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CSA A23.3-24

Tension development length

Verified against CSA A23.3-24, 2026-10-01

Development length of a straight reinforcing bar in tension, to CSA A23.3-24 Cl. 12.2. Calculate the development length of a straight reinforcing bar in tension per CSA A23.3-24 Cl. 12.2. Input concrete strength, steel yield strength, bar size, clear cover and clear spacing, the transverse reinforcement crossing the splitting plane, and the location, coating and density conditions that apply. The calc works out the general expression of Eq. 12.1 and, where the cover and spacing allow it, the simplified expression of Table 12.1, and takes the shorter, since Cl. 12.2.1 permits either. The five modification factors of Table 12.2 are each shown with the condition that sets them. Bars in compression are the Compression development length page, and hooks the Standard hook development length page.

Given

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\(f_{c}\) \(\mathrm{MPa}\) 20-80
\(f_{y}\) \(\mathrm{MPa}\) 300-500
\(\mathrm{rebar}\)
\(c_{c}\) \(\mathrm{mm}\) 10-200
\(s_{c}\) \(\mathrm{mm}\) 10-1,000
\(A_{\mathrm{tr}}\) \(\mathrm{mm}^{2}\) 0-5,000
\(s\) \(\mathrm{mm}\) 25-1,000
\(n\) 1-50
\(\mathrm{horiz}_{\mathrm{reinf}}\)
\(\mathrm{coating}\)
\(\mathrm{conc}_{\mathrm{density}}\)
\(\mathrm{min}_{\mathrm{ties}}\)
\(A_{s,\mathrm{ratio}}\) 0.1-1
\(\mathrm{bundle}\)
critical section db = 16.0 mm ld = 369 mm
Straight bar embedded past the critical section, drawn from the values above.

Title block

Optional. Printed under the title of the PDF.

This printed copy omits the derivation. The full report, with every step, is the PDF at https://calc.struct.work/calc/development-length-tension.pdf.

Results

Quantity Description Value Unit
\(\htmlClass{sym-l_d}{l_{d}}\) Development length required in tension 368.6 \(\mathrm{mm}\)
\(\htmlClass{sym-l_d_general}{l_{d,\mathrm{general}}}\) General expression, Eq. 12.1 368.6governs \(\mathrm{mm}\)
\(\htmlClass{sym-l_d_simplified}{l_{d,\mathrm{simplified}}}\) Simplified expression, Table 12.1, where Cl. 12.2.3 allows it 460.8 \(\mathrm{mm}\)

Derivation

S.1 \[\begin{aligned} \htmlClass{sym-d_b}{d_{b}} &= 16\ \mathrm{mm} \quad \left(\text{Bar diameter | 15M}\right) \end{aligned}\]
S.2 \[\begin{aligned} \htmlClass{sym-k_l}{k_{l}} &= 1 \quad \left(\text{Other bar location | Table 12.2}\right) \end{aligned}\]
S.3 \[\begin{aligned} \htmlClass{sym-k_c}{k_{c}} &= 1 \quad \left(\text{Uncoated | Table 12.2}\right) \end{aligned}\]
S.4 \[\begin{aligned} \htmlClass{sym-k_d}{k_{d}} &= 1 \quad \left(\text{Normal-density concrete | Table 12.2}\right) \end{aligned}\]
S.5 \[\begin{aligned} \htmlClass{sym-k_s}{k_{s}} &= 0.8 \quad \left(\text{20M and smaller | Table 12.2}\right) \end{aligned}\]

Branch: \(f_{y} \leq 400\ \mathrm{MPa}\) held

S.6 \[\begin{aligned} \htmlClass{sym-k_g}{k_{g}} &= 1 \quad \left(\text{Yield strength up to 400 MPa | Table 12.2}\right) \end{aligned}\]
S.7

Table 12.2, note 1

\[\begin{aligned} \htmlClass{sym-k_lc}{k_{\mathrm{lc}}} &= \min\left(\htmlClass{sym-k_l}{k_{l}} \cdot \htmlClass{sym-k_c}{k_{c}}, 1.7\right) \\ &= \min\left(\htmlClass{sym-k_l}{1} \cdot \htmlClass{sym-k_c}{1}, 1.7\right) \\ &= 1 \end{aligned}\]
S.8

Cl. 3.2, d_cs

\[\begin{aligned} \htmlClass{sym-d_cs}{d_{\mathrm{cs}}} &= \min\left(\htmlClass{sym-c_c}{c_{c}} + \frac{\htmlClass{sym-d_b}{d_{b}}}{2}, \frac{2}{3} \cdot \left(\htmlClass{sym-s_c}{s_{c}} + \htmlClass{sym-d_b}{d_{b}}\right)\right) \\ &= \min\left(\htmlClass{sym-c_c}{40\ \mathrm{mm}} + \frac{\htmlClass{sym-d_b}{16\ \mathrm{mm}}}{2}, \frac{2}{3} \cdot \left(\htmlClass{sym-s_c}{100\ \mathrm{mm}} + \htmlClass{sym-d_b}{16\ \mathrm{mm}}\right)\right) \\ &= 48\ \mathrm{mm} \end{aligned}\]

Branch: \(s < 12 \cdot d_{b}\) held

S.9

Cl. 12.2.2

\[\begin{aligned} \htmlClass{sym-K_tr}{K_{\mathrm{tr}}} &= \frac{40 \cdot \htmlClass{sym-A_tr}{A_{\mathrm{tr}}}}{\htmlClass{sym-s}{s} \cdot \htmlClass{sym-n}{n}} \\ &= \frac{40 \cdot \htmlClass{sym-A_tr}{200\ \mathrm{mm}^{2}}}{\htmlClass{sym-s}{150\ \mathrm{mm}} \cdot \htmlClass{sym-n}{2}} \\ &= 26.67\ \mathrm{mm} \end{aligned}\]
S.10

Cl. 12.2.2, Eq. 12.1, with the 8 MPa cap of Cl. 12.1.2

\[\begin{aligned} \htmlClass{sym-l_d_general}{l_{d,\mathrm{general}}} &= 0.9 \cdot \frac{\htmlClass{sym-k_lc}{k_{\mathrm{lc}}} \cdot \htmlClass{sym-k_d}{k_{d}} \cdot \htmlClass{sym-k_s}{k_{s}} \cdot \htmlClass{sym-k_g}{k_{g}}}{\frac{\min\left(\htmlClass{sym-d_cs}{d_{\mathrm{cs}}} + \htmlClass{sym-K_tr}{K_{\mathrm{tr}}}, 2.5 \cdot \htmlClass{sym-d_b}{d_{b}}\right)}{\htmlClass{sym-d_b}{d_{b}}}} \cdot \frac{\htmlClass{sym-f_y}{f_{y}}}{\min\left(\sqrt{\htmlClass{sym-f_c}{f_{c}} \cdot 1\ \mathrm{MPa}}, 8\ \mathrm{MPa}\right)} \cdot \htmlClass{sym-d_b}{d_{b}} \\ &= 0.9 \cdot \frac{\htmlClass{sym-k_lc}{1} \cdot \htmlClass{sym-k_d}{1} \cdot \htmlClass{sym-k_s}{0.8} \cdot \htmlClass{sym-k_g}{1}}{\frac{\min\left(\htmlClass{sym-d_cs}{48\ \mathrm{mm}} + \htmlClass{sym-K_tr}{26.67\ \mathrm{mm}}, 2.5 \cdot \htmlClass{sym-d_b}{16\ \mathrm{mm}}\right)}{\htmlClass{sym-d_b}{16\ \mathrm{mm}}}} \cdot \frac{\htmlClass{sym-f_y}{400\ \mathrm{MPa}}}{\min\left(\sqrt{\htmlClass{sym-f_c}{25\ \mathrm{MPa}} \cdot 1\ \mathrm{MPa}}, 8\ \mathrm{MPa}\right)} \cdot \htmlClass{sym-d_b}{16\ \mathrm{mm}} \\ &= 368.6\ \mathrm{mm} \end{aligned}\]

Branch: \(c_{c} \geq d_{b}\ \text{and}\ s_{c} \geq 1.4 \cdot d_{b}\) held

Branch: \(s_{c} \geq 2 \cdot d_{b}\ \text{and}\ c_{c} \geq 1.5 \cdot d_{b}\) held

S.11

Table 12.1, with the 8 MPa cap of Cl. 12.1.2

\[\begin{aligned} \htmlClass{sym-l_d_simplified}{l_{d,\mathrm{simplified}}} &= 0.45 \cdot \htmlClass{sym-k_lc}{k_{\mathrm{lc}}} \cdot \htmlClass{sym-k_d}{k_{d}} \cdot \htmlClass{sym-k_s}{k_{s}} \cdot \htmlClass{sym-k_g}{k_{g}} \cdot \frac{\htmlClass{sym-f_y}{f_{y}}}{\min\left(\sqrt{\htmlClass{sym-f_c}{f_{c}} \cdot 1\ \mathrm{MPa}}, 8\ \mathrm{MPa}\right)} \cdot \htmlClass{sym-d_b}{d_{b}} \\ &= 0.45 \cdot \htmlClass{sym-k_lc}{1} \cdot \htmlClass{sym-k_d}{1} \cdot \htmlClass{sym-k_s}{0.8} \cdot \htmlClass{sym-k_g}{1} \cdot \frac{\htmlClass{sym-f_y}{400\ \mathrm{MPa}}}{\min\left(\sqrt{\htmlClass{sym-f_c}{25\ \mathrm{MPa}} \cdot 1\ \mathrm{MPa}}, 8\ \mathrm{MPa}\right)} \cdot \htmlClass{sym-d_b}{16\ \mathrm{mm}} \\ &= 460.8\ \mathrm{mm} \end{aligned}\]
S.12

Cl. 12.2.1 and 12.2.5

\[\begin{aligned} \htmlClass{sym-l_d_single}{l_{d,\mathrm{single}}} &= \max\left(\min\left(\htmlClass{sym-l_d_general}{l_{d,\mathrm{general}}}, \htmlClass{sym-l_d_simplified}{l_{d,\mathrm{simplified}}}\right) \cdot \htmlClass{sym-A_s_ratio}{A_{s,\mathrm{ratio}}}, 300\ \mathrm{mm}\right) \\ &= \max\left(\min\left(\htmlClass{sym-l_d_general}{368.6\ \mathrm{mm}}, \htmlClass{sym-l_d_simplified}{460.8\ \mathrm{mm}}\right) \cdot \htmlClass{sym-A_s_ratio}{1}, 300\ \mathrm{mm}\right) \\ &= 368.6\ \mathrm{mm} \end{aligned}\]
S.13 \[\begin{aligned} \htmlClass{sym-k_bundle}{k_{\mathrm{bundle}}} &= 1 \quad \left(\text{Single bar | Cl. 12.2.7}\right) \end{aligned}\]
S.14

Cl. 12.2.7

\[\begin{aligned} \htmlClass{sym-l_d}{l_{d}} &= \htmlClass{sym-l_d_single}{l_{d,\mathrm{single}}} \cdot \htmlClass{sym-k_bundle}{k_{\mathrm{bundle}}} \\ &= \htmlClass{sym-l_d_single}{368.6\ \mathrm{mm}} \cdot \htmlClass{sym-k_bundle}{1} \\ &= 368.6\ \mathrm{mm} \end{aligned}\]

Questions

Why is l_d the shorter of l_d_general and l_d_simplified?

Cl. 12.2.1 lets l_d come from either the general Eq. 12.1 of Cl. 12.2.2 or the simplified Table 12.1 of Cl. 12.2.3, and either one is a code-compliant answer. The simplified table only applies with clear cover of at least d_b and clear spacing of at least 1.4 d_b. Where it applies the calc takes the shorter of the two, and l_d is never less than 300 mm.

When does l_d_simplified use 0.45 instead of 0.6?

Table 12.1 gives the smaller coefficient to members containing minimum ties per Cl. 7.6.5 or minimum stirrups per Cl. 11.2.8.2 throughout l_d, and to members with clear spacing of at least 2 d_b between the bars being developed and clear cover of at least 1.5 d_b. Either is enough.

What is k_g, and when does it raise l_d?

The reinforcement grade factor of Table 12.2. It is 1.0 for f_yg up to 400 MPa and f_yg / 900 + 0.56 above that, so a 500 MPa bar takes about 1.12 on top of the higher stress.

How do A_s_ratio and k_bundle change l_d?

Cl. 12.2.5 lets l_d 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; leave it at 1.0 then. The 300 mm minimum still applies after it. Cl. 12.2.7 then lengthens each bar of a bundle by 10, 20 or 33 per cent for two, three or four bars.

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