An Alternate Method for the Determination of Aircraft ...

An Alternate Method for the Determination of Aircraft Carrier LimitingDisplacement for Strength

by

Michael L. Malone

B.S., Electrical EngineeringPrairie View A&M University, 1987

Submitted to the Department of Ocean Engineering and theDepartment 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 MASSACHUSETTS INSTITUTEOF TECHNOLOGY

at theMassachusetts Institute of Technology JUL 11 2001

June 2001 1

2001 Michael L. Malone. All rights reserved. LIBRARIESBARKER

The author hereby grants to MIT permission to reproduce and to distribute publicly paper and electronicc~9 ies of hl tpfis document in whole or in part.

Signature of Author .... .. ..................................................................................

Department of Ocean Engineering and theDepartment of Mechanical Engineering

May 11, 2001Certified by ..............................................................

David V. Burke, Senior LecturerDepartment of Ocean Engineering

Thesis SupervisorC ertified by ........................................................................ .. ................................

Nicholas M. Patrikalakis, Professo d Mechanical Engineeringwasaki Professor of Engineering

Thesis ReaderAccepted by .............. ......

~ of Ocean Engineeringe-e pai i Committee on Graduate Students

Department of Ocean EngineeringA ccepted by ............................ . ................................... 4.........................................

Ain A. Sonin, Professor of Mechanical EngineeringChairman, Department Committee on Graduate Students

Department of Mechanical Engineering

An Alternate Method for the Determination of Aircraft Carrier LimitingDisplacement for Strength

by

Michael L. Malone

Submitted to the Departments of Ocean and Mechanical Engineeringin partial fulfillment of the

requirements for the Degrees ofMaster of Science in Naval Architecture and Marine Engineering

andMaster of Science in Mechanical Engineering

ABSTRACT

Aircraft Carriers are currently exceeding design displacement limits, with minimalService Life Allowance margin. Current aircraft carrier displacement limits are basedprimarily on structural strength criteria under very limited load and environmentconditions. Traditional methods of determining hull girder displacement strength utilizedan arbitrary safety factor of 15 percent which was allowed between the CalculatedPrimary Stress and the Design Primary Stress. The use of this safety factor and othershas resulted in the establishment of a conservative displacement limit. This establisheddisplacement limit fails to provide an adequate margin of comfort for the addition of postconstruction weight to aircraft carrier hulls and does not provide an accurate indication ofthe 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 HullCharacteristic Program (SHCP) were utilized in forming an alternate method fordetermining the limiting displacement for strength for aircraft carriers. Although thepresent aircraft carrier displacement limit takes into account numerous other limitations,this process deals only with the hull girder displacement limit for strength. This studydoes not provide a specific number for the displacement limit for strength for aircraftcarriers; however, it does show that the NIMITZ aircraft carrier hull is potentially capableof sustaining significant additional weight without exceeding established MaximumAllowable 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 andsteadfast support, this thesis could not have been completed.

Secondly, I would like to thank Dr. David Burke for providing me the necessaryguidance 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 herconfidence, encouragement and support, and my son, Brandon for understanding whyDad couldn't always play. You two are my light and the wind beneath my wings. I loveyou.

To Delphina and Brandon

Cambridge, Massachusetts, June 2001

3

Table of Contents

L ist of F igures........................................................................................4List of A ppendices...... ......................................................................... 51 Introduction ...................................................................................... 62 P ast Practices.......................................................................................93 Present Practices..................................................................................144 Developments Supporting Determination of Longitudinal Strength......................155 Computer Analysis Tools.....................................................................17

5.1 Ultimate Strength Program (ULTSTR). ................................................................ 185.2 Ship Hull Characteristic Program (SHCP) ....................................................... 25

6 Estimated Effect of Bending Moment on Determination of Limiting Displacement................................................................................................. 3 1

7 C onclusions.................................................................................... 437.1 Specific C onclusions........................................................................................... 437.2 R ecom m endations............................................................................................... 45

List of FiguresFigure 1. Generic Moment-Rotation Curve................................................................. 19Figure 2. CVNX (CVN 77) Failure Bending Moments............................................... 21Figure 3. Aspect Ratio vs. Buckling Coefficient. ......................................................... 25Figure 4. CVN 77 Sagging Baseline Bending Moment Comparison .......................... 32Figure 5. CNV 77 Hogging Baseline Bending Moment Comparison ......................... 33Figure 6. CVN 77 Full Load and Limiting Displacement Hogging Bending Moment

C om p arison ................................................................................................................ 34Figure 7. CVN 77 Full Load and Limiting Displacement Sagging Bending Moment

C om p arison ............................................................................................................... 3 5Figure 8. Sagging Bending Moment with 11,000 LTON point load applied at stations 0

to 4 . ........................................................................................................................... 3 6Figure 9. Sagging Bending Moment with 11,000 LTON point load applied at stations 5

to 9 . ........................................................................................................................... 3 7Figure 10. Sagging Bending Moment with 11,000 LTON point load applied at stations

10 to 14 . .................................................................................................................... 3 8Figure 11. Sagging Bending Moment with an 11,000 LTON point load applied at

stations 15 to 20. ................................................................................................... . 39Figure 12. Hogging Bending Moment with 11,000 LTON point load applied at stations 0

to 4 . ........................................................................................................................... 4 0Figure 13. Hogging Bending Moment with 11,000 LTON point load applied at stations 5

to 9 . ........................................................................................................................... 4 0Figure 14. Hogging Bending Moment with 11,000 LTON point load applied at stations

10 to 14 . .................................................................................................................... 4 1Figure 15. Hogging Bending Moment with 11,000 LTON point load applied at stations

15 to 2 0 . .................................................................................................................... 4 1

4

List of Appendices

Appendix A CVN 77 hull with 2,000 Long Tons applied at each station

................................................................................. . 4 8

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

................................................................................ . . 6 0

Appendix D CVN 77 hull with 15,000 Long Tons applied at each station

................................................................................ . . 6 6

Appendix E CVN 71 hull with 2,000 Long Tons applied at each station

................................................................................. . 7 2

Appendix F CVN 71 hull with 10,000 Long Tons applied at each station

.................................................................................... 78Appendix 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................................................................................. . 9 0

5

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.

SHIP Delivery Estimated CurrentDisplacement Displacement

(LTONS) (LTONS)

68 93,282 101,080

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

1 Sieve, 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 = (GL / IC) *Ac

where: 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

2 Naval Sea Systems Command Code 55Y1, "Design Standard for Hull Girder Primary Strength," DesignData Sheet 100-1, 28 June 1983.

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 HY-

80 and HY-100 as 10.5 tons per square inch (tsi), for HTS as 9.5 tsi, and for OS as 8.5 tsi.

3 ibid.

4 Naval Sea Systems Command Code 55YI, "Design Standard for Hull Girder Primary Strength," DesignData 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 Method7. 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.

13

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.

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 EmergingTechnologies," 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 EmergingTechnologies," 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

17

12 Adamchak, J. M., "A Ship Structural Synthesis Capability Utilizing Gross Panel Elements,"Massachusetts Institute of Technology, September 1969.

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.

13 Adamchak, J. C., "ULTSTR-A Program for Estimating the Collapse Moment of a Ship's Hull UnderLongitudinal 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 orHull Components under Longitudinal Bending or Axial Compression," Naval Surface Warfare Center,Carderock Division, NSWCCD-TR-65-97/21, July 1997.

18

I

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 orHull Components under Longitudinal Bending or Axial Compression," Naval Surface Warfare Center,Carderock Division, NSWCCD-TR-65-97/21, July 1997.

19

UtimateMoment

HoG

SltGmateSAG NMment

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 cross-

section. 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

s MAXIMUM ALLOWABLEFAI.UREIMOMENT

1ST FAIL RE 0 ME T

Comp- -ssion-

Temns ____n

14,000,00013,000,00012,000,00011,000,00010,000,0009,000,0008,000,0007,000,0006,000,0005,000,0004,000,0003,000,0002,000,0001,000,000

p 0-1,000,000-2,000,000-3,000,000-4,000,000-5,000,000-6,000,0100-7,000,000-8,000,000

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 orHull Components under Longitudinal Bending or Axial Compression," Naval Surface Warfare Center,Carderock Division, NSWCCD-TR-65-97/2 1, July 1997.

21

2C

IL

2

C

20 19 18 17 16 15 14 13 12 11 10 9 8 7 6

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 1st 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


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


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 / (b2 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). 20

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.

215.2.2 Design Condition (DESIGN).

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 = Volume / (LBP * beam * depth)

5.2.3 Hydrostatics (HYDRO). 22

The HYDRO module allows the user to request standard

hydrostatic properties for 1 to 100 waterlines or displacements for a

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 = volume * Bi / (12 * Cfton * LBP)

Where, 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


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 LimitingDisplacement.

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

010 0

-1000000-2

-- _ -2000000

-30000 -x E

0-000000 -

-5000000r

-7000000

CVNT/ baselire

- 1st Faikre Bening Mon-t

Main Alawable FalureBenin Mxmert

Station

Figure 4. CVN 77 Sagging Baseline Bending Moment Comparison.

32

0

X

CVN 77 Hogging Bending Moment

4000000

3500000c030000001Y

2500000E

- -10000000 X

1000000

S 016 10 A -0000

Station

Figure 5. CVN 77 Hogging Baseline Bending Mo

CVN77 baseline

1st Failure Bending Moment

-Maxdmurn Alowable FailureBending Moment

ment Comparison.

2. The 1" Failure Bending Moment of the hull girder is calculated utilizing

ULTSTR. This 1st 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 MomentE CVN 77 Full Load Moment

- - 500000

S02) 15 10 5

-500000

Station

Figure 6. CVN 77 Full Load and Limiting Displacement Hogging Bending MomentComparison with 11,000 LTONS added proportional to full load weight distribution.

34

CVN 77 Sagging Be

0 15 10 5 G

-A 9

Statio-n

8 0

Station

nding Moment

500000

00

-500000 0

-1000000 )E

-1500000 0

-2000000-)

-2500000

o CVN 77 LimitingDisplacement Moment

4 CVN 77 Full Load Moment

Figure 7. CVN 77 Full Load and Limiting Displacement Sagging Bending MomentComparison 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

2

CVN 77 Saggng Bendng Moment+11KtonR at staios 0 to4

Am- 6 0 0

3000000

2000000

1000000

10

>-1000000

-2000000

-3000000

-4000000

-5000000

-6000000

-7000000

0

0.-

E0

0>

*0

a)

Stabon

--- 1st FaklreNbtmart

Alombe Failure

FuJ LoadDsplacmentMnermt

0 0

A 2

o 3

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

CVN 77 Sagging Bencing Moment+11 Ktons at stations 5 to 9

10

0

P~ 6

Station

Figure 9. Sagging Bending Moment with 11,000 LTON point load

-500000

10

)-500000

-1000000

-1500000

-2000000

-2500000

-3000000

-3500000

-4000000

0

012

E0

0,*0

0)

- 1st FailureMbnent

-e- MaximumAlcoebleFailure lovment

- Full LoadDisplacementMoment

A 7

0 8

a 9

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 1St 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

0 15 10 5

o _

A J

500000

0

-500000

-1000000

-1500000

-2000000

-2500000

-3000000

-3500000

-4000m0

C,)C0

010

E0M

'V'

a)

-4-- 1st Failure lornnt

-e- MdmumAllca ble FailureMont

Full Load DisplacemEnt

0 10

0 11

a 12

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

2

+ +

+ xx +

A 0

go --n--- 0

CVN 77 Sagging Bencing Moment+11Ktons at stations 15 to 20

2000000

1000000-g

(0

1 0

---1000000E0

10o E

-2000000

-3000000

-400000

-o- 1st Failure Moment

-e- MaximumAllowable FailureMoment

-Full LoadDisplacementMoment

0 15

0 16

A 17

0 18

x 19

Station

Figure 11. Sagging Bending Moment with an 11,000 LTON point load applied at

+ 20

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

I

could be refined and does not necessarily indicate an immediate failure with applied

loads.

CVN 77 Hogging Bending Moment+11 Ktons at stations 0 to 4

9000000

8000000

7000000

6000000 0

5000000

40000000

3000000 2

2000000 S~

1000000 a

0

-1000000

-*- 1st FailureMoment


-+ Full LoadDisplacementMoment

0 0

A 2

o 3

- 0

10 0

Station

Figure12. Hogging Bending Moment with 11,000 LTON point load applied at stations 0 to 4.


I %J I U

Station

9000000

8000000

7000000

6000000

5000000

4000000

3000000

2000000

1000000

0

) -1000000

U)000

'4'-

45a

E0C0)0

0)

-+-- 1st FailureMoment

-e- MaximumAilowableFailure Moment

-e- Full LoadDisplacementMoment

o 5

o 6

o 8

Figure 13. Hogging Bending Moment with 11,000 LTON point load applied at stations 5 to 9.

40

- -~ - 4-r -------- __---------- - - -- __________

(

CVN 77 Hogging Bending Moment+11Ktons at stations 10 to 14

- 1st FailureMoment

- 00

7

1I

-e- MaximumAllowableFailure Moment

4000000-.- Full Load

3500000 DisplacementMoment

3000000 c. o 10

2500000'0

2000000C

1500000 E0

500000 ;6C

:0 CO

-500000

Station

0 11

& 12

o 13

X 14



10

9000000

8000000

7000000 0

6000000 +r0

5000000

4000000 0E

3000000 0

2000000

1000000!C0

-1000000

Station

1st FailureMoment



o 15

0 16

& 17

o 18

X 19

+ 20


41

5 n) r,

--- + + +

- -- - -

+

X 0

X C,--------- oi l

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 1st 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 1st 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 StabilitySpeed RequirementsSide Protection System ImmersionNuclear PropulsionHull StrengthReserve BuoyancyPropeller Immersion, andTrim 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


-Il -

15S 10 5

Station

9000000

8000000

7000000 E

6000000.005000000 t-

4000000 @E

3000000 0

2000000

1000000

0

-1000000


--- 1st FailureMoment


o Full LoadDisplacementMoment

0 0

A 2

o 3

- 1st FailureMoment

3 10

t- t0on

Station

1000000

0

-1000000 04-j0

-2000000 2

-3000000E0

-4000000 2(M

-5000000 5

-60000001M

-7000000



0 0

A 2

o 3

49

2


7'I

9000000

8000000

7000000

6000000

5000000

4000000

3000000

2000000

1000000

.0

-1000000

0,

0

0

E0

a,

-e- MaximumAilowableFailure MomentFull LoadDisplacementMoment

S5

0 6

A 7

Station


-0- 1st FailureMoment

500000

10

-- 500000 E0

-1000000 *o

-2100000 0

-2500000a,

-2000000

-3500000

-4000000



0 5

a 7

X 9

1st FailureMoment

2 S15 _ 10 5

-- A

Station

50


t15 10 5

tton

9000000

8000000

7000000 c06000000 .L0

0 05000000 ::

4000000 a,E

3000000 0

2000000 ~

~1000000

10 0) -1000000

-1st FailureMoment

-e- MaximumAlcwableFailure Moment

- Full LoadDsplacementMoment

0 10

* 11

a 12

o 13

X 14


500000

0

-5000000

-1000000I40

-2500000 aooo

0

-2500000 ~

-3000000 *

-3500000

-4000000

Station

- 1st FailureMoment

-e- MaximumAJlmable FailureMoment

-.- Full LoadDisplacementMoment

0 10

0 11

A 12

o 13

x 14

51

i7\

2 -1 -

__ 15_1_____0

-_ _ __ I_ _ _

CVN 77 Hoggng Bending Moment+2Ktons at stations 15 to 20

Station


0 15 10 5

Station

- 1st FailureMoment

-e- MadnumAlawabeFalure Moment

9000000 -- Full Load

D8000000 isplacementMoment

7000000 | o 150

60000000

5000000 40 16

4000000E a 17

3000000 0

2000000 10 18

10000000

0x 19)-1000000

+ 20

0 1st FailureMoment

-e- MaximumAdlowable FailureMoment


o 15

0 16

& 17

o 18

x 19

+ 20

52

500000

0

-500000 u.0

-100000000

-1500000 m

0

-2000000 E

-3500000

-4000000

__ ~t ~ -~ ___ - __ ____

____ ~1 - - - -, ___________ ____________ ____ - - ____ - ------ - ______

* 41 -IA

2

APPENDIX B:


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 1st 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

CVN 77 Hogging Bending Moment+1OKtons at stations 0 to 4

-~ijiiii~ ai 0- -0riir ~ -n--7~ 7

- - - -

9000000

8000000

07000000 ~060000000

5000000

4000000E

3000000 0

2000000

1000000

0

-1000000

Station

CVN 77 Sagging Bending Moment+1lKtons at stations 0 to 4

-e- MaximumAilowableFailure Moment

--- Full LoadDisplacementMoment

0 0

A 2

-c- 1st FailureMoment

0 0 0 00_ 0 0

-- X -

Station

3000000

2000000

1000000 c0

0

-1000000

-2000000 oE

-3000000 0

-4000000 c

-5000000 5

-6000000

-7000000

-e- MaximumAllowableFailure MomentFull LoadDisplacementMoment

o 0

o 3

55

1st FailureMoment

2

--1000000


Station

9000000

8000000

70000000

6000000 g05000000

4000000 0E

3000000 0

2000000

1000000

0

-1000000

CVN 77 Sagging Bending Moment+1 OKtons at stations 5 to 9

- 1st FailureMoment

-e- MaximumAllowable FailureMomentFull LoadDisplacementMoment

0 5

A 7

-k-- 1st FailureMoment

0 10

0

A 0

Station

500000

0

-5000000

-1000000 0

-1500000

-2000000 E

-2500000 0)

-3000000

-3500000

-4000000



0 5

A 7

56

2

..

CVN 77 Hoggng Bending Moment+1Ktons at stations 10 to 14

9000000

8000000

7000000

6000000

5000000

-4000000

3000000

2000000

1000000

00

-1000000

CD

0

0

E0

0)2

co

Station

CVN 77 Sagging Bending Moment+1OKtons at stations 10 to 14

1st FailureMomert

-e- MaximumAllocambe FailureMoment

. Full LoadDsplacementMoment

0 10

o 11

a 12

o 13

x 14

- 1st FailureMoment

- 15 10 5

_ 0

- - --- _- ---o

Station

500000

00

-500006 C

0-

-1000000 *0

-1500000

-2000000 E0

-2500000 0

-3000000

--3500000

-4000000

-- MadmumAlcableFailure MomentFull LoadlDsplacementMoment

o 10

o 11

, 12

o 13

x 14

57

4 A- i I

z

CVN 77 Hogging Bending Momen+1Ktons at stations 15 to 20

-4-

-- tion

CVN 77 Sagging Bending Momen+1 OKtons at stations 15 to 20

S-- --

t ++

--- o

Station

-- 1st Failuret Moment

-e- MaximumAllaceble FailureMoment

9000000 + Full Load

8000000 DisplacementMoment

7000000 r o 150

*0-N

-6000000 4o 0 165000000 1

4000000E A 173000000 0

2000000 m. 18

0

0 19)-1000000

+ 20

--- 1st Failuret Moment

-e- MaximumAdlowable Failure

1000000 MomentFull Load

500000 DisplacementSMoment

o 0 15-500000

00-1000000 . o 16

-1500000E

-20000000 a 17

-2500000 $o 18-3000000

-3500000 x 19-4000000

+ 20

58

APPENDIX C:


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

CVN 77 Hoggng Bencing Moment+11 Ktons at stations 0 to 4

- 0

Station

9000000

8000000

7000000

6000000

5000000

400000

3000000

2000000

1000000

0

-1000000

CVN 77 Sagging Bending Moment+11 Ktons at stations 0 to 4

0)

0

C00

"0

-o- 1st FailureMoment

-e- MaximumAllable FailureMoment

Full LoadDisplacementMoment

0 0

A 2

o 3

,- 1st FailureMoment

-- - --Q KR

0 )-

0 0

3000000

2000000

1000000 r0

0 400-1000000 %

-2000000E

-3000000 0

-4000000o)

-5000000 Ca)

-6000000

-7000000

-e- MaximumAilowableFailure MomentFull LoadDsplacementoment

0 0

a 2

o 3

Station

61

2

r..

1


___ - __ - 1 '-~~* ~

'1

in

9000000

8000000

7000000

6000000

5000000

4000000

3000000

2000000

1000000

04wd4-

0

40E0

ra


- MaximumAdlcabeFailure MomentFull LoadDsplacementMoment

o5

A 7

o 8)-1000000

Station


1st FailureMoment

-e- MaxmumAlloaebleFailure Moment

- Full LoadDsplacementMoment

0 5

4000000

Station

62

_ 10 5

- 0

-000

500000

0

-500000 0

-1000000

-1500000 -0

-2000000o E0

-25000000)m

-3000000 Mc0

-3500000 c

x ;V FS -TI U I

k.1

CVN 77 Hogng Bencing Moment+11Ktons at staltions10 to 14

- -

-

SWtO

9000000

80000007000000

04d

6000000 w00

5000000 -4000000

E3000000 0

2000000w

1000000

00

-1000000

-e--MaxinumAlomble Failure

-.- Full LoadDsplacementMonert

o 10

4 11

a 12

o 13

x 14

CVN 77 Sagging Bending Moment+11Ktons at statons 10 to 14

- 1st FailureMoment

-500000

1 0

-1000000 0---00000 0

I.-

-1500000

-2000000 E0

-2500000 o,

-3000000 *

-3500000

-4000000

Station

-e- MaximumAlcable FailureMomentFull LoadDisplacementMoment

o 10

o 11

a 12

0 13

x 14

e- 1st FailureMoment

0 15 10

- 1

0

63

2

2

J8


- 1- t- o+9+-

2n- -- a-ion

9000000

8000000

70000000

6000000 +-0

5000000

4000000 )E

3000000 0

20000001000000C

00

-1000000

- --- 1st FailureMoment

-e- MaximumAllcobe FailureMoment

-- Full LoadDisplacementMoment

o 15

0 16

a 17

o 18

X 19

+ 20


- +- -______-------______-__ -__

+ + ++ rr~ +

6 AA- - - - -

0

Station

2000000

4000000

00

4.-

-1000000E0

-2000000 co

-3000000

-4000000

- 1st FailureMoment

-e- MaximumAilowable FailureMomentFull LoadDisplacementMoment

o 15

0 16

A 17

o 18

x 19

+ 20

64

2

APPENDIX D:


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


0 A

X 0 0 9

Station


9000000

8000000

70000000

6000000 . 0

4000000 a)E

3000000 0

20000001000000 r

0-1000000

- 1st FailureMoment

e MaximumAllcwableFailure Moment


0 0

A 2

- 1st FailureMoment

-0

10 5

Station

e MaximumAdlcwable Failure

6000000 Moment

4000000 - Full Load4 ) Displacemento Moment

2000000 *000

-2000000 0

-4000000. A 2

-6000000 i

-8000000

67

2


10000000

-8000000

-6000000

4000000

2000000

00

-2000000

-4000000

04.0

0

CI

0E0

0,

V

- 1st FailureMoment

e MadmumAlcowable FailureMoment

o Full LoadDsplacementMoment

A 73 15 0

AL 8

Station


500000

-i 0 0

0 0-500000

* *)-1-1900.,

00

-20000000E

-2500000 -

-4000000

Station

- 1st FailureMoment

-e- Maximum,AlloableFailure MomentFull LoadDsplacementMoment

A 7

68

0

2


11 7

9000000

8000000

7000000 C0IV

6000000 0

5000000 Z

4000000 wE

3000000 0

2000000

1000000

00-1000000

Station

- 1st FailureMoment


0 10

0 11

a 12

o 13

X 14


500000

010 5/ -500000 e

-1000000 '0

-1500000--

-2000000 E0

___ ___- -2500000 .,-3000000 E

A -3500000X

-4000000

Station

1st FailureMoment

e MaximumAllowable FailureMomentFull LoadDisplacementMoment

0 10

0 11

a 12

o 13

X 14

69

2 15

0

0

00x0

A0

- -0

__ - --- 0 - __

- -0

CVN 77 Hogng Bending Moment+15Ktons at stations 15 to 20

-1i~ 4nA

__________ _________ ____ ____ i-I- __

Stato


-+

+ 0x +

0 O9I~~5 X0, LO

+

__ _ _ __ _ -1-n'00r

0000 b__ 0 0__

Station

-e- MdniumAlcmble FailureMrment

9000000 -e Full LoadDisplacement

8000000 Dslcnt

7000000 r 0 150

60000000

o 0 165000000

4000000E a 17

3000000 0

2000000 c0 18

1000000 C:0

x 19)-1000000

+ 20

1 1st FailureMloment

-e- MadmumAlomble FailureMomentFull LoadDisplacementMoment

0 15

0 16

a~ 17

o 18

x 19

+ 20

70

2000000

10000000

0 0160

-1000000aE0

-2000000m

-3000000D

4000000

1st FailureMom~er

~~~~~1~ -

xK~x

+ w -OA

T 0_

n

2

d

a 2 11

I

l

-'A g

)

APPENDIX E:


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

CVN71 Hogging Bencing Moment+2Ktons at stations 0 to4

9000000

70=00 C_ _ 8000000

600=000

400000 .E

300000D r

n -1000000

Station


Station

1000000

0Un

.-10000000.0

-2000000 a

-3000000 aE0

-400000010

-6000000

-7000000

0 1st FaiureMoment

- MadimAlo ble FailureMoment

.Ful LoadDisplamementMoment

a 2

o 1st Failure Moment

-e- MaximumAllcamble FailureMomentFull LoadDisplacementMoment

73

2 ) _ 10 __ _ _ _ _


AS~I4~iA~7 \~ -

'iU

Station

Z)

900000080000007000000600000050000004000000

30000002000000

1000000

0-1000000

Co0

aE00I.

'05

0E


500000

0

-5000000-V0

-10000000

-1500000,

-2000000 E0

-2500000 o,

-3000000 *

-3500000

_4000000

+ 1st Failure Moment

--- Maximum AlowableFailure Moment

+ Full Load[Dsplacement

Moment0 5

o 8

x 9

1st Failure Moment

-e- Maximum AdlowableFailure Moment

Full LoadDsplacementMoment

S5

a 7

o 8

74

Ui 10

z D 15 1_ 10

0

A 0

Station

-

I


9000000

8000000

7000000

600000

5000000

4000000

3000000

2000000

1000000

0

-1000000

00

4.E00)

Staton

- 1st Failure Moment

--e-- Maxmum AlableFailure Moment

- Full LoadDisplacement

o10

o 11

A 12

o 13

x 14


15 10 __

0

Station

500000

0U)

-500000 C0

-10000000

-15000000

-2500000 i>a,

-3000000

-3500000

-4000000


-e- aximum Aloa eFailure Moment

Full LoadDsplacementMoment

o 10

0 11

& 12

o 13

x 14

75

7 7

10 4r,


9000000

8000000

7000(W0

6000000

_ _ -- -- 500000

_ 4000000

3000000

-- 2000000

3k 1000000

0

a 1E 1j5 -1000000

Station


-e- Maximum AllowableFailure Moment

U)

0

0

0

E00)

CD.E

-. Full LoadDisplacementMoment

o 15

0 16

a 17

0 18

x 19

+ 20


10

-t-~1

0 ~/

/I\AI

500000

0

-500000 r-0

-1000000 *

-1500000 +

-2000000 E0

-2500000 cm

-3000000

-3500000

-4000000

Station

0 1st Failure Moment


o 15

o 16

A 17

o 18

X 19

+ 20

76

2

-A- 0

L

0 1:5

APPENDIX F:


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

CVN71 Hoging Bencing Moment+1OKtons at stations 0 to 4

9000000

8000000

7000000

6000000

5000000

4000000

3000000

2000000

1000000

0

-1000000

-0 1st Failure Mbment

-e- Maximum AllaebleFailure Moment

(0

0

E00II-

E0

C0,

e Full Load[DisplacementMoment

a 2- n

- 0

Staion

CVN 71 Sagging Bending Moment+1 OKtons at stations 0 to 4

C]

o0 0 0

6S

Station

3000000

2000000

10000000

0-1000000.2

-2000000 0E

-3000000 0

4000000

-5000000 C

-6000000

-7000000


-e- Maximum AllowableFailure Moment

Full LoadDisplacementMoment

a 2

79


9000000

8000000

7000000

6000000

5000000

4000000

3000000

2000000

1000000

0

-1000000

0

0

E0

0)

1st Failure Moment

-e- MaximumAlcmable FailureMomentFull LoadDisplacementMoment

0 5

A 7

Station


500000

00

1 -500000 c0

-1000000 IW

-1500000

-2000000 E0

-2500000 0

-3000000

-3500000

-4000000

-o-- 1st Failure Moment

-e- Maximum AlwableFailure Moment


o 5

a 7

o 8

Station

80

Ac"___

n

2 ___ 110__ _ _ _

_ bx0 b

0_ 0

"'K

01

17


__ - __ __ ____ - - F

____ I--' ____ _____ I _____ - ____ _______- ____ ____ _____ ____ I ____

9000000

8000000

7000000

6000000

5000000

4000000

3000000

2000000

1000000

0

0

4-

0

E0

2)


-e- MaximumAliowable FailureMoment


o 10

0 11

A 12

o 13-1000000

Station X

CVN 71 Sagging Bending Moment+1OKtons at stations 10 to14

0 15

U/

___- _ n ~-<-

0

A/ 0

-500000

-1500000

100

0

-21000000 E--

-1500000 -C

-2000000 E0

--2500000 im

--3000000 *

--3500000 I

-4000000

Station

14


-e- MaximumAlawable FailureMoment

-. Full LoadDisplacementMorment

o 10

o 11

A 12

0 13

x 14

81

2

k

10

0Q

e%

CVN 71 Hogging Bending Moment+1 OKtons at stations 15 to 20

+ 4

20 15 1IQ

Station

9000000

8000000

7000000

6000000

5000000

4000000

3000000

2000000

1000000

0

-1000000


-e- Maximum AliowableFailure Moment

C

0

0

00CI

+ Full LoadDisplacementMoment

o 15

0 16

A 17

o 18

x 19

+ 20


1000000

500000

10,

0)-500000

0

-1000000.

-1500000 oE

-2000000

-2500000 ~

-3000000 m

-3500000

-4000000

Station

1st FailureMoment

-e- MaximumAdlcwable FailureMomentFull LoadDisplacementMoment

o 15

o 16

A 17

o 18

x 19

+ 20

82

'4

+ +

+

r) 2W

Aj 00 0A

400

1in

APPENDIX G:


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


--- 0--

Station

IL

Si;

9000000

8000000

70000000

60000000

50000004000000

E3000000 0

2000000

1000000

0-1000000


0 7

OA

0 0

A

-V

Station

3000000

2000000

10000000

0-1000000 4

*-f

-2000000 2E

-30000000

-4000000

-5000000 CW-6000000

-7000000

-- 1st FailureMoment

--e- MaximumA ell Ue FailureMomnent


0 0

a 2

o 3

--- 1st Failure Moment

-e- MaximumAlowable FailureMoment


0 0

A 2

o 3

85

0

-

a 0

- b

2


Station


9000000

8000000

7000000 0

6000000 *10

5000000

4000000 0E

3000000 0

2000000 g1000000 r

00-1000000

500000

0

-100000000

-15000000

-2000000 E0

-2500000 ,

-3000000

-3500000

-4000000

-e-- MaxmumAelcoeble FailureMoment

- - Full LoadDisplacementMoment

0 5

A 7

0 1st Failure Moment

-e- aximumAllovable FailureMomentFull LoadDsplacementMoment

0 5

A 7

Station

86

1st FailureMoment

- - -

D 10i _- 0

04 FO _

-4- - -

- - --- -

CVN 71 Hogging Bencing Moment+11Ktons at stations 10 to 14

Station

9000000

8000000

7000000

6000000

5000000

4000000

3000000

2000000

1000000

0

-1000000

0

00

'-

4a

0

E0o

0 1st Failure Mloment

-e- MadmumAloaMble FailureMomert

-e Full LoadEDsplacementNbment

o 10

o 11

a 12

o 13

14

CVN 71 Sagging Benring Mormrt+11Ktons at stations 10 to 14

0 15 104-

_ _ _ A rv _ _ _

- - -_ _00

Statio

500000

00

)-500000

0-W-10000000

-1500000

0

-25000000

-3000000*

-3500000

-3000000

- 1st Failure Mbment

-e- MmdrumAllcmble FailureM4omnt

Full LoadDoaen~ttvpbment

o 10

0 11

A 12

o 13

x 14

87

r.


9000000

8000000

7000000

6000000

5000000

4000000

3000000

2000000

1000000

0

-1000000


-e-- MaxumAllwamble FailureMoment

+ Full LoadDisplacement

- M5ment$ 0 150

00a

E0

Co2

Im

Station

0 16

& 17

o 18

x 19

+ 20

- ++

+o +

_ 0-- 0 -

0

CVN71 Sagging Bending Momwnt+11Ktons at stations 15 to 20

1000000

500000

- 0 0

10 _V-50000000-1000000

0 0-1500000E

-2000000 0

__ -2500000

___ ___-300000

-3500000

-4000000

Station


-e- Maximum AllcvableFailure Moment

-- Full LoadDsplacementMoment

o 15

0 16

& 17

o 18

x 19

+ 20

88

I

2

APPENDIX H:


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


-I -- _

A 3

XP

0 0- 0

9000000

8000000

7000000

6000000

5000000

4000000

3000000

2000000

1000000

0

)-1000000

(00

00

0E0

Co:5C

-o- 1st FailureMoment

-e- MaximumAdloable FailureMomentFull Load[DisplacementMoment

0 0

A 2

Station



- 0u 0

~i--- 0 Q 0 Q 4 0- ^0

Station

-e- Maximum

6000000 Abeoble FailureMoment

4000000 ~Full LoadDsplacement

0 Moment2000000 *1*L 0

00

0-2000000 0

00)

-4000000 c

0-6000000 wo

-8000000

91


9000000

8000000

7000000 C0

6000000 V0

5000000

4000000 wE

3000000 0

-2000000

-1000000

Station

CVN71 Sagging Bending Moment+15Ktons at stations 5 to 9


-e- MaximumAlowable FailureMoment

-- Full LoadDisplacementMoment

o 5

A 7

0 8


500000

0

)-500000 C0

-100000000

-1500000

-2000000 E0

-2500000 o,

-3000000 X-3500000

-4000000

-e- MaximumAlco&eble FailureMomentFull LoadDsplacementMoment

0 5

A 7

- - 0

0 0 0

0

" 0 4a

0 0 00

- x /

Station

92

-1000000e

2


__ ____ __ __ __ __ _____ __ I __ I _____ __ __ __

-A

0~a 151 3 60

9000000

8000000

7000000 C0

6000000 00

5000000

4000000E

3000000 0

2000000

1000000!

0 I

-1000000

Station


50000

-00

_1 10 )_ -5000000

-1000000 0

00 -1500000

_-___ L-- -- 2500000)A 0 0

0~ 0

-25=

0--3500000

-4000000

Station

- 1st Failure

-e- MadmumAblleLe Failure

--- Full LoadDisplacementMoment

o 10

0 11

A 12

0 13

x 14

o1st Failure Moment

-e- Ma umAlabe FailureMomentFull LoadDisplacementMoment

0 10

0 11

A 12

0 13

x 14

93

'i

2


9000000

8000000

_ _7000000

6000000

- - 5000000

+- 20000002000000

1000000

n-1000000

Station


-x 1st Failure Moment

-x- Maximum AllowableFailure Moment

0-t

040

E0

:510

2000000

1000000 -0

0

-1000000 0E0

-2000000 m

-300000010

-4000000

Station


o 15

4 16

A 17

o 18

W 19

+ 20

- 1st FailureMoment

-e- MaxinumAllwamble FailureMoment


o 15

0 16

A 17

o 18

X 19

+ 20

94

+

+

0 0 0 0

0

0 + +

0~ 0

2

Date post:	09-Nov-2021
Category:	Documents
Upload:	others
View:	2 times
Download:	0 times

An Alternate Method for the Determination of Aircraft ...

Documents