| 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 | \(\displaystyle 76.2\ \mathrm{mm}\) | | CISC SST 12.1, L76x76x6.4, D (76.2 mm, equal legs) | 2026-10-01 |
| t | \(\displaystyle 6.35\ \mathrm{mm}\) | | CISC SST 12.1, L76x76x6.4, T (6.35 mm) | 2026-10-01 |
| A_0 | \(\displaystyle 927\ \mathrm{mm}^{2}\) | | CISC SST 12.1, L76x76x6.4, A (A_Th = 927 mm^2; A_A6 = 929 mm^2) | 2026-10-01 |
| r_x0 | \(\displaystyle 29.8\ \mathrm{mm}\) | | CISC SST 12.1, L76x76x6.4, Rxp (29.8 mm, major principal axis) | 2026-10-01 |
| r_y0 | \(\displaystyle 15\ \mathrm{mm}\) | | CISC SST 12.1, L76x76x6.4, Ryp (15.0 mm, minor principal axis) | 2026-10-01 |
| x_0 | \(\displaystyle 25.8\ \mathrm{mm}\) | | CISC SST 12.1, L76x76x6.4, Xop (25.8 mm, centroid to shear centre along the major principal axis) | 2026-10-01 |
| I_x1 | \(\displaystyle A_{0} \cdot r_{x0}^{2}\) | | Geometry (accepted by owner): I = A r^2, the definition of r; checks against SST 12.1 Ix + Ixy = 826e3 mm^4 (823e3 here, r rounded) | 2026-10-01 |
| I_y1 | \(\displaystyle A_{0} \cdot r_{y0}^{2}\) | | Geometry (accepted by owner): I = A r^2, the definition of r; checks against SST 12.1 Ix - Ixy = 210e3 mm^4 (209e3 here, r rounded) | 2026-10-01 |
| M_fx | \(\displaystyle 0.707 \cdot \left(e + \frac{t_{p}}{2}\right) \cdot T_{f}\) | | Statics (accepted by owner): T_f at the gusset mid-plane on the bolt line, (e, -t_p/2), lies 0.707 (e + t_p/2) from X' | 2026-10-01 |
| M_fy | \(\displaystyle \left| 0.707 \cdot \left(e - \frac{t_{p}}{2} - t\right) - x_{0} \right| \cdot T_{f}\) | | Statics (accepted by owner): the load's offset along X' from the centroid, 0.707 (e - t_p/2) - x_c, with x_c = 0.707 t + x_0 | 2026-10-01 |
| lambda_s | \(\displaystyle \frac{L}{r_{y0}}\) | S16 Cl. 10.4.1, a tension member's L/r, no K | CSA S16-19 Cl. 10.4.1 (slenderness of a member in tension: unbraced length L over the corresponding r, no K; r_y0 the least) | 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 |
| S_x1 | \(\displaystyle \frac{I_{x1}}{0.707 \cdot b}\) | | Geometry (accepted by owner): S = I/c (CSA S16-19 Cl. 3, S); the tip corner (b, 0) is the fibre farthest from X', b/sqrt(2) = 0.707 b | 2026-10-01 |
| M_y | \(\displaystyle F_{y} \cdot S_{x1}\) | AISC 360-22 F10.1, the yield moment, at the tips | AISC 360-22 Definitions and F9.1 (M_y the yield moment, at the extreme fibre: the tips, 0.707 b from X') | 2026-09-30 |
| M_nx1 | \(\displaystyle 1.5 \cdot M_{y}\) | AISC 360-22 F10-1 | AISC 360-22 Eq. F10-1 (M_n = 1.5 M_y) | 2026-09-30 |
| M_cr | \(\displaystyle \frac{9 \cdot E \cdot A_{0} \cdot r_{y0} \cdot t}{8 \cdot L}\) | AISC 360-22 F10-4, C_b = 1, beta_w = 0 for equal legs | AISC 360-22 Eq. F10-4 (M_cr = 9 E A_g r_z t C_b / (8 L_b) [sqrt(1 + (4.4 beta_w r_z/(L_b t))^2) + 4.4 beta_w r_z/(L_b t)], beta_w = 0 for equal legs, C_b = 1) | 2026-09-30 |
| M_nx2 | \(\displaystyle \min\left(\left(1.92 - 1.17 \cdot \sqrt{\frac{M_{y}}{M_{\mathrm{cr}}}}\right) \cdot M_{y}, 1.5 \cdot M_{y}\right)\) | AISC 360-22 F10-2 | AISC 360-22 Eq. F10-2 (M_y/M_cr <= 1: M_n = (1.92 - 1.17 sqrt(M_y/M_cr)) M_y <= 1.5 M_y) | 2026-09-30 |
| lambda_l | \(\displaystyle \frac{b}{t}\) | | AISC 360-22 F10.3 and B4.1a(b) (b/t, b the full leg width) | 2026-09-30 |
| lambda_p | \(\displaystyle 0.54 \cdot \sqrt{\frac{E}{F_{y}}}\) | AISC 360-22 Table B4.1b case 12, legs of single angles | AISC 360-22 Table B4.1b case 12 (legs of single angles, lambda_p = 0.54 sqrt(E/F_y)) | 2026-09-30 |
| lambda_r | \(\displaystyle 0.91 \cdot \sqrt{\frac{E}{F_{y}}}\) | AISC 360-22 Table B4.1b case 12, legs of single angles | AISC 360-22 Table B4.1b case 12 (legs of single angles, lambda_r = 0.91 sqrt(E/F_y)) | 2026-09-30 |
| leg | \(\displaystyle 1\) | | AISC 360-22 Table B4.1b case 12 (b/t = 12.0 <= lambda_p = 13.9 at the defaults: compact) | 2026-10-01 |
| M_nx3 | \(\displaystyle 1.5 \cdot M_{y}\) | AISC 360-22 F10.3(a), compact: does not apply, F10-1 stands | AISC 360-22 F10.3(a) and Eq. F10-1 (compact leg: leg local buckling does not apply, M_n = 1.5 M_y) | 2026-09-30 |
| M_nx | \(\displaystyle \min\left(M_{\mathrm{nx}1}, M_{\mathrm{nx}2}, M_{\mathrm{nx}3}\right)\) | AISC 360-22 F10, the lowest of the limit states | AISC 360-22 F10 (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 |
| x_c | \(\displaystyle \frac{1.414 \cdot t}{2} + x_{0}\) | | Geometry (accepted by owner): shear centre at the leg midlines, 0.707 t from the heel along X', plus Xop; checks against sqrt(2) X = 30.26 mm (30.29 here) | 2026-10-01 |
| x_t | \(\displaystyle 0.707 \cdot \left(b + t\right) - x_{c}\) | AISC 360-22 F10.3, S_c to the toe, its inside corner | AISC 360-22 F10.3 (S_c, elastic section modulus to the toe in compression); the toe's extreme fibre about Y' is its inside corner (b, t), 0.707 (b + t) from the heel along X' | 2026-10-01 |
| S_y1 | \(\displaystyle \frac{I_{y1}}{x_{t}}\) | | AISC 360-22 F10.3 (S_c to the toe in compression, I over the toe distance x_t) | 2026-10-01 |
| S_yh | \(\displaystyle \frac{I_{y1}}{x_{c}}\) | | Geometry (accepted by owner): S = I/c (CSA S16-19 Cl. 3, S); the heel, 30.3 mm from Y', is farther than the tips' 28.1 mm, so it is the extreme fibre of AISC 360-22 Definitions (yield moment) | 2026-10-01 |
| M_ny1 | \(\displaystyle 1.5 \cdot F_{y} \cdot S_{\mathrm{yh}}\) | AISC 360-22 F10-1, M_y at first yield, the heel | AISC 360-22 Eq. F10-1 (M_n = 1.5 M_y) with M_y at yielding of the extreme fibre (Definitions), the heel, farther from Y' than the tips | 2026-09-30 |
| M_ny2 | \(\displaystyle 1 \cdot M_{\mathrm{ny}1}\) | AISC 360-22 F10.3(a), compact: does not apply | AISC 360-22 F10.3(a) (compact leg: leg local buckling does not apply) | 2026-09-30 |
| M_ry | \(\displaystyle \phi \cdot \min\left(M_{\mathrm{ny}1}, M_{\mathrm{ny}2}\right)\) | AISC 360-22 F10, the lowest, S16 Cl. 13.1 a) phi | AISC 360-22 F10 (M_n the lowest value of the limit states), phi per CSA S16-19 Cl. 13.1 a) | 2026-09-30 |
| I_a | \(\displaystyle \frac{T_{f}}{T_{r}} + \frac{M_{\mathrm{fx}}}{M_{\mathrm{rx}}} + \frac{M_{\mathrm{fy}}}{M_{\mathrm{ry}}}\) | S16 Cl. 13.9.1 | CSA S16-19 Cl. 13.9.1 (T_f/T_r + M_fx/M_rx + M_fy/M_ry <= 1; M_r taken from AISC F10, not Cl. 13.5) | 2026-09-29 |
| I_b | \(\displaystyle \frac{M_{\mathrm{fx}}}{M_{\mathrm{rx}}} + \frac{M_{\mathrm{fy}}}{M_{\mathrm{ry}}} - \frac{T_{f} \cdot S_{x1}}{M_{\mathrm{rx}} \cdot A_{0}}\) | S16 Cl. 13.9.3 b) | 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) | 2026-09-30 |
calcsheet