| E | \(\displaystyle 200\ \mathrm{GPa}\) | | CSA S16-19 Cl. 3 (E = 200 000 MPa assumed) | 2026-09-29 |
| d | \(\displaystyle 247\ \mathrm{mm}\) | | CISC SST 12.1, W250x49, D | 2026-09-29 |
| b | \(\displaystyle 202\ \mathrm{mm}\) | | CISC SST 12.1, W250x49, B | 2026-09-29 |
| t | \(\displaystyle 11\ \mathrm{mm}\) | | CISC SST 12.1, W250x49, T | 2026-09-29 |
| w | \(\displaystyle 7.4\ \mathrm{mm}\) | | CISC SST 12.1, W250x49, W | 2026-09-29 |
| k | \(\displaystyle 32\ \mathrm{mm}\) | | CISC SST 12.1, W250x49, K | 2026-09-29 |
| S_x | \(\displaystyle 572000\ \mathrm{mm}^{3}\) | | CISC SST 12.1, W250x49, Sx | 2026-09-29 |
| phi_be | \(\displaystyle 0.75\) | | CSA S16-19 Cl. 13.1 f), 14.3.2 b) (phi_be = 0.75, end reaction) | 2026-09-29 |
| B_r1 | \(\displaystyle \phi_{\mathrm{be}} \cdot w \cdot \left(N + 4 \cdot t\right) \cdot F_{y}\) | S16 Cl. 14.3.2 | CSA S16-19 Cl. 14.3.2 b) i) | 2026-09-29 |
| B_r2 | \(\displaystyle 0.6 \cdot \phi_{\mathrm{be}} \cdot w^{2} \cdot \sqrt{F_{y} \cdot E}\) | S16 Cl. 14.3.2 | CSA S16-19 Cl. 14.3.2 b) ii) (0.60 phi_be w^2 sqrt(F_y E)) | 2026-09-29 |
| h_c | \(\displaystyle d - 2 \cdot k\) | | AISC 360-22 J10.4 (h = clear distance between flanges less the fillet radius for rolled shapes, d - 2k; S16-19 Cl. 3 k as the toe of the fillet) | 2026-09-29 |
| alpha | \(\displaystyle \frac{\frac{h_{c}}{w}}{\frac{L}{b}}\) | | AISC 360-22 J10.4 ((h/t_w)/(L_b/b_f); L_b the largest unbraced length of either flange at the load) | 2026-09-29 |
| M_y | \(\displaystyle S_{x} \cdot F_{y}\) | | AISC 360-22 J10.4 (M_y = F_y S_x, no phi) | 2026-09-29 |
| C_rs | \(\displaystyle 6.62\ \mathrm{TPa}\) | | AISC 360-22 J10.4 (C_r = 960,000 ksi when M_r < M_y, 480,000 ksi otherwise; 6.62e6 and 3.31e6 MPa are the exact conversions, the text prints 6.6e6 and 3.3e6) | 2026-09-29 |
| B_r3 | \(\displaystyle \frac{0.85 \cdot C_{\mathrm{rs}} \cdot w^{3} \cdot t}{h_{c}^{2}} \cdot \left(1 + 0.4 \cdot \alpha^{3}\right)\) | AISC J10.4 (a) | AISC 360-22 J10.4 a) J10-6 (phi = 0.85, C_r t_w^3 t_f / h^2 [1 + 0.4 ((h/t_w)/(L_b/b_f))^3]); the restrained-flange arm, the free arm J10-7 drops the 1 + | 2026-09-29 |
| B_r | \(\displaystyle \min\left(B_{r1}, B_{r2}, B_{r3}\right)\) | | S16-19 Cl. 14.3.2 and AISC 360-22 J10.4 (least of the limit states that apply; J10.4 does not apply past 2.3 restrained or 1.7 free) | 2026-09-29 |
| B_r4 | \(\displaystyle \frac{0.9 \cdot 7 \cdot t^{2} \cdot F_{y}}{2}\) | S16 Cl. 21.3 (b), halved at the end by AISC J10.1 | S16-19 Cl. 21.3 b) i) (T_r = 7 phi t^2 F_y, phi = 0.90) and AISC 360-22 J10.1 (halved within 10 t_f of the end; halved here at the end, which is d or less, so conservative unless d < 10 t_f); for information | 2026-09-29 |
| B_r5 | \(\displaystyle \frac{0.9 \cdot 12 \cdot w^{3} \cdot \sqrt{E \cdot F_{y}}}{h_{c}}\) | AISC J10.5, halved at the end | AISC 360-22 J10.5 J10-8 (24 t_w^3 sqrt(E F_yw) / h, phi = 0.90, halved within d/2 of the end; halved here within d, conservative); for information | 2026-09-29 |
| h | \(\displaystyle d - 2 \cdot t\) | | S16-19 Cl. 3 (h = clear depth of web between flanges) and Cl. 14.4.2 (KL = 0.75 of the stiffener length) | 2026-09-29 |
| F_ye | \(\displaystyle \min\left(F_{y}, F_{y1}\right)\) | | S16-19 Cl. 13.3.1.1 and 13.10 a) (weaker part in contact); the lesser of F_y and F_y1 for the mixed column, owner agreed 2026-09-29 | 2026-09-29 |
| A_0 | \(\displaystyle 12 \cdot w^{2} + 2 \cdot t_{1} \cdot b_{1}\) | S16 Cl. 14.4.2, 12 w of web | CSA S16-19 Cl. 14.4.2 (pair of stiffeners plus a web strip of 12 w at the end, area 12 w * w) | 2026-09-29 |
| I_s | \(\displaystyle \frac{t_{1} \cdot \left(2 \cdot b_{1} + w\right)^{3}}{12}\) | | S16-19 Cl. 14.4.2 (a column of the stiffener pair and a web strip; no formula given); the pair as one plate 2 b_1 + w wide, web strip's own inertia neglected, owner agreed 2026-09-29 | 2026-09-29 |
| r_s | \(\displaystyle \sqrt{\frac{I_{s}}{A_{0}}}\) | | S16-19 Cl. 14.4.2 and 13.3.1.2 (r = sqrt(I/A)) | 2026-09-29 |
| lambda_s | \(\displaystyle \frac{0.75 \cdot h}{r_{s}} \cdot \sqrt{\frac{F_{\mathrm{ye}}}{1.974\ \mathrm{TPa}}}\) | | S16-19 Cl. 13.3.1.1 and 13.3.1.2 (lambda = sqrt(F_y/F_e), F_e = pi^2 E / (KL/r)^2, KL = 0.75 h per 14.4.2) | 2026-09-29 |
| C_r1 | \(\displaystyle 0.9 \cdot A_{0} \cdot F_{\mathrm{ye}} \cdot \left(1 + \lambda_{s}^{2 \cdot 1.34}\right)^{\frac{-1}{1.34}}\) | S16 Cl. 13.3.1, n = 1.34 | S16-19 Cl. 13.3.1.1 (C_r = phi A F_y / (1 + lambda^(2n))^(1/n), phi = 0.90, n = 1.34 hot-rolled and fabricated sections) | 2026-09-29 |
| phi_w | \(\displaystyle 0.67\) | | CSA S16-19 Cl. 13.1 h) (phi_w = 0.67) | 2026-09-29 |
| V_r1 | \(\displaystyle 4 \cdot 0.67 \cdot \phi_{w} \cdot 0.707 \cdot D \cdot h_{c} \cdot X_{u}\) | S16 Cl. 13.13.2.2, weld metal | CSA S16-19 Cl. 13.13.2.2 (V_r = 0.67 phi_w A_w X_u; A_w = 0.707 D h_c per weld, four welds, theta = 0 so no enhancement; welds stop at the fillet; X_u is an input, W59 matching electrode) | 2026-09-29 |
| V_r3 | \(\displaystyle 0.9 \cdot 1.5 \cdot F_{\mathrm{ye}} \cdot 2 \cdot \left(b_{1} - \left(k - t\right)\right) \cdot t_{1}\) | S16 Cl. 13.10 (a), clear of the fillet | S16-19 Cl. 13.10 a) (B_r = 1.50 phi F_y A, phi = 0.90) and 14.4.2 (only the part outside the fillet bears; A = 2 (b_1 - (k - t)) t_1) | 2026-09-29 |
| B_rs | \(\displaystyle \min\left(V_{r1}, V_{r3}\right)\) | | AISC 360-22 J10.8 (stiffener welds and bearing sized for the difference between the load and the web) and S16-19 Cl. 14.4.2 | 2026-09-29 |
| C_r2 | \(\displaystyle B_{\mathrm{rs}} + B_{r}\) | | AISC 360-22 J10 (stiffeners sized for the difference between the required and the available web strength) and J10.8; S16-19 Cl. 14.4.1, 14.4.2 | 2026-09-29 |
| C_r | \(\displaystyle \min\left(C_{r1}, C_{r2}\right)\) | | S16-19 Cl. 14.4.2 (column) and AISC 360-22 J10.8 (welds and bearing); the column is checked against the whole load, conservative | 2026-09-29 |
calcsheet