Am I Missing Something?

[Lion06]

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.

 

[bkal]

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.

 

[PMR06]

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

 

[Lion06]

n was taken into account for each case individually.

 

[graybeach]

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.

 

[PMR06]

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?

 

[Lion06]

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?

 

[miecz]

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.

 

[MarcbSE]

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.

 

[haynewp]

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.

 

[PMR06]

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".

 

[UcfSE]

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.

 

[Lion06]

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.

 

[haynewp]

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.

 

[miecz]

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."

 

[haynewp]

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.

 

[par060]

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

 

[haynewp]

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.

 

[miecz]

haynewp-

The axial stress, f_a, doesn't change, and so it is correct to refer to it as an axial "component." The bending stress, f_b, 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.

 

[haynewp]

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.