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# Development of Bundled Bars

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**To**: **"SEAINT List (E-mail)" <seaint(--nospam--at)seaint.org>**
**Subject**: **Development of Bundled Bars**
**From**: **"Adair, Joel" <JAdair(--nospam--at)Halff.com>**
- Date: Tue, 4 Feb 2003 14:05:14 -0600

I have a question
regarding the interpretation of section 12.4 of ACI 318 (-99 or -02) about the
development length of bundled bars. 12.4.1 states that the development
length of a 3-bar bundle is 20% greater than a single bar, and a 4-bar bundle is
33% greater. That seems simple enough. Then, 12.4.2 states, "For
determining the appropriate factors in 12.2, a unit of bundled bars shall be
treated as a single bar of a diameter derived from the equivalent total
area." So, I use the equivalent diameter in determining my alpha, beta,
gamma, and lambda factors of 12.2.2 or 12.2.3. That seems pretty
straightforward, too.

Now the
confusion: If I'm using 12.2.3 to calculate my lengths, the right side of
equation uses d_b in the (c+K_tr)/d_b term. My thinking is that I should
use the equivalent diameter here, as well, because the commentary R12.4.2 says,
"...it is necessary to use an equivalent diameter of the entire bundle derived
from the equivalent total area of bars when determining factors in 12.2, which
considers cover and clear spacing and represents the tendency of concrete to
split." It seems that since the (c+K_tr)/d_b term is dealing with the
resistance of the transverse reinforcement to splitting, I should use the
derived diameter here, rather than the actual bar diameter. Any
comments?

Now, for the other
point of confusion: Should the d_b on the left side of the equations in
12.2.2 and 12.2.3 be the equivalent diameter or the actual diameter?
My thought is that this one should be actual bar diameter, not the equivalent
one. This is because of my interpretation of the first part of R12.4.2:
"Although splice and development lengths of bundled bars are based on the
diameter of individual bars..." What are your thoughts on this
one?

Thanks in
advance.

--
Joel

------------------------------------------------------------------

**Joel C. Adair,
PE**

Halff Associates, Inc.

8616 Northwest Plaza Drive

Dallas, Texas 75225

Phone: (214) 346-6287

Fax: (214) 739-0095

E-mail: jadair(--nospam--at)halff.com

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