DESIGN OF DOE FACILITIES FOR WIND-GENERATED MISSILES ...

DESIGN OF DOE FACILITIES FOR WIND-GENERATED MISSILES

Geyergy Kuilanoff and Richard M. DrakeFluor Daniel, Inc.

3333 Michelson DriveIrvine, CA 92730

ABSTRACT

This paper presents criteria and procedures for the design of structuresand components for wind-generated missiles. Methods for determiningmissile-induced loading, calculated structural response, performancerequirements, and design considerations are covered. The presentedcriteria is applicable to Safety-Related concrete buildings as a wholeand to all their exposed external components including walls, roofs, andsupporting structural systems and elements.

INTRODUCTION

Department of Energy (DOE) designcriteria [1] [2] often requires that facility designsconsider the effects of wind-generated missiles.This paper presents criteria and procedures forthe design of concrete structures andcomponents for wind-generated missiles.

The two types of effects which must beconsidered in designing for missile impacts arethe local effects and the overall structuralresponse effects. Local effects are dependentprimarily on the hardness of the missile relativeto the target structure it is impacting andconsider their ability to penetrate, perforate,spall, or scab the structure. The overallstructural response of the structure dependslargely on the location of impact and the kineticenergy of the missile.

If the local deformation characteristics ofthe missile or target structure can be determinedaccurately, and the assumption of plasticcollision is acceptable, an applied force timehistory can be developed and the overallresponse to the force can be treated as that for

an impulsive load. If the local deformationcharacteristics cannot be determined accurately,and for all cases of elastic and semielastic impact,the overall response to the force can be arrived atutilizing the principles of conservation of Energyand Momentum.

REQUIREMENTS SUMMARY

The requirements for consideration of wind-generated missiles are identified in DOE Order6430.1A [1] and UCRL-15910 [2]. In addition,specific DOE sites and facilities may providesupplemental design requirements.

DOE ORDER 6430.1ASections 0111-2.3 and 0111-99.0.2 require

that wind and tornado loadings shall be obtainedfrom UCRL-15910.

UCRL-15910Chapter 2 provides definitions and

performance goals for facility usage categories;general use, important or low hazard, moderatehazard, and high hazard. Chapter S provides

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Site-Specific wind and tornado loadings for eachfacility usage category. At DOE sites wheretornados are a viable threat, tornado missiledesign criteria are specified for moderate andhigh hazard facilities. At other DOE sites, windmissile criteria are specified for moderate andhigh hazard facilities.

The wind missiles specified are 2x4 timberplanks, 3 inch diameter steel pipes, and anautomobile. Weight, velocity and height aboveground are specified for each missile, dependingon facility usage category.

DESIGN FOR LOCAL EFFECTS

The Design for local effects must considerpenetration, perforation, spoiling, and scabbing.

Penetration - The displacement of a missileinto the target.

Perforation - The displacement of a missilethrough the target, with or withoutmissile exit velocity.

Spalling - The ejection of target materialfrom the front face.

Scabbing - The peeling-off of targetmaterial from the back face.

Perforation and scabbing are unacceptablelocal effects for Safety-Related structuresserving as containments.

RELATIVE HARDNESSMissile penetration formulas are dependent

on the relative hardness of a missile and target.A missile is hard relative to a concrete target(i.e., missile penetrates target) if Gm > G|, andsoft (i.e., no penetration) if <Jm < Gt; whereOm = average crushing or buckling limit stressof the missile based on net contact area of themissile; and G, = average contact stress requiredto cause local crushing and penetration of thetarget.

For reinforced concrete targets, Gt is setequal to the bearing stress given in ACI 349,

Section 10.15 (0 = 1) increased by the dynamicincrease factor of 1.25 given in ACI 349, SectionC.2. [3]. This results in a value of CF, slightlygreater than 2i£. For purposes of design, let G, =2&

Wood plank missiles are considered spitrelative to concrete targets since the missilecrushing stress (Om=4 ksi) is less than theconcrete crushing stress (O,=2f£= 8 ksi).

THICKNESS FOR HARD MISSILESThe concrete thickness required to resist

hard missiles should be at least 1.2 times thescabbing thickness, t,.

For missiles which are determined to behard relative to a reinforced concrete target, thefollowing NDRC formulae should be used todetermine the missile depth of penetration (x) andthence scabbing thickness (t,): [4]

x = 4KMWd L - H(lOOOd

J.80

X =

. .

KNW

l

lOOOd

.80

-

effective m

, for - i S 2.0d

+ d, for ± > 2.0d

180K = , concrete penetrability factor

firWhere N = missile shape factor (0.72 for flat-nosed missiles); W= missile weight, pounds; f£ =specified compressive strength of concrete, psi;Ac = missile contact area, square inches;x = missile penetration depth, inches; and v0 =striking velocity of missile, feet per second.


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The scabbing thickness (Q is computed d = the smaller offrom the following formulae:

0.2674Vn

J- or .1.07 V.

ii= 2.12 + 1.36 (l\ for 0.65 <S ! £ 11.75d Id) d

i i * 7.91 fii) - 5.06d d I

(it, for 1 £ 0.65

THICKNESS FOR SOFT MISSILESSoft missiles will cause no local

penetration with the exception of possiblepunching shear. However, if it can bedemonstrated by applicable foimulae or pertinenttest data that concrete thickness is at least 20percent greater than that required to preventperforation and punching shear failure, design toprevent punching shear failure is not required.See ACI 349, Appendix C [3].

Concrete thickness to prevent perforationfrom soft missiles can be determined byassuming the missile is a nondeformable (hard)missile. Compute the penetration depth (x) andeffective missile diameter (d) as for hardmissiles and then compute the perforationthickness (t,) using the following equations:

± d, for 1.35 <±£13.5i d I d

3.19 \1 -0.718 \1 d, for ±d

The required thickness to prevent perforation isequal to 1.2 .̂ If the concrete barrier thickness(t) does not exceed 1.2 t,. then a potentialpunching shear failure should be investigated asfollows:

Vp = The smaller of 1.625 AcCm or Wm

(See discussion on RectangularImpulsive Loads Herein)

t = d+c

Where: A,. = missile contact area, square inches;CTm = crushing stress, psi (=4,000 psi for woodmissiles); JJC = ratio of long side to short side ofthe concentrated load; d = effective depth ofsection, inches; fc = specified compressivestrength of concrete, psi; Vp = punching shearload, pounds; b0 = perimeter of critical section,inches; c = reinforcement concrete cover, inches;and t = concrete barrier thickness, inches. Theequation for d is based on a dynamic increasefactor of 1.10, a strength reduction factor (0) of0.85, and an ultimate load factor of 1.00.

DESIGN FOR OVERALLSTRUCTURAL RESPONSE

In addition to local impact effects, Safety-Related structures serving as containments mustalso be designed to resist the overall effects ofmissile impact.

The response of a structure to missile impactdepends largely on the location of impact, on thedynamic properties of the structure (target), andon the kinetic energy of the missile. For wind -generated missiles, the assumption of a plasticcollision between the missile and concrete targetis acceptable. This type of impact ischaracterized by significant local deformation ofthe missile or target. Wind-driven objects whichare hard relative to the target structure, such aspipe missiles, will penetrate into concrete targets.Soft missiles such as wood will deform uponstriking the concrete structure.

If the local deformation characteristics of themissile or target can be determined accurately,and the assumption of plastic collision isacceptable, the applied force rime history can bedeveloped and the analysis for overall response to


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the force can be carried out as for impulsiveload. Interface force-time history for steel pipeand wood missiles striking reinforced concretetargets can be characterized as a rectangularpulse with the average force value F, appliedover a time duration ta.

For the cases where local deformation of amissile or target structure cannot be determinedaccurately or local deformation on impact isnegligible, and for all the cases of elastic andsemielastic impact, the conservation of energyand momentum method should be used.

INTERFACE FORCING FUNCTION FORNONDEFORMING MISSILES

When a nondeforming missile penetratesinto the target structure upon impact, theinterface forcing function applied to the structureby the missile can be developed based onapplication of the equation of motion duringdeceleration of the missile. It is assumed thatthe velocity varies linearly to zero as a functionof time as the missile penetrates the structure.Implicit in this assumption is a constantacceleration, and consequently a constant forceof impact. The total kinetic energy of themissile before impact is expended as itpenetrates into the structure. If it is alsoassumed that the overall deflection of thestructure during impact is negligible whencompared to penetration; then the work done bymissile as it penetrates the structure is equal tothe initial kinetic energy. Thus:

Wv*

Where F, = force of impact; g = acceleration ofgravity; W= weight of missile; v0 = initialvelocity of missile; and x = missile depth ofpenetration. Based on the assumption that the

velocity reduces linearly to zero immediatelyfollowing impact, the time of impulse or durationof the impact force is:

2x

The value of Fj and td completely define arectangular impulse loading appl ied to thestructure.

It is convenient to combine these formulas,rearrange the terms, and solve for F, .

Wv03

T"mv0

t,

and impulse, i = F|td = mv0; where m is the massof the missile. '

INTERFACE FORCING FUNCTION FORDEFORMABLE MISSILE

When a deformable missile crushes uponimpact with the target structure the impact timehistory is developed based on the defonnation ofthe missile, assuming the target is rigid. The loadimposed on a rigid structure by an impactingdeformable missile is composed of two parts.The first part is the crushing strength, and thesecond pan is the inertial force, or time rate ofchange of momentum of the missile:

pc + yV2 = F,

where Pc = missile crushing strength at impactinterface; y = mass per unit length of uncrushedmissile at impact interface; V = velocity ofuncrushed portion of missile; and F, = forceapplied to rigid struck -x. Pc and y are functionsof the crushed length x of the missile which, inturn, is a function of time.

For the typical wood plank missile, thesecond term (7V2) in the formula is negligible.Therefore the force (Fj) applied to the rigidstructure is then approximately equal to the


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missile crushing strength (Pc). The crushedlength of the wood missile is then equal toinitial kinetic energy divided by the missilecrushing strength,

x = _

Assuming that the velocity reduces linearly tozero as a function of time, the duration ofimpact force:

2x

determined from published tables (e.g., Biggs[5]).

For the elasto-plasric response, and in theabsence of static loads, Wm is equal to therequired structure collapse load R^. A ductilityratio is selected in accordance with ACI 349,Appendix C [3] and the ratio (t/rj is caJculatedas for the elastic case. The DLF which is equalto RJF, can be determined for specific i/Te

ratios and ductility ratios from published tables(e.g., Biggs [5]).

For short duration loading where the naturalperiod of the structure is five or more times theload duration, the Dynamic Load Factor can becomputed without appreciable error by:

where Pe = force of impact = cmA; x = crushedlength, inches; om = crushing stress, psi(= 4,000 psi for wood missiles); and A = missilecross-sectional area, square inches. It isconvenient to combine these formulas, rearrangethe terms and solve for Pe:

mv.

and impulse, i = Pctd - mv0. These equationsare the same equation as derived for hardmissiles.

ANALYSIS FOR RECTANGULARIMPULSIVE LOADS

The equivalent static missile load (Wm)concentrated at the impact point for the structurewhich responds elasdcally is equal to:

Wm = DLF Fl

where F, is a suddenly applied constant loadwith a limited duration t̂ . After calculating theeffective period of the structure (Te) at the pointof impact, the ratio ( t /TJ can be calculated, andth?. dynamic load factor (DLF) can be

DLF =

= A. / M.fe =

Te = l/fe

where: toe = effective radial frequency (ofstructural element subject to impact load), radiansper second; fe = effective natural frequency,cycles per second; Te = effective natural period,seconds; and u = ductility ratio.

If a conservative error of up to 30 percent isaccsptable, then the same equation with the upperlimit shown can be used throughout t/Te range:

The equivalent static missile load then is equal to:

W o = DLF


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Recall that F, = — - , therefore

W. mv0 _

Note that, for very long duration loading, thedynamic load factor is at maximum and thelimiting value of dynamic load factor is 100percent accurate.

DLF »

For elastic response (u = 1.0), DLF = 2.0.The lowest permissible ductility ratio is 1.3

for shear carried by concrete alone. Therefore,the largest dynamic load factor to be used indesign does not need to be larger than 1.625.The equivalent static missile load is then equalto:

Wm £ 1.625F,

For other permissible ductility ratios theequivalent static missile load should be limitedby:

1

2p

Note that for flexure to control design, the loadcapacity of the structural element in shearshould be at least 20% greater than the loadcapacity in flexure.

For conservative design without regard toduration (td) or effective period of the structure(Te), and other permissible ductility ratios, theequivalent static missile load can be taken asequal to:

Wm = 1.625FS

For structural elements that are expected todeform beyond their elastic limit, the effects ofstatic loads on the available resistance should beaccounted for. The effective ductility ratio withthe effective available resistance equal to R^-R,described in ACI 349, Appendix C [3]commentary should be used.

CONSERVATION OF ENERGY ANDMOMENTUM METHOD

The conservation of energy and momentummethod for evaluation of overall structuralresponse is predicated on the assumption thatlocal deformation on impact is negligible. Whilethis ideal situation rarely exists in actual impacts,it is reasonable and acceptable to employ themethod described in this section for cases wherelocal deformation of missile or target structurecannot be determined accurately. This method isconservative with respect to overall failure in thatit neglects energy absorption through localdeformation upon impact. Before impact, thekinetic energy of the missile is known. Duringimpact, some portion of this energy is transmittedto the structure to be absorbed as strain energy.Conservation of momentum and energy are usedto calculate the transmitted kinetic energy andmaximum displacement. Structure displacementlimits or energy absorption capability aredetermined by the allowable ductility criteria.

For conservation of momentum,

mv0 =

For conservation of energy,

1 mv02 - 1 mv,2 + 1 MeV,2

where m = missile mass; Me = target effectivemass; v0 = velocity of missile before impact; v, =velocity of missile after impact; and Vj = velocityof target after impact.

An additional equation may be writtendenning the coefficient of restitution:


275

V

For ideal plastic impact, energy isdissipated and the two masses move off a? thesame velocity (V1 = vx) and e = 0. For idealelastic impact, e = 1 and energy is conserved.Note that it is always conservative to assumeelastic impact, though in some cases a value ofless than one for the coefficient of restitutionmay be justified based on experience.

Solving above equation for v,, andsubstituting into the momentum equation yieldsexpressions for post-impact target and missilevelocity:

It is i m p o r t a n t to n o t e t h a t anunderestimation of the target mass leads to aconservative estimation of the energy transmittedto the structure. In terms of the allowableductility and collapse load, the energy absorptioncapability of the structure (area under theresistance-displacement curve) is:

SE =

where SE = strain energy absorption capability ofthe structure; R^ = static collapse load; Xe =effective yield displacement (elastic displacementunder a static load RJ ; and Xg, = allowabledisplacement.

V,=.

m

1 + m[vo(l +e)] (post-impact target velocity)

(post-impact missile velocity)

Note that for m/N^ >e, the missile velocityis a positive value which indicates that themissile is still moving toward the target afterimpact. The residual velocity represents kineticenergy which the target must absorb in additionto that imparted to it during the initial impact.In equation form, the energy absorptioncapability of the target must be greater than:

KE, = i . MeV,2, for JL < e

R

mDISPLACEMENT

Substituting the definition of allowableductility (p = Xn/XJ into the equation above,results in the expression:

SE = R_X.

KE, = 1 MV,1, + 1 mv2, for — > e1 2 e ' 2 l McThe structure resists impact if SE is greater thanKE,.

For a wind generated missile under thegeneral case of semielastic impact and elasto-


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plastic response (without static loads present),where m/Me £ e. the above equations willreduce to the following:

KE = 1 M.1 2 eM

1m

SE = RmXe (M - i.) = i ^ L (2u - 1)

Setting KE, = SE, results in

-LM(1 + e) vo

(1ML

m

y^ (2M - 1)

(1

m

The equivalent static missile load, Wm, forelasto-plastic system is equal to the requiredresistance R,,, = X&. Substituting Xe fromabove results in:

ke (1 + e) von»Me

(m

substituting O)e = 1 results inM

e)vo mMe

(m + Me)

for M e » m

«,(i+e)vom (2rrfo)(l+e)vom

/2JT-TNote that for plastic impact e=0, the equation willreduce to

Then proceed as before

2jtfe vom

This is identical to the equations derivedconsidering missile penetration and/or missilecrushing upon impact.

For a wind-generated missile under the generalcase of semielastic impact and clastoplasticresponse with static loads present the availablestrain energy is

SE =R.(Xe-X0)

x -

where Xo = displacement due to static load.

USED BYSTATICLOADS

DISPLACEMENT

u X - XCalculate LL- = I 1

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(Note that w.ffw) > p)

then proceeding as before, one obtains

W . =

where

(R, =

= resistance required for static load

TARGET STRUCTURE EFFECTIVEMASS AND STIFFNESS

The effective mass and stiffness of thetarget structure can be established by staticanalysis. The target is represented by a discretebeam, frame, and/or finite element structuralsystem where a static unit load is applied at theimpact point. The expressions for k, and Mt

follow:

1

j— m v 1 dA — m. V:iM 2 '

Effective mass (Mc), effective stiffness (Kr).effective frequency (fc), and maximum moment(Hnw) n a v e been derived in general terms forsimply supported, fixed-fixed, and cantileverbeams for the elastic range of analysis and aresummarized in Table A.

Table A is applicable for \y < '* (1-1/2M)

. When

, W., is at maximum, constant, andW =m ( 1 M

does not vary with the location. The maximummoment is then computed by conventional means:

W Lfor simply supported beam M = m : for

* * * * mix A

4W Lfixed-fixed beam M = m ; for cantilever

beam MmM=Wn)L. The maximum beam shear isequal to Wm, for all conditions.

EFFECTIVE SLAB WIDTHCONSIDERATIONS

In evaluating flexural stresses in rectangularplates or slabs for equivalent static concentratedloads, the following considerations should bebom in mind:

Assuming v = CA, where C is a constantrelating displacement and velocity, and ve iseffective velocity:

•*>

where \ = deflection at impact point caused byunit load: \ = deflection at node i caused byunit load at impact point; m, = mass of targetassociated with node i; and n = number of nodesin the structural model.

a) A slab supported on four edgescan be designed as a two-way slab providedthe ratio of the longer to the shorter spanswithin a panel is not greater than 2.0. Theslab may be designed using the direct designmethod or the equivalent frame methoddescribed in Section 13.6 and 13.7 ofACI318.16}.

b) A slab supported on all four edgesshould be designed as a one-way slab in theshort direction if the ratio of the longer spanto the shorter span exceeds 2.0.

c) A slab supported on two oppositeedges should be designed as a one-way slab.


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d) A slab designed as a one-wayslab may be designed as a beam providedthat for concentrated loads the equivalentwidth is determined by yield-line analysistheory, and summarized as follows:

EFFECTIVE SLAB WIDTHRatio of Moment Capacity

Perpendicular to Span Directionto Moment Capacity in Span Direction

,25 JO J S LOLoad at Center l.OOL 1.41L 1.73L 2.00LLoad at Edge .44L .62L .76L .87LWhere L = Span Length

e) The loads resulting from adetailed finite element analysis may also beused in lieu of the above.

SUMMARY AND CONCLUSIONS

Criteria and procedures have beenpresented for the design of DOE concretestructures and components for wind-generatedmissiles. Local missile effects that consider therelative hardness of the impacting missile andthe target structure are addressed by relatinggenerally accepted ASCE and ACI publications

Overall structural response effects thatconsider the kinetic energy of the impactingmissile and the location of impact on the targetstructure are addressed by relating dynamictheory [5], ACI Publications [3][6], and originaldynamic derivations. The presented criteria isapplicable to safety-related buildings as a wholeand to their exposed external componentsincluding walls, roofs, and supporting structuralsystems and elements. Fomuias for evaluationof overall response of concrete targets struck bywind-generated missiles are summarized inTable B.

REFERENCES

[1] DOE ORDER 6430.1 A, General DesignCriteria. 1989.

[2] UCRL-15910, "Design and EvaluationGuidelines for Department of EnergyFacilities Subjected to Natural PhenomenaHazards", 1990.

[3] ACI 349, "Code Requirement for NuclearSafety Related Concrete Structures,"American Concrete Institute, 1985.

[4] Structural Analysis and Design of NuclearPlant Facilities. Manuals and Reports onEngineering Practice - No. 58, AmericanSociety of Civil Engineers, 1980.

[5] Biggs, J.M., Introduction to StructuralDynamics. McGraw-Hill, 1964.

[6] ACI 318, "Building Code Requirements forReinforced Concrete," American ConcreteInstitute, 1989.

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TABLE A

EFFECTIVE MASS. STIFFNESS. FREQUENCY. AND MAXIMUM MOMENT INBEAMS DUE TO IMPACTIVE LOADS

effective.Mo *»(».*)*

(S> K~ O S

ul ^

ptr Oni4

C. £ F mJ Ce«w«.+e.

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TABLE BFORMULAS FOR EVALUATION OF OVERALL RESPONSE OF CONCRETE TARGET

STRUCK BY MISSILE

Penetration Depth, x

Crushing Length, x

Duration, td

Impulse ,i

Impact Force, F!

effective StaticMissile Load WQ:Vm for /<=1.0(Wo< 2Ft)

Wa for /« ?« 1.0

(- • H^ 2/4 /

Basis of Analysis

Penetration(Steel Pipestriking

concrete target

NDRC formula

2x

mv0

mv0

td

mvowe

iivoo>e

MissileCrushing

(Wood Plank fipole missile:

mvj

2Pe

2x

v0

mv0

mvo . p

mvoa»e

mv0toe

/2^T

Conservation of Energyand Momentum

e - 0

mvoa>e

mvow,

i j 2 ^ - l '

e f 0

mvocu.(l+e)

where, a>» « | —kke • effective stiffness at impact pointMe - effective mass at impact point

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DESIGN OF DOE FACILITIES FOR WIND-GENERATED MISSILES ...

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