WIND RESISTANT DESIGN MANUAL FOR HIGHWAY

Keywords: Wind resistant design; Manual; Highway bridges; Turbulence effects 1.. With regard to wind resistant design, the Specification prescribes design wind load of bridges and dimen

WIND RESISTANT DESIGN MANUAL FOR HIGHWAY

BRIDGES IN JAPAN

Hiroshi Sato

Director, Structures Research Group, Public Works Research Institute,

Independent Administrative Institution (Minamihara 1-6, Tsukuba-shi, Ibaraki-ken, 305-8516, Japan, Tel.: +81-298-79-6726, Fax: +81-298-79-6739, E-mail: hsato@pwri.go.jp)

Abstract

In Japan, wind-resistant designs of highway bridges up to the span length of 200m are

conducted according to the Wind Resistant Design Manual for Highway Bridges This Manual is also applicable to the highway bridges up to the span length of 300m with minor modification of its provisions In this paper, the Manual is outlined first to illustrate wind resistant design procedure in Japan Then turbulence effects included in the Manual are described with Dr Davenport's contributions to the Manual

Keywords: Wind resistant design; Manual; Highway bridges; Turbulence effects

1 Introduction

Highway bridges up to the span length of 200m in Japan are designed according to the Specification for Highway Bridges With regard to wind resistant design, the Specification prescribes design wind load of bridges and dimensions of pipe structures, however, there is no sufficient provision on wind- induced vibrations in the Specification

The wind resistant designs of long-span bridges in Japan were mostly based on the Wind Resistant Design Criteria for Honshu- Shikoku Bridges The Criteria was originally formulated in

1964 and revised in 1976 by the ad hoc committee in the Japan Society of Civil Engineers The Criteria prescribes the design wind load including the effect of gust and the evaluation method of wind-induced vibrations based on wind tunnel testing

Since the revision of the Criteria, wind engineering had made a remarkable progress and a considerable amount of aerodynamic data of bridges had been acquired It was thought that wind resistant designs for limited kind of bridges could be made without wind tunnel testing if reliable formulae for the estimation were provided It was also thought that prediction of wind-induced vibration would become more reasonable and reliable if the effect of turbulence was incorporated appropriately in the design

From these reasons, the working group was organized in the Japan Road Association in

1984 to prepare the Wind Resistant Design Manual for Highway Bridges The working group was reformed into the Wind Resistant Design Committee in 1986, and the Manual was published

in 1991

At present in Japan, wind-resistant designs of highway bridges up to the span length of 200m are conducted according to the Wind Resistant Design Manual for Highway Bridges This Manual is also applicable to the highway bridges up to the span length of 300m with minor modification of its provisions If span length of a bridge becomes longer than 300m, the specific design specification will be established for the bridge

In this paper, Wind Resistant Design Manual for Highway Bridges is outlined to illustrate wind resistant design procedure in Japan

2 Procedure of Wind Resistant Design Using the Wind Resistant Design Manual

The procedure of wind resistant design using the Manual is as follows The wind properties

(basic wind speed, design wind speed, turbulence intensity etc.) are decided first The design wind load is calculated, and the static design of the bridge is made

At this stage, where major dimensions of the bridge are determined, wind-induced vibrations to be studied further are chosen considering the design wind speed, the deck width and the span length of the bridge For a bridge with short span length, no study on wind-induced vibration is required

For long-span bridges, wind-induced vibrations specified above should be predicted using the formulae provided in the Manual Then the wind-induced vibrations are evaluated The formulae were established considering past wind tunnel test results Since the formulae are expressed by means of only a few parameters, the prediction error of the formulae is not negligibly small Therefore, the formulae were established, so that their prediction may become safer It means that evaluation 'good' based on the formulae is almost always 'good', however, evaluation 'no good' based on the formulae is not always 'no good' because of the safety margin

of the formulae In case that the evaluation based on the formulae turns out to be 'no good', the bridge engineer can modify the design or he can predict wind-induced vibrations more accurately

by means of wind tunnel testing The evaluation based on wind tunnel testing has priority over that based on the formulae

3 Wind Properties Used in Design

Wind properties are modeled fundamentally according to Davenport [1] The terrains are classified into four, namely rough sea (TerrainⅠ), open farmland (TerrainⅡ), suburbs (Terrain

Ⅲ) and city centers (TerrainⅣ)

3.1 Basic Wind Speed U 10

The basic wind speed U10 is defined as the mean wind speed over open farmland (Terrain

Ⅱ) at an elevation of 10m, averaged over a period of 10 minutes Using the meteorological data

at weather stations in Japan, extreme wind speeds were estimated The return period was 100 years The basic wind speeds were classified into 4 categories, namely 30m/s, 35m/s, 40m/s and 45m/s

3.2 Design Wind Speed U d

The power law matched with the log profile at an elevation of 30m was applied to the mean

wind speed profile The design wind speed for dynamic design can be obtained from the following formula

where, E1: correction factor for altitude and terrains

3.3 Turbulence Properties

Typical values for turbulence properties such as turbulence intensities and power spectral density functions are provided in the Manual σu , r.m.s of longitudinal velocity fluctuation, was assumed to be 2.5u*, where u* is the friction velocity

4 Design Wind Load

The design wind load Pd for static design can be obtained from the following formula

where, Cd: drag coefficient, An: projected area, G: gust factor

Design wind speed Ud for design wind load is 40m/s Gust factor G was determined so that the shear force induced by the design wind load may become equivalent to those estimated by the gust response analysis proposed by Davenport [2] 1.9 is used for gust factor G In the Manual, the typical values for Pd or Cd are provided according to the type of bridges and members

5 Wind-Induced Vibration

5.1 Prediction of Wind-Induced Vibrations by the Formulae

The critical wind speed for flutter and galloping can be predicted by simple formulae as well as by wind tunnel testing The formula for prediction of critical wind speed of flutter is as follows:

where, Ucf: critical wind speed for flutter, fθ: natural frequency of the 1st torsional mode, B: width of bridge section

The formula for prediction of critical wind speed of galloping is as follows:

U cg = 8 f h B ; when angle of attack is almost 0 deg (4)

U cg = 4 f h B ; when angle of attack is positive (5)

where, Ucg: critical wind speed for galloping, fh: natural frequency of the 1st bending mode The amplitude of vortex-induced vibrations can be predicted by simple formulae as well as

by wind tunnel testing The effects of turbulence on vortex-induced vibrations are incorporated The formulae for prediction of critical wind speed and amplitude of vortex-induced vibrations are

as follows:

U cv = 1.33 fθ B - for torsion (7)

A c = A e E ms E t (8)

A e =βds･ 0.05･ (d/B)/ (m r δh ) -for bending (in h/B) (9)

A e =βds･ 13.2･ (d/B) 3 / (Ip r δθ) -for torsion ( in deg.) (10)

E t = 1-15βt (B/d) 1/2 Iu 2≧0 - for bending (11)

E t = 1-20βt (B/d) 1/2 Iu 2≧0 -for torsion (12)

where, Ucv: wind speed for the maximum amplitude of vortex-induced vibration, Ac: corrected maximum amplitude of vortex-induced vibration, Ae: maximum amplitude of vortex-induced vibration for rigid model in smooth flow, Ems: correction factor for vibrational mode (about 4/π), Et: correction factor for the effect of turbulence, βds: correction factor for sectional shape, d: depth of bridge section, mr, Ipr: reduced mass or reduced mass moment of inertia (mr = m/(ρB2), m: mass per unit length of the bridge, Ipr = Ip/(ρB4), Ip: mass moment of inertia per unit length of the bridge), δh, δθ: structural damping (logarithmic decrement), βt : correction factor for sectional shape, Iu: intensity of turbulence 5.2 Prediction of Wind Induced Vibrations by the Wind Tunnel Testing

Wind tunnel testing increases the reliability of wind resistant design of bridges Since the prediction of wind-induced vibrations based on the formulae may often provide safer value, there is a fair chance that wind tunnel study provides more economical design Turbulence has significant effects on wind-induced vibrations Therefore, standard wind tunnel testing methods in turbulent flow (full aeroelastic model test, taut-strip model test) were described in the Manual as well as conventional testing methods (spring-mounted rigid model test, measurement of steady aerodynamic forces)

5.3 Evaluation of Wind-Induced Vibrations The method of verification of flutter, galloping and vortex-induced vibrations are provided in the Manual For flutter and galloping, the following inequalities shall be satisfied, U cf > U r -for flutter (13)

U cg > U r -for galloping (14)

U r = U d E r1 E r2 (15)

U d = U 10 E 1 (16) where, Ucf: critical wind speed for flutter, Ucg: critical wind speed for galloping, Ur: reference wind speed for flutter and galloping, Ud: design wind speed, Er1: correction factor for the effect of gust, Er2: safety factor(1.2), U10: basic wind speed, E1: correction factor for altitude and terrains

It was found that onset velocity for negative damping, which caused galloping, increased remarkably in turbulent flow [3][4] It suggested that Ucg would be high enough when turbulence intensity is high Therefore Er1, correction factor for the effect of gust, was determined as 1 for

galloping, while Er1 for flutter was 1.1 to 1.25 depending on wind turbulence

For vortex-induced vibrations, unless the following inequality (17) is satisfied, the maximum amplitude of the vortex-induced vibration shall be less than the allowable amplitude shown in equations (18) or (19)

h a =0.04/f h - for bending (in m) (18)

θa =2.28/(b fθ) -for torsion (in deg.) (19)

where, Ucv: wind speed for the maximum amplitude of vortex-induced vibration, ha: allowable amplitude for bending vortex- induced vibration, fh: natural frequency of the 1st bending mode,

θa: allowable amplitude for torsional vortex-induced vibration, b: distance between the deck center and the center of outmost lane, fθ: natural frequency of the 1st torsional mode

6 Dr Davenport's Contributions

One of the main features of the Manual is incorporation of turbulence effects on wind- induced vibrations, where Dr Davenport has made a great contribution Therefore, the Manual was influenced directly and indirectly by Dr Davenport's works Some of the direct contributions

of Dr Davenport’s to the wind resistant design methods described in the Manual are as follows: (1) In the Manual, simple formulae for predicting amplitude of vortex-induced vibrations are provided The effects of turbulence on vortex-induced vibrations are incorporated Wind turbulence properties can be predicted based on the model proposed by Dr Davenport [1]

(2) Design wind load shall be calculated considering the effects of gust response, which was predicted according to the methods proposed by Dr Davenport [2]

(3) Er1, correction factor for the reference wind speed for galloping, was determined as 1, because onset velocity for negative aerodynamic damping, which causes galloping, would increase remarkably in turbulent flow The aerodynamic damping was measured by the author under the supervision of Dr Davenport [3]

Since the gust response analysis methods are so well known, there may be no need for me

to describe Dr Davenport's contribution here Our research on the wind resistant design methods for vortex-induced vibrations and galloping and Dr Davenport's contributions are described in the following sections

6.1 Design for Vortex-induced Vibrations

Vortex-induced vibrations may take place to long-span bridges at wind speeds considerably lower than their design wind speed For the design of long-span bridges, therefore, prediction of amplitude of vortex-induced vibrations becomes very important The mechanism and countermeasures of the vortex-induced vibrations were studied in Japan in 1970's, but most of the studies were based on wind tunnel experiments in smooth flow To understand the effects of turbulence on the vortex-induced vibrations, wind tunnel studies were conducted at the Public Works Research Institute in 1980's

In the study, vortex-induced vibrations of taut-strip models for 16 types of bridge cross section were measured in smooth flow and in 3 types of turbulent flow Used bridge cross sections were rectangular section, trapezoidal section, hexagonal section, two-plate section and

two-box section B/d of the cross section ranged from 4 to 10 Scale ratio of the model was assumed as 1/200, and the model length was 1.2m Turbulent flow was generated by spires and floor roughness Turbulence intensities for longitudinal wind speed (Iu) and vertical wind speed (Iw) were as follows: Iu=6.8%, Iw=5.1% for turbulent flow 1; Iu=11.5%, Iw=7.8% for turbulent flow 2; and Iu=22.4%, Iw=14.1% for turbulent flow 3 Integral scale of longitudinal wind speed (Lxu) was a little smaller than 1/200 of typical natural wind's scale, and that of vertical wind speed (Lxw) was about 1/200 of typical natural wind's scale

In smooth flow, vortex-induced vibrations of vertical bending mode were observed for 14 types of cross sections It was found that amplitude of the vortex-induced vibrations decreased in the turbulent flow Relationship between the maximum amplitude and turbulence intensity Iw is shown in Figure 1 In the figure, non-dimensional amplitude (h/B) was multiplied by reduced mass mr and structural damping δh The ratios of the amplitude (h/B) mrδh to that in smooth flow are shown in Figure 2 From the figures it was found that maximum amplitude decreases with turbulence intensity The turbulence effects on vortex-induced vibrations were a little smaller for hexagonal sections than for other sections It also seemed that the turbulence effects increased a little with B/d

Figure 1 Effects of turbulence on vortex-induced vibration amplitude (h/B) mrδh

Based on these results and others, the formulae for predicting amplitude of vortex-induced vibrations were developed as were shown in Equations (8)-(12) To utilize these formulae, turbulence intensities at the bridge site should be predicted In the Manual, wind properties are modeled fundamentally according to Dr Davenport [1] Dr Davenport's model was also applied

to prediction of turbulence intensities as follows

In the Manual, the power law matched with the log profile at an elevation of 30m was applied to the mean wind speed profile Intensity of turbulence Iu was calculated first at an elevation of 30m assumingσu = 2.5u* and the log profile Then the effect of altitude on Iu was corrected by the power law profile Therefore, Iu can be predicted by the following formula:

0

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

0.018

Iw

section (B/d=4, 7)

B/d=5

B/d=7, 10

Iu=(30/z) a /[ln(30/z 0 )] (20) where, z: altitude of the bridge (in m), a: exponent of the power law profile, z0: roughness length (in m)

Figure 2 Ratios of the amplitudes (h/B) mrδh to those in smooth flow

6.2 Design for Galloping

When a model of a long-span bridge with bluff box section is tested in smooth flow, divergent vibration called galloping is sometimes observed In turbulent flow, the divergent amplitude vibration may turned to be less divergent but more random vibration

In order to understand the turbulence effects on galloping, unsteady aerodynamic forces acting on the 1:2 rectangular prism were measured in smooth and turbulent flow at the University

of Western Ontario by the author under the supervision of Dr Davenport [3] The measurement

of lift force on the model, whose longer side was set along the wind, is described here

Turbulence was generated by a coarse grid placed upstream of the model The mesh size and the bar size were 0.61m and 0.15m respectively The intensity of turbulence used in the experiment was slightly smaller than that usually found in the natural wind The ratio of the integral scale of the turbulence to the width of the model was smaller than the ratio of the integral scale of natural wind to the width of a long-span bridge section

The model had a relatively large aspect ratio (0.10m x 0.20m x 2.13m) End plates were not attached to the model The lift force was measured by the pneumatic averaging method This consists of two kinds of averaging methods, i.e continuous averaging by porous material and discrete averaging by a manifold

Power Spectral Density Functions (PSDF's) of the fluctuating lift on the model at rest, SL, are shown in Figure 3 The turbulence broadens the peaks of the PSDF of the lift and also lowers the peak reduced frequency (from 0.16 in smooth flow to 0.12 in turbulent flow)

Unsteady lift force was measured by the forced oscillation method Then aerodynamic

0

0.2

0.4

0.6

0.8

1

1.2

Iw

hexagonal section (B/d=4, 7) B/d=5

B/d=7, 10

damping ratio for heaving motion ζah was estimated The results are shown in Figure 4 In smooth flow, sharp peak of positive aerodynamic damping appears at fB/U = 0.17 The aerodynamic damping turns to negative at fB/U < 0.15 According to the free vibration test of the model conducted in smooth flow, divergent heaving vibration, which can be regarded as galloping, was observed in the corresponding wind speed range Aerodynamic damping in the turbulent flow is also shown in Figure 4 The pattern is similar to that of smooth flow, however, the positive damping peak shifts to the lower reduced frequency and the peak becomes broader in the turbulent flow The turbulence decreased the critical reduced frequency to fB/U=0.10 (or increase the critical reduced wind speed to U/(fB)=10) where the aerodynamic damping turns to negative The wind-induced vibration observed in the free vibration test was less divergent in the turbulent flow than in smooth flow

Figure 3 Power Spectral Density Functions of the fluctuating lift on the rectangular model at rest Similar studies were conducted at the Public Works Research Institute for a continuous box girder bridge [4] It was also concluded that turbulence decreases the reduced frequency (or increases the reduced wind speed) for the onset of negative damping that causes galloping

As was described in Equation (14), critical wind speed for galloping should be higher than the reference wind speed that can be obtained from Equation (15) So far Er1 for galloping in Equation (15), correction factor for the effect of gust, had been the same as Er1 for flutter, which was larger than 1 Considering the turbulence effects on galloping, Er1 was determined as 1 for galloping

Wind

Lift

Turbulent flow Smooth flow

fB/U

Figure 4 Aerodynamic damping for heaving motion of the rectangular model

7 Revision of the Manual

Although the formulae to predict wind-induced vibrations of bridge girders are provided in the Manual, only the outlines are described for towers and cables Detailed description of the design methods for towers and cables has been required

In the Manual, assumed bridge types were suspension bridges, cable-stayed bridges and box girder bridges Recently, plate girder bridges with very small torsional rigidity have been applied to relatively long span length in Japan Noise barriers, which make girders bluff, are often attached to highway bridges in city area In some cases, two bridges are constructed very closely

to each other, which may cause buffeting problems Wind resistant design methods for these bridges have been also required

From these reasons, the committee for the Wind Resistant Design Manual was reorganized

at the Japan Road Association in 2000 to revise the Manual The revised Manual will be published in 2003 hopefully

8 Conclusions

In this paper, the Wind Resistant Design Manual for Highway Bridges was introduced The main features of the Manual are as follows

(1) The critical wind speed for flutter and galloping can be estimated by simple formulae as well

as by wind tunnel testing

Wind

h

Turbulent flow

fB/U

(2) The amplitude of vortex-induced vibrations can be estimated by simple formulae as well as by wind tunnel testing The effects of turbulence on vortex-induced vibrations are incorporated (3) Wind properties and design wind load are determined according to the models or methods proposed by Dr Davenport

Acknowledgements

The author would like to express his gratitude to the members of Wind Resistant Design Committee in Japan Road Association The discussions at the Committee were essential for preparing the paper as well as the Manual

References

[1] Davenport, A.G 1982, "The interaction of wind and structures", Engineering Meteorology, Amsterdam, Elsevier, pp 527-572

[2] Davenport, A.G 1962, "Buffeting of a suspension bridge by storm winds", Proc ASCE, Vol.88, ST3

[3] Sato, H 1983, "On the aerodynamic forces on a rectangular prism in smooth and turbulent flow, including motion-induced effects", Thesis for Master of Engineering Science, University

of Western Ontario

[4] Narita, N., Yokoyama, K., Sato, H and Nakagami, Y 1987, "Aerodynamic characteristics of continuous box girder bridges relevant to their vibrations in wind", Seventh International Conference on Wind Engineering, Aachen, V 4, pp 283-29