Hello,
I am looking for a closed from analytical solution for the critical bucking load of a beam subjected to axial compression as well as uniformly distributed transverse load. I spent few hours searching for it and could not find one, but somehow I have the feeling that somebody should have worked out the solution. If anybody can point me in the right direction I will really appreciate it.
Ultimately, I want to see what's the affect of uniform transversely distributed load on critical buckling load, also FYI the end conditions are fixed -fixed. I know somebody might say why not use FEA to solve this eigenvalue problem however, I am interested in closed form solution.
Thanks in advance
Nitesh
Forums
You can find the result in the books.
The materials mechanics gives us the result. Also, you can use the Euler Theory to solve it by yourself.
materials mechanics ?
Thanks for your response, are u referring to some book ?
Yeah
Yes, I reffer to some books may called Mechanics of Materials or Material Strength written by some people. Or maybe you can see the URL:http://www.core.org.cn/OcwWeb/Mechanical-Engineering/2-002Spring2004/LectureNotes/index.htm
Applications: Beam Bending, Buckling and Vibration PDF1
to find waht you want.
Thank Yeah
Yeah,
Thank you so much, I saw a similar problem in Timoshenko, that was a beam on ealstic spring with axial loading.
Thank you so much
Nitesh
critical buckling load : closed from solution
R. Chennamsetti, Scientist, India
Hi Nitesh,
You may refer 'Theory of Elastic Stability' - Timoshenko.
The problem outline is like this...
You will get a second order non- homogeneous ODE as a governing equation. The non-homogeneous part is appearing because of transverse load. Generally, transverse loads, eccentricities etc appear as non-homogeneous part.
This non-homogeneous ODE can be solved in two parts [1] complementary function (CF) - because of homogeneous part and [2] particular integral (PI)- the whole equation. Total solution => CF+PI. Substitute boundary conditions.
Ofcourse I didn't solve this problem. I just gave the outline ...
Good luck!!!