moment along a rebar lap splice

huangyhg

moment along a rebar lap splice
a cantilevered retaining wall that i am designing has vertical bars, lapped with vertical footing dowels.  the wall height from top of footing is 8-feet.  there are footing dowels (#4 @ 9") which extend from the footing, 3-feet into the wall.  they are lapped with vertical wall reinforcing (#4 @ 18") which is 8-feet long; therefore, the lap is 3 feet at the bottom of the wall.
the footing dowels are designed for the moment at the top of the footing.  the vertical reinforcing bars are designed for the moment at the top of footing dowels - at the 3-foot height.  but the moment changes pretty rapidly along the length of the lap, because it is a cantilevered retaining wall.  
how do i know that i don't have a development deficiency at any particular cross section along the lap?

i can see that you are trying tosave steel here, but atwhat cost - your confidence in your design?  why not just design both bars to the moment at the top of the footing and be done with it?  peace of mind is a good thing.
mike mccann
mmc engineering
i agree with mike--however, to answer your question, unless the moment diagram is convex (which it isn't on a cantilever), the bar will always be "more" developed than the moment in the wall.
daveatkins
dave, but the loading is triangular for a cantilevered retaining wall, so the moment is indeed "convex," isn't it?  that was actually the source of my concern, as i imagine a critical section at various positions along the lap, i wondered if moment could increase faster than the gradual development (starting from zero) of the footing bar side of the lap.
thank you both for your input.

no, a convex moment diagram bulges outward, like the moment diagram for a simple span beam.  since the moment diagram for a retaining wall is linear, and development occurs in a linear fashion, your bars will always be developed at least as much as the moment in the wall.
daveatkins
sorry dave, i think i meant concave.  the momenent diagram for a linearly-varying load is parabolic, not linear, right?
jsa2:
randomly check required reinforcing at two locations, say 1' and 2' above the footing. for each location, calculate the reinforcing required and make sure the reinforcing ratio is maintained wthin the range of one development length above this specific location/plane. done.     
i agree with mike.  some extra bars doesn't hurt anyone.   
yes, the moment diagram will be parabolic, and concave.  my mistake.
but, in any event this is better than a linear moment diagram, in terms of development of reinforcing.
daveatkins
the moment diagram for a linearly varying load is concave (cubic, i think).  for a uniform load due to surcharge, it's also concave (parabolic, i think).  so if you have the required reinforcing developed at both ends of the splice, you'll have enough developed in between.  the problem with adding reinforcing when it's not necessary is that, after a while, people start to think that it is necessary.  besides which, somebody has to pay for that extra reinforcing.
kslee, this was my thought too.  i haven't done that yet, but i suspect when i do, i will concur with miecz too. thank you all for your input.