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?

 

[kslee1000]

Can you post the equation for Pe calculation?

 

[waldo459]

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

 

[BAretired]

What happens if you grout at 32" centers?

BA

 

[kslee1000]

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")?

 

[Lion06]

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.

 

[waldo459]

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.

 

[frv]

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.

 

[kslee1000]

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.

 

[Lion06]

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.

 

[kslee1000]

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?

 

[waldo459]

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.

 

[kslee1000]

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.

 

[Lion06]

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.

 

[JAE]

I did some full calculations looking at e = 0 and e = 2 inches (and also for h/r < 99 and h/r > 99) and these are attached to this post. The result is that the 8" fully grouted wall always takes MORE load than the 16".

See attached.

 

[JAE]

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

 

[waldo459]

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.

 

[Lion06]

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.

 

[waldo459]

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.

 

[waldo459]

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?