Moment-Curvature Analysis in Reinforced Concrete
Moment-Curvature Analysis in Reinforced Concrete
(OP)
Can anyone explain in simple terms the practical application of Moment-Curvature curves (M-Phi Curves)?
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Moment-Curvature Analysis in Reinforced Concrete
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RE: Moment-Curvature Analysis in Reinforced Concrete
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).
RE: Moment-Curvature Analysis in Reinforced Concrete
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.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Moment-Curvature Analysis in Reinforced Concrete
RE: Moment-Curvature Analysis in Reinforced Concrete
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Moment-Curvature Analysis in Reinforced Concrete
RE: Moment-Curvature Analysis in Reinforced Concrete
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.
Is that what you wanted to know?
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Moment-Curvature Analysis in Reinforced Concrete
RE: Moment-Curvature Analysis in Reinforced Concrete
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?
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Moment-Curvature Analysis in Reinforced Concrete
RE: Moment-Curvature Analysis in Reinforced Concrete
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.
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Moment-Curvature Analysis in Reinforced Concrete
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.
RE: Moment-Curvature Analysis in Reinforced Concrete
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.
RE: Moment-Curvature Analysis in Reinforced Concrete
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!
Doug Jenkins
Interactive Design Services
http://newtonexcelbach.wordpress.com/
RE: Moment-Curvature Analysis in Reinforced 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.
RE: Moment-Curvature Analysis in Reinforced Concrete
RE: Moment-Curvature Analysis in Reinforced 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.
RE: Moment-Curvature Analysis in Reinforced Concrete