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# Development of Bundled Bars

• To: "SEAINT List (E-mail)" <seaint(--nospam--at)seaint.org>
• Subject: Development of Bundled Bars
• 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?

-- Joel

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