The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7)
Shanghai, China; September 2-6, 2012
Benchmark wind tunnel study of wind loading on
rectangular sign structures
Delong Zuo, Douglas A. Smith, Kishor C. Mehta
Wind Science and Engineering Research Center, Texas Tech University, Mail Box 41023,
Lubbock, TX, USA
ABSTRACT: Wind-tunnel tests were conducted to study wind loading on elevated rectangular
sign structures of various configurations. Based on these tests, the wind-induced force and moment acting on the sign models were evaluated. The data obtained from the wind tunnel tests
were analyzed in the context of the results of previous wind tunnel tests as well as those of a fullscale investigation. It is revealed that the configuration of the rectangular sign faces significantly
affects the loading on these structures. It particular, the outcomes of the present study indicate
that the torque acting on rectangular sign structures is overestimated by a standard that guides the
design of such structures.
KEYWORDS: rectangular sign, wind loading, wind tunnel tests.
1 INTRODUCTION
Rectangular boxes and plates are frequently used as signs to display information and to function
as a structural component. These sign systems with rectangular faces are structurally quite simple: They usually consist of a rectangular sign board or box and a simple support, such as 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 that fact that rectangular boxes and plates
are among bluff bodies of the simplest shapes, the wind loading of sign structures can be complex and is dependent on the size of the sign, the ratios between the three dimensions of the sign,
whether the sign is elevated or located on the ground and, in the case of elevated sign, the
amount of the clearance between the sign and the ground.
Perhaps due to the perceived simplicity of the structure, to date, very few studies have been dedicated to expressly investigate the wind loading of sign structures. Previous studies related to
wind loading of rectangular sign structures evolved from wind tunnel experiments conducted in
smooth, uniform flow (e.g., the early work done by Flachsbart, as summarized in [1]) to turbulent uniform flow (e.g., [2]) to both wind tunnel and full-scale studies in turbulent boundary layer
flow (e.g., [3-9]). Most of these studies, however, were conducted to study wind loading on freestanding walls, which resemble a class of rectangular signs on the ground. Only very few studies
(e.g., [5, 9]) were dedicated to the study of sign structures, and the focus of these studies were on
signs formed by thin plate-like rectangular elements. This paper presents the outcomes of a
benchmark study, which is a subset of a more comprehensive research effort, conducted to assess
wind loading on sign structures of a number of configurations. These outcomes are interpreted in
the context of the results from previous studies on wind loading on rectangular sign structures
and the specifications of design standard.
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2 EXPERIMENTAL CONFIGURATIONS
2.1 Models
Models of four sign structures with rectangular sign faces were tested in the wind tunnel at a
length scale of 1:50. The first has a single-plate of 3 mm in thickness, which will subsequently
be referred to as the single-plate sign model. The second is composed primarily of two parallel
thin plates of 3 mm in thickness as the sign faces, which will be referred to as the double-plate
sign model. This model is open on all sides, and the two sign faces are connected by eight 6mm
by 6 mm struts, four at the top and the other four at the bottom of the sign at equal spacing. The
third is a model also composed of two thin plates of 3 mm in thickness as the sign faces, but these two plates form a 30q angle instead of being parallel to each other. The two faces of this
model are also connected by eight 6mm by 6 mm struts, four at the top and the other four at the
bottom of the sign at equal spacing. This model will be subsequently referred to as the V-shaped
sign model. The fourth is cubic in shape with all the sides closed, which will subsequently be referred to as the box sign model. The sign double-plate, the V-shaped and the box sign models
were printed out by a three-dimensional printer, and the sign face of the single-plate sign model
was an aluminum plate. All four sign models were supported by a circular steel rod of 0.95 cm in
diameter. Figure 1 schematically shows the configuration and major dimensions of the models.
In this figure, b 15.2 cm , h c 7.6 cm , and t 3.7 cm . At a length scale of 1:50, these
dimensions correspond to full-scale sign faces with a width of 7.6 m and a height of 3.8 m. In
current design practices, sign structures are often characterized by their aspect ratio ( b / h ) and
clearance ratio ( h / ( h c ) ). These specimens represented sign models with an aspect ratio of 2
and a clearance ratio of 0.5.
b
t
Top View
Front View
b
Single-Plate Sign
h
b
V-Shaped Sign
t
t
c
b
Double-Plate Sign
Box Sign
Figure 1 Sign models tested in the wind tunnel (not to scale)
2.2 Simulation of boundary layer
A wood 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 atmospheric boundary flows representing those over exposure C specified by the loading
standard published by American Society of Civil Engineers [10] (subsequently referred to as
ASCE 7-10). Figure 2 shows the mean wind speed profile of the simulated atmospheric bounda-
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The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7)
Shanghai, China; September 2-6, 2012
ry layer at a length scale of 1:50. In this graph, the mean wind speeds at the measurement heights
were normalized by that measured at a height of 0.2 m above the wind tunnel floor. A leastsquares fit of the height against mean wind speed assuming that the profile is logarithmic in nature yields an equivalent full-scale roughness length value of z0 0.015 m , which is close to the
representative roughness length scale associated with exposure C specified by ASCE 7-10. Also
shown in Figure 2 is the estimated auto-spectral density function of the along-wind speed at a
height of 0.2 m above the wind tunnel floor as well as the corresponding Kaimal spectrum ([11])
at this height. In this figure, n is frequency, U is the mean wind speed, V u is the standard
deviation and S n (n, z ) is the auto-spectral density function. It can be observed that the simulated boundary layer has slightly higher energy content at higher frequencies and slightly lower energy content at lower frequencies than the flow represented by the Kaimal spectrum. This is a
typical shortcoming of larger scale wind tunnel simulations.
Height, z (m)
0.5
0
Simulated
Kaimal
Exposure C (z0 = 0.02 m)
nSu(n,z)/V2u
0.6
10
Simulated (z0 = 0.015 m)
0.4
0.3
10
10
0.2
-1
-2
0.1
0
0
-3
0.25
0.5
0.75
Mean speed ratio
1
10 -3
10
1.25
10
-2
-1
10
nz/U
10
0
10
1
Figure 2 Mean wind speed profile of boundary layer flow and spectrum of along-wind speed at a height of 0.2 m
above wind tunnel floor
2.3 Measurements
During the tests, the rods that supported the sign models were clamped to a six-component force
transducer (ATI Industrial Automation, Inc. Gamma series, calibration SI-32-2.5), which has a
resonance frequency of more than 1000 Hz for all components, for direct measurements of the
forces and moments acting on the sign structure models. The mean test wind speed was approximately 10 m/s at a height of 20 cm above the wind tunnel floor, which is equivalent to 40 m/s at
10 m above ground level. The reference wind speeds for calculation of the reference dynamic
pressure were measured by a Cobra probe (Turbulent Flow Instrumentation, series 100), which
was placed at a position that was at the same height as the top of the sign model and at least one
sign face width away from the side of the model. The single-plate, double-plate and box sign
models were tested for 6 orientations represented by yaw angles of 0q to 75q at a 15q increment, relative to the mean direction of the wind, respectively; and the V-shaped sign model was
tested for 13 orientation represented by yaw angles of 90q to 90q at a 15q increment. Figure 3 schematically indicates the definition of the yaw angle ( E ) for the four types of sign models tested. For the V-shaped sign model, clockwise rotation of the sign axis relative to the direction normal to the wind direction results in positive yaw angles and counterclockwise rotation
result in negative yaw angles. In addition to testing the whole sign models, a separate series of
tests were also performed for the supporting rods without the sign faces attached. With the reasonable assumption that the effect of the secondary flow induced by the rod can be neglected,
this enables estimation of the net forces and moments acting on the sign faces only.
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el
Wind
od
Wind
M
Mo
del
All the measurement channels were sampled at a frequency of 250 Hz. Ten tests were conducted
for each sign configuration as well as the rod to facilitate estimation of the coefficients representing the wind-induced forces and moments. The duration of each test is 72 seconds, which is
equivalent to 15 minutes at full-scale.
E
E
(b)
(a)
Figure 3 Definition of yaw angle for (a) single-plate, double-plate and box signs and (b) V-shaped sign
3 RESULTS
3.1 Mean force and eccentricity coefficients
To estimate the mean force coefficients, the forces acting on the sign structure models and those
acting on the supporting rods were first evaluated independently. For all specimens, the forces
measured by the two orthogonal axes of the force transducer were decomposed into an alongwind drag component and a cross-wind lift component. The mean drag and lift forces acting on
the rod are 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 are subtracted from the drag
and lift force time histories obtained from the 10 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, which will subsequently be denoted Fi (t ) , in which i is the test number and t is time. For each net force time
history, the corresponding force coefficient time history is estimated as
Fi (t )
(1)
C Fi (t )
1
UU 2 A
2
where U is the air density calculated based on the temperature, barometric pressure and relative
humidity measured in the wind tunnel, U is the mean wind speed measured at the height of the
top of the sign, and A is the area of the sign faces. For each sign model, a 15-minute mean
force coefficient, CFi mean(CFi (t )) is computed based on time histories obtained from each
individual test. The mean force coefficient of a sign model is then estimated as the average of
these 10 15-minute mean force coefficients. That is
CF
1 10
¦ CFi
10 i 1
(2)
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The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7)
Shanghai, China; September 2-6, 2012
Figure 4 shows the mean force coefficients of the four sign models tested for the yaw angles
tested. It can be seen that the mean aerodynamic behavior of the 4 sign models were quite different. While the largest mean force coefficient for all four models are expectedly associated with
smaller absolute values of yaw angles, the detailed evolution of these mean force coefficients
with the yaw angle is quite model dependent. For the single-plate sign model and the box sign
model, the mean force coefficients remain mostly constant for yaw angles of 0q to 30q . At
yaw angles of 45q and above, however, these two models behaved very differently due to the
difference in the depth of the signs. In particular, while the single-plate sign is seen to attain a
maximum mean force coefficient at a yaw angle of 45q , the mean force coefficient of the boxsign at a yaw angle of 45q is much smaller than those at yaw angles of 0q to 30q . By comparison, the evolution of the mean force coefficients of the double-plate sign is quite similar to
that of the single-plate sign except that the existence of a second rectangular plate make the mean
force coefficients of the double-plate sign slightly lower at yaw angles of 0q , 15q and 45q
and slightly higher yaw angles of 30q , 60q and 75q than those of the single-plate sign at the
corresponding yaw angles. By contrast, the loading of the V-shaped sign model is the most different from that of the other three sign models due to the fact that the orientation of this sign relative to wind is asymmetrical about the yaw angle of zero degree.
Figure 4 Mean force coefficient vs. yaw angle
While the mean force coefficients of the single-plate, double-plate and V-shaped sign models
shown in Figure 4 are quite similar to those reported by Letchford [5] and Warnitchai [9] for corresponding equivalent sign models tested at the same yaw angles in similar simulated boundary
layers flows, it is noteworthy that, as can be observed in , the critical (i.e., maximum) force coefficient of the box sign model, which was not tested by either Letchford [5] or Warnitchai [9], is
considerably lower than those of the other three sign models, which are quite similar. This suggests that closing the sides of rectangular sign structures results in reduction of wind loading of
these structures. Also, in the standards and specifications that guide the design of rectangular
sign structures (e.g., [10]), the force coefficients are mostly derived based on wind tunnel tests of
single-plate sign models, this means that the currently design practice likely overestimates the
wind loading on box sign structures.
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Table 1 Critical mean force coefficients
(C F ) max
single-plate
double-plate
V-shaped
box
1.41
1.35
1.44
1.23
To characterize the mean torque acting on the sign structure due to wind loading, an eccentricity
coefficient, which is the moment arm of the torque normalized by the width of the sign model, is
defined as:
Ti (t )
Cei (t )
(3)
Fi (t )b
where Ti (t ) is the time history of the torque acting on the base of the supporting rod during the
ith test run. For each sign model, a 15-minute mean eccentricity coefficient, Cei mean(Cei (t ))
is computed based on time histories obtained from each individual test. The mean force coefficient of a sign model is then estimated as the average of these 10 15-minute mean force coefficients. That is
1 10
(4)
¦ Cei
10 i 1
Figure 5 shows the mean eccentricity coefficients of the four sign models tested for the yaw angles tested. It can be seen that the difference in the mean force coefficients of the 4 sign models
were also present in the wind-induced torque acting on them. It can be seen that for the singleplate, double-plate and box sign models, the mean eccentricity coefficients exhibit a general
trend of increasing with increasing yaw angle. For yaw angles of 0q and 15q , the mean eccentricity coefficients of the single-plate, double-plate and box sign models are almost the same.
With increasing yaw angle, the mean eccentricity coefficients of the single-plate and doubleplate sign models become much higher than those of the box sign model at the corresponding
yaw angles, with the double-plate sign having the largest mean eccentricity coefficient at a given
yaw angle. Compared with these three sign models, the behavior of the torque acting of the Vshaped sign model is much more complex again owning to the fact that the orientation of this
sign relative to wind is asymmetrical about the yaw angle of zero degree.
Ce
Figure 5 Mean eccentricity coefficient vs. yaw angle
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The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7)
Shanghai, China; September 2-6, 2012
Table 2 Critical mean eccentricity coefficients
(Ce ) max
single-plate
double-plate
V-shaped
box
0.19
0.20
0.21
0.12
3.2 Force and eccentricity coefficients based on extreme values
In addition to the mean coefficients, the measurements made in the tests were also used to estimate the pseudo-steady force coefficients. For each sign model, at each yaw angle, the maximum
force coefficients was identified based on the force coefficient time history obtained from each
test. the 10 maximum force coefficients were then fitted to a type I Fisher-Tippett extreme value
distribution using the Lieblein method [12]. The mode and dispersion of the fitted extreme value
distribution were used to estimate the mean hourly extreme force coefficient as
(5)
Cˆ F mode10 minute [0.577 ln(6)] u dispersion10 minute
The pseudo-steady force coefficient is then estimated as
Cˆ F
C F
G2
(6)
where G is the gust factor calculated based on the expression [13]
(7)
G 1 0.42 ln(3600 / t0 )
In this study, t0 is taken as 3 seconds, the gust factor obtained using equation (7) therefore represents that associated with 3-second gusts.
Figure 6 shows the pseudo-steady force coefficients of the four sign models against the yaw angles. The mean force coefficients based on full-scale equivalent 15 minute records and the pseudo-steady force coefficients based on hourly extreme values are comparable since both time durations fall in the spectral gap (e.g., [14]). Comparison of Figure 6 with Figure 2 reveals that for
the critical loading cases associated with small yaw angle (i.e., less then 60q ), the pseudo-steady
force coefficients for all four models are close to the corresponding mean force coefficients. At
larger yaw angles, the pseudo-steady force coefficients for a given sign model differs from the
corresponding mean coefficients because for these yaw angles, the effect of the structure-induced
turbulence becomes more pronounced.
Figure 6 Pseudo-steady force coefficient vs. yaw angle
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Table 3 lists the critical pseudo-steady force coefficients for the four sign models tested. It is apparent again that while the critical pseudo-steady force coefficients of the single-plate, doubleplate and V-shaped sign models are close, that of the box sign model is considerably lower. This
again suggest that it is likely to be conservative if force coefficients derived based on study of
wind loading on single-plate signs are used to design box sign structures.
Table 3 Critical pseudo-steady force coefficients
(C F ) max
single-plate
double-plate
V-shaped
box
1.37
1.41
1.42
1.25
Using the same procedure used to estimate the hourly extreme force coefficients, the hourly
mean extreme force ( F̂ ) and absolute torque ( | Tˆ | ) acting on a sign model. These mean extreme
values can then be used to estimate a mean extreme value based eccentricity coefficient for this
sign model:
| Tˆ |
(8)
C e
ˆ
Fb
Figure 7 shows the mean extreme value based eccentricity coefficients against the yaw angles
tested. It is evident that for the single-plate, double-plate and box sign models, the eccentricity
coefficients increase with increasing yaw angle. It also can be seen that except for the case of zero yaw angle, for the same yaw angle, the single-plate and the double-late sign models have
higher eccentricity coefficients than the box sign model. In addition, the graph suggests that, as
in the case of mean eccentricity coefficient, the relationship between the mean-extreme value
based eccentricity coefficients of the V-shaped sign and the yaw angles are much more complex.
Figure 7 Mean extreme value based eccentricity coefficient vs. yaw angle
For a typical design situation, the design extreme torque is likely calculated based on the design
extreme force, which is the maximum extreme force for all the possible yaw angles. For codification purposes, an alternative synthesized eccentricity coefficient can be defined as
| Tˆ |
C e '
(9)
Fˆmax b
in which F̂max is the maximum of the mean extreme force for all wind directions.
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The Seventh International Colloquium on Bluff Body Aerodynamics and Applications (BBAA7)
Shanghai, China; September 2-6, 2012
Figure 8 depicts the synthesized eccentricity coefficients against the yaw angles. This graph indicates that for a given yaw angle, the two sign models consist of two plates as sign faces, i.e., the
double-plate sign and the V-shaped sign generally have larger synthesized eccentricity coefficients. It also suggested that although the synthesized eccentricity coefficients of the single-plate
sign model and the box sign model are close for small yaw angles (i.e., up to 30q ), with increasing yaw angle, the synthesized eccentricity coefficients of the single-plate sign model becomes
much larger than the corresponding ones of the box sign model.
Figure 8 synthesized eccentricity coefficient vs. yaw angle
Table 4 lists the critical (i.e., maximum) synthesized eccentricity coefficients for the four sign
models tested. Except that of the V-shaped sign model, these synthesized eccentricity coefficients are smaller than that specified in a typical standard. For example, in ASCE 7-10, the eccentricity coefficient recommended for the design of rectangular sign structures is 0.2. This value
is obviously overly conservative for box sign structures similar to full-scale equivalent of the box
sign model tested in the wind tunnel.
Table 4 Critical synthesized eccentricity coefficients
(C e ') max
single-plate
double-plate
V-shaped
box
0.13
0.18
0.25
0.09
4 CONCLUSIONS
Models of four types of sign structures with rectangular faces are tested in a wind tunnel as a
benchmark study of wind loading on rectangular sign structures. The data obtained from the
wind tunnel tests were used to evaluate the wind-induced force acting on the models represented
by mean and pseudo-steady force coefficients of these four types of structures as well as the
wind-induced torque about the vertical sign axis represented mean and mean-extreme loading
based eccentricity coefficients. It is revealed that for the four models with the same sized sign
faces, different configuration of the signs can result in quite different loading on the structures.
In particular, it was found that rectangular sign structures with all sides closed are subjected to
less wind loading in terms of both horizontal force and torque about the vertical axis than are
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signs consisting of either a single-plate or two plates with open sides. This means that design
specifications derived based on study of wind loading of single-plate sign structures can potentially overestimate the wind force acting on box type sign structures. In addition, the outcome of
the study also suggests that current design practice potentially overestimate the torque acting on
many types of rectangular sign structure.
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