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

## 19 posts in this topic

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

##### Share on other sites



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).

Edited by alberto

##### Share on other sites

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.

##### Share on other sites

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

##### Share on other sites

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

Edited by rigid_joint

##### Share on other sites

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.

##### Share on other sites

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.

Edited by rigid_joint

##### Share on other sites

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!

##### Share on other sites

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

##### Share on other sites
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!

##### Share on other sites
The unit of the result is in seconds.

And δ in centimeters?

Anyway, It's a strange formula because somebody has to know what δ value is. Only in performance based design seems that it could be used, but in that case formula involves δ and k (stiffness).

##### Share on other sites

"d is the lateral displacement of the top of the building in meters due to the gravity loads applied horizontally."

Anyway, It's a strange formula because somebody has to know what δ value is.

Yes, I agree!

##### Share on other sites

Yes, right in meters. In centimeters is making no sense at all .

##### Share on other sites

I guess it's a simple variation of T=2π(Μ/K)^0.5 for a SDOF system.

F=Kd, F=mg and (g)^0.5=π.

##### Share on other sites

Marios has right. In general is an equation without any special meaning. It's just for check.

##### Share on other sites
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.

I just found this formula in EN 1998-1-1 clause 4.3.3.2.2 (5)!

##### Share on other sites

Equation 4.9. But, it seems that it needs much work to take T when at the same time, you can have it with modal analysis faster and accurate.

##### Share on other sites

This one shouldn't be used in Europe, because it was formulated on the basis of experimental data of Californian Earthquakes, and California is a high seismic zone. The "formula" that you should use is the Rayleigh formula (you can find the formula on Dynamics of structures books). The masses and displacements there should be, in an approximate way, the gravitational masses in each floor. Don't know if I made my point!

## Create an account

Register a new account

• ### Similar Content

• By Gurudev
I was working on seismic design of steel structure.
There are two methods for linear seismic analysis
1. Lateral force method and
2. Modal response spectrum analysis
Now my structure is not satisfying all criteria for both methods i.e.,
First mode of vibration criteria is satisfied for 1 st  method while regularity criteria is satisfied for 2 nd  method.
So I am confused which method Shall be used.