Bridge Engineering

A structured learning path from bridge planning through advanced analysis. Master structural systems, load distribution, prestressed and composite bridges, bearings, expansion joints, and inspection methods per AASHTO LRFD.

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Level 1

Beginner — Bridge Types and Loads

Start here if you are new to bridge engineering.

Bridge Classification and Structural Systems

Bridges are classified by material (concrete, steel, timber, masonry), structural system (beam, arch, truss, cable-stayed, suspension, rigid frame), span length (short: ≤ 20 m, medium: 20-100 m, long: 100-300 m, very long: 300+ m), carrying function (highway, railway, pedestrian, pipeline), and construction method (cast-in-place, precast, incremental launching, balanced cantilever, segmental). The choice of bridge type depends on span length, site conditions, foundation constraints, construction access, budget, and aesthetic requirements.

Beam bridges (slab, T-beam, box girder) are the most common for short and medium spans. Slab bridges are simple and economical for spans up to 15 m. T-beam bridges with cast-in-place RC or prestressed I-girders are standard for 15-40 m spans. Box girder bridges provide high torsional stiffness for curved alignments and spans of 30-200 m. Truss bridges efficiently carry heavy loads over medium spans (30-150 m) using triangulated steel or timber members. Arch bridges excel at spanning valleys with rigid rock abutments (40-300 m). Cable-stayed bridges (200-800 m) and suspension bridges (500-2000+ m) dominate long-span crossings.

Bridge Loads per AASHTO LRFD

AASHTO LRFD Bridge Design Specifications use limit states design: Strength I (basic load combination without wind), Strength II (with special vehicles like permit loads), Service I (operational checks), Service II (steel structure yielding control), Fatigue (crack growth prevention), and Extreme Event (earthquake, vessel collision, ice). The HL-93 design live load consists of either the design truck (three-axle 325 kN total) plus design lane load (9.3 kN/m) OR the design tandem (two-axle 220 kN) plus lane load — whichever produces the maximum effect. Dynamic load allowance (impact) of 33% is applied to the truck or tandem, but not to the lane load.

Other loads include: dead load DC (structural components and non-structural attachments), wearing surface DW (future overlay), wind load on structure and live load (per AASHTO 3.8), temperature gradient (positive and negative through the superstructure depth), earth pressure for abutments and retaining walls, buoyancy for submerged elements, vehicle collision force on bridge rails and parapets, and vessel collision force for navigable waterways. Load combinations use specified γ factors: γ_DC = 1.25 for Strength I, γ_LL = 1.75, γ_DW = 1.50. The multiple presence factor for multi-lane loading is 1.20 for one lane, 1.00 for two lanes, 0.85 for three lanes, and 0.65 for four or more lanes.

Load Distribution and Live Load Distribution Factors

Load distribution factors (LDFs) in AASHTO LRFD approximate the fraction of a live load applied to one girder, enabling simplified girder analysis without a full 3D finite element model. The LDF method in AASHMO Table 4.6.2.2.2b-1 provides simple formulas based on girder spacing S, span length L, girder depth, deck thickness ts, and stiffness parameter Kg. For interior girders with concrete deck on steel or concrete beams: one lane loaded gives g = 0.06 + (S/4300)^0.4 · (S/L)^0.3 · (Kg/L·ts³)^0.1.

Distribution factors differ for moment and shear, interior and exterior girders, and one lane vs. multiple lanes loaded. Exterior girder distribution uses the lever rule (simple statics) for one lane and modifications of interior formulas for multiple lanes. Skew effects modify distribution factors when the skew angle exceeds 30°. Refined analysis (grillage or FEM) is recommended for curved bridges, very wide bridges, or structures with irregular geometry. The approximate distribution method is not applicable for post-tensioned concrete box girders or segmental bridges — those require refined analysis. Use the Load Distribution Calculator to compute AASHTO distribution factors.

Level 2

Intermediate — Reinforced and Prestressed Concrete Bridges

Build on fundamentals with concrete bridge design.

RC Slab and T-Beam Bridge Design

Reinforced concrete slab bridges are the simplest bridge type for short spans (3-15 m). The slab is designed as a 1 m wide strip with the HL-93 design truck positioned for maximum moment. The AASHTO LRFD empirical design method for slab bridges uses correction factors for continuity, skew, and edge beams. The minimum slab thickness is typically L/20 for simply supported spans, with reinforcement satisfying both strength and crack control requirements per AASHTO 5.7.3.4. Distribution reinforcement perpendicular to traffic is at least 67% of the main reinforcement for primary reinforcement parallel to traffic.

T-beam bridges consist of a cast-in-place concrete deck on cast-in-place concrete girders. The effective flange width for interior T-beams is the minimum of L/4, center-to-center beam spacing, or 12ts + bf. The deck overhang is designed for the wheel load placed 300 mm from the face of the rail. Shear connectors at the deck-to-girder interface are provided by extending stirrups into the deck. The transverse deck is designed as a continuous slab over girders for wheel loads, with the strip method per AASHTO Table 4.6.2.1.3-1 for a 1 m wide transverse strip. Dead load includes the self-weight of the structural section, wearing surface, barriers, and utilities.

Prestressed Concrete Girder Design

Prestressed concrete girders use high-strength steel strands (7-wire strand, diameter 12.7 mm or 15.2 mm, fpu = 1860 MPa) tensioned before (pretensioned) or after (post-tensioned) concrete placement. Pretensioned I-girders (AASHTO Types I-VI, PCI bulb-tees) are widely used for spans from 15-45 m. The transfer length (typically 50-60 strand diameters) is the distance required to develop the prestress force from the girder end, and the development length is approximately l_d = (fps - fpe)·db/7 + 60db per AASHTO 5.11.4.2.

Prestress losses are time-dependent and include: elastic shortening (immediate, released at strand detensioning), shrinkage (concrete volume change over time), creep (concrete deformation under sustained compression), and steel relaxation (reduction in strand stress under constant strain). Total losses typically range from 15-25% of the initial jacking stress for pretensioned members and 10-20% for post-tensioned members per the refined AASHTO method. Service limit states include: tensile stress limits at transfer and service, compressive stress limits (0.60f'c under sustained loads), and deflection/camber control. Strength limit states check flexural capacity at ultimate using strain compatibility. Use the Prestress Losses Calculator to compute time-dependent losses.

Substructure Design: Abutments and Piers

Bridge substructures include abutments (end supports retaining the approach embankment) and piers (intermediate supports). Abutment types are gravity (masonry or mass concrete), cantilever (RC stem on spread footing or piles), and stub (low-height with retained embankment slopes). Abutment design considers vertical loads (dead + live reaction, self-weight, backfill), horizontal loads (earth pressure, braking force, temperature, seismic), and longitudinal loads. The abutment backwall must resist horizontal earth pressure and vehicle collision loads behind the approach slab.

Pier types include solid wall (hammerhead, solid shaft), multi-column bent (two or more columns with bent cap), and pile bent (extended piles with pile cap). Pier design loads: vertical reaction from superstructure, wind on the exposed structure and live load on the bridge, braking and acceleration forces from traffic (25% of design truck weight applied at bearing level), temperature and shrinkage effects, stream flow pressure and scour, vessel collision (for navigable waterways), and seismic forces. Column design for piers follows ACI 318 modified by AASHTO requirements including larger minimum reinforcement (1% Ag minimum), closer tie spacing (300 mm maximum), and capacity design for seismic ductility. Foundation piles are designed for group action with lateral load distribution per AASHTO 10.7.2.

Level 3

Advanced — Steel Bridges, Bearings, and Inspection

For senior students and practicing engineers.

Steel Girder and Composite Bridge Design

Steel girder bridges use rolled wide-flange sections (W-shapes) for short spans (10-25 m) and built-up plate girders for longer spans (25-100 m). Composite action between the steel girder and concrete deck through shear studs significantly increases stiffness and strength. The effective flange width, cross-section classification (compact/non-compact/slender), and flexural capacity per AASHTO 6.10 follow the same principles as AISC 360 but with bridge-specific modifications including the hybrid factor for girders using different steel grades for flanges and web.

Plate girder design includes proportioning the web depth (typically L/15 to L/20), flange width and thickness, intermediate and bearing stiffener spacing, and the shear connection. The constructibility check ensures the steel section alone can support the wet concrete weight before the concrete hardens and composite action develops. Fatigue design per AASHTO 6.6 follows infinite-life and finite-life procedures with detail categories ranging from A (plain rolled members, fatigue threshold 165 MPa) to F (fillet welds, threshold 31 MPa). The fatigue load is a single HL-93 truck with a constant amplitude fatigue threshold based on the number of cycles. Cross-frame or diaphragm spacing controls lateral-torsional buckling during construction and distributes loads between girders.

Bridge Bearings, Expansion Joints, and Appurtenances

Bearings transfer loads from the superstructure to the substructure while accommodating movements (thermal, creep, shrinkage, prestress shortening) and rotations. Steel rocker and roller bearings accommodate large movements but require maintenance. Elastomeric bearing pads (laminated rubber with steel shims) are most common for moderate-span bridges — designed for compressive stress, shear strain from horizontal movement, and rotation. Pot bearings consist of an elastomeric disc in a steel cylinder, suitable for high loads and rotations. Spherical bearings use a concave/convex steel interface for multi-directional rotation capacity.

Expansion joints accommodate thermal movement at the deck ends and at piers in continuous bridges. Compression seal joints are economical for movements up to 50 mm. Strip seal joints use an elastomeric gland clamped between steel edge beams for movements up to 100 mm. Modular expansion joints (multiple seal elements) accommodate movements exceeding 100 mm—used for long-span bridges. Approach slabs transition from the bridge deck to the roadway pavement, preventing the bump at the end of the bridge caused by approach fill settlement. Bridge rails (traffic barriers) must meet AASHTO MASH test levels: TL-3 for typical highway bridges, TL-4 for high-speed highways, and TL-5 for heavy truck routes.

Bridge Inspection and Health Monitoring

Bridge inspection is mandated in the US by the National Bridge Inspection Standards (NBIS) — every bridge carrying vehicular traffic must be inspected at intervals not exceeding 24 months. Routine inspection covers all visible elements: deck condition (cracking, spalling, delamination), superstructure (girder condition, bearing alignment, corrosion), substructure (scour, cracking, settlement), and waterway adequacy. Fracture-critical members (FCMs) — tension members whose failure would cause bridge collapse — require hands-on inspection within the 24-month cycle. Underwater inspection is required for bridges over water at a maximum 60-month interval.

The AASHTO bridge element inspection manual assigns condition states to each element (Good, Fair, Poor, Severe) using a 1-4 rating scale. The Sufficiency Rating (0-100) determines federal funding eligibility — bridges below 50 are eligible for replacement, below 80 for rehabilitation. Structural Health Monitoring (SHM) uses sensors to track bridge behavior: strain gauges for load response, accelerometers for vibration and modal analysis, inclinometers for rotation, corrosion potential sensors, and fiber optic sensors for distributed strain measurement. Nondestructive evaluation (NDE) methods include acoustic emission, ground-penetrating radar for deck delamination, impact echo for concrete condition, ultrasonic testing for welds, and magnetic particle testing for surface cracks. Use the Prestressed Girder Calculator for girder analysis.

Practice Exercises

Exercise 1: Live Load Distribution

A bridge has a 200 mm thick concrete deck on steel plate girders at 2.4 m spacing with span 30 m. The girder stiffness parameter Kg = 1.5 × 10¹¹ mm⁴. Using AASHTO LRFD Table 4.6.2.2.2b-1, calculate the live load distribution factor for moment in an interior girder for two or more lanes loaded. Use the Load Distribution Calculator to verify.

Exercise 2: Prestress Loss Calculation

A pretensioned bridge girder uses 12-12.7 mm diameter strands stressed to 0.75fpu = 1395 MPa initially. The concrete strength at transfer f'ci = 35 MPa, f'c = 45 MPa. Estimate the total prestress losses using the AASHTO refined method: elastic shortening, creep, shrinkage, and relaxation losses. Use the Prestress Losses Calculator to verify.

Exercise 3: Composite Section Properties

A W760×173 steel girder (A = 22000 mm², Ix = 1.89×10⁹ mm⁴) is made composite with a 200 mm thick, 2.4 m wide concrete slab (f'c = 28 MPa, Ec = 26700 MPa). Calculate the transformed composite section properties: modular ratio n, transformed section moment of inertia, and section modulus for the top of steel and bottom of steel.

Exercise 4: Abutment Stability Check

A cantilever abutment 6 m tall retains granular backfill with γ = 19 kN/m³, φ = 32°. The abutment stem is 0.6 m thick, base width is 4.0 m, base thickness is 0.6 m. The bridge bears a vertical reaction of 400 kN/m and horizontal braking force of 50 kN/m at the bearing level (0.5 m from top). Check overturning, sliding, and maximum bearing pressure per AASHTO Strength I load combination.

References

AASHTO. LRFD Bridge Design Specifications. 9th ed., American Association of State Highway and Transportation Officials, 2020.
Barker, R.M. and Puckett, J.A. Design of Highway Bridges: An LRFD Approach. 4th ed., Wiley, 2021.
O'Brien, E.J. and Keogh, D.L. Bridge Design with IRC and Eurocodes. ICE Publishing, 2014.
Chen, W.F. and Duan, L. Bridge Engineering Handbook. 2nd ed., CRC Press, 2014.
Memmott, J. Bridge Inspection Manual. FHWA, 2019.
ACI 318-19. Building Code Requirements for Structural Concrete. American Concrete Institute, 2019.
Civil Engineering Handbook — Bridge Engineering chapter.
Engineering Formula Library — Bridge design formulas.
Engineering Standards Reference — AASHTO LRFD, Eurocode provisions.
Engineering Glossary — Definitions of bridge engineering terms.