Bond, Anchorage, and Development Length

Bond, Anchorage, and Development Length

Reinforcement must be embedded in concrete a sufficient distance to develop its yield strength. This distance is called the development length ($l_d$).

Development Length in Tension ($l_d$)

The basic development length equation for deformed bars in tension:

$l_d = \left( \frac{f_y}{1.1 \lambda \sqrt{f'_c}} \frac{\Psi_t \Psi_e \Psi_s}{c_b + K_{tr}/d_b} \right) d_b$

Where:

• $\Psi_t$: Reinforcement location factor (Top bars).
• $\Psi_e$: Coating factor.
• $\Psi_s$: Size factor.
• $c_b$: Smaller of (a) distance from center of bar to nearest concrete surface, or (b) one-half the center-to-center spacing of bars.
• $K_{tr}$: Transverse reinforcement index (often taken as 0 for simplicity).

Standard Hooks

Hooks are used when straight development length is not possible due to space constraints. Standard hooks are 90-degree or 180-degree bends.

---

Solved Problems