Eccentric weld group
A group of fillet welds under an in-plane load whose line of action misses the centroid, by the instantaneous center of rotation (IC) method or the elastic method of the AISC Manual, 16th Edition, Part 8, with the weld strength of AISC 360-22 Section J2.4. The result is the coefficient C, the required size, the available strength against your load and the force along the welds. Use it for a bracket, a seat, a welded tab or any pattern the Manual does not tabulate.
Inputs of the eccentric weld group #
- Load: service loads by type (each ASCE 7-22 2.3.1 or 2.4.1 combination of the types present is evaluated, all along the same load line) or the required strength directly. See Loads and combinations.
- Load line: the angle θ from the vertical (0 is straight down; a positive angle turns the load clockwise, as in the Manual tables), the distance of the line from the vertical weld at the level of the centroid, and, for an inclined load that does not pass through the centroid level at that point, the height of the load point above the centroid. The Manual's a l is the distance less the centroid distance x̄ l; the calculation shows both.
- Weld group: a single line, two vertical lines (Table 8-4), two horizontal lines (Table 8-5), a box with l vertical or horizontal (Tables 8-6, 8-7), a C with returns toward or away from the load (Tables 8-8, 8-9), an L with its return toward or away from the load (Tables 8-10, 8-10a, 8-11, 8-11a), or up to 60 custom segments. Two vertical lines with kl = 0 are one on each face of a single plate, the k = 0 column of Table 8-4. For two horizontal lines, l here is the spacing and kl the line length, the reverse of Table 8-5; the table note converts.
- Weld: the leg size and the electrode. The IC method uses C1 of Manual Table 8-3, the elastic method FEXX. That the filler suits the base metal (AISC 360-22 Table J2.6) is yours to confirm.
- Connected parts: the thinner part, which sets the size limits and the base metal check; its material; whether the welds share a shear plane (Manual Part 9: 3.09 D / Fu or 6.19 D / Fu); whether the weld runs along the edge of the part, which is what brings in the maximum size of J2.2b(b).
- Code options: the strength method, and the directional strength increase kds. The tables assume the increase. Turning it off is your judgment, for example for a single-sided fillet whose root can open (AISC 360-22 J2.4(a)).
Auto-design varies the fillet size (1/8 to 3/4 in.) and the length l (4 to 48 in.), least weld metal first; the return, the load line, the electrode and the parts stay as you entered them. A custom group keeps its segments and varies the size only.
Checks performed #
| Check | Basis |
|---|---|
| Weld group, chosen strength method | Required strength against φ C C1 D l or C C1 D l / Ω, φ = 0.75, Ω = 2.00 (Manual Eq. 8-30; AISC 360-22 J2.4, Table J2.5), or the elastic method (Manual Eqs. 8-11 to 8-17) |
| Weld group, the other method | The same comparison, shown and not counted in the status |
| Manual table value (note) | The tabulated C for the shape, linear in k and a, at the next lower tabulated angle, beside the C of the actual load line; the IC value is the one used |
| Minimum fillet size | Table J2.4, on the thinner part |
| Maximum fillet size | t, or t − 1/16 in. from 1/4 in. up, along an edge (J2.2b(b)) |
| Minimum length | 4 w on every segment (J2.2b(c)) |
| Long welds (advisory) | Where a line longer than 100 w is end-loaded, the factor of Eq. J2-1. It is reported and not applied, as in the Manual tables; whether the weld is end-loaded is your judgment |
| Base metal | 3.09 D / Fu or 6.19 D / Fu on the part, with D the smaller of the provided and the required size (Manual Part 9) |
IC method. Each element carries 0.60 FEXX (1 + 0.50 sin^1.5 θ) f(p) times its throat area. Its deformation is in proportion to its distance from the instantaneous center, and the element with the least ultimate deformation over distance reaches its limit (Manual Part 8). The calculation finds the center by equilibrium and reports C on l. It is solved for your load line, not read from the table.
Load through the centroid. This takes the a = 0 row of the tables, which the Manual says follows AISC 360-22 J2.4: for a linear group Eq. J2-5; for others the greatest of deformation compatibility, the elements summed with kds = 1.0, and Eq. J2-6 for groups of longitudinal and transverse lines.
Elastic method. Direct shear P / L plus the moment shear at each weld end, added as vectors, with kds = 1.0. It ignores ductility and is more conservative.
Manual table note. Between tabulated angles the Manual warns that straight-line interpolation may be wrong and says to use a rational analysis or the next lower angle: the note reads the next lower angle, and the check uses the analysis at your angle. For an L, the sign of θ picks 8-10 or 8-10a and 8-11 or 8-11a, with the return at the bottom; for a return at the top, change the sign of θ.
Limitations of the eccentric weld group #
- Fillet welds in one plane under a load in that plane. PJP and CJP grooves, plug welds and out-of-plane moment on the weld are not covered.
- The connected parts are not designed beyond the base metal thickness that develops the weld: no net section, block shear, plate bending or the member behind.
- The Manual's special case of a load out of the plane of the group is not a separate input.
- Eq. J2-1 for long end-loaded welds is reported, not applied.
- A group with short lines far apart under an inclined load (outside the tables, k above 2) can have more than one equilibrium solution, up to about 7 % apart in a study of such cases. The calculation keeps the one nearest the elastic estimate and says so for custom and out-of-range groups: compare the elastic method there.
Verification examples #
Verification status: 166 values compared in 134 examples (134 published, 0 hand calculations from the cited equations): 161 within tolerance, 5 recorded deviations. Code basis: the provisions it uses were read in the target edition.
From the AISC Design Examples v16.0 Vol. 1: II.A-26 (Solutions for a vertical load and a load at 75 degrees: C 1.88 and 3.45, 84.8 and 155 kips LRFD, 56.5 and 104 kips ASD) and II.A-27 (elastic: Ip 385, 47.2 kips LRFD, 31.5 kips ASD), and the weld groups inside II.A-2A, II.A-2B, II.A-10, II.A-11B, II.A-21, II.A-23, II.A-29 and II.C-1 (C, x̄, a and the required size). All are within tolerance.
From the AISC Manual 16th Ed.: every readable coefficient of Tables 8-4 to 8-11a, 21,308 of 21,344 cells (two machine reads of the page images; 36 cells were not read and are not compared), against the method. All but 15 are within 1 % or half a printed digit, plus one more that matches the errata:
- Table 8-4, 30 degrees, k = 2.0, a = 0.40 is printed 3.54; the Manual's errata correct it to 3.34, and the method gives 3.33.
- Table 8-11a, 75 degrees, a = 0.10 and 0.15, k from 0.8 up, 11 cells: the printed values equal the a = 0 row and the method gives 1.1 % to 1.6 % more.
- Table 8-10, 0 degrees, k = 2.0, a = 0.10: printed 7.10, the method 7.19 (1.3 %), one solution; not explained.
- Table 8-4, 0 degrees, k = 2.0, a = 0.70, 2.4 and 2.6: printed 1.0 % to 1.1 % above the method; both reads agree.
Hand calculations, no published example: kds off, E60 and E80 to E110 (scaling by C1 and FEXX only), metric input, custom segments and the load point above the centroid. The 6.19 D / Fu base metal option is the Manual's formula with no worked example here.