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Calhoun: The NPS Institutional Archive
Theses and Dissertations Thesis Collection
1946
An investigation of the shear stress distribution in a
simply supported I-beam with a concentrated load
acting near one end
Wright, Clarence Chandler
Cambridge, Massachusetts; Massachusetts Institute of Technology
http://hdl.handle.net/10945/6475
l-HlfiAM WfTH A CONCENTRATED LOADAcimG hbjkr om mo
CLARENCE CHANDLER WRIGH'JACK ANTHONY LA^iPADA
Library
U. S. Naval Postgraduate School
Monterey, California
library
U. S. Naval Postgraduate School
Monterey, California
0<^^ Wm BSAD OF P0ST0a4ZmAtI SCHOOti
Libicary
U. S. Naval Postgraduate Scfeool
Annapolis, Md,
0<HFf Vm HSAP OF FO8TORAD0ATB SOHOOti
Library
U. S. Naval Postgraduate Sct}OQl
Annapolis, Md,
(Intej>Dapartnifintal
)
MASSACHUSETTS INS 'TI TUTS OF TEGHNOLOGI
Cambridge > Ifeisso
Office ofW„ Mo Murray
Room 3-257
September 25, 191^6,
Captain Wc Ho Buracker,Hoom 5-233
Thesis Work of LCDR CO, WRIQHT, USNLCDR JoAo LaSPADA, USN
Dear Captain Burackers
In response to your request for informationon the thesis work carried out by Lto Comdro Co Co Wright andLto Comdro Jo Ac LaSpada it is a pleasure to tell you that I harebeen very favorably impressed with the irork which they have domand that I am hoping to find someone else to carry on where thevleft off
o
^
, ^These gentlemer. selected an interesting
and important problem which they attached in a most thoroughand businesslike mann^ro From the procedure which they adoptedI am aura uhat they have gained valuable e>:perience for t.hem=.selves and at tho sam^ tiise I feel that they have producedresults which will ba of considerable value to other peopletoterested in stresses in beams when conditions do not ccn-rom to the conditions and lianitations of the beam theory'
o
tsrr^r,^^^ X. X ^" ^ opinion, the work of these two
f f^!!f\r^°^ ^^ T^""^
caliber, and, in addition, it ^aa
of'Ssif^dX:.!'^^sociated with the. in the capacity
Sincerely yourS;,
/s/ W. Mo K-orray
Wo Mo Murray
C:.imbrii,^;e, Mass&chu setts3epte."aber IG, 1346
Professor J. S. Hi^^Qxl
Secr©tcir>" o£ the FacaltyM£ii>Gachu3»tts Iiu.titute of Tochuoioj^-Caiabridge, iA^xj^achusett^
Dear ;-.dr:
Ir. ficcor-iancti with the requirements
for the desroe ox Matter of l>cience in Naval Confetruotioji
&.nd En^ineariri,^, v;e isubmit hdrevi^itli a thesis entitled "An
IriVosti£ation o: th« 51ic.ar Stress Distribution in a Si;2ply
Supporteci I-35£lt. wit>? 2i Concer.trated :,oad -^ctiag Near One
End,"
AM limSTLQATlOll OF TllZ iMUR OTREi^ DI^TRIBUTIOIi 11^ A SIMPLY
SUPPOHTSD 1^3Zm ;:iTH A COliCEUTI^TED i:A)AD ACTING ii:.AH OKf S©
Ciarerice C. fright Jack kT UiSpadaLieutenant Odmu:jid^, U.^.tk^ry Lieu'ton^lt Comaumder, U.,S.Nc.wB.O., U.o.liaval Acadoay, ilJ-U B.C., 0,;:,2,avai Aca:ienr;, IMl
SubEdtted in pca-tiul iUIi'illment o: the
reqiiirari'-jntG Tor the degree of
MA3TEI( Oi- SGIiii^Ci; IT. iiAVAL CCLoTKOCTION /liD iSJGlJSt^EHIKG
at t).lQ
MAi-SACnUni^Tt:: XXTITUT" 05 TECHKOLCGY
IC'46
Tfie authora rSnh to e:;pres;i tiioir appreciation an^l indsbted-
no3s to the foliowins persona:
To Profeasor Williari lA, Murray for hid asciistanoe and guidance
in helping us select the approach to the prolij-em.
To Mr. ^/. L, Tfai.jh for his inctructiorj in the uee o: strain
gages, Rn:\ lor tJic ujo of i-:is por.r;ontil strain gage iiidicator.
lo ivlr* T, A. HeWv?on for instnicting u^ in tho corrv^ct proccdurtJ
for u:io tind applic5?.tiox'; ol i^ti-eiii^coat, for su£^astin>i thf- uce of iTin
strain rocotte uon!Oe:rriph, eji:". Tor ot';sr h&lprul su&«:©stioii» on the
detaiis or this tLe.ilj.
To Mr. if., L. Sinclair nrid Ikr. A. r\ Lynch o£ the Muteriala
Section, Boston Maval Chivr.ard, Tor their prorept procunisent of the-
noceasary m.-i serial a.
11G67
TAliLIG OF^ C0I-1TEKT8
Zm©.
List of Figures 1
List oi' Tables Z
Table of Syjabois 5
Summery 4
I. Introductiozi G
II. Procedure- 10
III, R«SUlt3 11
XV, Discussion of ^'-esults 12
V, Conclusion^ ar«a uecoiaraenuaiioiiia 14
VI. Appendix Ir**
A. JDet^llii of Procedure 17
B. Table.3 of Resu3.tD 31
C. Sample Calculation 60
D. Observed Data 65
E. iUbliogrupUy S2
LIHT OF riGUI^S
Fji^re Title; Pege
I. Locations D.r Strain Garjos on Botton: Fl^n;e 22
II (o). Locf.'.ti.;ii.-. of Str^xin Rc.-sttes oii i'lo.r.j/o 25
T.'$b and Strain Gages on Upper Pl&nge
11(b), DiagroRi of LocctioniJ of Star&in Ga^es 24
III. Heo otan.mlar ;?train Hoaette !-ioiso»^raph 25
IV. Rio}\l9 Universal TsEtlng Kachine vith Bfism £6
in Position
V. Goaeral Vi&w of 'i^eiting Mschine, 'Qe'xsi, and 27
"train Indicator
VI. Typical Stre^scoat Crack Pattern 28
VII, T>i5icBj 3tr&dseoat Ci-e.ck Pattern S9
VIII. Strain Indicator Rnd Connector Strips for 30
LeadD to 3tredi^. Gagos
IX. Cui'veii of •Results 52
X. CurTGC of Results 33
XI. Curves of Kesults 54
XII. Curvoo of Hesiilts 35
Lx •.j'i' 0..'' iA.i.Lii. o
CsLlouIL'it^d .Strrdr. Cr^ge U«.tf. 36-51
Etres^icoat C^^'^.ck Aii;^!*-} Data,
5£-i.;9
Stresiticoat LoafUn.;! Drata fhS^7'b
Stroln ''j-.^:e Ke/^^-din:, r^um-.-ere 74
vs . Strair: ^e^e i^ii'inbor^
XXnV-XLI Ob-itrved ir'tr^ln Gse Data 7^'-.91
A - Distance frara load to ix^hs upport, f^et.
a - AiLxlllaiy >'i::c factor (no urito)
,
B - Di;'tance from load to Tar r.-Jp>?art, feet,
b - iV;icJ5:ne53 o.f beajr. at any posi'cion, iiiche?.,
C - Diauuice of point iros neutral cixis, inchta,
E - Modulus of £i.a?^ticlty, pour^/.i2 per square inch,
I - Momunt o: iner&ia oi ::ection, (inc'ie 'O'^^*
L - Lon^^th or beac span, Tec-t,
M - Ben:;ing inarcent ':t Eection, foot-pounds.
Q - ^ir:jt raomcnp ox oruii outride of any line about the rjoutrol bj-J.'^,
(incbt.n)2»
V - Vertica.l ii'u-.ar, pounua,
T." - Applied Lo-aii, pounds,
X - Horizontal dictari-ce fro-i left support to -in^' point, feet.
^, - Strain in micro-inch.-; rj -p^r inch nic-aeurc^d by strain ro-joite in
thG vertical diraction,
6^-.itrvHin in ?r.icro~irtcbe& per inch inoe.surea by strain rosette in•1 dirf^.ction e,-ui dijtant from £, aod 6.-1,.
£3 - Strain in :r/icro-i?iche3 por inch rutCiaAured by otrain rosette iri
the hori ^or.:tal (ili*feCtion.
£_ - Corrected vn-lue of L;tra.lK in ::iicro-irich'ii;i per inch mefii^ured
in tV;e vortical iii-oction
^^- Corrected vr-lur.s 0'''Gtr<'^<in in silcro-inchou per inch "ensured
6<vai distant from £, and 63.
^j-Corrocted valus of jtrain in ziicro-inches Bt^r inch measuredin the hori^nt<:\l Qiri;Ction.
^ -The at;^;le mea.mred countcrclockwi.oe fro.'n 6 to ti-a dir&ct/ion of ^ r^
degrees
.
cT - Vertical Direct stress, poun-'s por square inch.
0" - Lor.A,lor,:iir:al direct r-ti' ^ --inOa per tsquart- inch.
'T^ - i^f-xl^nuM i>i:.^i-^r cx,rc^3, poui^I.^ pur irqiio.re inch.
1- - J!-hGi.r sC-resa in tKt, 5-1 ;;^lane, pouj:^.s poir G^.uar?; in;;h.
I » OB JZCT
Tiio objeco o.' thi.;: U^aoij invG..itigi;.ticn v::i^ to deteiT:iine tli©
chear ctre^i; JLitrlbutlon in a .-.in-ply uupportc<:i I-bennj ^itha c.jm-
centrated load actirj noar ona end,
II. ?;cQC£DUI^?L
An e" :c y X e.6# alun:iinu::i I-beau ^a:, tested. Thir^ baaa v;a.5
auppcrtfcd " inche;. i'xor. one enui aiu by r^ovii^g the iupport.i, bot:*
length oi' jp-in ^m;'. positioi. af load Tron r.oar rjuppart were vai-ied.
Vertical static lo.-;.;s in iricrrL^iint, incronynts ivere applied in vach
position. (Seo i^i^ure V /.'or pliotocrr.p''. oi* the Isboratorv set up.)
One seriej oT to.!st njn:^ -."ao :tta.'le to obtfi.iri ^lat?; from StrerKicowt
cracl: pr.ttorna. A -j-t-coiK' >:erics of runs ra^ naas to provide duta
Troffi SR-4 str-iin g'ice sieajurement:;.
III. It£SULX;:
Plots oi' vsluos of iraxiaa'n shQiv i^tress st various point:, on
the beam Jor euch oi' Tour ^sparivto tent runs are prtiiiented.
Strain r.^^o dntp. for tht^ roinaiiader gi" the ntriin t^ago t<:>st runs
i J inciudtx-l in Tablea £ to XV I ,
Data obt'^ined fro?n c\'-cb oi" tho Strasscoet test ruiu, ;3ivia^;
loading dats an;i crack. rir4:levT, .'"'.re rourrV; in TsVslea XVll to XXXI.
COra:LUK;IOI^^
The object or the thesij^ «ts s.tt∫(.i in a pr&ctlcabie
laanner ^iU\ -^ooo tii^incroriT);:; accuracy.
The Stresscoat Mtitiiiod of £tret-s Analysis 'Joa:; not provide
Eufficier-t ii}f3i"^ativ-)r! to obt^iin nucintitativc values oi hho&r
stress, but doe;-; provide a i^oo^^ ^uaiitative teii,*.ilc ftrjxin
picture oi' a loaded specijaeii.
l-lI-:COMI^i.rJDATIQKo
This ilivesti[;iition should bo cojitiiraecl Tor the ontirfc 3feri«
of I-besrfls in .'^ener&l U£>e,
Furti:jer invefctl|j,atioru; should bt inade ir. cuch ffianni;r a;:; to
provide (i mazi;nuja of data readlniis ior e&ch pattern oT ga^toD, to
aiiov; tl'ie graphical roif-ulto ercpectud U:> bs ea3i3.y iaired*
I. XriTKODUCnOM
A. Concept oi' the Probl««a.
During ?/orld Tinr II B30.it atructurfiil inveotigations not
directly rela.t&ii trn- vdnninji the "w&r voro nocosi^arily deferred.
Anion*; tbv: iriVesti^.:;?.tion3 postponed by the Buroau of Ship?:,
U.S. Kav-y, ii the profcics orsiJoiitev"; in t:iis theiii;: TVxe Inventi'-n-
tion or th.e Shear fJtresj Dlritrlbiation in -^ tzimply supporteu I--Da*3.!a
wit):i a concentrzitsd load acting nuar one end.
As stated by the Burcr.u ox* ohips- in a if.=tter to the authors,
"The solution o^^' tliii^ proble;^ i.j of interwat in the deiigin of crun
girders havinj^ e lull vfcb pinto, in the doaii^ of manj/ iypcis of
foun^lations for C'irr:.-in.:i; concentrated ioc>J.3, of flight deck longi-
tudinals, and, in -^jencrul, in ail probie{r.5 of transfer of lor-d
throiitjh shear in a boawi. Uitiniotely, it Us desired to wake design
rcconuRondiition,';] in crier to acaicvc t;rt>ator econoniietJ vihen propor-
tioning bea-as to reiiiat lihear,"
Arbitrary liirdtiticns on t,hii> investij:ation, i^.'hich i;5 ii^ub-
alUo«i SiS the firi.;t Et^^eL of a ivork ^itdch EU;:.t cortrinly be co:>-
tinued to include tiie ©iitirw- acopo of this problem, vrera dsai^'iiated
by the Bureau of iJhips >ia bcini;'
1. The invtistii^r.t.ion of t. rijn;;e'i section, profprwbXy •> built-
up or rolled "I" aectlon.
£. Tba inve£itife'«tiori oi Sitatic oonditioas, in vlgv^ of pix)bal:ile
lirsitatlona i;upoi.;ed by labor^At-ory faciiitiej.
3, Tho study of xh'2 3trt>sr^ field produced under load iii a
flaTi^ed crouD-cecticn, rut^ier than an invfcatisiition of aef-iodis of
reduciriji; atresia conditioni;.
B. 8tabua oi the Probleia*
Preiiffiirasry iseaxch i'or published articles ar^ texta relating
to ah©«.r iitre^s diiitribution In I-be«jfi dectiona has rwL=iuiteNS in
tiie optnlon by Wic; autiiori^, that no extoniive tests to deterisirie
«}iear etresa JListributioiia in X-baiufiS loaded other tJian at the
center or the spcai hivo bo<3n urd&rtiaken.
In tee pr-;li;air^i.ry anaiysic; it waa dccidc»u to iimit the lo?\d-
tZLg to values '*?t2ii be3.o'.i th© elastic lissit of the waterialK used,
both to elialnatG pcrciroriont dafor-iiatior. or the apeciBen during' eaeh
tsst Tun an-} to obi)e.in t-ast coiiiitiona which f^ouXd raore nearly
rofiliz© thie loadiutii' normtilly occtjrring in aervico.
The decision of the mothod of approach i'ollowea from ex^.t^^Sri^"
tion of laboratory lacilitioG available, vraich indicated -Umt use
of "Stre^scoat" (Brittl© Lacqusr Metiiod for Strosa Anedysis) would
be valuable in seoxchliif^ for tb© generrd appearance ox' the stress
field, at leaijt the atrosc; fiold forced by tenaiio and coraprt-'Salvc-
BtrQSsea due to loading;. Furtror, a transition froni these ti'enoral
stress fioids to specific quantitative shear stresses could bo gc~
coniplished by solx'lni;; for ehear streGse-s froa directional sti-ains
Obtaintid from SE-4 type- slectric otrsin ga^'t'B, Tie photo-elastio
metriod of stress en^ilyisis xm^: ©iL^.irmted ta an approiich to our
pi-oblea, for the prcaent, on advice from the tucEis 3Upervii;or,
Professor ^urraj^.
One factor vtitioh eiaerged frorc U-.o- preliniiriary analy.sio of the
problena ynna the value of solectiici^: a apeciGon ubich w&a a Bembor o£
d geometrically r-i'iilnr sei'issj cliat i^, 'whic-i could be coDii.>Qr«d
to either It^ger or ,-..;;:ailer I-i^^ctioiia by ra tios s^ich as thv-j
ratio oi.' depth of f'cction to r;Gb tliickneBs, or the ratio of dopt^i
of section to section nojiiluc, etc, 3y tliiL aGiecticD one or tnti
veriabies prcaent Hi.,;ht be clisiinaited in tae appllcs>tloB of
results oI te^tt of oni: p&x'ticuic.r specixjn to ;:;cneral practice*
This process o" ^olactiorj vt^^ not eriployed. To reduce Vie project
corjt nnd to uti.'.ise surplus rnater.-cil, reridily avtilable, a single
alurainum sec tier. -.?ai-: ocosen -r.rbitrarily ',-ith Uie ^ollo-xinc connidera-
tionss
1. T^.e section Jopt!'. t.ao to be large enout:h to periuit ioca-
tior. of r.oore tliRi; tsso roi\-.o oi' !,tr«in roiiettca*
Z,. TIio i5n>p:th o_' sjor-.-ulori ^.??ii: to be -jhort er;ouf;.h to provi.?e
a spen t.-~ell -^dthin tha linJt'-. oC the tujtiii^ rn£ic:;ii;e, v .t ^iruat
enou,4i to ellov.' the lanj;^th oi' d,p&r. to bo iivtroducod a-d s vi.riaI:J.e
factor in the probieffi.
Presentiition o£ r^.-salts ''^y ::^rnip!.;icil nicons (f.ce pp JZ^^35)
appeared ti;) be oi' \n'.Llnc, in tluj.t, rince a ::,tand<ird U.:r«Ii£vy
I-Gcction miy tooted tVtO r',suit;> could b© dircctl;/ applied to tl r,%
section, A ,-ar^t!.arj-iiticrlL ^orim.U?ition of <:-be«j:' stress div^tributlon
in & b«a:fl o. the tyjx inve;'ti.^a-ccd (fro?i toet data obtninod) ^.^>g
dea'iied too lo!i.[;thy a j^ro^jl.fT. lor tA.he j^hort period rillotted by the
curriculum to thcslo, Ihr.'^^verj it i:: ':ioped that the date obt":i.:'.i;.ad
in t}yi5 Inve.iiticjation rpc e>:t^:^n .;iv3 oncujdi to allow future tr-'me—
po;;itioa into a Hit:th3rr:-jitical c:;lutiot: of tht: probiy^.
A coir.parison of the o^^ -served .'md th*-;oroticGl valuG of sheer
strof:.Me3 (obt?ilt:$d .'ro -. jinpie bci^.i theory formulas) is iriaie to
llluistrute the divcrgcnoo of ihvTi^ tpIu^-s.
Ij
'Ihe esaentiiu ivtt^pa folloy/(Ki in thi;;. invei'titiation v^ere as
follovst
1. Ja^lection oi" t-3at ^pecir.en.
2, Selectiori or iststlvovl of testing and m&atitj oi obtaialng
dat£»
5. DetonRlnatioii of .'ijtresu fields by u^-se of 5tres»coat, unne-r
varied conditionrj of span icrm^th and poiiitioii of loading.
4. DGtermlnfition of iitrairic- at specific points by .'neans of
strft-ic ga^ea, uiiler varied conditions of i^pan Itmyth an- po::.ition
of loading,
• - 5. Gfdcuiht,ion ot value of maz-imirR nhe^xr titrezs at eccV. gar;0
poeition fron obaervoci i- train ^z^ d&tii,
6. CelcaUtion of tM-roretical maximira cheap stres;^ at each
atrain ga^jo locitioM fr:?.i; simplcv beani fomulaa.
7. Coniparison of ob:;orvec] '^inci tticoretical ro£ultf>,
F r detailof^ Jlscoiriiioa o^' dc;icriptioii of ©quipiaent and method
of taatin- 3eo Apponuix A.
Ill
.
hi .liuLJlj
1. Plots Ox vtiiucs of max.i?niini shear 3tre;:!u obteinfid .I'roni
strain ro;:.etts data ui-l vyJlues oi' rcaxiffium shear ctrehs o:>tnined
Xroni simple • beaa: formolfis r^m] Mohr* o circle vs. distance along
ti":e beam ara GhoKn on ps.£;e3 2f2 to 35"
£. Sxperimental t>traln G:.[,'e Data arc prcseuted oa patios 3fe
to S-r
to ^9 .
4. In t:ib Stresscor.t tcits p/jde in tbie iriVestie^cLticn it
vifiii noted, that the a>d.o of vertical cr£-.ck;-. in the loTor hsli. of
the bey«iffi ^fi-> in all 'ja.itjo dii-rplaced approxinuiteiy one inch froni
the load po^iition tr^t^sjrd. tiie center of the beeju, irreopectivo oi'
the bea:;i aonn,
5. Superpoidtio'i of the to:. ..dor. '^nci conipret-.'seJ. on Stre.-jscoat
cri:>ck contours s::o;ved t.^at in .sost c*k.-3.s th€: ir.tersQctior;a oT the
cracl:soltained .('roTi thu t-'-o riiri'orenf types o>' lo-iidiii are per-
pendicular, 4i.3 v;as exptjcttd,
6. \"ithin the li:-.:ito Oi" Uic loads u.ed, the an,J.e of cro.clr-
ing: at a ^ivcn poii;t iii thr- 5,tr-ec5co:it cracl p'.ttern is invlependent
ol" the load.
IV. Di:XL::::ior! op ei:jults
The r^-iSiiitw d'ovf t.i:;f.rl the sheer .itro;;:s 'diotribution in a
simply 3uppo2-ted I-l>occi with i, concentriitea lo€ui &Cviii^ near one
end is riot exactly that Ccvlculat';-^d from tiiiiiple bean iormuias and
Mohr*s Circle.
In ^^'noToJl , U'c ;-c^u*u" str^i^yS in the upp:;i- i.aj.:' of the i^-eb
is ^eater than calcuia^ed vfiiueG. In the loiser halT or Ihe besjs
web u'ie exporiaieiitcil nxnCi ci:.lcnlv.ted she^ir 8tre;5ses arc in cioee
agreeaent, t;.vcept in the vicinity oi" the support, -.'here an incr^..aJe
in shesir strev.^i is observe-ci in all cai:-.;*:!^:. . In tb^ uppt.r hair of t^ie
beam v;eb the Maxiiauw v&iua- of ..hssr .:.trc;i:.:y does not occur at the
position or loaiiri^^, but the location of thij fr;a:ciiaum value is
displaced torarua the center o£ th^^ apan.
Ho'w. enouiih data hat: been 'ivorked up tt present to determir-e
accurately the ai'xeeti, oi span ien^^th an-l po,.:iwion oT load froL:
nsar support on the rauio of obcierved mfuri>T.um shear ^:trei-.. to
calculated ruci^^iiaujn ^htL^ar iitrei^-a.
It is belioved tliat th;. ^treaocont Crack Aji,;ie- D^ta pre-
sented ai::;ove couli be coiaL^iii^-'d v'lU. cslculatod Vvilues oI" direct
stre'Ji^es to jive a. jnaximu.T. sl^ear ytrer^s Tor coraparison 'r.ith that
obtained froin Entrain ga^e deto.,
£inc« for a p&rticulcir test run the crack contours appeaxed
Identical and ind<-jpendent oi load, r. ain,;!© io£idin{i- near, but
safely below, tlie elastic iirdt, coupled T'dth the lr;crG^ije^
sensitivity produced by a ^'cooline" agent, should be julTicient
to delineate the dii-*cctior. of principal 3tr©j5::;e3. In t\x±3 respect.
too ^any te.^t runs v.:irc .T.r-...I«^ lo o'-t^in Ltvti., .oo..t (Inta be/oio
the siaiiiarity bct-..oe£i crac;; p-iVtcins; &-jpc£ruci.
It is bellsvcd th^-t L^.c cui-^/it of reviuit>:i coulJ h:.vt '.v:;(;ri
i'aired '::ore erju-^ily \m\ r, ^'r-^L.t'.-r nnvsirj'.r ol' ;;oirtt^ been ol-tr.in-od
Vjy sd'^li t/ional iitr-iiii. £.a/c "-0;jw mriG.
The method oi' o'^tsiniiir itr.. ividu:.! otr:iiri ja^:e roai-i)i ,..,
t?iat OI' Ubin.^- screTs" ty^ifc btnUn,- pot-tt. tc connsct the test le.sid
to ti:e ga^e xFad^ t;iou,::i ir>crc>abii:t the time r.:'ce-6i.e.r:; for each
run, appears to iilve rsor;v accuratt readin;;a an^. hiripiiTies t^.e
proc«sdure o." if^olatiR,, any indivicual derfecLiVii ga^ie Loim.i.
rIn or.ier to rsuace onu oI' the po; ci-.-le exptirimentcJ. errot^,
ob&erved strain j-'ago raas-iri,;'"^: ^vere i'sii-'ed to obtain values Uoed
in calculations. In toMO c^.;-;ri;-i u t-reater nucL-or oi ob.-3©rvatioiis
would have peniiitted rrore accurate reirintj.- To aliov prerjer.te-
tior> 01 :5tffiilar Qui^va^ i'or c^ich ce^it run, fair: d VMiues corro::por.d-
iri^^ to 1^ic 3ame arbitraiy loads •.••'©ra uaeu for cclcui.atloii in .'ill
cases.
The effect of reducing: atraintJ to fevcn ra-nberc-; ij considered
as negliicible, since the loji'i scale o-: the tcstinr Eiacliine proviaed
accuracy only to vflthiri 5 oounclp.
The reaultc ar-^; not a;: extensive A3 desired by the eut^i0rc,
However, it iia bolievec; that tiif: resultb !3^.o^.'n ar-c- representative
Ox the jhear iitrons di .tribution in an 1-bon.ia v-eb ur. ier the condi-
tionti 01 loading] e?elv..ctud for thio invosti^.fitioTi.
1. T]ic object Oil* tLfc th^wxo X. considLiad P^cconipiiuh'Jd.
Z. Tnc raduiJi U;!jLa to obtain shear stress is practicable,
end the nomo.ijraoh solution provisos engineering,: acour-^cy r-"ith
saviDf^ Oi tira€
.
5. Stre33CO£it ruiiii rovcai^'d the foliovdn.s concldera^lonc.
s, Ui^e of ^trersco&t id- «iJvantf:-ge*ouc; in castja -..hore
an overaii str-iin r.dcLure ic de;;lrfe(i. Thia -A-ouid bo parti culai'^ly
valueble in e^-jjnir.atiouo oi a conioiicat^d .itructure rhich coald
not be isolcted or o~ vhich a rroriol couid not be builb v^ithout
cxccv;.ive coj;t,
b. The utio oi' COo as c "coolinis" ag^nt ij extreaely
"aserul, altiiooijh la&tchin,; ob&erved aiid calibrated strains i^ not
pri^ctic&ble uiivier tlife? coolc-d conditions.
4. A checd on tlie accuracy oI w'trs..;;coat coritour-s can be
made by super position ^ of the t^-^naile crack pattern end the
eo3ipre. wioii crtick patUirn.
Th^j i^uithors recoinnend the- rollo-;fin-ji
1. That this .inveoti^v:?.Vcion be coLtinuod an:; enlcr^,od to
inclu..e tOots oi' i-be-tunc ol....r then the 8" x 4^ y.'^'.6" Giui'iinua
I-beaffl airoudy teatod, and tiiat the result.,^ b« coorJijietec to
deteiiainf relatioiu'j bettoci: obLjf.rved te:>t resulto on or.t nc.tevijil
fc-nd cmticipfitod Tt-i.\i.tz In aiiother xetai toid to ue t«. rmiiie; the in-
fluence Ox v&ryin^^ dl2ienj:;ion£, on ' ;:,h->i:.u:' atrei:^ distribution.
2. Thnt in oxh-r liiv^sti:;r-tiorrie; of this
type, v^hert. appiic>?.tion oi' Ltr .:::coat te^ti i'3 ccmtenplatcd,
the iivaaUiV proportior cT avails, bia '.irue be >,pori1i in ruanoita-
tlve strain G^i^c tcrt.s ratlier thar. in qualitative Strefscoat
testii'iii.
2. That ir er^^ contiiiucmce of tiiits invc2ti-
t'fttion the b'.'ara be tested in iiuch rwimier ft;3 to provide data at
shorter intervsls U-:.ixn one TQc.-liim Tor eacri six inc}\eG o-~ boara
length in eacl'; ro".': oi ^"ragei?, sni v.h^jre practicable more rows of
gc^jss be- introduceii.
VI- AP?E!:i:ix
tlU. «. -^-'^Jm
1 • JLftii
roliod btiui i.i^Lt Irtt i:. ^.o-ji^;^-" "^-^ pr^>pi?rtiOvi o: Llii;- rLCio'i^rial
are £ici roXiovtjj
Xcnsiie CU^en^tii /Il^t^OOO Ibj/oc ir.. (;.a::iiauja)
Silicon 0.1 - 0.07i)
Copper 0.10 - J.0
Iron 0,7'/ (BUixinuni)
Chroaiurj 0.15 - 0.25^-
Zinc 0,10*^ (int.-inam)
Tit-'-ni-un j.l^ (ai^ximuia)
Manganese 0.15!;^ (me-xlmus)
Otiivr el'iisinta 0.15a (:aa;d.iBajB)
AlaniiiiUB . RGCU..in4er
The tciit Bftciion v.a:. reannealed ^y th\i .r^ilovdr;-- h/.-at trciat-
aent;
1. Hc^at frar. x'oom tonspf^^r ^ tarn? to 8S0^? -it rate, of 50^ per hour.
2. Bai^e .it 850° for S hours.
3. Cool iron 850° to room teritperature at rate of 25<5 per
hour. Triiu -joctiori was tvciected lor the following
1, It vffts dinieaaionfilly identical 'fdth the .
I" X 4" X i8.4# siteel I-aection that in in, general us© in the
U.S. Kavy,
in handling,
2. It'; relatively ii{;ht woii^^ht provided for ease
3. Hi© externally applied loads requirad to produce
reasonable dtiflectionL, vibt& m."li withiii th© capacity of any testing
apparatus normally u.ied In laboratory- e:<iJiination.
4. The sm^ftt-ce scal^- forjiation uuually preosnt
vaa easily rer^oved "to provide -hs saooth aiirrr'Ce prer<5 . uiiiite to
even distrilation of '->trafsccof.t lacquer and n«ces:iar^' to at'tablish
c cl05e bondinji bet'..^ifcn strsiiin ^ie^^es Jiiv-I the .'a^tal.
£. T£^TIi!{G KkCmiiZ
TTiS testing machine uaod in all tcot ruzis \<U3 the Kiehle
tfeiveraal Testing Kachino, having r gsALKirauni Ct'Ai>aGity o.? 100,000
pourdc. {^&e i^ii^ures IV and V,)
2. SrilD^GaUT
!i!hi3 inaterial in :r.Rnufactared by tiie Stre^^coat DivLiion,
Mognafluvc Corporation, Itt: application and interpretation, folloTved,
basically, the principles act Tcrtii in iho Stresscoat "Manual
of OpersLting In^tractiono".
The raeansurixiij gages v/ere atandiird types of SR-4
Bonded Hosiiitanco Fire Str^iic Gti^ies, oT types illustrated in
Fi^aires I and II, manurtictured by Baldwin Soubhwark i/iviaion,
Baldwin Locoaouive fforke. Both single gagea of t^pes A~l and
A-6, and reotan,iul€.r strain rosettes of type AE-1, vsere used.
The single ea^-es ^v&re lociited on the boaa flanges w!iero uni-
diroctional stroscee '.^jre expQct&d* The strain rosettes rare
bonded to the beacri ^eb.
c. KOMQGrJlFHa
Aa a meanji of reducinti time of solution for shear
stress from strain rosotte dtiUi, tiid nomograph (See Figure 1X1),
developtsd by l\r, T. A- lie^Tson of the Division of Indu.3trial
Cooperation, ii.I.T., waii a vory valuable aid, A comparisjon of
accuracy of riOttOi,rnph solutions arnJ ciiiculated solutions sho^/ed
a diiTerenc<3 of froB! 0,^% to 5,^ in over 100 cai^es.
B> Di::.CP.X?'nQN 07 TE5.T3
1. agLTHOD OF LOADING
Ths bea:;i waii subjected to various static loadings in
the testing aachine. Ti-iOro Vjerc no '.^Rajaic load tests due both
to preliminary arbitrai'y lisiitat?l.onE placad on the; investigation
and to lack of available facilities in th» Materials Tosting
Laboratory'. Tiie arrarigeaont of iiiov&bl<s supports of the testing
machine (see Fit^ures IV and V) s-llov^ed for variation in length of
beaoj span i/Jd V'-iriirtioii in diatanca ;>©t'>.-t-Gn point of application
of load and point of s'lipport, inr]e...c>ri:ient of cc/. oth-r>r. Tlie
supports and los^Cii:^ ited^'e vore Taced T.'ith one inch difimc-tor hclf-
i»ound, transveroe atoei bax'S r/liicii provided support arj^ lotiJin^,
respectively, acroijs the crrbiro vddth ol i'ltitiQc aivi of a length of
not Eiore than J of an inch. (Soe Figure II). It r^fi conoidcred,
therofore, that these nsmber© ?ere "knife edges", providing line,
rigid support
,
Cti'Ow^ccocit tej^t;3 vvijrti juade i'or imornctive roaaons, to
deterniin^tf the appc.?.rfince o.f the tonsile and ccnprejjsiv?i r-traiiJ
fitilo^ under lo-iding. (A typical Streameoub pattern for a
3** X 2 3/6" X 2.0// olaTiinvKi I~boen» is illui.trated ir. Titrures 71
arid VIZ). Tlio load posit3.0B una l^u/^th o-" sp:\n :?rere Vc?ried li;
soroe oi those test runw. 2inoo r;tr9.:;£Coat r<;^''-ct3 ':x)th tc ten^^ilc
lo&diiu^, &-r-A to co.TiprcsL'ive io.a:]ing under certain conditions, souic
runs >?sr-a ro.ade for each of fiose t\TO types oi.' lo^ids. The corapres-
aion load strain patterns v^y^TQ conipared 'Krith. the tsnsilo strain
patterns. Ho effort r;a3 nr.ada to match observed anl c^^l lbrated
strc-ina. In the cajaa -b^isre istr&in patterns vrere laatched 'side
divergence of results 7/^2 noted. It i;3 not kno?7n whether this
divergc?rx© vt&s due to inability of tho authors to correctly match
sti-aina or to variation in the sensitivity ol the beam pc tterna
and t:io£e on the calibration iitripe. To obtain fjroatiy erJ.arged
areas of strcin patt^^rn^, U\q b^am surfaces were coolad suddenly
by neana oi' blasts o- cosnpreLi^f^a ^aaaous carbon dioxide expandi^^jj
against t.he metal i:-ur£^i.CQix. Tr-ii coolinij procei.c ha£> i^'reat advaiita^je
in e. quailtiitive wootino. Gii-dtiy incroct^cd strain .sensitivity of
Streaecoat at loiv temperatui'ea allows e much more coauiote ;;itr.".in
picture^ prcvldin.'; the aid of t/i:; overall pf.ttern oi the entire
specimen ^jfcsraTer strains &re present. In the test vjnh of tUis
tliesis, for instance, cooIIzh; the wob surfaces provides strain
p&ttsrns on the conpreysion fiide of tho neutral axis of the beasa.
1^0 att&cpt 7*as aad« to deteinaine th© lacquer sensitivity under the
"cooled" condition ij*'
3. STRAIK GAai^ TKSTS :
Thfc ffiijuhod Oi ioaaiiij; applied to oh'taiii a&«ii fur couiputatioii
of sliear stress ia deycrihed in p^j'aGrsph B (X), abov^j. Refiv^iintiS
of each straiii gage's ro;?ir-"tanco \Ter6 taken by iri&ans of tho iilw-l
-Strain Indicator {3eo Fii:7vir6 VIII) nx. c'-:.cl; io«c. in eacii teat run.
That is, for each vxa o load %'s.."3 applied enu tUt; ctr'i-in rsadinge
were takcift; tlao lo.?.d ''SlS incroao«d and roadin^^s were again tr.Kenj
and CO on, Xutj r^uniiij-^i^ zajx.ov. at appro:€isi^-vC-xy 500 poun. e Io«id
^or6 Ui^ed ns checiu readini,G since it Tjaa fouiid teot re<idin*rs ior
zero lofxd could not be corap»irs.id ivith &n^ e^ccuracy.
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( "^ / ^ REFERENCE LINE
ON
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^^ 28
A_:^^- 27
Figure III. SaEple Koraograph used for solution of Sliesr
Stress from Etrain Gage Data*COPYRI GHT , 1945 , THOMAS A HEWSON
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TABLE I .
CALcuuiiTi;D j;t!uii^ gage data
Ruii I^hiffiber; 1
De>aj:i vpan 7 feet
Lou-d 2500 pounds
17 Aajur5t 1946
Load Poiiition 2 feet I'r^m near support
E-1E~2E-5S-4E-5£-6
E~7F-lF-2F-3F-4F-5F-.6
G-1Gw2
G~5G-4G-5G-eG-7
-182
1-171753418
-11-12S-28-142-29-16-12-27-58
-62lis
-SO
-U2-156-152-212-21
12-1281
-158-984153
-159-81-68-6486
66
-25-67-73-187-178
-li€-
-125-.8
15
21-26
-il
46
65lij;
100-4292
-18
4
2-15
11937
21-11
123-26
-142
-28
-18
-12
.2e
-30
-68
-64
-113-137-154-212-20+214
-1513
-140-97
43
55
-162-83-91-€6
87
66
-73-187-178-147-123-8
-2
1624
-25-U
46
66116101
-4495
-816-1000-1080-1542-1550986
-8821078810
-794620446
-1400904-1034-1136960
750
44
26i
45
24^-40i
45^»
4sJ-44-34|'
-!52
-22420
16i
CALCULATED STRAIN GAGK DATA
Hun liunibert 1
Beaia Span 7 feet
Load 5500 pounds
17 Au^Ui:t, 1946
Load Position 2 feet from near support
e. ^z €3 £. ez ^3
E-l -25 -159 -32 -24 -161 -31E-2 5 -188 -95 7 -190
'
-i^S
3-5 2 -215 -103 4 -215 -103&-4 -22 -297 -261 -17 -297 -261£-5 160 -29 -240 165 -28 -251
E-6 51 -202 65 3 -203£-7 26 17 -17 S 29 20 -174
F-1 -15 -180 -11 -i:r -185 -11
F-2 -172 1 -172 4 3
F-3 -40 -ISl 24 -40 -106 25
F-4 -20-0 -136 4-29 -201 -Ico 53
F-.5 -36 69 -56 -37 62 -;55
F-6 -25 no -14 -25 52 -15G-1 -15 -223 -15 -228G-2 -58 -114 65 -59 -117 640-5 -56 -121 90 -50 -124 91G-4 -90 -88 161 -93 -92 163G-5 -85 120 138 -80 121 140G-6 160 -GO 181 -65G-7 -69 94 129 -72 95 1:^0
TABLE m.CP^.ajLAH2D :'jTiiMU GAGii: DATA
Run KusiLert 1 17 Aujuat 1046
Eeca£ Span 7 jT&ct Lead Position 2 f?eot frosi r.ear support
Load 45uO r>ounds
e; ^z1
t, £z £3 C 4>
E-1 -52 -£04 -45 -;u -20S -42 15GG -44 1/5E-2 6 -245 -la 8 -246 -121 1850 -35^lA8£-3 3 -J:7 3 -153 6 -275 -133 1979 35:5-
£-4 -30 -502 -oiJ7 -25 -565 -o56 2272 2G
E-5 207 -57 -514 214 -5S -518 257G -liE-G 64 -2i^3 70 4 -2G0 1786 -IS^3t~7 n £!1 -£20 56 ico -221 1504
-44tF-i -20 -252 -15 -20 -256 -13 1920F-.2 "ZZZ £ -222 o 4 isi^e 23
F-5 -Gl -249 29 -.''•*•"' -254 SO 214C -40iF-4 -2oG -176 37 -269 -175 42 1460 -15 S^-lB
?-£ -49 74 -46 -46 77 -45 1100 44;F-6 -32 63 -21 -52 65 -20 814 42 5/6G-1 -es -286 -25 -292 251Q -44
G-C -19 -146 82 -51 -147 85 1588 -?4
G-3 -C8 -157 117 -66 -15S 113 1784-£ljG-4 -118 -Uo 208 -122 -119 211 2062
G-i -HE 1 r.r.JLutJ 173 -liG 155 181 1742 19|
G-G 205 -79 207 -85G-7 -89 116 l-^f. -3.5 IIB 168 1384 16
CALCUI.ATi'D oTKAIK GAGE DATA
Bon Jmmber: 1 17 Auvj-uc^t 1946
Beam Span 7 feet Load Position Z feet from near support
Load(Pounrls)£500 55^00 45(30
A-^1 -115 -165 -207
k-Z -596 -555 -604A-5 -254 -558 -453
B-l 5 i:^ 15
B-4t -^^5 -S6 -47
B-S 19 £6
B-4 -115 -159 -205B-5 45 63 80
B-6 -38 -156 -203
B-7 6S 88 mB«-d -:203 -284 -568
B-9 218 505 597
B-10 -249 -343 -442B-U 73 ion 132B-lIc -254 -35G -459
B-15 -168 -25^ -545C-1 -56 -50 -65
C-2 -226 -515 -298
C-5 -404 -554 -724C-4 -172 -£41 -3oeD-1 -E6 -37 -47
D-.2 -136 -190 -245H«-l 54 78 101H-S 91 128 165H-3 148 Z'J? 266H-4 372 582 491H-5 295 391 514H-6 372 382 491fl-7 214 201 386
CiULCULATi-D oTKAIIv GAGE DATA
Run Number: 3
Beajn Span 5 feet
Load 2500 pounds
19 Au,;ust 1D4Q
Loed Position 2 feet near support
£, ^E-1 -57 -134 -50 -56 -152 -49 -770 -40
E-e -19 -155 -70 -18 -135 -81 -840 35
£-5 -155 -61 -136 -81 -940 53iE-4 -47 -202 -164 -44 -198 -16? -1006 28 :
E-S -7 -7 -169 -3 -:^ -169 1060 -25B-6 -13 -139 o -10 -15S 854 -20E-7 -108 2 2 -108 B94 -22
F-1 -17 -133 -70 -16 -157 -70 -870 56 ;
F-£ -14S -30 -29 -148 -26 -26 -7G0
40|?-5 -?.2 -lo6 -eo -28 -134 -59 -3:58
F~4 -131 -1^0 25 -132 -88 28 -786 -12F-S -20 23 -27 -15 27.5 -57 500 -40F~6 -26 25 -15 -26 £6 -14 420 4lf
44I
Q-1 -17 -121 -27 -15 -120 -27 -D02G~2 -16 -101 -18 -le -100 -18 -748G-5 -55 -101 20 -53 -100 21 -8?2 -52jG-4 -84 -96 68 -sr5 -38 70 -lOlS -C5G-5 -74 bO 75 -78 50 77 8i!0 16-4^
G-6 50 -101 52 -102G~7 -45 55 20 -45 54 21 654 32
CALCULATED STRAIN GAGE DATA
Run ISun^er: 3
Beam Span 5 feet
Loed 5500 pounds
19 August 1946
Load Position 2 feet from near support
Ir-1
E-2E-3E-4E-5E-6E-7F-1F-2F-3F.4F-6F-6Q-1G-gQ-S&«40-60-6Q-?
-81-32-0-67
-0~
-24-208-42-185-20-58-23-25
»iie-10470-65
-188-217
-168
-284
-9
-18
-194
42-188
12655
35
169141-144
'134
66
75
-69-129-115-251-238-194-151-99-41-85
35-50-20-38-2426
95105
-14250
80.29
62-4
4
3
-22
-207
-40
-186
2738222876.118
1067366
=185.214
-278
-4
-14
5
-192
-37
-185
-123
15436
-168
-140
-145
-154
66
74
^5
-67
-230
-238
-194
-151
-99
-37
-84
39-49
-19
582428
97
10714351
TAB>L,e VII.
CALCOIJITLD S'WxUl CxAQ'£ DATA
Hun Numbers 5
Beaa Span 5 feet
Load 4500 pounds
13 kxi^UQt 1D46
Load Pcaition 2 feet froja near i^upport
E-1B~2B-5£-4S^B*6E-7F-XF-2F-3F-4F-.6
F-6G^l
G-5G<-4
G-5G-^0-7
e. ^z £3 e. ^z £3 T.
•104 -.?.4S -83 -102 -243 -87 -1570 -40•38 -.t'79 -150 -5G -281 -129 -if-:60 35
"2^0 -148 5 -242 -143 -1640 sai•83 -S66 -{^97 -77 -565 -295 -1876 29tdl ~1£ -505 -5 -8 -5*35 1890 -22
-24 -249 5 -15 • -249 143C -20-193 4 4 -1?5 1274 -22^
.££ -251 -127 -29 -255 -1?16 -1610 -37ZfO -5o —63 -269 -60 -48 ISBG 22^.55 -239 -no -55 -241 -109 -1442 40237 -162 43 -258 -162 48 -1420 -12^
-4441|
56 46 -67 -55 49 -G3 88049 45 -27 -48 46 -26 77 J
.30 -?.!? -49 -23 -219 -48 -160-0 4Sj50 -182 -SO -29 -184 -29 -1580 45•95 -1Q5 54 -96 -187 56 -I5:ic -352150 -175 ?-n2 -175 125 -1816 -25154 86 152 -157 88 135 1454 17
90 -18 94 -185•80 95 57 -81 98 39 11-90 32
TABt-E: VI u.cai.cula:.:l ^'nuii gage data
Hun Number: 3 19 August 11>46
Qgam Span 5 fset l»c>?-d Pa;;.itioii 2 ffcet Trom ne^ir support,
£500 5500 45'>)
A-1 -118 -1G6 -S15A-2 -182 -256 -329A-5 -£30 -32?. -414B-1 -23 -50
B-£ -63 -95 -lf:2
B«S -25 -4.5
B-4 -120 -180B-.6 -4 -6 -9B-6 -.l.>5 -235 -304B~7 11 16 £0B-8 -214 -501 -369B-9 91 125 1114
B-10 -256 -S31 -42GB-11 11 lo on
E~12 -21?7 -31S -^HOB-IS -194 -2V4 -.55^.
C-1 -76 -lOi^ -156C-£ -21.5 -J»SO -384C-5 -E14 -501 -589C-4 -156 -217 -£P0D-1 -72 -102 -lolD-2 -18'5 -257 -350H-lH-2 44 61 70il~3 82 U4 147H-4 163 .^57 550H-6 210 234 580H-6 144 200 257
H-7 87 121 155
"TA b L-e IX.
CALCULAxi:D SiTlAlI^ GAGE DATA
I^iin llumbtirj4 23 Au^;ust 1946
BeajTi Span ? feet Load Positioji 1^- feet from nc-ar .support
Load 2500 pounds
E-1£-22-5E—
4
E-SE-6E-7
jF-4
F-6G-1
u—
o
G-4G~5G-6G-7 -?.l 52 70 -22 a 70 482 Ifri
E. t^. fs e. e^, 63•55 -117 -27 -34 -lin -26•5 -1 s* -55 —V -152 -55
-£17 -17 G 4 -213 -L7614 -52 -135 18 no -18525 -9 -113 25 -7 -1132£ -2 -94 -9410 -7B 11^ 1 -76.10 -154 -19 -10 -153 -19•14g -14 -14i: 3 -11•134 -7tJ -15 -154 -7£ -£
i^ -32 1 £1 -52.^U 21 'Zb -C8 ££ -27•4 7 -4 7
-25 -147 6 -C3 -147 6
•14 -56 66 1 i;—^w 65.51 -114 62 -114 65•80 45 96 -8i; 45 97•31 45 69 -3r 42 7065 -51 8G -S5.?.! 52 70 -22 51 70
r. 4>
.780 -45i-•ll'OO 59
1580 27
1038
-I5I
--5f
702612500 -ist•iog; 43918 26.596 -2j360452 4591 S9f1240 -4l|
-52I'8(Cic
•1176 -32
868 11500 12
TABLE X..
Sun NuflQber: 4 25 Augu- 1 1946
Bearu Cpan 7 feot Load ?0£it»lon 1^ feot from near support
Load 35'DO oounciy
l^S£-3
E-4E-6£-6
E-7F-lF-£F-5F-4
F-r.
G-1G-2G-3G~4G-5G-5G-7
£. £.
52 -l^G7 -221
-31520 -47
62 -14
SI -2
1516 -193205194 -114
2742 50
5 935 -214JiO -8374 -1G7lis 66
44 G312S30 73
^3 e. e^ ^B40 -ra -167 -39
79 -5 -219 -79
r.54 5 -510 -254269 25 -U5 -26916 o 33 -11 -1G4136 34 • -157
no 17 £ -11027 -15 -1G5 -27
18 -205 4 -1422 -1^4 -110 -1847 1 28 -47
40 -41 £2 -o9»-• 9
6 -35 -2if> e
S5 -22 -85 95
39 -75 -1{>7 901S9 -118 66 14196 -46 62 •39
44 124 -47
100 -52 71 101
TABue XI.
CALCUi.AT7.D LyTBAlli GAGE DATA
Kun Number I 4 23 Au^-ust 1946
Ream Span 7 feet Load Position 1^ feet from near support
Load 4500 pounJa
e. ^z C e. ^z ^3 r^ <^
£-1 -S8 "ZU -52 -67 -51 -1456 46tE-2 -6 -28^ -105 -6 -287 -103 jai4 S9£-5 "410 -551 7 -403 -331 2572 27*
l4E-4: £7 -65 -550 54 -55 -351 -1978£-5 40 -18 -J>14 46 -IS -U5 1358 14-E-6 41 -5 -li'S 45 -160 1196 15: r
E-7 20 -144 ZZ 5 -144 353 l^.
F-1 -19 -26^ -56 -13 -251 -36 a04a 49]^
F-2 -269 -26 -£88 6 -SO 1768 a5|F-.5 -253 -147 -29 -'^5£ -143 -£e 1000 i|F-4 .*)8 -60 fX 40 -60 364 -33F--5 -55 40 -52 -54 42 -51 82B 44^F-^ -6 12 -6 12 1156 38G-1 -44 -277 9 -44 -276 10 2258 42G-2 -H7 -110 124 -29 -112 125 1650 32|
52|G-.3 -95 -S18 119 -97 -216 121 2270G-4 -150 89 18i -154 88 1S4 1650 11?G-5 -58 8^: 129 -61 80 150 S58 iztGw6 162 -55 163 -58
G-7 -37 98 131 -40 96 132 896
CALCULAx::D 5>TIIAI!J GAGE DATA
Run Wuml.>er: 4 £3 Au^^u-'t 19 tG
Beaim Span 7 feet Lend Position 1^ feet frore necir support
Load (poon:^)
2500 5500 4500
A-1 -123 -i7C -229A-£ -X78 -257 -?38
A~5 -184 -26S -.^47
B-l -25 -57 -49
B-2 -29 -43 -56
B-5 21 20 38
B-4 -11^4 -a79 -2:54
B-5 38 55 703-6 -153 "ZZQ -501
B-7 120 IS*/ 247
B-3 -18« -272 -557
B-CJ S8 59 80B~1J -161 -262 -54:5
3-U 47 65 86
B-i2 -173 -2d9 -329B-13 -1G2 -2o3 -"04
C-1 -4.Q -68 -75
c-z -151 -21y -286C-2. -188 -273 -5SGC-.4 -160 -231 -5':}2
D«l -3(3 -55 -70D-2 -16i^ -239 -514H-1 49 72 34
H-2 100 146 190H~3 186 263 S52H-4 208 500 393H-5 189 274 3GSE-.6 155 226 298H-7 146 212 277
TABL-E xni.C^.LCUT.AT£D STRAIN GAGE DATA
Run Number : 6
Besni uipan 4 feet
ho^d 2500 poiuada
26 Augus-t ir.46
Load Poisition l| feet froni near Jiupport
e: e'z
1
€3 €, ^2 ^3 C ^E-1 -18 -97 -3-i -18 -96 . -11 -7ro 4&fE-2 13 —xlS -G^ 14 -114 -5j. GOj S5^E«3 7 -135 -100 -loS -100 1200 52 7/8&-4 Ji5 -lOt-l 25 -102 -324
24|£-6 13 Icii -oa ll» It'
7
-GO -5S2E^6 HO ;5^ -51 21 41 -54 -514 28
E-7 e 44 -^.7 45 -^7 3£ 5/8F^l -4 •^Lj^O* -17 -^i -US -17 944 42|
GliF-;a -117"1
-Id -117 4 -Ifl 800F-.5. -136 -GO o9 -100 -80 41 -6-:^0 -8^,F-4 1 49 -Id GO -1-1 -574 40|
45^^
44??-5 57 -4 im — -t -540F-6 (} 54 —1 60 -1 -49CG-^ -^6 —li-^D -25 -128 ^' -1078
6l|G-2 -U -0^. 5C> -12 -87 -90;:
G-5 -A2 -70 67 -7£ 66 -9^0G-4 ^65 37 74 -57 68 75 780 G9^G-6 -IC 4o '^,'^-
•^i'-! -17 46 3S tm 62^G-6 "IZ 4:: -15 42G-7 -18 56 -16 S7 19 S2% 55|
CALCDLATB^D :>TRAiri GAGE DATA
Run Nuiaber: Q 26 August 1946
Boaia Spaji 4 feet Load Poetlon ij feet froa near iiupport
Load 3500 pounds
e. ^z ^3 £. ^Z ^3
2-1 -25 155 -17 -25 139 -17
E-S ie -158 -71 19 -IGO -71
E-3 u -226 -141 14 -228 -141E-4 41 -140 -3 45 -140
E-5 £6 55 -95 26 37 -94
E-6 28 55 -75 30 58 -76
E-7 12 61 -38 13 63 -38F-1 -6 -1S8 -23 -G -ICl -25F-.2 -161 2 -26 -150 at -25F-S -152 -85 55 -15S -89 54
F-4 69 -21 Q 70 -21F-5 79 -6 81 -6
y-e 77 -2 79 -2
G-l -51 -174 -31 -177 1
G-2 -15 -118 4-42 -16 -121 42G-5 -67 -97 94 -53 -101 95
G-4 -74 93 104 -7G 95 102G-5 -22 62 45 -23 82 44G-6 -18 58 -19 57
G-7 -22 76 27 "ZZ 80 27
TABLE XV.CpXculatid ij'£?jan gage data
Run Number 1
6
26 Au^iiu^t l?'1i6
Beam Span 4 feet Load Position 1| feet from n-jar ,mpport
Lo^d 4500 pounds
^' ^^ £3 C e, c, C£-1 -27 -174 -S4 27 -176 -22 -1558£-2 ^5 -205 -92 25 "ZOCy -92 -16356
E-3 20 -290 ~ieO^ 24 -292 -180 -2140E-4 51 -182 4 56 '-182 -1560E-5 35 45 -i::0 3S 48 -l:Li -1076E-6 55 70 -e7 37 7£ -28 -llOOE-7 15 79 -50 16 82 -GO -90£F-1 -7 -193 -£?^ -f^ -201 -51 1610F-2 -20r^ 2 -33 -207 7 -C9 1570F-3 -10^ -108 71 -197 -1:)^ 713 -1S86F-4 89 -SC 1 92 -26 -953F-5 101 -9 105 -2 -976
F-6 96 -2 100 -2 -9200-1 -41 -224 1 -41 -227 Z -ISGOG-2 -20 -152 ?:: -21 "l^'i £5 -1584Q-:^ -75 -125 12^5 -75 -129 123 -164GG-4 -9? U8 1:20 -56 119 127 1560G-5 -25 81 +tiS -28 85 60 728G-6 -25 -75 -23 -74G-7 -cO 101 55 -JSl 105 54 962
TABL.E ^^>-calgulat:6D irnvj'.ui cage data
Ban Huraberi 6 2G Au;;vi^-t 1046
Beaa Span 4 feet Load Position l| feet i'rom noar cupport
Lo; .d (pounds])
2500 3600 4530
A-1 -83 -125 -1[^3
A-2 -43 -1C>^ -255
A-5 -98 -158 -178
B-lB-2 -:a -*7
B-3 1:0 :-! ^'I^
B-4 . -87 -ICOB-5 57 52 07
B-6 -11.3 -1S5 -213B-7 107 150 192
B~^ -1?S -lac -2::8
b-y 46 G'l
B~1J -itc5 -177 — ..- v*
B-li 25 y'r / "^
Bl^ —yl -127 -iGGB-l 5 -5? -79 -101O-l -It' -26 -: »:
C~2 -116 -io9 -:?03
C-5 -150 -ISOC--4 -47 ^e^ -85
J>^1 -24 -o2 -44
D-£ -15; -216 ^277H-i ^3 73 95
H-2 80 114 146Ii-3 154 21G £79H~4 16G 234 &02
H«6 123 172 222H-6 79 112 145
H-7 44 62 80
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Part I. Co'/;cut:^t._;:r; ci S-;oar ^trer^G fro*" ^tritin Gv-.^-e Rea.HnjL:.
i O.I - , i. . ; • i •" » »^« JU V-
e.i_ _ r .-— ^ (.57)
£, = - .. f 0»7i5
£,=. (1.02) (;a^)^(.C2io) (-1)7)
E^-z -o: « (.or^ij)(-;:o)
6^- -•'•/•4. ,43
rTom I^oiaograph oolut/ion lor Sii^^or ^^trfess
c-x»
Part II, Coiaoutation of Sh&nr StrcsJ*- froin Sirapl© Bn&r. ForrauiRSl
For Run ^o, 5, 19 Avi^at IC'C, Position F-5
A - £ ft.
B = 5 it.
L ~ :; rt
V ^ -
V =i - 1000 lbs.
Q = 0.O4 iii.^ (obtsi^'^a D> iuUo.7r.itu.,. tracin-r. oi beiim
cross-.>>ctiou)
I = 56.6 in, 4 (obtained a?., above)
b = ,?.? in, (.fratti (Jir::ct sii&s.)
n"V/Q
bi I b
. (-i-:>ao)(6.ai)
(5C.6) ( .28)
a. -1^ (L-x)T
^ (r'5J0)(2)(;:.7i3)
M =^ ;t7r0 ft. ii:-i:.
= 3
V= (aj^uaed)
y^5i^-4- rr'
3.
7"^ = -L 51C lb;:5/3q.in
vT
b. for Ivun Ko. i, 17 Autjui.t IfMf', C^^e PosiUon £-2
A s 2 ft
L = 7 ft
C - £ in.
b = .ZB in.
By intGgrxti'jn oi' aac tion
Q = 7.54 in.
2
r. (4500) (t)
7
V ~ ?23:0 lfc.:y?5.:;.in
" lb
« ( 91:10) (7,54 )
Tw"'Y' op)
=^ 15S7 lbv'::v .1:
L
U = £41x3 rt* i;.L?.
cr - Mc
cT^ = 1Q40 ibc/sq.in
r {24XJ)(2 )( 1^) ^ V^Sa)' (1557)2
r-
l»n- ± 164^;5 ibs/sr.in.
Aprmmx d
T!ii:". Jata is pre&er.itc'i .s-i- ioauii::^ data una crac*. au,^;lo lata.
The lo.vJinft daU. provldoe inror ;:•! oicn en type oT Lori, position
of load, G-tc, Tor each tent rur*. The crac": iiMf.iu data sum^ftriics
the an^ios of tho iiidlviaacLl CtrooSCOLit crac^LL*, The^e anglee ware
aeasured fro;:: U\^ "ixrisontal in c couiitcr clockTi;«3 direction I'vom.
the ritV-'t. Tlieae d&ta proviae inrorri'^ii-icn ^rhich v.-ould entbie arijr
peri^on to reconstruct tlic tensile strain pritterii Tor e^ch load
listet^I. 7V:Ci ineths>i or obtainlixg thib crftcl-: aii;;ie ufita /.as as
foilo7;8:
1. Afte^r coe:plction oi the teiit run ani <\pplic<itioii of C0/>,
tiio beaja wa^ reinovad rron; the ttstin^j ntichine and a rectarvu^^r
reference t^rid ^.yzt<::^ 'iKU-kod off covgrlriii the Gr':>a of tht; cracK.
ps-ttern. The reroroncc lines \terQ rup. paraliel to tlie <i;}u-j3ne'd
noutral ciid.L- arid at right C'.i\^;3.ci3 to the i:;.>v:Uwod ncutr:il c.xi.3»
The colur^;!!^ ( nuuiberGM.''i i, '<., ^, etc.) rt;p2"o;:i£nt liucij drawn per-
pendicular to t\ia r.LutroI B-:<ic, cmC ilne-s {itottei-od A, ^, C, iitc.)
rcpre>;<int line a parollol to uho nnu-orol axia«
;». The <':a,;lc ci' crac'iin.;^ .^6 then m-ifiiurc';' Rt ouch in&er-
iiection oi the jriv. rofcronoe iircs,
2. Explanation oi irballini; of refc^rer-ce lines.
a. Low rjiia'wiTj^ ar<3 y«5 %^i^ U-ft, lookin;^ towards the
h, Uiilfeiiu otr;3rYd..>e .,tate-i, the ihort span i;j to the
left.
c. Longitudinal rti-iTtirenc© lines an-: iupaoed i; inch
betv/eer* liiiesj vcrtic'd r«3iVrcrice iiiifci^ £.1*0 i;;:aced as noted, ou
"each dfiita ah«.ct.
4. The position of U.e beani neutral aixis i;* on rererciice
line G.
nTIi/iXIi GAGE DATA
Data i$F pi'^aeutod Tor i>c.o}i tost load of each run m.Hd«, in
the Eeqiienco oi' loading. 7rav. tliis obciervwl data the observed
values ivczo iaircKl, an^. tl2o TairtKl c'.&ta Ui.sd to obtain viuiafi of
iitrain xov colcu-^ation of rosults, Tn.e str,«riin Indicator rurerence
position value wasa olmlttod iYoja thtssc t!ibi6;s or obiscrvcsd data,
^iincti r.Il -lata un:lr,r en&.\ vQTx-iin^ eh'c htkzod on the i-yr^c rcrc;rr-nce
position. Tae valuco ip.veic ir. the- colarins under eiicth loci ^rc?
tj:ipreri;;ed in iaicro~lnch.*a poir inch.
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a
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Reading; Ga^ie Jleadin^-; Ga/ce Ji.eBHtn^ o^^ce
number HuJiaber ^?i^ili^5i! i'Ju2lb«r Niiabfcr liueber
1 13-5 (51 E-5-3 6C G-r.-3
Z B-6 32 i;-s-2 67 G-5-e5 C-2 35 K-6-1 68 G-,5-i
4 B~7 34 E~5-S G9 H-5S A-2 35 £-5-2 70 G-4-SG B-8 ^•e E-5-1 73 G-'^-g
7 B-D 37 E-4-3 Tr G-4-18 E-iO S8 E-4-2 7fj H-49 C-6 59 E-4-1 7G G-3-5
10 B-11 40 B-5-5 77 G-5-211 A-3 41 E-S-2 78 G-5-112 B-12 42 E-S-1 79 H-5IS 3-15 43 F-5-1 80 G-2-514 G-4 44 F-5-3 81 G-2-i:
15 E-2-3 45 F-l-S 82 c-n-116 E-2-2 46 F-4-2 as H-217 E-2-1 47 F-4^1 84 G-1-313 £-1-3 <i8 F-:^--3 87 G-i-1
19 E-1-2 43 F-5-2 8a G-1-2
ZQ E-1-1 50 ?-5-i S9 li-l
21 D-1 51 F-2-.3 90 F-G-1
22 D-Z 52 F-2-2 91 ?-e-2}d3 3-1 53 ^ — *..—
X
92 J-6-3
24 B-2 64 F-1-1 9$ G-7-125. C-1 55 F-5-2 94
/* ^* r'^
26 B-5 SI H-7 S5 G-7-3zr A-1 62 G-e-3 96 i;-7-l
2d 3-4 64 G-6-1 97 K-7-229 F-1-3 85 * H-6 3B £-7-5
30 F-1-J2
TA-BLB XXXII)
Gage Ga^-e Auxiliary' CalibratedNumber Factor Factor Res, (ohms)
A-1 2.04 119.6A-2 2.09 120.0A-
5
2.09 120.-)
B-1 2.04 119. c
B-2 2.04 119.03-2. Z,OA - 119.6B-4 ?..04 119.6E-5 Z,iH lis. 6B-G ^.04 119.6B-7 Z,OA 119,6B-6 £.jy 120.0B-9 Z,'}d 120,0B-10 2,09 120.0B-U ^,0B IJ^O.O
B-l£ 2.09 120,0B-IS ^.09 120.0C-1 ^?.04 U9.6C-£ Z,04: U9.6C-3 5: .09 iJiO.O
D-1 2.09 120,0D-2 2.00 120.0E-l 2.07 .0200 120,1L-Z 2.07 .0200 120,13i^3 2.07 .0200 119.9
E-4 2,0? .0200 119.9E-5 2.0? .021o 120.3£-6 2.0? ,021? 120.1E-7 2.07 .0213 120,1F-1 £.07 ,0200 120.1f-2 2,07 .OSOO 119,9
F-5 2, '07 .02'00 113,9
F-4 2.07 ,0213 120.3
F-.5 2.07 .0213 120.3
F~6 2,07 .021: 120.1
G-1 2.07 ,0200 120.1
G-2 2,C'7 .0200 120.1
G-S 2,07 .0200 119.9
G-4 2.07 .0215 120,5G-5 2.07 .0213 120.3
G-G 2.07 .0213 ;20.1
G-7 2,07 .0213 . 120.1
H-1 2,09 120*0
H-£ 2.02 120,0
H-3 2,09 120.0
H^4 2.09 120.0
H-6 2.0 s} 120.0H-6 2.09 120.0H-7 2.03 120.0
TABLE XKy\\/
oasxiirvEi) siRfdu qaoz data
Ruri T^umber: 1 Detc: 17 Auur. t IT? 'IS
Boafa Sj^xin 7 feet Lo&d Ponitlon 2 feat Tro-: n. r support
Reading LoaJ (pound 3)
Xuraber
12
o
4
5
6
7
8
9
10111215141516
17181920£12E23242526
87
28
29SO
31
52
335456
36
57
38
594041
424344
45
500 2530 ?^ilO ^ACO'
100(3 1050 1360 imsi;a7 lOSl 1009 9228P9 771 682 599
1I3S 1185 1<09 1200
042 680 545 218
llo4 972 381 676
1172 13G5 1420 15521201 1109 085 679
2S8 lis 942 622
590 449 480 553
520 357 221 018
1104 802 7C^0 GOO1259 1006 983 853800 750 680 590
lOCV 1011 968 3C0440 530 271 225102 110 110 118
622 809 830 788629 638 489 440450 420 420 418
205 260 250 251735 629 570 517
150 158 158 1G5£19 492 485 481
1032 1009 Q90 980559 569 5(^3 578
205 18£ 141 097
1012 521 873 040903 909 900 8C;8
S94 289 240 193570 460 298 202890 8?0 890 880290 SIS MO 379
1040 800 778 53:
599 432 ^79 423
GOC 651 3^7 7'^0
529 381 ^32 158
7fcO 547 475 548
5SC 582 616 6701G9 109 068 082
948 051 775 7206'00 621 327 652552 521 532 542
677 647 851 6o9
402 422 452 472
Hun NuTxber: 1Date: 17 Au,,;u^t 1S46
Been: S^aii ? i'eet |,oaa PoaitXon £ foet fror. n-ar .uptjort
Lo^-ci (pounae)-^ ^^m 3G£o 44eo
Sb^"^ ... ^?^l^p°^"^?^
46
47
46
49605152
655455
616364656667
6C
6370737475
7677
7679806182838487
88
8990919Z9S9495
36
9798
868 815 771 71291S 300 751 689599 380 562 59551>0 479 427 575720 702 707 711800 7^;:i0 790 798
^ 470 450 470 430828 716 673 620159 121 1£0663 693 722 76060S 779 873 102029S 244 228 «i.<.0
052 112 173 511894 1088 123-3 1490535 615 609 87570S 753 702 900
1140 loee 1040 971619 367 1102 1705710 796 888 1062eeo 200 171 170979 911 900 842o81 1104 1273 1708
1367 1452 1462 1510S84 610 570 547
1075 1038 1030 1035?7i 4Q0 580 6756^6 645 667 697291 209 186 150700 671 662 673S3£ 456 4i?l 540274 297 276 235745 701 696 710
1459 1540 1C74 12061450 14 Ji 1555 1545810 797 799 785792 821 854 850761 765 760 75'920 885 865 86051£ 368 587 430Z5'6 522 567 445922 ^39 350 990£71 £36 272 290£55 455 406 560
TABLe XXXV
liiin Kurober: 2 Date: IS Aufruiit l>i46
Beara Span 6 i"eet Load Position '.3 feet frora utar tiupport
o
4L'
6•7I
8
9
1011121214151617
181920?.l
2225242526
27
282D
30SI
52
35
54
35
36
S7
38
30
404142454445
LoMd (pour.:\g)
500 ^51^ 5435 4480 510
1230 1J:19 1260 1290 110013.^1 12.51 1105 u:53 15751013 853 800 740 10001 '^'f-'. 1372 1471 14;:8 13:^3
951 713 730 585 920
13S0 1170 U15 lOiO 3^40582 669 740 772 5V0
1£63 1072 1009 002 1240502 199 14S 012 350
629 65d 708'
720 612710 520 446 556 70S500 500 £40 140 400
15&0 1221 1170 1088 1372881 710 6V0 530 878
1265 1189 1189 1158 1257620 499 464 411 611
1230 1219 1242 1323 12r:2
1015 eB7 380 069 991732 606 670 623 790610 , 580 600 5C1 605
473 422 450 410 451
1146 1003 965 001 11331570 1328 1359 1540 1540712 66a 695 660 609
1161 1129 11S9 1110 1151714 710 748 710 698
1560 1238 1275 1219 157::
U60 1068 1042 1005 UGl1152 1124 1140 1122 1139613 480 4S8 508 5S8
630 542 521 457 642S75 360 090 963 961
1510 1348 1540 1340 1310069 852 730 700 040
520 52S 501 518
842 781 813 S15 8251550 1402 1555 1:^75 1449310 610 547 4G8 792l^G 750 759 740 768
607 615 539 540 (577
11(10 1002 965 910 1125S37 812 880 855 812eiiQ G5Q 654 6iyz 688
880 868 821 810 629eos 62-3 641 625 570
Run Number: Z
Beam Span 6 feet
OaSiuIlVSD SXIiAI!^ GAGS DATA
Date: 1:? Auju^t i',:46
Lcati Position 2 feet fron nwar support
Reading Load (poua^-uj)
ilumbor 500 £1315 ..1495 4480
851
510
46 365 890 872 95147 991 859 820 770 978
48 7*^6 700 390 660 GISO
49 320 730 659 596 793SO 0^:7 882 886 679 90951 1080 1002 1057 1050 10456E 706 707 690 GCy,^ 67065 967 928 8S2 802 98064 l'^78 1290 1305 12Su 120656 819 855 870' 889 829
61 960 1140 1195 1245 9n2
63 1535 1529 1276 1251 150064 1247 1325 1359 1371 i:.04
65 1477 1640 1732 1803 145266 1550 lr34£ 1655 1678 153967 785 319 825 842 77268 1200 1172 1120 1097 118069 705 950 1040 1144 715
70 1017 1168 1177 irae 102473 1598 15B7 1517 1501 157274 1066 1073 1031 1000 • loeo75 £76 785 852 950 550
75 695 763 797 770 656
77 385 846 773 743 353
78 1275 1270 1221 1212 125C79 1704 1352 1902 1970 I'-dZ
80 1718 1766 1779 17;^7 1711
81 1445 1406 1585 1506 14-: 4
82 872 689 900 840 844
85 1563 1G26 1652 11:78 i-:i7
84 1410 1421 1410 1-101 iiOi
87 945 959 936 900 932
08 780 6J:7 652 570 750
as 73o 879 642 662 76090 898 918 905 910 ^00
91 930 988 965 fV'T; 099
92 dZi) 8JC0 795 800 792
93 1030 1000 983 970 1010
94 1555 1315 1410 1442 1317
95 1570 1480 1480 UIZ 1362
96 1060 1105 1100 1115 100297 4:'58 442 435 441 402
98 700 G65 503 555 690
TA0L£ itxxVt
OuLi^i^j w^ilAIi^ GAGE DATA
}lim Kuaber; 3 Datei !: Auj:;ijst 1^46
Beara Span 5 feet Load ?o;jitiQi; 2 r^et L'rom near support
T^Qtidin^ Los^d (pouiv:is)
Kucaber 490 2460 5510 4535 515
1 "1155 1160 1159 1152 1163
2 134i> 1200 1129 1000 12665 1010 845 749 661 8054 37 4 354 360 362
6 878 691 523 639 7:^7
6 1343 1151 1055 973 12407 dZ3 612 649 676 459
a 1228 1045 939 341 11259 lo2G 1132 1066 970 1227
10 57;; 532 585 690 49011 660 489 378 280 6681 ^ 480 2S5 212 113 3-.30
13 13€G i2oe 1131 1052 1252
14 89B 739 680 613 81215 1221 nss 1098 1064 1119lf3 585 401 396 332 49[>
17 1212 1160 nzo 1141 iiOB
18 ::;71 910 830 870 068
19 788 049 596 540 672
20 586 518 501 480 462
21 1580 1298 1273 1238 126422 1130 988 501 856 103523 135a 1262 1249 1239 1210
24 ie(M 1597 1502 1552 1548
25 1152 lOGf) 1040 1009 102926 698 649 541 630 r.70
27 405 270 232 laa 296
28 lll'j lOOG 9G5 909 102G
29 1143 1055 1044 1012 1029
30 1500 1377 1331 1261 ^420
51 ei2 501 440 389 529
32 972 920 922 912 861
23 1353 1280 1293 1291 1231
54 905 766 700 630 8U55 1471 1409 1403 1401 1361
36 870 789 787 785 759
57 56C 394 356 2G0 440
58 778 691 509 427 689
39 778 750 712 693 699
40 C50 543 525 480 572
41 1145 980 910 360 103
42 65G 779 770 772 730
43 682 631 615 619 509
44 839 752 740 725 720
45 £80
,
539 552 559 472
:lun Nuin;j«r: 3
Beaa Span C fee-t
IIe<;diri}.';
ikimber
4G
47
43
40
5051
5JI
53
tabl€ JSJS3J: Cco^t)
Oi^.;£i:VED STIJ^II^ GiiCi: DATA
D-rite: i: i^u./u;.t l£.'4f
Load position T: feet Troiu na:ir support
490
'J 50
»^ ;•!,-
3101038G'30
931
i;-5 830CI 9^263 3.iO
G? 8ie68 llci2
63 707
70 1018
11 IMG74 107275 :53r:
76 C4C
77 83078 ir;40
79 7?-0
80 77281 140082 17(;3
83 1471o4 xocki
87 31^0
88 7o509 737
90 90591 372£'& 767
D3 1000L'4 131895 31^2
96 1020•J/ 357
G50
Lo'td (pounds)
t\m * 3510 4555 ..,_.i?iL
ei7 811 775 8i:i
830 770 720 892
602 .091 5S0 668
639 £65 b:52 oao030 320 802 79296 ?. 950 936 922COS S9? 500 56Ct-
u31 770 705 SC21101 UGl iieo 1160£01 819 820 708
990 1030 1060 8405O0 C70 232 262
1^05 1222 1240 locoICIO 1570 1628 1325655 665 712 580eCK3 312 836 7(31
1X1 1042 1015 1000er.4 912 905 690
1030 1058 x03<;^ 00015^56 1220 1180 12429BE ^50 892 960e-fio 720 702 41S630 648 553720 G30 632 7o8
ilii4 1132 1110 112881G 812 QL6 617746 756 730 860
1£30 1224 1194 12021722 1704 17O0 16821018 1G23 H.47 1404V69JS 1304 1205 1270300 7S4 790 770674 317 472 G20749 745 746 660Ooo 855 826 810892 000 \:10 C02757 740 752 723G54 SOO 88i 002
1330 1338 1565 1233410 417 427 322
1017 1000 1000 065367 357 5B0 0^7
580 ^>20 480 5^0
TA^i-B yxx i//r
Diite: il5 Aa-:,ajt lI,)46
Beam Cpan 7 l^eet
iieaciiiit:
I-iumber
6
101112
I'C
1415IS1718
19(C vj
21
2425
26
<c /
23
29
50
33
54o5
oG
o7
38
53
4041
4^4544
Lo^ ?oi3itl.on 1^ itt,t iron- near support
o.)0
Load (pourx..":s)
•o^O 4520
473 439 4S0 500 4;S8
Oiil 528 440 402 1541237 lllB 1055 908 1210
8 1.5 050 7401205 1057 087 02275*: 498 450 755'7r T, 809 028 841 755o-'j.i 557 £30 200 502
7eo S05 538 455 7 ' ^y1 -iO
340 8e3 822 807 821t41 732 712 611 054960 ,822 720 861 l:05
iC15 lc..4 1328 153!^
652 080 G^^G 561 810li^S l?^v" 1370 1040 1440882 7 44 •390 627 5G0548 C2a 1^'.- 550 522
1231 ilOii 1165 1210lu47 851 373 629
"> -NO*?X.Vf. /
soe 680 80I 852 C
lo34 1612 1500 15'i0 irooli306 1322 1100 115G 13711682 1525 1521 1545 1551051 890 C580 870 021
a.600 1510 1295 1205 1545
830 975 S71 998 052Col 555 457 400 GOO
lc4i 12-a 1190 1147 132o1419 i40C 1557 1540 1582874 728 (36S GIO C29802 780 740 698 C54
ueao 1192 1177 1183 1100r):-:"; 610 611 850 505
llGl 1058 1010 070 11427^0 74J 754 734 747
llL'S 1180 117 C 1107 114G811)
.» r» •-
f ,..' 500 402 Cv:l
1147 1111 J.\Jl -J 1005 10051178 1141 11 :v.
1 C^" 12001101 i'GCj 085 81
5
990
1415 1248 U4n 1078 i;-5oo
1210 1153 1105 1190 1212
1040 1001 060 000 10211031 io:vr: 1042 1051 10!f2
OoO 790 70: 7C5 800
-s
Run Ka-ubsr: 4
Boar, -pan 7 Tg-:
Tf^^L£ xxt^n Cc6*i7:)
^'•toj Z?^ Auj.;unt i: ^^
Lo'jd Position l'-' :"eet irijfe no^r ou:';v^Grt
45
47
48
40505152
535455
6165G46566
G7
63
6970737475787773
7980318283848788
89909192'33
9495
06
37
98
Load (•ioui;-:::}
_ 500 rif>30 _34i:5
1282
r; tr\ '.:
1201 1270 1269 124512;>8 1201 1260 1201 1E3G1028 1015 1022 10151110 1045 j80 919 104312^^ 1105 1045 11021340 12S0 1279 1274 12981040 905 DOS 999 10101250 1090 1040 078 12101393 1520 154G 1541 155711'29 ins 1119 1130 1065li-'oG 1563 1413 1494 1250657 SG5 551 541 509
643 551 5S3 634 500307 900 1073 1140 377
64E 873 900 ^.7C0
107G lOCO lOJO ilOG 10301430 13C4 1387 1373 1420X»-.'J(,j 1348 1440 1525 12181250 1502 1362 1403 12401G17 1853 1G83 1714 ICoC157-3 1272 1280 1240^ 1328
SC5 1^10 1135 1235 ^ 878
027 ^48 1000 1044 010114£ 1030 1000 950 108956G 515 518 510 57 S
1087 1207 1307 1450 11201033 1013 1043 1071 9021G35 1565 1540 1514 1CG21130 1072 1087 loco 1102
1084 1925 17521G57 1507 1C17 1622 1G17i;:55 1182 ua3 1133 12231104 049 905 340 10721075 1007 1133 1170 1078lino xi55 1148 1138 1146lies 1100 1195 1192 1155125 37 60 83 831247 1107 1100 1180 12.U505 Pili 875 oCO 580
680 7 DO 739 76S 652
15^0~
1 1 'V 1373 13526 '5 O .:; L 653 mz nr2
9c:0 020 '7 O O :;15
Han Miimbcr: 5
lieara Span 5 feet
Date* llo Au^raet iU.iG
i»o.';":t PoTiitlon 1; feet Tror near suppo2-t
lluaiber •00
LfOa.i (pouHis)^ZOO 'i-V.
K '.r,'
4
5
G
7
8o
1011
T r.
1415161718
19
202122£3;!4
252627
28
29
5031
32
32
54
^o
37
158
59
40414243
4445
381 47.^ 4D7r^ V, 430
G16 520 468 400 6321178 783 738 652 87371.: 1;;;12 1233 1302 1120
1225? 1109 1046 068 1232778 072 610 642 7Of
7r;l 7':io ai3 B33 739144? 1230
-; .- <j -V 1202 1455
7J0 mo 502 548 73273G 030 832 870 003
940 632 803 736 350
^304 908 655 805 1010652 570 631 490 650963 002 800 051 082
1430 1306 • 1372 1 y u ."i "i .1 y« •;
817 030 6 CO 301459 4f9 4C4 469 4G0
1183 1180 iyl72 1100 1103.^8v 'K}7 863 315 902
840 853 832 846 872340 659 &f:o 609 050
1424 1047 9^3 808 113011)50 1350 1533 1638 1550003 903 002 381 920
1328 1335 1321 1293 1350040 983 9G1 1002 DCl
489 U8 420 573
1313 1243 1200 1101 13231331 14.17 1307 1302 1-412
cie 706 655 e03 802
941 810 770 730 001
1170 1103 1172 114B/DO croc 530 541 520
•< 1 « T 1112 loco 1038 X.L72
i383 725 723 70a 717
1105 1122 1122 1133 1110
14::2 092 932 888 1072
1043 1017 1015 1017 1017
1110 1293 1208 13)1 rrlOll
1031 1260 12J.0 1108 134013G3 1302 1320 12 30' 13441130 1199 1132 1100 1220970 000 003 092
1041 1072 1071 J. j( 'J
-; >!->,
77 l C07 700 7:'^ 310
Hun Ihjjnber; Z
Beam ijjaa ,'> Tect
T^&L£ XX;<VIM (coiST)
Date: 2C Au,u.t iJ'tf;
46
47
48
49
5051
52
£3£45fc
61Ci-
64656G
G7
68
60707374757677
78
79eo3182
64878089300132959495
j6
97
DC
inioIorr.
i- v^ O
945
10271110i:50S
9781182573
1083o25-ro /
£01900
85015^5i2:a.
67?;
151707;;;
10^3577
11^010007i:5
108:^
80.:.
680isur100010271117lino
11041124G41
b..4
Load (pounds)2520 S500
147)?
1268900640821
132510529li8
G201115400
137914101718lOO-J
1183lir9W^J96057 f*
11001047640
c:o705120687?
1210
1152~> to
11701462677
: '.: V, V
886
'i'y .:io
1^80 1500 12421 '"'.'A'^ 1261 1276015 950 870615 578 v:iQ
775 72^/ 0251318 1509 1358
1030 1054 1047S49 805 1100651 642 G40
li:^0 . 1143 1X1439 478 351560 550 535573 596 505
1057 1107 010595 G43 - 590387 C2G 870
1572 13G2 14021485 1549 1 u- L
1758 leoo 10521024 1045 0551168 1140 1224'
1250 1337 102015C0 133«j 1270955 005 1020^'SC
fX
r", ''. G141550 1064
10B5 1030 1019GIO ^00 714
11 .':X 1143 1153330 036 ^iS)
707 708 7081200 1257 1242830 705 .•)07
1232 1252 11751117 1117 11201172 1120947 ?50 958
11C7 IIGO 11801485 1520 1455G;<6 715 G45
Iv' At.) 1552 Vf.TyO
875 G82 C45ta7 343 026
Date: 26 Aur'u.^t 1' 4^
o
4
6
7
10u121"
14lo
16
17IB
1j2021Cii
£224
27
28
29
31
3o
54' r
se
37
38
o2
404142
434445
ho::..: [poau-.L)
\i^%J.....„...^^.^J:^
3520 .._.„.i^y^„.__ i^O^
12j7 1440 15.54 1U.0GZiS :^40 4^-0 448 6416^8 802 74j / ^ uOG
1119 1209 12';' i;.>j.: 112C124^ 110?; 106 r x022 1240800 gb:: G4:: ii)^i
759 7ah 700 QIZ 7511436 1-Gl 121b 1280 148^;
GIO 719 670 805 80330G 828 8 o9 8 48 001060 872 S'6b 800 957
1025 C'48 912 878 1021GSS 620 600 570 682
1017 078 053 020 10151150 1404 1587 1448800 719 673 83c 810
465 478 482 4uO 47 c
ii«':. 1182 IISO 1172 11929^*f^ ::;16 075 842 o:s3*5 L; 358 3:>^ 8.1.1 872GGi: 640 CoO 622
1220 1095 1028 1210
i'jQ 100 530 500 c80
924 : oe 80S 3-1 020135[^ 1527 1317 lc>20 i;5o2
Ool 979 088 Oi;-;;(:»\Ci
lo4i 1432 1432 13ii? 11:40
IodO 12^34 1221 1187 1327
1416 lae 15'iS 13;:1 14167:^;^ 700 aco 61-0 < / J-
J
372 S32 810 71,^; 871
1151 UGO ii:a iro"' 1161l^i81 1502 1400 14821180 112C 10^5 ion^ 1179720 742 7:51 7Ci 70
1
1122 1142 ii::r 11:9 ii;'2
100 i 1000 '-()0 913 1081
1027 lOGC IOC 5 1075 10:^8
1340 i3J)r> is.:o 1358 IcGo
IvcZ 1272 1253 1108 1352
618 4;''l 450 572 651
IT.SX 1280 lr:G2 126- l:721005 ioo:: 1005 loo;: 10101060 107S 1072 1060 1070
BIS 809 800 790 Bir
TAB^C K)tX|x (Coti^r)
ODCLinvrx :^lTJ^Xli gage "^1-::^
Eun I\'u:r.bor: H Date
:
2^ Au/;U::t 1. ::
Begins i^pan 1 I'ce-u ,:.on 1^ Tfeot rroE riG^r support
Leriitnc Lc^iri (pourtis)
number c^5_„.. ZUZd 4500 4:^0
4o i::4e 12D2 1312 i3o547 l:!c-o 12i^3 120G 12i;e 130140 678 :;12 029 D42 . SGI43 703 So8 651 612 71250 1^41 8c C 812 770 960CI 1540 1327 liio 1510 134052 10/) c- 1050 1052 1055 106155 iO^.'8 1003 r „?T 110354 'ZkZ C20 620 G2f> 65155 1030 11^9 1149 1171 ioai61 1250 1287 1300 1316 124363 5?'5 662 .:78 577 500O'i ex 553 547 559 409C5 BOG oe.i 933 1024 8'>0
66 15GS li:75 i;-oo 1610 1^'47
6? S75 015 963 878i4l'i 1307 1505 1390 1415
69 i^eo 1380 1433 . 1400 120570 700 7G3 792 022 'S^c
75 lOOo 102G 10S37<. 22B 210 1^ 27075 1005 1142 1207 127 S 0^076 i^ea 1322 1:^48 1575 I2e277 lOOC 943 021 897 10057G 612 G70 'cm 552 GIG7<; lOS^ ?.180 122^ 130^0 1040
eo 1017 1044 1055 1-0€G 1013
ei Ct7 C2R oj7 o^e GV.9
8£ 11^7 1128 11;'0 1123 1140
85 om 878 •09 957 CIO
84 70G 704 703 703 705
67 1107- 1170 1177 1163 1203
88 950 SuO 312 9G1
89 1170 1204 1220 1232 ilG3
90 1131 1120 11 oi 1133 1132
91 112;^ 116G 1167 1210 1119
92 9C3 962 9G0 dCO y63
S3 1202 1190 iieo 1192 1202
94 1429 147 4 1497 ir)22 1420
iro: 1006 1612 1612 1&81
JO 1553 IZV6 1343 1532
i-7 J.O vi o 1628 1645 1655 15C8
D8 937 912 901 887 <135
l\\in KuKbtr 7
;c-a:a Span 7 roL.-t
oii:'iaiVi:D S1l^Alu gag:: data
Lo.'-;;; Po.-iition 2^ Tot I irar.i near fupport
Kuraber
^
5
G
7
8
9
101
1
l;^
14i;s
in17
18
199n
23
27
51
VtJ
S435
5C
57
404142
43
4445
Load (pounclii)
'•i • ./04-. S :5;j35 4480 -_J05_
lay 155£ 1570 1330 130 :?
iolO loSO 1315 1255 140581^0 609 G3S:
' -* *". 7001050 1071 lOOB 1121 1011117. 971 672 700 115261C 634 042 4£1 700
16^S 1G95 1701 1749 iol913ol iiec 1072 ? 2 h 1230958 OvOO GOO 410 7S1772 9i^ 900 11^7 040800 700 501 420
1503 1128 09? 45;^ 3oG
1489 1165 810 1221lo70 lAze 13r.3 r;,_!', 15CI0
i5eo 1339 1510 1297 137?730 G3S ^eo 545 751
1513 isn 1S29 ISOo1110 1103 IOCS 1001 1115920 B59 790 7G2 02177'j 700 750 772
l52o 1 f '^.'^ 1^90 1180 1^.25
1^10 1302 1240 liH2 141014S1J 1481 i;oi 1462 i47r'
847 0^8 HI8 £10 341
l^CJ 1240 1250 1221 1255873 eo7 000 Oil 672
1458 151. i5 1K15 12B2 142C1257 11^0 1121 1100 12201560 1349 1H4 1338 1S5S710 6i:G S82 542 7207 f •} 500 4S6 059 530070 971 941 806 800
i2/;7 120 J 1532 1402 1451117
:
951 820 571 8401470 1331 1201 1131 1502CCS 066 1010 1105 107B
1032 035 882 059 lOSOCIO soo 752 o90 010
lt2^ 12G2 1260 1270 1220l.>t0 1170 1 * T.C 1401 1550
ir^^.o 1419 13f.O 1310 1521ll<^7 1J.85 1102 1 r -it 11660(7 r 7^0 717 65^^ 332099 1020 1041 ^81
7 06 7,1'^ 720 7i€ '7;.''0
Lmr Nuzn'ber 7
Bean :>-oan 7 leot
7"/V0i-6 XI- Ccc*ir,)
03.:.i^;V..D /'riAIIi GAGK DATA
Date: 30 Aa.-u/t 1'j4G
Lo^.J Po:;it.lon 2^ feet x'roui near support
I>.oading
470Load(poun..ls)
Zid' 44C0 505
47
48
49
CO511 » ;
55
54£5
31
64C566G7
88
7073747576
77
787G
80818£8584C7
3889
00919293940596
97SB
1110 iOlO 972 042 .1x50
1151 1140 1160 1160 1170m7 361 359 65 5 664071 5D7 541 500 678071 662 862 860 071
1510 1S1£ 1500 1302 1518<;74 970 071 'j7i.i i'72
lOi^O ^^31 8c 3 840 1021
1456 1460 146f 1471 1460e5i 90i? 352 792 886
1240 1452 1560 i:48 1550lao 15565 1355 1196 1504429 540 692 1025 750055 1558 1515 S03
i(r/3 1157 1151 1253 11144G0 442 410 355 425
1267 1219 1104 1108 1225
673 51.0 1050 1567 910617 698 758 755 616
ar>o 780 755 715 855illG 1083 1077 1012 1122
040 1115 l:cO£ 1265 950
1220 1275 1500 1505 1225950 873 644 305 057
515 402 485 462 610
1035 1154 1213 1246 1040iM6 975 090 962 949
1565 1501 1436 14;!2 1570
1010 1005 1002 987 1017
740 8^03 840 847 74365-5 653
/^ '/ ty
610 654
1072 1050 1050 1057 1075067 866 822 765 972
1146 1107 11-0 1153 ^
lOOO 1105 1014 1000 1022t-So 1051 1050 1077 1021780 • 767 744 740 7641050 1020 1002 957 10201 «>o«^ 1502 1555 1410 1280570 667 715 632 700
1240 1274 129S 1553 1200547 563 555 550
726 663 483 723
Run I^uinben 8 Di?te: iJ Au;>ust 1" 16
Beim lipan G feet Lo:.id ^'o^ition 2^ leot iron near ;>upport
:<uffibcr 4B0 ):l>3:} 347?: 4510 £9i:3 510
4
5
G
7
8
S
10111215141516
17
1619£0
21Z:2<:•!.>. «J
<^ ,"
(. k
26£7
28ft ,->
30
31
32t -'J
543r>
5G
o7
38
39
4041
42434445
1315 134^ J. uCJ l^VJ 1507 1?^15
1502 loee 1530 127S Xi;:i 1158-1 i'> 1 71.- f'GO 6c:i 503 515
lOSl lif'O IISS 1111 1150 10101173 D71 cot CIS
,*i ^s »-•
11 vo
dZo G51 r.72 ^vl f>?-X "'T
CCo 8SU 760 7e9 11.1'J . 570ir.Go IOCS £^71 C75 1535 1517
^09 G:;0 C7D 470- .-jp I
•
045 io;;o lira 1148 1432vg£1411 i::o?j 1110 1005
-> r. ,' c;
837 700 go;:: 498 1057 IGGS1^52 lOCG 975 579 255 76915!:^0 las 111:1 lOiil 320 832i;?ro 1-41 1522 1502 1 -r^r-' 1577VoG 043 605 5G1 TOO 732
l-^SOG 1318 15:^1 1552 1306!11C 1103 1O08 1001 loei U12023 e49 81:: 773 725 521782 7no 755 751 750 7di
lf:J^9 1509 14O0 14;;;-. K70 1/251^-JtiO 12GD V^lb 11::7 1412147'.;. 1460 1480 1470 1470 147G
G41 c3^5 810 CIO 709 037
1^59 1JJ40 1231 1219 1200 1252B7: 000 800 505 015 070KGJ i3£l i;:5G 1248 1425123S 1102 11:50 100 5> 1045 122C
1557 i:;46 1340 !uc02 i..::i 1557
7:::: C3<; GO^ J'., .1' 5 -' '^5 725
1CG9 iii:3 1058 100* 1855 22^5675 esci 8Ci5 o.^i ^:::} 785
1440 lino 1470 1 .'OX 1705 1720
CoO 7^:7 66 ri" ,
"' C' i;-oi
15C7 1 •." ' t\ IIJO 1122 'I'-j-
'
'.'5 «;);;';
1078 1090 10..e 1105 1281 1246
lOoS jOO 05^ 752 1128
Olo «10 770 7£0 G21 887
Ifjp.n l^;;!ri 1 r^,'^ i;:73 1289 1224
1540 1477 1-1 4ii 1110 l^v:f: 1:^58
1 rr-.l-,i'K-0 lo64 15-09 1270 1525
11G8 1181 1159 115b 1205 1105^^'5 'J'\Z 7X) 8i..5 454 7049^0 loi:; 1029 1040 1050 05074<- / 60 720 711 710 752
TABLE )fLl fcflA/rJ
o:)..i.:rv:'D tpaij: .iAGE data
Ijin liunbor: 8 Date: ^0 hxV-^^X 1945
Dear;, t-pan :> i'eut TjO^..'-i Porvition ii\. 'Cant i'roM ri;.ai- Kiupport
l>u:f;ber
47
48
49SOfji
52
52
5455
616364S5r>6
C7
G8
o9
707'6
74757677
76
79CO81oZ£384878889V:lO
91
^2GS
S495
06
c?7
98
Lofici! vpO'iridia)
n^30 .^.170 4"10 _i^;iJi^._ 510
111^0 i04o lOOIi 'J! "^ CGI1170 i:xi 1102 1100 IIJJO 119006 o OGO 30B 851 343 B66f5C0 r;',?7 6(17 Clf'. 45:5 670072 8(?5 861 e,eo G£9 070
1315 1310 1305 i;::i 1313
.'?t una €60 089 07ri 071
lonr: 001 SCO 803 10E2i4C8 1456 14L0 1472 1463
CSO Gol S2£ 81/i 7^0 8201^310 1G?6 1786 1877 102s 1070
lo07 12£5 1£30 120^: Of..7 1090
77B 881 935 987 1738 1437
733 101'} llf^3 i::47 044 2941073 1145 1181 1220 1717 1003400 570 7,r;!.-: 547 o05 378
1 rs f1 .! 1172 1150 11^:5 082 1110
G;'^Si 1112 1220 1557 1100 436
jl'j:^<j li--^2 lc60 1702 1747 1555
054 700 7G0 7S.> 707 65611'^ 3 109^ 108 a 1069 1119
I'^.'Vt'") 10:^2 lie9 i2C45 155? 9451^217 1267 1:^00 1510 1350 1220337 877 S50 81.4 700 036
147G | / r «;Jl'j:«..^»-. 1448 1458 14?7 1461
1030 Ij.40 lli'O 1^:40 1507 1035
070 9B:^ ;^0i3 1001 94315G3 . ii;oO 1^175 144:5 1410 1560
J.0i!3 y:;G 005 095 1;.>05 1015i::3o 1745 1774 ICOO
', < ^ 'I I.', 1367
11.78 ir.78 1;.;78 107 5 ii:c:; 1578
107:;. 1002 1052 1052: -i J'.-(v 1068.•7-5 15P5 bzb 783 7^2 970
114S 117 & IIDO lr!02 1210 U50lono 1017 1016 1014 . 10^7 1027
1015 ltif»5 1087 1110 ili^o 1050
77 5 765 757 740 720 7S410'*:Q OiiU 974 960 900 975
ooZ> 410 443 43:5 680 484
os/c; 781 S20 360 U13 895
i;:e5 1013 15S;7 1 i;,iO 144o i;^oO
530 fc47 551 550 562 55075^0 602 o8^ 5^9 215 400
APPiiJiDIX E
BirLIOGIcAPKY
Title
1. Philo^iOp'cAcnl Maj^acine,
fier. 5, Vol. Z:-\ 1801
2. Piiilasop;:ici - Trt-n.:;c:;cLipii;i,
Koyal Society, LondonSer. A, Vol. 2£8, rj2£?
£. Philosophical Tr&naactiorisKoysl .Tociety, Loiidori
3er. A, Vol, 201, 1^07., p,35
4. Streue ir. Gun Turrate, MeaiS ,;^75
5. Htndbuch der E:<:poriEi9ntcjL
Ph: /ilk, Vo. 4
6. linicirfDUchen abai* dadGlttichgewiaht dcj
IlavAijcben 3taba3
7. Trantaction o iloyal ^oclt ty
Edinburj-h, Vol, 40, 1914, p. 3^5
8. Theory' of Plfite^. -•jria -hells
9. Ttieoiy oT Llaoticity
10. Strength ol" iiitariclc, P.?rt II
11. Theory ol Sti^uct-ii-as
Autfaoi'
Csruti 1^11son
A. E. 11.Love
Ii»I*.G.FiloR
?:m, Hovgaard
Krafts
L. Pochbaamjtrr
J. Do'iJig?-ll
S. Tiirx3shenko
S
,
Tiisoahenko
S. Tinoshenko
i>. '-tlnioGhenko
11667
m- ^^'^lavesw^^^^^^tication of ^^^
Mstri^utioJi^^-^ rnr supported I-
^- "'ttb a concentrated
J.
11667
ThosT-; WrightW9 An InveBtl^ption of the shear
Btrees distritution in a simplysupported I-be8jn with a concen-trated load acting near one end.
library
U. S. Naval Postgraduate SchndMonterey. Califorr)ip
