Cracked inertias for static analysis 1

[darkjmf1]

Hello,
ACI 318-19, cl. 6.6.3.1.1, provides reduced inertias for different structural elements.
It's clear to me that these values have to be considered for a lateral deflection anlysis, but should they be used as well for obtaining the design forces of those elements in a static (not seismic) anylisis?
With reduced stiffness, internal forces tend to be lower and thus required reinforcement will be lower too.
For columns, maybe it is compensated by usisng amplified moments in a second order analysis, but what about flexural elements like beams or slabs?
My concern is obtaining an unconservative design.
Thank you in advance.

 

[KootK]

I believe that you, as the designer, are permitted to use your judgment with respect to how you modify the stiffness of your members outside of the context of lateral, seismic design. Some engineers do use the ACI values to estimate member deflections but I do not believe that it is a mandatory approach. As you've intimated, this needs to be done judiciously.

 

[JoshPlumSE]

The main issue here is that there are different levels of stiffness for different levels of loading. For seismic, you are expected (even required) to go significantly past the normal elastic behavior in order to get ductile behavior required to resist the expected event without collapsing.

It is reasonably common to use different stiffness levels for service level forces when compared to ultimate level forces. For other loads, you may be pretty close to uncracked / elastic stiffness of a member. Think gravity deflection of a beam.

I believe there is a section in ACI that talks about using 1.43* the stiffness of 6.6.3.1.1 for service loads. I can seem to find the exact code (or commentary reference) for this right now. I'm pretty sure that's what RISA did when I worked there.... Automatically multiple the cracked stiffness by 1.43 for service level load combinations. Essentially, perform two different linear analyses with different assumed stiffness levels.

 

[Celt83]

My take on this has been that ACI 318-11 and under the reduced inertia tables for placed under the "Effective stiffness to determine lateral deflections" heading which to me indicated that the intent was for those values to be used in full structure lateral analysis. Additionally traditional slab design utilized the equivalent frame method which permitted the use of gross cross section properties outside of the joints (ACI 318-11 13.7.3.1 and ACI 318-14 8.11.3.3).

ACI 318-14 revised the section heading for the reduced inertias to simply state "factored load analysis" the commentaries in this section all speak to lateral analysis so the intent to require the use of the reduced inertias for gravity analysis is unclear. However the Equivalent frame method is still part of the code body in 318-14 and section 8.11.3.3 permits the use of the gross cross sections for analysis.

ACI 318-19 retains the "factored load analysis" heading and also removes the equivalent frame method from the code body but adds section 6.3.1.1 which says relative stiffnesses of members shall be selected based on a reasonable set of assumptions.

For me I have leaned on the allowance of gross sections under the equivalent frame method to satisfy ACI 318-19 6.3.1.1 for gravity analysis.

I have run test models both ways and with reduced inertias and regular bays in a two-way slab system I noticed a trend of more steel required in middle strips and increases in punching demand.

 

[milkshakelake]

I use an enveloped approach. I use uncracked for gravity (like Celt83) because I don't think things will crack without significant lateral loads. I use cracked for lateral strength. Lateral serviceability is a mixed bag; I usually just use cracked to save time, but I also don't do high rises, where it would have a significant effect on things like building period. I haven't compared the results like Celt83 has, but this approach makes sense to me.

For things like member deflections, I do an actual cracked analysis (with Icr). I don't think the ACI stiffness reduction factors are accurate enough for local design, though they get fairly close.