Well, laps can transfer axial force, but I’ve never heard of a lap splice (or a bar, for that matter) that can transfer bending.
Lap splice provisions in ACI are a conservative yield envelope based on a bunch of tests that can be found in the referenced research. Anything less than that and you run the risk of bar pull-out (bond failure) or concrete breakout (substrate failure).
I do not envy you this task. Just have the contractor redo it!
Can you elaborate more on your situation? Are you actually trying to size the reinforcing for bending, or just determine the lap required for steel in a flexural element so you maintain the original bending capacity of the specified beam?
Lap splices only speak to the transfer of axial bar stresses from one bar to the next. Even if the member is being designed for bending, the bar stresses are still axial.
Speaking to tension laps in general terms, it goes like this:
1) Use code provisions like the one below to work out the development length of the bars as a function of their diameter (loosely reflecting bond stress).
2) Take your lap / splice length to be a multiple of the development length. 1.30 X or something like that depending on your code. This theoretically allows you to transfer the full yield stress of the bars being considered across the splice.
3) In some, but not all situations it maybe be permissible to prorate your splice tension capacity for a partially lapped bar configuration.
