What is the general thing to do incase two modes are close to each other in modal analysis. 1

[ITsSB]

What is the general thing to do incase two modes are too close to each other? Eurocode 8 requires two modes (both translational and torsional modes) to have at least 10% of the higher period gap.

 

[SWComposites]

Modify the structural stiffness of portions active in one or both modes.

 

[HTURKAK]

My points ,


- you did not mention if the two modes on the same direction,

- consider CQC ( complete quadratic combination) .Pls look clause 4.3.3.3.2 Combination of modal responses

...(3)P If (1) is not satisfied, more accurate procedures for the combination of the modal maxima, such as the "Complete Quadratic Combination" shall be adopted.



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NEW ENGLAND MAXIM

 

[JoshPlumSE]

Yeah, I was going to say that (in the US) this isn't a problem, provided you use CQC (or a similar method) to account for the interaction of closely spaced modes.

 

[mronlinetutor]

I would say omega=sqrt(m/k). When the two modes move away from each other, the combined mode is a resonance. When the modes are approaching each other, the combined mode is cancellation. So the frequency of the combined mode is sqrt[(m1^2/k1^2+m2^2/k2^2). Now (M-lamda *K)=(dx/dt). Resonance occurs when dx/dt-->infinity. When dx/dt-->infinity, k1*k2-->zero. So you adjust the stiffness of the upper floor and lower floor to avoid resonance. But according to F=Kx, x would be K^-1*F. Now x=K^-1Ma^-1, v=(K/M) Assuming K is constant, you adjust the mass of the lower and upper floor beams, the stiffness of the mass and stiffness of the columns are not included; because the building is theorized to be a mass pendulum. Therefore stiffness remains constant and torsion can be neglected. The upper floor and lower floor usually twist together. Resonance does not care if you increase the mass or lower the mass, the point is to get resonance away from its spectral center.






disclaimer: all calculations and comments must be checked by senior engineers before they are taken to be acceptable.

 

[GregLocock]

"I would say omega=sqrt(m/k)" I wouldn't. There are still 2 modes. I couldn't be bothered to decipher the rest, presumably your senior engineer gets to red line a lot.

Cheers

Greg Locock


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[ITsSB]

@HTURKAK The two modes are in different directions (translational).
So, as long as i used CQC combination for modal maxima it's fine?

 

[JoshPlumSE]

Yes, that's what the US codes say.... If the modes are closely spaced then you have to use a modal combination method that accounts for the interaction of closely spaced modes. That's normally CQC. There are other methods that can work to. But, they're not used as often.

 

[HTURKAK]

It is fine but i would like to remind some points ;

- ( 3.2.2.1 3P) The horizontal seismic action is described by two orthogonal components assumed as being independent and represented by the same response spectrum.

- Clause 4.3.3.3.2 Combination of modal responses is applied for each separate direction and if the response in two vibration modes i and j on the same direction may be taken as independent of each other, if their periods Ti and Tj satisfy Tj ≤ 0.9 Ti . If the subject building totally symmetric and square or circular in plan , the response in two vibration modes i and j at different directions could have similar periods.




Use it up, wear it out;
Make it do, or do without.

NEW ENGLAND MAXIM