End Plate Connection — Moment Connection Design

Steel end plate moment connection design per AISC Design Guide 4. Bolt prying action, plate yielding, stiffener requirements, and column web checks. Educational use only.

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End Plate Connection Configurations

End plate moment connections are categorized by the bolt layout relative to the beam flanges. The configuration determines the yield line pattern, effective lever arm, and moment capacity.

Flush end plate — The plate does not extend beyond the beam flanges. Bolts are placed between the flanges, typically in two rows. Moment capacity is limited because the lever arm between the tension and compression bolt rows is small. Flush end plates are suitable for moderate moment demands where a simple shear connection also needs to transfer a small amount of moment.

4-bolt extended unstiffened (4E) — The plate extends beyond the beam tension flange, with two bolt rows above the flange and two below. This is the most common configuration for steel moment frames. The extended portion increases the lever arm, providing significantly higher moment capacity. The column flange must be checked for bending between the outer bolt rows.

8-bolt extended stiffened (8ES) — Similar to the 4E but with four bolt rows on each side of the beam flange, plus stiffener plates on the end plate between the outer and inner bolt rows. This configuration provides the highest moment capacity and is used for heavy moment demands. The stiffeners prevent the end plate from developing certain yield line mechanisms, forcing the failure mode into a higher-capacity pattern.

4-bolt extended stiffened (4ES) — An extended end plate with stiffeners on the tension side only. The stiffeners extend from the beam tension flange to the outer bolt row on the tension side.

Yield Line Analysis of End Plates

The end plate thickness is determined by yield line analysis. The yield line method models the plate as developing plastic hinges along specific patterns, and the plate capacity is the moment at which the full yield line mechanism forms.

For a 4-bolt extended unstiffened end plate, the critical yield line pattern consists of four yield lines radiating from the beam tension flange to each of the four tension-side bolts. The end plate bending capacity per AISC Design Guide 4 is:

Mp = Fyp * tp^2 / 4  (per unit width)

The required plate thickness depends on the applied moment, the bolt force lever arm, and the plate width. For the 4E configuration, the minimum plate thickness per the yield line mechanism is:

tp_req = sqrt(4 * Mu / (Fyp * bp * Yp))

Where Yp is a yield line parameter that depends on the bolt gage, flange width, and distance from the bolt to the beam flange. The Design Guide provides tabulated Yp values for standard configurations.

For a flush end plate, the yield line pattern is different: it involves yield lines running along the bolt rows and between the beam flanges. The flush configuration has a shorter effective lever arm, which reduces both the moment capacity and the required plate thickness compared to an extended configuration with the same applied moment.

Bolt Prying Action

Prying action is a critical phenomenon in end plate connections. When the end plate bends under the applied tension force, the contact point between the end plate and column flange shifts outward, creating a lever effect that amplifies the bolt tension.

The total bolt force including prying is:

T_total = T_applied + Q

Where Q is the prying force. The magnitude of Q depends on the plate flexibility, bolt stiffness, and the geometry of the connection.

Thick plate model (rigid plate): When the plate is thick relative to the bolt gage, prying is negligible (Q approaches zero). The plate remains essentially flat, and the bolt force equals the applied tension. This is the most desirable condition but requires a thicker plate.

Thin plate model (flexible plate): When the plate is thin, significant prying develops. The Kennedy method computes Q based on the relative stiffness of the plate and bolts. The prying force can increase bolt tension by 20% to 40% or more, potentially causing bolt failure if not accounted for.

The simplified AISC approach for prying action determines whether prying occurs by comparing the plate flexural capacity to the bolt tensile capacity:

If alpha <= 1.0: Q = 0 (no prying, thick plate behavior)
If alpha > 1.0: Q is computed from equilibrium of the prying mechanism

Where alpha is a parameter that compares the plate bending strength to the bolt tension demand at the prying contact point. Designers can eliminate prying by making the plate thick enough, which simplifies the bolt check but increases material and fabrication cost.

Column-Side Checks

The column flange and web must resist the concentrated forces delivered by the beam flanges through the end plate and bolts.

Column flange bending: The column flange is modeled as an equivalent T-stub. The T-stub has three possible failure modes:

The governing mode depends on the flange thickness, bolt capacity, and the distance from the bolt to the web (the "b" dimension in the T-stub model).

Column web yielding: The beam compression flange delivers a concentrated force to the column web. The web yielding length depends on the dispersion angle through the column flange and end plate. Per AISC Chapter J10.2:

phi*Rn = phi * Fyw * tw * (5k + lb)

Where k is the column flange-to-web fillet distance, lb is the beam flange thickness plus 2 times the end plate thickness (for bearing length), tw is the column web thickness, and Fyw is the column web yield stress.

Column web crippling: Web crippling checks the column web against local buckling under the concentrated compression force. Per AISC Chapter J10.3:

phi*Rn = phi * 0.8 * tw^2 * [1 + 3*lb/(d-2*tf)] * sqrt(E*Fyw/tf)

Where d is the column depth and tf is the column flange thickness. Stiffeners (continuity plates) are required when the demand exceeds the crippling capacity.

Panel zone shear: The column web panel zone must resist the shear generated by the beam flange forces. For an interior connection with balanced moments:

Vpz = Mu / (d_b - t_fb) - V_column

Where d_b is the beam depth and t_fb is the beam flange thickness. If the panel zone shear demand exceeds the web shear capacity, doubler plates are required.

Worked Example: 4-Bolt Extended End Plate Connection

Problem: Design an end plate connection for a W18x50 beam (ASTM A992, Fy = 50 ksi, Fu = 65 ksi) framing into a W12x96 column (ASTM A992). The factored moment Mu = 250 kip-ft and factored shear Vu = 40 kips.

Step 1: Determine bolt tension from applied moment.

For a 4E configuration with bolt rows above and below the beam flange:

Lever arm (tension to compression) = d_b + t_p = 18.0 + 0.75 = 18.75 in
Tension per bolt row = Mu / lever arm = 250 * 12 / 18.75 = 160 kips (per row of 2 bolts)
Tension per bolt = 160 / 2 = 80 kips

Step 2: Check bolt capacity (ASTM A325, 7/8-inch diameter).

Bolt nominal tension (AISC Table J3.2): Fn = 90 ksi
Bolt tensile area: Ab = 0.6013 sq-in (7/8-in bolt)
phi*Tn = 0.75 * 90 * 0.6013 = 40.6 kips per bolt
Required bolts per row = 80 / 40.6 = 1.97, use 2 bolts (OK)

Note that this does not yet include prying action, which will increase the demand on each bolt.

Step 3: Determine end plate thickness.

Assume a 9-inch wide end plate (bp = 9 in), 3/4-inch thick (tp = 0.75 in), ASTM A572 Gr. 50 (Fyp = 50 ksi). For the 4E yield line mechanism:

Mp per unit width = Fyp * tp^2 / 4 = 50 * 0.75^2 / 4 = 7.03 kip-in/in

The total plate bending resistance depends on the yield line pattern. For a 4E configuration with gage g = 4 in and distance from bolt to beam flange a = 1.5 in, consult AISC Design Guide 4 Table 3.3 for exact Yp values. For typical geometry, Yp is approximately 4 to 6.

Step 4: Check prying action.

For the 7/8-inch A325 bolts with 3/4-inch end plate, compute the prying parameter alpha. If alpha <= 1.0, no additional prying force develops. If alpha exceeds 1.0, the prying force Q must be computed and added to the bolt demand. With a 3/4-inch plate, prying is likely for this bolt gage.

Step 5: Check column flange bending.

For the W12x96 column: tf = 0.570 in, tw = 0.550 in, k = 1.16 in.

Using the equivalent T-stub model for Mode 1 (complete flange yielding):

Mf = Fyf * tf^2 / 4 = 50 * 0.570^2 / 4 = 4.06 kip-in/in

The column flange bending capacity depends on the T-stub geometry. If the demand exceeds the capacity, continuity plates (column stiffeners) are required.

Step 6: Check column web yielding.

lb = t_fb + 2*t_p = 0.570 + 2*0.75 = 2.07 in
phi*Rn = 1.0 * 50 * 0.550 * (5*1.16 + 2.07) = 187 kips
Compression flange force = Mu / (d_b - t_fb) = 250*12 / (18.0 - 0.570) = 172 kips
172 kips < 187 kips => Column web yielding OK without stiffeners

Step 7: Summary.

The connection requires 7/8-inch A325 bolts in a 4-bolt extended configuration with a 3/4-inch end plate. Column stiffeners are not required for web yielding at this load level but must be verified for flange bending.

Design Parameters Reference

Parameter Symbol Typical Range Notes
End plate thickness tp 5/8 to 1-1/2 in Governed by yield line analysis
End plate width bp 7 to 12 in Usually matches or exceeds beam flange width
Bolt diameter d_bolt 3/4 to 1-1/4 in A325 or A490 per AISC Table J3.2
Bolt gage g 3.5 to 6 in Horizontal distance between bolt columns
Bolt pitch p 2 to 4 in Vertical distance between bolt rows
Plate-to-flange distance a 1 to 2 in Distance from outer bolt row to beam flange
Prying parameter alpha 0 to 1+ Less than 1 means no prying (thick plate)
Beam flange yield Fy 50 ksi ASTM A992 default
Plate yield Fyp 50 ksi ASTM A572 Gr. 50 typical

Common Design Errors

Ignoring prying action. The most common error in hand calculations is neglecting prying forces. For plates less than 1 inch thick with standard bolt gages, prying can add 20% or more to the bolt tension. Always check prying per AISC Design Guide 4 or AISC Manual Part 9.

Insufficient plate width. The end plate must be wide enough to develop the full yield line mechanism and provide adequate edge distance for the bolts. A plate that is too narrow forces the bolts too close to the plate edge, reducing bearing capacity and potentially causing edge tear-out.

Omitting column-side checks. Engineers sometimes focus on the beam-side design (bolts and end plate) but neglect the column flange bending and web checks. The column is often the limiting element, especially when a relatively light column receives a heavy beam moment.

Incorrect lever arm. For extended end plates, the lever arm between the tension bolt rows and the compression flange includes the plate thickness. Using the beam depth alone (without the plate thickness) underestimates the lever arm and overestimates the bolt tension, which may seem conservative but can lead to selecting an unnecessarily heavy connection.

Not checking panel zone shear. In moment frames, the column panel zone shear can exceed the web capacity, requiring doubler plates. This check is separate from the end plate and column flange checks.

Additional Design Considerations

Weld design: The weld between the beam and the end plate must develop the full capacity of the beam flanges and web. Complete joint penetration (CJP) groove welds are typical for the beam flanges to ensure the full flange strength is developed. The web weld may be fillet welded for shear transfer.

Stiffener detailing: When continuity plates are required, they should be sized to match the beam flange thickness and width. The stiffener-to-column flange weld must transfer the excess force not resisted by the column flange or web. Fillet welds on both sides of the stiffener are typical.

Erection considerations: End plate connections require tight fabrication tolerances. The end plate must be perpendicular to the beam web, and the bolt holes must align between the end plate and column flange. Shims are sometimes required to accommodate column out-of-plumbness. Specify acceptable gaps in the construction documents (typically 1/16 inch for bearing-type connections).

Fatigue: For structures with cyclic loading (crane buildings, bridges), the end plate connection detail must be checked per AISC 360 Appendix 3. The weld at the beam flange-to-end plate interface is typically Category B or C. The bolt hole at the end plate edge is Category D. The allowable stress range decreases with the number of cycles.

Inputs and outputs

Typical inputs: beam section, column section, end plate width and thickness, bolt diameter and grade, bolt layout (gage, pitch, number of rows), steel grades for plate and members, and factored moment and shear demands.

Typical outputs: bolt tension including prying, end plate bending capacity, column flange bending capacity, stiffener requirements (continuity plates, doubler plates), and overall connection moment capacity.

Computation approach

The calculator follows the AISC Design Guide 4 procedure. For extended end plates, the bolt force including prying is computed using the Kennedy method or the simplified AISC approach. The end plate thickness is checked against yield line mechanisms. Column-side checks include flange bending (using the equivalent T-stub model), web yielding, web crippling, and web compression buckling. If any column-side check fails, the required stiffener size is computed.

Frequently Asked Questions

What is prying action in bolted end plate connections? Prying action occurs when the end plate or column flange flexes under the applied tension, causing the contact point near the bolt line to act as a fulcrum. This increases the bolt tension beyond the applied tension by an additional prying force Q. The magnitude of Q depends on the plate thickness, bolt gage, and the distance from the bolt to the beam flange. Thick plates have minimal prying; thin plates can increase bolt tension by 20-40%.

What is the difference between flush and extended end plates? A flush end plate does not extend beyond the beam flanges; bolts are placed between the flanges. An extended end plate extends beyond one or both beam flanges, with bolt rows above and/or below the flanges. Extended plates have higher moment capacity because the outer bolt rows have a longer lever arm. The 4-bolt extended unstiffened (4E) and 8-bolt extended stiffened (8ES) are the most common configurations.

When are column stiffeners required? Column stiffeners (continuity plates) are required when the column flange is too thin to resist the concentrated force from the beam flange without excessive local bending, or when the column web cannot resist the compression or tension delivered by the beam flanges. The need for stiffeners depends on the column flange thickness, web thickness, column depth, and the magnitude of the beam flange forces. Stiffeners add fabrication cost, so selecting a heavier column to avoid stiffeners is often more economical.

Can end plate connections be used for seismic moment frames? End plate connections can be used in seismic moment frames, but they must be prequalified per AISC 358 or justified by testing and analysis. AISC 358 includes prequalification for several end plate configurations, including the 4E and 8ES types. The prequalification specifies limits on beam depth, column depth, plate thickness, bolt diameter, and other parameters. Connections outside these limits require project-specific qualification testing.

How do I select between A325 and A490 bolts for end plate connections? A325 bolts (Fnt = 90 ksi) are adequate for most end plate connections with moderate to high moment demands. A490 bolts (Fnt = 113 ksi) provide higher tensile capacity per bolt and are used when the bolt tension demand exceeds A325 capacity and increasing the bolt count or diameter is impractical. A490 bolts are more expensive and have stricter installation requirements. They should not be galvanized due to hydrogen embrittlement risk.

What is the minimum end plate thickness? There is no universal minimum, but AISC Design Guide 4 recommends that the end plate be at least as thick as the bolt diameter for extended unstiffened configurations to limit prying action. For 7/8-inch bolts, use at least a 7/8-inch plate for a no-prying design. Thinner plates can be used if prying is explicitly checked and the bolt capacity is verified including the prying force.

How does the panel zone doubler plate interact with the end plate connection? The doubler plate is welded to the column web to increase the panel zone shear capacity. It does not directly affect the end plate or bolt design, but it is part of the overall connection system. The doubler plate thickness is selected so that the combined web-plus-doubler shear capacity exceeds the panel zone shear demand. The doubler plate must be detailed with plug welds or fillet welds to the column web to prevent local buckling of the thin gap between the doubler and the web.

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