determination of "c" of Boundary Element from ACI

[jenofstructures]

Good day everyone,

this topic is a big question for me for so long
its all about the ACI 318-08 Section 21.7.6.2 on how to know if a certain shear wall needs a boundary element

the formula is ok, but I still dont get how some examples I see in the internet is solving the neutral depth "c" in this computation. Those examples are already uses a value of "c" thAt is already coming from an "in house" computer program.

how did they determine the "c" value?
and it will be a big help also if there's a reference regarding any manual calculation regarding "c"

thank you in advance!!!!



Poems are made by fools like me, but only God can make a tree. engineers creates wonderful buildings, but only God can creates wonderful minds

 

[ishvaaag]

Normally the of the neutral axis is derived from one compatibility of deformations analysis of the studied section under the standing moment of interest. It can also be derived with enough accuracy from any of the accepted simplified compressed block models again with the same moment of interest.

 

[jenofstructures]

@ishvaag, what do you mean with the under standing moment of interest?

Poems are made by fools like me, but only God can make a tree. engineers creates wonderful buildings, but only God can creates wonderful minds

 

[ishvaaag]

I mean than when looking for a depth or position of a neutral axis you are essentially studying a case of status of some section under some specific moment. Every different moment will give a different depth of neutral axis. Normally, for a situation like the one looking for strength for a seismic shearwall at the extreme event being considered, this would be the maximum moment appearing at the factored level in the tentative analysis (without boundary elements) and then looking on that decide if such boundary elements need to be included.

Seeing that the code says that

"c in Eq. (21-8) corresponds to the largest neutral
axis depth calculated for the factored axial force and
nominal moment strength consistent with the design
displacement ?u. Ratio ?u /hw in Eq. (21-8) shall not
be taken less than 0.007"

it is clear it is a (factored) flexo-compression loadcase producing ?u, then look within it for the section producing the highest c anywhere in the height of the shearwall for such hypothesis.

So you need a mathcad worksheet or excel sheet or any other tool doing the referred sectional analysis for the P-M solicitations at the investigated sections. The simplest (but only approximate) way is to assume a rectangular ACI stress block satisfying the P-M equilibrium, and if only considering tension steel compression-tension equilibrium can be established even by hand; otherwise it is better to use one of the referred tools.

 

[ash060]

It would be equal to (Compression force/0.85f'cb)/ Beta. The compression force is equal to the tension force plus the applied compression Pu.

To make it simple you can assume that only the tension chord steel yields and add that to the applied compression force Pu also assume that the compression steel does not contribute to the compression force. From the way I am reading that section if your "c" is small enough you don't need a special boundary element. Once you have that number use the expression above and that will get you a "c" that is a good guess.

I am not very familiar with Chapter 21 as I don't do much seismic stuff, but I would think that you could get a good idea if you need this element from the numbers above.