Column and plate compressive strengths of aircraft structural materials 24S-T aluminum-alloy sheet

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Material Information

Title:
Column and plate compressive strengths of aircraft structural materials 24S-T aluminum-alloy sheet
Series Title:
NACA WR
Alternate Title:
NACA wartime reports
Physical Description:
21, 21 p. : ill. ; 28 cm.
Language:
English
Creator:
Lundquist, Eugene E
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 -- Testing   ( lcsh )
Aerodynamics -- Research   ( lcsh )
Genre:
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
Summary: Column and plate compressive strengths of 24S-T aluminum-alloy sheet were determined both within and beyond the elastic range from tests of thin-strip columns and from local-instability tests of formed Z- and channel-section columns. These tests are the first of a series in an extensive research investigation to provide data on the structural strength of various aircraft materials. The results, which are presented in the form of curves and charts that may be used in the design and analysis of aircraft structures, supersede preliminary results published previously.
Bibliography:
Includes bibliographic references (p. 10).
Statement of Responsibility:
by Eugene E. Lundquist ... et al..
General Note:
"Originally issued June 1945 as Advance Restricted Report L5F01."
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."

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003804757
oclc - 123897073
System ID:
AA00009392:00001


This item is only available as the following downloads:


Full Text

ARR No. L5F01


I

NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS





WAIRITIME REPORT
ORIGINALLY ISSUED
June 1945 as
Advance Restricted Report L5FOl

COLUMN AND PLATE COMPRESSIVE STRENGTHS
OF AIRCRAFT STRUCTURAL MATERIALS
24S-T ALUMINUM-ALLOY SHEET
By Eugene E. Lundquist, Evan H. Schuette,
George J. Heimerl, and J. Albert Roy

Langley Memorial Aeronautical Laboratory
Langley Field, Va.


,,U.' t.F I' -, i -': r- .,L*r -* i
P 1,. i0 11
C.:,i, LJ .LE, FL 32611-7011 USA



NACA'


WASHINGTON

NACA WARTIME REPORTS are reprints of papers originally Issued to provide rapid distribution of
P advance research results to an authorized group requiring them for the war effort. They were pre-
viously held under a security status but are now unclassified. Some of these reports were not tech-
nically edited. All have been reproduced without change in order to expedite general distribution.


L 190



































Digitized by the Internet Archive
in 2011 with funding from
University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation


http://www.archive.org/details/columnplatecompr001ang









NACA ARR No. L5F01


NATIONAL ADVISORY CC"'ITT:SE FOR AERONAUTICS


ADVANCE RESTRICTED ';PORT


COLUMN AND PLATE CC'Y3RESIVE STRENGTHS
OF AIRCRAFT STRUCTURa:L 1 TRIALSS

24S-T ALi-'. lii;'-ALLOY 3SEET

By Eugene E. Lundquist, Evan H. Schuette
George J. Heimerl, and J. Albert Roy





Column and plate compressive strengths of 24S-T alu-
minum-alloy sheet were determined both within and beyond
the elastic range from tests of thin-strip columns and
from locel-instability tests of formed Z- end channel-
section columns. These tests are the first of a series
in an extensive research investigation to provide data
on the structural strength of various aircraft materials.
The results, which are presented in the form of curves
and charts that may be used in the design and analysis
of aircraft structures, supersede preliminary results
published previously.


INTRODCT ION


Column and plate members in an aircraft structure are
the basic elements that fail by instability. If efficient
structures are to be designed, the strength of these ele-
ments must be known for the various aircraft materials.
An extensive research program has therefore been under-
taken at the Langley Memorial Aeronautical Laboratory to
.establish the column and plate compressive strengths for
a number of the alloys available for use in aircraft
structures. Reliable and rapid procedures for testing
such materials have already been developed and are
described in references 1 and 2.

The first material tested during the present investi-
gation was 24S-T aluminum-alloy sheat, The results for
this material, given herein, sit rs:de those contained
in a preliminary report (reference 2).









N1ACA ART No. LSPFO


SYMBOLS


L length of column

p radius of ":,.tion

c fixity coefficient used in Eulir column formula

_-L effective slenderness ratio of thin-strio column
PIe
b width of p~lte

bV. width of flange of Z- or channel section (see fig. 1)

b width of web of Z- or channel section (see fip.. 1)

r inside radius of bend of Z- or channel section
(see fig. 1)

t thickness of piste

k nondimensional coefficient used in plate-buckling
formula

k-v coefficient k used with bW and t in plate-
buckling formula (see fig. 2 and reference 3)

Ec modulus of elasticity in compression, taken as
10,700 ksi for 2LS-T aluminum alloy

T nondimensional coefficient for columns (The value of
T is so determined that when the effective
modulus TEc is substituted for E in the
equation for elastic buckling of columns, the
computed critical stress *.'r e with the
exer'imentnlly observed value. The coefficient T
is equal to unity within the elastic range and
decreases with increasing stress beyond the elastic
rsn e.)

rI nondin;ensionr~ coefficient for plates corresponding
to T for columns

P oisson': r,'tio, tfken as ).3 for 2~S-T aluminum alloy









NACA A'R No. L5F01


Ocr critical compressive stress

anax average compressive stress at mi:ximum load

a compressive yield stress


:"TEODS OF TESTING AND A ALYSIS


All tests were made in hydraulic testing machines
accurate to within three-fourths of 1 percent. The ends
of the stress-strain specimens and the columns were ground
flat end square.

Stress-strain curves.- The comniressive stress-strain
data, w:h-.i' "imint- ; r:. material for correlation with
its column and plste compressive strengths, were obt'-.rei
from tests of single-thickness specimens in a compression
fixture of the :rt-t'omery-Te .,lin tyne shon in fiIur- 3.
This fixture was used only for fl-t c~p-ression specimens,
which represented the mraterisl before forming. Infor-
mItion on the technique used in miskin; these tests is
presented in reference 4.. For the bent material in the
corners of the formed Z- and channel sections, compression
snecinens were cut from the corner portion and tested in
the special fixture shown in fi-'.. -.

Colwurn str-noth.- The column strength end the asso-
ciated e-lective colinm modulus were obtained by testing
thin-strip columns of the material with the ends clamped
in fixtures of the type shown n figure 5. The use of
end fixtures of this t;:e is discussed in detail in
reference 1. The f'.:tures used hvea been improved, and the
method of analysis lhs been modified since the publication
of reference 1. The method now used results in a column
curve representative of nearly perfect column specimens.
In addition, the method now takes into account the fact
that columns of the dimensions tested are actually plates
with two free edges.

PIl~- corr. res l e .r-en ,.- The plate compressive
strentr. of th' -r er':- l 'TT;: obtained from c:.:-:ression
tests on Z- and channel-section columns so proportioned
as to develop local instability, that is, instability of
the plate elements of which they are comprised. (See
fig. 6.) Inasmuch as the flanves and webs of such columns
are in realii-r plates with various kinds of ed .- support,











iKCA ARR


. L5J-1


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I;ACA ARK No. LCF01 5


and 49 ksi in the cross-grain direction. The modulus of
elasticity in compression was taken as 10,700 ksi, the
accepted value for 24S-T aluminum alloy.

When the flat sheet material is bent to an inside
radius r of 3t to form a Z or channel, the cold work
done on the materiel evidently raises the compressive
yield stress for the curved corner portion above that for
the flat web or flenge, about d1 percent for the with-
grain and 10 percent for the cross-grain direction. (se
fig. 10.) Because the curved corner specimens included
along their edges some flat material (about 1|0 percent
of the total area) for which the yield stress is lower
than that for the curved portion, the actual increase in
the compressive yield stress for the corner portion may
be soewhet greater than the increase indicated in fig-
ure 10. The important result to note is that the com-
pressive properties of a formed section may not be uniform
over the cross section.


Column Strength

The results of the tests of the thin-strip columns
are given by the column curves of figure 11 for the two
directions of grain.

At stresses beyond the elastic range, the experi-
mental values of acr are lower than those computed by
the Eul-.r column formula (see elastic-buckling curve,
fig. 11), because of the reduction in the effective
modulus of elasticity. The effective modulus to be
substituted for Ec in the Euler column formula to bring
calculated and experimental values of cr into agreement
is given as TEc, where T is a coefficient that is equal
to unity in the elastic range and decreases with increasing
stress beyond the elastic rcn:.1 In structural calculations
in which it is impossible to use directly values obtained
from the column curve (fig. 11), the value of T for a
given stress must be known. The variation of T with
stress for columns is therefore shown in figure 12 for
both directions of grain.










0o ACA AR PNo. L5F01


lfotne Cc.:7r-essive 3tor nth

Ihe ies~Its o' thla local-i5 st7-ility tects of the
for" ed L- rnd chr io-,~ -se:tioan ecoli;s, :ed to determine
t .1- '"la cm n: e s Fsltrr t e ;-iV :. in t .b1 le 2
; 1 l i.,tm :t r .tlroa r bi)s fo cion.ro.-c se~ I l. t s
cbtini e froI ; thes test" er3 h.'. : on tlio cuvtS Es a
d3.-' jn chert3s Pr,-.sted in t. fll .int trarhs.h.

Pl he-bjck] int curve.- The l t ',t-buiC :]in, cuove,
ur3I 13 fcr .l t lo i-ded in the wi -oin dix' eclion.
T ? i a f b ire Is is s ~g 'd bs, trs n losing the
plate-btici, 9- auti :n


CF (1)
12(1-,..)2"

to t l:3 0oronfi

Tr,
Scr -- __ (2)





wi-2e' t e subscrpt :l a dded to ~se the terr.s b
psd k o- the eq-t':ici corner s-cnl to the entries in
tablf s 2 :ri 5. Th s:.'i.riTy btvtoan the form0 of
creti, (C,) no fcht c 'll ninr fc'r oC the Eular e-~lr::.r,



r r>
tr (r)






?,.r"!lvcer1 tt-n Ihoj3 p'iv>an b o:r io (2) fo eEla:tc..

cf t-e rf ti t.3 f:te io.l of ec fLrt i l'.
e LT2
1f- -









--C
ccl 1iAt elV,.: O ,:: :5. tis V. rI '1 :tniv.eC ri i' tor, cas..tit
l' :' e ;: : ec o:i r a cop aes -:. .0 7~ to :.0c fer








ITA3A ARR 'o. L5'K1l


stress is given, together with the variation of T, in
fi--. 12. The crossing of the T- and r,-curves shown
in fij-ur? 12 occurs because the formed columns r::--arently
had an :r-:reciable derr-ee of imperfection, which resulted
in the deviation of the --curve from unity at a lower
stress than that at which th3 T-curve, representative
of nearly perfect columns, deviates .~.:;. unity.

Relationship of or to Ocr/T1 for plates.- In
proble,- cotrcerner ...ith Lhe s n th :.f ;i ., it is
sometimes desirable to insert the value of rEc for Ec
in the plate-buckling formula, equation (1), and to write
the equation in the transposed form

~-- 2
cr 2't

r, lell-,-;b-


In this form the value of acr/r.is given b, the modulus
of elasticity, Poisson's ratio, the ceometric dimensions
of the elate, and the coefficient k. The value of opc
can then be obtained '-' use of the curve of Ocr against
Ocr/r given in figure 114. This curve r, %' be obtained by
plotting: the data directly or by plotting from the faired
curves of figure 13.

As in the case of equation (1), the subscripts W
may be added to k and b of equation (4), and CGr/T
may be determined for a Z- or channel-section by the use
of the formula and curve of figure 2.

'.`,;i: :uir, compressive strength of plate elements.- In
the case -; .-.l t. i l .: 1 : n l :.si-itu. i nl ':.T .:,:r ss ion,
the supported, or restrained and supported, side ed-.:.s
remain essentially straight after buckling and ore capable
of carrying additional load. As a consequence, there is
a im i:r.u: stri-:-.th for the plate that is greater than
the bucklin: stren-th.

Theoretical studies that appear in the literature
concerning the ultimate strength of plates and the asso-
ciated effective width of the plates after buckling
indicate that the average stress at maximum load is
related to the critical stress. It is therefore reason-
able to assume that the average stress at maximum load













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'E. a i ......'p t 1 -, ./ .


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T1.?" r.;

arid t. ;

ec '


7ACA ARR ?o:. L5o01


e :ents thet rlk.:'e u,
: rel te to th'
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ur"es 15 -r ':i 1 3- '.1ito cn m" v : of b. /t is not,

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>of T: le c cr .riven
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c." ;-- '*: ? 1n c l .:in l *) oL0 ; E C : <1 0, :.- ;: n l .








!rACA A:R No. L5F01


for crrm- arisen with curves taken from figures i1 end 16
for the with-grain columns. COnly at the higher stresses,
where the stress-strain curve foil the cross-..rain direction
differs noticeably from the stress-strain curve for the
with-grain direction, are the values of 0r and ax
or max
_-reater for the cross-grain columns than for the with-grain
columns. The average increase in the high-stress region
was abcut 4 percent for cr and about 2 percent for omax
whereas the cross-grain compressive yield stress was approx-
imately 11 percent greater than the with-_ --i:, cr!,.ressive
yield stress.

Charts for local instability of Z- and channel-section
column7. T. .T. te c V.?,] -- :1 E.tr-^.g'tr. .:" >.. :".-,:-.' i 1
was evaluated from tests of Z- and channel-section columns.
The results of these tests, which provided this information
regarding plates, may also be applied directly to formed
Z- and channel-section columns that fail by local insta-
bility. These results can be conveniently summarized in
the form of charts that give directly, in terms of the
dimension ratios bF/by and -../t, the critical stress
and the aver:c-e stress at maximum load. Such charts,
based on the theoretical curve of figure 2 and the experi-
mental data, are given in fi-'.urs 19 to 21.


COT 7LUDJ IN U REA' '


The important conclusions of this report are embodied
in the test data of column and plate compressive strengths,
which are presented in the form of curves and charts that
may be used in the design -nd Pnalysis of aircraft
structures of 24S-T aluminum-alloy sheet.


Langley memorial Aeroniuticcl Laboratory
[' ttongl Advisory Cominitt-a ior Aeronautics
Langley Field, Vs.









'A CA Ar ITo. L5,T 01
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S-l. 3r lrtinl Stress for
. nn .3 th I-, Z-, Channl,
ti '. 'ACA A.R i;o. :iCOLi,


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t i f ..' .I2 :, 70 tre n rv s. IACA


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NACA ARR No. LDF'?1 11

TABLE 1.- C-F"'F'ESSI"E PROPERTIES OF 21S-T ALUMTIfUM-ALLOY SHEET

[E = 10,700 ksi]


Columns to which stress-strt.n Compressive yield
curves apply Stress- stress, cy
---F-- strain -
Direction curve With Cross
Type of Designation (fig.9) grain grain
loading tables 2 and (ksi) (ksi)
l- ^. ----- -- --.--- ll'-l.-ll -" -- --. -- -- -- lll. 1- ... lldll.illl- ..-.. .-- i.*-lr -*- 11- l lllnl g~ l.illlll~l l.l -- -- ----- -- -


With grain
and cross
grain

With grain




7Vith grain



Cross
grain

V.ith grain


Channel With grain


With grain


Cross
grain


Thin
strip


Z




Z



ZChanne


Channel


42.9



414.o




146.3



43.4


43.1


la to 6a, 6c, 7a, lOa,
10b, lla to 19a, 26b,
27a, 27c, 28a, 29a,
31b to 32c

6b, 7b to 9, 10c, 19b
to 26a, 26c, 27b, 28b,
28c, 29b to 31a

la to h4c


1 to 6a, 7a, 8a, 9a,
10a, lla, 12a, 13a,
14a, 15a, 16a, 17a,
18a, 19a, 20a, 21a,
21b, 22a, 23a, 24a,
25a, 27a to 28a, 2-',
50a to 31a, 32a, 33a,
3ha, 35a, 36a

6b, 6c, 7b, 7c, 8b,
8c, 9b, 9c, 10b, lOc,
llb, llc, 12b, 12c,
13b, 13c, 14b, 14c,
15b, 15, 16b, 16c,
17b, 17c, 18b, 18c,
19b, 19c, 20b, 22b,
23b, 23c, 24b, 24c,
25b, 25c, 26a, 26b,
28b, 29b, 29c, 31b,
32b

31c, 32o, 33b, 33c,
34b, 35b, 56b, 360

la to 4o


47.9


16.8




51.3



48.5


48.9








19.7











17.9


18.5


43.9


13.41


Channel


Channel








NACA ARR No'. L5FO1 12



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NACA ARR No. L5F01 13



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COMMITTEE FOR AERONAUTICS


Figure I. -"


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of Z-and channel-


section columns.


Fig. 1






NACA ARR No. L5F01


Buckling of web
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NATION. L ADVISORY
0 IMMIIEE OR AERONAiIIICS
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cr kwlrEctt
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Fig. 2







NACA ARR No. L5F01


a..


(a) Unassembled.


(b) Assembled with Tuckerman optical strain gage in
place on specimen.

Figure 3.- Fixture for obtaining compressive stress-strain
curves of flat sheet.


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Fig. 5






NACA ARR No. L5FO]


,I I





NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS

Figure 6.- Typical cross -sectional distortion
of columns that develop local instability.


Fig. 6







NACA ARR No. L5F01


Figure 7.- Z-section column under test for study of
instability of plates.


Fig. 7







NACA ARR No. L5F01


I I I
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Figure 8.- Illustrative stress -distortion curve for
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section columns loaded in compression
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Figure 10.- Effect of forming on compressive
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Fig. 10








NACA ARR No. L5F01 Fig. 11








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.4



.2.


NATIONAL AD FSORY
SC COMMITTEE FOR A RONAUTICS
0 10 ZO 30 40 50 68

Stress ksi



Figure 12.- Variation of T and T1 with stress for
2.45-T aluminum- alloy sheet. (T1 obtained from
tests of formed columns.)


Fig. 12








NACA ARR No. L5F01


c

C

C__
0

-c
o -
4 0
-- -

o oI

o
c6







IJ



\ --'^**

-'a^ ^------


6 o 6 o 6
a c


Fig. 13


0


o

0




o






















o
a


















oo,
0
0O







o




o


.C








21
0-5




I)




oa

EE






Cu


-4




u.
g 0



0.
L. 4--






oq
0.S







1-c


(






Fig. 14


NACA ARR No. L5FO1


Scr ksi


20










c / ,0 40n 6A0 60 10 12
/ COMMITTEE OR N AERONAUTICS

Figure 14.- Variation of aoc with Oacr/T for plates of 24S-T
aluminum- alloy sheet loaded in fhe with-grain direction,
obtained from tests of formed columns; ay= 44 ksi .








NACA ARR No. L5F01
4


Fig. 15a,b


C
E
o
-5

0





.C
E



(-
I




LOn















LC
.-











II"
C-








0 0
in








"*i

LL-










NACA ARR No. L5FO] Fig. 16a,b


C
E




0




E







LO



+4-





C4
U_=
E






















-c-







-0-
I-

0-
L.















00
>"-
>o
S-
r









L.
cr>

















-J

LL:


'I.
a -

'6
L
I-
0








NACA ARR No. L5F01


- I I I=


U4-,




U,
0

u


^^--I-
c_

___ _M _


i I


Fig. 17a,b


o
0 T!
T------
0*

E
0,-- -.

M- 0

- ___







'C
-^- E







e


*
--4 4-
i : --- --- --- ---


-c
L

-0
o11



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0 C5
D .0



Ct
o-4




:c






Q 0




o a









U-



CU
0r4
Ic-
o L

t-a

L L















0~c


...,, A








;ACA ARR No. L5F01


Fig. 18a,b


U,
._ u
YL





-5
u


.4-m

- C
-o r

c




5 E

c

Lu a
I 0
C 'n





Eb
- C

CL

SCO
-t
cs
EU




0 C0

2C
> .9





0C0
QLo






u C
o ca




co
C -0



Uc



C
Oo's
QGX t3
L--C
0.St







NACA ARR No. L5F01


50

26


40








20

o44
20 -








0
0 .2 4 .6 .8 .0

b NATIONAL ADVISORY
COMMITTEE FOR AERONAUTICS

Figure 19. Design chart for ocr for formed 245-T
aluminum-alloy Z-and channel -section columns that
develop local instability loaded in the with-grain
direction; o'c = 44 ksi.


Fig. 19







NACA ARR No. L5FO1


60




50




40




30

cmax ,
ksi
20




(0




0


bw
bw


Figure 20.- Design chart for max for formed 24S-T
aluminum- alloy Z- section columns that develop local
instability loaded in the with-grain direction; cry.44ksi.


bw
l 18 16 15






26,


















NATIONAL )VISORY
COMMITTEE FOR AERONAUTICS


Fig. 20







NACA ARR No. L5FO1


40




30


'max ,
ksi
20




10


Figure ZI. Design chart for ,,mox for formed 24S-T
aluminum-alloy channel-section columns that develop
local instability loaded in the with-grain direction ;
ocy = 44 ksi .


D14
























NATIONAL Al VISORY
COMMITTEEE FOR AERONAUTICS


Fig. 21







UNIVERSITY OF FLORIDA


3 1262 08106 493 2


I


tU' .'ERSITY OF FLOR,-



-F. 3- 117011
v -. FL 32611-7011 *, ,


I.

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