Supplemont to
, BUCKIING Or rlAT plyWOOD PIATIS lN CO,ftpptSSION'
SHIAR, OR COI|,IBINTDCOI{PRTSSTONAND SHEAR
Plates tlaving the Graln of the Jace Plles
lnclined to the Edges
LOAN COPY
Please return to.
Wood Engineering Research
Forest'Products Laboratory
Madison, Wisconsin S3lO5
Supplernent to
BUCKLING OI'FLAT
PLYWOOD PLATES IN COMPRESSION'
SHEAR, OR COMBINED
COMPRESSION AND SHEAR
Plates Having the Grain of the
tr'ace Plies Inclined to the Edgesl
By
Forest Service
Forest Products Laborato"y,L
U. S. Departrnent of Agriculture
In Forest Products Laboratory Report No. 1316, rrBuckling of Flat Plywood Plates in Cornpression, Shear, or Cornbined Cornpression and
Shearrrr exact or approxirnate formulas were given for calculpting the
buckling stress of very long (infinite) flat plates under cornpression,
ehear, or cornbined cornpression and ehear when the grain of the face
plies is perpendicular or parallel to the edgee or inclined to thern at an
angle of 45", In certain cases forrnulas for the buckling of finite platee
were given. In others it was pointed out that the buckling stress for a
finite plate could be estirnated with the aid of the curve given in figure
12 of Reirort No. 1316 frorn that of the corresponding inflnite plate. The
forrnulas for the critical compressive and shearing stresses were written in the forrns:
P"t=*"tLT
.z
n
( r)
a
I
:This
progress report wae originally issued by the Forest Products
Laboratory in 1943.
ZM.irrr"ined at Madison,
'Wisconsin.
Report No. f 316-C
Wis.,
in cooperation with the University
.]-
Agriculture
of
-Madison
9"r = k"
respectively.
h
""
2
(z)
z
a
Values of the constants k. and k"
were given in tables and
curves for several types of plywood inTeportTo.
1316. Sirnilar values
for further t14res of plywood are given in Supplernent B to Report No. f 316.
In the preeent supplernent approxirnate forrnulas are glven for calculating
the buckling stress of long plywood plates under the types of loading
speeified above when the grain of the face plies is incllned at any given
angLe to the edges.
The resultg obtained by using the forrnulas for cerinclinations
grain of the face plies and for certain typ^es of plyof
the
taln
wood are shown in table 9 and in the curvea of figures 43 to 70.2
It is
also pointed out that certain equations in Report No. l316 can be written
in sirnpler forrns.
1. Notation
The notation of Report No.
stants are defined in terrns
Kl=Ercos4e+Ez
Kz = El
" i r,4
o * Ez
l316 is used.
Irr addition the following
of congtants previously
defined:
e i n 4 o + zA sinz o
" o r4
e + 2A eir r z e
K5 = a(Et - A) sin3 0 cos g - t(Ez-A)
"o"2
"o"z
con-
o
e
sine .o"3 o
K5 = +(Et - A) sin0 cos3e - a(Ez-A) sin3 0 cos 0
?
:The figures and tablee in this supplement are nurnbered coneecutively
with those of Report No. 1316 and previous supplernents.
Report No. f 316-C
-2-
Rl = 6(n, + E2) sinz e
o + 2 A ( s i r r 4 e + c o a 4o
"osz
- 4 sinz e cosz e)
The choice of axee and the angle 0 are shown in figure 4 of Report No.
13f6.
It is to be observed that tfr angle 0 ls the angle rnade by the
direction of the grain of the face plies with the axis OX which ie perpendicular to the sides of the long plates under consideration.
2. Long Plates
Under Uniforrn
Cornpression
The energy rnethod wae used as explained on pages 4 and.5 of Report No.
1316. As before the forrn of the buckled gurface was taken to be represented by the eguation
w=Hs1n31
s r' n
a
7Jt
5.[y
- t x ,I
(3)
By the processes previously described it was found that k"
(1) is given by the forrnula
o. =
+where
[r",
z and 1 satisfy
z
4 4= y
z
,z + 6xrvz+Rr - ,", ,]
the sirnultaneoug
of equatlon
(4)
equations
Kz+Rtv2-Ksy-K6y
+
(5)
Kt
3 K 5 tz + K 5 - zR t y - 4Kl y3
lzKl v - 3K6
Report No. l3f6-C
-3-
(6)
3. Long Platee
Under
Uniforrn
Shear
By using the energy rnethod and equation (3) for the buckled
was found that k" of equation (Z) is given by the formula
1T'
.k" =7;;;;;
eurface
?.
f t*,
^-- z-z ..
+ 6Kry" * Rl - 3Iq ']
it
(?)
ULl
where z and l satisfy the eirnultaneous equations
z
4 =y 4.
+
2
z=
Kz* Rt v' - Ks y - K6 v3
(8)
Kl
zKz - zKl y4 - Ks y + 15 v3
(e)
6x, vz - R,
4. Long Plates Under Uniforrn Compreseion
(or Tension) and Shear
Let the shear stresg be f tirnes the conrpreesive
tions ( 1) and (z)
stress.
Then by equa-
k" =fk.
(10)
By using the energy method and equation (3) for the buckled surface lt
was found that
fi
Report No. l3L6-C
2
,z+6krv2+Rt-3K6
-4-
']
( l1)
where
z and l
satisfy
4.
4
z =y +
. z2=
the sirnultaneous
equations
Kz+ Rr vz - Ks y - K6v3
(1z)
*t
4*zr.- 4Kr (y3 * rva) - zRly + Ks(r - zry)+ K5(stl +zrv3)
tzKt (v + fvz) - zRtf - 3K6
( 13)
Values
of k" and k" are given in table 9 and ln figuree
43 to 70 for vari-
of the grain of the face
oue types of plywood and various inclinations
The
plies.
The constants of Douglas-fir
were used in the calculations.
construction
and use of the figures are explained on Page 14 of Report
construction other than
No. 13f6. For types of plywood of symmetrical
can be
those glven in table 9 and figures 43 to ?0 the constants k" and \
found frorn the values given in these tables
(or extrapolation) on the baeis of the ratio
and figures by interpolation
+ EZ) because, aB exEI/ (tl
p1ainedinReportNo.l3l6.B,theconstantElffinctionsofthie
ratio are found to lie on or very neat to srnooth curves.
From the values of the constants for very long flates as given in this report an estimate of their values for shorter platee can be rnade by using
the curve.of figure LZ oL Report No. 1316.
The constants given in
rnethod.
Compression
struction and angles of
k. that appear to be in
this Supplernent were obtained by an approxirnate
tests over a considerable range of types of conthe face grain have yielded values of the constant
good agreenrent with the approxirnate
sufficiently
theoretical
values, coneidering the nature of the testand the variability
of the plywood.
In buckling tests of panels the reeults are very sengitive
to the effects of edge conditions and initial curvature.
Definite conclusions will not be drawn until the test prograrn has been cornpleted.
Report No. 1316-C
-5-
Sirnplified
Forrns
of Certain
ione in R
rt No. 1316
Equations(12), (zB), (321, (3?), and(43) of Report No. l316 canbe simplified by collecting the terrns in Llzz and ueing the expressions (tl),
(29)-, (33), (38), and (44), tu"p..@.
The sirnplified equations, nurnbered as before, are written below.
n"=+
1""'+6oyz+R-
l,o*
+6cy2+R
z + 6 n 1 v z-
ks
( r7)
(28)
,^]
(32l
[,","
k"=
k"=
nz
lzt (l + Zyf) E,
t2
IzI (1 + zyf) E"
Report No. r3 16-C
+ 6E1vz
+ 6cyz +
-6-
(3?)
(43l,
.3-19
lbble
of -IohE pllrrcoil
!.--Buckllag
E. hzh?.
(or tenslle)
!
Loadtng :
r
r
€r
!
uader coroblned oompresslon or tenston
For ooupresslou p"r.
eupported.
q- g r 6- Lk
plates
ko EL\2/a2,
l{€getlw
ud
shear.
kc d€not€s tsnslon.
For coublnedgbregg ths eh€ar etrese ls equal to f,timo6
Edgei sluply
For phear
the oomprosslrr
atrese.
:k":2-p}y:
ftor
!
r ke i lrl
:Inflalte-ply
|
9-p1y
5-ply:
:
:
t
t L z 2 z 2 t 2 c rI l r l r I : l : I : 1 : 1 : I r I :
!
s
J-ply3
r
I:I:l r
J-pIyt
O.@.2
0.16 z
0.94 r
f.05
:
l.ll
L,11 z
I.l+9
:
5-ply
3
lr2rI:111:IrIrl
:E&-!B:.:333::
C o B p r e s s l o nI:! : . . . . r
k" t
I.2?
:
1.50
I.2J
1.Il
t
.
1.58
,
t.59
-2.57 z
-2.16
z
-2.2)
.97
.q8
:
|
1.0!
.52
.
.6j
.76
i
.el
'&
i
tttt::33:l
: l!
thoar
r....:
k" :
rIl:....:k-:
Shsar
Ooryrcalloar I!
auilshr.rr
t
.85 t
-.96.
.55 ,
.Z7t
'a
t
:15:l.0rkcr
3
|
fr
3 ,
,
. 5 1,
.#
i
,ee :
.86
|
.99
.18:
.2Jt
,27t
.71;
.9o,
t.os:
3
:
3----
3----:----:-------
'|
,*",
'a
,
.*'.
(
, t t €,
.\o'
-.@z
;
3
.e.
:
-:
i n"
.97 ;
-.972
i.o7:
:
.6r'
' -.6r
; -?.,
'; -e.p
rk"zl.!6
r.o9 ,
-1.09:
.g5;
t.ols
-I.412 -I.52.
:
.2Q?
-
.6r:
.70;
.tro z
r.r9 ,
z
.rt:
,.1" i
3--------:----------:----------
.9o:
.rl,-r.f,t",
:
!
tk.t
!
3
zn
;k; , -.29': -.'+5; -.54,
-.q6.
:
2
-^
l--------
,ket
r
,9'
.tz
,J..Z)'t
' et
:
I.OI
t
.lJ
,.ll
i
3----------------
!----
1.]? '.
t.zj
3
t.zl+
'
1.24
-.59 ,
-,el ,
-.az
i
-.62
r.14
,
r.t4 ,
-r.r4
:
L.oJ i
-1.54:
r.rz ;
-1.I2
:
.gg,
-1.44:
:
:
.623
.76
.59'
z. -2.16 '.
:. -?.\6
-]. 14
r.oo
-I.50
i
t.oz
:
-1.07
,
3
.So
-L.t5
:
|
.55
3
-z.oe ,
-r.rg
:
-r.se
-ao.rr+
:
.
-r5.56
-7.19
:
-4.J8
.5I
', -"1.9
i -"s.lS i -">.gl
: -rs.re .
s-14.16 t-I2.J6c
-LI.82
:
-8.06
-?.I9
.
-5.55 r
-5.t5
-5.ii.:.
-6.1j
:,
-10.0J
.l+7
Stli3tl:3:
-6,60 r
315,1.0:k6;-I.!l+r
.
i
:
;15;1.5;
3
t
-?.88t
I
:n"i-t.g+:-s.6oit.te
kc:-1.05:.
-\.Sl:
-r.rg:
-l+.16'. -l.et'
-?.97'
3ks3-1.56i-e.soi -e,z+l -1.2. i
: rl , r+.oit" i -.zs i -r.16; -r.os,
t
:
:krt-1.163
:
I
tk_t.?.81
t
t
r
- l + . 6 1 + .- \ , 1 2 .
g.2, t
6.51 :
6.02 ,
|
:
:
I l5
r-1.or ko : -r.66. t
-4.09 t
-l{rell t
r
I
1.56;
4.o9;
[.d+:
-L.8J z
2.75t
-1.9o :
2.852
rks!
lllzirt
, l'! 1-1.!; ko ;
3
t
!k.r
t
t
-:
r 15 r-l+;Orko r
:
Er!€o. lrl6G
z y \5019 F
:
-.9o
z
L.J5,
!
:
-.25 ,
-.40 !
'
i *" i r.ol
-3,9i
1.9'
-L.>a
3i
.
2.66.
6 .-5 6 :
-1.5)
:
t-
l,S+
-lio,
-1.49
t
!
-'70
-2.61
7.rr
,.
3
5.88
-r.to
,
-t.f+
-t.lo
J.la
:"
2.7+ 3
-1.86
<.or
t
-.lg :
1 . 5 9 ' , r . 6 0'
-4.78
-2.56
-3,65
,''-4.y0
3:
r
o:
:
'
z
-1.27
-+.W,
-1.0o,-.80r-.87
:4.0o z -J.?o,
.
I
t
:
.gt
.772
:15:-l+.0:k^3
i
t
:
.7O t
.61,
:kr:
Tanlleurna] r5 , .fl t"
ft
:
.62t
. 4 2;
;
"
t
.5Or
?
3
.5\,
t
"
:
.U+!
I.Ol
.jO
.i6'.
!
:
ancar
:
|
3
,k",
, r5 ,-i.0, t" ,
n
.86
.\j
: rr , i.ri r" :
;
n
.76,
.tgt
.50;
a
'
.6L t
.JIt
.44:
;
'15'-.5tk":
"
,
r.r. 2
!15s4.0!kc:
-----------
-l.If
3
;.
"
-j.}Ot
E'
: O.!: ko : .
t
tk",-r
:
:
-1.Mt
.
1.OL
a
-.1+7 ,
-.\g
.
-.49
r.9o i
,.gt ;
L.95
:
t
-.48
r.92
Table
plates
}ong pllwod
of
t.--Buckling
:Dag.;
I
under
conbined
or tension
conpression
:
I
i
:
ko :
0.56 :
0.82 :
1.05 :
f.Zj
:
I
k" :
.87 ,
.79 ,
1.04 :
r.ZJ
z
I.J8
:
k" : -1.01 :
-4,21 :
-J.89 ,
-J.58
t
-Z.BJ
t
.59 t
.j5 ,
.75 ,
1.I7
:
.Jo;
.?g:
.Jgi
:
(continuad)
I
I
,iii::ti
C o m p r e s s i o n3;0 t . . , . :
and shoar.
I+J
F]
li:::::::
Shoar
i
z JO r....:
1.41
;
l.Jl
::i:::::i
Shoar
, JQ ,....:
C o m p - r e s s i o nJ :0 ! 0 . 5 : k c :
r
andshear:
,*"i
'
''g ',
.62
.47:
.'r.i
.47r
.\?,
.J{t
'57',
.J).
'50;
.45,
'51'.
.ra;
.74;
.]-5;
.65:
.?z:
.87:
.6J t
-.J? ,,
r.?2 t
-.6, t,
1 . 1 + 23
-.i1
,
-./o
r.la
t.sz
1. 5 r
L.J6
-I.J6
-2.02
-r.7J
:
:k":
3J0:1.!:k":
;
'
;
;0";
:Jo34.o:kc:
I
i
,k"l
, Jo r -.5r kc ,
o"
:
:
,
,
"
'
;
J o : - 1 . 0 :k o :
:
;
: t o i - r . r .t " I
;
:
:
;
: J0 :-4.0: kc :
;
;
;o";
.5?
-.5?,
;ksr
o"
"
.5+
:
. 5 1:
.51,
'& i
.68 |
.
1.og
.59;
;3oir.o.t".
?
.98
.98
:
;
-I .+8.
,
|
.)+
.26 ',
1.04 ,
.J\ :
t.l>;
r.53
1.57
-.79
-1.52,
-2.I5 :, -2.r0 |
.?I z
,94 :
_.s4; _j.J6"
.79 ,
_J.r4"
:
1.05 :
.Lz: r..44: r.,*o,
-.6+ t
.(L
.8r r
.b)
.98
t. f o
7a
al
-r.85
1.05
-r.57
)o
'
-rJ'58
'6.79
:
-4,l+7
;
"
--:-.-------
i
:
:
|
;
;u";
-.98,
1.14,
1.45:
1 . 8 r:
-.r4
;
.97:
-.JZ',
L.z6:
-."6:
;Jo:-4.0!kcr
:
i
,ku, r.0l;
i----
3----:
----
! -------:
--_--___
-1.21:
!________
-I.J6
2.04
-I.52:
|
i
-,J7 .,
r.49,
i ______-_-_;
".+l ,
-.46 .
r.sf,
__________
L
l'5
-?.5O
-3'75
r
-.()
'.
-2.92
:
-10.02
5.ry
-2.89
,
',
f .ot
-).og
2.89
t
J.O6
-1.54
:
-1,70
-10.11
i,it::ai;:
-.89t
|.b
7.27
-r.27
z
'J0;-1.!:kor
-.
.6+
-2.57
1a
-.5t, kc t. -r.J? 3 -10.09 ! -10.49 , -Lo.J5 : -Io.zt
: 30 i
i,o._:
;
5 . 1 I +;
;
, t" , 2.66 ;
5.r8 ,
t.rr
',
',
', -?.9?
-t.g
-a.oe
-2.\J
-2.65
u"
.-r.ol
.
I
fo
;
'kur
?
i
t.6Jt
?.oEz 2.\J:
2.65 r
z.g9
lrz
t-.r]4
-1.114
l.lo
-..
r
Itr{
-.79
:' ,
t
.0+
.89 :
3
"
7.28
;
',
"
-<.rc
3::t:::
'f
"
.9O r
',
.r5
-J.II
,.1,
_.+l
r.ZA
,
i
i
,.;s
_.lo
r.gs
:-__________-____-:__-__
( continued
t{arao. IJIGC
z u 45035 F
)
hbl.
9.--B
(continued)
.
3
:
i
Loadlag
-:
9:
|
:k":2-plyr
f:or
i
: k" :
l:l
:Deg.:
3
::33i
C o m p r e s s i . o n :6 O : . . . . :
k"
J-ply:
3
:
:
:
:
0.68
5-ply:
i
:l:l:I:l:l
l:2:I
:Infinite-ply
:
9-ply
!
Iz2zZ:Z:I:l:l11:l:1:l:1:1:l:
'-ply:
i
::!!3
:
:
0.99
l:33:
Shear
J-pIy,
:
:
l:I:I
l.JO:
1.46 .
I.59 :
1.!8
z
f.57
z
I.6J
:
2.48
i
-1.68
:
-1.J1
::ii!
:50:....:
k":
I.0l:
.58
t
.97:
l.Jl
:
2.Il
k" :
-.87 t -Z,Oj
z
-Z.OZ :
-1.!g
:
-1.62
!i!3!3!i:
Shear
: 60 :....:
r.32
.66
:
r.o3
:
.16
r.27
rnzT
'
'
:503r.5'k"'
.\?:
.??,
.,*zi
:
.64:
.44:
.7or
r
rks:
k" '
.59 r.l€
;60,-.5:
i
.
k
:
:
, " , -.1o, _.74 ,
:
:
3
:
z^
r ^3 ,
. t+, -t z ! . z o :
; 60 :-r.0: kc .
,
-.47:-1.a5 t
:
3
:ku:
tr
"
t.fr:
_.ts,
3
-r- . Z
Ji
-L.ZJ:
.e" ,
.9j
:
r.r+ ,.
_.2'* ..
-
z
t.rg
-l.l!:
:
:::333:::
3 5o :-1.!: kg :
"
:
3
,o.i
50 !-4.0: ko :
:
:
:
,ku,
'
.jE , t.oo z
.97 ,
-.r7 1-r.5o:
-r.46,
.T
.46 :
.r*l
;
- . 7 + . - L . g z z _ r . 7 9 :,
.g";
r.1g
L.27
;
.62
!
L,Jl :
_.&
,
.
r,o5 ,
_1.06 r
1.05
r.57
t
'
1.42
1.26
-.5)+
1
tl
-1.11
.gA ,
-r.t+l
:
.44 ,,
_r.71,
.j9
;
-1.56:
-r.54
_s.gt+ .
-4.L2 z
_g.lS ;
-4.g7:
-+. ()
.
"
.)o
,
-,gg
.Al .
-r."j;
AQ
-t.to
.7A
.41
------.---.:--'
3!!33:!3;
Tenstonand; 5o , .5, kc : -5.J2 r -7.9j
snear
t
3ks:-2.55r-j.96
:: ; a ' t a : : i a
: 50 : l.O: kc | -I.61
:
, -s.+g ,
3 -4.a4:
-Z.gS :
-1.O5 2
I r" I -r.e3i -".ge i -l.oe,
:
,
i go i r.ri r" : -.eg: 4.te , -r.tg i
3
:
-?.692
:k.:-t.J4t-2.6\.
ii:::33
n
: 50 : 4.0: ko : -.26 z -.j6
r
3
:
:k-t-l.oli
'-?.26.
:3:-s::3:
-.16 t
-2.26.
'.
, 60 -.5i kc: -5.97i -1.", : ->.zs,
'
!
2.99: r.50 z
?.5J:
: 5O:-1.0: k" : -1.8! , -.96 :
1 . 6 93 . 9 6 !
:
:
: k "- ::
-I.6tr z
1 . 4 +z
:
:k":
t.IL
|
-f.rt ';
-r.so i
-Z.lo
t
3:
- . -) o/ |
-2.21 '
-).LJ
-t.tl
-r.ts
-2.5J
3
:
:
:
i
t
i
-.>a 3
-2.o9 3
-t.r" 1 -rr.5z
i
j.56 |
5.76,
i:::333i
3
I'.
-2.?7 ,
?.27 |
3
-j.77
:i
:
J.77 '
- 9 .5 0
-i'tu
-3')-4
-I'78
s
'
:
'
t
,
-.)+
!
-s.g+
\.97
-J,23
t.zJ
-J.O8
-i.*
;
-<.o(
-2. rb
-10.02
-5.ur
-l'70
-?.55
-. 50
-r.96
:
.
-!).>6
ien
:
'
-4.47
4.47
( rcutinued
lllneo.
IJIGC
zY4tuj7 N
)
of
Table !.--Buckling
:
,
3
Loadlng
plywood
lonB
platas
3 k":2-PlV,
f.or-,
I:I
: ks:
3
€ :
r
under
l-plyr
:
3
conblned
conrnession
l:1:I3
(continued)
and shear.
: Infiaite-ply
:
:
9-ply
5-ply
:
:
:
rLt?t2:?zI:l:l:l:l:l:1:I:I:1.:
---3 --..--------------------:
J-ply:
;
or tension
5-ply
:
l;2:1:1:l:l:l:l
, Dee..
i
3
3:3::::::3
Conpresslon:75.....,kc,
0.62t
0.8!;
l.Ol:
z
r.r7
I.26:
1.24
.
L.25
L.75
?
2.29
.
-I.59
! :
ShoAr
z75t....tk"t
3:::!:3!::
Shear
:75:....:ks3
.98.
.58:
.96t
-.65,
-t.OZ:
-I.Z?r
L.g9 |
f.Z).
-I.j6
?
-I.!,5:
-I.!0
3:l::33::i
.58:
^ ^ :.
.a)
.4s :
.lt8 :
.rlo:
/^
a
.ou
:
.20'
(1
:
. 5 6'
.2S;
.)> .
.t+
. 5 e:
.7\.
.?9'
.l+4'
.TJ ,,
.46 r
.69'.
.59
.86
.52 ,
.64.
3
.84
-.84
-.8)
-1.08 :
'
_?.O5t
,59 3
-.9'
- I . I O
"
:
3
"
n
, n. i -t.lf
,
,F
:
t'
^:
|
, 75 . +.o. kc
3
3
t:3:33:
:
-.",
^_
-t.ll
!
;
rk":-I.O1:
-.26
^_
-l.lJt
3
;
-.35 ',
-L.J6t
: z l , - r . 0 ,t " , - r . * i
',
a
, o" ; r.94;
"
'
t-r.5'. kc -r.05 ': 75
;
:
'
,
,n.,
: 75 ,-4.0: k" :
;
:
-t.01
-I.JI
.J2
-l .28
-1.33
.t1
',
-9.2L
,
-Lr'77
-5.88
z
'
-l.Jo
-3.30
:
_r,74
i
.
r- c^. o
t
3:
-2.3Lr-3.O2r-?.78
-I.JO
|
-t.s5 i
'.Js i
-r.56 :
-J.O? t
-2.79
3
-1.5?
4.6t
-r.++ ;
-.'ts ;
-.44
-1.84 :
-r./b
-l .s,
-r".gg :
i
6.jo ,
t.7G',
-rr.0z
,
z
-.*
-I.)Z
:!
'. -.5'. kc t. -6.1?,: -2.60 '. -s.zl
: 75
i
t.r{o; 2.6r:
:
8
:ks: j.r6,
"
.8J
-,6J
AZ
.o/
-7.r5i-ro.ll"
, -r.e. i
lnE
-1.o0
-).)ot-).1(.-+,o.1
-?,3r'
.60
.o(
-j.ti..
, 7 5 r L . O t k o : - r . 5 6 , - 1 . 4 g r _ 1 . g 5:
3 ks : -1.66
-r.U, '. -1.95
.
:
:
,
,. r.5' kc ,. -.90
-.Ss
-1.12 :
: 75
:';
:
f
-1.01
_ ? . 9 61
:::133:
"
\1
.a0
-.80
.?1,
-.92 |
!ks3-2.9J
.41
.16
r .06
'.5J
,
.90
L.12
r .05
-.5J
-.68
and:75
.fi o" : -S.aS: -4.r0 :
;
r.?t
t.oJ
-.52
.52 .
-.78:
1.07
I .07
rl
.99 t
- .l+9 ,
.Jb:
!
.9r
.9r
oa
r.o)
,75
.o{ :
.oz
r.rl
:
.90 :
I.TJ
.99
!
ar
.1!
-.75'
-.71 ;
:
-^i
.-?
1c
:
.ou
-.57,
-.)+:
snear
r.19
.4s
-.44;
.r]4
*:ff::'
.97
.l+o:
.)) 'z
.39
i
.55 ,
- , 2 7'
.81 3
:n":
r.5s;
-,29',
I'16'
- . g ri t . e e i
.9r r.66t.
;
-.5? |
.76;
-.16
''u;
;
-.93 3
rtgi
-.2s
,
r'10:
-2.15:
2.3j
-L.)V
aa
t
'
1.9r+i
-.to
I.5r
i
I
r
-4.00 i
4.oo !
s.S,
-J,4r
3.4r
't
7.79
'
'
|
-Z.LO
l."o :
^
- . OrU
i
:
2.41
?
2
aq
4.79
-2RA
!
z
:
?.og
-4.78
t
:
).o)
-'70
2.81
( oonotuded )
Uireo.
I,IGC
za 4w76 ?
EXPLANATION
OF F'IGURES 43 TO 70
The following figuree show aseociated values of k" and k", the constante
in equations (35) and(a0) of Report No. 1316, toiitte UrFtfing of long
rectangular platee of plywood under cornbined uniform corrrpression (or
teneion) and shear. The edges were taken to be simpty supported. The
constants for rotary-cut Douglas-fir plywood were used in the calculations of the coordinates of the points on these curves. Curves showing
the ratio of the half wave length b to the width a and the slope y of the
wrinklee ae functions of k" are pTotted to the tift in each figurE.
Report No. 1316-C
/
'[,u,'
I
/
0
0
'[,n,
il
_EL
S\
&
EI
S\
i\
I
0
ffi
llt
7
s
^l
v
fr
-t
0
2
SCALEFOP A N D ,
.--t
3\
FIG43
v
1',M-t
l"l
FIC 44
\
*l
I
lx
t-
r-l.
I
-totz
F-
,ffiL
FT
t_
t-
YI
|rll
'v
t-
A
X
Jt(L
z-cw(,)e =n'
/
'1
0
\
7
z - e w( ' t ) e = t s '
I
:_x
hml
E\
-t0
SCALEFOR
,a
a
t,,;
I
1cY
r/
sf
-EL
lot
,il, , lnotLonlo
'
JCALE FOR 6/AAIID
"
r r-r[J?,ifr=*.
z M+\175
Ft6.46
z-ew(') e.ts'
L
fi\
a
I
"i
x
iltil
II
I
| ,r"
s
\
[*r,t
M-
/l
F
YI
olj
F
s
\l
;
I
€x
I
7
+,
\'l
v-.,
-to
CALEFOR
t[lr, ?or/t"ort,,
Ftc.47
J-PLY (t:t:t) e =/5'
/
z
r
2
AI,ID I
Ftc.48
s-nv('r,)e=to"
(
rl
Yl,rrur 1l
n!
,M
s
.$,
t.\Y
-.rf
;\
(y
)
w
t/ort?or{"ori,
z u 44176 F
Fl6 4e
t-ctv (r,t,)e=eo'
rrt. so
s - e u( t , t ' ) e = t s '
-3
-J
tu
tttt
I
0t
0
\
0
I
4
.\
as
a
s
1l
=!_
n
0tl
tl
4--r
rilt -
t.z
SCALE OR la AilD 7
.IU
SCALE FOR
..
AND,
Fl6 5t
3 - P L Y( t : 2 : D 0 = t 5 ' ,
I
l
-T
-T
0
0
/
a
s
.\
FIG 52
3-PtY(r,z:)e=so'
-T
1
s
I
0t
1
:*\
/
tl
Vk.
s-l
"f,
-s'
N)
7
4
2
I
I
l
t
-to
SCALE
FON ttl
..
z M,t*r77 F
-I
SCALE
,
FtG.53
*pw'(i,z,,)e-eo.
liltt
ilInr
fiililtt
1
\
I
,/)'
.l
CR
AIID '
FlG. 54
t-Pw (r'z:r)e-ls'
-
1-lWtTtFflJUJt _
ilil1
II
Yl
-
/tl
lillil
,ffi
I
I
I
)
\,ffir
t/ li
.{
rl
_st
I
I
J
-\
L]
L 2-z
S C A L E CR
t
AND7
5C
\
E :0R la At'il
7
FIG 55
5-PLY (t:l:t:t:t)e =t5'
F t G .5 6
5 -PLY(t :| :t :t :t) 0 =30'
lt
I
\
I
I
I
0
l\
l
I
$
,!
q
;/
_$
Yll
/
-t
0
S C A L EF O P ; AND .,
z M\ut76, ,_0,,
flfi,it'r=*.
'ffii
-*\
0
0)
I
rl _
tliifi,tilililh
o-iIW
Iilt
tl
-l
0
SCALEFOP
AND7
FIG.5E
5 - P L Y( t : t : t : t : D e = 7 5 '
-
vl.,
I
,W
Yl
Itlrir
lllll1
€
rl,
-2
W
tli.Zt
Yt
lrll
ral
tvAl
ililf
W
vt
ll
I
."1"ttzl
ia,
I
II
iai x
iei
"i"-
-sL
*\
_S
Yl
-3
_ Et_
'f,,,,
iai
rlw
/:
trl
v
A
tzal
ililt
\
-t
0tz
STALEFlR b/aAtlD 7
I
-t
412
r r a t r r n p b / . n u nv
FIG 59
Ftc.50
) 30'
5 - P L Y( t : Z : ? . ' Z :gt =
5 -PLY (t : 2: 2: 2,t) e =/5'
l
"1,,,u
I
3
iwnl
I
I
) v///Ai
tlLUt
I
I
Y
IW,
'i,,,,,
. "lu
ivllili
ivlllxi
!w14i
illtt
-5
rr
JL
s
vl
si,
.-s[
lw'
'ivui
,r,rt,
,
lllr
et
vl
lfiill
iWNI
iW,
W
x
({-,
lril{
l
),./,
sil
s/l
z
"
7
u i lN[ l aj .-z) ?t 'o r '
FIC AI
;-,S'Pw(t,2;z:z:t)e=60"
,ril*
{1" i
YI
|*lt
W
I
ijrl
illtt
I
,t
SCALE 1B o/" AND
,W
I "/
YI
lilill
E
\
oroo z
4, 4ND
"
Ft6 62
5 - P L Y( l : z :2 : 2 :1 )g = 7 5 "
3
I
ial
-z
Yl
ilfil
HIttt
W
x
ilil1
ia,
I
I
w
lllll I
I
ia,
n+ftl
I
Yl
tYzt
(
vl
-3
Yl
llw
X
TVZI
I
I
(
^.
I
vl
YI
hll
rl2t
rei
I
t%!
, tzzl
rffiA
rillt
'v1
I
s
I
,W
ltttit
-,
vl
X
.-J
-a
ililt
Iilill
I
W
'*t
-st
\l
$l
-"-f,
I
-t
u
z
SCALEFOR AND 7
E
5Cl
'oR
% ANI
FtG. 54
e - 30"
9 - p Ly (1,l, t,t,1,t,t,1,)
Fl6 63
9-PLY(1,r,
t't'r,r,1,1,)
e=ts"
I
I
I
YI
lrlrr
W
vl
I
tW)lx
ivui
.J
YI
|llilt
'1,,,,,
I
iwl
IW
ivtnl
nmrnFI
tuJlal
|illt
\l
I
i
\
I
YI
^\L
ru
q7
v1
${
u,-
|rr
tfi,
tr/,
, !91
il
x
-2,
FtG.65
9-p1y (1'1:1,1:l:t:l:t:De=60'
Yl
,W
^(l
YI
Ill
iwnl
W,
-t()t2
S C A L EF o R b / d A N D
"
z M 4 4 1 + 4 rr
I
x
q"/
s/
iY
I
-
-Y
.z
-t()t
scAtt ronl" AIID
FtG.65
9 -PLy (l,t,t,l,l,t,t,1,le =7i'
vl
llllrl
IW\NI
wnr,
I
Yl
fltilt
I
I
Wi
ililr
I
I
X
vl
tbt
tV.2al
iW
x
5
YI
httrr
W
)S
iL
vi
tai
iai
Yl
iS
t{iit}
s/
v
,
tal
"1,,
u,
iai
ltW
s
s
s]
tat
I
"i' I
o
JC
E F IIR
2
AI,ID 7
I
0,,!
2
Ftc.57
^ - P L Y 0 =t 5 "
FtG.58
* - P L Y 0 =3 0 "
vl
I
,W
YI
Ilrr
X
lt
"1,u,,
iW
IW
fltr
I
I
'1,,,,,
t-
-a
I
iVIIili
iwui
i
illl{
iwnl
,il|lilr
\
ttual
lrilt
ts
\
,,/
vl
I
^\L
vl
[illt
-R
sll
,u/n-
\
lv,/ly't
S'
illttf
W
'tu,, 7
Yl
[*rr
ivm!
Iiltl
I
,Z'ou?*l^
ori7
FtG. 69
--PLY e =60"
a
iwlttr,
t
"iuI
t2
op l- nnn ,
z u 44495r
iF
SI
7
}Y
SCALE
\/
_qL
\-/
W
ul',-
-:Sl
Ftc. 70
a-PLY0=75"