Ventana de parámetros Lluvia – Valor umbral 1 – Salida

Typical arch bridges consist of two or more parallel arches that carry the bridge’s deck through hangers. The hangers are connected with a plane grillage system of transverse and longitudinal beams that supports the deck slab; see Figure 2.27. This is a very elegant configuration that is preferred in cases of rivers and canals because it gives enough under clearance. Arch bridges are usually simply supported systems that are used for span lengths ranging from 50 to 180 m. The maximum value of the total construction depth is in most cases between 1/5 and 1/6 of the span length. More demanding slenderness values can be asked due to architectural reasons and not structural ones.

The structural performance of arched bridges is schematically demonstrated in Figure 2.26. The dead weight of the deck together with the traffic loads is transferred from the transverse beams to the edge girders that are also known as stiffening girders. The hangers behave as inter- mediate supports for the stiffening girders and transmit the vertical loads to the upper part of the structure, the arches. Obviously, the arches are under compression, and therefore, buckling is highly possible. Due to this reason, arches are made of reinforced concrete or of steel closed cross sections. In pure arched bridges (Figure 2.26a), the stiffening girders are connected to the arch only by the hangers. The arch thrust is transferred to the foundation and the soil. When the stiffening girders and the arches are rigidly connected with each other at the bridge ends (Figures 2.26b, c and 2.27), the thrust is transferred to the stiffening girders that behave as ten- sion ties. These systems are known as bowstring arches [2.13] or arch-and-tie bridges.

The arches have usually parabolic form that follows the bending moment diagram of a simply supported beam with a uniform loading. This ensures that arches are uniformly com- pressed under self-weight and bending moments remain low. Biaxial bending due to wind or earthquake can take place, and therefore, symmetrical cross sections of closed geometry are chosen. It has to be stated that a precise buckling analysis must be conducted. This has to be done by calculating the critical buckling factors for every load combination and the corresponding buckling modes. This is a demanding design procedure that severely affects the morphology and the cross-sectional geometry of arches. EN 1993-2 provides buckling factors and imperfection values for a second-order theory analysis of arched structures.

Without stiffening girder

With stiffening girder

Tension (a) (b) Comp ressio n force s (c)

A validation of the code’s proposed buckling factors with the results of a buckling analysis of a 3D model is in any case to recommend.

Stiffening girders behave as continuous systems with equally spaced concentrated forces; these are the support reactions of the transverse beams. As mentioned earlier, they also act as tension ties due to their “cooperation” with the arches. Thus, an interaction between bending and tension must be carefully taken into account in different positions along the bridge’s length. The most critical verification points are usually those of the hangers. For this reason, designers place the hangers at positions that are coincident to those of the trans- verse beams. This obviously allows a more direct and economical force transfer.

Hangers are compact tension rods with the commonly used diameters ranging from 50 to 140 mm. They are connected with the arches and the stiffening girders through gus- set plates; see details 1, 2, and 3 in Figure 2.27. In details 1 and 2, one can see that the

Detail 1 h Arch girder Hanger _{Detail 3} X _“X” a a Detail 2 Gusset plate Gusset plate Stiffening girder Composite transverse beam

After concreting Before concreting Cross section L Elevation Section a–a Plan view Figure 2.27 Arch-and-tie-bridge.

hollow-box cross section of the arc is penetrated by a thick plate. The external part of the gusset plate transfers the tension load from the hanger to the internal part that works as a diaphragm. It is welded with the hanger through double-sided fillet welds; different types of welds are also possible. It is important to note that hangers constantly vibrate under the action of wind and therefore, a careful fatigue detailing is necessary. The dynamic behavior of the hangers needs therefore to be investigated since measurements have shown that their damping capacity is very low [2.51]. In case of resonance, the stress variations at the edge connections will be maximized and may be the reason of an unexpected brittle failure. Central hangers are usually more sensitive against wind-induced vibrations due to higher slenderness. Designers usually calculate the natural frequencies of the hangers (as isolated elements) by taking into account the effects of the axial forces due to the imposed loads and the shrinkage stresses of the welds and by considering different types of supports at the edges; the natural frequencies should be greater than a minimum value (recommended is 7 Hz); otherwise, dampers are installed. EN 1993-1-11 covers issues of tension members but does not offer adequate guidance on the vibration control of hangers. Finally, hangers should be replaceable since they cannot endure the total design working life of the bridge.

Arch bridges with inclined hangers are shown in Figure 2.28. The main advantage of such structures is mainly aesthetical since the inclination of the hangers gives to the structure an aerodynamic shape. Due to their increased length, inclined hangers are more sensitive to vibrations and construction difficulties arise especially at the connections with the arches and the stiffening girders. In order to minimize the effects of vibrations, additional hori- zontal stabilizing elements connecting adjacent hangers may be used, but this will have a negative effect on the appearance of the bridge.

In Figure 2.29, one can also see that the arch girders may be connected through top bracings. These braces are necessary for increasing the stability of the arch girders due to compression but also for enhancing the lateral stiffness in case of wind or seismic actions. Designers can choose different shapes for the bracing systems such as X, K, and Λ-diagonals or rigid frames; see also the network arched bridges in 2.4.7 that are preferably chosen for railroad applications. The decision of applying or not a top-bracing system is a difficult one since heavier arches may be finally more cost-effective and elegant alternatives.

The concrete slab may be separated from the stiffening girders in which case concrete is allowed to shrink or expand without affecting the steel elements. This may be seen advanta- geous, but the positive effects of the composite action are lost. However, the structure loses its redundancy that is a necessary characteristic for modern bridges. In other arch bridges, the concrete slab is connected with the steel elements and in bowstring arches additionally prestressed by tendons in the longitudinal direction; this is due to the fact that concrete is part of the tie and its cracking may not be taken into account in design realistically. Figure 2.29 shows a bowstring arch where a horizontal end bracing system is provided to allow for the participation of the entire bridge deck in the transfer of the arch thrust. The deck is a cracked composite tension member with effective cross-sectional properties, as provided by EN 1994-2. This leads to more slender structural members and raises the com- petitiveness of the “arched solution.”

A sensitive point in design of a concrete deck under tension is its shear resistance against the point loads of the wheels. When the crack width is excessive, the shear transfer is achieved by the dowel action of the reinforcement. The aggregate interlock becomes negligible, and the shear resistance decreases. In such a case, the reinforcing bars are constantly under cyclic bending, and fatigue failure is highly possible. For this reason, the maximum crack width should be limited to 0.1 mm for normal forces and to 0.2 mm for combined local bending and normal forces [2.13]. These values are smaller than those of EN 1992-2 for durability.

The erection of pure arch bridges starts with the construction of the arch that is done either on temporary falsework, if possible in swallow valleys, or by cantilevering in steep valleys or over water. In cantilevering, construction starts from the two springing points and continues with the position of new segments until the two halves are joined at midspan. During the progress of works, the parts of the arch in place must be temporarily tied back by cables. The prefabricated deck modules are then lifted and hung from the deck hangers that are connected to the arch.

Arch-and-tie bridges have the advantage of been external statically determinate. All steel parts including arches, hangers, and stiffening girders may be erected near the site and the entire bridge moved in place by barges. This is a common solution for medium-span river bridges. At the end, the deck is concreted. In that manner, the weight of the bridge during its put in place is reduced. Additional braces to ensure diaphragm action of the deck and temporary compression elements between the arch and the deck during moving operations are needed since the hangers are not in tension and therefore not effective.