End Plate Moment Connection -- AISC DG4 and DG16 Design Reference

The end plate moment connection is the dominant field-bolted moment connection in US steel construction. A steel plate is shop-welded to the beam end and field-bolted to the column flange. The bolts resist tension from the moment couple while the beam web transfers shear through the plate. AISC Design Guides 4 (Extended End-Plate Moment Connections) and 16 (Flush and Extended Multiple-Row End-Plate Moment Connections) provide the design methodology.

This page covers the yield line bolt force model, plate thickness determination, prying action, bolt design, and column-side checks. For broader connection type selection guidance, see Connection Types Explained. For the general limit state equations, see the Connection Design Guide.

End Plate Configurations

AISC DG4 and DG16 define standard configurations based on the number of bolts and plate extension:

Flush End Plate

The plate height equals the beam depth. Bolts are placed between the beam flanges (inside the profile). This configuration is for shear-only or light moment connections. Moment capacity is limited because the bolt lever arm is constrained to the beam depth minus flange thicknesses.

Extended End Plate -- 4E (Four-Bolt Extended)

The plate extends beyond both flanges. Two bolts are placed above the top flange (tension side) and two below the bottom flange. This is the most common moment end plate configuration for beams up to approximately W24 depth. The bolt lever arm is approximately d + 2 x (extension beyond flange), providing a 20-30% larger moment arm than a flush end plate on the same beam.

Extended End Plate -- 4ES (Four-Bolt Extended Stiffened)

Same as 4E but with stiffener plates welded between the end plate and the beam flanges. The stiffeners reinforce the extended portion of the end plate, increasing the plastic moment capacity of the plate in bending. This is required when the unstiffened plate thickness would otherwise exceed 2 inches.

Extended End Plate -- 8ES (Eight-Bolt Extended Stiffened)

Eight bolts total: four on the tension side (two rows above the flange, two bolts per row) and four on the compression side. The stiffened configuration provides the additional plate flexural strength required for the wider bolt pattern. This configuration is used for deep beams (W27 and larger) and high-moment applications. The larger bolt group on the tension side provides a longer yield line pattern and greater tension capacity.

Multiple-Row Extended (MRE) 1/2 and 1/3

Multiple rows of bolts on the tension side. MRE 1/2 has two rows of two bolts each above the top flange (four tension bolts total per side). These configurations developed in DG16 extend the 8ES concept to beams with even larger moment demands.

The Yield Line Bolt Force Model

The core of the DG4/DG16 method is the yield line mechanism. The end plate is idealized as a plate fixed along the beam flange and free at the edges, loaded by the bolt tension forces. The plate forms a yield line pattern -- plastic hinge lines radiating from the bolt locations -- at failure. The method determines:

  1. The required plate thickness to develop the bolt tension without premature plate flexural failure.
  2. The prying force amplification -- when the plate bends, it levers against the column flange, multiplying the bolt tension beyond the applied force.

Plate Thickness for the 4E Unstiffened Configuration

The required end plate thickness per DG4:

tp_req = sqrt( (M_u * 4 * b_p) / (phi_b * Fy * Y_p * (h_o - p_fo - t_fo)) )

where:

The yield line parameter Y_p is the critical term. It accounts for the four plastic hinge lines that form: two at the bolt line (tension and compression sides) and two at the beam flange-to-plate junction (inside and outside the flanges). For a 4E configuration:

Y_p = b_p/2 * [h_1 * (1/p_fi + 1/s) + h_o * (1/p_fo + 1/2s)]

where h_1 is the distance from the centerline of the compression bolts to the tension flange face (not intuitive -- this is the DG4 notation), p_fi is the bolt pitch inside the tension flange, s is the bolt gage, and p_fo is the bolt pitch outside the tension flange.

Prying Action

Prying is the amplification of bolt tension due to plate bending. As the end plate bends under bolt tension, the plate edge bears against the column flange, creating an additional reaction that increases the bolt force. The ratio of total bolt force to applied tension is the prying amplification factor, typically 1.1 to 1.4 for practical end plate geometries.

The bolt tension including prying per DG4:

T_b = T_applied * (1 + alpha * delta / (delta + rho))

where alpha is the ratio of the bending moment per unit width at the bolt line to the plastic moment capacity, delta is the ratio of net section area at the bolt line to gross section area, and rho = b_p / (2 * p_fo).

Engineers can minimize prying by:

Column-Side Checks

The end plate connection loads the column through the bolts in tension. The column must be checked for:

Column Flange Bending (AISC 360 Section J10.1)

The column flange acts as a plate loaded by the bolt tension. For unstiffened column flanges, the flange bends about the column web. The design strength:

phi Rn = phi * 6.25 * t_fc^2 * Fyfc
phi = 0.90

per bolt pair (two bolts across the flange width), where t_fc is the column flange thickness and Fyfc is the column flange yield strength. This is from AISC 360 Equation J10-1 (simplified yield line analysis of the column flange).

For a W14x90 column (t_fc = 0.710 in., Fy = 50 ksi): phi Rn = 0.90 x 6.25 x 0.710^2 x 50 = 0.90 x 6.25 x 0.504 x 50 = 141.7 kip per bolt pair. If the required bolt tension per pair exceeds this, continuity plates are required.

Column Web Yielding (J10.2)

phi Rn = phi * Fywc * twc * (5 k + lb)
phi = 1.00

where k = distance from the column flange outer face to the web toe of the fillet, lb = the loaded length (for end plate, typically the end plate thickness plus the weld leg).

Column Web Crippling (J10.3)

For compressive force delivered through the flange into the column web:

phi Rn = phi * 0.80 * twc^2 * [1 + 3*(lb/d)*(twc/t_fc)^1.5] * sqrt(E * Fywc * t_fc / twc)
phi = 0.75

Panel Zone Shear (J10.6)

The panel zone is the column web region between the beam flanges. Under the beam moment, the panel zone experiences high shear from the tension-compression couple. The required panel zone shear strength:

Vu_pz = (M_u_bm1 / (d_bm1 - t_f1) + M_u_bm2 / (d_bm2 - t_f2)) - V_col

If the panel zone yields prematurely, the frame stiffness degrades and story drift increases. AISC 341 (Seismic) requires the panel zone to develop sufficient strength to participate in the inelastic response. Doubler plates (additional plates welded to the column web) are added when the panel zone shear demand exceeds the column web capacity.

Worked Example -- 4E Extended End Plate (W18x55 to W14x90 Column)

Given:

Step 1 -- Trial plate geometry:

Step 2 -- Bolt tension (no prying -- preliminary): h_o = 18.1 + 2.0 = 20.1 in. (center of compression flange to tension bolt line, approximated) Tension per bolt pair = Mu / h_o = 3,000 / 20.1 = 149.3 kip per pair. Per bolt: 149.3 / 2 = 74.6 kip.

Step 3 -- Bolt tensile capacity: For 3/4 in. A325, Fnt = 90 ksi, Ab = 0.442 in^2. phi Rn = 0.75 x 90 x 0.442 = 29.8 kip per bolt. Two bolts: 59.7 kip < 74.6 kip. Insufficient!

Upgrade to 7/8 in. A325 bolts: Ab = 0.601 in^2. phi Rn = 0.75 x 90 x 0.601 = 40.6 kip per bolt. Two bolts: 81.1 kip > 74.6 kip. OK for applied tension (before prying).

Step 4 -- Check prying: The plate bending increases bolt tension. For this geometry (unstiffened 4E), the prying amplification factor is approximately:

Q = (tp^2 _ Fy _ b*p * w') / (8 _ a' * p_fo) where w' = bolt head width = 1.25 in., a' = distance from bolt center to plate edge = 1.5 in.

Try tp = 1-1/4 in. = 1.25 in.: Q = (1.25^2 x 50 x 8.5 x 1.25) / (8 x 1.5 x 2.0) = (1.5625 x 50 x 8.5 x 1.25) / 24 = 830 / 24 = 34.6 kip per bolt.

Total bolt force including prying = 74.6 + 34.6 = 109.2 kip >> 40.6 kip. Not OK.

Step 5 -- Add stiffeners (4ES configuration): With stiffeners, the end plate is fixed along the beam flange and the stiffener edges, dramatically increasing the plastic moment capacity. The bolt line is now inside the stiffened zone, and prying is significantly reduced. For the 4ES configuration per DG4 Table 4.2, the yield line parameter Y_p is approximately 1.5x larger than for 4E.

Revised tp for 4ES: approximately tp = sqrt(3,000 x 4 x 8.5 / (0.90 x 50 x (larger Y_p) x 20.1)). This algebra yields approximately tp = 1.0 in.

With tp = 1.0 in. and stiffeners, prying amplification factor drops to approximately 1.15. Total bolt force = 74.6 x 1.15 = 85.8 kip. With 7/8 in. A325: 81.1 kip < 85.8 kip. Slightly insufficient.

Upgrade to 1 in. A325 bolts: Ab = 0.785 in^2. phi Rn = 0.75 x 90 x 0.785 = 53.0 kip. Two bolts: 106.0 kip > 85.8 kip. OK.

Step 6 -- Shear check: The beam shear Vu = 45 kip is transferred through the end plate into the column via bearing and friction. With four bolts in shear (two compression-side bolts resist shear directly, two tension-side bolts resist shear after tension interaction):

For bolts with combined tension/shear per J3.7: frv = 45 / (4 x 0.785) = 14.33 ksi. F'nt = 1.3 x 90 - (90 / (0.75 x 54)) x 14.33 = 117 - 2.222 x 14.33 = 117 - 31.8 = 85.2 ksi < 90 ksi. phi Rn_tension_reduced = 0.75 x 85.2 x 0.785 = 50.2 kip per bolt. Two tension bolts: 100.4 kip > 85.8 kip. OK.

Step 7 -- Column flange bending: For W14x90 column flange: phi Rn = 0.90 x 6.25 x 0.710^2 x 50 = 141.7 kip per bolt pair. Required = 85.8 kip per pair. OK. No continuity plates required.

Step 8 -- Panel zone shear: Vu_pz = 3,000 / (18.1 - 0.630) = 3,000 / 17.47 = 171.7 kip (assuming no beam on the opposite side). Column shear V_col is approximately 20 kip at this level. Net panel zone demand = 171.7 - 20 = 151.7 kip.

Column web shear capacity: phi Rn = 0.90 x 0.60 x 50 x 14.0 x 0.440 = 166.3 kip > 151.7 kip. OK. No doubler plate required.

Final design:

Fabrication Notes

Related Tools and References

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. End plate moment connection design must be performed by a licensed Professional Engineer (PE) or Structural Engineer (SE) for the specific project. The site operator disclaims liability for any loss arising from the use of this information. Results are PRELIMINARY -- NOT FOR CONSTRUCTION.