Experimental study of wind loading of rectangular sign structures

J. Wind Eng. Ind. Aerodyn. 130 (2014) 62–74

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Experimental study of wind loading of rectangular sign structures Delong Zuo n, Douglas A. Smith, Kishor C. Mehta Department of Civil and Environmental Engineering, Texas Tech University, Lubbock, TX 79409, USA

art ic l e i nf o

a b s t r a c t

Article history: Received 11 December 2013 Received in revised form 31 March 2014 Accepted 15 April 2014

A three-phase experimental campaign was conducted to study wind loading of sign structures with rectangular sign faces. Full-scale measurements and wind-tunnel tests conducted in phase 1 of the studies showed consistent results for wind loading of a prototype rectangular box sign and its scaled model, validating the methodologies used in the wind tunnel tests. Five models of representative rectangular signs of different configurations were tested in the wind tunnel as the second phase of the study, the results of which revealed the significant influence of the geometrical configuration of rectangular sign structures on their wind loading. Motivated by the observations made in this phase of comparative investigation, an extensive series of wind tunnel tests were performed in the last phase of the study to evaluate wind loading of rectangular box signs of various configurations. The effects of the aspect and clearance ratios on wind loading of rectangular box signs are highlighted based on this phase of the study. Published by Elsevier Ltd.

Keywords: Rectangular sign Wind loading Full-scale measurement Wind tunnel tests

1. Introduction Rectangular boxes and plates are frequently used as signs to display information and to also function as a structural component. These sign systems with rectangular faces are structurally quite simple: they usually consist of primarily up to two rectangular sign boards or an enclosed rectangular box and a simple support in the form of a mono-pole or a truss. In some other cases, the rectangular signs are simply fixed to the ground. Despite the structural simplicity of these structures and the fact that rectangular boxes and plates are among bluff bodies of the simplest in shape, the wind loading of sign structures can be complex and is dependent on the size of the sign, the ratios between the three dimensions (i.e., width, height and depth) of the sign, whether the sign is elevated or located on the ground and, in the case of an elevated sign, the amount of clearance between the sign and the ground. To date, although extensive research have been performed to investigate wind loading of bluff bodies that resemble signs of rectangular plate or box in shape, few studies have been conducted to expressly investigate the wind loading of rectangular sign structures. Flachsbart conducted one of the earliest wind-tunnel

n

Corresponding author. Tel.: þ 1 806 834 6535; fax: þ1 806 742 3446. E-mail address: [email protected] (D. Zuo).

http://dx.doi.org/10.1016/j.jweia.2014.04.005 0167-6105/Published by Elsevier Ltd.

experiments to measure the wind pressure acting on a rectangular plate of various aspect (i.e., width to height) ratios in uniform smooth flow. His study highlighted the difference in the loading of the rectangular plates when they are on and elevated from the ground plane. The results of this investigation, which are summarized by Simiu and Scanlan (1996) formed a benchmark for subsequent studies motivated by the application in the design of flat plates. In particular, a number of studies used wind-tunnel experiments to highlight the wind loading of two dimensional plates in turbulent uniform flow (e.g., (Bearman, 1971)) and turbulent boundary layer flow (e.g., (Good and Joubert, 1968; Sakamoto and Arie, 1983)) as opposed to smooth uniform flow as in the case of the study by Flachsbart. These early wind tunnel studies were followed by a number of wind-tunnel, full-scale and numerical studies that were conducted to assess wind loading of free-standing walls, which resemble signs composed of a single rectangular plate fixed to the ground. For example, Letchford and Holmes (1994) performed independent wind-tunnel tests to study wind loading of models of infinite (i.e., spanning the entire width of a wind tunnel) and semi-infinite (i.e., spanning half the width of a wind tunnel) walls as well as finite walls of various aspect ratios in appropriately simulated boundary layer flow. In these tests, transducers were used to measure wind pressure acting at discrete locations on portions of the wall models, based on which the pressure coefficients at the instrumented locations of the models as well as the force

D. Zuo et al. / J. Wind Eng. Ind. Aerodyn. 130 (2014) 62–74

The focus of the paper is on the outcomes of the wind tunnel tests of scaled sign models, while the results from the full-scale study are used only for validation of the methodologies used in the wind tunnel tests. The data collected from the study are processed and presented in the forms of force coefficients and eccentricity coefficients, the latter of which are measures of the wind-induced torque acting on the sign or sign models subjected to testing. Based on an interpretation of these coefficients, the effects of the geometric configuration of rectangular sign structures on their wind loading are highlighted, and the dependence of the wind loading of rectangular box signs on the aspect and clearance ratios are evaluated.

2. The full-scale structure and the measurement system As part of a research effort to understand the wind loading of rectangular signs, a full-scale sign structure was installed at the field test site at Texas Tech University for long term monitoring. Fig. 1 shows this structure and its immediate surrounding terrain, which is flat and homogeneous with few obstructions. Fig. 2 shows the histogram of the roughness length (z0) of the terrain shown in Fig. 1, which is estimated based on 10-min mean wind speed values measured by two ultrasonic anemometers located at 0.91 m and 2.44 m, correspondingly, above ground level on an adjacent 200 m meteorological tower with the assumption that the mean wind speed profile is logarithmic in nature and that the effect of the atmospheric stability can be neglected, that is,   un z UðzÞ ¼ ln ð1Þ z0 k

Fig. 1. A prototype rectangular sign structure subjected to monitoring.

500 400 Density

coefficients of the whole models were estimated. The results of these wind-tunnel studies were subsequently codified and introduced into design standards despite some inconsistencies in the data sets obtained in the wind tunnel tests (Robertson et al., 1996). To address the inconsistencies, full-scale measurements using pressure transducers were conducted to study wind loads on free-standing walls (Robertson et al., 1995–1998) of various aspect ratios. In addition, both numerical studies based on computational fluid dynamics (Robertson et al., 1997) and additional wind tunnel experiments (Letchford and Robertson, 1999) were also conducted. In particular, the numerical study suggested that it is challenging for the model to adequately simulate the complex threedimensional flow created by the wall of simple rectangular shape. Although these previous studies on wind loading of freestanding walls were quite comprehensive and thorough, the outcomes of the studies apparently are only applicable to sign structures composed of a single thin plate fixed to the ground. As indicated in (Robertson et al., 1997), the pressure and force coefficients of these thin walls can be much higher than those of the ground level signs composed of thick rectangular boxes. Also, the wind loading of elevated rectangular sign structures had not been systematically studied. Subsequently, Letchford (2001) conducted wind tunnel experiments to specifically investigate wind loading of structures consisting of a single thin rectangular plate, which can be either on the ground or elevated. He used force transducers to directly measure the forces and moments acting on rectangular plates of various aspect ratios and, on this basis, estimated the mean and pseudo-steady force coefficients of these models for a number of wind directions. In addition, the study also evaluated wind-induced torque about the vertical axis of the sign models. The extensive data set obtained in this investigation were subsequently combined with those from previous studies on wind loading of free-standing walls and codified to form standards (e.g., (ASCE, 2010)) to guide the design of sign structures. These early data sets, as well as a more recent studies that investigated the effect of the porosity of the rectangular panels (Briassoulis et al., 2010; Giannoulis et al., 2012) on their wind loading, however, were all derived from studies of wind loading of a single thin plate and may not be applicable to rectangular signs of other types of configuration. Indeed, a recent study based on wind tunnels tests (Warnitchai et al., 2009) has shown that the force and moment coefficients of a sign structure consisting of two rectangular sign plates in either parallel or oblique configurations can be significantly different from those of a sign composed of a thin rectangular plate of the same aspect (i.e., the width to height of the sign face ) and clearance (i.e., the height of sign face to the total height of the structure) ratios. Also, although many studies have been conducted to study wind loading of rectangular cubes, such studies were either conducted in uniform smooth or turbulent flow (e.g., (Laneville et al., 1975)) or in turbulent boundary layer flow but for shapes on the ground plane representing a rectangular building but not a typical rectangular sign box. This paper presents the results of a three-phase experimental campaign that incorporated both full-scale and model-scale studies to investigate the wind loading of rectangular sign structures. In the first phase of the campaign, the wind loading on a full-scale rectangular sign structure was monitored in the field and a scaled model of this structure was tested in the wind tunnel using both pressure and force measurement techniques. In the second phase, five models of representative rectangular signs of different configurations were tested in the wind tunnel using the force measurement technique validated in the first phase of the study to reveal the significant influence of the geometrical configuration of rectangular sign structures on their wind loading. In the third phase, an extensive series of wind tunnel tests were performed to evaluate wind loading of rectangular box signs of various configurations.

63

300 200 100 0

0

0.002 0.004 0.006 0.008 z0 (m)

0.01

0.012 0.014

Fig. 2. Histogram of estimated roughness length of the field test site.

64

D. Zuo et al. / J. Wind Eng. Ind. Aerodyn. 130 (2014) 62–74

where U(z) is the mean wind speed at height z above ground level, un is the friction velocity, and k is the Von Kármán constant, taken as 0.4. For this estimation, only records with 10-min mean wind speed greater than 7 m/s measured by an ultrasonic anemometer (also on the 200 m meteorological tower) at 10 m above ground level were used. The mean value of the estimated roughness length is 0.0023 m. The broad distribution of the roughness length shown in Fig. 2 is partly due to the fact that these values are estimated without considering the thermal effects on the wind flow in the boundary layer (i.e., Eq. (1)). The sign structure subjected to monitoring consisted of a rectangular sign box of 7.5 m in width, 3.75 m in height and 1.75 m in depth, and a circular steel monopole of 3.75 m in height, 0.274 m in outer diameter and 0.092 m in wall thickness. These dimensions of the structure give an aspect, clearance and depth to height ratios of 2, 0.5 and 0.47, respectively. A total of 12 differential pressure transducers (Model 265, Setra Systems, with a range of 71.245 kPa) were used to measure the difference between the wind pressure at 12 pairs of mirrored locations on the two faces of the sign. Fig. 3 shows schematically the locations of the pressure taps (represented by the circles) on one of the two sign faces. To enable an estimation of the reference dynamic wind pressure, a propeller-vane anemometer (R.M. Young Company, model 05103V) was installed on an adjacent monopole at the height of the top of the sign for measurement of the wind speed at this height. To monitor the oscillation of the structure, three tri-axial accelerometers (Memsic Inc., model CXL04LP3 with a measurement range of 739.24 m/s2) were installed on the top of the sign at locations near the two vertical sides and at the center, respectively. In addition, the primary meteorological

b/4

b/4

b/8

b/4

c/6 c/3

c = 3.75 m

c/3 c/6

3. Configurations of wind tunnel tests The wind tunnel experiments were conducted in the Texas Tech University Boundary Layer Wind Tunnel, which is of a closedcircuit type and capable of generating wind speeds up to 50 m/s. The boundary layer section of this wind tunnel is 1.83 m wide, 1.25 m high, and has 17.7 m of upstream fetch for development of desired boundary layer wind. The wind tunnel experiments were conducted in three phases. In the first phase, a scaled model of the full-scale structure subjected to monitoring was tested in a simulated boundary layer that represents that over the field test site, which has an estimated mean roughness length of 0.0023 m. The results from these tests were compared with those from the full-scale study to validate the methodologies used in the wind tunnel tests. In the second phase, five different types of rectangular sign model with the same sign-face dimensions were tested in a boundary layer representative of that over an open terrain exposure (e.g., exposure C specified by ASCE (2010), with a typical roughness length of 0.02 m) to illustrate the effects of the geometrical configuration of the sign on the wind loading of rectangular sign structures. In the last phase, rectangular boxshaped sign models of various aspect and clearance ratios were tested in a simulated boundary layer that is the same as the one used in the second phase of the tests. 3.1. Wind tunnel models

b = 7.5 m

All the models tested in the study had a nominal length scale of 1 to 50. The scaled model of the full-scale sign subjected to monitoring, which was tested in the wind tunnel in phase one of the study, was built from ABS plastic by a three-dimensional

Fig. 3. Configuration of pressure taps.

Elevation t

b

Plan

t

b/8

conditions at the site were monitored by temperature, relative humidity and barometric pressure transducers. The onsite data acquisition system monitored the wind speed continuously. When a one-minute mean wind speed exceeded 6.7 m/s, the system triggered and sampled all channels at 30 Hz for 15 min. In this paper, the full-scale data will be used only as a benchmark for the wind-tunnel investigation to be described subsequently. A detailed interpretation of this full-scale data set will be presented in a separate paper. Also, since no significant oscillation of the structure was observed, the acceleration measurements are primarily used to estimate the power spectral density functions of the structural response, which indicate that the fundamental frequency of the structure is 1.2 Hz. A detailed interpretation of the acceleration data will not be presented herein.

b Box Sign

b

c

b h

30° V-Shaped Sign

t

Single-Plate Sign

t

b

b Double-Plate Sign

10° V-Shaped Sign

Fig. 4. Sign models tested in phase 2 of the wind tunnel experiments.

D. Zuo et al. / J. Wind Eng. Ind. Aerodyn. 130 (2014) 62–74

printer, and the support for this model was a brass monopole of 1.27 cm in outside diameter. While the dimensions of the sign box matched those determined by the prescribed length scale, the ratio of the diameter of the brass pole to that of the full-scale pole was 1 to 21.6. The larger length scale of the pipe was used to allow the tubing of the pressure measurement system used in phase one of the experiments to pass through this pipe and reach the pressure transducers. The mismatch of the length scale for the pipe is not expected to introduce significant secondary flow effects that could significantly influence the wind loading of the sign box. A total of five sign models were tested in phase 2 of the wind tunnel experiments. As schematically depicted in Fig. 4, the width (b) and height (c) of the sign faces as well as the height of the support (h–c) were all the same for the five sign models. In particular, the rectangular sign box of the “box sign” model tested was identical to the one subjected to testing in phase one of the wind tunnel study. The single-plate sign model shown in Fig. 4 had a single aluminum plate of 3 mm in thickness. The double-plate sign model and the two V-shaped sign models were built from ABS plastic by a three-dimensional printer. They were composed primarily of two thin plates of 3 mm in thickness as the sign faces, and were open on all sides. For these three models, the two sign faces were connected by eight 6 mm by 6 mm struts, four each at the top and at the bottom of the sign model, respectively, at equal spacing. The two plates of the double-plate sign model were parallel to each other; those of the 301 V-shaped sign model formed a 301 angle, and those of the 101 V-shaped sign model formed a 101 angle. All five sign models tested in this phase were supported by a steel circular rod of 0.95 cm in diameter. In phase 3 of the wind tunnel experiments, 39 rectangular boxshaped sign models of various aspect (b/c) and clearance (c/h) ratios were tested. Although the depth of a rectangular box sign was expected to affect wind loading, all these sign models were chosen to have a depth of 3.68 cm, which is equivalent to 1.84 m at full scale, because many prototypical box sign structures have a similar depth and it was not practical to test an enough number of models to adequately quantify the effect of the depth to height (t/ c) and depth to width (t/b) ratios on the loading of this type of structure. Table 1 lists the aspect, depth to height and depth to width ratios of the box sign models tested in phase 3 of the experiments, based on which the dimension of the models can be calculated. The same rectangular box was used for the models of a given aspect ratio, regardless of the clearance ratio. The boxes were supported by steel rods of either 0.95 cm or 1.59 cm in diameter, depending on the size of the sign. During the wind tunnel tests, the rods or the pipe that supported the models were clamped to an aluminum connector, which was either fastened to a force transducer mounted on a rigid supporting system, when the force transducer was used to directly measure the loading, or bolted to an aluminum plate mounted on the wind tunnel frame, when pressure transducers were used to measure the pressure acting on the sign faces. For the models with a clearance ratio of 1, a clearance of 3 mm was kept between the bottom of the sign model and the wind tunnel floor, and a piece of clear tape was used to seal the gap around the bottom of the models. The tape was carefully placed so that it adhered to the model but not the wind tunnel floor.

Table 1 Aspect ratio, depth to height ratio and depth to width ratio of sign models tested in phase 3 of the wind tunnel experiments. b/c

0.2

0.3

0.5

1

2

4

5

7.5

t/c [t/b]

0.145 [0.725]

0.145 [0.483]

0.242 [0.483]

0.290 [0.290]

0.483 [0.242]

0.580 [0.145]

0.527 [0.105]

0.725 [0.097]

65

Fig. 5. A sign model installed in the boundary layer simulated to represent opencountry exposure.

For all the sign models tested in the wind tunnel experiments, the blockage ratio was less than 1.2%. This suggests that blockage effect is negligible in assessing the wind loading of the sign models (Cermak et al., 1999). 3.2. Simulation of atmospheric boundary layer A wooden grid system right outside of the settling chamber of the wind tunnel, a barrier upstream of the boundary layer section and a combination of a carpet and wood blocks were used to simulate two types of boundary flow. For illustration, Fig. 5 shows a rectangular sign model installed in the wind tunnel in which the devices were in place to simulate an open terrain exposure. Fig. 6 shows the mean wind speed and longitudinal turbulence intensity profiles, at equivalent full-scale, of the simulated atmospheric boundary layers. In these figures, z is the height above ground level, U(z) is the mean longitudinal wind speed at height z (in meters), U(10) is the mean longitudinal wind speed at 10 m above ground level, and Iu is the longitudinal turbulence intensity. As indicated in the graph showing the mean wind speed profiles, least-squares fit of the heights against mean wind speeds assuming that the profile is logarithmic in nature (i.e., Eq. (1)) yields an equivalent full-scale roughness length of z0 ¼ 0.003 m for the boundary layer simulated to represent that over the field site, and an equivalent full-scale roughness length of z0 ¼0.017 m for the boundary layer simulated to represent that over a typical open terrain exposure. These roughness length values are quite close to those of the target boundary layers. Also, as shown in Fig. 6, the longitudinal turbulence intensity profiles are quite close to those with the assumption that the mean speed profile is logarithmic in nature and that the standard deviation of the longitudinal turbulence is given by su ¼ 2:5un (e.g., Holmes, 2007). Fig. 7 shows the estimated auto-spectral density functions of the longitudinal turbulence of the flow in the two simulated boundary layers based on the measurement at the level of 20 cm above the wind tunnel floor, which corresponds to 10 m above ground level at fullscale. It is evident that the estimated spectra of the longitudinal turbulence are reasonable representations of the empirical Kaimal spectra ((Kaimal et al., 1972)), which are also shown in Fig. 7. 3.3. Wind tunnel test procedure During phase one of the wind-tunnel experiments, a method based on measurement of wind pressure acting on the sign faces and one based on direct force and moment measurements were

66

D. Zuo et al. / J. Wind Eng. Ind. Aerodyn. 130 (2014) 62–74

30

simulated field site log fit (z0 = 0.003 m)

30

simulated field site Iu=1/ln(z/0.003)

25

simulated open country log fit (z0 = 0.017 m)

25

simulated open country Iu=1/ln(z/0.017)

20 z (m)

z (m)

20 15

15

10

10

5

5

0

0

0.25

0.5

0.75

1

1.25

0 0.05

1.5

0.1

0.15

0.2

0.25

Iu

U(z)/U(10)

Fig. 6. Mean speed and longitudinal turbulence intensity profiles of simulated boundary layers.

10

10

-1

10

0

-1

2

nSu(n,z)/σu

nSu(n,z)/σu

2

10

0

10

10

-2

10

Simulated Kaimal

-3

10

-4

10

-2

10

0

10

-2

Simulated Kaimal

-3

10

-4

10

-2

10

0

nz/U

nz/U

Fig. 7. Auto-spectral density functions of longitudinal turbulence of simulated boundary layers at a full-scale equivalent 10 m height.

used independently to assess the wind loading of the scaled model of the full-scale sign structure monitored in the field. In the experiments based on pressure measurements, a total of 24 pressure taps were placed on the two faces of the sign model at locations that are equivalent to those of the pressure taps on the full-scale sign in the field, which are indicated in Fig. 3. These pressure taps were connected to 24 ports of a Scanivalve pressure transducer (ZOC33) through a tubing system that consists of 25.4 cm long urethane tubes of 1.37 mm in inside diameter, which connected the pressure taps to 24 brass connectors, and 12.7 cm long urethane tube of 0.86 mm in inside diameter, which connected the connectors to the pressure transducer. In the experiments based on direct force measurements, the support of the model was clamped to an aluminum connector, which was fastened to a six-component (forces and moments in three mutually orthogonal directions) force transducer (ATI Industrial Automation, Inc. Gamma series) mounted on a supporting system beneath the wind tunnel floor. The wind loading on the whole model and that on the support without the sign attached were measured independently to enable an evaluation of the net force acting on the sign only. This same procedure based on measurements by the force transducer was also used in phases 2 and 3 of the wind tunnel experiments. In all three phases of the wind tunnel experiments, each nonV-shaped sign model was tested for 6 orientations, which can be represented by model yaw angles of 0–751, at 151 increments, relative to the mean direction of the wind, respectively. The 101 Vshaped sign model was tested for 15 orientations represented by model yaw angles of 901 to 901 at 151 increments as well as yaw angles of 51 and 851. The 301 V-shaped sign model was tested for

13 orientations represented by model yaw angles  901 to 901 at 151 increments. Fig. 8 schematically illustrates the definition of the model yaw angle for the non-V-shaped and V-shaped signs. Ten independent test runs were conducted for each model at each orientation. For all the tests of a particular model, a Cobra probe (Turbulent Flow Instrumentation, 100 series) was used to measure the wind speed at the height of the top of the model without the model present to enable calculation of the reference dynamic pressure. This experimental configuration for measurement of reference wind speed matches that used in the full-scale study. According to Cook (1990), this will result in a slight over estimation of the mean dynamic pressure at the top of the models, the amount of which depends on the turbulence intensity of the flow at the height of the measurement. The similarity equation that governs the length, velocity and time scales used in the wind tunnel tests is (Cermak et al., 1999) tm V m tp V p ¼ Lm Lp

ð2Þ

where t, V and L represent time, velocity and length, respectively, and the subscripts m and p indicate model scale and prototype scale, respectively. In this study, with a model to prototype length scale (i.e., Lm/Lp) of 1–50 and with the wind velocity scale (Vm/Vp) chosen to be 1–4, the time scale (tm/tp) is 1–12.5. During each test run in phase one of the wind tunnel experiments, the transducers were sampled at 250 Hz, which is equivalent to 20 Hz at full scale, and the data were divided into 72-s records, which is equivalent to 15 min at full scale. The duration of these records was chosen so that the equivalent full-scale time matches that of the time histories recorded in the full-scale

D. Zuo et al. / J. Wind Eng. Ind. Aerodyn. 130 (2014) 62–74

Wind

M od

el

Mo del

Wind

67

β

β Fig. 8. Yaw angle of the wind tunnel models.

experiments. During phases two and three of the wind tunnel experiments, the sampling rate was kept at 250 Hz, but the duration of each test run was 48 s, which is equivalent to 10 min at full-scale.

4. Data interpretation The data obtained in the field and in the wind tunnel tests were used to estimate non-dimensional coefficients that can be used to assess the wind loading of rectangular sign structures. The measurements by the pressure transducers or the force transducer were first used to form time histories of the wind-induced forces and torques acting on the full-scale sign or the sign models tested in the wind tunnel. Based on measurements by the pressure transducers either in the field or in the wind tunnel, the force and torque time histories were computed as n

F i ðtÞ ¼ ∑ r j P ij ðtÞAj j¼1 n

T i ðtÞ ¼ ∑ r j P ij ðtÞAj dj j¼1

ð3Þ

sign model did not generate mean torque about the axis of the rod, which coincided with the vertical axis of the sign model, the torque measured by the force transducer in the vertical direction was used directly as that acting about the vertical axis of the sign models (Ti(t)). With each force time history Fi(t), a corresponding force coefficient time history, CFi(t), was calculated as C Fi ðtÞ ¼

in which i is the test run number, Fi(t) is the force time history, Ti(t) is the torque time history, Pij(t) is the pressure measured by tap number j at time t, Aj is the area of the rectangular tributary centered at tap number j and bordered by the dash lines shown in Fig. 3, rj is the influence coefficient for tap number j, which is unity for the taps on the wind ward sign face and  1 for the leeward face, dj is the horizontal distance (moment arm) from the center of sign face to the jth pressure tap, and n is the total number of pressure taps. To form the loading time histories based on the measurements by the force transducer, the forces measured by the two orthogonal horizontal axes of the force transducer were decomposed into an along-wind drag component and a cross-wind lift component. The mean drag and lift forces acting on the supporting rod were estimated as the mean value of the drag and lift force time histories obtained from 10 tests of the rod. These mean drag and lift forces acting on the rod were subtracted from the drag and lift force time histories obtained from the tests of each sign structure model to yield time histories of the net drag and lift forces acting on the faces of this sign model. These net drag and lift time histories were then used to compute the resultant net horizontal force time histories (Fi(t)). Since the wind loading on the supporting circular rod of a

ð5Þ

where ρ is the air density calculated based on the temperature, barometric pressure and relative humidity measurements, U is the mean wind speed measured at the height of the top of sign for the full-scale study and the top of the sign model for the wind tunnel experiments, and A is the area of the sign faces. For each wind tunnel test, the mean value of the force coefficient, C Fi , was computed. The mean force coefficient of a sign model at a specific orientation was then estimated as the average of these mean values. That is CF ¼

ð4Þ

F i ðtÞ ð1=2ÞρU 2 A

1 m ∑ C m i ¼ 1 Fi

ð6Þ

where m is the number of test runs. In addition to the mean coefficients, the direct force measurement data were also used to estimate the pseudo-steady force coefficients of the models tested in phases 2 and 3 of the wind tunnel experiments. For every sign model at each orientation relative to the mean wind direction, the maximum force coefficient was identified based on the individual force coefficient time histories. The 10 maximum force coefficients were fitted to a type I Fisher–Tippett extreme value distribution using the Lieblein method (Lieblein, 1974). The mode and dispersion of the fitted extreme value distribution were then used to estimate the hourly mean extreme force coefficient as C^ F ¼ mode10 min þ ½0:577 þ lnð6Þ  dispersion10 min

ð7Þ

This hourly mean extreme force coefficient was used to estimate the pseudo-steady force coefficient as C^ F C~ F ¼ 2 G

ð8Þ

where G is the gust factor calculated based on the expression (Cook, 1990) G ¼ 1 þ 0:42I u lnð3600=t 0 Þ where Iu is the longitudinal turbulence intensity.

ð9Þ

68

D. Zuo et al. / J. Wind Eng. Ind. Aerodyn. 130 (2014) 62–74

In this study, the value of t0 is taken as 3 s, which indicates that the gust factor obtained using Eq. (9) is associated with 3-s gusts. To characterize the mean torque acting on the full-scale sign structure and the sign models due to wind loading, an eccentricity coefficient was defined as the mean moment arm of the torque normalized by the width of the sign model T ðtÞ C ei ðtÞ ¼ i F i ðtÞb

1.5

1

CF

ð10Þ

0.5

For each wind tunnel test run, the mean value of the eccentricity coefficient, C ei , was computed. The mean eccentricity coefficient of a sign model at a tested orientation was then estimated as the average of these mean values as Ce ¼

1 m ∑ C m i ¼ 1 ei

ð11Þ

0 -180

0

jT i j F max b

ð12Þ

1 m 0 ¼ ∑ C m i ¼ 1 ei

0.1

ð15Þ

where F^ max is the largest mean extreme horizontal force for all the orientations of a specific sign model.

0

45

90

135

180

Full-Scale Wind Tunnel Force Wind Tunnel Pressure

0.075

Ce '

0.05

0.025

0 -180

-135

-90

-45

0

45

90

135

180

β (°) Fig. 10. Comparison of mean synthesized eccentricity coefficients estimated based on full-scale and wind tunnel data.

1.6 1.4

ð14Þ

as well as a synthesized mean extreme value based eccentricity coefficient as ^ 0 jTj C~ e ¼ ^F max b

-45

ð13Þ

Using the same procedure for estimation of the hourly mean extreme force coefficients, the hourly mean extreme absolute ^ acting on a sign model was also estimated. This mean torque ðjTjÞ extreme value was then used to estimate a mean extreme value based eccentricity coefficient for this sign model as ^ jTj C~ e ¼ ^Fb

-90

Fig. 9. Comparison of mean force coefficients estimated based on full-scale and wind tunnel data.

where jT i j is the mean torque for test run i and F max is the largest mean horizontal force for all the sign orientations tested. The mean synthesized eccentricity coefficient for the sign model at a certain orientation is then estimated as 0 Ce

-135

β (°)

Alternatively, the torque acting on a sign model at each orientation can also be evaluated with the largest mean resultant horizontal force acting on the sign for all the tested orientations as a reference. To enable this evaluation, an alternative eccentricity coefficient, which will subsequently be termed the synthesized eccentricity coefficient, was defined for each test run as C ei ¼

Full-Scale Wind Tunnel Force Wind Tunnel Pressure

1.2

CF

1 Single-Plate 0.8

Double-Plate V-Shaped (10 deg)

0.6

V-Shaped (30 deg) Box

0.4 -90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

β (°)

5. Results 5.1. Comparison of results from full-scale and phase 1 wind tunnel studies Figs. 9 and 10 show a comparison of the 15-min mean force and mean synthesized eccentricity coefficients, respectively, of the fullscale sign structure based on each individual test run, and those of the scaled model of this structure defined by Eqs. (6) and (12), respectively. The full-scale data presented in these two graphs were all derived based on stationary records with the 15-min mean wind speed at the top of the sign being higher than 6.7 m/s, and the data for the scaled model were based on pressure and force measurements conducted in the wind tunnel tests in phase one of the study. Also, although the wind tunnel tests were conducted only for yaw angles between 01 and 751, the results are also compared to full-scale results over the yaw angle range of

Fig. 11. Mean force coefficient vs. yaw angle for the five sign models tested in phase 2 of the wind tunnel experiments.

 1801 to 1801 by taking into consideration that the model is symmetric about its horizontal axes. Remarkably good agreement between the results from the full-scale and model-scale studies is apparent. It is particularly noteworthy that, the results from the wind tunnel tests based on force and pressure measurements are generally in good agreement, although differences become more pronounced when the wind direction is more oblique to the sign face likely because the pressure measurement system could not measure wind pressure on the side panels. Nonetheless, Figs. 9 and 10 particularly suggests that according to both the full-scale and the model-scale studies, the mean force coefficient is the largest when the wind direction is close to be normal to the sign and that the mean torque about the vertical axis of the sign is

D. Zuo et al. / J. Wind Eng. Ind. Aerodyn. 130 (2014) 62–74

1.6 1.4 1.2

∼ CF

1 Single-Plate 0.8

Double-Plate V-Shaped (10 deg)

0.6

V-Shaped (30 deg) Box

0.4 -90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

β (°) Fig. 12. Pseudo-steady force coefficient vs. yaw angle for the five sign models tested in phase 2 of the wind tunnel experiments.

the largest when the sign is yawed approximately 451 to the mean wind direction. 5.2. Comparison of wind loading of different types of rectangular sign Figs. 11 and 12 show the dependence of the mean and pseudosteady force coefficients, respectively, on the yaw angle for the five sign models tested in phase 2 of the wind tunnel experiments. It can be seen that for the single-plate and the box sign models, except for when the wind is significantly oblique to the sign faces (i.e., the absolute value of the yaw angle being larger than 451), the mean and pseudo-steady force coefficients for a specific model orientation are quite close. For the other three models, however, the mean and pseudo-steady force coefficients can be quite different even when the models are close to being normal to the mean wind direction. This is due to the fact that the loading of these three sign models with open sides are more affected by the entrained turbulent flow in the wake of the windward face than the single-plate and the box sign models. In addition, Figs. 9 and 10 also reveal that although all the five sign models had the same aspect and clearance ratios, different configurations of the sign can result in quite different wind loading of the models. In particular, it is seen that the mean and pseudo-steady force coefficients of the box-sign model are consistently lower than those of the singleplate sign model except for when the yaw angle is 751. Similar to the case of different wind loading of rectangular plates and cubes in uniform flow, as reported by Laneville et al. (1975), when the sign face is normal to the wind, the lower drag of the box sign model of the particular aspect and depth to width ratios compared with that of the single-plate sign model is primarily due to partial reattachment of the flow after being separated at the edges of the windward face of the box sign model. Although the study by Laneville was not done in boundary layer flow, the explanation given is still fundamentally applicable to the case in consideration here. The same reason likely can be used to explain the difference in the loading of these two types of sign models at yaw angles up to 601. To identify the factors that contribute to the differences in the loading of the single-plate and the open-sided sign models, however, necessitates further, more detailed comprehensive study. Table 2 lists the critical (largest for all the model orientations tested) mean and pseudo-steady force coefficients of the five sign models tested in phase 2 of the wind tunnel experiments as well as the corresponding yaw angles (β). The critical force coefficients of the single-plate sign model are similar to those reported by both Letchford (2001) and Warnitchai et al. (2009) for similar single-plate sign models of the same aspect and clearance ratios.

69

The critical force coefficients of the double-plate sign model and those of the 301 V-shaped sign model are also close to those of similar sign models of the same aspect and clearance ratios tested in a wind tunnel by Warnitchai et al. (2009). Since the results from the previous studies were mostly reported in graphic form, however, a quantitative comparison between the results from the previous and the present studies is not pursued herein. In addition to these observations, the information presented in Table 2 also suggests that the critical force coefficients of the double-plate and V-shaped sign models are close to those of the single-plate sign model. The same observation was reported by Warnitchai et al. (2009). It must be noted, however, that this observation is only made for single-plate and open-sided signs similar to the particular ones tested in this study and those tested by Warnitchai, as the loading of other double-plate and V-shaped signs will depend also on the aspect and clearance ratios as well as the size of the gap between the signs composed of two plates. Table 2 also suggests that both the critical mean force coefficients and the critical pseudo-steady force coefficients of the boxsign model are considerably lower than the corresponding force coefficients of the single-plate sign model. Since the design standards for free-standing rectangular signs are mostly based on the results from wind tunnel tests of single-plate sign models, this means that the currently practice can over design rectangular box sign structures. The difference in the loading between the single-plate and box signs will be investigated in more detail when the results from phase 3 of the wind tunnel experiments are presented subsequently. Figs. 13 and 14 show the dependence of the mean and the mean synthesized eccentricity coefficients, respectively, on wind direction for the five models tested in phase 2 of the wind tunnel experiments. It can be seen in Fig. 13 that while the mean moment arm of the torque about the vertical axis of the non-V-shaped models increases with increasing yaw angle, the mean moment arm of the V-shaped sign models attain the largest value when the absolute value of the yaw angle is within 151 of 451. Fig. 14 indicates, however, that for all five models, the largest mean Table 2 Critical mean and pseudo-steady force coefficients of the five sign models tested in phase 2 of the wind tunnel experiments. singleplate

doubleplate

ðC F Þmax ½β 1.41 [451] ðC~ F Þmax ½β 1.37 [451]

101 V-shaped 301 V-shaped box

1.35 [451]

1.35 [  301]

1.44 [  301]

1.23 [151]

1.41 [451]

1.39 [  301]

1.42 [  151]

1.25 [01]

0.25

0.2

0.15

Ce 0.1

Single-Plate Double-Plate V-Shaped (10 deg)

0.05

V-Shaped (30 deg) Box 0 -90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

β (°) Fig. 13. Mean eccentricity coefficient vs. yaw angle for the five sign models tested in phase 2 of the wind tunnel experiments.

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D. Zuo et al. / J. Wind Eng. Ind. Aerodyn. 130 (2014) 62–74

0.25

0.3

0.2

0.25

0.2

0.15

∼ Ce ' 0.15

Ce ' 0.1

Single-Plate Single-Plate

Double-Plate

0.1

Double-Plate

V-Shaped (10 deg)

0.05

V-Shaped (10 deg)

V-Shaped (30 deg)

0.05

Box

V-Shaped (30 deg)

0

Box

-90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

0 -90

β (°) Fig. 14. Synthesized mean eccentricity coefficient vs. yaw angle for the five sign models tested in phase 2 of the wind tunnel experiments.

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

β (°) Fig. 16. Synthesized mean extreme value based eccentricity coefficient vs. yaw angle for the five sign models tested in phase 2 of the wind tunnel experiments.

0.3 Table 3 Critical synthesized mean eccentricity coefficients and mean extreme value based eccentricity coefficients of the five sign models tested in phase 2 of the wind tunnel experiments.

0.25 0.2

Singleplate

∼ C e 0.15 Single-Plate 0.1

Double-Plate

Doubleplate

101 Vshaped

301 Vshaped

Box

0 ðC e Þmax ½β 0.116 [601]

0.158 [451]

0 ðC~ e Þmax ½β 0.13 [601]

0.18 [601]

0.181 [  451] 0.212 [  301] 0.074 [601] 0.19 [  601] 0.25 [  151] 0.09 [601]

V-Shaped (10 deg) 0.05

V-Shaped (30 deg) Box

0 -90

-75

-60

-45

-30

-15

0

15

30

45

60

75

90

β (°) Fig. 15. Mean extreme value based eccentricity coefficient vs. yaw angle for the five sign models tested in phase 2 of the wind tunnel experiments.

torque is associated with an absolute yaw angle between 151 and 451. This is because, as can be seen in Fig. 11, the mean force coefficients of all five models are significantly larger when the absolute value of the yaw angle is between 451 and 451 than when it is above 451. Figs. 13 and 14 also suggest that for most wind directions, the mean and synthesized mean eccentricity coefficients of the double-plate and the V-shaped sign models, which have open sides, can be significantly higher than those of the single-plate and box sign models. Since the critical mean force coefficients of the double-plate and V-shaped sign models are close to those of the single-plate sign model and significantly higher than that of the box sign model, Fig. 14 suggests that for the same mean wind speed, double-plate and V-shaped signs represented by the corresponding models tested in this study can be subjected to much higher mean wind-induced torque about the vertical axis that can be single-plate and box signs. Figs. 15 and 16 show the mean extreme value based and the synthesized mean-extreme value based eccentricity coefficients for the five models tested in phase 2 of the wind tunnel experiments. These two figures again clearly show that except for the 301 V-shaped sign model, the largest moment arm of the torque about the vertical axis is associated with large absolute yaw angle values. However, according to Fig. 16, for all five models, the largest mean extreme torque is associated with a range of absolute yaw angle value between 151 and 451. Fig. 16 also shows that for almost all the wind directions tested, the two mean extreme value based eccentricity coefficients of the

three signs with open lateral and horizontal sides are higher than those of the single-plate and the box sign models, illustrating the pronounced susceptibility of open-sided signs to wind-induced torque about their vertical axis. Table 3 summarizes the critical values of the synthesized mean eccentricity coefficients and the synthesized mean-extreme value based eccentricity coefficients and the associated yaw angles for the five sign models tested in phase 2 of the wind tunnel experiments. Apparently, both the synthesized mean eccentricity coefficient and the synthesized mean extreme value based eccentricity coefficient of the singleplate sign model are significantly smaller than the corresponding ones of the signs with open sides but larger than the corresponding coefficients of the box sign model. Since the current standards for the design of sign structures are mostly based on previous study of wind loading of single-plate signs, this means that the current practice may under-design for the wind-induced torque acting on structures similar to those represented by the doubleplate model and the two V-shaped models and over-design for the torque acting on box-shaped rectangular signs such as that represented by the box sign model tested in this phase. The problem can be particularly significantly for signs with open sides, as Table 3 also shows that for the sign models consisting of two thin plates, the critical values of the two types of synthesized eccentricity coefficients increases when the angle between the two plates increases. Further, by incorporating the information listed in Tables 2 and 3, it is evident that for a particular sign model, the critical values of the force coefficients and those of the eccentricity coefficients often are not associated with the same yaw angles. This fact must be considered when a sign structure is designed for a combined loading of horizontal force and torque about the vertical axis. Since only a limited number of models were tested in this phase of the study, however, development of a general guide for this design situation is not attempted herein.

D. Zuo et al. / J. Wind Eng. Ind. Aerodyn. 130 (2014) 62–74

71

Table 4 Comparison between the force coefficients of rectangular box sign models estimated based on the present study and those of single-plate sign models reported in a previous study (Letchford, 2001). c/h

b/c 0.2

1 0.9 0.8 0.5

0.5

ðC F Þbox ½ðC F ÞPlate ; ðC F ÞPlate =ðC F Þbox  1 1.13 1.13 [1.42, 26%] [1.17, 4%] 1.27 1.21 [1.44, 13%] [1.45, 20%] 1.33 1.20 [1.46, 10%] [1.44, 20%] 1.21 [1.47, 21%]

1

2

4

1.11 [1.15, 4%] 1.13 [1.34, 19%] 1.28 [1.43, 12%] 1.25 [1.38, 10%]

1.06 [1.14, 8%] 1.12 [1.33, 19%] 1.21 [1.39, 15%] 1.22 [1.42, 16%]

1.00 [1.08, 0.98 [1.20, 1.09 [1.32, 1.21 [1.45,

5.3. Loading of rectangular box-shaped signs As presented above, the box sign model tested in phase 2 of the wind tunnel experiments is less susceptible to wind loading, in terms of both horizontal force and torque about the vertical axis of the sign, than the single-plate sign model of the same aspect and clearance ratios. The same observations are be made for a large portion of the box sign models tested in phase 3 of the wind tunnel experiments and single-plate rectangular signs of the same aspect and clearance ratios. As an illustration, Table 4 shows a comparison between the mean force coefficients of a subset of the box sign models tested in phase 3 of the wind tunnel experiments and those of the single-plate signs of the same aspect and clearance ratios, which were reported by Letchford based on his comprehensive wind tunnel experiments (Letchford, 2001). The comparison is done only when both the aspect and the clearance ratios of the models tested in the two studies coincide and only for the yaw angle of 01 because Letchford only reported mean force coefficients of the single-plate signs at this model orientation. Also, as will be seen subsequently, the largest force coefficient of a particular sign model tested in phase 3 of the wind tunnel experiments is often associated with a yaw angle of, or close to, 01, and the same is indicated for the single-plate sign models tested by Letchford. Table 4 suggests that for the aspect and clearance ratio combinations listed, the mean force coefficients of the box sign models are indeed lower than the corresponding values of the single-plate sign models. This, according to previous study of wind loading of rectangular plates and cubes (Laneville et al., 1975), is again primarily due to the partial reattachment of flow after it separates at the edges of the windward face of the box sign models. It is of particular interest to see that the difference between the mean force coefficients of the two types of sign is small when the clearance ratio is unity and the aspect ratio is equal to or greater than 0.5. A similar observation was made by Letchford (2001) when he compared the results of his wind tunnel study on wind loading of thin rectangular plates with a previous study of wind loading of plates that are 20 times as thick as his thin-plate models. The small difference between the mean force coefficients of the single-plate and the box sign models on the wind tunnel floor in these situations can be explained by the fact that because the models are on the ground plane, no separating shear layer exists beneath the bottom of the sign models to interact with the shearing layer above the top of the models and, as a result, the effect of the depth of the models in the range under consideration is insignificant. As a contrast, the difference between the mean force coefficient of the box sign model with an aspect ratio of 0.2 and a clearance ratio of 1 and that of the singleplate sign model with the same aspect and clearance ratios is large. In this case, because the models are very slender, the depth

5

8%]

1.00 [1.04, 4%]

22%] 21%] 20%]

1.27 [1.44, 13%]

of the model significantly affects the interaction of the separating shear layers on the two vertical sides of the model. A similar comparison between the wind-induced torque on rectangular box and single-plate sign models will not be pursued herein because only limited information on the torque loading was reported by Letchford for single-plate sign models. Table 5 lists the critical mean force coefficients of the box sign models tested in phase 3 of the wind tunnel experiments as well as the yaw angles associated with these critical mean force coefficients and the synthesized mean extreme value based eccentricity coefficients of the models at these yaw angles. It is evident that for most of the models tested, the mean force coefficient is the largest when the sign face is normal to the mean wind direction. For the few models of which the critical force coefficient is associated with a small yaw angle, the difference between the critical mean force coefficient and the mean force coefficient at a yaw angle of 01 is less than 3.5%, which is essentially negligible. Based on the information listed in Table 5, Fig. 17 plots the critical mean force coefficients of the box sign models tested in phase 3 of the wind tunnel experiments against the aspect ratios for fixed individual clearance ratios. It can be seen that when the aspect ratio is greater than 0.5, the force coefficient decreases with increasing aspect ratio when the clearance ratio is larger than 0.5 and can increase with increasing aspect ratio when the clearance ratio is smaller than 0.7. A similar observation was made by Letchford for single-plate sign models (Letchford, 2001). This dependence of the mean force coefficient on the aspect and clearance ratios can be explained as follows. As noted by Letchford, when the models of larger aspect ratios (i.e., b/c40.5) are on or close to the ground plane, the presence of the ground plane either prohibits or attenuates the interaction between the shear layer above the top of the sign and that beneath the bottom of the sign. In this case, when the aspect ratio of the sign model increases, the interaction between the shear layers beyond the vertical sides of the models becomes weaker, resulting in increased base pressure on the leeward face and, consequently, decreased drag force. On the other hand, when the models of large aspect ratios (i.e., b/ c4 4) are well cleared of the ground plane, they increasingly resemble a model of infinite width subjected to uniform flow, the mean force coefficient of which, for the depth to height ratio in consideration, is much larger than that of, say, a rectangular box with an aspect ratio of 1 (Cengel et al., 2011). Fig. 17 also suggests that when the aspect ratio is small (i.e., b/ co0.5), for the same clearance ratio, the mean force coefficient increases with decreasing aspect ratio. This can be similarly explained by the facts that the models become more like rectangular prisms when the aspect ratio becomes smaller and that in this case, the interaction between the shear layers on the sides increases.

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D. Zuo et al. / J. Wind Eng. Ind. Aerodyn. 130 (2014) 62–74

Table 5 Critical mean force coefficients of the box sign models tested in phase 3 of the wind tunnel experiments and the corresponding yaw angle and synthesized mean extreme value based eccentricity coefficients. c/h

b/c 0.2

0.3

0.5

1

2

4

5

7.5

1.13 [01, 0.046] 1.17 [151, 0.040] 1.20 [01, 0.038]

1.10 [01, 0.044] 1.23 [01, 0.045] 1.21 [01, 0.042] 1.21 [01, 0.047] 1.21 [01, 0.044]

1.11 [01, 0.067] 1.13 [01, 0.058] 1.28 [01, 0.058] 1.28 [01, 0.051] 1.25 [01, 0.056]

1.07 [151, 0.084] 1.14 [151, 0.070] 1.21 [01, 0.071] 1.21 [151, 0.073] 1.23 [151, 0.073] 1.39 [01, 0.067]

1.00 [01, 0.110] 0.99 [151, 0.092] 1.1 [151, 0.080] 1.15 [01, 0.082] 1.21 [151, 0.095] 1.33 [151, 0.078]

1.00 [151, 0.149] 1 [151, 0.092] 1.06 [01, 0.083] 1.15 [01, 0.091] 1.30 [151, 0.107] 1.41 [01, 0.074]

0.94 [01, 0.116] 0.98 [01, 0.120] 1.06 [151, 0.129] 1.09 [151, 0.110] 1.34 [01, 0.111] 1.36 [01, 0.097]

0 ðC F Þmax ½β; C~ e 

1

1.15 [01, 0.047] 1.27 [01, 0.052] 1.33 [01, 0.072]

0.9 0.8 0.7 0.5 0.25

1.5

1.4

1.3

(CF ) max

1.2 c/h=0.25 c/h=0.5

1.1

c/h=0.7 c/h=0.8

1

c/h=0.9 c/h=1

0.9 0

2

4

6

8

10

b/c Fig. 17. Critical mean force coefficient vs. aspect ratio for box sign models tested in phase 3 of the wind tunnel experiments.

1.5

1.4

1.3 b/c=0.2

(CF ) max 1.2

b/c=0.3 b/c=0.5 b/c=1

1.1

b/c=2 b/c=4 b/c=5

1

b/c=7.5

0.9 0

0.2

0.4

0.6

0.8

1

c/h

Fig. 18. Critical mean force coefficient vs. clearance ratio for box sign models tested in phase 3 of the wind tunnel experiments.

Also based on the information listed in Table 5, Fig. 18 plots the critical mean force coefficients of the box sign models tested in phase 3 of the wind tunnel experiments against the clearance ratio for fixed individual aspect ratios. This graph reveals that except for when the aspect ratio is between 0.5 and 2, the mean force coefficient decreases with increasing clearance ratio. As has been discussed above, for the models with large aspect ratio (i.e., b/

c42), this is partly due to the attenuation or prohibition of the interaction between the shear layer above the top of the sign and that beneath the bottom of the sign with the wind tunnel floor acting practically as a splitter plate when the models are close to the wind tunnel floor. For the models with small aspect ratios, the presence of the ground plane acts like an end plate for a slender cylinder, which significantly changes the flow around the lower end of these slender models and affects the wind pressure in that area. In addition, different clearance ratios apparently place the sign model in different portion of the boundary layer. When the clearance ratio is small, a model would be subjected to loading from wind flow that is less sheared than when the clearance is large. While Figs. 16 and 17 indicate a clear dependence of the wind loading of the box sign models on the aspect and clearance ratios, a more quantitative assessment of the manner in which the aspect and clearance ratios of a rectangular box sign affects its wind loading can be achieved only if the pressure on the faces of the sign box is measured. It also must be noted that the discussions herein are only applicable for the depth to height and depth to width ratios in consideration. The effects of the depth to height and depth to width ratios are not investigated while they can significantly affect the wind-induced force acting on rectangular cubes or prisms (e.g., (Holmes, 2007)). Table 6 lists the critical synthesized mean extreme value based eccentricity coefficients of the box sign models tested in phase 3 of the wind tunnel experiments as well as the yaw angles at which the critical values are achieved and the corresponding mean force coefficients. It can be seen that as a general trend, for a specific clearance ratio, the critical synthesized mean extreme value based eccentricity coefficient increases with increasing aspect ratio. The dependence of this coefficient on the clearance ratio, however, is less clear, due to the unclear effects of the presence of the ground plane, the sheared nature of the free stream, as well as the depth of the models on the shedding of the vortices off the vertical edges of the sign models. Nonetheless, it is noteworthy that the critical synthesized mean extreme value based eccentricity coefficients are associated with a broad range of yaw angles that are often quite small. This is because the synthesized coefficient is defined based on the mean extreme torque at a specific model orientation, which is largely influenced by the vortex shedding off the edges of the models, and the largest mean extreme horizontal force for all the sign orientations tested instead of the mean extreme torque and the mean extreme force pair at a specific model orientation. Since no corresponding coefficients have been reported in the literature for single-plate rectangular sign structures, a comparison

D. Zuo et al. / J. Wind Eng. Ind. Aerodyn. 130 (2014) 62–74

73

Table 6 Critical synthesized mean extreme value based eccentricity coefficients of the box sign models tested in phase 3 of the wind tunnel experiments and the corresponding yaw angle and the mean force coefficients. c/h

b/c 0.2

0.3

0.5

1

2

4

5

7.5

0.061 [151, 1.11] 0.064 [151, 1.17] 0.052 [301, 1.06]

0.066 [151, 1.03] 0.056 [301, 1.11] 0.069 [301, 1.13] 0.061 [301, 1.09] 0.068 [301, 1.06]

0.074 [301, 1.00] 0.066 [301, 1.02] 0.058 [01, 1.28] 0.059 [301, 1.2] 0.055 [451, 1.06]

0.086 [301, 1.00] 0.079 [01, 1.12] 0.073 [151, 1.15] 0.082 [451, 1.03] 0.086 [601, 0.77] 0.086 [451, 1.03]

0.118 [301, 0.95] 0.095 [301, 0.97] 0.085 [301, 1.03] 0.089 [451, 0.89] 0.105 [301, 1.15] 0.087 [451, 0.97]

0.149 [151, 1.00] 0.096 [301, 0.97] 0.095 [451, 0.86] 0.116 [451, 0.96] 0.117 [451, 1.25] 0.093 [451, 1.09]

0. 135 [151, 0.90] 0.125 [151, 0.97] 0.129 [151, 1.06] 0.116 [301, 1.02] 0.111 [01, 1.34] 0.109 [151, 1.35]

0 ðC~ e Þmax ½β; C F 

1 0.9 0.8

0.061 [151, 1.09] 0.066 [151, 1.18] 0.064 [151, 1.16]

0.7 0.5 0.25

between the wind induced torque about the vertical axis of these two types of structures is not pursued in this study. It must be noted that although Table 5 lists the synthesized mean extreme value based eccentricity coefficients together with the critical mean force coefficients and Table 6 lists the mean force coefficients together with the critical synthesized mean extreme value based eccentricity coefficients, this does not imply that the combination of this coefficients should be used directly in a design situation. Rather, more research need to be done to investigate the correlation between the horizontal force loading and the torque loading to facilitate appropriate load combination in the design of rectangular box sign structures. Nonetheless, Tables 5 and 6 do suggest that for most rectangular box sign tested, the critical horizontal force and the critical torque about the vertical axis occur at different sign orientation.

6. Conclusions This paper presents the outcome of a comprehensive wind tunnel study conducted to investigate the wind loading of rectangular sign structures and part of the results of a full-scale study that validated the methodologies used in the wind tunnel experiments. The wind tunnel experiments show that the types of configuration of rectangular sign structures can significantly affect their wind loading. It was revealed that for the five types of sign model of the given aspect and clearance ratios, the models with open sides are more susceptible to wind induced torque about the vertical sign axis than the single-plate sign model and the rectangular box sign model and that the wind loading of the rectangular box sign of the given depth to height ratio is lower than that of the single-plate sign in terms of both the total horizontal force and the torque about the vertical sign axis. By comparing the results from the phase of the wind tunnel experiments in which box sign models of various aspect and clearance ratios were tested with those from previous wind tunnel tests of single-plate signs, it is found that for the depth to height and depth to width ratio considered, the mean force coefficients of the box signs are smaller than those of the single-plate signs of the corresponding aspect and clearance ratios. Since the present standards that guide the design of rectangular sign structures are based on experimental study of wind loading of single-plate sign structures, this means that rectangular box sign structures similar to those represented by the wind tunnel models can be over designed in the current practice.

Based on the extensive wind tunnel tests of rectangular box sign models, the study also revealed the dependence of windinduced force on the aspect and clearance ratios of this type of structure. The results of these tests suggest that for the range of depth to height ratio of the sign models tested, when the sign is not slender along the vertical axis (i.e., the aspect ratio being greater than 0.5) the mean force coefficient decreases with increasing aspect ratio when the sign is relatively close to the ground plane (i.e., the clearance ratio being larger than 0.5) and can increase with increasing aspect ratio when the sign is further elevated. The results also shows except for when the sign face is close to being a square (i.e., the aspect ratio being between 0.5 and 2), the mean force coefficient of the box-shaped signs increases when the sign becomes increasingly elevated. On the other hand, the outcome of the wind tunnel tests reveals that the windinduced mean extreme torque of a rectangular box sign with depth to height ration similar to those tested increases when the sign becomes wider and that the dependence of the torque loading of the clearance ratio is much less clear.

Acknowledgments The material presented herein is based on work sponsored by the International Sign Association and the Outdoor Advertising Association of America. The supports by these associations are gratefully acknowledged. Any opinions, findings, conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the International Sign Association and the Outdoor Advertising Association of America.

References ASCE, 2010. Minimum Design Loads for Buildings and Other Structures (ASCE7-10). American Society of Civil Engineers, Reston, VA, USA. Bearman, P.W., 1971. An investigation of the forces on flat plates normal to a turbulent flow. J. Fluid Mech. 46, 177–198. Briassoulis, D., Mistriotis, A., Giannoulis, A., 2010. Wind forces on porous elevated panels. J. Wind Eng. Ind. Aerodyn. 98, 919–928. Cengel, Y., Turner, R., Cimbala, J., 2011. Fundamentals of Thermal-Fluid Science, 4th ed. McGraw-Hill Higher Education, New York. Cermak, J.E., Davenport, A.G., Durgin, F.H., Irwin, P.A., Isyumov, N., Peterka, J.A., et al. Wind tunnel studies of buildings and structures. In: Isyumov, N. (Ed.). ASCE Manuals and Reports on Engineering Practice No. 67, 1999. Cook, N.J., 1990. The Designer's Guide to Wind Loading of Building Structures, Part 2: Static Structures. BRE/Butterworths, London.

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