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.

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/(2tf) <= 0.56sqrt(E/Fy) for compact flanges.
• Minimum flange proportion: bf >= h/6 (to prevent lateral instability and ensure adequate LTB resistance).

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).

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.

Transverse stiffener design (Section G2.3)

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

• Moment of inertia: Ist >= btw^3j, 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

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)

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 = 720.4375 = 31.5 in^2. h/tw = 72/0.4375 = 164.6. kv = 5 + 5/1.33^2 = 5 + 2.82 = 7.82. 1.37sqrt(7.8229000/50) = 1.3767.4 = 92.3. Since 164.6 > 92.3, Cv2 = 1.517.8229000/(164.6^2*50) = 252.6 = 0.253.

With tension field: phiVn = 0.900.65031.5(0.253 + 0.747/(1.15sqrt(1+1.77))) = 850.5(0.253 + 0.390) = 850.5*0.643 = 547 kips > 450 kips OK.

Without TFA: phiVn = 0.900.65031.50.253 = 215 kips -- FAILS. Tension field action increases capacity by 154%.

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]

For a 72-inch girder with 20x1.5 flanges at maximum shear, typical weld sizes are 5/16" to 3/8" continuous fillet welds. The weld must be continuous (not intermittent) in 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. As a rule of thumb, web material cost is about 40% and fabrication (cutting, welding, stiffeners) about 60% of total girder cost.

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.

Run this calculation

• Beam Capacity Calculator
• Section Properties Database
• Welded Connections Calculator

Related references

• Lateral-Torsional Buckling
• Weld Joint Types
• Minimum Fillet Weld Size
• Plate Weight Reference
• 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.