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"What are the requirements for overlapping splices of rebar?"

My experience of working with re-bar in concrete for many years is that splices should be made at least 24 times the diameter of the re-bar being used (1/2-inch re-bar overlapped a minimum of 12-inches, etc.). This is also true at corners, where just crossing over an opposing piece would be essentially useless. A proper overlapping joint is very important. The purpose of using re-bar is to hold the concrete in compression, which is where concrete has its strength.

Typical minimum overlap at splices of reinforcing in a wall is 40 times the diameter of the reinforcing bar, therefore, reinforcing bar should be overlapped at splices a minimum of 20 inches.  The American Concrete Institute (ACI) basically writes the code for concrete construction.  For more information, look up ACI and specifically, chapter 318.