| e_b | \(\displaystyle \frac{d_{b}}{2}\) | | AISC Steel Construction Manual 14th ed. Part 13, Uniform Force Method (e_b = half the beam depth) | 2026-09-30 |
| beta_1 | \(\displaystyle \frac{L_{c1}}{2}\) | | AISC Steel Construction Manual 14th ed. Part 13, Uniform Force Method (beta locates the gusset-to-column centroid; L_c/2 assumes the bolt line starts at the beam flange face) | 2026-09-30 |
| alpha_1 | \(\displaystyle \beta_{1} \cdot \tan\left(\operatorname{radians}\left(\phi_{1}\right)\right) + e_{b} \cdot \tan\left(\operatorname{radians}\left(\phi_{1}\right)\right) - e_{c}\) | | AISC Steel Construction Manual 14th ed. Part 13, Uniform Force Method, Eq. 13-1 solved for alpha | 2026-09-30 |
| r_1 | \(\displaystyle \sqrt{\left(\alpha_{1} + e_{c}\right)^{2} + \left(\beta_{1} + e_{b}\right)^{2}}\) | | AISC Steel Construction Manual 14th ed. Part 13, Uniform Force Method, Eq. 13-6 | 2026-09-30 |
| F_v1 | \(\displaystyle \frac{e_{b}}{r_{1}}\) | | AISC Steel Construction Manual 14th ed. Part 13, Uniform Force Method, Eq. 13-4 over P (V_b/P) | 2026-09-30 |
| F_h1 | \(\displaystyle \frac{\alpha_{1}}{r_{1}}\) | | AISC Steel Construction Manual 14th ed. Part 13, Uniform Force Method, Eq. 13-5 over P (H_b/P) | 2026-09-30 |
| V_c1 | \(\displaystyle \frac{P_{f1} \cdot \beta_{1}}{r_{1}}\) | | AISC Steel Construction Manual 14th ed. Part 13, Uniform Force Method, Eq. 13-2 | 2026-09-30 |
| H_c1 | \(\displaystyle \frac{P_{f1} \cdot e_{c}}{r_{1}}\) | | AISC Steel Construction Manual 14th ed. Part 13, Uniform Force Method, Eq. 13-3 | 2026-09-30 |
| beta_2 | \(\displaystyle \frac{L_{c2}}{2}\) | | AISC Steel Construction Manual 14th ed. Part 13, Uniform Force Method (beta locates the gusset-to-column centroid; L_c/2 assumes the bolt line starts at the beam flange face) | 2026-09-30 |
| alpha_2 | \(\displaystyle \beta_{2} \cdot \tan\left(\operatorname{radians}\left(\phi_{2}\right)\right) + e_{b} \cdot \tan\left(\operatorname{radians}\left(\phi_{2}\right)\right) - e_{c}\) | | AISC Steel Construction Manual 14th ed. Part 13, Uniform Force Method, Eq. 13-1 solved for alpha | 2026-09-30 |
| r_2 | \(\displaystyle \sqrt{\left(\alpha_{2} + e_{c}\right)^{2} + \left(\beta_{2} + e_{b}\right)^{2}}\) | | AISC Steel Construction Manual 14th ed. Part 13, Uniform Force Method, Eq. 13-6 | 2026-09-30 |
| F_v2 | \(\displaystyle \frac{e_{b}}{r_{2}}\) | | AISC Steel Construction Manual 14th ed. Part 13, Uniform Force Method, Eq. 13-4 over P (V_b/P) | 2026-09-30 |
| F_h2 | \(\displaystyle \frac{\alpha_{2}}{r_{2}}\) | | AISC Steel Construction Manual 14th ed. Part 13, Uniform Force Method, Eq. 13-5 over P (H_b/P) | 2026-09-30 |
| V_c2 | \(\displaystyle \frac{P_{f2} \cdot \beta_{2}}{r_{2}}\) | | AISC Steel Construction Manual 14th ed. Part 13, Uniform Force Method, Eq. 13-2 | 2026-09-30 |
| H_c2 | \(\displaystyle \frac{P_{f2} \cdot e_{c}}{r_{2}}\) | | AISC Steel Construction Manual 14th ed. Part 13, Uniform Force Method, Eq. 13-3 | 2026-09-30 |
| A_f | \(\displaystyle H_{f} + P_{f1} \cdot F_{h1} + P_{f2} \cdot F_{h2} + P_{f3} \cdot \cos\left(\operatorname{radians}\left(\phi_{3}\right)\right) + P_{f4} \cdot \cos\left(\operatorname{radians}\left(\phi_{4}\right)\right)\) | AISC 14th ed. Part 13, Uniform Force Method, Fig. 13-2 | AISC Steel Construction Manual 14th ed. Part 13, Fig. 13-2(d) for the H_f and H_b terms; the plan-brace terms P_f3 cos(phi_3) and P_f4 cos(phi_4) are statics, not in the manual (owner accepted) | 2026-09-30 |
| S_f | \(\displaystyle V_{f} + P_{f1} \cdot F_{v1} - P_{f2} \cdot F_{v2}\) | AISC 14th ed. Part 13, Uniform Force Method, Fig. 13-2 | AISC Steel Construction Manual 14th ed. Part 13, Fig. 13-2(d): beam-to-column shear R_b - V_b, V_b up for a tension brace above the beam and down for one below | 2026-09-30 |
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