ACI 318-19 Moment of Inertia Change

[GA_Engineer]

I was wondering if anyone else had come across the slight change in ACI 318-19 to the calculation for the effective moment of inertia for non-prestressed sections. I ran across it while trying to replicate an existing design but using the new code and my concrete beam deflections shot way up. After looking into the code a bit further, I determined that the new equation will change the deflection for concrete beams depending on the applied moment. Based on the graph below, there is a pretty good sized reduction in effective moment of inertia with the new equation. I hadn’t seen a discussion on this new change but it could become a big deal since we will have to make some beams larger to meet deflection criteria that in similar situations worked as small beams using older code. Owners and GCs won’t like that. The first image below is from ACI 318-19 and the second from ACI 318-14. I found some more information here:

https://blog.risa.com/post/why-does-my-slab-deflection-increase-using-aci-318-19?hs_amp=true

 

[bookowski]

I hadn't seen this but aci 209 has always recommended using 4 sqrt vs 7.5 for rupture, so my guess would be that this is to put them more in line. How big of a difference this makes depends on how you're doing your calcs. Most people I know just take 0.35Ig and call it a day.

 

[GA_Engineer]

For computer programs that can easily calculate Ie, this seems to have the ability to increase deflections. I understand that many people might use 0.35Ig for hand calcs or spreadsheets to be conservative but in cases where programs are used that can quickly calculate the code Ie, if I’m reading the code right, this will have a big effect on deflections.

 

[andrews2]

Similar to the new shear equations, I imagine this change will receive a lot of industry push back and might be changing again in the next code cycle. The new moment of inertia equation just hasn't been talked about as much yet. This isn't a slight change either. In the cases I've seen, it absolutely kills long term deflections. The effective moment of inertia for some cases is half or a third of what it would be under 318-14. I haven't heard of any real world issues the old equation was causing, but someone has to justify their research money somehow I guess?

Also in response to both of your comments about most people taking 0.35Ig, the code does not allow this for deflections. The 0.35 factor is for analyzing factored loads to obtain strength demands, not for checking deflections. I know a lot of people, myself included, may use the 0.35 for some quick initial deflections checks, but it isn't always conservative as you say. Especially with the new codes, I see beams now get down as low as 0.2Ig. If deflection checks are close with 0.35Ig, you should be using the equations in the original post.

 

[bookowski]

I shouldn't have said conservative since it's not always the case.

However, you said that your "beam deflections shot way up". For beams other than very lightly loaded ones it should not make a large difference. Icr is a lower bound, Ieff will always be => Icr. You can quickly calculate Icr for various reinforcement ratios in beams. I think that it's at about 3/4% you hit Icr ~= 35% Ig. If you've got a beam with min reinf but moments well above cracking then you'd be lower, I don't encounter those often but would be aware to lower the estimated cracking if I did. I think that around 1.5% you're at about Icr ~= 50% Ig. You can calc Icr as a % of Ig independent of beam size/shape pretty quickly in xls and convince yourself that for beams with some lower bound of steel 35% is reasonable enough, and at around 1.5% you can start moving up. Since those are Icr they're a lower bound.

Slabs are a different story, but you said beams. Slabs - depends how you're doing them. If they are doing this to move the fr more in line with other aci docs then it would depend on how the software is doing lt, cracking, etc. for deflections. safe already uses 4sqrt(fc) for rupture by default, I'd think that applying another 2/3 to that is unnecessary. ram uses 7.5 but it also uses a larger creep factor than safe, putting them roughly in line in most cases.

 

[andrews2]

Yes I don't see a problem using 0.35Ig if you're also providing an amount steel that you feel comfortable will provide an appropriate corresponding Icr value. I worry some are not as thoughtful as you and use the 0.35Ig value without a second thought about what the actual cracked or effective moments of inertia are.

Perhaps that's what many are doing and that's why this change hasn't been discussed as much as the shear equation changes. Many people using 318-19 may not realize how much quicker the new equation approaches Icr than the old one..

I was talking only about beams in my reply. I don't see me changing anything about my design of 2-way slabs because of this code change. As you say, SAFE and other sources have already been providing recommendations for lower fr or higher creep factors that should cover what I think this change is intended to do.

 

[JAE]

For computer programs that can easily calculate Ie, this seems to have the ability to increase deflections

This depends on how the program handles the application of an "Ix" to the beam - specifically what I'm talking about is the fact that Ie is based on the applied moment to the beam at the section considered. Moment varies a lot across the span and ACI 318 tries to address this by allowing the designer to take the Ie value as the average of Ie at the critical positive and negative moment sections. This then uses an Ie based on high moment values and ignores the lower moment regions of the beam (i.e. near inflection points).

I think there have been studies that show the high moment regions (and the resulting Ie values) have a dominant effect on the derivation of accurate deflections but it is conservative.

Should a program actually derive Ie values along the span - and use those in each analysis of each load combination - then the deflections would be smaller than that derived by the "worst case Ie" values.

 

[GA_Engineer]

@Bookowski and @JAE, You both make great and valid points. I probably should have looked at the commentary in the code, which explains what you said:

I just have a situation where the beam is fairly small and lightly loaded as it’s in-fill beams and has a reinforcement ratio that is above code minimum but not above 1% like the commentary says. So I fall into an area where I am greatly affected. Main beams and girders probably won’t be as much affected for all the reasons stated.

 

[Celt83]

GA: I also imagine beams traditionally designed as pin-pin for simplicity may get hit hard also as there are not negative end moments to average Ie against so most software will give you Ie based on the critical mid span moment.