| phi | \(\displaystyle 0.9\) | | CSA S16-19 Cl. 13.1 a) (phi = 0.90, structural steel) | 2026-09-30 |
| E | \(\displaystyle 200\ \mathrm{GPa}\) | S16 Cl. 3.2, E = 200 000 MPa | CSA S16-19 Cl. 3.2 (E = elastic modulus of steel, 200 000 MPa) | 2026-09-30 |
| G | \(\displaystyle 77\ \mathrm{GPa}\) | S16 Cl. 3.2, G = 77 000 MPa | CSA S16-19 Cl. 3.2 (G = shear modulus of steel, 77 000 MPa) | 2026-09-30 |
| A_0 | \(\displaystyle 14300\ \mathrm{mm}^{2}\) | | CISC SST 12.1, WT460x111.5, A (A_A6 = A_Th = 14300 mm^2) | 2026-10-01 |
| b | \(\displaystyle 304\ \mathrm{mm}\) | | CISC SST 12.1, WT460x111.5, B (304 mm) | 2026-10-01 |
| t | \(\displaystyle 23.9\ \mathrm{mm}\) | | CISC SST 12.1, WT460x111.5, T (23.9 mm) | 2026-10-01 |
| d | \(\displaystyle 456\ \mathrm{mm}\) | | CISC SST 12.1, WT460x111.5, D (456 mm) | 2026-10-01 |
| w | \(\displaystyle 15.9\ \mathrm{mm}\) | | CISC SST 12.1, WT460x111.5, W (15.9 mm) | 2026-10-01 |
| y | \(\displaystyle 122\ \mathrm{mm}\) | | CISC SST 12.1, WT460x111.5, Y (122 mm, centroid below the flange's top) | 2026-10-01 |
| r_x | \(\displaystyle 143\ \mathrm{mm}\) | | CISC SST 12.1, WT460x111.5, Rx (143 mm) | 2026-10-01 |
| r_y | \(\displaystyle 62.7\ \mathrm{mm}\) | | CISC SST 12.1, WT460x111.5, Ry (62.7 mm) | 2026-10-01 |
| y_0 | \(\displaystyle 110\ \mathrm{mm}\) | | CISC SST 12.1, WT460x111.5, Yo (110 mm, centroid to shear centre) | 2026-10-01 |
| J | \(\displaystyle 2.08 \times 10^{6}\ \mathrm{mm}^{4}\) | | CISC SST 12.1, WT460x111.5, J (2.08e6 mm^4) | 2026-10-01 |
| C_w | \(\displaystyle 1.24 \times 10^{10}\ \mathrm{mm}^{6}\) | | CISC SST 12.1, WT460x111.5, Cw (1.24e10 mm^6) | 2026-10-01 |
| lambda_3 | \(\displaystyle \frac{200}{\sqrt{\frac{F_{y}}{1\ \mathrm{MPa}}}}\) | S16 Cl. 11, Table 1, flanges | CSA S16-19 Cl. 11.2 Table 1 (flanges of T-sections: 200/sqrt(F_y)) | 2026-09-29 |
| lambda_f | \(\displaystyle \frac{0.5 \cdot b}{t}\) | | CSA S16-19 Cl. 11.3.1 c) (b_el one-half the T-section flange), and AISC 360-22 F9.3 (lambda = b_f/2t_f) | 2026-09-30 |
| A_b | \(\displaystyle 0\ \mathrm{m}^{2}\) | | CSA S16-19 Cl. 13.3.4 a) (no reduced width: the flange is within Table 1's 200/sqrt(F_y)) | 2026-09-30 |
| lambda_s | \(\displaystyle \frac{d}{w}\) | | CSA S16-19 Cl. 11.3.1 b) (b_el the full stem of a T-section) | 2026-09-30 |
| lambda_3s | \(\displaystyle \frac{340}{\sqrt{\frac{F_{y}}{1\ \mathrm{MPa}}}}\) | S16 Cl. 11, Table 1, stem of a tee | CSA S16-19 Cl. 11.2 Table 1 (stems of T-sections: 340/sqrt(F_y)) | 2026-09-29 |
| A_d | \(\displaystyle \left(\lambda_{s} - \lambda_{3s}\right) \cdot w^{2}\) | S16 Cl. 13.3.4 a), stem past Table 1 | CSA S16-19 Cl. 13.3.4 a) (A_e from reduced widths meeting Table 1: stem cut to 340 w/sqrt(F_y)) | 2026-09-30 |
| A_e | \(\displaystyle A_{0} - A_{b} - A_{d}\) | | CSA S16-19 Cl. 13.3.4 a) (effective area from reduced element widths) | 2026-09-30 |
| r_0 | \(\displaystyle \sqrt{y_{0}^{2} + r_{x}^{2} + r_{y}^{2}}\) | S16 Cl. 13.3.1.2, x_0 = 0 | CSA S16-19 Cl. 13.3.1.2 (r_o^2 = x_o^2 + y_o^2 + r_x^2 + r_y^2, x_o = 0) | 2026-09-30 |
| F_ex | \(\displaystyle \pi^{2} \cdot \frac{E}{\left(\frac{k_{x} \cdot L_{x}}{r_{x}}\right)^{2}}\) | S16 Cl. 13.3.1.2 | CSA S16-19 Cl. 13.3.1.2 (F_ex = pi^2 E / (K_x L_x / r_x)^2) | 2026-09-30 |
| F_ey | \(\displaystyle \pi^{2} \cdot \frac{E}{\left(\frac{k_{y} \cdot L_{y}}{r_{y}}\right)^{2}}\) | S16 Cl. 13.3.1.2 | CSA S16-19 Cl. 13.3.1.2 (F_ey = pi^2 E / (K_y L_y / r_y)^2) | 2026-09-30 |
| F_ez | \(\displaystyle \frac{\frac{\pi^{2} \cdot E \cdot C_{w}}{L_{x}^{2}} + G \cdot J}{A_{0} \cdot r_{0}^{2}}\) | S16 Cl. 13.3.1.2, K_z = 1 and L_z = L_x | CSA S16-19 Cl. 13.3.1.2 (F_ez = (pi^2 E C_w / (K_z L_z)^2 + G J) / (A r_o^2), K_z = 1, L_z = L_x) | 2026-09-30 |
| F_e | \(\displaystyle \operatorname{root}_{\min F > 0}\left((F - F_{\mathrm{ex}})(F - F_{\mathrm{ey}})(F - F_{\mathrm{ez}}) - F^{2}(F - F_{\mathrm{ey}})\left(\frac{0\ \mathrm{m}}{r_{0}}\right)^{2} - F^{2}(F - F_{\mathrm{ex}})\left(\frac{y_{0}}{r_{0}}\right)^{2}\right)\) | S16 Cl. 13.3.1.1 b) and c) | CSA S16-19 Cl. 13.3.1.1 c) cubic with x_o = 0, whose least root is the lesser of F_ex and F_eyz of Cl. 13.3.1.1 b) for a singly symmetric section (worked through) | 2026-09-30 |
| lambda_e | \(\displaystyle \sqrt{\frac{F_{y}}{F_{e}}}\) | | CSA S16-19 Cl. 13.3.1.1 (lambda = sqrt(F_y/F_e)) | 2026-09-30 |
| f_s | \(\displaystyle F_{y} \cdot \left(1 + \lambda_{e}^{2 \cdot 1.34}\right)^{\frac{-1}{1.34}}\) | S16 Cl. 13.3.1, n = 1.34 | CSA S16-19 Cl. 13.3.1.1 (C_r = phi A F_y / (1 + lambda^2n)^(1/n), n = 1.34 hot-rolled, lambda = sqrt(F_y/F_e)) | 2026-09-29 |
| C_r | \(\displaystyle \phi \cdot A_{e} \cdot f_{s}\) | S16 Cl. 13.3.4 a) | CSA S16-19 Cl. 13.3.4 a) (C_r = phi A_e F_y / (1 + lambda^2n)^(1/n)) | 2026-09-30 |
| I_x | \(\displaystyle 2.92 \times 10^{8}\ \mathrm{mm}^{4}\) | | CISC SST 12.1, WT460x111.5, Ix (292e6 mm^4) | 2026-10-01 |
| I_y | \(\displaystyle 5.61 \times 10^{7}\ \mathrm{mm}^{4}\) | | CISC SST 12.1, WT460x111.5, Iy (56.1e6 mm^4) | 2026-10-01 |
| S_xt | \(\displaystyle 874000\ \mathrm{mm}^{3}\) | | CISC SST 12.1, WT460x111.5, Sx (874e3 mm^3 = Ix/(D - Y), at the stem tip); the S_x of AISC 360-22 Eq. F9-3 for a stem in tension | 2026-10-01 |
| S_xc | \(\displaystyle \frac{I_{x}}{y}\) | | CSA S16-19 Cl. 3 (S, elastic section modulus) and AISC 360-22 F9.3 (S_xc referred to the compression flange): I_x over y, the flange's top to the centroid | 2026-10-01 |
| M_y | \(\displaystyle S_{\mathrm{xt}} \cdot F_{y}\) | AISC 360-22 F9-3 | AISC 360-22 Eq. F9-3 (M_y = F_y S_x, S_x at the stem tip, the extreme fibre) | 2026-09-30 |
| M_nx1 | \(\displaystyle 1.6 \cdot M_{y}\) | AISC 360-22 F9-1 and F9-2, M_p = 1.6 M_y, under F_y Z_x for every tabulated WT | AISC 360-22 Eq. F9-1 and F9-2 (M_p = F_y Z_x <= 1.6 M_y, stem in tension); plate Z_x is at least 1.74 S_x for every tabulated WT, so 1.6 M_y governs (test_1_6_m_y_is_under_f_y_z_x_for_every_tabulated_tee) | 2026-09-30 |
| L_p | \(\displaystyle 1.76 \cdot r_{y} \cdot \sqrt{\frac{E}{F_{y}}}\) | AISC 360-22 F9-8 | AISC 360-22 Eq. F9-8 (L_p = 1.76 r_y sqrt(E/F_y)) | 2026-09-30 |
| L_r | \(\displaystyle \frac{1.95 \cdot \frac{E}{F_{y}} \cdot \sqrt{I_{y} \cdot J}}{S_{\mathrm{xt}}} \cdot \sqrt{\frac{2.36 \cdot \frac{F_{y}}{E} \cdot d \cdot S_{\mathrm{xt}}}{J} + 1}\) | AISC 360-22 F9-9 | AISC 360-22 Eq. F9-9 (L_r = 1.95 (E/F_y) sqrt(I_y J)/S_x sqrt(2.36 (F_y/E) d S_x/J + 1); the markdown copy closes the root before the + 1, which is dimensionally impossible; checked M_cr(L_r) = M_y at the defaults) | 2026-09-30 |
| B | \(\displaystyle 2.3 \cdot \frac{d}{L_{y}} \cdot \sqrt{\frac{I_{y}}{J}}\) | AISC 360-22 F9-11 | AISC 360-22 Eq. F9-11 (B = 2.3 (d/L_b) sqrt(I_y/J), L_b = L_y) | 2026-09-30 |
| M_cr | \(\displaystyle 1.95 \cdot \frac{E}{L_{y}} \cdot \sqrt{I_{y} \cdot J} \cdot \left(B + \sqrt{1 + B^{2}}\right)\) | AISC 360-22 F9-10 | AISC 360-22 Eq. F9-10 (M_cr = 1.95 E / L_b sqrt(I_y J) (B + sqrt(1 + B^2)), L_b = L_y) | 2026-09-30 |
| M_nx2 | \(\displaystyle M_{\mathrm{nx}1} - \frac{\left(M_{\mathrm{nx}1} - M_{y}\right) \cdot \left(L_{y} - L_{p}\right)}{L_{r} - L_{p}}\) | AISC 360-22 F9-6 | AISC 360-22 Eq. F9-6 (M_n = M_p - (M_p - M_y)(L_b - L_p)/(L_r - L_p)) | 2026-09-30 |
| lambda_pf | \(\displaystyle 0.38 \cdot \sqrt{\frac{E}{F_{y}}}\) | AISC 360-22 Table B4.1b case 10, flanges of tees | AISC 360-22 Table B4.1b case 10 (flanges of tees, 0.38 sqrt(E/F_y)) | 2026-09-30 |
| lambda_rf | \(\displaystyle 1 \cdot \sqrt{\frac{E}{F_{y}}}\) | AISC 360-22 Table B4.1b case 10, flanges of tees | AISC 360-22 Table B4.1b case 10 (flanges of tees, 1.0 sqrt(E/F_y)) | 2026-09-30 |
| M_nx3 | \(\displaystyle 1 \cdot M_{\mathrm{nx}1}\) | AISC 360-22 F9.3(a)(1), compact flange: does not apply | AISC 360-22 F9.3(a)(1) (compact flange: flange local buckling does not apply) | 2026-09-30 |
| M_rx | \(\displaystyle \phi \cdot \min\left(M_{\mathrm{nx}1}, M_{\mathrm{nx}3}\right)\) | AISC 360-22 F9 but lateral-torsional buckling, S16 Cl. 13.1 a) phi | AISC 360-22 F9, the lowest of yielding and flange local buckling, for CSA S16-19 Cl. 13.8.2 b) ii) (Cl. 13.5, no lateral-torsional buckling); phi per Cl. 13.1 a) | 2026-09-30 |
| M_rxl | \(\displaystyle \phi \cdot \min\left(M_{\mathrm{nx}1}, M_{\mathrm{nx}2}, M_{\mathrm{nx}3}\right)\) | AISC 360-22 F9, the lowest, S16 Cl. 13.1 a) phi | AISC 360-22 F9, the lowest of all its limit states, for CSA S16-19 Cl. 13.8.2 c) ii) (Cl. 13.6.1); phi per Cl. 13.1 a) | 2026-09-30 |
| C_ex | \(\displaystyle \frac{\pi^{2} \cdot E \cdot I_{x}}{L_{x}^{2}}\) | S16 Cl. 13.8.5, L the unbraced length (Cl. 10.3.2, K = 1) | CSA S16-19 Cl. 13.8.5 (C_e = pi^2 E I / L^2), L the unbraced length per Cl. 10.3.1, K = 1.0 for in-plane bending per Cl. 10.3.2; AISC 360-22 Appendix 8 P_e1 agrees | 2026-10-01 |
| U_1x | \(\displaystyle \frac{\omega_{1}}{1 - \frac{C_{f}}{C_{\mathrm{ex}}}}\) | S16 Cl. 13.8.5 | CSA S16-19 Cl. 13.8.5 (U_1 = omega_1/(1 - C_f/C_e)) | 2026-09-29 |
| I_m | \(\displaystyle \frac{C_{f}}{C_{r}} + \frac{U_{1x} \cdot M_{\mathrm{fx}}}{M_{\mathrm{rx}}}\) | S16 Cl. 13.8.4 b) | CSA S16-19 Cl. 13.8.4 b) (C_f/C_r + U_1x M_fx/M_rx + U_1y M_fy/M_ry <= 1.0, M_fy = 0) | 2026-09-30 |
| U_1xl | \(\displaystyle \max\left(U_{1x}, 1\right)\) | S16 Cl. 13.8.2 c) v), not less than 1.0 | CSA S16-19 Cl. 13.8.2 c) v) (U_1x not less than 1.0 for members in braced frames) | 2026-09-30 |
| I_l | \(\displaystyle \frac{C_{f}}{C_{r}} + \frac{U_{1\mathrm{xl}} \cdot M_{\mathrm{fx}}}{M_{\mathrm{rxl}}}\) | S16 Cl. 13.8.4 c) | CSA S16-19 Cl. 13.8.4 c) (C_f/C_r + U_1x M_fx/M_rx <= 1.0 with M_rx of Cl. 13.6.1, M_fy = 0) | 2026-09-30 |
calcsheet