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ADB816330
Approved for public release; distribution isunlimited.
Distribution authorized to DoD only;Administrative/Operational Use; APR 1942. Otherrequests shall be referred to David TaylorModel Basin, Washington, DC. Pre-dates formalDoD distribution statements. Treat as DoD only.
DWTNSRDC ltr dtd 4 Aug 1978
UNCLASSIFIED
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E.O. 10501 dtd 5 Nov 1953
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]<C AID <D|] ctnTflflL in Documinis-offici WRIGHT-PATTERSON AIR FORCE B A S E - D A Y T O N . O H I O
REEL-C
A. T.I
cfnim IS ABSOLVED
FROM ANY LITIGATION WHICH MAY ENSUE FROM ANY
INFRINGEMENT ON DOMESTIC OR FOREIGN PATENT RIGHTS
WHICH MAY BE INVOLVED.
m r
T RESTRICTEn
' MSlBiCfED
'
ATI ®Q/&Z> THE DAVID W. TAYLOR
+V j?
MODEL BASIN
UNITED STATES NAVY
EFFECTS OF IMPACT ON SIMPLE ELASTIC STRUCTURES
APRIL 1942
BY J. M. FRANKLAND, Ph.D.
<*:><j>},^ • *Q}
REPORT 481
RESTRTeiSBSL
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I 23
APPENDIX 1 FORMULAS FOR RESPONSE TO IMPACT DISTURBANCE
NOTATION
m is the mass, pounds divided by 386 Inches per second per second k is the spring constant, pounds per inch P is the applied force, or load, pounds P0 Is the maximum value of applied force p = P/Pn Is the disturbance factor, or disturbance * is the displacement In Inches x( = P%/k is the static displacement due to Pt
u = */*0 is the response factor, or resDonse T is the natural period In seconds / = 1/T is the natural frequency in cycles per second K = 2ir/ is the circular natural frequency In radians per second ( is the time in seconds t0 is the time of rise of gradually applied load (see Figure 4) tt is the duration of pulse
u, it are the first and second derivatives of u with respect to time n is the dynamic load factor u Is the circular frequency of cyclic part of disturbance In
radians per second r = U/K IS the frequency ratio
4> is the phase angle e,fi are constants
GENERAL EQUATIONS The system of Figure la acted upon by a force P gives rise to the
following differential equation:
mU{t) + kx(t)- Pit) [1]
where x is the acceleration. In non-dimensional terms, this equation is
*-*u(t) + u(n= pit) 12]
where K2 = k/m. The differential equation is to be solved subject to the condition
that the system starts from rest at zero time, that is,
M(0)=- 0 and tt(0) =0 [3]
A solution may be obtained In the form of a definite integral as
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5<4
It Is Interesting to compare the foregoing statements with some
experimental findings of R. N. Arnold (9). His apparatus consisted of a
simply supported beam subject to Impacts at mid length. Figure 27 consists
of scratch photographs Indicating variation of bending moment along the beam.
Though the horizontal scale In this figure Is not linear with time, the rec-
ord does Indicate how the bending moment varies. These records 3hould be
compared with the theoretical curves In Figure 23(c), and Figure 24(c).
Curve S In Figure 27 corresponds to a/l = 1/8 and curve A to a/I ='1/2. The
author states that the Impact loads at the center of the bar (obtained by
four Independent means) are In all cases 2.5 times those predicted by the as-
sumption of statical equivalence.
B
Reproduced by
IS & flD © ctniiiL flifl Docum£nTs office
WRIGHT-PATTERSON AIR FORCE BASE- OAVTON.OHIO
li in < nw I A A. T.I
<%£ (BCVKBIMIIV IS ABSOLVED
FROM ANY LITIGATION WHICH MAY ENSUE FROM ANY
INFRINGEMENT ON DOMESTIC OR FOREIGN PATENT RIGHTS
WHICH MAY BE INVOLVED.
B0IHrCW69»(!Jra4T) Frankland, J. U.
AUTHOR(S)
UGSTHICTGB <r- 7 - / - A.
DIVISION: Stress Analysis and Structures (7) SECTION: Loads, Criteria and Specifications (1) CROSS REFERENCES: Impact loads (50921.); Structures,
Aircraft - Gun blast resistance (90864.5)
ATTD- 16566 ORIG. AGENCY NUMBER
R-A81
REVISION
AMER. TITLE: Effects of impact on simple elastic structures
FORGN. TITLE:
ORIGINATING AGENCr: David Taylor Model Basin, ','iashington, D. C. TRANSLATION:
COUNTRY
U.S. LANGUAGE j
Eng. ORG-N.CUSS U. S.CLASS.
Restr. OAK
Apr'42 PAGES u IUUS.
33 FEATUBES
diagrs, graphs ABSTRACT
The characteristic features of stresses arising from rapidly applied or brief loads such as gun blast or gun recoil, referred to as impact loading, are presented. Repre- sentative cases of impact loading and their effects upon a simple undamped system with one degree of freedom are investigated for oscillating and nonoscillating disturbances. Weans of judging to what degree the behavior of the idealized system is realized among actual ships and other structures is discussed. Application of this to the strength of structures under impact is considered.
T-2. HO.. AIR MATERIEL COMMAND AIR ITECHNICAL INDEX EESTQOCVED
WRIGHT FIELD. OHIO. USAAF Wf-O-31 MAS 47 M,M0
BCMFcmraA (ismur) Frankland, J. U.
AUTHORS!
'V- 7 - / -A. DIVISION: Stress Analysis and Structures (7) SECTION: Loads, Criteria and Specifications (1) CROSS REFERENCES: Impact loads (5C920; Structures,
Aircraft - Gun blast resistance (9086A.5)
ATI- 16556 ORIG. AGENCY NUMBER
R-A81
AMER. TITLE: Effects of ijr.pact on simple elastic structures
FORGN. TITLE:
ORIGINATING AGENCY: David Taylor liodel Basin, Washington, D. TRANSLATION:
COUNTRY U.S.
LANGUAGE Sng.
FORG'N.CLA SS U. S.CLASS. DATE Restr. kpr'UZ
FEATURES diagrs, graphs
ABSTRACT The characteristic features of stresses arising from rapidly applied or brief loads
such as gun blast or gun recoil, referred to as impact loading, are presented. Repre- sentative cases of impact loading and their effects upon a simple undamped system with one degree of freedom are investigated for oscillating and nonoscillating disturbances, "eans of judging to what degree the behavior of the idealized system is realized among actual ships and other structures is discussed. Application of this to the strength of structures underimpact is-^considered.- , _ »¥—.»» T ~ ^- «-*
LO fObtfl 3d o NCV i953 T-2, HQ., AIR MATERIEL COMMAND AIR TE. .XAl-hiatt WRIGHT FIELD, OHIO, USAAF
WF-O-21 MAS 47 22.5CO