Column, crushing, and torsional strength of duralumin tubing: Part 1. Column strength, Part 2. Crushing strength, Part 3. Torsional strength (Material Section report)

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File D 52.313/20 McCOOK FIELD REPORT, SERIAL Nos. 2302-3-4
AIR SERVICE INFORMATION CIRCULAR
<AVIATION)
PUBLISHED BY THE CHIEF OF AIR SERVICE, WASHINGTON, D. C.
Vol. V July 1, 1924
COLUMN, CRUSHING, AND TO.~SI
STRENGTH OF DURALUMIN 1f uB
PART I: COLUMN STRENGTH
CRUSHING STRENGTH
TORSIONAL STRENGTH
PART II
PART III
~·
(MATERIAL SECTION REPORT )
Prepared by S. W. Thompson
Engineering Division, Air Service
McCook Field, Dayton, Ohio
March 24, 1924
WASHINGTON
GOVERNMENT PRINTING OFFIGE
1924
••
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CERTIFICATE: By direction of the Secretary of War the matter contained herein is published as adminis­trative
information and is required for the proper transaction of the public business.
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COLUMN, CRUSHING, AND TORSIONAL
DURALUMIN TUBING
STRENGTH OF
PART I- COLUMN STRENGTH
ABSTRACT
A series of tests were made on cold-drawn tubing
to determine the maximum loads (P/A) for values of
the ratio of length to radius of gyration (L/r) varying
from 10 to 541. The ends of the column were mounted
on parallel knife edges. The physical properties of
the tubing were: MATERIAL
Tensile strength, pounds per square The following sizes of duralumin tubing were used in
inch ___ ___________ _________ . ___ ___ 56, 000-64, 000 these tests:
Elongation in 2 inches, per cent__ ____ 10-28
The empirical loads were compared with the cal- Diameter_ __ ___ l2. 2512. 2512. 0011. 7511. 7511. 75Ji. 2511. 2511. 2511. oolio. 7510. 75 Thickness ___ ___ .125. 093. 0625 . 093 . 0625. 049
1
. 093. 065 . 035 .. 065 . 049. 035
culated loads as determined by several formulas, and
graphs are given showing the range of experimental
error and its relation to the calculated results. These tubes were manufactured by the Aluminum
The best combination of formulas from the stand- Co. of America.
point of accuracy of results and ease of application is
the use of Euler's formula for values of L/r of 90 and
above, and the use of formula P/A=48,000-400 L/r
for values of less than 90. This combination will not
give loads in excess of the yield point except for L/r
ratios of less than 40.
A comparison of the empirical results with the cal­culated
data is summarized as follows:
(a) Euler's formula can be relied upon for values of
L/r of 80 and above.
(b) J. B. Johnson's parabolic formula checks with
test data for values of L/r of 60 to 90, a very short
range. Below 60 the results are quite conservative.
It has the advantage, however, of not giving results
above the yield point of the material.
(c) T. H. Johnson's straight-line formula, with the
constants shown in the formula P / A=48,000-400
L/r, gives a good approximation to test results with
values of L/r from 0 to 90.
(d) The Gordon-Rankine formula is intended to be
used throughout the entire range of L/r, but gives too
conservative values between L/r of 40 and 120, a
range that many columns come under. ·
(e) The Natalis formula, based on the yield point
in compression and the modulus of elasticity, gives the
best results as a ~ingle formula to be used for all values
of L/r. For values of L/r of 90 and above the results
check accurately with t est data. Below 90 the results
are conservative and are limited to the yield point in
compression.
(j) The Natalis fo~mula, with the ultimate strength
in compression substituted for the yield point of the
METHOD OF PROCEDURE
The dimensions of the tubes were carefully checked.
The diameter represents an average of several meas­urements,
and the wall thickness an average of four
points taken at each end of the tube.
Each tube was squared off on the ends to leave the
longest length possible for the first column test. After
this test a tension, a torsion, and several· compression
specimens were cut from each tube and the remainder
cut into column specimens of different lengths.
The tension specimens were 18 inches long. The
test was made on the full section, using steel plugs in
the ends. These plugs were well rounded on the ends
and extended inside the tube to a point from one-half to
1 inch beyond the point reached by the grips on the
outside.
The specimens were center-punched every inch as a
basis for measuring elongation. The tests were run
in an Olsen 100,000-pound Universal testing machine.
A Ewing extensometer was used and a stress-strain
curve plotted for each specimen. The proportional
limit was taken at the point at which the stress ceased
to be proportional to the strain, and the curve started
to leave the straight line section. The modulus of
elasticity was calculated as the slope of the line.
The column tests were made in an Olsen 20,000-
pound Universal testing machine, except a few which
required the capacity of the 100,000-pound machine.
Knife-edge bearings shown in Figure 14 were used in all
tests and increased the column length by 1.480 inches .
Special centering blocks were made to insure the accu--
(1)
rate cent~ring of the tube ends on the face plates of
the knife edges. Especial ca re was used to make the
knife edges parallel and directly in line vertically. The
upper knife-edge bearing was bolted to the center of the
under surface of the mova ble head . The lower knife­edge
bearing was laid ori the t esting-machine table and
the mo" able head lowered until the knife-edge encl
!at es were ne.arly in contact. The lower knife edge
was then shifted until it was directly under the upper
knife edge and pa rallel to it. All specimens were care­fully
inspecteu for initial curvature eccentricity and
other defect s. Weak points were placed in the plane
of the knife edge~ so as to have the minimum effect on
the strength of.the column.
i\1eans were taken to measure the deflection of the
column as the load was applied. A small hole was
drilled near each end of the tube, and a st eel wire was
placed in the hole and allowed to project some 2Y2
inches. A fine wire was stretched between these points
and held straight by the t ension of a rubber band. A
steel scale reading to 0.01 inch and a r eading glass
"\\ere used to measure the di stance between the tube
and the wire. At intervals, as the load was applied,
lateral defl ection readings were taken which became
greater or less according to. whether the tube bent away
from or toward the wire. After the maximum load
had been reached, all load was removed and another
reading taken. The difference between t h.is last read­ing
and t he original reading indica ted the amount of
permanent set.
2
The compression specimens were cut 3 inches long
and were t ested in a special jig which consisted of a
steel plunger held in a cast-iron frame. This plunger
was free to move vertica!Jy , but was held rigidly against
any side play due to shift ing of t he t est ing machine
h ead. The compression specimens were t ested be­tween
flat plates, the knife edges not being used. A
Berry strain gage reading to one ten-th ousandth of an
inch over a gage length of 2 inch es was used in these
test s. Suffi cient readings were t aken to plot an a c­curate
curve for each specimen. The proportiona l
limit and yield point were obt a ined from t hese curves.
The yield point was taken as that point at which the
slope of the stress-strain curve was 50 per cent greater
than it was below t he proportional limit .
In checking each formula against actual r esults, the
theoretical values of P /A were calcula t ed for each L/r
"ratio. The modulus of elasticity, the ultimate com­pressive
strength, and the yield point in compression
were found from tests on each tube. These constants
for the material, which had been det ermined experi­mentally
for each tube, were substituted in the formu­las.
The theoretical value of P /A was then found for
each L/r rat io.
RESULTS
The results are recorded in T a bles 1 and 2 and are
a naly zed graphically in Figures 1 to 13.
DISCUSSION OF RESULTS
The symbols used in this discussion are as follows:
P = Loacl in pounds.
A= Cross-sectional a rea in square inches.
L = Length of column in inches.
r = Least radius of gyration.
E = Modulus of elasticity.
Sc= Ultimate compressive strength in pounds
per square inch.
Sy= Yield point in compression in pounds
per square inch.
The duralumin tubes were first tested as columns,
using their full length as received from the mill. Only
enough material was cut from each encl to squa re it off
properly. This gave columns with lengths of 100 to
130 inches and with L/r ratios of 160 up to as high as
541. The P /A stresses in t hese columns did not
reach 4,000 pounds per square inch in any case, so it is
unlikely that these first t ests injured the tubes in any
way. Not only was the loading light, but there was
not the slightest indication of any permanent set in the
t ubes after the t est. The t ests run with shorter L/r
ratios were on tubes cut out of these long columns, but
it is believed t hat no error was introdu ced on t hat
account.
Readings were t aken of t he permanent set of the
columns after t est. There was no measurable set in
t hose columns tha t were t ested with L/r rat ios of 70
or above. This means t ha t column wit h L/r ratios
of over 70 may be loaded in tests to their limit without
rniury. For columns with a n L/r ratio of less ·than 70
it is likely that the stress a t some local point will
exceed the yield point of the ma terial. The maximum
P /A corresponding to a column with L/r = 70 is 20,000
pounds per square inch. The yield p oint for the
columns t ested averaged 31,730 p ounds per squa re
inch. The assurance of not injuring long columns
a pplies only to t ests on columns made in a t esting
machine where the t est is stopped immediately after
passing the inaximum load. Any column in service
would be destroyed if stressed to the maximum load,
because it is not likely that t he load would be removed
immediately and the deflection would therefore con­tinue
indefinitely.
The theoretical curves showing the r elation of P /A
to L/r were drawn, and the values obtained from actua l
test were plotted on top of t hese curves. Figures 1,
2 4 6 8 10 and 12 show t hese results and make it
v~r; e~s; to 'see· t he accuracy of each formula at any
value of L/r.
J
In addition to this, the theoretical values were
clivi.ded by the corresponding test values. This ratio
also is a measure of the a ccuracy of the formulas.
A ratio of unity gives a perfect check between formulas
• and a ctual test results. These ratios are plotted on
Figures 3, 5, 7, 9, 11, and 13 and show very clearly the
range of L/r through which a given formula can be
relied upon.
All points found experimenta lly or t h eoretically were
plotted, although some of them were wild. Those
lying away from the general average were not con­sidered
in drawing the curves.
Figure 1 shows a graph representing Euler's formula
(P/A= (~/~2) for values of L/r of 90 and above, and
a graph representing T . H . Johnson's straight-line
formula, (P/A=48,000-400 L/ r) , for values of L/r less
than 90. The plotted points represent t est result s.
From t he standpoint of accuracy of results and ease of
applicat ion, t he combina t ion of these two formulas seems
t o be t he most satisfactory. For values of L/r of 90
and above, use Euler 's fo rmula . For values of L/r of
less than 90, use the straight-line formula.
The straight -line formula is simpler t han Johnson 's
parabolic formula, and it ch ecks with test data through
a grea t er range of L/ r . The combina tion with Euler's
formula will ch eck quite a ccurat ely with test data for
any value of L/r; however, for L/ r ra tios of less than
40, the columns held a greater load per squa re in ch
than the yield point in compression of the ma terial.
Therefore, it should be noted in using the straight-line
formula that for L/r ratios of less than 40 this formula
will give results in excess of the y ield point of the
material. The average yield point in compression
was 31,730 pounds per square inch.
It will be observed tha t the points plotted from t est
data lie quite accurately in line for the h igher values
of L/r. For the lower values of L/r the points are
more scattered and form a band rather tha n a line.
This is what Salmon 1 calls the "Area of experimental
result s." The width of t his band is part ly due to the
fact that ver y small eccentricities of loading and small
errors in squaring the ends of the t ubes have a very
great effect upon t he strength of t h e shorter lengths
of columns. Small imperfect ions in the tube itself have
a similar effect. These causes may be classed as
exper imental errors. Such sources of inaccuracy would
probably exist to a greater ext ent wh en the column is
used as a member of a st ru cture.
The ent ire width of this band, however, is not trace­a
ble to experimental inaccuracies. A part of t his width
is directly due to actual differences in the individual
t ubes. The high points on this band are the results
of "tests on t ubes Nos. 4 and 19. The same centering
blocks used on t ube No. 4 were used on tube No. 2,
but the results on No. 2 were uniformly along the
center of this band . T i.1be No. 22 gives r esults along
t he lower edge of t his. band. The following table
indicates the cause of t his :
1 "Columns," by E . H. Salmon, p . 201. P ubli shed by H enry Frowd
and H odder & Stough ton, London .
3
I Yield in Ultimate
compres- crusb_ing
Tube N o. lVIodulus of sion, strength, elasticity pounds pounds
19 _ - - - --- - - - - -- - - - -- - -- - - - - - -- - - - - -- - - 11, 239, 000
4 _ - - - - - - -- - - - - - - - -- - -- -- - - - - - - - - - - - - -- 10, 237, 400
2_ . - - - - - ----- - - - - -- - -- ----------- - - - -- 10, 997, 900
22 _____ __ ____ _______ __ ________ _____ __ _ 11, 117, 100
per square per square
inch in ch
36, 330
34, 910
32, 200
24, 930
61, 090
56, 840
57, 840
58, 720
Apparently the difference in the yield point in com­pression
is t he cause of most of t he width in this " band
of experimental result s." The height of the points
does not vary with eit her the modulus or with t he
ul t imate compressive strength, but with the yield
point in compression . The value of P /A does not vary
solely with L/r, but throughout the lower range of
lengths, P /A also varies with t he y ield point in com­pression
and possibly with other factors. The r esult is
certainly to be that in plotting P /A against L/r the
points will distribute themselves into a band according
to t he variation of t he factors which are not included.
Figure 2 shows a section of Euler' s curve drawn on
t he same scale with the t est data points. For valu es
of L/r of 80 and above, Euler's curve checks very well.
Below 80 the curve runs a bove the t est data points.
Figure 3 also indica t es that Euler's curve is quite
accurate for the high er values of L/r and may be used
clown to L/r of 80.
Figure 4 is the graph of a straight line drawn t hrough
test data points. The line was drawn so as to r epre­sent
the best a verage of r esults. It can be seen that
t he equation of this line is P/A=48,000- 400 L/ r .
This formula gives t he best approximation to t est
results (for t he sh orter lengths of columns) of any ·of
the formulas a nalyzed. The average compressive
strength of 3-inch samples of t hese tubes was 55,580
pounds per square inch. The average yield point was
31,730 pounds per squa re inch. The const ant chosen
(48,000 pounds p er square inch) is much more sat is­factory
than either of these. This constant averages
0.86 t imes the crushing strength or 1.5 times the yield
point; but any substit ul ion of eit her of these t erms
for their average const a nt of 48,000 gives very poor
results. The a verage position of points calculated
would be the same, and t he same curve would result ,
but the substitution of terms involving t he physical
charact eristics of individual t ubes throws the points
calculat ed into a broader b and.
Figure 5 shows t he proba ble error in using t he
straight-line formula, and indicat es its use for values
of L/r of 90 and below.
Figure 6 is a graph of J . B. J ohnson's pa rabolic
formula-s
2 P /A= Sy - _ y_ (Lir )2 . 4 ,,-2 E '
drawn to the same scale wit h t est data p oints. The
formula does not check with t est r esults on duralumin
t ubes for values of L/r of more than 90 or less t han 60.
Not only is t he range of accuracy limited, but the
curvature is in the opposite direction to t he general
4
curve of test data. It has the advantage of never · rate for L/r ratios of 90 and above and approaches
giving results greater than the yield point of the ma- Euler's curve at infinity. Below 90 the results are
terial.
Figure 7 shows the probable error in using this
formula for various L/r ratios.
Figure 8 is a graph of the Gordon-Rankine formula
drawn on the same scale with test data points. The
formula was used with Ritter's constant and reads-
P/A
Sc
1+ 7r~~(L/r)2
The fraction (7r~~) is known as Ritter's constant.
This curve gives values higher than test data on very
short lengths. Throughout the range of L/r ratios
from 40 to 120 the formula gives results that are too
conservative. For higher L/r ratios the curve coin­cides
with test data and approaches Euler's curve at
infinity. The objection to its use is the fact that it is
not sufficiently accurate through a large part of the
range for practical columns.
Fi-gure 9 shows the probable error in using this
formula.
Figure 10 is a graph of the Natalis formula drawn
on the same scale with test data points. The formula
is-where
1+c
P/A= Sy 1+c+c2
C= Sy (L/r) 2 7r2 E
This formula is of German origin and was published
;n " Technische Berichte, Band III, Heft 6." A dis­cussion
of its merits is given in the "Comparison of
Column Formula," by J. S. Newell and A. S. Niles, jr.,
Airplane Section, McCook Field. The curve is accu-less
than those plotted from test data. The formula
has the advantage that it will never give r esults
greater than the yield point of the material. It can
be used for any L/r ratio whatsoever and it coincides
accurately with test data for the longer columns.
The principal objection to its use is the labor involved
in solving by such a long and involved formula.
Figure 11 shows the probable error for various L/r
ratios.
Figure 12 is a graph of the Natalis formula drawn
on the same scale with test data, but with the ultimate
compressive strength substituted in the formula instead
of the yield p oint. The purpose of this was to raise the
curve through the lower range of L/r. By this substi­tution
the formula will check with test data for all
values of L/r down as low as 70. Below this point
the curve runs above test data and is useless. The
formula involves too much labor to be used generally.
Figure 13 shows the probable error for various L/r
ratios.
BIBLIOGRAPHY
"Columns," by E. H. Salmon. (Oxford Technical
Publication.)
"The Elasticity and Resistance of the Materials of
Engineering," by William H. Burr. (John Wiley &
Sons.)
"Comparison of Column Formula," by Airplane
Section, McCook Field. (Information Circular No.
395, Vol. IV.)
"Investigation of Thin Wall Seamless Steel Tubing,"
by Material Section, McCook Field. (Information
Circular No. 247, Vol. III.)
"Strength of Materials," by James E. Boyd. (Mc­Graw-
Hill Book Co.)
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. I• I I I I I I I I I I I
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GQR!20N-RA"'1Klt-IE \:ORMUU. f=POM ~R
. . ACTUAL Tc&T VA!..!JE:~ .~
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FIG. 9
. I I I I I I I I
I I I I I I I I I I
. VARIA'l"ION Of. '-~J '\"ME- Hl\T,6,L\S l'ORMUl A ~ = ::f >r.Tt 'A'
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Fm.11
60I "
.s6i RELATION OF TEST VALUE5
• TO
' T\-\E NATAU5FORMULA , - . P=f> ltC WHE:-R£; C::. ;iE ~r- A Y1+Ct0!·
52
"'18 .. .. ·C..URVE: I& Pl.OTT~D F-ROM VBl.UEoli! ... C.OM PUTaO 6~ 1'0£!!:lV!.e POlNT S SHOWN AR~ A.C:.TUA.\.. TE.&TS
44
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28
24
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16
12
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4
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().. ............. . / 1--- f, 11/TA• l.S c (//i'Y.~
II) .......... .
t ~ v
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........ ~
............
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10 z.o JO 40 .50 60 70 eo S" IO" 110 120 /JO 140 15o Ibo 170 /Ro 190 200 ZIO 220 230 240 250 260 270 280 :2.!Jo 300 J/C JZO 3.30 ~ J5o
FIG . 10
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s
4.
4
4
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0
lb 9.
l'l 'Z
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4
0
;-..., RE.LATION OF TE5T VALUE:S
"' TO '\ THE- NATALIS rORMULAWITH Sc. SUBSTITUTl:O F-OR 5~
.. • \ p= 5o IHi WHERC: C=iczi::('R)2. .. A 1+c.tc.z. -- ... ' ~ C.UR\IE: IS PL.OTTE:-D F-!\OM VAL.Ul!!.$
"AT , ... ,. - b ..... . ""' \ / C.OMf:!.!"TED et EOf!~VL.~ U61N UL IHAT ~ er MPR t.l>I' i: eol!:!:I:Z :2~0WH MU! ACTUAL. T~l!>T '·· 5T~I M&T fl .. .. VAL.\Jl!;.S - \ . . \ . , '
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10 1.0 30 .-.o so 60 70 eo 90 100 110 12.0 l'SO 140 1so \oO 110 180 190 ioo iro t?O Z.?>O Mo 2.50 u.o 2.10 tao ?.90 300 310 :no !I'S<> 340 !So
FIG. 12
f--1.
f--1.
12
. . . I I I ~ ~
I I I I
. '• VARIATION OF- t-r-~ THSO NATALI& FDRt!ULA •• ITH S< SU8JkbWTio FQR :2f ==~ . ) C.TUAl Tf:ST VA u~s
t-t-j
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t!> ~ !I> ·~ p ' ' I .,
Fm. 14.-Knife edge bearing and centering block
13
TABLE 1.-Column data on duralumin tubing
(Listed according to L/r ratio) •
P/A by different formulas Ratio or calculated values to test
1 2 3 4 5 6 7
__ _ _ _ ___ _ _ _________8_ 1
1
_ 9_ 10 11 12 13 14 15 16 11 18 19
Out- Max Nata-side
Wal! Length load i;, P/A Joh;i- Joh;i- Gor- Nata- li.s .
Tube diam- thick- . 10 pounds. L/r from Euler 's sons son .s don- hs (usmg Col. 8 Col. 9 Col.10 Col. ll Col. L9 Col. 13
No. eter, .ness, m ches . P from test par!"- s traight- R::in- (usmg cr.ush- Col. 7 Col. 7 Col. 7 Col. 7 Col. 7 Col. 7
4
2
6
10
12
8
18
16
14
20
24
22
4
2
6
12
8
10
18
16
14
20
24
22
4
18
16
20
24
22
23
21
17
19
2
6
12
IO
21
19
17
15
3
1
23
12
JO
18
16
14
5
23
15
11
8
9
13
7
20
21
24
4
3
24
1
2
5
6
11
9
22
7
12
10
13
8
14
17
16
15
18
20
19
23
24
21
22
inches mches L test bohc !me kme Y. P.) mg
str.)
2. 250
2. 252
2. 005
1. 752
1. 753
1. 756
1. 251
1. 253
1. 251
1. 004
. 740
. 742
2. 250
2. 252
2.005
L 753
L 756
L 752
L 251
L 253
L 251
L004
• 740
. 742
2. 250
L251
L 253
L 004
. 740
. 742
. 748
. 744
L 261
1. 002
2. 252
2. 005
L 753
L 752
. 744
L002
1, 261
L 252
2. 250
2. 253
. 748
1. 753
L 752
L 251
L 253
1. 251
1. 999
. 748
L 252
L 749
L 756
1. 753
1. 252
L 755
L 004
. 744
. 740
2. 250
2. 250
. 740
2. 253
2. 252
L 999
2.005
I. 749
L 753
. 742
L 755
L 753
1. 752
L 252
1. 756
L 251
1. 261
I. 253
I. 252
L 251
I. 004
1. 002
. 748
. 740
. 744
. 742
0.093
.128
. 0655
.064
. 052
. 095
. 0375
. 067
. 095
. 0645
. 035
. 051
. 093
. 128
.0655
.052
. 095
. 064
. 0375
. 067
. 095
.0645
. 035
.051
. 093
. 0375
. 007
. 0045
. 035
.041
.0365
. 0535
. 038
. 063
.128
. 0655
. 052
. 064
. 0535
. 063
. 038
. 067
. 0965
.1265
. 0365
. 052
. 064
. 0375
. 067
. 095
. 065
. 0365
. 067
. 049
.095
. 0045
. 0935
. 0945
. 0645
. 0535
. 035
. 093
. 0965
. 035
.1265
.128
. 065
. 0655
. 049
. 0645
. 051
. 0945
. 052
. 064
. 0935
. 095
.095
. 038
. 067
. 067
. 0375
. 0645
. 063
. 0365
. 035
. 0535
. 051
9.12
9. 01
8. 34
7. 45
7. 51
7. 35
5. 77
5.68
5.60
4. 81
3. 98
3. 93
16. 75
16. 52
15. 20
13. 51
13. 24
13. 44
10. 08
9.88
9.68
8. 14
6. 47
6.38
32. 01
18. 65
18. 28
14. 80
11. 48
11. 28
15. 09
14. 67
25. 94
19. 82
46, 62
42. 64
37. 58
37. 32
17. 12
23,07
30. 26
e9. 35
53. 36
56. 68
20.13
49. 61
49. 26
35. 79
35. 08
34. 28
6L40
22. 65
37. 74
58. 41
60. 30
61.90
43. 30
69.08
41. 43
34. 25
36. 42
124. 11
125. 13
41.41
132. 43
132. 61
120. 98
132. 98
12L 13
121. 28
50. 47
128. 58
133. 36
133. 36
96. 63
138. 86
107. 86
124. 33
12L 48
121. 43
127. 23
119. 48
120. 28
119.13
119. 42
120. 68
132. 61
34, 000
38. 650
17, 490
14, 520
11, 660
21, 820
5, 900
10, 500
15, 640
8, 200
3,300
4, 320
30, 060
33, 820
16, 080
10, 380
18, 980
11, 985
4,800
8, 760
13, 570
6, 940
2,900
3, 690
22, 480
4,220
7, 240
5, 840
2.100
3, 040
1 554
2:300
3, 750
5, 080
20, 500
8, 570
6, 510
8,240
1,860
3,900
2, 540
4, 980
12,840
15, 190
1, 165
4, 300
5, 180
2,000
3, 900
5, 000
5, 140
960
3, 060
2, 770
4,800
3, 300
2, 950
3,800
1,440
612
600
2, 470
2,370
322
2,640
2, 780
1, 330
1,360
624
818
300
1, 047
697
840
644
900
518
168
367
306
190
206
215
50
86
100
88
lL 95
lL 98
12. 15
12.47
12. 48
12. 50
13. 44
13. 52
13. 65
14. 45
15. 95
16. 04
21. 94
21. 97
22.15
22.45
22. 50
22.50
23. 48
23. 52
23. 60
24. 45
25. 92
26.04
41. 93
43. 45
43. 52
44. 45
46. 00
46. 05
59. 90
59. 93
59. 96
60. 08
61. 97
62. 15
62.45
62. 49
69. 93
69. 93
69. 95
69. 95
69. 98
75. 26
79. 91
82. 45
82. 48
83. 38
83. 53
83. 59
89. 74
89. 92
89. 94
97.14
102. 50
103. 62
105. 38
117. 48
124. 44
139. 91
145. 94
162. 59
164. 10
165. 93
175. 84
176. 27
176. 83
193. 82
201. 45
203. 01
206. 03
218. 66
221. 65
223. 30
235. 15
236. 07
263. 02
228897.. 4205 1
289. 37
296.41
358. 861
364. 59
447728.. 5963 1
492. 85
54L 33
53, 950 707, 540 33, 470 43, 220
45, 250 756, 300 31, 850 43, 210
43, 820 716, 650 32, 210 43, 160
42, 780 692, 610 30, 300 43, 010
41, 970 729, 940 33, 100 43, 000
44, 020 695, 050 31, 110 43, 000
47, 960 648, 100 30, 950 42, 620
42, 050 631, 940 30, 500 42, 590
45, 320 561, 560 30, 610 42, 540
43, 070 547, 620 32, 310 42, 220
42, 580 416, 070 31, 020 41, 620
39, 020 426, 460 24, 550 41, 580
47, 700 209, 900 33, 450 39, 220
39, 600 224, 880 31. 040 39, 210
40, 290 215, 630 31, 320 39, 140
37, 360 225, 570 32, 220 39, 020
38, 290 214, 520 30, 320 39, 000
35, 310 212, 740 29, 540 39, 000
39, 020 212, 350 30, 120 38, 610
35, 080 208, 7 40 29, 720 38, 590
39, 320 187' 850 29, 940 38, 560
36, 450 191, 270 31, 360 38, 220
37, 420 157, 550 30, 240 37, 630
33, 330 161, 810 23, 940 37, 580
35, 670 57, 470 29, 610 31, 230
34, 310 62, 010 27, 260 30, 620
29, ()()() 61, 080 26, 990 30, 590
30, 670 57, 870 27, 980 30, 220
27, 100 50, 020 26, 780 29, 600
27, 460 51, 740 21, 810 29, 580
19, 040 28, 300 20, 160 24, 040
19, 830 28, 650 20, 020 24, 030
25, 680 28, 930 24, 110 24, 020
27, 340 30, 730 25, 590 23, 970
24, 000 28, 260 23, 030 23, 210
21, 470 27, 390 22, 890 23, 140
23, 430 29, 150 23, 870 23, 020
24, 280 27, 580 22, 130 23, 000
16, 030 21, 040 17, 910 20, 030
20, 990 . 22, 680 21, 780 20, 030
17, 400 21, 260 20, 450 20, 020
19, 970 21, 860 20, 200 20, 020
19, 660 21, 230 19, 980 20, 000
17, 970 18, 460 18, 320 17, 890
14, 280 16, 290 15, 620 16, 030
15. 480 16, 720 16, 720 16, 020
15, 260 15, 830 15, 810 15, 000
16, 750 16, 840 16, 410 14, 650
15, 620 16, 580 16, 670 14, 590
14, 490 14, 970 16, 490 14, 560
13, 010 13, 490 13, 130 12, 100
11, 760 12, 870 12, 870 12, 030
12, 270 13, 220 12, 710 12, 020
10, 580 11, 090 9, 490 9, 140
9, 683 10, 340 7, 580 7, 000
9, 650 11, 010 5, 320 6, 550
8, 670 10, 740 6, 450 5, 850
7,710 7, 410___ ____ 1,010
7, 563 7, 380 ------- -- - -- ----
5, 280 5, 250 ------- - --- - - ---
7, 742 4, 970 - - -- --- -------- -
3, 919 3, 822 ------- --- -- - - --
3,630 3,859 _______ ---- - - - --
4, 155 3, 844 - -- ---- ---- - --- -
3, 124 3, 383 ------- - - -- - - - --
3, 255 3, 493 ------- --- ---- --
3, 367 3, •174 - - ---- - -- - --- - - -
3,408 2, 816 ----- - - - - -- - ----
2, 384 2, 577 - -- ---- ------ - --
2, 391 2, 860 ------- --- - - - ---
2, 710 2, 585 --- - - -- - - -------
2, 124 2, 138 -- - - --- -- - - -----
2, 513 2,309 ------- -------- -
2, 475 2, 160 ------ - - - - ------
1,892 2, 156 ------- -- - --- - --
1,816 1,949 _______ -- - ------
1, 501 l, 512 ------- ------ - --
1, 151 1, 259 ------- - -- ------
1, 470 l , 383 ------ - - - - - - ----
1, 227 I, 277 _______ - · - - - ----
~:~ !,~ ::::::: ::: :::: : :
1, 157 835 --- - --- ------ ---
1, m :g~ ------- :::::::::\
862 423 --- --- - - -
795 374 - - - -- - -- -
52, 620
53, 730
45, 220
46, 450
44, 940
51, 940
47, 470
50, 900
57, 640
54, 610
49, 110
51, 610
44, 730
46,000
41,410
39, 500
44, 490
40,350
41, 270
43, 770
47, 870
46, 050
41, 140
43, 080
28, 580
28, 050
29, 040
29, 620
26, 350
27, 500
18, 930
19, 660
18, 160
20,440
18, 990
17, 850
18, 120
17, 750
15, 750
16, 540
14, 810
15, 640
15, 480
14, 020
12, 540
12,400
12, 010
12, 670
12, 760
12, 140
10, 560
10, 410
10, 660
8, 970
8, 730
9,000
9, 240
5,410
6, 580
4,850
4, 563
3, 582
3,620
3, 596
3, 190
3, 295
3, 240
2,670
2, 444
2, 710
2, 476
2,060
2, 207
2, 070
2, 090
1,884
1, 513
1,230
1, 349
1,250
1,299
875
820
461
442
421
372
34, 829 55, 920
32, 140 57, 528
32, 506 51, 010
30, 580 49, 550
33, 410 4 7, 690
31, 410 55, 800
31, 240 50, 920
30, 770 54, 963
30, 910 63, 490
32, 720 60, 000
31, 440 54, 810
24, 850 57, 750
34, 070 . 53, 080
31, 630 54, 950
31, 940 49, 020
32, 880 46, 160
30, 890 53, 250
30, 090 47, 670
30, 730 48, 920
30, 270 52, 440
30, 270 63, 490
32, 020 56, 360
30, 580 50, 970
24, 430 53, 550
28, 390 37, 710
26, 770 37, 290
26, 370 33, 680
27, 240 39, 480
25, 390 35, 100
21, 550 36, 620
18, 250 24, 480
18, 110 25, 020
20, 800 23, 710
22, 150 26, 300
20, 040 24, 360
19, 790 23, 090
20, 740 23, 700
19, 335 23, 030
15, 430 19, 400
18, 3CO 20, 610
17' 180 18, 770
17, 050 19, 630
16, 810 19, 290
15, 580 16, 400
13, 120 15, 250
14, 360 15, 340
13, 460 14, 700
14, 100 15, 570
13, 950 15, 510
12, 940 14, 340
11, 950 12, 730
11, 050 12, 310
11, 770 12, 630
10, 110 10, 610
9, 560 10, 050
10, 255 10, 590
10, 000 10, 500
7, 080 7, 300
7, 090 7, 285
5,081 5, 220
4, 865 4, 934
3, 781 3, 783
3, 811 3, 844
3, 796 3, 827
3, 350 3, 224
3, 469 3, 482
3, 437 3, 458
2, 797 2, 808
2, 560 2, 570
2, 843 2, 844
2, 560 2, 580
2, 128 2, 138
2, 304 2, 309
2, 150 2, 156
2,148 2,154
1, 948 1, 946
1, 509 1, 512
1 258 1, 258
1: 380 1, 383
1, 275 1, 276
1, 331 1, 332
887 887
834 834
:g~ :g~I 423 424
374 374
13. 11 0. 64 0. 80
16.711 .70 .95
16. 35 . 73 . 98
16. 19 . 71 L 01
17.47 .79 L02
15. 791 . 71 . 98
13. 51 . 64 . 89
15. 03 . 73 1. 01
12. 39 . 67 . 94
12. 71 . 75 . 98
9. 77 . 73 . 98
10. 93 . 63 L 07
4.40 .70 .82
5.68 .78 .99
5.35 .78 .97
6.03 .86 1.04
5.60 . 79 1.02
6. 03 . 84 1. 10
5.44 .77 . 99
5. 95 . 85 1. 10
4.78 . 76 . 98
5. 25 . 86 L05
4. 21 . 81 1. 01
4.85 .72 1.13
L 61 . 83 . . 88
1. 81 . 79 . 89
2.11 .93 l.05
1.89 .U I .99
1.85 . 99 1.09
L88 .79 1.08
L 49 L 06 L 26
1. 45 L 01 L 21
1. 13 . 94 . 93
1.12 . 94 . 88
1. 18 . 96 . 97
L28 L07 L08
1.24 L02 .98
1. 14 . 91 . 95
1. 31 L 12 L 25
1.08 L04 .95
1. 22 L 18 I. 15
1. 09 L 01 1. 00
L08 1.02 L02
1.03 L02 1.00
1.14 L 09 L 12
1.08 l.08 .97
1.03 1.04 .98
LOO .98 . 88
1.06 L07 . 93
1.03 L 14 LOO
1. 04 L 01 . 93
1.09 L09 L02
1.08 1.03 .98
1.05 .90 .86
J.07 .78 .72
1. 14 . 55 . 68
1. 24 . 74 . 67
.96 ____ __ . 13
. 96 ---- -- ----- -­.
99 -- ---- - - - ---­.
64 ------ - - -- - - -
. 98 •• ____ - -- ----
1. 06 ___ ___ ---- - --
. 93 ------ - -- ----
1. 08 ___ ___ - - -- - --
L 07 - - ---- - -- --- -
1. 03 ----- - - -- ----
L. 8038 -_-_-_-_-_-_ -_-__-_--_-_-_
L 20 - - - - -- - -- ----
. 95 - - ---- ---- - --
L Ol ______ - ------
. 92 - - ---- ---- - --
. 87 ------ ------­!.
14 - - --- - ------­L
07 ------ - ----- -
L Ol ______ -- - ----
L09 ______ --- -- --
. 94 - - --- - ------­L
04 - - ---- - ------
. 86 ------ ---- - -­.
82 ------ -- - ----
. 72 ------ - - -- - --
. 76 ------ - ---- --
. 41 ----- - - -- - - -­.
49 - ----- - -- ---­.
47 -- ---- - - --, --
0. 98
1.19
1.03
L08
L 07
L 18
.99
1. 21
L 27
1. 27
1.15
1. 32
. 94
1.16
1. 03
1.06
L 16
1.14
L06
1. 25
L 22
1. 26
1.10
1. 29
.80
.82
LOO
. 87
. 97
L 00
. 99
. 99
. 71
. 75
. 79
.83
. 77
. 73
. 98
• 79
. 85
.85
. 79
. 78
.88
. 80
. 79
• 76
. 82
. 84
. 81
. 89
. 87
. 85
. 90
. 94
L07
. 70
. 87
. 92
. 59
.91
LOO
. 87
1. 02
L 01
.96
. 78
1. 02
L 13
. 91
. 97
.88
. 84
1. 10
L 04
L 01
L 07
. 92
L 02
. 84
.81
. 71
. 75
. 40
. 49
. 47
0. 65
. 71
. 74
. 71
. 80
. 71
. 65
. 73
. 68
. 76
. 74
. 64
. 71
.80
. 79
. 88
.81
. 85
. 79
. 86
. 77
.88
.82
. 73
. 80
. 78
. 91
.88
. 94
. 78
. 96
.91
. 81
.81
. 83
. 92
.88
. 79
. 96
. 87
.99
. 85
. 85
. 87
. 92
. 93
. 88
. 84
. 89
. 89
. 92
. 94
. 96
.95
.99
L 06
L 15
.92
.94
. 96
.63 .96
I. 05
. 91
1. 07
I. 07
1. 02
. 82
1. 07
L 19
. 94
LOO
. 92
. 87
1. 14
1. 07
LOO
L09
.94
1. 04
. 86
. 82
. 72
. 76
. 42
. 49
.471
1. 04
L 27
1. 16
L 16
1. 14
1. 27
L 06
1. 31
I. 40
L 39
1. 29
L 48
L 11
1. 39
1. 22
1. 24
1. 39
1. 35
1. 25
I. 49
1.61
1. 54
1. 36
1. 61
L 06
I. 08
L 33
L 28
I. 20
1. 33
]. 28
L 26
.92
.96
1. 01
L 07
LOl
. 95
1. 21
. 98
L08
. 98
. 98
. 91
1. 07
. 99
. 96
. 93
. 99
. 99
. 98
L 05
1. 03
LOO
. 97
L 10
L 21
. 95
. 96
. 99
. 64
. 97
L06
. 92
L 03
J. 07
L 02
. 82
L 08
L 19
. 95
L 01
. 92
.87
L 14
L 07
L 01
1. 09
. 94
L04
. 86
.82
. 72
. 76
. 42
. 49
. 47
-
14
TABLE 2.-General properties of duralumin tubes (material "as received")
T ension Per cent elon•g ation Torsion Compression tests on 3- inch specimens
Out- Modu- Modu-
Tube side Wall Propor- Tensile Modulus Propor- !us of Modulus lusrup- Propor- Yield Crush-
No. diam- thick- tional strength, of elas- tional rup- of elas- D/T ture, ti on al point, ing
eter ness limit, pounds ticity, 2 4 8 limit, ture, ticity, tensile limit, pounds strength,
pounds per pounds 11uches inches inches pounds pounds pounds strength pounds per pounds
per square per square I per per per per square per
square inch inch square square square square inch square
inch inch inch inch inch inch
-------- ------ - - - ------ - -----
1 2.253 0. 1265 26, 270 60, 530 10, 597, 000 1 20. 0 18.5 19. 5 20,440 33, 720 3, 843, 100 17.8 o. 557 32, 300 33, 840 58, 220
2 2.252 .128 22, 010 58, 960 10, 997, 900 23. 0 20.5 19. 25 18, 720 30, 510 3, 882, 240 17. 6 . 517 30, 440 32, 200 57, 840
3 2. 250 .0965 31,240 60, 670 10, 533, 000 19. 0 17. 5 15. 0 18, 540 30, 410 3, 854, 500 23.3 .501 28, 790 32, 160 57, 160
4 2.250 . 093 28, 560 61,000 10, 237, 400 20. 5 18.0 15. 25 19, 910 30,640 3,888,610 24.2 .502 31, 740 34, 910 56, 840
5 1. 999 . 065 21, 010 60,960 11, 007, 000 24. 0 21.5 20. 5 17,030 23, 660 3, 982, 100 30. 7 . 388 30, 380 31, 390 48, 610
6 2.005 .0655 25, 060 63, 370 10, 719,200 28.0 26.5 23. 75 18, 140 23,540 3,893, 540 30. 6 .371 30,070 32, 570 51, 260
7 1. 755 . 0945 21, 910 59, 820 10,358,000 22.0 20.5 18. 75 15,440 31,220 3, 933, 900 18. 6 .522 28,400 30,830 57,220
8 1. 756 . 095 1 22, 190 59. 270 . 11, 003, 700 23.0 21. 5 19. 75 16, 130 30, 180 3, 811,050 18.5 • 509 29,860 31, .470 56, 140
9 1. 75.1 . 0645 24, 550 63, 080 11, 941, 000 27. 5 24. 5 22. 25 21, 530 24, 300 ·3, 727, 800 27.2 .385 35, 370 36, 250 51, 740
10 1. 752 .064 24, 750 56, 450 10, 912, 500 14.0 12.0 11. 5 17,010 24, 350 4, 002, 220 27.4 .431 29,460 30, 640 49, 790
11 1. 749 . 049 22, 930 60,370 10,597,000 12.0 12. 5 12. 5 18, 020 20, 570 3, 810, 300 35. 7 . 341 28,660 30, 570 47, 110
12 1. 753 . 052 22, 320 59, 610 11, 519, 100 17. 5 15. 5 14.0 20,040 22,650 3, 917, 680 33. 7 . 380 32, 400 33, 480 47, 880
13 1. 252 . 0935 20,860 62, 090 12, 080, 000 27.0 23.0 20. 5 20, 150 37, 210 3, 661, 300 13. 4 • 599 34, 380 34, 670 66,380
14 I. 251 . 095 23, 180 60, 270 10, 601, 400 25.0 22.0 19. 5 14, 280 36, 250 4, 028, 380 13. 2 • 601 28, 110 31, 000 64, 240
15 1, 252 . 067 23, 260 58,420 10, 837, 000 20. 5 18. 75 17. 5 17,390 27, 660 3, 655, 300 18. 7 .473 28,870 31, 670 54, 930
16 I. 253 . 067 18, 820 57, 750 11, 721, 300 18.0 14. 5 14.0 18, 670 28,850 3, 703, 960 18. 7 .500 29,840 30, 840 55, 350
17 1. 261 .038 24, 660 56, 920 10, 538,000 17. 0 15. 0 15.0 16, 150 21, 760 3, 715, 200 33.2 .382 30, 140 34, 250 48, 830
18 1. 251 .0375 25, 040 62,600 11, 861, 500 10.0 9.5 9.0 16, 270 21, 340 4, 004, 140 33.4 .341 30,080 31,300 51, 220
19 l. 002 .063 34, 980 62,860 11, 239,000 18. 0 17.0 16. 25 18, 630 32, 910 4, 355, 900 15. 9 .559 35, 520 36, 330 61,090
20 l. 004 .0645 28, 890 59, 610 11, 585, 500 17. 5 16.0 15. 5 17, 360 34, 900 3, 941, 500 15. 6 .585 30, 720 32, 830 60,660
21 . 744 .0535 40,000 60, 340 10,423,000 27.0 22.5 19.5 14, 100 33,400 3, 968, 100 13. 9 .553 22,840 25, 860 62, 670
22 . 742 . 051 37,400 56,910 ll, 117, 100 27. 5 24.0. 20. 75 16, 750 34,280 4, 294, 400 14. 5 . 602 21, 680 24, 930 58, 720
23 . 748 .0365 38,480 61, 270 10, 542,000 16. 0 16. 25 15. 5 14, 450 25, 460 4, 180. 600 20.5 . 415 24, 510 25, 980 54, 530
24 . 740 .035 36, 160 61, 670 10, 724,800 19. 5 17.5 15. 0 20, 690 30, 840 4, 198, 200 21.1 .500 30, 320 31, 610 55, 680
------
26, 850 1 60, 190 ==1 17,750 3. 927, 200 I·----------- -----
Average __ ------- ---- -- - 10, 987, 000 ----- - --- ---- 29, 170 .487 29, 790 31, 730 55, 580
PART II- CRUSHING STRENGTH
ABSTRACT
Crushing tests were made on several sizes of cold­drawn
duralumin tubing cut to various lengths. The
variation of the crushing strength due to diameter,
wall thickness, and length of test specimen was deter­mined.
(a) The crushing load that a tube of given dimen­sions
will stand is independent of its length, within
certain limits. The shortest length which will permit
the tube to make one complete fold when loaded to
failure comes within these limits. Increasing the
length of the specimen until several folds can be made
does not affect the crushing load. A length is finally
reached at which it is impossible to load the specimen
accurately enough to cause failure by folding, and the
tube will collapse on one side. Beyond this point the
crushing load will decrease with increase of the length
of the specimen.
(b) Crushing specimens cut to the length L = 6 T+
390 T3/D2 will have a crushing strength numerically
equal to the tensile strength of the tube.
MATERIAL
The following sizes of duralumin tubing were used in
these t ests :
DiameteL ----- [2. 2512. 251 2. 0011. 751 1. 7511. 7511. 251'1. 2511. 251 1
1. 0010. 75,0. 75 Thickness ______ . 125 . 093 . 0625 . 093. 0625 . 049 . 093 . 065 . 035 . 065. 049 . 035
I
These tubes were manufactured by the Aluminum
Company of America.
METHOD OF PROCEDURE
The specimens were tested square ended and between
flat plates. Great care was taken to have both bearing
edges square with the axis of the tube. A special jig,
consisting of a steel plunger held in a cast-iron frame,
was used in these test s. This plunger was free to move
vertically, but was held rigidly against any side play
due to si1ifting of the testing machine head. An Olsen
100,000-pound Universal testing machine was used for
applying the load.
One object in making these tests was to find a length
to cut specimens such that the crushing strength would
be equal to the tensile strength. A series of tests
was made on specimens cut from several of the tubes
to lengths of 6 T, 8 T, and 10 T. The results of these
tests were compared with the tensile strengths of the
tubes and an estimate made of the required lengths for
the entire series of tubes. Specimens cut to these
lengths were tested and a new estimate made. Thus,
by the cut and tr method, the proper length was soon
found for each of the twelve sizes of tubing, such that
the crushing strength equaled the strength in tension.
A chart of lengths was laid out, as shown in Figure
15. Various formulas were tried with various con­stants
in an effort to express these lengths in terms of
the dimensions of the tube. The best formula found
was L=6 T+390 T3/D2 •
Two specimens from each of the 12 sizes of tubing
were -cut to lengths calculated from this formula.
The results of crushing tests on the two specimens of
each size were averaged and found to check with the
tensile strength of the tubes to within less than 3 per
cent in every case.
RESULTS
A formula was found connecting the crushing
strength with the tensile strength. The accuracy of
this formula is shown graphically on Figure 16, and
exact numerical data are recorded in the table.
It was found also that the curve representing P / A
plotted against L was horizontal throughout quite a
range. In other words, the crushing load that a
tubular specimen will stand is independent of the
length of the specimen, within certain limits, and the
specimen may be cut any length within these 1imits
without affecting the crushing load that the specimen
will withstand. The shortest length within these
limits is that length which will permit the tube to
make one complete fold when it is loaded to failure.
The upper limit is set by the longest length at which
the tube will still fail by folding, instead of by col­lapsing
on one side.
DISCUSSION OF RESULTS
The meaning of the symbols used in t his discussion
a re as follows:
P = Load in pounds.
A=Cross sectional area 111 square inches.
L = Length of tube in inches.
r = Least radius of gyration.
Sc= Ultimate crushing strength in pounds per
square inch.
St= Ultimate tensil e strength in potincls per
square inch .
X = An unknown term.
Figure 15 shows a chart of the lengths determined .
for each tube size such t hat the crushing streugth
would equal the tensile strength. The clotted line
shows the lengths calculated from the formula.
Figure 16 shows a graph of the results obtained by
testing crushing specimens cut to lengths set by the
formula L=6 T+390 T3/D2.
Each point is the average of two crushing tests
checked against one tensile t est on the same tube.
The table gives the exact numerical r esults. The
t ests were run on a wide va riety of sizes-from 0.75
to 2.25 inches in diameter and from 0.035 to 0.125
(15)
-
;16
inches in wall thickness, twelve sizes in all. Most of
the results check with the tensile strength to within
less than 2 per cent, and none of the results miss the
tensile strength as much as 3 per cent. It is believed
that this is sufficiently accurate for p1"actical use, at
least within the limits of the tube sizes tested. It will
be possible by the use of this formula to take a very
short piece of duralumin tubing, square off a crushing
specimen and test it, and get a close approximation
to the tensile strength. Occasionally, in an airplane
wreck, for example, it is impossible to get a long
enough piece of tubing to make a tensile test. In such
a case a crushing test would answer the purpose.
There are cases also in which it is necessary to save
the material for some other purpose, and a tension
test would require more than could be spared.
Figure 17 shows graphically a peculiarity of crushing
specimens. Varying the length within certain limits
did not affect the crushing strength. This curve is
plotted from tests on tube No. 6, but it is character­istic
of the results obtained on other tubes. If the
tube were long enough to make one fold, its crushing
strength was around a certain value. Increasing the
length so that two or three folds were made did not
change this value. In the case of tube No. 6 (2.005X
0.0655) the curve leveled off at about 50,000 pounds
per square inch. The curves on other tubes leveled
off at other values, depending upon the diameters and
the wall thicknesses. The tensile strength of tube No.
6 was 63,370 pounds per square inch. This point on
the curve is not on the horizontal portion, but is at a
position where the crushing strength changP.s very
rapidly for small changes in the length. In cutting
crushing specimens to check with tensile tests, it is
not possible, then, to use the horizontal portion of this
curve and cut specimens at any length along this line.
The formula worked out had to be accurate and had
to determine a particular point on each curve.
Figure 18 is a photograph of some typical crushing
specimens after test. The top row shows some speci­mens
cut from tube No. 6. From left to right the
data on these tubes are as follows :
L ength, inchcs _ ____ ___ __ _ l 3. 001 2. 83211. 0071 0. 6301 0. 5041 0. 3781 0. 280
Crushing strength, pounds,
per square inch. ________ 51, 260 49, 600 48, 825 49, 950 54, 790 65, 530 82, 300
These data were used in plotting the curve in Figure
17. It is seen that there is even a slight increase in
strength by increasing the length from 1 to 3 inches.
This is explained on the grounds that a slight inaccu­racy
in cutting the specimens, such as making one side
of the specimen longer than the opposite side, would
produce an effect which would be concentrated in 1
inch in one case and distributed over 3 inches in the
other. This would weaken the short tube more than
it would weaken the long one.
While running the tests, the behavior of the tubes
indicated ·the reason for the similarity of results on
different lengths. The extremely short tubes were not
long enough to make one complete fold. The actual
crushing of the material took place throughout the entire
cross sectional area. I ncreasing the length slightly
permitted the tube wall to bend in a complete fold.
This created a neutral axis such that the material
around the outside circumference was under tension
parallel to the tube axis while the material around the
inside circumference was under compression. This is
well illustrated by the central specimen in the top row.
This specimen was 0.630 inches long and was the short­est
one to give a point on the horizontal portion of the
curve. The photograph shows a crack running
around the tube, proving that the material around the
outside was under tension due to the bending of the
tube wall.
Increasing the length of the specimen still more
causes more folds to be made. It was noticed that one
fold would be made completely before the rest of the
tube had been distorted not iceably. After one fold
was made another one was started . This second fold
was completed before the third fold was started, and
so on. The specimen was of the same dimensions
throughout its length, and the load required to produce
one fold was the same as that required to produce
another fold, so the crushing strength of a specimen
long enough to produce several folds was the same as
that of a specimen only long enough to produce one
fold. There is a limit, of course, to the length at which
a specimen will still fail by folding. Beyond this limit
the tube fails by bending as a unit and collapsing on one
side. This upper limit depends upon the accuracy of
loading the specimen, the homogeneity of the material,
and other factors. It is possible by making a careful
set-up to get as many as four folds at least. When
the tube fails by bending, any increase in length causes
a rapid decrease in crushing strength and the curve
starts down again. It is interesting to note that the
specimen from this tube 0.630 inches long had an L/r
ratio of 0.92, and the specimen 3 inches long had an
L/r ratio of 4.38.
The two bottom rows on Figure. 18 show photo­graphs
of one specimen of each size tested at a length
calculated from the formula L = 6 T+390 T3/ D2.
It is evident that tension existed in the outside layers
of ' the tube along lines parallel to the tube axis, as
mentioned before; and also that, due to the expansion
of the tubes, considerable t ension ex ists along a line
drawn around. the tube at a point halfway between its
ends. This tension extends through the wall of the
tube and has caused some of them to split lengthwise.
The L/r ratios of each of these tubes are recorded in
the table. They vary from 0.56 to 1.90.
Results of crushing tests on duralmnin tubing when the
specimens are cut to length L=6 T-390 T3/ DZ
L ength of
Tube crushing
No. Tube s ize speci- L /r
mens,
inches
-- - - -- ------
1 2. 253XO. 1265 0. 914 1. 21
4 2. 250X . 093 . 620 . 81
6 2. 005 x . 0655 . 423 . 62
8 1. 756X . 095 . 678 1. 15
10 1. 7o2X . 064 . 420 . 70
12 1. 753X . 052 . 323 . 54
14 1. 251X . 095 . 77f} 1. 90
16 1. 253X . 067 . 478 l.l4
18 !. 251X . 0375 . 240 . 56
19 1. 002X . 063 . 476 1. 44
22 0. 742X . 051 . 401 1. 64
24 0. 740X . 035 . 242 . 97
'Average of two t ests.
Ultimate crushing 'rcnsilc stren gth, strength, lb. per lb. per sq. in.1 sq. in.
- -----
59, 200 60, 530
61, 650 61, 000
62, 270 63, 370
58,000 59, 270
57, 890 56, 450
59, 120 59, 610
61,000 60, 270
.56, 290 57, 750
62, 240 62, 600
61,680 62, 860
56, 320 56, 910
59, 930 61, 670
I
T en s ile
strength
obtained
by
crushing,
per cent
97.
101.
98.
97. (
8
l
3
9
5
2
4
5
4
1
0
2
102.
99.
101.
97.
99.
98.
99.
97.
17
~ ! I -- RcLATIO~ OF CTAOL CULATH> LHl~TllS • ....
- LHlG"Tll& FOUNt> 8'/ H.PERll'1cttT
- -- LEHGTHS DETEl(MIMEO FR.OM E.XPE.Rll"\E.. .1 SI 'EO~ TO C>IVc CRIJSH\HIO 5Tl(H~GTH 5 EQU•\. TOTHt F /C>c; - Ti;,>lSILE. 5TRcl'luTH5
- ------LENGT>I<'> CALCULATED •~OM FO~liULA : -
~~ ~ L% GT+ 3'l0 :f! -
- oz. ,IV
!..- ....
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FIG 15
C.OMPARl&ON OF- C.~US.HINt!> 5TR£-N(;TH
WITH
, . Tt:-N51Lf: STR~KGTH, WH£-K L"-~T+3CJo~i
lj NOTE::- THI& FORMULI'. WAS OE:R.l'IE:O TO .<:.1vl-. A
~(;TH To C~USHl~C. Sf'l::C.IMIC:NTS SUCH THAT
) THE: CRVSHINC. ST~E:NC::.TH WOULO SE: &.QUA\..
TO TH'& "TC-!-IS!LE STRC-l-IG.Tl-\ .
I ,,,,... V(JO ' ~ .... _......_
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Fm. 16
18
•
~
~ VAR\ATION OF CRUSHING STRENGTH
... WITH LEN~TH OF 5PECIME:N"
Ii RcSULTS OF TESTS ON A
11 TUBE 2.00SlC.Ob55
~
- ~ ,_
t
•
~ - ~
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lo !...c -. gA ":. q_ =~ 3 >
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f IG. 17
FIG . 18.- Photogrnph of crushing specimens
Top row: Specimens of different lengths cnt from the same tnbe. (Tu he No. 6-size 2.005 by 0.0655)
Two bottom rows: One tested specimen from each size of tubing-arranged in order according to size, as listed in tbe table. These specimens
were cut to the lengths set by the formula L ~ 6T+390 T •/D2
PART III.- TORSIONAL STRENGTH
ABSTRACT
The torsional strength of several sizes of duralumin
tubing was determined, and a study was made of the
effect upon the fiber stress of the ratio of the diameter
to thickness. The method of failure depends upon
the D/t ratio. For small tubes, the failure is due to
the shear stress; for intermediate tubes, a combination
of shear and localized collapse; and for large tubes,
the failure is entirely by localized collapse. This
investigation shows that the D/t ratio must be taken
into consideration as limiting the maximum fiber
stress, and this relationship is given by the formula
TM=45000-700 D/t for duralumin tubing with an
ultimate strength in tension of 60,000 pounds per square
inch. A more general formula is Tm=.75-.0017 D/t
X St.
MATERIAL
The following sizes of duralumin tubing were used in
these tests :
TABLE I
Diameter _____ _ 1 2~ 1 2~ 1 2.oo j 1%I H4 1 1% 1 1!4 1 1!4 1 1~ 1 i.oo\ % I% Thickness ______ . 125 . 093 . 062.5 . 0931. 0625_. 049 . 093 1" 065 . 035 . 065. 049. 035
These tubes were manufactured by the Aluminum
Company of America.
METHOD OF PROCEDURE
Torsion specimens were cut 30 inches long for the
small diameter tubes, and 36 inches long for the larger
ones. The ends were plugged with steel plugs. The
tests were made in an Olsen Torsion Machine. The
116,000 pounds-inch poise was used on the larger sizes,
and the 11,600 pounds-inch poise on the smaller tubes.
A Troptometer of the arc and pointer type, reading to
.01 inch on a radius of 12 inches was used to measure
deflections. The gage length was made as long as
possible (20 to 28 inches) and was carefully measured
with a steel scale in each case. Enough readings were
taken to plot an accurate load-deflection curve for each
specimen. The proportional limit and the modulus of
elasticity were obtained from these curves.
RESULTS
The results are recorded in Table 3 in convenient
form for reference. This table also contains the gen­eral
properties of these tubes as found from previous
tests. Figures 19 and 20 show some of these results
graphically.
DISCUSSION OF RESULTS
The meaning of the symbols used in this disc ussion
are as follows :
D = Outside diameter of tube in inches.
T= Thickness of the wall of the tube in inches.
d = lnside diameter of tube in inches.
M = Twisting moment in inch pounds.
Tm= Extreme fiber stress in torsion in pounds
per square inch- modulus of rup_ture in
torsion.
St= Ultimate tensile strength in pounds per
square inch.
DISCUSSION OF RESULTS
Figure 19 shows in curve No. 1 that the tensile
strength of the tubes was not affected by drawing to
different diameters and thicknesses. The fact that
all the tubes were of nearly t he same strength eliminates
t his factor as a variable. · Any differences in the tor­sional
strength are due to the variation in the D/T
ratio.
Figure 19, curve No. 2, shows the variation of t he
modulus of rupture in torsion with the D/T ratio.
The modulus of rupture in torsion was computed from
the formula-
M
Tm= 5.093--cJ.4
D•-15
An increase in the D/T ratio decreased the torsional
strength. Those tubes with a low D/T ratio tended
to fail in shear. Those with a large D/T ratio failed
by crumpling or collapsing. Curve No. 2 is drawn
through points plotted from data. This curve,
however, may be represented by the formula-
Figure 20 shows the ratio of torsional strength to
tensile strength plotted against the D/T ratio. The
curve is drawn thTOugh the points plotted from data.
This curve may be represented by the following
straight-line formula-
Tm = (. 75- .0117 ¥) S,
The two formulas may be combined, and Tm
eliminated.
45000 - 700¥=(.75-.0117 ¥) s,
Evaluating for S,
45000-700 ¥
D =S,=60000
.75-.01171'
This value of 60,000 pounds per square inch is the
average tensile strength of the tubes tested. This
furnishes a check between t he constants used in the
two formulas. It is believed that these two formulas
will be found useful in determining the maximum fiber
stress allowable in torsion tubes of diHerent sizes. A
solid rod has a D/T ratio of 2. Substituting this value
in the first formula we get 45000 - (2X700) =43600,
the modulus of rupture for a solid rod. This
value checks very closely with a value of 43260 for
torsional strength of solid duralumin bars of similar
properties obtained from previous tests.
(19)
20
""
7~-
VA~lf'iTION IN
PHYSICAL f'ROPE!!:TI f:S
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17:2 - t>l)RALUMIN-"l'fu BING
. . . . . . . . ·. .
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PHYSIC.AL PRO?E:RTIE:S
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FIG. 20
21
TABLE 3.-General properties of duralumin tubes (material "as received")
I
Tensio·n Per cent elongation Torsion Compression tests on 3-
inch specimens
Out- Wall Pro-
Tensile\
Pro- Modu- Modulus Modu- Pro-
Tube side Yi Id I Crush- thick- portion- Modulus portion- !us of of elas- D/T lusrup- portion- .e ing
N o. diarn- al strength, of elas- al rup- ture, al pomt, strength
eter ness limit, pounds ticity, 2 ins. 4 ins . 8 ins. limit, ture, ptoicuintyd,s tensile limit, pounds pounds pounds per pounds pounds pounds per strength pounds per per
per square per square per per per sg.uare square
square inch inch square square square square mch inch
inch inch inch inch inch
- --- - - - - - --- - -- --- ----- -- - - - --- ---- - -
1 2. 253 0.1265 26, 270 GO, 530 10, 597, 000 20.0 18. 5 19. 5 20, 440 33, 720 3, 843, 100 17. 8 o. 557 32, 300 33, 840 58, 220
2 2.252 . 128 22, 010 58, '960 10, 997, 900 23.0 20.5 19. 25 18, 720 30, 510 3, 882, 240 17. 6 .517 30, 440 32,200 57, 840
3 2.250 . 0965 31, 240 60, 670 10, 533, 000 19.0 17. 5 15. 0 18, 540 30, 410 3, 854, 500 23. 3 • 501 · 28, 790 32, 160 57, 160
4 2. 250 . 093 28, 560 61, 000 10, 237, 400 20. 5 18.0 15. 25 19, 910 30,640 3, 888, 610 24.2 . 502 31, 740 34, 910 56, 840
5 1.999 .065 21, 010 60, 960 11,007,000 24.0 21.5 20. 5 17, 030 23, 660 3, 982, 100 30. 7 . 388 30, 380 31,390 48, 610
6 2. 005 . 0655 25, 060 63, 370 10, 719, 200 28.0 26. 5 23. 75 18, 140 23, 540 3, 893, 540 30. 6 . 371 30, 070 32, 570 51, 260
7 1. 755 .0945 21. 910 59, 820 10, 358, 000 22. 0 20. 5 18. 75 15, 440 31,220 3, 933, 900 18. 6 .522 28, 400 30, 830 57, 220
8 1. 756 .095 22, 190 59, 270 11, 003, 700 23.0 21. 5 19. 75 16, 130 30, 180 3, 811, 050 18. 5 • 509 29, 860 31,470 56, 140
9 1. 753 .0645 24, 550 63, 080 11, 941, 000 27. 5 24. 5 22. 25 21, 530 24, 300 3, 727, 800 27. 2 .385 35, 370 36, 250 51, 740
10 1. 752 . 064 24, 750 56, 450 10. 912, 500 14. 0 12. 0 11. 5 ' 17,010 24, 350 4, 002, 220 27. 4 1 . 431 29, 460 30, 640 49, 790
11 1. 749 .049 22, 930 60, 370 10, 597, 000 12. 0 12. 5 12. 5 18, 020 20, 570 3, 810. 300 35. 7 . 341 28, 660 30, 570 47, 110
12 1. 753 . 052 22, 320 59, 610 11, 519, 100 17. 5 15. 5 14.0 .20, 040 22, 650 3, 917, 680 33. 7 .380 32, 400 33. 480 47, 880
13 1. 252 . 0935 20, 860 62, 090 12, 080, 000 27. 0 23. 0 20.5 20, 150 37, 210 3, 661, 300 13. 4 . 599 34, 380 34, 670 66, 380
14 1. 251 . 095 23, 180 60. 270 10, 601, 400 25. 0 22. 0 19. 5 14, 280 36, 250 4, 028,380 13. 2 . 601 28, 110 31,000 64, 240
15 1, 252 . 067 23, 260 58,420 10, 837, 000 20. 5 18. 75 17. 5 17, 390 27, 660 3, 655, 300 18. 7 .473 28, 870 31, 670 54, 930
16 1. 253 . 067 18, 820 57, 750 11, 721, 300 18. 0 14.5 14. 0 18, 670 28, 850 3, 703, 960 18. 7 . 500 29, 840 30, 840 55, 350
17 1. 261 .038 24, 660 56, 920 10, 538,000 17. 0 15.0 15. 0 16, 150 21, 760 3, 715, 200 33. 2 . 382 30, 140 34, 250 48, 830
18 1. 251 . 0375 25, 040 62, 600 11, 861, 500 10. 0 9. 5 9.0 16, 270 21, 340 4, 004, 140 33.4 .'341 30, 080 31, 300 51,220
19 1. 002 . 063 34, 980 62, 860 11, 239, 000 18. 0 17.0 16. 25 18, 630 32, 910 4, 355, 900 15. 9 . 559 35, 520 36, 330 61,090
20 1. 004 . 0645 28, 890 59, 610 11, 585, 500 17. 5 16. 0 15. 5 17, 360 34, 900 3, 941, 500 15.6 . 585 30, 720 32, 830 60, 660
21 . 744 . 0535 40, 000 60, 340 10, 423, 000 27.0 22. 5 19. 5 14, 100 33, 400 3, 968, 100 13. 9 . 553 22, 840 25, 860 62, 670
22 . 742 . 051 37,400 56, 910 11, 117, 100 27. 5 24.0 20. 75 16, 750 34, 280 4,294, 400. 14. 5 . 602 21,680 24 .. 930 58, 720
23 . 748 .0365 38, 480 61,270 10, 542, 000 16.0 16. 25 15. 5 14, 450 25, 460 4, 180, 600 20. 5 . 415 24, 510 25, 980 54, 530
24 . 740 . 035 36, 160 61, 670 10, 724, 800 19. 5 17. 5 15. 0 20, 690 30,840 4, 198, 200 21. l . 500 30, 320 1 31, 610 55, 680 ==1== 60, 190 \ 10. 987, 000
---- - - ---
Average __ 26, 850 ---- -- - ---- -- ---- --- 17, 750 29, 170 3, 927, 200 ----- 487 29, 790 31, 730 I 55, 580
I
0