EFFECTS OF SHEAR DEFORMATION I N
THE CORE OF A RAT RECTANGULA R
SANDWICH PANE L
Stiffness of Flat Panels of Sandwich Constructio n
Subjected to Uniformly Distributed Loads Norma l
to Their Surfaces -- Simply Supported Edge s
INEGs
_ WED
AND REAFi= iWE D
196 2
N . 1583-A
LOAN COP Y
Please return to :
Wood Engineering Researc h
Forest Products Laborator y
Madison, Wisconsin 5370 5
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FOREST PRODUCTS LABORATOR Y
UNITED STATES DEPARTMENT OF AGRICULTUR E
FOREST
MADISON 5, WISCONSIN
In Cooperation
with the
SERVIC E
University
of
Wisconsin
Supplement tQ
EFFECTS OF SHEAR DEFORMATION IN 'Ii[ CORE OF A
FLAT RECTANGULAR SANDWICH PANE L
Stiffness of Flat Panels of Sandwich Construction Subjecte d
to Uniformly Distributed Loads Normal to Their Surface s
-- Simply Supported Edge d
By
W . J . KOMMERS, Enginee r
and
C . B . NORRIS, Enginee r
Summary
This supplementary report presents the results of experimental testing in sub stantiation of formulas (89) and (90), given in Forest Products Laborator y
Report No . 1583 . These formulas were derived for the central deflection o f
flat sandwich panels having simply supported edges and subjected to a uniforml y
distributed transverse load . They incorporate the increase in the centra l
deflection due to shear deformation in the low-density core materials . Fifty seven tests were performed on 15 flat panels of sandwich construction havin g
facings of 0 .032-inch, 24ST alclad aluminum or eight-ply laminated glas s
cloth . The core materials were balsa wood, cellular cellulose acetate, o r
Forest Products Laboratory corrugated-type paper honeycomb . Evaluation of the
elastic properties of these materials was determined by auxiliary tests .
•
The deflections obtained from the tests of the panels agreed reasonably wel l
with those calculated by use of the formulas presented .
This progress report is one of a series prepared and distributed by the
Forest Products Laboratory under U . S . Navy, Bureau of Aeronautics No .
NBA-PO-NAer 00619, Amendment No . 1, and U . S . Air Force No . USAF-PO (33-038)48-41E . Results here reported are preliminary and may be revise d
as additional data become available .
Report No . 1583-A
Introductio n
the increasing use of sandwich materials in'the building of structures requir ing a high ratio of strengt h - to weight indicates the need for determining th e
strength and elastic properties oP .such materials . Forest Products Laboratory
Report No . 1583 presents the- mathematical analysis for the buckling of sand wich materials under compressive end load and the deflection under unifor m
transverse Load . It is believed that a determination of the adequacy of th e
mathematical fnethods employed can be better obtained from the deflections o f
panels under uniformly distributed transverse loads than from the critica l
loads of panels subjected to edgewise compression because the latter usuall y
are not sharply defined, being obscured to a greater or lesser extent by th e
initial lack of flatness of the sandwich panels'.
.
Facing materials of aluminum or laminated glass cloth were combined with end grain balsa, paper honeycomb, or cellular cellulose acetate core materials t o
make sandwich panels composed of either isotropic•or ..anisotropic materials .
Specimens of various core thicknesses were made and tested over various span s
. to produce a representative range of shear deformations in the low-densit y
core materials . Simply supported edge conditions were maintained throughou t
this series of tests, as fixed edge conditions are usually not completel y
maintained under test, particularly with specimens having comparatively lo w
compressive strength in the direction of clamping . .The central deflection s
of the specimens tested under uniform load normal to the surfaces are cam , pared with the deflections as calculated by the method presented, using th e
elastic properties of the separate materials for each sandwich panel .
Description of Material s
Balsa
-
-
Balsa obtained from a commercial source passed the following specification :
"Balsa lumber, surfaced two sides, weight 6 to 9 ,pounds per cubic'foot, kiln- dried, random widths (3 inches minimum), random lengths (6 feet minimum) .
. Thickness, 1-1/2 inches or 2-1/2 inches with not less than 50 percent of the
material 2-1/2 inche s ' in thickness with tl/8 inch allowable tolerance . "
Cellular Cellulose Acetat e
The cellular cellulose acetate was manufactured commercially in a pilot plan t
from 'cellulose acetate and approximately 3 percent chopped-glass fibers by an
extrusion process employing heat and pressure . The material was received in
the form of extruded bars white'in color, 5/8'by 2-5/8 inches in cross section, : and from 4' to 10 feet in length . The outer surface of the bar was composed '
of a dense, firm skin . After removal of this skin, the density of the materil l
ranged between 6 .0 and 6 .8 pounds per cubic foot .
Report No,. 1583-A
-2-
Corrugated-type Paper Honeycom b
The paper honeycomb core material was fabricated at the Forest Product s
Laboratory from corrugated sheets of 45-pound commercial kraft paper which
had been pretreated with 10 percent, by weight, water-solubl e "phenolic resin .
The sheets were laminated by gluing together the crests of the corrugation s
of adjacent sheets ; the block so formed was treated with .approximately 55
percent hot-setting polyester resin and cur eg at"250° ' . . The .density•of this
material was approximately & pounds per cubic foot .
-
7
Aluminu m
. The aluminum sheet material used for facings was commercial 0 .032-inch, 24ST' alclad aluminum 48 inches wide .
.
Laminated Glass Cloth
The glass cloth used for facing material was commercial heat-cleaned clot h
chemically treated with a chromecomplex bath . In laminating the cloth,_a
resin content of approximately 45-50 percent was desired .
Preparation of Test Specimen s
all
The procedures followed in the fabrication of
sandwich panels- in thi s
series weKe similar to those described in Forest Products'Laboxatcary Repor t
No . 1574 .: The bonding resins and adhesives used for the .vari{ous combinations
of cores and facings are as follows :
••A . A high-temperature-setting, high-visc6'sity, contantpressure ;
laminating resin of the polyester type .
I
B . A high-.temperature-setting, -two component resin with 'a thermo setting'•iiguisd and thermoplastic powder .
C. •A high-temperature-setting, modified thermoplasti,e' meal-to
- wood glue .
- D . A high-temperature-setting mixture of thermosetting resin an d
synthetic rubber .
E . A high-temperature-setting, acid-catalyzed, phenolic. i sin .
All specimens having glass cloth facings were fabricated entirely with the us e
of resin (A), which was used for laminating the facings and bond=ing them to th e
cores .
2B . G . Heebink, A . A . Mohaupt, and J . J . Kunzweiller, "Fabrication of Light weight Sandwich Panels of the Aircraft Type, " FPL Report No . 1574, 1947 .
Report No . 1583-A
-3-
The aluminum-balsa wood specimens were fabricated with adhesive ' (B) . The
specimens with aluminum facings and cellular cellulose acetate cores wer e
fabricated 334th glue (C) .
The aluminum-honeycomb paper specimens were fabricated, with resin (E), follow ing a precoat on the, aluminum with mixture (b) .
The finished panels were 48 inches square with nominal core thicknesses rang ing from 1/4 inch to 3/4 inch . The facings of laminated glass cloth consisted
of eight plies, with a total thickness of approximately 0 .024 inch . Actual
specimen dimensions were measured at time of test .
All specimens were conditioned to equilibrium moisture content in a room main =
tained at 74° F . and 65 percent relative humidity .
Test Apparatu s
Aluminum-faced Sandwich Plate s
The apparatu s , designed to apply a uniformly distributed load normal to th e
facings of the aluminum-faced sandwich panels having simply supported edge s
is shown in figure 1 . This apparatus consists of a wood box sealed on th e
four sides and bottom, with knife edges on the top of the four, sides finishe d
so as to be square and in a . plane . The test-panel is positioned on the to p
of the box with thin rubber gasket material between the knife edges and th e
panel . Uniform load over the area of the panel is produced within the perim eter of the-knife-edge s . by reducing the pressure inside of the box by mean s
of a vacuum pump .• The pressure differentials between the two,side s , of the
panel .are measured with a water manometer . .A dial gage, which indicateAc .
deflection in 0 .001-inch units, is attached to-a beam supported above-the
panel, with its stem in contact with the center of the panel (fig . 2) . Supports for the beam ;reat .on the panel and are adjustable to coincide with the
span of the box . Thus, compression of-the gasket material when the panel i s
loaded does not influence the dial readings . The four corners of the pane l
were cJ.amped to the box to prevent their lifting nuider load and-thus releasing
the seal .
.
Load-deflection data are recorded, for each panel tested by readi!cg the manometer for equal increments of panel deflection . Two tests were made on eac h
panel, one with the pressure applied to one side of the panel and one with i t
applied_ to, the . other side_ of the panel . % Following the completion of the tests of the large panels (48 inches square) ,
the sides of the woodbox'were adjusted to reduce its dimensions from 44 t o
38 inches square . Strips 6 inches wide were cut from two sides of the panels ,
thus maintaining a 2-inch overhang beyond the knife edges, and the pane l
retested . This procedure . was repeated for box .dimensions of•32, 28, and 22
inches .
Sandwich Plates Facedwith GlassCloth
-
The 48-inch square sandwich panels having laminated glass clath facings wer e
originally tested on the sealed wood frame apparatus . It was found, however ,
Report No . 1583-A
-4-
i,,,€
that for panels of this size, the effect of shear deformation - was small . Cal ar
culation indicated that much smaller spans were required to produce
check
time:
t
qry
deformations in the cores that were sufficiently large to
adequately . Three welded steel boxes with the top edges of the sides machine d
flat and in a plane were made nominally 12, . 8,, and 6 , inchea . aquare . two test's
were made of each panel on each of the three boxes, reducing the size of the
panels for each span . , The overhang of the plate eras 1/2 inch on the 1214inc h
box and 1 inch on the 8- and 6-inch boxes . ;• ,
_
Figure 3 is A schematic diagram of the apparatus :, Specimen . ,(Ai is AR"supported on 'the .sealed steel-box (D) . Load Is .app]4ed - y m
of
r. _
tor . The pressure differentials produced were meaeu'edewtth a meter ti e
containing either mercury or bromoform . The central deflects
pt.]a. :
were too small to be accurately measured with a 0 .001 inch diEail
~.•~.,~
was used cfox; ;the large aluminum-faced -specimens . Either a Mai' mirror -oxi-'
Lamb's roller extensometer was attached to yoke (B) and support lock (C) .
Small 1/8-inch diameter disks of cardboard were glued to t11 .faci' gs of the .
panels at the, intersection of the .diagonals, and the_ .aupp haoe*s were i n
turn glued to the .disks . Load-deflection data were--'r=ecorded for ea0h panel
tested by reading the manometer gage for equal increments of paneldefle,ctions .
. I. The density of the liquids in the manometer at 22° C . eras-used to determ n-e
the unit pressures .and loads on the sandwich plates . In some cases it was
necessary to place a film of cellophane over the top face of the specimen t o
prevent leakage of air through the sandwich material .
de- >.
Tests of Minor Coupon s
All the sandwich panels for this series of tests-were fabr-idated48 inchep
square . As the panels were reduced in size for the normal loading tests, the
strips cut from the edges of the panels were used: to da:termlie the elasti c
properties of the material . Four such strips from eacd panel were tested i n
simple static besting over t full span, then each stripy :,aut
:thm e
- pieces of equal_-length and these were retested . In these tests the eentiter
deflections were,limited in order to prevent the stresses from selling th e
elastic limit of the materials . The tests were made in conformnce with the
.methods as given in Forest--Products Laboratory Report No . 1556 .Values for Poisson's ratios for-the materials-were obtained - from inforration'
available at the Laboratory .
. .r
5.
'_
Equations jised in the Analysi s
r
Experimental Values
L .
,
a
Experimental values of the quantity (1?) in the correction"factor (1 °+ : 1►) chi
be obtained from equation (89) of Forest Products Laboratory Report No . 1583
:. , i. % .
in the form :
3 "Methods for Conducting Mechanical Tests of Sandwich Constructions . "
Forest Products Laboratory Report No . 1556, revised 1948.
Report . No . .1583-A
-5-
;
K
(138)
in which
C = the central deflection measured by test an d
Co = the central deflection without allowance for shear deformatio n
ab calculated by equation (88) .
It is evident that accurate values of m t will not be obtained from tests of
large panels because the ratio of C to C o will usually be near unity .
'1 '
-
For the calculation of C o , values of the over-all elastic properties of th e
sandwich panels are obtained from tests of coupons cut from the panels . For
use with these values and for square plates, equation (88) can be put in th e
form
Co
192aX
7T
(139 )
(h 3 -c 3 ) H
in which
= Ex + Ey + 2A, and
A = E$,. + 2Aµxy ,
(139,a )
(139, b ), "
(all elastic constants of the facings) . For square panels having isotropic facings, equation (139) becomes
Co = 48a4,p
El
7160
X.
(144)
and for square sandwich panels having anisotropic facings the equation become s
Co =
,192a4p
~r6 { E(~l + E2 )h3+ 2A ( h3 -.
A
• (141 )
in whic h
El
X
= the over-all modulus of-elasticity of a plate in bending, i n
the x-directio n
E2 = the same in the y-direction .
A is computed by formula (139,b) using the elastic constants of the facings .
For isotropic facings A = E .
Experimental values of
El
and E2 were obtained from bending teats of strips o f
the sandwich materials cut from the panels . The strips were supported nea r
Report No . 1583-A
-6-
their ends and loaded at their centef's . To eliminate the effect of shear
deformation in the core materiel, the'strips we ':rirst•tested over a long
span and then cut Into shorter lengths and tested Over 6horter spans .
.,
'The Over-all -, flexural stiffness' cif -si L!~h a stri pr'af sandwich meteri&l tested in
this way is given .by'equation (50 of Forest Products LaboraioreRepor t
No . 1505 -4 and can be :put in the form :
.
h
Pl
= 1/4 Aw
112 .
(1 + 2 e)
_
.
1
(142
s
.1141
,, s .
1
.-+ : p
l
in whic h
P = central load
=-central deflection at ti at load
l = length of Span
w = _width of strip
h = thickness of sandwic h
e is associated with the deflection due to shear deformation i n
the core .
6.
When the results of ttio•tests made on two differen t 'spans are substituted in
equation. (142), two equations are obtained which can be solved for E1 , thus
eliminating the unknown value of e . Tests of specimens of this kin in whic h
the .width (w) was successively reduced indicate that values of E1 rather than
El are obtained, even when the specimens are quite narrow,!
Experimental values for the shear modulus of a sandwich plate, in the plane
of the plate, can be determined directly by the method described in Fores t
Products Laboratory Report 'No' . '13C'15.However ; a's equat:~on -(140) shows, such
values are not needed for sandwich plates having isotropic facings . For
sar,:wich plates having `•laminated glass cloth Facings, for which equation (141 )
if to be used, tests according to Report . NO .,- 1301 . for . the shear.,modulu of'th e
sandwich were not made . In equation (141) we have '(h - c3) , an d- by relation
March, H . W . and Smith, C . B . "Flexural Rigidity of a Rectangular Strip o f
3andhrich Construction ." FPL Report No . 1505 .
.March, H . W ., Kue,pzi,,E . W .. .andr .d comers, W . J . "Method of Measuring th e
Shearing Moduli in Wood ." FPL Report No . 1301, 1942 .
Report No, 1583- A
following equation (139), this is equal to
(Exo•yx + 2Aµxy) (h3 - c3 ) . It
i
was considered that values computed from the known elastic properties of th e
laminated glass cloth would be sufficiently accurate for the purpose of thi s
report . The modulus of rigidity of the laminated glass cloth associated wit h
the x and y axes is 500,000 pounds per square inch . Other values for elastic
constants used in the calculations were w yx = 0 .23 and X = 0.947 .
Values of modulus of elasticity for the glass cloth facing material ( Ex and E )
were calculated from the following equation :
E = E _
y
(Elh3)
x
( h3
-c(Et3)
c3)
(i43 )
The term ( E1h3 ) was calculated from equation (142) and estimated values wer e
taken for E t ) . For E t , the Young's modulus of the core, average values fo r
the respective core materials were used . Since these values are small i n
comparison with E, and a considerable change in them would not materiall y
change the computed values of Ex and Ey, the average of the values of E t for
directions parallel to the x and y axes was used . Since the facings had eigh t
cross-banded laminations and the stiffness of the sandwich was approximatel y
the same in the x and y directions, it has been assumed that Ex and Ey are
equal for this series of tests .
Calculated Value s
Calculated values of the quantity n, in the correction factor (1 +n ), were
obtained from equation (90) which, for square panels, can be put in the form
1)
c
= n
16a 2p
(144 )
Coh(µ yZ + µ t xZ )
by use of the approximatio n
h3 - c3 = 6 c f h (approximately if f <<c) .
Values of µ t yx and µtxz, shear moduli of the core, were obtained from bendin g
tests of strips of sandwich materials made in connection with equation (142) .
The simultaneous equations were solved for e rather than for-,
This valu e
of e was substituted in equation (54) of Forest Products Laboratory Repor t
No . 15051 and the equation solved for µt . It was found that, for the purpos e
of this report, a good approximately of this equation is obtained if all bu t
two terms are neglected . Thus it can be shown tha t
3Exc
c2
approximately
(145) '
h2)
xz 2 eh X (1
In this formula Ex is the modulus of elasticity of the facing material in th e
x-direction . Corresponding values for µt yz are obtained from the tests of th e
strips of sandwich cut from the plate in the y-direction .
Report No . 1583-A
-8-
Presentation,of Dat a
The results of the tests of the sandwich panels having aluminum and laminate d
glass cloth facings are listed in tables 1 and 2, respectively . Dimensions ,
elastic properties as determined from tests of minor coupons, loads and corres ponding central deflections of test panels, and computed deflections are give n
for each specimen . The values of the quantity ( Tit) in the factor (1 + 71 t' ) )
for the correction of central deflections due to shear deformation in the low density core materials as obtained from the tests of the normally loaded panel L
and equation (138), are tabulated together with the computed values of th e
quantity
c ) as calculated from equation (144) .
(n
The individual results of the static bending tests of the minor coupons cu t
from the panels having aluminum facings are listed in table 3 . The average
flexural stiffness values ,Eh3 ) given for each panel were computed from
equation (142), and the average flexural rigidity values (µ') for each cor e
material were computed from equation (145) . Table 4 is a similar tabulatio n
of the static bending test data for the minor coupons cut from the panel s
having laminated glass cloth facings . In addition to the data given i n
table 3, table 4 includes values for the modulus of elasticity of the glas s
cloth facing material . These values were computed from equation (143) .
An additional series of tests was made to determine the effect of the widt h
of a panel on the flexural modulus of a sandwich construction when tested a s
a centrally loaded beam over a constant span length . One sandwich panel
30 inches square made with 1/2-inch balsa wood core and 0 .032-inch aluminum
facings was tested over a span of 28 inches and retested with successivel y
reduced widths . The specimens were simply supported over their full widths o n
rigid parallel knife edges . The load was applied over their full widths by
means of a I/2-inch round steel bar . Stresses in the material were kept wel l
below the elastic limit to prevent any permanent damage to the specimens . The
averages of the data obtained from this series of tests are given in table 5
in terms of flexural stiffness per unit width (ElI ) .
b
Discussion of Result s
The central deflection of a flat sandwich panel of sandwich construction unde r
uniform transverse load is increased by the effect of shear deformation in the
low-density core material . This increase in deflection can be calculated with
reasonable accuracy by the method presented in Forest Products Laborator y
Report No . 1583 . Figures-Nos . 4 and 5 show the relation between the increas e
in deflection of the sandwich plates tested and the increase as calculate d
from equation (90) . The points on figure 4 are plotted from the data give n
in table 1 for the sandwich panels having aluminum facings . The values fo r
the quantity D in the correction factors ( 1 + r)) vary from approximatel y
0 .05 for the large panels to approximately 0 .6 for the small panels . If all
the plotted points were on the dotted lines, there would be perfect agreemen t
Report No . 1583-A
-9-
between the theory presented and the test results . There is, however, th e
normal scatter of points about the line . Variables in specimen thicknesses ,
nonuniformit y t of the materials, and other alight inaccuracies account fo r
this scatter . The points near the origin of the graph, however, appear t o
diverge more from the theoretical .ones ; the values these points represent
are those obtained from the large test panels, for which corrections wer e
very small. Since the quantity ('q t ) is found by differences of two, almos t
equal numbers, a small inaccuracy in one of the numbers produces a larg e
error in the difference .
Figure 5 similarly shows the relation between the test and computed values fo r
the quantity ri for the panels having glass cloth facings . The test points o n
this figure are plotted from the data given in table 2 and again show reasonabl e
agreement between the theory and the test results . The sandwich panels havin g
facings of laminated glass cloth, which have a modulus of elasticity approxi mately 25 percent that of aluminum, were tested over much smaller spans tha n
the panels having aluminum facings to produce shear deformations in the core s
sufficiently large to check the theory adequately . The dimensions of the squar e
test boxes were from 44 to 22 inches . for the aluminum plates and from 12 t o
6 inches for the glass cloth plates . The largest value of 7 (greater than
unity) was calculated for a small panel having a 1/2-inch cellular cellulos e
acetate core and glass cloth facings . The values of 71 for the panels having
balsa wood or honeycomb-type paper core materials were considerably smalle r
because the shear moduli of these cores were approximately twice . .-that pfLth e
acetate core material .
:A
The effect of specimen width on the flexural stiffness of a sandwich'ain :suc-'
tion is not considered significant as a result .of . -the . Matra , .hown .on figure' 6 .;.,
al stiffness per unit. . .
Since no significant difference between the f
width of 30- and 3/4-inch-wide strips of .sani rich . onstruotion is►ehown in ,
figure 7 it is assumed that the Poisse •'s. ratio ei9 ct on, -the . narrow .pale].
is the same as on the wide panel . Thus, the stiffness va&ues! ►per lit= l,dath _
determined for the 'sandwich panels f]omt tests of etw4row specimens• .ar.e sume .- `: .
to-be
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Sable 3 .-8aealteof toots of Mvtar aoayene catfrtet the emdrloh
ele has;ag0,0}r lash
alualamatimings ;Inclndinthe average flexuralstiffness for eanhpanel and
the average shear modulus firsackacrematerial
Specimen t o»rage s Average s Lsagth
a thick-
number
a
s
nos s
s
Span
width a
s
:
a
-:-- - t
t-
t
t
t
t Inch a Inch s Inches
t
t
t
a
Inches
(BS)t
11h3
s
-A-
t
t
s Shea r
1
modnlna
t of con
1
t
s
a
V)-"- -
t P .e
.1 ,
tInch-poumdsa Inch-pound,
A=1201-BALSA SANDWICH MLTUTAI.
AB-4A a 0 .572 a 5 .43
t
.572 t 5 .43
t
a
AB-4B s
.572 a 5 .44
.572 t 5 .44
18-40 s
t
.578
.576
t
t
a
t
e
Average (4 )
AB-4D
42 .00 a
a 13 .91 s
e
a
47 .55
s 15 .74
a
s
3 .00 a 35.00 s
t 3 .00 t 11 .62 t
s
s
a
.581 a 3 .01 t 42.03 t
.561
a 3 .01 t 13 .93 a
:
a . . . . . .. ....
a
1
13 .90
a
Average (4)
Average (8)
,445
.445
t
a
t
t
t
34 .96 a
11 .61
a
s
s 42 .03 a
AB-3 0
a
a
42.00
a
a 47 .52
a 15 .74
a
AB-3 B
AB-3D
a
t
Ab-3 A
t
t
t
a 3.01
s 3.01
s
a 13 .95
a
12.00
t 44 .00
t
s
a 47,485
t 32,595
a
38 .00
a
a
t
12 .00 t
s
31 .00
9 .00
t
a
:
597.034 a
13 .571
a
a
612,658 t
12,703
49,147
s
a
32,809
45,569
t 22,306
s
36 .00 a 47,317
9 .00
a 24,663
a
t
38 .00
t
1
s
t 29.294
12 .00
t
a
a
a
a
t
363 .776 a
t
ta
t
t
a
t
21,840
12 .00
31 .00
a 26,784
9 .00
t 16,812
36 .00 ,
9 .00
t
a
t
a
a 30,178
t 22,037
t
44 .00
s
604,396 t 10,120
7
t
602 2Z t 12 .276
,2
a
t:
27 .741
372,446
338,656
t
t
t
16,616
13,540
12,949
t
13,610
a
349,220 a
356 .024 s
12.610
t
12,672
17AMI20M-CBLLULAR CBLI2LOSB =TATE SANDWICH
AO-4A
s
AC-4B
t
:
t
t
.554
.554
t 5,44
t 42 .02
: 5 .44
t
t
t
: 5 .43
.552
.552 t 5 .43
t
1
38 .00
47 .52 t
15 .73 a
44.00
12.00
ACac t
t
.561
.561
AC-4D a
.559 t 2.99 t 42 .07
t
t
.559
Average (4)
AO-3A t
s
t
L0-33 t
t
12-30
a
a
a
a
AC-3D a
a
s
Average (4)
Average (6)
a 3 .00
a 3 .00
a
13 .93
t
a
t
:
t 35 .00 t
a 11 .61 a
t
: 13 .914
,
2.99
t
a
t
.431 a 5 .44 a 42 .00 t
.431
.431
.431
: 5 .44
a
t 5 .44
a 5 .44
a 13 .91 t
a
a 47 .52 a
a 15 .73 a
a
=
a
.432 a 3 .00 a
a
34.99 t
.432 a 3 .00 a 11 .62 t
a
a
a
.436 a 3 .00 a 42.03 a
.436
s 3 .00
a
t 13.93
a
a
a
t
12 .00
t
43,860
23 .712
39 .930
s 19
.299
a
t
t
a
a
579 .675 a
s
t
a
t
6 .526
a
t
t
5,31 2
38.00 a 40,810 a
a
523,355
:
31 .00 a 35,486 t
a 10,996 :
9.00
9.00
:
:
535.6c* aa
3 .991
s 17,727
I
VOLVO t
8,165
t
541,841
38 .00 a 26,413 t
s
a
12.00 a 16,079 t
a
a
44 .00 a 25,782 a
12 .00
a 13,097 a
339,~t a
t
$
a
31 .00 a 22,082
9 .00 a 8,475
a
38 .00 t 25,319
9 .00
a
a
12,238
s
a
6,579
a
4,423
t
a
a
334,061
a
309,612 a
4,341
3 648 a
32781 a
7.376
a
t
a
t
5,84 2
LL11eI7101f?1228 20flTCOaS Bm2D8I0 8
A7,4A a
_
:
A7 ,4B
A7-4C
a
t
a
A2-4D a
a
a
Average (4 )
AY-3k ,
a
AP-3B a
a
t
AP-30 a
t
t
1773D t
a
t
Average (4)
Average (6)
7 M 78827 P
.621 a 5 .42 t 42.02 a
.821 a 5 .42 t 13.91 a
t
t
a
.616 t 5 .43
.816
a 5 .43
a
.822 t 3.00
.822 t 3.00
a
.819 a 3.01
a 47.53 a
t
15 .75
t
35,05 a
a
a
a
a 11 .63 a
,
t 42.05 a
.819 a 3 .01 t 13 .94 s
a
5 . 44 a 42,01 t
5 .44 a 13 .92 t
a
.701 t 5 .43 t 47 .53 t
.701 a 5 .43 t 15 .74 a
t
t
s
.702 t 3 .01 t 35 .04 a
.702 t 3 .01 t 11 .62 a
a
a
t
.700
.700
t
t
a
.701 s
3 .02
.701 s 3 .02
a
t 42.05 a
t
13 .94 s
38 .00
12 .00
44 .00
12 .00
31 .00
9 .00
38 .00
9 .00
a
a
a
t
s
a
a
60,574 a
a
a 1,362,153 a
12,174
a
1 .289 .973 s
9,21 9
104,414
99,221
t
t
50,077 a
t
a
:
a
40,882 t
t
a 1,151,832 s 14,09 6
91,031 a
a
a
t
.
38 .00 t
12 .00
s
t
44 .00 s
12 .00
a
t
31 .00 s
9 .00 a
a
36 .00 t
9 .00 a
86,201 a
32,163
78,849
49,591
a
99990o7i
1 .254 , 966 a
t
a
t
a
73,032 a
41,231 a
s
62,483 t
28,864 a
a
67,620 t
1,010,091
8 .799
t
a 12,740
926,104 t 10,21 1
t
t
639.709 t 11,14 2
36,359 a
a 6gp 711
906,171
t
t 16 4
t
11,859
!able 4 .--Aesulteoftests of minor cvnpone ant frost sandwich panels having eight-ply glass cloth facings ;
Includingaverageflexuralstiffness foreach panel . averageshear modnlas for each core
material . and2oun6'smodules for the laminated &less cloth
:
Specimen
number
: Average
s thick-
.
noe s
s
Inch
s
s
: Average :
s width
Length
s : Inches s
Inches
:
:
Span
s
s
(ZI) t
s
:
s
llh3
s
s
Inches
Inch-pounds
: Inch-mounds :
f
A(
s
$ P .s .i :(10 )
P .s .i .,
GLASS CLOTH-C&LLULAR CZLLUL08S ACDTATZ SANDWIC H
O0-3A
s
0 .537
.537
s
s
2 .89
2.89
:
:
48 .05
14 .02
s
s
46 .00
12 .00
s.
:
$
.541
.541
2 .89 . 8
2 .89 s
42x.04
13 .95
40 .00
s
s
.12 .00
:
s
s
.541
.541
:
2 .93
2 .93
s
41 .02
11 .98
s
$
39 .00
10 .00
s
8
9 .075
7,546
s
.545
.545
s
s
202
2 .92
s
s
35 .96
s
:
34 .00
10 .00
s
s
2 .90
2 .90
:
:
48 .05
14 .02
$
:
46.00
12 .00
s
42 .03 '
13 .92
s
s
40 .00
12 .00
s
41 .06
11 .98
s
:
35 .98
11 .92
t
00-38
00-30
00-3D
average (4)
00-20
s.
s
00-22
'
.416
,416
.415
.415
s
2 .89
2 .89
11 .93
8,745
7,807
s )
s )
9,010 .
6,962
8
105 , 840
s
110,280
9, 020
9, 055
6,535
s•:
: -.
112,680
:
1113
:
5,182
4,862
: )
: )
s
s
5,215
4,322
)
)
63,840
39 .0o
10 .00
s
$
' 5,515
4,822
s
t 1
66,840
:
9 .540 . :
:
s
34 . 00
10 .00
s
s
5,428
: )
4,172
s )
.. ... ... ...
67,080
:
4,490
65
:
32,364
:
8 '
62,520 :
.425
.425
s
s
2 .93
2 .93
00-2D
:
s
.426
.426
s
:
2 .93
2 .93
t
8
00-1A
8
.292
.292
s
2 .89
2.89
:
:
48 .04
14 .03•
s
s
46 .00
12 .00
s
s
2,671
.2,378
00-18
s
s
,294
.294
s
s
2.90
2 .90
s
$
42 .03
13 .93
:
40 .00
12 .00
s
2,730
2,2'42
s ).
)
33,480
00-10
:
.
.303
.303
:
:
2 .94
2 .94
s
s
41 .05
11 .98
8
:
39 .00
10 .00
s
s
2,758
2,417
i
33, 480
00-1D
's
.297
8
2 .93
2 .93
8
35 .96
11 .92
:
s
34 .00
10 .00
s
2,596
2,151
8-
Average (4)
Average (12)
Z M 78828 F
.297
s
1
1
4,080
s
Average (4)
10,460
111,240
:
00-20
1
s
. : )
s )
)
31 .740 :
s )
...
-5i:76F :
....... ... ...
s
4,490
2 .86
1 3 .220
4,000
:
2 .83
:
2 .8 2
2 .88
:
4,920
2,697
:
3 .1 3
6,380 i
4,220
:
6,459
:
(Continued)
2 .98
Table 4 .--Results of teats of minor canponi eat fro* saadmich•panel■ having eight-ply glass cloth facings ;
including average flexural stiffness for each panel, average shear modulus for each cor e
material, and Toung s e modulus for the laminated glass clot h
1
:
s Average
t thicknose
t Average t
Specimen
number
s
:
Inch
:
width
t
I
Length
Span
t
I
I
s
Inches, :
Inches, s
t
t
t
(SI) t
t
Inches
.slh3 .
s
s Inch pounds
t
1
s
s
t
1
t
Inch-pounds t
l .~ .i .
t P 0 0 01 00.00 )
GLASS CLOTH-BALSA SABDVIO H
GB-3A
:
's
0 .543
' .543
GB-33
:
.544
.544
t
t
' :
s
s
8,940
8,393
s )
108,000
s
18,950
s
8,775
7,886
: )
)
106,320
t
11,230
8,915
7,926
:))
t
34 .00
10 .00
:
:
9,625
8,371
r
s
5,212
4,707
)
s )
63,000
8
7,900
:•
61,8oo
:
20,830
2 .90
2.90
:
48 .03
14 .02,
,t
:
46 .00
12 .00
2 .90
2 .90
s
42 .05
13 . 93
:
i
40 .00
12 .00
2 .92
2 .92
t
41 .02
11 .96
3
39 .00
10 .00
:
t
2 .93 .t
2 .93 t
35 .96
11 .92
t
t
: )
t
t
2 .74
GB-3C
t
.543
.543
GB-3D
3
.554
.554
:
.418
.418
s
:
2.90
2 .90
s
s
48 .03
14 .02
s
s
46 .00
12 .00
s
3
:
.419
.419
s
t
2 .90
2.90
s
:
42 .04
13 .93
t
40 .00
12 .00
s
.044
s
s
.428
.428
:
2.93
2.93
:
$
41 .04
11 .98
s
:
39 .00
10 .00
s
Z5
.793
)
t )
67,440
:
8,450
s
.423
.423
$
s
2 .92
2.92
: 35 .96
s . 11 .92
t
34 . 00
10 .00
t
:
5,365
4,902
s )
$ )
64,920
t
14,000
~i4,2 o
s
s
s
s
GB-1A
.: '
s
.289
.289
t
s
2.90
2.90
:
:
48 .03
14 .02
:
s
46 .00
12 .00
:
s
2,420
2,109
s )
)
29 .40o
s
4,010
t
s
GB-1B
s
.287
.287
s
:
2.90
2 .90
s
42 .04
13 .93
s
40 .00
12 .00
t
s
2 .240
2,038
8 )
:
)
27,180
ss
5,810
t
t
2 .79
GB-10
s
.294
.294
:
s
2.92_ 8
2.92 t
41 .03
11 .98
:
:
39 .00
10 .00
t
t
2,445
. 2,233
s )
29,520
s
9,29 0
GB-1D
s
.291 '
.291
:
2.92
2.92
35 .96
11 .94
34 .00
10 .00
:
1
2,338
2,117
28,320
28-,'
s
t
8,200
s
2 .78
Average (4)
GB-2A
:
GB-2B
GB-20
GB-2D
Average (4)
s
Average (4 )
Average (12)
Z M 78829 F
s
:
s
I
117 .000
109,740
)
15,250
107 . 64°
W
'
s
s
11,920
2 .8 3
t
11,320
t
s
2 .7 7
s
(Continued)
2 .84
Ti'ble 4 .--Results of tests of minor coupons eat from sandwich panels having eijht-ply Klasscloth facings ;
including average flezural stiffness for each panel, average shear modulus for each cor e
material, and Tousles modulus for the laminated glass clot h
t
Specimen I Average 4 Average : Length :t Span
number
4 thick- t width
:
4
i1 mess
t
r
t
t
Inch
t•
InFhei t
Inches
87-33
t
61-30
GP63D
Average
t
t
'2.90
2.90
t
t
s
2.92
2.92
t
t
t
2.93 : 35.94
2.93 : 11 .91
t
.789
.789
i
:
.T90
.790
t
.?92
(4)
2.90
2.90
t
.791
t
:
t
t .
48 .03
14 .02
41.05'
11.96
t
t
39.00
10.00
,20,685
17,900
t )
t )
2507- 800
20,125
16,571
t ]
t)
t
t
.666
.666
8
:
2.92
2.92
I
t
41.03
11.97
.672
.672
t
t
2.92
2.92
t
t
35.93
11.90
u
.537
.537
:
t
a7-1D s
.539
.539
.542
.542
81=10
(4)
t
2.90
t
34 .00
1
1
10.00
46.00
:
2.90
2.90
t
8
t
8
2.93
2 .93
t
t
Average for all glass-cloth panels t
846 .600 t
t
247,350 t
2.91
18,100 t
12,430
t
t
_
14,000
170,880 tt
12,403 . :)
t )
11,800 `t
40.00 s
12 .00
s
14,460
12,676
: ) 175 .920 t
10,820 st
t
t
39.00
10.00
t
t
13,730
11,730
t)
t )
t
t
34 .00
10.00
t
14,775
13,290
t )
t
t
12 .00
,
:
169,200
t) 179,160
t
t
t
6 .37
20 •200
2 .91
8,325
8 )
110,040
13,640 t
: ) 40.00
t
12 .00
:
t
5,615
8,253
t )
t)
103,920 :t
25
: 39.00
: 10 .00
t
8
' 9,340
8,512
: 34.00
10.00
t
t
t
9,070
8,005
.400
s
: ) 112,680 t
1 )
16 .720 t
) 110,160 '
t
109,200 t
13,910 $
s
t
15,568 t
t)
2.92
t
t
35.96
11.92
2.91
:
14.02 s 12.00
42.04
13.93
: 2.92 : 41.02
t • 2.92 t
11.97
t
Average (12)
Z M 78830 P
•:
)
7137116
t
Average
HONITCOMB SANDWICH
10,230
t
t
f
t P .s .i .(10 )
P .s .i .
243,'600
t
1
87-18
i Inch-pounds t
_
2.90 : 41.96
2.90 t 13 .93
t
s
19,715
16 .693
t
.542
t
40.00 :1.
12.00
.666
.666
t
s
t ■
8
t
87-1A
t
13 .93
42.02
07-28 s
(4)
'
25,200
:
Average
h3
248 400 t
2.90 t 48 .03
2.90 : 14 .02
1 .
£
t
s
8 )
t
GP-2D s
Inch-pounds
t
20,550
19,066
.667
.667
'GP-20
-A-
46 .00
12.00 i
:
:
t
(II)t
t
t
81. 2A t
:
t
Inches
t
GLASS MOTH-PAM
87-3A t 0 .790
t
.790
t
4
2.75
2.91
2.866
Table 5 .--Average flexural stiffness value s
determined from simple bending
tests of strips of aluminum
balsa sandwich material of var ious widths, tested over a 28 -,
inch span
Specimen
width
Inches
Number of .
: specimens ,
tested
.
Average
stiffness
1,000 p .s .i .
30
4
45 .175
15
4
43 .975
'3-5/8
24
44 .579
1-3/4
32
43 .82
7/8
64
44 .868
r
Report No .
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EXPERIMENTAL VALUES OF(1? ) IN CORRECT/ON FACTOR (/*Vt)
Z M 78823 F '
Figure 4 .--Experimental values of the quantity (>) t ) in the shear deformation
correction factor (1 + 74) and computed values of the quantity (i7 c ) fo r
for central deflections of simply supported flat sandwich panels wit h
aluminum facings, subjected to uniformly distributed loads normal to thei r
surfaces .
0. 7
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0
//
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o
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o
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04
0.6
0.8
1.0
/.P
/. 4
0P
/
t~
EXPERIMENTAL VALUES OF (Nr 17IN CORRECT/ON FACTOR
1
(/
Figure 5 .--Experimental values of the quantity (A7 t ) in the shear deformation
correction factor (1 + tit ) vs . computed values of the quantity (ro c ) fo r
central deflections of simply supported flat sandwich panels with glas s
cloth facings, subjected to uniformly distributed loads normal to thei r
surfaces .
2K78822F
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0
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