ML18117A370
Text
TMI-1 UFSAR APPENDIX 5A 5A-1 REV. 18, APRIL 2006
- 1. INTRODUCTION
The vital structures of the Three Mile Island Nuclear Station Unit No. 1 as listed in Section 5.1.3
of the Final Safety Analysis Report are designed to withstand the following hypothetical aircraft impact loadings (Reference 1):
Case Item Weight Velocity Effective Area
A Object 6,000 lbs. 200 knots 5 ft. diameter B Object 4,000 lbs. 200 knots 3 ft. diameter C Total Aircraft 300,000 lbs.
- 200 knots 16 ft. diameter D Total Aircraft 200,000 lbs. 200 knots 19 ft. diameter
This report presents results of the aircraft impact study, which includes the analysis of the Reactor Building shell for various locations of the above loadings; and, the plate analysis for the
Case D loading, which is the basis for wall and roof slab designs for vital structures other than
the Reactor Building shell. The paper entitled "On t he Stress Analysis of Structures Subjected to Aircraft Impact Forces" is applicable to this work except for the static analysis of flat plates
and a minor deviation in the dynamic load factors.
Also presented are additional studies to determine if the aircraft impact loading will produce a
loss of prestress force in the Reactor Building shell and, if the loss of prestress does occur, what effect this loss would have on the structure.
The final study presented is concerned with the possibility of the spalling of the anchors of the
liner due to an aircraft impact on the Reactor Building shell.
- 2. DYNAMIC LOAD FACTORS
The technique used to analyze these structures is based upon establishing a dynamic load
factor and applying this factor to a static solution.
In determining the DLF curve the response of an undamped, linear elastic one-degree-of freedom system is used.
- The analytical check on the basis of this loading considered a uniform collapse resistance of the fuselage which indicated that the integrity of the Reactor Building would
not be jeopardized. Further investigation indicated that the assumption regarding
uniform deceleration is not conservative. When a revised description of deceleration for
Case C was assumed, based on a variable distribution similar in principle to that shown
in Figure 5A-35 for Case D, the analytical methods employed did not demonstrate that
the Reactor Building would remain stable. As described in Section 3.1.1.2, the check
was made for the Case C aircraft based on a constant loading and was found to be less
severe than the Case D aircraft analyzed is described in Section 3.1.1.3. Because of the
extremely remote probability of the Case C aircraft impacting at the most unfavorable
location and attitude, the Case D aircraft for impingement was finally adopted as the
design basis.
The idealized total reaction vs time curve is as shown in Figure 5A-1. This total reaction vs time
curve describes quite well the results obtained from Tables 5A-6 and 5A-7 and Figures 5A-35
and 5A-36. The time variable t n and the ratio factor for a Boeing 720 airplane (Figure 5A-1) are shown in Table 5A-1.
TMI-1 UFSAR APPENDIX 5A 5A-2 REV. 18, APRIL 2006 The equations for dynamic load factors (DLF) for an undamped linear elastic one-degree-of-freedom system (Reference 2) are shown in Table 5A-2 in terms of the fundamental period T. The dynamic load factor is defined as the ratio between the dynamic response at any tine (t) and the static response to the peak load P.
The maximum response as a function of the period T for Boeing 720 impact is calculated by the
equations of Table 5A-2 and shown graphically in Figure 5A-3. Since this maximum response
curve is obtained, the analysis of plate and shell st ructures can now be analyzed statically once the dynamic load factor is chosen from Figure 5A-3 with reference to appropriate period T.
Figure 5A-3 represents a revised curve obtained from plotting additional points at
5 _ 2 cps frequency steps.
1000 100
Basically this curve is similar to the prev ious one but does pick up some oscillation which has been considered in the design.
- 3. ANALYSIS
The analysis of the vital structures as defined in Section 5.1.3 of the Final Safety Analysis Report is divided into two concepts: Section 3.1, Shell Analysis; and Section 3.2, Plate Analysis of this appendix.
3.1 SHELL
ANALYSIS
This analysis is used for the Reactor Building. The areas of impact that are considered to be
the most critical are; Apex of the Dome, Dome to Girder Transition, Girder to Cylinder
Transition, Impact at Grade.
3.1.1 APEX OF THE DOME
This analysis is divided into three parts.
3.1.1.1 Analysis For Case A & B Impact Loadings
A study of the protection against missiles res ulting from a hypothetical aircraft impact was made. The hypothetical missiles are defined as follows:
Case Weight Velocity Impact Surface A 6,000 lb 200 knots 5 ft diameter B 4,000 lb 200 knots 3 ft diameter
This study consisted of an investigation of the overall structural response due to central impact of the missile on a spherical dome as well as the resistance to penetration due to a local
material failure.
TMI-1 UFSAR APPENDIX 5A 5A-3 REV. 18, APRIL 2006 3.1.1.1.1 Structural Response
- a. Introduction An upper bound of permanent displacements was determined resulting from direct central aircraft impingement on a spherical dome. The basic tool used was the
displacement bound theorem for rigid- plastic continua (Reference 3). The initial velocity
distribution is determined on the basis of an inelastic collision between the missile and
the structure.
- b. Limit Analysis for Ring Loads First we considered a simply supported spherical cap under a ring load (See Figure 5A-4). The intensity of the load is "P" per unit length (i.e. the total load = 2Pa). A lower bound on the limiting value of "P" is found by determining a stress field which satisfies equilibrium condition and which nowhere violates the yield condition.
To obtain a lower bound, we assumed that for r a N = O, M = M o where "M o" is the fully plastic moment per unit length. On this basis it can be then determined that:
where "2Pa" is the total ring load. For this condition where "a" approaches zero.
R
- c. Determination of the Initial Velocity Field
From the elastic solution for a concentrated load at the apex of a shell investigators have determined that "r e," the length over which the initial velocity distribution is felt is approximately 2hR where "h" is the shell thickness (References 4 and 5). Therefore the initial velocity is sensibly zero for r = r
- e.
The initial velocity distribution is considered proportional to the elastic static deflection due to a concentrated load at the apex. Because it is difficult to
determine these deflections in closed form for a spherical shell it was necessary
to approximate the deflection by several functions each one of which were used to determine M velocity of the missile immediately after contact. These functions included the following:
- 1. Linear variation
- 2. Simple trigonometric variation ++= )sin-(1 )sin (1)sin-(1 )sin (1 ln 1
cos sin M 4 Pa 2 o1.81 M Pa 2 o=
TMI-1 UFSAR APPENDIX 5A 5A-4 REV. 18, APRIL 2006
- 3. Variation suggested by a simply supported circular plate under a central concentrated load. 4. Variation suggested by a clamped circular plate under a central concentrated load.
For these cases the numerical values of " ", v o and T o are as shown on Table 5A-3. where: = fraction of responding dome mass as previously described v o = velocity of M immediately after contact T o = initial kinetic energy of the dome
- d. Application of the Displacement Bound Theorem
Using the displacement bound theorem it can be shown that
where W o U.B. is the upper bound of the deflection at r = O.
"M o ," the fully plastic moment per unit length, is conservatively developed considering that at plastic collapse the tendons are not carrying any load and that
only the 3/8 in. steel liner acts as reinf orcement with a yield strength of 30,000 psi. Therefore, M o = 393,000 lb ft/ft which results in a conservative lower bound.
Considering the previous cases for distribution of initial velocity, the upper bound
of displacements are therefore as shown on Table 5A-4.
The average value of 0.97 inches for W oU.B. is considered to be a reasonable and representative number for an upper bound deflection. It should be noted that this
analysis provides only an order of m agnitude determination of the upper bound of displacement and based upon comparison with actual displacement of a flat
circular plate with "a/R = O," that is a concentrated in lieu of a ring load, the
upper bound errs on the high side.
The conclusion can be drawn on the basis of this analysis that the structural response of the dome does not produce a condition of collapse. This solution
does not consider the problem of local material failures which could lead to a
more serious problem than the overall structural response.
3.1.1.1.2 Local Material Failure
A study was made of the problem of local penetration making use of the modified Petry formula, wherein:
D = k Ap V'
where: D = depth (in feet) of penetration
k = experimentally obtained material's coefficient for penetration
o o U.B.o M 1.81 T W=
TMI-1 UFSAR APPENDIX 5A 5A-5 REV. 18, APRIL 2006 Ap = sectional pressure obtained by dividing the weight of the missile by its maximum cross-sectional area (expressed as pounds per square foot)
V' = velocity factor expressed as log 10 (1 + V 2 ) 215,000 where "V" represents the terminal or striking velocity in feet per second.
On the basis of "k" being equal to 0.0023 the penetrations are as follows:
Case A D = 0.128 ft = 1.54 in.
Case B D = 0.237 ft = 2.85 in.
both of which are less than the limit established for valid use of this equation. The material
coefficient "k" has been determined by experimental re sults for reinforced concrete with different compressive strengths. Variation in material pr operties will affect the k-value used and thereby the depth of penetration. However, the thickness of the reinforced concrete used for aircraft
protected structures exceeds the lower limit fo r use of the modified Petry formula. A study of missile penetration was made using the Ballistic Research Laboratories formula (Reference 22)
which resulted in deeper penetration but well within acceptable limits.
The impact of detached aircraft elements such as engines etc., will hit at a distance away from the center of impact. The top and bottom surface of the shell (See Figure 5A-15) in this location
will be in compression, and the combined flexural stress less than at the center of impact. The
engines have not been considered to hit at center of impact, however, the effect of the whole Class D aircraft remaining intact has been evaluated as discussed in Section 3.1.1.3.
3.1.1.2 Analysis For Case C Impact Loading
A study was made of the protection against a hypothetical aircraft impingement by an aircraft weighing 300,000 pounds, traveling at a velocity of 200 knots and impacting over an area with an effective diameter of 16 feet. The stability of the reactor containment structure was verified
by means of dynamic elastic analyses fo r the impingement of the total aircraft.
The effect of a large aircraft impingement against t he apex of the reinforced concrete dome was as studied by calculating the dynamic response of an elastic solid of revolution to
time-dependent forces acting on the area of impact, as shown in Figure 5A-5. The magnitude
and duration of the impact forces were determined according to the mass, structural
characteristics, and vertical component of the velocity of the aircraft. The grid for the
finite-element idealization of the dome is given in Figure 5A-6. Based on virtual work, the
equilibrium equations for the entire structure are formulated as follows:
TMI-1 UFSAR APPENDIX 5A 5A-6 REV. 18, APRIL 2006
.. .
(m)d + [ (k) + 2 (m)] d + (k) d = f
where:
(m) = mass matrix
(k) + 2 (m) = damping matrix
(k) = stiffness matrix
d = displacement vector
Dots indicate time derivatives. These equations are integrated by means of a
Predictor-Corrector method with a Runge-Kutta-Gill starting procedure using a computer
program developed at Franklin Institute Research Laboratories. FIRL is acting as Consultant to
GAI in connection with this problem.
Evaluation of the results, in conjunction with a procedure proposed by Dr. Steven Batterman and utilized in the study described herein to calculat e limit (final) displacements in a rigid-perfect plastic shell will lead to safe estimates of the size and velocity of the largest aircraft that may
impinge upon the containment building without jeopardizing its structural integrity.
An analysis was performed considering the following loading condition (Refer to Figure 5A-5 for
nomenclature):
P n = 200 psi
t 1 = 0 t 2 = t 3 0.16 sec.
The diameter of the impact area was considered to be 16 feet. In order to obtain a preliminary
indication of displacements, this analysis was performed on the basis of the conservative
assumption of no internal damping. Also to simplify the solution, the steel liner was not
considered.
The equivalent diameter of the fuselage of the B707 type aircraft is approximately 13.3 feet.
The assumed impact area is considered to be reas onably indicative of the impact area of such an aircraft considering the significant distortion which will occur to the fuselage as well as the
load distribution afforded by the concrete to the middle surface of the dome.
The loading pressure of the 300,000 lb aircraft without impact would be 10.4 psi. Therefore the
loading considered represents a constant deceleration of the impacting aircraft of 20g. That
means that the entire aircraft remains intact and all elements decelerate at 20g. This
represents an equivalent load on the fuselage of the aircraft of 5,800,000 lb, which it is
estimated would result in gross collapse of the aircraft.
The analysis indicates that the maximum displacements and stresses all of which occur at the
center of impact (i.e. the apex of the dome) are as follows:
TMI-1 UFSAR APPENDIX 5A 5A-7 REV. 18, APRIL 2006 Displacement (in). Stress (psi)
Maximum -0.98 -2264
+ 354
Static -0.66 -1832
+ 346
The displacement at the apex of the dome as a function of time is depicted in Figure 5A-7. This
graphical representation of displacements indicates that the most severe duration of the loading
is equal to or greater than 0.16 seconds. The static displacement is that produced by the 200
psi loading applied for an infinite period. Figure 5A-8 depicts the displacements and stresses
which occur at time 0.16 seconds after impact w hich is the instant of maximum displacement at the dome apex.
The loading considered in this analysis represents the case where the aircraft with all its
engines, fuel tanks, and wings remains intact and the total resulting load is applied on the nose
of the aircraft. It has been concluded that the resultant load due to one or both wings shearing
off the fuselage and impacting against the dome will result in a less critical condition than that
previously considered. The static displacement of the dome at the point of impact of one engine is approximately 0.1 inches. The displacem ent results from a loading equivalent to a 20g deceleration applied for an infinite period. The physical separation of engines is sufficient to
produce only a minimal increase in displacements due to the fact that the wings or engines upon separation from the remainder of the aircr aft would be traveling at significantly reduced speed.
The results obtained from the Analysis for Case C Impact Loading were not used for the final
design of the Reactor Building Dome and Shell.
3.1.1.3 Analysis For Case D Impact Loading
A study was made of the protection against a hypothetical aircraft impingement by an aircraft weighing 200,000 pounds, traveling at a velocity of 200 knots and impacting over an area with an effective diameter of 19 feet using the same analytical techniques described in Section
3.1.1.2 of this appendix. The final design of the Reactor Building was based upon the case D
Impact Loading Analysis.
The load-time curves for the 200,000 lb. aircraft as shown on Figure 5A-2 were used as the
design basis and was derived from the geometry , structure characteristics, and mass distribution of the B720 type aircraft.
Two loading cases were considered; one in which the outboard engines, wing structure, and
outboard fuel are separated from the aircraft at a prescribed time following impact (Table 5A-6 and Figure 5A-2), and one in which the aircraft is assumed to remain intact after the initial
impact (Table 5A-7 and Figure 5A-2).
TMI-1 UFSAR APPENDIX 5A 5A-8 REV. 18, APRIL 2006 The reaction load can be derived as follows:
Linear Impulse = Linear Momentum and: [][]1 2 V delta-V L t delta LM XV LV LM Rµµµ+=
()()V X V delta L t delta Rµ+µ= ())(t delta X delta t delta V delta L R Vµµ+= In the limit: R =
µLa + µV 2 and µL = M= mass of uncrushed aircraft thus µLa = Ma = P B (the unbalanced force on the uncrushed
portion of aircraft)
therefore: R = P B + µV 2 where:
R = Total reaction load on rigid surface in pounds
P B = Load in pounds required to crush or deform fuselage longitudinally
µ = mass of aircraft per unit length (slugs/ft)
V = velocity in ft/sec of uncrushed portion of aircraft at any time or distance during the impact
Instrumented data from a full-scale C-119 aircra ft impact into a vertical wall indicated that the results given by the above momentum exchange pr inciple for a B720 aircraft were of the right order of magnitude; however, the actual reaction load (P B) to the wall by the C-119 aircraft was not recorded. The rate of change of the air craft velocity was determined, however, by high speed film analysis and compared with the rate of velocity change with the B720 aircraft as
shown in Figures 5A-9 & 5A-10. This comparison shows that both aircraft decelerate at
approximately the same rate; however, the B 720 required more than twice as much crush distance because of its higher initial impact velocity.
- Structural properties of the aircraft considered in Reference 1 were obtained from The Boeing Company.
TMI-1 UFSAR APPENDIX 5A 5A-9 REV. 18, APRIL 2006 The reaction load as a function of time is presented in Figure 5A-2 and 5A-35 for the B720.
Note that the peak reaction occurs as the wing and fuselage are crushed between the front and rear spars. This is caused by the fact that the "µV2" is largest at this location ("µ" is very high here as shown by the mass distribution in Figure 5A-11). Also note that the fuselage
deceleration is highest when the reaction load is rather low. This phenomena is caused by the
reduced mass of the uncrushed portion of t he aircraft being decelerated by the relatively constant buckling load (P B) acting on the uncrushed portion. See Tables 5A-6 and 5A-7, and Figure 5A-2. The buckling load (P B) of the fuselage is shown in Figure 5A-12
- . The average diameter of the fuselage for the B720 aircraft is 13.3 feet. As can be seen from the load-time
curve the peak load occurs after the wings hav e impacted against the dome. Considering that the wings constitute a large proportion of the total mass, it is considered justifiable to consider a
portion of the wings that is in contact with the dome at the peak load as additional impact area.
Considering this additional area and the load distribution afforded by the concrete to the middle
surface of the dome, the effective diameter of the impact area is 19 feet.
The analysis indicates that maximum induced extreme compressive fiber stress of 7742 psi and
displacement of 1.81 inches occurs at the center of the impact area.
For the two loading cases, the displacements of the apex of the dome as a function of time are
shown in Figures 5A-13 and 5A-14. For comparis on, the displacement of the points at a radius of 115.2 and 268.8 inches are also shown. Stresses due to the aircraft impingement and
prestress near the apex and at a radius of 85 inches are shown in Figures 5A-15 and 5A-16.
The maximum combined extreme compressive fiber stress is approximately 9372 psi. This includes stresses due to aircraft related loads and the prestress loads. It has been recognized
that biaxial stress conditions as produced in the Reactor Building due to prestress, increases
the ultimate strength of concrete. Consider ing that the minimum cylinder strength of the concrete for the Reactor Building is based upon a 28 day curing time, an increase of 20 percent
in strength can be justified (Reference 12) considering that the concrete will have cured more
than two years when the plant is in operation. The present records of the 90 day compressive
strength of the same concrete used in the shell is in agreement with this strength increase. The strength of concrete under biaxial stress when was determined by Rosenthal and Glucklich (Reference 26) to be c f 2.2 = 2.2 x 6000 = 13,200 psi.
The local radial tensile stresses around the dome tendon conduit was determined utilizing the
Finite Element Method including in the model in the effect of the 5"f, Schedule 40 steel tendon
conduit. The model shown in Figure 5A-40 consist of an axisymetric solid of revolution. The loads applied to the model are:
- a. Radial prestress from each of the three tendon layers
- b. Meridional prestress
- c. Meridional stresses due to aircraft impact
The resulting radial tensile or compressive stresses are shown on Figure 5A-41. The radial
stresses shown in parenthesis are the results of the loads described above excluding the
external dome pressure due to the crushed fuselage. The radial stresses have been adjusted
for this external pressure. The stress concent ration around the conduit was greatly absorbed by TMI-1 UFSAR APPENDIX 5A 5A-10 REV. 18, APRIL 2006 the steel conduit and thereby reduced the expected larger tensile and compressive stresses in the adjacent concrete. Two local areas of concrete tensile stresses exist on an axis +/- 45 W from the axis parallel with the dome surface. Any tensile cracking in this region would be limited by the confining compressive stresses. A local tensile crack in these regions of the concrete close
to the conduit will increase the biaxial concrete compressive stress to approximately 9.150 psi
<13,200 psi considering an average stress over the uncracked portion of concrete. This is the
worst condition which exists approximately 8 inches from the dome surface, and is a conservative method for evaluating the load carrying capability of the concrete. In fact, essentially all concrete is subjected to triaxial compressive stresses which further increases the
concrete capacity. A schematic showing the stress state of the dome in relationship to the
conduit is shown in Figure 5A-42.
The maximum compressive stress at the center of the first tendon conduit is f C = 5000 psi, with no radial tensile stresses.
The loading considered in this analysis of the dome were:
- a. Prestress load
- b. Radial tensile stresses due to tendon curvature
- c. Stresses introduced due to aircraft impact.
Stresses in the dome at the edge of the loaded area of the aircraft are for wings and engines
attached:
Meridional Hoop
f C top = - 6268 psi f C top = -6419 psi f C bottom = - 4931 psi f C bottom = +128 psi Shear v C = 470 psi
The concrete compressive stresses are acceptable; and the shear stress below that permitted
by ACI 318-63, Chapter 26.
Stresses in the dome 36 inches out from the loaded area of the crushed aircraft for wings and
engines attached (Figure 5A-37) are:
Meridional Hoop
f C top = -3600 psi f C top = -5268 psi f C bottom = -3440 psi f C bottom = -342 psi Shear v C = 356 psi
The concrete compressive stresses are acceptable; and the shear stress below that presented
by ACI 318-63, Chapter 26. (Figures 5A-38 and 5A-39)
It is of interest to note that the high fiber stresses at the apex of the dome are reduced
significantly to the location at the periphery of the loaded area and at a distance "d" from the
periphery of the loaded area.
No special investigation has been made for the ca se of simultaneous impact of the partially disabled aircraft and the detached elements (outboard engines, wing structure, and outboard TMI-1 UFSAR APPENDIX 5A 5A-11 REV. 18, APRIL 2006 fuel) on separate locations. The impact of the aircraft with a 19 ft-0 in. diameter impact area is the most critical load case. It will be seen by inspection of Figure 5A-15 that detached elements
will impact in areas at significantly lower st ress level. It is considered improbable that the partially disabled aircraft can impact on the stru ctures at a location that has been damaged by the previous impact of the detached elements.
The impact of the entire aircraft on the dome has been analyzed and the results are shown in Figure 5A-16.
Therefore, the conclusion can be safety drawn that the dome will not collapse due to the
established loading condition.
3.1.2 DOME TO GIRDER TRANSITION
This analysis is in accordance with the methods described in Section 5.2.4.1 and was made for
Case D loading by a hypothetical aircraft described in Section 3.1.1.3. The non-axisymmetrical load is represented by a Fourier Series and has the general dimensions and shape as shown in
Figure 5A-17. The stress resultants are shown in Figure 5A-18.
3.1.3 GIRDER
TO CYLINDER TRANSITION (SPRING LINE)
Analyzed the same as 3.1.2 above. The stress resultants are as shown in Figures 5A-19 and
3.1.4 IMPACT
AT GRADE
Analyzed the same as 3.1.2. The stress resultants are as shown in Figure 5A-21.
3.2 PLATE
ANALYSIS
This analysis was made for the Case D loading by a hypothetical aircraft as described in
Section 3.1.1.3.
3.2.1 FUNDAMENTAL
FREQUENCY
It is readily seen in Figure 5A-3 that as long as the fundamental frequency of the plate is greater
than 10 cps, or less than 6 cps, the dynamic load factor will be less than 1.32. In the present plate analysis, all of the slabs have the fundamental frequency greater than 10 cps. The
fundamental frequency calculated for each slab (except two slabs which will be explained
subsequently) is based on the assumption of simply-supported boundary conditions. This
assumption will lead to a lower value of fundamental frequency for the current plates because
their boundaries are actually restrained rather than simply-supported. The value of E employed in the dynamic analyses was equal to the static modulus, and no account was taken of the
increase in E resulting from the dynamic load effect in order to compensate for any reduction of E due to high stress levels. This approach is felt to be conservative because (1) the structure
fundamental frequencies fall to the left if the peak in the maximum DLF vs. frequency curve and
(2) the area of impact, where the highest stress lev els occur, is relatively small compared with the total structure. These low values of f undamental frequency will give a conservative dynamic load factor as can be seen in Figure 5A-3. Consequently, variation of the elastic properties and
edge conditions from the assumed parameters w ould lead to a reduction of the magnitude of the dynamic response. When the dynamic load factor value falls below unity, a minimum factor of 1.0 is used. The theoretical background of calculating fundamental frequency of simply TMI-1 UFSAR APPENDIX 5A 5A-12 REV. 18, APRIL 2006 supported plate is straightforward and well documented. (References 2, 13, and 14). The well known formula of natural frequency is:
a mn = X 2 D (m)2 + (n)2 ph a b
where m and n denote the mode number; D is the flexural rigidity; p is the density; and a, b, and
h, are length, width, and thickness of plate, respectively.
For the two exceptional plates where the boundary c onditions are more likely to be fixed, the fundamental frequencies are calculated based on fixed boundaries. There is no exact solution
of fundamental frequency for such cases; howev er, numerical approximations which are based on energy principle are available. (References 2, 15, and 16). The present calculations of
fundamental frequency of fixed plate are obtained from the tables and suggested formulae in
Chapter 5 of "Introduction to Structural Dynamics" (Reference 2).
After obtaining the fundamental frequency of each slab and the dynamic load factor, the
remaining work is a statical slab analysis.
This approximate dynamic analysis technique is equivalent to the assumption that the DLF's of all modes are equal to that of the fundamental mode. For the computation of maximum response for design purposes, this approach is
conservative for the following reasons:
- a. The fundamental periods of all the slabs fall to the left of the peak in the diagram of maximum DLF vs. period, thus indicating that the higher modes have smaller
maximum DLF's.
- b. The maximum DLF's of the various modes do not occur simultaneously.
- c. The maximum bending moment results when the impact occurs at the center of the slab. For this case, the fundamental mode dominates the response.
- d. The maximum transverse shear is obtained when the impact takes place near a supporting edge, in which case most of the load is transferred directly to the
support with little dynamic participation of the slab.
In order to assess the validity of these assertions, the study reported in Reference 21 was
recently extended to evaluate the dynamic res ponse of a typical slab subject to impact at various locations (center, edge, and intermediate points). In this study, mode superposition, using up to 900 modes (30 harmonics in each c oordinate direction), was employed with the expressions for the DLF given in Table 5A-2 to c alculate the time history of the displacements and stress resultants at critical positions for the Boeing 720 impact. The maximum values of
these quantities were compared with the corresponding static values, and it was found that for
every one the ratio of maximum dynamic value to static value was less than the maximum DLF
for the fundamental mode. Therefore, the design values obtained by factoring the static responses by the maximum fundamental DLF would in every case be larger than the actual
maximum, indicating that this procedure will yield a conservative design.
TMI-1 UFSAR APPENDIX 5A 5A-13 REV. 18, APRIL 2006 3.2.2 FINITE-ELEMENT ANALYSIS FOR SLABS
The present finite-element analysis is based upon a rectangular plate element (Figure 5A-22) as developed in References 5A-16 and 5A-17. Each nodal point has 6 degrees-of-freedom. A
comprehensive explanation of the satisfaction of the "completeness" and "compatibility" of the chosen displacement function is given in Referenc es 5A-18 and 5A-19. The convergence of the solution accuracy vs grid refinement is monotonic and rapid as evidenced in various References
5A-16, 5A-17, 5A-18, and 5A-19. For the problem of plate in bending, 16 elements
discretization can lead the solution of deflections to a small error of less than five percent as
compared with classical solutions. The element number used in the present calculation ranges
from 25 to 64 for various slabs.
Since the finite-element method is much less restricted to the geometry and boundary
conditions than the classical solution, the actual geometry and boundary conditions are
represented in the present calculation without modifications.
As an illustration of the present slab analysis and design, an example of roof slab at the heat exchanger vault of the auxiliary building at E levation 305 ft is chosen. The dimensions and boundary conditions are shown in Figure 5A-23(a). The dynamic load factor, based on the
elastic undamped one degree-of-freedom assumptions, was found to be 1.188.
As shown in Figure 5A-23(a), nine critical impact positions, which produce the critical moments and shears at various sections, were examined.
As a simplified demonstration, the moment diagrams along line AA are shown in Figure 5A-23(b). The top and bottom reinforcements
corresponding to the moments in Figure 5A-23(b) were designed and shown on GAI Drawing
422030. The shear reinforcement designed for this slab is shown on GAI Drawing 422031. The
shear reinforcements were designed on the basis of the aforementioned finite-element
computer program output of shears.
The slab is a rectangle 121'-0 by 55'-0 by 6'-0 as shown on GAI Drawings 422030 and 422031.
The slab is supported along all four edges and along the East-West centerline. For the purpose
of this analysis, only the southern half has been considered. Moment curves have been plotted for the different impact positions. Five im pact positions have been considered. An envelope was then constructed in order to obtain maximum moments at any point along section A-A, Figure 5A-23. This envelope was used to calculate the required reinforcement. A similar
procedure was used to calculate the moments for another 4 strips of the slab in the North-South
direction and 5 strips in the East-West direction.
3.2.3 DESIGN
CRITERIA FOR REINFORCING
The wall and roof slabs exposed to aircraft impact have been designed according to the
following criteria.
- a. The main reinforcing is designed on the basis of bending moment diagrams obtained from computer printouts using Case D loading and according to the ACI
318-63, Ultimate Strength Design Method, Chapter 15.
- b. The shear reinforcing is designed on the basis of the shear force diagram obtained from computer print-outs using the Case D loading and according to the
ACI 318-63, Ultimate Strength Design Method, Chapter 17.
TMI-1 UFSAR APPENDIX 5A 5A-14 REV. 18, APRIL 2006
- c. Anchorage for the reinforcing bars is provided by carrying the reinforcing bars past the theoretical cut-off point a distance sufficient to develop the ultimate
strength of the bar.
- d. The allowable bond stresses are calculated on the basis of ACI 318-63, Chapter
- 18.
- e. No welding has been done on reinforcing bars.
- f. In the design no special construction methods were specified.
3.2.4 DESIGN
CHECK
It is recognized that the elastic analysis employed for the flat slabs is conservative and that the
resulting design does have a capacity in excess of that implied by the load considered for slab
design.
As a conclusion of this design, each wall and roof slab exposed to aircraft impact was checked
utilizing the Yield Line Theory (Reference 25).
These aircraft-protected structures can withstand at least a load equal to 1.52 x (17,500,000) =
26,400,000 lbs. This load represents the maximum load as determined in the previous section, with the peak DLF = 1.52 as shown in Figure 5A-3.
- 4. ADDITIONAL DETAIL STUDIES
Some additional studies on the detail structural analysis of the aircraft impact on the
containment vessel have been made:
- a. Bearing failure of concrete in the neighborhood of anchors of tendons under direct impact.
- b. Shear-off of the anchors of the dome tendons, vertical tendons, and hoop tendons.
- c. Spalling due to aircraft impact on the outside wall.
- d. Impact effects on equipment and components.
4.1 BEARING
FAILURE OF CONCRETE UNDER DIRECT IMPACT The bearing capacity of concrete, according to ACI-318-63, is 1.9 x 0.375 c f = 3560 psi. The aircraft impact force of 21,100 kips (assuming a dy namic load factor of 1.2), according to the 19 foot diameter (283.5 ft
- 2) circular normal impact area, produces an impact pressure of 21.1 x 10 6/283.5 x 144 = 517 psi. It is readily seen that the aircraft impact does not cause bearing failure as long as the total impact force is distributed on an area greater than 41.1 ft
- 2. (Reference 2) (corresponding to a bearing stress of 3560 psi). Thus, it may be concluded that TMI-1 UFSAR APPENDIX 5A 5A-15 REV. 18, APRIL 2006 bearing failure can be prevented as long as the impact force is distributed on an area greater than 5.14 283.5 41.1=percent of the normal impact area.
Intuitively, it is believed that no matter where t he aircraft hits, the impact area should be at least 14.5 percent of the area of the case when the aircraft impacts on a flat wall.
The anchors of the dome and vertical tendons are embedded in concrete at least one foot in
depth. No damage of the anchors is possible when the aircraft hits normal to the anchorages.
Although the hoop tendon anchorages are not embedded in concrete, the aircraft would have to
hit in a tangential direction to the containment vessel to produce a bearing failure of the
anchorage.
This being the case, it is unlikely that the total impact force will be concentrated over less than
14.5 percent of the normal impact area; therefor e, a bearing failure of the concrete at the hoop tendon anchorages will not occur.
4.2 SHEAR-OFF THE ANCHORS
Three cases have to be investigated when considering the possibility of shearing-off the
anchors of the tendons due to aircraft impact, particularly the impact of engines and sharp
object.
4.2.1 CASE A: SHEAR-OFF THE ANCHORS OF VERTICAL TENDONS
The aircraft may travel in the direction shown in Figure 5A-26 such that the anchors of vertical
tendons may be sheared-off. Based on the investigation conducted in Reference 1, the
information is available that the maximum response of statically equivalent impact load is 21.1 x
10 6 lb (assuming conservatively a dynamic load fact or of 1.2) and the maximum impact area is a 19 ft diameter circle (assuming the aircraft strikes normal to a flat wall). The shear strength at Section A-A shown in Figure 5A-27 governs whether or not the aircraft will shear the concrete and impinge at the anchors. The shear stress at Section A-A must be calculated for the worst
condition of impact loading and compared with the shear capacity.
Considering the maximum aircraft impact area with a diameter of 19 ft, the maximum number of
covered tendons are:
7.47 30.5 12 x 19 anchors b etween dist. C. to C.ft 19 N===
As a very conservative estimation, the impact force on the area between two anchor centers is:
lb/tendon 10 x 2.83 7.47 10 x 21.1 N response Max.P 6 6===
TMI-1 UFSAR APPENDIX 5A 5A-16 REV. 18, APRIL 2006 The area available for resisting the shear can be estimated from Figures 5A-27 and 5A-28.
A = 28" x 30.5" = 853 sq in.
It is reasonable to assume that the load applied above Section A-A is proportional to the area of impact.
[]lbs. 6 10 x 21.1 25 x 15 25 x d where d = 2'-2".
The applied load = 3.1 x 10 6 lbs which results in a shearing stress across Section A-A equal to psi 600 psi 369 28 (12) 25 lbs. 6 10 x 3.1<= Ultimate shear strength of concrete f ult = 600 psi. Although unlikely, it is, however, assumed that nine anchors are sheared-off by the aircraft impact.
As illustrated in Figure 5A-29(a) it is seen that Section AA is of primary concern if vertical tendons fail under the impact. The moment m 1 , caused by the aircraft impact, has to be resisted by the moment m
- 2. The moment caused by the aircraft impact is:
m 1 = 21.1 x 10 3 x 166.5 x 12 = 4.2 x 10 7 in-kips The moment due to the undestroyed tendon prestressed forces resisting, m 1 is:
m 2 - T(d 1 + d 2) where T is the total prestressed forces on tension side of N.A., for the case when there is no
tensile force in section AA. The tendons do not exceed their prestressed forces. Then,
T = 37 x 2 x 1090 = 8.06 x 10 4 kips d 1 and d 2 are the distances from the neutral axis to the centers of gravity of the active tendons on the tension and compression sides of the neutral axis respectively as shown in Figure
Therefore:
m 2 = T(d 1 + d 2) = 8.06 x 10 4 x 987 = 7.95 x 10 7 (k-in)
It is now concluded that even with a dynamic load factor 1.2 and a very conservative
assumption that nine tendons are covered by t he airplane impact and are destroyed, the safety factor for not causing
tension at section AA is:
S.F. = m 2 = 7.95 x 10 7 = 1.90 m 1 4.2 x 10 7
In order to shear-off nine vertical tendon anchorages, the aircraft must impact as shown in
Figure 5A-26. A reasonable assumption is that the impact load will be concentrated above the
ring girder. As a conservative estimate of the resulting forces, the forces shown on Figure TMI-1 UFSAR APPENDIX 5A 5A-17 REV. 18, APRIL 2006 5A-18 due to the aircraft impact at the girder to dome transition were used. Figure 5A-18 shows that the maximum moments and shears occur in the dome. Therefore, the resisting prestress
forces in the critical dome area are not affected by a loss of vertical prestress.
The shear stresses in the wall are of concern because the allowable shear stress reduces when
the meridional axial force is lost due to the failure of nine vertical tendon anchorages. The
shear stresses at three locations were determined and compared with an ultimate shear stress
of 2ff C (ACI 318-63).
The three locations are:
- a. Cylinder wall to ring girder transition
- b. Base of wall
- c. Ten feet above the base of the wall (Haunch to typical wall transition)
Although the shear stress at location a. exceeds 2 o f C , the shear reinforcement required is less than that pr ovided for the normal loading cases under no loss of prestress. The shear stresses at locations b.
and c. are less than the ultimate shear stress.
4.2.2 CASE B: SHEAR-OFF THE ANCHORS OF DOME TENDONS
If the aircraft impact occurs as shown in Direction 2 of Figure 5A-30, the shear resisting capacity
of the concrete at Section AA has to be greater than the impact force so that no force will be
transferred to the anchors of the roof tendons. The shear resisting area, assuming a 19 ft width
of impact area is:
A = 19 ft x 6.416 ft x 144 = 17,554 in
- 2. The total shear capacity of concrete against the vertical impact is:
F = 600 x 17,554 = 10.53 x 10 6 lb which is smaller than the aircraft impact load 21.1 x 10 6 lb (with a conservative assumed dynamic load factor 1.2).
It is reasonable to assume that the applied load is proportional to
the area of impact. [1.25 x 19
] 21.1 x 10 6 lbs. 15 x 19
The applied load = 1.76 x 10 6 lbs which results in a shearing stress across section A-A of Figure 5A-30 = 1.76 x 10 6 lbs = 100 psi <600 psi.
19 (6.416) (144)
Under the above analysis, the dome tendon anchorages will not fail in shear.
The dome tendons are composed of three layers ly ing on top of each other. Each layer is composed of parallel and equally spaced tendons (Figure 5A-31). As can be seen from Figure
5A-32, the orientation of the three layers is such that the tendons cross each other with a
constant angle of 60 degrees. Since the dome tendons are so close to each other, crossing TMI-1 UFSAR APPENDIX 5A 5A-18 REV. 18, APRIL 2006 each other, and overlying each other is intuitiv ely believed that no damage will occur to the dome even if a few tendons are assumed to be broken under the aircraft impact.
In addition to the previous logic, providing the failure of the dome tendon anchorages is caused
by an aircraft impact as shown in Direction 2 of Figure 5A-30, the major portion of the impact load will be resisted by the cylindrical wall and not by the dome which has lost the prestress forces due to 8 broken dome tendons.
If the aircraft travels in the Direction 3 as shown in Figure 5A-30, it is seen that the concrete
bearing failure is relatively small.
Previously, a calculation has shown that as long as the actual impact area is at least 14.5 percent of the maximum theoretical impact area, no bearing failure
will occur. Therefore, impact Direction 3 is of no critical concern.
4.2.3 CASE C: SHEARING-OFF THE HOOP TENDONS
The aircraft may travel in the direction shown in Figure 5A-33. Since there is no concrete cover
to protect the anchor, direct impact on the anchors may shear-off several tendons. As shown in
Figure 5A-33 the minimum vertical spacing between anchors on one side of the buttress in 33
inches. Each hoop tendon is anchored in one buttress, then passes by the adjacent buttress, and is finally anchored in the next adjacent buttr ess.The aircraft impact area has a minimum depth of 19 ft which can cover seven (i.e., (19 x 12)
= 6.9) anchors of hoop tendons.
33
If the most conservative assumption is made that all of the seven anchors are sheared-off due
to aircraft impact, one-half of the hoop prestress force in a cylindrical panel with a depth of 19 ft
and a curve length of one third of the cylinder periphery would be eliminated. An analysis is made considering the containment vessel with nor mal prestress conditions with the exception that a cylindrical segment with a depth of 15 ft has only one half of the hoop prestress. The
resultant axial forces and shears with half of the hoop tendon forces lost in the range between
800 inches and 965 inches above the base of the cylindrical wall are listed in Table 5A-5. It is
seen that the out of plane shear and hoop force have changed due to the failure of the hoop
tendons. The shear has increased considerably, but, is in the opposite direction of the shear
due to aircraft impact, and therefore aids in resisting the aircraft impact. When the aircraft
impact diminishes and the hoop tendons are still broken, the remaining shear is much less than
the ultimate shear stress according to ACI 318-63.
The above analysis does not consider the moment s caused by the loss of 8 hoop tendons.
Referring to Figure 5A-34, which is a comparison of (1) the loading due to aircraft impact plus
total prestress and (2) the loading due to aircraft impact plus total prestress minus the hoop
prestress due to the loss of hoop tendons, it can be deduced that the resulting moments will
tend to counteract the moments caused by t he aircraft impact. When the aircraft impact diminishes, the axial compression due to the remaining prestress forces (see Table 5A-5)
should be sufficient to overcome the tension due to the moments caused by the loss of hoop
prestress.
Based on the above logic and conservative numerical calculation, it is believed that the aircraft
impact in the direction shown on Figure 5A-33 does not jeopardize the stability of the structure.
TMI-1 UFSAR APPENDIX 5A 5A-19 REV. 18, APRIL 2006
4.3 SPALLING
DUE TO AIRCRAFT IMPACT ON THE OUTSIDE WALL
Spalling is the kind of fracture which results from the interference between the incident
compressional wave and its reflected counter-part. The mechanics of spalling can be described
graphically as follows:
Compressive wave before Part of the compressive wave reaching the free surface reflected back from the free surface
The spalling will occur at a distance Y from the free surface, if the net tensile stress AB exceeds
the tensile fracture strength of the material (References 23 and 24). From these we can see
that the spalling is influenced by two factors, (a) the duration and shape of the stress pulse, and (b) property of the material acted on.
The plane dilatational wave will travel through the plate at the speed of S + 2T , were delta, T are Lame's constants and Y is the
p density of the material.
Transform (S + 2T) to a form in terms of Young's Modulus E, and Poisson's ratio U, which engineers are more familiar with. We have:
S + 2T = E (1 - U)
(1 + U) (1 - 2U)
For concrete, with E = 4,000 ksi, U = 0.15, pg = 145 lb/ft 3 , the wave velocity is: c = 1.4 x 10 5 in./sec = 11,650 ft/sec.
Hence, for the structure we are concerned with, the spalling may occur only for the stress pulse
duration of the order of microseconds. The first unloading of our impact force occurs at
0.19 seconds. In other words, for a wall of 5 ft thickness, the wave has to travel back and forth
almost 220 times before the impact force reaches the unloading point. Due to the internal
friction, the stress wave is long dispersed before it can build up tensile stress in the structure.
So the spalling effect is almost impossible to occur.
Nevertheless, the anchors on the containment vessel liner above grade will be deeply anchored
into the concrete wall with one inch diameter bolts (form 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.
The design criteria for the liner anchors is described in Section 5.2.3.2.5 "Liner Anchor". The
liner angle welds have been tested by 20 percent liquid penetrant test 100 visual inspection in
accordance with the requirements of Section VIII of ASME Boiler and Pressure Vessel Code.
Three specimens of the liner angle welds were tested by Pittsburgh Testing Laboratory and the
factor of safety was found to be 2.7 against the worst possible load on the liner anchor.
TMI-1 UFSAR APPENDIX 5A 5A-20 REV. 18, APRIL 2006
4.4 IMPACT
EFFECTS ON EQUIPMENT AND COMPONENTS
To eliminate the shock effect caused by an aircraft impact, the concrete floor slabs in the
Control Building have been separated by a 2 inch wide joint from the exterior walls exposed to an aircraft impact. The concrete slabs are supported by steel beams which in turn are
supported on elastromeric pads which act as vibration dampeners.
4.5 REFERENCES
- 1. Haley, Jr., J. and Turnbow, J., "Total Reaction Force due to an Aircraft Impact into a Rigid Barrier," AvSER Report prepared for Gilber t Associates, Inc. by Dynamic Science, Phoenix, Arizona, April 1968.
- 2. Biggs, J. M., "Introduction to Structural Dynamics," McGraw-Hill Book Co., N.Y. 1964, Section 2.3.
- 3. J. Martin, "Impulsive Loading Theorem For Rigid-Plastic Continua," J. Engineering Mechs. Div., ASCE, EM5, October 1964, pp. 27-42.
- 4. K. Forsberg and W. Flugge, "Point Load On a Shallow Elliptic Parabaloid," To Appear in Journal of Applied Mechanics.
- 5. A. Kalnins and P.M. Naghdi, "Propagation of Axisymmetric Waves in An Unlimited Elastic Shell," Journal of Applied Mechanics, 27 , 1960, pp 690-695.
- 6. C. H. Norris 'et al': "Structural Design for Dynamic Loads
," McGraw Hill, 1959.
- 7. J. N. Cernica and M. J. Charignon: "Ultimate Static and Impulse Loading of Reinforced Concrete Beams." ACI Journal , V. 50, No. 9, 1963, pp. 1219-1228
- 8. Walter Cowell: "Dynamic Properties of Plain Portland Cement Concrete." Naval Civil Engin. Lab
., Port Huenema, Calif. Report NCEL 447, 1966.
- 9. H. Weigler and G. Becker: "Der Bauingenieur
," Berlin, Vol. 36, No. 10, 1961, pp.
390-396.
- 10. J. Peter: "Zur Bewehrung von Scheiben und Schalen fur Hauptspannungan Schiefwinklig zur Bewehrungstrichtung , Doctoral Thesis, Technische Hochschule Stuttgart, 1964.
- 11. G. W. D. Vile: "Strength of Concrete Under Short-Time Static Biaxial Stress."
Proceedings of International Conference on Structural Concrete , London, 1965.
- 12. Fritz Leonhardt: "Prestressed Concrete Design and Construction" Wilhelm Ernst &
Sohn, 1964, pp. 59.
- 13. Volterra, E. and Zachmanoglou, E., "Dynami cs of Vibrations," Charles Merrill Books, Inc., Columbus, Ohio, 1965.
TMI-1 UFSAR APPENDIX 5A 5A-21 REV. 18, APRIL 2006
- 14. Timoshenko, S. and Young, D., "Vibration Problems in Engineering," 3rd Ed., D. Van Nostrand Co., Inc., 1955.
- 15. Harris, C. and Crede, C., "Shock and Vibration Handbook," McGraw-Hill Book Co., N.Y., 1961.
- 16. Bogner, F., Fox, R, and Schmit, L., "The Generation of Interelement-Compatible Stiffness and Mass Matrices by the Use of Interpolation Formulae, "Proc. Conf on Matrix
Methods in Structural Mech., Dayton, Ohio, 1965.
- 17. Gallagher, R., "The Development and Evaluat ion of Matrix Methods for Thin Shell Structural Analysis," Ph.D. Dissertation, State University of New York at Buffalo, 1966.
- 18. Gallagher, R. and Yang H., "Elastic Instability Prediction of Doubly Curved Shell Structures," 2nd conference on Matrix Methods in Structural Mechanics, Wright-Patterson Air Force Base, Dayton, Ohio, Oct. 1968.
- 19. Yang, H., "A Finite-Element Formulation fo r the Instability Prediction of Doubly Curved Shell Structures," Ph.D. Dissertation, Cornell University, Ithaca, N.Y., Oct. 1968.
- 20. Timoshenko, S. and Goodier, J. N., "Theory of Elasticity," McGraw-Hill Book Co., 1951.
- 21. Riera, J. D., "On the Stress Analysis of Structures Subjected to Aircraft Impact Forces", Nuclear Engineering and Design, August, 1968.
- 22. Gwaltney, R. C., "Missile Generation and Protection in Light-Water-Cooled Power Reactor Plants" U.S. Atomic Energy Commission, DRNL-NSIC-22, September, 1968.
- 23. Rinehart, John S. and Pearson, John, "Behavior of Metals under Impulsive Loads" Dover, 1965.
- 24. Kolsky, H. "Stress Waves," Dover, 1963.
- 25. Wood, R. H. "Plastic and Elastic Design of Slabs and Plates," Ronald, 1961.
- 26. Rosenthal, I. and Glucklich, J., "Strength of Plain Concrete under Biaxial Stress," ACI Journal, November 1970.
TMI-1 UFSAR APPENDIX 5A 5A-22 REV. 18, APRIL 2006 TABLE 5A-1 TIME VARIABLE t n
Boeing t 1 t 2 t 3 t 4 t 5 t 6 I
0.06 0.14 0.19 0.24 0.26 0.33 0.219
TMI-1 UFSAR APPENDIX 5A 5A-23 REV. 18, APRIL 2006 TABLE 5A-2 DYNAMIC LOAD FACTORS (DLF)
DLF 1 = { t - T sin at} I (0 to t
- 1) t 1 2X t 1 DLF 2 = {1 + T
[sin a(t-t
- 1) - sin at]} I (t 1 to t 2) 2X t 1
DLF 3 = DLF 2 + {2(t-t 2) - T sin a(t-t 2)}(1-I) (t 2 to t 3) t p Xt p DLF 4 = DLF 2 + {1 - 2t-t 3 + T [2 sin a(t-t 3)-sin a(t-t 2)]}(1-I) (t 3 to t 4 t p Xt p DLF 5 = DLF 2 + T {- sin a(t-t
- 4) + 2 sin a(t-t 3)-sin a(t-t 2)}(1-I) (t 4 to t 5) Xt p
DLF 6 = DLF 5 - {t-t 5 - T sin a(t-t 5)} I (t 5 to t 6) t 6-t 5 2X(t 6 - t 5)
DLF 7 = DLF 5 - {1 + T
[sin a(t-t
- 6) - sin a(t-t 5)]} I (after t
- 6) 2X (t 6 - t 5) where:
a = 2X (radians/sec)
T
TMI-1 UFSAR APPENDIX 5A 5A-24 REV. 18, APRIL 2006 TABLE 5A-3 KINETIC ENERGY OF THE DOME
r e = 37.0' S v 8 T 8
(fps)
(ft-lbs)
Case 1 0.1667 5.8 0.182 x 10 6
Case 2 0.172 5.6 0.172 x 10 6
Case 3 0.228 4.3 0.133 x 10 6
Case 4 0.130 7.4 0.23 x 10 6
TMI-1 UFSAR APPENDIX 5A 5A-25 REV. 18, APRIL 2006 TABLE 5A-4 UPPER BOUND DISPLACEMENTS
r e = 37.0'
W 8U.B. Case (inches)
1 0.995
2 0.925
3 0.715
4 1.245
Average 0.97
TMI-1 UFSAR APPENDIX 5A 5A-26 REV. 18, APRIL 2006 TABLE 5A-5 COMPARISON OF STRESS RESULTANTS FOR PRESTRESS LOADINGS
E OUT OF PLANE SHEAR MERIDIONAL FORCE HOOP FORCE
L E Q(10
- 2) Nf (10
- 5) NP (10
- 5) V.* lbs/in lbs/in lbs/in
(1) (2) (1) (2) (1) (2)
800 -0.33 18.508 -.3730 -.3730 -.7166 -.5628 816 -0.32 14.446 -.3730 -.3730 -.5519 833 -0.309 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 -.7151 -.5305 899 -3.74 -.3730 -.3730 -.5317 915 -7.314 -.3730 -.3730 -.5355 932 -10.99 -.3730 -.3730 -.541 948 -14.83 -.3730 -.3730 -.5505 965 -0.010 -18.86 -.3730 -.3730 -.7150 -.5610
- INCHES ABOVE THE BASE CYLINDRICAL WALL
(1) WITHOUT LOSING TENDON
(2) 1/2 OF HOOP TENDON FORCES LOST TMI-1 UFSAR APPENDIX 5A 5A-27 REV. 18, APRIL 2006 Table 5A-6 Reaction Load (R) Calculations Case 1: With Wing and Engines Detached (C = 200 kts = 338 fps; M = 200,000 lb. = 6200 slugs)
TIME STRENGTH MASS MASS MASS MASS
OF FRAME
/FT CRUSHED LOST INTACT 0.0 0.0 0. 0. 0. 6200. 0.010 0.154 5. 9. 0. 6191.
0.020 0.307 9. 23. 0. 6168.
0.030 0.459 12. 35. 0. 6132.
0.040 0.565 18. 49. 0. 6083.
0.050 0.565 22. 69. 0. 6014.
0.060 0.565 25. 81. 0. 5933.
0.070 0.565 28. 89. 0. 5844.
0.080 0.565 28. 94. 0. 5750.
0.090 0.565 28. 93. 0. 5658.
0.100 0.565 28. 92. 0. 5566. 0.110 0.565 28. 91. 0. 5474. 0.120 0.565 28. 91. 0. 5383.
0.130 0.565 28. 90. 0. 5293.
0.140 0.629 28. 89. 0. 5204.
0.150 0.817 47. 109. 0. 5095.
0.160 1.007 62. 187. 0. 4909.
0.170 1.193 86. 236. 336.* 4336.
0.180 1.378 112. 319. 0. 4017.
0.190 1.550 156. 401. 962.** 2654.
0.200 1.550 167. 501. 0. 2153.
0.210 1.550 157. 485. 0. 1669.
0.220 1.550 89. 405. 0. 1264.
0.230 1.550 33. 128. 0. 1136.
0.240 1.550 32. 88. 0. 1048.
0.250 1.550 31. 79. 0. 969.
0.260 1.550 30. 72. 0. 897.
0.270 1.550 29. 64. 0. 832.
0.280 1.550 28. 57. 0. 776.
0.290 1.495 27. 50. 0. 726.
0.300 1.438 27. 43. 0. 683.
0.310 1.389 26. 36. 0. 646.
0.320 1.347 25. 30. 0. 616.
0.330 1.313 25. 24. 0. 592.
0.340 1.287 25. 18. 0. 574.
0.350 1.269 24. 12. 0. 561.
0.360 1.259 24. 7. 0. 555.
0.367 1.257 24. 2. 0. 553.
MAXIMUM REACTION LOAD = 17.213 LBS*10.0E 6
- Inboard engines stopped without significant deformation at barrier.
- Outboard engines, wing structure, and outboard fuel are separated from wing.
TMI-1 UFSAR APPENDIX 5A 5A-28 REV. 18, APRIL 2006 Table 5A-6 Reaction Load (R) Calculations Case 1: With Wing and Engines Detached (C = 200 kts = 338 fps; M = 200,000 lb. = 6200 slugs)
TIME DECEL VEL VELOCITY CRUSHED IMPACT DECEL CHANGE LENGTH CORCE G'S 0.0 0.0 0.0 338.00 0.0 0.0 0.0 0 010 24.9 0.13 337.87 3.41 0.71 0.77 0.020 49.8 0.37 337.50 6.79 1.30 1.55 0.030 74.9 0.62 336.87 10.16 1.84 2.33 0.040 92.9 0.86 336.02 13.49 2.60 2.89 0.050 93.9 0.93 335.08 16.85 3.07 2.92 0.060 95.2 0.95 334.14 20.19 3.38 2.96 0.070 96.7 0.96 333.18 23.53 3.65 3.00 0.080 98.3 0.98 332.19 26.89 3.65 3.05 0.090 99.9 0.99 331.20 30.21 3.62 3.10 0.100 101.5 1.01 330.20 33.51 3.60 3.16 0.110 103.2 1.02 329.17 36.81 3.57 3.21 0.120 105.0 1.04 328.13 40.09 3.54 3.26 0.130 106.7 1.06 327.07 43.37 3.51 3.32 0.140 120.8 1.09 325.99 46.60 3.57 3.76 0.150 160.4 1.41 324.58 49.85 5.72 4.99 0.160 205.1 1.84 322.74 53.12 7.41 6.37 0.170 275.1 2.32 320.42 56.34 10.05 8.55 0.180 343.0 3.08 317.34 59.53 12.63 10.66 0.190 584.0 4.99 312.34 62.68 16.81 18.15 0.200 719.8 6.47 305.87 65.77 17.20 22.37 0.210 928.8 8.10 297.77 68.76 15.46 28.87 0.220 1226.3 10.78 286.99 71.68 8.91 38.11 0.230 1364.3 13.07 273.92 74.49 4.05 42.40 0.240 1479.0 14.36 259.56 77.18 3.71 45.97 0.250 1600.4 15.40 244.17 79.70 3.40 49.74 0.260 1728.7 16.65 227.52 82.06 3.10 53.73 0.270 1862.5 17.96 209.56 84.25 2.82 57.89 0.280 1998.3 19.12 190.44 86.23 2.57 62.11 0.290 2060.6 20.35 170.09 88.03 2.29 64.04 0.300 2107.2 20.84 149.25 89.63 2.03 65.49 0.310 2149.7 21.29 127.96 91.02 1.81 66.82 0.320 2187.4 21.91 106.05 92.20 1.63 67.99 0.330 2218.7 22.04 84.01 93.15 1.49 68.96 0.340 2243.2 22.32 61.69 93.88 1.38 69.72 0.350 2260.4 22.30 39.39 94.38 1.31 70.26 0.360 2270.2 22.66 16.73 94.66 1.27 70.56 0.367 2272.4 16.81 -0.08 94.73 1.26 70.63 MAXIMUM REACTION LOAD = 17.213 LBS*10.0E 6
See Figure 5A-31, Reaction Load and Fuselage Deceleration.
TMI-1 UFSAR APPENDIX 5A 5A-29 REV. 18, APRIL 2006 5A-7 Reaction Load (R) Calculations Case 2: With Wing and Engines Attached (V. = 200 kts = 338 fps; M = 200,000 lb. = 6200 slugs)
TIME STRENGTH MASS MASS MASS MASS OF FRAME /FT CRUSHED LOST INTACT 0.0 0.0 0. 0. 0. 6200. 0.010 0.154 5. 9. 0. 6191.
0.020 0.307 9. 23. 0. 6168.
0.030 0.459 12. 35. 0. 6132.
0.040 0.565 18. 49. 0. 6083.
0.050 0.565 22. 69. 0. 6014.
0.060 0.565 25. 81. 0. 5933.
0.070 0.565 28. 89. 0. 5844.
0.080 0.565 28. 94. 0. 5750.
0.090 0.565 28. 93. 0. 5658.
0.100 0.565 28. 92. 0. 5566.
0.110 0.565 28. 91. 0. 5474.
0.120 0.565 28. 91. 0. 5383.
0.130 0.565 28. 90. 0. 5293.
0.140 0.629 28. 89. 0. 5204.
0.150 0.817 48. 110. 0. 5094.
0.160 1.007 84. 217. 0. 4877.
0.170 1.193 111. 318. 0. 4559.
0.180 1.378 134. 300. 0. 4168.
0.190 1.550 156. 458. 0. 3711.
0.200 1.550 167. 505. 0. 3206.
0.210 1.550 157. 492. 0. 2714.
0.220 1.550 141. 450. 0. 2264.
0.230 1.550 123. 391. 0. 1873.
0.240 1.550 102. 314. 0. 1559.
0.250 1.550 94. 273. 0. 1286.
0.260 1.550 82. 232. 0. 1054.
0.270 1.550 50. 161. 0. 893.
0.280 1.502 41. 104. 0. 789.
0.290 1.426 33. 79. 0. 709.
0.300 1.358 27. 58. 0. 652.
0.310 1.296 25. 44. 0. 608.
0.320 1.242 24. 37. 0 571.
0.330 1.196 24. 31. 0. 540 0.340 1.159 24. 26. 0. 514.
0.350 1.129 24. 20. 0. 494.
0.360 1.107 24. 15. 0. 480.
0.370 1.094 24. 9. 0. 470.
0.380 1.088 24. 4. 0. 467.
0.381 1.088 24. 0. 0. 467.
MAXIMUM REACTION LOAD = 17.580 LBS*10.0E 6 See Figure 5A-32, Reaction Load and Fuselage Deceleration.
TMI UFSAR APPENDIX 5A 5A-30 REV. 18, APRIL 2006 5A-7 Reaction Load (R) Calculations Case 2: With Wing and Engines Attached (V. = 200 kts = 338 fps; M = 200,000 lb. = 6200 slugs)
TIME DECEL VEL VELOCITY CRUSHED IMPACT DECEL CHANGE LENGTH CORCE G'S 0.0 0.0 0.0 338.00 0.0 0.0 0.0 0 010 24.9 0.13 337.87 3.41 0.71 0.77 0.020 49.8 0.37 337.50 6.79 1.30 1.55 0.030 74.9 0.62 336.87 10.16 1.84 2.33 0.040 92.9 0.86 336.02 13.49 2.60 2.89 0.050 93.9 0.93 335.08 16.85 3.07 2.92 0.060 95.2 0.95 334.14 20.19 3.38 2.96 0.070 96.7 0.96 333.18 23.53 3.65 3.00 0.080 98.3 0.98 332.19 26.89 3.65 3.05 0.090 99.9 0.99 331.20 30.21 3.62 3.10 0.100 101.5 1.01 330.20 33.51 3.60 3.16 0.110 103.2 1.02 329.17 36.81 3.57 3.21 0.120 105.0 1.04 328.13 40.09 3.54 3.26 0.130 106.7 1.06 327.07 43.37 3.51 3.32 0.140 120.8 1.09 325.99 46.60 3.57 3.76 0.150 160.4 1.41 324.58 49.85 5.89 4.99 0.160 206.4 1.85 322.73 53.12 9.79 6.42 0.170 261.7 2.33 320.40 56.34 12.56 8.13 0.180 330.5 2.95 317.45 59.53 14.84 10.27 0.190 417.7 3.74 313.71 62.68 16.93 12.98 0.200 483.5 4.49 309.22 65.80 17.56 15.03 0.210 571.1 5.21 304.01 68.83 16.03 17.75 0.220 684.6 6.26 297.75 71.84 14.05 21.28 0.230 827.5 7.54 290.21 74.78 11.93 25.72 0.240 994.1 9.19 281.03 77.67 9.64 30.90 0.250 1205.2 10.96 270.06 80.43 8.39 37.46 0.260 1470.6 13.34 256.72 83.06 6.98 45.71 0.270 1736.3 16.12 240.59 85.55 4.45 53.96 0.280 1904.9 18.16 222.43 87.84 3.54 59.21 0.290 2010.6 19.61 202.83 89.97 2.80 62.49 0.300 2083.4 20.50 182.33 91.90 2.26 64.76 0.310 2133.4 21.10 161.23 93.62 1.94 66.31 0.320 2176.6 21.77 139.46 95.14 1.71 67.65 0.330 2216.2 21.97 117.49 96.42 1.53 68.88 0.340 2252.6 22.35 95.14 97.49 1.38 70.01 0.350 2283.6 22.46 72.68 98.32 1.26 70.98 0.360 2308.2 22.97 49.71 98.93 1.17 71.74 0.370 2324.4 23.17 26.54 99.31 1.11 72.24 0.380 2330.9 23.28 3.26 99.46 1.09 72.45 0.381 2331.0 3.26 -0.01 99.46 1.09 72.45 MAXIMUM REACTION LOAD = 17.580 LBS*10.0E 6
See Figure 5A-32, Reaction Load and Fuselage Deceleration.