effect of underwater explosions on ship and …
TRANSCRIPT
----~ ---. _.:::, _ •• _-_. __ 1 __
RESTRICTED
FIRST STATUS REPORT
-ly " "'-
EFFECT OF UNDERWATER EXPLOSIONS
ON SHIP AND SUBMARINE HULLS
I
',. '. .. -.-,~'
W::': .. - .:: -
OFFICE OF NAY Al RESEARCH
Contract N6onr-0713 2, Task Order 32
Project NR-360-004
DEPARTMENT OF CIVIL ENGINEERING
UNIVERSITY OF ILLINOIS
URBANA, ILLINOIS
DCc.TDlrTcn
.~ ---~~·.3-~..;
. ' .......... -~
FIRST STATUS REPORT
Co~t~act N6onr-07132 Task Order 32 Project Designation No. ~~-36o-004
EFFECT OF UNL'ER~ATER EXPLOS IONS ON SHIP AND SUB1iARINE HuLLS
by
Jo E~ Stallmeyor, J. A. Brooks) WD J. Hall
vith th9 collcboration of
L." E ~ Gooc.rr;2.r.., Essearch Assistant. Professor' of Civil" Engir::3cl~in8 ane.
H ~ tL r!0Y .. "1rY~rk7 R8search P!"ofes~~or of S true tura18ngi21eerir:.5
A s~atws report of a proJect in cooperation with
In::1! aN~:--:lEt\3 !T'! 01i' TI->L IN 0 IS , DE.rAR~~IT OF c rJIL ENGINEEEING
anc.
THE OFFICE- OF NAVj~ EESEAR~H
Urbane.;! Illincis 1 October 1951
RESTRICTED
.--.. ---~~==========--------
TABLE OF CO~lTS
Sumwery
l.. Laboratory Tests of Scale Models
II. Static Analysis of Hull Segment
IlIa Initial Specifications of Dynamic Tests
IV. Loadins of a Submerged structure by Interaction with the Effects of an Underwater Explosion
v~ Ferscn::lsl
RESTRICTED
SUMMARY
'rhis report describes in outline farm progress under
con:.ra,ct Noonr-07132 for the period 1 Februa.:-y 1951 to 1 October" •
1951 " Complete stat.ic tests of two 1/8-s:ale hull,·segment mod.els
have bean conducted. These havo provided numerica.l values of the
structurel pe.rarnsters needed to supplement the dynamic ar~al ysas and
tests.,
Ccmpleta analyses have been made for t~.e static casc:o
Apparatus for dynamic tests of hull models has bsan
(tes~.gnod "
Pl"81imLc1ry studiss of the 1oa.ding of e. submerged strl...';c=
tUf'O by interactiGD. with th.3 effects cf an UndfJl"~J/a. tijr ~?AplD8i0n hS,Ta
In gensral attention has been dire:ted tO~Brd two obj8Ctivss~
(=--) Flndi.ng the sl!lfJ.119E-'c ~ractical sGeli~ e.:!:. whIch
ee.c b3 8.ssu .... srJ .•
~~ ~os3itlD to decide, on the basis of s rGl~tively simple tgst,
RESTRIC1'ED
I. LABORATORY TESTS OF SCALE MODlruS
1.. Introduction
The use of scaled models for astimation of the performance
of marine structures is so well established that no detailed justifica-
tion for the development of a reliable small-soale tasting procedure
for submarine hulls is necessary. Such 8 procedure can effer-t savings
in time, materia.l., a.nd the use of technically trained personnel. At
the same t.ime , it must be recognized that the succ,~ss of any model
program depends partly on its ability to provide information from
which full-scale performance can be predicted and pertly on its ability
to decide the rela.tive merits of e.lternative designs. Work unier the
program reported here has been directed toward t70 objectives:
(A) How small a scale can be used in the model without
losing reproducibility of structural behavio~?
(B) What criteria can be used to establish 8 figura-of~
merit for alternative designs of pressure hull, stiffeners and cuter
. hull?
In connection with these objectives work has been directed along the
-following lines:
(A) Static and dynamic laboratory tests of modal sectionsQ
(B) Structural ana.lysis of simplified hull repre3entations~
(C) Estimation of the loading of a submerged cylinder by
interaction with the effects of an underwater explosionn
The work described in this report is a preliminary approach
to the objectives of the prograro u It covers a part of the activities
under Contract N6onr-01l32. Work has been carried out in the Structural
RESTRICTED
Research Laboratory, Department of Civil Engineering, University of
Illinois, over the period 1 February 1951 to 1 October 1951~
The unknown factors in the effects of submerged structures of
very large explosions are so many and so important that the development
a.t this time of e. laboratory test which will "model" prototype conditions
cannot be oontemplated. On the other hand, a d~~ic model test intended
to produoe structural failure does not require that the time-dependence
of the impulsive forces be sealed exactly, so long as the dynamic test load
ing has the same general charaoteristics as that which acts en the proto
type. The extent of the prototype duplicatad (struoturally) ne~d be large
only oompared ~Bith the extent ot the structurally damaged submarine hull.
In attacking the problem of determining the limiting scale factor, it was
decided to start with test specimens which were soaled segments of ths
submarine hul1~ Approximately a 60 degreo segment was chosen for a
standard tast specimenD Such a specimen is relatively easy to test both
sta.tic.ally aI1.d dynamica,llyo Moreove:::.", a single concentrated load at the
center of such a segment gives a representation of the behavior of 8 fairly
well distributed load over a la.rger segment, or even 8. complete ringo With
the latter type of speciman, one is faced with the difficul"ty of a.pplying
simultaneously or with definite time phases, a series of rad"ial loads,)
Although sever::.l complete rings may B'IJ'0ntually have to be tasted.., it seemed
wiser to start with the simpler problemo
2., Static T~sts
The primary purpose of the static tests is the quantitative
determination of some of the paramete~s whioh are needed in the development
of 8 suitable dyr~mic testing prooedurso
For preliminary tests a number of 1/8-scale semi-dam3.gad
caissons ware obtained from the Underwater Explosions Research
l~·ln.L\j·.l.11iiJ
4.
Division (UERO) at the Norfolk Naval Shipyard. Specimens from these
caissons were used in the preliminary static tests and will also be
used in establishing a dynamic testing procedurso
Two preliminary static tests have been run to date
(1 October 1951). In the first test (Specimen 1 Static), a 90
degree segment was chosen, but this was modified in the second
static test to a 60 degree specimen.
Specimen 1 Static.
This specimen consisted of a 90 degree segment ta.ken from
an end section of one of the UERD 1/8-scale caissons. The specimen
was 9 in. wide with the two stiffeners 4 in. apart and centered on
the specimen (edge distance of 2~1/2 in.). The shell was 5/32 in.
MoSo plate with 00281 in. by 0 .. 75 in. HTS bar stiffeners welded to
the shell.
In this first test a combination roller-hinge reaction was
used at both ends, the horizontal reactions being measured by two
calibrated tie bars. The specimen was essentially a tied arch, "the
tie being a structural replacement for the remainder of the hull
segment. A single centra.l concentrated load was applied to the '5tiff~
eners through a loading bar laid across the top of the stiffenerso
The test set-up is shown in Fig" l~l.
The instrumentation included:
1. SR-4 electric resistance strain gages mounted at
various points on the plate and stiffeners, and used "also to measure the
load in the tia-rodso
2. Two ro~s of Ames dials at 10 deg. and 30 degQ from
the vertical. These dials ware moved transversely to pick up the
plate deflectionso
RESTRICTED
5.
3. A series of 35 mmo photographs taken before, during
and ~~ter the taste These were used (somewhat unsuccessfully) to
compute a load-defleotion ourve for the load point~
4q Stresscoat was applied on the top and bottom of
one-half of the specimen. This yielded no information of value~
An elastic arch analysis made before the test predioted
very aocurately the load at whioh first yielding occurred (for this
test at a load of approximately 4,000 lb~). Initial yielding bege.n
under the load points at the top of the stiffeners.
The redie.l defleotions as measured with the Ames dials
showed that the pls-te had a tendency to bulge upwards during the testo:!
This affeot is illustrated in one of the figures of Specimen 2 Statico
Tne ultimate load carried by this sepcimen was 17,200 lb.
Figure 1--2 shows the deflected shape of the specimen at a
load of 11,400 lb., after it had passed the ultimate load o As is
seen in the figure~ the specimen failed in an unsymmetrical shapso
This was prime,rily the result of two factors;-the specimen was slightly
out of round since it came from a. semi·=>de.ma.gad caisson, and -the load
was not applied exactly at the cantero The spherical loading block
allowad the loading system to rotate and thus accentuated the failurso
Directly under the loading block the stiffener buckled
slightlyo
Considera.ble difficulty was experienced with the end sup
ports and the spherical loading block during this testo These oondi-,
tions were improved for the seoond and more elaborate static testo
RESTRICTED
6.
Specimen 2 Statico
Originally it had been thought that it might be desirable
to test specimens with two radial, concentrated loads. An invastiga-
tion'showed that this would be difficult and expensive. It was
decided that a single concentrated load would be applied to a spec i-
men trade of a 60 degree segment. Specimen 2 ... sta.tic was obtained from
the relatively undamaged portion of one of the liB-scale UERD caissons~
The specimen was 9 in. wide with a 4-1/2 in. stiffener spacing, thus
allowing a 2-1/4 in. overhang on each side. A new type of end
reaction_which, it was feltj could easily be modified for the 15te~
dynamic tests was designed a~d used~ The specimen, as fabricated,
actually subtended en arc of 68 degrees between centers of pins~ In
this test, as in the first test,. tie rods were used to maas~re the
horizontal reactions~ 'rhese tie rods were one of the major sources
of difficulty, a.s will be pointed out la.ter.. The instrumentation
used on this specimen included:
l~ Two Ames dials, one mounted under ~he load point
of each stiffener to meesure the cenier deflection.
2~ Two Ames dials, one at each end, for measuring
the ~orizontal movement of the ends of the specimen. The~e dials
were in linG with the stiffener on which horizontal and vertical
def13ctions ware being measured at five different pointso
)0 A drum reco~d8r mounted on the 120,000 loo
hydraulic ffiBcnina which automatically recorded a load-deflection
cu~ve" The l.Ja.d-daflection curve obte.ined from the drum record
agreed closely in all respects with the curve computed from the Ames
dia.l !"se.dingso
RESTRICTED
40 Nine Starret rtL.a.st VJord" dials Vlhich wer~ used to
measure the horizontal and vertical deflections of five points along
one of the stiffeners. These dials have a travel of only Ov030 ina;
yet both thoborizontsl and vertical movements of the points along
the stiffener were obtained fairly accurately up to 8 load of 16,000
Ibo
5~ A 35 mm. camera which provided a photographic
saqusnce of speci~en behavior throughout .the testo
60 SR-4 resistance strain gages mounted on the
of -t~he second or outer "plas ti~ hinge 0 "
Figure 1-3 shows tbe specimen -,~it.h all of the ins trumenta. ,g
tion in plsoao
For this t9St, the spherical loading block W3S replaced
by [, loading blccJ-~ so wounted trJ.8..t i.t could not rot.e..te" This load-=>
i~1g condi tim:r, in conjunction with a truer specimen and ;nor~ 73.GCura.'te
cent8l"ing of the load, caused the specimen to deflec.t in a sY!nme-:~ri ~81
snap·s as is shewn in the series of photographs (FiGs., l.~4, l·~5~ DoDd
F'ibllra 1=7 shows clearly the tar:d-sncy of the platGs to
bulge -outwal"'fi when the specimen is testedo
Th(; load dGflGction curve for s)6ci:118n 2 stE.t:~c is shown
in F-igo 1-8" The ultiu:ete load fo:,:" this specimen was 19,,96c 10"
as indicated on the load deflection cu~vea
As was -:he case in the f irst s-t .. e .. ~ic test, a nHQbe~ of dif"
ficGlties were encountered with respeot to t~e loading of the speci~en
and the speciman supports. It we.s found that one of thr, stiffeners
was loaded bElfere the other because of ma.chining inaccuraciQso Another
RESTRICTED
80
complication arose from the plastic yielding of thG tie rods and
end pins which were designed for the first static test end which
Wer{3 strained boy'ond the ela.stic limit by the grea.ter horizontal
thr7.1st developed in test 2 statioo
It is planned that a third sta~ic test will be completed
in the near futurso In this test the speci~en end supports, which
wil!. allow rotati,on while preventing horizontal movement, ':till be
lds'ntical to tilos 6 tha.t will be used for the imp9.ct tests 0 It is
s.nt1.cipeterl that results bearing directly on the dynamic tests will
s,3ct,ion of this !,,?-pcrt) prepara.tions for the initial dyr:a.mic tests
h3.v'8 procGfld:21~ be/ond the initial planning st.a.ge ...
RiTISTRICTED
Fig. I Specimen I Static - No Load
. :., .... Fig.2 Specimen I Static - Load 11,400 lb .
After Passing Ultimate
(~.~: 1 {:~ -;~ ::.-, • ,~~ '}' J" \
~ ~ ~~) d ~~ r~ . ~i 1{ ~~ - ~
RESTRICTED
Fig.:3 Specimen 2 Static - No Load
.~.
Fig. 4 Specimen 2 Static - Load IO,OOO-lb.-
fit~' HICTED
Fig. 5 Specimen 2 Static - Ultimate Load
Fig.6 Specimen 2 Static - Load 8~OOO lb.
RESTRICTED
Fig. 7 Specimen 2 Static - Showing
Bulging of Plaie
r I J I ;..:
i I G
1 i
I i !
! , , ! i I ;
i
I I
i I I :1
1
;. i i
1-' i
it :1 ! ;
I I • ' ; r---------I---------r-------.----i I I ; i
I:! !
! !
!! i i i 1 ~
I 'j ! 1 ~-'T-·--------- - ---~---.-.t__.--.----. ___ . ___ ~ ________ -l-.. _._ ... ------------.. --:-:.-------.---.~-----~
i i . ~ \ ) I j
I ~ ". ~ \ £ ~ I J
.~ I 1
~} t:S
~~ ... ZJ
'; I I i ---.11.------------:---- _. ___________ . _.i ________ _____ .. ____ ~--_- ___________ ~ ~
': I ~ ')
\ i \ \.
"
\ \. 1-
\
. \.. i
~
~ ~ l
----=:t;-'---- t------ i i ~~ -----1---------;--------'-----1 -i ~) ~
'\ . '\
~ "-,,_ i
'l~
'. '-..."
..... ""·c.! , ;
.... , 1 ' ~
'~'- i I ~ ----.--- ._-" , .. ~~;:-- ---.: ---------------.:-----------------------1.: -'-">~
~ l ~ ,.,
! ~ .... '-J ij \~ i ~ ~
i I~ I ~ <"...) 1l..,J. ~ ~ ~
"~, ~ ;I
,--~,
" ' ~
~ c: . . ~~
:!.. ()
~:-.... 1
~ ... ",~ }< ?\~ ,-~
:-""l ~,!.... t~ ,
,(-::: '. ~ '.,'.
,~;', ~i~~~ ~¥~~~~;:';~{·~~~i~i~~~'::~~· , . ".:: .~< .... -~-,. ~~~'.: .. --: ::.:
RES TH ICTlID ,~ .. . ~~.:7i~.L_ .. -'-.. -
-9-
1. Introduction -
The purpos~ of static tests CD. hull segment-'X:Qdels is to
obtain numerical values of f~ndamental physical par~t~rs needed
in the dynamic tests" The purpose~:f the static analysis has been
to make possible t,he computation of these Q.uantities from the experi-
ment.al data ..
Tests were ,conducted by applying essentially Gon~entrated
described else'dbere in this Report {s#'};e Sectlon I}. The res-traint
which would ordin~.rily be provided by the reQ8.j,nder of ·the section
wes 6imulat,~,I. by .a.:l elastic tilt! cOl~Jecting the ends of the eegn:.ent 0
LJnde~ thes~ CirCU!lli3tanc~s the principal physical ps:rameters are
1) the ansle~~cha:a.;e ~r. unit of length due t.:) u~:t t 'bending
this quant:1 ty is e. cc·nstant. At m.gher loads} as tbf..: behav.:tor in.
the Yi~:l.uj.ty oi" the concentl"ated load.s becomes inel3.5t1c,; it may be
pos i tion on tb~ hl:11 segment ~
1ently expres~ed as the ratio of the fo'tee ~ EJ carried by the tie to
the ~xternal fo:rc~'} P ..
t1exa(~t" analJlsis {in the elastic rang~) as e tied erICh o;r curyed
beam 0 The analysis employed has not been of this 8ort~ how~vero
RESTRICTED
RESTRICTED
-10-
The hull segment has baen considered to have elasticity concentrated
8t a number of points (5 in the example worked out in this section)
rather than distributed throughout the structurs. This device is one
which can later be employed for dynamic analysis. The advantagas of
having the principles of the static analysis coincide with tho3e to
be employed in later investigations seem great enough to justify what
would otherwise be an unneoessary idealization.
20 Notation
H = Horizontal force applied as shown in Figo 2-10
p = Vertical force applied as shown in Figo 2 ... 10
:to ::L = % - coordinate of the i th point,
i = -3, ... 2, -1, 0, 1, 2, 30
Yi = Y - coordina.te of the i th pointo
Li = Distance between the points, i and i + 10
%1+1 - :x~ (Xi :: ..i-
Li
Y1+1 - Yi 0. 2 :2
~i = -I- t3i = 1 L.! l. ~
U· :: X - displacement of -the i ..r,.', pointo l un
V1. :: y - displaoement ox the i th pointt.> .J.
Mi :: Bending moment at the i th point .. Positive as shown in Fig .. 2-20
RESTRICTED
., 1 - . .\.~-::>
the arch or curved bea~ being analy~ed~
t~e angular rotation of the link jgiulng the 1 =
l::·t :PQi.o.t to the i th pOintl) mod th~ i tb point.
I 'I
f
.A B ~n . .lGnti~Y~s ~~--:- .-
:2 c ':;h~ ~,~ending lLOment a~; th~ i tb. pain t r,xi; f lexibili ty
RES TB J:C TED :-~ -.----:-:::.-==-.~
l
The b4!ud.1ng moment at any point,9 1.9 is giv~=n b)-I th;:
expression (Si~e Fig", P'c:>l) ..
Mi z:: ~ P (x.J = Xi) = H {Y, .::> Y1)9 i s 0.0 l,li 2) 3
M,,,,1 :: Ni
By d~Z'init1on~ D.; is given by the <e~rpZ'eDa1cn .&
All ~i ar~ eq~!al ~~d the subscript -my be d!"ap~-edQ
'J 't tlC:-1 'by as;sumptic:a ;~2!i s
K \L\1<>1 11 j ){31 = {vi't}l C.vi)ai {ui C ui~l)~i:l '-', {:r:L " ;it~lJa'i_~l =~-=== ~~'---=.~...:z-=~.~._ -::=> =::::;::z:.===-=--~=~.::-:-=.::...--=---==---=-c-=-=.-==--=-- .. __ ....::::::::-.~.-=:=-~::::.O
L L L
lim ~M. .. ;; M(x,V ~ 2 ..
""000] ;;
, ,. '; '~,b,;J
EquE. tion (6) and GUb8'.eq\~ent eque,tigns 113 not iJ exc~pt in the 1:Lzit
of
~
~~ --1
~,..
i.
'! ;;:
\
T~v:~ dlB;)l~~,:~·~rr:.euts (u.t 11 1f.,t:: of pOints 00 t.a:e h:3,l:~ 6~F1]1·~-:lt cl\. 2.
1-- ,I 'l!.<" r," ':-,.x
.1 '.
:,":1.::
-.1 =.~
::-::f.
,; 1
0
CO· ,.,,-.+ _"= .'.J.J ~) .~
.0
~ 0 ~.
i~ ('\ = ,I
11,..., ''', '~ t I) ,'I
RES~qIGjrEJ:. -~.,-=~-.---
x,J~ =1 --)
"J
;; ,
2;/ ~ ..... ;' 4~:
1 / 2 "J
i
b ... ;:'9o .2 :')
.J .""\ . ..., ,J
"...
.~ !. •• ,,:.
2
~ j .~ 0
The retll.lU~:o.deX' Qf' the analysis consists in J:"eplaicing a j b, B.D.d C in
Equations {8} by t.heir corre~t values?} given by Equntions (10; J) then
;repla~1ng e 1 'by M~ L/EX d in vie~ of Equation {6j g. and finally r~!?la~1ng ~ d
M by its value: in terms of losds and coordinates as given by Equation i ',1
d.ire~tly in t-srm..:J ()i~ the loads E and P.;) the stiffness Elt' the element
length 10,1 anc. th<t} i:noT1f"11 ~oordinates of points in the unstraine:d geg.r;~D.t.
For: COmI~B..ri8on with other analYB~!3 ~; it. :is more cgnv~n1ent to
l.J.S~ th{! ~adi~3 of the pressure h~113 R) than the segment len.gth L ..
the deformatiot!.s rredicted by the analysis .ore given. in Table l~ Th~
solution satisfies Raylt;!ighi)s reciprocal rele.tio!lBhips which provide
two horiz,on"ta~t loads H is twic~ th~ horizgntal end. dte.fle~t,1oD. due to
~l ver:tical load. P :: H'.> The ditfe.re:ace in sign is due to the choice of'
d~fle~tiG:n H-::9 tn.:l.t a positive E ,{Se?} F:tg::, 2-"1) p:rod1;lces llegati'fe c-.l
Cax r~"i:n.g o~:t an I:~xact n anal,yois ~".rbich \iould correspond to
using an infinite nulI!be:r of segments] the f:;er.ter and end defl~ction5 are
found to be
By :r.:ompari80n with the .first line of Table 1B a:ld th~ lest lin.e of
Tabl~ J.A,9 it may 'be 'seen that even with elasticity lConcentr~t;ed at
"exa:::t" solution 1:0 bett,~r than 6 ~rc~nt in 811 stati~ ~e.S02S"
Ex~eri~!ntal values of u_ a~d v are given in FiSc 2~5A ;) ()
2-=- ;)'dud 2"--1'r,, Va11,.1es (j'f thes:! quantities correspondiug to a given
if~.l1,.'.~ of ? can be j.n5~X'ted into the left=ba.nj aide of Equations {Lle,y
and. :( 11b ;." When T~his is done the Ifalu-es of aiR and EI toX' the lc..:s.d
The H=>? re).,atiQnship is sho1.f1.l in Fig 0 2=5·~ It sp-peurs to
From the fisur;~
(12)
the
rt.l-~ ) \\ 0,)./ fJ
It is ~"r.idep.t t.b,a:t the dimensions Qf the tie were su~h a.s to provide
about 97 p~rcent Qf ~omplet~ fixity",
RESTRICTED --=-=.===-
1 j
dteflections 101" and. Vo are shown in Fig" 2,,-,60 .For loods less than
9000 lb '.> in magnitude ZI ap~ars to have bce::l very ne~rly~gudtant '"
'r-. 6ti.f.f~ner9 Er '~~l,c1J,le::';,~d by {:on~n:;ntional m,,~thQda ~is 1.,[)4 x 10° Ib __ in,,'c,o
i5 quit·~ lin~~.r~
Fig" 2.:=.5 are ~6ed in the analytical for12llJ.l~ of Equation (lJ1a,),v the
RESTRICTED
center detle~tiona are given by the upper (computed) curve of Fig" 2:>4"
The comparison between theory and experiment, when appropriate ¥alues
of st.irfness :rmd t.ie restraint are ~mployedJ is not lJllS&ti6f'sctoryo
As -l part o.f the analJ-'tical program, an In'iestigatio71 of
intfol ving systems gf ordinary differentiltl equations whi~h a;r'e not
nf,l!~essar11)' lin~ar:. Of the numerical met,hods e"9'ailable step=by=step
p!"oc~dv.rea s~':Jm to. ~e ID(}st suit,uble and efforts have "bee!l ~oT?~!@ntrated
by :finite diftereni~es;) Studies havt:: been p"!.lblish~d j,u whi,ch '?X/dt2
1 d ...... I" (,-. + '\ ,i~2 ud ·rn_ c:;. ..... ·4..... .1 I')
~las rep a(Cl! ;.cy ;\Xn<i?l o,.;::Xn Xn=lOA~'" a \~~n ~d'Xnol -'r "'"n=2 =An~3J/:Cb=r:r;.J
r~B:pe(~ti'l!elyo Fairly satisfa~tQry results are obtaiued by so doing.
~er~ g'btain~d Wh08:~ roots d~t~rmin~d the nature of the solutloos of the
~orresponding d1f'fi!ren~e equs.tioIlS \ The solutions of t.he latter ~quat1ons
RESTRICTED ~- .. -~
RESTRlCTE.U ..:cr~=-~
could then be cornpared yith those of t.he differential eql..\ation.:. It
\{~uld seem ~t first glance» that a. more a.ccurate formula. for the
second deri v~n.1 ve ·..;ould lead to results that are a ~loser approxi=
matioo to th~ CQrr~ct sQlut1on~ 1~is is not necessarily true J howe¥eru
1
(.6t)2 divergent r~sult8 are obtainedo On the other haudg the approxi~te
tOK'L1Ula ;! ., =C~"""'. ~7;;2 '\ ,I 2 . 1 ~ t . l' \~.L. + 12 J Gl X eaMS 0 gOC-G. ;r~slJ.- ·~s
when used to aolxe (l)~
. .:ri;,:;.,
1·) S_~~.arr
RESTRIC~
I ~ J
1 i ; 1
1
I I :1
l~
RESTRICTED' ____ _
---~=- .~~
RESTRICTED
I I I
I I I , i ! i .
1 ~
! ~
I --.-xJ
~~ ..
~----------------------r----------~--------__ RESTRICTED 1 ~/!
i ! ,/'/ t I l/~ ~
I I /1 I /4~~. ____ ~ ____ ~ ______ ~! _______ ~~~·~ _____ ~i ____ ~t
I I/V I I I a ! I l4,o~o~--------~---------~~.----.----~I~--------~----------~--------~
//f I / i l
/2000t _________ -4 __________ ~~~~-~~------~I----------~----------~---------! I' ,//1 i
i I
I:
~ ! / i I
i / iii' ,I f
/qooo~--------~-----~,-l~~~~--------~----------rl!----------~I--·--------}
l I I '.~.!,: I iii
8 000 / I ; I L ! ~---------~,~/~~·-~-----4----------~--------~--------! ----------~:
~·V ! i P I' 1 i.1
Ii i 1 j ,.
J U"J ..;,......------.~ ~.f..3 I! :
/' ~.....,.-; I""' ,
: f ~ l:5ao.c ----.---uo-.----.JJ. ____ .... _ .. ____ . ___ .... _____ I - I t-- -.. I
/ : I ! 1 ,1 : I I ;
__ --4?.l.l
f-1 _____ 1 ____ --------------J- L __ i ~ '. I i
/ I Iii .{ ! i . ; , i!! j I I 1 '
-]~~-----Lc_-- .. --- -- -----t-.. -.------",-----+--- L- _______ ; I I .
I I I ; ;J i 1
j Iii / !; I I
~1 II I I I (,) t i L-____ . __ ~
o O. !.J.2 c.' ... 04';'~'
Fi 6', ,,? -.3 ~------------------------------~~~fl------------------------------------
=r !
.,~~a W, ___ ~~;.l I ! _II.-' __ _
I !
~ /~lcoO -I - Ii
l' l I I! . f i I I ! I ~ I I I
8ccoJ ~I ---l~------+------+------+------.l j r-- I I I j /: I i I " :
61700 t---,Lji------L,-----+-I------+--· ___ -+--____ 1
1 f I ! I I ~o l I l ! :,/) .' l ~ . I I
. .(/ ,......--~ I-! ' '?'j .-' . . I 1
t i i --'J..e>-rth., I - t:-- .i~ ~- 1 ~ } l i-I ~c~VI=- ! I
~jl 000 f---- / I -1 1 /! ~ 1 - j I I
I I , i J J !
.2170<0 !-L ! -l-----J ! / t ; J j ? I ~. ~ i i }
If I I I a V -4.-____ i I I
0.; ~,.. -,,~,-,---0--1 '-"., /r/ //vCHE.S I F/G. 2-4 1. ""'--------------------------------...,_ .. /
c
y/ .. ' 0/
I /
I I
I ~ i I
1 I
1 I I
! I I -' _ l
ti.2
.~
I "
; j 1
.;
RESTRICTRD ~
...... ~,.,.~~~~'S~:(*.;wt:l ~
I 8 .4
I ~ j .~ .
~
/f~1
"2~J .I 3
. ~ 1 ~ , ~
J ~
~
• /
j I
.1 !
-- ·~-T~7i ~ ........ ._'i,IIE; __ ~:-
I I ! '/ I I / I
j
/ - .-
/ I p
I ~'
I i I
I ~.
i .~ l
------+---1--~------~------~------~
I· I 11 80<70 I I III ~/D
~ ! I -d~~,;si-----~);J~ ,~s ! I' I I 'I! 'II
,,1 GcJaJ I / I ---+-. -----I-. ----t-----1
~ I I/i I I ! .~aY.) I k-·· ___ ---l _______ ---+-l ___ +-! ____ -+-___ ~ '~/ll I II 1- ' I I r
5. j j ! i .~ 1,' I 1
~ )' - : I ~ I i I
2 d~O L- 4'_-r ___ --+ ___ ~~~===~FL =-=~~~-.... --~ __ ~
I" f } I .
~ I j
; / ! . 1 :! ~ )'
l I It f I
11/ ! o /L._-----_I ~ ____ ..:--..... __ _= __ I,
.~~"'":11104&
o
r---I J r;
---+-------+-----~~ ~ ~ B\
~_I!:-_.<\~XJ_'~ -+-----m---~-__+_--- -- --------I~ I
' I ~ L I ~
I ~~y j /1" I
I /I! I I. • ~:\ I I / I I : 1 ':j
~ / I • 'I ! (~J i---,I i /4- ----,-----'--- __ ,l _____ . ___ ~-- ---- ----~, rji
11,._1 I/o I ,"
"t Ii I ,. CJ
"l if I I' .:
t~!: ~irJ 1! --·----------~--------+--------l, ! ~:j i 1t ' ! t (\'
I i,l 1'J Q II i ~ i --".,) f I! I 1\)-' , lit !~., !; 3 , ' 1 I I ':J
i D 0 il I ' · \t - 1. I ~ i~ Ii I ' j" f C - --- --!-'!- ~ ___ ...1-
1
: ---- --- - - - -- -- --- -----11
-- - - - --- -------l ~.~ " :-.... ! 1 1
J 1-... /',! - I i ~ ! (r~ I i j
~ \;~ rI" 0 ; ! i 1 - r I r;1 ~ i r ~ I ,\ ,,~ d I I Iii ~ t·t} i i ! I I 1 ~J ~ 1, e-:-=- .---- t' ·----'-·'-r··------------+---------·l-- j~ ! If' -- - -11- --- i I ! l r;
l i i~ \)
~ i Ii,:, I'
\~~t.-__ .-.. ~_--1L_____ ' ; ~~ ~
\0
:,---,---' -' .,-'-
\) ~j
<
i ~ ~~----"'------,-; \:~ ~~ \\~ \}
\
I :r-. i V ,
(
f f'-I 1 ~:.e
~ ,-
V) J ~~ i
\ ~ ! "~''''~ j
l 1
~ i 4
~
i j
1 1 j
-1 1
TABLE I
DEFORMATIONS OF h1ILL S~
(A) Horizontal De·i'orr"'.....a tions 1 u., ..
~ Point I D~.le to E:<terne.l Force,~ Due to Rest.reining Fares, H ] I 0 I 0 r 0 I !
I I I I l
A 10-3 PR3/EI :x 10-3 EF.3/E1 1 I 0.5084 If"
-0.3045
! 2 3.9689 n' -2~8145 I
~ l j
3 I 11.,1147 -8,,5134 J iil
eBl Vertical Dafcn:.ations,., vi .------~---------------------o.. 1,': -----------------------------~ I Point Due ·~o Extll""'1lal Force, II· Due to Restraining Forca, R-i
,e 30. -:~B43 : ~o-3 PR~/EI I -2202254 x 10-3 PR3/EI !
I '/ 1
I 1 21~.9845 ~ -19 .. 0981 1 I l i
! i I 1 2 15~OTI3 i ~lO~7497 I
l 3 0 __ L ______ o_. j
RESTRICTED
-{ :.", ~',' • '._:Of •. !.. '. ~
~ ...... "; .. ~ ," .............. ;1 ,
. -. '.'
." 1
f'· ~; ........ • ~ • .: .• 1 -, •
::J."J:~. , ~ ... ", \ -'t"I' 'Atl.~ ......
.~.)~
" :'~.ot.
-, oJ !. ;::'::; ~ " "<.' ., . , ' ... ~'
(. '\,",::
.I.!.!' ••• M , ":- ... 1".1· ... \ :.
~ ... ',J '~. ,._~ t1 '\::"
'. --, .1:
.: "i '.: .... ',: ...
tee gra'3~Gt r~rlod of I?ibratlon of the specimen \.(il1 a11lia.)'~ b~ 3hprt~l'
than the load.ing pulse so that the puls~ may "be var1~d withj,n quite
wide limi'ts t,11thout, appreciably ex/:::1ti;ng t.he higher mt.2ld.es o.f' "!;1.,br"a
t<iOD of the b.!!J.11l I;rt.rl)~ tUX'.e >
Bot.h meC.b.:3.n,lcal and h:ydraulirc 8),atems were conBic,er~d. in. t..h:e
design of a spri~ system \fith a modulus of 65,000 lbo ~r in·ch" The
id;ea of a me'>':han1.:<::sl system vas dis.:::arded be~aur;e the l!laSo c':(' t,h~
.~.~ .• ~
. , ,~ ,
. ,- ,
,.)'.'1.
/ .'
, '" -', ~ ...... !
__. ___ .:.--=.:L.-_-.......... ~._......,~ __ '..r •• ,.-_~-~- • ..:::.-
OF'
\
., ~ \ .. .,:, ''-'.:). t, s~ t'} ;:;"4~'~ G
., - . ',I
:~' r~: . ,':
, .... , ...
.~ ;1" .' \ .~, ,
:,\,,;,,'), ..... ::.t ok
t '-",,'
. :~
.' ... : \,.' ~. 'j ' .. '-.
:- -.
; ... '.' ,:
" ., r::..~, 7 ..
..,j:
.. :: . ~ .
" I,
"J _',
. "" ,-;,.' .... ,;1 .....
l.. ,I
tre~tment ep~ars .1J'l the literature i.)(d.) for th.::;: simplest COn.figur8::-:-'··~-'····
tionB {Light..hill~>.I ThOXnhill'~ fo;: a plane shock 1.f3Ve passing concave
fgrmf\4».5l'6
.,... "l ~ - !
1
i
"'l',' :"
" • ;. I" •
'. ~:~
:_ ~", ,"l. "
,; ;.
:;.. l ' ....
, .... : "
J .,1
.: -:".:'
.. : :..~ ~.: -
•. J 1 :.. ..... -. 1: ~ ",
~. ~, .'.
I"
;
I", ~~ :\·.:3 ;~ '_ ',_ .~. J- i.;!
t,.',: .. )f
Z 01,(, ",- ...
RESTRICTED
"Diffraction of Shock Waves around Va.rious Obstacles,"
oy G. Uhlenbeck, E.R.I., Univo of Michigan, Report No. 50-1, March
1950 ..
5. liThe Passage of Shock Waves over Oblique Obsta.cles,"
by R. N. Hellyer, Jr., and AQ C. Hunting, E.R.I., Univ. of Michigan,
Report No a 51-1~ j Augus t 1951.,
6., "'The Diffra.ction of Shock Wa.ves around Obsta.clss 2.Ed
the Transient Loading of Structures, f, by W .. Bleakney, Princeton
Un.!.versity, D9pt., of Phy3i~s} T8chn1.cal R8pO~t 11>·3, !IR 061~,,020;t
Noori-105, Task II.
L
RESTRICND
RESTRICTED
a e
d h
Fig. I Shock Wave Diffraction Around Cylinder
(Wat~r Tabfe Analogy)
RF~TR~rT~n
S tallr.;'jeye1''') Hali;; VL J" 5,:'00'::---:3, .j.. ri. Ho'~.Jl.3.r:d, F" L. co:~, Ho L. hlasse.rd, J ,. U. Cherry, She.le (~["l hlGDC:7',c~l::ij I, ,,J~
C~r~[' 2.scn ~ .~ ~ (i J
?l'" (; j e ~~ .. t S tt~ ·21" ~ .. r- _tsc t~ AssIsten-::' Project St',)G~visc::' fc:' ::'·y;)sri::: ::C.,3·.:' -o:j;"'~~rr
Assista.n-j~ Pro.10lct SqJ0rviso:"" :f0~' s:~c:~12'-':L;;,::.J_ .:::' i ;ac~::,
Research Assistant Research Assi:Ttar.t Resaarch Assistant Research Assistant He S Bare h !~s s i::; tar'! t Ras9a~ch Assistant Res9arah Asais~a~t
.~'
~~ ~'- r -.~"'. i"':' ;> ..... _J __ J .... v "",' ... 1 ~
'..l ?,. --' . '-: ... ' ._ -:',,/ ·.'!fi