Steel Girder-to-Column Moment Connections — Engineering Reference

Girder-to-column connections transfer moment, shear, and sometimes axial force from beams and girders into columns. Moment connections are classified as fully restrained (FR, Type FR, or moment connections) or partially restrained (PR), and are designed per AISC 360-22 Chapter J and (for seismic applications) AISC 358-22. This reference focuses on the most common fully restrained connection types.

Common moment connection types

| Connection Type — Description — Typical Application — AISC 358 Prequalified? | | ---------------------------------- — ----------------------------------------------- — ------------------------------- — ---------------------- | | Bolted Flange Plate (BFP) — Plates bolted to beam flanges, welded to column — Wind moment frames, non-seismic — Yes (SMF, IMF) | | Welded Unreinforced Flange (WUF-W) — CJP weld beam flange to column, bolted web — SMF gravity + seismic — Yes (SMF) | | Reduced Beam Section (RBS) — Dog-bone cut in beam flanges — SMF primary seismic — Yes (SMF, IMF) | | Extended End Plate (EEP) — End plate welded to beam, bolted to column — Rigid frames, portal frames — Yes (SMF, IMF) | | Bolted Stiffened End Plate (BSEP) — End plate with stiffeners, high-moment capacity — Heavy girders — Yes (SMF) | | Kaiser Bolted Bracket (KBB) — Cast steel bracket bolted to both flanges — Retrofit, renovation — Yes (SMF) |

Design procedure for an extended end plate connection

The extended end plate connection is popular for portal frames, industrial buildings, and mid-rise structures because all field work is bolted (no field welding).

Worked example — 4-bolt extended unstiffened end plate

Given: W18x50 beam to W14x90 column. Factored moment M_u = 220 kip-ft (wind combination). Factored shear V_u = 40 kips. A992 steel (Fy = 50 ksi). A325 bolts (Fnt = 90 ksi, Fnv = 54 ksi). End plate: A36 (Fy = 36 ksi).

Step 1 — Bolt tension from moment (simplified method per AISC DG4):

The moment is resisted by bolt couples. For a 4-bolt extended configuration (2 bolts above the top flange, 2 bolts below the top flange, using top flange as reference):

Bolt row lever arms from the compression flange centerline:

• Row 1 (above top flange): h_1 = d_b - t_f/2 + p_f = 18.0 - 0.570/2 + 2.0 = 19.72 in.
• Row 2 (below top flange): h_2 = d_b - t_f/2 - p_b = 18.0 - 0.285 - 2.0 = 15.72 in.

where p_f = 2.0 in. (distance from face of flange to first bolt row above), p_b = 2.0 in. (distance below flange to bolt row).

Sum of bolt forces times lever arms = Mu: 2 * Tbolt * h1 + 2 * Tbolt * h_2 = M_u (assuming equal bolt forces for simplification, though actual distribution varies)

This simplified approach gives: Tbolt = M_u / (2 * (h1 + h_2)) = 220 * 12 / (2 * (19.72 + 15.72)) = 2,640 / 70.88 = 37.2 kips per bolt

Step 2 — Check bolt tension capacity: phi _ r_nt = phi _ Fnt _ A_b = 0.75 _ 90 * 0.6013 (for 7/8 in. bolt) = 40.6 kips > 37.2 kips (OK, 92% utilization)

Consider using 1 in. bolts (Ab = 0.7854 in.^2): phi * rnt = 0.75 * 90 * 0.7854 = 53.0 kips (more comfortable margin).

Step 3 — End plate thickness (yield line analysis per AISC DG4): The minimum end plate thickness is governed by yield line patterns forming in the plate around the bolt holes. Per AISC DG4 Table 3.4:

tp_req = sqrt(2 * Mu / (phi_b * Fy_p * Y_p))

where Y_p is the yield line parameter depending on bolt layout geometry (typically 150-300 in. for common configurations).

Assuming Y*p = 200 in. for this layout: t_p_req = sqrt(2 * 2640 / (0.90 _ 36 * 200)) = sqrt(5280 / 6480) = sqrt(0.815) = 0.903 in.

Use 1 in. end plate.

Step 4 — Column flange check: The column flange acts like the end plate but loaded from the outside. The same yield line analysis applies. For the W14x90 column (t_f = 0.710 in.), check if the column flange thickness is sufficient or if a stiffener (continuity plate) is needed.

Panel zone design

When moment is transferred into the column, the web panel zone between the beam flanges experiences high shear. Per AISC 360-22 Section J10.6:

phi _ R_v = 1.0 _ 0.60 _ Fy _ dc _ tw _ [1 + (3 * bcf * tcf^2) / (db * dc * tw)]

For the W14x90: dc = 14.0 in., tw = 0.440 in., bcf = 14.5 in., tcf = 0.710 in.:

phi _ Rv = 0.60 _ 50 _ 14.0 _ 0.440 _ [1 + 3 _ 14.5 _ 0.710^2 / (18.0 _ 14.0 _ 0.440)] = 184.8 _ [1 + 21.93/110.88] = 184.8 * 1.198 = 221 kips

Panel zone shear demand from M_u = 220 kip-ft: V_pz = M_u / (db - tf) = 220 * 12 / (18.0 - 0.570) = 2640 / 17.43 = 151 kips

Since 151 < 221 kips, the panel zone is adequate without a doubler plate.

Code comparison

| Aspect — AISC 360/358 — EN 1993-1-8 — AS 4100 Sect. 9 — CSA S16-19 | | ------------------------- — ------------------------------- — ------------------------------------- — ------------------------------ — -------------------------------- | | Connection classification — FR, PR, simple — Rigid, semi-rigid, pinned — Rigid, semi-rigid, pinned — Type A (rigid), Type B (simple) | | Prequalified connections — AISC 358 catalog — No formal catalog — No catalog — CISC Handbook tested connections | | Panel zone check — AISC 360 J10.6 — EN 1993-1-8 Section 6.2.6 — AS 4100 Clause 9.4 — CSA S16 Clause 21.3 | | End plate design method — AISC DG4 (yield line) — EN 1993-1-8 T-stub model — Murray/Hogan model — CISC Moment Connections guide | | Bolt tension capacity — phi = 0.75, Fnt = 90 ksi (A325) — gamma_M2 = 1.25, f_ub = 800 MPa (8.8) — phi = 0.80, f_uf (Table 9.2.1) — phi = 0.75 (same as AISC) |

The Eurocode T-stub method (EN 1993-1-8 Section 6.2.4) models the end plate as equivalent T-stubs and identifies three failure modes: complete yielding of the plate (Mode 1), bolt failure with prying (Mode 2), and pure bolt failure (Mode 3). This is analytically equivalent to the AISC yield line method but uses different notation.

Key clause references

• AISC 360-22 Section J10.6 — Panel zone shear strength
• AISC 360-22 Chapter J — Connection design (bolts, welds, affected elements)
• AISC 358-22 — Prequalified connections for seismic applications
• AISC Design Guide 4 — Extended End-Plate Moment Connections
• AISC Design Guide 16 — Flush and Extended Multiple-Row Moment End-Plate Connections
• EN 1993-1-8 Section 6.2 — Design of beam-to-column joints

Topic-specific pitfalls

• Neglecting prying action on bolts — when the end plate is flexible relative to the bolt stiffness, the plate bends and introduces additional prying tension in the bolts. AISC DG4 accounts for prying through the yield line method; ignoring it can underestimate bolt demand by 20-40%.
• Using the wrong bolt grade — A325 (Group A, Fnt = 90 ksi) and A490 (Group B, Fnt = 113 ksi) have different strengths. A490 bolts cannot be galvanized and have specific tightening requirements. Verify the bolt grade matches the design calculations.
• Omitting the column web stiffener (continuity plate) when required — when the concentrated beam flange force exceeds the column web local yielding, crippling, or sidesway buckling capacity (AISC Section J10.2-J10.4), continuity plates are required. This check is separate from the panel zone shear check.
• Designing the connection for the beam demand instead of the beam capacity — for seismic moment connections, the connection must develop the probable maximum moment of the beam (Cpr * Ry * Fy * Z_x), which can be 30-50% higher than the factored design moment.

Moment connection classification

Girder-to-column connections are classified by their ability to transfer moment and their rotational stiffness:

For FR connections, the connection must develop at least the full design moment without significant rotation. For PR connections, the moment-rotation characteristics must be explicitly modeled in the structural analysis. Simple connections are designed for vertical shear only, with the beam rotation accommodated through flexible connection details (angles, single plates, or end plates with short bolts).

AISC 358 prequalified connections summary

AISC 358-22 (Prequalified Connections for Special and Intermediate Moment Frames) provides a catalog of connection types that have been tested and demonstrated to achieve the rotation capacity required for seismic moment frames. Using a prequalified connection eliminates the need for project-specific testing.

The RBS (dog-bone) connection is the most widely used SMF connection because it shifts the plastic hinge away from the column face, protecting the critical beam flange-to-column weld. The radius cuts in the beam flanges reduce the section modulus by approximately 30-40% at the center of the cut, ensuring yielding occurs within the reduced section rather than at the weld.

Panel zone shear design per AISC J6

Panel zone shear is one of the most critical limit states in moment connections. The column web between the beam flanges experiences high shear as the unbalanced moment from the beam is transferred into the column.

Panel zone shear demand: V_pz = M_u / (d_b - t_fb)

where d_b = beam depth and t_fb = beam flange thickness.

Panel zone shear capacity per AISC 360-22 Section J10.6:

phi × R_v = phi × 0.60 × Fy × dc × tw × [1 + (3 × bcf × tcf²) / (db × dc × tw)]

The bracketed term accounts for the contribution of the column flanges to panel zone resistance through frame action. For columns with thin flanges (e.g., W12x sections), this contribution is small; for columns with thick flanges (e.g., W14x120+), it can increase capacity by 20-30%.

When doubler plates are needed: If V_pz > phi × R_v, a doubler plate must be welded to the column web to increase the panel zone thickness. The doubler plate is typically plug-welded or fillet-welded to the column web and must extend at least to the k-distance above and below the beam flanges.

Stiffener (continuity plate) requirements

Continuity plates are required when the concentrated forces from the beam flanges exceed the column web's local capacity. Per AISC 360-22 Section J10:

Stiffener sizing: If required, continuity plates must be proportioned to resist the excess force. Minimum stiffener width = bf_beam/3. Minimum stiffener thickness = t_fb/2. The stiffener is typically welded to both the column web (CJP or double fillet) and column flanges (double fillet).

Connection design forces from analysis

The design forces for a girder-to-column connection are not simply the beam end moments and shears from the structural analysis. For seismic moment frames, the connection must be designed for the probable maximum moment that the beam can deliver:

M_pr = Cpr × Ry × Fy × Zx    (probable maximum moment)

where Cpr = 1.2 (peak connection strength coefficient) and Ry = 1.1 for A992 steel. This amplifies the nominal plastic moment by approximately 32% above Fy × Zx. The corresponding shear is:

V_pr = M_pr / (L_clear) + V_gravity

For wind-governed moment frames (non-seismic), the connection is designed for the factored moment from the load combinations, and the probable moment approach is not required.

Worked example: W24x68 girder to W14x82 column moment connection

Given: W24x68 girder (A992) frames into a W14x82 column (A992). Factored moment Mu = 280 kip-ft (wind combination). Factored shear Vu = 48 kips. Design a bolted flange plate (BFP) connection.

Step 1 — Connection configuration: Use 3/4" A325 bolts in standard holes. Flange plates: A36 (Fy = 36 ksi, Fu = 58 ksi). Web plate with bolts for shear transfer.

Step 2 — Flange force from moment: Flange force Fu_flange = Mu / (d - tf) = 280 × 12 / (23.73 - 0.585) = 3360 / 23.15 = 145.1 kips.

Step 3 — Bolt shear in flange plate connection: Number of bolts per flange = 4 (2 rows of 2). Shear per bolt = 145.1 / 4 = 36.3 kips. phi × Rn (single shear) = 0.75 × 54 × 0.4418 = 17.9 kips (threads included, 3/4" bolt). For double shear (plate on both sides): phi × Rn = 35.8 kips. 36.3 / 35.8 = 101% — marginally over. Use 6 bolts per flange (3 rows of 2): shear per bolt = 145.1 / 6 = 24.2 kips < 35.8 (OK).

Step 4 — Flange plate tension capacity: Flange plate = 8" wide × 3/8" thick. phi × Pn = 0.90 × 36 × 8 × 0.375 = 97.2 kips < 145.1 kips. Increase plate thickness: try 5/8" plate. phi × Pn = 0.90 × 36 × 8 × 0.625 = 162.0 kips > 145.1 (OK).

Step 5 — Column flange check: W14x82: tf = 0.855 in, bf = 14.7 in. Check local flange bending from concentrated force. phi × Rn = 0.75 × 50 × 6 × 0.855² = 164.4 kips > 145.1 kips (OK — no stiffener needed for flange bending).

Step 6 — Panel zone check: dc = 14.3 in, tw = 0.510 in, bcf = 14.7 in, tcf = 0.855 in. phi × Rv = 0.60 × 50 × 14.3 × 0.510 × [1 + 3 × 14.7 × 0.855² / (23.73 × 14.3 × 0.510)] = 219.0 × [1 + 32.2 / 173.3] = 219.0 × 1.186 = 259.7 kips. V_pz = 280 × 12 / 23.15 = 145.1 kips < 259.7 (OK — no doubler plate needed).

Result: BFP connection with 5/8" A36 flange plates and six 3/4" A325 bolts per flange is adequate. No continuity plates or doubler plates required.

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Related references

• K-Factor Guide
• Column K-Factor
• How to Verify Calculations
• Connection Design Workflow
• Seismic Design
• Moment Frame Design
• steel beam capacity calculator

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Column Buckling Theory

Euler Buckling

The Euler buckling load represents the theoretical critical load for an ideal elastic column:

Pcr = π²EI / (KL)²

Where:

• E = modulus of elasticity (200 GPa for steel)
• I = moment of inertia about the buckling axis
• K = effective length factor
• L = unbraced length

Real Column Behavior

Real columns deviate from Euler theory due to:

• Initial out-of-straightness (typically L/1000)
• Residual stresses from manufacturing (hot-rolling or welding)
• Eccentricity of applied load
• Inelastic material behavior

These effects are accounted for through column strength curves that reduce the theoretical Euler capacity based on slenderness ratio (KL/r) and section type.

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Frequently Asked Questions

What is the recommended design procedure for this structural element?

The standard design procedure follows: (1) establish design criteria including applicable code, material grade, and loading; (2) determine loads and applicable load combinations; (3) analyze the structure for internal forces; (4) check member strength for all applicable limit states; (5) verify serviceability requirements; and (6) detail connections. Computer analysis is recommended for complex structures, but hand calculations should be used for verification of critical elements.

How do different design codes compare for this calculation?

AISC 360 (US), EN 1993 (Eurocode), AS 4100 (Australia), and CSA S16 (Canada) follow similar limit states design philosophy but differ in specific resistance factors, slenderness limits, and partial safety factors. Generally, EN 1993 uses partial factors on both load and resistance sides (γM0 = 1.0, γM1 = 1.0, γM2 = 1.25), while AISC 360 uses a single resistance factor (φ). Engineers should verify which code is adopted in their jurisdiction.

Design Resources

Calculator tools

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Design guides

• Column Capacity Worked Example
• Column Buckling Guide
• Column Buckling Calculator Guide
• EN 1993-1-1 Column Buckling Worked Example