Text

Summary of Aircraft Impact Design.
	ML19276H107
Person / Time
Site:	Three Mile Island
Issue date:	08/28/1969
From:	; GILBERT/COMMONWEALTH, INC. (FORMERLY GILBERT ASSOCIAT
To:	;
References
	GAI-1716, NUDOCS 7910100502
	Download: ML19276H107 (47)
	v • d • e

{{#Wiki_filter:'s REPORT NO.1716 METROPOLITAN EDISON COMPANY THREE MILE ISLAND NUCLEAR STATION UNIT 1

SUMMARY

OF AIRCRAFT IMPACT DESIGN 1415 073 GILBERT A S S OC I ATES, INC. 79101oo7O]

r . August 26, 1969 FR ORT 170. 1716 SU'&ARY OF AIRCRA?" D?ACT T:.SIG:! 1415 074

                                                  ?repared ?7.

Gilbert Associates , Inc.

e , TABLE OF CONTE"TS Pare

1. GriERAL - 1

2. DYNAMIC I.OAD FAC*0RS 2

3. A'IALYSIS 3 3.1 SELL ANALYSIS 3 3.2 PLATE ANALYSIS 3 L. FINITE ELEENT ANALYSIS FOR SLAES 5 5 ADDITIONAL DETAIL S"tJIES 7 5.1 EARING FAILUFI 0F CONCE"E UNDER DIRECT IA!?ACT T 5.2 SEAR-OFF THE A'ICHOF,S S 5 2.1 Case A: Shear-Off the Anchors of Vertical Tendons 8 5.2.2 Case E: Shear-Off the Anchors of De=e Tendons 13 5.2.3 Case C: shearinz-Off the Ecce Tendens 15 5.3 SPALLING OF ANCHORS OF LINER INSIDE TE CONTAINEN"' VESSEL DUE TO AIRCRAFT I!GACT ON TE OUTSIDE WALL 17

6. REFERENCES 19 TABLES Table I Time Variable t ,

Table II Dynamic Load Factors Table III Cc=parisen of the Stress Resultants for Prestress Leadings. FIGURES 1415 075 i

e . LIST OF FIGURES Figure 1 Total Reaction Vs. Ti=e Curve Figure 2 Mav' ~ ~ Dynamic Load FLetor Vs. Period Frequency of A One-regree-Freedo= Syste= Under the I= pact of Boeing 720 Figure 3 Pressure Distribution For Aircraft I= pact Figure h Aircraft I= pact at Girder to Dome Transition Figure 5 Aircraft I= pact at Spring Line Figre 6 Radial Deflection - I= pact at Spring Line Figure 7 Aircraft I= pact at Grade Figure 8 Rectangular Finite Element Figure 9 Heat Ixchanger Vault Mc=ent Diagrs= for the Roof Slab Figre 10-A Auxiliarf Building - Concrete Heat Exchanger Vault - Roof Slab Elevation 305'-0"

    ,      Figure 10-B Auxiliary Building - Concrete Heat Exchanger Vault - Roof Slab Elevation 305'-0" Figure 11    Critical Aircraft I= pact Direction 1
   ,       Figure 12    Concrete Cover to Protect Against Aircraft I= pact Figure 13    Detail of Anchor Block Figure lh    Prestress Stresses After Nine Tendons Fail Figure 15    Critical Aircraft I= pact-Directions 2 and 3 Figre 16     Equal Spacing of Roof Tendons Figure 17    Do=e Tendons Figre 18     Mini === Spacing of Hoop Tendons Figre 19     Cc=parison of Prestress Loadings 1415 076 11

1

1. General The vital structures of the '"hree Mile Island Iiuclear Station Unit lo.1 as listed in Section 3 of Supplement 27o. 5 of the PSAF are designed to withstand the following hypothetical aircraft i= pact loadings. (Eased on the load time - described in Append $ces 3 and C of Supplement 5 of the PSAR).

C as e Ite: Weicht Velocity Effective Area A Object 6,000 lbs 200 knots 5 ft diameter B Object h,000 lbs 200 knots 3 ft diameter C Total Aircraft 300,000 lbs 200 knots 16 ft dia eter D Total Aircraft 200,000 lbs 200 knots 19 ft dia=eter This report presents results of the aircra't i= pact study not previously presented in the PSAR. Tnis includes the analysis of the reacter building shell for various locations of the Case D loading; and, the plate analysis for the Case D loading, which is the basis for vall and roof slab designs for vital structures other than the reactor building shell. Also presented in this report are additional studies to htermine if the aircraft i= pact loading vill produce a less of prestress force in the reactor building shell and, if the less of prestress does occur, what effect this loss would have en the structure. The finni study presented in this report is concerned with the possi-bility of the spalling of the anchors of the liner due to an aircraft i= pact en the reactor building shell. 1415 077

2 2 DY:iAMIC LOAD FAC*CES 3e technique used to analyze these structures is based upon estab-lishing a dynamic load factor and applying this facter to a static solution. In deter =ining the DLF curve the response of an unda= ped, linear elastic ene-degree-of freede syste= is used. The idealized total reaction vs time curve is as shown in Figure 1. The time variable t and the ratio factor for a 3ceing 720 airplane n (Figure 1, Appendix C of Supplement No. 5) are shown in Table I. The dyna =ic load factors (DLF) for an unda= ped linear elastic ene-degree-of-freede system are adopted frc= Reference 2 and shown in Table II in te:=s of the Pandamental period T. The dynamic lead factor is defined as the ratio between the dynamic response at any time t and the static response to the peak load P. The maximu= response as a function of the period T for Boeing 720 in-pact is calculated by the equations of Table II and shown graphically in Figure 2. Since this maxi =um response curve is obtained, the analysis of plate and shell structures can new be analyzed statically ence the dyna =ic 1 cad factor is chosen frc= Figure 2 vith reference to appropriate period T. 1415 078

e , .

             .                                                                                                  3 3     ANALYSIS The analysis of the vital structures is divided into two concepts as follows:

3.1 SEELL ANALYSIS This analysis is used for the reactor building. The areas of i= pact that are considered to be the most critical are analyzed as follows:

a. Apex o:? the Ec=e. Analyzed as presented in Supple =ent No. 5 cf the PSM.

b. De=e to Girder transition. This analysis is in accordance with the methods described in the Answer to Questio*. 7.h.1 of Supple-

                          =ent No. 1 of the PSAP.. The non-axisy==etrical lead is repre-sented by a Fourier Series and has the general dimensions and shape as shown in Figure k.

c. Girder to Cylinder transition (spring line) . Analyzed the same as "b" above . The stress resultants are as shown in Figu.es 5 a*.d 6.

d. Impact at Grade. Analyzed the sa=e as "b" above. The stress re-sultants are as shown in Figure 7.

3.2 PLATE ANALYSIS Funda= ental Frequency: Frc= Figure 2, it is readily seen that as 1cng as the fundamental frequency of the plate is greater than 10 c;s , or less than 6 cps , the dynamic load factor vill be less than 1.32. In the present plate analysis, all of the slabs have the funda ental frequency greater than 10 cps. The fundamental frequency calculated for each slab f except two slabs which vill be explained subsequently) are based on the assu=ption of si= ply-supported boundary conditions . This assu=ption vill lead to a lover value of fr.damental frequency for the currint plates because their boundaries are actually restrained more regidly than =erely si= ply-supported. '"hese lov values of "und-

                                                                          .           1415 079

1. c ental frequency vill give a censervative dynL=ic load factor as ca. be seen from Figure 2. 'w' hen the dyna =ic lead facter value falls te-lov unity, a =ini=u facter of 1.0 vill be used. The theoretical background of calculating fundamental frecuency of si= ply supported plate is straightforward and well docu=ented. (2), (3), and (h). The vell known for=ula of natural frequency is: w

                                            =n
                                               =n

5 ( _."J ' , ( n 2 pn vhere = an n denote the mode number; D is the flexural rigidity; p is the density; and a, b, and h, are length, vidth, and thick.ess of plate , respectively.

For the two exceptional plates where the boundary conditions are =cre likely to be fixed, the fundamental frequencies are calculated based on f1xed boundaries. There is no exact solution of fundamental fre-quency for such cases ; however, nu=erical approxi=ations which are based on energy principle are available. (2), (5), and (6). Sie present calculations of funda= ental frequency of fixed plate are obtained frc= the tables and suggested for=ulae in Chapter 5 of Reference (2) . After obtaining the fundamental frequency of each slab and the dynamic lead factor, the re=aining work is a statical slab snalysis.

                                                                               . 1415 080

5 M.*t56 7. rv ??.fdT*

ih1'As'

                .4         --       .          v. c '. c .On p c.,

J.. .fa s.t_ Q The present finite ele =ent analysis is bas: 2pon a rectangular plate element as developed in References 6 and 7 (Figure 8) . Each todal point has 6 degrees-of-freedc=. A ec=prehensive explanation of the satisfaction of the "ce=pleteness" and "cc=patibility" of the chosen displacement function is given in References 8 and 9 The convergence 4 of the solution accuracy vs grid refine =ent is menctonic and rapid as evidenced in various literature. ( 6, 7, 8, and 9 ) . For the proble= of plate in bending,16 elements discretication can lead the solutien of deflections to a small error of less than five percent as ec=p are d with classical solutions. The element nu=ber used in the present calculation ranges frc= 25 to 6L for various slabs. Since the finite ele =ent method is =uch less restricted to the gec=etry and boundary conditions than the classical solution, the actual gec=e-try and boundan conditions are represented in the present calculation without modifications. As an illustration cf the present slab er.alysis and design, an example cf roof slab at the heat exchanger vault of the auxiliar-/ building at Elevation 305 ft is chosen. 2e dimensions and boundary conditions are shewn in Figure 9-A. The dynamic lead factor, based on the elastic unda ped one degree-of-freedc= assu=ptions , was fcund to be 1.183. As shown in Figure 9-A, nine critical i= pact positiens , which produce the critical =c=ents and shears at various sections , were examined. As a simplified de=cnstraticn, the =c=ent diagrams alcng hnt E a"e shown in Fig re 9-3. Se top and bottc= reinforcements corresponding 1415 081

c

the =c=ents in Figne 9-A vere designed er.d shown in Figre 10-A.

                      ~he shear reinforce =ents and ancher plates designed for this slab are sher. in Figre 10-3.      The shear reinforce =ents were designed on the basis of the aforementioned f. nite ele =ent ec=puter prog a= output of shears.

The slab is a rectangle 97 ft by 60-1/2 ft by 5 ft. As shown in Farre 9-A, five critical i= pact positions have to be considered. Fcsition (1) causes the =ax1=u= center =c=ent, pcsitions ( 3) and (4), which are near the quarter lengths of the two orthogonal =iddle lines , cause the

                      =ax1=u= edge =c=ents. Fositions (2) and ( 3) cause the ~=v'=1:: edge shears. The =c=ent diagrams along axis E due to i= pact       at pcsitions (1), (2), sr.d (k) calculated bf the afore=entioned method are show.

in Figre 9-3. 1415 082 t __ . .- - .... - .4. -.

_ . _ _ _ _ . . _ . . 7 5 ADDITIONAL DETAIL S"'UDIES So=e additional studies on the detail structural analysis of the aircraft i= pact on the contain=ent vessel have been made:

a. Bearing failure of concrete in the neighborhood of anchors of tendons under direct i= pact.

b. Shear-off of the anchors of the dc=e tendons , vertical tendons ,

and hoop tendons. j

c. Spalling of the anchors of the liner inside the containment vessel

         ,                           due to aircraft i= pact on the outside vall.

The result and conclusions made in the studies are discussed in the following sections. 51 BEARING FAILURE OF CONCRETE UNDER DIRECT IMPACT The bearing capacity of concrete, according to ACI 318-63, is 1.9 x f O.375 fc = 3560 psi. The aircraft i= pact force of 18,000 kips I (assu=ing a dynamic load factor of 1.2), according to the 15 x 25 = i 375 ft 2. nor=al i= pact area, produces an i= pact pressure or 18 x 106 /15 x 25 x lbh = 333 psi. It is readily seen that the aircraft i= pact doesn't cause bearing failure as long as the impact area is 278 approx 1=ateV greater than 333 3650 = 3h.h ft 2 Tnat is , the bearing failure can be prevented as long as the impact area stays within 3h.h

                                      = 9 2 percent of the i= pact area of the case when the aircraft 375
     ;                         hits normal to a flat plate. Intuitively, it is believed that no
                               =atter where the aircraft hits, the i= pact area should be at least t

9 2 percent of the area of the case when the aircraft 1.: pacts on a flat vall. 14'" 183

g . S The anchors of the de=e and vertical tendens are e= bedded in concrete . at least one foot deep. ?!o da= age of the anchers is possible when the aircraft hits nor=al to the anchorages . Although the hoop tendon anchorages are not e= bedded in concrete, the 4 aircraft would have to hit in a tangential direction to the contain-

                   =ent vessel to produce a bearing failure of the anchorage.

i This being the case, it is unlikely that the total impact force vill be concentrated over 9.2 percent cf the nor=al impact area; therefore, a bearing failure cf the concrete at the hoep tenden anchcrages vill not occur. 52 SEAR-OFF TE A?!CEOP.S Three cases have to be investigated when considering the possibility j of shearing-off the anchors of the tendons due to aircraft i= pact, l particularly the i= pact of engines rad sharp object. 5.2.1 Case A: Shear-Off the Anchers of Vertical Tendons The aircraft =ay travel in the direction as shown in Figure 11 such that the anchors of vertical tendens =ay be sheared-off. I Based on the investigation conducted in Reference 1, the infor-i

                  =ation is available that the =axi=u= response of statically equivalent i= pact 1 cad is 16.0 x 100 lb (assu=ing conservatively a dyna =ic load factor of 1.2) and the =aximum i= pact area cf 15 ft i

by 25 ft (assu=ing the aircraft hits nor=al to a flat vall) .

                  "he verst condition of aircraft i= pact, as can be seen frc= Fig-ure 12, is when the aircraft i=pinges at such a pcsition that the

__ ._____ b d_'_EL._OM._..

9 total i= pact lead is concentrated en the portien of concrete vbich is abcVe the line E. In other words, the shear strength of section E has to be calculated to decide whether the air-eraft vill shear the concrete and i=pinge at the anchors. Tenta-tively, the lengths a, b, c, and d are decided as fo11cus: a = 2 ft - T-3/h in. b = 1 ft 1/2 in. e = 10 ft d=2ft Considering the =c.xi=um aircraft i= pact area with a width cf 25 ft, the maximum nu=ber of ecvered tendens are:

                       ,                    25 ft                                          2 5 x 12 J=                                                        =                   = 9.89 C. to C. dist, between anchors                                  30 5 As a very apprcxi= ate esti=ation, the i= pact force on the area between two anchor centers is:

Max. restonse 18.0 x 10 6 P= ,, a

9. ee_

                                                                               =       1.83 x 106'lb/tenden The area available fer resisting the shear can be-estimated frc=

Figures 12 and 13. A = d x 10" + a x 20-1/2" = 120 x 10 + 31.75 x 20.5 = 1850" 1415 085

   . . _ . . . _ . _ .           _ _ _ _              .m . .             .,..               _._._ _.        . . . _ _ _ .

                                                                           .na The conservatively esti=ated maxi =u= shearing stresses applied at surface AI (Figure 12) due to aircraft i= pact is then:

T = 1.83 x 1c6= 990 :si, 1850 Fro: ACI-31S I ulti= ate = 300 psi i

   ,   The re=aining portion of the shearing feree F = (990 - 300) 1850 = 1275 kips / tendon is assu=ed to b: re'tsted by the anchors. The shear resisting capacity of each anchor can be cale lated as:

T tendon = P.S. force x Coule=b static coefficient of friction + Ult = ate shear stress x Area

                 = 1090 x 0.2 + 1hh x 8.28
                 = lLO8 kips / tendon Therefore, an esti=ation can be made that about nine tendons (with 25 ft vidth of aircraft i= pact) are under:

1275 140d " 9 E'#

of their capacity to resist shee. failure. It is likely that no anchors vill be sheared-off since the above calculations are based on very censervative assu=ptions.

Although the above analysis shows that no anchors will fail, it is , however, assumed that nine anchors are sheared-off by the aircraft i= pact. As illustrated in Figure lk-A, it is seen that Section AA is cf pri=ary cencern if vertical tendens fail under kk\

11 the impact. The 20 cent m, caused by the aircraft i= pact has to be resisted by the =osent =2 caused by the undestroyed ten-dens on the left hand side of the neutral axis as shown in Figure IL-B. Because of the loss of nine tendon forces , the real neutral axis lies slightly on the right hand side of the ; r N.A. axis as shown in Figne ik-B. It is however, assu=ed to ' cross the center of the cylinder for simplicity and conservative- , ness. The =0=ent caused by the aircraft impact is: 3 I my = 18 x 10 x 146.5 x 12 = 3.6 x 10 in-kips 3e merent due to the undestroyed tenden prestressed forces en the left hand side of the neutral axis is: l m2 = F x d t where F is the total prestressed forces, for the case when there is no tensile force in section AA and all of the tendons do not exceed their prestressed forces , so: F = 37 x 2 x 1090 = 8.06 x 10b kips

   ,                         and d is the distance frc= r: enter of gravity of the active ten-dons to the neutral axis as shown in Figure L-C:

d= rsn23 ,800 sin 1.L

                                                   ..h 8001.4 x 0.085 = 565 in.

2a 1415 087

                              "herefore:
                                  =2
                                     =       =     8.0 x 10 x 565 = k.65 x 107 kip-in so:

I I

                                  =2 = k .65 2. 10 k-in>=1 = 3.6 x 10 r.ip-in It is now concluded that even with a dyna:::ic load fsetor 1.2 and a very conservative assu=ption that all of the nine tendons covered by the airplane i= pact are destroyed, the safety factor
                           - for not causing tensien at section AA is:
                                         =            L.56 x 107 S.F. = =,2     =

3.6 x 10,

                                                                   * *,*27 2

In order to shear-off nine vertical tendon anchorages , the air-craft must i= pact as shown in Figure 1. A reasonable assu=ption

      ;                      is thnt the i=pnet Iced vill te concentrated above the ring girder.

As a conservative esti= ate of the resulting forces , the forces shown en Figure k due to the aircraft impact at the girder to dc=e transition vere used. Figure k shows that the maximu=

                             =0=ents and shears occur in the dc=e . "herefore , the resisting prestress forces in the critical area are not affected by a loss of vertical prestress.

The shear stresses in the vall are of concern because the allev-able shear stress reduces when the =eridional axial force is Ics: 4 due to the failure of nine vertical tendon anchorages. The shear stresses at three locatiens vere deter =ined ar.d ec= pared with an ultimate shear stress of 26 x { (AC: 315-63).

     - - - - - ~ ~ - - -                       - - - - -               -     - - - - - - - - - - -   - -

13

                          ':he three locations are:

1) Cylinder vall to ring girder transition

2) Base of vall

3) Ten feet above the base of the vall (Haunch to typical vall transition)

Although the shear stress at location 1 exceeds the ulti= ate shear stress, the shear steel reinforce =ent required is less than that provided for the nor=al loading cases under no loss of pres-stress. The shear stresses at locations 2 and 3 are less than the ulti=ste shear stress . 5.2.2 Case 3: Shear-Off '"he Anchers of Dore Tendons If the aircraft i= pact occurs as shown in Direction 2 of Figure 15, i the shear resisting capacity of the concrete at section AA has to be greater than the i= pact force so that no force vill be transferred l to the anchors of the roof tendens. "he shear resisting area, assu=ing i a 25 ft. vidth of i= pact area is:

    ,                          A = 25 ft x 7 f 3/L in. = 28,825 in.

t The total shear capacity of cencrete against the vertical i= pact is: F = 1 9 x 1L1 x 28825 =7.Th x 10 6 lb. which is s= aller than the aircra't i= pact load 18 x 106 lb. (with a conservative assu=ed dyna =ic load factor 1.2) . Let it ce assu=ed that after overec=ing the shear resistance of the concrete, (18 - 7.7h) x 105 = 10.26 x 1C lhs is applied to the anchors of the

                                                                         .. .-- 7 41 5- 089-

3 - roof tendons. Only the ec=penent cf := pact feree which is per-pendicular to the tenden direction is res;cnsible for shearing-off the anchors. This component can be calculated as: 10.26 x 106 ces 18 = 9.75 x 106 lb 6 Lec it be assuned that the force 9.75 x 10 lb acts perpendieu-larly at the anchors vite a covered width of 25 ft. The spacing betvcen tnchors of the upper lgyer of deme tendons is 2h-1/2 in. (Figure 16 ) . According to the calculation: 25 x 12 24.5

                                         = 12.25 = 12                                       -

C a total of 12 anchors are under the i= pact of 5.75 x 10~ lbs. Iach 6 anchor is under the shear force of 0.75 x 10 = 7.96 x 10 lb. 12.25 When c = pared with the shear resisting capacity of each tenden, lh08 kips /tenden, it is found that the safety factor for each tenden anchorage against shear failure is: 6 S . F. = 1. h0 8 x 10 = 1.T,a 7 96 x 105 Under the above analysis , the de=e tenden anchorages will not fail in shear. The doce tendens are cceposed of three layers lying en top of each other. Iach layer is ce=pesed of parallel and equally spaced tendons. As can be seen from Figure 17, the orientation of the three layers is such that the tendons crci each other with a censtant angle cf 60 degrees . Since the dere tendens are so close to each c her, crossing each other, and overlying each cther 1415 090

                                                                                                      .c it is intuitively believed that no da ace vill occur to the de=e even if a fev tendens are assu=ed to be broken under the air-craft i= pact.

In addition to the previous logic, providing the failure of the dc=e tenden anchorages is caused by an aircraft i= pact as shown in Direction 1 of Figure 15, the =ajor portien of the i= pact load will be resisted by the c'/lindrical vall and not by the do=e which has 1 cst the prestress forces due to 12 broken dO=e tendens.

f the aircraft travels in the Direction 2 as shown in Figure 15; it is seen that the concreta bearing failure is likely the proble=

necessitating consideration. Previously, a calculation has shev. that as long as the i= pact area stays within 9.2 percent of the i= pact area, no bearing failure vill occur. Therefore , i= pact Direction 2 is of no critical concern. , 1,

   .               5.2.3 Case C: Shearint-Off The Hoot Tendens The aircra't =ay travel in the direction shown in Figure 18.

Since there is no concrete cover to protect the anchor, direct i= pact en the anchcrs =ay shear-off several tendens. As shown in Figure 18 the =ini=u: vertical spacing between anchors on ene side of the buttress is 33 inches. Each hoop tenden is anchered in One butt,ress , then passes by the adjacent buttress , and is finally anchored in the next adjacent buttress. 1415 091

                                                                                                                           ,a
                             '~ne aircraft impact area has a =ini=u= d:pth cf 15 ft. which can 15 x 12 cover five (i.e.,

33 = 5.k5 ) archers of hoep tendocs . If the most conservative assu=ption is =ade that all of the five anchors are sheared-off due to aircraft impact, one-half of the hoop prestress force in a cylindrical panel with a depth of 15 ft. and a curve length of one third of the cylinder periphery would be eliminated. An analysis is =ade censidering the contain=ent vessel with .or=al prestress conditions with the exception that a cylindrical seg=ent with a depth of 15 ft. has only one-half cf the hoop prestress. The resultant axial forces and shears with half of the hoop tenden forces Icst in the range between 800 in. and 965 in. above the base cf the cylindrical vall are listed in Table 1. It is seen that the out of plane shear and hoop force I have changed due to the failure of the hoop tendens. The shear has increased considerably, but, is in the opposite direction cf 1 the shear due to aircraft i= pact, and therefore aids in resisting

     ,                      the aircraft i= pact. 'Inen the aircraft i= pact di=inishes and the hoop tendons are still broken, the re=aining shear is =uch less than the ulti= ate shear stress according to ACI 318-o3.

The scove anclysis does not consider the =c=ents caused by the loss of 12 hoop tendons. Refering to Figure 19, which is a ec=parison of the loading due to aircraft i= pact plus total pre-stress and the loading due to aircraft impact plus total pre-stress =inus the hoop prestress due to the loss of hoop tendons, it can be deduced that the resulting =c=ents vill tend to counter-act the =o=ents caused by the aircraft i= pact. 'inen the air-1415 092

                                                                                     -t l

craft i= pact di=1nishes , the axial ecupression due to the re-

             =aining prestress forces (see Table 1) should be sufficient te overcome the tension due to the =c=ents caused by the less of hoop prestress.

Based on the above logic and conservative ut=erical calculation, it is believed that the aircraft i= pact in the direction shown

           ' on Figure 18 does not jeopardize the stability of the structure.

53 Spalling of Anchors of Liner Inside the Contain=ent Vessel due to Aircraft != pact on the Outside Wall In rigid dynamics it is assu=ed that when a force is applied to any one point on a body, the resultant stresses set every other point in motion instantaneously, and the force can be considered as producing a linear acceleration of the whole body. In the theory of elasticity, on the other hand, the body is censidered as in equilibriu= under the action of applied forces , and the elcstic defor=ations are asscred to have reached their static value. These treat =ents are sufficiently accurate for the proble=s in which the ti=e between the application o'f a force and the setting up of effective equilibriu: is short ec=- pared with the ti=e in which the observations are =ade. When, hev-ever, cne is considering the effects of forces which are applied for enly very short periods of ti=e or are changing rapidly, the effects

            =ust be censidered in ter:s of the propagation of stress vaves.

1415 093

7 IS. I In the present case , the aircraft i= pact is a relatively long ten ,t process. The total i= pact duration for a Boeing 720 aircraft lasts 0.33 seconds when ec= paring with a concrete vall with a thickness of 3-1/2 ft. FrcT a conservative one di=ensional wave propagation con-sideration, the vate propagation velocity can be approxi=ated as (10): C=i = h x 10 6 = 1.33 x 105 in./sec. p C.087/32.2 x 12 Tnerefore, the setting up of effective equilibriu of forces under aircraft i= pact can be sufficiently made in this case. No streas wave effect is needed fer consideration. Nevertheless , the anchors en the centain=ent vessel liner above grade vill be deeply anchored into the concrete vall with one inch diameter bolts (fom ties ). These bolts have a capacity to resist 1.7 kips per foot of anchor. This measure further protects the liner anchors against failure due to spalling even though such behavior is not anticipated, as previously described. t 1415 094

w 4 6 REFERENCES

1. Haley, Jr. , J. and Turntov, J. , " Total Reaction Force due to an Aircraft I= pact into a Rigid Barrier," AvSER Report prepared for Gilbert Associates , Inc. by Dyna =ic Science , Phoenix, ,ei:ena,

      ,                    April 1968.

2. Siggs , J. M. , " Introduction to Structural Dyna =ics , "McGraw-Hill look Co., N.Y. 196h, Section 2.3.

3. Volterra, E. and Zack moglou, E. , " Dyna =ics of Vibrations ,"

Charles Merrill Books , Inc. , Cc:.u= bus , Ohio,1965

      ,                k. Timoshenko, S. and Young, D. , " Vibration Proble=s in Engineering,"

3rd Ed. , D. Van Nostrand Co. , Inc. ,1955 5 Harris , C. and Crede , C. , " Shock and Vibration Handtosk," McGraw-Hill 3cek Co. , N.Y. ,1961.

6. Scgner, F. , Fcx, R, and Schmit , L. , "Se Generation of Inter-ele =ent-Co=patible Stiffness and Mass Matrices by the Use of Inter-polation Fer=ulae, " Proc. Conf on Matrix Methods in Structural Mech., Dayton, Ohio, 1965 7 Gallagher, R. , ""'he Develep=ent and Evaluation of Matrix Methods for Thin Shell Structural Analysis," Ph.D. Dissertation, State University of New York at Buffalo,1966.

6. Gallaghe. R. and Yang H. , " Elastic Instability Prediction of Doutly Curwd Shell Structures," 2nd Conference on Matrix Methods in 3tructural Mechanics, Wright-Patterson Air Force Base, Dayton, Ohio, Oct. 1968.

9. Yang, H. , "A Finite Element For=ulation for the Instability Pre-diction of Doubly Curved Shell Structures ," Ph.D. Dissertation, Cornell University, Ithaca, N.Y. , Oct.1968.

   ,                   10. Timesheuko, S. and Goedier, J. N. , "3 sory of Elasticity,"

McGraw-Hill Scok Co., 1951. i

                                                                                      \4\b D95

TABLES h 1 1415 096

       . . - - -                       , i! h !. b ' >* *

tis - - - - - - - - - - - - - - - -

TABLEI TIME VARIABLE fn B ing t t t t " 1 2 3 h *5 *6 0.06 0.1h 0.19 0.2h 0.26 0.33 0.219 TABLE ll DYNAMIC LOAD FACTORS DLF, O to ty T sin wt a 4 2n t 1 m

DLF2 1 to t2 1+ a t 27 t, sin w(t-ti) - sin et DLF, t2 to t 3 DLF2+ .' T sin (t-t 2) (1-0) s :- nP t-t DLF 4 t to t g DU + - + (1-a) 3 2 tp r P 2 sin w(t-t3) - sin w(t-t2) T DLF *h* DP 2 + "*p 5 *5 - sin w(t-t h) + 2 sin w(t-t3) - sin w(t-t2) Il-") t-** T " DLF 6 t to t 5 6 DLF. - sin w(t-t5) t6-ts 27(*6 - ts) DLF after t 6 a 7 DLF5-1+ 27 (t -t$) sin w(t-t6) - sin w(t-t5) 2. Where u = T (radians /see) 1415 097

TABLE 111 COMPARISON OF STRESS RESULTANTS FOR PRESTRESS LO ADINGS OUT OF PLANE SHEAP. MERl010NAL FORCE HOOP FORCE 2 5 h 0 (10 ) No (10 ) No (105 ) d (1) (2) (1) (2) (1) (2) 800 -0.33 18.508 .3730 .3730 .7166 .5628 816 -0.32 14.446 .3730 .3730 .5519 333 -3.309 10.589 .3730 .3730 .7157 .5429 849 6.892 .3730 .3730 .5362 866 3.308 .3730 .3730 .5320 882 -0.219 -0.22 .3730 .3730 . )j 51 .5305 899 -3.74 .3730 .3730 .5317 915 -7.314 .3730 .3730 .5355 332 -10.99 .3730 .3730 .541 948 -14.83 .3730 .3730 .5505 965 -0.010 -18.86 .3730 .3730 .7150 .5610

INCHES ABOVE THE BASE CYLINORICAL VALL (1) WITHCUT LOSING TENDON (2) 's 0F HOOP TENDON FORCES LOST.

GILBE RT ASSOCI ATES, INC.

G 9

                       ~ "" ~ "" * * " " " ' = - -

ee-..., .,, ,, , _ ,

4 FIGURES 1415 099 _ - - . . . - - - a t i e. ;. P * *s4'C;

                                                     .              't*       -    - - - - - - - - - - - - - - - - - -

w

                                                 ~ JL 10 u

x w

       '          S if

_,a. x w Q. M e N (Od N0ll3v3M 1415 100 TOT AL RE ACTION VS, TIME CURVE GILBERT ASSOCI ATES, INC, FIGURE 1

F REQUENCY (CPS) P00R DifSINAL 100 50 40 30 20 10 5 4 3 2 1 1.7

                                                 '                              '       3        i       #            . i m

e i 1 3 f , e

                                                 '                i                                      t                                                               I

t I e 3 , 1 8 i i s i e t 8 ' I t 8 I

t i g g g i e e i ! d I I

i I e

[ f 9 4 8 t l 1.5 ' ' ' ' ' ' ' ' ' ' t , p i i i i i I e i l e a 9 Q !

' ' ' ' I t '8 i # q , ,
g ' ' ' ' ' ' ' O ' I e 6 e ,
>=
i U ' l i I 8 i [ t
~~
4 ],] e 6 i 6 t ! , t , , , Q _I I
< i A. I I- 1 , i t i O i /~1 ' / 7 A , i ,
J ' / . V i i
. T i g , .f ." r ' '\~ '~~ '- ~ ~ ~ ' i x
i i _ _ _ . _ . 2__ .
- f i , i 4 , i , i AE i t '
Z l i e N EX , # J. __ 6 I e a 6
, I e i 3 %I e Q U+Y i
1
. . , - j -
i g , e m' 6 3 I l , l \ l I ( 1 P \t g .i. , 4 i 6 i . N i . . T ' ' UNECONOMIC ZONE e- i I e
\i e i .i . e i ; i ), .
e r , i i1 .I , ' t e t T i i e ! t i e e ! 1I - t 3 i e i e i i l 4 UI i i i
, , , . . . 1 , l I
i , 4 l .\ 9

i I < i j 6 i , i \t t ' I 3 ' ' '
t I I e I i , g i e ' l , ,' I 4 6 t. e 1 i e i . i l
' ' ' ' ' i- i 0.5 I e i t ! '
t i 4
1. I a 4 i
i =9 l- g e e i. e
-I 8 e ! t 4 t- i t e t 4 i e t i I I I l i I I ' ! i i i .i. , , ,' , i i ' , i , , i , , i 0.3 0.01 0.02 0.03 0.04 0.05 0.1 0.2 0.3 0.4 0.5 1.0 TIME (SECONDS) 1415 101 MAXIMUM DYN AMIC LO AD FACTOR VS. PERIOD OR FREQUENCY OF A ONE DEGREE FREEDOM SYSTEM UNDER THE IMP ACT OF BOEING 720 CILBERT ASSOCIATES, INC. FIGURE 2
FOURIER SERIES = .07955 .1575 ? 05 6 + .1558 COS 2 6 .1446 CCS 3 e + .133 CCS de .
- 1208 . COS SG +.1058 COS 66 .0894 COS 78 + .0722 COS 86 .0551 COS 96
( 0- l 1 #,6*4g$sf o* &
/ l! s pg.s,4 ,gif ' / < W J I r "o i
y ; ku lll li.I
!II ii i.u 1,I j
I o llll.l; 1 i',, . .
<! ' I i l !!li I ;i , 1 1.
j'.1t l
- : I 1
lw :l:,o 1 i
! ,; l : 11 ' l'>,I i
tu
! ; 1: 11 ! IIIf;lq I r } '\' ! *,1 !<l l':., , l l> l i
1, 11 1 ljl I!iIll i ' I.? j lllllli,
; ,,: ll l 1415 102 l I ' ! ll l ' : : ! '
lI;l;';il' llll ""'$f5!!'/r"ly'#I'r*"" GILBE RT As50CIATES, Inc, FIGURE 3
"3 5
S N O I T C
,I E I
L F E T D F K 8 5 4 1 7 2 S R A E l i S T F K T 5T S 6 T F 5
0. F- N 9K 1 -
E 0 9 6T M 7 1 F O M f L A N lO DI R E M
- p"L"i ~ . U 0 0 0 0 0 0 0 0 0 0 0 0 0 0 o 0 5 4 3 2 1 0 9 8 7 6 5 4 3 2 j 1 1 1 1 1 1 FyLL ;2Qto y $S >' - ' n4 $ 9mo$
4o
- 8I myr45z-o_Inm s- h8- m { M* m cmm
5 0
5 3 9 c S N O I !!,I , ,' i' T C E L
> F E
D 2 2T 1 F 2 9 'K 2 ; S R A E H S 3. 2F T 2'
> 1- K ' I ,! ' ,
li ! S
T N
E M O M L
> A N > i. , i .
O I D T I F R E K.- M T T F F K 5 T 4 9 F 8 8 9 4 4 I l'
. 4- "OA 'zgE 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 4 3 2 1 0 9 8 7 6 5 4 3 2 1 1 1 1 1 1 1 emWI.yeQ>Um L
n$mH _r'>Q ,8 Y aZ Czm 9EE >gO$mev' go n
- ; c = m <a
N
/ \ / \ / \ / \ ' \
l
\ \ .93273" \ g i I I /
1
/
1
\ / \ /
N j ELEV.149' 1" 1415 105 RADI AL DEFLECTION IMPACT AT SPRING LINE GILBERT ASSOCI ATES, INC. FIGURE 6
+ >
4 ' 0 1 5 4 t O I T C E
- L F
E D T F
/
2 K 6 T 9 T 6. F 2 / 9 8 F
/
0 2 K 5 1 K - 4 5 : 6 1
\
S R A
E l
i S
\>
4T 6. 3/ F 6K 1 - 1 T F S T N E M O M T L F A
/
K N
- O T I F D I
8 R 8 E 4 M 1, s _A - W Oa iI l k l !<! q 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 4 3 2 1 0 9 8 7 6 5 4 3 2 1 1 1 1 1 1 1 la* . 9ts" m j o_E 4
- h8~ U' _ E" h $ y.2I .
n~ D o ng
- ~
% -- ' N - . _ _ . 2 y A Fy
/
Fr b a g(xy / t i 3 F, ;x I M
Y (b) SIX FORCE COCONENTS AT (a) GEOMETRY NODAL POINT 1415 107 i -
RECTANGULAR FINITE EL EMENT GILBERT ASSOCIATES, INC. FIGUR E 8
2,8N) e.c<n 2,410 , 2.20e Y
- t,a w i = gg.a. = /,th > / / / / / / /// / ///
e ! r t/>xtire ,s = e Lo g l /, f$ '-1200
," l ,)s1 0 / p h an**P3 /
T 5 x 4 ? /
;, /"u 'g , _J f
sco (
/ =
s.~ey o ,i>;i 4 ,,,,
.R ~ / l -/ /
1.x. / w___ L' a 5 oircraft impact positions cu .w, 5 _ _ . . . - . -p- -
- f,u ,
y n .
./ //
2, Iown , t,200 ,
--=* 1,900 l
n @
, b 5 moonerit.s otong section A-A /,ano . /. < * /* /-
e O ' l'~ 'l *1' f I'0 ' ' b '*1
~~~ - - 2,000 rio rea,/ .D:aysvons at Sec/o<- ^ -l CD @ HE AT EXCH ANGER VAULT WOMENT DI ACR AM FOR THE ROOP 5L AB cet er a t anociair s, enc. FIGURE 9 'l I
I*I.
!! i l .i i,S,!. .!,, ! j '!1.
I . s 1 1' ,1 t 3
'. . - . . i i' l .'e~ ' ,I;
f. ;
i[.f'l;l l l .'! ll h:n-l:!
! l.t 1 -~~
er - g- ,.
o. . 9.
u L :.
) .a :s ,,- . n ; 3 * .I n l - ~
it; :Tiu P00R ORHE l !s't
. . . .3 I . * ,, ,s l ; e .,, , , [r ,
rw* .t. .= .!
~ .. .- t. i .i; -. . i. __.
y . i , .. F6 '
!' ic - J;} : '- ' . -
ji -
.I- : #s s.1 .. , l' __.
v e:- = -_.s lI 9* **v ft - !i ;
.i - . . . -.- ei f . ~ ", * - ,_ m . .f . .=r .- __ . , . ,r p.- m m ,
Q '"* f ' .k'7
!l l ""i * ' .1 j' , T l l j 1 N
m, . L, , ___ -) l'. 5
= *(a,,
8, g .
; , ~ ,
I
! l '! f.lI !
11 l } I e i
5 a55 $,,,- $
a nl I (, i t. : i i eya r=- 9,,, 4-wi--'
'==ar = 9 [ ,..,' 7 ,r.;i- e , g. - B ..c , ,, i E l , -.-- ,
v..
.s , ., 'a zg 3Nd , j .) l l r = -L M j, . . -l = '3 1 '.t ( ',
l l 4 3 4.[ 4
.s 15 3 . } ,
l 4!'lii i.! __'!) 1 1 .-- 1, i
'. _ .m> -- - +i g . -"1M 5
[* - I Q..
... *1 I
d
! s l
l 1a Ah'T t
<.~.- )'s,nge e! ::i ' i l* - ;
j
.j i l r 7; , ....--,........~., , _ : . .. . , ._
_ m __ . J a u i i . , i
- * :te-d fb7 '
I I 8
)* ! ! ~ ,. l' .
g
.,e_. - .. % ~ M6 . ! s e l .j - -- i .
a !.. hMF ~
~ j- -
1-
,b I ,
a
-l 1415 T09 -
1 I e
. n.
e
,el s-I, .i , 'p. . '. - r : ~ ~ .c it. i' ;. .) * !
3 8
-l ri 3 i . m. ,I _ - . a.. , . *..s v-w . - l-:
l1.s e . . ,-
; ',)' gi G i1 .b I l\l! * :;. l a, . n h[ '
__..m ? , ap
w.'
u -- !
. e. -- .- .I g .. - --- [ . ,. , . d ,,'( -- .3i I .. ,{ .I ff *k .g . .i ?!
4 ~~ ---
~* ,- . . a_s w o, , ..o.r- --.
_,-{ ps
...._.._ _ . ,. .......... a 7 -9 . = ...............- .. - --. . . .
i ;.
.. . I i !. i Ji *li !! 11 if ! -' %* , ,,- ,,.. - .
L.-
.t ...--r,------- .
v e
.- - i ', -* I" , t z R O *.m ,:
l. t i s. i. 'l a
v>3
'li 'l ! ' }l '1 1 i d l a"a4 -.: . . 2- t . - -St .- - - - = ~ + ~ - ~' =4-5gaw g, . --_i - 7 ~'
g5.! 3
- jl j .
4 !!
! i b. c'-~ ar-d <1 i: ,, 9 ..<. ! J.i ..,._ ; ._,.,_ s .# i. .. ,. g g p.
2, !. .
. = -tl :*
18 il. d
.' 'l}
x
. ;iX 8 a . y ~~}, ,~ '. '. i H * . f '.w.
1-f g- . 18
** !l i .il: t{
j$ I P -- ve - - * =
= I ,e . .s I
i 2 ,,.3 ^ e- L.e g w t' m . *7 y t 11 n
- jl - n.i.
i ;li e c -
a
.. g i - a . -
4. g J , '* -
. . e 11 !! ri i b 6..
il s>. . j! ji i! jj 3 !. r-
.Q. . . . . -
5
~ , g~ . .. t t
I f{
f if - 4
t. r'. -I -
J
. .0',. ,_7- t... . m. . . . eeeew' . . _ , ' ., .....P . ,.
z -- I 1415 110
V
= / \ /
CRITICAL AIRCR AFT IMPACT DIRECTION 1 clLBf RT ASSOCI ATES, INC. FIGURE 11 1415 111
- C - o .
6 _ d A A I i.3-
\
CONCRETE COVER TO PROTECT AGAINST AIRCRAFT IMPACT GILBERT ASSOCI ATES, INc. FIGURE 12 1415 112
I e l'-8b" 10 : l'-8 *i
/ / ,-/~ 7 ' c7 a ,Q l /Q ,l -~
l~ l- (
~ l--l l ( - li !I/I/ Id -l- l)I-l! ,'-l- f E- l l _'/ / E, _ii_' //
I I l l
> ll l _1 W- GY, L ll l +
I I I I I rl I lll I I l I l i l Il 1l l1 i i l I I l.) LJ ! DETAll OF ANCHOR BLOCK GILBERT ASSOCIATES, INC. FIGURE 13 1415 113
[ f MPACT DlQECTION _ g t
.R di di A A ._!
[ 1 (aJ gCQb
/ s l
i 2== l,7 QADinN3
/ i ~~ '
l e ,
~,
R / ' p CG- ,-
=>
D '
' S'N 2" d
2 ct i ASSUMED N.A. (b) (C) PRESTRESS STRESSES AFTER HINE TENDONS Fall GILBERT ASSOCI ATES, INC. FIGURE 14 1415 114
~
IMPACT DIRECTION @ 1,
\
N o
/,'
ss E a ,/ ,'
/ /
o u s '
/ , /
h s 's , ' i
). ' ,v-N /
N ,s' ' o ,
, / ~
CRITICAL AIRCRAFT IMPACT DIRECTIONS 2 AND 3 clLBERT ASSOCIATES, INC. FIGURE 15 1415 115
e . . e l, e. & e e e N / OUTSIDE VIEW OF FIG.16 EQUAL P AGNG OF ROO F TENDONS GILBERT A550CI ATES, INC. FIGURE 16 1415 116
/// = .=; , r come TENooNg EQUAq 'o' To sA S? . ^S3o HEQ A*t- / // '
i
' ll /
y p// STENDOy3
#SSOCIATE S, g FIGUgg gy 1415 117
$BUTTRE55 I
Y x 'X N
~ ^ IM DAC T i *)iDECT CN 11'-8* q. / \ ~
l'~ ' ' Q~ ~ g/A,v - , N q s
~ _ . _ ,'a --
s s
% N s -
u
~ ~ ',- '- -- -~- ~. .'N N ' ~~~ % ' - f % -. ~
s ;, -
-- , ~ _ __
i]'_ m N / N # MINIMUM SPACING OF HOOP TENDONS GILBERT ASSOCIATES, INC. FIGURE 18 1415 118
gDUE TO VERTICAL -DUE TO VERTICAL PRESTRESS pegsregss e, h.* Id i.' Ai DUE TO HOOP i' DUE TO HOOP N PRESTRESS ' PRESTRESS AQUETO LOSS
= OF HOOP PRESTRESS DUE TO AIRCRA DUE TO AIRCRAFT I MPACT I MPACT y aa 9
s. 9 .
E LEVATION ELEVATION DUE TO AlRCRAFT IMPACT b -- Dut Tb AIRCRAFT IMPACT
\ '
o p- HO P ESTR ESS cop PRE TRESS Cut To HMP NG PLAN PLAN LOADING I LOADING 2 TOTAL PRESTRES5 LOS$ OF HOOP PRESTRESS COMPARISON OF PRESTRESS LO ADING GILBERT ASSOCIATES, INC. FIGURE 19
/ /
1415 119}}

ML19276H107

Text

SUMMARY

Navigation menu

Search