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.

 

[haynewp]

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.

 

[miecz]

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.

 

[haynewp]

"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.

 

[haynewp]

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.

 

[miecz]

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.

 

[haynewp]

See page 5. ACI 530 uses (fa+fb)/Fb < 1.0 instead of the standard interaction equation. ie. fa+fb<Fb

http://www.nwcma.org/Articles/Masonry_Design_Method_Choices.pdf

 

[JAE]

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.

 

[haynewp]

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

 

[JAE]

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.

 

[haynewp]

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.

 

[haynewp]

Klingner

http://www.concrete.org/tkc/documents/allowable_stress_design_of_RC_masonry_shear_wall.pdf