| lamb | \(\displaystyle 1\) | | CSA A23.3-24 Cl. 8.6.5 a)-c) | 2026-10-01 |
| phi_c | \(\displaystyle 0.65\) | | CSA A23.3-24 Cl. 8.4.2 | 2026-10-01 |
| phi_s | \(\displaystyle 0.85\) | | CSA A23.3-24 Cl. 8.4.3 a) | 2026-10-01 |
| d_s | \(\displaystyle 11.3\ \mathrm{mm}\) | | CSA metric bar sizes, nominal diameter and area | 2026-10-01 |
| d_b | \(\displaystyle 25.2\ \mathrm{mm}\) | | CSA metric bar sizes, nominal diameter and area | 2026-10-01 |
| A_sb | \(\displaystyle 100\ \mathrm{mm}^{2}\) | | CSA metric bar sizes, nominal diameter and area | 2026-10-01 |
| theta | \(\displaystyle \operatorname{radians}\left(35\right)\) | A23.3 Cl. 11.3.6.3, simplified method | CSA A23.3-24 Cl. 11.3.6.3, theta = 35 deg | 2026-10-01 |
| d | \(\displaystyle h - c_{c} - d_{s} - \frac{d_{b}}{2}\) | | Geometry: h - c_c - d_s - d_b/2, one bar layer inside the stirrup | 2026-10-01 |
| d_v | \(\displaystyle \max\left(0.9 \cdot d, 0.72 \cdot h\right)\) | A23.3 Cl. 3.2, effective shear depth | CSA A23.3-24 Cl. 3.2, definition of d_v | 2026-10-01 |
| x_0 | \(\displaystyle b - 2 \cdot c_{c} - d_{s}\) | | Geometry: stirrup centreline at c_c + d_s/2 from each face | 2026-10-01 |
| y_0 | \(\displaystyle h - 2 \cdot c_{c} - d_{s}\) | | Geometry: stirrup centreline at c_c + d_s/2 from each face | 2026-10-01 |
| P_h | \(\displaystyle 2 \cdot \left(x_{0} + y_{0}\right)\) | A23.3 Cl. 3.2, p_h | CSA A23.3-24 Cl. 3.2, p_h on the stirrup centreline | 2026-10-01 |
| A_0h | \(\displaystyle x_{0} \cdot y_{0}\) | A23.3 Cl. 3.2, A_oh | CSA A23.3-24 Cl. 3.2, A_oh on the stirrup centreline | 2026-10-01 |
| cot_theta | \(\displaystyle \frac{1}{\tan\left(\theta\right)}\) | | CSA A23.3-24 Cl. 11.3.6.3, cot of theta | 2026-10-01 |
| A_v_min_per_s | \(\displaystyle \frac{0.06 \cdot \sqrt{f_{c} \cdot 1\ \mathrm{MPa}} \cdot b}{f_{y} \cdot 1\ \mathrm{mm}}\) | A23.3 Cl. 11.2.8.2, Eq. 11.1 | CSA A23.3-24 Cl. 11.2.8.2, Eq. 11.1 per unit s | 2026-10-01 |
| total_stir_provided | \(\displaystyle \frac{n \cdot A_{\mathrm{sb}}}{s \cdot 1\ \mathrm{mm}}\) | | All n legs per s, no clause | 2026-10-01 |
| b_w | \(\displaystyle 1 \cdot b\) | A23.3 Cl. 11.2.10.1, minimum web width within d | CSA A23.3-24 Cl. 11.2.10.1 for a rectangle, Cl. 11.2.10.5 spalled to the stirrup centreline past 11 A_v,min | 2026-10-01 |
| beta | \(\displaystyle 0.18\) | | CSA A23.3-24 Cl. 11.3.6.3 a) and b), Eqs. 11.9a/b; Eq. 11.9 also used below the minimum stirrups, which is conservative | 2026-10-01 |
| V_c | \(\displaystyle \phi_{c} \cdot \lambda \cdot \beta \cdot \sqrt{f_{c} \cdot 1\ \mathrm{MPa}} \cdot b_{w} \cdot d_{v}\) | A23.3 Cl. 11.3.4, Eq. 11.6 | CSA A23.3-24 Cl. 11.3.4, Eq. 11.6 on b_w | 2026-10-01 |
| A_v | \(\displaystyle n \cdot A_{\mathrm{sb}}\) | | All n legs, no clause | 2026-10-01 |
| V_s | \(\displaystyle \frac{\phi_{s} \cdot A_{v} \cdot f_{y} \cdot d_{v} \cdot \mathrm{cot}_{\theta}}{s}\) | A23.3 Cl. 11.3.5.1, Eq. 11.7 | CSA A23.3-24 Cl. 11.3.5.1, Eq. 11.7, A_v = n A_sb | 2026-10-01 |
| V_rmax | \(\displaystyle 0.25 \cdot \phi_{c} \cdot f_{c} \cdot b_{w} \cdot d_{v}\) | A23.3 Cl. 11.3.3, Eq. 11.5 | CSA A23.3-24 Cl. 11.3.3, Eq. 11.5 on b_w, V_p = 0 | 2026-10-01 |
| V_r | \(\displaystyle \min\left(V_{c} + V_{s}, V_{\mathrm{rmax}}\right)\) | A23.3 Cl. 11.3.3, Eqs. 11.4 and 11.5 | CSA A23.3-24 Cl. 11.3.3, Eqs. 11.4 and 11.5 with V_p = 0 | 2026-10-01 |
| shear_utilization | \(\displaystyle \frac{V_{f}}{V_{r}}\) | | Ratio of V_f to V_r, no clause | 2026-10-01 |
| A_c | \(\displaystyle b \cdot h\) | A23.3 Cl. 3.2, A_c | CSA A23.3-24 Cl. 3.2, definition of A_c | 2026-10-01 |
| P_c | \(\displaystyle 2 \cdot \left(b + h\right)\) | A23.3 Cl. 3.2, p_c | CSA A23.3-24 Cl. 3.2, definition of p_c | 2026-10-01 |
| T_cr | \(\displaystyle \frac{0.38 \cdot A_{c}^{2} \cdot \lambda \cdot \phi_{c} \cdot \sqrt{f_{c} \cdot 1\ \mathrm{MPa}}}{P_{c}}\) | A23.3 Cl. 11.2.9.1, Eq. 11.2 | CSA A23.3-24 Cl. 11.2.9.1, Eq. 11.2 with f_cp = 0 | 2026-10-01 |
| A_v_per_s | \(\displaystyle \max\left(\frac{V_{f} - V_{c}}{\phi_{s} \cdot f_{y} \cdot d_{v} \cdot \mathrm{cot}_{\theta} \cdot 1\ \mathrm{mm}}, 0\right)\) | A23.3 Cl. 11.3.3 and 11.3.5.1, Eqs. 11.4 and 11.7 | CSA A23.3-24 Eqs. 11.4 and 11.7 for A_v/s, floored at 0; Eq. 11.1 minimum checked separately | 2026-10-01 |
| A_0 | \(\displaystyle 0.85 \cdot A_{0h}\) | A23.3 Cl. 11.3.10.3 | CSA A23.3-24 Cl. 11.3.10.3, A_o = 0.85 A_oh | 2026-10-01 |
| A_t_per_s | \(\displaystyle \frac{T_{0f}}{2 \cdot A_{0} \cdot \phi_{s} \cdot f_{y} \cdot \mathrm{cot}_{\theta} \cdot 1\ \mathrm{mm}}\) | A23.3 Cl. 11.3.10.3, Eq. 11.17 | CSA A23.3-24 Cl. 11.3.10.3, Eq. 11.17 solved for A_t/s, A_o = 0.85 A_oh | 2026-10-01 |
| torsion_stir_provided | \(\displaystyle \frac{A_{\mathrm{sb}}}{s \cdot 1\ \mathrm{mm}}\) | | One outside leg per s, no clause | 2026-10-01 |
| torsion_stir_utilization | \(\displaystyle \frac{A_{t,\mathrm{per},s}}{\mathrm{torsion}_{\mathrm{stir},\mathrm{provided}}}\) | | Ratio of A_t/s to one leg provided, no clause | 2026-10-01 |
| total_stir_required | \(\displaystyle A_{v,\mathrm{per},s} + 2 \cdot A_{t,\mathrm{per},s}\) | A23.3 Cl. 11.3.10.1 | CSA A23.3-24 Cl. 11.3.10.1, shear plus torsion, A_t on two legs | 2026-10-01 |
| total_stir_utilization | \(\displaystyle \frac{\mathrm{total}_{\mathrm{stir},\mathrm{required}}}{\mathrm{total}_{\mathrm{stir},\mathrm{provided}}}\) | | Ratio of required to provided, no clause | 2026-10-01 |
| shear_stress | \(\displaystyle \frac{V_{f}}{b_{w} \cdot d_{v}}\) | | V_f over b_w d_v, no clause | 2026-10-01 |
| threshold | \(\displaystyle 0.125 \cdot \phi_{c} \cdot \lambda \cdot f_{c}\) | A23.3 Cl. 11.3.8.3, as a stress on b_w d_v | CSA A23.3-24 Cl. 11.3.8.3, 0.125 lambda phi_c f'c over b_w d_v | 2026-10-01 |
| S_max | \(\displaystyle \min\left(300\ \mathrm{mm}, 0.35 \cdot d_{v}\right)\) | A23.3 Cl. 11.3.8.3, half of Cl. 11.3.8.1 | CSA A23.3-24 Cl. 11.3.8.1 halved by Cl. 11.3.8.3 on shear or torsion | 2026-10-01 |
| s_w | \(\displaystyle \frac{x_{0}}{n - 1}\) | | Geometry: n legs evenly spaced over the stirrup centreline width | 2026-10-01 |
| s_w_max | \(\displaystyle \min\left(d_{v}, 600\ \mathrm{mm}\right)\) | A23.3 Cl. 11.3.8.4 | CSA A23.3-24 Cl. 11.3.8.4, lesser of d_v and 600 mm | 2026-10-01 |
| alpha_T | \(\displaystyle 1 - \frac{0.005 \cdot f_{c}}{1\ \mathrm{MPa}}\) | A23.3 Cl. 11.3.10.4 | CSA A23.3-24 Cl. 11.3.10.4, alpha_T = 1.0 - 0.005 f'c | 2026-10-01 |
| torsion_stress | \(\displaystyle \frac{T_{0f} \cdot P_{c}}{0.85 \cdot \alpha_{T} \cdot A_{c}^{2}}\) | A23.3 Cl. 11.3.10.4 b), torsion term | CSA A23.3-24 Cl. 11.3.10.4 b), torsion term | 2026-10-01 |
| combined_stress | \(\displaystyle \sqrt{\mathrm{shear}_{\mathrm{stress}}^{2} + \mathrm{torsion}_{\mathrm{stress}}^{2}}\) | A23.3 Cl. 11.3.10.4 b) | CSA A23.3-24 Cl. 11.3.10.4 b), non-box section, V_p = 0 | 2026-10-01 |
| stress_limit | \(\displaystyle 0.25 \cdot \phi_{c} \cdot f_{c}\) | A23.3 Cl. 11.3.10.4 b) | CSA A23.3-24 Cl. 11.3.10.4, right-hand side of Eq. 11.18 | 2026-10-01 |
| torsion_section_utilization | \(\displaystyle \frac{\mathrm{combined}_{\mathrm{stress}}}{\mathrm{stress}_{\mathrm{limit}}}\) | | Ratio of combined stress to its limit, no clause | 2026-10-01 |
| A_vs_per_s | \(\displaystyle \max\left(\mathrm{total}_{\mathrm{stir},\mathrm{provided}} - 2 \cdot A_{t,\mathrm{per},s}, 0\right)\) | A23.3 Cl. 11.3.10.1, shear share | CSA A23.3-24 Cl. 11.3.10.1, provided less 2 A_t/s, the share left for shear | 2026-10-01 |
| V_s_shear | \(\displaystyle \phi_{s} \cdot A_{\mathrm{vs},\mathrm{per},s} \cdot 1\ \mathrm{mm} \cdot f_{y} \cdot d_{v} \cdot \mathrm{cot}_{\theta}\) | A23.3 Cl. 11.3.5.1, Eq. 11.7 | CSA A23.3-24 Cl. 11.3.5.1, Eq. 11.7 on the shear share | 2026-10-01 |
| V_s_lt | \(\displaystyle \min\left(V_{s,\mathrm{shear}}, V_{f}\right)\) | A23.3 Cl. 11.3.9.2, V_s not over V_f | CSA A23.3-24 Cl. 11.3.9.2, V_s not over V_f - V_p | 2026-10-01 |
| shear_term | \(\displaystyle V_{f} - 0.5 \cdot V_{s,\mathrm{lt}}\) | A23.3 Cl. 11.3.10.6, V_p = 0 | CSA A23.3-24 Cl. 11.3.10.6, V_p = 0 | 2026-10-01 |
| torsion_term | \(\displaystyle \frac{0.45 \cdot P_{h} \cdot T_{0f}}{2 \cdot A_{0}}\) | A23.3 Cl. 11.3.10.6 | CSA A23.3-24 Cl. 11.3.10.6, torsion term with V_p = 0 | 2026-10-01 |
| F_lt | \(\displaystyle \sqrt{\mathrm{shear}_{\mathrm{term}}^{2} + \mathrm{torsion}_{\mathrm{term}}^{2}} \cdot \mathrm{cot}_{\theta}\) | A23.3 Eq. 11.14 with Cl. 11.3.10.6 | CSA A23.3-24 Eq. 11.14 with Cl. 11.3.10.6, M_f = N_f = V_p = 0 | 2026-10-01 |
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