End Plate Connection — Engineering Reference

Extended end plate moment connection design — AISC DG4/16, 4E and 8ES configurations, yield line bolt force model, plate thickness, and column-side checks.

Overview

An end plate moment connection consists of a plate welded to the end of a beam and bolted to the face of a supporting column flange. Unlike clip-angle or shear-tab connections that transfer shear only, end plate connections develop the full or partial moment capacity of the beam, making them a primary choice for moment-resisting frames. AISC Design Guide 4 (DG4) and Design Guide 16 (DG16) provide the detailed design procedures used in North American practice.

End plate configurations are classified by the number and position of bolt rows:

• 4E (Four-bolt extended unstiffened) — two bolts above and two bolts below the tension flange, extended end plate, no stiffener.
• 4ES (Four-bolt extended stiffened) — same as 4E but with a vertical plate stiffener welded between the end plate and the beam flange, increasing the plate's bending resistance.
• 8ES (Eight-bolt extended stiffened) — four bolts above the tension flange (two rows of two) and four bolts below, with stiffener. Used for heavy moment connections.
• Flush end plate — bolts are entirely within the beam depth. Lower moment capacity but simpler to fabricate and suitable for wind-moment frames.

Yield line theory for plate thickness

End plate design per AISC DG4/DG16 uses yield line analysis to determine the required plate thickness. The yield line pattern depends on the bolt layout, the distance from the bolt centerline to the beam flange (p_f), and the plate width (b_p). The required end plate thickness is:

t_p = sqrt(2 x M_u / (phi_b x F_yp x Y_p))

where M_u is the factored beam moment, phi_b = 0.90, F_yp is the end plate yield strength, and Y_p is the yield line mechanism parameter from the applicable DG4/DG16 table. Y_p is a function of the bolt geometry (s, p_f, p_b, g) and the plate width.

Bolt force model

The bolt force in the tension zone is not simply M_u / (n x d). Because the end plate flexes, prying action increases the bolt tension. DG16 accounts for this using the split-tee analogy: each bolt row is modeled as a T-stub in which the plate acts as the T-stub flange. The bolt force including prying is:

B = T + Q

where T is the applied tension and Q is the prying force. When the plate is thick enough to prevent prying (the "thick plate" condition), Q = 0 and the bolt force equals the applied tension. When the plate is thin, Q can increase the bolt force by 30% or more.

Worked example — W18x50 beam, 4E configuration

Given: W18x50 beam (d = 18.0 in., b_f = 7.50 in., t_f = 0.57 in.), M_u = 250 kip-ft, end plate F_yp = 50 ksi, A325 bolts 3/4 in. diameter, bolt gage g = 5.5 in., p_f = 1.75 in. (distance from flange face to first bolt row centerline), b_p = 9.0 in.

1. Yield line parameter Y_p: For a 4E configuration, Y_p = (b_p/2) x [h_1 x (1/p_f) + h_0 x (1/s)] + 2/g x [h_1 x (p_f + s)]. Using h_1 = 15.68 in., h_0 = 17.43 in., s = 3.5 in.: Y_p = 138.2 in.
2. End plate thickness: t_p = sqrt(2 x 250 x 12 / (0.90 x 50 x 138.2)) = sqrt(6000/6219) = 0.98 in. Use t_p = 1.0 in.
3. Bolt tension: Flange force = 250 x 12 / (18.0 - 0.57) = 172 kip. Per bolt (4 bolts in tension) = 172/4 = 43.0 kip. A325 3/4 in. bolt available tension = phi x F_nt x A_b = 0.75 x 90 x 0.4418 = 29.8 kip. Not adequate — need 7/8 in. bolts (phi x R_n = 40.6 kip) or add bolt rows.

Code comparison — end plate connections

Column-side limit states

The column must be checked for several limit states caused by the concentrated flange forces from the end plate:

• Column flange bending — the column flange acts like a T-stub loaded by the bolt tension. If the column flange is too thin, stiffening with continuity plates is required.
• Column web yielding (AISC J10.2) — the beam compression flange force can yield the column web directly opposite. R_n = F_yw x t_w x (5k + l_b).
• Column web crippling (AISC J10.3) — at concentrated compression loads, the column web can buckle locally.
• Column panel zone shear (AISC J10.6) — the moment couple from the beam creates a shear force in the column web panel. R_v = 0.60 x F_y x d_c x t_w for single-sided connections. Doubler plates may be needed.

Common mistakes to avoid

• Ignoring prying action — using T = M/(n x lever arm) without the DG16 prying model can underestimate bolt forces by 30% or more, leading to bolt fracture.
• Wrong bolt position — the distance p_f from the beam tension flange to the first bolt row is critical. Values outside the DG4 recommended range (typically 1.5 to 2.0 in.) produce unreliable yield line solutions.
• Omitting column-side checks — even when the end plate and bolts are adequate, the column flange may be too thin or the panel zone may be overstressed. Continuity plates and doubler plates are frequently required.
• Using flush end plates for large moments — flush configurations have limited moment capacity because all bolts are within the beam depth. For moments exceeding about 60% of the beam plastic moment, extended configurations (4E or 8ES) are generally required.
• Not checking the weld to beam flange — the CJP or fillet weld connecting the beam tension flange to the end plate must develop the full flange force. Undersized welds at the tension flange are a fracture-critical failure mode.

AISC Design Guide 4 — Extended End Plate Configurations

AISC Design Guide 4 (DG4), originally authored by Thomas M. Murray and later updated in Design Guide 16 by Murray and Sumner, classifies extended end plate connections into four principal configurations. Each configuration is defined by its bolt arrangement, the presence or absence of end plate stiffeners, and the resulting moment and shear capacity. The selection of configuration depends on the magnitude of the design moment, the available column flange thickness, and architectural or fabrication constraints.

8ES — Eight-Bolt Extended Stiffened

The 8ES configuration is the highest-capacity end plate connection covered by DG4. It features four bolt rows (two above and two below the beam tension flange) with a vertical stiffener plate welded between the end plate extension and the beam tension flange. This stiffener prevents the extended portion of the end plate from bending independently, forcing the full plate width to participate in resisting bolt tension.

The 8ES is used for heavy moment connections where the factored moment exceeds the capacity of the 4ES configuration. Typical applications include moment connections to W14x500+ columns in high-rise frames, connections at seismic link beams in eccentrically braced frames, and retrofit connections where the existing column flange is too thin for unstiffened configurations. The yield line pattern for the 8ES involves six distinct yield line segments that form around the bolt rows and the stiffener, creating a more complex mechanism than the 4E configuration. The Y_p parameter accounts for these additional segments and is significantly larger than for comparable unstiffened configurations, resulting in a thinner required plate.

Bolt tension forces in the 8ES are distributed across four bolt rows rather than two, reducing the demand on each individual bolt. However, the stiffener weld must develop the full force transferred from the extended portion of the end plate to the beam flange. The stiffener is typically designed as a pair of vertical plates (one on each side of the end plate extension) with a combined thickness at least equal to the beam web thickness.

8E — Eight-Bolt Extended Unstiffened

The 8E configuration places eight bolts in four rows (two above, two below the tension flange) but without the vertical stiffener plate. This reduces fabrication cost and eliminates a potential source of weld defect, but the end plate must be thicker to compensate for the lack of stiffening.

The 8E is economical when the design moment is moderately high and the column flange is thick enough to resist flange bending without continuity plates. Because the extended portion of the end plate is unstiffened, the yield line mechanism involves the plate bending in two directions (transverse and longitudinal), which increases the required plate thickness compared to the 8ES. The typical t_p for an 8E ranges from 1.0 to 1.75 in., depending on the moment and bolt diameter.

A key consideration for the 8E is the distance p_f from the beam tension flange to the first bolt row. If p_f is too large (greater than approximately 2.5 in.), the plate extension behaves as an unsupported cantilever, and prying forces increase dramatically. DG4 recommends p_f values between 1.5 and 2.0 in. for 8E configurations.

4E — Four-Bolt Extended Unstiffened

The 4E is the most common extended end plate configuration in current practice. Two bolt rows (one above and one below the tension flange, each with two bolts) provide moment resistance through a simple, economical layout. The 4E is prequalified for use in Special Moment Frames per AISC 358 Chapter 6 (BUEEP — Bolted Unstiffened Extended End Plate), making it the default choice for seismic moment connections.

The 4E yield line mechanism involves four yield line segments: two running from the inner bolt row to the beam flange (across the plate width) and two running from the outer bolt row along the plate edges. The parameter Y_p is computed from these segments and is sensitive to the bolt gage g and the distance p_f. The design tables in DG4 and DG16 provide pre-computed Y_p values for standard W-shapes and bolt layouts.

For the 4E configuration, the plate thickness typically falls between 5/8 and 1-1/4 in. The critical limit state is often end plate yielding near the tension flange, where the plate bends about a horizontal axis aligned with the beam flange. The bolt force includes prying action when the plate is relatively thin (the "thin plate" condition per DG16), which increases the required bolt diameter.

Flush End Plate

Flush end plates have all bolt rows within the beam depth, typically one row near the top flange and one row near the bottom flange. Because the lever arm between tension and compression bolt rows is limited to the beam depth minus two flange thicknesses, the moment capacity is significantly lower than extended configurations for the same bolt size.

Flush end plates are suitable for wind-moment frames (where full moment resistance is not required), pinned connections with nominal moment transfer, and secondary beam connections. They are simpler to fabricate (no plate extension) and easier to erect because the connection is entirely within the beam profile. However, AISC 358 does not prequalify flush end plates for Special Moment Frame connections, limiting their use to Ordinary Moment Frames or gravity frames with wind moments.

The yield line pattern for flush end plates involves the plate bending between the beam flanges, with yield lines running from the bolt holes to the web and flanges. Because the plate is confined within the beam depth, the yield line mechanism is simpler than for extended configurations, and Y_p values are generally smaller.

Limit States for End Plate Connections

End plate moment connections must satisfy multiple limit states to ensure safe performance. These limit states are categorized into bolt limit states, plate limit states, and column-side limit states. Each must be checked independently, and the lowest capacity governs the connection design.

Bolt Tension (AISC J3.6)

Each bolt in the tension zone must resist its share of the flange force plus any prying action. The nominal bolt tensile strength is:

R_n = F_nt x A_b
phi x R_n = 0.75 x F_nt x A_b

where F_nt is the nominal tensile stress (90 ksi for A325, 113 ksi for A490) and A_b is the nominal bolt area. For a 3/4 in. A325 bolt: phi x R_n = 0.75 x 90 x 0.4418 = 29.8 kip. For a 7/8 in. A325 bolt: phi x R_n = 0.75 x 90 x 0.6013 = 40.6 kip.

When prying action is present (thin plate condition), the bolt force increases to B = T + Q, where Q is determined from the DG16 prying model. The prying force depends on the ratio of plate flexibility to bolt stiffness and can range from zero (thick plate, no prying) to 30-40% of the applied tension for thin plates with large p_f values.

Bolt Shear (AISC J3.6)

The bolts must also resist the beam shear reaction. For end plate connections, the shear is distributed among all bolts in the connection. The nominal shear strength per bolt is:

R_n = F_nv x A_b (threads excluded from shear plane)
phi x R_n = 0.75 x F_nv x A_b

where F_nv = 48 ksi for A325-SC (slip critical) or 60 ksi for A325-N (bearing type, threads included). For a 3/4 in. A325 bolt in bearing: phi x R_n = 0.75 x 60 x 0.4418 = 19.9 kip per bolt. Combined tension and shear on bolts must satisfy the interaction equation per AISC J3.7.

End Plate Yielding (Yield Line Analysis)

The end plate must be thick enough to develop the required moment without excessive plate yielding. The yield line method assumes the plate forms a mechanism of plastic hinges along specific lines, and the work done by the applied forces equals the internal energy dissipated by the yield lines. The required plate thickness is:

t_p,required = sqrt(2 x M_u / (phi_b x F_yp x Y_p))

where phi_b = 0.90, F_yp is the plate yield stress (typically 50 ksi for A572 Gr 50), and Y_p is the yield line parameter from DG4/DG16 tables. The actual plate thickness must exceed t_p,required. Common practice is to specify the next standard plate thickness (e.g., if t_p,required = 0.92 in., specify 1.0 in.).

Prying Action

Prying action is the increase in bolt tension caused by the flexibility of the end plate. When the plate bends under the flange force, the edges of the plate press against the column flange, creating a prying force Q that adds to the bolt tension. The magnitude of Q depends on:

• The plate thickness relative to the bolt pitch and gage
• The distance from the bolt centerline to the plate edge
• The bolt stiffness (diameter and grade)

DG16 classifies the plate as "thick" (no prying, Q = 0) or "thin" (prying present, Q > 0) based on a comparison of the required plate thickness for the no-prying condition versus the actual plate thickness. When the actual thickness exceeds the no-prying threshold, Q = 0 and the bolt force equals the applied tension. When the plate is thinner, Q is computed as:

Q = (3 x B x b' / (8 x a^2)) x (delta / 2 - b' x t_p^2 / (3 x B x a))

where B is the bolt force, a is the distance from the bolt centerline to the plate edge, b' is the distance from the bolt centerline to the beam flange face, and delta accounts for bolt elongation. This equation is solved iteratively or using the DG16 tabular method.

Worked Example — 4-Bolt Unstiffened End Plate for W18x50

This worked example demonstrates the complete design of a 4E extended end plate connection for a W18x50 beam framing into a W14x90 column.

Given:

• Beam: W18x50 (A992, F_y = 50 ksi), d = 18.0 in., b_f = 7.495 in., t_f = 0.570 in., t_w = 0.355 in., S_x = 88.9 in.^3, Z_x = 101 in.^3
• Factored moment: M_u = 200 kip-ft
• Factored shear: V_u = 45 kip
• End plate: A572 Gr 50, F_yp = 50 ksi, b_p = 9.0 in.
• Bolts: 7/8 in. A325-N, standard holes, g = 5.5 in., p_f = 1.75 in.
• Column: W14x90, t_fc = 0.710 in.

Step 1 — Determine flange force:

The beam flange force is the couple force from the applied moment:

F_f = M_u / (d - t_f) = 200 x 12 / (18.0 - 0.570) = 2400 / 17.43 = 137.7 kip

Step 2 — Bolt tension check (no prying initially):

With 4 bolts in the tension zone, the applied tension per bolt is:

T = F_f / 4 = 137.7 / 4 = 34.4 kip

Available bolt tension (7/8 in. A325): phi x R_n = 0.75 x 90 x 0.6013 = 40.6 kip

Since 34.4 < 40.6, bolts are adequate without prying. Check prying to confirm.

Step 3 — End plate thickness (yield line analysis):

For the 4E configuration with the given geometry, the yield line parameter from DG4 Table 3-3:

Y_p = b_p x [(h_1 / (2 x p_f)) + (h_0 / (2 x s))] + 2/g x [h_1 x (p_f + s)]

With h_1 = 14.93 in. (distance between inner bolt rows), h_0 = 17.43 in. (distance between outer bolt rows), s = 3.0 in. (bolt spacing in longitudinal direction):

Y_p = 9.0 x [(14.93 / (2 x 1.75)) + (17.43 / (2 x 3.0))] + 2/5.5 x [14.93 x (1.75 + 3.0)]

Y_p = 9.0 x [4.27 + 2.91] + 0.364 x [70.9] = 9.0 x 7.18 + 25.8 = 64.6 + 25.8 = 90.4 in.

Required plate thickness:

t_p = sqrt(2 x 200 x 12 / (0.90 x 50 x 90.4)) = sqrt(4800 / 4068) = sqrt(1.180) = 1.09 in.

Use t_p = 1-1/4 in. (1.25 in. plate)

Step 4 — Prying action check:

With the 1.25 in. plate (thicker than required 1.09 in.), the plate is in the thick plate regime. The prying force Q is negligible. Bolt demand remains at T = 34.4 kip < 40.6 kip. OK.

Step 5 — Bolt shear check:

All 8 bolts (4 tension + 4 compression) resist the shear of 45 kip:

V_per_bolt = 45 / 8 = 5.6 kip
phi x R_nv = 0.75 x 60 x 0.6013 = 27.1 kip >> 5.6 kip. OK.

Step 6 — Combined tension and shear interaction:

f_t = T / A_b = 34.4 / 0.6013 = 57.2 ksi
f_v = V_per_bolt / A_b = 5.6 / 0.6013 = 9.3 ksi

AISC J3.7 interaction: f_t <= (1.3 F_nt - f_v) x phi when f_v > 0.2 x phi x F_nv

f_t,allowable = (1.3 x 90 - 9.3) x 0.75 x (1/1.3) = (117 - 9.3) x 0.577 = 62.2 ksi > 57.2 ksi. OK.

Step 7 — End plate summary:

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