Problems with eigen analysis of a two-story shear frame

[KIMYONGWOO]

hi,
I want to solve eigen analysis of a two-story shear frame.

http://opensees.berkeley.edu/wiki/index ... hear_frame
This example used Ib as a large number.

The analytical solutions are omega1=sqrt(k/(2m)), omega2=sqrt(2k/m)

I compared with the result of this example and analytical solution.

I used k=24EIc/(h^3) *(12*rho+1)/(12rho+4)
where, rho=Ib/(4Ic)
(10page from "Dynamic of Structures" book by Professor Anil K. Chopra)

case 1) Ib=infinite, the results are same.
Opensees, omega1=12.20 omega2=24.40
Analytical, omega1=12.20 omega2=24.40

case 2) Ib=Ic, the results are different.
Opensees, omega1=6.91 omega2=20.55
Analytical, omega1=9.22 omega2=18.45

Is those analytical solution wrong?
Did I missed some conditions?
How do I fix the example file to solve when Ib=Ic?

[selimgunay]

Yes the analytical solution is not correct when Ib=Ic. The k that you use in omega1=sqrt(k/(2m)), omega2=sqrt(2k/m) is only valid for a single bay, single story structure because it is derived from the static condensation of the stiffness matrix of that structure, it is not valid any more for the 2 story.

If you want, you can construct the stiffness matrix for the two story and using the mass matrix, you can get the eigenvalues from Matlab, they should match the OpenSees results.

[KIMYONGWOO]

Thanks. I have an question. Where can I get the k(multi or two story sturcture), if Ib=Ic? Do you have a reference? or link?

[selimgunay]

I don't know of a reference. But you can obtain the stiffness matrix either by using the Direct Stiffness method or by following an approach similar to what is described in Example 1.1 of Chopra's book.

[KIMYONGWOO]

Thanks.