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IVERSITY LIBRARIES

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This is to certify that the
dissertation entitled
Probabilistic Models to Represent

Loads Due To Human Activities

presented by
Bassem K. Khafagi

has been accepted towards fulfillment
of the requirements for

Doctor of Philosophy degree in Civil Engineering

Major professor

Mew

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LIBRARY
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TO AVOID FINES return on or before date due.

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PROBABILISTIC MODELS TO REPRESENT
LOADS DUE TO HUMAN ACTIVITIES

By

Bassem K. Khafagi

A DISSERTATION
Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Civil and Environmental Engineering

April 1993

 

 

 

ABSTRACT

PROBABILISTIC MODELS TO REPRESENT LOADS
DUE TO HUMAN ACTIVITIES

BY

Bassem K. Khafagi

Human loads are random and produce dynamic force components which cannot be
predicted with certainty. Current codes account for human loads by assuming a static load
equivalence that included the maximum dynamic effect of human movements. The
primary objective of this research is to generate probabilistic functions which accurately
represent the dynamic force caused by several human actions.

Measured data were obtained from three sets of experiments, two designed to measure
forces due to the action of an individual on a force platform; and the third designed to
measure the forces due to the action of a group on a floor system. The study included
six different in-place human movements grouped into two categories; transient motions
(single jump, standing up suddenly, and dropping into a seat), and periodic motions
(jumping, jouncing, and swaying side to side).

Transient actions were modeled by passing straight or curved lines through control points
that define the force-time history. Best-fit distributions for the control points were
determined. Model error was developed as a Gaussian random process and was
incorporated into the model to better represent the modeled actions. Periodic loadings
were analyzed as a series of cycles where each cycle is a full period of the motion
considered. The period and peak force ratio of each cycle were modeled as first order
autoregressive processes. Model verification was applied to the different motions
considered in the study. Stochastic models were compared with experimental data and
feedback from the process was used to refine the models.

A computer program; Human Load Simulation, HLS, was developed to simplify
generating load distributions for any combination of human loading conditions. Output
of the program includes the statistical parameters of the control points associated with the
time histories, amplitudes of peaks and their arrival time, spectral energy distributions for
periodic motions, and force—time history for each simulation. A modified version of HLS
was developed to simulate group loading conditions.

Several potential applications of HLS were presented. Code values were examined and
found to be acceptable except for the transverse force component where a value of 45
lb/ft was recommended to replace the current 10 lb/ft value in the code. An example
showing the advantage of using probabilistic loads was presented. Other potential
applications of the research outcome were discussed. It is anticipated that research
findings will have an impact on standards for structural design and serviceability control.

 

 

 

Copyright" by

BASSEM KAMAL KHAFAGI

April 1993

 

 

 

 

To Ekram,

Yasmeen, Louai, and ........

iv

 

 

 

ACKNOWLEDGE/IENTS

In the course of this project, I have received assistance in a variety of forms from
many pe0ple. I am indebted to them, and I wish to acknowledge this debt. My heartfelt
thanks to Professor W. Saul and Professor R. Harichandran for their cooperation,
enlightening advice and devoting part of their time to guide and help me to overcome the
difficulties I have faced during my research program; Professor T. Wolf, Professor F.
Hatfiled, and Professor G. Ludden, other members of my Graduate Committee, for their
recommendations and review of the dissertation; Special thanks go to Ahmad Al-
Ghamedi and Abdulrahman Al-Hadlag for their friendship and incessant help.

I am grateful to my enlightened parents who supported and encouraged me
throughout my education. Finally, I believe that God is behind any success I have

reached. So, my thanks to Him. .....

 

 

 

 

 

TABLE OF CONTENTS

LIST OF TABLES ..................................... viii
LIST OF FIGURES ....................................... x
CHAPTER 1.0 INTRODUCTION ............................. 1
1.1 General ...................................... 1

1.2 Problem Statement ................................ 2

1.3 Objectives of the Study ............................. 3

1.4 Research Description ............................... 5
CHAPTER 2.0 CURRENT STATE OF KNOWLEDGE ............... 8
2.1 Introduction .................................... 8

2.2 Literature Review ................................ 8

2.3 Current Project ................................. 14

2.4 Current Practices ................................ 16
CHAPTER 3.0 EXPERIMENTAL MEASUREMENTS .............. 18
3.1 Instrumentation ................................. 18

3.2 Data Collection ................................. 21

3.3 Data Processing ................................ 24

3.4 Statistical Output Summary .......................... 27
CHAPTER 4.0 MEASUREMENT ANALYSIS .................... 35
4.1 General ..................................... 35

4.2 Methodology .................................. 35

4.3 Transient Loading ................................ 39

4.3.1 Single Jump .............................. 40

4.3.2 Sitting Down ............................. 50

4.3.3 Standing Up ............................. 53

4.4 Periodic Loading ................................ 55

4.4.1 Periodic Jumping .......................... 57

4.4.2 Periodic Jouncing .......................... 63

4.4.3 Side Swaying ............................. 64

vi

 

 

 

 

CHAPTER 5.0 HUMAN LOAD MODELING .................... 67
5.1 Introduction ................................... 67
68

.................................

 

5 .2 Basic Concepts
5.2.1 Random Processes .......................... 68
5.2.2 Random Number Generation ................... 71
5 .2.3 Generation of Correlated Random Variables .......... 73
5.2.4 Monte Carlo Simulation ...................... 74
5.3 Transient Load Modeling ........................... 75
5.3.1 Mathematical Approach ...................... 76
5.3.2 Load Simulation ........................... 85
5 .4 Periodic Load Modeling ............................ 86
5.4.1 Stochastic Analysis ......................... 88
5.4.2 Load Modeling ............................ 92
CHAPTER 6.0 MODEL APPLICATIONS ...................... 95
6.1 Introduction ................................... 95
6.2 Group Simulation ................................ 95
6.3 Code Verification ................................ 99
6.4 Reliability-Based Design ........................... 102
6.5 Other Potential Applications ........................ 105
CHAPTER 7.0 CONCLUSIONS ............................ 107
7.1 Summary .................................... 107
7.2 Conclusions .................................. 109
7.3 Future Work .................................. 110
APPENDIX A DATA PROCESSING PROGRAMS ................ 112
APPENDIX B LOAD SIMULATION PROGRAMS ......... . ...... 159
LIST OF REFERENCES ................................. 186

vii

 

 

Table

2.1
2.2
2.3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17

Lainipioi-u

LIST OF TABLES

Periodic actions ..................................
Representative activity and their applicability to actual structures .....
Bounds for Natural Frequencies of Structures subject to Human Loads . .
Transient Data-base .................................
Periodic Actions Data-base ............................
Typical Output Files from "DATA.FOR" ...................
Output summary of Single Jump (One~Individual) ..............
Maximum Force Ratios (Single Jump) .....................
Peak Statistics for Floor System Data ......................
2 Hz.—Periodic Jumping Peak Analysis .....................
Human Movements Considered in The Study .................
Human Movements Considered in The Study .................
Control Points for Single Jump ..........................
Single Jump Control Points Statistics ......................
Correlation Matrix (Single Jump) ........................
Best-Fit Distributions (Single Jump) .......................
Sitting Down Control Points Statistics ......................
Correlation Matrix (Sitting Down) ........................
Best-Fit Distribution (Sitting Down) .......................
Standing Up Control Points Statistics ......................
Best-Fit Distribution (Standing Up) .......................
Correlation Matrix (Standing up) ........................
2-Hz. Periodic Jumping ..............................
Peak Analysis (Periodic Jouncing) ........................
Control Points Statistics (Periodic Jumping) ..................
Periodic Jouncing Statistics (One Individual, 2 Hz.) .............
Max. Peaks (Side Swaying) ............................
Typical Side Swaying Data ............................
Measured Versus Simulated Control Points for Single Jump ........
Measured Versus Simulated Control Points For Sitting Down .......
Measured Versus Simulated Control Points For Standing up ........
Periods and Peaks for a Typical Periodic Jumping ..............
Constants a1, and aT for the Periodic Motions .................

viii

14
17
22

33
35
37
44
46
47
5 1
52
53
54
54
55
57
61
63
63
66
67
67
87
88
89
94
95

 

 

Table Page
5 .6 Measured Versus Simulated Data (Periodic Jumping) ............. 95
6.1 Measured Versus Simulated Maximum Force Ratios ............. 98
6.2 Measured Versus Modified Simulated Maximum Force Ratios ....... 100
6.3 Dynamic Force Ratios for One Individual ................... 104

 

 

 

Figure

1.1
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8

 

 

LIST OF FIGURES

Page
Human Loads As Static and Dynamic Forces .................. 2
View of the Force Platform, Saul et. a1. ( 1990) ................ 19
The Floor System Lab, Saul et.al. (1990) .................... 20
Human Load Experimental Data-base ...................... 21
DATA.FOR Flow Chart .............................. 24
Force Type History (DATA.FOR Screen Output) ............... 27
Spectral Analysis (DATA.FOR Screen Output) ................ 27
A Typical Force-Time History (Floor.For Output) .............. 31
Mean, Min, Max Peaks For 2 Hz. Periodic Jumping ............. 33
Log-Linear Regression Model ........................... 34
A Single Jump .................................... 38
Control Points for A Single Jump ......................... 39
Control Points for a Periodic Motion ....................... 39
A Typical Single Jump ............................... 41
Best-Fit Distribution for Response Lag ..................... 50
A Typical Sitting Down Motion .......................... 53
A Typical Standing up ............................... 55
A Typical Periodic Jumping ........................... 59
Control Points for a Typical Periodic Jumping ................ 6O
CONTROLFOR Output (Periodic Jumping, 2 Hz. , Parallel Ratio) . . . . 62
CONTROLFOR Output (Periodic Jumping, 2 Hz., Vertical Ratio) . . . . 62
A Typical Periodic Jumping Response Period ................. 64
A Typical Periodic J ouncing ............................ 65
A Typical Swaying Side to Side .......................... 66
Typical Samples in the Random Process F(t) .................. 71
HLS Screen Output (Single Jump, One Individual) .............. 78
HLS Screen Output (Sitting Down, One Individual) .............. 78
Error Function (Single Jump, One Individual) ................. 82
Error Spectrum (Sitting Down, One Individual) ................ 82
Straight and Curved Lines of Single Jump Model ............... 83
Single Jump Error Function, b = 0.73 Hz. ................... 85
Single Jump Error Function, b = 0.36 Hz. ................... 85

 

 

 

 

Figure Page
6.1 A Typical GROUP.FOR Output, 10 Individuals ................ 99
6.2 A Typical GROUP.FOR Output, 40 Individuals ................ 99

xi

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1.0 INTRODUCTION

1.1 General

Human loads are random and therefore cannot be predicted with certainty. In
addition to the forces due to static weights, the movement of persons produces dynamic
force components. Human loads vary from event to event in an apparent pattern and
therefore it was postulated they could be shown to obey the laws of probability and hence
would be predictable. In addition to many other possible applications, these loads are the
primary concern in the design and analysis of assembly structures. A challenge a
structural engineer faces is how to quantify the uncertainty associated with loads due to
, human movements and provide corresponding measures to assure safety and serviceability
of the structure at a reasonable cost. This was the initial motivation for attempting to
provide procedures for generating functions to represent forces due to human movements.

When a person on a horizontal surface is absolutely motionless a vertical force is
brought to bear on the support due to gravitational acceleration acting on the mass of the
person's body, the weight of the person, as shown in Figure 1.1.a. The value of the
static force could be predicted by a probability distribution model of the individual
weights of a population sample of pe0p1e. When activity takes place, such as jumping,

sitting down, or swaying, there are resultant vertical and horizontal forces which fluctuate

  
  

ith time due to the changing acceleration of the person's mass, as illustrated in Figure

 

 

 

2

1.1.b. The vertical component of this force varies from zero to several times the
person's weight. Horizontal components do not exist in the static situation. The time
variation for any one of various human actions, for instance a single jump in place,

provides a pattern characteristic of that action. Similar to the distribution model for

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

No Force
Force
Time Time
Force Component h the x-dlr Force Convonent h the x-dlr
Face NoFOmQ Rm W
Tune Tune
ForceComponenthmey-dlr ForceComponenthuIey-dlr
Time Time
Force Component h the z-dk Force Component in the z-dlr

Figure 1.1 Human Loads As Static and Dynamic Forces

  
  
  
 
 
  
  

 

predicting the weight of an individual in a group of people, the parameters defining the
characteristic pattern of a force due to a human action vary randomly within the bounds
of distribution models.
1.2 Problem Statement

For the design of structures to avoid catastrophic failure, the uncertainty of human
oads was Traditionally accounted for by assuming a static load equivalence that included

e maximum dynamic effect of human movements. Recent incidents of occupant

 

 

 

 

3

discomfort, and strong vibration of assembly structures, Bachmann (1992), have
reinforced the need for quantification of dynamic human loadings. In recent years,
researchers have been utilizing probabilistic methods to model loads and calculate the
probabilities associated with combined load effects. A number of investigations have been
conducted on human loads variabilities which have resulted in several important
achievements, Allen (1990), Bachmann (1992), and Murray (1991). However, up until
this study, no satisfactory method existed for determining the statistics of the dynamic
load one person in a group would generate when performing various types of human
movements.
The focus of this study is the modeling and analysis of human loadings to include and
quantify their random nature. The impact of the research on the evaluation of safety of

assembly structures and determination of design loads and load combinations in building

  
 
  
  
  
  
  
  
  
  

codes is summarized.

1.3 Objectives of the Study

 

The primary objective of the research is to generate probabilistically-based functions
which will accurately represent the dynamic force pattern and values caused by several
types of human actions. The force due to each person in a group of n persons is of the
form {F(t)} where F,(t) represents a single force and i = 1, 2, 3, . . . ,n. The parameters
ceded to generate these probability-based-functions will be determined utilizing measured
alues. Data from tests conducted by the author are supported with data from earlier

tages of the research. The force functions produced will represent the dynamic load of

 

 

 

 

 

 

 

 

 

4

an individual in a crowd of people who are also active. With accurate correlations, the
entire group action will then be modeled with a matrix of discrete forces.

In addition to the interest in having these forces derived and available, there are a

number of ancillary objectives which will have benefits and future possibilities:

I The models will be especially important in cases where sustaining human loading
is the primary purpose of the structure such as stadium or grandstand seating. In
these cases the models would be valuable for design and analysis.

I The models may be used to determine limits or maxima; for example, for the
verification of specific building code values which are based on avoidance of
catastrophic failure. The code values used in the design of grandstand seating
areas, such as for stadium design, will be derived and compared with published
code values for verification.

I The models provide for the ability to conduct simulations to study any of a
number of possible events. An example is the post-elastic response of a
grandstand element subjected to a person jumping on it.

I The models are valuable for reliability-based design methods where the design
input needs to be probabilistically presented.

I The load models may eventually have a major impact on standards for structural
design such as those produced by ANSI, the American National Standards
Institute, from which many building codes are derived.

I The models will be necessary for the design of active controls to minimize

vibration of structures subjected to human movements. Accurate definition of

 

 

 

 

 

 

 

5

time-varying forces where humans are the primary source of the forces, such as
for the design of stadiums, are essential for providing active damping of the
structure.

I The models may be used to define parameters, such as acceleration, based on
serviceability of the structure. Serviceability criteria should be a requirement for
acceptable design.

I It is expected that the process evolved in developing the load models will provide
a methodology for extending the list of models to additional human actions such
as for aerobics, climbing or descending stairs, and the " heel drop" test.

I The models and the methodology should provide the insight needed to extend

definitions of load functions to forces from actions due to persons moving such as

dancing, walking or marching.

 
  
  
  
  
  
  
  

1.4 Research Description

The load modeling of human movements was accomplished through four tasks:

a) Experimental measurements: Force histories from tests performed on a small force

 

platform and on a large floor system were used to statistically characterize dynamic

loading due to human activities.
b) Model identification: Digitally recorded responses due to specific motions were

eviewed to obtain all available information on how the force histories are generated and

hat factors affect the shape and magnitude of the generated force .

 

 

 

 

m'fid” L L
__-__r.

 

6
c) Load Modeling: The experimental data were analyzed and inferences were made

regarding parameters needed to develop the load models. Modeling methodologies are
presented along with detailed procedures for simulating the different human actions
considered in the study.
(1) Model verification : The proposed models were used to generate extensive load
histories which were compared statistically to the measured test data. The intent of the
process was to reveal inadequacies of the model and therefore, through iteration, improve
the proposed model.

This dissertation is organized in the following parts:
Introduction (Chapter 1.0): It is a condensed outline of the topics herein, defined and
more fully explained in the main body of the dissertation. It is intended as a broad
mapping of areas covered by the research.
Current State of Knowledge (Chapter 2.0): A detailed review of the current state of
knowledge in the field of modeling human loads is presented. Earlier development of the
project of which this research is part of is outlined. The chapter also includes an
overview of current practice in the design process and how the present U. S. codes
characterize human loads on assembly structures.
Experimental Measurements (Chapter 3. 0): An overview of procedures of data

ollection, the experimental setup, data manipulation, and data representations is

  
  
   
 

resented. Computer programs were developed to automate the process of converting
aw voltage data into time-force histories. Data available from earlier measurements

ere utilized as well as data from new tests.

 

 

 

 

 

 

7

Measurement Analysis (Chapter 4. 0): For each human movement type chosen for the
study, the forcing function model is hypothesized. The parameters needed to define each
motion are evaluated and analyzed statistically.

Probabilistic Load Modeling (Chapter 5.0): The chapter describes an iterative model-
building methodology whereby the stochastic models introduced in Chapter 4.0 are related
to actual time series data. The process of model verification was applied to the different
motions considered in the study. A model to simulate group loading is provided. The
developed forcing functions are compared with experimental data. Feedback from this
process is used to refine the forcing functions.

Model Applications (Chapter 6. 0): The impact of the research findings on the current
state of knowledge is described. Several Applications showing the use of the Human
Load Simulation program, HLS, are developed from the study. Recommendations on
handling dynamic human loads in the design stage are presented.

Conclusions (Chapter 7. 0): A summary of the research along with the major findings
and conclusions is presented. The chapter also includes recommendations for designers
and code agencies for incorporating research findings in future reliability-based-codes.

A list of tasks for future research is outlined.

 

 

 

 

. .~.---‘~.;v‘
mum- ' -

 

2.0 CURRENT STATE OF KNOWLEDGE

2.1 Introduction:

In this chapter, a detailed review of the current state of knowledge in the field of
modeling human loads is presented. First, an overview of the history of measuring force
parameters of human loads is demonstrated. Then earlier deve10pment of the project of
which this research is part of is outlined. Finally, the chapter outlines the current

practice in both the design and analysis phases that relates to human load modeling.

2.2 Literature Review

Studies of human live loads, from before the turn of the century, have been reported
in depth by Saul and Tuan (1986). Tilden (1913) is the first person reported to have
measured the parameters of forces due to human movements; his work formed the basis
for the parameters used in present day building codes for grandstands and similar places
of assembly. Much of the intervening work focused on finding the statically equivalent
code values used for design today (ASA 1941). A series of incidents involving the
collapse of portable grandstands in the early 1920's led to tests conducted under the
supervision of the American Standards Association (now American National Standards

Institute) to measure horizontal forces exerted by spectator movements. Other code

 

 

 

9

associations adopted the design values recommended by the American Standards
Association Committee in 1941, and the values remain the same today. These tests
focused on determining the upper bounds forces and neglected dynamic content.

Bachmann (1984) examined the hypothesis that resonance behavior in a structure can
be avoided if its natural frequency is higher than that of the forcing frequency and
discovered that the assumption is not always correct. He found that lightly damped
structures may be forced into significant resonance if their natural frequency is an integer
multiple of the forcing frequency. A case study of a gymnasium where vibrations with
large amplitudes due to resonance occurred at twice the forcing frequency is discussed
in detail in his paper. He proved that the second and third harmonic of the forcing
frequency may produce significant dynamic loading.

Allen, et al (1975, 1982,1987) found that although structures in most cases were built
to code, serviceability problems such as unacceptable vibrations due to occupants'
movements occur. They related structural resonance to thirteen cases of serviceability
problems caused by dancing, spectator activity at rock concerts, aerobics, exercising, and
walking. Their studies were concerned with response of the structure and gave negligible
treatment to the input function. Greimann and Klaiber (1978) generated a continuous
forcing function to successfully model a resonance condition caused at Iowa State
University stadium by spectators moving together on a grandstand.

Tuan and Saul (1985) focused upon measuring the loads produced by an individual
performing prescribed maneuvers on a small force platform. The loads produced by an

individual performing prescribed maneuvers measured on a small force platform were

 

 

 

10

categorized and some statistical analyses were done on the data to produce tentative load
functions. The research was continued by McDonald (1984) who designed and
constructed a 4 by 8 foot force platform for measuring loads produced by up to five
people. The platform was used to acquire data for actions due to one or more persons.

Ebrahimpour (1989) , proposed group forcing functions to produce an equivalent
vertical dynamic load to be compared to code presented values. A sinusoidal Fourier
series was used to describe the total force developed by a symmetrically placed group of
people jumping in unison at a fixed rate. VanKleek (1988), constructed and instrumented
a 12 foot by 15 foot floor system to accommodate up to 40 people. The floor system was
used to obtain experimental measurements and test the accuracy of the group load model
pr0posed by Ebrahimpour. Statistical modeling was performed for periodic jumping
conducted at frequencies of 2 and 3 Hz and also for a single jump. The results showed
that for the specific conditions of the test, the equivalent maximum uniform floor load
approached an asymptotic value comparable to the code value.

Rainer, et a1 (1988), investigated the dynamic loading and response of footbridges
using a force platform and asking individuals to walk or run along the span at a
predetermined pulse rate. They concluded that for walking, running, and jumping, the

excitation force can be represented as F(t):

N
F(t) = P [ 1 + E ansin(2mtfi + 91.)] .......... [2.1]
n=l

where:

P = static weight of a person; a = Fourier amplitude or coefficient;

 

 

 

 

 

11

n = harmonic order of footstep rate; = footstep rate in steps per second;
t = time in seconds; ¢ = relative phase angle; and
N = total number of harmonics.

Allen (1990) introduced some revisions to the Canadian Building Code design criteria

Table 2.1 Periodic actions*

 

3.; .;.;.

 

 

 

I Walking I Footbridges
I Running , I Office buildings
I Jumping I Gymnasia and sports halls

 

I Dance and concert balls with no fixed
I Dancing seating

 

I Hand clapping with body bouncing while
standing I Concert halls with fixed seating as well

I Hand clapping only as galleries

 

 

I Lateral body swaying while seated or while
standing I High-diving platforms in swimming pools

 

 

 

 

" Afler Bachmnn (1992).

for floor structures to reduce building vibrations due to human activities. He studied a
number of recent vibration problems in concrete building structures due to dancing and

aerobics exercises and suggested the following design criteria for minimum natural

 

 

frequency:
f 2 f 1 + 1.3 . E22 ............... [2.2]
O ao/g to
where:
= forcing frequency; a = natural frequency of the structures;

 

 

 

l2
a/g = acceleration ratio; o ---= mass weight; and
a», = Weight of the person. a = dynamic load factor

He recommended increasing the factor (1 .3) to (2.0) in the case of aerobics activities.

Considering the problem of floor vibrations, Murray (1991) provided a methodology
for controlling annoying floor movement in residential, office, commercial, and
gymnasium type environments. His criteria states that the motion of floor systems would
not be objectionable to occupants of residential and office environments if the following

inequality is met:

D > 35 A0 f + 2.5 ................. [2.3]

where D = damping in percent of critical, A, = maximum initial amplitude of the floor
system due to heel-drop excitation (in.) defined as the force by a person standing on the
toes and dropping suddenly from that position, and = first natural frequency of the floor

system (Hz). For commercial environments (such as shopping centers), the criteria is

 

based on an acceleration tolerance limit of 0.005 g due to walking excitation so that
maximum deflection under 450 lbs. force applied anywhere on the floor system does not
exceed 0.02 in. Murray (1991) confirmed the usefulness of Eq. [2.2] proposed by Alan
(1990), to be used for gymnasium environments.

Bachmann (1992) suggested the following function for the dynamic forces due to

rhythmical body motions shown in Table 2.1:

 

 

 

 

 

13
Fp(t)=G+AGlsin(2rrj;t)+Astin(41tj;t-<p,) +AGssin(6nj;t-tp3) +....... - [2.4]
with:
p = fundamental frequency of excitation (frequency of the motion, i.e. frequency of

walking, running, jumping, dancing, etc.), G = weight of person in motion, AG,- = part

Table 2.2 Representative activity and their applicability to actual structures’“

 

   
 

 

 

 

 

 

 

 

€932;
vertical 2.0 0.4 0.1 102 0.1 1112
2.4 0.5 ~ 1
forward 2.0 0.5(0t,,=0.1) 0.2
lateral 2.0 OLA—=01 (1,150.1
Running 2.0-3.0 1.6 0.7 0.2 -
Jumping normal 2.0 1.8 1.3 A 0.7 A in fitness training ~0.25
3.0 1.7 1.1 A 0.5 A (in extreme cases up to 0.5)
high 2.0 1.9 1.6 A 1.1 A A: (92 = q” = "(I ' f't’)
3.0 1.8 1.3 A 0.8 A
Dancing 2.0-3.0 0.5 0.15 0.1 ~4Qn extreme cases up to 9
Hand clapping with 1.6 0.17 0.10 0.04 no fixed seating ~4
body bouncing while (in extreme cases up to 6)
standing 2.4 0.38 0.12 0.02 with fixed seating ~2 to 3
Hand clapping normal 1.6 0.024 0.010 0.009
2.4 0.047 0.024 0.015 ~ 2 to 3
intensive 2.0 0.170 0.047 0.037
Lateral body seated 0.6 (1,504 - -
swaying ~ 3 to 4
standing 0.6 0.50.5 - -

 

 

 

 

 

 

*Afler Bachmann, (1992).

of force of the i—th harmonic with i=2,3,. . .. (Fourier amplitudes), (p,- = phase lag of the
i-th harmonic relative to the first harmonic. Table 2.2 shows the characteristics of
representative human load dynamic forces as published by a working group of the

Comité Euro-International du Béton (CEB).

 

 

 

14
2.3 Current Project

The current field of research started in 1983 with a study to determine the sources
and accuracy of building code prescribed load values for the design of stadiums. The
research focused on live loads due to human movements on assembly structures such as
grandstands, stadiums and bleachers. It was found that present codes are based on
experience and tests conducted around 1930 to satisfy safety criteria, i.e. , the avoidance
of catastrophic failure, due to live loads. These loads are presently specified in various
building codes as statically equivalent forces having a uniform vertical load over the
surface plus three components along the seats (one vertical and two in the horizontal
plane, one along the seats and the other perpendicular to the seats). Ignoring the dynamic
effect of human loads on assembly structures has led to vibration and serviceability
problems in some modern assembly structures. A fairly complete history of U.S.
practice, code sources, and background on the issue has been compiled and published by
Saul and Tuan (1986).

The loads produced by an individual performing prescribed maneuvers was measured
on a small force platform, Tuan (1983) and Tuan and Saul (1985). The maneuvers were
categorized and some statistical analyses were done on the resulting data to produce trial
model load functions. The research was continued by McDonald ( 1984) who designed
and constructed a 4 foot by 8 foot force platform for measuring loads produced by up to
five people. The platform was used to acquire additional data for actions due to one or
more persons. This data was used to develop a preliminary model to describe loads due

to a crowd of people. Descriptive random parameters were defined for periodic jumping,

 

 

 

 

15

periodic jouncing, and single jumps. A sinusoidal series was used to describe the total
vertical component force developed by a symmetrically placed group of people jumping
in unison at a fixed rate, Ebrahimpour (1987).

The objectives of the second phase of the study were to measure dynamic loads
generated by large groups of people performing coherent movements and to test the
accuracy of the analytical load model derived earlier in the project.

VanKleek (1988) constructed and instrumented a 12 foot by 15 foot floor system to
accommodate up to 40 people. The stiffness, mass, and damping matrices of the floor
system were determined. The floor system was used to obtain experimental
measurements and test the accuracy of the group load model proposed by Ebrahimpour
(1987). Load tests were conducted with groups of 10, 20, 30, and 40 participants.
Statistical modeling was performed for periodic jumping conducted at frequencies of 2
and 3 Hz and also for a single jump. The load-time histories were determined and
comparisons were made between computed and measured results.

The results showed that for the specific conditions of the test the equivalent maximum
uniform floor load approached an asymptotic value comparable to the code value. Also,
it was found that the average deviation between measured and simulated values was less
than 8%, Ebrahimpour and Sack (1989).

The preceding research projects provided extensive data and led to the hypothesis that
forces due to the various human actions may be accurately modeled as probabilistic
functions. These functions would be very valuable analytical tools for further and

extensive research on projects involving such forces.

 

 

 

 

 

16
2.4 Current Practice:

The 1982 Edition of the Uniform Building Code defines Assembly Structures as:
"A building or a portion of a building used for the gathering together of 50 or more
persons for such purpose as deliberation, education, instruction, worship, entertainment,
amusement, drinking or dining or awaiting transportation", UBC (1982). The code

suggests using a uniform static vertical live load of 120 pounds per linear foot of seating,

Table 2.3 Bounds for Natural Frequencies of Structures subject to Human Loads

 

 

 

 

 

 

 

 

 

 

Footbridges 1.6 to 2.4 Hz and 3.5 to 4.5 Hz to be avoided
Office buildings > 4.8 Hz (C > 5%) and > 7.2 Hz (C < 5%)resp.
Gymnasia and sports halls > 7.5 Hz > 8.0 Hz > 8.5 Hz > 9.0 Hz
Dance and concert halls > 6.5 Hz > 7.0 Hz > 7.5 Hz > 8.0 Hz
without fixed seating

Concert halls and theaters Vertical: > 6.5 Hz

with fixed seating (incl. Horizontal: > 2.5 Hz

pop concerts)

 

 

 

lateral sway bracing loads of 24 pounds per foot parallel to the seating and 10 pounds per
foot perpendicular to seat and footboards for grandstands, reviewing stands, and
bleachers. It also recommends using a uniform vertical live load of 100 pounds per
square foot for assembly structures with moveable seating.

A design criteria for assessing the acceptability of floor structures subjected to human
periodic movements was introduced into the Commentary to the 1985 National Building

Code of Canada.

 

 

 

 

 

 

l7
Bachmann (1992) showed that rhythmical human body motions can induce

considerable dynamic forces on assembly structures. Table 2.3 presents bounds for the
natural frequency of structures subject to man-induced vibrations to reduce the probability
of resonance when the forcing frequency approaches the natural frequency of a structure.

In general, recent studies to include the dynamic effect of human loads represents an
advance in representing the effect of human loads. However, work was needed to derive
load models that simulate different human movements as sole individuals or as individuals
in a group. This research takes a fundamental look at the problem of modeling individual

forcing functions and characterizing the correlation between individual forcing functions.

 

 

 

 

 

3.0 EXPERIIVIENTAL MEASURENIENTS

3.1 Experimental Devices
The goal of the experimental measurements was to accurately measure dynamic force
components due to specified human activities. Data taken from tests performed on a

force platform and a floor system were obtained from three sets of experiments, two

 

Figure 3.1 View of the Force Platform, Saul et. al. (1990)

designed to measure forces due to the action of an individual; and the third designed to
measure the force due to the action of a group. Two different test devices were utilized.
One was a 4 ft by 8 ft force platform designed and instrumented as described by

McDonald (1984) and Ebrahimpour and Sack (1988) used for measuring the vertical and

18

 

 

 

19
horizontal components of loads produced by individuals and small groups up to five

participants, Figure 3.1. The platform has an approximate fundamental natural frequency

 

Figure 3.2 The Floor System Lab, Saul et.al. (1990)

of 20 Hz. which provides a flat transfer function so that imposed loads are transmitted
to the sensors without distortion in the frequency range of the load; this is essentially the
definition of a force platform. The platform is supported vertically by five transducer
assemblies (load cells), and horizontally by three in each direction.

The other device, as shown in Figure 3.2, is a 12 ft by 15 ft floor system designed
to measure total vertical loads generated by a group of people, up to forty participants,
Ebrahimpour (1989). The floor system has a fundamental frequency of about 26.4 Hz and
was instrumented with load cells and linear variable differential transformers (LVDTs)
to measure the vertical component of human loads,Vankleek (1988). More detailed

information on the data acquisition hardware is provided by Sack and Ebrahimpour

(1988), and Burke et. a1. (1985).

 

 

20

Data-Set N0. 1

 

 

 

[101

[85]
Transient Periodic dom
Single Jump Penodc Jumping Random Jumping
[26] (431 [121
L l i
1-Person 2-Persons 5—Persons 1-Eerson 2-Persons
[10] l§L El [5]
1 arson 2-P ersons anions
[$01 1201 [91
l l T T l 7
1 Hz 2 Hz 3 Hz 5 Hz 1 Hz 2 Hz 3 Hz 5 Hz
[5] [51 1'5) 15] [21 (2] [21 171
m. 2‘... l... in.
[51 [51 [5] l5]
Data-Set N 0. 2
13511
J
Transient Random Jumping PerLdle
I154: I391 [“181
L
Single Jrimp Sitting down Standirjg up 114:: 2-Per.r(s) 4901(5)
[58] 1481 1481 l 191 15]
1-Per. 2-Per. (s) 4-Per.(s) 14:1“ 2433“! s) 44394, 5)
1451 I91 [41 I351 191 I41
1 , —Per. 5) 4-Per.(s)
[351 [4]
Jam rrig Jouncing Shalying
[1 81911“! (“I41
F I l T It 4H1l l l
2 Hz 3 Hz 4H: 3 Hz 4 Hz

 

 

 

 

 

 

 

 

 

 

 
 
   

 

 

 

 

 

 

 

[5°] [49] [49]

1-Per. MZ-PerSs). 4—P‘esr)(s) hiflZ-Pl 5) 44°19?) l——T—_——‘|l‘———1—-—l 1-Pelr Mtg} 4—Per(s)

1-gerj 2-Per(s) 4-Per(s).1-Per2-Per(s).4-Per(s).1-Pler. 2—Per(s). 4vPer(s) 1-Pler. 2-Per(s)4-Pen(ls)

 

r481 :48:

[49]
931.243 s). 4-P Ws)|p£—1——j1-PerJZ-Pegsl Mafia)

 

Data-Set N0. 3
[11"]
V V 1
sale are warm
1 I i l T
14’ . 9-P . 10-P . 20-P . 30«P .
[546]! [9? (s) [631(5) [1 8elds) [g]! (S)

 

Figure 3.3 Human Load Experimental Data-base

40-Per.(s)
151

 

 

 

 

 

21

In contrast to the force platform which by definition is designed so that input equals
output, the floor system is modeled as a nine-degree of freedom vertical dynamic system

where the output is read as vertical displacement of the floor.

3.2 Data Collection

Dynamic human loading can be categorized as transient, periodic, and random.
Transient loads are temporary non-repetitive loads from which the structural response is
damped out before the next transient action is expected to occur, McDonald (1984).
Types of transient actions could include a single jump, suddenly standing up, or falling
into a seat. Human load modeling in this

study is limited to the transient and

 

 

periodic motions.

 

 

 

 

 

 

 

 

 

1 45
As illustrated in Figure 3.3, large
Single Jump 2 19 74
number of tests, were conducted on both 4 4
5 6
the force platform and the floor system for
1 35
individuals and groups of up to 40 Sitting down 2 9 48
participants. Prerecorded pulses (prompts) 4 4
were played at the desired rate through Standing up 1 35 48
2 9
loud speakers, and the participants were 4 4

 

 

 

 

 

requested to perform a specific action at
the pulse rate. The output from these tests were utilized to derive and verify the

individual and group effect of human movements. Table 3.1 summarizes the collected

 

 

 

 

 

 

22

transient actions by the type of action (single jump, sitting down, and standing up). In
Table 3.2, the periodic actions are categorized by the stimulus frequency for the motions

in the study (jumping, jouncing, and swaying).

Table 3.2 Periodic Actions Data-base

 

 

 

 

23

LSelect motion I<

L
Iread parameters I

L
+I New File I
l
I Read Raw Data ]
I
I Find Force-Historiesj

 

 

 

 

 

 

 

 

 

 

 

N0 Motion is No
Periodic Transien Random

 

 

 

 

 

 

 

I Find Peaks I I Find Max. Peak I
J

r { Compute Statistics I‘
l

I Save forces I
We w

L Plot Forces I
L

 

 

 

 

 

 

 

 

 

 

 

Calculate Autocorrelation
and Autospectra

I Plot Spectra I
T

—>I Save to Output I

 

-———>J

 

 

 

 

 

 

 

No

 

 

 

 

 

(Save Statisticsj
I

 

 

Calculate Average
Spectral Data

 

 

 

 

ast No
Motion

Figure 3.4 DATA.FOR Flow Chart

 

 

 

 

 

24
3.3 Data Processing

The raw data was collected in digital format as voltage readings. To use this data
for the development of load models, a FORTRAN program, "DATA.FOR" was
developed. For each motion type, the program reduces the transducer data into force—
time series in the three principal axis of motion; vertical, and two perpendicular
horizontal components Then the program calculates the statistical parameters of each
force history, plots the forces in the three directions, computes and plots autocorrelation
and autospectra for periodic motions, and calculates the average autocorrelation and
average autospectra for force-time histories considered in the analysis. A listing of the
program is included in Appendix A. Figure 3.4 is a flow chart to illustrate the
components of the program "DATA.FOR".

Input to the data processing program consists of three sets of files; a) raw data files,
b) processing files, and c) calibration files. The raw files contain the voltage readings
and information about the type of test, weight of person or persons performing the
experiment, and time and date of the test. The processing files include "PARAM.DAT"
which is a collection of parameters needed to process the raw data and to compute the
statistical and spectral information. Font files which were needed to plot graphs on the
monitor are also a part of the processing files set. Calibration files hold the calibration
factors needed to convert voltage into forces. These calibration factors were computed
in an earlier stage of the research project and the process of obtaining these factors are

documented in Ebrahimpour (1988), and VanKleek (1989).

 

 

 

 

 

25

The program saves the computed statistical information and spectral analyses in

separate files which have the same file names as the raw data, but with different

 

    

 

 

 

 

 

 

 

 

l SJT1A010.FRC Force Forces in the x1, and 2 directions

2 SJT 1A010.ACN Autocorrelation Autocorrelation for XJ, and 2 directions
3 SJT1A010.ASP Autospectra Autospectra for the three directions

4 SJ-SUMM.OUT Final output Statistical information

5 SJ—AVG.ACN Correlation When more than one file grocessed

6 SJ—AVGASP Spectra When more than one file processed

 

 

 

 

 

extensions. For example, a raw data file name "SJT1A010.RAW" which contains data
from a single jump (SJ) performed as a transient action by one person (Tl), from data
set (A), and was saved as test number (010) of the raw data collection (.RAW) would
produce the files shown in Table 3.3 when processed by the program "DATA.FOR":

Output to the monitor is composed of force-time plots and spectral analysis plots (for
periodic actions). Figures 3.5 and 3.6 are views of typical output from DATA.FOR.
Maximum peak values in the three perpendicular axis and the weights of the participants
are among the statistical information reported on the figures.

The vertical forces measured using the floor system were computed from transducers
voltages using the Fortran program "FLOOR.FOR". The listing of the program is
provided in Appendix A. The program provided an effective and accurate method to
process the test data gathered from the floor system. The procedure employed in the

program to convert LVDTs voltage readings to vertical forces is explained in detail by

 

 

 

 

 

 

26

 

DATAF O R Output

 

 

 

 

 

   

 

 

 

 

 

 

 

 

 

 

 

FXAS A name to WEIGHT w as A RATIO ro wsraur
.30 .08
r: .25 F .04
O O a
2 3° 2 a
E .15. E .00 .
n '10 n on
A ~05. A. '
.7 .00' '7 '-°‘
0 .35 0 “£3
-.10 -.09
as. -.10.
FILE I PJ318002.RAW WITH 1 PER.
F
g PERIODIC MOTION - PJ TEST - 002
E l Q ; weights - 140. 0. 0. 0. 0.
n ,5 g g Total-- 140. ES'rrrtxrz- 143.17 lbs
A ‘ 'i i l i
1T ' ' m ' 3’ L” " 6 or 15 max ram:
0 " LUII L X-dir .316 3.912
Y-dir -.090 3.610
30 do Z-dir 3.134 3.618
TlMEUN-I 211' marooottrnru....

 

 

Figure 3.5 Force Type History (DATA.FOR Screen Output)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

DATA. F O R Output
SPECTRAL ANALYSIS
AUTOCORRELATION AUTOSPECTRUM
1.00 1.29 _
.eo«
1.00«
f: a
t c .901
3 -40‘ 5
o .
1 .201 ' .601
f 0
3 .00" 3
i s .40«
l
:3. -.20- ;
.zoi
’-“°I
.o 20.0 :0? 303 33.070110 120.0 .000 rfo in 3:0 {.0 6.0 do 7:0 $5.0 3:01:10
Les Fmfl-ltl
FILE: PJ313002 HMS: 1.1612 FEAK: 3.18 MEAN: .06

 

Figure 3.6 Spectral Analysis (DATA.FOR Screen Output)

 

 

 

 

 

 

 

 

 

27

VanKleek, ( 1988). The floor system was modeled as a nine degree-of-freedom system

and the program FLOOR.FOR was used to solve the following equation of motion:

mm [M] [A] + [61m + [K] [x] -------- [3.11

where :

FM : applied nodal force vector

M9,, : mass matrix AM : acceleration vector
C9,, : damping matrix V9,, : velocity vector
K M : stiffness matrix 179,, : displacement vector

LVDTs Readings were converted from voltages to displacements using the proper
calibration factors. Displacement histories were differentiated numerically to obtain
velocity and acceleration. The vectors were used in Eq. [3. 1] to calculate the force
vector 17,. The total force-time history on the floor were computed by summing the force
vector at every time t.

Input to FLOOR.FOR consisted of the raw data files, calibration matrix, and the
predetermined mass, damping, and stiffness matrices. Output files included force-time
history generated at each node location (LVDT location) on the floor, total force-time
history, and a summary of statistics of force peaks. Figure 3.7 shows a typical plot of

force-time output from FlOOR.FOR

3.4 Statistical Output Summary:
The force history, or shape of the force function with time, for each of the actions

measured, proved to be consistent. Since each action appeared to result in a reproducible

 

 

 

 

 

 

28

function, it was hypothesized that each function could be accurately modeled. Although
each force history for the same action is similar in shape, each is statistically different;
that is, the force functions vary within narrow bounds. As a result an accurate model
would be probabilistic.

Statistical Results from the data processing program DATA.FOR output are stored
on magnetic media for later use in the analysis. They are arranged by motion type
(Transient, Periodic, and Random). For each motion type, output forces are normalized
with respect to the participants' weights and referred to as ”Dynamic Force Ratio ”.
Absolute maximum dynamic force ratios and actual and estimated static weight are
reported for an individual and for a group. Following are abbreviations that apply to
values in these tables:

Fxmax : absolute maximum force ratio (to individual's weight) in the x- direction.

Var : sample variance

STD : sample standard deviation

C.O.V. : coefficient of variation

Table 3.4, a typical statistical table, shows the absolute maximum dynamic force
ratios by one individual performing a single jump in-placc. It can be seen from the table
that force ratios in the vertical direction are significantly more than the other two

components in the horizontal direction. The table shows also that an individual would
generate an average vertical force of about 3.19 times his weight when performing a
single jump. The minimum vertical dynamic force ratio observed in this collection of

tests was 1.54. Thirty five males and fourteen females participated in this experiment.

 

 

 

29

Their average weight was 161.36 lbs. with a standard deviation of 30.80 lbs. and weight

range from 103 to 242 lbs.

 

 

 

 

 

 

 

 

 

 

 

 

 

   

 

251-342;, if,- _ . 7

 

 

 

 

 

 

 

 

 

 

30

For each motion type, a table summarizing the statistical information of individual

and group force ratios is prepared for later analysis. Table 3.5 , for single jump motion,

Table 3.5 Maximum Force Ratios (Single Jump)

Fymax
l 2 4

.60 .37 .24 .28 .21
.10 .21 .03 .04 .09

1.24 0.65 1.49 0.73 .31

.11 0.03 . 0.06 0.03 0.01

0.33 .17 . 0.25 .18 0.09
45.79 102.3 63.78 .41

 

10 Persons (Perlodlc Jumplng at 2 Hz.)

 

ll /\ fl

«Li ill --

f \1 U \/ if
\f U \«x’ W V

1.5 2 2.5

 

 

0.5

 

Dynamic Force R0110
o
I

 

 

 

 

 

 

 

 

d

0 0.5
Time (see)

Figure 3.7 A Typical Force-Time History (Floor.For Output)

presents a typical sample of such tables. It shows that an increase in the number of
people performing the same action at the same prompt tends to decrease the overall
dynamic force. A single jump exemplifies this phenomena since it is difficult for typical

individuals to maintain coherency in a pulse action like a single jump.

 

 

 

 

 

 

 

 

31
Tests performed on the floor system were analyzed for peak statistics using

FLOOR.FOR. Some of the statistics are tabulated in Table 3.6. Data collected from the

floor system are limited in two aspects; only the vertical component of the dynamic force

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

was recorded; and data collection is limited to only periodic jumping at 2Hz. It was
observed that individuals could maintain better coherency at this frequency range. Data
collected from the floor system were used in this study to verify a load model
hypothesized to simulate a large crowd.

Table 3.7 shows that the larger the group that performs the same action at the same
time, the harder it is for individuals to maintain coherency. The maximum dynamic force
ratio decreased from 4.54 for one persons to 1.14 for forty persons performing periodic
jumping at 2 Hz. Figure 3.8 shows the group dynamic ratios for groups of individuals
up to forty. The sample size of the four participants was the smallest among all other

groups. Therefore, the standard error of the mean for that particular group shows a

 

 

 

 

32

wider range than all other groups. The figure also suggests that the relationship between

the number of participants and the dynamic force ratios may not be linear.

Table 3.7 2 Hz.-Periodic Jumping Peak Analysis

 

Group Dynmalc Force Ratios (Periodic Jumping, 2 Hz.)

5 .00
4.50

4.00

Dynamic Force Ratio
!° N S" 9’
0 or 0 or
o o o o

-n
01
o

1 .00

0.50

0.00

 

1 2 4 1 O 20 30 40
No. of Participants

Figure 3.8 Mean, Min, Max Peaks For 2 Hz. Periodic Jumping

Since periodic jumping at 2 Hz. was found to produce the maximum coherence

among participants, it would constitute an upper limit of dynamic load ratios of one

 

 

 

 

 

33

individual in group. A non-linear regression model is proposed to estimate "Dynamic
Group Factor " DF; an empirical factor to generate dynamic force ratios as function of
group size n . The model is in the form :

where regression coefficients b, m are estimated by transforming Eq. [3.2] to a linear

form and solve the linear regression, Chapra (1988):

Log(DF)==nLog(m)+I.og(b) .......... [3.3]

D F = b * m n .................. [3.2]
The regression model was solved to estimate the regression coefficient for mean,

minimum, and maximum dynamic factors. Figures 3.9 presents the regression model in

 

comparison to the measured values. The figure also shows that the range between the

 

Dynamic Factor Ratio (DP) (Exponential Mode

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

4 i» * "m"
min
3 5 IN / max
.I AWW [fathered Maxinurn Peekd + actual mean
3 _
1‘ W \ —I-— actual min
2:: 2 5 3‘ \ m A aotualmax
a ' ' ‘N
33 N
.9 \
s 2 -- s
3‘ I
1.5 ir‘ LIIL

 

 

 

 

  

 

llmlll—rlll—l—ilWlWlllililT‘lTilimllWTllillllliTl—Tlllflfliliil—Fllll—WTIIlilTfllllllITlll—T‘l
0 10 20 30 4O 50 60 7O 80 90
NeolWln)

 

Figure 3.9 Log-Linear Regression Model

 

   

 

34

maximum and minimum dynamic group factors decreases as the crowd size increases.
This formulation could be used as a tool to estimate an upper bound for the mean and

range of the dynamic force ratios of any group size n. The pmposed Log-linear

 

 
 
    
   
   

Single Jump A single jump in place from a standing position

 

I Standing Up Standing up from a sitting position ]I

I Sitting Down Dropping into a seat from a standing position I

Jumping Periodic jumping in place

 

 

I Jouncing moving up and down without leaving the floor

 

 

 

..... LSWaying Swaying side to side from a sitting position

 

regression can be simplified to take the form:

 

DF = a * B" .................. [3.4]

 

where :
or is 2.98, 1.73, and 4.08 for the mean, minimum, and maximum Dynamic Group factors

and B is a constant factor equals to 0.97.

 

Although several other regression forms were examined, the proposed regression in
Eq. [3.4] proved to be the best—fit model. Nevertheless, it is important to emphasize the
preliminary nature of the proposed regression. It is beyond the scope of this research to
further investigate the theoretical aspects of the regression models in spite of their
practical importance. Further statistical analysis could provide a better and more

representative form to describe DF.

 

   

 

 

4.0 MODEL ANALYSIS

4.1 General

In this part of the research, the focus is analyzing human loadings data to include
and quantify their random nature. For each transient action in the study, a method
based on passing straight lines through control points that define the force-time history
is used to simulate human loading. Best-fit distributions for the control points were
determined. Periodic loadings were analyzed as a series of impulses where the forcing
function is divided into cycles, each of which is a full period of the motion considered.
Statistics of each impulse in the force-time history were computed and analyzed for

correlation and peak distribution.

4.2 Methodology

The dynamic force resulting from a single activity, such as a jump, is a time varying
function F,(t) graphically represented as a single pulse with force changing with time over
a relatively short interval, Fig. 4.1.a. This dynamic load will vary somewhat from
individual to individual and from one time to the next for the same individual. In
addition, when two or more individuals attempt the same action at the same time, the

resulting loads will vary somewhat from one another but may be influenced by each

35

 

 

 

 

 

36

other, Figure 4.1.b. The function F,(t) due to the action of a single person i may be a

pulse or a continuing response. Table 4.1 summarizes motions considered in the study:

Table 4.1 Human Movements Considered in The Study

   
  

  

Single Jump

   
  
 

A single jump in place from a standing position

 

Standing Up Standing up from a sitting position II

. I Sitting Down Dropping into a seat from a standing position I

Jumping Periodic jumping in place

 

 

 

 

 

[Jouncing moving up and down without leaving the floor

Swaying Swaying side to side from a sitting position

 

 

For each movement type, the forcing function is assumed to be a function of several

independent random variables such as time, response lag, and group effect. The

 

parameters of the function due to an individual performing a predefined human movement

 

can be represented as F,(t):
5,0), = w l 1 +fz (t, ¢,f)l ............. [4.1]
Fin), = w j, ( t, o, f) ............... [4.2]
F,(t)y = w fy ( t, ¢,f ) ............... [4.3]

where the random variables are:

w : Weight of individual

t : Time in seconds

(I) : Response Lag (Time lag between the prompt and the individual reaction)

f : Frequency of motion (not a factor in transient actions)

 

   

 

 

 

 

37

The dynamic components of the forces due to one person is approximated by passing
line segments through control points defined as shown in Figure 4.2 for the case of a
single jump, Tuan (1985). Periodic motion is modeled as a series of impulses, where
the shape of each impulse is defined by passing line segments through control points as
shown in Figure 4.3. The mean and the variance of arrival time and amplitude is
determined for each control point. The probability density functions for the best-fit
distribution is evaluated for arrival times and amplitudes of control points.

To simplify the modeling process, several assumptions were made. They are:

 

 

1.0
0.6 ~
0.2 I

-0.2 '1

-05 l

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Dynamic Ratio

 

 

 

 

 

 

 

 

 

 

 

 

 

.00 1.00 2.00 3.00 4.00 ‘ .00 1.00 2.00 SOT 4.00
Tlmslsn) Time(sec.)
a) One Individual 0) Three Individuals

Figure 4.1 A Single Jump

l Initial computations are confined to the vertical component of the dynamic force.

 

 

 

 

 

38
A Single Jump, One Person

 

 

 

 

A J‘A‘

—P V-“

A

 

 

 

w m m m m o
2 2 1 1
73:88“.

 

 

Time ( sec. )
Time ( sec.)

 

 

10 Persons Periodic Jumping

 

 

Figure 4.2 Control Points for A Single Jump

 

 

 

 

 

Figure 4.3 Control Points for a Periodic Motion

-50 4
~100 a
-150

 

 

39

I Random processes used in the analyses were assumed to be adequately characterized
by second-order models (models that can be sufficiently defined with the mean and
the standard deviation).

I To account for participants weight variabilities, a general model based on the
statistics of the weight distribution of the US . p0pulation were assumed for the
study.

I For periodic motions, A model assuming that the person is always trying to maintain

coherency with the prompt was assumed.

4.3 Transient Loading

 

The study includes single jumps, standing up from a sitting position, and sitting
down. A typical transient forcing function F,(t) has the following random variables:

Response Lag (I) : A random variable that represents the time between the prompt
and the response of an individual. Available data were utilized to find the probability
distribution function of the Response lag, and to determine whether it depends on the
type of the transient motion.

Amplitudes a 1,, a,,,..., am: Amplitudes of the control points that best—represent the
transient function considered were determined. Covariance matrix and correlation
with individual's weight were computed and analyzed.

Arrival Times tfi, thy”, t": Similar to the amplitude coefficients, statistics on
arrival times were computed. The first arrival time t,,. for an individual i, is always

assumed to be equal to the response lag (I) assumed for the individual.

40
4.3.1 Single Jump

The single jump motion is used to explain in details the process of analyzing the
measured data. Other types of transient actions considered in this study (Standing up, and
Sitting down) are analyzed similarly. Differences in the analyses process are explained
later in this Chapter.

For each measured force—time history, as a stochastic process, the weight of the

person performing the test was removed from the process by subtracting it from all

Vertical Force Ratio (Single Jump, One Individual)

 

.2
E
i
ll.
0
'E
i
o 0.5 1 1.5 2 2.5
Time (See)

Figure 4.4 A Typical Single Jump

force-time series points. The process was normalized by dividing each reading by the

weight of the participant. Figure 4.4 shows a typical vertical component of a single

jump.

 

 

41

Eight control points were assumed sufficient to describe the vertical component of
the forcing function, as shown in Figure 4.4. The prompt marks the beginning of the
process. The first control point denotes the start of the individual's motion. The time
lag from the beginning of the process to the first control point is defined as the Response
Lag 0. The individual is in a static position at this portion. The process consists of three
segments; first is the preparation for the jump, from control point 1 to 4; then airborne
time between control point 4 and 5; and finally the landing portion where control point
6 marks the peak landing. The process ends at control point 8 when the person returns
to the static position, Figure 4.4.

A program, CONTROL.FOR was developed to automate the process of analyzing
the measured data. Input to the program consists of a parameter file and the collection
samples of force-time histories for the chosen action. CONTROL.F OR proceeds as
follows.

I Reduce the force-time history to 2.5 seconds after the prompt. It has been
observed that 2.5 seconds is well beyond the duration of any action period
considered herein. Force-time histories were aligned such that the prompt marks
the beginning of the file.

I Differentiate the reduced function with respect to time to compute the slope

function. The slope function is used to find the control points.
I Find control points using two criteria. First, the change in the slope direction will
define peak control points 2,3,6, and 7. Control points 1,4,5, and 8 are defined

as points where the slope values changes significantly. The program compares the

 

 

42

slope before and after each point and determines whether it exceeds a preset range
value. The range value establishes the second criteria.

The response lag (I) is determined as the time from the prompt to the first control
point. The response lag is then removed from the process and treated as an
independent random variable. This assumption is verified later in the analysis.
Arrival times are then adjusted so that actual dynamic motion starts at time
g=aa

Reduced force-time history data along with amplitudes and arrival times of the
control points are saved in a file which has the same name as the input force-time
history with an extension ".CRL",

The Subroutine PLOTXY, is then called to plot the reduced function and control
points on the same axes to visually ensure that control points were properly
captured. Arrival times and amplitudes of control points are also shown on the
screen.

The program repeats the previous steps for all samples of force-time histories in
the selected human motion (a single jump in this case).

An output file (SJ -CRL.OUT) saves arrival times, amplitudes of control points,
and peak values in the three principal axes from each sample in the collection of
files processed by the program, Table 4.2.

Subroutine MYSTAT is called to compute the important statistics of control points
amplitudes and arrival times, Table 4.3. The computed statistics are saved in the

output file.

 

43

Table 4.2 Control Points for Single Jump

 

 

 

 

WT (I) T1 T3 T4 T5 T6 T7 T8 A1 A2 A3 A4 A5 A6 A7 A8
M“ 165 0.18 0.12 0.32 0.44 0.85 1.00 1.29 1.62 -0.10 -0.64 2.17 -1.00 -l.00 1.41 -0.45 0.00
172 0.15 0.15 0.41 0.56 0.97 1.03 1.41 1.53 -0.04 -0.68 1.92 -0.97 -0.98 2.55 -0.57 0.09
162 0.21 0.09 0.41 0.59 1.06 1.15 1.79 2.00 -0.18 -0.54 1.54 -l.03 -l.01 1.44 -0.45 0.02
181 0.29 0.09 0.35 0.44 0.88 0.97 1.27 1.38 -0.15 -0.45 2.24 «0.95 -0.92 2.38 -0.51 0.21
175 0.15 0.00 0.21 0.35 0.82 0.94 1.38 1.62 -0.05 -0.05 2.07 -0.95 -0.97 4.24 -0.20 0.03
165 0.21 0.12 0.27 0.38 0.74 0.79 1.18 1.35 -0.06 -0.74 2.42 -1.01 -l.00 2.69 -0.53 0.02
172 0.15 0.12 0.32 0.44 0.85 0.91 1.24 1.59 -0.04 -0.98 2.25 -1.01 -l.01 4.36 -0.49 -0.03
162 0.18 0.15 0.41 0.68 1.15 1.24 1.91 2.09 -0.08 0.52 1.29 -1.00 -l.01 2.04 -0.51 0.10
181 0.32 0.09 0.32 0.44 0.79 0.88 1.09 1.24 -0.07 -O.62 1.86 -l.00 -l.01 3.24 -O.7l 0.07
176 0.27 0.00 0.09 0.18 0.53 0.59 0.85 1.53 -0.03 -0.03 2.56 -l.02 -l.07 3.86 -0.79 -0.25
196 0.27 0.09 0.47 0.59 0.97 1.06 1.29 1.47 -0.03 -0.47 1.61 -0.93 -0.97 3.49 -0.34 0.20
140 0.50 0.06 0.35 0.50 0.94 1.06 1.24 1.27 -0.23 -0.41 1.70 -0.92 ~0.94 2.62 -0.11 0.03
186 0.53 0.09 0.65 0.77 1.32 1.38 1.82 1.94 -0.06 -0.38 1.41 -l.03 ~0.97 3.43 -0.43 0.11
150 0.32 0.09 0.24 0.38 0.77 0.85 1.12 1.24 -0.08 -0.72 2.65 -0.89 -0.95 4.60 -0.32 0.03
189 0.35 0.12 0.38 0.53 1.00 1.09 1.27 1.44 ~0.07 -0.65 2.06 -0.98 -0.99 5.04 -0.74 0.07
163 0.24 0.18 0.47 0.65 1.09 1.18 1.50 1.62 -0.01 -0.56 1.60 -0.91 -0.92 1.95 -0.45 -0.14
125 0.38 0.09 0.38 0.53 0.94 1.00 1.47 1.68 -0.07 -0.49 1.56 -0.89 -0.90 5.04 -0.18 0.03
234 0.35 0.09 0.29 0.47 0.65 0.77 0.97 1.06 -0.06 -0.29 1.46 -0.85 -0.88 2.12 -0.23 0.06
132 0.29 0.12 0.27 0.38 0.85 0.94 1.21 1.50 0.02 -0.72 2.93 -0.88 o0.87 5.94 -0.58 -0.12
130 0.24 0.12 0.27 0.41 0.71 0.82 1.00 1.18 -0.04 -0.60 2.13 -0.95 -0.94 2.43 -0.34 0.00
146 0.27 0.12 0.24 0.35 0.71 0.82 1.00 1.18 -0.01 -0.85 2.47 -0.90 -0.96 2.31 -0.28 0.19
242 0.18 0.12 0.44 0.56 1.03 1.09 1.56 1.71 -0.07 -0.43 1.31 0.98 -0.98 3.49 -0.42 0.01
184 0.35 0.12 0.38 0.50 0.94 1.03 1.27 1.47 -0.06 -0.31 2.44 -0.98 -0.97 4.05 -0.53 -0.03
155 0.35 0.18 0.44 0.59 1.09 1.15 1.44 1.62 -0.05 -0.41 1.84 -0.96 -0.96 3.12 -0.69 0.06
200 0.21 0.18 0.47 0.59 1.00 1.09 1.29 1.50 -0.01 -0.36 1.86 -0.97 -l.02 4.47 -0.36 -0.04
191 0.21 0.09 0.21 0.35 0.56 0.62 0.82 1.03 -0.03 -0.70 1.86 -0.93 -0.93 3.82 -0.54 -0.09
166 0.35 0.09 0.27 0.41 0.71 0.79 1.06 1.18 -0.11 -0.49 2.08 -0.90 -0.95 2.13 -0.56 0.08
215 0.38 0.09 0.27 0.38 0.79 0.85 1.12 1.24 ~0.01 -0.54 2.27 -0.90 -0.87 2.84 -0.63 0.13
154 0.32 0.12 0.27 0.41 0.77 0.85 1.15 1.29 -0.04 -0.82 2.20 -0.98 -0.97 4.24 -0.53 0.07
153 0.21 0.12 0.35 0.50 0.97 1.06 1.29 1.44 -0.03 .0.62 1.99 «0.90 -0.90 2.97 -0.63 0.43
164 0.18 0.06 0.27 0.38 0.79 0.85 1.12 1.59 -0.10 —0.59 2.79 -1.01 -l.01 8.85 -0.40 0.01
120 0.29 0.09 0.24 0.38 0.56 0.62 0.77 0.79 -0.05 -0.42 1.29 -0.92 -0.99 1.85 -0.13 0.04
103 0.27 0.09 0.21 0.32 0.50 0.59 0.77 0.79 -0.05 -0.72 2.23 -0.88 -0.90 2.80 -0.15 0.01
126 0.27 0.00 0.06 0.18 0.32 0.47 0.74 0.85 -0.04 -0.04 1.34 -l.01 -l.10 1.56 -0.53 0.01
116 0.21 0.18 0.38 0.50 0.88 0.91 1.21 1.38 0.04 -0.41 1.94 -0.85 -0.86 1.77 -0.59 0.49
185 0.24 0.12 0.38 0.47 0.85 0.91 1.21 1.56 0.05 -0.38 2.07 -0.94 -0.96 4.27 -0.34 0.02
145 0.35 0.09 0.38 0.53 0.88 0.97 1.32 1.38 -0.11 -0.43 1.38 -0.82 -0.93 2.03 -0.08 0.01
140 0.24 0.06 0.18 0.27 0.50 0.59 0.85 1.00 -0.07 -0.57 2.57 -0.69 -0.86 2.23 90.28 0.04
170 0.29 0.09 0.32 0.47 0.82 0.91 1.12 1.24 0.01 -0.42 1.60 -0.87 -0.89 3.06 -0.46 0.01
120 0.41 0.06 0.21 0.29 0.65 0.74 0.94 1.12 -0.22 -0.58 2.70 ‘0.83 -0.93 3.54 -0.69 0.21
171 0.27 0.09 0.27 0.38 0.68 0.77 1.06 1.35 0.03 -0.78 1.66 -0.86 -0.87 1.95 -0.32 0.20
177 0.24 0.12 0.27 0.41 0.65 0.74 0.94 1.09 -0.03 -0.49 1.65 -0.87 -0.91 2.72 -0.47 0.14
124 0.29 0.06 0.32 0.47 0.77 0.88 1.12 1.06 -0.21 -0.59 1.32 -0.93 -0.96 2.13 -0.37 -0.29
128 0.32 0.06 0.38 0.53 0.82 0.91 1.12 1.38 -0.16 -0.46 1.06 ~0.79 -0.86 1.89 -0.05 0.02
110 0.24 0.12 0.29 0.41 0.71 0.79 1.06 1.24 -0.05 -0.41 1.71 -0.89 -0.94 3.04 -0.32 0.02

 

 

 

 

 

 

 

44

I All output files are closed and the program report the number of processed files

and any errors during the run.

Output from the program is used next to study the correlation among control points
and to find the best-fit distribution for arrival times and amplitudes of each control point.
Correlation Analysis

In order to better understand the relationship between the control points arrival times
and amplitude ratios, a correlation analysis was conducted. The correlation coefficient
r was calculated for all control points pairs and the results are tabulated in Table 4.4.
The coefficient of correlation is a measure of the degree of linearity in the relationship
between any two variables X, Y, Pollard, (1979). The correlation coefficient is calculated

from the covariance matrix as follows:

N
COV(x,y) =—;i£(xi-xm)(yi—ym) ......... [4.4]
r = ———"°"("’y) ................. [4.5]
x” oxoy

where cov (x , y) is the covariance matrix between variable X and variable Y, N is the
number of samples, x, is the value of the X variable from sample 1', and x, and o, are
the mean and the standard deviation of X. The coefficient of correlation takes values
from -1 to +1 where the negative values suggest negative correlation (high values of x
are associated with low values of y) and positive values indicate positive correlation (high
values of x are associated with high values of y). The perfect positive linear correlation

will result in a value of 1 for the coefficient. An r value of zero does not imply

 

 

 

 

 

45

independence between .1: and y. It only indicates lack of any linear relationship between
x and y.

In general, 1001’ gives the percentage of the total variation of the variable Y which
is explained by, or is due to, the relationship to variable X, Freund (1980). It is however
important to emphasize that r measures only the strength of the linear relationship and that
high correlation values does not necessarily imply a cause-effect relationship. If the

considered variables were drawn from a bivariate normal distribution, the correlation

 
  

 

   

 

 

 

 

 

 

0.10 0.45 0.82 0.90 1.19 1.37 -0.0 -0.5 1.93 -0.93 -0.9 3.16 -0.43 0.05
103 0.15 0.00 0.06 0.18 0.32 0.47 0.74 0.79 ~0.2 -0.9 1.06 -1.03 -1.1 1.41 -0.79 -0.29
242 0.53 0.18 0.65 0.77 1.32 1.38 1.91 2.09 0.05 -0.0 2.93 -0.69 -0.8 8.85 -0.05 0.49
139 0.38 0.18 0.59 0.59 1.00 0.91 1.18 1.29 0.28 0.95 1.88 0.34 0.24 7.45 0.74 0.78
949 0.01 0.00 0.01 0.01 0.04 0.04 0.07 0.08 0.00 0.04 0.21 0.01 0.00 1.88 0.03 0.02
31 0.09 0.04 0.11 0.12 0.19 0.19 0.26 0.29 0.06 0.20 0.46 0.07 0.06 1.37 0.18 0.13
. 19 30.96 41.47 33.22 25.91 23.41 20.70 22.03 20.82 -100 -37. 23.74 -7.50 -5.7 43.4 -42.5 264.2
@3555; 5 0.01 0.01 0.02 0.02 0.03 0.03 0.04 0.04 0.01 0.03 0.07 0.01 0.01 0.21 0.03 0.02

   
     
   

 

 

 

 

coefficient can be further examined by using the Fisher Z transformation which estimates
the confidence intervals for calculated coefficient of correlation. The test is based on a

change of scale from r to Z which is given by:

 

where the distribution of Z is approximately normal and a direct function of the true
population coefficient of correlation p. The confidence interval for p is constructed from

known statistical tables and the following (1-01) confidence interval:

 

 

 

46

 

Z-_zLfl—<P<Z+zupoeoooeoeoeoool407]
Z
n—3 n-3

where It; is the mean of the transformation variable Z.

Table 4.4 Correlation Matrix (Single Jump)

 

       
  
  
  
  
  
  
  
  
  
 
    
 

-0.0 -0.1 0.07 0.03
0.39 0.29 0.36 -0.4 -0.0 -0.0 0.16 -0.0 -0.2 0.25 0.01 -0.1 ~0.0 -0.0 -0.0
0.80 0.65 -0.0 -0.0 -0.4 -0.2 0.07 -0.0 0.05 0.17 0.06 -0.0 -0.0 -0.1 -0.0
0.84 0.66 -0.0 -0.0 -0.5 -0.2 0.06 -0.0 0.08 0.14 0.04 0.02 0.02 -0.1 -0.0
-0.1 0.15 0.27 -0.0 0.19 -0.2 0.12
-0.0 0.13 0.23 -0.0 0.18 -0.2 0.08
-0.0 0.10 0.33 -0.0 0.28 -0.2 0.03
-0.1 0.01 0.52 -0.2 0.42 ~0.3 0.23
-0.1 0.16 0.16 -0.1 0.03 -0.1 0.14
0.06 -0.1 0.04 -0.1 0.09 -0.1 -0.1
-0.3 0.01 0.28 -0.0 0.25 -0.1 0.54
0.42 0.24

 

 

    
     
          
     
     
           
       
             
   

0.16 0.07 0.06 -0.0
-0.0 -0.0 -0.0 0.12 0.08 0.03 0.22 0.14 -0.1
-0.2 0.05 0.08 —0.1 -0.0 -0.0 -0.1 -0.1 0.06
0.25 0.17 0.14 0.15 0.13 0.10 0.01 0.16 -0.1
0.01 0.06 0.04 0.27 0.23 0.33 0.52 0.16 0.04
-0.1 -0.0 0.02 ~0.0 -0.0 -0.0 -0.2 -0.1 -0.1 0.22 0.01
-0.2 -0.0 -0.0 0.02 0.19 0.18 0.28 0.42 0.03 0.09 0.25 -0.2 -0.2 0.09 -0.3 -0.2
0.16 -0.0 -0.1 -0.1 -0.2 -0.2 -0.2 -0.3 -0.1 -O.l -0.1 0.15 0.06 -0.0 0.25 0.17
0.0 -0.0 -0.0 -0.0 0.12 0.08 0.03 0.23 0.14 -0.1 0.54 -0.2 -0.1 1.00 -0.1 -0.1

 

      

 

 

 

 

 

 

The process could be explained by considering the correlation between the amplitude
ratios of maximum force in the X—direction and maximum force in the Y-direction. The
value of r from Table 4.4 suggests a positive correlation of 0.64. Assuming that both of
the variables are normally distributed, the confidence interval for the true strength of the
linear relationship between the two variables is estimated by first calculating the Z

transformation of 0.64 from Eq. [4.6] which is be 0. 767. Substituting the values, 1: =45,

 

 

 

47
and zm,2 =1.96 (from the standard normal distribution tables at n =45 and 0c =0. 05) in Eq.

[4.7], the 0. 95 confidence interval is

z-_z°-_°5L2_<pz<z+_zL°6L2_ ............ [4.8]
[45 -3 [45—3
0.465 < pz < 1.069 ................ [4.9]

These two values are then interpolated from the Z Tables or from using Eq. [4.6] to get

0.434 < p < 0,739 ............... [4.10]

So, it can be said that with a 0. 95 confidence, the true linear relationship between the

maximum force in the X-direction and the maximum force in the Y-direction lies between

 

0.434 and 0. 789 with an estimate of 0. 64 provided from 45 independent samples. This
process has been implemented in this study to compute correlation coefficients and
provide confidence intervals for each significant correlation.
Best-Fit Distribution

In the use of statistical distributions, observed data is used to estimate any parameter.

The process should be the best possible to estimate the desired value. Maximum

 

likelihood is one of the most widely used methods for estimating the parameters of
probability distributions. The estimators derived by this method usually have the
desirable properties of being consistent, unbiased, and efficient. The principle of this
method is to select as an estimate of 9 the value for which the observed sample would

have been most "likely" to occur. That is, if the likelihood of observing a given set of

 

 

 

 

 

 

48

observations is much higher when 6 = 91 than when G = (~32, then it would seem
reasonable to choose 91 as an estimate of 9 rather than 92.

A good estimator must have three properties, which are summarized using the

following notation :
9 = parameter being estimated
8' = best estimator of 8
I 6' must be a consistent estimator of 9. This means that it is possible to take a
sample size 11 large enough so that the absolute difference '9 - 8' I is smaller
than some small value 8 .
I 9' must be an unbiased estimator of 9. To be unbiased, the expected value of 9'
must equal 8.
l (9' must be an efficient estimator of 8. The variance of an efficient estimator 8'
must be smaller than the variance of any other estimator, Blank ( 1980).

The theoretical probability distributions considered for fitting the results of the control
program are the normal, inverse Gaussian, and log-normal distributions. The difference
between each probability distribution and the actual sample distribution is obtained at each
sample point. The maximum difference (for a given theoretical distribution and over the

entire sample) D", is the Kolomogorov-Smirnov statistic, denoted as the K-S statistic:
D" = max I F (x) -— Sn (x) I ............. [4.11]
where Sn(x) is the empirical cumulative distribution function of a sample of a size n

drawn from a population in which random variable X has a continuous cumulative

distribution function F(x), Gibra (1973)-

 

 

 

 

 

49

The K—S statistic determines the level of probability at which it is possible to reject
the null hypothesis that a random variable has a particular type of probability distribution,
Eliashakoff (1983). The hypothesis is rejected if the observed value of the Statistic falls

in the critical region at the desired level of significance which can be calculated as:

[_b;(_:)]1fl ................ [4.12]

The statistical model underlaying the test assumes the sample observations have zero
probability of being equal (i.e. continuous distribution), Pollard (1979).

Table 4.5 shows the means of the control point coefficient and their corresponding
standard deviations, and the K-S statistic values. By visual inspection and examining the
K—S statistic values in table 4.5, probability distribution functions were selected as best-

fit distribution for each control point random variable. Figure 4.5 shows a typical plot

Response Lag (Slngle Jump

 

0.026 ‘

 

0.02 -

 

0.015 —<

 

    
 

Probabflily (pdf)

 

  
   
 

 

Will“

a all“

0 0.05 0.10.2 0.25 0.3 0.35 0.4 0.45 0.5 0.65 0.0 0.05
Rnponu Lag (See)

Figure 4.5 Best-Fit Distribution for Response Lag

 

 

of a data histogram and the best-fit distribution. The same process explained earlier was

applied to all other random variables.

4.3.2 Sitting down

Seven control points were assumed to describe the vertical component of the forcing

function as shown in Figure 4. 6. The same process, explained earlier in the case of

single jump motion, was used to find the control points and their statistics. The program

.............................................................

.......

   
   

Table 4.5 Best-Fit Distributions (Single Jump)

 

161.356

STD

K-SNOR 3355331613}? ,. ‘ .5323

 

   

0.277

 

   

0.098

 

   

0.319

 

   

0.452

 

   

0.818

 

   

0.903

 

   

1.192

 

   
   

1.373
-0.068

 

   

-0.519

 

   

1.934

 

   

0.927

 

   

0.951

 

   

3.155

 

   

-O.427

 

   
   

0.094
0.530

 

   

 

    

 

? 0.618 0.493
|; 0.170 0.145
0.208 0.251

   

 

   

3.189

 

 

 

 

 

 

 

 

 

 

51
CONTROLFOR was modified to analyze the sitting down motion. Arrival times,

amplitudes of control points, and peak values were saved and analyzed for important

statistics as shown in Table 4.6. The table shows that the average peak force in the

 

 

Table 4.6 Sitting Down Control Points Statistics

13 T4 T5 T‘ 1‘! Al 1 T 1 “ " "

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

vertical direction for a person dropping to a seat was about 2.11 times his weight. Force
ratio components in the orthogonal horizontal directions were 0.26 for the average force
perpendicular to the seating and 0. 07 for the average parallel force ratio. The table also
reveals that the average time needed to perform the motion was 0.86 seconds with a delay
after the prompt (response lag) of 0. 25 seconds.

Linear correlation coefficients were calculated for all points pairs with the results
tabulated in Table 4.7. Finding the best-fit probability distribution to represent each
variable in the motion was accomplished by examining the K-S statistic values shown in
Table 4.8. The best-fit distribution for the response lag was found to be the Log-Normal
distribution. This is consistent with the finding in Table 4.5 for the case of a single
jump. The table reveals that amplitudes can be best-represented by a Log-Normal

Distribution.

 

 

52

Table 4. 7 Correlation Matrix (Sitting Down)

 

 

   
 

-0.05 -0.01 0.05 0.07 -0.02

 

 

0.34 -0.36 -0.37 -0.17 0.27

 

-0.08 0.26 -0.33 0.40 -0.1

  

 

    

 

-0.0
0.16

 

0.02 -0.23 -0.08 0.00 0.04
-0.14 -0.10 -0.02 -0.01 -0.16

  
  
  
  
  
  
 

-0. 36 0. 67 -0 66 .0. 66 '40. 66

.022 0.45 -033 -032 .0.27 0.41.53

. -0.2

-0.76 0.58 -0.67 0.26
-0.23 0.31 -0. 56 039

-0. 06 -0 07 -0. 03 -0. 01 -0. 03 -0.07 0.32 -035 -034 -023 -0.01 0.16 -0.10 0.26 -029 0.24 .0.2
-0.0 ' -020 0.16 0.10 0.10 0.25 0.02 01 -005 .019 0.26 -0.24 0.25
-0.0 -0.01 0.04 0.48 0.48 0.55 -023 —0.1 0.31-0.41 0.54 -032 0.55
-0.0 -011 0.19 0.18 0.18 0.26 -0.08 -0.0 0.09 .021 0.29 -0.16 0.26
.0.0 .. -014 0.25 0.04 0.05 0.13 0.00 .0.0 -0.00 -0.10 0.18 -0.10.13
00 0.69 0.62 0.80083 -; .024 0.21 .004 -0.05 -0.01 0.04 -0.1 -0.06 .001 0.19 -0.18 -0.0
-0.0 0.70 072 0.83 0.83 0.9623532; -0.05 0.07 0.16 0.16 0.19 .013 -0.2 0.13 -014 0.4 .034 0.19
-0.0 -020 -0.01 -011 .014 .024 . 3"’9€-0.48 0.49 0.49 0.39 -0.36 -0.2 0.59 -0.17 0.35 -035 0.39
0.32 0.16 0.04 0.19 0.25 0.21 0.07 __ 071-071-055 0.67 0.45 .071 0.72 -O.62 0.39 -0.5
-0.3 0.10 0.48 0.18 0.04 -o.04 0.16 0.49-0.71;; 0.99 0.89 -0.66 .03 0.76 -0.76 0.82 -0.56 0.89
-0.3 0.10 0.48 0.18 0.05 .0.05 0.16 0.49 .071 0.99 .35; 50.89 -0.66 .0.3 0.76 -0.75 0.82 -0.56 0.89
-0.2 0.25 0.55 0.26 0.13 .0.01 019 0.39 .055 0.89 0.89 0.74 -074 0.83 -055 1

-O.6
-0. 2

 

-0. l
0.26
-0.2
0.24
-0.2

 

 

 

 

-0.05 0.31 0.09 -0.00 -0.06
-0.19 -0.41 ~0.21 -0.10 -0.01
0.26 0.54 0.29 0.18 0.19
-0.24 -0.32 -0.16 -0.1 -0.18

 

0.25 0.55 0.26 0.13 -0.01 0.19

 

0.39 -0.55 0.89 0.89

0.59 -0.71 0.76 0.76 0.74 -0.76
-0.17 0.72 -0.76 -0.75 -0.74 0.58
0.35 -0.62 0.82 0.82 0.83 -0.67
-0.35 0.39 -0.56 -0.56 -0.55 0.26
l -0.66

.0.2

0.31
-0.5
0.39

-0.2

Vertical Force Ratio (Sitting Down, One Individual)

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

El
0.8
E 1
3 0.4
a B \
3 o B 3.-
E
5..
. 1?
v1.2
0 0.2 0.4 0.6 0.8 1 1.2 1.4
Tlme(Sec.)

Figure 4.6 A Typical Sitting Down Motion

325.065 0.63 .040 074

 

 

Table 4.8 Best-Fit Distribution (Sitting Down)

 

53

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

> .. « ...-- :: i ; z: . .. @1082;
158. 5714 34. 7261 0.0922 0.0895 LOG-NOR
0.2521 0.1088 0.1672 0.3588 NORMAL
0.2445 0.1035 0.1448 0.087 LOG-NOR
0.4631 0.1372 0.1354 0.0895 LOG-NOR
0.5328 0.1523 0.1737 0.128 LOG-NOR
0.6025 0.1568 0.217 0.1614 LOG-NOR
0.7479 0.1713 0.146 0.1001 LOG-NOR
0.8622 0.1746 0.158 0.1272 LOG-NOR
0.0417 0.0544 0.2608 0.2315 LOG-NOR
-0.7595 0.6027 0.2467 0.1394 NORMAL
0.8298 1.3254 0.3551 0.0847 LOG-NOR
0.8609 1.3101 0.342 0.1299 LOG-NOR
2.1178 1.7622 0.224 0.0905 LOG-NOR
-0.3263 0.2298 0.2434 0.1171 NORMAL
0.1072 0.0816 0.1857 0.0817 LOG-NOR
0.2497 0.1541 0.1555 0.1033 LOG-NOR
0.2608 0.184 0.2095 0.0899 LOG-NOR
0.0766 0.0738 0.3124 0.1689 LOG-NOR
0.0808 0.0672 0.2444 0.164 LOG-NOR
2.1 178 1.7622 0.224 0.0905 LOGoNOR

 

 

 

4.3.3 Standing up

The vertical component of the forcing function for the standing up motion was found
to be sufficiently approximated by six control points, Figure 4.7. The program
CONTROLFOR was modified to analyze the motion. Statistics for control points and

peak values are shown in Table 4.9. The table shows that the average peak force in the

Table 4.9 Standing Up Control Points Statistics

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

54

Vertical Force Ratio (Standing up, One Individual)

Dynamic Force Ratio

 

0 0.5 1 1.5 2 2.5
Time (See)

Figure 4.7 A Typical Standing up

 

 

..........................................................................................
........................................................................................................................................

158.5714 34. 261 0.0922 0.0895

 

    

 

   

 

  

 

  

 

  

 

  

 

  

 

  

 

  

 

  

 

  

 

   

 

 

  

 

 

  

 

  

 

  

 

  

 

 

 

 

 

 

0.3135 0.1576 0.1319 0.1196 LOG-NOR
0.2344 0.1113 0.115 0.1298 NORMAL
0.5285 0.1232 0.0985 0.0884 LOG-NOR
0.621 0.1568 0.1199 0.1335 NORMAL
0.7941 0.2276 0.1621 0.1096 LOG-NOR
0.9471 0.2416 0.1205 0.0799 LOG-NOR
0.0159 0.0088 0.1104 0.1623 NORMAL
1.0104 0.8999 0.2032 0.1074 LOG-NOR
0.9604 0.8472 0.308 0.1619 LOG-NOR
0.9419 0.846 0.305 0.1574 LOG-NOR
1.0809 1.2655 0.2624 0.1917 LOG-NOR
0.0805 0.0893 0.2452 0.1862 LOG-NOR
0.3708 0.3255 0.2508 0.136 LOG-NOR
0.5074 0.4085 0.3124 0.1742 LOG-NOR
0.1071 0.1523 0.3053 0.1304 LOG-NOR
0.145 0.1323 0.1946 0.1015 LOG-NOR
1.4718 1.2511 0.229 0.1477 LOG-NOR

   

 

 

 

 

 

 

55

vertical direction for a person standing up from a sitting position was about 1.47 times
his or her weight. Force ratio components in the orthogonal horizontal directions were
0.5 for the average force perpendicular to the seating and 0.14 for the average parallel
force ratio. Comparison with same statistics for the sitting down motion reveals that the
later produced larger forces in the vertical direction. This observation is expected since
the person standing up is moving against gravity while moving with it in sitting down.
The same argument could also be used to explain the finding that the average time
needed to perform the motion was 1.003 seconds with a delay after the prompt (response
lag) of 0.291 seconds in comparison with only 0.86 seconds to perform the sitting down
motion and a response lag of 0.25 second.

Linear correlation coefficients were calculated for all control points pairs with the
results tabulated in Table 4.10. Finding the best-fit probability distribution to represent
each variable in the motion was accomplished by examining the K—S values shown in
Table 4.11. The best-fit distribution for the response lag was found to be the Log-Normal
distribution. This confirms the finding in Table 4.5 for the case of a single jump. The
table reaffirms again that amplitudes can be best-represented by a Log-Normal

Distribution.

4.4 Periodic Loading
Periodic Loading includes: periodic jumping, jouncing, and swaying. The dynamic
component of the vertical force due to one person performing a periodic motion is

approximated by a series of impulses, where the shape of each impulse was defined by

 

56

 

Table 4.11 Correlation Matrix (Standing up)

 
 
 

 
  
  
 

 

............................................................................................................................................................................................................................................................................... '2'?"
:3 . 0.339 -0.29 0.253 0.246 -0.00 -0.20 -0.33 0.359 -0.36 0.275 -0. 11

.017 .025 -0.19 .023 -020
-0.18 .015 -0.10 -0.17 -0.25 0.008 -0.38 0.341 0.344 -0.12 0.114 032 0.298 .032 0.158 -0.27
0.631 0.704 0.479 0.389 -0.28 0.441 -0.47 .048 0.285 -0.06 0.526 -0.46 0.488 .037 0.43
01.0736 0.629 0.566 -0.18 0.551 -052 -0.52 0.225 -0.10 0.388 -054 0.482 -027 0.40
.027 0.439 -042 -043 0.545 0.067 0.481 -042 0348 -0.60 0.59

.005 0.291 -019 .019 0.142 .005 0.243 -022 0.198 -0.31 0.25
5771-001 0.456 .0. 34 .035 0.501 -0.08 0.409 .037 0.248 .055 0.56
' -0. 29 0.231 0.209 0.058 .010 -0.26 0.235 0.32 0.319 -009
' -0.83 0.441 -0.01 0.804 .079 0.617 -0.36 0.70

‘ . .044 0.113 -0.89 0.947 -0.77 0.429 -0.64
. 0.12 -0.89 0.949 -o.77 0.445 -0.66

“ -039 0.193 -0.62 0.92
-0.07 0.064 0.06

 

 

   
 

-0.17 -0.18 §§§§§§
.025 -015
-019 -0.10
-0.23 -0.17
40.20 .025
;§; 0339 0.008 -0.28 -0.18 -0.27 -0.05
-029 -O.38 0.441 0.551 0.439 0.291 0.456
0.253 0.341 -047 -0.52 -042 .019 -034
0.246 0.344 -0.48 -0.52 -043 -0.19 .035
" 0.00 -0.12 0.285 0.225 0.545 0.142 0.501
. .0.20 0.114 -0.06 -0.10 0.067 -0.05 -0.08

   
 

 
  
   
     
  
  
  
  
  
  

 

  
    
   
   
   
 
  
  
 
 
  

 

 

 

-0.33 -032 0.526 0.388 0.481 0.243 0.409 -0.50 0.67
0.359 0.298 -0.46 -0.54 -0.42 -0.22 -037 0.537 .0. 59
.0. 40 0.45

-0.36 -0.32 0.488 0.482 0.348 0.198 0.248
0.275 0.158 -0.37 -0.27 -0.60 -0.31 -0.55 0.319 ~0.36 0.429 0.445 -0.62 0.064 -0.50

' -0.11 -0.2710.431 0.406 0.592 0.254 0.566 -0.09 0.707 -0.64 -0.66 0.92 0.069 0.678 .0. 59 0457 .

 

 

 

 

 

 

passing line segments through predetermined control points. Impulses were saved as series

of transient actions with the following assumptions:

I If the prompt frequency is within the physical limits of an individual to perform
the prescribed motion, the individual in general attempts to synchronize the motion
to follow it. It has been observed that when an individual is out of phase with the

prompt in one cycle, an effort is made in the next cycle to adjust to it. Findings
from the measured data asserted this observation.

I When a person, due to physical limitations, is unable to maintain coherency with
a high prompt rate (frequency higher than the range of 2-3 Hz.), Reiner (1987),
The person would perform the action at the highest frequency rate possible with

no attempt to adjust to the prompt. Although insufficient data were available to

verify this assumption, visual observation of tests conducted at frequencies of 4

 

 

 

57

 

and 5 Hz. demonstrated the leaning of individuals to perform actions at their
highest possible rate.
I The dominant forces on the platform due to the side swaying motion is the
horizontal longitudinal component (parallel to the seating).
I It is assumed that individuals maintain the same level of activity throughout the
length of the studied motion (approximately 10 seconds).
I The studied motions are treated as weakly stationary processes. The validity of
this assumption is discussed later in the chapter.
I The analyzed motion is confined to the periodical part of the motion. Initial
stages of the motion would be simulated separately as transient actions. This is

necessary to preserve the assumption made earlier about the stationarity of the

studied process.

4.4.1 Periodic Jumping

Force-time histories were divided into cycles, where each cycle is a full period of
the action considered. Three control points were sufficient to describe each cycle. One
is the peak point in the cycle and the other two define the airborne time. Figure 4.8

presents a typical vertical force ratio of one individual jumping at 2 Hz.
For each measured force-time history, the analysis was conducted using the program
CONTROLFOR which was described in Section 4.3.1 for the case of single jump
motion. The program was modified, however, to accomplish the following additional

steps for analyzing periodic motions in this study:

 

 

58

 

: j. W..."
l 1 1‘
l l J
.0 0 J UUJU 0000‘

o 2 4 6
Time (Sec.)

Figure 4.8 A Typical Periodic Jumping
I The number of cycles was computed for each measured load-time history. The

 

 

 

 

 

 

__

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Dynamic Force Ratio

 

 

 

 

 

 

 

 

 

starting time of each cycle was recorded along with the peak force in the cycle.
I For each cycle, arrival time and amplitudes of control points were defined.
Figure 4.9 shows the control points for the periodic motion in Figure 4.8.
I An output file is created in which the periods of each cycle and control points data
are saved. Table 4.12 is a sample of information reported in the output files.
I Subroutine SPECTRAFOR is called to compute the autocorrelation, autospectrum
fimction and the root mean square of the process considered. Typical screen
output is shown in Figure 4.10 and 4.11 for the forces in vertical and parallel axes
of motion.
Output from CONTROLFOR shows that the average peak force ratio in the vertical
direction for a person jumping periodically in place at a 2 Hz. prompted frequency was

about 2.273 times the person 's weight, Table 4.13. This ratio decreased to 2.154 at 3 Hz.

 

 

 

59

Control Points Periodic Jumping (2 Hz., One Individual)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

'1‘ M 1111‘ ii
00/010111 1
111 0 11111111111111 J

Time (sec.)

Figure 4.9 Control Points for a Typical Periodic Jumping
and 2.002 at 4 Hz. This finding shows that the higher the jumping frequency the lower
the average peak force ratio a person generates. Maximum peaks also followed the same
pattern and dropped from an average of 2.852 for 2 Hz. jumping to 2.750 and 2.448 for
3 and 4 Hz. respectively.

At a prompt of 2 Hz. (0.5 sec. period), the period of the jumping ranged from 0.472
to 0.59 seconds with an overall average of 0.509 seconds. This means that on the
average, individuals were jumping at a frequency of 1.95 Hz. while the prompt frequency
was 2 Hz. This difference between prompt and response increased at 3 and 4 Hz. as
shown in Table 4.14. The average response period for persons jumping at a prompt of
0.333 seconds (3 Hz.) was 0.36 seconds (2.77 Hz.) and for the case of a prompt period
of 0.25 seconds (4 Hz.), it was 0.285 seconds (3.51 Hz.). This observation verifies the

assumption made earlier about the inability of a person to maintain coherency with the

 

 

 

 

60

Table 4.12 2—Hz. Periodic Jumping

 

 
   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1 .
2 173 0.478 0.045 2.22 0.416 3.331
3 126 0.477 0.033 3.148 0.39 3.94
4 160 0.497 0.021 3.627 0.468 4.219
5 205 0.476 0 032 2 539 0.404 3.175
6 196 0.509 0.042 2.397 0.252 2.883
7 140 0.501 0.039 2.685 0.246 3.186
8 186 0.492 0.104 3.222 1.395 4.536
9 150 0.507 0.023 2.513 0.136 2.824
10 189 0 524 0.035 3 126 0.485 3.736
11 163 0 521 0.013 2 746 0.132 3.006
12 125 0 55 0.173 2 669 0.352 3.517
13 234 0 488 0 027 1 524 0.166 2.002
14 132 0 587 0 025 3 825 0.326 4.227
15 130 0 498 0 037 1 784 0.218 2.462
16 146 0 526 0 023 1 93 0.197 2.372
17 242 0 505 0 026 1 542 0.136 1.774
18 184 0 472 0 028 2 451 0.469 3.107
19 155 0 547 0 076 1 094 0.24 1.579
20 200 0 504 0 034 2 537 0.32 3.069
21 191 0 505 0 05 1 066 0.252 1.861
22 166 0 493 0 035 1 894 0.261 2.522
23 215 0 517 0 024 3 459 0.435 3.935
24 154 0 472 0 03 2 608 0.193 3.084
25 153 0 533 0 03 2 454 0.47 3.198
26 164 0.504 0 027 3 213 0.171 3.473
27 120 0.51 0.1 2 188 0.176 2.487
28 103 0 51 0.039 1 399 0.323 2.243
29 126 0 52 0.024 1 337 0.219 1.732
30 116 0 522 0 097 1 129 0.224 1.512
31 185 0 489 0 053 1 684 0.253 2.189
32 145 0 504 0 042 2 444 0.42 3.029
33 140 0 496 0 044 2 013 0.148 2.3
34 170 0 513 0.025 1 758 0.16 2.008
35 120 0 511 0.028 2 044 0.287 2.542
36 177 0 59 0.267 2 142 0.167 2.384
37 124 0 518 0 017 1 924 0.235 2.282
38 128 0 513 0 029 1 334 0.334 1.829
39 110 0 498 0 038 2 107 0.369 3.413
AVG 159.179 0.509 0.048 2.273 0.319 2.852
MIN 103 0.472 0.013 1.066 0.132 1.512
MAX 242 0.59 0.267 3.825 1.395 4.536
RNG 139 0.118 0.254 2.759 1.263 3.024
VAR 1135.89 0.001 0.002 0.498 0.044 0.651
STD 33.703 0.026 0.046 0.706 0.21 0.807
cov 21.173 5.113 95.406 31.053 65.763 28.278
SER 5.397 0.004 0.007 0.113 0.034 0.129

 

 

 

 

 

 

 

 

 

 

 

 

 

 

61

a .. Dos Ea
PERIODIC JUMPING

FIAS A RATIO TO WEIGHT

 

0.4)! "1030‘"

 

 

 

 

 

 

 

 

0 20 4.0 810 6.0 10.0
TlMEtsoc.)
CONTROL POINTS 3 Aurospecrnuu
E I
FILE - paztnooaJnc WITH 1 91:11.; :
Weight:- 186. ESTIMATE-186. lbs ‘ :
.80-
Val-1&1. no 11.: are l'
Portodfl‘) .492 .669 .104 0 j
Peak (F3) 3.222 4.636 1.396 . -40
cum (1. ) .003 n
11111941811 was ~1.026 1.00 . _ A '
t .0 2.0 4.0 6.0 ao 100
y flamumyoki

 

 

 

Figure 4.11 CONTROLFOR Output (Periodic Jumping, 2 Hz., Vertical Ratio)

 

PERIODIC JUMPING

Fy AS A RATIO TO WEIGHT

 

0“!)3) "1030“

    

 

 

 

4:0 60
TIMEuec.)

AUTOSPECTHUM

CONTROL POINTS

FILE 8 pJ218003.FRC WITH 1 PER.
Weight= 186. ESTIMATE=186. lbs

 

 

 

Variant. we an STD '20
Period (T ) .492 .559 .104
Peak (P2) 3.222 4.536 1.395
Chain (6 ) .003
81: Peak VII .... -1.026 .00

 

'C”-‘DOO ‘0‘"00003
.0
O

.0 20 4:0 610 6.0 10.0
firmnnoflHfl

1W1
Figure 4.10 CONTROLFOR Output (Periodic Jumping, 2 Hz., Parallel Ratio)

 

 

 

 

62

 

 

 

.....................................

Table 4.13 Peak Analysis (Periodic J ouncing)

    

.........
..............

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

high prompt frequency.

To further study this pattern, the period of each cycle of a typical periodic jumping
at 2, 3, and 4 Hz. were plotted against the cycle number as shown in figures 4.12. The
figure shows that when the person performs the motion at a period less than the prompt
frequency, an attempt is made in the next cycle to increase the period to adjust to the
prompt frequency. This assumption proved to be valid for most of the recorded cases for
jumping at 2 Hz. The figure also shows that this particular person started at frequency

different from the prompt. However, as the test proceeded, the person adjusted to the

 

 

63

Individual Jumping Period ( Prompt at 2, 3, and 4 Hz.)

Puiod 0.5 2112.]

Period (880.)

 

0 5 10 15 20 25
Cycle No.

Figure 4.12 A Typical Periodic Jumping Response Period

prompt and the variation around the prompt period decreased. On the contrary, when the
prompt period decreased to 0.33 (3 Hz.) and 0.25 (4 Hz.), the two individuals were
jumping consistently at lower frequencies than the prompt frequency with very few
attempt to adjust to it. This observation will be used in the modeling process as explained

in the next chapter.

4.4.2 Periodic J ouncing

Five control points were sufficient to describe vertical force ratios for each cycle in
the periodic jouncing motion One is the peak point in the cycle and the other four define
the shape of the negative part. Figure 4.13 presents a typical vertical force ratio of one
individual performing periodic jouncing at 2 Hz.

Average peak force ratio in the vertical direction for a person jouncing in place at
a 2 Hz. prompted frequency was about 0.84 times the person's weight, Table 4.15. This

ratio increased to approximately 1.0 at 3 Hz. and 4 Hz. Maximum peaks also followed

Vertical Force Ratios (Periodic Jouncing, 2 Hz., One Person)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

“W

 

 

 

 

Dynanic Force Ratio

 

 

 

 

 

 

 

 

 

 

b

In
P__.______.___——.—

I...—

I:
.2
III:

 

 

 

 

 

 

 

Time (Sec.)

Figure 4.13 A Typical Periodic J ouncing
the same pattern and increased form an average of 1.06 for 2 Hz. jouncing to 1.37 and
1.33 for 3 and 4 Hz. respectively. The average period of individuals jouncing
periodically at 2 Hz. (period of 0.5 seconds) was found to be 0.501 seconds. This means
that on the average, individuals were jouncing at the same prompted frequency of 2.0 Hz.
As in the case of periodic jumping, individuals were unable to maintain coherency with
higher frequency (3 and 4 Hz.) and their average jumping period were 0.368 (2.71 Hz.)

and 0.28 (3.57 Hz.) respectively.

4.4.3 Side Swaying

Side swaying forces were dominant in the horizontal direction and parallel to the
individuals' seating. The recorded motion is shown in figure 4.14 where the presented
force ratio is in the horizontal plane. Only peak forces were collected for the analysis.

Typical force ratios in the horizontal plane are presented for the case of periodic swaying

65

1
2
3
4
5
6
7
8
9

NHHI—‘D—‘i—lh—Ip—Ip—IHH
oxoooxio‘m-AuNHO

 

Horizontal Force Ratio (Side swaying, One Individual)

1111111

 

””1-
:5.-

 

 

Dynarnic Force Ratio
o
“I—
"H
R

. I

“7' vyviirygi

 

 

 

 

 

 

 

-0.4

Figure 4.14 A Typical Swaying Side to Side

 

 

 

 

66

 

at 2 Hz, Table 4.16. Maximum force ratios in the horizontal direction were found not

to correlate with the individuals weights. The same conclusions that were obtained from

the analysis of periodic jumping and
Table 4.16 Max. Peaks (Side Swaying)

periodic jouncing regarding the inability of
individuals to maintain coherency at higher
frequencies were observed in this motion

also. Table 4.17 shows typical statistics for

 

reported average and maximum peaks in the

horizontal direction. It shows the average Table 4 17 Typical Side Swaying Data

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

force was about 0.125 times the person's ,
196 0.096 0.199

weight with a range from 0.03 to 0.274. 140 0034 0-175
186 0.03 0.147

The Maximum peak ratios were in the range 150 0.053 0.149
189 0.274 0.337

of 0.112 to 0.354 times the persons' weight 125 0.197 0389
, 234 0.11 0.211
wrth an average of 0.208. 132 0.112 0.182
146 0.103 0.204

191 0.147 0.222

166 0.122 0.179

215 0.209 0.259

331 0.177 0.227

153 0.184 0.354

307 0.1 0.112

103 0.089 0.17

126 0.129 0.283

282 0.086 0.156

145 0.122 0.169

340 0.081 0.144

 

 

 

 

 

 

 

 

 

 

5.0 HUMAN LOAD MODELING

5.1 Introduction

A computer program; Human Load Simulation, HLS; utilizing the understanding of
the nature of each motion and factors that affect its force history was developed giving
researchers an advanced tool to use in design and analysis. The forcing functions
produced by the program simulate several types of human movements. The probable
levels of instantaneous or peak values of human loads are represented by probability
density functions. The program may be used to generate load distributions for any
combination of human loading conditions, composed of those presented herein. Input to
the program includes information about the type of action to be simulated, group size,
and parameters necessary to define the individual loads. The program calls an array of
subroutines to calculate forcing functions for different human actions and these forcing
functions are combined in any form requested by the analyst. Output of the program is
based on the type of action and can be summarized as follows:

Transient loading (pulse loading): Statistical parameters of the control points associated
with the time histories of the transient action are reported. The amplitudes of peaks and
their arrival time are calculated. The program would also provide the probability density

function of the peaks or the impact factors for the input action.

67

 

 

 

68
Steady state loads (periodic loading): The program produces force-time histories,

 

estimates the probability densities of peaks, and computes the spectral energy distributions
in the frequency domain in the form of power spectral density functions (PSD). Power
spectra are determined by taking the Fourier transform of the autocorrelation functions
associated with the simulated time histories, Clough and Penzien (1975). Fast Fourier
Transform (FFT) method outlined by N ewland (1975), and implemented by Harichandran
(1984) is adopted in the program.

In order to develop the above mentioned Human Load Simulation program, HLS,
several steps were required. First, model hypotheses were examined and summarized in
the previous chapter. In this chapter, an attempt to describe an efficient methodology to
simulate human actions is presented. The next chapter illustrates several applications to
explain different ways of using the developed software.

This chapter explains the random processes application to the development of the
program, the generation of correlated random variables to use in estimating control points
for each load type considered, and development of the Monte Carlo simulation process.

The intention of the next section is to briefly explain the mathematics involved in these

steps for the use in modeling human loads.

5.2 Basic Concepts
5.2.1 Random Processes

Since loads due to human movements vary randomly, current methods of handling

them are fundamentally deficient because they do not provide quantitative information

 

II)

 

 

69

 

regarding load variabilities in a rational way. Random process theory deals directly with
uncertainty by characterizing random excitations, human loads in this case, with a
statistical approach. In this way, a large portion of the uncertainty in defining the forces
due to human actions can be investigated and expressed in a way that can be better
understood and used. The application of the concept of random processes to the modeling
of the loads due to human movements seems to be very appropriate in this sense.

The function describing the force due to a human action is a " random process "
because it varies with time. A random process cannot be defined by a single measure or
function. The set of all possible "samplefimctions" constitutes the random process, and
is called the "ensemble". Figure 5.1 displays three typical samples in an ensemble of
random process F(t). The figure shows that, a different sample function is obtained every
time the load is recorded. The random process can then be described through its
probability properties, which allow estimates or forecasts within some degree of
confidence, Augusta (1984). Some of the important definitions in using random processes
are described as follows:

Ensemble Average: Is the average of the random process F(t), measured at time t:

N F
EIFUIH = ”mum; J—(ni-L .......... [5.1]
i=1

where N: is the number of samples in the ensemble.
Stationary Random Process: If all joint probability density functions obtained for the
ensemble do not depend on time, the random process is said to be stationary. If all the

average values (moments) remain constant over a change in time, the process is called

 

 

 

70

 

a "strong stationary process". If only the first and the second moments (mean and
covariance) of the process remain constant with respect to time, the process is a " weak

stationary process", where the first and second moments expressions are

121:17iitjii] := ‘E:[ [7( QB) ] [5:2]
E[F(tl)F(t2)] = E[F(tl+T)F(t2+T)]

2 Hz. Periodic Swaying

4.14/\MAA “MIAMI/WIMP t»
WVVWUVWWVWVWW.WW.

inflHMMMMMM MMMN t,
UUIWWWWVIVIWISWW“

,gthWMMMMAMMAI u,
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Figure 5.1 Typical Samples in the Random Process F(t)

 

 

Force

 

 

 

 

 

Ergodic Process: The process is called "ergodic" , if in addition to being stationary, the

average taken at any sample is the same as the ensemble averages. If the process is

ergodic, it is stationary.

 

 

 

 

 

 

71

<F(t,-)> = Limm%,f_:ll:F(t,)dt = E(F(t))..-- [5.3]

Autocorrelation: Autocorrelation is the average value of the product of the forcing
function at time t and at time (t+‘c) for a random process F(t) , sampled at time t and then
again at time t+t. If the process is weakly stationary, the autocorrelation depends only

on t and is equal to the mean square of the process F(t):

19(1) =E[F(tl).F(tl+1:)] .......... [5.4]

forergodicprocess Rf(r) = %LTF(t)F(t+r)dt, T—ooo [5.5]

Power Spectral Density: It defines the frequency composition of the forcing function

F(t), and is the Fourier Transformation of the autocorrelation function.

Sim) = 31;]_:Rf(c)exp(-im)dt ........ [5.6]

where 00 = is the circular frequency.

5.2.2 Random Number Generation

Random number generation is an important component of every stochastic simulation
model. An essential property of every random number generator is the ability to generate
random variables that are uniformly distributed on the interval (0,1) and stochastically
independent. John von Neumann (1951) and others suggested using the computer's
arithmetic operations to produce sequences of numbers that, while being entirely

deterministic, had the appearance of randomness. The numbers resulting are generally

 

 

 

72

termed pseudorandom numbers. That is, since the numbers are generated algorithmically,
they are not actually random. However, for practical purposes, pseudorandom numbers
are considered to behave as random numbers, i.e. , to be uniformly distributed and
mutually independent provided that the random generator has a long- enough cycle length.
The cycle length is the number of pseudorandom numbers generated before the same
sequence of numbers starts again.

Several methods may be employed to generate uniformly distributed random numbers
(Motooka 1954) . The first method uses a recurrence relation to generate successive
random numbers by employing any algorithm consisting of arithmetic and logical
operations. The second method employs a special computer accessory, namely a physical
random-number generator, that transforms the results of a physical random process (like
electrical noise generators, pulse detectors of ionizing radiation events, or gas discharge
tubes) into a sequence of binary digits in the computer (Golenko and Smiryagin 1960).
This method increases the speed of computation, since the generated numbers are written
in a fixed standard location of the memory. A third, rarely-used, method consists of
inserting tables of uniformly distributed random numbers into the working memory of the
computer. The fourth method, which is used in this study, is to obtain uniform random
numbers by the mixing method. This method is based on utilizing specific features of the
electronic computer to generate pseudorandom numbers. The method begins by assigning
an initial integer number, which is placed in a certain location in computer memory.
Then, the random numbers are calculated by shifting the image of the bits of the

previously generated number a certain number of places. This technique of shifting

 

 

 

73

registers in the computer memory is used by the UNI uniform random generator
subroutine to generate uniform pseudorandom numbers for this study.

The advantages of pseudorandom numbers over purely random numbers is that the
computer can generate them. Moreover, an important statistical advantage is the ability
of such subroutines to reproduce the same sequence of pseudorandom numbers if it starts
with the same initial value in the generating formula.

5.2.3 Generation of Correlated Random Numbers:

From the analysis of different human load motions, it was found that correlation
exists among control point arrival times and in some cases among the control point
amplitudes. It is therefore necessary to preserve the same correlation structure if these
variables are to be estimated as random variables to simulate the motion of an individual.
The procedure explained here to generate correlated random variables was programmed
by Harichandran, (1992), and is based on a methodology explained by Johnson, (1987)
for the generation of multivariate normal distributions.

Assume that it is desired to generate y,- random variables which maintain a correlation
structure preserved in the covariance matrix cov 0’10.)- The samples of y could be
generated from a sample of independent standard normal random variables x,- using the

following linear transformation :

[Y]=[H][X]+[p.] ............. [5.7]

where H is a lower triangular transformation matrix that relates to the covariance matrix

of the correlated variables y,, and 11 is a vector of the mean of each variable y,, Then it

can be shown that

 

 

 

74

E[YYT] = E[HxxTHT] = HE[XXT]HT---- [5.8]

E[YYT] = HHT ................ [5.9]

since the product of E[ X X’] is an identity matrix because the random variables xi's are
independent and have a unit variance. Then knowing the left hand side of eq. 5.9 which
is the definition of the covariance matrix, the entries of the matrix resulting from the
product H HT is found and therefore the matrix H could be obtained. Equation 5.9

represents the Cholesky factorization of the symmetric positive definite covariance matrix

of Y.

5.2.4 Monte Carlo simulation

Generally, a simulation model seeks to duplicate the behavior of a phenomena
knowing the statistical properties of its random variables and the interactions between its
components. Simulation results will reach steady state only after the numerical
experiment is repeated a sufficiently large number of times. Thus, in order for the output
of a model to be representative of what would be expected in the long run, simulation
must produce a large enough sample (or be repeated enough times) to ensure
representative results.

Monte Carlo methods are those in which pr0perties of the distributions of random
variables are analyzed by use of simulated random numbers. The Monte Carlo method
can be defined in a broad sense as " any technique for the solution of a model using

random number or pseudorandom numbers" (Hammersly and Handscamb 1964). One

 

 

 

75

 

application of the Monte Carlo method is to find the distribution or some of the
parameters of the distribution of a stochastic variable (probabilistic variable). This
variable is a known function of one or more other stochastic input variables that have
known distributions. The method involves the determination of the distributions of the
parameters, selection of a random sample of each parameter, and combination of these
samples to obtain a measure of overall performance or reliability. The process of random
selection and determination of response effects is repeated a large number of times, each
repetition resulting in another independent estimate of the modeled function. As the
sample size increases, the distribution of the sample becomes a better representation of
the distribution of the population.
In this study, Monte Carlo simulation is used to produce a lOOO-point sample of

force-time history values for each load type combination provided by the user of HLS.

5.3 Transient Load Modeling

Transient loads are modeled in HLS in a process consisting of four stages:

I a) Input from the analyst provides the program with the necessary information to
determine the type of transient action, number of participants, and type of output
media (printer, screen, or files).

I b) The program reads the parameter files for the selected motion which contains
the control points statistics, phase lag parameters, and the model error (explained

next). The seed array for the random number generator is read at this stage.

 

 

 

 

76

I c) HLS then calls the appropriate subroutines for the selected actions to determine
the force-time history in the vertical direction, and computes the maximum
positive and negative horizontal components. The model error is generated at this
stage. The group force-time history is also calculated, and the maximum and
minimum values of the generated forces are prepared for the output stage.

I (1) Calculated individual force-time histories along with the group force time
history are sent to the requested output media at this stage. The program plots
force-time histories to the screen with the important statistics and saves all output

files in the same directory that the program is running from.

Figures 5.2 and 5.3 shows typical screen output for the case of a single jump and
sitting down by one individual.

In the next section, the mathematical approach used in developing load models for

transient motions is explained. The single jump motion is used to demonstrate the

methodology and the steps for arriving at a reliable estimate of the load produced by an

individual, any number of individuals, or a group.

5.3.1 Mathematical Approach

Vertical forces from transient actions are modeled in HLS as a series of lines or
curves that closely fits data measured earlier and maintains the same control points
statistics and correlation between different arrival times and amplitudes. Horizontal

components are modeled as two impulses with magnitudes and arrival times that conforms

to the observed measurements.

 

 

 

 

 

 

 

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Figure 5.2 HLS Screen Output (Single Jump, One Individual)

SITTING DOWN

 

FRAS A RATIO TO WEIGHT

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

FyAS A RATIO T0 WEIGHT
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Figure 5 .3 HLS Screen Output (Sitting Down, One Individual)

 

 

 

 

 

 

 

 

78
Random Variables

The process of transient load modeling starts by determining the weight of the person
or persons performing a certain type of transient motion. Two options are available to
the user of HLS ; one is to provide weights, the other to use the random number
generator to estimate this variable. Currently, simulated weights are based on a model
suggested by Sidney (1974). The model is a log-normal probability density function with
a mean of 163 lbs, and a standard deviation of 17 lbs.

The response lag 0, for any sample is predicted as a log-normal random variable with
a mean of 0.27 7 seconds and a standard deviation of 0.087 seconds. Generating a log-
normal random variable is based on the assumption that if a variable 0 is log-normally
distributed with a mean of 11, and a standard deviation of 6,, then the natural logarithm

of 0, denoted as Ln ((1)), is normally distributed.
assuming )1 = 111(9)) .............. [5.10]

coefficient of variation as follows:

a
with Coeflicient of Variation V10) = p—i’ -------- [5-11]
0

and mean and standard deviations are calculated as:

 

 

 

 

79

 

Estimating a log-normal random variable is a three-step process. First the transformed
variable y is obtained by from Eq. [5-10] and treated as a normal random variable with
a mean and standard deviation calculated from Eq. [5.12] and Eq. [5 .13]. Then a
random variable is generated for the variable y , within the given mean and standard
deviation, using random generations techniques discussed in Section 5 .2. Finally, the

random value (1) is computed as :

It is essential to note that log-normally distributed random variables cannot assume
values less than zero. This assumption is suitable for the Response Lag in this case since
participants always wait for the prompt to perform the intended motion.

Correlated Random Variables

Arrival times and amplitudes are generated as correlated random variables using the
procedure in Section 5 .2. Random variables with any probability distribution function
other than the normal were transformed to normal equivalence. The covariance matrix
of the correlated variables were computed by multiplying the correlation coefficients by
the appropriate standard deviations. The subroutine HMATRIX was used to perform
linear transformation of standard normal variables to obtain the correlated variables. The

mean values of the correlated variables were then added to the generated random
variables. Then the new correlated random variables were transformed back to their
original assumed distribution. It was found that the best-fit distributions for all random
variables in the study were either normal or log-normal. Therefore, the transformation

was performed using the process outlined in Eq. [5.10] through Eq. [5.14].

 

 

 

 

80
Model Error

The load model is constructed by fitting straight or curved lines to the randomly
estimated control points. The determination of using straight lines or curves was based
on minimizing the error or the difference between generated and measured load histories.
A program MODEL.FOR, was used to fit the control points to the measured data and
connect the points first by straight line and then by second degree curves. Estimates of
the error associated with each trial were calculated. Figure 5 .4 is a typical screen output
from the program which shows an average error calculated from 45 samples of a single
jump by one individual. The error spectrum was calculated for the average error and it
is shown in figure 5.5. It was found that straight lines provided less error in most cases.
Figure 5 .6 shows a typical single jump where only one curve line was needed to connect
control points 5 and 6.

Further analysis was conducted on the error function which was defined as the
difference in amplitude between measured and fitted data. Treating the error function as
a random process shows that over a large number of samples, the random process
approach stationarity and therefore realizations of the error can be predicted from its
amplitude spectrum, Newland (1987).

It is essential to note that for this particular case of single jump, a part of the process
is known to be deterministic; that is the airborne time where the dynamic force ratio is
always -1 . This deterministic part of the motion disturbs the assumption of stationarity.
The problem could be avoided by removing the error terms from the deterministic porion

of the motion. Another alternative would be to divide the error process into three

 

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82

segments; one before the airborne time, then the deterministic part followed by the
landing part. The first and third segments could then be treated as two separate random

processes. Removing the error term from the deterministic part was chosen in this study

to simplify the modeling process.

Model Error Simulation

The error functions were simulated from their spectra for each generated sample and

Control Polnts for a Single Jump

  
 

3 2
g.
.3 1
.9
g .

-1

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
Time (Sec.)

Figure 5.6 Straight and Curved Lines of Single Jump Model
then added to the simulated force ratios in the three principal axes of motion. Taking
advantage of the central limit theorem and assuming that the error variable is the result
of summing many statistically independent variables, the error function is assumed to
approximate a Gaussian random process, Newland (1979). The mean and variance of the
error stationary Gaussian process is computed for each motion considered in the study

using the program MODEL.FOR.

 

83

To ensure consistent estimates of the error function realizations using the computed
power spectrum, several smoothing band widths were considered. Figures 5 .7 and 5 . 8
are two of the error spectra where the smoothing bandwidth in the first figure was about
0.73 Hz. while it was 0.36 Hz. for the second. It can be concluded from visual
inspection of the two figures that the bias introduced into the spectrum when using the
higher bandwidth is not significant. The power spectrum in figure 5 .7 was used in this
study to generate error functions for the case of single jump.

Assuming the process to be a zero-mean, real-valued, stationary Gaussian process
E(t) , and using the one-sided power spectral density function 6(0)) , the subroutine SIM U,
adopted from Harichandran (1992), is used to generate samples (realizations) of E(t) using
the following simulation technique, Soong (1992):

l. Minimum and maximum frequencies are determined for the simulation such

that the area under the one-sided power spectra could be approximated as:

5(w)=a(m),for0sws3 ......... [5.15]

l The reduced power spectra is then partioned into non-overlapping intervals I: of
width A0)" and amplitudes 8,, determined from the one-sided reduced spectra.

I The variance 6 7,, for each interval is calculated as the area under the spectra,
Figure 5 .7.

l A series of independent random variables (1),, are generated to be used in the Fast
Fourier Transform algorithm, FFT, to obtain a sample of size m of the estimated

error function. The variable (1),, is distributed uniformly over the range (0, 21:).

 

 

84
' The approximate sample (realization) of the error process E0) is then generated

Error Spectrum (Single Jump), b=0.73

 

 

0 1 2 3 4 5 6 7 8 91011121314151617
Frequency (Hz.)

Figure 5.7 Single Jump Error Function, b = 0.73 Hz.

Error Spectrum (Single Jump), b = 0.36

1.00
7

 

 

 

0 1 2 3 4 5 6 7 8 91011121314151617
Frequency (Hz.)

 

Figure 5.8 Single Jump Error Function, b = 0.36 Hz.

 

 

 

 

85

using the SIMU subroutine which applies a Fast Fourier Transformation on the

following stochastic process, Soong (1992) to obtain the error function:

Zm(t) = fiancos(wnt+()n) ......... [5.16]

MI

I The process is repeated for each simulation of the human load and the resulting

error function is added to lines and curves connecting control points.

Horizontal Force Ratios

Horizontal force ratios were estimated as correlated random variables based on the
measured data statistics. For each horizontal component (parallel and perpendicular to
seating), the maximum and minimum force ratios were computed. Arrival times to these
force ratios were determined as correlated random variables to the arrival time of the
maximum force in the vertical direction. Amplitudes of the force ratios were found from
the respective probability distributions, means, and standard deviations. Modeling error

was established using the same process explained earlier for vertical force ratios.

5.3.2 Load Simulation

The procedure explained in Section 5 . 3.1 were applied to each of the three transient
motions considered in this study (single jump, sitting down, and standing up). Typical
screen views of HLS output were shown earlier in figures 5 .2 and 5 .3. For each
simulation, the program provides the dynamic force ratios in the three principal axes of

motion along with the control points and the peak amplitudes of the sample.

 

 

 

 

 

 

 

86

 

For each motion type, HLS was used to simulate an ensemble of lOOO-samples of
the motion and mean, standard deviation, and probability distributions of the control
points of the ensemble were estimated. These values were then compared to the ensemble
of measured data. Tables 5.1 through 5.3 present these statistics and show the absolute
difference between the measured and simulated values as percentages of the measured
. data. The tables demonstrate that the simulated samples converged to the measured data

with differences of no more than 5 % of the measured data.

5.4 Periodic Load Modeling
Periodic loads are modeled in HLS, in a process consists of five stages
I a) Input to the program provides information needed to determine the type of

periodic action, prompt or stimulus frequency, number of participants, and type

 

 

 

 

 

 

 

 

 

 

1.90%

. Simulation 0.323 0.915 . .
Tune Difference 0.20% 1.60% 1.40% 1.40% 1.30% 1.30% 1.40% 1.20%
St. Dev Measured 0.086 0.041 0.106 0.117 0.192 0.187 0.262 0.286
1:12;]? Simulation 0.088 0.04 0.106 0.116 0.188 0.183 0.249 0.273

Difference 2.90% 1.30% 2.10% 5 .00% 4.40%

 

 

 

Measured

3.155.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Mean -0.062 1.134 -0.427
Aum Simulation -0.06 -O.Sl6 1.144 -0997 -0.992 3.22 -0.43 0.051
Difference 3.70% 0.50% 0.90% 0.00% 0.10% 2.00% 0.70% 0.90%
St. Dev Measured 0.063 0.196 0.459 0.069 0.055 1.372 0.132 0.134
Amplit simulation 0.063 0.2 0.458 0.067 0.054 1.409 0.186 0.132
Difference 0.40% 2.00% 0.10% 2.40% 1.40% 2.70% 2.40% 1.30%

 

 

 

 

 

 

  
    
   

87

 

 

Measured
Simulatio
Difference
Measured
Simulatio
Difference .

 

 

 

 

 

 

 

 

 

Measured

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Simulatio

Difference 1.40% 1.30% 0.50% 0.40% 1.40% 0.90% 1 1.10%
St. Dev. Measured 0.064 0.594 0.306 0.291 0.737 0.227 0.131
Amplit. Simulatio 0.067 0.596 0.291 0.277 0.697 0.228 0.134

mffprpnm: 4 50% a 30% 4 30% o 5 40% Q 40% o

 

 

of output media (printer, screen, or files).

 

I b) The program reads parameter files which contains control points statistics,
phase lag parameters, model error spectra, and the seed array for the random
number generator.

I c) HLS then calls the appropriate subroutines for the selected actions to determine
the force-time history, and computes peak statistics for the selected motion. The
model error function as a random process is generated at this stage and added to
the force-time histories.

I d) The one-sided power Spectra for the simulated dynamic force ratios is

computed and plotted to the screen.

 

I e) Calculated individual force-time histories along with the group force time

history, if requested, are sent to the requested output media at this stage. The

 

program is set up to plot force-time histories and spectra to the screen. Other

important statistics are saved in a summary file.

 

 

 

88

The stochastic approach to deve10p load models for periodic motions is explained.
in the next section. A first order linear Markov process is used to approximate the
arrival time and amplitude peak of control points. The process as an autoregressive
function is explained in detail for the periodic jumping motion. Application of the
process is then extended to other motion types.

5.4.1 Stochastic Analysis

Statistical analyses of measured periodic loadings revealed a consistent pattern of

 

Table 5.3 Measured Versus Simulated Control Points For Standing up

 
 

 

Measured
Aviva! Mean Simulation 0.298 0.231 0.529 0.611 0.865 1.009

11'
ms Difference 2.30% 1.00% 0.30% 0.50% 0.90% 0.60%

Measured 0.17 0.12 0.181 0.195 0.37 0.379

5‘ De“ Simulation 0.173 0.118 0.175 0.192 0.377 0.379

Difference

 

 

 

 

 

 

  

 

 

 
 
 

 

 

Measured
Simulation 0.005 0.986 -0.672 -0.644 0.73 0.026
Difference 8.70% 0.50% 1.90% 2.20% 1.90% 1 1.10%
Measured 0.016 0.33 0.35 0.39 0.268 0.088
St‘ Dev. Simulation 0.016 0.328 0.347 0.386 0.264 0.092
Difference 0.30% 0.70% 0.90% 1.10% 1.60% 5.00%

   

 

 

Amplitudes

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

arrival times and amplitude peaks of cycles within each recorded sample.

For arrival times, It was observed that participants always attempted to adjust their
motion period to match that of the prompt. This behavior was shown in Section 4.4.1
to be consistent from one individual to another and suggests some dependency between

the period of the current cycle and the next one. If the probabilistic behavior at the

   

 

 

89

present, given all of the past behavior, depends on only the most recent past, the process
is called A Markov process. Understanding the phenomena of human jumping would

further suggests that the motion in a present cycle may be approximated by considering

only the previous cycle.
The process X is considered a first order linear Markov process, or a first order

autoregressive process if it satisfies the difference equation:

Xt—aXt_l = C(t) ............... [5.17]

where a: is a constant and C(t) is a stationary purely random process to represent the
"random disturbance" portion of the process, Priestley (1981). If the jumping period of

a participant is assumed to be a first order Markov process , then Equation [3 8] could be

rewritten as:

T" - a TM = C ( n) .............. [5.18]

where T, is the period at cycle n. Equation [5.18] could be interpreted as a linear

regression equation to estimate the period T at cycle It knowing the value of the period

at cycle n-1 .
Tn = a Tn-l + c ( n) .............. [5.19]

The process is then simplified by assuming initially conditions the period has a value of

zero and Eq. [5.19] will results in :

T1 = c ( 1 ) ................. [5.20]

and Eq. [5 .19] is then rewritten as:

 

 

 

 

 

 

90

Tu = (n + a ( (H + a Tm2 ) ............ [5.21]
Tn = (n + a (H + a2 (H + a3 (H + ,,,,,,, + art-1 T1 . . . . [5.22]
and using Eq. [5 .20]:
T,I = C” + a CH + a2 Cm2 + ....... + a"‘1 C1 ------- [5-231
and if E(T,_) = pg, then
E(Tn) = “c(a+02+ ,,,,,,, .an-l) ......... [5.24]

II

 

EN.) = 16(1‘“

) for a at 1 ........ [5.25]
1 — a

and E(T,,) = [Lg n for a =1. If the mean of the disturbance function is zero, then the
expected value of the period is zero and does not depend on the cycle number; i.e a
stationary process up to the first order. If the mean of the disturbance function is not
zero, then the expected value of the period will be a function of the cycle number and the
process is not stationary. However, if the absolute value of the constant coefficient a is
less than zero, it can be proved that for large cycle numbers n, the process T" will be

" asymptotically stationary" to the first order and computed as follows, Priestley, (1981):

 

E(Tn) = 1‘: forlargen. la|<1 ...... [5.26]

A similar process is then repeated for evaluating the variance and covariance of the

process T(n), and the following equations are obtained:

 

 

 

 

 

91

 

)= 5(7; T,.,) e of a for |a|<1.[5.27]

cov ( T", T
l-a2

11+?

and it can be said that the process T, will be "asymptotically stationary" to the second

 

order given the absolute value of a is less than one. The autocorrelation function for the

process is thus:

R(r)=al'l, r=0¢112131 .............. [5°30]

which decays to zero exponentially as I r 1 increases.

The outlined procedure from Eq. [5.17] through [5.30] is also applied to amplitude
peaks which was observed to have the same pattern of the Markov property. The process
of preparing and analyzing measured data consisted of the following steps:

I The CONTROLFOR program was used to determine the period and peak ratio
of every cycle of each sample in the ensemble of measured data. The program
reports the value of the current and last period and peak ratio for each cycle in the
periodic process. Table 5 .4 shows a typical sample of this process for a periodic
jumping test 2 Hz for one individual.

I The constant value a was estimated from each sample in the ensemble of

measured data for the considered motion using correlation program CORREL.

 

 

 

92

Two values of the constant a are estimated from Eq. [5.28]. These are a], and
a, for the arrival times T and peaks P which are the random processes of each
sample.

I The value of the disturbance function C(n) associated with each process was also
computed and analyzed for determining its statistical properties.

I The mean and the standard deviation of a, and a, were calculated over the
ensemble of measured data to determine the probability distribution function that
best-fit the variables.

Table 5 .5 shows the statistics of the constants a, and a, for the case of periodic
jumping at frequencies 2, 3, and 4 Hz. It can be seen from the values in the table that
the positive correlation between each cycle and the cycle before it was stronger for the
2 Hz. jumping in comparison with the 3 and 4 Hz. jumps. This was found to be valid
for both the period and the peak ratios and it also verifies the observation made earlier
in chapter 4.0 about the inability of participants to adjust to the prompt at Integer

frequencies higher than 2 Hz.

5.4.3 Load Modeling

The periodic motions were modeled in HLS, as first order linear autoregressive
processes where the period the amplitude peak of each cycle are generated from the
procedure explained earlier. For each periodic motion considered in the study (Jumping,
jouncing, and side swaying) the program provides the dynamic force ratios as a time

series and computes the spectral density function for the simulated motion.

 

 

 

93

Table 5 .4 Periods and Peaks for a Typical Periodic Jumping

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0.000 3.371 0.000
0.471 3.001 3.371
0.558 2.891 3.006
0.559 3.171 2.891
0.530 3.594 3.171
0.559 4.535 3.595
0.500 3.354 4.536
0.558 4.533 3.544
0.530 4.200 4.532
0.529 4.418 4.200
0.265 3.331 4.418
0.559 -1.023 3.330
0.294 3.854 4.027
0.559 3.918 3.854
0.530 4.357 3.199
0.500 2.883 4.357
0.558 3.209 2.883
0.265 -0.935 3.209
0.265 3.615 4,935
0.529 3.523 3.615
0.559 3.728 3.523
0.529 2.756 3.728
0.559 3.265 2.756

 

 

 

 

For each periodic motion, three ensembles of lOOO—samples of the motion were
Simulated at the frequencies 2, 3, and 4 Hz. The mean and the standard deviation of

peak force ratios and motion period were compared with measured data statistics to verify

 

 

 

94

Table 5.5 Constants a, and a, for the Periodic Motions

 

 

 

 

 

 

 

 

 

 

 

 

 

 

the proposed model. Table 5.6 presents these statistics and shows the absolute difference
between the measured and simulated values as percentages of the measured data. The
table demonstrates that the simulated samples converged to the measured data with
differences of no more than 1% of the mean measured data. Simulated data from all
motions showed smaller standard deviations than the measured data. This is due to the
fact that in measured data there were always cases where some individuals chose to end

their m0tions earlier than others in the same group.

Table 5 .6 Measured Versus Simulated Data (Periodic Jummng)

...............................................................................................................................................

 

 

 

 

     

.........

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6 .0 Model Applications

6.1 Introduction

This research provides an accurate model of loads due to several human actions. The
model could be used to verify existing code values, provide a tool for use in reliability~
based designs, and study the effects of human loads on various special structures.
Modeling Transient action would be useful in the design of elements that support mainly
transient loads such as spring boards and staircases steps. Periodic loads are more likely
to govern in the vibration prevention design stage especially if the loading frequency is
close to the natural frequency of the structure. It has been confirmed that periodic
loadings are major contributors to most of the documented cases of human discomfort
due to vibration of assembly structures, Bachmann (1988). It has also been observed and
verified that periodic motions would produce the maximum forces on structures when
compared with transient and random motions produced by the same group of persons.

It is expected that the research conclusions would provide a basic tool to be used in
changing building codes to provide designs which are not only safe against catastrophic
failure but serve their purpose without harmful or annoying vibrations or deflections.
6.2 Group Load Simulation

A modified version of The Human Load Simulation program, HLS is used herein to

generate loads for a group of participants and compare it with similar measured data.

95

 

 

96
The periodic loading module is used to illustrate the ability of the program to generate

group loadings. The modified model, GROUP.FOR uses the procedure outlined in last
chapter to generate periodic jumping for individuals. Force-time series from each
individual is then added to a new array denoted here as the group force-time series. This
process takes into account the fact that each individual would start the periodic motion at
a different time (the response lag). Although the main focus in this process is to obtain
the maximum force ratio of the group of individuals, the program does not attempt to
align the peaks of different individuals. The assumption here is that every individual
would jump independently and the overall force is the result of adding individual forces
at each discrete time point in the time series. Statistics from measured data showed that
the larger the group that performs the same action at the same time, the harder it is for
individuals to maintain coherency and the lower the overall generated dynamic force-
ratios, Table 3.7. Using the same weights from measured data, a simulation of 100-
samples per group of individuals were conducted using GROUP.FOR.

Output Showed that simulated mean peak forces were always lower than the measured
data. Moreover, the ratio of the difference to the measured data was found to have a
consistent pattern. Table 6.1 summarizes this finding. It shows the measured versus the
simulated maximum peak force ratios for groups up to 40 participants.

The table illustrates the possibility of a non-linear correlation between the group size
and the dynamic force-ratio generated by an individual within a group. This phenomena
has been addressed in earlier Stages of this project, Tuan (1981), and Mcdonald (1984).

However, insufficient data hindered studying the pattern.

 

 

97

Although other potential factors may have contributed to the pattern shown in table
6.1, the " group factor " may still be the dominant part of the shown trend. It has been
observed throughout the data collection process that individuals motions were always

influenced by neighbors motion. Having active individuals within a group seemed to

Table 6.1 Measured Versus Simulated Maximum Force Ratios

 

 

 

 

 

 

 

 

 

 

 

 

 

 

energize other individuals in the same group. It is important to emphasize however, that
this conclusion has not been studied statistically to justify it due to the lack of sufficient
measurement. The measuring devices utilized in this study were not designed to measure
individual motions of participants in a group. The output force-time histories were
always the recording of total motion on the device.

The program GROUP.FOR was modified to include a non-linear regression model
to account for the trend explained earlier, and denoted as the " group factor ". Screen
output from the modified program are shown in Figures 6.1 and 6.2. The figures show
that the simulated group of 10 individuals produced a maximum peak ratio of 1.87 while
the simulation for 40 individuals produced a dynamic force ratio of 0.511. Since the
simulated experiment starts with a response lag that was drawn from a distribution with
a small coefficient of variation, high peaks have more probability of occurring at the first

portion of the force-time series. The pattern was observed in the simulated data figures

 

 

 

98

 

GROUP SIMULATION

 

Fl AS A RATIO IO \AIEIGHT

Minimum ninth/17
.. iv . v VVVIV

 

i

 

o-q)r moron
.-"
3 8

 

 

 

 

'ZW f l r
.0 20 40 $0 00 100
TIMEtsocJ
SIMULATION : 1 meme...

 

Periodic Jumping with 1 Person
Weight-156. Lbs. Prompt- 2.00 Hz.

‘0‘”00'010

Jumping Frequency --> 2.002 83.
Jumping Period II) .500 Sec.

net. Peak Ratio --> 1.314

_- A_-_

Sinuletioa: 1 out at 10 .o 2.0 '.o 80 10.0

'.o 8
ur am To com-1mm. .. “MW”
Figure 6.1 A Typical GROUP.FOR Output, 10 Individuals

m

GROUP SIMULATION

 

8838888888

 

 

‘C"‘”¢300

 

 

 

 

FzAS A RATIO TO WEIGHT

 

 

 

 

 

 

é... [LEA/1117414111411 10111.14...
:. UUUVVVVVVWWWWVW‘
:E;|'V1l-Jl-J‘\:T-lc:)r\l : IE5 AUTOQWKHRUM

 

Periodic Jumping with 40 Per(s).
AVG. Wt-163.Lbs. Prompt-2.00 Hz.

nub-A

seeaagg

Jumping Frequency II) 1.958 Hz.
Jumping Period II) .511 Sec.

Hex. Peek Ratio II) .626

 

 

.0 do I) 6.0 do 1110
ananufla

 

“"V‘DOO ‘e"'flID(n

Simulation: 5 out of 40

II? INTER TO 60371101....

Figure 6.2 A Typical GROUP.FOR Output, 40 Individuals

'4:

 

 

 

 

 

 

 

99

6.1 and 6.2 reaffirm the observation Table 6.2 summarizes the modified simulated

maximum peak ratios. Maximum difference between measured and simulated group loads

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

was found to be less than 5%
6 .3 Code Verification

The focus of this study was to define the force—time history produced by one
individual or a group of individuals performing a predefined typical motion. Measured
and simulated human loads in the research provide a limited sets of data in the much
larger spectrum of activities, motions, frequencies, and participants composition. In order
to transform these load values into structural design loads, other variabilities such as
spatial and temporal variations must be considered. However, knowing the maximum
force ranges produced from each motion simulated in the study may help in verifying

current code values for assembly structures where human beings are the major source of

 

live loads.

The highest loading effects were simulated using the Human Load Simulation

program, HLS developed in this study. Statistics from the collected data confirmed that

 

 

 

 

100

 

periodic motions produced the highest vertical load ratios. Swaying side to side in a
standing position presented the maximum force ratios in the horizontal direction and
parallel to the rows of seats. Maximum transverse horizontal force ratios (perpendicular
to the seating) was always associated with motions that produced maximum vertical force
ratios. The single jump by an individual was found to produce the highest vertical and
transverse force-ratios among all actions considered in the study (Periodic and Transient).
Table 6.3 is a summary of the load ratios obtained from the current research. The log-
normal distribution was found to be the best-fit distribution for all the dynamic force
ratios in the table.

It is proposed here to consider two separate cases of loading conditions for code
verifications. One case is for structures subjected mainly to the forces of one person.
Typical examples would be spring boards, car seats, and steps of a stair case. The other
case is assembly structures where dynamic forces are typically generated by a group of
individuals. Dynamic force ratios in Table 6.3 could be utilized when designing
structures from the first case. Group loading conditions will form the bases for
suggesting dynamic load ratios for structures from the second case.

To illustrate the use of Table 6.3, a single jump by one individual is considered. A
typical individual would generate a peak vertical dynamic force ratio of about 3.2.
Assuming the individual occupies an area of 3.5 square feet, UBC (1982), and has an
average weight of about 163 lb, Sidney (1979), the mean dynamic force would be about

150 lb/ftl. Similarly, the mean transverse and parallel forces could be obtained from the

table considering that the code assumes parallel and transverse forces to be linearly

 

 

 

 

101

 

distributed over a length of 28 inches. The mean dynamic forces would therefore be
about 26 and 35 lb/ft for the parallel and transverse horizontal forces. The values in the
vertical and the transverse directions differ significantly from the current code values of
100 lb/ft2 for the vertical force and 10 lb/ft for the transverse force. This finding is
affirmed by other studies Tuan ( 1981), and McDonald (1984). It is emphasized however
that the suggested values are based on statistically limited data collection. Experimental
data is still needed to arrive at more reliable estimates of load ratios.

Periodic motions would be utilized for load verification of the second type of
structures; assembly structures where dynamic loads are typically produced by a group
of individuals. It has been found that coherency among individuals performing transient
actions is generally low and therefore it significantly reduces the overall group force-
ratio.

Periodic jumping at about 2 Hz. was found to produce the largest vertical and
transverse force ratios. The inability of individuals to maintain perfect coherency tends
to reduce the group force ratios when more than one person attempts the action. It has
been observed however, that a group effect exists in periodic motions where individuals
may influence the motions of others in the same group. Taking both observations into

account and reviewing the measured and simulated data, it is proposed to use the
"Dynamic group factor" introduced in chapter 3 .0 to modify the mean dynamic force

ratios in Table 6.3. The Dynamic Group Factor, denoted as DF, has the following form:

DF = 0,97" 4 Fr ................. [6.1]

 

 

 

 

 

 

 

102

1",: Mean dynamic force ratio of one individual

n : Crowd size
Equation [6.1] should be used to reduce the mean dynamic force ratio for periodic actions
in Table 6. 3. The corrected force ratios could then be employed to estimate an upper
bound to the dynamic force by a group of individuals performing any of the actions
simulated in the study. When periodic jumping was used to verify code values, it was
found that the code values would provide acceptable maximum ranges for both the
vertical and the parallel components of the periodic motions. However, the transverse
component was found to be significantly higher than the code value. It is therefore
suggested to increase the load value of 10 lb/ ft in the transverse direction to 45 lb/ ft.
Other literature showed the finding to be valid. Tuan (1983), suggested a value of 43

lb/ ft for the same force component.

6.4 Reliability-Based Design

Generally, the reliability of any system is defined to be the probability of performing
adequately for the period of time intended under the operating conditions encountered.
The reliability of a structure is also defined as the probability that the structure will not
exceed any of its limit states during a specified time period. In the case of human, one
of the limit states loadings on assembly structures could be considered as the probability
of not exceeding a certain vibration level. A certain value of acceleration may be another
form of a limit state. Defining the statistical parameters of the dynamic human loads is

therefore an important and essential ingredient in finding the overall reliability of the

 

 

 

 

103

Table 6.3 Dynamic Force Ratios for One Individual

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

structure under analysis.

A currently used measure to describe structural reliability is the reliability index, B.

It represents the distance, in Standard deviations, from the set of variable values that is

 

most likely to occur to the set of variable values that is most likely to cause failure. The
reliability index 13 is directly pr0portional to the difference between the mean values of
the load L and resistance R. where 6L, O'R are the standard deviations of load and

resistance respectively. It should be noted that this formulation for the reliability index

 

 

 

 

 

 

 

104

is valid only if both of the load and resistance are normally distributed. Moreover, the

same principles apply for other distributions.

R -L
13 - Z "'2 .................. [6.2]
o, + 01.

Although the reliability index does not directly indicate a value for the reliability of
a structure, it can be used to indicate a lower bound on the reliability and also to serve
as a relative measure for the level of safety of different structures. Beyond that, we can
only state that, for a given structure, larger values of the reliability index represent
greater reliabilities than smaller values.

The reliability index usually varies from 2.0 to 8.0. Analysis of 3 values for
specifications governing the design of buildings in the United States indicates that B
typically ranges from 3.0 to 4.0. These values are for members designed to resist gravity
loads in situations where failures are ductile, Ellingwood (1980). It is however
important to emphasize at this point that, whereas the reliability index (B) is not a direct
measure of the reliability, it is a useful comparative measure and can serve to evaluate
the relative safety of various structures.

The advantage in simulating dynamic loads produced by human actions may greatly
benefit the reliability design concepts. Knowing the load statistics enables a designer to
simulate over all probable values for loads and resistance and then determine the
acceptable level of safety. The load ratios developed in this study for several human

movements could be used in design cases where the knowledge of load variabilities would

 

 

 

 

 

105

 

enhance the ability to assume the appropriate safety measures and reliability for the

intended structure.

6.3 Other Potential Applications

It is anticipated that the results of this research will be very useful for a broad range
of building industry. following are some potential examples:
Floor Vibrations

Modern structures which have slender and elegant elements can be very sensitive to
vibrations. Increasing numbers of excessive floor vibration incidents caused by human
movements have been reported recently, Buchmann (1992), and Sterareh (1992). The
coincidence of the natural frequencies of the floor system with human movement
frequency is the major cause of this problem. The correspondence of the structure' 8
natural frequency with the frequency of a higher harmonic of the time history of the
dynamic excitation has also been realized to lead to resonance. To reduce the effect of
annoying vibrations on the serviceability of structures, several solutions have been
suggested. Among them, are the modifications of the floor stiffeners or mass, increasing
the system damping, and/ or limiting the vibration amplitudes. The accurate
representation of the dynamic forces applied on the structure is essential to develop a
reliable solution to the excessive vibration problem.

Manufacturers of floor systems, timber, pre-stressed concrete, open-web steel joists,

and other combinations of geometry and materials may be willing to conduct a computer

 

 

 

 

106

simulation to anticipate potential problems rather than doing a full scale test or risk an

adverse design for prototype installation.

Safety Studies

Insurance companies concerned with adverse or potentially harmful loading due to human
actions or occupancy, such as occurred at the disastrous Kansas City Hyatt sky bridges,
could be interested in a tool which has the capability of simulating a situation in a

computer prior to construction, or in another scenario, analyzing an occurrence so as to

remedy a problem.
Education

The Human Load Simulation program, HLS, could be used as an educational tool for
graduate courses dealing with reliability design, random processes, theory of random
vibrations, and dynamic of structures. The ability of the program to simulate several
loading conditions (transient and Periodic) and to produce pseudorandom processes could
help in illustrating many of the concepts and applications of these courses. An instructor
could utilize the random number generation features in HLS to produce random variables,

correlated variables, or Markov random processes for any application since the produced

variables would be dimensionless.

 

 

 

 

7 .0 CONCLUSIONS

7 .1 Summary

In addition to many other possible applications, human loads are the primary concern
in the design and analysis of assembly structures. Human loads vary from event to event
in an apparent pattern and they can be shown to be predictable statistically. The focus
of this research is to quantify the uncertainty associated with the loads due to human
movements. Providing accurate models of probabilistic functions to represent forces due
to several predefined human movements was the main objective of the study.

A detailed review of current state of knowledge in the field of modeling human loads
is presented. The study also provides an overview of current practice in the design
process and how the present U.S. codes characterize human loads on assembly structures.

Data taken from tests performed on a force platform and a floor system were
obtained from three sets of experiments; two designed to measure the force due to the
action of an individual and the third designed to measure the force due to the action of
a group. Two different test devices were utilized. A 4 ft by 8 ft force platform was used
for measuring the vertical and horizontal components of loads produced by individuals
and small groups up to five participants. The other device was a 12 ft by 15 ft floor
system designed to measure total vertical loads generated by a group of people of up to
forty participants. The study includes six different in-place human movements grouped

into two categories; transient motions which includes single jumps, standing up suddenly

 

 

 

 

 

108

 

from a sitting position, and dropping into a seat from a standing position; and periodic
motions which includes periodic jumping, jouncing, and swaying side to Side.

For each transient action in the study, a method based on passing straight or curved
lines through control points that define the force-time history is used to simulate the
forces due to human actions. Best-fit distributions for the control points were determined.
An error function was developed and incorporated into the model to better represent the
modeled actions.

Periodic loadings were analyzed as a series of impulses where the forcing function
is divided into cycles each of which is a full period of motion considered. Statistics of
each impulse in the force-time history were computed and analyzed for correlation and
peak distribution. The motions were modeled as first order autoregressive processes.

An iterative model-building methodology whereby the stochastic models are related
to actual time series data was conducted. Model verification was applied to the different
motions considered in the study. A model to simulate group loading is provided. The
developed forcing functions are compared with experimental data and feed back from the
process is used to refine the forcing functions.

A computer program, Human Load Simulation, HLS; was developed giving
researchers an advanced tool to use in design and analysis. The forcing functions
developed by the program simulate several types of human movements. The program
may be used to simplify generating load distributions for any combination of human

loading conditions, similar to those presented in this research. Input to the program

includes information about the type of action to be simulated, group size, and parameters

 

 

 

 

 

 

109

necessary to define the individual loads. The program calls an array of subroutines to
calculate forcing functions for different human actions and these forcing functions are
combined in any form requested by the analyst. Output of the program is based on the
type of action and includes the following:

I Statistical parameters of the control points.

I Amplitudes of peaks and their arrival times.

I Spectral energy distributions for periodic motions.

I Force-time history for individuals.

I Group force histories (for group loading).

Several potential applications of the program developed from the study are presented.
Code values were examined and recommendations regarding the transverse horizontal

force is outlined. Other potential applications of the research outcome are also discussed.

7.2 Conclusions
This study indicates several conclusions with respect to the modeling of human load
movements:
I Measured data Showed that human movements can be reproduced using
probabilistic procedures.
I Periodic motions produced the highest vertical load ratios.
I Swaying side to side in a standing position presented the maximum force ratios in

the horizontal direction (parallel to the seatings).

 

 

 

 

 

 

7.3

110

Maximum transverse horizontal force ratios (perpendicular to the seatings) were
always associated with motions that produced maximum vertical force ratios.
The single jump was found to produce the highest vertical and transverse force
ratios among the actions considered in the study (periodic and transient).
Log-normal distribution was found to be the best-fit distribution for all peak force
ratios.

The developed program HLS, will simplify generating load distributions for any
combination of human loading conditions, similar to those presented in this
research.

Code values were examined and found to be acceptable except the transverse force
component where a value of 45 lb/ ft is recommended to replace the current 10

lb/ ft value.

Future Work
The study leads to the following areas of needed further work:

I The human load program developed in the study needs to be expanded to include

other types of human loadings.

I More statistical work is needed to establish the model error for human loads

provided by HLS.

I A study is needed to understand the effect of area of occupancy, floor type, and

coherency among participants on the overall force ratios of one individual in a

 

 

111

group. A state of the art force platform would enable measuring individual
forcing functions for individuals in a group.

Aerobic motions are interesting class of human motions which deserves to be
studied and modeled. Higher jumping frequencies and higher degree of coherency
are expected in this class of motions.

Studies on the effect of the prompt frequencies on the output forcing functions is
still needed. Available data are very limited in this perspective.

Taking advantage of the developed software may raise other potential possibilities
of using CAD interface systems to show the performed motions and generated
forces in real-time.

Additional work is needed to translate the results of this research into formats

suitable for use in design specifications.

 

APPENDIX A

DATA PROCESSING PROGRAMS

 

lldinthZhR

$STORAGE:2
$LARGE*

*
* * * * * * * * * * * * * * * * * * * i * * * * * * i * * * * * *

g.
‘-
4
It
I-
4
:1-
:1-
:1-
1(-

* * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * *

44
44
44
44
4*
44
44
44

APRIL 15, 1992

MAY 05, 1992

June 15, 1992

June 20, 1992 BASSEM K. KHAFAGI
AUG 16, 1992

Aug 24, 1992

Aug 30, 1992

Oct 5, 1992 MICHIGAN STATE UNIVERSITY
EAST LANSING, MI 48823
U.S.A

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * k * * * * * * * * * * * * * * * * * * * * * * * * * * * i *
*****************************************************************

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

++++++++++++++++ 1. DATA INPUT/OUTPUT ++++++++++++++++
++++++++++++++++++++++++++++++++++

*4-44'4*=$*fl-*N-**I+*X-**ik*flr**
*fi-**'**ik*fl'**it*I-#*'441+41'44

0000004444444444444444444444»

PROGRAM DATA.FOR

DIMENSION XVOLT(512,11), FX(512), FY(512), FZ(512)

DIMENSION BVOLT(1,11), VOLT(512,11), PROMPT(512)

DIMENSION TIME(512), PR(512), PRP(200)

DIMENSION XCALIB(11),YCALIB(11),ZCALIB(11)

DIMENSION XCALIBA(11),YCALIBA(11),ZCALIBA(11)

DIMENSION XCALIBB(11),YCALIBB(11),ZCALIBB(11)

DIMENSION FXP(512) FYP(512), FZP(512)

DIMENSION Fme(2001, Fme(200), Fme(200),twgt(200)

INTEGER WEIGHT(5),NAA(20)

LOGICAL*1 XABS

CHARACTER REPORT*12,INPUTS*40,JOB*40,dataset*1,TT*5,EXT*12,DP*1
CHARACTER FNAME1*3,FNAME2*3,FNAME3*3,FNAME4*3,FNAME*12,0UTPUTS*40
CHARACTER Filefla *2,fileflagn*2

CHARACTER*8 NAME( 0,200

COMMON /CMP/ M,N,FS,IWIN,L,NFFT,DF

COMMON /FILES/ INPUTS,OUTPUTS,LINP,LOUT

FLAG FOR THE OPEN SCREEN

OOO

DP='y'
OFLAG=1

Read INPUT Data from PARAMETER FILE "PARAM.DAT"

COO

OVJA
'11
E
El

112

 

113

DETERMINE THE LOCATION OF INPUT AND OUTPUT FILES

1.0 INPUTS

OOOOOO

LINP= LEN TRIM(INPUTS)
IF(LINP. NE. 0) THEN
INPUTS= —INPUTS(1: LINP)//' \'
LINP=LINP+1

END IF

2.0 OUTPUTS

LOUT=LEN TRIM(OUTPUTS)
IF(LOUT. NE. 0) THEN
OUTPUTS=OUTPUTS(1: LOUT)//' \'
LOUT= LOUT+1

END IF

START FILES' PROCESSING

READ (1,*) NG

DO 5 LL=1,NG

READ (1,*) NA

NAA(LL)=NA

DO 20 I= 1, NA

READ (1,16) FNAMEl, FNAMEZ, FNAME3, DATASET, FNAME4
10 FORMAT (A2, A1, A1,A1,.A3)
20 WRITE (NAME(LL, I), 30) ENAME1,ENAME2,ENAME3,DATASET, PNAME4
30 FORMAT (A2, A1 AL A1, A3)

IF (LL. EQ. 1 THEN
WRITE (EXT,9)JOB,fname2

GOO

000

9 FORMAT (A2,'-',a1,'-SUM.OUT')
OPEN (7,FILE=OUTPUTS(1:LOUT)//EXT)
END IF
5 CONTINUE
C
C
C Read spectral estimation parameters
C
READ (1,*) M
READ (1,*) IWIN
READ (l,*) L
READ (1,*) NFFT
READ (l, *) OF
CLOSE (l)
C
C
c +++++++++++++++++++++++++++++++++++++++
C +++++++++++++ 2. READING CALIBRATION EACTORS +++++++++++++
C +++++++++++++++++++++++++++++++++++++++
C
C
C READ THE CALIBRATION FACTORS FILES IN THE THREE DIRECIONS X,Y,Z
C USE THESE FACTORS TO CALCULATE THE FORCES IN EACH DIRECTION BY
C MULTIPLYING THE VOLT(I,J) * CALIB-X FOR THE X FORCES AND THE SAM
C FOR THE OTHER TWO DIRECTIONS Y,Z
C
C READ CALIBRATION FACTORS FOR THE X, Y, Z FOR DATA SET A,B
C
C
C OPEN THE CALIBRATION FILES IN THE X, Y, Z DIRECTIONS.
C
C

DO 35 NN=1,2
IF (NN.EQ.1) THEN
OPEN (3,FILE='X-CALIB.DSl')
OPEN (4,FILE='Y-CALIB.DSl')
OPEN (5,FILE='Z-CALIB.D81')
DO 40 J=1,11
READ (3,50) XCALIBA(J)
READ (4,50) YCALIBA(J)
READ (5,50) ZCALIBA(J)

40 CONTINUE
CLOSE (3)
CLOSE (4)

45

35
50

000

000

60
70

000

75

85

000

80

0000

90

100
110

00000

 

114

CLOSE (5)

ELSEIF (NN.EQ.2) THEN

OPEN (3,FILE='X-CALIB.DSZ')
OPEN (4,FILE='Y-CALIB.DSZ')
OPEN (5,FILE='Z-CALIB.DSZ')
DO 45 J=1,11

READ 3,50) XCALIBB(J)

READ 4,50) YCALIBB(J)
READ (5,50) ZCALIBB(J)
CONTINUE

CLOSE (3)

CLOSE (4)

CLOSE (5)

END IF

CONTINUE

FORMAT (11(E18.3))
START THE FILES-PROCESSING LOOP

DO 480 LL=1,NG
NA=NAA (LL )
DO 380 K=l,NA

E.G. THE LOOP CAN BE CHANGED TO K=1,5 IF WE WANT TO PROCESS 5 FILE

WRITE (FNAME, 60) NAME(LL, K)

FORMAT (A8, W)

WRITE (REPORT, 70) FNAME

FORMAT (A8,'.FRC')

READ (FNAME,10) FNAMEl,FNAME2,FNAME3,DATASET,FNAME4

determine the calibration files to use and the sampling rate for the test

IF é;DATASET.EQ.'A}).OR.(DATASET.EQ.'a')) THEN
FS= .

DO 75 J=l,11

XCALIB(J)=XCALIBA(J)

YCALIB(J)=YCALIBA(J)

ZCALIB(J)=ZCALIBA(J)

CONTINUE

ELSEIF ((DATASET.EQ.'B').OR.(DATASET.EQ.'b')) THEN
FS= .

DO 85 J=1,11

XCALIB(J)=XCALIBB(J)

YCALIB(J)=YCALIBB(J)

ZCALIB(J)=ZCALIBB(J)

CONTINUE

ENDIF

BEGIN BY OPENING FILES TO READ DATA

OPEN (2, FILE= INPUTS(1: LINP)//FNAME)
OPEN (6, FILE= OUTPUTS(1: LOUT)//REPORT)
READ (2,80) (WEIGHT(I), I= 1, 5)

FORMAT (/, 5(I4)//)

Now add the weights of participants to get TWEIGHT

TWEIGHT= O. 0

DO 90 I=1,5

TWEIGHT= TWEIGHT+WEIGHT(I)
CONTINUE

IF((Fname2.eq.

't'). or. (FnameZ. eq. 'T' ). or. (Fname2. eq. 'R' ). OR.
1(Fname2.eq.'r'))

N= 256
D0 100 I=1,N
READ (2,110) (XVOLT(I,J),J=l,11),PROMPT(I)
CONTINUE

FORMAT (11(F8.0/),F6.0)

+++++++++++++++++++++++++++++++++++++++
+++++++++++++ 3. NORMALIZING VOLT. READINGDS +++++++++++++
+++++++++++++++++++++++++++++++++++++++

000000

120

00000 000

144
134

000

140
130

000000

150

160

0000

000

115

 

SELECT THE FIRST (OR THIRD) VOLTAGE READING AS THE BASE TO NORMRLIZE
THE VOLTAGE READING AGAINST THE PART. WEIGHTS AND SAVE IT IN
MATRIX "BVOLT"

DO 120 I=1,11

IF ((DATASET.EQ.PA').OR.(DATASET.EQ.'a')) THEN
BVOLT(1,I)=XVOLT(1,I)

ELSE

BVOLT(1,I)=XVOLT(3,I)

END IF

CONTINUE

DETERMINE THE TIME STEP USED IN COLLECTING DATA
TIMESTEP=1.0/FS

NORMALIZE DATA BY SUBTRACTING EACH RAW OF DATA FROM THE FIRST
VLOTAGE READING WHICH REPRESENT THE STATIC WEIGHT OF THE FLOOR
AND PARTICIPANTS.

DO 134 I=1,N
DO 144 J=1,ll
VOLT(I J)=0.0
TIME(I)=0.0
PR(I)=0.0
CONTINUE
CONTINUE

DO 130 I=1,N

DO 140 J=1,11

VOLT(I J)=XVOLT(I,J)-BVOLT(1,J)
TIME(I)=TIME(I—l)+TIMESTEP
PR(I)=ABS(PROMPT(I)-PROMPT(1))
IF (I.EQ.1) THEN

TIME(I)=0.0

END IF

CONTINUE

CONTINUE

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

+++++++++++ 4. FINDING FINAL FORCES X, Y, z , P +++++++++++
+++++++++++++++++++++++++++++++++++++++

DO 150 I=1,N
FX(I)=0.0

FY(I)
FZ(I)
FXP(I
FYP(I
FZP(I
CONTINUE

DO 170 I=1,N

DO 160 J=l,11

FX (I)=FX (I) +VOLT (I, J) *XCALIB(J)
FY(I)=FY(I)+VOLT(I,J)*YCALIB(J)
FZ(I)=FZ(I)+VOLT(I,J)*ZCALIB(J)
CONTINUE

SWITCH FX WITH FY FOR DATA SET A (TO MATCH DATA SET B COORD. SYSTEM)
aLSO TAKE THE WEIGHT OFF FROM THE FZ(I) FOR DATA.SET A

.0
.0

II II ll CO
000

.0
.0
.0

IF ((DATASET.EQ.'A}).OR.(DATASET.EQ.'a')) THEN

FXSWgFX(I)
FYSW=FY(I)
FX(I)=FYSW
FY(I)=FXSW
FZ(I)=FZ(I)-TWEIGHT
ENDIF

FIND FORCE RATIO

170

000000

000000000000000

000

180

0000

116
FXP(I)=FX(I)/TWEIGHT
FYP(I)=FY(I)/TWEIGHT
FZP(I)= Z(I)/TWEIGHT
CONTINUE

NOW FIND THE MAXIMUM VALUE OF THE FORCE FX,FY,FZ, AND USE EACH
AS A.VALUE FOR THE PROMPT SPIKE.

CALL MAX (FX,FXMAX,TX,TIMESTEP)
CALL MAX (FY,FYMAX,TY,TIMESTEP)
CALL MAX (FZ,FZMAX,TZ,TIMESTEP)
CALL MAX (FXP,FXPMAX,TX,TIMESTEP)
CALL MAX (FYP,FYPMAX,TY,TIMESTEP)
CALL MAX (FZP,FZPMAX,TZ,TIMESTEP)
CALL MIN (FX,FXMIN,TXM,TIMESTEP)
CALL MIN (FY,FYMIN,TYM,TIMESTEP)
CALL MIN (FZ,FZMIN,TZM,TIMESTEP)
CALL MIN (FXP,FXPMIN,TXM,TIMESTEP)
CALL MIN (FYP,FYPMIN,TYM,TIMESTEP)
CALL MIN (FZP,FZPMIN,TZM,TIMESTEP)

FOR THE CASE OF SINGLE JUMP OR PERIODIEC JUMPING WHERE THE PERSON
LEAVE THE FLOOR, IT MAY BE POSIBLE TO ESTIMATE THE STATIC WEIGHT
OF THE PERSON(S). THIS IS USEFUL IF THE WEIGHT IS UNKNOW OR AS
AS MEASURE OF DATA AQUISITION ACCURACY.

IT HAS BEEN FOUND THAT A PERSON LEAVES THE FLOOR WHEN JUMPING FOR
ABOUT 0.6 SECONDS (ABOUT 20 READINGS) AND COMES FOLLOWED DIRECTLY
BY THE FZMAX (THE HIT).

EWEIGHT=0.0

IF ((FNAME1.EQ.'SJ').OR.(FNAMEl.EQ.'sj').OR.(FNAMEl.EQ.'PJ').OR.
1(FNAME1.EQ. 'pj ' ) ) THEN

EWEIGHT=-fzm1n

END IF

REPORT THE LOCATION OF THE PROMPT (IF ANY) FOR TRANSIENT ACTION

IF ((ENAME2.EQ.'t').OR.(ENAME2.EQ.'T')) THEN
CALL MAX (PR,PRMAX,TP,TIMESTEP)

DO 180 I=1,N

PR(I)=0.0

CONTINUE

NP=INT(TP*FS)+1

PRMAX=100.

PR(NP)=PRMAX

ELSE

FIND PEAKS FOR THE PROMPT FOR PERIODIC ACTION

CALL MAX (PR,PRMAX,TP,TIMESTEP)
CUTOFF=PRMAX/4.0

NPK=O

DO 190 I=1,N

 

 

 

190

000

200
210

000000000

220

230
240

00000

250

00000

260
270

000

280

000

290

117

IF (PR(I).LE.CUTOFF) THEN
PR(I)=0.0

ELSE

NPK=NPK+1

PRP(NPK)=I

PRMAX=100.

PR(I)=PRMAX

END IF

CONTINUE

THIS LOOP IS TO ENSURE ONLY ONE READING PER PROMPT

DO 210 Nz=1,NPK
I=PRP(Nz)

DO 200 NN=1,4
PR(I+NN)=0.0
CONTINUE
CONTINUE

END IF

+++++++++++++++++++++++++++++++++++++++
+++++++++++++ S. START THE FINAL OUTPUT +++++++++++++
+++++++++++++++++++++++++++++++++++++++

PRINT TIME VS FORCES IN X,Y,Z DIR. PLUS THE PROMPT

WRITE (6,220) , '
FORMAT (///,10X,'TIME ',3X,'X-FORCE Ratlo ',2X,'Y-FORCE Ratlo',

12X,'Z-FORCE Ratio',2X,'PROMPT',/)

DO 230 I=1,N

WRITE (6,240) TIME(I),FXP(I),FYP(I),FZP(I),PR(I)

CONTINUE

FORMAT (7X,F8.3,3(F14.6),3X,F10.0) \

PRINT INFORMATION ABOUT THE FILE NAME TO THE SCREEN TO ENSURE THAT
CORRECT FILE IS BEING HANDLED

WRITE (6,250) FNAME,FNAME3
FORMAT (//,20x,' INPUT FILE INFORMATION',///,3x,'FILE NAME = ',

1A12,10x,'PARTICIPANTS = ',A3,2x,'PERSONs.'/)

REPORT AN EXPLAINATION OF THE INFORMATION STORED IN THE FILE
THIS INFORMATION WILL BE PRINTED TO THE SCREEN AND SAVED IN
THE REPORT FILE (*.#RP)

IF ((FNAME2.EQ.'t').OR.(FNAME2.EQ.'T')) THEN
WRITE (6,260) FNAME1,FNAME4

ELSE

WRITE (6,270) FNAME1,FNAME4

END IF

FORMAT (3x,'TRANSIENT ACTION
FORMAT (3X,'PERIODIC ACTION

THEN, PRINT OUTPUT SUMMARY

WRITE (6,280) (WEIGHT(I),I=1,5) TWEIGHT,EWEIGHT
FORMAT }//,1X,'WEIGHT(S) z',5(Ié),3x,'Tota1 :',F7.0,5X,‘ Estimate
)

',A3,5x,'TEST NO. = ',A3/)
',A3,5x,'TEST NO. = ',A3/)

1:',F7.2

FINALLY, WRITE A SUMMARY ABOUT THE FORCES.

WRITE (6,290) REPORT
FORMAT (20x,' FORCES INFORMATION ',///,13x,'FINAL REPORT FILE N

1AME = ',A12///)

WRITE (6,300) FXMAX,FXPMAX,TX
WRITE (6,310) FYMAX,FYPMAX,TY

WRITE (6,320) FZMAX,FZPMAX,TZ

IF ((FNAME2.EQ.'t').OR.(FNAME2.EQ.'T')) THEN
WRITE (6,330) PRMAX,TP

ELSE

WRITE (6,340) PRMAX

END IF

 

000000000000000

0.30000

0000000000

000000000

300
310
320

330
340

50

118
FORMAT (2x,'FXMAx =',F12.4,' LBS RATIO TO WEIGHT=‘,F8.4,8X,'AT T
1IME = ',F5.3,' SEC.',/)
FORMAT (2X,'FYMAX =',F12.4,' LBS RATIO TO WEIGHT=',F8.4,8X,'AT T
lIME = ',F5.3,' SEC.',/)
FORMAT (2X,'FZMAX =',F12.4,' LBS RATIO To WEIGHT=‘,F8.4,8X,'AT T
lIME = ',F5.3,' SEC.',/)

FORMAT (2X,'PRMAX =',F12.2,' ',26x,'AT TIME = ',F5.3,' SEC.',/)
FORMAT (2X,'PRMAX =',F12.2,' ',26x,'AT TIME = PERIODIC',/)
+++++++++++++++++++++++++++++++++++++++
+++++++++++++ 6. PREPARING PLOTS TO THE SCREEN +++++++++++++
+++++++++++++++++++++++++++++++++++++++
CALL THE OPENING MENU FOR FINAL ON—SCREEN OUTPUT(UNDER DESIGN)

THE OPEN FLAG‘WILL OPEN THE MENU ONLY THE FIRST TIME THE PROGRAM
THE COLOR FLAG WILL BE SET TO (0) OR
(1) DEPENDING ON THE ITERATION NO. THIS FLAG'WILL INTERCHANGE
THE BACKGROUND COLOR.

IF (OFLAG.GT.0.0) THEN

IF((DP.EQ.'Y').OR.(DP.EQ.'y')) THEN

CALL OPEN (OFLAG,BW)

READ (*,*)

END IF

ELSE

GO TO 350

END IF
CALL PLOTXY SUBROUTINE TO PLOT THE TIME VERSUS THE FORCE IN THE
X, Y, z DIRECTIONS.

CONTINUE

IF((DP.EQ.'Y').OR.(DP.EQ.'y')) THEN

CALL PLOTXY (TIME,FXP,FYP,FZP,PR,FXPMAX,FYPMAX,FZPMAX,NP,TX,TY,TZ,
1WEIGHT,TWEIGHT,CFALG,K,NA,FXPMIN,FYPMIN,FzPMIN,TXM,TYM,N,FNAME,
2EWEIGHT,BW)

ELSE

print *,'GROUP: ',ll,'FILE: ',k

END IF

CLOSE (2)

CLOSE (6)

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

+++++++++++ 7. SPECTRAL ANALYSIS ESTIMATION OF FORCE-SERIES ++++++++

+++++++++++++++++++++++++++++++++++++++++++++++++++++++
spectral analysis will be called out only if the action is
periodic. Also if more than on action is being processed, the
average correlation and average spectrs Will be disabled

IF((Fname1.eq.'ss').or.(Fname1.eq.'SS').or.(Fnamel.eq.'jn').or.

l(Fnamel.eg.'JN').or.(Fname1.eq.'PJ').or.(Fnamel.eq.'pj')) THEN
if(k.eq. ) then

noav%=0

file lag=fname1

endif

fileflagn=fname1
if(filef1agn.ne.fileflag)noavg=l
CALL SPECTRA (LL,K,NA,NAME,OF,RMS,ZMEAN,BW,noavg)
END IF

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

+++++++++++ 8. Reporting max forces to file "SUMMARY.OUT" ++++++++

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

Find absolute maximum forces and report them.to the matix fxmx(i)

fxmx(k)=fx max .
if(fxpmax. t.abs(fxpmin)) fxmx(k)=abs(fxpmin)
fymx(k)=fypmax

 

 

000

00000 000000

0000) 000

000

000

360
370

380

371

372

480

119

if(fyim ax. 1t. abs(fypmin)) fymx(k)=abs(fypmin)
fzmx ) =fzpmax
twgt(k)=tweight

IF (K.EQ.1) THEN

WRITE (7,360)fname3,FNAMEZ

ENDIF

WRITE (7, 370) K, TWGT(K), FXMX(K), FYMM(K), FZMM(K)

FORMAT(//, 5x, SUMMARY OF TESTS OF' ,As, PERS. AT ',al,‘ Hz.',//,
llX, 'Test 'Weight Fxmax Fymax Fzmax')

FORMAT (2X,IZ, 5X, F8. 2, 3(4X,F6.3))

DONE .....

print *,ll,k
CONTINUE

CALCULATE AND REPORT IMPORTANT STATISTICS FOR THE OBSERVED ACTION
This is done only if the same action is considered

if(noavg.eq.0)then

XABS=.TRUE.

CALL MYSTAT (TWGT,NA,WMIN,WMAX,NWIN,NWAX,WMEAN,WVAR,WSTD,WVX,
1W5KE,WKUR/WSE,XABS)

CALL MYSTAT (FXMH,NA,XMIN,XMAx,NXIN,NXAX,XMEAN,XVAR,XSTD,xvx,
1XSKE,XKUR,XSE,XABS)

CALL MYSTAT (FYMX,NA,YMIN,YMAX,NYIN,NYAX,YMEAN,YVAR,YSTD,YVX,
1YSKE,YKUR,YSE,XABS)

CALL MYSTAT (FZMx,NA,2MIN,ZMAx,NzIN,NZAx,ZMEAN,ZVAR,ZSTD,zvx,
lZSKE,ZKUR,ZSE,XABS)

BLANK LINE T0 SEPARATE DATA

WRITE (7,373)
FORMAT (1X)

REPORT TO THE OUTPUT FILE

TT='MEAN'

WRITE (7, 371) TT, WMEAN, XMEAN, YMEAN, ZMEAN
FORMAT (1X,.A5, 1X, F10. 2, 3(2X, F8. 3))
FORMAT (1X, A5, 1X, IlO, 3(2X, I8), 3X, Ill)

TT='MIN'
WRITE (7, 371) TT,WMIN,XMIN,YMIN,ZMIN
TT=' MAX'
¥¥ITE (7, 371) TT,WMAX,XMAX,YMAX,ZMAX
WRITE (7, 371) TT,WVAR,XVAR,YVAR,ZVAR
TT='STD'
WRITE (7,371) TT,WSTD,XSTD,YSTD,ZSTD
TT='C.O.V'
WRITE (7,371) TT,WVX,XVX,YVX,ZVX

TT='NMIN'
WRITE (7, 372) TT,NWIN,NXIN,NYIN,NZIN
TT=' NMAX'
WRITE (7,372) TT,NWAX,NXAX,NYAX,NZAX
TT='SKEWN'
WRITE (7,371) TT,WSKE,XSKE,YSKE,ZSKE
TT='KURTO'
WRITE (7,371) TT,WKUR,XKUR,YKUR,ZKUR
TT='ST- -ER'
WRITE (7, 371) TT,WSE,XSE,YSE,ZSE

end
CONTINUE
CLOSE(7)

ALL DONE

CALL ENDGRAPHICS()

 

120

STOP

END
MAN PROGRAM DATArP
#################################f#####################################

* * k * * * * * * * * * * * * * * * * * * * i * * * * * * * * * * *

x»

**
*-

SUBROUTINE OPEN

* * * * * * k * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

APRIL 15,1992 OPENING LOGO......

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
*****************************************************************

**-#*-**’*W-**
*fi-*i-*1~*i-**

++++++++++++++++++++++++++++++++++
++++++++++++++++ 1. DATA INPUT/OUTPUT ++++++++++++++++
++++++++++++++++++++++++++++++++++

0000000***w****»****00

SUBROUTINE OPEN (OFLAG,BW)

LOGICAL*1 INITGRAPHICS,INITBORDER,INITWINDOW,INITAXES,INITFONTS,
1PLOTMETHOD,INVERTX,INVERTY,TITLEONLY,SCRONLY,Y2PLOT,y3plot,
2PLOT2METHOD

INTEGER*2 BORDERCOLOR,WINDOWCOLOR,AXISCOLOR,LABELCOLOR,PLOTCOLOR,
1TITLECOLOR,NUMBER,PLOTZCOLOR,FONTHEIGHT,FONTWIDTH,PLOT3COLOR

CHARACTER TITLE*280,XAXISTITLE*80,YAXISTITLE*80

C INCLUDE 'PLOT.DIF'
C 7 INITIALISE THINGS FOR THE FIRST PLOT

INITGRAPHICS=.TRUE.

INITBORDER=.TRUE.

INITWINDOw=.TRUE.

INITAXES=.FALSE.

INITFONTS=.TRUE.

PLOTMETHOD=.TRUE.

Y2PLOT=.FALSE.

Y3PLOT=.FALSE.

SCRONLY=.TRUE.

FONTHEIGHT=28

FONTWIDTH=16

C SET UP THE FANCY COLORS

BORDERCOLOR=14
WINDOWCOLOR=15

IF (BW.EQ.1) THEN

BORDERCOLOR=0
WINDOWCOLOR=15

END IF

C SET UP THE PLOT LIMITS

XMIN=0.0

XMAX=1.0

YMIN=0.0

YMAX=1.0

C POSITION THIS PLOT AT THE TOP LEFT OF THE SCREEN

XBOTTOMLEFT=0.0

YBOTTOMLEFT=0.0

XTOPRIGHT=1.0

YTOPRIGHT=1.0

TITLE=' ** D A. T .A . F O R **'

CALL PLOT (INITGRAPHICS, INITBORDER, INITWINDOW, INITAXES, INITFONTS,
1XDATA, YDATA, Y2DATA,NUMBER, PLOTMETHOD, INVERTX,INVERTY, XMIN, XMAX,
2YMIN, YMAX, XTICSPACE, YTICSPACE, XBOTTOMLEFT, YBOTTOMLEFT ,XTOPRIGHT,
3YTOPRIGHT, PLOTZCOLOR, BORDERCOLOR, WINDOWCOLOR, AXISCOLOR, LABELCOLOR,
4PLOTCOLOR, TITLECOLOR, XAXISTITLE, YAXISTITLE, TITLE, TITLEONLY,
5FONTHEIGHT, FONTWIDTH, SCRONLY, Y2PLOT, Y3PLOT, PLOT3COLOR, X3, Y3, NUM3,
63W, PLOTZMETHOD)

C WAIT FOR USER TO HIT RETURN
C READ(*.*)
CC CALL ENDGRAPHICS()

OFLAG=0

RETURN

ENDN

OF MODULE SUBROUTINE OPENING
C#######################################################################

 

OOOOOOJFX'IPII’fiiI-fl-X'fl-X'I'I-I’

000

w:~*n-**=+*x~*x-**

10

 

SUBROUTINE PLOTXY

********************************
********************************

*x-sw:9s1~*s~*n~**

++++++++++++++++++++++++++++++++++
++++++++++++++++ 1. DATA INPUT/OUTPUT ++++++++++++++++
++++++++++++++++++++++++++++++++++

SUBROUTINE PLOTXY (TIME,FX,FY,Fz,PR,FXMAx,FYMAx,FZMAx,NP,Tx,TY,Tz,
1WEIGHT,TWEIGHT,CFALG,K,NF,FXMIN,FYMIN,FZMIN,TXM,TYM,N,FNAME,
2EWEIGHT,BW)

DIMENSION TIME(512), FX(512), FY(512), FZ(512), PR(512)

INTEGER WEIGHT(5)

INCLUDE 'PLOT.DIF'

LOGICAL*1 INITGRAPHICS,INITBORDER,INITWINDOW,INITAXES,INITFONTS,
lPLOTMETHOD,INVERTX,INVERTY,TITLEONLY,SCRONLY,Y2PLOT,y3plot,
2PLOT2METHOD

INTEGER*2 BORDERCOLOR,WINDOWCOLOR,AXISCOLOR,LABELCOLOR,PLOTCOLOR,
1TITLECOLOR,NUMBER,PLOT2COLOR,FONTHEIGHT,FONTWIDTH,PLOT3COLOR

CHARACTER TITLE*280,XAXISTITLE*80,YAXISTITLE*80,FNAME1*3,FNAME2*3,
1FNAME3*3,FNAME4*3,FNAME*12,TITLE1*80,TITLE2*80,TITLE3*80,TITLE4*
280,TITLE5*80,TITLE6*80,TITLE7*80,TITLE8*80,TITLE9*80,TITLE10*80

NUMBER=N

INITIALISE THINGS FOR THE FIRST PLOT

INITGRAPHICS=.TRUE.

INITBORDER=.TRUE.

INITWINDOW=.TRUE.

INITAXES=.TRUE.

INITFONTS=.TRUE.

PLOTMETHOD=.TRUE.

PLOT2METHOD=.TRUE.

TITLEONLY=.FALSE.

SCRONLY=.FALSE.

Y2PLOT=.TRUE.

FONTHEIGHT=10

FONTWIDTH=5

SET UP THE FANCY COLORS DEPENDING ON THE VALUE OF CFLAG (0 OR 1)

BORDERCOLOR=14

IF (CFLAG.EQ.0.0) THEN
WINDOWCOLOR=8

CFLAG=1.0

ELSE
WINDOWCOLOR=1

CFLAG=0.0

END IF
AXISCOLOR=10

LABELCOLOR=11

PLOTCOLOR=14

PLOT2COLOR=4

PLOT3COLOR=4

TITLECOLOR=15

IF(BW.EQ.1.0) THEN

BORDERCOLOR=3
WINDOWCOLOR=15
AXISCOLOR=0
LABELCOLOR=0
PLOTCOLOR=0
PLOT2COLOR=1
PLOT3COLOR=3
TITLECOLOR=4

END IF

Set file name Component

READ (FNAME,10) FNAME1,FNAME2,FNAME3,FNAME4
FORMAT (A2,A1,A1,1x,A3)

000 000 0000000000

000

20

0000

0000000000

000 000

 

122

++++++++++++++++++++++++++++++++++
++++++++++++++++ 1. FORCE IN THE x-DIR ++++++++++++++++
++++++++++++++++++++++++++++++++++

SET UP THE PLOT LIMITS for the screen part only

PRED=2.0
XMIN=1.0
XMAX=6.0
XTICSPACE=2.0

Call scale subroutine to set Ymin, Ymax, Yticspace
CALL SCALE (FXMIN,FXMAX,YMIN,YMAX,YTICSPACE)
POSITION THIS PLOT AT THE TOP LEFT OF THE SCREEN

XBOTTOMLEFT=0.00
YBOTTOMLEFT=0.50
XTOPRIGHT=0.50
YTOPRIGHT=1.00
GIVE IT.A TITLE
TITLE='FX AS A RATIO TO WEIGHT '
XAXISTITLE=' T I M E ( s e C . )'
YAXISTITLE='FORCE RATIO'

PLOT THE SECOND SET OF DATA (THE PROMPT)

IF ((FNAME2.EQ.'t').OR.(FNAME2.EQ.'T')) THEN
PR(NP)=FXMAX/PRED

ELSE

DO 20 I=1,N

IF (PR(I).GT.0.0) PR(I)=FXMAX/PRED

CONTINUE

END IF

READY TO CALL PROGRAM PLOT.FOR

CALL PLOT (INITGRAPHICS,INITBORDER,INITWINDOW,INITAXES,INITFONTS,
lTIME,FX,PR,NUMBER,PLOTMETHOD,INVERTX,INVERTY,XMIN,XMAX,YMIN,YMAX,
2XTICSPACE,YTICSPACE,XBOTTOMLEFT,YBOTTOMLEFT,XTOPRIGHT,YTOPRIGHT,
3PLOT2COLOR,BORDERCOLOR,WINDOWCOLOR,AXISCOLOR,LABELCOLOR,PLOTCOLOR,
4TITLECOLOR,XAXISTITLE,YAXISTITLE,TITLE,TITLEONLY,FONTHEIGHT,
5FONTWIDTH,SCRONLY,Y2PLOT,Y3PLOT,PLOT3COLOR,X3,Y3,NUM3,BW
6,PLOT2METHOD)

++++++++++++++++++++++++++++++++++
++++++++++++++++ 2. FORCE IN THE Y-DIR ++++++++++++++++
++++++++++++++++++++++++++++++++++

SET UP THE PLOT LIMITS

XMIN=1.0
XMAX=6.0
XTICSPACE=2.0

Call scale subroutine to set Ymin, Ymax, Yticspace
CALL SCALE (FYMIN,FYMAX,YMIN,YMAX,YTICSPACE)
POSITION THIS PLOT AT THE TOP RIGHT OF THE SCREEN

XBOTTOMLEFT=0.50
YBOTTOMLEFT=0.50
XTOPRIGHT=1.00
YTOPRIGHT=1.00

GIVE IT A.TITLE '
TITLE='FY AS.A RATIO TO WEIGHT '
XAXISTITLE=' T I M E ( s e c . )

0000

000000 0000 0000

0 000 000

0000

0000

30

40

123

YAXISTITLE='FORCE RATIO'

Prevent a new screen

INITGRAPHICS=.FALSE.
INITFONTS=.FALSE.
INITAXES=.TRUE.

PLOT THE SECOND SET OF DATA (THE PROMPT)

IF ((FNAME2.EQ.'t').OR.(FNAME2.EQ.'T')) THEN
PR(NP)=FYMAx/PRED

ELSE

DO 30 I=1,N

IF (PR(I).GT.0.0) PR(I)=FYMAx/PRED

CONTINUE

END IF

READY TO CALL PROGRAM PLOT.FOR

CALL PLOT (INITGRAPHICS,INITBORDER,INITWINDOW,INITAXES,INITFONTS,
1TIME,FY,PR,NUMBER,PLOTMETHOD,INVERTX,INVERTY,XMIN,XMAX,YMIN,YMAX,
2XTICSPACE,YTICSPACE,XBOTTOMLEFT,YBOTTOMLEFT,XTOPRIGHT,YTOPRIGHT,
3PLOT2COLOR,BORDERCOLOR,WINDOWCOLOR,AXISCOLOR,LABELCOLOR,PLOTCOLOR,
4TITLECOLOR,XAXISTITLE,YAXISTITLE,TITLE,TITLEONLY,FONTHEIGHT,
5FONTWIDTH,SCRONLY,Y2PLOT,Y3PLOT,PLOT3COLOR,X3,Y3,NUM3,BW
6,PLOT2METHOD)

++++++++++++++++++++++++++++++++++
++++++++++++++++ 3. FORCE IN THE z-DIR ++++++++++++++++
++++++++++++++++++++++++++++++++++

Call scale subroutine to set Ymin, Ymax, Yticspace
CALL SCALE (FZMIN,FZMAX,YMIN,YMAX,YTICSPACE)
POSITION THIS PLOT AT THE BOTTOM LEFT OF THE SCREEN

XBOTTOMLEFT=0.00
YBOTTOMLEFT=0.00
XTOPRIGHT=0.50
YTOPRIGHT=0.50
GIVE IT A.TITLE
TITLE='FZ AS.A RATIO TO WEIGHT
XAXISTITLE=' T I M E ( s e c . )'
YAXISTITLE='FORCE RATIO'

PLOT THE SECOND SET OF DATA (THE PROMPT)

IF ((FNAME2.EQ.'t').OR.(FNAME2.EQ.'T')) THEN
PR(NP)=FZMAX/PRED

ELSE

DO 40 I=1,N

IF (PR(I).GT.0.0) PR(I)=FZMAX/PRED

CONTINUE

END IF

READY TO CALL PROGRAM PLOT.FOR

INITAXES=.TRUE.
CALL PLOT (INITGRAPHICS,INITBORDER,INITWINDOW,INITAXES,INITFONTS,

R NUMBER PLOTMETHOD,INVERTX,INVERTY,XMIN,XMAX,YMIN,YMAx,
2§T¥§SPAC§,YTICSPACE,XBOTTOMLEFT,YEOTTOMLEFT,XTOPRIGHT,YTOPRIGHT,
3PLOT2COLOR,BORDERCOLOR,WINDOWCOLOR,AXISCOLOR,LABELCOLOR,PLOTCOLOR,
4TITLECOLOR,XAXISTITLE,YAXISTITLE,TITLE,TITLEONLY,FONTHEIGHT,
5FONTWIDTH,SCRONLY,Y2PLOT,Y3PLOT,PLOT3COLOR,X3,Y3,NUM3,EW

6,PLOT2METHOD)

0000000

000

0 00000

OOOOOOfi-X'Ififlki-fl'li'i-‘f’ffl'ifoo

50

60
70

80
90

100
110

130
140

#

**

*
*

**=+*l-**Ik*I-*i-W#

###

124

++++++++++++++++++++++++++++++++++
++++++++++++++++ 4. OUTPUT VALUES ++++++++++++++++
++++++++++++++++++++++++++++++++++

just plot the title on this one
XBOTTOMLEFT=0.50
YBOTTOMLEFT=0.00
XTOPRIGHT=1.00
YTOPRIGHT=0.50

TITLE=' FORCE—RATIOS '
WRITE (TITLE1,50) FNAME,FNAME3

FORMAT ('FILE = ',A12,2x,'WITH ',A2,2X,'PER.')

IF ((FNAME2.EQ.'t').OR.(FNAMEZ.EQ.'T')) THEN
WRITE (TITLE3,60) FNAME1,FNAME4

ELSE

WRITE (TITLE3,70) FNAME1,FNAME4

END IF

FORMAT ('TRANSIENT MOTION = ',A3,2x,'TEST = ',A3/)
FORMAT ('PERIODIC MOTION = ',A3,2x,'TEST = ',A3/)
WRITE (TITLE4,80) (WEIGHT(I),I=1,5)

FORMAT (”Weights = ',5(I3,','))

WRITE (TITLE5,90) TWEIGHT,EWEIGHT

FORMAT ('Tota1= ',F4.0,' ESTIMATE= ',F7.2,' lbs')

Find the max. value of force in the x,y directions (absolute force

IF (ABS(FXMIN).GT.ABS(FXMAX)) FXMAX=FXMIN
IF (ABS (FYMIN) .GT.ABS (FYMAX) ) FYMAX=FYMIN

IF (ABS(FXMIN).GT-ABS(FXMAX)) TX=TXM

IF (ABS(FYMIN).GT.ABS(FYMAX)) TY=TYM

WRITE (TITLE6,100) K,NF

WRITE (TITLE7,110) FXMAX,TX

WRITE (TITLE8,120) FYMAX,TY

WRITE (TITLE9,130) FZMAx,Tz

WRITE (TITLE10,140)

FORMAT (IZ,' of '13,2x,' FMAx TIME')

FORMAT ('x—dir',3x,F8.3,6x,F6.3)

FORMAT ('Y-dir',3X,F8.3,6X,F6.3)

FORMAT ('z-dir',3x,F8.3,6x,F6.3)

FORMAT ('HIT ENTER TO CONTINUE....’)

CALL OUTPUTS (XBOTTOMLEFT,YBOTTOMLEFT,XTOPRIGHT,YTOPRIGHT,TITLE,

lTITLEl,TITLE2,TITLE3,TITLE4,TITLE5,TITLE6,TITLE7,TITLE8,TITLE9,
2TITLE10,CFLAG,BW)

WAIT FOR USER TO HIT RETURN ( only for testing the program
, otherwise let the program run With no stops

READ (*,*)
IF (K.EQ.NF) CALL ENDGRAPHICS ()
RETURN
ENEND OF SUBROUTINE PLOTXY
###
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SUBROUTINE MAX

*****************

***************
***************

**************~k**

MAY 05,1992 FINDING THE MAX. VALUE OF DATA

** **-**-*t-**-*

++++++++++++++++ 1.

SUBROUTINE MAX (DATA,FMAX,T,TIMESTEP)

000

000 OOOQOO*************OO

OEEEEEEEEEEEEOOO

10

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125

TO FIND THE MAX. FORCE

DIMENSION DATA(512)
T=0.0
N=0
=-1E14

NMAX=0
DO 10 I=1,512
N=N+1
IF (DATA(I).GT.FMAX) THEN
FMAX=DATA(I)
NMAX=N
GO TO 10
END IF
CONTINUE
T=REAL(NMAX)*TIMESTEP
RETURN
ENDN

OF SUBROUTINE

*

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* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * k *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
*****************************************************************

SUBROUTINE MIN

MAY 05,1992 FINDING THE MIN. VALUE OF DATA

Ex-Ex-EEarEx-EE

++++++++++++++++++++++++++++++++++
1. DATA.INPUT/OUTPUT ++++++++++++++++
++++++++++++++++++++++++++++++++++

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

SUBROUTINE MIN (DATA,FMIN,T,TIMESTEP)
TO FIND THE MIN. FORCE

DIMENSION DATA(512)

T=0.0

N=O

FMIN=0.0

NMAX=0

DO 10 I=1,512

N=N+1

IF (DATA(I).LT.FMIN) THEN
FMIN=DATA(I)

NMAX=N
GO TO 10
END IF
CONTINUE
T=REAL(NMAX)*TIMESTEP
RETURN
END UBROUTINE MIN
END OF S
####################################################################
f#f*f# .#f#f*f”f”f#f*f#f#f#f#f*f#f#2#f#f#f#f#f#f#f*f#f*f#f#f*f#f*f#f#
* * * * * * * * * * * * * * * * * * * * * * * * * * * k * * * * * *
*
SUBROUTINE outputs :
* * * k * * * * * * * * * * * * * * * * * i * * * * * * * * * * k *
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
MAY 15,1992 Plotting the final values of Forces :
* * * * * * * * * * * k * * * * * * * * * * * * * * * k * * * * * *
* * * * * * * *

* * * * * * * * * * * * * * * * * * * * * * * * *

START OF MODULE outputs.for
INCLUDE 'FGRAPH.FI'

0

00000

0000

000 0000

10

20

126

SUBROUTINE OUTPUTS (XBOTTOMLEFT,YBOTTOMLEFT,XTOPRIGHT,YTOPRIGHT,
1TITLE,TITLE1,TITLE2,TITLE3,TITLE4,TITLE5,TITLE6,TITLE7,TITLE8,
2TITLE9,TITLE10,CFLAG,BW)

INCLUDE 'FGRAPH.FD'

INTEGER*2 DUMMY,XWIDTH,YHEIGHT,IX1,IY1,IX2,IY2,IX,IY,FONTHEIGHT,
1FONTWIDTH

REAL*4 XWl,YW1,XW2,YW2,XBOTTOMLEFT,YBOTTOMLEFT,XTOPRIGHT,
1YTOPRIGHT,YT

CHARACTER TITLE*80,FONTCOMMAND*10,FONTSTRING*7,FONTFILE*12,TITLE1*
180,TITLE2*80,TITLE3*80,TITLE4*80,TITLE5*80,TITLE6*80,TITLE7*80,
2TITLE8*80,TITLE9*80,TITLE10*80

RECORD / VIDEOCONFIG / SCREEN
RECORD / WXYCOORD / WXY
RECORD / XYCOORD / POSITION

COMMON SCREEN
SET UP FONT FOR USE

FONTFILE='HELVB.FON'

FONTCOMMAND="T'HELV'"

IF (REGISTERFONTS(FONTFILE).LT.0) THEN

WRITE (*,10) FONTFILE

FORMAT (' FONT FILE ',A12,' NOT FOUND IN PLOT')

STOP

END IF

FONTHEIGHT=28

FONTWIDTH=16

WRITE (FONTSTRING,20) FONTHEIGHT,FONTWIDTH

FORMAT ('H',I2.2,'W",Iz.2,'B')

DUMMY=SETFONT(FONTCOMMAND//FONTSTRING)

GET SCREEN DIMENSIONS
XWIDTH=SCREEN.NUMXPIXELS
YHEIGHT=SCREEN.NUMYPIXELS

SET A VIEW PORT, WITH CORNER COORDINATES DEFINED As A

FRACTION OF THE TOTAL SCREEN SIZE

(0.0,o.0) IS BOTTOM LEFT OF SCREEN

(1.0,1.0) IS TOP RIGHT OF SCREEN

TRANSLATE CORNER COORDINATES TO PIXEL COORDINATES
IX1=INT(XBOTTOMLEFT*FLOAT(XWIDTH))
IX2=INT(XTOPRIGHT*FLOAT(XWIDTH))
IY1=YHEIGHT—INT(YTOPRIGHT*FLOAT(YHEIGHT))
IY2=YHEIGHT—INT(YBOTTOMLEFT*FLOAT(YHEIGHT))
CALL SETVIEWPORT (IX1,IY1,IX2,IY2)

CREATE.A REAL COORDINATE WINDOW
XW1=0.0
YW1=0
XW2=1.0
YW2=1.0
DUMMY=SETWINDOW(.TRUE.,XW1,YW1,XW2,YW2)

SET THE COLOR OF THE BACKGROUND WINDOW DEPENDING ON THE FLAG
"CFLAG" ... NOTE THE SETUP HAS TO BE OPPOSITE TO THE PLOTXY

IF (CFLAG.EQ.1.0) THEN

DUMMY=SETCOLOR(8)

ELSE

DUMMY=SETCOLOR(1)

END IF

IF(BW.EQ.1.0)DUMMY=SETCOLOR(15)

DUMMY=RECTANGLE W($GFILLINTERIOR,XW1,YW1,XW2,YW2)
DRAW.A BORDERIAROUND THE VIEWPORT

DUMMY=SETIOU?RUMMY SETCOLOR(3)

IF BW.E . . D =

DUMMY=RECTANGLE;W($GBORDER,XWl,YW1,XW2,YW2)

This is the screen design of the data output

TITLELENGTH=50
POSITION THE TITLE CENTERED (MORE OR LESS) ABOVE GRAPH

YT=0.9*(YW2+YW1)

CALL MOVETO W (0.9*(XW2+XW1),YT,WXY)
CALL GETCURRENTPOSITION (POSITION)
IX=POSITION.XCOORD
IY=POSITION.YCOORD
IX=IX—(TITLELENGTH*FONTWIDTH)/2
IY=IY-FONTHEIGHT/2

000

00000

000M

0000

127

enter the program name (Title: from the main program)

DUMMY=SETCOLOR(15)

CALL MOVETO (IX,IY,POSITION)

CALL OUTGTEXT (TITLE(1:TITLELENGTH))
DUMMY=SETCOLOR(4)

CALL MOVETO (IX,IY+2,POSITION)

CALL OUTGTEXT (TITLE(1:TITLELENGTH))

CHANGE THE FONT TO.A FIXED FONT TO CREATE THE FORCES' TABLE
HERE, COURIER FONTS WILL BE USED.

FONTFILE='courb.fon'
FONTCOMMAND="T'courier'"

FONTHEIGHT=12

FONTWIDTH=9

IF (REGISTERFONTS(FONTFILE).LT.0) THEN
WRITE (*,10) FONTFILE

STOP

END IF

WRITE (FONTSTRING,20) FONTHEIGHT,FONTWIDTH
DUMMY=SETFONT(FONTCOMMAND//FONTSTRING)

YT=0.8*(YW2+YW1)

CALL MOVETO W (0.73*(XW2+XW1),YT,WXY)
CALL GETCURRENTPOSITION (POSITION)
IX=POSITION.XCOORD
IY=POSITION.YCOORD
IX=IX-(TITLELENGTH*FONTWIDTH)/2
IY=IY—FONTHEIGHT/2

DUMMY=SETCOLOR(0)

CALL MOVETO (IX,IY+10,POSITION)

CALL OUTGTEXT (TITLE1(1:TITLELENGTH))
CALL MOVETO (IX,IY+25,POSITION)

CALL OUTGTEXT (TITLE2(1:TITLELENGTH))
CALL MOVETO (IX,IY+40,POSITION)

CALL OUTGTEXT (TITLE3(1:TITLELENGTH))
CALL MOVETO (IX,IY+60,POSITION)

CALL OUTGTEXT (TITLE4(1:TITLELENGTH))
CALL MOVETO (IX,IY+75,POSITION)

CALL OUTGTEXT (TITLE5(1:TITLELENGTH))
IF(BW.EQ.1.0)GOTO 22
DUMMY=SETCOLOR(11)

CALL MOVETO (IX,IY+11,POSITION)

CALL OUTGTEXT (TITLE1(1:TITLELENGTH))
CALL MOVETO (IX,IY+26,POSITION)

CALL OUTGTEXT (TITLE2(1:TITLELENGTH))
CALL MOVETO (IX,IY+41,POSITION)

CALL OUTGTEXT (TITLE3(1:TITLELENGTH))
DUMMY=SETCOLOR(10)

CALL MOVETO (IX,IY+61,POSITION)

CALL OUTGTEXT (TITLE4(1:TITLELENGTH))
CALL MOVETO (IX,IY+76,POSITION)

CALL OUTGTEXT (TITLE5(1:TITLELENGTH))
CONTINUE

Change font size

FONTHEIGHT=10

FONTWIDTH=8

WRITE (FONTSTRING,20) FONTHEIGHT,FONTWIDTH
DUMMY=SETFONT(FONTCOMMAND//FONTSTRING)

Filling the Table of Forces

DUMMY=SETCOLOR(14)
IF(BW.EQ.1.0)DUMMY=SETCOLOR(4)

CALL MOVETO (IX,IY+110,POSITION)

CALL OUTGTEXT (TITLE6(1:TITLELENGTH))
DUMMY=SETCOLOR(15)
IF(BW.EQ.1.0)DUMMY=SETCOLOR(0)

CALL MOVETO (IX,IY+130,POSITION)

CALL OUTGTEXT (TITLE7(1:TITLELENGTH))

 

 

000

**I+*I-**-**-**-**

O()O()*i-**l$*i-*i'**-**

0000000

*
*

128

CALL MOVETO (IX,IY+145,POSITION)

CALL OUTGTEXT (TITLE8(1:TITLELENGTH))
CALL MOVETO (IX,IY+160,POSITION)

CALL OUTGTEXT (TITLE9(1:TITLELENGTH))
DUMMY=SETCOLOR(0)

CALL MOVETO (IX,IY+180,POSITION)

CALL OUTGTEXT (TITLE10(1:TITLELENGTH))
DUMMY=SETCOLOR(4)

CALL MOVETO (IX,IY+181,POSITION)

CALL OUTGTEXT (TITLE10(1:TITLELENGTH))

ALL DONE

CALL UNREGISTERFONTS ()
RETURN
END

***********
**

********
********* ********

SUBROUTINE SCALE

*******************
*******************

AUG 22,1992

*
*

**
**

VERTICAL PLOT SCALE

‘1:********************************
*********************************
*****************************************************************
++++++++++++++++++++++++++++++++++
++++++++++++++++
++++++++++++++++++++++++++++++++++

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

SUBROUTINE SCALE (FMIN,FMAX,ST,FIN,TICK)

REAL*8 U,C
TT=ALOG10(FMAx-FMIN)
MT=IRINT(TT)
TT=10.**(TT-MT)

IF (TT.LE.2) THEN
TT=2.

ELSE IF (TT.GT.5) THEN
TT=10.

ELSE

TT=5.

END IF
TICK=TT*10.**(MT—l)
U=1.00001*TICK
C=DLOG10(U)

IF (C.LT.0) THEN
L=IDINT(C)~1

ELSE

L=IDINT(C)

END IF
C=DBLE(10.)**L
TICK=C*IDNINT U/C)
N1=IRINT(FMIN TICK)
N2=IRINT(FMAX/TICK)+1
ST=N1*TICK
FIN=N2*TICK

RETURN

 

1. DATA INPUT/OUTPUT

FIN = Ending value;

TICK

1-##-** **-*1-** EE

-----—-—-—-—-----------—------—--------------—------—_----—-—-—-—--—-~_

This routine determines the starting and ending values to be used in
a full scale plot.
OUTPUT : ST = Starting value;

THIS IS A.MODIFIED VERSION OF.A PROGRAM WRITTEN ORIGINALLY BY R. HARIC

——_-————-—-—-————-.————-u-————————————u——————---—~————-————_——_—————-c———--

 

129

$ SRECTRA.FOR
STORAGE:

SUBROUTINE SPECTRA

* * * * * * * * * * * * * * * * * * * * * * * * * * * k * * * * *

AUG 22,1992 AUTOCORRELATION AND AUTOSPECTRA PLOTS

* * * * * * * * * k * * * * * * * * * * * * * * * * * * * * * * *
* * * * k * * i * * * k k * * * * * * * k * * * * * * * * * * * *

*I-*I-**-**>+*i-**#H#

f
*
*
*
*
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
*
k
'k
*
*
*
*

*****************************************************************

++++++++++++++++++++++++++++++++++
++++++++++++++++ 1. DATA INPUT/OUTPUT ++++++++++++++++
++++++++++++++++++++++++++++++++++

——_————-—..---‘_-———————-----—-——_———————-———--——--_--——————————————-—_—_

Description:
PROGRAM TO ESTIMATE THE AUTOCORRELATION, AUTOSPECTRA,
AVERAGE AUTOCORRELATIONC, AND AVERAGE AUTOSECTRUM OF
FORCE-TIME SERIES. IT IS A.MODIFICATION OF A PROGRAM ORIGINALLY
WRITTEN BY:
Ronald S. Harichandran, and E. Vanmarke, "Space-Time
Variation of Earthquake Ground Motion", Research Report
R84—12, Dept. of Civil Engineering, MIT, 1984.

————~--———————--——--—————-—-—-——-——-——-—-——-————-—————-—--—————————-———

The autocorrelation function and the one—sided, normalized (i.e.

area) autospectrum of each force-series are stored in files with

the same name as the force-series and with filetype .ACN and .AS

respectively. The average of all the autocorrelation functions a

of the normalized autospectra are stored in files named AVERAGE.

and AVERAGE.ASP; If autospectra are estimated, then a file name

SUMMARY.OUT, containing useful summary tables, is created.
Description of input:

Input are received from a file named "PARAM.DAT" which contains:

(1) General Informatio about the run:

N No. of Samples

FS Sampling Rate
(2) For autospectral estimation:

NA Number of force-series

Name(L,I) Names of force-series (Each in a separate lin
(3) Input for autospectral computations:

M Section size (must be a power of 2), 2 <= M <= 2
IWIN Window t e, l for rect. window, 2 for Hamming wi
L Half-widt of lag window, 2 <= L<=(M/2+1);
NFFT FFT size used for the spectral estimate, (2L-l)
OF Output frequency (<= fs/2)

C
*

*

*

1|:

*

1k

*

*

~k

*

*

1k

*

C

C

C

C

C

C

C

C

c

C

C

C

C

C

c

C

E Description of output:

c

C

c

C

C

C

C

C

C

c

C

C

C

C

C

C

C

C

c

C

C

C

C _______________________________________________________________________
SUBROUTINE SPECTRA (LL,K,NA,NAME,OF,RMS,XMEAN,BW,noavg)
COMPLEX SXY(513)

REAL SACORR(1025),SASPEC(513)

REAL SX(513),CCF(1025),XA(1025),AXIS(1025),NULL(1)
CHARACTER FILE1*12,C*80,XLAB*80,YLAB*80,INPUTS*40,0UTPUTS*40
CHARACTER*8 NAME(20,200)

COMMON /FILEs/ INPUTS,OUTPUTS,LINP,LOUT
COMMON /CMP/ M,N,FS,IWIN,L,NFFT,DF
COMMON /CMPD1/ MAXM

COMMON /OUT1/ C

COMMON /SM/ FMAX,NP

DATA (SACORR(I),I=1,512)/512*0./,(SACORR(I),I=513,1025)/513*0./
DATA.(AXIS(I),I=1,1025)/1025*0./
DATA.SASPEC/513*0./

C
C Begin spectral estimation

 

000

000

10

000

20

30

CCC
CCC

4O
CCC
ccc

000

50

C

130

DF=Fs/FLOAT(NFFT)

NF=NFFT/2+1

XA(1)=0.

XA(2)=FMAX- DF

CALL AUTOSCL (XA, 2, FTICK, FST, FMAX)
NFMAX= FMAX/DF+1. 00001
NOF=ANINT(OF/DF)+1

IF (NOF.GT.NF) NOF=NF

Compute the autocorrelation functions and autospectra.

II=K
OPEN (6,STATUS='OLD',FILE=OUTPUTS(1:LOUT)//NAME(LL,II)//'.FRC')

skip information lines at the top of the input file (5 lines)

READ (6,10)

FORMAT (5(/))

CALL CMPSE (CCF,SXY,VAR,PA,XMEAN)
CLOSE (6)

VAR=SQRT(VAR)

RMS=VAR

ADD THE MEAN TO THE PEAK (IT WAS REMOVED IN THE SPECTRUM CALC.)

IF (PA.GT.0) THEN

PA:PA+XMEAN

ELSE

PA=PA—XMEAN

END IF

DO 20 J=1, M/2+1

XA(J)=J-1
SACORR(J)=SACORR(J)+CCF(J)/NA

WRITE (FILE1,30) NAME(LL,II),'.ACN'
FORMAT (8A)

='AUTOCORRELATION '
OPEN (8, FILE=OUTPUTS(1: LOUT)//FILE1)
CALL OUT (8, M/2+1, CCF, 0.,1.)
XLAB= 'Lag'
YLAB='Autocorrelation'
XTICK=0.
YTICK=0.
CALL AUTOSCL (XA, M/2+1, XTICK, XST, XFIN)
CALL AUTOSCL (CCF, M/2+i, YTICK, YST, YFIN)
CALL PLTS (0.,FLOAT(M/2+1), YST, 1.,XTICK, YTICK, XLAB, YLAB, C, AXIS, XA,
1CCF, M/2+1,11,BW)

WRITE (FILE1, 30) NAME(LL, II),' .ASP'

='AUTOSPECTRUM
DO 40 J=1, NF
SX(J)=CABS(SXY(J))
XA(J)=(J- 1)*D F
SASPEC(J)=SASPEC(J)+SX(J)/NA
OPEN (9, FILE= -OUTPUTS(1: LOUT)//FILE1)
CALL OUT (9, NOF, sx, 0.,DF)
XLAB='Frequency (Hz)'
YLAB='Spectral Density'

YTICK = -2.

YTICK=0.
CALL AUTOSCL (SX, NFMAX, YTICK, YST, YFIN)
CALL PLTS (0.,FMAX, YST, YFIN, FTICK, YTICK, XLAB, YLAB, C, AXIS, XA, SX,
1NFMAX, 2, BW)

call plts for the final information on the screen

=' S P E c T R A.L A.N A L Y s I 5'
CALL PLTS (0.,1. o.,1.,1 1. ,XLAB, YLAB, C, AXIS, NULL, NULL, 1, 5, BW)
WRITE (C, 50) NAME(LL, II), RMS, PA, XMEAN

lFORMAT (1x, FILE: ,A8, T25, 'RMS:',F9.4,T42,'PEAK:',F7.2,T62,'MEA
N: F7.2)
CALL PLTS (0.,1.,0.,1.,l.,1.,XLAB,YLAB,C,AXIS,NULL,NULL,1,7,BW)

g Output average correlations and spectrum

if(noavg.eq.0) then

 

60

70

000

131

IF (II.EQ.NA) THEN

FILE1='ANERAGE. ACN'

C='AVERAGE CORRELATION

OPEN (10, FILE=OUTPUTS(1: LOUT)//FILEl)

CALL OUT (10, M/2+1, SACORR, 0.,1.)

DO 60 J=1, M/2+1

XA(J)=J-1

XLAB='Lag'

YLAB='Autocorrelation'

XTICK=O.

YTICK=O.

CALL AUTOSCL (XA.,M/2+1, XTICK, XST, XFIN)
CALL AUTOSCL (SACORR, M/2+1, YTICK, YST, YFIN)
CALL PLTS (O. ,FLOAT(M/2+l),YST,1.,XTICK,YTICK,XLAB,YLAB,C,AXIS,XA,

lSACORR, M/2+1,3 3,BW)

FILE1='AVERAGE.ASP'

C='AVERAGE SPECTRmM '

OPEN (11, FILE=OUTPUTS(1: LOUT)//FILE1)

CALL OUT (11, NF, SASPEC, 0. ,DF)

DO 70 J=1, M/2+1

XA(J)= (J—1)*DF

XLAB='Frequency (Hz)'

YLAB='Spectra1 Density'

YTICK=O.

CALL AUTOSCL (SASPEC,NFMAX,YTICK,YST,YFIN)
CALL PLTS (0.,FMAX,YST,YFIN,FTICK,YTICK,XLAB,YLAB,C,AXIS,XA,

13ASPEC,NFMAX,4,BW)

call plts for the final information on the screen

=' A v E R.A G E A.N A L Y S I 3'

CALL PLTS (0.,1.,0 .,1.,1.,1. ,XLAB, YLAB, c, AXIS, NULL, NULL, 1, 6, BW)
=' E N D O F F I L E P R O C E S s I N G'

CALL PLTS (0.,1.,0.,1.,1.,1.,XLAB, YLAB, c,AXIs, NULL,NULL,1,8,BW)
END IF

END IF

END
SUBROUTINE OUT (IF,NN,X,XMIN,XINC)

——————--_-———n—-_——-———————-——-———-———————_——_————————_—-—————————_—

C This subroutine outputs an array to a file. I

C____.

10
20

30

4O

00
#41:

00000000

##3##:
t1!

—-_..

~-———_-————-—-——---————-—--—————————-————_————-—--—-—-——————————————

REAL X(*)

CHARACTER*80 c

COMMON /CMP/ M,N,FS,IWIN,L,NFFT,DF
COMMON /OUT1/ c

FORMAT (A80/)

FORMAT ' M= ,I5, '; No. of Samples =' ,IS, ; Sampling Frequency
éf‘,g?.l ' Window = Hamming' ,'; ‘Window half-width =' I4, ; NFFT =
,I
FORMAT ' M =' ,15, '; NO. of Sm mples =' ,IS, Sampling Frequency
1=',F6.l ' Window = Rectangular' , Window half-width = ,I4, NF

2FT =',I5)

OPEN (IF,STATUS='UNKNOWN')

WRITE (IF,10) 0

IF (IWIN.EQ.1) WRITE (IF,30) M,N,FS,L,NFFT
IF (IWIN.EQ.2) WRITE (IF,20) M,N,FS,L,NFFT
WRITE (IF,*)

DO 40 I=1,NN

WRITE (IF *) XMIN+(I-1)*XINC,X(I)

CLOSE (IFS
RETURN

ND
#######################################
#######################################
SUBROUTINE CMPSE (CCF,SXY,XVAR,PA,XMEAN

~w¢#=

-———————_--—-——-_-———-—--————————-—-_———————--——-—————-——————q————-—--

This subroutine estimates the auto correlation functions, and the
normalized auto amplitude spectra.

The correlation method for power spectrum estimation is used. Thi
modification of the program written by:

L. Rabiner, Bell Laboratories, MUrray Hill, New Jersey 07974

R. Schafer, et. a1, Georgia Institute of Technology, Atlanta, Georgi

 

132

This method is based on the technique described by C. M. Rader,
In the IEEE Trans. on Audio and Elect., VO1. 18, No. 4, pp 439-442
Input: M is the section size (must be a power of 2);
2 = M <= 1024.
N is the number of samples to be used in the analysis.
MODE is the data format type;
_MDDE = 0 for autocorrelation and autospectrum;
FS 18 the sampling frequency in Hz (i.e., number of samp
second).
IWIN is the window type;
IWIN = 1 for rectangular window;
IWIN = 2 for Hamming window.
(2L-1) is the window base width used in the spectral est
2 <= L <= (M/2+1).
NFFT is the FFT size used in the spectral estimate;
(2L-1) <= NFFT <= 1024.
Variables returned to calling program:
CCF(M/2+1) = Autocorrelation function for +ve lags;
SXY(NFFT/2+1) = Autospectrum (take absolute of SXY);
XVAR = variance of the force-series;
PA = Absolute peak of the force-series.
REAL XA(1025),CCF(*)
COMPLEX X(1025),Z(1025),XMN,XI,YI,SXY(*)
COMMON /CMP/ M,N,FS,IWIN,L,NFFT,DF
PARAMETER (PI=3.141592654)

000OOOOOOOOOOOOOOOOOOOOOO

c
C DEFINE CONSTANTS. NSECT IS THE TOTAL NUMBER OF ANALYSIS SECTIONS.
c LSHFT IS THE SHIFT BETWEEN ADJACENT ANALYSIS SAMPLES
C
LSHFT=M/2
MHLF1=LSHFT+1
NSECT=(FLOAT(N)+FLOAT(LSHFT)-l.)/FLOAT(LSHFT)
c
C 33 IS THE GENERATOR SAMPLE NUMBER. AT THE VERY FIRST CALL TO SUBROUTI
c GETX THIS IS SET AT zERo SO THAT ANY NECESSARY INITIALIZATION
C CAN BE PERFORMED IN THESE SUBROUTINES.
c NRD IS NUMBER OF SAMPLES OF GENERATOR OUTPUT To BE COMPUTED OR READ.
c
SS=0.
NRD=LSHFT
XSUM=0.
YSUM:0.
XXSUM?0.
YYSUM=0.
PA=0.

LOOP TO CALCULATE MEANS AND VARIANCES OF X AND Y DATA
USE GETX TO READ NRD SAMPLES FROM X GENERATOR STARTING AT SAMPLE SS

0000

DO 30 K=1,NSECT
IF (K.EQ.NSECT) NRD=N-(K-1)*NRD
CALL GETX (XA,NRD,SS,N)
DO 10 I=1,NRD
XSUM:XSUM+XA(I)
10 XXSUM?XXSUM+XA(I)*XA(I)
C
C COMPUTE THE ABSOLUTE MAXIMUM OF THE NRD VALUES OF XA.
C

DO 20 I=1,NRD
20 IE‘ (ABS(XA(I)).GT.ABS(PA)) PA=XA(I)
IF (K.EQ.1) SS=1.
SS=SS+ELOAT(NRD)
30 CONTINUE
FN=FLQAT(N)
XMEAN=XSUM/FN
XVAR=XXSUM/FN-XMEAN*XMEAN
SQVAR=SQRT(XVAR*XVAR)
XMN=CMPLX(XMEAN,XMEAN)

REMOVE THE MEAN FROM THE PEAK (MEAN WILL BE A DELTA FUNCTION AT ZE

000

IF (PA.GT.0) THEN
PAFPA-XMEAN

 

133

ELSE
PA=PA+XMEAN
END IF

C
C LOOP TO ACCUMULATE CORRELATIONS
C

SS=1.
NRDY=M
NRDX=LSHFT
DO 40 I=1,NHLE1

40 Z(I)=(0.,O.)
DO 110 K=1,NSECT
NSECT1=NSECT-l
IF (K.LT.NSECT1) GO TO 60
NRDY=N—(K-l)*LSHFT
IF (K.EQ.NSECT) NRDx=NRDY
IF (NRDY.EQ.M) Go TO 60
NRDY1=NRDY+1
DO 50 I=NRDY1,M

50 X(I)=(0.,0.)

c
c READ NRDY SAMPLES FROM x GENERATOR STARTING AT SAMPLE SS
C
60 CALL GETx (XA,NRDY,SS,N)
DO 70 I=1,NRDY
70 X(I)=CMPLX(XA(I),XA(I))
DO 80 I=1,NRDY
80 X(I)=X(I)-XMN
NRDx1=NRDx+1
DO 90 I=NRDX1,M
9o X(I)=CMPLX(0.,AIMAG(X(I)))
c
c CORRELATE x AND Y SECTIONS
C DO EVEN-ODD SEPARATION AND ACCUMULATE CONJG(X)*Y
C
CALL FFT (X,M,O)
DO 100 I=2,LSHFT
J=M+2—I
XI=(X(I)+CONJG(X(J)))*.5
YI=(X(J)-CONJG(X(I)))*.5
YI=CMPLX(AIMAG(YI),REAL(YI))
Z(I)=Z(I)+CONJG(XI)*YI
100 CONTINUE
XI=X(1)
Z(1)=Z(1)+CMPLX(REAL(XI)*AIMAG(XI),0.)
XI=X(MHLF1)
Z(MHLF1)=Z(MHLF1)+CMPLX(REAL(XI)*AIMAG(XI),0.)
SS=SS+FLOAT(LSHFT)
110 CONTINUE
C
c INVERSE DFT TO GIVE CORRELATION
C

DO 120 I=2,LSHFT

J=M+2—I

X(I)=Z(I)

X(J)=CONJG(Z(I))

120 CONTINUE

X(1)=Z (l)

X(MHLF1)=Z(MHLF1)
C CALL FFT (X,M,1)

g STORE NORMALIZED CORRELATIONS FOR POSITIVE LAGS.

DO 130 I=1,MHLE1
XA(I)=REAL(X(I))/FN
CCF(I)=XA(I)*M/SQVAR
XA(I)=CCF(I)
C130 CONTINUE
C WINDOW CORRELATION USING (2L-l) POINT WINDOW. FOR AUTOCORRELATION USE
C OF SYMMETRY.
g In section below, K = —1 for negative lags and K = l for positive lags

K=-1
J2=1
L2=L
NLAST=NFFT~L2+1

 

134

IF (IWIN.EQ.2) THEN
DO 140 I=J2,L2
140 éfigl§FXA(I)*(0.54+0.46*COS(PI*FLOAT(K*(I-l))/FLOAT(L-1)))

C Put negative lag values at right end of XA(I)
C

IF (K.EQ.-l) THEN
DO 150 I=2,L2

J=NFFT+2-I
150 XA(J)=XA(I)
END IF
C
C

DO 160 I=L2+1,NLAST
160 XA(I)=O.

DO 170 I=1,NFFT
17o X(I)=CMPLX(XA(I),0.)

C
C COMPUTE NORMALIZED ONE-SIDED AUTOSPECTRUM OR CROSS SPECTRUM
C

CALL FFT (X,NFFT,0)
DO 180 I=1,NFFT/2+l
180 SXY(I)=2.*X(I)/DF

RETURN

END
C#######################################################################
C#######################################################################

SUBROUTINE AUTOSCL (X,N,TICK,ST,FIN)
C This routine determdnes the starting and ending values to be used in P
C for a full scale plot. '
C INPUT : X = X or Y array; N = Number of elements in X;
C TICK = Distance between tick marks; a) >0 to use supplied valu
C b) =0 to choose automatically
C OUTPUT : ST = Starting value; FIN = Ending value; TICK (If originall

—————-—u-——--——-_————-——-————————--—~-—‘--—-——————-—~————-----~-—-—-—_~

O

FIN=X(1)

ST=X(1)

DO 10 I=1,N

IF (X(I).GT.FIN) FIN=X(I)
10 IF (X(I).LT.ST) ST=X(I)

IF (TICK.GT.0.) THEN
ST=TICK*IRINT(ST/TICK)
FIN=TICK*(IRINT(FIN/TICK)+1)
ELSE IF (TICK.EQ.0) THEN
TT=ALOGlO(FIN-ST)
MT=IRINT(TT)
TT=10.**(TT-MT)

IF (TT.LE.2) THEN
TT=2.

ELSE IF (TT.GT.5) THEN
TT=10.

ELSE

TT=5.

END IF
TICK=TT*10.**(MT-l)
U=1.00001*TICK
C=DLOG10(U)

IF (C.LT.O) THEN
L=IDINT(C)-l

ELSE

L=IDINT(C)

END IF

C=DBLE(10.)**L
TICK=C*IDNINT(U/C)
N1=IRINT(ST/TICK)
N2=IRINT(FIN/TICK)+1
ST=N1*TICK
FIN=N2*TICK

NT=N2-Nl

END IF

 

135

RETURN

END

INTEGER FUNCTION IRINT(X)
IF (X.LT.0) THEN
IRINT=INT(X)-1

ELSE

IRINT=INT(X)

END IF

RETURN

##################
##################
SUBROUTINE FFT (X,

mm:
#m¢
##tm

z:w#

~ #mt

H3ߢ

Earn:
ma:

~vma:
am:
am:
*at

C This subroutine computes the discrete Fourier Transform or the inverse
C transform of X.

C ———————————————————————————————————————————————————————————————————————
C Input: X = 2**M complex array that initially contains the input

C and on return contains the transform;

C N = 2**M points. (Must be power of 2, else infinite loop resu
C INV = 0 for direct transform; 1 for inverse transform.

———————————--——-—-—-u—————_————-—--——_----—---——————————_———-———————_———

00

COMPLEX X(*),U ,
MFALOG(FLOA T(N )
Nv2=N/2
NM1=N- 1
J=l
DO 40 I=1,NM1
IF (I.GE.J) GO TO 10
T=X(J)
X(J)=X(I)
X(I)=T
10 K=NV2
20 IF (K.GE.J) GO To 30
J=J-K
K=K/2
GO To 20
30 J=J+K
40 CONTINUE
PI=4.0*ATAN(1.0)
DO 70 L=1,M
LE=2**L
LE1= LE/z
U=(1.0, 0.0)
w=CMPLX(COS(PI/FLOAT(LEl)),-SIN(PI/ELOAT(LE1)))
IF (INV. NE. 0) w=CONJG(W)
DO 60 J=1,LE1
DO 50 I=J,N,LE
IP=I+LE1

W,T
)/ALOG(2.)+.1

T=X(IP) *U
X(IP)=X(I)-T
X(I)=X(I)+T
50 CONTINUE
U=U*W
60 CONTINUE
7O CONTINUE
IF (INV.EQ.1) RETURN
DO 80 I= 1, N
X(I)=X(I)/N
80 CONTINUE
RETURN

END

###########################
###########################
SUBROUTINE GETX (X, NRD, SS, N

#mt
aw:
~«wsc

_-_______—--_—____-—---_—__—_——----_--___——_—-_-_-_-.-—~__---_—--——_-_-—

C This subroutine passes the required length of a TIME SERIES to the cal
C program. On the first call to this subroutine SS = 0, and the ent
C values of the force- series is read from logical unit 11, and the f
C values are placed in array X. On all subsequent calls NRD values
C force- series starting from sample SS are placed in array X.

-——-—-~—---—-—_---——----‘—----_—————----_——--~——---——-—--—---——-——‘-~—-

REAL X(*),XSTORE(7500)
10 FORMAT (45X,F13.6)

 

OOOOOOO»**»»*******»OO

0000

000

N
0

:m#

136

J=SS

IF (J.EQ.0) THEN

§EID (6,10) (XSTORE(I),I=1,N)

END IF

DO 20 I=1,NRD

X(I)=XSTORE(J+I-l)

RETURN

END .
######################################################################
######################################################################
******'k****************************
********‘k**************************
* *
* SUBROUTINE PLTS *
* *
***at-*******************************
******'k****************************
* 'k
* AUG 22,1992 TO PLOT CORRELATION AND SPECTRUM :
'k
* * * * * * * * * * * * i k * * * * * i * * * * * * * * * * * * * * *
* k * * * * * * * * * * * k * * * * * * * * * * * * * * * * * * * * *
* ***************************************************************** *

++++++++++++++++++++++++++++++++++
++++++++++++++++ 1. DATA INPUT/OUTPUT ++++++++++++++++
++++++++++++++++++++++++++++++++++

SUBROUTINE PLTS (XMIN,XMAX,YMIN,YMAX,XTICSPACE,YTICSPACE,
lXAXISTITLE,YAXISTITLE,TITLE,AXIS,X,Y,NUMBER,NN,BW)

LOGICAL*1 INITGRAPHICS,INITBORDER,INITWINDOW,INITAXES,INITFONTS,
lPLOTMETHOD,INVERTX,INVERTY,TITLEONLY,SCRONLY,Y2PLOT,y3plot,
2PLOT2METHOD

INTEGER*2 BORDERCOLOR,WINDOWCOLOR,AXISCOLOR,LABELCOLOR,PLOTCOLOR,
lTITLECOLOR,NUMBER,PLOTZCOLOR,FONTHEIGHT,FONTWIDTH,PLOT3COLOR

DIMENSION X(NUMBER), Y(NUMBER), AXIS(*)

CHARACTER TITLE*280,XAXISTITLE*80,YAXISTITLE*80

INITIALISE THINGS FOR THE FIRST PLOT

INITGRAPHICS=.TRUE.
INITBORDER=.TRUE.
INITWINDOw=.TRUE.
INITAXES=.TRUE.
INITFONTS=.TRUE.
PLOTMETHOD=.TRUE.
TITLEONLY=.FALSE.

y2plot should be set to "true" to show the zero axis

Y2PLOT=.TRUE.
Y3PLOT=.FALSE.
FONTHEIGHT=10
FONTWIDTH=5
SET UP THE FANCY COLORS
BORDERCOLOR=14
WINDOWCOLOR=1
AXISCOLOR=10
LABELCOLOR=11
PLOTCOLOR=14
PLOT2COLOR=4
PLOT3COLOR=4
TITLECOLOR=15
IF(BW.EQ.1.0) THEN
BORDERCOLOR=3
WINDOWCOLOR=15
AXISCOLOR=0
LABELCOLOR=4
PLOTCOLOR=0
PLOT2COLOR=1
PLOT3COLOR=3
TITLECOLOR=0

 

00000 00000 00000 00 00000

00000

137

END IF
IF (Nn.EQ.l) THEN

++++++++++++++++++++++++++++++++++
++++++++++++++++ 1. Auto Correlation ++++++++++++++++
++++++++++++++++++++++++++++++++++

XBOTTOMLEFT=0.00
YBOTTOMLEFT=0.1O
XTOPRIGHT=0.50
YTOPRIGHT=0.90

ELSE IF (Nn.EQ.2) THEN

++++++++++++++++++++++++++++++++++
++++++++++++++++ 2. Auto Spectra ++++++++++++++++
++++++++++++++++++++++++++++++++++

INITGRAPHICS=.FALSE.
INITFONTS=.FALSE.
INITAXES=.TRUE.
WINDOWCOLOR=1
IF(BW.EQ.1.0)WINDOWCOLOR=15
XBOTTOMLEFT=0.50
YBOTTOMLEFT=0.10
XTOPRIGHT=1.00
YTOPRIGHT=O.90

ELSE IF (Nn.EQ.3) THEN

++++++++++++++++++++++++++++++++++
++++++++++++++++ 3. Average Correlation ++++++++++++++++
++++++++++++++++++++++++++++++++++

WINDOWCOLOR=O
IF(BW.EQ.1.0)WINDOWCOLOR=15
XBOTTOMLEFT=0.00
YBOTTOMLEFT=0.10
XTOPRIGHT=0.50
YTOPRIGHT=0.90

ELSE IF (Nn.EQ.4) THEN

++++++++++++++++++++++++++++++++++
++++++++++++++++ 4. Average Spectra ++++++++++++++++
++++++++++++++++++++++++++++++++++

WINDOWCOLOR=0
IF(BW.EQ.1.0)WINDOWCOLOR=15
INITGRAPHICS=.FALSE.

XBOTTOMLEFT=O.50

YBOTTOMLEFT=O.10

XTOPRIGHT=1.00

YTOPRIGHT=O.90

ELSE IF ((Nn.EQ.5).OR.(Nn.EQ.6)) THEN

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

++++++++++++++++ 5. Top Title on the Screen ++++++++++++++++
++++++++++++++++++++++++++++++++++

INITGRAPHICS=.FALSE.
TITLEONLY=.TRUE.
INITAXES=.FALSE.
INITFONTS=.TRUE.
FONTHEIGHT=28
FONTWIDTH=16
WINDOWCOLOR=7
TITLECOLOR=4

IF (BW.EQ.1.0) THEN
WINDOWCOLOR=15
TITLECOLOR=4

END IF
XBOTTOMLEFT=0.00
YBOTTOMLEFT=0.90
XTOPRIGHT=1.00
YTOPRIGHT=1.00

ELSE IF ((Nn.EQ.7).OR.(Nn.EQ.8)) THEN

 

0000

000

00000

138

+++++++++++++++++f++++++++++++++++
++++++++++++++++ 6. Bottom Title Screen ++++++++++++++++
++++++++++++++++++++++++++++++++++

INITGRAPHICS=.FALSE.
TITLEONLY=.TRUE.
INITAXES=.FALSE.
INITFONTS=.TRUE.
FONTHEIGHT=18
FONTWIDTH=9
WINDOWCOLOR=7
TITLECOLOR=0

IF (BW.EQ.1.0) THEN
WINDOWCOLOR=15
TITLECOLOR=4

END IF
XBOTTOMLEFT=0.00
YBOTTOMLEFT=0.00
XTOPRIGHT=1.00
YTOPRIGHT=0.10

END IF

Call plot to print graphs to the screen

CALL PLOT (INITGRAPHICS,INITBORDER,INITWINDOW,INITAXES,INITFONTS,
1X,Y,AXIS,NUMBER,PLOTMETHOD,INVERTX,INVERTY,XMIN,XMAX,YMIN,YMAX,
2XTICSPACE,YTICSPACE,XBOTTOMLEFT,YBOTTOMLEFT,XTOPRIGHT,YTOPRIGHT,
3PLOT2COLOR,BORDERCOLOR,WINDOWCOLOR,AXISCOLOR,LABELCOLOR,PLOTCOLOR,
4TITLECOLOR,XAXISTITLE,YAXISTITLE,TITLE,TITLEONLY,EONTHEIGHT,
5FONTWIDTH,SCRONLY,Y2PLOT,Y3PLOT,PLOT3COLOR,X3,Y3,NUM3,BW
6,PLOT2METHOD)

WAIT FOR USER TO HIT RETURN ( only for testing the program
, otherwise let the program run w1th no stops)

IF ((Nn.EQ.7).OR.(Nn.EQ.8)) THEN
READ * *)

I
END IF
IF (Nn.EQ.8) CALL ENDGRAPHICS ()
RETURN
END

 

139

MYSTAT. FOR
C#######################################################################
C#######################################################################

SUBROUTINE MYSTAT(X,Nn,XMIN,XMAX,NMIN,NMAX,XMEAN,XVAR,XSTD,XVX,

1XSKE,XKUR,XSE,XABS)

DIMENSION X(Nn)

LOGICAL*1 XABS

=-1El4

XMIN=1e14

NMAX=O

NMIN= 0

XSUM=0.0

XSUM2=0.0

XSUM3=0.0

XSUM4=0.0

DO 10 I=1,Nn

if(xabs) then

DO 20 II=1,Nn

X(I)=ABS(X(I))
20 CONTINUE

END IF

DETERMINE THE MEAN

000

XSUM:XSUM+X(I)
XSUM2=XSUM2+X(I)**2.0

FINDING MAXIMUM.AND MINIMUM

IE (X(I).GT.XMAX) THEN
XMAX=X(I)
NMAX=I
END IE
IE (X(I).LT.XMIN) THEN
XMIN=X(I)
NMIN=I
END IE

10 CONTINUE
XN=FLOAT(Nn)
XMEAN =XSUM/XN
XVAR =XSUM2/XN-XMEAN**2.0
XSTD=SQRT XVAR)
XVX=(XSTD XMEAN)*100.0
XSE=XSTD/SQRT(XN)

COEFFICIENT OF SKEWNESS AND COEFFICIENT OF KURTOSIS

000

000

DO 30 I=1,Nn

XSUM3=XSUM3+(X(I)-XMEAN)**3.0

XSUM4=XSUM4+(X(I)-XMEAN)**4.o
30 CONTINUE

XSKE=XSUM3/XSTD**3.0

XKUR=XSUM4/XSTD**4.0

RETURN

END

$STORAGE:2
$LARGE

140

PLOT.FOR

C################################################
C START OF MODULE PLOT FOR #######################

INCLUDE 'EGRAPH.EI'

SUBROUTINE PLOT (INITGRAPHICS,INITBORDER,INITWINDOW,INITAXES,
1INITEONTS,XDATA,YDATA,Y2DATA,NUMBER,PLOTMETHOD,INVERTX,INVERTY,
2XMIN,XMAX,YMIN,YMAX,XTICSPACE,YTICSPACE,XBOTTOMLEFT,YBOTTOMLEFT,
3XTOPRIGHT,YTOPRIGHT,PLOTZCOLOR,BORDERCOLOR,WINDOWCOLOR,AXISCOLOR,
4LABELCOLOR,PLOTCOLOR,TITLECOLOR,XAXISTITLE,YAXISTITLE,TITLE,
5TITLEONLY,FONTHEIGHT,FONTWIDTH,SCRONLY,Y2PLOT,Y3PLOT,PLOT3COLOR,
6X3,Y3,NUM3,BW,PLOT2METHOD)

PURPOSE

PROGRAMMER
REVISION
NOTES

CALLS
GRAPHICSMODE()

ON ENTRY
LOGICAL*1

LOGICAL*1
LOGICAL*1
LOGICAL*1
LOGICAL*1
REAL*4
REAL*4
INTEGER*2
LOGICAL*1
LOGICAL*1
LOGICAL*1
REAL*4
REAL*4
REAL*4
REAL*4

REAL*4
REAL*4

000000000000000000000000000000000000000000000000000000000000000

TO PLOT A SET OF X-Y DATA USING THE MICROSOFT
FORTRAN 5.0 GRAPHICS LIBRARY. PLOT WILL PLOT
AN 'UNLIMITED' SET OF X AND Y DATA USING

CGA, EGA, VGA OR HERCULES GRAPHICS WITH

USER DEFINED PLOT POSITIONING, AXIS LABELLING
AND TITLING.

LIAM E. GUMLEY, CURTIN UNIVERSITY OF TECHNOLOGY
20 APRIL 1992 BY BASSEM K. KHAFAGI

HERCULES GRAPHICS USERS MUST RUN

MSHERC.COM (MICROSOFT HERCULES RESIDENT VIDEO
SUPPORT ROUTINES, SUPPLIED WITH MICROSOFT
FORTRAN 5.0) BEFORE ATTEMPTING TO CALL PLOT.
PLOT ALSO USES THE MICROSOFT FORTRAN 5.0 FONT
FILE HELVB.FON TO GENERATE CHARACTERS.
HELVB.FON MUST BE IN THE CURRENT DIRECTORY WHEN
PLOT IS CALLED OTHERWISE THE PROGRAM WILL

STOP WITH A 'FONT FILE NOT FOUND' MESSAGE.

NOTE THAT THE FONT FILE HELVB.FON ONLY

NEEDS TO BE INITIALISED ONCE, ON THE FIRST
CALL TO PLOT. THE FONTS REMAIN RESIDENT IN
MEMORY FOR SUBSEQUENT CALLS TO PLOT.

ALSO NOTE THAT SELECTION OF COLORS MAY NEED TO
BE CHANGED ON CGA OR MONOCHROME MONITORS, AS
THESE ONLY SUPPORT TWO COLORS (BLACK OR WHITE).
THE X AND Y AXIS LABELS ARE WRITTEN IN
SCIENTIFIC NOTATION. THE BASE IS WRITTEN NEXT
TO THE TICS, AND THE EXPONENT PORTION, TAKEN
FROM THE AXIS MAXIMUM VALUE, IS WRITTEN AT THE
END OF THE AXIS.

SET HIGHEST RESOLUTION ON CGA/EGA/VGA/HGC

ALSO CALLS ROUTINES EROM MICROSOFT FORTRAN 5.0
GRAPHICS LIBRARY GRAPHICS.LIB. MAIN PROGRAMS
WHICH CALL THIS SUBROUTINE (PLOT) MUST BE LINKED
WITH GRAPHICS.LIB.

E.G.
>FL MAIN.FOR PLOT.FOR GRAPHICS.LIB

TRUE : ENTER GRAPHICS MODE
FALSE: NO ACTION

TRUE : DRAW WINDOW BORDER

FALSE: NO ACTION

TRUE : ERASE INSIDE WINDOW
FALSE: NO ACTION

INIT GRAPHICS
INIT BORDER
INIT WINDOW

INIT AXES TRUE : DRAW AXES AND LABELS
FALSE: NO ACTION

INIT FONTS TRUE : INITIALISE FONT FILE
FALSE: NO ACTION

XDATA ARRAY OF ORDINATES (ASCENDING)

YDATA ARRAY OF COORDINATES

NUMBER # OF ELEMENTS IN XDATA, YDATA

PLOT METHOD = TRUE : JOIN POINTS WITH LINES

= FALSE: DRAW DOTS ATTEBINTS
T X = TRUE : X AXIS INVER
INVER = FALSE: NO ACTIIHVERTED
Y = TRUE : Y AXIS

INVERT = FALSE: NO ACTION

XMIN MINIMUM TO PLOT FOR X AXIS

XMAX MAXIMUM TO PLOT FOR X AXIS

YMIN MINIMUM TO PLOT FOR Y AXIS

YMAX MAXIMUM TO PLOT FOR Y AXIS

X TIC SPACE TIC-LABEL INTERVAL FOR X AXIS

Y TIC SPACE TIC-LABEL INTERVAL FOR Y AXIS

 

0000000000000000000000

10

20

0

00000

00 000

141

 

REAL*4 X BOTTOM LEFT SCREEN PLOT LOCATION (0.0-1.0)
(0.0,0.0) = SCREEN BOTTOM LEFT
(l.0,1.0) = SCREEN TOP RIGHT
REAL*4 Y BOTTOM LEFT SCREEN PLOT LOCATION (0.0-1.0)
REAL*4 X TOP RIGHT SCREEN PLOT LOCATION (0.0-1.0)
REAL*4 Y TOP RIGHT SCREEN PLOT LOCATION (0.0-l.0)
INTEGER*2 BORDER COLOR COLOR FOR WINDOW BORDER
INTEGER*2 WINDOW COLOR COLOR FOR WINDOW BACKGROUND
INTEGER*2 AXIS COLOR COLOR FOR PLOT AXES AND TICS
INTEGER*2 LABEL COLOR COLOR FOR AXIS LABELS
INTEGER*2 PLOT COLOR COLOR FOR PLOTTED DATA
INTEGER*2 PLOT2 COLOR COLOR FOR PLOTTED DATA (2ND SET)
INTEGER*2 TITLE COLOR COLOR FOR TITLE TEXT
CHARACTER*80 X AXIS TITLE TITLE TEXT FOR X AXIS
CHARACTER*80 Y AXIS TITLE TITLE TEXT FOR Y AXIS
CHARACTER*80 TITLE TITLE TEXT FOR PLOT
LOGICAL*1 TITLE ONLY = TRUE : BORDER AND TITLE ONLY
= FALSE: NO ACTION
INTEGER*2 FONT HEIGHT CHARACTER FONT HEIGHT (PIXELS)
INTEGER*2 FONT WIDTH CHARACTER FONT WIDTH (PIXELS)
ON EXIT NOTHING CHANGED, NOTHING RETURNED

INCLUDE 'FGRAPH.FD'

LOGICAL*1 INITGRAPHICS,INITBORDER,INITWINDOW,INITAXES,INITFONTS,
lPLOTMETHOD,INVERTX,INVERTY,TITLEONLY,SCRONLY,Y2PLOT,Y3PLOT,
2PLOT2METHOD

INTEGER*2 DUMMY,XWIDTH,YHEIGHT,IXl,IY1,IX2,IY2,BORDERCOLOR,
1WINDOWCOLOR,AXISCOLOR,LABELCOLOR,PLOTCOLOR,TITLECOLOR,NUMBER,I,IX,
2IY,TICLENGTH,PLOTZCOLOR,FONTHEIGHT,FONTWIDTH,TITLELENGTH,
3PLOT3COLOR

REAL*4 X,Y,XMIN,YMIN,XMAX,YMAX,XDATA(NUMBER),YDATA(NUMBER),
lY2DATA(NUMBER),XWl,YW1,XW2,YW2,XTICSPACE,YTICSPACE,XBOTTOMLEFT,
ZYBOTTOMLEFT,XTOPRIGHT,YTOPRIGHT,XT,YT,X3(NUM3),Y3(NUM3)

CHARACTER TICLABEL*8,FONTFILE*12,FONTSTRING*7,TITLE*80,
lXAXISTITLE*80,YAXISTITLE*80,FONTCOMMAND*10,TITLE1*80,TITLE2*80,
2TITLE3*80,TITLE4*80,TITLE5*80,TITLE6*80,TITLE7*80,TITLE8*80

RECORD / VIDEOCONFIG / SCREEN
RECORD / WXYCOORD / WXY
RECORD / XYCOORD / POSITION

COMMON SCREEN
SET THE NAME OE THE EONT FILE To USE (MUST BE IN CURRENT DIR)
FONTFILE='HELVB.FON'
FONTCOMMAND="T'HELV'"
SET THE GRAPHICS MODE To HIGHEST POSSIBLE RESOLUTION
IE (INITGRAPHICS) CALL GRAPHICSMODE ()
REGISTER FONT FOR LABELS
IE (INITFONTS) THEN
CALL UNREGISTEREONTS ()
IE (REGISTEREONTS(FONTFILE).LT.0) THEN
WRITE (*,10) FONTFILE
EORMAT (' EONT FILE ',A12,' NOT FOUND IN PLOT')
STOP
END IE
SET UP EONT FOR USE
WRITE (FONTSTRING,20) FONTHEIGHT,FONTWIDTH
EORMAT ('H',I2.2,'W',IZ.2,'B')
DUMMY=SETEONT(FONTCOMMAND//FONTSTRING)
END IE
GET SCREEN DIMENSIONS
XWIDTH=SCREEN.NUMXP;§§EES
YHEIGHT=SCREEN.NUMY
SET A.VIEW PORT, WITH CORNER COORDINATES DEFINED AS A
FRACTION OF THE TOTAL SCREEN SIZE
(0.0,0.0) IS BOTTOM LEFgFogcgggfiEN
. 1.0 IS TOP RIGHT
TRANSLATE CORNER COORDINATES TO PIXEL COORDINATES
Ix1=INT(XBOTTOMLEET*FLOAT(XWIDTH))
IX2=INT(XTOPRIGHT*FLOAT(XWIDTH))
IYl=YHEIGHT—INT(YTOPRIGHT*FLOAT(YHEIGHT))
IY2=YHEIGHT-INT(YBOTTOMLEFT;§L%$§(YHEIGHT))
TVIEWPORT 1x1 IY , ,
CACREATE.A REAL COORDINATE WINDOW, WITH GRAPH AREA SIZED AT
60% OF THE TOTAL VIEWPORT SIZE (LEAVES 15% EITHER SIDE FOR

LABELS AND TICS)

SCALE=0.60
IF THE GRAPH OCCUPIES LESS THAN 50% OF THE SCREEN IN

EITHER THE X OR Y DIRECTION, THEN THE LABELS WON'T FIT.

00

000 000 000 0000

0000

30

40

142

80 IF THE GRAPH IS LESS THAN 50% OF SCREEN IN X OR Y,
THEN SIZE THE GRAPH AREA AT 30% OF THE VIEWPORT SIZE.
IF (XTOPRIGHT-XBOTTOMLEFT.LT.0.5.0R.YTOPRIGHT-YBOTTOMLEFT.LT.0.5)
ISCALE=0.30
IF (SCRONLY) THEN
XW1=XMIN
YW1=YMIN
XW2=XMAX
YW2=YMAX
GO TO 30
END IF
XW1=XMIN-0.5*(1.0-SCALE)*ABS(XMAX-XMIN)
YWl=YMIN-0.5*(l.0-SCALE)*ABS(YMAX-YMIN)
XW2=XMAX+0.5*(1.0-SCALE)*ABS(XMAX-XMIN)
YW2=YMAX+0.5*(1.0-SCALE)*ABS(YMAX-YMIN)
DUMMY=SETWINDOW(.TRUE.,XW1,YW1,XW2,YW2)
DRAW A BORDER AROUND THE VIEWPORT
IF (INITBORDER) THEN
IF (INITWINDOW) THEN
DUMMY=SETCOLOR(WINDOWCOLOR)
DUMMY=RECTANGLE WK$GFILLINTERIOR,XW1,YW1,XW2,YWZ)
END IF _
DUMMY=SETCOLOR(BORDERCOLOR)
DUMMY=RECTANGLE_W($GBORDER,XWl,YW1,XW2,YWZ)
END IF
SKIP TO TITLE DRAWING IF REQUIRED
IF (TITLEONLY) GO TO 90
IF (SCRONLY) GO TO 40
IF (.NOT.SCRONLY) GO TO 50

This is the screen design of the openning logo

TITLELENGTH=80

DUMMY=SETCOLOR(8)

IF (BW.EQ.1.0)DUMMY=SETCOLOR(15)

YYW1=YW1+0.42

YYW2=YW2-0.42

DUMMY=RECTANGLE W($GFILLINTERIOR,XW1,YYW1,XW2,YYWZ)
DUMMY=SETCOLOR(I2)

IF (BW.EQ.1.0)DUMMY=SETCOLOR(0)
DUMMY=RECTANGLE;W($GBORDER,XWl,YYW1,XW2,YYW2)

POSITION THE TITLE CENTERED (MORE OR LESS) ABOVE GRAPH

YT=0.5*(YMAX+YMIN)

CALL MOVETO W (1.0*(XMAX+XMIN),YT WXY)
CALL GETCURRENTPOSITION (POSITION)
IX=POSITION.XCOORD

IY=POSITION.YCOORD
IX=IX-(TITLELENGTH*FONTWIDTH)/2
IY=IY—FONTHEIGHT/2

enter the program name (Title: from the main program)

DUMMY=SETCOLOR(0)

CALL MOVETO (IX,IY,POSITION)

CALL OUTGTEXT (TITLE(1:TITLELENGTH))
DUMMY=SETCOLOR(11)

IF (BW.EQ.1.0)DUMMY=SETCOLOR(0)

CALL MOVETO (IX,IY+2,POSITION)

CALL OUTGTEXT (TITLE(1:TITLELENGTH))

Standard logo
TITLE1=' DEPARTMENT OF CIVIL ENGINEERING'

TITLE2=: ' MICHIGAN STATE UNIVERSITY'
TITLE3=

TITLE4=' LOAD RESEARCH'
TITLE5=' PROGRAMS FOR DISSERTATION'
TITLE6=' '

TITLE7=' BASSEM K. KHAFAGI'
TITLE8=' OCTOBER 1992'

Drawing the screen

000

50

0000

C60
61

70

143

DUMMY=SETCOLOR(15)

CALL MOVETO (IX,IY-200,POSITION)

CALL OUTGTEXT (TITLEl(l:TITLELENGTH))
CALL MOVETO (IX,IY-160,POSITION)

CALL OUTGTEXT (TITLE2(1:TITLELENGTH))
CALL MOVETO (IX,IY-120,POSITION)

CALL OUTGTEXT (TITLE3(1:TITLELENGTH))
CALL MOVETO (IX,IY-80,POSITION)

CALL OUTGTEXT (TITLE4(1:TITLELENGTH))
CALL MOVETO (IX,IY+80,POSITION)

CALL OUTGTEXT (TITLE5(1:TITLELENGTH))
CALL MOVETO (IX,IY+120,POSITION)

CALL OUTGTEXT (TITLE6(1:TITLELENGTH))
CALL MOVETO (IX,IY+160,POSITION)
CALL OUTGTEXT (TITLE7(1:TITLELENGTH))
CALL MOVETO (IX,IY+200,POSITION)
CALL OUTGTEXT (TITLE8(1:TITLELENGTH))

Adding shadow to the text

DUMMY=SETCOLOR(4)
CALL MOVETO (IX,IY-198,POSITION)
CALL OUTGTEXT (TITLE1(1:TITLELENGTH))
DUMMY=SETCOLOR(1)
CALL MOVETO (IX,IY-158,POSITION)
CALL OUTGTEXT (TITLE2(1:TITLELENGTH))
DUMMY=SETCOLOR(4)
CALL MOVETO (IX,IY-118,POSITION)
CALL OUTGTEXT (TITLE3(1:TITLELENGTH))
CALL MOVETO (IX,IY—79,POSITION)
CALL OUTGTEXT (TITLE4(1:TITLELENGTH))
CALL MOVETO (IX,IY+84,POSITION)
CALL OUTGTEXT (TITLE5(1:TITLELENGTH))
CALL MOVETO (IX,IY+122,POSITION)
CALL OUTGTEXT (TITLE6(1:TITLELENGTH))
DUMMY=SETCOLOR(1)
CALL MOVETO (IX,IY+162,POSITION)
CALL OUTGTEXT (TITLE7(1:TITLELENGTH))
DUMMY=SETCOLOR(4)
CALL MOVETO (IX,IY+202,POSITION)
CALL OUTGTEXT (TITLE8(1:TITLELENGTH))
SKIP THE AXES DRAWING IF NOT NEEDED
IF (.NOT.INITAXES) GO To 140
DRAW AXES
DUMMY=SETCOLOR(AXISCOLOR)
CALL MOVETO W (XMIN,YMAX,WXY)
DUMMY=LINETO‘W(XMIN,YMIN)
DUMMY=LINETO‘W(XMAX,YMIN)
DUMMY=LINETO‘W(XMAX,YMAX)
DUMMY=LINETO_W(XMIN,YMAX)
PUT TIC MARKS AND LABELS ON AXES AT USER DEFINED SPACES
TIC MARKS ARE ALWAYS 2 PIXELS LONG
TICLENGTH=2
TIC MARKS AND LABELS EOR X AXIS
DO 70 X=XMIN,XMAX,XTICSPACE

INVERT X AXIS PLOTTING IE REQUIRED
XT=X
IE (INVERTX) XT=XMAX-ABS(XT—XMIN)
CALL MOVETO W (XT,YMIN,WXY)

CALL GETCURRENTPOSITION (POSITION)
IX=POSITION.XCOORD
IY=POSITION.YCOORD
DUMMY=SETCOLOR(AXISCOLOR)
DUMMY=LINETO(IX,IY+TICLENGTH)

TIC LABEL IS 5 CHARACTERS LONG
WRITE (TICLABEL,60) X
EORMAT (1PE8.1)

EORMAT (1F5.1)
EORMAT (1F6.2)

MAKE ROOM FOR THE TIC LABEL
IX=IX—(5*FONTWIDTH)/2
IY=IY+(FONTHEIGHT/2)

CALL MOVETO (IX,IY,POSITION)
DUMMY=SETCOLOR(LABELCOLOR)
CALL OUTGTEXT (TICLABEL(1:5))

CONTINUE
PUT TIC MARK AT XMAX IN CASE IT WAS MISSED

 

80

90

100

110

144

XT=XMAX
IE (INVERTX) XT=XMIN
CALL MOVETO W (XT,YMIN,WXY)
CALL GETCURRENTPOSITION (POSITION)
IX=POSITION.XCOORD
IY=POSITION.YCOORD
DUMMY=SETCOLOR(AXISCOLOR)
DUMMY=LINETO(IX,IY+TICLENGTH)

TIC MARKS AND LABELS FOR Y AXIS
DO 80 Y=YMIN,YMAX,YTICSPACE
YT Y INVERT Y AXIS PLOTTING IE REQUIRED
IF (INVERTY) YT=YMAX-ABS(YT-YMIN)
CALL MOVETO W (XMIN,YT,WXY)
CALL GETCURRENTPOSITION (POSITION)
IX=POSITION.XCOORD
IY=POSITION.YCOORD
DUMMY=SETCOLOR(AXISCOLOR)
DUMMY=LINETO(IX—TICLENGTH,IY)

TIC LABEL IS 5 CHARACTERS LONG
WRITE (TICLABEL,61) Y
MAKE ROOM FOR THE TIC LABEL

IX=IX-(6*FONTWIDTH)
IY=IY-(FONTHEIGHT/2)
CALL MOVETO (IX,IY,POSITION)
DUMMY=SETCOLOR(LABELCOLOR)
CALL OUTGTEXT (TICLABEL(1:6))
CONTINUE

PUT TIC MARK AT YMAX IN CASE IT WAS MISSED
YT=YMAX
IF (INVERTY) YT=YMIN
CALL MOVETO W (XMIN,YT,WXY)
CALL GETCURRENTPOSITION (POSITION)
IX=POSITION.XCOORD
IY=POSITION.YCOORD
DUMMY=SETCOLOR(AXISCOLOR)
DUMMY=LINETO(IX-TICLENGTH,IY)

WRITE THE GRAPH TITLE AT TOP OF GRAPH REGION
DUMMY=SETCOLOR(TITLECOLOR)

POSITION THE TITLE CENTERED (MORE OR LESS) ABOVE GRAPH
TITLELENGTH=80
IF (TITLE(TITLELENGTH:TITLELENGTH).EQ.' ') THEN
TITLELENGTH=TITLELENGTH-1
GO TO 100
END IF
YT=YMAX
IE (TITLEONLY) YT=0.5*(YMAX+YMIN)
CALL MOVETO W (0.5*(XMAX+XMIN),YT,WXY)
CALL GETCURRENTPOSITION (POSITION)
IX=POSITION.XCOORD
IY=POSITION.YCOORD
IX=IX-(TITLELENGTH*FONTWIDTH)/2
IF (TITLEONLY) THEN
IY=IY—EONTHEIGHT/2
ELSE
IY=IY-2*FONTHEIGHT
END IF
CALL MOVETO (IX,IY,POSITION)
DUMMY=SETCOLOR(TITLECOLOR)
CALL OUTGTEXT (TITLE(1:TITLELENGTH))

Go To RETURN STATEMENT IF ONLY TITLE TO BE DRAWN
IE (TITLEONLY) GO To 170

WRITE THE XOAXIS TITLE
TITLELENGTH=
IF (XAXISTITLE(TITLELENGTH:TITLELENGTH).EQ.‘ ') THEN
TITLELENGTH=TITLELENGTH-1
Go TO 110

END IF
POSITION THE TITLE CENTERED (MORE OR LESS) BELOW GRAPH

CALL MOVETO W (0.5*(XMAX+XMIN),YMIN,WXY)
CALL GETCURRENTPOSITION (POSITION)
IX=POSITION.XCOORD

IY=POSITION.YCOORD
IX=IX-(TITLELENGTH*FONTWIDTH)/2

IY=IY+(3*FONTHEIGHT)/2
CALL MOVETO (IX,IY,POSITION)
DUMMY=SETCOLOR(TITLECOLOR)

000

120

130
140

150

145

CALL OUTGTEXT (XAXISTITLE(1:TITLELENGTH))
WRITE THE Y AXIS TITLE VERTICALLY, SINCE WE CAN'T ROTATE
TITLELENGTH=80
IE (YAXISTITLE(TITLELENGTH:TITLELENGTH).EQ.' ') THEN
TITLELENGTH=TITLELENGTH-l
GO TO 120
END IF
POSITION THE TITLE CENTERED (MORE OR LESS) TO LEFT OF GRAPH
CALL MOVETO W (XMIN,0.5*(YMAX+YMIN),WXY)
CALL GETCURRENTPOSITION (POSITION)
IX=POSITION.XCOORD
IY=POSITION.YCOORD
IX=IX-8*FONTWIDTH
IY=IY-(TITLELENGTH*FONTHEIGHT)/2
DUMMY=SETCOLOR(TITLECOLOR)
NOW WRITE THE CHARACTERS ONE AT A.TIME VERTICALLY
Do 130 I=1,TITLELENGTH
CALL MOVETO (IX,IY,POSITION)
CALL OUTGTEXT (YAXISTITLE(I:I))
IY=IY+EONTHEIGHT
CONTINUE
PLOT THE DATA.IN XDATA AND YDATA
DUMMY=SETCOLOR(PLOTCOLOR)
DEFINE CLIPPING REGION
GET TOP LEFT POSITION
CALL MOVETO W (XMIN,YMAX,WXY)
CALL GETCURRENTPOSITION (POSITION)
CALL GETPHYSCOORD (POSITION.XCOORD,POSITION.YCOORD,POSITION)
IX1=POSITION.XCOORD
IY1=POSITION.YCOORD
GET BOTTOM RIGHT POSITION
CALL MOVETO W (XMAX,YMIN,WXY)
CALL GETCURRENTPOSITION (POSITION)
CALL GETPHYSCOORD (POSITION.XCOORD,POSITION.YCOORD,POSITION)
IX2=POSITION.XCOORD
IY2=POSITION.YCOORD
SET UP NEW VIEWPORT FOR CLIPPING
CALL SETVIEWPORT (IX1,IY1,IX2,IY2)
DUMMY=SETWINDOW(.TRUE.,XMIN,YMAX,XMAX,YMIN)
PLOT THE FIRST POINT, INVERTING IE NECESSARY
XT=XDATA(1)
YT=YDATA(1)
IE (INVERTX) XT=XW2-ABS(XT—XW1)
IE (INVERTY) YT=YW2-ABS(YT—XW2)
CALL MOVETO W (XT,YT,WXY)
IE (.NOT.PLOTMETHOD) DUMMY=SETPIXEL W(XT,YT)
PLOT THE REST OF THE DATA, INVERTING IF NECESSARY
Do 150 I=2,NUMBER
XT=XDATA(I)
YT=YDATA(I)
IF (INVERTX) XT=XW2—ABS(XT-XW1)
IF (INVERTY) YT=YW2—ABS(YT—YW1)
IF (PLOTMETHOD) THEN
DUMMY=LINETO_W(XT,YT)
ELSE
CALL MOVETO W (XT,YT,WXY)
DUMMY=SETPIXEL;W(XT,YT)
END IF
CONTINUE

PLOT THE SECOND SET OF DATA ON THE SAME X-Y AXIS

IE(.NOT.Y2PLOT) Go TO 170

DUMMY=SETCOLOR(PLOTZCOLOR)

XT=XDATA(1)

YT=Y2DATA(1)

IF (INVERTX) XT=XW2-ABS(XT—XW1)

IE (INVERTY) YT=YWEEAaiéYT-XW2)

CALL MOVETO W XT, ,

IF (.NOT.PLOT2METHOD) DUMMY=SETPIXEL W(XT,YT)
PLOT THE REST OF THE DATA, INVERTING IE NECESSARY

DO 160 I=2,NUMBER

XT=XDATA(I)

YT=Y2DATA(I)

IF (INVERTX) XT=XW2-ABS(XT-XW1)

IE (INVERTY) YT=YW2-ABS(YT-YW1)

IF (PLOT2METHOD) THEN

 

 

160

000

165
C

c
170

146

DUMMY=LINETO W(XT,YT)
ELSE -

CALL MOVETO W (XT,YT,WXY)
DUMMY=SETPIXEL;W(XT,YT)
END IF

CONTINUE

PLOT THE THIRD SET OF DATA ON THE SAME X-Y AXIS

IE(.NOT.YSPLOT) GO TO 170
DUMMY=SETCOLOR(PLOT3COLOR)
XT=X3(1)
YT=Y3(I)
IE (INVERTX) XT=XW2~ABS(XT-Xw1)
IF (INVERTY) YT=YW2-ABS (YT-XW2)
CALL MOVETO W (XT,YT,WXY)
IE (.NOT.PLOT2METHOD) DUMMY=SETPIXEL W(XT,YT)
PLOT THE REST OF THE DATA, INVERTING IF NECESSARY
DO 165 I=2,NUM3
XT=X3(1)
YT=Y3(I)
IF (INVERTX) XT=Xw2-ABS(XT—Xw1)
IF (INVERTY) YT=YW2—ABS(YT-YW1)
IE (PLOT2METHOD) THEN
DUMMY=LINETO W(XT,YT)
ELSE ‘
CALL MOVETO W (XT,YT,WXY)
DUMMY=SETPIXEL W(XT,YT)
END IF —
CONTINUE
ALL DONE
CALL UNREGISTERFONTS ()
RETURN

END
C#############################??########################################

000

000

SUBROUTINE GRAPHICSMODE
INCLUDE 'FGRAPH.FD'

INTEGER*2 DUMMY,MAXX,MAXY
RECORD /VIDEOCONFIG/ MYSCREEN
COMMON MAXX,MAXY

FIND GRAPHICS MODE.

CALL GETVIDEOCONFIG (MYSCREEN)
SELECT CASE( MYSCREEN.ADAPTER )
CASE( $CGA )
DUMMY=SETVIDEOMODE($HRESBW)
CASE( $OCGA )
DUMMY=SETVIDEOMODE($ORESCOLOR)
CASE( SEGA, $OEGA )
IF (MYSCREEN.MONITOR.EQ.$MONO) THEN
DUMMY=SETVIDEOMODE($ERESNOCOLOR)
ELSE
DUMMY=SETVIDEOMODE($ERESCOLOR)
END IF
CASE( $VGA, $OVGA, $MCGA )
IE (MYSCREEN.MONITOR.EQ.$MONO) THEN
DUMMY=SETVIDEOMODE($VRESZCOLOR)

ELSE
DUMMY=SETVIDEOMODE($VRE316COLOR)
END IF

CASE( $HGC )

DUMMY=SETVIDEOMODE($HERCMONO)
CASE DEFAULT
DUMMY=0
END SELECT
IF (DUMMY.EQ.0) STOP 'ERROR: CANNOT SET GRAPHICS MODE'

DETERMINE THE MINIMUM.AND MAXIMUM DIMENSIONS.
CALL GETVIDEOCONFIG (MYSCREEN)

MAXX=MYSCREEN.NUMMPIXELS-l
MAXY=MYSCREEN.NUMYPIXELS-l

END
C############################?f#########################################

SUBROUTINE ENDGRAPHICS
INCLUDE 'FGRAPH.FD'

 

 

 

 

147

INTEGER*2 DUMMY
DUMMY=SETVIDEOMODE($DEFAULTMODE)
RETURN

END

 

*1-*I-**)f*fi-**if*i-**’+**'**>f*i-**'**it*fl-**Jf*i-**16*fl'*1-**

0000000*************#**#*********t******#***********

0000000000

148

FLOOR.FOR

* * * k * * * * * * i * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * k * * * * * * * *

FLOOR.FOR

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

THIS PROGRAM READS THE VOLTAGE DATA COLLECTED FROM.THE PLATE FORM
AND FINDS THE CORRESPONDING FORCES. THE DATA IS STORED AT A.RATE
OF 100Hz BY 'TRAP.BAS'.

THIS PROGRAM USED WITH ANY PERIODIC JUMPING TEST. HOWEVER, THE

DEFAULT IS NOW 2 HZ PERIODIC JUMPING. IF THE FREQUENCY DIFFERS
FROM 2 HZ, YOU MAY NEED TO CHANGE THE COUNTER IN DO LOOP 80. THE
VALUE OF THE COUNTER IN THIS LOOP (30) DETEMINES THE RANGE OF
SEARngNG FOR THE FIRST MAJOR PEAK. SEE THE COMMENT JUST BEFORE
LOOP .

THE PROGRAM NOW DOES NOT INCLUDE THE MASS OF THE PARTICIPENTS IN
THE CALCULATION OF THE MASS, DAMP, AND TOTAL FORCE MATRICES.

IF YOU NEED TO CONSIDER WITH THE MASS OF THE FLOOR PLUS PART.,

YOU MAY HAVE TO CHANGE THE MATRIX FMASS(I) IN LOOP 250 TO M(I).
ALSO, YOU WILL NEED TO CHANGE THE DEFINITON OF MASS MA IN LOOP 360
TO BE EQUAL TO MASS(I,J) INSTEAD OD TMASS(I,J)

#*
#*
**
**
**
**
+*
#*
**
**
**
**
**
**
**
**
**
**
*1
**
*w
#*
**
**
**
**
#fi

**
**

**

**

t¥

#*

OCTOBER 4, 1989

BASSEM K. KHAFAGI
YING X. CAI

UNIVERSITY OF IDAHO
MOSCOW, ID 83843

*fi'**lf*I-*X-*fi'**=f**'**J&*X-**>+*I-*I-**l$*fl'**!f*I-**I¥*1-**
**'**'**'*i-*#'**-*i-*I-*i-*#~*fl-**-*fl-ii-*I~*I-¥*'** *I-#i-*1-**-*

U.S.A
* * * * * * k * * * * * * * * * * * * * * * * * * * * * * * k * *
* * * * * * * * * * * * * * * * * * * * * * * * * * i * * * * * *
*****************************************************************

++++++++++++++++++++++++++++++++++
++++++++++++++++ 1. DATA.INPUT/OUTPUT ++++++++++++++++
++++++++++++++++++++++++++++++++++

PROGRAM FLOOR

DIMENSION VOLT(1000,9),X(300,9),CALI(9),D(150,9),DEF(128,9)
DIMENSION A(128,9),B(128,9),VEL(128,9),ACCL(128,9),EIT(128,9)
DIMENSION PHIT(9),MN(9),MNN(9),MA(9,9),DA(9,9),DAA(9,9),DAM(9,9)
DIMENSION DAMP(9,9),VNODE(9),ANODE(9),XNODE(9),FA(9),FV(9),FX(9)
DIMENSION STIF(9,9),EORCES(128,9),PART(40),FMASS(9),TOTEORCE(124)
DIMENSION TMASS(9,9),BVOLT(1,9)

I

REAL*8 K(9,9),M(9) LAMBDA(9),E(9),PHI(9,9),MASS(9,9),NODE(9)
REAL MN,MNN,MA

CHARACTER FNAME*12,DATE*12,STIME*12,ETIME*12,FORCE*12,TFORCE*12
CHARACTER FNAMEl*3,FNAME2*1,FNAME3*1,FNAME4*1,FNAME5*6,REPORT*12
LOGICAL WANTX

NOW, WE READ THE FILE NAME OF THE DATA SET. WE WILL USE THIS FILE
NAME AS A BASE FOR NAMING THE OUTPUT FILES. IF THE DATA FILE NAME
IS 20PJ2-10.0C9, IT MEANS THAT THIS DATA SET FOR 20 PEOPLE
PERFORMING PERIODIC JUMPING (PJ) AND THIS IS GROUP (2) AND TEST NO.
(10) THAT WAS DONE IN OCT. 1989 (0C9). THE OUTPUT FILES WILL BE
IN THE FORM OF 20PF2F10.0C9, 20PF2T10.0C9, AND 20PF2R10.0C9. THE
PART (PFZF,PF2T,PF2R) REPRESENT PERIODIC JUMPING (P), FINAL FORCES
(F) FOR GROUP (2) THEN THE LAST LETTER IN THIS PART REPRESENT THE
FILE CONTENT. (F) REPRESENTS NODAL FORCES FOR THIS TEST, (T) REP-

000

0 000000000000

000000

0000000000

Tocoqmmawm

12

10
15

18

19
210
211
212

 

149

RESENTS TOTAL FORCES FROM THE PERIODIC JUMPING ON THE FLOOR, AND
(R) REPRESENTS THE FINAL REPORT FOR THIS TEST.

PRINT 2

READ(*,3)NODEBASE

PRINT 5
READ(*,4)FNAME1,FNAME2,ENAME3,FNAME4,ENAME5
WRITE(ENAME,6)ENAME1,ENAMEz,ENAME3,FNAME4,FNAME5
WRITE(EORCE,7)ENAME1,ENAME3,FNAME5
WRITE(TEORCE,8)ENAME1,FNAME3,FNAME5
WRITE(REPORT,9)ENAME1,FNAME3,FNAME5
EORMAT(1X,' WHICH NODE WILL BE USED AS A.BASE FOR CALCULATIONS')
EORMAT(Il)

FORMAT(A3,A1,A1,A1,A6)

FORMAT(1X,' WHAT 13 NAME OF INPUT FILE?')
EORMAT(A3,A1,A1,A1,A6)
FORMAT(A3,'F',A1,'F',A6)
FORMAT(A3,'E',A1,'T',A6)
FORMAT(A3,'F',A1,'R',A6)

OPEN(1,FILE=ENAME)

OPEN(2,EILE='INPUT')

OPEN(3,FILE=EORCE)

OPEN(4,FILE=TEORCE)

OPEN(5,FILE=REPORT)

OPEN(6,FILE='PHI')

+++++++++++++++++++++++++++++++++++++++
+++++++++++++ 2. REDUCING DATA TO 128 SAMPLE +++++++++++++
+++++++++++++++++++++++++++++++++++++++

READ THE DATE, STARTING TIME, AND ENDING TIME OF THE TEST. THEN,
DELETE THE FIRST FOUR-COLUMNS OF DATA.(STRAIN GAGE DATA), AND SAVE
THE LVDT VOLTAGE IN THE FILE "LVDT.VLT"

READ(l,12)DATE,STIME,ETIME
EORMAT(A12//,A12/,A12)

DO 10 I=1,1000

READ(1,15) Y,Y,Y,Y, (VOLT(I,J) ,J=1, 9)
CONTINUE

FORMAT(13F8.0)

SELECT THE FIRST VOLTAGE READING AS THE BASE TO NORMALIZE
THE VOLTAGE READING AGAINST THE PART. WEIGHTS AND SAVE IT IN
MATRIX "BVOLT"

DO 18 I=1,9
BVOLT(1,I)=VOLT(1,I)
CONTINUE

SEARCH THE FIRST MAJOR VOLTAGE PEAK VALUE AND SELECT 300

SAMPLE POINTS SUCH THAT 149 READINGS BEFORE IT AND 150 AFTER.

THE SEARCH WILL USE LVDT NO 5 AS A BASIS SINCE IT IS A.MID. NODE

IN THE FLOOR SYSTEM. .ALSO IF NVMAX IS >850 WE WILL ASSUME IT 850
AND IF IT IS < 150 WE WILL ASSUME IT 150. IF THE TEST ENDED BEFORE
1000 SAMPLES THE SEARCH WILL BE TERMINATED AT "NEND" VARIABLE

J=NODEBASE
N=0
NEND=1000
DO 19 I=1,1000
N=N+1
IF((VOLT(I,J).EQ.0.0).AND.(VOLT(I+1,J+1).EQ.0.0)) GO TO 210
CONTINUE
NEND=N
WRITE(*,212) NEND
FORMAT(1X,'THE TEST ENDED AT SAMPLE NO: (',I4,')‘)
VMAX=0.0
N=0
DO 20 I=1,1000
N=N+1

0000 0000000000

000000000000

00000

20

LAMA

80

150

IF (ABS (VOLT (I, J) ) .GT.VMAX) THEN
VMAX=ABS(VOLT(I,J))
NVMAX=N
Go To 20
ENDIF
CONTINUE
=NVMAX
MEND=NEND—150
IF(NVMAX.GE.MEND)THEN

NVMAX=MEND

ELSE IF(NVMAX.LE.150)THEN

NVMAX=150

END IF

DO 22 I=1,300
DO 25 J=1,9
VOLT(I,J)=VOLT(NVMAX+I-150,J)
CONTINUE

CONTINUE

NORMALIZE DATA BY SUBTRACTING EACH RAW OF DATA.FROM THE FIRST
VLOTAGE READING WHICH REPRESENT THE STATIC WEIGHT OF THE FLOOR
AND PARTICIPANTS. THEN THE DEFLECTION IS CALCULATED BY DIVIDING
EACH COLUMN BY THE CORESPONDING CALIBRATION FACTOR OF THAT LVDT.
EACH COLUMN REPRESENT THE DATA READ BY ONE OF THE LVDT'S. THE
CALIBRATION FACTORS ARE STORED IN THE FIRST PART OF FILE "INPUT"

DO 30 J=1,9
READ(2,*) CALI(J)
DO 40 I=1,300
X(I,J)=(VOLT(I,J)—BVOLT(1,J))/(-3276.7*CALI(J))
CONTINUE
CONTINUE

THE DEFLECTION WILL BE REDUCED NOW TO 150-SAMPLE BY DELETING
EVERY OTHER SAMPLE, AND SAVE AS MATRIX D(150,9)

DO 60 I=1,300,2
N=(I+1)/2
DO 70 J=1,9
D(N,J)=X(I,J)
CONTINUE
CONTINUE

SEARCH THE FIRST MAJOR DEFLECTION PEAK VALUE AND SELECT 128
SAMPLE POINTS SUCH THAT 4 READINGS BEFORE IT AND 123 AFTER.

THE SEARCH WILL USE LVDT NO 5 AS A BASIS SINCE IT IS A MID. NODE
IN THE FLOOR SYSTEM.

SINCE THE FREQ. OF THE TEST IS 2 HZ, AND THE RATE OF COLLECTING
DATA IS NOW REDUCED TO 50 HZ, A FULL JUMP WILL BE REPRESENTED BY

25 SAMPLES. IN ORDER TO BE ABLE TO GET TO THE MAX. PEAK, WE MUST

SEARCH FOR IT IN A.RANGE GREATER OR EQUAL THAN 25. SO, WE SET
THE LOOP COUNTER TO 30.

J=NODEBASE
DMAX=0.0
NMAX=0
N=o
DO 80 I=1,3o
N=N+1
IE (D(I,J).GT.DMAX) THEN
DMAX=D(I,J)
NMAX=N
GO To 80
ENDIF
CONTINUE
MAX=NMAX

NOW THE REDUCED SAMPLE OF DEFLECTIONS WILL BE STORED IN MATRIX
DEF(128,9) TO USE IT IN THE PROGRAM.
THE REDUCED NO. OF SAMPLES (128) WILL BE DENOTED AS "NS"

NS=128
DO 90 I=1,NS
DO 100 J=1,9

 

0000000000000

000

000000000000

0000000000

151

 

DEF(I,J)=D(NMAX+I-S,J)
100 CONTINUE
9o CONTINUE

+++++++++++++++++++++++++++++++++++++++
+++++++++++++ 3. FINDING FITTED DEFLECTION +++++++++++++
+++++++++++++++++++++++++++++++++++++++

PERFORM PERIODIC REGRESSION OF SELECTED DEFLECTION SAMPLES
BY USING THE FOURIER SERIES TO GET FITTED DEFLECTION.

CALCULATE FOURIER COEFFICIENTS

PI=3.141593
DO 110 J=1,9
SUM1=0.
DO 120 I=1,NS
SUM1=SUM1+DEE(I,J)
120 CONTINUE
.A(0,J)=SUM1/NS
DO 130 I=1,20
SUM2=O
SUM3=O
DO 140 IJ=1,NS
SUM2=SUM2+DEF(IJ,J)*COS(2*I*PI*IJ/NS)
SUM3=SUM3+DEF(IJ,J)*SIN(2*I*PI*IJ/NS)
14o CONTINUE
.A(I,J)=2*SUM2/NS
B(I,J)=2*SUM3/NS
13o CONTINUE

CALCULATE PREDICTED DEFLECTION HISTORY

D0 150 I=1,NS
SUM1=0
SUM2=0
DO 160 JJ=1,20
SUM1=SUM1+A(JJ,J)*COS(2*PI*JJ*I/NS)
SUM2=SUM2+B(JJ,J)*SIN(2*PI*JJ*I/NS)
160 CONTINUE
FIT(I,J)=A(0,J)+SUM1+SUM2
150 CONTINUE
110 CONTINUE

+++++++++++++++++++++++++++++++++++++++
+++++++++++++ 4. VELOCITY AND ACCELERATION +++++++++++++
+++++++++++++++++++++++++++++++++++++++

************‘k****************************************************

PROGRAM TO DO CENTRAL DIFFERENTIAL
NOTE: H IS THE TIME INTERVAL, H= l/(FREQUENCE OF SELECTED SAMPLE
POINTS). SINCE THE SAMPLES HAVE BEEN REDUCED TO 50 HZ, H=.02 SEC.

H=0.02
DO 180 J=1,9
DO 190 I=3,126
VEL(I,J)=(-§IT(I+2,J)+8*FIT(I+1,J)-8*FIT(I-l,J)+FIT(I-2,J))
2 H

( )
ACCL(I,J)=(-FIT(I+2,J)+16*FIT(I+1,J)-30*FIT(I,J)+16*FIT(I-1
,J)-FIT(I-2,J))/(12*H*H)
190 CONTINUE
180 CONTINUE

+++++++++++++++++++++++++++++++++++++++
+++++++++++++ 5. FLOOR AND PART. MASS +++++++++++++
+++++++++++++++++++++++++++++++++++++++

HERE, WE CALCULATE THE MASS MATRIX FOR THE FLOOR
SYSTEM AND THE PARTICIPANTS USING THE WEIGHT AND LOCATION OF
EACH PARTICIPANT AND APPLYING IT TO THE CORRECT NODE.

 

 

00000000000

220

000

*

000

225

000

226

000

227

0000

240

000

 

152

THE ARRAYS INCLUDE:

PART(40) - WEIGHTS AND LOCATIONS OF PARTICIPANTS
M(9) - MASSES OF PARTICIPANTS BROKEN UP INTO 9 NODES
NODE(9) - PARTICIPANT AND FLOOR MASS FOR 9 NODES

MASS(9,9) - MASS MATRIX TO BE SAVED IN FILE "MASS"

READ THE PARTICIPANT WEIGHT-LOCATION FILE, (THIS IS IN THE SECOND
PART OF THE FILE "INPUT".

N=0
DO 220 J=1, 4o
READ(2, *) PART(J
PART(J) =PART(J)/386. 4
N=N+1
IF(PART(J).GT.0.0) THEN
NPART=N
GO To 220
ENDIF
CONTINUE

CALCULATE TOTAL WEIGHT CORRESPONDING TO EACH NODE

NODE(1)— =P?RT$32£;§ART(29)+2. ./3. *(PART(37)+PART(27)+PART(19))
T
NODE(2)- =1. /3. *(PART(19)+PART(20))+2. /3. *(PART(7)+PART(8))
2./9. *(PART(17)+PART(18))+PART(9)+PART(10)
NODE(3)=PART(30)+PART(40)+2. /3. *(PART(20)+PART(28)+PART(38))
+4. /9. *PART(18)
NODE(4) =PART(35)+PART(25)+2. /3. *PART(15)+2. /9. *(PART(17)+PART(13))
+1./3 .*(PART(37)+PART(27)+PART(33)+PART(23))
NODE(S) =1. /9. *(PART(17)+PART(18)+PART(13)+PART(14))
+1 ./3. *(PART(7)+PART(8)+PART(3)+PART(4)+PART(15)+PART(16))
+PART(5)+PART(6)
NODE(6) =PART(26)+PART(36)+2. /3. *PART(16)+2. /9. *(PART(18)+PART(14))
+1. /3. *(PART(28)+PART(38)+PART(24)+PART(34))
:NODE(7) =PART(31)+PART(21)+2. /3. *(PART(33)+PART(23)+PART(11))
+4 /9. *PART(13)
NODE(8)- =PART(1)+PART(2)+2. /3. *(PART(3)+PART(4))
+2 9.*(PART(13)+PART(14))+1 /3. *(PART(11)+PART(12)
NODE(9) =PART(22)+PART(32)+2. /3. *(PART(24)+PART(3 4)+PART(12)
+4. /9. *PART(14)

 

 

)
)

INPUT THE MASS OF THE FLOOR ALONE IN ARRAY FMASS(9)

DO 225 I=1,9
FMASS(I)=0.358592

CONTINUE
FMASS(2)=0.222567
FMASS(5)=O.222567
FMASS(8)=0.222567

PUT FLOOR MASSE IN THE FORM OF A 9X9 FLOOR MASS MATRIX

DO 226 I= 1, 9
J=I

CONTINUE
ADD MASS OF PARTICIPANTS TO MASS OF FLOOR FOR EACH NODE
DO 227 I= 1, 9

M(I)=NODE(I)+FMASS(I)
CONTINUE

TMASS(I,J)=FMASS(J)

PUT NODAL MASSES IN THE FORM OF A 9X9 MASS MATRIX

DO 230 JI=1, 9
=I
MASS(I,J)=M(J)
CONTINUE

FORMAT(9F10.6)

 

00000000000000000000000000000000000

00000

000 000

000

000 000 000

153

+++++++++++++++++++++++++++++++++++++++
+++++++++++++ 6. DAMPING MATRIX +++++++++++++
+++++++++++++++++++++++++++++++++++++++

PROGRAM TO SET UP AND SOLVE CHARACTERISTIC VALUE PROBLEMS OF THE TYPE:
(LAMBDA)*M*X = K*X

THIS PROGRAM READS THE MATRICES K AND M AND CONVERTS IT TO THE STANDARD
EIGENVALUE FORM, (LAMBDA)*X = AFK BY THE FOLLOWING TRANSFORMATION:
(L.AMBDA)*(M**0. 5)*X = (M**- -.0 5)*K*(M**- -.0 5)*(M**0. 5)*X

WE THEN SOLVE FOR THE EIGENVALUES OF THE X' = (M**0.5)*X. (SOME
REFERENCES DESCRIBE THIS AS SOLVING FOR THE EIGENVALUES IN THE
GENERALIZED COORDINATES. WE FINALLY SOLVE FOR X = (M**-0.5)*X'.

IMPORTANT ASSUMPTIONS:
K = IS SYMMETRIC AND REAL STIFFNESS MATRIX
M = IS DIAGONAL MATRIX OF THE MASS USED IN CALCULATION.

N-VECTOR OF REAL DOUBLE PRECISION VALUES. THE CALCULATED
EIGENVALUES ARE PUT IN THIS VECTOR.

N-VECTOR. WORKING VECTOR.

X = N-BY-N MATRIX OF REAL DOUBLE PRECISION VALUES. THE CALCULATED
EIGENVECTORS ARE PLACES COLUMN-BY-COLUMN IN THIS MATRIX.

LAMBDA

NDIM = THE ACTUAL DIMENSION OF THE ARRAYS IN THE MAIN PROGRAM.
N = THE ORDER OF MATRICES K AND M.

WANTX = LOGICAL. IF WANTX = .FALSE. THEN SYMEIG SKIPS THE CALCULATION
OF THE EIGENVECTORS, SAVING SOME TIME.
NDIM = 9
WANTX = .TRUE.
N=9

READ MATRIX K, ROW-BY-ROW. ALSO, CALCULATE M*** *0. 5.
IF YOU NEED TO WORK WITH THE MASS OF THE FLOOR PLUS PARTICIPANTS,
YOU HAVE TO CHANGE THE MATRIX FMASS(I) IN THIS LOOP TO M(I)

DO 250 I = 1, N
READ(2, *) (K I, J), J=1, N)
IM(I) = 1. 0D0 DSQRT(FMASS(I))
250 CONTINUE

CALCULATE (M**-0.5)*K
DO 260 I = 1, N
DO 260 J = 1, N
PHI(I,J) = M(I)*K(I,J)
SAVE THE STIFFNESS MATRIX IN THE ARRAY STIF(9,9)

STIF(I,J)=K(I,J)
260 CONTINUE

CALCULATE (M**-0.5)*K*(M**-0.5)
DO 270 I = 1, N
DO 270 J = 1,

N
K(I, J) = PHI(I, J)*M(J)
270 CONTINUE

CALCULATE THE EIGENVALUES (AND EIGENVECTORS IF DESIRED).

CALL SYMEIG (NDIM,N,K,LAMBDA,E,WANTX,PHI)

SKIP THE EIGENVECTORS IF WE DIDN'T ASK FOR THEM

IF (.NOT.WANTX) Go To 320

TRANSFORM THE EIGENVECTORS BACK FROM THE "GENERALIZED COORDINATES"

DO 310 J = 1, N

 

0000

0000

000

0000

0000

0000000

310
320

330
340

360
350

370

390

380

410
400
395

154

D0 310 I = 1, N
PHI(I,J) = PHI(I,J)*M(I)
CONTINUE
CONTINUE

WRITE THE EIGENVECTORS INTO FILE='PHI'. THE EIGENVECTORS PHI(J),
J=1,2,...,9, ARE PLACED ROWFBY-ROW IN THIS FILE.

DO 330 J=1,9
‘WRITE (6,340)(PHI(I,J),I=1,9)
CONTINUE
FORMAT(9E12.6)
REWIND 6

DO 350 I=1,9
DO 360 J=1,9
MA(I,J)=TMASS (I,J)
CONTINUE
CONTINUE

CALCULATE MNN(N)=[PHIT](N)*[MA]*[PHI](N),[PHIT](N) IS THE
TRANSPOSITION OF NTH EIGENVECTOR.

DO 370 I=1,9
READ(6,340)(PHIT(J),J=1,9)
II=l
JJ=9
KK=9
CALL MATRIX(PHIT,MA,MN,II,JJ,KK)
II=1
JJ=9
KK=1
CALL MATRIX(MN,PHIT,MNN(I),II,JJ,KK)
CONTINUE
REWIND 6

CLEAR OUT THE MATRIX DA BEFORE STARTING

DO 380 I=1,9
DO 390 J=1,9
DA(I,J)=0.0
CONTINUE
CONTINUE

SUM. OF (2*XIN*OMEGAN/MNNN)*[PHI]*[PHIT])

CALCULATE DA
SUM. OF (2*XIN*OMEGAN/MNNN)*DAA)

XIN=0.015
DO 395 I=1,9
READ(6,340)(PHIT(J),J=1,9)
II=9
JJ=l
KK=9
CALL MATRIX(PHIT,PHIT,DAA,II,JJ,KK)
DO 4004.51,}1 9
D0 =
DA(J,L)£DA(J,L)+(2*XIN*DSQRT(LAMBDA(I))/MNN(I))*DAA(J,L)
CONTINUE
CONTINUE
CONTINUE
REWIND 6

CALCULATE [DAMP] = [MA] * [DA] * [MA]

II=9

JJ=9

KK=9

CALL MATRIX(MA,DA,DAM,II,JJ,KK)
CALL MATRIX (DAM, MA, DAMP, II, JJ, KK)

+ ++ +++++4
+++++++++++++ 7. OTAL FORCES +++++++++++++

 

 

155

CALCULATE [EA]=[M]* ANODE , FV = DAMP * VNOD ’ = *
[FORCE]=[EAJ+[FV19[FX] 1 [ ] [ ] [ E] [FX] [K] [XNODE],AND

DO 420 I=1,124
DO 430 J=1,9
XNODE(J)=DEF(I+2,J)
VNODE(J)=VEL(I+2,J)
ANODE(J)=ACCL(I+2,J)
430 CONTINUE
II=9
JJ=9
KK=1
CALL MATRIX (MA, ANODE, FA, II, JJ, KK)
CALL MATRIX(DAMP,VNODE,FV,II,JJ,KK)
CALL MATRIX(STIF,XNODE,FX,II,JJ,KK)
DO 440 J=1,9
FORCES(I,J)=FA(J)+FV(J)+FX(J)
440 CONTINUE
WRITE(3,470) (FORCES(I,J),J=1,9)
420 CONTINUE
DO 450 I=1,124
DO 460 J=1,9
TOTFORCE(I)=FORCES(I,J)+TOTFORCE(I)
460 CONTINUE
WRITE(4,*)TOTFORCE(I)
450 CONTINUE
470 FORMAT(9F11.4)

TO FIND THE MAX. FORCE ON THE FLOOR

000000

000

N=o
FMAX=0.0
NMAX=0
DO 480 I=1,124
=N+1
IF (TOTEORCE(I).GT.EMAX) THEN
FMAX=TOTFORCE(I) (
NMAX=N I
GO TO 480 ‘
ENDIF ‘
480 CONTINUE I
WRITE(*,490)FNAME,NPART,DATE,STIME,ETIME,NODEBASE,NV,VMAX (
WRITE(S,490)FNAME,NPART,DATE,STIME,ETIME,NODEBASE,NV,VMAX
WRITE(*,500)NODEBASE,MAX,FMAX,FMAX/NPART,FMAX/NPART/3.5
WRITE 5,500)NODEBASE,MAX,FMAX,FMAX/NPART,FMAX/NPART/3;5
490 FORMAT(l ,28X,'OUTPUT SUMM?RY},//,1X,'INPUT FILE NAME : ,A12,//

*,1X,'NO. OF PART. : ',I , .
*,1X,'DATE OF TEST : ',A12,//,1X,'TEST STARTED AT : ,A12,//,1X,
*'TEST ENDED AT : ',A12/;,1X,'MAX. VOLT. (NODE ',I1,') IS SAMPLE
*NO. ' I3 2X '=' 1X,E10.2, )

500 EORMAT(1X,'MAX.'PEAK (NODE ',I1,') IS SAMPLE NO.',I3,3X,'= ',F9.2
*,2X,'lb',//,1X,'THE AVERAGE DYNAMIC HUMAN LOAD IS = ,F9.2,3X,
*'1b/PERSON',//,1X,'THE DESIGN EQUIVELANT LOAD IS = ,1x,
*F7.2,4X,'PSF',/)

STOP
END

C
C****************************************************************************

C
SUBROUTINE SYMEIG (NDIM,N,A,D,E,WANTX,X)
INTEGER NDIM,N

LOGICAL WANTX
REAL*8 A(NDIM,NDIM),D(NDIM),E(NDIM),X(NDIM,NDIM)
REAL*8 ALPHA,BETA,GAMMA,KAPPA,AIJ,T,C,S,F,DABS,DSQRT

S EIGENVALUES AND EIGENVECTORS OF REAL SYMMETRIC MATRICES
FHOHUELINEAR MATHEMATICS FOR ENGINEERING APPLICATION" BY JOEL

H. FERZIGER (1978).

NDIM = DECLARED ROW DIMENSION OF A (AND X)
N = ORDER OF.A

= — - TRIX DOUBLE PRECISION)
‘A .A IS ASEUMED TO BE SYMMETRIC. ONLY THE DIAGONAL AND LOWER

0000000000

000000000000000000000000

000

0000

0000

WANTX =

 

156

TRIANGULAR PORTIONS OF A.ARE USED. IF POSSIBLE, PUT THE
BIGGEST ELEMENTS IN THE UPPER LEFT CORNER. UPPER TRIANGLE
PORTION OF A.IS UNALTERED UNLESS A.AND X ARE IN THE SAME

N-DIMENSIONAL VECTOR, (DOUBLE PRECISION)
STORES THE OUTPUT EIGENVALUES.

N-DIMENSIONAL VECTOR, (DOUBLE PRECISION) USED FOR WORK SPACE.

.A LOGICAL VARIABLE. IF WANTX = .TRUE. THEN THE EIGENVECTORS ARE
CALCULATED. IF WANTX = .FALSE. THEN THE EIGENVECTORS ARE NOT
CALCULATED.

N-BY-N MATRIX (DOUBLE PRECISION)
IF WANTX = .TRUE. THEN THE OUTPUT X(I,J) IS THE EIGENVECTOR
ASSOCIATED WITH EIGENVALUE D(J).

CALCULATES THE EIGENVECTORS AND REPLACES THE INPUT MATRIX, A, WITH ITS
EIGENVECTORS.

HOUSEHOLDER TRIDIAGONALIZATION

D(1) = A(1,l)

IF (N.LE.2) GO TO 8

NMl = N-l

DO 7 K = 2, NMl

FIND REFLECTION WHICH ZEROS A(I,K-1), I=K+1,...,N
ALPHA = 0.

DO 1 I = K N

D(I) ='A(I,K—1)
ALPHA = ALPHA + D(I)*D(I)

CONTINUE
ALPHA = DSQRT(ALPHA)
IF (D(K).LT.0.) ALPHA = -ALPHA

D(K)

= D(K) + ALPHA

BETA = ALPHA*D(K)
IF(BETAJEQ.0.) GO TO 6

APPLY REFLECTION TO BOTH ROWS AND COLUMNS OF REST OF A
USE AND COMPUTE ONLY LOWER TRIANGLE

KAPPA = 0.
DO 3 I = K, N

GAMMA = 0.

DO 2 J = K, N
IF (I.GE.J) AIJ A(I,J)
IE (I.LT.J) AIJ A(J,I)
GAMMA = GAMMA + AIJ*D(J)

CONTINUE

E(I) = GAMMA/BETA

KAPPA = KAPPA + D(I)*E(I)

CONTINUE
KAPPA = 0.5*KAPPA/BETA
DO 5 I = K, N

E(I = (I) - KAPPA*D(I)

)
J - K, I
DO 4A(I,J) = A(I,J) — D(I)*E(J) - E(I)*D(J)

CONTINUE

CONTINUE

.A(K,
D(K)

K-1) = D(K)
=.A(K,K)
K) = BETA

=.A(N,N)
= A(N,N—1)

ACCUMULATE TRANSFORMATIONS
PRODUCES X SO THAT XT*(INPUT A)*X IS TRIDIAGONAL

IF(.

X(N,

NOT.WANTX) GO TO 20
N) = 1.

 

 

11

12

13
15

0000

20

21

000

22

000

000

000

23

24

157

DO 15 KB = 1,NM1
K = N-KB
BETA = A(K,K)
DO 11 I = K, N

X(I,K) = 0.
X(K,I) = 0.
CONTINUE
X(K,K) = .
IF (K.EQ.1 .OR.BETA, EQ.0.) GO TO 15
DO 14 J = K, N
GAMMA = 0.
DO 12 I = K, N
GAMMA = GAMMA + X(I,J)*A(I,K-1)
CONTINUE

DO 13 I = K, N
X(I,J) = X(I,J) - GAMMA*A(I,K-1)
CONTINUE
CONTINUE
CONTINUE

TRIDIAGONAL QR ALGORITHM
IMPLICIT SHIFT FROM LOWER 2-BY-2

DO 27 MB = 2, N
M = N+2-MB
MM1 = M-l
ITER = 0
L = 1
E(L) = 0.

FIND L SUCH THAT E(L) IS NEGLIGIBLE

L M

S DABS(D(L-l)) + DABS(D(L))
T S + DABS(E(L))

IF (T.EQ.S) GO TO 23

L L-l

IF (L.GE.2) GO TO 22

IF E(M) IS NEGLIGIBLE, THE D(M) IS AN EIGENVALUE, SO...

IF (L.EQ.M) GO TO 27
IF (ITER.GE.30) GO TO 27
ITER = ITER + 1

FORM IMPLICIT SHIFT

T (D(M—l) - D(M))/(E(M) + E(M))
S DSQRT(1. + T*T)

IE (T.LT.0.) S = -S

S = D(M) - E(M)/(T+S)

E(L) = D(L) - S

E = E(L+1)

CHASE NONZERO F DOWN THE MATRIX

DO 26 J = L,MM1
T = DABS(E(J)) + DABS}F)
ALPHA = T*DSQRT((E(J) T)**2 + (F/T)**2)
C = E J)/ALPHA
= F ALPHA
TA = S*(D(J+1) — D(J)) + 2.0*C*E(J+1)
) = ALPHA
+ ) = E(J+l) - C*BETA
*BETA
= D(J) + T
) = D(J+1) - T
J.EQ.MM1) GO TO 24
E = S*E(J+2)
E(J+2) = —C*E(J+2)

S

BE
E(J
E(J 1
T = S
D(J)
D(J+1
IF (

IF(.NOT.WANTX) Go TO 26

DO 25 I = 1, N
T = X(I,J)
X(I,J) = C*T + S*X(I,J+1)
X(I,J+l) = S*T - C*X(I,J+l)

 

0000000

25
26

27

30
10

158

CONTINUE

CONTINUE
GO TO 21

CONTINUE
RETURN
END

******************************************************************

SUBROUTINE MATRIX.FOR

******************************************************************

SUBROUTINE MATRIX(A,B,C,M,N,L)
INTEGER M, N, L
DIMENSION A(M,N),B(N,L),C(M,L)
DO 10 I=1,M
DO 20 K=1,L
C(I,K)=0.0
Do 30 J=1,N
C(I,K)=C(I,K)+A(I,J)*B(J,K)
CONTINUE
CONTINUE
CONTINUE
RETURN
END

 

 

 

 

APPENDIX B

LOAD SIMULATION PROGRAMS l

 

.SIIHLSJWZR

$STORAGE:2

O 0000000*********$**********X-li-li-X-fl-X-ifi-fl-

000

0000

$LARGE
*

*-**-**-**-** **-**-**-**-**-**-**-*x-**-*

***********************
***********************

**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**

OCT 23 , 1992

BASSEM

MICHIGAN STATE UNIVERSITY
EAST LANSING, MI 48823

U.S.A

**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**
**

THIS PROGRAM READS THE PROCESSED *.CRL FILES
AND PERFORMS THE FOLLOWING TASKS:

K. KHAFAGI

FOR.A CERTAIN ACTION

*it-X-X-X-li-X-fl-X’N-i-Xvi-*IQ-i-fl-X-Ifl-Jffl-l-fl-i-i-i-i-JP

++++++++++++++++++++++++++++++++++
++++++++++++++++ 1. INPUT/OUTPUT MANAGEMENT ++++++++++++++++
++++++++++++++++++++++++++++++++++

PROGRAM hls.FOR

INTEGER WEIGHT(1000)

INTEGER WEIGHT(lO)

CHARACTER INPUTS*40,FOUT*12

CHARACTER FNAME1*2,FNAME*12,0UTPUTS*40
COMMON /CMP/ M,N,FS,IWIN,L,NFFT,DF
COMMON /FILES/ INPUTS,OUTPUTS,LINP,LOUT

common statement to save the array u from function uni between calls

common u(l7)

in order to assure that no sequence of random numbers 9

enerated by

function uni will be used twice, the seed array for uni (array u)

18 saved from run to run in file 'Seedarray'.

160

in order to get

161

c started, for the first run only, a separate program is run the only
c purpose of which is to invoke the function rstart that is in uni.
c rstart initializes the seed array u. for all subsequent runs the
0 seed array from the prev1ous run will be used instead of invoking
c rstart by running the separate program.
c
open(l,file='sj-hls.dat')
do 4 i=l,17 .
read(l,9) u(1)
9 format(1x,e27.20)
4 continue
C
c DATA.INPUT PROVIDED BY THE USER
c
c
1000 format (/1X,a,' ? '$)
PRINT *,'
1 I
PRINT *,'
1 I
C

write (*,1000) 'NO. of Persons Performing this Actions'
5 read (*,*) NPART
if (NPART.lt. 0.) then
write (*.'(/a)')
* ' *** ERROR *** NPART is less than 0 - Reenter'

go to 5
else if (NPART.gt.1000.) then
wrlte (*,'(/a) )

* ' **In this BETA.version...No. of Part. can not exceed 1000'
go to 5
end if
C
c . . . .
16 write (*,1000) 'Do you Want to input Part1c1pants Weight..(Y/N)
read (*,'(a)') IWT
IF((IWT.EQ.'Y').or.(IWT.EQ.'y')) THEN
C
C I
do 6 i3=l,npart .
239 write (*,1010) I] . . ' ' '
1010 format (/1X,fWeight of Part1c1pant No.: I4, ? $)
read (*,*) weight(ij)
if (weight(13).le. 0.0) then
write (*,'(la)') , , '
* ' *** ERROR *** Weight is less than 0 - Reenter
goto 239.
elseif(weight(11).gt.300.0) then
wrlte (":(/a2') ' ' 300 lb R t '
* ' Sorry,!!! My limitation is a Weight less than . een er
goto 39.
elseif(weight(il).1t.30.0) then
write ( ,'(/a)') . . "' |
* ' Sorry,!!! Infants were not conSIdered 1n HLS ..... Reenter
goto 239
6 endif
continue
else IF((IWT.EQ.'N').or.(IWT.EQ.'n')) THEN
C
C
C
DO 17 In=1,NPART
c
c Weight r.v.:
: a normally distributed deviation from the nominal value Will
c be used.
C (mean=+l73 lbs, std.dev.=16 lbs) for men
C (mean=+l43 lbs, std.dev.=20 lbs) for women

 

 

162

c see REFRENCE: .....
c
rnum=rnor(0)
AVGWT=160.0
STDWT=17.0
18 weight(in)=AVGWT+rnum*STDWT
if((weight(in).lt.0.0).or.(weight(in).gt.300.0))go to 18
if(npart.le.15) print *,'Weight of Participant No.:',In,' is = '
l,weight(in),' lbs.’
17 continue
else
goto 16
end if

000

fnamel='SJ'

WRITE (FNAME,40) FNAMEl

WRITE (FOUT,41) FNAMEl
40 FORMAT (A2,'-HLS.DAT')
41 FORMAT (A2,'-HLS.OUT')

FLAG FOR THE OPEN SCREEN
OFLAG=1
Read INPUT Data from PARAMETER FILE "hls.DAT"

000 000

READ (1,10) INPUTS
READ (1,10) OUTPUTS
READ (1,3) BW

3 format (f3.l)
na=1
n=90

10 FORMAT (A40)

DETERMINE THE LOCATION OF INPUT AND OUTPUT FILES

1.0 INPUTS

000000

LINP=LEN TRIM(INPUTS)

IF (LINPTNE.0) THEN
INPUTS=INPUTS(1:LINP)//'\'
LINP=LINP+1

END IE

2.0 OUTPUTS

000

LOUT=LEN TRIM(OUTPUTS)

IF (LOUTTNE.0) THEN
OUTPUTS=OUTPUTS(1:LOUT)//'\'
LOUT=LOUT+1

END IF

OPEN NEEDED FILES
OPEN (7,FILE=OUTPUTS(1:LOUT)//'hls.OUT')

OPEN (4,FILE=OUTPUTS(1:LOUT)//fout)

00

call sjump(Npart,weight,fname,oflag,avgwt,stdwt)

000000 00
U
0
Z

 

163

l ,
lPRINT *,' SUCCESSFUL RUN !!!! HERE IS THE SAVED OUTPUT
1 I

1 I
l I
PRINT *,' TWO'FILES WERE GENERATED AS OUTPUT ......
l I

1 I
PRINT *,' FILE NO. 1 ... NAME : SJ-HLS.OUT
l

lPRINT * ' ' CONTENT : FORCE-TIME HISTORIES
l I
1 I
PRINT *,' FILE NO. 2 ... NAME : HLS.OUT

I
PRINT *,' CONTENT : STATISTICAL OUTPUT
1 I
1 I
I

PRINT * ' HLS.FOR, V8.1.0, NOV. 1992 ...... B. KHAFAGI, MSU
I

END
C END OF THE MAIN PROGRAM DATA—P1.FOR
C#######################################################################
C

* * ~k * * * ~k * ~k * * * 'k * 'k * * 'k 'k * 'k * * * 'k * * 'k * * -k * * 'k 'k *
* * * * * * * * * ~k * 'k * * * 'k * * * * 'k 'k 'k * * 'k * * * * * * * ~k * ~k
* * ****iv):*********************************************************** *

++++++++++++++++++++++++++++++++++
++++++++++++++++ SUBROUTINE SJ (SINGLE JUMP)

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

000+000

SUBROUTINE s'um (N art weight fname oflag,av wt,stdwt)
DIMENSION avgtIB)? sgdt(8),avga(8),stda(8),avg%(5),stdf(5)
DIMENSION allin(22,5),ALLOUT(22,5),d1ff(22,5)

DIMENSION COVt(7I7)'COVIé358)ICEY§(3)5)Ih(?889)X(8)

DIMENSION corf 5 crv cor cora ,

DIMENSION FXT(( 5 )FYT(90),'FZT(90), TIMET(90), AT(8), TT(8)
DIMENSION A(10 T(1000,8),PHI(1000),ALL(22,1000),DATA(1000)

9

0 )
dimension Error 5;CONTROL(90),e(90)
INTEGER WEIGHT(
C DIMENSION A(lO, T(10,8),PHI(10),ALL(22,10),DATA(10)
C INTEGER WEIGHT(

LOGICAL*1 XABS

5
O
0
(
1
8
1

I
,8
90
00
)r
0)

164

CHARACTER INPUTS*40,outputs*40
CHARACTER FNAME*12

COMMON /CMP/ M,N, FS, IWIN, L, NFFT, DF
COMMON /FILES/ INPUTS, OUTPUTS, LINP, LOUT

common statement to save the array u from function uni between calls
common u(l7)
Read Spectral estimation parameters for the error term

var=0.0244720
frmin=0.0
frmax=10.0

FS=37.

dtt=1.0/FS
nfft=128

TIMESTEP= 1. O/FS

do 23 i=1,n
timet(i) =timet(i-1)+timestep
if(i. eq. 1) timet(i)=
continue

000 000

O)

 

++++++++++++++++++++++++++++++++++
3. FILES' PROCESSING
++++++++++++++++++++++++++++++++++

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

0000000N

npt=7

npa=8

npf=5 . . . ' _ .
read (1,110) avgph1, stdphi,(avgt(1),1=l,npt),(stdt(1),1=l,npt)
do 112 i=1, npt

read (1,114) (cort(i, j), j=—1,npt)

continue . .

read (1,116) (avga(i), i=1,npa),(stda(i),i=1,npa)

do 118 i=—1,npa

read (1,119) (cora(i, j), j= -1, npa)

continue

read (1,122) (avgf(i), i=—1,npf),(stdf(i), i=1, npf)

do 124 i=1, npf

read (1,126) (corf(i, j), j= -1, npf)

t.
SnichnirtWE(137.3;S/,7(f7.3),/,7(f7.3))
3),/.8(f7.3))

format

format
3))
8333/,5(f7.3))
8)

(
(
format E
(
(

112

118

124
110
114
116
119
122
126
136

format
format
format

HIU'IU'ICDQQ

HAAAAA

NHH‘hHH‘hI'h
CDQQ\.'I\)Q

whi
hi

V

{MOO-ti:

167

168

169

allin(i+
allin(i+
continue
do 168 i=
allin(i+9,
allin(i+9,
continue

do 169 i=

1)
2)
1)
2)
:1,
2,2
l,

1
2

—1,

allin(i+17,1)=avgf
allin(i+17, 2)=stdf

continue

(1'4 'O'OS
QAQ

t
t

Ia-H-

AA AA
P-IJ-
vv vv

)
)

(i
(i

165

 

C

c

c now the log normal varables are calculated
c

c ++++++++++++++++ hase lag

ccc phivx2=(stdp i/avgph1)**2.0

ccc stdphi=sqrt(log(1.0+phivx2))

ccc avgphi=1og(avgphi)-( og(1.0-phivx2)/2.0)

c ++++++++++++++++ loads as log normal

ccc do 47 i=1,npa

ccc if((i.e3.3).or.(i.eq.6)) then

ccc vx2=(st a(i)/avga(1))**2.0

ccc avga(i) =log(avga(i))-(lo (1.0-vx2)/2.0)

ccc stda(i) =sqrt(1og(1.0+vx2?)

ccc endif

47 continue

ccc do 45 i=1,npf . .

ccc if((i.eq.1).or.(1.eq.3).or.(1.eq.5)) then
ccc vx2=(stdf(i)/avgf(1))**2.0

ccc avgf(i) =log(avgf(1))-(log(1.O-vx2)/2.0)

ccc stdf(i) =sqrt(log(l.0+vx2))

ccc endif

45 continue

C I
C now find the cov. matrix for amplit. (a), t1me t, force f .
C by multiplying correlation coeff1c1ent times st.dev (1), (j)
c

c

do 125 i=1,npt
do 127 j=1,npt . . . '
covt(i,j)=cort(1,j)*stdt(1)*stdt(j)
127 continue
125 continue
do 135 i=1,npa
do 137 j=1,npa . . . .
cova(i,j)=cora(1,j)*stda(1)*stda(j)
137 continue
135 continue
do 155 i=1,npf
do 157 j=1,npf . . . .
covf(i,j)=corf(1,j)*stdf(1)*stdf(j)

157 continue
155 continue
0
c

DO 380 K=1,Npart
C ZERO THE FLAG Zi (USED IN THE LOAD MODELING PROCESS)
C

Zl=0.0

22:0.0

Z3=0.0

Z4=0.0

25:0.0

Z6=0.0

Z7=0.0

TIl=0.0

T12=0.0

now pick the random variables that represent the control points

response lag phi

a log-normally distributed deviation from the nominal value will

b d.
(ge:::+0.28 s, std.dev.=0.091bs) for men

see REFRENCE: .....

0000000000

IL

 

CCC

0000

CCC

CCC

CCC

CCC

OOOOO

0000000000000

166

rnum=rnor(0)
an=avgphi+rnum*stdphi
avp=exp(an)
phi(k)=an

each of the time control will be assumed at this point noramllg
distributed With correlated random variables called for time t -t7

call hmatrix (covt,crv,npt,npt,h,x)
tt(l)=0.00
tt(2)=avgt(1)+crv(l)
tt(3)=avgt(2)+crv(2)
tt(4)=avgt(3)+crv(3)
tt(5)=avgt(4)+crv(4)
tt(6)=avgt(5)+crv(5)
tt(7)=avgt(6)+crv(6)
tt(8)=avgt(7)+crv(7)

call hmatrix (cova,crv,npa,npa,h,x)
at(1)=avga(1)+crv(l)
at(2)=avga(2)+crv(2)
at(3)=avga(3)+crv(3)
at(3)=exp(av a(3)+crv(3))
at(4)=avga(4 +crv(4)
at(5)=avga(5)+crv(5)
at(6)=exp(avga(6)+crv(6))
at(6)=avga(6)+crv(6)
at(7)=avga(7)+crv(7)
at(8)=avga(8)+crv(8)

call hmatrix (covf,crv,npf,npf,h,x)
fxx=avgf(l)+crv(1)
fxx=exp(avgf(1)+crv(l))
fxm=avgf(2)+crv(2)
fyx=exp(avgf(3)+crv(3))
fyx=avgf(3)+crv(3)
fym:avgf(4)+crv(4)
DO 195 I=l,n

CALCULATE THE VALUES OF THE CONTROL MODEL CONTROL(I) FOR AMPLITU
ERROR BY USEIN THE SAMPLE TIME CONTROL POINTS INSTEAD OF MEAN TI

CONTROL POINTS.

IF (TIMET(I).LT.AVP) THEN
CONTROL(I)=0.0

GO TO 195

ELSE IF (TIMET(I).LT.(TT(2)+AVP)) THEN
STEP=((AT(2)-AT(1))/(TT(2)-TT(1)))/FS
CONTROL(I)=CONTROL(I-1)+STEP

21:21+1.

IF (Zl.EQ.l.0) CONTROL(I):AT(1)

GO TO 195

ELSE IF (TIMET(I).LT.(TT(3)+AVP)) THEN

AL
USE A SECOND DEGREE PARABOLA TO MODEL THIS PART. THE INITI
CONDITIONS FOR THE PARABOLA IS A.VALUE OF A(Z) AT TIME—0 (AT T2)
AND A.VALUE OF.A(3) AT TIME=dt (AT T3) AND SLOPE OF 0 AT 0

F(t) =.ATA2 + BT + C

AO=dA/dT“2

BO=0

CO=A2

dT=T3-§3

dA=A3-

T(6) IS THE REFRENCE INITIAL TIME

DT=TT(3)-TT(2)
DA;AT(3)-AT(2)
AO=DA/DT**2.0
BO=0.0
CO=AT(2)

 

 

CC
CC

000000000000

195

196

0 0000000

167

CONTROL(I)=AO*TI1**2+BO*TIl+CO
TIl=TI1+1.0/FS
STEP=((AT(3)-AT(2))/(TT(3)-TT(2)))/FS
CONTROL(I)=CONTROL(I-1)+STEP
zz=zz+1.
IF (ZZ.EQ.1.0) CONTROL(I)=AT(2)
GO TO 195
ELSE IF (TIMET(I).LT.(TT(4)+AVP)) THEN
STEP=((AT(4)-AT(3))/(TT(4)-TT(3)))/FS
CONTROL(I)=CONTROL(I—1)+STEP
z3=z3+1.
IF (Z3.EQ.1.0) CONTROL(I)=AT(3)
GO TO 195
ELSE IF (TIMET(I).LT.(TT(5)+AVP)) THEN
IF ((Z4.EQ.0.0).AND.(CONTROL(I-l).LT.-1.0)) CONTROL(I-1)=AT(4)
STEP=((AT(5)—AT(4))/(TT(5)-TT(4)))/Fs
CONTROL(I)=CONTROL(I-l)+STEP
z4=z4+1.
IF (Z4.EQ.1.0) CONTROL(I)=AT(4)
GO TO 195
ELSE IF (TIMET(I).LT.(TT(6)+AVP)) THEN
STEP=((AT(6)-AT(5))/(TT(6)-TT(5)))/FS
CONTROL(I)=CONTROL(I—1)+STEP
zs=zs+1.
IF (ZS.EQ.1.0) CONTROL(I)=AT(5)
GO To 195
ELSE IF (TIMET(I).LT.(TT(7)+AVP)) THEN

USE A SECOND DEGREE PARABOLA TO MODEL THIS PART. THE INITIAL
CONDITIONS FOR THE PARABOLA IS A.VALUE OF A(6) AT TIME=0 (AT T6)
AND A VALUE OF.A(7) AT TIME=dt (AT T7) AND SLOPE OF 0 AT dT

F(t) = ATAZ + BT + C
AO=[A6-A7]/dT“2

BO=-2*A*dT

CO=A6

dT=T7-T6

T(6) IS THE REFRENCE INITIAL TIME

DT=TT(7)-TT(6)
Ao=(AT(6)-AT(7))/DT**2.0
BO=-2*AO*DT
co=AT(6)
CONTROL(I)=AO*TI2**2+BO*TIZ+CO
TIZ=T12+1.0/FS
GO To 195
ELSE IF (TIMET(I).LT.(TT(8)+AVP)) THEN
STEP=((AT(8)-AT(7))/(TT(8)-TT(7)))/FS
CONTROL(I)=CONTROL(I—1)+STEP
z7=z7+1.
IF (Z7.EQ.1.0) CONTROL(I)=AT(7)
GO To 195
END IF
CONTROL(I)=0.0
CONTINUE
do 196 i=l,8
t(k,i)=tt(1)
a(k,i)=at(1)

 

 

CONTINUE
+++§++%#+%%%4+%:++4+%4++%+%%4+++++
++++++++++++++++ 5. ERROR MODELENgLLLIILLL +++++++++++++++
+++++++++++++++++:L++++...11....T.
call simu (VAR,FrMIN,FrMAX,DTt,NFFT,error)

DO 210 I=1,n

 

I;

 

0000000

000

0000000000

210

240

250
260

300

310

320
330

340

 

 

 

168

e(i)=error(i)

FZt(I)=CONTROL(I)+e(i)

Fxt(I)=e(i)/10.0

Fyt(I)=e(i)/30.0
ti=t1mestep*i-an

cut =ti-tt(6)
if((ti.ge.tt(4)).and.(ti.1e.(tt(5)+0.03)))then
FZt(I)=CONTROL(I)
endif
1f((cut.lt.timestep).and.(ti.ge.tt(6)))then
fxt(i)=fxx

fxt(i-1)=fxm

EYE“???

yt 1- =
endif ym
CONTINUE

+++++++++++++++++++++++++++++++++++++++
+++++++++++++ 5. START THE FINAL OUTPUT +++++++++++++
+++++++++++++++++++++++++++++++++++++++

PRINT TIME VS FORCES IN ACTUAL VERSUS ESTIMATED MODEL, AND ERROR
IF (NPART.GT.10) THEN

if(k.eq.1) then
PRINT * ' FOR MORE THAN 10 PART., LOAD HISlTORIES ARE NOT SAVED'

I
PRINT *,' HOWEVER, CONTROL POINT STATISTICS ARE STILL SAVED.‘
PRINT *,' Press any key when ready.‘
read(*,*)
endif

ELSEIF (NPART.LE.20) THEN

WRITE (4,240) . .
FORMAT (///,10X,'TIME ',3X,'Z-FORCE Ratio ',2X,'MODEL Ratio',2X,'

1ERROR ARRAY'/)

DO 250 I=1,90

WRITE (4,260) TIMEt(I),FZT(I),CONTROL(I),E(I)
CONTINUE

FORMAT (7X,F8.3,2X,F14.6,2X,F14.6,2X,F14.8)
WRITE (4,300) WEIGHT(K)

FORMAT (//,1x,'WEIGHT(S) :',I5,)

FINALLY, WRITE A SUMMARY ABOUT THE FORCES.

WRITE (4 310) fname
FORMAT (50x,' FORCES INFORMATION ',///,13X,'FINAL REPORT FILE N

1AME = ',A12///,5X,'POINT',5X,'TIME',5X,'AMP.'/)

DO 330 I=1,8
WRITE (4,320) I,T(K,I),A(K,I)
FORMAT (1X,I3,3X,F8.3,3X,F14.6)

CONTINUE

WRITE (4,340) PHI(K)

FORMAT (1X,'Response Lag (PHI) = ',F7.4)
ENDIF

PHIK=PHI(K)

CALL PLOTXY SUBROUTINE TO PLOT THE TIME VERSUS THE FORCE IN THE
X, Y, Z DIRECTIONS.

NOW FIND THE MAXIMUM VALUE OF THE FORCE FX,FY,FZ, AND USE EACH
FOR THE RANGE OF SCREEN PLOTS.

3

00000

0000

000 000

FZMIN=0.0

CALL
CALL
CALL
CALL
CALL
CALL

MAX
MAX
MAX
MIN
MIN
MIN

 

169

(FXT,FXMAX,TX,TIMESTEP)
(FYT,FYMAX,TY,TIMESTEP)
(FZT,FZMAX,TZ,TIMESTEP)
(FXT,FXMIN,TXM,TIMESTEP)
(FYT,FYMIN,TYM,TIMESTEP)
(FZT,FZMIN,TZM,TIMESTEP)

FWEIGHT=WEIGHT(K)

IF (NPART. GT. 10) THEN

IF (K. EQ. 1) PRINT * ,'NO OUTPUTS TO THE SCREEN ....
1LIMITATIONS . "' '

PRINT *,

ELSE

SIMULATION No. : ',K

IF (OFLAG.GT.0.0) THEN
CALL OPEN (OFLAG,BW)

ELSE

GO TO 350
END IF

 

 

50 CALL PLOTXY (TIMET, FZT, CONTROL, FZMAX, FWEIGHT, BW, K, Npart, FZMIN
1, 90, FNAME, AVP, TT, AT, 8, FxT, foIN, foAX, fyt, fymin,fymax)
ENDIF

+++++++++++ 8. Reporting control points to fIiE.T§i?LQETTILTTTI+

IF (K. EQ.1) WRITE (7,360)
WRITE (7,370) K, WEIGHT(K), PHIK,(TT(J), J=2, 8),(AT(I),I=
11, 8),FXMAX, FXMIN, FYMAX, FYMIN, FZMAX

360 FORMAT (//, 25X,'OUTPUT SUMMARY', //, 73X,'No WT PHI T2
1 T3 T4 T5 T6 T8 A1 . A2
13 A4 A5 A6 A7T A8 FXmax FXmin FYmax
l FYmin FZmax' )

370 FORMAT (1X, I3, 1X,i4, 21(2X, F6. 3))

PREPARE DATA FOR THE STATISTICS PACKAGE
.ALL(1, K)= float(WEIGHT(K))

ALL(6E K) ;:tT

ALL(16,K)=
ALL(17,K)=a

)
)
)
)
)
)
)
1)
2)
3)
4)
5)
6
7
8

)
)
)

ALL(18, K) =FXMax
ALL(19, K) =FXMin
ALL(20, K) =FYMax
ALL(21, K) =FYMin
ALL(22, K)=FZMAX

DONE WITH ALL FILE PROCESSING

380 CONTINUE

add counter for the no. of time to call mystat

nms=22
XABS=.false.
C
C CALCULATE AND REPORT IMPORTANT STATISTICS FOR THE OBSERVED
ACTION

do 600 i=1,nms

do 610 k=l,NPART

data(k)=all(i,k)
610 continue

if(npart.eq.l)go to 611

CALL MYSTAT (data,NPART,DMIN,DMAX,DMEAN,DSTD,DSE,XABS)
611 continue

c
c same estimated variables in a new arrat ALLOUT in which the
parameter . . . .
c l is the variable being processed (eg. weight, ph1,..) and the
parameter . .
c nout is the output variable number defined as follows:
c
nest=2
allout(i,1) =Dmean
allout(1,2) =Dstd
600 continue
C
C REPORT THESE VALUES TO THE SUMMERY OUTPUT FILE
C
c
c BLANK LINE T0 SEPARATE DATA
c

do 666 i=1,22 . .
diff(i,1)=abs((allin(i,1)—ALLOUT(I 1))/a111n(i,l)*100.0)
diff(i,2)=abs((allin(i,2)-ALLOUT(I,2))/allln(1,2)*100.0)

666 continue
WRITE (7,633)

633 FORMAT (1X/)
WRITE (7,361)

361 FORMAT 25X 'OUTPUT SUMMARY',//,3X,'No WT PHI T2
1 T3 (/T& ' T5 T6 T7 T8 A1 A2
13 A4 .A5 A6 .A7 .A8')
WRITE (7,653) (ALLin(I,1),I=1,17)
WRITE (7,650) (ALLOUT(I,1),I=1,17)
WRITE (7,655) (d1ff(1,1),I=l,l7)
WRITE (7,654) (ALLln(I,2),I=1,17)
WRITE (7,650) (ALLOUT(I,2),I=1,17)
WRITE (7,655) (d1ff(1,2),I=1,17)

650 FORMAT (' Sim',f6.0,f8.3,15( 8.3))

653 FORMAT (1x,'Mean valuesf,/,' Act',f6.0,f8.3,15(F8.3))

654 FORMAT (1x,'Std. Deviat10ns',/,' Act',f6.0,f8.3,15(F§.3))

655 FORMAT (' Dif',3x,f3.0,'% ',f5.l,'% ',15(F5.l, % )/)

C
CALL ENDGRAPHICS ()
RETURN
*ENE‘kiri'****************************

‘-
X-
X-
*
)I-
*-
1-
3(-
*
*-
#-

***‘k‘k

*1-*#—*s—»»~*x~*x-+
x-
x-
a(-
*
i-
X-
x.
»
g.
)1-
fl-
*
*
3‘.
*
*
a(-
*-
*
2(-

(70 »»-**-*x-*x-*x-*x-*

 

$i-*fi-*fl-*i-*i-*fi-*

IL

 

00000

00

***-***lt-X-X-i-i-OO

*
9:
'k
*-
*
*
*
*
*
*
*

l. 4. +
++++++++++++++++ 1 . DATA ++++++++++++++++
% +

SUBROUTINE OPEN (OFLAG,BW)
LOGICAL*1 INITGRAPHICS,INITBORDER,INITWINDOW,INITAXES,INITFONTS,
lPLOTMETHOD,INVERTX,INVERTY,TITLEONLY,SCRONLY,Y2PLOT,Y3PLOT
INTEGER*2 BORDERCOLOR,WINDOWCOLOR,AXISCOLOR,LABELCOLOR,PLOTCOLOR,
lTITLECOLOR,NUMBER,PLOTZCOLOR,FONTHEIGHT,FONTWIDTH,PLOT3COLOR
CHARACTER TITLE*280,XAXISTITLE*80,YAXISTITLE*80
INCLUDE 'PLOT.DIF'
INITIALISE THINGS FOR THE FIRST PLOT
INITGRAPHICS=.TRUE.
INITBORDER=.TRUE.
INITWINDOW=.TRUE.
INITAXES=.FALSE.
INITFONTS=.TRUE.
PLOTMETHOD=.FALSE.
Y2PLOT=.FALSE.
Y3PLOT=.FALSE.
SCRONLY=.TRUE.
FONTHEIGHT=28
FONTWIDTH=16
SET UP THE FANCY COLORS
BORDERCOLOR=5
WINDOWCOLOR=7
LABELCOLOR=4
SET UP THE PLOT LIMITS
XMIN=0.0
XMAX=1.0
YMIN=0.0
YMAX=1.0
POSITION THIS PLOT AT THE TOP LEFT OF THE SCREEN
XBOTTOMLEFT=0.0
YBOTTOMLEFT=0.0
XTOPRIGHT=1.8
$¥$E§i§HT 1 ** s J - H L s . F o R **'
IF(BW.EQ.1) THEN
BORDERCOLOR=O
WINDOWCOLOR=15
LABELCOLOR=1

END IF
CALL PLOT (INITGRAPHICS,INITBORDER,INITWINDOW,INITAXES,INITFONTS,

Y2DATA NUMBER PLOTMETHOD,INVERTX,INVERTY,XMIN,XMAX,
$§MINé§M£X?XTICSPACE,YTICSPACE,XBOTTOMLEFT,YBOTTOMLEFT,XTOPRIGHT,
3YTOPRIGHT,PLOTZCOLOR,BORDERCOLOR,WINDOWCOLOR,AXISCOLOR,LABELCOLOR,
4PLOTCOLOR,TITLECOLOR,XAXISTITLE,YAXISTITLE,TITLE,TITLEONLY,
5FONTHEIGHT,FONTWIDTH,SCRONLY,Y2PLOT,Y3PLOT,PLOT3COLOR,X3,Y3,NUM3)
WAIT FOR USER TO HIT RETURN
READ(*r")
CALL ENDGRAPHICS()

OFLAG=O

RETURN

END
END OF MODULE SUBROUTINE OPENING

############
###§#§#f#§#f#f#§#g#g#f#f#f#f#f#f#f#f#f#f#f#f#f#f#f#f#f#f#§#. . . . . .

*********************************

SUBROUTINE PLOTXY

****************~k

*************
** ****************

****************

»»
*1—*x-*x—**-*»

APRIL 15,1992 PLOTTING FORCE-TIME HISTORIES

*
******i-*************************

 

172

*******'k***************************
* ****************in):*****-kink**************************************** *

000000 ’1' *

000

00000

000

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

++++++++++++++++ 1. DATA.INPUT/OUTPUT ++++++++++++++++
++++++++++++++++++++++++++++++++++

SUBROUTINE PLOTXY (TIME,FZ,PR,FZMAX,WEIGHT,EW,K,NF,FZMIN,N,
1FNAME,PHIK,X3,Y3,NUM3,fx,foIN,foAX,fy,fymin,fymax)
DIMENSION TIME(90), FZ(90), PR(90)
DIMENSION X3(NUM3), Y3(NUM3),XNULL(8),YNULL(8)

INCLUDE 'PLOT.DIF'
LOGICAL*1 INITGRAPHICS,INITBORDER,INITWINDOW,INITAXES,INITFONTS,
lPLOTMETHOD,INVERTX,INVERTY,TITLEONLY,SCRONLY,Y2PLOT,Y3PLOT

INTEGER*2 BORDERCOLOR,WINDOWCOLOR,AXISCOLOR,LABELCOLOR,PLOTCOLOR,
lTITLECOLOR,NUMBER,PLOT2COLOR,FONTHEIGHT,FONTWIDTH,PLOT3COLOR

CHARACTER TITLE*280,XAXISTITLE*80,YAXISTITLE*80,
lFNAME*12,TITLE1*80,TITLE2*80,TITLE3*80,TITLE4*
280,TITLE5*80,TITLE6*80,TITLE7*80,TITLE8*80,TITLE9*80,TITLE10*80,
3TITLE11*80,TITLE12*80,TITLE13*80

NUMBER=N

INITIALISE THINGS FOR THE FIRST PLOT

INITGRAPHICS=.TRUE.
INITBORDER=.TRUE.
INITWINDOW=.TRUE.
INITAXES=.TRUE.
INITFONTS=.TRUE.
PLOTMETHOD=.TRUE.
TITLEONLY=.FALSE.
SCRONLY=.FALSE.
Y2PLOT=.false.
Y3PLOT=.TRUE.
FONTHEIGHT=10
FONTWIDTH=5

SET UP THE FANCY COLORS DEPENDING ON THE VALUE OF CFLAG (0 OR 1)
BORDERCOLOR=14
IF (CFLAG.EQ.0.0) THEN
WINDOWCOLOR=8
CFLAG=1.0
ELSE
WINDOWCOLOR=1
CFLAG=0.0
END IF
AXISCOLOR=10
LABELCOLOR=11
PLOTCOLOR=14
PLOT2COLOR=4
PLOT3COLOR=15
TITLECOLOR=15

++++++++++++++++++++++++++++++++++
++++++++++++++++ 1. FORCE IN THE x-DIR ++++++++++++++++
++++++++++++++++++++++++++++++++++

XMIN=0.0
XMAX=2.5
XTICSPACE=O.5

CREATE THE ZERO AXIS USING THE ARRAY XNULL

XNULL(8)=xmax
YNULL(8)=0.0 _ . .
Call scale subroutine to set Ymin, Ymax, Yticspace,XMIN,XMAX,...

 

 

 

 

IL

 

000

000 000000

000

173

CALL SCALE (1.3*fxmin,l.3*fxmax,YMIN,YMAX,YTICSPACE)
POSITION THIS PLOT

XBOTTOMLEFT=0.00

YBOTTOMLEFT=0.45

XTOPRIGHT= 0. 50

YTOPRIGHT= O. 90
GI ITA

TITLE
TITLE= Fx AS A RATIO TO WEIGHT '
XAXISTITLE=' T I M E ( s e C . )'

YAXISTITLE='FORCE RATIO'
USE THE BLACK AND WHITE COMBINATION IF SCREEN CAPTURING IS NEEDED

IF(BW.EQ.1) THEN
BORDERCOLOR=0
WINDOWCOLOR=15
AXISCOLOR=1

PLOT3COLOR=2
TITLECOLOR=1
ND IF

READY TO CALL PROGRAM PLOT.FOR

CALL PLOT (INITGRAPHICS, INITBORDER, INITWINDOW, INITAXES, INITFONTS,
lTIME, Fx, PR, NUMBER, PLOTMETHOD, INVERTX, INVERTY, XMIN, XMAX, YMIN ,YMAX,
2XTICSPACE, YTICSPACE, XBOTTOMLEFT, YBOTTOMLEFT, XTOPRIGHT, YTOPRIGHT,
3PLOT2COLOR, BORDERCOLOR, WINDOWCOLOR, AXISCOLOR,LABELCOLOR, PLOTCOLOR,
4TITLECOLOR,XAXISTITLE,YAXISTITLE,TITLE,TITLEONLY,FONTHEIGHT,
5FONTWIDTH,SCRONLY,Y2PLOT,Y3PLOT,PLOT3COLOR,XNULL,YNULL,NUM3)

++++++++++++++++++++++++++++++++++
++++++++++++++++ 1. RCE IN THE y—DIR ++++++++++++++++
++++++++++++++++++++++++++++++++++

CALL SCALE (l.2*fymin,1.2*fymaX,YMIN,YMAX,YTICSPACE)
POSITION THIS PLOT

INITGRAPHICS=.FALSE.
XBOTTOMLEFT=O.5O
YBOTTOMLEFT=0.45
XTOPRIGHT=1.00
YTOPRIGHT=O.9O
GIVE IT A TITLE
TITLE=' Fy AS A RATIO TO WEIGHT '
XAXIS MT E= ' TIME ( s e c .
YAXISTITLE= 'FORCEI RATIO'

USE THE BLACK AND WHITE COMBINATION IF SCREEN CAPTURING IS NEEDED

IF(BW.EQ.1) THEN
BORDERCOLOR=0
WINDOWCOLOR=15
AXISCOLOR=1
LABELCOLOR=4
PLOTCOLOR=0
PLOT2COLOR=1
PLOT3COLOR=2
TITLECOLOR=1

END IF

READY TO CALL PROGRAM PLOT.FOR

 

I;

 

 

000 0000000

000 000

00000

000

40
50

174

CALL PLOT (INITGRAPHICS,INITBORDER,INITWINDOW,INITAXES,INITFONTS,
1TIME,Fy,PR,NUMBER,PLOTMETHOD,INVERTX,INVERTY,XMIN,XMAX,YMIN,YMAX,
2XTICSPACE,YTICSPACE,XBOTTOMLEFT,YBOTTOMLEFT,XTOPRIGHT,YTOPRIGHT,
3PLOT2COLOR,BORDERCOLOR,WINDOWCOLOR,AXISCOLOR,LABELCOLOR,PLOTCOLOR,
4TITLECOLOR,XAXISTITLE,YAXISTITLE,TITLE,TITLEONLY,FONTHEIGHT,
5FONTWIDTH,SCRONLY,Y2PLOT,Y3PLOT,PLOT3COLOR,XNULL,YNULL,NUM3)

++++++++++++++++++++++++++++++++++
++++++++++++++++ 1. FORCE IN THE z-DIR ++++++++++++++++
++++++++++++++++++++++++++++++++++

Call scale subroutine to set Ymin, Ymax, Yticspace,XMIN,XMAX,...
CALL SCALE (l.2*fzmin,l.2*fzmax,YMIN,YMAX,YTICSPACE)
POSITION THIS PLOT

XBOTTOMLEFT=0.00
YBOTTOMLEFT=0.00
XTOPRIGHT=0.50
YTOPRIGHT=O.45
GIVE IT A TITLE
TITLE=' FZ AS‘A RATIO TO WEIGHT '
XAXISTITLE=' T I M E ( s e C . )'
YAXISTITLE='FORCE RATIO'

USE THE BLACK AND WHITE COMBINATION IF SCREEN CAPTURING IS NEEDED

IF(BW.EQ.1) THEN
BORDERCOLOR=O
WINDOWCOLOR=15
AXISCOLOR=1
LABELCOLOR=4
PLOTCOLOR=0
PLOT2COLOR=1
PLOT3COLOR=2
TITLECOLOR=1

END IF

READY TO CALL PROGRAM PLOT.FOR

CALL PLOT (INITGRAPHICS,INITBORDER,INITWINDOW,INITAXES,INITFONTS,
lTIME,FZ,PR,NUMBER,PLOTMETHOD,INVERTX,INVERTY,XMIN,XMAX,YMIN,YMAX,
ZXTICSPACE,YTICSPACE,XBOTTOMLEFT,YBOTTOMLEFT,XTOPRIGHT,YTOPRIGHT,
3PLOT2COLOR,BORDERCOLOR,WINDOWCOLOR1AXISCOLOR,LABELCOLOR,PLOTCOLOR,
4TITLECOLOR,XAXISTITLE,YAXISTITLE,TITLE,TITLEONLY,FONTHEIGHT,
5FONTWIDTH,SCRONLY,Y2PLOT,Y3PLOT,PLOT3COLOR,XNULL,YNULL,NUM3)

++++++++++++++++++++++++++++++++++
+++++++++++++++ 2. OUTPUT VALUES ++++++++++++++++
++++++++++++++++++++++++++++++++++

just plot the title on this one
XBOTTOMLEFT=O.50
YBOTTOMLEFT=0.00
XTOPRIGHT=1.00
YTOPRIGHT=O.45
INITGRAPHICS=.EALSE.

TITLE=' CONTROL POINTS '
WRITE (TITLE1,40)

FORMAT ('Single Jump With One Person')

WRITE (TITLE2,50) WEIGHT

FORMAT ('Weight= ',F4.0,' lbs')

Find the max. value of force in the x,y directions (absolute force
WRITE (TITLE3,60) K,NF

I=0
WRITE (TITLE13,80) PHIK

 

 

 

I;

 

175

1:1
WRITE (TITLE4,70) I,X3(1),Y3(1)
I=I+
WRITE (TITLE5,70) I,X3(2),Y3(2)
I=I+
WRITE (TITLE6,70) I,X3(3),Y3(3)
=I+
WRIT? (TITLE7,70) I,X3(4),Y3(4)
I= +
WRITE (TITLE8,70) I,X3(5),Y3(5)
= +
WRIT? (TITLE9,70) I,X3(6),Y3(6)
= +
WRITE (TITLE10,70) I,X3(7),Y3(7)
= +
WRITE (TITLE11,70) I,X3(8),Y3(8)
6O FORMAT (IZ,' OF'I3,1X,'POINT TIME AMP.')
70 FORMAT (8X,IZ,2X,F8.4,2X,F10.5)
80 FORMAT (1X,'Response Lag (PHI) = ',F7.4)

WRITE (TITLE12,90)

9O FORMAT ('HIT ENTER TO CONTINUE....')
CALL OUTPUTS (XBOTTOMLEFT,YBOTTOMLEFT,XTOPRIGHT,YTOPRIGHT,TITLE,
lTITLEl,TITLE2,TITLE3,TITLE4,TITLE5,TITLE6,TITLE7,TITLE8,TITLE9,
2TITLE10,TITLE11,TITLE12,TITLE13,CFLAG,BW)

 

C
C
C ++++++++++++++++++++++++++++++++++
C ++++++++++++++++ 3. Top Title on the Screen ++++++++++++++++
C ++++++++++++++++++++++++++++++++++
C
INITGRAPHICS=.FALSE.
TITLEONLY=.TRUE.
INITAXES=.FALSE.
INITFONTS=.TRUE.
FONTHEIGHT=28
FONTWIDTH=16
WINDOWCOLOR=7
TITLECOLOR=4
XBOTTOMLEFT=0.00
YBOTTOMLEFT=0.9O
XTOPRIGHT=1.00
YTOPRIGHT=1.00
C TITLE='S I N G L E J U M P'
E USE THE BLACK AND WHITE COMBINATION IF SCREEN CAPTURING IS NEEDED
IF(BW.EQ.1) THEN
WINDOWCOLOR=15
TITLECOLOR=1
END IF
CALL PLOT (INITGRAPHICS,INITBORDER,INITWINDOW,INITAXES,INITFONTS,
lTIME,FZ,PR,NUMBER,PLOTMETHOD,INVERTX,INVERTY,XMIN,XMAX,YMIN,YMAX,
2XTICSPACE,YTICSPACE,XBOTTOMLEFT,YBOTTOMLEFT,XTOPRIGHT,YTOPRIGHT,
3PLOT2COLOR,BORDERCOLOR,WINDOWCOLOR,AXISCOLOR,LABELCOLOR,PLOTCOLOR,
4TITLECOLOR,XAXISTITLE,YAXISTITLE,TITLE,TITLEONLY,FONTHEIGHT,
C 5FONTWIDTH,SCRONLY,Y2PLOT,Y3PLOT,PLOT3COLOR,XNULL,YNULL,NUM3)
C WAIT FOR USER TO HIT RETURN ( only for testin the program
g , otherwise let the program run Wlth no stops?
READ (*,*)
IF (K.EQ.NF+1) CALL ENDGRAPHICS ()
RETURN
END

END OF SUBROUTINE PLOTXY
###################################################################
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

*****3"****************************
*

**»»n()
m:
=23:

*xq:

 

 

000 000000It-i-1I-1t-x-It-1-1-1-fl-

176

SUBROUTINE MAX

MAY 05,1992 FINDING THE MAX. VALUE OF DATA

* 'k * 'k 'k * * * 'k 'k * * * 'k 'k * 'k * 'k 'k ‘k * * * * 'k * * * * * * ~k
* * 'k * * 'k 'k * 'k 'k 'k 'k * 'k * * * 'k * 'k 'k 'k 'k 'k 'k * * 'k -k * * 'k 'k
*****-****‘k********************************************************

*x-**-**-**-**
*1—*fl-*fi-+i-**

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

++++++++++++++++ 1. DATA INPUT/OUTPUT ++++++++++++++++
++++++++++++++++++++++++++++++++++

SUBROUTINE MAX (DATA,FMAX,T,TIMESTEP)
TO FIND THE MAX. FORCE

DIMENSION DATAX90)
T=0.0

N=0

FMAX=-1El4

NMAX=0

DO 10 I=1,9O
N=N+1

IF (DATA(I).GT.FMAX) THEN
FMAX=DATA(I)
NMAX=N

GO TO 10

END IF

lO CONTINUE

DOC) nooonnx-x-x-x-x-x-x-x-x-x-x-x-zt-OO

# ##################################################################
********* ********************
********************

T=REAL(NMAX)*TIMESTEP
RETURN
END

END OF SUBROUTINE MAX

** *3?

*************

SUBROUTINE MIN

1*
*
*
*
*
****it*****************************
*
*
9:
*-
*
*
*

**-**-»x-+x-*:-»x-*§:
=11:

++++++++++++++++++++++++++++++++++
++++++++++++++++ 1. DATA INPUT/OUTPUT ++++++++++++++++
++++++++++++++++++++++++++++++++++

SUBROUTINE MIN (DATA,FMIN,T,TIMESTEP)
TO FIND THE MIN. FORCE

DIMENSION DATA(90)

T=0.0

N=0

FMIN=0.0

NMAX=0

DO 10 I=1,90

N=N+1

IF (DATA(I).LT.FMIN) THEN

 

 

 

I;

 

 

10

o********+**»000

0

00000

***$****#***#3¥2

10

20

177

FMIN=DATA(I)

NMAX=N
GO TO 10
END IF
CONTINUE
T=REAL(NMAX)*TIMESTEP
RETURN
END
END OF SUBROUTINE MIN
###################################################################
###################################################################
*********************************
*********************************
*
SUBROUTINE outputs *
*
**************************~k******
*********9:***********************
*
MAY 15,1992 Plotting the final values of Forces *
*
*********************************
*********************************

START OF MODULE outputs.for

INCLUDE 'FGRAPH. FI'

SUBROUTINE OUTPUTS (XBOTTOMLEFT, YBOTTOMLEFT, XTOPRIGHT, YTOPRIGHT,
1TITLE,TITLE1, TITLEZ, TITLE3,TITLE4,TITLE5,TITLE6,TITLE7,TITLE8,
ZTITLE9, TITLEIO, TITLE11,TITLE12,TITLE13, CFLAG, BW)

INCLUDE 'FGRAPH. FD'

INTEGER*2 DUMMY,XWIDTH, YHEIGHT, 1X1, IYl, IX2, 1Y2, IX, IY, FONTHEIGHT,
1FONTWIDTH

REAL*4 XW1,YW1,XW2, YW2,XBOTTOMLEFT,YBOTTOMLEFT,XTOPRIGHT,
lYTOPRIGHT, YT

CHARACTER TITLE*80, FONTCOMMAND*10, FONTSTRING*7, FONTFILE*12, TITLE1*
180, TITLE2*80, TITLE3*80, TITLE4*80, TITLE5*80, TITLE6*80, TITLE7*80,
2TITLEB*80, TITLE9*80, TITLE10*80, TITLE11*80, TITLE12*80, TITLE13*80

RECORD / VIDEOCONFIG / SCREEN
RECORD / WXYCOORD / WXY
RECORD / XYCOORD / POSITION

COMMON SCREEN

SET UP FONT FOR USE
FONTFILE='HELVB.FON'
FONTCOMMAND="T'HELV'"
IF (REGISTERFONTS(FONTFILE).LT.0) THEN
WRITE (*,10) FONTFILE
FORMAT (' FONT FILE ',A12,' NOT FOUND IN PLOT')
STOP
END IF
FONTHEIGHT=28
FONTWIDTH=16
WRITE (FONTSTRING, 20) FONTHEIGHT, FONTWIDTH
FORMAT (' H', IZ. 2,'W', I2. 2, 'B'
DUMMY=SETFONT(FONTCOMMAND//FONTSTRING)

GET SCREEN DIMENSIONS
XWIDTH=SCREEN.NUMXPIXELS
YHEIGHT=SCREEN.NUMYPIXELS

SET A.VIEW PORT, WITH CORNER COORDINATES DEFINED AS.A

FRACTION OF THE TOTAL SCREEN SIZE

(0.0,0.0) IS BOTTOM LEFT OF SCREEN

(1.0,1.0) IS TOP RIGHT OF SCREEN

TRANSLATE CORNER COORDINATES TO PIXEL COORDINATES
IX1=INT(XBOTTOMLEFT*FLOAT(XWIDTH))
IX2=INT(XTOPRIGHT*FLOAT(XWIDTH))
IY1=YHEIGHT-INT(YTOPRIGHT*FLOAT(YHEIGHT))
IY2=YHEIGHT-INT(YBOTTOMLEFT*FLOAT(YHEIGHT))

CALL SETVIEWPORT (IX1,IY1,IX2,IY2)

CREATE.A REAL COORDINATE WINDOW
XW1=0.0
YW1=0

 

 

 

 

 

00000

000 000 0000

00000

178

XW2=1.0
YW2=1.0
DUMMY=SETWINDOW(.TRUE.,XW1,YW1,XW2,YW2)

SET THE COLOR OF THE BACKGROUND WINDOW DEPENDING ON THE FLAG
"CFLAG" ... NOTE THE SETUP HAS TO BE OPPOSITE TO THE PLOTXY

IF (CFLAG.EQ.1.0) THEN

DUMMY=SETCOLOR(8)

ELSE

DUMMY=SETCOLOR(1)

END IF

IF(BW.EQ.1) DUMMY =SETCOLOR(15)

DUMMY=RECTANGLE W($GFILLINTERIOR,XW1,YW1,XW2,YW2)
DRAW A BORDERIAROUND THE VIEWPORT

DUMMY=SETCOLOR(14)

IF(BW.EQ.1) DUMMY =SETCOLOR(0)

DUMMY=RECTANGLE_W($GBORDER,XW1,YW1,XW2,YW2)

This is the screen design of the data output

 

TITLELENGTH=50
POSITION THE TITLE CENTERED (MORE OR LESS) ABOVE GRAPH

YT=0.9*(YW2+YW1)

CALL MOVETO W (0.9* (XW2+XW1) ,YT,WXY)
CALL GETCURRENTPOSITION (POSITION)
IX=POSITION.XCOORD
IY=POSITION.YCOORD
IX=IX-(TITLELENGTH*FONTWIDTH)/2
IY=IY-FONTHEIGHT/2

enter the program.name (Title: from the main program)

DUMMY=SETCOLOR(15)

IF(BW.EQ.1) DUMMY =SETCOLOR(O)

CALL MOVETO (IX,IY,POSITION)

CALL OUTGTEXT (TITLE(1:TITLELENGTH))
DUMMY=SETCOLOR(4)

IF(BW.EQ.1) DUMMY =SETCOLOR(0)

CALL MOVETO (IX,IY+2,POSITION)

CALL OUTGTEXT (TITLE(1:TITLELENGTH))

CHANGE THE FONT TO A FIXED FONT TO CREATE THE FORCES' TABLE
HERE, COURIER FONTS WILL BE USED.

 

FONTFILE='courb.fon'
FONTCOMMAND="T’courier'"

FONTHEIGHT=12

FONTWIDTH=9

IF (REGISTERFONTS(FONTFILE).LT.O) THEN
WRITE (*,10) FONTFILE

STOP

END IF

WRITE (FONTSTRING,20) FONTHEIGHT,FONTWIDTH
DUMMY=SETFONT(FONTCOMMAND//FONTSTRING)

YT=0.8*(YW2+YW1)

CALL MOVETO W (0.73*(XW2+XW1),YT,WXY)
CALL GETCURRENTPOSITION (POSITION)
IX=POSITION.XCOORD
IY=POSITION.YCOORD
IX=IX-(TITLELENGTH*FONTWIDTH)/2
IY=IY-FONTHEIGHT/2

 

 

I;

 

179

DUMMY=SETCOLOR(O)

IF(BW.EQ.1) DUMMY =SETCOLOR(1)

CALL MOVETO (IX,IY+10,POSITION)

CALL OUTGTEXT (TITLE1(1:TITLELENGTH))

CALL MOVETO (IX,IY+25,POSITION)

CALL OUTGTEXT (TITLE2(1:TITLELENGTH))

DUMMY=SETCOLOR(11)

IF(BW.EQ.1) GOTO 22

CALL MOVETO (IX,IY+ll,POSITION)

CALL OUTGTEXT (TITLE1(1:TITLELENGTH))

CALL MOVETO (IX,IY+26,POSITION)

CALL OUTGTEXT (TITLE2(1:TITLELENGTH))
22 CONTINUE

FONTHEIGHT=10

FONTWIDTH=8

WRITE (FONTSTRING,20) FONTHEIGHT,FONTWIDTH
DUMMY=SETFONT(FONTCOMMAND//FONTSTRING)
DUMMY=SETCOLOR(14)

IF(BW.EQ.1) DUMMY =SETCOLOR(0)

CALL MOVETO (IX,IY+40,POSITION)

CALL OUTGTEXT (TITLE3(1:TITLELENGTH))
DUMMY=SETCOLOR(15)

IF(BW.EQ.1) DUMMY =SETCOLOR(1)

CALL MOVETO (IX,IY+55,POSITION)

CALL OUTGTEXT (TITLE4(1:TITLELENGTH))
CALL MOVETO (IX,IY+68,POSITION)

CALL OUTGTEXT (TITLE5(1:TITLELENGTH))
CALL MOVETO (IX,IY+81,POSITION)

CALL OUTGTEXT (TITLE6(1:TITLELENGTH))
CALL MOVETO (IX,IY+94,POSITION)

CALL OUTGTEXT (TITLE7(1:TITLELENGTH))
CALL MOVETO (IX,IY+107,POSITION)

CALL OUTGTEXT (TITLE8(1:TITLELENGTH))
CALL MOVETO (IX,IY+120,POSITION)

CALL OUTGTEXT (TITLE9(1:TITLELENGTH))
CALL MOVETO (IX,IY+133,POSITION)

CALL OUTGTEXT (TITLE10(1:TITLELENGTH))
CALL MOVETO (IX,IY+146,POSITION)

CALL OUTGTEXT (TITLE11(1:TITLELENGTH))

DUMMY=SETCOLOR(2)

IF(BW.EQ.1) DUMMY =SETCOLOR(O)

CALL MOVETO (IX,IY+164,POSITION)

CALL OUTGTEXT (TITLE13(1:TITLELENGTH))

DUMMY=SETCOLOR(O)

CALL MOVETO (IX,IY+185,POSITION)

CALL OUTGTEXT (TITLE12(1:TITLELENGTH))
DUMMY=SETCOLOR(4)

CALL MOVETO (IX,IY+186,POSITION)

CALL OUTGTEXT (TITLE12(1:TITLELENGTH))

ALL DONE
CALL UNREGISTERFONTS ()

RETURN
END

000

 

******************
******************

w+
**
u-x-
*»
**
* *
*$
*$

SUBROUTINE SCALE

**********************
***~k**************~k***

n~

a»

x-

1.
2+2:-
*3!-
2+:-
x-x-
»*
$a+
*$

***-***fi-fl-X-
*****$***
:9
x-
x-
a(-

AUG 22,1992 VERTICAL PLOT SCALE

 

 

 

I;

 

 

 

180

*
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
***************************************************************** *

++++++++++++++++++++++++++++++++++
++++++++++++++++ 1. DATA INPUT/OUTPUT ++++++++++++++++
++++++++++++++++++++++++++++++++++

*-*fl-*

()0(3C)* *X-*

SUBROUTINE SCALE (FMIN,FMAX,ST,FIN,TICK)
This routine determines the starting and ending values to be used in
a full scale plot. . .
OUTPUT : ST = Starting value; FIN = Ending value; TICK .

THIS IS A MODIFIED VERSION OF.A PROGRAM WRITTEN ORIGINALLY BY R. HARIC
REAL*8 U,C
TT=ALOG10(FMAX-FMIN)
MT=IRINT(TT)
TT=10.**(TT-MT)

IF (TT.LE.2) THEN
TT=2.

ELSE IF (TT.GT.5) THEN
TT=10.

ELSE

TT=5.

END IF
TICK=TT*10.**(MT-l)
U=l.00001*TICK
C=DLOG10(U)

IF (C.LT.0) THEN
L=IDINT(C)-1

ELSE

L=IDINT(C)

END IF
C=DBLE(10.)**L
TICK=C*IDNINT(U/C)
N1=IRINT(FMIN/TICK)
N2=IRINT(FMAX/TICK)+1
ST=N1*TICK
FIN=N2*TICK

RETURN

END

INTEGER FUNCTION IRINT(X)
IF (X.LT.O) THEN
IRINT=INT(X)-l

ELSE

IRINT=INT(X)

END IF

RETURN

END

###############################

###############################

function uni(jdum): uses mcgill ufierduper to generate uniform

random numbers between 0 and 1. t e argument (jdum) is just a

dummy argument - i.e. it isn't used in the subpro ram. for
more information contact dr. george marsaglia was ington state
university pullman,washington.

0000000

#flm
mum

2 ##########################§#

#
# ######################### figgfifigfi
s

the function rstart is invoked once at the beginning of the main
program to initialize uni. the arguments for rstart can be
chosen arbitrarily.

********************************************************************

function uni(jdum) .
integer nbits,i,j,m,11
common u(l7)

 

 

 

lg;

 

000

0000000000

00

 

 

181

data nbits,i,j,m,i1/48,17,5,32707,1971/ .
THIS SEED WAS USED TO SIMULATE random motions
jdum:0

uni=u(i)-u(j) _

if(uni.lt.0.) uni=uni+l.

u(i)=uni

i=i-1

ifgi.eq.0) i=1?

if(j.eq.0) j=17

return

rstart initializes uni

entry rstart(is,js) ' _ . .
initializes u(1) to u(l7) bit-by-bit, uSing fibonaccl mod m, lag 2
1 =13

i3='s

do 2 I=1,17

s=.5

u(l)=0.

do 2 ll=1,nbits
k=i3-il

il=i2

i2=i3

i3=k

if(i3.gt.0) go to 2
i3=i3+m
u(l)=u(l)+s

s=.5*s
rstart=is*10000+js
return

end

*********************************************************************

function rnor(j): generates normally distributed random numbers be-
tween -infinity and +infinity With a mean=0.0 and a standard devia-
tion=l.0.

********************************************************************

 

function rnor(j) .
patchwork normal, 0<x<2.290094, linear and cubic pretests.

i=0

rnor=2.290094*(2*uni(O)-l.)

x=abs(rnor)

if(x.le.l.098) return

y=uni(0)

if(x+¥.le.2.084) return

if(.7 3398*x+y.1t.1.89122) go to 3
rnor=sign(2.290094-x,rnor)

return
h=l.66244+x*(.5088388-x*(1.310391-x*.3513116))
if(y.gt.h) go to 2

g=2.71622-x (1.961507-x*.3628954)

if(y.le.q) return
if((q+.0054.lt.¥).and.(¥.lt.h-.002)) go to 4
if(alog(y).le.. 02802-. *x**2) return
if(.602802-.5*(2.290094-x)**2. t.alog(2.-y)) go to 2
x=sqrt(5.244531—2.*alog(uni(0)?)
if(unig0)*x.gt.2.290094) go to 4
rnor=Sign(x,rnor)

return

end

 

 

182

C 'k*******************************************************************

c
CCC FROM DR. RONALD HARICHANDRAN

subroutine hmatrix (cov,crv,m,n,h,x)

DIMENSION cov(m,n),h(m,n),crv(m), X(m)

REAL CIJ
130 format (lx,7(f7.3))
DO 10 J=1,N

H(J,1)=COV(J,1)/SQRT(COV(1,1))
IF(J.EQ.1)GOTO 10
DO 30 K=1,J
IF(K.EQ.1)GOTO 20
IF(K.EQ.J) THEN
CIJ=0.0
DO 40 I=1,J-1
CIJ=CIJ+(H(J,I))**2
40 CONTINUE
H(J,J)=SQRT(COV(J,J)-CIJ)
GOTO 10
END IF
CIJ=0.0
DO 50 I=1,K-l
CIJ=CIJ+H(J,I)*H(K,I)
50 CONTINUE
H(J,K)=(COV(J,K)-CIJ)/H(K,K)
20 H(K,J)=0.0
30 CONTINUE
10 CONTINUE

C now multi ly the matrix h.time a vextor of standard R.V. to get
C the corre ated random variables
c

 

do 70 i=l,m
x(i)=rnor(0)
70 continue
DO 80 I=1,M
Crv(I)=0.0
DO 90 J=1,N
Crv(I)=Crv(I)+h(I,J)*x(J)
9O CONTINUE
8O CONTINUE
RETURN
END
C############################
C############################
SUBROUTINE MYSTAT(X,Nn,
DIMENSION X(Nn)
LOGICAL*1 XABS
=-1E14
XMIN=1e14
XSUM:0.0
XSUM2=0.0
DO 10 I=1,Nn
if(xabs) then
DO 20 II=1,Nn
X(I)=ABS(X(I))
20 CONTINUE
END IF

C

C DETERMINE THE MEAN

C
XSUM=XSUM+X(I)
XSUM2=XSUM2+X(I)**2.0

C

C FINDING MAXIMUM AND MINIMUM

C

IF (X(I).GT.XMAX) THEN
XMAX=X(I)
END IF

I2;

 

 

183

IF (X(I).LT.XMIN) THEN
XMIN=X(I)
END IF

10 CONTINUE
XN=FLOAT(Nn)
XMEAN =XSUM/XN
XSTD=SQRT(XSUMZ/XN-XMEAN**2.0)
XSE=XSTD/SQRT(XN)
RETURN

END
C#######################################################################
c

c Program to generate a random function from a specified SDF
c Calls: fft, urng from nswclib

SUBROUTINE SIMU(VAR,FrMIN,FrMAX,DT,NFFT,error)
com lex x(128)
rea r(513),error(90)
intrinsic sin, cos, cabs
parameter (pi=3.141592654, maxfft=1024)
data x / 128*(0., O.)/
c Define arithmetic function to compute area under two—sided SDF
sint(fl,f2) =(f2-f1)*(s(f2)+s(f1))/2
df = 1./dt/nfft
dfoZ = df/2
nf = nfft/2 + 1
do 12 ii=l,513
r(ii)=uni(0)
12 continue
c take care of end regions
nfl = ifix(frmin/df) + 1
nf2 = ifix(frmax/df) + 2
f1 = frmin
dfl = frmin - (nfl-1)*df
if (dfl .gt. df02) then
phi = r(nf1+1)*2.*pi
if (frmax-frmin .le. df) then . ' .
x(nf1+1)=sqrt(abs(sint(frmin,frmax)))*cmplx(cos(phi),Sin(phi))
go to 35
end if
n1 = nfl + 2
f2 = df*nfl + dfoZ . _ _
x(nf1+1) = sqrt(abs(sint(fl,f2))) * cmplx(cos(phi),31n(phi))
else
phi = r(nfl)*2.*pi
if (frmax—frmin .le. df) then _ . .
x(nf1)=sqrt(abs(Sint(frmin,frmax)))*cmplx(cos(phi),Sin(phi))

go to 35
end if
n1 = nfl + 1
f2 = df*(nfl-l) + dfoZ _ . .
x(nfl) = sqrt(abs(Sint(f1,f2))) * cmplx(cos(phi), Sln(phl))
end if

f2 = frmax

df2 = (nf2—1)*df - frmax

if (df2 .gt. df02) then
n2 = nf - 2
fl = (nf2-2)*df - df02
phi = r(nf2—1)*2.*pi

x(an—l) = sqrt(abs(sint(fl,f2))) * cmplx(cos(phi), sin(phi))
else
n2

= nf2 - 1

fl = (nf2gé):gf*-'df02
hi = r n . i . . .

E(an) ; sqit(abg(sint(f1,f2))) * cmplx(cos(phi), Sln(phl))

 

 

I2;

 

184

end if
c Assign transforms to middle region

f1 = (n1-1)*df
31 = s(fl)
do 30 i = n1, n2
f2 = fl + df
$2 = s(f2)
ssint = df * (31+32)/2
phi = r(i)*2.*
x(i) :zsqrt(abs(ssint)) * cmplx (cos(phi), sin(phi))

fl-
sl.= 82
30 continue

c Make x conjugate symmetric

35 n1 = maxO (2,nf1)
n2 = minO (nf2, nf- 1)
do 40 i = n1, n2 .
40 x(nfft+2— —i) = conjg(x(i))
c Let x(1)= 0 (zero freq. ), and im[x(nf)]- -O (Nyquist freq. ). This ensures
zero
c mean, real, series. Power at Nyquist freq. must also be doubled.
0 Power at zero freq. (— =2*cabs(x(1))**2) is lost.

x(1) = cmplx (0., O. )
x(nf) = sqrt(2. ) * cmplx (cabs(x(nf)), O.)

c Obtain inverse fft
call fft (x, nfft, l)

c Scale x to obtain target variance

sum = 0.
sum2 = 0.
do 50 i = 1, nfft
x(i) = x(i) .
sum = sum + real(x(i))
50 sum2 = sum2 + cabs(x(i))**2

sum = sum/nfft

sum2 = sum2/nfft - sum*sum
vcrn = sqrt(abs(var/sum2))
c
c
c
do 60 i = 1, 90
x(i) = (x(i) - sum) * vcrn
error(i) =real(x(i))
60 continue
end
c
c
function s(f) _________
c ______________________________________________________________
c Compute the value of the error spectrum at freq F
c ———————————————————————————————————————————————————————————————————————

dimension freq(512),process(512)
if(ijump. eq. 0) then
READ (1, 10) ifreq
10 formAT(I5)
do 144 i=1, 512
read (1,138)freq(i),process(i)
144 continue

'2‘

 

 

 

 

  

185
138 format (2f16.11)
ijump=1

fstep =freq(2)

endif

itest=int(f/fstep)+l

i=itest

if(f. eq. freq(i)) then

s=process(i)

elseif((f. gt. fre (i)). and. (f. le. freq(i+1))) then
fper=( (f-freq (i))7fstep

s= (process(i+1)-process(i))*fper+process(i)
endif
return
#######################
#######################

arm:
#41:“,

.—---———---------------—----~---—--—-—--—-———-----—-—--————-——-—-—---——

C This subroutine computes the discrete Fourier Transform or the inverse
C transform of X

C _______________________________________________________________________
C Input: =2**M complex array that initially contains the input
C and on return contains the trans om
C -2**M points. (Must be power of 2, else infinite loop resu
C INV = 0 for direct transform; 1 for inverse transform.
C _______________________________________________________________________
C
COMPLEX X(*),U ,W,T
M=ALOG(FLOAT (N ))/ALOG(2. )+.1
NV2=N/2
NM1=N-1
J=l
DO 40 I=1,NM1
IF (I.GE.J) GO TO 10
T=X(J)
X(J)=X(I)
X(I)=T
10 K=NV2
20 IF (K.GE.J) GO TO 30
J=J-K
K=K/2
GO TO 20
30 J=J+K

4O CONTINUE
PI=4.0*ATAN(1.0)
DO 70 L=1,M
LE=2**L
LE1= LE/Z
U=(1. 0, 0. 0)
W=CMPLX(COS(PI/FLOAT(LE1)),-SIN(PI/FLOAT(LE1)))
IF (INV. NE. 0) W=CONJG(W)
DO 60 J=1,LE1
DO 50 I=J,N,LE
IP=I+LE1
T=X(IP)*U
X(IP)=X(I)-T
X(I)=X(I)+T

50 CONTINUE
U=U*W

60 CONTINUE

7O CONTINUE
IF (INV.EQ.1) RETURN
DO 80 I=1,N
X(I)=X(I)/N

80 CONTINUE
RETURN

END
C#######################################################################

 

 

 

 

'2‘

 

 

 

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3. Allen, D.E. , and Pemica, G. , " Floor Vibration Measurements in a Shopping
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4. Allen, D.E., Pemica, G., and Rainer, J .H., "Building Vibration Due to Human
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5. Allen, D.L. , and Swallow, J .C., "Annoying Floor Vibrations-Diagnosis and
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6. American Standards Building Requirements, "American Standard Specifications for
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7. Bachmann, H. , " Case Studies of Structures with Man-Induced Vibration, " Journal
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8. Bachmann, H. , " Vibration of Building Structures Caused by Human Activities; Case
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Bachmann, H. , "Vibration Upgrading of Gymnasia, Dance Halls, and Footbridges",
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187

11. Box, George E. P., "Time series analysis; forecasting and control," San Francisco,
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13. Clough, R. W. , and J. Penzien, "Random Processes," Dynamics of Structures, 1st
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15. Ebrahimpour, A. and R.L. Sack, "Modeling Dynamic Occupant Loads," Journal of
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18. Eliashakoff, 1., "Probabilistic Methods in the Theory of Structural," John Wiley &
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19. Ellingwood, B. et a1. , "Structural Serviceability: a Critical Appraisal and Research
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20. Ellingwood, B., Galambos, T., MacGregor, J ., Cornell, C.,"Development of a
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degree of Master of Science in Civil Engineering, Sep 1988.

 

 

 

 

LIBRQRIES

WW

312930 897

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