Prestressed Bridge Design - A step by step Approach

Concrete is strong in compression but weak in tension; however, prestressing can be used to ensure that it remains within its tensile and compressive capacity under the range of loading applied. Prestressing in bridgeworks is normally applied as an external force to the concrete by the use of wires, strands or bars, and can greatly increase the strength of the concrete alone.

This can result in longer or slender spans, which improves aesthetics while providing economy in the construction.

Prestressed concrete bridges include a wide variety of different forms:

• from cast in situ to precast; from beams to box girders;

• and from simply supported to cable-stayed.

Their functions range from the carrying of pedestrians and cyclists to road or rail traffic and they make up a significant proportion of the bridge stock in existence today.

The design of prestressed concrete bridges both greatly influences and is dependent on the construction process envisaged. The construction sequence and practical considerations in positioning the tendons influence the prestress layout much more than the desire to achieve a concordant profile.

Precast girder design must address three basic stages of performance—transfer, service, and strength—as well as additional stages if posttensioning is introduced. Precast girder design, including section size, prestress force (number and size of strands), strand layout, and material properties, may be governedby any of these stages. Although design for flexure dominates the precast girder design process, other aspects must also be considered such as prestress losses, shear and interface shear strength, anchoragezones, deflection and camber, diaphragms, and seismic connections.

In general, the design of precast–pretensioned concrete girders includes the following: select girdersection and materials, calculate loads, perform flexural design and determine prestressing force, perform shear design, check anchorage and horizontal shear transfer (shear friction), and estimate camber and deflection.

Either the precast manufacturer or the design engineer is responsible for design of the girder forhandling, shipping, and erection. The engineer confirms that the girder is constructible and conforms to the required design criteria.

In most precast girders, a relatively large value of fci′ is used in design, which typically controls the overall concrete mix design. If an excessively large value of fci′ is required in design to resist temporary tensile stresses at transfer in areas other than the precompressed tensile zone, such as the top flange at girder ends, then bonded reinforcement or prestress strands may be designed to resist the tensile force in the concrete, per AASHTO LRFD. This helps reduce the required fci′ used in design.

The relatively large value of fci′ used in design also results in a relatively large value of fc′ (e.g., often in excess of 7 ksi), which is normally larger than that required to satisfy the concrete compressive strength requirements at the serviceability and/or strength limit state. In cases where a larger fc′ is required to produce an economical design (e.g., girders of longer span, shallower depth, or wider spacing), a 56-day compressive strength may be specified to achieve the higher strength, rather than the normal 28-day strength.

Advantages of the concrete used in precast girders produced under plant-controlled conditions are wide ranging. Higher modulus of elasticity and lower creep, shrinkage, and permeability are by-products of the relatively higher compressive strength and steam curing process used for precast girders.

SCC is being more commonly used in precast plants. Although slightly more expensive than traditional concrete, it provides significant advantages such as elimination of consolidation, reduced manual labor, and smoother concrete surfaces, often combined with high strength and durability.

For economy, precast girders commonly use 0.6-in diameter, 270 ksi (Grade 270), low-relaxation strands. Use of 0.5-in diameter strands is less common because the 0.6-in diameter strands provide a significantly higher efficiency due to a 42% increase in capacity. The 3/8-in diameter strands are commonly used for stay-in-place, precast deck panels. Epoxy coated prestressing strands may be used in corrosive areas.

The limit state design which characterizes the AASHTO LRFD specifications utilizes specific load types. These load types include dead loads, live loads, accumulated locked-in force effects, construction loads, wind loads, force effects due to superimposed deformations, friction forces, and blast loading.

The load types presented in this chapter apply primarily to the design of bridge superstructures, and additional loads must be considered in the design of bridge substructures. In addition, the load types presented in this chapter do not include those associated with extreme events, nor do they include those which apply exclusively to less common signature bridges.

Dead loads include all loads that are relatively constant over time, including the weight of the bridge itself. In LRFD bridge design, there are two primary types of dead load:

• Dead load of structural components and nonstructural attachments, designated as DC

• Dead load of wearing surfaces and utilities, designated as DW

For strength and extreme event limit states, the maximum load factors for DW dead loads are generally greater than the maximum load factors for DC dead loads due to the greater uncertainty of the presence and the exact value of DW dead loads Other dead loads are specified by the AASHTO LRFD specifications and are included specifically in some load combinations. These loads are due to the effects of earth pressure (both vertical and horizontal), earth pressure surcharge, and other geotechnical effects. These loads are not discussed in this section, as they influence the design of substructures and rarely, if ever, influence the design of a bridge superstructure.

In addition to dead loads, which are continually acting on a bridge, and construction loads, which generally act on a bridge only during its construction, a bridge must also be designed to resist live loads. The primary difference between dead loads and live loads is that dead loads are permanent but live loads are transient. That is, dead loads act on the bridge at all times, but live loads are not necessarily present at all times. In addition, dead loads are stationary loads, but live loads are moving loads. Two common forms of live loads are vehicular loads and pedestrian loads.

A design lane generally has a width of 12 feet. The number of design lanes is simply computed as the roadway width divided by the 12-foot design lane width, rounded down to the nearest integer. For example, if the distance between the curbs is 70 feet, then the number of design lanes is five. When computing the number of design lanes, possible future adjustments to the roadway should be considered. For example, if a median is currently present on the bridge but may be removed in the future, then the number of design lanes should be computed assuming that the median is not present.

Although the automobile is the most common vehicular live load on most bridges, the truck causes the critical load effects. In a sense, cars are “felt” very little by the bridge and come “free.” More precisely, the load effects of the car traffic compared to the effect of truck traffic are negligible. Therefore, the AASHTO design loads attempt to model the truck traffic that is highly variable, dynamic, and may occur independent of, or in unison with, other truck loads.

The principal load effect is the gravity load of the truck, but other effects are significant and must be considered. Such effects includeimpact (dynamic effects), braking forces, centrifugal forces, and the effects of other trucks simultaneously present. Furthermore, different design limit states may require slightly different truck loadmodels. Each of these loads is described in more detail in the following sections. Much of the research involved with the development of the liveload model and the specification calibration is presented in Nowak (1993, 1995). Readers interested in the details of this development are encouraged to obtain this reference for more background information.

Design Lanes The number of lanes a bridge may accommodate must be established and is an important design criterion. Two terms are used in the lane design of a bridge:

• Traffic lane

• Design lane

The traffic lane is the number of lanes of traffic that the traffic engineer plans to route across the bridge. A lane width is associated with a traffic lane and is typically 12 ft (3600mm).

The design lane is the lane designation used by the bridge engineer for live-load placement. The design lane width and location may or may not be the same as the traffic lane. Here AASHTO uses a 10-ft (3000 mm) design lane, and the vehicle is to be positioned within that lane for extreme effect.

The mechanism of fatigue failure is believed to begin at the surface of a member where there are microscopic imperfections (present at the time of fabrication), which act as stress raisers. As a result, the stress at this location becomes much greater than the average stress acting over the cross section.

As this higher stress is repeated, it leads to the formation of minute cracks.  Occurrence of these cracks causes reduction in the member cross section at those locations (at tips or boundaries of members such as eye bars), which results in increased stresses.

The close relationship between the failures of metal parts (failures of axles of railroad cars were a major problem at the time) was amply recognized by McConnell (1849), who made an exhaustive study of the failure of axles of railroad cars.  Based on this study, the French engineers recommended a careful inspection of coach axles after 70,000 km of service to avoid problems of sudden fracturing.  Now, fatigue is believed to be responsible for a large percentage of failures in connecting rods and crank shafts of engines, steam or gas turbine blades, connections or supports of bridges, and railroad wheels and axles.

The required number of strands is usually governed by concrete tensile stresses at the bottom fiber for the load combination Service III at the section of maximum moment or at the harp points. For estimating the number of strands, only the stresses at midspan are considered.

It is instructive to understand the concepts of limit states, which form the foundations of the strength design, and the LRFD philosophies. Stated simply, a limit state is a condition which represents the limit of structural usefulness (AISC 1986). Or, in the context of structural reliability, a limit state can be defined as a boundary between desired and undesired performance of a structure (Nowak and Collins 2013).

The use of plural limit states is intentional as there may be, and usually are, many conditions that, if violated, would impair a structure’s ability to satisfactorily carry extreme loads. These limit states are owner/designer-driven conditions and their intents are specified in the design codes. Intended service life is prescribed in the design codes, usually 50 or 75 years.