analysis of industrial slabs-on-ground
TRANSCRIPT
ANALYSIS OF INDUSTRIAL FLOOR SLABS-ON-GROUND FOR DESIGN PURPOSES
by
KANCHEEPURAM N. 6UNALAN, B.E., M.E.
A DISSERTATION
IN
CIVIL ENGINEERING
Submitted to the Graduate Faculty of Texas Tech University in
Partial Fulfillment of the Requirements of
the Degree of
DOCTOR OF PHILOSOPHY
December, 1986
ACKNOWLEDGEMENTS
The author expresses his deep sense of gratitude to Dr. Warren
K. Wray for his encouragement and guidance throughout the course of
this work. He also thanks Dr. C.V.G. Vallabhan, Dr. James R.
McDonald, and Dr. Necip Guven for their valuable guidance. Thanks
are also due to Dr. K.C. Mehta for willing to be an examiner and to
Dr. D. Chou for all his help. The author is indebted to Dr. E.W.
Kiesling, Chairman of the Department of Civil Engineering, for the
financial assistance throughout the course of his study at Texas
Tech University.
The author thanks his parents for their constant encouragement,
guidance and moral support. He also thanks his wonderful wife,
Duru, for her unselfish support, patience and encouragement.
The author wishes to thank everyone at Terra Testing, Inc. for
their encouragement and assistance. Finally, thanks are also due to
Mrs. Sherry Smith for the wonderful job of typing this manuscript.
n
ABSTRACT
Slab-on-ground foundations refer to ground supported floor
slabs used to transfer loads safely to the subgrade without under
going distress themselves. These foundations have been used in
residential, light commercial and industrial buildings for many
years. Since the loading conditions and magnitudes in industrial
buildings are wery different from those in residential and light
commercial buildings, their design must be approached differently.
Various design procedures have evolved for the thickness design of
industrial floor slabs, but most of them have been developed for a
specific use or have certain limitations. Therefore, there is still
a need for a rational design procedure which will eliminate some of
these limitations.
In order to develop a rational design or analysis procedure, a
parametric study involving slab length, slab width, slab thickness,
modulus of elasticity of soil, aisle width between stacks, stack
loading, and forklift loading was conducted to study their influence
on deflections, bending stresses, bending moments, and shear forces
occurring in the slab. The study was conducted by considering the
influence of stack and forklift loadings, both separately and
together. The values used in the study were over a realistic range.
Regression analysis was performed on the results of 618 individual
problems and equations for the thickness design of industrial floor
ii i
slabs were developed. Correlation coefficients for these equations
ranged from 0.78 to 0.99.
As the modulus of elasticity of the soil is an important
parameter in the design of industrial floor slabs, a survey of eight
practicing engineers and commercial testing laboratories was con
ducted to determine the most practical and economical means of
evaluating the modulus of elasticity of soil.
Equations rather than nomographs have been developed for
maximum bending stresses, maximum shear forces and maximum differen
tial deflection for each loading condition. These equations permit
solving for the required slab thickness to resist the imposed loads.
TV
CONTENTS
ACKNOWLEDGEMENTS ii
ABSTRACT i i i
LIST OF TABLES viii
LIST OF FIGURES x
1. INTRODUCTION 1
1.1 Concrete Floor Slabs 1
1.2 Winkler Foundation 2
1.3 Previous Work 4
1.4 Scope of Research 22
2. A BRIEF INTRODUCTION TO APPLICABLE THEORY 24
2.1 Introduction 24
2.2 A Brief Review of
the Theory of Plates 25
2.3 Finite Element Method 26
2.4 Finite Element Computer
Program, SLAB4 27
3. EVALUATION OF MODULUS OF ELASTICITY OF SOIL 32
3.1 Introduction 32
3.2 Characteristics of the Modulus of Elasticity of Soil 33
3.3 Testing Procedures for Determining Modulus of Elasticity of Soil 37
3.4 Evaluation of the Most Practical and Economical Testina Procedure ^4
4. PARAMETRIC STUDY 49
4.1 Introduction 49
4.2 Material Parameters 50
4.3 Structural Parameters 53
4.4 Utility Parameters 55
4.5 Accomplishment of Parametric Study 66
5. DEVELOPMENT OF REGRESSION EQUATIONS ".. 74
5.1 Introduction 74
5.2 Regression Analysis 74
5.3 Development of Regression Equations 75
5.4 Discussion on Regression Equations 81
5.5 Limitations of Using the Regression Equations 83
5.6 Analysis of the Regression Equations 86
6. DESIGN PROCEDURE USING
THE REGRESSION EQUATIONS 92
6.1 Introduction 92
6.2 Soils Investigation 92
6.3 Safety Factor 93
6.4 Design Procedure 94
7. CONCLUSIONS AND RECOMMENDATIONS 98
7.1 Introduction 98
7.2 Conclusions 98
7.3 Recommendations 101
VI
LIST OF REFERENCES 103
APPENDICES
A. USER' S GUIDE FOR COMPUTER PROGRAM SLAB4 108
B. LISTING OF PROGRAM SLAB4 WITH SAMPLE OUTPUT 122
C. QUESTIONNAIRE FOR SURVEY 184
D. VALUES OF DESIGN PARAMETERS DUE TO FORKLIFT LOADING AT 15 LOCATIONS USED IN QUASI-STATIC ANALYSIS 188
E. COMPARISON OF RESULTS FOR DIFFERENT ASPECT RATIOS OF FINITE ELEMENT 205
F. STRESS, MOMENT, SHEAR, AND DIFFERENTIAL DEFLECTION RESULTS FROM PARAMETRIC STUDY 207
G. MOMENT EQUATIONS 237
H. DESIGN EXAMPLE USING EXISTING PROCEDURES 238
I. DESIGN EXAMPLE USING THE REGRESSION EQUATIONS 243
J. A COMPARISON BETWEEN THE PCA METHOD AND THE REGRESSION EQUATIONS 252
v n
LIST OF TABLES
1.1 Vehicle Categories 17
1.2 Traffic Categories for Design Index 18
3.1 Means of Weights of Relative
Importance Assigned to Variables 46
3.2 Computed Weights and Their Sums 47
4.1 Variation in Values of Design Parameters Due to Variation in E 52
4.2 Maximum Deflection Values Correspondi ng to E Val ues 54
4.3a Comparison of Values of Design Parameters with Stacks Oriented Along the Long and Short Directions of a Slab with an Aspect Ratio of 1.33 57
4.3b Comparison of Values of Design Parameters with Stacks Oriented Along the Long and Short Directions of a Slab with an Aspect Ration of 4.0 58
4.4 Details of Forklifts Used in the Analysis 60
4.5 Ratios of Values of Design Parameters for Forklift Loading Alone at Locations Where Maximum Values Occurred with Respect to Values at Position 1 63
4.6 Ratios of Values of Design Parameters for Stack and Forklift Loadings at Locations Where Maximum Values Occurred with Respect to Values at Position 1 64
4.7 Ratios of Values of Design Parameters with Forklift Truck Oriented Perpendicular to the Aisle with Respect to Values with Forklift Truck Oriented Along the Aisle 67
4.8 Values of Parameters Used in the Parametric Study 70
viii
5.1 R-Squared Values from Regression Analysis for Principal Equations 84
5.2 Increase in Design Parameters Due to Increase in Slab Thickness 91
6.1 Comparison Between Regression Equations and Existing Procedures 97
IX
LIST OF FIGURES
1.1 Subgrade and Slab Stiffness Relationship 5
1.2 Uniform Load Design and Slab
Tensile Stress Graphs 6
1.3 Wheel Loading Design 7
1.4 Design Graph for Axles with Single Wheels 9
1.5 Design Graph for Axles
wi th Dual Wheel s 10
1.6 Design Graph for Post Loads 12
1.7 Effective Load Contact Area Depends on Slab Thickness 13
1.8 Design Curves for Concrete Slabs: Warehouse Fl oors and Open Storage Areas 15
1.9 Design Curves for Concrete Slabs: Warehouse Floors and Open Storage Areas (Category VI, Forkl i fts) 16
1.10 Design Curves for Slab-on-Grade - Central Loadi ng 19
1.11 Design Curves for Slab-
on-Grade - Edge Loading 20
2.1 Def 1 ecti ons Due to Loadi ng 29
2.2 Stresses Due to Loading 30
3.1 Gibson Soil Model 35
3.2 Mixed Stratigraphy Model 36
3.3 Load-settlement Curve from Plate Bearing Tests 39
3.4 Variation of f. with Plasticity Index 42
x
3.5 Impact Value versus Elastic Modulus from Theory and Tests 43
4.1 Locations of Forklift for
Quasi-Static Analysis 62
4.2 Forklift Along and Perpendicular to Aisle 65
4.3 Combination of Parameters for Stack Loading Condition 71
4.4 Combination of Parameters for Forklift Loading Condition 72
4.5 Combination of Parameters for Stack Plus Forklift Loading Condition 73
5.1 Comparison Between Computer Analysis and Regression Equations 87
XI
CHAPTER 1
INTRODUCTION
1.1 Concrete Floor Slabs
A need for an economical foundation for residential and light
commercial buildings following World War II led to the use of ground
supported slabs, usually referred to as slab-on-ground, or slab-on-
grade if the subgrade has been prepared. The term "slab-on-ground"
is applied to both unreinforced and reinforced floor slabs. These
slabs have been grouped (7)* into four categories based on the
amount of reinforcement provided. The four categories are:
1. Plain concrete slabs.
2. Plain, nonstructurally reinforced slabs.
3. Structurally reinforced slabs.
4. Post-tensioned slabs.
Although plain concrete slabs have the advantages of economy
and ease of construction, it has become a practice to provide a
minimal percentage of reinforcement in all plain concrete slabs to
compensate for shrinking effects. Thus, in practice the first two
categories complement one another and therefore when plain concrete
floor slabs are referred to both here and elsewhere, it implies
concrete slabs with shrinkage reinforcement. Plain, nonstructurally
*Numbers in parentheses refer to entries in the List of References
1
2
reinforced slabs have also been found to be economical and have been
successfully used for a wide variety of loading and site conditions.
Structurally reinforced and post-tensioned slabs have been used
where unusual loading or very poor site conditions were anticipated.
In general, a concrete floor is expected to give good service
for many years without deteriorating. In particular, large area
concrete floors for industrial buildings must be designed and
constructed with the greatest possible economy to give trouble free
service. However, in spite of these requirements and in spite of
being in use for many years, their design has been more of an art
than a science. Various design procedures have evolved in recent
years for slab-on-ground foundations in residential and light
commercial buildings (7,15,25,46,53). On the contrary, less atten
tion has been paid to the development of a design procedure for
these foundations in industrial buildings. The few procedures
available to assist in the thickness design of industrial floor
slabs have a shortcoming in common, i.e., the inappropriate modeling
of the soil. All of them model the soil as a Winkler foundation.
Why modeling the soil as a Winkler foundation is inappropriate is
explained in the following section.
1.2 Winkler Foundation
Winkler, in 1867 (52), proposed that the deflection of the soil
surface can be modeled by a simple equation:
p = kw (1.1)
where
p = pressure acting on the soil surface, psi
k = proportionality constant called modulus of subgrade
reaction, pci
w = deflection of loaded region, in.
Over the years engineers have made use of Winkler's model because of
its simplicity in representing the soil in soil-structure inter
action analyses. Many empirical formulae were proposed for k, even
though there is no unique value of k for soil. The modulus of
subgrade reaction is not a property of the soil alone; it also
depends on the rigidity of the structure, duration of loading,
loading type and depth of soil medium. Other limitations of
modeling the soil as a Winkler foundation are discussed below.
For instance, in the field when a load is applied on a semi-
infinite elastic half space the surface deflects not only under the
load but it also deflects in the neighborhood of the load with the
magnitude of deflections diminishing with distance away from the
load. With the Winkler model only the surface under the loaded
region will deflect.
The differential equation for slab on elastic foundation is:
Dv w + kw = p(x,y) (1.2)
where D is the flexural rigidity of the plate. Consider a uniform
slab carrying a constant uniform load, p , over the entire slab.
The solution of the governing equation (1.2) for a free edge condi
tion (zero bending moments and shear forces) is a constant displace
ment indicating that there is no bending moment or shear force in
the slab. We know that this is not true because under any given
loading, the slab will experience some bending moment and shear
4
force. Therefore, the design of slabs on ground with the Winkler
assumption will yield unsafe results if the slab carries fairly
large and uniformly distributed loads.
1.3 Previous Work
Design procedures for industrial floor slabs-on-ground were
primarily based on experience or they were accomplished using one of
the following:
1. The Corps of Engineers method (12).
2. The American Concrete Institute method (2).
3. The Concrete Reinforcing Steel Institute method (10).
These methods were found to be more empirical (based on per
formance experience) than rational by researchers in this area
(29,30) and that there was a need for a rational design procedure.
As a result, a number of attempts have been made and there are a few
procedures available today to assist in the thickness design of
industrial floor slabs. These procedures are briefly discussed
here.
1.3.1 Panak's Method (29,30)
The first reported rational design procedure was that of Panak.
He studied deflections, stresses, and moments in large area concrete
slabs using the discrete element slab theory (21) over a range of
practical variables. From the analysis, he developed graphs shown
in Figures 1.1, 1.2 and 1.3. The graph shown in Figure 1.1 provides
a ratio of the slab stiffness to the modulus of subgrade reaction
D/k, required in subsequent graphs. It is based on assumed
CVi
c o •r-+J to 0)
a: CO (/I
C
</)
fO
"O
c
<u
.a 3
t/1
i-=3
O ^ ro oj = o O <Ti CO jv* CD i n
Nl SS3NX3IH1 9V"1S
O < "• u. 5 w»
3
o o a o o o o o o O 00 CD
O o
o ^ ^ -
(u/»*-qi) iN3i/^oi^ 9NiaN3a a v i s lAini/Mixvw /
i l l I I I/I I—I i H l l l I I—I 1 II I I I O \ n c v i — i n c v j — i n ~ / Ci C> O O
O O ^ O o O Q Q Q 00 o <>J
CM
+->
CO - C
Q . fO s-
as
to a> s-
• M
cu
to
n3
• o c ea
c en
•r— to
• a
o
E S -
o
CO
cu s-3 CD
(u /u -q i ) 1N3IAI0IAI 9NiaN3a avis 1/ niAiixviAj
5 10 15 20
EQUIVALENT LOADED DIAMETER -
Figure 1.3: Wheel Loading Design (after [29])
m.
8 thickness of the slab and known values of concrete modulus and
effective subgrade modulus. The graph shown in Figure 1.2 provides
design bending moments in terms of aisle width, D/k ratio, and
magnitude of uniform loading. The graph shown in Figure 1.3 pro
vides design bending moments for a loaded forklift on the slab in
terms of single wheel load, distance between load wheels, effective
tire footprint diameter and D/k ratio. The work of Panak was the
first step towards developing a rational design procedure for
industrial floor slabs-on-ground and has been incorporated into the
Wire Reinforcement Institute (WRI) and the American Concrete Insti
tute (ACI) methods.
Though still considered to be the most rational design pro
cedure available, Panak's method has shortcomings. The primary
shortcoming is that the soil has been modeled as a Winkler founda
tion. The other limitation of this method is that short term values
of m.odulus of subgrade reaction have been used in the analysis and
even if long term value (needed in the case of clayey soils) can be
determined, the design graphs do not permit their use in design.
Also, it has been reported by Wray (53) that the length and width of
the slab influence the values of design parameters such as moments
which have not been considered by this and other procedures dis
cussed in the following sections.
1.3.2 Portland Cement Association (PCA) Method (28)
The design graphs included in Figures 1.4 and 1.5 are based on
computerized solutions by Packard (27) and on Pickett's formulae
4 0 i
o.
d^oi < o -1
y 20-: < :
a 15-
R ' o o
-r '°-LJ 9 -
8 -co !S 7 : ^ 6-CO
5-
4--
3-
^^ —
\ ^
_ ^
WI-
V
\
IFF
\
\ \
\
\ ^
~ ^
\
^
\ ,
A \ '
•1 .N SPACING^ in.
, _ ^ 1
/
k
4ri ^
20^
ci
t s
,1
-f^
^ 1
yS
> /
•
^
• ^
N. ^
2 D I AT
1
V 1 /
y v r—
/
• ^~
/
' 'OOy^ ^ 200
!
EFFECTIVE
:\REA isa m.
\\^ 1
.10
.8 CO
7 Z^
y 50 100 '200 SUBGRADE k. pci.
Figure 1.4 Design Graph for Axles with Single Wheels (after [28])
10
0.90
0.85
O80
0.75
0.70
0.65
0.60
0.55
O I-O
£ <
o
liJ
I O UJ
0.50
1.5: Design Graph for Axles with Dual Wheels (after [28])
11
(31). The graphs were developed for a Poisson's ratio of 0.15 and a
concrete modulus of elasticity of 4000 ksi. The graphs for concen
trated wheel loads were developed considering the flexural strength,
factor of safety, wheel spacing, effective wheel contact area and
modulus of subgrade reaction. Post load graphs, such as the one
shown in Figure 1.6, were developed for other modulus of subgrade
reaction values of 100 pci and 200 pci, based on Hetenyi's method
(17). Figure 1.7 provides effective contact area which is based on
load contact area and assumed thickness of the slab. When analyzing
for dual wheels. Figure 1.5 is used to obtain an equivalent load
factor which is based on dual wheel spacing, effective contact area,
and assumed thickness of the slab. The equivalent load factor is
multiplied with the dual-wheel axle load to obtain the equivalent
single-wheel axle load, which is then used with other values in
Figure 1.4 to arrive at the required thickness of the slab.
In this procedure, the soil beneath the slab is modeled as a
Winkler foundation and also, long term values for the modulus of
subgrade reaction have not been included. Panak (30) reports in his
work that the negative moments in the middle of the aisle for a
uniform loading condition with aisleways approximately 10 ft or less
in width were found to control the design, indicating that the aisle
width and uniform loading are important parameters that need to be
considered. But these parameters have not been considered in
developing this procedure.
12
N
/ /
\
\ V ^
V"'
?(iin
/ /
/ / J
\
\
\
\ \
\
V \
1 1
1
V19' \ 1 V eo\
100
/
/
\
/
SUE
1
• — H I
1
X
/ \
y
/
^ ^ ^
' / /
k V ^
V V
?ol/ ^ 6 0 / ^100 V
GRADE k 5 0 pel
/
, i i
/
A
•? "fi:
/
/
S
14
13
12 -cn en
II ^
10 y X
8 < - J CO
6
5
80 40 20 10
EFFECTIVE CONTACT AREA
sq in. Figure 1.6: Design Graph fo r Post Loads (af ter [28])
13
LOAD CONTACT AREA, sq in.
Figure 1.7: Effective Load Contact Area Depends on Slab Thickness (after [28])
14 1.3.3 Corps of Engineers Design
Curves (4,13,14)
The design curves shown in Figures 1.8 and 1.9 were produced
from computer solutions based on Westergaard's formula (48) for free
edge stress with some joint transfer ability. The curves were based
on a transfer coefficient of 0.75, an impact factor of 25 percent, a
concrete modulus of elasticity of 4000 ksi and a Poisson's ratio of
0.20. The variables considered are: modulus of rupture at 28 days,
wheel spacing, axle loading, wheel contact area and modulus of
subgrade reaction. To account for different types of vehicles and
traffic volumes. Category I, II, III, IV, V and VI have been ex
pressed in terms of equivalent operation of a basic axle loading.
The basic loading was assumed to be a 25,000 lb single-axle load
with two sets of dual wheels spaced 52 inches apart with 11 inches
between dual wheels. These categories are included in Table 1.1.
Also, a parameter called "design index" has been included to express
various axle loads and traffic volume in terms of relative severity.
Table 1.2 contains these design index values.
In developing the curves, the soil beneath the slab has been
modeled, as a Winkler foundation and, therefore, requires a modulus
of subgrade reaction value. The procedure considers only the wheel
loading condition and even for this, the categories used are based
on some arbitrarily selected loading.
1.3.4 Corps of Engineers Curves (34,35)
The curves shown in Figures 1.10 and 1.11 were developed by
Ringo using Westergaard's formula (48). These curves were plotted
15
CO UJ
o
(f) en u
it:
o X I-\-z: UJ
UJ
I
540
Figure 1.8: Design Curves for Concrete Slabs: Warehouse Floors and Open
Storage Areas (after [13])
16
(n X o I
en u z it: o h-
I-
UJ
UJ >
2
540
Figure 1.9: Design Curves for Concrete Slabs: Warehouse Floors and Open Storage Areas ' (Category VI, Forklifts) (after [13])
17
CO
to OJ
s-o Ol O) 4J rtJ
OJ
OJ
(O + J fO o
a o>
•r-CO CD
O
t — 1
>
>
> 1—4
1—t
t — 1
1—4
t — 1
» - H
t—H
> 1
s-o CT (D +-) ro
C_3
O O O CJ I D
O O O O CM
O O O *X) 1—1
O O O o T—t
o o o »XJ
o o o ' ^
to j Q
»_^
> , 4-> •r— O 03 Q . ea
e )
o o o o CM 1—1
o o o CO • ^
o o o <o CO
o o o un CM
o o o ID I—1
o o o o T—1
to X i r— "— -a as o
- J
(U
to •r—
ca:
a C7>
to CD
Q
ȣ>
•^
«£>
<X)
«>f
^
to (D S_
• r-1—
M-O
S-CU
J 3 E 3
z :
o •^ 4-J «3 E =3
. (D C
O •^ 4-> rt3 E 3
Pne
o • 4-> «o E =3 <D C
o .
(J •^ -M «o E 3
Q-
"O • I —
r— o
CO
-o •r—
r— o
oo
<D S-
• 1 —
1—
M-O
CD C L >>
h-
*£> I—1 CO
cr> 1—1
T—t
o o f—1
LD •
CM ^£)
1—1
• VO CO
o •
t ^ CM
rtJ CD s-
< :
- • - > o fO
4 - > ^ - ^
c • o c
O - 1 -
<D • s_ cr
•r- to 1— ^-^
i n CT>
o cy>
o cr»
o o t—i
<X) o CM
U^ CO t — t
+-> (J (T3 +->- -^ C - i -O to
o o. • — ' •
CD > <D
• I - S -
+-> 3 (J to CD to
M- CD M- S-UJ Ci.
O 1—1
CT>
CT
0 0
r^
W3
— .
c •r-
• • ^ » '
x : +-> • o • 1 —
2 CD s-
•f—
h-
o CO
1 <T»
20
-7
CO 1—1
1 CO t n
1 CO 1—1
CO I—1
1 CO LO
1 CO t—1
»—1
I—1 1
CVJ LO
1 f—1
.—1
CO CO
1—1
CO
• c
• 1 —
-—' CD c
•r— U (O a.
LD
— CD CD
.c s
CM cr> 1—1
*:i-'^f T—l
«^ «;l-1—1
CM CO I—i
o CT>
O C3
'--^ .
c •r—
' —'
.^ 4-> •o •n-I S
CD — to
•n-
<c
^
- > * •
«51-
co
1 1
1 1
r— (T3 13
Q ^ -
• S= C <D • • -OJ v _ ^
S +J to CD CD
J D S-• 1 —
C7>|—
a •r- r—
u a> (T3 CD
to 3
18
CO
X
•o
CD •r-to (D
O
S-o
<+-
to CD
S -
o C D CD
O
CM
CD
to c o
•r-• » - >
fC >> S- ro CD O Q .
O S-CD
E Q . Z3 E
•r— X to
-a rtj o
_ i
X CD
• o c
t—l
c c^
•r-to <D
Q
O LO
. ^ U =3 S-
+J
+-> M-• n -r— .:K:
s-o
<+--o rT3 O
r— 1
CD ^— X fO
Q . •r— .ii^
o I—1
1—1
o o un 1—1 CM
J>^ . ^ CJ u r j 3 S- S-
+-> •«->
+-> 4-> C4- M-
r^ ^— J!^ .^ s- s-o o
4 - M-
T3 - O n3 fO O O
1 1 CD CD
^ ^ P"" X X (T3 (Q
Q . a .
. ^ .:><:
O un T - l 1—1
CM
o o LO O CM .—1
. ^ .^ CJ CJ 13 :3 S- i_
-(-> +-> 4-> ^J 4 - M-
r— r— j » : .:>£ s- s-o o
4 - M-
-o -a <n m o o 1 1
CD CD r^ r"" X X <0 (O
CL Q .
. : i ^ . ^
o i n 1—1 1—1
CO
o Ln LO CM
. ^ jid:
o u 3 3 S_ S-
-»-> +-> +J +-> M- «4-
r— r^ J ^ Ja<£ S- S-o o
4 - 4 -
• o - o fO m o o 1 1
CD CD ^— r"~ X X m ro £DL Q .
.i^ Ji^
LD i n t - l CM
• ^
19
< O -J UJ -J X <
u. O Q. "^
c
3 CO
CO en UJ oc
S A F E T Y FACTOR AND MODULUS OF RUPTURE NOT INCLUDED WITHIN THE GRAPH
CONTACT AREA 25 sq in. SHRINKAGE COMPESATING CEMENT CONCRETE SOLID TIRES; TWO PER AXLE
SUBGRADE MODULUS
K 50. pel 100.
S=30 in.
S=30ln.
S=40in.
60 40 30 (4)
WHEEL SLAB THICKNESS H, in. SPACING,in.
Figure 1.10: Design Curves for Slab-on-Grade - Central Loading (after [34])
20
THE GRAPH
SUBGRADE MODULUS K 50. pc»
100. 200. 300.
S=30 in.
5=40 in.
S=60 in.
60 40 30 (4)
WHEEL SPACING, in.
6 8 »o le
SLAB THICKNESS H, in.
(14)
r.irvps for Slab-on-
21
for specific use and were based on a transfer coefficient of 0.25,
Poisson's ratio of 0.20, wheel area of 25 sq in. and a concrete
modulus of elasticity of 4000 ksi. The variables that were con
sidered are allowable concrete tensile stress per 1000 lbs of axle
load, wheel spacing, and modulus of subgrade reaction.
The curves have been developed by modeling the soil as a
Winkler foundation and do not include the long term values. Also,
the curves consider only one contact area, namely, 25 sq. in.,
implying that they have been developed only for a specific use. The
curves further consider only the wheel loading condition and do not
include uniform (stack) loading condition.
1.3.5 Interactive Computer Solution (36)
The program has been developed by Ringo and Steenken on a soft
disk for a microcomputer. Westergaard's six loading cases (48,49)
based on the classical Hertz solution have been programmed. The
variables that were considered are modulus of rupture, factor of
safety, joint transfer coefficient, Poisson's ratio, axle load,
wheel spacing, wheel area, aspect ratio of wheel area, and modulus
of subgrade reaction. The program provides the thickness required
for the concrete slab based on the above variables.
The solution is based on modeling the soil as a Winkler founda
tion and requires a value for the modulus of subgrade reaction. It
also considers only the wheel loading condition.
22
1.4 Scope of Research
Although there are a number of design procedures already
available to assist in the thickness design of large area or indus
trial type floor slabs, most of these procedures have been developed
for a specific application or by considering only a limited number
of variables over a limited range of values. Therefore, the purpose
of this dissertation is to analyze the slab-on-ground used for
industrial appilcations and to develop a more rational design or
analysis procedure which will overcome the shortcomings of the
existing design procedures.
Based on extensive literature review, it was found that slab
length, slab width, slab thickness, modulus of elasticity of soil,
aisle width between stacks, stack loading and forklift loading are
considered to be important in the design of an industrial floor
slab. So, in order to develop a rational design or analysis
procedure, it was proposed to conduct a parametric study involving
the above parameters to study their influence on deflections,
bending stresses, bending moments, and shear forces occurring in the
slab.
The study would be conducted over a realistic range of values for
the parameters mentioned above. The soil was modeled as an elastic
continuum and a finite element FORTRAN program called SLAB4 was used
for the analyses. The theory and structure of this program is
discussed in Chapter 2.
In order to model the soil as an elastic continuum, the values
of Poisson's ratio and the modulus of elasticity of the soil are
23
used in the analysis. To enable the design engineer to decide on a
method of evaluating the modulus of elasticity of the soil to be
used for the analyses, a survey was conducted on some of the com
monly available testing procedures. Based on the survey, the most
practical and economical means of evaluating this property is
recommended. Details of the testing procedures considered, the
survey, the analysis, and the recommendation are presented in
Chapter 3.
Details of the parametric study, such as parameters considered,
combinations of these parameters, and range of values used for these
parameters are presented in Chapter 4. Discussion on the regression
analysis used to develop the regression equations and the equations
themselves are presented in Chapter 5. A different design procedure
based on regression equations rather than nomographs is presented in
Chapter 6. Finally, conclusions regarding the results of this study
and how well the principle objectives were achieved, along with some
recommendations, are presented in Chapter 7.
CHAPTER 2
A BRIEF INTRODUCTION TO APPLICABLE THEORY
2.1 Introduction
Application of the principles of soil mechanics to the behavior
of structures in practice has explained the behavior of structures
supported on soil reasonably well. The reason for this is that the
behavior of a structure and the underlying soil are interdependent
and, therefore, they need to be analyzed together. This understand
ing has changed the approach to solving soil-structure interaction
problems. For instance, slab-on-ground foundations are being
analyzed by representing the problem as a plate resting on an
elastic foundation (8,19,20,47,53). The problem of bending of a
plate resting on an elastic foundation can be solved in closed form
only for a relatively small number of boundary conditions and,
therefore, approximate numerical methods have to be used.
A finite element program (a numerical method) was developed
(8,19,20,47,53) to analyze concrete slabs-on-ground by representing
the problem as a plate on an elastic continuum. As the objective of
the study reported herein was to develop a rational design procedure
for thickness design of industrial floor slabs and not to develop a
numerical procedure to conduct the parametric study, the existing
finite element program, with suitable modifications and now called
SLAB4, was used. The structure of the program is explained in
24
25
Section 2.4. Also, a brief introduction to the theory of plates and
the finite element method are given in the following sections.
2.2 A Brief Review of the Theory of Plates
To a large extent, bending properties of a plate depend on its
thickness. There are two types of plates: thin plates and thick
plates. A plate is said to be thin if its ratio of thickness to the
smaller span length is less than 1/20; otherwise it is said to be a
thick plate. Associated with these two types of plates are three
types of problems, namely:
1. Thin plates with small deflections.
2. Thin plates with large deflections.
3. Thick plates.
By small deflections it is meant deflections that are smaller than
or equal to the thickness of the plate.
Analysis of thin plates subjected to lateral loads (loads
applied perpendicularly to the plane of the plate) are commonly
accomplished by using the linear theory which assumes that the
lateral displacements due to loads are small in comparison to its
thickness. This theory has been found to apply very well to rein
forced concrete slabs (43,55).
The linear theory, sometimes referred to as the classical
Kirchoff's theory of plates, is based on the following assumptions:
1. The middle plane is free from deformation.
2. Forces normal to the middle plane of the plate before
deformation remain normal after deformation.
26
3. The normal stresses in the direction perpendicular to the
plane of the plate can be disregarded.
Based on the above assumption, Kirchoff developed a theory in
which all stress components can be expressed by a single variable,
w, the deflection of the middle surface of the plate. The develop
ment and final equations for both isotropic and orthotropic plates
can be found in any standard textbook, (e.g., 43).
2.3 Finite Element Method
The advent of high speed digital computers with the aid of
approximate numerical methods have made it possible to solve prob
lems which were once not possible to solve by hand. Of the various
numerical methods known, the finite difference and the finite
element methods have been used extensively for plate bending prob
lems. The philosophy of the finite element formulation is consid
erably different from that of the finite difference formulation. In
the finite difference method, a numerical approximation is made to
the exact mathematical differential equation governing the problem
by concentrating on a number of selected values of the unknown
function at specified mesh points. In the finite element method,
the plate is divided into a series of small elements and these
elements are assumed to be joined only at specified nodal points.
Continuity, together with equilibrium, are established at these
points.
Of the two methods, the finite element method is often found to
be more adaptable because of such things as variations in material
properties, geometry, etc., can be more conveniently handled. The
27
formulation of this method can be found in any standard textbook
(e.g., 55).
2.4 Finite Element Program, SLAB4
After the development of the finite element method, it did not
take yery long to find applications for this method in the field of
civil engineering. The simplicity of formulation with capabilities
of handling odd geometric shapes and varying material properties has
made this method quite popular. Also, the systematic way in which
the procedure reaches a solution makes it well suited for program
ming on a digital computer.
The method of finite elements has been extended to the problems
of bending of slabs and a computer program was developed by
Zienkiewicz and Cheung (54) to analyze elastic, isotropic and ortho-
tropic slabs. Later it was used by Cheung and Zienkiewicz (8) to
analyze plates and tanks on an elastic (semi-infinite half space)
foundation. For their analyses, they assumed that the plates
remained in contact with the subgrade at all times. They demon
strated that there was very little additional difficulty in modeling
the subgrade as an elastic continuum. Boussinesq's equation (44) is
used to obtain the flexibility matrix of the subgrade, which is then
inverted to obtain the stiffness matrix. The stiffness matrix of
the subgrade is added to the stiffness matrix of the plate and the
unknown displacements are solved for, first and then the stresses
obtained. The program was then used by Wang, Sargious, and Cheung
(47) for the analyses of rigid pavements. The program was modified
to analyze two slabs (simulating two lanes of pavement)
28 simultaneously which were assumed to be connected by dowels that
were 100 percent efficient. Effects of temperature differentials
such as warping (cupping) were also included. This modified program
can handle loss of contact between slab and subgrade due to warping
and pumping. However, a major difficulty in terms of large computer
storage (memory) was required because the overall stiffness matrix
was not banded (due to the stiffness matrix of the subgrade). Huang
(19) developed an iterative scheme which makes the stiffness matrix
banded and solves the excessive storage problem. Huang (20) also
incorporated a scheme which makes use of symmetry, thereby further
reducing the storage required and also the time required to solve a
problem. The reliability of the results of an analysis using this
program was compared by Huang (19) with analytical and experimental
results. Based on the comparison, Huang reports that the deflec
tions predicted by the program checked reasonably well with experi
mental measurements and that the edge stresses checked within 6% of
analytical solution (Figs. 2.1 and 2.2). Wray (53) used the program
for analyzing slab-on-ground foundations for residential and light
commercial buildings supported on expansive soils. He modified the
program to be able to handle non-constant rectangular sections
(slab-on-ground foundations with stiffening beams), and also in
cluded a subroutine to calculate bending moments and shear forces.
The program with the above features was named SLAB2 by Wray (53).
Although all of the features described above are not required
for the analysis of an industrial floor slab, additional modifica
tions were made by the writer to make this program more efficient
29
LOAD y-FREE EDGE
t LOAD 'I UONGITUDINAL
JOINT
^H4iW4^ O
0.1 0.2
0.3
0 4
0.5
E E
I -o ui _i b-liJ O
7in.(l80mm)SLAB, 7,000 lb (31 kN) LOAD
' O
o UJ -J
UJ
o
lO 'O
8 in.(200mm) SLAB, 12,000 lb (53 kN) LOAD
z o » -o UJ - I u.
0
5
10
15
20
i
A ^o
X 7^ w
<
r ^Oin.
/ (51 cm) 1 1
^ ^ ^
1 •^ i> , i
\
0 .
kf M
) ^
> 0
0.1
0.2
0.3 0.4
0 5
E E
O I -
- I b . UJ O
9 in.(230mm)SLAB, 15,000 lb (67 kN) LOAD
FULL CONTACT -—PARTIAL CONTACT
o EXPERIMENTAL
Figure 2.1: Deflections Due to Loading (after [19])
30
UJ s
&> CO
(/>
< «
to K
Q CO
Ui - s CO 2 UJ > > <o ( O CO
z ^
Bco' t - CO — UI
q OT
& UI
i2 UJ CO > CO CO UJ Z IT
< h: Q: lO
^1 z . ^ CO O CO 3 Ui o CO
200
0
200
400
600
200
0
200
4 0 0
600
1 /
J »
ir-^
20 jr
^ ^ ^
1.
(51 cm) J 1
_-a ~ 0 - N . t ' "fc
t ^
^
-a_
CM
> CO CO
2
3
4
7 in. (180 mm) SLAB, 9,000 lb (40 kN) LOAD
• 9'
v" / f
r
fo- ^"o-i-"*"
20i!
'^ ^
1.
(51 cm) 1 i . . . .
0 Q -SL, *
• JO—O -rr-
S^"'1 V ^
«
2 3 4
8 in. (200 mm) SLAB, 12,000 lb(53 kN) LOAD
± 9_C
L , ^ - Q D
^ / V
«
rr^ ' ' ' *
••
u Tf
J
I
0
I
2
3
4
9 in. (230mm) SLAB, 15,000 lb (67 kN) LOAD
CO
H CO
-ICJ
I* - t CO
CM U J ^
i
» - CO iCM ii
O S gco t CO (!) UJ Z cc
UJ - ^
UJ ^
^ ^
t CO
_ l < ^
il I - CO
THEORETICAL - FULL CONTACT - PARTIAL CONTACT
EXPERIMENTAL o TRANSVERSE '^ LONGITUDINAL
Figure 2.2: Stresses Due to Loading (after [19])
31
when used in a parametric study such as the one being reported
herein. In order to study the behavior of a slab under both the
stack loadings representing the stored materials and the forklift
loadings, the program was modified to permit two loading conditions
of different intensities to be imposed simultaneously. Differential
deflections are an important aspect of the analysis and so an
additional routine to calculate the twenty greatest differential
deflection over distance ratios (A/1) has been added. These results
are now printed along with deflections, bending stresses, bending
moments and shear forces. Deflections, bending moments and shear
forces are printed both in the order of the finite element nodes and
also in ascending order of magnitudes. This program has now been
named SLAB4. A user's guide for program SLAB4 is included as
Appendix A and the program source listing with a sample output is
included as Appendix B.
CHAPTER 3
EVALUATION OF MODULUS OF ELASTICITY OF SOIL
3.1 Introduction
Analysis of slab-on-ground foundations have been carried out in
the past by representing the soil beneath the slab by a system of
springs (a Winkler foundation) having a constant modulus of subgrade
reaction, k^. Because of the simplicity of the model, it has been
quite popular and is still used by many engineers. Even though the
concepts of elasticity apply to soils only in a wery approximate
range, it would be more appropriate to model the soil as an elastic
continuum rather than modeling it as a Winkler foundation, for
reasons discussed in Section 1.2.
To represent the soil as an elastic continuum, the two basic
elastic properties, modulus of elasticity of soil, E and Poisson's
ratio of soil, v^ aJ e required. Despite trying to represent the
soil more realistically, the results of an analysis are only as
meaningful as the values of E chosen. Unfortunately, tabulated
values based on simple correlation are too often used. Therefore,
in order for any analysis to be meaningful, the value of the modulus
of elasticity of the foundation soil needs to be evaluated for the
site rather than assumed.
A number of testing procedures have evolved by which the value
of E can be estimated. Thus, an engineer is faced with the task of
32
33
choosing the type of testing procedure to make this empirical
evaluation. An attempt is made below to present the characteristics
of the modulus of elasticity of soil, some of the commonly available
testing procedures and, in a general way, to recommend the most
practical and economical way of evaluating E .
3.2 Characteristics of the Modulus of Elasticity of Soil
Although in many situations soil is assumed to be homogeneous,
isotropic and linearly elastic, in reality it is far from being so.
It is very difficult to represent the soil with all its complexities
and even with the assumptions, the complexity of the material has
its influence on E in the form of (22):
1. Stress history.
2. Stress level.
3. Soil type.
4. Time (thixotropic, aging and strain-rate effects).
5. Type of loading.
6. Soil disturbance.
Thus, it is clear that there can be no general value of E^ and,
hence, the modulus needs to be evaluated on a site-by-site basis.
The evaluation of E is not an easy task because of the above
factors. Associated with the complexity is its variability in both
the horizontal and vertical directions. The variation of E^ with
depth was first considered by Gibson (16). He considered the
influence of variation of E with depth on the stresses and dis
placements in an isotropic elastic half-space subjected to loading
34
normal to its plane boundary. The model proposed by Gibson, now
called Gibson's model, is given by:
E3 = E^ + n,.z (3.1)
where
E = modulus of elasticity of soil
E^ = modulus of elasticity of soil at the surface
m = slope
z = depth
The model is represented in Figure 3.1. Recently a study of fifteen
buildings in the Houston area for foundation settlements during
construction showed that the Gibson model successfully provided
elastic solutions for a soil (overconsolidated Beaumont clay)
exhibiting increasing undrained modulus with depth (50,51). For the
study, an equivalent constant modulus value was used. The equiv
alent constant modulus value will tend to increase with foundation
size, which is supportive of the Gibson model. However, large mat
and combined footings impact deeper soil masses and, typically,
require higher values of normalized modulus as a function of
increasing footing size. This concept of equivalent Gibson model,
which has shown to be useful for cohesive foundation media in the
Houston area, has subsequently been expanded to consider the
presence of sand layers within the supporting layers (Fig. 3.2).
At the present, variations in the horizontal directions cannot
be handled in any way but to use judgment tempered with experience.
35
f f / ^ / //?/y/////////
CLAY
EQUIVALENT CONSTANT Eg MODEL
GIBSON MODEL Ec= EQ+m-z
Figure 3.1: Gibson Soil Model (after [16])
36
• ^ ^ ^ ^ ^
CLAY
wzm^ SAND
CLAY
Eg FOR CLAY MODEL
Eg FOR MIXED MODEL-
GIBSON MODEL
Figure 3.2: Mixed Stratigraphy Model (after [51])
37
3.3 Testing Procedures for Determining Modulus of Elasticity of Soil
Generally, sophisticated testing procedures are used for
research purposes; on the other hand, simple and commonly available
testing procedures are typically used for obtaining soil properties
to be used for design purposes. Therefore, only the commonly
available testing procedures have been considered here. These
procedures include uniaxial compression test (triaxial test),
unconfined compression test, plate bearing test, California bearing
ratio test, pressuremeter test, static cone test, standard penetra
tion test, and vane shear test. The results of these various tests
have been correlated by others in earlier work to the modulus of
elasticity of soil. The various correlations with references are
given below.
3.3.1 Uniaxial Compression Test
The modulus of elasticity of soil is obtained from the stress-
strain relationship of the soil. The slope of the tangent drawn to
the initial point is called the initial tangent modulus and the
slope of the line joining any two separate points is called the
secant modulus. The initial tangent modulus is reported to be used
quite often, but it has been recommended (22) that the secant
modulus value obtained by picking the initial point and a point
corresponding to 1/2 or 1/3 of the peak deviator stress be used.
38
3.3.2 Unconfined Compression Test
The modulus of elasticity value from this test is said to
correspond to one-half the ratio between the failure stress and its
corresponding strain (38).
3.3.3 Plate Bearing Test
From a series of plate load tests using plates of the same
shape but of different size, a curve is drawn between measured
settlement and loading (Fig. 3.3). Then the slope of this line is
related to E by (5):
[(1 - v^s^/^s^ ^w = '/ ^ ( • '
where
s = settlement, in.
q = loading on footing, psi
B = width of footing, in.
E = modulus of elasticity of soil, psi s
V = Poisson's ratio of soil s
I = influence factor which depends on shape of footing and w
its rigidity (refer to Table 5.4 in Ref. 5)
3.3.4 California Bearing Ratio Test
In situ California bearing ratio value is approximately related
to E^ by (11):
E = 500 X CBR (3.3) s
where
E = modulus of elasticity of soil, psi s
CBR = California Bearing Ratio
39
i
qB ^ Es >^ w
0 0
qB
Figure 3.3: Load-Settlement Curve from Plate Bearing Tests (after [5])
40
3.3.5 Pressuremeter Test
The modulus of elasticity of soil is obtained from the pres
suremeter test using the following relationship (24):
h = ^sp (3.4)
where
a = structural coefficient = 2/3 for clays
= 1/2 for silts
E^ = modulus of elasticity of soil, tsf
E^ = spherical modulus of elasticity, tsf
3.3.6 Static Cone Test
The static cone results are related to E by (37):
E3 = 2q^ (3.5)
where
, Kg/crr
2
E = modulus of elasticity of soil, kg/cm'
q = cone resistance value, kg/cm
3.3.7 Standard Penetration Test
The blow count values of the standard penetration test are
specifically related to E by (5):
E = 10 (N + 15) for sands (3.6)
E = 6 (N + 5) for clayey sands (3.7)
where
E = modulus of elasticity of soil,ksf
N = field blow count/foot
and is generally related to E by (41):
E^ = 130 f. N (3.8)
41
where
2 E = modulus of elasticity of soil, kN/m
f. = constant value
2
The value of f. ranges from 4.0 to 6.0 kN/m , based on the plasti
city of the soil. The relationship between f. and plasticity index
is illustrated in Fig. 3.4.
3.3.8 Vane Shear Test
The relationship between the results of the vane shear test and
E is given by (26):
E, = (T/e I d^) (3.9)
where
T = torque required to generate a rotation of
e = angular rotation
d = diameter of blades
IQ = 2/N H/d ([S^]"^{r*})^r*}
The undrained modulus of a saturated soil is said (26) to be easily
obtained from T vs. e plot.
3.3.9 Clegg Impact Test
The relationship between the results of the Clegg impact test
and E is given by (9): s
L = u.u/ ^Liv;
where
E = 0.07 (CIV)"^ (3.10)
E = modulus of elasticity of soil, MPa s
CIV = Clegg impact value
The above relation is illustrated in Fig. 3.5.
8 i
42
6
4H
2-
• _ • .
• LONDON CLAY o BOULDER CLAY o LAMINATED CLAY D BRACKLESHAM BEDS -I- KEUPER MARL • FLINZ
. 4 (kN/tn )
10 20 30 40 50
— • • .
60 70 PI(%)
A OXFORD CLAY AKIMMERIDGE CLAY • WOOLWICH a READING SUPPER LIAS CLAY
lo 20 30 40 50 60 70 PI(%)
Figure 3.4: Variation of f| with Plasticity Index (after [41])
43
o CL
CO
O O
O
CO < -J Ld
500
200
100
50
20
10
10 psi FROM VAN TIL et aL (45)
#
-107/psi / / / FROM U.C. TESTS ON CEMENT STAB, CRUSHED ROCK.
FROM THEORY Es = .07(IV)'
E 2 ' = 1 . 6 6 ( I V ) ^ - 2 . 9 7
•16* psi (AVE. CONFINING STRESS 85kPa)
I I '
20 40 60 80 100
IMPACT VALUE Figure 3.5: Impact Value versus Elastic Modulus from Theory and Tests (after [9])
44
This procedure, which is relatively new in the United States,
came to the attention of the writer much after the survey, explained
in Section 3.4, was conducted. Therefore, this procedure will not
be found in the survey but has been included here to enable the
reader to be up to date on the procedures available to evaluate the
modulus of elasticity of soil.
3.4 Evaluation of the Most Practical and Economical Testing Procedure
The testing procedures described above have their advantages
and disadvantages, but their relative merits are not apparent to
most users when choosing one testing procedure over another.
Therefore, to enable the design professional to choose an appropri
ate testing procedure, a survey was conducted among eight geotech-
nical testing laboratories located across the state of Texas and
four competent individuals from universities.
The survey included an evaluation procedure based on the
following variables (a) availability, (b) reliability, (c) famili
arity, (d) cost of equipment, (e) cost of test, (f) interpretation
of results, and (7) ease of performance. The relative importance of
each of these seven variables was weighted by three knowledgeable
individuals according to the following scale:
1. Very important.
2. Important.
3. Neither important nor unimportant.
4. Unimportant.
5. ye.ry unimportant.
45
The means of these weights were computed and tabulated. The results
are shown in Table 3.1.
The individual variables considered in the evaluation procedure
were weighted on a scale of 1 to 5 in relation to a testing pro
cedure as shown in the sample questionnaire survey included in
Appendix C. For example, this writer would weigh the availability
of unconfined compression test as "1", since it is very likely that
most geotechnical testing laboratories will have the capability to
conduct this test. On the other hand, this writer would weigh the
availability of the pressuremeter test as "5", since it is wery
unlikely that everybody will have the facility to conduct this test.
The results of the survey were compiled and the means of the
weights of all the variables corresponding to each testing procedure
were calculated. These means were then multiplied by the corres
ponding means of weights of relative importance given in Table 3.1.
For example, the mean of weights corresponding to availability of
unconfined compression test was found to be 2.400. This was mul
tiplied by 1.333, which is the mean of weights of relative impor
tance of availability in the evaluation procedure, to give a value
of 3.199 (which can be rounded off to 3.2). The values thus
obtained were tabulated and are included in Table 3.2. The values
obtained for each variable were numerically added for each testing
procedure.
The lowest sum obtained corresponded to the most practical and
economical testing procedure.
Table 3.1: Means of Weights of Relative Importance Assigned to Variables
46
Variable
Availability
Reliability
Familiarity
Cost of Equipment
Cost of Test
Ease of Interpretation
Ease of Performance
Means of Weights of Relative Importance
1.333
1.333
2.667
3.667
2.333
2.333
2.667
47
E 3
I/O
s-*r" (U <~
I—
" O c fO
t o
(U
3
ited
- J o. E o o
CM
• CO Q)
JDi ro
\—
dure
*
cu o o J -
o . •»->
t n (U
1 —
0 0
p-*
VO
LO
-si-
CO
O J
t - H
(U
(O
S-fO
CsJ
un
VO
t—t
CO
i n
I T )
VO
«—1
CO
t — l
I D
r^
T—«
CM
CO
> » -»-> • r -
abi
• r" <T3 > <c
VO
CO
o^
CO
t - H
CO
r-
CM
CM
CO
«—1
CO
«—1
CO
0 0
CM
>> +->
bil
03
P _
CD Qc:
CM
o^
t - H
i n
CM
cy>
o t — l
C3^
i n
r^
VO
CM
CO
0 0
' ^
>> +-> •r—
iar
• r -E 03
U -
CM
O «—1
0 0
0 0
VO
CM 1—4
«—1
LO «—1
^ 1—«
1—t
cr>
CO 1—4
CM
cn
VO
CM r—1
pmen
t
•r— 3
cr U J
o -i-> CO O c_>
o
LO
CT>
CO
i n
L n
CT»
p ^
o VO
o
0 0
VO
CO
o i n
•»->
a; h-
V4-O
4-> t o
o o
^
LO
VO
i n
o
r*>.
CO
0 0
T—l
LO
t — l
VO
l O
CO
<T>
^
rpre
tati
on
c I - H
4 -O
OJ CO
<o U J
0 0
VO
0 0
^
0 0
VO
*d-
o T—l
CM
r^
o
0 0
LO
CO
r^ VO
orma
nce
<v O -
v + -O
CU to
m U J
^
LO
r^
CO CO
LO
en
en «—1
VO
C3^
.—1
^
cn
o LO
0 0
CM
o
o
Sum
^-. ^~ fO
X fO
Z. +-> 1 — to
00 H -4_> O) +-> c/) 1 — O to
O fO VO
O to »— o • r - to +-> C7^4-> - i -i n CD I/) c to S- + J to S- cu • • - CD <D 03 <U C L I — S- 1 — +-> &- +-> S- E "3 cu +-> to C ^ O O I C U S - E C U O !
E t j > c : c Q < u o c : » — o ••- +-> s- cu
< _ ) - a S - n 3 C U 4 - > C i _ S -CU fO "f- £ cu rtJ
1 — C C U C C U C T J C U
(O •>- ca s- s- cu s-.iz • 1 - V|_ O 3 D - fO V/1 X C <U 4 - to " O
f a o - M T - i n c u c c u • r - C J r O i — ( U C r O C £ Z C i — f O J - O - M f O
: 3 r 3 Q - C _ > C i _ C _ 3 C O > '
1 1 1 1 1 1 1 1
T - l C M C O ^ L O V D t ^ O O
cu s -
:edu
Proc
• • ->
to
48
From this analysis, the unconfined compression test was found
to be the most practical and economical testing procedure. The
standard penetration test and the uniaxial compression test ranked
second and third, respectively. However, it should be understood
that the findings are based on the survey which reflects the common
practices in this geographic region (southwestern U.S.). Therefore,
even though any one of these procedures could be used to evaluate
the modulus of elasticity of soil, it is recommended that their
respective applicabilities and reliabilities in relation to existing
conditions be clearly understood. For instance, the unconfined
compression test can be performed only on samples with some
cohesion. In addition, disturbance resulting from sampling
procedures in slightly cohesive soils can result in large errors in
the value of E . s
V
"c V
c
CHAPTER 4
PARAMETRIC STUDY
4.1 Introduction
The parameters involved in designing an industrial floor slab'
on-ground can be grouped into: (1) material parameters, (2) struc
tural parameters, and (3) utility parameters. Specifically, these
parameters include:
1. Material parameters
a. Modulus of elasticity of concrete, E
b. Poisson's ratio of concrete,
c. Modulus of elasticity of soil, E^
d. Poisson's ratio of soil, v
2. Structural parameters
a. Slab length, L
b. Slab width, W
c. Slab thickness, h
3. Utility parameters
a. Stack loading, p^
b. Forklift loading, p^
c. Aisle width between stacks, A^
In accomplishing this study, three of the material parameters
were assumed to be constant throughout the analysis. These three
parameters were the modulus of elasticity of concrete, Poisson's
49
50 ratio of concrete, and Poisson's ratio of soil. The values of these
three parameters, together with other assumptions made regarding the
range values and the reasoning behind them, are explained below.
4.2 Material Parameters
4.2.1 Modulus of Elasticity of Concrete, E c
A minimum compressive strength of 4,000 psi at 28 days is
usually recommended for any type of industrial or commercial floors
(40). Although lower strengths have been found to be adequate for
supporting the loads on these floors (40), the additional strength
is required to provide satisfactory resistance to wear. But to
account for variations in weather conditions at time of placing,
poor placing or finishing practices, variations in gradation of
aggregates, etc., a low value of 2,770 psi for compressive strength
was used in Eq. (4.1) to determine the modulus of concrete (3):
E = 57,000 VT (4.1)
where
f = compressive strength of concrete, psi
This provided a modulus of elasticity value of 3,000,000 psi for the
concrete used in the analysis model. The empirical formula given by
Eq. (4.1) can be used for general construction grade concrete,
usually exhibiting a 28 day compressive strength of 2,500 psi or
more (3).
A study involving other modulus of elasticity values namely,
3,600,000 psi and 4,000,000 psi, indicate higher values of design
parameters as compared to those obtained with a modulus of
51
elasticity of 3,000,000 psi. These values are normalized with
respect to values obtained with E = 3,000,000 psi and are reported
in Table 4.1. The equations presented in Chapter 5 are based on an
E value of 3,000,000 psi. However, to enable the use of other
values of E in the range between 3,000,000 psi and 4,000,000 psi, a
modulus factor, E or E has been introduced in the equations for
maximum bending stresses, maximum bending moments and maximum shear
forces. The modulus factor, E or E , can be calculated from Eqs. X y' ^
4.2a and 4.2b for the range, 3000 psi ^ f' ; 5000 psi:
E = 0.0167 W + 0.1208 (4.2a) X c
E = 0.0141 ^ + 0.2565 (4.2b)
y c
However, it should be recognized that its application will be appropriate only within the range of E discussed.
4.2.2 Poisson's ratio of concrete. V c
Poisson's ratio of concrete is known to range between 0.15 and
0.20 (32). A conservative value of 0.15 was used in this study.
4.2.3 Modulus of Elasticity of Soil, E^
A wide variation of this property is reported in the literature
(5,22), ranging from 50 psi to 2,000,000 psi. In order to narrow
this range, a study of maximum slab deflection was conducted by
varying only the value of the modulus of elasticity of soil while
holding all other parameters constant. Percent change in maximum
deflection due to changes in E^ were computed. For example, percent
change in maximum deflection due to change in E^ from 2000 psi to
10,000 psi was calculated as (2.84 in. - 0.57 in.)/2.84 in. x 100 =
Table 4.1: Variation in Values of Design Parameters Due to Variation in E
52
Maximum Differential Deflection
Maxmum Stress in x-direction
Maximum Stress in y-directi on
Maximum Moment in x-directi on
Maximum Moment in y-directi on
Maximum Shear Force in x-direction
Maximum Shear Force in y-Directi on
3,000,000
1.00
1.00
1.00
1.00
1.00
1.00
1.00
E^. psi
3,600,000
1.00
1.18
1.15
1.18
1.15
1.18
1.14
4,000,000
1.00
1.29
1.24
1.29
1.24
1.29
1.22
NOTE: Results were obtained using
slab length, L = 150 ft slab width, W = 100 ft slab thickness, h = 6 in. modulus of elasticity, E = 7500 psi aisle width, A = 5 ft ^ stack loading,^p = 8.0 psi
53
80%. These results are given in Table 4.2. The values of other
parameters used in this study are noted at the end of the table.
For values of E lower than 1,500 psi, the total deflections
were found to exceed 5 in. which were considered to be unreasonable.
Although the percentage change in maximum deflection values appeared
to be significant for values of E greater than 15,000 psi, there
really was no practical change in magnitudes of maximum deflection.
Consequently, as a result of this study, values of 1,500 psi and
15,000 psi were selected as the lower and upper bounds, respec
tively. A value of 7,500 psi was also used as an intermediate
value.
4.2.4 Poisson's Ratio of Soil, v
Poisson's ratio of soil is known to range typically (42) from
0.15 to 0.50, where a value of 0.50 corresponds to a compressible
medium. For similar analysis, values of 0.35 or 0.4 have been used
(5,22,53). Because the magnitude of computed deflections are not
highly sensitive to changes in Poisson's ratio, a constant value of
0.40 was adopted in this study.
4.3 Structural Parameters
4.3.1 Slab Length, L, and Slab Width, W
Slab length and width are usually governed by the requirements
of the user. For industrial warehouses, the width may sometimes
exceed 300 ft and the length may exceed 1000 ft. These dimensions
are much larger than those for slabs in residential and light
commercial buildings. However, in this study, clear dimensions
54
Table 4.2: Maximum Deflection Values Corresponding to E Values
Modulus of Elasticity of Soil, E
(psi) '
1,000
2,000
10,000
20,000
30,000
50,000
Maximum Deflection
(in.)
5.00
2.84 1
0.57
0.28
0.19
0.11 •
Maximum Change in Deflection due to Change in E
(%) '
43
80
51
32
42
NOTE: Results were obtained using
slab length, L = 150 ft slab width, W = 50 ft slab thickness, h = 10 in. aisle width, A = 5 ft stack loading,^p = 4 psi
''^-
I,
n n
tm
55
ranging from 50 ft to 250 ft, which commonly occur in practice, are
considered. The specific combinations of lengths and widths are
assumed to cover the range of aspect ratios (1 to 5) normally
encountered.
4.3.2 Slab Thickness, h
Slab thickness contributes to the stiffness of the system and
is therefore an important parameter in the design of floor slabs.
Generally, the preliminary design involves determination of the
optimum uniform thickness of the slab-on-ground for a specific
loading condition. Based on this information, the decision is then
made as to whether the slab needs to be stiffened by grade beams to
reduce the uniform thickness or to structurally reinforce it.
Because a uniformly thick slab is usually the design objective., in
this study only a constant thickness slab is considered. Even
though a minimum thickness of 6 in. has been recommended (3) for
plain concrete floor slabs-on-ground in industrial warehouses, slab
thicknesses of 4 in. have also been found in the literature (33).
Therefore, in order to cover the ranges most likely to occur in
practice, slab thicknesses of 4 in. and 10 in. were selected as the
lower and upper bounds, respectively, for this study. Slab thick
nesses of 6 in. and 8 in. were also used as intermediate values.
4.4 Utility Parameters
4.4.1 Stack Loading
Stack loadings are due to stored materials. Their magnitudes
and locations are usually determined by the user. However, for this
56 study, the following assumptions were made:
1. Stacks are 5 ft wide when access is from one side alone,
and/or 10 ft wide when access is from both sides.
2. Stacks are assumed to be continuous and parallel to the
long dimension of the slab.
3. Concentrated loads due to rack posts cause only a punching
shear problem (34), which can be readily analyzed using conventional
reinforced concrete design procedures.
The lower and upper bounds of the loading intensity due to stacks
were computed based on information obtained from local warehouses.
The values used were 2 psi and 8 psi, respectively. An intermediate
value of 4 psi was also used.
In order to compute the difference in values obtained between
having the stacks oriented parallel to the long dimension of the
slab and parallel to the short dimension of the slab, a separate
analysis was conducted. The values obtained for the various design
parameters with stacks oriented along the long and short directions
of the slab, respectively, are reported in Tables 4.3a and 4.3b.
The analysis indicates that there will be a significant change
(increase and decrease) to the order of about 500% in the values of
design parameters between having the stacks oriented along the long
side of the slab and along the short side of the slab.
Therefore, if any layout other than having the stacks along the
long direction of the slab is contemplated, care should be exercised
in applying the results of this study.
57
OICO C CO
o •
-o cu +-> e cu
•r—
^ o to
. ^ ( J 03
4-> C>0
-c: +-> • r -
S t o S-cu
4-» CU
o
o •r—
+-> n3
C i
+ J O CU CL to
<:
c 03
- C -»->
• 1 ^
S J 3 (O
,— E 00 ra s-fC
Q -
£Z CD
• r -to CU
Q
v+-O
t o CU Z5
^ fO :> V4-O
C o to
•^ s-fO CL E O
o
fO
M -O
to
c: o
• r—
+ J o cu s-
•^ Q
+-> ^ o
- C <y)
• o e fO
CJ) d o
_ l
cu ^ 4->
CO
cu
03
CO
—
o •^ • M
<« OC
•»-> tJ (U Q . i/>
<:
• " ly) a .
o •
00
• r " I / I
^
2.0
en c
• r *
•o <o o
_ l L
c o
• M - r -
o u
to u a
c o
c u o a;
- J L .
o
o 4-> • ! -k 4->
o u f a> t/i i .
o
c o
Ot-M C tJ O 0)
_ l t -• r -
O
c o
CT»T" C •«->
• » - U " O (U ns S-O • • -
- J O
o o o ir> »«H
o o L D
f * «
o o LT) t — l
o o o m t—4
o o i n r«»
o o m 1 - ^
o o o i n t - H
O o I D
r^
o O m t—t
o o o i n t - H
O o i n p«»
o o m f—1
• 1 —
1/1 o .
•* i /t LLl
lO r*.
o
1—1 m
1—1
1 1
O) i»>.
o
00 i n t - H
1 1
r^ CM
• O
m i n
• o
CO 1 ^
• CM
00 CM
• o
VO i n
• o
T - l
00 • CM
c o
• p >
E -M 3 VJ E <U
• p - r ^ X >* - • l O (U c
Z Q - t -
CO
i n
m i n
.49
a» (Ti
1
I - H
• a t I - H
r-4
.44
r^ !>«.
1 1
CM P ^
• r^ t - H
o ^ CM CO
CM i n
• f—1 CSJ r - l
0 0 o
• CM CO
l O T - l
• at ^
t—l
o • I - H
CO 1—1
• c: • T -
a-i n
"^ " </t X J 3
a r—
00
« CO t — l
T - l
.67
CO p-> t - H
1
V O CO
CO VO
CM 1—1
o 1 - H
1—1
1 1
VO VO
• o 0 0
m m
• 0 0
^
CM CM
• CM CO T - l
VO 0 0
• o CM
<J\ a>
• V O CO
a\ CM
« CO CM T - l
• c .^ C T « 1
«» " «/» X JH
o •—
<Tt
^ m CM <Tt
CM t—l
00 i n V O t - H
1 1
i n t - l
o <T>
T H
CM
r^ i n
CM
1 1
a\ CO
• i n o^ CM
CM o
C D
^ i n
« r CO
• i n CM O CM
CO V O
• «3-CO i n
VO CO
• CT> l -H 0 0
T—l
«a-. CO
0 0
CSi
• c • r -
•*>^ £1
— 1 M
X C z : - T -
r». CM
I - H
a» 00 T - l
^• o> 00 CM
1
'
CO o
VO m o t -H
CO CO
i n CO 00 l -H
1 1
o o
1—1
T - <
m
o t - H
. a\ o 0 0
CM VO
CO o CM CM
l - H
VO
• r^ ^ CO
CM
^ . VO
T H
VO
i n 00
• «r i n o CM
• c •^ • ^ ^
X )
^-1 M
>.= :E .-
^ 1—1
m 1
T - l CM
O I
1 1
CO CM
CM
«*
.98
r*» i n
1
^ VO
l - H
1
^ 1—1
. CO
CO 0 0
CO l - H
CM
(^ • o »—1
<Ti 0 0
»3-l - H
i n VO
• CO CM
• C
•^ ^ 1 . ^
M ( />
X ^
> «—
m VO
CT> CO
CM 0 0
i n m
1 1
o 0 0
0 0 1
o CO
m I - H
'
1
1
o I - H
o t—l
l - H
^ ^
VO r~.
CO CM
o a t
CM 1
CO I - H
• i n 1
CM I - H
• r^ T - l
1
• c • r—
^•^ iA
>»^ 3 » 1 —
58
CDO C O O •
I — ^
<c X3 (U •M
C CU •^ s-o
to -^ CJ fC
4-o
o r— 4-» fC
ai + j
CJ <v (/) CL
+J «sC 00
x: • » - >
• -3
to s-
e fO
x: 4J •r^
s O) -O
•*-i
cu 03 r ^
E oo 03 S-m Q.
c en •r—
to CU C=3
M-O
to CU 3 r— 03
>
M-
fO
M-O
to c o •r-
+-> o cu s_ • r—
o
+J s-o x: oo
o -o
C o to
• f —
s-03 Q. E
c: 03
CD sz o _J
cu o -c: C_) -•->
CO •
CU
JO 03
o o •
o
J j
Aspe
c
• 1/1 Q .
O •
00
J
(/) a. o •
CM
C3>
Load
li
c o
+J t-& . ••->
o u
• o
c o •T"
Ot-M C tJ O 0) _l t-
o
c o
i. *J o u .C V to u o
c o
a>4J c u o <u
o
c o
•I- <J
o ••— -J o
o o o m t-H
O o m rx
O O m I-H
O o o m t-H
o o m r~
o o m I-H
O o o in I-H
O o in 1^
o o m T-l
o o o m T-l
o o in
o o in l-H
(A/l UJ o.
VO CO . o
I-H
P*. • o
«!• in • CO
r»» CO • o
"* r-. . o
00 VO . CO
CO T-l
• o
VO CM . o
I-H
CO . I-H
•* t-H
d
r«. CM
O
in CO •
1—•
c o •
E •!-> 3 tJ
axim
ef
le
n.
S:Q —
r o • C>J
a>
00 CO • CTt
^ l-H
VO T-H
. OJ « » •
^
o CO • 00
CM I-H
VO CM . VO
at l-H
at * » •
a
1—1 l-H
in
^ CM . r CM
00 t-H
• VO «r
t-H
o . r«.
^ l-H
00 CO
Kj-
CO
CTt VO
CO m
VO in
.3" in l-H
c • r -
o-
X ^ D ^
00 at • VO
l-H 1—1
in m • 1^
VO T-H
^ o .
O in CO
00 •d-. CO
VO
r*. CM . o I-H .-1
CM ^ • VO
^ CO
CM .* • o CO
CM CO
• ^ ^
in
«r • t-H
O l-H
00 00
o CM
CM at
VO CO
VO CO
o CM I-H
C •T—
CT
« (/)
O I—
in ^ .
^ CO m T H
o !»«. . at
00 ^ CM
CM CO •
at VO CO r*.
VO CM .
CO CO T-l CM
CM
o . I-H
r CM CO
CM 00 •
^ CM in 00
00 CTt • CO
in ^
CM VO
• at VO r».
00
o • o in
CM
<• o CO 1^ in
CTt 00
« * •
at 00
CM
o VO
r in CM
c •t"
.o 1
X c ac •<-
00 at .
r> ^ at l-H
I-H
in • CM
at 1^ CM
CM crt •
CO ^ CO m
m o • 00
in
o I-H
^ 00 • p^
CO 00 I-H
o VO • CO
r*» P-. in
l-H
at •
Co o in
at VO
• CO CO p».
I-H
00
• o ai VO l-H
I-H
at
t^ ^ •
CO
l-H
CO
in I-H
VO
CO at
in
o o CM
c • ^ 1
0> *
2: •'-
at VO .
t—l
CM 1
I-H
^ •
t-H
CO 1
o m • CM
r«. 1
m 00 • 00
CO 1
!*>. 00 • r-4
m 1
l-H
CM •
r«. r-» 1
CO in •
«s-1
o at ' VO 1
o t-l
• CO CM 1
Oi VO
at 1
cr> 00
CM I-H
1
t-H
CO
o CM 1
c
X ^ > I—
00 00 • CM
^
in CO •
r*. in
CO
r«» • C7» (
CM 00 • 00 1
CM CO •
m I-H
1
I-H I-H
• 00 <• 1
un r». •
o l-H
o "S-
• ^ I-H
CTt
^ • o CM
o at
CVi 1
CO l-H
in 1
CM
r>«. VO I-H
1
c
•> in
^ r —
59
4.4.2 Forklift Loading
The types and rated capacities of forklifts used in this study
are based on manufacturer's information obtained from local ware
houses and forklift truck dealers and are given in Table 4.4.
Forklifts with rated capacities of 2,000 lbs and 15,000 lbs are used
as lower and upper bounds, respectively. To avoid the problem of
colinearity (which means that a nearly exact linear relation among
the predictor variables exists, causing coefficient estimates to be
inflated and to predict unreasonable values), a third type of
forklift with an intermediate rated capacity of 4,000 lbs was used
in sixteen cases, the details of which are also included in Table
4.4. It is recommended (28) that if information regarding wheel
contact area is not available, it can be roughly approximated for
solid or cushion tires by using:
contact area = tire width x 3 or 4 (4.3)
Therefore, the contact area of the rear tires of the forklift was
calculated by multiplying the tire width by 4. The contact pressure
is then obtained by dividing the single wheel load by the contact
area of the tire. In order to obtain uniform contact pressure under
all four wheels, the contact area of the front wheels was adjusted.
Additionally, forklifts are assumed to operate only along the aisles
between the stack locations, even when the slab is not loaded with
stack loadings.
4.4.3 "Worst Case" Forklift Truck Location
A separate, quasi-static analysis was carried out by systemati
cally placing the forklift loading at different points on one
Table 4.4: Details of Forklifts Used in the Analysis
60
Rated Capaci
Front Cushion Tires
Rear Cushion Tires
Loads, lbs: Empty Condition
Loads, lbs: Fully Loaded Condition
Contact Area, sq. in.
1
Axle Width, in.
Distance between
ty, lbs
O.D., in.
I.D., in.
Width, in.
O.D., in.
I.D., in.
Width, in.
Front Wheels
Rear Wheels
Front Wheels
Rear Wheels
Front Wheels
Rear Wheels
Axles, in.
Basic minimum aisle for right angle stacking, in.
2,
16
11
• 5
13
8
4
2,
2,
4,
2,
31
18
34
43
119
000
.25
.25
.00
.00
.00
.50
700
700
700
700
.35
.00
.60
.00
.00
4,
18
12
7
16
10
5
3,
4.
7,1
4,
35
20
39
53
130
000
.00
.12
.00
.00
.50
.00
350
150
350
150
.42
.00
.10
.50
.00
15.
28
22
12
22
16
8
8,
11.-
32,
11.'
91
32
54
70
164
000
.00
.00
.00
.00
.00
.00
500
100
500
100
.23
.00
.00
.00
.50
NOTE: Details obtained from manufacturer's specifications provided by local dealers.
61
quadrant of a slab and assuming it to be symmetrically loaded in
order to determine the location of the loaded forklift truck that
produced the most severe or "worst case" loading condition. The
locations studied are shown in Fig. 4.1. As the maximum values of
deflection, stress, bending moment and shear force are critical for
the design, locations where maximum values of these design param
eters occurred were identified. The values were then converted into
fractions with respect to values obtained at the first or
"benchmark" location. Because of their relevance, only these
maximum values from the "benchmark" location were tabulated and are
included in the text (Tables 4.5 and 4.6). However, the values of
the design parameters obtained at all 15 locations shown in Fig. 4.1
are included in Appendix D for reference by the interested reader.
These results were then carefully analyzed to arrive at the most
critical location which will produce the largest combination of
values for all the design parameters. Based on the analysis for
aisle width of 10 ft, location 12 was used for forklift loading
alone, and location 14 was used for the combined (stack plus fork-
lift) loading. Similarly, for aisle width of 15 ft, location 6 was
used for forklift loading alone, and location 5 for the combined
(stack plus forklift) loading.
A separate study was also accomplished with the forklift
directed or oriented along the aisle, as well as oriented perpen
dicular to the aisle as in loading or unloading from the stack (Fig.
4.2). The results of this study were then normalized with respect
to values obtained with the forklift oriented along the aisle, and
62
AISLE
O - J CO
<
10 8
AISLE -15 -14
posi"noN I
•13-- L i z l II
AISLE u - J CO
<
50 ft
AISLE WIDTH = 10 ft
Figure 4 .1 : Locations of Forklift for Quasi-static Analysis
63
r—
-^ S -
o U -
s-o
M -
0 1
s-( U
- l - >
<u E fO
s-03
D -
c: CJ>
" I —
CO CU
Q
M -
O
U l CU 3
— fO
^>
to CU 3
03
>
l-H
c o 1 —
E -t-> 3
E • r -
X 03
^ CU
s-cu
-SZ
s to c: o
• 1 —
+ J 03 CJ
o —' +-> 03
CU
c o
r—
M - < :
o to O
• r-+•>
n3 Q ;
C T
e •r—
XJ rC O
• 1 —
to o
OL.
+-> ra
to CU ^ fO
>• o
- l - >
- M
o cu C L 0 0
cu Dl
- C - M
•^ s
T 3 CU S -
s-Z3
o o
_ J O
m
o in
o m
o o o i n i n
LD
CU
- Q 03
+ J <4-
m
c o
• 1 —
lA c (U E
•f—
o ^ lO
— t o
c •^
« </> «/l (U c .^ u •^ .c 1—
^ <a ^ t o
IQ
<4- Q . O
i/» I— 3 • • -
1— O 3 OO
-o O M -
£ O
o.
o»
• o
o
i . o
GO at O t-H CM t-H CM 0%
o at
CO
o CO
a\ at o
r^ CO
VO t-H CM
m CO CM
m m
CM CM
m
o
CM
in CO
m CO
CO
m CO
CO
CM
in CO CO
CM
^ o
CO CM CM CTl CM t - l
CO as VO
a\ CO CM
at
l O CM
in at
CM VO
o CM O
o CM
l-H O
CO CO in o
VO o o>
CT> r-o CO
VO
O
at VO o
l-H o
a;
o
IQ
> 3
X lO
0) s-
c o
l/t o a.
l/t •r -
0) tJ i~ o
t -(U
. a E 3
lO o o
u
o
X rt3
C O C O o) •!- a< •>-e ••-» E *J o u o u Z V £ a;
X L . s-E 3 0 3 0 3 0 3 0
^ = E I E l E l E l ,— - t - X - f- > , • • - X • • - >> -«o. X X X X < ( O C I O C r o c ( O C
c c i. o s- o (O -r - (O - t -
.c u . c u oo a; oo O)
o Q .
(/) <U u i . • o -o u •a <u •M lO
I—• 3
X I lO +->
( / I
c o •r~
•»->
<o u o
_ j
(U i . t . 3 U tJ o
(/> (O .c Vrt (U
r— .o (O
• s-(O
>
64
• o c fO
J ^
U) (U 3
03 o > to
• ! - >
0 0
&-o
t4-
to s-CU
-M CU E «a s-(O
Q .
£=
E 3 E
• r -X 03
5?"
I - H
c o
• 1 —
4-> •^ to o
CU Q -S-<u t ~
3
to c o
'r-
+-> CD fC •^ in cu
o
M-O
to cu =3
^-03 > M-O
to o
•r— +J 03
CJ o
_ I
+J 03
to O ) c
• f—
+J 03
to 0 ) =3
r— 03
> O +J
-M CJ CU CL to Q)
a:
- o ^ fO o
_ l
4-> M-• r -
^ .^ s-o
oe: u-
• • (£>
•«d-
cu r-" j D 03
+ j •r—
S "O cu s-s_ 13 CJ u
o
8 9
O LD
O LO
O
o 0 0 IT)
r>o
LD
«X)
CO cr>
I «-H
o OJ ^
o Lfi C£>
a> t - H
r».
CSJ CO o
r~o r-o •^
O . t-H
i n CO cr>
CO 0 0 CVJ at
0 0 i n CO
CO
CO o
cr> Ln o LD
CT»
ro. CO cr>
CO t-H CO
+•> <4-
to c cu
. a 03
c>o
to oi cu sz
.^ o
j Q 03
to ex
o oo
O
•r-U - 1 -
•r- to +J Q . to 03 *>
I— a>
c>o ro. LO o
r^ CM t - H
t ^ f - H
CO
o LO CO
*d-cr> cr>
LO
C7>
O CO O
ro. LO
o
LO o LO
C3 LO
o
CO LO at
0 0 1—I
to
C3>
to
• o o
03 • I - O -O —1 03 O +->
_ l <+-
. : i ^ O 03
4-> C/)
S-
o
cu
to •r— < 3 :
cu J 2
c o
+-> .13 U O
o
o cu
cu
X 03
c o
+-> o cu s-
Q I
X
CU E o
c o
+-> o OJ
s-Q
I X
c o
••—
o cu s-
• I - E Q - 1 -
I > , CU
u c s-
• I - o
X 03
X 03
c cu
Z5 E
• I — X 03
S -ro CU
sz oo E 3
X 03
o
CJ cu s-
I
CU CJ s_ o
03
sz oo
X 03
cu -c: •«->
«+-o
03
cu
03
> E 13 E X 03
E 03
CU
s-cu
to
o
to o O-
• o c o o. (/•)
cu s-s- . o - o (J (U
&-L.
CJ OJ LJ
• o CU
J D to fiJ 03
+-> - C
to to c cu O I—
• I - J 2 +-> 03 03 • • -U S-O 03
__1 >
65
AISLE
UJ - J en
STACK LOADING
AISLE 1
1—1
i2,
|1
STACK LOADING
AISLE
STACK LOADING
AIS
LE
1 ALONG AISLE 2 PERPENDICULAR TO AISLE
Figure 4.2: Forkl i f t Along and Perpendicular to Aisle
66 are included in Table 4.7. As can be seen, the values obtained with
the forklift truck oriented perpendicular to the aisle (as if it
were loading or unloading the stack) are greater than when the
forklift is oriented along the longitudinal axis of the aisle.
Therefore, the study was conducted with the forklift truck per
pendicular to the aisle. It was also found that the values obtained
for forklift trucks facing the stack with both sides of the aisle
loaded was lower than when there was no load behind the forklift due
to stacks; however, analysis for forklift loadings was carried out
with both sides of the aisle being loaded as it is wery difficult to
generalize such a situation.
4.4.4 Aisle Width Between Stacks
An aisle is a passage between stacks, provided to permit
movement of forklift trucks which are used to handle the material
stored. The width of the aisle provided is governed by the turning
radius of the forklift in use and also by the storage requirements.
Aisle widths of 5 ft, 10 ft, and 15 ft were used in the study
because they are known to be commonly used in warehouses. Although
an aisle width of 5 ft does not permit passage of most forklifts, it
was used in this study as a lower bound to understand the influence
of aisle width on results for stack loading conditions alone.
4.5 Accomplishment of Parametric Study
The parametric study was accomplished with the aid of the
finite element program SLAB4, described in Chapter 2. The study was
conducted in three phases: (1) analysis with stack loading alone.
67
+-5 v+-•r— r— J:^: s-o
U -
- C +-J •1—
2 lA S-
<u 4-> CU E 03 s-03
Q -
C
cn •^ lO cu
Q
M -O
to OJ 3
r— 03
>
«•-O
to
o •^ +-> OJ
Q ;
• • r-o
^
cu
- Q 03
+-) U CU cu
cu r ^ t o
to cC cu
Ci :
J Z - M •^ S
CU — t o
•r—
«=c cu
sz •\->
CU - E • M
cr> c o
1 ^
<c -o cu
• M c cu
• r -S_
o o +-) i -03
1 —
3 U
•r—
-o C CU
.2^ LJ 3 ^
I— • M M-•r—
,— a..i^ S-
<u o. • o cu
•*->
cu •f—
s-o
. ^ o 3 S-y—
i_
o L L .
. E -<-> •p—
s to cu 3
1 —
OJ r=-
o 4-J
s-<a
" 3 0 ) O I— CO CO
•»- i/» CO CO
C C C t -H — I <U Q . O i - -M 01
a.
VO at m at CM
O) 'I- o < o
o o o
o o o
o o o
o
c o
I. <o 3 01 U f— •^ (/» o X > - ^ I -H c <c Oi O I-H o. o i- 4.) 0)
O -
o o o
VO
|o» CM as
CM . H
r-^
[• i-^ • --• S
^
< &
o
SI
to
a. o o i n
0) j Q E 3
fO u o
0)
(/) • t - o <: o
o o o
o o o
o o
o o
at c o
o
o c o
u OJ
s-
c o
o OJ
0)
a 3 E
•f— X (O
X 10
a; E c o o
u <u
X o l O I
0» E C o o
E U 3 <U E s-
• r - 't— X o 10 I 2: >»
s. o (O • • -0) •«->
.c u t o OJ E — 3 O E I
• I - X X <o c
0) u k. o
10 •
X ro
O 0>
i o ; I
o>
1/1 3
• 0 0) c •^ 10 •M .O 0
OJ i . 0) 2 l/t
••-> p ^ 3 lA 0
CC
'f—
•»-» >•- - U «3->4-
0 m 0 II
in .c II
II • _ i (/>
3 (/) •» ^
-C • C •M f .:^ Ol+J 0 C T3 -i-V - JZ
— 3 •*->
.0 ^ .a 10 lO IO — — — (/I i/i 10
^- (/> • I - Q . O (/) CO
• 1 - 1 ^ v»- m l -H 0 ••-> O .
<«- II > . CO
• M O «4-• 1 - l -H II Q . u • I - II WI » •M a. at 1/1 3 c 10 < " ' ^
r— W O 01 * C 10
_ J : - I - o v»- -iJ " a I— O "O 10
• t - o •(-> 10 s . — vt-3 •<-
r— Oi .^ I— 3 f— O J i
TS m 10 ^ O - I - •(-) O E lO </) >4-
•1- 2 : -r-
68
(2) analysis with forklift loading alone, and (3) analysis with
stack plus forklift loading.
These assumptions were made for the study:
1. The slab is monolithic and of constant thickness.
2. The slab is in full contact with the subgrade at all times.
3. The slab is subjected to maximum loading and symmetry could
be used.
4. Since the slab will not be exposed to severe weather, there
will be no significant temperature differential across the thickness
of the slab. Also, perimeter (structural) loading was not con
sidered in this study. The reason it was not considered because the
exterior wall loads are typically carried directly by continuous
perimeter footings and generally the slab is isolated from these
footings by isolation joints. Because of symmetry, only the top
right quadrant of the slab was analyzed. The longest (length)
dimension of the slab was always assumed to be along the y-axis.
The slab was discretized into rectangular elements with aspect
ratios less than three, as larger aspect ratios gave unreasonable
values for the design parameters. Comparison of results for similar
problems with different aspect ratios of element is included in
Appendix E. For more details on computer code, input information,
the reader is referred to the user's guide to SLAB4, given in
Appendix A.
With these basic assumptions, the parametric study was con
ducted in a systematic manner. Although the reasons for and
selected ranges of values of parameters have already been discussed,
69
they have been summarized for convenient reference in Table 4.8.
The parametric study was conducted over the range of values for
parameters indicated in Table 4.8. It was accomplished by varying
one parameter at a time in a specific manner for the three loading
conditions, thereby including all possible combinations. This is
indicated schematically in Figures 4.3, 4.4 and 4.5.
The scope of the study used in the overall problem analysis and
subsequent development of the equations was quite extensive. The
study included a total of 618 cases for all three loading
conditions. The values of the several design parameters as cal
culated by the computer code for each of the 618 cases studied are
included in Appendix F. The results of this analysis included
values of deflections, bending stresses, bending moments and shear
forces. Deflections, bending moments and shear forces were listed
both in the order of finite element nodes and in the ascending order
of magnitude in the computer output for each problem. The results
also included the twenty greatest ratios of differential deflection
over distance (distance between corresponding nodes). However, only
the absolute maximum values of these design parameters were used in
the regression analysis described in Chapter 5.
Table 4.8: Values of Parameters Used in the Parametric Study
70
Parameter Symbol Unit Value
Modulus of Elasticity of Concrete
Poisson's Ratio of Concrete
Modlulus of Elasticity of Soil
Poisson's Ratio of Soil
Slab Length
Slab Width
Slab Thickness
Aisle Width
Wheel Spacing
Stack Loading
Forklift Loading
V
V
psi
psi
3,000,000
0.15
1500, 7500 ,15000
0.40 s
L
W
h
A w
S
Ps
Pf
ft
ft
in.
ft
ft
psi
psi
50, 150, 250
50, 100, 200
4, 6, 8, 10
5, 10, 15
2.5, 3.26, 3.5
2, 4, 8
75, 103, 178 _i
71
ill ill 111 II 11 II )i II II II II •>
^ ^ ^ ^ ^ ^ ^ ^ ^ l - f J L^ I—i-J
O O. O IO
> — — g
in
00
« I
r-CJi. I O
I IO
o IO II - I
s 8 CM II
* o o IO
o 8H
>-
o »-< _ _ l ^
c o d UJ
0 0 X
GO.
I 10 • I — 1 0
< M — ^ Q
' IO
e v j — — g
L_ 10
10
Q
10
10
10
10
00-4—2 « ' — 10
M
*> o.
o (O
10
I ^
X I -o
UJ -J (O
CO UJ CO < o u. o CC UJ CD
3
UJ O
(T O U.
O UJ CO 3 •»
O
•r—
C o
c_>.
T 3
O
u
+->
s-o
to
OJ ^ - » a; E ro S-rtJ
0 .
c o •r -+J 03
E o CJ
ro
(U
3
72
o 8'
o — ^
I !P
to
^
IO
g IO
g IO
g lO
g IO
-C
IO
g lO
g lO
s-
CO X I -z Ui ^
o •f— +l> •r— -o c o C_3
c •r-
•o o
s-o
o
to
s.
+->
E (O s-<o
c o
•r -4-> (O
c .o E o
CJ
0) s-3 C7>
O —
73
lOCVi I I II
^ ^ ^T"
s o lO H
• o oo lOOJ II II
^ ^
•v «^
o IO csi II
lO
CD
CVJ
O O-IO
^
CD I IO
g IO
g IO
o
lO
g IO
g jO
g IO
o o lO
H CM H EH
IO
g lO
g IO
o o—^ lO
H
g
HlO — g
00 • «
IO
>- CM—^
CO CO UJ
z o X I-
co < _ l ^
U.3
coo
1 o z o a o
CO
g lO
g to
CJ> • -
o 3 » -u.
o - * u.
X I -o
UJ -J
O CO
<
c o
c o
CJ
cn
(O
o
o
to 3
u <o
c/>
s-o
CO
cu
cu E «o
<o
c o
•r— 4-> 03
c •r— E o
CJ
ir>
cu t -3 cn
CHAPTER 5
DEVELOPMENT OF REGRESSION EQUATIONS
5.1 Introduction
The results of the parametric study described in Chapter 4
included deflections, bending stresses, bending moments and shear
forces. Having acquired all of this information, the next step was
to relate the design parameters as dependent variables to other
parameters involved, such as slab length, slab width, slab thick
ness, etc., as independent variables. To do this, a regression
analysis, which is a statistical technique for modeling and
investigating the relationship between two or more variables was
used. The details of the regression analysis are described in the
following sections.
5.2 Regression Analysis
Regression analysis was accomplished using a select calling
computer program (18,23). The program is designed for variable
selection in least squares regression models. The selection proce
dure is the Hocking-LaMotte-Leslie method as implemented in
LaMotte's select subroutine. Select subroutine is the core of this
program and the method used guarantees selection of the minimum mean
square error (MSE) model. The program may read or generate a
variable pool not to exceed 80 variables. Variables may be
74
75 generated or read directly by a user written subroutine named
"INPUT." Various output options are available to the user. The
result is either a linear equation of the form:
y = a + ^^1 ^ h \ ^ ^ S- i f - '
or a logarithmic equation of the form:
B- Bp B.- B. y = a^x^ X2 X3 x . "• (5.2)
For more information on the regression analysis, the reader is
referred to References 18 and 23.
5.3 Development of Regression Equations
The regression analysis was carried out by representing the
following parameters as independent variables:
1. Slab length, L, ft
2. Slab width, W, ft
3. Slab thickness, h, ft
4. Modulus of elasticity of soil, E , ksf
5. Aisle width between stacks, A , ft
6. Stack loading, p , ksf
7. Forklift loading, p., ksf
8. Wheel spacing, S, ft
and the following design parameters, one by one, as dependent
variables:
1. Maximum differential deflection, A
2. Maximum bending stress in x-direction, a^
3. Maximum bending stress in y-directi on, o
76 4. Maximum shear force in x-direction, V,
X
5. Maximum shear force in y-directi on, V
The variables are read directly with the aid of an INPUT
subroutine. The logarithmic regression, Eq. (5.2), was used in this
3 -3 study. The magnitude of variables ranged from about 10 to 10 .
If the linear regression (Eq. 5.1) was used, the importance of
_3 variables with magnitudes of 10 would be very much suppressed by
variables with larger magnitudes. In order to avoid this problem,
the logarithm of the variable value was used to bring the magnitude
of each variable to within a unit, whereby the importance of one
variable will not override the importance of another just because of
magnitude. Correlation coefficients for a linear regression were in
the order of 0.55 compared to 0.98 for a logarithmic regression,
indicating that the logarithmic regression is more suited for the
data on hand. Therefore, in the INPUT subroutine, the variables
were first converted to a consistent system of units (kips and feet)
and then converted in terms of their logarithms (base 10) before
being used for the regression analysis.
The results of the regression analysis include regression on
the full model, along with optimal regression for a specified number
of subset sizes. For this study, as an input parameter, the number
of subset sizes was specified as four. This means after regression
on the full model, the program will eliminate variables one by one
in a specific manner up to four variables and regress on the remain
ing variables. These results, along with the corresponding corre
lation coefficients are used in deciding on an appropriate model to
77 represent the data. Analysis of all these results for this study
indicated a decrease in the value of correlation coefficient with
fewer variables, reinforcing the fact that all variables considered
are important in the thickness design of industrial floor slabs and
need to be included. Therefore, the results of the regression on
the full model alone have been taken into account.
Regression equations (stack loading condition alone) were
developed by considering (1) ratio of loaded area to area of slab
instead of aisle width, (2) ratio of loaded area to area of slab for
cases with stacks back to back, (3) aisle width for cases with
stacks back to back, (4) lesser data sets (deleting data sets with
radical values of design parameters), (5) thickness h, in inches,
(6) no thickness, etc. These equations were not superior (based on
correlation coefficient) to those reported in this section; on the
contrary, in some cases they were found to be far less superior.
Therefore, none of these equations have been included here. For the
design procedure, stress equations were found to be suitable and
easy to compare directly with the allowable value. Therefore, only
the stress equations have been included in the text. However,
equations for bending moments for all three loading conditions were
developed and are included in Appendix G. Also, if a reinforced
floor slab is contemplated, the moment equations could be used to
determine the design moments.
The study was carried out for the three loading conditions and,
therefore, there are three sets of equations involved. Equations
78 are listed by the loading condition and in turn by the dependent
variables in the following sections.
Stack Loading Condition
(L)0.44 („)0.62 ( ,0.20 ^^ ^0.78 A = (0.47) 5 (5.3)
(E ,0.99 ( )0.29 ^ s' ^ w'
(L)0.14 (y)O.Ol ( ,0.30 ( )0.27 ( ,0.97 a = (EJ(1026) !!! 5 (5.4)
(, ,0.74
(„)0.18 ( ,0.59 ( ,0.91 o„ = (EJ(30,045) 5 (5.5) y y (L}0-*s (E/-^^ (Ajo-18
(,)0.30 (,)1.82 ( ,0.02 ( ,0.98 V^ = (E J(15.14) ^ 5 (5.6)
(„)0.09(,)1.83( )0.74 V = (E )(1467)- ^ (5.7) y y (,)0.83 (,^)0.57 (, ,0.44
Forklift Loading Condition
(L)°-21 (W)O-" (h)°-^l (,,)'•'' A= (0.12) (5-8)
(, ,0.98 (,y.21 (s)1.81
79
(L)°-l^ {h)0-30 (pj2-04 a = (E )(22.25) 1 / c QX
{W)0-O^EjO-72 (A )0-02 (s)2.04 ^^'^^ J w
(W)°-0^ (h)0-34 (pj2-39 a = (E ){347.71) 1 (5 JQ)
^ {L)0-15 (EjO-72 (A )0-51 (s)3.48 w W
(,)0.28 (, 1.80 ( )0.52 ( ,2.80 V = (E )(13.33) "H 'J. (5.11)
(L)0-21 (E )0-57 (s)3.96
(L)C.03 (,)0.11 (,)1.90 ( .0.22 ( ,2.13
\ = (EJ(0.19) i f (5.12) ' ' (E^)^-^^ (S)2-64
Stack Plus Forklift Loading Condition
(, 0.41 (, 0.62 (,)0.19 )0.15 ( 0 . 7 0 ( 0.19
(0.12) ^ 5 ^ (5.13) ( )0.97 (3)0.26
(L)0.25(,)0.02(,)0.14()1.02()0.55 (3)1.81 a^ = (EJ(10.17) "^ ^ (5.14)
(, )0.69 (p^)0.08
(,)0.06 (,)0.18 ( )0.70 ( ,0.50 (^0.68 (3^0.42 a = (E )(131.92) "^ ^ '- (5.15) y y (L)°-28 (E^)0-'2 ^ ^
80
„)0.39,„0.23„)1.77(,0.81(,0.66( ,0.21,5,1.29 V, = (EJ(C.03) ^ 5 i (5.16)
(„,0.01 (,,1.79 (, ,0.84 ( ,0.59 , ,0.84 ,s,0.19 V = (EJ(3.09) !! 5 ! (5.17)
y y ,,,0.48(^^,0.59
where
L = length of slab, ft
W = width of slab, ft
h = thickness of slab, ft
A = aisle width between stacks, ft w E = modulus of elasticity of soil, ksf s
p = stack loading, ksf
p^ = forklift loading, ksf
S = wheel spacing, ft
E = modulus factor in x-direction x E = modulus factor in y-directi on
A = maximum differential deflection, ft 2
a = maximum bending stress in x-direction, kips/ft X
2 a = maximum bending stress in y-direction, kips/ft
V = maximum shear force in x-direction, kips/ft X
V = maximum shear force in. y-direction, kips/ft y
x-direction corresponds to short direction (width) of slab
y-direction corresponds to long direction (length) of slab
81 5.4 Discussion on Regression Equations
Regression equations in terms of independent parameters have
been developed based on studies conducted. A brief discussion
relating to the importance of a parameter in an equation, its
position in the equation, and the reasoning behind it, are included
here.
The relative significance of a parameter in an equation is
measured by the magnitude of its regression coefficient or exponent
in the equation. For example, in Eq. (5.3) the most significant
variable would be the modulus of elasticity of soil with an exponent
of 0.99 and the least significant parameter would be the thickness
of the slab with an exponent of 0.20. Although exponents of magni
tude less than 0.1 can be considered to be insignificant and the
corresponding parameters excluded from the equations, they have been
included so that the user will feel that all the variables of
significance have been considered and included. Therefore, the user
does not have to contemplate on the relative significance of a
parameter, but could directly use it in the equation. The position
of the parameter (whether it is in the numerator or in the denom
inator) relates whether it would increase or decrease the magnitude
of the design parameter, corresponding to an increase or decrease in
its magnitude. In Eq. (5.3) slab length, slab width, slab thickness
and stack load are in the numerator, implying that an increase in
their magnitude will cause the magnitude of maximum differential
deflection to increase, whereas an increase in the magnitude of
modulus of elasticity of soil and aisle width would tend to decrease
82 the maximum differential deflection. The reason for this is that
larger slabs are more flexible, i.e., deflect more; thicker slabs
contribute to greater deflection (due to different model responses
involved), and stack loadings add to the deflection. On the other
hand, as the soil gets stiffer, i.e., greater modulus of elasticity,
the magnitude of deflection decreases. Also, as the stacks are
placed further apart, i.e., greater aisle width, the magnitude of
deflection midway of aisle width decreases.
Equations for design parameters in the x and y directions
exhibit a certain trend due to plate action. For design parameters
in the x-direction (short direction), an increase in slab length
would increase the magnitude of the design parameters; whereas for
parameters in the y-direction (long direction), an increase in the
magnitude of slab length would decrease their magnitude. This
appears to be logical as the aspect ratio of the entire slab in
creases, magnitudes of design parameters in the x-direction would
increase and those in the y-direction would decrease. However,
there appears to be exceptions to this general rule in Eqs. (5.4),
(5.11), (5.12), (5.14) and (5.16). In Eqs. (5.4), (5.12) and
(5.14), the exponents of variables (W, L and W, respectively) are
less than 0,1, indicating that they very well could be in the
denominator. Also, an exponent less than 0.1 indicates that the
variable is of no great significance to the equation and that it
would not change the magnitude of the design parameter significantly
(in Eq. (5.4) when W = 100 ft, (W)°-°^ = 1.047 and when W = 300 ft,
(H)O-Ol = 1.059), so as not to cause any serious error. However, in
83 Eqs. (5.11) and (5.16), this could be attributed to data used from
the analysis of slabs with aspect ratio of 1.
In Eq. (5.14) the forklift loading appears in the denominator
instead of the numerator, implying that an increase in its magnitude
would decrease the magnitude of the design parameter. This is due
to the reduction in deflections and bending moments in aisles as a
result of forklift loading at the same location in certain cases.
An identical finding is reported by Panak (30).
The correlation coefficient, expressed as "R-squared," measures
how well the regression model fits the data. R-squared values near
zero are expected for completely random data, whereas an R-squared
value of 1.0 would imply all data to fall evenly about the curve of
best fit. R-squared values for the regression equations resulting
from the analysis of the various SLAB4 data sets are listed in Table
5.1 and indicate equations provide a good to very good fit.
5.5 Limitations of Using the Regression Equations
The equations presented in Section 5.3 are for thickness design
of industrial floor slabs subjected to normal loadings anticipated
in a warehouse. These equations have been developed based on
certain assumptions and considerations. Therefore, it is essential
that the limitations on the validity of these equations be clearly
understood before attempting to use them. The assumptions made in
developing these equations are:
1. Stacks are 5 ft wide when access is from one side alone,
and/or 10 ft wide when access is from both sides.
1 m 'I
84
e o
• 1 —
to to OJ s-CD O)
OC
e o s-
^-
to cu
to e o
• 1 —
+ j fO
3 cr
L U
— f O C L
u <o
- a Q.
i . s-rO O 3 M-cr
(/) to
Q : to
• • ro
LD
OJ
. Q IT3
• o 0 ) S- 0 ) <0 3 3 ^ -O" <o
t / ) > 1
0 £
. • o- o
LU Z
bol
E >>
«/>
&. 0)
4->
a> E IQ U l O
Q .
c CD
( / I
c
tio
Cond
i
c • o
IO
o - J
0 0 at
o
c*> t n
<3
c o
•^ 4.^ t J 0 )
«^ o
_ I O
•^ . M c a> L. 0)
i « -
(^ o
mum
,^ X IO
z:
a% CO
o
«• t n
X D
ion
* j
u Ol L
•^ o
1 X
c •^ l/t (/) 0) u
4.>
(/) CT c
•^ • ^
c w
CQ
E 3 E X (O
0 0 0 0
o
i n
m
>) o
ion
•*j
u 0) i .
*f—
a 1
> f
c • r -
«/> l /t
a> i~
• ^
t o
O t c
• " "O c O)
CO
E 3 E
•f—
>< I O
0)
Alo
Load
ing
IO ••-> t /1
CM at
o
VO
m
X >
c o
•r— •«->
U 0) u
>.* o
1 X
c • r -
a> u i~ o U -
i . IO O)
.c oo E 3 E
•r— X l O
CO l>«
o
r m
>» 5 »
C O
•^ • M
u (U L.
• r—
a 1
>. c
•^ a; t j
^ o
L l -
i~ I O 0)
.c l/»
E 3 E X l O
0 0 CT>
o
0 0
i n
<
c o
•^ •4-) u <u
r—
>*-(U
o ^ K
(O • ^
4 J
c <u l~ <u <•-
14-• ^
o E 3 E
• * X I O
CO at
o
at
itt
X
o
UOL
•M U 0) &.
• p -
o 1
X
c "^
l /t l /t 0) L.
•• ->
t o
CT C
• » • o c <u
OQ
E 3 E
•^ X IO
o ^ CT CT
O O
O —' t-l 1—1
m LO
> » X D >
ion
•)-> c o o (U • ! -U 4->
•f - o o <u
1 L. >» ••-
a C 1
•<- X
l/t c l / t T -0) w <u
4-> t J 0 0 1 -
o CT t i .
c ••- &. - a IO C (U (U . c
CQ t o
E E 3 3 E E
• ^ 'f— X X lO (O
:E. Z :
ing
Load
if
t
r— 0)
&. O o •—
«—1 CT
O
CNi r - l
m
>» >
c o
•^ •!-> O (U w T *
o 1
>» c
•^ 0) u s-o L I .
i-«a 0)
j =
i / >
E 3 E
• r—
X IO
CT CT
O
CO r H
l / >
<
c o
•^ • M tJ <u — <•-0)
o — IO
• r—
4->
c (U
^ 0) <•->*-•.— o E 3 E
•r-X 10
CVJ CO
o
*r f - H
t n
>< o
ion
•M U <U i .
•^ o 1 X
c •f—
l/t l /t 01 i-
• t J VO
CT
c • . "O c <u CQ
E 3 E
• » X lO
«o o 0 0 CT
O O
t n t o l - H 1—1
t n t n
«>> *< D 3 »
UO
L
•«-> c u o 0) • • -i . -)->
•r- U O (U
1 k =*» :^
o C 1
• ^ X
l/t c 1/1 •<—
<u i . Ol 4-> tJ t o s-
o CT t i -
c • 1 — ^
"O lO C Q) 0) JZ
CO t o
E E 3 3 E E
•^ •^ X X IO IO
4 J >4-
rkli
us
Fo
Q . CT C
o -o IO lO
4-> O oo _ J
o CT
O
r». f - H
t n
>» >
c o
•^ 4 ^
u 01 &.
•.— a 1
>» c
*^ OJ tJ L-O
u. &-lO Ci
.c t o
E 3 E
•^ X lO
z:
!1 Hi
85
2. Stacks are assumed to be continuous and parallel to the
long dimension of the slab.
3. Concentrated loads due to rack posts cause only a punching
shear problem which is not considered here.
4. Stresses caused at edges due to moving loads and high stack
loads are recognized but have not been considered here (as these
could not be considered on an individual basis).
5. Aisle width is considered to be uniform.
6. Forklift truck is assumed to operate only in the aisles,
even when the slab is unloaded.
Other features that need to be recognized are:
1. A unit analysis on these equations will not yield conven
tional units for bending stress, shear force or differential
deflection. This appears to be an inherent problem when using
regression analysis to develop equations, but the unit "problem" is
accommodated in the coefficient of regression equation.
2. Input values of all parameters must be in consistent units
of kips and feet. Substituting parameters into equations in any
units other than in kips and feet will produce incorrect results.
However, if units of pounds and inches, for example, are desired,
the conversion must be made after obtaining solutions to the
regression equations.
3. It should be recognized that the equations have been
developed using parameters over a range of magnitudes typically
encountered in warehouses. Therefore, the equations will only
predict reliable values for ranges given in Table 4.8. For values
86
outside the ranges indicated in Table 4.8, the equations may not
give reasonable results.
5.6 Analysis of the Regression Equations
A number of examples were worked out using the regression
equations presented in Section 5.3. The results obtained and the
observations made during this exercise are discussed in detail
below.
As a first step, the reliability of the regression equations
was established. As was reported in Section 2.4, the reliability of
the results of an analysis using the finite element program SLAB4
was established by Huang (19) by comparing results predicted by the
program to field measurements. The results obtained by Huang using
the program were shown to compare reasonably well with experimental
measurements. Therefore, it can be concluded that the results from
the analyses used in developing the equations reported in this study
also can be considered to be reasonable reliably and that the
equations themselves will be equally reliable. However, as a check
on the ability of the regression equations to reproduce the data
used in their formulation, results (deflections, moments and shear
forces) from approximately fifteen cases (formed 3 to 18 percent of
the total cases analyzed for the different loading conditions) of
computer analyses were compared to those predicted by the regression
equations. The results were then plotted as shown in Fig. 5.1. As
can be seen, the points plot reasonably well about the 1:1 line
indicating that the equations represent the results of the analyses
reasonably well. Thus, having shown the equations to produce
CO
<
<
cr LiJ
h-
o o
87
0.0 0.1 0.2 0.3 0.4
REGRESSION EQUATION
FOR MAXIMUM DIFFERENTIAL DEFLECTION
0 1000 2000 3000 4000
REGRESSION EQUATION
FOR MAXIMUM STRESS IN X-DIRECTION
Figure 5.1: Comparison Between Computer Analysis and Regression Equations
T ^
88
acceptable results, examples were worked out to analyze the
predictions from these equations. An example used to analyze the
equations is discussed below.
Magnitude of the various parameters used are as follows:
Slab length, L = 250 ft
Slab width, W = 125 ft
Aisle width, A = 10 ft
Modulus of elasticity of soil, E = 1805 psi = 260 ksf
s
Stack loading, p = 8 psi = 1.152 ksf
Forklift loading, p^ = 110 psi = 15.84 ksf
Wheel spacing, S = 37 in. = 3.08 ft
Concrete compressive
strength, f' = 5000 psi
Factor of safety, FS = 1.5
Allowable tensile stress, F. = 7.5 = 353.55 psi = 50.91 ksf
FS
Allowable shear stress, v = 4 \ ^ = 188.56 psi = 27.15 ksf
Concrete modulus of elasticity factors:
E = 0.0167 V 5 0 M + 0.1208 = 1.30 X
E = 0 .0141 VFOOO'+ 0 .2565 = 1.25 y
The design parameters for the three loading conditions, assuming a
slab thickness, h, of 4 in. were found to be:
Stack Loading Condition
a = 76.42 ksf > 50.91 ksf N.G. X
a = 26.04 ksf < 50.91 ksf O.K. y
'^m
89
V = 0.23 ksf < 27.15 ksf O.K.
Forklift Loadino Condition
a^ = 16.39 ksf < 50.91 ksf O.K.
a, = 13.12 ksf < 50.91 ksf O.K. y
V = 6.65 ksf < 27.15 ksf O.K.
Stack Plus Forklift Loading Condition
a = 74.37 ksf > 50.91 ksf N.G. a = 39.63 ksf < 50.91 ksf O.K.
V = 0.20 ksf < 27.15 ksf O.K.
As the 4 in. thick slab was found to be insufficient for the stack
loading condition and stack plus forklift loading condition, the
slab thickness was increased to 6 in. The stresses in a 6 in. thick
slab for the three loading conditions were found to be greater than
those in the 4 in. thick slab. This will appear to be contrary to
what one would intuitively expect, but Panak reported an identical
finding (30). Panak reports that as the slab thickness increases,
bending moments and stresses also increase (bending moment being a
product of bending stiffness and curvature). One reason for this is
at the stack-aisle interface there is a reversal in bending moments
and, as the slab gets thicker, the values of the bending moments
increase. To the contrary, a thinner or more flexible slab will be
able to accommodate this reversal better. Panak (30) reports that
while the phenomenon of moment and stress reductions seems to lead
to the conclusion that a very thin slab is ideal for uniform
loading, the necessity for forklifts and trucks to operate on the
slab and the presence of cracks due to shrinkage and other causes
90
limit the advantage to be gained. But he does not discuss the
effect of increasing thickness for forklift loading on the stresses
due to uniform loading. Results of other procedures discussed in
Section 1.3 indicate that for the forklift loading (which do not
discuss uniform loading condition either), as the slab thickness
increases, stresses decrease. This is due to the difference in
modeling of the subgrade. The other procedures model the subgrade
as a Winkler foundation rather than an elastic half-space and use a
single value for the modulus of subgrade reaction. With such a
model, as the slab becomes more rigid, the deflection becomes more
uniform (tending toward rigid body motion) and, therefore, result in
lower bending moments and stresses. It is also not known if the
other procedures take into account the additional load due to the
increased weight of the slab (due to increased thickness) or con
sider the additional thickness for stiffness calculations alone.
This increase in values of design parameters with an increase
in thickness was observed in all the examples attempted. However,
for every problem, there is a certain "threshold" value of soil
modulus below which even slab thicknesses in excess of 10 inches
will not provide acceptable results for the given loading. For
values of soil modulus above this "threshold" value, any thickness
(4 <^h i l O in.) of slab will provide acceptable stresses. The
above findings with the example problem discussed above are
summarized in Table 5.2.
T^
91
_ o +-> QJ 3
O
U) S-O) +J to (U to E cu fO c i- J ^ fC o
Q_ •!—
c f— CD
•r- j a to fO OJ 1—
( 3 t/0
c c • ^ 'r—
OJ O) to to n3 fO O) <u s- s-o o c c
1—t »—t
<NJ •
LD
<u t—
1—
-a r—
o J C = M-co too a; LLJ . ^ i_ =
,c h-
0 1 c
•r— to "O 3 ro r— O • — 1
CO • ! -+J 1— CO .i<:
&-o
U -
CD c
•r—
-o <o o
_ J
-> H -
1 —
o U -
CT) c:
• 1 —
fO o
_ J
ack
I/O
M -to
. ^
M-to
J:<:
^ -to
J ^
4 -to
Ja^
M-lO
.:^
M-to
. ^
^-to
^-to
H -to
to to a> c
(O o c r ^ . ,— • ! • -
(>o x: h -
,,_^ •r— to
t o O . •
CO o «;1- LO ^ t - t
CO
o CVJ
• o
ro VO
• CTt CO
r«. CO
• ^ r^
Ln wo
• t o
Csl I - H
• CO t - H
at CO
• VO f - H
CO C J
•
o
«:i-o
• VO CO
CVJ «:d-
• VO r^
<d-
^ ^ • 1 —
to C\J Q .
• r o «;!• O Lf) 0 0
CO
'vi-CM
• o
^ «;*•
• CvJ < ; * •
at VO
• 0 0 r-
CO 0 0
• r«.
CM o
• i n « - H
< -<d-
• 0 0 1 - H
I O OJ
•
o
LO o
• CO CO
r-». at
• LO 0 0
VO
,._^ • 1 —
to CO Q .
• >!d- O o o t o CJ
"?!•
ir> 0 0
• •si-«!3-
LO 0 0
• «d-^
LO r H
• CM 0 0
VO ^
• 0 0
^ LO
• VO l - H
VO CNJ
• o CM
0 0 CM
•
o
VO LO
• CTt CO
VO *:^
•
at
0 0
^ - ^ •^-Ul
^ a. • CM O VO O VO VO
">1-
r^ CM
• o
0 0 r>-
• VO «!d-
LO r^
• <:i-0 0
O O
• at
r^ 0 0
• r»> t - H
CO VO
• t - H
CM
O CO
•
o
r^ o LO « *
CO CO
o o t - H
o t - H
CHAPTER 6
DESIGN PROCEDURE USING THE REGRESSION EQUATIONS
6.1 Introduction
A step-by-step procedure is presented in this chapter to assist
the user in using the regression equations. Parameters considered
to be important in the thickness design of industrial floor slabs
are presented in Chapter 4 and the regression equations for maximum
bending stresses, maximum shear forces, and maximum differential
deflection for stack loading, forklift loading, and stack plus
forklift loading conditions are presented in Chapter 5.
The design process begins with the determination of field
conditions and the required site preparation. As this step is
critical to a successful design of an industrial floor slab, a brief
introduction to a soils investigation is presented in the following
section.
6.2 Soils Investigation
A soils investigation at the proposed site should be conducted
to determine: (1) type or types of soil at the site, (2) depths and
distribution of each soil type, (3) consistency of clay soils and
density of granular soils, and (4) modulus of elasticity of the
soils.
92
93 The modulus of elasticity of soil which was shown in Chapter 5
to be the most important of the parameters, can be determined by
using the unconfined compression test which has been recommended in
Chapter 3 as the most practical and economical means of evaluating
this property of the soil. If cohesionless soils are encountered,
then the second choice, namely the standard penetration test, may be
used. However, it is left to the judgment of the geotechnical
engineer to decide on a testing procedure based on availability,
types of soil present and site conditions. It is also left to the
judgment of the geotechnical engineer to decide on the locations and
types of soil to be tested so as to provide realistic values for the
design. Further, it is recommended that special preparation of the
site be carried out if unstable soil conditions are present.
6.3 Safety Factor
A safety factor is incorporated into a design procedure to
account for deviations that are bound to occur between conception
and completion. The selection of a value to use as safety factor
depends on other assumptions, but should result in a design that is
reasonably conservative but not excessively so.
With this concept, various design procedures use different
values for safety factors for different loading conditions. But all
of the values fall within the range between 1.25 and 2.0 (32), where
a safety factor of 2 is generally used for unlimited repetitions of
wheel loads. For normal warehouse conditions, safety factors in the
range between 1.4 to 1.7 are used. In the design examples using the
94
regression equations in Appendix I and Appendix J, a safety factor
of 1 has been assumed.
6.4 Design Procedure
The first step towards design would be to gather information
regarding the soil, structural and utility parameters described in
Chapter 4. Also, the compressive strength of concrete, f , and the
allowable tensile stress of the concrete, f., need to be specified.
Slabs of irregular shape (e.g., L-shaped) should be divided into
rectangles and each rectangle designed individually.
The design process begins by first considering the stack
loading condition. The design steps are as follows:
1. Assume a trial slab thickness. Based on construction
practices, it is recommended that it would not be practical to
construct such a floor slab less than 4 in. thick (33). Therefore,
as a starting point, the trial slab thickness could be assumed as 4
in.
2. Calculate the allowable tensile stress from (1),
f. 11 KT = 7.5^71 (6.1) t allowable c
where f ' = compressive strengh of concrete, psi
3. Maximum shear force was found to occur under the load and
toward the middle of the slab. Therefore, it can be assumed to be a
two-way action and the maximum allowable shear stress for two-way
action is determined using (1)
y = ^ \rr' (6.2) c c
where
V = maximum allowable shear stress, psi c
95 f^ = compressive strength of concrete, psi
4. Calculate the stress that the slab would experience in both
directions due to the known imposed loads using Eqs.(5.4) and (5.5.)
If the allowable value is exceeded, then consider improving the
subgrade (with higher modulus of elasticity value) or increasing the
required strength of concrete, namely, f;. Analysis presented in
Chapter 5 showed that if the soil modulus is inadequate, that even
slab thicknesses in excess of 10 in. will not satisfy bending stress
requirements.
5. Calculate expected maximum shear force in each direction in
the section using Eqs. (5.6) and (5.7).
6. Calculate the maximum design shear stress using
V 1000 v = b;d^-l44 (6.3)
where
V = maximum design shear stress, psi
V = maximum shear force, kips/ft
b = minimum perimeter = (1 + 2d) x 4, ft
d = effective depth = 0.8h, ft
h = thickness of slab, ft
If the maximum design shear stress value is greater than the maximum
allowable shear stress, then consider improving the subgrade or
increasing the required strength of concrete, namely, f'. Analysis
presented in Chapter 5 showed that increasing the slab thickness
will not solve the problem.
96 7. Following the same procedure, check the adequacy of the
section for forklift loading condition and stack plus forklift
loading condition.
8. If there is a limit on the allowable differential deflec
tion for the floor slab, calculate the maximum differential
deflections for the three loading conditions using Eqs. (5.3),
(5.8), (5.13) and compare it to the allowable value. If this
allowable value is exceeded, then consider improving the subgrade,
as increasing the thickness will not solve the problem.
A design example illustrating the procedure is included in
Appendix I. Also, a comparison of the required slab thickness
resulting from the equations to the required slab thicknesses from
three other methods has been made and shown in Table 6.1. Details
of design steps of the other procedures are included in Appendix H.
The design example used to illustrate the PCA method (28) has been
worked out using the regression equations in Appendix J to make a
one-to-one comparison between the two. However, such a one-to-one
comparison was not possible with Panak's method (29,30) and the
Corps of Engineers method (4,13,14) because some of the variables in
the examples fell outside the ranges indicated in Table 4.8.
The design procedure presented here is for the required thick
ness of the slab section to satisfy the expected service loading
conditions. However, to control shrinkage cracking it is often
recommended (13) to provide 0.10 percent (of the cross-sectional
area) distribution steel in both directions.
97
to e o
• r --M ro 3 cr
LU
c: o
•r— to to CU S-cn OJ
Q i
c O) OJ 2
- l - > O)
CQ
c o to
•^ &. ro Q . E O c_>
to cu i-3
-o cu u o s_
O-
CT) e
• 1 —
-M to
•r— X
LU
T3 e IO
V D
CU
!o (O
l / t o C l/t o
• 1 - l/» • ! -l/t 0) •!-> 3 L. (O
CT 3 a» O"
Q g L U
l / t
o a> 91
l/t c Q.'r-i~ CT o c
<-> t l J
IO
(O
o.
o o o m t n
o o o i n
CSJ
o o o
* t n
o o o tn
o o o o o o
o in 0 0 1-4
>» i.
I o I CT
0 )
f O
o •a-
CO r
lO
o
tn
o a.
t—l
»* CM
O O o t n
o o o m
o
4,00 o
• 00
o o o r"*
• .
Mome
nt
whee
l
1—t 1 CO 1
VO 00
i n
t n f ^
« » •
CSJ
o o o tn
o o o o o o
<4- i n o CO
.a in I— CO
O II o o -o r— IO •>^ o l/t r— l /t
a> 01 U r -
• M X l / > l O
CO CM
3 vt in < IO o .
I/I
<u £> <o r" U IO
_ l
•* .c *-> CT C OJ
OJ
l/t ^-3 ••-
«— O 3 t o -o O M -s: o
0) •o l O i . -f-CT O
. O Q . 3
O * c I/I o 3 • • -
I — ••-) 3 U
-o <o O 0 ) s:o£
CT C • • -0 1 V t L . O .
•l-> 0 0 "
u 0 ) * * ->
• t - • l /t O) Wt •!->
0) a; C3. U E c o o
>» tn u ca.
i / i t j I O I x J
OJ
O OJ
in u 3 C
»— O 3 O
• D O < • -
s o
l /t • I - Q . l/t Q .
l /t • O . CT
C
CT C IO ••- o • a _ j lO o +J
. ^ r -t J . ^ IO w
•!-> O lyO t i .
«/)
CT
U lO o.
1/1
ID OJ
• a cr OJ • l /t " O c
IO ' ^ • •> o .a c
IO _ i c r IO - f -OJ l/t r— s_ 4-> t o •>
< c " m 0) ^ "O l/t
••-> »— O) O) 0) U IO •<-> i . c (O > a; •!- . ^ *-> •-- e 3 o c 3 IO cr-«-o cr-i- 01 . c
o tu o a: h-
Chapter 7
CONCLUSIONS AND RECOMMENDATIONS
7.1 Introduction
The principal objective which initiated the work presented here
was to develop a design or analysis procedure which would:
1. Be rational.
2. Be capable of producing values of bending stress, shear
force, and differential deflection resulting from expected service
loads.
3. Be applicable to all industrial floor design in general.
4. Be easy to use.
There are certain limitations to the work presented here. A
brief discussion of these limitations are included. Conclusions
based on analysis of the regression equations presented in Chapter 5
are also summarized here.
7.2 Conclusions
7.2.1 Rational Procedure
All the properties needed for the equations presented in
Chapter 5 can be either directly measured or computed and none have
to be assumed.
98
. ».£«
99 7.2.2 Specific Design Values
The design equations developed in Chapter 5 and incorporated
into the design procedure in Chapter 6 will produce values of
bending stress, shear force, and differential deflection. By this it
is meant that these values can be directly compared with the allow
able values, whereas in the other existing procedures it is not
possible to study the variation in any of these design parameters
corresponding to a change in any of the parameters discussed in
Chapter 4. These procedures yield only the thickness required for a
particular set of parameters.
7.2.3 General Application
The procedure presented herein was not developed for a specific
problem or by considering only specific values for parameters and,
therefore, facilitates its use for a wide range (within those
indicated in Table 4.8) of parameters. These values (values of
design parameters) are not dependent on any type of reinforcing
system and therefore can also be used to design a reinforced or a
post-tensioned floor slab.
7.2.4 Ease of Use
The equations are simple, easy to use, and can be easily pro
grammed for a personal computer or a hand calculator.
7.2.5 Limitations
As discussed in section 5.5, the equations developed here have
been based on certain assumptions, which were made in order to
facilitate the analysis. The assumptions made should be clearly
1 in
100 understood before attempting to use the equations. Also, the
equations were developed by considering a wide range of values for
parameters. Therefore, it should be recognized that the use of
these equations for values of parameters outside the limits given in
Table 4.8 will likely yield unreasonable results.
7.2.6 Conclusions Based on Analysis of the Regression Equations
1. At any given value of soil modulus, with all other
parameters held constant, bending stress is shown to increase as
slab thickness increases.
2. Above some "threshold" value of soil modulus, any thickness
of slab will prove to be acceptable with respect to bending stress
(4 £ h £lO in., E^ £ 15,000 psi).
3. Below this "threshold" value of soil modulus, no slab
thickness ( 4 ^ h £ 10 in.) will provide acceptable results.
4. Conclusions 2 and 3 are contingent upon the given set of
parameters, i.e., the "threshold" value of soil modulus varies with
the magnitudes of the parameters and, thus, the "threshold" value is
not a constant value from one problem to the next.
5. Conclusion 1 is consistent with the previously reported
findings of Panak.
6. With all other parameters held constant, as the value of
soil modulus increases, the resulting bending stresses decrease.
Further, as the value of soil modulus increases, the magnitude of
the resulting bending stress becomes less sensitive to variations of
the ratio of E /h.
101
7. From analyzing the same problem where the only varying
parameters are slab thickness and soil modulus, increasing slab
thickness will not result in an acceptable design if the problem
exceeds the allowable bending stress at a given value of soil
modulus. This is due solely to the increase in section stiffness
resulting from an increase in slab thickness. The only way to
reduce bending stress at any given slab thickness (assuming all
other parameters are held constant) is to improve the value of soil
modulus.
7.3 Recommendations
As with any research work, the work presented here has room for
improvement. Based on the experience gained from this study, the
following recommendations are made:
1. Units of design parameters, namely bending stress, shear
force and differential deflection produced by the regression equa
tions are not of the conventional form typically expected, i.e., a 2
dimensional analysis would not strictly result in units of F/L for
stress, e.g. kips/ft^. This is due to the use of regression
analysis to derive the equations (which considers only the numerical
values and not the units for the solution). It should be recognized
that the unit "problem" is accommodated (or accounted for) in the
coefficient of the regression equation. Thus, it is y/ery important
that only the units specified in Chapter 5 be used in solving the
equations. If other units are desired, the conversion must be made
following the solution of the equation and not before. If this
inconsistency in units is not desired, then it is recommended that
102
the design equations be developed in terms of nondimensional param
eters.
2. Constant thickness monolithic slabs alone were considered
and, therefore, the design parameters at an edge need to be fully
analyzed. This analysis would improve the flexibility of this
procedure.
3. The forklift loading analysis was a quasi-static analysis.
This approach was taken to save computer time without sacrificing
principles of statics or dynamics. However, for future use in a
similar analysis, it is recommended a table of values of design
parameters be developed for various loadings, locations, dimensions,
soil conditions and properties.
4. The work presented here needs to be extended to include
larger stack and forklift loading.
LIST OF REFERENCES
1. American Concrete Institute, "Building Code Requirements for Reinforced Concrete," ACI Committee 318, September 1983.
2. American Concrete Institute, "Recommended Practice for Concrete Floor Slab Construction," ACI Committee 302, August 1968.
3. American Concrete Institute, "Manual of Concrete Practice, "Floor and Slab Construction," Part 1, 1978, pp. 302-303.
4. American Concrete Institute, "Design of Slabs on Grade: State of the Art," Preliminary Draft, 1984.
5. Bowles, J.E., Foundation Analysis and Design, McGraw-Hill Book Co., New York, 1968.
6. Brown, P.T. and Gibson, R.E., "Surface Settlement of a Deep Elastic Column Whose Modulus Increases Linearly with Depth," Canadian Geotechnical Journal, Vol. 9, No. 4, 1972, pp. 467-476.
7. Building Research Advisory Board, "National Research Council Criteria for Selection and Design of Residential Slabs-on-Ground," U.S. National Academy of Sciences, Publication No. 1571, 1968.
8. Cheung, Y.K. and Zienkiewicz, O.C, "Plates and Tanks on Elastic Foundations--An Application of Finite Element Method," International Journal of Solids and Structures, Vol. 1, 1965, pp. 451-461.
9. Clegg, B., "Design Compatible Control of Basecourse Construction," Australian Road Research 13(2), June 1983, pp. 112-22.
10. Concrete Reinforcing Steel Institute Design Handbook, 1968, pp. 426.
11. Crossley, Robert W. and Beckwith, George H., "Subgrade Elastic Modulus for Arizona Pavements," Executive Summary submitted to Arizona Dept. of Transportation, Highways Division, March 1978.
103
104
12. Department of the Army, "Rigid Pavement for Roads, Streets Walks and Open Storage Areas," Technical Manual No. 5-822-6 April 1969.
13. Department of the Army, "Concrete Floor Slabs on Grade Subjected to Heavy Loads," Technical Manual 5-809-12, Construction Engineering Research Laboratory, Champaign, Illinois, April
14. Department of the Army, "Engineering and Design of Pavement for Roads, Streets, Walks and Open Storage Areas," Technical Manual TM 5-822-6, April 1977.
15. Frazer, B.E. and Wardle, L.J., "The Analysis of Stiffened Raft Foundations on Expansive Soil," Proceedings, Symposium on Recent Developments of the Analysis of Soil Behaviour and Their Application to Geotechnical Structures, University of New South Wales, Kensington, N.S.W., Australia, July 1975, pp. 89-98.
16. Gibson, R.E., "Some Results Concerning Displacements and Stresses in a Non-Homogeneous Elastic Half Space," Geotechnique 17, 1967, pp. 58-67.
17. Hetenyi, M., "Beams on Elastic Foundations," The University of Michigan Press, Ann Arbor, Michigan, 1946.
18. Hocking, R.R. and Leslie, R.N., "Selection of the Best Subset in Regression Analysis," Technometrics, Vol. 9, 1967, pp. 531-540.
19. Huang, Y.H., "Finite Element Analysis of Slabs on Elastic Solids," Transportation Engineering Journal, May 1974, pp. 403-416.
20. Huang, Y.H., "Analysis of Symmetrically Loaded Slab on Elastic Solid," Technical Notes, Transportation Engineering Journal, May 1974, pp. 537-541.
21. Hudson, William R. and Hudson, M., "Discrete Element Analysis for Discontinuous Plates," Proceedings of the American Society of Civil Engineers, Journal of the Structural Division, ASCE, October 1968, pp. 2257-2279.
22. Lambe, T. W. and Whitman, R. V., Soil Mechanics, SI Version, 2nd Edition, John Wiley and Sons.
23. LaMotte, L.R. and Hocking, R.R., "Computational Efficiency in the Selection of Regression Variables," Technometrics, Vol. 12, 1970, pp. 83-93.
IF»^
105 24. Lukas, R.G. and de Bussey, B. L., "Pressuremeter and Laboratory
Test Correlations for Clays," Proceedings of the American Society of Civil Engineers, Journal of the Geotechnical Engineering Division, No. GT9, Vol. 102, September 1976, pp. 945-962. ^
25. Lytton, R.L., "Design Criteria for Residential Slabs and Grillage Rafts on Reactive Clay," Report for the Australian Commonwealth Scientific and Industrial Research Organization, Division of Applied Geomechanics, Melbourne, Australia, November 1970.
26. Madhav, M.R. and Ramakrishna, K.S., "Undrained Modulus from Vane Shear Test," Technical Note, Proceedings of the American Society of Civil Engineers, Journal of the Geotechnical Engineering Division, Vol. 103, No. GTll, November 1977, pp. 1337-1340.
27. Packard, R.G., "Computer Program for Airport Pavement Design," SR029P, Portland Cement Association, 1967.
28. Packard, R.G., "Slab Thickness Design for Industrial Concrete Floors on Grade," IS 195.OlD, Portland Cement Association, 1976.
29. Panak, J.J., McCullough F.B. and Treybig, H. J., "Design Procedure for Industrial Slabs Reinforced with Welded Wire Fabric," an interim report prepared for the Wire Reinforcement Institute by Austin Research Engineers, Inc., March 1973.
30. Panak, J.J. and Rauhut, J.B., "Behavior and Design of Industrial Slabs on Grade," American Concrete Institute Journal, May 1975, pp. 219-224.
31. Pickett, G., "A Study of Stresses in the Corner Region of Concrete Pavement Slabs Under Large Corner Loads," Concrete Pavement Design, Portland Cement Association, 1951, pp. 77-86.
32. Pierce, D.M., "A Numerical Method of Analyzing Prestressed Concrete Members Containing Unbonded Tendons," Dissertation presented to the University of Texas at Austin, Texas in partial fulfillment of the requirements for the degree of Doctor of Philosophy, 1968.
33. Rice, P.F., "Design of Concrete Floors on Ground for Warehouse Loadings," Journal of the American Concrete Institute, Vol. 29, No. 2, August 1957, pp. 105-113.
34. Ringo, B.C., "Desian, Construction and Performance of Slabs-on-Grade for an Industry," American Concrete Institute Journal, 1978, pp. 594-602.
»»»>< '
106
35. Ringo, B.C., "Planning, Design and Construction of Slabs on Grade," Design of Industrial Floors, American Concrete Institute, SCM-5, 1983.
36. Ringo, B.C. and Steenken, J.M., "Industrial Floor Slabs: A Thickness Solution," American Concrete Institute, COM 1/83, 1983.
37. Schmertmann, J.H., "Static Cone to Compute Static Settlement Over Sand," Proceedings, American Society of Civil Engineers, Journal of Soil Mechanics and Foundations, Vol. 96, SM3, 1011, May 1970.
38. Simons, N., "Settlement Studies on Two Structures in Norway," Proceedings of the 4th International Conference on Soil Mechanics and Foundation Engineering, London, 1957, p. 431.
39. Singer, F.L., Strength of Materials, 2nd Edition, Harper and Row, New York, 1962.
40. Spear, R.E., "Concrete Floors on Ground," Portland Cement Association Journal, 1978.
41. Stroud, M.A., "Standard Penetration Test in Insensitive Clays and Soft Rocks," Proceedings of the European Symposium on Penetration Testing, Stockholm, June 1974, pp. 367.
42. Terzaghi, K. and Peck, R.B., Soil Mechanics in Engineering Practice, John Wiley and Sons, Inc., New York, 1948.
43. Timoshenko, S. and Woinowsky-krieger, S., Theory of Plates and Shells, 2nd Edition, McGraw-Hill Book Co., New York, 1968.
44. Timoshenko, S. and Goodier, J.N., "Theory of Elasticity," McGraw-Hill Book Co., New York, 1951.
45. Vantil, C.J., McCullough, B.F., Vallerga, B.A. and Hicks. R.G., "Evaluation of AASHO Interim Guides for Design of Pavement Structures," NCHRP Rep. 128, Highway Res. Board, 1972.
46. Walsh, P.F., "The Design of Residential Slabs-on-Ground," Division of Building Research Technical Paper No. 5, Commonwealth Scientific and Industrial Research Organization, Highett, Victoria (Australia), 1974.
47. Wang, S.K., Sargious, M.A., and Cheung, Y.K., "Advanced Analysis of Rigid Pavements," Proceedings of the American Society of Civil Engineers, Transportation Engineering Journal, February 1972, pp. 37-44.
107 48. Westergaard, H.M., "Computation of Stresses in Concrete Roads,"
Proceedings, Highway Research Board, Vol. 5, Part I, 1925, pp. 90-112.
49. Westergaard, H.M., "Stress Concentrations in Plates Loaded Over Small Areas," American Society of Civil Engineers, Transactions, Paper No. 2197, 1943.
50. Williams, C.E. and Focht, J.A. Ill, "Initial Response of Foundations on Stiff Clay," ASCE National Convention, New Orleans, Louisiana, October 1982.
51. Williams, C.E. "Initial Response of Foundations on Mixed Stratigraphies," Transportation Research Board Meeting, Washington, DC, January 1986.
52. Winkler, E., "Die Lehre von Elastizitat und Festigkeit," Prague, The Netherlands, 1867, pp. 182.
53. Wray, W.K., "Development of a Design Procedure for Residential and Light Commercial Slabs-on-Ground Constructed Over Expansive Soils," Dissertation presented to Texas A&M University, College Station, Texas in partial fulfillment of the requirements for the degree of Doctor of Philosophy, 1978.
54. Zienkiewicz, O.C. and Cheung, Y.K., "The Finite Element Method for Analysis of Elastic Isotropic and Orthotropic Slabs," Proceedings, Journal of Institute of Civil Engineers, Vol. 28, 1964, pp. 471-488.
55. Zienkiewicz, O . C , The Finite Element Method in Engineering Science, 2nd Edition, McGraw-Hill Book Co., London, 1971.
APPENDIX A
USER'S GUIDE FOR COMPUTER PROGRAM SLAB4
108
109
A.l Comments on the Use of the Guide for Uata Input for Program SLAM
A.1.1 General Program Notes
1. The data cards must be stacked in the proper order for the
program to run.
2. A consistent set of units must be used for all input data,
e.g., pounds and inches, except where specified otherwise.
3. The input data cards, or sets of data cards, are presented
in the order in which they would be required to be arranged if the
analysis option selected (Option 1, 2, 3 or 4) required that par
ticular data. For example. Option 2 would require the nodal numbers
at which subgrade reaction is assumed to be zero as input data; this
data would be Data Set 7. Option 1 does not require nodal numbers of
zero reaction and, thus, the input data deck for this option would
not contain a Data Set 7.
Data Set 1
Defines the number of problems to be solved (data decks to read
in) without recompiling the source deck.
Data Set 2
Defines the rated capacity of the forklift used in the analysis
and the aisle width in which the forklift operates.
Data Set 3
This data set identifies the problem: slab length and width,
beam depth, edge moisture variation distance, maximum amount of soil
110 movement, the swelling mode, the exponent in the exponential equation
that describes the shape of the swelling soil profile, whether the
structural stiffness will be determined as a stiffened slab section
or as a constant depth section, and if there is a second loading on
the slab.
Data Set 4
1. Provides dimensions of the stiffening beams and their
spacing, dimensions of the slab portion of the total cross-section,
and moments of inertia in both directions.
2. This data set is not included if a constant-depth section is
being analyzed.
Data Set 5
1. The first card of this two-card data set identifies the
number of slabs to be analyzed (1 or 2), material properties
(Poisson's ratio and modulus of elasticity of soil and concrete), and
several programming constants, e.g., type of symmetry, if any;
presence of non-contact locations; if pre-calculated deflections are
to be input; and if punched output is desired.
2. The second card defines the number of x and y coordinates
occurring in each slab, the number of iterations to be allowed in
establishing subgrade contact, the number of nodes and the nodal
numbers at which output calculations are to be printed.
3. The coordinates in the x-direction begin at zero and in
crease from left to right. Coordinates at the joint must be counted
twice if two slabs are being analyzed. Y coordinates also begin at
zero and increase from bottom to top. The number and coordinates of
n im
111
the y-direction nodes is the same whether one or two slabs are being
analyzed.
Data Set 6
The coordinates of the x- and y-direction nodes are read in
according to F8.3 format. If two slabs are being analyzed, coor
dinates for the nodes at the joint must be read in twice. More than
one card may be necessary to read in all of the coordinates.
Data Set 7
If NOTCON is not zero, the nodal numbers at which there is no
soil-slab contact are input in accordance with 15 format. More than
one card may be necessary to define all nodal numbers.
Data Set 8
This single card data set identifies the total number of nodes
at which a gap exists between the soil and the slab, the number of
elements experiencing loading, the amount of loading (as a pressure,
e.g., psi or psf), whether temperature is to be considered in the
solution, the temperature difference between the slab top and bottom,
the number of nodes at which convergence will be checked, and itera
tion and tolerance limits.
Data Set 9
Input the nodal numbers at which convergence will be checked in
accordance with 15 format. More than one card may be required to
input all check nodes.
Data Set 10
This Data Set reads in the amount of gap previously calculated
as existing between the slab and subgrade at each node where a gap
112 exists. More than one data card may be required to read in all gap
data. If NREAD = 0, there are no previously calculated gaps and this
Data Set will not be included in the problem data deck.
Data Set 11
If gaps exist at specified nodes, this Data Set identifies those
nodes in 15 format. More than one card may be necessary to identify
all nodal locations. If NREAD = 2, this Data Set is not needed and
will not be included in the problem data deck.
Data Set 12
This Data Set assigns the magnitude of the gap at each location
specified in Data Set 11. The input format is F8.4 and more than one
card may be required to input all data. There must be as many gap
values as there are gap locations in Data Set 11. If NREAD = 2, this
Data Set is not needed and will not be included in the problem deck.
Data Set 13
If a uniformly distributed load acting over the entire slab
surface in addition to any live loading specified in Data Set 8 is to
be considered in the analysis, set NWT = -1 and the uniformly dis
tributed load will be read in on a single card in F8.3 format.
Data Set 14
1. The elemental numbers which are to receive some loading 0 are
identified in 15 format. More than one card may be necessary to
identify all loaded elements.
2. Elemental numbers increase from bottom to top and from left
to right. There are (NX-1) x NY-1) elem.ents.
113 Data Set 15
1. The area being loaded by Q is described by XDA and YDA. The
load is distributed over the elemental area from the center of the
rectangular element on a fractional basis in both directions ranging
from -1.00 to +1.00. For example, if the load were to be applied
over the rightmost 75 percent of the element in the x-direction, the
input values would be: XDA(l) = -0.50 and XDA(2) = +1.00. If the
same load were to cover only the bottom half of the element in the
y-direction, the input values would be: YDA(l) = -1.00 and YDA(2) =
0.00. If the entire element is to be loaded, the load distribution
would be -1.00 and +1.00 in both directions.
2. The distribution cards must be stacked in the proper order
to ensure distribution of load over the corresponding element, NL(I).
Data Set 16
Defines the number of elements on which the second loading Q2,
acts in 15 format and the loading intensity in F10.5 format.
Data Set 17
The elemental numbers which are to receive the second loading Q2
are identified in 15 format. More than one card may be necessary to
identify all loaded elements.
Data Set 18
1. The area being loaded by Q2 is described by XDA2 and YDA2.
The load is distributed over the elemental area from the center of
the rectangular element on a fractional basis in both directions
ranging from -1.00 to +1.00 (Refer to data set No. 15).
114
2. The distribution cards must be stacked in the proper order
to ensure distribution of load over the corresponding element,
NFL(I).
115
U J
o I—I
o <c o _ J CO
t / 1 HH •«LU _ J
C_3 ^ L U C_3 •« X Z > -
l-H o : t—
t/^ 2 : o X I—I 0 0 X >-*
_j 2 : s : X >- s : X X 2 :
Q
o _ J I / )
>-a: \— o
o VO
LO LO
O LO
LO
LT) O
> 3 -
>-X
. 0 CO
LU X
o "CM
t/T ;< X
CM
O h—I
CO
o
•a: t —
o
CO
o LO
u. L U t /0
o
D-
c_)
I—
X X
116
OQ
zn.
C_)
O
£5
8 2:
O 00
LO
.0
.LO VO
. 0 VO
LO LO
. 0 I—
LO "VO
O "VO
LO •'LO
CXL CL.
LU CQ
00 LU Q O
•a: J— CO
o
LU C/1
<
LU C_)
Q . tyO CQ
O-C/)
z: <c LU CQ
<: LU OQ
00
<: LU CO
LU OQ
00 "si-
CD
.CM CO
CM
oo CC CL.
.LO
t/
LO CO
CJ to CM
>-t-H
o .VO
.LO
CO
•00 •X t — l
o
to
o
J — LU 00
<: I — Q
ca Q-
CQ <c _J 00
•LO
CC CL.
C_) >-
CM X
o "LO
LO
o
LO "CO
. 0 CO
LO "CM
o •CM
LO
•LO
>-CC <c CO t/1 LU
o
CO
>-<c 2: 00 Q
<: C_)
o l-H
I—
O CJ
117
t o
•
o •z. \-LU OO
•a: I— <
6 64
72
0 48
5
6 24
32
4
t-H
00
o LU CJ OO
Q «a:
3 : t-« Q O u_ cr: _ i O _ J LU o o H- o u- <:
2 : _ i t / ) I—I _ j LU Q ea; \ - CC
2r o 00 »—I C_3 t—I O _1 Ct: X o o O I— I— CJ C/7
<: >-> - _ j Q :
<c ••>LU CO
I— 3 1 0 0 0 0 I— LU CC O t—I CO LU
00 3 LU LU O CQ \— -J CC _J 5-z o «a: t—I u- 2: o ce: >- 00 o _-J o o LU a: o I— <c
< o X I—* I— LU O 00 s: "-I •-I 2: t—
r-•
0 z h-LU t/1
•a; J— «a; Q
'"^ ' 1 ^^^ r-J z.
0 t^
LO VD
0 VO
LO LO
<-1 LO
LO
<^
LO CO
0 CO
20
25
LO r—t
0 t-H
LO
r-\
U-0
C/7 LU 0 0 •z.
-J _1 <
t— I — 1
_l
0 1—
>-CC <: oo
NECE
S
LU CQ
>-«sC 2: 00
cn
N CA
R NU
ATIO
I — 1
t— •zz 0 CJ
^ LU 1— 0 z.
CJ
o CJ
00
o
I— LU 00 < I— <x.
Ll-_I CJ 1—1
•-0 LL. Qi
U-_J LU Q
_J LU 0
CJ-
O-SI LU I—
\-3 2:
:^ CJ
^
_ j C_) 1—1
Q ea: 0 _J 2:
u. *. '.ij (— P' 0.
-^
0 CO
LO
0
0 VO
r-> to
0
0 CO
LO CM
0 CM
LO 1—1
0 f-H
LO
118
.CO
o
LO VO
o VO
LO LO
en •
o z h-LU OO < <
O LO
LO
O ^3-
LO CO
o CO
LO CM
CJ CM
LO
^1 1
2l
LO
t/0 LU
O
<: h-00
CC ZD CJ
U-
o
oo
CC
OQ
>-<3:
oo CD CC
<c CJ
o I —
o CJ
.1^ VO
CO
I —
Q
CC
CJ
CM LO
at CO
VO CM
<: I— oo
>-CC
oo CO
CQ
>-
OO o Q: «a: CJ
o I — I
I —
o CJ
CO
CO
«a; I— <: Q
CD
,o
LO VO
o VO
LO LO
o LO
LO
o
LO CO
o CO
LO CM
o CM
LO
LO
QC L U <C oo t / 0 oo LU O LU "ZZ
LU CQ
>-<c 2 :
oo Q CC <: C J
•z.
LU CC CL.
L U CC <SL
OO CL. ca: CD
2 : LU 3 1 3
oo LU Q
o o <: —1
2: <:
•2L 00 CJ t-H CJ _J
LU
119
r CM
VO
_ VO LO
CO
CO
CM
VO
C/0 CL. < : CD
(— OO
>-oc CO
oo LU CJ
CQ
>-<t
OO C3 CC ct CJ
o I — I
I— «t
o CJ
CM CO
OO
< I— <
CD
_j oc
CJ
00
U o o
I—
CQ ct _J OO oo
c t I — «=t C2
o
LO VO
o VO
LO LO
o LO
LO
O
LO CO
o CO
LO CM
O CM
LO
LO
OC . ct CD OO LU OO o LU <C C J O
LU CC CQ
O >- I— ct 2; 00
h-OO 2: CZi LU OC 2: e^ LU C J _ J
I— <c
z. 00
o o CJ h-
120
o
CM
a >-
o CO
LO
CO
Ct I— ct
ct O >-
CM
Q X
ct O X
o CsJ
CC LU • Ci- O o z oc CL. I—
LU LU OO
I— ct I—
Z ct t-H Q
O LL. LU O CD 2: 00 ct 1— CC Z. OC LU ct 2:
LU 00 _J O LU CC ct Q CJ LU
Q z cj;
o o
CQ n: •-H \— CC I— 31 00 I— t-H I—I
C3 3 Q Q ct Z o o _J O-Z. I/)
LU LU CC CQ CC
O \- o 00 ID O LU CC CC LU LU C3 3: cs: I— o
VO r-H
•
o I— LU 00
c t I—
o
CM CD
o ct o
LO
LO
r l-H
• 0 ^
1— LU 00
ct t— ct Q
*—» l-H
_I LL-Z.
0 r
LO VO
55
60
0 LO
LO «5l-
0 •SI
LO CO
0 CO
LO
5 20
2
I-H
0 I-H
LO
I-H
Q ct 0 _J
LU CQ
0 1—
ENTS
s. LU _I LU
ST AL
L
1—1
_ i
0 1—
ARY
00
ECES
LU OQ
S MA
Y N
CARD
ON
TINU
ATIO
CJ
LU 1— 0 Z.
121
. o
CM
CM
< >-
o O LU LU O CD c t
z. o c t _ l CC CC LU c t 3 1
\-OO Q 3 : O i I— e t t-H CJ 3 Z O
o z. i - i o I— C5_ = 3 CO CQ LU t—I a : r^ cccc r-^ I— o oo c_) • t-H O Q O Z
I— Q I— CSC oe: LU O LU C>0 - J Q u . cd < : ^ O I—
c t \±^ CC a CO LU
Q- Ll_ I— o o (/) a: =5 Ci_ oo .o
CO
LU
CC LU
CM c t a >-
CM
. O CJ
00 CsJ
o X
CD
00
c t I— <
CM «a: o X u
APPENDIX B
LISTING OF PROGRAM SLAB4 WITH SAMPLE OUTPUT
122
123
/ / JOB l M K y » V 0 , U ^ 9 , 2 O , 3 0 , 0 9 l , • 6 U N A L A N • , C L A S S = ^ , l » e 6 I O N = 5 1 2 0 I C / / EKEC FORTGCL»PARM,FORT=»MOSOURCE» / / S V S I N 00 *
C C' c c c c c c c c c c c c c c c c c c c c c< c c c c c c c c c c c c c c c c c c c c c c
THE ORIGIMAL APPLICAFION OF THIS PROCtAN I S DESCRIBED I N TWO PAPERS BV THE AUTHOR, V .HUANG: 111 - F I < I I T £ ELEHENT ANALrS IS OF SLABS ON E L A S T I C S O L I D S * . TRANSPORTATION ENGINEERING JOURNAL OF ASCEf VOL 1 0 0 , NO. T E 2 8 , HAV, 1 9 7 4 , PAGES 4 0 3 - 4 0 6 ; AND C2I -RECTANGULAR PLATES PARTIALLY SUPPORTED ON AN ELASTIC HALF S P A C E - , PRO-CEEDINGSt 1ST INTERNATIONAL CONFERENCE ON COMPUTATIONAL METHODS IN NONLINEAR ^tECHANICSt 1 9 7 4 , PAGES 4 0 5 > 4 1 4 .
THE ORIG INAL PROGRAM BY HUANG WAS MODIF IED AND GIVEN THE HUANG WAS M O D I F I E D AND GIVEN THE NAME - S L A B 2 " BV W. K. WRAV AND R. L . LYTTON, J U L Y , 1 9 7 7 .
TSLAB2" WAS nOOIF IED TO I T S PRESENT F3RM AND GIVEN THE NAME - S L A B 4 - BY K. N . GUNALAN AND W. K. WRAY* DECEMBER, 1 9 8 6 . A DESCRIPTION OF THE MODIF ICATIONS AND EXAMPLE PROBLEMS ARE GIVEN I N K. N . GUNALAN'S DOCTORAL DISSERTATION E N T I T L E D : - ANALYSIS OF I N D U S T R I A L FLOOR SLABS-ON-GROUND FOR DESIGN PURPOSES-, AT TEXAS TECH U N I V E R S I T Y , LUBBOCK, TEXAS, 1 9 8 6 .
THIS PROGRAM PROVIDES SOLUTIONS FOR THE DEFLECTIONS, STRE S S E S , BENDING MOMENTS, AND SHEAR FORCES DUE TO LOADING AND/OR WARPING I N A SINGLE RECTANGULAR SLAB, OR TWO SLABS CONNECTED BY DOWEL BARS AT THE J O I N T , RESTING ON A FOUNDAI ION OF THE ELASTIC SOLID TYPE.
THE SLAB VARIOUS S I Z E S . THE F I N I T E ELE THE SOLUTION I CONSECUTIVELY TO RIGHT ALONG BARS AT THE JO T W I C E , ONE FOR THE DOWELS ARE THE J O I N T ARE E ITHER OR BOTH SLAB MAY BE CO DEFLECTIONS DU E ITHER COMBINE
S ARE DIVIDED HOWEVER* FOR
MENTt THE SOLU S TERMINATED. FROM BOTTOM TO THE X AXIS. INT, EACH NODE THE LEFT SLAB ASSUMED loot
THE SAME FOR B SLABS, AND TH
MPUTED. THE P E TO DEAD LOAD D OR SEPARATEL
INTO RECTAN ASPECT RAT
TIONS WOULD THE ELEMEN TOP ALONG
IF TWO SLAB AT THE DOW AND THE OT
EFFICIENT, OTH SLABS. E STRESSES ROGRAN CAN V TEMPERATU Y.
GULAR FINITE ELEMENTS OF IO*S SREATER THAN THREE FOR BE ERRONEOUS AND THEREFORE
TS AND NODES ARE NUMBERED THE Y AXIS AND FROM LEFT S ARE CONNECTED BY DOWEL ELLED JOINT MUST BE NUMBERED HER F3R THE RIGHT SLAB. SO THAT THE DEFLECTIONS AT LOADS MAY BE APPLIED TO AT ANY NODE IN EITHER DETERMINE THE STRESSES AND RE WARPING* OR LIVE LOAD*
r*00000010 00000020
r*000O003O *00000040 *OO00O0SO #00000060 *00000070 *00000080 *0 0000090 *00000100 *00000110 *00000120 *00000130 *00000140 *000001S0 *00000160 *00000170 *00000180 *00000190 *00000200 *00000210 *00000220 *00000230 *00000240 *000002SO *00000260 *00000270 *00000280 *00000290 *00000300 *00000310 *000 00320 *00000330 *00000340 *000003S0 *00000360 *00000370 *00000380 *00000390 *00000400 *00000410 *00000420 *00000430 *00000440 *00000450 *00000460
124
c
c
r I.e. w I " ! '•"OSRAM CAN NOW HANDLE TWO L3ADING CONDITIONS S I H U L T A N E O - » 0 0 0 0 0 4 7 0 C " S L Y * E . G . , STACK LOADING CONDITION TOGETHER WITH A FORKLIFT * 0 0 0 0 0 4 8 0 I L O A D I N G . * 0 0 0 0 0 4 9 0
. , „ , *00000500 C THE PROGRAM L I S T S DEFLECTIONS* MOMENTS AND SHEAR FORCES BOTH * 0 0 0 0 0 S 1 0 C I N THE ORDER OF NODES AND I N THE ASCENDING ORDER OF NAGNITUDE. • 0 0 0 0 0 S 2 0 C T H I S I S DONE WITH THE AID OF A IHSL LIBRARY CALLED VSRTR AVAILABLE * 0 0 f t 0 0 5 3 0 C AT TEXAS TECH U N I V E R S I T Y . * 0 0 0 0 0 5 4 0
*00000550 C THE >»ROSRAM NOW PROVIDES THE TWENTY MAXIMUM DIFFERENTIAL * 0 0 0 0 0 5 6 0 C DEFLECTION R A T I O ' S TOGETHER WITH NODE NUMBERS* DISTANCE BETWEEN T H E * 0 0 0 0 0 S 7 0 C NODES, D I F F E R E N T I A L DEFLECTION BETWEEN THE N3DES ETC. * 0 0 0 0 0 5 8 0
* 0 0 0 0 0 S 9 0 C THE PROGRAM PROVIDES THE FOLLOWING FOUR OPTIONS: * 0 0 0 0 0 6 0 0 C OPTION 1 : SLAB AND SUBGRADE ARE I N FULL CONTACT* AS * 0 0 0 0 0 6 1 0 C ORIGINALLY ASSUMED BY P I C K E T T . — > SET NOTCON»00000620 C TO 0* NWT TO 0 * AND CYCLE TO 1 . * 0 0 0 0 0 6 3 0 C OPTION 2 : SLAB AND SUBGRADE ARE I N FULL CONTACT AT * 0 0 0 0 0 6 4 0 C SOME POINTS BUT COMPLETELY OUT OF CONTACT AT * 0 0 0 0 0 6 5 0 C THE REMAINING POINTS BECAUSE OF LARGE GAPS * 0 0 0 0 0 6 6 0 C BETWEEN THE SLAB AND TME SUBGRADE. — > SET * 0 0 0 0 0 6 7 0 C NOTCON TO THE NUMBER OF POINTS NOT I N CON- * 0 0 0 0 0 6 8 0 C TACT* NGAP TO 0 * NWT T3 0 * AND NCYCLE TO 1 . * 0 0 0 0 0 6 9 0 C OPTION 3 : SLAB AND SUBRAOE MAY OR MAY NOT BE I N CON- * 0 0 0 0 0 7 0 0 C TACT BECAUSE OF WARPING OF THE SLAB. WHEN * 0 0 0 0 0 7 1 0 C THE SLAB I S REMOVED* T)« E SUBGRADE WILL FORM * 0 0 0 0 0 7 2 0 C A SMOOTH SURFACE WITH « 0 DEPRESSIONS OR I N I - *0O0O073O C T I A L GAPS. — > SET NOTCON TO 0* NGAP TO 0 * ^ 0 0 0 0 0 7 4 0 C NCYCLE TO MAXIMUM NUMBER OF CYCLES FDR CHECK-*000007SO C ING CONTACT* * 0 0 0 0 0 7 6 0 C OPTION 4 : WHEN THE SLAB I S REMOVED* THE SUBGRADE WILL * 0 0 0 0 0 7 7 0 C NOT FORM A SMOOTH SURFACE BUT SHOWS IRREGULAR*00000780 C DEFORMATION. — > SET NOTCON TO 0 * NGAP TO * 0 0 0 0 0 7 9 0 C NUMBER OF NODES WITH I N I T I A L GAPS* NCYCLE TO * 0 0 0 0 0 8 0 0 C MAXIMUM NUMBER OF CYCLES FOR CHECKING C a N T A C T * 0 0 0 0 0 8 1 0 C * 0 0 0 0 0 8 2 0 C * 0 0 0 0 0 8 3 0 C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 0 0 0 0 0 8 4 0 C * 0 0 0 0 0 8 5 0 C — — I W P U T DATA: * 0 0 0 0 0 8 6 0 C NORMALLY* INPUT DATA I S I N CONSISTENT UNITS OF POUNDS* * 0 0 0 0 0 3 7 0 C I N C H E S * POUNDS PER SOUARE INCH ( P S I l * E T C . HOWEVER* SLAB WIDTH A N O * 0 0 0 0 0 8 8 0 C LENGTH OF THE SLAB AND THEIR RESPECTIVE NODAL DISTANCES ARE INPUT * 0 0 0 0 0 8 9 0 C I N F E E T . THE INPUT DIMENSIONS I I N F E E T I ARE CONVERTED INTERNALLY * 0 0 0 0 0 9 0 0 C TO INCHES FOR PROGRAM CALCULATIONS. * 0 0 0 0 0 9 I 0 C * 0 0 0 0 0 9 2 0 C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ^ * * * * * * * * * * * * * * * * * * * * * 0 0 0 009 30 C * 0 0 0 0 a 9 4 0 C NOTES ON DIMENSIONS TO BE S P E C I F I E D BY THE USERS: * 0 0 0 0 0 9 5 0
125
THE DIMENSIONS OF C AND G SHOULD NOT BE LESS THAN:
THE DIMENSION
THE THE
DIMENSION DIMENSION
THE DIMENSION
N 0 B ( 2 I = INX14-NX2 I *NY*NB OF H AN HD SHOULD NOT BE LESS THAN:
NOO s CNONY4- l l *NONY/2 ; I F N S L A B ^ l * NONY = N X l * N Y ; I F NSLAB»2* NONY = I N X 1 ^ N X 2 - 1 I * N Y
OF CO SHALL NOT BE LESS THAN N r * N B * 3 OF F SHALL NOT BE LESS THAN N 0 2 * WHERE:
N02 - I N X 1 « - N X 2 I * N Y * 3 OF D F * GAP* P P F * PF* CURL* FO* DEF* AB* AND NCC
SHOULD NOT BE LESS THAN INX1«-<I X2 l *NY
THE DIMENSIONS INDICATED ABOVE ARE A MINIMUM* THOUGH LARGER DIMENSIONS MAY BE REQUIRED.
P R I N C I P A L NOTATION FOR SLAB2
ABI I AOB ADB2 AISLWD ASPACE
ATB ATB2 B
BDA BDA2 BEAML* BEAMS
BEAMLL
BEAMLW
BEAMSL
BEAMSW
BSPACE
CC I
C0( I CURLtNGAPI)
DISTAN ELEMEN SLAB A Af I ADB SO AISLE CENTER STIFFE Af I ATB SO DISTAN ELEMEN B( I BOA SO LONG 0 BEAM* LONG D SECTIO LONG 0 SECTIO SHORT SECTIO SHORT SECTIO CENTER STIFFE (It SL STIFFN STIFFN AMOUNT
CE BETWEEN MIDPOINTS OF ADJACENT TS* IN X - D I R E : T I O N REA INFLUENCED BY EACH NODE DIVIDED BY B( I UARED WIDTH IN FEET -TO-CENTER SPACING OF LONGITUDINAL NIN6 BEAMS M U L T I P L I E D BV B( I UARED CE BETWEEN MIDPOINTS OF ADJACENT TS* I N Y - D I R E C T I O N D I V I D E D BY A l I UARED IMENSION AND SHORT DIMENSION OF GRAD IN I N C H E S . IMENSION OF LONGITUDINAL BEAM CROSS-N IMENSION OF TRANSVERSE BEAM CROSS-N DIMENSION OF LONGITUDINAL CROSS-N DIMENSION OF TRANSVERSE BEAN CROSS-N -TO-CENTER SPACING OF TRANSVERSE NING B EAMS AB STIFFNESS MATRIX* OR 121 OVERALL ESS MATRIX OF SYSTEM ESS COEFFICIENTS AT THE JOINT
OF GAP BETWEEN SLAB AND SUBGRADE
* 0 0 0 0 0 9 6 0 * 0 0 0 0 0 9 7 0 * 0 0 0 0 0 9 8 0 * 0 0 0 0 0 9 9 0 *00001000 *00001010 *00001020 *00001030 *00001040 *000O10S0 *00001060 *00001070 *00001080 * 0 0 0 0 1 0 9 0 *00001100 *00001110
00001120 00001130 00001140 00001150 0 0 0 0 1 1 6 0 00001170 00001180 0 0 0 0 1 1 9 0 00001200 00001210 00001220 00001230 00001240 00001250 0 0 0 0 1 2 6 0 00001270 00001280
E 0 0 0 0 1 2 9 0 00001300 00001310 00001320 00001330 00001340 00001350 0 0 0 0 1 3 6 0 000J)1370 00001380 0 0 0 0 1 3 9 0 00001400 0 0 0 0 1 4 1 0 00001420 00001430 00001440
126
c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c
OEFI 1
OEFF
DEL
DELF
OFI 1
OKI 1
OXYFAC* DVFAC
DYI 1
EIX EIY Fl 1 FLRCAP FOI 1
FRX
HI 1 ICL
ICLF
lER
ISOTRY
LIFT
MOIX
HOIY
MMM
MXOIFI 1
UNIT DEFLECTIONS FROM SUBGRADE FLEXIBILITY 0 0 0 0 1 4 5 0 MATRIX 0 0 0 0 1 4 6 0 WORKING VARIABLE WHOSE VALUE IS DEPENDENT 0 0 0 0 1 4 7 0 UPON DEF( I ANO LOCATION IN FINITE ELEMENT00001480 6RID 0 0 0 0 1 4 9 0 TOLERANCE TO CONTROL CONVERGENC* GENERAL- 0 0 0 0 1 5 0 0 LY USE 0 . 0 0 1 FOR COARSE CONTROL 0 0 0 0 1 5 1 0 TOLERANCE TO CONTROL CONVERGENCE* GENERAL- 0 0 0 0 1 5 2 0 LY USE 0 . 0 0 0 1 . FOR FINE CONTROL 0 0 0 0 1 5 3 0 DIFFERENCE IN DEFLECTIONS AT THE SAME NODE 0 0 0 0 1 5 4 0 BETWEEN TWO CONSECUTIVE ITERATIONS 0 0 0 0 1 5 5 0 DISTANCE BETWEEN ADJACENT NODES IN THE 0 0 0 0 1 5 6 0 X-DIRECTION 0 0 0 0 1 5 7 0 FORMS OF THE ELASTIC CONSTANTS OF AN ORTHO-00001580 TROPIC SLAB IWHOSE PRINCIPAL DIRECTIONS OF 0 0 0 0 1 5 9 0 OF ORTHOTROPY COINCIDE WITH THE X- AND Y- 0 0 0 0 1 6 0 0 AXESI 0 0 0 0 1 6 1 0 DISTANCE BETWEEN ADJACENT NODES IN THE 0 0 0 0 1 6 2 0 V-OIRECTION 0 0 0 0 1 6 3 0 FLEXURAL RIGIDITY IN LONGITUDINAL 0IRECTION00001640 FLEXURAL RIGIDITY IN TRANSVERSE DIRECTION 0 0 0 0 1 6 5 0 DEFLECTION AT A NODE 0 0 0 0 1 6 6 0 FORKLIFT'S RATED CAPACITY IN POUNDS 0 0 0 0 1 6 7 0 FORCE DUE TO WEIGHT OF SLAB AND/OR UNI- 0 0 0 0 1 6 8 0 FORMLY DISTRIBUTED LIVE LOAD ON ELEMENT 0 0 0 0 1 6 9 0 FLEXURAL RIGIDITY PER UNIT WIDTH* IN L 0 N G I - 0 0 0 0 1 7 0 0 ITUOINAL DIRECTION 0 0 0 0 1 7 1 0 SUBGRADE STIFFNESS MATRIX 0 0 0 0 1 7 2 0 MAXIMUM NUMBER OF ITERATIONS ALLOWED* GEN- 0 0 0 0 1 7 3 0 ERALLV USE 1 0 FOR COARSE CONTROL. 0 0 0 0 1 7 4 0 MAXIMUM NUMBER OF ITERATIONS ALLOWED* GEN- 0 0 0 0 1 7 5 0 ERALLV USE 30 FOR FINE CONTROL 0 0 0 0 1 7 6 0 INSTABILITY ERROR OCCURRING DURING MATRIX 0 0 0 0 1 7 7 0 INVERSION 0 0 0 0 1 7 8 0 SWITCH TO DETERMINE IF STIFFNESS OF CON- 0 0 0 0 1 7 9 0 STANT THICKNESS SLAB OR OF STIFFENED SLAB 0 0 0 0 1 8 0 0 IS TO BE USED IN PROBLEM SOLUTION—> ASSIGN00001810 0 IF CONSTANT THICKNESS; ASSIGN 1 IF 0 0 0 0 1 8 2 0 STIFFENED SLAB 0 0 0 0 1 8 3 0 DETERMINES MODE OF SOIL SWELLING: ASSIGN 0 0 0 0 1 8 4 0 1 IF CENTER LIFT* AND ASSIGN 2 IF EDGE L I F T 0 0 0 0 1 8 5 0 MOMENT OF INERTIA OF STIFFENED SLAB SECTION00001860 IN LONGITUDINAL DIRECTION 0 0 0 0 1 8 7 0 MOMENT OF INERTIA OF STIFFENED SLAB SECTION00001880 IN TRANSVERSE DIRECTION 0 0 0 0 1 8 9 0 EXPONENT OF EXPONENTIAL EOUATIDN DESCRIBING00001900 PROFILE OF SWOLLEN SUBGRADE. EQUATION IS 0 0 0 0 1 9 1 0 OF THE FORM V=C*X**M 0 0 0 0 1 9 2 0 NUMERICAL DIFFERENCE BETWEEN MOMENTS AT 0 0 0 0 1 9 3 0
127
c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c
MXVDIFI 1
MYDIFI 1
MYXOIFI 1
NB
NCK
NCYCLE
NELEM NFLINFLOADI
NFL OAD
NGAP .
NGINGAPI
NKENT NLINLOADI NLOAD
NO! 11
N0I2I
NOB! 11 N08t2l NONY
NOO NOOCKINCKI
NOTCON
NOl N013 N02 N023 NPINPRINTI NPRINT
ADJACENT NODES IN THE X -O IRECTION NUMERICAL DIFFERENCE BETWEEN TWISTING MOMENTS AT ADJACENT NODES NUMERICAL DIFFERENCE BETWEEN MOMENTS AT ADJACENT NODES I N TME Y -D IRECT ION NUMERICAL DIFFERENCE BETWEEN TWISTING MOMENTS AT ADJACENT NODES HALF BAND WIDTH* EQUAL TO OR GREATER THAN I NY • 2 1 * 3 NUMBER OF NODAL POINTS FOR CHECKING THE CONVERGENCE MAXIMUM NUMBER OF CYCLES FOR CHECKING SUB-GRADE CONTACT* GENERALLY USE 10 NUMBER OF ELEMENTS I N F I N I T E ELEMENT GRID ELEMENT NUMBERS OVER WHICH SECOND LOAD I S APPLIED NUMBER OF ELEMENTS ON WHICH SECOND LOAD I S APPLIED TOTAL NUMBER OF NODES AT WHICH A GAP EXIST BETWEEN SLAB AND SUBGRADE. ASSIGN 0 IF NO GAP EXISTS OR THE GAP IS VERY LARGE NODAL NUMBER OF THE NODE AT WHICH THE GAP GAP BETWEEN SLAB AND SUBGRADE IS S P E C I F I E D COUNTER TO CALL SUBROUTINE •SHEAR* ELEMENT NUMBER OVER WHICH LOAD I S APPLIED NUMBER OF ELEMENTS 3N WHICH LOAD I S APPLIE USE 0 IF THERE I S NO LOAD TOTAL NUMBER OF COMPONENTS CONTRIBUTING TO INTERNAL WORK I N SLAB t l TOTAL NUMBER OF COMPONENTS CONTRIBUTING TO INTERNAL WORK I N BOTH SLABS N 0 I 1 I * N B N 0 I 2 ) * N B NUMBER OF NODES I N SLAB S i OR NUMBER OF NODES IN BOTH SLABS LESS NY INONY • I I * (NONY) / 2 NODAL NUMBER OF THE POINTS FOR CHECKING CONVERGENCE TOTAL NUMBER OF NODES AT WHICH REACTIVE PRESSURE I S PRESUMED TO BE 0 . I F NCYCLE-1
WILL NEVER BE I N CONTACT; I F THESE N3DES MAY OR MAY NOT BE DEPENDING ON CALCULATED RESULT
THESE NODES NCYCLE > 1 * IN CONTACT* N X 1 * N Y * 3 TOTAL NUMBER NX*NV»3 TOTAL NUMBER OF NODES IN BOTH SLABS NODAL NUMBER OF THE PRINTED POINTS. NUMBER OF NODES AT WHICH STRESSES ARE
OF NODES IN SLAB tl
TO B
00001940 00001950 00001960 00001970 00001980 00001990 00002000 00002010 00002020 00002030 00002040 00002050 00002060 00002070 00002080 00002090 00002100 00002110 S000021.20 00002130 00002140 00002150 00002160 00002170 00002180 0000 02190 00002200 00002210 00002220 00002230 00002240 00002250 00002260 00002270 00002280 00002290 00002300 00002310 00002320 *00002330 00002340 00002350 S00002360 00002370 00002380 00002390 00002400 00002410 E00002420
128
c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c
NPROB
NPUNCH
NREAD
NSLAB NSLOAD
NSVM
NTEMP
NWT
NX NXl HK2
NY NYNB NZINOTCONI
PA PB PFf 1 PPF I 1 PR PRS Q
PRINTED NUMBER OF PROBLEMS TO BE SOLVED. I NOTE: OPTIONS 3 AND 4 MAY BE SOLVED IN TWO SEPARATE PROBLEMS. THE F I R S T PROBLEM COMPUTES THE GAPS ANO PRECOMPRESS IONS DUE TO WEIGHT OF SLAB ANO TEMPERATURE BY SETTING NWT TO 1 * ANO THE SECOND PROBLEM COMPUTES STRESSES AND DEFLECTIONS DUE TO L I V E LOAD ONLY BY SETTING NWT TO 0 . 1 ANY GAPS OR PRECOMPRESSION TO BE PUNCHED7 ASSIGN 1 I F YES AND ASSIGN 0 I F NO. ANY GAPS OR PRECOMPRESSIONS TO BE READ IN7 ASSIGN 1 I F YES* ASSIGN 2 IF GAPS ANO PRE-COMPRESSIONS ARE FROM THE PREVIOUS AND ASSIGN 0 I F OTHERWISE.
0 0 0 0 2 4 3 0 0 0 0 0 2 4 4 0 0 0 0 0 2 4 5 0 0 0 0 0 2 4 6 0 0 0 0 0 2 4 70 0 0 0 0 2 4 8 0 000024 90 00002500 00002510 00002520 000 02530 00002540 00002550
PR0BL£M*00002560 0 0 0 0 2 5 70
NUMBER SLABS* EITHER 1 OR 2 0 0 0 0 2 5 8 0 SWITCH TO DETERMINE IF THERE I S A SECOND 0 0 0 0 2 5 9 0 LOADING ON THE SLAB. ASSIGN 0 WHEN THERE I S 0 0 0 0 2 6 0 0 NO SECOND LOADING AND ASSIGN 1 WHEN THERE I S A SECOND LOADING ON THE SLAB CONDITION OF SYMMETRY. ASSIGN 1 WHEN NO SYMMETRY E X I S T S * 2 WHEN SYMMETRIC WITH RESPECT TO Y A X I S * 3 WHEN SYMMETRIC SPECT TO X A X I S * 4 WHEN SYMMETRIC SPECT TO BOTH X ANO Y AXES* ANO 5 SLABS SYMMETRICALLY LOADED. CONDITION OF WARPINS. ASSIGN 0 IF
0 0 0 0 2 6 1 0 0 0 0 0 2 6 2 0 0 0 0 0 2 6 30 0 0 0 0 2 6 4 0 0 0 0 0 2 6 5 0 0 0 0 0 2 6 6 0 0 0 0 0 2 6 7 0 0 0 0 0 2 6 8 0
TEMPERA-00002690
WITH R E -WITH R E -FOR FOUR
TURE GRADIENT I S 0 AND ASSIGN 1 I F I S NOT 0 METHOD EMPLOYED. ASSIGN NOT CONSIDERED* ASSIGN 1
GRADlENTOOO02700 00002710
0 WHEN WEIGHT IS 00002720 WHEN WEIGHT IS 00002730
CONSIDERED FOR SLAB OF NON-CONSTANT CROSS- 0 0 0 0 2 7 4 0 SECTION* ANO ASSIGN - 1 WHEN SLAB I S OF C 0 N - 0 0 0 0 2 7 5 0 STANT* RECTANGULAR CROSS-SECTION TOTAL NUMBER NODES I N THE X DIRECTION NUMBER OF NODES I N X D IRECTION FOR SLAB H NUMBER OF NODES I N X D IRECTION FOR SLAB 12 ASSIGN 0 WHEN THERE IS ONLY ONE SLAB. NUMBER OF NODES I N Y D IRECTION N Y * 3 * N B
0 0 0 0 2 7 6 0 0 0 0 0 2 7 7 0 0 0 0 0 2 7 8 0
. 0 0 0 0 2 7 9 0 0 0 0 0 2 8 0 0 0 0 0 0 2 8 1 0 0 0 0 0 2 8 2 0
NODAL NUMBER OF THE NODES AT WHICH R E A C T I V E 0 0 0 0 2 8 3 0 PRESSURE I S I N I T I A L L Y SET TO ZERO WORKING VARIABLE* EaUAL TO A WORKING VARIABLE* ERUAL TO B A PREVIOUS NODAL DEFLECTION A PREVIOUS NODAL DEFLECTION POISSON'S RATIO OF THE CONCRETE POISSON'S RATIO OF THE SOIL LOADING ON SLAB* EXPRESSED AS A PRESSURE
0 0 0 0 2 8 4 0 0 0 0 0 2 8 5 0 0 0 0 0 2 8 6 0 0 0 0 0 2 8 7 0 0 0 0 0 2 8 8 0 0 0 0 0 2 8 9 0 0 0 0 0 2 9 0 0 0 0 0 0 2 9 1 0
129
c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c c
c c
Q2
OK QK2
QO QSLAB
RFJ RM SMI 1
STRI * 1
T TEMP
TEX
TEY
TRBL
TRBW
V L * VM
V X I 1 VXMAXN VXMAXP VVI 1 VYMAXN VVMAKP XT! 1 Y T I 1 WK X I N K 1 ^ N X 2 I
XOAINLOAO* 1 ) XOAINLOAO* 21
X 0 A 2 I N F L 0 A D * 1 > X D A 2 ( N F L 0 A D » 2 I
AND
ANO
SECOND LOADING ON PRESSURE FORCE DUE TO APPLI FORCE DUE TO APPLI ELEMENT WK WEIGHT OF SLAB EXP D ISTRIBUTED LOAD. SLAB I S NOT CONSTA CROSS-SECTION ANO RELAXATION FACTOR R I G I D I T Y MODULUS STIFFNESS MATRIX F OF AN ORTHOTROPIC CALCULATED STRESSE SUPPORT CONDITIONS THICKNESS OF THE C DIFFERENCE I N TEMP BOTTOM OF SLAB. U UPWARD AND NEGATIV EQUIVALENT CONSTAN LONGITUDINAL DIREC EQUIVALENT CONSTAN TRANSVERSE D I R E C T I TORSIONAL R I G I D I T Y DIRECTION
TORSIONAL R I G I D I T Y DIRECTION LOAD MATRICES USED STIFFNESS MATRIX SHEAR FORCE IN THE MAXIMUM NEGATIVE S MAXIMUM P O S I T I V E S SHEAR FORCE IN THE MAXIMUM NEGATIVE S MAXIMUM P O S I T I V E S TEMPORARY STORAGE TEMPORARY STORAGE WEIGHT OF CONCRETE X COORDINATES STAR ING FROM LEFT TO R READ TWICE AT JOIN NATE DISTANCES ARE LOWER AND UPPER L I X D I R E C T I O N . USE ERS THE WHOLE LENG LOWER AND UPPER L I SECOND LOADING IN IF THE LOAD COVERS
SLAB* EXPRESSED AS A
ED LOAD ON AN ELEMENT ED SECOND LOAD ON AN
RESSED AS A UNIFORMLY
0 0 0 0 2 9 2 0 0 0 0 0 2 9 3 0 0 0 0 0 2 9 4 0 0 0 0 0 2 9 5 0 0 0 0 0 2 9 6 0 0 0 0 0 2 9 7 0 0 0 0 0 2 9 8 0
( T H I S INPUT I S USED WHEN00002990 NT DEPTH RECTANGLULAR N t f T s l . l AT THE J O I N T * USUALLY 0 .
OR A RECTANGULAR ELEMENT MATERIAL S DUE TO LOADING AND
ONSTANT DEPTH SLAB EKATURE BETWEEN TOP AND SE P O S I T I V E IF CURLED E IF CURLED DOWNWARD.
0 0 0 0 3 0 0 0 0 0 0 0 3 0 1 0
5 0 0 0 0 3 0 2 0 0 0 0 0 3 0 30 0 0 0 0 3 0 4 0 0 0 0 0 3 0 5 0 0 0 0 0 3 0 6 0 0 0 0 0 3 0 7 0 0 0 0 0 3 0 8 0 0 0 0 0 3 0 9 0 0 0 0 0 3 1 0 0 0 0 0 0 3 1 1 0
T THICKNESS SLAB DEPTH I N 0 0 0 0 3 1 2 0 TION 0 0 0 0 3 1 3 0 T THICKNESS SLAB DEPTH I N 0 0 0 0 3 1 4 0 ON
OF BEAM I N LONGITUDINAL
OF BEAM I N TRANSVERSE
TO DETERMINE ELEMENTAL
X - O I R E C T I O N
0 0 0 0 3 1 5 0 0 0 0 0 3 1 6 0 0 0 0 0 3 1 7 0 0 0 0 0 3 1 8 0 0 0 0 0 3 1 9 0 0 0 0 0 3 2 0 0 0 0 0 0 3 2 1 0 0 0 0 0 3 2 2 0
HEAR FORCE I N X - 0 I R E C T I O N 0 0 0 0 3 2 3 0 HEAR FORCE IN X - 0 I R E C T I O N 0 0 0 0 3 2 4 0
Y - D I R E C T I O N 0 0 0 0 3 2 5 0 HEAR FORCE I N V - 0 I R E C T I O N 0 0 0 0 3 2 6 0 HEAR FORCE IN V - D I R E C T I O N 0 0 0 0 3 2 7 0 F I L E FOR XI 1 F ILE FOR V I 1
I N P S I TING FROM 0 ANO INCREAS-I G H T . I N O T E : X MUST BE T IF TWO SLABS. COOROI-
INPUT I N F E E T . I H ITS OF LOADED AREA I N X
0 0 0 0 3 2 8 0 0 0 0 0 3 2 9 0 0 0 0 0 3 3 0 0 0 0 0 0 3 3 1 0 0 0 0 0 3 3 2 0 0 0 0 0 3 3 3 0 0 0 0 0 3 3 4 0 0 0 0 0 3 3 5 0
- 1 TO • I I F THE LOAD C O V - 0 0 0 0 3 3 6 0 TM OF ELEMENT. 0 0 0 0 3 3 7 0 HITS OF LOADED AREA FOR 0 0 0 0 3 3 8 0 X - O I R E C T I O N . USE - 1 TO « -100003390
THE WHOLE LENGTH OF THE 0 0 0 0 3 4 0 0
130
c c c c c c c c c c c c c c c c c c c c c c c c c c< c c
XEC XMOM XYMOM XXIll XXI2I XXL xxs XYMX
YINYI
VDAINLOAD* I I YOAINLOAD* 2 1
Y D A 2 I N F L 0 A 0 * 1 I Y 0 A 2 ( N F . 0 A D * 2 I
YM YMOM VMS W i l l Y Y I 2 I
ANO
AND
ELEMENT EDGE PENETRA BENDING NOME TWISTING MOM X-COORDINATE X-COORDINATE SLAB LENGTH* SLAB WIDTH* AMOUNT OF DI INCHES
V COORDINATE CREASING TO LOWER ANO UP D I R E C T I O N . WHOLE WIDTH LOWER ANO UP SECOND LOADI IF THE LOAD ELEMENT YOUNG'S MODU BENDING NOME YOUNG'S MODU V-COORDINATE V-COORDINATE
TION OIS NT I N X-ENT S OF CEN S OF CEN
I N FEET IN FEET FFERENTIAL SHRINK OR SWELL* I N
TANCE* I N F E E T . •DIRECTION
ITROIO OF SLAB B l ITROIO OF SLAB C2
S STARTING FROM ZERO AND I N -TOP* I N FEET PER L I M I T S OF LOADED AREA I N V USE - 1 TO -1-1 I F THE LOAD COVER OF ELEMENT. PER L I M I T S OF LOADED AREA FOR NG IN Y - D I R E C T I O N . USE - 1 TO * COVERS THE WHOLE WIDTH OF THE
LUS OF THE CONCRETE NT IN V-OIRECTION LUS OF THE SOIL S OF CENTROID OF SLAB • ! S OF CENTROID OF SLAB 12
DIMENSION S N ( 9 0 1 * S M 1 ( 9 0 ) * S M 2 ( 9 0 I » S N 3 ( 9 0 I * S M * 0 I *XYMOM(6S0 I * MXOIF I 6 5 0 1 * MYDIF I 6 5 0 1 f N X Y O I F I * » V I 6 5 0 t * X T I 6 S 0 l * Y T I 6 5 0 1 * 0 X 1 6 5 0 1 * DYI 6 5 0 1 *HDI * * N O O I 4 I * N O B ( 2 I * C ( 1 5 0 0 0 0 I * G A P I 6 5 0 I * H ( 2 0 8 0 0 0 I * O O O I f C O ( 5 5 0 0 l » P F ( 6 5 0 l * C U R L ( 6 5 0 l * N O D C K I 7 5 l * X
* S O I DIMENSION X D A ( 5 0 0 * 2 I * V D A ( 5 0 0 * 2 1 * K O I 4 1 t V O I 41
* D C F I 6 5 0 I * A B ( 6 5 0 I * N C C ( 6 5 0 I * N Z I 6 5 0 I * S T R I 6 5 0 * 6 * V X I 6 5 0 1 * V V I 6 5 0 1 * I R I 6 5 0 1 * G U N A ( 6 5 0 1 * X D A 2 I 5 0 0 *
4 ( 9 0 I * X M O M 1 6 5 0 I * V M O M I 6 65 01 *MYXDIF I 65 01 * X ( 6 5 0 2 0 8 0 0 0 1 * O F I 6 5 0 1 « N L I 6 5 0 * P P F ( 6 5 0 I * F I 2 1 0 0 I * 6 I 1 5 X I 2 I * Y V I 2 I * Y Y Y I 2 1 I * F 0 I
* N P I 6 5 0 I * N 0 I 2 I * Z Z I 2 1 I * l * N G 1 6 5 0 l * Y X n O M ( 6 5 0 l * 2 1 * Y 0 A 2 ( 5 0 0 * 2 1 * N F L ( 6 5 0
COMMON C » F * G » N 0 * N 8 * X » V * S T R » N P * X M 0 M * V M 0 M * X Y M 0 M * X T * V T * D X * D Y » M X 0 I F * * M V 0 I F » M K Y O I F » M Y X D I F * V X M O M * V X * W * N X Y * N Y X * VXMAXN* VXMAXP* *VVMAXN»VYMAXP
REAL n X D I F * M Y D I F f MXYDIF* MVKOIF* MOIX* MO lY
—FOR REFERENCE ON DATA BLOCKS* SEE Z I E N K I E W I C Z * O . C * -THE F I N I T E —ELEMENT METHOD I N ENGINEERING S C I E N C E " * CHAPTER 1 0 * MCGRAW-HILL —BOOK C O . * 1 9 7 1 .
DATA SMl/60.* 0.* 30.*5*0.* 20.* 30.* 0.* 15.* 3*0.* 15.* 0.*
00003410 00003420 00003430 00003440 00003450 00003460 00003470 00003480 00003490 00003500 00003510 00003520 00003530 S00003540 00003550 00003560 100003570 00003580 00003590 00003600 00003610 00003620 00003630 00003640 00003650 *00003660 00003670 00003680 500003690 100003700 100003710 000003720 600003730 00003740 00003750 00003760 100005770 00003780 00003790 00003800 00005810 00003820 00003830 00003840 00003850 00003860 00003870 00003880 00003890
131
* 1 0 . * - 6 0 . * 0 . * 3 0 . * 3 » 0 . * - 3 0 . * 0 . * 1 0 . * - 3 0 . * 0 . * 1 5 . * 3 * 0 . * 00003900 * - 1 5 . * 0 . * 5 . * 6 0 . * 0 . * 3 0 . * 5 * 0 . * 2 0 . * - 3 0 . * 0 . * I S . * 3 * 0 . * - 1 5 . * 0 0 0 0 3 9 1 0 * 0 . * 5 . * - 6 0 . * 0 . * 3 0 . * 3 * 0 . * - 3 0 . * 0 . * 1 0 . * 6 0 . * 0 . * - 3 0 . * 5 * 0 . * 00003920 * 2 0 . * 3 0 . * 0 . * - 1 5 . * 5 * 0 . * - 1 5 . * 0 . * 1 0 . * 6 0 . * 0 . * - 5 0 . * 5 * 0 . * 2 0 . / 0 0 0 0 3 9 3 0
00003940 DATA S M 2 / 6 0 . * - 5 0 . * 0 . * 0 . * 2 0 . * 4 * 0 . * - 6 0 . * - 5 0 . * 0 . * 5 0 . * 1 0 . * 00005950
* 4 * 0 . * 5 0 . * - l S . * 0 . * - 1 5 . * 1 0 . * 4 * 0 . * - 5 0 . * - 1 5 . * 0 . * 1 5 . * 5 . * 00005960 * 4 * 0 . * 6 0 . * 5 0 . * 0 . * 0 . * 2 0 . * 4 * 0 . * - 5 0 . * I S . * 0 . * - 1 5 . * 5 . * 4 * 0 . *00003970 * 5 0 . * 1 5 . * 0 . * 1 5 . * 1 0 . * 4 * 0 . * 6 0 . * - 5 0 . * 0 .» 0 . * 2 0 . * 4 * 0 . * - 6 0 . * 0 0 0 0 5 9 8 0 * - 5 0 . * 0 . * 5 0 . * 1 0 . * 4 * 0 . * 6 0 . * 5 0 . * 0 . * 0 . * 2 0 . * 4 * 0 . ^ 00003990
00004000 DATA S M 5 / 5 0 . * - 1 5 . * 1 5 . « 0 . * 0 . * - 1 5 . * 5 * 0 . * - 5 3 . * 0 . * - 1 5 . * 5 * 0 . * - 1 5 . 0 0 0 0 4 0 1 0
* * 0 . * 0 . * - 5 0 . * 1 5 . * 0 . * 1 5 . * 5 * 0 . * 5 0 . * 8 * 0 . * 5 0 . * I S . * 1 5 . * 0 . * 0 0 0 0 4 0 2 0 * 0 . * 1 5 . * 5 * 0 . * 5 0 . * 8 * 0 . * - 5 0 . * - 1 5 . * 0 . * - 1 5 . * 5 * 0 . * 5 0 . * - 1 5 . * 00004050 * - 1 5 . * 0 . * 0 . * 1 5 . * 5 * 0 . * - 5 0 . * 0 . * 1 5 . * 5 * 9 . * 1 5 . * 0 . * 0 . * 5 0 . * 00004040 * 1 5 . * - 1 5 . * 0 . * 0 . * - I S . * 5 * 0 . / 00004050
00004060 DATA SN4/ 8 4 . * - 6 . * 6 . * 0 . * S . * 5 * 0 . * 8 . * - 8 4 . * - 6 . * - 6 . * 6 . * - 2 . * 0 0 0 0 4 0 7 0
* 0 . * - 6 . * 0 . * - 8 . * - 8 4 . * 3 * 6 . * - 8 . * 0 . * - 6 . * 0 . * - 2 . * 8 4 . * 6 . * 00004080 * - 6 . * - 6 . * 2 . * 0 . * 6 . * 0 . * 2 . * 8 4 . * 6 . * 6 . * 0 . * 8 . * 5 * 0 . * 8 . * 8 4 . * 0 0 0 0 4 0 9 0 * —6 . * - 6 . * 6 . * 2 . * 0 . * 6 . * 0 . * 2 . * - 8 4 . * - & . * 6 . * - 6 . * - 8 . * 0 . * 00004100 * - 6 . * 0 . * - 2 . * 8 4 . * - 6 . * - 6 . * 0 . * 8 . * 5 * 0 . * 8 . * - 8 4 . * - 6 . * 6 . * 6 . * 0 0 0 0 4 1 1 0 * - 2 . * 0 . * 6 . * 0 . * - 8 . * 8 4 . * 6 . * - 6 . * 0 . * S. * 5 * 0 . * 8 . / 00004120
00004130 101 FORMAT l / * 4 0 X * ' F I N I T E ELEMENT ANALYSIS OF INDUSTRIAL FLOOR SLABS'*00004140
* / 4 0 X * 4 9 ( ' - ' l « / / 5 l X * ' S L A B 4 * BY K.N.GUNALAN* 19 8 5 . ' * / 5 1 X * 2 7 ( • - ' I I 00004150 102 FORMAT l / / 5 X * ' T H I S INDUSTRIAL FLOOR SLAB PROBLEM HAS: ' * 00004160
* / 5 X * 3 9 l ' - ' l l 00004170 103 FORMAT (/ /*SX*'SUMMARY OF VAR I A B L E S ' * / 5 X * 2 1 ( ' - • 1 1 00004180 104 FORMAT I 1 4 I 5 I 00004190 105 FORMAT l 4 F l 0 . 4 * 4 l 5 t 00004200 106 FORMAT I 9 F 8 . 5 I 00004210 107 FORMAT I 6 E 1 5 . 6 I 00004220 108 FORMAT I I 5 9 2 F 1 0 . 4 * 2 E 1 0 . 5 * F I 0 . 4 » S I 5 I 00004250 109 FORMAT l / * 5 X « ' S L A 6 L E N G T H * ' * 1 7 X * F 7 . 2 * 7 X * ' F T ' * / / 5 X * ' S L A B WIOTHxt, 00004240
* 1 8 X * F 7 . 2 * 7 X * ' F T ' * / / 5 X * ' T H I C K N E S S OF S L A B = « * 9 X * F 1 0 . 4 * 6 X * ' I N ' * / / 5 X * 00004250 *'MODULUS OF CONCRETEs ' *10X*E10 .5*2X* 'PSI ' *^ /5X* 'POISSOi lS RATIO OF'00004260 * * • CONCRETE-««F10.4*/ /5X**V.MODULUS OF SUB.RADE' ' *8X*E10 .5* 00004270 * 2 X * ' P S I ' * / / 5 X « ' P O I S S O N S RATIO OF SUBGRADE" *F10 .4 I 00004280
110 FORMAT l / / 5 X * ' D I M E N S I 0 N OF GRADE BEAMS IN I N C H E S ' » / 5 X * 5 4 l ' - • » * 00004290 * / / 4 0 X * ' 0 £ P T H ' * 1 0 X * ' W I D T H ' * 1 0 X * ' S P A C I N G ' * / 4 0 X * 5 l ' - ' l » 1 0 K * 5 l ' - ' l * 00004500 * 1 0 X » 7 ( ' - ' I * / / 1 0 X * » T R A N S V E R S E GRADE BEAM'*6X*F10 .5*5X*F10 .5*7X* 00004310 * F 1 0 . 5 . / / 1 0 X * ' L O N G I T U D I N A L GRADE BEAM'*4X*F10. 5*5X*F10 .5 *7X* 00004320 * F 1 0 . 5 , / / I 00004350
111 FORMAT I 6 I 5 * 4 F 1 0 . 5 * F 5 . 2 * 1 5 1 00004540 112 FORMAT l / / *5X* 'PR0GRAM C0NSTANTS'*/5X* 1 7 1 ' - ' I I 00004550 115 FORMAT l / / 5 X * ' N S V M » ' * 2 X * I 5 * / / 5 X * ' N B « ' * 4 X * I 5 l 00004560 114 FORMAT | / / 5 X * « N X 1 « ' * 5 K * I 5 * / / 5 X , ' N V - ' * 4 X * I 5 * / / 5 X * ' N C Y C L E = ' * I 5 * / / 5 K * 0 0 0 0 4 5 7 0
* ' N P R I N T . ' * I 5 I 00004380
132
115 *s??2iT^^5I ' *7 ' -? /c : * * ' " '^^ ' * ' " ' • ' • • " • "•'^5X*'NCK='.5X*I5*/, w i : l " ^ ^ • " • " • ' ^ * * ' ' * • * * ^ " ° * 5 ' 2 X * ' P S I ' * / / 5 K * ' 0 E L . ' * 2 X * F 1 0 . 5 * • / / 5 K * ' 0 E L F = ' * 1 X * F 1 0 . 5 , / / 5 X * ' R F J = ' * 2 X * F 1 0 . 5 * / / 5 X , ' I C L F « ' * 1 X * I 5 I
/ / 0 0 0 0 4 5 9 0 00004400 00004410
OF X IN INCHES ARE: • * / * 1 1 I 4 X * F 8 . 5 I I 00004420 OF V I N INCHES ARE: ' * / * 1 1 I 4 X * F 8 . 5 1 1 00004430
FOLLOWING NODES ARE USED TO CHECK CONVERGENCE:'*00004440 00004450
ARE APPLIED ON THE FOLLOWING ELEMENTS'*
I INCHESI IN THE ORDER OF N0DES'* /5X»
116 FORMAT l / / 5 X * ' V A L U E S 117 FORMAT l / / 5 X * ' V A L U E S 118 FORMAT l / / 5 X * ' T H E
• / / * 1 2 I 1 0 I 119 FORMAT I 9 F 8 . 4 I 120 FORMAT I F 7 . 5 I 121 FORMAT ( 7 F 1 0 . S I 122 FORMAT ( / / * 5 X * ' L 0 A D S
* 'AND COORDINATES:'! 123 FORMAT I l O X * I 5 * 4 F 15 .51 124 F0RMAr(/ /5X»'DEFLECTIONS
* 4 2 ( ' - ' l l 125 FORMAT I / / * & X* 'NODE'*7X* 'DEFLECTION' *6X* 'NODE'*7X* 'DEFLECTION' *
*6X* 'NODE' *7X* 'DEFLECTION' *6X* 'NODE' *7X* 'DEFLECTION* I 126 FORMAT 1 4 1 4 X * I 5 * 5 X * E 1 3 . 6 I I 127 F0RMATI/ /5X*'DEFLECTIONS I INCHESI I N THE ASCENDING ORDER OF**
* • M A G N I T U D E ' * / 5 X * S 5 l ' - ' I I 128 FORMAT l / / 3 5 X * ' M I N I M U M DEFLEC T IONs '«E15 .6*2 X* * I N ' * / / 5 5 X *
* • MAXIMUM D E F L E C T I 0 N s ' * E 1 5 . 6 * 2 X * ' I N ' I 129 F0RMATI/ /5X* 'STRESSES I L B S / S O . I N I IN THE ORDER OF N00ES ' * / 5X*
* 4 2 l ' - * l l 130 FORMAT I / / * 6 X * ' N 0 0 E * * 8 X * * S T R E S S X**10X*'STRESS V ' *10X*
*'STRESS XY'* 12X* 'MAJ0R ' *15X* *MIN0R**15X* *SHEAR** / I 151 FORMAT I 5 X * I 5 * 6 I 5 X * E 1 5 . 6 I I 152 FORMAT I / / / / / I 155 F0RMATI//5X**M0MENTS ( I N . L B S I 154 F0RMAT( / /6X* 'N00E ' *8X* 'M0MENT 155 F0RMAT(//5X*'MOMENTS I I N . L B S )
* * OF M A G N I T U 0 E ' * / 5 X * 6 0 ( * - * I )
IN THE ORDER OF NODES • * / 5 X * 2 9 l ' - ' I I X**10X*'MOMENT Y'*9X*'MOMENT X Y ' * / ) K AND Y IN TNE ASCENDING ORDER**
X* *6X *• NODE **8X**MOMENT Y**6X**NO0E**8X**MOMENT
X * * / l Y * * / )
OF N O D E S * * / 5 X * 5 3 l * - * l l DIRECTION I L B S / I N I * * / / * 6 I 6
136 F 0 R M A T I / / 6 X * * N0DE**8X**M0MENT 157 FORMAT(//6X*•NODE•*8X**MOMENT 138 F 0 R M A T ( 2 ( 5 X * I 5 * 5 X v E 1 3 . 6 l l 139 FORMAT!'1*1 140 F0RMAT(/ /5X**SHEAR FORCES I N THE ORDER 141 FaRMATI//10K**CALCULATED SHEAR IN LONG
* X * ' I N C R ' * 3 X * ' S H E A R X ' l * / I 142 F 0 R M A T I 6 ( 6 X * I 5 * 5 X * F 8 . 5 I I 145 FORMAT(//10X*'CALCULATED SHEAR IN SHORT DIRECTION ( L B S / I N I • * / / * 6 (
*6X* ' INCR**5X**SHEAR Y * l * / I 144 F0RMATI/ /5X**SHEAR FORCES I N THE ASCENDING ORDER OF MAGNITUDE'*
* / 5 X * 4 7 ( ' - * l ) 145 FORMAT(/ /55X*'MAX NEGATIVE SHEAR FORCE IN K -0 IRECTION* ' *F8 .5» •
* L 8 S / I H * * / 5 5 X * * M A X POSITIVE SHEAR FORCE IN K-D IRECTION** *F 8 . 5 * • * L B S / I N * * / / 5 5 X * * M A X NEGATIVE SHEAR FORCE IN Y -D IRECTION** *F8 .3 * * • L B S / I N * * / 3 5 X * * M A X POSITIVE SHEAR FORCE IN Y-DIRECTION=**F8 .5* * • L B S / I N * I
00004460 00004470 000044 80 00004490 00004500 00004510 00004520 00004550 00004540 00004550 00004560 00004570 00004580 00004590 00004600 00004610 00004620 00004630 00004640 00004650 00004660 00004670 00004680 00004690 00004700 00004710 00004720 00004730 00004740 00004750 00004760 00004770 00004780 00004790 00004800 00004810 00004820 00004830 00004840 000048 50 00004860 00004870
133
c c c c
c< c
c c-c
c c-c-c
c
c c-c
c* c c-
146 FORMAT ( F 7 . 1 * F 1 0 . 4 I
'''*^A;;LTirD?;::;j5x'!^;.;:jj;.p"Tr;'="^=-"'^^-^'''''-^«-'^'"-14? FSSMJT aslFfi ' .s?"**'"" ° ' ""*"* ^°''°''*'^ CONDITION.,/5X*37(.-.) }?? IZltl ;^^V*^'^*-°'*°=*''^»^^5*'*«^=*'5X*Fia.5*2X*.pSI.| 1 5 1 FORMAT ( / / * 5 X * * S E C 0 N 0 LOADING APPLIED ON THE FOLLOWING ELEMENTS*.
** ANO C O O R D I N A T E S : * , / 5 X * 6 5 ( * - * I * / I .-• ."-*•«». C L t n t n i b ,
READ I N THE NUMBER OF PROBLEMS TO BE SOLVED ON THIS RUN
READ ( 5 * 104 1 NPROB
READ 1 5 * 1 4 & I FLRCAP* AISLWD WRITE ( 6 * 1 0 1 1 WRITE ( 6 * 1 3 2 ) WRITE ( 6 * 1 4 7 1 FLRCAP* AISLWD
WRITE ( 6 * 1 0 3 )
— B E G I N PROBLEM SOLUTION
DO 9 5 0 LLL - 1* NPROB —READ I N SLAB DIMENSIONS AND OTHER DESCRIPTIVE VARIALBE OF SLAB-ON-—GROUND TO BE ANALYZED
READ ( 5 * 1 0 5 J XXL* XXS* XEC* XYMX* MMM, I S 3 T R Y * L I F T * NSLOAO
NKENT = 0
I F ( I S O T R Y . E Q . O ) GO TO 8
-READ I N DIMENSIONS OF GRADE BEAMS AND GRADE BEAM SPACINGS
READ ( 5 * 1 0 6 ) BEAMLW* BEAMSW* BEAMLL* BEAMSL* ASPACE* BSPACE
- — R E A D IN MOMENT OF INERTIA I N LONG AND SHORT DIRECTIONS READ 1 5 * 1 0 7 1 MOIX* MOIY
C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * i C C READ I N SLAB GEOMETRY* ELASTIC CONSTANTS* ANO OTHER CONSTANTS C
3 READ ( 5 * 1 0 8 1 NSLAB* PR* T* YM* VMS* PRS* NSYM* NOTCON* NREAD* *NPUNCH* NB
C* c
00004880 00004890 00004900 100004910 00004920 00004930 00004940 00004950 00004960 00004970 00004980 00004990 00005000 ^00005010 00005020 00005030 00005040 00005050 00005060 00005070 00005080 00005090 00005100 00005110 00005120 -00005130 00005140 00005150 00005160 '00005170 00005180 00005190 00005200 00005210 00005220 00005230 00005240 00005250 00005260 00005270 00005230 00005290 00005300 00005310 00005320 00005330 00005340 00005350 00005360
134
c-c
c c-c
WRITE 1 6 * 1 0 9 ) XXL* XXS* T* YM* PR* VMS* PRS
CALCULATE R I G I D I T Y MODULUS
RM * Y M * T * * 3 / ( 1 2 * ( 1 - P R * * 2 ) I
CALCULATE E L A S T I C I T Y OF S O I L
YMSPRS = Y M S / I 1 . - P R S * * 2 I
I F I I S O T R Y . E Q . O I GO TO 9 WRITE ( 6 * 1 1 0 1 BEAMLW* BEAMSW* BSPACE* BEAMLL* BEAMSL* ASPACE
CALCUALTE FLEXURAL R I G I D I T Y
EIX = YM*MOIX EIY = YM*MaiY FRX = E I X / ( 1 2 . * X X L I
C c-c
CALCULATE CONCRETE WEIGHT CONSTANT FOR SLAB OF CONSTANT THICKNESS
9 WK = 0 . 0 3 7 * T IF IISOTRY.EQ.OI GO TO 7
—CALCULATE TORSIONAL R I G I D I T Y OF TEE SECTION
TRANSVERSE GRADE BEAM TRBW - ( B E f t M L W * B E A M S W * * 5 / 1 6 . 1 * ( ( 1 6 . / 5 . I - ( 5 . 3 6 * B E A M S W / B E A M L W I
* * ( 1 . - ( B E A M S W * * 4 / I 1 2 . * B E A M L W * * 4 I I I I / B S P A C E -LONGITUDINAL GRADE BEAM
C C-c
z* c
TRBL = I B E A M L L * B E A M S L * * 5 / 1 6 . l * l l l 6 . / 5 . 1 - 1 5 . 56*BEAMSL/BEAMLL) * * I 1 . - ( B E A M S L * * 4 / ( 1 2 . * B E A M L L * * 4 ) ) I I / A S P A C E
DXYFAC s I I 6 . * X X L * R M * ( 1 . - P R | | 4 ^ T R B L « - T R B W 1 I ^ E I X OVFAC - ( X X L / X X S I * ( M O I Y / M O I X I
CALCULATE AN EQUIVALENT SLAB DEPTH
TEX = ( ( l . -PR**2l*MOIX/XXLI**0.555555 TEY « TEX*(0YFAC**0.555555I
READ IN NUMBER OF NODES IN EACH DIRECTION ANO NODAL PRINTING INFO
7 READ (5* 104 1 NXl* NX2* NY* NCYCLE* NPRINT, (NP(I)*I-1* NPRINTl
NX - NX14-NX2 N0(2I * NX*NY*5 N02 = NOl 21 N025 - Na2/3
00005370 00005380 00005390 00005400 00005410 00005420 00005430 00005440 00005450 00005460 00005470 00005480 00005490 00005500 00005510 00005520 00005530 00005540 00005550 00005560 00005570 00005580 00005590 00005600 00005610 00005620 00005630 00005640 00005650 00005660 00005670 00005680 00005690 00005700 00005710 00005720 00005730 00005740 00005750 00005760 00005770 00005780 00005790 '00005800 00005810 00005820 00005830 000058 40 00005850
135
c c-C
C C C-
c
N O I l l = N X 1 * N Y * 3 NOl = NOl I I N 0 1 5 s N O l / 3
— R E A D I N COORDINATES OF F I N I T E ELEMENT GRID SYSTEM
READ 1 5 * 1 0 6 1 I X I I I * 1 = 1 * N X l * f V C I l * 1 = 1 * NYI
—CONVERT GRID SYSTEM COORDINATES FROM FEET TO INCHES
DO 1 6 0 I = 1 * NX X ( I ) = X ( I I * 1 2 .
160 CONTINUE 0 0 1 6 1 1 = 1 * NY Y d ) = Y( 1 1 * 1 2 .
1 6 1 CONTINUE
: CALCULATE THE VARIOUS CONSTANTS USED THROUGHOUT THE SOLUTION
LA = NB-1 N O B d l = N0( 1 ) * N B N 0 B ( 2 I = N 0 ( 2 I * N B NOBl « N O B d ) N0B2 3 N0B(2 ) N013P = N013«- l NOIP = N014-1 N015NY = N015*NY
: I N I T I A L I Z E AND SET TO ZERO THE MATRIX OF NODES NOT I N CONTACT I N I
0 0 5 2 0 0 1 = 1 * N025 5200 N C C d l = 0
I F ( N O T C O N . E Q . O I 60 TO 5 2 2 0
: READ IN THE NODAL NUMBERS AT WHICH SUBGRADE REACTION IS PRESUMED : TO BE ZERO
READ (5* 1341 (NZdl* 1 = 1* NOTCONI
DO 5210 1 = 1 , NOTCON 5210 NCC(NZ(I1I = 1 5220 IF (NSLAB-ll 11* 11* 15
11 NONY « Nai3 GO TO 15
13 NONY s N023-NY 15 NOO = ( NQNY«-ll*N0NY/2
00005860 00005870 00005880 00005890 00005900 00005910 00005920 *00005930 00005940 00005950 00005960 00005970 00005980 00005990 00006000 00006010 00006020 00006030 00006040 00006050 00006060 00006070 00006080 00006090 00006100 00006110 00006120 00006130 00006140 00006150 T00006160 00006170 00006180 00006190 00006200 00006210 00006220 00006230 00006240 00006250
*00006260 000062 70 00006280 00006290 000 06300 00006310 00006320 00006330 00006340
136
c C INITIALIZE VARIABLES ANO MATRICES C
ICC = 0 ICCC = 0 NIC - 0 DO 9 5 5 1 = 1 * N023
9 5 5 F ( ( I - 1 1 * 3 > 1 I = 0 C C DETERMINE NUMBER OF ELEMENTS IN FINITE ELEMENT MESH C
NELEM = ( N Y - l ) * ( N X - N S L A B t NYI = NV-1
I F THE SLAB AND SUBGRADE ARE NOT ASSUMED IN FULL CONTACT*
UNTIL THE SAME CONTACT CONDITIONS ARE OBTAINED
965 NIC = NIC4-1
INITIALIZE SUBGRADE STIFFNESS MATRIX
ITERATE
0 0 16 I = 1* NOO 16 H i l l s 0
IC = 0 0 0 55 I = 1* N023 P P F d ) « F ( ( 1 - 1 1 * 3 * 1 1
55 A B d l = 0
C INITIALIZE SLAB STIFFNESS MATRIX
00 19 I = 1 * N0B2 19 C d l s 0
PA s 0 PB = 0
GENERATE STIFFNESS MATRIX OF EACH ELEMENT
DO 2 0 0 K = 1* NELEM 11 = ( K - l l / N Y l 12 = K-I1*NY1 IF (NSLAB-21 2 1 * 22f 22
21 N O D d l = K«-I1 GO TO 2 7
22 IF I K - N Y 1 * ( N X 1 - 1 ) ) 2 1 * 2 1 * 23 23 I I = 11*1
NOO(l ) = K*I14^NY1 27 N0D(2 I = NaD( 11 *1
N0D(3 I = N0D(1I4-NY N0D(4) = N3D(3)«-1
00006350 00006360 00006370 00006380 00006390 00006400 00006410 00006420 00006430 00006440 00006450 00006460 00006470 00006480 00006490 00006500 00006510 00006520 00006530 00006540 00006550 00006560 00006570 00006580 00006590 00006600 00006610 00006620 00006630 00006640 00006650 00006660 00006670 00006680 000066 90 00006700 00006710 00006720 00006730 00006740 00006750 00006760 00006770 00006780 00006790 00006800 00006810 00006820 00006830
137
A = ( X d l * 2 ) - X ( I l 4 ^ 1 ) l / 2 00006840 B = ( V d 2 4 - l l - Y ( I 2 } l / 2 00006850
C 00006860 C TEST FOR DUPLICITY OF CALCULATIONS 00006870 C 00006880
I F ( A B S ( A - P A ) . L T . O . O O l . A N D . A B S ( B - P B I . L T . 0 . 0 0 1 1 GO TO 100 00006890 PA = A 00006900 PB = B 00006910 ATB = A*B 00006920 ATB2 * ATB**2 00006930 AOB = A/B 00006940 BOA = B/A 00006950 A0B2 = AD8**2 00006960 B0A2 = B0A**2 00006970
C 00006980 C COMPUTE THE ELEMENT FLEXIBILITY MATRIX OF SUBGRADE 00006990 C 00007000
XXX = 0 00007010 Y Y Y f l l = A L a 6 ( 2 . 0 l 00007020 00 24 I = 2 * 21 00007030 XXX = XXX4-0. 05 00007040
24 Y Y Y d l = A L 0 G ( l * S O R T ( l * B D A * * 2 * X X X * * 2 l l 00007050 CALL OSF ( 0 . 0 5 * YYY* ZZ* 211 00007060 0EF(K I = ( Z Z ( 2 1 I - A L 0 G ( B D A I * 1 I / ( 4 * 5 . 1 4 1 5 9 5 * A I 00007070 XJ s 0 00007080
C c-c
00007090 —FORMULATE LOAD MATRICES VL AND VM 00007100
00007110 00 95 I = 1* 4 00007120 00 95 J = I* 4 IJ = IJ^l
50 VL = 2*B GO TO 50
IF (M-2) 60* 70* 80 60 VM = 1
GO TO 90 70 VM = 2*B
GO TO 90 80 VM = 2*A 90 CONTINUE
00007130 00007140
DO 95 L = 1* 3 00007150
IF (L-2) 20* 50* 40 JJSJIJJS 20 ui - » 00007170
GO TO 50 00007180
40 VL = 2*A 50 00 95 M = 1* 5
IJLM = M«-(L-11*3*(IJ-11*9 „ « « « , , . n IF d.EO.J.ANO.L.GT.M) GO TO 95 °A^Aliti
00007190 00007200 00007210 00007220 00007230
00007250 00007260 00007270 00007280 00007290 00007300 00007310 00007320
138
CALCULATE I S O T R Y = l :
THE ELEMENTAL I F SLAB I S OF
STIFFNESS <4ATRIX ( I F SLAB HAS GRADE BEAMS CONSTANT THICKNESS* I S O T R Y = 0 . )
I F ( I S O T R Y ) 9 5 0 * 9 2 * 93 92 S M d J L M ) = R M * ( B 0 A 2 * S M l d J L M ) * A 0 B 2 * S M 2 d J L M I « - P R * S N 3 ( I JLM)
* * 0 . 5 * ( 1 . - P R ) * S M 4 ( I J L M ) ) * V L * V M / ( 6 0 . * A r B ) GO TO 95
93 S M d J L M ) = F R X * ( B 0 A 2 * S M 1 ( I J L N I « - 0 Y F A C * A O B 2 * S M 2 ( I J L M l * D X Y F A C * S M 4 ( * I J L M ) I * V L * V M / ( 6 0 . * A T B )
95 CONTINUE GO TO 189
100 D E F ( K I = D E F ( K - 1 I 189 I J = 0
DO 200 1 = 1 * 4 A B ( N O O d ) ) = A B ( N 0 0 d ) ) « - A T B
C C-c-c
—SUPERIMPOSE THE ELEMENT STIFFNESS MATRIX TO FORM THE OVERALL —STIFFNESS MATRIX
C c-c-c
DO 200 J = I * 4 IJ = IJ^l 00 200 L = 1* 3 DO 200 M = 1* 3 IJLM » M*(L-1)*3«-(IJ-1)*9 IF (I.EQ.J.ANO.M.LT.L) GO TO 200 IH s (N0D(I)-l)*Na*3*l*(L-l)*NB*(N3D( J)-NO0(I ))*34-M-L C(IH) = C(IH)*SM(IJLM)
200 CONTINUE
SUPERIMPOSE THE ELEMENT FLEXIBILITY MATRIX TO FORM THE OVERALL FLEXIBILITY MATRIX OF THE SUBGRADE
1502 502 504
506 508
510
512
DO II 12 IF IF H(( 60 IF IF DEF 60 IF DEF GO DEF 60 IF
541 1 = 1 * NONY = d-l)/NY*l = I-(I1-1 )*NY (I.GT.NX1*NY( 11=11*1 (NCC(dl-l)*NY*l2).EQ.O) GO TO 1502 I*l)*I/2) = H((I*1I*I/2I*1 TO 541 (I-(I-1I/NV*NY-1) 512* 502* 512 d-1) 506* 504* 506 F = 4*0£F(1) TO 600 d-NONY«-NYl) 510* 508, 5 10 F = 4*DEF((NX-1-NSLAB1*NY1+1) TO 600 F = 2*(DEF(I-I/NY)*0EF(I-I/HY-NY1)) TO 600 (I-(I-1)/NY*NY-NY) 522, 514* 522
*00007330 00007340 00007350 00007360 00007370 00007380 00007390 00007400 00307410 00007420 00007430 00007440 00007450 00007460 00007470 00007480 00007490 00007500 00007510 00007520 00007530 00007540 00007550 00007560 00007570 00007580 00007590 00007600 00007610 00007620 00007630 00007640 00007650 00007660 00007670 00007680 00007690 00007700 00007710 00007720 000077 30 00007740 00007750 00007760 00007770 00007780 00007790 00007800 00007810
139
514 I F ( I - N Y ) 5 1 8 * 516* 518 516 OEFF = 4*0EF(NY1)
GO TO 600 518 I F d-NONY) 510* 520* 510 520 OEFF = 4*0EF( INX-NSLAB)*NY1)
522 I F d - N Y ) 5 2 4 * 600* 526 524 OEFF = 2 * ( 0 E F d ) * D E F ( I - l ) )
00007820 00007830 00007840 00007850 00007860
?? !? ^°? ... 00007870 00007880 00007890
00007910 00007920
< ° TO 600 00007900 526 IF d-NONY* NVl) 550* 600, 52 8 528 OEFF = 2*(0EF(I-I/NY-NY1)*0EF(I-I/NY-NY))
GO TO 600 00007950 530 OEFF = DEFd-I/NYI*OEF(I-I/NY-ll*DEFd-I/NY-NYlI*DEF(I-I/NY-NY) 00007940 600 00 542 L = 1, NSYM 00007950
IF (L.EQ.5) 60 TO 542 00007960 IF (L-2) 270* 272* 274 00007970
270 SIGX = 1 00007980 SIGY = 1 00007990 GO TO 290 00008000
272 IF (NSYM.Ea.3l GO TO 542 00008010 SIGX = -1 00008020 SI6V = 1 00008030 GO TO 290 00008040
274 IF (L-3) 276* 276* 278 00008050 276 SIGX = 1 00008060
SI6V = -I 00008070 GO TO 290 00008080
278 SIGX = -1 00008090 SIGV s -1 00008100
290 00 540 J = I* NONY 00008110 Jl = (J-ll^NY-fl 00008120 J2 = J-(J1-1)*NV 00008130 IF (J.GT.NK1*NY) Jl = Jl*l 00008140 IF (L.EQ.1.AN0.I.EQ.J.0R.L.EQ.2.AND.I.LE.NY.AND.I.EQ.J.0R.L.E0.5. 00008150
*ANO.I.EQ. (I-1)/NY*NY*1.AND.I.EQ.J.0R.L.EQ.4.ANO.I.EQ.1.ANO.J.EQ.1100008160 00008170 00008180 00008190 00008200
224 AAA = l/(5.141595*SQRT((Xdl)-SIGX*X( J1))**2*(Y(I2)-SISY*Y(J2))** 00008210 *2)) 00008220
226 H((J*l)*J/2-J*I) = H((J*l)*J/2-J*I)*AAA 00008230 540 CONTINUE 00008240 542 CONTINUE 00008250 541 CONTINUE 00008260
C 00008270 C STORE THE FLEXIBILITY MATRIX OF THE SUBGRADE 00008280 C 00008290
00 9541 I = 1* NOO 00008300
*G0 TO 60 TO
222 AAA 3 GO TO
222 224 OEFF 226
140
9 5 4 1 C
C
190
1 9 1 192
171 172
C c-c
H O d ) = H I D / Y M S P R S
• INVERT THE F L E X I B I L I T Y MATRIX T3 OBTAIN THE STIFFNESS MATRIX OF -THE SUBGRADE
CALL SINV I H * NONY* l . O E - 0 7 * l E R * NOOl I F I I E R . N E . O ) GO TO 6 0 0 0 0 0 545 1 = 1 * NOO H I D = HI I ) * Y M S P R S
-ST IFFNESS MATRIX OF THE SUBGRADE IS ADDED TO THE STIFFNESS MATRIX -OF THE SLAB TO OBTAIN THE STIFFNESS MATRIX OF THE SYSTEM
DO 1 7 2 1 = 1 * N 0 2 * 3 I F ( N C C ( ( I - l ) / 3 * l ) . N E . O ) GO TO 1 7 2 I F d . 6 T . N O l . A N O . I . L E . N 0 1 * N Y * 3 ) GO TO 172 I F d - N O l l 1 9 0 * 1 9 0 * 191 IK = d - l ) / 3 * l GO TO 192 I K = d - l ) / 5 * l - N Y DO 1 7 1 J = 1 * NB* -3 16 = IK*( J-1 ) / 3 I F ( I . L E . N 3 1 . A N 0 . I G . G T . N 0 1 3 . 0 R . I G . G T . N O N Y I GO TO 1 7 1 I F ( N C C K I - l ) / 3 * l * ( J - l ) / 3 ) . N E . O ) GO TO 1 7 1 I H = ( I - 1 ) * N B * J C ( I H ) = C I I H l * H ( ( I G * l ) * I G / 2 - ( J - 1 ) / 3 ) CONTINUE CONTINUE I F ( N S L A B . E Q . l ) GO TO 2 0 7 NYNB = NY*3*NB
—STORE THE S T I F F N E S S COEFFIC IENTS AT THE JOINT
0 0 2 0 5 1 = 1 * NYNB C O d l s C ( N O B l * I » 203
C C ADJUST THE S T I F F N E S S COEFF IC IENTS AS A RESULT OF SYMMETRY C
0 0 2 0 5 I = 1 * NY 205 C K I - 1 1 * N B * 3 * 1 * N 0 B 1 I = l . O E 2 0 207 I F ( N S Y M . E Q . l . O R . N S Y M . E Q . 5 1 GO TO 203
I F I N S Y M - 3 1 1 7 3 * 1 7 5 * 173 173 DO 174 I = 1 * NY 174 C K d - l >*3«-2 l * N B * l l = l . O E 20
I F ( N S Y M . E Q . 2 I GO TO 2 0 8 175 DO 176 I = 1 * N 0 2 3 * NY 176 C(((I-l)*3*l)*NB*1) = l.OE 20
C C APPLY GAUSS ELIMINATION TO FORM AN UPPER TRIANGULAR COEFFICIENT
00008310 00008320 00008330 00008340 00008350 00008360 00008370 00008380 00008390 00008400 00008410 00008420 00008430 00008440 00008450 00008460 00008470 00008480 00008490 00008500 00008510 00008520 00008530 00008540 00008550 00008560 00008570 00008580 00008590 00008600 00008610 00008620 00008630 00008640 00008650 00008660 00008670 00008680 00008690 00008700 00008710 00008720 000087 30 00003740 00008750 00008760 00008770 00008780 00008790
141
C M A T R I X * WHICH WILL BE USED LATER FOR ITERATION C
208 00 215 N = 1, NSLAB 215 CALL TRIG(N)
IF (NIC.GT.l) GO TO 931
DETERMINE THE COORDINATES OF THE CENTER OF EACH SLAB FOI — W A R P I N G
IF (NSYM-2) 7020* 7030* 7040 7020 X X d ) = X ( N K l ) / 2 .
Y Y l l ) = Y l N Y ) / 2 . 60 TO 7070
7050 XXIl l = 0 . Y V d ) = Y ( N Y ) / 2 . GO TO 7 0 7 0
7040 I F (NSYM-41 7 0 5 0 * 7 0 6 0 * 7 0 2 0 7050 XX( 1) = X ( N X l ) / 2 .
Y V d ) = 0 . 6 0 TO 7 0 7 0
7 0 6 0 X X d l = 0 . Y Y d l = 0 .
7070 I F ( N S L A B . E Q . l ) 6 0 TO 7 0 8 0 X X ( 2 ) = ( X ( N X I * X ( N X l l l / 2 . Y Y ( 2 ) = Y ( M Y ) / 2 . I F ( N S Y M . E 3 . 3 . O R . N S Y M . E Q . 4 ) Y Y ( 2 ) = 0 .
C C READ I N GAP, TEMP, AND LOAD DATA C
7080 READ ( 5 * H I ) NGAP* NTEMP* NLOAD* I C L * NCK* NWT * TEMP, * O E L F , R F J , I C L F
WRITE ( 6 , 1 1 2 ) WRITE 1 6 , 1 1 3 1 NSYM* NB WRITE ( 6 * 1 1 4 1 N X l * NY* NCYCLE* NPRINT WRITE ( 6 * 1 1 5 1 NLOAD* I C L , NCK, NWT, Q* DEL* DELF* R F J , WRITE ( 6 , 1 1 6 1 ( X ( I 1 , I = 1 * NXl WRITE ( 6 * 1 1 7 ) ( Y ( I I * I > 1 * NY)
C C — — R E A D I N NODE LOCATIONS USED TO CHECK CONVERGENCE C
READ (5* 104) (NOOCKdl* 1 = 1* NCKl C< C
C
c-
WRITE (6* 1181 (NOOCKdl* 1=1* NCK) If INREAO-1) 678, 677, 981
—READ IN LOCATIONS OF SPECIFIED OR PRE-CALCULATED CURL
00008800 00008810 00008820 00008830 00008840 00008850
COMPUTINC00008860 00008870 00003880 00008890 00008900 00008910 00008920 00003930 00008940 00008950 00008960 00008970 00008980 00003990 00009000 00009010 00009020 00009030 00009040 00009050 00009060 00009070 00009080 00009090 00009100 *00009110 00009120 00009130 00009140 00009150 00009160 00009170 00009180 00009190 00009200 00009210 00009220 *00009230 00009240 00009250 00009260 00009270 00009280
0, DELi
ICLF
7 C 74
142
6 7 7 READ 1 5 , 1 3 7 ) ( C U R L I I ) , 1 = 1 , N 0 2 3 )
6 0 TO 983 6 7 8 0 0 6 8 0 1 = 1 * N 0 2 3 6 8 0 C U R L I I ) = 0 .
I F ( N G A P . E a . O ) GO TO 1 0 6 9 C C' c
—READ I N GAP LOCATIONS
READ 1 5 * 1 3 4 ) ( N G d ) * 1 = 1,NGAP)
C READ I N LOCATIONS OF S P E C I F I E D OR PRE-CALCULATED CURL C
READ ( 5 , 1 1 9 ) ( C U R L ( N G ( I ) I , 1 = 1 * NGAPI
C COMPUTE THE CURLING OF SLAB DUE TO TEMPERATURE DIFFERENTIALS AND C ADO I T TO THE CAP TO FORM TOTAL CURLING ANO GAP C
1069 I F ( N T E M P . E Q . O ) GO TO 9 8 1 DO 3 I = 1 * NX I F ( I - N X l ) 7 1 0 0 * 7 1 0 0 * 7 2 0 0
7 1 0 0 N = 1 GO TO 7 3 0 0
7200 N = 2 7300 0 0 3 J = 1 * NY
5 C U R L K I - 1 ) * N Y * J I = O . O 0 0 0 0 2 5 * T E M P * ( (X d ) - X X (N ) ) * * 2 * ( Y( J ) - Y Y ( N) ) * * * 2 ) / T * C U R L ( d - l ) * N Y - t - J )
9 8 1 CONTINUE I F (NWT) 2 ? 6 * 9 8 3 * 292
C C I f NUT IS NOT ZERO* COMPUTE THE VERTICAL N30AL FORCES DUE TO THE C WEIGHT OF SLAB C C . . . R E A D I N WEIGHT OF SLAB FOUNDATION OF N0N-C3NSTANT CROSS-SECTION C AND/OR L I V E LOAD AS UNIFORMLY DISTRIBUTED LOADING
C 292 READ ( 5 * 1 2 0 ) QSLAB
c ***************************************************************** *****' C
OQ = QSLAB 00 295 I = 1* N023
295 FOd ) = QSLAB*AB( I) GO TO 931
C DISTRIBUTE WEIGHT OF SLAB OF CONSTANT* RECTANGUALR CROSS SECTION
00009290 00009300 00009310 00009320 00009330 00009340 00009350 00009360 00009370 00009380 00009390 00009400 '00009410 00009420 00009430 00009440 00009450 00009460 00009470 00009430 00009490 00009500 00009510 00009520 00009530 00009540 00009550 00009560 00009570 00009580 00009590 00009600 00009610 00009620 00009630 00009640 00009650 00009660 00009(»70 00009680 00009690 '00009700 00009710 00009720 00009750 00009740 00009750 00009760 00009770
143
c c-c
296 DO 2 9 7 I = 1 * N 0 2 3 2 9 7 F O d I = W K * A B d l
0 0 = WK GO TO 931
I F NWT IS ZERO* I N I T I A L I Z E THE NODAL FORCES TO ZERO
9 8 3 0 0 9 5 2 I = 1 * N023 9 5 2 F O d I = 0 9 3 1 0 0 1 9 5 1 1 = 1 * N023
1 9 3 1 P F d ) = 0 . DO 18 I = 1 * N02
18 F i l l = 0 I F I N I C . G T . I ) GO TO 8 7 1 I F I N L O A O . E Q . O ) GO TO 9 3 3
—COMPUTE NODAL FORCES DUE TO APPLIED LOADINGS
— R E A D I N LOCATION OF APPLIED LOADS
READ 1 5 * 1 3 4 ) ( N L ( I ) * 1 = 1 * NLOAD)
C
c
c
c * * * *
c
c
c 201
C**** c
DO 2 0 1 I . = 1 * NLOAD
-READ I N D I S T R I B U T I O N OF LOAD ON EACH LOADED ELEMENT
READ ( 5 * 1 2 1 ) X D A ( I * 1 I * X D A ( I * 2 l * Y D A ( I * 1 ) * Y 0 A d * 2 )
C c-c
WRITE (6* 122) 00 202 1 = 1 * NLOAO
202 WRITE 16* 123) N L d ) * XDA(I*1)* XDA(I*2)* Y0A(I*1)* YDA(I*2)
FIND FORCE DUE TO APPLIED LIVE LOAD
DO 300 K = 1 * NLOAO IF (NSLAB.EQ.l) GO TO 803 IF (NL(K)-(NX1-1)*NY1I 803* 803* 801
801 II = (NLIK)-11/NY1*1 12 = NL(KI-(I1-11*NY1 NODdl = NL(K)*NY1*I1 GO TO 804
803 II = (NL(K)-1I/NY1 12 = NL(K)-I1*NY1 NOOd) = NL(K)*I1
804 N00(2) = Nao( 1)*1 N00(3) = N0D(1)*NY
00009780 00009790 00009800 00009810 00009820 00009830 00009840 00009850 00009860 00009870 00009880 00009890 00009900 00009910 00009920 00009930 00009940 00009950 00009960 000099 70 00009980 00009990 ^00010000 00010010 00010020 00010030 00010040 00010050 00010060 ^00010070 00010080 00010090 00010100 00010110 00010120 00010130 00010140 00010150 00010160 00010170 00010180 00010190 00010200 00010210 00010220 00010230 00010240 00010250 00010260
144
N0D(4) = N U D ( 3 ) * 1 C 0 0 0 1 0 2 7 0
^ f * D CONTRIBUTING LOADED AREA FOR EACH NODE 00010290 ^ 00010300
00010310 00010320 00010330
C DETERMINE FORCE ACTING ON NODE DUE TO APPLIED LOADING 00010340
A = (X(Il*2)-Xdl*l))/2 B a (Y(I2*l)-Y(I2)l/2
C
OK = Q*A*B 00010350 00010360
00010450 00010460
N0D13 = (N00(l)-ll*3 00010370 NOD33 = (N30(3I-11*3 00010380 X O d ) = XDA(K*2I-XDA(K,1) 00010390 YD(1) = YDA(K,2)-YDA(K,1) 00010400 X0(2) = (XDA(K*2)*X0A(K*l))/2 00010410 YD(2) = (YDA(K,2)*YDA(K,l))/2 00010420 DO 300 I = 1 , 4 00010450 IF (1-2) 210, 220* 230 00010440
210 XI = -1 YI = -1 GO TO 260 00010470
220 XI = -1 00010480 YI = 1 00010490 60 TO 260 00010500
250 IF d-5) 240* 240* 250 00010510 240 XI = 1 00010520
YI = -1 00010530 60 TO 260 00010540
250 XI = 1 00010550 YI « 1 00010560
2 6 0 F O I N O O d ) ) = F O ( N O O ( I ) I * 0 . 2 5 * Q K * ( 1*XI*XD(2I ) * ( 1 * Y I * Y D ( 2 ) 1 * X D ( 1 ) * 0 0 0 1 0 5 7 0 * y O ( l ) 0 0 0 1 0 5 8 0
300 CONTINUE 00010590 C 00010600 C CHECK FOR SECOND L0ADIN6 ON SLAB 00010610 C 00010620
If (NSLOAO.EQ.O) 60 TO 935 00010630 C 00010640 C——COMPUTE NODAL FORCES DUE TO SECOND LOADING 00010650 C -READ IN INTENSITY OF SECOND LOADING AND NUMBER OF ELEMENTS LOADED 00010660 C BV THIS 00010670 C 00010680
READ ( 5 * 149 ) NFLOAD* 02 00010690 C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 0 0 0 1 0 7 0 0 C 000 10710
WRITE (6* 143) 00010720 WRITE (6* 150) NFLOAD* 02 00010730
C 00010740 C READ IN LOCATION OF SECOND SET OF APPLIED LOADS 00010750
145
READ ( 5 * 104 ) ( N F L ( I ( * 1 = 1 * NFLOAOI
C c-c
——-READ IN DISTRIBUTION OF SECOND LOADING ON EACH LOADED ELEMENT
DO 401 1 = 1 * NFLOAD 401 READ 15* 121 ) X D A 2 ( I * 1 1 * X 0 A 2 ( I * 2 I * Y D A 2 ( I , 1 I , YDA2( 1,21
C * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * c
WRITE ( 6 * 1 5 1 1 00 402 1 = 1 * NFLOAD
402 WRITE ( 6 * 1231 N F L d I * X 0 A 2 ( I * 1 1 * X 0 A 2 ( I * 2 I * V D A 2 ( I * 1 I * YDA2( I *21 C C FIND FORCE DUE TO APPLIED SECOND LOADING C
DO 405 K = 1 * NFLOAD I F ( N S L A B . E Q . l l 60 TO 404 I F I N F L I K 1 - I N X 1 - 1 I * N Y 1 I 404* 404* 405
405 I I = I N F L I K l - 1 1 / N V l * ! 12 = N F L I K I - I I 1 - 1 1 * N V 1 N O O d l = N F L I K 1 * N V 1 * I 1 6 0 TO 406
404 I I = I N F L I K l - l l / N Y l 12 = N f L I K l - I l * N Y l N O D d l = N F L I K I * I 1
406 N0D(2 I = N 0 0 ( 1 I * 1 N00(51 = NOOdl^NY N0D(41 = N0DI514-1
C C-
c -FIND CONTRIBUTING LOADED AREA FOR EACH NODE
A = I K d l * 2 1 - X d l * l l l / 2 B « I Y d 2 * l l - Y ( I 2 1 1 / 2
C C DETERMINE FORCE ACTING ON NODE DUE TO APPLIED LOADING C
0K2 « Q2*A*B N0015 = ( N 0 D ( 1 I - 1 1 * 5 N0055 = ( N 0 D ( 5 1 - 1 1 * 5 X D d l = XDA2(K*2 I -XDA2(K*11 V O I l l = V 0 A 2 ( K * 2 ) - Y D A 2 I K * 1 ) X 0 I 2 ) = I X 0 A 2 I K * 2 ) * X D A 2 I K * l ) ) / 2 Y 0 I 2 ) = I Y D A 2 I K * 2 ) * Y 0 A 2 I K * l l l / 2 00 405 1 = 1 * 4 I F 11 -21 4 0 7 * 4 0 8 * 409
407 X I = - 1 Y I = - 1 6 0 TO 410
00010760 00010770 ^00010780 00010790 00010800 00010810 00010820 00010830 ^00010840 00010850 00010860 00010870 00010880 00010890 00010900 00010910 00010920 00010930 00010940 00010950 00010960 00010970 00010980 00010990 00011000 00011010 00011020 00011030 00011040 00011050 00011060 00011070 00011080 00011090 00011100 00011110 00011120 00011130 00011140 00011150 00011160 00011170 00011180 00011190 00011200 00011210 00011220 00011230 00011240
146
00011250 408 XI = - 1 YI = 1 00011260 GO TO 410 00011270
409 IF 11-31 411* 411* 412 00011280 411 XI = 1 00011290
YI = - 1 00011300 60 TO 410 00011510
412 XI = 1 00011320 YI = I 00011350
410 FOINOOIIII = F O I N O 0 I I l l * 0 . 2 5 * O K 2 * l l * X I * X D l 2 l l * l l * V I * Y D I 2 l l * X D t l l * 00011540 •VOID 00011550
405 CONTINUE 00011560 955 I F INSLAB.EQ. l l 60 TO 871 00011570
DO 875 I = 1 * NY 00011580 875 FOIN015-NY4-I1 = F 0 I N 0 1 3 - N Y * I 1 *F 01 N 0 1 3 * I I 00011390
C 00011400 C FIND D E F L E : T I 0 N DUE TO SLAB WEIGHT AND/OR UNIFORMLY DISTRIBUTED 00011410 C LIVE LOAD 00011420 C 00011430
871 DO 502 1 = 1 * N025 00011440 502 F I ( I - 1 1 * 5 * 1 1 = F O d I 00011450
I F (NLOAD.EO.O.AND.NWT.EQ.O) GO TO 1505 00011460 C 00011470 C COMPUTE DEFLECTIONS AS IF ONLY ONE SLAB EXISTS 00011480 C 00011490
CALL LOAOM ( I I 00011500 1503 CONTINUE 00011510
C 00011520 C UNDER A GIVEN CONTACT CONDITION* APPLY ITERATION PROCESS UNTIL THE00011550 C——-DEFLECTIONS CONVERGE 00011540 C 00011550
510 IC s IC*1 00011560 0 0 2 I = 1* N025 00011570 IF ( IC.EQ.1 .AN0.I .GT.N0131 CO TO 1952 00011580
2 P F d l « F ( ( I - 1 I * 5 * 1 1 00011590 1952 I F INSLAB.EQ. i l 60 TO 526 00011600
IF l i e . E Q . l l 60 TO 511 00011610 0 0 945 I = NOIP* N02 00011620
945 F i l l = 0 00011650 00 947 I = N015P* N025 00011640
947 F I ( I - 1 1 * 5 * 1 1 = F O d l 00011650 C 00011660 C If TWO SLABS EXIST* DETERMINE THE NODAL FORCES IN THE RIGHT SLAB 00011670 C DUE TO THE DEFLECTIONS OF THE SUBGRADE. 00011680 (. 00011690
DO 797 I = N015P* N025 00011700 IF (NCC(I).NE.O) GO TO 797 00011710 IF (I.LE. NOl 3*NY) GO TO 797 ???ff!?? K = I-NY
00011730
147
00 795 J = 1 * N023 00011740 I F ( N C C ( J ) . N E . O ) GO TO 795 00011750 I F ( J . 6 T . N 0 1 5 . A N O . J . L E . N 0 1 5 * N Y I GO TO 795 00011760 I F ( J - N 0 1 5 ) 1050* 1050* 1052 00011770
* ° " an'ri i « . . 00011780
, o « - ^°. IV^ 00011790 1052 M « J-MY 00011800 1054 IF I J . 6 T . I -NB/5 .ANO.J .LT.I*NB/3 .AND.J .6T.N013I 60 TO 748 00011810
I f IK-M) 7 i 2 * 742* 744 00011820 742 HH = HIIM*l)*N/2-M*K) 00011850
« 0 TO 754 00011840 744 HH = HIIK*l)*K/2-K*MI 00011850 754 I f INTEMP.EQ.O.ANO.NLOAD.NE.O.ANO.CURLIJI .LE.01 60 TO 746 00011860
f K I - l l * 5 * l l s f ( I I - 1 I * 5 * 1 1 - ( P F I J I - C U R L ( J ) ) * H H 00011870 6 0 TO 795 00011880
746 F ( ( I - 1 ) * 5 * 1 ) = F I I I - 1 I * 5 * 1 1 - P F I J I * H H 00011890 60 TO 795 00011900
748 I F I K - M I 7 8 6 * 786* 788 00011910 786 HH = H ( I M * l l * M / 2 - M * K I 00011920
60 TO 792 00011950 788 HH = H I ( K * l l * K / 2 - K * M l 00011940 792 IF INTEMP.EO.O.ANO.NLOAO.NE.O.AND.CURLIJI .LE.01 60 TO 795 00011950
F I I I - 1 I * 5 * 1 I = F l d - l l * 5 « - l l * C U R L I J}*HH 00011960 795 CONTINUE 00011970 797 CONTINUE 00011980
C 00011990 C——EQUATE THE DEFLECTIONS OF THE JOINT AT THE RI6HT SLAB TO THOSE AT 00012000 C THE LEFT SLAB 00012010 C 00012020
511 00 512 I = N015P* N015NY 00012050 512 F I I I - 1 I * 5 * 1 1 = l .OE 2 0 * I P F I I I * R F J * l f l l I - N Y - l l * 5 * l l - P f ( I l l l 00012040
C 00012050 C — - C O M P U T E DEFLECTIONS OF THE RIGHT SLAB 00012060 C 00012070
CALL LOAOM ( 2 1 00012080 C 00012090 C DETERMINE THE NDOAL FORCES IN THE LEFT SLAB DUE TO THE DEFLECTIONS00012100 C Of THE SUB6RA0E 00012110 C 00012120
526 00 515 I = 1* NOl 00012150 515 f i l l = 0 00012140
00 1100 1 = 1 * N015 00012150 1100 F l d - l l * 3 * l l = F O d l 00012160
001595 I = 1* N015 00012170 IF (NCC(I) .NE.Ol 60 TO 1395 00012180 DO 395 J = 1 * N023 00012190 I F (NCC(J1 .NE.01 GO TO 595 00012200 I F ( J . G T . N 0 1 3 . A N O . J . L E . N 0 1 5 * N Y I 60 TO 395 00012210 IF (J -N015) 2050* 2050* 2032 00012220
148
2050
2052 2054
542
544 554
546
548 586
588 592
595 1595
>AN0.J .LE.N015I 60 TO 548
M = J 6 0 TO 2054 M = J-NY I f ( J . 6 T . I - N B / 5 . A N 0 . J . L T . I * N B / 5 . I f d - M ) 5 4 2 , 542* 544 MM = H((M*l)*M/2-M*II 60 TO 554 HH = H ( ( I * l l * l / 2 - I * M l I f «NTEMP.tO.O.ANO.NLOAD.NE.O.AND.CURL(JI .LE.01 60 TO 546 f 1 ( 1 - 1 1 * 5 * 1 1 = F ( ( I - 1 1 * 5 * 1 I - ( P F ( J I - C U R L ( J I 1 * H H 6 0 TO 595 f ( d - l l * 5 * l l = f ( ( I - l ) * 5 * l ) - P f ( J | * H H 6 0 TO 595 I f (I-MI 586* 586* 588 HH = H((M*ll*M/2-M*Il 6 0 TO 592 HH = H ( ( I * l l * I / 2 - I * M l I f (NTEMP.EQ.O.AND.NLOAD.NE.O.AND.CURL(Jl.LE.O) 60 TO 395 f ( ( I - l ) * 3 * l ) = f ( ( I - 1 I * 3 * 1 I * C U R L I J 1 * H H CONTINUE CONTINUE I f INSLAB.EQ. l ) 60 TO 524
COMPUTE THE VERTICAL NODAL fORCES AL0N6 THE JOINT IN THE LEfT SLA DUE TO THE DEfLECTIONS OF THE RI6HT SLAB
00 516 I = 1 * NY J = I I - 1 1 * N B * 5 * 1 N5 = I N 0 1 5 - N Y - 1 * I 1 * 5 * 1 DO 514 K = 1 * NB JLBK = J - I L A * 1 - K 1 * L A I f I J L B K . L E . O I 60 TO 514 f l N 5 l = F I N 5 1 - C O I J L B K l * F l d - l l * 5 - L A * K * N 0 1 I
514 CONTINUE DO 516 K = 1 * LA I f I I . E 0 . N Y . A N D . K . 6 T . L A - 5 I GO TO 524
516 f l N 5 1 « F I N 5 1 - C 0 ( J * K 1 * F I I I - 1 I * 5 * 1 * K * N 0 1 1 C c-c
c c-c-
COMPUTE DEFLECTIONS OF THE LEFT SLAB
524 CALL LOAOM I I I
CHECK CONVERGENCE UNDER A GIVE CONTACT C0N9ITI0N AND REPEAT THE ——PROCESS IF DESIRED ACCURACY IS NOT OBTAINED. 551 0 0 540 1 = 1 * NCK
I F ( F ( ( N O O C K ( I ) - 1 ) * 3 * 1 ) . E Q . 0 . ) 60 TO 340 If( ABS(OF(NODCKd))/F((NODCK( 11-11* 5*111.6T .OEL.AND. IC. LT.
*ICLI 60 TO 310 540 CONTINUE
00012250 00012240 00012250 00012260 00012270 00012280 00012290 00012500 00012510 00012520 00012550 00012340 00012350 00012360 00012570 00012580 00012590 00012400 00012410 00012420 00012450 00012440 00012450 B00012460 00012470 00012480 00012490 00012500 00012510 00012520 00012550 00012540 00012550 00012560 00012570 00012580 00012590 00012600 00012610 00012620 00012650 00012640 00012650 00012660 00012670 00012680 00012690 00012700 00012710
149
c c-c
I F ( I C C C . E O .
— A S S I 6 N A NEW
DO 54 50 I = C A P d l = F ( ( I F ( 6 A P ( I 1 1
5410 N C C d l = 1 6 0 TO 5 4 3 0
5420 N C C d l = 0 5450 CONTINUE
1.OR.NCYLE.EQ.il 60 TO 9541
CONTACT CONDITION
1* N025 I-11*5*11-CURLI II 5410* 5420* 5420
— C H E C K C0NVER6 REPEAT THE PR
00 5452 I =
IF (F(INOO:K I F l A B S K F d
* . 6 T . O E L . A N D . 54 52 CONTINUE
; UNDER THE F l ; DELF TO OBTA 9 5 4 1 I f d C C C . E Q .
ICCC = I C C C * I C L = ICLF DEL = DELF 6 0 TO 510 I C C 3 I C C * 1
ENCE BETWEEN TWO DIFFERENT CONTACT CONDITIONS AND OCESS I F DESIRED ACCURACY IS NOT OBTAINED
1 * NCK ( I I - l ) * 5 * l ) . E Q . O . I CO TO 5452 NOOCK ( I ) - l ) * 5 * 1 1-PPF ( N O O C K d l I I / F ( I N O O C K d l - 1 1 * 5 * 1 1 1 N I C . L T . N C Y L E l 6 0 TO 965
NAL CONTACT C O N D I T I O N , CHAN6E ICF TO ICLF AND DEL TO I N MORE ACCURATE RESULTS 11 GO TO 5 4 1 1
541
IF I f
( I C C . E Q . l (NUT . E Q . O
— — D E T E R M I N E TH — C U R L ANO THE
958 0 0 9 5 8 1 = 1 CURL I I I = F l
I GO TO 350 ) GO TO 550
E F I N A L CURL AS THE DIFFERENCE BETWEEN THE I N I T I A L DEFLECTION AT EACH NODE
, N025 ( I - 1 ) * 5 * 1 ) - C U R L ( I )
C c-c-c
ON VALUE OF CURL: NEGATIVE SIGN INDICATES GAP BETWEEN —SLAB ANO SUBGRADE —CHANGE SIGN
C c« c
DO 5820 I = 5820 CURLII) = -C 550 CONTINUE
OMPUTE THE
IF (ISOTRY)
1* N025 URLdl
STRESSES AT DESIGNATED NODAL POINTS
950* 8000* 8100
00012720 00012730 00012740 00012750 00012760 000127 70 00012780 00012790 00012800 00012810 00012820 00012830 00012840 00012850 00012860 00012870 00012880 00012890 00012900 00012910 00012920 00012930 00012940 00012950 00012960 00012970 00012980 00012990 00013000 00013010 00013020 00015050 00015040 00015050 00013060 00015070 00013080 00013090 00013100 00013110 00013120 00013130 00013140 00013150 00013160 00013170 00013180 00013190 00013200
150
C CALL SUBROUTINE SOLID I F SLAB IS CONSTANT THICKNESS SLAB C
8000 CALL SOLID (NPRINT* NY* N X l * NX* PR* RM* T* NSYM* NKENTl GO TO 8500
C C CALL SUBROUTINE TEE IF SLAB IS STIFFENED SECTION SLAB C
SlOO CALL TEE (NPRINT* NY* NXl* NX* OXYfAC* fRX* TEX* TEY* NSYM* *OVfAC* NKENTl
8500 NKENT = 1 I f d C C . L T . 2 1 GO TO 510
900 CONTINUE 950 CONTINUE
6000 CONTINUE C C PRINT DEfLECTION RESULTS C
WRITE 16* 1241 WRITE ( 6 * 1251 WRITE ( 6 * 1261 ( I * f ( d - l l * 5 * l l * 1 = 1 * N0151 DO 999 1 = 1 * N015
999 C U N A d I = F ( d - l ) * 5 * l l OEFLMX = 0 . 0 DO 996 1 = 1 * N013
996 I F ( O E F L M X . L T . 6 U N A d l l OEFLMX = 6UNA( 11 OEFLMN = GUNAI l l DO 997 1 = 1 * N013 I F IDEFLMN.LT.GUNAdl l 60 TO 997 DEfLMN = 6 U N A d l
997 CONTINUE 0 0 998 1 = 1 * N015
998 I R d l - I CALL VSRTR (6UNA* N015* I R l WRITE 16* 1271 WRITE 16* 1251 WRITE ( 6 * 1261 ( I R d l * 6 U N A ( I 1 * 1 = 1 * N0131 WRITE ( 6 * 1281 DEfLMN* DEfLHX
C c-c
-CALCULATE AND PRINT DIFFERENTIAL DEFLECTIONS
CALL MSLP (N0151
C — — P R I N T STRESS RESULTS C
WRITE 16* 1291 WRITE (6* 1301 DO 887 1 = 1 * NPRINT
887 WRITE 16* 1311 NPdl* (STR(I*J1* J* 1»61
00013210 00013220 00013230 00013240 00013250 00013260 00013270 00013280 00013290 00013500 00015510 00015520 00015550 00015540 00015550 00015560 00015570 00015580 00015390 00013400 00013410 00015420 000154 50 00015440 00015450 00015460 00015470 00015480 000154 90 00015500; 00013510 00015520 00015550 00015540 00015550 00015560 00015570 00015580 00013590 00013600 00013610 00013620 00015630 00013640 00013650 00015660 00015670 00015680 00013690
151
c
c
00 888 I « 1* NXY
C c-c
00013700 C — PRINT MOMENT RESULTS 00015710 C 00015720
WRITE (6* 1321 00015750 WRITE (6* 153) 00013740 WRITE 16* 154) 00015750 DO 886 1 = 1 * NPRINT 00015760
886 WRITE (6* 151) NP(I)* XMOM(I)* YMOMd)* XYMOMd) 00015770 00 776 1 = 1 * NPRINT 00015780
776 I R d ) = I 00015790 CALL VSRTR (XMOM* NPRINT* IRl 00015800 WRITE (6* 1521 00015810 WRITE (6* 1551 00015820 WRITE (6* 1561 00013830 WRITE (6* 1381 (IRdl* XMOMIII* 1= 1* NPRINTl 00015840 00 775 1 = 1 * NPRINT 00015850
775 IRdl = I 00015860 CALL VSRTR IYMOM* NPRINT* IRl 00015870 WRITE (6* 1521 00015880 WRITE (6* 137) 00015890 WRITE (6*1531 (IRdl* YMOMdl* 1= 1* NPRINTl 00015900
00015910 C PRINT SMEAR RESULTS 00015920 C 00015950
WRITE (6* 1591 00015940 WRITE (6* 1401 00013950 WRITE (6* 14110021130 00013960 WRITE (6* 1421 (I* VXdl* I* 1* NXYI 00015970 WRITE (6* 1451 00015980 WRITE (6* 1421 (I* VYdl* 1= 1* NYX1 00015990 WRITE (6* 1591 00014000 WRITE 16* 1441 00014010 WRITE 16* 141) 00014020
00014050 888 I R d l = I 00014040
CALL VSRTR IVK* NXY* I R l 00014050 WRITE 16* 1421 l I R d l * V X I I l * I « 1 * NXYI 00014060 WRITE 16* 1451 ! ? ! } * ! ' ; DO 777 I = 1 * NYX 00014080
777 I R d l = I 00014090 CALL VSRTR IVY* NYX* I R l ° ° ° ! t l ? « WRITE 16* 1421 l I R d l * V Y d l * 1= 1 * HYXl 00014110
00014120
PRINT MAXIMUM SHEAR VALUES ?°°!tlf« 00014140
WRITE 16* 1451 VXMAXN* VXMAXP* VYMAXN* VYMAXP J J J J t J ! °
00014180 END
152
SUBROUTINE SOLID INPRINT* NY* NXl* NX* PR* RM* T* NSYM* NKENTl 00014190 C 00014200 C SUBROUTINE CALCULATES STRESSES FOR SLAB OF CONSTANT THICKNESS 00014210 C 00014220
DIMENSION C11500001*FI21001*6(1500001 *NOl21*XI6501*YI6501«STRI650*00014250 *6>*NPI 6501 *XMOMI6501*YMOMI6501*XYM0M(6501*MXDIF(6501*NYDIF(6501* 00014240 *XT( 6501*VT( 6501*0X16501*DYI6501*MXYDIFI 6501tNVXOIFl6501*VX16501* 000142 50 *VYI6501*YXMOM16501*IRl6501*6UNAI6501 00014260
C 00014270 COMMON C*F*6*N0*NB*X*Y*STR*NP*XM0M*YM0M*XYM0M*XT*YT*DX*0Y*MX0IF* 00014280
*M YD IF*MXYDIF*MYXDIF*YXMOM*VX*VY*NXY*NYX*VXMAXN*VXMAXP*VYMAXN* 00014290 *VYMAXP 00014500
C 00014510 REAL MXOIF* MYOIF* MXYDIF* MYXDIF* MOIX* MOIY 00014520
C 00014330 C 00014540
NOl = NX1*NY*5 00014550 N013 « NOl/3 00014560
C
557 N s NOl
C c-c
00014570 C — — B E 6 I N S0LVIN6 STRESS MATRIX FOR INTERNAL MOMENTS 00014580 C 00014590
DO 450 I = 1* NPRINT 00014400 11 = I N P d l - l l / N Y * l 00014410 12 = N P I I I - I l l - l l * N Y 00014420 IF I N P d l - N 0 l 5 l 555* 555* 557 00014450
555 N = 0 00014440 Ml = 0 00014450 NXX = NXl 00014460 NPl = I N P d l - l l * 5 00014470 GO TO 558 00014480
00014490 Nl = Nal3 00014500 NXX~= NX 00014510 NPl = ( N P ( I I - N 0 1 5 - 1 » * 5 ° ° ° J t H S
558 NP2 = NP1*5*NY S J J l t " ? NP5 = NP1-5*NY Tr.^ltr^
00014550 ZERO OUT OLD STRESS MATRIX 00014570
00014580 00014590 0 0 1359 J = 1* 5
1559 STR(I*J1 = 0 . ftnft,i.*.An C DETERMINE IF NODE IS ON PERIMETER OF SLAB " J J l t ^ ? ; C CORNER N0DE7 OoSiJtJS
IF (NP(II.Ea.NY*NXXI 60 TO 450 J « « , ! t * n C TOP ED6E NODE? 2 S 2 } r l ! S
IF ( N P ( I l . E Q . ( N P d l - l l / N Y * N Y * N Y l 60 TO 575 J S J I t t t o C SIDE ED6E NODE? S S J } ! t ! n
I f (NP(I ) .6E.NV*(NXX-1)*1) 60 TO 420 S J S u t J o C
153
I T " ? " " ; ; ? ^ , " ? ! ? " " ^ " ^ * " " ' • DIMENSIONS AND SOLVE FOR M( I ) 0 0 0 1 4 6 8 0 « - 1 XI 11*1 l - X d l ) ) / 2 0 0 0 1 4 6 9 0 : • ^y[\l*l*'y*l2n/2 0 0 0 1 4 7 0 0 * ° " " • < • 0 0 0 1 4 7 1 0 "O** = B/« 0 0 0 1 4 7 2 0 S T R d * l ) = ( 6 * ( B D A * P R * A D B ) * F ( N * N P 1 * 1 ) - 8 * A * P R * F ( N * N P 1 * 2 ) * 8 * B * F ( N * 0 0 0 1 4 7 3 0
* N P l * 5 l - 6 * A 0 B * P R * f ( N * N P l * 4 l - 4 * A * P R * f ( N * N P 1 * 5 » - 6 * B 0 A * F I N * N P 2 * 1 I * 4 * 0 0 0 1 4 7 4 0 * B * F I N * N P 2 * 5 1 1 / I 4 * A * B 1 0 0 0 1 4 7 5 0
S T R d « 2 1 = ( 6 * ( A 0 B * P R * B 0 A I * F ( N * N P 1 * 1 I - 8 * A * F ( N * N P I * 2 1 * 8 * B * P R * F I N * 0 0 0 1 4 7 6 0 * N P l * 5 l - 6 * A D a * F l N * N P l * 4 1 - 4 * A * F l N * N P l * 5 l - 6 * B D A * P R * F I N * N P 2 * l l * 4 * B * 0 0 0 1 4 7 7 0 * P R * F ( N * N P 2 * 5 I I / ( 4 * A * B 1 0 0 0 1 4 7 8 0
S T R ( I * 5 1 = 0 . 5 * ( 1 - P R I * ( - 2 * F ( N * N P 1 * 1 1 * 4 * B * F ( N * N P 1 * 2 I - 4 * A * F ( N * N P 1 * 0 0 0 1 4 7 9 0 * 5 I * 2 * F ( N * N P 1 * 4 1 * 4 * A * F ( N * N P 1 * 6 1 * 2 * F I N * N P 2 * 1 I - 4 * B * F I N * N P 2 * 2 1 - 2 * F I 0 0 0 1 4 8 0 0 * N * N P 2 * 4 1 1 / I 4 * A * B 1 0 0 0 1 4 8 1 0
——DETERMINE LOCATION OF NODE IN NODAL 6R ID WORK 0 0 0 1 4 8 2 0 I f I N P I I I - 1 - N l l 5 7 0 * 5 6 0 * 5 7 0 0 0 0 1 4 8 5 0
560 CON = 6 0 0 0 1 4 8 4 0 « 0 TO 4 5 5 0 0 0 1 4 8 5 0
I N P I I I . E 0 . I N P I I 1 - 1 I / N Y * N Y * 1 1 6 0 TO 420 0 0 0 1 4 8 6 0 0 0 0 1 4 8 7 0
DETERMINE C0NTRIBUTIN6 AREAL DIMENSIONS ANO SOLVE FOR MIJl 0 0 0 1 4 8 8 0 0 0 0 1 4 8 9 0
A « I X ( I l * l l - X ( I l l } / 2 0 0 0 1 4 9 0 0 B » ( Y ( I 2 l - Y I I 2 - l l l / 2 0 0 0 1 4 9 1 0 AOB = A/B 0 0 0 1 4 9 2 0 BOA = B/A 0 0 0 1 4 9 5 0 S T R d * l l = S T R I I * 1 1 * I - 6 * A D B * P R * F I N * N P 1 - 2 I * 4 * A * P R * F I N * N P 1 - 1 1 * 6 * I 0 0 0 1 4 9 4 0 *B0A*PR*ADB}*FIN*NP1*1I*8*A*PR*FI N*NPl*21*8* B*FI N*NP1*51-6*B0A*FI 000149 50 *N*NP2*1I*4*B*FIN*NP2*511/I4*A*BI 00014960
S T R d * 2 l = S T R I I » 2 1 * I - 6 * A D B * F I N * N P 1 - 2 I * 4 * A * F I N * N P 1 - 1 1 * 6 * I A 0 B * P R * 0 0 0 1 4 9 7 0 *BDAI*f l N * N P l * l l * 8 * A * f I N*NP1*2 l*8*B*PR*f IN*NP1 *5 1-6* BDA*PR*f I N*NP2*000 1 4 9 8 0 * 1 I * 4 * B * P R * F I N * N P 2 * 5 I I / I 4 * A * B 1 0 0 0 1 4 9 9 0
STRI 1*5) = S T R l I * 5 1 * 0 . 5 * d - P R l * ( - 2 * F ( N * N P l - 2 1 - 4 * A * F ( N * N P l l * 2 * F ( 0 0 0 1 5 0 0 0 * N * N P l * l l * 4 * B * F ( N * N P l * 2 l * 4 * A * F ( N * N P l * 5 1 * 2 f t F ( N * N P 2 - 2 1 - 2 * F ( N * N P 2 * l l - 0 0 0 1 5 0 1 0 * 4 * B * F ( N * N P 2 * 2 1 I / ( 4 * A * B I 0 0 0 1 5 0 2 0
C — — — — D E T E R M I N E LOCATION OF NODE IN NODAL 6RI0W0RK 0 0 0 1 5 0 5 0 I f ( N P d l . E O . N Y * N l l GO TO 5 6 0 0 0 0 1 5 0 4 0 I F ( N P d l . E a . ( N P ( I I - l l / N V * N Y * N Y I GO TO 4 5 0 0 0 0 1 5 0 5 0 I f ( N P d I - N Y - N l l 4 1 0 * 4 1 0 * 4 2 0 0 0 0 1 5 0 6 0
4 1 0 CON = 5 0 0 0 1 5 0 7 0 GO TO 455 0 0 0 1 5 0 8 0
C 0 0 0 1 5 0 9 0 C — — — D E T E R M I N E CONTRIBUTING AREAL DIMENSIONS AND SOLVE FOR M(Kl 0 0 0 1 5 1 0 0 C 0 0 0 1 5 1 1 0
4 2 0 A « ( X ( I l l - X ( I l - l l l / 2 0 0 0 1 5 1 2 0 B » ( Y ( I 2 * l l - Y d 2 l ) / 2 0 0 0 1 5 1 3 0 ADB « A/B 0 0 0 1 5 1 4 0 BOA « B/A 0 0 0 1 5 1 5 0 S T R I I * 1 1 * S T R I I * 1 1 * I - 6 * B 0 A * F I N * N P 3 * 1 1 - 4 * B * F I N * N P 5 * 5 1 * 6 * I B 0 A * P R * 0 0 0 1 5 1 6 0
154
c c-c
* 4 * A * f l N * N P l * 6 1 l / l 4 * A * B l I f I N P I I ) . E Q . N V * I N X X - 1 I * 1 1 GO TO 560 I f l N P d l - l N P I I l - l ) / N Y * N Y - l ) 4 3 0 * 4 1 0 4 3 0
—DETERMINE CONTRIBUTING AREAL DIMENSIONS AND SOLVE FOR M I L )
430
00015240 00015250 00015260 00015270 00015280 00015290 00015300 00015310 00015320 00015330 00015340 00015350 00015360
B = IY(I2)-V(I2-l))/2 A = IX(ri)-X(Il-l))/2 AOB = A/B BOA = B/A
STRd*l) = STR(I*1)*(-6*BDA*F(N*NP3*1)-4*B*F(N*NP3*3)-6*A0B*PR*F( *N*NP1-2)*4*A*PR*F(N*NP1-1I*6*(BDA*PR*AD3)*F(N*NP1*1)*S*A*PR*F(N* *NP1*2)-8*B*F(N*NP1*3))/(4*A*B) STRd*2) = STR(I*2)*(-6*8OA*PR*F(N*NP5*ll-4*B*PR*F(N*NP3*31-6*AOB*00015370 • F (N*NPI-2)*4 *A*F(N*NP1-11*6*(A0B*PR*B0AI*F( N*NP1*11*8*A*F(N*NP1* 000153 80 *21-8*B*PR*F( N*NP1*311/(4*A*B1 STR(I*31 = STR(I*31*0.5*(1-PRI*(-2*F(N*NP3-21*2*F(N*NP3*1I*4*B*F(
*N*NP5*21*2*F(N*NP1-21-4*A*F(N*NP1I-2*FIN*N*1*1I-4*8*FIN*NP1*21* *4*A*FIN*NP1*5)1/(4*A*B)
DETERMINE LOCATION OF NODE IN NODAL GRID WORK IF (NP( I).Ea.NY*NXX) 60 TO 360 IF (NP(I).EO.(NP(I)-1)/NY*NY*NY.OR.NP(I).GE.NY*(NXX-11*11
*6 0 TO 410 CON = 1.5
SOLUTION OF STRESS MATRIX COMPLETED
CONVERT INTERNAL MOMENT TO STRESS
455 DO 4 56 J = 1 * 5 4 5 6 S T R ( I * J 1 ' R M * C 0 N * S T R ( I * J 1 / T * * 2
I F ( N P ( I I . E a . ( N P ( I I - 1 1 / N Y * N Y * 1 . A N 0 . N S Y M . N E . 5 . A N D . N S Y M . N E . 4 . a R . * N P d l . E Q . ( i l P ( I l - l l / N Y * N Y * NYI S T R d * 2 1 = 0 .
I F ( N P d I . L E . N Y . A N D . N S Y M . N E . 2 . A N D . N S Y M . N E . 4 . 0 R . N P ( I 1 . G T . ( N X 1 - 1 ) * N V 0 0 0 1 5 5 70
00015390 00015400 00015410 00015420 00015430 00015440 00015450 00015460 00015470 00015480 00015490 00015500 00015510 00015520 00015530 00015540 00015550 00015560
9 8 7 6 4 50
* . A N D . N P d I . L E . ( N X 1 * 1 I * N Y . O R . N P ( I I . S T . ( N X - 1 I *NY) S T R ( I * 1 I = I F ( S T R ( I * 1 ) . E Q . O . O R . S T R d * 2 ) . E Q . O ) S T R ( I * 3 ) = 0 .
—DETERMINE MAJOR ANO MINOR STRESSES AND HORIZONTAL SHEAR X-Y S T R ( I * 6 ) = S Q R r ( 0 . 2 5 * ( S T R ( I * 1 ) - S T R ( I * 2 ) I * * 2 * S T R ( I * 3 ) * * 2 ) S T R ( I * 4 ) = I S T R ( I * l ) * S T R ( I * 2 ) ) / 2 . - S T R ( 1 * 6 ) S T R ( I * 5 ) = ( S T R ( I * l ) * S T R d * 2 ) ) / 2 . * S T R ( I * 6 ) CONTINUE CONTINUE
0.
PLANE
00015580 00015590 00015600 00015610 00015620 00015630 00015640 00015650
155
^ 0 0 0 1 5 6 6 0 C CONVERT STRESS TO MOMENT 0 0 0 1 5 6 7 0 ^ 0 0 0 1 5 6 8 0
PZOP = T * T / 6 . 0 0 0 1 5 6 9 0 DO 475 LP = 1 *NPRINT 0 0 0 1 5 7 0 0 XMOM(LP) = S T R ( L P * 1 ) * P Z 0 P 0 0 0 1 5 7 1 0 YHOM(LP) = S T R ( L P » 2 ) * P Z Q P 0 0 0 1 5 7 2 0 XYMOM(LP) = S T R ( L P * 3 ) * P Z Q P 0 0 0 1 5 7 3 0
475 CONTINUE 0 0 0 1 5 7 4 0 I F ( N K E N T . E Q . O ) GO TO 6 0 0 0 0 0 1 5 7 5 0
C 0 0 0 1 5 7 6 0 C CALCULATE SHEAR FORCES 0 0 0 1 5 7 7 0 C 0 0 0 1 5 7 8 0
CALL SHEAR (NX* NY) 00015790 C 00015800
600 RETURN 0 0 0 1 5 8 1 0 END 0 0 0 1 5 8 2 0 SUBROUTINE TEE ( N P R I N T * NY* N X l * NX* DXYFAC* FRX, TEX, TEY, NSYM, 0 0 0 1 5 8 3 0
* O Y F A C , NKENT) 0 0 0 1 5 8 4 0 C 0 0 0 1 5 8 5 0 C SUBROUTINE CALCULATES STRESSES FOR SLAB WITH GRADE BEAMS 0 0 0 1 5 8 6 0 C 00015870
DIMENSION C( 1 5 0 0 0 0 ) , F ( 2 1 0 0 I * G ( 1 5 0 0 0 0 1 * NO(21 *X ( 6 5 0 1 * Y ( 6 5 0 ) » S T R ( 6 5 0 , 0 0 0 1 5 8 8 0 * 6 1 * N P ( 6 5 0 I * X M O M ( 6 5 0 ) * Y M O M ( 6 5 0 ) * X Y M O M ( 6 5 0 1 * M X O I F ( 6 5 0 ) * M Y O I F ( 6 5 0 ) * 0 0 0 1 5 8 9 0 * X T ( 6 5 0 ) * Y T I 6 5 0 1 * 0 X ( 6 5 0 ) * 0 Y ( 6 5 0 ) * M X Y D I F ( 6 5 0 ) * M V X D I F ( 6 5 0 ) * V X ( 6 5 0 ) * 0 0 0 1 5 9 0 0 *V Y ( 6 5 0 ) , y X M 0 M ( 6 5 0 ) * I R ( 6 5 0 ) *CUNA(65.0) 0 0 0 1 5 9 1 0
C 0 0 0 1 5 9 2 0 COMMON C * F * G * N O , N B * X * Y * S T R * N P * X M O M * Y M O N * X Y M O M * X T * Y T * O X , 0 V , M X 0 I F , 0 0 0 1 5 9 30
*MYD I F * M X Y D I F *MYXOIFtVXMOM*VX*VY*NXY* NY X*VXMAXN*VXMAXP,VYMAXN, 0 0 0 1 5 ^ 4 0 *VYMAXP 0 0 0 1 5 9 5 0
C 0 0 0 1 5 9 6 0 REAL MXOIF* HYDIF* MXYDIF* MYXDIF* MOIX, M3 lY 00015970
C 00015980 C 00015990
NOl = NX1*NY*3 00016000 N015 = NOl/5 00016010
C 00016020 C BEGIN SOLVING STRESS MATRIX FOR INTERNAL MOMENTS 0 0 0 1 6 0 3 0 C 0 0 0 1 6 0 4 0
0 0 5 0 0 1 = 1 , NPRINT 0 0 0 1 6 0 5 0 11 = INPI I I - 1 1 / N Y * 1 00016060 1 2 = N P d l - l I 1 - 1 1 * N Y 0 0 0 1 6 0 7 0 I F ( N P ( I ) - N 0 1 3 1 5 * 5* 10 0 0 0 1 6 0 8 0
5 N = 0 N l = 0 NXX = NXl N P l = ( N P d ) - l ) * 3 GO TO 15
10 N = NOl
00016090 00016100 00016110 00016120 00016150 00016140
156
Nl = N013 NXX = NX NPl = (NP(I)-N013-1)*3
15 NP2 = NP1*3*NY NP3 = NP1-3*NY
C C ZERO OUT OLD STRESS MATRIX
00016150 00016160 00016170 00016180 00016190 00016200 00016210 00016220 00016230 00016240
.,, 00016250 C DETERMINE IF NODE IS ON PERIMETER OF SLAB 00016260
C 00 50 J = 1*
50 STR(I*J) = 0 C
c C — — — C O R N E R NODE?
00016270 00016280
IF (NPd) .Ea.NV*NXX) 60 TO 300 00016290 C TOP EDGE NODE? 00016300
IF (NP(I).EO.(NP(I)-1)/NY*NY*NY) 60 TO 120 00016310 C SIDE E06E N00E7 00016320
IF INP(I).6E.NV*(NXX-1(*1) 60 TO 210 00016330 C 00016340 C DETERMINE CONTRIBUTING AREAL DIMENSIONS AND SOLVE FOR M d ) 00016350 C 00016360
A « (Xdl*l)-X(Il))/2. 00016370 B = (Y(I2*l)-Y(I2)l/2 00016380 DENOM = 4.*A*B 00016390 ADB = A/3 00016400 BDA = B/A 00016410 STR(I*11 = I6*BDA*F(N*NP1*1 )*8*B*F(N*NP1*31-6*BDA*F(N*NP2*11*4*B* 00016420 *F(N*NP2*3ll/OENOM 00016430 STR(I*2I = (6*ADB*F(N*NP1*11-8*A*F(N*NP1*21-6*A0B*F(N*NP1*41-4*A* 00016440
* F ( N * N P l * 5 1 l * (0YFAC/0ENaNI 000164 50 S T R ( I * 3 1 = D X Y F A C * ( - 2 * F ( N * N P 1 * 1 I * 4 * B * F ( N * N P 1 * 2 I - 4 * A * F ( N * N P 1 * 3 1 * 2 * 00016460
* F ( N * N P 1 * 4 1 * 4 * A * F ( N * N P 1 * 6 ) * 2 * F ( N * N P 2 * 1 ) - 4 * B * F ( N * N P 2 * 2 ) - 2 * F I N*NP2* 000164 70 * 4 ) 1 / ( 4 * A * B ) 00016480
C — D E T E R M I N E LOCATION OF NODE I N NODAL GRIOWORK 00016490 I F ( N P ( I ) - l - N l } 110* 100* 110 00016500
100 CON = 6 00016510 6 0 TO 400 00016520
110 I F (NPl I ) . E Q . ( N P ( I ) - 1 ) / N Y * N Y * 1 ) 60 TO 210 00016530 C 00016540 C DETERMINE CONTRIBUTING AREAL DIMENSIONS ANO SOLVE FOR MIJ I 00016550 C 00016560
120 A = ( X ( I l * l ) - X ( I l ) ) / 2 00016570 B = ( Y d 2 ) - Y ( l 2 - l ) ) / 2 00016580 DENOM = 4 . * A * B 00016590 AOB = A/B 00016600 BOA = B/A 00016610 S T R ( I * 1 ) = S T R d * l ) * ( 6 * B D A * F ( N*NP1*1) *8*B*F ( N * N P 1 * 3 ) - 6 * BDA*F ( N*NP2000 16620
* * 1 ) * 4 * B * F ( * 4 * N P 2 * 3 ) ) / D E N O M 000166 50
157
S r R d * 2 ) = S T R ( I * 2 I * ( - 6 * A 0 B * F ( N * N P 1 - 2 1 * 4 * A * F ( N * N P 1 - 1 ) * 6 * A D B * F ( N * 0 0 0 1 6 6 4 0 * N P 1 * 1 ) * 8 * A * F ( N * N P 1 * 2 ) ) * ( 0 Y F A C / 0 E N 0 M 1 0 0 0 1 6 6 5 0
S T R d * 3 } = S T R ( I » 3 1 * a X Y F A C * ( - 2 * F ( N * N P l - 2 1 - 4 * A * F ( N * N P l l * 2 * F ( N * N P l * 0 0 0 1 6 6 6 0 *l)*4*B*F(N*NPl*2t*4*A*F(N*NPl*5l*2*F(N*NP2-21-2*F(N*NP2*ll-4*B* 00016670 *F(N*NP2*?I1/(4*A*B1 00016680
C — ~ ~ DETERMINE LOCATION OF NODE I N NODAL GRIOWORK 0 0 0 1 6 6 9 0 I F ( N P ( I l . E a . N Y * N l l GO TO 100 0 0 0 1 6 7 0 0 I F ( N P ( I ) . E Q . ( N P ( I ) - 1 ) / N Y * N Y * N Y ) GO TO 5 0 0 0 0 0 1 6 7 1 0 I F ( N P ( I ) - N Y - N 1 ) 2 0 0 * 2 0 0 * 2 1 0 0 0 0 1 6 7 2 0
200 CON = 3
C
0 0 0 1 6 7 3 0 50 TO 400 00016740
0 0 0 1 6 7 5 0 C DETERMINE CONTRIBUTING AREAL O IMENSI f f iS ANO SOLVE FOR M(K) 0 0 0 1 6 7 6 0 ^ 0 0 0 1 6 7 7 0
210 A = ( X ( I l ) - X ( I l - l ) ) / 2 00016780 B = ( Y d 2 * l ) - Y ( I 2 ) ) / 2 0 0 0 1 6 7 9 0 DENOM = 4 . * A * B 00016« i00 AOB = A/B 0 0 0 1 6 8 1 0 BOA = B/A 0 0 0 1 6 8 2 0 STRI 1 * 1 ) = S T R d * 1 ) * ( - 6 * B 0 A * F ( N * N P 3 * 1 ) - 4 * B » F ( N * N P 3 * 3 ) * & * B O A * F ( N * 0 0 0 1 6 8 3 0
* N P 1 * 1 ) - 8 * 3 * F ( N * N P 1 * 3 ) ) / D E N 0 M 0 0 0 1 6 8 4 0 S T R d * 2 ) = S T R ( I * 2 ) * ( 6 * A D a * F ( N * N P l * l ) - 8 * A * F ( N * N P l * 2 ) - 6 * A0B*F ( N * N P 1 0 0 0 168 50
* * 4 ) - 4 * A * F ( N * N P l * 5 ) ) * ( 0 Y F A C / D E N 0 M l 0 0 0 1 6 8 6 0 S I R ( 1 * 5 ) = S T R d *31 *DXYFAC* ( - 2 * F ( N * N P 3 * 1 1 * ( * B * F ( N * N P 3 * 2 ) * 2 * F ( N * N P 3 0 0 0 168 70
* * 4 ) * 2 * F ( N * N P 1 * 1 ) - 4 * B * F ( N * N P 1 * 2 ) - 4 * A * F ( N * N P 1 * 3 ) - 2 * F ( N * N P 1 * 4 ) * 4 * A * 0 0 0 1 6 8 3 0 * F ( N * N P 1 * 6 ) ) / ( 4 * A * B ) 0 0 0 1 6 3 9 0
I F ( N P d ) . E a . N Y * ( N X X - l ) * l ) 60 T3 100 0 0 0 1 6 9 0 0 I F ( N P d ) - ( N P d ) - l ) / N Y * N Y - l ) 3 0 0 * 2 0 0 * 3 0 0 0 0 0 1 6 9 1 0
C 0 0 0 1 6 9 2 0 C DETERMINE CONTRIBUTING AREAL DIMENSIONS AND SOLVE FOR MIL) 00016930 C 00016940
300 B = ( Y ( I 2 ) - Y ( I 2 - l ) l / 2 0 0 0 1 6 9 5 0 A = ( X d l l - X ( I l - l l l / 2 0 0 0 1 6 9 6 0 DENOM s 4 . * A * B 0 0 0 1 6 9 7 0 ADB = A/B 0 0 0 1 6 9 8 0 BOA = B/A 0 0 0 1 6 9 9 0 S T R d * l l = S T R d * 1 I * ( - 6 * B 0 A * F ( N * N P 3 * 1 1 - 4 * B * F ( N * N P 3 * 5 } * 6 * B D A * F ( N * 0 0 0 1 7 0 0 0
* N P 1 * 1 1 - 8 * S * F ( N * N P 1 * 5 I I / 0 E N 0 M 0 0 0 1 7 0 1 0 S T R ( I * 2 1 = S T R ( I * 2 1 * ( - 6 * A 0 B * F ( N * N P 1 - 2 1 * 4 * A » F ( N * N P 1 - 1 I * 6 * A D B * F ( N * 0 0 0 1 7 0 2 0
* N P 1 * 1 1 * 8 * A * F ( N * N P 1 * 2 I I * ( O Y F A C / D E N O M I 0 0 0 1 7 0 50 S T R ( I * 5 I = STRI I * 5 1 * D X Y F A C * ( - 2 * F ( N * N P 3 - 2 I * 2 * F ( N * N P 3 * 1 1 * 4 * B * F ( N * N P 3 0 0 0 1 7 0 4 0
* * 2 ) * 2 * F (N*»|P 1 - 2 ) - 4 * A * F I N*NP l l - 2 * F ( N * M P l * l 1 - 4 * B * F ( N * N P l * 2 ) * 4 * A*F I N * 0 0 0 1 70 50 * N P 1 * 3 1 I / ( 4 * A * B ) 0 0 0 1 7 0 6 0
C 00017070 C DETERMINE LOCATION OF NODE I N NODAL GRIOWORK 0 0 0 1 7 0 8 0 C 0 0 0 1 7 0 9 0
IF INP(II.Ea.NY*NXXl GO TO 100 00017100 IF (NP(I).EQ.(NP(I)-1)/NY*NY*NY.0R. NPd).6£.NY*(NXX-l)*l) 00017110
*C0 TO 200 00017120
158
CON = 1.5 00017150 C 00017140 C SOLUTION OF STRESS MATRIX COMPLETED 00017150 C 00017160 C — — C O N V E R T INTERNAL MOMENT TO STRESS 00017170 C 00017180
400 STR(I*1) = ( FRX*C0N*STR(I*1 ))/dEX**2) 00017190 STR(I*2) = (FRX*CON*STR(I*211/(rEY**21 00017200
450 STR(I*3) = I FRX*CON*SrR(I»3))/(TEX**2} 00017210 IF (NP( I).Ea.(NP( I)-1)/NY*NY*1.AN0.NSYM.NE. 3. AND. NS YM.NE. 4.0K. NP( 1000172 20
*I.EQ.(NP( I)-1)/NY*NY*NV) STR(I*2) = 0. 00017230 IF (NPl II.LE.NY.AN0.NSVN.NE.2.AND.NSYM.NE.4.3R.NP(I).CT.I NX 1-1)*NY000172 4O
*.AND.NP(I).LE.(NXl*l)*NY.OR.NPd).CT.(NX-l) *NYI STR(I*1) = 0. 00017250 IF (STR(I*1) .EQ.0.0R.STR(I*2I.EQ.01 STR(I*31 = 0. 00017260
C 00017270 C —DETERMINE MAJOR ANO MINOR STRESSES AND HORIZONTAL SHEAR (X-Y PLANE00017230 C 00017290
STRd*6) = SQRT(0.25*(STR(I*l)-STRd*2))**2*STR(I*3)**2) 00017300 STRd*4) = ( STRd*l)*STR(I*2) )/2.-STR(I*6) 00017310 STRd*5) = ( STR(I*1)*STR(I,2) )/2.*STRd*6) 00017320
9876 CONTINUE 00017330 500 CONTINUE 00017340
C 00017350 C CONVERT STRESS TO MOMENT 00017360 C 00017370
00 490 1 = 1 * NPRINT 00017380 XMOMd) = ( S T R d * l ) * T E X * * 2 ) / 6 . 00017390 YMOMd) = ( S T R d » 2 ) * T E Y * * 2 ) / 6 . 00017400 XYMOMd) = ( STRI I , 5 l * T E X * * 2 ) / 6 . 00017410
490 CONTINUE 00017420 I F (NKENT.EQ.O) GO TO 600 00017430
C 00017440 C CALCULATE SHEAR FORCES 00017450 C 00017460
CALL SHEAR (NX* NY) 00017470 (. 00017480
600 RETURN 00017490 g^O 00017500 SUBROUTINE MfSO (A* N* EPS* lER* NT I 00017510
g 00017520 C SUBROUTINE IS ALGORITHM TO FACTOR A SYMMETRICAL POSITIVE DEFINITE 00017530 C MATRIX ••.'"> ^ DIMENSION A(NT) °'!!i\lltl - 00017570
DOUBLE PRECISION OPIV* OSUM* DSQRT, 08LE So017590 C TEST ON WRONG INPUT PARAMETER N 2°21It?«
00017540 00017550
C 00017610
159
1 lER = 0 0 0 0 1 7 6 2 0 C 0 0 0 1 7 6 3 0 C I N I T I A L I Z E DIAGONAL LOOP 0 0 0 1 7 6 4 0 C 0 0 0 1 7 6 5 0
K P I V = 0 0 0 0 1 7 6 6 0 DO 11 K = 1 , N 0 0 0 1 7 6 7 0 K P I V = K P I V * K 0 0 0 1 7 6 8 0 INO = KPIV 0 0 0 1 7 6 9 0 LEND = K - 1 0 0 0 1 7 7 0 0
C 0 0 0 1 7 7 1 0 C CALCULATE TOLERANCE 0 0 0 1 7 7 2 0 C 0 0 0 1 7 7 3 0
TOL = A B S ( E P S * A ( K P I V ) ) 0 0 0 1 7 7 4 0 C 00017750 C START F A C T 3 R I Z A T I 0 N LOOP OVER THE KTH ROW 0 0 0 1 7 7 6 0 C 0 0 0 1 7 7 7 0
DO 11 I = K, N 0 0 0 1 7 7 8 0 OSUM = 0 . 0 3 0 0 0 1 7 7 9 0 I F (LEND) 2 , 4 * 2 0 0 0 1 7 8 0 0
C 0 0 0 1 7 8 1 0 C START INNER LOOP 0 0 0 1 7 8 2 0 C 00017830
2 DO 3 L = 1 , LEND 0 0 0 1 7 8 4 0 LANF = K P I V - L L I N O = I N D - L
3 OSUM = D S U M * D B L E ( A ( L A N F ) * A ( L I N O I ) 0 0 0 1 7 8 7 0 000 17830
END OF INNER LOOP 0 0 0 1 7 8 9 0 0 0 0 1 7 9 0 0
C 9 OP IV = DSQRTIOSUMl
A ( K P I V 1 = D P I V O P I V 2 l . D O / O P I V GO TO 1 1
C C CALCULATE TERMS I N ROW
0 0 0 1 7 8 5 0 0 0 0 1 7 8 6 0
C c-c C TRANSFORM ELEMENT A I I N D I ^ ^ ' ^ I ' ^ l ^ g 0 0 0 1 7 9 2 0
4 OSUM = 08LE I A d N O U - D S U H ? ? ? ^ I ? ? ? IF d - K l 10* 5* 10
C C TEST FOR NEGATIVE PIVOT ELEMENT ANO FOR LOSS OF S IGNIF ICANCE C
5 I F I S N 6 L I O S U M l - T O L l 6 * 6* 9 6 I F (OSUM) 1 2 * 1 2 * 7 7 I F ( l E R l 8* 8 * 9 8 lER = K-1
C C COMPUTE PIVOT ELEMENT
00017940 00017950 00017960 00017970 00017980 00017990 00018000 00018010 00018020 00018030 00018040 00018050 00018060 00013070 00018080 00018090 00013100
160
C 0 0 0 1 8 1 1 0 10 AIINDI * DSUM*DPIV 0 0 0 1 8 1 2 0 11 INO = IND*I 0 0 0 1 8 1 3 0
C 0 0 0 1 8 1 4 0 C — — E N D OF DIAGONAL LOOP 0 0 0 1 8 1 5 0 C 0 0 0 1 8 1 6 0
RETURN 0 0 0 1 8 1 7 0 C 0 0 0 1 8 1 8 0 C NEGATIVE PIVOT ELEMENT FOUND 0 0 0 1 8 1 9 0 C 0 0 0 1 8 2 0 0
12 lER = -1 00018210 RETURN 00018220 END 00018230 SUBROUTINE TRIG (Nl 00018240
C 00018250 C THIS SUBROUTINE APPLIES THE GAUSS ELIMINATION METHOD TO FORM A 00018260 C UPPER TRIANGULAR BAND MATRIX. FOR A GIVEN CONTACT CONDITION* THIS00018270 C TRIAN6ULATI0N IS PERFORMED ONLY ONCE AND THE RESULTS CAN BE USED 00018280 C REPEATEDLY. 000182 90 C 0 0 0 1 8 3 0 0
DIMENSION C( 1 5 0 0 0 0 I * F ( 2 1 0 0 I * 6 ( 1 5 0 0 0 0 I * N O ( 2 1 * X ( 6 5 0 1 *YI6501 * S T R I 6 5 0 * 0 0 0 1 8 3 1 0 *6 l*NP(650)*XMOM(650l*YMOM(6501*XYMOM(650l*MXDIFI650)*MY0IFI650l* 0 0 0 1 8 3 2 0 *XTI 6501*YTI 6501*OKI 6501*DYI6501*MXVOIF 16501*MYXDIFI650)*VX1650)* 0 0 0 1 8 5 50 *VVI650)*YXM0MI65 0 ) * I R I 6 5 0 ) * 6 U N A I 6 5 0 I 0 0 0 1 8 5 4 0
C 0 0 0 1 8 3 5 0 COMMON C*F*G*NO*NB*X*Y*STR*NP*XMOM*YMOM*XYMOM*XT*YT*OX*OY*MXDIF* 00018360 *M VO IF *MXYDIF* MYXDIF* YKMOM*VX*VY* NXY *NYX* VXMAXN* VXMAXP* VYMAXN* 00018570 *VYMAXP 00018580
C 00018590 MOIX* MOIY 00018400
00018410 00018420 000184 50 00018440 00018450 00018460 00018470 00018480 00018490 00018500
fi'j* ' ciJi ;;;!!cis 6 i j * K i = c ( j * K i ; « ! ; ! c ? ;
10 c i j * K i = c i j * K i / 6 i j i ? ? „ ? , : : LC = LA DO 50 L = 1* LA MI = J*L*NB-1 DO 2 0 K = 1* LC
20 CIMI*KI = CIMI*K1-CIJ*K*LA-LC1*6IJ*L1
REAL MXOIF* MYOIf* MXYOIf*
NOE - NOINI LA = NB-1 LB = NOE-LA I f I N - 1 1 2* 2 * 4
2 I B = 1 6 0 TO 6
4 I B = N 0 ( 1 1 * 1 6 00 50 I = I B * LB
J = NB*t-LA
MYXOIf *
00018550 00018560 00018570 00018580 00018590
161
1 S ~ ^o"I 00018600 1 J * , \ 00018610 LO = LA-1 00018620 00 90 I = LB* NOE 00018650
C
J » NB*I-LA 00018640 6IJ)= CIJI 00018650 If (1-LDI 52* 52, 56 00018660
52 DO 54 K = 1* LD 00018670 54 6(J*K1 = C(J*KI 00018680 56 DO 40 K = 1* LA 00018690 40 C(J*KI = C(J*KI/6(J1 00018700
LC = LA-1 00018710 If (I-NOEI 50* 90* 50 00018720
50 DO 70 L = 1* LD 00018750 MI = J*L*NB-1 00018740 00 60 K = 1 * LC 00018750
60 C ( M I * K I = C ( M I * K > - C ( J * K * L A - L C - 1 I * 6 ( J - H . I 00018760 LC = LC-1 00018770 I f d - L C l 7 0 * 7 0 * 80 00018780
70 CONTINUE 000 18790 80 LO = LO-1 00018800 90 CONTINUE 00018810
RETURN 00018820 END 00018850 SUBROUTINE LOAOM (N l 00018840
00018850 SUBROUTINE USED THE TR lANGULARIZ ED MATRIX FROM SUBROUTINE 00018860
-TRIG AND COMPUTES THE DEFLECTIONS OF THE SLAB. 00018870 00018880
DIMENSION C ( 1 5 0 0 0 0 1 * F ( 2 1 0 0 1 * G ( 1 5 0 0 0 0 1 * N 0 ( 21 * X ( 6 5 0 1 * Y ( 6 5 0 ) * S T R ( 6 5 0 * 0 0 0 1 8 8 9 0 *6 l *NP(6S01*XMOMI6S0l*YMOMI650l*XYMOMI650l*MXDIF(6501*MYDIf ( 6 5 0 1 * 00018900 * X T I 6 5 0 I * Y T ( 6 5 0 1 * 0 X ( 6 5 0 1 * D Y ( 65 01 * MXYOIf (6501 *MYXOIf( 6501 *VX (6501 * 00018910 * V V I 6 5 0 1 *YXMaMI6S0 l * IR(6501 •6UNA(6501 00018920
00018950 COMMON C,f,G*NO*NB*X*Y*STR*NP*XMOM*VMOM*XYMOM*XT*YT*DX*DY*MX0IF* 000189 40
*HYD IF *MXVDIF*MYXDIF*VXMOM*VX*W* NXY *NYX* VXMAXN* VXMAXP* VYMAXN* 0001895 0 *VYMAXP 00018960
0 0 0 1 8 9 7 0 REAL MXOIF* MYOIF* MXYDIF* MYXOIF* MOIX* MOIY 0 0 0 1 8 9 8 0
00018990 NOE = NOINI 00019000 LA = NB-1 00019010 LB = NOE-LA 00019020 I F ( M - l l 2* 2 * 4 00019030
00019040 C ONLY ONE SLAB TO BE CONSIDERED 00019050 C 00019060
2 IB = 1 00019070 60 TO 6 00019080
162
c c-c
c C ' c
c c-C" c
c c-
— T W O SLABS TO BE CONSIDERED
4 IB = N0(11*1 6 DO 20 I = I B * LB
J * NB*I-LA f d l = f ( I t / 6 ( J l DO 20 L = 1 * LA
20 f d * L l = F d * L l - F I I I * 6 l J*L1 LB = LB*1 LD = LA-1 0 0 60 I = LB * NOE J = NB*I -LA F d l s F ( I 1 / G ( J 1 LC = LA-1 I F ( I - N O E l 5 0 * 7 0 * 50
50 DO 40 L = 1 * LD F d * L I = F I I * L l - f d l * 6 l J*L1 LC = LC-1 I f l l - L C I 4 0 * 4 0 * 50
40 CONTINUE 50 LO = LO-1 60 CONTINUE 70 0 0 80 IK = I B * NOE
1 = N 0 E - I K * 1 * I N - l l * N O d l J s NB* I -NB*2 00 80 K = 1 * LA I f I I * K . 6 T . N 0 E 1 60 TO 80 f d l = f ( I l - f ( I * K I * C ( J * K - l l
80 CONTINUE RETURN END SUBROUTINE SINV (A* N* EPS* lER* NT I
THIS SUBROUTINE INVERTS A SYMMETRICAL POSITIVE DEf lNITE MATRIX
DIMENSION AINTI
DOUBLE PRECISION DIN* WORK* DOLE
fACTORIZE GIVEN MATRIX BY MEANS OF SUBROUTINE MFSD — A » TRANSPDSE(T1*T
CALL MFSD (A* N* EPS* lER* NT 1
CHECK FOR INSTABILITY IF (lERl 9* 1* 1
INVERT UPPER TRIANGULAR MATRIX "T*
00019090 00019100 00019110 00019120 00019150 00019140 00019150 00019160 00019170 00019180 00019190 00019200 00019210 00019220 00019250 00019240 00019250 000192 60 00019270 000192 80 00019290 00019500 00019510 00019520 00019550 00019540 00019550 00019560 00019570 00019580 00019590 00019400 00019410 00019420 00019430 00019440 00019450 00019460 000194 70 00019480 00019490 00019500 00019510 00019520 00019530 00019540 00019550 00019560 00019570
163
c c-c
c c c-c
c c-c
c c-c
c C' c
c c-c
c c-c c-c-c c-
— P R E P A R E I N V E R S I O N LOOP
1 IPIV « N * ( N * l l / 2 . INO « IPIV
— I N I T I A L I Z E I N V E R S I O N LOOP
DO 6 I = 1 * N D I N = 1 . 0 0 / O B L E ( A d P I V l l A d P I V l = D I N M I N = N KEND = I - l LANF = N-KEND I F (KENOl 5 * 5 * 2
2 J = INO
I N I T I A L I Z E ROW LOOP
0 0 4 K = 1 * KEND WORK = 0 . 0 0 MIN = M I N - 1 LHOR = I P I V LVER = J
— S T A R T INNER LOOP
0 0 5 L = LANF* MIN LVER » L V E R * 1 LHOR s LHOR*L
5 WORK s W 0 R K * 0 B L E ( A ( L V E R 1 * A ( L H 0 R I 1
— E N D OF INNER LOOP
A I J I = -WORK*DIN
4 J « J-MIN
END OF ROW LOOP
5 IPIV * IPIV-MIN 6 INO = IND-1
EMO OF INVERSION LOOP
CALCULATE INVERSEIAI BY MEANS OF INVERSEdl* WHERE INVERSEIAI INVERSEdl * TRANSPOSE( INVERSE( Tl 1.
—INITIALIZE MULTIPLICATION LOOP
00019580 00019590 00019600 00019610 00019620 00019650 00019640 00019650 00019660 000196 70 00019680 00019690 00019700 00019710 00019720 00019750 00019740 00019750 00019760 00019770 00019780 00019790 00019800 00019810 00019820 00019850 00019840 00019850 00019860 00019870 00019880 00019890 00019900 00019910 00019920 00019950 00019940 00019950 00019960 000199 70 00019980 00019990 00020000 00020010 00020020 00020030 00020040 00020050 00020060
164
c c« c
0 0 8 I = 1* N IPIV * I P I V * I J = IPIV
— INITIALIZE ROW LOOP
0 0 8 K = I* N WORK = 0 . 0 0 LHOR = J
C C START INNER LOOP C
0 0 7 L = K* N LVER = LHOR*K-I WORK = W 0 R K * 0 B L E ( A ( L H 0 R I * A ( L V E R 1 I
7 LHOR = LHOR*L C C-c
c c-c
c c-c-c
END OF INNER LOOP
A I J I - WORK 8 J X J4.IC
END OF ROW ANO M U L T I P L I C A T I O N LOOP
9 RETURN END SUBROUTINE OSF ( H , Y* Z * N D I M I
- — - T H I S SUBROUTINE COMPUTES THE VECTOR OF INTEGRAL VALUES FOR A 6 I V E N E Q U I D I S T A N T TABLE OF FUNCTION VALUES.
C C-C C-C
DIMENSION YINDIMI* ZINDIMI
HT « .5555555*M
If INOIM-51 7* 8* 1
—NOIM IS GREATER THAN 5.
PREPARATION Of INTEGRATION LOOP 1 SUMl = V(2)*Y(21
SUHl = SUM1*SUM1 SUMI = HT*(Y(11*SUM1*Y(51I AUXl s Y(41*Y(41 AUXl = AUX1*AUX1 AUXl s SUM1*HT*(Y(51*AUX1*Y(5 11 AUX2 = HT*(Y(11*5.875*(Y(21*Y(5I1*2.625*(Y(5I*Y(411*Y(61I SUM2 > Y(51*Y(51
00020070 00020080 00020090 00020100 00020110 00020120 00020150 00020140 00020150 00020160 00020170 00020180 00020190 00020200 00020210 00020220 00020250 00020240 00020250 000202 60 00020270 00020280 00020290 00020500 00020310 00020320 00020350 00020540 00020550 00020560 00020570 00020580 00020590 00020400 00020410 00020420 00020450 00020440 00020450 00020460 00020470 00020480 00020490 00020500 00020510 00020520 00020550 00020540 00020550
165
c c-c
c c-
SUM2 s SUM2*SUM2 SUM2 = A U X 2 - H T * ( V ( 4 I * S U M 2 * Y ( 6 I I Z d l = 0 . AUX = V ( 5 1 * Y ( 5 1 AUX = AUX*AJX Z ( 2 1 = SUM2-HT*( Y ( 2 I * A U X * V ( 4 I 1 Z ( 5 I = SUHl Z ( 4 1 = SUM2 I f (NDIM-61 5* 5* 2
-INTEGRATION LOOP
00 4 I SUMl = SUM2 « AUXl = AUXl ' AUXl = Z ( I - 2 1
NOIM* 2 = 7* AUXl AUX2 Y ( I - 1 1 * Y ( I - 1 I AUX1*AUX1 S U M 1 * H T * ( Y ( I - 2 ) * A U X 1 * Y ( I I 1 = SUMl
I f d - N D I M l 5* 6* 6 AUX2 = Y( I I * Y d l AUX2 = AUX2*AUX2 AUK2 = S U M 2 * H T * ( V ( I - 1 I * A U X 2 * Y ( I * 1 1 I Z d - l l = SUM2
C
c
U
c-c
END OF INTEGRATION LOOP 5 Z ( N D I M - 1 I = AUXl
Z INOIMl = AUX2 RETURN
6 Z ( N 0 I M - 1 I s SUM2 Z INOIMl = AUXl RETURN
NOIM IS LESS THAN 5
7 IF (NOIM-51 12* 1 1 * 8
—NOIM I S EQUAL TO 4 OR 5
SUM2 « 1 . 1 2 5 * H T * ( V d l * Y ( 2 1 * Y ( 2 1 * Y ( 2 l * Y ( 5 l * Y ( 5 l * Y ( 5 1 * Y ( 4 1 l SUMl = y ( 2 l * Y ( 2 1 SUMl s SUM1*SUM1 SUMl = HT* (Y( 1 I *SUM1*Y I51 I Z d l = 0 . AUXl = Y ( 5 I * Y ( 5 ) AUXl = AUX1*AUX1 ZI2I = SUM2-HT*(Y(21*AUX1*VI41I If INOIM-51 10* 9* 9
00020560 00020570 00020580 00020590 00020600 00020610 00020620 00020650 00020640 00020650 00020660 00020670 00020680 00020690 00020700 00020710 00020720 00020750 00020740 00020750 00020760 00020770 00020780 00020790 00020800 00020810 00020820 00020850 00020840 00020850 00020860 00020870 00020880 00020890 00020900 00020910 00020920 000209 50 00020940 00020950 00020960 00020970 00020980 00020990 00021000 00021010 00021020 00021030 00021040
Ifi6
10
A U X l = A U X l « Z I 5 I » Z d l « Z ( 4 1 = RETURN
Y I 4 I * Y I 4 1 AUX1*AUX1 S U M 1 * H T * I V I 5 1 * A U X 1 * V I 5 I 1 SUMl SUM2
C C NOIM I S EQUAL TO 5 C
11
12
SUMl SUM2 SUM2 Z ( 5 I Z l l l Z I 2 I RETURN END SUBROUTINE
H T * l l . 2 5 * Y d l * Y I 2 1 * Y ( 2 l - . 2 5 * Y ( 5 1 1 Y I 2 1 * Y ( 2 1 SUM2*SUM2 H T * 1 Y I 1 1 * S U H 2 * V I 5 I I 0 . SUMl
SHEAR I N X * NYI C c-c-c C' c-c-c
—SUBROUTINE USES A NUMERICAL INTEGRATION TEC —SHEAR f O R C E . UNITS ARE fORCE PER LENGTH* E
—SUBROUTINE WAS WRITTEN S P E C I f l C A L L V FOR USE —SLAB SYMMETRICAL TO BOTH THE X AND Y AXES. —FOR SLABS WITH OTHER SYMMETRY.
HNIQUE TO CA . 6 . * LBS PER
WITH A RECT I T HAS NOT
DIMENSION : i 1 5 0 0 0 0 I * F I 2 1 0 0 I * 6 I 1 5 0 0 0 0 ) * N O I 21 * 6 1 * N P I 6 5 0 I * X M O M I 6 5 0 1 * Y M O M I 6 5 0 I * X V M O M I 6 5 0 1 * M * X T I 6 5 0 l « V T I 6 5 0 l * 0 X l 6 5 0 1 * 0 V I 6 5 0 1 * M X Y D I f l 6 5 01 * V Y I 6 5 0 1 * V X M 0 N I 6 5 0 I * I R I 6 5 0 I * 6 U N A I 6 5 0 I
COMMON C * f * 6 * N 0 * N B * X * Y * S T R * N P * X M 0 M * V M 0 M * X Y M * M Y D I f * M X Y D I F * M Y X O I F * V X M O M * V X * V Y * N X Y * N Y X * V X M *VVMAXP
* X I 6 5 0 1 * Y I 6 5 X D I F ( 6 5 0 1 * M Y * M Y X D I F I 6 5 0 1
OM*XT*YT*DX* AXN*VXMAXP*V
LCULATE INCH.
AN6ULAR BEEN TE
0)*STRI DIFI650 *VXI650
DY*MXDI YMAXN*
REAL MXOIF* MYOIF* MXYOIF* MYXOIF* MOIX* M3 lY C C STORE NODAL COORDINATES C
DO 6 0 0 I = 1 * NX X T I I ) = X d l
6 0 0 CONTINUE 0 0 6 0 5 I = 1 * NY Y T d l * Y d l
605 CONTINUE C c-c
—ESTABLISH W0RKIN6 VARIABLES
NZl = NX*NY
00021050 00021060 00021070 00021080 00021090 00021100 00021110 00021120 00021150 00021140 00021150 00021160 00021170 00021180 00021190 00021200 00021210 00021220 00021250 00021240 00021250 00021260 00021270
STED00021280 00021290 00021500
650*00021510 I* 00021520 1* 00021550
00021540 00021550
F* 00021560 00021570 00021580 00021590 00021400 00021410 00021420 00021450 00021440 00021450 00021460 00021470 00021480 00021490 00021500 00021510 00021520 00021550
167
6 0 8 C c c-c
NXX = N X - 1 NYY = N Y - 1 NYX = ( N Y - 1 I * N X NXY = ( N X - 1 1 * N Y HZl = ( N X - 1 I * ( N Y - 1 1 KX = N X * 1 KV = N Y * 1 KZ = KX*KY KXV = N Y * ( N X * 1 I KYX = N X * ( N Y * 1 I 0 0 6 0 8 1 = 1 * N Z l Y X M O M d l X - l . * X Y M O M ( I l
C c-c-c-c-c C'
NUMBER THE COLUMNS AND ROWS OF THE F I N I T E ELEMENT 6R ID
0 0 6 1 0 J = 1 * NX 0 0 6 1 0 I = 1 * NY
6 1 0 Y d * ( J * N Y l - N V l = Y T d l L = 0 0 0 6 1 5 J = 1 * NX DO 6 1 5 I = 1 * NY L * L * l
615 X ( L 1 = X T ( J I J J J = 0
B E 6 I N SOLUTION FROM UPPER RI6HT CORNER (NODE N Z I I OF UPPE — — Q U A D R A N T . NUMBERIN6 OF DIFFERENCE ELEMENTS INCREASES FRO — T O BOTTOM OF 6 R I 0 PATTERN* THEN FROM R I6HT TO L E F T . NODE — — I N 6 REMAINS THE SAME.
C-C-
——CALCULATE DELTA-Y*S 00 700 I « 1* NYY
700 OVdl » YCNZ1-I*1I-V(NZ1-II DISTRIBUTE OELTA-Y*S THR0U6H0UT
— OELTA-Y*S BELOW HORIZONTAL LINE OYINYI = OY(NV-ll DO 710 J = 1* NY 00 710 I = 1* NX OYdI*NYYI*J*Il = OVIJI
710 CONTINUE CALCULATE DELTA-X* S
00 720 J = 1* NXX OXIJl = X(NZl-(J*NYl*NYl-X(NZl-(( J*1)*NY)*NY)
720 CONTINUE DISTRIBUTE 0ELTA-X*S
00 750 J = 1* NXX DO 750 I = 1* NY OK(I*(J*NV)-NV) = DX(J)
6RI0. ALSO GENERATE OF SYMMETRY.
THROUGHOUT GRID.
00021540 00021550 00021560 00021570 00021580 00021590 00021600 00021610 00021620 00021650 00021640 00021650 00021660 00021670 00021680 00021690 00021700 00021710 00021720 00021750 00021740 00021750 00021760 00021770 00021780 00021790
R RIGHT 00021800 M TOP TO 00021810 NUMBER- 00021820
00021830 00021840 00021850 00021860 00021870
IMAGINAR00021880 00021890 00021900 00021910 00021920 00021930 00021940 00021950 00021960 00021970 00021980 00021990 00022000 00022010 00022020
168
730 CONTINUE GENERATE IMA6INARY DELTA-X*S TO THE LEFT OF VERTICAL L NT = (NY*NXX)*1 wcKiit*!!. L
NPP s NT*NYY 00 740 I = NT* NPP • X d ) = O X d - N V )
740 CONTINUE CALCULATE OELTA-XMOM'X ANO DELTA-XYMOM'X
L = 0 00 750 J = 1 * NXX 00 750 I = 1 * NY L = L * l MXDIF IL) = X M O M ( N Z l - ( J * N Y I * N V - I * l l - X M O M ( N Z l - ( J * N Y I - I * 1 I MXYOIf (L l = X Y M 0 M ( N Z 1 - ( J * N Y I * N Y - I * 1 I - X Y M 0 M ( N Z 1 - ( J * N Y 1 - I * 1 I
750 CONTINUE CALCULATE IMA6INARY DELTA-XYMOM'S
DO 755 I = NT* NPP M X Y D I f d l = M X Y O I f d - N Y l
755 CONTINUE ——CALCULATE DELTA-VMOM'S
L = 0 DO 765 J = 1 * NX DO 760 1 = 1 * NYY L = L * l MYDIF IL I = Y M O M ( N Z l - ( J * N Y ) * N Y - I * l l - Y M O M ( N Z l - ( J * N V I * N V - I I
760 CONTINUE MVOI f (J *NYl = MYOIf ( ( J * N Y 1 - 1 1 L = L * l
765 CONTINUE —CALCULATE DELTA-YXMOM'S
770
775
L * 0 DO 775 J = 1 * NX 00 770 I = 1 * NYY L « L * l MYXOIf ( L l » YXM0M(NZ1- (J*NYI*NY- I *1 I -YXM0M( N Z 1 - ( J * N Y I * N V - I 1 CONTINUE MYXOI f (J*NYl = M Y X O I f l l J * N V l - l l L » L * l CONTINUE
——CALCULATE SHEARS
-INCREMENTS OVER WHICH SHEARS ARE CALCULATED ARE NUMBERED BE6 -AT THE UPPER RIGHT CORNER Of THE SLAB PORTION IN THE UPPER R -OUAORANT. INCREMENT NUMBERING INCREASES fROM TOP TO BOTTOM -fROM RIGHT TO LEfT. NODAL NUMBERING REMAINS UNCHANGED.
00022030 INE OF 00022040
00022050 00022060 00022070 00022080 00022090 00022100 00022110 00022120 00022150 00022140 00022150 00022160 00022170 00022180 00022190 00022200 00022210 00022220 00022250 00022240 00022250 00022260 000222 70 00022280 00022290 00022300 00022310 00022320 00022350 00022540 00022550 00022560 00022570 00022380 00022590 00022400 00022410 00022420 000224 30 00022440
INNIN600022450
I6HT ANO
867 — C A L C U L A T E SHEAR DO 870 1 = 1 * NXY
IN X-DIRECTION AND WRITE RESULTS
00022460 00022470 00022480 00022490 00022500 00022510
169
c c-c
8 7 0 V X I I l = I M X 0 I F I I l / O X I I l l * l M Y X 0 I F d l / D Y I I l l CALCULATE SHEAR IN Y-DIRECTION
K = 0 L = 0 0 0 875 J = 1 * NX 00 875 I = 1 * NY L « L * l I f d . E Q . N Y l 60 TO 875 K = K * l V Y I K l = ( M Y D I F ( L I / D Y ( L 1 1 - ( M X Y D I F ( L I / D X ( L 1 1
875 CONTINUE J J J = 1
SORT TO FIND MAXIMUM SHEAR FORCE IN EACH DIRECTION
VXMAXN = 0 . 0 VXMAXP = 0 . 0 VYMAXN = 0 . 0 VYMAXP = 0 . 0 DO 880 1 = 1 * NXY I F ( V X M A X N . 6 T . V X ( I I 1 VXMAXN = V X d l
880 I F ( V X M A X P . L T . V X d l l VXMAXP = V X I I l 00 885 1 = 1 * NYX I F (VYMAXN.6T.VY( I11 VYMAXN = V V ( I 1
885 I F ( V Y M A X P . L T . V Y d l l VYMAXP = V Y d l RETURN END SUBROUTINE MSLP (N015I
C C——SUBROUTINE CALCULATES DIFFERENTIAL DEFLECTION C
DIMENSION C ( 1 5 0 0 0 0 1 * F ( 2 1 0 0 1 * 6 ( 1 5 0 0 0 0 1 * N D ( 2 1 * X ( 6 5 0 1 * Y ( 6 5 0 ) * S T R ( 65 *6 I *NP(650 I *XMOMI650 I *YMOMI6501*XYMOMI650 I *MXDIF (650 I *MYOIF I650 I * * X T 1 6 5 0 1 * Y T I 6 5 0 1 * D X I 6 5 0 1 * D Y I 6 5 0 I * M X Y D I F I 6 5 0 ) * N V X O I F I 6 5 0 ) * V X I 6 5 0 ) * * V Y ( 6 5 0 ) * Y X M O M ( 6 5 0 I » I R ( 6 5 0 I * 6 U N A ( 6 5 0 I * A ( 2 0 I * B ( 2 0 I * C X ( 2 0 1 * L X ( 2 0 I * * 0 I 2 0 I * I A I 2 * 2 0 1
C COMMON C*F*G*N0*NB*X*Y*STR*NP*XMOM*YMOM*XYMOM*XT*YT*DX*0Y*MXOIF*
*MYD IF*MXYOIF*MYXDIF*VXMOM*VX*VY*NXY*NYX*VXMAXN*VXMAXP*VYMAXN* *VYMAXP
C 7 FORMAT I / /SX* 'TWENTY MAXIMUM DIFFERENTIAL DEFLECTION RATIOS'*
* / 5 X * 4 5 l ' - * l ) 8 FORMAT I / / 6X* *N0DE1* *8X* *N0DE2* *12X* *DELTA* * 1 2 X * * D I S T * , 1 2 X , * D I ST
* 1 2 X , * 0 E L T A / L * , 1 2 X , * L / D E L T A * , / 5 6 X * * I N C H E S * * 1 O X * * I N C H E S * * 1 2 X * * F T * 1 9 FORMAT I / 6 X * I 5 * 1 0 X * I 5 * 1 0 X * E 1 5 . 6 * 5 X * E 1 5 . 6 * 5 K * F 6 . 2 * 8 X * E 1 3 . 6 * 1 1 X * I 3
DO 11 IM = 1 * 20 11 A f l M ) = 0 .3
00 1 I = 1* N015
00022520 00022550 00022540 00022550 00022560 00022570 00022580 00022590 00022600 00022610 00022620 00022650 00022640 00022650 00022660 00022670 00022680 00022690 00022700 00022710 00022720 00022750 00022740 00022750 00022760 00022770 00022780 00022790 00022800 00022810 00022820
0*00022850 00022840 00022850 00022860 00022870 00022880 00022890 00022900 00022910 00022920 00022950 00022940
* *00022950 00022960
) 00022970 00022980 00022990 00023000
170
IF IK IF 00 I I I J
GO TO 4
60 TO 5
TO
DO 2 J = 1* N015 I F ( J . E Q . l ) 6 0 TO 2
DIST = S Q R T ( ( X ( J ) - X ( I ) ) * * 2 * ( Y ( J I - Y ( 1 1 1 * * 2 1 ODIFF = F ( ( J - 1 I * 5 * 1 I - F ( ( I - 1 1 * 5 * 1 1 SLP « OOIFF/OIST FOIST = D I S T / 1 2 0 0 5 K = 1* 2 0 I F ( S L P . 6 T . A ( K 1 I CONTINUE 6 0 TO 2
( A ( K ) . E Q . O . O l = 20-K ( I K . E Q . O l 6 0 6 IL = 1* IK = 20- IL = 11*1
A d J I = A d i l B d J l = B d l l o d j i = o d i i cxdji = cxdii IA(1*IJ1 = IA(1*III IA(2*IJ1 = IA(2*III A(KI = SLP BIKl = ODIFF OIK) = DIST CX(K) = FOIST IA(1*K) = I IA(2*K) = J CONTINUE CONTINUE WRITE (6*71 DO 10 M = 1* 20 NSLP = 1/A(M1*0.5 LX(M) « NSLP CONTINUE WRITE (6*8) WRITE (6*91 RETURN END
//LKEO.SYSLIB DO // DO // DO DSN=EDR.IHSL.V90.SINGLE.LIB*DISP=SHR // DO OSN=EOR.IMSL.V90.DOUBLE.LIB*DIS»=SHR //LKED.SYSLMOO OO DSN=WYL.VO.WKW.LOADLIB(GUNA)* 01SP=OLD*UNIT = //
6 5
2 1
10
((IA(J*I)*J = 1*2)*8(I)*0(I)*CX(I )*Ad)*LX ID* 1 = 1*20)
00025010 00023020 00023050 00025040 00025050 00025060 00025070 00025080 00025090 00023100 00023110 00025120 00025150 00025140 00023150 00025160 00023170 00023180 00023190 00023200 00025210 00025220 00025230 00023240 00023250 00025260 00025270 00023280 00023290 00025500 00025310 00023520 00025330 00023540 00025350 00023560 00025570 00025380 00023390 00023400 00023410 00023420 00023430 00023440 00023450
171
- i « ta^
a: ^ 1/1 3 Q
y tart
u. O
un tart
WI V .J <z 2 « ^ S UJ s: tu _ l
lu
1 l/« 1 1 K 1 1 O' 1 1 •< 1 1 1 1 •- 1
Z 1 <S 1 -I 1 <Z 1
3 1 It 1 • 1
y 1 • 1
^ 1 1
>- 1 n 1
1 ••1
'^ 1 a 1 « 1 -J 1 u» 1
VO a -1 u. a . •-' t/t
CL Q.
•• 1 tft 1 « 1 X 1
I r 1 Ui 1 _J 1 so 1 a 1 ae 1 a. 1
1 0 1 «x 1 - t 1 t« 1
1 oe t a 1 O 1 ^ 1 a. 1
1 1 ae 1
SI 3 1 O t Z 1 — 1
1.1 k^ 1
X 1 ^ 1
o • o
I I
>> tart
u a a. a u
a UJ
^ « ae
^ I i .
^ _ j
^ oe O l b
o o • o
« 4
M X M Q ta4
3
liJ - J lA tart
«
l^l Ui 1 -1 1
SI - 1 et 1 « 1 > 1 1 *k i O 1
1 V 1 ee 1 <X 1 c 1 r 1 3 1 1/) 1
o o • o
l/< tart
I I X ^ o z U i
_l
OB
a u i/«
o o • o
o tart
I I X
*-a *• 3
B « U I / I
O O o o • >o
II
a a .J l / t
I k
o tA l/t UJ
z ^ u tart
X ^
o U i
o o >r • o
11
UJ
*-UJ
oc u z o u I k
o l/t
3 .J 3 a o z
o o / tart a
O
I I UJ
^ UJ 9C U
z o u
UL
o
o tart hta
a OK
l A
z o l/t i / i tart
O a.
o UJ
o l/^ tart
• o
II U i a « oe o m 3 l /t
I k
O
l/t
3 .J 3 a a c • ^
o o o »t • o
II UJ
a a oe m 3 ut
I k O
o tart kB
« oe l/t
z s ut >/) tari
O ^
l / t 1 >- 1 Z 1
«1 • - 1 Irt 1 Z j O 1 U 1
1 C 1 « 1 ^'l u i ° 1 oe 1 ft. 1
«r
II
z > l/t z
»M tart
It
>
O .O
(J ae a.
a <x o
O ta
ll
o o o •
o o
o o o •
a -r l/t
o o o •
o
00 1/1
o o o
• 9 INJ •* ISJ
I/*
o o o •
O XS
O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O o • • • • •
• • <# tarttart^tartMtartMtarttartMtarttarttarttarttartM O O e o
l/t UJ
O O t* « o o o o o o o o o o o o o o o o
O O xi z o o o o o o o o o o o o o o o o
O O ta-OOOOOOOOOOOOOOOO • • a o o o o o o o o o o o o o o o o o e oeoooooooooooooooo • # IN •• 0 « * * » * * * « * * * « * * * « A i ta Ui O .rt»< tart tart « tart »« tart «tart »«w«tartX«-<tart
U U I I I I I I I I I I I I I I I I z UJ a 19 flO Z oe ^ «
O O UJ 1 o o > ^ e o z z • . 3 U J O O O O O O O O O O O O O O O O o o u z o o o o o o o o o o o o o o o o 90 ^ U J O O O O O O O O O O O O O O O O tart 1/1 ^ . ( O O O O O O O O O O O O O O O O
U U J O O O O O O O O O O O O O O O O UJ M • • • • • • • • • • • • • • • • X <v ia»rt...-.rt-rt-rt^tart,rt...4tart^tart.rt-rt u z
O O O 3 o o ^ o O O -J • • a .1
O O UJ o ff\l axO l/t Ik UJtart UJ"*' 3 <A O O O O O O O O O O O O O O O O « « tart U J O O O O O O O O O O O O O O O O 4 « UJ z o o o o o o o o o o o o o o o o
QC k t a O O O O O O O O O O O O O O O O l/t l/t « O O O O O O O O O O O O O O O O
172
l /t
0.
e O O o o •
«
II 9
o O ^rt
O o •
o
I I _J U i
a
o tart
O o o •
o
II I k -1 UJ o
e o o o l / t
• o
H
^ I k
oe
o PO
I I I k . J u **
UJ z o uo z o tart •
o z-o tart
K
Ik O
l/t u i O 3 • U O
« »
UJ z e uo z o M •
o zao tartvrt
> Ik o
U J O 3 • taJO
« »
DE
S
o z VA
z tart
OL
LO
U
I k
UJ
X
^
O tart
•*
z
o UJ tart ml OL CL
«
AR
E
I / I
a « o taj
I I I I I I I I I t I I I I I I
r^N>aoO>«^ooe>
173
ooooooooooooooooo tart
^ U i U i i M I U U J U J I U l U U J U J I U I M l U U J I U U J U O e O V t ' \ J t a r t u ^ . M ^ > « , 0 7 « O > O ^ H > , ^ UJ . » N . ^ (^J ••O ^ U M A >0 « 0 0 > O »> ^M1/1 taj rg o IM * '> • ^ ^ ta^ "-»o» v/t • * »^«r «e l/t u. •*••» ta >o O »# uM/t o ta^ o "- « oe fu rg UJ 9 0 t a r t l / 1 i ^ » l ^ > e O m l ^ ' 4 >#tartWt M 1 0 a (M K t tart fNJ »M rt l> i I O tart H i ^ tart ^ ( \ ) tart ( \ j
O O O O O O O O O O O O O O O O
UJ a «»ae IM >a o«»eo ru <a O ' ^ oefM^o o « r O - r t - r t l M ' \ J ( M N l t a n % f . ^ , * | ^ l / 1 . 0 > 0
Ztarttart tart . • tart tart tart tart-rttartMtMMtart tart tart
ooooooooooooooooo tart ^ U J I l i U J U J U J U i U i u i U J U J l l i l i J U J U J U J U J U I / 1 ^ ^ ' ' - » ^ » 0 « 0 » 0 1 j K . « « t a r t l i ^ ^ . ^ O . U J s 0 u » O ' ^ i M i / t « * O » ' . * 5 0 i / t ^ ^ O i / t ^ p<ta ee 1/1 o> ^ « o » o e >o tan >o tart 1^ pg Ok K-1 u.».«»oetart«r^0>oevi\0»t»uiiart«reo UJOtart.rtee»OaeOtart^<«oo«i<^#wtart a r<11^ I J f M <M AJ I M f>1 <M <SJ l \J tart I M is j M l \ j
O O O O O O O O O O O O O O O O
O " O ^ t a r t lAW>»»1^ktart W^O> tanfc.tart 1/1 o > » n O tart tart tart ( M I M » n ( < n » < n , # . r i ^ l / M / 1 > 0
z
Zta r t tart tart tart tart tart tart tart tart tart . r t^tarttart tart . 4 ^ o e o o o o o o o o o o o o o o o o tart
^ UJ M UJ UJUUJ U UJ U U I U U IU U UJ u<A tart o>«rAj tart ^9><»<0^oe -o ••"AW uJoao»^i^Oi^oo(M^».ao>ri^*>Otart>»' »j»>«* i r »•«»»« "nose oo»<>o»>»^ ># "no-
t / t I k k • • ^ K n • > 1 ^ e • ' t a r t N 1 e ^ ^ > » ' ^ O O r U ^ 0 • « UJ I U J f \ J l ^ h t a ^ l / M ^ O l / 1 ^ 0 0 « » ( M ' * ' ^ t a r t ( M ^ Q I Otantar t / \ i f«J»r t (M«<nta* /U IMtar t /M«r t . r t (MIMtar t
O l • • • • • Z t O O O O O O O O O O O O O O O O O
I u. I O I
I ae I UJ I lU a i a#M<co«#«o<M>flO'.#ooiM>oo>*oo'M>o « I O tart .rt tart fM/M-i^fl^n-^-^i/n/i 1/1 >e>« f l I z
I UJ I Z I k- I
I Z I tart I a» .,tart,rttart-rttarttarttarttarttart.rttart-rt»«.rt-rt
I a o o o o o o o o o o o o o o o o o 1/1 I t—UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ Ui UJ UJ UJ UJ UJ J ^Jo.«oo»o>^fco>oo^^•rtl/1^»«rt<oo«#^ Z I U J O > / M l ^ * P » / 1 < C l / t ' ^ " ^ O O ^ t a r t W 1 t a r t ( / l ^ u I ^«oe><e«o>o><#«^rsjvii/^o>»aeaotr Z I u.«/ i '^00P«»00*#1J<^O*'>OK.9k»a0^ tart I UJ«^Jf1J9>0^o^Otart>>oun.«^.f^JrM>C . I a « n « M ' M I M < M ( M P « r j ^ ( M f \ J ( M P u ^ / M / M . -
lA I o o o o o o o o o o o o o o o o o Z l O l «-• I ^ I U I UJ t UJ _ J I a . ^ -
O tart^rMiM(Mxi«^«r">»«#ini/i<o>0 z
a I
174
ooooooooooooooooo ^UJUJUJUJUJIiJUJUJUJUJUJUJuJUJUJUJ O > V/1 > 1»" r t ^ . * » f f».Ui^ Ok Otart > ^ ^ e UJ » • » » i ^ O l/t i/» 0> lM»H/^ «# • « 00 un j « J ^ * 1/1 lA »^ tan ao >* l/t un i/tiM ( v >0 Ki ao u. •« >o (M IM oe oo ao o o <»i «r o !»• l/t «# UJ »»1/1-o o "rt—«^ xn l/t »s'O o> o> o tart
a—'••tartiMIMIMiMIM'MlMiMiMIMiMxitan
O O O O O O O O O O O O O O O O
OM^^^^^oe^^rtrtsoi^-^o^^oxn/Ni^ 0<# IM~0<OI /1 '0>Ol /1«r^ taa fMtarttan
z
aoooooooooooooooo ^taUJlJJUJllJlUUiUJUJUJUJUJlUUJUJUJUJ o ^^tart tart . o > o « n tart I\JO«»»I tart N. 00 oe Uj>iMB0i/n«/iOtart^.«rtnjfc.^OiMi/i^ J"no»r"*<0»#«<nunOkf>ooo>»M»#0'0 Ik a-*n Pk. o . o»-O >01^ >0 O tart O . ^ «* tart UJ X l 1/1 l / t 0 0 O tart I M >^ • ^ 1/1 f ^ 00 Ok Ok O tart
a tart tart tart tart r j l t IM ivj f j «M/VI/sj fig isj wn tan
OOOOOOOOOOOOOOOO
o«»o<fl^^'^JlMtartOk^o,HA^.^^/^ao Oun-n s#Mi/ikOt/ii«tartmtarti>ntart'M
UJ z a 3
19 { a ZI oooooooooooooooooo ^ I ^ i i i i A i i i i i t i i £ l i i i i n u j i i i i i i i i i ^ ] i ^ | i m u i i f ^ t i i
(jwn ^taatveOiMkOOoe tart tart O>oe^ ^1/19> UJ (M va "n 1/1 * ' » j tart 1/11/11/ < c # tai ae 00 O"
ae I j X t a ^ « j o > > o ^ o o p o k » n ^ . O k * " n " n ^ . < o UJ I ^k^JO^•Okf^ta•l,^Ok•#»#l/l^«Ok«»tartO«l/^ a I uj '^i / i i / t^Ota«'Mr\ i>#i / t '«fwaoOkOO^ oe I O I
O O O O O O O O O O O O O O O O O
z tart
a z
UJ u I ao-oi* UI I OkOtan* « I z
UJ 00
«* » « f\i tart
• e
I I
z o tart
to> U UJ u Ik UJ a c 3 z tort
Z tart
Z
UJ » •
»• kO i/n <M tai
• O
II
z o tart
tta
u UJ taJ u. UJ
a z 3 z tart
X
<x z
oooooooooooooooooo tart ^UlUJUJIiJUJUJlUUJIUULJIUUJIUUJUJUJIiJ uso«0 'MO>l />^^<c^«'4• '1r^ .r«r»>o<o
X I u i > » o e o e o ^ e « » « # ^ o o « » n > u n ^ o o u I ^9>w«^Oki/i<'i /t-oiM»<o«nooo>OkooO' 2 ik>Or<.<o»#Kt<MoeOktart»nNn'OkOxnaooOtart tart j UJIM^I/ iPkO«"««<M»»l/ t^^>a0^»OiM
Otart tart tart tart ryj^/^iMlJ'tJiM^^JIJ'Mxntan un i OOOOOOOOOOOOOOOOO Z 1 O I
u UJ I — _
a^'MOO*»rtO>"rt>OunOtan^oo»*^tartiM O ««•# tart un . # M.M«# 1/1 .#^i»n tan— >
UJ
a
175
>e (M <M
OO
I M
I M
I M
»n I M
^ >r I M
l / t
-e <\i
k O
k O
i \ i
0 0
<o »M
O
. (M
k *
K .
O J
O 0 0
I M
M
OO
I J
>* ao IM
•kT
0 0
I M
•* ar M
k *
OO
<\l
V/1
ao I J
k f l
ao (M
^ k
ao I J
o-oe I M
O o (M
o I
« kO k - ^
UJ k^
a >*
I M I M 0 o 1 I
UJ Ol -* -o un wn tart tan
o o •n "1
o o
•M I M o o I I
kO
i/k
O
00
" 0 •% 0 o 1 I
UJ UJ " 1 tan I M O o •# IV ^k
It t
I M I M fVJ 'kj o o o o 1 1 ) 1
U i UJ UJ UJ kO • * o e 0> » • kfl Ok <e o nj o > 1/1 ^ l/t • f i >C 1/1 1/1
o I
l U UJ •# oo tart O k # tart (M I M 1/1 l A
•M ^ O O I I
"M O I
UJ 0 0
o-
IM o I
UJ
IM IM o e I I
UJ -O I M « *
l/n ^ O Ok lA ^
' M I M O O I I
UJ UJ or I M >o >e » f f l .
•e »»•
O O o o o o
o o k. O O
o o
o o
•o o o o
o o
a o
O rt* tart O fM ao
o o
O M O oo
O tart O tart tart tal
o oe o k oe o 0 0 O O i f i O t a r t i / i o O i / i i / i i r O
</> 1 O 1 <- 1 k- 1 <T 1 ae 1
• Z 1 O 1 « 1 ^ 1 u 1 UJ 1 .J 1 u. 1 U J 1
a 1 1
_ i 1 « 1 ^ 1 w- 1 Z 1 UJ 1
* UJ 1 u . 1
u. 1
l / l
^ U J
l / t X • r t U
a z
i « « U J
fc-X . J U U J Z
a k r t
fVJ
U J
I M
o U J
o o o o o k O
o
o o U J
ao
^ tart
i r k O
I M
O
i M
o U J
o o o o o k O
o
o o U J tart
o -r tan k O
I M
O
I M O
U J
o o o o o k O
o
o o U J
rg o I M
3 0
l/n I M
o
o U J
o O O O O yO
O
O O
U J k O
». tart
xn
«# • v j
O
O
U J t n
f t
«n <c tart
O
o o U J
<o ^ rvj
^ tart
0 0
O
o U J
o o o o f U
o
• o o U J 0 0
< M
I M tart
V A
«# o
o U J
o o o o (M
o
o o U J
« t oc o oo
^ >» 3
o U J
o o o o 0 0
o
o o U J
i«n l / k
%r l / >
-o k O
o
o u. o o o o »\J
o
o o U J ( M tart
tart
0 0
•»1
^ o
o U J 0 0 l /n
un •r l / t
o
o o U J
>» »»1
>.» o-o o> o
o U J
^ tan
. Os
0 0
o
o o U J
K .
-^ K .
x n
h .
k O
o
o U J
o o o o l \ i
o
o o U J
k O
o-ao ( M A J
•k»
o
o U J
o o o o >«
o
tart
o U J
9-i r p ^
k O
" M
** o
o U J A .
X I
^ » ao
o
o o U J
^ X I
k O
o» k O
k O
o
o U J
o o o o 9 0
o
o o U J
k O K t
I M X I
p<n
sO
o
o U J
^ xn
^ » c
o
o o U J N .
un O i /»
<« k O
o
o U. '
o o o o Art
o
o o U J
k O
>o xn 9-tart
• *
o
o U J k f i
k O O k
«» yO
O
tart
o U J h .
fv o sO
<M tart
o
o U J A .
X I
N .
o> ao
o
o o U J k C
^k.
• r k .
l / t
<c o
o
U J xn X I
xn >e ^^
e
o o U J
• xn ao ( A
•* Pk.
o
Ok O xn NT
. # t a r t M i / t x n » r » f ^ . « » i / < i / t i A O O . # k # > »
z UJ
UJ a o
^ un -O k * k O tart O k IM O IM
k. I
176
o o o o o o o oe S UJ M 1 ^ UJ IM UJ UJ UJ x ^ k O k ^ O O ^ i / l r t r t X O t a r t O O t a r t ^ . O k l/t ^.OPwflo<oo>9e
a e k O O O i / M M « r O O t a ^ l / i k f l O k ' * •O P^xniM tart tart • «
O O O O O O O O O O O O O O O O O O O O O O O O O O O UJUJUJUJUJUJlUUJl^UJlUUJ k0unxn^«<0^>.0un0k0k0 - 09ekOtaao<ekO^K.iMun >M^oi/iiAk#ekOo<oiAO ao lA IM kO Aj ^ k O O <*kO«r x i • r t X n i A > r ^ O O t a r t K t O t a r t O kOkOxn^OkiMAjAjAjtartrtk/tj
u j u j u j u J i ^ ; u u j i u u J u j ^ u J . u i U u j tart.#aoiAkOO>oiJxnkOOk#OkAj«» ^ t a r t O ' * » i A O 0 » " « 0 ' " — O O k v A O un^«AAJun>lA^tar txn* iMkO-Otar t I A 0 0 ( M " 1 l A I A O O a 0 O ^ . ^ • • # O • O > O O x n O x n a e ^ a O O e o Ok tart tart tart lA (VJ Aj IM tart - O ' O kO xn o Ok XI • « x t AJ
O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
o o o o o o o o o o o o o o o o o e o o o o o o o o o o o o o o o o oe O UJUJUJUjUJuJUJUJUJUJUJUJUJUJUJUJUJUJUJIUUJUJUJIUUJIiJUJUJUJUJUjUJUJUJ Z *^xnAj«*o>*>0"tkOiAxniAxn^. iAOkkO'* tar tkOOk>OkaoaoO»»«ta - 'MkO«MkO«o tart *xnxnkOtart (AuniMaexnkOO'eun>#iAxno«*krxn.Ok#tartxniAOk>«<0 380>N.aoxi Z O x n » r t > ^ 5 0 ^ » A > > t a r t 0 ^ l A A « » » t a r t l M X 1 0 k A j . * I M t a i ' ^ - < A . o e k O O k O k l / t 0 . i M e e - «
* * k 0 x n r » i A « » k * ' M a 0 x n a 0 a 0 k 0 « » f l 0 > 0 A j a 0 k 0 l A t a r t A I N . I M A j O > 0 0 > 0 k < 0 ^ . x t 0 k k # . * k # ^ ^ a o ^ . ^ . A . ^ i k j a o i > . ^ ^ ^ ^ . . ^ ^ ^ „ , ^ . . ^ . ^ 3 0 o o , M > ^ ^ ^ ^ ^ ^
o o o o o o o o o o o o o e o o e o o e o e o o o o o o o o o o o o I I I I I I I I
o o o o o o o o o o o o o o e o oe I O ^ U J l ^ U J W * | i i ^ ^ i ^ i n i i | ^ i » i ^ | i i » i n f n i n f •1 iMiMiAka-a ao .««nok» ,#o .o iA iAM « Oio<M«*AJ iAkeHita<«e<n.aoooxnoo> z <oxn^oe^• h.^«#.o<*^-oiAiAxiOk
•rtfi»»»tartvA xnA.o^<.xi>Aaeoetartxnk# x n x l A i > 0 - a l A O i A A J l A l A U n i A . e i A X 1
O O O O O O O O O O O O O O O O I I
tU '^ ' i l ' i l ' 'VUf i^Hf" - ' i^ ' "" t i * ' " -^ ' f *^^ ' lA fv Aj 9> k#«#«rka 91 v-r^. lA ao xn tan a I M I M l A ^ ^ f V k O H t a O ' ^ A k X n a O K . o e x n O k O O O k ^ ^ ^ . » y i , # x i ^ ( ^ i A a o u n O k un 1/1 o e o O " n i A K . u n » A t a r t O i M ^ k # o l A l A l A > A x l i A l A O k # x t ^ ^ > A » l J M ' A
(.# « r ' • • T A J Ok k#iA>r tart tart tart—tart tart IM
o o e o o o o o o o o o e o o o o o o o o o o o o o o e o o o o o o I I I I I I I I I I I I
V
UI l /t UJ oe k -l A
0*"rttarttarttart
O O O O O
t i i i i i H H i 1111
A J k « 0 ^ l A « # 9 k . < o a o 0>Ak#AJ<0 l^r tMPAwrt lA 0 > 0 tart kO tart
tartOO/^JIJ O O O O O
11 1 U H A I I l 1^^ 1
" • O O O I M l A l A K l A « 0 > * OOtartrtrtAJMI AJ lAOOkOta* Ok tart Ok tart xn
A j O t a r t A j A J O O O O O
^ U J UJ UJUJ kO«A(M«#.a > i » t M ^ a o O ^ M A J t a r t • n » t a r t . # O k i M k ^ t a r t O a o
A J « * » * A j O J O O O O O
UJ IW W M UJ I A N . « » * < « t a a < « 0 0 O f l O u n . * ' * •A^OO tart tart O k A j A j x n o
tart tart tart AJAJ
O O O O O
l l j ^ i i | m l i j i
k O O k « k O ^ « A ^ « r X 1 » X l t a r t X I n ^ O O k t a r t X n ^ ^ ^ » n . ^ x n » n
X I tart tart — o o e o 1 U J U J I U U J ^ O l A x t A r t O f l O l A A k l A O O k A i — O O O A . O ^ < «
O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O I I I I I I I I I
xnxn>APAfg H(AjAjxn»rt AJAJAJAJAJ
OOOOO e o e e e e e o o e I ^ U J U J U J i U l y i M u i l u l U u t u i ^ i ^ U J
l/t xnAJAk^kK. O O i ^ O l A — vAkOkO^IA l/l O k O < M « r ' « wnf^xniAxn k 0 ^ f f c A j ' « UJ . ^ x n ^ o O K ^ ^ . # x n i M ^.^tar tx i f lo ae tartMrt^^tartiA xnA>oA>ke te-a^ffyo-^. xnxnAj<4<e unoiAk#-* »«#tarttanao l / l
A J A J A J A J A J O O O O O
A J I M
oo
•OOk
U J u U u u AJ — ^ 0 < 0 «^ao»iAoc A J « * k * « # ^ ^ ^ B O k O l A ^ ^ l A ^ O k - k * - X i a o
I M « A I M O O O
UJUJUJ lAf lO^«. l A l A A J O ^ I A
i A O > r « r o tart «rt tart iM«*Ok#unk# ta r t^ O k * « *>» r t * 'MO 'k *« *« r tart A j 0 « # l A « » t a « — 0
x t i A x i x n o o o o
oo^iAxn oo tatart . lAOOkOO A j f k . ^ t a r t xnxiAjo — AJ
fnoooo O O O O O oooo o o o o o o o o o o o o o o o o o o o o III I III I
O O O O O O O O O O o o o o o o o o o O O O O O O o o o o o o o o o
0 I 1
l /» l a I taJI
" I UJ I l/t I lA
lUUJIUUJUJIiJUJUJUJIUUilUUJUJUJ UJUJUJIMUJUJUJUJUJ l/t O i « * ( M x n > > » 0 « * l ^ » ^ " < k * x n O > ^ t A A j O k O l A » A ^ A . O * l/t O k M l t t k O O l / l i A M S O e x n O O O ^ x n — . ^ O A J A J I M I M " * -UJ o » t « - < k # a o o . x i ' * — » A i A i A « u n w n k # « 0 * * a o ^ — A j — K ^ 0 . . 0 > A ^ l A > * k # A J « O t a < « 0 0 « 0 « — A J ^ . A j l A I A 0 0 O < O ^ ^ « ^ . # ^ k A r « a s ^ ^ f v ^ O k 0 0 w n i / i k O m ^ k # i A i A u n i A A j « r l/t r« .^ .^ .^«xn«A»• ta •» • • r taOtar t •^>r •^ •^AJta •^<* •#" * lM—
U J U J I M ^ U i U U J U U J U J 0 0 l A l A tart tart I M k O i A u n i A PA X I X I » ^ , M OO » • kO l A Ok ^ 001/1 un * un * AJ 00 O-AJAjOlAkC9>kO^PA00 ooaeoeooxn»kO<o«^ tarttarttart—<Oktart^^Artr^
o o o o o o o e o o o o o o o o o o o o o o o o o o o o o o o o o o 1 I I I I I I I I I
21 </• I
i UJ tartPNiXt^un-OP^oeoO—'Mxn^unkOPn.oOOO-^iMxn^uikpA.aOOiO—AJPA^ I Q ^ ^ ^ t a r t — t a r t — — t a r t — ( M A J I M A J A J I M A j A J I M A j x n p A x n P A l r t t
177
O O O o o o o o O O O O O O O O O O O O O O O O O O o o o o o
• • • J • • • • • • « . . . O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O UiuJUJUiUiUiUJUJIlJUJUJUJUJUJUJUJUJUJUJuJUJUJUJUJuJUJUJUJUJUJ » ' " ^ « » ' * ' 0 ' v ^ O o e p « . 0 > O i > » O k a O k O ( M j n ^ x n x n O k O O k A J O O » " A O k ^ , r O ' » o — r v ^ O i A x n u i k O ^ a o o x n - o — ^ , » A j o o A . » O k O > * A . k O k O ^ l A ' A . ^ i e O - — K . u n ^ u n A j l A N . i M « » O k A . A J i M u l O k X i O k O k X ^ O ^fcoeoooo—A.OkOO>p^iM—oaeaose~e»*iAxn.#kOO«Ajfk»xi • " ^ ^ - • " - O - ^ u n A j - k O u n o o * - k # O o e - * k O t a i k n o O i M < O i A A j A . O xnunAjAJAj iM—Aj.#x^«A — ^ A ( » « l t a ^ A j — A j t a n x n » n x n ^ x i — f v O O O O
O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O C I I I I I I I I
rg AjAjAj«nAjiA«Axn"Axn«AvAxnxnxntanPAunAiAiiMPAAi kOun -rt o o o o o o o o o o o o o o o o o o o o o o o o oo o
I I I I I UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ Ui UJ Ui UJ UJ UJ UJ UJ UJ UJUJ UJ
fle tart tart>iAoeooxn^keruiA<APAxn<oiAAjiAPAiviAk#oe» K x k o O kO lAunAj^iAN-xntart^oiM^-xnAikOtartunArt tan-O^rOkn >Ofik O "^ <C x n . ^ A J u n a o O * » " * A i i A O ^ » ^ . a o > O l A O k O a o « » 0 ' * x n o Ok « ^ oopAkOAjo^'>»^>.eoaiioo>AjAjAjAjiAOki>PA^tan«r I A - > •O Z «*o»ri/n^-<xnta<PAPAxnpAA(tartxnPAPAxitart»rtiA>oiAtartAjoOk—oo-oo
o o o o o o o o o o o o o o o o o o o o o o o O O O O O O O O O i I I I I I I I I I I I I
AJ tarttarttartAJIM AjtarttartAJAj tarttarttartrtrttart A J t a r t v ' ^ r t O
V o o o o o o ooooo o o o o o o o o o o X I I I I
UJ i ^ u J U J U J U i ^ u j U J U J U J UJUJUJUJUJ UJ " J U ' l U Vif l /t * . tarttartaeaO»* tartlAk,»*eaO tart.«OOk<<l A j O - r t A J O k
l/t o. o O A i « * » tart—.#.r» tan-un—<0 ^». * lA««# UJ un O x n e e O k O « « ^ t a r t O « * -OPwulkOOk .#aoO>>HA oe o xnOoo—<« » k # x n o e O o>#oopn.ao OkOkOkPviv ^ tart O x n . - A J ^ AkkOiA^tart U 1 » k O O ^ ' « — k O O A k I/i " r t O A I A J « * » r A . O A . A J I A « A k t f O t a X A ( K . 0 0 l A O > O « A a 0 I A « # O O O O O O O
o o o o o o o o o e o o o o o o o o o o o o o o o o o o o o o o I I
IM (MAJAjxniM A J P M I M I M A J A J A J A J A J I M A J A J A J X I A J A J A J — A J —
V o o o o o o o o o o o o o o o o o o o o o o o o o o UJ ^ UJ UJ UJ UJ UJUJUJUJUJ UJUJUJUJUJ UJUJUJUJUJ 11111 m l UJ u I
lA l/t tartkO^ta^lA O A j O k O " " AktarttartAJO ki#tartiAUnO AJOO^xnfV UI — tarttanpAoOkO Pfc-PAOkO A . a o « A j O ^oOtartrt-rt- O k O « r ^ o UJ AJ l A » x n O k t a r t tartPA-OOlA A l O O - O x n - P A O U I A J * * O k O - x n O k Q X O X l ta r t tan -Ok* OkOtar tOkXn tartOOkdtart . O ^ A . O » r 0 O A J ^ . x n » ^ 0 0 a O ' t ' O ^ A J tartkOlAlAAJ « r O ^ ^ ^ O k P A , o « r t ^ A j K ^ O ^ T k O l/t « ro«* i jn * r ta r t—o>*"Axn—Ajoxn«n(M—ou^kOiA-A jo—»^oo<«o
OOOOoaoOOOOOOOOOOOOO'SOOOOmOOOO'-^O I I I I I I I I I
O O O O O O O O O O O O O O O O O O O O O O O O O O
UiUiUiUJUJUJIUUJlWUJUJUJUJUJUJUJlUUJUJIUUJUJUJUJUJUJ l/l ^ x n « » o e o ' ^ ) ' M r t a ^ l A ^ » ^ . > ^ » P A u 1 ' M A J O u n ^ — k o ^ r t o o * UI i i A i > t a « * i / i ^ t a r t » r r > . » « # x n o o k ^ x n i A ^ p « A j — » » o - r t i A k o a o UJ xn>o«#uniM*^iAOk' ' i tartOOOflOi /»xiAj^* 'X- i^MMOk«»»pA oe iveoooeeooor taO>^tar t»^Aj^rwgountA««# iAAj^^O kta eeOk««tar tOta^OAJP«^OO^ae>nAi (MIM'>J I /1xnOOOAjkClA l/l •niA(M'VlM(Mta«Aj»APAxnPAtartA(xnxiPA«AtartAjxniin»APA—PAOOOOOO
o o o o e o o o o o o o o o o o o o o o o o o o o o o o o o o o I I I I I I I I I I
Ui iAkaA.000kO"«MP'l.*lAkO^»00O«O«rtAJ»A^U1'O^a0O>OtartAJxn,#U1-0 Q wnxnx^xn>A^>rsr^«r«rk^^k#^iAiAUiiAiAiAiAiAuniA^<0^'0^-0-0 O
178
o o — O — O — x n x n A.>—— xnx^ — A J A J X I — A J A J X I X I AJAJAJ O O O O O o o o o o o o o o o o o o o o o o o o o O O O
> I I I I X UJUJUJUJUJ UJUJUJUJUJ UJUJUJUJUJ UiUiUJUJUi UJUJUJUJUJ UJUJUJ
"l^kOSk^flO tartAJlAA»^>. l A O O < r A J f^PAtart^i/k >A.»eOAjnn >«Otart to l A x n i A A j O tartO^Uno ^•^N.kOtart A j O * * l A ^ —OOO'OlA • O O l A z Ajao»*Aktart A.tartan^>oe I A O O A J I A I A esek«rt<rek O k O O ^ A j •OOkan UJ Ok00>0«r iA^flO»oo ao>^Ajxn tA<0A.eoO « A J . # > A A J xnoao z PA^»eetart^ tartaefk.aofw «A«»kOAj>A •AkOOkaeae O>OOO«#AJ OAj-e o keAj<oAj<ootarttarttarttartxioiv^keta4AjOAjA.rtrt^tartooevrtAjtarttaietarttartAi K • • • . . . . . * • • • • • • . • . • . • « . . • . . • . . . • •
ooooooooeooooaoooooooooooooeooooo I I I I I I I I I
o o o o o o o o o o o o o o o o o o o o o o o o o O O O > l/t U J U U J I U U J UJUJUJUJUJ u j IWtUUJULJ U J I u u j I k U J l U l ^ u i u j U J l U UJ UJ u i kta ^ A J P A O O O lA«*aOtar tOk 0 > ^ k A | / i ^ lAOk^tar t tar t aOOOxiOkOk k O M t a c a Z l A t a r t k O O k O l A k Q l A X l P A l A ^ • 0 « # t a r t k # a e O k O A . ^ A > x n > # i / t PMAkOe O UJ tartaO»Atart..^ AjkOAJtart^ A J O O w n ^ ^ OkOOiMAkkO Aj'O'Mun- unAj'^ at z o x n a o i v ^ Aj«ro«rA> ^AkOOunxn OO^^^^TAJ "A^roooOk lAKi^»
O OkAj^i^K. A-o^kOOkO ^kO..*tan(i. ^k f l^A jK . K i O ^ a e o OkAj«# I k Z ^aeN>«MAJO>NJ*' l 'M00lAOAJAJ'M00tartOlMAjAj00pMOAiPAAjeei>OO^>0eA> o • • • • • • • . . . » * • . . . • * . « . . . . • • . .
O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O K I I I I I I I I I UJ a ae I
o O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
K U M M M M \U W U UJ UJ UU U U U J \U ^UJ U U M M M M U ^ ^ ^ U M U M UJ
p» 0»O0k(<»%#OAiiAOOO»M«#^epk«r>run,r.C<0-0wnPA—lA'OOkOOOkxn Z i^OPta^ao^w«i/n—aeAjOta'>#^>#aoxn«A»iAPwunvrt.#OiMiMk#«#»un— UJ »^^keo«iA<«<0PAek»tartAjtart9"k#un>#iA>rxno^^<0^-xtxntartp<tartPAPA Z OkOkA-oo«—^<rxn««^«AiAwn>Otart<e^xnpAi/iounAj^O>oo—Aj^OOoo
l/l i o k#k#.#i^AjxnoooopAtart^fwA.A.»Ai/iA.^fcA.Kxnaoooo—-OtartkO-ow^ OB I Z >#rtr<#«#AilMtartv<tarttartuntartfMIMAJPM—oe/tiAJAJAitartOO—taXtart—|A«rt«r«r^
O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O I I I I I I I I I I
UJ • r tAJ»Ak#u1<<JPt»000 'Otar tAJ«^k# lA>a^ .«0kO"*AJPAk»unke^00*O —AJXI a — — — — — AJAJIMAJAjAJAjAJAJAJtanxnxnxt
o
179
> oo ooooo ooooo ooooo ooooo *< I I I
UJUJ UJUJUJUJUJ UJUJUJUJUJ UJUJUJUJUJ UJUJUJUJUJ ^ A j x n tarttartAkOkA. A > l 9 > l v a C O > eekOkOtartOk x ^ ^ ^ t a r t j ^ o * Z fwao eoo^Ajrtrt ^Aj f lO'M^ aoAjxn^pv oeorvf^Aj UJ l A l A OOtar tAJkAO AkOOOeoOAJ PVOOtartlAPA ' O O k O k ^ r i / l Z kOxn tartOOtartAJ^ AkOOtartOe-C x n k O v r t ' k ^ - tarttarttart^k^'O O tartkO A j P A l A l A k f i ^ U l x n O k O O ^ - > C 0 0 k # O O k A J O O e C u n ' « O t a r t t a r t A J A J k # e « # > r t P A A j x n o » — k # ' ^ > A O . » t a r t l A P A A J O O O e o e O
O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O I I
oo ooooo ooooo ooooo ooooo ooooo UJUJ g j u j u j m i ^ u j l k U J I k M UJUJUJUJUJ | ^ uJ UJ m u j | ^ UJ 1 ^ l u UJ
— < r ^ ^ A i > A ^ t a r t l M ^ « # » t a r t ^ O k O - A J O ' k # 0 0 » A j k O tarti^O'-'k^ Z ^ A j OkOOoo» Oaoooxto ^AjOPAkO Aj^rOOk^r lAkiTOooO UJ k^tart — t a r t o a o ^ tart^^iAta* A.ui«rOk-« oo«riAAi<« Ok^.#xtk# Z -000 O^a0tartk# ^OkOk^kT ^Ok^rwAj ^xnOtart^ p^xi^^^^a O lAOO ^ • r t A . a O ' k * k # . « — u n p A O O O A k A k O l A O O k * 0 0 « ^ A . O A J O O Z • r t A j O A J > A I M a O ^ O A J A J A J O k » " O A j t a r t t a r t a O t a r t O x n x n x n ^ t a r t O r f c t a « ' * l A ^ O
ooooooooooooooooooooooooooooooooo I I I I I I I I I
O O O O O O O O O O O O O O O O O O O O O O O O O O O K
tAj^|iHfiiikimjin^im^^f^i^uji^iitAjii^i|ji^i^l^^^tmj^^l^tiJUimiiJ
tta ^O^^iA'^^—-Oae^Ajk^k^—O—roOkfvOkaOtaxe^tartPA Z e>00«>^^k#i/noexn*Oeex'i«*0^rviAtartki^^AjunA.aopA UJ •Ak#AiAixnekAjAjN'<0«#vrt«#OkiA>rxnoiA9ktarteetart^..A.rtAj C N'AJO^kOkO>r^ta•'«f^^>»^O^<0ke^un—AjAjxntart«#oO O kOPAiAAjAjAjAjijnxniMAjAjAj—Aj»^*^xnk#aoooaoo>0— Z > r ' M » ' l — — ^ — I M A j A J t i — — — O k — — — t a r t i M O O O O O O
O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O I I I I I I I I I I
UJ , # t A k O A , 0 0 l > O " r t A J P A k * l / 1 - * ^ a O O k O t a r t A J P A ^ l A ' t f N i O e O k O t a r t A J • A ^ U n k ^ a «Atanxnp<n»nPA«#«r«r^k#k#k*.^^knAuni/ii/niAuniAi/iwniA'0>0<0<CkO>*^
a
180
UJ I O I 3 I N. I - I Z I o I « I Z I
I k r . » . # ^ ^ > # ^ ^ v x t A jA jxn tanxnxnk#^k^^k^^ .« .#^^kr .#^ i^ "• ' O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O a I
I UJUJ UJ ^ U ^ W UJ l U UJ i k n i i i n i ^ ^ i k i i i j i i i n i l i j i ^ f i i i i ^ ^ ^ ^ u j ^ i j y j ^ ^ i ^ n f l i i
ae I X ^OKis^kOaek^OkOtate o>»^tart^kOtartAjOxniAPki/ioe'^oOk^eef< UJ I iA«*»^«AooiAiAtart A>»no^^«raAtartae,^Aj«#>A«#rk.oijnr^9>Ok a I ^ xn«rtk,^Okek#«^unPkOk un«#tarti/ itarttart«rt<09><0*AAjxnoo«k#«rO—xn 2 I Z l A u n P A O A ^ ^ k O l A l A t a r t tartA.xt^PUlMO«#'4ektartkOk0IM<*AjekaOO^ O I UJ ^ . ^ A . A . A J l M * O k x n > A • n i / » - r t A j « # i « O O O O t a r t l M A J 0 e O ' « A . # l A ^ < e
I Z A J A j A J A j A J A j — — » O O O A j O e — — u n — — — — A J ^ ^ ^ ' k T ^
(Jl o . • • . • • • * • . . . • . • • • • * • « • • • • • • • • • • . • Z I z o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o ^ j I I I I I I I I I I Z I UJ I U I l/l t * i • " • > * O A j x i , o ^ ^ « A i r t n ^ ^ A j , O O O i M « e < ' * 0 » ^ O i / i o o O o O u n a o u n t a r t ^ — . *
I A J " » A J A j k # « » ^ v A A J i / t k O ^ « 0 tarttartk^iAAJlA »rt Aj Aj • * xn i/t un «A x l iA UJ I UJ X I Q * - I O
I z z I « I
I V I
I >«' >y.fsrk«' *r.#'<i# AjAjiMxn>Axn»i^^^k#^^v.r>#^<.r^^ a I OOOOOOOOOO o o o o o o o o o o o o o o o o o o o o Z I X ^ I ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ i | f^ | imi i i i^ i^ ju j t i iU jmtAjmujml lJ iA juJ lULAJl i j
I k- o ^ i A A k A j A k ^ k t a r t ^ ^ K n > r i / n » k A O t a r t e u n t a r t t a r t > # ^ O t a r t . # » O x n » X I Z ^ — « A ^ O a O f V ^ e O P A l A O — ^ O O A j l A — l A A i O ^ k O u n A J O O ^ O t a r t l A
I UJ O - A J l / t k ^ t a r t k ^ O P A l A O k ( M A j ^ A . r f c ^ l M P A k O P A ^ » A J A . t a « 0 ^ k O x n x n • • I Z kOiAPA.- iOkA.A.kekOO O O ' / V l O k ^ ^ t a ^ x i ^ o O ^ ^ ^ k O t a r t x n k O A ^ ^ O O O 1^ I O ^^»^A.AJAJOk9k•ntar t . r t iAaOta<xnMnwneeoOlMAi f lOOOAj«rk*wnke a I C AJAJAJAJAJIMtarttart—«rtOOOAJ*nflOta«»«l/1kOta<"" — — « - l — • " t a r t A j ^ « # ^ r « # - J l • • . • • • • • • • . • • • • • • I e o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o
Z I I I I I I I I I I I tart I
I UI I te I Z | UJ u n x n O k k O i A ^ y — e n . A . — u n x i o - A . # O A J — » a e A . . O O k A . h . k 0 i A P A A J - n A j UJ I Q tarttarttarttart'kr^ununtart«rkO<o<OkOP'nAjPA^tartk# AjAjxnxniAun xnxn Z I O O l z Z I
181
oeoooooo ooooooooooooooooooo UJ UJ UJ Ui UJ UJ UJ lU UJ UJ UI UJ Ui UJ UJ UJ UJ UJ UJ UJ UJ UJ Ui UJ UJ UJ UJ
> u n ^ k O ^ k f i ^ t a r t o » . r t . r t A i i / i « » n u n t a n O k « » i M . » ^ x n k O A J ^ » < B 0 «*AkO«o<oo^»>o p'i*o"''«**'ii«OAj>OkOAjaokOiA"<«»PAo
^ » f l e i ^ r > A > ^ k O ^ ^Ok^^^AJAJOtartkOtartaOXIPttartOOlAtarttart r oop^oo^kkT^AJAj K>»r<k#A.KnaoAjQeoo>»OkpvkAeeop'iO»r'v UJ » > a • * • • o ^ - ^ o >0'^Aj^O'Ork.^oeotartiAO«#OkAjflo«oi/t Z <MAJ AJAJ AjtarttartrtrtO O O O O O l / l ^ e e o O t a M I M AJAJAJ tanxntaniA^ArtOOOOaO-o • • • • • • • • • • . • • . • . • • • • . • • . . . • • z OOOOOOOOOOoooooOOOOOOooooooooooeo
I I I I I I I I
0> <* lA .#^ tar t xn xn k# 00 Aj »# kOflO tart tart A l A J A ( A . ^ * l A « O a O u n « * x n tart Aj O O O ' * — - ^ ^ ^ l A J M u n u i - — AJ k*—•k#AJlA>OIM X1.A xniAkO A j —
UJ a o
0 0 0 0 0 0 0 0 0 o o o o o o o o o o o o o o o o o o o M U J U I U U U ^ U U J i fmH£^im^i iJ i j - i iA jm^| i^ in i^ fy^nf i i iu /^ | i^ j^
— »»A.Aj»#^Oktartk,» OkOkta^unOki ooaeokOoo^aoooAj-OPAOk^ z unoeokOooAj—oo o»«iA«rxn^iA^'«0^0«#oo»Aj^oOk# UJ AjOeAJtartOkUnOktart.* k^-rt^^l/lkOIMAJk^tartkOlA^rkOAJlAAjOOkO Z »A.^<OOOx«^tart .^O-xnun^r^Oxn^O^^Oxi^tartiAPw-<« O *kO^.^—ao^xno AjO^xniAk^^^AkOkO^oo^aeOkAiooiA c AJAJ AJAJ Ajta*x""««rooooOk#<«rfcao»ta<»iiiJ»MAjxnxnxnA.ffcA.oooOtart
o o o o o o e o o o o o o o o e o o o o o o o o o o o O O O O O O 1 I I I I I I I I
ui xno»^xni/io^f^i^O<0O>0AjPA0ktartke^i9k0»uniAA.k0^-0xna0ta«iMOk# a »r tAJAJ^'* l /1 tar t^>0xn-0<0xn. , *k0AJ-0tar t .# lA AJ xnAJl/1lAxniAX1PA«r xn
o
182
X lAtartaeAJtartOkOkk#<><r ^ • o o ^ • ^ A l A O P A A J ^ o
ae ^ t a r t « r t O A » p A a e n j x i ^ a • • * • • . • • • •
UJ oxnunokunaoxnoxifs. S "Ak© lAuniAke ^OlA < I I I I I
V unao<MOkkO»—xn tartAkPAOkkriA^unO
Oi aO'^-.rv^tartOkOkAjiA
UJ 0 > f i M O O O O O O X I I I
oe U O A j n O k ^ O ^ A j V ^ O Z —tartAJPAPAi««riA^
U <0 iMae«»O<0Aja0k# z ——iMPAxi«r*run
X o^AjaopkkOaoxiun— (MXn»l / t«#^0>AAJO
oe i A » « o O A « x n a o A j « A i / t 4 • • • « • • • • • . UJ O P A l A > l A a O i A O x n A > X xn>o lAiAi / tkO -e\/t l/t I I I I I
V ^ O O ^ l A ^ • • < k O , ^ A J >o r>» 00 O • * xn-O Ok—
Q: ^ l A x n o ^ t a r t O k ^ k ^ tf • . • . « • . * • UJ oooooooo-Z I — Ut I
untart^xnOkun»<A.xtOk ae u
« UJ X l/t
A j ^ O » » O l A k ^ k # ^ » I A 0 0 O " * I A « # O k 00 ^ AJ Oktart «rtk<n AJ OBtart xn PA
OAjun»i/taexnO«AA. xi<« uiununk0 ^ l A I I I I I
V »^iiAkOP>n^OIAPA lMtaM^,#»k#Ajv4A>
UJ O O O — O O O x n X tart I I — lA I I
ae u •^OkflAjOO^OkOAjaO U k#O<OPNj00srO<OIM
X >«O«»fl0Aj0ex.)kOlAO ^ • « » tart AJ O AJ fV tart ao
ae ^tar tAjOktar t iMun^^iA
« • * • • * • . • • • UJ AjiAun»ae»k#oxno> X x n ^ un iA iA -0 kOiA l/l I I I I I
z •> l/t
UI O lA • » » Aj .#tart xn 00 «* O tart A. ae tart X I un 0«A—k#un.#—tartun
x n o o o x n ^ r o o -I I — I t
^ ae l/t u xnoklAtart^xn»^/^^^,
l/l a
U X NkAjAkOOunxlAklAkOkO UI UJ ^aexntar tkesoaeo^tar t
ae a : k O x n o A j o ' n j * A » i M O k •rt « • . • * . • « • . •
O I a UJ < o i M x n o * > i M O i M ^ S "XPA PAAJAJXI xnAj
19 un I I I I I
u UJ > a o O - - A J — O k O x n x n oc ao<*ao—O^OPAiA tart oe >A.ta«tart^tartAJO*« a tf . . . . . . . . .
UJ A J P V J O O - A J I A O O te X I I I I I ae l/l O
ut A I « e < r O < O A j e O a r O «
w« Aj AJ PA xn »H /MA Ajoo •»o<OAjoe«# o
oe I a
u oe o
l/t I
oe tf
l/t
a X oxnxnta r tow^"^""^ Ui i/noxnee^Aj>o<o«#o ^ oe •AOk^ao^OAi^aOkO tf tf • • . • * • • • * • J UJ O I M O — k * - — O O x n 3 X 1 1 I I I U un « u
oe « UJ X l/t
a > KniAOi/nxnoeOuniAO UJ AjOxna0P'tPA^<e^^ hta oe iMO""Oxxx->"'*'-^ta« a tf . . . . . . . t * . ^ UJ O x n > # o O O u n A i O O 3 X I I I I U l/l
tf u
ae u tart ^ PA 0> un tart A . xn Ok uik
tart rtrt I M PA PA k « « # l A
183
X O'k^kOunOkOAjA.tartO » O C i > ^ i / i A . ^ o e o > 0
ae lA-^AjOxnNkOOktarttart tf * . . • • . • . . . UJ O A k A j O k O O l / l A J x n i A 3 lAlAPAAJ I " A ^ ^ <A I I I I
V a O ^ l A l A t a r t t a r t O k O k O ao•rt^>oxnlAlA^O
ae »k*AjOtart"goir»iM tf . • • . * . . . « UJ A J O O O O O O A j u * X I I I wt
ae u ^oo^—lA^oeAjOk Z u n < O l A A J kTtartPAtart
oe U AJ^OPAunoOkOOOOO Z Aj>rAjxn,rxn PA
X O O t a r t k O k O P P I i A O A J ^ r x t — 0 ' « r — O O ^ O O l A A j
ae ^ l A ' ^ ^ ^ A r t i M x n O k i A tf . • . . . • • . . « UJ » A » A i O k O O ' ^ A J ' M > r X lAUnxl-vj I •AkO^O l/t I I I I
> l / 1 P A l A P A t a r t « A u n i M l M O O — P A P A A J ^ P A O O
ae ounxno—<Mhtak#^ tf • • • . • . . « ( UJ P A O O O O O O i M * * Z I I I I l/l
ae u z
tart^PA^xl^lA ao O O k A J i A l A ^ ^ A j p r tX l
X v A i M ^ a O ! a " A k # P A a O u n AJ AJ tart tart fM P A O a e O ' k *
ae xntart,/tAjo^k0^^ao tf . . • . • • • . . • UJ x t O O l A O t a r t O P A O k O > x n Z • ^ u n u i P A I A j i / i > 0 •Jt I I I I
U P A A . a o O t a r t x n u n A j P A O Z l A A J A j A j P A — l A P A t a ^ . *
'v«rkO«#iAtart.Ooexn i/n^>#«r ——xn
V >#iAoei/iooOAjoo »—xnaoAj^Ak—A.
oe ^ a n P A O t a r t t a r t l A k # k ^ tf * • • . . • • • • UJ o o o e o o O t a 4 « r X — I I I l/t I
ae u A k k O t a r t O k O l A t a r t P A A j
• r x n — » # u l — U I —
lAlA oao -J .J
unO —-O
^— . • PAlA
1
II II Z Z O O tart tart
N t a » >
uu UJUJ aeae tart tart
?? X X
\A\A a a . J U
» o A . » l A ^
* • xnun tart
II II X'X o o krt tart
I B ^
u u UJUJ aeae tartta*
a e 1 1
> >
a I 3 I
z I 19 I tf I Z I
I U. I O I
o: I UJ I a I ae I O I
I (J I Z I
a I z I UJ I u I t/t I tf I
I
1 ^ 1
I
51 I
l/l I
SI oc I O I U. I
I ael « I 1 ui I
X ^ a n t a r t A j k C ^ ^ k f kOOk AJ lA xn Ok kO I t PA Ok N> O
ae PAO^>\jAjAjOAjxnae tf . . . . • • • . • • UJ "nOkiAOta^OxniAOOPA X kOlAunPA I lAkO l/t I I I I
V ^ P A O - ^ A k k A ^ x n o ^ VA ( T tarttart l A AJ Ok PA
ae tartlAPAtarttarttartUnAJpta) tf • • • • • • • * • UJ —eoooo—»» s — I I I
• . l/t I
•X ae lA l/l u 'k»PAO.rP^ee«*iAi/iiM a: O Z unAJX* PA,^»rtta.pA«r U taJ tart tata
z o
A J — » » O O < # « 0 * AjiA tan^rtun Ajta
o X ^KMr^unp^iPAtartO^ao UJ apAks^^oxnooaoiAO ae ae xnof^k^OAjoe-xnoo ^rt ^ . . . . . . . . . . a UJ x n f > k i A O ' s i O " < i A * « A
Z -eunun-n i un<fi •J l/l I I I I Z o
U A i ^ O x O ^ f f c ^ ' O ' f l x * Z UirUAj .#tarttartPAk#
X l/l
a X l/1ek•#e^»#«'<<Bon> UJ —orwAiOk^'kroi/tPA ^ oe Ki rtrt xnun<0*<ae tart A i tart tf tf • • • * • . • • * • U UJ P A ^ A t a O - O O O l ^ O O P A 3 Z <Ol/1iA«A— IA<0 U l/l I I I I I .J tf u
UJ V PAtartPiwtartAJkOkewaiA
ae A>Onraotar t« rkeekac tart ae PA kO PA tart tart tart k # Ok o a tf • • •
UJ x n t a r t O O O O O O x n ^ Z — I I I ae >/i I o X un
oc z u Ai-A^r^roei/iAjp^ — Z lAAJPOtartAJPA ^
oe tf UJ X lA
a > Okfr«#o>unPAr>takOiAo UJ r w » — ^ o p o o o k O ^ ^ ^ oe u n — ^ — — P A ^ ' O ' ^ ^ tf tf • # • • • • • • • • _J UJ x n A j O e o O O O i M u n 3 Z — I I I U </» I
« u
Z Z Z Z
UJUJ UJUJ u u u u aeee aeae O O o o I k l k I k l k
aeoe oeae « « tftf UJUJ UJUJ X X X X lAIA lAIA
UJUJ UJUJ
« — tf— U l / t I9 t / t U J O UJO za. za. X X X X tftf tftf Z Z Z Z
ae u tartAI«0lAAi<O^0e^.-
lAAJlA ^^rtrtPAtart
oe u z
APPENDIX C
QUESTIONNAIRE FOR SURVEY
184
185
Texas Tech University Department ol Civil Engineering
May 23, 1985
Dear Sir:
I am a graduate student in the Department of Civil Engineering at Texas Tech University, working on my Ph.D. under the guidance of Dr. Warren K. Wray. Part of my dissertation requires that I evaluate the most efficient/economical way of determining the modulus of elasticity of soil. This will be based on statistical analyses that I will carry out on some of the commonly available testing procedures. To carry out these analyses, I am conducting a survey in order to gain the necessary reliable data. Each of the testing procedures listed on the enclosed form will be evaluated based on the following factors:
1. Availability 2. Reliability 3. Familiarity 4. Cost of Equipment 5. Cost of Test 6. Interpretation of Results 7. Ease of Performance
Each of these factors is to be individually weighted on a scale of 1-5 as indicated below.
Availability 1. Very likely that everybody will have 2. Likely that everybody will have 3. Not sure 4. Unlikely that everybody will have 5. Very unlikely that everybody will have
Reliability 1. Reliable 2. Fairly reliable 3. Not sure 4. Not very reliable 5. Unreliable
Familiarity ^ .,. . ^ , , 1. Very likely that everybody is familiar with the procedure Z. Likely that most persons are familiar with the procedure 3. Note sure ^ ^ 4. Likely that most persons are unfamiliar with the procedure 5! Very unlikely that everybody is familiar with the procedure
Bo« 4069/Lubbock, Texas 79409 (8061 742-3523
186
Pace 2
Cost of Equipment (from testing laboratory's viewpoint) 1. Very inexpensive 2. Inexpensive 3. Neither expensive nor inexpensive 4. Expensive 5. Very expensive
Cost of Test (as perceived by the client/user) 1. Very reasonable 2. Reasonable 3. Neither reasonable nor unreasonable 4. Unreasonable 5. Very unreasonable
Interpretation of Results 1. Very simple 2. Simple 3. Neither simple nor difficult 4. Difficult 5. Very difficult
Ease of Performance of Test 1. Very easy 2. Easy 3. Neither easy nor difficult 4. Difficult 5. Very d i f f i c u l t
If you are familiar with at least five of the testing procedures and are also familiar with at least five of the factors listed above, please fill out the enclosed table, using the indicated scale, by placing the appropriate number in the applicable box. The survey should take less than five minutes of your time. If you are unable to complete the survey, please return this letter and the uncompleted survey in the envelope provided. I would appreciate it if you could return your survey by June 15, 1985.
Thank you for your assistance,
Sincerely yours.
K.N. Gunalan
KNG/sh
Enclosure
187
CO re
di O c re E &-c S-O)
Q-
I
s- o Q - ' i -
OJ re +-> -l->
to J cu
CO h
o O
O OJ E
+-> Q. CO •!— O :
O CT UJ
I— +->
i L re re
I -M
CC JZt
re
I + J
re T -> ^
ca: re
CO
a;
c: o
re r— X re r— C 3
CO CO
cu s-Q . E O
C-)
(U
o CJ
o CO CO OJ s-a .
cz o I D C_J
re X re
CJ>
re a;
CO
cu
re
re • r-E= S-O
14-• r— r—
re C_)
CC CO C_3
O l — -c
• 1 - 0 S- • ! -
re 4-> <u re
CQ oc
s _ (U
4-> CU E <U s -:D CO CO OJ S-a.
O) c o
CJ>
XJ i -re
- D c re +-> CJO
c: 0
• r-
+-> re s_ +-> OJ c (U
Q_
I— O-c/
-M V)
a; h-
re (U
.£= uo
(U
re
APPENDIX D
VALUES OF DESIGN PARAMETERS DUE TO FORKLIFT
LOADING AT 15 LOCATIONS USED
IN QUASI-STATIC ANALYSIS
188
189
r>»
V£>
L O
^
CO
CM
<—1
c o • ~ •M • F —
U I O
o.
.00
o i r >
o o
• o
o o
C3
o o C 3 I T )
O o o i r >
o o
• o LT)
O o
• o i r >
• M I * -
« t
_ l
at
. c • ! - >
a t c 0)
_ l
.00
o ir>
o o
o L O
o o
o
o o o ir>
o o o* ir>
o •
o m
o o
• o L O
4-> H-
m
3
«» . c 4-> • o
•^ 3
.00
na-
o o
^
o o
• «*•
o o
^
o o «T
o o
• ^
o o
« ^
• c • r -
«» .c ta
l / l l / l 0) c .^ u .c 1—
.00
o ,—1
o o
o l -H
o o
o <—1
o o o
o o
• o 1—1
o o
• o . — 1
o o
• o 1—1
•)-> «•-
A
X <:
« . c • M • o
•^ 3
(U
l / l • r " e t
.00
o o 1—1
o o
o o ir> 1—1
o o
o o m 1—1
o o o o ir> 1 — •
o o o o m 1—1
o o
• o o l -H
O o
• o o t n 1—1
>» -M 'f—
u •^ + J - f -l / l </l I O C3.
(. 1 1 1 ta
u l I4_ U J
O ta
l / l 1 — 3 ••-
1 — O 3 CO
• o O <*-s : o
.00
i n
o o i n
O O
i n r«».
o O
i n
o o m r^
o o
• i n p ^
o o
• m p ^
« ot c
• r -• o ITS
o _ l
• ! ->
14- - i -• r - l / l 1 — Q .
^ i- • o u-
L i - Q .
«-H
o
CD
m «-H
o
m l - H
o
i n l - H
o
^ ^ • o
CO l - H
. o
c • r -
M
c o .^ ••-> u OJ
r-> «•-01 o
E 3
_E X 10
z :
(X) o o
o
o
CO o o
00 o o
ao o o
1 ^
o •
o
V O
o •
o
. f— c n j T -
•^ • M « C X
o V O
CO
«a-
VO
i n
CO VO
i n
^ m m
CTt
r^ . vn
i n CO
• m
ii»-^
<u <a^ S- E 01 <
»•-u- • • 1 - c o o
•^ e + j 3 U E 01
X « ^ >0 OJ
s: o
1
o l - H
X
_ X IO
E f —
• — .
< -
1 X
c •^ i n lA 01 s.
• ! ->
</) E 3
E •r—
X (O
CT> i n
CSJ
VO CO
CO
m m l -H
^ m
l -H i-rt
V O
^ i n 1—1 1—1
VO CVJ
. n l -i—1 i-rt
VO
r^ . m
l-H 1—1
X
o^-~ . " c
c ••-o
. 1 - cr ••-> VJ1
u ^ . OJ lA
i. .o • ^ 1 ^
S : Q ^ - '
t r
l -H O r - l
CO 1—1
o l - H
CM VO
^ at
VO
i n r^ CSJ at
1 — •
CO
. t—l
CO
r^ r*
• r>x CO
1
>> c
*r—
lA lA > , OJ D ' - x i -
4-> « C IJO C r -
O E ••- O-3 • M vn
E O - ^ •r- 01 lA X L . ^ fO • • - r—
Z Q > - '
c • r "
• ) - >
C 0 )
£ o :£
E 3
E • p "
X (O
z :
i n CVJ
• CVJ l-H CVJ
m CVJ
l-H CO CV)
CT^ O
CO o CO
CO
^ vn o CO
0 0 CO
r^ o CO
CO VO
• t r
o CO
00 VO
• 00 o CO
k z:
-•— « •
c c o •<-
• r - - ^ 4 J i n
u -o <U •— &. 1
•r— .
o c 1 ' ^
X ^ ^
o m
CVJ
<—1 CO
CVJ
l-H CO
t r
CVJ
CO ^ H
i n o CVI
CVI CO
r«x t r CVJ
CVJ CO
VO l -H CVJ
VO o
• t r CO CVJ
c • p »
>, • M s : C '-'• (U . .
E c c o o •>-
: E •-- ^ +-> in
E u X I 3 0 ) 1 — E S- 1
• r - ' ^ .
X o c IO 1 -r-
S. > , — '
OJ
v.>
m
t r
CVJ i n
VO
CVJ 00
m
CO CO
i n
l - H
0 0
i n
CO 0 0
i n
VO O
• VO
X i - > o
u.
s. (O OJ
J = t o
E
M
c o
• 1 —
• » - >
o < U ^ - N i . •
• r - C
3 a •<-E
'f—
X l O
Z
1 ^ * ^
X m . Q
c .— • ^ ^ i — ^
CT^ O
t n 1
VO i n
i n
t r i n
1
i n
CO
00 CO
^ 1
t r VO
CO
o CVJ
• m 1
OJ
o > , S- 3 » O
U - •>
c i- o fO • • -OJ 4 ^
.c u 1/1 <u •—»
i . •
E ••- = 3 Q • • -E 1 ^ ~
• 1 - > , m
X . o <o C p -
Z •!- >_-
190
^ T - H
CO l - H
CVJ . - 4
l - H
1—1
o l - H
at
00
Position
o o
• o m
o o
• o in
o o
• o m
o o
• o m
o o
• o i n
o o o m
o o
. o m
4 J
<*-
Length,
L,
o o
• o m
o o
• o m
o o
• o tn
o o
• o m
o o
• o m
o » o
m
o o o m
<4-
Width,
W,
o o
• ^
o o
• «3-
O O
• ^•
O O
• t r
o o
• t r
o o t r
o o
^
c
1 .
f
_
ickn
ess
1 -
o o
• o 1—1
o o
• o l - H
o o
• o l - H
o o
• o l - H
o o
• o l - H
o o
• o l - H
o o
• o t - l
4 J 14-
«
- c ^
J-i
sle
Widi
<:
o o
• o
150
o o
• o o m r—1
o o
• o
150
o o
• o o in 1—1
o o
• o o i n l-H
o o
• o
150
o o
• o o m l -H
>. 4->
.^ • r -•«-> - t -l / l </l lO C L
1 1 1 »
t/1 U— LiJ
dulus
01
Soil, 1
o<*-z o
o o
• m r^
o o
• m p ^
o o
• m r^
o o
• in 1 ^
o o
• in i»«.
o o
• m p ^
o o
• m p>»
* O l c
• r " •o •o o
1
rkli
ft 1
. ps
i
cu Q.
P x l - H
. o
r^ l - H
. o
to l - H
* o
i n l - H
. o
VO l - H
* o
VO 1 - ^
. o
VO l - H
. o
c • '
» c o
•^ •«->
u 0)
I t -01
ximum Di
<o z :
o l - H
. o
o l - H
. o
o^ o
• o
CO o
• o
CT1
o •
o
at o
• o
at o
• o
• r - C (O • ! -
• • J » C X
V O CVI
• t r
p ^ p ^
• ^
p>x CO
• VO
i n CVI
• t r
o% CVJ
• m
CVJ CVI
• i n
m l - H
. m
^—.^ 01 <o ^ i- E (U <
v»-
• 1 - c
ximum
D fl
ecti
oi
•O OJ
1
o t—l
X
X IO
<
1 X
c • p "
m m 01
•(->
ximum
S
0 CVi
• tn p ^
CO
at m
CVJ CT1
t r CO
• 0 CO
CO l - H
. CO 0 0
t r VO
• CT1 CO
CVJ
in • t r
r^
i»» CVJ
• l - H
CT1
X D ' - ~
« C
rect
i on
bs/sq
i
(O - 1 - >—
2: o —
1
>. c •^ 1/1
m 01 i-
*J
ximum
S
0 p ^
. CO 0 l -H
0 1—1
• CT1
0 l-H
i n p ^
• CO 0 1—1
0 i n
. l - H
l-H l-H
0 0
at . l - H
0 l -H
CT1 CO
. t — l
0 l-H
i n CO
• l - H
0 1—1
> 1 0 - — «
• c
rect
ion
bs/s
q i
10 - 1 - 1 —
CO in
. 0 0 CVI
0 CO P- . •a-CVJ
CO i n
• i n l-H CVi
i n 1—t
. tn CO CVI
CVI 0
• a> CO CVi
l - H
r». . CO
at t—l
0 t r
• CO
t r CVJ
c •^ X + j s : c —» E E C 0 0 - r -
ximum
M Di
rect
i n.
-lbs
/
(O 1 • » -2: x - ^
VO CO
CT1 0 0 CVI
^ CT1
0 at CVJ
0 0
0 0 1 CVJ
CVI CO
. r«. a\ CVI
t r
at . I - H
CVJ
at CO
• 0
CVI
0 VO
• l - H
CVI
c *^ , _ > i •!-> £ C ' — •
E c c 0 0 •<-
ximum
M Di
rect
i n.
-lbs
/
fO 1 •<-
CVJ CVI
CVI
at VO
CVJ
Ol
^ ^
CTi t r
• VO
0 p*.
. Csl
VO CVI
. CVJ
cn VO
• CVJ
01 CJ X i . 3 » 0
ii- •>
c i . 0 (O • • -01 *->
.c u
ixim
um S
I x-Dire
bs/i
n.)
2: •,->—
at at
i n 1
CT1 0 0
i n 1
CO l - H
a
VO 1
VO CVJ
• VO 1
^ 0
• m
1 - ^
1 - ^
• i n
«r 0
• m
OJ
1 - > 0
IL. *>
c i- 0 (O ••— 01 *•>
.c u
Maximum
S in
y-Dire
(lbs
/in.
)
191
VO
m
^
CO
CVJ
l - H
t n l - H
Position
o o
• o i n
o o
• o m
o o
• o i n
o o
• o i n
o o
• o t n
o o
* o m
o o o i n
Length,
L, ft
o o
• o m
o o
• o m
o o
• o m
o o
• o i n
o o
» o i n
o • o
i n
o o o i n
Width,
W, ft
o o
• <*
o o
• ^
o o
• t r
o o
• t r
o o
• ^
o o
• ^
o o ^
c • 1 —
Thickness, h
o o
• o l - H
o o
• o l - H
o o
• o l - H
o o
• o l - H
o o
• o l - H
o o
• o l - H
o o
• o 1—1
•«•>
<4-
*
Aisle
Width,
o o
• o
150
o o
• o
150
o o
• o o m l -H
o o
• o
150
o o
• o o t n 1—1
o o
• o o i n »-i
o o o o t n l -H
>»
icit
4 J • • -m m <a Q .
Modulus of E
of So
il,
E ,
CO t - H
• 0 0 p^ t - H
CO »—1
. CO p». l -H
CO l - H
. 0 0 p^ l -H
CO 1—1
. CO p^ l -H
CO l - H
. 0 0 p -l -H
CO l - H
. 0 0 p". r-l
O o t n r»»
A 6uip
r^ CVi
• o
00 CVi
• o
0 0 CVJ
• o
p » CVi
• o
p^ CVi
• o
VO CVI
• o
r -l - H
o
• c
• t "
on.
ecti
Forklift
Loai
Pf. psi
Maximum
Defl
at t—l
• o
o CVi
• o
o CVi
• o
o CVI
• o
o Csi
• o
CO 1—t
. o
1—1 l - H
o
•
tial
. in
i n CO
• l - H
l - H
CSi 0 0
• o 1—1
t n VO
• CO l - H
t - H
o . l - H
I - H
t o i n
• ^ t - H
VO CT1
• O l - H
o> o CO
C X - ^ Ol IO ^ S- E 1 OJ <3 O
Maximum
Diff
De
flec
tion
,
l -H X
X IO
<
1 X
c
<n m
o ^ a
o CO l -H
at CO
• 0 0 0 0 CVI
l - H
CO
• CSi t r CO
p". CSI
• CO CO CVi
0 0 CVi
• CVi t r CO
t r l - H
. CO at CVi
CSJ t - H
l - H
at
X
Maximum
Stre
Di
rect
ion, o
(Ibs
/sq in.)
1
c •r—
in l/l
^ at
« CSJ p». CVJ
t r CO
• CTI CVi l -H
CT1 CTi
• t r t o CVI
00 l - H
. o CO l -H
CT> P«.
. i n t o CVI
m f ^
• CO CO l -H
CO l - H
(Jl
o l -H
>>
Maximum
Stre
Dire
ctio
n,
a (I
bs/s
q in.)
CO p«»
. p*. t r CO
*r o CTI VO
CO CO
• CVI l -H at
CO p^
• 0 0 VO p^
VO p^
. CSJ t-l O l
l - H
p *
• l - H
CO pv.
0 0 at
CVI
CVI
c
X • u a i :
Maximum
Mome
x-D
irect
ion
, (i
n.-l
bs/i
n.
CO 0 0
p^ CVJ
CO CVI
a
VO t r CO
i n VO
• t o o p »
m l - H
. P~ t r CO
1— P-.
. 0 0
o
VO VO
• VO i n CO
CVJ
o t - H
at CVJ
c
Maximum
Mome
y-Direction,
(in.
-lbs
/in.
VO l - H
. CO l - H
CO CO
t r l - H
t r o
• 00 l - H
i n 0 0
• ^ l - H
t r
o • CO
l - H
CO CVJ
• VO f - H
CTI t o
CVJ
01 U X S- 3»
o cu •>
c i- o
Maximum
Shea
in x-Directi
(lbs
/in.
)
p>» ^ «a-l - H
p.. I - H
. i n 1
CTI •
0 0 l - H
^• i n
• i n 1
<T> 0 0
• CO l - H
i n VO
" i n 1
CTI CO
i n 1
OJ o > ,
o LU •
c ( . o
Maximum
Shea
in
y-Directi
(lbs
/in.
)
192
CO t — l
CSJ I - H
l - H
1—1
o I - H
at
00
r«>.
Position
o o
• o in
o o
• o m
o o
• o m
o o
• o tn
o o o in
o o o tn
o o
50.
Length,
L, ft
o o
• o in
o o
• o in
o o
• o tn
o o
• o in
o o
• o in
o o in
o O
50.
Width,
W,
ft
o o
• ^
o o
• "*
o o
• t r
o o
• ^
o o
• t r
o o
• ^•
o o t f
c
Thickness,
h o o
• o l - H
o o
• o l - H
o o
• o l - H
o o
• o 1—1
o o
• o 1—1
o o
• o I - H
o o
t - l
«4-
• k
Aisle
Width,
o o
• o o m I-H
o o
* o o m l -H
O o
• o
150
o o
• o o tn l -H
O o
• o o . in <-<
o o
• o o m l -H
o o
1500.
> i
icit
m m IO o.
Modulus
of E
of Soil,
E ,
CO l - H
. CO p«. t - H
CO l - H
« 00 PN. t -H
CO I—1
. 00 p^ l -H
CO t - H
. 00 1—1
CO l - H
. CO p-» I-H
CO l - H
. CO I - H
CO l - H
00 p^ I-H
M
ding
CTI CVJ
• o
CTI CVI
• o
CO Csl
• o
at CSI
• o
O l CVI
• o
00 CVi
• o
00 CVi
• o
c • -
on.
ecti
Forklift
Loa
Pf.
psi
Maximum
Defl
»-l CVi
• o
l - H
CSJ •
o
o Csi
• o
I - H
CSJ •
o
l - H
CVJ •
o
l - H
CVI •
o
t - H
CVI
o
• 1— c IO • ! -
•r-•u> «
CTI tn
• o l - H
CO O l
• t r l - H
cn o
• o t - H
t - H
^ • CSJ
l - H
CO i n
• CO l - H
CTI Csl
• CSi t - H
p>. CO
t r t—l
C X — » OJ IO « r s- ^ ' OJ <J o
Maximum
Diff
Deflection,
l -H
X
X
<o E
X
c
in 1/1
o p«.
• o CO t -H
t - H
CVI •
CO VO CVi
CO l - H
. in CO t-l
at to
• VO CVi I—1
CO i n
• CTI i n CVi
CTI p~
• p«« CSI l -H
r»» «r
260.
X
Maximum
Stre
Direction,
o (I
bs/s
q in.)
p». VO
« CSi CTI CSJ
CVi 00 CO m CO
CTI VO
• CVJ o CO
o CSJ
• p». VO CSi
i n VO
• o CVi CO
CVJ l - H
. p^ VO CVJ
CO in
320.
>> c
•t—
l/l 1/1 > ,
Maximum
Stre
Direction,
o (I
bs/s
q in.)
^ in CO t r CO
CO 00 I - H
o 1 ^
to CO
• o VO CO
<r 00
. p» CO CO
o CVI
• CVI CTI VO
p^ r»»
• o t r CO
CO m
694.
c X
+f 2 :
Maximum
Mome
x-Direction,
(in.-lbs/in.
m ^
0 00
CVJ tn
« CO
0 1
VO t - l
. p^ 0 CO
CO tn
• Csl I-H P^
VO 0
• i n i n 0 0
Csl CO
• CVJ l - H
00 CO
854
c
* . 2 : ^ c - ^
Maximum
Mome
y-Direction,
(in.-lbs/in.
CVJ CO
i n
t - H
in a
at 1
CVJ CVI
• CO l - H
VO l - H
. i n
CO CO
• 0 I - l
CJI CO
" i n
t r 0
CTI
OJ 0 X
0 LU -
c s- 0
Maximum
Shea
in x
-Directi
(lbs/in.)
CO p-»
. in 1—1
1
CTI 0
a
CJt l -H
1
tn <j>
a
t o I-H
1
r». 0
. CO l -H
1
t r in
. tn l -H
1
00 0
* CO
1
t r
in I-H
1
0) 0 > 1
LU •> c
i~ 0
Maximum
Shea
in y-Directi
(lbs/in.)
193
i n
t r
CO
CVi
I - H
i n t — t
^ I -H
tion
Po
si
o o
• o m
o o
• o i n
o o
• o t n
o o o t n
o o
a
O t n
o o
50.
o o
50.
L, ft
th.
Leng
o o
• o m
o o
• o t n
o o a
O i n
o o
• o i n
o O
a
O i n
o
50.
o o
50.
* 3
m
Widt
o o
• ^
o o
• t r
o o a
<a-
o o ^
o o
a
^
o o «*
o o ^
s, h,
in
kn
es
Thic
o o
• i n t - H
O o
. i n t - H
o o
• i n l - H
O o
« t n l - H
o o
a
m 1—1
o o
10.
o o
• o t - H
4-> t»-
dth,
A
3
OJ
Aisl
o o
• o o m I-H
O o
« o
150
o o a
O
150
o o a
O O m l -H
o o
a
O O m l -H
o o
1500.
o o
1500.
>,
4 J •«-l/l m lO o .
1 1 1 . .
I/I I f - UJ
o
lus
oil,
Modu
of S
o o
• i n r
O O
• m r
o O
. i n i*»
o o
• t n p>.
o o
a
i n p^
CO l - H
178.
CO t-l
0 0 p -I-H
«
Load
ing
lift
ps
i
i n l - H
. o
t n l - H
. o
t n l - H
. o
^ t - l
. o
CO I - H
a
o
o CO
o
o CO
o
^ c
. t —
« c o
Defl
ecti
mu
m
J- - X O *4- IO
Lu Q . Z
CTI o a
O
CO o
a
O
CO o a
O
p". o a
O
ps. O
• O
CVI CVJ
o
CVI CVi
o
• t— c lO '^
•t—
t r o a
i n
CTI CTI
a
^
t - H
CTI
• t r
«r p^
. t n
t - H
CO
• «r
0 0 VO
oi
CO CO
CO t -H
C X - - ^ OJ IO ^
^ s '^ 0) < o
14- ^ 14- •> X • 1 - c ^
o o
mum
ecti
Ma
xi
Defl
lO
<"
VO VO
• t n p«.
CTI O
a
CO p>«.
CO VO
. i n p».
p>» CVJ
• CO
r
t r CVI
• ^ p~
CVI i n
129,
o t—l
292
1 X
c
Maximum
Stress
i Di
rect
ion,
°
(Ibs
/sq
in.)
^
CO CVJ
a
CO CO
r p *
• t r t o
t o t n
• t r CO
CJI VO
• CJI to
r-» ^
• CJt p -
CO i n
292
.87
353
1
>> c
<A 1/1 ^ > » 01 o -—• c • ! - > » £ : 1/1 C t -o E •<- CT 3 •»-) m E o-- .
•I— OJ l/l X s- . a l O • • - t —
S. Q — '
p * r
. t - H
O CVJ
l - H
CT> a
t r CTI l -H
CO t o
. I - H
o CVi
CO CO
. i n as l -H
CO CTI
• P^ CTI l -H
o ^
345
.92
698
c
Moment
i ti
on,
M s/in.)
^
imum
ir
ec
.-lb
X o c IO 1 • < -
Z X w
i n CJI
. l - H
CVi CVi
CVJ p *
. CVi 1 ^ l -H
CTI " T
. t n CVI CVi
CO 00
. t n 0 0
. -H
CTI
• t - H
I-H CVJ
0 0
o
780
.65
943
c
OJ ' ' E c = 0 0 •<-
2 : — ^
imum
ir
ec
.-lb
X 0 c 10 1 -t-
z > 1 - ^
CJI to
• CVI
p». t o
. CVI
CTI VO
• CVI
i n VO
• CVI
VO VO
' CVJ
.07
i n
.20
0 l -H
OJ U X
Shear
Fon
rect
ion,
V
.)
imum
x-
Di
s/in
X J3 10 C 1—
2 : - r - - ^
1— 0
• H T
CSJ CSJ
. CO 1
CO CJt
• CO 1
CO I - H
. CO
t — l
r s
^ 1
p~
..
-15
.90
CO t -H
1
OJ
1 Shear
F(
rect
ion,
.)
imum
y-
Di
s/in
X . a 10 c >—
2 : - I - - ^
194
C V i
l - H
o l - H
at
00
p ^
t o
c o
Posi
ti
o o o i n
o o
• o i n
o o
• o t n
o o
• o i n
o o a
O i n
o o a
O m
o o o m
4 ^
•+-^
_ l
Length
o o o i n
o o
• o m
o o
• o m
o o
• o i n
o o
• o i n
o a
O i n
o o o m
4 - J t ^
3
^
Width
o o
• ^
o o
• ^
o o
• ^
o o
• ^
o o
• « •
o o a
t r
o o t r
, c
m
.c m
1 Thickness
o o m l - H
o o
• i n l - H
o o
• i n l - H
O o
• m l - H
O o
• m I -H
o o a
m l - H
O o
« t n l - H
H.J I4_
m
3 <c
^ ^J
• o
3
Aisle
O o
• o o in l - H
O o
• o 091
o o
• o
150
o o
• o
150
o o
• o o in l - H
o o
• o
150
o o
• o o tn t - H
>» 4-> • r -
o • r -4 J - t -
l / l l / l
(O ^
11 i * 1/1
I f - U J
o t .
m t— •^ •!—
Modu
li
of So
CO f*
CO p ^ f H
CO t - H
. 00
t - H
O o
• t n p ^
o o
. i n p>«
o o
• i n p ^
o o
• t n p ^
o o a
i n
p *
A
O l
c "O I O
o _ i
4-> 1 * - •<-• 1 - 1/1
Fork
l Pf.
P
p>» CSJ
o
V O CSJ
• o
t o I -H
. o
VO l - H
. o
VO l - H
. o
i n t - l
. o
t o l - H
. o
c •^
«k
c o
• 1 —
4 J
u 0)
14-OJ
o E 3
Maxi
mi
o i t - H
o
CO l - H
• o
o t - H
. o
CTI
o • o
CTI
o • o
CO o
« o
at o
• o
• 1 — c IO T -
+ J «
C X
CVJ CO
t r l - H
CO CO
a
o I - H
VO t r
• t r
C O CO
• t r
CO t r
• ^
CO CTI
• i n
r» CJI
• i n
^—^ O J 1 0 < r
S- E OJ <
1 4 -
t 4 - " • I - C
o o E -^ 3 U
Maxim
Defle
1
o r - H
X - -
X IO E
>
1 X
c '^ m m OJ
H - l
E 3
CO VO
C3 CO CVJ
i n I - H
. i n
o CVI
i n
CO
• C O
0 0
t r CO
. CVI
(^
00 o
• o CTI
l - H
f ^
. P ^ P«.
VO to
• l - H
CTI
X D ^ ~
« c o
• r - CT 4 - > m
Maxim
Direc
(lbs
/
I - H
tn
V O C V i
CVJ
t n o
• t n o l - H
i n
CTI a
0 0
C O
i n
o • 00
00
p « .
00 •
0 0
G O
i n
o •
0 0
C O
t n
p »
• C V I C V i l - H
1
>> c
• t —
l / l
• «>» OJ o ^—*
H-> " C t / 1 c • . -
o E -r- CT 3 H J l / l
Maxim
Direc
(lbs
/
CO l - H
m l - H
to
m o p ^
t r i n
o to
a
t n CO CVI
o CJI
. CVJ CT^ I - H
o CVI
• o CVJ
CVJ CVJ
. p ~ .
o CVJ
f l
t r
• t r
t r CVI
c •^ X
+-»£ C ' — OJ t l .
E c c o o ••-
2 : ••- - ^ H ^ m
E CJ - O
3 OJ t —
Maxim
x-Dir
(in.
-
^ o t r o VO
CO l - H
. o CO CVJ
o CVJ
a
p>«
C O CVJ
CTI P ~
. ^ CO CVJ
00 CJI
• to CO CVI
o 00
• t r CO CVJ
t r CO
• p * C V I
C O
c • t —
>» • u > "S.
c --^ OJ •» .
E c c o o •>-
2: ••- — 4 -> m
E u .ca 3 0 ) I —
Maxim
y-Dir
(in.
-
p ^
VO
0 0
CTI P *
p>«
CTI t n
. CVI
0
. CVI
<J1 i n
• CVJ
< j i CSJ
. t r
CVJ
r^ • t o
O J 0 X S - 5 >
0 C u •
c L. 0 1 0 f OJ H->
.c 0 t / 1 QJ ^
1;=; '= 3 Q - 1 -
Maxim
in X-
(Ibs
/
0 0
VO t - l
i n
t n a
i n
1
CO CVJ
a
t r 1
to CO
. t r
1
CO CVI
• t r
1
VO i n
. ^
00 p ~
• VO 1
OJ 0 > , 4 . ^ 0
L U -C
L- 0 ro •< -01 H->
. S U 1/1 QJ - — •
i . • E — C
3 Q - ^
Maxi
IT
in y-
(Ibs
/
195
at
00
p>.
t o
m
^
CO
c o
Posi
ti
o o
• o m
o o
• o m
o o
• o i n
o o
• o t n
o o a
O m
o o o t n
o o o m
4-> <4-
Length,
L,
o o
• o i n
o o
• o m
o o
• o i n
o o
• o i n
o o a
o m
o o i n
o o o m
t 4 -
3
Width:
O o
• ^
o o
• t r
o o
• t r
o o
• ^
o o a
t r
o o ^
o o t r
c • t ^
I .
- C
-
Thickness
o o
• m l - H
O o
* t n l - H
o o
• i n l - H
O o
• t n t - H
O o a
i n f*
o o a
m l - H
O o
• i n t - H
^J «4-
• 1
3 « t
J ^
Widi
Aisle
o o
• o 150
o o
• o o m l -H
O o
• o
150
o o
a
O
150
o o
• o
150
o o
a
O O i n l-H
O o
a
O
150
>» 4.>
CJ . r -4-J • ! -I / I t /1 fO CL
11 1 « .
t/1 14— L U O
Modu
li
of So
CO t - H
. 00 p ^ t -H
CO I-H
. CO
I—1
CO t - H
. CO p>» l-H
CO l - H
. CO p« . l -H
CO l - H
. CO 1 ^ I-H
CO t - H
. CO p -l -H
CO l - H
. 00 p ^ t - l
• k
O l c
•^ "O IO
o 1
14- " -'t— l / l f— ca.
I . » O <4-
Lu ca.
CTI CVI
• o
00 CSJ
• o
CO CVi
a
o
VO CO
• o
CO CVJ
• o
.00 CSJ
a
o
p * CSJ
• o
^ c
• r *
«k
c o
• r -
••-> (J 0)
14-OJ o E 3
Maxi
mi
l - H
CSi a
O
00 CSJ
• o
l - H
CVI
« o
CO CVi
• o
o Csi
• o
o CVI
a
o
o CVJ
• o
• 1— c IO -r-
• f j • C X
CTI t — l
• CO t — l
o t r
a
O t - H
O 00
a
t r l - H
O l t r
a
p«» t - H
CSJ 00
a
o l - H
C O
p *
. CVJ I - H
p^ CO
a
O l - H
< — . OJ IO ^ t- ^ E OJ <
• 4 -Vf- « • t - c
um D
ctio
i Ma
ximi
De
fies
1 o l-H X
max
'(l/v)
1 X
c •^ m m OJ
H-> t / 1
E 3
l - H
O a
t o t r CVI
CVJ CO
• 00 CVJ t -H
CVJ CTI
a
VO t r CVJ
CTI 00
a
CO CTI CVI
i n i n
• VO
o CVJ
o f ^
. o CO CVI
VO t n
• t o
o CVI
^x o.-.. " c C - t -
o •r- CT H-> m
Maxim
Direc
(lbs
/
o CTI
. t—l
at Csi
CTI
^ • CO
t r CVI
CVI CO
. I - H
CTI CVi
CTI P^
. o o t r
o p«.
• i n CVI l-H
CO CTI
• t n CVI CVi
o p > .
* V O
CVi t - 4
1 >» c
• ^
m <A > , 0) D ' - ^
•»-> « C
um S
tion
sq i
Maxim
Direc
(lbs
/
CVi o VO i n t o
00 l - H
. C S i
CO
«r «o-
« CO m VO
o p^
. CO CO
CTI 1 ^
. O i n i n
O CSJ
. i n l-H VO
CO 00
• o i n i n
c •^ X ••-> s C '-^ OJ t» •
E c c o o ••-
um M
ecti
lbs/
Maxim
x-Di
r (i
n.-
at CO
CO
p *
^ VO
a
CVJ t o VO
o CVJ
• CO
1 ^
CO p^
. CO VO
o I—1
cn l - H
. i n CO CO
CO t r
• CVJ
o VO
00 00
• p -CO CO
c • p -
^ t c - * * H-> Z C ' - ^ OJ *» •
E c c o o ••-
lum M
ecti
lb
s/
Maxim
y-Dir
(in.
-
i n I - H
. CTI
VO t o
a
t r
i n CO
. r^ l - H
^ O
• CO CVI
CO CVJ
. p ^
CO VO
• CO
^ (^
' p^
01 CJ X
o Cu •> c
C- o IO - i -OJ ••->
.£: u
lum S
Dire
in
.)
Maxim
in X-
(Ibs
/
so r*»
. <r I -H
1
t r r>«.
. CVJ l-H
1
VO CTI
a
t r l - H
CO CTI
• O CVI
1
t n <J>
• ^ 1
CO
o • t o
l - H
O l CO
• •
t n 1
OJ
o Lu ^ c
c o IO • ! -OJ H->
. C CJ
lum S
Dire
in.)
Maxim
in y-
(Ibs
/
196
o t -H
c o • . •4->
l / l
o Q .
O o
a
O i n
H-> I4-
t .
_ J
t l
J C 4-> 0 1 c 01
- J
0 0
• 0 i n
H-> I f -
t .
3
«» . c 4-> • 0 •r—
3
0 0
a
^
• c
t .
.c M
in l / l 01 c .^ (J
x: 1—
0 0
• m t -H
H-» t f -
« i
3 <C
t k
.s H-> "O
3 OJ
m •t—
««
0 0
• 0
150
>> H-> • 1 —
CJ
•»-> - t -m m 10 a.
UJ •• in
14- LU • ca
t .
in r— 3 -t-
1— 0 3 CO
• 0 0 14-s. 0
CO t -H
. 00 p^
• k
0 1 c
• 0 10 0
_ J
H-> >4- - t -•r- l/l r— Q .
.^ t . -0 <4-
c u a .
CTI CSJ
• 0
c • *
«k
C 0
• r -4-» U OJ
r ^ 14-QJ
0
E 3
_E X 10
2 :
l -H CVI
• 0
. 1— c 10 • ! -
• t —
H-> » C X
i n CO
• 0
^—^ OJ 10 t r s- _ E OJ <
<•-t4- » • 1 - C o 0
•^ E •>-> 3 0 E <U
•r— r— X 14-10 OJ 2: a
1 0 l - H
X N _ ^
X 10
E r—
^•^ < *—'
1 X
c
•^ l / l m OJ i-
H-> t/O
E 3 E
*r^ X 10
m 0
. p>. CVi l-H
X 0 ' •"*
" c c •<-0
• I - CT 4-> m 0 ""^ OJ in i- . 0
• ^ ^ —
Z Q « . ^
1
>> c •^ m m OJ s-4-)
t / l
E 3 E
• r -X (O
CVJ i n
• CO t r CM
> 1 D •--»
» C C • ! -0
•<- CT H-> l/l 0 ^ « . OJ m i- . 0
• ^ r^ Z Q ^ - '
c • t —
•U> c OJ E 0 2: E 3 E •^
I-H 0 0
• 0 0 CO CO
X 2 :
"* » c c
0 ••-•^ ^^ 4-> m u . 0 OJ t— t - 1
• - . X c a c 10
z 1 •»-x^--
c •^ •-> c OJ E 0
2: E 3 E •^
CSI r»»
. CM t o VO
__>. S. "^^
« c c 0 •<-
't— ^ * ^
•*-> tn CJ . a OJ 1— S - 1
• 1 — .
X c a c: 10
Z 1 • ! -
>>~-'
OJ u
CM t r
a
•a-
X
;- > 0 Lu
L (O OJ
.c t /1
E 3 E •^ X (O Z
m
c 0
•^ H-> U 0 1 ^ — c . • 1 - c
0 ••-1 " "
X in . O
c <— "~^
CO 1—
. CM l - H
1
OJ 0 > , 5- > 0
LU t> C
s- 0 10 • ! -OJ H->
. c u 1/1 OJ ' • ^
c E ••- c 3 Q ••-E 1 •>--
• 1 - > , in X X ) 10 C 1—
: E •>- —-
197
p »
VO
m
^
CO
CM
t - H
tion
Po
si
o o
• o t n
o o
• o i n
o o
• o m
o o
a
o i n
o o o m
o o
50.
o o
50.
L, ft
th.
Leng
o o
• o i n
o o
• o m
o o
• o i n
o o
a
O i n
o o o i n
o
50.
o o
50.
•f-> •*-
3 *
Widt
o o
• ^
o o
• t r
o o
• ^
o o
a
t r
o o
^
o o t r
o o
•
s, h,
in
knes
Thic
o o
• o l - H
o o
• o l - H
o o
• o l - H
o o
a
o l - H
o o
•
o l - H
o o
10.
o o o l -H
dth,
A^,
3
OJ
Aisl
o o
• o
150
o o
• o 091
o o
• o
150
o o
a
o
150
o o
a
O
150
o o
1500.
o o
1500.
> i
icit
of Elast
E . psi
m t — 3 ' t -
1— o
Modu
of S
o o
• t n r^
O O
• i n f»»
o o
a
t n p~
o o
a
i n
(^
o o
a
i n p>«
o o
75.
o o
75.
«»
Loading
H-i 14- - r -• I - i n I — Q .
o o
• CO
o o
• 0 0
o o
a
0 0
o o
• CO
o o
• 0 0
o o CO
o o CO
• t —
l / l
t o CTI
• O
t r CTI
• O
P^ CTI
a
o
CTI CTI
a
O
CO CTI
a
o
^ CTI
O
l -H
at o
c • t —
a. » c in o
ladi
ng,
p
_ i
j ^ t J ^ - to O <4- •»->
Lu O . 1/1
Deflecti
mum
Maxi
CO i n
. o
t n i n
a
O
CO t n
• o
o VO
a
o
i n t n
• o
t n t n
o
CO
m O
•
tial
,
in
CO CM
a
i n CM
i n t o
a
CO CM
VO CO
a
VO CM
CO 0 0
a
VO CM
0 0 VO
• t r CM
i n CM
25.
CO l -H
t n CM
C X — OJ IO ^ s- E 1 0) < o
<4- "* Vf- • X •r- C — '
o o E •»-> 3 U E 01
Maxi
De
fl
l O
E
<3
1 X
c
stress
i mu
m Ma
xi
o i n
. m t - l CM
t r CTI
a
CO tn t-t
i n 00
. I - H
l - H
o p N .
. VO 0 0 I-H
CJI CTI
• CTI CO t -H
CTI t ^
VO l -H
O CM
CO CO l -H
Direction,
o (I
bs/s
q in.)''
CO r^
. t r m CO
t r r»«.
. r^ in CO
o p^
. CO t o CO
i n o
• CM CM t r
I - H
CO
• CO CO CM
CO CM
406.
CO CO
450
> i
c
tn tn > , OJ D - - ^ i .
•4-> •> C t /1 c • • -
O
Maximum
Dire
cti
(Ibs
/sq
r^ to
a
t r p^ i n
t r CO
a
CO CM t r
t n CVI
. CO i n t r
0 0 0 0
. p~ CJI
o CO
• CO
CO
CM t o
-452.
.54
488
c
Moment
i tion,
M s/in.)
""
imum
ir
ec
.-lb
X a c l O 1 -t-
z x ^ -
c
Moment
i im
um
Max
CM
^ • CO
m CVI t -H
1
i n CTI
a
CO CTI l -H l -H
1
VO CO
• CJI VO
CO CO
. r«» CO CVI l -H
1
i n I - H
• CM CM t o
CJI
-111
2.
.89
1200
>>
« • c c o —
* j m
irec
.-
lb
o c 1 - I -
i n to
. I - H
l -H 1
o •a-
• t r l - H
CTI O
. I - H
l -H 1
P^ CO
. CO t -H
1
l - H
t r
• O l 1
CM VO
t r
1
.92
CTI 1
Shea
r Fo
rce
rection, V
imum
x-
Di
s/in
X j a lO C 1 —
S - I - - - -
VO CO
• t o CO
CM o
• t o CO
1
CM i n
. CTI CO
cn CO
' t n CO
1
p~
^ " CTI
1
I-H
o CTI
.69
-26
Shear
Forc
e rection,
V im
um
y-Di
s/
in
X JU IO C r—
j r — —
198
"a-f H
CO
CM l -H
t - H
f H
O f H
CTI
CO
c o
*J
t/1 o
a .
.00
o m
o o
• o tn
o o
• o in
o o
• o m
o o
• o in
•
o o
• o tn
o o
• o m
4-> i«_
1 .
_ i
»> £ * j
O l c OJ
- J
.00
o in
o o
d in
o o o tn
o o
• o m
o o
• o tn
o •
o tn
o o
• o m
4-> v»-
« 3
» . C 4-> "O
3
O O
t r
o o
^
o o •a-
o o
• ^ •
o o
• ^
o o
• ^
o o
• «•
. c .^
t l
. c t .
l / l t/1 OJ c .^ u .c t—
.00
o t -H
o o
d f H
O
o o t . ^
o o
• o f H
o o
•
o l - H
o o
• o l - H
o o
« o f H
4-> 14-
t k
3 <t
m
.c 4.J • o
3
OJ
l / l
i <
> 1 - M
u •iJ m IO
L U
Vf-O
m 3
.00
0 0 tn f H
0 0
c> 0 in t . ^
0 0
C J 0 m l -H
0 0
• 0 0 in 1—1
0 0
• 0 0 tn I—1
0 0
• 0 0 tn I-H
0 0
• 0 0 in I-H
.^ m a .
m
m L U
t .
p ^
.^ 0
3 CO • o O 14-2: 0
.00
in p ^
0 0 tn p>.
0 0
tn p ^
0 0
• tn p ^
0 0
• in r^
0 0
• tn p -
0 0
• tn r^
* O i c
• 0 • 0 0
_ J
H-> V » - 1 -• 1 - m •— Q .
.^ i . ' 0 "4-
U . Q .
.00
CO
0 0
0 0
0 0
0 0
0 0
• CO
0 0
a
0 0
0 0
• CO
0 0
• CO
l / l 0 .
1 .
m O L
* 0 1
c •^ - 0 10 0
_ l
.^ u 10
4-> 0 0
t -H 0
l - H
P ^ 0 1
d
0 0 0 1
0
in CTI
• 0
f H
0 . a
^ - 4
0 0
ov • 0
i n CTI
• 0
c •r—
* c 0
. 1 —
H-> U OJ
p ^
14-OJ
0
E 3
E •--X
<o 2 :
f —
10 t—
•4->
c QJ i . OJ
14-Vf-. p —
0
E 3
E t—
CM
to 0
CTI
m 0
CTI in 0
to m
• 0
CM VO
a
0
0 to
•
0
r>» tn
• 0
. c .^
t l
X
CM - H
CJI CM
CM CO
0 0 CM
1 — •
t o
1 0 CM
^ 0
a
^ CM
CO
r»« . CM
CM
l - H
CO
• VO CM
CO
in • VO
CM
.—^ ro t r E
<3
«k
C 0
• -H->
u OJ
— X t f -10 OJ
s. a
1 0 — H
X
_ X (O
^ f.-
^^ <3
—
1 X
c • -<A lA 0 1 i .
4-> L O
E 3
E •^ X
<o
D
t .
C 0
t —
4-> U OJ i .
t —
2 : 0
CTI VO
l -H f H C O
CO CO
CM CO CO
I - H
0
t r CO CM
CVI P- .
. tn tn f H
to tn
a
0 CM CM
CM CO
. t n
CM
CO CO
• CTI CTI CM
X
^—^ . c •^ CT l / l
** m .o f —
—'
1
>> c
. t —
m t n OJ i~
H-> t / 1
E 3
E *^ X
<o
0 1
CO
tn CO
l -H 0
t—l CO
t . ^
^ CO CO CO
l - H
as 0 0 CO
t r CO
a
0
C O
t r i n
. CM
CO
CM CO
. p ^ t n CO
>> D
« C 0
• r -
H-> U OJ
s-*^ z 0
..—* . c • 1 —
CT
m .* m
. 0
— ""^
c 't—
H->
c OJ
E 0
£
E 3
E • 1 —
X 10
2 :
2 :
m
c 0
•r—
.-> VJ OJ i-
•^ o 1
X
P-. t—l
l -H CO CO
CO t n
CO 0 0
CO 0
^ CM t o
«• CM
t n
^
r
. CO 0 0 t n
CM t n
. t n CO
CM
• CO
as
X
^—^ • c
• I —
• ^ ^
i n J3 f —
t
• c •^ '"'
c ^^-H->
c OJ
E 0
2 :
E 3
E •
2:
* c 0
•^ H->
u 0 )
&. • X ca
•o S.
i > 1
t—1 VO
0 1 in f H
1
a\ tn
0 CM 0 l -H
0 VO
0 t r I-H I-H
1
r.^
. P ^ l -H CTI
1
l - H
0
CO* 0 CM l -H
1
CO CM
. CO p ~ CM l -H
1
CO VO
• CO CO l -H ^ H
1
>» — • c
• — •
^^ i n . Q
— 1
• C
•^
OJ
u s-0
L u
;_ 10 01
.s t / 1
E
g E •^ X 10
2 :
CTI P«.
CTI 1
t n 0 0
CT^ 1
0 CTI
l - H
t -H 1
0 0 VO
CM —H
1
^ CO
. VO 1
t n t r
• 0 1 1
to to
•
0
^^
X 5 »
«k
c 0
• r -
4-> U 0 )
u • t -
0 1
X
c •r—
^—^ • c
•*— ^ i n . O i ^
_ .
OJ 0 i . 0
L u
C-(O OJ
.c I / )
c
g =
• - -
X 10
2 :
1 —
i n CO
p . . CTI
0 CO
t—l
t r
^ CO
0 CT^
CO CM
t n CO
. VO CO
1
t n CO
. p ~ CO
1
0 CO
. t n CO
1
>> :> -c
0
* - M U OJ ' ^ C-
• ^ —
0 •<-1 " ^
>> l/l
^ c <—
199
VO
m
«a-
CO
CM
t - H
in t - H
tion
• t —
m o
O -
o o
• o in
o o
• o i n
o o o m
o o o m
o o o tn
o o
o in
o o o i n
4-> <4-
H-> O l c OJ
—J
o o
• o in
o o
a
O t n
o o
a
O i n
o o o i n
o o o in
o o i n
o o o i n
4-» t 4 -
* H-» • o
3
O o
• t r
o o
a
<•
O o
• t r
o o
^
o o ^
o o t r
o o t r
c •t—
t.
t/i l / l OJ c CJ
1 —
o o
• o l - H
o o
a
o l - H
o o
a
O t - l
o o
« o f H
o o o l -H
o o o f H
o o o l -H
H - l
1 4 -
t .
3 ««
m
+-> - o
3
01
1/1 • I T
o o
• o o m t -H
O o
a
O O in l -H
O o
• o o in t -H
O o
a
o o i n l -H
O o d o m I -H
o o o o m t -H
O
o o o t n I - H
>) • I —
CJ
+J - 1 -m m (O o.
1 I 1 M
l/l Vf- c u o
t l
l / l I — 3 • • -
1 — O
Modu
of S
CO t - H
. CO p -l -H
CO I - H
* 0 0 p». I -H
CO f H
• 0 0 p>. t -H
CO t - H
. 0 0
I - H
CO l - H
0 0 p^ t . ^
CO 1—1
0 0
l - H
o o m p »
«» O l c
• o lO o
_ l
H-> 14- - t -• 1 - m 1 — o .
O o
• 0 0
o o
• 0 0
o o
a
CO
o o
a
CO
o o CO
o o CO
o o 0 0
• 1 —
l/l o.
p*. O l
• o
o o
. l - H
CO o
. I - H
p«. at
• o
r«« CTI
o
t r CJI
o
CO
o t - l
c •^
« l
t> fc^
m o o.
O l
c • o IO
o _ J
^ CJ C » lO O *4- H-J
l u Q . 1/1
• t —
+J CJ QJ
**-01
O
E 3
E X IO
2:
!»«. in
. 0
1—1
to a
0
CO VO
• 0
p>» i n
. 0
p^ in 0
t r i n
0
i n t o
0
. f - c 10 - t -
H-J " C X
CM f H
. r»» CM
CM CM
a
p». CM
0 i n
. CO CM
CO CM
. P>» CM
l - H
CM
CM
i n CTI
i n CM
p *
CM CM
" " s
OJ <0 t j -i- E 1 OJ < 0
14- f H
• I - c 0 0
E •U 3 0 E 01
Maxi
Defl
X 10
E
>
X
c • ^
l/l in OJ
• f j t /1
E 3 E X lO
VO CTI
. t - H
VO t—l
CO CTI
a
CO f H CM
CM in
• CM CO CM
to CO
• t—l
t o l -H
i n CTI
l-H CSJ CM
P-. CTI
CO f H
CSJ
CO f H
t n CO CM
X D ^ - »
Direction,
(Ibs
/sq
in
0 i n
• CTI in CO
0 p^
a
t r to CO
^ l - H
. CO CM
«r
p * t r
• •a-CO CM
t - H
«a-p>. 0 t r
l - H
i n
I - H
i n
i n
CTI t o CO
> 1
c ''~ tn
0) D ^—* «_ •
Maximum
St
Direction,
(Ibs
/sq
in
CJ> 0 0
. I - H
CO «3-
CM VO
a
0
t n
< j i
CO
. CO i n p^
CTI CM
t
0 CO
r-» CO
l-H CTI i n
CTI t n
0 p«. t n
CO
p -CM VO
c
•t-> 2 : C ' — 0} * .
E c c 0 0 ••-
2 : • • - ^ H-> vn
E VJ - O 3 QJ <— E s- I
X a c 10 1 • ! -
2 : X ^ '
r^ CM
. P^ 0 CM l -H
1
CM tn
. CM 1 ^ CJI
i n l - H
. t o CO CSJ l-H
1
1 0
CM t
i n CM t o
0 CTI
t o 0 1—1 l-H
1
t r 0
t r 0 CM l-H
CO t o
CO CO I - H
I - H
1
c >>
C ' — 0 ) tl .
E c c 0 0 • • -
2 : - t - ^ 4-> 1/1
E u -o 3 OJ 1 —
E i- • X ca c (O 1 • • -2: >. -^
CM t n
. •a-l-H
1
0 0 CO
• CM f H
r»« CO
• t o
CTI t r
• CTI 1
0 at
CO l-H
1
t r
I - H
I - H
CM i n
t o 1
OJ U X
0 Cu • c s- 0 10 - f OJ H->
t / ) 0 1 - — • 1 . •
imum
x-
Di
s/in
X . Q 10 C 1 — 2 . , -«- .
CM P^
• VO CO
CM t n
• CTI CO
t o CO
• . t n CO
1
CO
^ • CTI
1
CO 0
CTI t r
VO
t o CM
1
CM t n
t n CO
OJ 0 > , s- >
l u • C
4- 0 (O • ! -QJ 4->
f CJ 1 0 QJ ^ - «
imum
y-
Di
s/in
X . 0 (O C 1 —
200
CO l -H
CM I—1
t - H
l - H
O l - H
CTI
CO
p -
C
o 4->
t/1 o o.
o o o i n
o o o m
o o
• o m
o o
• o m
o o
• o i n
o o
a
O i n
o o o m
^.t 14-
* - J
•t-> o>
OJ _ l
0 0
d m
0 0
0 i n
0 0
• 0 i n
0 0
• 0 m
0 0
• 0 t n
0 • 0
m
0 0
0 m
4 J l ^
m
3
^ • f -J
3
0 0
•a*
0 0
• ^
0 0
• «r
0 0
• «a-
0 0
• t r
0 0
a
^
0 0
• ^
a
c
m
JZ
« 1/1 m OJ c
1—
0 0
• 0 l - H
0 0
• 0 t - l
0 0
• 0 t - H
0 0
• 0 t - H
0 0
• 0 t - H
0 0
a
0 I - H
0 0
a
0 f H
4-> 1 ^
«« 3 <
n
^ 4.J • 0
3
OJ
1/1 •p—
cC
0 0
d 0 t n l -H
0 0
• 0 0 m l - H
0 0
• 0 0 m t -H
0 0
• 0 0 i n t -H
0 0
• 0 0 i n t -H
0 0
a
0 0 m t -H
0 0
a
0 0 m t -H
>> 4^ .^ ( J . f »
• ) -> l/l 10
CU
I f -0
in 3
3 • 0
• f -
m 0 .
M
l/l cu
t l
• t —
0 t /1
0 <4-2 : 0
m
0 1 c
• 0 10 0
^ j
H-» 1 ^
0 C U
co t - H
CO
l - H
CO f H
CO
f H
CO t - l
. CO p« . l -H
CO t - H
. 00
t — l
CO t - H
t
CO p>» l-H
CO l - H
. CO
l - H
CO l - H
. 00 p». l-H
• t —
l/l a.
«k
t f -
0 0
• CO
0 0
CO
0 0
• 00
0 0
• CO
0 0
• 00
0 0
a
CO
0 0
• 00
•^ tn 0 .
t l
r^ 0
t — l
"a-0
t - H
<JI CTI
a
0
CTI 0
. l - H
1 ^ 0
. t - H
t r 0
. f H
l - H
0 • f H
C •^
t .
c l/l b
Q .
m
as c
•r— • 0 10
_ l
U 10 4-> CO
•^ ••->
CJ OJ
t ^ OJ ca
E 3 £
• t —
X IO
2 :
f —
10 • p -
• f -J
c 01 u OJ
t+-<4-• 1 —
1 ^ t o
0
^• VO
• 0
CJI i n
a
0
CTI VO
a
0
CO t o
• 0
t r VO
a
0
l - H
VO
• 0
• c •^
m
X
i n f H
t - H
CO
0 0 t r
0 CO
CM t - H
• «a-CM
t - l l - H
. VO CM
00 0
• CM CO
l - H
00 a
CTI CM
VO VO
• 00 CM
.—. 10 ^ _ E <
t .
c a 0 E ••-> 3 u E OJ
X < ^ 10 OJ
z ca
1 0 l - H
X ^.^
X lO E
r.-
<3
1 X
c •^ m tn OJ i -
•u> t / )
E 3 E X
D
m
c 0
• t —
•)->
0 OJ
(O - 1 -
2 : 0
0 t o
CM m CO
0 CO
0 CM CO
CO CM
a
CO t n l - H
t r t n
« VO CO CM
t o f H
• CTI I-H CO
CTI t . ^
. 0 CM CO
t r CO
• 0 l-H CO
X
-—* . c
CT l/l
l/l
.o ^
1 > 1
c • r -
tn 1/1 OJ i-4-> t/>
E 3 _E X
D
« c 0
• f "
•u> CJ OJ
s -(O • < -
2: 0
^ I - H
•a* 0 CO
t - H
CTI
t n CO CO
f H
ps. a
r«-l -H CO
CO p^
• l - H
CO
CM 0
a
CO 1 ^ CO
f H
CM
• CM VO CO
CO 0
• CO i n CO
>, — • c
• 1 —
CT m m .o ^
c • t —
H-> c OJ E 0 2: £ 3
2 :
c 0
H->
u OJ
E s_ X Q •0 2:
1
X
fv. CM
0 t r CJI
CM l - H
t r i n CO
i n <ji
f H
CM
•a-
1 ^ r^
a
0 CO VO
0 l - H
. t - H
i n 0 0
CO 0 0
. CO t n 00
p» i n
t
p~ CM CO
X
^ • - .
. c •^ in
.£3 r—
1
C
•^
c •^ H-> 2 c 01 E 0
2 :
£ 3
* c 0 H-> U OJ
E ^ X 0 <o 1
>
0 0
CO CM 0 1
1
0 0
CO t r 0 f H
1
0 f H
. CTI CM at
1
CM
^ . I - H
<J1
as
0 0 p-»
• CO 00 l-H t.^
1
t n 0 0
. I - H
0 CM I-H
1
0 CM
• CM 00 f H l-H
1
> 1
^ • ^
c 't—
m . 0 — 1
OJ u
CO 0 0
CTI 1
CO VO
l - H
CM
CTI t r
^ I-H 1
t o 0
p~ 1
CTI "a-
• 0 l - H
1
P^ 00
• CTI 1
^ i n
• t - H
CVI
X u > 0
t u
i-l O
QJ f 1/1
E 3 £ X 10
• 1
c 0
1 ^ -
H-> U 0)
0
X
c
c '^ in .a
^
OJ u i. 0
LU
l. (O QJ
. C t o
E 3 E X 10
2:
3»
* C 0 '^ H->
U OJ
0 1
>• c
at t r
CTI CM
t n CO
^ CO
t o i n
a
0 CO
CM 00
a
0 CO
1
CTI CO
• VO CO
1
CM CM
. VO CO
1
i n l - H
t
t o CO
>>
c 'f—
1/1
^
201
i n
^
CO
CM
l - H
i n
^ l - H
c
o • f -
•4->
•^ t n O
Q -
.00
o i n
.00
o m
.00
o t n
.00
o m
.00
o t n
o o o i n
o o
• o i n
H-J 14-
«k
- J
m
.c •• ->
O l c OJ
_ l
.00
o t n
.00
o i n
.00
o i n
.00
o t n
.00
o m
o • o
t n
o o
• o m
•• ->
< • -
^ 3
f
J C 4-> • o • f .
3
.00
t r
.00
t r
.00
t r
.00
t r
.00
^
o o
« ^
o o
• ^
• c
•^ m
. c
t .
m m Ol c
.^ u
•^ . c 1 —
.00
m f H
.00
m f H
.00
t n t - H
.00
m l -H
.00
i n f H
O
o o l - H
o o
• o t - H
- M
<*-m
X <C
M
. s
• * - > • o
•^ 3
QJ
^— l / l
•^ •X.
.00
1500
.00
1500
.00
1500
.00
1500
.00
1500
o o o o t n l -H
O
o • o o
i n f H
>> H-J
•^ u •^ +•» • > -m m l o ca .
— 1 I 1 M
m l f_ L U
o A
m r— 3 • ! -
I — O 3 t n
• o O «4-
2 : 0
.00
t n pv .
.00
t n p ^
.00
m
.00
m
.00
i n
CO f H
0 0 1 ^ t - l
CO t - H
. 0 0 p ^ t -H
t l
0 1 c
*t—
• 0 10 0
_ l
H-> t * - • ! -• 1 - t /1 r - Q .
-^ u •> 0 t * -
L u ca .
.00
0 0
.00
0 0
.00
CO
.00
CO
.00
CO
0 0
CO
0 0
• CO
•^ l / l Q .
t .
m 0 .
M
0 1 C
• t —
• 0 10 0
_ l
.^ 0 fO
4.J
m
p« . 0 CTI P«»
0 0
VO CTI CTI VO
0 d
t r r-* 0 0 m
d d
t n 0 0 0 0 t n
d d
f H ^ CO . i n
d d
CO CO f H r ^
f H 0
0 0 l -H p« .
. . f H 0
c • ^ t
1 — c M 10 * ^
C • ! -0 H-> «
• 1 - C X
CTI CTI
t r CO
0
32.
CO VO
VO CM
CTI CO
d CO
m t o
CM
t n CM
VO CM
CO f H
. t r CO
1 X
c
*— .^ •!-> 0 1 ( 0 t r 0 s - E OJ OJ <3
1 — 14-Vt- I f - " OJ • • - c
0 0 0
•^ E E - M 3 3 0 £ E OJ
• I — . ^ ^ — X X V| -10 10 OJ
z 2: a
1 t n 0 1/1 t -H 01 X i .
' 4-» t / l
X
2 E E 3
—' E f — 't—
>«>. X < ] (O
CO
462.
p«» CO
450.
CM CO
99.
CM
t o
29.
CO
CM CO "082
t r l - H
1 ^
^ CM
0 0
• 0 0
CO
^ x 0 . — .
* « c
C • ! -0
• r - CT 4-> m 0 ^ s . OJ t / l b . JU
• t — ^—
— ' 2 : Q « —
0 m
853.
CM
m
741.
t - H
0 0
42.
CO
CO p*.
43.
^
0 VO
496.
r ^ CM
I-H i n CO
CO t r
. l - H
i n CO
1
>. c
•^ l / l
^ ^>t OJ D * — . S-
H-> t. c I / ) C 1 -
0 E — CT 3 H-» m £ o - ^
• t - OJ i n X c . 0 (O • ! - f -
: E Q — '
^ 0 CO f H 0 HS-
1233.
2276.
-18.
CM CO t n CO CO VO
1202.
1977.
-17.
CO VO 0 1—1 l -H f H
CO t r fH^ CTI t -H f H P * CTI 1
0 0 0 ^ CTI CM t r
• t •
CTI CO CM P ^ 0 0 f H CO l-H 1
l -H
l-H 1 0 VO t n CVI CM
747.
1324.
-10.
^ CM CM 0 P ^ t-H
CTI t o ^ - . i n CO 1 VO CTI
0 CM CM 0 0 0
* • • 0 0 1 ^ f H CM t O l-H CTI 0 1
f H 1
OJ 0 X
C C L . 5 > • 1 - - I - 0
X > t L U « • M 2 : * J S . C C - - » C - — s_ 0 Q) » • (^ « • f^ ' r * E c c E c c Q j 4 - > 0 0 - 1 - 0 0 • • - . C O
Z ' t - ^ . > 2 : > - ^ t > o o ) ^ - ~ •!-> lA * i lA C •
E U . O E U . O £ • • - £ 3 0 J f - 3 O J 1 — 3 Q ' f -E S . 1 £ S- 1 £ 1 - ^
• I - - 1 - . • ! - - t - • • ! - X m x o c X O C X . 0 lO 1 • > - 10 1 • • - <o C 1 —
Z X — 2 > , > . ^ 2 : — « - '
01 u s . 0
L U
i-lO 01
. c t / 1
E 3 E X 10
s:
i n l -H
-60.
CTI
36.
VO 0
26.
'
CJl 0 0
42.
t — l
34.
0 t r
0 0 CM
l - H
CO
^ CO
>, >
0,
c 0
-l-> VJ OJ ^-^ i- •
•1- c c a - 1 -
1 •~ . . > > 1/1
. a C t —
• I - ^ ^
202
CM
l - H
o I - H
at
CO
p ^
V O
ion
4 J • t —
1/1 o
Q .
O
o
d m
o o o t n
o o
• o t n
o o
" o t n
o o
• o i n
o o
a
O t n
o o o i n
^.^ • 4 -
0k
.c
O l
OJ —1
o o
d i n
o o
• o i n
o o
• o i n
o o
• o i n
o o
• o i n
o a
o t n
o o
a
o i n
^J i > _
« 3
^ JC. H-> " O
3
O o t r
o o t r
o o
• V
o o
• ^
o o
• t r
o o
a
^
o o
a
t r
• c •^
«k
g *
^ (/) ( / I
c .^ u
1 —
o o
• m l - H
o o m l - H
o o
• i n l -H
O
o • t n
I - H
o o
• t n l - H
o o
• i n t - H
O o
a
t n t - H
4-)
^. t l
s < • *
t .
JZ. ^J " O
3
OJ
l / l
5
*
0 0
« 0 0 t n l -H
0 0
d
150
0 0
•
1500
0 0
• 0 0 t n l -H
0 0
• 0 0 i n t -H
0 0
a
0
150
0 0
• 0 0 i n l -H
>, • f j •r— ( J
" 1 —
H ^ l / l
I O
L U
1*-
o l / l 3
.»— m a .
. 1
l / l
L U
M
.^ 0
' 3 CO " O 0 « 4 -
2 : 0
CO l - H
d p>. t -H
CO t - H
d ps. t -H
0 0
• i n
0 0
• t n r v .
0 0
a
i n | S s
0 0
a
i n P«s
0 0
a
t n p s .
t t
0 1 c
• 0 10 0
_ i
H J 1 ^ • ! -• t - ( / I t — a .
i . -0 vu.
L u a .
0 0
d
0 0
• CO
0 0
• CO
0 0
• CO
0 0
a
CO
0 0
• CO
0 0
• CO
't—
m a.
t .
i n Q .
M
0 1 C
• t —
• 0 10 0
J^ CJ r o
H-J < /1
CO 0 0
• 0
CO 0 0
d
0 CTI
• 0
P ^ CO
• 0
CM CO
• 0
CM CO
• 0
O l p s .
• 0
. c
• f -
t l
c 0
•^ •u 0 0 )
l l -
01 0
E 3 £ X 10
2 :
f —
IQ
•^ H->
c OJ i . OJ
14-14-
0
£ 3 E
0 V O
d
t n t n
• 0
CO t o
a
0
l - H
VO a
0
i n i n
a
0
t n i n
• 0
CM i n
« 0
• c •^
A
X
CM P ~
CTI CM
t r
m • ^
CM
p s .
at a
| s < .
CM
t r i n
a
0 CO
CM VO
a
t o CM
CTI p ^
. i n CM
CM 0
• CO CM
j ^ . .
10 t r
Ja <
M
C 0
4-> CJ OJ
• 1 — f —
X >4-10 OJ 2: 0
i 0 l - H
X
_ X 10
E
i
1 X
c •r—
1/1 1/1 OJ
&. 4 - >
t / )
E 3
_£ X
0
« c 0
•f->
u OJ
10 - f -2: ca
CM CO
CTI l -H CO
CTI m i n t n CM
0 CSJ
•
325
0 t n
a
CO p ^ CM
CO CTI
a
CM CO CM
CJl t o
• CTI VO CM
0 0 O l
• 0 0 CM
X
^—^ . c • t —
CT 1/1
^ s .
I / I . O
^
1
>» c •^ l / l i n OJ
s-4-> ( / I
E 3 £
X
„•. 0
m
c 0
• f -
H-> U OJ
(O • ! -
co ^ CM t r t r
m CM
, _ H
0 i n
CO t r
t
I -H t-l CO
CTI CO
a
CO CTI CM
0 CO
a
CO p . . CM
CM
^ • CJI
CTI CM
CO CO
• CO i n CM
> i ^ — s
. c •^ CT
m • • s . .
i n . 0
^
c •^ H->
c 01
E 0
2 :
£ 3
E
s
« c 0
' t —
•u>
u OJ i-
• r - •!— X o IO 1
X
CO t n
I - H
i n CO
r^ m l - H
CO t o
0 CM
a
867
l - H
t o
• CM
p »
t n f H
. t.H
CSI t o
0 0 l - H
. CTI l - H
1 —
t n < j i
• i n CO i n
X
* — s
c • f -
s s . *
t n . O r-~
1
c
^
c •^ H->
c 01
E 0
Z
E 3
E • r -X 10
2:
"Z. t .
c 0
• r -
H-> U OJ I .
0 1
> •
0 CO
CTI ps. I—1 I-H
P ^ t o
VO CO CO f H
f H
i n a
-882
CTI CTI
a
CO 0 0 CJI
1
t r t r
. l - H
0 t X I
1
l - H
0
• CM P ^ 0 1
1
CO CTI
• ^ t - l
CO 1
> 1
-*—s
c • ^
^ s ^
1/1
.a ^-1
c • r -
01
u ;-0
L u
i-(O QJ
^ 1/1
E
CO l - H
CO I—1
1
p ^ CO
t—l
"
t o CO
a
0 t - H
1
p s .
CM
. CJl
0 CO
. P . s
p s .
i n
. CM f H
i n CM
• CTI l - H
X 3 »
« c 0
•'— H-> CJ OJ
3 c^
E X lO
2 :
1 X
c
^ — s
C • t —
' ^ ' s .
i/1
.a ^
QJ U
c 0
l u
i -10 01
f t / 1
E 3
E X 10
r» t l
c 0
•^ H-) 0 0 )
u 0
1
f H
0
CO
^
CTI CO
^ CO
CM VO
a
CTI l - H
1
l - H
C s l
. I - H
CM
VO CO
• 0 CM
l - H
t n
. CM CM
as CM
• CTI l - H
>»
^^ c •^ ^ s .
> , i n
.a •r— —'
203
O l
CO
p> .
V O
i n
^
CO
c o
Posi
ti
o o o i n
o o
• o i n
o o
• o m
o o
• o i n
o o
a
O t n
o o o i n
o o o t n
4.J
14-
_ l
Leng
th
0 0
0 i n
0 0
• 0 i n
0 0
• 0 t n
0 0
• 0 i n
0 0
» 0 m
0
0 m
0 0
0 m
14-
3
_
Widt
h,
0 0
^
0 0
• ^
0 0
• ^
0 0
• ^
0 0
a
t r
0 0
a
t r
0 0
t r
. c
t .
- C
A
ickn
ess
1—
0 0
m t -H
0 0
• t n I -H
0 0
• i n t -H
0 0
• i n t - H
0 0
a
i n t - l
0 0
a
i n f H
0 0
. i n t - H
^J I4_
t .
^^
Widi
( / I
0 0
d 0 m t -H
0 0
• 0 0 i n t - H
0 0
• 0 0 m l - H
0 0
• 0 0 i n f H
0 0
• 0 0 t n l - H
0 0
• 0 0 m t -H
0 0
a
0 0 t n t - H
>. 4->
•^ ^J
•^ 4-> 1/1 lO
L U
l f_
0
t/l 3
• r -t / l Q .
t / l L U
M
. - V
t - 0 3 1/1
"O 0 H -
£ 0
CO t -H
t
CO 1 ^ t -H
CO I -H
. 00 p s . f H
CO f H
. CO p ^ t -H
CO f H
. CO pss l-H
CO l - H
. 00 1 ^ f H
CO l - H
. 0 0 1 ^ t - H
CO I -H
. CO p ~ l - H
.. 0 1 c
" O IO 0
_ J
4->
• f 1/1 t — Q .
4 - • 0 <4-
L U Q .
0 0
d
0 0
• 00
0 0
• 00
0 0
• 00
0 0
a
CO
0 0
a
00
0 0
• 00
•r— 1/1 O L
t l
i n CTI
d
CTI CO
• 0
CO CO
• 0
CM CO
• 0
t — l
0 . t - H
f H
0 . I - H
CO CO
• 0
• c
•^ * c
1/1 0 Q .
«k
0 1 C
• 0 10 0
_ J
u 10
H-> I / )
• t —
H-> CJ OJ
14-QJ
0
E 3
X <o
2 :
^ <o •^ 4-»
c OJ s-OJ
<4-t f -• p -
0
£ 3
rss t o
d
l - H
VO
• 0
0 VO
a
0
t r t n
a
0
CO
r^ . 0
CO ps.
a
0
0 VO
• 0
t
c • f
t l
X
0 CO
CO CO
0 0 t r
a
CO CM
CM f ^
a
i n CM
CO i n
a
CO CM
l - H
CO a
CM CO
CO CO
• l - H
CO
1 ^
m • t r
CM
. ^ • s
10 ^ E
< t l
c 0
4-> U
£ OJ
X t ^ 10 OJ
1 0 l - H
X
X 10 £
<
1 X
c •^ m l / l OJ
H->
in E 3
^E X
D «•
C 0
4-> U OJ i-
10 - t -2 : 0
t r t n
CO 0 0 CM
to t o
a
1 ^ t r CM
CO CM
a
CM i n CM
r^ CM
. I - H
0 CM
P ^ CM
• 00 CO t r
r^ 0
• 1 ^ CM
<«• ^
• P * ps. CM
X
• C
CT l / l
m . 0
^
1 > i
c •^
l / l i n OJ
H-> t / )
E 3
X
0
c 0
H->
at CM
CTI
m CM
CM CO
a
0 0 t r CM
t r CO
• CO CO CM
CTI r^
• t r i n CM
0 t n
• 0 0 i n CO
i n t r
• CO t r rs»
CM CM
• <J1
CO
>> ""*
c
CT m
0 " s . . OJ 1/1
(O - r -
2: ca ^
c • t —
•f->
c 01
£ 0
2 : E 3
Z
c 0
H-» U OJ
£ V. X Q 10
S. 1
X
l - H
l - H
VO t n
CM «r 0 VO t o
CM t o
a
CM
VO
CM p . .
a
VO CO
m
CO p ^
• CO VO f H
f H
t n 0 0
• CO CO l - H
^ 0 0
• CTI CO ps.
X
^ - s
c •^
1/1
.a f —
1
c
• ^
c •r—
H-> C QJ
£ 0
2:
£ 3
'Z.
0 H-> 0 QJ
E s-X 0 10
^ VO
CO f H
00 1
VO VO
CTI f H
CO 1
CTI VO
a
t n CO CO
0 CTI
. I - H
CM CO
1
CO CO
. at CO CM CM
VO CO
• t n CTI CTI f H
t n CM
• f H
CO CTI
>> —. c
'^ m
.a — 1
c >>sl^
OJ 0
s- > 0
L u
c 10 OJ
J C t o
£ 3
£ X 10
2:
n
c 0
H J
u OJ s -
• 1 —
0 1
X
c
^ ^ CTI
t o m VO
CTI VO
. P.S t—l
p . . CO
a
CJI r-H
VO CTI
. P » l - H
1
CTI l - H
• 0 0 l - H
1
CTI 0 0
• . — I f H
1
X
c *t—
m .a ^
QJ CJ
&-0 U .
c 10 OJ
J C 1/1
£ 3
£ •F—
X 10
5 »
" C 0
• ! - >
u OJ
0
0 0 i n
0 0 l - H
CO CM
a
0 0 l - H
0 0 i n
a
CM CM
C J ps.
. 0 CM
f H
l - H
. 0 VO
1
CO 0
. p ^ CO
0 0
• VO CM
1
>)
c ''—
> » l / l . 0
c —'
204
o f H
c o •^ 4-»
•^ 1/1 o
a .
o o
• O m
+J <4-
M
_ l
M
. C H-> O l c OJ
_ l
o o
• o i n
H-> 14-
M
3 A
. C H-> • 0
3
0 0
• ^•
• c •^
«k
.c t .
m tn OJ c .^ CJ
.c 1—
0 0
• t n l -H
•4->
<•-• k
3 «*
«« . C H-> - 0 • f .
3
01 f —
1/1 >r -
<e
0 0
• 0 0 i n 1—1
> i H-> •t—
u •t— H-> -f-m m 10 Q .
I — i i I t l
1/1 t f - c u 0
t *
m r— 3 • • -
1— 0 3 t /1
- 0 0 <4-
2 : 0
CO l-H
. CO p^ I-H
t l
0 1 c .^ T3 10 0
_ l
4-> 14- • • -• t - m f - ca.
.^ 1 . tl 0 t f -
Lu a .
0
• 0 0
•t— l / l 0 .
* in o.
M
CJI c
• 1 —
• 0 •0 0
_ J
.^ u 10 4-> CO
p> CTI
• 0
c •^
m
c 0
.t— H-J u 01
r ^ 14-QJ ca E 3 £
• P "
X 10
2 :
CT> VO
• 0
. t— C 10 • ! -
• 1 —
* J •> C X
CTI i n
• 0 CO
^—.. OJ 10 t r S- £ OJ <
14-••- « • 1 - c 0 0
• p -
E H-> 3 U £ (U •^ " X <4-•0 OJ 2 : 0
1 0 f H X
s ^ ^
X 10 £
^— ^^. < • ^ s ^
1 X
c •t—
in tn 01
&. H-/ t /1
E 3 £ •^ X 10
CM i n
• CO CO CO
X D — .
. - c C - 1 -0
• 1 - CT H-> m 0 "s.. OJ l/l i - . O
•r- r^ 2 : 0 ^ '
i n l -H
. CJI t n CM
1
>» c
•t—
in m ^ > , OJ 0 -—. i . H-> - C t/> C f -
0 E -r- CT 3 4J m E CJ ^
• 1 - OJ in X s- . a 10 - f r— Z Q w .
c •^ H-> c QJ E 0
Z
E 3 £ •^
CM f s .
. CM 0 CJl
X •s.
^"^^ m. a
c c 0 •<-• P - S S ^
H-> in u .a 0) .— i - 1
•t— . x o c <o z
1 -f-X «—'
c • I—
H-> c OJ E 0
2 :
£ 3 E •^
1 ^ 0
0
f H CTI t o
> i 2 : ^ ^
« . c c 0 -t-
't— s . ^
H-l in U JU OJ 1 — S- 1
•^ . x o c 10
z 1 - I -
> l ^ —
CO i n
a
0 l - H
1
OJ U X J- > 0
Lu K C
i- 0 «3 -t-01 H->
. C U ! • ) 01 - - ^
s . . E ••- c 3 0 - 1 -£ 1 ^
• I - X tn X . O 10 c .—
S - i - ^ —
OJ CJ
(-0 Lu
S_ 10 OJ .c t / >
£ 3
_£
X IO
z
i n ^ a
CO
1
>, =>
•« c 0
•^ H-> U 0 ) , . ^ i - .
• 1 - c a - 1 -
1 . . ^ > ) t/1
.a C t—
• 1 - — .
APPENDIX E
COMPARISON OF RESULTS FOR DIFFERENT
ASPECT RATIOS OF FINITE ELEMENT
205
206
i n
i n
o o
o U l
O O O O O O
c o m i n I-H
o o o h-O O i-H I f
o o in
CO = > l -H
o ce t / 1 L U
o o o o o o o o o o o tn i n t n f H
O o o o
CO CO
o o in
CO CO f H
.82
l - H
- H
t o
p . . t *
f H
l - H
o l - H
i n
o t r
VO t n CO
p ^ 0 0
l - H
o i n 0 0
CO CTi
cn CO cn t n
t o m VO p ^
1
o VO
O l CO
1
o CM
i n
1—1
o o o t n
o o o i n —H
o o o t n
o o o i n
o o o I - H
o o o l - H
o o t n
o o t n
o o o o t n I-H
o o o o m l - H
o o 0 0
o o 0 0
l - H
CO
CO
o CO
CO
0 0
l - H
1—1
oc t—l
0 0 VO
^ t n
t r l - H
CM t n
0 0 as
p s .
o m
o VO
t r CM CO
P * CO
sLi Vi3 t r 0 0
f ^
o o l - H
t r t n
f H
O l
l - H
0 0 1
t r " T
l - H
t o 1
l - H
CO
VO
o i n
p ^ CM
0 0 CM CO
t n 00
VO t o t r 0 0
r^ o l - H
r^ t r i n
t o t o
r^ p ^
1
CM CO
t n t n
1
O
o o i n l - H
o o o i n
o o o t - H
o o t n
o o o o i n l -H
o o CO
I - H
CO
CO
CM 0 0
f H
CM t o
ro i n
O O
CO o m
t . ^
as o p ^ CO
CO ps.
VO VO t r CO
i n 1 —
l - H
CO l - H
VO
o ps.
r^ p ^
1
CTI P ^
CM p . .
1
t 4 -O H-l
c O OJ
•-- E H-> OJ •0 1—
0£. L U
H-) Q ;
o +-> OJ -t-
o. c tn • ! -
<C L U
4-> i f -
• _ l
t l
SZ H-> O l
OJ _ J
H-> t f -
f
3
V I
. C H->
't—
^
• c •t—
t .
. c
* t n t n OJ
c .^ o .c 1 —
4 - >
* f
3 •4
«« . C
+-> • o *r^ 3
0,
i n * f —
<:
> i H-> • t —
CJ
*^ H J T -m in IO a .
— 1 1 1 t .
i n l | _ L U
o t l
m 1 — 3 • < -
1 — o 3 1/1
O •*-2 : o
• r—
t o
o.
^ m CL
t*
CD C
• t —
T3 o3 O
^ .^ CJ IO
4-» I / )
c • I —
•* c o •^ 4-> CJ OJ
— l l -OJ
o E 3
£ X (O
2 :
. «— c rs • ! -
• I —
H-> • C X —. OJ 10 H T s- E QJ <
1 4 -V| - « • f - C 0 0
• r-E H-> 3 U E 0 )
X t i -10 01
2 : 0
1 0 l - H
X
..^ X 10
E ^ — s
' <
• — '
1 X
c • 1 —
i n L l QJ S-
H J t / 1
E 3
E • t —
X «3
^
f
X D — .
. « C c • < -0
• f CT H-> t n 0 ^ s . OJ in i- . o •^ — " O s ^
1
>> sz
•^ m t. m > , QJ D - - ^ S-
H-) " C 1/1 C - i -
0 E • • - CT 3 H J m E 0 ^
• • - OJ m X 1 - . 0 10 • • - I —
Z T J s . ^
c • ^
X H-" ZtL C - ^ 0 ) t. . E C C 0 0 • - -
' J * I f ^ . ^
H J i n
E u .o 3 OJ 1 — E s_ 1
x o c J O 1 • ! -
c .f—
>, +-> s c ^ OJ t. . E C C 0 0 - 1 -
2 : • < - s . ^ H-> i n
E VJ . Q 3 OJ 1 — E i- 1
x o c 10 1 • ! -
Z > , ^ -
c c •<-• f - ' ^ . .
m 01 j a 0 1 — S - - — 0
U - X
=» 10 ' 0) c
J C 0 t / l • . -
H-> E u 3 OJ E i-
X Q 10 1
Z. X
c C • ! -
t n OJ ^ 0 1 — 4 - • — •
0 Cu > ,
> i . 10 • 0) c
-c c oo • . -
H-> E 0 3 OJ E '_ X 0 10 1
Z > >
APPENDIX F
STRESS, MOMENT, SHEAR, AND DIFFERENTIAL
DEFLECTION RESULTS FROM
PARAMETRIC STUDY
207
208 H
EA
R
/IN
tJ i K
a:
ULJ t i«
t / l ) <
C l b
o > > • •
tm
t b
C I k
z ^ X t
14.
oe M ^ trt t/1 a .
ee M ^ tn in a .
l b
^H kH
o
- J t / 1
t /1
O 3 l» U U.
«
^ H
t « t ^
tu il
m*
e • o
o e • o
i i »
o •
e
<o •NJ
•
w t
^ J 9 0 •
o o
o
liO
•
| ^ J
o o •
o o o . l A
o o \fl
<o o o •
o
o o •
a
I M
o •
o
> 0
e
i \ j ac
• »r I M
m
o •
o
I M
o •
o o o •
\/^
o o \/t
o o • o
o o • C3
o • o
. e
0 0
• m*
ao .
I M
I M
ca .
o
fsj
o
o
o o o . t r
o o o
•«r o •
o
v H
o • o
(M
• . 4
« 4
O •
ft. 0 0 OO •
<o »r
o
•
un 0 0
o •
m*
ae
o •
o C3 O
• in
o o t /^
I M
O •
a
o o •
o
eo in
• e
O l l /S
fVJ
•
<M
I M •
fv» O
* 4
(M
• o
eo
o o •
o
o o o . l/t
o o sn
O • o
»o o o •
o
0 0
• M
• o
•n
*M
o •
\n
• o i r«
^ mm
9
O
ee
o •
o o o . \n
o o o
t M
I M
o o
m*
(M O
o
r t i
ee
(M •
»M
<o
•o
• »M
s T <n f M •
s T u n
f s .
O »o
o
rvj o
o •
o o o • t /^
o o \n
mt
O
O
o o
o
ao •o
e
o f M
•
o •14
• o
o I M •
1 ^
s T
I M SO
C •
«M
•
o o o •
l / ^
O o \n
0.0
11
\n o o
o
o • M
•r o
o I M >r •
o
Ov o •>o
•
t J
o> «r I M •
sn I M
r \ j
o •
o
rti
o •
C3
O O O
• l/S
O o o
0.0
72
ao ^> e •
o
^.
•#
•
- r
•
xn s T
ao •
\n o s T
^ s
O
•
eo
o o •
o
o o o • \n
o o \n
o o
o •
o O l
• •M
Ok
•
0 0
vO
»o •
«o f H
\n
f H •
I M s T m*
f M • O rvj •
o
0 0
o •
o o o •
\n
o o in
o •
tn (M
o - o
o
tm
mt
\n y*
• mm
tn \n (M •
I M o
0 0
f M O .
flO
0 0
• 4
• o
ao o
•
o o o • in
o o o
O l
o o
t
o
o o o
o
o
o> «r
ao •* •
PH V.H
«r 0 0 Os »
\n in
>n
f t
• o
o o •
o o o .
o
o o sn
tn o o •
ml
o o
a O
*r
o
o »r o •
o
I M
I M
• in
W I
oo > •
s T «t4
» wn
O •
o
(M O
• o
o o o •
o
o o l /^
I M
O
o •
o
m* O O
• o
n t
\n o •
v «
(M o .
0 0
o o-
«M o> •
O I M
O •
o
« J
o o •
o o o .
o
c o o
•*
o o
o •
o
»r m
• « 4
O sn in
o
0 0
<M •
O
o >o
m
>o O I M
on sn
m O
an
o o •
o o o .
o
o o in
m*
O •
tn
o o •
in
ce tn
t
o
o»
• o
0 0 « 4
«r •
»r
in ar 0 0
• m sn
0 0
f H
• O
eo o
•
o o o
o
o o l/n
90
0
• o
I M
O o •
o
eo o I M
• o
»
o m
O
o> •
> oo sn
• OJ
o> sn es
«
0 0 o o •
o o o
o
o o o
> mm
o •
o
I M
o •
fS I t
o
• mm
-O
«r I M •
"O
o> in
• ar
I M
• o
f M O o •
C3
o o o
o
o o m
«*
o •
\n o o •
o
sn •
O
o mm
•
ao \n
m
m «o
l O rv. \n •
I M
m o •
o
I M O o •
o o o
o
o o un
^ O O O O O O O O O O O O O O O O C O C o
" ^ ^ c s o o o o o o o o o o o o o o o c o o e ^ l ^ . * * • • • • • • • • • • • • • • * • •
^ > r s r * r . * s * » r o o o o o c « r « r » r . r s r s * o o t / t f ^ f H f K f H f H f H . - f H
z b -Q ^ M l b
3 in
z ^ z ^ UJ l b
vn
o o o
o sn
o o o
o
o o o
o tn
o o o
o
o o o
o i r t
o o o
o
o o o
o sn
o o o
o
o o o
o in
o o o
o
o o o
o in
o es o
o
o o o
o un
o o o
o
o o o
o in
o o o
o
o o o
o i n
o o o
o
o o o
o m
o o o
o
o o o
o m
o o o
o
o o o
c m
o o o C5
O o o
o tn
o o o
o
o o o
o i n
o o o
o
o o o
o in
o o o
o
o o o
o i n
o o o
o
o o o
o i n
o o o
o
o o o
o m
o o o
o
o c o
o i n
o o o
o
<n es o
o m
o o c
o
209
X S» tn ^
rsi m* O
ao ^» o
<0 tn sn «# o o
ao fM
o o o o • •
o o
e o
o tn o •
ao O
o o
o o .
o
in m»
o o
o o o
in fM
o <o o o
<\i m*
O o
o o
^ m o in o o • •
o o ae a z tW M X ^ vn ^
O o
m o
I M m fM • * o o • .
o e
m wt es o e o • •
o o
o o
o (M o
tn o o
o o •
o
fM o o
o
ca o o
>n
o
fM
o o o e
o •
o
eo IM O
eo m
<« I M tn
># •* O iM ^ ^
o o
tn • «
eo tn in "o >n tn <M
O
o «o OO
• M
o> o o 00
m ao nj
tn M •O
P*. « un «f O (30
» t «i« O O M » t o M o .••
«M
(M
O
•n o
m ee fVJ
fM (M oe ^ fM O
ee tn e o
fM
o ee fM
o r g IM
o o
I M fM fM
m m m
eo ae m
m in 00
o ^ o ^ e O fM fM -H fM
in &
oe M
m a.
a z
» i n M n u n ' A t O f M r k a o . t « i » i ) r j o o ^ e o i n > n f M i n f \ j o e e ^ N . ' 4 * n ^ 9 i 0 . f t t . H e o o < t H m o e o o > 9 e ' n i n ^ ^ e o « 4 u n > i H . 4 e o a o o H p k O « ^ n r p > i ' H > r f > > .
k ^ ^ ^ ^ r g ^ k ' n f M ^ O a o o ^ a o . M n e P ^ O i u n v r ^ ^ ^ a O w 4 * ^ ^ ( M ^ p i » e o ^ ' « s r Q O u n u n o i r \ j » « . 0
" H « ^ " < >e mm mm m rsl mm Kn
> c ^ ^ • % r ^ « l r • * f M O ' O l O > • o o ^ o ^ » . r n J O ^ ^ l n f M . H m ^ a e O « » n « n m . * a e f t o . ^ . o - o » H > o o > i n i n ^ O i n ^ o ^ « t « « r > n r u f H O f M ^ u n O * o r « . o > t f <
n r s H t v f > . i n < o . r ^ i n i n ' n f M i n » H — « « o o a o » H K . t M , # ^ . ^ 0 ( M . H O O i n » o . * i M » » i n o » i M i n « * «
fM «H ^ mm mm ^ f H f M - Q i
0 ' i n » n ^ " H a O s r ' n ' ' i ' s . r s j " n n j » o i n » H i n ^ o n t - » l M " n ^ n ^ » t n ^ r ^ J ^ n ^ / n ^ > o o ^ ' n l / ^ u n o e ^ » n ^ o ^ o ^ o « • H O f M O O ^ > ^ o l M O o ^ O t M O ^ 0 f - e a l n
O O O O O O O O O O O O O O O C o C S O i M
« o .J ^ m
a 3
ISL
«
tn UJ
^ u hH
tn
X ^ a
SW
I
T ^ 3» UJ
m
hri
in ^
^ kb
h4
tn ^
z taH
^ u.
k-lb
m o o
o
o o e o
o o o
f .
o o o o f H
o o
o
o o o •
m
en o o
o
o o o o
o o in
o o o o IM
o o
o
o o o •
m
eo o o
e
o o o o
o o in
o o o o **
o o
o
o o o • in
ao o o
o
o o o o
o o o
f H
o «3 o o «tH
o o
o
o o o •
m
nj o o
o
o o o
o o m
ca a o »r
o 3 o
o
o o o • o m
nj e o
o
o o o
o o m
o o e sT
o ca o o
o o o • o m
m o o
o
o o o
o o o
f H
o o o 1 *
o o o o
o o o • o m
eo o o
o
o o o
o o sn
o o o sT
C3 o o o
o o o • o un
ee o o
o
o ea o
o o tn
o C3
c sT
O o o o
o o ca • o m
eo o o
a
o o o
o o o
f H
o o ea »r
o o o o
o o o • in
fM
o o
o
o o o
o o m
o o o o
o o o o
o o o • o m
ni
o o
o
o o o
o o m
e o o o
o o o o
o o o • o m
IM
ca o
o
o o o
es C! o
f H
O ca o o
o o o a
o c o • o in
00
o o
o
o o o
o o sn
o o c o
o o o o
o o o • o m
ao o o
o
o o o
o o m
c o o o
o o o o
ca o o • o m
ao o o
o
o o o
o o o
f H
o o o o
o o o o
o o o • o m
IM O o
o
o o o
o o in
o ca o »r
o o o o
o c o o o
IM
ea o
o
o o o
C3
o tn
o o o •r
o 3 O
e
o o o o o
fVJ
o o
o
o o o
o o o
mm
o 3
o • *
o ca o o
o c
10
0.C
30
o o
o
o o o
o o in
o o o
o o o o
c o o o
210
ae « z UJ M X V tn M
ae a z UJ »m
X "V
¥m
Z lb a ^ c ^ > •
ka lb N>
C lb
O "v c ^
ae •* k- in tn a. V
ae 1^ S" Ul
tn a. •X
lb lU
a z a
a
o « J m h» ^ t/l
m
.01
o
«
• o
m m
0.4
tn
^ >o • o
»> fH tn
^ ».
» o. fM
fM
m IM
80 fH
m o
ae o o o
r> o o • o
o • o
>* >n
0.2
t-l
un tn
• o
in
eo » oo .*
m Ol
un — » •n "* O « nj
O
ao o o o
o .0
8 o
IM
m o • o
^ 'C •
Pi*
»n 90 r*
• «#
i*n
.* mm
ao
tn
^ o> o tn IM
fs. O >o o
fM
o o o
in
.02
o
ao fM
• o
o tn
0.8
«r >c ^o . fH
m ^ <c o .
»• tn eo
Ok
o>
tn in f H
O
nj O o o
fw
.03
o
fSi
• o
o m
1.0
>r • o .
«H
. 00
o> o> i-n
eo ^ ao O
<o
ao . ea o
fM O o o
m
•n
o
fM
mm
• O
tn ao fM
•
d •4 N. . ee
tn •o in
y *
tn
«n O fM f H
m iM ml
"2 vfl «» fM
ee o o o
pfc fM
o
IM in o • o
ao n.
4.1
oo «n fM * >c
m IM > to xn -H
O ca •o vf N. tn
IM IM m o
an o o o
>
.07
o
1^ tn o • o
o fM
2.6
m «
tn
. o
oo o. o> (M ae
ae •<n o. »r fM rg
•«f
»n fM
o
00
ea o o
m*
O O
O
o • o
PH
o
0.1
ee eo fM • O
« >e eo .
m
>* in mm
00 3 -* •tn O IM
o
IM O o 3
mt*
O O
O
tn 3
• o
in IM
0.0
ft. 00
o • 8
mi*
fV in
o.
*H OC
m IM m
o-\n o o
fM 8 3
8
*iH
0.00
fM
o • o
•n fH
0.0
fv N »
o . 8
m «o 00
s»
o-mm
in
IS. « H
8 Xl 3
O
nj 8 8
8
tn
0.00
o
tn rw in a
8
eo ee .« • .•<
m 8 'O
8 >f
90 fM »n fM
»# •» * mm
O-
8
en 8 8
8
fH
0.00
m*
8 a 8
•* >
0.0
oo un m . 8
m ps un fM •n
8 •n fH
«» •n . H
«r eo — 8
eo 8 8
3
mm
8 8
8
3 8
8
d sT
0.0
IM Os m*
• 8
». 8 •n 00
"*
3 «# d
fH
«.
IM
o> 3
3
eo 3 3
3
f» 8 8
8
o>
8
8
sT •4
1.1
8 rs tn a
mm
« (M 00
<o •o
Ok
o>
pg oe
t> fH
«» 8
fM 8 3
8
fM 8 8
O
m
8
8
« oe
0.2
8 3 >o a 8
o» m o« "O '-'
rfi 00 o» un tn
«* eo 8
3
fM 3 8
3
•H
8 8
a
fM m* 8
8
<o in
0.1
•n fVJ sT
3
^ »n o> o»
•n 3 sf
in IM
(M .* a 3
fM 3 3
3
.f fM 8
3
>
3
8
o» in
3.1
fH 00 »n m
3
m o> m4
y *
f>. as fM
o <M
. . 3
-
00 3 3
3
8 «H 3 a
a
in 8
a
fH -*
0.9
fH in 90
fH
wn r«> sf
>e un
30 •n 3
fH
fH
tm
>o 3 IM
3
oe 8 3
3
(S.
3 3 a 3
0.0
f .
m
0.5
r» s»
f H
"t
8
•n •n
IM vO IM
nr rC
>»•
3 mm
3
00 3 3
3
O 8 8 3 8 8 8 8 8 8 8 8 8 3 8 3 8 8 3 3 3 3 ^ 8 8 8 8 8 8 8 3 8 8 8 8 8 8 8 3 8 3 3 3 ^ I b 8 8 8 8 a 3 8 8 8 8 8 3 8 3 8 3 3 3 3 3 i n » 9 » » m 9 » » » » 9 * » » * » » » * »
M i / s i n u n i n i n i n u n t n 8 8 8 8 8 e 8 3 8 e 3 3 « f . f « ^ f H . « . H f H f H f H f H . H t - l
WH tn in UJ ^
CJ M z Z l-H
in
z a ^ M tb 3 tn
z k-z >-UJ u.
in
50
0 0
00
vf
00
0
e tn
00
0
8
a
8 8 a
f H
a a 3
vT
00
0
3 in
00
0
3 3
50
0
8 3 8
a
00
0
3 sn
3 3 3
3 O
50
0
00
0
3
00
0
3 in
00
0
3 3
000
-
8 3 3
3
00
0
3
m
00
0
3 3
50
0 0
00
3
00
0
3 m
000
3 a
50
0
3 3 3
3
00
0
3 m
00
0
3 3
8 3 8
-
3 3 3
3
00
0
3 un
3 3 3
3 3
50
0 0
00
00
0
3 m
00
0
3
a
50
0
3 3 3
3 3
3 in
3 3 3
O 3
000
mm
00
0 0
00
3
m
.00
0
3 3
50
0 .0
00
00
0
3 un
.00
0
3 3
50
0
00
0
00
0
3
m
.00
0
3 3
00
0
-
00
0
00
0
3 sn
,00
0
3 3
50
0
00
0*
3
00
0
3 un
.00
0
s 3
oos
.00
0
3
00
0
3 in
.00
0
3 3
00
0
^ 4
00
0'
c
.00
0
3 tn
.00
0
3 3
50
0
00
0*
3
00
0
3 tn
.00
0
3 3
50
0
3 3 3
3
00
0
3 in
.00
0
3 3
00
0
md
.00
0
3
00
0
3 tn
00
0-
3 3
} <^
211
oc <X Z UJ mm
a: « z UJ fcH I Vi
in ^
^ IT lb
a •v
lb
h-
r tb
a*^ te a
m a a . a
ao a a a
a
s»
a fM
a
a
» ee s# a a
" • .0
0
a
fM
3
0.0
fs.
^ a a a
K.
a
a
«4
a a a
a
a
0.0
sf
fM 3
a
a
f H
a a
a
>f fH
a a 8
o> fM
OaO
<e o-a
a
N.
a
mm
•n
aOO
a
ao a
OaO
m ae tiH
a
a
f H
a
a
fM
aOO
a
a
OaO
m ». 8 a
8
oe 1*1
(M a
a
ee tiH
a a
IM
xn
0.0
a 00 in
a ^4
f H
fM
a
•n
^ a a a
un fH
OaO
.H
fn m a a
un 8 (M a
V H
•* a a 8
f .
OaO
o» a tn a 8
in
IM
fs.
a a
p-
fs.
a a
<M
wn
Oal
m fM
a a m
^
a V H
fM
0.03
CO un
0.0
» in Ol a
«4
f>» IM m a
^
»
OaOl
a
0.0
o» m fH 8
vH
^ m a
(M
sT
a a a
un
a
0.0
o in IM
a a
N.
"n a
a
f H
3 3
a
»»i B
OaO
tn
<c 3 a
8
.# a
a
^ a 3
8
IM O
OaO
fl 1 ^
a • a
<o a a
a
oe fH
a a
fM fM
a a
a
un pk 9 a 3
m 00 IM
mm
in
a 3 a
8
<M
0.0
IM tn (M
3
. m
3
•n 8 3
• a
30
0.0
f H
tn
fH
a
tn
IM
S
020
•
O
K>
O.Oi
•n
a fM
no Ol
IM
fM
r 3 3
a
a
a
0.0
00
-o a
m
rsi
a
- H 0 0 < i * O ' ^ . v O f M f M i / i » O « » n j 8 i n e 0 ( » s . O f M t n > n ~ . _ ! 2 ' ^ i " * ^ ' * ' ^ ' ^ ^ ^ ' ^ ' * ' ^ 8 a . » f M v r 3 w n a e • - l ^ n , 0 0 • n w n ^ f w e o ^ / ^ ^ n l n u n e O ( M l n l * l 0 3 ^ o ^ o t n a . > c f s . d a o o u n i * « H a e * - ^ o - i n s r i M u n . # o J * M e >• P » f H ' ^ > o » n d t t n f H 3 f H . « o i i M - H i o o . ^ ( v > f
IM « s fH . n fH
f f c P . f H ^ . . ^ a ( ; ^ ^ p ^ ^ , ^ ^ , . < ^ , t i , ^ ^ ^ l ^ ^
3 • n N . s f M i n p . N . o . e o > « n > n f M f . » . 3 3 r > O f . . « > a : M n j o > o i s . O i n j . * ( M « f 3 i n f M r s i K n o » o . f i . i » n » o o ^* i n a a a a a a a a a a a . a a a a a . . . t n Q L ' o • n ( ^ J X n J d . . ^ l ^ J • n ^ O f H m a o > n o > f H f H . ^ ^ . . , ^ J X a : > » « M » H p » a o ^ ^ . ^ r ^ > s . > 0 ^ « . * ^ ^ 5 ( 5 ' M N . " n . ^
f H P t e f H aH l A I M f H f H . ^ t x _
u. ' n • . * ^ w . * l ^ J l ^ J , M ^ . d t n l n a l n « * ^ . 3 « C v f - H , o lu • C ^ . » < n a 3 . f f M > o & > . . f o e i n i . n i O » H m f N j 3 c o i f M v f Q 2 t ^ O O m m t \ l m m , ^ O O m m f \ j , ^ l ^ m m O O - l t m m f > ^ ^ ,
a 3 a e . * a a 8 a e » H a 3 e 8 3 f H 3 8 3 3
a <r fM O <- 3
J m 3
b. a
in o
•M a a
nj a a
eo a 3
eo 3 a
00 8 3
IM 8 a
fM a a
fM ee a a 3 3
on 3 3
en 3 8
nj 8 8
rsj 3 3
IM 3 3
on 3 3
ac 3 3
00 3 3
IM 3 3
fM 3 8
O 8 8 8 8 8 8 8 8 8 3 8 8 8 8 3 3 3 3 3 3 3 ^ 3 8 8 8 8 8 8 8 8 8 8 8 3 3 3 3 8 3 3 3 ^ 0 . 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 3 3 3 Ul m m 9 » 9 9 » » 9 9 9 » m » » t 9 t » t
kH
m Ul UJ ^
3 3
m
8
3 tn
a a a
a a m
a a m
a a a
a 3 un
a a m
3 3
a
a a m
a 3
m
3 3 3
3 3 tn
3 3
tn
3 3 3
3 3
m
3 3
m
o 3 3
3 3
m
3 3 tn
^ 0 3 3 3 3 8 3 3 3 3 3 3 3 3 3 3 3 3 3 3 O 0 0 0 0 0 8 S 3 0 3 3 3 3 3 3 3 3 3 3 3 I . H Z 3 0 8 0 3 3 3 3 3 3 3 3 3 3 3 B 3 3 S 3 Z M a a a a a a a a a a a * . • • . « . • . b- ^ , ^ > ^ » » > » ' v a 3 3 a 3 3 > f > » ' v » - ' . f > f » * 3 3 Vrt „ , ^ f ^ f H f * » H f . f «
Z
a 3 in
z UJ
o r) 3
f-> m
f-i 8
a 3 3
3 3 3
3 m
a 3 3
3 8
3 3 3
8 in
3 3 3
8
a
a a a a in
a 3 8
3
o
3 3
a 3 in
3 3 3
3
a
3 3 3
3 tn
8 3 3
3
a
a 3 3
3 in
3 3 3
3
a
a 3 3
a tn
a 3 3
a a
3 3 3
3
m
3 3 3
3
a
3 3 3
3
m
3 3 3
3 3
3 3 3
3
un
3 3 3
3 3
3 3 3
3
m
B C 3
3 3
3 3 3
3 US
3 B 3
B 3
fM
3 S 3
3 in
3 B 3
3 3
fM
B B 3
3 in
3 B 3
3 8
fM
3 B 3
3 in
3
3 3
3
3 fM
3 B 3
B in
3 3 B
3 3
nj
3 3 3
3
m
3
3 3
3
O fM
3
3 3
3 un
3 B 3
3
3
3 3 3
B
m
3
B 3
3
CJ
fM
212
« z UJ M
X >s
>
m 3 a
a a
a a
8
a 8
(M
a a a a
3
a a
m a a
a
a
a a a
a a a •
8
fM — a a a 3 • •
a a
«# a
a a • a
8 a
a 3
a 8
3
a a 3
a a
a a a
a
a
X V i Ul ^
fs. a a
30 in
a a a
a
un (M a
a
a
a a
a
a
•n a a a
8
IM 8 a
a
a
< # t - «
a a
a
a 8
a a
a
a
a IM a
a 8
a a
a
IM
a a
a
o> <o f* in
a a • a
8 a
v f a
ao a a
»M a 3
a a
a 8
C U .
c ^ > a
O. 8 a n j
s f fM
a fM
ao 00 un
fM a
a
tn fM
a a
8
a 8
a Ps f n
a a
o> a
eo
a a
a
s# ^. a
a
O fM
IM - H a a
8 a
m a
fM O l
a
a
v f un
IM
a fM a
a
a
v f IM
a a
a
o. 00
a
a
a " v m 1*1
a
a
ee K i eo
a
m fM eo
a fM
OO 00 IM
a
a
p. eo a
ps.
a m 30
N . fw tn ^
O l (M • f
fM >C 8 fM
a •H a
a 8 «H
tn a
N l fM Ol
eo a a a
- H WH 8
ee f H mm se
Ol n j
a 8 3 M
IS. i n O"
^ t n t n 0 .
a : sH b . m tn a .
UJ
a z
Ol 3
a a fM
a
n j
a
m f H in
«M a
•n • c
Pv 3
i n fM t n un «M fM
a a
fM 8
m
m a ee
a
Pv O v f
00 a f H fV/ >« 00
a a ao v f
in s f
a fM Ps ^ .
a a «o O^
fM fM
a
>n f H ^ f H
v f un fM
a m m
3 in
a Ok
fM i n 00
a fs.
fln ee IM
a o> •n ^ f H o
v f Pv v f
a fM
3 v f fM
n j >C m
a m
3
OO m
p .
IM
3 00
a m
fM
3 f H 00
•a n j
3 a
a
fM P . v f
a wn 3
a IM
o>
f H
v f a
3
>e 3
00 3 IM
3 o>
v f v f
0> fH f n fM 8 n j
a a a »H
00 n j
v f fM
IM P H
a
a
un un
-H <0 fH un fH a
f H O
pg f H
un >o
an n j a a
M 8
O-
BO ^
>o v f
in
3
f\j IM
00 v f 3
AJ Pv
m an i n
8 t - l
a « a « . J i n ^ 3i£ t n
fM 8 a
ee a a
00 a a 8
a a a
a a
pg a a
an 8
a
00 3 3
ae a a
p j a a
n j fM a a a e
00 3 3
00 8 a
oo 3 3
fM 3 3
fM 3 3
3 3
eo 3 3
a 8 8 8 8 8 6 8 8 8 8 8 8 8 8 8 8 3 3 3 3 3 b > 3 8 8 a a a 3 8 a e a a 8 a e 8 8 3 8 8 _ j i b 3 a a e a e 8 8 8 3 8 e a 3 a 8 a 3 a 8 U l a a a a a a a a a a a a a a a a a a a a
t" t n i n i / s t n e e e a e a a a e 3 3 3 u n u n u n m
an tn in UJ ^
^ o bt Z Z M
tn
z a ^ SH lb
3 tn
z z •-UJ lb .J ul
8 3 8
mm
8 3 3
8 f H
000
3
000
3
a pg
a 3 m
3 3 3
3 "
000
3
000
a a fM
a a un
a a a a t-l
000
a
000
a a pg
a a a
V 4
a 3
a a '
000
a
000
200.
a a un
a a e
000
3
000
3 a pg
a a in
a a a
000
a
000
200.
a a a
f H
a a a
000
3
3 3 3
200.
3 8 tn
3 3 3
000
3
000
3 8 fM
3 3 un
3 3 3
000
e
.000
•002
a a a
-
3 3 3
000
8
a 3 3
200.
3 3 in
3 3 3
3
000
3
000
3 8 pg
3 3 m
3 3 3
3
000
3
.000
200.
3 3 3
^ 4
8 3 3 3
000
3
.000
3 B pg
3 3 m
3 3 3
3
000
a
.000
200
3 3 m
3 3 3
3
000
3
.000
3 a pg
3 3 8
fH
3 3 3
3
000
B
3 B 3
3 3 pg
3 3 un
3 3 3
vf
000
B
3 3 3
3 O pg
3 B m
3 3 3
vf
000
B
B 3 a
200
3 3 3
m^
3 3 3
vf
000
3
.000
3 3 pg
3 3 Ul
B 3 B
vf
000
3
.000
3
o pg
213 YSHEAR
K/IN
ae
« z
XSHE
K/I
^ C lb
> •
m
0.00
ce 8 O
'O
. eo «H a a
fM 0.
00
.#
a a . a
vf
» a a
eo I O
'O
PK an O
'O
<e tn m f H
^
0.00
wn • H
0.0
pg pg
a
vf
0.00
fH
f H O'O
m a tn • a
fs>
0.07
t\i
>n
0.1
^
a a
vf
PU
0.0
3
ee in
0.0
m mm
o a •*
»
0.01
a ^
0.0
^ vf tiH a
f H
nj
0.00
fs.
a
0.0
WI Ps
a
a
.* OO
'O
in
a
OaO
o> m a a a
f H
0.00
pg
a O'O
a pg
a a a
K OO
'O
t^
t^
0.0
eo o-m a a
pg
0.00
m P H
0.0
« WI mm a
8
• H
0.00
a
0.0
o >o a a a
a
0.02
m PJ
0.0
00 o> p.
.H
Pa OO
'O
8 f H O
'O
a ao m a
vf
0.00
Pa 3
0.0
fb r\j tn
a
•^
0.05
m m
0.0
\n vf vf
m
oo
0.01
. ai
0.0
Ol ^ «o f H
wm
a a a
IM •m
0.0
1 ^
vf o a
X a
^ tn in a. >
ae sn ^ tn tn a. X
l b UJ
s f » i n » f M 9 o o u n a f M e o ^ o e o > . - i f H f H u n i n a ' * ^ r ; r * r ' ^ " ° ^ * ' ^ * ^ * * ^ » ^ ' ^ « ' N . o i i n v f P J • n f ^ J ^ . ^ ^ / ^ f ^ f V J 5 ^ 0 , ^ ^ ^ ^ ^ ^ ^ y n ^
8 e » P I ^ 8 a H ^ ( M a e 8 f H O a f M 3 s ( > a i V f ^ t-H
o i f M ^ a f ^ P . o ^ f n i n f - o « n j i n f M f ^ w i u n p . f ^ t > f H ( M s f « n 3 a o a e » n f H f H » « g a n a O v f p a f H ( M O » f H i n e o ^ t a « f n a n a o o e o a ^ ^ « « e o e o e o e o > o < 0 0 > i e
9 0 v n P M f H O O v f . » a o u n > f f b ^ 8 u n ^ . « f o . o a e ^ o • O w n ^ a i t M ^ f H ^ v O f ^ ( V l l / > f V j O a n f H " j i > v n
fM "^ fM an "n
f M > 0 ^ » n o o u n a v f f M o e i M O ' O i a > O u n u n f v j O f H ^ s f p . i n a n o . n j f H a e u n N n f H ^ f l o a o c o p « 3 3 e s a o f ^ o O f H ^ i O f H m t n t . H t . H > n e o P v 8 e e a o i n f S i f s .
" n o > o o " n » n e e s f . ^ 3 e P » . # e o » H . O O > P s . i M e r i n ^ . P s « o » p . . ^ a O f « . ^ 3 n j f H » f f H m i M a n n j « f i n o i m* mm « e r M a H . M > r f H fH . # , - (
r M f ^ < 0 > O v f f M " n O ' ' n ' n f M v f f M ' ^ « f . o p » o c > o p > f H i n a n j ^ f ^ « n « O f H O i ^ . . f u n f ^ m m . o f n ^ . o o
a n f H s 0 f H 8 t n a n f H i n f H 8 ^ a n f « . 0 » H B 3 C - V f H
3 a 8 a 8 a H 3 3 8 8 a M 8 8 8 a a f H 3 3
a « B l-H -I sn tm a Ul
OB 3 a
ae 3 3
PJ 3 3
IM a a
pg a a
00 a a
00 a a
00 a a
fM 3 3
IM 8 3
fSJ 00 8 8 8 a
00 3 3
on 3 3
PJ 3 3
fM 3 3
PO 3 3
00 B 3
3 3 3 3
Q 8 3 3 8 3 3 8 3 3 8 8 8 8 3 8 3 3 3 3 3 3 ^ 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 3 8 3 3 ^ I b 8 8 a a 3 a a 8 a a a a 8 a 8 a 3 3 3 3 Ul 9 m m » * » » » » » * » m » m * » * » »
« f H f H f H ^ ^ - H f H f H
an Ul tn UJ ^
^ o an Z
X an
tn
z bf
a •-an tb 3 tn
X kf
z ^ UJ lb -J m
a a m
a 3 a vf
3 3 3 a
8 in
3 3
a
2 00
.
8 3 3
f H
3 3 3
vf
3 3 3
3 tn
3 3 3
2 00
.
8 3 un
8 3 3
3
3 3 3 a
3 in
3 3 3
200.
3 3 m
3 3 B
3
3 3 3 a
3 tn
3 3 a
200.
a 3 3
f H
3 3 .3
3
3 3 3 .
3 •n
3 3 3
2 00.
3 3 m
3 3 3
3
3 3 8 .
3 in
B 3 3
200.
3 3
m
3 3 3
3
3 3 3 a
a un
3 3 3
2 00.
3 3 8
f H
a a a a
a 3 3 a 3 un
3 3 3
200.
3 3 in
3 3 3
vf
3 3 3
. B tn
3 3 3
8
3 3
m
3 3 3
vf
3 B 3 a 3 in
3 B 3 a 3
3 3 8
f H
8 3 3
vf
a 3 3 a 3 in
3 3 3 a 3
3 3
un
B 3 B
vf
3 3 3
• 3
m
3 3 B
3
3 8 m
3 3 3
vf
3 3 B
. 3
un
3 3 B a 3
3 r> 3
p H
3 3 3
vf
3 B 3
• 3 sn
B 3 B
3
3 3 in
3 3 3
3
3 3 B
3
m
3 3 3
3
3 3
m
3 3 3
3
3 3 3
3 in
3 3 O
B
3 3 3
-
3 3 3
3
3 B 3
B in
3 3 B
3
3 3
m
3 3 3
3
3 B B
S
3 B 3
3
3 3 un
3 B B
3
3 3 3
3
m
3 3 3
3
3 O 3
-
3 3 3
3 3 B
3
B
3 3
1 50.
214
oe 4 z UJ "* X 's* «n ^ >
«
a z
XS
HE
K/1
N»
C lb
a N, > 8
ib
t>
c u. a > z ^ K a
Ik
a: b. bt tn Ul a. V
ae a. ^ Ul
tn a. X
u. tu
a z an md
a
a
a ^ _i tn Sm U m
a 3 *-_l u. in
an in Ul tu ^
•iH
a 3 a
a
00
a a a
a
« ^ a a
a <« IM
a
f H
vf
un 00
nj
00 PU
o> vf
!>•
m in an
a
fM
a a a
a a a a
a a m
I.H
f H
a a 8 a
PK
a a 8
a
eo ^ 8
8
m p» a a -
• *
eo yO
<o
PJ
<o vf
yj (M
f H
P.
a a
pg 3
a a
a a a a
a a m
p.
P 4
a 0.
0
•4
a
0.0
o» a a a
a .# a a
(M «1
^ tn
o> ..# Ol
an mm
ye wn a a
pg
a a a
8 a a a
a 3 3
. 1 .
a
0.0
<o •* O
'O
Ol
pg aiH
a
fM
wn m
a
a Ol
wn
00 vf
in wn vf
pg p .
l*
3
>o a
vf
a a a
a a a a
a a m
mm
a
0.0
tn 8
0.0
mm WI
a a
sf
tn f .
a
Ol
a m M
V H
fb
fM
eo 00 vf
PI-
pg f H
8
vf
a a a
a a a a
3 3 un
*H
a
0.0
Wl
a
0.0
yO
mm a a
pg
en a a
wn fM O-
un
wn
a oo tn pg
P H
iC
a a
V *
a a a
a a a a
3
a a
<o a
0.0
pg PJ
0.0
v#
tn mm
"•
o« wn vf
mm
^ PJ pg
Ol
>o
m vf
wn
-o 00
in
a in
a
PSJ
a a a
a a a a
a 3 tn
<M
3 O'O
m mm
0.0
mm O-nj
a
pg v»
so
a
o» p> V *
p .
•*
K. vf
m
ao an
^ a ItH
a
PJ
a a a
a a a a
a a m
aH
a
0.0
«H
••«
0.0
Wl
<« -"
a
s# Wl v#
o
un m Ps
o>
00
an e
«o pg
^ m 3
a
pg
a a a
a a a a
3 3 3
» a
0.0
eo •n
0.0
m mm >o f H
eo WS mm
pg
pg
eo eo
"O
o>
o> un pg
90 pg
00 vf Pv
a
sf
a a a
a a a a
3 3 tn
pg
a
0.0
00 <M
0.0
ee f H
sf
a
» Ol Ol
a
wn a
in
pg
wn in
o>
o> •n
^ m -H
a
vf
a a a
3
a a a
a a in
P H
a
0.0
fM fM
0.0
« Wl
fM
8
Ol OS «
a
p. ^ pg
.* •*
wn us O-
.—
.f
>o p. 3
3
.f 3 3
a
a a a a
a 3 3
aH
3
0.0
IM wn
0.0
m wn nj
a
10 ^ a V H
tn 00
a 00
00
fH
un vf
K pg wn
Pg
a fH
mm
eo a a a
a a a a
a 3 in
^
a
0.0
» a
0.0
<« in a a
•n ^
8
« m f H
W H
pg
a lO
m
wn Oy
pg
fM Pg
3
ee a a a
3 3 3
a
a 3
un
f H
a
0.0
m 3
0.0
Ol fM
a a
>e >o
a
Pa
a o. a P H
3 f-H
tn
o-vf
^ t.H
f H
3
00 3 3
3
8 8 3
3
3 3 3
vf
f H
0.0
fs. Pa
0.0
<e wn m
fM
vf
wn
wn
m*
m f H
(M
in fH
3 fM 3
pg wH fM
vf Wl IM
fH
eo 3 3
3
a a a a
a 3 in
^ *a
0.0
m tn
0.0
Wl
p. <o 8
ee m
"•
pg tn wn
a vf
o-PH
»
pg 3
3 in fM
8
eo 3 3
3
8 8 8
3
3 3 in
fM e5
0.0
<M vf
0.0
9" 90 Wl
a
f H
tm
aw
«M trs
wn pg
wn vf «
wn Pv
un PJ pH
a
00 3 3
3
3 3 3
3
3
3 3
rm o
0.0
eo a
0.0
vf ..f
a
IM O^
3
N. Ol
an
un
pg le in
>f
tm
.f an
.f
a
PH 3 3
3
3 3 3
m
3 3
m
^^ m
0.0(
fM 3
0.0
fM Wl
a a
in
a
.# 3 3
pg
VH
00
» 3
an vf
•w H V
3
3
pg 3 3
3
8 3 3
in
3
3
m
^ 0 8 8 8 8 3 8 8 8 3 3 3 3 8 3 8 3 3 3 3 CJ 0 3 0 0 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 a H Z 3 3 8 3 3 3 3 3 3 3 3 3 3 3 3 3 3 B 3 3 Z S H . . . . . . . . . . . . . . . . . . . .
b- ^ ^ , . ^ , ^ v f v f B 3 3 3 B 3 v f v f » f 3 B 3 v f > f tn ^ f - f , . H f H f - .., — -H
z ^ a ^ an tb 3 tn
z b.
z w-
-J tn
3 3 3
3 m
3
o 3
3 m
3 3 3
3 m
3 3 3
3 un
3 3 3
a m
a 3 8
8 tn
8 3 3
3 in
3
3 .
a a tn
3 B 3
e m
a . a a a m
a a a a un
a 3
a a tn
3 3 3
3 in
a B 3
3 m
a 3 3
8 sn
3 3 3
3
m
3 3 3
a m
3 3 3
3 tn
3 3
a 3
m
3 3 3
3 un
3 3 3
a tn
3 3 3
3
m
3 3 3
B in
3 3 8
3
un
3 3 3
3
m
3 3
a a tn
3 3 3
3 in
3 3 3
3 tn
3 3 3
3 in
3 3 3
3 tn
3 3 3
3
m
3 3 3
3
m
3 3 3
3 in
3 3 3
3 tn
3 3 3
3 in
3
B 3
3
m
3 3 3
3 tn
S 3 3
3
wn
3 B 3
3 in
3
3 3
3
un
215 Y
SH
EA
R
K/I
N
XS
HE
AR
K/I
N
M C lb a n^
> a
lb
^ Z lb
a'v z ac 8
w-ib
hf in tn a > p
oe an »- in Ul 0. X
u. UJ
a z an an
a
a
a WH .J in w. ^
lOO
'O
0.0
01
<o
0.0
1
o» m a a
P H
a mm
yQ
^ -« a IM pg
vf vf
3
a
fM
a a
a 8 a
0a
01
6
un
0.2
8
fM ^ ».
a
PJ
a ao
>e a tm wn pg
vO
vf
Wl
an
>o fs.
a
.# a a
0.0
0 1
0
.00
4
wn
0.0
6
^ fM pg
a
a a 00
Wl
pg
ae ao rvj
un • «
in
m mm
a
vf
a a
I OO
'O
0.0
02
fM
0.0
3
K
^ "*
a
eo * a PU f H
ps.
oo >o m vf
en p. a a
vf
a a
20
0'0
0.0
32
a
1.3
1
^ Wl in
tn
o> mm
>e 00
Pte
^ f H
pg
a a pg
>e tn in
a
PJ 3 8
0.0
03
0.0
17
a
0.3
9
N. PJ pg
•*
a ep wn an IM
OO
9-in
wn ^
«o f H
f H
a
fM a a
20
0'0
0.0
12
». 0
.21
Wl .n fb
a
pa lO mt
Wl
"*
a a a sf 1 *
o> in
a a
pg
a a
0.0
17
0.0
66
>
2.3
8
i #
K a <«
wn fH
m wn vf
•f wn .»
vf
Wl
o> vf 00
a
< a a
90
0'0
0.0
32
^
0.7
5
a « wn
pg
m 00
a un •*
a a >o fH vf f"
3 00 f H
a
vf
a a
»0
0'0
0.0
22
>o
0.4
2
aW
fM •#
••
^ 00
m m pg
rsi
pg IM
m oo
p H
o> a a
^ a a
SO
O'O
0.0
31
^.
0.5
6
tn Wl Ol
WH
Wl
fb sf
PU
IM
» •
vf 00
vf <M Ps
3 pg vf
**
en 3 8
lOO
'O
0.0
08
>o
0.1
2
Wl
m .f
a
a * Wl
pb vf
a o> «o o. ^
o. oo PJ
a
ee a a
lOO
'O
0.0
04
>*
0.0
6
pg Wl pg
8
vf O' a vf pg
a wn o» lO
eo
m vf fl.
a
00
a a
0.0
35
0.0
99
00
4.5
4
a m un
WH
Pa < 00
pg fb <M
rg a a an o>
N l
wn vf
pH
00
a a
0.0
13
0.0
63
in
1.4
7
rb fM <o sf
ye fs. vf
eo eo
a a <«
p. Pv pg
p-a an
a
ao 3 3
0.0
07
0.0
43
a
0.8
4
in Ol p.
»M
Pa pg
vf
a m
in » •
lO
fb
H5 fH
>o in •H
a
00
a a
20
0'0
0.0
07
Wl
0.1
7
Wl
tn (M
a
Ps a p.
•* •o
•n O' o> vf
o»
fl. p. p.
a
fM a a
I OO
'O
0.0
03
Ol
0.0
3
>e .fi a 3
eo pg
m
vf fH
vf N. lO
.f nj
•e m fH
3
pg 3 a
0.0
01
0.0
02
a
0.0
2
fs Wl
a a
« 00 wn
m.
Wl pg
i>
an
'^
00 Pv 3
a
fM 3 8
0.0
07
Of O
'O
«f
0.5
9
Pa 8
mm
00
o. >o Pg pg
'M
vf
p. v3
^ 3 .f
e an O
Pg
on 3 3
tn
o a a a a a a a a a a a a a a a a a a a a 3 k . o e a a a a a a a a a a a a a a a a a a ^ t b 8 a a a a e a a a a a 3 8 a a 3 8 8 8 3 m . a a a a a a a a a a a a a a a a a a .
<S p M ^ f H « H f H - H f H . > l p H p H f H f « f H . « f M f 4
SH in m UJ w
a a a
a a in
a 3 tn
a a a
a a m
a 3 m
a a a
3 3 in
a a us
a 3 3
3 3 un
3 3 m
8 3 3
8 a in
a 3 m
3 3 3
8 3 un
3 3
m
3 3 3
3 O US
un fH tn fH in fH p. un PH fH ps. un
^ 3 8 8 8 3 3 8 8 3 8 3 3 3 3 3 3 3 3 8 3 O 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 S H Z 3 3 3 3 3 3 S 3 3 3 3 B 3 3 3 3 3 B 3 3 Z M . . a . a a a . a . . . . a 8 b. . f v f > f v f 3 3 3 3 3 3 v f v f » f 0 3 3 v f . # v f . f i n f i < f a t . H p H f N f H f H p H f H
z b-
a b-aa Ib
3 •n
z ^ z UJ lu -1 tn
3 3 3
3 in
3 3-8
3 in
3 a a 3 un
3 3 3
3 m
3 3 3
3 in
3 3 3
3 in
3 3 3
3 in
3 3 3
3 un
a a a 3 tn
3 3 8
3 un
3 3 3
3 in
3 3 3
3 in
3 3 3
3 in
8 a a a m
a 3 8
8 un
8 3 3
3 tn
3 3 3
3 in
8 3 3
8 in
3 3 B
3 sn
3 3 3
3 m
3 3 3
3 in
3 3 3
8 un
B 3 3
3 un
3 3 B
3 m
3 B 3
B m
3 3 3
3 un
3 3 3
3 m
B B 8
8 m
B 3 a 3 tn
B 3 3
3 m
3 3 3
3 •n
3 3 3
3 m
3 3 3
3 3
3 3 3
3 m
B 3 3
3 3 tm
a 3
3
3 tn
3 3 8
3 3 fH
3 3 a a m
3 3 3
3 3 tH
3 3 a 3 m
216
oe <z z
YS
HE
K/I
oe <s z UJ WH
X "v Ul M X
^ C Ib aN» C M > •
tb
ha Z Ife
a >s Z M X a
W-tb
« -H ^ Ul Ul a. >
a: "H w. tn tn a. X
u. tu a z sa tH
a
a a SH U Ul ^ it tn
a 3 b. ml U. tn aa
«
»m tn in UJ ^
^ CJ PH Z X SH
in
SU
IDT
H
FT
SL
EN
TH
F
T
fM
a a 8
m • *
a a a
m Wl f H
a
fM fM wn
8
un ># in
a in
a ec o-pg
a fH
3 Wl
in
8
eo a a a
a 8 a a tn
8 8 m a Ps
3 8
a a vf
10
0.0
00
50
.00
0 1
tm
a a 8
o> a a . 8
Ol
lO 8
8
N.
ee mm
a
pg Pb lO
tn pg
* ye
m pg
m
un lO PJ
a
00 a a a
a o a 9
m
o a a
15
.
a a a a
vf
10
0.0
00
50
.00
0 1
W H
pg
8
a
pii PJ 8 a 8
8
m ao f H
pg
•# wn "•
v# p. o> a f H
pg
* .f
a 90
<o 3 3
f H
fM 3 8
a
a a a •
i^
1
a o un a
fH
3 8 3
3 '*
10
0.0
00
50
.00
0
:
« a a a
a « •
a 8
a
a oo un a
fb
>o m a
vf
> p.
vf
ft
pg
a a
an
pg
a fM
a
pg
a a a
a a a a m
8 8 m a N-
8 3 3 a 3 -*
10
0.0
00
50
.00
0
]
-* a a 8
p.
a a 8
a
-c PU Wl
8
•# «o Wl
8
f H
N. m > W H
wn vf
eo
p j
fH
a mm
a
pg
a a a
a a a a un
a 3 a
15
.
a 3 3 a 3 f H
10
0.0
00
50
.00
0
eo m 8
8
pg
m a 8
a
Pb
.* >o m
wn >n o. sf
oe eo Pa
00 Wl
wn
un in p.
o> pg
a vf 00
pg
an a a a
a a a a m
a 3 m a
fH
a 3 3 a
3
•*
10
0.0
00
50
.00
0
eo m*
8
8
>0 wn a a a
Wl v#
<«
"*
a Wl mm
fM
<o P. m 00 *
>e fb
N.
pg
^ p. m a
ee a a a
a a a . m
a a in a
Ps
a a a a "*
10
0.0
00
50
.00
0
a .H
a a
fM wn a 8
a
Ol
Wl Ol
a
W H
. 4
• *
wH
IM <a wn <o m
"O 00 yt)
30
fb
00 IM
a
on a 8
a
a a a a un
a a a
15
.
a 3 3 • a f H
OO
O'O
Ol
50
.00
0
f H
a a a
o a a a a
^ pg 9m
a
un sf
.# a
fM vf in
fb
vf
tn an p.
<o >o
in
^ »o a
fM
a a a
a a a a a -
a a m a
a e a vf
10
0.0
00
OO
O'O
Sl
mm
a a e
Wl
a a a a
8 Wl
a 8
v) a .a.
a
Wl
eo •* a •"
<M aa
O'
o> wn
•o wn f H
a
pg
a a a
a a a a a "*
a a m a p.
a 3 3 a
vf
10
0.0
00
OO
O'O
Sl
f H
a a e
f H
a a a a
sf f H
a a
m m a a
un W H
Wl
m
a p. .* a pg
no <C a a
fM a a a
a a a a a f H
a a a
15
.
a 3 3 a
vf
10
0.0
00
15
0.0
00
fH
a 3
a
Ni
mt
a 8
a
fM Wl pg
a
a oe 00
a
>o Wl
o> lO 00
a vf
a a an wn
wn o> fH
**
^ a a a
a a a a a "
a a m 9
a a a a
vf
10
0.0
00
15
0.0
00
mm
a a a
Ul
a a a a
rsj m a a
«« P H
fM
a
m fH
wn
o. fH
a 00
3
o ^
f H
vf pg
a
vf
a a a
a a a a a **
3
a m a Pv
3 3 3
vf
10
0.0
00
OO
O'O
Sl
f H
a a 8
Wl
a a a a
lO
pg
a a
eo a f H
a
in a 00
o.
tH
^ m
a vf
fH
IM fH
a
' * •
a a a
a a a a a "*
a 3 a
15
.
a 3 3
vf
10
0.0
00
15
0.0
00
O' a a a
ae pg a a a
Ol
vf m
**
sf pg in
nj
a f H
9
o>
^ Pg vf
f H
m ttH
Pg
O-f)
a
fM
a a a
a a a a a f H
a a m «
fH
a 3 B • 3
10
0.0
00
15
0.0
0 0
PU a a 8
>e f H
a a a
pg wn .# a
a vf
a •a
Wl
a >
pg
Wl
Oy
an
fM •n
a 00 "H
a
«M
a a a
a a a a a f H
3 3 tn
N.
3 3 B 9
3
10
0.0
00
15
0.0
00
mm
a a a
wn . a a a
ao Wl pg
a
ao sf
>e a
N.
>o pg
«H
pg
un 30
OO as
..H
e> 3
a
fM
a a a
a a a a
a p H
a a a
15
.
3 3 3
3
10
0.0
00
15
0.0
00
Wl fH
3
a
un un a a a
ao o> Wl
pg
Ps fb
un vf
a ye 00
vf -H
ao 00
un
^ P. IM
fs. OO wn
fH
vf
a a a
a a a a 3 fH
3 3 in a
3
3 3 3
10
0.0
00
15
0.0
00
vf
a a a
^ Wl a a a
a a p..
a
sf
a a pg
9-ye 9-
vf
.t5 in pg
a pg m*
l\l
m iM
a
.f
a a a
a a a a 3 f H
3 B m a Pv
3 3 3
3
10
0.0
00
15
0.0
00
pg
3 3
8
Wl "M 3 a 3
pg
> an
a
> un pg
**
90
» .f
pg
fH
pg
un
in fs.
pg vf fH
3
vf
3 3
3
3
a a 9
a f H
3 3 3 • un
B B 3
3
10
0.0
00
15
0.0
00
217
ae <z z UJ SH
X >a Ul ^
>
ae « z
XS
HE
K/I
a a 8
a
m wn a a
a a a a
a fH
a a
a a a a
m a a a
fM
a a a
ao a aH
a
a a a a
f H
>o a a
a a a 8
<o .# a a
a a a a
90
a a a
a a 8
a
pg
a a a
a a a a
f H
a a a
a a a a
« •H
a a
a a a a
«# a a 8
a a a a
pg a a a
a a a a
•o an a a
Wl
a a a a
Ps fH
a a
pg a a a a
(M f H
a
a
'fl f H
a a a
P H
fb a
a
<o a a
a
fM wn a a
vf a a a a
pg pg a a
un a a a a
fH
1^
a a
fH
a o
a
eo a a a
• - f M * a < C i n o » > o f M P » o e . # w i i n e o v f a w n w i w n f l o C i b v f ^ i / i ^ w n ^ ^ a n f H a e . o m f M o « f M w H . o w i t s , f M a ^ v f 8 a a ( M < « M a a p g a a w n w i / v j v f P b . ^ u n f H C ^ * 8 8 8 8 8 8 8 8 v a o a e v f w ^ a a a a a a a ^ a a p g a e a a
N. tb
Z i b w n f M " H ( 5 i w n o o P s . * u n . * p g . « » > 0 « o a p v > O P s O ' v f a N , ^ s f ( M > O O i v f « f f H e * l M p H a e f H p » w i f M w n 3 0 . * Z M a a s a a a a 8 a a a . a a a a . a a .
x a f H 8 8 a o w n p g e 8 a a a a f M w H o v n p j a H f H e
ac SH b- tn tn ^
>
a: 'H b> tn ul a. X
lb tu a z an an a
a
a WH ..J tn
^ it Ul
a 3 ^ -1 u.
an
^ in tn UJ ^
^ u an Z X WH W-in
SU
IDT
H
FT
SL
EN
TH
F
T
a tn fb
in O
sf 90 l O
>o m •e 9 pg pg
pg
er a a
a
8 a a
a
8 8 un
f H
o 3 8 a
vf
00
0*0
01
O
OO
'OS
rsi 00 9
yO
vf pg vf
fb
m -" ^ m vf
a
an 3
a
a
a a a
a
8 a in a P»
a a a a
vf
OO
O'O
Ol I
OO
O'O
S
wn eo fb
oe
tn Pa N l
a oo
lO pg pg
a
ao a a
a
a a a
a
o 3 a a m t.H
a a a a
vf
OO
O'O
Ol
OO
O'O
S
f H
ye fb
un
pg
00
a ye
mm
n j
un
oe N. an
pg
00 3 3
8
3 a a
a
8 a tn a
f H
a a 3 a 8 "*
OO
O'O
Ol
OO
O'O
S
in Ol
a
.#
o» ps. 9
tn Wl pg
<o 00 sf
a
oo a a a
a a a
a
a 8 m a
p.
a a a a f H
OO
O'O
Ol
50
.00
0
eo un 9
f H
a 00 00
00 vf f H
in sf
pg
a
00
a a a
a a a
a
a a a a
m f H
a a a a
a
00
0*0
01
0
00
*05
m a ps
sf
ae pg vf
> p. f H
o> a <o
a
pg 8
a a
a a a in
a 3 m a
l-H
3 S 3 a vf
00
0*0
01
0
00
*05
vf .* P H
fM
nj sf
a pg .f
.n pg f H
a
a a a
a a a tn
a a m .
N.
a a a a vf
OO
O'O
Ol
OO
O'O
S
a Pa P H
>o
9
wn m
i 4
pg
IM «o a
a
a a a
a a a tn
a 3 8 a
in mm
8 3 3
vf
00
0*0
01
0
00
*05
Pa 10
a 00
8
a a a
>o m Wl
00
un a f H
a a 3
8 3 8
m
3 3 in a
f H
3 3 3 • vf
00
0*0
01
50
.00
0
fH
vf
a
•*
a rg m Wl 00
i # P H
pg
a
a a a
a a a in
a a un a
N.
a o 3 vf
10
0.0
00
50
.00
0
eo f H
fM
pg
wn ^ p.
pg
.f
pv 3 fH
8
3 8
8
a a a in
a 3
a • in f H
3 3 3
vf
00
0*0
01
00
0*0
51
un eo sf
O"
pg
fM ps.
f H
P. '* >o fH
10
a
3 a a
a a a in
a 3 m a
" H
a a a a
00
0*0
0 1
0
00
*05
1
eo vf
ee Wl
p. pg
N.
O->o
N ye "H
a
a a a
a a a tn
a 3 in a
fb
3 3 3
10
. 1
00
.00
0
OO
O'O
Sl
9 tm
"-t
m
N. P H
fH
pg
.
m no 3
a
3 8
8
8
a 3
sn
8 3 3 a
un **
3 3 3
10
.
OO
O'O
Ol
OO
O'O
Sl
•o
« pg
N.
30
>o tn
pg
pg an
vf I t
pg
f H
3 a a
a a a un
a a un fH
3 3 3
10.
10
0.0
00
1
50
.00
0
m Pa fb
m
.f fb
oo
m wn
"* in
m fM
8
3 3
a
a a a m
a a in
. N.
a a 3
10
.
OO
O'O
Ol
00
0*0
51
P H
fb
o> in
•e fy.
vf
pg
oo
i>
pg " H
3
3 3
3
8 8 8
un
3 3 3
m
3
3 3
10
. 10
0 .0
00
OC
O'O
Sl
00 mm 00
vf
pg
vf
o> md
9 3 fb
Pv
tn 9
tm
«? 3 3
3
8 3 3
m
3 3 m
"*
3
3 3
vf
OO
O'O
O 1
O
OO
'OS
l
00
wn 00
Ps
P H
N vf
>o •o
" fs.
c> m
3
no 3 3
3
3 3
3
sn
3
3 n ^
3 3 3
vf
10
0.0
00
OO
O'O
Sl
218
a: « z UJ mi X ^ Ul V
ae <z z tu SH
Z N. tn it X
^
C lb
VMO
T
FT
.K/
C lb av. z >< X a
^ lb
ae WH b- Ul tn a. V
a: a. W- Ul tn a. X
tb tu
a z SH mm
a
a
a <-pJ tn ^ ^
a a a a
sf
a a a
in
<o a a
ee pg fM
a
wn tt.
wn
vf
fM
f H
a an
un 00
9 9 tm
a
ar a a
Wl
a a
a
a sf f H
a
.^
ae m •<#
mm 9 wn
a f H
wn sn eo vf fb
fM
in m vf
an pg -e
9 •e a pyj
eo a a
^
a a
8
^
a a
vf > sf
fH
> •
•« .»
^
ee ftj 'O
o 90
vf
<c f H
eo ye
a an vf
a
ee a a
a a a
a
•*
a a
^ m eo a
a fM fb
pg
N Pa
a f H
in
in N. f H
wn ye mm
30 f H
IM
a
eo a a
a a a
a
8 8
a
fb
m pg
a
>e p. pg
a
>
m .n lO
o»
a f H
vf
& •
^
ye an f H
"*
PU
a a
a a a
a
a a a
IM <«
a 8
PJ
a fH .
a
wn f H
Wl
Wl pg
o> pg p j
00 wn
oe pg fu
a
»M
a a
a a a a
a a a
pg Wl
a a
^
<o a a
a vf
o> f H
f H
O f H
a fn fM
vf mm mm
a
pg
a a
a a a 8
.H
a a
pg sf PJ
a
^
Ul vf
a
^
wn ee a 9
fb
fb
PM
O-ye
Pv ps. Pv
a
eo a a
a a a 8
a a a
• *
fM
a
fM fb pg
a
00 f H
«o lO vf
pg Ol 9
mm
a fH
o-en wn
a
00
a a
pg
a a
8
fM fM
a a
tn 9
rsi
m m ee f H
in pg Pa
P H
wn
in
a wn
fH
P H
mm
vf pa vf
fH
pg
a a
a a a 8
OO
a a a
fM
a
8
00 00
un a
>o a .H
PJ vf
eo in pg
m Wl
vf
o» PSJ
a
n.1
a a
a a a
a
<o a a a
Pb
a
a
^
<e wn
a
f H
a <#
vf pg
m us «o f H
pg
N. vf f H
a
pg
a a
wn a 8 8
00 wn a a
« PVJ
Pll
• *
• ^
Wl
pg
>o fb in
9 an t.H
00 tn
>o 3 vf
3 vf
oe
3
00 3 3
pg
a a
a
l>b
PM
a a
•• mm
mm
9 fM
m f H
o> a ao vf
00
p. lO P.
f H
O
a pg vf
a
00
a a
a a a
a
^
a a a
in 00
a
tn ^ .*
a
eo >A f H
9
<o
lO pg
on «e >n
a an 9
a
nj
a a
a a a
a
Wl
a a a
pg vf
a a
ee a a. a
wn ^
^ un "*
an 9 an
3 vf
p«. 00 fH
a
PJ
a a
a a a a
fM a a a
fH
pg
a a
m un
s 8
mm pg
a ao
P. an Pv
3 pg
vf
9 3
a
PSJ 3 3
a a a
a
fb f H
a a
Wl
« Wl
a
m « ee a
an p. O'
un w^ f-
an 3 Pv
PH
an Wl
yO
an iC
vf
3 8
8
a 8
a
m a a a
Wl
oo a a
sf f H
fM
a
IM «
a P H
an
^ 3 vf
3 «
3 an an
3
vf
3 8
3 8 a
a
wn a a a
PVJ sf
a a
a f H
f H
a
vf vf
eo m "*
oo « pg
PH
vf
in
>o ""
a
vf
3 3
tn B a a a a a a a e a a 8 8 8 8 o o o o c 3
a o a a a a e a e a a a a a a a a e a a a 3 ^ . 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8
- J i b 8 8 a a 8 a a a a a e a 8 a a 8 a a 3 3
i - u n u n u n u n u n u i J u n u n u n i n i n i n u n i n 8 a 3 8 e 3 A J f H f H f H f H f H f H f H f H t - t f H
tn tn UJ ^
^ «j
— z Z an W>
m
z ^ a ^
3 tn
z
z w-UJ Ik
- J
3 3 3
tn f H
3 B a a
vf
8 3 8
3
o o o a 3
f a
O o in
o 8 a a
3 t-H
3 3 a a
8 a
8 8 a a
a f H
a 8 m ^
a e 3
3
*-
8 3 a a
8 a
a 3 3 a
a mm
a a a a
m f H
a 3 3 a 3 f H
8 3 3 a
3 3
3 3 3 a 3
f H
a a tn a
f H
a 3 3
vf
3 3 a a
3 in
S 3 3 a 3
a pg
a a in a
^
a a a a
vf
a a a a a in
a 3 3 a 3
a pg
a a a a wn
-*
a 3 3 a
vf
3 3 3 a
3 tn
3 3 3
00.
fM
8 3
m a p.
3 3 3 a
vf
8 3 8 a
8 in
3 B 3
00.
pg
3 3
a a m "
a a a a
vf
3 3 3 a
3 tn
3 3 3
00.
pg
3 3 in a
f H
3 3 3 a 3
3 3
a a 3 in
a a a
00.
pg
3 3 un a
p.
3 3 3 •
a
3 B 3 a
3
m
3 3 3
00.
pg
3 8 3 a
in
^
3 3 3
3
3 3 B a
3 us
3 3 3
00.
pg
a 3
un a Pv
a 3 3 a
3
3 3 3 . B in
3 3
a
CO
.
pg
a 3 8 a
us fH
3 3 3
3
3 3 3 .
3
m
3 3 3
00.
pg
8 3 tn .
mm
8 3 3
vf
3 3 S a
3
m
3 3 3
00.
pg
B 3
m a p.
a 3 3 a >f
3 3
a a 3 in
3 3 3
00.
pg
3 3 3 a
in
B 3 3
vf
B 3 3
3
3
C B
00.
pg
8 3 in .
fH
3 3 3
vf
3 3 3
3
vn
3
3 3
00
.
fM
3 3
m N
3 3 3
vf
000
O
00
0
3 8 pg
3 3 3
m
3 3 3
vf
00
0
O
00
0
3 8 pg
219
ac a z X ^ tn u
ae
« z
XS
HE
K/I
b t
C lb a >s z a > 8
lb
b .
Z lb a V r it X a
w>
ae mm b- tn ul a. >.
ae an a- Ul Ul e.
Ol
a a a
a ^ fM
a a
a 91
PW >0 8
a^
fb
fb mm
IM
^
a fb
N.
Ol
a 0^
un
a
^
a a a
a un H *
OaO
tn
> vf a
a
an 0 0.
a
un ^ >o o* PJ
>o f H
m
0
fM
3
0.0
fM f H
a a
a sf
oo fM
8
Wl
Wl
<o
a
fs.
fM
a Pa fH
fb
un ac l>b
a fM
0.0
Wl
un 0
.0
Ol
(M 00 8
pg
sf
fM mm
sf
pg
mm ^
0.
<0 f.
tn
o> Wl
p .
pg
^ a
0.0
f H
wn
0.0
Pa
fM Ol 8
8
«r sf 0
W H
00 0. tn
in
un
PH
wn wn
116
m
a
0.0
wn pg O
'O
^ vf
m a 8
lO s #
pg
"*
^ • *
.#
pg
wn
9 sn Wl
vf
00
a
0.0
.# wn
0.0
». . M
Pb 8
a
vf
'O N.
M .
•* wn un
O-
pg
N
un in
65
6
pg
a
0.0
mm mm
0.0
un >e mm 8
a
ao pg vf
a
a tn N
f H
ye
9 3
o>
15
8
f H
a O'O
«e 8
0.0
•# eo a a
a
a IM fM
a
sO
oe sf
«H
an
ec yO in
mm
9 mm
0.0
«H
lO
0.0
mm 9 S.
a f H
lO vf
eo
wn
in .f vf
Pa
3
Ps. Wl
0
22
9
pg
P M
0.0
un vf
a a
a
in
un a a
f H
^ Ps
<«
PVJ
in
ee pg
an
vfi
9 ye wn
14
7
Wl
a
0.0
oe a
OaO
pg
a PJ a
8
•n fb
^
a
o> Wl
eo
Ul Ps.
p. mm Wl
177
mm
3
0.0
fM 8
0.0
Pb
^ a . a
sf f H
.«
a
a Wl
un
Pw f H
^0 an fb
pg
aH
a
0.0
vH
3
0.0
sf
pg
a . a
0^ un a
a
wn •0 »
ee
a «o 3
PVJ
ps
3 O'O
m ,iM
0.0
00
o> Wl a
a
00 m 9
a
>o a wn
» .f
m oc N.
35
1
fM 3
0.0
^ 3
0.0
fM Ol
a a
a
« fM fM
a
^ m ye
sf
wn
« 9 30
•«f
W H
8
0.0
fM 3
0.0
Pa vf
a a
a
Ps f H f^
a
<o fM P.
p.
**
00 fM 00
an
pa
mm
0.0
in •n a 8 a
fM sf tn
IM fb P>.
nj
a IM un
Pg
9
ye
9 pg
166
Pb
et
OaO
<«
0.0
fb
PVJ in
a
fM m^ mm
-
wn 9 Ul
f H
•n
m 3 0.
p.
vf
8
a a
a
, a a
a
90
a Wl
a
o-oo <e
3
eo m vf
an • •
3 us wn
m^d
l b f b i v . O f H f H P . a o m s o O > N 3 P . . * t n 3 u n o > f H v O tu • ^ i n f M w n o . f b ^ f a O > O w n w n > o o r w n O ' > ^ i t v a n , . ^ a Z f M f M f H P f c w n p H 3 > O w n ^ w n e e f H 3 » f p g f H . H P v i f H w H a H a . a a a a a a a a a . . . a a a . . .
o f H a a f H B a w n s e a a a a a f H e e f H B B
a «• i M P g p g v f v f « f a n e e a e f l o e c P J p j p g v f > f v f i s j f M P g a s H o a a a a a 8 a 3 a e 3 3 3 3 3 3 3 3 3 . J t n 8 8 8 a a a 8 a 8 a 8 8 3 8 3 8 3 3 3 3 ^ N ^ a a a a a a a a a a a a a a a a a . . . m 8 8 8 8 8 3 8 8 8 8 8 8 8 8 8 8 3 3 3 3
a 3 ^ -t u. Ul
SH
tn in UJ ^
8
a a a
a 0
m
a a a a
a a in
a a a a
a 0
a
a a a a
a a in
a a a a
a a Ul
a a a a
a a a
a a a a
3
a tn
a a a a
a a m
a a a a
3 3 8
a a a a
3 3 m
a a a a
a 3 8
a a a
3 3 in
3
a a
a a tn
a a a
a a a
a a a
a a tn
a a a
a 3 tn
3 8 8
3 3 3
a a a
3 3 un
3
a a
a 3 tn
a 8 3
3 3 3
^ 0 a- Z Z SH b-tn
z ^ a t-
3 3 3
3
3 3 3
a a a a
3 3 8
a a a a
a a a
a a a a
a a a
a a a 3
a 3
a
a a a a
a a a
3
3 3
vf
3 3
a
a a 3
vf
3 3 8
3
3 3
vf
3 3
a
3
3 3
3
"*
3 3 3
8
3 3
3
•
3 3 3
3
3 3
vf
3 3 B
3
3 3
vf
3 3 3
3
3 3
vf
3 3 3
3
3 3
vf
3 3 3
3
3 3
vf
3 3 3
3 3 3
.f
3 3 3
3
3 3
3 f*
3 3 3
B
3 3
3 p H
3 3 3
3
3 3
3
^
3 3 3
Z w-tU lb
tn
a in
3 3 3
3 in
3 3
a
a un
a a a
a un
a 3
a
a un
a a a
a in
a a a
a tn
3
B
a
a in
3 3 3
a un
3 3 3
3 tn
a 3 3
3 in
3 3 3
3 n
3 3 3
3
un
B 3 3
3 in
3 3 3
3 un
3
3 3
3 in
3 3 B
3 in
3 3 B
3 tn
3
3 3
3
m
3 3 3
B tn
3 3 3
8
a a a pg
a 8 Pg
a a PJ
3 8 8 8 .-M PJ
8 3
3
a 3 3 3 3 Pg ryj
3
a n j
a 3 pg
3 3 pg
3 3 pg
3 3 pg
a a pg
a a a 3 pg pg
3 3 3 3 pg Pg
220
ae « z UJ mm
X b ^
m it > ae 9 z UJ a. X b^ tn %e X
Wa
C tb a " V 8
»• C tu O >s IP V X .
b.
ae SH ^ in in O.
>>
ae WH ha tn Ul 0. X
u. UJ
a z a
a
a WH _i tn kf ^
tn
>e w a . a o. «o a a
a < a
pg
00
a nj
in
Pa
ee \n 9
•n
9 ye vf
pg fH
wn in tiH Pv
-*
vf
a a a
•o M H
a a
a
a Wl
a a a
.« O' Ol a
a
vf
a fM
pg
fH
vf vf
o> un
tn in pj
pg
an Pb
a un an
a
vf
a a a
^ a a a
a
. 4
pg a a a
o 00
sn a a
o> vf Wl
mm
oe a wn in
•n
pg
fH 9
3 00
p. N. " a
vf
a a a
vf
fH O'O
a Wl
a a a
a » Ps a
a
oe <« eo »H
m «o pg
lO Oi pg
vf
wn <o 3 3 N.
yC vf
>n pg
ao 3 3
8
Wl
a O'O
ae a a a a
vf
00 fH a
a
P H
un <# a
eo a * oo >o
fM fH
pg
o-ye mm
vf an
m a
00
a a a
pg
a
0.0
«# a a 8 8
•# OS
a a a
Wl
wn pg
a
eo in fM
m wn
oe >« wn
(b. 80
OC »o pg
a
ee a a a
un fb
0.0
ee wn ft.
8
a
un OS
eo 8 sf
a eo a a fH
O ^ ye
wn O" pg
vf pb
<o «* 3
«o no •e ao fM
oo 3 3
a
pg «n
0.0
o> in a a a
o> P H
8
•*
Ol vf Wl
sf
un vf
"* un
-
>o fH
cn
a iC pg
ac OP m a
ao 3 3
8
a fM
0.0
a vf
a a
a un fH a
•*
ae >A <o IM
vf PH
a 9
>o
9 vf
3
8 vO fH
N
o> fM
3
an 8 a a
pg a
0.0
Ps a a a a
pg fb
WH a
a
^ Ol pg
a
f^
>0
vf
ye
m wn fH
9 3 fH
pg 3 <o 3
PJ 8 a a
M
a
OaO
m a a a a
00 Wl
a a a
Wl
Pa
a a
^
a pg
sf
•*
fb
>e nj
Pa nj
PH pg fH
a
fM
a a a
mm
a O'O
pg
a a 8 a
o> WH
a a a
oe Wl
a a
fb fb WH
fb
wn oo fH
Vf -H
^ -C 3
a
fM
a a a
eo a
0.0
fH
wn a 8 8
un N.
a a
^
a pg
mm
00
un "• wn Ul nj
un o-— a un .* wn vf
3
pg
00 8 3
a
fM a
0.0
sn fM
a a
vH
un fH
a a
o o« pg
a
tn a N.
*o tn
pg
pg pg
pg mm
'^ pg
P H
vf
a
00 3 3
a
fH
a
0.0
^ a a a
p. pb
a a
o> m fH
a
Pa N. >o 00 pg
ae Pv 9
>o in
<o 3 pg
3
ee 8 8
3
fH
fM
0.0
vf
nj
a 8
fM a a
mm
mm 90 aH
fM
O md fH
vf
pH
in
p.
no a •n • 30
>e p.
a
nj
a a a
90
o
0.0
o
3
a
aW fH
in 8 a
ae Wl
>e a
PVJ
o« >e a «n
an >o fM
00
•n
«o in pH
3
pg 8 8
8
tn 3
0.0
>o 8 a a
fM N. PJ a a
.# eo wn
a
o» wn Wl
o "
vf
un 3
as
PJ
35 fv.
3
3
fM 3 3
3
8 sn
OaO
<e in 8
a
Wl
vf
Ol
un
-O vO in
fb
<o m un
>o in an
30 vf 9
wn un .* t.H
-o — pg
00 3 3
3
X
0.0
.f Wl
3
3
fH
o> N.
..#
>e PVJ
fH US sf
pa
o
90 ^M
on
vO us pH
^ vf vf
8
an 3 3
3
a 3 8 8 8 8 8 8 8 8 3 3 8 3 3 8 3 3 3 3 3 s w - a a a a a a a a a a a a a a a a a a a a j i b 8 o a a a a 3 a 8 e a a 8 3 3 8 8 8 3 3 t n a a a a a a a a a a a a a a a a a a a a
« f H f H f H f H f H f H f H f M f H
an tn m UJ ^
V o — z Z SH b-
tn
z ^ a ^ an Ik
3 tn
z b.
z »-
_J in
3 3 m
3 3 8
3 PH
3 3 8
3 m
3 3 3
3 3 pg
3 3 sn
3
3 3
3 tt-
8 3 a 3 tn
3 3 a 3 8 fM
a a a
fH
a a a a -*
a 3
a a un
3 3 3
8 8 PVJ
3 3 in
8 3 3
vf
a 3 a a tn
a a a a 3 fM
8 3 un
3 3 3
vf
8 3 3
3 m
3 3 a a a pg
a a a
fH
a 3 3
>f
3 3 8
3 in
3 3 a a a pg
3 3 US
8 3 3
3 "
3 3 8
3 tn
3 3 8
3 8 pg
a 3 m
3 3 3
3 "
3 3 3
3 us
8 3 3
3 3 pg
a 3 a
-
3
3 3
3 •
3 3 3
3 in
3 3 3
a 8
pg
3 3 un
3 3 8
vf
8 3 3
8 m
3 3 3
3 m pg
3 3 un
3 3 3
vf
3 3 a B in
3 3 3
3 m pg
8 3 8
-
3 3 3
vf
3 3 3
3 m
3 3 B
3 m pg
3 3 tn
3 3 3
vf
8 3 3
3 un
3 3 3
8 m pg
3 3 m
3 3 3
.f
3 3 a 3 m
3 3 3
3 m nj
3 3 3
md
3 B 3
vf
B 3 3
3 in
3 3 3
3 m rg
3 3 un
3 3 3
3
3 3 3
3 m
3 3 3
3 m pg
3 3 in
3 3 3
3
3 3 3
B m
3 3 3
3
m pg
3 3 3
t.H
3 3 3
3
3 3 3
3 in
3 3 3
3 in pg
3 3 in
3 3 3
3
3 3 3
3 m
3 3 3
3 in pg
3 3
m
3 3 3
3
3 3 3
B in
3 3 3
3 in fM
221
ae •X z
YS
HE
K/I
ec
c z
XS
HE
K/I
hf C tb O >s
> a
tk
^ Z tk
o ^ ^ w X a
ae b. b. m ui a. V
ne PH w- m in a. X
u. tu Q Z an tm
a fH
a 8 8
pg
»n a a
a >o a a a
«H
Ol Wl
<« a
Wl
ee wn a VI
N. wn Wl
00
^
pg nj pg
a a 8
Ol
a a a 8
a
a 8
8
tn
m fM
a
Pa tn fH
>c nj
un oo
m in
o
•H pg vf
a a a a
Wl
a a a
a
eo
.01
a
PVJ en
a . a
^ OS un
>o
fb
>n Pa
P. •SJ
m 00 B
a a a a
fH
a a a a
^ a a 8
8
sf vf
a a
a
8 Wl vf
l> un
^ vf p H
Pg vf
a
a
0.0
Wl Wl
0.0
tn
.25
a
s* vf fH
a f H
m pg un
9
in Pg in
a as an
» •
P H
•n
a
0.0
a fH
0.0
in
.06
a
»• Wl wn a
a
pg ye t
pg
eo <n >o 00 -fc
ye ye pg
a
OaO
sn a
OaO
.
.03
a
m*
ze mm
. a
a a pa
"
00 pg lO
pg us
sn wn fH
a
0.0
mm IM
0.0
un
.06
fH
<o vf vf
. "*
vf
a o-
<n
m vf Pv
ye 00
00
o-in
a
0.0
wn fH
0.0
«
.27
a
^ mm yO
. a
, in
m >o "*
a un f H
p. W".
a pg f H
a
0.0
pg aW
0.0
tn un •H 8 8
eo PVJ sf a
a
9 sf fH
o.
vf 9 ye
in fM
a ye
e
f H
OaO
OO Pa
0.0
Ps Ps wn a
pg
a p. un a
»n
m fM
<o pg .f
Wl 00 fH
vf fH fM
>o fb vf
a O'O
un un
OaO
a
.63
a
fH mm 00 a
"*
pb pg oe
N wn
^ 00 P.
eo o
30 9 pg
a a a a
Wl vf O
'O
vf
.37
a
un PJ vf a
WH
^ -» y *
fM pg
9 N. 3
an N.
3 tn f H
3 O'O
00 3
0.0
vf
.18
a
fM o> sf . a
in .# 9
ee ye
9 pv un
vf no fH
Vf 3 m
3
0.0
PVJ 3
0.0
.04
a
Pb mm mm . a
sf 9 •f
Ul mm
9 ye P-
wn vf
PVJ
a fH
a
0.0
a
0.0
.02
a
a <« a a a
Ol 00 flO
^
90
a in
pg pg
mm un B
a
OaO
a an
0.0
vf nj pa
a
o IM »
un PVJ • ^
fH
Pa PVJ
o-PVJ Wl
an pg
o vf
>o
a
0.0
30 a
0.0
Wl -C
a
9 in vf
a
<o a PJ
J ye
an P.
a Pg
fH
un wn t
mi
0.0
. B O
'O
Wl 00
a a
.« •n PVJ
a
K. N
aH an
^
.n in
00 oa
00
>c P H
0.0
fM •^
0.0
in
wn
mm >f •n
Wl
fH p. lO
pg 9
^^ b. ^r
3 3 PJ
pg tn ifc^
•H 8 fH a a mm
i3 3 WH -J in W- it tn
a 3 »-aJ U. tn mm
« •
mm Ul in tu ^
it
o WH Z
T mm b* in
z k-a b. an u. 3 in
z b-
z ^ UJ Ik _J Ul
an
a a a
a 8 8
in
3 3 a
f H
a 3 3
3
3 3 3
a in
3 B 8
a tn Pg
PJ
a a a
a a a a
a a un
3 3 3
3 3 3
3 tn
3 3 3
o m PJ
fM 3 3
3
3
a a 3
8 a tn
a 3 3
3 3 8
8 tn
B 3 3
3 tn pg
pg 3 3
3
3
a a a
a a a
f H
a 3 8
3 B 3
3 in
a a a a in ryj
ee a a a
a a a a
a a in
a a a
a 3 3
3 un
3 3 3
o in pg
in 3 3
3
3
a a a
a a m
a 3 3
a 3 8
3 in
3 3 3
a tn PVJ
on
a a a
a a a a
3 3 8
f H
8 3 3
3 3 3
3 tn
3 3 3
3 m pg
fM
a a a
a a a a
a a un
a 3
a 3
3 3
a a tn
3 3 3
3 tn pg
PVI
a 8
a
3
a a a
a a un
a 3 3
3
3 3 3
3 un
3 3 3
3 in fM
pg 3 3
8
3 3
a a
a 3 8
fH
3 3 3
S
3 3 B
3 un
3 3 3
3 in pg
n 3 3
3
3 8 3
3
3 3 in
3 3 3
3
3 3 3
3 in
3 3 3
3 m Pg
nn
a a a
a a a a
a 3 m
3 3 3
S
3 3 3
3 in
3 3 3
3
m pg
an 3 8
3
3 8 8
8
a a a
^ H
3 3 3
3
3 3 3
3 in
3 3 3
3 m nj
pg 3 3
3
3 8 3
wn
3 3 m
3 3 3
vf
3 B 3
3 un
3 3 3
3 US pg
nj 3 3
3
3 3 3
in
3 3 tn
3 3 3
vf
3 3 3
3 m
3 3 3
3 in pg
fM 3 3
a
a 3 3
m
3 3 3
fH
8 3 3
vf
3 3 3
3 sn
3 3 3
3
m pg
CO 3 B
3
8
a a m
a a us
3 3 3
vf
3 3 3
3 m
3 3 3
3 m Pg
ae 3 3
3
3 3 8
m
3 3 un
8 3 3
-f
3 3 B
3 us
3 3 3
3 tn rtj
eo 3 3
3
8 8 3
in
3 3 3
-
3 3 3
vf
3 3 3
3 in
3 3 8
3
fM
pg 3 3
3
3 3 3
m
3 3 in
3 3 3
3
—
3 3 3
O •n
3 3 3
3 m Pg
222 H
EA
R
/IN
tn u >
HE
AR
/I
N
Wl it X
bp
C Ib a "v X w >. 8
tm tb
^ C Ik
a "N r tit X a
Wa Ik
ae an ^ Ul in a. ^
ac an
^ tn tn a. X
tk
tu
a z an an a
a
a WH -1 tn
^ ^ tn
a 3 t--J u-tn
«
aa tn in UJ ^
^ u w- Z Z an b-tn
.00
5
a
.01
6
a
0.4
90
>e
1.2
2
wn Pa in a
IM
P. Wl
tn a
Wl PI.
m ws a H
a
PM
a 3
a
a a a
a a in
a 3 3
3
a0
03
a
• O
il
a
0.2
79
vf
•n fb a a
lO
•n pa 8
mm
oe vf
a • vf
vf
OC
vO 3
a
fM
a e
a
a a a
a a a
f H
a 3 3
3
80
57
8 a
l33
a
5.2
74
f H
tn
. mm
» pg sf
.
wn
<« fb
>o a an
f H
o-ye
^
oe a a
a
a a a
a a m
a a a
a
.02
2
a
8
a a a
1.8
45
f .
Os in
>
o
0.6
fH fH
mm 00 vf
. m Pv fM
p.
m wn
a
eo
a a
a
a a a
a 3
m
3 3 3
a
.01
3
a
.04
1
a
1.0
67
fM
2.7
8
pb
nj
4.0
>o
f H
* 00
a >o -n fH
pg
oc f H
a
en 3
a
a
a a a
a a a
P H
a 3 a
a
.00
2
8
.00
7
a 0
.17
3
N. 52
'0
a
^
4a
9
>o
vf 9 mm a »o l>
90 vf
9
a
PU
a a
a
a a a
3
a m
a 3 3
vf
a a 9 e
.00
3
a
0.0
38
ye 90
'0
m wn
4.3
"^
N. vf fb
a sf
PVI
3 O-P H
a
fM
a a
a
a a a
a a in
a 3 3
vf
0.0
01
.00
2
a
0.0
19
fb
0.0
3
<•
.*
7.2
N l
9 ao . Wl
"
tn 9 8
a
pg
a a
a
a a a
a a a
f H
3 3 3
vf
0.0
02
.01
5
a
0.1
52
pg
0.3
2
in
o.
7.1
in
m vf
m .
wn
a PH
m if
ye
a
ee a a
a
a a a
a a in
a a a
vf
10
0'
w
a
.00
9
a
0.0
77
fb
0.1
8
> mm
8.9
fM
a p. lO a pg tn
an Pj an
a
ee 3
a
a
a a a
a 3 3
ItH
8 3 3
vf
02
2
•
a
tn pg
a •
a
1.9
54
sf tn Wl
mm vf
7.2
fH fH
>e pg fM
. fH
00
9 PVJ rvi
•
fM 8 a
a
a a a
a a m
3 3 3
3
00
8
a
a
01
0
a
a
0.5
14
a
0.5
7
fb fH
0.8
Wl
Ul
8 pg a
vf an
pa vf ryj
a
PVJ
a a
a
a a a
3 3 in
B 3 3
3
00
4
a
a
00
6
a 8
P. pg a
a
>o
Oa
36
•o (M
6.4
"*
o> -o Ol
. mm pg
sf pg f a
a
PJ a a
3
8
a a
m
a 3 3
-
3 3 3
3
01
8
a
a
03
6
a
a
pg
9
a «H
fb
2.1
5
sf fH
7.5
3
vf PJ vf a
9 nj fH
Pv
9 •e
a
eo 3 a
a
a a a
un
a a in
a 3 3
3
01
0
8
8
03
2
a
a
1.0
10
f H
1.4
3
vf Pa S
'O
-o
Pa
nj ao .
sn OO
9 y *
wn
a
on a a
3
a a a
m
3 3 3
-
3 3 3
3
0.0
1
a
a
00
9
8
a
0.1
28
p H
0.4
5
OS in
7.8
'
.f
N
„ 9 a
00
-n fH
3 Wl
ao
3
pg 8 8
8
a a a
a
a 3 m
3 3 3
•*
00
1
a
a
00
3
a
a
0.0
29
eo
O.l
Oi
wn p.
0.7
•^
Cs 3 tn a 8 vf
N vO mm
3
fM 3 a
a
a a a
3
3 3 un
3 3 3
vf
00
1
a
a
fH
a a a
a
0.0
15
m
0.0
5'
3 an
5.4
1
3 pv fb
. 3 pg
vf ac 3
a
pg 3 3
3
3 a a
a
3 3 3
-
3 3 3
vf
00
4
a
a
03
5
a
a
0.4
98
^ fb Pb a
>o L/S
6.6
'
30 fH
an in m
m m
ye
mm vf
^.
pg
ao 3 3
3
3 a a
a
a a m
3 3 3
vf
3 B a
a
01
0
a
a
0.1
13
%A
0.4
21
%^ liA
2.2
if
tn N. P.
. 9 m
vf
tn m
3
oe 3 3
3
3 8 8
3
3 3 in
3 3 3
vf
X 3 8 3 3 8 8 8 8 3 3 3 3 3 3 3 3 3 3 3 3 W- 3 B 3 3 B 3 0 3 3 3 3 3 B 3 B 3 3 3 3 3 a ^ - 8 a a a a a a 3 3 a a a o 3 3 3 B B B o k H t k 8 a a a a a a a . a a . . a . . a a . . 3 3 3 3 3 8 3 3 3 3 3 3 3 3 3 3 3 3 3 8 3 tn t n t n i n i / s i n 3 3 3 3 3 3 B 3 3 3 3 3 B B 3
Z 8 3 8 8 8 8 3 8 8 3 3 3 3 3 3 3 3 3 3 3 w- 3 8 3 3 3 3 8 3 3 3 3 3 3 3 3 3 3 3 3 3
z ^ a a a a B a a a e a a a B B B B B B B B U J u . * 8 a . . a a . . . . . . . . . • • • • _J 3 8 3 8 8 3 8 3 3 8 3 3 3 3 3 3 3 3 3 3 Ul i ^ u n m u n m i n t n i n u n v n i n u n i n m i n i n i n i n i n i n
f M f M P g f M f M f M f M P g f M f M P g f M P g P V j f M P g f M f M P g f M
223
at 4 z UJ SH
X V t f l M
a a
^ wn
a a a a
a a
a 8
a a
a a
8
a
wn pg
a a a a
a a
8 a
a a a
a
Ol
a a
PVJ
a a
a a
a a
a
a
fM f H a
a
a
Ul a a
a
a
a 3
a a
^0 Ul
a PJ
a
pg mm
a a a a
a a a a
ae * ^ « < O P g w H < o e o p g f H a o o v f t n > O p H O i o « - P w w i « Z 8 P g " * f H i O v f 0 3 a w i a a w n « H f H m i O v f 8 a ^ "< a e a a a a e a a a a a a a a w H o a a a
' ^ ^ a a a a a a a a a a a a a a a a a a a a X
* - f b f H v f f M f M « o i n f M - » f b ^ w n m v f ( M P b i , f w i w n a e C t b w n ' O o O w H p ^ w n a O v f p g r w ' C a e ^ O i e o o w n P a N . w n O ' n s a w n w i f v j f M f i a f . i O O N . f H a i n v f f M n j o o a . M a
> » 8 a * a a f H a 8 a e a a a . x e a w n . ^ p H 8 a
hf
C Ib a Nl z ^ X 8
Ib
ae SH •- in tn (L >
a; an b. Ul Ul O. X
tb
tu a z SH SH
a
a
a «-ml SA
^ ^ m
a 3 •» aJ U. tn WH
<Z
mm Ul m UJ ^
^ u an Z Z SH b-tn
z ^ a w-
3 in
z t—
Z w. UJ Ik _J to
». f H
fM
a
N. * vf
f H
Pg
ao m o. f H
30
N.
p. pg
a
on a a a
a a a a
a a a
f H
a 8 3
vf
3 B 8
3 3
3 a 3 o m pg
vf vf
in
fM
00
in so P H
00
un f H
ve
pg
in mm
9 9 3
f H
PJ 8 a a
a a a a
a a m
a 3 a a
3 3 3
8 3
a a a 3 m pg
o> vf a **
'O pg
a wn fM
9
m O'
pg
>o
PM pg
fM
a
nj
a a a
a a a a
a a m
3 3 3
3
3 3
a a a
a 8 a a
8 m PM
4 m <e a
in mm Pa
pg W H
a tn wn
^
pg f H
fH
a
fM
a a a
a a a a
a a a
f H
a a a 3
a 3
a a a
a 3 3 a
8 m pg
fM ^ OS
ws
in
a Wl
<o N.
ye 9 ye
p .
pg
an e> m
a
eo a a a
a a a a
a a un
a a a a
a 8 a a a
8 3 3 a
3 •m pg
OS
a un pg
a Wl f H
i #
vf
ye vf
in
a -
nj
3 Wl
a
00 3 8
a
a a a a
a 3 3
fH
3 3 3
8
3 3 a 8 3
3 3 3 a
3 m pg
«e pte sf
a
a in
.n
> •o
Pa
N sf
OO
P H
fb
vf
Ps
a
PVi 3 a a
a a a
a a in
a a a vf
a 3 3
3 3
3 3 3 . 3 wn pg
Wl
P H
f H
a
oo ye
sn
m "*
nj pg
m p j
^ un fH
a
fM
a a a
a a a
a a tn
a a a vf
a 3 a a a
a a a a 3 un fM
ee in a a
us PVJ
o» N.
00 N. 00
f H
in Ps 3
a
pg 3 a a
a a a
a a a
f H
3 3 3
vf
3 a 3
3 3
3 3 8 . 8 tn PJ
ee ps
ee
"*
o> vf
tn
pg Pa pg
^ pg f H
vf
3 N fH
8 vf
pg
ao a a a
a a a
a a US
a 3 3
vf
3 3 3
3 3
3 3 3 a 3 in
pg
00 sf
^
a
w mm sf
f H
lO
a pg f H
00
f H
>o 00 vf
a
eo a a a
a a a
a 3
m
8 3 3
vf
3 B 3
3 3
3 3 3 . 3 m PJ
mm m IM
a
vf Pa pg
f H
wn
PVJ pg tn
<o 30
wn vf
pg
a
eo a a a
a a a
a 3 3
f H
3 3 3
sf
3 3 B
3 3
3 3 3 . 3 in pg
<C <o 90
pg
.f fM N.
pg
9
.f wn O
pH
fb
P. 8 3
fH
PSJ 3 8
3
a a a
a 3 in
3 3 3
3
r^
3 3
3 3
3 3 3 . 3 in pg
fM in .« f H
00 vf
<o o pg
f f
PJ PH
o. e
ye
8 Pg
8
pg 3 8
3
a a a
a a m
3 3 3
3
3 3 B
3 3
3 3 3 . 3 in pg
ee » -e a
f H
o. ae
>o f H
9 90 OO
P H
vf
vf
a fH
a
fM 3 3
8
a a a
a 3 3
f H
3 3 3
3
3 3 3
3 3
3 3 3 . 3 in pg
9 mm
m 3 fH
O mm 3
lO
an
Wl
an pH
9 mm
ye
00
>o m
P j
an 3 3
3
3
a a
B 3 in
3 3 3
3
3 3 3
3 3
3 3 8 . S in pg
sf
a sf
sf
IM
m pg
f H
fH fH
8 lO fM
vf
vO pg
3 wn m
8
00 3 3
3
3 3
3
3 3 m
3 3 3
3
3 3 B
3 3
3 3 3 . 3 in pg
ttH
» ye
pg
<3 >o Wl
vf
«o
wn in vf
t.H
f H
nc >e pg
e
00 3 3
a
a a a
B 3 S
f H
3 3 3
B
3 3 3
3 3
3 3 3 .
3
m pg
lO in IM
8
ao vf 9
sf
•o
<o 3
^ vf
>•
mm
sf vf
pH
Pit
3 3
3
3 3 3
3 3 m
3 3
3
vf
3 3 3
3 O
3 3 3 . 3 m p j
o> ye
a 8
US fa
an
>f "*
PV) vf
9
in n j
9 rs •nj
a
pg
a 3
3
3 B 3
3 3 m
3 3 3
vf
3 3 3
3 3
3 3 3 . 3
pg
224 H
EA
R /I
N
Ul ^
HE
AR
/I
N
tn it X
C lb
a>N
> a
Ik ^
Z tk
a-N c X a
bp Ik
at WH
^ tn m V
.00
1
8
• 0
02
a
0.0
19
a >0
'0
so
fM
.00
2
8
.01
5
8
0.1
52
Ps
0.3
3
N. v#
tn
.00
1
a .0
09
a
0.0
77
tn
a
fb
ae eo eo fM
.02
2
a
.02
0
a
1.9
56
<o
1.3
4
vf
00
•n N
"*
.00
8
8
.00
9
a 0
.51
2
»n
0.5
3
wn Wl Ps
a wn
.00
4
a
• 0
06
a
0.2
74
Ol
0.3
4
ao o> wn ye mm
.01
8
a
.03
7
a
1.7
89
le
2.1
4
N.
a Wl
fb
a
.01
0
8
.03
2
a
1.0
08
\n
1.4
2
mm 9 -* a <o
a a 8
.00
5
a
0.1
04
•#
0.3
0
ye 9 a o-Wl
0.0
0 1
0
.00
1
0.0
22
»
0.0
6
fH fb
wn
00
00
1
a
0.0
01
o
.on
in
0.0
3
ye fM pg
vf
00
1
a
0.0
04
0.0
87
pg
0.2
7
wn <o vf
PVJ
wn 0
01
a
00
2
a
0.0
44
ae
0.1
3
'O 9 m ye fH
00
9
a
02
6
8
1.2
75
00 o <M a
PVJ
>o a m ye p.
00
2
8
8
a a
0a
33
4
m
0.7
9
IM Wl
a a PJ
10
0
a
a
00
7
a
0.1
79
in
0.4
5
Wl M ^
Ps
a mm
00
6
a
04
5
8
1.1
13
en
2.9
8
fH
eo Pa
>e «o
00
3
a
a
02
7
a
a
0.6
13
Ol v f
N .
a
ye ^ P.
'O m
00
1
a
a
00
5
a
a
Oa
lSl
8
0.5
5
pg 'C m
>o tn
mm
a a 8
a
00
1
a
a
Oa
03
2
«b
0.0
7
(/
"M ^
P a i n w n f H p f c ^ O s f j ^ ^ O s f u n a p . p . o > . < n > o « i _ _ ' ' ^ " ^ i ^ . f p g p g > o e f b i n o . ^ 8 f b a i f b u n u n a n m * ' ; ; * ' s f 8 N 8 ^ P s p H C ^ P . 3 8 O l 0 0 ^ O P g p g O > f - P > '
t n a . v f > o w n 8 f \ / 0 3 e v f w i u i w n ( s g f H P a ( s . N . O ' s f - H n s X - w ' M f b 5 0 a n P s j f M O O f H P g f H 3 u s w n ^ f M K . O a n r O
^* tm mm f a f H f H f H p a
lb v f v f f M f H w n p . w n K i » » 3 a o ^ ^ 8 a v f f M 3 f H . . y T O UJ v f o o O ' > O f b a o > o w n e e " n » H r s o . « H i n j v O i c . n a v o Q 3 S f H & . . f a o w n f H 3 u n f H p g p « _ f b K n , O w n f H a ; ^ O i M s H S H . a . . a a a a a . a a a . . . . . . .
a a e e f H a a » H 8 f H a 8 8 8 f H o a a a a H O
a "-_i in b. ^ a tn 8
pg a a
eo ao a a a a
pg a a
PVJ a a
pg a a
ee a a
an a a
PJ a a
pg
a 8
PJ a a
ee a a
eo a a
IM a a
PSJ a a
PVJ 3 3
eo 3 3
00 3 3
pg 3 3
n j 3 3
a 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 3 3 3 ^ 8 8 8 8 8 8 8 8 8 8 8 8 3 8 8 8 8 8 8 8
^ u - e a a a a a a a a a a e a a a a a B B a U l » 9 » * m » 9 » t » m t » » m 9 , » m »
mm t n t n i n i n i n i n i n w n 8 8 8 8 a a 8 a a 3 i n t n « f H p t H f H f H M f H ^ P H f a f - p M p M
tn tn UJ ^
^
ST
HIC
IN
z a SH Ik
3
Ul
X bp
Z »-UJ Ik
.J tn
OO
O'S
l
a
4a 0
0
00
0
a a IM
00
0
a
a 3 in
a
4.0
0
00
0
a a fM
OC
O
a
15
.00
0
a
4.0
0
00
0
a a pg
000
a
a 3 un
a
10
.00
0
00
a a pg
00
0
a
a 3 un
3
lOa
OO
0
00
3 8 pg
00
0
8
ISa
OO
O
3
10
.00
0
00
3 3 pg
00
0
8
CC
5'2
3
10
.00
00
0
3 3 nj
00
0
a
15
.00
0
a
10
.00
0
00
3 3 pg
00
0
3
CO
S'I
8
4.0
0
3 3 3
3 3 pg
00
0
3
OO
S'2
3
4.0
0
00
0
3 3 pg
00
0
3
OO
O'S
l
8
4.0
0
00
0
a 3 pg
00
0
3
7.5
00
3
4.0
0
00
0
3 3 PJ
00
0
3
OO
O'S
l
3
4.0
0
000
3 3 pg
00
0
3
OC
S'I
3
10
.00
00
0
3 3 nj
00
0
3
7.5
00
3
10
.00
00
0
3 3 fSj
00
0
3
15
.00
0
a
10
.00
00
0
3 3 PVJ
000
3
7.5
00
3
10
.00
00
0
3 3 IM
oco
3
15
.00
0
3
10
.00
00
0
3 3 PJ
00
0
3
OC
S'I
3
4.0
0
00
0
3 3 PJ
00
0
3
00
5'2
3
4.0
0
00
0
3 3 M
00
0
3
PVJ p g p g f M p g PVJ p g p g p g PVJ p g p g p g
225
ae « z UJ SH
X N. tn it >
ec « z UJ b.
z ^ Wl M X
^ C lb ,
a V. c ^ > 8
I B
u. ^
C tb
eN. «• w X 8
^ u.
ac SH ^ tn in a. >
ae i-b. tn
tn a.
tk UJ
a ;w an a-
a
a « a SH -J tn b- w tn
a 3 ^ -J lb Wl WH
a
a. Ul in UJ ^
^ CJ SH Z X SH b.
tn
X ^ a w-aH Ik
3 Ul
z b-
z ^ tu tk _i Ul
fH
a a • a
P H
a a . a
sC tt.
a a 8
o> Wl
a a
a
vf PH fH
ye
,.« p. vO a vf
sf
a fH
a
PSJ
a a a
a
3 a a a
tn
a a a
-H
a a 3 .
vf
3 3 a a
a a PVI
a a a a
a tn pg
pp.
a a a a
tn
a a 8
a
fb
fM «H 8
a
<e a wn a
a
^ vf vf
vf
sTs 9 00 a
11
4
pa
in
>o a
eo a a a
a
a a a a wn
a 3 m
a a a a
vf
3 3 3 a
3 3 Pg
3 3 3 a
3 m pg
«H
a a a 8
fM
a 8 8
a
. so a a a
tn in fH a
a
wn un o«
pg
fb aH
fM a
no
i> pg an
8
ae a a a
a
a a a a
m
a a a
fH
a a a a
vf
a a a a
3 3 pg
a a a a
a wn Pg
90
a a a a
». pg
a a
a
00 wn s# a
.M
.a fH
PVJ a
PVJ
^0 P. vf
90
^ ^ ye a
132
o vf vf
fH
pg
a a a
a
a a a a
m
a 3 sn
a 3 3 a
3
a a a a a a PVJ
a a a a
a un fM
Wl
a a a a
wn PH
a a
a
wn Wl
vf a
a
fb
Os
ae a
a
f4
lO
>
pg
oo oe rs a
wn
o> pg
a
fM
a a a
a
a a a a
tn
a a in
a 3 3 a
3
a 3 a a a a PJ
a 3 3 a
3 in fM
pg
a a a a
fs.
a a a
a
ao wn fM a
a
PSJ pg
m a
a
00 un pg
"
a sf
wn a
fH
P. vf f H
a
pg
3 a a
a
a a a a
in
a a a
fH
a a a a
a
a a a a a a pg
a a 3 a
3
un pg
vf
... a 8 8
a un 8 8
8
90 »> in a
WH
a Ol
.* a
Wl
>o 00 eo
9
vf
a vf a
20
9
«o •n fb
a
on 3 a a
a
a a a a
m
a a m
a a a a
3
8 3 8 a
3 B fM
3 3 3 a
3 tn pg
00 a a a 8
8 wn a a a
fH
9 eo 8
a
fH vf
a a
PJ
9 wn sf
m
00 Pb vf a
12
2
a Pv an
a
on a a a a
a a a a
un
a 3 a
fH
a a 3 a
3
3 3 3 a
3 3 nj
a 3 a a
a tn pg
UJ <J
CL tb Wl
3
a un
a a un
a a un
a a un
a a un
a a m
a a a a in un
a a a a m m
a a m
a a m
226 a a tn
a a in
a a m
a a m
a a tn
a a m
a a a a un wn
pg pg pg pg pg pg pg PM pg pg PVI pg
oe z 3 an UJ V
X ^ cn >
a a
a a
pg fH
a
a
a a
a a
•m m a Wl a a
pg in WH
a a a a
pg
a
>o a a
fH
a
a
pg
a a
in
a
eo PH
a
o
a a
a a
un .* -H a a a
a: z « SH UJ N X ^ tn
wn a a a
a
•^ «0 vf a a a
a
a a
a
a a 8
a
o>
a a
a
a a 8
a
PH « .« PVJ
a a a a
a a
a a
a a a
a
pg fM a a a
o> a a
pg a a
vf
<o a a
a
00 mm
a a
a
fM
a a a
a
a a
«o a a a
a
a a a
a
C U.
a «v z >t > a
a pg
a wn a
a
a a wn
•f vf
yQ
a
PVJ eo a
ao .9 vf a m *
wn .* vf wn pg a
Ul
pg ye
00 wn
a
a Pa 00
a eo •e
eo
vf fM
a
vf
un Ul
«* 8 Wl o a an a vf •H a
z u. a *b z
9 0 > * a » n p . ^ ( n w i ^ i n » H > o w i f b o ^ p H e a e o s o flefMfH>f>oa9efM(MwnoiapgwiN.fHfHwi(Mvf " H 8 v f W > N t ^ O i p H f M a O s v f w i o ^ u ^ i M a w i « n
8 e t M 8 8 a w i f H 8 8 a a a a p j 8 a a f H a
9 e w H a 0 f H r b f H w i i n f H w i N w n w H w i r M » 3 ^ « H 8 ^ . f H N P M w i w i f H u n o ' f H O . p g i n w n ^ i n f b B o o f M a a a a p v j a p g a a a a a p g e p g a e a a a
in Wl
> u
ac b- SH in Ul
X it
u. lU
a z SH an
a
a
a an aJ Ul -J ^ Ik
a 3 h-.J lb tn an
^ in in UJ ^
^ o SH Z Z w-
in
SU
IDT
H
FT
S
LE
NT
H
FT
a
a ^ a
a
an 00
a
a
in p. a
a
a 8 a
a
o a m
f H
8 a 3 a vf
50
.00
0
OO
O'O
S
a
o. a a
a
o a a
a
tn N a
a
a a a
a
a 3 8 a
tn fH
8 a a a vf
OO
O'O
S
OO
O'O
S
a
in
oc a
a
wn Pv fH
a
m Pa a
a
a a a
a
8 3 US
f H
3 3 3
10.
3 OO
'OS
O
OO
'OS
a
f H
pg
a
a
00 f H
8
a
in Pv
a
a
a a a
a
a 3 3 a
wn ^ H
8 3 3
10a
B OO
'OS
O
OO
'OS
8
oo 00 pg
8
Ps pg fM
a
00 N. f H
a
a a a
a
a a in a
ttH
a a 3 a
.f
8 OO
'OS
O
OO
'OS
a
e> Wl 3
a
m pg
a
a
00 Pv p H
a
a a a
a
a a a a
wn fH
a a a a
vf
8 OO
'OS
O
CO
'OS
a
> Wl pg
a
.# ws fM
a
00 fb f H
a
a a a
a
a a wn a
f H
a a a
10
a
a
50
.00
OO
O'O
S
a
Ps
>o a
a
a an 3
a
ae fb f H
a
a a a
a
a a a a un
a a 3
10
.
3
50
.00
OC
O'O
S
a
sf ac a
a
PJ
rs a
a
in p.
a
a
a a a wn
3 3 m a
pH
3 3 3 a
vf
3
SO
aO
O
OC
O'O
S
a
wn f a
a
a
ae a a
a
m Ps
a
a
a a a un
3 3 a a
in
3 3 3
vf
a
50
.00
5
0.0
00
a
o m a
a
m m t—
a
in N. a
a
a a a m
a a in a
fH
3 3 3
10
.
3 OO
'OS
5
0.0
0 0
a
vf pg
a
8
>o p H
3
a
in N. a
a
a a a wn
3 3 3 a
m
3 3 3
10
.
3 OO
'OS
O
OO
'OS
a
^ PVJ mm
a
p H
c f H
a
00 N fH
a
a a a tn
a 3 m a
P H
3 3 3
vf
3 OO
'OS
O
CO
'OS
a
vf fH
a
a
a Pg
a
a
an N ttH
a
a a a un
a a a a
m pH
a 3 3 a
vf
3 OO
'OS
O
OO
'OS
a
N wn fH
a
, fH pg
a
an N "*
a
a a a m
a a m a
a 3 3
10
.
3 OO
'OS
O
OO
'OS
8
fH
an 3
3
>C Pg 8
8
ao p.
•*
3
3 8 8
un
a 3 3
wn
3 3 3
10.
3
50
.00
5
0.0
00
8
O fb
3
3
on PH
t-"
B
m rs 3
3
8 8 8
3
3 3 tn
fH
3 3 3
vf
3 OO
'OS
20
0.0
00
3
^ fH
3
3
nj mm
3
8
m fb
3
3
8 8 8
3
3 3 3
in
3
3 3 vf
3 OO
'OS
20
0.0
00
a
3 30 3
3
9 00
Pg
a
sn pv 8
3
a a a 3
a 3 in
3 3 3
10.
3
50
.00
2
00
.00
0
a
^ fM
a
3
«> n.' 3
3
un Ps 3
8
8 3 O
B
3 3 a
m md
8 3 3
10.
a
50
.00
20
0.0
00
US
PA
CE
F
T
YS
HE
AR
K
/IN
H
EA
R
K/I
N
tn X
YM
OM
F
T.K
/FT
z u. a N. r ^ X a
b> tk
YS
TR
K
SI
oc ^ SH tn tn X K
tb UJ a z a
FL
LO
AB
K
SI
AIS
LU
D
FT
tn tn UJ it
ST
HIC
K
IN
SU
IDT
H
FT
z
Z w-UJ tk ml in
OO
S't
0.0
16
.0
09
a
0.7
65
0.6
34
fb
00 pg a a
a2
38
a
24
5
a
ee
I'O
.00
0
a
laS
OO
4
.00
0
OC
O^
OS
00
0
20
0.
3.5
00
0.0
02
.0
01
a
0.1
03
28
0'0
0.0
39
fH
WS
a a
.02
6
a
oo
o.i
; .0
00
a
15
.00
0
4.0
00
5
0.0
00
a a a 3 a pg
OO
S't
0.0
54
.0
41
a
3.9
22
Pa
wn . Wl
0.2
35
.2
14
a
29
2
a
ae
O.l
i .0
00
a
1.5
00
1
0.0
00
50
.00
0
00
0
20
0.
3.5
00
0.0
2 1
.0
12
8
1.1
16
0.9
11
0
.06
7
m m a
a
03
5
a
ao
0.1
0
00
a
OO
O'S
l
a 3 3
a
OO
CO
S
a a a a a pg
2.5
00
0
.00
5
<n a a a 8
0.2
23
pg
a a
0.0
84
.0
91
a
11
2
a
m
0.0
-.0
00
wn
OO
S'l
4.0
00
S
Oa
OO
O
00
0
a 8 PM
2.5
00
0.0
01
.00
1
8 0
.03
5
0.0
34
0.0
13
.0
13
a
mm
a a
un
a a
.00
0
un
OO
CS
l
4a 0
00
OO
O'O
S
00
0
a 8 pg
2.5
00
0.0
21
21
0'
8
0.9
63
1.6
48
0
.05
8
,09
9
a
27
8
a
tn
a a
a a a in
OC
S'I
10
.00
0
SO
aO
OO
a 8 a a e PVJ
2a
50
0
0.0
09
.00
4
a
0.4
01
98
t'0
0.0
24
.0
23
a
02
3
a
in
0.0
] .0
00
in
OO
O'S
l
10
.00
0
50
.00
0
00
0
20
0.
3.5
00
0.0
06
80
0*
a
0.3
21
0
.67
1
0.1
20
.2
52
a
20
5
a
ee
0.1
] .0
00
wn
1.5
00
a a a vf
50
.00
0
00
0
a a pg
OO
S't
0.0
0 1
.0
01
a
0.0
37
0.0
87
0
.01
4
.03
3
a
22
0
a
ee
o.n
a a a tn
OO
O'S
l
4.0
00
OO
CO
S
00
0
20
0,
3.5
00
0.0
31
0.0
45
2
.21
6
4.3
90
0
.13
3
.26
5
a
28
1
a
00
o.i
; .0
00
tn
1.5
00
1
0.0
00
5
0.0
00
.0
00
a 8 pg
3a
50
0
0.0
10
0.0
11
0.5
04
0.9
91
0
.03
0
.05
9
a
oe pg 3
a
00
0.1
] .0
00
m
00
0^
51
CC
CO
l
50
.00
0
.00
0
20
0.
2.5
00
0.0
03
0
.00
4
0.1
86
0.2
10
0
.07
0
,07
9
a
12
6
a
sn
0.0
]
00
0'
a
1.5
00
4
.00
0
OC
C^
OS
.00
0
25
0.
2.5
00
0.0
0 1
0
01
a
0.0
24
OtO
"0
6
00
^0
fH
a a
01
3
a
m
0.0
] .0
00
a
15
.00
0
4.0
00
co
co
es
CO
O'
25
0,
2.5
00
0.0
15
0
12
a
1.3
52
1
.32
6
0.0
81
0
80
a
30
9
a
un
0.0
] 0
00
8
1.5
00
1
0.0
00
00
0^
05
,00
0
25
0
2.5
00
0.0
04
0
06
a
0.3
35
0.3
46
02
0*0
02
1
a
05
1
a
tn to*o
.00
0
a
15
.00
0
10
.00
0
OC
O'O
S
.00
0
25
0
OO
S't
0.0
19
00
9
a
0.7
65
Wl ye a a
0.2
87
23
8
a
24
4
a
no
o.n
0
00
a
1.5
00
4
.00
0
50
.00
0
,00
0
3 m pg
OO
S't
toc
o
100
a
0.1
03
0
.08
2
0a
03
9
03
1
a
02
6
a
30
Oa
l]
00
0
3
15
.00
0
4.0
00
5
0.0
00
.0
00
2
50
3.5
00
29
0*0
03
5
a
22
6*t
3.5
75
5t2
*0
21
4
a
51
1
a
oo ll'O
00
0
a
1.5
00
1
0.0
00
5
0.0
00
,0
00
2
50
OO
S't
0a
02
6
01
2
a
a
1.1
16
0.9
11
0
.06
7
05
5
a
05
3
a
3C
0.1
7
00
0
a
15
.00
0
10
.00
0
oo
co
s
.00
0
3 m pg
227
UJ CJ <Z *m a. lb m 3
YS
HE
AR
K/I
N
XS
HE
AR
K/I
N
b-
YM
Or
FT
.K/F
^ C lb a >s z X 8
lb
ae kf WH tn Wl > it
ar ^ an ul Ul X it
.50
0
pg 0
.00
6
0.0
05
wn ?2
'0
Wl
vf fM a
a
vf 00
a 8
a
f H
9 B
8
.50
0
pg
0.0
01
0
.00
1
m
0.0
3
y *
Wl
a a
a m f H
a a a
wn fH
8
a
.50
0
fM
0.0
21
0
.02
1
wn 96
'0
Ol
1.6
4
eo in
a a a
o» eb a a
a a in
fM
0.0
09
0
.00
6
fH
0.4
0
>o eo Wl a a
.# fM
a a a
Wl pg
a a
a a un
ptn
Oa
01
2 0
.01
4
f4
0.3
2
p «
0.6
7
a pg fH
. a
PVJ
wn pg
a
/ a a m Wl
O.O
Oi
0.0
02
pb
0.0
3
Pa
0.0
8
vf fH
a . a
t
wn a a
.50
0
Wl
0.0
65
0
.05
6
Wl 2
.21
^
4.3
9
wn Wl fH
a a
wn >o pg
a
OO
S't
0.0
18
0
.01
8
wn
0.5
0
fH
0.9
9
a w^ a a a
OS
un a a
.50
0
pg
0.0
03
0
.00
3
a
0.1
8
fM
0. 15
fb
«o a a
a
fb
un a a
50
0
PJ
0.0
0 1
0
.00
1
Wl
0.0
2
WH
0.0
2
o a a . a
oe 3 8
3
50
0
fM
0.0
15
0
.00
9
a St'l
sf
0.8
3
fH
00
a a
a
a m a a
50
0
pg
0.0
04
0
.00
3
a
0.3
2
pg
0.2
1
Ol ^t
a a
tn f^
a a
50
0
»
0.0
23
0
.02
7
HH 16
'0
in
1.1
3
pg vf Wl a a
«o pg vf
a
50
0
a Wl
*0
0'0
S
OO
'O
oo
0.1
3
<«
0.1
8
pj un a a
a fb
a a
00
5
a Wl
0.0
66
0
.07
1
fb
4.0
3
Wl a eo a
wn
PVJ vf PVJ a a
00 PVJ pg
8
50
0
8 wn
0.0
30
0
.03
5
^
1.2
7
fM
1.4
8
fb N a a
9 ee a a
00
5
a pg
0.0
06
SO
O'O
fM
0.2
2
tn
0.2
2
Wl eo a a
«# ao a a
00
5
a PJ
0.0
01
a a a
a
.«
Oa
03
Wl
0.0
3
Wl
a a
pg
3
3
00
5
a PVJ
Oa
02
2 0
.02
0
pn
0.9
81
V *
1.0
9
O' sn a a
<o >o a 3
50
0
a
Pj
OIO
'O
0.0
07
eo 9y wn a
a
ai IfO
vf
a a
9
3
3
228
lb a n J 0 0 3 l n p u f H 3 » f ^ f S J a n c ^ P . l n v f a n O l f H « n lU P J f H ^ s p | o f M 3 . ^ & f M w n N w n w s w i p . O i f M s n f b a Z f H 8 n j 3 f M a w s B P u 3 r s 3 w n 3 N 3 P g 3 ^ 0
a 8 8 8 8 8 8 8 8 8 8 8 8 8 8 3 8 3 3 8 3
a <t i n t n t n t / s o e a o a e e o i n i n i n i n o n a o e n o o i n i n i n i n O W H W a N . N P . N P v N r s N P s f b f s . N N . N P v r s r s P v r s
. j t n o o a a f H f H f H f H 8 e a 8 » H a H f H f H 3 3 3 B a J ^ a a a a a a a a a .
UP e a e a a a e e a a a a s s a a a s B B
a a a a a a a a a a a a a a a a a a a a a 3 > a . o 8 e a a a a 8 8 a 8 a a a 8 8 8 a 3 3 - J i b 8 a 8 a a a a a 8 a a a 3 3 3 3 a a 3 3 Ul m » 9 9 » » t » 9 9 m m m » m 9 » 9 » m mm i / s u n i n t n i n t n t n i n e a a a B a a s t n i n u n t n <r , „ f H f H f H f H f H f H , - l f H f H f a f H - H - H f H , ^ , H f < ^ ^
in m UJ ^
a a un
a 3
a
a a o a in a
a 3 a a m a
a 3 un
8 3 8
a a m
3 3 3
8 3 un
a a 3
3 3 us
3 3 3
3 3 in
3 3 3
8 3 m
3 3 3 3 3 m
3 3 3
U ap Z Z an
3 3 3
a a 3
a 3
a
a 3 3
a a a
a a 3
3 3 3
a a a
a a 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
3 3 3
ul
z b. a h. WH tb
3 i.t
Z h-
z >-UJ Ik
tn
3 8 a 8 tn
a B a a un pg
a a a e tn
3 3
a 8 m pg
3 3 a 8 un
a B a a tn pg
a 3 8
3 in
B 3 3
8 un pg
8 a a 3 in
a 3 3
3 m pg
8 3 3
3 m
3 3 3
3 tn pg
3 3 8
3 m
8 3 8
3 m pg
3 3 a a tn
3 3 a a m pg
a a a a 3 IM
3 3 3
B m Pg
3 3 3
3 3 pg
3 3 3
3 m pg
3 3 a 3 3 pg
B 3 8
e m pg
8 3 3
3 3 pg
3 3 3
3 tn pg
3 3 a 3 3 fM
3 3 3
O m pg
3 B a 3 3 nj
B 3 3
3 in nj
3 3 3
3 3 pg
3 3 3
3
Pg
3 3 o 3 3 pg
3 B 3
3
m fM
3 3 8
3 3 pg
3 B 3
3
pg
B 3 3
3 3 nj
3 3 3
3 m pg
3 3 3
3 3 PVj
3 3 3
3
PU
3 B 3
3 3 pj
3 3 3
3
pg
lU (J
« ^ Q. U. tn 3
ac z <X SH
UJ * b z ^ tn
>
ae z • « SH
UJ N . X >c tn X
^ C Ib a b b
c ^ V • ^m
u. b p
z u. a s v «- ^ X a
a a i n
a wn
pg f H
a a
a
v f f H
a 8
a
ao f H
wn a
a
pg 1 *
^O a
a
a a un
a wn
mm
a a
a 8
;M a a
a
a
f b
wn a
a a
wn 00 a
a a
8 a i n
a tn
ye ye a
a 8
f b in a
8
a
a f H
fM a
fM
O N . N l '
a wn
a a in
a wn
eo f H
a •
a
00 mm
a a
a
<o Os • *
8
a
o> a Ol a
a
229
^ SH fH O mm
Ul m a I ^ it a c
fH pg
ae ^ SH
tn Ul X i<
s f PVJ
a
a
a H
a
a
^ pg PVI
a a
3
sn in 3
tk tu
a z aa f 4
a
o
« n SH -J Ul ml it
mm
B wn
a 8
oe p . l - H
a
p H
wn 3
a 8
an N f H
a
v f Wl Pv
a a
00 N . f H
a
w^ N .
a a
a
en ps f H
a
a 3 »-.J u. tn b H
«
S H
Ul tn LU ^
a a a
a i n f H
a 3 tn
a
a a a
a
m "*
a 3 8
a
a a a
a in f H
a 3 in a
a a a
a un "*
a a a
a fH in fH l/S
^ ( J
a- Z Z SH W-.
tn
X
^ a • -an tk 3 i n
z ^ Z t -UJ Ik - J i n
3 3 3
a v f
8 3 3
a a 3 fM
8 3 3
a 3 m pg
3 8 a
a v f
a a a
a
a 3 pg
3 3 3
a 3 US pg
a 3 8
a 3 -*
3 3
a .
a a n j
a a 8
. a i n PVJ
a 3 3
a 3 t - H
8 3 a
a
a a p g
3 3 8
a 3 m pg
u a ha a. tk Ul
a a m
a a wn
a a Ul
PJ fM
a a m a pg
a a a a a a m tn in 8 8 8
<M PM fM
a a
pg
a a m a
a a m a
a a wn
a a in
a a in a
8 a in 8
a a wn a
a a un
a a in a pg
a a wn a
pg
a e in
a a m a fM
230
at z a an UJ N X it in
Os a a
in p". Wl 8
a a a a
•o •*( •H fb
a a a a
8 a
a a
a
1 ^
vf a a
a 8
vf
a a a
a a
vf
a
oo o, a
pg fM
8
<o in
a a 8
fM >0
a a
a
a a
a
PVI a a
N a a a
a
« SH UJ N X it in
C lb a ba
> 8
a 'v r M
pg a a a
a
<o IM
pg 8 pg
-e m* a a a 8 8 a
a a
"O «o >o -* mm e a a HH 8
©• sf •^ PVJ in a a a
a a
a a
a
pg fM wn fH Wl o
a a a
wn a 1^ 00 eo m sO Wl Wl 8 a a «"* ^ a
eo Wl ^ fb fM a o. oo wn 8 8 8
"< Sf 8
00 a a a
a
Wl
m
fM pH « a
a
ee un eo a
a
sf
eo a
a
ee IM -H a a a
8 so sf fH in fH a 8 aw O
fM
m
WH 8
Wl 8
a a 8
N •H fM a
a
Ps 9 mm a
a
<e tn
a a 8
Ol
^ Wl 8 ^
Pa
a Os a sf
00 in
a a a
f H
<« > a <«
ae 8
eo a
ps
^ f H
a a 8
^
a IM a ««
un «H fM a ««
wn PVI
a a 8
<o » a a fM
^ 9 00 a an
sf
a a a a
es m a
a
Pa
» pg a
a
N
^ a a a
« sf fM 8 fM
m a pg a
f H
f H
a a a a
« eo 8 a
a
a vf
a a a
w> a 3 a a
«H
.n m 8
a
Wl
« fH
a
a
' * < e l n » O e e e e v f r a | / ^ l M | n J l n ' ^ e f b a o f b « f e o - , ^ t r * ' i « ' ^ £ ' * ' M e e , f . o w i o i n j P a w n i / s w n e f b - n a t w H f v , , / n f M . * a a o p g o > a O v f w n , r p . . o a f b f b . f w i f H ^ in u • • a . . 8 8 . a a a a a a a a a a a t n a , f M s O w l p g f H f M - « ^ — b . w n w H f g K P u i n - . f M P g M -> * i n . H i n a > o p g f b f M P b v f o e ^ - H i b f M f M s f « n f n j
"^ a w f M . n u n p j i # » H « M o e fH a " H ^ ^ v f ^ ^ , . » w i a e f M > O w n a O B w i r M i n a w n
as f > > w n « e i n i n N . 8 e a « H p g w n f H r s , K 4 « f b . f r g ^ • w i / s O e e P a < C w n i . f p a . f O v f P . . # . ^ e O s f f M < « 8 f M 1^^ * * * * * • • » m » » » » » m » m m m m x a . i n < O e e w n o o » i e e e o e o p a 8 w s ^ e Q i M w n f . f a i / i f a
N a f M f H e e f H « f . H a s f N o . s 0 f b f a . M m f H . « nj " H f M w n u s f M ' * f H « a . f
tu • H f M P v j i O o ^ o w n ^ ^ . r i n r s f b P s j v f e o w s o . f s j t ^ a p v i « o o 3 w n i f i 8 e w s » f c O a w n r s e a f M w i 3 8 mm Z a . a a a a a a a a a ' a a a a a . ' . . . a - t s e a a B a a a a a e a a e s a a a a B
a i n m w n t n i n w n i n t n o o o o o e a o a e n n a e a o i n i n i n u n a r s r b P s h a N P v r b p s N N P . N . N r s N N b . f b b . r s 8 W H 0 0 8 8 0 8 3 a a H f a f H f . f P f 4 . a f a 0 0 3 3 - J U l . a a a a a a a a a a a a a a . a a . .
i ^ ^ a a a a a a e a e a e a a a a e a a a a
a «t a SH aJ Ul
m
a 3 -i b. in tb bH
Ul aa UJ in
^
^ o aa Z
X sa
Ul
Z ^ a b. SH Ik
3 tn
Z ^ z ^ UJ tk .J Ul
pg
a a a
a a a a
a B in
a 8 a
a 3 a
a 3 a a
00
a a a
a a a a
a a us
a a a
a a a a
a a a . a
fM
a a a
a a a a
a 3 a
-
a a a
a 3 a 8
a 8 a a
a
ee a a a
a a a a
a a a
f H
a a a
a 3 3
3
8 3 8 a 8
fM
a a a
a a a a
a a tn
a a a a fH
3 3 3
3
3 3 3 a 3
no 3
a a
a a a a
a a wn
a a a a fH
a a a a
a a a a
a
PVJ
a a a
a a a a
a a a
-
a a a a "
a a a a
a 3 3 a
3
ee a a a
a a a a
a 3
a
fH
a 3 8
3
"
3 3 3
3
3 3 8 a
3
fM
a a a
a a a a
a a m
a a a vf
3 3
a 8
a a a a
a
an a a a
a a a a
3 3 un
a 3 3
vf
8 3 3
3
3 3 3 a
a
fM 8
a a
a a a a
a a a
-
a 3
a vf
a 3
a a
3 3 3
. 3
as a a a
a a a a
3 3 8
f H
a 3 8
vf
3 3 3
3
3 3 3
. 3
nj
a a a
a a a 8
a a m
a a a a *
a 3 3
3
3 3 3
. a
eo a a a
a a a a
a a in
a 3 8
a PH
3 3 3
3
3 3 3
• 3
fM
a a a
a a a a
a 3 3
-
a 3 3
8
**
3 3 3
3
3 3 8
. 8
eo 3 3
3
a a a a
3 3 3
PH
3 3 3
a **
3 3 3
3
3 3 3
. 3
PJ 3 3
a
a a a in
a 3 un
3 3 3
vf
3 3 3
3
3 3 3
. 3
eo a a a
a a a us
8 3 un
3 3 8
vf
3 3 3
3
3 3 3
. 3
fM
a a a
a a a in
3 3 3
mm
3 3 3
vf
3 3 3
3
3 O 3
. 3
eo e a a
a a a tn
a 3
a
-
a 3 3
vf
3 B O
C
3 3 8
• 3
UJ
u c ^ a. lb
m 3
ae z « mm UJ >s
z ^ Wl
>
ae z « an UJ N X it in
a a in a fM
pg wn a a a
.« fM
a a a
a a in 8
pg
fH
PVJ fH
a
a
« o> a a a
a a un a fM
<o fH
a a
a
wn a a a a
a a in a
pg
». m a a
a
wn fM
a a a
a a m a wn
a Wl
a a
a
m fH
a a 8
a 8 m 8 WS
fb vf
a 8
a
fH pg
a 8
a
a a in a .n
wn a a a a
pg
a a 8
a
a a m a
"n
p.
a a a
a
wn a o a
e a a a a a e a a a m in in wn l/S 8 8 8 8 8
wn wn w> .n PVJ fM ^ ae fH an N Pg an lO a 8 ^ a a a • a 8 a a
8 8 8 8 8
te yc 9 eo ^ vf o> fH "M a 8 a a a a
a a in a
fM
a a
a a in a
PM
a a in a
fM
a a in
fH »H rg a a • a
a a
a a
a a
a a
a
fM fH
a a 8
a a m a
PM
vf
an
a
a a a a in tn a a
pg fM
231
a a a
a a
in a a
9 a a
fM pg
a
•H Ol wn C b. nj a >s a Z ^ a
m ae
fM
« vf
•O
-o sn
m fM pg
•w in 9 fM
nj N Os
a fH
sn eo * 00 pg fH
a wn
pg pg a
fM <o a
00
m <o
Ol wn
pg N
pg a wn a M m
^ ee r lb pg
a N sn X *£ a X a pg
«o Os
wn fH vf fb a 8 a fH
sf PH fM pg vf l/l a a tb
» • » HH .H 8
in Sf pa 00 «a 4 «f wn fH e Pa l/S aH sO fH .f .f fV, a a 8 a a a
a sf fb fH «H e
a m in sf 8 a
a
Wl
^ fH a
a
< Ps N a •a
Os
o. in a •#
wn in
•r a
a
•# > fM a
« H
i n s f i / s » H m N ' « " H ^ ( O f H w n p a w n . H O i « O u n O . v f a H i O ^ » m o w s w i ^ O a H , ^ O i n a o o > u n i O ^
a e w a r v ^ ^ f a g o w f f V j r g O s f v f W l N i n ^ f M f M f M e O N i p H
' ' * ^ " " ' 0 " ' ' M e e f b * . « « . f b 9 e s f o a o w n w n « > , o w s > « o > O t n e o . f a o o o f M s # w i » H O . f b o e a O f M O > - H a H f M
a H i n « « i n e 0 a M W l i O a H f . fH f\|
P v « H O > f H « O a P g f H . O f b » . 8 f H < 0 8 s f f M f l O P g N
ae e n a n o v r P v a B i n a w n e e o > v f f H w i u n P a i e w n e e a o ^ ^ > 0 N u n ^ a 6 a H a H f M 8 ^ * f M < 0 ^ i n P V J « f 0 « p H P g S A s A a 9 , t t f . , ^ , f , ^ , , , f ^ , ^ X & O ' > f b ( M w ^ e f b v f e e < C ^ 0 0 8 N 8 f H i O w S f H 8
* n . r r s j o a e » i n i p s w s n j c o o e o > . f w i i n 3 r s n j p > " H v f f a w i w i p g . * a n f H mm !\i
Ik N i > a n e e w s P a a e f M P g w n a n u n v f » H o ^ » n i n > 0 8 lu a n P v j a n f b » f ^ a n o o i n O ' v f e n » a n v f f M ' * o e i n * f a P g ' O a a . n N 8 B * n ^ 3 a " n f > j O f a | ^ a n B p H ^ Z m t m m m » m » » 9 9 » » m » m m a m m a a H o o e a a a a 3 8 a e a a f H 3 8 a . * 3 3
a i n i n i n i n a o o e s o o o o e o o o o o n ^ i n i n u n u n u n u n u n « r s N . p v ^ . N . P a ^ . P . r s N r b P . N . N N r s P . p s ^ . r s P n a H 0 3 3 3 f H f H f H f H f - f H . . . f H 8 8 e 3 8 e 3 3 - i m . a a a a a a a a a a a a . . . . . . . ^ ^ 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 3 3 3 8
a fM « a a aa 8 _ j i n . h> ^ a m
an a a
PVJ a a
ee a a
PJ a a
00 fM a a a a
eo a a
fM ee a a a a
pg 00 a a a a
PJ a a
eo pg a a a a
er fsi a 8 a a
on a
pg an 8 a a 8
a a a a a a a a a a a a a a a a a a a a a 3 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 ^ ^ - 0 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 l / t l k . a a a a a a a a a a a a a a a a a a a WH t n i / i u n i n i n u n m i n u n t n i n i n 8 3 3 8 3 3 3 8 « ^ ^ ^ ^ « . f a » . f H f H ^ f H « H . « f H f - f « f H f - . a f H
tn an tu tn
^
^ u aa Z X aa b. in
^ ^ a b. SH Ik
3 Ul
Z
Z s-U.' Ik _) in
3 3 US
a B a a —
8 3 3
3 m
3 3
a 8 tn
a a un
a 3 3
8
-"
3 8 3
3 us
3 3 3
8 m
a a a
-
3 3 8
8
3 3 8
3 m
8 3 a 8 m
8 3 3
-
a 3 8
a
a 3 8
a un
a 8 a 8 wn
3 3 m
8 3 8
*
8 3 3
a in
a 3 8 a
a m
a 3 un
a 3 3
vf
3 B 3
8 m
8 8 a a
a tn
a 3 8
fH
3
a a vf
a a a a tn
a 3 8
. 8 in
3 3
a
-
a a a vf
3 3 8
3 un
3 3 3
. 3 sn
8 3 in
B 3 B
3 fH
3 3
a a un
a 3
a . 3 US
3 3 in
3 3 3
a "*
a 3 3
3 in
a 8
a . a un
a a 3
-
8 3 3
3
"
3 3 3
8 un
8 B 8
. 8 m
3 3 3
tm
8 3 3
S PH
3 3 3
3 in
3 B 3
. 3 m
3 3 in
3 3 3
vf
3 3 3
3 in
3 3 8
. 8 8 PVJ
3 3 m
3 3 3
vf
3 3 3
3
m
8 3 8
. S 3 Pg
3 B 3
-
3 3 3
vf
3 3 3
3 in
3 3
a 3 3 pg
3 3 3
-
3 3 3
vf
3 B 3
3 in
3 3 3
3 3 ni
3 3 m
3 B 3
3 fH
3 3 3
3 in
3 3 B
3 B Pg
3 3 in
B B
3
3 3 B
3
3 3 3
. 3
a pg
3 3 3
-
3 3 3
1 3
""
3 3
a o us
3 B O
3 3 pg
3 3 3
-
B 3 8
3 PH
3 3 3
3
3 3 O
. 3 3 n.
0. Ib Wl
a a wn
a a m
a a in
8
a a wn
a
a a m
a a m
a 8 in
8
8 a m
a
a a a e a a a a o e a a 8 8 8 8 8 8 8 8 8 8 8 3 t n m i r s i / n m w n m w s t n ^ i / s u s
• 8 8 8 8 8 8 8 8 8 8 8 ^ f M r M f s j r v j f M r g f M w % . r w n w n
232
ac z « SH tu Nl Z it in
a pg
a a
a
pg wn
a a
a
a a
un a a a
a
a
a a
a
pg a
vf
a
m a a
PM
a a a
a a a
a
a a
a
Pv fb a
ye a a
ao pg
a a
a
a 0> an Wl PH 8 8 8 8 8
oe z a SH UJ N X it in X
a a a
fM fM
a a
a
»M a a 8
a
a a 8
8
a a
a
fM fb
a 8
8
wn PH a a 8
eo pg
a a a
pg
a a a
a a a
a
fH a a a
a p. a
ao a a a
a
a a a
in pg a
a a a 8
a a a
a
s c
^ vf fM
a
a
•e tn mm ml 8 8 8 8 a -H 8 a
m a
sf
fM O' eo
fH 8
pg 00 a
<0 fH fH
nj
fM fH a a a M
ee Wl
a a
8
a 8
fM fb 8
Wl 9 sf a in
a sf a 8
m m
P. a a a a
fH O
no 9
PH f>
a
a
C tb
X a
fM <o 90 a
a
in fH wn PH a a
M O
nj a
a
in sf a
pg
m ee a fM
« rb m
8 fM
<o a
a pg
ee
a a
a
in pg ps
a Wl
00
a fM
O-a
a
fM Os pg
ye vf
o»
a fM
m fM PVJ a
a
a sf
^ r 5 l ! ' * ' ^ ' ^ * " * ' * » ' ' * " ^ ' * - i ^ 8 u s f H 0 O b. ^ ' ^ " ^ ' ^ * ' ^ 0 ' ^ « W * » n > f M f b * - a ^ . ^ i ^ t , i
' " • • • • • • • 8 8 8 8 8 8 8 8 . . . •
w H i > w i N . r b O f b 0 8 . H « H i n a n j p g O > P s > e S w s • ^ ^ P g s f f H f H * l - i w n W S W l
i n N o o - o o ^ O f M w n w n f M e o f M P g ^ m v f f l O O ' f H O
b . a - t H 9 0 , f e o - H 8 , / s O ' * * P s w n u n e o - H u i o > o * a f
x t ' . X m Z . X . l . l m Z J : • a . a x a . w S f H w > f H N i 0 > P g . 0 - H P a P g u n w ^ ^ , 0 f , . O ^ ^ ^
n j a e * e O s e f M P . p g - S N . a n p g p g p g u s o u n o i « ) i s u 1^ sn P M s f p a f M O O p H P S J P s . H I / S 3 0 . P
u. ' ^ > n « o i n > o a e p . 8 f v i w n a o a o < M a H . ^ O t n « ' i > x UJ ' ^ ' ^ « f P V J < O e C i ^ s f P a w n ^ V f V , « 0 0 v O N . f v . a n * u n ^ y * > ^ O m d i n t n O m m ^ ^ f s O m m ^ i n O m m ^ , / ^ O m d
^ " " a f H 8 e a f H 8 o o f H o a a t - i e a 8 f - 3 3
a o r a r G O a o o e a o a o e P i n m m i n u n i n u n u n r e « c c 9 C 9 ^ N r s N f b N r s P - r s N r s N N f b r s . f b r s P s f s . r b n s H f f f a f a f H — H f H f H f H o a a a a a 3 3 f H f - . - i t - i H i 5 _ ! ^ _ f • - ! • • • • • • • • • a a a a a . J i ^ a a a a a a e a a a o e a a a a a a e a
a « a SH -J tn Wa it in
a 3 U bl in Ik
«
tn SH UJ tn
^
^ u a- Z Z a-
in
z b-
a tm mm Vk
3 in
z b-Z b. UJ tk PJ in
pg
a a a
a. a a a
a a un
a 3 8
8 3 a a
a a a a 8 pg
eo a a a
a a a a
a a in
a a a
a a a a
3 8 8
8 8 pg
pg
a a a
a a a a
a 3
a
-
3 3 3
8
a a •a
a a a a a pg
en a a a
a a a a
a a a
w<
a a 3
8 8
a a
a a a a a pg
PJ
a a a
a a a a
8 3 in
a a a a **
a 3 3
a
a a a a a pg
en a a 8
a a a a
a a m
a a a a ""
a a a a
a a a a a fM
fM
a a a
a a a a
a 3 3
-
3 3 3
a "
a a a a
a a a a a pg
00
a a a
a a 8
a
a a a
f H
a 3 3
a "*
a a a a
3 3 8
a a pg
pg
a a a
a a a
a a m
a a a sf
a 3 3
3
3 3
a 3
a pg
00
a a a
a a a
a a m
a a 3
vf
3 3 3
3
a a 8
a 8 pj
pg
a a 8
a a a
a a a
pH
a a 3
vf
3 3 3
8
3 3 3
8 8 pg
00
a a a
a a a
3 3 3
-
3 3 3
vf
8 3 3
3
a a 3 8 8 pg
PJ
a a a
a a a
e 3 un
8 3 3
3 fH
3 3 8
B
3 3 8
8 8 pg
00
a a a
a a a
e a m
a 3 3
3
*"
3 3 3
B
8 3 3
3 8 pg
pg 8 a a
a a a
a 3 8
fH
3 3 3
8 t-t
o 3 3
3
3 3 3
8 8 PV,
ee a a a
a a a
a e a
-
8 B 3
3
•"
3 3 3
3
3 3 B
8
o pg
fVJ 3 a a
a a a
3
e in
a 3 3
*
3 3 O
3
3 3 3
3 8 nj
OC 3 8
8
a a a
8 3 in
8 3 3
vf
3 3 3
3 tn
3 3 3
3 a pg
nj 8 8
a
8 a 8
3 8 8
-
8 3 3
vf
3 S 3
3 m
3 3 O
o 8 fM
ec 8 3
a
a a a
3 3 3
fH
3 3 3
vf
3 3 3
3 in
B 3 B
8 3 P.
« • -a. lb tn
3 a un
a a m
8 a a a in m
a 8
a a m
a fM
a a m
a pg
a a in
a fM
a a in
a 8 a a tn m
a a i n
•M fM fM fM
a a a a a a a e a 8 8 8 8 8 8 3 8 0 i n i n i n i n t n m i n i n w n
f M w n w n w i w n w n w n w s M s
233
ae z
Ul N
z Wl
>
Ps vf 8 a
a
a
m in fM PVI
a a
pg a a a
a
>0 fH a a a 8 8 a a a
a a a
a
-H r^ — nj a a a a
a a
a a a
a
f^ 3 3 mm
8 a a a
a 8
a a a
pg a a
an Ps
a w a a a a
a a
in
a
sf ws PH fM
a a
« -H *
Z ^ Ul
a a a
a pg
a a
a
pg Wl a a a
00
8
a 8
a a a
<0 N. fH .O a a
a Wl sf
a a
a
a a 8
vf vf
a a a a
a
a a a 8
a a
fM C pg un a a
r u. a N c it > a
pg 8
fb W^ fb fb
ee eo a
tn
pg fM a
pg sO a
fM a Wl >o
o> fb fM
fM
a fH w,
fM
a fH
a
a
a
oo fM US a
wn
>o
vf pg 90 pg t- 90
<0 -H fH
a N K a
sf 00
pg a (M ee GO Os a o> pg 8 8 8
PSJ aw tn
tn m PVJ
a Wl
m a
tn
o-in a
a >o
a PH
wn a
a
00 fM wn « fM ao a a
•H O
PVJ
m m a
a
a
30 fH fM a
a
m m sf
so wn
a fb
00 «0 8 fH pg PH
a a PH fM
•X aa
us a.
Ul in
X a.
lu
O SH Z a a.
09 oo Os
tn pg
p. >n
a
in
3
eb Ol a
a
o* sf a fM N.
sf
in
8 9 sn 8
fM ee
Psi
ee
PJ oe
Ul eo PSJ PSJ 90 m a a 00 p. fH ».
m 8 ye fb
a mm
oe •f a
a pa
pg wn
e a
a
PV)
a vf
00
oe
vf
a
a pg
N. in
a
9 'O pg
PVJ
Wl fM fH ». Ol 9 a a
N 00 Os -H
pg
N a aH mm
wn a
a in
<0 wn
00 fM a
w^ OO
vf >o 9 9 ye
00
fM vf fH
fH > PJ fH fH
P. fb O fM *
30 in tn nj 8 tn a a
fH 9.
N a
in a pg a
in
pg a PV)
fb Wl f. vf fH m
m pg
a 8
a Ps fH pg
vf a
a cb >0 vf
«0 fH
ye 3
m tn fb PSJ
in
3 fb tn an mm *
vf 00
00 tn
90 pg
wn
vf
ye •* 6
wn N eo
-H 9 3 wn
>e nj
3 <e
9 pg
vf
fM
pg
a un a
PJ
vf
ac
. pg
•O m
3 — PH O 3 — a -H 8 -H 3 -H
a <r n sa _j ul -I at
00 00 in
8
a
un
3
a
un
a a
un
8
a
tn
3
a
m 8
a
un
a tn
a
a w. -J tn *m X tn
fM a a
00 a a
pg a a
ao a a
a a
00 a a
pg a a
eo a a
pg a a
00 a a
PJ a a
oc PJ a 8 8 a
eo a a
PVJ
3 8
ao a a
Pg ao fM 3 8 8 3 8 8
on a a
a a a a a a a a e a a e a a a a a a a a e 3 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 ^ ^ . 8 8 8 8 8 8 8 8 8 3 8 3 8 8 8 8 8 8 8 8 tnib a a a a a a a a a a a . a a a a . . . .
SH i n i n u s t n a a a a a a e B B B B B a a a e « . H f H f H . H f H f a f 4 f H f H f H t - l p . f a . H f H f H f H p H f a _ M
tn aa a- Ul
^
u a- Z T SH
^
z k-a b. •a Ik
3 Ul
..
t— Z b. UJ Ik fJ
m
a 3 m
PH
a 3 3
a
a 3
a 8
a 3 3
3 8 Pg
3 8 m
fa
8 3 3
3
3 3 a a
a a a a a pg
a 3
a m "*
a a a a
a 0 3
3
s 3 a 3
a pg
a a a Ul fH
a 3 3
a
a a 0
a
a 3 8
a a rvj
a 3 m
3 8 3
*
8 3 8
3
3 3 3
3 in pg
3 3
m
8 3 8
vf
8 8 8
a
a a a a m PM
8 8
a
""
a a a vf
a 3 8
8
8 8
a 3 un nj
8 3
a
f H
a a a vf
a 3
a a
a a 3
a in pg
8 3 in
a 3 B
3
3 B 3
3
3 3 3
3 m pg
3
a un
3 3
a a f-
3 3 3
a
a 3 3
3 m pg
a 3 8
•"
8
a a a fH
3 ^^ 3
3
3 3 S
3
m pg
3 3 3
**
3 3 B
3 PH
3 3 3
3
3 3 3
3
m pg
8
e m
3 3 3
*
3 3 3
3
3 3 8
3 in pg
e e in
3 3 3
vf
3 0 3
B
3 B 3
3 tn fM
B B 3
«H
3 B 3
vf
3 3 B
3
3 B 3
3 m nj
3 B
a
mm
a 3 3
vf
3 3 3
3
B 0 3
3 us fv.
8 B in
3 3 3
3
3 3 3
3
3 3
B tn PV.
3 3 in
3 3 3
3 PH
3 3 3
3
3 3 3
3 m pg
3 3 8
"
e 3
s a fH
3 ^v 3
3
3 3 3
3 m fM
3 3 8
fH
8 3 3
3
3 B 3
3
3 3 3
B uv fM
US
PA
CE
F
T
ac z <X a .
SU N X it-Ul
>•
XS
HE
AR
K
/IN
Y
MO
M
FT
.K/F
T
XM
OM
F
T.K
/FT
Y
ST
R
PS
I
Ul tn
X &
u. UJ
a a- Z ^ Ml
a « 3 SH
-1 Ul
U.
a « a WH -J Wl
t- u m
00
5'2
sf 3 3 a a
0.0
12
0
.27
2
00
0.6
1
ee fB'lO
l
fM tn m a
^ •n fM
<n
a in
3
in
Ps 3 a
a
PSJ
3 a a
2.5
00
fb fH
3
a
0.0
4 5
ye
mm
a
PH
mm
2.3
4
a
41
8a
3«
00
©• a
fb Pa 30
>o wn •e mm
in fb
a a
a
00
8 a a
2a
50
0
a a a a
0.0
02
BtO
'O
Pa
00 a 8
a
Ps
14
.35
a tn Ps .
pg 1^
f H
in
o
a
un Ps 3 a
a
pg
a a a
2a
50
0
wn
a a a a
Oa
00
7 0
.15
7
in
0.3
3
a.
o> .
00
m
wn wn m . in pg
ae o "*
a
m N
a a
a
ao a a a
2a
50
0
PM
a a a
fb
Wl
a a
a
6I/'l
ee 22
't
un
10
3.1
3
fM 00
<o a w> pg fM
m in
>e a
in Pv
a a
a
Pg
a 8
a
2a
50
0
WS
a a
0.1
36
5
.48
9
a
12
.09
•*
32
9.3
1
00
ee wn .
sn "M Pa
PJ
O <e **
in rs 3 a
a
ee a a a
2a
50
0
in
8 a a
0a
01
6
0.4
07
Pa
0.9
3
9 0*'*
2
o> WS pg
. <o in
9 <« a a
m N. 8 a
a
Pg
a a a
OO
S'2
vf fM
a a
0.0
60
1.5
52
^
3.2
9
««
93
.14
vf
tn -e .
fb
> f H
.. 30 p H
a
m N a a
a
eo a a a
OO
S't
wn
a a
a
Oa
03
0
20
0'1
Ps la
46
sf
pg fb a P. Pb in
P.
a PH a
a in
m »o a in
a
oe rs
a
a
pg 8 8
a
OO
S't
02
1
a
0.0
45
0
.98
3
fM
2.3
9
a
36
8.4
5
N
^ 00
. •c 9 no 00
wn <o **
ee p.
a
a
ee a . a a
OO
S't
20
0
8
0.0
05
ISl'O
in
0.2
2
wn 5
6.5
2
Wl
a sf
. vf
eo
fM
m a a
eo N
a a
fM
a a a
3.5
00
too
a
0.0
0 7
0
.13
9
a
0.3
4
Pa
o. a
in
pg vf vf
a Pa pg ""
00
>o *"
a
00 N
a
a
ee a a a
OO
S't
« vf
a a a
Oa
07
2 4
.22
7
fM
5.7
8
m
25
3.6
2
pg
Wl
o. a
•O vf Wl
fb
sn ye
a
ao P.
a a
pg
a a a
OO
S't
•n
o> a a 8
0.1
36
5
.11
1
12
.09
in
30
6.6
5
so N vf
m fM fb
in > •«
fH
00 pv
a a
ee a a a
3a
50
0
> fH
a a a
0.0
38
1
.37
6
o
la9
8
<e
82
.56
p. PVJ 00 a eo . aH
9
«o a a
00 Pv
a
fM
a a a
3.5
00
oo PJ
a a a
0a
06
0
22
t'l
vf
3.2
9
se
82
.33
o> in •e
N
»
^ ee
a
<c N
8
ae a 8
a
00
5*2
an a a a
a
0.0
09
0.2
10
0
.45
a
78
.71
00
tn
b.
vf
vf 8 Pg
—
sn p. o
a
pg
a a 8
00
5*2
a 3 a 8
Oa
OO
l
52
0*0
in 90
'0
•n
9a
48
ml wn
fb
„
PH
fM •H
B
m P. 3
a
PJ
e a a
OO
S'2
a a a
a S
OO
'O
00
a a
a OD
0.2
5
8 fb
a a
fM
•n 9 N
a eo <o
>o 9 an
a
in p.
3
8
ec a a a
2.5
00
PVJ fH
a a
0.0
29
1
.84
3
vf
pg
a pg
^
llO
aS
S
eo tn
m
mm
tn
yO
-
in rs 3
8
PJ
8 8
8
234
a 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 0 3 8 8 . 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 3 8 8 ^ b . a a a 8 8 a a 8 8 a 8 a a a 8 8 e 8 8 3 I A S k » » » m » » » m » » » m » » t » » , m ,
mm t n u n i n w n i n t n t n t n w n i n i n w n i n i n i n i n e e a a a f H v H f H p H f H f H f H f H f H f H P H f a t M f H M f a ^ f a f H f a
in "H Ul tn
it
^ u aa Z
T WH
Ul
Z ^ a m-mm Ik
3 Ul
•m
^ Z ^ UJ lb
- J Ul
a a tn
a 3 3
a a a a
a a a a pg
a a m
a a 3
3 3 8
3
3 3 3
3
PVI
3 3 8
f H
a a a
• 3
3 3
3
S a a a pg
3 3 3
-
a 8 8
a 3 a a
a a a a pg
a 3
m
3 3 8
a "*
a a a a
a 3 a a pg
a a m
a a a a ""
a a a a
a 3 8
3
PJ
3 3 a
fH
a a a a • •
a B 3
3
3 3 a a pg
3 a a
f H
a a E
a **
a 3
a 3
3 3 8
a PJ
a 3 tn
a a a vf
a a a 3
8 3 8
8
pg
3 3 m
8 8 8
vf
a a a a
a 8 8
a pg
a a a
-
a a 3
vf
8 3 a 3
B 3 a 3
pg
3 3 3
-
a a a vf
a a a a
a 3 a 3
pg
3 3 m
8 3 3
8 " •
8 3 8
8
8 3 8
3
pg
8 3 m
3 3 8
3 "*
3 3 3
3
3 3 3
3
pg
3 3 8
-
8 3 3
3 ""
8 3 3
3
8 3 3
8
pg
3 3 a
fH
a 3 3
8 ""
8 3 3
8
3 3 3
8
pg
3 3 m
a a a vf
8 3
3
a 3
PJ
3 3 3
O
pg
8 3 8
-
8 3 3
vf
3 3 3
3 B
3 3 3
8
pg
3 3 8
-
a a a vf
a 3 3
B 3 pg
3 3 3
3
PSJ
3 3 in
a 3 3
a "*
a 3 3
3 B pg
a 3 3
3
pg
u Q. u. Ul
3
a a m .
pg
a a 3 8 m tn a a
PJ wn
a a un
a a in
a a sn
a a un 8
a a in
a a m a
Pg
a a m
a a wn a
PVI
a a m a
fM
8 8 8 8 8 8 a a a 3 8 a WS in wn m in m
235
ar z C WH
UJ N .
Z « in
a a 3
a
a
pg
a a
a a
pg
vf
a a 8
8 a
a
vf
a a
a a
m a a
vf
PVJ
a a a
a
pg
a a a
a
3 a
m o. p. .f PH fSj
a a a
UJ N X it in
a a
a
eo eo «# pg a 8
m ^ a a a a a a
a a
<o a
Wl
WS
a a
a
p.
a a a a
pg
a a a
a
a a 8
m in
a a
a
PJ
a a a
a a a
a
Ps if
<0 wn a a
tn
a a
a
C lb
a N. c ^ > 8
Ol a p. eo a > a a
WH O
»• sf
wn o fH fM a a
a a
vf Wl 00
a
Wl
Wl
a
Ps eo wn >c 9 fM a a
-< a
a a
a
a vf
a a
vf in Ok
a
a
eo sf
a
a
fH ye fH ^
IM an
pg
C Ib
a N, X a
a a
a
PVJ
fM fH
Ol 00 fH pg a a a a
Ol a
•C WS
wn
00 eo wn a
pg
pg fM fH
N wn
a Ps a a
a a
pj m fb
pg eo a PVJ
00 > pg
•H »M ^ fb fH 00 » 90 00
PJ -H sf fH pg
Sf -n tn a.
Ul Ul
a a- Z a SH
in ee 0>
00
pg 9 m mm Ps «
fb fH pg wn
a vf fM
pg eo a
vf
<o
sf
Wl .#
P. a wn pg
a a
•PI vf
fb
a
pg
us « fH M
9 pg
-H a Pa
ee
a
pg
•e
ao m CO o
Wl e
p .
m 00
00
in
9 <0 m 00 >0 fM
pg pg oo o o. -n
fM
sn 00
<0 fH O'
PH ye Pg O.
pg
yO pg
pg
o.
vf
>o
a a
PJ
c
in
HH rg PVI
o>
Pv
o« Nl a
pg
fH O, «0 Ps eo fH
un
e
a -H a PH a -H
a
a
a tn ec
a
a 9 ps
eo
u a tn wn
00 pg pg N WH lO a a
eo PH
ae pg 8 sf
pg fH fM tn ae 30 fM
y* OZ mm
•n m yQ pg Pv an
• m , X 30 sn 9 3 ' Ps M tb f«
pg
oc a fH
in ne
•H O — a
a a "-_i tn
- i it
tn
a
a
m ae CO m
3
8
tn
a
a
un
B
a
tn
8
8
00 W
a fM
a a a WH o
J Wl a WP ^ a tn
00 a a
pg
a a
Nl a a
an a a
PVJ
a a
fM a a
a a
P J
a a
fM a a
P J
a a
ao a a
Pg a a
pg en
a 8 8 8
pg
8 8
pg
3 8
en 3 a
a a a
a a a
a a a
a a a
a a a
a a a
a a a
a a a
a a a
a 8 3
3 8 3
8 8 3
3 8 3
a a a
tn Ik
a a a
a a a
a 3 a
a a a
3 8 8 8 8 8 3 3 3 3 3 3 3 8 8 8 3 3 3 8 e a 3 a e 3 S 3 S 3 B 3 3 3 B 3
t n a H 3 8 i n 3 8 i n a 3 i n 3 3 3 t n B B i n O S UJin a a a a s . a a . . . . . . . . . .
^ u n u s f H i r i n - H i n u n p H i n i n i n f H u s u v f . i t f v i ^
^ u WH Z
Z — ^ tn
^ ^ a w. SH Ik
3 ul
Z ^ z ,-UJ Ik
_J U3
a a 3
8
*"
3 3 8
3 3 pg
3 3 a a in pg
a a a
a ""
3 3 a
s 3 pg
3 3 a a wn pg
a a a vf
3 3 3
3 3 fM
3 3 3
3 m fM
3 B 8
vf
8 3 3
3 3 pg
3 3 3
8 in pg
a 3 3
vf
8 3 3
3 3 pg
3 3 8
8 m rvj
a 3
• 3
3
•
3 3 3
3 3 fM
3 3 8
8 in pg
8 8 3
3 mm
3 3 3
3 3 pg
3 B 3
3 in pg
a a a 3
""
3 B 3
3 3 pg
3 3 3
3 in pg
3 3 3
•
3 3 3
B 3 pg
3 3 B
3 m fM
8 3 3
vf
3 3 3
3 3 PO
8 3 8
3 m pg
3 3 3
3 f H
3 t-l
B
3 3 IM
3 3
a 3
m pg
3 3 3
3
"*
3 3 O
o 3 pg
3 3 B
3 in fM
3 3 3
vf
3 3 3
3 3 fM
3 f^
3
3 gv pg
3 3 3
vf
3
o o
o 3 n.' B B 3
3
m PV)
8 3 3
•
3 3 3
3 3 -VJ
B 3 3
3
m Pg
3 B 3
3
""
3 C C
3 3 pg
3 3 3
O gv pg
3 3 3
3
"
3 C 3
O 3 "g
3 3 3
3 in pg
3 3 3
3
""
3 B 3
3 3 -u 3 3
o 3
m nj
APPENDIX G
MOMENT EQUATIONS
236
237
Stack Loading Condition
(L)0.18 ( 2.27 (, 0.27 ( 0.97
{W)°-^^ {h)2-57 (p )0.91 M = (E^)(7752) 'l (G.2)
(L)0-52 (E )0.82 (, )0.07
Forklift Loading Condition
(L)°-^2 (,)2.30 ( 2 . 0 4 M, = (EJ(3.66) f (G.3)
(,)C.04 (^0.72 ( )0.02 (3)2.03
(,)0.16(,)2.57 0.41
M = (E )(56.84) 5 (G.4) y y (,)0.15 ( )0.72 (, )0.50 (3)3.47
5 W
Stack Plus Forklift Loading Condition
(L)0.26(^^)0.06(^)2.18(^ )1.09(p )0.63( ,0.17(3)1.30
M^ = (EJ(1.25) "^ ^ i (G.5) (, )0.72
(,)0.09(j^)2.22()0.75(i0.54( 0.78(3)0.24
ri = (Ej(2i.2i) ^ ^ (G.6) y y (L)0.30 (, )0.73
APPENDIX H
DESIGN EXAMPLE USING EXISTING PROCEDURES
238
239
H.l Introduction
A design example is used here to compare the results obtained
from three procedures which are in common use among practicing
professionals. The three procedures are:
1. Portland Cement Association method (PCA).
2. Panak/Wire Reinforcement Institute method (Panak/WRI).
3. Corps of Engineers method.
Brief descriptions of each of the procedures are given here.
However, for more details, the reader is asked to refer to the
specific references indicated.
H.2 Design Data
A warehouse floor slab, 100 ft x 50 ft, needs to be designed for
the following conditions:
Aisle width between stacks, A^ = 7.5 ft
Modulus of elasticity of soil, E^ = 5000 psi = 720 ksf
Stack loading, p^ = 8 psi = 1.15 ksf
Design Axle Load = 10*000 ^^s
Contact area = 27 sq in.
Forklift truck loading, p^ = 185 psi = 26.64 ksf
Wheel Spacing, S 31 in. = 2.58 ft
Compressive strength of concrete, f^ = 5000 psi = 720 ksf
240 The three procedures stated here use a modulus of subgrade
reaction, k^, value as opposed to the modulus of elasticity of the
soil. Therefore, in order to be able to really make a comparison,
all parameters involved should be identical. Therefore, the modulus
of elasticity value is converted to an equivalent modulus of sub-
grade reaction value using the following equation (47)
k = 60 (E /1000)°-^^^ (H.l)
where
E = modulus of elasticity of soil, psi
k = modulus of subgrade reaction, pci
The value of k corresponding to an E value of 5000 psi is
calculated using Eq. (H.l) as follows:
,865
= 241.41 pci
H.3 Portland Cement Association (PCA) Method
k^ = 60 (5000/1000)'
The design chart used is shown in Figure 1.4. A safety factor
value of 1.5 is used. The design steps involved in thickness design
for single-wheel axle loads are:
1. Flexural strength of concrete, MR:
MR = 7.5 VT" = 7.5 V^OOO c
= 530.33 psi
2. Concrete working stress, WS:
WS = MR/SF = 533.33/1.5 = 353.55 psi
241
3. Slab stress per 1000 lb of axle load:
WS/axle load, kips = 353.55/10 = 35.35 psi/1000 lb
4. Enter Fig. 1.4 at left with stress of 35.4 psi; move right
to effective contact area of 27 sq in. down to wheel spacing of 31
in.; right to read an approximate slab thickness of 4.5 in. on the
imaginary line of subgrade modulus, k , of 241 pci.
H.4 Panak/Wire Reinforcement Institute Method (Panak/WRI)
The design charts used here are shown in Figs. 1.1, 1.2 and 1.3.
The design steps involved are:
1. Assume a slab thickness, say 6 in.
2. Enter Fig. 1.1 at left at 6 in. on the line of concrete
modulus, E , of 4 X 10 psi; move right to effective subgrade Vf
5 modulus, k of 241 pci; then down to read D/k ratio of 3.75 x 10
. 4 in. .
3. Enter Fig. 1.2a at bottom with aisle width of 90 in.; move
5 4 Straight up to D/k of 3.75 x 10 in. ; move right, cross over to
Fig. 1.2b with uniform load of 1.15 ksf to intersect maximum slab
bending moment at 350 Ib-ft/ft; move right to intersect tensile
stress curve of 354 psi (7.5 VTr/1.5); down to read an approximate
slab thickness of 4.0 in.
4. Calculate the equivalent loaded diameter from
d = \/(4/7T) (contact area) (H.2)
d = \/(4/7T) (27) = 5.86 in.
5. Enter Fig. 1.3 at bottom with equivalent loaded diameter
value of 5.86 in.; move straight up to intersect D/k curve at
5 . 4 ^ ^ 3.75 X 10 in. ; move left to read unit moment corresponding to 1000
lb wheel, which is 270 Ib-in./in.
6. Enter Fig. 1.3b at bottom with wheel spacing of 31 in.; move
up to intersect D/k curve of 3.75 x 10^ in.^; move left to read
additional unit moment value of 25 Ib-in./in.
7. Add values from steps 5 and 6 and multiply this sum by total
load on wheel in kips.
8. Enter Fig. 1.2b with a maximum slab bending moment value of
1475 Ib-ft/ft; move right to tensile stress curve of 354 psi; down to
read a slab thickness of approximately 5.5 in.
9. Compare values obtained in Step 3 and in Step 8. Use the
larger of the two, which would be 5.5 in this case.
H.5 Corps of Engineers Method
The design chart used is shown in Fig. 1.8. The type of fork-
lift truck used corresponds to Category I and Design Index 1 as given
in Tables 1.1 and 1.2. As the values used here fall outside the
bounds of the curve, the curves will have to be extrapolated in order
to come up with a value for the thickness of the slab. The design
steps involved are:
1. Enter chart at left with a flexural strength value of 354
psi; move right to subgrade modulus, k , value of 241 pci; move to
curve corresponding to DI 1; move right to read a thickness value of
7.75 in.
The same example is worked out using the regression equations in
Appendix I, and the result is compared with those obtained here and
are tabulated in Chapter 6.
APPENDIX I
DESIGN EXAMPLE USING THE
REGRESSION EQUATIONS
243
244
1.1 Introduction
A design example is used here to demonstrate the use of the
regression equations and to compare the result with those obtained
using three existing procedures included in Appendix H.
1.2 Design Data
A warehouse floor slab, 100 ft x 50 ft, needs to be designed for
the following conditions:
Aisle width between stacks, A = 7.5 ft
Modulus of elasticity of soil, E^ = 5000 psi = 720 ksf
Stack loading, p^ = 8 psi = 1.15 ksf
Design Axle Load = 10000 lbs
Contact Area = 27 sq in.
Forklift truck loading, p^ = 185 psi = 26.64 ksf
Wheel Spacing, S = 3 1 in. = 2.58 ft
Compressive strength of concrete, f ' = 5000 psi = 720 ksf
1.3 Design Calculations
1. Assume trial slab thickness of 4 inches.
2. Calculate allowable stresses:
f = 7.5 Vf^ = 530.33 psi = 76.37 ksf
V = 4 ^ = 282.84 psi
245 Stack Loading Condition:
3. Calculate design stresses:
(L)°-lV)0-°l{h)°-30(A )0-27(p )0-97
°x = (Ex)(l°26.00) TT^^^'" s
W' "S
nnn^0.14/(.«x0.01/./T^i0.30,7 t-N0.27/H ic^O.97 = (1.29)(1026.00) !^^ ^-^ Wl^) (7.5) [WIS)
(720)^*^^
(1.29)(1026.00) (1.906)(1.040)(0.719)a^
28.60 k ips / f t2 < f^ ^^^^^^^^^
(^^^0.18(,)0.59( .0.91
ay = (Ey)(30,045.00)^^^Q^^3^^ ^032^^ ^0.18
, . n v 0 . 1 8 , . / H ^ v 0 . 5 9 , H 1 0 0 . 9 1 = (1.24)(30,045.00)^^Q^ n ,^n^^^^\ .,^^'^^1 o
(100)°-^^(720)°-^^(7.5)°--^^
/ I o>.^/on nAC rtn^ ( 2 . 0 2 2 ) ( 0 . 5 2 3 ) ( 1 . 1 3 6 ) (1.24)(30,045.00)(^^^^Q)J330 g99)(l 437)
= 15.50 k i p s / f t ' < f^ allowable
4. Calculate expected shear forces: ( L ^ 0 . 3 0 ( , ) 1 . 8 2 ( , y . 0 2 , p ^ ) 0 . 9 8
V, = (E,)(15.14) ( , )0.n(E^)0.6U
246 = M oo>M. ..^(100)Q-^Q(4/12)^-B^f7.5^0-0^M 1.^0.98
(50)^-^^(720)°-^°
= (1 29)(15 i/|)(3.981)(0.135)(1.041)(1.147) ^ ^ ^ -^^^ (1.538)(51.808)
= 0.157 k i p s / f t
(W)0.09(^)1.83( jO.74
V^^V(^^^^-^\,)0.83(,^)0.57j^)0.44
= (1.24)(1467.0) (50)Q;0 ; (4 /12)^>^3, ,^^ , ,0 .74 (100)0.83(720)0.57(7 5)0.44
= f l ?4UUfi7 n^ (1.4222)(0.134)(1.109) ^^'^^^^^^^^'^) (4b.709)(42.529)(2.427)
= 0.082 kips/ft
5. Calculate maximum design shear stress:
„ , „ 0.157 '- 1000 (1+2x0.8x0.3333)x4x0.27 ^ 144
0.66 psi < V ,, ^ c all owable
6. Calculate maximum differential deflection
A = (0.47)
(L)0.44(^)0.62(^)0.20(p ,0.78 s
(. )0.99(^ ,0.29
._ (0 47) (100)Q-^^(50)Q'^^(4/12)Q-^Q(1.15)Q-^^
(720)^-^^(7.5)°'^^
(n Ai\ (7.586)(11.307)(0.803)(1.115) ^ ^^'^^^ (674.154)(1.794)
= 0.030 ft
Forklift Loading Condition
7. Calculate design stresses:
(L)0.12(^)0.30( ,2 .04
a , = ( E J ( 2 2 . 2 5 ) ^
247
X > X" • ' („)0 .04(^ )0.72(^ )0 .02(3)2.04
= (1 .29)(22.25) ^ ^ Q Q ] ' ' ' ' ( y ^ ^ ) ' ' ' ' l ^ ^ ; ^ ^ ) ' - " ' (50)0.04(720)0.72(7^5)0.02(2^33)2.04
(1.738)(0.719)(809.263) [l.d^)[dd.db} ( i . i 6 9 ) ( l l 4 . 0 9 8 ) ( l . 0 4 l ) ( 6 . 9 1 4 )
= 30.24 k ips / f t ^ < f . , , . , ^ t allowable
(^)O.04(^)0.34(p^)2.39
oy = (Ey)(347.71)^^^o.l5(^ )0.72(^ )0.51(3)3.48
^i;n^0.04,. , ^ ^ . 0 . 3 4 , . . ^>,N2.39 = (1 24)(347 71) (50) (4/12) (26.64)
(100)°-^^(720)°-^^(7.5)°-^^(2.58)3-^^
n ^AU- ziT 7^) (1.69)(0.688)(2552.859) [i..d^)K:i^/./i) (1.995) (194.098) (2.794) (27.067)
43.70 kips/ft^ < f, ^^^^^,^^
8. Calculate expected shear forces:
(„,0.28(,,1.80(,^)0.52(p^,2.80
^x = (Ex)(13.33) ^^j0.21(^ ,0.57(5,(3.96)
n „ w n 331 (50)°-^^(4/12)^-^°(7.5)°-^^(26.64)^-^° = (1.29)(13.33) (ioO)0-21(720)°-"(2.58)3-96
248 n PQUi? - ^ (2 .990)(0.138)(2.851)(9806.089) U . ^ y n i J . ^ s j ; (2 .630)(42.528)(42.659)
= 41.57 k i p s / f t
( L ) 0 . 0 3 ( , ) 0 . 1 1 ( , ) 1 . 9 0 ( , )0.22( )2.13
\ = (E ) (0 .19) n .Q ;> ^4 ^ y y (^^)0.59(3)2.64
= (1 .24) (0 .19) (100)^'^3(50)Q-^^(4/12)^-^Q(7.5)Q-^^(26.64)^-^3
(720)°*^^(2.58)^-^^
- n oA\fn 1Q^ (1.148)(1.538)(0.124)(1.558)(1087.396) " U . 2 4 ) ( 0 . 1 9 ) (48.509)(12.209)
= 0.148 kips/ft
9. Calculate maximum design shear stress:
41.57 ^ 1000 ^ " (1+2x0.8x0.3333)x4x0.27 ^ 144
= 174.33psi < v^ ,n,^,t)le
10. Calculate maximum differential deflection: (^,0.21(„)0.53(^^,0.71(p^)1.12
A = (0-12) (E^)0.98(,^)0.21(3)i.81
,n ^-,^ (100)°-^^(50)°-"(4/12)°-^^(26.64)^-^^
" *°-^'' (720)0-58(7.5))"-^l(2.58)i-«^
,„ ,,, (2.630)(7.9521(0.458)(39.050) = (0-12) (631.227)(l.527)(b.bbU)
= 0.010 ft
249
oo
0 0
t>0
LT)
to O-
CM
o
c o
• 1 —
+-> *r-
-a c o o ai c
• ^ T 3 ca o
_ j
4-> M -•^-r— - ^ S-
o L u
(/) 13
r ^ Q -
- ^ U 03
• • t o (U </) l / l OJ s-+-> (/>
c CD
• r-</) CU
• o
OJ
n3 r— 3 U
<T3 (_3
•
CSJ
o •
o
Lf) O J
• o
0 0
o
(/)
T — l
o
0 0
0 0 i n
CM
i n t n
• o
Ln
CvJ
o
Ln
i -H
o CM t—t
•=t
CM CD
O Ln
i n CM
o o
0 0
o
V O CM
cn lO
o CM
I—<
o
cr> CM
o LO
i n
Ln
o 0 0 o
0 0 o 0 0
Ln CO
0 0
o
CNJ LO
CO
< 3 CO
LO LO
• CO at
C\J
o
0 0 LO
o i n
to
cu
- a rt3
o
o
00
LO
o
r . — 1
• o « — t
•—^
at CM
CM + J L»-
~~ to Q .
•r— J ^
cn r-
CM
00 CM
to
CM at
CO
CM
CO t n
CM
0 0 ^ LO
LO •
LO CM
O
i n
o Ln
o
o Ln
0 0 ~ ' t—t
• o
CM
LO O
O i n
CM
o CM r^
CO CM
O
o
CM
cn
ro
CM
o as LO
at t—t CO
at
CM
o
CO at o
CM 0 0
Ln LO CM
CO at o
CO LO
• CO
O)
-Q
o
fO
-t
CM CTi
l - H
CO 1—1
-—' «^ CM
• I—t
+->
V
CM
+-> M -
to CL
•^ . ^
r>«. CO
• 0 0 CM
250
cr> CM
at CM
oo
CM
o
O.
LO LO
to O-
00
o
r r
Ln
UJ to
to <u o i-o <4-
$-fd
a; sz to
-o (U 4-> U <u CL X OJ
cu +-> fO
f —
ZZ u
t—
ro CJ
'^^' CO CM
• o "5" ^^^
cy» CO
• o
_ j • — - '
CO o
• o
LU'
II
^mm
»
00 Ln
CM
CM •
O
«^ LO •
LO CM
LO LO •
o LO
CM
CO CM
O
in
at CO
o o
CO •
o •—^
in
r y ^ - ^
Px. r^
r* Ln
• o
o CM r^
CO
o
as CM
LO
CO •
CO
CO at at
o o
in
in
CO
in
CM
VO CM o VO
00 CM in
Csi
Os
•
o oo
00
at Ln
to
Q.
00
a>
o
o
cn tn
00
cn
00 in
CM
to
CO
VO •
VO OJ
<n Ln •
o Ln
00
o in
en «
f-H
CM f—I
«^
»-H
o <Z)
o Ln
en tn
o
CM
00
o o
CO
o
cn CM
to CL
o o II
<n o CO
cn o CO
CM
cn
LO LO
Ln
LC 00 o
cn o LO
CO
CO CO
• in
o
o o
o CM
cn o CO
CM
Q.
T—
I-H
O
II
CM
251 13. Calculate maximum design shear stress
^ ^ ^ 0.14 100 (1+2x0.8x0.3333)x4x0.27 ^ 144
= 0.59 psi < V TT ^ c all owable
14. Calculate maximum differential deflection:
(L)0.41(^)0.62(^)0.19(^ )0.15( )0.70( )0.19
^ = (0-12) 0 .7 0 26 " ' (^^)0.97(3)0.26
__ (o^^2)(100)"'^'(50)Q-^^(4/12)Q-^^7.5)Q'^^(1.15)Q-^Q(26.64)^-^^
(591.034)(1.279)
.^ ,^^(6.607)(11.307)(0.812)(1.353)(1.103)(1.866) " ^^'^'^^ (591.034)(1.279)
= 0.03 ft
Therefore the assumed slab thickness of 4 inches would be suf
ficient to sustain the imposed loading.
A safety factor of 1 was assumed in using the regression
equations. However, even with a safety factor of 1.4 to 1.5, a 4 in.
thick slab will be found to be sufficient.
APPENDIX J
A COMPARISON BETWEEN THE PCA METHOD
AND THE REGRESSION EQUATIONS
252
253
A design example is used to illustrate the PCA method and to
compare the PCA method with the regression equations on a one-to-one
basis. However, in order to adopt the equations, certain assumptions
had to be made. For example, the PCA method does not require the
length or the width of the slab, but these dimensions are required in
the equations and therefore a reasonable value for these had to be
assumed. Design data used are given in Section 0.1. The design
example as worked out to illustrate the PCA method is presented in
Section J.2 and the example is worked out using the equations in
Section J.3.
J.l Design Data
Axle load = 25 kips
Wheel spacing, S = 3 7 in. = 3.08 ft
Number of wheels on axle = 2
Tire inflation pressure, p^ = 110 psi = 15.84 ksf
Tire contact area = 114 sq in.
Subgrade modulus, k = 100 pci
Concrete flexural strength, MR = 640 psi C« 28 days
Compressive strength of concrete, f^ = 4000 psi = 576 ksf
Assumed values are as follows:
Slab length, L = 150 ft
Slab width, W = 100 ft
Aisle wid th , A w
10 f t
Stack loading, p^ = 4 psi = 0.576 ksf
Calulated values are as fo l lows:
254
k^ = 60 1000
0.865
E = 10
hog 6.55917 k 0.865
= 10
nog 6.55917 x lOo" L 0.865
= 1805 psi
= 260 ksf
J.2 Design Example Using PCA Method
1. Safety factor, SF:
For frequent operations of this forklift truck in
channelized aisle traffic, select a safety factor of 2.0 (permits
unlimited stress repetitions).
2. Concrete working stress, WS:
,,c MR 640 WS = fTF = 3P = 2:0 = 320 psi
3. Slab stress per 1,000 lb of axle load
WS axle load, kips
320 25 = 12.8 psi
4. Enter Fig. 1.4 with stress of 12.8 psi; move right to
contact area of 114 sq in.; then down to wheel spacing of 37 in.;
255 then right to read a slab thickness of 7.9 in. on the line for
subgrade k^ of 100 pci (use 8 in. thick slab).
J.3 Design Example Using the Regression Equations
1. Assume trial slab thickness of 4 inches.
2. Calculate allowable stresses:
^t " '^'^ ^ " 474.34 psi = 68.31 ksf
V = 4 VT~ = 252.98 psi
Stack Loading Condition:
3. Calculate design stresses:
(L)0-l^W)0-01(h)°-30(A ) 0 - " { p )0-97 \ = (E,)(1026.00) 0 .74" ^
S
= (1.18)(1026.00)(^^°'°- ' ' ( l°°)°-°'(^/ l^)°i^°>°-' ' (°-^^^)'- ' ' (260)°-'*
= (1.18)(1026.00) (2-017)(1.047)(0719)(1.862)(0.586) (61.246)
= 32.75 k ips/ f t^ < f t allocable
,„)0.18(,,0.59( ,0.91
"y = (Ey)(30,045.00) ^^^o.48(g ,0.82(ft ,0.18
(150)°-*^(260)°-^2(10)°-l^
M iOr-5n riA^ nnK(^-^91j(0.523)(0.605) - (1.15) (30,045.00)^^_pgo)(g5_5go)(i_514j
= 15.63 kips/ft2< f^ allocable
256 4. Calculate expected shear forces:
(L)°-30(h)l-82(A )0-02(p )0-98 ^x = (Ey)(15.14) ,, . > \ ^;'' X y- j y jO . i i ^g ,0.60
/ ,f .pix0.30/./ .^vl.82,,nx0.02,^ C7c^0.98 = (1.18) (15.14)^^-5^^ WlLl (10) (0.576)
(100)°-^-(260)°-^°
= (1 18H15 l/l^(4.496)(0.135)(1.047)(0.582) • ^^•^«Hib. i4j (l.660)(28.118)
= 0.142 k ips/ f t
(,)0.09(^)1.83(p^)0.74
\ - (^)(1^67-0) (^)0.83(,^)0.57(;^)0.44
= (1 15)(1467 0) (100)^'^^(4/12)^-^3(0.576)Q-^^ (1.15)11467.0) (^50)0.83(260)0.57(10)0-^^
- n iRUiAfi7 n^ (1.514)(0.134)(0.665) (63.996)123.798)(2.754)
= 0.054 kips/ft
5. Calculate maximum design shear stress:
0.142 1000 ^ " (1+2x0.8x0.3333)x4x0.27 ^ 144
= 0.593 psi < v^ allowable
257 6. Calculate maximum differential deflection:
(L)0.44(^)0.62(^)0.20(p^)0.78
^ (0 47) (150)Q-^^100)0'^2(4/12)Q-2Q(0.576)Q'^^
(260)°-^^(10)°-2^
(0 A7\ (9.067)(17.378)(0.803)(0.650) ^ • ' (245.937)11.950)
= 0.081 ft
Forklift Loading Condition
7. Calculate design stresses:
(L)0.12(^,0.30( ,2.04
o„ = (EJ(22.25) 'x - ^^x'^"-"' („)0.04(E^,0.72(^y.02(s,2.04
- (1 18U22 25) '150l°-l^(4/12)°-^°(15.84)2-°^ - (1.18)(22.25) (^oo)0-0^260)°-"(10)0-02(3.08)2-04
/, ,o\^,o ,c^ (1.825)(0.719)(280.221) = (1.18)(22.25) •(i.202)(54.800)(l.047)(9.923)
= 14.107 kips/f t2< f t allowable
(w)°-°^(h)°-3^P,)2-^^
258 = (1.15)(347.71) (100)^-Q^(4/12)Q-34(i5^84)2.39
(150)0-15(260)0.72(10)0.51(308)3.48
= (1.15)(347 71) (1.202)(0.688)(736.911) ^ ^^^ - ^ (2.120)(54.80)(3.236)(50.137)
= 12.928 kips/ft^ <f. ,, ., t allowable
8. Calculate expected shear forces:
(W)0-28(h)l-80(A )0.52( )2.80 V = (E )(13 33) ^ w ^^f X xH13-33) (L)U.21(,^)0.57(3)(3.96)
= (1.18)(13.33) (100)^-^^(4/12)l-^Q(lO)0-52(15.84)2-^0
(150)0-21(260)0-5^3.08)3-^^
= (^ ifiUi- o'^\ (3.631) (0.138) (3.311) (2287.255) U.iOMi^.oJJ (2.864)(23.798)(86.032)
= 10.179 k ips/ f t
(L)0.03(^)0.11(^)1.90(^ ) 0 . 2 2 ( ) 2 . 1 3
\ - ' ^y^ ( ° -^^ ' (E^)0.59(3)2.64
= (1 i5)(o 19) (150)Q-03(100)0-11(4/12)1-^0(10)°-22(15.84)2-13
(260)0-5^(3.08)2-^^
, , -^w^ ,^t (1.162) (1.660) (0.124) (1.660) (359.318) = (1-15)(0.19) (26.597)(19.488)
= 0.060 k ips/ f t
9. Calculate maximum design shear stres:
^ _ ^ 10.179 1000 (1+2x0.8x0.3333)x4x0.27 ^ 144
259
= 42.501 psi < V ,, ^ c all owable
10. Calculate maximum differential deflection: (L)0-21(w)0-53(h)0.71(p^)1.12
(E )0-^^(A )0-21(s)1.81
,n ION (150)0-21(100)0-53(4/12)0-^1(15.84)1-12
" ^ ^ ^ (260)0-98(io))0.21(3.o8)l-81
f^ m^t (2.864)(11.482)(0.458)(22.066) " ^ -- ^ (232.634)(1.622)17.661)
= 0.014 ft
260
c o
• p— 4->
Con
d"
CT)
oadi
ni
Fo
rkli
ft L
to 3
r— CX
.^x: u ra
-t-J oo
. • t n CU
t o
stre
at
e d
esig
r
3 U
r— fO
C_3
• T - H
1 - H
t - H
0 0 •
t - H
««^ OO - -
L n L n
• o
^—^ to
Q -^ -
CM O
• t - H
,.— 5
ca:
^ t - H
• o
c-
^ ^ CM o
• o
3
t n CM
• o
_ J
0 0 o
• o
^—^ v»-
Q . • • . .
cn VO
• o
to L U
" ^ t - H
• o T-H
X LU
II
X D
t - H
CO •
t - H
^^"^ 0 0
o •
CO
^ - L n i n
• o
^'""^ VO
r^ i n
• o
^ . f ^
O J
o •
t - H
^—., o t - H
s •
«* t - H
« o
, — X
O J t - H
>».^ «d-
CM o
• o
o o t - H
> .. i n CM
• o
o i n t - H
y . ^ ^
0 0 o
• o
. .—» ^ 0 0
• L n t — l
> ^ cn LO
• o
o LO CM .. ^
1 ^ T—t
(1.1
8)(
10
.
II
\
— t - H
LO VO
• r->.
> ' .»—* 0 0 CO r x .
• o > ' «.—^ t - H
r-* «?!-
• o t - H
' . . — N
r L n 0 0
• o —• < • — »
r- cn o
• t - H
s — . ^
— o o i n
• CO
—-*
.. s
r-« «:r CM
• T - H
> •> .»—. o CO CO
• VO • ^
r t - H
ft
(1.1
8)(
10
II
OJ 1 —
Jin n3 5 o r—
r— rtJ
4-> VK
V
CM
/ft
to
40.4
20 k
i|
II
CM •vT
• O
— OO
y . - ^
0 0 VO
• o
.•—» M -
Q -— '
o i n
• o
— N
to Q .
% ' O
r •
o . « — N
5 <
" • — ^
0 0 t - H
• o
'—» - C ^_^
LO
o •
o '—' 3
CM 1 ^
• O
^—» to
LU V •
CO OJ
• o
—» _ J ^—'
OJ cn • t - H
CO t - H
LU
II
>, D
CM
'>r o
0 0 o
• CO -.^^
0 0 VO
• o
, — V
«=*-0 0
• t n t - H
% •
o i n
• o
. • s
VO t ^ i n
• o *—'
o r»~
• o
f—»
o t - H
• '
0 0 t - H
• o
^—^ CM r - t ~ » s .
^ > — '
VO
o •
o ' — » o o t - H
'
CM
r-•
o * s
o VO CM » *
0 0 O J
• o
*—* o LO 1-H
» — '
92)
• t - H
(1.1
5)(
13
II
-— "^l-o VO
• t - H
^—^ * — » ^ ' ^ l -L n
• VO '—^ * • — »
cn i n
r^ •
o — *—^ CM t - H
O
• i n — ' ' — » 1—1
CM 0 0
• o
' — 0 0 r-H CO
• T-H
o o 0 0
• ^ L n
r LO
o •
^
92)
• l -H
(1.1
5)(
13
II
(U t—
JZl
ea ? o
f ~
— fO
+ J Vt-
V
CM
+->
to
29.4
1 k
ip
II
cn CM
261
cn CM
to
CM
o
CL
LO VO
to CL
00
o
to (U LJ i-O
V I
SITS CU f—
t o
• o
cu +-> o <u CL X
cu cu +-> (TJ
n— 3 LJ
I —
03 C_3
CO O J
• o
cn CO
• o
Ln
LU to
CO
o
LU
00 o CO
OJ
o
00
Ln
LO VO
LO 1^ in
00
o o
CM
CO CM
O O
cn CO
o in
in
o LO CM
CO
o o 00
00 VO OJ
VO 00
Ln cn VO
in
LO
CO
00 00 •
CM
00 LO
o
CO cn •
CO CM
CO
o
00
cn t-H
o
oo
CO
en Ln
to
a. 00
cn
o
o
cn tn
00
cn
to
to CL
00
o II
cn o
CO
0 0
o CO
_ ^ 0 0
o * > » — * S i
«d-0 0
• t n 1 - H
* ^ cn i n
• o
* — » VO t ^ L n
• o « '
•i:d-0 0
• o
—y.
o t - H
N _ ^
cn r
• t - H
^ — y .
O J t - H
^ y^^^
1 - H
o •
o o o t - H
cn Ln
• o
.^•^^>. o VO O J
y^—y
0 0
<^ •
o —y.
o L n I - H
>_
^-^ cn o
• CO > ' , s
L n
''—y
0 0 CO OJ
• t - H
• — '
— t - H
0 0 t—t
m
o 1-H
• — '
f — *
CM CM
r •
o » -^—s
0 0 l - H
cn •
VO • ^ — '
^—* o I - H
• o
• > — ^
— r>. ^r o
• t - H
-—» 1—
cn L n
• LO CM
o 0 0
o •
t - H
t - H
^-^ cn o
• CO
> — ' f—»
L n
a.
o II
CM
\ 1
s-o
• p LJ 03
4 -
>) •*->
CU l l
03 to
i -O +J o 03
4 -
>> •»-> CU
M -03 to
03
262
cn
cn
to to cu & -
• • - >
t o
S-03 CU
to
c cn to (U -a
X 03
CU
03
Z3 U
03 C_)
O O
0 0
CM •
O X
X
CO CO CO CO
• o X
00 •
o X
OJ
II
>
cu JZt 03 :? o
r—
. . c o
't—
+ J LJ CU
M -CU
T 3
r— 03
• I —
+-> £= CU
s-cu
o r>. o
— to
Q -
> . _ ^ i n t - H
• o
*-—*» 5
«a: ^—^
cn t - H
• o
~» x: —
CM LO
• o
LO O J
• o
oo r^ cn
• C 3
L U
03
U >
V
•r— to Q -
0 0 I — t
VO
o
II
X 03
CU • ! ->
03
Z5 LJ
03 O
«
o
CM t - H
O
in
00
t n
o
LO ^ « . LO
o Ln t - H
o o t - H
cn T-H
o OJ
CM VO
o o
VO CM
O
O LO
CM T-H
o
00
o CO
cn
o VO CM
o cn VO
o CO VO
CO t - H
• t - H
CM t - H
00
o
CO
CO
CM o 00
OJ
II
<3
,—.. o *d-CO
• t - H
«_ ,—., t — t
i n o
• o CM CM »_
1
•»->
*+-CO
r o
• o
II
cn £=
•r— • o 03 C
• "
•a <u to o CL
E • r -
(U
.c •l->
c •r— 03
+ J VO :3 I/)
o 4->
+-> c cu
. f —
LJ 'r—
^-4 -3 to
LO •r—
.a 03
— to
J ^ VJ
• 1 —
sz • t ->
• c: '*" ^ 03
O
GJ S_
o Vf-O)
c cu > <u c: <u cu to
to OJ
W<t
<u > cu 2: o I C
• I/)
c o
'r— +-5 03 3
cr cu c: o
• f —
to to
cu s-cn cu s-cu .c • M
cn c • r— to 3
C •r—
-o cu E 3 to to 03
UT o; S
. — (
. +-> OJ
• 1 —
LJ • t —
M -M -3 to
1 —
r— • I —
+-> to
to • T —
.a OJ
f —
to
J>t.
u •r— x: + J
. c:
• • "
^ 03
#* UO
• '"'
CO