Simple buckling problem

[kiso]

My goal is to program a buckling analysis program. I'm using the "Concepts and applications of the finite element analysis" by Cook (second edition).

I'm having trouble with the exercise problem 12.9b:

P 1 2 3 P
-----> o==========o=========o <------
A A
L
/--------------------/


PROBLEM:
Find the buckling load P for a two-element system. Impose symmetry about the center node 2, so that the eigenvalue problem involves only two d.o.f associated with element 1-2.

ANSWER: -9.944EI/L^2

Ok, I can do that. But when I'm trying to do the same with 2 elements, 4 global d.o.fs (without imposing symmetry), I get weird answers. I might do something wrong or then MathCad2001 (which I'm using for testing) cannot compute the eigenvalues properly.

Could someone tell me if the answer should be the same or not?

Thanks
Kim

 

[kiso]

aaargh ..... different font.... the pic got messed up

you probably get the idea

L is for the total structure (2 beams).
Nodes from left to right: 1 2 3 marked with o.


kim

 

[jayachan]

Hello Kiso,

Find the textbook C.K.Wang, Advanced Matrix Structural Analysis, International Text Book Co., 1972 from University of Wisconsin, Madison, Wisconsin, 53706, Engineering Library or some other book store.

Prof.C.K.Wang also has another text, Matrix Methods of Structural Analysis, International Text Book Co., 1971.

Prof.Robert D.Cook is also from UW, Madison, Wisconsin.

These books have Fortran Programs for Buckling and Second order analysis. You can type them and they work. No errors in them.

I am sure that Engineering Library, UW, Madison has them.

Profs.Wang and Cook have retired. Call (608)-262-3491 to find where they are now. This is UW, CEE Department, Structural Engineering Divison.
visit

http://www.uwisc.engr.edu

and find CEE Department.

Prof.P.Jayachandran
WPI, Worcester, Mass, 01609.