How to understand Buclking length ?

Replies to This Discussion

Permalink Reply by Karamba3D on November 29, 2016 at 12:48pm

Hi Jason,

the buckling length of an element depends on its support conditions and is the distance between the inflection points of the buckled shape.

Maybe you find this blog entry interesting: http://www.thestructuralmadness.com/2014/03/charlie-chaplin-and-his...

Best,

Clemens

Permalink Reply by Jason Chen on November 29, 2016 at 6:56pm

Hi Friends ,

 The blog is very good you recomended .it  explains the Euler's  formula in detail .

But i  still don't know what is buckling length  of a element .In this blog ,it doesn't propose the concept of buclking of length. 

I want to know how to calculate the buclking length of element.

  the picture  as below  about  Euler’s formula in the blog.

Permalink Reply by Karamba3D on November 30, 2016 at 12:13pm

Hi Jason,

for an axially loaded beam which is simply supported on both sides the member length is equal to the buckling length (see the blog cited above, picture with the euler cases above the video, case 'd'). This is because the curvature of the buckled beam at the hinges is zero.

For a beam which is fixed against rotation on both sides (case 'a') the distance between the points where the buckled shape has zero curvature is equal to half the beams length.

The importance of the buckling length stems from the fact that if it is known a problem at hand can be reduced to that of finding the buckling load for a simply supported system.

In order to calculate the buckling length of an element with arbitrary spring supports at its end one needs to solve the eigenproblem which is connected to the differential equation for a beam under axial load. This is not trivial but doable. A good textbook on this matter is 'Theory of Elastic Stability' by S.P. Timoshenko.

Best,

Clemens

Permalink Reply by Jason Chen on December 1, 2016 at 4:55am

Thank you，i think i see your meanings.In my country ,buclking length = calculate length.In  the blog 'Leff'=buclking length,isn't it ?

Permalink Reply by Karamba3D on December 1, 2016 at 12:24pm

Yes you are right.

C.