Beam Splice Design Worked Example — W18x55 Bolted Flange & Web Plates per AISC 360-22

Complete step-by-step beam splice design for a W18x55 floor beam. The splice uses bolted flange plates (top and bottom) and bolted web plates (both sides). Every limit state is checked with actual numbers and code references. This is a bearing-type connection with A325N bolts and standard holes.

Problem Statement

PRELIMINARY — NOT FOR CONSTRUCTION. All results are for educational and reference use only. Must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) before use in any project.

A W18x55 beam in a commercial office building requires a field splice at approximately the quarter-point of a 40 ft span. The splice is located where the factored moment is 60% of the maximum midspan moment and the factored shear is the full end reaction (conservative). The beam is ASTM A992 (Fy = 50 ksi, Fu = 65 ksi).

Section Properties — W18x55 (ASTM A992):

Property Value Units
d 18.1 in.
bf 7.53 in.
tf 0.630 in.
tw 0.390 in.
kdes 1.06 in.
A 16.2 in.²
Ix 890 in.⁴
Sx 98.3 in.³
Zx 112 in.³

Loads at Splice Location (factored, LRFD):

Splice Plate Material: ASTM A36 (Fy = 36 ksi, Fu = 58 ksi) Bolts: 3/4 in. diameter ASTM A325N (Fnv = 54 ksi), standard holes (dh = 13/16 in.)

Step 1: Flange Force Calculation

The flange force at the splice location is the axial tension/compression couple that resists the moment:

P_f = M_u / (d - tf) = M_u / (d_eff)

Where d_eff is the distance between flange centroids. For W18x55:

d_eff = d - tf = 18.1 - 0.630 = 17.47 in.
P_f = M_u / d_eff = (180 × 12) / 17.47 = 2,160 / 17.47 = 123.6 kips per flange

Each flange splice plate pair must transfer P_f = 123.6 kips. This is the demand on the flange connection.

Step 2: Flange Splice Plate Sizing

Select flange splice plates: PL 7 × 3/8 in. (A36), one each side of the flange.

Plate Properties (per plate):

Note: The hole deduction is 13/16 in. + 1/16 in. = 7/8 in. per bolt per AISC B4.3b (damage allowance). Using 2 bolts across the width (2 gauge lines):

A_n = [7.0 - 2 × (7/8)] × 0.375 = (7.0 - 1.75) × 0.375 = 5.25 × 0.375 = 1.969 in.²

Effective net area (AISC D3, shear lag factor U = 1.0 for flat plate with all elements connected):

A_e = U × A_n = 1.0 × 1.969 = 1.969 in.²

Step 3: Flange Plate Tension Yielding Check (AISC J4.1)

Nominal tensile strength for yielding on gross section:

R_n_yield = Fy × A_g = 36 × 2.625 = 94.5 kips (per plate)

Design strength (LRFD, phi = 0.90):

phi × R_n_yield = 0.90 × 94.5 = 85.1 kips per plate

For 2 plates (one each side of flange):

Total phi R_n_yield = 2 × 85.1 = 170.1 kips

Check: P_f = 123.6 kips < 170.1 kips. Tension yielding OK. Utilization = 0.727.

Step 4: Flange Plate Tension Rupture Check (AISC J4.2)

R_n_rupture = Fu × A_e = 58 × 1.969 = 114.2 kips (per plate)

Design strength (LRFD, phi = 0.75):

phi × R_n_rupture = 0.75 × 114.2 = 85.7 kips per plate

For 2 plates:

Total phi R_n_rupture = 2 × 85.7 = 171.3 kips

Check: P_f = 123.6 kips < 171.3 kips. Tension rupture OK. Utilization = 0.722.

Rupture governs (85.7 < 85.1 per plate), as expected for net section.

Step 5: Flange Bolt Shear Check (AISC J3.6)

Bolt configuration: 4 bolts per flange side (2 rows of 2 bolts). Bolts are in single shear (one shear plane per bolt, since splice plates are on both sides of flange and each plate pair shares the load).

Single A325N bolt shear capacity (AISC Table J3.2, Fnv = 54 ksi):

A_b = pi × (3/4)² / 4 = 0.442 in.²
r_n = Fnv × A_b = 54 × 0.442 = 23.9 kips (nominal single shear)

For threads excluded from shear plane (X condition, standard for bearing-type), the nominal strength can be increased per J3.6. For threads included (N condition, conservative):

r_n = 23.9 kips per bolt

Design strength (LRFD, phi = 0.75):

phi × r_n = 0.75 × 23.9 = 17.9 kips per bolt

For 4 bolts per flange side:

Total phi R_n_bolt = 4 × 17.9 = 71.6 kips

Wait -- this is per side. The total for the splice (both sides) requires checking each side independently since the force path is: beam flange → bolts → flange plates → bolts → beam flange. Each bolt group must transfer the full flange force P_f = 123.6 kips.

4 bolts × 17.9 kips = 71.6 kips < 123.6 kips — NOT ADEQUATE with 4 bolts.

Increase to 6 bolts per flange side (3 rows of 2 bolts):

phi R_n_bolt = 6 × 17.9 = 107.4 kips

Still not adequate. Try 7/8 in. diameter bolts or increase to 8 bolts.

Use 8 bolts per flange side (4 rows × 2 bolts) with 3/4 in. A325N:

phi R_n_bolt = 8 × 17.9 = 143.2 kips > 123.6 kips. **Bolt shear OK.** Utilization = 0.863.

Step 6: Flange Bolt Bearing Check (AISC J3.10)

Bearing at bolt holes in flange splice plates (t = 0.375 in. A36 plate):

Edge distance: L_e = 1.5 in. (minimum per AISC Table J3.4M: 1.25 in. for 3/4 in. bolt)

For L_e = 1.5 in. < 2d = 1.5 in., use bearing strength governed by tearout:

r_n_bearing = 1.2 × L_c × t × Fu ≤ 2.4 × d × t × Fu
L_c = L_e - dh/2 = 1.5 - (13/16)/2 = 1.5 - 0.406 = 1.094 in.

r_n = 1.2 × 1.094 × 0.375 × 58 = 28.5 kips per bolt (tearout)

Upper bound:

2.4 × d × t × Fu = 2.4 × 0.75 × 0.375 × 58 = 39.2 kips per bolt
r_n = min(28.5, 39.2) = 28.5 kips (tearout governs)

Design strength (LRFD, phi = 0.75):

phi × r_n = 0.75 × 28.5 = 21.4 kips per bolt

For 8 bolts per flange side:

phi R_n_bearing_plate = 8 × 21.4 = 171.2 kips > 123.6 kips. **Bolt bearing on plate OK.**

Bearing in beam flange (tf = 0.630 in., A992, Fu = 65 ksi):

For interior bolts (spacing s = 3.0 in. > 3d = 2.25 in., so tearout does not govern for interior bolts):

L_c_interior = s - dh = 3.0 - 0.875 = 2.125 in. (using dh_eff = 7/8 in.)
r_n_interior = 2.4 × d × tf × Fu = 2.4 × 0.75 × 0.630 × 65 = 73.7 kips

For edge bolts:

L_c_edge = 1.5 - (7/8)/2 = 1.5 - 0.438 = 1.063 in.
r_n_edge = 1.2 × 1.063 × 0.630 × 65 = 52.2 kips

Flange bearing is less critical than plate bearing. Bolt bearing on flange OK.

Step 7: Flange Block Shear Check (AISC J4.3)

Block shear on flange splice plate. For 4 rows of 2 bolts (8 bolts total), the potential block shear failure path is:

Gross shear area: A_gv = L_gv × t_p × 2 shear planes = 13.5 × 0.375 × 2 = 10.13 in.² Net shear area: A_nv = A_gv - 4.5 × dh × t_p × 2 = 10.13 - 4.5 × 0.875 × 0.375 × 2 = 10.13 - 2.953 = 7.17 in.²

(4.5 holes deducted — 4 full holes + 1 half hole at each shear plane edge)

Gross tension area: A_gt = 3.0 × 0.375 = 1.125 in.² Net tension area: A_nt = [3.0 - 1 × 0.875] × 0.375 = 2.125 × 0.375 = 0.797 in.²

Per AISC J4.3, U_bs = 1.0 (uniform tension stress):

R_n_bs = 0.60 × Fu × A_nv + U_bs × Fu × A_nt ≤ 0.60 × Fy × A_gv + U_bs × Fu × A_nt

= 0.60 × 58 × 7.17 + 1.0 × 58 × 0.797 ≤ 0.60 × 36 × 10.13 + 1.0 × 58 × 0.797
= 249.5 + 46.2 = 295.7 kips ≤ 218.8 + 46.2 = 265.0 kips

Governing R_n_bs = 265.0 kips (gross shear yielding + net tension rupture controls).

Design strength (LRFD, phi = 0.75):

phi × R_n_bs = 0.75 × 265.0 = 198.8 kips per plate

For 2 plates:

Total phi R_n_bs = 2 × 198.8 = 397.5 kips

Check: P_f = 123.6 kips << 397.5 kips. Block shear OK. Utilization = 0.311.

Step 8: Web Splice Design

The web splice must transfer V_u = 35.0 kips. For splice location at quarter-span, the web also carries a small portion of the moment, but for simplicity, we design the web splice for the full shear. Use 2 web splice plates (one each side), PL 12 × 1/4 in., A36.

Bolt layout: 3 bolts per side in single vertical row at 3 in. spacing. Bolt gage from top of plate = 1.5 in.

Web Splice Plate Properties:

Step 9: Web Splice Plate Shear Yielding (AISC J4.2)

Per plate:

R_n_shear = 0.60 × Fy × A_gv = 0.60 × 36 × (12 × 0.25) = 0.60 × 36 × 3.0 = 64.8 kips

Design strength (LRFD, phi = 1.00 per AISC G1 for webs with h/tw meeting limits):

phi × R_n_shear = 1.00 × 64.8 = 64.8 kips per plate

For 2 plates:

Total phi R_n_shear = 2 × 64.8 = 129.6 kips > 35.0 kips. **Shear yielding OK.**

Step 10: Web Splice Plate Shear Rupture (AISC J4.2)

Net shear area (3 bolts, dh_eff = 7/8 in.):

A_nv = (12 - 3 × 0.875) × 0.25 = (12 - 2.625) × 0.25 = 9.375 × 0.25 = 2.344 in.² per plate

R_n_rupture_shear = 0.60 × Fu × A_nv = 0.60 × 58 × 2.344 = 81.6 kips per plate

Design strength (phi = 0.75):

phi × R_n = 0.75 × 81.6 = 61.2 kips per plate

For 2 plates:

Total = 2 × 61.2 = 122.4 kips > 35.0 kips. **Shear rupture OK.**

Step 11: Web Bolt Shear Check

3 bolts per side, 3/4 in. A325N single shear:

phi r_n = 17.9 kips per bolt (from Step 5)
phi R_n_bolt = 3 × 17.9 = 53.7 kips > 35.0 kips. **Web bolt shear OK.**

Step 12: Web Block Shear (AISC J4.3)

For web splice plate with 3 bolts in single row:

Shear path: L_gv = (3 - 1) × 3.0 + 1.5 + 1.5 = 9.0 in. (distance from first to last bolt center + top and bottom edge distances) Tension path: L_gt = 1.5 in. (edge distance from bolt line to plate edge)

Gross shear area: A_gv = 9.0 × 0.25 = 2.25 in.² per plate Net shear area: A_nv = (9.0 - 2.5 × 0.875) × 0.25 = (9.0 - 2.188) × 0.25 = 1.703 in.²

(2.5 holes deducted — 2 full + 2 half holes at edges)

Gross tension area: A_gt = 1.5 × 0.25 = 0.375 in.² Net tension area: A_nt = (1.5 - 0.5 × 0.875) × 0.25 = (1.5 - 0.438) × 0.25 = 0.266 in.²

(0.5 holes in tension plane — half hole at the top of the shear path)

R_n_bs = 0.60 × Fu × A_nv + U_bs × Fu × A_nt ≤ 0.60 × Fy × A_gv + U_bs × Fu × A_nt

= 0.60 × 58 × 1.703 + 1.0 × 58 × 0.266 ≤ 0.60 × 36 × 2.25 + 1.0 × 58 × 0.266
= 59.3 + 15.4 = 74.7 ≤ 48.6 + 15.4 = 64.0 kips

Governing R_n_bs = 64.0 kips.

Design strength (phi = 0.75):

phi R_n_bs = 0.75 × 64.0 = 48.0 kips per plate

For 2 plates:

Total phi R_n_bs = 2 × 48.0 = 96.0 kips > 35.0 kips. **Web block shear OK.**

Step 13: Beam Web Check at Splice

The beam web (tw = 0.390 in., A992, Fy = 50 ksi, Fu = 65 ksi) must also be checked for block shear and bearing.

Bolt bearing on beam web:

L_c_edge = 1.5 - 0.438 = 1.063 in.
r_n_edge = 1.2 × 1.063 × 0.390 × 65 = 32.3 kips
r_n_interior = 2.4 × 0.75 × 0.390 × 65 = 45.6 kips

For 3 bolts (1 edge + 2 interior):

R_n_bearing_web = 32.3 + 2 × 45.6 = 123.5 kips
phi R_n = 0.75 × 123.5 = 92.6 kips > 35.0 kips. **Web bearing OK.**

Beam web block shear (similar to plate but with beam web properties):

Shear path length through beam web: 9.0 in. (same layout)

A_gv = 9.0 × 0.390 = 3.510 in.²
A_nv = (9.0 - 2.5 × 0.875) × 0.390 = 6.812 × 0.390 = 2.657 in.²
A_gt = 1.5 × 0.390 = 0.585 in.²
A_nt = (1.5 - 0.5 × 0.875) × 0.390 = 0.414 in.²

R_n_bs = 0.60 × 65 × 2.657 + 65 × 0.414 ≤ 0.60 × 50 × 3.510 + 65 × 0.414
= 103.6 + 26.9 = 130.5 ≤ 105.3 + 26.9 = 132.2 kips

Governing R_n_bs = 130.5 kips (net shear rupture controls for higher-Fu web).

phi R_n_bs = 0.75 × 130.5 = 97.9 kips > 35.0 kips. **Beam web block shear OK.**

Step 14: Summary — Pass/Fail

Limit State Reference Demand Capacity D/C Ratio Status
Flange plate tension yielding AISC J4.1 123.6 k 170.1 k 0.727 PASS
Flange plate tension rupture AISC J4.2 123.6 k 171.3 k 0.722 PASS
Flange bolt shear (8 bolts) AISC J3.6 123.6 k 143.2 k 0.863 PASS
Flange bolt bearing (plate) AISC J3.10 123.6 k 171.2 k 0.722 PASS
Flange block shear AISC J4.3 123.6 k 397.5 k 0.311 PASS
Web plate shear yielding AISC J4.2 35.0 k 129.6 k 0.270 PASS
Web plate shear rupture AISC J4.2 35.0 k 122.4 k 0.286 PASS
Web bolt shear (3 bolts) AISC J3.6 35.0 k 53.7 k 0.652 PASS
Web plate block shear AISC J4.3 35.0 k 96.0 k 0.365 PASS
Beam web bearing AISC J3.10 35.0 k 92.6 k 0.378 PASS
Beam web block shear AISC J4.3 35.0 k 97.9 k 0.358 PASS

All checks pass. The governing limit state is flange bolt shear at D/C = 0.863. The splice is adequate for the design loads.

Final Splice Details:

Related Calculators

Use the Splice Connection Calculator to check your own beam splice designs. For beam capacity verification before splice design, use the Beam Capacity Calculator. For bolted connection checks including bolt shear and bearing, try the Bolted Connection Calculator.