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Tension development length: validation

Every formula and clause of Tension development length was compared by hand with CSA A23.3-24, and every row matched, on 2026-10-01. The rows below are read from the calculation itself at its declared values, so they are the formulas the page runs today.

Formulas

NameSymbolicClauseAgainstDate
d_b\(\displaystyle 16\ \mathrm{mm}\)CSA metric bar sizes, nominal diameter2026-10-01
k_l\(\displaystyle 1\)CSA A23.3-24 Table 12.2, bar location2026-10-01
k_c\(\displaystyle 1\)CSA A23.3-24 Table 12.2, coating2026-10-01
k_d\(\displaystyle 1\)CSA A23.3-24 Table 12.2, concrete density2026-10-01
k_s\(\displaystyle 0.8\)CSA A23.3-24 Table 12.2, bar size2026-10-01
k_g\(\displaystyle 1\)CSA A23.3-24 Table 12.2, reinforcement grade2026-10-01
k_lc\(\displaystyle \min\left(k_{l} \cdot k_{c}, 1.7\right)\)Table 12.2, note 1CSA A23.3-24 Table 12.2, note 12026-10-01
d_cs\(\displaystyle \min\left(c_{c} + \frac{d_{b}}{2}, \frac{2}{3} \cdot \left(s_{c} + d_{b}\right)\right)\)Cl. 3.2, d_csCSA A23.3-24 Cl. 3.2, definition of d_cs2026-10-01
K_tr\(\displaystyle \frac{40 \cdot A_{\mathrm{tr}}}{s \cdot n}\)Cl. 12.2.2CSA A23.3-24 Cl. 12.2.2, K_tr and the 12 d_b spacing limit2026-10-01
l_d_general\(\displaystyle 0.9 \cdot \frac{k_{\mathrm{lc}} \cdot k_{d} \cdot k_{s} \cdot k_{g}}{\frac{\min\left(d_{\mathrm{cs}} + K_{\mathrm{tr}}, 2.5 \cdot d_{b}\right)}{d_{b}}} \cdot \frac{f_{y}}{\min\left(\sqrt{f_{c} \cdot 1\ \mathrm{MPa}}, 8\ \mathrm{MPa}\right)} \cdot d_{b}\)Cl. 12.2.2, Eq. 12.1, with the 8 MPa cap of Cl. 12.1.2CSA A23.3-24 Cl. 12.2.2, Eq. 12.1, and Cl. 12.1.22026-10-01
l_d_simplified\(\displaystyle 0.45 \cdot k_{\mathrm{lc}} \cdot k_{d} \cdot k_{s} \cdot k_{g} \cdot \frac{f_{y}}{\min\left(\sqrt{f_{c} \cdot 1\ \mathrm{MPa}}, 8\ \mathrm{MPa}\right)} \cdot d_{b}\)Table 12.1, with the 8 MPa cap of Cl. 12.1.2CSA A23.3-24 Cl. 12.2.3, Table 12.1, and Cl. 12.1.22026-10-01
l_d_single\(\displaystyle \max\left(\min\left(l_{d,\mathrm{general}}, l_{d,\mathrm{simplified}}\right) \cdot A_{s,\mathrm{ratio}}, 300\ \mathrm{mm}\right)\)Cl. 12.2.1 and 12.2.5CSA A23.3-24 Cl. 12.2.1 and Cl. 12.2.52026-10-01
k_bundle\(\displaystyle 1\)CSA A23.3-24 Cl. 12.2.72026-10-01
l_d\(\displaystyle l_{d,\mathrm{single}} \cdot k_{\mathrm{bundle}}\)Cl. 12.2.7CSA A23.3-24 Cl. 12.2.72026-10-01

Clauses

ClauseStepsAgainstDate
Table 12.2, note 1k_lcCSA A23.3-24 Clause 12, as cited2026-10-01
Cl. 3.2, d_csd_csCSA A23.3-24 Clause 3, as cited2026-10-01
Cl. 12.2.2K_trCSA A23.3-24 Clause 12, as cited2026-10-01
Cl. 12.2.2, Eq. 12.1, with the 8 MPa cap of Cl. 12.1.2l_d_generalCSA A23.3-24 Clause 12, as cited2026-10-01
Table 12.1, with the 8 MPa cap of Cl. 12.1.2l_d_simplifiedCSA A23.3-24 Clause 12, as cited2026-10-01
Cl. 12.2.1 and 12.2.5l_d_singleCSA A23.3-24 Clause 12, as cited2026-10-01
Cl. 12.2.7l_dCSA A23.3-24 Clause 12, as cited2026-10-01