AISC 360-22 Bearing Stiffener Design — W24x55 Full Worked Example (Section J10)

Complete step-by-step bearing stiffener design following AISC 360-22 Section J10 provisions (LRFD). This worked example covers a W24x55 simply supported beam with a concentrated end reaction: web local yielding (J10.2), web crippling (J10.3), determination of whether stiffeners are required, stiffener plate sizing per J10.8, effective column check, and weld design for the stiffener-to-web connection. Every calculation is shown with actual values and code clause references.

Problem Statement

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

A W24x55 beam spans 36 ft in a commercial building and is simply supported at each end. The bearing at each support is over a 6 in. long bearing plate (lb = 6 in.) placed directly on a concrete or masonry support. The beam is not restrained against rotation at the support (typical pinned-roller beam support). The factored end reaction is Ru = 85 kips.

Design parameters:

• Beam: W24x55, ASTM A992 (Fy = 50 ksi, Fu = 65 ksi)
• Factored end reaction: Ru = 85 kips
• Bearing length at support: lb = 6 in.
• End distance from beam end to bearing edge: 3 in.

Section Properties (W24x55)

Step 1: Web Local Yielding (AISC 360-22 Section J10.2)

Web local yielding occurs when the compressive stress from the bearing load exceeds the web yield capacity. The load spreads through the flange and into the web at an assumed slope.

For an interior condition (bearing not at the end), the effective bearing length includes a contribution from both sides of the bearing plate:

AISC Equation J10-2 (LRFD):

Rn = Fy × tw × (5k + lb)   for interior condition with lb ≤ d

For an end bearing condition, the load spreads through the flange to one side only. Additionally, the end distance from the beam end to the bearing must be at least k_det for the full 2.5k dispersion:

AISC Equation J10-3 (LRFD) for end bearing:

Rn = Fy × tw × (2.5k + lb)   for lb ≤ d

where the end distance from the beam end to the bearing plate edge ≥ k_des (1.01 in.). For our case, the end distance is 3 in. ≥ 1.01 in., satisfying the end distance requirement.

Rn_yield = 50 ksi × 0.395 in. × (2.5 × 1.01 + 6.0)
         = 19.75 kips/in. × (2.525 + 6.0)
         = 19.75 × 8.525
         = 168.4 kips

Design web local yielding strength (phi = 1.00 per J10.2 for LRFD):

phi × Rn = 1.00 × 168.4 = 168.4 kips

Check: Ru = 85 kips < 168.4 kips. Web local yielding OK. Utilization = 85/168.4 = 0.505.

Step 2: Web Crippling (AISC 360-22 Section J10.3)

Web crippling is a localized buckling of the web near the junction with the loaded flange. The resistance depends on whether the concentrated load is applied at a distance from the member end greater than or less than d/2 (the beam depth divided by two).

Location check: The bearing is at the beam end. The point of load application is at lb/2 = 3 in. from the beam end. Since 3 in. ≤ d/2 = 11.8 in., the load is at a distance from the member end less than d/2. Use AISC Equation J10-5a (LRFD):

Rn = 0.40 × tw^2 × [1 + 3 × (lb/d) × (tw/tf)^1.5] × sqrt(E × Fy × tf / tw)

Substitute values:

lb/d = 6.0 / 23.6 = 0.2542
tw/tf = 0.395 / 0.505 = 0.7822
(tw/tf)^1.5 = 0.7822^1.5 = 0.6917
3 × (lb/d) × (tw/tf)^1.5 = 3 × 0.2542 × 0.6917 = 0.5274
[1 + 0.5274] = 1.5274

tw^2 = 0.395^2 = 0.1560

sqrt(E × Fy × tf / tw) = sqrt(29,000 × 50 × 0.505 / 0.395)
                        = sqrt(29,000 × 50 × 1.2785)
                        = sqrt(1,853,825)
                        = 1,361.6 (units: kips^0.5)

Rn = 0.40 × 0.1560 × 1.5274 × 1,361.6
   = 0.09533 × 1,361.6
   = 129.8 kips

Design web crippling strength (phi = 0.75 per J10.3 for LRFD):

phi × Rn = 0.75 × 129.8 = 97.4 kips

Check: Ru = 85 kips < 97.4 kips. Web crippling OK. Utilization = 85/97.4 = 0.873.

The web crippling utilization is higher (0.873) than web yielding (0.505), but both are acceptable. Web crippling is the governing web limit state for this configuration.

Step 3: Web Sidesway Buckling (AISC J10.4)

Web sidesway buckling is a lateral instability of the web under a concentrated compressive force. This limit state only applies when the compression flange is not restrained against relative lateral movement of the loaded and unloaded flanges.

For this beam, the top flange is laterally braced by the floor deck. The bottom flange is unrestrained at the support, but sidesway buckling requires relative movement between the loaded flange and the flange opposite the load. At a bearing support, both flanges are typically restrained by the bearing plate and bolted connections.

Additionally, if the compression flange is restrained against rotation (which occurs when the flange is attached to a slab or deck), sidesway buckling is not applicable per J10.4 commentary. Since this is an end support where the beam bears directly on a plate, and the deck provides lateral restraint:

Web sidesway buckling is deemed not applicable for this condition because the combined restraint from the deck and bearing plate prevents relative flange movement.

Step 4: Stiffener Requirement Decision

Summary of web limit states:

All web limit states are satisfied without bearing stiffeners. However, if the end reaction were increased to, say, Ru = 110 kips (a 30% increase), web crippling would exceed capacity (110/97.4 = 1.13 > 1.0), and bearing stiffeners would be required.

For educational purposes, we proceed with stiffener design as if the load exceeds capacity.

Step 5: Bearing Stiffener Design (AISC J10.8)

Step 5a: Stiffener Plate Geometry

Bearing stiffeners are provided in pairs, one on each side of the web. The stiffeners must:

• Extend from the loaded flange to within a close distance of the opposite flange (or bear on the opposite flange for end reactions).
• Be attached to the web with a continuous fillet weld or intermittent weld capable of transmitting the stiffener force to the web.

Stiffener width (bs): The stiffener width is limited by the flange width minus fillet radius minus web thickness allowance:

bs_max = (bf - tw) / 2 = (7.01 - 0.395) / 2 = 3.31 in.

Use bs = 3.0 in. on each side (provides clean bearing on flange).

Stiffener thickness (ts): The stiffener outstand must be compact. Per J10.8, the width-to-thickness ratio of the stiffener outstand must satisfy:

bs_stiff / ts ≤ 0.56 × sqrt(E/Fy) = 0.56 × sqrt(29,000/50) = 0.56 × 24.08 = 13.5

For bs_stiff = bs = 3.0 in. (full width from web face to stiffener edge), the minimum thickness is:

ts_min = bs / 13.5 = 3.0 / 13.5 = 0.222 in.

Use ts = 3/8 in. = 0.375 in. > 0.222 in. OK.

Stiffener clip: Provide a 1 in. × 1 in. clip at the web-flange junction to clear the fillet radius. The effective bearing width of the stiffener on the flange is:

bs_effective = bs - clip = 3.0 - 1.0 = 2.0 in. per stiffener

Bearing check on flange: The stiffener bears on the loaded flange. Bearing area of the pair of stiffeners:

A_bearing = 2 × bs_effective × ts = 2 × 2.0 × 0.375 = 1.50 in^2

Required bearing stress:

fp = Ru_required / A_bearing = 110 / 1.50 = 73.3 ksi

Compare to allowable bearing: phi × 1.8 × Fy = 0.75 × 1.8 × 50 = 67.5 ksi (per J8). 73.3 ksi > 67.5 ksi — marginal. Increase stiffener thickness.

Use ts = 1/2 in. = 0.50 in.:

A_bearing = 2 × 2.0 × 0.50 = 2.00 in^2
fp = 110 / 2.00 = 55.0 ksi < 67.5 ksi → OK.

Revised stiffener: Pair of plates, bs = 3.0 in., ts = 1/2 in., with 1 in. clip at the web-flange junction.

Step 6: Effective Column Check (AISC J10.8)

Bearing stiffeners at the end of a beam act as a short column carrying the concentrated reaction. The effective column section consists of the stiffener plates plus a portion of the web.

Step 6a: Effective Column Area

For end stiffeners, the effective web width on each side is 12tw (not to exceed the actual available web width):

web_width = 12 × tw = 12 × 0.395 = 4.74 in. ≤ available web width → OK.

Effective column area:

A_eff = 2 × (ts × bs) + 25 × tw^2   (note: 12tw per side for end stiffeners)
       = 2 × (0.50 × 3.0) + 2 × 12 × 0.395^2

Wait — the web area contribution: For interior stiffeners, the effective web strip is 25tw centered on each stiffener. For end stiffeners, the effective web strip is 12tw per AISC J10.8 Commentary. The area contributed by the web is:

A_web = 2 × 12 × tw × tw = 24 × 0.395^2 = 24 × 0.1560 = 3.745 in^2

Stylized: The web strip is effectively a rectangle of width 12tw and height tw (the web plate). So the cross-sectional area contributed by the web is 24tw^2 (12tw per side, two sides, each with area tw wide × plus 2 × 12tw × tw).

A_eff_stiff = 2 × 0.50 × 3.0 = 3.00 in^2
A_eff_web = 2 × 12 × tw × tw = 24 × 0.395^2 = 3.745 in^2
A_eff_total = 3.00 + 3.745 = 6.745 in^2

Step 6b: Moment of Inertia of Effective Column

The effective column is cruciform in shape: the web plate and two stiffener plates. The moment of inertia about the web axis (the buckling axis of the cruciform column) is:

I_eff = (ts × (2 × bs + tw)^3) / 12   (stiffener contribution about web axis)
        = (0.50 × (2 × 3.0 + 0.395)^3) / 12
        = (0.50 × 6.395^3) / 12
        = (0.50 × 261.5) / 12
        = 130.75 / 12
        = 10.90 in^4

Step 6c: Effective Length and Slenderness

For end bearing stiffeners, the effective length factor K = 0.75 per AISC J10.8 (both ends of the stiffener are connected, but the connection at the web provides partial fixity). The unbraced length is the clear web depth between fillets:

h_web = d - 2 × k_des = 23.6 - 2 × 1.01 = 21.58 in.

Effective length:

KL = 0.75 × 21.58 = 16.2 in.

Radius of gyration of the effective column:

r_eff = sqrt(I_eff / A_eff_total) = sqrt(10.90 / 6.745) = sqrt(1.616) = 1.271 in.

Slenderness:

KL/r = 16.2 / 1.271 = 12.74

Step 6d: Column Buckling Strength

For such a low slenderness, inelastic buckling governs. The column curve per Chapter E:

Fe = pi^2 × E / (KL/r)^2 = pi^2 × 29,000 / (12.74)^2 = 9.8696 × 29,000 / 162.3 = 1,764 ksi

Fy/Fe = 50 / 1,764 = 0.02835

Fcr = [0.658^(Fy/Fe)] × Fy = 0.658^0.02835 × 50 = 0.988 × 50 = 49.4 ksi

Step 6e: Design Column Strength

Pn = Fcr × A_eff_total = 49.4 × 6.745 = 333.1 kips
phi_c × Pn = 0.90 × 333.1 = 299.8 kips

Check: Required load Ru = 110 kips < 299.8 kips. Bearing stiffener column OK. Utilization = 110/299.8 = 0.367.

The effective column strength far exceeds the demand because the cruciform column is very stocky (KL/r = 12.7). Bearing stiffeners sized to meet the bearing stress requirement typically satisfy the column check by a wide margin.

Step 7: Weld Design — Stiffener to Web

The fillet weld connecting each stiffener to the web must transmit the stiffener force to the web. The required weld strength is the difference between the applied reaction and the capacity of the web alone.

Force that must be transferred through the stiffeners:

P_stiff = Ru - phi × Rn_web (where Rn_web is the governing web limit state)

The web alone (without stiffeners) can carry 97.4 kips (web crippling governs). For Ru = 110 kips:
P_stiff = 110 - 97.4 = 12.6 kips (the stiffeners carry the excess capacity)

For a more conservative design, assume the full reaction passes through the stiffeners.

Weld length per stiffener: The stiffener is welded to the web along the full web depth between the flange fillets:

L_weld_per_stiff = h_web = 21.58 in. (approximately)
Total weld length = 4 × 21.58 = 86.3 in. (two stiffeners, each welded both sides)

Minimum fillet weld size per AISC Table J2.4: For the W24x55 web thickness of 0.395 in. and stiffener thickness of 0.5 in., the minimum fillet weld size is 3/16 in. Use 1/4 in. fillet weld.

Weld strength per inch (E70XX electrode):

phi × 0.6 × FEXX × 0.707 × w = 0.75 × 0.6 × 70 × 0.707 × 0.25 = 10.47 ksi × 0.177 = 1.85 kips/in. (per sixteenth)
phi × Rn_weld_per_inch = 1.392 × D (in sixteenths)
                        = 1.392 × 4 = 5.57 kips/in.

Design weld strength:

phi × Rn_weld = 5.57 × 86.3 = 480 kips >> 110 kips → Weld is adequate.

Summary of Design Checks

For the design load of Ru = 85 kips, bearing stiffeners are not required. A 6 in. bearing plate is adequate. However, for the 110 kip condition, a pair of 3.0 in. × 1/2 in. bearing stiffeners with 1 in. clips and 1/4 in. fillet welds to the web provides adequate bearing capacity.

Frequently Asked Questions

When are bearing stiffeners required for steel beams?

Bearing stiffeners are required when the factored bearing force exceeds the design bearing strength of the web alone per AISC 360-22 Section J10. The four web limit states checked are: web local yielding (J10.2), web crippling (J10.3), web sidesway buckling (J10.4), and web compression buckling (J10.5). If any limit state is exceeded, bearing stiffeners must be provided. They are commonly needed for concentrated reactions exceeding 100 kips on rolled beams and at support reactions for deep slender-web girders.

How are bearing stiffeners sized per AISC J10?

Bearing stiffeners are sized as a pair of plates welded to the web and bearing on the flanges per J10.8. The stiffener width is governed by the bearing area on the flange and the local buckling limit (outstand width-to-thickness ≤ 0.56 sqrt(E/Fy)). The stiffener thickness is determined from the required area of the effective column section (stiffener plates plus web contribution of 12tw per side for end stiffeners or 25tw per side for interior stiffeners). The effective column length is 0.75h for end stiffeners and 0.75h for interior stiffeners checked per Chapter E.

What is the difference between web yielding, crippling, and buckling?

Web local yielding (J10.2) is crushing of the web directly under the bearing plate. Web crippling (J10.3) is compression buckling of the web near the flange-web junction. Web sidesway buckling (J10.4) is lateral buckling of the web relative to the compression flange. Web compression buckling (J10.5) is overall buckling of the web panel under a concentrated load applied to one flange. Each limit state has its own equation in AISC J10.

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Related References

• AISC Beam Design Example — W24x55
• Stiffener Design Reference
• Weld Design Reference
• AISC Steel Construction Tables
• How to Verify Calculations
• Steel Connection Types

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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.