Deflection of an elastic curve

Hi:


In mechanics of materials. I learned that the deflection of a beam can be characterized by its elastic curve which is the deformed neutral axis.


But I am bothered by the fact that, if two end of a beam is fixed, and the elastic curve is continuous in between, then it must mean that the length of the neutral axis has elongated.

However, this seems to be inconsistent with the fact that neutral axis should experience no longitudinal strain or stress by definition.



can anyone care to explain this to me?


thanks