Shear buckling N

Bending buckling

, Shear buckling

Horizontal stiffener

Vertical stiffener

FIGURE 25.18 Stiffeners of web: (a) buckling of web and (b) stiffeners of web.

supported girder, the longitudinal (horizontal) stiffeners are usually located here. The longitudinal stiffeners are not recommended due to its poor fatigue resistance. Transverse (vertical) stiffeners, on the other hand, prevent shear buckling and provide postelastic shear buckling capacity by the tension field action. The most transverse (vertical) stiffeners are placed near the support since the largest shear force occurs at those locations. Bearing stiffeners are also required at the supports to combat large reaction forces, which are designed independently just as any other compression member would be. Buckling patterns of a web are shown in Figure 25.18. If the web is not too deep nor its thickness is too small, no stiffeners are necessary and fabrication costs are reduced.

2. Variable sections. The variable cross-sections may be used to save material and cost where the bending moment is smaller, that is, near the end of the span (see Figure 25.15). However, this reduction increases the manpower required for welding and fabrication. The cost of manpower and material must be balanced and traded off. In today's industrial climate, manpower is more important and costly than the material. Therefore, the change of girder section may not economic. Likewise, thick plates are often specified to eliminate the number of stiffeners needed, thus to reduce the necessary manpower.

25.4.3 Composite Girder

If two beams are simply laid one upon the other as shown in Figure 25.19a, they act separately and only share the load depending on their relative flexural stiffness. In this case, slip occurs along the boundary between the beams. However, if the two beams are connected and slip prevented as shown in Figure 25.19b, they act as a unit, that is, a composite girder. For composite plate girder bridges, the steel girder and the concrete slab are joined by shear connectors. In this way, the concrete slab becomes integral with the girder and usually takes most of the compression component of the bending moment while the steel plate girder takes the tension. Composite girders are much more effective than the simply tiered girder.

Let us consider the two cases shown in Figure 25.19 and note the difference between tiered beams and composite beams. Both have the same cross-sections and are subjected to a concentrated load at mid-span. The moment of inertia for the composite beam is four times that of the tiered beams, thus the resulting vertical deflection is one fourth. The maximum bending stress in the outer (top or bottom) fiber is a half that of the tiered beam configuration.

The corresponding stress distributions are shown in Figure 25.20. Points "S" and "V" are the center of area of the steel section and the composite section, respectively. According to beam theory, the strain distribution is linear but the stress distribution has a step change at the boundary between the steel and concrete.

FIGURE 25.19 Principle of tiered beam and composite beam: (a) tiered beam and (b) composite beam (Tachibana and Nakai 1996).

Effective width of slab (b)

Effective width of slab (b)

FIGURE 25.20 Section of composite girder: (a) composite girder section and (b) stress distribution (Tachibana and Nakai 1996).

Three types of shear connectors, studs, horse shoes, and steel blocks, are shown in Figure 25.21. Studs are most commonly used since they are easily welded to the compression flange by the electric resistance welding, but the weld inspection is a cumbersome task. If the weld on a certain stud is poor, the stud may shear off and trigger a totally unforeseen failure mode. Other types are considered to maintain more reliability.

Shear connectors are needed most near the ends of the span where the shear force is largest. This region is illustrated in Figure 25.19a, which shows the maximum shift due to slip occurs at ends of tiered beams. It is this slip that is restrained by the shear connectors.

25.4.4 Grillage Girder

When girders are placed in a row and connected transversely by floor beams, the truck loads are distributed by the floor beams to the girders. This system is called as "grillage girder.'' If the main girders are plate girders, no stiffness in torsion is considered. On the other hand, box girders and concrete girders can be analyzed assuming stiffness is available to resist torsion. Floor beams increase the torsional resistance of the whole structural system of bridge.

Let us consider the structural system shown in Figure 25.22a to observe the load distribution in a grillage system. This grillage has three girders with one floor beam at midspan. In this case, there are three nodal forces at the intersections of the girders and the floor beam but only two equilibrium equations (V = 0 and M = 0). Thus, it becomes one degree statically indeterminate. If we disconnect the intersection h

FIGURE 25.21 Type of shear connectors: (a) stud; (b) horse shoe; and (c) steel block (Nagai 1994).

FIGURE 25.21 Type of shear connectors: (a) stud; (b) horse shoe; and (c) steel block (Nagai 1994).

FIGURE 25.22 Grillage girders: (a) one-degree indeterminate system and (b) statically determinate system (Tachibana and Nakai 1996).

between the main girder B and the floor beam and apply a pair of indeterminate forces ''X' at point "b" as shown in Figure 25.22b, X can be obtained using the compatibility condition at point "b." Once the force X is found, the sectional forces in the girders can be calculated. This structural system is commonly applied to the practical design of plate girder bridges.

25.4.5 Widely Spaced Plate Girder

To compete with concrete bridges, a new design concept of steel bridge has been developed by minimizing the number of girders and pieces of fabrication blocks, thus reducing the construction cost. The space between girders is taken wide and the lateral bracing is neglected. An example of the bridge is shown in Figure 25.23, which has only two girders with the space 5.7 m and the prestressed concrete slab deck thickness of 320 mm.

25.4.6 Box Girder

Structural configuration of box girders is illustrated in Figure 25.24. Since the box girder is a closed section, its torsional resistance is high with no loss of strength in bending and shear. On the other hand, plate girders are open sections generally only considered effective in resisting bending and shear. Orthotropic decks — steel plates with longitudinal and transverse stiffeners — are often used for decks on box girder or thin-walled structures instead of a concrete slab (Figure 25.24b) for long-span bridges.

Torsion is resisted in two parts: pure torsion (St Venant torsion) and warping torsion. The pure torsional resistance of I-plate girders is negligible. However, for closed sections such as a box girder, the pure torsional resistance is considerable, making them particularly suited for horizontally curved bridges or long-span bridges. On the other hand, the warping torsion for box section is negligible. The I-section girder has some warping resistance but it is not so large compared to the pure torsion of closed sections.

FIGURE 25.23 Widely spaced girder bridge (Chidorinosawagawa Bridge, Japan, from Kawasaki Heavy Ind., Ltd., with permission).

Lower flange

FIGURE 25.24 Box girder: (a) with reinforced concrete deck and (b) with steel deck (Nagai 1994).

Lower flange

FIGURE 25.24 Box girder: (a) with reinforced concrete deck and (b) with steel deck (Nagai 1994).

25.4.7 Fabrication

Gas flame cutting is generally used to cut steel plates to designated dimensions. Fabrication by welding is conducted in shop where the bridge components are prepared before being assembled (usually bolted) on the construction site. 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. These both use an electric arc that is generally considered the most efficient method of applying heat. SMAW is done by hand and is suitable for welding complicated joints but less efficient than SAW. SAW is generally automated and can be very effective for welding simple parts such as the connection between flange and web of plate girders. A typical placement of these welding methods is shown in Figure 25.25. TIG and MIG use an electric arc for heat source and inert gas for shielding.

(b) Flux nozzle
FIGURE 25.25 Welding methods: (a) shielded metal arc welding; (b) submerged arc welding; and (c) gas metal arc welding (Nagai 1994).



An electric beam weld must not be exposed to air; 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 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 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: fillet and groove welds (Figure 25.26). The fillet weld is placed at the junction of two plates, often between a web and a 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 25.26b.

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 require expensive equipment. Use of color paint or magnetic particles, on the other hand, is a less-expensive 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. 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 a 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) esthetically bolts are less appealing. In special cases that need to avoid these disadvantages, the welding may be used even for site connections.

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