Structure Configuration Based on Wind Engineering

13.1 Introduction 13-1

13.2 Effects of Wind Load 13-2

Mechanism of Wind Load • Configuration Effect for Single Bluff Body • Vicinity Arrangement Effect of Multiple Bluff Bodies

13.3 Control of Aeroelastic Responses 13-14

Mechanism of Aeroelastic Vibration of Structures • Control of Aeroelastic Vibration of a Single Bluff Body • Control of Aerodynamic Interference Caused by Multiple Structure

13.4 Wind Design Data 13-33

Estimation of Wind Load and Onset Wind Velocity • Estimation of Amplitude

13.5 Examples of Real Bridges 13-39

Collapse of Tacoma Narrows Bridge • Vortex-Excited Vibration of the Great-Belt Bridge • Vortex-Excited Vibration of the Box Girder Bridge in Trans-Tokyo Bay Highway • Vortex-Excited Vibration of the Tower of the Akashi-Strait Bridge During Self-Standing State

13.6 Summary 13-44

References 13-45

Further Reading 13-47

13.1 Introduction

When a structure is immersed in an air stream, aerodynamic forces are induced in the structures by the air stream and the aerodynamic forces apply on the structure as wind load generating deflection and vibration. Flexible structures like high-rise buildings and long-span bridges are susceptible to deflection and vibration under wind action. In order to reduce the deflection or to control the vibration of the structure, the effect of aerodynamic/aeroelastic forces should be reduced. The best method for the reduction of the aerodynamic force effect is to adapt a structural configuration that can reduce the aerodynamic/aeroelastic force effect. For this purpose, when designing a flexible structure susceptible to vibration under wind action, it is necessary and useful for structural engineers to understand the mechanism of the process generating aerodynamic forces and the relationship between structural configuration and aerodynamic forces.

The following steps are an outline of the design for the structure susceptible to vibration under wind action:

1. Decide the design wind speed for the structure by using data measured previously at meteorological observatories close to the construction site.

2. Estimate the wind load applying on the structure under the design wind speed.

3. When the wind load exceeds the design wind load, improve the proposed structural configuration so as to possess a smaller wind load based on the data previously measured or the results of wind tunnel tests conducted to find a better configuration.

4. Check the occurrence of aeroelastic vibrations, after confirmation that the wind load is smaller than the design wind load. If the occurrence of aeroelastic vibrations is predicted, the structural configuration should be further improved to be the vibration amplitude less than the allowable value so as not to induce the aeroelastic vibrations.

This chapter deals with the mechanism of the process generating aerodynamic forces and the relationship between the structural configuration and wind load or aeroelastic vibration induced in the structure.

Aerodynamic forces are drag force, lift force, and aerodynamic moment. The drag force is a force parallel to the wind direction, the lift force is a force perpendicular to the wind direction, and the aerodynamic moment is a rotating force around a specified point. When the terminology of wind load is used, the wind load usually indicates the drag force.

13.2.1 Mechanism of Wind Load

A cross-sectional shape of structural member is usually a nonstreamline shape, which is called a "bluff body.'' The representative shapes of a bluff body used in a structure are circular and rectangular cross-sections.

Figure 13.1 shows flow visualization around a circular cross-section structure [1]. The approaching flow separates at an angle 6 of about 80°, which is measured at the center of the circular section from the stagnation point to downstream direction along the surface. The separated flows on upper and lower sides roll up from both separation points and vortex streets are generated in a wake of the bluff body. The vortex vibrates with frequency linearly proportional to the wind velocity as discovered by Strouhal [2]. Figure 13.2 shows the mean pressure distribution around the circular structure [3]. Positive pressure is induced on the upstream surface and negative pressure on the downstream surface and on both upper and lower side surfaces. The drag force is calculated by subtracting pressure on downstream surfaces from pressure on upstream surface of the structure. That is, the drag force is generated by the pressure difference between upstream and downstream surfaces. The mechanism generating drag force is simple for a single bluff body as mentioned above, but complicated for multiple bluff bodies. In this section, the drag force coefficients for a single body and multiple bodies are introduced for structural engineers.

Coefficients for drag and lift forces and aerodynamic moment are CD, CL, and CM, respectively, and defined as follows:

13.2 Effects of Wind Load

FIGURE 13.1 Flow visualization of the wake of a circular structure [1].

where p, U, A, and B are air density, wind velocity, representative area (usually projected area perpendicular to wind direction), and representative width, respectively. FD, FL, and FM are the drag and the lift forces and the aerodynamic moment, respectively.

Strouhal number St is useful to predict the onset wind velocity of vortex-excited vibration. The definition of Strouhal number is

where fv, D, and U are frequency of vortex in the wake, representative length (usually height projected perpendicularly to wind direction), and wind velocity, respectively. In some following figures, Strouhal number is indicated with drag force coefficients.

13.2.2 Configuration Effect for Single Bluff Body Side Ratio Effect of Rectangular Cross-Section Structure

The drag force of a rectangular cross-section structure (rectangular structure) changes with a variety of side ratios as shown in Figure 13.3 [3]. When side ratio B/D = 0, the rectangular structure is

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