calcsheet
Standard hook development length
Verified against CSA A23.3-24, 2026-10-01
Development length of a standard hook in tension, to CSA A23.3-24 Cl. 12.5. Calculate the development length of a standard hook in tension per CSA A23.3-24 Cl. 12.5. Input concrete strength, steel yield strength, bar size and hook type, the side cover, the ties or stirrups enclosing the hooks and the spacing of the hooked bars, and the coating and density conditions that apply. The four factors of Table 12.5 are worked out from those inputs and each is shown with the row that set it. Excess reinforcement may shorten the length per Cl. 12.5.5, never below 150 mm or eight bar diameters, and at a member end the calc checks the enclosing ties of Cl. 12.5.6. Straight bars are the Tension development length and Compression development length pages.
Given
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This printed copy omits the derivation. The full report, with every step, is the PDF at https://calc.struct.work/calc/development-length-hooked.pdf.
Results
| Quantity | Description | Value | Unit |
|---|---|---|---|
| \(\htmlClass{sym-l_dh}{l_{\mathrm{dh}}}\) | Hook development length required | 229 | \(\mathrm{mm}\) |
| \(\htmlClass{sym-l_hb}{l_{\mathrm{hb}}}\) | Basic hooked bar development length, Cl. 12.5.2 | 229 | \(\mathrm{mm}\) |
Derivation
Branch: \(c_{\mathrm{side}} \geq 6 \cdot d_{b}\) did not hold
Cl. 3.2, A_hs
\[\begin{aligned} \htmlClass{sym-A_hs}{A_{\mathrm{hs}}} &= \htmlClass{sym-n_h}{n_{h}} \cdot \htmlClass{sym-A_b}{A_{b}} \\ &= \htmlClass{sym-n_h}{2} \cdot \htmlClass{sym-A_b}{200\ \mathrm{mm}^{2}} \\ &= 400\ \mathrm{mm}^{2} \end{aligned}\]Branch: \(A_{\mathrm{th}} \geq 0.4 \cdot A_{\mathrm{hs}}\) did not hold
Branch: \(s_{h} \geq 6 \cdot d_{b}\) held
Cl. 12.5.2, with the 8 MPa cap of Cl. 12.1.2
\[\begin{aligned} \htmlClass{sym-l_hb}{l_{\mathrm{hb}}} &= \frac{\htmlClass{sym-k_l}{k_{l}} \cdot \htmlClass{sym-k_c}{k_{c}} \cdot \htmlClass{sym-k_d}{k_{d}} \cdot \htmlClass{sym-k_r}{k_{r}} \cdot \htmlClass{sym-f_y}{f_{y}} \cdot \left(\frac{\htmlClass{sym-d_b}{d_{b}}}{1\ \mathrm{mm}}\right)^{1.5} \cdot 1\ \mathrm{mm}}{30 \cdot \left(\frac{\min\left(\htmlClass{sym-f_c}{f_{c}}, 64\ \mathrm{MPa}\right)}{1\ \mathrm{MPa}}\right)^{0.25} \cdot 1\ \mathrm{MPa}} \\ &= \frac{\htmlClass{sym-k_l}{1} \cdot \htmlClass{sym-k_c}{1} \cdot \htmlClass{sym-k_d}{1} \cdot \htmlClass{sym-k_r}{0.6} \cdot \htmlClass{sym-f_y}{400\ \mathrm{MPa}} \cdot \left(\frac{\htmlClass{sym-d_b}{16\ \mathrm{mm}}}{1\ \mathrm{mm}}\right)^{1.5} \cdot 1\ \mathrm{mm}}{30 \cdot \left(\frac{\min\left(\htmlClass{sym-f_c}{25\ \mathrm{MPa}}, 64\ \mathrm{MPa}\right)}{1\ \mathrm{MPa}}\right)^{0.25} \cdot 1\ \mathrm{MPa}} \\ &= 229\ \mathrm{mm} \end{aligned}\]Cl. 12.5.1 and 12.5.5
\[\begin{aligned} \htmlClass{sym-l_dh}{l_{\mathrm{dh}}} &= \max\left(\htmlClass{sym-l_hb}{l_{\mathrm{hb}}} \cdot \htmlClass{sym-A_s_ratio}{A_{s,\mathrm{ratio}}}, 8 \cdot \htmlClass{sym-d_b}{d_{b}}, 150\ \mathrm{mm}\right) \\ &= \max\left(\htmlClass{sym-l_hb}{229\ \mathrm{mm}} \cdot \htmlClass{sym-A_s_ratio}{1}, 8 \cdot \htmlClass{sym-d_b}{16\ \mathrm{mm}}, 150\ \mathrm{mm}\right) \\ &= 229\ \mathrm{mm} \end{aligned}\]Questions
When does k_l drop to 0.8?
Table 12.5 gives 0.8 to a 35M or smaller hook with side cover normal to the plane of the hook of at least 6 d_b, or to one ending inside a column core with that side cover at least 60 mm. 45M and 55M hooks take 1.0.
When does k_r drop to 0.6?
For 35M and smaller hooks enclosed by ties or stirrups with A_th of at least 0.4 A_hs, or spaced at least 6 d_b centre to centre. The ties have to satisfy Condition 1 or 2 of Cl. 12.5.4. At a discontinuous end Cl. 12.5.6 allows it only for a hook anchored in a column with both the side cover and the top or bottom cover over 60 mm, and the calc applies that.
What sets the floor on l_dh?
Cl. 12.5.1: l_dh is never less than 8 d_b or 150 mm, whichever is greater, and that holds after the A_s_ratio reduction of Cl. 12.5.5. Eight diameters passes 150 mm from 20M up, since 8 x 19.5 = 156 mm.
What does Cl. 12.5.6 ask for at the end of a member?
Where both the side cover and the top or bottom cover to the hook are under 60 mm, the hook is enclosed along l_dh by ties perpendicular to it at no more than 3 d_b, and the first tie encloses the bend within 2 d_b of its outside. The calc checks both, from s_t and e_t.