Plate Girder Design — AISC 360 Chapter G Shear and Stiffener Reference

Plate girders are built-up I-shaped members fabricated from individual plates welded together, used when rolled W-shapes cannot provide the required depth, span, or capacity. Unlike rolled sections, plate girders have slender webs that require explicit checks for web shear buckling, tension field action, and stiffener design. AISC 360-22 Chapter G governs shear design and AISC 360-22 Section F13 covers proportioning limits.

When to use a plate girder

Rolled W-shapes go up to about W44x335 (44 inches deep, 335 lb/ft). When spans, loads, or clearance requirements exceed what rolled shapes can handle, plate girders fill the gap. Typical applications include transfer beams carrying column loads, long-span roof girders (80-200 ft), bridge girders, and crane runway girders supporting heavy moving loads.

Plate girder vs. rolled beam decision guide

Proportioning limits (AISC 360 Section F13)

• Web slenderness: h/tw <= 260 (without stiffeners). With transverse stiffeners: h/tw up to 11.7*sqrt(E/Fy) = 280 for Fy = 50 ksi.
• Flange width-to-thickness: bf/(2*tf) <= 0.56*sqrt(E/Fy) for compact flanges.
• Minimum flange proportion: bf >= h/6 (to prevent lateral instability and ensure adequate LTB resistance).

Proportioning limits by Fy

Web shear strength (Chapter G)

Without tension field action (Section G2.1)

phiVn = phi * 0.6*Fy*Aw*Cv1     [phi = 1.00 for h/tw <= 2.24*sqrt(E/Fy)]
phiVn = phi * 0.6*Fy*Aw*Cv1     [phi = 0.90 otherwise]

Where Aw = d*tw (web area), and Cv1 is the web shear coefficient from AISC Table G2-1:

The plate buckling coefficient kv = 5 for unstiffened webs, and kv = 5 + 5/(a/h)^2 for stiffened webs (where a = stiffener spacing).

Cv1 values by h/tw and stiffener spacing (Fy = 50 ksi)

With tension field action (Section G2.2)

For webs with transverse stiffeners spaced at a/h <= 3.0, post-buckling strength from tension field action can be utilized:

phiVn = 0.90 * 0.6*Fy*Aw * (Cv2 + (1 - Cv2)/(1.15*sqrt(1 + (a/h)^2)))

Tension field action develops diagonal tension in the web after initial shear buckling, similar to a Pratt truss. This can increase shear capacity by 30-80% for slender webs.

Tension field action capacity increase

Values assume Aw = 31.5 in^2 (72 in. x 7/16 in. web), Fy = 50 ksi.

Transverse stiffener design (Section G2.3)

Transverse (intermediate) stiffeners prevent web shear buckling and anchor the tension field. Requirements:

• Moment of inertia: Ist >= b*tw^3*j, where j = 2.5/(a/h)^2 - 2 >= 0.5
• Width: bs >= h/30 and bs >= bf/6 (for adequate bearing area)
• Thickness: ts >= bs/15 (to prevent local buckling of the stiffener itself)
• Fit: stiffeners may be fitted to the compression flange but must be stopped short (4tw to 6tw) of the tension flange to avoid fatigue-sensitive welds in the tension zone

Stiffener sizing by web depth

Stiffener pairs (one each side of web) are standard for webs deeper than 48 in.

Bearing stiffener design (Section J10.8)

Bearing stiffeners are required at concentrated load points and supports where the web cannot resist the full bearing force. They are designed as columns using a cruciform cross-section consisting of the stiffener plates plus a strip of web (25tw on each side for interior stiffeners, 12tw for end stiffeners).

Effective column area: Aeff = 2*bs*ts + (25tw)*tw  [interior]
Effective length: KL = 0.75*h (AISC recommends K = 0.75)

Bearing stiffener capacity by web depth (Fy = 50 ksi)

Check this effective column against compression per Chapter E with phi = 0.90.

Worked example — 72-inch plate girder

Given: Span = 100 ft, Vu = 450 kips. Web: 72 x 7/16 in (tw = 0.4375 in). Flanges: 20 x 1.5 in. Fy = 50 ksi. Transverse stiffeners at a = 8 ft (a/h = 96/72 = 1.33).

Web shear: Aw = 72*0.4375 = 31.5 in^2. h/tw = 72/0.4375 = 164.6. kv = 5 + 5/1.33^2 = 5 + 2.82 = 7.82. 1.37*sqrt(7.82*29000/50) = 1.37*67.4 = 92.3. Since 164.6 > 92.3, Cv2 = 1.51*7.82*29000/(164.6^2*50) = 0.253.

With tension field: phiVn = 0.90*0.6*50*31.5*(0.253 + 0.747/(1.15*sqrt(1+1.77))) = 850.5*(0.253 + 0.390) = 850.5*0.643 = 547 kips > 450 kips OK.

Without TFA: phiVn = 0.90*0.6*50*31.5*0.253 = 215 kips -- FAILS. Tension field action increases capacity by 154%.

Worked example — bearing stiffener at support

Given: Same 72-inch girder. Reaction Ru = 350 kips. Web: 72 x 7/16 in. Bearing stiffeners: PL5/8x6 each side of web.

Step 1 — Effective area: Aeff = 2(6 x 0.625) + (25 x 0.4375) x 0.4375 = 7.50 + 4.79 = 12.29 in^2

Step 2 — Effective length and radius of gyration: KL = 0.75 x 72 = 54 in. Cruciform section I = 2(0.625 x 6^3/12) = 22.5 in^4. r = sqrt(22.5/12.29) = 1.35 in.

Step 3 — Slenderness and capacity: KL/r = 54/1.35 = 40. Fe = pi^2 x 29000/40^2 = 179 ksi. Fcr = 0.658^(50/179) x 50 = 46.0 ksi. phiPn = 0.90 x 46.0 x 12.29 = 509 kips > 350 kips OK.

Flange-to-web weld design

The flange-to-web fillet weld must transfer the horizontal shear flow:

q = V*Q/(I)    [shear flow, kips/in]

Typical flange-to-web weld sizes

phi x Rn per inch for 5/16 fillet = 6.95 kips/in (E70XX). Two-sided 5/16 fillet = 13.9 kips/in capacity. Continuous welds required for seismic applications per AISC 341.

Practical tip: optimizing plate girder economy

The most economical plate girder typically has: (1) the deepest web the structure can accommodate, (2) the thinnest web allowed by shear with tension field action, (3) compact flanges sized for moment, and (4) stiffeners spaced to provide adequate shear capacity without being so close that fabrication cost exceeds the material savings.

Cost optimization: web thickness vs. stiffener spacing

The 7/16 in. web with 8 ft stiffener spacing is the sweet spot for a 72-in. girder at this shear demand. Web material cost is about 40% and fabrication about 60% of total girder cost.

Code comparison for plate girder design

AISC 360-22 Chapter F Plate Girder Overview

AISC 360-22 Chapter F governs the design of plate girders for flexure. The key distinction from rolled beam design is the treatment of slender webs that buckle before the full plastic moment is reached. The applicable sections are:

For plate girders, Section F4/F5 provides the nominal flexural strength Mn based on the lateral-torsional buckling (LTB), compression flange local buckling (FLB), and web plastification limit states. The flange strength is reduced by the plate girder bending strength reduction factor Rpg (per AISC Section F5.3) to account for web bend-buckling.

Web Slenderness Classification

The web slenderness ratio determines whether tension field action can be used and what shear strength equations apply per AISC Chapter G:

For ASTM A992 (Fy = 50 ksi), the compact web limit is h/tw = 2.24 _ sqrt(29,000/50) = 53.9, and the noncompact limit is h/tw = 3.76 _ sqrt(29,000/50) = 90.6. Most plate girders have h/tw > 90 and are classified as slender.

Stiffener Design per AISC Chapter G

Plate girder stiffeners are required to prevent web shear buckling and enable tension field action. AISC Chapter G2.2 and G2.3 provide the design requirements:

Intermediate stiffener requirements per AISC G2.3:

Required moment of inertia:
Ist >= (j^2 / 50) * (2.5 / (a/h))^2 - 2 >= 0.5 (in4)

Where: j = a/h - 0.192 * (h/tw) * sqrt(Fy / E)

• Stiffeners must extend full depth of web
• Minimum width of each stiffener element: 2 in. plus half the web thickness per side
• Maximum stiffener spacing: a/h <= 3.0 for tension field action (no limit without TFA)
• Bearing stiffeners are designed as columns per AISC J10.8 with an effective cross-section including the stiffener plus a strip of web

Tension Field Action (TFA) per AISC G2.2

Tension field action is the post-buckling shear resistance provided by the web acting as a diagonal tension field between stiffeners. This can increase shear capacity by 30--60% over web shear buckling alone:

TFA is NOT permitted in the following situations (AISC G2.2 exceptions):

• End panels of girders (no anchorage available at the support)
• Panels where the aspect ratio a/h > 3.0
• Girders with slender webs where no intermediate stiffeners are provided
• Panels subject to significant combined shear and moment interaction without proper checking

The economic impact of TFA is substantial. Without tension field action, a typical plate girder web might need to be 40--50% thicker to meet the same shear demand, adding 15--25% to the total girder weight.

Weld Requirements for Plate Girders

Welds connecting flanges to web and stiffeners to web must be carefully designed for plate girders:

Flange-to-web weld size:

Required weld strength per unit length:
w = V * Q / (I * 2)  (for weld on both sides of web)

Where:
V = maximum shear at the point
Q = first moment of flange area about neutral axis
I = moment of inertia of girder
2 = two welds (one on each side of web)

The weld size should be checked at multiple points along the span because shear varies. In many plate girders, the flange-to-web weld is smallest at midspan (low shear) and largest at supports (high shear), leading to variable weld sizing along the length.

Plate Girder vs. Rolled Beam Comparison

Economical crossover point: for spans exceeding 60 ft or column reactions exceeding 500 kips, a plate girder typically becomes more economical than the heaviest rolled W-shape despite higher fabrication cost, because the web and flanges can be optimized independently.

Common mistakes

1. Using rolled-beam shear equations for plate girders. Rolled beams use Cv1; plate girders with slender webs need the full Cv2/TFA treatment.
2. Forgetting bearing stiffeners at supports. Even if web shear is adequate, concentrated reactions can cause web crippling or yielding at supports.
3. Ignoring stiffener fit-up details. The gap between stiffener and tension flange is critical for fatigue -- this detail is often missed in detailing.
4. Not checking web bend-buckling (Section F13.4). For deep webs under flexure, phi*Rpg reduction applies to flanges.
5. Using kv = 5 for stiffened webs. The stiffener spacing reduces kv; using the unstiffened value (kv = 5) is unconservative for a/h < 3.

Frequently asked questions

When should I use a plate girder instead of a rolled beam? When span exceeds 60 ft, or when the required depth exceeds 44 in. (deepest rolled W-shape), or when a lighter section than any rolled shape can handle the loads.

What is tension field action? After a slender web buckles in shear, diagonal tension stresses develop that carry additional load, similar to a Pratt truss. This post-buckling reserve can increase shear capacity by 30-80%.

Do I always need stiffeners in a plate girder? Not always. If the web is thick enough that h/tw < 1.10*sqrt(kv*E/Fy) and Cv1 = 1.0, stiffeners are not needed for shear. However, bearing stiffeners are almost always needed at supports and concentrated load points.

How do I size flange-to-web welds? Calculate the shear flow q = VQ/I at the flange-web interface. Select a continuous fillet weld size with phiRn >= q. For plate girders, 5/16 to 3/8 in. fillet welds each side are typical.

What is the maximum web slenderness for a plate girder? AISC limits h/tw to 260 without stiffeners. With transverse stiffeners, the limit increases to 11.7*sqrt(E/Fy) = 280 for Fy = 50 ksi.

Can I use partial penetration welds for flange-to-web joints? No. Flange-to-web joints should use continuous fillet welds or CJP groove welds. Intermittent welds are not permitted for plate girders in seismic applications per AISC 341.

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Related references

• Lateral-Torsional Buckling
• Weld Joint Types
• Minimum Fillet Weld Size
• Plate Weight Reference
• Compact Section Limits
• Slender Wall Design
• Weld Electrodes
• Steel Grades
• How to Verify Calculations

Disclaimer

This page is for educational and reference use only. It does not constitute professional engineering advice. All design values must be verified against AISC 360-22 Chapters F and G and the governing project specification. The site operator disclaims liability for any loss arising from the use of this information.