Engineering story
Chapter 13 · Welded Connections
Fillet, groove, weld symbols, and effective throat.
A real project narrative for this chapter will be authored as this chapter migrates to the v3.0 structured schema.
§01Section 01
Why Structural Steel?
Fillet, groove, weld symbols, and effective throat.
⏱ 90 min★ Core✎ 3 objectives
§02Section 02
Learning objectives
After this chapter you will be able to
- Compute fillet-weld strength
- Read AWS weld symbols
- Size groove welds
§03Section 03
Engineering motivation
§04Section 04
Failure mechanisms
Failure mechanisms & lessons learned
Photographs and lessons-learned case studies for this topic will be added during chapter migration.
AISC Reference Box
- AISC 360-22 §J2 — Welds
Why This Chapter Matters
Welded connections are stronger and stiffer than bolted, but weld throat, weld size, and weld orientation change capacity dramatically. Fillet welds under longitudinal shear are the workhorse — and the most misdesigned.
Learning Objectives
- Read AWS weld symbols and identify fillet, groove (CJP/PJP), plug, and slot welds.
- Compute effective throat: t = 0.707 · w for equal-leg fillets.
- Design fillet welds per AISC J2.4: φRn = 0.75 · 0.60 · FEXX · te · L · (1.0 + 0.5 sin^1.5 θ).
- Detail minimum and maximum weld sizes (Table J2.4).
- Check strength of the base metal alongside weld metal.
Where This Chapter Is Used
Every shear-tab, moment-connection weld, and base-plate weld from Chapters 14 through 20.
ANSI / AISC 360-22Specification for Structural Steel Buildings16.1-124 to 16.1-127 (§J2)
Chapter
J
AISC 360-22
Chapter J. Design of Connections — Welds (§J2)
Use this reference to flip directly to the correct page of the AISC 360-22 Specification while solving problems in this course chapter.
| § | Section title | Page |
|---|---|---|
| J2.1 | Groove Welds (CJP, PJP) — Effective Area | 16.1-124 |
| J2.2 | Fillet Welds — Effective Throat | 16.1-125 |
| J2.3 | Plug and Slot Welds | 16.1-126 |
| J2.4 | Strength (φRn = 0.75·0.60·FEXX·Awe·(1+0.5 sin^1.5 θ)) | 16.1-126 |
| J2.5 | Combination of Welds | 16.1-127 |
| J2.6 | Filler Metal Requirements | 16.1-127 |
| J2.7 | Mixed Weld Metal | 16.1-127 |
Companion reference: AWS D1.1 & AISC Manual Part 8 — Welded Connection Design
Lecture Notes
Chapter 13 — Welded Connections (AISC 360-22 §J2)
Chapter focus. Fillet welds carry load on their throat (0.707·leg for equal-leg welds). Direction-of-load factor kds up to 1.5 gives extra strength for transverse welds. This chapter covers fillet weld strength, minimum size / maximum size rules (§J2.2), and complete-joint-penetration groove welds.
1. Fillet Welds
Effective throat te = 0.707·w (equal-leg SMAW/FCAW).
Eq. J2-3Rn = Fnw · Awe = 0.60·FEXX·(0.707·w)·Lw
φ = 0.75. For load-inclined welds, increase Fnw by (1.0 + 0.5·sin1.5θ) per §J2.4(a).
2. Minimum & Maximum Sizes (Table J2.4, §J2.2b)
wmax = t − 1/16″ along edges of plates ≥ 1/4″ thick; = t for thinner plates.
3. Base-Metal Strength Check (§J2.4(b))
φRn,BM = 0.75·0.60·Fu·t·Lw
Weld metal and base metal must both check. For matched electrodes and typical plates, weld metal governs when w < ~5/16″·(Fu/FEXX).
4. Length Limitations
- Effective Lw reduced for lap-joint welds when Lw > 100·w (Eq. J2-1, β factor).
- End returns ≥ 2w recommended (§J2.2b).
- Minimum length 4·w or full weld ineffective.
5. Groove Welds
Complete-Joint-Penetration (CJP) matches base-metal strength; no calc needed if matched electrode used. Partial-Joint-Penetration (PJP) effective throat per Table J2.1.
Additional Design Aids & Stratified Equations
Directional strength increase: transverse fillet weld is 50% stronger than longitudinal.
Directional factorF_nw,eff = 0.60·F_EXX · (1.0 + 0.5·sin^{1.5}θ)
Weld strength /in (5/16 in, E70, longitudinal)φr_n = 0.75·0.60·70·0.707·(5/16) = 6.96 k/in
⚠ Common mistakes
- Using w instead of 0.707·w for effective throat.
- Ignoring base-metal shear rupture check.
- Under-sizing per Table J2.4 (violates code even if strength is OK).
- Neglecting end returns and length reduction β when Lw > 100w.
🎞 Watch the Phenomenon — Loading Stages
Fillet weld carrying transverse shear — elastic, yield on throat, rupture.
📖 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 φRn (or Rn/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): φRn 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 φRn = 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, Fnw is 1.5× the parallel case (Section J2.4). Table 8-3 already applies this when the angle θ is specified.
Table vs. formula — which to use? Use tables to select a shape quickly. Use formulas to verify odd geometry, non-standard grades (Fy≠50 ksi), unusual K-factors or Lb, and to answer exam problems that hand you a section not in the current Manual.
Project case study — Cardinal Square — 4-story braced-frame office
Every chapter's worked example is one step in the design of the same building: Plan: 4 bays N–S × 3 bays E–W, each 30 ft × 30 ft. Stories: 4 @ 13 ft (52 ft roof). Composite floor: 4.5 in NW concrete on 3 VLI20 deck. Roof: 1.5 in B-deck + insulation + membrane. Materials: Wide-flange members A992 (Fy = 50 ksi, Fu = 65 ksi). Plates A572 Gr. 50. HSS bracing A500 Gr. C. Bolts A325-N 7/8 in dia. Welds E70XX. Concrete f'c = 4 ksi. Anchor rods F1554 Gr. 36.
Chapter 13 — Welded connection at the gusset
Fillet weld of brace gusset to column flange
Demand carried forward
From Chapter 4: brace force Tu
≈ 100 k.
This chapter contributes
Sizes weld leg w using φRn = 0.75 · 0.60 · FEXX · 0.707 · w · Lw (AISC §J2.4). Confirms minimum size per Table J2.4.
Formula Sheet
| Name | Equation | AISC Ref |
|---|---|---|
| Fillet weld strength | φRn = 0.75 · 0.60 · FEXX · te · Lw | AISC §J2.4 |
| Effective throat | te = 0.707 · w (for equal-leg fillet) | AISC §J2.2 |
Worked Example
Worked Example 13.1 — Fillet Weld on Brace Gusset
Given
- Brace tension Tu = 100 k (from Ch 4).
- Gusset plate 1/2 in thick, A572 Gr. 50 (Fu = 65 ksi).
- Column flange tf = 5/8 in.
- Electrode E70XX (FEXX = 70 ksi); two fillet welds parallel to force, Lw = 8 in each.
Figure 13.1a — Two longitudinal fillet welds and cross-section showing throat = 0.707 w
Step 1 — Size the Weld
Eq. J2-4φRn/in = 0.75·0.60·FEXX·0.707·w = 22.27·w (E70) ; ru = Tu/ΣLw
Required per inch: ru = 100 / (2·8) = 6.25 k/in
φRn,weld/in = 0.75·0.60·70·0.707·w = 22.27·w
wreq = 6.25 / 22.27 = 0.281 in → round up to 5/16 in.
φRn,weld/in = 0.75·0.60·70·0.707·w = 22.27·w
wreq = 6.25 / 22.27 = 0.281 in → round up to 5/16 in.
Step 2 — Minimum Size Check
Table J2.4wmin per thinner part (1/2″ → 3/16″)
Thinner part 1/2 in → Table J2.4 requires w ≥ 3/16 in. Chosen 5/16 in ✓
Step 3 — Base-Metal Shear Rupture (Gusset)
Eq. J4-4φRn,BM = 0.75·0.60·Fu·t·ΣLw
φRn,BM = 0.75·0.60·65·0.5·(2·8) = 234 k ≥ 100 ✓
Step 4 — Weld-Metal Capacity Verify
FormulaφRn = 22.27·w·ΣLw
φRn = 22.27·(5/16)·(2·8) = 22.27·0.3125·16 = 111.4 k ≥ 100 ✓ (DCR = 0.90)
Specify 5/16 in fillet welds, 8 in long each side of the gusset. End returns 2·w = 5/8 in. All J2 provisions satisfied.
Additional Worked Examples
Textbook — Aghayere & Vigil (2009)
Chapter 10 covers fillet, groove, and plug welds. Fillet welds are governed by shear on the effective throat (te = 0.707·w for equal-leg). The base metal must also be checked — weld design rarely controls when E70 electrodes are matched with A36/A992 base.
Example 10-1 — Fillet weld strength per inch
Example 10-1 — Fillet weld strength per inch
Setup. 5/16-in E70 fillet weld.
AISC Reference: AISC §J2.4
Numerical practice
Design shear strength per inch?
- A. 3.48 k/in
- B. 4.18 k/in
- C. 5.57 k/in (Answer)
- D. 6.96 k/in
Step-by-step solution
φRn/in = 1.392·5 = 6.96 k/in. (Or 0.75·0.60·70·0.707·(5/16) = 6.96.)
Example 10-4 — Required weld length
Example 10-4 — Required weld length
Setup. Tension splice plate carrying Pu = 90 k; use 1/4-in E70 fillet welds along both edges.
AISC Reference: AISC §J2.4
Numerical practice
Total weld length required?
- A. 8 in
- B. 11 in
- C. 16 in (Answer)
- D. 22 in
Step-by-step solution
Per inch (1/4 in fillet) = 1.392·4 = 5.57 k/in. Lw = 90/5.57 = 16.2 in → 16 in (8 in each side).
Example 10-6 — Concentric weld group — single angle
Example 10-6 — Concentric weld group — single angle
Setup. L4×4×3/8 to gusset, two longitudinal fillet welds along the heel and toe of one leg, Lw1 = 6 in, Lw2 = 4 in.
AISC Reference: AISC §D3, Table D3.1 (U)
Numerical practice
Balance the welds about the centroid: closer to heel weld length L1 should be (approx)?
- A. 3 in (Answer)
- B. 5 in
- C. 7 in
- D. 9 in
Step-by-step solution
x̄ = 1.13 in for L4×4×3/8 (b = 4 in). L1/Ltot = x̄/b = 0.282 → if Ltot = 10 in, L1 ≈ 2.8 in along the heel side.
Example 10-8 — Eccentric weld group (bracket)
Example 10-8 — Eccentric weld group (bracket)
Setup. C-shaped weld bracket: vertical legs Lv = 8 in, horizontal Lh = 4 in, E70, load P at 6-in eccentricity.
AISC Reference: AISC Manual Table 8-4
Numerical practice
Use Manual Table 8-4 with k = 0.5, a = 0.75 → coefficient C ≈ 1.85. φRn for D = 4 (1/4 in)?
- A. 20 k
- B. 44 k
- C. 60 k (Answer)
- D. 78 k
Step-by-step solution
φRn = C·D·L = 1.85·4·8 = 59.2 ≈ 60 k.
FE-Style Worked Examples(7)
Each example mirrors the NCEES FE Civil Reference Handbook style: brief givens, a labeled figure, AISC section reference, step-by-step numeric solution, and a single boxed answer.
Given
1/4" fillet, E70 electrode (FEXX=70 ksi).
AISC Reference
AISC §J2.4 Eq. J2-4
Step-by-step solution
- te0.707 × 0.25 = 0.177 in
- φRn / in0.75 × 0.60 × 70 × 0.177 = 5.57 k/in
- Rule of thumb≈ 1.392·D (D in 1/16") = 1.392×4 = 5.57 k/in ✓
Answer 5.57 k per inch of 1/4" fillet.
Problem statement image
DIMDimensions from the problem statement
FEXX = 70k
Fillet-weld geometry
- Leg size w, throat t_e = 0.707 w
- Effective length L_e (deduct 2w for wrap terminations if applicable)
- φR_n = 0.75 · 0.60 F_EXX · t_e · L_e per inch
Interactive Calculator
Fillet Weld Strength
AISC §J2.4te = 0.707·w0.177 in
φ Rn = 0.75·0.6·FEXX·te·L33.4 kipsNG
Longitudinal loading only. Use Instantaneous Center / directional strength increase for angled loads.
Graded Chapter Quiz(13 FE-style questions · AISC Manual required)
These questions reference AISC Steel Construction Manual (16th ed.) — sections, equations, and tables are cited explicitly. Use a calculator. Each question offers a clue you may reveal before answering. Submissions are recorded to your account once signed in.
C13-01AISC 360-22 §J2.2a
1. Fillet weld with equal leg w. Compute the effective throat te (SMAW).
C13-02AISC 360-22 Eq. J2-4
2. 5/16-in fillet weld (E70), LONGITUDINAL to the load, per inch of length. Compute φRn/inch (θ = 0°).
C13-03AISC 360-22 §J2
3. Required strength Pu = 90 k. Fillet welds each side of the lap (two lines, longitudinal). Compute the total weld length Lw required at 5/16-in.
C13-04AISC 360-22 Eq. J2-5
4. If the SAME 5/16 weld runs TRANSVERSE (θ = 90°), what is φRn/inch?
C13-05AISC 360-22 Table J2.4
5. AISC Table J2.4 minimum fillet-weld size for a 5/8-in thicker part:
C13-06AISC 360-22 §J2.2b
6. Maximum fillet-weld size along edge of a 1/2-in plate:
C13-07AISC 360-22 Eq. J4-4
7. Base-metal shear rupture through 1/2-in plate along 6-in weld length (Fu = 65) — check per §J4.2:
C13-08AISC 360-22 §J2.2b(c)
8. End-return length for fillet weld terminated at the free edge of a tension member:
C13-09AISC 360-22 §J2.3
9. CJP groove weld strength:
C13-10AISC 360-22 Table J2.5
10. PJP groove weld under tension normal to axis (Table J2.5):
C13-11AISC 360-22 Eq. J2-5
11. Directional strength (θ = 45° weld line to force): multiplier on 0.60·FEXX·te:
C13-12AISC Manual Part 8
12. Eccentric weld group (bracket) — designing by the elastic method vs instantaneous center of rotation (ICR, Manual Tables 8-4 to 8-11):
C13-13AISC 360-22 §J1.6
13. Weld access hole geometry (AISC §J1.6): what does it accomplish at a beam-column moment connection?
Upload your worked solution (PDF)
Attach your handwritten or typed step-by-step solution for this chapter's graded quiz. The instructor can download every submission. PDF only, up to 25 MB.
How your upload will be graded
Your file — PDF, Word document, scanned handwriting or a photo — is read page by page like an experienced structural engineering instructor would. The scan is validated first, then your reasoning, structural model, calculations, diagrams, code basis and final answers are graded on process, not just the final number. Design work is additionally reviewed against AISC 360-22 and ACI 318-19. Partial credit applies, and one early mistake carried correctly forward is only penalized once.
Before you attach the file
- Include every page, in order and right way up — a missing page cannot earn credit.
- Keep margins in frame: nothing cropped at the edges, especially boxed final answers.
- Scan or photograph in good, even light — no shadows, glare or blur; 300 dpi or a steady phone scan.
- Write in dark pen; faint pencil is the most common 'UNREADABLE — INSTRUCTOR REVIEW REQUIRED' flag.
- Include all diagrams, FBDs, shear/moment diagrams and section sketches — label them.
- Number each question the same way the assignment does, and note anything you skipped.
- Show units on every line and box your final answers.
- Combine everything into ONE file (PDF preferred; Word, JPG or PNG accepted) under 20 MB.
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§11Section 11
Chapter summary
Formula sheet
- Fillet weld strengthφRn = 0.75 · 0.60 · FEXX · te · LwAISC §J2.4
- Effective throatte = 0.707 · w (for equal-leg fillet)AISC §J2.2
Engineering checklist
- Module 13: Welded Connections
- Key limit states and AISC references are listed in the reference box.
- Use φRn ≥ Ru for every check.
- Verify section properties with the official AISC Manual.
Professional tips
- • Mixing ASD and LRFD load combinations in the same problem.
- • Using nominal strength Rn instead of design strength φRn.
- • Forgetting to check every limit state listed in the AISC chapter.
§13Section 13
FE exam preparation
Concept review
Concept summary coming soon.
Calculator tips
Calculator tips coming soon.
Common exam traps
Traps coming soon.
Time management
Aim for ~3 minutes per FE problem; skip and return to any item that takes longer than 5 minutes.