foundamental period

[Anonymous]

Hello,
I can’t explain the fundamental period of this structure by hand calculations.
I thought its dynamic behavior was a single degree of freedom system (cantilever beam).
Mass in the top : 19555059 kg (very similar to RSA)
J (25 circular R.C. columns 1 m diameter) : 1.2265 m4
E : 4000000000 daN/m2
L : 9 m
T = 1,9542 s (2 π √ M/K)
RSA calculate 0,63 s.
Thank you for your answers.

[Anonymous]

Hello,

I saw these differences between the model and the hand calculation (maybe you can tell me different):

1. as I can see, the behaviour is not a cantilever one, but I would say your stiffness should be 12EJ/L^3

2. The mass is not only on the top but also you have the mass of the columns.

3. I don't think is a rigid diaphragm. 

4. The J of the columns is different from the one you have used.

[Anonymous]

Thank you for your answer.

Here’s my remarks:

• All beams are released and so I’ve hinge in all column-beam joints. For that reason I think it’s a cantilever. Seismic deformations seem to support this concept.
• You’re right. But the mass of the columns is around 22% of the total. I would be surprised if it’s the only reason of such a difference. Hand calculated period is 1.95 s, RSA period is 0,63 s.
• If I am not mistaken, I modeled a rigid diaphragm in XY directions.
• You’re right. There is a small difference. Moment of inertia of a filled circular section is π D4/64. I find 4906250 cm4, RSA calculates 4908738 cm4.

[Refaat]

Hi  @  paolo-bartoli

“ Mass in the top : 19555059 kg’’

Which loads were include in this mass?

Refaat

[Anonymous]

Thank you.

I made a mistake in the mass in the top.

Mass in the top is 1563961 kg (not 19555059 kg ).

But, I’m still far from RSA solution.

Here’s my calculations:

Surface: 3601,76 m2

Dead load purlins: 43,8213 daN/m2 

Dead load concrete slab 10 cm : 250 daN/m2 

Live load parking: 234x0,6 = 140,4 daN/m2 

Mass in the top: 3601,76x(43.8+250+140,4) = 1563961 kg

K= 3EJ/l^3 = 3x400000x1.2265/9^3 = 20190329 daN/m

T = 2x3.14x(1563961/20190329)^0.5 = 1,7478 s

RSA: T1 = 0,63 s

I still don’t consider column mass (441562 kg), which vibrate with a smaller period.

Is that the only reason of this difference?

[Anonymous · Accepted solution]

Ok I found the issue.

It is all fine, you forgot to divide per g=9.81m/s2

What you find was kg / (kg/m2 * m4 / m3) = m

[Anonymous]

Thank you very much,

Paolo