Chapter 12 — Bolted Connections (AISC 360-22 Chapter J)

1. Why Connections Deserve More Care Than Members

Structural failures overwhelmingly begin at connections, not at midspan. Three reasons:

• Stress concentration. A member carries stress smoothly; a connection funnels the entire member force through a handful of small holes. Local stresses at a hole edge are 2–3× the average.
• Multiple materials and modes. Bolt steel, plate steel, weld metal and base metal all interact — and each has a different ductility.
• Fabrication and erection tolerance. Members are rolled to tight tolerance in a mill. Connections are drilled, punched, fitted and bolted by people, often at height in bad weather.

This is why AISC assigns rupture-mode resistance factors (φ = 0.75) that are stingier than member yielding (φ = 0.90), and why the entire philosophy of connection design is to make the ductile mode govern where possible.

2. Bolt Types, Grades and Installation

AISC 360-22 organizes high-strength bolts by strength group rather than by the historical A325/A490 designations. All are covered by ASTM F3125/F3125M.

Read the "N" and "X" carefully. N means threads are iNcluded in the shear plane; X means eXcluded. The 26% difference between 54 and 68 ksi is entirely about whether the shear plane cuts the threaded root area or the full shank. In practice, always assume N unless you can guarantee the geometry — a shop that substitutes a longer bolt will put threads back in the plane and you will never know.

Installation classes (RCSC Specification, §J3.1)

• Snug-tight. Plies in firm contact from the full effort of an ironworker with a spud wrench. Adequate for most bearing-type connections, which is the majority of building steel.
• Pretensioned. Installed to at least T_b from Table J3.1 (turn-of-nut, calibrated wrench, twist-off, or DTI washer). Required for: joints subject to fatigue or significant load reversal, joints with A490 bolts in tension, and column splices in tall/slender frames.
• Slip-critical. Pretensioned and with a specified faying-surface condition. Required where slip cannot be tolerated: oversized holes, slots parallel to load, fatigue with reversal, and connections to existing structures.

3. Bolt Shear Rupture (§J3.7)

A_b = πd_b²/4 is the nominal shank area — always, even for thread condition N. The thread reduction is already baked into the lower F_nv value, so never reduce A_b as well (a classic double-count).

Counting shear planes

Multiply R_n by the number of shear planes the bolt crosses. A lap splice (two plies) → 1 plane. A butt/double-lap splice (three plies) → 2 planes. A double-angle framing connection → the web bolts are in double shear, the support bolts are usually single shear. Getting this wrong is a factor-of-two error, and it is the single most common student mistake in this chapter.

Long joints (§J3.7 User Note)

In connections longer than 38 in. between extreme fasteners in the line of force, the end bolts pick up more load than the interior ones (shear lag in the fastener group). The Specification's F_nv values already contain a modest reduction for this; for very long splices, refer to the Commentary.

4. Bearing and Tearout at Bolt Holes (§J3.11)

These two modes describe the plate, not the bolt, and they are checked at every bolt individually because each bolt has a different clear distance.

"Deformation at the bolt hole at service load is a design consideration" means you care whether the hole ovalizes by more than about ¼ in. For nearly all building work the answer is yes, so use the 2.4/1.2 forms. The 3.0/1.5 forms apply only where hole elongation genuinely does not matter (e.g. a redundant, non-architectural, non-fatigue connection).

Computing the clear distance l_c

• Edge bolt: l_c = l_e − d_h/2, where l_e is the centre-to-edge distance in the direction of force.
• Interior bolt: l_c = s − d_h, where s is the centre-to-centre spacing in the direction of force.

At each bolt, the plate strength is the lesser of bearing and tearout. Then the bolt's contribution to the joint is the lesser of that plate value and the bolt shear value — this "effective strength per bolt" logic is stated in the User Note to §J3.7 and is exactly how AISC Manual Part 10 builds its tables.

Additional Design Aids & Stratified Equations

5. Bolts in Tension (§J3.7) and Prying Action

Where a bolt loads a flexible flange or plate (hanger connections, tee stubs, end-plate moment connections), the fitting bends and bears back on the bolt at its toe. This prying action adds a force q to the applied tension:

Prying can add 20–60% to the bolt force in a thin fitting. The design cure is thickness: a fitting thick enough that it does not bend has no prying. AISC Manual Part 9 gives the closed-form t_min to eliminate prying entirely.

6. Combined Tension and Shear in Bearing-Type Joints (§J3.8)

A bolt resisting both tension and shear has a reduced tensile strength. AISC uses a straight-line clip of the true elliptical interaction:

where f_rv = required shear stress = V_r/A_b. Exemption: per the User Note, the interaction may be ignored if either the required shear stress or the required tensile stress is ≤ 30% of the corresponding available stress. Note that the equation reduces the tensile capacity; the Commentary gives the mirror form if you prefer to reduce shear instead.

7. Slip-Critical Connections (§J3.9)

Resistance factors depend on hole type — this is where slip-critical design bites:

8. Combined Tension and Shear in Slip-Critical Joints (§J3.10)

Applied tension partially un-clamps the joint, so there is less normal force available to generate friction. The nominal slip resistance is multiplied by k_sc:

T_u and T_a are the total tension on the bolt group and n_b is the number of bolts carrying that tension — the per-bolt division is already inside the formula. Omitting k_sc is the most common slip-critical design error, and Worked Example 12.5 shows a case where including it moves the joint from 71% to 99% utilization.

9. Hole Types, Spacing and Edge Distance (§J3.2–J3.5)

• Minimum spacing (§J3.3): s ≥ 2⅔d_b; 3d_b preferred (2¼ in. for a ¾ in. bolt, 3 in. is the shop standard).
• Minimum edge distance (§J3.4): Table J3.4 — 1 in. for a ¾ in. bolt, 1⅛ in. for ⅞ in., 1¼ in. for 1 in. Detailers routinely use 1¼ in. as a universal minimum.
• Maximum spacing (§J3.5): 24t or 12 in. for painted members; tighter for weathering steel in the elements, to keep moisture out of the faying surface.
• Maximum edge distance (§J3.5): 12t or 6 in.

Note that spacing and edge distance are not merely detailing rules — they feed directly into l_c, and hence into tearout strength. Tightening an edge distance to save an inch of plate can cost you 25% of the connection.

10. Affected Elements: Yielding, Rupture and Block Shear (§J4)

U_bs = 1.0 when tension stress is uniform (most gusset plates, angles, coped beams); U_bs = 0.5 when it is non-uniform (e.g. a coped beam with two bolt lines). In net-area calculations, remember §B4.3b: add ⅟₁₆ in. to the hole diameter to allow for damage from punching, so a ¾ in. bolt in a standard hole removes ⅞ in. of material.

11. Design Workflow — Work It in This Order

1. Compute required strength R_u / R_a from ASCE/SEI 7 load combinations.
2. Choose bolt diameter, grade, thread condition and hole type. Choose bearing-type vs slip-critical and justify it.
3. Bolt shear (Eq. J3-1) × number of shear planes → strength per bolt.
4. Bearing and tearout at every bolt, in every connected ply (Eqs. J3-6). Take the minimum at each bolt.
5. Effective strength per bolt = min(shear, bearing, tearout). Sum over the group.
6. Connected-element checks: tensile yield (J4-1), tensile rupture (J4-2), shear yield (J4-3), shear rupture (J4-4), block shear (J4-5).
7. If slip-critical: slip resistance (J3-4) with the correct φ for the hole type; apply k_sc (J3-5) if tension is present.
8. If bolts carry tension: bolt tension (J3-1), combined interaction (J3-3), and prying action (Manual Part 9).
9. Verify spacing, edge distances and maximum spacing (J3.3–J3.5). Report the governing limit state and D/C.

12. Practice and Detailing Judgment

• Standardize. One bolt diameter and one grade per project wherever possible. Mixed ¾ in. and ⅞ in. bolts on the same job guarantees a field error.
• Shop weld, field bolt. Welding is cheapest downhand in a controlled shop; bolting is fastest and safest in the field.
• Leave room for the wrench. An impact wrench needs roughly 1¾ in. of clearance around the nut. A connection that calculates perfectly and cannot be installed is a failed design.
• Design for ductility. Prefer configurations where bolt shear or plate yielding governs over brittle tearout or block shear at low utilization.
• Do not over-specify slip-critical. It is a real cost with a real inspection burden. Use it where the code or the behaviour demands it.

📖 Using the AISC Manual — Bolted Connections

Companion reference: Manual Part 7 — Tables 7-1 (φr_n 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 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.

Example — 6 bolts, 3/4″ A325-N, single shear, 1/2″ ply: Table 7-1 → φr_n = 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 → φR_n = 6 × 17.9 = 107 kip. Two look-ups, done.