Numerical study on wind pressures caused by the variation of the rounding
radii of the industrial shed eaves
GUILHERME S. TEIXEIRA, MARCO D. DE CAMPOS
Institute of Exact and Earth Sciences
Federal University of Mato Grosso,
Av. Valdon Varjão, 6390, Barra do Garças, 78605-091, Mato Grosso, BRAZIL
Abstract: This work approached a typical industrial shed with varied rounded eaves, which is pointed out, in
the few papers on it, as favorable to structural safety against the action of the winds. Since the literature has
neglected this building configuration, the external pressure coefficients were obtained by CFD with the aid of
the Ansys Workbench software, applying tetrahedral meshes in the domain discretization. Furthermore, the
boundary layer around the building was modeled for greater accuracy in data capture. Using the RNG K-
Epsilon model, were determined the turbulent flow effects. The results indicated a reduction in the pressure
coefficients in the most sensitive regions and prone to accidents caused by wind on the roof. Finally, the flow
pattern can be measured using the presented velocity fields.
Key-Words: Wind action, industrial shed, eaves, Ansys, pressure coefficient.
Received: April 9, 2022. Revised: March 5, 2023. Accepted: April 3, 2023. Published: April 25, 2023.
1 Introduction
In the last 50 years, it has taken advantage of
electronic instrumentation development and
computer-based statistical analysis techniques for
conducting various surveys of wind loads on low-
rise buildings. Despite this, there were few studies
about the wind loads in the curved eaves in
industrial and commercial low-rise buildings [1].
This approach is necessary since curved eaves may
mitigate the high suctions that develop with
conventional sharp eaves over the lower part of the
windward roof slope. It is precisely this suction that
usually causes damage to the structure [2].
In this context, a low-rise buildings experiment of
1986/87, the Silsoe Structures Building, in the
United Kingdom, was idealized for full-scale wind
pressure measurements. This building, constructed
in an open country, constituted an optional eaves
geometry with either traditional sharp or curved
eaves. As well as seventy pressure tapping points on
the building roof and walls, the building was
equipped with twelve strain gauge positions on the
central portal frame to enable measurements of
structural response to be made ([1], [3]).
Despite the studies already carried out on geometric
factors of buildings such as roof slope, height-depth
ratio, and width-depth ratio, few studies have
focused on analyzing the influence of eaves. Among
these, few presented results for rounded eaves. Few
authors in literature, such as the Silsoe Structure
experiments ([4],[5],[6]), addressed this
architectural element. Thus, this work analyzed the
influence on the pressure coefficients caused by the
variation of the rounding radii of the eaves.
2 Methodology
ANSYS Workbench (often ANSYS WB) is a multi-
disciplinary business software widely used in
industry and academia applications. It is known by
researchers in the computational field, especially in
Wind Engineering, its integrity, and cost-
effectiveness in the study of wind action on
buildings. For these reasons, the present work was
almost entirely developed using the software, from
geometry modeling, meshes, equations solution, and
post-processing, and described next.
Geometry, domain, and subdomain
The basic geometry of this work consists of a shed
located in the farmland of the Silsoe Research
Institute. It is a building with a rectangular plan
measuring 12.90x24.10x4.16 m (WxLxH), eaves
rounding radius of 635 mm (varying in the
simulations), and roof pitch of 10º [2], modeled
using SpaceClaim, Ansys WB CAD platform (Fig.
1a). For the domain, were adopted the
recommendations of [7], being the length of
5H+L+15H, the width of 5H+B+5H, and the height
of H+5H, dependent on the building height of
(H=4.16 m), of the length L of the building in the
flow direction and width B. Note that the reference
height H=4.16 m is measured from the ground to the
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Guilherme S. Teixeira, Marco D. De Campos
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projection of the sharp eaves, as in the studies
conducted in [8], instead of the height up to the
ridge. For better accuracy of the effects of the flow
in the vicinity of the building, a subdomain with
dimensions of 0.5H in all directions of the building
was developed (Fig. 1b). The blockage ratio varied
from 4.47% to 5.14% in the simulations, above the
3% recommended by [7] but below the maximum of
10% indicated, which may be enough to avoid
artificial acceleration of the flow over the building.
(a)
(b)
Fig. 1 (a) Geometry cross-section, with roof, equally divided into six zones, and (b) domain, subdomain, and
building (both in meters).
Mesh
Mesh represents a fundamental step in attaining the
numerical solutions to the governing partial
differential equations using CFD because the mesh
selected for CFD simulations will define the
accuracy and resolution of the simulation results,
both of which will affect the computation time and
level of detail in the results [9]. Likewise, in this
work, some precautions were adopted, which used
unstructured meshes composed of tetrahedral,
allowing better parameterization and control in
critical regions [10].
It's them:
i) The capture of proximity and curvature: these
parameters are relevant to capture the effects in the
rounded regions of the eaves.
ii) In the meshes were considered four refinement
levels (Fig. 2). The first is in the fluid domain, with
a controlled dimension of the elements; the second
is in the subdomain, with a lesser in size element
than the previous one (half); in the third level, the
control of the size of the elements on the faces of
the building and, finally, the modeling of the
boundary layer.
Fig. 2 Mesh refinement levels used of one numerical
application in this work
For the external flows, i.e., bodies immersed in fluid
streams with unconfined flows, viscous effects will
be present at the solid-fluid boundaries [11]. Global
effects on the flow can happen due to the tensions
existing in these thin boundaries (called boundary
layers, described in [12]). For this reason, its CFD
modeling is relevant and used in the present work.
To determine the boundary layer parameters were
adopted the recommendations of the ANSYS CFX-
Solver Modeling Guide [13]:
δ=0.035 L Re
δ is the boundary layer thickness, L = Dh the
hydraulic diameter, and Re the Reynolds number,
given by:



being A the cross-sectional area of the wind tunnel
to the airflow, a, b the horizontal and vertical
dimension of the cross-section of the control volume
to the airflow, respectively, V the flow velocity
[m/s] and the air kinematic viscosity (=1,56E-5
[m²/s]).
In addition, 10 nodal points in the direction
orthogonal to the flow obstruction wall, according to
[13]. This number of points was adopted to
guarantee a good performance of the turbulence
model. It was also considered the boundary layer on
the 4 facades, on the roofs, and on the eaves of the
shed. Although the expansion rate applied to the
meshes is 1.1 (below the maximum 1.2 usually
recommended by ANSYS), in the boundary layer,
exclusively, the expansion rate of the elements was
[14]:
Growth rate = 󰇡
󰇢
where  represents the thickness of the first
element and is given by [13]:

iii) In this work a grid sensitivity analysis was to
ensure that the results, depending on the mesh
employed, did not present significant changes. Thus,
three different grids were applied for each
simulation (coarse, medium and fine), having
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approximately 660k, 1.13Mi, and 2.30Mi grid cells,
respectively. This addition of cells at each new
mesh iteration was always greater than 1.5 times the
previous mesh, as indicated by [16]. Even with the
meshes not showing significant differences in the
results, the fine meshes.
iv) Mesh quality parameters are also fundamental
factors to guarantee an acceptable mesh. Here, the
aspect ratio, skewness, and orthogonal quality were
analyzed, as they describe well the geometric
aspects and connectivity between elements. For
three-dimensional elements, the aspect ratio is the
ratio between the radius of the circumscribed and
inscribed circles in the base geometry (in our case,
the triangles). The skewness indicates how close to
the ideal geometry (in this case, tetrahedron) the
mesh cells or faces are (recommended values
between 0 and 0.5). Lastly, the orthogonal quality
metrics the element's orthogonality (recommended
values close to 1) [15].
v) Finally, concomitantly with the grid sensitivity
analysis, studies were carried out with meshes of
different methodologies to certify the independence
of the results.
Thus, in the analysis, it was restricted to meshes
with one level of refinement. In these, only the size
of the element in the fluid domain would be under
the user's control.
Although, for these two methodologies, the
differences in the results were not significant, the
first methodology resulted in values closer to those
of the literature adopted in the validation and,
therefore, was adopted in this work.
Setup and solver setting
The vertical profile of wind speeds on the INLET
face is described below by the Power Law, which is
widely accepted in Engineering applications [17]:
 󰇧
󰇨
where is the wind speed (in meters per second) at
height Z (in meters), and is the pre-established
wind speed at a reference height , adopted as
10 m. The exponent α is an empirically derived
coefficient that varies depending on the terrain
roughness and the time interval. Also, α=0.16
representing a terrain with high grass, and
=30m/s were adopted.
At different points and times within the fluid
domain, a turbulence model frequently used in Wind
Engineering, the RNG K-Epsilon, was employed to
model the random properties of the turbulent flow
[18].
According to Franke et al. [19], the advective terms
must be discretized using higher-order schemes
when transforming the governing differential
equations into algebraic equations.
For this, in the present work, the High Resolution
schemes for such terms and numerical turbulence
were defined. As the simulations involve a notably
free surface [13], was applied the Double Precision
scheme (16 digits) to improve the convergence.
In addition, the chosen stopping criterion was the
RMS equal to 10E-4, followed by three verification
steps to determine the reliability of the results:
i) Interpretation of the results of the residual values
of the mass, momentum, energy, and additional
turbulence equations due to the RNG K-Epsilon
model employed. That is, residual RMS, in addition
to the simulation stopping criterion, was used as a
convergence criterion.
ii) Monitoring the Principle of Conservation of
Mass.
According to [13], the difference in mass on the
INLET and OUTLET faces must be less than 1%.
iii) On the physical coherence of the results.
The external pressure coefficients, defined by
Cpe=Δp/q, where Cpe is the external pressure
coefficient; Δp is the difference in external pressure
coefficient, and q is the dynamic pressure, in
addition to being used to analyze each application,
provide parameters for interpreting the correct
physics of the values obtained with the simulation.
This fact is due to the range of expected values for
this parameter. For positive values, which indicate
overpressures, a maximum of Cpe=1.0 is expected
(disregarding errors associated with CFD). For
negative values, which indicate suction, in defined
regions of geometry, the magnitude can be from 6 to
8 times the pressure obstruction [20]. Finally,
Table 1 shows the rest boundary conditions adopted.
Table 1. Boundary conditions and parameters.
Condition
Method of mesh
Capture curvature and proximity
Reference pressure
Air temperature
Turbulence intensity
Flow regime
Inlet
α
Zref
Uref
Relative pressure of outlet
Wall - Ground
Model wall roughness
Roughness
Advection scheme
Turbulence numeric
Minimum number of iterations
Maximum number of iterations
3 Numerical results
Application 1 (validation): To validate the
methodology, the T-test was used to evaluate the
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significant differences between the means of the
samples of the present work and of [2]. In [2], the
results used the full-scale field experiment, which
has a significant quality in terms of benchmark if
compared with the reduced models, which
minimized the scale effects ([21], [22]). The angle
of incidence was 90º with wind reaching the
building transversally (named Model 1, where the
notation “R plus three digits” represents the
rounding for the eaves, in mm), and Tables 2 and 3
show the mesh parameters.
The sensitivity of roof pressures as a function of
eaves configurations is well described in the
literature ([23], [24], [25]). Thus, to adequately
represent the results, the samples for the test were
composed of the average external pressure
coefficients of the windward and leeward roofs (not
including the eaves themselves) (Fig 3a). A
transverse cut sectioned the surface into six equal
parts (Fig 1a). Table 4 shows the Cpe values for six
zones using Model 1 in comparison with [2].
Considering the null hypothesis (H0) that the means
are not different, assuming two samples with
equivalent variances, two-tailed distribution, and
significance ' = 0.05, using Microsoft Excel
software obtained a p-value = 0.836, approximately.
As p-value > ', we do not reject the null hypothesis
(H0) and, therefore, consider the difference between
the means in the Cpe values insignificant.
Table 2. Mesh quality parameters.
Results
Parameter
Range
Classification [12]
Model 1 (R635)
(average)
Model 2 (R335)
(average)
Model 3 (R935)
(average)
Aspect ratio
up to 100
recomended
51.364
59.786
54.655
Skewness
0.25-0.50
good
0.25065
0.2566
0.25389
Orthogonal
quality
0.70-0.95
good
0.74538
0.73935
0.74254
Table 3. Results for the boundary layer of Models 1, 2 and 3 with vent at 90º.
V (m/s)
a (m)
b (m)
A (m²)
Dh (m)
Re
δ (m)
Δy (m)
Growth rate
30
65.7
24.96
1639.87
36.18
69569821
9,59724175E-2
1,62477E-5
1.859
Table 4. Cpe values for six zones using Model 1 in comparison with [2].
Cpe medium
Model
Zones
1
2
3
4
5
6
[2]
-0.80
-0.55
-0.79
-0.80
-0.39
-0.25
Present work
-0.91
-0.49
-0.94
-0.96
-0.32
-0.17
(a)
(b)
Fig. 3 Pressure distributions over roof for curved eaves with transverse wind for (a) Model 1, and (b) Models 2
and 3.
Application 2 (eaves rounding radii): Here, the
rounding radii of the eaves were varied to analyze
their influence on the pressure coefficients.
According to the results, the roofs presented a
similar distribution pattern, with suction peaks on
the windward eaves and ridges. Despite this, the
intensity at the point immediately beyond the
windward eaves (i.e., close to 0.00% of the roof
span) in Model 2 was 41.18% higher than in Model
3, although it was 22.06% lower in the ridge (Fig
3b). Analogously to the results of [2], the smaller
the rounding radius (in this work, R335 < R935, and
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in [2], R000 (sharp eaves) < R635), the more intense
were the pressure coefficients at the most windward
point of the roof (~0.00 % span). As in [2], an
inversion of intensities in the ridge. The values were
close on the leeward face of the roof, with an
absolute difference for Cpe of 0.10.The results also
showed that in the eaves themselves, the smaller the
radius, the greater the suctions (Fig. 4a-b).
In consonance with this result, a sharper curve with
smaller radii will cause an increase in the flow
velocity (Fig. 4c-d). Hence, based on the literature,
[26], [27, [28], or on Bernoulli's Theorem, it is
concluded that the most intense velocities generated
the highest negative pressure peaks. Also, the point
of displacement occurred approximately in the
middle of the leeward roof, compared to the
building with the eaves with a larger radius (Model
3), in line with [2] (Fig. 4c-d).
(a)
(b)
(c)
(d)
Fig 4 Top view Cpe contour and the transverse plane of the velocity fields, respectively, for (a), (c) Model 2,
and (b), (d) Model 3.
4 Conclusions
The effects of wind on the roofs of buildings with
curved eaves were measured using computer
simulation.
The results for two rounding radii presented here
corroborate the literature, i.e., increasing the radius
of the eaves can decrease the pressures on the roof
portions closer to the windward side, despite
generating great efforts on the ridge.
Furthermore, the configurations of the rounded
edges can be considered of little relevance when the
leeward faces are analyzed.
These results help to create more references for
Wind Engineering, considering that the literature
addressing rounded eaves is scarce. Future research
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should test new radii and seek to establish
connections with roof slopes, height-depth ratio, and
width-depth ratio, among other relevant geometric
aspects.
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Contribution of individual authors to
the creation of a scientific article
Guilherme Teixeira was responsible for the
methodology, carrying out the simulation, and
writing the results. Marco Campos carried out the
conceptualization, review, and editing.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflicts of Interest
The authors have no conflicts of interest to declare
that are relevant to the content of this article.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
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