Masonry wall problems calculating neutral axis outside face shell

[mjl23]

Hi, I'm looking for a little more guidance on calculating the neutral axis for a masonry wall when the neutral axis is not within the face shell thickness. I worked through one scenario below, but the result obviously looks wrong. The formula to calculate k looks wrong under further scrutiny, doesn't look like a positive value would result in any case?


I assumed the following:
(1) Allowable stress design
(2) 8" thick wall
(3) Partially grouted with 1-#5 at 24" spacing

From NCMA Tek 14-7A:
[tt]
k = [-As n - tfs(b - bw)] / (d b)

NCMA Tek 14-1B gives the following:
tfs = 1.75 in
tweb = 0.75 in
wblock = 15 + 5/8in

Where:
b = width of section
bw = for partially grouted walls, width of grouted cell plus
each web thickness within the compression zone


|<---->|---S_core

-------------------------------------------
|| || || || || || ||
|| @ || || || @ || || ||
|| || || || || || ||
-------------------------------------------

|<------S_grout----->|

So I would do the following:

b = width of section = grout spacing = S_grout
bw = b - b_cores

b_cores = summation of ungrouted core widths
b_cores = N_core x b_core

b_core = width of core = (wblock - 3*tweb) / 2 = 6.688

N_core = number of ungrouted cores
N_core = (S_grout - S_core) / S_core

S_core = spacing of cores = 8"

N_core = ( 8 - 8)/8 = 0 ungrouted for 8" spa
N_core = (16 - 8)/8 = 1 ungrouted for 8" spa
N_core = (24 - 8)/8 = 2 ungrouted for 8" spa
N_core = (32 - 8)/8 = 3 ungrouted for 8" spa
N_core = (40 - 8)/8 = 4 ungrouted for 8" spa
N_core = (48 - 8)/8 = 5 ungrouted for 8" spa


bcores = 2 x 6.688 = 13.375
bw = 24- 13.375 = 10.625
d = middle of 8" wall = 3.8125
n = 29,000,000 / 1,350,000 = 21.48

As = 0.155 sq. in. (1 - #5 at 24" spacing, 0.31 sq. in per bar)

k = [-As n - tfs(b - bw)] / (d b)
k = (-0.155*21.48 - 1.25*(24-10.625)) / (3.8125*24) = -0.2191
[/tt]

 

[haynewp]

I think you messed up when you figured the NA is not in the face shell. I get k=0.3156 and kd=1.2 in which is less than face shell t=1.25 in.

 

[mjl23]

Oops. You are correct. I come up with the same.

However, if I change the spacing to 16", then the neutral axis is not within the face shell.

[tt]
rho x n = 0.005082 x 21.4815 = 0.1092
k = (2 x rho n + (rho n )^2)^0.5 - rho n
k = (2 x 0.1092 + (0.1092)^2)^0.5 - 0.1092
k = 0.3707
kd = 1.413 > 1.25 face shell

So then using previous formula with:
b = 16
sgrout = 16
score = 8
Nungrouted cores = 1
bcore = 6.6875

bcores = 6.6875
bw = 9.3125

k = [-As n - tfs(b - bw)] / db = -0.2189
[/tt]

So negative k makes no sense. I have the MSJC Designers Guide, but they conveniently make everything fully grouted, or when it's partially grouted, the neutral axis falls within the face shell. I find no examples when the neutral axis is outside of the face shell. I'm trying to put together a spreadsheet that will address this case when it comes up.

 

[haynewp]

It looks like you are using "b" in the denominator instead of "bw". But I think it still comes out negative, I think the formula is wrong.

A common approximation that I have used before can be found on page 5-7 here:

http://www.wbdg.org/ccb/ARMYCOE/COETM/tm_5_809_3.pdf

I tried to derive the formula you are using with the web contribution and I got an answer that was very close to the one using the approximate formula.

 

[UcfSE]

The TEK says to use the equation you reference when the NA is located within the core. It references equation 10 "with the neutral axis in the compression
face shell". Do you use the MDG put out by ACI?

 

[mjl23]

UcfSE

I have the Masonry Design Guide found here:

http://www.cement.org/bookstore/profile.asp?itemid=lT305

I'm not sure if I understood your comment about the TEK. If I use eqtn 10 then the neutral axis is not in the face shell, so I tried to use the other formula which seems bogus. I've read elsewhere the data/formula in the TEKs are not so reliable.

haynewp

I had just actually gave up on the TEK formula and calculated based on the Army Corp formula. I was hoping to do something more accurate but that may be the best I can get for now. The Army Corp formula basically disregards the web contribution completely.

One thing I realized I was probably doing wrong was not using the same 'b'. When I calculated rho (As/bd) I had b = 12inch design width.

I was reluctant to use the Army Corp publication because of it's age. I'm a little surprised the ACI manual or the design guide doesn't offer more guidance in the way of section properties, wall weights, and this subject.

The design guide doesn't say where they come up with the wall selfweight either.

Thanks for your help.

 

[UcfSE]

You can use the equations provided in the MDG. The one you reference is the same I was thinking of. It is probably easier to leave the NA location as a variable to be iterated and write a different equation for each zone the NA can be in, i.e outisde the wall, inside the tension flange, in the core, in the compression flange. Working this way you can create a moment-axial interaction curve for your specific wall properties and reinforcing.

It is not necessary to check this explicitly each time you design a wall. Some of the equations can be simplified if you are not checking axial interaction like you would in the diagram (not the same as the linear interaction equation). Are you trying to create an interaction diagram?

JK = (2M)/(bd²F_b)

K = 0.5*(3-[&radic;](9-12JK))

J = 1-K/3

A_s = M/(F_sJd)

 

[mjl23]

UcfSE

Thank you. I was diverted from this task for a bit and needed to ponder what you said.

I guess my problem of "solving" for the neutral axis goes away if I create an P-M interaction diagram like you say. I should be able to to isolate the contributions of the web and flange more easily.

Reviewing the MDG and your post above I am confused about the neutral axis being "outside of the wall". I see in the MDG where the kd value exceeds the wall thickness, so I gather this is what you are referring to. I haven't made many interaction diagrams (maybe not since college) so I guess the reality of that point never hit me.

I'm more familiar with the LFD approach in general, but most of the examples I found dealt with ASD so I went that direction initially. It's good to understand both approaches anyway.

Do you guys cook your own calculations or use commercial software?

I'd post my spreadsheet, but I guess this forum doesn't permit it.

 

[UcfSE]

I have a spreadsheet that uses VB to interate over a broad range of NA values. This creates a P-M interaction diagram. Then it's just plotting points of (M,P) and seeing if you are inside the curve.

You can use the equations I posted pretty easily to calculate moment strength. These will not reflect the moment increase due to axial load, so it's a bit conservative depending on your load. You should derive those relationships, for your own benefit. It's not difficult at all, just a few lines. Initially they look curcular but they work and you can avoid the charts for NA and steel ratio.

 

[mjl23]

I recognized / confirmed all but
K = 0.5*(3-?(9-12JK))

VB huh? That's nice. I thought about just doing it originally in mathcad so I could actually plot the curves, etc. but opted to keep it in excel.

I'd be interested to see how you coded that. Are you writing from VB to cells and then graphing, or do you graph straight away from VB?

Going that route (VB) I imagine you can plot a wide range of demand values as well (doing several load combinations and various points of wall height to get a wide range of P-M).

I had started to do the wall forces analysis using a UDF (user defined function), but I noticed the calculation time increased significantly compared to leaving it in excel so aborted that approach.

Back to my original topic, what do you use for the web width? MDG conveniently makes all their examples fully grouted or NA in the face shell. I derived something on my own above, but I saw where the Army Corp publication just assumes 7 1/2", regardless of grout spacing apparently.

 

[JAE]

I went to a masonry seminar a few years ago - taught by two profs - Max Porter from Iowa State and Richard Klingner from Texas. They had a spreadsheet set up to create a P-M interaction diagram for masonry which they shared with the attendees.

I took the thing and formatted it for our office use. Turned out OK. I hate to say it but there's been enough time gone by that I would need to get back into the spreadsheet to see how we used it.

But if you tried to contact either of those two at their respective universities, they might be able to send you a copy.

 

[DaveVikingPE]

USACE is about to release a new Masonry Structures Design UFC to replace TM 809-05-3; strength design is "in" ASD is "out."

 

[UcfSE]

I take the web/core to be the width of the core from out to out of web plus the width of the filled core.

The VB plots a table of values at each iteration of NA. Besides having just the final P and M value, you can have it return other things like steel stress, masonry stress, stress in each piece used to make the whole, etc. It's pretty to have it return other values as well that help with error checking and hand-verification. It does take a bit to get into but once you have an application and work it through, it's not so bad. The interaction diagram itself can be plotted on another sheet in the same workbook based on the values in the table returned by the VB.

 

[mjl23]

That's what I ended up doing. I calculate strains, stresses for masonry/steel, then calculate compression/tension forces for each component and then the resisting moment for each component. I just did it in the excel cells though rather than VB.

Now that I've gained some comfort level with ASD I'll probably create a parallel worksheet to do LFD. Again I found more examples in ASD so I was checking my results. I agree that LFD is probably the way to go, I just didn't find any worked examples for verification.

I was unable to find any worked examples for either ASD or LFD for partially grouted though. For now I'm using a "web width" I originally posted above. I guess it would be alot easier to just use the width of 1 filled core and its adjacent webs, but I was looking to be more accurate.

The P-M diagram I get is not "smooth" for the partially grouted condition. Is there a way to post pictures on this forum so you could tell me if you think the diagram looks reasonable? I have a smooth curve for the fully grouted condition, but I get a small break in the plot roughly around the maximum moment location. It seems like it might be ok (basically the curve is different only in the region of the graph that corresponds to the height of the core).

 

[UcfSE]

thread507-113569

Check my first reference in the first response. Amrhein's text is generally well-liked so I've heard. It is a bit old and doesn't use the ACI but the principles still apply. This book also has some good tables in the appendices you may find useful or at least informaitonal.

Click on the "Process TGML" link just above the "Submit Post" button for information on posting pictures.

The P-M curve won't be smooth. It will have kinks, or sharp turns. It should be continuous though.

 

[mjl23]

Thanks, that looks like a real good reference. Looking at the table of contents looks like it might have answered most of my questions.

I'll try to post my P-M diagram.