| 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 |
| b_0 | \(\displaystyle 102\ \mathrm{mm}\) | | CISC SST 12.1, 2LE102x102x11, B (102 mm) | 2026-10-01 |
| d_0 | \(\displaystyle 102\ \mathrm{mm}\) | | CISC SST 12.1, 2LE102x102x11, D (102 mm) | 2026-10-01 |
| t | \(\displaystyle 11.1\ \mathrm{mm}\) | | CISC SST 12.1, 2LE102x102x11, T (11.1 mm) | 2026-10-01 |
| A_0 | \(\displaystyle 4280\ \mathrm{mm}^{2}\) | | CISC SST 12.1, 2LE102x102x11, A (A_A6 = A_Th = 4280 mm^2, both angles) | 2026-10-01 |
| y_c | \(\displaystyle 29.6\ \mathrm{mm}\) | | CISC SST 12.1, 2LE102x102x11, Y (29.6 mm, centroid to the flange's outside face) | 2026-10-01 |
| r_x | \(\displaystyle 31.3\ \mathrm{mm}\) | | CISC SST 12.1, 2LE102x102x11, Rx (31.3 mm) | 2026-10-01 |
| r_y2 | \(\displaystyle 46.6\ \mathrm{mm}\) | | CISC SST 12.1, 2LE102x102x11, Ry10 (46.6 mm, the pair at a 10 mm gap) | 2026-10-01 |
| r_z | \(\displaystyle 20\ \mathrm{mm}\) | | CISC SST 12.1, 2LE102x102x11, Ryp (20.0 mm, one angle's least radius about its minor principal axis); L.csv L102x102x11 Ryp 20.0 | 2026-10-01 |
| T_r | \(\displaystyle \phi \cdot A_{0} \cdot F_{y}\) | S16 Cl. 13.2, gross section yield | CSA S16-19 Cl. 13.2 a) i) (T_r = phi A_g F_y) | 2026-09-29 |
| lambda_x | \(\displaystyle \frac{L_{x}}{r_{x}}\) | S16 Cl. 10.4.1, L/r for a member in tension | CSA S16-19 Cl. 10.4.1 (tension: unbraced length L over the corresponding r, no K) | 2026-10-01 |
| lambda_y | \(\displaystyle \frac{L_{y}}{r_{y2}}\) | S16 Cl. 10.4.1, L/r for a member in tension | CSA S16-19 Cl. 10.4.1 (tension: unbraced length L over the corresponding r, no K), r_y of the pair | 2026-10-01 |
| lambda_1 | \(\displaystyle \frac{\max\left(L_{x}, L_{y}\right)}{n \cdot r_{z}}\) | S16 Cl. 19.3.1, one angle between spacers | CSA S16-19 Cl. 19.3.1 (component of a tension member between interconnections, slenderness <= 300) with Cl. 10.4.1 (L/r); spacing max(L_x, L_y)/n, r_z the one angle's least | 2026-10-01 |
| J | \(\displaystyle 176000\ \mathrm{mm}^{4}\) | | CISC SST 12.1, 2LE102x102x11, J (176e3 mm^4, both angles; L102x102x11 87.9e3 each) | 2026-10-01 |
| I_x | \(\displaystyle 4.19 \times 10^{6}\ \mathrm{mm}^{4}\) | | CISC SST 12.1, 2LE102x102x11, Ix (4.19e6 mm^4, both angles) | 2026-10-01 |
| I_y | \(\displaystyle r_{y2}^{2} \cdot A_{0}\) | | Definition r = sqrt(I/A) (accepted by owner); the table gives Ry per gap but no Iy for the pair | 2026-10-01 |
| e_v | \(\displaystyle \left| g - y_{c} \right|\) | | Statics (accepted by owner): T_f on the bolt line g from the flange's face, the centroid y_c from it | 2026-10-01 |
| M_fx | \(\displaystyle e_{v} \cdot T_{f}\) | | Statics (accepted by owner): T_f at eccentricity e_v about the x axis | 2026-10-01 |
| stem | \(\displaystyle 1\) | | AISC 360-22 F9.1(a) and F9.2(a) (web legs in tension), statics (accepted by owner): with g >= y_c the load line is on the stem side, so the stem tip is the more tensile fibre | 2026-10-01 |
| S_xt | \(\displaystyle 57800\ \mathrm{mm}^{3}\) | | CISC SST 12.1, 2LE102x102x11, Sx (57.8e3 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 | \(\displaystyle \frac{I_{x}}{y_{c}}\) | | CSA S16-19 Cl. 3 (S, elastic section modulus) and AISC 360-22 F9.3(b) (S_c referred to the compression flange): I_x over y_c, the flange's face 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_n1 | \(\displaystyle 1.6 \cdot M_{y}\) | AISC 360-22 F9-1 and F9-2, M_p = 1.6 M_y, under F_y Z_x for every tabulated pair | AISC 360-22 Eq. F9-1 and F9-2 (M_p = F_y Z_x <= 1.6 M_y, web legs in tension); plate Z_x is at least 1.72 S_x for every tabulated pair, so 1.6 M_y governs (test_1_6_m_y_is_under_f_y_z_x_for_every_tabulated_pair) | 2026-09-30 |
| B | \(\displaystyle 2.3 \cdot \frac{d_{0}}{L_{y}} \cdot \sqrt{\frac{I_{y}}{J}}\) | AISC 360-22 F9-11 | AISC 360-22 Eq. F9-11 (B = 2.3 (d/L_b) sqrt(I_y/J), d the web leg in tension, 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 |
| L_p | \(\displaystyle 1.76 \cdot r_{y2} \cdot \sqrt{\frac{E}{F_{y}}}\) | AISC 360-22 F9-8 | AISC 360-22 Eq. F9-8 (L_p = 1.76 r_y sqrt(E/F_y), r_y of the pair) | 2026-09-30 |
| L_r | \(\displaystyle \frac{1.95 \cdot \frac{E}{F_{y}} \cdot \sqrt{I_{y} \cdot J}}{S_{\mathrm{xt}}} \cdot \sqrt{\frac{2.36 \cdot \frac{F_{y}}{E} \cdot d_{0} \cdot S_{\mathrm{xt}}}{J} + 1}\) | 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 |
| M_n2 | \(\displaystyle M_{n1} - \frac{\left(M_{n1} - M_{y}\right) \cdot \left(L_{y} - L_{p}\right)}{L_{r} - L_{p}}\) | 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_l | \(\displaystyle \frac{b_{0}}{t}\) | | AISC 360-22 F10.3 and B4.1a(b) (b/t, b the full leg width), by F9.3(b) | 2026-09-30 |
| lambda_p | \(\displaystyle 0.54 \cdot \sqrt{\frac{E}{F_{y}}}\) | AISC 360-22 Table B4.1b case 12, legs of angles | AISC 360-22 Table B4.1b case 12 (legs of angles, 0.54 sqrt(E/F_y)), by F9.3(b) and F9.4(b) to F10.3 | 2026-09-30 |
| lambda_r | \(\displaystyle 0.91 \cdot \sqrt{\frac{E}{F_{y}}}\) | AISC 360-22 Table B4.1b case 12, legs of angles | AISC 360-22 Table B4.1b case 12 (legs of angles, 0.91 sqrt(E/F_y)), by F9.3(b) and F9.4(b) to F10.3 | 2026-09-30 |
| M_n3 | \(\displaystyle 1 \cdot M_{n1}\) | AISC 360-22 F10.3(a), compact leg: does not apply | AISC 360-22 F10.3(a) (compact: leg local buckling does not apply), by F9.3(b) | 2026-09-30 |
| M_nx | \(\displaystyle \min\left(M_{n1}, M_{n2}, M_{n3}\right)\) | AISC 360-22 F9, the lowest of the limit states | AISC 360-22 F9 (M_n the lowest value of the limit states) | 2026-09-30 |
| M_rx | \(\displaystyle \phi \cdot M_{\mathrm{nx}}\) | S16 Cl. 13.1 a), phi on the nominal strength | CSA S16-19 Cl. 13.1 a) (phi = 0.90 on the nominal strength) | 2026-09-30 |
| I_a | \(\displaystyle \frac{T_{f}}{T_{r}} + \frac{M_{\mathrm{fx}}}{M_{\mathrm{rx}}}\) | S16 Cl. 13.9.1 | CSA S16-19 Cl. 13.9.1 (T_f/T_r + M_fx/M_rx <= 1.0, M_fy = 0) | 2026-09-29 |
| I_b | \(\displaystyle \frac{M_{\mathrm{fx}}}{M_{\mathrm{rx}}} - \frac{T_{f} \cdot S_{\mathrm{xc}}}{M_{\mathrm{rx}} \cdot A_{0}}\) | S16 Cl. 13.9.3 b), S at the compression fibre | CSA S16-19 Cl. 13.9.3 b) (M_fx/M_rx + M_fy/M_ry - T_f S_x/(M_r A) <= 1.0, class 3 form), M_fy = 0 | 2026-09-30 |
calcsheet