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Eluer Buckling ACI 530
3

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?

RE: Eluer Buckling ACI 530

Can you post the equation for Pe calculation?

RE: Eluer Buckling ACI 530

(OP)
Pe = [pi^2*Em*In/(h^2)]*(1-0.577*e/r)^3

RE: Eluer Buckling ACI 530

What happens if you grout at 32" centers?

BA

RE: Eluer Buckling ACI 530

Case I - grout @8" ctr. I = 443
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

because for case 2 you are adding material to the inside of the section.  It's the same reason that the r of a HSS with a 1/8 wall thickness is greater than the r of the same HSS with 5/8 wall thickness.

RE: Eluer Buckling ACI 530

(OP)
r=(I/A)^0.5

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

I'm really not familiar with Masonry design, but my guess is that it's exactly what StrEIT mentioned.

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

Good point. But while I can understand the HSS, I am ignorant on properties of CMU block, thus, I still don't understand.

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

If I am remembering correctly, that equation attempts to account for second order effects (that is what the (1-e/r)^3 factor is in there for).  If you take that out it is the traditional EULER buckling equation and your capacity goes up as the number of grouted cells increases, as you would expect.  
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 think StrEIT got this one right (about 1-0.5779(e/r)^3) term). Per properties taken from NCMA manual (standard block with faceshell bedding), and the simplified Pe expression stated before, below are the results for grout space arranged from 0" (no grout) to 72", with e = 2":           

    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

(OP)
For an interior wall with 5 psf load (dealing with stack bond here so it is a little different than running bond). Allowable Pe is 1/4Pe I get the following

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

I have little different take on this.
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

Alright, I did a little more looking into this.  First of all the Euler buckling load for the wall is only applicable for h/r>99 per MSJC 2.2.3.1.  
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

I might add that these calcs are based upon ACI 530-05.

RE: Eluer Buckling ACI 530

(OP)
Great discussion.  My design is working out fine with the lower buckling stress for 8" on center, so I'm going with the reduced load based on 1/4 Pe.

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

JAE-

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

(OP)
I too am in ACI 530-05, maybe equation numbers are different in other versions.  

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

(OP)
So I just read something.  That Pe for unreinforced masonry is 0.25 because of the reduced moment of inertia and inherent eccentricity due to the cracked section.  The Pe is not something checked in ACI 530 section 2.3.  Can anyone verify this?

RE: Eluer Buckling ACI 530

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).

RE: Eluer Buckling ACI 530

StructuralEIT,
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

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

RE: Eluer Buckling ACI 530

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).

RE: Eluer Buckling ACI 530

(OP)
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?

RE: Eluer Buckling ACI 530

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

RE: Eluer Buckling ACI 530

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.

 

RE: Eluer Buckling ACI 530

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

 

RE: Eluer Buckling ACI 530

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.

RE: Eluer Buckling ACI 530

"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.

RE: Eluer Buckling ACI 530

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

RE: Eluer Buckling ACI 530

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

RE: Eluer Buckling ACI 530

Good!  And the sooner the better!

BA

RE: Eluer Buckling ACI 530

Nice catch, Waldo459.

RE: Eluer Buckling ACI 530

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.

RE: Eluer Buckling ACI 530

(OP)
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.

RE: Eluer Buckling ACI 530

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.

RE: Eluer Buckling ACI 530

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!   

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