Structural Steel Connections, AWS D1.1 Welding & AISC 360 LRFD
Fillet Weld Effective Throat & AISC/AWS LRFD Strength Formula
Calculate 45° Fillet Effective Throat t_e = w / SQRT(2) (mm), Total Effective Weld Shear Area A_w (mm²), Design Strength per Millimeter (kN/mm), and Total Connection LRFD Capacity phi*R_n (kN).
Fillet welds fail in shear across the 45° throat w / SQRT(2)—NOT across the full leg size w!
Equal-leg 90° structural fillet welds specified by leg size w (mm) rupture along the minimum 45° bisector plane from the weld root to the hypotenuse face: Effective Throat Thickness is t_e = w * COS(45°) = w / SQRT(2) = 0.7071 * w (mm)! Under AISC 360 J2.4 and AWS D1.1 LRFD rules for longitudinal shear connections using filler metal of nominal tensile classification F_EXX (MPa, e.g. 480 MPa for E70XX electrodes), Nominal Weld Metal Shear Stress is F_nw = 0.60 * F_EXX with resistance factor phi = 0.75—giving Unit Design Capacity per Millimeter of Single Weld q_design = (0.75 * 0.60 * F_EXX * (w / SQRT(2))) / 1,000 kN/mm and Total Connection Capacity phi * R_n = q_design * L_each * N_welds!
Verify on a Double-Sided Gusset Lap Splice—Fillet_Leg_Size w = 8.0 mm (B2 -> Effective Throat t_e = 5.66 mm in E2), Weld_Length_Per_Line L = 150.0 mm (B3), Number_of_Weld_Lines N = 2 (B4 -> Effective Throat Area A_w = 5.6569 * 300 = 1,697.06 mm² in E3), and Electrode_Strength F_EXX = 480.0 MPa (E70XX, B5): Unit Design Capacity per mm hits 1.222 kN/mm (E4), and Total Connection LRFD Strength phi * R_n equals 366.56 kN (E5)!
| AISC/AWS Fillet Weld KPI (w = 8 mm, 2 x 150 mm Lines, FEXX = 480 MPa) | Formula | Verified Output |
|---|---|---|
| Effective Throat Thickness te (mm) | Fillet_Leg_w_mm / SQRT(2) | 5.66 mm (7.07 mm @ w = 10 mm) |
| Total Effective Throat Area (mm²) | (w / SQRT(2)) * Length_mm * N_Welds | 1,697.06 mm² (2,121.32 @ w = 10 mm) |
| Design Strength per mm (kN/mm) | (0.75 * 0.60 * FEXX * (w/SQRT(2)))/1000 | 1.222 kN/mm (1.527 @ w = 10 mm) |
| Total LRFD Weld Capacity (kN) | (0.75 * 0.60 * FEXX * Aw_mm2) / 1000 | 366.56 kN (458.21 kN @ w = 10 mm) |
AISC 360 / AWS D1.1 LRFD Fillet Weld Shear Strength Formula
Validate Leg_Size w >= 3 mm, Effective_Length L >= 4 * w (AISC minimum fillet weld length rule!), integer Weld_Lines N >= 1, and Electrode F_EXX in [410, 830] MPa!
=LET(lg_w, B2, ln_m, B3, nw_l, B4, fx_m, B5, IF(OR(lg_w < 3, ln_m < 4 * lg_w, nw_l < 1, INT(nw_l) <> nw_l, fx_m < 410, fx_m > 830), "Invalid Fillet Weld Input", LET(te_m, lg_w / SQRT(2), aw_t, te_m * ln_m * nw_l, ROUND((0.75 * 0.6 * fx_m * aw_t) / 1000, 2))))10 mm Multi-Pass Fillet Upgrade & 4*w Minimum Length Guard Check (Set w = 10 mm)
Step Fillet_Leg_Size B2 up from 8.0 mm to 10.0 mm: Effective Throat E2 increases to 7.07 mm, Unit Strength E4 rises to 1.527 kN/mm, and Total LRFD Capacity E5 climbs 25% to 458.21 kN! (Also test B3 = 20 mm < 4 * 8 = 32 mm to verify the AISC minimum length guard!)
=IF(ISTEXT(E5), E5, ROUND((0.75 * 0.6 * B5 * (B2 / SQRT(2))) / 1000, 3))Try the example
Use the original values or change them to test your understanding.