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Basic Theory of Plates and Elastic Stability - Part 10

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Tài liệu tham khảo giáo trình cơ học kết cấu trong ngành xây dựng bằng Tiếng Anh - Yamaguchi, E. “Basic Theory of Plates and Elastic Stability” Structural Engineering Handbook Ed. Chen Wai-Fah Boca Raton: CRC Press LLC, 1999 - Bridge Structures

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Nội dung Text: Basic Theory of Plates and Elastic Stability - Part 10

  1. Toma, S.; Duan, L. and Chen, W.F. “Bridge Structures” Structural Engineering Handbook Ed. Chen Wai-Fah Boca Raton: CRC Press LLC, 1999
  2. Bridge Structures 10.1 General 10.2 Steel Bridges 10.3 Concrete Bridges 10.4 Concrete Substructures 10.5 Floor System 10.6 Bearings, Expansion Joints, and Railings Shouji Toma 10.7 Girder Bridges Department of Civil Engineering, Hokkai-Gakuen University, Sapporo, Japan 10.8 Truss Bridges 10.9 Rigid Frame Bridges (Rahmen Bridges) Lian Duan 10.10Arch Bridges 10.11Cable-Stayed Bridges Division of Structures, California Department of Transportation, Sacramento, 10.12Suspension Bridges CA 10.13Defining Terms Acknowledgment Wai-Fah Chen References School of Civil Engineering, Further Reading Purdue University, Appendix: Design Examples West Lafayette, IN 10.1 General 10.1.1 Introduction A bridge is a structure that crosses over a river, bay, or other obstruction, permitting the smooth and safe passage of vehicles, trains, and pedestrians. An elevation view of a typical bridge is shown in Figure 10.1. A bridge structure is divided into an upper part (the superstructure), which consists of the slab, the floor system, and the main truss or girders, and a lower part (the substructure), which are columns, piers, towers, footings, piles, and abutments. The superstructure provides horizontal spans such as deck and girders and carries traffic loads directly. The substructure supports the horizontal spans, elevating above the ground surface. In this chapter, main structural features of common types of steel and concrete bridges are discussed. Two design examples, a two-span continuous, cast-in-place, prestressed concrete box girder bridge and a three-span continuous, composite plate girder bridge, are given in the Appendix. 1999 by CRC Press LLC c
  3. c 1999 by CRC Press LLC FIGURE 10.1: Elevation view of a typical bridge.
  4. 10.1.2 Classification 1. Classification by Materials Steel bridges: A steel bridge may use a wide variety of structural steel components and systems: girders, frames, trusses, arches, and suspension cables. Concrete bridges: There are two primary types of concrete bridges: reinforced and prestressed. Timber bridges: Wooden bridges are used when the span is relatively short. Metal alloy bridges: Metal alloys such as aluminum alloy and stainless steel are also used in bridge construction. 2. Classification by Objectives Highway bridges: bridges on highways. Railway bridges: bridges on railroads. Combined bridges: bridges carrying vehicles and trains. Pedestrian bridges: bridges carrying pedestrian traffic. Aqueduct bridges: bridges supporting pipes with channeled waterflow. Bridges can alternatively be classified into movable (for ships to pass the river) or fixed and permanent or temporary categories. 3. Classification by Structural System (Superstructures) Plate girder bridges: The main girders consist of a plate assemblage of upper and lower flanges and a web. H- or I-cross-sections effectively resist bending and shear. Box girder bridges: The single (or multiple) main girder consists of a box beam fabricated from steel plates or formed from concrete, which resists not only bending and shear but also torsion effectively. T-beam bridges: A number of reinforced concrete T-beams are placed side by side to support the live load. Composite girder bridges: The concrete deck slab works in conjunction with the steel girders to support loads as a united beam. The steel girder takes mainly tension, while the concrete slab takes the compression component of the bending moment. Grillage girder bridges: The main girders are connected transversely by floor beams to form a grid pattern which shares the loads with the main girders. Truss bridges: Truss bar members are theoretically considered to be connected with pins at their ends to form triangles. Each member resists an axial force, either in compression or tension. Figure 10.1 shows a Warren truss bridge with vertical members, which is a “trough bridge”, i.e., the deck slab passes through the lower part of the bridge. Figure 10.2 shows a comparison of the four design alternatives evaluated for Minato Oh-Hasshi in Osaka, Japan. The truss frame design was selected. Arch bridges: The arch is a structure that resists load mainly in axial compression. In ancient times stone was the most common material used to construct magnif- icent arch bridges. There is a wide variety of arch bridges as will be discussed in Section 10.10 1999 by CRC Press LLC c
  5. FIGURE 10.2: Design comparison for Minato Oh-Hashi, Japan. (From Hanshin Expressway Public Corporation, Construction Records of Minato Oh-Hashi, Japan Society of Civil Engineers, Tokyo [in Japanese], 1975. With permission.) Cable-stayed bridges: The girders are supported by highly strengthened cables (often composed of tightly bound steel strands) which stem directly from the tower. These are most suited to bridge long distances. Suspension bridges: The girders are suspended by hangers tied to the main cables which hang from the towers. The load is transmitted mainly by tension in cable. 1999 by CRC Press LLC c
  6. This design is suitable for very long span bridges. Table 10.1 shows the span lengths appropriate to each type of bridge. 4. Classification by Support Condition Figure 10.3 shows three different support conditions for girder bridges. Simply supported bridges: The main girders or trusses are supported by a movable hinge at one end and a fixed hinge at the other (simple support); thus they can be analyzed using only the conditions of equilibrium. Continuously supported bridges: Girders or trusses are supported continuously by more than three supports, resulting in a structurally indeterminate system. These tend to be more economical since fewer expansion joints, which have a common cause of service and maintenance problems, are needed. Sinkage at the supports must be avoided. Gerber bridges (cantilever bridge): A continuous bridge is rendered determinate by placing intermediate hinges between the supports. Minato Oh-Hashi’s bridge, shown in Figure 10.2a, is an example of a Gerber truss bridge. 10.1.3 Plan Before the structural design of a bridge is considered, a bridge project will start with planning the fundamental design conditions. A bridge plan must consider the following factors: 1. Passing Line and Location A bridge, being a continuation of a road, does best to follow the line of the road. A right angle bridge is easy to design and construct but often forces the line to be bent. A skewed bridge or a curved bridge is commonly required for expressways or railroads where the road line must be kept straight or curved, even at the cost of a more difficult design (see Figure 10.4). 2. Width The width of a highway bridge is usually defined as the width of the roadway plus that of the sidewalk, and often the same dimension as that of the approaching road. 3. Type of Structure and Span Length The types of substructures and superstructures are determined by factors such as the surrounding geographical features, the soil foundation, the passing line and its width, the length and span of the bridge, aesthetics, the requirement for clearance below the bridge, transportation of the construction materials and erection procedures, construction cost, period, and so forth. 4. Aesthetics A bridge is required not only to fulfill its function as a thoroughfare, but also to use its structure and form to blend, harmonize, and enhance its surroundings. 10.1.4 Design The bridge design includes selection of a bridge type, structural analysis and member design, and preparation of detailed plans and drawings. The size of members that satisfy the requirements of design codes are chosen [1, 17]. They must sustain prescribed loads. Structural analyses are performed on a model of the bridge to ensure safety as well as to judge the economy of the design. The final design is committed to drawings and given to contractors. 1999 by CRC Press LLC c
  7. c 1999 by CRC Press LLC TABLE 10.1 Types of Bridges and Applicable Span Lengths From JASBC, Manual Design Data Book, Japan Association of Steel Bridge Construction, Tokyo (in Japanese), 1981. With permission.
  8. FIGURE 10.3: Supporting conditions. FIGURE 10.4: Bridge lines. 10.1.5 Loads Designers should consider the following loads in bridge design: 1. Primary loads exert constantly or continuously on the bridge. Dead load: weight of the bridge. Live load: vehicles, trains, or pedestrians, including the effect of impact. A vehicular load is classified into three parts by AASHTO [1]: the truck axle load, a tandem load, and a uniformly distributed lane load. Other primary loads may be generated by prestressing forces, the creep of concrete, the shrinkage of concrete, soil pressure, water pressure, buoyancy, snow, and centrifugal actions or waves. 1999 by CRC Press LLC c
  9. 2. Secondary loads occur at infrequent intervals. Wind load: a typhoon or hurricane. Earthquake load: especially critical in its effect on the substructure. Other secondary loads come about with changes in temperature, acceleration, or tempo- rary loads during erection, collision forces, and so forth. 10.1.6 Influence Lines Since the live loads by definition move, the worst case scenario along the bridge must be determined. The maximum live load bending moment and shear envelopes are calculated conveniently using influence lines. The influence line graphically illustrates the maximum forces (bending moment and shear), reactions, and deflections over a section of girder as a load travels along its length. Influence lines for the bending moment and shear force of a simply supported beam are shown in Figure 10.5. For a concentrated load, the bending moment or shear at section A can be calculated by multiplying the load and the influence line scalar. For a uniformly distributed load, it is the product of the load intensity and the net area of the corresponding influence line diagram. 10.2 Steel Bridges 10.2.1 Introduction The main part of a steel bridge is made up of steel plates which compose main girders or frames to support a concrete deck. Gas flame cutting is generally used to cut steel plates to designated dimensions. Fabrication by welding is conducted in the shop where the bridge components are prepared before being assembled (usually bolted) on the construction site. Several members for two typical steel bridges, plate girder and truss bridges, are given in Figure 10.6. The composite plate girder bridge in Figure 10.6a is a deck type while the truss bridge in Figure 10.6b is a through-deck type. Steel has higher strength, ductility, and toughness than many other structural materials such as concrete or wood, and thus makes an economical design. However, steel must be painted to prevent rusting and also stiffened to prevent a local buckling of thin members and plates. 10.2.2 Welding Welding is the most effective means of connecting steel plates. The properties of steel change when heated and this change is usually for the worse. Molten steel must be shielded from the air to prevent oxidization. Welding can be categorized by the method of heating and the shielding procedure. Shielded metal arc welding (SMAW), submerged arc welding (SAW), CO2 gas metal arc welding (GMAW), tungsten arc inert gas welding (TIG), metal arc inert gas welding (MIG), electric beam welding, laser beam welding, and friction welding are common methods. The first two welding procedures mentioned above, SMAW and SAW, are used extensively in bridge construction due to their high efficiency. Both use an electric arc, which is generally considered the most efficient method of applying heat. SMAW is done by hand and is suitable for welding complicated joints but is less efficient than SAW. SAW is generally automated and can be very effective for welding simple parts such as the connection between the flange and web of plate girders. A typical placement of these welding methods is shown in Figure 10.7. TIG and MIG use an electric arc for heat source and inert gas for shielding. An electric beam weld must not be exposed to air, and therefore must be laid in a vacuum chamber. A laser beam weld can be placed in air but is less versatile than other types of welding. It cannot be 1999 by CRC Press LLC c
  10. FIGURE 10.5: Influence lines. used on thick plates but is ideal for minute or artistic work. Since the welding equipment necessary for heating and shielding is not easy to handle on a construction site, all welds are usually laid in the fabrication shop. The heating and cooling processes during welding induce residual stresses to the connected parts. The steel surfaces or parts of the cross section at some distance from the hot weld, cool first. When the area close to the weld then cools, it tries to shrink but is restrained by the more solidified and 1999 by CRC Press LLC c
  11. FIGURE 10.6: Member names of steel bridges. (From Tachibana, Y. and Nakai, H., Bridge Engineering, Kyoritsu Publishing Co., Tokyo, Japan [in Japanese], 1996. With permission.) cooler parts. Thus, tensile residual stresses are trapped in the vicinity of the weld while the outer parts are put into compression. There are two types of welded joints: groove and fillet welds (Figure 10.8). The fillet weld is placed at the junction of two plates, often between a web and flange. It is a relatively simple procedure with no machining required. The groove weld, also called a butt weld, is suitable for joints requiring greater strength. Depending on the thickness of adjoining plates, the edges are beveled in preparation for the weld to allow the metal to fill the joint. Various groove weld geometries for full penetration welding are shown in Figure 10.8b. Inspection of welding is an important task since an imperfect weld may well have catastrophic consequences. It is difficult to find faults such as an interior crack or a blow hole by observing only the surface of a weld. Many nondestructive testing procedures are available which use various devices, such as x-ray, ultrasonic waves, color paint, or magnetic particles. These all have their own advantages and disadvantages. For example, the x-ray and the ultrasonic tests are suitable for interior faults but 1999 by CRC Press LLC c
  12. FIGURE 10.7: Welding methods. (From Nagai, N., Bridge Engineering, Kyoritsu Publishing Co., Tokyo, Japan [in Japanese], 1994. With permission.) require expensive equipment. Use of color paint or magnetic particles, on the other hand, is a cheap alternative but only detects surface flaws. The x-ray and ultrasonic tests are used in common bridge construction, but ultrasonic testing is becoming increasingly popular for both its “high tech” and its economical features. 10.2.3 Bolting Bolting does not require the skilled workmanship needed for welding, and is thus a simpler alternative. It is applied to the connections worked on construction site. Some disadvantages, however, are incurred: (1) splice plates are needed and the force transfer is indirect; (2) screwing-in of the bolts creates noise; and (3) aesthetically bolts are less appealing. In special cases that need to avoid these disadvantages, the welding may be used even for site connections. There are three types of high-tensile strength-bolted connections: the slip-critical connection, the bearing-type connection (Figure 10.9), and the tensile connection (Figure 10.10). The slip-critical (friction) bolt is most commonly used in bridge construction as well as other steel structures because it is simpler than a bearing-type bolt and more reliable than a tension bolt. The force is transferred by 1999 by CRC Press LLC c
  13. FIGURE 10.8: Types of welding joints. (From Tachibana, Y. and Nakai, H., Bridge Engineering, Kyoritsu Publishing Co., Tokyo, Japan [in Japanese], 1996. With permission.) the friction generated between the base plates and the splice plates. The friction resistance is induced by the axial compression force in the bolts. The bearing-type bolt transfers the force by bearing against the plate as well as making some use of friction. The bearing-type bolt can transfer larger force than the friction bolts but is less forgiving with respect to the clearance space often existing between the bolt and the plate. These require that precise holes be drilled and at exact spacings. The force transfer mechanism for these connections is shown in Figure 10.9. In the beam-to-column connection shown in Figure 10.10, the bolts attached to the column are tension bolts while the bolts on the beam are slip-critical bolts. The tension bolt transfers force in the direction of the bolt axis. The tension type of bolt connection is easy to connect on site, but difficulties arise in distributing forces equally to each bolt, resulting in reduced reliability. Tension bolts may also be used to connect box members of the towers of suspension bridges where compression forces are larger than the tension forces. In this case, the compression is shared with butting surfaces of the plates and the tension is carried by the bolts. 10.2.4 Fabrication in Shop Steel bridges are fabricated into members in the shop yard and then transported to the construction site for assembly. Ideally all constructional work would be completed in the shop to get the highest quality in the minimum construction time. The larger and longer the members can be, the better, within the restrictions set by transportation limits and erection tolerances. When crane ships for erection and barges for transportation can be used, one block can weigh as much as a thousand tons 1999 by CRC Press LLC c
  14. FIGURE 10.9: Slip-critical and bearing-type connections. (From Nagai, N., Bridge Engineering, Kyoritsu Publishing Co., Tokyo, Japan [in Japanese], 1994. With permission.) and be erected as a whole on the quay. In these cases the bridge is made of a single continuous block and much of the hassle usually associated with assembly and erection is avoided. 10.2.5 Construction on Site The designer must consider the loads that occur during construction, generally different from those occurring after completion. Steel bridges are particularly prone to buckling during construction. The erection plan must be made prior to the main design and must be checked for every possible load case that may arise during erection, not only for strength but also for stability. Truck crane and bent erection (or staging erection); launching erection; cable erection; cantilever erection; and large block erection (or floating crane erection) are several techniques (see Figure 10.11). An example of the large block erection is shown in Figure 10.43, in which a 186-m, 4500-ton center block is transported by barge and lifted. 10.2.6 Painting Steel must be painted to protect it from rusting. There is a wide variety of paints, and the life of a steel structure is largely influenced by its quality. In areas near the sea, the salty air is particularly harmful to exposed steel. The cost of painting is high but is essential to the continued good condition of the bridge. The color of the paint is also an important consideration in terms of its public appeal or aesthetic quality. 1999 by CRC Press LLC c
  15. FIGURE 10.10: Tension-type connection. 10.3 Concrete Bridges 10.3.1 Introduction For modern bridges, both structural concrete and steel give satisfactory performance. The choice between the two materials depends mainly upon the cost of construction and maintenance. Generally, concrete structures require less maintenance than steel structures, but since the relative cost of steel and concrete is different from country to country, and may even vary throughout different parts of the same country, it is impossible to put one definitively above the other in terms of “economy”. In this section, the main features of common types of concrete bridge superstructures are briefly discussed. Concrete bridge substructures will be discussed in Section 10.4. A design example of a two-span continuous, cast-in-place, prestressed concrete box girder bridge is given in the Appendix. For a more detailed look at design procedures for concrete bridges, reference should be made to the recent books of Gerwick [7], Troitsky [24], Xanthakos [26, 27], and Tonias [23]. 10.3.2 Reinforced Concrete Bridges Figure 10.12 shows the typical reinforced concrete sections commonly used in highway bridge su- perstructures. 1. Slab A reinforced concrete slab (Figure 10.12a) is the most economical bridge superstructure for spans of up to approximately 40 ft (12.2 m). The slab has simple details and standard formwork and is neat, simple, and pleasing in appearance. Common spans range from 16 to 44 ft (4.9 to 13.4 m) with structural depth-to-span ratios of 0.06 for simple spans and 0.045 for continuous spans. 2. T-Beam (Deck Girder) The T-beams (Figure 10.12b) are generally economic for spans of 40 to 60 ft (12.2 to 18.3 m), but do require complicated formwork, particularly for skewed bridges. Structural 1999 by CRC Press LLC c
  16. FIGURE 10.11: Erections methods. (From Japan Construction Mechanization Association, Cost Estimation of Bridge Erection, Tokyo, Japan [in Japanese], 1991. With permission.) depth-to-span ratios are 0.07 for simple spans and 0.065 for continuous spans. The spacing of girders in a T-beam bridge depends on the overall width of the bridge, the slab thickness, and the cost of the formwork and may be taken as 1.5 times the structural depth. The most commonly used spacings are between 6 and 10 ft (1.8 to 3.1 m). 3. Cast-in-Place Box Girder Box girders like the one shown in Figure 10.12c, are often used for spans of 50 to 120 ft 1999 by CRC Press LLC c
  17. FIGURE 10.12: Typical reinforced concrete sections in bridge superstructures. (15.2 to 36.6 m). Its formwork for skewed structures is simpler than that required for the T-beam. Due to excessive dead load deflections, the use of reinforced concrete box girders over simple spans of 100 ft (30.5 m) or more may not be economical. The depth-to-span ratios are typically 0.06 for simple spans and 0.055 for continuous spans with the girders spaced at 1.5 times the structural depth. The high torsional resistance of the box girder makes it particularly suitable for curved alignments, such as the ramps onto freeways. Its smooth flowing lines are appealing in metropolitan cities. 4. Design Consideration A reinforced concrete highway bridge should be designed to satisfy the specification or code requirements, such as the AASHTO-LRFD [1] requirements (American Association of State Highway and Transportation Officials—Load and Resistance Factor Design) for all appropriate service, fatigue, strength, and extreme event limit states. In the AASHTO- LRFD [1], service limit states include cracking and deformation effects, and strength limit states consider the strength and stability of a structure. A bridge structure is usually designed for the strength limit states and is then checked against the appropriate service and extreme event limit states. 1999 by CRC Press LLC c
  18. 10.3.3 Prestressed Concrete Bridges Prestressed concrete, using high-strength materials, makes an attractive alternative for long-span bridges. It has been widely used in bridge structures since the 1950s. 1. Slab Figure 10.13 shows Federal Highway Administration (FHWA) [6] standard types of pre- cast, prestressed, voided slabs and their sectional properties. While cast-in-place, pre- stressed slab is more expensive than reinforced concrete slab, precast, prestressed slab is economical when many spans are involved. Common spans range from 20 to 50 ft (6.1 to 15.2 m). Structural depth-to-span ratios are 0.03 for both simple and continuous spans. FIGURE 10.13: Federal Highway Administration (FHWA) precast, prestressed, voided slab sections. (From Federal Highway Administration, Standard Plans for Highway Bridges, Vol. 1, Concrete Super- structures, U.S. Department of Transportation, Washington, D.C., 1990. With permission.) 2. Precast I Girder Figure 10.14 shows AASHTO [6] standard types of I-beams. These compete with steel girders and generally cost more than reinforced concrete with the same depth-to-span ratios. The formwork is complicated, particularly for skewed structures. These sections are applicable to spans 30 to 120 ft (9.1 to 36.6 m). Structural depth-to-span ratios are 0.055 for simple spans and 0.05 for continuous spans. 1999 by CRC Press LLC c
  19. FIGURE 10.14: Precast, prestressed AASHTO (American Association of State Highway and Trans- portation Officials) I-beam sections. (From Federal Highway Administration, Standard Plans for Highway Bridges, Vol. 1, Concrete Superstructures, U.S. Department of Transportation, Washington, D.C., 1990. With permission.) 3. Box Girder Figure 10.15 shows FHWA [6] standard types of precast box sections. The shape of a cast-in-place, prestressed concrete box girder is similar to the conventional reinforced concrete box girder (Figure 10.12c). The spacing of the girders can be taken as twice the structural depth. It is used mostly for spans of 100 to 600 ft (30.5 to 182.9 m). Structural depth-to-span ratios are 0.045 for simple spans and 0.04 for continuous spans. These 1999 by CRC Press LLC c
  20. sections are used frequently for simple spans of over 100 ft (30.5 m) and are particularly suitable for widening in order to control deflections. About 70 to 80% of California’s highway bridge system is composed of prestressed concrete box girder bridges. FIGURE 10.15: Federal Highway Administration (FHWA) precast, pretensioned box sections. (From Federal Highway Administration, Standard Plans for Highway Bridges, Vol. 1, Concrete Superstructures, U.S. Department of Transportation, Washington, D.C., 1990. With permission.) 4. Segmental Bridge The segmentally constructed bridges have been successfully developed by combining the concepts of prestressing, box girder, and the cantilever construction [2, 20]. The first prestressed segmental box girder bridge was built in Western Europe in 1950. California’s Pine Valley Bridge, as shown in Figure 10.16 (composed of three spans of 340 ft [103.6 m], 450 ft [137.2 m], and 380 ft [115.8 ft] with the pier height of 340 ft [103.6 m]), was the first cast-in-place segmental bridge built in the U.S., in 1974. The prestressed segmental bridges with precast or cast-in-place segmental can be classified by the construction methods: (1) balanced cantilever, (2) span-by-span, (3) incremen- tal launching, and (4) progressive placement. The selection between cast-in-place and precast segmental, and among various construction methods, is dependent on project features, site conditions, environmental and public constraints, construction time for the project, and equipment available. Table 10.2 lists the range of application of segmental bridges by span lengths [20]. 1999 by CRC Press LLC c
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