Slender Wall Design - Iterative Deflection vs. Direct Calculation

[UCFEngineer]

Section 14.8.3 of the alternative design of slender walls for ACI 318-02 (as well as '05 and '08) states that the moment at the midheight section of the wall due to factored loads and P-Delta effects (Mu) can be obtained by iteration of deflections using equations 14-4 and 14-5 or by direct calculation using equation 14-6. The problem I have is that if you put equation 14-5 into 14-4, you get equation 14-6...therefore, I get the same value and there is no difference between these 2 methods.

Is there something I'm missing? I could see if you were allowed to use the full section (Igross) up to the cracking moment and then use a cracked section (Icracked) from the cracked moment to the factored moment (Mu), but that is not how Section 14.8.3 reads.

 

[JAE]

There is no difference that I see. I think what the code is doing here is first presenting the "pure" format of the concept and then rearranging the terms to make the calculation easier.

This is even implied by the language -

first they say iterate the deflections until the Mu on both sides of equation 14-4 are equal (the Mu on the left and the Mu that shows up in the [Δ]).

then they say "or by direct calculation" which implies that these are finding the same result.

The iteration is no sequential [Δ]'s from a second, third, fourth order analysis, but rather iterations finding equivalency on either side of the equation.

 

[UcfSE]

I see no difference either.

Go Knights?

 

[UCFEngineer]

Thank you both for the responses.

If these equations are part of the same "method", then this portion of the code makes more sense, but I don't understand why they would show the development of the direct calculation equation. It seems to be redundant.

On top of that, I sent this exact question to ACI and got the following response:

"The calculation of the second order moment by iteration of deflections using equations 14-4 and 14-5 of ACI 318-02 is done in an iterative fashion with the number of iterations depending on the power of the computing tool.

If one plugs Eq. 14-5 into Eq. 14-4 to obtain Eq. 14-6, that results in an estimated ultimate condition and that is termed as the direct calculation procedure."

To me, this response makes it seem as though the are not the same method. Maybe I am reading into it too much?

And UcfSE, GO KNIGHTS! Class of 2000

 

[JAE]

OK - I won't mention what school I went to - but I think you had our past football coach there for a while...or was that USF?

Anyway - one comment on the ACI response. They may not always be right. Depends on who answered it.

 

[haynewp]

I see them as different methods. A p-delta iteration versus direct amplification to estimate Mu.

(Mu) can be obtained by iteration of deflections using equations 14-4 and 14-5 or by direct calculation

My ACI-05 doesn't say "using equations 14-4 and 14-5", it just says "Mu shall be obtained by iteration of deflections, or..".

 

[UcfSE]

Typically I would think of P-[Δ] as an iterative process as we see in the first set of equations. In this particular case there is a closed-form solution so I don't see why they retain 14-4 and 14-5 unless perhaps for historical reasons.

c/o 2001.

 

[UCFEngineer]

I thought they were supposed to be different methods as well, but if you place equation 14-5 into 14-4 you get equation 14-6...so they seem to be the same.

However, if they are the same method, I'm not happy with the way it is presented.

 

[miecz]

PCA's Notes on ACI 318-02 says that 14-6 is derived from 14-4 and 14-5. It also says that the whole method was first published in the UBC, but that ACI has modified the method. I believe that, in the earlier UBC versions, equation 14-6 didn't exist. Also, notice that the deflection in the following section is iterative.

 

[haynewp]

The older UBC examples I remember reviewing a long time ago iterated to get Mu. I don't care for the way ACI has this section presented. ENERCALC still gives the option to use a direct or an iterated method to get Mu. Comparing the two gives significantly different results.

 

[strucguy]

Here's an interesting article on why the slender wall design section in ACI318-02 &05 has been modified in ACI318-08.

http://www.gostructural.com/article.asp?id=1474

As you all know, the method given in ACI-318 is similar to what's given in Unified Building Code. And, the article clearly explains why ACI has decided to adopt the method given in UBC.

Also, there is difference between using the iterative method and direct P-Delta analysis method.

In iterative method(ACI318-08) the value of Delta_u is varied using equations 14-8 & 14-9, until the value of M_u converges in eq. 14-4.

Whereas in direct design method, the concrete is assumed to be cracked. Delta_u is calculated by using eq 14-5 and then applied in eq 14-4 to get M_u. This mehtod is true if the out of plane loads are significantly high such that the concrete cracks. But, that isn't always the case.

Hope my explanation helps. I can be a little bit more specific on the iterative method. Please let me know.
Thanks.

strucguy