TITLE: Is the moment-curvature relation for an elastic beam general?
QUESTION [2 upvotes]: The relationship between the moment and the curvature for an elastic beam is
$$M = -EI\kappa$$
Previously, I have only used this with small deflections in static calculations. I am currently working on a dynamic cable model with bending stiffness for a physics simulation. Does this relationship hold for large deflections and dynamic behavior? If not, why?

REPLY [2 votes]: Not sure you care anymore, but - for large deflections, this does not hold.  As the pretty pictures at wikipedia show, an elemental does not remain perpendicular to the neutral axis when bending deep beams, so that goes out the window.  The second is the neutral axis in general shifts towards the compression side, because there is less material on that side of the centroid, so I becomes a function of the curvature. (See below).  Both of these effects mean different approaches need to be used.
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