Finding damping coefficient MDOF

[Batzo]

Hi,
For damped MDOF system, how do I find damping coefficient "c" without using Modal Analysis?
I have m and k matrices.

https://files.engineering.com/getfi...e50-d63b961611c0&file=IMG_20210723_091249.jpg

 

[Retrograde]

What type of structure is it?

Some typical values expressed as a % of critical:

Single Mast 0.2%
Bolted lattice 0.5%
Building (service) 1%
Building (ultimate) 3%
Car shocks ~20%

 

[Batzo]

It is a reinforced concrete building,
but it isnt matter,what is the formula?

For SDOF, Is:

But how do I find c for each floor in MDOF?

 

[WARose]

Why not just assume a value? You are never going to get a super accurate one in any case.

By the way, is this a new or existing structure?

 

[271828]

Are you designing a building that doesn't exist yet or are you trying to determine the actual damping for a building that exists?

If you're in design, then you'll need to use a design value. These are very inexact.

If you're working on an existing building then you'll need to use some variety of Experimental Modal Analysis.

 

[Batzo]

Im designing.
Damping ratio for reinforced concrete is 5% (Chopra).

But i ask if there is any way to determine c coefficient other than Modal Analysis.
And I can assume a value, but there is a calculation for it for MDOF system?

 

[Retrograde]

In the Rayleigh damping model, the damping matrix of a structure is a linear combination of mass and stiffness matrixes.

 

[GregLocock]

" i ask if there is any way to determine c coefficient other than Modal Analysis."
Sure, get a hammer and an accelerometer and a similar building. Spend a happy day bashing the structure and measuring the vibration and looking at the damped curve. This is a modal analysis I suppose. Hitting things with hammers is fundamental to /correlated/ structural models.

Cheers

Greg Locock


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