calcsheet
Compression development length
Verified against CSA A23.3-24, 2026-10-01
Development length of a reinforcing bar in compression, to CSA A23.3-24 Cl. 12.3. Calculate the development length of a reinforcing bar in compression per CSA A23.3-24 Cl. 12.3. Input concrete strength, steel yield strength, bar size, clear cover and clear spacing, the transverse reinforcement crossing the splitting plane, and the coating and density of Table 12.3. The calc works out the transverse reinforcement index K_tr, caps it at 1.75 d_b, and applies the general equation of Cl. 12.3.2. The result is never taken as less than 300 mm. Straight bars in tension are the Tension development length page, and hooks the Standard hook development length page.
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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-compression.pdf.
Results
| Quantity | Description | Value | Unit |
|---|---|---|---|
| \(\htmlClass{sym-l_d}{l_{d}}\) | Development length required in compression | 508 | \(\mathrm{mm}\) |
| \(\htmlClass{sym-l_dc}{l_{\mathrm{dc}}}\) | General equation, Cl. 12.3.2 | 508 | \(\mathrm{mm}\) |
Derivation
Branch: \(s < 12 \cdot d_{b}\) held
Cl. 12.3.2
\[\begin{aligned} \htmlClass{sym-K_tr}{K_{\mathrm{tr}}} &= \frac{40 \cdot \htmlClass{sym-A_tr}{A_{\mathrm{tr}}}}{\htmlClass{sym-s}{s} \cdot \htmlClass{sym-n}{n}} \\ &= \frac{40 \cdot \htmlClass{sym-A_tr}{200\ \mathrm{mm}^{2}}}{\htmlClass{sym-s}{150\ \mathrm{mm}} \cdot \htmlClass{sym-n}{2}} \\ &= 26.67\ \mathrm{mm} \end{aligned}\]Cl. 12.3.2, with the 8 MPa cap of Cl. 12.1.2
\[\begin{aligned} \htmlClass{sym-l_dc}{l_{\mathrm{dc}}} &= \left(\frac{\htmlClass{sym-k_c}{k_{c}} \cdot \htmlClass{sym-k_d}{k_{d}} \cdot \htmlClass{sym-f_y}{f_{y}}}{1.3 \cdot \left(1 + \frac{0.1 \cdot \min\left(\htmlClass{sym-K_tr}{K_{\mathrm{tr}}}, 1.75 \cdot \htmlClass{sym-d_b}{d_{b}}\right)}{\htmlClass{sym-d_b}{d_{b}}}\right) \cdot \min\left(\sqrt{\htmlClass{sym-f_c}{f_{c}} \cdot 1\ \mathrm{MPa}}, 8\ \mathrm{MPa}\right)} - 21\right) \cdot \htmlClass{sym-d_b}{d_{b}} \\ &= \left(\frac{\htmlClass{sym-k_c}{1} \cdot \htmlClass{sym-k_d}{1} \cdot \htmlClass{sym-f_y}{400\ \mathrm{MPa}}}{1.3 \cdot \left(1 + \frac{0.1 \cdot \min\left(\htmlClass{sym-K_tr}{26.67\ \mathrm{mm}}, 1.75 \cdot \htmlClass{sym-d_b}{16\ \mathrm{mm}}\right)}{\htmlClass{sym-d_b}{16\ \mathrm{mm}}}\right) \cdot \min\left(\sqrt{\htmlClass{sym-f_c}{25\ \mathrm{MPa}} \cdot 1\ \mathrm{MPa}}, 8\ \mathrm{MPa}\right)} - 21\right) \cdot \htmlClass{sym-d_b}{16\ \mathrm{mm}} \\ &= 508\ \mathrm{mm} \end{aligned}\]Cl. 12.3.1 and 12.3.4
\[\begin{aligned} \htmlClass{sym-l_d_single}{l_{d,\mathrm{single}}} &= \max\left(\htmlClass{sym-l_dc}{l_{\mathrm{dc}}} \cdot \htmlClass{sym-A_s_ratio}{A_{s,\mathrm{ratio}}}, 300\ \mathrm{mm}\right) \\ &= \max\left(\htmlClass{sym-l_dc}{508\ \mathrm{mm}} \cdot \htmlClass{sym-A_s_ratio}{1}, 300\ \mathrm{mm}\right) \\ &= 508\ \mathrm{mm} \end{aligned}\]Cl. 12.3.5
\[\begin{aligned} \htmlClass{sym-l_d}{l_{d}} &= \htmlClass{sym-l_d_single}{l_{d,\mathrm{single}}} \cdot \htmlClass{sym-k_bundle}{k_{\mathrm{bundle}}} \\ &= \htmlClass{sym-l_d_single}{508\ \mathrm{mm}} \cdot \htmlClass{sym-k_bundle}{1} \\ &= 508\ \mathrm{mm} \end{aligned}\]Questions
How does K_tr shorten the compression length?
Cl. 12.3.2 divides by 1.3 (1 + 0.1 K_tr / d_b) sqrt(f'c), so ties crossing the splitting plane at a spacing under 12 d_b reduce l_d. K_tr is 40 A_tr / (s n) and is not taken greater than 1.75 d_b, so the most it can do is divide the first term by 1.175.
Why is l_d longer than the old 0.24 d_b f_y / sqrt(f'c) gave?
CSA A23.3-24 replaced the compression expression of the earlier editions with Cl. 12.3.2 and raised the minimum from 200 mm to 300 mm. For a 15M bar at f_y = 400 MPa in 25 MPa concrete with no ties the new expression gives about 40 d_b, where the old one gave 19 d_b.
Does a hook shorten l_d in compression?
No. Cl. 12.5.7 does not count a hook as effective in compression, and a hooked bar in compression is developed as a straight one, by Cl. 12.3.
How do A_s_ratio and k_bundle change l_d?
Cl. 12.3.4 lets l_dc be multiplied by A_s required over A_s provided where there is more steel than analysis needs, but not where development of f_yg is specifically required, for Clause 21 seismic design, or for splice lengths. The 300 mm minimum still applies after it. Cl. 12.3.5 then lengthens each bar of a bundle by 10, 20 or 33 per cent for two, three or four bars.