Eluer Buckling ACI 530
Eluer Buckling ACI 530
(OP)
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?
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?






RE: Eluer Buckling ACI 530
RE: Eluer Buckling ACI 530
RE: Eluer Buckling ACI 530
BA
RE: Eluer Buckling ACI 530
e = 2", r = 2.2"
f(Pe) = 443*[1-0.577*(2/2.2)^3] = 443*0.566 = 250.7
Case II - grout @16" ctr. I = 378
e = 2", r = 2.43" (?)
f(Pe) = 378*[1-0.577*(2/2.43)^3] = 378*0.678 = 256.3
Ok, your cal appears correct.
But question here, why r for case II (2.43") is larger than case I (2.2")?
RE: Eluer Buckling ACI 530
RE: Eluer Buckling ACI 530
At 8" o.c. At 16" o.c.
Aavg=91.5 Aavg=65.8
Iavg=443.3 Iavg=387.1
r=2.2 r=2.43
Although the I increases 14%, the A increases 40%, driving down the r.
At 8" centers, Pe=25470#/lf
at 16" centers, Pe=29300#/lf
at 32" centers, Pe=32900#/lf
Anyone have any insight into what is going on here? It appears that the less cells filled, the more load it takes to buckle the wall. However, the strength of the wall is also limited to Fa and Fb, and these will allow for more load on walls that have more filled cells. So it looks like Euler buckling load increases with fewer cells filled, while strength goes down.
RE: Eluer Buckling ACI 530
The Euler buckling STRESS goes down, but you have a greater area over which to apply that lower stress; ultimately you get a net increase in capacity.
RE: Eluer Buckling ACI 530
Let's try to figure out together:
A1 = 443/2.2^2 = 91.53 (8" spa)
A2 = 378/2.43^2 = 64.01 (16" spa)
A1 = b1*t1, A2 = b2*t2; let t1=t2=constant
b2/b1 = A2/A1 = 64.01/91.53 = 0.7
Thus, the effective/equivalent block width of grout in 16" spacing is 70% of that in 8". Is the above proportion correct? Sorry, I don't have the manu on hand.
RE: Eluer Buckling ACI 530
Additionally, I am getting different numbers than you are. I am getting 31021.3klf for the 8" wall grouted at 8". That is WAY higher than the squash load, Pa, so it isn't really even an issue.
RE: Eluer Buckling ACI 530
I r f(Pe) Ratio = f(Pe)i/f(Pe)8
0" 334 2.84 266.7 1.08
8" 440.2 2.19 246.7 1.0
16" 387.1 2.43 262.6 1.06
32" 360.5 2.59 264.7 1.07
64" 347.2 2.7 265.8 1.08
72" 345.8 2.71 265.6 1.08
It looks like the term 1-0.577...is the best approximation. Any thought, comment?
RE: Eluer Buckling ACI 530
8" 16"
Pa=approx 11,000plf Pa=approx 7250plf
Peallow=6370plf Peallow= 7320plf
So yes, the fa (therefore Pa) increases with more cells filled, but the allowable Euler buckling force controls for the 8" on center, and almost controls for the 16" on center. From what I'm getting out of the consensus here, the results of the number is correct, that the 8" on center will have a lower Euler buckling load than the 16" on center, although the allowable force as a result of fa will be higher for 8" on center than 16" on center. Euler buckling will control for 8" on center, fa controls for 16" on center. Just seems wrong, that's all.
As for a comparison with steel, there is nothing that limits steel to 1/4 of the allowable Euler buckling load. This is a penalty for using masonry I guess.
RE: Eluer Buckling ACI 530
From table present above, it appears the euler buckling stress for the standard block stands at 266, except the case for 8" grout spa. Since the deviation is less than 10%, the higher stress could be used with confidence. Also keep in mind, when CMU buckles, it's mainly a phenonmenon on faceshell, which suffers the highest compressive force, the grout really has little contribution.
RE: Eluer Buckling ACI 530
Additionally, because this in only a requirement for unreinforced masonry, the Euler buckling equation was modified for a member having resistance in compression, but NOT in tension.
RE: Eluer Buckling ACI 530
See attached.
RE: Eluer Buckling ACI 530
RE: Eluer Buckling ACI 530
Ok, MSJC 2.2.3.1 equations 2-10 and 2-11 are for all members subject to axial compression and/or flexure. Only Fa is different depending whether or not h/r is less than or greater than 99. For compression, isn't all masonry unreinforced unless the bars in the cells are tied, as for columns with 4 bars or more? See 2.3.2.2.1 and eqs 2-17 and 2-18 become 2-12 and 2-13. The reinforcement comes into play for flexural strength for walls. I don't see how Pe doesn't come into play here.
RE: Eluer Buckling ACI 530
Is it the intention of the standard to use Pe/A in place of Fa in the interaction equation? I thought that the Pe check was a completely separate check from the interaction.
I am getting the same values that you get for everything except with e=2 for h/r>99.
For grout @ 16" o.c., I am getting 12,680plf (which you do get), but for grout @ 8" o.c., I am getting 11,021plf (which is much less than your 102,544plf). It appears that your Pe for e=0 and e=2" are identical.
I want to make 2 other points. First, you have to check both equations 2-13, and 2-14, not just one or the other.
Second, while the code doesn't make this clear, I think it's appropriate to do two checks for a wall for equation 2-13. For most walls with an eccentricity at the top, the base is considered pinned, therefore the moment goes from Pe at the top to 0 at the bottom. I check the mid-height of the wall using Fa= eq. 2-15 and M=Pe/2. I would check the top of the wall using Fa=0.25f'm and M=Pe. The reason for this is that there is no stability concern at the top of the wall where the max moment is, and there is a reduced moment at the mid-height of the wall where the real stability concern is. You penalize yourself too much by using the worst case of both.
I also want to say that I typically do use the worst case for both, but see nothing wrong with the approach mentioned above if you're in a pickle.
RE: Eluer Buckling ACI 530
JAE- why no check of Pe in h/r less than 99? If you do check it, then P for 8" o.c. would be less than Pa. From the Pe equation for 8" o.c. I get 7648 lb/lf with E=1350000, In=443,e=2, h=12'. And 8782 lb/lf for 16" o.c.
RE: Eluer Buckling ACI 530
RE: Eluer Buckling ACI 530
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).
RE: Eluer Buckling ACI 530
My appologies - the 102,544 lbs was a mistake - should be 11,021 lbs which you also got.
Is it the intention of the standard to use Pe/A in place of Fa in the interaction equation?
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.
First, you have to check both equations 2-13, and 2-14, not just one or the other.
No, the two equations are for different things - one for Fa and the other for Fb.
check the mid-height of the wall using Fa= eq. 2-15 and M=Pe/2.
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!
RE: Eluer Buckling ACI 530
RE: Eluer Buckling ACI 530
RE: Eluer Buckling ACI 530
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?
RE: Eluer Buckling ACI 530
RE: Eluer Buckling ACI 530
One is for Fa and one is for Fb so I guess yes, both need to be checked.
RE: Eluer Buckling ACI 530
******************************************************
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
RE: Eluer Buckling ACI 530
RE: Eluer Buckling ACI 530
RE: Eluer Buckling ACI 530
BA
RE: Eluer Buckling ACI 530
RE: Eluer Buckling ACI 530
BA
RE: Eluer Buckling ACI 530
RE: Eluer Buckling ACI 530
If you reinforce the section, then it does have tensile capacity and this particular buckling equation doesn't apply anymore.
RE: Eluer Buckling ACI 530
RE: Eluer Buckling ACI 530
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.
RE: Eluer Buckling ACI 530
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!