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Am I Missing Something?

Am I Missing Something?

Am I Missing Something?

(OP)
I am trying to verify some masonry spreadsheets and I am having a hard time with some things.  
If you have a section with axial load and moment, is it correct to assume that you can analyze the section for each individually and superimpose the results to get max stresses?  This is reinforced masonry.
I got some results for the combined loading that surprised me a little, but I took the results blindly and verified them through mechanics, not design.  Needless to say, it did work out.  I then analyzed the section for axial load only, and for moment only.  I thought I could superimpose the masonry stresses and the steel stresses to get the same stresses that I got when using the combined loading, but it isn't working out that way.  Does anyone have an idea why?  
Am I just completely missing something.
This is ASD, and I thought that for the elastic range of stresses (I know it's not really elastic if it cracks, but we assume so for design), that the principle of superposition applies.

RE: Am I Missing Something?

Without knowing more details about what you did and how, my first thought is: Is it really elastic/linear?

For axial load, it probably behaves elastically, but for bending, I would imagine that your masonry behaves as a non-tension material, i.e. non-linear behaviour.

RE: Am I Missing Something?

Did you remember to multiply by the modular ratio "n"?

RE: Am I Missing Something?

(OP)
n was taken into account for each case individually.

RE: Am I Missing Something?

Is your axial compression greater than or equal to MC/I?  If so, it should behave elastically, no? If not, I think you need an interaction diagram, like in reinforced concrete columns.

RE: Am I Missing Something?

You should be able to superimpose the stresses, P/A +- Mc/I, where A and I have been appropriately "transformed" using n.

What method are you comparing this to?

RE: Am I Missing Something?

(OP)
PMR-
I was using P/A+bending stress due to moment only.  Since this already took n into account, I thought that should work.  Am I thinking about it wrong?

RE: Am I Missing Something?

I don't believe you can superimpose axial and bending analyses.  You need to analyze the section for combined bending and axial load.  An axial force puts the masonry in compression, which allows the masonry which would otherwise be in tension to contribute to the bending resistance.  An example of the analysis for beams is given in the old ACI SP-3 publication.   

RE: Am I Missing Something?

miecz is right on.  The axial load will actually increase the moment capacity of the masonry in most cases.  This is because masonry capacity is typically limited by flexural tension.  Since the axial compression reduces the net tension the flexural capacity increases.  As a result superimposing the axial and flexural stresses will not work out.

RE: Am I Missing Something?

If you are assuming a cracked section for either case (same properties if superimposing or combined axial + bending), I don't know why the results are coming up differently. Same section modulus, same effective area, linear elastic. The spreadsheet may not be calculating based on a cracked section if the axial is high enough under the combined case.  

RE: Am I Missing Something?

The more I really think about, I think others are correct in that you may not be able to directly add P/A and Mc/I if the section is cracked.  The neutral axis location is not a function of applied axial or flexural loads, therefore it is not as straight forward as I originally thought.

Hmmm... something to think about next time I'm "sitting on the throne".

RE: Am I Missing Something?

You can use the unity equation and check for interaction of axial and flexural stresses calculated independently.  You can also check them as combined axial-moment interaction similar to what we do with concrete columns.  Both are acceptable, but the P-M interaction will give you a more efficient design.  As you noted, what you work out with one will not necessarily give the same results as the other.  

RE: Am I Missing Something?

(OP)
Part of what I am having trouble rectifying is that for certain cases, the spreadsheet is telling me that the steel is in compression (i.e. there is a negative stress in the steel), but the kd value it is giving me is less than the d distance.  kd is the depth of the compressive stress triangle and I don't know how you get compression in the steel if the steel doesn't fall within that zone.   

RE: Am I Missing Something?

I think by ACI 530 section 2.3.3.2.2 and commentary you are supposed to add the stress from bending and axial directly and not use the unity equation, but I have seen the unity equation used a lot for reinforced masonry anyway.

In the case where the properties you are using are the same throughout, then I don't see why the results are different between applying the combined load versus adding the axial effects to the bending effects. Remember to also check as T-beam as required.  

RE: Am I Missing Something?

I don't read section 2.3.3.2.2 that way.  I see where it says not to use the unity equation, but I don't see that it says to add the stress from bending to the stress from axial.  Commentary section 2.3.3.2 says "a second compressive stress calculation must be performed considering the combined effects of the axial load component and flexure at the section."

RE: Am I Missing Something?

2.3.3.2.2 The compressive stress in
masonry due to flexure or due to flexure in combination
with axial load shall not exceed (1/3) f'm provided the
calculated compressive stress due to the axial load
component, fa , does not exceed the allowable stress, Fa ,
in Section 2.2.3.1.

RE: Am I Missing Something?

NCMA TEK 14-7A says you can use the unity equation

RE: Am I Missing Something?

2.3.3.2.2- See Commentary for Section2.2.3.1 for information on Fb.The interaction equation used in Section 2.2.3 is not
applicable for reinforced masonry and is therefore not
included in Section 2.3.

RE: Am I Missing Something?

haynewp-

The axial stress, fa, doesn't change, and so it is correct to refer to it as an axial "component."  The bending stress, fb, changes depending an the axial force. Notice there is no mention of a bending "component."  I think the commentary to 2.3.3.2 is more clearly written than section 2.3.3.2.2, but that may be because it says what I believe.

The ACI publication (SP-3) that I referred to in my original post was for ASD of concrete under compression and bending.  I believe the same approach is valid for masonry.  However, my reinforced masonry textbook by Schneider and Dickey uses the unity equation, which, as you say, is clearly dismissed by the commentary 2.3.3.2.2.

RE: Am I Missing Something?

The second part refers to checking the axial "component" against Fa. Again, maybe I am missing why you cannot superimpose axial + bending stresses as long as you are using the same section properties and linear assumption. f=P/A+Mc/I

A side note, all my older examples use the unity equation.

RE: Am I Missing Something?

When set to ACI 530, RISA Masonry uses computes (fa+fb)/Fb for a wall with bending plus axial.

When set to UBC 97, it checks the interaction equation.

RE: Am I Missing Something?

If I understand SP-3 for concrete, the section properties of a bending member change when you add an axial force.  The more compression, the more of the section remains uncracked under bending, and the greater the resistance against bending.  The formula for "k" reflects this, so the compression region, kd, grows with axial compression.  Conversely, a bending member with axial tension will tend to crack more, kd shrinks, and the bending resistance diminishes.

From what I can tell, the unity equation is always conservative, if the axial force is compressive.  It is not conservative if the axial force is tensile.

RE: Am I Missing Something?

"The more compression, the more of the section remains uncracked under bending"

This is what I have been saying, it seems you have to assume a cracked section the whole time to superimpose stresses in this way. There may be some approximation being allowed by ACI 530 to add the stresses directly as RISA is doing. I am not sure at this time what to do exactly, I am going to have to look more into all of this. But it is clear the interaction equation is not to be used for reinf. masonry per ACI 530 commentary.   

RE: Am I Missing Something?

It looks like it is taking the standard axial stress fa based on the uncracked wall area (P/Agross like you normally get checking axial) and adding that to fb which is based on the cracked section properties. Then adding these stresses together for the comparison to Fb. Which is what I have been saying, with the difference that the area for axial is based on the uncracked section. So it appears to me now to be a code allowed approximation to add these stresses together in this manner for axial plus bending on a reinf. member.

RE: Am I Missing Something?

Try to get a hold of ACI SP-3.  It's called the "Reinforced Concrete Design Handbook."  It's ASD and so it's out of print but I was able to get one used on biblio.com for $19.  It treats concrete bending members with tension, compression, double reinforcing, and T sections, if kd exceeds the thickness of the wall.  It's the only publication I've ever seen that addresses this in this manner.

RE: Am I Missing Something?

I once attended a seminar put on by two professors (Porter from Iowa State and Klingerer from Texas) and they both offered a spreadsheet that used an interaction method similar to concrete columns (Per UcfSE's comment above).  

I don't think this is directly found in ACI 530, but the seminar they were giving was ACI 530 based.

 

RE: Am I Missing Something?

Do you remember if the diagrams were set up using
fa/Fa+fb/Fb < 1.0 or (fa+fb)/Fb < 1.0?

RE: Am I Missing Something?

They aren't a direct ratio of actual/allowable.  They are just like concrete columns where there is a P/M interaction "bulb" diagram.  I have a spreadsheet that is written for them but there is a bug in it right now that deals more with excel finding the relative value between the P/M applied vs. the capacity at that P/M value and correctly reporting the unity value.   

RE: Am I Missing Something?

Amrhein has one for reinf. masonry but it is set up for strength design.  Macgregor's concrete has some set up for ratios compared to unity for elastic material then goes into the standard bulb for reinforced concrete.  

I am actually working on some heavily loaded cmu pilasters right now so I will be coming up with some myself based on ASD.    

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