An investigation was conducted to determine whether there are significant size effects in compressive strength of large Z-stiffened sheet-stringer panels as compared with geometrically similar smaller models and thus to ascertain whether the prediction of the strength of large panels by model tests is reliable. The specimens studied were manufactured from 7075-T6 aluminum alloy and included four representative types of panel designs, with full- and one-quarter-scale panels of each type

Doman, J P

Schwartz, Edward B

English

NASA Technical Reports Server

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~ ~ NATIONAL ADVISORY COMMITTEE 
~ FOR AERONAUTICS 
TECHNICAL NOTE 3756 
STUDY OF SIZE EFFECT IN SHEET-STRlliGER PANELS 
By J. P . Doman and Edward B. Schwartz 
Naval Air Material Center 
NACA 
Washington 
July 1956 
https://ntrs.nasa.gov/search.jsp?R=19930084675 2020-06-17T18:53:42+00:00Z

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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
TECHNICAL NOTE 3756 
STUDY OF SIZE EFFECT IN SHEET-STRINGER PANELS 
By J. P. Doman and Edward B. Schwartz 
SUMMARY 
The object of this study was to determine whether there are signif-
icant size effects in compressive strength of large Z-stiffened sheet -
stringer panels as compared with geometrically similar smaller models 
and thus to ascertain whether the prediction of the strength of large 
panels by model tests is reliable. 
The specimens for the study were manufactured from 7075-T6 aluminum 
alloy. There were four representative types of panel designs) with full-
scale and one-quarter-scale panels of each type . 
A comparison of the average failing stresses shows that there is no 
significant effect due to the panel size. 
For the panels tested) which failed by general instability) there 
was no significant compressive-strength size effect between the large 
z-stiffened prototype and geometrically similar model panels. 
INTRODUCTION 
With the advent of large aircraft and high ~ing loadings) it has 
become necessary to test scale-model panels because of limitations of 
testing-machine sizes and loading capacities. Geometrically similar 
models of different sizes should) theoretically) all fail at the same 
stress; however) size effects of various sorts might influence the failing 
stress . The size effects may be present because of variation of mate-
rial properties with sheet thickness) accuracy of construction) the 
impracticability of extending the geometrical similarity to the riveting) 
and various other factors. 
The object of this project was to determine whether there are sig-
nificant size effects in compressive strength' of large Z-stiffened sheet-
stringer panels as compared with geometrically similar smaller models and 
thus to ascertain whether the prediction of the strength of large panels 
by model tests is reliable. 
2 NACA TN 3756 
This work was conducted at the Aeronautical structures Laboratory 
of the Naval Air Material Center and has been made available to the 
National Advisory Committee for Aeronautics for publication because of 
its general interest. 
DESCRIPTION 
The test specimens for this study were manufactured by standard pro-
cedures using standard sheet material of 7075-T6 aluminum alloy and 
available aluminum-alloy rivets. The stiffeners were extruded from 
special dies in order to have Z- stiffeners of desired proportions and to 
obtain geometric similarity, but standard Aluminum Company of America 
extrusion tolerances, outlined in reference 1, were used. 
The panels were designed in accordance with the method of designing 
for maximum structural efficiency, as outlined in reference 2. The basic 
parameters and their representative values used in the four types of 
panel designs are presented in table I. Reference 2, which deals with 
2024-T, was used because, at the time of designing the panels, no design 
charts for 7075-T6 panels were available. Without actual test work there 
was no way of accurately obtaining analogous sets of curves for 7075-T6. 
Therefore, for lack of a better method, it was assumed that the nondimen-
sional, optimum-panel-proportion curves for 2024-T would hold with suffi-
cient accuracy for 7075-T6. The diameter and pitch for the rivets of the 
panels were chosen in accordance with references 3 and 4 in order to 
obtain optimum strength and practical spacings. 
Three panels of each of the four types were manufactured . Geometri -
cally similar panels, one-~uarter scale of the designed panels, were also 
manufactured, using standard procedures and standard sheet thicknesses. 
Comparing the panel designs for this study against the subse~uently pub-
lished design charts for 7075-T6 in reference 5, the charts show that the 
panel proportions were not far from the minimum weight proportions and 
that the panels were to fail as columns without previous sheet buckling. 
The ends of all panels were machined to give good contact surfaces. 
Each panel was installed in the testing machine and loaded to 3 percent 
of the predicted failing load. The contact surfaces were visually checked 
and remachined, if necessary, to give a good contact with the testing-
machine platens. 
The final machined dimensions of the full- and one-~uarter-scale 
panels are presented in table II. The symbols for the dimensions are 
defined in figure 1 and in appendix A. 
All panels had SR-4 electrical resistance-wire strain gages installed 
back to back across the center of the panel on the sheet in the middle of 
• 
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NACA TN 3756 3 
each bay. The full-scale panels had additional back-to-back gages 
installed across the center of the panel on the outstanding flanges of 
the Z-sections. 
METHOD 
The panels were tested in compression to failure in the 5,000,000-
pound-capacity, universal, hydraulic, testing machine. Figure 2 shows a 
full-scale panel being installed in the testing machine. The panels were 
centered in the testing machine, held straight and in position by the 
testing-machine alining bars, and loaded to 3 percent of the estimated 
failing load. The alining bars were withdrawn from the panel in order to 
,check the contact surfaces between the machine platens and the specimens. 
Strain readings were taken at convenient increments of load in order to 
determine whether the panels were loaded evenly between the sheet and 
stiffeners and across the panel width. The two tapered "leveling disks" 
of the testing machine were moved as necessary in order to tilt the 
loading surface of the testing machine to obtain even load distributions. 
Less than 10-percent variation in strain readings at 15 percent of the 
estimated failing load was considered even load distribution. The strain 
gages were read during tests in order to detect, by the strain-reversal 
method, the presence of buckling. The loads indicated were accurate to 
within tl/2 percent of the true load applied. 
Compression coupons were made and tested from each component of all 
panels in order to find a 0.2-percent-offset compressive yield stress for 
the panel materials. 
RESULTS 
The failing loads and calculated stresses (piA) for the panels are 
presented in table III. In order to obtain data comparable on the basis 
of the same material strength, the mean stresses for the one-Quarter-
scale panels were corrected for difference in material strength between 
the full- and one-Quarter-scale panels according to the nondimensional 
material correction chart for 7075-T6 clad sheet in reference 6 . Both 
corrected and uncorrect ed stres ses are included in table III. 
Figures 3 to 14 show the failed specimens in order of type. 
two views of each large panel type are shown and then one view of 
small type is shown. All panels failed suddenly, as columns, and 
interrivet or sheet buckling occurred. 
First, 
each 
no 
4 NACA TN 3756 
The average compressive yield strengths (O. 2-percent offset) of 
the 7075 -T6 material were: 
Full-scale sheets, psi 
Full-scale stiffeners, psi 
1/4- scale sheets, psi .. 
1/4-scale stiffeners, psi 
77,160 
80,200 
70,555 
74, 630 
Because two of the failing stresses for the full-scale type D panels are 
very nearly equal while the third is considerably larger, there is a 
tendency to reject this large value as being an "outlying observation." 
Although this could not be justified on the basis of these three stresses 
alone, it can be shown after an estimate of the experimental error based 
on 21 other failing stresses that the difference between the largest type 
D panel observation, 58, 650 psi, and the other D panel observations is 
statistically significant at the O.5-percent level. (See appendix E.) 
This means that if the largest observation is rejected the probability is 
only 1/200 that a wrong decision was made. In view of this, the high 
stress for the one type D panel can be r e j ected . 
It can be seen, by comparing the average failing stresses in 
table III, that the greatest variation between full- and one-quarter-scale 
panels is only 2 .8 percent. Comparing the full- 9 cale-panel stresses with 
the corrected one -quarter - scale stresses shows a reduction of variation 
to 2 .4 percent . 
The only size-effect factor observed during the study was the type 
of failure. At failure of the one -quarter-scale panels, the web and out-
standing leg of a few of the Z-section stiffeners jumped off the panels. 
At failure of full-scale panels, nearly all the Z-section stiffeners 
either jumped off or shattered . This effect can be observed by comparing 
the figures showing the failed specimens. 
CONCLUDING REMARKS 
There was no significant size effect in the compressiye strength of 
the large -scale Z-stiffened panels tested as compared with geometrically 
similar small-scale panels. Therefore, the compressive strength of large-
scale panels failing by general instability may be predicted from model 
tests or accepted design data presented as nondimensional parameters. 
Aeronautical Structures Laboratory, 
Naval Air Material Center, 
Philadelphia, Pa., June 13, 1955. 
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NACA TN 3756 
A 
bA 
bF 
bS 
bw 
c 
d 
L 
P 
Pi 
P 
r tw 
s 
ts 
tw 
W 
APPENDIX A 
SYMBOLS 
cross - sectional area 
width of attached flange) in . 
width of outstanding flange) in. 
spacing of stiffeners on sheet) in. 
width of stiffener web) in . 
coefficient of end fixity 
rivet diameter) in . 
length of panel) in . 
load) kips 
load per inch of panel width) kips/in . 
rivet pitch) in . 
rivet spacing) in . 
thickness of sheet) in . 
thickness of stiffener web) in. 
width of specimens) in . 
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6 NACA TN 3756 
APPENDI X B 
STATISTI CAL ANALYSIS 
By Edward B. Schwartz 
Formula 12.7 . 4 on page 333 , of "Statistical Theory With Engineering 
Applications" by Hald (ref. 7) may be written 
X( ) - X 
n P ~ ~P (1 + 2) rn-=-l Sf 1 f ~=-n-= 
where 
1 - P 
n 
n number of observations in sample (3 herein ) 
P-fractile of cumulative distribution of X(n ) 
X(n) largest observation in a sampl e of n 
X 
f 
sample mean 
estimate of population variance computed from a second inde-
pendent sample from same population (herein, the remaining 
21 observations) 
number of degrees of freedom of this estimate (herein, 
7 X 2 = 14) 
normally distributed variable with zero mean and unit variance 
The sample of n is assumed to be drawn from a normally distributed 
population. 
Each group of three stresses furnishes an estimate, with t wo degrees 
of freedom, of the population variance. On the assumption that all 7 
such values are estimates of the same population variance, they can be 
pooled to give a single estimate of 14 degrees of freedom. Doing this 
NACA TN 3756 
gives 
Sf = 1 )650 lb 
Values of can be obtained from standard s t at istical tables . 
Application of the above formula now shows that 
x( ) = 58 650 > X( ) n ) n 99 . 5 percent 
Therefore ) the value 58) 650 psi can be rejected as an "out lying obser -
vat i on" with 99 . 5-percent certaint y . 
7 
8 NACA TN 3756 
REFERENCES 
1. Anon. : Alcoa Structural Handbook. Aluminum Co . of Am. (Pittsburgh)) 
1950 . 
2 . Schuette) Evan H.: Charts for the Minimum-Weight Design of 24s-T 
Aluminum-Alloy Flat Compression Panels With Longitudinal Z-Section 
Stiffeners . NACA WR L-197) 1945 . (Supersedes NACA ARR L5F15 .) 
3. Dow) Norris F .) and Hickman) William A.: Effect of Variations i n 
Diameter and Pitch of Rivet s on Compressive Strength of Panels With 
Z-Section Stiffeners - Panels of Various Lengths With Close Stiffener 
Spacing . NACA TN 1421) 1947. 
4 . Dow) Norris F.) and Hickman) William A.: Effect of Variation in Diam-
eter and Pitch of Rivets on Compressive Strength of Panels With 
Z-Section Stiffeners. I - Panels With Close Stiffener Spacing That 
Fail by Local Buckling . NACA WR L-44) 1945. (Supersedes NACA 
RB L5G03 .) 
5 . Hickman) William A.) and Dow) Norris F. : Direct-Reading Design Charts 
for 75S-T6 Aluminum-Alloy Flat Compression Panels Raving Longitudinal 
Extruded Z-Section Stiffeners. NACA TN 2435 ) 1952. 
6 . Anon. : Strength of Metal Aircraft Elements . ANC-5, Munitions Board 
Aircraft Committee) Revised ed .) J une 1951. 
7 . Rald) A.: Statistical Theory With Engineering Applicat i ons . J ohn 
Wiley & Sons) Inc.) 1952 . 
L _____________________________ _______ _ 
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NACA TN 3756 
TABLE I 
PANEL DESIGN PARAMETERS 
Structural 
Panel loading 
twi ts type parameter, tWJ in. tSJ in. bp 
Pi/Live 
(a) (a) (a) (a) (a) 
A 0.4 0·5 0.25 0·5 0.5bw 
B .4 LO .25 .25 
.5bw 
C .8 
·5 . 25 .5 .5bw 
D .8 LO .25 .25 .5bw 
a Pi load per inch of panel width, in. 
L length of panel, in. 
c coefficient of end fixity 
tw thickness of stiffener web, in. 
ts t hickness of sheet, in. 
bF width of outstanding flange, in. 
bW width of stiffener web, in. 
bA width of attached flange, in. 
9 
bA 
(a) 
9tw 
9tW 
9tw 
9tw 
10 NAeA TN 3756 l 
TABLE II 
PANEL DIMENSIONS 
Panel Sheet Z-stiffener Rivets 
Type Scale Number L, W, ts, Number ~, hA, b\(, tw, d, p, s, in. in. in . in. in . in. in. in. in. in . 
1 1611 8 622 8 
Full 2 1611 8 622-8 1/2 6 21 8 
21 
4 6.1-32 1/4 3/4 21 1; 12 
3 161~ 622 8 
A l~ 1 ~ 16 
1/4 2 ~ l~ 1/8 6 ll/16 9/16 115. 1/16 3/16 9/16 3 2 16 32 
3 401 2 l~ 16 
l 1722 8 4~ 32 
Full 2 171 4i 1/4 8 21 8 
21 
4 61:-32 l/4 1/2 11 2 a 8 
3 1722 8 4~ 16 
B 
1 ~ 121 2 
1/4 2 W. 4 121 2 l/l6 8 ll/l6 9/16 Ll5 32 l/l6 l/8 3/8 Lll 16 
3 44ft 121 2 
l L07~ 16 54J 8 
Full 2 L071 54J l/2 8 21 21: l l/4 3/4 21: 71: 8 8 2 4 532 4 2 
3 l06 541 8 
c 
l 27 l~ 4 
l/4 2 27 l~ l/8 8 5/8 9/ 16 11: l/l6 3/16 9/16 11 
. 4 4 8 
3 27 l~ 4 
l 12at ~ 8 
Full 2 1287 ~ l/4 LO 2~ 21 l l/4 l/2 11 ~ 8 16 2 4 5-3'2 2 4 
3 12iL 8 ~ 8 
D 
l 33 II 
l/4 2 33 l~ 8 l/l6 lO 5/ 8 9/16 11 4 l/l6 l/8 3/8 12.. 32 
3 33 II 
L 
TABLE III 
FAJI.,nm LOADS AND CALCULATED STRESSES 
Load, lb Stress, P /A, psi Mean stress , psi 
Panel 
type Full 1/4 scale 
Full 
1/4 scale 
Full 
1/4 scale scale scale scale 
2,290,000 135,000 47,720 45 , 3&::l 
A 2 , 350 ,000 150,400 49,010 50 , 550 48,460 47,393 
2 , 330,000 137,600 48,590 46,250 
1, 532,000 95 , 400 44,490 44 , 290 
B 1,516,000 91 , 200 44,030 42 ,340 44 , 960 44 ,083 
1,600,000 97,000 46,360 45 , 620 
2 , 850 ,000 173,000 60 , 220 58, 620 
C 2,750,000 170,000 58,170 57 , 610 59, 930 59,077 
2 ,900,000 120 ,000 61, 340 61,000 
1,790,000 109,000 51, 210 48,920 
D 1,&::l0,000 110,000 51, 520 50 , 270 a51,365 49,910 
2 ,050,000 112,600 58, 650 50 , 540 
aHighest failing panel stress rejected (see appendix B). 
Corrected stress , 
1/4 scale 
48,340 
44,303 
60, 554 
50,159 
--
~ 
~ 
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--.1 
\Jl 
CJ'I 
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12 NACA TN 3756 
s 
• 
I ~ ...,.1 r" ~ ~ 
'-t-" 0J 
bl 
i'l 
tw- - 1_ / r 
• 
Figure 1.- Symbols for panel dimensions (see table II and appendix A). 
~~--------- - -- ----- - -----
NACA TN 3756 13 
L-93499 
Figure 2.- Installing full-scale panel in 5,OOO,OOO-pound-capacity 
testing machine. 
14 
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NACA TN 3756 
L-93500 
Figure 3.- Stiffener side of failed full-scale type A panel. 
NACA TN 3756 15 
Figure 4.- Sheet side of failed full-scale type A panel. L-93501 
16 
L. ____ . 
NACA TN 3756 
L- 93502 
Figure 5. - Stiffener side of failed full - scale type B panel. 
NACA TN 3756 17 
L-93503 
Figure 6.- Sheet side of failed full-scale type B panel. 
18 
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NACA TN 3756 
L-93504 Figure 7.- Stiffener side of failed full-scale type C panel . 
NAeA TN 3756 19 
Figure 8 . - Sheet side of failed full - scale type C panel. L- 93505 
20 NACA TN 3756 
L- 9~50 6 
Figure 9 .- Stiffener side of failed full- scale type D panel . / 
NAeA TN 3756 21 
Figure 10 . - Sheet side of failed full- scale type D panel. 1- 93 507 
22 NACA TN 3756 
Figure 11.- Failed one-~uarter-scale type A panel. L-93508 
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NACA TN 3756 23 
Figure 12.- Failed one-quarter- scale type B panel. L-93509 
24 NACA TN 3756 
Figure 13.- Failed one- quarter- scale type C panel. L-93510 
NACA TN 3756 25 
Figure 14.- Failed one-quarter-scale type D panel. L-93511 
NACA - Langley Field, Va. 


Study of Size Effect in Sheet-stringer Panels

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