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

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

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.

Run this calculation

• Column Capacity Calculator
• Section Properties Database

Related references

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

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against the applicable standard and project specification before use. The site operator disclaims liability for any loss arising from the use of this information.