eigen value

02-Getting started with the modelling
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karabi
Posts: 18
Joined: 21 Jul 2020, 12:46

eigen value

Post by karabi »

Dear Sir/Madam,

I am modeling multibay 3D (G+3)building frames. In my study, I am working
on 3D buildings with different bays such as 3x5, 4x5, 4x7, etc. These are
all symmetric plans and each bay length is 4m. I have considered rigid
diaphragm because my buildings are of RC. So I have considered the most
probable center node(though exact center node not defined) as the master
node and the remaining nodes as slave nodes. I have run the eigenvalue
analysis to check if my modeling is correct. For 3x5 and 4x7 I do get nodal
displacement in the y-direction and zero nodal displacement in x for mode 1
and vice versa in mode 2. For 4x5 frame I get nodal displacement in the
y-direction and zero nodal displacement in x for mode 1 however, for mode 2
I get nodal displacement in x-direction as well as y. As far as I know,
I should not get such an eigenvalue solution for 4x5 frame. It's a
symmetric plan. So the first two modes should not have a rotation in Rz.
Please help me in this regard. I am stuck in this for quite a long time.
huffte
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Joined: 22 Jul 2011, 10:19
Location: Cookeville, Tennessee, USA
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Re: eigen value

Post by huffte »

If the exact center of mass has, indeed, not been defined, then you likely have eccentric mass distributions at one or more levels, which would indeed produce multi-directional displacements, even if the stiffness is symmetric. Both mass and stiffness must be perfectly symmetric in order to expect no orthogonal effects.
Last edited by huffte on 31 Aug 2020, 16:01, edited 1 time in total.
Tim Huff
karabi
Posts: 18
Joined: 21 Jul 2020, 12:46

Re: eigen value

Post by karabi »

Hello Huffte,

Thank you so much for your reply. Can you please instruct me to define the exact center in Seismostruct if there is no beam-column joint(node) that lies exactly at the center of the plan? how to define such a node? because taking any other node near the center as the master node results in these types of multidirectional nodal displacements.

with best regards,
Karabi
huffte
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Location: Cookeville, Tennessee, USA
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Re: eigen value

Post by huffte »

You can place a node in the exact center and connect it to the corners with rigid links. Depending on your intended model, you may have to use rigid links to more than the corners.
Tim Huff
karabi
Posts: 18
Joined: 21 Jul 2020, 12:46

Re: eigen value

Post by karabi »

Hello Tim Huff,

I am so thankful to you. I tried a few combinations with a node in the exact center and connected it to the corners with rigid links. Finally I got the desired results of nodal displacements. Thanks once again.

with best regards
Karabi
karabi
Posts: 18
Joined: 21 Jul 2020, 12:46

Re: eigen value

Post by karabi »

Hello,
I am again getting some unusual results with eigen value. The structure is symmetric, column dimension 400mmx300mm and I got unidirectional nodal displacements in the 1st and 2nd mode as expected. However if I rotate the columns by 90 degrees (or change the RC column section to 300mmx400mm) I get multidirectional nodal displacement in 2nd mode which should not be the correct result. how can changing the column orientation make the same structure eccentric? Please help.
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seismosoft
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Joined: 06 Jul 2007, 04:55

Re: eigen value

Post by seismosoft »

how do you know that the results are not correct?
In non-symmetrical buliding it is very typical to get modes that are a combination of translational and rotational parts.
Seismosoft Support
karabi
Posts: 18
Joined: 21 Jul 2020, 12:46

Re: eigen value

Post by karabi »

thanks for your response.
the building plan is symmetric, the only variation I made was changing the column orientation by 90 degrees. how can that make the building nonsymmetric?
regards,
Karabi
huffte
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Joined: 22 Jul 2011, 10:19
Location: Cookeville, Tennessee, USA
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Re: eigen value

Post by huffte »

First, I would make certain that indeed all of the columns on any given level have been rotated. If only some of the columns are rotated, then a stiffness asymmetry will exist. Also make certain that the same element type and subdivision strategy has been used for all columns on a given level. Make certain that the lateral force resisting systems (LFRS) at each level are symmetrically placed. Are moment connections and releases symmetric? Did column rotation alter the LFRS? Are leaning columns identical in terms of releases at each level? . . .

Finally, realize that even a plan-symmetric structure has a torsional mode of vibration. It may be possible that the observed bi-directional displacements are accurate.
Tim Huff
karabi
Posts: 18
Joined: 21 Jul 2020, 12:46

Re: eigen value

Post by karabi »

Thanks a lot for your detailed explanation. It is quite helpful to clear my modelling concepts regarding plan symmetry and eigen value.
regards,
Karabi
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