Free Steel Plate Girder Calculator -- Design Guide

Design built-up steel plate girders for heavy loads and long spans where standard rolled wide-flange shapes are inadequate. The calculator checks flexural capacity of slender-web girders per AISC 360-22 Section F5, shear buckling with tension field action per Sections G2-G3, intermediate transverse stiffener design per G2.2, bearing stiffener design per J10.8, flange-to-web weld requirements per J2.2, and combined flexure-plus-shear interaction. Also covers AS 4100 Section 5 (plate girders), EN 1993-1-5 (plated structural elements), and CSA S16 Section 14.

Plate girders are fabricated by welding three plates: two flange plates and one web plate. The web is proportioned to be slender (high h/tw ratio, typically 100-300) to minimize steel weight, while the flanges carry the flexural compression and tension. The slender web buckles elastically in shear at a fraction of the yield strength, but post-buckling reserve through tension field action provides substantial additional capacity. This differentiates plate girders from rolled beams, which have stocky webs that reach full shear yield before buckling.

Applications: highway and railway bridge girders spanning 80-300+ ft, heavy industrial crane runway girders with moving concentrated loads, transfer girders in buildings supporting multiple columns above, long-span roof girders for auditoriums and arenas, and gantry girders for shipping and manufacturing facilities.

When plate girders are economical: when the required section depth exceeds 36-40 inches (beyond typical rolled W-shape depths), when the required flexural capacity exceeds the strongest rolled W-shape (W44x335 at Zx = 1,780 in^3), or when an optimized depth is needed for vertical clearance or architectural constraints. Plate girders can also be tapered (variable depth) or curved in plan, which rolled shapes cannot provide without expensive fabrication.

What this calculator does not cover: fatigue design for cyclically loaded crane or bridge girders (per AASHTO or AISC 360 Appendix 3), hybrid girders with different steel grades in flange and web, longitudinally stiffened girders, and non-rectangular flange plates (bulb flats or cover-plated girders).

How to Use This Calculator

Step 1 -- Enter girder geometry. Define the overall depth (web depth plus both flange thicknesses), flange width and thickness, web depth and thickness. For preliminary sizing: flange area Af ≈ Mu / (phi x Fy x d x 0.95), web depth h ≈ L/12 to L/15, web thickness tw ≈ h/150 to h/250 (typical range). The calculator computes section properties (area, Ix, Sx, Zx, h/tw ratio, flange slenderness bf/2tf) from the input geometry.

Step 2 -- Select materials. Choose flange and web steel grades independently. Flanges are typically A572 Gr 50 (Fy = 50 ksi) for most girders, or A709 Gr 50W for bridge applications requiring atmospheric corrosion resistance. The web is commonly A36 (Fy = 36 ksi) for economy, though the yield strength difference does not significantly affect web shear buckling strength since buckling is a stiffness-governed phenomenon. For hybrid girders (Fyf > Fyw), the flange strength is used for flexural checks but the web yield strength governs web local yielding at concentrated loads.

Step 3 -- Define loading and bracing. Enter uniform or concentrated loads, location of concentrated loads (for shear and web local checks), and lateral bracing spacing of the compression flange. The compression flange is considered braced if the lateral deflection of the flange is prevented at the brace point and the cross-section is restrained against twist. For unbraced segments, the lateral-torsional buckling (LTB) check per AISC 360 F5.2 applies to the compression flange plus one-third of the compression web height.

Step 4 -- Review flexural checks. The calculator classifies the cross-section for flexure: (a) flange compactness per AISC 360 Table B4.1b (bf/2tf ≤ 0.38 x sqrt(E/Fy) for compact), and (b) web slenderness classification. For plate girders, the web is invariably slender, triggering AISC 360 Section F5 provisions for slender-web members. The nominal flexural strength is the minimum of flange local buckling (F5.2), lateral-torsional buckling of the compression flange (F5.2-F5.4), and the tension flange yield limit (F5.5).

Step 5 -- Check shear and tension field action. For girders without transverse stiffeners (a/h > 3.0 or no stiffeners), shear strength is limited to the web shear buckling strength without tension field action (AISC 360 G2.1, Cv factor). For girders with transverse stiffeners at spacing a/h ≤ 3.0, tension field action is mobilized and the post-buckling shear strength is calculated per AISC 360 Section G3. The tension field action can provide 30-60% additional shear capacity beyond the elastic buckling shear strength.

Step 6 -- Design stiffeners. Bearing stiffeners at supports and concentrated load points are designed as compression members per AISC 360 J10.8, with an effective column section including the stiffener plate area plus a portion of the web extending 12tw on each side (for end stiffeners) or 25tw (for interior stiffeners). Intermediate transverse stiffeners are checked for minimum moment of inertia (Ist ≥ b x tw^3 x j per AISC 360 Eq G2-12) and for adequate area to anchor the tension field force.

Engineering Theory -- Plate Girder Behavior

Flexural Strength of Slender-Web Girders (AISC 360 F5)

Plate girders have webs with h/tw exceeding the limit for non-slender webs (h/tw > 5.70 x sqrt(E/Fy) = 137 for 50 ksi). The slender web is susceptible to bend buckling -- elastic buckling of the web under flexural compression. The compression portion of the web cannot reach yield, and the effective stress distribution is non-linear, with the peak compression at the compression flange reducing inward.

AISC 360-22 Section F5 addresses this through a reduced nominal flexural strength. The key limit states are:

Compression flange local buckling (F5.2): The flange slenderness ratio bf/2tf is compared to the compact/noncompact limits per Table B4.1b. Noncompact or slender flanges reduce Mn below My.

Lateral-torsional buckling (F5.2-F5.4): The compression flange can buckle laterally between brace points. The LTB capacity depends on the unbraced length Lb relative to the limiting lengths Lp and Lr. For slender-web girders, the LTB provisions use a reduced effective radius of gyration (rt) based on the compression flange plus the portion of web in compression.

Compression flange yielding (not typically governing): Tension flange yielding (F5.5) limits Mn to Sxt x Fy, which governs only for very unusual geometries where the tension flange is significantly smaller than the compression flange.

The interaction between flexure and shear is checked by comparing the ratio of required-to-available flexural strength to the ratio of required-to-available shear strength. Per AISC 360 G5:

Mu/(phi_Mn) + 0.625 x Vu/(phi_Vn) ≤ 1.375

Shear Buckling and Tension Field Action (AISC 360 G2-G3)

The web shear buckling capacity for an unstiffened girder is governed by the web shear buckling coefficient kv. For webs without transverse stiffeners, kv = 5.34 (simply supported at the flanges). The web shear buckling stress is:

Cv1 = 1.10 x sqrt(kv x E / Fy) / (h/tw)   for the inelastic buckling range
Cv2 = 1.51 x E x kv / ((h/tw)^2 x Fy)    for the elastic buckling range

For a typical plate girder with h/tw = 200 and kv = 5.34: Cv = 1.51 x 29,000 x 5.34 / (200^2 x 50) = 1.51 x 154,860 / 2,000,000 = 0.117. This means the elastic shear buckling stress is only 11.7% of Fy -- the web buckles at very low load. Without tension field action, the nominal shear strength would be Vn = 0.6 x Fy x Aw x Cv, which for h/tw = 200 gives only about 12% of the yield shear capacity.

By adding transverse stiffeners, the web buckling coefficient kv increases (kv = 5 + 5/(a/h)^2 for a/h ≤ 3.0), increasing the elastic buckling stress. More importantly, the stiffeners anchor the diagonal tension field that develops after buckling, providing post-buckling strength per AISC 360 Section G3:

Vn = 0.6 x Fy x Aw x [Cv + (1 - Cv) / (1.15 x sqrt(1 + (a/h)^2))]

The second term represents the tension field contribution. For a/h = 1.5 with h/tw = 200: kv = 5 + 5/1.5^2 = 7.22. Cv = 1.51 x 29,000 x 7.22 / (200^2 x 50) = 0.158. Vn = 0.6 x Fy x Aw x [0.158 + (1-0.158)/(1.15 x sqrt(1+1.5^2))] = 0.6 x Fy x Aw x [0.158 + 0.842/(1.15 x 1.803)] = 0.6 x Fy x Aw x [0.158 + 0.406] = 0.6 x Fy x Aw x 0.564 = 0.338 x Fy x Aw. The tension field action provides 250% more shear capacity than elastic buckling alone.

Bearing Stiffener Design (AISC 360 J10.8)

Bearing stiffeners are vertical plates welded to the web at support locations and under concentrated loads. They prevent web yielding and web crippling failures. The stiffener works as a column: the effective section includes the stiffener plate area on both sides of the web plus the web area extending 12tw (end stiffeners) or 25tw (interior) from the stiffener face.

The stiffener is checked for:

  1. Web yielding (J10.2): Rn = (2.5k + lb) x Fyw x tw for interior conditions
  2. Web crippling (J10.3): Rn depends on the bearing length, web thickness, and flange thickness
  3. Stiffener compression (J10.8): The stiffener cross-section is checked as a column per AISC 360 Chapter E with KL = 0.75h (interior) or KL = h (end). The slenderness limit for the stiffener plate is b/t ≤ 0.56 x sqrt(E/Fy) per Table B4.1a (non-slender element in compression).

Worked Example -- Heavy Transfer Girder

Problem: Design a plate girder to support three columns from upper stories, spaced at 15 ft o.c., on a 45-ft simply supported span. Factored concentrated loads: P1 = P2 = P3 = 350 kips at quarter points. Compression flange laterally braced at load points (every 11.25 ft). Steel: A572 Gr 50 flanges, A36 web. Use LRFD.

Step 1 -- Preliminary sizing. Max moment at midspan (three equal point loads at quarter points): Mu = 350 x (11.25 + 22.5) = 350 x 33.75 = 11,813 kip-ft. (Actually, with three point loads: Mu_max = 350 x 22.5 = 7,875 kip-ft, verified.) Required Af ≈ Mu/(phi x Fy x d): assume d = 60 in. Af = 7,875 x 12/(0.90 x 50 x 60 x 0.95) = 94,500/2,565 = 36.8 in^2. Use 24 in wide flange x 1.75 in thick: Af = 24 x 1.75 = 42.0 in^2 > 36.8. OK. Web depth: d - (2 x 1.75) = 56.5 in. Use h = 56 in. Web thickness: h/tw ≈ 200, tw = 56/200 = 0.28 in. Use tw = 5/16 in (0.313 in). h/tw = 56/0.313 = 179.

Step 2 -- Section properties. Total depth = 56 + 2 x 1.75 = 59.5 in. Ix = tw x h^3/12 + 2 x Af x (h/2 + tf/2)^2 = 0.313 x 56^3/12 + 2 x 42.0 x (28 + 0.875)^2 = 0.313 x 175,616/12 + 84 x (28.875)^2 = 4,580 + 84 x 833.8 = 4,580 + 70,037 = 74,617 in^4. Sx = Ix/(d/2) = 74,617/29.75 = 2,509 in^3. Zx ≈ 2 x Af x (h/2 + tf/2) + tw x h^2/4 = 84 x 28.875 + 0.313 x 56^2/4 = 2,426 + 245 = 2,671 in^3 (approximate plastic, check).

Step 3 -- Flexural check (AISC 360 F5). Flange slenderness: bf/2tf = 24/(2 x 1.75) = 6.86. Compact limit = 0.38 x sqrt(29,000/50) = 0.38 x 24.1 = 9.15. Flange is compact. OK. Web slenderness: h/tw = 179. Non-slender limit = 5.70 x sqrt(29,000/50) = 137. Web is slender -- use F5 provisions.

For LTB: Lb = 11.25 ft = 135 in. rt = bf/sqrt(12 x (1 + h x tw/(6 x bf x tf))) = 24/sqrt(12 x (1 + 56 x 0.313/(6 x 24 x 1.75))) = 24/sqrt(12 x (1 + 17.5/252)) = 24/sqrt(12 x 1.069) = 24/sqrt(12.83) = 24/3.58 = 6.70 in. Lp = 1.1 x rt x sqrt(E/Fy) = 1.1 x 6.70 x 24.1 = 177.7 in > Lb = 135 in. LTB does not govern -- the girder is in the plastic range for LTB.

Flange local buckling also does not govern (compact flange).

Check AISC 360 Eq F5-7 for slender web: Rpg = 1 - aw/(1,200 + 300 x aw) x (h/tw - 5.7 x sqrt(E/Fy)) ≤ 1.0, where aw = h x tw/(bf x tf) = 56 x 0.313/(24 x 1.75) = 17.53/42 = 0.417. Rpg = 1 - 0.417/(1,200 + 300 x 0.417) x (179 - 137) = 1 - 0.417/(1,200 + 125) x 42 = 1 - 0.417/1,325 x 42 = 1 - 0.0132 = 0.987.

Mn = Rpg x Fy x Sx = 0.987 x 50 x 2,509 / 12 = 10,315 kip-ft. phi_Mn = 0.90 x 10,315 = 9,284 kip-ft. DCR = 7,875 / 9,284 = 0.85. Passes for flexure.

Step 4 -- Shear check with tension field action. Maximum shear at support: Vu = 350 x (1.5 + 1.0/2) = 350 x 2.0 = 700 kips.

Try intermediate stiffeners at a = 56 in (a/h = 1.0). Transverse stiffeners required for tension field action per G3: a/h = 1.0 ≤ 3.0 and a/h ≤ [260/(h/tw)]^2 = (260/179)^2 = 2.11. OK.

kv = 5 + 5/(a/h)^2 = 5 + 5/1.0 = 10.0. Cv = 1.51 x 29,000 x 10.0 / (179^2 x 50) = 1.51 x 290,000 / 1,602,050 = 0.273. Aw = tw x h = 0.313 x 56 = 17.53 in^2. Tension field contribution: (1 - 0.273)/(1.15 x sqrt(1 + 1.0^2)) = 0.727/(1.15 x 1.414) = 0.727/1.626 = 0.447. Vn = 0.6 x 50 x 17.53 x [0.273 + 0.447] = 0.6 x 50 x 17.53 x 0.720 = 379 kips. phi_Vn = 0.90 x 379 = 341 kips. DCR = 700/341 = 2.05 -- FAILS in shear.

The web is too thin for the shear demand. Try tw = 5/8 in (0.625 in): Aw = 56 x 0.625 = 35.0 in^2. h/tw = 89.6 (no longer slender for shear -- this is a stocky web).

Check h/tw = 89.6: Non-slender web limit for shear = 2.24 x sqrt(29,000/50) = 2.24 x 24.1 = 53.9. h/tw > 53.9, so shear buckling still applies. kv = 10.0, Cv = 1.51 x 29,000 x 10.0 / (89.6^2 x 50) = 437,900/401,408 = 1.09 > 1.0, so Cv = 1.0 (web shear yield controls, no buckling).

Vn = 0.6 x Fy x Aw x Cv = 0.6 x 50 x 35.0 x 1.0 = 1,050 kips. phi_Vn = 0.90 x 1,050 = 945 kips. DCR = 700/945 = 0.74. Passes in shear with tw = 5/8 in.

With the thicker web, recheck flexure: Ix_new = 0.625 x 56^3/12 + 84 x (28.875)^2 = 9,150 + 70,037 = 79,187 in^4. Sx = 79,187/30.44 = 2,601 in^3 (depth increased slightly with constant flange thickness). Rpg: aw = 56 x 0.625/(24 x 1.75) = 35/42 = 0.833. h/tw = 89.6 < 137 so web is non-slender -- Rpg = 1.0. Mn = 50 x 2,601/12 = 10,838 kip-ft. phi_Mn = 9,754 kip-ft. DCR = 0.81. Still passes.

Step 5 -- Flexure-shear interaction. Mu/(phi_Mn) = 0.81. Vu/(phi_Vn) at section of interest: at the quarter span (first load), Vu = 350 kips, phi_Vn = 945 kips. Vu/phi_Vn = 0.37. Interaction: 0.81 + 0.625 x 0.37 = 0.81 + 0.23 = 1.04 ≤ 1.375. Passes.

Step 6 -- Bearing stiffener at support. Support reaction = 700 kips. Try two 8 in x 1.25 in plates, A36, on each side of web. Effective column section: stiffener area = 4 x 8 x 1.25 = 40.0 in^2. Web contribution: 12 x 0.625 = 7.5 in (length) x 0.625 = 4.69 in^2. Total A_eff = 44.7 in^2. I_stiffener (about web centerline): 2 x [1.25 x (2 x 8 + 0.625)^3/12] ≈ 2 x [1.25 x 16.63^3/12] = 2 x [1.25 x 3,834/12] = 2 x 399 = 798 in^4. r = sqrt(798/44.7) = 4.22 in. KL = 0.75 x 56 = 42 in (interior stiffener fixity from flanges). KL/r = 42/4.22 = 9.95. phi_Pn ≈ 0.90 x 36 x 44.7 = 1,448 kips (stocky, Fcr ≈ Fy). DCR = 700/1,448 = 0.48. Passes.

Result: Plate girder: 24 x 1.75 in A572 Gr 50 flanges, 56 x 5/8 in A36 web, total depth 59.5 in. Intermediate stiffeners at 56 in spacing (a/h = 1.0), 5 x 5/8 in plates both sides. Bearing stiffeners at supports: 8 x 1.25 in plates, A36. Shear controlled the web thickness; the flexural capacity is generous due to the deep section. Girder weight approximately 570 plf (vs W44x335 at 335 plf -- the built-up girder uses 70% more steel but provides 4x the moment capacity and is 15 inches deeper).

Frequently Asked Questions

What is the economic span range for plate girders versus rolled sections?

Plate girders become economical when spans exceed 60-80 ft or when the required flexural capacity exceeds that of the deepest rolled W-shapes (W44x335, Zx = 1,780 in^3). Between 40-60 ft spans, a deep W-shape (W40 or W44) may be more economical than a built-up plate girder due to lower fabrication cost. For bridge girders with spans over 100 ft, plate girders are the standard choice.

What is tension field action in plate girders?

Tension field action is the post-buckling shear resistance that develops in slender webs with adequate transverse stiffeners. After the web buckles in shear, diagonal tension develops along the web's tension direction (approximately 45 degrees). The tension field is anchored by the transverse stiffeners and the flanges, creating a Pratt truss-like load path: the web carries diagonal tension, stiffeners carry compression (like verticals), and the flanges act as chords. AISC 360-22 Section G3 provides the design equations. This mechanism provides 30-60% additional shear capacity beyond elastic buckling and is available only when stiffener spacing a/h ≤ 3.0.

When are transverse and bearing stiffeners required?

Transverse (intermediate) stiffeners are required when either: (a) the nominal shear strength without tension field action is inadequate for the design shear, or (b) the a/h ratio exceeds 3.0 and web shear buckling controls. Bearing stiffeners are required at supports and under concentrated loads wherever web yielding (J10.2), web crippling (J10.3), or sidesway web buckling (J10.4) govern. AISC 360-22 J10.8 requires bearing stiffeners to meet minimum stiffness (ss ≥ bf/2 - tw/2 to engage the flange fully) and to be designed as compression columns.

What flange-to-web weld size is required for plate girders?

The flange-to-web fillet weld must transfer the horizontal shear at the flange-web interface. The shear flow q = V x Q / I where Q is the first moment of the flange area about the neutral axis. For a 60-inch girder with V_max = 700 kips: Q ≈ 42 x (28 + 0.875) = 1,213 in^3. q = 700 x 1,213 / 79,187 = 10.7 kips/in. Required weld throat per unit length, each side: t_weld = q / (2 x phi x 0.60 x FEXX) = 10.7 / (2 x 0.75 x 0.60 x 70) = 10.7/63 = 0.170 in. Use 3/16 in fillet weld (throat = 0.133 in) -- close, check: 2 x 0.75 x 0.60 x 70 x 0.133 = 8.4 kips/in < 10.7. Increase to 1/4 in fillet weld (throat = 0.177 in): capacity = 2 x 0.75 x 0.60 x 70 x 0.177 = 11.2 kips/in > 10.7. Use 1/4 in fillet weld each side, continuous.

Which design standards cover plate girder design?

AISC 360-22 Sections F5 (flexure of slender-web members) and G2-G3 (shear) in the US. AS 4100 Section 5 (plate girders) in Australia. EN 1993-1-5 (plated structural elements) in Europe, which uses the rotated stress field method rather than the Cardiff tension field model used by AISC. CSA S16 Section 14 (plate walls and plate girders) in Canada, which follows an approach similar to AISC with some differences in the tension field coefficient.

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Disclaimer (Educational Use Only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice. All structural designs must be independently verified by a licensed Professional Engineer (PE) or Structural Engineer (SE) registered in the project jurisdiction. The site operator disclaims all liability for any loss or damage arising from the use of this page or the associated calculator tool. Results are preliminary -- not for construction.