should neglect any reinforcement in compression.
RE: Beams with compression reinforcement
RE: Beams with compression reinforcement
RE: Beams with compression reinforcement
RE: Beams with compression reinforcement
RE: Beams with compression reinforcement
As long as you account for the moment imposed by the axial force by the moment arm (distance between neutral axis and centroidal axis), it doesn't matter.
Having said that, however, I know it's more common to sum moments about the centroidal axis for columns.
RE: Beams with compression reinforcement
RE: Beams with compression reinforcement
RE: Beams with compression reinforcement
RE: Beams with compression reinforcement
For a slab poured monolithic with beam (T-beam), does this mean that any reinforcing provided in the slab (outside the stirrups) should not be considered when using the rho prime for deflection calcs?
RE: Beams with compression reinforcement
Compression reinforcement in and of itself does little to increase capacity. What it DOES do is increase the ductility of the beam, which in turn will allow you to add more tension steel with an accompanying increase in capacity.
StrEIT.. I do that all the time.. you had me doubting myself with your second post.
RE: Beams with compression reinforcement
If the steel requires tieing, it should be tied whether you include it in the capacity analysis or not.
As for the location of the axis for moments in compression (or tension) members, it depends on the position of the beam/strut in the structural analysis. Assuming that the columns were modelled as line members placed on the centroidal axis then the resistance moment should also be about the centroidal axis. You can do that either by taking moments about the centroidal axis or by taking moments about the neutral axis, then adding the moment due to the applied axial load applied at the centroid (making sure to get the sign right!)
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Beams with compression reinforcement
I have a very simple example that I think will make my point. The example is for a homogeneous material, but the same principle applies. Look at a 1"x12" plate with an axial load of 100k and a moment of 200k-in (about the strong axis). This results in a stress distribution of 16.67ksi at the top and 0 at the bottom (putting the neutral axis at the bottom fiber). Because the entire section is in compression, it will be much easier to see my point. We have a single compressive force acting at 2" above the centroidal axis (12*2/3-6). If you take this compressive force about the centroidal axis you will get the correct moment of 200 k-in. If, however, you take the moment about the neutral axis (the bottom fiber that is unstressed), you will get a moment of 100k * 8" = 800 k-in, which is not correct.
RE: Beams with compression reinforcement
RE the original question, this has been answered above.
RE Tying of compression reinforcement, different codes have different rules on when steel must be tied. Some do not require tying os smaller bars, some do not require tying depending on the stress level in the bar. At service level stresses, tying is not normally necessary, only for ultimate strength.
RE: Beams with compression reinforcement
You're forgetting that the sum of internal AND external forces provides equilibrium.. you've just accounted for the interior forces.. Take that 800 k-in moment from the interior forces and add the moment from the point load -100 kip*6in=-600k-in and you get 200 kip-in, which is the applied external moment.
I don't know why several people have said that you must take moments about this or that axis.. We could take moments about any axis we want.. For some reason, a lot of engineers tend to forget this very fundamental concept..
RE: Beams with compression reinforcement
And in doing so, you have just transferred it to moments about the centroid!
However, if you have a material like reinforced concrete or prestressed concrete where you are combining materials of different types, the plastic centroid and elastic centroids are not necessarily the same so you cannot assume the elastic centroid, you have to calculate the location of the plastic centroid and do your "transfer" as in your case, or moments about as the rest of us are calling it, in relation to the plastic centroid!
RE: Beams with compression reinforcement
In doing what, exactly, have I "transfered" the moments to the centroid?
The beam can "feel" where I'm summing moments about?
How can so many engineers not get it?! This is one of the most fundamental concepts in statics. It does not matter AT ALL where you choose to sum moments. Equilibrium MUST be maintained no matter how you look at a problem! We choose to sum moments about certain axes for convenience, but ONLY for convenience. I can sum moments about the center stripe of Broadway Avenue and the answer will be EXACTLY the same.
RE: Beams with compression reinforcement
I am just changing the axial load and moment to be a stress distribution. If you consider the forces on one side and the stress distribution on the other you will always get zero moment otherwise there is no equilibrium. You have to look at only the internal forces to get the internal forces.
RE: Beams with compression reinforcement
RE: Beams with compression reinforcement
Yeas. That's what we are saying.
StrEIT.. I'm not sure what we're arguing about. It seems to me that you have proven my point.
You are not really "changing" anything. What you are describing is the internal stresses that RESULT FROM the externally applied loads.
If you take your beam and cut a section somewhere along the length (and assuming your loads are applied at the end and self weight is neglected, the section cut may be anywhere along the length), then the resulting FBD must be in equilibrium. The resulting interior moments and compression result in the stress distribution you have described.
You may sum moments about any point you wish: centroid, PNA, my kitchen counter; the resulting "interior" moment will be the same. In this particular case, the internal moment is exactly the same as the exterior moment, as we neglected self weight. I'm really failing to see how we are disagreeing on this.
RE: Beams with compression reinforcement
If you read my example above, I think it shows that pretty clearly. The stress distribution (0-16.67 ksi) needs to match the internal (or external forces) to be in equlibrium. If you sum moments of the stress distribution (0-16.67ksi) about the neutral axis (the bottom fiber) then you get a different moment than if you sum moments about the centroidal axis. The only reason for this is because there is a net axial load.
RE: Beams with compression reinforcement
From Macgregor (page 492),
RE: Beams with compression reinforcement
It doesn't matter what your loading is. Statics is statics. You cannot choose to sum only internal moments and disregard the free body diagram. An axial load will not change the beauty of statics.
The stress distribution is what it is as a result of the externally applied loads. In the end, what you are trying to determine is the maximum stress in the member.
Try this: apply your axial load somewhere other than the centroid and sum your moments about the centroid. You cannot disregard shear anymore, or the reactions at the support. Now your internal stresses vary depending on where along the beam you cut your section. Which axis would you sum moments about?
RE: Beams with compression reinforcement
I think my statics are working out fine. When you look at the moment acting at a section of a beam - I think I just figured out EXACTLY where we are missing each other. Tell me if I'm wrong. You are thinking of a single element that has applied forces on one side and internal forces on the other side. In that case, I agree that it doesn't matter when you take moments about, they must always sum to 0 to maintain equilibrium. The point I was making earlier in this thread, and trying to reiterate here is that if you have a concrete section with a strain analysis only (such that you don't know what the applied forces are), it is critical that you take moments about the centroidal axis to get the moment acting on the section. In this case you will get a net moment and axial load, it won't sum to zero, because you have no applied forces taht you know about - only an assumed strain profile.
RE: Beams with compression reinforcement
you are specifically referring to columns and the traditional way of computing the moment capacity of a section with a predetermined external axial load.
Summing moments about the centroid in this case certainly makes it easier, as you essentially neglect the axial load itself, as the stresses from the assumed equally loaded cross section essentially "cancel out" when summed about the centroid.
I'm not arguing that it's done traditionally this way (read one of my first few posts); I was just thrown for a loop when people started arguing that the answer (read "physical interpretation") could change depending on how you chose to view a problem. Like you, I also wrote a few Excel spreadsheets to calculate the interaction diagrams in school and now that I remember, I did sum about the centroid.
My argument is that it shouldn't and doesn't matter how you look at it. You could choose to make it easier on yourself by summing about the centroid or you could make more work for yourself by choosing to sum about some other axis. The answer is the same.
RE: Beams with compression reinforcement
RE: Beams with compression reinforcement
You guys need to read what each other is writing, because you are both correct. I believe this to be the case:
You may take the sum of the moments at any point and if in equilibrium they will equal zero. So to solve for an externally applied moment you must consider the externally applied loads i.e. the compressive force. However to simplify this procedure because the compressive force is unknown we can take the moment about the centroid creating a 0 length moment arm. Therefore your both correct!
EIT
RE: Beams with compression reinforcement
In your summation about neutral axis, you are not accounting for the axial force (100 kip) based on which you ended up with your stress distribution. The net result will still be 200 k-in.
RE: Beams with compression reinforcement
Quoting Cool Hand Luke.. "what we've got here is failure to communicate.."
I now understand what you're saying, and you are right. I kept on thinking in the other direction. You've assumed a profile and want to determine the forces that led to that profile.
RE: Beams with compression reinforcement
which summation are you referring to? I think the PDF I posted is fairly clear.
frv-
I wish I got big bucks - I'd settle for middle-of-the-road bucks. I figured we were talking past each other. Once I realized that you were using the full FBD with the applied external loads then it all made sense and I agree.
RE: Beams with compression reinforcement
Agreed. I was doing the summation of moments based on an axial load being applied at the centroid and moments taken about the neutral axis.
RE: Beams with compression reinforcement
Anyway, my 2 cents worth.
In a very lightly loaded beam, taking the compression reinforcement into account may actually reduce the calculated moment capacity (but not the actual capacity). I ignore it in these cases.
Where you have a highly loaded beam and the compression extends well below the level of the reinforcement then it does actually increase the moment capacity significantly.
RE: Beams with compression reinforcement
2 things:
Why would the compression reinforcement reduce the calculated moment capacity? If you are referring to a situation where the compression reinforcement may end up in tension at the top, then yes; but I have never seen a case where the neutral axis is close enough to the compression block for tis to be the case. Maybe it does.
I disagree with your second point; If you start with a beam without compression reinforcement and add some steel within the compression block, all you'll do is reduce the depth of the compression block (which under normal circumstances is a small percentage of the depth of the beam to begin with) meaning your moment arm from your tension steel (the quantity of which which is unchanged) to the centroid of your compression is slightly increased, resulting in marginally higher calculated moment capacity (certainly well below 10%).
RE: Beams with compression reinforcement
It may be helpful to think in terms of an eccentric axial force, rather than an axial force + moment. In the case of the posted example it is immediately obvious that the eccentricity of the axial force is 8 inches above the NA, or 2 inches above the centroid, and that those two statements are saying the same thing.
This discussion reminds me of the history of beam bending theory, where Galileo's incorrect theory continued to be used for literally hundreds of years after Antoine Parent, then Bernoulli and Euler, then Coulomb had all come up with the theory we use today.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Beams with compression reinforcement
that is true and very clear IF you know the external forces. If, however, you're going on just a strain or stress profile than you cant't do that. Well maybe for a steel plate you could, but not for a RC section.
RE: Beams with compression reinforcement
If you know the stress profile of a RC section, you can do something similar. But when would you know the stress profile without knowing the applied loads?
BA
RE: Beams with compression reinforcement
the reason I say it's more difficult for a RC concrete section where you don't know the applied loads (admittedly, the only time I can think of this happening is when constructing an interaction diagram or trying to determine a moment capacity for a given axial load - something in which you're staring with a strain profile instead of applied loads), is because you won't have a neat stress distribution as shown in the PDF I posted. It will have discrete stresses or forces and by the time you determine the location of that axial force you'll have already found the moment anyway.
RE: Beams with compression reinforcement
When you are calculation an interaction diagram for a concrete shape with some reinforcement in it! It is completely unrelated to applied loads.
In doing this calculation at any point on the curve you adjust the moment by a moment equal to the Force at that point on the curve * distance to plastic centroid. This is exactly the same as doing the initial calculation about the plastic centroid, even if frv cannot see that is what he is actually doing!
RE: Beams with compression reinforcement
I carefully chose my words there, I said 'calculated' for a reason. If you use the compression nreinforcement then your lever arm is to the centroid of the reinforcement, but what if your compression block lies entirely in the cover concrete then your centre of thrust from the concrete gives a longer lever arm and therefore a greater moment.
If your compression block is only a small percentage of your total depth then it is not a highly stressed beam of the type that I was referring to. If you have an exceptionally reinforced beam then the compression zone can be in the realm of 30% of the beam depth.
These are obviously the two extreme cases and are definately not the norm.
RE: Beams with compression reinforcement
I think I disagree. If we assume that the minimum tensile reinforcement is 0.0033bd, using 4ksi concrete you get a minimum compression block dimension of 0.00097d (let's say 0.001d for talking purposes). In this case, any "compression" reinforcement will actually be tension reinforcement. Though it may add little to the capacity because it is so close to the neutral axis, it definitely won't be reducing the capacity.
If we look at a case where the compression steel lies in the compression zone, but outside of the compression block (in that area encompassed by c-a)......... this is the only opportunity I see for a reduced moment capacity using compression steel. Here are my thoughts, though, without diving into it too deeply right now. If you have the condition noted above and arrive at a moment capacity, then take away the compression reinforcement, two things will happen - first, the compression block gets bigger meaning the moment arm gets smaller for a portion of the moment capacity. Second the moment arm gets longer for a portion of the moment capacity (the portion using compression steel). I'm not sure how this would shake out with real numbers, though.
RE: Beams with compression reinforcement
I have done the numbers for both extremes and can assure you that it can make a difference though I would never take the compression steel into account unless it was necessary for strength/ductility. My comments above are based on personal experience.
RE: Beams with compression reinforcement
Please re-read the thread. StrEIT and I were kind of talking through each other. We were addressing different issues. Since he had given a specific example, I thought we were talking a specific case with specific known loading. What he was talking about was something else.
csd72.. If you have MacGreagor, read the chapter on compression reinforcement. If not, I'm sure whatever concrete book you have will cover it as well.
The centroid of the compression is most certainly not the centroid of the compression steel. The forces on the cross section must still equal zero. Since you haven't added any tension reinforcement, your compression force must be exactly the same with and without compression steel.
RE: Beams with compression reinforcement
never said that the centroid was in the compression steel, in reality most of it will be in the concrete.
But if you design it using the compression steel then a portion of the compression force will be at a lower level thus lowering the centroid.
I chose my words very carefully but you have demonstrated that you did not read them as carefully.
RE: Beams with compression reinforcement
Brad
RE: Beams with compression reinforcement
csd is saying that adding compression reinforcement can LOWER your bending capacity (on paper, at least).
RE: Beams with compression reinforcement
your words:
"If you use the compression nreinforcement then your lever arm is to the centroid of the reinforcement"
How did I misinterpret that?
The reason I keep harping in this, csd, is because I clearly remember the parametric comparisons of beams in college; keep all other variable the same and modify one to see how it affects the capacity compared to a baseline capacity. Compression reinforcement, concrete compressive strength have very little effect on overall strength. It is misleading to claim otherwise.
Nowhere in my notes, nowhere in Macgregor and thus far never in practice have I seen or heard of compression reinforcement giving you "significantly" more capacity.
What you are describing in your example, is not a "lightly" loaded beam. It is a very lightly reinforced beam (loading is independent of capacity in a flexural member). Again, in this case, your neutral axis will be very close to the top of the beam and maybe you get the answer you experienced; I don't know, but I suspect that if you did, you had reinforcement ratios way outside the norm (as in likely not permitted), but maybe not.
What I'm getting at is that MacGregor, at least, lists 4 reasons for providing compression reinforcement. Increase in strength is NOT among them.
RE: Beams with compression reinforcement
Yes, csd did say it but I doubt that he meant what you have interpreted. He also goes on to talk about the centre of the concrete compression, so maybe he is thinking in terms of 2 separate components of the compression force rather than a single resultant force.
Try designing a heavily reinforced beam that is over-reinforced without compression reinforcement. The compression reinforcement will give a significant increase in capacity if that is the route you take to making the design ductile. The increase in capacity is from a combination of the increase in the lever arm and the increase in the capacity reduction factor (.65 to .9). You do not need MacGregor to figure that out.
RE: Beams with compression reinforcement
You are jumping ahead one step. Please, read my post responding to kikflip.. I stated exactly that point. Compression steel will give you additional DUCTILITY which, IN TURN allows you to add more tension steel and thus increase capacity.
Compression steel in and of itself doesn't do much to increase capacity. That's the whole point of this now-bordering-on-absurd discussion.
Pointing to MacGregor was an obviously failed attempt to end this discussion. I've designed a sufficient amount of concrete beams to know what I'm talking about.
And if memory serves me (I've already begun holiday celebrations), you are not allowed to design a compression-controlled conventionally reinforced concrete beam to begin with. Nobody here was talking about prestressed.
RE: Beams with compression reinforcement
thanks a million.
you brought back my sanity.
who would even think about steel yielding in compression.
RE: Beams with compression reinforcement
Perhaps it's the early holiday celebration, but I'm not sure what you're referring to.
RE: Beams with compression reinforcement
It's known when you design a normal concrete beam section you add two bars in compression to support your stirrups, gives you better sevicablity, or to meet some siesmic detaile requirements.
In case if you have a shallow beam where you need to please the architect, you will need to add the compression reinforcement, having this in mind it is very obvious to double reinforce you section to meet the required strength with abalanced area of steel.
RE: Beams with compression reinforcement
In 99% of cases the contractor puts rebar in as a cage with shear reinforcement so a nominal top reo would always be called up to complete the cage even though its not normally required in the majority of cases.
RE: Beams with compression reinforcement
NO!! .... What are you afraid of? If you do that you been conservative. You should consider the compression steel area.
That statics should be:-
Tensile force on tension reinforcement = Compressive force on reduced balanced section of concrete that your code permit + compressive force on compression reinforcement.
To calculate compressive stress on the steel, calculate the compression steel strain from the proportions of the strain diagram and multiply this value by steel elastic modules.
.....
Compression reinforcement does increase section moment capacity. And also help to form plastic hinge for moment distribution as per code requirement if you don't have the luxury to increasing section depth. Use it!
RE: Beams with compression reinforcement
I chose my wording of the first post carefully, subsequent posts not so much.
My comments are not based on any individual code but on concrete in general. I am on my 4th concrete code now, if you include revisions then it is probably my 12th. Each one has different rules on maximum and minimum reinforcement.
I just do not think that you can make all encompasing statements regarding this.
I did say I was talking about extremes and not the norm.
RE: Beams with compression reinforcement
Actually, some codes do allow design of compression controlled RC beams, Eurocode 2, BS8110 and to a limited extent AS3600 all allow it with appropriate reductions in capacity due to reduced ductility. ACI code was not mentioned in this discussion so it is not a code based discussion but a general one. But it does allow a tension strain of .004 which is in the transition zone and requires a reduction in the capacity reduction factor to about .8 instead of .9!
RE: Beams with compression reinforcement
Guilty as charged; I did not even consider other codes.
RE: Beams with compression reinforcement
RE: Beams with compression reinforcement
BA
RE: Beams with compression reinforcement
RE: Beams with compression reinforcement
BA
RE: Beams with compression reinforcement
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Beams with compression reinforcement
RE: Beams with compression reinforcement
No-one has suggested that it will.
I'm just interested to see what code provisions, in which code, results in the calculated design bending capcity being reduced when you add compression reinforcement.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Beams with compression reinforcement
I cannot believe that there have been 35 replies to this!
Anyway, my 2 cents worth.
In a very lightly loaded beam, taking the compression reinforcement into account may actually reduce the calculated moment capacity (but not the actual capacity). I ignore it in these cases.
Where you have a highly loaded beam and the compression extends well below the level of the reinforcement then it does actually increase the moment capacity significantly.
I don't know how to make the pretty boxes show up when you're quoting someone's post, but this post suggests that the calculated moment capacity can be reduced by adding compression reinforcement.
RE: Beams with compression reinforcement
BA
RE: Beams with compression reinforcement
(quote) quoted text (/quote)
but with square brackets instead of round ones.
BAretired - code provisions often have unintended consequences, and if some code provision results in the design bending capacity being reduced by including compression steel in the calculation I thought it would be interesting to have a look at it, that's all.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Beams with compression reinforcement
BA
RE: Beams with compression reinforcement
As someone said it is possibly an unintended consequence of a code rule..
RE: Beams with compression reinforcement
BA
RE: Beams with compression reinforcement
I have double checked my theory using a spreadsheet based on british standards and have confirmed that it is correct to that code. So I stand by my comments as valid.
As most of the people on this thread are based in the US then I will try and do my proof calcs to ACI code but I will have to wait until I am at home and can access my pdf copy.
RE: Beams with compression reinforcement
RE: Beams with compression reinforcement
I'm not sure whose posts you are referring to, but I have just been asking for information.
Great. Can you supply details please? i.e. cross section details, concrete grade, axial load, code, and bending capacity with and without compression reinforcement. I'd be very interested to see it.
At least two of us are based in Australia. The Australian codes are close to US (at least for beam and column ULS design) but I'm very familiar with UK codes (5400 more than 8110 though, so if there is a significant difference in this context perhaps you could point it out).
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Beams with compression reinforcement
Yes I am talking about extremely light reinforcing and extremely heavy reinforcing. I used the term lightly and heavily loaded which has caused some misinterpretations - hey that comes from doing it in spare 10 second slots between my paid work.
Anyway as I say in my second post these are extreme cases and not the norm.
My point was that you should not always make broad statements about these things.
IDS,
I bet your a Melbournite!
The differnces are mostly in the minimum reinforcement and the material factors although BS8110 has a specific formula for bending which is a bit different to the standard compression block formula.
This definately applies to the Australian method too.
I am working from home today so am not able to scan the calcs in.
RE: Beams with compression reinforcement
Just the cross section details and concrete grade etc will be fine.
(And the picture at the top of my blog front page should give a hint that I'm not from Melbourne)
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Beams with compression reinforcement
Anyway, it doesnt really matter what section you use as long as you have extreme amounts of reinforcement.
A 600x600 section will do, grade 25 concrete.
First case 200mm^2 of tension reinforcement with/without 100mm of compression steel.
Second case same section with 10000mm of tension steel with/without 2000mm of compresion steel.
These are probably outside code limits for reinforcement but I tried to pick some that would significantly show the issue.
I dropped the squared on the above.
RE: Beams with compression reinforcement
According to AS 3600 the first one seems to have marginally higher capacity with the compression steel, and the second one has much higher capacity with compression steel, but it's late here now. I'll have a proper look tomorrow.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Beams with compression reinforcement
RE: Beams with compression reinforcement
I say top steel because it is in tension, past yield in the AS 3600 calc and close to yield in BS 5400.
I used 30 mm cover top and bottom, and 4 no. 8 mm bars on the bottom, 2 no. 8 mm bars on top. I reduced the concrete strength to 20 MPa for the AS 3600 sections, because it is based on a cylinder strength, and used the standard high yield bars (500 MPa and 460 MPa). As you say, the reinforcement is way under the minimum required for a flexural member, but I'm interested in why we get different results.
You can download the spreadsheet I used for the AS 3600 calculation from:
http:
if interested. Let me know if you want a copy of the BS5400 one.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Beams with compression reinforcement
That spreadsheet is based on strain compatability formulii and therefore takes into account the effect that i refer to for a lightly loaded beam. It appears to have an error though as it is showing full tensile stress in both top and bottom steel (something that seems to violate strain compatability).
If you use the classic formulii for concrete bending then you get two formulii
The first is the lever arm between equal amounts of top and bottom steel i.e Asfy(d-d1)
The second is the standard concrete stress block formulii for the remainder of the moment not taken from the first.
If you use this method then you can get less calculated moment capacity when you add top steel. This happens when the centre line of the steel is below the centre line of the rectangular stress block.
It really highlights how different the results can be from different methods.
RE: Beams with compression reinforcement
It doesn't violate strain compatability. The depth of the Neutral Axis is only 17.39 mm (for AS 3600 with top steel) and the depth of the top reinforcement centroid is 34 mm, so the strain at the top steel is:
0.003*(17.39-34)/17.39 = -2.86x10^-3
Elastic stress = -573 MPa > yield
I don't know exactly what you mean by the "classic method", but if it is an approximate method that doesn't take the difference between the top and bottom steel into account, then it isn't surprising that it gives some odd results with extreme steel ratios.
Any method using strain compatability should give almost exactly the same results for any given stress block and steel parameters, possibly with some small variation depending on how the steel in the compression zone is handled. If you deduct the full concrete stress from the steel stress in all steel above the NA (to account for the displaced concrete), then it is possible that if the compression steel is between the bottom of the concrete rectangular stress block and the NA, then there could be some reduction in calculated bending capacity, but it would be very small.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Beams with compression reinforcement
RE: Beams with compression reinforcement
I was using the same formula that I have always used for beams with discrete top and bottom steel, it is also the formula that I was taught at university and what features in some of the texts for the eurocodes.
All formulii are approximate, particularly those for reinforced concrete. But I agree that it is important to understand the limitations of the formulii that you use. This is the point that my original post was aimed at - broad brush statements dont really cover it.
Structural EIT,
A very valid point and I do mention that these are extreme cases. Though if you look at beams with minimum reinforcement and high strength concrete I believe that you can get the same type of thing happening.
When I get the chance to sit down for more than 2 minutes I will calculate some examples based on min and max steel ratios.