NIST BUILDING SCIENCE SERIES 180 

Database-Assisted Design for Wind: 

Concepts, Software, and Examples 

for Rigid and Flexible Buildings 

Joseph A. Main and William P. Fritz 

 
Cover Photo: Boundary Layer Wind Tunnel Laboratory, The University of Western Ontario
NIST BUILDING SCIENCE SERIES 180 

Database-Assisted Design for Wind: 

Concepts, Software, and Examples 

for Rigid and Flexible Buildings 

Joseph A. Main 

William P. Fritz 

Building and Fire Research Laboratory 

National Institute of Standards and Technology 

Gaithersburg, MD 20899-8611 

March 2006 

U.S. Department of Commerce 

Carlos M. Gutierrez, Secretary 

National Institute of Standards and Technology 

William A. Jeffrey, Director 
Disclaimer

Certain commercial entities, equipment, or materials may be identified in this document in order to 

describe an experimental procedure or concept adequately. Such identification is not intended to imply 

recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended 

to imply that the entities, materials, or equipment are necessarily the best available for the purpose. 

National Institute of Standards and Technology Building Science Series 180 

Natl. Inst. Stand. Technol. Bldg. Sci. Ser. 180, 99 pages (March 2006) 

CODEN: NBSSES 
Abstract 

Database-Assisted Design (DAD) represents a unified framework for analysis and design of 

buildings for wind loads that makes direct use of pressure time histories measured at a large 

number of pressure taps on one or more wind tunnel models. Local climatological information 

on extreme wind speeds and their direction-dependence can be used in conjunction with the 

measured pressures to obtain estimates of peak wind effects with specified return periods for use 

in structural design. Wind effects of interest may include internal forces and bending moments, 

demand/capacity ratios, or deflections and accelerations. Through direct use of measured 

pressures, rigorous accounting for wind directionality, and accurate modeling of structural 

dynamics for flexible buildings, DAD enables more accurate estimation of peak wind effects 

than is allowed by simplified procedures in current use, thus facilitating more risk-consistent 

designs. It is anticipated that in the not-too-distant future, pressure time series obtained by 

Computational Fluid Dynamics (CFD) may also be used in DAD. 

This report provides an overview of DAD and presents details of its implementation for both 

rigid and flexible buildings, for which separate software packages have been developed. The 

report is intended as a companion to these software packages, which are being made publicly 

available at <http://www.nist.gov/wind>. The software for rigid buildings incorporates an 

interpolation scheme which allows for estimation of peak wind effects using wind tunnel models 

whose dimensions do not precisely match the dimensions of the structure of interest. To facilitate 

efficient implementation, the details of the DAD procedure are presented herein using matrix 

notation. However, no use of matrix algebra by design engineers is required, and the 

accompanying software packages incorporate graphical interfaces to make the procedure 

transparent and user-friendly. Example calculations are presented to illustrate the DAD 

approach. 

Key words: building technology; aerodynamics; extreme winds; database-assisted design; 

structural dynamics; wind directionality; wind forces; wind tunnels. 

iii 
Acknowledgements 

The authors have been supported through the NRC/NIST Postdoctoral Research Associateship 

Program and would like to thank their postdoctoral research advisor, Emil Simiu, for initiating 

and providing direction for this work; Eric Ho of the University of Western Ontario for 

providing the wind tunnel pressure measurements used for the examples in this report; Mihai 

Iancovici of the Technical University of Civil Engineering of Bucharest, Romania, who made 

useful initial contributions to the development of the software for flexible buildings; Ilaria 

Venanzi of the University of Perugia, Italy, who provided valuable feedback on that software; 

and Jean-Paul Pinelli of the Florida Institute of Technology, Ben Schafer of The Johns Hopkins 

University, and Ted Stathopoulos of Concordia University, for providing valuable comments on 

the work presented in this report. 

iv
Contents 

Abstract.........................................................................................................................................iii 

Acknowledgements ...................................................................................................................... iv 

Contents......................................................................................................................................... v 

List of Figures.............................................................................................................................. vii 

List of Tables..............................................................................................................................viii 

1. Introduction – Joseph A. Main and William P. Fritz............................................................ 1 

2. Overview of Database-Assisted Design – Joseph A. Main and William P. Fritz................ 3 

2.1. Aerodynamic databases: pressure time series................................................................. 3 

2.2. Evaluation of peak wind effects...................................................................................... 5 

2.2.1. Transforming wind pressures to structural loads.................................................... 6 

2.2.2. Evaluating time series of wind effects.................................................................... 6 

2.2.3. Estimating expected peaks of time series ............................................................... 7 

2.3. Climatalogical databases: directional extreme wind speeds........................................... 8 

2.4. Peak wind effects with specified return period............................................................. 11 

2.5. Implementation in structural design.............................................................................. 13 

3. Application to Rigid Buildings: Static Analysis and Interpolation Issues – 

Joseph A. Main...................................................................................................................... 14 

3.1. Overview....................................................................................................................... 14 

3.2. Transfer of wind loading from cladding to structure.................................................... 16 

3.2.1. Determination of tributary areas for pressure taps................................................ 16 

3.2.2. Assumed form of structural system ...................................................................... 17 

3.2.3. Resultant forces on structural frames.................................................................... 19 

3.2.4. Assembly of “tributary matrix” ............................................................................ 20 

3.3. Analysis of structural response ..................................................................................... 23 

3.3.1. Expressing responses in terms of influence coefficients ...................................... 23 

3.3.2. Time series of structural responses....................................................................... 24 

3.3.3. Directional Influence Factors (DIFs).................................................................... 25 

3.3.4. Exploiting model symmetry.................................................................................. 26 

3.4. Estimation of structural responses from models with different dimensions................. 29 

3.4.1. Scaling of pressure tap coordinates....................................................................... 29 

3.4.2. Interpolation between DIFs from different building models ................................ 31 

3.5. Estimation of peak responses with specified return period .......................................... 37 

3.5.1. Resampling of DIFs .............................................................................................. 37 

3.5.2. Interpolation between DIFs for different terrain conditions................................. 38 

3.5.3. Computing peak responses from directional wind speeds.................................... 39 

v
4. Application to Flexible Buildings: Dynamic Analysis – William P. Fritz ...................... 41 

4.1. Introduction................................................................................................................... 41 

4.2. Dynamic modeling........................................................................................................ 41

4.2.1. Transforming wind pressures to structural loads.................................................. 42 

4.3. Modeling of wind effects.............................................................................................. 43 

4.3.1. Interpolation methods for peak wind effects ........................................................ 44 

4.4. The high-frequency force balance (HFFB) method...................................................... 45 

4.5. Accompanying software ............................................................................................... 46 

4.5.1. General overview of the accompanying software................................................. 46 

4.5.2. Example: A 66-Story Building ............................................................................. 48 

4.5.3. Single-degree-of-freedom (SDOF) oscillator ....................................................... 50 

4.6. Summary....................................................................................................................... 52 

References.................................................................................................................................... 53 

Appendix A: User’s Manual for windPRESSURE, Database-Assisted Design Software 

for Rigid, Gable-Roofed Buildings – Joseph A. Main ........................................55 

Appendix B: Notes for Installation and Use of HR_DAD, Database-Assisted Design 

Software for Flexible Buildings – William P. Fritz ............................................89 

vi
List of Figures1

Figure 1. Plan view of example building showing definition of wind direction..........................4 

Figure 2. Plan view showing definition of building orientation and relationship between 

alternative definitions of wind direction.....................................................................11 

Figure 3. Simple gable-roofed building. ....................................................................................14 

Figure 4. Definition of local coordinate system for each building face.....................................17 

Figure 5. Identification of tributary areas for taps on a particular face. (a) Simple tap 

array; (b) More complicated tap array with varying tap density. ...............................17 

Figure 6. Typical form of structural system for low-rise building.............................................18 

Figure 7. Plan view of example building showing wind direction and selected frame. ............18 

Figure 8. Elevation view of selected frame showing unit force vectors at cladding 

attachment points (girt and purlin locations)..............................................................19 

Figure 9. Identification of pressure taps that are tributary to a selected cladding panel............21 

Figure 10. Distribution of pressure loading to resultant forces at the corners of a 

cladding panel.............................................................................................................21 

Figure 11. Influence coefficients associated with moment at left knee (circled).........................24 

Figure 12. Schematic plan view of building model showing symmetric wind directions 

corresponding to reflection of pressure tap array about axes of symmetry................27 

Figure 13. Directional Influence Factors (DIFs) giving maximum values of moment at left 

knee for a unit wind speed from each direction θ (units of ). ...............28 2 N m/(m/s) ⋅

Figure 14. Scaling of pressure tap coordinates to match dimensions of structure of 

interest.........................................................................................................................30 

Figure 15. Interpolation for different eave height of DIFs for bending moment at left knee 

of first interior frame (units of , plotted against wind direction)............35 2 N m/(m/s) ⋅

Figure 16. Comparison of interpolated (different eave height) and calculated DIFs for 

bending moment at left knee of first interior frame (units of , 

plotted against wind direction). ..................................................................................36 

2 N m/(m/s) ⋅

 

1

 Figures in the Appendices are not included in this list. 

vii
Figure 17. Interpolation for different roof rise of DIFs for bending moment at left knee of 

first interior frame (units of , plotted against wind direction)................36 2 N m/(m/s) ⋅

Figure 18. Comparison of interpolated (different roof rise) and calculated DIFs for 

bending moment at left knee of first interior frame (units of , 

plotted against wind direction). ..................................................................................37 

2 N m/(m/s) ⋅

Figure 19. Maximum value of moment at left knee (units of kN m⋅ ) having 50-year and 

500-year return periods, for varying building orientation. .........................................40 

Figure 20. Schematic of the MATLAB file organization for HR_DAD. ....................................47 

Figure 21. Typical plan view of the 66-story building.................................................................48 

Figure 22. SDOF oscillator example and assumed variable values.............................................50 

List of Tables 

Table 1. Equations of motion for x, y and φ directions ............................................................42 

Table 2. Selected members of the 66-story building example and their locations...................49 

Table 3. Summary of wind effects using wind loads from the preliminary design and 

from the DAD procedure (load combination: 1.2D+L+1.6W)...................................50 

Table 4. Summary of input variables for SDOF oscillator example ........................................51 

viii
1. Introduction 

Joseph A. Main and William P. Fritz

Advances in wind tunnel technology over the past several decades now enable simultaneous 

measurement of pressures at hundreds of pressure taps on the surface of building models, and 

parallel advances in computational and digital storage capabilities enable analysis of such large 

quantities of pressure data on standard desktop PCs. Database-Assisted Design (DAD) represents 

a unified framework for making direct use of such measured pressures in the analysis and design 

of structures. Local climatological information on extreme wind speeds and their directiondependence is also used in conjunction with the measured pressures in order to obtain realistic 

estimates of peak internal forces with specified return periods for use in structural design. 

Currently, wind loads are typically represented fairly coarsely in design using standards such as 

the American Society of Civil Engineers (ASCE) 7-02 Standard (ASCE 2003). Such standards 

are based on the results of wind tunnel tests, but reducing these results into a simple and 

generally applicable tabular format necessitates considerable simplification and loss of 

information. For tall, flexible buildings, simplified approximate procedures such as the HighFrequency Force Balance (HFFB) methodology are in common use. Through direct use of 

measured pressures, rigorous accounting for wind directionality effects, and more accurate 

modeling of structural dynamics for flexible buildings, the DAD approach enables more accurate 

estimation of peak wind effects, with a view to achieving more risk-consistent building designs. 

It is anticipated that in the not-too-distant future, pressure time series obtained by Computational 

Fluid Dynamics (CFD) may also be used in DAD. Improvements in sensor technologies are also 

enabling measurement of pressures on buildings at full scale. Such full-scale measurements will 

play an important role in the validation of pressures obtained from wind tunnel tests and CFD 

simulations, and full-scale pressures may eventually be used in DAD as well. 

The DAD approach was originally conceived for predicting the linear, static response of 

low-rise buildings (Whalen et al. 1998, Rigato et al. 2001, Simiu et al. 2003). Whalen et al. 

(2002) developed a user-friendly pilot software package known as WiLDE (Wind Load Design 

Environment), which implements the approach for low-rise metal frame structures. 

Subsequently, the DAD approach has been extended to consider nonlinear static response of low 

buildings (Jang et al. 2002) and linear dynamic response of high-rise buildings (Fritz et al. 2004). 

For high-rise buildings, wind tunnel tests are routinely conducted in the design stages, and the 

pressure measurements required for the DAD approach can be obtained from such tests. For lowrise buildings, however, constraints on project budgets and timelines generally do not permit 

specialized wind tunnel testing. To facilitate more widespread use of the DAD approach for lowrise buildings, an aerodynamic database is being assembled at the U.S. National Institute of 

Standards and Technology (NIST), containing measured pressure time series for a fairly large 

number of gable-roofed building models with various dimensions, as discussed in Ho et al. 

(2005). 

To illustrate and facilitate implementation of the DAD approach, software has been 

developed using the MATLAB language (MathWorks 2005) and is being made available through 

the internet at <http://www.nist.gov/wind>, along with other information, software, and data 

1
related to extreme winds and wind effects on buildings. At this website, separate software 

packages are available for rigid, gable-roofed buildings (developed by J.A. Main) and for tall, 

flexible buildings (developed by W.P. Fritz). These software packages, along with user 

instructions, can be obtained from the website by following the links for Database-Assisted 

Design software. The software for rigid, gable-roofed buildings is similar in concept to that 

previously developed by Whalen et al. (2002). However, the present software (a) eliminates the 

need for preprocessing of pressure data through automated handling of pressure databases in the 

standard HDF format developed by Ho et al. (2005) and (b) incorporates an interpolation scheme 

for cases in which the building dimensions do not precisely match those of an available wind 

tunnel model. 

In this report, an overview of the DAD methodology is first presented in Section 2, which 

discusses the format and requisite scaling of the wind pressure time series and directional wind 

speed data used in DAD, describes the different stages of the analysis in general terms, and 

highlights some of the differences in implementation for rigid buildings and flexible buildings. 

Section 3 presents further details specific to the treatment of rigid buildings (i.e., buildings with 

negligible dynamics effects), for which a number of simplifications can be introduced. An 

interpolation scheme is also presented in Section 3, to enable treatment of cases in which the 

building dimensions do not precisely match those of an available wind tunnel model. Section 4 

discusses the application of DAD to flexible buildings, for which dynamic effects cannot be 

neglected. Sections 3 and 4 also include brief descriptions of the corresponding software 

packages for rigid and flexible buildings – available through the website discussed above – and 

present example calculations illustrating the application of these software packages. Further 

details related to the setup and operation of the software packages for rigid and flexible buildings 

are presented in Appendices A and B, respectively. 

 

2
2. Overview of Database-Assisted Design 

Joseph A. Main and William P. Fritz

A variety of wind effects must be considered in structural design. Wind effects of interest 

include internal forces and bending moments in structural members, from which 

demand/capacity ratios must be evaluated and interaction equations considered (e.g., for 

combined flexure and axial loading). Global wind effects such as overturning moment and base 

shear may also be of concern, and deflections and accelerations are commonly required for 

serviceability considerations. For design purposes, it is necessary to evaluate the values of such 

wind effects corresponding to a specified return period, where the return period (also known as 

the mean recurrence interval) is defined as the inverse of the annual probability of exceedance. 

In computing wind effects corresponding to a specified return period, the DAD approach 

makes use of two distinct types of databases in conjunction. The first type of database, described 

in subsection 2.1, represents the building aerodynamics, containing pressure time series 

measured in the wind tunnel for various wind directions. These pressure time series are 

combined with structural analysis, as described in subsection 2.2, to compute peak wind effects 

corresponding to winds with various speeds and directions. In laying out the basic DAD 

procedure in this section, it is assumed for simplicity that pressure data are available for the exact 

structural dimensions of interest. This is generally the case for high-rise buildings, for which 

specialized wind tunnel tests are routinely conducted in the design stages. This is generally not 

the case when using the NIST aerodynamic database for low-rise buildings, however, and this 

assumption is relaxed in Section 3, which discusses the use of pressure time series from models 

with differing dimensions and presents an interpolation procedure. The second type of database, 

described in subsection 2.3, represents the extreme wind climate at the site of interest, containing 

directional wind speed data based on simulation or historical observation. These directional wind 

speed data are combined with the peak wind effects computed for various wind speeds and 

directions, as described in subsection 2.2, to obtain peak wind effects corresponding to specified 

return periods. Subsection 2.5 concludes this section with some brief comments on integration of 

the DAD approach within the structural design process. 

2.1. AERODYNAMIC DATABASES: PRESSURE TIME SERIES 

Pressure time series used in representing the spatio-temporal distribution of wind pressures on a 

building surface are obtained using boundary layer wind tunnels, which enable simulation of the 

turbulent flow characteristics and the variation in mean flow velocity with elevation that are 

associated with specified terrain conditions. For a given building model, tests are conducted for 

different terrain conditions by varying the height of roughness elements on the upwind floor of 

the wind tunnel and/or reproducing to model scale the built environment upwind of the building 

being tested. For each terrain condition, tests are conducted for a range of different wind 

directions, and in each test, pressure time series are recorded simultaneously using a large 

number of pressure taps distributed over the surface of a building model. Letting p denote the 

3
number of directions for which tests are conducted, it is convenient to introduce the symbol 

1 2 [ ] = θ θ p θ " θ to denote the 1× p vector of wind directions for which pressure time series 

are available. The wind directions in θ are measured relative to a reference axis on the building 

model, which typically coincides with one of the building’s primary axes, as illustrated in Figure 

1. While the present report is limited to the treatment of buildings with rectangular plan 

dimensions, as in Figure 1, it is noted that the approach described herein could be applied in a 

fairly straightforward manner to buildings with more complicated geometry. For symmetric 

building models (e.g., gable-roofed buildings), wind tunnel tests can be conducted over a range 

of less than 360°, and as discussed in Section 3.3.4, symmetry can be exploited to extend these 

results over a full 360° range. Symmetry seldom exists for tall buildings, for which the built 

environment is usually reproduced at model scale, and in such cases, wind tunnel tests are 

generally conducted over a full 360° range. 

θ

Figure 1. Plan view of example building showing definition of wind direction. 

Measured pressures are typically stored in nondimensional form as pressure coefficients, 

from which pressures for any particular wind speed can be obtained by appropriate scaling. 

Letting denote the number of pressure taps and the number of samples in each time series, 

the measured pressure coefficients for specified terrain conditions and for a given wind direction 

l s

θ j can be expressed as an l s × matrix P,θ j C , where the ith row of P,θ j C is the measured time 

series for the ith pressure tap. In scaling the pressure coefficients to obtain pressures for a given 

wind speed, it is important to ensure that the elevation, the averaging time, and the terrain 

conditions associated with the wind speed of interest are consistent with those of the wind speed 

used in referencing the pressure coefficients. While pressure coefficients in ASCE 7-02 (ASCE 

2003) are referenced using 3 s gust wind speeds at 10 m (33 ft , pressure coefficients herein are 

referenced using the mean wind speed at roof or eave height, and the averaging time associated 

with the mean wind speed is taken to be 1 h, which is a typical approximate duration for a wind 

tunnel test (after conversion to prototype scale). Pressure coefficients referenced using a wind 

speed at a different height can be re-referenced to roof-height wind speed as discussed by Ho et 

al. (2005), and the influence of averaging time can be accounted for as discussed in Simiu and 

Scanlan (1996, Section 2.3.6). Letting 

)

VH denote an hourly mean wind speed at roof (or eave) 

height H for the appropriate terrain conditions, an l s × matrix of pressure time series associated 

with winds of this speed from direction θ j can then be obtained by scaling the measured 

pressure coefficients as follows: 

1 2

2 P, j H j P C θ = ρV θ (1) 

4
where ρ = air density, and ρ = 1.225 kg/m3

 ( ρ = 0.002377 lbf⋅s

2

/ft4) for dry air at sea level 

under standard atmospheric conditions. In the treatment of dynamic response in Chapter 4, it is 

convenient to partition the pressure time series in Eq. (1) to separate the pressures producing 

forces along each of the building’s primary axes. 

The prototype-scale sampling frequency associated with the pressure time series follows 

from the requirement of equivalence between the reduced frequencies at model scale and at 

prototype scale, which can be expressed as follows: 

m p

Df Df

V V

⎛⎞⎛⎞ ⎜⎟⎜⎟ = ⎝⎠⎝⎠ (2) 

where D denotes a characteristic dimension of the structure, f denotes the sampling frequency, 

 denotes the mean wind velocity at a consistent height (e.g., roof height), and the subscripts m

and p denote “model” and “prototype” scales, respectively. Letting 

V

/ λ L = D D m p denote the 

length scale of the wind tunnel model, the prototype sampling frequency can be expressed as 

follows by rearranging Eq. (2): 

p

p m

m

V

f f V

λL

⎛ ⎞ = ⎜ ⎟ ⎝ ⎠

 (3) 

The model-scale sampling frequency mf , the model-scale wind speed , and the length scale Vm

λL are constants determined by the wind tunnel testing conditions. In contrast, it is generally 

necessary to consider a range of values of the prototype-scale wind speed , to reflect the 

statistical variability of the extreme wind speeds from each direction at the site of interest, as is 

discussed in the following subsection. Because the prototype-scale sampling frequency 

Vp

p f is 

proportional to the prototype-scale wind speed , as shown in Eq. Vp (3), each wind speed that 

is considered corresponds to a different sampling frequency 

Vp

p f . As is further discussed in 

subsection 2.2.2, this dependence of the sampling frequency on the wind speed is particularly 

important for dynamically sensitive structures, for which responses can be strongly affected by 

the frequency content of the loading. 

2.2. EVALUATION OF PEAK WIND EFFECTS 

This section describes the evaluation of peak wind effects of interest (e.g., internal forces and 

bending moments) from the pressure time series discussed in the previous section. This process 

can be divided into two main stages. The first stage, described in subsection 2.2.1, involves 

transforming the wind pressures, which are applied to the cladding of the building, to resultant 

wind forces, which are applied to the primary structural system at a number of discrete locations. 

The second stage, described in subsection 2.2.2, involves the use of structural analysis to 

evaluate time series of wind effects produced by these resultant wind forces. This second stage is 

conveniently accomplished using influence coefficients. Peak wind effects are of greatest interest 

in structural design, and subsection 2.2.3 discusses the estimation of expected peak values from 

time series of wind effects. 

5
2.2.1. Transforming wind pressures to structural loads 

While wind pressures are applied to the cladding of a building, numerical models used in the 

analysis and design of the building’s primary structural system generally do not include cladding 

elements. Therefore, some approximate procedure is required to represent the transformation of 

wind pressures on the cladding to resultant loads on the primary structural system. The first step 

in such a procedure is to determine the tributary area associated with each pressure tap, which 

defines the area over which the measured pressure is assumed to act. Tributary areas can be 

determined from the coordinates of the pressure taps, and this process is further discussed in 

Section 3.2.1. The wind load associated with a particular pressure tap is then given by the 

product of the measured pressure with the corresponding tributary area. The wind load associated 

with each of the pressure taps must then be distributed to the primary structural system at a 

number of discrete locations. Sections 3.2.2 through 3.2.4, present an approach for rigid, gableroofed buildings, based on that presented by Whalen et al. (2000), in which the wind loads are 

distributed to the structural frames at the attachment points of girts and purlins which support the 

cladding panels. This approach is based on structural analysis of a cladding panel simply 

supported along two edges by girts or purlins, which in turn are attached to the structural frames 

by hinges. Using this procedure, a “tributary matrix” is assembled, which represents the transfer 

of wind pressures to structural loads at the girt and purlin attachment points. A simpler approach 

is used for flexible buildings in Section 4, in which the load associated with each pressure tap is 

applied to the structure as a point load at or near the position of the pressure tap. In both cases, 

time series of structural loads are obtained from the measured time series of wind pressures for 

each wind direction. 

2.2.2. Evaluating time series of wind effects 

Once time series of resultant wind loads on the primary structural system have been obtained, 

time series of the wind effects of interest (e.g., bending moments, shear forces, and 

displacements) can be evaluated from these by structural analysis. This is conveniently 

accomplished using influence coefficients, which give the values of the wind effects of interest 

resulting from unit forces at each loading point. Influence coefficients can be obtained using 

standard structural analysis software by defining load cases corresponding to unit forces at each 

loading point and computing the resulting wind effects of interest. Static loads are used in 

computing the influence coefficients, even in the treatment of dynamic responses in Chapter 4. 

The influence of structural dynamics on the wind effects of interest is handled in Chapter 4 by 

defining “inertial” influence coefficients associated with unit translational and torsional loads at 

each floor of the building. Time series of inertial loads associated with translational and torsional 

accelerations of each floor of the building are computed using modal analysis, and the dynamic 

contributions to the wind effects of interest are then evaluated from the product of these inertial 

loads with the “inertial” influence coefficients. 

An important distinction between the treatment of static and dynamic responses (i.e., rigid 

and flexible buildings) concerns the influence of the sampling frequency associated with the time 

series of wind loads. As shown previously in Eq. (3), the prototype-scale sampling frequency, 

which determines the time scale of the loading, depends on the wind speed for which responses 

are required. This dependence is relatively unimportant in evaluating linear, static responses for 

rigid buildings, because the responses at each instant are simply proportional to the loads at that 

6
instant and are independent of the time scale. Consequently, for rigid buildings it is sufficient to 

simply compute time series of the wind effects of interest corresponding to a unit wind speed. 

Because wind pressures in Eq. (1) are assumed to be proportional to the square of the wind 

speed, wind effects corresponding to any wind speed of interest can then be obtained from the 

effects induced by a unit speed through multiplication by the square of the wind speed, as is 

further discussed in Chapter 3. In contrast, the dynamic response of flexible buildings can be 

very sensitive to the time scale of the loading. Because of the dependence of the time scale on 

wind speed, dynamic responses are not simply proportional to the square of the wind speed, but 

must be computed independently for each wind speed of interest using the appropriate prototypescale sampling frequency from Eq. (3). 

2.2.3. Estimating expected peaks of time series 

Peak wind effects (i.e., maximum and minimum values) are of greatest interest in structural 

design, and therefore it is necessary to evaluate peaks from the time series of wind effects 

discussed in the previous section. While the maximum and minimum values of a time series are 

readily evaluated, these observed peaks can exhibit wide variability from one realization to 

another, due to the highly fluctuating nature of wind pressures (i.e., significant differences might 

be expected in the peak wind effects computed using several different sets of pressure time series 

obtained under nominally identical conditions in the same wind tunnel). Therefore it is generally 

preferable to use a more stable estimator for the expected peaks. Sadek and Simiu (2002) present 

a procedure for estimating peaks that involves evaluation of probability distributions for the 

peaks through extension of classical results for Gaussian processes. As part of the software 

development in this study, a modified version of this procedure has been implemented as a set of 

MATLAB functions. These MATLAB functions for peak estimation are included with the DAD 

software packages for rigid and flexible buildings and can also be downloaded independently 

from <http://www.nist.gov/wind> by following the link for “Estimation of peaks from time 

series.” Further details on the peak estimation procedure are provided at this website. Using such 

an approach, expected values of the peaks can be estimated and used in place of observed peaks. 

It should be noted that the expected maximum and minimum value of a time series depend 

on the duration of the record under consideration, with increasing record duration leading to 

higher expected maximum values and lower expected minimum values. It is also noted that the 

prototype-scale duration of a wind tunnel test varies depending on the wind speed of interest, 

because of the dependence of the sampling frequency on wind speed, according to Eq. (3). The 

wind tunnel tests of Ho et al. (2005), for example, had a sampling frequency of and 

a duration of 100 s. For a model with a length scale of 

500 Hz mf =

1/100 λL = and a wind speed of 

 at model eave height, a prototype-scale test duration of 1 h then 

corresponds to a prototype-scale wind speed of 

6.1m/s (20 mi/h) Vm =

25 m/s Vp = (56 mi/h), while a duration of 0.5 h 

corresponds to a wind speed of 50 m/s Vp = (112 mi/h) and a duration of 2 h corresponds to a 

wind speed of . Because of the dependence of expected peak values on 

record duration, the same prototype-scale duration should ideally be used in evaluating all peaks, 

with an appropriate duration being 1 h, for consistency with the averaging time associated with 

the directional extreme wind speed data discussed in Section 

12 m/s Vp = (28 mi/h)

2.3. The peak estimation procedure 

of Sadek and Simiu (2002) can be used to accomplish this, as it allows for estimation of expected 

7
peaks for a duration that differs from the actual duration of the time series under consideration. 

However, using this procedure for a number of computed time series of bending moments for a 

rigid, gabled-roofed building, it has been observed that as the duration used in estimating peaks 

is varied from one-half to twice the actual record duration, the expected peak values differ by 

less than 5 % from the expected peaks using the actual record duration. This range in duration 

corresponds to quite a wide range of wind speeds – from 12 m/s to 50 m/s 

for the example from Ho et al. (2005) above. It is therefore concluded that peaks estimated using 

the actual record duration are in most cases acceptably close to peaks for a 1 h duration. 

(28 mi/h) (112 mi/h)

This simplification, that is, neglecting variations in record duration with wind speed, is 

particularly useful in evaluating peak wind effects for rigid buildings. Peak wind effects for any 

wind speed of interest can then be evaluated by simply multiplying the peak wind effects for a 

unit wind speed by the square of the wind speed, without further adjustment to account for 

variations in record duration due to wind speed. The values of the peak wind effects 

corresponding to a unit wind speed from each direction are referred to as Directional Influence 

Factors (DIFs), as in Rigato et al. (2001), and they are further discussed in Section 3.3.3. As 

noted previously in Section 2.2.2, wind effects for flexible buildings are not simply proportional 

to the square of the wind speed, but must be computed independently for each wind speed and 

direction, accounting for dynamic effects. An interpolation procedure is used in Chapter 4 to 

facilitate evaluation of peak wind effects for any wind speed and direction of interest for flexible 

buildings. In this procedure, peak responses are evaluated for a number of different wind speeds 

over the range of interest, and this is repeated for each wind direction for which pressure 

measurements are available. A polar grid of wind speed and wind direction values is thus 

defined, with values of the peak wind effects available at each grid point, and peak wind effects 

for intermediate wind speeds and directions are then estimated from their values at these grid 

points by interpolation. 

2.3. CLIMATALOGICAL DATABASES: DIRECTIONAL EXTREME WIND SPEEDS 

Directional wind speed data, based on simulation or historical observations, are used in 

representing the probability distribution of extreme winds from each direction at the location of 

interest. Because events with long return period are of interest in structural design, data 

representing a significant span of time are required. Available meteorological data cover a 

relatively short time span (typically about 100 years for hurricanes; even shorter time spans are 

covered for non-hurricane regions), and therefore, statistical extrapolation techniques are 

generally required to obtain peak wind speed estimates with long return periods. Hurricane-prone 

regions and non-hurricane-prone regions require different techniques for estimation of longperiod extreme wind speeds, as discussed in Simiu and Scanlan (1996, Chapter 3). 

Simulated hurricane wind speeds from Batts et al. (1980) represent estimates of the largest 

wind speeds from each of 16 directions for 999 hurricanes, generated by Monte Carlo simulation 

using analytical and empirical models of hurricane winds. The 999 extreme wind events are 

provided for a large number of locations (mileposts) along the Gulf of Mexico and North 

Atlantic coast. These simulated data are publicly available at <http://www.nist.gov/wind> by 

following the links for extreme wind data sets. The simulations are based on the assumption that 

the hurricane frequency of occurrence is governed by a Poisson process with a constant rate, and 

this occurrence rate is provided with the wind speed data for each location. The data are reported 

8
as one-minute averaged wind speeds in nautical miles per hour at 10 elevation over 

open terrain. Because peak wind speeds depend on averaging time and because pressure 

coefficients are referenced using hourly averaged wind speeds, these one-minute averaged wind 

speeds must be converted to hourly averages through division by a factor of approximately 1.25 

(Simiu and Scanlan 1996, Figure 2.3.10). In this report, simulated hurricane wind speeds are 

used for illustration; Section 3 uses wind speeds for Miami (milepost 1450), while Section 4 uses 

wind speeds for New York City (milepost 2550). 

 m (33 ft)

In non-hurricane regions or in hurricane regions where significant non-hurricane winds can 

occur, directional non-hurricane wind speed data are needed. Non-hurricane directional wind 

speed data are also available at <http://www.nist.gov/wind> in the form of largest annual wind 

speeds from each of eight directions at 37 locations in the continental United States where 

hurricanes are not expected to occur. These data are reported as peak gust speeds in miles 

per hour at 10 elevation over open terrain, which must be converted to hourly 

averages using the procedure described in Simiu and Scanlan (1996, Section 2.3.6). For each of 

these non-hurricane locations, data are available for about 30 years. Another source of 

directional wind speed data for the United States is the Automated Surface Observing System 

(ASOS), which provides climatological observations at most of the nation’s airports. ASOS 

records, which can be obtained from the National Oceanic and Atmospheric Administration, 

contain hourly reports of peak gust wind speeds and corresponding wind directions, along with 

many other climatological observations. Software to extract directional wind speed data sets 

from ASOS records is currently in development at NIST. 

3 s

 m (33 ft)

After appropriate scaling to account for the averaging time (e.g., Simiu and Scanlan 1996, 

Figure 2.3.10), directional wind speed data for a given location can be represented as an h q ×

matrix VZ of hourly averaged wind speeds at elevation Z over terrain with roughness length 

Z0 , where denotes the number of hurricanes (or the number of years, in the case of nonhurricane wind speeds) and denotes the number of wind directions. The simulated directional 

hurricane wind speed data cited above correspond to 

h

q

Z = 10 m and open terrain, for 

which 

(33 ft)

Z0 = 0.03 m ( 0.1 ft ) is representative. In the case of hurricane wind speeds, each row of 

VZ corresponds to a particular hurricane, while in the case of non-hurricane wind speeds, each 

row corresponds to a particular year. In the former case, the occurrence rate ν of hurricanes at 

the location of interest is also required. For both hurricane and non-hurricane wind speeds, each 

column of VZ corresponds to a particular wind direction, and it is convenient to introduce the 

symbol 1 2 [ ] α = α α " α q to denote the 1×q vector of wind directions for which extreme 

wind speeds are available. 

Since roof-height wind speeds are generally used in referencing the pressure coefficients 

(e.g., Ho et al. 2005), the matrix VZ of wind speeds at elevation Z must be scaled to wind 

speeds at roof height H. The ratio of mean wind speeds at different elevations depends upon the 

terrain conditions, as characterized by a roughness length parameter, and a vector of roughness 

lengths can be defined for the site of interest, giving the roughness 

lengths associated with winds from each of the directions in the vector α . Assuming a similarity 

model for the mean velocity profile (e.g., Simiu and Scanlan 1996, Section 2.2.5), a mean wind 

speed at elevation 

0 01 02 0 [ q z = zz z " ]

Z over terrain with roughness length Z0 , denoted VZ , can be converted to a 

9
mean wind speed at height H over terrain with roughness length 0 j z , denoted VH , through 

scaling by the following factor: 

0.0706

0 0

0 0

ln( / )

ln( / )

j j

j

Hz z

ZZ Z

λ ⎛ ⎞ = ⎜ ⎟ ⎝ ⎠

 (4) 

It is noted that some practitioners use the power law, rather than the similarity model, and the 

power law is used in the software for flexible buildings in open or suburban terrain. However, for 

buildings in large cities neither the similarity model nor the power law may be applicable, and 

the scale factors must be estimated for each direction from wind tunnel tests. An h q × matrix 

VH of hourly averaged wind speeds at eave height can then be obtained by multiplying each 

column of VZ by the corresponding scale factor. This operation can be expressed as follows: 

diag( ) V V H Z = ⋅ λ (5) 

where 1 2 [λ ] = λ λq λ " is a 1×q vector of scale factors for each direction, with its elements 

defined by Eq. (4), and diag( ) λ is a q q × diagonal matrix formed by placing the elements of 

along the main diagonal, with zeros elsewhere. The directional extreme wind speeds in 

λ

VH then 

represent hourly averages at roof height for appropriate terrain conditions and are thus consistent 

with the wind speeds used in referencing the pressure coefficients. 

It is generally necessary to shift the wind directions in so that they are defined 

consistently with the wind directions in θ , introduced in subsection 

α

2.1, for which pressure time 

series are available. As shown in Figure 2, the wind directions in α are measured in degrees 

clockwise from the north, in contrast with the wind directions in , which are measured relative 

to a reference axis of the building model. Letting 

θ

α0 denote the orientation of this reference axis, 

measured in degrees clockwise from the north, the wind directions in α can be shifted by the 

orientation angle α0 as follows to obtain a 1×q vector 1 2 ˆ ˆ ˆ [ ˆ ] θ = θ θ " θ q of wind directions 

that are defined consistently with those in θ : 

 (6) 

360

0 0

ˆθ αα j j = − c f d g e h

where the brackets and specified bounds indicate that the resulting values are shifted by 360°, as 

necessary, to ensure that . While the shifted wind directions in are defined 

consistently with those in , the values in these two vectors generally will not coincide. The 

reason for this is that wind tunnel pressure measurements are typically recorded at smaller 

increments in wind direction than directional extreme wind speed data are available. Therefore 

interpolation or resampling is generally required to evaluate peak wind effects corresponding to 

the wind directions in from peaks computed using pressure time series corresponding to the 

wind directions in . 

ˆ 0 360 ≤ < θ j ˆ

θ

θ

ˆ

θ

θ

10
θ

N

E

α 0

α θ

N

E

α 0

α

Figure 2. Plan view showing definition of building orientation and 

relationship between alternative definitions of wind direction. 

2.4. PEAK WIND EFFECTS WITH SPECIFIED RETURN PERIOD 

The final stage of the analysis is to combine the site-specific climatalogical information with the 

building aerodynamics to evaluate peak wind effects with specified return period, rigorously 

accounting for building orientation and wind directionality. For each directional wind speed in 

the matrix VH from Eq. (5), corresponding peak values of the wind effects of interest can be 

evaluated by interpolation from the peak values computed as described in Section 2.2. For rigid 

buildings, the influence of wind speed is represented by multiplying Directional Influence 

Factors by the square of the wind speed, and interpolation is performed only with respect to wind 

direction, as discussed in Section 3.5.1. For flexible buildings, interpolation of peak responses is 

performed with respect to both wind speed and direction. It is emphasized that because of the 

dependence of the wind directions in Eq. (6) on building orientation, the interpolation process to 

evaluate peak wind effects corresponding to each element of VH , as well as the subsequent 

procedure for evaluating return periods, must be repeated for each building orientation of 

interest. If the building orientation is unknown, then peak wind effects with a specified return 

period can be evaluated for a number of possible building orientations. Expected values of peak 

wind effects for the specified return period can then be estimated as a weighted combination of 

the results for each orientation, with weighting factors equal to the probability of occurrence of 

each orientation. 

Each row of VH corresponds to a particular hurricane (or year, for non-hurricane winds), 

and the highest peaks corresponding to each hurricane (or year) are of interest. For a given wind 

effect, the maximum (or minimum) value corresponding to each row of VH is evaluated to 

obtain a time series of the maximum (or minimum) value of that wind effect in each hurricane 

(or year). Statistical analysis of these time series can then be used to estimate annual probabilities 

of exceedance associated with different values of the wind effect. These annual probabilities can 

be converted to return periods, where the return period is defined as the inverse of the annual 

probability of exceedance. Long return periods (e.g., 50 years or 500 years) are of interest in 

structural design, and because directional wind speed data are typically available for only a few 

11
decades, extrapolation is generally required to estimate peak wind effects with long return 

periods. This can be accomplished by best-fitting an extreme value distribution to the time series 

of peak wind effects. 

When using simulated directional hurricane wind speed data (Batts et al. 1980), time series 

of peak wind effects corresponding to 999 hurricanes are obtained, and because of the long 

duration of these time series, values with long return periods can be estimated fairly simply using 

order statistics, without the need to fit an assumed probability distribution. The time series of 

maximum values of a particular wind effect in each hurricane can be expressed as an h×1 vector 

, where h is the number of hurricanes. Let the elements of this vector be 

sorted in descending order, so that . The probability that the wind effect b will 

exceed the kth ranked value in any given hurricane can then be estimated as follows: 

max max max

1 [ h b = b b " ]

max max b1 = max( ) b

max

k b

( ) max 1 hurricane

1 k

k Pb b

h

> = +

 (7) 

The simulated hurricane wind speeds of Batts et al. (1980) were based on the assumption that the 

frequency of hurricane occurrence at a given site is governed by a Poisson process with constant 

occurrence rate. For hurricane winds, it is therefore consistent to make this same assumption in 

computing the annual probability of exceedance of based on the probability of exceedance 

per hurricane given in Eq. 

max

k b

(7), whereby the following result is obtained (see e.g., Simiu and 

Scanlan 1996, p. 115): 

( ) max 1 year 1 exp 1 k

k Pb b

h

⎛ ν

> =− −⎜ ⎞

⎟ ⎝ ⎠ +

 (8) 

where ν denotes the hurricane occurrence rate, having units of . The return period 

associated with exceedance of is then given by the inverse of this annual probability: 

1 year−

max

k b

1

1 exp 1 k

k N

h

ν −

⎡ ⎛ ⎞⎤ =− − ⎢ ⎜ ⎟⎥ ⎣ ⎝ ⎠ + ⎦ (9) 

Responses of interest in structural design are generally associated with long return periods, for 

which νk h /( 1) 1 +  . Replacing the exponential in Eq. (8) with its Taylor series expansion and 

neglecting terms of second and higher order, the annual probability of exceedance of can 

then be approximated as 

max

k b

νk h /( 1) + , which corresponds to a return period of ( 1) /( Nh k k  + ν ) . 

The return period given by this approximation is within 1 % of the exact value for return periods 

greater than 50 years. Using this approximation, or the original expression in Eq. (9), an h ×1

vector 1 2 [ T N = NN N " h ] can be assembled, giving the return period associated with each 

element of . The maximum value of the wind effect b corresponding to a specified return 

period 

max b

N can then be computed from the vectors N and by interpolation. The minimum 

value of the wind effect b corresponding to a specified return period can be evaluated in an 

analogous manner, starting with a time series of minimum values in each hurricane, sorted 

in ascending order. 

max b

min b

12
2.5. IMPLEMENTATION IN STRUCTURAL DESIGN 

It is noted that the DAD approach requires a preliminary structural design, so that influence 

coefficients corresponding to the wind effects of interest can be computed and used to evaluate 

peak wind effects as described in subsection 2.2. Preliminary member sizes for this purpose can 

be established using wind loads from standard provisions such as ASCE 7-02, and preliminary 

influence coefficients can be obtained by structural analysis using these member sizes. After 

peak wind effects with the specified return period have been evaluated using these preliminary 

influence coefficients, demand/capacity ratios can be evaluated and structural members can be 

resized. Updated influence coefficients can then be computed using the modified member sizes, 

and the DAD procedure can be repeated. This iterative process should be repeated as necessary 

until acceptable convergence is achieved in the wind effects of interest corresponding to the 

specified return period. 

13
3. Application to Rigid Buildings: Static 

Analysis and Interpolation Issues 

Joseph A. Main 

This section describes an implementation of the DAD approach for predicting the linear, static 

response of rigid buildings to wind loading. The term “rigid” denotes a structure with negligible 

dynamic response to wind loads, and the defining criterion used in the ASCE 7-02 Standard is 

that the fundamental natural frequency is ≥ 1 Hz (ASCE 2003). The requisite computations in 

this section are presented using matrix notation to facilitate efficient implementation. While the 

basic approach described in this section is applicable to more general types of rigid buildings, the 

accompanying software is limited to the relatively simple type of gable-roofed building depicted 

in Figure 3, as are the example calculations presented in this section, which were performed 

using the accompanying software. The geometry of this relatively simple type of building can be 

represented by four independent length dimensions: the width W , length , eave height , and 

roof rise 

L H

R . The software has also been developed specifically to handle aerodynamic databases 

in the standard HDF format developed by Ho et al. (2005). The use of this standard format 

allows the pressure time series to be loaded directly by the software and automatically applied to 

the structural model, eliminating the preprocessing of pressure data previously required by 

WiLDE-LRS (Whalen et al. 2002). 

W

H

R

x

y

z

L

W

H

R

x

y

z

L

Figure 3. Simple gable-roofed building. 

3.1. OVERVIEW 

The outline of this section is as follows. Section 3.2 presents the approach used for transforming 

the wind pressures to structural loads, which was previously discussed in general terms in 

Section 2.2.1. A “tributary matrix” is introduced to represent the distribution of wind pressures 

from the cladding of the building to its primary structural system, and a procedure for assembling 

the tributary matrix is presented, which is implemented in the accompanying software. Section 

3.3 presents the approach used to compute structural responses (i.e., wind effects such as internal 

forces and bending moments) from the resultant wind loads. The responses of interest are 

expressed using a matrix of influence coefficients associated with unit forces at the cladding 

attachment points, and a formal expression for the influence coefficient matrix is presented in 

14
Section 3.3.1. Influence coefficients can be obtained using standard structural analysis software, 

and in the accompanying DAD software influence coefficients for the responses of interest are 

included in a building input file in spreadsheet format (comma-separated values). This building 

input file also contains additional information that defines the building, such as its dimensions, 

the frame locations, and the terrain conditions. As in Rigato et al. (2001) peak responses are 

expressed using Directional Influence Factors (DIFs), discussed in Section 3.3.3, which define 

peak responses corresponding to unit wind speeds from each direction and can be scaled to 

obtain peak responses for any wind speed of interest. Section 3.3.4 describes a formal procedure 

for exploiting model symmetry to extend the DIFs over a full 360° range of wind directions 

using measurements recorded over a smaller range. 

Section 3.4 discusses the estimation of peak structural responses using pressure 

measurements from models with differing dimensions. Given the wide range of structural 

geometries encountered in design as well as practical limitations on the number of building 

model variations for which measured pressures can be obtained, it is unlikely in practice that 

measured pressures would be available for a model with dimensions that precisely match the 

dimensions of the structure of interest. Establishment of DAD as a broadly applicable 

methodology therefore requires some reliable means of interpolation to enable prediction of 

internal forces for structures with dimensions intermediate to those for which pressure 

measurements are available. Previous efforts to develop such means of interpolation have made 

use of artificial neural networks in attempting to account for the complexities in the spatiotemporal distribution of wind pressures and pressure dependence on model geometry and wind 

direction (Chen et al. 2003a; Chen et al. 2003b). While the predictions of these models were 

found to be fairly good, the complexity of these approaches could potentially be a hindrance to 

broader application in design. 

In Section 3.4, a relatively simple method of interpolation is proposed, in which peak 

structural responses (e.g., bending moments and axial forces) are interpolated, rather than wind 

pressures, thus eliminating the necessity for the interpolation scheme to account explicitly for 

spatial and temporal distributions of the pressures. In the proposed approach, separate analyses 

are performed using measured wind pressures from a number of building models with 

dimensions that bound those of the structure of interest. In each of these bounding analyses, the 

coordinates of the pressure taps are scaled to match the dimensions of the structure of interest, as 

discussed in Section 3.4.1, and the measured pressures are then treated as if they had been 

measured on a model with the same dimensions as the structure of interest. The pressure tap 

coordinates and building dimensions are provided with the measured pressure time series in the 

standard HDF pressure database format. In the accompanying software, the procedures in 

Section 3.4.1 are implemented to automatically scale the tap coordinates, if necessary, before 

assembling the tributary matrix to transfer the pressures to the structural system. 

This scaling procedure is clearly a simplification of the true building aerodynamics, 

resulting in inaccurate correlations between pressures at different locations due to the artificial 

adjustment of the separation distance between pressure taps, as well as failing to represent 

changes in the physics of the wind flow due to changing building geometry. However, the errors 

are considerably reduced when the peak responses for the structure of interest are obtained by 

interpolation between the peak responses estimated from each of the bounding analyses. In 

Section 3.4.2 a fairly simple multi-dimensional interpolation scheme is presented for this 

purpose, in which greater weight is given to results from building models that more closely 

match the dimensions of the structure of interest. The proposed approach is illustrated using 

15
pressure measurements from Ho et al. (2005) for models with the same plan dimensions and roof 

slope but with three different eave heights. Peak responses generated by interpolation from the 

models with the largest and the smallest eave height are compared with values obtained by 

applying the pressures actually measured on the model with intermediate eave height, and 

remarkably good agreement is observed. In contrast, it is found that the interpolation procedure 

is not as successful for different roof slopes. Pressure measurements from Ho et al. (2005) are 

also considered for models with the same plan dimensions and eave height but with three 

different roof slopes, and peak responses generated by interpolation from the models with the 

largest and the smallest roof slope are found in some cases to be about 50 % less that the values 

obtained by applying the pressures actually measured on the model with intermediate roof slope. 

This example corresponds to a difference of 22° between the larges and smallest roof inclination 

angles, and it is therefore concluded that pressure data are required from models with smaller 

increments in roof slope in order for the proposed interpolation scheme to give reliable results. 

Finally, Section 3.5 discusses the estimation of peak responses with specified return period. 

The accompanying software allows the extreme wind speed climate to be represented using 

simulated hurricane wind speed data from Batts et al. (1980) and could be readily extended to 

make use of other databases that may become publicly available. Section 3.5.1 presents a 

procedure for resampling DIFs to coincide with wind directions for which directional extreme 

wind data are available. Section 3.5.2 presents a simple, approximate procedure for interpolating 

DIFs obtained from pressure measurements for different terrain conditions, to accommodate 

cases in which the terrain conditions at the location of interest differ from those of available 

pressure measurements and may vary with direction. Section 3.5.3 then discusses the evaluation 

of time series of peak responses from the directional extreme wind speeds, from which responses 

with specified return period can be estimated as discussed previously in Section 2.4. 

3.2. TRANSFER OF WIND LOADING FROM CLADDING TO STRUCTURE 

3.2.1. Determination of tributary areas for pressure taps 

In making use of measured pressures to predict structural responses, it is necessary to evaluate 

the tributary area associated with each tap, where “tributary area” denotes the area over which 

the pressure measured at a particular tap is assumed to act. A procedure has been developed that 

automatically evaluates tributary areas using the tap coordinates, which may be either scaled 

coordinates or actual coordinates. The procedure for evaluating tributary areas is applied to each 

face of the building in turn, and the coordinates of the taps on each face are expressed using a 

local s-y coordinate system in the plane of that face, as depicted in Figure 4. The y-coordinate 

coincides with the global y-coordinate, while the s-coordinate is obtained from the global x- and 

z-coordinates by transformation. Taps on the end walls are not considered, as structural 

responses in the y-direction are not evaluated at present. 

16
y

s

y

s

y

s

y

s

y

s

y

s

y

s

y

s

Figure 4. Definition of local coordinate system for each building face. 

Figure 5(a) depicts a simple tap array plotted in the s-y plane (taps are indicated by the + 

signs). For this simple type of tap array, which has the same number of taps in each row and the 

same number of taps in each column, the bounds of the tributary areas are simply lines midway 

between the adjacent rows and columns of taps, while the exterior tributary bounds for the 

outermost taps are defined by the edges of the face. For taps located on the boundary between 

two faces, such as those shown along the top edge of Figure 5(a), the tributary areas are assumed 

to extend over both adjoining faces, and therefore, the taps must be included in both faces when 

evaluating tributary areas. More complicated tap arrays, such as that depicted in Figure 5(b), can 

in many cases be treated by dividing the array into a number of simple tap arrays, for which the 

tributary areas can be determined as described above. The portions of the tap array on each side 

of the vertical arrows in Figure 5(b) are simple arrays, having the same number of taps in each 

row and the same number of taps in each column. 

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + +

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + +

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + + + + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

y

s

y

s

(a) (b)

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + +

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + +

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + +

+ + +

+ + + + + + + + + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

+ + + + + +

y

s

y

s

(a) (b)

Figure 5. Identification of tributary areas for taps on a particular face. 

(a) Simple tap array; (b) More complicated tap array with varying tap density. 

3.2.2. Assumed form of structural system 

The structural system of the building under consideration is assumed to be of the general form 

illustrated in Figure 6. The primary structural system consists of frames spanning the width of 

the building, in the x-z plane. These frames are plotted with heavy lines in Figure 6. The 

structural frames need not be equivalent, and some may have interior columns, like the end 

frames in shown Figure 6. The columns of the frames need not be pinned at the base. Girts and 

purlins, which are plotted with thin lines in Figure 6, span between the frames in the y-direction. 

The cross-members on the walls are called girts, while those on the roof are called purlins. Roof 

panels and wall panels, which form the exterior envelope of the building, are attached to the girts 

17
and purlins, and the shaded area in Figure 6 indicates a roof panel. For conciseness, the term 

“purlin” is used in this paper to represent either a girt or a purlin, and the term “cladding panel” 

is used to represent either a roof panel or a wall panel. 

y x

z

Figure 6. Typical form of structural system for low-rise building. 

A number of simplifying approximations are introduced in analyzing the structural system 

of Figure 6. The major simplification is that the purlins and cladding panels are not included in 

the structural model, and only the structural frames are explicitly modeled. Further, responses to 

loads in the y-direction are not considered. The coupling between frames introduced by the 

cladding system is then neglected, and the response of each frame in the x-z plane is analyzed 

independently. Even though the purlins are not included in the structural model, it is noted that 

the out-of-plane restraint provided to the frames by the purlins can be important (e.g., for 

preventing lateral-torsional buckling) and should not be neglected in design. Because the purlins 

and cladding panels are not included in the structural model, it is necessary to determine how the 

wind pressures, which are applied to the cladding panels, are distributed as resultant wind loads 

to the structural frames at the girt and purlin attachment points. 

In illustrating the DAD procedure in this section, a building is considered with dimensions 

given by W = 36.6 m (120 ft), L = 57.2 m (187.5 ft), H = 5.5 m (18 ft), and R = 1.5 m (5 ft). 

Pressure measurements for a 1:100 scale model with these dimensions are available from Ho et 

al. (2005), with tests performed over a range of 180° in 5° increments, for a total of 37 

directions. A structural system consisting of 11 equally spaced frames is considered, as indicated 

by vertical lines in Figure 7, and the first interior frame, which is highlighted in Figure 7, is 

selected for analysis. A preliminary design for the selected frame was established using wind 

loads from ASCE 7-02 for open terrain, in combination with applicable dead and live loads. 

θ

Figure 7. Plan view of example building showing wind direction and selected frame. 

18
3.2.3. Resultant forces on structural frames 

The procedure for predicting structural responses makes use of a discretized structural model 

(e.g., a finite element model). Let the number of unconstrained degrees of freedom in the 

structural model be denoted . Assuming linear behavior and neglecting dynamic effects, the 

 vector of generalized displacements (which generally includes both nodal displacements 

and nodal rotations) can be related to the corresponding 

n

n ×1 u

n ×1 vector of generalized forces f

through an n n × global stiffness matrix K : 

Ku f = (10) 

It is assumed that the wind pressures are applied to the cladding of the building, which is not 

included in the structural model, and that the cladding is attached to the primary structure at a 

number of discrete locations. For simplicity, it is assumed that the cladding is attached by hinges, 

so that no moments are transferred to the structure by the cladding. Since pressures by definition 

act normal to the surface of application, it is further assumed that the resultant forces are oriented 

normal to the cladding surface at each attachment point. For cases in which cladding surfaces 

with differing orientation are attached to the structure at a particular point, separate resultant 

forces are defined for each surface. The kth resultant force can then be represented as the product 

of a scalar coefficient φk with an n ×1 vector of unit magnitude that defines the orientation 

of the resultant force. The vector has nonzero entries only for degrees of freedom associated 

with the relevant attachment point, and these nonzero entries correspond to the components of a 

unit vector normal to the relevant cladding surface at this attachment point, oriented in the 

direction of positive pressure. 

wk

wk

Figure 8 shows the unit force vectors for the selected frame of 

the example building of 

wk

Figure 7. The points of application of these unit loads correspond to the 

locations at which girts and purlins are attached to the structural frame, and these are spaced at 

intervals of approximately 1.2 m (4 ft). 

w1

w5

w6

w20w21

w35

w36

w1 w40

w5

w6

w20w21

w35

w36

w40

Figure 8. Elevation view of selected frame showing unit force vectors at cladding 

attachment points (girt and purlin locations). 

Letting m denote the total number of resultant forces, the net global force vector f can then 

be expressed as a summation of all of the resultant forces, =φ11 2 2 + ++ φ φ m m fw w w " . In 

expressing this summation, it is convenient to define an m×1 vector of 

scalar coefficients (the superscript T denotes transposition) and an matrix 

1 2 [ ]T φ = φφ φ " m

n m×

19
Www w = [ 1 2 " m ] whose columns are the unit vectors . The summation of resultant 

wind forces can then be expressed as follows: 

wk

f W= φ (11) 

With the orientation of resultant forces having been assumed in the definition of the unit vectors 

, what remains to be done is to define the coefficient vector wk φ as a function of the applied 

pressures. In Eq. (1), an l s × matrix θ j P of pressure time series was defined, with each row 

being the time series for a particular pressure tap. Let p denote an l ×1 vector formed by taking 

one column from such a matrix, which thus defines the distribution of pressures at the various 

taps at a particular instant of time. The vector φ of resultant force coefficients at that instant can 

then be expressed as a linear transformation of the vector p in the following general form: 

φ = Ap (12) 

The m l × “tributary matrix” A has units of area and can be expressed as Aaa a = [ 1 2 " l], 

where the kth column specifies how the tributary area associated with the kth pressure tap is 

distributed to the various cladding attachment points. (The “tributary area” associated with a 

given tap is the area over which the measured pressure at that tap is assumed to act.) The validity 

of the general form of linear transformation in Eq. 

k a

(12) can be verified conceptually by using a 

matrix condensation approach, presuming the existence of a detailed discretized model of the 

structure that includes the cladding. However, a detailed structural model that includes cladding 

elements is generally unavailable, and simpler approximate techniques are therefore generally 

required for assembling the matrix . An approximate procedure for this purpose is described in 

the following subsection. Combining Eqs. 

A

(11) and (12), the generalized force vector f

corresponding to the pressure distribution p can then be expressed as f WAp = . 

3.2.4. Assembly of “tributary matrix” 

In this subsection, a relatively simple approximate procedure is introduced for assembling the 

tributary matrix for gable-roofed buildings with the general form of structural system 

illustrated in 

A

Figure 6. The approximations used in this procedure are essentially equivalent to 

those used by Whalen et al. (2000) in WiLDE-LRS, while the present implementation using a 

tributary matrix introduces some significant efficiencies. Firstly, the automated assembly of the 

tributary matrix using information provided in standard UWO HDF files eliminates the manual 

preprocessing required in WiLDE-LRS, in which pressure time series corresponding to distinct 

rows of pressure taps must be extracted and saved as separate files. Secondly, since the pressure 

tap layout remains constant for a given wind tunnel model, the same tributary matrix can be used 

for pressure measurements from all wind directions, so that the load transfer calculations need to 

be performed only once at the outset of the analysis. In WiLDE-LRS, by contrast, the load 

transfer calculations are performed as part of the response analysis, and are thus repeated for 

each wind direction. The preprocessing of pressure time series described above must also be 

performed separately for each wind direction when using WiLDE-LRS. 

The tributary matrix A is assembled by independently analyzing each rectangular cladding 

panel in turn. For each cladding panel, such as that indicated by shading in Figure 6, the pressure 

taps are identified whose tributary area overlaps the selected cladding panel. This procedure is 

20
illustrated schematically in Figure 9, in which the boundary of the selected cladding panel is 

superimposed over the pressure tap layout for that face. Circles in Figure 9 indicate those taps 

whose tributary area overlaps the area of the selected panel. In general, only a portion of the 

tributary area associated with each of these taps will overlap the selected panel, and the 

remaining portions of tributary area are handled when considering neighboring cladding panels. 

Each portion of tributary area that overlaps the selected cladding panel is then distributed to the 

attachment points at the four corners of the selected panel according to the procedure illustrated 

in Figure 10. 

y

s

+ + + + + +

+ + + + + +

+ + + + + +

y

s

Figure 9. Identification of pressure taps that are tributary to a selected cladding panel. 

Rc

ad q

Ra

Δy

Δs

y′

s′

ΔY

ΔS

qad

pk

qbc

d

c

a

b

bc q

Rb

Rd

k p

Rc

ad q

Ra

Δy

Δs

y′

s′

ΔY

ΔS

qad

pk

qbc

d

c

a

b

bc q

Rb

Rd

k p

Figure 10. Distribution of pressure loading to resultant forces at the corners of a cladding panel. 

The rectangular shaded area in Figure 10 corresponds to the shaded area in Figure 9, 

representing the portion of tributary associated with a particular tap, denoted tap k , that overlaps 

the selected cladding panel. The pressure acting over this area is then equal to the pressure 

measured at tap k , which is denoted . The points labeled through in k p a d Figure 10 are the 

four corners of the selected panel, at which points the purlins are attached to the structural frames 

21
and resultant forces are to be evaluated. The heavy lines at the upper and lower edges of the 

selected panel (i.e., segments bc and ) represent purlins spanning in the y-direction between 

adjacent frames. The upper and lower edges of each cladding panel are assumed to be hinged to 

the purlins, while the left and right edges (i.e., segments and ) are assumed to be free. The 

resultant forces at the four corners of the selected panel are evaluated by analyzing each purlin as 

a simply supported beam, as shown by the free-body diagrams at the upper and lower edges of 

ad

ab cd

Figure 10, and the resultant forces are equal to the reactions, denoted , , , and . Ra Rb Rc Rd

The loading intensity (force per unit length) on the purlins due to the distributed pressure 

is evaluated by isolating a strip of cladding panel with unit width, spanning in the s-direction 

between adjacent purlins and passing through the region over which the pressure is applied, 

as illustrated by the shaded vertical strip in 

k p

k p

Figure 10. Because a strip of unit width is considered, 

the loading intensity on loaded portion of the strip is equal to . Neglecting shear forces on the 

left and right edges, the isolated strip is then analyzed as a simply supported beam, as shown in 

the free-body diagram at the right-hand edge of 

k p

Figure 10. It is noted that cladding panels 

typically have ribs aligned perpendicularly to the purlins, making them much stiffer for bending 

in that direction. Therefore, plate action is not expected to dominate, and analyzing a strip of the 

cladding panel as a simply supported beam is considered a reasonable approximation. The 

reactions at the upper and lower ends of the strip give the loading intensities on the upper and 

lower purlins, denoted and , respectively. The values of these load intensities can be 

obtained by static equilibrium from the free-body diagram at the right-hand edge of 

bc q ad q

Figure 10, 

and are given as follows: 

( ) 1

2 1/ / ad k q ps = Δ − −Δ Δ s′ ΔS sS ; ( ) 12 / / bc k q p ss S s S = Δ Δ+Δ Δ ′ (13) 

With the loading intensities and determined, the reactions at the ends of the upper and 

lower purlins can be similarly determined from the free-body diagrams at the upper and lower 

edges of 

bc q ad q

Figure 10. Each of these reaction forces is proportional to the applied pressure , and 

it is convenient to express them as follows: 

k p

; R pA a k = a R pA b k = b R pA c k c R pA d kd ; = ; = (14) 

where Aa , Ab , Ac , and Ad denote the portions of the tributary area Δs yΔ distributed to each of 

the four attachment points at the panel corners and are given as follows (it is noted that 

Aabcd + + + =Δ Δ A A A sy ): 

( )( ) 1

2 1/ / 1 / / a

1 A 2 =Δ Δ − Δ − Δ Δ − Δ − Δ Δ sy s S s S y Y y Y ′ ′ (15) 

( )( ) 1

2 / / 1/ / b

1 A 2 =Δ Δ Δ + Δ Δ − Δ − Δ Δ s ys S s S y Y y Y ′ ′ (16) 

( )( ) 1 1

2 2 / // / Ac =Δ Δ Δ + Δ Δ Δ + Δ Δ s ys S s S y Y y Y ′ ′ (17) 

( )( ) 1 1

2 2 1/ / / / Ad =Δ Δ − Δ − Δ Δ Δ + Δ Δ sy s S s S y Y y Y ′ ′ (18) 

The areas Aa , Ab , Ac , and Ad can then be added to the appropriate entries in the kth column of 

the tributary matrix , and this can be repeated for each of the taps whose tributary area 

overlaps the selected cladding panel. By repeating this procedure for each cladding panel, the full 

tributary matrix can be assembled. It is noted that if only a subset of the structural frames are to 

A

22
be analyzed, only the cladding panels that have an edge adjoining the selected frames need to be 

considered in assembling the tributary matrix. 

3.3. ANALYSIS OF STRUCTURAL RESPONSE 

3.3.1. Expressing responses in terms of influence coefficients 

The relationship in Eq. (10) can be solved for the displacements, which can be expressed as 

. The matrix inverse notation is used for convenience, while it is noted that Eq. −1 u Kf = (10) can 

generally be solved more efficiently without forming the explicit inverse (e.g., by Gaussian 

elimination). With all forces applied at element nodes, as ensured by the assumed form of in 

Eq. 

−1 K

f

(11), internal forces in structural elements, which are of interest in design, can be expressed 

as a linear combination of the generalized displacements in the following general form: 

 (19) T

i i r = e u

where is an vector, and the subscript i is simply an index to differentiate among the 

various internal force quantities of interest. The response quantity can generally be expressed 

most directly in the local coordinate system of the element in which it occurs, as 

i e n ×1

i

r

T

i i r = e u , where 

the overbar denotes quantities expressed in local coordinates. For a prismatic planar frame 

element, for example, the generalized displacements of the two ends can be expressed in the 

element’s local coordinate system as 111 2 2 2 [ ]

T u = uv uv θ θ where u , v , and θ denote axial 

displacements, transverse displacements, and in-plane rotations, respectively. The axial force in 

the frame element (positive in tension) can then be expressed in terms of u as T P = e u , where 

( / )[ 1 0 0 1 0 0 T e = − EA L ], L = element length, A = cross-sectional area, and = 

modulus of elasticity. Similarly, the bending moment at end 1 of the frame element can be 

expressed as 

E

1

T M = e u , where in this case 2 ( / )[0 6 4 0 6 2 T e = − EI L L L] and I = 

moment of inertia for in-plane bending. Displacements u in an element’s local coordinate 

system can be expressed as a linear transformation of the global displacements in the form 

u Cu = , where the nonzero entries of C are direction cosines. Substituting this transformation 

into the expression T

i i r = e u allows the response quantity to be expressed in the global form of 

Eq. 

i

r

(19) through the relationship T T e e i i = C . It is noted that when displacements or differential 

displacements are of concern (i.e., for serviceability considerations), these can also be readily 

expressed in the form of Eq. (19), so that may represent either a displacement response or an 

internal force response. 

i

r

Letting r (with no subscript) denote the number of response quantities of interest, it is 

convenient to define an n r × matrix E , whose columns are the vectors : i e

Eee e = [ 1 2 " r ] (20) 

Letting [ 1 2 ]

T

r r = rr r " denote the r ×1 vector of response quantities of interest, it then 

follows from Eqs. (19) and (20) that r can be expressed as 

 (21) T r Eu =

23
Combining Eq. (11) with the inverse of Eq. (10), the displacements u can be expressed as −1 u KW = φ . Substituting this relationship into Eq. (21), the vector r of responses can then be 

expressed in terms of the vector φ of force coefficients as follows: 

T r N= φ (22) 

here is an matrix of influence coeffici

(23) 

he matrix can be expressed as 

w N m r × ents defined by its transpose as 

T T −1 N EK W =

N Nnn = [ 1 2 " ]

ith the ith response q

nr , where the ith column ni T is a vector 

of influence coefficients associated w uantity. The jth element f the vector 

ni gives the value of the ith response quantity ir resulting from a unit value of the jth force 

efficient (i.e., 1 j

 o

co φ = and 0 φk = for k j ≠ , so that = j f w ). While Eq. (23) represents a fairly 

general expression for the influence coefficients of inte st, it is noted that in some cases, 

particularly for simple frames, the influence coefficients may be evaluated more efficiently 

through the use of the Müller-Breslau Principle (e.g., Sack 1984). The influence coefficients can 

also be evaluated using commercial structural analysis software by applying unit forces with 

appropriate orientation at the cladding attachment points and evaluating the resulting values of 

the response quantities of interest. For the selected frame of the example building in 

re

Figure 7, the 

moment at the left “knee” (circled in Figure 7 and in Figure 11) is taken as the response quantity 

of interest and is denoted 1

r . Figure 11 shows a plot of the corresponding vector n1 of influence 

coefficients, with each element of n1 plotted in the direction of the corresponding unit vector wk

shown in Figure 8. While numerical values are not shown in Figure 11, the largest influen 

coefficient, associated with w21 , has a value of 1 21 [ ] 4.71 N m / N

ce

n = − ⋅ ( −15.5 lbf ft / lbf ⋅ ). The 

influence coefficients shown in Figure 11 correspond to columns pinned at the base, but as noted 

previously, fixed column bases can also be considered, as well as more complicated frames with 

interior columns. 

Figure 11. Influence coefficients associated with moment at left knee (circled).. 

3.3.2. Time series of structural responses 

While Eq. (22) defines the vector r of response quantities at a particular instant of time, it is 

necessary to evaluate time series o each response quantity from the measured pressure time 

series. In Eq. 

f

(1), an l s × matrix θ j P of pressure time series associated with winds from 

direction θ j was defined, and corresponding to this, an r s × matrix θ j R of response time series 

24
can be defined, where the ith row of θ j R is a time serie r the ith response quantity i

r. Each 

column of 

s fo

θ j R then represents a vect of response quantities at a particular instant, and an 

expression f

or r

or θ j R can be obtained using the results of the preceding sections, by replacing the 

vectors p, φ , and r with corresponding matrices. Replacing p with θ j P , Eq. (12) then becomes 

θ j θ j Φ = AP (24) 

where the m s × m trix a represents series time of the force coefficients φ . Replacing φ with Φθ j

Φθ j in Eq. (22), the matrix θ j R of response quantities can then be expressed as 

j j

T R N θ = Φθ (25) 

Combining Eqs. (1) and (24), the matrix of force coefficients can be expressed as Φθ j

1 2

2 P, j H j Φθ = ρV AC θ , and substituting this expression into Eq. (25), the matrix θ j R of response 

quantities can be expressed directly in terms of the measured pressure coefficients as follows: 

1 2

2 P, j j

T R N AC θ = ρVH θ (26) 

he two stages in evaluating structural responses are c

3.3.3. Directional Influence Factors (DIFs) 

uctural desig and therefore it is necessary to 

term

T learly seen in Eq. (26), where the matrix 

A represents the transfer of pressure loading from the cladding to the primary structural system, 

and the influence coefficient matrix N expresses the response quantities of interest in terms of 

the forces applied to the primary structure. 

Peak responses are of greatest interest in str n, 

evaluate peaks from the response time series discussed in the previous section. Peak responses 

can be evaluated for a unit wind speed from each direction, which are called Directional 

Influence Factors (DIFs). Responses for a given wind speed from a particular direction can then 

be obtained simply by scaling the appropriate DIF by the square of the wind speed. It is often 

necessary to exploit model symmetry in order to obtain DIFs over a full 360° range. 

An r ×1 vector max

θ j r of the maximum value of each response quantity can be expressed in 

s of atrix the m θ j R of response time series as follows: 

( ) max r R = max j j rows θ θ (27) 

where the notation max ( ) denotes the row-wise maximum of its matrix argument, in which rows

the maximum value in each row is evaluated and the resulting values are assembled to form a 

column vector. Eq. (27) represents observed peaks, which can exhibit wide variability from one 

realization to another, and it may therefore be preferable to use a more stable estimator for the 

expected peaks, as discussed in Section 2.2.3. The examples presented in this section use 

observed peaks, as indicated in Eq. (27). It is noted that the minimum values of the response 

quantities min

θ j r should generally be computed in addition to the maximum values, as either value 

may govern in design. For the sake of conciseness, only expressions for maxima are presented in 

25
this section, but these expressions are readily extended to minima by simply replacing “max” 

with “min” in each expression. 

Substituting Eq. (26) into Eq. (27) and dividing by , the vector of maximum responses 

for a

2 VH

 unit wind speed from direction θ j , denoted max x , can be expressed as θ j

( ) max max 2 1

2 P, / max j j

T

H rows θ θ = =⋅ V ρ θ x r N AC j (28) 

rs of peak responses for unit wind speeds from each di

max max max

θθ θ p

The vecto rection can then be assembled 

into an r p × matrix max X as follows: 

max ⎡ 1 2 = ⎤ ⎣ ⎦ x x " (29) 

It is convenient to introduce the symbol 

X x

max

i χ to denote the ith row of , whereby can 

χχ χ " (30) 

ents of the vector 

max max X X

be alternatively expressed as 

Xmax max max max

1 2 [ ]T = r

The elem 1× p max

i χ are then the Directional 

ty. 

3.3.4. Exploiting model symmetry 

If the wind tunnel model is symmetric about the axis corresponding to 

Influence Factors (DIFs) 

associated with the ith response quanti

θ = 0 , then pressures 

measured for a wind direction of θ could also have been measured for a wind direction of 

360° −θ on an identical model with the pressure tap array reflected about the axis θ = 0 , as 

shown in Figure 12(b). The tap array itself need not be symmetric. Similarly, if the l is 

symmetric about the axis corresponding to 90

mode

θ = °, then pressures measured for a wind direction 

of θ could have been measured for a wind direction of 180° −θ on an identical model with the 

pressure tap array reflected about the axis θ = 90°, as shown in Figure 12(c). If the model is 

symmetric about both θ = 0 and θ = 90°, then press easured for a wind direction of ures m θ

could also have been measured for a wind direction of 180° +θ on an identical model with the 

pressure tap array reflected about both axes, θ = 0 and θ = 90°, as s

ive ain pre

hown in Figure 12(d). For a 

doubly symmetric model, it is then possible to effe ly obt ssure measurements for four 

different wind directions from a single set of measurements, by exploiting model symmetry. It is 

convenient to introduce the symbols 

ct

b θ , c θ , and d θ to denote the 1× p vectors of symmetric 

wind directions depicted in Figure 12, where the e m ese vectors are defined as 

follows, in terms of the elements of θ : 

360 b θ θ = °− c f ; c θ θ = °− 180

le ents of th

d g e h 0 j j 0

360 j j

360 c

d g e h ; (31) 

unds indicate that the resulting values are shifted by 360

f 360 d

0

180 θ θ j j = °+ c f d g e h

where the brackets and specified bo °

degrees, as necessary, to ensure that they are ≥0° and < 360°. 

To compute structural responses corresponding these to symmetric wind directions, it is 

necessary to assemble tributary matrices, corresponding to A in Eq. (12), that specify the 

manner in which pressures from each of the reflected tap layouts are distributed to the cladding 

attachment points on the primary structural system. The matrices corresponding to the symmetric 

wind directions defined in Eq. (31) are denoted Ab , Ac , and Ad , representing the reflected tap 

26
layouts depicted schematically in Figure 12(b), (c), and (d), respectively. Responses for unit 

wind speeds from each of the symmetric wind directions can then be computed by replacing A

in Eq. (28) with Ab , Ac , or Ad , as appropriate. The r ×1 vector of maximum responses for a 

unit wind speed from direction b θ j , for example, is denoted max

bθ j x and is computed as 

max 1

b b 2 max ( ) P, j j

T

θ θ = ⋅ ρ rows x N A C . The aximum responses from each of the p wind directions can 

 matrix 1 2

max max max max

b bb b [ ] θθ θ p X xx x = " of DIFs. Using Ac and 

Ad , matrices max Xc and X for the wind directions in 

and d θ , res vely. 

 m

then be assemb ×

 can be sim DI

led as an r p

max

d ilarly assembled, giving Fs 

c θ pecti

+ + + + +

+ + + + +

+ + + + +

+ + +

+ + +

θ + + +

+ + +

+ + +

+ + +

+ + + + +

+ + + + +

+ + + + +

+ + +

+ + + θ

+ + +

+ + +

+ + +

+ + +

+ + + + +

+ + + + +

+ + + + +

θ + + +

+ + +

+ + +

+ + +

θ

+ + + + +

+ + + + +

+ + + + +

+ + +

+ + +

+ + +

+ + +

+ + +

+ + +

(a)

(b) (d)

+ + + (c)

+ + +

+ + + + +

+ + + + +

+ + + + +

+ + +

+ + +

θ + + +

+ + +

+ + +

+ + +

+ + + + +

+ + + + +

+ + + + +

+ + +

+ + + θ

+ + +

+ + +

+ + +

+ + +

+ + + + +

+ + + + +

+ + + + +

θ + + +

+ + +

+ + +

+ + +

θ

+ + + + +

+ + + + +

+ + + + +

+ + +

+ + +

+ + +

+ + +

+ + +

+ + +

(a)

(b) (d)

+ + + (c)

+ + +

Figure 12. Schematic plan view of building model showing symmetric wind directions

corresponding to reflection of pressure tap array about axes of symmetry. 

A 1× p vector 1 2 [ ] θ = θ θ θ " p of wind directions can then be formed with its 

m s giv nion of the elements ent en by the u in θ , b θ , c θ , and d ele θ (with no repetitions), where p

denotes the total number of unique elements in he v tors. In the case of a singly symmetric 

model, 

 t se ec

θ is formed from the union of θ with b θ or c θ , depending on the axis of symmetry. The 

resulting vector θ will span the full ran e of 3 ° if spans a range of at least 90° for a doubly 

symmetric model or at least 180° for a singly symmetric model. If the range of θ exceeds these 

specified values, then overlap will generally occur between the ranges of θ , 

g 60 θ

b θ , c θ , and d θ . 

Consequently, for a given wind direction θ j in the resulting vector θ, multi le tim tes of the 

corresponding DIFs may be available. Let the notation 

p es a

max |

θ=θ j

X denote the column (if any) in the 

matrix max X for which the corresponding element of θ equals θ j . Similarly, let b

max

b |

θ =θ j

X

denote t lumn (if any) in the matrix max he co Xb for which the corresponding element of b θ equals

θ j , and let c

max

c |

θ =θ j

X and d

max

d |

θ =θ j

X be d d likewise for the matrices max Xc and m Xd . These 

lumn vect provid ny as four estimates of the DIFs corre ding 

efine ax

co ors then e as ma spon to θ j , from 

which improved estimates of the expected peaks can be obtained by averaging. An r ×1 vector 

27
max

θ j

x of peak responses corresponding to a unit wind speed from direction θ j can then be 

evaluated by taking the average of all the available estimates: 

b c

max max max max max mean b c j rows jjj θ === θθθ

⎛ ⎞ ⎡ ⎤ = ⎜⎢⎣ d d =θ j

⎟⎥ ⎝ ⎠⎦ θ

X (32) 

here the notation denotes the row-wise mean of its matrix

responses for each direction in 

θθ θ

x XX X

w mean ( ) argument. The peak rows

θ can then be assembled into an r p × matrix max X as follows: 

1 2

x max max max

θθ θ p

ma = ⎡ ⎤ ⎣ ⎦ X xx x " (33) 

max The matrix X gives averaged values of the DIFs for th

uantity for each of the wind directions in the vector 

e maximum value of each response 

q θ, wh

(3

ich extends over the full 360° range. 

As in Eq. 0), max X can be alternatively expressed in terms of its rows as max max max max

1 2 [ ]T X = r χχ χ " . 

45°

0°

90°

135°

180°

225°

270°

315°

200

400

600

800 max

1 θ χ,

b max

b1 θ χ,

c max

c1 θ χ,

d max

d1 θ χ,

max

1 θ χ,

45°

0°

90°

135°

180°

225°

270°

315°

200

400

600

800 max

1 θ χ,

b max

b1 θ χ,

c max

c1 θ χ,

d max

d1 θ χ,

max

1 θ χ,

max

1 θ χ,

b max

b1 θ χ,

c max

c1 θ χ,

d max

d1 θ χ,

max

1 θ χ,

Figure 13. Directional Influence Factors (DIFs) giving maximum values of moment at left knee 

for a unit wind speed from each direction θ (units of ). 2 N m/(m/s) ⋅

28
Figure 13 shows the DIFs associated with the maximum value of the moment at the left knee 

of the selected frame, plotted against the wind direction θ , as defined in Figure 7. The DIFs 

associated with θ and b θ , denoted max

1 χ and max

b1 χ , are plotted in the right-hand sector, between 

270° and 90°, while the IFs associa with nd d θ , denoted max

c1 D ted c θ a χ and maxd1 χ , are plotted in 

the left-hand sector, between 90° and 270°. The averaged DIFs ma

1

x χ , associa ith ted w θ , extend 

around the full circle, with the largest value being 2 621 N m / s) ⋅ ( 2 45.6 lbf ft ft / s) ⋅ ), 

corresponding to 

/(m /(

θ 4 = 15°. 

3.4. ESTIMATION OF STRUCTURAL RESPONSES FROM MODELS WITH 

The procedure described in this paper is applicable to rigid buildings with the general form 

DIFFERENT DIMENSIONS 

depicted in Figure 3. While Sections 3.2 and 3.3 treated cases in which a wind tunnel model is 

available whose full-scale dimensions exactly match the dimensions of the structure of interest, it 

is assumed in this section that a model with exactly matching dimensions is unavailable. 

Therefore, a number of models must be selected with dimensions that are reasonably close to the 

dimensions of the structure of interest. Preferably, the dimensions of these models should bound 

the dimensions of the structure of interest, so that improved estimates of the peak responses of 

interest can be obtained by interpolation. Letting b denote the number of building models 

selected, it is convenient in subsequent manipulations to use the subscript i b =1, 2, , ... as an 

index for each building model. The full-scale dimensions of the ith building m wn in odel, as sho

Figure 3, are then denoted Wi , Li , Hi , and Ri . The dimensions of the building of interest, for 

which no wind tunnel model is available, are denoted using the subscript i = 0 , as W0 , L0 , H0 , 

and R0 . 

3.4.1. Scaling of pressure tap coordinates 

The basic approach proposed in this paper for making use of pressure measurements from a 

model with differing dimensions is simply to scale the coordinates of the pressure taps to match 

the dimensions of the structure of interest. Let i x , i y , and i z be vectors specifying, respectively, 

the x-, y-, and z-coordinates of the pressure taps on the ith b ilding model. With the origin of the 

coordinate system at a lower corner of the building, as depicted in 

u

Figure 3, vectors i x and i y of 

scaled x- and y-coordinates that match the dimensions of the structure of interest can be obtained 

as follows: 

0

i i

i

W

W

x x  = ; 0

i i

i

L

L y y  = (34) 

Scaling of the z-coordinates is somewhat more complicated because it depends on the two 

independent vertical dimensions H and R . It is convenient to partition the row vector i z as 

[ ] H R z zz i ii = , where H

i z contains the values of i z that are ≤ Hi (i.e., the z-coordinates of taps on 

low eave height) and R

i z contains the values of i z that are i the walls be > H (i.e., the z29
coordinates of taps on the roof and on the end walls above eave height). The

taps above and below eave height can then be scaled separately as follows: 

z-coordinates of 

H H0 H z z  = ; i i Hi

0 ( ) R R R z 1z1 i i =+ − H H 0 i Ri

(35) 

where is a vector of ones with the same size as . The full vector of scaled z-coordinates 

n

imensions are sto

1 R

i z i z

can the be formed as [ ] H R z zz   i ii = . After partitioning and scaling, the elements of i z should be 

reordered, as necessary, for consistency with i x and i y , so that the scaled coordinates of the kth 

pressure tap are given by ([ ] ,[ ] ,[ ] ik ik ik xyz  . As ted previously, both the pressure tap 

coordinates and the building d red in the standard UWO HDF pressure database 

files, and using this information, the scaling of tap coordinates represented by Eqs. 

) no

(34) and (35)

can be performed automatically for specified dimensions of the structure of interest. 

This scaling of pressure tap coordinates is illustrated schematically in Figure 14, in which 

the tap coordinates from two models with eave heights H1 and H2 (shown in the left column) 

are scaled to match the dimensions of the model of inter , with eave height 0 est H (shown in the 

right column). For clarity, scaling of the tap coordinates is illustrated only for the taps on the left 

face in Figure 14, and the other building dimensions (W , L , and R ) are equivalent to those of 

the structure of interest. It is noted that the correlation etween pressures measured at different 

taps depends on their separation distance, and because scaling of tap coordinates artificially 

adjusts their separation distance, some misrepresentation of the correlation in pressures should be 

expected. For the building with eave height 1

 b

H in Figure 14, for example, scaling leads to 

increased separation distances between taps, and therefore, the measured pressures might be 

expected to be more highly correlated than would be expected for taps at the scaled locations. 

Conversely, for the building with eave height H2 , the separation distances between taps are 

reduced by scaling, so that the measured pressures might be expected to be less highly correlated 

than would be expected for taps at the scaled locations. 

H2

H0

H0

H1

H2

H0

H0

H1

Figure 14. Scaling of pressure tap coordinates to match dimensions of structure of interest. 

30
3.4

ind tunnel model exactly 

proach outlined in these 

.2. Interpolation between DIFs from different building models 

Sections 3.2 and 3.3 treated cases in which the dimensions of the w

match the dimensions of the structure of interest. However, the ap

sections can be directly extended (in an approximate sense) to cases in which the dimensions 

differ, by assembling a tributary matrix using tap coordinates scaled to match the dimensions of 

the structure of interest. This allows influence coefficients for the structure of interest to be used 

in conjunction with pressure coefficients measured on a model with different dimensions, 

effectively treating the pressure measurements as if they had been recorded on a model with the 

same dimensions as the structure of interest. In this manner, peak responses can be estimated 

using pressure measurements from a number of models whose dimensions are close to the 

dimensions of the structure of interest, assembling a different tributary matrix for each model. 

The DIF matrix obtained using pressure measurements from the ith model (with dimensions Wi , 

Li , Hi , and Ri ) is then denoted max Xi , where the subscript i b =1, 2, , ... denotes the index of the 

building model. It is assumed for simplicity that the columns of the DIF matrix max Xi for each 

mod corres nd to the same set of wi el po nd directions, given in the vector θ. If necessary, 

interpolation can be performed to ensure that this is the case. 

With DIF matrices max Xi having been obtained using pressure measurements from a number 

of building models with differing dimensions, it is necessary to combine these estimates in some 

manner to obtain a “best” estimate of the DIF matrix for the structure of interest, which is 

denoted max X . Consider first the simple example depicted in Figure 14, in which two models 

with heights H1 and H2 are available, and the response of a structure with height H0 is of 

interest, w e her H102 < < H H . The other dimensions of the models are assumed to match those 

of the structure of inter . In this case, an appropriate means of estimating the DIF mat max X

for the structure 0

est rix

of height H is by linear interpolation between the DIF matrices max X1 and 

max X2 , corresponding to the models with heights H1 and H2 , respectively. This li

interpolation can be expressed as follows: 

near 

max 20 0 max max

2 1

HH H

H H

1

1 2

2 1

H

H H

− − = + − X XX  (36) −

he simple form of linear interpolation in Eq. (36) is applicable

odel dimensions match those of the structure of

tages of 

simp

T only in restrictive cases in which 

all but one of the m interest and in which results 

from only two building models are used. In general, as many as four of the model dimensions 

may differ from those of the structure of interest, and more than two building models may be 

required to adequately bound the dimensions of the structure of interest. A more general multidimensional interpolation method is thus required for realistic cases of practical interest. 

While a number of different multi-dimensional interpolation approaches could be used to 

estimate the DIF matrix max X , an approach is proposed in this paper that has the advan

licity and ease of implementation. The approach can be viewed as a generalization of Eq. 

(36) to higher dimensions, and it is first noted that Eq. (36) can be written in the following 

alternative form, for H102 < < H H : 

31
max max max

1 H H 1 22

γ γ = +

Δ Δ

X X  X (37) 

where ΔH1 , ΔH2 , and γ are defined as follows: 

Δ= − H1 1 H H0 ; Δ = H2 2 H H− 0 ; 

1

1 2

1 2 21

1 1 H H

H H HH γ

−

⎛ ⎞ Δ Δ

=+ = ⎜ ⎟ ⎝ ⎠ ΔΔ − (38) 

It is thus noted that the linear interpolation of Eq. (36) can be viewed as a weighted average of max X1 and max X2 , with the weighting factor for max Xi being inversely proportional to the deviation 

ΔHi of the building height from the height of the structure of interest. The sum of the weighting 

factors is unity (i.e., 1 2 γ / / Δ+Δ = H H γ 1). 

In generalizing the weighted average of Eq. (37) to accommodate deviations in more than 

one building dimension, it is helpful to introduce a vector to represent the dimensions of the 

simple type of gable-roofed building shown in Figure 3. The full-scale width of the building 

model is selected to represent the absolute dimensions of the model, and the remaining 

dimensions are represented using three ratios: the aspect ratio , the height-to-width ratio 

Wi

/ L Wi i

i / Hi W , and the roof slope . Each of these four parameters is then normalized by its value 

for the building of interest to define the vector of dimensions for the ith building model : 

2 / R Wi i

di

0 00 00 00

/ //

/ //

T

i ii ii ii

i

W LW HW RW

W LW HW RW

⎡ ⎤ = ⎢

⎣ ⎦

d ⎥ (39) 

where the superscript T denotes transposition. The subscript i = 0 denotes the building of 

interest, and it is noted that by definition. A vector of deviations in the 

normalized dimensions can then be defined as follows: 

0 d =[1 1 1 1]

Δddd i i = − 0 (40) 

In generalizing Eq. (37), a scalar measure of this deviation in building dimensions is 

required in place of ΔHi , as a measure of the overall “closeness” of the model dimensions to the 

dimensions of the structure of interest. Perhaps the simplest scalar measure would be the norm 

, which represents the four-dimensional “length” of the vector . A 

disadvantage of this measure is that deviations in each of the model dimensions are given equal 

weight, while it is known that building aerodynamics are more sensitive to changes in some 

dimensions than others. For example, a deviation of 50 % in the roof slope of the model might be 

expected to have a more significant influence on the wind pressure distribution than an 

equivalent deviation in the aspect ratio of the model. To compensate for such disparities in 

aerodynamic sensitivity, each component of the deviation vector can be scaled by a factor 

representing the sensitivity of peak responses to changes in that dimension, to obtain a scaled 

deviation vector : 

1/2 || || ( ) T Δdi ii = Δd Δd Δdi

Δdi

Δdi



 (41) Δd S 

i = Δdi

where S is a 4 4 × diagonal matrix containing scale factors for each of the building dimensions: 

32
 (42) / // diag( , , , ) W LW HW RW S = SS S S

Larger scale factors in S correspond to dimensions on which peak responses depend more 

sensitively, and it might then be expected that , the scale factor associated with the roof 

slope, would be greater than , the scale factor associated with the aspect ratio, as discussed 

previously. Appropriate values of the scale factors in can be determined empirically by using 

pressure measurements for available wind tunnel models to investigate the sensitivity of peak 

responses to changes in the various dimensions, and efforts along these lines are currently 

underway. Only the relative magnitude of the scale factors in is of consequence, and it is 

convenient to scale the matrix S so that the largest scale factor equals unity. In the case of equal 

weighting, then reduces to the identity matrix, and . The norm of , given as 

follows, is then used to represent the “closeness” of the building model dimensions to those of 

the structure of interest: 

R W/ S

L W/ S

S

S

S Δd

i = Δdi Δdi



T Δd 

i i = Δd Δdi

 (43) 

A generalized weighted average that accommodates deviations in more than one building 

dimension can then be obtained by substituting || || in place of Δdi

 ΔHi in Eq. (37). The 

summation in Eq. (37) can also be expanded to include an arbitrary number b of building 

models, whereby the following expression is obtained: 

max max

1

b

i

i i

γ

=

X = ∑ Δd

  X (44) 

The value of the constant factor γ follows from the condition that the sum of all the weighting 

coefficients equals unity (i.e., ), and is given as follows: 1 / || || 1 b

i i γ Σ = Δd =

1

1

1 b

i i

γ

−

=

⎛ ⎞

= ⎜

⎜

⎝ ⎠

∑ Δd ⎟

⎟ (45) 

Eq. (44) represents a relatively simple multi-dimensional interpolation scheme that can be 

applied regardless of the number building models or the number of dimensions for each model 

that differ from those of the structure of interest. The scheme has the property that when the 

dimensions of the structure of interest approach the dimensions of one of the models , the 

DIF matrix converges exactly to the corresponding DIF matrix 

d0 di

max X max Xi . It should be noted 

that Eq. (44) does not extrapolate; rather, as the dimensions pass beyond the range of the 

available models, the estimated DIF matrix ax tends to a uniformly weighted average of all 

the available DIF matrices. The accuracy of the interpolated DIFs depends on the availability of 

results from building models with dimensions that are reasonably close to the dimensions of the 

structure of interest. The scaled deviation vector could potentially be used to select 

appropriate building models for use in interpolation from all the models available in the 

aerodynamic database, by forming the vector for the dimensions of each model and 

selecting models for which the norm || is smallest. 

d0

m X

Δdi



Δdi



|| Δdi



33
Figure 15 presents interpolated DIFs for a case like that illustrated schematically in Figure 

14, in which models are available with two different eave heights, H1 and H2 , and peak 

responses are desired for a model with intermediate eave height H0 . Pressure measurements 

from Ho et al. (2005) are used, which correspond to 1:100 length scaling and “open” terrain. The 

larger eave height is H2 = 7.3 m (24 ft), the smaller eave height is H1 = 3.7 m (12 ft), and peak 

responses are desired for an intermediate height of H0 = 5.5 m (18 ft). The other dimensions are 

the same in all cases, and are given by W = 36.6 m (120 ft), L = 57.2 m (187.5 ft), and R = 1.5 

m (5 ft). As shown previously in Figure 7, a structural system consisting of 11 equally spaced 

frames is considered, and the selected response of interest is the moment at the left “knee” of the 

first interior frame, with corresponding influence coefficients shown previously in Figure 11. For 

the interpolation example shown in Figure 15, pressure measurements are actually available for 

the intermediate eave height as well, and DIFs computed using these measurements were shown 

previously in Figure 13. Figure 16 shows a comparison of the DIFs obtained by interpolation for 

H0 = 5.5 m (18 ft) with those computed using the actual measured pressures. The agreement is 

remarkably good, and it is noted that the discrepancies are of comparable magnitude to the 

uncertainty in the computed DIFs themselves. This can be verified by comparison with the DIF 

plots in Figure 13, in which model symmetry was exploited to obtain two DIF estimates for each 

direction, with the difference between these estimates giving a measure of the uncertainty. It 

therefore could hardly be hoped that the interpolation scheme would perform much better. 

Unfortunately, the interpolation is not nearly as successful when using models with differing 

roof rise R , as shown in Figure 17 and Figure 18. Figure 17 presents interpolated DIFs for a case 

in which two models are available with roof rise given by = 1.0 m (3.3 ft) (corresponding to 

an inclination angle of 4.8°) and = 6.1 m (20 ft) (inclination angle of 27°), and peak 

responses are desired for a model with intermediate roof rise of = 3.0 m (10 ft) (inclination 

angle of 14°). Pressure measurements from Ho et al. (2005) are used, corresponding to 1:100 

length scaling and “open” terrain. The plan dimensions and eave height are the same in all cases, 

and are given by W = 24.4 m (80 ft), = 38.1 m (125 ft), and = 7.3 m (24 ft). In this case, a 

structural system consisting of 7 equally spaced frames is considered, giving a bay spacing of 7.6 

m (25 ft). The selected response of interest is the moment at the left “knee” of the first interior 

frame, and the influence coefficients shown previously in 

R1

R2

R0

L H

Figure 11 are used in computing this 

response, with the girt and purlin locations scaled to match the building dimensions. In this 

example, pressure measurements are actually available for the intermediate roof rise as well, and 

Figure 16 shows a comparison of the DIFs obtained by interpolation with those computed using 

the actual measured pressures. 

The agreement in this case is not very good, with the interpolated values about 50 % less 

than the computed values in some cases. It is noted that in this case, the DIFs computed from the 

intermediate model are actually larger than the DIFs from either of the bounding models for 

many wind directions. This example corresponds to a difference of 22° between the roof 

inclination angles of the bounding models, and it is therefore concluded that pressure data are 

required from models with a smaller difference in roof slope in order for the proposed 

interpolation scheme to give reliable results. It is noted, however, that most industrial metal 

buildings have quite shallow roof slopes. Because more pressure data are available in the NIST 

database for buildings with shallow roof slopes, it would not be necessary to interpolate between 

models with such a large difference in roof slope in many cases of practical interest. Further 

34
research is required to establish bounds on the applicability of the proposed interpolation scheme 

given the current set of building models for which pressure data are available. 

45°

0°

90°

135°

180°

225°

270°

315°

200

400

600

800

H1 = 3.7 m (12 ft)

H0 = 5.5 m (18 ft)

(interpolated)

H2 = 7.3 m (24 ft)

45°

0°

90°

135°

180°

225°

270°

315°

200

400

600

800

H1 = 3.7 m (12 ft)

H0 = 5.5 m (18 ft)

(interpolated)

H2 = 7.3 m (24 ft)

Figure 15. Interpolation for different eave height of DIFs for bending moment at left knee of first 

interior frame (units of , plotted against wind direction). 2 N m/(m/s) ⋅

45°

0°

90°

135°

180°

225°

270°

315°

200

400

600

800

H0 = 5.5 m (18 ft)

(interpolated)

H0 = 5.5 m (18 ft)

(computed)

45°

0°

90°

135°

180°

225°

270°

315°

200

400

600

800

H0 = 5.5 m (18 ft)

(interpolated)

H0 = 5.5 m (18 ft)

(computed)

35
Figure 16. Comparison of interpolated (different eave height) and calculated DIFs for bending 

moment at left knee of first interior frame (units of , plotted against wind direction). 2 N m/(m/s) ⋅

45°

0°

90°

135°

180°

225°

270°

315°

200

400

600

R1 = 1.0 m (3.3 ft)

R0 = 3.0 m (10 ft)

(interpolated)

R2 = 6.1 m (20 ft)

45°

0°

90°

135°

180°

225°

270°

315°

200

400

600

R1 = 1.0 m (3.3 ft)

R0 = 3.0 m (10 ft)

(interpolated)

R2 = 6.1 m (20 ft)

Figure 17. Interpolation for different roof rise of DIFs for bending moment at left knee of first 

interior frame (units of , plotted against wind direction). 2 N m/(m/s) ⋅

45°

0°

90°

135°

180°

225°

270°

315°

200

400

600

R0 = 3.0 m (10 ft)

(interpolated)

R0 = 3.0 m (10 ft)

(computed)

45°

0°

90°

135°

180°

225°

270°

315°

200

400

600

R0 = 3.0 m (10 ft)

(interpolated)

R0 = 3.0 m (10 ft)

(computed)

36
Figure 18. Comparison of interpolated (different roof rise) and calculated DIFs for bending 

moment at left knee of first interior frame (units of , plotted against wind direction). 2 N m/(m/s) ⋅

3.5. ESTIMATION OF PEAK RESPONSES WITH SPECIFIED RETURN PERIOD 

DIFs evaluated as discussed previously, either by interpolation or by direct computation, can be 

used in conjunction with a matrix VH of simulated wind speeds, as in Eq. (5), to compute peak 

values of the response quantities of interest over a significant time duration, from which 

responses with specified return period can be estimated. To enable this, it is generally necessary 

to resample the DIFs to coincide with the wind directions for which wind speeds are available in 

the matrix VH . 

3.5.1. Resampling of DIFs 

In Eq. (6), a 1 vector of wind directions was defined that corresponds to the columns of the 

 matrix 

×q ˆ

θ

h q × VH of simulated wind speeds. The wind directions in generally do not coincide 

with those in 

ˆ

θ

θ, the 1× p vector of wind directions corresponding to the columns of the DIF 

matrix max X (generally q p < ). Therefore resampling is generally required to make use of the 

DIFs in conjunction with the directional wind speeds. 

A wind speed reported for direction ˆθ j could potentially correspond to any wind direction 

within the sector bounded above by the midpoint between ˆθ j and 1 ˆθ j+ , and bounded below by 

the midpoint between ˆθ j and 1 ˆθ j− . (“Wrapping” of wind directions about 360° must be 

accounted for in establishing these bounds.) It is convenient to introduce the symbol ˆ Δθ j to 

denote this sector associated with direction ˆθ j . In a similar manner, a sector Δθ k can be defined 

for each wind direction θ k in θ. Because θ is sampled more finely than , each sector ˆ

θ ˆ Δθ j will 

generally overlap several sectors Δθ k . With maximum responses for winds in each sector Δθ k

given by max

θ k

x , the expected maximum responses for winds in sector ˆ Δθ j , denoted , can be 

expressed as follows: 

max

ˆ ˆ

θ j

x

( ) max max

ˆ

1

ˆ ˆ j k

p

k j

k

P θ θ θ θθ θ =x = ∈Δ ∈Δ ⋅ ∑ x (46) 

where ˆ ( | P k ) θ ∈Δ ∈Δ θθ θ j denotes the probability of winds in sector Δθ k given that winds are 

known to be in sector ˆ Δθ j . This probability is nonzero only for sectors Δθ k that overlap ˆ Δθ j , 

and it is convenient to let ˆ Δ ∩Δ θ k θ j denote the sector defined by the intersection of Δθ k and 

ˆ Δθ j . Assuming that winds from any direction within the sector ˆ Δθ j are equally likely, the 

37
probability ˆ ( | P k ) θ ∈Δ ∈Δ θθ θ j is simply given by the fraction of ˆ Δθ j that is overlapped by 

Δθ k , which can be expressed as follows: 

( ) ˆ ( ) ˆ ˆ ( )

k

k j

j

P

θ θ j θ θθ θ

θ

∠ Δ ∩Δ

∈Δ ∈Δ =

∠ Δ (47) 

where ˆ ( ) ∠ Δ ∩Δ θ k θ j and ˆ ( j ∠ Δθ ) denote the interior angles associated with the sectors 

ˆ Δ ∩Δ θ k j θ and ˆ Δθ j , and ˆ ( k ) ∠ Δ ∩Δ θ θ j is nonzero only if Δθ k and ˆ Δθ j overlap. The estimates 

of resulting from Eqs. max

ˆ ˆ

θ j

x (46) and (47), giving expected maximum responses for unit wind 

speeds from each direction in , can then be assembled into an ˆ

θ r q × matrix as follows: max Xˆ

1 2

max max max max

ˆˆ ˆ ˆ ˆˆ ˆ

θθ θ q

⎡ ⎤ = ⎢⎣ ⎥⎦ X xx x " (48) 

As in Eq. (30), the symbol x is introduced to denote the ith row of the matr max ˆ , which 

can be alternatively express max ˆ ]

T

r χ . The wind directions 

associated with the c ns of max Xˆ are then the same as those associated with the lu

ma ˆi χ ix X

ed as 1 2 ˆ

X = [χ χ ˆ ˆ "

olum co mns of 

max max max

VH . 

3.5.2. Interpolation between DIFs for different terrain conditions 

denoted 

While terrain conditions were not mentioned in the previous discussion of DIFs, it is important to 

note that DIFs are computed using pressure coefficients corresponding to specific terrain 

conditions, and therefore, the DIFs themselves are specific to these terrain conditions. For 

building models in the NIST aerodynamic database, pressure measurements are generally 

available for two different terrain conditions, described as “open” and “suburban” (Ho et al. 

2005). Let the two terrain conditions be denoted C and B, with corresponding roughness lengths 

0C z and 0B z , where 0C z < 0B z . Typical values are 0 z C = 0.03 m (“open” terrain) and 

0 z B = 0.3 m (“suburban” terrain). Using the distinct sets of pressure measurements for terrain 

condition and B o DIF matrices can be obtained for the ith building model, which are 

denoted 

s C , tw max XC i, and max XB i, . The interpolation scheme in Eq. (44) can then be applied separately to 

the results m all building models for each of the two terra condi s to obtain two DIF 

matrices, max XC  and max XB  , corresponding to roughness lengths 0C

 fro in tion

z and 0B z . These DIF mat s 

can then be resampled, as described in Section 

rice

1 o ob DIF m trices and , 

who

The roughness leng

om 

direction. This column-wise interpolation can be expressed as follows: 

3.5. , t tain a max ˆ

XC

max ˆ

XB

se columns correspond to the wind directions in α . 

ths associated with each wind direction in α are given in the vector 

0 01 02 0 [ ] q z = zz z " , which was used previously for scaling directional extreme wind speeds 

in Eq. (4) atrix of DIFs corresponding to appropriate terrain conditions fr each direction, 

denoted max Xˆ , can then be obtained by interpolating each column of max Xˆ between the 

corresponding columns of max ˆ

XC and max ˆXB , using the specified roughness length for that wind 

. A m

38
 (49) max max max ˆˆ ˆ diag( ) diag( ) X X=⋅ +⋅ C CB μ X μB

where diag( ) μC and diag( ) μB denote the q q × diagonal matrices obtained by placing the 

elements of the 1 vectors and along the main diagonals with zeros elsewhere, and the 

jth elements of the vectors and are defined as follows, in terms of the roughness length 

×q μC μB

μC μB

0 j z associated with direction α j : 

0 0

0 0

B j

Cj

B C

z z

z z

μ − = − ; 

0 0

0 0

j C

Bj

B C

z z

z z

μ − = − (50) 

It is noted that for cases in which 0 0 j B z z > or 0 0 j C z z < , the weighting factors in Eq. (50) lead to 

linear extrapolation. If extrapolation is undesirable, the interpolation can be truncated at the 

limits 0C z and 0B z by setting 0 μ Cj = and 1 μ Bj = when 0 0 j B z z > and by setting 1 μ Cj = and 

0 μ Bj = when 0 0 j C z z < . 

3.5.3. Computing peak responses from directional wind speeds 

The notation is introduced to denote the 2 VH h q × matrix formed by squaring each element of 

the matrix VH : 

2 [ ] ([ ] )2 V V H kj H kj ≡ (51) 

The maximum value of the ith response quantity corresponding to each of the directional wind 

speeds in the matrix VH can then be evaluated by multiplying each column of by the 

corresponding entry of the 1 vector 

2 VH

×q max ˆi χ of DIFs. The resulting matrix of directional 

maximum responses has the same dimensions as , and it can be expressed as , 

where denotes the matrix formed by placing the elements of 

2 VH2 m diag( ) ˆ H i V ⋅ χ ax

max diag( ) ˆi χ q q × max ˆi χ along the 

main diagonal, with zeros elsewhere. Of interest is the maximum value of the ith response 

quantity in each hurricane, regardless of direction (or the maximum in each year, for nonhurricane winds). This can be expressed in the form of an h×1 vector max , obtained by 

evaluating the maximum element in each row of the matrix of directional responses: 

ˆ

i r

( ) max 2 max ˆ max diag( ) ˆ i H rows

r V = ⋅ χi

)

rˆ ) k

 (52) 

The vector is then sorted in descending order, so that and 

, where denotes the kth element of . In this manner, an 

max ˆ

i r max max

1 [ ] max( ˆ ˆ r r i i =

max max [ ] min( ˆrih i = max [ ] ˆ

i r max ˆi r h ×1

vector of ranked responses can be determined for each of the r response quantities of 

interest, from which responses with specified return periods can be evaluated as described 

previously in subsection 

max ˆ

i r

2.4. 

Figure 19 shows maximum values of the bending moment at the left knee of the selected 

frame corresponding to return periods of 50 years and 500 years, plotted against building 

orientation α0 , as defined in Figure 2. These results correspond to simulated directional 

hurricane wind speeds from Batts et al. (1980) for Miami, for which the estimated hurricane 

39
occurrence rate is . Responses corresponding to different building orientations 

were obtained by using Eq. 

1 ν 0.560 year− =

(6) to define a new vector of wind directions for each value of ˆ

θ α0

and repeating the procedure described above from Eq. (46) onwards for each orientation. The 

largest value of the 500-year maximum response is 886 kN m⋅ (654 ki ), corresponding to 

an orientation of 

p ft ⋅

α0 = 202.5° (SSW). 

SE

E

S

SW

W

NW

N

NE

400

600

800

1000

200

500 year

50 year

SE

E

S

SW

W

NW

N

NE

400

600

800

1000

200

500 year

50 year

Figure 19. Maximum value of moment at left knee (units of kN m⋅ ) having 50-year and 500-

year return periods, for varying building orientation. 

40
4. Application to Flexible Buildings: 

Dynamic Analysis 

William P. Fritz

4.1. INTRODUCTION 

Flexible buildings are defined as buildings that have significant dynamic effects when subjected 

to extreme loads. The application of DAD to flexible buildings is straightforward owing to the 

systematic conversion of wind tunnel pressures into wind effects. The wind effect of interest 

accounts for the applied loads due to wind and to the inertial forces they induce. 

4.2. DYNAMIC MODELING 

The combination of the pressure time series from wind tunnel measurements for winds blowing 

from direction θ, P,θ j C , and directional extreme wind speeds that represent hourly averages at 

roof height, VH , yield external pressures at each of the pressure taps in the wind tunnel model as 

given in Eq. (1). These pressures are separated into their directional components: those normal to 

a rectangular building’s principal axis y induce pressures in the x direction and those normal to 

the building’s principal axis x induce pressures in the y direction. At a tap location denoted by l, 

the components of the wind-induced pressures are summarized as follows: 

( ) lxθ ρ CVtp plxH θ

2

2

1 = acting in the x direction (53) 

( ) lyθ ρ CVtp plyH θ

2

2

1 = acting in the y direction (54) 

The function of time is expressed explicitly in these equations as will be the wind effects they 

induce. Positive and negative pressures correspond to pressure acting towards and away from the 

building face, respectively. Wind forces in the x and y directions, Flxθ(t) and Flyθ(t), can be 

obtained from the pressures plxθ(t) and plyθ(t) through multiplication by the respective tributary 

areas, Alx and Aly, of each pressure tap l. The static effects of these forces on the structure are 

determined by using influence coefficients described in Section 4.3, for which the sign 

convention (positive toward the building face) is the same as for the pressures. For the 

calculation of dynamic effects, positive forces are forces whose direction is the same as the 

direction of the building’s principal axis x or y. 

The structure is assumed to be linearly elastic and to have coincident elastic and mass 

centers. The case of non-coincident centers is considered in Venanzi et. al (2005). The dynamic 

model of the building consists of a lumped mass at each floor with applied forces Flxθ(t) and 

Flyθ(t) accumulated at each floor using tributary areas. Moments about the elastic center, Μlθ, are 

produced by the wind forces Flxθ multiplied by their distance from the elastic center, yl, and by 

41
the wind forces Flyθ multiplied by their distance from the elastic center, xl. These forces and 

moments at each floor act as forcing functions in the equations of motion for the lateral 

deflections in the x and y directions and for the angular rotation about the z direction, φ. This 

approach can be easily adapted for non-rectangular buildings. 

The lateral deflections at elevation z in the x and y directions and the angular rotation about 

the z direction, φ, induced by a speed VH blowing from direction θ can be written in terms of 

generalized coordinates and modal shapes of vibration as 

∑ (55) =

=

n

i

xii tzxtzx

1

ξ )()(),( θ

∑ (56) =

=

n

i

yii tzytzy

1

ξ )()(),( θ

∑ (57) =

=

n

i

ii tztz

1

)()(),( φθ ξφ φ

where t)( ξ xi , t)( ξ yi and t)( ξ φi are the generalized coordinates in the i

th mode corresponding to 

motions in the x, y and φ directions, respectively, induced by wind from direction θ ; xi(z), yi(z) 

and φi(z) are the i

th modal shapes; and n is the number of modes of vibration being considered. 

The equations of motion, fundamental modal mass and generalized force are summarized in 

Table 1 for each direction. 

Table 1. Equations of motion for x, y and φ directions 

Dir. Equation of motion Modal mass 

Mxi,Myi,Mφi

Generalized force 

Qxiθ,Qyiθ,Qφiθ

Eq. 

No. 

x )()(2)( )( 2 1 t tQMtt xiθ xiixix θ ξωξωςξ ixix θ xixi θ

− + + =   ∑=

n f

k

mzx kki

1

2 )( ∑=

l n

l

lxli tFzx 1

)()( θ (58)

y )()(2)( )( 2 1 t tQMtt yiθ yiiyiy θ ξωξωςξ iyiy θ yiyi θ

− + + =   ∑=

n f

k

mzy kki

1

2 )( ∑=

nl

l

lyli tFzy 1

)()( θ (59)

φ )()(2)( )( 2 1 t tQMtt iθφ iii θφφφ ξωξωςξ ii φθφ ii θφφ

− + + =   ∑=

f n

k

kki Iz 1

2 φ )( ∑=

Μ l n

l

lli tz 1

)()( φ θ (60)

The variables nf and nl are the total number of floors and taps, respectively; ωi and ζi are the 

circular frequency and damping ratio in the i

th mode; mk is the mass of floor k; and Ik is the mass 

moment of inertia of floor k. Solutions of the equations of motion combined with the modal 

shapes yield the lateral deflections and angular rotation in Eqs. (55), (56) and (57). 

Differentiating these equations twice yields the respective accelerations. 

4.2.1. Transforming wind pressures to structural loads 

The pressures in Eqs. (53) and (54) are measured at taps located on the building model in the 

wind tunnel. The pressure tap locations and their tributary areas are scaled to the prototype 

building to generate wind loads. The calculated forces at their specified locations induce wind 

effects within the structure, and are referred to as applied wind loads. They also induce 

vibrations about the mass center. Inertial loads result from multiplication of the accelerations, 

42
found through solution of the equations of motion in Table 1 at each floor, by the floor mass or 

mass moment of inertia, and are referred to as inertial wind loads. A flexible building and its 

elements are designed for the combined effect of the applied and inertial wind loads. 

4.3. MODELING OF WIND EFFECTS 

We assume that the structural system consists of beams, columns, and trusses, but the procedure 

can be easily adapted to other systems. The structure is subjected to known, time dependent 

aerodynamic forces at the pressure tap locations and inertial forces at each floor’s center of mass. 

The wind effects at any cross-section of any member j, roof accelerations, and interstory drift, 

can therefore be calculated at each time t by summing up the products of the aerodynamic and 

inertial forces by the respective influence coefficients that convert the forces into the wind effect 

being sought. 

For this report, the model utilizes the following influence coefficients characterizing the 

system and obtainable by using standard structural analysis programs: mjXWl and mjYWl, 

representing the bending moments induced about the local X and Y axis of member j by a unit 

load perpendicular to the building face at tap l (the subscript W indicates that the influence 

coefficients are associated with the calculation of effects due to wind forces); PjWl, the axial force 

in member j due to a unit load perpendicular to the building face at tap l; mjXIxk and mjYIxk, the 

bending moments about the axes X and Y in member j due to a unit horizontal force acting 

through the center of mass in the x- direction at floor k (the subscript I indicates that the 

influence coefficients are associated with the calculation of effects due to inertial forces); mjXIyk

and mjIyk, similar moments due to a unit horizontal force acting through the center of mass in 

direction y at floor k; PjIxk and PjIyk, the axial forces due to a unit horizontal force acting through 

the center of mass in the x- and y- directions at floor k; mjXTk and mjYTk, the moments induced 

about axes X and Y by a unit horizontal torque about the elastic center at floor k; PjTk, the axial 

force induced by a unit horizontal torque about the elastic center at floor k. Other wind effects 

can be considered using similarly defined influence coefficients. 

These sets of influence coefficients are combined with the wind forces based on the 

recorded pressures at the pressure taps and the calculated inertial forces to obtain the windinduced internal forces. (In the expressions that follow we omit the subscripts x and y where they 

are not necessary.) The wind speed VH therefore induces in member j and at time t a total axial 

load and total moments about local axes X and Y 

( ) ∑ ∑[ ] () () () (61) = =

= − + +

f l n

k

kkjIxk kkjIyk kkjTk

n

l

j lljWl tIPtymPtxmPAtpPtP

1 1

)( θ θ θ θ φ θ   

( ) ∑ ∑[ ] ( ) () () (62) = =

= − + +

f l n

k

kkjXIxk kkjXIyk kkjXTk

n

l

jX lljXWl tImtymmtxmmAtpmtM

1 1

)( θ θ θ θ φ θ   

( ) ∑ ∑[ ] ( ) () () (63) = =

= − + +

f l n

k

xkkjYIxk kkjYIyk kkjYTk

n

l

jY lljYWl tImtymmtxmmAtpmtM

1 1

)( θ θ θ θ φ θ   

where mk is the mass of the kth floor, (tx ) kq  and (ty ) kq  are the accelerations in the x- and ydirection at floor k, and Ik and (t) φ kq  are the mass moment of inertia and the rotational 

acceleration of floor k, assumed to be infinitely rigid, about the elastic center. 

43
For design purposes it is not the individual internal forces that need to be considered, but 

rather combinations of internal forces governed by interaction equations and by load 

combinations. For example, for steel structures, the following design interaction equations 

(AISC, 2001, 16.1-38) – or variants thereof – could be used for member j:

 For ( ) ≥ 2.0

j

jf

P

tP

φ

θ : ( ) ( ) ( ) 1

9

8 )( ≤⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+= +

njyb

jYf

njxb

jXf

nj

e jf

jf M

tM

M

tM

P

tP

tW

φφφ

θ θ θ

θ (64) 

 For ( ) < 2.0

nj

jf

P

tP

φ

θ : ( ) ( ) ( ) 1

2 )( ≤⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+= +

njyb

jYf

njxb

jXf

j

e jf

jf M

tM

M

tM

P

tP

tW

φφφ

θ θ θ

θ (65) 

where is the wind effect of interest for wind direction θ; P e Wjfθ nj, Mnjx, and Mnjy are the nominal 

axial and flexural strengths of member j; φ and φb are axial and flexural resistance factors, and 

the quantities in the numerators are the total axial load and moments due to the specified factored 

combinations (hence the subscript f). For example, applicable load combinations specified by the 

ASCE 7-02 Standard, are: 

1.2D + 1.6L (66) 

1.2D + 1.0L + 1.6W (67) 

0.9D + 1.6W (68) 

where D=dead load, L=live load, and W=wind load. 

Some wind engineering consultants use methodologies requiring designers to consider as 

many as 20 separate combinations of axial loads and/or moments. These are affected by guessedat combination factors or such methods for adding peak effects as the so-called “point-in-time” 

method, and are specified in accordance with a variety of in-house criteria. The difficulty 

experienced by the design engineer is to relate meaningfully those combinations to the 

interaction equations for the members being designed. The methodology just described covers 

simply and exhaustively all cases of interest as reflected clearly and unambiguously in 

interaction equations and load combinations specified by the ASCE 7 Standard or other 

standards, and in a manner that is directly relevant to and usable in the design process. 

4.3.1. Interpolation methods for peak wind effects 

In view of their dependence on time t, Eqs. (64) and (65) yield the observed or estimated peaks 

of the functions (refer to Section 2.4). These peak maximum or minimum values are of 

direct interest in design, and reflect rigorously the superposition of wind effects in the x and y 

directions and in torsion. As noted in Section 

e Wjfq

2.2.2, wind effects for flexible buildings are not 

proportional to the square of the wind speed. Using site specific wind speeds from the 

climatological databases described in Section 2.3 would require the performance of the dynamic 

analysis for every wind speed and wind direction. An interpolation procedure is therefore used to 

facilitate evaluation of peak wind effects for flexible buildings. 

The analysis is performed for the building using a number of wind speeds evenly 

incremented for each wind direction for which wind tunnel pressure data are available. The range 

of wind speeds should be broad enough to properly span the wind speeds in the climatological 

44
database, i.e., the maximum wind speed in the range should be larger than the largest value in the 

database and the minimum wind speed in the range should be small enough to include the speeds 

that influence the return period of the wind effect (Section 2.4). This minimum value is specified 

as Vth on p. 5 of the software described in Section 4.5. The wind speeds in the database are used 

explicitly, but the wind effects they induce are obtained by interpolation from the polar grid 

created as explained in Section 2. 

The software allows two interpolation methods of the wind effects from this polar grid of 

wind speeds and directions. Method A interpolates linearly between wind speeds and wind 

directions. Method B interpolates linearly between wind speeds, but considers only the larger of 

the two values corresponding to the two bounding wind directions. Method B is slightly more 

conservative. 

4.4. THE HIGH-FREQUENCY FORCE BALANCE (HFFB) METHOD 

The methodology described can also in principle be applied to results obtained by the High 

Frequency Force Balance (HFFB) approach, which owes its popularity to its simplicity. 

Currently, HFFB is implemented in the frequency domain, in spite of a certain lack of 

enthusiasm on the part of some practicing engineers for spectral methods, perceived to be less 

transparent than time domain methods. However, the HFFB approach may equally well be 

implemented in the time domain. One potential advantage is that wind-induced effects in the x, y 

directions and in torsion can be added to each other exactly, whereas in spectral methods the 

phase information is lost and such exact addition is not possible. We also note that spectral 

methods were used in the 1960s and 1970s largely because time domain methods were 

prohibitive computationally. This is no longer true today. 

In the HFFB approach the information available consists of base moments measured in the 

wind tunnel for the x and y directions and in torsion. For the particular case of fundamental mode 

shapes that are linear in z, the base moments in the x and y directions are proportional to the 

generalized force in Eqs. (58) and (59). If the fundamental mode shapes are not linear in z, it is 

possible to adjust the results, but this requires making guesses on the distribution of the pressures 

over the building height. For buildings in open terrain this is possible to some reasonable extent, 

but informed guesses are more difficult for buildings in a built environment. 

In addition, base torsional moments are proportional to sums of torsional moments applied 

at each floor, whereas the generalized force in torsion consist of sums of torsional moments 

applied at each floor, weighted by the respective ordinate of the torsional modal shape. Here too 

it is possible to make adjustments based on guesses concerning the distribution of the torsional 

moments with height, but in general such guesses are again difficult to make reliably; the errors 

can be considerable in structures with significant wind-induced torsion affected by the building’s 

specific built environment. 

The non-inertial terms (i.e., the terms involving pressures) in Eqs. (61), (62), and (63) must 

also rely on guessed-at distributions of the wind pressures. To assess approximately the potential 

for errors inherent in such guesses, recall that the pressures are responsible for the non-resonant 

response (i.e., the response not associated with inertial forces), that is, typically, for perhaps half 

the total dynamic response or more. The effect of unavoidable errors in the guessed-at 

distribution of the pressures with height is therefore, typically, far from negligible. 

Finally, the HFFB approach does not allow accounting for more than one mode of vibration 

in the x or y direction or in torsion. 

45
The situation with respect to the use of the HFFB approach is similar to the situation that 

prevailed before the advent of structural analysis software, when approximate methods were 

widely used for the calculation of internal forces in tall buildings. Such methods worked 

reasonably well, but were thoroughly displaced once digital computation became firmly 

established. The HFFB approach has served the profession well, but in our opinion it is 

unwarranted for the structural design of very tall structures, given the superior accuracy of the 

DAD procedure. 

The HFFB procedure is less expensive, but for tall buildings the difference in cost is likely 

to pale in comparison with the benefits inherent in the more accurate DAD approach. Also, when 

cost considerations are involved, it should be remembered that, typically, pressure measurements 

are needed anyway, and some wind tunnel laboratories perform both an HFFB test, and 

measurements of (non-simultaneous) pressures for the design of glazing. The HFFB method also 

has the advantage of being fast and versatile, with possible changes in building design being 

easily accommodated during the design stage. Advances in manufacturing techniques may, 

however, allow changes in models with pressure taps to be comparably fast. 

Procedures similar to DAD have been used on an ad-hoc basis in a variety of wind 

engineering projects. However, the objective of the DAD approach is the development of a 

systematic approach that meets optimally the structural designers’ needs, and allows designers to 

scrutinize effectively or, given the requisite recorded aerodynamic database and climatological 

information, to actually perform the estimates. 

4.5. ACCOMPANYING SOFTWARE 

A software program called High-Rise Database-Assisted Design (HR_DAD) has been developed 

to calculate wind effects corresponding to specified mean recurrence intervals (MRIs) for 

structural members within a flexible building. Currently, the wind effects covered by the 

software only include the quantities defined by the interaction formulas in Eqs. (64) and (65) and 

floor deflections and accelerations. This section contains a general overview of the software and 

its MATLAB files, an example of the use of interaction formulas for members of a 66-story 

building, and a simple example that uses the software to calculate a peak wind-induced 

displacement. The software was developed with a user-friendly graphical interface and is 

available on the website <http://www.nist.gov/wind>. 

4.5.1. General overview of the accompanying software 

This subsection is intended as an overview of the MATLAB files, their inter-relation, and the 

graphical-user-interface. The latter is particularly helpful for the calculation of wind effects other 

than those associated with Eqs. (64) and (65), for example deflections and accelerations. 

The HR_DAD software is comprised of 34 MATLAB files, which are arranged as shown in 

Figure 20. 

46
maxminest.m 

F_Cp_tr.m 

F_Ft.m 

F_Load_Vector.m

.m and .fig 

files for each 

HR_DAD.m Page_Main 

Page_Open 

Page_One 

Page_Two 

Page_Three 

Page_Four 

Page_Five 

Page_Six 

Page_Seven 

Page_Eight 

Output1.m

Program2.m

Program1.m

HurrData.m

stdgaminv.m 

stdnormcdf.m 

stdnorminv.m

modal eom solve.m

Figure 20. Schematic of the MATLAB file organization for HR_DAD. 

The program is started by typing “HR_DAD” at the MATLAB command prompt. This file 

initializes all the variables and opens up 10 pages: 2 introductory pages (Page_Main and 

Page_Open) and 8 other pages (Page_One through Page_Eight) that run the program. Each page 

contains the eight menu tabs located along the left-hand side of the graphical interface. Selection 

of one of these tabs brings that page to the top of all the opened pages. Pages 1 to 5 contain areas 

to input values for the variables and open files pertinent to the program. Purple icons within each 

page that contain the symbol “?” provide additional information for the specific item. For 

example, the menu labelled “1.Building Info.”, which calls the Page_One.m routine, contains an 

input box for the variable “RNmodes”. Clicking on the purple information icon produces a popup window that indicates that the variable name within the MATLAB program is RNmodes, that 

its matrix size is 1 X 1 (i.e., it is a constant), and that the variable specifies the number of 

vibration modes considered in the analysis. The user defines the necessary variables in pages one 

through five, which automatically change the values of the (global) variables within the program. 

The pages and the variables can be selected in any order. The default values specified in the 

HR_DAD.m file are otherwise used. 

The actual calculations are performed in page six by selecting the “Run1” and “Run2” 

buttons, which run the files called Program1.m and Program2.m, respectively (refer to Figure 1). 

Program1.m uses all the defined variables to generate the peak (either observed or estimated) 

wind effect of interest (defined in page five) for the wind directions and wind speeds (WD and 

WS, respectively, defined in page three) for specified structural members (if the wind effect is 

member specific). Several defined functions are used, some of which call other defined functions 

as shown in Figure 20. Comments within the MATLAB script files describe details for these 

functions. The routine in Program1.m establishes a matrix of peak values that has dimensions 

length(WS) by length(WD) and saves it under the file location and name specified in page six. 

The user also has the option of saving the actual wind effect time histories in page six for each 

combination (WS,WD) bearing in mind that they generate many large files. 

The matrix saved in Program1.m is used in Program2.m. The routine in Program2.m cycles 

through each member, loads the saved table of peak wind effects from Run1 (Program1.m), 

loads the particular hurricane wind speed database (specified in page five) and calculates the 

peak wind effect for each MRI (specified in page three). The peak wind effect as a function of 

MRI is saved for each member under the file location and name specified in page six. 

47
Page seven summarizes key input variables and provides the graphical output for a specified 

member. When the “Go” button is clicked, the file Output1.m is called, which displays the 

results from Program2.m. The Output1.m page allows the user to redefine the structural member 

and the MRI. Page eight, “8. Save/Load Data”, allows the user to save the current set of variables 

to a specified file location or load a previously saved file. Finally, the “Exit” button closes all 

pages and exits the HR_DAD program. The variables, however, still remain in memory. 

The user can change the program to suit their particular needs. The graphical interface is 

modified through the MATLAB figure files, e.g., Page_Four.fig, by typing “guide” at the 

MATLAB command prompt. The callback functions for these figure files as well as the program 

routines and functions are found in the MATLAB m-files. 

4.5.2. Example: A 66-Story Building 

The procedure was applied to a 66-story, 198 m (650 ft) high symmetric building with a 37 

by (121 by 121 ) square plan (

 m

37 m ft ft Figure 21), located in an urban environment. Wind 

tunnel data, supplied by the Boundary Layer Wind Tunnel at the University of Western Ontario 

for a 1:400 model of the building, consist of wind pressure coefficient time-histories, CPl(t), 

simultaneously measured at 201 pressure taps arranged on the four faces of the building model at 

10 levels, for 36 wind directions in 10° increments. 

12.34 m 12.32 m

37.00 m

6.17 m 6.17 m

North

20°

y

x

Figure 21. Typical plan view of the 66-story building. 

Measurements were made for duration of 59.78 s with a sampling rate of 400 Hz and an hourly 

mean wind speed at the top of the model of 11.72 m/s (26.2 mi/h). This information is entered 

into page two of the software. The condition that the reduced frequency nD/V (D and V are the 

characteristic length and velocity, respectively) be the same for model and prototype must be 

used for every mean hourly wind speed at the top of the building being used in the calculations 

(refer to Eqs. (2) and (3)). The data suggest the existence of aerodynamic interference effects due 

to the presence of neighboring buildings. 

A preliminary design of the structural members was based on the along-wind loads 

approximately equal to those provided in the ASCE 7 Standard for a 42.4 m/s (95 mi/h) mean 

hourly wind speed at the building’s roof height. The structural system consists of steel beams and 

48
columns, and a lateral force resisting system. The 48 periphery columns are spaced evenly at 

3.08 m (10.1 ft), and the nine core columns are spaced evenly at 6.17 m (20.2 ft). The base 

restraints of the perimeter columns are hinges, while the core columns have fixed supports. 

Floors are spaced evenly at 3 m (9.8 ft) and the column sizes decrease at the 24th and the 44th

floors. Perimeter and core columns are connected at each floor by beams extending in both 

perpendicular directions from the corners of the core area. Wind bracing consists of a system of 

outrigger and belt trusses between floors 21 and 24, 42 and 45, 63 and 66. Core bracing is 

provided at all floors. Floor systems, assumed rigid at each floor, are modeled as concrete shells, 

0.1 m (.3 ft) thick, located over the entire area of each floor. Gravity loads include the structure 

self-weight (D), a superimposed dead load (SD) of 0.48 kPa (10 lb/ft2

), and a live load (L) of 

2.39 kPa (50 lb/ft2). The SD and L loads were distributed uniformly over each floor and were 

applied as vertical point loads to the column joints using appropriate tributary areas. 

A modal analysis was performed on the model to evaluate the eigenvalues and 

eigenfrequencies for the system. The system’s displacements were expressed in terms of the first 

three generalized coordinates corresponding to the three fundamental modes of the structure. 

These correspond to two purely translational mode shapes (x and y) and one rotational mode 

shape (φ). The natural periods (T) for these modes are 4.28 s, 4.28 s and 3.99 s, respectively. The 

fundamental damping ratios (D) are assumed 1.5 % for all three modes. This information is 

entered in page one of the software. 

The software used for the preliminary design and modal analysis is also used to calculate 

dynamic influence coefficients (page three) and member static load reactions to dead and live 

loads (page four) for select members. The user must decide the loads for analysis (page one), the 

interpolation method for direction (page three), load factors for dynamic model (page four) and 

points considered in time histories (page five). A database of simulated hurricane wind speeds is 

selected in page five and an appropriate range of wind speeds (WS) and wind directions (WD) is 

used in page three. The peak wind effect tables are generated in page six as are their mean 

recurrence intervals. 

Selected results are presented for four members whose locations within the structure are 

described in Table 2. 

Table 2. Selected members of the 66-story building example and their locations 

Member number Member type 

x coordinate (m) 

beginning / end 

y coordinate (m) 

beginning / end 

z coordinate (m) 

beginning / end 

3838 chord 6.17 / 6.17 0 / 6.17 30 / 30 

4093 diagonal 6.17 / 0 6.17 / 6.17 30 / 33 

5818 column 18.5 / 18.5 0 / 0 27 / 30 

3235 column 18.5 / 18.5 18.5 / 18.5 0 / 3 

The hurricane database selected corresponds to New York City, NY, for which the estimated 

hurricane occurrence rate is 0.305 per year. The wind effect in either Eq. (64) or Eq. (65) is 

calculated for the wind loads from the preliminary design and from the DAD procedure using the 

load combination in Eq. (67). These results are shown in Table 3. 

49
Table 3. Summary of wind effects using wind loads from the preliminary design and from the 

DAD procedure (load combination: 1.2D+L+1.6W) 

Wind effect, e Wjfθ

Member Number Preliminary design DAD procedure 

3838 0.22 0.41 

4093 0.07 0.15 

5818 0.15 0.31 

3235 0.34 0.42 

As expected, the wind effects calculated by using DAD are greater than those used in the ASCE 

7-based preliminary design. 

DAD offers the engineer the capability to refine the member designs so that the performance 

of the members is efficient – and that risk-consistency among members be achieved. For the 

example of the interaction equation used above, the sizes of members with wind effect ( ) 

values greater than unity need to increase, whereas – to the extent allowed by serviceability 

constraints – members with values much less than unity can be decreased. Resizing 

individual members within the structure, although possible, may be impractical, but groups of 

structural members (e.g., large quantities of columns with similar properties) may be changed 

from the preliminary design to achieve better structural efficiency and risk consistency. 

e Wjfθ

e Wjfθ

4.5.3. Single-degree-of-freedom (SDOF) oscillator 

A simpler application designed to provide a simple check of the software considers a SDOF 

oscillator excited by a sinusoidal force. The wind effect of interest here is the maximum 

displacement in the lateral direction. Figure 22 depicts the SDOF model and the requisite 

parameter values. 

x(t) 

F(t)=cosωt= cos(10t) m = 1 kg 

L = 1 m 

k = 100 N/m 

ζn = 1 % 

ω = 10 rad/s 

ωn = k m/ = 10 rad/s 

Period, Tn = 2π/ωn = 0.628 s 

fn = 1/Tn = 1.592 Hz 

Figure 22. SDOF oscillator example and assumed variable values. 

50
The input variables for this problem are summarized in Table 4. The variables are organized 

by their respective pages within the program. The definition of the variables can be found within 

the pages of the software and variables not applicable to this particular wind effect of interest are 

omitted. 

Table 4. Summary of input variables for SDOF oscillator example 

Page 1 Page 2 Page 3 Page 4 

Nfloors = 1 Ntaps = 1 mem_lista

 = 1 massa = 1 kg 

H_bldg = 1 m tapsa

 = [0 0 1 1 1] difa = [1 1 1 1 1 1 

 1 1 1 1 1 1] 

frames_DLa = [1 0 0 0] 

Fdofs = 1 Cp_tra,b = cos(10*t) propsa

 = [1 0 0 0 0] frames_SDLa = [1 0 0 0] 

RNmodes = 1 Vm = 1 WS = 1 m/s frames_LLa

 = [1 0 0 0] 

T = 0.628 s freq = 50 WD = 0o 

D = 1 % ms = 1 MRI = 1 yr 

evectorsa

 = 1 Npoints = 9421 

a

 Saved within a separate file (e.g., evectors is within a file specified in flnMode_shape) 

b

 t = [0:dt:188.4] where dt = (1/freq)*(Vm/WS)*ms = 0.02 s. 

Variable assignments are made either directly through direct entry in their respective page or 

through uploaded files specified by file location and name. The analysis is performed by clicking 

the “RUN 1” button on Page 6, which executes the MATLAB file “Program1.m”. The 

generalized displacements (local variable gen_d), velocities and accelerations are obtained 

through the “F_Load_Vector” function called within Program1.m. The actual displacement 

values are obtained thereafter through multiplication by the eigenvector (local variable faix). 

MATLAB code for the maximum value from this time history can be added to that line; it cannot 

be typed at the MATLAB command prompt since these variables (e.g., disp_x) are not global. 

All code beyond these lines is irrelevant for this particular wind effect, so any variables used or 

errors encountered after these lines are meaningless. Following the above procedure, a maximum 

displacement of 0.4972 m is obtained. The units result from units used in the input variables. 

We are interested in steady-state response, which for an excitation force ( ) cos Ft F t = o ω is: 

= ωtfHFtx −φ)cos()()( o . 

The mechanical admittance function, H f ( ), is 

2

2

2 2

22 14 4

1 )(

⎟

⎠

⎞ ⎜

⎝

⎛ ⎥ +

⎦

⎤ ⎢

⎣

⎡ ⎟

⎠

⎞ ⎜

⎝

⎛ −

=

n n n n f

f

f

f mf

fH

π ς

Since ω/ωn = f/fn = 1, we have 

51
5.0

)01.0)(2)(1()592.1(4

1

24

1 )( 22 2 2 = = = mf nn πςπ

fH 0 

Therefore, 

5.0)( max tx = m

which is very close to the value yielded by the HR_DAD software. Although this particular wind 

effect is not explicitly programmed into HR_DAD, it is easily determined through simple 

modifications to the program files. 

4.6. SUMMARY 

This chapter describes the application of DAD to flexible buildings and the calculation of 

structural response by accounting for the applied loads due to wind and the inertial forces they 

induce. The procedure presented in this chapter: (1) is capable of accounting for nonlinear 

fundamental modal shapes, including the fundamental modal shape in torsion, and for higher 

modes of vibration; (2) automatically adds up in a correct manner time histories of wind effects 

associated with motions in the x and y directions and torsional motions; (3) readily 

accommodates load combination requirements specified by standards; (4) accounts for the actual 

distribution of the wind pressures over the building height; (5) yields for direct design purposes 

wind effects on all individual members of the structure; and (6) integrates in a simple, 

transparent, and physically correct manner wind directionality effects associated with the 

extreme wind climate and the building aerodynamics. Most of these features are not present in 

procedures based on the measurement of base moments and shears, such as the High Frequency 

Force Balance (HFFB) method. Like the HFFB method, our procedure is applicable to tall 

buildings without significant aeroelastic effects. The procedure is applicable for any wind 

effects, including deflections, accelerations, and internal forces or linear combinations thereof. 

This procedure achieves improved accuracy and conformity with the physics underlying 

dynamic tall building response, as well as clarity, transparency, effectiveness, and userfriendliness from the point of view of the structural designer. To apply the procedure it is 

necessary that the wind tunnel operator supply the time histories of the pressure data, the wind 

speeds (unless they are available in the public domain), and the relation between airport speeds at 

10 m above ground in open terrain and mean hourly speeds at the top of the building. The 

procedure then allows the analysis to be conducted by the structural engineer. This restores full 

control of the design process to the engineer in charge of the project. 

52
References 

American Society of Civil Engineers (ASCE). (2003). Minimum Design Loads for Buildings and 

Other Structures, SEI/ASCE 7-02, 2nd Edition, Reston, VA. 

Batts, M.E., Russell, L.R., and Simiu, E. (1980), “Hurricane wind speeds in the United States.” J. 

Struct. Div., ASCE, 100(ST10), 2001-2015. 

Chen, Y., Kopp, G.A., and Surry, D. (2003a), “Prediction of pressure coefficients on roofs of 

low buildings using artificial neural networks.” J. Wind Eng. Ind. Aerodyn., 91, 423-441. 

Chen, Y., Kopp, G.A., and Surry, D. (2003b), “Interpolation of pressure time series in an 

aerodynamic database for low buildings.” J. Wind Eng. Ind. Aerodyn., 91, 737-765. 

Fritz, W., Iancovici, M., and Simiu, E. (2004), “Applicability of database-assisted design to tall 

buildings.” Proceedings of 8th International Conference on Flow-Induced Vibrations, Paris, 

France, 6-9 July 2004, (CD-ROM). 

Ho, T.C.E., Surry, D., Morrish, D. and Kopp, G.A. (2005), “The UWO contribution to the NIST 

aerodynamic database for wind loads on low buildings: Part 1. Archiving format and basic 

aerodynamic data.” J. Wind Eng. Ind. Aerodyn. 93, 1-30. 

Jang, S., Lu, L., Sadek, F., and Simiu, E. (2005), “Database-assisted wind load capacity 

estimates for low-rise steel frames.” J. Struct. Eng., 128(12), 1594-1603. 

Main, J.A. (2005), “Combining wind pressure databases with structural analysis to predict peak 

responses for rigid buildings.” Proceedings, 6th Asia-Pacific Conference on Wind 

Engineering, Seoul, Korea, 12-14 September 2005, (CD-ROM). 

Main, J.A. (2005), “Interpolation issues in the estimation of peak internal forces using wind 

pressure databases.” Proceedings, 6th Asia-Pacific Conference on Wind Engineering, Seoul, 

Korea, 12-14 September 2005, (CD-ROM). 

The MathWorks, Inc. (2005). MATLAB and Simulink for Technical Computing.

<http://www.mathworks.com> (accessed Oct. 27, 2005). 

Rigato, A., Chang, P. and Simiu, E. (2001). “Database-assisted design, standardization, and wind 

direction effects.” J. Struct. Eng., 127(8), 855-860. 

Sadek, F. and Simiu, E. (2002). “Peak non-Gaussian wind effects for database-assisted low-rise 

building design.” J. Eng. Mech. 128(5), 530-539. 

Sack, R.L. (1984). Structural Analysis, McGraw Hill, Inc., N.Y. 

Simiu, E., Sadek, F., Whalen, T.M., Jang, S., Lu, L.-W., Diniz, S., Grazini, A., and Riley, M.A. 

(2003). “Achieving safer and more economical buildings through database-assisted, 

reliability-based design for wind.” J. Wind Eng. Ind. Aerodyn., 91, 1587-1611. 

Simiu, E. and Scanlan, R.H. (1996). Wind Effects on Structures, 3rd Ed., Wiley-Interscience, 

N.Y. 

53
Venanzi, I., Fritz, W.P., and Simiu, E. (2005). “Effect of distance between the elastic center and 

the mass center on the wind-induced dynamics of tall buildings.” Proceedings, 6th AsiaPacific Conference on Wind Engineering, Seoul, Korea, 12-14 September 2005, (CD-ROM). 

Whalen, T.M., Sadek, F. and Simiu, E. (2002), “Database-assisted design for wind: basic 

concepts and software development.” J. Wind Eng. Ind. Aerodyn. 90, 1349-1368. 

Whalen, T.M., Shah, V., and Yang, J.S. (2000), “A pilot project for computer-based design of 

low-rise buildings for wind loads – The WiLDE-LRS user’s manual.” NIST GCR 00-802, 

National Institute of Standards and Technology, Gaithersburg, MD, USA. 

Whalen, T.M., Simiu, E., Harris, G., Lin, J. and Surry, D. (1998), “The use of aerodynamic 

databases for the effective estimation of wind effects in main wind-force resisting systems: 

application to low buildings.” J. Wind Eng. Ind. Aerodyn. 77&78, 685-693. 

54
Appendix A: 

User’s Manual for windPRESSURE, DatabaseAssisted Design Software for Rigid, Gable-Roofed 

Buildings 

Joseph A. Main 

55
PRESSURE P R E S S U R E EAKESPONSE STIMATION for TATICTRUCTURES SINGECORDED XPERIMENTS wind

Database-Assisted Design Software 

for Rigid, Gable-Roofed Buildings

wind

EAKESPONSE STIMATION for TATICTRUCTURES SINGECORDED XPERIMENTS

PRESSURE P R E S S U R E PRESSURE P R E S S U R E R E S S U R E wind EAKESPONSE STIMATION for TATICTRUCTURES SINGECORDED XPERIMENTS EAKESPONSE STIMATION for TATICTRUCTURES SINGECORDED XPERIMENTS

Database-Assisted Design Software 

for Rigid, Gable-Roofed Buildings

User’s Manual 

developed by Joseph A. Main 

Building and Fire Research Laboratory 

National Institute of Standards and Technology 

Updated February 10, 2006 

Current version available at www.nist.gov/wind

Disclaimer: Certain trade names or company products are specified in this document to specify adequately t

identification does not imply recommendation or endorsement by NIST, nor does it imply that the product is tpurpose. The “stand-alone” version of this software requires installation of the MATLAB1 Component Runtime 

by The MathWorks, Inc. The author’s limited rights to the deployment of this program are limited by a liceNIST and The MathWorks. The license agreement can be found at www.mathworks.com/license/. The 

MathWorks and its licensors are excluded from all liability for damages or any obligation to provide remedial ac

1 MATLAB®. © 1984 – 2005 The Mathworks, Inc.

56
Installation and Setup 

The following files are required for use of the windPRESSURE software, and are being www.nist.gov/wind. The files can also be obtained on CD by request. 

• windPRESSURE program files: provided in the following alternative forms: 

o MATLAB m-files (requires version 7 of MATLAB) o Stand-alone executable (for Windows 2000/XP; requires installation 

of MCRInstaller.exe, which is also provided) 

• Building input files: two sample files are provided: 

o BLD_W=120,L=187.5,H=18,R=5,Open_Country.csv o BLD_W=120,L=187.5,H=18,R=5,Directional.csv 

• HDF pressure databases: Results are provided from four tests conducted at 

the University of Western Ontario, and results from three different wind directions are provided from each test. All models have the same roof slope of 1:12, length scaling of 1:100, width of W = 36.6 m (120 ft), and length of L = 57.2 m (187.5 ft), but the eave height and terrain conditions are different, as follows: 

o eave height of H = 3.7 m (12 ft), “Open_Country” terrain o eave height of H = 5.5 m (18 ft), “Open_Country” terrain o eave height of H = 5.5 m (18 ft), “Suburban” terrain o eave height of H = 7.3 m (24 ft), “Open_Country” terrain 

• Simulated directional hurricane wind speed data: data files are provided 

from 55 different locations (mileposts) along the Gulf of Mexico and North Atlantic coasts. 

Figure 

windPR

It is recommended that users create a single folder named “windPRESSURE” on their local to save all downloaded files and folders, and a recommended directory structure is shown 

files” folder contains all MATLAB m-files (required only for execution within MATLAB), anfolder contains the stand-alone executable and related files (required only for stand-alo“bldg_files” folder contains the building input files, the “HDF_files” folder contains HDF pre(separate subfolders must be created within this folder for each of the four tests list“hurr_files” folder contains simulated directional hurricane wind speed files. As shown in 

57
recommended that separate folders be created for the following three types of output files: 

Factor (DIF) output files, Time Series output files, and Mean Recurrence Interval output filesFor execution within MATLAB, add the “m-files” folder to the MATLAB search path, and save 

Figure 2. Adding “windPRESSURE\m-files” to the MATLAB search path. 

The windPRESSURE software can then be executed by typing “windpressure” at the 

prompt. 

For stand-alone execution, the MCRInstaller must first be installed by executi“MRCInstaller.exe”. The windPRESSURE software can then be launched by doub“windpressure.exe” within the “stand-alone” folder. The stand-alone version of windPRESS

a minute to initialize upon execution, so please be patient. 

58
Graphical User Interface 

Launching the windPRESSURE software opens the graphical user interface shown in Finterface, a building input file can be selected and its contents displayed graphically, and t

HDF pressure databases can also be selected, upon which all subfolders will be searched f

Figure 3. Graphical interface for calculation, interpolation, and display of Directional Influence Fa

59
available results listed. The folder in which DIF output files should be stored and retrieved 

through this interface, and the results to be stored the output file can be selected by p

options...” button, which opens the dialog box shown in Figure 4. Directional Influence 

computed by selecting an available set of HDF pressure databases and pressing the “Com

the dimensions of the wind tunnel model do not match the dimensions of the structure of intap coordinates will be automatically scaled to match the structure of interest. 

Figure 4. Output options for computation of Directional Influence Factors. 

If the option “Display time series during analysis” is selected in the dialog box shown in series of computed responses will be plotted during the analysis, as shown in Figure 5, with 

these results to a Time Series output file. Once DIFs have been computed, the user will be 

the name with which to save the file, and the listing of available DIF files within the interfac

updated. The results in the DIF files can then be displayed graphically by selecting a D“Display”, which opens the graphical interface shown in Figure 6, in which the quantitie

selected. 

60
Figure 5. Graphical interface for plotting and saving of response time series 

(Observed peaks circled, estimated peaks shown as horizontal lines). 

61
Figure 6. Graphical interface for displaying DIF file contents. 

The windPRESSURE software incorporates an interpolation scheme to allow estimation of Dof interest from DIFs computed from several different wind tunnel models with dimensionthe dimensions of the structure of interest. Interpolation can be performed within the i

62
simply by selecting several DIF files computed from different HDF files (with the same ter

pressing the “Interpolate” button. The interpolated results will then be saved and displayed panels shown in Figure 3. The interpolation scheme performs a weighted average of the selthe “closeness” of the model dimensions to the dimensions of the structure of interest, a

different dimensions used in assessing this “closeness” can be adjusted by pressing the “Inte

Factors” button in the interface of Figure 3, which opens the dialog box shown in Fig

sensitivity factors can be adjusted and saved. 

Figure 7. Dialog box for adjusting sensitivity factors used in interpolation of DIFs. 

63
By pressing the “Mean Recurrence Intervals” button at the bottom center of the graphica

Figure 3 , another graphical interface is opened, which is shown in Figure 8. This interface major stage of the analysis, in which DIF results files are combined with simulated directspeeds to compute peak responses with specified Mean Recurrence Intervals. The fosimulated hurricane wind speed data files can be selected through the interface, and the bui

Figure 8. Graphical interface for computing responses with specified Mean Recurrence Interva

64
then be selected from the list of available mileposts. The MRIs for which responses are 

selected through the interface, along with the DIF results file(s) to be used, and results caby pressing the “Compute responses with specified MRIs” button. The results are displayed in Figure 9 and Figure 10, and they can then be saved to an MRI output file, if desired. 

Figure 9. Graphical interface for displaying responses with specified Mean Recurrence Interva

65
Figure 10. Graphical interface for displaying resampled DIFs used in computing responses with speci

66
Building Input File 

This section describes the contents and format of the building input file, a comma-delimited the characteristics of the building to be analyzed. The building input file can be createstandard spreadsheet software and must be saved in the comma-separated values (CSV) fibe properly interpreted by the windPRESSURE software. This CSV file can then be selected the graphical user interface. A sample building input file is shown in Figure 11. The building input file consists of keywords followed by tabular input data. Keywords begand the following keywords are required in each building input file (underscores are used in than spaces): 

*UNITS*BUILDING_DIMENSIONS*TERRAIN*FRAME_LOCATIONS*ATTACHMENT_LOCATIONS*RESPONSE_NAMES*INFLUENCE_COEFFICIENTS

Input data begins on the row immediately following each keyword, and the purpose and formcorresponding to each keyword are described in the following sections. The keywords and data can be entered in the input file in any order, but no extraneous rows are permitted. Er

input data does not match the expected format for the specified keyword. Header rows a

input data for most keywords, so that columns can be labeled, making the input file eaheader rows must not be omitted, or the input data will not be properly read and errors wcolumn labels for the header rows are indicated in the following sections. However, the erows are not actually read by the software, and alternative column labels can be used, or thbe left blank. Additional annotation can be added to the input file by using the % symbol: % are treated as comments and are ignored in reading the building input file. 

2 Any line that begins with an asterisk will be interpreted as a keyword, and an error will result if the text follow

recognized keyword. 

67
continued on next column...

...continued from previous column: 

Figure 11. Sample building input file (BLD_W=120,L=187.5,H=18,R=5,Open_Country.csv). 

68
*UNITS 

Purpose: Define units used in the building input file and in the output of results. Format of Input Data: 

Length Force Wind Speed Å header row 

length_units force_units ws_units Å text entries 

Currently, only the units shown in the following table are supported, and the units must bfile exactly as shown in the second column of the table. 

Quantity Units 

Length ft 

Force lb 

Wind Speed ft/s 

The length units specified here apply to the building dimensions specified in the *BUILsection, the roughness lengths specified in the *TERRAIN section, the y-coordinate*FRAME_LOCATIONS section, and the s-coordinates specified in the *ATTACHMENT_LOCAforce units specified here apply to the unit force used in evaluating the influence coefficie*INFLUENCE_COEFFICIENTS section. The units of the influence coefficients themselves *RESPONSE_NAMES section and do not need to match the units specified here, as lo

coefficients result from a unit force with the force units specified here. The wind speed 

Directional Influence Factors (DIFs) that are output by the software: these DIFs give the response quantity of interest corresponding to unit wind speeds with the units specified directions. 

69
*BUILDING_DIMENSIONS 

Purpose: Define the dimensions of the building to be analyzed. The building dimensions arlength dimensions: the width W0, length L0, eave height H0, and roof rise R0, as shown in F

units specified in the *UNITS section must be used to define these dimensions. 

Format of Input Data:

Width Length Height Roof Rise Å header row 

W0 L0 H0 R0 Å numerical values 

W0

H0

R0

x

y

z

L0

W0

H0

R0

x

y

z

L0

Figure 12. Definition of building dimensions 

70
*TERRAIN 

Purpose: Define roughness of the terrain surrounding the building to be analyzed, which may direction. Format of Input Data:terrain Å text entry 

N NE E SE S SW W NW Å header row 

z0(1) z0(2) z0(3) z0(4) z0(5) z0(6) z0(7) z0(8) Å numerical values 

The terrain entry in the first row specifies the type of terrain, and must be one of the follow

Open_Country Suburban Directional 

The second and third rows of input data should be included only if “Directional” terrain is 

row. “Open_Country” terrain corresponds to a roughness length of z0 = 0.03 m (0.1 ft

directions. “Suburban” terrain corresponds to a roughness length of z0 = 0.3 m (1 ft) directions. Specifying “Directional” terrain requires that roughness lengths be defined for eight different wind directions. These directions begin with the north and increase by 45clockwise direction, as indicated by the column labels in the header row above (the second The roughness lengths corresponding to each of these directions are specified in the third rothe length units specified in the *UNITS section must be used to define these roughness leng

71
*FRAME_LOCATIONS 

Purpose: Define the location of each structural frame to be analyzed, along with the locatioframes, and assign an identifying number to each frame to be analyzed, for use in the outpuFormat of Input Data: 

Number Previous y Current y Next y Å header r

1 frame_coords(1,1) frame_coords(1,2) frame_coords(1,3) Å numerica2 frame_coords(2,1) frame_coords(2,2) frame_coords(2,3) Å numerica

... ... ... ... 

f frame_coords(f,1) frame_coords(f,2) frame_coords(f,3) Å numerica

y x

z

current y

previous y

next y

z

x

θ

y

current y

previous y

next y

θ

Figure 13. Definition of frame locations 

The input data consists of f rows (preceded by one header row), where f is the numbanalyzed, which can be as few as one. Each of these f frames must be identical. If mostructural frame is to be used in the building (e.g., if some frames have interior colum

properties of the frames differ), then separate building input files must be created for e

structural frame, and separate analyses must be performed for each type of frame, ubuilding input files. The frames to be analyzed do not need to be adjacent. Each framassigned a number in the first column of the input data. These frame numbers, which are uresults, must start at 1 and increment by 1, ending with f. For each frame to be analyze

define the y-coordinates of three frames: the previous frame, the current frame, and 

72
illustrated in Figure 13 (the frames span in the x-direction). These coordinates are defined 

and fourth columns of the input data, respectively. The “current” frame is the frame to bshown in red in Figure 13. The “previous” frame and the “next” frame are the neighboring f

are blue and green in Figure 13. The positions of these neighboring frames are required in 

the lengths of the girts and purlins that span between the current frame and the neighboriand purlins spanning between the current frame and the neighboring frames are highlighted 

spanning in the y-direction. If there is no “previous frame” (i.e., if the current frame is at thnear y = 0) then the y-coordinate of the current frame should be specified for both the “Previous y” (i.e., in both the second and third columns of the input data). Similarly, if ther(i.e., if the current frame is at the end of the building near y = L0), then the y-coordinate 

should be specified for both the “Current y” and the “Next y” (i.e., in both the third and foinput data). As shown in Figure 13, y = 0 corresponds to the windward face of the building 

of θ = 0°. It is noted that the origin of the coordinate system shown in Figure 13 is at the obuilding from the origin used in defining the pressure tap coordinates in the standard HDfile. 

73
*ATTACHMENT_LOCATIONS 

Purpose: Define the locations at which girts and purlins are attached to the structural framesFormat of Input Data:

Index Face s-coordinate Å header row 

1 attach_pts(1,1) attach_pts(1,2) Å numerical values 2 attach_pts(2,1) attach_pts(2,2) Å numerical values 

... ... ... 

m attach_pts(m,1) attach_pts(m,2) Å numerical values 

s

face 2

1

2 3 45

face 1

s

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

x

z

face 3

34 33 32 31 30 29 28 27 26 25 24 23 22 

35 s

face 4 

s

face 2

1

2 3 45

face 1

s

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

x

z

face 3

34 33 32 31 30 29 28 27 26 25 24 23 22 

35 s

face 4 

Figure 14. Definition of girt and purlin attachment locations 

The input data consists of m rows (preceded by one header row), where m is the number 

girts and purlins are attached. Each attachment location is assigned an index in the first 

data, and these indices must start at 1 and increment by 1, ending with m. These indi

*INFLUENCE_COEFFICIENTS section to define the influence coefficients corresponding to attachment location. The location of each attachment point is defined by specifying the 

second column of the input data) and a local “s-coordinate” in the plane of that face (in the 

input data). The face numbers and s-coordinates are defined as shown in Figure 14, in w

locations are indicated by arrows normal to each face. The x- and y-coordinates in Figure 1

global coordinate system shown in Figure 13, and it is noted that face 1 corresponds to x = 

74
attachment locations must be assigned in order of increasing face number and then – for ea

increasing values of the s-coordinate. This ordering is illustrated in Figure 14, in which the a

attachment locations are labeled with the index number, using the same color as the correattachment location coincides with the boundary between two faces, then separate indices the attachment location on each of the adjoining faces. This is illustrated at the ridge of t

14, where index 20 is used to denote the ridge location on face 2, and index 35 is used 

location on face 3. It is noted that if the attachment locations are symmetric about the 

coordinates of the attachment locations on faces 1 and 2 are equivalent to the s-coordinatelocations on faces 4 and 3, respectively. 

75
*RESPONSE_NAMES 

Purpose: Assign numbers to the response quantities to be computed, which must coincidnumbers used in the *INFLUENCE_COEFFICIENTS section, and provide descriptive names (e

knee”, “Vertical displacement at ridge”) and units (e.g., “lb-ft”, “in”) for these response qlabeling of results. 

Format of Input Data:

Number Name Units Å header row 

1 resp_names{1} resp_units{1} 2 resp_names{2} resp_units{2} 

... ... ... 

r resp_names{r} resp_units{r} • 

numerical

• 

text entries

• 

text entries

The input data consists of r rows (preceded by one header row), where r is the number of rebe computed, which can be as few as one. Each response to be computed is assigned a 

column of the input data, for use in the output of results. These response numbers mincrement by 1, ending with r. For each of these response quantities, a descriptive name the second column of the input data, and the corresponding units must be provided iInfluence coefficients for each of these response quantities must also be 

*INFLUENCE_COEFFICIENTS section, and the units of the influence coefficients must be 

units provided in this section. Apart from this requirement of consistency, there are no restthat can be used, as the units provided here are not actually interpreted by the software. T

and units are used only for labeling of the results, as a convenience to the user. 

76
*INFLUENCE_COEFFICIENTS 

Purpose: Define influence coefficients for each of the responses to be computed, for whic

and units are provided in the *RESPONSE_NAMES section. The influence coefficients defin

response quantity resulting from a unit force at each of the girt and purlin attachment loca

*ATTACHMENT_LOCATIONS section. The unit forces used to evaluate these influence coefficforce units specified in the *UNITS section. Format of Input Data:

Index Response 1 Response 2 ... Response r Å header row 

1 N(1,1) N(1,2) ... N(1,r) Å numerical values 2 N(2,1) N(2,2) ... N(2,r) Å numerical values 

... ... ... ... ... 

m N(m,1) N(m,2) ... N(m,r) Å numerical values 

34 33 32 31 30 29 28

27 26

25

24

23 22

21

35

6 7 8

9

10

11

12

13 14 15 16 17 18 19 20

1 2

3 4 5

34 33 32 31 30 29 28

27 26

25

24

23 22

21

35

6 7 8

9

10

11

12

13 14 15 16 17 18 19 20

1 2

3 4 5

Figure 15. Influence coefficients associated with bending moment at left knee (Response 1). 

Attachment indices, as defined in Figure 14, are labeled. 

The input data consists of m rows (preceded by one header row), where m is the nu

locations. The first column of the input data specifies the attachment index, as define

*ATTACHMENT_LOCATIONS section, and the attachment indices must start at 1 and incr

with m. The next r columns, where r is the number of responses to be computed, defin

77
response quantity resulting from a unit force at each attachment location. These unit force

corresponding face in the direction of positive pressure (i.e., towards the center of the buildthe arrows at each attachment point shown in Figure 14. The unit forces used to evalu

coefficients must have the force units specified in the *UNITS section. There are no restric

the resulting influence coefficients, but the units must be consistent with those *RESPONSE_NAMES section. 

78
Directional Influence Factor (DIF) Output File 

This section describes the contents and format of DIF output files, which are comma-delimitcomputed Directional Influence Factors are saved. DIF output filenames must begin with “Dby the windPRESSURE software. DIF output files contain the following sections. 

*UNITS*BUILDING_DIMENSIONS*MODEL_DIMENSIONS*WEIGHTING_FACTORS (included only the results were obtained by interpolation)*MODEL_TERRAIN*FRAME_LOCATIONS*ATTACHMENT_LOCATIONS*RESPONSE_NAMES

If “Observed peaks” are selected in the output options (Figure 4), then the following sections 

*DIF_OBS_MAX *DIF_OBS_MIN

If both “Observed peaks” and “Store multiple peaks for each wind direction” are selected i(Figure 4), then the following sections will be included: 

*DIF_OBS_MAX_ALL *DIF_OBS_MIN_ALL

If the DIFs were obtained by interpolation and “observed peaks” were contained in the originterpolation, then “bounding” results from each original DIF file will be included in the follow

*DIF_OBS_MAX_BND *DIF_OBS_MIN_BND

If “Estimated peaks” are selected in the output options (Figure 4), then the following section

*DIF_EST_MAX *DIF_EST_MIN

If both “Estimated peaks” and “Store multiple peaks for each wind direction” are selected i

(Figure 4), then the following sections will be included: 

*DIF_EST_MAX_ALL *DIF_EST_MIN_ALL

If the DIFs were obtained by interpolation and “estimated peaks” were contained in the originterpolation, then “bounding” results from each original DIF file will be included in the follow

*DIF_EST_MAX_BND *DIF_EST_MIN_BND

79
If “Store load distributions producing peak responses” is selected in the output options 

following sections will be included: 

*LOAD_DISTRIBUTION_MAX *LOAD_DISTRIBUTION_MIN

If both “Store load distributions producing peak responses” and “Store multiple peaks for are selected in the output options (Figure 4), then the following sections will be included: 

*LOAD_DISTRIBUTION_MAX_ALL *LOAD_DISTRIBUTION_MIN_ALL

If the DIFs were obtained by interpolation and load distributions were contained in the originterpolation, then “bounding” results from each original DIF file will be included in the follow

*LOAD_DISTRIBUTION_MAX_BND *LOAD_DISTRIBUTION_MIN_BND

The purpose and format of each of the preceding sections are described in the following. *UNITS Format and Purpose are the same as in the building input file. *BUILDING_DIMENSIONS Format and Purpose are the same as in the building input file. *MODEL_DIMENSIONS Purpose: Provide the dimensions of the wind tunnel models used in computing the DIFs. Format: 4 columns; 1 header line, b lines of data, where b is the number of building mod

results were obtained by interpolation: 

Width Length Height Roof Rise (header) 

W1 L1 H1 R1 W2 L2 H2 R2 

... ... ... 

Wb Lb Hb Rb 

80
*WEIGHTING_FACTORS 

This section is included only if the DIF results were obtained by interpolation. Purpose: Report the weighting factors for each model used in computing DIFs by interpolatioFormat: 

Model 1 Model 2 ... Model b (header) 

WF1 WF2 ... WFb 

The output data consists of 1 row with m columns, where m is the number of models used in *MODEL_TERRAIN Purpose: Report the terrain of pressure database files used to compute the DIFs. Format: The output data consists of one entry (1 row, 1 column), which specifies type of 

either “Open_Country” or “Suburban”. 

*FRAME_LOCATIONS Format and Purpose are the same as in the building input file. *ATTACHMENT_LOCATIONS Format and Purpose are the same as in the building input file. *RESPONSE_NAMES Format and Purpose are the same as in the building input file. *DIF_OBS_MAX Observed maximum values of each response for a unit wind speed from each direction. If obtained for some wind directions (by symmetry), then only the averaged results are report*DIF_OBS_MIN Observed minimum values of each response for a unit wind speed from each direction. If obtained for some wind directions (by symmetry), then only the averaged results are report

81
*DIF_OBS_MAX_ALL 

Observed maximum values of each response for a unit wind speed from each direction. Al

symmetry are reported, with each tested wind direction resulting in results for four differ

denoted Wind Direction A, B, C, and D. 

*DIF_OBS_MIN_ALL Observed minimum values of each response for a unit wind speed from each direction. Alsymmetry are reported, with each tested wind direction resulting in results for four differdenoted Wind Direction A, B, C, and D. *DIF_OBS_MAX_BND This section is included only if the DIF results were obtained by interpolation, and it reports values from each model used in interpolation, if “observed” peaks were available. *DIF_OBS_MIN_BND This section is included only if the DIF results were obtained by interpolation, and it reports values from each model used in interpolation, if “observed” peaks were available. *DIF_EST_MAX Estimated maximum values of each response for a unit wind speed from each direction. If obtained for some wind directions (by symmetry), then only the averaged results are report*DIF_EST_MIN Estimated minimum values of each response for a unit wind speed from each direction. If obtained for some wind directions (by symmetry), then only the averaged results are report*DIF_EST_MAX_ALL Estimated maximum values of each response for a unit wind speed from each direction. Alsymmetry are reported, with each tested wind direction resulting in results for four differdenoted Wind Direction A, B, C, and D. 

82
*DIF_EST_MIN_ALL 

Estimated minimum values of each response for a unit wind speed from each direction. Alsymmetry are reported, with each tested wind direction resulting in results for four differdenoted Wind Direction A, B, C, and D. *DIF_EST_MAX_BND This section is included only if the DIF results were obtained by interpolation, and it reports values from each model used in interpolation, if “estimated” peaks were available. *DIF_EST_MIN_BND This section is included only if the DIF results were obtained by interpolation, and it reports values from each model used in interpolation, if “estimated” peaks were available. *LOAD_DISTRIBUTION_MAX This section reports the load distribution producing the maximum observed value of each r

each wind direction. Load values are given for each index defined in the *ATTACHMENT_

and the units of these load values are given by the force units in the *UNITS section. If obtained for some wind directions (by symmetry), then averaged peak load distributions are *LOAD_DISTRIBUTION_MIN This section reports the load distribution producing the minimum observed value of each reach wind direction. Load values are given for each index defined in the *ATTACHMENT_and the units of these load values are given by the force units in the *UNITS section. If obtained for some wind directions (by symmetry), then averaged peak load distributions are *LOAD_DISTRIBUTION_MAX_ALL This section reports the load distribution producing the maximum observed value of each r

each wind direction. All results obtained by symmetry are reported, with each tested wind results for four different wind directions, denoted Wind Direction A, B, C, and D. Load valueindex defined in the *ATTACHMENT_LOCATIONS section, and the units of these load valu

force units in the *UNITS section. 

83
*LOAD_DISTRIBUTION_MIN_ALL 

This section reports the load distribution producing the minimum observed value of each reach wind direction. All results obtained by symmetry are reported, with each tested wind results for four different wind directions, denoted Wind Direction A, B, C, and D. Load value

index defined in the *ATTACHMENT_LOCATIONS section, and the units of these load valu

force units in the *UNITS section. *LOAD_DISTRIBUTION_MAX_BND This section is included only if the DIF results were obtained by interpolation, *LOAD_DISTRIBUTION_MAX values from each model used in interpolation, if load distributio*LOAD_DISTRIBUTION_MIN_BND This section is included only if the DIF results were obtained by interpolation, *LOAD_DISTRIBUTION_MIN values from each model used in interpolation, if load distributio

84
Time Series Output Files 

If “Display time series during analysis” is selected in the output options Figure 4, then resp

be saved through the graphical interface shown in Figure 5. Time series can only be saveone response at a time (each response can be saved in turn, if desired), and responses are for the four different wind directions obtained by symmetry (Wind Directions A, B, C, and dialog of Figure 16, the time series can be saved in one of two formats: in comma-delimited 

or in MATLAB format (*.mat). 

Figure 16. Dialog box for saving of time series. 

A portion of a time series output file in CSV format is shown in Figure 17. As shown, identwritten in header rows at the top of the CSV file. If the time series is saved in MATLAB format (*.mat), then the time series and identifying inin a structure array named “TS_structure” in a MATLAB file with the specified name. Thwithin MATLAB using the syntax shown in the following example: load 'TS_ADW100o100N018d0150_f1r1.mat' 

85
Figure 17. Portion of sample time series output file. 

The times series and identifying information given in the headers of the CSV file shown in 

in fields with the following names: 

TS_structure.HDF_filename 'ADW100o100N018d0150.HDF' (HDF preTS_structure.frame_label 'Frame 1: y = 18.75 ft' TS_structure.resp_label ‘Response 1: Moment at left knee (lb-ft)' TS_structure.n_s 49792 (Number TS_structure.theta_a 15 (Wind Dir TS_structure.theta_b 345 (Wind Dir TS_structure.theta_c 165 (Wind Dir TS_structure.theta_d 195 (Wind Dir TS_structure.ts_a [1x49792 double] (Time SeTS_structure.ts_b [1x49792 double] (Time SeTS_structure.ts_c [1x49792 double] (Time SeTS_structure.ts_d [1x49792 double] (Time Se

86
Mean Recurrence Interval (MRI) Output File 

The MRI output files contain the following sections. *UNITS Format and Purpose are the same as in the building input file. *BUILDING_DIMENSIONS Format and Purpose are the same as in the building input file. *MODEL_DIMENSIONS Format and Purpose are the same as in the DIF output files. *FRAME_LOCATIONS Format and Purpose are the same as in the building input file. *MODEL_TERRAIN Format and Purpose are the same as in the DIF output files. *RESPONSE_NAMES Format and Purpose are the same as in the building input file. *MRI_LIST Purpose: Define the Mean Recurrence Intervals for which peak responses where Format: One row with values in one or more columns giving the Mean Recurrence Intervals 

were requested. 

*MRI_MAX_OBS This section is included if “observed” peaks were available in the selected DIF file(s), and it values of each response quantity corresponding to the specified return periods, computpeaks. 

87
*MRI_MIN_OBS 

This section is included if “observed” peaks were available in the selected DIF file(s), and it values of each response quantity corresponding to the specified return periods, computpeaks. *MRI_MAX_EST This section is included if “estimated” peaks were available in the selected DIF file(s), and it values of each response quantity corresponding to the specified return periods, compute

peaks. 

*MRI_MIN_EST This section is included if “estimated” peaks were available in the selected DIF file(s), and ivalues of each response quantity corresponding to the specified return periods, compute

peaks. 

88
Appendix B: 

Notes for Installation and Use of HR_DAD, 

Database-Assisted Design Software for Flexible 

Buildings 

William P. Fritz

89
High-Rise Database-Assisted Design (HR_DAD) 

DAD Software for Flexible Buildings 

How to download and install the software:

The HR_DAD software has been developed using the MATLAB language and is available 

through the internet at <http://www.nist.gov/wind>. All 34 MATLAB files required to run the 

software are zipped into one file, HR_DAD.zip, for a single download. Simply download this zip 

file and copy the 34 files into a directory whose path is accessible by MATLAB. To run the 

software, simply type “HR_DAD” at the MATLAB command prompt, which runs the script file 

of similar name and opens ten figure files. 

Basics of using the HR_DAD_software:

The ten opened figure files (i.e., pages) are used to input the values for the required variables 

used by the HR_DAD software. All variables are initially assigned an empty set in the 

HR_DAD.m script file. Variable values can be assigned in any order in pages one through five. 

The variable names within the software are typically shown in parentheses before the input box 

on the page. In several instances, a saved MATLAB file is opened within a page to load 

variables that contain vectors or matrices. Purple help icons with a “?” sign provide the required 

variable name, the variable size, a description of the variable and the specific organization of the 

variable’s contents. 

Once the variables are assigned values by the user, the first portion of the HR_DAD program is 

run on page six. The results of this first run are saved at the location specified with the “Save As” 

button. Tables of peak wind effects must be saved and are used for the second portion of the 

program that calculates mean recurrence intervals of the wind effects. The results of run two are 

also saved at a specified location. Graphical output is displayed through page seven, which uses 

the Output figure file. Page eight allows the user to save the current variable set at any point in 

the assignment process or load a previously saved set of variables into the software. 

A wind speed database is required to estimate the mean recurrence intervals of the wind effect. 

The simulated hurricane wind speeds are available on the website. Simply save a file to the same 

location as the software and then specify its milepost in page five as the variable “Hmp”. These 

data are used in conjunction with the tables of peak wind effects in the second portion of the 

program. 

Examples for the HR_DAD software

Two examples are provided with the HR_DAD software: 1) a 66-story building with 

accompanying directional wind tunnel measurements and 2) a single-degree-of-freedom (SDOF) 

oscillator with a sinusoidal force. 

The first example illustrates the full use of the software. The example is downloaded in two 

stages. The first stage involves downloading the complete set of variables, which are contained 

90
in the zip file named “66-story Example.zip”. Once the files are copied to a location that is 

accessible by MATLAB, run HR_DAD and load the file called “Bldg66_122905” through page 

eight of the software (see Basics above). This updates all variable values and the displayed 

values within the pages. The second stage involves downloading the 36 files that contain 

directional wind tunnel measurements in 5° increments. These files are large and timeconsuming to download, but are necessary to estimate the mean recurrence intervals of peak 

wind effects. Note that the downloaded zip file contains results that do not need these large files; 

the wind tunnel measurements are only needed if the analyses are rerun. A subset of the 36 

pressure files can be used bearing in mind that the tables of peak wind effects are calculated for 

each wind direction (specified through the variable “WD” in page three) and that the directional 

extreme wind speeds (e.g., simulated hurricane wind speeds mentioned above) are interpolated 

among these tables of peak wind effects. Thus, the fewer wind directions used, the coarser the 

mesh of available peak wind effects and the greater the variability in the estimates of mean 

recurrence intervals. Further details are provided in Section 4.3.1 of this report. 

The second example illustrates the ability to easily manipulate the software and obtain a peak 

wind effect other than the interaction equation for individual members. This example is 

downloaded through the single zip file named “SDOF example.zip”. Once the files are copied to 

a location that is accessible by MATLAB, run HR_DAD and load the file called “sdof” through 

page eight of the software (see Basics above). This updates all variable values and the displayed 

values within the pages. As described in Section 4.3.1 of this report, the wind effect of interest is 

the maximum deflection of the single mass. This requires slight modification to the script file 

Program1.m: the maximum deflection should be calculated right after the equations of motion 

are integrated. 

91