Supplemontto
BUCKIINGOt flAT plywooD pliTts tN coilpRrsstoN,
sHfAR,OR COftBtNrDCoftpRtsstoNANDs]trAR
Buchling of f,lat Plyuood Plates in Uniform Shear
With face Grain at Angles of Oo,+46o, and 9Oo
Revised July l9OO
I N F 0 R M A T t 1CiN
i l ,1i 1" 'l.]i
A N DR l A i - F i f i i r ' i l i l
l9ri2
No. t3l6-H
UNITED STATESDEPARTMENTOF AGRICULTURE
,
FOREST
SERVICE
FOREST
PRODUCTS
LABORATORY
. Madison
S,Wisconsin
ln Coopcration with thc Univcnity ol lVimoarin
SUCKf,INGOF TT.A[ PIYTfOODPI"AfES IN UNISORI,ISHEAB
WIIH FACSGRAINAT AI{GI,ESOT OO, +II(O. ANDAOO
3y
A. W. VOSS,Englneer
C. 3. ITORRIS,&rglneer
and.
JgStrE PAII,IA, Jr.*
1
Sorest Prod.ucts laboratoryrS Sorest Serviee
U, S. Department of Agrieul-hrre
Introtl.uc,tion
X'orest Proclucts Laboratory Report No. 1316-H, lssued ln FebnraTy 1945,
presented.prelimlnary resulte of an experimental stucly of a nathenatical
anaLysls for the buckltng of flat plywood plates subJected to ghear. The
fornula that hacl been prevtously ilevelopetl tn Forest Proclucts Laboratory
Report No. tJ16 was fouad satisfactory for the plates tested. Curves were
dran'mto show the correlatlon between the tests .and.conputatlons rnad.ewlth
constants for both clauped. and. slmplf, supportetl edges. Fron the linlted
nrnber of tests reported., an effectlve uLtlmate-stress curve was obtainetl
for cleslgn pur]poses
lhe Arny-Navy-Clvl1 Subconnlttee, aftef revtewlng Report No, 1315-8,
requosted. that results of ad.clitlonal tests, lncludlng 'square plates wlth
face grain at angles of +4Jo and. 45o, together with whatever check tests
nlght be roqulrecl to exanlnb the effect of the stlffness of the load.tng
fra^nes on observed. stresses, be inc!.ud.ed.ln thls revlsed. raport.
Y
Thls report supersed.esReport No. 1315-H and.presents a more extensive
experlrnentaL stutl.y of the nathenatieal analysls presentetl. ln Forest Prodlucts
laboratory Report No. 1J15 for the buckllng of fLat plywood"plates und.er
shear Ioad.. Inclucled. in it are results of tests nade on plwood. plates of
soveral. proportions and. with their face graln at varimrs angles' as follows:
lFornrerLy an englneer at the Forest Products laboratory.
The other authors
assume responslblltty
for the present revision.
4{aintalned at Madlson, Wls., ln cooperatlon wtth the Uaiverslty of WisconsLn.
Rept. No. 1J16-Ii, Revtserl
Agricul.turo-Madlsoa
Wlth the face graln at 0o (paral-}el to short d.imenslons)
Plates 10 by 20 inches
PLates L0 by l0 inches
Wtth the face graln at 90o (perpenclicular to short d.lnensions)
Plates 10 by 20 lnches
Plates 10 by J0 tnches
With the faee grain at +4J.o (paralle1
to tension diagonal)
Plates sqlrsre.(slze varied)
Plates 10 by 20 inehes
Plates 10 by J0 lnches
With the face graln at AJo
(per?endlcular
to teaslon d.iagonal)
Plates square (size vartett)
Plates 10 by 20 lnches
Plates L0 by l0 inches
In each of these condltlons the thlckness of the pLate and. the stlffness of the loatllng' frame were variedl,
$he forsnrLa d.eveloped.in Report No. 1115 rdas found satisfactory.
A
group of curvss for applylng the buckLing coefficlent,
k"r, for lnfinltely
lon€ pS.ates to flnlte plates ls presentod.. Curves showlng the relatlonship
betr'reenobserved. stresses and computerl stresses with ed.gesof the plates
Adjustnent factors
s1ryLy supported. antl. with eclges clamped are included.
requlrod. to brlng theorettcal and observed. stresses lnto agreement aro
presented.
Analysis of the data on frame stiffness
of this stlffness on buckllng stresses.
showed.no coosistont effect
The effectlve ultlnate-shear stresses were obtalneil ancLplotted.
agalnst a nond.inenslonal p,araneter of paneL wid.th to establlsh a curve for
the d.eslgn of plates subJecteil to shear.
Pumose
Secau.seof the presslng neetL for d.eslgn criterla necessary to the
d.urlng the war, forrnr]-as aatL constadts rvoro
butLt[1ng of wooil aircraft
d"evelopeclby mathenatical analysos. Ono such analysis was presontod. ln
Forest Products Laboratory Report No. 1J16 on the btrckllng of flat plyt*ootl
p3.atos ln conpresslon, shoar, or conbinecl corupresston and. shear. Ehe forrmrla
for coupresslon r,ras subsequently substantlatecl experimentalLy, and. tho results
Rept. No. 1J15-H, Revlsod
-?-
lrere $rbllshetl tn Forest Proclucts laboratory Report $o, L316-D. Bhe uork
presented. hereln was an experfuoental lnvestlgation of forrtrLa 2L.(energy aethotl), of Forest Products Laboratory Report No. L3L6
gcr = k"\]?1"2
for the crltlcal
buckllng stress of plywoocl.plates untler ualforn slroar, together with an enplricaL study of the ua^:rfunrnshear stress that plyrlrood panels
rtl,l zustaln after buckllng.
Descrlptlon of MateriaL
The pLywood.for thls serles of tests r,rasnade from Sltka strlruce logs
obtained. as-part of a shipment fron the state of Washingto# and iron yetfowpopLar logs obtalnetl fron Tennessee. The Sitka spruce was cut into flttches
and shlpped to a plywood nanufacturer to be quarter-sLlcecl to the speclfleiL
thlclaresses.
The sLlced. veneer r,vasreturnect to the Forest Products T,aboratory
to be clried, edge-glued, and.'prossetLinto 2- by 6-foot plywood.paneLs. The
yellor'r-poplar was rotary cut, drled., and pressed. into paneLs at the laboratory.
Tbe faeo graln of tbe ftnlsheil plywooct uas at angles of 0o, 9Oo, and 45o wlth
refcrcnce to the ehort sld.o of the panels.
Marklne and Matchlne
Panelp were numbereclaccorcLing to constnrctlon and specios' as shom
ta tablo L5.it Constnictlons 4 to 21, lncLuslver w€f,o of, the usual plywood
constnrctlon; that is, the graln directlon of each ply nas perpend.icuLar to
Constructions I+Oto I+5, lncluslve,
the grain d.lrectlon of, the adJacent plies.
were cllfferent only ln that the graln d.lrectlon of the center two.plies trae
para3-1-e1".In add.ition to the constnrctlon number, srnall. letters (a,' b, c,
etc,) were used. to,distlngulsh panels of llke specles and constnrction fron
one a,yrother,
A typlcaL laycut of speclnens ls shor,nrla figure 108.5 tlne 45o rnaterlal
was used. both in negatlve and positive shear, Eo that the face graln was
[he
para1LeL and. perpend.icglar, respectlveLy, to the compression tliagonaI.
deslgnattons for lndtvidual spectnms suffixedl to the paneL d.esignatlons and
the tests thereby lnd.lcated. were as follows:
3shtpnent 1580.
&Ur" t"Utes and figures In thls supplement aTe nustbered eonsectrtivcly wlth
G. Figures
thoso of Report No. LJ16 and its iuppleurents 3, C, D, g, F, a^nd.
1J4 through 138 have been d.eletetl, however, ln the revlsloa of Beport
No. 1JL6-H.
53o"ro.e tho plwood paacls t{ere narufachued. to rneet speclflcatlon AI{-NN-PJL1a anit were thougtrt equal to commerclal alreraft grad.e, no attorapt r.ras
nacle to avold. ninor d.efocts tn the face pLies, since there was probabLy as
nnrch varlation ln tho inner plles as la the faco pIles
Rept. l{o. 1316-H, Revlserl
-3-
-Desfunatlon
[est
L, 2, etc.
Plate buckllng
81, 82, etc.
Shear strength (pane1)
Plate shear test for nodulus
ln shear
of rigidtty
D and. E
Statlc benillng wlth the face
grain paraL1.e1 to span
3 and. G
Statlc benillng wtth the face
graln perpend,torLar to span
$ach frane nernler wae assigned the sane ld-entificatlon
as the plate
plus
an addtfron uhich lt was cut, after the buckllng test was coqgleted,
tlonal number to fulentlfy each nernber of the f,rarne.
All speclnens and coupons were condttloneb to produce a noisture content betr+eefr,
3-Ll2 and"5-Ll2 percent at tine of test so as tb avold. results
that woulcl'requlre correctton for moisture content.
Method of 1e.g_t
Preparatioq gl Specinens
ALl test speclmens werE eut on ftne-euttlng,
shaqp, clrsular saus
after the panels narkecl as lndlcatecL ln ftgure 108 had been cut on a bandl saw
lnto sectlone.
,
Suckllng test spectnens were prepared. as shown ln flgure 10p. Flrst
the corners uere cut by drllllng
l-lnch-tllanoter
hoLes centered. 1/2 tnch fron
the corrcer of the test area and Llz lnch away fron the corner on a llne at
&5o to the eclges. The pLate wae thon cut to slze on a cirsular sorrro Ehe
specinen rrras then gluecl lnto a frane of uhlte plno, hartl mapJ.e,or yellow
blrch.
I'lhlte plne franes wore used on a few of the very thln spoclnons (three
f/tl8-lnch plles),
slnce the hoavy'hardwood. franes caused sone breakago at the
0n thcso thln
corners of tho fragtle platos during hand.llng bcfore tost.
plates frre,nos wore-ma.d.eof Jl4- by 2-inch memborsglueil to each sid.o of the
plyvrood., whlle on the thlckest pLates the frane members were l-Jl9 AV Z$lt+
lncheg. i'or the bulk of the spectnens between these two extremes, the frame
rnenbers were 314 ly z-)14 lnebes, A gap of approxlnately f/f6 inch vras rnaintained. at the comers between the encls of the fra.ne nenbers to prevent thelr
Holes to recelve the loaillng plns were locatetl
bearing otr one another.
aecor€.ing to the table of d.lnenslons glven on flgure 109 andl were clrtIled
3.arge to provltlo the aecessary bedrlng area on the frane.
sufficientLy
Rept. No. $16-8,
Bevised.
-lr-
Frane nenbers were prE)ared for static bentllng tests after tha plate
buckllng test was coqgleteil. Eaeh rnenber, nade up of tlro blocks wlth the
pl5nvood.glued between then, was r€noved. fron the test plate by neans of a
band.-saw cut along the edlge of the area testecl for shear buckllng.
Ehts
satiled.surface of the fra.ne nembers was then Jolneredl to a flat, srnooth surface for abottt 2 lnches fron each end. to bear on the supports tlurlng the
'!
static bend.tngtest.
fest Pro_cedures
The proeedures for the statlc bencl.lng test of frane nenbers and. for
the shear streugth test of pltrnroocl(coupons sI ana s2)are glven in the appond.lx. Statlc bend.ing tests nad.e on coupons D, E, tr', and. G are ttescrlbod. ln
the append.lx to I'orest Products Laboratory Report No. 1316-D. [llrg p}?te
shear tost on coupon C ts tllscussed, and. tlescrlbed ln X'orest Procluetd':laboratory RErort No. 1301, rrMethodof, Measuring the Shearlrg Moitull of:Wood.tt
The procedure for the buckling test of plywootl plates ln shear ras
eetabllshed only after rnrch tlmo and effort had been d.evotecl to experlnentatlon wlth nethocls of supportlng and loaillng plates and wtth noth.oils of
observlng the crtticaL buckllng load..
: Ihe method of obtalning the crltical
buckJ.lng stress of pL5nrood.
pLates in shear ls illustrated. ln flgure 110, r,lbleh shows a spoelnen uncler
l-oad. Load.was applled to the frane of the speclnen thro4h wood loacling
blocks fltted with I-lnch-sqrrare steel bars. Ilard.enotl-stool rollers and
loacLing plns transmltted the load. to the frame, ancl the frame transnltted
the Loadl to the plywood. panel by glue shear.
The test proeedure was as foLlows: The loadlng plns and. rolLers hrere
assembled.lnto the drl}leil hol-es. Whennecessary, the holes were reamed.
wlth a hancl rearner to provide a snug fit for the pins.
A tLlal gage graduatecl
to 0.0001 lnch vas then adjusted to oae menber of tbe frane of the speclmen
to measure the flexure of thd rnember1n the plane of the plyr'rood.. [hls frame
gage was adJustetl so that tts sptnil.le contacteil. the eclge of the pLyr*ood.at
the center of the frame member
Diagoruil d.efornatton (when record.ecl) was neacured on the eouprssslon
d.lagonal across the center of the pane}. To obtain this neasurenent two
tlla1 gages (not shordaln flg; 1L0) graduateit to O.OOOIlnch were mor:nted.
oppoeite one another on opposite sld.es of one of the longer frane nernbers.
Bhe spindles of the dlals rrrere connectedl to the opposlte frane neurber by
flne wlres that passed.over the center of the panel, one oa each sld.o, ancl
rnad.eangLes of 4Jo wlth the ed.ges of the paaol. The readings of tho two
tlia1s were averagerl to nlnlnlze the effects of arrf, sltght trvlstlng of the
framo caused.by trrarptng and of anf, sllght eecentric drtlling
of tho holes
for the loatllng pins.
The speclmen was thon placett la the tosting nachine. To prevent tho
panel fron twlstlng antl to keep the frane properly alinocl, guld.o ralls were
Rept. {o. }315-H, Revteed,
-5-
claaped. to the frane at the two corners not loaded.. fhese raiLs were
cla,rpeil. tlghtly to one frame nember, but were shimneil to allow approximately
0.002-lnch eLearance for the ad.Jacent frane member. A smaLl loacl r,ras then
app1leil to hold the speclnen between the head.s of the nachlne whlLe pLrmblng
and. centerlng the set-up on the load.ing blocke. DlaI gage6 were tben bror:ght
lnto posltlon to measure lateral clef].ectlon (buckllng) at the center anrl
approxinately at the quarter polnts of the longitudtnal. center Llne of the
dpocinen. llhe potnte of contact between the splnd.les of the ga€es ancl the
panel were narkecl wlth a pencll, thumb taeks to whlch silver contact polnts
bad beea.soltLered were forcedl lnto the plywood, anil the necessary electrlcal
connecttons ldere nade to a couple of clry-cell battorles ancl a buzzcr.
Slnce the oxact posltlons of the crosts of the buchles lrero unprodlctable, especialLy ln very thin pl.ywood, a Bnall prebuckllng load. was appLledl,
antl thp contacts were spotteil on the panel at the polnts of naxinum lateral
movementas shownby a stralghtedge.
Thls procedlure usuall.y resuJ.ted ln a
gootl set of eurves fron whleh the buekllng Load was easlLy read,.
The questlon as to whether thts procedure weakened the paael and.
caused. lt to sustaln lesi load. before buckllng lvas ansveredl by maktng several
test runs, consecutlvely, on each of several paneLs. No weakenlng was evldent, and. buckllng took pLace at about the sane Ioad. on al-l nurs. fhis
repeatetl. loading proeedure appllecl to only a few of the thln speclnens that
hacl.a 1ow ratlo of buekllng.strese to estlslatecl proportlonal-Ilnlt
stress.
-A1thoughon sone of the thick panels the eLectrical coatact was ellninated for the gages neasurlng lateral defLection, lt was felt that the pressure
of the d.lal spindles on thln speclnens wouLd,tnfLuence ttre buckLlng. The
system of electrieal eontact rvas therefore used, D.rring test the splndles
were kept free of the spoeineas oxcept at tfune of reading, when contact hras
nacle with onl-y enough prossuro to corrplote thc circult and to onergize the
buzzer. To tako the'road.lngs of thc frame and.tliagonal gagos was no problon,
gages hail to be read. one at a timo and. r.rlth conbut the latoral-d.oflectlon
"sld.erablo caro to prcvent lateral pressure on the panol by the spindle.
Wltilo the readings uero belng taken, the Load"on the speclaten was heltl.
constant. Und.er thls arrangement some scatter of polnts could alwa,ys be
ergrected.,partly because of the d.tfficulty of..hoLdtlng an even load (especially
at the hlgher Load.s) ana partly because of the factor of hunan er?or'ln.the
technlque of measurlng the Lateral defLecttons.
flhe loatl was applled la lncrenents so estlmated as to glve at least
l0 rearlings before ]uckltng occurred, fhe speed of the h'eaclof, the testtng
machlne durlng the appllcatlon of load hras approxtmately 0.018 lnch per
Readings were taken ae rapiclly as posslble ln'ord.er to prevent
ninute.
unnecessary ereqp of the specinen and. wero contlnued past bucklr,ng. The
ga.ges for neasurlng lateral d.eflectlon were then renoved., antl tho buckles
Sallure
were narked on, the speclnon as lt rsas betng loaded to fallure.
usuaLly occurred. ln one of two rrrays-- bXr conpro'sslon and. bsniling at ono of
the corncrs not load.ed, or by shear along the frqmo'. Failurc by shear along
the fra,no r,ras typlcal for tho 0o and. !0o face-grain pane3.s.
Rept. t{o. J.JI6-[I, Revl^sod
-6-
Methotl of Choosi.ne the Observed 3uckllne Load.
fo d.eternine the crltlcal
buckllng load., the follou'tng neasurementg
were takea at each increment of loatl. and were plotted agalast the loa.d-.
1.
2.
3.
Lateral cleflections of the plywootl pLate.
Dl.agonel compresslon acfoss the plate at 45o to the edges.
DefLectlon of the frames ln the plane of the plate.
0f tirese measurenents the lateral deflections were the nost conslstent antl
were therefore conetd,erocL
0f second.ary
the best tndlcators of buckling.
luportanrce were the readlngs of the diagonal courpression. The chief d.ifficulty ln uslng these ctlagonal measllrenents to d.eternine the crltlcal
loact
was that usuallj' sevoral changes of slope of the pl.ottecl cufire were obtalned
before buckllng, as evldenced by Lateral d.efLections, occurred.. However, the
dctertlnation of the critical
Loatl by use of these dlagonaL moasurements
appoarod. fairly reliable for tho thlcker panols. The frane itcfLections urere
too inconsisteat to bo used as inrlicators of buckllng.
Whlle the curves
plottccl fron these measurementsgenorally followed a given pattcrn for panels
havLng a certaln face-graln d.lreetlon, the cha^ngesln slope of tbe curve were
too irregular to be of value. lfheaever the lateral deflections gave a sbarp
tlefinltion of a critlcal
buckltng Loacl, the plots of the other measurenents
lndlcated the sane erltical
load.,
The loarl, latera].-d.efleetlon
curve seldom changecl.d.lrection wltb a
sharp and.prectse break at the crittcal
buckllng loatl (I'orest Products
Laboratory Report No. 1316-D), probably on account of an inittal
curvature
la the plate.
The curve usr:alIy assustedla nelr slope ln a graclual na,nner.
The buckllng load. was chosen Just above the knee of the curve. tr'lgure /5
of I'orest Products Laboratory Report No.-13L5-D illustrates
the marurerof
selecting the Ioad., as follolrs:
3y extrapolating the cun'e of rrrn No. 4,
the buclcllng load. chosen on run No. 5 wouLtl have been read. at a polnt uhere
the eurve'beglns to level off.
A slnllar sitr.ratlon ls shown agaln in
figure )Z of I'orest Products l.,aboratory Roport No. 1J16-G, ln whlch the
buckllng d.eflectlon curve is conqlared.to strains neasured. wlth nete,lectrlc
gages set at the center and. edges of the panel. These exanples arc taken from
the buckLing of plywood.plates uniLer compresslon.
lhe fol-l-owing oxarples show that thts eamenethod ls applicabLe to
plates und.er unlform shear. Specimens 5xc-1 antL 6xc-2 were sut fron the
same 2- by 6-foot plywooiLpanel. It so happened that spectmen 5xc-1 (fig.fff)
unttl
behavecl.wrder test in an ld.eal nanner; the lateral novenent uas sllght
the bucl<ling load. was reached., and then rapid nrovernentwas record.ed.. There
buci<llng load on thls speclmen r.ras
ls no questlon but that the crltical
21450 pound.s; Specimen 6xe-2 (trg. 112) behaved.ln a contrary fashion. If
the methocl of chooslng buckllng load.s were appIied., 2,100 pound-sruould be
No
chosen because at this load two of the curves become straight Ilnes.
buctcllng load. was chosen for thls specimen because of lts noncritlcal behavior, but it ls d.esiretl to polnt out that, even in such an extreme case'
the critlcal
buckllng loacl can be approxinatecl.
Rept. ITo. I315-H, Revlsect
-7-
Specioen lftrn-2 (fig. 1lJ) firtfrer
shows this nethod of choosing the
type
Strain gages of the electric-resistance
buckling load to be correct.
were glued to bottr faces of the plate opposite each other, and stralns were
and of frane
deflection
recorded in addition to measurerrents of lateral
the buckling load chosen fron the strains recorded by the
deflections.
gages rras approxi:nat'eIy 3 ,2OO pounds. ltris load vras also indinetalectric
cated by all dial. gages. Dletalectric gages nurnbered 3 and B increased ln
strain wrder compression until buckling Tras reached, when compresslve strain
was relieved, and a slight jncrease ln tension vras noted lrith gages nrrnbered
I and 5. Gages nurnber 2 and 7 should theoretically
have renained at zero
strain ntrjLe tension and coupression equalized each other, but at buckling,
a new relationship
developed. the buclcling load plcked fron the lateralcurves agreed vni.th that indicated by the el-ectrio-resistance
deflection
strain gages. Matched to this spcluen lyas sp€ci.uen ldtxn-lr cunres for
which are shorrm in figure 111+. Ttris is a ttrrylcal set of curres ttrat agaln
indicates the correctness of Ure method of chooslng buokling Load,
A different
type of behavlor io shown in the curves of figure 115.
these curves are representative of specimens that begi.:r to borrvin one di.rection on the application
of Load and that at buckUng change into a uave
pattern of a quite different
form. ftre buckllng load is then relatively
simple to read fron the cunres and is usuaLly at a point wtrere one of the
lateral gages reverses.
The curv€s for specinen 17dr-l (fig. It5) iffustrate
The cunres for ttre rnatched speci.nen 1?xh-2 (fig. 1t6) are also shovun
this.
jn order to conpare the nethods of reading buclcling loads.
The selection of a critical
buckling load frequentJy required personal
judgroent in the interpretation
of the load-deformation cul:\res, To eliminate
any possibility
of ttre results being influenced by this judgnent, all of the
obsenred critical
loads rryereestablished, and the observed critical
stress
lras deternined, before the critical
stresses nere conputed by use of ttre
theory.
Presentatlon
of Data and Computations-
ltre data obtai.ned from the plyvuood tests and the resuli s of conputations are presented in tables 1Z to 26 and in figures 11? through 126r- J.L|
(wit'h figure L27,l,2B, and 129 being used in computatioas) and 130 througtr
133.
fn tabl-es lJ through 26, colurnn 1 gives the panel designation, and
column 2 identifies
the buclcling test plates.
Data pertaining to the buckling
test are Blvgn i-n colurnns 3 througfu J and include widt]r (a), length (b), and
thiclmess (ft) Aimensions in colr:nns 3r hr aurrd5, The obsenred critical-buckling stress given in cohrnn 6 and the effectlve
ultimate stress 'r,abulated in
column 7 were courputed from loads obserrred in test by the formrla:
qr
Report No. 1316-H, Revised
-
P
h ''Etrba
-8-
(1)
WhenP is the crltlcal
buckllng load, q ls the critical
buckllng stress; and
when P is the narlna:tn load, g is the effeettve ultfunate stress, J-abelecl.I'"
tn thls report.
Data fron the shear strength test specliens ( sI and s2) matchstLwlth
the bucklLng test plate are glven ln coLunns 8, 9, and. 10. ftre thlcloess (t)
ls glven ln colunn 8, and. the length of the sid.es (w) of the square test area
ls g5.ven ln eolumr t.
fhe rnaxinu.nload (\1tr) attained. tluring..t1le.test was
used. to compute the uLtlnate stress (fr6) by the followlng forrnula:
W,,t +
Fs6=ffi
This ultimate
(a)
stress ls given ln colu.m 10.
fhe notlu.ll of el.asttcity 31 and. 32 were conputecl fron bencling tests
of specimens D, E, T, anil G by the forrnrla:
E'r o r E cQ=
where P
I
D
I
lPIl
48DI
(:)
= load. upon the centrally load.ed.coupon ln pouatl.s
= length of span over which the coupon vras tested in tnches
= deflecttoa of the coupon at Loail P ln lnches
'= noment of inertia of the eross section of the coupon in lnches.
[he nodu].us EI results when the face grain of the coupon ls paralj-el to the
span, aad. the nodulus E2 when the face graln ts perpend.leular to the span.
The load rvas kept sufftcieatly
low so that the proportlonal- llntt
hroulclnot
be exceed.ed.. The vaLues obtalned are tabulateiL ln colrrnns tI andl 12 of the
tables.
The ratlo Ef (Sf + E2) ls glven ln cohlnn g of the tabl-es.
The ruotlulus of elasticlty
ft, 1o the cllrectlon of the grain of the wood
used. ln nalclng the plywood was comtrnrtetl from the fonnula:
Et=#(nr+12)
which resuLts
fron
(lt)
the forrnula:
Ef,+Sf=31
+32
(5)
tt be assulned that gT
of
- 2=
0 ! += F{,, and where 3f = rodolus of elasticlty
(See Forest Products Laboratory Beport
rvood.in the tangential tl.lrectton.
No. L3L6-3, p€€e 3.) Thls assurptlon ls not groatLy ta erxor for thls use.
lf
Rept. No. 1316-8, Rev1sed.
-9-
buckllng stresses given ln colurm 14 for slrrply strpported.
,[he critlcal
and,
ed.ges
ln colunn:lJ for claqred, eilges wefe..co{prited by forruul.a (Z?) ot
Forest Products Labdratory Report' l{ot, fJff,; ltArqf, rs :
Q 'car = o " h where
rt=
h=
a=
i<'-
-2
the noilulus of elastielty
of the wood
the thlc}rlees of the plyruootl plate (col. 5)
the wld.th of the plywood,pLate (col. 3)
a coefflctent
that d.epend,son the plate and that was
determined. as follows:
Fron the dlata on statlc
bend.lng tests the ratlo
nhlch is
glven ln colrlnn $, was obtalnedl, [hls ratio $as used. to enter. the curves iu
figure 127 fot cla4>ecl etlges and ln flgure L29 for strply supportetl edges and
to obtain the proper values of k.r, the coefficlent
long
for tnflnltely
plates subJeited. to shear. These coefflcients then w€re corrected. for the
flnite pLate, as follows:
Sga1n the ratlo
flgure
"t* Pz
was used -- this
128 for claupeil ed.gosand. ln figure
to obtain the corresponrdttngvalue ot
buckle length ln an lnfinttely
lflre Length-width ratlo
two' valuee or 4
*,
plato
long
to obtaln thearatlo of L
to enter ihe cunres ln
130 for sinply
l.o.r
the ratio
supportetl edges and
of the theorotical
to tho wlitth of the pLate.
I fo" each plate
abrl.
tlne
testeil was then divid.ecl by tbe
for each ectgeconcll.tlon.
These
of + were then usetl to obtain the ratio 61 IE91o" each ed.gecond.itloo
br
ks
by applicatlon of the proper curve fron figure.l3L when the face graLn was at
0o or pOo, or fron flgure IJ2 when the face graia was at +Jl'5o. 3y taking the
regiprocals antl mrl.tipLylng by the k". for each ed.gecond.ition a value of k"
ratios
supported. edges and a value of k" for cla.nped eclges were cleternlaed..
fhe two vaLues of eer, one for simply supporteil ed.gesand. one for clanpefl
for sirply
ed.ges, rvere then easlly
cornputed by the forunrlai
Ratios of the criticaL bucldtng stresses to the shear strength (col.10)
were computed.by using the observed. stress (col. 6), the stress for sirply
supported. eclges (col. 14), and. the stress for clanpeil. adges (cot. 15), aad'
were tabul.ated" ln columRe l-6, I?, and IB, respectlvely.
Rept. 1To. 1J15-H, Revlsecl
-10-
Ehe ratto .E- glven ln coh:.nn 19 ts a nondlnenslonaL paraneter of
Bo
panel ryid.th obtalnad, by the formrla:
e-
(8q.. (3) of Forest Proclucts
Laboratory Report No. 916-I.)
ao
The values tabulated
the reclprocal
tn colrrnn 19 r,uereobtalned. by taklng the square root of
QcI obs
of the values o,
glven in coLruur L6.
3sd
The ratio of the effectlve ultlnete stress of the plates tested. for
buckling to the ultlmate stress of the matchecLcoupons tested. ln shear ls
glven ln cohrnn 20.
Tor conpartson of the stresses computeclfor sinply supported. eclges
and. the obserred. stresses flgures llft,through 126were prepared, r,rith the
q^_
(slmpty supported) frour column L? ot the tables plotted. as
values of #
Fsd
8""
abscissas *i
tn. values of
fron column 15 as ord.inates.
Fed
3or couparlson of the stresees eor;nrted for fireit ed.ges and. the ob'servecl stresses flgures ll7l through 125r lrere prepared. in a slnilar Eanner.
An eqpirlcal
curve obtalaect fron a conrposlte pLotting
of all
tests
gro;, colr:mn 20 for the
wfth !i fron coh.rmnLp for the absclsgas ancl b
ao
Fsg
orcllnates ls given in flgure LJ].
I'ron this curre the effeetlve uLtlnate
shearlng stress of flat pl-ywoodlp3-ates can bs estlnated for d.eslgn pur1)oses.
Stre datl obtainecl fron tests of frane nerobers are presented. la
tables lfa thror:gh 26a.
::'
The plate speclmen fron which the frane menbers were cut is ld.entlfied ln cohunn 1'of these tables, and. the nr:mber of the frame menbers tested.
for eaeh pLate ls shown 1n colurnn 2. Colurnns3, 4, anr[,5 show, respectively,
the span, nlclth, andl clepth of the nember at test.
Wlil.th iac].ud.es the thicknese of the plyuood and. two thiclcnesses of the materlal forming the frane.
The varue of Er courrputed.
for each memberls glven ln coiunn 6, and. the
average value of SI for the two long sldes of the fra,ne, or aLl sid.es tested
1nthecaseofsq1]arep1ates,1sg1ventnco1unnf.Inco1umn81sthe
ratio of the critlcal
stress observed.$urlng the test of the platd to the
crltlcaL
stress computed.for siuply supportetl eclges obtalned. fron tables 1?
through 26 by dlvlcllng colu-ton6 by colrrrnr 14.
Rept. No, 916-8,
Revlsed.
-1r-
'
Critlcal
Dlscusslon of Results
.
*,..,
Suckllne Stresses
Ehe critlcal
buckllng stresses obtalned by test are conpared. with
those cor;nrtetl by rneans of the theory presented. ln Forest Products Laboratory
Reports Nos. 1J16 and. 1116-8 and wlth attdltton;I theoretlcal results.
The
follorving egtratlon, nrrmber (ef) of report 13L6, was usad:
.2
Qcr = k"Ef*
a'
ln whlch Etr = nodulus of eLastlclty
l.
a=
b=
kb-
ln the dHrectlon of the graln of the
wood of which the plp*ood ls rad.e
thlcloess of the pLywood
sualler dinension of t*re pl5nrood plate
larger dt.nenslon of the p15'wooilplate
a coefflclent,
the value of which clErends-upon the conetnrctlon of the plyuood. antl the ratlo I
a
The procedlure was to flnd that value of k , that ls kor, that appltes
to lnfinltoly
long panels ancl then to ad.Just this value to apply to panels
of flnite length by neaas of curves obtalued fron varlous nrithenatlcaL a^nalyses.
The values of k* were obtalned. froro the cur"res plottecl ln figures 127 to L29,
lncluslve, as previously ileserlbecl. flbese figures were pl-otteil fron the
origlnal nathenatlcal tlata obtained la coanreetlon with Report $o. 13L6-3. The
adJustnent of k", to ks was nacle by neans of the curves of figuros 1JL and. 132'
For plyt'roocL
shlch were obtalned fron varlous mathenatlcaL investlgatlons.
havlng its face graln para1Lel to oae of the edges ancl the od.ges slmply supportod., the work of E.Seydlel was usod, fron whtch the curvs of figure 12 of
Report No. 3.J16was obtalneil aacl'replotted. ln flgure L)Z of the prosont.rqlort.
l'lhon thc otlges of theso panels wero clarrtrlod.,the work of R. C. T. Snitl$g was
usod.. A curvo obtained. fron Snithrs roport rvae also plotted. 1n flgure $2.
Ehc ctrsp ln the qurvo was usod, ln the computatlons ln tho prescnt report,
ln orror, coultl
althorrgh the srnooth dlashed sulrro, wh{ch ls only sllghtly
gralp dlrcctlons at 45o to
havo been usod. For panols havlng thollfe.ce
their od.gos, forutrlae tl.'orivoil by Green aad. Hearroon4were used. The deterrainalts ln these forduLas rvere expand.ed.,andsolved to obtaln the grbup of
curres d.rawn ln flgure 1J1. The use of these curnres has been prevlously
d.escribed.
9R. c. E. sni.th. 'r3uckllng of PlyrvooclPlates in Shear.tr Australlan
for
Sclentiflc
antl lad.ustrtal
Researcb - Dtvlslon
of Aeronautlcs.
Cor:ncll
Report
sM51.
4.
I'The Suckltng of Flat Rectangular Pl-ywooti
Magazlne. L945 Ser. f, voL. xx:rvl, rrp. 659-688.
E. Green a"odB. F. s, Hearnon.
Plates.rl
Phllosophlcal
Rept. No. 1116-8, Revlseil.
-l,2-
In figures ll?Ato L2&and 11?nto 1268, lncluslve, values of the
stresses are plotteil agalast'contrnrteclvalues' r'ilth both
observed.crittcal
yalues dlivldletl by the approprlate strength of the pL5rwoocl. In generaL' thg
stress are greater than the conputed. values for
obseflred. values of critlcal
plates wtth stqgly supported. edges, and are less than those coutrruteclfor
plates with clanrped ed.geswhen the courputed stresses are less than the
The stratght Llne shown ln each ftgure ls ertencletl
stress.
proportlonal-limlt
hrckllng stress ls Less
fron 0 over the lang€ ln whlch the computed crltical
If tho computetl
shear.
proportlonal-llmlt
in
stress
than the approxi.nate
to the slopes of
eqtral
buckllng stresses are corrected. by factors
crltical
these Ilnes, the observed.Etresses are approxlnateLy obtalnecl. For each
graln d.lrection two such f,actors were obtalnecli one to apply to computecL
stresses when aEsr:mlngedges ere etuplY. supForted, and the other to corymtefl
stresses when assr:nfng the edges are clampedl. An average factor was obtalned
for each graln d.lrectlon and for each of the two nethod.s of couputatlon.
lhese factors
are aE follows:
0
Slrply
supporteil etlses
1.05
1.111
1.00
1.30
0o
900
-450
+45"
Cla'nped.ettees
o.64
.?l+
.66
.8ll
[he factors applyln€ to computations basecl on simply sugrportetl edges
are suUstantlally unity, with the ereeptlon of the one appl-ying to a facegra5.n directlon of +4Jo. It is ind.icatetl, tberefore, that the pLates tested
were uor6 neaily sln$ly sulporteil ttra^u clanpecl.
She d.ata showlng the effect of the supportlng frames on the crlticaL
'in tables lfa througt.'26a. .Analysls of
buckllng stresses are preeentedt
thego. aita tnatcateil that the stiffness o.f the frames, over the lfurlted. ran€e
bucltltng stresses.
stutlletL, had no conslstent effect on the observqd crltlcal
Fffoc_tlve Ul-tlnate Stl:esses
Ehe effective ultlmate stress of plywood plates antl, the sheat strength
of the pllrwooit were both obtainetl ln thls stud5r. l{hen buckllng occurs ln a
pLate srrbJeetetl to shear before lt fai],s, tbe average or effectlve ultl-nate
(f*) fs lower than the ultlnate stress (f"r) attalned when the p3.ate
"tte""
falls r'rlthout bucklLng.
t'ron the forrmrld for the crlttcal- buckllng stress It ls obvtous that
glven
natertal a plate can be nad.Esufflclentl-y narrow to buckle at the
fron a
wid.th, labe1ed, aor l.s
sa,mestress at wl:-i.chfallure occurs. llhls partlcular
stress andLsolvlng for ao.
obtaiued. by uslng the strength for the critlcal
[]nrs:
Rept. No. 1316-U, Revised,
-L3-
plate nay be erpressed ln terns of the
Stnilarly,
the wid.th of a partlcular
obserrred.criticaL load. fhus:
,e-ksE,h3
9cr obe
Ehe ratio
that wlll
of the lrtdth of a finlte plate of a given naterlal
caus€ buckltng to occur at fallure le:
g%
to the wid.th
''"4
whlch, fron the above equations, equals
\/,
V 9cr obs
Iao obtalned by taklng the above sqtrare root of obserred. stresses
ls therefore a noncllnenslonaL parameter of paneJ. wldth that d.oes not d.epentL
on the edge or end. cond.ltlons of the plate except as they enter the shear-test
da.ta.
The ratlo
with 9- for abscigsas and..1g'- gsa
Fs@
'o
graln
and.
ord.lnates fitterl separate pLots of the clata for each panel size
Ttre llghtnelght Llnes ind.icate the area in whlch the plots of
d.lrectlon.
Of course, nost of the plots rvere brrnchecl
lnd.lvltlual tests were scatteretl.
aLoag the curve. fhe broken Ilne shows, for corparisoa, the curve resultlng
when the absclssas are the recLprocals of the ord.inates.
Ehe general eurve in ftgure
lll
[he general curve shoun ln flgure 1-33wy be used as follotus to obtain
. the effectlie ultinate streis that a plate- wttt- carry if the strength and
elastlc propertles of the materlal ln the pl.ate are lmown. Ftrst solve for
(a") fn the forsula for the crltlcal
buclcllng stress by uslng the shear
buckllng stress. llhen with the d.lnension (a) of the
strength as the crltleal
and read'
piate, ottatn the
_ _ -ratlo (=).
' a o T . Entsr the curve at thls valuo og (*)
&o
'
ltultlply
this ratlo by the shear strength
tbe corresponitlng va}1e of #.
tsd
of the naterlal- (Fre), and. the result wiLl be the effectlve ultlmate strese
for the plate.
rr (ao) ls computedby assuntng s1nply supported edges, tho value wtlL
be snaller ttran for a:ry other etlge contlltion because the ratlo 9- is l-arger
&o.
rr^
than f,or any other od.gocond.ltlon aniL tho read.lng ef --.:- f1'e6 the cunro ls a
!sg
minlnum for the plate.
Rept, No, 1J16-H, Rovisod
-LlF
Conclusions
fhe nathenatlcal anaLysls glven ln Forest Proclucts Laboratory Report
No. lJ15 givcs buckLing stresses tLue to shear thatse ln reasonabLo agreement
with e:qgorinental resuLtd''lf the ecl.geffurltles of the plates are taken into
accouat. The use of conputations based on plates with siurpl-y supported. ed.ges
lead.s to slightly conservative results.
The ultinate effectlve btress can be obtalned fron figure IIJ wtth
sufflclent accurbclr for ilesign Inrryoges if the ed.geflxity of the plate ls
estimated.. This curve wiLl gtve conservatlve values lf the ed.gesof the
plates are assuned.to be simply supported..
Appendlx
Method. of _Tggt for Ultlmate Shear
Stress of Plywood Plate.s
A stand.ard test for determinlng the ulttmate shear stress of plywood.
had not been established. when thls series of tests was performed.. A tentativo nethod.that hatt
glven consistent results at the Forest Procluets
T.raboratory was followed.;
fhe coupon for test was shapedLas shown in flgure L08, coupons 51 and.
52. The d.etail at the eorner of the couDon lras the same as that shormrfor
the buckLing test specinen tn flgure 10pl The cllameter of the pin was 1/4
Lnch,.rrAttuas 1/4 inch, rr3l' uas Jll6 j.:nc]n,anrdthe clia^neterof tbe roLler
was JlV lnch for all the coupons
Dinensions of the coupons were such that the sqrlare area woul-d.not
buckLe before failure occumed. and. that the area gluecl to the blocks rvould.
be sufficieat to transmlt the forces between the blocks and the plywoocl
without failure.
[hic]nress of the pl5rwood.rangecl.fron abouf LlL6 lnch to
1/4 lneh, and the slde of thq sqr:ar- rqngedt fron I-1/4 lnches to 4-tl2 inches,
tlepend.ingon the direction of strese antl the thlclmess of the pLyrvood.
'
Iia.rtl.woocl
bLocks tlt6 lnch shorter ttran the siiles of the square were
Iocatecl. on the plywood. coupons by the use of a jlg and. were gluett to the
plyrvooclwith a'coltl-sotttng urea-resln glue. Pressure was applled. tq the
glued parts by wood.clqmps for at least 15 hours. After the glue was set,
the coupon was conpLetectfor test by d.rilllng 1/4-lnch-diameter hoLes wlth
the spoclnen heltL .ln a J 19.
- .."i
In settlng up the apparatus for test , If4-tnch-d.ianeter plns ana liilt+,-,'
lnch-d.laneter rollers were assenbled. on the colrpon; aad. two steel wcd.gcshapcd. hoad.s wlth surfacos at 45o to the vertical were contored. ln a lrydraullc
testing nachlne. The specirnen was then placeil between the head.s as shoronin
Rept. No. L116-8, Revtsed
-L5-
flgure IJp. .A load of 10 pounds was nalntained. on the speclnen whtle the
ellnenent andl bearlng between the parts ln the set-up nere checked..
The load. was then lncreased until the specirnen falIed[, a&d.a maxfumm
Ioad rvas obtained., I'allures occurred elther in shear parallel
to the sldes
of the square or Ln coqpresslon or tenglon along the ttlagonals of the square,
tlependh! upon the constructlon of tho plyr.rood.and. the relatlvo strengths
la shoar, coarpression, and tensl.on.
The ultlnate
(Z) as 'folLows:
where Fsd = ultlnate
Ehear stress was eomputeclfron the naxlur:m loail by formrla
shear stress
trfittt= uLttnate load., regard.Iees of type of fallure
= thlekness of plywood
t
Ir = length of one slde of square.
fhls nothod assunes that the sffect of ths load.lng plas locatett t/4 lnch
outelfle the ed.goof the sqlrare ls the sarneas if the plns were centered, at
the odge of tho squarer
Trvo coupoas were testeil for each 2- by 6-foot panel, and. the average
ultlnate stress was used. for the cornputatlon of the effoctive rvidiths of
buckled pLates. fhe clata on theso tests of coupons ar€ glven in tables I7
'ccLr.unns p,
througb Z6 Ln
8,
anit L0.
Test of FraraoMombers
I'tane memberswere tested. ln statlc bencllng, as lllustratecL ln
flgure 140, to d.etermlne the stlffness of the franes tn the plane of the
plywood.n Srds were supported. on l-lnch roller plates centsred. 1 luch fron
each end. on the smoothed.surfaces. Ehe d.lstance bei;ween the l-ateralljr adJustable knlfe-ecl.ge supporis was record.ed.as the spa.n. loacl. was applied.
at the center through a curved. wood.enloadlng bl-ock. Deforoatlon ln lnches
was obtatned. fron a dlaL read.lng to 0.001 tnch that was nountecl on the supporting base anil bore on the plyr.rootl between the solld-wood. coqgoaents of
the frane.
Lroad.-d.eflection curves were plotted., ancl the slope tras usecl to
compute the value of II by the formtrla:
Ef=
where
1 PIJ
165-
load. ln pound.s
L = span ln lnches
D = d.eficction ln inchee
D-
Rept. i{o. 1316-H, Revlsed,
-16-
Table 15. --Pllrwood constructlons and specLes
Con8
r tnrc tlon
.---.-.-.:
No a
tVpe
-.-;
o 11 : 1 : 1
L6
t7
18
L9
20
thlclmese
t/zo
L/'t+B
.1
I: I:1
t/zo
L/L6
L/'+B
e'l
1 :l : 1 : 1 : I
t/zo
t/t6
L/\8
:l I:1: I: I: I
r/zo
L/L6
2L
L/!e
l+O
l+r
\2
1:2:1
,+,
U+
t+Z
1 :2 : 1
Rept. No. 1515-E, Revisetl
Specles
:
t/16
6
7
I
9
Prv
L/48
I
,
:
:
Ll20
L:/16
l'+8
t/zo
L/L6
Yellolr-poplar
Do.
Do'.
Sltka spruce
Do.
Do.
YeJ.Iow-poplar
Do.
Do.
Sttka spruce
Do.
Do.
YeIIow-poplar
Do.
Do.
Sltka spruce
Do.
Do.
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Table
224.--Reeults
bf
test6
for
stltfro8s
ot
frue
Ddbera
buckllpa
@tchlpa
1.9 by r0
IEeIs.
Fr@
BuckllDg:
:--------test
--------:FretglEr
glEcta@:tro.
no,
i -----
(r)
-----
LrJ-I
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t2
---
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i--*-:
|
:Il:
5rL-2
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t 2 8 z ) . 7 7 8I I . 9 8 8r
I,695,8 | I,687,5 |
L,62
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9e-1
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ta
r 28 I r.l8o I L.977 |
| 2 8 : 1 . 7 9 1z+L . 9 7 7t
L,829,' 2 L,72r.' '
1.r'
I,62I.7t.....,,...:.....,.,..,..
9a-2
|
r2
r 28 r 1,8c4 r 1.9€6 |
| 28 r 1.?82 | 1.91% r
r,816.7,I,92r,7t
r.18
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15rn-1
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t2
2 28 | L.772 | r.99, t
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t2
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2
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r 28 r !.1%6 | 2.757 |
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2
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1
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2
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: 28 : 2,908 .2.7e I
8,1+12.\ . 6107l.5 :
I.0Z
7 ' 6 9 9 . 9. . . . ' . . . . . . i ' . . . . . . . . ' . . .
:
I
2
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t 28 | 2.Y4 '. 2.702 . ? , 7 8 l + .r4, . . , , . . , , . : . . . , . . . . . . . . ,
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t
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1.42
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: 28 r L?98 | 2.?79 |
: 28 : 1.f85 | z,TlL I
2orl-l
3 1
1 27 r ,.001 ; I.1t4 3
| 27 |,.OIO : I.Lto !
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| 28 2 I.78, ; 2.758 |
: 28 r 1.180 | 2.77I I
l+,P81.3: l+,?D..or
I.2?
l + r ! 4 0 . :1. . . . . . . . , . : , , . . . . . . , , , . .
t
r,t+r9,6 |
1.42
1,ffir.r15,95r.rt
.?[0 l
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8,z4o.zt 8,rlr,8r
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8,02r.4 : . . . . . . . . , . : , . . . . . . , . , . . .
I+rztr-z
r
:
!
: 28 : 2.900 | 2.711 |
z 28 r 2,902 | 2.727 |
: I
------:
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fE,
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!
II
:
I
(r)
at
BFl!
dete
I Depth:
(r+) :
-r-----
:
test
tace
| 8 | 2.%l .2,719 |
? 28 | 2.91+t : 2.?40 |
3 28 : 1.912 t 2,7)\
t2
4r!J-1
:
:
r
1----:-------
! (2) r(l)
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1.58
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l+rJ-2
i
:
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tliith
bche6.
l+Ode-l r
l
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| 27 | 2,0& r
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776,6:
720.0:
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rz
: 28 s l.8or | 2.7\2 |
| 2A I I.791 | 2.727 |
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!
4rrl-2
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t2
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l+,)@,0 : !,581.t+ :
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2
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fhl-]
!
I
2
t 28 t 2.918: 1.125 I
z 2 8 t 2 . 9 1 \| L . W r 3
fLl-z
r
2
t 2 8 ; 1 , 6 & . r , 7 r o 3 2 7 , r r 8 , \ : 2 ? , I o 8 . 1:
| 2 8 . 5 . 6 7 >t r . 7 r 2 | 6 , 6 7 7 . 8 : . . . . . . . . . . :
Irl+tl-l
:
I
2
3 28 | 1.915 | 2.72, |
3 2 8 | f , y 2 , | 2 . 7 5 6|
\,9L7.5 | 5,181.0;
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l+l+rl-2
!
2
! 28 r 1.914 t 2.71\ t
2,414.4 r
l+ttk-r
:
l
. 28 | 2.9\5 . 2.Tt2 |
? 28 | 2.9N t 2.nI |
8,6Q\.6 t 8,55r.5 |
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5r:.-t
:
1
2
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. ? 8 | 2 . 9 0 2t 2 . 7 o ) .
8,??0.8 I 7,912.5 |
,77
7 , 0 9 1 + .; t. +. . . . . . . . . t . , , . . . , , , . . . .
i,4t*.1+ :
.89
4l+rJ-l
z vr 81282 T
t 28 z 2.925 | L.127 |
t2832.9rorl,Ito:
:
1
z 27 . 2,96, I L.Lr7 ,
. 2 7 . 2 . 9 1 9 ! 1 . 1 t 1r
819.5 !
769.6 t
79\.6 .
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6)9.2 t
7 1 1 . 9: . . . . . . . . . . 3 . . . . , . . . . . . . .
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E"bb zr..--Ea4lt!
lE
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L6
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r.672 | 2.7@.
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L'592 | 2.na
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L,fu z 2.lg
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D
1,588 t 2.74
r.r97 2.74O
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4
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1.07
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r.620
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r.608
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X'lgure 1i?.--4,
ior the conluted stresges together rrlth tlata pJ.ottedl for the couparlson of obeerved str€iees'wlth stresses contr[t€d by assnnlng slnply supportetl etlges. pr
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Tlgure 1t8.--4r the ou:re rlth a alope that ls reconnentletl as an ailJustnent factor
ior {:he conrpl1teaEtresses togetber with tlata pLottedl for the conlnrleon of obeerred st1,eeeeevlth etreesee conqrutedby aeeunlng sinply supported edlges. E,
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C?ITICAL STREgS + MAXII'IUM gTRESS OF MATCHEO COUPON.
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Flgure 119.--$ the cunre wlth a slope that le necormendlerlae an adJuetuent
factor for thE couputeil gtresseE together wlth data pLottetl for the coaparleon of obserretl sttessee rrlth stresses corputetl by assunlng eiuply supported
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obserretl stresses wlth etresses corlnrtetl by assunlng Blrply eupp,ortett edgee.
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Flgure 121.--A, the cruve rlth a elope that ls reconnentleil as an adJuetuent faotor
for the conrputetletresses together with data plottetl for the conparlson of observeil etregses rtth gtreeses conryrutettby aeeunlng slnply eupporteil edges. p,l
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FLgure L22.--A, the currre rrtth e dlope that ls reconrendlecl as an ad.Justnent factor
for {:he coqrutecl etreseee togother rrtth ttata plottetl for the ccinparlson of obselllred stresgge rlth gtreeses corputetl by aesrrmlngeirply supportecl eclges. BJ
the ea're except tJrat claqred etlgee were asaunod lnetead of slnply supBorted
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Ftgure L25,--L, the currre rrlth a slope that ls reconnended' as aa
the complottecl
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data
vith
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Ftgure 124 ---4, the curve wlth a slope that ls recormend.ed as an adJustnent
tlata plotted for the comiactor for Ehe coryutetl etregses together'vlth
parLsoa of observed stresses lrith stresses computed by assr:mlng slnply
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Ftgure 125.--L, the cu:rre wlth a slope that te reconnencletl as an aiUustnent
iactor for Ehe computedlstresseg together rrtth dtata plottecl for" the conprarlson of obseflecl stresses nlth etresses conputecl by aeeunlng einplyl
supported edgbs. Er the eame except that clarnFed eclges v€re assumecl tnsteaa or srnply supporterl etlges. Test speclnene were 10 x 5O lnches.
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