Steel Bridge Girder Design — Plate Girders, I-Girders, Tub Girders

Steel bridge girders form the primary load-carrying elements of steel bridges. This guide covers design and detailing of plate I-girders, box/tub girders, stiffeners, and cross-frames per AASHTO LRFD.

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Core calculations run via WebAssembly in your browser with step-by-step derivations across AISC 360, AS 4100, EN 1993, and CSA S16 design codes. Results are preliminary and must be verified by a licensed engineer.

Overview of Steel Bridge Girder Systems

Steel bridge girders are the primary load-carrying members in steel bridges. They span between supports (abutments and piers) and directly support the bridge deck. Girder systems are categorized by their cross-section and structural behavior:

Rolled beam bridges — The simplest steel bridge, using standard W-shapes (W27 through W44). Limited to spans up to approximately 60 ft (18 m) due to the maximum available rolled section depth (~44 inches). Economical for short-span bridges where fabrication cost must be minimized.

Plate I-girders — Fabricated by welding three plates (two flanges and one web) into an I-shaped section. The depth, flange width, and flange thickness can be optimized for the specific span and loading. Typical for medium spans (60-200 ft / 18-60 m). The web depth can vary from 36 to 120 inches or more, and flange plates can be up to 4 inches thick.

Box/tub girders — Closed-section girders (rectangular or trapezoidal) that provide superior torsional stiffness. The trapezoidal tub girder is commonly used for horizontally curved bridges. Tub girders typically range from 4-12 ft (1.2-3.7 m) in width and 4-15 ft (1.2-4.6 m) in depth.

Hybrid girders — Plate girders with higher-strength steel in the flanges (typically HPS 70W or HPS 100W) and lower-strength steel in the web (Grade 50). This optimizes material usage and reduces fabrication costs.

Plate Girder Design per AASHTO LRFD Section 6

Section Proportion Limits (AASHTO 6.10.2)

For I-section plate girders, AASHTO LRFD specifies:

Web depth D: web thickness tw ≤ 150 for webs without longitudinal stiffeners, ≤ 300 with longitudinal stiffeners
Flange width bf: bf ≥ D/6, bf ≥ 12 inches, and bf / (2tf) ≤ 12.0 for compression flanges
Flange thickness: tf ≥ 1.1 × tw (for weather zone considerations)
Flange overhang: for compression flanges, λf = bf/(2tf) ≤ 0.38√(E/Fyc) for compact sections

Flexural Design (AASHTO 6.10.6)

Flexural design of I-girders follows a hierarchy of checks:

Compact section positive flexure — For sections satisfying web slenderness Dcp ≤ 3.76√(E/Fyc): the nominal flexural resistance Mn = 1.3 × Rh × My for the compression flange, where Rh is the hybrid factor (1.0 for homogeneous girders, 0.90-0.95 for hybrid girders) and My is the yield moment at the section.

Non-compact section positive flexure — For sections not satisfying compact limits: Mn = Rb × Rh × My, where Rb is the web load-shedding factor that accounts for web bend-buckling. Rb = 1 - (ar/(1200+300ar) × (Dc/tw - λb) where ar is the web area ratio.

Negative flexure — For composite sections in negative moment (over piers): the steel girder alone (without concrete slab in tension) must resist negative moment. The concrete slab is assumed cracked in tension. The nominal flexural resistance is the minimum of the compression flange strength (based on local buckling and LTB) and the tension flange strength (based on yield).

Lateral-torsional buckling (AASHTO 6.10.8): For discretely braced compression flanges:

Lb ≤ Lp: Mn = Rb × Rh × Myc (full plastic capacity)
Lp < Lb ≤ Lr: Mn = Cb × Rb × Rh × Myc × [1 - 0.5 × (Lb-Lp)/(Lr-Lp)] ≤ Rb × Rh × Myc
Lb > Lr: Mn = Cb × Rb × Rh × Myc × (Lr/Lb)² ≤ Rb × Rh × Myc (elastic LTB)

The limiting lengths Lp and Lr are per AASHTO 6.10.8.2.3. The moment gradient factor Cb accounts for the shape of the moment diagram between brace points.

Shear Design (AASHTO 6.10.9)

Shear design considers both the web contribution and the tension field action (for stiffened webs):

Unstiffened webs: Vn = C × Vp, where C is the ratio of shear buckling resistance to yield strength, and Vp = 0.58 × Fyw × D × tw.

Stiffened webs (transverse intermediate stiffeners): Vn = Vp × [C + 0.87(1-C)/√(1+(do/D)²)], where do is the transverse stiffener spacing. For interior panels (not adjacent to supports), the term 0.87 represents the post-buckling tension field action. For end panels, the tension field action is limited and Vn = C × Vp.

The shear resistance is φvVn with φv = 0.90 (AASHTO 6.5.4.2).

Stiffener Design

Transverse Intermediate Stiffeners (AASHTO 6.10.11.1)

Transverse stiffeners are required when the shear demand exceeds the shear resistance of the unstiffened web. Design requirements:

Stiffener spacing do: The spacing must satisfy: do/D ≤ 3.0, and for end panels: do ≤ 1.5D
Projecting width: bt ≥ 2.0 + D/30 (inches), where bt is the stiffener width
Thickness: bt/tp ≤ 0.48 × √(E/Fys) (local buckling limit)
Moment of inertia: It ≥ do × tw³ × J, where J = 2.5/(do/D)² - 2.0 ≥ 0.5
Area: Ast ≥ 0.15 × B × D × tw × (1-C) × (Vu/Vr) × (Fyw/Fys), where B = 1.0 for stiffener pairs

Bearing Stiffeners (AASHTO 6.10.11.2)

Bearing stiffeners are required at supports and at concentrated load points. Design per AASHTO 6.10.11.2:

Must extend from the full depth from flange to flange
Designed as columns resisting the full reaction: φcPn = φc × Fcr × As × (0.80 factor for eccentricity)
The effective column section = stiffeners + a strip of web of width 12tw (on each side of the stiffener)
Minimum stiffener width: bf - 2 inches (to clear the flange-to-web weld)
Stiffener-to-web weld: full-length fillet weld on both sides
The stiffener-to-flange connection must develop the full bearing reaction through direct contact (snug fit) or weld

Tub Girders (AASHTO Section 6.11)

Tub girders (trapezoidal box girders) are used for horizontally curved bridges where torsional stiffness is critical:

Advantages: (1) Closed cross-section provides superior torsional resistance (J is 10-100× that of an I-girder), (2) Curved alignment is naturally accommodated — the cross-section rotations due to torsion are much smaller, (3) Narrower deck overhang reduces deck cost, (4) Aesthetic appearance for urban settings.

Design requirements per AASHTO 6.11:

Cross-section: Minimum web inclination: 1:4 (horizontal:vertical). Maximum web inclination: 1:1. Minimum bottom flange width: 4 ft (1.2 m).
Internal cross-frames: Required at maximum spacing of 25 ft (7.6 m). Must be designed for the internal distortion of the box under torsional loading.
Top flange lateral bracing: Required during construction before the concrete deck cures. Lateral brace spacing: maximum 20 ft (6.1 m).
Web slenderness: D/tw ≤ 150 for straight girders, ≤ 120 for curved girders
Bottom flange width-thickness: wfc/tfc ≤ 0.38√(E/Fyc) for compact sections
Top flange bracing: For tub girders without a cured concrete deck, the top flanges require discrete lateral bracing to prevent LTB.

Construction sequence: (1) Erect tub girder sections on temporary support towers, (2) Make field splices (full-penetration groove welds for flanges, bolted splice plates for webs), (3) Install top flange lateral bracing, (4) Place precast or cast-in-place deck panels, (5) Connect shear studs and place deck closure pours.

Hybrid Girders

Hybrid girders use different steel grades for flanges and webs to optimize material cost. Common combinations:

Grade 50 web with HPS 70W (70 ksi) flanges — most common, 30% increase in flexural capacity for ~15% increase in flange cost
Grade 50 web with HPS 100W flanges — for very long spans where girder depth must be minimized
Grade 50 web with Grade 50 flanges — homogeneous girder, simplest to fabricate

Per AASHTO 6.10.1.4, hybrid girders must use the hybrid factor Rh ≤ 1.0. For flanges with Fyf > 1.25Fyw: Rh = (12 + β(3ρ - ρ³)) / (12 + 2β), where β = (Dn/D) × (tw/tfc) × (Fyw/Fyf) × (bfc/tfc) and ρ = Fyw/Fyf.

Cross-Frame Design

Cross-frames (also called diaphragms) provide lateral stability and load distribution between girders:

Intermediate cross-frames: Per AASHTO 6.7.4, intermediate cross-frames are required: (1) at maximum 25 ft (7.6 m) spacing, (2) at points of abrupt changes in girder cross-section, and (3) for curved girders, at closer spacing based on curvature.

End cross-frames: Required at all supports to provide lateral restraint to the girder compression flanges and to transfer lateral loads to the bearings.

Cross-frame types: X-type (most common), K-type (for deep girders where X-type would have excessive member slenderness), and single-diagonal (for shallow girders).

Design forces: Cross-frames are designed for: (1) lateral wind loads transferred through the deck, (2) lateral seismic loads, (3) centrifugal forces on curved bridges, and (4) constructability loads during steel erection.

Girder Splice Design

Field splices connect girder sections shipped from the fabrication shop. Per AASHTO 6.13.6.1:

Bolted splices: Most common for field splicing. Designed as slip-critical for bolt groups. The splice must develop the full flexural and shear capacity of the smaller connected section, or the design forces at the splice location. Bolted splice plates typically use Grade 50 steel. Minimum two rows of bolts on each side of the splice.

Welded splices: Full-penetration groove welds used for flange splices and web splices. Require backing bars and quality control inspection (ultrasonic testing of groove welds). More sensitive to fit-up conditions in the field.

Frequently Asked Questions

What is the difference between a plate girder and a rolled beam? Plate girders are built-up sections fabricated by welding plates together (web + flanges), allowing custom depths and flange sizes beyond the limits of rolled W-shapes. Rolled beams are limited to standard AISC shapes (max depth ~40 inches). Plate girders are used for longer spans (typically > 60 ft / 18 m) and can be designed with variable depth, tapered flanges, or hybrid grades. Per AASHTO 6.10, plate girder slenderness limits are more permissive than rolled sections.

How are stiffeners designed on plate girders? Per AASHTO LRFD 6.10.8 and 6.10.11: (1) Transverse intermediate stiffeners — required when shear capacity exceeds D/tw limits, designed for required stiffness ratio and area, (2) Bearing stiffeners — at supports and concentrated loads, designed as columns resisting the full reaction, (3) Longitudinal stiffeners — optional, placed at D/5 from compression flange to improve bend-buckling resistance. Minimum stiffener width is 2 inches + d/30 (AASHTO 6.10.11.1.2).

What is a tub girder and when is it used? A tub girder (trapezoidal box girder) is a closed-section steel girder used for horizontally curved bridges where torsional stiffness is critical. The closed cross-section provides superior torsional resistance compared to open I-girders. Per AASHTO LRFD Section 6.11, tub girders require: (1) internal cross-frames spaced at max 25 ft (7.6 m), (2) top flange lateral bracing during construction, (3) minimum web thickness D/tw ≤ 150 for straight girders, and (4) fatigue design of diaphragm connections to curved flanges.

What is a hybrid girder and why use one? A hybrid girder uses different steel grades for flanges and web — typically Grade 50 (50 ksi) web with HPS 70W (70 ksi) flanges or HPS 100W (100 ksi) flanges for longer spans. The web stress at the flange-web junction is limited by the web yield stress, but higher-strength flanges allow more compact flange sizes for the same flexural capacity. Per AASHTO 6.10.1.4, hybrid girders use the hybrid factor Rh (typically 0.90-0.95) to account for the reduced web contribution at yield. Cost savings: 5-15% compared to homogeneous Grade 50 girders using HPS 70W flanges, and 10-20% using HPS 100W flanges, due to reduced flange plate sizes and welding costs.

How are cross-frames designed for steel bridge girders? Cross-frames (diaphragms) between girders are designed per AASHTO 6.7.4 and 6.9 for: (1) Wind loads — lateral wind on the bridge superstructure is distributed to the cross-frames as axial forces in the X-brace or K-brace members, (2) Lateral seismic loads — the seismic response of the bridge mass is transferred through the cross-frames to the bearings, (3) Constructability — cross-frames provide stability to girder compression flanges during deck placement, (4) Curved girder forces — for curved bridges, cross-frames resist torsional warping forces. Cross-frame member slenderness is limited to KL/r ≤ 140 (tension members) and KL/r ≤ 120 (compression members). Cross-frame connections must be designed for the full member force, typically using bolted gusset plates with slip-critical bolts.

Disclaimer (educational use only)

This page is provided for general technical information and educational use only. It does not constitute professional engineering advice. All results must be independently verified by a licensed Professional Engineer.