Chapter 13 — Welded Connections (AISC 360-22 §J2)

1. Weld Processes — Where the Numbers Come From

Structural steel is almost always joined with an arc-welding process. SMAW (shielded metal arc, "stick") is used for field welds and repairs. FCAW (flux-cored arc) and SAW (submerged arc) dominate shop fabrication because they are faster and produce more consistent quality — SAW in particular gives full-strength, low-defect welds and is standard for shop-fabricated built-up girders. The electrode classification (e.g., E70XX) tells you the nominal tensile strength of the deposited weld metal, F_EXX, in ksi — "70" means 70 ksi. Matching filler metal (F_EXX ≥ F_u of the base metal) is required unless the engineer specifies otherwise, so that the weld does not become the weak link before the connected material yields.

• SMAW — stick electrode, manual, versatile, common in field erection.
• FCAW — cored wire, self- or gas-shielded, fast deposition, common in shop and field.
• SAW — wire feed under a granular flux blanket, highest quality/deposition rate, shop-only (flat position).
• GMAW — solid wire, gas-shielded ("MIG"), fast but wind-sensitive (shop use).

2. Weld Types

A fillet weld is a triangular weld deposited in the corner formed by two plates; it is by far the most common structural weld because it needs no edge preparation. A complete-joint-penetration (CJP) groove weld fuses the full thickness of the joint — with matching filler metal it develops the full strength of the thinner connected part, so no calculation of weld strength is needed (only the connected-part checks govern). A partial-joint-penetration (PJP) groove weld only fuses part of the joint thickness (effective throat < full thickness) and must be checked like a fillet weld using the effective throat from Table J2.1. Plug and slot welds fill a round hole or elongated slot in one plate to fuse it to an underlying plate — used for stitching lapped plates together or hard-to-reach shear transfer, not for primary load path connections.

3. Reading the Weld Symbol

The weld symbol is drawn on a reference line with an arrow pointing to the joint. Information placed below the line describes the weld on the arrow side of the joint; information above the line describes the other side. For a fillet weld, the leg size is given to the left of the triangle symbol and the length (if not "weld all around") to the right. A filled circle at the bend in the leader is the field weld flag — it means this weld is made in the field, not the shop, which affects both cost and quality-control planning.

4. Effective Throat and Effective Area (§J2.2)

A fillet weld does not fail on its leg faces — it fails by shearing along the plane through the throat, the shortest distance from the root to the weld face. For an equal-leg fillet made by a process with a flat (or slightly convex) face, that throat is the leg size times cos 45° = 0.707. Submerged-arc welds get credit for deeper penetration: for legs ≤ 3/8 in the whole leg may be taken as the effective throat, an SAW-specific bonus.

• w — nominal fillet leg size (in).
• t_e — effective throat (in).
• L_w — effective weld length (in), excluding starts/stops and craters.

Physically: doubling the leg size does not double the "amount of steel doing the work" in the same simple way people assume for bolts — the shear plane area scales with 0.707·w, so the strength per inch of weld is directly proportional to leg size w.

5. Fillet Weld Strength (§J2.4)

Weld metal fails in shear on the effective throat, regardless of the direction of the applied force relative to the weld axis. But the ductility of that shear failure depends on direction: a weld loaded transverse to its axis (θ = 90°) fails at a higher stress than one loaded longitudinally (θ = 0°), because the transverse geometry mobilizes a larger fraction of the throat before rupture. AISC captures this with a direction-of-loading multiplier k_ds.

• F_EXX — electrode classification strength (ksi); 70 ksi (E70XX) is standard.
• θ — angle between the line of action of the force and the weld's longitudinal axis (0° = longitudinal, 90° = transverse).
• k_ds — ranges from 1.0 (θ=0°) to 1.5 (θ=90°); use the User Note strain-compatibility limits before applying k_ds > 1.0 to certain weld groups (elements loaded in different directions).

Physically: a transverse fillet weld can be sized 33% smaller than a longitudinal one for the same load, because it is inherently stronger per unit throat area — but engineers often ignore this bonus for simplicity and conservatism.

6. Minimum and Maximum Fillet Weld Size (Table J2.4, §J2.2b)

A weld that is too small relative to the plate thickness cools too fast and can crack; hence Table J2.4 sets a minimum leg size that increases with the thickness of the thinner connected part — this is a heat-input/quality requirement, not a strength requirement. A weld along the edge of a thin plate must not overrun the edge, so the maximum leg is capped as well.

Physically: the minimum-size table exists so that the weld deposits enough heat/volume to fuse properly into thicker material without excessive quench cracking — it must be checked independently of the strength calc, and it can govern even when the calculated required size is smaller.

7. Minimum Effective Length and the Length-to-Size Penalty (§J2.2b(d))

A fillet weld's effective length must be at least 4 times its nominal size, or the size is treated as 1/4 of that length (a strength penalty for stubby welds — stress does not redistribute uniformly at the ends). At the opposite extreme, very long, end-loaded fillet welds (loaded only at the ends, e.g. lap splices) suffer a reduction because stress is not uniform along a long weld — the ends see more load than the middle before the whole length yields.

• l — length of the end-loaded fillet weld (in).
• w — leg size of the fillet weld (in).
• If l/w > 300, use β = 0.60 (Note: for l/w beyond that range, effectiveness plateaus).

Physically: this is why splitting a long lap splice into two shorter parallel welds (or adding transverse end welds) is often more efficient than one very long weld of minimum size — the reduction factor β directly de-rates the nominal strength you calculated from Eq. J2-4.

8. End Returns

At the end of a fillet weld that resists a tension load parallel to the weld (as in a lap-splice angle or bracket), the weld should be returned around the corner for a short distance (typically 2·w) rather than stopping abruptly. This "end return" reduces the stress concentration at the weld terminus, where premature cracking is otherwise common — a detailing best practice rather than a strength calculation, but commonly required by AISC Manual connection tables.

9. Base-Metal Strength Check (§J2.4(a))

A weld connection can fail two different ways: the weld metal can shear through its throat, or the base metal adjacent to the weld can tear (shear rupture along the fusion face). Both must be checked — the weld can be strong enough while the thin plate beside it isn't, especially for thin gusset plates welded with an oversized fillet.

Physically: for typical E70 electrodes on A36/A572-50/A992 steels, weld metal governs (is weaker) when w is smaller than roughly 5/16 in per inch of connected-plate thickness ratio; base metal tends to govern for thin, high-strength plates joined with an oversized weld.

10. Eccentrically Loaded Weld Groups

Brackets, single-plate shear connections, and gusset-to-column welds are rarely loaded through the centroid of the weld group. The eccentricity produces a moment M = P·e that the weld group must resist in addition to the direct shear. Two methods are used:

• Elastic (vector) method — treats the weld group like a bolt group: direct shear P/A_w is added vectorially to a "torsional" shear M·r/J (polar analogy), and the largest resultant vector governs. Conservative, hand-calculable, and independent of load direction relative to any one weld segment — this is what students should master first.
• Instantaneous center (IC) method — recognizes that the weld group actually rotates about an instantaneous center (not its centroid) and that each weld element can develop different amounts of the k_ds directional bonus and inelastic deformation before rupture. It is the basis of AISC Manual Tables 8-4 through 8-11 and gives higher (less conservative, more accurate) capacities, but requires iteration or the tables/software.

• A_w — total weld throat area treated per unit throat (usually work per inch of L_w, i.e., analysis is done for a 1-in throat and scaled by w at the end).
• J — polar moment of inertia of the weld line group about its centroid, J = I_x + I_y.
• c — distance from the weld-group centroid to the farthest weld point.

Physically: welds located far from the centroid (the corners of an L- or C-shaped weld group) see the highest combined stress and govern the required weld size; increasing the depth of a bracket weld group is a far more efficient way to reduce stress than increasing its width, because c and J both grow with depth.

11. Weld Quality, Inspection, and Common Defects

AWS D1.1 governs welding procedure specifications (WPS), welder qualification, and acceptance criteria. CJP groove welds in tension resisting seismic or fatigue loads typically require UT or RT; routine fillet welds usually rely on visual inspection by an AWS Certified Welding Inspector (CWI), supplemented by MT/PT for suspect areas.

Design Workflow

1. Determine required strength (LRFD: factored load; ASD: service load).
2. Select weld type (fillet vs. groove) and geometry based on the joint configuration.
3. Check Table J2.4 minimum size and §J2.2b(b) maximum size against connected-part thickness.
4. Compute F_nw = 0.60F_EXX·k_ds, apply φ = 0.75 (LRFD) or Ω = 2.00 (ASD).
5. If end-loaded and l/w > 100, apply β reduction (Eq. J2-1).
6. Check base-metal shear rupture on both connected parts (Eq. J2-2/J4-4 form).
7. For eccentric groups, compute the weld-group centroid, J, and check the maximum resultant r_u by the elastic method (or use IC tables for efficiency).
8. Detail end returns, minimum length, and specify inspection level.

Additional Design Aids & Stratified Equations

🎞 Watch the Phenomenon — Loading Stages

📖 Using the AISC Manual — Welded Connections

Companion reference: Manual Part 8 — Tables 8-3 (fillet weld strength per 1/16″ per inch), 8-4 to 8-11 (eccentric weld coefficient C for common shapes). In practice, engineers rarely compute every quantity from first principles — the AISC Steel Construction Manual (16th Ed.) tabulates φR_n (or R_n/Ω) for every rolled shape so you can pick a member in seconds. Formulas remain essential for understanding, verifying, and for anything the tables do not cover.

Fillet weld shorthand (E70XX): φR_n per inch of weld = 1.392·D kip/in, where D is the weld size in sixteenths (5/16″ → D=5 → 6.96 kip/in). Table 8-3 tabulates this so you never re-derive 0.75·0.6·70/√2·(1/16).

Eccentric weld groups (Tables 8-4/8-11): the instantaneous-center coefficient C lets you write φR_n = C·C₁·D·L, where C is by geometry & load angle, C₁ is the electrode-strength adjustment (1.0 for E70), D is weld size in sixteenths, L is the characteristic length. Replaces the fictitious "elastic" vector method that under-predicts capacity by 30–100%.

Directional strength increase: when load is perpendicular to the weld axis, F_nw is 1.5× the parallel case (Section J2.4). Table 8-3 already applies this when the angle θ is specified.