Determination of desirable lengths of Z- and channel-section columns for local-instability tests

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Material Information

Title:
Determination of desirable lengths of Z- and channel-section columns for local-instability tests
Series Title:
NACA WR
Alternate Title:
NACA wartime reports
Physical Description:
8 p., 5 leaves : ill. ; 28 cm.
Language:
English
Creator:
Heimerl, George J
Roy, J. Albert
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Publisher:
Langley Memorial Aeronautical Laboratory
Place of Publication:
Langley Field, VA
Publication Date:

Subjects

Subjects / Keywords:
Airplanes -- Design and construction   ( lcsh )
Aerodynamics -- Research   ( lcsh )
Genre:
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
Summary: Local-instability tests of 24S-T aluminum-alloy formed Z- and channel-section columns were made in order to determine a length of test specimen that would avoid the increased strength associated with short lengths and also permit the occurrence of a convenient buckling pattern. The effect of column length on the critical compressive stress, on the average stress at maximum load, and on the number of half-waves of the buckling pattern is shown. A buckling pattern of three half-waves is indicated as desirable for test purposes. A curve is presented from which may be determined the lengths of Z- or channel-section columns that give a buckling pattern of three half-waves. When the strength for local instability is very high, a reduction in the length indicated by the curve may be necessary to prevent column failure. In order to avoid the increased strength associated with short lengths, a ratio of length to web width above 3.5 should be used.
Bibliography:
Includes bibliographic references (p. 5).
Statement of Responsibility:
by George J. Heimrl and J. Albert Roy.
General Note:
"Originally issued October 1944 as Restricted Bulletin L4H10."
General Note:
"NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were previously held under a security status but are now unclassified. Some of these reports were not technically edited. All have been reproduced without change in order to expedite general distribution."
General Note:
"Report date August 10, 1944."

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003806705
oclc - 124096347
System ID:
AA00009406:00001


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Full Text



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RB No. L4E10 .


,. ;." "
."::i .. :


AL ADVISORY COMMITTEE FOR AERONAUTICS


WART IKE REPORT


ORIGINALLY ISSUED
October 1944 as
Restricted Bulletin L4H10


DETERMINATION OF DESIRABLE LENGTHS OF

Z- AND CHANNEL-SECTION COLUMNS


FOR BOCAL-IMSTABILITY TESTS


By George J. Heimerl and J. Albert Roy


Langley Memorial Aeronautical Laboratory
Langley Field, Va.


UNIVERSITY OF FLORIDA
i : DOCUMENTS DEPARTMENT
120 MARSTON SCIENCE LIBRARY
SP.O. BOX 117011
GAINESV WIE.FL 32611-7011 USA






WASHINGTON

R: i"Ei RPORTS are reprints of papers originally issued to provide rapid distribution of
-Ws*ru t to an authorised group requiring them for the war effort. They were pre-
"i- :meity s.t~ s fbu are: now unclassified. Some of these reports were not tech-
Fv": bel Zreproduced without change in order to expedite general distribution.


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NACA RB No. L4H1O

NATIONAL ADVISORY COMMITTEE iFO .AEFONAUTICS


RESTRiICqED BULTLETIN




2- AT. 1' ,'.. \.'II' LJ COLU'iT I

F3R lOC4 L-II N'-'.TALI LITTY TE'? S

Ey C-ecrgo J. Ieimeri sr.i J. Albert Roy


S U M"AP'i


Lo.:s.-lr- .stgo:l it.y tests of 2 '2"-T allir.nlim-alloy
formed : -. r.'. ch :;nel- section co1lur.ns w re made in
orc.er to .d:l lioith te t s'. ec.en that v'ould
a'oi t*. .a. .n csc;r: c ir.tiedi vith rhort
len, 2 &1' I'.lo Tr: r,- Lh co .'ir..r nce ?f 3 convenient
bu. ..: 'h i o .f olu.ni lengt-> on the
cr i .-,1 r;:, 3 .; te tr .s, orn tne aver ,a e .tress .t
ma;. -.r I, J '. id or. t.: r nu-i -: r of half--waves cf Lhe
bu.r:! l.I n ; patt --' sh,''T .4 b'u .it ng ipttern of three
hnall 1 s s ind.i.;ate- i as dr :-. rab r for test purposes.
A c. r;: is prcsentieJ rrom which ma; be deterrmined the
lengths of Z- or chann'l-seCti] on colurruis that give a
buckling pattern oi three half-waves. "Tien the strength
for local instability is very high, a reduction in the
length indiated by the curve ray be necessary to Frevent
column failure. In order to avoid the increased strength
associated 'with short lengths, a ratio of l-enth to web
width above 5,.5 should be use.cd.


I I"RODTTCTI IN


In local-instab li ty tests of Z- and ,hannel-secti-n
columns, suitable specimen lengths should be determined.
As the flanges and webs of such ,oluirns maj be considered
plates vith various kinds of edge supports, the local
instability of these columns becomes a plate-buckling
problem 'When a plate is long, the critical conmressive
stress tends to be ind-ependent of length: whereas, if
the plate is :ery shDrt, the stress increases appreciably.
(See fie.. 6 of reference 1.)









2 NACA RB No. L -10


For an investigation of columns that develop local
instability, therefore, the Jrecinen s should be made
long, enough to avtri an appreciable increase in stress
and yet not long enough to result .n column failure.
In order' to determinne lengths of columns that meet
these reruirerents, tests were nade of f'orred Z- and
channel-section -soliurns of various lengths. This reFort
present, the test resuls and a carve fnr deterrl-ning
desirable Iolur-n lengths fcr test purposes.


S Y' rBOLS


bp -Tidth of flange, Iricheis

b-.;: width of w-b, inches

L length, inches

t *hickness of veb cr. frirne, :;nches

E modulus of r-lastici ty, ksl

Oc, critical -ompr.es-iv e stress, ksi

a P.verage stress -Lt naxirrurr lobd, ksi

cv compressive yield stress, ksi


SP ECT .MNS


-orred Z- and channel-section columns were made
frorr 2'S.-T *3li.min2mr elloy with the grain of the material
PcrsEll 1 to ti.:- length of th: column: ne sheet of
material was used for each ty e of colurn, and 75 columns
of each typ were tested. The ends of the specimens were
ground flat, parallel, acnd at riTht angles to the length
3f th column. i'Pgure 1 sh-rws the nominal dimensions of
th' three cross S-ctions used for the Z- and channel-
section columns. The measur-d dimensions of the columns
anld the test results arc- given in table 1. For each
cross suction, the ratio of length to wob width was
varied -rmc abbiru 1 to about 10.








NACA RB No. L4L10


Stress-strain tests of the material were made with
single-thickness specimrcns in a r!ller-t1pe compression
fixture similar to that show-v in figure 2 of reference 2.
Corpressive stress-strain curves are shown in figure 2.
The values of the comr-x-essive yield stress, determined
by the C.2-percent-offs-t method, and of the modulus of
elasticity are given in t&ble 2.


METHOD OF TESTING


Phe coluirn tests were made in a 35C0,000-pound-
capacity compression testing machine that is accurate
within three-quarters of 1 .-ercent for the r.srge of load
used in the tests.

A Z-sectibn colunxi under test is shown in figure 5.
The displacement of pointers, supported by sxtensicn
arms attached to the flanges of the oiurrns, was ricssured
by the opti~ S1 ni-ror'eters that can be s:-en in figures .
The critical conmressive stress was obtained from stress-
distortion curves in ti.e manner described and illustrated
in reference 5. In this method, the critical stress is
determined as the point near the top of the knee of the
stress-distortion curve where a marked increase in distor-
tion first occurs .ith small increase in stress.


RESULTS AND DISCUSSIOTO


The variation of ocr and Omax with L/b, for
each of the different types of column tested is presented
b, b_.
in figure L. Columns having I =- 21 and b = 0.5
t W
developed bending failure for > 7. A definite rise

in critical and maximum stress~ when the columns become
very short is showrn by these curves. For all except the
very short cluimns, however, the curves are relatively
level. The number of half-vaves of the buckling pattern
that occurred in each case is also indicated in figure 4.

It has been found desirable for test purposes to
make the column length such that an odd number of half-
waves develops, because of the convenience in measuring








NACA RB No. L4H10


cross-sectional distcrtion at the center of the column.
Economy of mrratpril and the pnisib'i1 ty of beiading failure
if the column is long I.e6.a to a choice of lengths such
thnt the colu-ars ;vill eveloo the least number of half-
waves aid still avoid an appreciable in-rease in stress
due to the effect of snort lengths. There considerations,
to.rg;th.?r with the test results shown in figure L, indicate
tiet a buckling paLteri of tihr e :alif-w-ves is the one
most de-irable for irnvstigaL!.ons oi lo-.al instability
of col' 1mnrs.

The length of the ha] f--wave v eveloped when local
instability ozc.-.rs var. P, for a givcn web width, with
the cross-sectional isat.o b, /b -. The number of half-
waves then dere'nds on tne tatio of length to web width L/bti.
By sho'-ir.'g the nur.ber of half-waves that occur for eivan
values of b/,'b, and L/b, as illustrated in figure 5,
curves m.ay b- drawn th-i. show. the rtlatiorship between
b /by; nd L/bA requirra to obtain any desired number
of half-waves. Tn order- to Tive proper r eight to the
test results shown in figure 5, the numbe-r of tests for
w'hi.ch .:ch nu.:.ber of half-vav 's occurred is indicated.

A reconmmi.ded curv-E is drawn in figure 5 to indicate
the prop.r:, tilns o. either a Z- or a channel-section column
req-uir to d.velo, a :,cklinc r.atte'rn of thr'=-.e half-
waves, v.rich .s d-eirable for test furpnses. This curve
can be .:sed *.irectly for sel-rting speimen lengths in
many ca.ts. In cascs in which the strength for local
instability is hi,-h (low values of -bw/t), however,
spEcime-? lengths s,-lect-cd according to the recommended
curve mnay not be short ncugh to prevent bending failure.
It is therefore necessa' to chec' the column strength
of the s[!eclrlens selected and, in rorme cases, to shorten
the s.,.c irr..ns:. In any case, figure L shows that, in
order to avoid en increase in .trer.-th due to the effect
of very rhort lengths, the v.lue of L/b,. used should
De above .5.

CONC LTST O-IS

For local-Instability tests of Z- and channel-
sqction colurmns, the sr-:cirrens should be just long
enough to avoid th. increased str..ng.tn associated with
short l.-neth3 tut of such length that a buckling pattern
conven!_nt fbr test purposes occirc. A buckling pattern
of thre.. half- avep rreets these requirements; the proper
length for this condition may be -btained from a curve








NACA RB No. L4~IO


based on tests. fhen the strength for local instability
is very high, a reduction in this length may be necessary
to prevent column failure. In order to avoid the
increased strength associated with short lengths, a
ratio of length to web width above 3.5 should be used.


Langley i."emorial Aeronautical Laboratory
National Advisory Comnurttee for Aeronautics
Langley Field, Va., August 10, 1944







REFE E IECES


1. Lundquist, Eugene F., rnd Stowell, Elbridge Z.,
Critical Compressive Stress for Flat Rectangular
Plates Supported alon? All Edges and Elastically
Restrained agAinst Potation along the Unloaded
Edges. NACA Rep. No. 755, 1942.

2. Paul, D. A., Howell, F. W., and Grieshaber, H. E.:
Comparison of Stress-Strain Curves Obtained by
Single-Thlckness and Pack 'Methods. NACA TN
No. 819, 1941.

3. Heimerl, George J., and Roy, J. Albert: Freliminary
report on Tests of 24S-T Aluniinum-Alloy Columns of
Z-, Channel, and iH-Section That Develop Local
Instability. NACA RB No. 3J27, 1943.








I NACA RB No. L4H10
, i .


TABLE 1
IIYASURED DIMENRTONE OF FOIRED SPECIkENS AND TESr FESIJLS

Sat t b. y L L b b or oaB Number
p lr (In.) fin.) (In.) (In.) b t 1b 1Ik1e Ikal) or hlf-


Z-sectlon column: asetion 1

Is 0.106 2.54 1.50 2.79 1.10 24.00 0.51 47.4 50.2 1
lb .106 2.54 1.50 2.79 1.10 2.o00 .51 b6.o0 0.2 1
2a .105 2.5 1.50 5.55 2.12 2.05 .51 44.2 16.7 1
2b 1 2 5.55 2.12 .9 .51 L. 6.5
b 106 2. 1 .50 7.92 3.11 2.00 .51 41.3 I.53 2
S .106 2.5 7.60 2.9 24.00 51 42.1 2
106 2.5 .50 7.82 07 2.o .51 46 .1
S .106 2. .50 10.0 .07 25.91 .51 20. L2.7
: lb .106 2. 1.2Q 10.30 .05 2 .98 .51 Lo.q L5.7 2
4 .106 2.54 1.50 10.50 4.05 2.00 .51 0.7 4.5. 2
1 .o106 .55 .50 12.92 5.07 24.05 .51 5.0 5
5b .106 1.0 12.95 5 .~ .o 1 1.0 2.
S106 2.5 1. 12.95 5.07 24.05 .51 59.8 5.)5
S 106 2.5 .30 15.50 0 4.00 .51 59.8 L2.7
6b .106 2.51 .)0 155 6.19 25.67 .52 q9.8 1.1
60 106 .5 1.50 15. 6.11 2.00o .51 0.0 L,).2 I
7 .106 2.52 1.0 17 6.97 2.81 51 59.7 Ll.9 5

I -setlon column: sebtlon 2

8a. 0.105 2.5 2. 2.72 1.07 .24l. 1.02 3.0 58-7 1
8b .105 2.55 2.5 2.68 1.5 24.2 1.01 35.8 c.o I
So .105 2.5 2.8 2.68 1.0 24.14 1.02 52.2 41.O 1
*9 .105 2.54 2. 5.28 2.08 24.1 1.02 21.0 30.9 1
9b .10o 2. 5L 2.8 5.5 2.10 24.4 1.02 22.8 51.2 1
104 .106 2.5 2.0 7.70 5.05 4.0 1.02 15.6 1.0 1
10b .106 2. 2.60 672 2. 02 1.02 15.5 51.1 1

11b .105 2. 2.5 107 .06 24 .00 15.2 29.8 2
11 :106 2.55 2.5 10.5 4.06 .09 .9 I.', 50.2 2
12* 105 25 2. 12.9 5.0 .99 1 2
12 b 2.1.5 09 16.9
2e o 2.5 2. 12.95 10 .19 1.00 16.2 29.3 2
15* 106 2.5 2. 15255 4.11 11 1.00 IL.q 29.2 5
15b o106 2.5 25 15.55 6.11 2.00 1.00 15.6 29.4 2
S106 2.5 2. 15.55 6.11 2.oo 1.oo 11 2Q.2 5
.106 2. 2.5 18.07 7.10 2.9' 1.01 7 5
b :06 2. 2.5 18.07 7.10 2 .0 1.01 2 2.9
S106 2.54 2.5 18.0 7.11 259 1.01 28.9
N.' 15, .106 2. 2.58 20.60 8.10 2.95 1.01 1.4 29.5
15b .106 2.5 2.58 0.60 8.10 25.98 1.01 1U.. 28.1
15 .106 2. 2. 20.62 8.11 295 1.01 19 29.
I6S .106 2.54 2.58 25.22 9.13 2k.00 1.01 1a.2 27.8
6b .106 2. 2.58 23.22 9.13 25.98 1.01 14.6 27.7
16a .106 2.5 2.58 25.22 9.15 2 .98 1.01 1.5 27.6
17s .106 2. 2.5 25.75 10.10 24.00 1.01 15.5 27.5 4
17b .106 2. 258 25.7 10.08 2.00 1.01 1. 27.5
17a .106 2.5 258 25.7 10.11 2 o 1.01 2.9

Z-aectlon column; eotlion 5

18* 0.105 1.0 1.48 1.71 1.23 15.29 I.o6 45.8 55.7 1
1Gb .15 1. 1.48 1.74 12 3.29 1. o6 5.9 55.5 1
19 .105 .2 1.6 07 2.1 1).52 1.05 4.9 1.2 1
206 .105 1.41 1.*8 4.7 5.11 15.8 1.05 4k.2 7.1 1
20b .10 140 .8 .9 .15 15.29 1.06 2.0 6.8 1
'"20 .106 1.0 1.46 15 15.22 1.0 89 6.L 1
21* .106 1.2 1.5 5.95 .6 1).50 1.02 52.6 .7 2
21b .106 1. 1 590 15.-5 1.02 .1 4. 2
S21 .106 5.90 ,.1 15. 5 1.05 k5.2 5
22. .106 1. 5 7.5 5.15 1.45 1.02 38.5 5.8 2
22b .106 1. 1.45 7.32 5.14 15.43 1.02 59.6 .2 3
S22 .106 511 5. 1 6 2
25, .o16 1. 1. .107 1 1.00 1.2 49
h .106 1.4 1. 8.7l 6.07 1 .58 1.0oo 2.
25e 106 1.5 1.5 8.7 6.10 1 .5 I.oo L2.k 4 4 5
2: 106 .2 1005 6.9W 7 .98 1.5 5.
6.o1 .98
.2b 106 1. 1.2 10.0 6.98 1. .98 0. 4.2 5
ale .106 1.44 1.l 10.10 6.99 13.62 .98 41.0
S .106 1.41 11.5 7.99 15.62 .98 4o.6 .8
25b .10 1. 1.2 11.52 .05 15.52 9 40.1 45.6
25' .106 1. 1.L1 11.54 7.99 15.62 .9 l.5 .437 4
26a .106 1. 1.142 12.92 .95 13.62 .98 41.6 5-5 4
26b .106 1. 1.42 12.92 8.99 1.58 .99 2.8 .5 4
I :26e .106 1. 1.1 12.98 8.95 15. a .97 5-9
27. .106 1 .2 .57 9.99 1.5.55 .99 L0.6 45
27b 106 1.4 1 10.01 1) 1.0 9 4
S27e .106 1.4 1 .1 164.6 9.95 15.0 8 0.7
9.95 1 .


NATIONAL ADVISORY
COOV I'r PR AERONAUTICS


.1S









NACA RB No. L4H10


TABLI I Conolutad
MASUR D DImSITONS Ooaoluded

speosm b L L or Om bmber
.) .) ( .) ( .) ) ( ) at balf-


ChUonl-sssttan oolum; motion I


Ii
lb
to
as
2*
2b


6b

ks
5.

Es


a


r!
0.07

.106
.106
.106
.106
.106
.106
.106
.106
.106

.106
.1016
.105
.20
.10
10I


a.,'
2.
2.
2.5
2.
2.
2.
2.
2.
a.
.,



2.
2.


6.a6
1.26
1.27
1.28

1.:2
1.26

I: a
1.26
1.,7




1.26
1.27
1.2:6


2.78
2.67
IM



10.15
10.5 V
l,.00
12.97

i1n

11.05


1.09

2.10
2.11
5.06
5.0






6.10
7.10

7.11
6.01
6. to

7 I


2 5.7


2 .91

2 .00
:8.19

2.00


:00
24 0
&.19
.215
.co


0.69
: ,

.9


It!
.6
6.0
".1
59




97
3.59
39.7


9.9



39.7
39.7


6r.s
1, .
69.6





42.6
.0





.i-

i I
.0


.M
w.


Chbaul-ueotlon solum: esstirW 2


89
Bb
,9
95
9b
lOb
10s
11b
lib
1e
12.
las
15.
1b


160
ISb

15a
15b


17
17b
17o


18
19s
19b
19e
20.
20b
21a
21b
21 l
22.
22b
22oa


2:
2 o
25.
25b
2 i

26b
a6b


.0 10
.105
.105
.106
106
.106
.106
.106
.to
.106
106



.106
. io6



.106



.106
.106
.105
106
.106
.106
.106
.106
.106
.105


0.106
.105
.105
.105
.105
.106
.106
.106
.106
.106
.106
.106
.1o6
.106
.106
.106
.106
.106
.106
.106


2.
2. 6


2. 2


2 57
2.55
2. 9
2.2
2.
2.5
2. 55












2-55


Chanl-Moatlom oloi; motion c)
1.6 1.6 1.00


1.41

1.-


1.2
1:t

1.
I.

:I.
1.42


.la
.41
1.4
1.40
1.64'
1.4


2.90
2.57
2.81
5.60



to
10.6
10. 8
12.98
12.96
12.97
15.52
11 3
It
18.01
20.65
20.63
20.6
25. :?
25.19
25.70
25.0


1.1a
1.00
1.11
2.12

5.10

6.o6





7 0
6.06
I.06
.091
.029
6.00


8.o0



9.09
10.18
10.0b
i 9:09


.5iE
.36

.12









ti:


24.0
2.30
ll l

.29:


1.40
1.2
1. 2

1. 6
1.2
l.62




1.62
1.65
I. L

1.5
'-62


102

10, I
5. 2










10.07
11.65
11.60
8U.B
12. 9
10.07
10. 07
11.65
11.R60
12.92


1.16
1.97
2.11
2.08
8.10
9.01.
.08
I.ll
.oh
5.09
5.05


.:a
6.2k
6.11



B.2:

9.0,


15.61
15.61


11.
I15.61


15.71





l:a
15.6~





1:25
1:5
1). e


1.00
.99

.98




1.0
.99
1.01
1.00
1.00
1. 00
.99
.99
1 02
1.01
1.0
1.00


n .
7.9





I2
12.9






15.1
15.0
1.i



1.05
12.5


.I1
62.1


o8:1
58.1









59.9


38.7


liT,
0.5



50.2
29.T



29.7
Ej:1
50.0




29.0
:2.
ag:
29.1
29



281

2. .
6.



.0


65.6

k.9
1.
.2
I .6




5.0



6.1


_____ ____ j ____ A A- A A ___ ___


nTIOWAL ADWI6SOW
Couunnm rpo MIug&AgWI


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NACA RB No. L:-10o


mAEBLE 2

CO.r'TRESSIVE PFOPERTIES O AT-.EFI AL


I.TI1L'./L ADVISORY
C9"'.'TTTTE FOR AFFOIIAUTITCS






































































































































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S NACA RB No. L4H10
Fig. 1





.102 2
T- r

5 2.__
|. 1 [ 50---|









2.50

SSection 2
102








i.: 250 550
ill ,.- t -so- L









Section 3

Z- section Channel section
NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS
Figure 1.- Column cross sections.




r.






NACA RB No. L4H10


60 --
Z-section Channel secti


50 Cros l CrossI
O qra in --7 qrin!



e--"
i th /ith
40 rain grain

5o

30



20



10



0 0-*

NATIONAL ADVISORY
Strain COMMITE FOR AERONAUTICS

Figure 2.-Compressive stress-strain curves.


Fig. 2









NACA RB No. L4HO1 Fig. 3






















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NATIONAL ADVISORY
COMMITTEE FOR AERONAUnCS


Figure 5.- Number of half-waves in buckle pattern
produced by various proportions of Z- and
channel- section columns of 24 5-T aluminum
alloy.


S3 I- 3(3) 4 (1)
(6) 2(6) 3(6) 3(6 (3) 4(6) 5(2)

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Recommended curve
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Number of Number
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g Location of test .
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UNIERSITY OFFLORIDA

3 1262 08 06 51



UNIVERSITY OF FLORIDA
DOCUMENTS DEPARTMENT
120 MARSTON SCIENCE LIBRARY
P.O. BOX 117011
GAINESVILLE, FL 32611-7011 USA





















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