Beam Bond & Development
Analyze tension development lengths ($\ell_d$), lap splices, and standard hook requirements for beam reinforcement based on ACI 318M-11.
1. Tension Development Length ($\ell_d$)
Based on ACI 318M-11 (Section 12.2) / McCormac & Brown Chapter 7 (SI Units).
$$ \ell_d = \frac{9}{10} \frac{f_y}{\lambda \sqrt{f'_c}} \frac{\psi_t \psi_e \psi_s}{\left(\frac{c_b + K_{tr}}{d_b}\right)} d_b $$
Required $\ell_d$:
-- mm
2. Tension Lap Splice
3. Tension Hook Development ($\ell_{dh}$)
$$ \ell_{dh} = \max \left( \frac{0.24 \psi_e f_y d_b}{\lambda \sqrt{f'_c}}, 8d_b, 150 \text{ mm} \right) $$
Note: Hooks are considered ineffective for compression bars (ACI 12.5.5).