In clause 220.127.116.11, in the text:
“Where a bar ends in a standard hook complying with Clause 18.104.22.168, the tensile development length of that end of the bar, measured from the outside of the hook/cog, shall be taken as 0.5 Lsy.t or 0.5 L_st as applicable”
I could not figure out what the “0.5 L_st as applicable” refers to. Since the bar ends in a standard hook/cog, shouldn’t the bent portion of the bar contribute to one half of Lsy,t as pointed out by Warner et al (reinforced Concrete 3rd Edition, p.173)?
I wonder if this clause was written to make design easier by assuming that the straight portion (measured to the outside of the cog) contribution as 0.5L_st (assuming that a full yield strength is not required) and the cog portion contribution conservatively assumed to be 0.5 L_st even though the cog portion contribution is actually 0.5 Lsy,t (> 0.5 L_st).
If I am evaluating the anchorage capacity of a rebar (in an existing structure) with a standard cog having a horizontal anchored portion (measured to the outside of cog) of length x (where x < 0.5 Lsy,t), is my total anchored length = x + 0.5 Lsy,t or is it 2x ?
0.5 Lsy.t and 0.5 Lst are the same concept, the length of a hook is half the straight development length. Use Lsy.t if you want the hook to develop the full yield strength (fsy) of the bar. Use Lst (22.214.171.124) if you only need to develop a portion of the yield strength.
I would say that if x is less than 0.5 Lsy.t then x = 0.5 Lst. Therefore, from 126.96.36.199, the stress than can be developed at x, sigma_st = fsy (2 x) / Lsy.t. It’s perhaps conservative but it’s defensible with a literal reading of the code. The development length of a hook is empirical so I would tend to be literal with the reading.
As a check you can look at it the other way around. Say you only want to develop half the yield strength of the bar. That would make Lst = 0.5 Lsy.t. With your first interpretation that would mean that with a hook x could be zero (the end of the cog) since the remainder of the hook would develop 0.5 Lsy.t… That wouldn’t seem unreasonable. Your second interpretation would give x = 0.25 Lsy.t.
Above is a snippet.