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INDUSTRY &, SCIENCE
File 629.13/Un3as/No. 706 AIR CORPS TECHNICAL REPORT No. 4217
AIR CORPS INFORMATION CIRCULAR
PUBLISHED BY THE CHIEF OF THE AIR CORPS. WASHINGTON, D. C.
Vol. VIII December 15, 1936 No. 706
THE COMPRESSIVE STRENGTH OF
STAINLESS STEEL SHEETSTRINGER COMBINATIONS
PART III CYLINDRICAL SPECIMENS
(AIRCRAFT BRANCH REPORT)
UNITED STATES
GOVERNMENT PRINTING OFFICE
WASHINGTON : 1937
Ralph Brown Draughon
LIBRARY
JUN 19 2013
Non·Depoitory
Auburn University
ULA IN.G
TABLE OF CONTENTS
Page
Su1nmary _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1
Object________________________________________________ ___________________________________ ___ 1
Descript ion __ ___ __ __ ____ ______________ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 1
Method of testing ____________________ __ __ ___ ___ ____ ____ ____ __ _____ ____ __ ______ __ ______ _______ 1
Di scus~on _ __ ___________ _ __________________ _ _________________________________________________ 1
Sy1nbols ___ _ ____ ___ ______ ______ ____ ________ ___ _____________ _______ ___________ ___________ 1
R eview of essential variables__ _______________ __ __ ____ _______________________ __ __ ____ _______ 2
Methods of expressing stren gth properties ___________________________________________________ 2
Average stress from PfN values _______________________________________________ __ _____ ___ ___ 3
R elat ionship between Pf N, average stress, and percent reinforcement __ __ __ __ ____ ____ ________ __ _ 3
The influence of curvature on PfN values ______ ___________ ____ __ _________________ __________ 3
The effective width coefficient " C"               4
The influence of curvature on column properties ___ __ __ ____________ ___ ____ ____ ____________ ___ 5
Conclusions and r ecommendatio11s ______ ______ __ __________ _______________________________ ____   5
References_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 5
Appendix A                6
TabulatiOn data ____ _____________ ___ ________ ___ ___ __ _____________ ·_____ _________ ______________ 8 10
F igures 1 to 37, in clus ive __ _______________________ ______ ·   11 24
LIST OF FIGURES
F1 ,1 u RE 1. T ypical stringer.
2. Column properties of flat sp ecimens .
3. P / N vers us t for flat specimens.
4. Stiffener failing load v.ers us pitch for vari ous cu rvatures, t = 0.014.
5. Stiffener fai ling load ver sus pitch for vario us curvatures, l = 0.020.
6.Stiffener failing load versus pitch for \r~i o u s curvatures, 1= 0.030.
7.StiffeneJ~failing load versus pitch for various curvatures, t = 0 .050.
8.Stiffener unit load increase due to cur va.t ure versus R2f pl, L = 11.
9 . Stiffener unit load increase due to cm vature ver sus R2f pt, L = 15.
10. Stiffener unit load in crease due to curvature versus R2f pt, L = 22.
11 . Stiffener unit load increase clue to curvature ver sus R2f pl, L = 3l.
12. Stiffen er unit load in crease due to curvature versus R2 fr,t, Log  Log Plot.
13. Stitfener uni t load ill crease due to curvature Ye rsus R,zf pt, Log  Log Plot.
14. R atio: (Pf l\T)cf (Pf N )1 versus Rf t.
15. Ratio: (Pf l\T) cf(PfN )1 versus Rf t.
16.Ratio: (Pf l\T)cf(Pf l\T)1 versus Rf t.
17.R atio: (Pf l\T)cf(PfN )1 \·ers us Rf t.
18. R atio: (Pf f\T)cf (Pf l\T)1 versus Rf t.
19. Ratio: (Pfl\T)cf(PfN )1 versus Rf t.
20. R atio: (PfN)cf(PfN )1 versus Rf t.
21. Ratio: (Pf Mcf (Pf N )1 versus Rf t.
22. Loads carried by stiffeners alone stabilized by a closing sheet of 1= 0.
23. The influence of curvature on effective width coeffi cient. L = 11 in ches.
24. The influence of curvature on effective width coeffi cient. L = 15 in ch es.
25. The infl.uence of curvature on effective width coefficient . L = 22 inches.
26. I nfluence of covering sheet on stiffener unit loads.
27. PfA vers us Rft at constant pitch. L = ll inches.
28. PfA ver sus Rft at constant pitch. L = l5 inches.
29 . PfA versus Rft at constant pitch. L = 22 inches.
30. PfA versus Rft at constant pitch. L = 31 inches.
31. PfA versus Lat varying pitch and Rft .
32. PfA versus Lat varying pitch and Rf t.
33. PfA versus Lat varying pitch and R/t.
34. PfA versus Lat varying pitch and Rf t.
35. Method of testing.
36. Method of testing.
37. Methocl of testing.
(Il)
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4 193
THE
\
COMPRESSIVE STRENGTH OF STAINLESS STEEL
SHEET~STRINGER COMBINATIONS
PART III (CYLINDRICAL SPECIMENS)
(Prepared by C. G. Brown, J. Matulaitis, and J. E. Younger, Materiel Division, Air Corps,
Wright Field, Dayton Ohio, June 2, 1936)
SUMMARY
T he most satisfactory method fo und for t he expression
of t he test results was on t he basis of Pf N, or load
per stiffener. Pf N values are a function of stiffener
shape, t hickness, and length and a re also influenced by
sheet t hickness, and for curved skin also by curvature
and stiffener pitch.
T he fun ctions of length and sheet t hickness were,
for the stiffener section employed >and for uncurved
sheet, fa irly well defined . It was fou nd t h!Jt for small
val ues of skin t hickness t he i11ft uence of curvat ure
co uld be represented, t,o a fair degree of acc uracy, in
terms of R2f lp. T he influence of curva t ure was to
increase th values of Pf N for curved sheetstiffener
combinations over t le values for uncurved. T he
increase over t he un curved sheetstr inger values
appeared to be a hyperbolic function of R2ftp. The
increase clue to curvat ure was observed to be great er
for short columns t han for long columns.
It was noted t hat results expressed on an a verage
stress basis were misleading and unconser vative when
a verage stresses were computed by dividing t he specimen
load by only t he actual area of the specimen,
When average stresses are computed from t he expression
p
N(fl.,+ A ,h) t he results become consist ent. Having
established a Pf N value for a given st iffenN, sheet, and
length, it is possible to p red ict accurately a verage
stresses in terms of stiffener p itch, or per cent reinfor
cement.
OBJECT
To comment furt her on t he behavior of stainlesssteel
sheetstri nger combinat ions and to report on an analysis
of data obta in ed from t he University of California on
tests of 40 reinforced stainless steel cylindrica l shell s.
DESCRIPTION
The cylindr ical shells used in t his series of tests were
of hard drawn 18 8 stainlesssteel sheet, ha ving an
ult imate tensile strength of 175,000185,000 pounds
per square inch.
Stiffener spacings of 1.24, 2.27, 4.33, and 10.51 inches
were employed . T ile fo regoing spacings were respect,
ively co nstant over a 90° quadrant to permit four
tests per cylinder.
The specimens we re spotwelded t hroughout.
METHOD OF TESTING
All tests were performed at t he Uni versity of Californ
ia between Ms.y 10 and May 14, 1935, using a
3,0_D0,000pouncl Sout hwark Emer.v universal testing
machine under the supervision o( Dr . .J. E. Younger.
The specimens were prepared for testing as shown in
fig ures 35, 36, and 37.
Tests were made by loading comp lete indi vid ual
q uadrants wherever poss ible. In some instances, clue
to unsatisfactory flatness of the ends, a complete
quadrant could not be loaded . In such cases calculat
ions \Yere based on t he estimated number of stiffeners
act ing.
Complete cylinders were employed in order to a\·o id
any effects res11lt ing from using specimens of Yery
small included a rc and la rge radius.
DISCUSSION
a. Symbols.
The following symbols have 11C'cn used in the discussion
t hat follows :
E= Modul us of elasticity, pounds per sq uare inch,
taken as 26,000,000 for stainless steel.
t= Thick ness, inches.
R = Raclius of cur vature, in ches.
p = Stiffener pitch, in ches.
A = Area, squa re inch.
A.,= Tot a l area of test specimen .
A.,=Al·ea of stiffener a lone, square inch.
A,,.= Al·ea of a sheet of width p.
P= Total load carried on a test specimen, pounds.
" =Failing stress of stiffener.
N = Number of stiffeners.
T he cylinders varied from 30 inches to 60 inches
diameter and had lengt hs of 11, 15, 22, and 31 inches.
Stiffe ners and sheet were ident ical in thickness, at 
values of 0.01 4, 0.020, 0.030, and 0.050. inches.
Sub1= Refers to flat, u ncurved specimens.
S 'ub.= Refers to curved specimens.
L =Specimen overall length.
I = Moment of iner t ia of stiffener .
C= Effective width coefficient .
114602371 (1)
2
b. R eview of essential variables.
Before taking up t he effects of curvature it is believed
that the case of flat specimens should be reviewed
briefl y. In dealing with flat platestringer combinations
it was observed that the effects of certain variables
must be accounted for in establishing the strength
properties of the combination . These variables, when
isolated, are:
(1) Length, or slenderness ratio effects: It has
been noted from reference 1 that the compressive
strengths of the stiffeners can, in
most cases, be represented by a form of
EulerJohnson curve, using proper end
fixity coefficients.
(2) End fixity, which varies with the method of support,
or t est , and probably with variations
in stiffener shape, is probably responsible for
a good share of scattering in test data.
(3) Stiffener shape: This variable is allimportant
and influences all other Yariables to the ext
ent that in the short column range the
effects of the other variables must be expressed
as applying only to a given stiffener
shape, or cross section. The stiffener shape
factor includes effects due to size, thickness,
flat width and curvature of the elements,
outstanding flange widths, et c. It has been
observed that, generally, the stiffener member
can be credited with carrying the greater
portion of the load supported by sheetstringer
combinations.
(4) Sheet thickness: The influence of sheet thickness
cannot always be completely isolated,
as its effect depends upon the thickness of
the stiffener to which it may be attached.
Its effect is great in the presence of thin
stiffeners and small in the presence of thick
stiffeners.
(5) Stiffener spacing: Stiffener pitch effects are
somewhat uniform, though not entirely detached
from skin thickness effects.
(6) Pitch of the rivets or welds attaching the sheet
to the stringers: Effects clue to pitch of
attaching welds, or rivets, have been observed
to be of a minor nature for reasonable
values of those pitches.
(7) Curvature effects.
c. Methods of expressing strength properties.
Various methods of expressing the strength of flat
sheetstringer combinations have been presented by
those who have conducted resear ch in that field. They
may be summarized briefly as follows :
Method A: Adding the ultimate load carried by
the stiffener alone to the ultimate load carried by
the sheet alone, assuming independent action of
each. It was observed in the work presented in
reference 1 that method A could lead to appreciable
discrepancies if open section stiffener tes.ts
were employed as a basis for the determination
of the strengths of sheetstringer combinations
involving sect ions closed by the sheet, clue to the
prevalence of twisting failures. This method
was not further in vestigated clue to lack of
sufficient test data on closed stiffeners.
Method B: Adding to the ultimate load carried
by the stiffener an effective width of sheet subjected
to the same stress as the stiffener; the
effective width being expressed as a function of
~~t,
On a basis of Pf N, a value of P/ N could be
established that was independent of stiffener
pitch. This stiffener unit consisted of the stiffener
and some unknown amount of sheet working
with it. For a given stiffener, values of P / N
increased somewhat parabolically with sheet
t hickness.
In order to det ermine the applicability of
method B, an empirical failing stress was establish
ed by means of extrapolating the test data
to give a failing stress on a stiffener closed by a
sheet of zero thickness. Then, assuming that
this stress only was developed, effective widths
of sheet were computed. While the stiffener
failing stresses computed on this basis appeared
reasonable, the developed widths appeared to
have unreasonable values. Values of the effective
width coefficient C, in the expression w= C
J!f}. appeared to be a fun ction of l.
Method C: Assuming the stiffener and its effective
width of sheet to behave as a column which fails
by bending normal to theplane of the sheet, the
strength of the column being determined from a
consideration of a slenderness ratio involving the
effective sheet width, and a typical column
curve for stiffeners of similar proportions.
While method C has been shown to be applicable
to opensection tests, the method did not
appear to produce refinements that justified its
application to the stainless steel specimens. A
particular stiffener and several sheet thicknesses
were investigated by calculating u for the
stiffener and its several effective areas of sheet.
No worthwhile variation of u from that of the
stiffener alone was noted. Due to the prevalence
of local failures the method was not extensively
applied.
Method D: On a basis of a verage stress, or total
load carried by a test specimen divided by its
total area. This average stress is often expressed
as a function of percent reinforcement.
Further comments on this basis will be found in
subsequent paragraphs.
Method E: On a basis of P / N, or total load
divided by the number of stiffeners acting. It
was observed that the most useful basic operation
in treating sheetstringer combinations,
curved and fiat, consisted of reducing the data
to a P/N basis. From P/N values, average
stresses, effective sheet widths, et cetera are
readily obtained. This method was found to
be most applicable to the data and will be the
basis for .the greater portion of the discussion
that follows.
d. Average stress f rom PIN values.
Having established values of P f N, and for fiat
specimens, knowing that P/N is independent of stiffener
pitch, it is possible to compute average stresses
directly for any desired pitch simply by dividing P/N
by the the area of the stiffener plus a width of sheet
having the pitch of the stiffeners. That is
P f A
p
When such Yalues were computed for the specimens of
reference 1 it was noted that the computed values
agreed well for low pitches, but did not agree at all for
the greater pitches. The explanation lies in the number
of stiffeners used on the test specimens and in the
manner of computing stresses. Average stresses in
reference 1 were simply computed from the expression
p
A, With only a slight error the latter expression may
be written as
p
NA,,+(Nl )A ,h
which, it will be noted, differs materially from the
expression
p
N(A,,+A,,,)
Since the total load carried is a function primarily of
the stiffener, with the sheet contributing only a relatively
small amount, while the total area is influenced
largely by the amount of sheet included, it may be seen
that omitting one panel of sheet from the area computations
greatly reduced the total area, without materially
influencing total load, and leads to apparent average
stresses that are too high.
In applying t est results, as allowables, to wing or
fuselage construction on an average stress basis, it is
customary to isolate critical stringers and, from a
consideration of the spacings of the adjacent stringers,
assign some allowable P f A, usually determined from
tests on panels of but few stiffeners and computed from
a consideration of only the actual area of the test
specimen. As has been pointed out, this procedure
may, depending upon the spacings involved and the
number of stiffeners in the test specimen, prove
unconservative.
A more conservativ e approach, and one more in
accord wit.h actual conditions, both in a wing or
ruselage and in test specimens, appears to be available
in expressing test results first on a P f N basis. Average
stresses can then be expressed quite simply in terms of
a ny desired pitch.
Where average stresses arc used in this report they
will be computed from PJN values; that is, on the basis
of an equal number of stiffeners and sheet panels.
e. The relationship between P /N, average stress, and percent
reinforcement.
From a consideration of the definitions of "average
stress", and percent reinforcement, an interesting and
3
significant relationship appears. Average stressP
/ N
P /A= A,,+ A ,h
p A,,
ercent reinforcement= A,h+A, ,
Therefore
A,,
or A , ,.+A,, percent reinforcement
P f A = ___P_ ,__/N ___
A, ,
percent reinforcement
=• p I !i. X percent r einforccmcn t
A,,
From the abo,e consideration it is apparent that P f A
is a linear function of percent reinforcement.
The P f A versus percent reinforcement cm~ves of Air
Corps Information Circular No. 697 do not pass through
the origin since P /A values were computed from a
consideration of only the actual· area of the specimen
and not from a consideration of P/N values.
The reader should not be confused by the case of
percent reinforcement= O, for which case, from the
preceding considerations, P /A= O. It is granted that
the expressions may not be strictly correct at very low
values of percent reinforcement, where the contribution
of the sheet to the total load carried will be large.
Though the contribution of the sheet may be large, the
total for an unreinforced sheet will be so small that it
is likely to be an unimportant case and can better be
treated by other considerations.
f . The influence of curvntu re on P f N values.
In order to compare the res ults of the tests on cylinders
with the test data on similar fiat specimens,
figures 2 and 3 were drawn to express the effects of
length and sheetstiffener thickness on P f N values for
fiat specimens. The data for these figures were obtained
from the "C" series tests of Air Corps Information
Circular 697. In the study of the tests on fiat
specimens it was noted that the load carried per stiffener
was independent of pitch, depending only upon length
and sheet or stiffener thickness.
Accordingly, the data for the curved specimens were
expressed on a P f N basis in figures 4 to 7, inclusive,
being plotted in terms of sheet R/t and stiffener pitch
for various lengths. There have been included on these
cu rvcs straight lines at constant P f N representing the
flat specimen test .results. The effects of curvature arc
represented by the departures of the data from these
lines.
The magnitude of the increase in P/N values for
curved specimens over flat values, in terms of R/t alone,
is seen to be rather too erratic to evaluate exactly for
it apparently varies with stiffener pitch, with specimen
length, and with curvature, and is obscured considerably
by the erratic nature of the t est data. In general,
however, P f N values in the presence of curved sheet
increase with diminishing values of R/t, with increasing
stiffener pitch, and with increasing stiffener thickness.
4
It has been shown in appendix I that the load carried
by a stiffener supported by curved sheet may be expressed
by the relationship
P= 'IT2EJ+E(I!_)tp
L' 'IT2 R'
While the above expression deals primarily with a
Euler column, it is believed permissible to substitute
'IT2EI
for the Euler load £2 the value of Pf N for a fiat
sheetstiffener unit, as obtained from the EulerJohnson
curve that expresses the column properties of that
specimen, and for P, the value of Pf N for the curved
specimen. The expression then reads
<PfN)c= (PfN) 1+~Gfz)v
It will be uoted that when p=O, (Pf N)c= (Pf N)1, which
. trend was observed to some extent in figures 4 to 7,
inclusive.
(Pfl'v)c=(PfN)1 again when R is infinite
Rewriting the expression it becomes(
P f N) c (Pf N)1= K~2
E
where K=;'J.£2
that the d ifference in Pf N values
may be a fun ction of tp fR2 for given
Using the same method for computing "C" that \vas
used in Air Corps Information Circular No. 697, values
were computed for the cylindrical specimens. The
stiffener failing stress used for the computations was
determined from figure 22, \vhich was computed from
the data of Air Corps Information Circular No. 697.
It should be pointed out that the values given in
figure 22 are for the stiffeners alone and that for the
purposes of this present discussion the stiffener is considered
closed, or stabilized, by a sheet of zero thicknese,
in order that the total sheet working may be expressed
by only the coefficient "C."
As would be expected from the rather erratic basic
data and from the nature of the necessary calculations,
which involve: First, the difference of test values of
Pf N and estimated values of P; N for stiffeners alone,
and secondly, operations invol ving t2, the results are
rather scattered. It is, however, possible to observe
trends in the results which are worthy of note.
When "C" is plotted against t, the sheet thickness,
trends similar to those noted for the fiat specimens, are
noted. The data are too spread, however, to be represented
by any one curve. It is possible to roughly
approximate the effects of R ft, as in figure 23, b11t, as
will be noted on figure 24, stiffen er pitch as well as Rft
influences "C" values.
Variations due to stiffener pitch 'rnuld be expected
for the curved specime11s, s ince PfN values have been
previously shown to be influenced by stiffener pitch.
gave an .unsatisfactory grouping of data. Accord An exact determination of "C" in terms of Rft is
ingly, figures 8 to 11, inclusive, have been plotted in handicapped by lack of large Rft values for the 0.050
terms of R2ftp, " ·hich gave a more useful grouping cylinders and lack of small R ft values for the 0.014
of the data. A fairly definite trend toward hyper cylinders. The above discussion concerns the case of
bolic variation is apparent from these curves. It will an assumed, or empirical, stiffener failing stress.
which indicates
previously noted
values of L.
tp It was found that a plot of (P/ N)c (Pf N )1 against R'
be noted, however, that there is a considerable separa The remaining case of using an effective width detertion
of the data for the higher thicknesses. mined by other means will also be discussed briefly, not
For a given length of specimen a single curve could because of any influence of curvature, but to add to an
well represent the data for the 0.014 and 0.020 speei understandi.ng of the case. Having isolated a stiffener
mens with reasonable accuracy. A fairly well clefined unit, comprising the stiffener and its effective width of
function is apparent for those thicknesses when the sheet, and knowing by test the total load, or Pf N, carried
data are plotted on loglog paper, as in figures 12 and by that stiffener unit, two unknowns still remainthe
13. The constants, however, vary rather erratically stiffener failing stress, and the effective sheet width.
due to the influence of length , and a consistent expres By assuming one of these the other may be calculated.
sion for the influence of R2 ftp is lacking. ln order to The procedure used in Air Corps I nformatio11 Circular
express the influence of curvature in a more quantita No. 697 was to establish a value for th e stiffener fa iling
ti ve sense, figures 14 to 21 \\·ere plott.id to shO\Y the 8tress and from that calculate all effecti ,.e width coeffiratio
of (PflV)cf (Pf N)1 j11 terms of Rft aud length. cient, as has bee11 discuseed in the paragraphs preceding .
While the data are quite scatt ered , certain trends a.re The reverse.procedure \\'Ou ld be for the flat specimens
apparent, namely: • to take the effecti,·e " ·id th as indicated by Von J\.arman ':;
(1) An increase ill the stiffe11er unit load ratio "·iU1 expressioudecreasing
llf t, as \\·oulcl be expected.
2
_
1 7 j!J.1
(2) An increase i11 the stiffellcr un it load ratio " ·ith w · ' O''
increasing specimen length. This effect and determine the value of O' , that \\·ould satisfy these
could be expected from a consi deration of conditions. This may be accomplished as fo11ows:
the variation of the effective " idth of sheet PfN= (A.,,.+ A,,) O'
with stress; namely, an increase of effective
width \vith decreasing stress .
(3) A decrease in the stiffener unit load ratio with
decreasing pitch.
g. The e:f!ective width coefficient . "C"
Let
and
For the purpose of comparing the results of tests on
cun·ed specimens \\·ith those on fiat specimens, the or
effective 11·idth coefficient will be investigated briefly .
. /E
= (1.7y;;:t',,.+A,,)O'
l'f N = l. 7JE;,J;12 ,,.+ A,,O'
K = l.7,/E
x=J;
PfN = Kxt' ,h+A,,x2
A , ,x'+ Kt2 ,,.x  Pf N = 0.
5
From which the stiffener failing stress necessary to
satisfy t he condition that the effective width of sheet
\rnrking with the stiffener is equal to l.7~t can be
found .
. ~~ Values of u for effectiv e sheet 'vidth = l.7  t. L =
• (J
9};, in ches.
u for Sheel t
sti ffener ~·~
. Stiffener t closed
by sheet 0.00\J
of 1=0
0.014 o.orn 0.029 0.049
_ _ __ , ___   
0014 .. ...•..... 92,000 11 6, 000 130, 500 131,500 136,000 104.000
0.019 __ __ __ __ ___ 105, 000 126, 000 134, 000 134, O:JO 147, 000 132, 000
0.029 ______ _____ 115, 000 124.000 122, 000 137, 000 1 134, 000 127,000
0.049 ___ ________ 11 5. 000 120, 000 122, 000 125, 000 135, 000 144, ()(){)
The tabulat ion above shO\VS a comparison of u values
for both bases of computation. The results appear
fairly consistent and reflect, to some extent, variations
that might be expected from an examination of figure 26.
Since the effective widths computed, when u is that
for a stiffener closed by a sheet of t = 0, appear unreasonably
large, exceeding in some cases the pitch of the
stiffeners, and since the values of u , computed for an
effective width of 1.7..j~t a rc not greatly different, t he
use of t he latter effecti ve \\'idth is probably t he more
desirable procedure.
It should be recalled that t he stiffeners employed in this
investigation were attached to the sheet by two rO\\'S of
welds. Should a stiffener be attached by a single row of
welds, or by two rows at a different spacing, the effective
widths of sheet would probably change somewhat.
h. 7.'he influence of curvature on column properties.
In discussing the effect of curvature on length, the re
must be grouped with length effects the variables fixity
and stiffener shape which were considered the same
throughout t he tests. While the ends of the circular
specimens were supported by circular rings, and the
flat specimens were not, it could not be observed t hat
t he end conditions were sufficiently different to ·wa rrant
t heir being considered as different .
In this discussion it must be borne in mind that the
results presented are for the particular case of stiffeners
and skin of equal t hickness, and a particular stiffener
shape. Figures 31 to 34, inclusive, where average
stresses at failure ha ,·e been plotted against length ,
illust rate t he effect of cunature to some extent. Ri11ee
both curvature and t hick11 ess were varied to obtai11 t he
plotted range of Rft values, t he possibility exists t ha t.
some of the variation noted may be clue to t he res ult
of changes in stiffener failing load \vith changing t hickness.
It " ill be noted t hat t he column effects could
well be represented by forms of EulerJohnson curves,
the constants of which would be greatly influenced by
pitch, skin thickness, and curvature. It will be observed
t hat pitch and curvature effects overlap to a
considerable extent. Plotting P fA against R/t for
eonstant lengths and pitches, a slightly different sha pe
of curve is obtained, as in figures 27 to 30, inclusi,·e.
Plotting in t his manner it " ·ill be noted that a general
continuity of t he data exists, t hough t he usual experimental
scattering is apparent.
The above means of representing the data are not
necessarily conclusive since insufficient data exist to
extend, for a given pitch and length, a curve throughout
t he R ft range for a given t hickness. It must be recalled,
t9o, t.hat t he part icular case of sheet and stiffener
of equal thickness is represented. For variations of
the skin thickness, t he stiffener remaining constant, t he
shape and position of t he above mentioned curves would
vary. The extent of these variations in shape and position
of curves with skin t hickness depends upon t he
shape and the thickness of the stiffener.
CONCLUSIONS AND RECOMMENDATIONS
The most satisfactory n1ethod found fo r the expression
of t he test res ults 'ms on t he basis of P f N, or load
per stiffener. P f N values a re a function of stiffener
shape, t hickness, and length and a re also influenced by
sheet t hickness, and for curved skin also by curvature
and stiffener pitch.
The functions oflength and sheet t hickness were, for the
stiffener section employed and for uncurved sheet, fairly
\Yell defined. It \Vas found t hat for small values of skin
t hickness t he influence of curvature could be represented,
to ~• fair degree of accuracy, in terms of R2 /tp. The
influence of curvature was to increase the values of P / N
for cm·ved sheetstiffener combinations over the values
for uncurved. The increase over the uncurved sheetstringer
values appeared to be a hyperbolic function of
RZftp. The increase due to curvature was observed to
be greater for short columns t han for long columns.
It was noted that results expressed on an average
stress basis were misleading and unconservative when
averaire stresses were computed by dividing the specimen
load by only the actual a rea of the specimen.
When average stresses a re computed from the expression,
p t he results become consistent. Having es
N(A81+ A,h)'
tablished a P f N value for a given stiffener, sheet, and
length, it is possible to p redict accurately average stresses
in t erms of stiffener pitch, or percent reinforcement.
Since the results obtained have been on a material
whose use is at prese'nt small it is recommended that the
applicahility of methods used in this report to aluminum
alloy sheetstringer combinations be in vestigated.
Such data as a re available indicate that P f N values for
uncurvcd aluminum alloy sheetst ringer combinations
arc independent of pitch. The data are too meager
to be conclusi,·e and should be supplemented by testi;
t hat are planned so as to prove t he particular point in
q uestion.
REFERENCES
1. Au Investigation of t he Compressive Strength
Properties of StainlessSteel SheetSt ringer Combinations
C. G. Brown and E . H. SchwartzAir Corps
Information Circular No. 697.
2. Analysis of Data on Compressive T ests of Reinforced
Cylinders V. J. Skoglund. Unpublished report
Uni versity of Californ ia.
3. Data on T ests of 40 Reinforced StainlessSteel
Cylindrical Shell s J. E. Younger. Unpublished report
University of Californ ia.
4. N. A. C. A. T echnical Note 455.
APPENDIX A
The equation for the loading on a stringer is (see
fig. A):
d'y Pd2 Efdx,+axzy =f(x) _________ ___ __ ( l )
In which E= Modulus of elasticity of the material.
I= Moment of inertia of the crosssectional
area of the stringer about the neutral
axis perpendicular to the radius of
the cylinder.
P = Load carried by each stringer.
p = L'>c=~• in which n is the number of n
stringers assumed uniformly spaced
around the circumference.
(The stringer is assumed to consist of the stringer
proper with a portion of the cylinder equal to the width
of the Etringer. A portion of the cylindrical surface
wider than this \\·iclth of the stringer may be assumed
if desirable.)
The t erm f(x) is the supporting force exerted by the
cylindrical wall on the stringer. A solution of the
problem depends upon the determination of the nature
of this force.
If we assume that the initial movement of the stringers
toward their buckling state causes a circumferential
stretching or compression of the skin of the cylinder,
we may obtain a solution. While this solution will
not be exact, it will probably give the relationship between
the variables involved. This relationship may
serve as a guide in correlating the experimental data.
The radial load f (x) causes a hoop tension in the skin
of F pounds
F  1 /2fL('x,c) J '" ·d ( · ) (
0
1 0 Slll 0 _____ _________ __ 2)
= + l /2f(x)r[ cos o] "
L'>c o
= +J/2!~:"[  1 (+ l) ] = _f~~r _____ . (3)
= _f(x)r
p
In terms of the deformation in the hoop element and
the physical characteristics of t he material
1,, = Et~ b c) _________________ ( 4 l
in whicht
= thickness of the skin.
c=the circumferentia l lengt h.
b,=the strain in the circumferential length.
In terms of t he radiu s, r 
In which L'>r is replaced by (y), see figure A.
Equating equations (3) and (5)
f(x) ._ t  1 E y _________ ________ (6)
p r
or + J(x) =  E':J!,y r
Thus equation (1) becomes
By lettingp
J2 = Er                  (9)
and
Equation (8) becomesd4y
cl'y
dx' +J2ax2 + n'y= O __           (11)
The solution of which isy=
A cosh a.i;+ B sinh ax+ C cos bx+ D sin bx _. (12)
in whicha=
v  P+.J,}'4n'    ~ (13)
and
b = Vj' + ,1~ 4n' ___ _____ __ ____ (14)
The limits to be satisfied are
(1) When x = O, the bending moment is zero, red2y
quiring that dx2=0
(2) vVhe11 x = L, the bending morneut it> zero,
d2y
req uiring that jx2= 0
(3) When .t = O, y= O
(4) When .c= L, y= O
Limit (3) req11ires t hat
A+ C= O ________________ ( 15)
Limit (J) requires that
Aa2 Cb2= 0_ ___________ ( l6)
Thus A = 0, C= O
Limit (2) requires that
Ba2 sinh aL  Db2 siu bL = O ________ ( l7)
Limit (4) requires that
B sinh aL+D siu bL = O _ _ ____ ( LS)
Solving equation (17) and (18) we o'Jtain 
B (a2tb2) sinh aL = O ___________ (l9)
D (a2+ b') sin bL= O _____ __ ____ (20)
7
Since D, B, a and b cannot be zero, then Thus we note that Euler's critical load is excee<lerl by
sin bL= O _____ _____ ____ _____ (21) an amount which is a function of
Thus for the critical loadbL=
m7r
· and for t he minimum critical load for the length L 
bL, or VP + V~4n' L = 7r _________ (22)
Solving for j2
J.2 = 7vr+2 n:•;L;2 _______________ (23J
s·m ce J· 2 EPI ' an d n ,_ tlpr 2
equation (23) becomes
? 7r2 tp L2 EI=v + 1r2 ~  __________ (24)
P=1r2vEJ+ Ertep (~V ) ________ __ _( 25)
or
P 7r2E tp 1 L2
A= (~)2 +ET' ;i A ___ ___ __ __ (26)
Tf we let
7r2E
( ~) 2 =Pc_ (27)
Where Pc= Euler's minimum critical load,
eq uation (26) becomes
~= Pc+~ (~) (¥)  C28)
11460237  ~
( f.¥) and ~2
_ _ _ _ _ _ _ _ _ _ __ __ (29l
I1  .....
t
I
I
I
·\
I
I
I
I
..,I
I
' " ',
L
! 
\I ,:.__  I CYLWDER
1 / l u.,,,oER LoAo
\ : i
''t~'  __J_
F IGURE A.Cylinder dimensions.
8
TABLE 1. Cornputation of effective width coefficient " C"
g~ ~ q
@ ~
~ q
~ Failing C=~ ~ Failing
~~
8,o Stiff w stress of ~~ ·a El en er 8P Stiff stress of C=t I st iffener =A,, =w =Wft
~~
·a s en er I stiffener = A~h =w =w/t
"' "' alone ~~ ~ "' "' alone rPn. Q alone 0. Q ~ alone
~ fiat tests °[JJ
~ fiat tests
          
lA 3, 400 2, 730 85, 000 0. 0321 2: 28 163 17. 50 Q. 3 21B       7, 320    0. 0861 2.S7 95. 7   5. 47
lB  2, 600  . 0306 2. lS 156     s. 9 21C ·   6, 630       .078 2. 60 S6. 7   4. 96 lC   2, 3SO      .0280 2. 00 143    s . 2 21D  6, 430       . 0756 2. 52 84. 0  4. SO
lD  1, 995        . 0235 1. 68         22A   4, 050       .0476 1. 5S6 52. 9  3. 02
2A     3, 030    . 0357 2. 55 1S3  10. 4 22B  4, 930       . 05SO 1. 935 64. 5  3. 69
2B   2, 320    . 02725 1. 95 139   7. 95 22C      4, 100       . 0482 1. 60S 53. 6      3. 06
2C   1, 600    . OlSS 1. 34 96  5. 55 22D  · 4, 750         .0559 1. S63 62. 1    3. 55
2D    1,690      . 0199 l. 42 SS. 5
   8~3 
23A 12, 500 23, 200 S7, 500 . . 265 5. 3 100. 6 17. 24 5. S3
3A  2,430   . 02S6 2. 04 146   23B    19, 000       . 217 4. 34 S6. s   5. 04
3B   I, 750    . 0204 1. 46 104. 5 5. 9 23C     16, 600      . 190 3. s 76. 0  4. 41
3C       1, 500     01765 1. 26 90      5. 15 23D    13, 500     . 1543 3. 09 61. 8  3. 58
3D       I, 550    .01S2 1. 30           24A 12, 500 13, 400 S7, 500 . 153 3. 06 6 1. 2 17. 24 3. 55
4A   1, 380      . 0162 1. 16 83   4. 75 24B      13, 300     .152 3. 04 60. s  3.53
4B   1,430    .0168 1. 20 so   4. 9 24C   11, 200        .12S 2. 56 5 1. 2   2. 97
4C   I, 060        . 0125 . 89 64       3. 75 24D    9, 300      .1063 2. 13 42. 6   2. 47
4D    1, 620    . 01905 1. 36            2fiA 2, 100 3,300 52, 500 . 0629 4. 49 321 22. 25 14. 45
5A 5, 600 4, 460 98, 000 . 0455 2. 27 113 16. 30 6. 93 25B     2, 460         . 046S 3. 35 239  10. 75
5B   3, 000     . 0306 1. 53 75. 1     4. 6 25C     2,000        . 03Sl 2. 73 195    S. 76
5C   2, 750   . 0281 1. 41 70    4. 3 25D      1, 710     · . 0325 2. 32 166      7. 45
5D   2,S30   . 0289 I. 44 72      4. 4 26A       2, 200          . 0419 2. 99 214    9. 62
6A    3, 560  . 0356 1. 7S S9    5. 3 26B      1, 930        .0367 2. 62 1S7  S. 40
6B    2, 920   .o29a 1.49 75     4. 6 26C     1, S20    . 0346 2. 47 176. 5    7. 93
6C   2, 560   . 0261 1.31 65     4.0 26D     l, 300    . 0247 I. 765 126    5. 66
6D    2,560  . 0261 1. 31 65    4. 0 27A 3, 400 3, 300 59, 400 . 0556 2. 7S 139 20. 9 6. 65
7A   5,400    . 0551 2. 75 137      8. 4 27B   2, 920     . 0492 2. 46 123   5. 88
7B   2,850   . 0291 1. 45 73   4. 4 27C   2, 290    . 03S6 1. 93 96. 5   4. 62
7C     2, 280  . 0233 1.16 58    3. 5 27D     1, 940   . 0327 1. 635 SL s    3. 91
7D   2, 3SO    . 0293 1. 21 61    3. 7 2SA    2, 700       . 0455 2. 28 114   5. 45
SA  760    .007S . 39 19. 5     1. 2 2SB       2, 430       . 0410 2. 05 102. 5  4. 90
SB  580   . 00593 . 296 14. 8     . 91 2SC    2, 090        . 0352 1. 76 88  4. 21
SC    S60        . OOS78 . 439 22. 0      I. 35 28D    1, 740       . 0293 I. 465 73. 2 26.7 3. 50
SD    1, 950    . 0199 . 995 49. 7    3. 05 29A 5, 200 9, 200 60, 600 .152 5. 07 169. 0 S. 17
9A S,900 s . 300 103, 500 . 0802 2. 67 89. 0 15. S4 5. 62 29B    6,050      . 0999 3. 33 111.0  5. 36
9B    6, 250    . 0604 2. 01 67. 0     4. 23 29C    5, 000    . 0825 2. 75 91. 7   4. 43
9C  6, 530      . 0631 2. 11 70. 3       4. 44 29D   3, 640      . 0601 2. 01 67. 0   3. 24
9D    5, 770       . 055S 1. S6 62. 0      3. 92 30A    3, 450    . 0570 1.90 63. 3  3. 06
JOA   9, 280    . OS96 2. 99 99. 6       6. 29 30B   2, 410    . 0398 1. 33 44. 4  2.15
lOB  6, 650         . 0640 2. 13 71. 0      4. 4S 30C    l , 410       . 0233 . 777 2. 59   1. 25
lOC  5, 650      .0546 1. S2 60. 6  3. S3 30D       930      . 0153 . 51 17. 0  . 82
lOD   5, 330       . 0515 1. 72 57. 3     3. 62 31A S,900 17, 800 62, 000 .'287 5. 74 114. s 20. 5 5. 6 llA    7, 930      . 0766 2. 55 S5. 0     5. 37 31B   14, 400     . 232 4. 64 92.S  4. 53 llB   4, 000        . 03S6 1. 29 43. 0   2. 71 3 tC   10, 000         .1613 3. 23 64. 6  3.1 5 llC   5, 270       .0510 1. 70 56. 7     3. 5S 31D       5, 300       . 0855 1. 71 34. 2   1. 67 llD   4, 750      . 0459 1. 53 51. 0   3. 22 32A     7, 330        . llS 2. 36 47. 2   2. 3 12A   3, 370      . 0326 l. 09 36. 3     2. 29 32B     7, 330          . llS 2. 36 47. 2  2. 3 12B    4, 140    . 0400 1. 333 44. 4   2. s 32C       3, 280     .0529 1. 06 21. 2  1. 04 12C S, 900 2, 680 103, 500 . 0259 . S63 2S. s 15. S4 l. 82 32D    3, 720     .0600 1. 20 24  1. 17 12D   3, 230     . 0312 1. 04 34. 7     2.19 33A 1, 300 4,430 32, 500 .136 9. 71 694 28. 3 24. 5 13A 15, 200 20, 400 106, 000 .1925 3. S5 77. 0 15. 67 4. 92 33B 2, 360        . 0726 5.19 371  13. 1 13B   17, 900    .169 3. 38 67. 6      4. 32 33C
    
13C    lS, 000 .170 3. 40 68. 0 4. 34     2, 030        . 062.5 4. 47 319   11. 3          33D 1, 710 . 0526 3. 76 269 9. 5 13D  10,000       . 0943 1.886 37. 7    2. 41           14A 22, 100 . 209 4. lS S3. 6 34A 2, 760 .0850 6. 07 434 15. 3              5. 34 34B   l,880       . 0579 4. 14 296  10. 5 14B    16, 300         . 154 3. OS 61. 6    3. 93           i4C 16, 500 .156 3. 12 62. 4 34C l, 450 . 0446 3.19 228    8. 05             3. 9S 34D      1, 470          . 0452 3. 23 231 S.1 7 14D  10, 300     . 0972 1. 944 38.9     2. 4S         15A   lS, 100      . 171 3. 42 6S. 4   4. 36 35A 2, 100 4, S60 36, 700 .132 6. 6 330 26. 6 12.4
15B  15, 300     . 1443 2. S9 57. s 3. 69 35B      3, 160      . OS61 4. 31 215. 5   S. l
15C    14, 700      . 1387 2. 77 55. 4      3. 54 35C     3, os o     . 0840 4. 20 210  7. 9 15D     10, 900  .1028 2.056 41. 1     2. 63 35D      3, 080        . OS40 4. 20 210  7. 9 16A    11, 400     . 1075 2.150 43. 0 2. 75 36A   3, 420       . 0932 4. 66 233  8. 76 16B   11, 700     . 1104 2. 21 44. 2    2. S2 36B        2, 720         . 0741 3. 71 185. 5  6. 97 16C       11, 200          .1057 2. 114 42. 3   2. 70 36C     2, 500         . 0681 3. 41 170. 5    6. 41 16D   S,SOO   . OS3 1. 66 33. 2       2. 12 36D       1, 850        . 0504 2. 52 126. 0   4. 73
17A 2, 900 3, 560 72, 500 .0491 3. 51 251 18. 93 13. 27 37A 3, 2CO 7, 230 37, 300 .194 6. 47 216. 0 26. 4 S. 19
17B      2, 700   . 0372 2. 66 190    10. 04 37B     4, 46 o __________ _ .1195 3. 98 132. 7  5.03
17C  2, 390    . 033 2. 36 16S. 5 S. 9 37C  2, 690      . 0722 2. 41 80. 3  3. 04
17D     2, 580     . 0356 2. 54 lSI. 5    9. 6 37D        2, 23 o ____ ______ _ . 059S 1. 994 66. 4  2. 51
lSA    2, 400     . 0331 2. 37 169. 5   8. 95 3SA   5, 980        . 1604 5. 38 179. 3  6. so
lSB       1, SlO     . 0250 1. 7S6 127. 5   6. 74 3SB     4, 370      .1173 3. 93 131.0  4. 96
18C      l ,S90      . 0261 1.865 133. 3 7. 05 3SC       3, 700    . 0992 3. 31 110. 4  4.19
!SD    1, 980     . 0273 1. 95 139. 3    7. 36 3SD      2, 910        . 07SO 2. 60 S6. 6  3. 28
19A 4, 700 5, 030 S2, 200 .0612 3. 06 153. 0 17. 7S s. 6 39A 5,600 19, 700 38, 900 . 506 10. 12 202. 4 25. S5 7. S3
19B        3, 11 o _____ _____ _ .037S l.S9 94. 5    5. 32 39B      16, 700       . 429 s . 5S 171. 6    6. 65
19C      3, 500     .0426 2.13 106. 5  5. 99 39C    9, 63 o _______ ____
. 2475 4. 95 99. 0   3. 83
19D  ...  3, 420    .0416 2.0S 104. o ______ 5. S5 39D   7, 07 0      . 182 3. 64 72. 8   2. S2
20A   3, 500      . 0426 2.13 106. 5   5. 99 40A    12, 37 o __ _________ . 31S 6. 36 127. 2   4. 92
20B     3, 08 o ___ __ ______ . 0375 l.S75 93. s  5. 28 40B      9,490      . 244 4. 88 97. 6   3. 7S
20C      2,S2 o __ ____ _____ . 0343 I. 715 85. s    4. S3 40C    6, 17 0        . 15S6 3. 17 63. 4  2. 46
20D    2, 74 o ___ ______ __
. 0333 1. 66S 83. 4   4. 69 40D     4, 28 0       . 110 2. 20 44. 0  I . 71
21A 7, 300 9, 770 S5, 000 .115 3. S3 127. s 17. 5 7. 3
I
Speci Failing Thickness
Test G men load, Stiffener+
no num· pounds sheet,
ber p inches (t)
  
100 l A 18, 400 o. 014
B 30, 000 . 014 c 52, 000 .014
D 90, 300 . 014
13 2 A 19, 300 . 014
B 40, 000 . 014 c 65, 100 . 014
J) 117, 000 . 014
9 3 A 17, 800 . 014
n 46, 400 . 014 c 83, 400 . 014
D 143, 700 . 014
97 4 A 23, 900 . 014
n 53, 200 . 014 c 93, 700 . 014
D 175, 600 .014
117 5 A 30, 200 . 020
B 43, 000 . 020 c 75, 200 .020
D 143, 400 .020
IOl 6 A 27, 500 .020
B 59, 600 . 020 c 106, 100 . 020
D 187, 800 . 020
17 7 A 33, 000 . 020
B 76, 000 .020 c 134, 600 . 020
D 231, 500 . 020
105 8 A 31, 800 . 020
B 68, 000 . 020 c 135, 800 . 020
D 264, 500 . 020
133 9 A 51, 600 . 030
B 75, 700 . 030 c 138, 900 . 030
D 249, 100 . 030
25 JO A 54, 500 . 030
B 108, 900 . 030 c 189, 200 . 030
D 327, 500 . 030
29 11 A 50, 500 . 030
B 116, 200 . 030 c 240, 600 . 030
D 396, 000 . 030
121 12 A 61, 300 . 030
B 143, 400 . 030 c 243, 300 . 030
D 425, 000 . 030
153 13 A 107, 000 . 050
B 165, 700 . 050 c 298, 500 . 050
D 428, 300 . 050
129 14 A 112. 100 . 050
B 251, 500 . 050, c 349, 200 . 050
D 588, 000 . 050
145 15 A 100, 200 .050
B 274, 000 . 050 c 509, 200 . 050
D 757, 000 . 050
149 16 A 133, 000 . 050
B 296, 000 . 050 c 554, 000 . 050
D 841, 000 . 050
93 17 A 19, 400 . 014
B 28, 000 .014 c 47, 600 .014
D 93, 200 . 014
89 18 A 21, 200 .014
n 51,800 .014 c 86, 300 . 014
D 156, 200 .014
45 19 A 29, 200 .020
B 39, 100 .020 c 73, 800 .020
D 138, 000 .020
81 20 A 32, 800 .020
B 70, 000 . 020 c 135, 500 .020
D 238, 000 . 020
125 21 A 51, 200 . 030 n 73, 100 . 030 c 125, 300 . 030
D 233, 400 . 030
113 22 A 56, 800 . 03G
B 134, 400 . 030
(' 239, 600 .030
D 421 '900 . 03 0
1 11 inches Lhroughout, including G 16D.
Length,
inches
(1 )
(1)
(1)
(1 )
(1)
(1)
(!)
(1)
(1)
(1)
(1)
(1)
(1)
(1)
(1 )
(1)
(!)
(1)
(1)
(1)
(1)
(!)
(1)
(1)
(1)
(1)
(1)
(1 )
11
11
11
11
11
Jl
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
11
lJ
11
11
11
II
lJ
lJ
11
11
11
11
15
15
15
15
15
15
15
~~
15
15
15
15
15
15
15
15
15
15
l!\
15
15
15
1'
9
TABLE 2
Stiffe ne r
numbe r
5
9
17
3
7
13
23
3
I
9
7
29
5
11
21
35
3
5
7
17
3
7
13
23
3
9
li
29
5
11
21
35
3
5
9
17
3
7
13
23
3
9
17
29
5
11
21
35
3
5
9
17
3
8
11
23
3
9
17
29
5
11
21
35
;J
5
9
17
4
11
18
32
3
5
9
17
4
9
18
32
3
5
9
i
5
I
l
!
1
2
3o I
Pitch,
inches
(p)

10. 51
4. 33
2. 27
1. 24
10. 51
4. 33
2. 27
1. 24
10. 51
4. 33
2. 27
1. 24
10. 51
4. 33
2. 27
]. 24
10. 51
4. 33
2. 27
1. 24
10. 51
4. 33
2. 27
1. 24
10. 51
4. 33
2. 27
1. 24
10. 51
4.33
2. 27
1. 24
10. 51
4. 33
2. 27
1.24
10. 51
4. 33
2. 27
1.24
10. 51
4.33
2. 27
1.24
10. 51
4. 33
2. 27
1. 24
10. 51
4. 33
2. 27
1.24
10. 51
4. 33
2. 27
1. 24
10. 5l
4. 33
2. 27
1. 24
10. 51
4. 33
2. 27
1. 24
10. 51
4.33
2. 27
1. 24
10. 51
4. 33
2. 27
1. 24
10. 51
4. 33
2. 27
l. 24
10. 51
4.33
2. 27
1. 24
10. 51
4.33
2. 27
l. 24
10. 51
•1.33
2. 27
1. 24
PitchX
sheet
thickness
As

0.147
. 0605
. 0318
. 01735






  

 



. 2102
. 0866
. 0454
. 0248
.. _______
 
 



  
 
  
  
 . 3153
.1299
. 0681
.0372
 
  
 
   



 

  


. 5255
. 2165
.1135
. 0620
 




 

 
  
  
  
 
  







  

  

       

  

 
 

 
 
 


Average
area Sheet each As+ AR R R/t
stiffener
AR
   
0. 0407  15 1, 070
    15 
   15 
    15  
  Q. 1877 20 1, 430
 . I0,12 20  
  . 0725 20   . 0407 . 0581 20  
     25 1, 786
  25 
   25  
    25  
    30 2, 142
    30 
   30  
  30  
. 0582   15 750
   15 
   15 
   15   
 . 2684 20 1, 000
    .1448 20   
 . 1036 20    
  . 0830 20 
     25 1, 250
     25 
     25  
       25 
  30 1, 500
    30  
    30  
    30   
  . 4026 15 500
   . 2172 15  
  . 1554 15   . 0873 . 1245 15 
    20 667
   20  
     20  
      20  
   25 833
    25  
   25  
   25  
      30 1, 000
    30  
   30   
     30   
  . 6710 15 300
  . 3620 15 
   . 2590 15  
. 1455 . 2075 15  
         20 400
       20 
     20 
     20 
    25 500
     25 
      25  
  ·· 25  
     30 600
     30 
       30  
   30   
   .1877 15 1070
   . 1012 15 
 .0725 15   
  .0581 15  
   30 2142
 · 30     
     30 
      30  
   . 2684 15 750
  . 1448 15  
   . 1036 15   
   . 0830 15  
   30 1500
     30 
   30  
  30  
    . 4026 1.5 500
  . 2172 15  
   . 1554 15  
 . 1245 15  
      30 1,000
    30 
      30 
  30 
Load R' per stiffener Pt

6, 130 1, 520
6, 000 3, 720
5, 780 7, 070
5,395 13, 000
6, 430 2, 710
5, 720 6, 600
5, 000 12, 600
5, 090 23, 000
5, 830 . 4, 240
5, 150 10, 300
4, 900 19, 700
4, 950 36, 000
4, 780 6, JOO
4, 830 14, 800
4, 460 28, 300
5, 020 51, 800
10, 060 l , 070
8, 600 2, 600
8, 350 4, 950
8, 430 9, 070
9, 160 I , 900
8, 520 4, 620
8, 160 8, 920
8, 160 16, 100
11, 000 2, 970
8, 450 7, 220
7, 880 13, 800
7, 980 25, 200
6, 360 4, 280
6, 180 10, 400
6, 460 19, 800
7, 550 36, 300
17, 200 7l3
15, 150 1, 730
15, 430 3, 300
14, 670 6, 050
18, 180 I, 270
15, 550 3, 080
14, 550 5, 880
14, 230 10, 700
16, 830 1, 980
12, 900 4,810
14, 170 9, 180
13, 650 16, 800
12, 270 2, 850
13, 040 6, 950
11, 580 13, 200
12, 130 24, 200
35, 600 428
33, JOO 1, 040
33, 200 1, 980
25, 200 3, 620
37, 300 760
31, 500 1, 840
31, 700 3, 520
25, 500 6, 450
33, 300 1, 190
30, 500 2, 890
29, 900 5, 500
26, 100 10, 100
26, 600 1, 710
26, 900 4, 150
26, 400 7, 940
24, 000 14, 500
6, 460 1,520
5, 600 3, 720
5, 290 7,070
5,480 13, 000
5, 300 6, 100
4, 710 14, 800
4, 790 28. 300
1,800 5(800
9, 730 1, 070
7,810 2, 600
8, 200 4,950
8, 120 9, 070
8, 200 4, 280
7, 780 10, 400
7, 520 19, 800
7, 410 36, 300
17, 070 713
14, 620 1, 730
13, ~30 3, 300
13, 730 6,050
11, 350 2, 850
12, 230 6, 950
11, 400 13, 200
12 050 24 200
Stress
based
on
whole
sectior!

32, 600
59, 300
79, 700
93, 000
34, 200
56, 500
69, 000
87, 600
31, 000
50, 900
67, 500
85, 200
25, 580
47, 700
61, 500
86, 500
37, 500
59, 400
80, 7 00
0
00
0
00
101, 50
34, 2
58,80
78,8
98,30 0
000
00
00
41,
58, 4
76, 1
96, 10 0
00
00
00
23, 7
42, 7
62, 5
91,
42, 7
000
00
00
()()
00
00
00
00
00
0
69, 7
99, 4
117, 8
45, l
71, 6
93, 6
114, 3
41,80
59, 4 00
00
00
00
00
00
00
00
00
00
00
()()
000
91, I
109, 7
30,4
60, 1
74,4
97, 5
53, l
91, 5
128, 2
121, 5
55, 6
87,
122, 5 00
000
00
00
00
00
00
00
123,
49, 7
84, 3
115, 5
126, 0
39, 6
74,3
102,
115, 80
000
0
00
00
34, 4
55,4
73,
94, 4
000
00
00
0
0
0
50
28, 2
46, 60
66,00
84,80
36, 2
54, 000
79, 20 0
00
00
00
00
00
00
00
97,8
30, 6
53, 7
72, 6
89, 6
42, 4
67, 4
89. 70 0
000
200
00
111,
28,
56, 4
73, 40 0
9 6, 800
10
TABLE 2 Continued
Speci Failing Thickness Pitcbx Aver 1 Stress
'l'est Pitch, sheet age area Load R • based no. G nmuernn ploouandd, s St isfhfeeneet,r + Liennchgeths , Snutimffebneerr inches t hick each As+An Sheet R/t per on ber p inches (t) (p) ness stiffener R st iffener Pt whole A s An section
                
141 23 A 107, 100 0.050 15 3 10. 51         0. 6710 15 300 35, 700 428 53, 200
B 157, 900 . 050 15 5 4. 33         . 3620 15    31, 500 1, 040 87, 000 c 261, 5CO . 050 15 9 2. 27       . 2590 15     29, 100 1, 980 lJ 2, 500
D 441, 600 . 050 15 17 1. 24       . 2075 15  26, 000 3, 620 125, 300
137 24 A 129, 600 . 050 15 5 10. 51               30 600 25, 900 1, 710 38, 600
Bc 283, 500 . 050 15 11 4. 33          30      25, 800 .4, 150 71, 300 498, 100 . 050 15 21 2. 27           30     23, 700 7, 940 91,500
]) 763, 000 .050 15 35 1. 24        30      21, 800 14, 500 105, 000
77 25 A 16, 200 . 014 22 3 10. 51             . 1877 15 1070 5, 4CO 1, 520 28, 750
Bc 22, 800 . 014 22 5 4. 33        . 1012 15       4, 560 3, 720 45, 100 36, 900 .014 22 9 2. 27         . 0725 15    4, 100 7, 070 56, 500
]) 64, 700 . 014 22 17 1. 24     . 0581 15      3, 810 13, 000 65, 500
41 26 A 17, 200 . 014 22 4 10. 51            30 2142 4, 300 · r., toe 22, 900
Bc 40, 300 . 014 22 10 4. 33        30     4, 030 14, 800 39, 800 70, 500 . 014 22 18 2. 27           30      3, 920 28, 300 54, 000
]) 105, 400 . 014 22 31 1.24       30     3,400 51, 800 58, 500
85 27 A 20, 100 .020 22 3 10. 51        . 2684 15 750 6, 700 1, 070 25, 000
Bc 31, 600 . 020 22 5 4. 33           . 1448 15   6, 320 2, 600 43, 700 51, 200 .020 22 9 2. 27         .1036 15     5, 690 4, 950 54, 900
D 90, 700 . 020 22 17 1. 24         . 0830 15        5, 340 9, 070 64, 300
33 28 A 24, 400 .020 22 4 10. 51              ao 1500 6, 100 4, 280 22, 700
Bc 52, 500 .020 22 9 4. 33               30      5,830 10, 400 40, 300 93, 400 .020 22 17 2. 27           30   5, 490 19, 800 53, 000
D 159, 600 .020 22 31 1. 24             30    5, 140 36, 300 61, 900
21 29 A 43, 300 .030 22 3 10. 51           . 4026 15 500 14, 400 713 3.1, 700
Bc 56. 200 . 030 22 5 4. 3:J         . 2172 15     11, 250 1, 730 51, 800 91, 800 . 030 22 9 2. 27            .1 554 15   10, 200 3, 300 65, 600
]) 150, 300 . 030 22 17 1. 24       .1245 15       8,840 6, 050 71, 000 n 30 A 34, 600 . 030 22 4 10. 51             30 1000 8, 650 2, 850 21, 500
Bc 68, 500 . 030 22 9 •1. 33        30    7. 610 6, 950 35, 000 119. 100 . 030 22 18 2. 27           30  6, 610 13, 200 42, 500
D 196; 300 . 030 22 32 l. 24         30     6, 130 24, 200 49, 200
37 31 A 80, 000 . 050 22 3 10. 51   . 67 lO 15 300 26, 700 428 39, 800
Bc 116, 500 . 050 22 5 4. 33 ·    . 3620 15     23, 300 1, 040 64, 400 170, 000 . 050 22 9 2. 27      . 2590 15   18, 900 l , 980 73. sso ]) 241, 000 . 050 22 17 1. 24     . 2075 15   14, 200 3, 620 68; 400
157 32 A 81, 200 . 050 22 5 10. 51             30 600 16, 230 1, 710 24, 200
Bc 178, 500 .050 22 11 4. 33              30    16, 230 4, 150 44, 800 256, 000 . 050 22 21 2. 27            30   12, 180 7, 940 47, 000
]) 442, 000 . 050 22 35 1. 24           30   12, 620 14, 500 60, 700
5 33 A 17, 200 . 014 31 3 10. 51        .1877 15 1, 070 5, 730 1, 520 30, 500
Bc 18, 300 . 014 31 5 4. 33           .1012 15  3,660 3, 720 36, 200 30, 000 . 014 31 9 2. 27         . 0725 15   3, 330 7, 070 45, 900
D 51, 200 ' 014 31 17 1. 24          . 0581 15       3, 010 13, 000 .'\l, 800
1 34 A 12, 200 .014 31 3 10. 51              30 2, 142 4, 060 6, 100 22, 100
Bc 31,800 . 014 31 IO 4. 33               30  3, 180 14, 800 31, 500 49, 600 . 014 31 18 2. 27               30     2, 750 28, 300 37, 900
]) 69, 400 . 014 31 25 1. 24               30       2, 770 51, 800 47, 600
53 35 A 20, 900 .020 31 3 10. 51        . 2684 15 750 6, 960 1, 070 26, 000
Bc 26, 300 .020 31 5 4.33            . 1448 15   5, 260 2,600 36, 400 46, 600 .020 31 9 2. 27      . 1036 15     5, 180 4, 950 50, 000
]) 88, 100 .020 31 17 1. 24            . 0830 15     5, 180 9, 070 62, 400
49 36 A 22, 100 .020 31 4 10. 51             30 1, 500 5, 520 4, 280 20, 600
Bc 43. 400 . 020 31 9 4. 33        30    4, 820 10, 400 33, 300 82, 800 .020 31 18 2. 27           30   4, 600 19,800 44,400
]) 126, 300 . 020 31 32 1. 24            30       3, 950 36, 300 47, 600
61 37 A 31, 300 .030 31 3 10. 51           . 4026 15 500 10, 430 713 25. 900
Bc 38, 300 . 030 31 5 4. 33        . 2172 15  7, 660 1, 730 35; 300 53, 000 . 030 31 9 2. 27       . 1554 15    5, 890 3, 300 37, 800
]) 92, 400 .030 31 17 1. 24        . 1245 15    5, 4:l0 6, 050 43, 600
57 38 A 35, 700 . 030 3 l 4 10. 51              30 1, 000 9, 180 2, 850 22, 800
Bc 75, 700 . 030 31 10 4. 33                   30      7, 570 6, 950 34. 900 124. 300 . 030 31 18 2. 27                  30   6, 900 13, 200 44, 400
]) 195, 800 . 030 31 32 1. 24                30    6, 110 24, 200 49, 100
69 39 A 76, 100 . 050 31 3 10. 51         . 6710 15 300 25, 300 428 37, 700
Bc 111. 500 . 050 31 5 4. 33        . 3620 15   22, 300 1, 040 61 , 600 137, 000 .050 31 9 2, 27     . 2590 15       15, 230 1, 980 58, 700
]) 215, 500 . 050 31 17 1. 24       . 2075 15        12, 670 3, 620 61, 000
65 40 A 71. 900 . 050 31 4 10. 51     30 600 17, 970 1, 710 26, 800
Bc 150; 900 . 0.50 31 10 4. 33                  30    15, 090 4, 150 41, 700 212, 000 .050 31 18 2. 27                30   11, 770 7, 940 45. 400
]) 316, 200 . 050 31 32 1. 24    .   30      9,880 14, 500 47, 600
.. 

11
Radius
R
\
PersPecl:~ve qJ l:!fpY:a.l section
7
14 d
_J_ 1
16 4
.500
St iftener section
FIGURE 1.
.......

;
i
12
FIGURE 2.
FIGURE 3
~: '
; I
: '
' =
13
FIGURE 4. FIGURE 5.
FIGURE 6 . FIGURE 7.
14
F IGURE 8.
FIGURE 9.
15
FIGURE JO.
FIGURE 11.
16
FIGURE 12.
FIGURE 13.
17
F IGURE 14. F' IGURIO 15.
F'1ou1rn 16. Ji' 1GUHE 17.
18
FIGURE 18. FIGURE 19.
FIGURE 20. FIGURE 21.
L
19
H •
FtGURE 22.
FIGURE 23. • F IGURE 24.
20
F !GUH.E 25, FIGURE 26.
+ ·~
''
FIGURE 27.
I
, ' '
~ · j~
I~ @l m .
1;  +
' 'H 1
21
' "
• I
".. · 1
FI G!:HE 28.
' [ ' .. it
., j, . Jt iJi ~ .
~I :i+ HI
1tl1 t!41: w
F IGURE 29.
" }
. . j I "
t  lo,
.;
I .
'.
1..i
. I
22
,+
j±
. HFIGUHE
30.
'I·
FIGURE 31.
23
FIGURE 32.
I I i
I I = =
:m  =
R':m Fffl ~
FIGURE 33.
24
FIGURE 34.
4,000,000pound testing machine in the civil engineer department of
the University of California on which the tests were made. The
heads were micrometered for parallelness of surfaces. They were
found to check to less than 0.001 inch. Pads of 1 inch by 1 inch
duralumin blocks about 3 inches long were used to make contact
Showing the bulkhead reinforcement arrangement to prevent local
failures due to contact of machine. The hoops are ~ inch by
2 inch steel, the internal one an expansion ring and the external
one a contraction ring. No local failures occurred due to end
conditions.
on surfaces to be tested.
FIGURE 35.
0
Specimen between t he heads of the machine. Noteduni.lum in bl •Jcks
nt test section.
Specimen between the heads of the machine. Note cluralumio blocks
at test section.
FIGURE 3fi.
Expansion and cootraction joints for the bulkhead rin gs. pecimen between the heads of t he machine. Note dural u7c1<s at test section.
FIGURE 37,
l L_ _ _ _