# Large or small deflections of a cantilever beam

1. Jun 14, 2012

### fmsrat

Hi,

I'm looking for a parameter or a design guideline that could say weather or not the classical bending theory can be applied to certain beam under certain load. I'm making my dissertation about some work on cantilever beam and it's first natural frequency, so in order to model correctly the beam i would like to know if could use the classical bending theory.

Thanks in advance

2. Jun 14, 2012

### DScheuf

fmsrat:

From what I remember, using the classical beam theory (euler-bernoulli) does not account for shear strain which would over or under estimate your natural frequency. I feel that the beam theory you should be looking is Timoshenko.

Again, this from what I remember. Hopefully someone can correct me if I am wrong.

Best of luck.

3. Jun 16, 2012

### nvn

fmsrat: (1) For a cantilever beam, you generally can use classical beam theory (Euler-Bernoulli beam theory) if beam length L ≥ 10*h, where h = beam cross-sectional depth.

(2) For a cantilever beam, if L < 10*h, you might want to use Timoshenko beam theory.

(3) For a cantilever beam, you generally can use beam small deflection theory (i.e., basic Euler-Bernoulli or Timoshenko beam theory, mentioned in items 1 and 2) if L ≥ 10*y, where y = beam maximum bending deflection.

(4) For a http://img72.imageshack.us/img72/9576/beam02.png [Broken] or http://img600.imageshack.us/img600/3467/beam03.png [Broken] (clamped, embedded, encased, encastre, built-in) beam, change each 10 to 20 in items 1, 2, and 3, above.

Last edited by a moderator: May 6, 2017
4. Jun 18, 2012

### fmsrat

Thanks for your reply, could you tell me what references(articles,books) did you use for that parameters.

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