Chapter 15 — Moment Connections (AISC 360-22 §J10 / AISC 358)

1. Classifying Connections: FR, PR, and Simple

Every beam-to-column connection has some moment-rotation (M–θ) relationship. AISC 360-22 Commentary §B3.4 sorts connections into three families based on how that curve compares to the beam's own flexural stiffness EI/L:

• Simple (pinned) — the connection transmits negligible moment; it is designed to allow the beam ends to rotate freely under gravity load. Initial rotational stiffness is roughly ≤ 2EI/L. Single-plate shear tabs and double angles fall here (Chapter 14).
• Fully restrained (FR) — the connection is stiff enough that the angle between beam and column axes essentially does not change under load; initial stiffness ≥ 20EI/L. The analysis can assume full continuity — the beam behaves as if rigidly built into the column.
• Partially restrained (PR) — anything between the two extremes. A PR connection carries a meaningful moment but also rotates a meaningful amount, and that flexibility must be included explicitly in the frame analysis as a rotational spring with a known M–θ curve.

Classifying a connection is not optional bookkeeping — it changes the frame analysis. If you analyze the frame assuming FR joints but detail a connection that is actually PR, the real beam moments and column moments will differ from what you designed for, and the real drift will be larger than predicted.

2. Directly Welded Flange Connections

The most direct way to make a moment connection is to weld the beam flanges straight to the column flange with complete-joint-penetration (CJP) groove welds, and to connect the web with a bolted shear tab (which carries only shear — the flanges carry essentially all of the moment). This was the standard pre-Northridge (1994) special moment frame detail; after several welded flange connections fractured brittlely in that earthquake, AISC 358 added supplemental requirements (weld access hole geometry, backing bar removal, CVN toughness of filler metal, continuity plates) before this detail can be used in seismic special or intermediate moment frames. In ordinary (non-seismic, wind-only) moment frames it remains an efficient, economical detail.

3. Force-Couple Idealization

To design the flange welds, plates, and bolts, and to check the column, the beam's bending moment must be converted into discrete forces that act at the flange locations. The standard AISC idealization treats the entire moment as an equal-and-opposite pair of axial forces acting at the flange centroids, separated by the lever arm (d − t_f):

• M_u — factored moment at the connection (often taken at the column face, or at the plastic hinge location for seismic RBS details).
• d — beam depth; t_f — beam flange thickness; (d − t_f) approximates the distance between flange centroids.
• P_uf — the tension (or compression) flange force used to size welds, flange plates, bolt groups, and column-side limit states.

This idealization ignores the small moment carried by the web, which is conservative for design of the flange connection and is the universal starting point in AISC design examples.

4. Bolted Flange-Plate (BFP) Connections

A bolted flange-plate connection welds a plate to the column flange in the shop, then field-bolts the beam flange to that plate — combining a reliable shop weld with a fast, tolerant field bolted splice. AISC 358 Chapter 7 pre-qualifies this detail for seismic use. Design requires four separate checks, each on the load path from beam flange → bolts → plate → weld:

1. Bolt group in the beam-flange-to-plate splice: shear, bearing, tearout under P_uf (Chapter 12/14 methods).
2. Plate tension yielding: φ_tF_yA_g, φ_t = 0.90 (Eq. J4-1 / D2-1).
3. Plate tension rupture through the bolt holes: φ_tF_uA_e, φ_t = 0.75 (Eq. D2-2).
4. Compression-side plate buckling: the compression flange plate is a short, stocky column between the column face and the first bolt row — check as a compression member per §E3 (often KL/r is small enough that F_cr ≈ F_y, but always verify).

5. Extended End-Plate Connections

An extended end-plate connection shop-welds a thick steel plate to the beam end, extending it beyond the flanges, then field-bolts the plate to the column flange with pretensioned high-strength bolts. AISC 358 Chapter 6 pre-qualifies four-bolt unstiffened (4E), four-bolt stiffened (4ES), and eight-bolt stiffened (8ES) geometries. The plate must be thick enough to force the bolts (not the plate) to be the ductile limit, and thin enough to avoid an oversized, uneconomical connection — this is governed by yield-line theory (§9 below).

6. Column-Side Limit States (§J10)

Every flange force P_uf delivered to the column must be checked against the column's own local capacity — a concentrated load applied to a thin flange and web can locally yield, crush, or buckle the column long before the global column strength is threatened. AISC 360-22 §J10 defines five limit states for this "concentrated force" problem, which apply on both sides of a moment connection:

6.1 Flange Local Bending (§J10.1)

A tension flange force pulls the column flange toward the beam, bending it like a plate about the column web. If the column flange is thin relative to its width, it deforms enough to load only the region near the web, wasting the outer part of the beam flange.

where F_yf and t_f are the column flange yield stress and thickness. If P_uf exceeds φR_n, a continuity plate is required opposite the tension flange.

6.2 Web Local Yielding (§J10.2)

The concentrated flange force spreads through the column web at a 2.5:1 slope from the point of application; if the resulting web stress exceeds F_yw, the web yields locally.

N is the bearing length (here, the beam flange thickness) and k_des is the design distance from the column outer face to the web toe of the fillet.

6.3 Web Local Crippling (§J10.3)

Crippling is a localized buckling/crushing failure of the web directly under the concentrated compression flange force, distinct from the yielding check above; it typically governs for thinner webs.

6.4 Web Compression Buckling (§J10.5)

When compression flange forces are applied to both flanges of the column at the same location (as at an interior beam-column joint), the entire web between the two forces can buckle like a column plate.

7. Panel-Zone Shear (§J10.6)

The panel zone is the rectangle of column web bounded by the beam flanges (depth d_c, thickness t_w). At an interior joint, the flange forces from beams framing in on both sides of the column act in the same rotational sense on the panel zone, generating a shear far larger than the shear in the column shaft above or below. Left unchecked, this shear causes a diamond-shaped shear distortion of the joint that concentrates rotation right where the beam plastic hinge is trying to form — a major contributor to pre-Northridge connection failures.

where b_cf, t_cf are the column flange width/thickness, d_b the beam depth, and d_c the column depth. If φ_vR_n < the panel-zone shear demand (approximately P_uf,left + P_uf,right − V_column), a doubler plate is required to add web area.

8. Continuity Plates and Doubler Plates

• Continuity plates are horizontal stiffener plates welded across the column web, aligned with the beam flanges, added whenever flange local bending or web local yielding/crippling capacity is insufficient. They give the flange force a stiff load path straight through the column and restore flange-bending stiffness.
• Minimum continuity plate thickness (AISC Design Guide 13 / 358) is typically t_cp ≥ t_bf/2 (one-sided connection) or ≥ t_bf (two-sided), and plates are CJP- or fillet-welded to both column flanges and the web, sized to develop the unbalanced flange force.
• Doubler plates add web area (and hence shear capacity) to the panel zone when §J10.6 governs. They are placed against the column web (either side) and welded around the perimeter, with a required minimum thickness so the composite web thickness (t_w + t_d) satisfies R_n ≥ demand.
• In seismic SMF/IMF construction, doubler plates and continuity plates additionally must satisfy AISC 341 detailing rules for welding sequence and plug welds to avoid introducing new fatigue-critical details.

9. Yield-Line Theory for End Plates (AISC 358 §6)

An extended end plate loaded in tension by the beam flange force does not fail by simple bending about one line — it fails along a pattern of plastic hinge ("yield") lines that forms around the bolt holes and the beam flange, redistributing moment across the whole plate width. AISC 358 tabulates the yield-line parameter Y_p (a function of bolt gage, pitch, and plate width) for each pre-qualified end-plate geometry, and the required plate thickness comes directly from equating the internal virtual work of the yield-line mechanism to the external work of the flange force:

• γ_r — bolt row factor accounting for prying uplift (=1.0 for outer bolt row on most configurations).
• p_f — distance from the flange face to the near bolt row (a "gage" dimension in the yield-line pattern).
• Y_p — yield-line mechanism parameter, in inches, from the AISC 358 tables for the specific bolt pattern (4E, 4ES, 8ES) — larger Y_p means a stiffer mechanism and a thinner plate is adequate.
• F_py — end-plate yield stress; φ = 0.90.

Physically: if t_p ≥ t_p,req, the plate stays essentially elastic and all inelastic deformation localizes safely in the bolts and the beam (thick-plate / ductile-bolt design philosophy). If the plate is thinner than required, it yields first, and — especially cyclically — plate yield-line hinging is far less predictable than bolt yielding, so AISC 358 does not allow a "thin-plate, ductile-plate" design philosophy for its pre-qualified details.

Additional Design Aids & Stratified Equations

10. Prequalified Seismic Connections — AISC 358 Overview

For special (SMF) and intermediate (IMF) moment frames, AISC 341 requires the moment connection to be either (a) qualified by cyclic testing per Appendix S/K1, or (b) selected from AISC 358's list of pre-qualified connections, each with its own chapter of prescriptive design rules:

Pre-qualification means the connection has documented cyclic test data over the applicable range of beam/column sizes; the designer follows the chapter's step-by-step procedure rather than re-deriving the design from first principles. All of these connections still require the §J10 column-side checks and panel-zone check from this chapter — pre-qualification governs the beam-side detail, not the column.

11. Summary of φ Factors and Limit States

12. Design Workflow — Moment Connection

1. Classify the connection intent (FR/PR/simple) and confirm it matches the frame analysis model.
2. Compute M_u and V_u at the connection (column face, or hinge location for RBS/seismic details).
3. Idealize flange force: P_uf = M_u/(d − t_f).
4. Design the beam-side detail (weld, flange plate + bolts, or end plate + bolts) for P_uf.
5. If end plate: size t_p from yield-line theory; check bolt tension with prying.
6. Check all five column-side §J10 limit states for P_uf against the column flange/web.
7. Check panel-zone shear (§J10.6); add doubler plate if needed.
8. Add continuity plates if flange bending or web yielding/crippling governs.
9. For seismic frames, confirm the whole detail matches an AISC 358 pre-qualified geometry and detailing limits.

📖 Using the AISC Manual — Moment Connections

Companion reference: Manual Part 12 (FR moment connections) + Design Guides 4 (extended end-plate) & 16 (flush end-plate). 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.

Fully-restrained moment connections have too many geometry variables for a single 2-D table, so the Manual gives step-by-step design procedures keyed to worked examples in Part 12 rather than pre-computed φR_n tables. However:

• Table 12-1 tabulates flange-weld strength per weld size for direct-welded flange connections.
• Design Guide 4 (4-bolt & 8-bolt extended end-plate) has a fill-in-the-blank spreadsheet template with every limit state.
• AISC 358 (Prequalified Seismic Connections) tabulates every dimension for RBS, WUF-W, and end-plate moment connections — you copy the geometry, do not design it.