AUTOMOBILE IMPACT FORCES ON CONCRETE WALL

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t NUREG/CR-2790CWA Report 4010-FR

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. Automobile Impact Forces onConcrete Wall Panels

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Prepared by R. L. Chiapetta, E. C. Pang

Chiapetta, Welch & Associates, Ltd.

Prepared forU.S. Nuclear RegulatoryCommission

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CR-2790 R t u.

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NOT;CL

Tha report was prepared as an account of work sporuoted by an agency of the Uruted States' Govo nment . Neither the United States Gesernrnent nor any ency thercof, or any of theirerr.pf riers, makes any warrant y, egressed or irnphed, or anun'es any legal ikhihty of re-t

sponso,hty for any thud party's use, or the resof ts of such use, of any udorrnation, appar Ws |product or process disclosed in this stport, nr represents that its use by such third party woofd '

r;ot mfrirge povately oy.ned rights. !

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E| Availabihty of Reference Materials Cited in NRC Pub;icatmns

Most cocuments cited in NRC pubucations wW be avadable from one of the foilevnng sources;

| 1 7 he NRC Public Document Room,1717 H Street, N.W.) i Washington, DC 20555

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{ 2. The NRC/GPO Sales Program, U.S. Nuckar Regulatory Commission,j Washington, DC 20555

1- 3. The National Technical Information Service, Springfield, V A 22161I

{ Although the hsting that follows repre'ents the majority of documents cited in NRC pubhcations,j it is not intended to be evhaustne

| Referenced docu nents availab!e for insnection ar,d copying for a fee from the NRC Pubhc Docu- |

| ment Room mcluda NRC corremondence and ir.ternal NRC mcmoranda: NRC Of fice of Inspectionand Enforcement hohetins, catulars, information notices, inspection and insesti phon notices: it

I Licensee E vent Reports, vendor reports and correspondence; Commn,sion pgem and apohcant and

| licer'.ee cocurnents and corresponuence.j4 The followna documents in the NUREG senes are avadable for purchase from the NRC/GPO Sales '

! Proyam: formal N RC staf f and contractor reports, N RC sponsored conference proccedmos. and'

|NRC book!ets and brochures. Alsa asadable arc Regulatory Guides. NRC requ!ations in the Coce of

i Fdera! Regulations and fiuctear Regulatory Cornmission issuances|

Docurnents <ivslable from the National Technical Information Service mclude NUREG ser;es,

repo ts and tech Ucal reports prepared by other federa! aarnca s and reports prepared by the Atomicr,

i Energy Commission, forerunner vocy to trie Nucle =r Regulatory Commission.! '

| Docurretits avM!able from public and special techrdcal bbranes include all open hierature items,i such as books. journal and penndical articles, and transactions. Feceral Register notices. federal and

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sute leaMat on, and congtess,onal reports can usuativ be obtamed from the-c hbrancs (i [

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Smq'e conms o' N RC draf t reports are availatue free upon written request to tne Division of Tech-nical lofomution and Document Control. U S. Nuclear Regubtory Commission, Washington, DC20555.

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~ ! Comss of industry codes and standards useit m a substantwe manner in the NRC regulatory process- me mamta'md at the NRC L brary. 7920 Norfolk Avenue, Bethnda. A*eyland and are avadable

them for rtference uw by the public. Codes and standards are usuMiy cenynghted and may be,

purchmen from the origin 3tmg en',anizat!oq or, if they are American National Standards, from the |>

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Anvrican Natione Standarns inst,tute 1430 Broadwiy, New York, N ( 10018. i

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NUREG/CR-2790CWA Report 4010-FRRD i

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Automobile Impact Forces onConcrete Wall Panels

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M:nuscript Completed: January 1982D:ta Published: June 1982

Prep: red byR. L. Chiapetta, E. C. Pang

Chiip;tta, Welch & Associates, Ltd.9748 Roberts RoadPalos Hills, IL 60465

Pr:p3 red forDivision of Engineering Technology

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Offica of Nuclear Regulatory Research ;|

U.S. Nuclear Regulatory Commission !

Wcchington, D.C. 20666NRC FIN B6609 !

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ABSTRACT

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The objective of this study was to develop force-time impact signaturedata for use in the design or evaluation of nuclear power plant structuressubject to tornado-borne automotive vehicle impact. The approach was basedon the use of analytical vehicle models to calculate impact forces. Toassess the significance of vehicle / structure interaction for head-on impactforce-histories, a lumped-mass model of a reinforced concrete wall panelwas coupleo to a one-dimensional vehicle model for numerous panel designconfigurations within the range of practical interest. Vehicle-structureinteraction was found to have relatively little effect on the force-histories. The sensitivity of structural response to variations in forcesignature characteristics was established and idealized impact force-timerelations were developed for five distinct impact speeds ranging from

; 20-60 meters /second. The use of these relations produce less conservative: estimates of structural deflection, for all impact speeds considered,

than the currently accepted design procedure.

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| TABLE OF CONTENTS

?.*L*.1. INTRODUCTION 1

2. BASIC APPROACH 2! 2.1 Data Collection 2

2.2 Vehicle Model Selection and Evaluation 22.3 Impact Force Calculation for Baseline Configuration 22.4 Effect of Structural Deformation 32.5 Effect of Impact Orientation 32.6 Derive Design Functions 4

3. MATHEMATICAL VEHICLE MODELS 'FOR IMPACT SIMULATION 5

3.1 Review 53.2 Parameter Data 73.3 Evaluation 73.4 Sensi tivity 113.5 Summary and Final Model Selection 13

4. FORCE SIGNATURES FOR HEAD-ON IMPACT INTO RIGID WALLS 47

5. EFFECT OF WALL DEFORMATION ON IMPACT FORCE 108

5.1 Coupled Vehicle / Structure Model 1085.2 Structural Parameters 1095.3 Results 109

6. EFFECT OF IMPACT ORIENTATION ON FORCES 125

7. DESIGN c'JNCTIONS 139

7.1 Baseline Configurations 1397.2 Structural Deformation and Impact Orientation Factors 140

i 7.3 Comparison with Currently Accepted Procedures 1427.4 Summary 143

8. CONCLUSIONS AND RECOMMENDATIONS 155

REFERENCES 157

APPENDIX A - DISTRIBUTED MASS VEHICLE MODEL AND STRUCTURAL MODEL 158

APPENDIX B - VEHICLE PARAMETER DATA 167

APPENDIX C - CONTMASS COMPUTER PROGRAM 197

APPENDIX D - WALL PANEL PARAMETERS 208

APPENDIX E - EFFECT OF TEMPORAL LOAD DISTRIBUTION ON STRUCTURALRESPONSE 240

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LIST OF ILLUSTRATIONS

Figure Page,

3.1 Instantaneous Momentum Transfer Vehicle Model 16

3.2 Constant Force Vehicle Model 16

3.3 Linear Model 17

3.4 Nonlinear Vehicle Model 17

3.5 Distributed Mass Vehicle Model 18

3.6 Multimass Vehicle Model 19

3.7 Development of Nonlinear Spring Properties 20

3.8 1972 Chrysler, 30 mph Impact 21

3.9 1973 Plymouth Satellite, 30 mph Impact 22



3.12 1973 Ford Torino, 30 mph Impact 25

3.13 1973 Ford Torino, 30 mph Impact 26

3.14 1973 Torino, 30 mph Impact 27

3.15 1975 Plymouth Gran Fury, 30 mph Impact 28



3.18 Model Predictions of Acceleration History with Test Data 31

3.19 Comparison of Impact Force on Various Models at Low-Speed Impact 32

3.20 1975 Honda CVCC, 40 mph Impact 33

3.21 1975 Honda CVCC, 40 mph Impact 34

3.22 1975 Honda CVCC, 40 mph Impact 35.

3.23 Comparison of Impact Force Between Lumped Massand Distributed Mass Models 36

3.24 Impact Force for Lumped Mass Representation of Engineand Body Masses - Distributed Mass Model Versus LumpedMass Model 37

3.25 High-Speed Impact Force for Compact Car 38

3.26 High-Speed Impact Force for Intermediate-Size Car 39

3.27 High-Speed Impact Force for Full-Size Plymouth 40

3.28 High-Speed Impact Force for Full-Size Ford 41

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LISTOFILLUSTRATIONS(Contd)

Figure Page

3.29 Effect of Crushing Strength on High-Speed Impact Force-- Minicar 42

3.30 Effect of Crushing Strength on High-Speed Impact Force-- Intermediate-Size Car 43

3.31 Effect of Value of Momentum Transfer Factor of Distributedliass Model on Impact Force 44

3.32 Effect of Body Mass Distribution on High-Speed Impact Force 45

3.33 Effect of Engine Mass Distribution on High-Speed ImpactForce 46

4.1 Car Body Force on Rigid Wall; SRI Car, 20 m/sec Impact Speed 45

4.2 Car Body Force on Rigid Wall; Calspan Car, 20 m/secImpact Speed 50

4.3 Car Body Force on Rigid Wall; Ford Pinto, 20 m/secImpact Speed 51

4.4 Car Body Force on Rigid Wall; Plymouth Gran Fury, 20 m/sec?mpact Speed 52

4.5 Car Body Force on Rigid Wall; Plymouth Satellite,' 20 m/secImpact Speed 53

4.6 Car Body Force on Rigid Wall; Plymouth, 20 m/sec ImpactSpeed 54

4.7 Car Body Force on Rigid Wall; Chrysler, 20 m/sec ImpactSpeed 55

4.8 Car Body Force on Rigid Wall; Ford Pinto, 20 m/sec ImpactSpeed 56

4.9 Car Body Force on Rigid Wall; Honda CVCC, 20 m/sec ImpactSpeed 57

4.10 Car Body Force on Rigid Wall; SRI Car, 30 m/sec Impact Speed 58

4.11 Car Body Force on Rigid Wall; Calspan Car, 30 m/sec ImpactSpeed 59

4.12 Car 3ody Force on Rigid Wall; Ford Pinto, 30 m/sec ImpactSpeed 60

4.13 Car Body Force on Rigid Wall; Plymouth Gran Fury, 30 m/secImpact Speed 61

4.14 Car Body Force on Rigid Wall; Plymouth Satellite, 30 m/secImpact Speed 62

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Figure Page_





4.19 Car Body Force on Rigid Wall; SRI Car, 40 m/sec ImpactSpeeo 67


4.21 Car Body Force on Rigid Wall; Ford Torino, 40 m/sec ImpactSpeed 69





4.26 Car Body Force on Rigid Wall; Ford Pinto 40 m/sec Impact :Speed 74 1

4.27 Car Body Force on Rigid Wall; Honda CVCC, 40 m/sec ImpactSpeed 75 |

4.28 Car Body Force on Rigid Wall; SRI Car, 50 m/sec ImpactSpeed 76

4.29 Car Body Force on Rigid Wall; Calsp:n Car, 50 m/sec ImpactSpeed 77





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Figure Page.




4.37 Car Body Force on Rigid Wall; SRI Car, 60 m/sec ImpactSpeed 85





4.42 Car Body Force on Rigid Wall; Plymouth, 60 m/sec Impact-Speed 90



4.45 Car Body Force on Rigid Wall; Honda CVCC, 60 m/sec Impac.t,

| Speed 93

4.46 Comparison of Body Force on Rigid Wall for Different Cars,20 m/sec Impact Speed 94


4.48 Comparison of Body Force on Rigid Wall for Different Cars,l 30 m/sec Impact Speed 96





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LIST OF ILLUSTRATIONS (Contd)

P_ ageFigure a

4.53 Comparison of Body Force on Rigid Wall for Different Cars,50 m/sec Impact Speed 101.



4.56 Impact Force for Various Impact Speeds - Baseline Config-uration, Plymouth Satellite 104.

5.1 Coupled Vehicle / Structure Model 111

5.2 Wall Panel Resistance Function 111

5.3a Percent Deviation of Engine Impulse, Simply SupportedPanel 116

5.3b Percent Deviation of Engine Impulse, Fixed Edge Panel 117

5.4a Percent Deviation of Body Mass Impulse Simply SupportedPanel 118

5.4b Percent Deviation of Body Mass Impulse, Fixed Edge Panel 119

5.5 Effect of Wall Flexibility of Impact Force for 12" ThickWall at 40 m/sec Impact Speed 120

5.6 Effect of Wall Flexibility of Impact Force for 24" ThickWall at 40 m/sec Impact Speed 121

5.7 Effect of Wall Flexibility of Impact force for 36" ThickWall at 40 m/sec Impact Speed 122

5.8 Effect of Wall Flexibility on Impact Force for 12" ThickFall at 20 m/sec Impact Speed 123'

5.9 Effect of Wall Flexibility on Impact Force for 12" ThickWall at 60 m/sec Impact Speed 124

6.1 GUARD Vehicle Model 127

6.2 Side Contact Panels for GUARD Vehicle Model 127

6.3 Impact Configuration for Orientation Study 128

6.4 Impact Panel Properties for GUARD Model,1973 Plymouth 129

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Figure Pm6.5 Comparison of Frontal Impact Force Functions, 40 m/sec

1973 Plymouth Satellite, 6, = 0 130

6.6 Impact Force,1913 Plymouth Satellite, 40 m/sec0, = 0 deg , O = 1 rev/sec 131

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6.7 Impact Force,,1973 Plymouth Satellite, 40 m/sec;O = 30 deg, 0, = 1 rev/sec 132g

6.8 Impact Force,,1973 Plymouth Satellite, 40 m/sec;O = 60 deg, o = 1 rev/sec 133

g g

6.9 Impact Force. 1973 Plymouth Satellite, 40 m/sec;'

O = 90 deg, O = -1 rev/sec 134g g

6.10 ImpactForce,}973PlymouthSatellite,40m/sec;O = 120 deg, 0, = -1 rev/sec 135g

6.11 Impact Force, }973 Plymouth Satellite, 40 m/sec;0, = 150 deg, o = -1 rev/sec 136g

6.12 Impact Force, }973 Plymouth Satellite, 40 m/sec;o = 180 deg, O = -1 rev/sec 137g g

6.13 Effect of Vehicle Yaw Orientation on Impact Force --Plymouth Satellite, 40 m/sec Impact Speed 138

| 7.1 Design Envelope for 20 m/sec Impact 145i

| 7.2 Design Envelope for 30 m/sec Impact 146

7.3 Design Envelope for 40 m/sec Impact 147

7.4 Design Envelope for 50 m/sec Impact 148

7.5 Design Envelope for 60 m/sec Impact; 149

7.6 Idealized Baseline Force Functions 151

7.7 Stiffness of a Partially Loaded, Simply Supported, SquarePlate 152

7.8 Effect of Yaw Impact Orientation on Wall Panel Displacement 153

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LIST OF TABLES

Table Pm4.1 SRI Full-T ~:ar, Baseline Configuration Results 105

4.2 Calspan Full-Size Car, Baseline Configuration Results 105

4.3 1973 Ford Torino, Baseline Configuration Results 105

4.4 1975 Plymouth Gran Fury, Baseline Configuration Results 106

4.5 1973 Plymouth Satellite, Baseline Configuration Results 106

4.6 Plymouth, Baseline Configuration Results 106

4.7 1972 Chrysler, Baseline Configuration Results 107

4.8 1974 Ford Pinto, Baseline Configuration Results 107

l 4.9 1975 Honda CVCC, Baseline Configuration Results 107

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5.1 Matrix of Wall Panel Geometries Considered 112;

| 5.2 Matrix of Wall Panel Geometries Considered 113

! 5.3 Comparison of Maximum Force and Impulse for Rigid

j and Flexible Walls, Fixed Edge Panels 114

| 5.4 Comparison of Maximum Force and Impulse for Rigidand Flexible Walls, Simply Supported Panels 115

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| 7.1 Response of " Typical" Structure to Calculated BaselineForce Signatures 150

7.2 Comparison of the Effect of Current and RecomendedImpact Load Calculation Procedures -- Design Car 154

7.3 Comparison of the Effect of Current and RecomendedImpact Load Calculation Procedures -- 1973 Plymouth

i Satellite 154

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1. INTRODUCTION.i

; The structural design of nuclear power plants in recent years has increas-ingly been concerned with the threat of main structure penetration ordamage caused by a variety of high speed missiles. Sources for suchthreats range from high speed fragments from internal equipment to impactingaircraft and tornado borne debris. The last category is generally takento include such miscellaneous wreckage as pipes and timbers but must alsoinclude air-borne motor vehicles as a credible possibility. Although asubstantial number of studies have been reported dealing with variousaspects of structural response and damage criteria for missiles, thesestudies have dealt either with the "hard" missiles (i.e., relatively small,stiff penetrators) or with the very large, " soft" missiles such 'as air-cra f t. Little information is available which specifically deals withmotor vehicle impact on nuclear facilities. Further, the automobile, con-sidered as a missile, is intermediate in mass and size between the hardpenetrators and the large missiles such as aircraft and is likely to in-volve force levels and damage mechanisms which do not fall within therange of effects included in either of these extremes.

The procedure currently acceptable to the Nuclear Regulatory Comission(NRC) for considering automobile impact loads on Category I structures innuclear power plants, consists of treating the automobile as a rigidmissile which imparts its total momentum instantly to the structure. Atlow impact velocities the adequacy of this simplistic approach is oflittle concern because other loadings govern the design of exterior wallsof Category I structures. However, recent studies (Ref. 1) suggest that

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i relatively high impact velocities are likely to be attained by an automo-I bile in a tornado in some geographical areas. At these velocities, auto-

mobile impact loads could very well dictate certain aspects of structuraldesign; e.g., the size and configuration of reinforcing bars in reinforced

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i concrete walls. It is therefore desireable to obtain a more accuratedefinition of automobile impact loads.

The objective of the investigation reported herein was to develop represen-tative design-oriented loading data for reinforced concrete wall panelssubjected to automobile impact considering the deformability of both thevehicle and structure.

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The study was solely analytical in nature and drew largely on the exten-sive body of low-speed automotive crash data and simulation techniquesavailable from prior vehicle crashworthiness studies as a source of load-ing information. Design data was developed for various impact speedsranging from 20 meters /sec to 60 meters /sec.

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2. BASIC APPROACH

The following steps outline the basic approach used to develop the resul-tant design orientated data in the fonn of loading functions.

2.1 Data Collection

Data relative to both automobiles and reinforced concrete walls in nuclearpower plant structures were necessary for the conduct of the analysis inthis investigation.

Descriptive data representative of the spectrum of passenger vehicles wascollected. This included mass and crushability characteristics. In addi-tion, crash test results for the impact of passenger vehicles into heavyreinforced concrete walls were compiled for validation of the analyticalmodels.

Ranges of reinforced concrete wall design parameters for nuclear powerplant structures were obtained for use in modeling their structuralproperties.

2.2 Vehicle Model Selection and Evaluation

A literature review was conducted for crash models to calculate impactforces. The vehicle deformation models used to date for application tovehicle impact with nuclear power plant structures have been confined toone-dimensional head-on orientation models. For purposes of this study,the baseline configuration was defined as head-on impact of an automobileinto a rigid wall.

The vehicle models reviewed were evaluated by comparison with each otherand against vehicle crash test data for the baseline configuration. Oneexisting model was modified and selected for subsequent use on thisinvestigation.

The sensitivity of the selected model to variation in mass and strengthdistribution and magnitude was studied.

2.3 Impact Force Calculation for Baseline Configuration

With the selected model, impact force-time functions were calculated fornine passenger automobiles ranging from full-size cars to minicars forimpact speeds of 20, 30, 40, 50 and 60 meters /sec.

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2.4 Effect of Structural Defonnation

The vehicle model was coupled with an elastic, plastic one-degree-of-freedom flexural model for the structural wall panels. This simplerepresentation of the wall panels was introduced to approximately deter-mine the effect of structural deformation on impact forces.

The impact of one automobile into a wide variety of walls representingthe practical range of structural design parameters was simulated. Cal-culations were made for impact speeds of 20, 40 and 60 meters /sec. Impactforce functions were compared to the corresponding ones for impact of thevehicle with a rigid wall. Results showed that structural deformationhas little effect on impact forces.

2.5 Effect of Impact Orientation

The relative severity of impact between frontal, rear, side and anyoblique angle impact between these orientations was determined. This wasaccomplished with the use of a three-dimensional vehicle model. The wallswere assumed to be rigid for the purpose of this part of the study.Rotational as well as translational velocity at impact was considered.

A translational velocity of 40 meters /sec in combination with zero andone revolution /sec angular velocity was used. The frontal impact crush-ing strength properties of the three-dimensional vehicle model weretaken to be approximately equal to those of the one-dimensional frontali

impact model and the side and rear crushing strength properties per unitarea were assumed equal to those of the front. One full-size passengervehicle was used in the calculations. It was found that the side impactorientation produced the greatest peak impact force by about a factor oftwo over the frontal impact force, and that the side impact force func-tion deflected a typical wall panel more than the force function for anyother orientation considered. Furthermore, the rotational velocity of1 revolution /sec at impact was found not to significantly alter the im-pact force function and the three-dimensional and one-dimensional vehiclemodels produced comparable force functions for both side and frontalimpact conditions even though the impact envelope, or " springs", of thethree-dimensional model are massless whereas those of the one-dimensionalmodel are not.

In view of the above findings, the simpler one-dimensional model was usedto compute force functions for side impact as well as frontal impact ofthe test vehicle into a rigid wall. Both functions were applied to astructural model of a typical wall panel. By trial and error, the mul-tiple factor, applied to the frontal impact function, necessary to pro-duce the same structural deflection as the side impact function wasdetermined. This was done for various impact speeds. This factor wasfound to vary between 1.65 and 2.45 depending on impact speed.

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2.6 Derive Design Functions

Baseline force functions generated for the various vehicles consideredat each of the five impact speeds (from 20 to 60 meters /sec) were inputto the simple elastic, plastic structural wall panel model for onetypical wall panel.

The vehicle whose baseline force function produced the greatest structur-al defomation was selected as the design car at the given speed. Thiswas done for each of the five impact speeds.

The force functions for the design cars at each speed were then idealizedsuch that the idealized function has the same total impulse and producesthe same structural deflection on the panel model mentioned above.

The final idealized impact force functions were derived by multiplyingthe baseline idealized functions by two factors; one to account for theeffect of structural defomation and one to account for impact orientation.

The structural deformation factor was recomended to be unity since theeffect of structural deformation was found to be insignificant. The im-pact orientation factor was reconteended to be between 1.65 and 2.45depending on impact velocity. The latter factors were derived as explainedin Section 2.5.

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3. MATHEMATICAL VEHICLE MODELS FOR IMPACT SIMULATION'

3.1 Review

There are at least three basic vehicle models which have been used tosimulate the impact of a vehicle with nuclear power plant structures asa result of a tornado.

The one currently accepted by the NRC consists of essentially a rigidmass representation of the vehicle as depicted in Figure 3.1 (Ref. 2).The basic assumptions inherent in this model are that the impact durationis very much smaller than the period of response and that the impact isfully plastic (no elastic rebound; the car moves with the same speed asthe structure after impact). For example, for a simple one-degree-of-freedom representation of the structure, the velocity of the structureimediately after impact is:

(1)s" M+M o

where M = car massM = structure masssVo = impact velocity of car

For brevity, this model will be referred to as the Instantaneous MomentumTransfer Model.

In the Constant Force Model (Figure 3.2) the vehicle is considered intwo parts: (1) the engine and transmission, and (2) the remainder of thecar. The engine and transmission are assumed to transfer momentum instan-taneously and plastically as in the preceding procedure and the remainderof the car is assumed to crush as a constant force spring over a finiteduration. This procedure has been employed in Ref. 3 where the magnitudeof the constant force was estimated from data on one car crash test.

The Linear Spring Model shown in Figure 3.3 treats the vehicle as a singlelumped mass with a linear spring representing its defomation properties.In Ref. 4 this model is used with a value for the spring constant ofK = 12.5W lb/ft (W = car weight, lb) based on head-on crash tests of numer-ous cars from the 1950's and 1960's. The displacement history of the carmass according to this model is given by

V

x= sin wt (2)

where w = (3)

t = time after impact

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The car acceleration is

X = -V u sin wt (4)o

and the force acting on the wall is

V

F=Kx=Kfsinwt (5)

For a linear spring which unloads in a completely plastic manner, Eqns(2),(4) and (5) are valid only up until

t=tmax " 2 m (6)

which is the time at which the displacement, acceleration and force achievetheir maximums. After that the force and acceleration are zero.

Three additional mathematical models were identified for consideration asvehicle models in the present application. The first of these is theNonlinear Model (Figure 3.4). It is a single lumped mass model like theLinear Model but has a nonlinear rather than a linear spring.

Another candidate vehicle model identified was the Distributed Mass Modelshown in Figure 3.5. This model has been used to compute aircraft impactforces on nuclear power plant structures (Ref. 5). In this model thevehicle is composed of a crushed region and a rigid uncrushed region.The impact force is a function of the crush force and mass density alongthe length of the vehicle as follows:

F = P (x) + sp(x)V (7)c1

where P (C) = crushing strength of the vehicle as a function |c of( = distance along length of vehiclex = crush distance

p(C) = mass per unit length of the vehicle as a func-tion of C

V = current velocity of uncrushed portion of vehicleB = a factor, the value of which depends on certain

assumptions.

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The vehicle acceleration is given by

P(*)dV ca=g=- (8)

M -/g* p(E)dg

A detailed derivation of Eqns(7) and (8) is provided in Appendix A.

Another type of vehicle impact model considered is a Multimass Model.The automobile industry has long used multimass tehicle models for crashsimulation to evaluate and revise the design of structural components ofvehicles so as to be able to meet government-imposed crash performancerequirements and to improve the impact crashworthiness of vehicles ingeneral. A schematic of this type of model is shown in Figure 3.6. Asindicated in the figure the model is composed of a number of lumpedmasses, corresponding to main structural components of cars, interconnectedby nonlinear " springs" or energy absorbers. The characteristics of theenergy absorbers are determined normally by dismantling a vehicle andtesting various subassemblies in a crush testing machine.

3.2 Parameter Data

Data characterizing the strength and mass distribution properties was com-piled for nine vehicles for use on this investigation. This data is pre-sented in Appendix B.

3.3 Evaluation

In Section 3.1, six vehicle impact models were described including theNRC accepted Instantaneous Momentum Transfer Model. The other five wereall evaluated as alternatives for subsequent use on this study to gener-ate impact force design curves.

In the Constant Force Model (Ref. 3) force F on a wall due to impact withthe bulk of a car, exclusive of engine and transmission, is computed fromthe energy equation,

fMV = FA (9)2o

where M2 is the mass of the bulk of the cars.(see Figure 3.2). The quan-tity A is the total length of crush which is determined by the test. Theconstant impact force F can then be computed from Eqn(9). The maincriticism of this model is that whereas the test vehicle may be represen-tative of a wide class of vehicles, the test or tests upon which A isdetermined are limited to a relatively small range of impact velocitiesat the low end of the velocity spectrum of interest. There is norational way of determining A, and hence F, at higher speeds outside of

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test range. The implication of this model is that the value of theaverage force F is independent of speed, but as will be shown later inthis report, this is far from true. Therefore, the Constant Force Modelwas dismissed from further consideration.

The spring characteristics in the Nonlinear Model are developed by usingacceleration readings from an accelerometer mounted on a relatively rigidsection of the uncrushed portion of a car during a crash test into arigid wall. The acceleration, multiplied by the car mass, is plottedagainst crush distance, as shown in Figure 3.7 to obtain the force-deflection properties of the spring in the model. In principle, thiscould be done for several cars for which low-speed test data is availableto develop a representative or average spring property. However, thishas not been done and therefore an average nonlinear spring property wasnot available for use on the current investigation. Even if it wereavailable, the nonlinear model would be subject to the same type of ques-tions regarding its validity for extrapolation to high-speed impact as isthe Linear 11odel since the Nonlinear Model is the same type (single mass-single spring) as the Linear Model. Consequently, evaluation of the non-linear model did not include numerical calculations.

The impact force predictions of the Linear,Multimass and Distributed MassModels were compared to each other and with test data for low-speed im-pact. For the Linear Model, numerical computations were performed usinga spring constant of K = 12.5W as explained in Section 3.1 and Eqn(5)was used to compute impact force. Vehicle characteristics necessary asinput to the Multimass and Distributed Mass Models were compiled and arepresented in Appendix B. The lumped multimass model used in this studyis depicted in Figure 3.6 which is programmed in the form of a computerprogram called COMPAT (Ref. 6) which was utilized to generate numericalresults for the Multimass Model in this study. The Distributed MassModel, Eqns(7) and (8), were programmed. The resulting computer programwas called CONTiiASS, which is described in Appendix C.

Numerical calculations were first performed for a 1972 Chrysler impactinga rigid wall in a head-on impact orientation at 30 mph. The calculatedimpact force history using the Linear Model, the COMPAT (multimass model)computer program, and the CONTMASS (distributed mass model) computerprogram is given in Figure 3.8. Two curves are shown in the figure forthe COMPAT results. One is relatively smooth and one is rather oscilla-tory at early time. The latter represents the force on the front facingof the bumper mass of the Multimass Model and the former is the sum ofthe forces in the three springs or " energy absorbers" connected to therear end of the bumper mass (see Figure 3.6). In subsequent usage ofthe COMPAT computer program on this study, the force on the rear end ofthe bumper is what was plotted to represent impact force on the wall.Figure 3.8 shows fairly close comparison of force predicted by CONTMASSand COMPAT (rear end of bumper force) up to the time of unloading. Thisis to be expected since the same mass and strength distribution inputsto the two computer programs were derived frem the same data as explainedin Appendix B. The Linear Model predicted somewhat smaller force than

8

the other two models. This is because the overall spring stiffness of12.5W used in the Linear Model is based on older model vehicles and istoo small for newer vehicle models.

The next set of comparisons between the Linear, Multimass and DistributedMass Models involved simulation of actual crash test events. Crash testdata for head-on impact of several automobiles into rigid flat barriersis presented in Ref. 7. In addition to acceleration measurements in thecar, the rigid barrier had load cells to directly measure the force trans-mitted to the wall during impact. On this study the impact tests of threeof the cars reported in Ref. 7 were simulated. The cars were

e 1973 Plymouth Satellitee 1973 Ford Torinoe 1975 Plymouth Gran Fury

The tests on these cars were conducted at 30 mph. The results of thesimulations with the Linear Model, the COMPAT (multimass) computer pro-gram and the CONTMASS (distributed mass) computer program are shown inFigures 3.9 through 3.17 where they are compared to the test data.

On each of these figures there are two curves generated by the CONTMASSmodel, one which includes strain rate effects and one which does not.The Linear Model implicitly includes strain rate effect in its springconstant since the constant is based on dynamic test data. The COMPATcomputer program has the following strain rate effect law built into it:

FD = FS(R1 + 0.021nly|) (10)

where FS = static spring forceFD = dynamic spring forcey = time rate of change of spring lengthR1 = curve fitting parameter

This law has a singularity in it at } = 0. For the purpose of this in-vestigation, the law was modified in COMPAT to be

FD = FS(R1 + 0.021nly|)(lla)for (R1 + 0.021n ji|) >_1.

otherwise FD = FS (11b)

This modified law was also programmed into the CONTMASS computer programwhere in this case i was interpreted to be the velocity of the car rela-tive to the wall. In all of the calculations with COMPAT and CONTMASSwhich included strain rate effect, a value of Rt = 1.4 was used. Thisvalue was suggested in Ref. 6 as a result of trial and error in correlat-ing predicted quantities with test Ata.

9

For each of the three cars -- Satellite, Torino and Gran Fury -- Figures3.9 through 3.17 include acceleration versus distance, impact force ver-sus distance and impact force versus time plots. The acceleration andforce versus distance plots contain test data for comparison with themodel predictions. No test data in the fonn of force versus time wasavailable.

Although there are detail differences between model predictions and testdata in the results in Figures 3.9 through 3.17, the models predictedforce levels and pulse shapes which would suffice for design purposes.

In addition to the test data described above for full- and intermediate-size cars, crash test data was obtained for a subcompact and minicar.toprovide further checkpoints for the models. In Ref. 8 test results werereported for 30 mph head-on impact of a 1974 Pinto into a rigid barrier.The only meaningful test measurement for use on the current study wasthe acceleration measured in the trunk of the car. Model predictions ofacceleration are compared with test measurements in Figure 3.18 and asso-ciated predictions of force-time are given in Figure 3.19. The corrla-tion with test data is not as good as for the heavier car but is stillacceptable.

In Ref. 9, a head-on impact test of a 1975 Honda into a rigid bar-rier at 40 mph is reported. Figures 3.20 through 3.22 show model pre-dictions compared to test results. The correlation is excellent.

All in all, the above comparisons show good predictive capability ofthe Linear, Multimass and Distributed Mass Models for low-speed, head-onimpact. However, at high-speed impact the Linear Model cannot be expectedto produce good results because the " spring constant" is speed dependentand impact of the engine cannot be accommodated adequately. Consequentlyin the next step of the evaluation process, which involved extrapolationof the models to high-speed impact, only the Multimass and DistributedMass Models were considered.

At the first attempt to extrapolate the Multimass Model to high-speedimpact, it was found necessary to arbitrarily stiffen the springs inthe model near the end of limit of their stroke in compression so as toavoid overlap of masses.

As explained in detail in Appendix B, mass distribution data for theDistributed Mass Model was derived from lumped mass data by taking eachof the lumped masses for a vehicle as shown in Figure 3.6, and distribu-ting each of them over their actual length at their location in thevehicle. For the first high-speed impact simulation of a 1973 FordTorino impacting a rigid wall, head-on, at 132 mph, the engine mass wasdistributed over a four foot length and the body mass was distributedover the entire car length. The results of the simulation with CONTMASSis shown in Figure 3.23 where it is compared to the COMPAT results whichwere obtained with the stiffened interconnecting springs in the Multi-mass Model.

10

The first " spike" in the COMPAT curve is caused by impact of the enginemass with the wall, i.e. , due to " bottoming out" of the springs andmasses in front of the engine mass. The second spike is due to impactof the body mass with the wall. The first spike is to be expected, butthe second is not realistic and would not occur if the body mass werereplaced by several interconnected masses. This could not be done inthe simulations because of limitations of the COMPAT program. TheCONTMASS curve shows no spikes. This is because the engine and bodymasses were " spread out" rather than lumped.

To demonstrate that the Multimass and Distributed Mass Models give com-parable results when masses are distributed in a similar fashion, asecond simulation of the Torino was conducted by " lumping" the engine andbody masses over 0.6 ft and 2 ft, respectively. The results are given inFigure 3.24 which shows similar force predictions for the two models.This demonstration also suggested that for the Distributed Mass Model,the engine mass should be artificially distributed over only a fractionof a foot in order to obtain forces which are comparable to those predictedby the Multimass Model. Therefore, in the next series of simulations con-ducted in the evaluation process, the engine masses were distributed inthis manner for the Distributed Mass Model. Further consideration of the

l Multimass Model was dropped at this point because of the limitations ofthe COMPAT program regarding the body mass mentioned above.

High speed (132 mph), head-on impact simulations were perfomed for fourvehicles with the CONTMASS program using the engine lumping proceduredescribed above. The impact force predictions are displayed in Figures3.25 through 3.28.

3.4 Sensitivity

With the CONTMASS program, some studies were perfomed to establish thesensitivity of impact force to variations in vehicle crushing strength,momentum transfer factor in the Distributed Mass Model, and body andengine mass distributions. These studies were all performed for high-speed (132 mph) impact.

Effect of crushing strength of a vehicle on impact force functions wasdetermined with the simulation of impact of a Honda and Plymouth Satel-lite with a rigid wall. The results are shown in Figures 3.30 and 3.31.The PC factor in these figures are scalar multipliers applied to theestimated strength distribution functions computed for the vehicles.Since results were obtained for PC factors of 1/2,1 and 2, the curvesgiven in Figures 3.30 and 3.31 show the effect on impact force varyingthe crush strength from one-half to twice the original estimated value.The results indicate that the impact force function is not appreciablyaer.sitive to these variations. This is to be expected because these sim-ulations were for the high-speed regime where the crushing strengthcontribution is small compared to the monentum transfer contribution tototal force in a distributed mass model.

11

_ .

There has been some controversy in the literature concerning the appro-priate value of a scalar factor, S, for the momentum transfer term indistributedmassimpactmodels(Eqn(7)). There are two schools of thoughton this. One insists the value of S should be unity and the other claimsit should be one-half. To determine what difference the use of the twodifferent values would produce, simulation of a high-speed impact of aPlymouth Satellite with a rigid wall was conducted. The results aredisplayed in Figure 3.31 which shows a substantial difference in peakforce resulting from the use of the two different factors. A study ofthis problem reported in Appendix A suggests that the factor of unity isnore appropriate for the current application of the distributed massmodel.

Conventionally, a lumped mass representation of a vehicle for crash analy-sis purposes consists of only a few masses such as the engine and trans-mission, front suspension, rear axle bumper and the so-called " body mass"(Figure 3.6). The latter mass represents the bulk of the vehicle, thatmass not represented by the other lumped masses. In using a distributedmass model of a vehicle there is some arbitrariness in the assumed dis-tribution of the body mass over the length of the vehicle. A study wasmade to establish the sensitivity of impact ' force to variations in theassumed distribution. Three different assumed distributions were con-sidered. Detailed definitions of these are given in Appendix B. Theresults for each of these is presented in Figure 3.32 which shows thatvariations in body mass distribution produce little change in the impactforce functions at high speed impact.

A distributed mass model, such as CONTMASS, produces impact forces whichare very sensitive to assumed length of distribution of engine mass ifthe engine crushing strength is fictitiously assumed to be equal to thatof the structural components fore and aft of it in the vehicle. Data tosupport this statement is presented in Figure 3.33 which shows the effectof a systematic variation in assumed length of distribution on impactforce, if actual engine length is used (i.e., on the order of 4 ft) a |very unrealistic relatively flat, force pulse results. Reasonable re-sults are obtained only for equivalent length distributions of a smallfraction of a foot. This suggests that perhaps a different representa-tion of the crushability of the engine mass may be more appropriate ina distributed mass model.

To follow-up on this idea, the engine mass of the Satellite was modeledas a crushable mass by itself without the remainder of the car. The ;

engine mass was distributed over its actual length and was given a uniform '

crushing strength distribution along its length based on the yield stressof steel. At an impact speed of 132 mph, a peak force of 13 x105 lb wascalculated and the duration of the impact pulse was computed to be0.0005 sec. Response times of a reinforced concrete wall panel in anuclear power plant structure are very much greater than this duration,and the peak force of the engine pulse is much greater than the maximumimpact force due to the remainder of the car. This suggests that in thecurrent application, the engine can practically be treated as rigid and i

that its momentum can be considered to be transferred to the wall imme-diately upon impact.

12

__ --- - --. -. _ .-.

. _ _

3.5 Sumary and Final flodel Selection

The evaluation of the candf ate vehicle models can be summarized as follows:

(a) General Observations: During impact of a vehicle with a wallthere are two major interaction mechanisms which determineloading on the wall: (1) momentum transfer and (2) crushing oralternately, mass and strength effects respectively. Distrio-uted nass models such as CONTMASS contain both mechanisms ex-plicitly. Multimass models such as C0?iPAT also accommodateboth nechanisms providing the springs connecting the masseshave sufficient stiffness or strength near the limit of theirstroke to allow " bottoming out" without overlap of masses.Single mass-spring models such as LINEAR or NONLINEAR can im-part load to the wall only by crushing or deformation of thespring.

At low-speed impact the momentum transfer is relatively smalland the crushing mechanism dominates generation of impactforces. At high-speed impact the reverse is true. This sug-gests that at low-speed all four types of models can adequate-ly represent the impact condition, but that at high-speed, thesingle mass-spring models are not suitable.

(b) Input Data Requirements: The spring stiffness for the LINEARmodel is based on the overall stiffness of vehicles as deter-mined from full-scale field tests. Detailed information onlocal structural stiffness and mass distribution is not re-quired. A disadvantage of this nodel is that the " equivalent"stiffness normally changes with impact speed. The springstiffness already has the strain rate effect incorporated init since it is based on dynamic loading data.The NONLINEAR model is a generalization of the LINEAR modelin that the deformation characteristics of the vehicle arerepresented by a nonlinear spring instead of a linear one.Only one lumped mass is still used for the vehicle mass. TheNONLINEAR model also requires full-scale dynamic field testdata to determine the spring properties. These propertieschange with increasing deflection. Again, . detailed informa-tion on local structural stiffness and mass distribution isnot required for the model.

The COMPAT and CONTMASS models require detailed informationon mass and crush strength distribution. The crush strengthis based on static load laboratory tests on subcomponents ofthe vehicle. Strain rate effect has to be explicitly in-cluded in these models since the crush data is based onstatic loading.

(c) Loa-Speed Impact Performance: Based on the model calculationsconducted thus far, it appears that all of the models can bemade to produce reasonable correlation with test data.

13

!

(d)High-SpeedImpactPerformance: At high-speed impact, typic-ally a proper impact force signature should contain a sig-nificant " spike" due to impact fo the relatively stiff enginewith the wall.The LINEAR model is not capable of predicting the engine spikeand it usually gives a load duration which is much too long ora load magnitude which is too high depending on the assumedvalue for the constant spring stiffnass in the model. Simi-larly, the NONLINEAR model does not exhibit the engine spikeand has the tendency to either provide a load duration ormagnitude which is too high.A multimass model such as COMPAT is subject to overlapping ofmasses unless the spring properties are substantially stiffenedat spring deflections approaching the maximum compression limit.When these stiffened springs are used, spikes in the force sig-nature occur as a spring tends to " bottom out". The characterand magnitude of these spikes will depend not only upon theintensity with which two masses tend to approach each other,but also upon the assumed bottoming characteristics of thestiffened spring interconnecting the two masses. This is es-pecially important for spring bottoming corresponding to enginemass impact with the wall because a large spike in the forcesignature is normally produced and the properties of this spikebecome extremely sensitive to the assumed bottoming characterof the spring (s) attached to the front of the engine mass.Another problem associated with the COMPAT model for high-speed impact is that the body mass of the vehicle (essentiallymost of the vehicle mass behind the firewall) is lumped into asingle mass. Consequently at high-speed the model predicts anunrealistic force spike due to body mass impact with the wall.This phenonenon is not inherent with multimass models in gen-eral, but occurs with COMPAT because of the limited number ofmasses available with which to model the vehicle. The bodymass could be represented by several masses instead of one.Another disadvantage of multimass models is that they arerelatively expensive computationally.A distributed mass model such as CONTf1 ASS also does not accur-ately predict the engine spike if the engine mass is assumeddistributed over the actual length of the engine and the crush-ing strength of the vehicle in the vicinity of the engine isset equal to that of the structural components attached to thefore and aft of the engine. If the actual crushing strengthof the engine is used and the engine mass is distributed overthe actual engine length, the model predicts an extremelylarge force spike which is probably realistic. However, the

; numerical integration time step necessary to produce accurateresults in this situation is extremely small thus making thesolution process very expensive.

14

._. _. ..

As a result of the model evaluation, the model finally selected as thehead-on vehicle impact model for use on this investigation is theDistributed Mass Model with the engine treated as a noncrushable mass andthe remainder of the vehicle as a continuous crushable mass. The de-tails of the final model are presented in Appendix A. The CONTMASS pro-gram was revised to incorporate the rigid engine.

15

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Figure 3.9 1973 Plymouth Satellite, 30 mph Impact

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Time (sec)Figure 3.18 Model Predictions of Acceleration History with Test Data

|

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f1974 Stock Pinto, 30 mph Impact

--- - Linear-- - -- CONTMASS without strain rate

100' --

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Time (sec)Figure 3.19 Comparison of Impact Force for Various Models at Low Speed Impact

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Time (sec)Figure 3.20 1975 Honda CVCC, 40 mph Impact

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Figure 3.22 1975 Honda CVCC, 40 mph Impact

- _ _ _ _

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1973 Ford Torino, 132 mph Impact_

Engine Distribution Over 4 ft Lengthp f. _ ,|

,t N Body Mass Distribution Over Entire Car Length/i ,/ t COMPAT----------

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Time (sec)Figure 3.23 Comparison of Impact Force Between Lumped Mass and Distributed Mass Models ,

_ _ - - _ _

h 1973 Ford Torino, 132 mph Impact

Engine Distribution Over 0.6 ft1600 - Body Mass Distribution Over 2 ft

?\ ~,COMPATri , N ----------

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Time (sec)Figure 3.24 Impact Force for Lumped Mass Representation of Engine and Body Masses

-- Distributed Mass Model Versus Lumped Mass Model

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Time (sec)Figure 3.26 High Speed Impact Force for Intennediate-Size Car

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Time (sec)Figure 3.28 High Speed Impact Force for Full-Size Ford

- - -___ _ ________

_ _ _ _ _ . _ _

1975 Honda, 132 mph

Linear Body Mass DistributionEngine Lumped Over 6 Inches

1600

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Time (sec)Figure 3.29 Effect of Crushing Strength on High-Speed Impact Force -- Minicar

-____

1973 Plymouth Satellite, 132 mph Impact(Bilinear Body Mass Distribution 0 c.g. of Car)

PC Factor 0.5----------

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PC Factor 2.0---

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Time (sec)Figure 3.30 Effect of Crushing Strength on High Speed Impact Force -- Intermediate-Size Car l

|

|

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4 1973 Plymouth Satellite, 132 mph Impact

CONTMASS Analysis

Linear Body Mass DistributionEngine Mass Distributed Over 0.8 ft

1800-

B Factor = 1.01600" S Factor = 0.5----------

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Time (sec) ,

Figure 3.31 Effect of Value of Momentum Transfer Factorof Distributed Mass Model on Impact Force

_ _ _ _ _ _ _ _

_ _ .__ _ _ _ _ _ . __. ___.

1973 Plymouth Satellite, 132 mph Impact

CONTMASS AnalysisEngine Mass Distributed over 0.8 ft

Bilinear body mass distribution 0 c.g. of body mass'

Bilinear body mass distribution 9 c.g. of car- ----------yg % - -- - Linear body mass distribution_

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Figure 3.32 Effect of Sody Ma'ss Distribution on High Speed Impact Force,

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1 1973 Plymouth Satellite, 132 mph Impactt |

|| CONTMASS Analysis,, Linear Body Mass Distribution

2 ~

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|t - - Engine mass distributed over 2.4 ft: I Engine mass distributed over 0.8 ft

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Time (sec)Figure 3.33 Effect of Engine Mass Distribution on High Speed Impact Force

_

4. FORCE SIGNATURES FOR HEAD-0N IMPACT INTO RIGID WALLS

The CONTMASS computer program was used to calculate impact forces and im-pulses for vehicles impacting a rigid wall in a frontal (head-on) orien-tation. The combination of rigid wall and head-on orientation will bereferred to as the baseline configuration throughout this report.

Calculations were performed for nine passenger cars ranging in size froma minicar to full-size cars.

Car Weight (lb) Size

1. SRI 4660 Full2. Calspan 4660 Full3. 1973 Ford Torino 4600 Intermediate4. 1975 Plymouth Gran Fury 4560 Full5. 1973 Plymouth Satellite 4380 Intermediate6. Plymouth A1507. 1972 Chrysler (Dodge Decon) 35008. 1974 Ford Pinto 2489 Subcompact9. 1975 Honda CVCC 2000 Mini

Five distinct impact speeds were considered:

Speed

meters /sec miles / hour

20 44.730 67.140 89.550 111.860 134.2

Calculated impact force pulses for each car, for each speed, are presentedin individual plots in Figures 4.1 through 4.45. These individual plotswere replotted to a common scale and placed on combined plots in Figures4.46 through 4.55. These figures contain either four or five curveseach for a given impact speed showing the effect of different cars im-pacting a wall at the same speed.

In Figure 4.56, force curves are presented for one car (Plymouth Satel-lite) at five different speeds which allows one to conveniently discernthe difference in impact force pulse as a function of impact speed.

The force pulses shown in all of the Figures (4.1 through 4.56) are theimpact force on the wall due to the crushable portion of the vehicleonly. In CONTMASS the effect of engine impact on the wall is an instan-taneously applied impulse. In Tables 4.1 through 4.9, the engine impulse,time of impulse, engine impact velocity are given as well as the maximumforce of the pulse of the crushable portion of the car, the area (impulse)

47

;

of the pulse and duration of the pulse. The impulse of force pulse wasobtained by numerical integration within the CONTMASS program. Notethat in the tables, the engine inpact velocity is less than the initialvehicle impact velocity. This is because the uncrushed portion of thevehicle, including the engine, undergoes some reduction in velocity afterinitial impact. This is accounted for in the computation of engine im-pulse in the CONTMASS program. It should also be noted that the totalchange in momentum of a car should equal the total impulse on the wall,i.e.,

MV, = IE*IC (12)

where IE = engine impulseI = impulse due to crushab,e mass of carg

It can be verified from Tables 4.1 through 4.9 that Eqn(12) is satisfiedfor each case considered.

48

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20 m/sec Impact Speed

49

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54

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67

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Figure 4.20 Car Body Force on Rigid Wall; Calspan Car, 40 m/sec Impact Speed

68

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Figure 4.22 Car Body Force on Rigid Wall; Plymouth Gran Fury, 40 m/sec Impact

70

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_ _ _ _ _ _

TABLE 4.1 SRI FULL-SIZE CAR, BASELINE CONFIGURATION RESULTS

Engine Igact N ximum Fo m Fo m -T M Area h attonVehicle Impact Engine Impulse Time at EngineSpeed (ft/sec) (kip-sec) Impulse (m-sec) Velocity B dy Pulse of Body Pulse of Body Pulse

(ft/sec) (kip) (kip-sec) (m-sec)

406.0547 9.32 50.065.62 0. -- --

98.43 1.1706 35.5 41.8802 434.4111 12.64 56.0131.24 2.6985 24.0 96.5460 469.7785 15.80 59.0164.05 3.8090 19.0 136.2770 512.3883 19.21 147.0196.86 4.8882 15.5 174.8875 565.9770 22.75 168.0

TABLE 4.2 CALSPAN FULL-SIZE CAR, BASELINE CONFIGURATION RESULTS

|'

Engine Impact Maximum Force Force-Time Area DurationVehicle Impact Engine Impulse Time at Engine Velocit of Body Pulse of Body Pulse of Body Pulse |aui Speed (ft/sec) (kip-sec) Iquise (m-sec) |(ft/sec (ktp) (kip-sec) (m-sec)

65.62 0. 300,8542 9.227 47.0-- --

98.43 1.4165 32.0 50.6804 327.2247 12.40 53.0131.24 2.7816 22.0 99.5178 366.0705 15.66 68.0164.05 3.9233 17.0 140.3674 477.5948 19.04 194.01 % .86 4.9608 14.t) 177.4874 608.2246 22.71 152.0

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TABLE 4.3 1973 FORD TORINO, BASELINE CONFIGURATION RESULTS

Engine Impact Maximum Force Force-Time Area DurationVehicle Impact Engine Iquise Time at Engine Velocit of Body Pulse of Body Pulse of Body PulseSpeed (ft/sec) (ktp-sec) Impulse (m-sec)(ft/sec (ktp) (kip-sec) (m-sec)

65.62 1.0509 48.50 34.7376 133.7989 8.353 93.098.43 2.4507 28.50 81.0107 166.8094 11.70 82.0

131.24 3.5840 21.00 118.4728 256.4856 15.24 110.0164.05 4.6617 16.50 154.0966 370.5452 18.84 142.01 % .86 5.7116 13.50 188.8049 510.6063 22.52 129.0

_ _ _ _

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TABLE 4.4 1975 PLYMOUTH GRAN FURY, BASELINE CONFIGURATI0fl RESULTS

Engie: Ispact e ximun Force Force-Time Area DurationVehicle !spect Engine Impulse Time at Engine Velocity of Body Pulse of Body Pulse of Body PulseSpeed (ft/sec) (kip-sec) Ispulse (m-sec) (ft/sec) (kip) (kip-sec) (m-sec)

65.62 0. 182.0213 9.309 65.0-- --

98.43 2.1762 29.50 72.4664 200.3374 11.85 71.0 ,

'

131.24 3.3%1 21.00 113.0877 307.8327 15.35 67.0164.05 4.5016 16.50 149.8986 453.4200 18.81 107.01 % .86 5.5676 13.50 185.3949 630.5082 22.38 125.0

TABLE 4.5 1973 PLYMOUTH SATELLITE, BASELINE CONFIGURATION RESULTS

Engine Impact e ximum Force force-Time Area DurationVehicle Impact Engine Impulse Time at Engine Velocity of Body Pulse of Body Pulse of Body PulseSpeed (ft/sec) (kip-sec) Impulse (m-sec) (ft/sec) (kip) (kip-sec) (m-sec)

E 65.62 0. -- -- 180.4406 8.973 64.0m 98.43 2.1494 29.6 71.5713 195.5096 11.30 71.0

131.24 3.3780 21.0 112.4841 298.6824 14.51 66.0164.05 4.4898 16.4 149.5051 436.8194 17.65 105.01 % .86 5.5497 13.6 184.8000 605.8858 21.49 117.0

,

|

|

|

TABLE 4.6 PLYMOUTH, BASELINE CONFIGURATION RESULTS

Vehicte Impact Engine Impulse Time at Engine Engine Impact N ximum Force Force-Time Area DurationSpeed (ft/sec) (kip-sec) Impulse (m-sec) Velocity of Body Pulse of Body Pulse of Body Pulse

(ft/sec) (kip) (kip-sec) (m-sec)

65.62 0. 283.8658 8.556 46.0-- --

98.43 1.2324 30.5 52.9097 305.2295 11.50 - 84.0131.24 2.3554 21.0 101.1253 331.8358 14.65 107.0164.05 3.3019 16.0 141.7620 377.5869 17.88 117.01 % .86 4.1432 13.5 177.8801 534.7388 21.59 161.0

____ - _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

_.

TABLE 4.7 1972 CHRYSLER, BASELINE CONFIGURATION RESULTS |

Engine tapact Maxisman Force Force-Time Area DurationVehicle Impact Engine Impulse Time at Engine Velocity of Body Pulse of Body Pulse of Body PulseSpeed (f t/sec) (ki p-se'.) Impulse (m-sec) (ft/sec) (kip) (kip-sec) (m-sec)

-- -- 188.0329 7.198 54.065.62 0.98.43 1.9781 28.5 69.2320 195.7785 8.737 72.0

131.24 3.1636 20.5 110.7247 224.3542 11.200 64.0

164.05 4.2326 16.0 148.1425 335.4876 13.820 59.0

1 % .86 5.2533 13.0 183.8653 473.7193 16.250 165.0

TABLE 4.8 1974 FORD PINTO, BASELINE CONFIGURATION RESULTS

Engine tapact Maximum Force Force-Time Area DurationVehicle Impace Engine lapulse Time at Engine Velocity of Body Pulse of Body Pulse of Body PulseSpeed (ft/sec) (kip-sec) Impulse (m-sec) (ft/sec) (kip) (kip-sec) (m-sec)-g

65.62 0.2430 41.0 18.3650 146.3681 4.888 48.0

98.43 0.9899 22.5 74.8209 166.9199 6.653 66.0

131.24 1.5221 16.0 115.0515 1 % .8348 8.694 64.0

164.05 1.9932 13.0 150.6599 299.5134 10.730 185.0

1 % .86 2.4660 10.5 186.3935 416.7365 12.860 104.0

TABLE 4.9 1975 HONDA CVCC, BASELINE CONFIGURATION RESULTS

Engine Impact Maximum Force Force-Time Area DurationVehicle Ispact Engine impulse Time at Engine Velocity of Body Pulse of Body Pulse of Body PulseSpeed (ft/sec) (kip-sec) Ippulse (m-sec) (ft/sec) (kip) (kip-sec) (m-sec)

65.62 0.2889 36.5 30.5047 107.9099 3.866 49.0-

98.43 0.7551 21.5 79.7214 135.9287 5.504 62.0

131.24 1.1118 16.0 117.3750 202.3457 7.233 113.0

164.05 1.4542 12.5 153.5288 305.0104 8.992 128.0

196.86 1.7806 10.5 187.9842 417.6232 10.730 89.0

_ . . . _ _ . . . _

.

5. EFFECT OF NALL DEFORMATION ON IMPACT FORCE

To compute the effect of wall panel deflection on impact force signatures,a simple single-degree-of-freedom structural model of the wall panel wascoupled to the Distributed Mass vehicle model. Structural model param-eters for a wide range of wall panel configurations were computed andused to determine the impact force on the wall with the coupled vehicle /structure model. Only overall flexural deformation of the wall panel wasrepresented by the structural model; local wall deformation was notconsidered.

5.1 Coucled Vehicle / Structure Model

The coupled model is shown schematically in Figure 5.1. The vehicle por-tion of the model is the same Distributed Mass Model used in the baselineconfiguration calculations. It consists of a crushable and uncrushable(engine) mass. The wall portion of the model is represented by a singlemass and spring with the spring having an elastic-plastic resistancefunction as shown in Figure 5.2. The governing equations for this sys-tem are:

R=P } ~ "c + U(6 (Ic

6where M =fp(y)dy=crushedmassofcar (14)c

and p(C) = mass per unit length function of crushable portionof car (excluding engine)

( = crushed length of car = n -xR = interaction force between wall and car

Also R=M + R (x) (15)s s

where Ms = effective structural massR (x) = resistance function for structural spring

s

Prior to engine impact, C < C #"de

c dt "uc +"e3 (P *-

M = / p(y)dy = uncrushed portion ofuc (17)crushable mass

M = engine masse

M =Msi = initial effective structural mass (18)s

108

,

After engine impact, E > C ande

d($ + *) g (39)P =-c dt uc

fis"Nsi + II (20)e

The detailed derivation of the above equations for the coupled model isgiven in Appendix A. They were incorporated into the CONTMASS programdescribed in Appendix C.

5.2 Structural Parameters

The range of geometric variables of the wall panels considered for struc-tural deformation calculations are as follows:

h = thickness: 12" - 36"a = span between columns: 10' - 36'b = span between floors: 10' - 36'

Structural spring properties (K and Rm) and effective structural mass,its were calculated for the 401 combinations of these parameters indicatedin Tables 5.1 and 5.2. The structural design variables (percent ofsteel, cover, etc.) and the formulas used are presented in Appendix Dalong with listings of the calculated properties for the matrix of geo-metries defined in Tables 5.1 and 5.2.

5.3 Results

The CONTMASS computer program was employed to calculate wall impact forcesfor both rigid and flexible walls. Eighteen representative square slab4

(a = b) configurations listed in Tables 5.1 and 5.2 were first considered.Calculations were performed for 20, 40 and 60 meters /sec impact speedsfor the 1973 Plymouth Satellite. In each case the engine impulse andmaximun force and area (impulse) of the pulse due to the crushable por-tion of the car for the flexible wall were compared to the correspondingquantities for the rigid wall. Results are given in Tables 5.3 and 5.4for fixed and simply supported edge wall panels. The deviation of thevalues of the three compared quantities for the flexible wall was a verysmall percentage of the corresponding rigid wall values in most cases.The exceptions are for thick, very short span slabs. In all other casesthe deviations are less than 13 percent, and for the more typical con-figurations, the deviations are all less than 6 percent. The deviationsfor the engine and body impulses are plotted in Figures 5.3 and 5.4.

109

_ ..

,

it should be noted that in reference to Tables 5.3 and 5.4, theoreticallythe total impulse (engine plus body) should be the same value for everycase corresponding to a given impact velocity and should be equal to thetotal mass of the vehicle times the impact velocity. Upon examinationof Tables 5.3 and 5.4 it may be observed that this is not exactly satis-fied. There are two reasons for this. One is that the body impulsesfor the flexible wall calculations were determined by integrating theforce pulse up until the time that the vehicle stopped crushing. Atthat time the vehicle generally still had a small residual nonzero vel-ocity (either plus or minus). The second reason is that the force pulsewas integrated numerically and therefore a small amount of error isintroduced.

*

For a flexible panel with a typical span (24 ft) the crushable body pulseis compared to the corresponding pulse for a rigid wall for 12, 24 and36 inch wall tnicknesses in Figures 5.5 through 5.7. The inpact speedwas 40 meters /sec. For the same thickness (12 inches) and a 24 ft span,the effect of speed on the deviation between flexible and rigid wallsmay be observed from Figures 5.5, 5.8 and 5.9. Figures 5.5 through 5.9all show the small difference in the shapes and magnitudes of the pulsesfor rigid and flexible walls.

In view of the small effect of wall flexibility on impact force calcu-lated for a wide range of square panel configurations, only one nonsquarepanel was considered (h = 12", a = 30 ft, b = 36 ft). The impulse andaaxinun force for the flexible panel deviated from the rigid wall values'

by less than 3 percent.

!

\

l

I

|

t

110

-_

g L 4 '

t

F) O/s

/ Mi e

M "s

| h "b$s

% At 2

Wall Vehicle

Figure 5.1 Coupled Vehicle / Structure Model

R3j ,

R'~m

K

1

' ; X

Figure 5.2 Wall Panel Resistance Function

111 |

TABLE 5.1 MATRIX OF WALL PANEL GE0METRIES CONSIDERED

b = 10' b = 14'a 10 14 18 24 26 28 30 32 34 36 10 14 18 24 26 28 30 32 34 36

h

12 x x x x x x15 x x x x x x182124 x

27303336 A

b = 18' b = 20'a 10 14 18 24 26 28 30 32 34 36 10 14 18 24 26 28 30 32 34 36

h

12 x x x x x x x x x x15 x x x x x x x x x x18 x x x x x x x21 x x x x x x x24 x x x x x x x27 x x x x x x x30 x x x x x x x33 x x x x x x x36 x x x x x x x

b = 22' b = 24'a 10 14 18 24 26 28 30 32 34 36 10 14 18 24 26 28 30 32 34 36

h

12 x x x x x x x x' x x x x x x15 x x x x x x x x x x x x x x18 x x x x x x x x x x x x x x21 x x x x x x x x x x x x x x24 x x x x x x x x x x x x x x27 x x x x x x x x x x x x x x30 x x x x x x ,x x x x x x x x33 x x x x x x x x x x x x x x36 x x x x x x x x x x x x x x

112

..

TABLE 5.2 MATRIX OF WALL PANEL GE0METRIES CONSIDERED

b = 26' b = 28'a 10 14 18 24 26 28 30 32 34 36 10 14 18 24 26 28 30 32 34 36

h

12 x x x x x x x x x x x x x x15 x x x x x x x x x x x x x x18 x x x x x x x x x x x x x x21 x x x x x x x x x x x x x x24 x x x x x x x x x x x x x x

27 x x x x x x x- x - x x x x x x30 x x x x x x x x x x x x x x

33 x x x x x x x x x x x x x x

x x- x x x x x x x x x x x x x

b = 30' b = 36'a 10 14 18 24 26 28 30 32 34 36 10 14 18 24 26 28 30 32 34 36

h

12 x x x x x x x x15 x x x x x x x18 x x x x x x x21 x x x x x x x

24 x x x x x x x x

27- x x x x x x x30 x x x x x x x33 x x x x x x x36 x x x x x x x x

113

-___. . _ _ _ _ _ _ _-

-__--. . . ..

. __. _ _ _ - _ _-

TABLE 5.3 COMPARIS0N OF MAXIMUM FORCE AND IMPULSEFOR RIGID AND FLEXIBLE WALLS, FIXED EDGE PANELS

Impact Engine Madmum BodySpan Thickness Percent Percent Percent*U ty p(ft) (inch) "Deviation Deviation Deviationm sec) { p ) )

10 12 20 0. O. 180.4616 -0.01 8.879 1.0510 12 40 3.0473 9.79 307.9031 -3.09 14.28 1.5910 12 60 5.0509 9.00 540.8536 10.73 21.08 1.9110 24 20 0. O. 180.7652 -0.18 8.889 0.9410 24 40 3.2170 4.77 362.7205 -21.44 14.48 0.2110 24 60 5.2945 4.60 604.4139 0.24 21.28 1.0010 36 20 0. O. 187.7392 -4.04 8.997 -0.2710 36 40 3.2605 3.48 433.7474 -45.22 13.97 3.7210 36 60 5.3764 3.12 687.2092 -13.42 21.30 0.8824 12 20 0. O. 177.8184 1.45 8.734 2.66 ,

24 12 40 3.2548 3.65 286.1394 4.20 14.66 -1.03-

% 24 12 60 5.3966 2.76 569.9810 5.93 21.60 -0.5124 24 20 0. O. 180.7409 -0.17 8.962 0.1224 24 40 3.3397 1.13 301.8945 -1.08 14.35 1.1024 24 60 5.4731 1.38 599.8923 1.00 21.49 0.00

|24 36 20 0. O. 180.8126 -0.21 8.969 0.0424 36 40 3.3620 0.47 301.9678 -1.10 14.62 -0.7624 36 60 5.5007 0.88 608.6716 -0.46 21.33 0.7436 12 20 0. O. 178.3032 1.18 8.588 4.2936 12 40 3.3324 1.35 289.9643 2.92 14.11 2.7636 12 60 5.4746 1.35 589.1554 2.76 21.50 -0.0536 24 20 0. O. 180.1211 0.18 8.882 1.0136 24 40 3.3590 0.56 296.2712 0.81 14.43 0.5536 24 60 5.5077 0.76 598.9463 1.15 21.49 0.0036 36 20 0. O. 180.6890 -0.14 8.968 0.0636 36 40 3.3684 0.28 298.8409 -0.05 14.62 -0.7636 36 60 5.5191 0.55 603.1302 0.45 21.21 1.30

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ - __________

- _ _ __ . . .___ . _ _ - _ . _ _ - .

TABLE 5.4 COMPARIS0N OF MAXIMUM FORCE AND IMPULSEFOR RIGID AND FLEXIBLE WALLS, SIMPLY SUPPORTED PANELS

Impact Engine Maximum YSpan Thickness Percent Percent Percent(ft) (inch) Velocity Impulse Force apulseDeviation Deviation Deviation(m/sec) (kip-sec) (kip) (kip-sec)

10 12 20 0. O. 180.7933 -0.20 9.116 -1.5910 12 40 3.0716 9.07 312.4383 -4.61 14.61 -0.6910 12 60 4.9795 10.27 528.7547 12.73 /. 86 -1.7210 24 20 0. O. 180.3454 0.05 8.887 0.9610 24 40 3.2127 4.89 331.8110 -11.92 13.72 5.4410 24 60 5.2869 4.74 641.0147 -5.80 21.18 1.4410 36 20 0. O. 180.4490 0.00 8.957 0.1810 36 40 3.2620 3.43 440.5942 -47.51 13.93 4.0010 36 60 5.3749 3.15 603.4936 0.39 21.63 -0.6524 12 20 0. O. 176.1396 2.38 8.44 5.9424 12 40 3.2570 3.58 281.7640 5.66 13.92 4.07-

g 24 12 60 5.4032 2.64 568.5085 6.17 22.22 -3.4024 24 20 0. O. 180.1630 0.15 8.964 0.1024 24 40 3.3343 1.29 295.5676 1.04 14.71 -1.3824 24 60 5.4730 1.38 592.7306 2.17 21.00 2.2824 36 20 0. O. 180.7733 -0.18 8.965 0.0924 36 40 3.3554 0.67 300.7935 -0.71 14.49 0.1424 36 60 5.4978 0.94 602.9802 0.48 21.54 -0.2336 12 20 0. O. 178.2462 1.22 8.588 4.2936 12 40 3.3351 1.27 290.0546 2.89 13.96 3.7936 12 60 5.4783 1.29 590.0296 2.62 20.98 2.3736 24 20 0. O. 179.7651 3.74 8.795 1.9836 24 40 3.3596 0.54 295.3693 1.11 14.25 1.7936 24 60 5.5093 0.73 598.7672 1.17 21.59 -0.4736 36 20 0. O. 180.3700 0.04 8.884 0.9936 36 40 3.3681 0.29 297.4853 0.40 14.45 0.4136 36 60 5.5198 0.54 602.3236 0.59 21.37 0.56

. _ _ _ _ _ _ _ _ - _ _ _ _

_ _ _ _ _ .____________ ___________ _____________ _ _ _ _ _ _

I

l *10' h = 12" 3

e 1

40 m/sec-*-*-g,." x-x - 60 m/sec-

8 6. .

.2%

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be I

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g -x-x- 60 m/sec

8 2.'D2>g 1. x

.. 'N ~x-.

0 ; :' ' "

6 12 18 24 30 36 Span (ft)

Figure 5.3a Percent Deviation of Engine Impulse Simply Supported Panel116

. ..

,

h = 12"10. ,

- e- e - 40 m/sec,

-x-x- 60 m/sec8. - -y

86. -e

.2%; 4. -

*

E*e

2. -A

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0 6 12 18 24 30 36 Span (ft)

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12 18 24 30 36 Span (ft)0

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40 m/sec- * - * -cO

- x-x - 60 m/sece,o 2. -

%'s$ l- x_e -n

,_.

h 12 18 24 30 36 Span (ft)O

Figure 5.3b Percent Deviation of Engine Impulse. Fixed Edge Panel

117

_

h = 12"6. +

e -+ - +- 20 m/secw~ +- +-+ - 40 m/secg 4,, ,_

3 -x-a- 60 m/sec-*

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@ -a-x-60 m/secS2-8

81s.2 'f

* I - +$06 12 1R h 30 36 Span (ft)

x-

Figure'S.4a Percent Deviation of Body Mass Impulse, Simply Supported Panel

118

_ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

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Figure 5.4b Percent Deviation of Body fiass Impulse, Fixed Edge Panel119

. _ _ _ _ _ . .-

_ - ______ _ _ _ _

o .

@ Rigido

A Nonrigid-

E. START TIME -

" 0: 0: 0

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8Y-

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8a3.0c o'.co th.oo 2'4 00 3'2 00 4'o .co 4's .oo s's.co 6'4.00 7'2.00

Time (m-sec)

Figure 5.5 Effect of Wall Flexibility of Impact Force for 12" Thick Wall '

at 40 m/sec Impact Speed

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. _ _ _ _ _ _ _ _ _ _ _ _ _

6. EFFECT OF IfiPACT ORIENTATI0ft ON FORCES

The effect of impact orientation on wall impact forces was studied usinga three-dimensional vehicle model computer program, GUARD (Ref. 10). Thevehicle model in this program is a lumped mass model as illustrated inFigure 6.1. The vehicle makes contact with objects via contact panelslocated on the exterior profile of the car as shown in Figure 6.2. Thedeformation characteristic of each panel is represented by a nonlinearspring.

Using the GUARD program, impact forces were calculated for different yaworientations of the vehicle defined by the angle s shown in Figure 6.3.oThe impact conditions considered were a normal (tp the wall) initial im-pact velocity V and an initial angular velocity Bo. Only one speed wasoconsidered, Vo = 40 m/sec. The specific combinations of Go and Oo studiedwere:

Oo (deg) o (rev/sec)0 0 and +1 -

30 +160 +180 -1 and +190 0 and -1

100 -1120 -1150 -1180 -1

Nonzero initial angular velocities were used in most of the cases becauseit was believed to produce a more severe impact than a zero angular vel-ocity situation (i.e., a " hammering" action). The magnitude of 1 revolu-tion /sec for the initial angular velocity was chosen because of aninvestigation reported in Ref.11 which predicted maximum spin velocitieson the order of 1 revolution /sec for automobiles in a tornado. As indi-cated in the above table, cases of zero initial angular yaw velocitywere also considered for the s = 0 and 90 deg angular impact ~configura-otions so as to be able to determine the effect of initial angular velocityon impact force. Results showed that, for these specific orientations(frontal and side-on), there was little influence of initial angularvelocity on the force signature.

Impact of the top and bottom of a vehicle were not considered in theorientation study, only impact on the sides, front and rear.

For the purpose of this study, the side, front and rear impact panelswere all assumed to have the same deformation characteristics per unitarea. There is some evidence to support this assumption based on pastexperience with GUARD and.other three-dimentional vehicle crash simula-tion computer programs, at'least for low speed impact.

125

- - - - _ - .. ._ .-

The front impact panel properties for the GUARD model were constructedon a trial and error basis to produce an impact force function whichclosely resembles that predicted by the CONTMASS model for frontal im-pact of the same car (1973 Plymouth Satellite) at the same speed (40 m/sec). The selected panel properties are given in Figure 6.4 and the com-parison of impact force functions for the GUARD and CONTMASS models isshown in Figure 6.5.

|

In order to apply the GUARD computer program to the subject problem, ithad to be modified to:

(a) allow nonzero initial angular acceleration, Eg

(b) determine when the engine impacts the wall and to computethe resultant impulse on the wall

(c) reduce the mass and mass moment of inertia of the sprungmass at engine contact due to loss of engine mass.

The impact force pulse from the crushable part of the vehicle as computedwith the GUARD program, is plotted in Figures 6.6 through 6.12 for dif-ferent impact orientation anglas at an initial angular velocity of1 revolution /sec. They have ail been combined on one graph in Figure 6.13for convenience in comparisor.. The magnitude of the engine impulse andthe time at which it ocured after impact is also tabulated on Figure 6.13.The results show that the greatest peak body force occurs for the side-on(90 deg) orientation. The peak force for 90 deg is approximately twicethat for zero deg (head-on). The engine impulses for these two orienta-tions are about the same size.

i

f

126

- -

.. .. _. ..

. _ _ _ _ _ _ .

0f h*

/ / W //

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Figure 6.1 GUARD Vehicle Model

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Plymouth Satellite, 40 m/sec Impact Speed

-.. _ _ _ _ _ .___ __ __ _ _ _ _ _ _ _ _ _ __

. . _ _

7. DESIGN FUNCTIONS_

7.1 Baseline Configurations

The first attempt at constructing design impact force functions involvedan enveloping procedure. For each of the five speeds, the baseline forcefunctions for each of the nine cars considered were plotted on the samefigure and an " envelope" of these curves was constructed. The resultantenvelopes are shown in Figures 7.1 through 7.5. Triangular-shaped approx-imations to the envelope functions, shown as dotted lines in Figures 7.1through 7.5, were input to the STRMODEL structural response computerprogram for a typical wall panel (24 ft x 24 ft x 24 in. - fixed edges).The maximum displacements obtained in this manner were found to be twoto three times greater than the corresponding displacement obtained byusing any one of the individual force functions for different cars.Therefore, the idea of using " envelopes" as design functions wasabandoned.

It was decided to use the force function for the car producing the great-est structural deflection as the design function at a given speed. Ateach speed the force functions for the seven heaviest cars were used to ,

compute maximum structural displacements for the typical wall panel men-tioned above. The results are given in Table 7.1, where the car numberslisted in the table are identified as follows:

Car Number Name Weight (1bs)

1 SRI Full-Size Car 46602 Calspan Full-Size Car 46603 1973 Ford Torino 46004 1975 Plymouth Gran Fury 45605 1973 Plymouth Satellite 43806 Plymouth 41507 1972 Chrysler 35008 1974 Ford Pinto 24899 1975 Honda CVCC 2000

Table 7.1 shows that the following cars produced the greatest structuraldeflection and therefore were selected as the " design" cars:

Impact Speed Design Car

20 m/sec SRI30 m/sec SRI40 m/sec Calspan50 m/sec SRI60 m/sec SRI

139

_ _____________________________ _____-_-____-

The baseline force functions and corresponding engine impulses for thesecars at the given speeds were presented in Section 4. For convenience incharacterizing the design functions, idealization or simplifications ofthem were constructed. This was accomplished with the use of a two-stepidealized force function as shown in Figure 7.6. The parameters F , F ,i 2ti and t2 were first selected to approximately fit the actual curves.These values were then refined so as to preserve the area under thecurve (body impulse) and maximum structural displacement produced by thepulses on the " typical" structure. The engine impulses, Ie, and time ofengine impact, t*, were kept the same as actual.

7.2 Structural Defomation and Impact Orientation Factors

The design functions derived in the preceding subsection were for thebaseline configuration, i.e., for rigid walls and head-on impact orienta-tion. To account for the wall flexibility and for nonfrontal impact,the concept of structural defomation and impact orientation factorswas introduced. In principle, these factors, applied as multipliers tothe baseline forcing functions, would account for the effects of walldeformation and impact orientation as follows:

F(t) =f xf x F(t) (21)S 0Total Base I

where f = structural deformation factorfs = vehicle impact orientation factor

The values of the factors are selected so as to produce the proper struc-tural deflection. The forces in Eqn(21) represent only the crushablebody force, they do not include the engine impulse. The " total" engineimpulse (and associated time of application) is the same as the baselineengine impulse.

The concept of using deformation and orientation factors is offered asan alternative to the direct use of the " total" functions as designfunctions to readily allow for incorporation of future refinements orbetter data on structural flexibility and effect of vehicle orientationon impact forces. With the use of this procedure, the baseline func-tions need not be changed.

Tne result of this study showed that structural flexibility has relativelylittle effect on impact force, as discussed in Section 5. Therefore,the structural deformation factor, f , was uniformly selected as unitysfor all speed ranges.

140

-__ -_

1

The effect of vehicle impact orientation on impact force was reported inSection 6. To determine the value of the orientation factor, fo, firstthe force functions generated in Section 6 for various yaw orientationswere input to the STRfiODEL computer program to calculate structural de-flections of a typical wall panel for the various impact orientationsconsidered. However, the STRMODEL program had to first be refined toaccommodate time variation of vehicle impact area on the wall becausewall stiffness is a function of loaded area of a wall panel. The varia-tion of stiffness with loaded area assumed was linear as shown in Fig-ure 7.7 by the dotted line. The exact variation of stiffness with loadedarea for a centrally-loaded square area on a square panel for an elastic,isotropic plate is indicated in Figure 7.7 by the solid line.

The maximum structural deflections of a typical wall panel computed withthe revised version of STRf10 DEL are shown in Figure 7.8 as a function viinitial yaw impact angle Oo. This shows that the side-on (90 deg) im-pact orientation is the most severe, with a maximum deflection ofapproximately twice that of the frontal impact (zero deg) orientation.Therefore, in this investigation, the side-on impact was considered tobe the worst orientation and the values of the orientation factor, fo,were based on this. It should be noted that the above conclusion wasreached on the basis of calculations performed with one car (PlymouthSatellite) at only one speed (40 m/sec). However, it is believed, dueto the basic assumption made in the orientation study, that the same con-clusion would result with other cars (including the design cars) andother speeds.

To derive the orientation factors the CONTMASS computer program was usedto generate impact force functions for a side-on impact for the PlymouthSatellite at a given impact speed. The resultant function was then in-put to the STRM0 DEL computer program to calculate the maximum structuraldeflection of a typical wall panel. The baseline design function for thecar was then multiplied by an estimated value of the orientation factor,fo, and the resultant function input to STRMODEL to compute structural

was found that,deflection. This process was repeated until a value of fowhen applied to the baseline force function, produced the same maximumstructural deflection as the side-on (90 deg) force function.

In order to implement this procedure a side impact model for the PlymouthSatellite had to first be derived for the CONTMASS program. The massdistribution function p was simply derived by taking the total car mass,exclusive of engine mass, and dividing by the width of the car. Thecrushing strength function Pc was derived from the following relation:

A93 (22)P =P -

c c A90 0 0

141

1

._____ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

where Pc

0A = frontal impact area of car

0

A = side impact area of car90

This relation is consistent with the basic assumption made in the orien-tation study that the side and frontal crush properties per unit areaare the same.

The values of the orientation factor and associated maximum structuraldeflection of a typical wall panel, computed by the above procedure,are:

Orientation Maximum DeflectionImpact Speed Factor of Wall PanelVo (m/sec) fn (inch)

20 2.45 0.205630 2.03* 0.300040 1.81 0.512950 1.71* 0.888160 1.65 1.4630

determined by curvilinear interpolation

7.3 Comparison with Currently Accepted Procedure

Structural deflections of the same typical wall panel described in thepreceding subsection were calculated using the currently accepted Instan-taneous Momentum Transfer vehicle model identified in Section 2 forcomparison with the design procedure developed on this investigation (rec-omended procedure). The comparison is given in Table 7.2 for the design car.

For speeds less than 60 m/sec, the recomended procedure producedsmaller wall deflections than the currently accepted procedure. However,

I at 60 m/sec impact speed, the two procedures resulted in approximatelythe same deflection. At speeds greater than 60 m/sec, the current pro-cedure predicted smaller deflections than the recommended procedure.This is theoretically not possible for a linear structure, but it canoccur for a nonlinear structural model such as we are dealing withhere. This is demonstrated in detail in Appendix E.

It is important to note that in the recommended procedure, the total de-sign force function F otal (Eqn(21)) and associated impulse should bet

applied to the wall panel over an area corresponding to the side impactarea of the design car (approximately 35 ftz). It should also be notedthat in Table 7.2 the deflections calculated with the currently accept-able procedure were based on the design car hitting the wall panelassigned a stiffness associated with a loaded area equal to the side

142

_ _ _ _ .

_ _ _ _ . - - _ . - -

impact area. Had the stiffness associated with a loaded area equal tothe frontal impact area been used, greater deflections would have re-sulted at each speed and the currently accepted procedure would appeareven more conservative than indicated by Table 7.2. To further illus-trate this point a comparison of the currently acceptable procedurewas made with the recommended procedure for the Plymouth Satellite.The currently acceptable procedure was applied to the typical wall panelusing both frontal and side impact areas. The results are summarizedin Table 7.3 which shows that the use of the frontal impact area pro-duces more conservative answers for the entire range of velocitiesconsidered.

7.4 Sumary

The recommended design procedure developed on this investigation involvesthe use of force functions associated with head-on impact of a specificcar (design car) at a given speed. The design cars, at each of the fivedistinct impact speeds considered, are identified in Section 7.1.

The force functions are composed of a force pulse due to impact of thecrushable portion (body) of the vehicle model and an instantaneous im-pulse due to impact of the rigid engine of the vehicle model.

Baseline (head-on, rigid wall) body force functions for the design carsare given in Figures 4.1, 4.10, 4.20, 4.28 and 4.37 for 20, 30, 40, 50and 60 meters /sec impact velocities respectively. The correspondingengine impulses and time of engine impact, relative to the ceginning ofbody force pulse, are listed in Tables 4.1 and 4.2.

Parameters for an idealized representation of the baseline body forcefunctions are tabulated in Figure 7.6.

To account for vehicle impact orientation, a factor fo, given in Section7.2, should be applied to either the calculated or idealized baselinebody force functions. This is not to be applied to the engine impulses.

To account for structural defonnation effects, a factor fs, discussedin Section 7.2, should be applied to either the calculated or idealizedbaseline body force functions. In this study, structural defonnationeffects due to flexural action of typical reinforced concrete wallpanels were found to be insignificant. Therefore, the fs factor forthis effect is unity. However, if estimates of local deformation

-

effects can be obtained, they can be used to determine an effectivevalue of fs which in general would be different from unity. Localdeformation effects on impact load signatures were not considered inthe current investigation.

143

The design force functions should be applied to the center of a wallpanel over an area corresponding to the side impact area of the designcar (approximately35ft). If for some reason it is not desired to2

consider orientation or structural defonnation effects, the baselineforce functions (calculated or idealized) should be applied to the cen-ter of the panel over an area egual to the frontal impact area of thedesigncar(approximately10ft).

For design of a wall panel for overall flexural action, either the cal-culate. or idealized baseline force functions, with appropriate fo andfs factors applied, may be used. However, for design of internal equip-ment or structural components sensitive to high frequency input (i.e.,frequencies higher than the fundamental frequency of the wall panel),only the calculated baseline force functions should be used because theidealized functions do not have the same frequency content as the calcu-lated functions, especially in the higher frequency range. It should alsobe noted that even the calculated force-function should be used withcaution for high frequency response calculations because the relativesimplicity of the vehicle model employed in generating the force func-tions may preclude accurate calculation of high frequency content ofthe functions.

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144

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TABLE 7.1 RESPONSE OF " TYPICAL" STRUCTURETO CALCULATED 8ASELINE FORCESIGNATURES

I" Pac p(ductility ratio)Sp,ed Car * max

(m/sec) (inches) " * max /* yield

20 1 0.1448 0.70222 0.1425 0.69113 0.06612 0.32074 0.08736 0.4237-5 0.08569 0.41566 0.1307 0.63397 0.1028 0.4985

30 1 0.2267 1.09942 0.2080 1.0093 0.1602 0.77694 0.1695^ 0.82205 0.1675 0.81236 0.1840 0.89237 0.1526 0.7401

40 1 0.3'056 1.48212 0.3201 1.55243 0.2458 1.19214 0.2612 1.26675 0.2493 1.20906 0.2459 1.19257 0.2143 1.0393

50 1 0.4953 2.40202 0.4670 2.26483 0.3725 1.80654 0.4106 1.99135 0.3689 1.78906 0.3327 1.61357 0.2910 1.4113

60 1 0.7043 3.41562 0.6448 3.12713 0.5817 2.82114 0.6395 3.10145 0.5893 2.85796 0.4696 2.27747 0.4040 1.9593

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Impact Speed

m/sec (mph) F1 2 l t t2 t*F3

(kips) (kips) (kip esec) (sec) (sec) (sec)

20 (44.74) 90 410 0. 0.035 0.05005 --

30 (67.11) 120 365 1.17 0.021 0.0486 0.0355

40 ( E 48) 180 330 2.78 0.010 0.0520 0.0220

50 (111.85) 370 30 3.81 0.045 0.1302 0.0190

60 (134.22) 440 70 4.89 0.032 0.1558 0.0155

Figure 7.6 Idealized Baseline Force Functions

151

_ _ _ _ _ _ _ _ _ _ -

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I = Bending Moment of Inertiaper Unit Width

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Figure 7.7 Stiffness of a Partially Loaded Simply Supported, Square Plate(Ref. 12)

| 152

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TABLE 7.2 COMPARIS0N OF THE EFFECT OF CURRENT AND REC 0m ENDED |IMPACT LOAD CALCULATION PROCEDURES -- DESIGN CAR

Maximum Wall Deflection (inch)Impact Sp)eed(m/sec Current Procedure Recommended Procedure

(*)

20 0.298 0.17530 0.523 0.26740 0.873 0.66450 1.24 1.1860 1.74 1.78

TABLE 7.3 COMPARISON OF THE EFFECT OF CURRENT AND RECOMMENDEDIMPACT LOAD CALCULATION PROCEDURES -- 1973 PLYMOUTHSATELLITE

Maximum Wall Deflection (inch)Impact Speed(m/sec) Current Pr ure

Recommended Procedure

20 0.29 0.31 0.2130 0.49 0.54 0.3040 0.79 0.86 0.5150 1.16 1.28 0.8960 1.62 1.78 1.46

(*) based on loaded area equal to side impact area of car(**) based on loaded area equal to frontal impact area of car

154

_

8. CONCLUSIONS AND RECOMENDATIONS

8.1 Conclusions

The following major conclusions may be made as a result of this investiga-tion:

e The effect of structural flexibility on the impact forcesignature of an automobile on typical reinforced concretewall panels of Category I structures in nuclear power ?lantsis relatively insignificant, i.e., for the determinintsforce signatures, the walls may be considered to be rigid.

e The effect of automobile impact orientation on impact forcesignatures and consequential structural deformation is ap-preciable and should be considered in the design procedure.Side-on impacts may produce structural deflections up totwice those of head-on impacts.

e The NRC currently acceptable procedure for considering auto-mobile impact loads is conservative for all impact speedranges up to 60 meters /sec. The degree of conservatism isdependent on the automobile, its impact speed and its impactorientation. For the so-called " design cars" defined inthis study, the NRC procedure, applied in conjunction witha side-on automobile impact orientation, can produce struc-tural deflections which are nearly 100 percent too large atan impact speed of 30 m/sec. This procedure is proportion-ally less conservative for higher impact speeds in thissituation up to a speed of 60 m/sec for which it producesapproximately the " correct" deflections. The NRC procedure,when applied for head-on impact, may produce an even higherdegree of conservatism.

8.2 Recommendations

e Local defonnation effects due to automobile impact have notbeen considered in this investigation. The reconnended de-sign procedure developed herein is readily amenable to in-corporation of these effects through the use of the struc-tural deformation factor f -s

e In principle, the recommended design procedure could beextenJed to steel construction walls as well. The baselineforce signatures generated on this study would still beva'. i d .

155

e The probability of various weight classes of automobilesattaining specific impact speeds should be considered inthe design process. In this respect, the force signaturesgenerated herein for a wide vehicle spectrum (minicars tofull-size cars) over a wide range of impact speeds (20 to60 m/sec) would be tremendously useful. Heavier vehicles,up to weight classes known to have a reasonable probabilityof being thrown about in a tornado, shculd then also be con-sidered. This would include, for example, school buseswhich have been known to have been picked up and thrownconsiderable distances in a tornado,

e The impact force signatures presented are based on analy-tical models which are unvalidated in the high speed rangeand for nonfrontal impact orientations. If feasible, a fewtests should be conducted to spot check the high speed andnonfrontal impact orientation results predicted by the models.

e The study of orientation effects here was limited to only in-plane (rotation about the yaw axis) variation and to only onecar at one speed. If warranted, the orientation study should jbe extended to consider more arbitrary impact orientation )

; angles and to include several cars at several speeds.

.

I

i

,

156

_ _ _ _ _

_-

/

REFERENCES

1. Simiu, E. and M. Cordes, " Tornado-Borne Missile Speeds," NBSIR 76-1050, National Bureau of Standards, Washington, DC; prepared for theU.S. Nuclear Regulatory Commission.

2. " Barrier Design Procedures," U.S. Nuclear Regulatory Commission Stand-ard Review Plan, Office of Nuclear Reactor Regulation, Section 3.5.3.

3. Shanahan, J. S., et al, " Missile-Barrier Interaction," Topical Reportprepared by Stone & Webster Engineering Corp. , SWEC0 7703, EMTR-801,September 1977.

I 4. Linderman, R. B., J. V. Rotz and G.C.K. Yeh, " Design of Structuras forMissile Impact " Topical Report BC-TOP-9-A, Revision 2, prepared byBechtel Power Corporation, September 1974.

5. Tsai, J. C. and R. S. Orr, " Development of Criteria and Design Applica-tion for Steel Missile Berriers," ASCE Boston Convention, Civil Engin-eering and Nuclear Power, Volume III, Preprint 3596, April 1979.

6. Attachment 1 "COMPAT Program," private communications from Gary Bell,Office of Vehicle Safety Research, Department of Transportation,National Highway Traffic Safety Administration, Washington, DC, Novem-ber 8, 1979.

7. Ryder, M. 0. , Jr. , " Classification of Automobile Frontal Stiffness /Crashworthiness by Impact Testing," Calspan Corporation Report D0T HS-801 966 for National Highway Traffic Safety Administration, August 1976.

8. Tanner, R. B., "Crashworthiness of the Subcompact Vehicle," Minicars,Inc. Report DOT HS-801 969 for National Highway Traffic Safety Admini-stration, Final Report, August 1976.

9. Ryder, M. 0. , Jr. , " Evaluation of Geometric Aggressiveness of Full-Size Automobiles," Calspan Corporation Report DOT HS-802 060 forNational Highway Traffic Safety Administration, October 1976.

10. Bruce, R. W., E. E. Hahn and N. R. Iwankiw, " Guardrail / Vehicle DynamicInteraction," IIT Research Institute Report FHRA-RE-77-29 for FederalHighway Administration, Contract D0T-FH-11-8ci March 1976.

11. Redmann, G. H. , et al, " Wind Field and inf etz./ Models for Tornado-Propelled Objects," Jet Propulsion Lab 3rrw(y vajact 308, Final Re-port EPRI NP-748 for Electric Power Resd3rch'lustitute, May 1978.

12. Timoshenko, S. Theory of Plates and Shells, New York: McGraw-Hill BookCompany, 1940.

157

_ _____________ _ _ _.

_

APPE? DIX ADISTRIBUTED MASS VEHICLE MODEL AND STRUCTURAL MODEL 1

A.1 DERIVATION OF VEHICLE MODEL EQUATIONS

Thissectioncontainsthederivationofi!heequationofmotionwhenadistributed mass car body, with a lumped engine mass, is impacted on arigid wall.

._6 r

wall I19 M M

'

4 e u

k

Figure A.1

In Figure A.1: M = crushed mass of carc

Mu " "b *"e = uncrushed mass of car| M = uncrushed body mass

bi M = lumped engine mass

e( = amount of crush

Now consider the crushed region and a mass di which will be crushed intime At, and do the momentum balance before and after the crush. Assumethe velocity in the crushed portion is zero.

| Vel.=0 .g Vel . = 0_

: P AM M * AME ' "c c c_

Before Crush After CrushFigure A.2

In Figure A.2: R = reaction at the wallP = crushing strength at the car cross-section

c

therefore,

(-R + P )At = (M + d) x 0 - (M x 0 + Nd)c c c

158

_ _ . . _ .

Simplifying and taking the limit At + 0, we have

-R + P = -$ (A1)c

but dm dm JdTt' " W dt

h = pi (A2)Of

where p = f = mass per unit length at the cross-section of car.

Combining Eqns(A1) and (A2), we have

R = P +p (A3)c

Now consider the whole body of car

g g $ + A$Vel.=0- = eVel.=0

; fi A" "u "c + "uc


LetthevelocityoftheuncrushedmassbechangedbyA$aftertheimpact(Figure A.3). Doing the momentum balance, we have

-rat = (M + AM) x 0 + M ($ + A$) - (M + AII)bc u u

Simplifying and taking the limit At + 0, we have

R=-M +p (A4)u

Comparing Eqns(A3) and (A4), we have

^P *~c u

159

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _.''

I

-___ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ .

The mass distribution of the car can be generalized as a continuous massdistributed over the car body plus a lumped engine mass as shown in Fig-ure A.4.

i

V s

s "es

s

] | j

ks

'

:g ;&N L , ,_ ,,

Figure A.4

Let the engine be located at a distance of E from the front face of thecar which has a total length of L. Thenbedretheengineimpact,i.e.,when E < Ee

^Pc " ~(N *"e)b

M , the uncrushed body mass, can be written as:b

H =/ p(y)dy (A7)b

Eqn(A6) becomes:

Pc"- # p(y)dy + M ] (A8)E e

Af ter the engine impact, i.e. , when E < g :g

LPc"~ # (y)dy (A9)

E

therefore,

R=P*" ^c

where Eqn(A8) and Eqn(A9) apply to P when E <6 and ( > g , respectively.c e e

160

- -. . _ _ ._ .. _ _ _ _ _

&wall / M I~ M*.

e

h 's ---e. F-

/, "e b m:

"b c b

2

Figure A.5

Now consider the impulse produced by the impact of the lumped engine andits effect on the velocity of the car body (Figure A.5). Let I be theimpulse, F be the force exerted between the engine and the car body dur-ing impact, and let the impact have a duration of At. Doing momentumbalance, we have

-I - fat = 0 - Me ei

-P at + fat = M I ~kbi}c b bf

where the subscripts i and f designate the state before and after theimpact of engine, respectively. It can be seen that

b "Ibi*Ilei

Taking the limit At + 0, the above equations become

I=M (All)e1

(A12)$ *ibf

Therefore, the impulse produced by the impact of engine and the velocityof the car body after the impact are governed by Eqn(All) and (A12),respectively.

161

_ _ _ - _ _ _ _ _ _ _ _ _ _ - _ _ _ -

A.2 STRUCTURAL MODEL

The structure is modelled by a simple spring-mass unit with a mass Ms

and stiffness Ks(FigureA.6).

WK

s

fW s < FN

Figure A.6

The equation of motion is obtained to be: '

MX+Kx=F (A13)3 s

Where F = force exerted on the structure.

The impact of the lumped engine on the wall is simulated by an impulseand afterward the mass of the engine is added to the mass of structure 1

and moves with it (Figure A.7).

S fi< ;

I d/ '

$h s /M M + M,M s ; p

d $#

Before Impact After Impact

Figure A.7

In Figure A.7, ij and if are the velocity of the structural mass beforeand after the impact of the engine. I is the impulse produced by theengine; F is the force exerted on the wall by the car body; and Me is themass of engine. Consider momentum balance before and after the impact,assuming the duration of impact is At, we have:

1 + fat = (M + M } f ~ "s is c

J

162

- _

Taking limit at + 0, we have:

I +M iS " g +*g (A14)f

s e

Therefore, the structural model is governed by Eqns(A13) and (A14).

A.3 COUPLED VEHICLE / STRUCTURAL MODEL

This section contains the derivation of the equation of motion when acar body, with a lumped engine mass, is inpacted on a nonrigid wall. Thewall is modeled by a spring-mass unit (Figure A.8).

N k/ K

# s Mj c u//

Figure A.8

In Figure A.8, C. Mc, Mu have the same meaning as in Section A.1. x isthe displacement of the wall. flow consider the crushed region and amass AM which will be crushed in time At, and do the momentum balancebefore and after the crush,

d A+( i + Ai

"cR ; : P AM R_._ fi + AM : Pc c


163

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _-

. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

Before the crush, the crushed mass travels at the velocity of the wall,k, and AM travels at a velocity A + &. After the crush, let the velocityof the wall be changed by AA, then:

(-R + P )At = (M + AM)( + A ) - (M + #( * k))c c c

Simplifying and taking limit At + 0, and taking|

p= (A15)

we have:

R=P - "c p (A16)c

Now consider the whole body of car before and after the crush.

|l

d I +__i ; $ +k i + Ai I + i + A( + Ai

R"c AM M = g ,63 g


The change of velocities for different masses is shown in Figure A.10.Doing the momentum balance before and after the crush, we have:

-rat = (M + AM)( + AS) + M ( + + ^ + }-"c -("u+0")( * )c u

Simplifying and taking limit At + 0, we have

d([ + i) 2R=-M -M + (A17)c

1

164

ComparingEqns(A16)and(A17),wehave:

P * 'N (A18)c u d

Taking the same generalized mass distribution of the car as in Section A.1(Figure A.4), the crushed mass can be expressed as:

CMc " I p(y)dy (Ab'o

For ( < g, Mu " "b + Ne(A20)

For C > (, Mu"Nb

where M , the uncrushed body mass, can be expressed asb

M =/ p(y)dyb

Therefore, from Eqn(A18)

, , d($ + i) gflc g (y)dy + M,] for E ig, (A21)P

d($ + I / g(y)dx for C > C, (A22)Pc"~ dt

Therefore, from Eqn(A16)

6 2R=P- I p(y)dy + pS (A23)c o

where Eqn(A21) and Eqn(A22) applies to Pc when (SCe and C > (e, respec-tively.

165

_ _ _ _ _ _ _____

d+ 5, +- I -, M,K M M

F s Fs s g ; ,g s.

iM e ,s b m +,j ~

M F~g cc M

b P* "bc

Figure A.11

Now consider the impulse produced by the impact of the lumped engine andits effect on the velocity of the car body (Figure A.11). Let I be theimpulse; F be the force exerted between the engine and the car body dur-ing impact; Fs be the force on the structure; and let the impact have aduration of At. Doing raomentum balance before and after the impact ofengine, we have:

3 3 c f i}-F At + I + P At = (M + M )I

-I - fat = M ( f + ef i ~ ei)~

e

-P at + fat = M ( f * bf i ~ bi}c b

where the subscripts i and f designate the state before and after the|

impact of engine, respectively. It can be seen that

&,4 =$bi " i=0 andef

Taking limit At + 0, and simplifying, we have:

I=M,5 ^bf

MI i + 1) *I"s *M ) ic, e ^*f " M+M+Me s c

$bf " i*i~f ^

Therefore, the impulse produced by the impact of engine and the velocityof the structure and car body after impact are governed by'Eqns(A24),(A25) and (A26), respectively.

166

_ _ _ _

APPENDIX BVEHICLE PARAMETER DATA

B.1 MASS DATA FOR MULTIMASS MODEL

The weights of the different masses of a car for the nine cases that areconsidered-in this report, are given in Table B.1. There are three basictypes of mass connections and they are shown in Figures B.1 through B.3.

TABLE B.1 WEIGHT OF DIFFERENT MASSES OF CAR MODELS

Weight (lb) g33Car

Model Engine & Front Body Rear Axle peBumper Transmission Suspension

1 60.0 967.0 383.0 2586.0 1--

12 68.4 1103.5 437.1 2951.0 --

13 54.2 974.1 270.6 3301.1 --

34 50.0 305.0 50.0 1595.0 --

35 75.0 920.0 274.0 2231.0 --

16 50.0 426.0 262.0 1751.0 --

7 50.0 900.0 250.0 3050.0 250.0 28 50.0 900.0 250.0 3050.0 250.0 2

9 100.0 750.0 378.0 2922.0 3--

3Car Model 1 - 1973 Plymouth Satellite *2 - 1975 Plymouth Gran Fury **13 - Torino**24 - 1975 Honda"5 - 1972 Chrysler"

86 - 1974 Pintol7 - Calspan Full-Size Car

8 - SRI Full-Size Car!9 - Plymouth'

*Superscript refers to reference number at end of this appendix.

**Mass of 1975 Plymouth Gran Fury is taken to be 1.141 of the mass

2of 1973 Plymouth Satellite .**

Mass of Torino is taken to be 0.9871 of the mass of 1973 Plymouth2Satellite ,

167

_ _________ _ __ _ __ . _ _ . . _ ,_ _.

1

|

|

Bumper

Sheet Metal,

Fore Frame

Aft FrameSu capEng Mts

B dyRadiatori

- i

$ Drive ShaftEngineTransmission Mts

Fire Walli

i

figure B.1 Car Model Mass Connection Type 1

__

|| j||

_

<..

pe

ryda o

C B

.

p es mu a

S rF

ra t 2e f

R A epyTnl ol

a re t . i

W al np tex os c

e RA ru er FS n

ni oF tf Ca

l h s sa S t st M ae e MM v g

i n l

t r E ee D d

oe MhS e s r

n n aCg& a.i

rn T

E e 2ma BrF e

re ur g

r o i

o F Ftai

daR

repmu

B

Ee

I IJ i

ryda oC B

emar 3F et pf yA T

noitc

l e"p l n

a nu W o

h Cer si sF a

l Ma st t l

e M eM d

g ot n Me Ee rh aS C

e sn n 3g& ai

r Be n Tm E ea rr uF g

i

e Fro rF o

tai

daR

r -epmu

B

o

:

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ .

B.2 CRUSH DATA FOR MULTIMASS MODEL

The crush data for the multimass models considered in this report aregiven in Tables B.2 through B.8

Car Model Table Number81973 Plymouth Satellite B.2

1975 Plymouth Gran Fury **1 B.2

Torino**2 B.2

1975 Honda' B.3

1972 Chrysler" B.4

1974 Pinto' B.5lCalspan Full-Size Car B.6

lSRI Full-Size Car B.7

Plymouth' B.8

** The crush strength of Plymouth Gran Fury is taken to be the sameas that of Plymouth Satellite.

** The crush strength of Torino is taken to be 0.6949 of the crushstrength of Plymouth Satellite.

171

. _ _ _ _ _ _ _ _ _ _ _ _ _ _

TABLE B.2 CRUSH DATA FOR 1973 PLYMOUTH SATELLITE

-40.0 0.0 5.1 9.3 10.1 11.2 13.2 12.6 13.0 50.0Radiator 0.0 0.0 6.9 17.0 26.2 33.1 50.0 24.4 47.2 105.0-40.0 -2.1 0.0 1.0 2.0 3.9 11.1 13.1 40.0 100.0Aft Frame -10.0 -10.0 0.0 25.0 30.0 24.2 36.8 32.1 32.1 32.1-40.0 -2.1 0.0 4.3 5.6 7.0 11.0 11.8 13.6 100.0Forward Frame -10.0 -10.0 0.0 37.2 37.2 49.7 49.7 38.8 42.2 42.2-40.0 0.0 3.0 7.0 10.0 11.6 13.0 14.7 40.0 100.0Sheet Metal 0.0 -10.0 12.1 15.1 12.1 6.1 6.1 4.2 4.2 4.2-40.0 0.0 12.5 17.6 20.0 30.0 40.0Fire Wall 0.0 0.0 7.4 45.2 52.6 93.4 134.2-40.0 0.0 5.9 7.1 9.0 10.1 11.4 13.0 40.0 100.0Ortve Shaft 0.0 0.0 17.9 16.7 21.5 10.0 17.0 11.0 11.0 11.0-40.0 -2.1 0.0 0.8 2.0 4.1 7.0 20.0 40.0 100.0En9ine Mount -10.0 -10.0 0.0 3.9 4.9 14.0 4.8 4.8 4.8 4.8

Transmission -40.0 -2.0 -1.5 0.0 1.0 2.9 4.8 6.3 40.0 100.0Mount 0.0 0.0 -5.5 0.0 2.8 0.7 4.0 10.0 10.0 10.0

TABLE 8.3 CRUSH DATA FOR 1975 HONDA

-50.0 10.5 13.5 15.5 18.5 120.0Radiator 0.0 0.0 5.0 20.0 45.0 45.0

-50.0 8.0 8.6 13.6 15.5 18.7 20.2 24.6 120.0$ et Metal 0.0 0.0 0.2 6.3 5.9 7.2 6.0 5.5 5.5-50.0 0.0 4.0 5.2 11.35 12.0 14.0 120.0Forward Frame 0.0 0.0 7.0 16.0 12.0 13.5 118.0 118.0-4.0 0.0 0.33 3.0 120.0Engine Mount -30.0 0.0 1.2 23.0 23.0

-50.0 0.0 0.4 2.0 4.4 10.1 120.0Af t Frane 0.0 0.0 14.6 15.5 14.0 20.0 20.0

-50.0 2.0 3.6 5.0 6.7 7.4 7.9 11.3 120.0Fire Wall 0.0 0.0 3.5 17.3 22.4 22.9 16.0 18.0 18.0

i'

TABLE 8.4 CRUSH DATA FOR 1972 CHRYSLER

-40.0 4.0 5.0 9.68 12.32 13.8 14.8 15.4 16.7 120.0Radiator 0.0 0.0 1.0 9.8 18.4 28.1 43.9 36.2 80.0 80.0

-40.0 5.0 5.7 7.34 13.82 14.84 16.0 17.2 23.6 120.0et Metal 0.0 0.0 9.5 22.9 13.7 17.8 11.1 15.5 5.9 5.9-40.0 0.0 1.74 3.15 6.72 11.5 13.5 14.2 15.2 120.0Forward Frame 0.0 0.0 12.3 7.2 10.0 7.36 35.6 35.6 29.4 29.4

-4.42 -4.16 -3.06 -1.77 -1.6 0.0 2.57 5.7 6.1 120.0Engine Mount 0.0 -7.88 -7.46 -4.5 -8.0 0.0 15.5 12.6 0.0 0.0Aft Frame -40.0 0.0 0.3 0.9 1.2 2.1 4.98 5.6 50.0 120.0 1

0.0 0.0 15.2 22.4 21.8 25.0 24.6 23.2 23.2 23.2

-40.0 0.0 4.86 7.71 8.54 8.88 9.62 11.88 52.2 120.0Fire Wall 0.0 0.0 3.16 10.5 14.0 13.0 15.5 16.5 178.4 178.4

Note: First row - amount of crush in inchSecond row - force in kip

172

-. . .. . _ - - _

TA8tE B.5 CRUSH OATA FOR 1974 PINTO

-40.0 0.0 1.7 2.9 3.8 4.7 6.0 8.0 24.0 30.0Radiator 0.0 0.0 4.0 6.0 10.0 19.0 27.0 43.3 100.0 115.0

-40.0 -1.2 0.0 0.8 10.0 10.0AIL I'*** -10.0 -10.0 0.0 26.0 26.0 26.0

-40.0 -1.2 0.0 0.8 0.9 3.9 4.9 6.4 16.2 20.0Forward Frame -10.0 -10.0 0.0 1.0 4.0 26.0 26.0 19.0 19.0 17.3

-40.0 0.0 1.8 5.0 7.0 7.9 26.0 36.3 50.0 100.0Sheet Metal 0.0 0.0 2.0 2.0 4.0 3.0 3.0 1.0 1.0 1.1

-40.0 0.0 10.0 20.0 30.0 40.0 50.0 60.0 80.0 100.0Fire Wall 0.0 0.0 18.0 36.0 54.0 72.0 90.0 108.0 144.0 180.0

-40.0 -1.2 0.0 8.1 11.1 12.0 13.1 14.1 40.0 100.0Orive Shaft -16.0 -10.0 0.0 16.0 16.0 8.7 9.7 11.3 11.3 11.3

-40.0 -4.0 -3.0 0.0 0.8 2.9 4.0 : 40.0 100.0.

Engine Mount -6.0 -6.0 -8.0 0.0 2.0 11.0 11.0 12.0 12.0 12.0

Transmission -40.0 -5.0 -3.3 -0.4 1.7 6.0 9.0 10.0 11.0 100.0Mount -5.7 -5.7 -2.3 -2.3 2.7 3.0 5.0 5.0 0.0 0.0

TABLE B.6 CRUSH OATA FOR CALSPAN FULL-SIZE CAR

-12.0 16.8 18.0 26.4 31.2 36.0Radiator 0.0 0.0 150.0 150.0 1.0x10' 1.0x10'

-12.0 6.0 8.4 14.4 18.8 40.8 60.0Sheet Metal 0.0 0.0 23.0 15.0 17.0 55.0 55.0

-12.0 0.0 0.12 3.0 3.6 6.6 12.0 48.0Forward Frame 0.0 0.0 16.0 16.0 75.0 55.0 30.0 30.0

-20. () -2.0 -0.96 0.0 0.96 2.0 20.0Engine Mount -20.0 -20.0 -10.0 0.0 10.0 20.0 20.0

-12.0 0.0 0.6 3.6 9.0 48.0 49.2Af t Frame 0.0 0.0 75.0 55.0 30.0 30.0 30.0

-24.0 0.0 1.2 2.4 3.6 36.0Drive Shaft 0.0 0.0 15.0 17.0 0.0 0.0

-12.0 -10.0 0.0 7.0 7.2 48.0Rear Suspension -17.0 -17.0 0.0 30.0 20.0 20.0

-36.0 0.6 6.6 18.0 36.0Fire Wall 0.0 0.0 100.0 25.0 10.0


173

TA8LE B.7 CRUSH OATA FOR SRI FULL-SIZE CAR

-12.0 22.8 24.0 30.0 31.2 36.0Radiator 0.0 0.0 150.0 150.0 1.0x10' 1.0x10'-12.0 6.0 7.2 18.0 24.0 26.4 36.0 54.0Sheet Metal 0.0 0.0 40.0 40.0 50.0 100.0 100.0 125.0-12.0 0.0 0.1 6.0 6.6 30.0 36.0 37.2Fonsard Frm -10.0 0.0 18.0 18.0 24.0 24.0 100.0 1000.0-6 6Engine Mount

-12.0 0.0 0.1 12.0 18.0 24.0Aft Fr m -10.0 0.0 24.0 24.0 100.0 1000.0-24.0 0.0 1.2 2.4 3.6 36.0Orive 5 haft 0.0 0.0 15.0 17.0 0.0 0.0-12.0 10.0 0.0 7.0 7.2 48.0Rear Suspension -17.0 -17.0 0.0 30.0 20.0 20.0-12.0 9.0 21.0 27.0 30.0 36.0Fire WaH 0.0 0.0 30.0 50.0 100.0 100.0

,

TA8LE B.8 CRUSH OATA FOR PLYMOUTH

-50.0 0.0 8.1 13.0 17.8 20.3 120.0Radiator 0.0 0.0 4.0 14.0 74.0 138.0 138.0-50.0 6.0 8.6 11.4 15.2 22.2 23.2 33.3 120.0Sheet Metal 0.0 0.0 9.2 13.6 12.5 6.8 4.2 3.0 3.0-50.0 0.0 1.5 2.7 6.5 15.3 17.8 20.2 21.7 120.0forward Frame 0.0 0.0 46.0 11.0 51.4 48.5 59.0 37.0 45.4 45.4-7.5 -4.0 -1.2 -0.2 U.0 0.7 0.9 1.6 2.5 120.0Engine Mount -9.9 -3.2 -9.8 -0.9 0.0 2.0 10.0 14.9 23.6 23.6

-50.0 0.0 1.4 1.9 4.1 10.4 11.4 120.0Aft fr a 0.0 0.0 31.7 31.2 22.4 25.7 31.7 31.7

-50.0 2.3 2.8 3.7 8.8 9.0 10.8 120.0I I '' "' N 0.0 0.0 0.6 5.5 12.9 17.1 20.8 20.8


174

. . . . .

B.3 CONVERSION OF DATA FOR DISTRIBUTED MASS MODEL USAGE

B.3.1 Construction of Distributed Mass Function

In the construction of the distributed mass function used in the distrib-uted mass vehicle model (see Appendix A), the lumped masses of the car(except the engine which is treated as a rigid mass) are distributedevenly over their actual length about their c.g.'s. The body mass isthen distributed linearly over the whole length of the car so that theoverall c.g. of the car matches the. actual c.g. of the car. The dis-tributed masses are then added up to give the distributed mass function,p. An example is shown in Figure B.4. The actual values for the carsare shown in Figures B.5 through B.12.

B.3.2 Construction of Crush Strength Function

In the construction of the crush strength function of the distributedmass model (PC Function) for various cars, the car is assumed to becrushed only at the impact face where the car makes contact with thebarrier. The rest of the car body remains undeformed. The PC functionis a plot of the force exerted on the barrier when a certain distanceof the car is crushed. The car is modeled with lumped masses connectedby nonlinear springs.

In the actual construction of the PC function, the front mass of the car

is pushed toward the other masses while holding the other masses fixed.The force required to push the mass is plotted against the displacement.This process continues until the front mass hits the second mass, thenthe second mass starts to move with the front mass while holding theother masses fixed. The process continues until the last mass is hit.An example is given in Figure B.13. The actual values used for the dif-ferent cars are shown in Figures B.14 through B.20.

175

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -

FrontSuspension

RearSuspension

Bumper_._

l i I | |

| | 1 | |

| | 1 1 I

I | | 1 I

I I I I_

l i l

I~ Car Body Mass

1 I I | |

1 1 I | |

1 | | | 1

| | | | |

1 | | 1|

I I I I

I ii g gIl I _ , _

I

~

'I

~ -

-

_

_

-

Distributed Mass for the Whole Car

Figure B.4 Construction of Distributed Mass Function

176

_ _ _ _

|| |1 ||

8.'l

.51

eti

l4 l'l e

taS

htu

'2 ol mylP

37

) 9t0'l f 1

(

rtn oe fmec na olp i

8 s tci

D nuf

- s- s- a

8 Mdetubir

4 tsi

D

5.

B2

erugi

0 0 0 F0 0 08 6 4

- 0

_:2C1

.

C~

||||| ||

gg

k g

o4 n

{iroTdroFh

t3791

)t rf o( f0'l tn ne ome ic ta clp ns ui

8 D f

ssaMdet& ubirtsi

D4

6 _Ber

- ui g

i

F

0 0 M0 0

90 _0 8 41

32Og__-

_

_

$

,800

;. 600

$-

]''400

a . .

|.

0 2 4 6 8 l'0 52 l'4.

Displacement (ft)

Figure 8.7 Distributed Mass Function for 1975 Honda

'

179

b

_

_.

_

-

:83

-

:61

,

rg e- g

lsyrhC

2Z 7,'l

91

ro)

t f- f

( n01 t o

n ie tme cc na ulp FsiD s

d saMdetub

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D

8.

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erugi

F2

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.

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|| ,1|| 1;111 ||l 1||| || !

61

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otniz'l P

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tn ne om iec ta cl nps us' Fi

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9_

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er

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.

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a(

t Cn

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si

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:2 er

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- F

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0 0 00 0 0

~ 0

_ *C b "

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,

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1

.BI

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raC

ez

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S-

lluF

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ro

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m ce nca u

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O sa.5 Mdetubi

. 6 rtsi

D

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B

erugi

F-'2

0 0 00 0 0 _ ,

05 4 3-

32Ca

Eta

P ;

'

8'l

6a'l

4:1

htuomy2

1 l

.

P_ r-

o) ftf( n

0 t o1 n i

e tme cc na ul

. p F _- s .

-i sD -

s8 aM

-

d.e

rub

.6 irtsi

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er- u

~ gi

F2,

0 0 0 -_

0 0 0

-5 4 3

0

7$Ca_

_

.

-.

-

M

c ||||

-

_ ~

Spring 1. , _

M1 M3Spring 2 Spring 3

M2

_

M Crush Strengthfor Spring 1

1 II

I

| Crush StrengthI

g for Spring 2It

I I

I I

I I

II , Crush StrengthI for Spring 3,

' i' l

I I

I ii i

OverallCrush Strength

Fig'ure B.13 Construction of Crush Strength Function

185

_ _ _ _ - - - _. .

_- .. . - . . .__

220--

i

200-

Constructed PC Function180--------- Simplified Input to CONTMASS

Program160

3 140'5.E 120-o / 1

/ t' I

5 100- -

/ 1e/ \ /,' ' I80 ' -

/\ I

# I /60 f g-

. / I'I

40-- r

20--

- .

: : . . 3

0 20 40 60 80 100 If0 l'40'


Figure B.14 Crush Strength Function for 1973 Plymouth Satellite

_ _ _ _ _

|| || 1| '1 |,

m 0E =

a 6rgorP

SSAMT

n No Oi C 0E -

t 5c on tuF t

uC p aP n d.

I rd oe d ) Ht e sc i e 5u f h 7r i 0 c 9

t

t l 4 n 1s p i

n m ( roo i

C S t fn

- e n- m o- e i

- c t- a c- l n- p u- s F

0 i- a . 3 D htgnertShsurC

0e ,

251

B

erugiF

- 0, ,1

's

- - - - 0

0 0 0 00 5 0 52 1 1

na 5 85u.

a"o

_

|1,|,lt

, ,

0.6

-

margor

P

SSAMT

. .05

n N ro Oi C e

lt sc on t y

ruF t h

CuC p ) 2P n s 7I

d e 9h 1e d 0

t e ~ 4 cn rc ii ou f ( fr i

t l t ns pn m n o

e i -o i m tC S e cc na u-l F-

- p- s h- . 0 i t3 D g- n-- e -r

- tS

_- hsur

~ C

~ 0 6. 2 1.

B -

er -

u -/ g// i

_ / F

_

01

_

- ""0 0' 0' 0_

0 5 0 52 1 1

â 7 eE*u.

-@

_

1|1

marg ;0o 7r

SAM /T

n No Oi C ;0t

6c on t ou tF t nu iC p PP n

I kd ce d ot e 0 tc i 0

u f S Sr i 4t l ) 7s p s 9n m e 1o i hC S c r

n oi f

- (- 0 n- t 4 t o|

- n i- \ e t- m c- e n- c u

/ a Fl' p hs ti g

0 D n: 3 e

rt

j S

hsur

C/02 7

/1

/ B/ e/ r/ uj g

/ iF

01/

//

//

j/

//

- - - .- - - .

0 0 0 0 0 02 0 8 6 4 21 1

2"6 ggw

ge

| |||j1|

. _ _ - _ _ _ _ _ _ __ _ _ _ _

!l

l

200,.

_ . _ _\ Constructed PC FunctionSimplified Input to CD.'!TMASS\

--------

g Program160. . g

/ \

' \

d \

\

120-ô.

$8isu. 80--

A s~

I sI s/ s

40-- d

//

I

II

: : ; ;"

,

1 2 3 4 5 6 7

Displacement (ft)

Figure B.18 Crush Strength Function for Calspan Full-Size Car

_ _ _

_ _ _ _ _ _ - _ _

,

Constructed pc Function320 - _________. Simpli fied Input to

CONTMASS Program

280.

240-

-

$200--

85"

160--

7 .

120-

80

-Y, ,

'

40- //

|/

/ .

0 1 2 3 4 ~5 6 7

Displacement (ft)

Figure B.19 Crush Strength Function for SRI Full-Size Car

191

-_

mar :7gorP

SSAMT

n No O

C :6dc on tuF t

uKp n

I hd te d u

5 ot e :

mc iu f yr i l

.

_Pls p _

n m r _

o _i

S f

) n- t o- f i

- :4 ( t- c- t n- n u- e F- me h

c ta g

_

l np es r

i t;3 D S

hsu -r ._C _

_

_

02

2 B:

erugi

F

1' :

s

-". .

.

0 0 0 0 00 6 2 8 42 1 1

^ o. 5 8iu. s.

-

-

2

_ - _ _ _ _ _ _ _ _

B.4 VARIATION ON BODY MASS DISTRIBUTION

Three types of body mass distributinns have been used; they are:

(a) linear distribution

(b)bilineardistributionwiththechangeofslopeatthec.g.of the car body mass

(c) bilinear distribution with the change of slope at the c.g.of the whole car

The purpose of using three different types of mass distribution is tofind out how the results would vary due to different types of body massdistribution. It has been found that the variation does not have a sig-nificant effect on the results and the linear distribution is adapted

for all the car models.

The three types of body mass distributions are shown in Figures B.21through B.23. In the figures, L is the length of the car, Xg is thedistance from the front to the c.g. of the car body, and XC 1s the dis-tance from the front to the c.g. of the car. In each case, there are two

cuantities to be solved, namely S, the slope and X in Figure B.21; Y andX in Figures B.22 and B.23. The two quantities in each case are solvedby considering the following two conditions: (1) the bounded area mustbe equal to the mass of the car body and (2) the c.g. of the boundedarea must lie on tne c.g. of the car body mass.

An example is given for the Plymouth Satellite and is shown in FiguresB.5, B.24 and B.25.

193

_ _ _ _ _ _ _ _ _ -

ir

1r LS + XX

JL JL

L :,I'r

Figure B.21 Linear Distribution

.

n

Yr

X |,, ,,

E:: XB: L J,

Figure B.22 Bilinear Distribution -- Change iof slope at c.g. of car body mass

!

)m

N l

1 ,

X

o o

XC d:- L Jr n

Figure B.23 Bilinear Distribution -- Changeof slope at c.g. of whole car

194

.

800

O3< 600

C.3 400 -

200

~

. . . . .

0 2 4 6 5 10 12 14 16 18

Displacement (ft)

Figure B.24 Bilinear Mass Distribution - W.R.T. C.G. of Car Body Massfor 1973 Plymouth Satellite

800

600

32 400 --

200

^

0 2 4 6 8 i0 I2 i4 16 18

Olsplacement(ft)

Figure B.25 Bilinear Mass Distribution - W.R.T. C.G. of the Whole Carfor 1973 Plymouth Satellite

195

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ -

- - - _ __ - _

APPENDIX B REFERENCES

1. " Study of Compatibility and Asymmetry in Car-to-Car Impact;" Holmes,B. S. and Gran, J. K., Stanford Research Institute, Contract DOT-TSC-843

2. " Classification of Automobile Frontal Stiffness /Crashworthiness byImpact Testing; " Ryder, M. 0., Calspan Corporation Final ReportD0T-HS-801 966, Contract D0T-HS-501099, August 1976

3. Attachment 3 " MINICAR Model"; private communications from Gary Bell, i

Office of Vehicle Safety Research, Dept. of Transportation, NationalHighway Traffic Safety Administration, Washington, DC; October 23,1979

4. Attachment 1 "1975 Honda into 1972 Chrysler A"; private communica-tions from Gary Bell, Office of Vehicle Safety Research, Dept. ofTransportation, National Highway Traffic Safety Administration,Washington, DC; October 23, 1979

5. Consumer Reports, " Mechanical Specifications of Cars;" 1972-75

6. Consumer Reports, " Basic Car Body Dimensions;" 1972-75

7. "Crashworthiness of the Subcompact Vehicle;" Tanner, Richard B. ,Minicars, Inc. Final Report 00T-HS-801 969, Contract D0T-HS-113-3-746, August 1976

8. " Evaluation of Geometric Aggressiveness of Full-Size Automobiles;"Ryder, N. 0. , Calspan Corporation Final Report DOT-HS-802 060, Con-tract D0T-HS-5-01099, October 1976

9. Attachment 2 " Honda-Plymouth 61.7 mph Frontal Impact;" privatecommunication from Gary Bell, Office of Vehicle Safety Research,Dept. of Transportation, National Highway Traffic Safety Administra-tion, Washington, DC; November 8,1979

I

i

196

_ . -_

APPENDIX CCONTMASS COMPUTER PROGRAM

C.1 INPUT INSTRUCTIONS

InputformatforCONTMASS(continuousmassmodel):

Card Entries Fomat

1 Title 20A4

2 Z0,DZ0,TI TF,DELT,CLEN, IPR,ND1,ND2,FD1,FD2,R.VC freeZ0 = initial displacement of car (ft)DZO = initial velocity of car (ft/sec)TI = initial time (sec)TF = final time (sec)DELT = size o'f time step for integration (sec)CLEN = car length (ft)IPR = print at every IPR time stepsND1 = number of entries in Table PCND2 = number entries in Table MUFD1 = PC multiplierFD2 = MU multiplierR = strain rate effect coefficient

= 0 - no strain rate effectVC = 1/2 or 1 - velocity coefficient

3 XME,XXE

XME = mass of engine (K-lbm)XXE = displacement of engine mass from front of

car (ft)

4 X0,0X0,XM,XK,ULF,KLME,KLMP free

XJ = initial wall displacement (ft)DX0 = initial velocity of wall (ft/sec)XM = mass of wallXK = spring constant of wall (kip /ft)ULF = ultimate strength of wall (kip)KLME = transfonnation factor in elastic rangeKLMP = transformation factor in plastic range

197

__ -

Card Entries Format

5 PC(I),I=1,ND1 free;

PC(I) = crushing strength of car along thelength of car (kip)

6 PCX(I),I=1,ND1 ~ free

PCX(I) = distance along the car correspond'eagto the PC values entered in Card 3(ft)

7 MU(I),I=1,ND2 freeMU(I) = mass per unit length of car along

the length of the car (K-lbm/ft)

8 MDX(I),I=1,ND2 freeMDX(I) = distance along the length of the car

corresponding to the MU values enteredin Card 4 (ft)

Note: for rigid wall, specify XM = 0.

For looping input: I

1. Title card 20A4

2. Initial velocity of car

3. X0,DX0,XM,XK,ULF,KLME,KLMP

To save the output in a file:

0ASG,UP FILE.

BUSE 8, FILE.:

P

198

_ _ - _ _ _ _

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . __

C.2 LISTING

MAIN PROGRAM

CnHnnN / t NP T / 7 0. n Z'n . T ! . TF .'nEL T . CI E* f pe . *n t . N0 2. F01. Fn2.'e . vt .toJe e' Pr(20).PCYt20).Muf20).Mvvf26).TPC(20).T"ilf20),in nto.YM rte e

to e .t:L F e rLME.KLMP.WEw.7EN4e Cod *0N/LPCNT/L0nPSe NATA LunP/0/4e 10 CALL INPilfTe 1F (v M.GT . .on t ) GO Tn 20ao CALL sul1ce Go 70 inIno 70 CALI 50L211e nn TO to12e END

INPUT

to C Tw!S PROGRAM SIMILATES A CONTINilotl3 C AR MASS w nn El. IMPACTING nu2* C & WTGTO FLAT AA981EW. THE FORCE EVE 9 fen nv THE aakw!EN. YdE3e C ACCFLFRATION. v FLilC f f V ann n!SPLACEMENT AS A FitNCT !:14 IIF Tt1E TSse C CALCULATEn AND PWTNTEn NUT. THE FORMULA Fod F0dCE CALCotAT!n* 135e CAo C FORCE e PCe(R+.02eALOG(ABS (VEL)))+MuovELea7To CAo C HEcE F09CE = REACT!nN AT THE nAoRTEues C PC e CditSH STRENGTd 0F CAR AT THAT CQOS9-SEritnNine C MU s MASM PER UNIT LENGTH OF CAR AT T4AT CWO59 S E C T !lu.lie C VEL e vel.0 CITY AT THE IMPACT FACF(FT12e C e e STRAIN RATE FFFECT COEFFICIENT13e C n MEANS NO STRAIN # ATE EFFECT14e C

150 C EYPl! CIT EULER IMTEGRATt0N METHnD IS ItSEO TO CALCIILATE niiPLACEME'T16e C VFLnCITY AND ACCELERATION AT $UCCES91vE TIME STEPS.ITo C

1Ae C INPUT 8 Yo a INITIAL DTSPLACEMENT19e C v0 e INITIAL VELnCITY2no C TI e INITIAL TIME21e C TF e FINAL TIME22e C nELT s SIZE nF TIME FOR INTEGRATt0N23e C CLEN e CAR LFNGTH2mo C Ipa e PRINT AT EvFRY IPW 9fEPSPie C Not e NtiM R E R OF ENTRIES IN TAMLF PC2Ao C Nn2 m NUMRER nF ENTp!Es 19 TA9LE MUPfe C Fnt a PC ARRAY MULTIPLIER2me C FD2 e MU ARRAY MULTIPLIER29e C R e STRAIN RATE EFFECT COEFFICIEdf30e C

3t* C -------------------------------------------------------------------3?e C

199

_ _ _ _ _ _ _ _ _ -

lie Soes00 TINE INPUTJoe COMMUN/ INPT /20,0Zo, T !, TF ,0EL T , CLEN, f PR, N01, N02, F01.F 02,W. vC,35e e PC(201 PCM(20).MU(20).MOVfin),TPCf20),7*U(231,so,nro,rM,vd3As e . tiL F ,4 L M E , K L H P . Y E h; . Z E N

37e CnMkON/LPCNT/L0nP3Pe OATA db/8/$9e NEAL MO,Mur,KLFE.4LMPene ntMFNSION ITITLE(201nie Lo0PsLDOP+147e 9 Fan (S.1007.ENDaln2) f f ! T r.4 5e 1007 FORMAT (7044)eue IF(LOOP.LE.1)45. eWEAn(5,1001.EN0sto2) 70,070,T!.TF,DELT,CLEN.!PH.Nnt.ND2 F01.FD2,44e eVC47* 1001 F0WkATC)ene frfLOOP.GT.1) WEAD(5,1001) 07009. vetTEf6,1005)ice 1005 FDRMAT(1Ht)5te We!TE(6,1nnA) !T!TLE57e 1008 FORMAT (ar,'eseee ',20A4,//)53e wp!TEf6.tn07) 20.nZn.T!,TF,0ELT.CLE4,fPR.FDt.FDP.4,1CSee ton 2 FnWWAT(10v e'!Nff!AL OfSPLACEMENT s', Fin.0,/104S%e e'fNfTfal. VELPCITV s'.F10.4./ing.l!N!ftal Tf"F s', Fin.u./Inv.She e' FINAL TIME s',Flo.a / lor.' TIME INCREMENT s',Flo.5.57e */10v.' CAR LENGTH sl.Flo.4,

808!NT TIME INTERVAL s',I4, |

54e e/10r ee/107.'PC MULTIPLIER s'. Fin.4,/ tog.lMll MULTIPLTER s'. Fin.4 'See

hoe e/10Y,'5 TRAIN RATE EFFECT COEFFICIENT s',F10.4,ble */10x.' VELOCITY CUEFFICIENT s'.F10.4)62e IF(t00P.LF.1)63 eREA0(5.1001) MEN, ZEN60e I F (L O O P , G T .1 ) MENexENe32.7 I

65e =RITEf6,1003) XEN,2FN6Ae NFNorfN/3P.267. 100 3 FOR" A T (/10Y , 8 M A SS OF ENG Ik'E s ' , F i n.4,has e/10y,'OTSTANCE OF ENGINE FRnN FRONT OF Cap s',F10.4)69 RFan(5,10nti V0,0Y0.rM.rt.ULF.<LME,WLMP76e IF(VM.LT. 001) GO in_ tut , , )7te WRITE (6,1020) WO,0X0 vM.xx.ULF.kLME.KLMP72e 1020 FORMAT (//,10X,' INITIAL WALL DISPLACEMENT e '.F10.a./10r,73e et!NITIAL WALL YELOCITV si,F10,4,/,10Y,' MASS OF WALL s',Flo.4,7ee e/lov e'8PRING CONSTANT OF WALL s'.Flo.475e e/10Ye'blTIMATE STRENTH OF WALL s',F10.4,

( 7he e/loy,' TRANSFORMATION FACTnR'IN FLASTIC GEG!nN s'. Fin.4,77e */10Y 'TRANSPORMATION FACTOR IN PLASTIC REGION s',F10.a)78e MMsWM/32.279e 161 IFfl.00P.GT.1). RETURN

i 80. REA0(S loot) (PC(!).!st.N01)Ble wPITEf6.1011) (PC(!).!st.wnt)82e 1011 FnRMAT(////10W ' PC s ' ,10F i n . 4 (/15 v ,10F i n . 4 ) 1ole REA0(5,tont) (PCX (!) . ! s t , N01 )See wn!TE(6,to12) (PC Y (!) , I s 1. ND 1 )8Me 1012 FORMAT (/10X,'PCr s',toFio.4,(/154,10Flo.4))44e WE A0 (S.10n!) (Mtf( f) . !s t , ND2)a7e *p!TE(6.1613) (MufI),f=1.kO2)

\200

_

_ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ . _ _ _ _ _ _ _ . .

,

Ace i nt i FnN> AT (/inY,' Mti s ' ,16F i o . 4, ( / t m r ,10F l o .41 )89e HEA0(5,10nt) (Mitr (!),Is t ,NDP)

90e wp!TE(6,1014) (MuY( f) , Is t , Ne ')'

91e 1014 FDWMAT(/10r lMilY s'e10Flo,s,(/15r,10Flo,4))e

ope on a Jet,H0191e a TDCfJ)sPC(J).F0194e DD 3 Jai,NO2

95c 3 tbil(J)sMU(J)/12.2eF0296o N F TilN N97e 102 END FILE NU9Ao STOP99e EPO

33e SitB00Ul f NF SOL 130e CnMMON/INPT/Z0,020,T!,TF,nELT CLENetPR,N01,NO2,F01,502,R,VC,

Pr (20) , PC Y (20) , MU (20) , MilY (20) . TDC (20) , TMU (20) , Y0,0 Y0, YM, X N35e e

36e e .IILF,NLME,KLMP,xEN,2EN

37e R F AL ML , M11Y , MilF , Mila , K LME , KLMP

34e OATA NU/8/39e ASSIGN 21 TO NGOene FwAYso,

ele AREA =042e uns7041e vn=0ZOese CALL INTGRT f f"U.Mtir , NO2,0. , CLEN. TH A SS)45e TPAS$s(TMASS+ YEN)e32,2Che We!TE(6,4001) THASSC7e 4001 FnHMAT(/////,71,'em TOTAL MASS OF CAR (K.LBM) s',F10.4)44e C40e C SFT 11P A PLOTTING FILEShe C

51e HFLTTsDELTe1000,

52e HCMuse53e we!TEfhlt) NCHN,DELTT5ee C

550 w9tTE(6,1609)

56e innq FnRMAT(tH1, thy,'REACTTON(KIP)',64.'ACCELERATIOufG)',17x,57e e ' T I M E f M-SE C) ' ,6Y ,8 0! ST A NCF (I N) ' ,10 X , l V El.nC I T y (F T /SEC ) ' , /)

SRe TfMETalf59e OfSTToro600 VELTsVOble OwsYEN67o Ns(TF=TI)/DELT+1,163e ICNTs060e Is06%e 00 1 Jn),466e CALL INTE0P(PCY,TPC.DISTT,PCF,N01,DllH1.DUM2)6To CALI INTG8T f 7MU, M1JY, ND2,'QISTT .CLEN NIIF )6Ae AvELT=AaS(vELT)

201

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -

4

)69e F8RsR+.02eALOG(AVELT)70s !F(FSR.L

IF(R.LT.Jil.3 FaRs!.7te 001) F8 Ret.72e ACCTsePCFeF8A/(MUF+DM)73e- 13 CONT!kUE'fee 0!STs0!877e12. ,

| 75e VElevtLT I'

765 ACCsACCT/32i277e T ! M F. s T I M E f * 10 0 0.7Ae CALL INTERP(MureTMU,0!STT.MHA.N02.00Mt.011M2179e FORCEsPCFeF34+MllAeVELTeetevC80s ARE4sAREA+FORCEe0ELTSte IF(FORCF.GT.FMAX) FMAvsFORCE ,

A t e- 1003 PORF A? (16Yi-E12.6,10Y,E12.6.10Y.E12.4.10Y,E12.4.10Y F12. A)83e WRITE (hu) FORCE.ACCe vtL,0!SThae IF(ICNT.LF. 0)45e- ewn!TE(6.1003) FORCEeACC T!ME.0187, VEL46e !F(!CNT.LT.0) GO 70 10187e 11 O!STT80!877+VELYe0ELT+.5eACC7e0ELTeelA A s- VFL T * VEL T + A CCT *0 El.T'49e TIMF.TeTIMET+0ELT

- 90s TF (0!ST T.LE. ZEN) GO TO 319te GO 70 KGO.(21.31)97e C93e C ENG!NF HIT 8 THE WALL. SAVE NECESSARY INFORMATIONS94e C VFLfMPsVELOCITY OF' CAR AT IMPACT OF ENGTNF95e C vis!MPUL8E PWODUCEO RY FNGINE96e C ftMPsT!"E AT !MPACT OF ENGINE9fe C94e 21 ohs 099e VFLIMPavELTtone YfayENeVELT10l* T!MPs?!METet000. I

finPe ASSIGN 31 TO KGO103e 31 IP(VELT.GT.O.) GO 70 12 '

tote ICNTest105e GO 70 13

.

10Ae 12 !CNTs!CNT+110's IF(TCNT.EO.!PR) ICNTs010Ae 1 CnNTINUE109e 101 CONTINUE110e AREAS &hfA,FORCEe0ELT-tile WRITEf6,2001) AREA117e ? cot FORPAT(////,2Y 'eeeet AREA HNOED F00CE= TINE CURVE s' F. n.a)tile wo!TEf6,3001) y!, VEL!MP.TIMP114e 1001 FORWAT(//10Me'!MPULAE PR0nuCEO MY ENGINE s'.F10.4flie e/ tor,'!MPACT VELOCITY s'.F10.e.116e e/ tore' TIME AT IMPACT OF ENGINE of.F10.8)117e WRITE (6e3002) FMAYttAs 3002 FORM AT (10ri 'M A Y!M'IM- FORCE s ' .F10.8)119e R F Ti> R N

120e Eku

i

202

.

.

- __-

. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ . _ _

to AUBROHTfNF SQLt . . .

2e COMw0N/fNPT/20,0!n,T! TF nti.T. CLEW, IPR,N01.N02,F0teFn2 U VC,PC(20).PCV(26).MU(20).MHvf20).TPCtan).TPHf20),vo,ntn,vM,1<3e e

,HLPetLME,tLMP. WEN,2EN.,es e

io RF Al MD.MllX e MllF,MU A.KLME.KLMPho DATA Hil/ 8 /To CAe C wR!TE HEADEN ON PLOT FILEto C

ino. DELTTsDELTe1000.tie NCHNef12e > R I T E (hll) NCHN.DELTT130 Cleo C FINE TOTAL MASS OF CAR150 C

160 .C ALL...!N1GRt(TMU e MUX hD2.0..CLEN.'TM ASS), , ,

17e TMAS$stTMASS+rEN)e32.2too wn!TEf6.en01) TMAS$19o anni FOR*AT(/////,7te lee TnTAL MASS nF CAR (W.L9M) s'. Fin.4)

200 C

210 WRITE (6,1001)220 1061.F.ORMAT(tH1,TX '.T!ME'e9xE' FORCE 8,t3x|'Z', 12r|80Z'.ttv 'nDZ'.

~

e

21e *13v 'v'.12v.90Y',11Y.'unt')24. C

25e C 7 s AMCllNT OF CRU$H OF CAR2Ae C y a WALL DISPLACEMENT27e C VFN e MASS nF ENGINE24e C VME e EQUfVALENT STRUCTURE MASS20e C

Ine AREAsn.31e FSAvs032e TfMEsT!33e ympn38e ysyn1%e 07enZnThe nyanto

1Te VFN7svLN34e vlt s UL F / X K39e twEsxMetLMEane ykYe0.

. .

ete Ns(TF=TI)/nELT+1.42e ICNTan43e ASSfGN 41 7n IGnsee C ALL INTGRT (TMlle MllY?ND2.'0. .'CLEN!TM ASS)

~

49e ASSfGN St To KG46e ASSIGN 81 TO NGnate ASSfGN 91 TO N70cae nn g Jag,na0e G0 to AG,(51.52)50e 51 CALL I NT E R P f p C r e T P C ,7. PC F ,gNnt.OllMt nUM2)

, ,

5te CALL INTGRT(TMU,MllX,N02.7.CLEN.MUF)52 CALL I N T E RP (Ml't ,7*U Z. MU A .'Nnt ,0yM t ,0tiw2)ble vMCsT* ASS.MitF

203

______ ______ _

__ _________ _

5ee An7sAR$(07)59e FSRsN+ n2eALOG(A07)She !F(FSR.LT.t.) FARet.57e IF(R.L1. 001) FARet.See C FORCEsPCF*F8R*MUA*(07ee2 eve +0re0Z)56e C 00rs(FORCE.YKY)/rMEAne c DDZs-PCFeFS4/MUF 00rhis nnys(PCFeF84+MUAe0ZeeParKY)/(YME+rMC)6Pe OnZe=PCFeFSR/(MUF+rENZ)=0Dr63e FORCEarNEeDor+rKr64e 52 CONTINUE

~

65* TTMOUTsTIMEe100066e 77sFet2.6Te Truret2.. ..6Ao Tnors00r/32.269e 7007s007/32.270e IF(FORCE.GT.FMAY) FMArsFORCE7te AREAsAREA+ FORCE *0ELT

~*72e WRITE (Nt!) FORCE.Tr.07e'T007.Tr.nr.70DrT3* !FCICNT.LE.0)._74e own!TE(6.10nP) T I M O U T . F O R C F . T 7. n z .' T 00 Z . T r . n r . T o o r79e 1002 FFRMAT(2r.8E14.6)The 11 IF(TCNT.LTen)._ GO 70. tot _77e ver+0reDELT+.5e00renELT**PTAe 7sZ+07e0ELT+.5e007*0ELTee279e nyopr+0nte0ELT40e nysnZ+0nZenFLTAto TTMFsT!HE+DELT87e 1F(7.LE. ZEN) GO in 7193e CAa* C THE ENGINE HITS THE WALL. 00!NG PROPER TRANSFnRMAT!nNS. SAVINGA5e C riefMPULSE PRODUCEO BY ENGINE

i

84e C fnysRATF OF CRUSH OF CAR AT IMPACT nF ENGTNE87e c MnysvELOCITv DF WALL AT IPPACT OF ENGINEAAe C TTMPsTIME AT IMPACT OF ENGINEA9e C96e Gn TO IGO.(41.21)gle 41 rLMsNLHF92. ntFer*L xMeKLME93 TF(AAS(n!F).GT..nn01) rLMs4t MPgoe f or s (VEve (Ov +07) + (rLMe rM+rMCl eDr) / (XEN+ rLMe rM+v MC)99e Tn7s02

i 9Ae Snysor

97e YMarM+rENgme rFN7sn.9oe nyonr+D7 70xone nysTOYOle vierEAnnZ02e TfMPsTIMEet00003* ASSTGN Pt 70_IGOOne 71 wurerketraro)0%e s*EarMeKLME06. IF ( ABS (vK r) .LT.ULF) GO TO KGO (et.'87)

~

i

204

_ _ _ _ _ _ _ _ _ _ -

- _ _ _ _ _ _ _ _ _ _ _ _ _

OTo C

OAo C IJLTIMAff (!MIT OF STRUCitl#E REACHE009e C

too !stGNetWM/AM8(VRW)tto vrretS!GNeULFtPo rost-!SIGNevit1,t o zwEsxMe<L*Ptoo GO 70 KGO.(81 82)lio Al IF(nZ,GT.0) GO TO 12

1Ao C

ife C CHUSH OF CAR STnPPED1Ae C

too AREAsARFA.FORCEe0ELT2no ASSTGN 52 70 KG

A2.,0..KGO .. ._..... _., ...12to ASS 7GN T

122e 42 !F(DX.GT.0.) GO TO KTO.f91.92)123o ICNTeet1240 GO TO 1125e C

12Ao C CAR BnDy AND STRUCTURE MARS NovE TOGETHER12To C

1280 91 OZs0.1290 00Zso.1300_ f0RCEs0..131o vlMsMLME132o n!FoxME.KMeKLME1330 IF(ABS (n!F).GT..on00..*LMaKLM813ao VMsTHAssern1350 XMEarMayLM

134e . ASSIGN 92.TO.KT.013Fe of noxe vnv/VME13Ao 12 TENTafCNTot139e IF(TCNT.EO.!PR) ICNT_sp1400 1 CnNTINUEisto 101 WRITE (6,1005) AREA142o 10n5 FORMAT (////.2X.'oenee ARE A' llNDER FORCE = TIME CURVE s ' .E tn.a)141e WRITE (6.tn03) v!.707.sov.TtHP1aso 1003 FnR>AT(//10Y.'!MPilLSE PRunUCEO My ENG!nF s'. Fin.4

185o e/ tor.'C8USMING VELOCITV.0F CAR AT IMPACT OF ENGtNE es.Flo s.ta6o e/30s.'STRi!CTURE VELOCITY AT IMPACT OF FNGINE es.F10.4lato e/ tor.' TINE Af IMPACT nF ENGINE s'.Flo.4)tone so!TE(6,'inge) FMAY , FnRCE s'. Fin.a)140. Inne FnRMAT(Inv.'MAYIMMM

. , ,

150e FND FTLE sti151e G F TitR N

952* Fwn

205

_____ -

i

SU8 ROUTINE INTGRT(FW,y,N,X0,X1,FF)C-

C INTEGRATION OF A FUNCTION ENTERED IN TA8ULAN FORM, LINEARC FUNCTION BETWEEN POINTS ARE AS8HMED.C Fu s. TABLE OF FUNCTION VALUEC 1 s TABLE OF CORRESPONDING VARIABLE VALUEC N e GIMEN8!ON OF TA8LEC Xo e 8 TARTING POINT OF INTEGRATIONC X1 e END PO!NT OF INTEGRATIONC FF a FINAL INTEGRATED VALUEC

O!MENSION FY(N),X(N)FFs0.

C

C FIND THE FUNCTIONAL VALUE AT wo,X1 AND THEI8 LOCATION IN THE |C ARRAY.C

CALL INTERP(X,FW,X0,F0,N,TLO,IVO) *

CALL INTERP(X,FX,X1.F1,N,IL1,!U1)C

C INTEGRATINGC

INQa!Lle!UQIF(IND) 11.12,12

C

C X0,v1 IN THE SAME STRIPC

11 FFs(F0+F1)*(X1=x03/P.RETURN

C

C 10,Y1 IN ADJACENT STRIPC

12 F F e (F0+F X (IHO)) * (Y (!UO)-xn) /2.+ (F 1+F X (!L1)) * (r1=r (IL1)) /2.IF(IND.EQ.0) RETURN

C

C X0,X1 IN SEPERATED STRIPC l

ILs!U0|IusIU0+1 '

00 1 !si,INDP F s FF+ (F X (IL) +F Y (!U)) * (Y (!U) =M (!L)) /2.ILs!UIUs!U+1,

1 CONTINUERETURNLNO

I

206

__ _. __

_ - _ _

.

|

|

SU$ ROUTINE INTERP(x,y,3X,3y,N,IL,10) |C TWIS 8UOROUTINE-00E4-TME LINEAR INTERPOLATION TO PIND THE VALUEC OF SY CORMESPONDING TO THE VARIABLE SX. Y IS AN ARRAY CONTAININGC THE CORRESPONDING FUNCTIONAL YALUES OF X.C

C NaO!MENSION Ufi THE ARRAYC

COMMON /PP!/PI.O!MENSION X(N),Y(N)

C

C CHECK THE I.!MITC

IF(SX.LT,X(1).0R.SX.GT.X(N)) GO TO 11C

00 1 I s t! , N

IF (S X .G T . X (!) ) GO TO 1ILo!=1lustGO TO 12

1 CONTINUE12 Sy s (SX.X (IL)) e (y (IU) .y (IL)) / (X (IU) .X (IL)) + y (IL)

RETURN11 hRITE(6,1001) SX

1001 FORMAT (10Xe' X IS IN UNPROPER RANGE WHEN Er4TERING SUBR0l' TINE INTL*P. Y s8,E12.6)

STOPEND

|

207

___ __ _ _ _ _.

___

APPENDIX DWALL PANEL PARAMETERS

1

D.1 DESIGN VARIABLES

The structure considered in this report is a concrete wall with reinforcingsteel bars running vertically and horizontally at both faces of the wall(Figure D.1). The design variables are:

e Range of dimensions

C = minimum cover for vertical reinforcement C = 1.5 inchy

Ch = minimum cover for horizontal reinforcement C = 1.5 + d inchd = diameter of vehicle steel bara = 10 - 36 f tb = 10 - 36 f th = 12 - 36 inches

e Type of steel bar associated with different thicknesses ofwall

1

Thickness Diameter '

of Slab Type of of BarsDirection (inch) Bars Number (inch)

Vertical 12 . 15 8 1.00Vertical 18 - 36 11 1.41Horizontal 12 , 15 8 1.00Horizontal 18 - 36 10 1.27

e Spacing

The spacing of the rods is such that the percent area of steelin the vertical direction is 0.75 percent and in the horizontaldirection is 0.5 percent.

D.2 STIFFNESS FORMULASI

D.2.1 Stiffness Formula

The wall is simulated by an orthotropic rectangular plate with fixededges and is loaded partially at the center (Figure D.2d). The stiffness,K , is obtained by considering the stiffnesses of three other cases andcombine them together. Those three cases are:

208

- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

. _ _ _ . __

k a 4r

O O

b.

O C

M I

e C,W MWd

I -* C l&h

h

R

Figure D.1 Concrete Wall

2094

_

_ _-

P \

Po

L L L 1 L e < v g--> - > r

| q p__ a/2-4- a/2 -.I,e a

,r ,r

b/26 &

b/2v. a

(a) (b)

PP, n

< l 1 1 1 1 c 4 e,,, ,...,

> - a rj k a d[- a

,r r

b>x b

J' :..

yv

(c) (d)l

l

Figure D.2 Load Cases for Rectangular Plate

I

210

(a) Isotropic rectangular plate with fixed edges, unifonn load(Figured.2a)

(b)Isotropicrectangularplatewithfixededges, concentratedloadatthecenter(Figured.2b)

(c) Orthotropic rectangular plate with fixed edges, unifonnload (Figure D.2c)

For the formulas that follow, the Poisson's ratio of the plate is taken tobe 0.3.

e Case A: For uniform load on an isotropic rectangular plate with fixededges:

4Pa*=C (0.2-1)max 1 3

Eh

where u = maximum deflection at center of platemax

E = Young's modulus of plate

h = thickness of plateC = coefficient depends on the value of b/a

g

b/a 1.0 1.2 1.4 1.6 1.8 2.0

C 0.013 0.019 0.023 0.0255 0.027 0.028-1

or Eqn(D.2-1) can be written in terms of the moment of inertia of thecross-section of the plate as:

4Pa0

w =C (D.2-2)max y

EI

where I = moment of inertia of the cross-section of the plate.

From Eqn(D.2-2) we can write the stiffness of the plate as:

P abg " EIb (D.2-3)KA"w C *3max lFor calculation of I, see Section D.2.2.

*The fonnulas for the Cases A, B and C are taken from " Theory and Analysisof Plates " Szilard, R. ; Prentice-Hall Inc. , Inglewood Clifs, NJ,1974.

t

211

;

e Case B: For concentrated load on an isotropic rectangular ~ plate withfixed edges:

Pa=C (0.2-4)" max 1 0

3Eh (0.2-5)D =

22(1-v)

where v = Poisson's ratio

C has the following value:1

b/a 1.0 1.2 1.4 1.6 1.8 2.0

C 0.0056 0.00647 0.00691 0.00712 0.00720 0.00722g

Again, Eqn(0.2-5) can be written in terms of the moment of inertia of thecross-section as:

EID= (D.2-6)22(1-v)

Then we can write the stiffness of the plate as:

P D (D.2-7)I B"w 2

',

max Cal

e Case C: Uniform load on orthotropic rectangular plate with fixed edges:|

The displacement of any point on the plate can be expressed as:

2 22 2

49P x_ y,g (D.2-8)8 4 22 4

7D b + 4Ba b + 7D ax y

where Exl'xg ,

2* 12(1-v )

EyI'yD =

2Y 12(1-v )

B = 1/2(vD + vD + 4D }x j t

I212

._ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

'I'*+I'Y 1D =Gt xy, 2 < 12;

f= i ExEyGxy 2(1+v)

I'x = moment of inertia of cross-section normal to the x-axisI'y = moment of inertia of cross-section normal to the y-axis

For reinforced concrete plates:

Ex = Ey = Ec = Young's modulus of concrete

For displacement at the center of plato, x = 0, y = 0, from the above equa-tion, we have

49P 44(0'2-9)"o " 2048 4 27D b + 4 b + 7D a

x j

Therefore, the stiffness of the plate can be written as:

4 22 4P ab 7D b + 4Ba 6 + 7D ag = 2048 x y(D.2-10)K = -

c w 49 33o ab

e Case D: Uniform load partially loaded at the center of an orthotropicrectangular plate with fixed edges (Figure D.2d)

To obtain the stiffness for this case, it is assumed that the stiffness ofthe plate varies linearly from the concentratedly loaded c5se, Case B, to thetotally uniformly loaded case, Case A. It is also assumed that for casesof tne same area of partial uniform load, the ratio between the stiffnessof the partially loaded case and the uniformly loaded case are the samefor isotropic and orthotropic plates. Based on the above assumptions, wecan write:

KDI " (K ~ K ) + K (D.2-11)A B B

KKC DI (*~KD* KA

where K = stiffness for isotropic plateDI

K = stiffness for orthotropic plateD

213

_ _ _ _ _ _ -

__ _ _ _ .

D.2.2 Calculation of Moment of Inertia for Reinforced Concrete Plate

Converting the area of steel to concrete (Figure D.3) the following equa-tions can be written:

(bkd)y+ (n-1)A's(kd-d') = nA (d-kd) (D.2-13)s

,b(kd)3 + (n-1)A's(kd-d')2 + nA (d-kd)2 (D.2-14)IC 3

whereE

8n = - - -C

E = Young's modulus of steel3

E = Young's modulus of concretec

A = area of steel in tensions

A's = area of steel in compression

I = m ment of inertia of the cross-sectionC

Eqn(D.2-13) is used to solve for kd which is then put into Eqn(D.2-14) tosolve for the moment of inertia I -C

D.3 ULTIMATE LOAD FORMULA

To obtain the ultimate load (maximum resistance) of the wall, first the ul-timate moment of the wall is calculated by using Eqn(D.3-10) or Eqn(D.3-11)and then Table D.1 is used to obtain the ultimale load.

i D.3.1 . Calculation of Ultimate Moment

To calculate the ultimate moment, we assume that the reinforced concreteplate is bent such that the steel bars at the lower part of the cross-section (as in Figure D.4a) have been yielded. From Figure D.4b, doingforce and moment balance, we have:

T = C + 0.85f 'wc (D.3-1)y c

M = C (c-d') + (0.85f 'wc) h + T(d-c) (D.3-2)1 c

where is crushing strength of concrete

I214

.. .

| | ||||1li| 1111I||1.||1| a

l

a sr it xuAeN d

s g ,k

fg ,A i,

A d

)1

' '- 2n ! ' '

( '

" ' g' ' n' ' i

i ' dn

' e' B

r'

e'd

' n'

U

eb ' t

as'

i A Pl

n'

e'

t' e

r' c

n' o' C

i '

' 'des i ' c

'A i '

or

i '

f\'d -ir

) ' n1ih- 2 en R(

rof

marga

O O i

D

aer

A

O O 3

D

eru

O O gi

F

~:

|I1

.

.

k w :! 0.85f'c

O O O Ih :I"c

1

c 2 0

1 n.a. p-.n.a.

:d

5m

" TO O O :

(a) (b) (c)

Figure D.4 Force Diagram for Reinforced Concrete Plate Under Bending

-. .

. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

. - . . _ _ _

but T=oA (D.3-3)ys

( d')C =aA = E csA =EA (D.3-4)g 33 s s ss p

where o, = yield stress of steel

A = area of cross-section of steels

E = Young's modulus of steel3

Put Eqns(D.3-3), (D.3-4) into D.3-1 and solve for C, we have:'

,o , -,

E+PsC = d'( '0.85f'c,) (D.3-5)E +P,s dp a,,

whereA

p=d'

Note that if < 0.8dp

*y dpd' O.85f'c < II

then C decreases with increasing p.

At the limit as p + 0 C + d',

C + rd'p+= ,

where

o

r = [ 0.85f'c

From Eqn(D.3-1) we have:

C =oA - 0.85f'c wey ys

y s .l0.85f'c we dd' "

(D.3-6)'

=oA c A dd,.ys

" "y^s ~

.

217

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ -

At the ultimate load condition, as p + 0, c -* d', we have :

= o A, 1 - k' (0.3-7)C1 y

But for r -* 1/2, the magnitude of C1 wculd be greater than ayAs which isimpossible. In this case, it means that the yield strength bf steel isreached before p becomes 0. In this case we have -

A (D.3-8)C1 " ~"y ,

PutintoEqn(0.3-6)andsolveforC,wehave

C = 2rd' (D.3-9)

Figure D.5 shows the relationship between C and p.

Then Eqn(0.3-2) is used to calculate the ultimate moment by using the cor-responding values for C1 and C for r > 1/2 and for r < 1/2.

For r >_1/2:

1+h -1 (D.3-10)M =A du sy

For r < 1/2:

= A c d 1 + h (1 - 2r)' (D.3-11)M3yu ,

C

r>1g

d, r2 = 1

1/2 < r3 * I|

2r d'4

r < 1/24

p

Figure D.5 Relationship Between r, e and p

'

218

- _ _ _ __ _ _

__ . _ _ _ . -

,s>,,,,,,

, ,

I 'e; a,

',,,,,,f1.. .

L b ---,1

TABLE D.1 MAXIMUM RESISTANCE FOR TWO-WAY SLABS:FIXED FOUR SIDES, UNIFORM LOAD

a/b Maximum Resistance

1.0 29.2 Mu

0.9 27.4 Mu

0.8 26.4 Mu

0.7 26.2 Mu

0.6 27.3 Mu

0.5 30.2 Mu

where

M = ultimate moment capacity per unit width at center ofu long edge.

Reference:

" Introduction to Structural Dynamics," John M. Biggs, McGraw-Hill,Inc., 1964.

219

_

_ _ - _ - - - - _ _ . . - . _

D.4 EFFECTIVE MASS

The structure shown in Figure D.6a could be approximated by a one-degreesystem with an equivalent forcing function, Fe(t), an equivalent mass, Me,and an equivalent spring with stiffness Ke. The equivalent system isselected so that the deflection of the concentrated mass is the same asthat for the central point of the plate. The quantities of the actual sys-tem and the equivalent system are related by transformation factors. Theyare:

M

K = * -M M

t

Ye

L " T-t

k R

K = e_ , MeR k R

M

and the resistance factor KR must always equal the load factor K . There-Lfore, the equation of motion can be written as:

K *

Mt Lx Lt(D.4-1)or

i

K M R + kx = Fgg t

whereKM

Kgg =7L

For a fixed rectangular plate, K ' K and K are shown in Table D.2.L M g

220

_ _ _ _ .

IlII1 I

)t( ee K

F /

/)v M b

/s(

metsy

S

eerge

D-en

Otn

, e,

la

" viuq

g' . Ei

6ov D

er

t e ug

F i' F'

n

)y a(

a

f y

a

t uM

my

|o

- _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _

|

iis,,i s i ii e .

I 'a| , , , , , ,e kTABLE D.2 TRANSFORMATION FACTORS FOR TWO-WAY SLABS: '

FIXED FOUR SIDES. UNIFORM LOADkr--- b ---W

Strain Range a/b Kt Kg KLM

1.0 0.33 0.21 0.630.9 0.34 0.23 0.680.8 0.36 0.25 0.69Elastic 0.7 0.38 0.27 0.710.6 0.41 0.29 0.710.5 0.43 0.31 0.72

1.0 0.33 0.17 0.510.9 0.35 0.18 0.510.8 0.37 0.20 0.54Plastic 0.7 0.38 0.22 0.580.6 0.40 0.23 0.580.5 0.42 0.25 0.59

Reference: " Introduction to Structural Dynamics," John M. Biggs, McGraw-Hill, Inc., 1974.

I

I

i

222

. .

___ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

D.5 CALCULATED VALUES

In this section, the stiffness and the ultimate moments for the 401 designcases listed in Table 5.1 are listed in Table D.3. These values are calcu-lated by using the formulas presented in Appendixes D.2 and D.3. In TableD.3, the variables have the following meaning:

XA = a = column spacing (Figure D.2)

XB = b = floor spacing (Figure D.2)

AK = K = stiffness of isotropic rectangular plate with fixedA edges, uniform load (Figure D.2a)

BK = K = stiffness of isotropic rectangular plate with fixedB edges, concentrated load at the center (Figure D.2b)

CK = K = stiffness of orthotropic rectangular plate withC fixed edges, unifonn load (Figure D.2c)

DKI = K = stiffness of isotropic rectangular plate with fixedDI edges, partially loaded (Figure D.2d)

DK0 = K = stiffness of orthotropic rectangular plate withD fixed edges, partially loaded (Figure D.2d)

ULTM1 = ultimate moment of plate in the vertical reinforce-ment direction

ULTM2 = ultimate moment of plate in the horizontal reinforce-ment direction

223

______________ _ __

_ _ _ _ _ _

TABLE D.3 THE STIFFNESS AND ULTIMATE M0MENTS OF WALL FOR THE DESIGN CASES

[ %/V F ;mh gtj ,), __ -,_ 7.),'

- * -__.,

' " "COVER = 1.5 (IN)

[ OtanE7tR OF $7tEL (IM) 1.4100 1.2700300w |t-seta-OP-STFtt 7w-TtwS10w/PT-tt) .iiss .s"

, ,.3000 )1 ANtA 0F STEEL IN COMPRESS 10N/P7 ft) 7500 * ' 4

.g* ~

ttT*fwStew tv-tMPact sRE*177i - 5s0000 Y 2.609u ,,

; 9o.-,

' "

O ,, | sy

....................................................................................................................... ,,

p,

) ITHICahtes nF MALL (twt e In.n000 --"

entA 07 S7fEL. COMPRESSION IN E.7 DIRN. (30.tN) e 1.6800, iTosssa.utss'

le0000 V . ' #

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_ _ _ _ _ _ _ _ _ _ _

APPENDIX EEFFECT OF TEMPORAL LOAD DISTRIBUTION

ON STRUCTURE RESPONSE

E.1 ELASTIC STRUCTURE

In this section, the effect of three kinds of load distrubution (FiguresE.2 and E.3) on one-degree undemped elastic systems is considered. TheF1 and td are varied so that the area under the force-time curve is keptconstant. The following equation is used to find the maximum displacementof the structure (Figure E.1) under various loads.*

y,,x = (DLF),,x [F (E.1)

where DLF = dynamic load factor

k = stiffness of springF = peak force of loady

k

M M.

Figure E.1 One-Degree Undamped Elastic System

Three tables are constructed for the three kinds of load (rectangularload having zero rise time, triangular load having zero rise time, andisosceles triangular load). In the construction of the tables, it ischosen for convenience that

k = 1.0 lb/ inchT = 1.0 sec/ cycleI = 0.5 lb-inch

whereT = period of structureI = total impulse of load

*" Introduction to Structural Dynamics," John M. Biggs, McGraw-Hill, Inc.,1964.

1

. ,

240,

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ .

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- !

|/,-

e- - ---

0.4 -p

/ I .-._

f

l I -- |00.05 0.10 0.2 0.5 , 1.0 2.0 5 10

~

Figure E.2 Dynamic Load Factors of One-Degree Elastic Systems (tJndamped)Subjected to Rectangular and Triangular Load Pulses HavingZero Rise Time

1.6

/'_ N1.4

~

) \''' ~

| \ p(/ \ /- N

,.o vf --

I jg o.s9 j z .-

0.6 -

-

I / !'

0.4I

q_

0.2b

IOO 1.0 2.0 3.0 4.0

tg/T

Figure E.3 Dynamic Load Factor of One-Degree Elastic Systems (Undamped)Subjected to Isost.eles Triangular Load Pulse

241_

----------m____ _%.____ __

__ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

TABLE E.1 TABLE E.2 TABLE E.3

MAXIMUM DISPLACEMENT OF ONE-DEGREE MAXIMUM DISPLACEMENT OF ONE-DEGREE MAXIMUM DISPLACEMENT OF ONE-DEGREEUNDAMPED ELASTIC SYSTEM UNDER UNDAMPED ELASTIC SYSTEM UNDER UNDAMPED ELASTIC SYSTEM UNDER

RECTANGULAR LOAD PULSE HAVING ZER0 TRIANGULAR LOAD PULSE HAVING ZER0 IS0SCELES TRIANGULAR LOAD PULSERISE TIME RISE TIME

= 1 = 0.5 ,H,17 7 ,H,1F1 td td I td td 1 td td

F (lb) (DLF) max Ymax(inch) td/Ttd/T F(1b) (DLF) max Ymax(inch) td/T F (lb) (DLF) max Ymax(inch)1 1 1

b 0.05 10.00 0.31 3.1 0.05 20.00 0.15 3.0 0.25 4.00 0.75 3.00.10 5.00 0.61 3.05 0.1 10.00 0.30 3.0 0.5 2.00 1.28 2.560.15 3.33 0.90 3.0 0.15 6.67 0.45 3.0 0.75 1.33 1.48 1.970.'20 2.50 1.18 2.9S 0.2 5.0 0.60 3.0 1.0 1.0 1.50 1.500.30 1.67 1.60 2.67 0.3 3.33 0.84 2.8 1.25 0.8 1.43 1.140.40 1.25 1.90 2.38 0.4 2.5 1.04 2.6 1.5 0.67 1.29 0.860.50 1.00 2.00 2.0 0.5 2.0 1.20 2.4 1.75 0.57 1.13 0.64

0.6 1.67 1.30 2.17 2.0 0.50 1.0 0.500.7 1.43 1.40 2.0

It can be noticed that for these three cases, the smaller the time interval the pulse isapplied to, the greater will be the displacement of the structure.

E.2 ELAST0-PLASTIC STRUCTURE

The effect of three load cases (an impulse applied at time zero, a steppedrectangular load pulse, and a stepped rectangular load pulse with an im-pulse at the cep) on an elasto-plastic structure is considered in thissection. The characteristics of the structure and load pulses are shownin Figures E.4 through E.7.

E.2.1 Impulse at Time Zero (Case A)

Consider Figure E.4 and Figure E.5:

For y _< y,j, solving the equation of motion

My + Ky = 0 (E.2)

we have ,

yy=fsinut

=i coswtg

where h= = initial velocity.g

For y > y,j, solving the equation of motion

My + R,= 0 (E.3)

we have -R2

y = ppt 3 + y ,t1 coset,) + y l (E.4)e

where

t =t-tg el

Sy,j=jsinet,)

The time at which maximum displacement occurs and the maximum displacementare obtained to be:

Mi,coswtel(E.5)t,= Ry

m

2y, = f p 2 cos wtel + #el (E.6)o

$

243

_ _ _ _ _ _ _ _ _ _ _ _ - _ _ _ _ __ __

- _ _ _ _ _ _ _ _ - _ _ _ _

k

! M M

k

R ~~~~

: : /im i i

i i i

#MYdYe1

Figure E.4 Resistance of Structure

I

r

t

Figure E.5 Impulse Applied at Time Zero

F1

F ~~~~

2 l

i1

t tel d

Figure E.6 Stepped Rectangular Load Pulse

F3

F~ ~ ~ ~

2 liI

t tel d

Figure E.7 Stepped Rectangular Load Pulsewith an Impulse at the Step

244

_ _ _ _ _ _ _ _ _ _ _ - _ _ _ _

. _ _ _ .

E.2.2 Stepped Rectangular Load Pulse (Case B)

Consider Figure E.4 and Figure E.6:

For y 1 y l, solving the equation of motione

My + ky = F (E.7)1

we have

y= (1 - coset)

j= esinet

I Y # Y , solving the equation of motionFor y l de

My + R =F (E.8)m 2

we have

y = h (F -R )t + wt sinut (E.9)2 g g y el + Yel

where

t =t-t1 el

yl= (1 - coswtel)e

For yd s y, solving the equation of motion

My + R =0m

we have-RM

t .10)t 20 2 * Y20y=2M 2 +Y

where

t =t-t2 d

F

- R )(td-tel)2 +p(td-tel)sinut,) + y,)11y20 " 2fi (F2 m

j20"M(F2 - R,) ( td -t,j)+ esinet,j,

245

. _ _ . ..


"520(E.11)t2m " R

m

(E.12)ym" 20 + Y20

E.2.3 Stepped Rectangular Load Pulse With an Impulse at the Step (Case C'

Consider Figure E.4 and E.7:

For y < y l, we have the same solution as in the previous section:e

F

y = f (1 - coset) (E.13)

For y l # Y # Y , we havee d

y=h(F2 -R )tg + p10 l * Y (E.14)2

tm el

where

t =t-t1 el

F

yl (1 - cosetgj)=e

$ esinatel +=

10

For yd 3 y, we have

-RN

t (E.15)t20 2 +Y20y= 2M 2+

where

t =t-t2 d

y20 i (F.2 - R,)(td-tel) + 10(td gj ) + y,)-t*

)20 (F2 - R,) ( t - tel) # 10=d

246

_ _ _ _


N20(E.16)t2m " R

m

y,=h(y20+Y (E.17)20

E.2.4 Numerical Examples

In order to show the relationship between Case A and Case B, Table E.4 isconstructed using the following parameters:

k = 1.0 lb/ inch M = 0.02533 slugR = 1.0 lb e = 6.2832 rad /secm

yl = 1.0 inch T = 1.0 seceF = 1.0 lb t -tel = 1.0 see1 d

TABLE E.4

COMPARISON BETWEEN CASE A AND CASE B

WITH VARYING F2 (Figures E.4. E.5 and E.6)

F I Case A Case B2

(1b) (lb-inch) Ym (inch) ym (inch)

1.0 1.0 71.96 7.783220.0 21.0 7824.3 7628.324.8 25.8 11809.4 11808.630.0 31.0 17049.0 17363.7100. 101. 180961.0 196050.0

A case for the Plymouth Satellite impact on the wall at 80 mph is used tocompare Case A and Case C. The following parameters are used:

247

. ._ _.

_ _ _ _ _ _ . _.

I* = 36.46 kip-sec

F =F = 1133 kip1 2

R = 678 kipm

4k = 4.07 x 10 kip /ftM = mass before tel = 3.26 k-slugy

M = mass after t = 2.64 k-slug2 el

y,) = 1.6658 x 10-2 ft

tel = 0.01034 seet = 0.026 sec

d

The results are obtained to be:

y = 0.2534 ftm

A

y*C

From the above numerical results, it can be seen that displacements causedby load patterns in Crse B and Case C could be larger than that caused byload pattern in Case A which has the same total impulse as in Case B orCase C.

248 .uioo m . m m u .oo,,, cia,,, 3. i _2,,n u , 13

_ _ _ _ _ _ _ _ _ .

-- - - - _ - _ _ - ____ _- _ _ _ _ _ _ _ . _ _ _ _ _ _ _

t.nc e oau 2x i % s c.m m . .. . . . e, ., : , j.

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Automobile Impact Forces on Concrete Wall Panels3 F(ECsPIE NTT. Acct WErd NCo

. 7. AUTHORts) . L. DATE REPORT COMPLE TEDR. L. Chiapetta, E. C. Pang u oni,, | ye aR

January 1982

9 PE RF ORMING ORGANIZATION N AME AND M AILING ADDRESS (sacivar 29 Coort DATE REPORT issVEDChiapetta, Welch & Associates, Ltd. wourn |vsAn9748 Roberts Road June 1982

Palos Hills, IL 60465 s. ft , u,4as

a ttue o ur,*r

D$v$sio$ Y Yn'gY $rin % c M fo^g f " " * '" " ### to. r Ao;E cT/T AsK/ WORK UNIT NO.

Office of Nuclear Regulatory ResearchU.S. Nuclear Regulatory Commission 11. CONT R ACT NO.

Washington, DC 20555 NRC FIN B6609

13 TYPE OF REPOB47 et nico covt REo (lacLPyf daaraf

Technical Report15. SUPPLEMENTARY NOTES 14. (te,v, unia)

16 ABSTR ACT 000 woras or Jessf

The objective of this study was to develop force-time impact signature data for use inthe design or evaluation of nuclear power plant structures subject to tornado-borneautomotive vehicle impact. The approach was based on the use of analytical vehiclemodels to calculate impact forces. To assess the significance of vehicle / structureinteraction for head-on impact force-histories, a lumped-mass model of a reinforcedconcrete wall panel was coupled to a one-dimensional vehicle model for numerous paneldesign configurations within the range of practical interest. Vehicle-structureinteraction was found to have relatively little effect on the force-histories. Thesensitivity of structural response to variations in force signature characteristics wasestablished and idealized impact force-time relations were developed for five distinctimpact speeds ranging from 20-60 meters /sec. The use of these relations produce lessconservative estimat9s of structural deflection, for all impact speeds considered, thanthe currently accepted design procedure.

17. CIE Y WORDS AND DOCUMENT AN ALYSis 17t DESCRIPTORS

17th IDENTIFIE Rs!DPEN-ENDE D TERMS

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