Engineering story
Chapter 12 · Bolted Connections
Bolt shear, bearing, tearout, slip-critical (Chapter J).
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?
Bolt shear, bearing, tearout, slip-critical (Chapter J).
⏱ 100 min★ Core✎ 3 objectives
§02Section 02
Learning objectives
After this chapter you will be able to
- Compute bolt shear, bearing, tearout
- Distinguish bearing vs slip-critical
- Detail hole types and spacing
§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 §J3 — Bolts and Threaded Parts
Why This Chapter Matters
Connections transfer forces between members. The Hyatt Regency (1981) and countless smaller failures traced back to bolt shear, bearing, tearout, or slip-critical assumptions that the designer got wrong.
Learning Objectives
- Distinguish A325 vs A490, snug-tight vs pretensioned vs slip-critical.
- Compute bolt shear rupture (φRn = φ · Fnv · Ab · Ns).
- Compute bearing and tearout at each bolt (AISC J3.10).
- Design slip-critical connections (AISC J3.8).
- Detail minimum edge distance, pitch, and gage per AISC Table J3.4.
Where This Chapter Is Used
Every bolted joint in Chapters 14 (shear), 15 (moment), 16 (base plates), 19 (framing), and the capstone.
ANSI / AISC 360-22Specification for Structural Steel Buildings16.1-127 to 16.1-140 (§J3)
Chapter
J
AISC 360-22
Chapter J. Design of Connections — Bolts (§J3)
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 |
|---|---|---|
| J3.1 | High-Strength Bolts (A325, A490, F3125) | 16.1-127 |
| J3.3 | Minimum Spacing | 16.1-129 |
| J3.4 | Minimum Edge Distance (Table J3.4) | 16.1-130 |
| J3.6 | Tensile and Shear Strength of Bolts | 16.1-131 |
| J3.7 | Combined Tension and Shear in Bearing-Type | 16.1-133 |
| J3.8 | Slip-Critical Connections | 16.1-133 |
| J3.10 | Bearing and Tearout at Bolt Holes | 16.1-136 |
Companion reference: AISC Manual Part 7 — Design Considerations for Bolts
Lecture Notes
Chapter 12 — Bolted Connections (AISC 360-22 Chapter J)
Chapter focus. Bolts fail in shear (through the shank), bearing (crushing the plate at the hole edge), or tearout (fracture from the hole to the plate edge). AISC Chapter J tabulates Fnv for A325/A490, then this chapter walks the limit-state ladder used on every connection in the rest of the course.
1. Bolt Types & Grades
- A325 / F3125 Group A — Fu = 120 ksi; most common structural bolt.
- A490 / F3125 Group B — Fu = 150 ksi; higher strength, weldability limitations.
- Bolts are specified as bearing-type (N = threads iNcluded, X = eXcluded) or slip-critical (SC).
2. Bolt Shear (§J3.7)
Eq. J3-1Rn = Fnv · Ab
φ = 0.75. Ab = π·db²/4 (nominal shank area). Double shear: multiply Rn by 2.
3. Bearing & Tearout (§J3.11)
Eq. J3-6a bearingRn = 2.4·db·t·Fu
Eq. J3-6c tearoutRn = 1.2·Lc·t·Fu
Lc = clear distance from edge (or adjacent hole) to bolt hole. Governing bearing/tearout = min of the two, per bolt.
4. Slip-Critical (§J3.9)
Eq. J3-4Rn = μ · Du · hf · Tb · ns
μ = 0.30 (Class A, mill-scale) or 0.50 (Class B, blast-cleaned). φ = 1.00 (standard) or 0.85 (oversized/slotted). Tb from Table J3.1 (e.g. 39 k for 7/8″ A325).
5. Spacing & Edge Distance (§J3.3–J3.5)
- Minimum spacing s ≥ 2⅔·db (preferred 3·db).
- Minimum edge distance Le from Table J3.4 (e.g. 1⅛″ for 7/8″ bolt, sheared edge).
- Maximum spacing 24·t or 12″, max edge 12·t or 6″.
Additional Design Aids & Stratified Equations
Clear distance L_c is measured hole-edge to plate-edge (edge bolt) or hole-edge to next hole-edge (interior).
Bearing per bolt (φ = 0.75)φR_n = 0.75 · 2.4 · d_b · t · F_u
Tearout per boltφR_n = 0.75 · 1.2 · L_c · t · F_u
⚠ Common mistakes
- Using shank Fnv = 68 ksi (X) when the threads are actually in the shear plane (N = 54 ksi).
- Forgetting to reduce for double shear vs single shear.
- Using nominal edge distance instead of Lc (clear) in tearout.
- Applying φ = 1.00 (slip-critical) with oversized holes — φ = 0.85 there.
📖 Using the AISC Manual — Bolted Connections
Companion reference: Manual Part 7 — Tables 7-1 (φrn shear), 7-2 (tension), 7-4/7-5 (slip-critical), 7-6 (bearing & tearout), 7-11 (eccentric bolt groups). 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.
Example — 6 bolts, 3/4″ A325-N, single shear, 1/2″ ply: Table 7-1 → φrn = 17.9 kip/bolt; Table 7-6 → bearing 39.2 kip/in × 0.5″ = 19.6 kip, tearout 40.8 × 0.5 = 20.4 kip. Bolt shear governs → φRn = 6 × 17.9 = 107 kip. Two look-ups, done.
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 12 — Bolted shear-tab connection
Filler-to-girder shear tab — 3 bolts, A325-N 7/8 in
Demand carried forward
From Chapter 7: Vu
= 25.5 k per bolt group.
This chapter contributes
Checks bolt shear (φRn = 0.75 · Fnv · Ab), plate bearing and tearout per §J3.7 / §J3.11. Verifies plate edge distance and bolt spacing.
Formula Sheet
| Name | Equation | AISC Ref |
|---|---|---|
| Bolt shear | φRn = 0.75 · Fnv · Ab | AISC §J3.7 |
| Bearing | φRn = 0.75 · 2.4 · db · t · Fu | AISC §J3.11 |
| Tearout | φRn = 0.75 · 1.5 · lc · t · Fu | AISC §J3.11 |
Worked Example
Worked Example 12.1 — 3-Bolt Shear Tab
Given
- Vu = 25.5 k at filler beam end (from Ch 7).
- Shear tab: 3/8 in thick, A36 (Fu = 58 ksi).
- 3 A325-N 7/8 in bolts vertical, s = 3 in, Le,top = 1½ in, Le,side = 1½ in, standard holes (dh = 15/16″).
- Single shear.
Figure 12.1a — Shear-tab geometry with three vertical bolts and edge distances
Step 1 — Bolt Shear per Bolt
Eq. J3-1Ab = π db²/4 ; Rn = Fnv·Ab ; φ = 0.75
Ab = π·(0.875)²/4 = 0.601 in²
Rn,shear = 54·0.601 = 32.5 k; φRn = 0.75·32.5 = 24.3 k/bolt
Rn,shear = 54·0.601 = 32.5 k; φRn = 0.75·32.5 = 24.3 k/bolt
Step 2 — Bearing per Bolt
Eq. J3-6aRn,brg = 2.4·db·t·Fu ; φ = 0.75
Rn,brg = 2.4·0.875·0.375·58 = 45.7 k; φRn = 34.3 k
Step 3 — Tearout per Bolt
Eq. J3-6cRn,to = 1.2·Lc·t·Fu ; Lc,edge = Le − 0.5 dh; Lc,int = s − dh
Edge bolt (top): Lc = 1.5 − 0.5·(15/16) = 1.031 in
Rn,to,edge = 1.2·1.031·0.375·58 = 26.9 k; φRn = 20.2 k
Interior bolts: Lc = 3 − 15/16 = 2.063 in
Rn,to,int = 1.2·2.063·0.375·58 = 53.8 k; φRn = 40.4 k
Rn,to,edge = 1.2·1.031·0.375·58 = 26.9 k; φRn = 20.2 k
Interior bolts: Lc = 3 − 15/16 = 2.063 in
Rn,to,int = 1.2·2.063·0.375·58 = 53.8 k; φRn = 40.4 k
Step 4 — Group Strength
Per boltφRn,bolt = min(shear, bearing, tearout); Σ over group
Per bolt φRn = min(shear 24.3, bearing 34.3, tearout as above):
Edge bolt governs = min(24.3, 20.2) = 20.2 k
Two interior bolts govern = min(24.3, 34.3, 40.4) = 24.3 k each
ΣφRn = 20.2 + 2·24.3 = 68.8 k ≥ Vu = 25.5 ✓
Edge bolt governs = min(24.3, 20.2) = 20.2 k
Two interior bolts govern = min(24.3, 34.3, 40.4) = 24.3 k each
ΣφRn = 20.2 + 2·24.3 = 68.8 k ≥ Vu = 25.5 ✓
Shear tab has DCR = 25.5/68.8 = 0.37. Edge bolt tearout is the weakest link — increasing Le to 2″ would move governance back to bolt shear.
Additional Worked Examples
Textbook — Aghayere & Vigil (2009)
Chapter 9 develops bolt mechanics. A bolt may fail in (a) shear of the bolt body, (b) bearing of the plate against the bolt, (c) tearout of plate material to the edge, (d) tension of the bolt body, or (e) slip in a slip-critical joint. AISC §J3 governs.
Example 9-1 — Shear capacity of A325-N bolt
Example 9-1 — Shear capacity of A325-N bolt
Setup. 3/4" A325-N bolt (Fnv = 54 ksi, Ab = 0.442 in²) in single shear.
AISC Reference: AISC §J3.7
Numerical practice
φrn per bolt?
- A. 12.0 k
- B. 15.9 k
- C. 17.9 k (Answer)
- D. 21.6 k
Step-by-step solution
φrn = 0.75·54·0.442 = 17.9 k.
Example 9-2 — Bolt group capacity
Example 9-2 — Bolt group capacity
Setup. 6 bolts (3/4" A325-N) in double shear connecting a tension splice.
AISC Reference: AISC §J3.7
Numerical practice
Total φRn?
- A. 108 k
- B. 144 k
- C. 180 k
- D. 215 k (Answer)
Step-by-step solution
Per bolt double shear = 2·17.9 = 35.8 k; 6·35.8 = 215 k.
Example 9-4 — Bearing on plate
Example 9-4 — Bearing on plate
Setup. 3/4" bolt through PL 3/8", A36 (Fu = 58 ksi), 3-in spacing, 1.5-in edge.
AISC Reference: AISC §J3.11
Numerical practice
φRn (bearing, deformation OK)?
- A. 29 k
- B. 39 k (Answer)
- C. 47 k
- D. 55 k
Step-by-step solution
φRn = 0.75·2.4·0.75·0.375·58 = 29.4 k. (Tearout is also OK: lc = 1.5 − 0.5·(13/16) = 1.09 in; φRn,t = 0.75·1.5·1.09·0.375·58 = 26.7 k → tearout governs ≈ 27 k; pick bearing/tearout min.)
Example 9-5 — Eccentric bolt group — elastic method
Example 9-5 — Eccentric bolt group — elastic method
Setup. Vertical bracket bolted with 6 bolts (3 rows × 2 cols) at 3-in spacing, load P at 6-in eccentricity.
AISC Reference: AISC Manual Table 7-7
Numerical practice
Direct shear component per bolt (P = 60 k)?
- A. 6 k
- B. 8 k
- C. 10 k (Answer)
- D. 12 k
Step-by-step solution
rv = P/n = 60/6 = 10 k. Add torsional rt,x and rt,y components vectorially to find resultant.
Example 9-7 — Slip-critical capacity
Example 9-7 — Slip-critical capacity
Setup. 3/4" A325 SC, Class A surface, single shear, Tb = 28 k pretension, single slip plane.
AISC Reference: AISC §J3.8
Numerical practice
φRn (slip)?
- A. 6.3 k
- B. 8.4 k (Answer)
- C. 10.5 k
- D. 13.4 k
Step-by-step solution
φRn = 1.0·0.30·1.0·1.0·28·1 = 8.4 k per bolt (Class A).
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
3/4" A325-N bolt, Fnv=54 ksi, Ab=0.442 in².
AISC Reference
AISC §J3.7 Table J3.2
Step-by-step solution
- φRn0.75 × 54 × 0.442 = 17.9 k per shear plane
Answer φRn = 17.9 k.
Problem statement image
DIMDimensions from the problem statement
Fnv = 54kAb = 0.442in²
Bolted lap — plate + bolt pattern
- Pitch s along the load, gage g perpendicular
- Edge distances L_ev (parallel), L_eh (perpendicular)
- Hole diameter d_h = d_b + 1/8 in (fabrication + damage)
- Net area A_n = A_g − Σ(d_h · t) + Σ(s²/4g)·t
Interactive Calculator
Bolt Shear / Bearing / Tearout
AISC §J3.7, §J3.11Ab0.601 in²
φ Rn (shear, all bolts)97.4 kips
φ Rn (bearing, all bolts)182.7 kips
φ Rn (tearout, all bolts)195.8 kips
Governing φ Rn97.4 kips
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.
C12-01AISC 360-22 Table J3.2 & Eq. J3-1
1. Single 7/8-in Ø A325-N bolt (Group A, threads in shear plane, Ab = 0.601 in²). Compute nominal shear Rn per shear plane (Fnv = 54 ksi).
C12-02AISC 360-22 Eq. J3-1
2. Same bolt in SINGLE shear. Compute design shear per bolt φRn.
C12-03AISC 360-22 Eq. J3-1
3. 4-bolt lap splice, single shear: design shear strength of the BOLT GROUP.
C12-04AISC 360-22 §J3.11
4. Same 3/8-in PL 6 wide (Fu = 65). For an INTERIOR bolt with s = 3 in, dh = 15/16, compute the clear distance Lc used for bearing/tearout.
C12-05AISC 360-22 §J3.11
5. Same bolt (interior, deformation not a design consideration). Compute φRn for BEARING / TEAROUT and identify which governs.
C12-06AISC 360-22 §J3.11
6. At the EDGE bolt with Le = 1.5 in, dh = 15/16: compute Lc and φRn (tearout).
C12-07AISC 360-22 §J3
7. Assemble the group strength for the 4-bolt lap (1 edge bolt + 3 interior bolts). Take the MIN of bolt shear, bearing, and tearout for each bolt, then sum.
C12-08AISC 360-22 §J3.3
8. Minimum spacing between bolt centers per §J3.3:
C12-09AISC 360-22 Eq. J3-4
9. Slip-critical strength (STD holes, Class A faying surface, 1 slip plane, μ = 0.30, Du = 1.13, hf = 1.0, Tb = 39 k):
C12-10AISC Manual Part 9
10. T-stub bolted hanger in tension: what phenomenon amplifies the bolt tension beyond the applied load / n?
C12-11AISC 360-22 Table J3.1
11. Minimum pretension Tb for a 7/8-in A325 (Table J3.1):
C12-12AISC 360-22 Eq. J3-3a
12. Combined bolt shear + tension (bearing bolt): reduced tension F'nt =
C12-13AISC 360-22 §J3.2 Table J3.3
13. Standard hole diameter for a ¾-in bolt (Table J3.3):
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.
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§11Section 11
Chapter summary
Formula sheet
- Bolt shearφRn = 0.75 · Fnv · AbAISC §J3.7
- BearingφRn = 0.75 · 2.4 · db · t · FuAISC §J3.11
- TearoutφRn = 0.75 · 1.5 · lc · t · FuAISC §J3.11
Engineering checklist
- Module 12: Bolted 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.