An Alternate Method for the Determination of Aircraft Carrier Limiting
Displacement for Strength
by
Michael L. Malone
B.S., Electrical Engineering
Prairie View A&M University, 1987
Submitted to the Department of Ocean Engineering and the
Department of Mechanical Engineering
in Partial Fulfillment of the Requirements for the Degrees of
Master of Science in Naval Construction and Engineering
and
Master of Science in Mechanical Engineering
at the
Massachusetts Institute of Technology
June 2001
2001 Michael L. Malone. All rights reserved.
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
JUL 11 2001
1
LIBRARIES
BARKER
The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronic
c~9 ies of hl tpfis document in whole or in part.
Signature of Author ....
..
..................................................................................
Department of Ocean Engineering and the
Department of Mechanical Engineering
May 11, 2001
Certified by ..............................................................
Certified by ........................................................................
Nicholas M. Patrikalakis, Professo
Accepted by
..............
David V. Burke, Senior Lecturer
Department of Ocean Engineering
Thesis Supervisor
.. ................................
d Mechanical Engineering
wasaki Professor of Engineering
Thesis Reader
......
~ of Ocean Engineering
e-e pai i Committee on Graduate Students
Department of Ocean Engineering
Accepted by ............................
.
...................................
4.........................................
Ain A. Sonin, Professor of Mechanical Engineering
Chairman, Department Committee on Graduate Students
Department of Mechanical Engineering
An Alternate Method for the Determination of Aircraft Carrier Limiting
Displacement for Strength
by
Michael L. Malone
Submitted to the Departments of Ocean and Mechanical Engineering
in partial fulfillment of the
requirements for the Degrees of
Master of Science in Naval Architecture and Marine Engineering
and
Master of Science in Mechanical Engineering
ABSTRACT
Aircraft Carriers are currently exceeding design displacement limits, with minimal
Service Life Allowance margin. Current aircraft carrier displacement limits are based
primarily on structural strength criteria under very limited load and environment
conditions. Traditional methods of determining hull girder displacement strength utilized
an arbitrary safety factor of 15 percent which was allowed between the Calculated
Primary Stress and the Design Primary Stress. The use of this safety factor and others
has resulted in the establishment of a conservative displacement limit. This established
displacement limit fails to provide an adequate margin of comfort for the addition of post
construction weight to aircraft carrier hulls and does not provide an accurate indication of
the actual hull girder displacement limit.
A first failure analysis of fifteen sections of the newest aircraft carrier design (CVN 77)
was conducted. The results of this analysis along with output data from the Ship Hull
Characteristic Program (SHCP) were utilized in forming an alternate method for
determining the limiting displacement for strength for aircraft carriers. Although the
present aircraft carrier displacement limit takes into account numerous other limitations,
this process deals only with the hull girder displacement limit for strength. This study
does not provide a specific number for the displacement limit for strength for aircraft
carriers; however, it does show that the NIMITZ aircraft carrier hull is potentially capable
of sustaining significant additional weight without exceeding established Maximum
Allowable Bending Moment limits.
Thesis Supervisor: David Valentine Burke, Ph.D.
Title: Senior Lecturer
2
ACKNOWLEDGEMENTS
I would like to give my most sincere thanks to Evelisse Martir, Nat Nappi, Sr,
John Rosborough, and CDR Kevin Torsiello of NAVSEA for without their help and
steadfast support, this thesis could not have been completed.
Secondly, I would like to thank Dr. David Burke for providing me the necessary
guidance and teaching me the "right way" to make point. I will always remember "Y."
Last and most importantly, I wish to thank my loving wife, Delphina for her
confidence, encouragement and support, and my son, Brandon for understanding why
Dad couldn't always play. You two are my light and the wind beneath my wings. I love
you.
To Delphina and Brandon
Cambridge, Massachusetts, June 2001
3
Table of Contents
L ist of F igures........................................................................................4
5
List of Appendices...... .........................................................................
6
1 Introduction ......................................................................................
2 P ast Practices.......................................................................................9
3 Present Practices..................................................................................14
4 Developments Supporting Determination of Longitudinal Strength......................15
5 Computer Analysis Tools.....................................................................17
18
5.1 Ultimate Strength Program (ULTSTR). ................................................................
25
5.2 Ship Hull Characteristic Program (SHCP) .......................................................
6 Estimated Effect of Bending Moment on Determination of Limiting Displacement.
31
................................................................................................
43
43
45
7 C onclusions....................................................................................
7.1 Specific C onclusions...........................................................................................
7.2 Recom m endations...............................................................................................
List of Figures
Figure 1. Generic Moment-Rotation Curve.................................................................
Figure 2. CVNX (CVN 77) Failure Bending Moments...............................................
Figure 3. Aspect Ratio vs. Buckling Coefficient. .........................................................
Figure 4. CVN 77 Sagging Baseline Bending Moment Comparison ..........................
Figure 5. CNV 77 Hogging Baseline Bending Moment Comparison .........................
Figure 6. CVN 77 Full Load and Limiting Displacement Hogging Bending Moment
C omp arison ................................................................................................................
Figure 7. CVN 77 Full Load and Limiting Displacement Sagging Bending Moment
C omp arison ...............................................................................................................
Figure 8. Sagging Bending Moment with 11,000 LTON point load applied at stations
to 4 . ...........................................................................................................................
Figure 9. Sagging Bending Moment with 11,000 LTON point load applied at stations
19
21
25
32
33
34
35
0
36
5
37
to 9 . ...........................................................................................................................
Figure 10. Sagging Bending Moment with 11,000 LTON point load applied at stations
10 to 14 . ....................................................................................................................
Figure 11. Sagging Bending Moment with an 11,000 LTON point load applied at
stations 15 to 20. ...................................................................................................
38
. 39
Figure 12. Hogging Bending Moment with 11,000 LTON point load applied at stations 0
to 4 . ...........................................................................................................................
40
Figure 13. Hogging Bending Moment with 11,000 LTON point load applied at stations 5
to 9 . ...........................................................................................................................
Figure 14.
10 to
Figure 15.
15 to
40
Hogging Bending Moment with 11,000 LTON point load applied at stations
41
14 . ....................................................................................................................
Hogging Bending Moment with 11,000 LTON point load applied at stations
41
2 0 . ....................................................................................................................
4
List of Appendices
Appendix A CVN 77 hull with 2,000 Long Tons applied at each station
.................................................................................
. 48
Appendix B CVN 77 hull with 10,000 Long Tons applied at each station
................................................................................
. . 54
Appendix C CVN 77 hull with 11,000 Long Tons applied at each station
................................................................................
. . 60
Appendix D CVN 77 hull with 15,000 Long Tons applied at each station
................................................................................
. . 66
Appendix E CVN 71 hull with 2,000 Long Tons applied at each station
.................................................................................
. 72
Appendix F CVN 71 hull with 10,000 Long Tons applied at each station
.................................................................................... 78
Appendix G CVN 71 hull with 11,000 Long Tons applied at each station
. 84
.................................................................................
Appendix H CVN 71 hull with 15,000 Long Tons applied at each station
.................................................................................
5
. 90
1 Introduction
All NIMITZ Class aircraft carriers are approaching their limiting displacement for
strength. This limiting displacement is due to calculated limitations based upon
longitudinal strength. Traditionally, longitudinal strength has been determined by
balancing the ship on a static wave. The ability to meet operational requirements using a
static balance method is implicitly based on the historical success of the method.'
Through the years, design practices and capability to assess the results of those practices
have undergone significant change. United States aircraft carrier design, in particular,
has improved significantly since its modest beginnings in the early 1940's. This thesis is
motivated by the present condition of NIMITZ class aircraft carriers regarding limiting
displacement for strength. In the following chapters, a fresh look will be taken into the
parameters underlying longitudinal strength.
Table 1 shows the commissioned displacement of this class of warship, and the
estimated current displacements, individually.
Table 1. CVN 68 Class Displacement.
Delivery
Displacement
(LTONS)
Estimated Current
Displacement
(LTONS)
68
93,282
101,080
SHIP
69
93,831
101,636
70
94,069
100,979
71
96,865
103,448
72
97,497
103,995
73
97,816
103,900
74
97,490
103,187
75
97,943
102,585
1Sieve, M. W., Kihl, D. P., Ayyub, B. M., "Fatigue Design Guidance for Surface Ships, Draft,"
CARDEROCKDIV-U-SSM-65- / September 2000.
6
For example, using current practice in determining the limiting displacement for strength,
an estimation of the CVN 68 limiting displacement would be as follows:
AL
where:
=
(GL / IC) *Ac
AL = Limiting Displacement (long tons (LTON))
AC = Contract Design Displacement (LTON)
aic = Calculated Primary Stress (tons per square inch (tsi))
GIL = Limiting Primary Stress (tsi)
If we assume the following:
AL= (8.00 tsi / 7.19 tsi) * 93,282 LTON
The estimated longitudinal displacement for strength would be: 103,790.82 LTON
The difference between AL and Ac is 10508.82 LTON, rounded to 11,000 LTON.
The added displacement is assumed to be equally distributed along the length of the ship.
A derivation of the previous equation is conducted in chapter 2. It is clear by comparing
the as commissioned displacement to the present displacement that this class of ship is
fast approaching its limiting displacement for strength. In fact, all NIMITZ class aircraft
carriers are presently in stability status two, which means that neither an increase in
weight nor center of gravity (KG) can be accepted without compensating for the increase
by a reduction elsewhere. It is the goal of this analysis to show that present methods of
determining the limiting displacement for strength are very conservative and that, indeed,
a significant amount of weight may be added to the hull and still not exceed the bending
moment capacity of this hull. It should be noted that numerous other limitations such as
speed requirements, Side Protection System Immersion, nuclear propulsion, and trim
requirements may limit the future growth displacement. The focus of this investigation is
7
squarely on hull girder bending moment limits. No other limitations are addressed in this
study.
The total weight of the ship, or displacement, is comprised of the hull girder steel
weight, the propulsion units, electrical, weapons, sensors, and anything else that has
"weight." The structural weight of the ship accounts for approximately forty-nine
percent of the displacement. The structure is composed of decks, bulkheads, and shell
elements. These elements are made up of plates and stiffeners whose dimensions are
often referred to as scantlings. The scantlings are a function of the ship length,
operational profile, and the overall displacement of the ship. Hull girder bending
moments subject the structure to hull girder primary bending stresses. These bending
stresses are limited to a particular value in order to preclude structural failure, fatigue,
and collapse. Traditionally, upon completion of the Contract Design Phase, the
difference between the Calculated Primary Stress (aic) and the Design Primary Stress
(@D),
should be at least 1.0 tons per square inch (tsi) for combatant ships.2 This
difference is known as the Stress Factor for Primary Stress (Ms), and accounts for
increases in hull girder stresses due to bending moment growth resulting from weight
growth or weight redistribution. Design Primary Stress is not allowed to exceed the
Limiting Primary Stress that normally varies from 8.0 tsi to 10.5 tsi depending upon the
hull material. Therefore, the future weight, or displacement, is limited by the increase in
the primary hull girder stress up to its limiting value. The value of this displacement is
referred to as the "Limiting Displacement for Strength." Traditionally, the added weight
is assumed to be distributed in the same proportion as the original full load weight
Naval Sea Systems Command Code 55Y1, "Design Standard for Hull Girder Primary Strength," Design
Data Sheet 100-1, 28 June 1983.
2
8
distribution. 3 These results may be a conservative estimate of the future weight growth.
In order to permit a larger limiting displacement for strength, an alternative method of
determining limiting displacement for strength is required.
2 Past Practices
Numerous records indicate that it has long been Navy practice to allow a factor
between the Calculated Primary Stress and the Design Primary Stress. Prior to World
War II, this factor allowed for rivet holes, stress concentrations, and instability in
compressive loadings, equaling approximately 15 percent. 4 After World War II, an
extensive review of past practices and experiences was conducted by a committee formed
by the Bureau of Ships. It was noted that "Wartime operations emphasized the necessity
of ruggedness as a characteristic of combatant vessels, which because of tactical
situations may be driven at high speed in heavy seas." 5 Ruggedness required, in the case
of the DD 927 Class, an allowance of approximately 50 tons of steel (approximately 1%
of displacement) and the increasing of the calculated bending moment by 10 percent.
Gradually, the concept of utilizing a "ruggedness" factor was discarded to prevent
confusion. By 1953, it had been replaced by the practice of requiring that the
combination of primary and secondary stress not exceed 80 percent of the allowable
strength of the material used. The Design Primary Stress Limit was established for HY80 and HY-100 as 10.5 tons per square inch (tsi), for HTS as 9.5 tsi, and for OS as 8.5 tsi.
3ibid.
4 Naval Sea Systems Command Code 55YI, "Design Standard for Hull Girder Primary Strength," Design
Data Sheet 100-1, 28 June 1983.
5 Ferris,
L. W., BUSHIPS 440 Note, 27 January 1948.
9
In the mid 1960's, the practice of monitoring hull weight growth led to the introduction
of the concept of "Limiting Displacement for Strength." This concept implied that there
was an upper limit on displacement determined by hull girder strength.
The basic equations utilized for estimating the bending moment and stress were as
follows:
(1) Bending Moment:
M
=
AcLBP/C
where M = Bending Moment
Ac = Displacement
LBP = Length Between Perpendiculars
C = Bending Moment Coefficient
(2) Stress:
aic =M/Z
where aic = Calculated Primary Stress
M = Bending Moment
Z = Section Modulus
The above equations may be combined to show that
CTc =M/Z = AcLBP/CZ
It should be noted that for a given ship, this practice assumes that LBP, Z, and C remain
constant, such that a new constant C', may be used, where:
C'= LBP / C Z
therefore,
aic = C' AC
10
The prime (') is utilized to indicate a new or changed displacement. If this new
displacement is to be determined, then the equation becomes:
aic /Ac
=
C'
=aIL /AL
thus,
AL =(GIL
GCy) *Ac
where cic = Calculated Primary Stress
GIL
= Limiting Primary Stress
AC = Contract Design Displacement, and
AL = Limiting Displacement for Strength
While it is obvious that there is a definite limit as to how much weight or displacement
that a hull can resist, the published Limiting Displacement for Strength is not an absolute
value but needs to be reevaluated based on weight increases, weight redistribution, and
configuration changes. 6 When a ship approaches the limiting displacement, the stress
situation should be reevaluated based upon the best weight information available. The
lack of information detailing the exact location of weight addition and removal makes
establishing a realistic modified weight distribution an extremely difficult and time
consuming task.
An alternate, and more versatile, method for estimating the bending moment due
to small changes in weight is the Ferris Method 7. This method is effective only for small
6
Ferris, L. W., BUSHIPS 440 Note, 27 January 1948.
7 Ferris, L. W., "The Effect of an Added Weight on Longitudinal Strength," SNAME Transactions, 1940.
11
changes in weight relative to the ship's displacement. The change in longitudinal
bending moment for the hogging or sagging condition is:
AM=Px/2 - PKL/4
where:
AM = change in bending moment in ft-tons
P
= change in weight in tons
L
= length between perpendiculars in feet
x
= distance of point P from midship in feet
K
= dimensionless hull shape coefficient.
P is positive for added weights and negative for removed weights, and x is always
positive whether forward or aft. The first term in the expression accounts for the change
in moment caused by the change in weight, while the second term accounts for the effects
of the opposing buoyancy wedge. Therefore, a positive answer indicates that the hogging
moment is increased or sagging moment is reduced; and a negative answer indicates that
the hogging moment is decreased or sagging moment is increased. For the hogging
condition, a weight added in the midsection of the ship reduces the longitudinal bending
stress, while a weight added near either end increases it.8 This indicates that there is a
point in the forebody and one in the afterbody at which weight can be added without
changing the stress. For sagging, the effects are similar but opposite to those for hogging.
The ship's weight, consisting of fixed and variable weights, is divided into 22
ship segments to give a realistic representation of weight distribution along the length of
the ship. These 22 segments correspond to the standard 20 segments between the
perpendiculars plus one forward and one aft of the perpendiculars. The cross sections of
12
the ship, known as stations, are numbered from zero at the forward perpendicular to 20 at
the after perpendicular. Light Ship (fixed weight) and Load (variable weight)
components of the weight distribution must be readily separable in order to facilitate
manipulation to simulate the various load conditions anticipated during the life of the
ship. Fixed weights consist primarily of hull, hull engineering, machinery, fittings,
equipment, and permanent ballast. Whereas variable weights consist of cargo, fuel,
embarked aircraft, water, lubricants, water ballast, crew, provisions, and ship's stores.
Since the mid 1950's the following thirteen steps have been followed in
calculating the longitudinal strength9 :
1. Tabulate the longitudinal distribution of weights
2. Define the wave height, wave length, and wave center
3. Balance the ship on wave and still water
4. Tabulate the forces of buoyancy
5. Determine the loads from weights and buoyancy
6. Integrate the loads to give shearing forces
7. Integrate the shearing forces to give bending moments
8. Determine the effective structure
9. Calculate the moments of inertia and section moduli
10. Calculate the bending stresses
11. Calculate the shearing stresses
12. Calculate the deflections
13. Assemble work in suitable form for record in a longitudinal strength
drawing.
8 Ferris,
L. W., "The Effect of an Added Weight on Longitudinal Strength," SNAME Transactions, 1940.
9 Naval Sea Systems Command Code 05P1, "Longitudinal Strength Calculation," Design Data Sheet 100-6,
29 May 1987.
13
3 Present Practices.
Present USN design criteria for longitudinal strength are specified in Naval Sea
Systems Commands Design Data Sheet (DDS) 100-6 and utilizes a standard wave
approach for determining primary stresses. This standard wave is of trochoidal form with
wavelength equal to the ship length between perpendiculars (LBP) and height equal to
1.1 ILBP. The standard wave approach determines the design bending moment by
statically balancing the ship on this trochoidal wave. The stresses derived from this
bending moment are then compared with allowable values and adjusted on a trial and
error basis, to reflect past experiences with ships already in operation. The standard wave
approach does not, however, specifically account for the effects of transient loads such as
whipping, green seas, wave slap, or fatigue or their effects on longitudinal distribution of
bending moments other than by empirical "rules of thumb". Due to all of these
uncertainties, large safety margins have been used to account for effects of slamming.
Since the current service life of Navy ships ranges from 30 to approximately 50
years, fatigue cracking is considered. The likelihood of fatigue cracks occurring is
minimized by controlling hull girder seaway stress ranges based on the fatigue strength of
the ship's structural details. Additionally, current practice requires that fatigue allowable
stress range be tied to the ship's lifetime bending moments. The lifetime bending
moments represent the magnitude (hog and sag) and number of vertical bending moment
cycles expected during the ships service life. These bending moments include those due
to changes in wave height and slam induced whipping. Ship speed and heading
probabilities, wave height and whipping probabilities, ship characteristics, service life,
operating time and geographic area have a great affect on lifetime bending moments.
14
Evolving practice has lifetime bending moments replace the traditional bending moments
based on 1.1 'LBP wave' 0 . The fatigue allowable stress range is calculated using Miner's
cumulative damage rule, the ship's lifetime bending moments, and the fatigue strength of
the critical structural detail. Miner's rule is a widely accepted method for calculating
damage resulting from cyclic stress.
4 Developments Supporting Determination of Longitudinal Strength.
Finite element methods have provided a capability to assess variations in design
and materials. In finite element analysis, the standard loads are still used in conjunction
with the standard design allowable stresses. The Navy, however, did not routinely use
full ship finite element models until the design of the SAN ANTONIO (LPD 17) class
and ZUMWALT (DD 21) class ships. Rather, hand calculations were used to determine
the strength of the hull girder. Finite element models are used for determining local
stresses as required.
Load and Resistance Factor Design is the newest approach utilized in designing
Navy ships. The San Antonio (LPD 17) class amphibious ship is the first to be designed
utilizing this approach. This method produces separate factors for loads and for strength
of members so that computed maximum lifetime loads can be used in conjunction with
strength computations in a reliability-based design. Reliability-based design requires
1 Ayyub, B. M., "Reliability-based Design of Ship Structures: Current Practice and Emerging
Technologies," SNAME Technical Report for Contract DTCG23-97-P-MMlC76, July 1998.
15
consideration of three components: (1) structural strength, (2) loads, and (3) methods of
reliability analysis."'
The computer program Ultimate Strength (ULTSTR) is used for the determination
of the structural strength component. The original version of the Ultimate Strength
(ULTSTR) program was envisioned to fill the need for an automated method of
determining ultimate hull girder strength that was fast and easy enough to use such that it
could be readily applied in the preliminary stages of structural design. This version was
released approximately 20 years ago and has since undergone significant improvements.
The original version of ULTSTR was unused for years after its initial development.
However, due to increased interest in ultimate strength, the current version of ULTSTR
has been brought back to the forefront.
An additional tool which is used is the Ship Hull Characteristics Program (SHCP).
SHCP automates the calculation of typical naval architecture equations.
Neither Finite Element Analysis methods nor Load and Resistance Factor Design
methods were considered viable for this study due to significant time and manpower
constraints. The use of ULTSTR, with the assistance of NSWC Carderock Division, and
SHCP provided the best opportunity for conducting a meaningful investigation into
limiting displacement for strength. The procedure presented in chapter 6 is, relative to
the two methods discussed above, a rudimentary way of determining if a detailed analysis
of hull girder primary stress is required. In this procedure, bending moment capacity,
determined by evaluating a section of a hull form utilizing the Ultimate Strength
(ULTSTR) computer program, is utilized as a trigger limit. The bending moment of each
" Ayyub, B. M., "Reliability-based Design of Ship Structures: Current Practice and Emerging
Technologies," SNAME Technical Report for Contract DTCG23-97-P-MMIC76, July 1998.
16
section of the hull is determined utilizing the Ship Hull Characteristic Program (SHCP).
One may modify section weights by manipulating input data files in SHCP. A graphical
comparison is made between the two and if the bending moment capacity curve is
exceeded by the section bending moment curve, then a detailed analysis should be
performed.
This method works very well as a indicator; however, it could be improved
by knowing the exact location of weights added post construction.
5
Computer Analysis Tools.
To examine the accuracy of displacement being limited by increasing the bending
moment associated with increased weight, this thesis examines the bending moment
using new tools. Determining the hull girder displacement limit for strength requires the
utilization of two computer programs, namely, the Ultimate Strength (ULTSTR) Program
and the Ship Hull Characteristics Program (SHCP).
ULTSTR has undergone substantial change since its initial beginnings as the
Gross Panel Synthesis Technique (GPST). GPST was presented by John C. Adamchak
as part of his doctoral thesis in 1969.12 ULTSTR is the logical progression of
programming technology from GPST. The current version of ULTSTR was issued in
1997 and includes several improvements to the original version issued in 1982.
SHCP was developed by the Naval Sea Systems Command and was initially
released in 1976. Since 1976, SHCP has undergone 14 revisions. Each revision either
improved the functionality of the program or improved ease of use. John Rosborough of
Adamchak, J. M., "A Ship Structural Synthesis Capability Utilizing Gross Panel Elements,"
Massachusetts Institute of Technology, September 1969.
12
17
Naval Sea Systems Command, Code 05P5, has largely maintained SHCP for the past
decade.
The major characteristics of each program are presented in the following sections.
5.1 Ultimate Strength Program (ULTSTR).
The Ultimate Strength Program was developed by Adamchak13 and is used for
estimating the collapse moment of a hull girder subjected to longitudinal bending.
ULTSTR is designed to estimate the ductile collapse strength of conventional surface
ship hulls under longitudinal bending. The program is based on a variety of empirical
solutions for the most probable ductile failure modes for grillage structure. This
procedure involves the incremental application of curvature (i.e. rotation) about the
neutral axis of a section of the hull and computing the resulting equilibrium longitudinal
moment. At each value of curvature, the program evaluates the equilibrium state of each
gross panel and hard corner element relative to its state of stress and stability
corresponding to its particular value of strain. 14This leads to a moment-curvature
relationship for the hull. The collapse (ultimate) moment at the section is defined as the
point at which the value of moment reaches its peak and then drops off. Figure 1
provides a generic Moment-Rotation Curve.
Adamchak, J. C., "ULTSTR-A Program for Estimating the Collapse Moment of a Ship's Hull Under
Longitudinal Bending," David W. Taylor Naval Ship Research and Development Center, Report No.
82/076, October, 1982.
14 Adamchak, J.C., "ULTSTR (1997): The Revised Program for Estimating the Collapse of Ship Hulls or
Hull Components under Longitudinal Bending or Axial Compression," Naval Surface Warfare Center,
Carderock Division, NSWCCD-TR-65-97/21, July 1997.
13
18
Utimate
Moment
HoG
I
SAG
SltGmate
NMment
Rotation (Radians)
Figure 1. Generic Moment-Rotation Curve.
As Figure 1 indicates, the peak moment is usually defined as the hulls' "ultimate
strength." It is possible for hulls with significant redundancy to have local moment
peaks, that is, "a moment-curvature behavior that builds up to a peak moment value,
drops off a bit, and then builds up to a greater peak value before dropping off in capacity
again."' 5 As curvature on an individual section is increased, the hogging or sagging
bending moment increases until the ultimate moment is reached. This effect results in a
change in slope of the moment-curvature diagram. The knuckle that is apparent on the
curve just prior to the Ultimate Moment indicates the "first failure." The "first failure"
could be a small element failure or it could be a component failure. In the interest of
maintaining the unclassified nature of this thesis, ultimate strength values are not utilized.
15 Adamchak, J.C., "ULTSTR (1997): The Revised Program for Estimating the Collapse of Ship Hulls or
Hull Components under Longitudinal Bending or Axial Compression," Naval Surface Warfare Center,
Carderock Division, NSWCCD-TR-65-97/21, July 1997.
19
Rather,
1 St
Failure Moments and Maximum Allowable Moments, both of which are
described later, are used in discussing the bending moment capacity of individual
sections.
Several ductile and instability failure modes are considered in evaluating the
equilibrium moment. Structural yielding is included as a ductile failure mode. Instability
failure modes incorporate Euler beam-column buckling and stiffener lateral-torsional
buckling (tripping).
In support of this study, Naval Surface Warfare Center (NSWC), Carderock
Division performed an ultimate strength analysis of several hull cross sections of the
CVNX class of aircraft carriers, specifically CVN-77. The results of this analysis were
provided to the author NAVSEA.
In this analysis, the ship cross section was represented
by a series of "gross panel elements" and "hard corners." The cross section was
modeled, and ULTSTR was executed to evaluate the ultimate moments of the crosssection. The collapse of the hull is addressed by the collapse behavior of the local
components that make up the cross section, i.e., gross panel, stiffened or unstiffened, or
hard corners. Figure 2 provides a graphical representation of the ULTSTR output data
provided by NSWC, Carderock.
It should be noted that ULTSTR provides a bending moment capacity for the
individual section under consideration. This bending moment capacity will be utilized in
a comparison analysis that will be discussed in later sections.
20
14,000,000
13,000,000
12,000,000
11,000,000
10,000,000
9,000,000
8,000,000
s MAXIMUM ALLOWABLE
FAI.UREIMOMENT
1ST FAIL
7,000,000
RE
0 ME T
2
C 6,000,000
5,000,000
4,000,000
IL
3,000,000
2,000,000
2 1,000,000
p
0
C
-1,000,000
-2,000,000
-3,000,000
-4,000,000
-5,000,000
-6,000,0100
-7,000,000
-8,000,000
Comp-
-ssion-
____n
Temns
20
19
18
17
16
15
14
13
12
11
10
9
8
7
6
5
4
3
2
1
STATIONS
Figure 2. CVNX (CVN 77) Failure Bending Moments.
The collapse of the hull in ULTSTR is addressed by the collapse behavior of the
local components that make up the cross section. At each value of curvature, the
program evaluates the equilibrium state of each gross panel and hard corner relative to its
state of stress and stability corresponding to its value of strain. 16 ULTSTR then computes
the total moment on the cross section by summing the moment contributions of all the
elements that make up the section being evaluated. This moment contribution is
calculated by taking the product of stress, effective area, and lever arm. It is quite
impossible to determine at a glance what failure mode may be most critical for a
particular gross-panel element; therefore, it has been assumed that, once instability is
' 6 Adamchak, J.C., "ULTSTR (1997): The Revised Program for Estimating the Collapse of Ship Hulls or
Hull Components under Longitudinal Bending or Axial Compression," Naval Surface Warfare Center,
Carderock Division, NSWCCD-TR-65-97/2 1, July 1997.
21
detected in a given mode, the behavior follows through to failure in that same mode.
17
Interaction among different modes of failure is an extremely complex problem and has
not received much treatment.
The first failure moments, as reported in ULTSTR, result from onset of buckling
for the plates, usually wide panels. Typically they do not have an adverse impact on the
ultimate moment capacity of the section; however, it is proposed to be used as the lower
bound for the moment capacity of a particular section ( 1 st Failure Moment). For a
stiffener, column buckling or tripping is the failure mode, which is equivalent to its
ultimate failure. Consequently, the local failure is ultimate failure for a stiffener.
However, it is proposed to be used as the upper bound for the moment capacity of a
particular section (Maximum Allowable Failure Moment). The 1 st Failure Bending
Moment from the ULTSTR output represents the first failure of an element on a section
and will occur at or below the Maximum Allowable Bending Moment. The Maximum
Allowable Bending Moment Hog or Sag represents the point at which the value of
moment in the section causes the first combined plate and stiffener element, or gross
panel, to fail by column buckling or tripping.
Note that ULTSTR does not report the ultimate failure mode of a plate,
consequently it may be possible, but rather unlikely, that a plate may buckle before a
stiffener fails. However, the formulas used for column failure use an effective width of
plate for determining the strength or failure capacity, hence, it assumes that the plate has
failed ultimately and no further reporting of plate failure is shown. Plate buckling is not
17 Adamchak, J.C., "ULTSTR (1997): The Revised Program for Estimating the Collapse of Ship Hulls or
Hull Components under Longitudinal Bending or Axial Compression," Naval Surface Warfare Center,
Carderock Division, NSWCCD-TR-65-97/21, July 1997.
22
included as an explicit separate failure mode because it influences collapse more
indirectly by influencing plating effectiveness relationships, i.e. effective breadth, width,
etc.'
8
Gross panel elements in the cross section can "fail" either through material
yielding in tension or compression, or through structural instability. The structural
instability failure modes are as follows:
1. Euler beam-column buckling, and
2. Stiffener lateral-torsional buckling, also known as "tripping."
The ULTSTR output file shows the following failure modes:
1. Gross panel unstiffened wide panel buckling.
2. Gross panel material yielding.
3. Gross panel Euler beam-column buckling occurring in the same
direction.
4. Gross panel Euler beam-column buckling occurring by an alternating
buckling pattern.
5. Gross panel stiffener lateral-torsional buckling or instability (tripping).
6. When the lower deck is in compression, and the tension side, usually
the upper deck, reaches yield stress before any additional compression
failure on the compression side and vice versa.
In the case of plate buckling, the wide panel buckling theory used by ULTSTR does not
account for the plate aspect ratio. Consequently, the compressive capability of the panel
may be too conservative for plates with an aspect ratio of a/b>1. The wide panel
buckling theory assumes a unit width of 1. This may be seen by comparing the critical
Adamchak, J.C., "ULTSTR (1997): The Revised Program for Estimating the Collapse of Ship Hulls or
Hull Components under Longitudinal Bending or Axial Compression," Naval Surface Warfare Center,
Carderock Division, NSWCCD-TR-65-97/21, July 1997.
18
23
stress for simply supported plate buckling to the wide plate critical buckling stress as
shown in Figure 3. The critical stress (ac) for simply supported plate buckling can be
calculated as follows:
acr = k I
2
D / (b 2 t)
where k
buckling coefficient
D
plate flexural rigidity
b = plate width, and
t
=
plate thickness
For simply supported plates, k is determined as follows:
k = ((mb)/a + a/(mb)) 2
where m = the number of half-waves in the
buckled shape
a/b = aspect ratio
b/a = inverse of the aspect ratio
When a/b << 1, m = 1, and k reduces to k = b2 / a2 ; therefore, for wide plate buckling the
critical stress is:
acr =72 D
/ (a2 t)
where a = plate length
The distance between the two curves in Figure 3 represents a measure of
conservativeness between the two results.
24
k
m=1 m=2
m=3 m=4
Simply supported plate
4
Wide Plate Assumption
(ULTSTR)
0
1
2
3
4
a/b
Figure 3. Buckling Coefficient vs. Aspect Ratio.
Plates of [a/b >/= 1] are typically found in aircraft carrier structures.
5.2 Ship Hull Characteristic Program (SHCP)
The Ship Hull Characteristic Program is an extremely capable tool that consists of
a basic geometry interpreter used to load various volumetric and centroid properties into
a ship data table (SDT) and a set of modules which interrogate the SDT for information
required to perform basic naval architectural calculations.1 9 The naval architectural
modules of SHCP provide a means of calculating or plotting the following:
Hydrostatics
Trim Lines
Floodable Length
Limiting Drafts
Intact Stability
Intact Statical Stability on Waves
Damaged Stability Cross Curves
Damaged Transverse Stability
19 Ship Hull Characteristic Program User's Manual, Version 4.20, March 2000.
25
Damaged Longitudinal Stability
Damageable Length, and;
Tank Capacities and Free Surface
In addition, SHCP contains several modules that are utilized to input or modify ship data.
These modules include the following:
Ship Offsets Input
Design Condition
Sheer Deck Input
Compartmentation Input
Subdivision Input, and;
Liquid Loads Specifications
Of these numerous modules, only the following were required to be utilized for this
analysis. Those modules were:
Hull, Appendages and Referenced Offsets (HULL)
Design Condition (DESIGN)
Hydrostatics (HYDRO), and;
Longitudinal Strength (STRNGH)
Each of these four modules will be discussed in detail in following sections.
26
5.2.1
Hull, Appendages and Referenced Offsets (HULL). 2 0
The HULL module calculates and stores the ship data table for the
main hull, appendages and referenced offsets. It also checks offsets
provided by the user for correctness. Any errors encountered are saved in
the output file. Plots of the vessel's bodyplan and isometric may be
generated and checked by the user. Station Spacing, offset scaling,
Length Between Perpendiculars (LBP), body plan scaling, and Main Hull
geometry type data is entered into the program via this module. Two
types of offset descriptions are utilized. Both types describe the ship as a
series of station cuts where each station is modeled by offsets consisting of
a series of heights and half-breadths (normal offsets) or a radius and
optional vertical offset value (circular offsets) at a series of longitudinal
locations. Three appendage types are provided: appendage by offset,
point volumes, and line volumes. Each record indicates appendage type,
whether buoyant, flooded, or null and a description.
5.2.2
Design Condition (DESIGN). 21
The DESIGN module allows the user to specify one of three
combinations of displacement, draft, trim, and longitudinal center of
gravity (LCG). This file may specify draft and trim, displacement and
20
Ship Hull Characteristic Program User's Manual, Version 4.20, March 2,000.
2
ibid.
27
trim, or displacement and LCG, only. The DESIGN module calculates the
design displacement, draft, longitudinal center of buoyancy (LCB), station
of maximum area, and other items for a particular vessel at an attitude
specified by the user. The longitudinal position (Xmax )of the station with
the maximum sectional area Amax at the design waterline is found by
determining the A and B coefficients of the curve segment which contains
+
that specific station and then setting the slope of that curve [(2*A*Xmx)
B] equal to zero and solving for Xmax. Taylor's second order interpolation
coefficients, found from Xmax and the three stations describing the curve
segment, are used to generate interpolated values of Amax, Ymax (the
maximum half-breadth), and depth. The beam is computed as 2*Ymax.
SHCP calculates the form coefficients utilizing the following equations:
a. Midships section coefficient (also called the section
area coefficient):
Cx = Amax / (beam * depth)
b. Prismatic coefficient:
Cp= Volume / (Amax * LBP)
c. Block Coefficient:
Cb
5.2.3
Hydrostatics (HYDRO).
= Volume / (LBP * beam * depth)
22
The HYDRO module allows the user to request standard
hydrostatic properties for 1 to 100 waterlines or displacements for a
22
Ship Hull Characteristic Program User's Manual, Version 4.20, March 2000.
28
maximum of seven different trim conditions. If none of the requested
waterlines or displacements is within 0.001 feet or meters of the Design
Condition draft or displacement, the Design Condition draft or
displacement is added to the list of waterlines or displacements for which
calculations are performed. The calculated properties for the Curves of
Form are presented in tabular form as a function of increasing waterline.
A different set of hydrostatic properties is calculated and printed for each
trim submitted. Ship specific information is interpolated at each waterline
and trim to obtain cross section properties. This module utilizes the
following formulas in determining ship specific information:
a. Displacement:
Displ = volume / Cfton
b. Prismatic coefficient:
C= volume / (Amax * LBP)
c. Waterplane coefficient:
CWP= Ap / (2 * LBP * Ymax)
d. Transverse waterplane inertia coefficient:
)
CWpi= Wpit * 1.5 / (LBP * (Ymax) 3
e. Longitudinal metacentric radius:
Bmi = Wpi / volume
f.
Transverse metacentric radius:
Bmt = Wpit / volume
g. Height of longitudinal metacenter above baseline:
Kmi = KB + Bmi
h. Height of transverse metacenter above baseline:
Kmt = KB + Bmt
i.
Tons per inch immersion:
TPI = Awp / (12 * Cfton)
29
j.
Change in displacement per foot of trim aft:
Ciofts- =
(-12) *TPI * LCF / LBP
k. Moment to trim one inch:
MTI
Where,
=
volume * Bi / (12 * Cfton * LBP)
Ama = cross sectional area at station of maximum area
A
=
waterplane area
KB
=
height of center of buoyancy above baseline
LCB = longitudinal center of buoyancy
LCF = longitudinal center of flotation referenced from midships
Volume = volume of displacement
Wpil = longitudinal moment of inertia of waterplane
Wpit = Transverse moment of inertia of waterplane
Ymax = beam at the waterline at the station of maximum area
Cfton = volume in cubic feet displaced by a ton of water
LBP = length between perpendiculars in feet
5.2.4
Longitudinal Strength (STRNGH).
The STRNGH module performs calculations of load, shear,
bending moment, and stress along the length of a ship in still water and
with the ship in both hogging and sagging conditions on a trochoidal
wave. A weight distribution curve of the ship is described by locating up
to 41 weight curve segments, and specifying the weights and their
longitudinal centers of gravity between successive segment endpoints. For
each wave condition trochoidal wave ordinates are generated for every
ship and appendage station. The ship is balanced on this wave and draft
23
Ship Hull Characteristic Program User's Manual, Version 4.20, March 2000.
30
and sectional area at 100 points along the length of the ship are printed.
After finding the balanced volume and it's LCB from the bow to each aft
weight curve segment boundary, buoyancy, shear and bending moments
for each weight curve segment are calculated. A standard wave length
equal to LBP and height equal to 1.1 *
1 (LBP) were utilized.
In this
analysis, the STRNGH module was the primary module utilized to
manipulate section weights.
6 Estimated Effect of Bending Moment on Determination of Limiting
Displacement.
Utilizing the traditional method of determining the Limiting Displacement for
Strength, as demonstrated in the example in the Introduction, results in the difference
between the limiting displacement for strength of the NIMITZ class aircraft carrier and
its full load displacement of approximately 11,000 long tons (LTONS). This traditional
approach indicates that the hull is capable of sustaining only 11,000 LTONS of additional
weight when distributed equally at each station. The estimates reported in this section
show that, in fact, the NIMITZ class hull is potentially capable of sustaining a
significantly greater weight than the traditional approach suggests without exceeding the
Maximum Allowable Failure Bending Moment.
The process consists of the use of the Ship Hull Characteristics Program (SHCP)
and the Ultimate Strength (ULTSTR) Hull Girder Collapse Program. A brief outline of
the steps involved follows:
1. The baseline longitudinal bending moment is determined utilizing SHCP.
This moment is indicated on following figures as the Full Load Displacement
31
Moment and is used as the basis for comparison with other derived bending
moments. This moment is due solely to the weight-buoyancy distribution of
the ship and no additional point loads are applied. A comparison between the
ULTSTR Failure and SHCP bending moments is provided in Figures 4 and 5.
One may note that in the hogging condition, it appears that the baseline CVN
77 bending moment exceeds the 1s' Failure Bending Moment capacity. Since
the 1st Failure Bending Moment and Maximum Allowable Bending Moment
curves are derived from ULTSTR outputs which are preliminary results and
are subject to the interpretation of an operator, this does not necessarily
indicate an immediate failure with applied loads.
CVN 77 Sagging Bending Moment
1000000
0
0
10
-1000000-2
CVNT/ baselire
-2000000
_
-30000
X
x
-000000
- 1st Faikre Bening Mon-t
-
--
E
0
Main Alawable Falure
-
0
Benin Mxmert
-5000000r
-7000000
Station
Figure 4. CVN 77 Sagging Baseline Bending Moment Comparison.
32
CVN 77 Hogging Bending Moment
4000000
3500000c
30000001Y0
CVN77 baseline
2500000E
-
-1000000
1000000
10
16
0
1st Failure Bending Moment
X -Maxdmurn Alowable Failure
Bending Moment
0S
-0000
A
Station
Figure 5. CVN 77 Hogging Baseline Bending Mo ment Comparison.
2. The 1" Failure Bending Moment of the hull girder is calculated utilizing
ULTSTR. This
1 st
Failure Bending Moment represents the first failure of an
element on a specific section. It will occur at or below the Maximum
Allowable Moment. In addition, the Maximum Allowable Bending Moment
for hogging or sagging conditions is also calculated utilizing ULTSTR. This
represents the point at which the value of the bending moment in the section
causes the first combined plate and stiffener element, or gross panel, to fail by
column buckling or tripping.
3. Weights, or loads, are added to various stations (iteratively) to determine
revised maximum longitudinal bending moments for the hull due to the
increased weight at a specific station. Weight additions are conducted by
modifying the STRNGH module data input file utilized by SHCP.
4. A comparison is made between the first failure moments (from ULTSTR) and
the revised maximum longitudinal bending moments (from SHCP).
33
5. Finally, when these two moments are equal, the maximum weight capacity
has been reached, and a revised limiting displacement can be determined.
Appendices A through H contain figures demonstrating the effect of various
combinations of added weight. The process remains the same for all cases; therefore,
only the case involving the addition of an 11,000 LTON point load will be discussed in
this section. The 11,000 LTON weight has significance in that this weight determines the
growth margin, from traditional methods, associated with the NIMITZ class aircraft
carrier. A weight greater than this would make a ship of the NIMITZ class exceed it's
limiting displacement for strength as calculated utilizing traditional methods. If this
weight were distributed along the hull proportional to the design weight distribution
curve, calculations show that there would essentially be no difference between the
bending moment at limiting displacement and the bending moment at full load. Figures 6
and 7 show these results.
CVN 77 Hogging Bending Moment
2500000
2000000
0
--
1500000 .2
CVN 77 Limiting
Displacement Moment
E
-
-
CVN 77 Full Load Moment
500000
S0
2)
15
10
5
-500000
Station
Figure 6. CVN 77 Full Load and Limiting Displacement Hogging Bending Moment
Comparison with 11,000 LTONS added proportional to full load weight distribution.
34
CVN 77 Sagging Be nding Moment
500000
0
20
10
15
5
G
-A
9
Statio-n
8
0
0
o CVN 77 Limiting
Displacement Moment
-1000000
)
-500000
0
-1500000
0
-2000000
-)
E
4 CVN
77 Full Load Moment
-2500000
Station
Figure 7. CVN 77 Full Load and Limiting Displacement Sagging Bending Moment
Comparison with 11,000 LTONS added proportional to full load weight distribution.
CVN 71 bending moment data is similar to the results presented in Figures 6 and 7. The
CVN 77 hull includes a bulbous bow whereas the CVN 71 hull does not. The bulbous
bow will have an impact on buoyancy; however, since added weight results in buoyancy
change around the full load immersion, it is expected to have little impact on change in
bending moment.
In this analysis, the weight is treated as a point load and is applied to each station
from 0 to 20, sequentially. Refer to Figures 8 through 15 for a graphical representation of
the effect on the hull girder bending moment of adding this point load.
35
---
CVN 77 Saggng Bendng Moment
+11KtonR at staios 0 to4
Alombe Failure
3000000
Am-
0 0
6
1st Faklre
Nbtmart
2000000
FuJ Load
1000000
Mnermt
10
>-1000000
Dsplacment
0
00
0
.-
-2000000
E
-3000000
0
-4000000
0>
-5000000
*0
-6000000
a)
A 2
o 3
-7000000
Stabon
x 4
Figure 8. Sagging Bending Moment with 11,000 LTON point load applied at stations 0 to 4.
As can be noted in Figure 8, an addition of a point load of 11,000 tons at stations 0
through 4 can easily be accommodated by this hull form from the sagging perspective.
Significant separation exists between the hull girder bending moments associated with
the weight added at stations 0 through 4 and the
1 st
and Maximum Allowable Failure
Moment curves in the sagging condition. This indicates that additional weight added to
each station has minimal impact on the overall hull girder sagging bending moment. In
fact, adding weight at certain stations can result in an improved bending moment curve,
i.e. increasing the separation between the SHCP generated bending moment curve and the
Maximum Allowable Failure Moment curve. Adding weight at the ends of the ship
results in an increase of the hogging moments, and a decrease of the sagging moments.
36
-e- Maximum
Alcoeble
-500000
)-500000
-1000000
Failure lovment
Full Load
Displacement
Moment
-
10
10
1st Failure
Mbnent
-
CVN 77 Sagging Bencing Moment
+11 Ktons at stations 5 to 9
0
120
-1500000
0
P~
6
-2000000 E
0
-2500000 *0
0,
-3000000
-3500000
A 7
0)
0 8
-4000000
Station
a
9
Figure 9. Sagging Bending Moment with 11,000 LTON point load applied at stations 5 to 9.
As shown in Figure 9, a similar pattern is noted when adding an 11,000 LTON point load
at stations 5 to 9. However, when the weight is added at station 9, the resulting bending
moment at station 9 is equal to the
1 St
Failure Moment and Maximum Allowable Failure
Moment. This indicates that some other form of failure has occurred at station 9. All
other resulting bending moments fall within satisfactory limits. Again, this hull form
demonstrates its capability to support an 11,000 LTON point load at all stations with the
exception of station 9 being marginal.
37
CVN 77 Sagging Bending Moment
+11Ktons at stations 10 to 14
500000
-4-- 1st Failure lornnt
0
20
15
5
10
-500000
-e- MdmumAllca ble Failure
C,)
C
0
-1000000 0
10
-1500000
_
-2500000
Full Load DisplacemEnt
0 10
'V'
-2000000 E0
o
Mont
0 11
M
a 12
-3000000 a)
A
J
-3500000
-4000m0
o 13
x 14
Station
Figure 10. Sagging Bending Moment with 11,000 LTON point load applied at stations 10 to 14.
Clearly, as shown in Figure 10, adding an 11,000 LTON point load at station 10 results in
the hull girder bending moment matching the 1St Failure Moment at station 10. The 1st
Failure Moment and Maximum Allowable Failure Moment are matched at station 9.
Likewise, if the weight is added at station 12, then the bending moment at station 12
barely remains below the 1st Failure Moment for that station.
38
CVN 77 Sagging Bencing Moment
+11Ktons at stations 15 to 20
-o- 1st Failure Moment
-e- Maximum
2000000
-Full
1000000-g
+xx
1
Load
Displacement
Moment
0 15
0
+
I
(0
+
+
Allowable Failure
Moment
A
go --n---
0
---1000000
10
o
E
0
E
0
0 16
A 17
-2000000
-3000000
-400000
Station
0 18
x
19
+ 20
Figure 11. Sagging Bending Moment with an 11,000 LTON point load applied at stations 15 to 20.
Notably, in the sagging condition, the NIMITZ class hull can support adding this
11,000 LTON point weight at any station greater than station 10. At no sections do the
revised bending moment curves approach the limits established by the 1st Failure and
Maximum Allowable Failure Moment Curves. Refer to Figures 10 and 11.
Figures 12 through 15 show similar results for adding an 11,000 LTON point load
to individual stations in the hogging condition. Figure 12 shows that if the point load is
added at stations 0, 1, 2, or 3, it is possible that the hogging Maximum Allowable Failure
Moment curve could be exceeded. Adding this point load to any other station results in a
moment that is much less than the Maximum Allowable Failure Moment. One may note
that the hogging 1" Failure Moment curve is almost immediately exceeded with any
weight addition. Since this curve was derived from the preliminary ULTSTR results, it
39
could be refined and does not necessarily indicate an immediate failure with applied
loads.
-*- 1st Failure
CVN 77 Hogging Bending Moment
+11 Ktons at stations 0 to 4
Moment
-e- Maximum
Allowable Failure
Moment
-+
Full Load
Displacement
Moment
9000000
8000000
7000000
0 0
6000000 0
5000000
0
-
4000000
0
3000000 2
2000000 S~ A 2
1000000 a
10
0 0
o 3
-1000000
Station
Figure12. Hogging Bending Moment with 11,000 LTON point load applied at stations 0 to 4.
-+--
CVN 77 Hogging Bending Moment
+11 Ktons at stations 5 to 9
1st Failure
Moment
9000000
8000000
7000000
6000000
5000000
U)
0
0
0
'4'-
4000000 a
3000000 0
-e- Maximum
Ailowable
Failure Moment
-e- Full Load
Displacement
Moment
o 5
o 6
45
2000000
-~
-
4
-r
0)
0
1000000
--------
I %J
__----------
-
-
--
0
__________
0)
o 8
) -1000000
I U
(
-
E
C
Station
Figure 13. Hogging Bending Moment with 11,000 LTON point load applied at stations 5 to 9.
40
-e- Maximum
Allowable
Failure Moment
-.- Full Load
Displacement
Moment
4000000
3500000
3000000 c
.
2500000'0
2000000
C
1500000 E
0
-
1st Failure
Moment
-
CVN 77 Hogging Bending Moment
+11Ktons at stations 10 to 14
o
10
0
11
0
0
7
& 12
500000 ;6
C
CO
:0
5 n)
1I
r,
o
13
X
14
-500000
Station
Figure 14. Hogging Bending Moment with 11,000 LTON point load applied at stations 10 to 14.
1st Failure
Moment
CVN 77 Hogging Bending Moment
+11 Ktons at stations 15 to 20
-e- Maximum
Allowable
9000000
-
8000000
7000000
0
Failure Moment
Full Load
Displacement
Moment
o 15
6000000 +r
---
0
5000000
+
+ +
- -- -
-
4000000
0 16
0
E & 17
3000000 0
+
2000000
X
1000000!C
0
--------oi
X l C,
o 18
0
10
-1000000
Station
X 19
+ 20
Figure 15. Hogging Bending Moment with 11,000 LTON point load applied at stations 15 to 20.
41
The analysis was conducted on two hull forms. The first analysis involved a
bulbous bow hull form, CVN 77. The second analysis involved the traditional NIMITZ
class non-bulbous bow, CVN 71. Section weights were similar for both hull forms;
however, hull offsets were significantly different. Specific section weights and hull
offsets were unique to each analyzed hull; therefore, the displayed hull girder bending
moment curves are unique to each hull. The 1 st Failure Moment and Maximum
Allowable Bending Moment were derived from an analysis of the CVN 77 hull stations 3
through 17 using ULTSTR. The full load displacements of these two hulls are within 5
percent of each other. Since the degree of redundancy of the hull structures of CVN 77
and CVN71 is nearly exact, it is assumed that the results of the CVN 77 ULTSTR
analysis also apply to CVN 71. Hence, the
1 st
Failure Moment and Maximum Allowable
Bending Moment curves are also presented on the CVN 71 figures. The complete results
of the analysis for CVN 77 are contained in Appendices A through D and for CVN 71 in
Appendices E through H. One may note that no significant differences exist in the results
of these analyses of the two hull forms under consideration. Each hull form was
evaluated by adding point weights (i.e. 2,000; 10,000; 11,000; and 15,000 LTON) at each
of 20 stations and obtaining a resulting bending moment for the hull after each weight
addition. The results are provided in groups of 4 to 6 sections. Each curve represents the
hull girder bending moment resulting from a point load applied at a single station. A
synopsis of the analysis results for each applied point load is provided at the beginning of
each Appendix.
42
7 Conclusions.
7.1 Specific Conclusions
All NIMITZ class aircraft carriers are quickly approaching their limiting
displacement for strength (as calculated utilizing traditional methods). The traditional
methods of calculating the limiting displacement results in a somewhat conservative
value. A less conservative limiting displacement would provide a better measure of the
estimated growth margin associated with the NIMITZ class aircraft carrier and could
alleviate some of the concerns about aircraft carriers exceeding their limiting
displacement. Several conclusions may be made:
1. The NIMITZ class aircraft carrier hull can accommodate more weight without
exceeding maximum bending moment estimated by ULTSTR.
2. The ability to make a more detailed assessment using readily available tools
exists.
3. The existence of the bulbous bow makes no difference in the analysis results.
7.1.1
Discussion of Conclusions
1. The process of determining limiting displacement for strength discussed
herein shows that the NIMITZ class hull is potentially capable of
sustaining additional weight which would exceed the currently
established limiting displacement. When utilizing traditional means, the
displacement growth allowed prior to exceeding limits is 11,000 LTON.
43
The current method assumes that the weight growth is distributed
equally over the 20 stations. Under this premise, as shown in Figures 6
and 7, the hogging and sagging bending moments remain virtually
unchanged. The effect of added weight on longitudinal strength is very
dependent on the distribution and location of the added weight.
Analysis results provided in the appendices indicate that as much as
15,000 LTON point loads could be applied at some locations without
exceeding 1 " Failure Bending Moment or Maximum Allowable Bending
Moment curves while limits were exceeded at other locations. This
indicates that the NIMITZ class hull has greater growth potential. Given
that most new installations contribute on the order of hundreds to
thousands of LTONS of additional weight and that the analysis results
show that the NIMITZ class hull is capable of sustaining additions of a
15,000 LTON point load at most stations, it is unlikely that installations
of individual systems will result in the Maximum Allowable Bending
Moment being exceeded.
2. The process presented in this paper provides a means for determining
whether a more detailed analysis must be conducted on a hull that is
approaching its traditionally calculated limiting displacement. It is only
as good as the weight data available for analysis. Section weights play
an important role in determining whether established bending moment
indicators will be exceeded or not. If the displacement of the ship is
allowed to increase so that the resulting hull girder bending moment
approaches the Maximum Allowable Bending Moment, then the
resulting bending stresses will also increase. These increases in stress
can have detrimental implications, particularly if the Ultimate Bending
Moment of a section is exceeded. ULTSTR results are sensitive to the
assumptions (load type, panel type, ... ) made in the preparation of the
structural data, and the availability of pre- and post-processors is
nonexistent. ULTSTR and SHCP are easily accessible and provide a
44
great capability in determining the longitudinal displacement for
strength.
3. The effect of added weight on the bending moment curves of the two
hull forms discussed in the previous sections can be readily observed.
The fact that the CVN 77 hull includes a bulbous bow has no effect on
the results. If one compares the results of the analysis of the CVN 77
and CVN 71 hulls (with and without the bulbous bow, respectively), it
may be observed that the results are nearly exact.
In the past, ship classes such as CV-4 1, CV-66, and FFG's have approached their
limiting displacement for strength when analyzed using the traditional method.
Additional structural detail analysis corroborated the need for additional strengthening as
the displacement increased. The present method of determining limiting displacement for
strength has been useful as a flag to conduct further structural analysis. The method,
previously discussed, provides a viable means of determining a refined limiting
displacement for strength.
7.2 Recommendations.
Although the process of determining limiting displacement for strength presented
here is viable, there are several things that could be done to improve its accuracy. It is
recommended that:
1. A Weight Management Program be established as the single source for
maintaining the location of weight additions and deletions. This
analysis is based upon original (as commissioned) full load weight
distribution. The accuracy of this method could be improved by
45
utilizing actual section weights which requires that the exact location
of weight changes be known.
2. A standard procedure be devised in order to interpret the results of the
ULTSTR analysis. Development of a Pre- and Post-Processor is
essential to improving ease of use.
3. Additional studies be conducted to determine the exact effect on other
limiting displacements of adding large weights. Although this analysis
was primarily concerned with the limiting displacement for strength,
there are in fact numerous other limiting displacements that require
consideration. Over the years some of the limits have changed;
however, the limiting displacement for strength has remained
unchanged since the design of CVN 68. Limiting displacement and
draft limits are also based upon requirements derived from:
Intact or Damaged Stability
Speed Requirements
Side Protection System Immersion
Nuclear Propulsion
Hull Strength
Reserve Buoyancy
Propeller Immersion, and
Trim Limits
Although this analysis demonstrates that the CVN 68 hull is capable of supporting
an additional increase in weight, it does not consider the effects of these weight additions
on the requirements associated with those factors listed above.
46
APPENDIX A:
CVN 77 HULL WITH 2,000 LONG TONS APPLIED AT EACH STATION
47
The figures in Appendix A show the resulting bending moments when a 2,000
LTON point load is applied at each station. Clearly, the bending moment capacity of the
hull will not be exceeded when a 2,000 LTON point load is applied at any station.
48
---
CVN 77 Hogging Bending Moment
+2Ktons at stations 0 to 4
-e- Maximum
Allowable
Failure Moment
9000000
o
8000000
Full Load
Displacement
Moment
7000000 E
6000000.
1st Failure
Moment
0 0
0
0
5000000 t4000000
@
E
3000000 0
2000000
A 2
1000000
15S
0
-
-Il
10
Station
5
o 3
-1000000
-
CVN 77 Sagging Bending Moment
+2Ktons at stations 0 to 4
1st Failure
Moment
-e- Maximum
Allowable Failure
Moment
Full Load
0
Displacement
Moment
-1000000 0
4-j
0 0
0
-2000000 2
1000000
2
3
10
-3000000
E
0
-4000000 2
t- t0on
(M
-5000000 5
-60000001M
-7000000
Station
49
A 2
o 3
1st Failure
Moment
CVN 77 Hogging Bending Moment
+2Ktons at stations 5 to 9
9000000
8000000
7000000
0,
6000000
0
5000000
4000000
3000000
2000000
-e- Maximum
Ailowable
Failure Moment
Full Load
Displacement
Moment
S5
0
0 6
E0
A 7
a,
1000000
.0
7'I
-1000000
Station
-0-
CVN 77 Sagging Bending Moment
+2Ktons at stations 5 to 9
-e- Maximum
Allowable
500000
10
2
S15
_
10
5
-- 500000
-1000000
-2100000
1st Failure
Moment
E
0
*o
Failure Moment
- Full Load
Displacement
Moment
0 5
0
a,
A
--
-2500000
a 7
-2000000
-3500000
-4000000
Station
X 9
50
Failure
-1st
CVN 77 Hogging Bending Moment
+2Ktons at stations 10 to 14
Moment
-e- Maximum
Alcwable
Failure Moment
9000000
Full Load
Dsplacement
Moment
-
8000000
i7\
7000000 c
0
0 10
6000000
.L
0
0
0
5000000 ::
4000000
a,
*
11
a
12
o
13
E
3000000 0
2000000 ~
~1000000
0
10
10
t15
5
) -1000000
tton
X 14
-e- Maximum
AJlmable Failure
Moment
-.- Full Load
Displacement
Moment
0
500000
0
2
-500000
-
-1
1st Failure
Moment
-
CVN 77 Sagging Bending Moment
+2Ktons at stations 10 to 14
0 10
-1000000I
40
_
__
I_
_
15_1_____0
_
aooo0
-2500000
0
-2500000 ~
-3000000
-3500000
11
A
12
o
13
*
-_
__
-4000000
Station
x 14
51
1st Failure
-
CVN 77 Hoggng Bending Moment
+2Ktons at stations 15 to 20
Moment
-e- Madnum
Alawabe
9000000
Falure Moment
Full Load
--
isplacement
D8000000
Moment
7000000 |
0
6000000
__
~t
____ ~1
~
-~
-
-
___ -
- -,
___________
____________
__
____ -
-
____ - ------
5000000
____
o 15
0
16
40
4000000
- ______
E
3000000 0
a 17
1
2000000
0 18
1000000
0x
*
41
-IA
0
19
)-1000000
Station
+ 20
CVN 77 Sagging Bending Moment
+2Ktons at stations 15 to 20
20
15
10
5
0 1st Failure
Moment
-e- Maximum
Adlowable Failure
500000
Moment
- Full Load
0
Displacement
Moment
-500000 u. o 15
0
-10000000
0
0 16
-1500000 m
0
& 17
-2000000 E
o 18
-3500000
x
19
-4000000
Station
+ 20
52
APPENDIX B:
CVN 77 HULL WITH 10,000 LONG TONS APPLIED AT EACH STATION
53
The figures in Appendix B show the resulting bending moments when a 10,000
LTON point load is applied at each station. Stations 0 through 4 are capable of
sustaining a 10,000 LTON point load in the sagging condition. Note that if the load is
applied at station 1 or 2, the potential exists that the Maximum Allowable Failure
Moment curve in the hogging condition may be exceeded. If the point load is applied at
stations 9 or 10 in the sagging condition, then the ship bending moment will intersect the
Maximum Allowable Failure Moment and
1 st
Failure Moment curve at station 9. This
indicates the potential for failure at station 9 with this applied load. All other stations are
capable of sustaining a 10,000 LTON point load without exceeding the Maximum
Allowable Failure Moment curve.
54
1st Failure
Moment
CVN 77 Hogging Bending Moment
+1OKtons at stations 0 to 4
9000000
8000000
7000000 ~ 0
6000000
5000000
-0 -n--
-
E
3000000 0
2000000
7
-
-
-
-~
0 0
4000000
-~ijiiii~ ai
0
riir 7~
0
0
-e- Maximum
Ailowable
Failure Moment
Full Load
--Displacement
Moment
A 2
1000000
0
-1000000
-
-1000000
Station
-c- 1st Failure
Moment
CVN 77 Sagging Bending Moment
+1lKtons at stations 0 to 4
-e- Maximum
3000000
0_
0
0
0
0
2000000
00
1000000 c
0
0
--
X
-
2
Allowable
Failure Moment
Full Load
Displacement
Moment
o 0
-1000000
-2000000 o
E
-3000000 0
-4000000 c
-5000000 5
-6000000
-7000000
Station
55
o 3
-
CVN 77 Hogging Bending Moment
+1OKtons at stations 5 to 9
1st Failure
Moment
-e- Maximum
Allowable Failure
Moment
9000000
Full Load
8000000
Displacement
Moment
7000000
0 0 5
6000000 g
0
5000000
4000000
0
E
3000000 0
2000000
A 7
1000000
0
..
-1000000
Station
-k-- 1st Failure
CVN 77 Sagging Bending Moment
+1 OKtons at stations 5 to 9
2
0
Moment
-e- Maximum
Allowable Failure
500000
Moment
- Full Load
0
Displacement
-500000
Moment
0
-1000000 0 0 5
10
0
-1500000
A
0
-2000000 E
-2500000 0)
-3000000
-3500000
-4000000
Station
56
A 7
1st Failure
CVN 77 Hoggng Bending Moment
+1Ktons at stations 10 to 14
Momert
-e- Maximum
Allocambe Failure
Moment
9000000
Full Load
.
8000000
Dsplacement
CD
7000000
Moment
0
6000000
0 10
0
5000000
o 11
-4000000
E
3000000 0
4
-
0)
2000000 2
A
i
I
a 12
1000000
co
00
o
13
-1000000
Station
x 14
-
CVN 77 Sagging Bending Moment
+1OKtons at stations 10 to 14
1st Failure
Moment
Madmum
--
Alcable
Failure Moment
Full Load
00
lDsplacement
-500006 C
Moment
o
10
0
-1000000 *0
500000
15
-
10
5
-
z
-1500000
-2000000 E
o 11
0
-2500000
0
_
0
,
12
-3000000
-
-
---
_-
o
--- --3500000
o 13
-4000000
Station
x 14
57
-- 1st Failure
Moment
CVN 77 Hogging Bending Momen t
+1Ktons at stations 15 to 20
9000000
-e- Maximum
Allaceble Failure
Moment
+ Full Load
8000000
Displacement
Moment
7000000 r
o 15
0
*0-N
-6000000 4
o
5000000
0 16
1
4000000
E
3000000
-4-
A
17
0
2000000 m
.
0
18
0 19
)-1000000
-- tion
+ 20
---
CVN 77 Sagging Bending Momen t
+1 OKtons at stations 15 to 20
-e- Maximum
Adlowable Failure
Moment
Full Load
Displacement
1000000
500000
SMoment
--
o
t
0 15
-500000
++
0
0
-1000000 .
-1500000
E
-20000000
o 16
a 17
-2500000
$
S--
1st Failure
Moment
-3000000
---
o
-3500000
o 18
x 19
-4000000
Station
+ 20
58
APPENDIX C:
CVN 77 HULL WITH 11,000 LONG TONS APPLIED AT EACH STATION
59
The figures in Appendix C show the resulting bending moments when a 11,000
LTON point load is applied at each station. The potential exists that the Maximum
Allowable Failure Moment curve in the hogging condition may be exceeded if the point
load is applied at stations 0 through 3. Additional comments are provided in Chapter 6.
60
-o- 1st Failure
CVN 77 Hoggng Bencing Moment
+11 Ktons at stations 0 to 4
Moment
-e- Maximum
Allable Failure
Moment
Full Load
9000000
8000000
Displacement
7000000
0)
6000000
0
Moment
0 0
5000000
400000
0
-
0
C
0
3000000
2000000
"0
A
2
1000000
0
o 3
-1000000
r..
Station
,- 1st Failure
Moment
CVN 77 Sagging Bending Moment
+11 Ktons at stations 0 to 4
3000000
2000000
0
1000000 r
0
10
)-
4
2
0
0
--
-
0
0
oment
0 0
%
KR
-1000000
-e- Maximum
Ailowable
Failure Moment
Full Load
Dsplacement
--Q
-2000000
E
-3000000 0
-4000000o)
a 2
-5000000 C
a)
-6000000
-7000000
Station
61
o 3
-0- 1st Failure
Moment
CVN 77 Hogging Bending Moment
+11Ktons at stations 5 to 9
9000000
8000000
7000000
0
4wd
6000000 4-
___
x
;V
-
FS
__
-TI
1
-
U
'-~~*
~
5000000
0
4000000
40
E
3000000 0
2000000
I
1000000
A 7
ra
'1
.1
k
Maximum
Adlcabe
Failure Moment
Full Load
Dsplacement
Moment
o5
o 8
in
)-1000000
Station
1st Failure
Moment
CVN 77 Sagging Bending Moment
+11Ktons at stations 5 to 9
10
_
5
-e- Maxmum
Alloaeble
500000
Failure Moment
Full Load
0
Dsplacement
-500000 0
Moment
5
0
-1000000
-
-1500000
0
-2000000o E
0
-
-25000000)m
0
-3000000 Mc
0
-3500000 c
-0
00
4000000
Station
62
e- 1st Failure
Moment
CVN 77 Hogng Bencing Moment
+11Ktons at staltions10 to 14
-e--Maxinum
Alomble Failure
9000000
-.-
8000000
Full Load
Dsplacement
Monert
7000000
0
10
6000000 0w o
4d
-
0
-
5000000
4000000
-
4
11
E
3000000 0
2000000w
a 12
1000000
00
2
o 13
-
-1000000
SWtO
x 14
-
CVN 77 Sagging Bending Moment
+11Ktons at statons 10 to 14
1st Failure
Moment
-e- Maximum
-500000
1
20
15
-
10
0
0
-1000000
--00000 0
1
Alcable Failure
Moment
Full Load
Displacement
Moment
o 10
I.-
-1500000
-2000000 E
o 11
0
0
J8
-3000000
-3500000
a 12
*
-2500000 o,
0 13
-4000000
Station
x 14
63
- ---
CVN 77 Hogging Bending Moment
+11Ktons at stations 15 to 20
-e- Maximum
Allcobe Failure
Moment
Full Load
--
9000000
Displacement
8000000
6000000
5000000
4000000
+9
+-
-
0
0 16
a 17
2000000
o 18
1000000C
2n
0
0
-
0
+-
E
3000000 0
1
t- o
-
Moment
o 15
)
7000000
--
a-ion
1st Failure
Moment
X 19
-1000000
+ 20
-
CVN 77 Sagging Bending Moment
+11Ktons at stations 15 to 20
2000000
0
+
rr~
-
-______-------______-__
-__
-e- Maximum
Ailowable Failure
Moment
Full Load
Displacement
Moment
o 15
+
+
4000000
+
+ +
1st Failure
Moment
0
2
4.-
0 16
-1000000
6
-
0
- -
-
-
E
AA
A 17
-2000000 co
o 18
-3000000
x 19
0
-4000000
Station
+ 20
64
APPENDIX D:
CVN 77 HULL WITH 15,000 LONG TONS APPLIED AT EACH STATION
65
The figures in Appendix D show the resulting bending moments when a 15,000
LTON point load is applied at each station. The first instance where the Maximum
Allowable Failure Moment curve in the hogging condition was exceeded occurred with
the application of a 15,000 LTON point load at stations 0 through 4. This is a clear
indication that detailed analysis should be conducted when considering the addition of a
weight of this size far forward in the ship. It is clearly indicated that adding this load at
stations 10, 11, or 12 in the sagging condition requires additional analyses since the
Maximum Allowable Failure Moment curve is clearly exceeded. If the load is applied at
station 16 in the hogging condition, then there exists the potential that the Maximum
Allowable Failure Moment curve could be exceeded indicating potential failure.
66
1st Failure
Moment
-
CVN 77 Hogging Bending Moment
+15Ktons at stations 0 to 4
e Maximum
Allcwable
Failure Moment
- Full Load
Displacement
Moment
9000000
8000000
7000000
0
6000000
0 0
.
0
4000000 a)
E
3000000 0
0 A
X 0
9
0
2000000
A 2
1000000 r
0
-1000000
Station
-
CVN 77 Sagging Bending Moment
+15Ktons at stations 0 to 4
1st Failure
Moment
e Maximum
Adlcwable Failure
6000000
4000000
10
2000000
*
0-
-
4)
o
0
5
2
Moment
Full Load
Displacement
Moment
00
-2000000 0
-4000000.
-6000000 i
-8000000
Station
67
A 2
1st Failure
Moment
-
CVN 77 Hogging Bending Moment
+15Ktons at stations 5 to 9
e Madmum
Alcowable Failure
Moment
10000000
o Full Load
Dsplacement
-8000000
Moment
0
-6000000
4.0
0
4000000
CI
0
2000000 E0
3
15
0,
00
0
A 7
V
-2000000
0 8
AL
-4000000
Station
-
CVN 77 Sagging Bending Moment
1st Failure
Moment
+15Ktons at stations 5 to 9
-e- Maximum,
Alloable
Failure Moment
Full Load
Dsplacement
Moment
500000
-i
0
0
2
*)
*
-1-1900.,
0
-20000000E
0-500000
00
-
-2500000
A
-4000000
Station
68
7
1st Failure
-
CVN 77 Hogging Bending Moment
+15Ktons at stations 10 to 14
Moment
-e- Maximum
Allowable Failure
Moment
9000000
Full Load
8000000
Displacement
Moment
7000000 C
0
IV
6000000
0
10
0
5000000 Z
0 11
4000000 w
E
3000000 0
2000000
7
11
a 12
1000000
00
o 13
-1000000
Station
X 14
1st Failure
Moment
CVN 77 Sagging Bending Moment
+15Ktons at stations 10 to 14
500000
0
2
10
15
5/
-500000 e
-1000000 '0 0 10
0
-1500000--0
-
0
-0
x0
__
-
--- 0
-
-
e Maximum
Allowable Failure
Moment
Full Load
Displacement
Moment
-2000000 E
00
___
___-
-2500000 .,
__
0 11
a
12
o
13
X
14
-3000000 E
A0
-0
-3500000X
A
-4000000
Station
69
1st Failure
Mom~er
CVN 77 Hogng Bending Moment
+15Ktons at stations 15 to 20
-e- Mdnium
Alcmble Failure
Mrment
__________
____
____
i-I
8000000
7000000 r
-
~~~~~1~
_________
-e Full Load
Displacement
Dslcnt
9000000
-
6000000
__
0
5000000
E
a 2
w
T
3000000 0
2000000 c
1000000 C
11
-OA
0_
:0
I
n
-1i~
4nA
o 0 16
a 17
0 18
x 19
ld)-1000000
Stato
+ 20
1 Failure
1st
Mloment
CVN 77 Sagging Bending Moment
+15Ktons at stations 15 to 20
-+
-e- Madmum
2000000
Alomble Failure
Moment
Full Load
1000000
Displacement
Moment
0
+
15
4000000
K~xx
+
0
0
g
0
15
0
+
0x
-'A0
,
0 O9I~~5
__
_
_
-1000000a
__
0r
0 16
)
X0
LO
E
-1-n'0
_
0
a~
17
-2000000m
+
2
160
000
0
b__
0
o 18
0__
-3000000D
x 19
4000000
Station
+ 20
70
APPENDIX E:
CVN 71 HULL WITH 2,000 LONG TONS APPLIED AT EACH STATION
71
The figures in Appendix E show the resulting bending moments when a 2,000
LTON point load is applied at each station. Clearly, the bending moment capacity of the
hull will not be exceeded when this point load is applied at any station.
72
0
CVN71 Hogging Bencing Moment
+2Ktons at stations 0 to4
-
8000000
70=00 C
_
600=00
Load
.Ful
Displamement
Moment
0
.
400000
Madim
Alo ble Failure
Moment
9000000
_
1st Faiure
Moment
E
300000D r
a
2
-1000000
n
Station
o 1st Failure Moment
CVN 71 Sagging Bending Moment
+2Ktons at stations 0 to 4
-e- Maximum
Allcamble Failure
1000000
Moment
0
2)
_
10
__
_
_
_
_
Un
.-10000000.
0
-2000000 a
-3000000
a
E0
-4000000 10
-6000000
-7000000
Station
73
Full Load
Displacement
Moment
+ 1st Failure Moment
CVN 71 Hogging Bending Moment
+2Ktons at stations 5 to 9
---
9000000
8000000
7000000 Co
6000000 0
5000000 a
+
Maximum Alowable
Failure Moment
Full Load
[Dsplacement
Moment
0 5
4000000
E
0
3000000 '05
00
2000000 E
\~
AS~I4~iA~7
-
-
I.
1000000
0
Ui
10
'iU
Z)
I -1000000
o 8
Station
x 9
1st Failure Moment
CVN 71 Sagging Bending Moment
+2Ktons at stations 5 to 9
-e- Maximum Adlowable
Failure Moment
500000
0
zD
10
1_
15
-500000
-1000000
Full Load
Dsplacement
Moment
S5
0
-V0
0
-1500000,
-2000000 E
0
-2500000 o,
0
-3500000
A0
_4000000
Station
74
7
*
a
-3000000
o 8
-
CVN 71 Hogging Bending Moment
+2Ktons at stations 10 to 14
1st Failure Moment
--e-- Maxmum Alable
Failure Moment
9000000
Full Load
Displacement
-
8000000
7000000
o10
600000
0
0
5000000
4000000
4.
3000000
0
0)
2000000
7
o 11
E
1000000
7
0
-1000000
10 4r,
o 13
Staton
x 14
-
CVN 71 Sagging Bending Moment
+2Ktons at stations 10 to 14
-e-
500000
0
15
12
A
10
U)
-500000 C
0
__
-10000000
-1500000
0
1st Failure Moment
aximum Aloa
Failure Moment
Full Load
Dsplacement
Moment
o 10
0 11
a,
-2500000 i>
0
& 12
-3000000
-3500000
o 13
-4000000
Station
x 14
75
e
1st Failure Moment
-
CVN 71 Hogging Bending Moment
+2Ktons at stations 15 to 20
-e- Maximum Allowable
Failure Moment
Full Load
Displacement
Moment
o 15
-.
9000000
8000000
U)
7000(W0
6000000
_
_
--
--
500000
_
4000000
3000000
--
2000000
3k
0
0
0 16
0
E
a
CD
.E
0 18
0)
1000000
0
x 19
a
-1000000
1j5
1E
Station
+ 20
0 1st Failure Moment
CVN 71 Sagging Bending Moment
+2Ktons at stations 15 to 20
-1000000
-t
-~1
*
10
1:5
-e- Maximum
Allowable Failure
Moment
500000
Full Load
Displacement
0
Moment
-500000 ro 15
0
-1500000
o 16
+
L
20
17
0
-2000000 E
0
A 17
-2500000 cm
-A-
0
0
-3000000
~/
/I\AI
Station
-3500000
o 18
X 19
-4000000
+ 20
76
APPENDIX F:
CVN 71 HULL WITH 10,000 LONG TONS APPLIED AT EACH STATION
77
The figures in Appendix F show the resulting bending moments when a 10,000
LTON point load is applied at each station. Close attention should be paid when
applying the point load in the hogging condition to stations 1 and 2. Although the
resulting bending moment curve does not exceed the Maximum Allowable Failure
Moment curve, it is very close to doing so. Likewise, if the point load is applied at
station 10, then the potential exists that the Maximum Allowable Failure Moment curve
may be exceeded at station 9. Application of the point load to any other station achieves
satisfactory results.
78
1st Failure Mbment
-0
CVN71 Hoging Bencing Moment
+1OKtons at stations 0 to 4
-e- Maximum Allaeble
Failure Moment
9000000
e Full Load
[Displacement
Moment
8000000
7000000
(0
6000000 0
0
5000000
0E
II-
4000000
3000000
n
-
2000000
E
0
C0,
a 2
1000000
0
0
-1000000
Staion
-
CVN 71 Sagging Bending Moment
+1 OKtons at stations 0 to 4
-e- Maximum Allowable
Failure Moment
3000000
C]
2000000
0
o0 0
6S
1st Failure Moment
Full Load
Displacement
Moment
1000000
0
0
-1000000.2
-2000000
0
E
-3000000 0
4000000
-5000000 C
-6000000
-7000000
Station
79
a
2
1st Failure Moment
CVN 71 Hogging Bending Moment
+1OKtons at stations 5 to 9
-e- Maximum
Alcmable Failure
Moment
9000000
Full Load
8000000
7000000
6000000
Displacement
Moment
0
0 5
0
5000000
4000000
Ac"___
E
3000000 0
2000000 0)
A 7
1000000
0
1
17
n
0 -1000000
Station
-o-- 1st Failure Moment
CVN 71 Sagging Bending Moment
+1Ktons at stations 5 to 9
-e- Maximum Alwable
Failure Moment
500000
-
00
2
110__
___
_
0
b
0_
_
1-500000 c
0
-1000000 IW
-1500000
bx
_
_
Full Load
Displacement
Moment
o 5
-2000000 E
0
0
"'K
-2500000
0
a 7
-3000000
-3500000
-4000000
Station
80
o 8
---
CVN 71 Hogging Bending Moment
+10Ktons at stations 10 to 14
-e- Maximum
Aliowable Failure
Moment
Full Load
-.Displacement
Moment
o 10
9000000
8000000
7000000
__
____
-
I--'
____
__
_____
__
____
I
_____
-
-
____
_______-
____
____
_____
____
4-
0
0
6000000
F
-
1st Failure
Moment
5000000
I
0 11
4000000
____
E
0
3000000
2)
2000000
A
12
1000000
0
o 13
-1000000
Station
X 14
-0- 1st Failure
CVN 71 Sagging Bending Moment
+1OKtons at stations 10 to14
Moment
-500000
20
15
100
10
0
-1500000
--1500000 CE
-21000000
-
/
U
-e- Maximum
Alawable Failure
Moment
-. Full Load
Displacement
Morment
o 10
n
0
_
Q
-2000000 E
~-<-
--2500000 im
e%
0
A/k
o 11
0
--3000000
--3500000 I
0
A 12
*
___-
0 13
-4000000
Station
x 14
81
1st Failure Moment
-
CVN 71 Hogging Bending Moment
+1 OKtons at stations 15 to 20
-e- Maximum Aliowable
Failure Moment
9000000
+
Displacement
Moment
8000000
7000000
6000000
5000000
+
4000000
4
Full Load
0
o
15
C
0
0 16
0
A
3000000 0
CI
17
2000000
o 18
1000000
0
20
15
x
-1000000
1IQ
Station
+ 20
1st Failure
Moment
CVN 71 Sagging Bending Moment
+10Ktons at stations 15 to 20
'4
-e- Maximum
Adlcwable Failure
Moment
1000000
Full Load
500000
Displacement
Moment
10,
o 15
0
)-500000
+
+
21in
W
r)
19
0
-1000000.
o
16
A
17
o
18
x
19
-1500000 o
Aj
0
0 0A
-2000000
E
-2500000 ~
-3000000 m
400
-3500000
-4000000
Station
+ 20
82
APPENDIX G:
CVN 71 HULL WITH 11,000 LONG TONS APPLIED AT EACH STATION
83
The figures in Appendix G show the resulting bending moments when a 11,000
LTON point load is applied at each station. The 11,000 LTON point load may not be
applied to station 0 without approaching the Maximum Allowable Failure Moment curve.
A more detailed analysis is required. Applying the point load at stations 9 or 10 in the
sagging condition results in the ship, 1st Failure, and Maximum Allowable Failure
Moments being coincident. This condition also indicates a need for a more in depth
analysis.
84
--e- Maximum
A ell
Ue Failure
Momnent
-.- Full Load
Displacement
Moment
9000000
8000000
7000000
-
6000000
1st Failure
Moment
--
CVN 71 Hogging Bending Moment
+11 Ktons at stations 0 to 4
0
0 0
0
5000000
4000000
a 0
E
3000000 0
2000000
-
b
--- 0--
2
1000000
IL
Si;
a
0
o 3
0 -1000000
Station
---
CVN 71 Sagging Bending Moment
+11 Ktons at stations 0 to 4
0
7
OA
0
2
1st Failure Moment
-e- Maximum
Alowable Failure
3000000
Moment
2000000
- Full Load
Displacement
1000000
Moment
0
0 0
0
0
-1000000 4
*-f
A
-2000000 2
E
-30000000
-4000000
-V
-5000000 C
W
-6000000
-7000000
Station
85
A 2
o 3
1st Failure
CVN 71 Hogging Bending Moment
+11Ktons at stations 5 to 9
Moment
-e-- Maxmum
Aelcoeble Failure
Moment
9000000
- - Full Load
8000000
7000000
Displacement
0
6000000 *1
0
Moment
0 5
5000000
4000000
0
E
3000000 0
2000000
g
A 7
1000000 r
0
0
-1000000
Station
0 1st Failure Moment
CVN 71 Sagging Bending Moment
+11 Ktons at stations 5 to 9
-e- aximum
500000
D
- 0
-
-
-
10
i
0
_
-10000000
0
-1500000
Allovable Failure
Moment
Full Load
Dsplacement
Moment
0 5
0
-2000000 E
04
FO
_
-
- - ---
-2500000
-
-
-3000000
-3500000
-4000000
Station
86
,
0
-4-
A 7
0
CVN 71 Hogging Bencing Moment
+11Ktons at stations 10 to 14
1st Failure Mloment
-e- Madmum
AloaMble Failure
9000000
-e
8000000
Momert
Full Load
EDsplacement
7000000
Nbment
0
o 10
'-
0
0
4a
6000000
5000000
0
4000000
o 11
E
3000000
0
o
2000000
a 12
1000000
0
r.
o 13
-1000000
Station
14
- 1st Failure Mbment
CVN 71 Sagging Benring Mormrt
+11Ktons at stations 10 to 14
-e- Mmdrum
Allcmble Failure
M4omnt
Full Load
500000
00
0
15
4-
10
Doaen~t
tvpbment
)-500000
-100000000
-W
o 10
-1500000
_
_
A
_
rv
_
_
0
11
A
12
_
0
-
-
-_
00
_
-25000000
-3000000*
-3500000
o 13
-3000000
Statio
x 14
87
-
CVN 71 Hogging Bending Moment
+11Ktons at stations 15 to 20
1st Failure Moment
-e-- Maxum
Allwamble Failure
Moment
9000000
+
Displacement
8000000
-
7000000 $
0
0
6000000
M5ment
15
0
0
a
0 16
E
& 17
2000000 2
Co
1000000
o 18
5000000
4000000
3000000
I
Full Load
0
Im
0
x 19
-1000000
Station
+ 20
1st Failure Moment
-
CVN71 Sagging Bending Momwnt
+11Ktons at stations 15 to 20
-e- Maximum Allcvable
Failure Moment
1000000
-
++
0
-
0
2
_V-500000
+
+
o
10
-1000000
0-
_
0
0
0-1500000
0
0
E
-
-
-2000000 0
0
__
Full Load
Dsplacement
Moment
o 15
--
500000
0 16
& 17
-2500000
o
___
18
___-300000
-3500000
x 19
-4000000
Station
+ 20
88
APPENDIX H:
CVN 71 HULL WITH 15,000 LONG TONS APPLIED AT EACH STATION
89
The figures in Appendix H show the resulting bending moments when a 15,000
LTON point load is applied at each station. The 15,000 LTON point load may not be
applied at station 0 or 1 in the hogging condition without exceeding the Maximum
Allowable Failure Moment curve. Additionally, if the load is applied at stations 9, 10, or
11 in the sagging condition, then the Maximum Allowable Failure Moment curve will be
exceeded at station 9 indicating a need for additional analysis. All other stations are
capable of supporting the addition of this 15,000 LTON point load without exceeding the
Maximum Allowable Failure Moment curve.
90
-o- 1st Failure
Moment
CVN 71 Hogging Bending Moment
+15Ktons at stations 0 to 4
-e- Maximum
Adloable Failure
Moment
Full Load
9000000
8000000
7000000
6000000
-I
-- _
5000000
A
3
XP
[Displacement
Moment
(0
0
4000000
0
3000000
0
E
2000000
0
-
A 2
Co
1000000 :5
C
0
0
0 0
0
0
0
)-1000000
Station
-
CVN 71 Sagging Bending Moment
+15Ktons at stations 0 to 4
-e- Maximum
Abeoble Failure
Moment
~Full Load
6000000
-
-
0
u
^0
4000000
Dsplacement
0
0Q0Q 4 0
~i---
Moment
0
2000000 *1*L 0
0
0
0
-2000000 0
0
0)
-4000000 c
0
-6000000 wo
-8000000
Station
91
1st Failure Moment
--- 1st Failure
Moment
CVN 71 Hogging Bending Moment
+15Ktons at stations 5 to 9
-e- Maximum
Alowable Failure
Moment
9000000
-- Full Load
8000000
Displacement
Moment
7000000 C
0
6000000 V o 5
0
5000000
4000000 w
E
-
3000000 0
-2000000
0
-
- 1000000
e
A
7
0
8
-1000000
Station
-0- 1st Failure
CVN71 Sagging Bending Moment
+15Ktons at stations 5 to 9
20
0
0
0
Moment
-e- Maximum
Alco&eble Failure
500000
Moment
Full Load
0
Dsplacement
)-500000 C
Moment
0
0
5
-10000000
0
-1500000
"0
4a
-2000000 E
0 00
0
0
-
/
-2500000 o,
x
-3000000 X
-3500000
-4000000
Station
92
A 7
1st Failure
-
CVN 71 Hogging Bending Moment
+15Ktons at stations 10 to 14
-e- Madmum
AblleLe Failure
9000000
Full Load
---
8000000
__
____
__
__
__
__
_____
__
Moment
7000000 C
0
II
__
Displacement
_____
__
__
6000000
__
10
0
11
A
12
0
13
x
14
0
5000000
'i
o
0
4000000
E
3000000 0
2000000
-A
0~a
1000000!
I
0
151 3 60
-1000000
Station
o1st Failure Moment
CVN 71 Sagging Bending Moment
+15Ktons at stations 10 to 14
um
Alabe Failure
Moment
Full Load
Displacement
Moment
-e- Ma
50000
-00
2
10
_1
)_
-500000
0
-1000000 0 0 10
00
-1500000
0
_-___
A
0
0~0
-- 2500000)
L--
0
11
A 12
-25=
0--350000
0
0
13
x
14
-4000000
Station
93
1st Failure Moment
-x
CVN 71 Hogging Bending Moment
+15Ktons at stations 15 to 20
-x- Maximum Allowable
Failure Moment
Full Load
-
9000000
Displacement
o
Moment
15
0
40
4
16
E
A
17
o
18
W
19
+
20
8000000 0-t
_
_7000000
6000000
-
-
5000000
2000000
+-
0
2000000
1000000
:5
10
n-1000000
Station
-
1st Failure
Moment
-e- Maxinum
Allwamble Failure
Moment
2000000
Full Load
Displacement
Moment
1000000
0 o 15
+
-
CVN 71 Sagging Bending Moment
+15Ktons at stations 15 to 20
0
0 16
0
+
+
2
-1000000 0
E
0~
0
0
A 17
-2000000 m
0 0 0 0
o 18
-300000010
X 19
0
-4000000
Station
+ 20
94