Concrete design is very codified. If you are performing a standard design (simple seismic design included) you will not need to do a moment curvature analysis.
Caveat: you really should understand where ductility requirements come from in the codes. You also need to learn how the steel and concrete interaction can change the ductility (e.g. what happens when the steel enters strain hardening).
That's a very general question. A very general answer is that to calculate deflections you need to calculate curvatures (either explicitly, or indirectly), and to calculate curvatures you need to know the moment-curvature relationship.
All codes put limits on deflections, so in fact you do need to do a moment-curvature analysis when working to a code, although sometimes it may be buried in some deemed to satisfy provisions.
Thank you Swivel and IDS. But I am still not very clear. Explain to me when you need to do such analysis with simple illustrations and something I can really relate with to grasp the concept. Thanks guys
If you ask some more specific questions, you will get some more specific answers. I don't have time to write a text book, or even to guess what it is you really want to know.
IDS that's ok. I'm not asking you to write any textbook all i'm asking for is a simple illustration. Please if you don't have time its fine, let those who have time put their comments here. Thank you
I'm just saying you would get more response if your question was more specific.
Probably the simplest example of applying a moment-curvature analysis is calculating the deflection at the end of a cantilever from a single point load applied at the end using FL^3/3EI.
If the moment-curvature relationship was not linear (so EI was not constant), which is usually the case for reinforced concrete, then you would need to divide the cantilever into a number of sections, and calculate the curvature, slopes and deflections of the ends of each section, based on the moment.
The next step up is finding displacement or ductility demand if any section reaches the yield moment.
Thank you IDS, your illustration is very helpful. It leads me to the next question, I am aware there are 2 methods used for moment-curvature analysis (Traditional approach and ACI method). Please do you any material that treats the traditional approach well? I am particularly having issues with the determination of ultimate moment. You need to determine fsu (ultimate stress in steel) which is a function of ultimate strain in steel. But ultimate strain in steel is a function of the depth of neutral axis which we assume initial and try other values depending if C=T. The problem becomes difficult if the steel material experiences strain hardening. Hope you got my question IDS?
I'm not sure what you mean by the "traditional" and "ACI" methods (I am not based in the USA, although I am an ACI member). Am I right in thinking your focus is on analysis approaching and after yield of the reinforcement?
The basic method, as I understand it is:
- Assume a strain at the compression face
- Find the depth of NA that satisfies equilibrium (i.e. resultant reaction = - applied axial force)
- Find moment and associated curvature
- Repeat for different strains until the required range of curvatures is covered
- Use the resulting moment-curvature relationship in a non-linear analysis
Is that different to the Traditional and/or ACI approach, or are you wanting to discuss difference in the more detailed methods of application?
Thank you IDS. Yes my focus is on the analysis after yielding of reinforcement and for beams without compression reinforcement. The procedure you highlighted is not quite similar to the traditional approach. In the traditional approach, we assume the depth of the neutral axis which we then use to calculate the ultimate strain in the steel. The strain is used to determine the ultimate stress in the steel and then we find out if C=T (i.e equilibrium is achieved). If equilibrium is not achieved we assume a new value for the depth of the neutral axis. My question is now if its a steel type that undergoes strain hardening how do we go about this approach.
Assuming a strain then finding a NA position that satisfies equilibrium is essentially the same as starting with the NA and finding the strain.
It isn't clear to me what the problem with strain hardening is. You can either ignore it, which will be conservative, or include the increased stress in your force calculation.
The only difference if strain hardening is included is that the stress keeps increasing (at a reduced rate) as strain increases past the yield strain. The remainder of the calculation method remains the same.
RE tradition approach, it depends on whose tradition you are following.
Basically you have to determine a strain diagram which results in C = T. The strain diagram is normally defined as an extreme compression fibre strain and a neutral axis depth. Which one you choose to fix as a starting point is up to you. You then adjust the other to get C = T. Then you try a new starting point until you get the strength condition you want.
Regarding the "when is moment curvature analysis necessary?" question, I would say that, in a production engineering office in North America, it is only really needed for performance based seismic design. In more general terms, it's needed whenever you need to understand the behaviour of a member that will be making serious excursions into the inelastic range. Technically, any investigation of flexural deformation is a study in moment-curvature relationships. However,I don't think that's what you mean here.
Jack Mohle has a new book out on seismic design that contains some excellent information on this subject.
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.
Regarding the "when is moment curvature analysis necessary?" question, I would say that, in a production engineering office in North America, it is only really needed for performance based seismic design. In more general terms, it's needed whenever you need to understand the behaviour of a member that will be making serious excursions into the inelastic range. Technically, any investigation of flexural deformation is a study in moment-curvature relationships. However,I don't think that's what you mean here.
I think you are right. It seems strange to me that when people talk about moment-curvature analysis they almost always are talking about situations where the steel is past yield. The reason that seems strange is that the section behaviour becomes seriously non-linear as soon as the concrete cracks, but in the context of this thread perhaps I had better forget about that.
An example of where I have used moment-curvature analysis (in the post-yield sense) in production design is in distributing longitudinal seismic forces to viaduct piers with varying heights.
rapt - I'm relieved to see we are in total agreement on the basic approach to the problem!
That's an excellent point regarding non-linear applications IDS. I myself first encountered moment-curvature analysis in the context of the fiber method in prestressef concrete.
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.
Thank you Rapt, KootK and IDS once again for your patience. You all gave me useful information and deduced so many things. KootK place what is the title of Jack Mohle's Book?
Link. It's available as an eBook which was fun for me. Got it read on the train / at the gym.
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.
