Development length

A bar can only work at full stress if it is anchored far enough into concrete on each side of the point where that stress is needed. The bond between bar and concrete transfers force gradually, so a certain length is needed to build up the full bar force. That length is the development length. If it is not available, the bar pulls out before it yields and the member fails early.

Development length is found by equating the bar force to the bond force: the bar force is its area times design stress, and the bond force is the perimeter times length times design bond stress. This gives Ld = φ σs / (4 τbd). Deformed (ribbed) bars grip much better than plain bars, and bars in compression need less length because the bar end bears on concrete. Codes give design bond stresses that rise with concrete grade. Bundled bars need extra length.

Where space is short, hooks and bends add anchorage, each counted as an equivalent length. Laps, where one bar ends and another starts alongside it, transfer force through the surrounding concrete and are sized from development length, with extra rules for tension laps and for laps in highly stressed zones. At simple supports, the positive moment bars must satisfy Ld ≤ M1/V + L0, and the M1/V term may be increased by 30 percent where the bar ends are confined by a compressive reaction; this limits bar size at supports. Good detailing staggers laps and keeps them out of plastic hinge regions in seismic design.