Bridge Loads and Design Principles
The design of any bridge requires a thorough understanding of all the forces and loads it will experience during its service life. Engineers must accurately calculate these loads and apply appropriate design philosophies to ensure the structure is safe, durable, and economical.
Types of Bridge Loads
Bridge loads are generally categorized into permanent loads, transient loads, and environmental loads.
Permanent Loads (Dead Loads)
Permanent loads remain relatively constant throughout the life of the bridge.
- Dead Load of Structural Components (DC): The weight of all structural elements (girders, deck, piers, abutments) and non-structural attachments permanently fastened to the bridge.
- Dead Load of Wearing Surfaces and Utilities (DW): The weight of the future wearing surface (asphalt overlay) and any utility lines (pipes, cables) carried by the bridge. This load can change over time due to resurfacing.
- Earth Pressure (EH): The lateral pressure exerted by soil against the abutments and retaining walls.
Transient Loads (Live Loads)
Transient loads change in magnitude, position, and direction. The most significant transient load for highway bridges is vehicular traffic.
Vehicular Live Load (LL)
The dynamic forces exerted by moving vehicles. In the United States and many other regions, the American Association of State Highway and Transportation Officials (AASHTO) specifies standard design vehicular live loads.
- Design Truck (formerly HS-20): A standardized truck model with specific axle spacings and weights used for design calculations.
- Design Tandem: Two closely spaced axles representing a heavy localized load.
- Design Lane Load: A uniformly distributed load ( or ) representing a line of lighter traffic, applied simultaneously with the design truck or tandem.
Dynamic Load Allowance (IM)
Also known as impact factor. Moving vehicles create dynamic effects (bouncing, vibrations) that increase the effective live load compared to a static vehicle. The static live load is multiplied by a factor (e.g., for deck joints, for fatigue, for other components) to account for this.
Pedestrian Live Load (PL)
Applied to sidewalks and pedestrian bridges, typically a uniformly distributed load (e.g., or ).
Environmental Loads
Forces imposed by nature that the bridge must withstand.
- Wind Load (WL and WS): Wind pressure acting on the structure itself (WS) and on the vehicles crossing the bridge (WL). It causes lateral forces and overturning moments.
- Seismic Load (EQ): Horizontal and vertical forces generated by earthquakes. In seismic zones, detailing for ductility is crucial to prevent collapse.
- Temperature Gradient (TG) and Uniform Temperature (TU): Changes in temperature cause materials to expand and contract. If restrained, this induces significant internal stresses. Differential heating (top of deck hotter than girders) causes bowing.
- Water Loads (WA): Forces from flowing water (stream pressure), buoyancy, and wave action on piers and foundations.
- Ice Loads (IC): Lateral pressure from floating ice sheets striking piers.
Other Forces
- Centrifugal Force (CE): The outward lateral force exerted by vehicles moving on a curved bridge.
- Braking Force (BR): The longitudinal force transferred to the deck when vehicles brake or accelerate.
- Vessel Collision (CV): The impact force from barges or ships striking piers in navigable waterways.
Dynamic Load Allowance (Impact)
Vehicles do not cross bridges perfectly smoothly. Bumps, potholes, expansion joints, and the vehicle's own suspension cause bouncing, which amplifies the static weight.
Calculating Impact (IM)
To account for this dynamic effect, the static weight of the design truck is increased by a percentage known as the Dynamic Load Allowance (IM).
- For standard deck joints, the IM is 75%.
- For all other components (girders, piers) under the Strength limit state, the IM is 33%.
- For fatigue design, the IM is reduced to 15%.
Note: Dynamic Load Allowance is applied only to the vehicular live load (truck/tandem), not to the uniform lane load or dead loads.
Dynamic Load Allowance (IM) Equation
Calculates the total vehicular live load acting on a bridge component by amplifying the static load to account for dynamic effects. Use cases: Determining the factored live load for girder flexure or shear design, Calculating extreme forces on bridge piers caused by moving traffic.
Variables
| Symbol | Description | Unit |
|---|---|---|
| Total vehicular live load including dynamic allowance | kN or kips | |
| Static weight or force from the design truck/tandem | kN or kips | |
| Dynamic Load Allowance factor (expressed as a decimal, e.g., 0.33 for 33%) | - |
Aeroelastic Effects of Wind
For long-span, flexible structures (such as suspension and cable-stayed bridges), simple static wind pressure calculations are insufficient. Dynamic, aeroelastic interactions between the bridge deck and the wind can lead to destructive oscillations.
Aeroelastic Phenomena
- Vortex Shedding: As wind flows past a bluff body (like a blunt bridge deck), it creates alternating vortices in its wake. This causes vertical oscillations that can be uncomfortable for pedestrians but are rarely structurally fatal.
- Flutter: A dangerous aeroelastic instability where the bridge's torsional (twisting) motion couples with its vertical motion. Energy from the wind is fed into the structure, causing the oscillations to grow exponentially until catastrophic failure (as famously seen in the original Tacoma Narrows Bridge).
- Galloping: High-amplitude, low-frequency oscillations typically affecting slender components like stay cables, especially when coated with ice or running water.
Seismic Design Principles
Bridges located in seismic zones must be specifically engineered to resist the severe ground shaking caused by earthquakes.
Designing for Earthquakes
The fundamental philosophy in seismic design is to allow the bridge to sustain damage during a severe earthquake but prevent it from collapsing, ensuring life safety.
- Ductility: Materials and connections must be capable of significant plastic deformation without fracturing. Concrete columns are heavily reinforced with tightly spaced transverse hoops or spirals to confine the core concrete and prevent the vertical rebars from buckling under extreme lateral shaking.
- Capacity Design: Engineers deliberately design specific locations (usually the columns) to yield and act as "plastic hinges," absorbing the seismic energy. All other components (foundations, cap beams, superstructure) are designed to remain elastic and stronger than the plastic hinge.
- Unseating Prevention: Adequate seat widths on abutments and piers must be provided so the girders do not shake loose and fall off during longitudinal or transverse displacement.
Influence Lines
Because transient loads (like vehicles) move across the bridge, the internal forces (shear, moment, axial) at any specific point on the structure constantly change. To find the maximum possible effect, engineers use Influence Lines.
Understanding Influence Lines
An influence line is a graph showing how a specific structural response (e.g., bending moment at midspan, or shear at a support) varies as a single unit load moves across the bridge.
- Purpose: By finding the peak value on the influence line, an engineer knows exactly where to place a moving vehicle (like the AASHTO Design Truck) to produce the absolute maximum force at that specific location on the bridge.
- Application: Once the critical position is found, the actual axle weights of the truck are multiplied by the corresponding values (ordinates) on the influence line to calculate the total design force.
Bridge Design Philosophies
Over time, design methodologies have evolved to provide more rational and reliable approaches to structural safety.
Load and Resistance Factor Design (LRFD)
LRFD is the current standard philosophy mandated by AASHTO for highway bridges. It is a reliability-based approach that separates uncertainties into two distinct categories: loads and material resistance.
Fundamental LRFD Equation
The fundamental LRFD equation requires that the factored resistance must be greater than or equal to the sum of the factored loads.
AASHTO LRFD Limit States and Load Combinations
LRFD requires checking the bridge design against several limit states. For each limit state, specific load combinations with varying load factors () are analyzed to ensure safety under different simultaneous loading scenarios.
Strength Limit States
Focuses on the structural stability and strength to resist the statistically maximum loads that could occur during the bridge's 75-year design life.
- Strength I: Basic load combination for normal vehicular use without extreme wind. Features high load factors for dead loads and maximum vehicular live loads.
- Strength II: For owner-specified special design vehicles, permit vehicles, or heavy construction traffic.
- Strength III: Bridge subjected to extremely high wind velocities (e.g., hurricanes). Assumes heavy traffic is absent because drivers stop or slow down in extreme weather. Features high wind load factors and low live load factors.
- Strength IV: Specifically intended for very long-span bridges where the ratio of dead load to live load is exceptionally high. Applies a massive load factor to dead loads.
- Strength V: Normal vehicular traffic occurring simultaneously with a moderate wind event (typically ).
Service Limit States
Focuses on restrictions regarding stress levels, deformations (deflections), and cracking under everyday operating conditions to ensure the bridge remains durable and comfortable to use.
- Service I: General load combination relating to normal operational use with normal winds. All load factors are typically . Used for checking general deflections and concrete compressive stresses.
- Service II: Used specifically to check yielding of steel structures and slip of critical bolted connections under design vehicular loads.
- Service III: Used to check tension stresses and potential cracking in prestressed concrete superstructures under normal traffic.
- Service IV: Relates to tension in prestressed concrete substructures under severe wind conditions.
Extreme Event Limit States
Ensures the structural survival of the bridge during major disasters. Severe damage is acceptable, but total collapse must be prevented.
- Extreme Event I: Evaluates the bridge's survival during a major earthquake (Seismic Load). Live load factors are significantly reduced, as peak traffic during an earthquake is statistically unlikely.
- Extreme Event II: Evaluates survival during events like vessel collision, vehicle collision on piers, massive ice loads, or major floods (scour events).
Fatigue and Fracture Limit State
Targets steel components, restricting stress ranges caused by repetitive loading to prevent fatigue cracking over millions of cycles.
- Evaluates the stress range caused by a single, standard fatigue truck (a modified design truck) to ensure cracks do not initiate or grow throughout the bridge's lifespan.
Historical Note: Allowable Stress Design (ASD) and Load Factor Design (LFD)
Before LRFD, older bridges were designed using ASD or LFD.
- ASD used unfactored loads and required stresses to be below an allowable stress (a fraction of the yield stress). It did not consistently account for the variability of different load types.
- LFD introduced load factors but still used a single format for resistance, serving as a transitional philosophy towards LRFD.
Key Takeaways
- Bridge loads include Permanent (dead loads, earth pressure), Transient (vehicular/pedestrian live loads, braking, centrifugal forces), and Environmental (wind, seismic, temperature, water, ice).
- Vehicular live load utilizes models like the Design Truck, Design Tandem, and Design Lane Load, augmented by a Dynamic Load Allowance (IM) for vibration impacts.
- Long spans require attention to Aeroelastic phenomena (flutter, vortex shedding) under wind loads.
- Seismic Design relies heavily on ensuring adequate ductility and utilizing capacity design principles to prevent structural collapse during an earthquake.
- LRFD (Load and Resistance Factor Design) mandates that factored resistance exceed factored loads ().
- Engineers must analyze multiple Limit States (Strength, Service, Extreme Event, and Fatigue) and numerous load combinations within those states to ensure overall bridge reliability.