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# Thread: Determination of the fundamental period of vibration (T1) of a building

1. ## Determination of the fundamental period of vibration (T1) of a building

Is there any mathematical formula for the approximate calculation of the fundamental period of vibration of a building?

2. $
\textrm{

T_{1}=C_{t}\times H^{\frac{3}{4}}

}
$

Ct=0.085 for moment resistant space steel frames,
Ct=0.075 for moment resistant space concrete frames and for eccentrically braced steel frames and
Ct=0.050 for all other structures.
H is the height of the building, in m, from the foundation or from the top of a rigid basement (EN 1998-1 section 4.3.3.2.2).

We can use this approximation for buildings with heights up to 40m provided that they follow the regularity criteria that are described in table 4.1 (EN1998-1 section 4.2.3.1).

3. An empirical type we use (for concrete structures) is T=n/10 where n=number of stories (typical storey~3m).

So for a 10 storey building T=1 sec.

4. There are also a couple of approximation formulae in EC1 (Wind).

5. In paulay-priestley's book there are some formulas e.g. for frame buildings T=0.061*(h^ 0.75).

6. An estimation of the fundamental period can also be made by the following expression: T1=2*(d)^0.5.
d is the lateral displacement of the top of the building in meters due to the gravity loads applied horizontally.

7. How does this formula come from?

It seems like a performance based design equation but in that case formula is a little bit different.

(I think T=δ/ks where δ=displacement target for mass center, not displacement at the top.)

T1=2*(d)^0.5
There is a unit problem with that formula except there is a unit decision in advanced.

8. I really don't know what is the theory behind this expression...
I will search through the internet and my notes... Probably I will find something!

9. I asked it just because I think that I have never seen it before.

10. There is a unit problem with that formula except there is a unit decision in advanced
The unit of the result is in seconds.
This expression works the same way as the formula described by Eurocodes.

I asked it just because I think that I have never seen it before.
No problem at all!