Four Stages of a Bridge Design
The bridge design process consists of four key stages: conceptual, preliminary, detailed, and construction design The conceptual design phase focuses on generating various feasible bridge schemes and selecting final concepts for further evaluation In the preliminary design stage, the best scheme is chosen, its feasibility is assessed, and cost estimates are refined The detailed design phase finalizes all structural specifics to prepare for tendering and construction Lastly, the construction design outlines the step-by-step procedures for building the bridge Each design stage must account for the requirements of the subsequent stages, ensuring that the conceptual design includes considerations for construction feasibility, structural details, costs, and aesthetics.
During the conceptual design stage of a bridge, it is not necessary to conduct detailed studies on every issue; rather, accumulated engineering experience plays a crucial role in assessing the feasibility of basic ideas For instance, while a 150-meter span prestressed concrete box girder bridge with a depth of approximately 7.50 meters is generally feasible based on past projects, a deeper girder of only 5.00 meters would require a thorough analysis due to its deviation from conventional depth ratios Therefore, the appointment of an experienced engineer for conceptual design is essential, as this process must encompass all bridge details from inception to completion, ensuring that the proposed design is feasible under specific conditions Feasibility extends beyond structural stability and constructability to include the four fundamental requirements of a bridge: safety, functionality, economy, and aesthetics.
The conceptual design stage marks the beginning of bridge design, serving as a creative process that challenges the engineer's innovative skills Starting with a blank slate, this phase is crucial for envisioning and developing unique design solutions.
The significance of conceptual design is often overlooked, leading to underdeveloped concepts due to time constraints This can result in future complications To enhance the quality of conceptual designs, it is essential to involve senior, experienced staff in this crucial process.
Establishing the Criteria
Bridge design must adhere to legal documents such as the “LRFD Bridge Design Specifications” by AASHTO, but these specifications may not always be current due to the slow adaptation to new developments The late Professor T.Y Lin emphasized the importance of considering the rules of nature alongside existing codes Therefore, bridge engineers should not only meet specification requirements but also account for local conditions and the needs of the communities they serve.
Overloaded trucks pose significant challenges that existing specifications often fail to address, leading to overstress in bridge structures and a reduced fatigue life For instance, when trucks exceed their design axle loads by 150%, the fatigue life of welded steel components can drop to less than 30% of their intended lifespan, transforming a 100-year design life into just 30 years Therefore, while adhering to specifications is essential, it is equally important to account for real-world conditions that impact infrastructure durability.
A bridge is engineered to fulfill specific functions while adhering to environmental conditions and constraints The design must comply with relevant specifications and codes, collectively referred to as the bridge's design criteria These criteria encompass various essential factors that guide the construction and functionality of the bridge.
1 Type, volume, and magnitude of traffic to be carried by the bridge
2 Clearances required by the type of traffic on the deck
3 Navigation clearance under the bridge
4 Environmental effects such as earthquake, wind, flood, and other possible natural phenomena
5 Geological formation and soil characteristics at the site
6 Economic conditions or available project funding
7 Expectations of the stakeholders on form and aesthetics
Before conceptualizing a new bridge, engineers must clearly define various conditions that can significantly influence the design Any violation of these conditions can render the design unacceptable The bridge must fulfill its intended functions, including safely supporting the loads it will bear, while also adhering to budget constraints Additionally, the bridge's aesthetic integration into its physical environment is of utmost importance.
The design criteria for the bridge outline essential constraints that influence its construction Key factors such as function dictate the deck's width and elevation, while navigational clearances impact height and span length Additionally, geological and topographic conditions at the site play a crucial role in shaping the bridge's geometry The goal of the conceptual design process is to develop an optimal bridge scheme that meets all specified criteria, focusing on safety, functionality, economy, and aesthetics.
Characteristics of Bridge Structures
When selecting the most appropriate bridge type, we categorize bridges into four main types: girder, arch, cable-stayed, and suspension bridges Additionally, there are innovative combinations, such as the cable-stayed and suspension bridge design by Franz Dishinger, as well as the cable-supported girder bridge, which merges a girder bridge with one of the primary types Notably, the extra closed bridge is a specific variation of the cable-supported girder bridge.
Traditionally, girder bridges and arch bridges are favored for short to medium spans, while cable-stayed bridges are optimal for medium to longer spans, and suspension bridges excel in very long spans In the 1960s, engineers estimated that the maximum span for cable-stayed bridges was around 450 meters and for girder bridges, about 250 meters However, these limits have been surpassed, as modern cable-stayed bridges now exceed spans of 1000 meters.
Advancements in construction materials and techniques have significantly increased the reasonable span lengths of various bridge types However, the relative comparisons between these spans remain valid, with only the numerical values of the span ranges having changed.
FIGURE 1.1 Four basic types of bridges.
Engineers should not be confined by traditional assumptions regarding bridge design It is crucial for them to grasp the actual limitations of each bridge type, informed by the latest advancements in construction materials and equipment As new materials emerge, engineers must be prepared to reassess these limitations using the same foundational principles A solid understanding of structural characteristics is essential for this process To start, we can examine the fundamental elements that constitute structures.
Structures, regardless of their complexity, consist of four fundamental types of structural elements: axial force elements (A), bending elements (B), curved elements (C), and torsional elements (T), collectively known as the ABCT of structures The first three element types—A, B, and C—are capable of forming nearly all types of structures, while torsional elements, although often derived from combinations of the first three, can enhance clarity in our understanding of structural design.
In cable-stayed and truss bridges, the primary role of cables, girders, and towers is to manage axial forces, classifying them as A elements Although local effects may induce bending moments in these structures, they are typically secondary In contrast, girder bridges primarily support loads through bending, categorizing them as B elements When an axial force element shifts direction, it generates a lateral force component, which can effectively counter lateral loads If these lateral loads are closely spaced, the structural element transforms into a curved form, designating it as a C element.
The “A-B-C” of basic structural elements
Curved elements in bridge design can be categorized based on the axial force they experience; compression results in an arch-like structure, while tension resembles a suspended cable, akin to the main cable of a suspension bridge By utilizing A, B, and C elements, engineers can construct frameworks for nearly all major bridge types Torsion, typically a localized effect, often occurs alongside these elements, particularly in eccentrically loaded girder bridges, where it coexists with bending moments Despite the presence of torsion, the bending moment remains the primary design consideration, allowing the structure to be classified predominantly as a B element.
In design, it is crucial to proportion structural elements to stay within allowable stress limits As illustrated in Figure 1.4, the A element allows for full utilization of its cross section, as all parts can reach the allowable stress simultaneously In contrast, the B element is less efficient, with only the extreme fiber able to achieve the allowable stress, leaving the majority of its cross section underutilized The C element, like the A element, demonstrates greater efficiency compared to the B element, making it a more effective choice in structural design.
Inefficient load distribution in bridge elements necessitates additional material to support the same weight, increasing dead weight and posing challenges, particularly for long-span bridges Notably, the Shibanpo Bridge in Chongqing, China, holds the record for the longest girder bridge span at 330 meters, while the Chaotianmen Bridge, also in Chongqing, is the longest arch bridge span at 552 meters The Vladivostok Bridge in Russia boasts the longest cable-stayed span at 1,104 meters, and the Akashi Kaikyo Bridge in Japan features the longest suspension bridge span at 1,991 meters Among these, the Shibanpo Bridge is the shortest, exemplifying the unique characteristics of girder bridges.
FIGURE 1.4 Stress distribution in A and B elements.
The Shibanpo Bridge, depicted in Figure 1.5, primarily relies on bending to support loads, classifying it as a B element B elements are known for their lower efficiency, resulting in bridges that predominantly feature them having reduced maximum spans.
Before designing a bridge, it is crucial to identify potential challenges and understand the specific limitations that may affect the project These limitations can include environmental, financial, social, historical, and technical boundaries, which are unique to each project While technical issues may have universal applicability, other constraints vary significantly from one project to another.
When designing a bridge, engineers encounter two main types of technical challenges: technical difficulties, which are solvable albeit potentially costly in time and resources, and technical limitations, which represent fixed constraints that cannot be surpassed A key technical issue is determining the maximum span length for various bridge types This article aims to analyze and provide insights into the maximum possible span lengths for four specific bridge designs.
When a bridge span is very long, we will face various technical problems The most prominent prob- lems are the following:
1 Girder stiffness in the transverse direction
2 Reduction in cable efficiency of very long cables in a cable-stayed bridge
3 Torsional stiffness of the main girder
4 Allowable stresses of the construction materials
The choice of construction materials significantly impacts the maximum span lengths of long-span bridges For over 150 years, steel and concrete have been the primary materials utilized in their construction Although fibers and composites are available, they have not yet reached a level of readiness for widespread use in major long-span bridge projects Consequently, this analysis will focus exclusively on steel and concrete, noting that in the case of very long-span bridges, steel remains the dominant material, with concrete serving a secondary role, except in girder bridges.
Steel became widely used in commercial applications starting in the mid-nineteenth century, following a period when iron was briefly utilized Prior to this, bridges were predominantly constructed from stones and bricks, materials known for their excellent compressive strength but lacking in tensile strength This limitation confined bridge design to arch structures, which are evident in historical records For thousands of years leading up to the nineteenth century, all longer span bridges were primarily built using stones and bricks, reinforcing the dominance of arch bridges in that era.
In order to estimate the maximum possible span of each bridge type, we must address the above- mentioned problems first.
1.4.3.1 Lateral Stiffness of the Main Girder
The minimum width of a bridge is influenced by its traffic pattern, with a standard six-lane bridge typically measuring around 34 meters in deck width For a 1000-meter span, this results in a span-to-width ratio of approximately 29.4, allowing the bridge to effectively withstand lateral loads from wind, earthquakes, and other forces However, increasing the span to 2000 meters raises the ratio to 59, posing challenges in resisting lateral loads, and further increases in span exacerbate this issue To enhance stability, one straightforward solution is to widen the bridge, as exemplified by the under-construction Messina Strait Bridge in Italy Additionally, there are various methods to improve the lateral stiffness of bridge girders, making this challenge manageable.
1.4.3.2 Effectiveness of a Long Stay Cable
Design Process
The load path refers to the route through which any load acting on a deck is ultimately transferred to the foundation In a cable-stayed bridge, for instance, the weight of a truck on the deck is conveyed from the wheels to the deck plate and floor beams, then to the edge girders, and subsequently through the cables to the tower, finally reaching the foundation Understanding this load path is crucial for structural integrity.
When transferring loads between structural members, it is essential for the load to pass through a joint or linkage connecting them These linkages, often more vulnerable than the main members, must be constructed with care For example, the cable anchorage linking a cable to a tower typically represents a weaker point in the load path compared to both the cable and the tower Therefore, in conceptual design, it is crucial to clearly define the load path and ensure all linkages are properly established.
FIGURE 1.18 New eastern spans of the San Francisco-Oakland Bay Bridge.
1.5.2 Taking Advantage of Redundancy: Permanent Load Condition
Traditionally, bridges have been viewed as two-dimensional structures, leading to their analysis based primarily on three fundamental equations of applied mechanics.
Any structure that can fully satisfy these three equations is a stable structure Any structure that can- not fully satisfy these three equations is not structurally stable.
In conceptual design, the ability to manipulate stress distribution is a powerful tool, particularly in statically indeterminate structures Unlike statically determinate structures, where stress distribution cannot be altered, statically indeterminate structures offer various stress distribution patterns For instance, a two-span bridge can be seen as two simply supported beams if the spans are not continuous However, if the spans are continuous, the bridge becomes a one-degree statically indeterminate structure, introducing one unknown in the calculation of forces and bending moments This flexibility allows for the assignment of any value to the unknown while still satisfying the fundamental equations, resulting in a stable structure.
For simplicity’s sake, let us assume the bending moment at the middle support, M b , is the unknown
Setting the bending moment M b to zero results in a bending moment in the bridge equivalent to that of two simply supported beams By assigning different values to M b, we can generate various bending moment diagrams for the bridge This variation allows us to optimize the efficiency of the bridge girder effectively.
To achieve the desired value of M b in construction, one effective method involves adjusting the reaction at the center support using hydraulic jacks, allowing for the attainment of any specified value of Mb.
A three-span continuous girder is classified as a two-degree statically indeterminate structure, featuring two unknowns whose values can be assumed at will In general, an N degree statically indeterminate structure will present N unknowns, also assumable For permanent load conditions, the stress distribution across the entire bridge can be calculated using the three fundamental equations outlined in Section 1.5.2 This calculation remains straightforward, even for complex structures like cable-stayed bridges with numerous cables.
A bridge is inherently a three-dimensional structure; however, for global design purposes, a two-dimensional analysis is often adequate When a three-dimensional analysis is required, it introduces six equations to consider, compared to the three fundamental equations of mechanics.
∑Fx= ∑0; Fy= ∑0; Fz= ∑0; Mx= ∑0; My= ∑0; Mz=0.
The fundamental principle remains unchanged, allowing us to assign any desired value to each unknown within the structure Ultimately, this enables us to determine the complete force distribution by utilizing these six equations.
For the majority of bridges, the permanent load is the primary load affecting the structure, while the live load typically constitutes less than 20% of the total load Consequently, a significant portion of the stresses within the bridge can be determined using straightforward calculations, as outlined in this section.
This calculation is significant as it does not consider the bridge's stiffness, allowing it to be performed prior to finalizing the dimensions of the bridge members.
Prestressing introduces artificial forces into structures, with parabolic prestressing tendons being a notable example that creates a uniform load against its curvature Similar in concept to the main cables of a suspension bridge, these tendons can effectively balance the dead weight of a bridge girder when arranged correctly The level of balance can be precisely controlled for optimal performance, and various tendon profiles beyond the parabolic shape can also be utilized.
Cable-stayed bridges exemplify a unique form of prestressing, where the tension in each cable can be precisely controlled to create diverse moment diagrams in the girder.
The original concept of prestressing aimed to precompress concrete to counteract tensile stresses under service loads, enabling the construction of numerous long-span concrete bridges over the past century However, in designing prestressed concrete bridges, it is crucial to consider the long-term deformation effects caused by concrete creep, shrinkage, and steel relaxation, as these factors can significantly impact the performance of long-span structures.
The application of prestressing is not limited to concrete We can prestress a steel bridge too Prestressing introduces artificial forces into the structure, no matter what the structural materials are.
1.5.4 Live Load and Other Loads
Once a bridge is completed and open for traffic, structural modifications are no longer feasible It is essential to calculate the stresses based on the actual stiffness of the bridge members, as live and other loads are applied after completion Anticipating the effects of these loads is crucial for estimating their magnitude during the conceptual design phase While specifications provide guidelines, they may not always reflect the latest data, necessitating site-specific studies Additionally, certain unique circumstances may require special considerations in the design process.
Earthquake and wind represent two different types of loads a bridge has to endure.
Conceptualization
The conceptual design of a bridge aims to identify the optimal solution that ensures safety, functionality, and aesthetic appeal while adhering to budget constraints This process often leads to two distinct approaches: either developing a new concept tailored to specific conditions or implementing a long-held idea from the engineer's experience.
Developing a new bridge design to meet specific boundary conditions is a common approach in engineering For instance, when an 800-meter span is required due to navigational criteria, options like cable-stayed or suspension bridges arise If soil conditions are inadequate for anchoring large horizontal forces, a cable-stayed bridge becomes preferable However, concrete cable-stayed bridges may be too heavy and costly for such spans, leading to a choice between steel or composite girders based on economic factors and local construction expertise The cross-section of the girder, whether a box girder or truss, and its shape—streamlined, trapezoidal, or rectangular—must be carefully considered alongside aesthetic elements like tower design, material selection, color combinations, and lighting arrangements Technical aspects such as aerodynamic effects, seismic movements, foundation settlements, thermal movements, durability, maintainability, constructability, life cycle costs, and environmental requirements are also crucial Gradually, these considerations lead to a bridge concept that fulfills all imposed conditions The Dagu Bridge in Tianjin, China exemplifies this derivative design process, featuring a 106-meter span over the 96-meter wide Haihe River, accommodating six lanes of traffic and two pedestrian paths while adhering to local aesthetic and functional requirements.
• Owing to navigation requirements of the river, the arches must be placed above the deck.
• A regular arch bridge would have two arch ribs, one each side of the deck They would have been over 32 m apart.
The girder's depth of less than 1.4 meters is inadequate for spanning a 32-meter-wide deck transversely; therefore, the two arches are repositioned to the edges of the traffic lanes, resulting in a separation of approximately 24 meters between them.
To prevent lateral buckling, unconnected arch ribs must be significantly bulky, which compromises aesthetics; two vertical arch ribs can appear unremarkable and lack visual appeal.
Connecting the two arch ribs with struts enhances stability, allowing for a more slender design However, this approach may appear visually unappealing for smaller spans, making it less acceptable from an aesthetic standpoint.
• For the 106-m span, a basket-handle configuration would appear too flat.
A three-dimensional structural system incorporates two planes of hangers for each arch rib, effectively addressing the issue of lateral buckling This innovative design allows for the creation of exceptionally slender ribs.
• With two planes of cables stabilizing each arch rib, it is possible to tilt the arch ribs outwards so passengers on the bridge deck will have a very open view.
The bridge's design features asymmetrical arches, with one arch intentionally taller than the other to reflect the surrounding landscape's irregularity This height difference enhances the bridge's visual appeal, while the steeper inclination of the taller arch ensures stability by preventing excessive outward lean.
• And, this becomes the Dagu Bridge (see Figure 1.22).
The design process of the bridge was influenced by specific constraints, yet it also prioritized aesthetics This methodical approach ultimately led to a distinctive concept, inspired by the owner's preference for an arch bridge.
( f) FIGURE 1.21 Development of the Dagu Bridge concept.
During the conceptual design stage, we evaluated construction methods, ultimately opting for a straightforward and economical approach due to the river's non-navigable condition at the time False work was utilized to construct the deck girder, with girder sections welded together while supported by piles Additional false work was established on the completed deck to support the arch ribs, facilitating the construction of the inclined arch ribs.
As engineers, we often have intriguing bridge concepts in mind that lack the right opportunity for application This could involve enhancing an existing bridge with specific modifications to better suit a landscape or exploring long-held innovative ideas When the right moment arises, it becomes clear that this is the ideal choice for implementation Essentially, it's about applying existing bridge concepts rather than creating new ones, with only minor adjustments typically required, as perfect conditions are rare.
The Twin River Bridges, which include the Dongshuimen Bridge over the Yangtze River and the Qianshimen Bridge over the Jialing River in Chongqing, China, exemplify a unique architectural vision The towers' design is reminiscent of an ancient Chinese weaving machine, featuring a gap at the top that allows sunlight to filter through, enhancing the visual appeal Despite a longstanding desire to create distinctive bridge towers, the majority of Chinese bridges are six-lane structures requiring wider decks, which can compromise aesthetic elegance However, the Twin River Bridges, with their four-lane upper deck and two transit tracks below, utilize a deep girder and narrower deck, making them ideal for this innovative tower shape This design reflects a long-awaited opportunity to implement a more graceful and culturally resonant bridge architecture.
The tower shape of the bridges, characterized by its curved formwork, incurs higher construction costs; however, aesthetics were prioritized due to their prominent location at the confluence of two rivers, resembling the city's gateway The lower transit level adheres to strict deformation limits, with a 13-meter-deep truss girder providing necessary stiffness and offering passengers stunning views of the river valleys through its large openings To maintain a transparent appearance and preserve the cityscape, a single plane of cables was utilized, and the bridge was designed as a cable-supported girder structure, minimizing the number of cables The constant curvature of the tower shafts simplifies formwork, with three towers sharing a uniform design, though some have longer bases due to varying ground levels, enhancing formwork efficiency This project exemplifies a unique application of a pre-existing design concept to a new bridge.
The development of bridge concepts often involves a blend of different approaches, such as adapting an existing design to suit local conditions or enhancing specific elements of a bridge to optimize both cost-effectiveness and visual appeal.
Aesthetics
A bridge can be charming and graceful; a bridge can also be spectacular and emit excitement Regardless, a bridge must be attractive Aesthetics are a basic requirement of bridge design.
Engineers often adhere to established rules found in books and specifications, yet aesthetics defy such guidelines The ancient Greeks exemplified this, dedicating immense effort to the aesthetics of their structures, with the Parthenon standing out as a pinnacle of architectural perfection This iconic building showcases meticulous attention to detail, where every element is carefully crafted to achieve a desired visual effect For instance, the upward curvature of horizontal lines and the varied spacing and diameters of columns create an illusion of uniformity, highlighting that these are not strict aesthetic rules, but rather thoughtful refinements to enhance visual appeal.
Despite numerous attempts by scholars to define the rules of structural beauty, a definitive standard remains elusive One prominent concept is the "golden section," which asserts that a rectangle with a side ratio of Φ (approximately 1.618) is the most aesthetically pleasing This idea has been explored for centuries, yet it remains controversial whether this rectangle universally surpasses the visual appeal of a square.
Aesthetics revolves around the concepts of proportion, balance, and harmony, as highlighted by Italian Renaissance architect Alberti, who described beauty as “a harmony of all the parts.” Our perception of beauty is primarily emotional rather than logical, allowing us to appreciate the dramatic, daring, graceful, and poetic qualities of objects like bridges Ultimately, the goal is to evoke an emotional and visceral response from the audience, making the process of achieving this response an art form in itself.
A bridge should seamlessly blend into its environment, appearing natural, simple, and original while harmonizing with its surroundings (Tang, 2006a) As a prominent feature in a city, it must convey its function clearly to the public, avoiding a superficial appearance Ultimately, the design should prioritize simplicity and authenticity to enhance its integration with the landscape.
Uniqueness is a vital aspect of art, and this principle applies equally to bridge design, where no two bridges should be identical Each bridge must address specific requirements and site characteristics to achieve originality, style, and character Much like a valuable painting, a bridge's distinctiveness significantly enhances its subjective worth, making it a unique architectural masterpiece.
Nature endorses simplicity Even the most important equations of nature are extremely simple, like
The human mind naturally favors simplicity, as evidenced by fundamental equations like F = ma and E = mc² In architecture, the simplest bridge designs often emerge as the most aesthetically pleasing and widely accepted solutions Achieving beauty in structure involves a process of simplification, where unnecessary elements are eliminated without compromising functionality This process demands both experience and a deep understanding of structural integrity and aesthetics.
A well-designed and aesthetically pleasing bridge can often be more economical, as it aligns with natural principles and simplicity However, the beauty of a bridge may sometimes come at a higher cost, prompting a necessary evaluation of the trade-off between beauty and expense The decision to invest in a more visually appealing structure depends on specific circumstances Beyond its primary function of facilitating traffic, a bridge can embody symbolic significance and aesthetic value If deemed a signature structure, the additional investment in beauty may be justified.
Everyday decisions, such as purchasing a house or clothing, involve balancing cost and personal preferences Most people choose homes that are affordable yet align with their aesthetic tastes, rather than opting for the cheapest or most expensive options Ultimately, we strive to find a harmonious blend of affordability and style in our choices.
A completed bridge will be prominently displayed for centuries, highlighting the importance of creating an aesthetically pleasing structure The visual appeal of a bridge significantly impacts the community, as a poorly designed bridge can have negative effects on the surrounding area While aesthetics should not be the sole focus in bridge construction, a well-designed bridge can enhance the overall beauty of a city, as no beautiful city can thrive with an unattractive bridge.
Creating a visually appealing bridge demands considerable time and effort; however, as design becomes routine, this process becomes less burdensome Bridge engineers must prioritize aesthetics, as an unattractive bridge can negatively impact a community, akin to a form of pollution that is challenging to eliminate swiftly.
Aesthetic lighting significantly enhances the visual appeal of bridges at night, with various lighting techniques available Suspension bridges often utilize lace lighting, where lights are affixed to the main cables, allowing for easier maintenance due to their walkable size In contrast, cable-stayed bridges require lights to be installed on the bridge deck since their cables are too small for such installations Visual representations of different aesthetic lighting schemes can be found in Figure 1.24.
Decoration in bridge design can be likened to cosmetics; a truly beautiful bridge does not require embellishments The most effective bridges express their beauty through their structural form, and minor details like covers for cable anchorages do not constitute decoration In the case of large bridges, their sheer scale and design can overshadow any decorative elements, making them appear less impressive However, when a bridge is intended to symbolize a specific meaning or commemorate an event, the use of decorations can be fitting and enhance its significance.
Urban bridges are typically smaller and designed for aesthetic appeal, enhancing their integration with the surrounding environment In contrast, bridges in natural settings should prioritize simplicity and a strong connection to nature, making elaborate decorations less suitable.