From: "Luc Huyse" <ljchuyse@ucalgary.ca>
Subject: Re: Cantilever deformation
Date: Tue, 4 May 1999 16:14:35 -0600
Newsgroups: sci.math.num-analysis
Keywords: bending of a beam

Hello:

Claude Gagnon wrote in message ...
>Hi,
>
>I want to get a reference or an article about the nonlinear analysis example
>of a cantilever beam subject to a tip load.
>
>Someone tells me that the final result of deformation is that the straight
>beam becomes a circle.
>
>Thanks for any information about a reference to this example,
>
>Claude
>

The curvature in a beam depends on the bending moment (forget about
the -usually very small-shear deformations for the time being). The bending
momnet in a cantilever beam subject to a tip load varies linearly. As a
result, as long as the beam behaves linear elastic the curvature will also
vary linearly along the beam axis.
If your material is perfectly elasto-plastic the moment does no longer
increase once the fully plastic moment is reached in a particular
cross-section. Consequently: you eventually obtain a constant moment along
your beam, which may lead you to believe than then also the curvature would
be constant and that you would end up with a circle. Unfortunately the
curvature of a fully plastic section is not defined, so you never really get
a circle, at least not from an engineering point of view.
You can find this is in any strength of materials undergraduate text, such
as: R.C. Hibbeler, Mechanics of Materials, Prentice-Hall.

Hope this helps
Luc Huyse ljchuyse@ucalgary.ca
University of Calgary