Why not, SEIT? In your example you can solve for the axial load P = 16.67*12/2 = 100, then M = P*S/A = 200.
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?
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.
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!
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.
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.
I never said it reduced capacity, only that if you take it into account in your calculations then you get a lesser capacity. In this case actual and calculated can be very different.
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.
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.
I agree with csd72. When your cross section is near the point of changing from under-reinforced to over-reinforced, you can add a little compression steel to increase the section strength and maintain the under-reinforced requirements (ie. compression steel in compression block zone). This is a simple case of the rebar increasing your compression block EI value. I have done this on precast jobs when the architect has spec'd a specific cross sectional size and the EOR has already generated a complete set of drawings without the precast company's input. I am not saying it is cost effective, but it sure did reduce the number of site changes.
"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.
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.
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.
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.
Without reading all reponses, I would have to say that compression reinforcement is ignored even if it is there.
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.
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!
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.
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!
