Improvement of aerodynamic stability of suspension bridges with H-shaped simplified stiffening girder

Abstract

Wind-tunnel study on the improvement of aerodynamic stability of simplified suspension-bridge girder structures was conducted with using a 1/40-scaled section model. Objective of the study is the development of an economically superior suspension bridge with 500–1,000 m center span length. The wind-tunnel test showed that an edge-girder type cross section exhibited large amplitude torsional vortex-induced vibration as well as torsional flutter at a low wind speed. Accordingly, aerodynamic countermeasures of open grating deck and triangular faring, and structural countermeasures of center stay, diagonal bracing and mass increase were tried to improve the aerodynamic stability. Finally, feasibility of the best combination to a full-scale bridge was examined by structural analysis.

Keywords

suspension bridge / aerodynamics / simplified girder / wind-tunnel test

Introduction

Suspension bridge is the most suitable form for super long-span bridges with a more than 1,000 m center span. It is also superior and competitive for less than 1,000 m span bridges even though recently cable-stayed bridge is very likely to be selected for such span length. From the viewpoint of aerodynamic stability, a truss or closed box girder is mostly adopted for long-span bridges. However, even box girder has a limit for realizing lower manufacturing cost due to complicated welding, and many stiffening structures.

In this study, aiming at the development of a simplified girder structure with adequate aerodynamic stability and economical efficiency for suspension bridge, model suspension bridges were designed and their aerodynamic stability were examined by section-model wind-tunnel tests. Then, the feasibility for such a simplified suspension bridge girder structure was discussed by complementary structural analyses.

A simpler girder structure proposed in this study is the so-called edge girder structure (H-shaped girder) in which main girders are arranged at the both deck edges and a composite deck slab is placed between the two girders, as shown in Fig. 1. However, it is well known that this edge-beam girder is inferior to aerodynamic stability as reported, for example, in cases of Tacoma Narrows Bridge [ 1] and Alex Frazer Bridge [ 2] and others [ 3− 7]. Authors also conducted a wind-tunnel test for such an edge girder structure of a suspension bridge [ 8− 10]. In fact, various aerodynamic countermeasures were applied for their decks to improve the aerodynamic stability. Typical aerodynamic countermeasures were open gratings on the deck to decrease pressure difference between over and under the deck, edge plates and triangular farings to control flow separation and baffle plates under the deck to disturb vortex actions on the deck. In addition, it was pointed out that edge girder location to inner position increases the aerodynamic stability. Therefore, in this study, in order to improve the aerodynamic stability of the edge girder structure of a suspension bridge, some aerodynamic countermeasures of a steel grating and triangular faring, and structural countermeasures of cable stay and diagonal bracing were tested. In addition, mass effect was investigated. Finally, the feasibility of the aerodynamically best and simplified girder structure to a full-scale bridge was examined by structural analysis.

Modeling of suspension bridges with simplified girder structure

Model bridge design

Suspension bridges with simplified girder structures studied here are designed. Model bridges are single span suspension bridges with the center span of 540 m and the sag ratio of 1/10 by referring to Toyoshima Bridge [ 11]. Details of structural design was also referred to the Design Specification for Road Bridges [ 12]. The 13.5 m wide and 1.0 m high bridge girder accommodates two traffic lanes. A simplified girder structure consists of two edge girders and a deck slab. Three types of the deck slab are adopted: RC deck, I-beam grid RC deck and steel grating deck. To investigate structural efficiency of the deck slab, three types of girders are adopted: two, three and six girders, as shown in Fig. 2. In addition, hanger interval in the longitudinal direction is varied at 10, 15 and 20 m. Asphalt pavement of 70 mm thickness is placed on the RC decks. Main cables are designed assuming the tensile strength of 1,800 MPa with the safety factor of 3.

Table 1 shows weight of suspended structures for model suspension bridges to be studied. Suspended structure weight varies from 15 to 20 t/m except for the steel grating deck type. Larger hanger interval tends to yield a heavier structure. Two edge-girder type also yields a heavier structure. On the other hand, steel grating deck girder is considerably light. Figure 3 shows the total weight of superstructures including towers and cables for models with the hanger interval of 15 m.

Based on the model bridge design, a multiple girder structure rather than two edge girder one is advantageous with respect to the total weight. However, construction cost of a bridge must be evaluated by not only total weight (material cost) but also simplification of structures (fabrication cost). In addition, a steel grating deck girder is quite advantageous with respect to structural simplification as well as the total weight. However, it should be noted that a suspension bridge requires mass effect to some extent for aerodynamic stability. This will be examined by a wind-tunnel test described later.

Natural frequency

To obtain fundamental dynamic characteristics of the model suspension bridges, natural frequencies are analyzed with 3D finite element models. These are also used for wind-tunnel test conditions. Table 2 shows natural frequencies for four fundamental modes: first symmetric vertical (1SV), first asymmetric vertical (1AV), first symmetric torsion (1ST) and first asymmetric torsion (1AT). Figure 4 shows vibration mode shapes for case No.11. Since the weight of suspended structures except for a steel grating deck type varies by only 20%, torsional frequency also varies by only 10%. On the other hand, a steel grating deck type yields much larger torsional frequencies.

Investigation of aerodynamic stability

Test cases and conditions

To investigate the aerodynamic feasibility of the simplified girder structure of suspension bridge, a section-model wind-tunnel test was conducted. The section-model test followed the Wind-tunnel Test Manual of Akashi Kaikyo Bridge [ 13]. A two-edge-girder with steel grating deck structure was originally intended to realize the simplification of a suspension bridge girder. The section model was fabricated for such geometry, as shown in Fig. 5. A steel grating deck was modeled as shown in Fig. 5(b). When a solid deck like a RC deck is tested, a cover plate was attached on the grating deck. Some aerodynamic countermeasures of triangular faring were prepared to improve the aerodynamic stability, as shown in Fig. 6.

Table 3 shows test cases. Twenty cases in total were conducted where three different mass conditions were considered to investigate the mass effect. Table 4 shows test conditions. The section model was fabricated as a 1/40 scaled rigid model. It was given two degrees of freedom (vertical and torsion) in the wind tunnel. Mass and polar moment of inertia per unit length were calculated by scaling (1/40)² and (1/40)⁴, respectively. They considered weight of girder, hangers and main cables as uniformly distributed all over the spans. Structural damping was adjusted by electro-magnetic dampers to logarithmic decrement of 0.02, however torsional damping could not be adjusted.

Test results of aerodynamic stability

Due to the limitation of space, some characteristic results of the wind-tunnel test are shown in Figs. 7–12. The result is presented in the non-dimensional amplitude and reduced wind speed U_r (normalized by deck width B) and prototype dimensions by quantities in Table 4.

Figure 7 shows wind-induced vibration response in vertical and torsion for Case 1 (grating deck, no faring, lowest mass). There is only small amplitude vortex-induced vibration at U_r of 1 in the vertical direction while there is quite large amplitude one at U_r of 1 − 3 in the torsion. On the other hand, no flutter was observed up to very high wind speed, which is due to the open grating deck. This result is similar to previous studies [ 14, 15]. In this study, three types of faring were prepared, however none of those could suppress this large amplitude torsional vortex-induced vibration. There is only one possible solution for the steel grating deck structure. Largest mass case (Case 15) showed an almost satisfactory result, as shown in Fig. 8. Maximum amplitude of 1 degree was observed in+3 degree angle of attack. It may be suppressed by additional damping and/or turbulence. However, large mass condition will spoil the advantage of light weight of steel grating deck.

Figure 9 shows wind-induced vibration response in vertical and torsion for Case 4 (solid deck, no faring, lowest mass). Vortex-induced vibration in both vertical and torsion was observed. In addition, flutter occurred at a low wind speed for all three angles of attack. This is due to aerodynamically unstable cross section of a two-edge-girder (H-shaped) deck with light weight. After trying to improve the aerodynamic stability of this cross section, it was found that Faring C was the most effective as shown in Fig. 10 (Case 7). Vortex-induced vibration was completely suppressed and flutter onset wind speed was increased to almost twice. It is understood that the longest faring can reduce flow separation at the leading edge and increase the flutter onset wind speed. However, it seems to be still short for the flutter requirement of a 500 m-class suspension bridge.

Figure 11 shows wind-induced vibration response in vertical and torsion for Case 14 (solid deck, faring C, middle mass). This case is a twice mass case of Case 7. The result proves the mass effect. Flutter onset wind speed was increased by the mass effect. However, mass effect also decreased natural frequencies so that a converted wind speed in the prototype bridge decreased to the level lower than that of the lighter case (Case 7), on the contrary.

Figure 12 shows wind-induced vibration response in vertical and torsion for Case 20 (solid deck, faring C, largest mass). This case is a triple mass case of Case 7. Mass effect was observed much more than in Case 14. Mass effect increasing flutter onset wind speed surpassed the reduction effect of natural frequency. However, it also seems to be still short for the flutter requirement of a 500m-class suspension bridge.

Structural countermeasures to improve aerodynamic stability

As a result of the wind-tunnel test, it was found that some simplified girder structures (e.g., solid deck with Faring C and heavy steel grating deck) have possible feasibility. To further improve the aerodynamic stability of those cases, structural countermeasures to increase torsional frequency were investigated.

Cable stays connecting main cables and girder at the span center, and diagonal bracing were applied to the original bridge models, as shown in Fig. 13. Then, torsional natural frequency was calculated. Four types of cable stays (two, four, six and eight stays) and three types of diagonal bracings (upper, middle and below girder) were applied. In addition, diameter of the stay cable was changed at 6.8, 9.6 and 11.8 cm. Since 15-3-I model (No. 9) in Table 2 showed the largest torsional natural frequency except for grating deck model, a girder structure of 15-3-I with the girder height of 1 m (same height as that in wind-tunnel test) was redesigned. Then, effect of the increase in flutter wind speed was examined by multiplying the wind-tunnel test result (Case 20: solid deck, Faring C and largest weight) by the frequency ratio between countermeasure model and base model.

Table 5 shows natural frequencies of 1st symmetric torsion (1ST) and 1st asymmetric torsion (1AT) modes for countermeasure cases. Since 1AT frequency does not increase larger than 1ST frequency even for six and eight stay cables, only two and four stay cable cases are shown. It can be also seen that the effect of diagonal bracing below the girder is significant.

Figure 14 shows flutter onset wind speed for structural countermeasures based on the wind-tunnel test result and torsional frequency calculation. Note that the original case was also converted from Case 20 result by reduced wind speed. Putting diagonal bracings below the girder (solid deck, faring C and largest weight) increased the flutter onset wind speed to more than 50 m/s and 80 m/s at −3 and 0 degree angle of attack, respectively. This will make the girder structure aerodynamically feasible for mild wind condition areas.

Conclusions

Feasibility and improvement of aerodynamic stability of simplified suspension-bridge girder structures for 500 − 1,000 m span was studied by structural analysis and wind-tunnel test. The wind-tunnel test showed that a solid deck supported by two edge girder structure with triangular-shape faring provided the possible feasibility of flutter onset wind speed. On the other hand, a steel grating deck structure exhibited large amplitude torsional vortex-induced vibration. Further improvement of flutter onset wind speed of the solid deck structure was realized by cable stays or diagonal bracings. Flutter onset wind speed with diagonal bracings increased to more than 50m/s and 80m/s at −3 and 0 degree angle of attack, respectively. This will make the simplified girder structure proposed in this study aerodynamically feasible for mild wind condition areas.

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