Eluer Buckling ACI 530 3

[waldo459]

Ok, calculators out!

Contrary to what I believe, apparently, a solid grouted masonry wall buckle at a lower load than one with grout at 16" on center. ACI 530, Equation 2.2.3-d with the following values:

8" wall
h= 12'
e= 2"
E= 1125000

Wall Properties
8" on center 16" on center
r= 2.2 r= 2.43
I= 443 I= 378

Pe= 25469 plf PE= 29300 plf

How can this be?

 

[Lion06]

Where did you read that? The code commentary says that the (1-0.577e/r) factor accounts for the cracking and inability of unreinforced masonry to sustain tension, not the 0.25. The 0.25 is just a factor of safety. This is also noted in the code commentary (in the '08 edition, on page cc-46 regarding the overal safety factor of 4).

There might not be a Pe check for reinforced masonry, but theFa equation for reinforced masonry still takes buckling into consideration with the (1-(h/(140r))^2) and (70r/h) ^2terms. These terms account for wall slenderness, which takes care of the buckling consideration. If you check out the code commentary, on page cc-47 (in the '08 edition) it talks about if you substitute in e=0.1t, and E=1000f'm that you get the f'm(70r/h)^2. The only difference is you're not doing the Pe, because it takes into account the fact that unreinforced masonry can't sustain tension (reinforced masonry obviously can).

 

[JAE]

StructuralEIT,
My appologies - the 102,544 lbs was a mistake - should be 11,021 lbs which you also got.

[red]Is it the intention of the standard to use Pe/A in place of Fa in the interaction equation?[/red]

No, the Pe is a separate check. The fa/Fa and fb/Fb check for strength interaction and I back-calculated a Pa at e=2" to get the unity = 1.0. The Pe check is a separate "lid" on the axial load as I see it. The Pe equation has the eccentricity in it so it doesn't make sense to combine it again with the fb.


[red]First, you have to check both equations 2-13, and 2-14, not just one or the other. [/red]

No, the two equations are for different things - one for Fa and the other for Fb.


[red] check the mid-height of the wall using Fa= eq. 2-15 and M=Pe/2. [/red]
I'm not sure that is right. You shouldn't substitute an Fa from Equation 2-15 in my view.


waldo:

I should have checked it as you suggest. I've edited my original calculation and it is attached....guess what? Now there are conditions where the 8" fully grouted wall takes less load!

 

[hokie66]

Which is ridiculous! ACI needs to take another look. The whole thing is much too complicated for loading on block walls.

 

[Lion06]

Ok, I think I have a realistic idea why this is true. Because the (1-.577e/r)^2 factor is accounting for buckling of a section that can't sustain tension, the fully grouted wall will actually crack first. Because A is so much higher in the fully grouted wall, the P/A portion of P/A-M/S precompresses the wall LESS than for the wall grouted a@ 16" o.c. The S is smaller for 16" o.c. but by a smaller % and the net result is the fully grouted wall cracks first, and therefore buckles first (for higher e, not for e=0).

 

[waldo459]

There is also the debate about what qualifies as eccentricity. I have always allowed for eccentricity for all conditions, as a minimum of 2", even for a full bearing beam on top of a pilaster. I think that the contractor will miss it, beam will be too short, etc. Would you agree or disagree, why? If e=0 the allowable loads are greatly increased over e=2. For 8" block, pilaster with two cells with (1) #6 each face will have about 40k with e=0, about 16k with e=2.

Also, I can't find in the ACI530 that the Pe is a required check for reinforced masonry, code or commentary. Should it even be checked unless masonry is unreinforced?

 

[Lion06]

No, it isn't a required check for reinforced masonry. I talked about that in a post higher up in this thread.

 

[JAE]

StructuralEIT - after getting some sleep and re-reading your statement above (6 May 09 16:06) where I countered your statement about checking both equations 2-13 and 2-14 I seem to think I misunderstood what you were saying.

One is for Fa and one is for Fb so I guess yes, both need to be checked.

 

[jheidt2543]

I'm sorry to enter into this so late (I've been catching up on old thread reading), BUT I found this thread very interesting in that the results of the Code provisions are more than a little confusing, if not down right goofy. So, I sent the entire thread to The Masonry Society (TMS) for their comments and here they are:

******************************************************
06/03/09
Mr. Heidt,
Following is the response to your question from TMS Member, Dr. Richard E. Klingner. Please note that the opinion below does not necessarily reflect the opinion of TMS. Thank you for contacting TMS.

Susan Scheurer
TMS Meeting Planner / Membership Coordinator / TMS Journal Managing Editor

************************************************************

Dear Susan:

Please feel free to forward this to Mr. Heidt. I emphasize that while this is a knowledgeable individual response, it does not necessarily reflect the opinion of the Masonry Standards Joint Committee.

What the email writer notes is correct. Because a solid or grouted wall has a smaller radius of gyration than an otherwise identical hollow wall, the Euler buckling capacity of the former is less than that of the latter. One actually reduces a hollow wall's buckling capacity by grouting it. This observation, while counter-intuitive, is a consequence of the formulation adopted by the MSJC Code for calculating the capacity of an unreinforced masonry wall. That equation modifies the Euler buckling capacity by a cubic penalty factor which is consistent with the assumption that the wall is unbonded (that is, that the masonry is dry-stacked). This issue is discussed further in the latest edition of the Masonry Designer's Guide, published by TMS. The MSJC has been working on consistent moment magnifier provisions for masonry that would address this issue in a less conservative way.

Regards, Richard Klingner

***********************************************************
----- Original Message -----
From: jheidt2543 [mailto:notifyme@eng-tips.com]
To: info@masonrysociety.org
Sent: Wed, 3 Jun 2009 08:12:23 -0400 (EDT)
Subject: Eluer Buckling ACI 530

Ladies/Gentlemen:

This is a thread from Eng-Tips Structural Forum and it raises some very interesting questions regarding ACI 530 and I thought you might be able to review the comments and provide some follow-up. Please direct this to the appropriate persons.

Thank you,

James F. Heidt, PE

 

[JAE]

Thanks, Jim. Good response from Dr. Klingner (Texas). I attended a seminar he gave once with Dr. Porter of Iowa State and both were very knowledgable in masonry.

 

[hokie66]

"One actually reduces a hollow wall's buckling capacity by grouting it" is a ridiculous statement. That may be the way the equations read, but I defy them to prove it by experimentation. Glad they are working to address the issue.

 

[BAretired]

hokie is right. The addition of grout cannot reduce the buckling capacity of a masonry wall. This means that the code equations are not realistic. Back to the drawing board.

BA

 

[JAE]

Well, he admits it is counter-intuitive and also states that they are working on a better formulation.

 

[BAretired]

Good! And the sooner the better!

BA

 

[miecz]

Nice catch, Waldo459.

 

[Lion06]

This check isn't required for reinforced masonry. The equation is specific for buckling of a material that has no tensile capacity. I believe that is the caveat that most are missing when thinking it is counterintuitive that adding grout reduces buckling capacity. In steel you can often think of having a lower allowable, but having so much extra steel that you end up with a higher capacity. The difference here is that steel can take tension, unreinforced masonry can't.

If you reinforce the section, then it does have tensile capacity and this particular buckling equation doesn't apply anymore.

 

[waldo459]

Structural EIT. I feel exactly the same way. But, even with tensile forces neglected, grouting the entire wall will lower axial stress significantly over 16" on center, so also this agrees with your extra masonry to end up with a higher capacity. However, the lower allowable due to the equation is so low that it indicates the wall will buckle with a lower force if completely grouted. I would seriously doubt that this is the case in reality.

 

[Lion06]

I agree that it may not be the case in reality. There are so many variables with masonry, however, that you have to make certain assumptions and run with it. The biggest assumption, in my mind, that lead the this rift between theoretical and real capacities is that there is no tensile capacity. The mortar will have some tensile capacity, not much, but some. Additionally, the grout has it's own tensile capacity, which is much higher than that of the mortar. We are treating a grouted masonry wall, with CMU, mortar, and grout as an isotropic material. In order to do that, you have to make the most conservative assumptions.

I do agree with you, as noted above, that this would likely not occur in a real world situation, but it would probably be difficult to quantify it because of the reasons listed above.

 

[jheidt2543]

Well, we design in the real world and I think our engineering theories are developed to describe that real world - sometimes rather crudely. However, we shouldn't be so conservative that it is unrealistic either.

When you look at some of the current masonry designs with #9 bars @ 8" o.c. and larger in fully grouted cores next to past acceptable designs without rebar and grout, how do those buildings stand up? Where are the failures that prove we need to be ULTRA-conservative?

These equations seem to give results that are, in some cases, so far from reality that they are nearly useless. When this happens, what is our response? The Code requires it. Why can't they develop equations based on the results of experimental programs?

That's my rant for today!