Cracked stiffness values in calculation of fundamental period

[k.aydin]

Hi all,

I am wondering if any property modifiers (cracked stiffness values) are used when calculating the fundamental period of vibration of a building according to ACI 318/ ASCE 7?

Regards,
Kamil

 

[Agent666]

Yes this is typical in ACI318.

 

[k.aydin]

Thanks Agent666 for your response.

That s what I also thought. But there s one thing that confuses me:

ACI says in R6.6.3.2.2 that "Analyses of deflections, vibrations, and
building periods are needed at various service (unfactored)
load levels (Grossman 1987, 1990) to determine the performance of the
structure in service. The moments of inertia of
the structural members in the service load analyses should
be representative of the degree of cracking at the various
service load levels investigated. Unless a more accurate
estimate of the degree of cracking at service load level is
available, it is satisfactory to use 1.0/0.70 = 1.4 times the
moments of inertia provided in 6.6.3.1, not to exceed Ig, for
service load analyses."

What I understand from the above is that if we re calculating
period of a building, we can use 1.4 times cracked stiffness of structural
members (except flat plates) which would basically give the properties of
uncracked sections.

Am I right?

Kamil.

 

[wannabeSE]

Have you seen section 6.6.3.1 in ACI 318-14?

 

[k.aydin]

Hey wannabeSE, thanks for the response,

Yes, I have seen the section 6.6.3.1 in ACI 318-14. There, the cracked values
are given for elastic analysis under factored loads. But the anlaysis of modal case
for fundamental period is made corresponding to the conditions of unfactored loads.
I think therefore the section R6.6.3.2.2 in ACI 318-14 should be followed when
computing the fundamental period. Is that correct?

Respect, Kamil.

 

[JoshPlumSE]

ACI 318 typically uses 0.35*Igross for beams and 0.7*Igross for columns. That's for strength level stiffness which would be appropriate for seismic loading. Keep in mind that for ASCE-7 Seismic loading it is assumed that you have inelastic behavior which allows you to use the response modification factor R to reduce the seismic loading by a lot. Hence, you are expecting a good deal MORE cracking at seismic level loading that you do at regular strength level loads.

For service level loading, like deflection or such, the commentary suggest using 1.5 * the strength level stiffness. Which turns out to be 0.5*Igross for beams or 1.0 Igross for columns. When that section mentions natural period they are probably talking about for comparison to operating period of dynamic equipment or such.

 

[k.aydin]

JoshPlum, I appreciate your reply. Thanks..