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UNCLASSIFIED AD NUMBER LIMITATION CHANGES TO: FROM: AUTHORITY THIS PAGE IS UNCLASSIFIED ADB816330 Approved for public release; distribution is unlimited. Distribution authorized to DoD only; Administrative/Operational Use; APR 1942. Other requests shall be referred to David Taylor Model Basin, Washington, DC. Pre-dates formal DoD distribution statements. Treat as DoD only. DWTNSRDC ltr dtd 4 Aug 1978

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Page 1: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · UNCLASSIFIED AD NUMBER CLASSIFICATION CHANGES TO: FROM: AUTHORITY THIS PAGE IS UNCLASSIFIED ADB816330 unclassified restricted E.O. 10501

UNCLASSIFIED

AD NUMBER

LIMITATION CHANGESTO:

FROM:

AUTHORITY

THIS PAGE IS UNCLASSIFIED

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

Page 2: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · UNCLASSIFIED AD NUMBER CLASSIFICATION CHANGES TO: FROM: AUTHORITY THIS PAGE IS UNCLASSIFIED ADB816330 unclassified restricted E.O. 10501

UNCLASSIFIED

AD NUMBER

CLASSIFICATION CHANGESTO:

FROM:

AUTHORITY

THIS PAGE IS UNCLASSIFIED

ADB816330

unclassified

restricted

E.O. 10501 dtd 5 Nov 1953

Page 3: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · UNCLASSIFIED AD NUMBER CLASSIFICATION CHANGES TO: FROM: AUTHORITY THIS PAGE IS UNCLASSIFIED ADB816330 unclassified restricted E.O. 10501

Reproduction Quality Notice

This document is part of the Air Technical Index [ATI] collection. The ATI collection is over 50 years old and was imaged from roll film. The collection has deteriorated over time and is in poor condition. DTIC has reproduced the best available copy utilizing the most current imaging technology. ATI documents that are partially legible have been included in the DTIC collection due to their historical value.

If you are dissatisfied with this document, please feel free to contact our Directorate of User Services at [703] 767-9066/9068 or DSN 427-9066/9068.

Do Not Return This Document To DTIC

Page 4: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · UNCLASSIFIED AD NUMBER CLASSIFICATION CHANGES TO: FROM: AUTHORITY THIS PAGE IS UNCLASSIFIED ADB816330 unclassified restricted E.O. 10501

Reproduced by

]<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.

Page 5: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · UNCLASSIFIED AD NUMBER CLASSIFICATION CHANGES TO: FROM: AUTHORITY THIS PAGE IS UNCLASSIFIED ADB816330 unclassified restricted E.O. 10501

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

f\

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Page 7: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · UNCLASSIFIED AD NUMBER CLASSIFICATION CHANGES TO: FROM: AUTHORITY THIS PAGE IS UNCLASSIFIED ADB816330 unclassified restricted E.O. 10501

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Page 8: UNCLASSIFIED AD NUMBER LIMITATION CHANGES · UNCLASSIFIED AD NUMBER CLASSIFICATION CHANGES TO: FROM: AUTHORITY THIS PAGE IS UNCLASSIFIED ADB816330 unclassified restricted E.O. 10501

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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

follows:

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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.

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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.

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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

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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