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Structural design of the DRDDC notional destroyer
John R. MacKay Malcolm J. Smith Liam Gannon Doug Perrault DRDC – Atlantic Research Centre
Defence Research and Development Canada Scientific Report DRDC-RDDC-2019-R081 July 2019
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IMPORTANT INFORMATIVE STATEMENTS
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© Her Majesty the Queen in Right of Canada (Department of National Defence), 2019 © Sa Majesté la Reine en droit du Canada (Ministère de la Défense nationale), 2019
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Abstract
This Scientific Report describes the structural design of a generic 7,600 tonne air-warfare destroyer, referred to as the DRDC Notional Destroyer (ND). The intent of the ND is to provide a test-bed for evaluating structural, stability, hydrodynamic and other naval engineering design standards, design concepts, analysis methods, and software. The ND is not based on either existing or future naval platforms. The current work is concerned only with the structural aspects of the ND design, which conforms with Lloyd’s Register’s Naval Ship Rules (NSR) for a worldwide service area. In addition to the standard Rules requirements for structures, the ND was designed against LR’s requirements for an Extreme Strength Assessment, Level 2. That entailed comparing the hull girder’s ultimate strength, as predicted using Smith’s progressive collapse method, against extreme lifetime global loads prescribed by the NSR. This Scientific Report describes the hypothetical performance requirements that drove the ND design, the modelling and analysis tools used, and the bottom-up design procedure employed by DRDC. The outcome of the design process is then presented, including the general arrangement; design loads; the final structural configuration and scantlings; and the results of the global and ultimate strength assessments. The evolution of the scantlings, from those meeting the standard NSR requirements to those meeting global and ultimate strength requirements, is discussed, as are the weight implications associated with meeting those requirements.
Significance to defence and security
The Notional Destroyer provides a benchmark against which the design and performance of existing and future RCN ships can be compared. It also serves as a test bed for studying alternative naval standards and classification society rules, design concepts and methods, novel design features, modelling and simulation techniques, and warship performance under environmental and military loads.
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Résumé
Le présent rapport décrit la conception de la structure du contre-torpilleur fictif (CTF) de RDDC, un contre-torpilleur générique de 7 600 tonnes destiné à la guerre aérienne. Le CTF vise à fournir un banc d’essai pour évaluer certaines normes de génie naval, notamment celles relatives à la structure, à la stabilité et aux qualités hydrodynamiques des navires, ainsi que certains concepts pour la conception, certaines méthodes d’analyse et certains logiciels. Le CTF n’est pas lié à une plate-forme navale actuelle ni à aucune future plateforme. Les travaux évoqués dans le présent rapport portent seulement sur les aspects structurels de la conception du CTF, laquelle est conforme aux Naval Ship Rules (NSR) de la Lloyd’s Register (LR) pour une zone de service mondial. En plus de respecter les exigences standard de la LR s’appliquant aux structures, le CTF a été conçu pour satisfaire à ses exigences en matière de résistance extrême (niveau 2). La résistance ultime de la poutre-coque a été évaluée en fonction des prédictions réalisées en appliquant la méthode d’effondrement en cascade de Smith et comparée aux charges globales extrêmes indiquées dans les NSR pour la durée de vie des poutres-coques. Dans le présent rapport scientifique, on décrit les exigences de rendement hypothétiques qui ont guidé la conception du CTF, les outils de modélisation et d’analyse employés et la procédure de conception de bas en haut utilisée par RDDC. On présente ensuite les résultats du processus de conception, y compris la configuration générale du navire, les charges théoriques, la configuration de la structure définitive, l’échantillonnage final ainsi que les résultats des évaluations en matière de résistance ultime et globale. Enfin, on discute de l’évolution des différents échantillonnages, en commençant par ceux qui satisfont aux exigences standard imposées par les NSR et en terminant par ceux qui respectent les normes de résistance ultime et globale, et on décrit les conséquences sur le poids du respect de ces exigences.
Importance pour la défense et la sécurité
Le contre-torpilleur fictif fournit un point de comparaison pour l’évaluation de la conception et du rendement des navires actuels et futurs de la Marine royale canadienne. Il servira aussi de banc d’essai pour étudier d’autres normes de génie naval et d’autres règles de société en matière de classification, des concepts et des méthodes de conception, de nouvelles caractéristiques de conception, des techniques de simulation et de modélisation ainsi que le rendement des navires de guerre lorsqu’ils sont assujettis à des charges militaires et environnementales.
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Table of contents
Abstract ...... i Significance to defence and security ...... i Résumé ...... ii Importance pour la défense et la sécurité ...... ii Table of contents ...... iii List of figures ...... v List of tables ...... vii 1 Introduction ...... 1 2 Design assumptions ...... 2 2.1 Performance requirements and particulars ...... 2 2.2 Hull form and lines ...... 3 2.3 Structural design assumptions ...... 7 3 Modelling and analysis tools ...... 9 4 Design procedure ...... 11 4.1 Specification of the general arrangement and structural configuration ...... 12 4.2 Derivation of local design loads ...... 12 4.3 Determination of scantlings to resist local loads ...... 12 4.4 Derivation of global hull girder design loads ...... 13 4.5 Modification of scantlings to resist global loads ...... 14 4.6 Verification of the structural design ...... 16 5 General arrangement and structural configuration ...... 17 5.1 Baseline configuration ...... 20 5.2 Engine room variants ...... 21 5.3 Watertight subdivision variants ...... 21 5.4 Structural variants ...... 22 6 Design loads ...... 23 6.1 Local design loads ...... 23 6.2 Global design loads ...... 25 7 Structural design ...... 30 7.1 Longitudinal structure ...... 30 7.2 Transverse structure ...... 35 8 Global strength ...... 37 8.1 Section properties ...... 37 8.2 Stress criteria ...... 37 8.3 Buckling criteria ...... 39 9 Ultimate strength ...... 44
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9.1 Ultimate bending moment results ...... 45 9.2 Extreme shear strength assessment ...... 50 10 Design evolution ...... 51 11 Geometric model and design modifications ...... 56 11.1 Forward end design ...... 57 11.2 Deck 1 openings ...... 58 11.3 Transverse bulkhead modifications ...... 59 11.4 Other modifications ...... 61 12 Conclusions ...... 62 References ...... 64 Annex A Frame table ...... 66 List of symbols/abbreviations/acronyms/initialisms ...... 67
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List of figures
Figure 1: Geometric model of a wind tunnel model used in the air wake study [6]...... 4 Figure 2: Body plan of the ND hull; showing station numbers. Scale in metres...... 5 Figure 3: Buttock and waterlines of the ND Hull. Scale in metres...... 6 Figure 4: Structural modelling and analysis procedure for the ND. Each box shows a software program, its function and the type of model it produces, if any...... 9 Figure 5: Bottom-up structural design procedure for the ND, with reference to applicable chapters in Lloyd’s Register’s Naval Ship Rules (NSR)...... 11 Figure 6: General arrangement of the baseline configuration and other variants of the ND. ...18 Figure 7: Detailed tank arrangement of the ND baseline configuration; showing diesel fuel oil in red, aviation fuel oil in purple, lube oil in orange, seawater ballast in green, fresh water in blue, black water in black, and grey water in grey...... 21 Figure 8: Local design pressures for the shell envelope amidships...... 23 Figure 9: Shell envelope design pressure at the keel between the forward and aft quarter points. . 24 Figure 10: Still-water vertical bending moment distributions for the baseline configuration. ...26 Figure 11: Distribution of mass for the baseline configuration at end of life with icing loads for the deep departure and arrival load conditions...... 27 Figure 12: Still-water and wave vertical bending moment distributions for the baseline configuration showing the worst-case loads in hogging and sagging...... 28 Figure 13: Design vertical bending moment distributions for the baseline configuration. ....28 Figure 14: Vertical shear force distributions for the baseline configuration...... 29 Figure 15: Midships cross-section for the baseline configuration (F34.1); all dimensions in millimetres unless otherwise noted; corrosion margins are not shown...... 30 Figure 16: Cross-section at the forward quarter point in way of a stores compartment (F16.8). . . 31 Figure 17: Cross-section at the forward quarter point (F16.8) showing scantlings from the revised forward end design [3]...... 32 Figure 18: Cross-section at the aft quarter point in way of double hull fuel tanks in the baseline configuration (F51.3) showing both effective and ineffective structure...... 33 Figure 19: Geometric model of the baseline configuration of the ND, showing the starboard side structure in aft engine room...... 34 Figure 20: Scantlings for the watertight transverse bulkhead between the engine rooms in the baseline configuration (F32)...... 36 Figure 21: Johnson-Ostenfeld relationship for the critical buckling stress...... 40 Figure 22: Midships cross section model for ultimate strength analysis...... 45
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Figure 23: Forward quarter cross section model for ultimate strength analysis, indicating effectiveness of structural elements...... 46 Figure 24: Comparison of the extreme design vertical bending moment (VBM) envelope for the baseline configuration and the ultimate strength at selected longitudinal positions. . . 47 Figure 25: Moment-curvature relationships for vertical bending of the hull girder at selected cross-sections of the baseline configuration...... 48 Figure 26: Bending moment interaction curves at selected cross-sections of the baseline configuration...... 49 Figure 27: Amidships cross-section showing the scantlings after designing for local loads, global strength and ultimate strength...... 51 Figure 28: Moment-curvature relationships for vertical bending of the hull girder amidships at various stages of design...... 55 Figure 29: Trident Modeller model of the baseline configuration of the ND; showing the starboard side of the hull...... 56 Figure 30: Revised forward end design: hull plate thicknesses in mm (top); internal structural arrangement (bottom)...... 57 Figure 31: No. 1 deck openings in way of engine rooms...... 59 Figure 32: Transverse watertight bulkhead at Frame 32 indicating plate thickness in mm. ....60 Figure 33: Modifications to aft end structure...... 61
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List of tables
Table 1: Performance requirements for the ND...... 2 Table 2: Comparison of AWD designs...... 2 Table 3: Hull particulars for the ND baseline configuration in the deep departure condition. . . 3 Table 4: Material properties for high-strength steel...... 7 Table 5: Basic structural design parameters...... 17 Table 6: Summary of ND variants...... 19 Table 7: Deck locations...... 19 Table 8: Tank and void space volumes for the baseline configuration...... 20 Table 9: Displacement of the baseline configuration under various loading cases...... 25 Table 10: Scantlings for primary transverse members...... 35 Table 11: Section properties of the design cross-sections.a ...... 37 Table 12: Maximum hull girder normal stresses for the baseline configuration resulting from the minimum rule vertical bending moment...... 38 Table 13: Maximum hull girder shear stresses for the baseline configuration resulting from the minimum rule vertical shear force...... 39 Table 14: Definitions of NSR buckling stresses...... 40 Table 15: Critical buckling stress criteria at selected locations on the amidships cross-section of the ND...... 42 Table 16: Applied stresses and safety factors on buckling failure for selected locations on the amidships cross-section of the ND...... 42 Table 17: Applied shear stresses and minimum safety factors for shear buckling failure at selected locations in the forward and aft quarter cross-section of the ND...... 43 Table 18: Ultimate strength of the baseline configuration under vertical bending...... 47 Table 19: Maximum shear stresses for the baseline configuration resulting from extreme vertical shear forces...... 50 Table 20: Section properties amidships at various stages of the structural design.a ...... 53 Table 21: Ultimate strength of the amidships section of the baseline configuration under vertical bending at various stages of design...... 54 Table 22: Dimensions of longitudinal stiffeners in the revised design [3]...... 58 Table A.1: Frame table for the ND...... 66
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1 Introduction
Defence Research and Development Canada (DRDC) developed a notional destroyer to create a test bed for comparing design rules and methods, for evaluating the performance of design features, and determining achievable design goals for modern warships. The Notional Destroyer (ND) is a conventional air warfare destroyer, but is not based on either existing or future naval platforms. It was designed to meet Volume 1 of Lloyd’s Register’s Naval Ship Rules [1], which is mainly concerned with structural and loading requirements, and the Department of National Defence’s (DND) stability standard [2]. With this design, the performance of a warship designed to classification society naval rules can be compared to more traditional hull designs. The ND also allows the software used in its design to be evaluated, as well as identifying the strengths and weaknesses of a variety of modelling and simulation tools that can be applied to engineering analysis of the design.
This report describes the structural design of a baseline configuration of the ND, along with a series of design variants used to explore the effects of specific design changes on aspects of ship performance. In particular, this report describes the general arrangement of the ND baseline configuration and variants, how the structural aspects were designed to meet LR’s Naval Ship Rules (NSR), as well as the structural capacity of the baseline variant. The structural design described herein covers (1) the amidships hull and deck structural design, taking into consideration global and local loadings on the hull and decks; and (2) the design of the main transverse and longitudinal bulkheads based on local loading requirements. Subsequent to the completion of the present work, the baseline ND design was further developed by Lloyd’s Applied Technology Group (ATG) [3] to comply with the NSR’s local pressure loading requirements in the forward end of the vessel. Separate studies will be published on aspects of the design related to stability, such as the detailed tank arrangements, weight distributions, and the intact stability performance, as well as on the verification of the global and ultimate strength of the ND using finite element analysis.
This document begins with a description of the performance requirements and initial assumptions that govern the design of the ND (Section 2). DRDC’s suite of modelling and analysis software that was used to design the ship is then described in Section 3. Section 4 summarizes the overall design procedure. The following sections describe each step in the design, including: development of the general arrangement and structural configuration (Section 5); derivation of the design loads (Section 6); structural design scantlings (Section 7); global strength assessment (Section 8); and ultimate strength assessment (Section 9). The evolution of the amidships structural scantlings through the local, global and ultimate strength design is presented in Section 10. Some additional refinements of the design and the development of the geometric model are summarized in Section 11. Conclusions and recommendations for future work are presented in Section 12.
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2 Design assumptions
2.1 Performance requirements and particulars
The ND is approximately 7,600 tonnes, 150 m long and is intended to represent a typical modern Air Warfare Destroyer (AWD). The performance requirements that drove the design of the ND, which are typical of modern surface combatants, are summarized in Table 1. The size and tonnage of the ship is dictated mainly by its combat role as an AWD with vertical launch capability. Table 2 compares particulars for some modern AWD designs currently used in NATO navies. The service area, service life, and speed requirements in Table 1 are factors in determining the short- and long-term loading that the ship must withstand.
Table 1: Performance requirements for the ND.
Combat role Air warfare destroyer Service area Worldwide Service life 30 years Cruise speed 18 knots Sprint speed 30 knots
Table 2: Comparison of AWD designs.
Class Displacement (t) Length overall (m) Beam (m) Draft (m) Zumalt 15,995 190 24.6 8.3 Daring 8,700 152.4 21.2 7.4 Arleigh-Burke 8,315 154 20 5.3 Horizon 7,050 152.9 20.3 5.4 De Zeven Provinciën 6,050 144.2 18.8 5.18 Álvaro de Bazán 5,800 146.7 18.6 4.75
The ND has a nominal design service life of 30 years. Service life affects the structural design through the global strength requirements and fatigue design of the vessel. In the NSR, service life mainly affects global strength through changes to the still-water loads on the vessel due to growth of the lightships weight over the life of the vessel; the effect of service life on the wave-induced loading is negligible when a worldwide service area is assumed. Fatigue design is not addressed in the current study and a fatigue design assessment (FDA) is left for the future work. However, previous work on the Halifax class design showed that a warship can be designed for an even longer lifespan (45 years) without a significant increase in costs [4].
In addition to the performance requirements, it was assumed that the ship would meet or exceed the pollution requirements of the International Maritime Organization (IMO) [5], especially with respect to
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protection of fuel oil tanks by double bottoms. Other basic design assumptions, such as a longitudinally framed hull structure, were based on conventional naval designs.
The general particulars of the hull are listed in Table 3 for the ship at the beginning of its service life (7,673 tonnes in deep departure), and at the end of its life, including a lightships weight growth margin of nearly 15% plus maximum allowable ice accretion (9,095 tonnes in deep departure). The growth in lightships weight over a 30 year service life and icing loads are determined from DND’s stability standard [2]. Initial calculations were performed assuming a beginning-of-life deep departure weight of 7600 tonnes; the final weight of 7,673 was determined once the details of the tank arrangements were established.
Table 3: Hull particulars for the ND baseline configuration in the deep departure condition.
Particulara Beginning of Life End of Life (No Icing Loads) (With Icing Loads) Length overall, 151.4 m Overall depth, 16.5 m Amidships depth 14.0 m Maximum breadth, 18.7 m Displacement, ∆ 7,673 tonnes 9,095 tonnes
Length along the waterline, 142.8 m 143.5 m
Length b/w perpendiculars, 137.8 m 138.5 Amidships locationb 68.9 m 69.2 m Longitudinal centre of gravityb 72.0 m 73.8 m
Waterline breadth, 16.8 m 17.0 Draft, 6.7 m 7.5 m
Block coefficient, 0.48 0.51
Waterplane area coefficient, 0.77 0.77 Length constant, Ⓜ 7.30 6.93 a. Hull size and shape parameters are defined in the list of symbols and abbreviations. b. Distance aft from the Forward Perpendicular (FP). The FP is 0.80 m and 1.48 m forward of Frame 0 for the beginning of life and end of life loading, respectively. Frame positions are defined in Annex A. 2.2 Hull form and lines
The ND hull form was designed by DRDC and NRC for an air wake study looking at the effect of topsides design on helicopter operations [6]. A rendering of one of the wind tunnel models used in the air wake study, consisting of the outer ship envelope above the waterline, is shown in Figure 1. The air wake model was extended below the waterline by adapting NRC’s Design 24 hull form [7] to fit the above
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waterline envelope. The resulting hull form and superstructure envelope wwere used as the starting point for the ND design.
Figure 1: Geometric model of a wind tunnel model used in the air wake study [6].
The body plan of the ND hull form is shown in Figure 2, and the sheer and half-breadth plans are presented in Figure 3. Not included are any appendages (bilge keels, sonar domes, A-brackets, etc.) as these do not contribute to the structural performance of the hull. The lines plan shows that the hull is not perfectly faired, especially in the amidships area. For example, Figure 3 shows a “bulge” in the 8 m buttock line between longitudinal positions 70 m and 85 m, which results from relatively steep local gradients in the hull form. That can be seen in the left-hand-side (stern half) of the body plan in Figure 2, where both the slope of the side shell and the curvature of the turn of bilge increase abruptly between stations 10 and 11. DRDC could properly fair the ND hull in the future; however, the imperfect fairness of this version of the hull will have a negligible effect on the structural and stability modelling that is the focus of the current work.
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Figure 2: Body plan of the ND hull; showing station numbers. Scale in metres.
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Figure 3: Buttock and waterlines of the ND Hull. Scale in metres.
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2.3 Structural design assumptions
The ND structural configuration and scantlings were designed to meet Volume 1 of LR’s Naval Ship Rules [1]. It was assumed that all structure would be fabricated from High-Strength Steel (HSS) in order to reduce structural weight and increase the weight envelope available for combat and marine systems. The nominal material properties for HSS are listed in Table 4. The design was performed specifically for the baseline configuration; however, with only minor modifications, the resulting scantlings could be made to meet the Rules for the other variants described in Section 5 as well. In the present work, the structural design of just the baseline configuration is considered.
Table 4: Material properties for high-strength steel.
Young’s modulus 207 GPa Poisson’s ratio 0.3 Yield strength 355 MPa Density 7,850 kg/m3
The targeted LR class notation for the ND is
NS2 Destroyer, SA1, ESA2 where NS2 indicates a frigate or destroyer, SA1 indicates that a worldwide service area is assumed, and ESA2 indicates that the hull design complies with extreme strength assessment requirements based on an elasto-plastic analysis of the hull strength. The current work does not include any calculations in support of Residual Strength Assessment (RSA), Structural Design Assessment (SDA), or Fatigue Design Assessment (FDA) notations. DRDC will present the results of a SDA of the ND in a separate report.
The Enhanced Scantling (ES) notation, which may be awarded if a corrosion policy is specifically developed and applied to the ship, is not applied. The Rules requirements for corrosion margins are not onerous. So long as adequate steps are taken to prevent material loss due to corrosion, such as preservative coatings and active or passive cathodic protection systems, the Rules specify only an additional 2 mm of plating, over and above the design scantlings for the keel plate, and an additional 0.5 mm for all plating below a line 1 m above the design waterline.1 DND’s structural design standard DMEM 10 [8] is less prescriptive, indicating that appropriate allowances should be considered for areas that are particularly susceptible to corrosion, such as the shell envelope around the waterline.2
A tailored corrosion policy was not developed for the ND, and all design scantlings presented herein are based on the structural dimensions without the Rules corrosion margins mentioned above. Fabrication drawings, were they to be produced, would of course need to include the corrosion margins for the appropriate structure.
1 It is unclear if the latter requirement applies only to plating on the hull envelope, or to all external and internal structure. 2 DMEM 10 does prescribe a 0.5 mm corrosion allowance for tank tops and other deck structures in corrosive environments.
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The ND design is a work in progress. The present work describes the development of the hull structural design using the NSR for the following structure: the hull envelope; the weather deck; internal decks; transverse and longitudinal bulkheads; the inner bottom; and tank structures. An additional study by Lloyd’s ATG provides the hull structural design for the extreme forward end [3]. What remains to be completed is the structural design for the superstructure, the flight deck, internal tank boundaries, hatches and penetrations, connection details, and machinery foundations. In the future, typical connection details could be designed in order to allow a Fatigue Design Assessment (FDA) to be carried out on the ND, but DRDC has no plans for that at present.
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3 Modelling and analysis tools
Several in-house and commercial software packages were used in the development of the ND design and analysis models. The structural modelling and analysis procedure is shown schematically in Figure 4.
Structural models were generated using DRDC’s in-house pprogram PW7600, which creates the input geometry and material data for the Trident Modeller geometric modelling software developed by Martec Limited. Trident Modeller is a ship structures modelling tool for creating geometric models and Finite Element (FE) meshes for structural analysis, and which is based on the SubSAS modelling tool for submarine structures [9]. A ship model can be produced within the graphical user interface of Trident Modeller; however, the model is stored in a human-readable XML data format called RMGScript. PW7600 produces ship models in the RMGScript format.
Figure 4: Structural modelling and analysis procedure for the ND. Each box shows a software program, its function and the type of model it produces, if any.
PW7600 allows the user to specify the main structural dimensions (e.g., primary and secondary member spacing, deck locations), the watertight subdivision, and the location of tanks, engine rooms, stores and
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void spaces. The structural scantlings can be based on default values specifically selected for a 7,600 tonne warship, user-defined values, or, to a limited extent, dimensions based on LR’s Naval Ship Rules, which were coded directly into PW7600.3 Furthermore, while the program was initially intended to produce models specifically for the 7,600 tonne ND, the user can also input the displacement and table of offsets for any arbitrary hull form. In that way, DRDC is not only able to produce the ND variants described herein, but can also use PW7600 to generate notional warships of various displacements and arrangements if necessary.
Structural models produced by PW7600 incorporate all watertight boundaries including the shell envelope, decks, tanks, and bulkheads, as well as all primary and secondary stiffening members. Stiffener end connections are not modelled in detail, and only very large penetrations, such as the uptake and intake openings, are included in the model. The current version of the program does not generate the superstructure.
Trident Modeller was used to produce finite element meshes for structural analysis, including linear-elastic global strength analysis and nonlinear ultimate strength calculations.4 The FE models were also used to generate two-dimensional cross-sections of the hull for ultimate strength calculations using DRDC’s STRUC program [10]. The ultimate strength calculations themselves, which were required to satisfy the ESA2 notation, were performed with DRDC’s ULTMAT software [11]. Ultimate strength calculations within ULTMAT are based on Smith’s progressive collapse method for hull girders [12].
3 The limitations of PW7600 with respect to automatically generating scantlings that meet the NSR are discussed in Section 4.3 on p. 12. LR’s software for determining compliance with the NSR was not used in the current work since it was not available to DRDC at the time. 4 Global finite element modelling and analysis of the ND are not described in this report.
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4 Design procedure
DRDC followed the procedure shown in Figure 5 in the structural design of the ND. That figure refers to the applicable sections of LR’s Naval Ship Rules [1]. DRDC’’s design procedure in Figure 5 is based on a bottom-up approach, whereby the scantlings are first designed to resist local loads, after which they are selectively enhanced to ensure that the hull can also resist global loads. Given the layout and structure of the Rules, the bottom-up procedure was the most practicall way to design the ship to meet the NSR requirements. Each step in the design procedure in Figure 5 is described in greater detail in the following sections.
Figure 5: Bottom-up structural design procedure for the ND,, with reference to applicable chapters in Lloyd’s Register’s Naval Ship Rules (NSR).
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4.1 Specification of the general arrangement and structural configuration
Step 1 in the design of the ND involves defining a general arrangement and the basic structural configuration and dimensions. The general arrangement for each variant is arrived at through a trial-and-error procedure aimed at ensuring that the predefined requirements for each variant are met (e.g., the number of longitudinal subdivisions, the location of engine rooms) and that the fuel and storage capacities are approximately uniform across the variants. Of course, certain features of the arrangements, such as the number of decks and location of tanks, are constrained by the initial design assumptions like the size and shape of the hull. The placement of fuel oil and other tanks is also influenced by trim and stability considerations. Other factors, such as providing adequate space for the Vertical Launch System (VLS) and an adjacent stores space for the magazine, also affects the general arrangement designs. The final general arrangement for each variant is presented in Section 5, along with the rationale for some of the design choices and trade-offs.
To a certain extent, the structural configuration is constrained by NSR requirements for a longitudinally framed hull. For example, the NSR requires the spacing of transverse and longitudinal primary members to fall within specified ranges. Otherwise, the basic structural dimensions, such as the spacing of secondary members, were selected based on typical existing warship designs. The basic structural dimensions are also described in Section 5. 4.2 Derivation of local design loads
Step 2 involves the calculation of local design loads as prescribed by the NSR, including hydrostatic and hydrodynamic loads on the hull envelope, and occupancy loads for internal decks. Local loads on the hull envelope are based on the displacement and draft associated with the deep departure, end of life loading condition with icing (see Table 3). Local loads due to slamming, helicopter operations on the flight deck, and the weight of the superstructure on the weather deck and adjacent structure are not considered. Ice build-up and collision loads are also neglected (however, icing contributions to global loads are considered, as described below). Slamming and helicopter landing may be taken into account at a future date, if the bow and flight deck structures of the ND are designed in greater detail. The local design loads derived for the ND are described in Section 6.1. 4.3 Determination of scantlings to resist local loads
In Step 3, the structural scantlings are designed to resist the local loads derived in Step 2, while at the same time ensuring that the minimum scantlings prescribed by the NSR are satisfied. Step 3 primarily involves ensuring that the NSR criteria for prescribed stress, displacement, and cross-sectional area are met for stiffened panels and primary members under the bending moments and shear forces that arise due to the local hydrostatic, hydrodynamic and occupancy pressure loads.
Calculations for determining local design loads (Step 2) and scantlings (Step 3) for the hull envelope are performed using tools embedded in PW7600. Calculations for internal structures, like decks and bulkheads, are done separately using spreadsheets. A basic scantling optimization procedure is employed in PW7600, whereby the scantlings are incrementally increased until the minimum criteria are satisfied. With the spreadsheet scantling calculations, a manual trial-and-error procedure is used to ensure that the
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plate thicknesses and stiffener dimensions satisfied the Rules. The interim scantlings designed to meet local loads are presented in the context of the evolution of the structural design in Section 10. 4.4 Derivation of global hull girder design loads
The global hull girder loads are determined in Step 4 of the design procedure. The NSR require global still-water loads to be determined by “direct calculation;” in other words, by deriving resultant bending moments and shear forces along the ship’s length based on given weight and buoyancy distributions, and by assuming static equilibrium. Any suitable stability or finite element software capable of performing static balance analysis may be used to assess still-water loads for assessment against the NSR. In the present work, the global still-water loads are generated using static balance analysis with the General Hydrostatics (GHS) software.
Design still-water loads are taken to be the maximum and minimum of twelve loading conditions. Those loading conditions are generated by combining scenarios related to the mission (deep departure, operational light, and arrival), life-cycle (beginning and end of life), and environment (with or without the maximum allowable amount of icing). The result of the GHS calculations is a set of design curves for the 5 hogging and sagging still-water vertical bending moment, , and shear force, .
A mass distribution for each of the twelve loading conditions first had to be determined as input to the GHS calculations. The following steps were taken to develop the mass distribution for the baseline configuration: The total mass of tank contents was estimated based on tank volume; The mass of other variable items and consumables was scaled from Halifax class data [13]; The lightship mass of the baseline configuration (including structural mass) was determined as 7600 tonnes minus the total mass of tanks, variable items and consumables; The distribution of the lightship mass was approximated by scaling the distribution from the design of the US notional destroyer to the target baseline lightships mass [14].
The mass of the baseline configuration (deep departure at beginning of life with no icing load) became larger than the target mass of 7600 tonnes (see Table 3) once the details of the tank subdivisions were developed. The final baseline mass distribution was adjusted to create the mass distributions for all twelve load conditions. These take into account: The differences in the tank contents, variable items and consumables in the deep departure, operation light and arrival conditions; The weight growth in the vessel between beginning and end of life, determined using the weight growth formula in DND’s stability standard [2]; The maximum allowable icing load of 397 tonnes situated on the weather deck with a longitudinal centre of gravity at /3 forward of midships [2].
5 The sign convention for vertical bending moments used throughout this report is positive (+) for hogging and negative (-) for sagging.
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Global wave loads are directly prescribed by the NSR based on the ship’s hull form (length, breadth and block coefficient), operational profile, and factors accounting for the distribution of the loads along the ship’s length. The NSR prescribe a minimum vertical wave bending moment, , and minimum vertical wave shear force, . The wave shear force distributions prescribed by the NSR are based on positive and negative shear force envelopes; they are only indirectly associated with shear forces arising from the design hogging and sagging conditions.
Wave loads for the ND are based solely on the deep departure, end of life loading condition (with ice loads), as summarized in Table 3 on p. 3. That loading condition results in the largest displacement and deepest still-water draft for all conditions considered. NSR wave loads increase with increasing waterline length and breadth, so that by using the deepest possible draft the most pessimistic wave loads are considered.
The rule bending moment is determined to be the maximum and minimum combinations of and , for hogging and sagging, respectively. In a similar manner, the rule shear force distribution is given by the maximum and minimum combinations of and , for positive and negative shear forces, respectively. The rule bending moments and shear forces are used in the standard NSR global strength assessment to determine resultant hull girder stresses, which are then compared against allowable stress levels.
The extreme strength assessment notation (ESA2) requires the extreme vertical bending moments and shear forces to be derived. The extreme bending moment is equal to the sum of and the extreme vertical wave bending moment, 1.5 . Likewise, the extreme shear force is taken as , where 1.5 is the extreme vertical wave shear force.
The various bending moment and shear force distributions that were derived for the ND are presented in Section 6.2, starting on p. 25. The assumed weight distributions associated with global loads are also discussed in that section. 4.5 Modification of scantlings to resist global loads
The aim of Step 5 of the design procedure is to ensure that the hull girder can resist the global loads determined in Step 4. This includes checking that NSR criteria for both global strength and ultimate strength are met. Global strength is determined by comparing normal and shear stresses under global bending moments and shear forces, respectively, to maximum allowable stresses based on yielding and buckling criteria with built-in safety margins. Global strength is based on linear elastic analysis. On the other hand, ultimate strength is concerned with ensuring that the nonlinear elasto-plastic collapse strength of the hull girder exceeds the most extreme global load that the ship must withstand over its service life.
For the ND, PW7600 is used to produce an interim structural model incorporating the scantlings designed for local loads (Step 3). A coarse FE mesh of the entire ship is then generated using Trident Modeller and is imported into STRUC to generate cross-section models at the forward quarter point, amidships, and the aft quarter point. Each cross-section is manually edited so that only longitudinally continuous structure is effective. An initial design assumption was that longitudinal bulkheads would be designed to resist local flooding loads only, and are therefore considered to be ineffective in global and ultimate strength calculations. Tank structures and the inner bottom are assumed to be completely ineffective since they were continuous through at most two or three compartments. Shadow zones forward and aft of large deck
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openings are assumed to be completely ineffective.6 The shape and extent of shadow zones are calculated according to the recommendations in the NSR.7 Longitudinally discontinuous decks passing through more than two compartments are assumed to be partially effective. Their effectiveness at a given longitudinal position was determined using the “Efficiency of Short Decks” curve provided by Chalmers [15].
Global strength criteria are applied first. The global stresses are determined using the rule bending moment determined in Step 4 and section moduli are calculated from the cross-section models using ULTMAT. The global stresses derived in this way are compared with LR’s maximum allowable stresses for longitudinally effective structure based on yielding and buckling. This check is performed at the forward and aft quarter points and amidships. Scantlings are increased in cases where the applied stresses exceeded any of the maximum allowable stresses. Any changes to one cross-section are applied uniformly over the length of the hull so that all cross-sections are affected. In that way, the general scantlings are the same over the entire length of the hull even though the structural configuration varies from compartment to compartment due to the type of compartment and shape of the hull. Adjustments to the scantlings to satisfy global strength are performed iteratively. Once scantlings are increased, the Trident Modeller model is recreated using PW7600 and re-meshed; cross-section models regenerated in STRUC; and the global stresses recalculated. The procedure is repeated until the scantlings are compliant with the Rules.
Once the global strength checks are completed, the ultimate strength of the hull is calculated for cross-sections amidships and at the forward and aft quarter points. Like the global strength checks, an iterative procedure is used to redesign the scantlings for ultimate strength. Scantlings are increased at selected locations when needed, and changes to any cross-section are applied to all other cross-sections. The revised scantlings are then fed back into PW7600, and the process is repeated until the ultimate strength is satisfactory at the design cross-sections. Additional ultimate strength calculations are then performed at 10 m increments along the length of the hull, including sections where the extreme bending moments are greatest in hogging and sagging. That satisfies the ESA2 requirement for evaluating ultimate strength at critical sections.
ULTMAT is capable of predicting stresses due to global loads and ultimate strength for any combination of vertical and horizontal bending moments; it can also predict the distribution of elastic shear stresses in a cross section for any combination of vertical and horizontal shear forces. However, it cannot predict ultimate strength in shear considering elasto-plastic effects and buckling. Thus, in Step 5, only the vertical bending aspects of elasto-plastic ultimate strength are addressed, while shear strength is evaluated using the elastic methodology in ESA1. Vertical bending tends to govern the sizing of scantlings, and as will be shown, it is unlikely that ultimate strength in shear is a limiting factor in the structural design.
Structural dimensions and scantlings for the ND are presented in Section 7, along with some of the details of the design procedure for specific structural items. Global strength calculations supporting the normal Rules requirements are presented in Section 8, while ultimate strength analyses required for the extreme strength assessment notation are described in Section 9. The adjustments that were made to the dimensions and scantlings to satisfy global and ultimate strength requirements are described in Section 10.
6 In particular, shadow zones were applied to Nos. 1, 2 and 3 decks in way of the intake and uptake openings. 7 Volume 1, Part 6, Chapter 4, Section 1.4 of Reference [1].
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4.6 Verification of the structural design
Step 6, the final stage in the design of the ND, is to verify the adequacy of the structural arrangement through linear and nonlinear finite element analyses. Linear analyses follow LR’s recommendations [16] for the structural design assessment, and are intended to satisfy the Structural Design Assessment (SDA) notation in the NSR. The aim of the SDA is to verify that global stress and buckling requirements are met while considering the full complexity of the geometry and loading of the hull. SDA analyses are performed for various global load cases using the ANSYS FE solver and a global FE model produced using Trident Modeller. SDA modelling and analysis methodology and results will be presented in a separate report.
Nonlinear FE analyses are used to verify that the ESA2 requirements for resisting extreme vertical bending moments and shear forces are met. This is especially important for shear loading since ultimate shear strength is not addressed in Step 5 of the design procedure. The analyses are performed with ANSYS using refined FE meshes of selected compartments where the global loads and structural resistance are most critical. Nonlinear FE analysis procedures and results will also be described in a separate report.
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5 General arrangement and structural configuration
Step 1 in the design of the ND involves creating a general arrangement consistent with conventional warship layouts and meeting the original performance and design requirements discussed in Section 2. Furthermore, the arrangement of the structural system and basic structural dimensions are selected based on conventional naval design. This section presents the general arrangement of the baseline configuration and four variants of the ND, as well as the overall structural configuration.
Profile views of the general arrangements of the baseline configuration and the four variants that involve changes to that general arrangement (i.e., the ER/1, ER/2, WT+2, and WT-2 configurations) are shown in Figure 6. The key structural dimensions that were fixed at the outset of the design procedure are listed in Table 5. The frame locations marked in Figure 6 correspond with the frame data provided in the frame table in Annex A.
The variants of the ND currently under consideration are described in the following sections. A summary of all variants is provided in Table 6. The hull particulars listed in Table 3, as well as the structural dimensions summarized in Table 5, the frame table in Annex A and the deck elevations given in Table 7, are applicable to all of the ND variants.
The arrangement of all ND variants is characterized by four decks, and port and starboard watertight longitudinal bulkheads at Nos. 2 and 3 decks. Nos. 1, 2 and 3 decks extend nearly the entire length of the hull, from the collision bulkhead at Frame 4 (F4) to the transom. No. 4 deck does not pass through the engine rooms, and terminates at the aft peak bulkhead at F67. There is a double bottom in stores compartments below No. 4 deck and a double hull in way of fuel oil tanks.8 The inner hull forming fuel tank boundaries was configured to ensure a minimum clearance of 0.5 m from the outer hull to allow access for maintenance and inspections.
Table 5: Basic structural design parameters.
Frame spacing 2.0 m Spacing of hull longitudinals 550 mm Vertical spacing of decks 2.75 m Spacing of deck longitudinals 575 mm Spacing of vertical stiffeners on watertight bulkheads 575 mm Transverse offset of longitudinal bulkheads 3.45 m Spacing of vertical stiffeners on longitudinal structure 500 mm
8 DRDC’s interpretation of the IMO regulations concerning the prevention of pollution by oil [5] is that special protection of fuel tanks against grounding or collision damage is only required for oil tankers. Thus, the ND could be designed with a single hull in way of the fuel tanks and still satisfy IMO requirements. Nonetheless, double hull protection of the fuel tanks was provided in order to ensure compliance.
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Figure 6: General arrangement of the baseline configuration and other variants of the ND.
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Table 6: Summary of ND variants.
Configurationa Perturbation from the baseline Number of Total capacity of configuration transverse fuel oil tanks (m3) watertight bulkheadsb Baseline N/A 10 1473 ER/1 One-compartment separation of engine 10 1565 rooms ER/2 Two-compartment separation of engine 10 1695 rooms WT+2 Two additional WT bulkheads 12 1674 WT-2 Two fewer WT bulkheads 8 1791 Cofferdam Cofferdam between engine rooms 10 1473 HS/A Enhanced scantlings at critical locations 10 1473 HS/B Box girders under Nos. 1 and 4 decks 10 1473 a. ER indicates changes to the engine room arrangement, WT indicates changes to the number of watertight transverse bulkheads, and HS indicates hull strengthening options. b. The cofferdam is counted as a single watertight bulkhead.
Table 7: Deck locations.
Deck Height above baseline (m) No. 1 Deck 14.0a No. 2 Deck 11.25 No. 3 Deck 8.5 No. 4 Deck 5.75 Inner Bottomb 3.0 a. No. 1 Deck height aft of amidships. b. General stores / accommodation compartments only.
By changing the general arrangement, and thus the longitudinal position of the double hull fuel tanks, the fuel capacities of the ND variants are not uniform. Fuel capacity varies within approximately 20% from the baseline configuration, depending on the tank arrangement (see Table 6). Those differences in the tank configuration are addressed in the stability design, where fuel tank spaces are added to or subtracted from the ND variants as necessary in order to produce arrangements with the same fuel capacity as the baseline configuration.
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5.1 Baseline configuration
LR’s NSR require a minimum of seven watertight bulkheads for the ND based on its length and amidships location of engine rooms. The baseline configuration was designed with ten watertight bulkheads along its length in order to provide some margin over the minimum Rules requirement and to allow other variants with fewer bulkheads to comply with the NSR.
The fore and aft engine rooms are adjacent to one another in the baseline configuration, and are situated amidships. The arrangement of the main fuel oil tanks is shown in Figure 6(a) and the tank capacities are listed in Table 8. The arrangement and subdivision of the fuel oil tanks has been further refined in the stability model, as shown in Figure 7. Some void spaces shown in Figure 6(a), or portions thereof, are used for fresh water, grey water, black water, etc., tanks in the stability design. The total fuel capacity of the baseline configuration is approximately 1,500 m3.
Table 8: Tank and void space volumes for the baseline configuration.
Compartment Type of tank Volume (m3) Volume between tank boundaries and outer hull (m3) No. 2 (F4-F11) Void spaceb 230.3 N/A No. 3 (F11-F18) Storesc 182.4 N/A No. 4 (F18-F25) Fuel oil tanka 527.3 272.9 No. 7 (F39-F46) Fuel oil tanka 551.3 283.8 No. 8 (F46-F53) Fuel oil tanka 394.8 271.3 No. 9 (F53-F60) Void spaceb 441.6 N/A No. 10 (F60-F67) Void spaceb 182.4 N/A No. 11 (F67-Stern) Void spaceb 18.6 N/A a. Tank volumes are based on a permeability of 97%. b. Volume of void space from keel to No. 4 deck. c. Volume of tanks under inner bottom in stores compartment.
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Figure 7: Detailed tank arrangement of the ND baseline configuration; showing diesel fuel oil in red, aviation fuel oil in purplee, lube oil in orange, seawater ballast in green, fresh water in blue, black water in black, and grey water in grey.
The locations of general stores and machinery spaces in the baseline configuration are indicated in Figure 6(a). The space above the forward stores compartment has been assigned to the vertical launch system. The stores space beneath the VLS would be a logical choice for thhe magazine; however, no special structural arrangements have been designed for either the VLS or magazine. Furthermore, the flight deck aft of the hangar has not been designed for helicopter landing loads. The superstruccture has not yet been designed, other than the shape of its external envelope. The remaining unmarked compartments in Figure 6 are considered accommodation, stores, marine system, sensor system, or combat system spaces. 5.2 Engine room variants
In the ER/1 and ER/2 variants, the forward and aft engine rooms are separated by one and two compartments, respectively. The length of the engine rooms is constant in the baseline and all variants. Only the aft engine room changes position in the ER variants, so that separation is achieved by moving that compartment towards the stern. The ER configurations may be used to study how isolating the engine rooms can improve survivability, and in particcular, vulnerability (e.g.,, by lowering the probability of damage to both engine rooms during combat). 5.3 Watertight subdivision variants
The WT+2 and WT-2 variants differ from the baseline configuration by adding and subtracting two transverse watertight bulkheads, respectively (see Table 6). The engine rooms in those variants are adjacent to one another and are the same length as in the baseline confifiguration; however, the enngine rooms have been moved forward or aft, as necessary, to accommodate the fuel oil tanks and vertical launch system. Typical compartments in the WT+2 and WT-2 variants are 10 m and 18 m in length, respectively, compared to 14 m in the baseline configuration. The WT variants are intended to be used to study the effect of the watertight subdivision on survivability aand damaged stability.
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5.4 Structural variants
Table 6 also lists three variants that involve changes to the structural configuration of the baseline configuration, but not to its general arrangement. The cofferdam variant is identical to the baseline configuration, except that the transverse watertight bulkhead between the engine rooms is replaced by a cofferdam. The cofferdam itself consists of two identical watertight bulkheads spaced 1 m apart and centred at F32. This model may be used to study how a cofferdam could be used to isolate the engine rooms for survivability purposes, instead of resorting to full compartment separation like that used with the ER variants described above.
The HS series of ND variants listed in Table 6 are aimed at studying how different hull strengthening options can improve the residual hull girder strength of the ship after damage. Strengthening may be achieved by increasing the scantlings at critical locations for longitudinal strength, such as the weather deck and the shear strake. Another way to improve residual strength is to insert longitudinally continuous box girders at strategic locations such as the corner of the weather deck and the shear strake or along the waterline. Box girders may also be used to replace or enhance existing primary structure such as the keel girder or the side stringers.
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6 Design loads
6.1 Local design loads
The NSR prescribe local design pressures for the hull envelope based on longitudinal and vertical position. Below the design waterline, the shell envelope pressure is , where is the hydrostatic pressure, and is an equivalent static pressure that accounts for hydrodynamic forces in waves. The NSR defines as the greater of the pressures ressulting from relative vertical motion between ship and wave, , and pitching motion, . The resulting distribution of varies piecewise linearly in the vertical direction , approaching the minimum design pressure for the weather deck, , at an elevation of , where is the keel elevation, is the design draft at the longitudinal position , and is the nominal wave limit height. The design pressure for the weather deck, , is determined following a similar procedure.
The local shell envelope design pressures amidships of the ND are shown in Figure 8, along with the hull offsets at that location. For this calculation, 0 and 7.5 m, i.e.,, the design draft at end of life (see Table 3). Using empirical formula provided in the NSRR, 12 kPa and 10.8 m. Since the weather deck height of 14.0 m is less than 18.3 m, over the entire side shell.
Figure 8: Local design pressures for the shell envelope amidships.
By way of comparison, Figure 8 also shows the local pressures prescribed by DND’s structural design standard DMEM 10 [8]. The DMEM 10 design pressure at an elevation, z, amidships is equivalent to a . hydrostatic head of 0.3 , but is never to be taken less than 50 kPa, i.e., a 5 m pressure head. The additional 0.3 . term is the contribution to the pressure head (for units in metres) due to pitching
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motion of the vessel. At longitudinal positions forward of amidships the head due to pitching motion increases linearly to 1.1 . at the forward perpendicular. These assumptions are similar to those used in the NSR to determine the pitching motion contribution, . The minimum 50 kPa pressure load in DMEM 10 allows for sea slap and dynamic interactions with the seaway other than slamming (green sea loads are also likely covered by the 50 kPa pressure, but that is not explicitly statedd in DMEM 10). The equivalent to the relative vertical motion prescribed by the NSR is not considered in DMEM 10. From Figure 8 it can be seen that the NSR design pressures are slightly greater than DMEM 10 requirements below the waterline, while the opposite is true above the waterline. Nonetheless, the two standards give maximum design pressures at the keel that agree within 2%.
The longitudinal distribution of the maximum design pressure, which occurs at the keel, is shown in Figure 9 for positions between the forward and aft quarter points. The NSR design preessure curve has a steep negative slope for 33.7 42 m, where the hydrodynamic wave pressure is governed by pitching motions. For 42 m, wave pressures associated with relative vertical motion govern, and the design pressure decreases more slowly towards the aft quarter point at 102.6 m. From amidships abaft, the rise in the keel elevation leads to smaller hydrostatic pressures and a corresponding decline in design pressure. The design curve derived from DMEM 10 rules follows a similar trend, and only diverges significantly from the NSR curve 42 70 m, where relative vertical motion, which is not considered by DMEM 10, has the greatest contribution to the NNSR design pressure.
Figure 9: Shell envelope design pressure at the keel between the forwward and aft quarter points.
Other local design loads include pressures on internal decks, bulkheads and tanks. The NSR design pressure for an internal deck is taken as the greater of: (1) a maximum static occupancy load based on the type of compartment (accommodation, workshop, stores, etc.); and (2) a lesser, but more typical occupancy load adjusted for inertial effects due to vertical accceleration.
Transverse and longitudinal watertight bulkheads are designed against hydrostatic pressure equivalent to flooding up to the watertight bulkhead deck, i.e., the weather deck. The NSR allow the designer to choose between that approach, which is based on the International Convention for the Safety Of Life At
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Sea (SOLAS), and a design philosophy based on the damaged stability draft and heel, i.e., V-lines. Tank structures are designed against two local load cases: (1) fuel oil pressures due to static head and inertial effects (sloshing is not considered); and (2) external pressure due to damage of the hull envelope and flooding of the adjacent spaces. 6.2 Global design loads
The still-water vertical bending moment distribution for each loading condition considered for the baseline configuration was determined using the GHS software.9 The ship’s displacement associated with each of those loading conditions is listed in Table 9, and the resulting distributions of vertical bending moment are shown in Figure 10. The still-water bending moments are greatest for the end of life arrival loading condition with ice accretion (ARIE). That loading condition is therefore used in determining the rule minimum (global strength) and extreme (ultimate strength) design bending moment curves for hogging. Still-water loads are the smallest for the deep departure conditions without ice loads (DDNB and DDNE), and these govern the minimum, or sagging, still-water bending moment envelope.
Table 9: Displacement of the baseline configuration under various loading cases.
Load Mission Environment Life-Cycle (t) Case DDNB Deep departure No icing Beginning of life 7673 DDIB Deep departure Ice accretion Beginning of life 8208 DDNE Deep departure No icing End of life 8787 DDIE Deep departure Ice accretion End of life 9095 OLNB Operational light No icing Beginning of life 6850 OLIB Operational light Ice accretion Beginning of life 7278 OLNE Operational light No icing End of life 7796 OLIE Operational light Ice accretion End of life 8550 ARNB Arrival No icing Beginning of life 6794 ARIB Arrival Ice accretion Beginning of life 7145 ARNE Arrival No icing End of life 7576 ARIE Arrival Ice accretion End of life 8449
9 The load cases in Table 9 and Figure 10 use the following naming convention for each loading condition: the first two letters refer to the variable loading state of the vessel (DD = deep departure, OL = operational light, and AR = arrival); the third letter refers to environmental condition (I = with icing loads, N = no icing loads); and the fourth letter is related to the life-cycle of the ship (B = beginning of life, E = end of life). For example, the DDIB curve in Figure 10 gives the deep departure, beginning of life loading condition, including loads due to ice accretion.
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Figure 10: Still-water vertical bending moment distribbutions for the baseline configuration.
As mentioned earlier, local design loads were based on the deep departuree, end of life loading condition with ice accretion (DDIE). The DDIE condition was chosen since it results in the largest displacement and deepest draft, and therefore produces the most pessimistic local loads. However, when global loads are considered, the DDIE condition (black triangles in Figure 10) results in a maximum still-wwater bending moment that is approximately 12% less than the worst-case ARIE loading (black squares).. That seems, at first, counter-intuitive since the displacement of the ship in the DDIE condition is approximately 8% greater than for ARIE load case (see Table 9). However, the apparent anomaly is explained by examining the mass distribution, rather than the total mass, for each loading condition.
Figure 11 shows the mass distribution for the DDIE and ARIE loading conditions, including masses that are distributed over the length and those that are applied at a single point, such as the helicopter and accreted ice. At arrival, the fuel oil tanks are assumed to hold only 10% of their capacity, compared to 95% at departure. That is reflected in Figure 11 by the smaller magnitudes of distributed mass in the ARIE condition in the area of the fuel tanks (40 60 m and 78 106 m) and lube oil tanks ( 64 m). On the other hand, black and grey water tanks that extend abaft 106 m are empty at departure and 90% full at arrival. Furthermore, seawater ballast needed to trim the ship in the ARIE load condition results in an abrupt increase in mass distribution at 20 m. Thus, the increase in hogging still-water bending moment from departure to arrival is the result of reducing mass amidships where buoyancy is greatest, and increasing mass near the longitudinal extremities of the hull.
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Figure 11: Distribution of mass for the baseline configuration at end of life with icing loads for the deep departure and arrival load conditions.
The design hogging and sagging still-water bending moment distributions are shown in Figure 12, along with the wave bending moment distributions prescribed by the NSR.10 The rule minimum and extreme bending moment distributions for the baseline configuration aarre shown in Figure 13.
10 See Section 4.4 on p. 13.
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Figure 12: Still-water and wave vertical bending moment distributions for the baseline configuration showing the worst-case loads in hogging and sagging.
Figure 13: Deesign vertical bending moment distributions for the baseline configuration.
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The still-water, wave, rule minimum and extreme verticall shear force distributions for the baseline configuration are shown in Figure 14. The still-water posittive and negative shear force curves were derived by taking the maximum and minimum shear forcess, respectively, for all loadding conditions at each longitudinal position. The rule minimum and extreme shear force distributions do not represent real-life load cases since the area under each curve does not sum to zero, and so static equilibrium is not achieved. Rather, the design shear force distributions are meant to represent the maximum positive and negative shear forces that may occur at a given longitudinal position over the ship’s life-cycle.
Figure 14: Vertical shear force distributions for the baseline configuration.
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7 Structural design
The structural design for the hull is described in the following, starting with the longitudinal structure in Section 7.1, and then the transverse structure in Section 7.2. The evolution of the longitudinal scantlings over the course the design procedure is described in Section 100. 7.1 Longitudinal structure
The longitudinal structural configuration and scantlings deterrmined for the baseline configuration using the loads of Section 6 are shown for the amidships section in Figure 15. All primary members (with the exception of plate girders beneath the inner bottom) are built-up T-sections, while secondary members are rolled tees.11
Figure 15: Miidships cross-section for the baseline configuration (F34.1); all dimensions in millimetres unless otherwise noted; corrosion margins are not shown.
11 Built-up sections (e.g., 1355×22W 255×21F) are denoted as W F. Rolled tees (e.g., 140x100x6x10 tee) are denoted as . All dimensions are in millimetres.
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The longitudinal structural configuration and scantlings at the forward quarter section are shown in Figure 16. The scantlings and stiffener dimensions in this figure were determined by extending the scantlings and stiffener dimensions forward of midships. Scantlings for the No. 4 deck, the inner bottom and deep girders were determined using the local design loads for decks and longitudinal bulkheads, with adjustments where required for global strength and buckling requirements. The deep girders below the inner bottom are vertical stiffened to prevent premature buckling under global loads. This design is referred to as the “original” design for the forward quarter section.
Figure 16: Cross-section at the forward quarter point in way of a stores compartment (F16.8).
Subsequent to the development of the scantlings in Figure 16, Pearson and Abbott [3] redesigned the forward end hull envelope taking into account the local pressure and impact loads on the external plating. Impact loads (i.e., slamming) were not considered in Section 6, since their contribution to the loading amidships is small. The local loading considered in the redessign was therefore more appropriate for the forward end structure. Global loading was not considered iin the redesign since it normally has little influence on the structural design forward of the forward quarter point or aft of the aft quarter point. The
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scantlings for the redesigned forward quarter section are shown in Figure 17. As the redesign only affected the external envelope, scantlings of the internal structure are the same as in Figure 16. This design is referred to as the “revised” design of the forward quarter sectioon. The redesign of the forward end is further discussed in Section 11.
Figure 17: Cross-section at the forward quarter point (FF16.8) showing scantlings from the revised forwarrd end design [3].
The longitudinal structural configuration and scantlings at the aft quarter section are shown in Figure 18. The scantlings and stiffener dimensions in this figure were determined by extending the scantlings and stiffener dimensions aft from midships. As in the forward quarter section (Figure 16), the scantlings for the No. 4 deck, tank structure and bottom girders were developed using the local loading requirements, and then adjusted as required for global loading and buckling considerations.
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Figure 18: Cross-section at the aft quarter point in way of double hull fuel tanks in the baseline configuration (F51.3) showing both efffeective and ineffective structure.
The amidships cross-section in Figure 15 is a structural arrangement typical of engine rooms: No. 4 deck and the inner bottom are removed to make room for the propulsion machinery; and horizontal stringers in the ERs maintain longitudinal structural continuity of those structures to other compartments. The bottom shell is stiffened by a centreline or keel girder, and inboard and outboard side girders, port and starboard. Deck girders provide vertical support beneath the longitudinal bulkheads above No. 3 deck. Similar girders are located port and starboard and at the centreline of decks in other compartments (see Figure 16 through Figure 18).
During the design for local loads it was found that the side stringers needded to be very deep (≈ 1 m) in order to meet LR’s criterion for bending stiffness (i.e., section modulus). The main factor leading to those large sections was determined to be the span length, normally equal to the compartment length less an allowance for end brackets. The effective length of the sttringers was reduced by introducing deep
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transverse web frames (see Figure 19) near the mid-length of the engine room compartments.12 This had the effect of relaxing the section modulus requirements, leading to correspondingly smaller stringer scantlings. The stringer scantlings in Figure 15 are reflective of the reduced dimensions enabled by the deep frames.
Deck girder scantlings were reduced in a similar manner to the side stringers. In this case, it was assumed that the effective length of the girders could be reduced through the placement of either deep deck beams or port and starboard pillars near the centre of the compartment. The deep beams / pillars themselves have not yet been designed to meet the Rules, and so have not been included in any of the analysis models. They will not affect ultimate strength calculations based on Smith’s method (Section 9) and are not expected to influence nonlinear finite element simulations to a great extent. Deep beams may interfere with equipment placement and passageways, but that may be at least partially mitigated by incorporating the beams into non-watertight subdivisions. In any case, it is likely that deep beams are preferable to pillars due to the risk of pillars puncturing the hull envelope unnder shock loading.
Figure 19: Geometric model of the baseline configuration of the ND, showing the starboard side structure in aft enginee room.
As shown by the cross section in Figure 15, the engine rooms differ from other parts of the ship in that No. 4 deck, inner bottom, and the central sections of Nos. 2 and 3 decks between the longitudinal bulkheads are all absent. The gaps in Nos. 2 and 3 decks are to accommodate the uptake and intake casings. Furthermore the longitudinal structure in No. 1 deck shown in Figure 15 will be discontinuous due to openings for the uptakes and intakes into and out of each engine room.
12 LR’s Naval Ship Rules allows for structural arrangements with deep transverse frames; see Reference [1], Volume 1, Part 3, Chaptere 2.
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The vertically stiffened longitudinal bulkheads between Nos. 1 and 3 decks, and beneath No. 4 deck in void spaces, were designed to be watertight. The scantlings for those bulkheads are based on regions of the transverse bulkheads with the same elevation (see Section 7.2 below). Figure 15 shows the scantlings for the port and starboard longitudinal bulkheads under No. 1 deck. Vertical stiffeners on the plate girders beneath the inner bottom in the stores compartment and tanks were designed in a similar way (see Figure 16 through Figure 18). 7.2 Transverse structure
The scantlings for all primary transverse members, including web frames, deck beams and plate floors, are listed in Table 10. The arrangement of some of the primary transverse members on Bulkhead 32, which separates the two engine rooms, can be seen in Figure 20. Web frames and beams on the weather deck (No. 1 deck) were designed to resist the combined action of hydrostatic and hydrodynamic pressure loads. Internal deck beams were designed to resist cargo, occupancy, or tank loads, as appropriate.
Table 10: Scantlings for primary transverse members.
Primary Member Location Typical Deep Scantling Scantling Transverse web Between Nos. 1 and 2 decks 191x7W N/A frame 40x9F Transverse web Between Nos. 2 and 3 decks 210x7W N/A frame 45x10F Transverse web Between Nos. 3 and 4 decks 230x7W 560x10W frame 50x10F 120x25F Transverse web Between No. 4 deck and inner bottom 273x7W 608x11W frame 60x12F 130x27F Transverse web Between inner bottom and keel 364x8W 651x11W frame 80x16F 140x29F Deck beam No. 1 deck 220x7W N/A 50x10F Deck beam Internal decks 225x8W N/A 120x15F Plate floora Engine rooms 1355x7W N/A 165x14F Plate floor Beneath inner bottom in stores compartments 10 mm web N/A and tanks a. Face plates of the built-up plate floors in the engine rooms are horizontal. Dimensions are listed for the deepest point of the built-up T-section at the centreline.
Each inter-deck region of the web frames was designed independently, assuming that rigid end support is provided by the decks (or stringers in way of decks). As a result, the built-up T-sections are heavier near the bottom shell where the loads are the greatest. Deep web frames are inserted in each engine room at the
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third frame location aft of the bulkhead, and extend from No. 3 deck to the plate floors (see Figure 19). They were designed based on the same loading as typical fraames, but the length of the frames was taken as the distance between No. 3 deck and the plate floors. That is because the deep frames are assumed to support the side stringers, as opposed to typical frama es, which are supported by the stringers (see Section 7.1). There are no deep web frames in the other compartments.
All main transverse bulkheads were designed to be watertight for flooding extending from the keel to No. 1 deck. Each intere -deck region of bulkhead, including the plating and vertical stiffeners, was designed independently. The bulkhead that separates the forward and aft engine rooms (at F32 in the baseline configuration) represents a special case, since all other transverse bulkheads are fully supported by the internal decks. Horizontal stringers are located on that bulkhead to compensate for the absence of deck support. Vertical girders are also introduced in order to shorten the effective lengths of the stringers, thus reducing their size. Scantlings for the bulkhead at F32 are shown in the drawing in Figure 20. The structural layout of other bulkheads is similar, but without the stringers at deck locations and with vertical girders replaced by typical vertical stiffeners.
Figure 20: Scantlings for the watertight traansverse bulkhead between the engine rooms in the baseline configuration (F32).
The stiffening arrangement shown in Figure 20 is highly simpliified, in that stiffeners are purely horizontally and vertically aligned. Vertical stiffeners are spaced so as to intersect with ddeck stiffeners. But as drawn in Figure 20, they will not connect up with the hull longitudinals, thereby creating weak connections between the bulkheads and hull. This shortcoming is corrected in the developmment of the geometric model in Section 11.
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8 Global strength
The global strength of the ND baseline configuration was verified in two ways. Fulfillment of the normal Rules requirements for global strength was confirmed using elastic stress analysis of two-dimensional design cross-sections. ULTMAT was used to calculate the relevant cross-section properties, such as the moment of inertia and neutral axis location, and applied stresses were determined based on elastic beam theory and the rule minimum vertical bending moments shown in Figure 13 (p. 28). The results of those analyses are discussed in this section.
A more realistic prediction of the applied stresses was achieved using a three-dimensional Finite Element (FE) model and linear elastic analysis under local and global loads. Those analyses were intended to satisfy LR’s requirements for the Structural Design Assessment (SDA) notation. The methodology and results of the SDA will be described in a separate report. 8.1 Section properties
Table 11 summarizes the section properties calculated with ULTMAT for four cross sections shown in Figure 15 through Figure 18.
Table 11: Section properties of the design cross-sections.a
Location Neutral Axisb Section Area Section Modulus (m3) Moment of Inertia (m4) (m) (m2) Horiz. Vert. Horiz. Vert. Fwd quarterc 8.205 1.067 2.847 3.490 22.937 28.637 Fwd quarterd 7.553 0.975 2.486 3.116 20.026 23.708 Amidships 6.992 0.884 3.693 3.396 34.445 23.963 Aft quarter 8.284 1.047 3.372 3.024 27.891 19.995 a. All cross-section properties are calculated neglecting longitudinally ineffective structure. b. Vertical position of the neutral axis with respect to the baseline. c. Forward quarter section data are based on the original design scantlings and dimensions in Figure 16. d. Forward quarter section data are based on the revised design scantlings and dimensions in Figure 17.
8.2 Stress criteria
The NSR prescribe the maximum permissible normal stress in longitudinally effective structure, , as
(1)
where is the yield stress of the material, is a factor accounting for the longitudinal position being considered, and is a knock-down factor on the yield stress for high-strength steel. The maximum permissible shear stress, p, is defined in an analogous way. 0.750 for longitudinal positions
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falling approximately within the quarter points, and 0.919 for HSS with 355 MPa, giving a maximum allowable normal stress equal to approximately 69% of the yield stress. The maximum permissible stresses for the ND structure between the quarter points are 245 MPa and 141 MPa.
A summary of the maximum normal stresses in the hull girder at the design locations is given in Table 12. Those data show that, in all cases, the design stresses are less than 50% of the yield stress for HSS, and are considerably less than the stress level of 245 MPa allowed by the Rules. That does not indicate over-design, however, since the scantlings are governed by local, global and ultimate strength criteria. Two sets of results are provided for the forward quarter section in Table 12, one based on the scantlings in Figure 16, and the other based on the revised forward quarter design shown in Figure 17. For convenience, rule bending moments for both forward quarter sections are assumed to be the same, although in reality slight differences would result from the different structural weights in the two designs.
The highest normal stresses tend to occur in the hogging condition, since the applied bending moments are greatest for that loading scenario. The detailed design of reinforced penetrations, stiffener end brackets, and other connections has not been carried out. Nonetheless, the relatively small hull girder stresses suggest that the ND will have good fatigue performance provided connections are well designed and proper weld procedures developed.
Table 12: Maximum hull girder normal stresses for the baseline configuration resulting from the minimum rule vertical bending moment.
Location Rule Vertical Bending Maximum Normal Maximum Normal Momenta (MN-m) Stress (MPa) under Stress (MPa) under Hoggingb Saggingc Hog Sag Tens. Comp. Tens. Comp. Fwd quarterd 374.7 -290.6 90.8 -106.5 82.6 -70.4 Fwd quartere 374.7 -290.6 120.3 -119.4 92.6 -93.3 Amidships 563.1 -390.1 165.4 -163.3 113.1 -114.5 AFT quarter 309.2 -297.7 88.2 -101.4 97.7 -84.9 a. Minimum rule vertical bending moment. b. Maximum hogging stresses in tension and compression occur at the weather deck and the keel, respectively. c. Maximum sagging stresses in tension and compression occur at the keel and the weather deck, respectively. d. Calculations for the forward quarter section are based on the original design scantlings in Figure 16. e. Calculations for the forward quarter section are based on the revised design scantlings in Figure 17.
A summary of the maximum shear stresses in the hull girder at the design locations is given in Table 13. The shear stresses were calculated using shear flow analysis with DRDC’s EBMS program [17]. The results in Table 13 indicate that the design shear stresses do not exceed 51% of the maximum allowable shear stress. In all three cross sections the maximum shear stresses occur in the side shell plating in Strake “D,” between the levels of No. 3 and No. 4 decks.
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Table 13: Maximum hull girder shear stresses for the baseline configuration resulting from the minimum rule vertical shear force.
Location Positive Shear Force Negative Shear Force VSFa (kN) Max Shear Stress VSFa (kN) Max Shear Stress (MPa) (MPa) Fwd quarterb 8642 46.3 -12807 68.6 Fwd quarterc 8642 41.2 -12807 61.1 Amidships 9717 53.5 -4507 24.8 Aft quarter 11360 71.5 -8424 53.0 a. Minimum rule vertical shear force. b. Calculations for the forward quarter section are based on the original design scantlings in Figure 16. c. Calculations for the forward quarter section are based on the revised design scantlings in Figure 17. 8.3 Buckling criteria
Global strength assessment following the NSR requires verification that the applied stresses are not great enough to cause premature buckling of the longitudinal structure between transverse frames and bulkheads. Maximum allowable or critical buckling stresses are prescribed for a variety of failure modes including local buckling of the shell or deck plating, overall buckling of stiffened panels, and local buckling of the secondary stiffeners themselves. The critical buckling stresses prescribed by the NSR are summarized in Table 14.
For each failure mode, the elastic buckling stress, , is first calculated according to classical formulas [1]. The effects of material plasticity are then accounted for using a Johnson-Ostenfeld correction factor for stresses greater than one-half of the yield stress. The critical buckling stress for each failure mode, , is given by
for , and (2) 1 for .
The strength-reducing interaction of elastic buckling and plastic collapse predicted by the Johnson-Ostenfeld relationship is shown in Figure 21. Critical buckling stresses derived in this way are compared to applied compressive stresses resulting from the rule minimum shear force and vertical wave bending moments for hogging and sagging.
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Table 14: Definitions of NSR buckling stresses.
Stress Description
critical buckling stress of a plate panel under uni-axial compression
critical buckling stress of a plate panel under pure shear
critical overall buckling stress of a stiffened panel under uni-axial comppression
critical torsional buckling stress for a secondary stiffener under uni-axial compression
critical web buckling stress for a secondary stiffener under uni-axial compression
critical flange buckling stress for a secondary stiffener undeer uni-axial compression
Figure 21: Johnson-Ostenfeld relationship for the critical buckling stress.
The amidships scantlings shown in Figure 15 (p. 30) meet all NSR buckling requirements with only a few exceptions. A few areas in the forward and aft quarter point cross-sections were found to exceed the buckling stress limits in the NSR. For example, the extreme outboard bay of plating on No. 2 deck in the forward section (see Figure 16 on p. 31) did not meet plate buckling requirements because its breadth was greater than a typical bay. This problem and others like it can be corrected when the arrangement of the deck longitudinals is worked out in detail.
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In addition to the absolute buckling stress criteria, the NSR require that the overall buckling strength of a longitudinally stiffened panel exceeds the torsional buckling strength of the stiffener (i.e., ). Likewise, the stiffener web and flange buckling stresses must also exceed the torsional buckling stress of the stiffener (i.e., and ). The final amidships scantlings shown in Figure 15 meet all absolute and relative buckling criteria with just a few exceptions. These are mainly in the shear strake in the forward and aft quarter sections, where the requirement could not be met without significantly increasing the stiffener depth in the final design. Nonetheless, does not exceed by more than 0.25% in any of the exceptional cases. This was considered sufficient to meet the Rules requirements within a small margin of error.13
It is impractical to present the critical buckling stresses for all locations on the design cross-sections because of the large number of individual stiffener and plate panels. Instead, by way of example, the critical stresses are presented for each deck and strake location on the amidships cross-section in Table 15. It can be seen that local buckling of the plating tends to be the most critical failure mode. Overall buckling of the stiffened panel and local buckling of the stiffeners are less critical due to the relatively heavy secondary stiffeners that are required to meet ultimate strength criteria.
The maximum compressive stresses arising in each deck and strake are listed in Table 16. Also listed are the minimum safety factors for each mode of failure considered. Those values are based on evaluation of buckling criteria and applied stresses on a panel by panel basis, so the safety factors are not the same as those produced by directly comparing the worst-case deck and strake stresses in Table 15 and Table 16. The overall safety margin on global strength, considering all amidships structure, is 1.23 after the scantlings were increased to meet ultimate strength requirements. That value represents the additional margin of safety over and above those safety factors that are built into the NSR formulation for design loading and allowable stresses.
13 The current discussion refers to the global strength analysis of the design, including scantling enhancements that were made to improve ultimate strength. In some cases, the relative buckling criteria were not met by the intermediate global strength design discussed in Section 10, either; however, the non-compliant stresses were all within 1% of the benchmark torsional buckling stress.
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Table 15: Critical buckling stress criteria at selected locations on the amidships cross-section of the ND.
Locationa Critical Buckling Stress Criteria(MPa) for Indicated Failure Modeb
Weather Deck 189.6 156.6 303.8 298.3 305.6 319.1 No. 2 Deck 85.1 125.7 257.1 229.8 277.3 321.3 No. 3 Deck 38.1 73.0 271.1 255.7 290.0 321.4 “A” Strake 205.6 158.9 291.6 288.9 299.2 320.3 “B” Strake 204.6 158.8 291.6 289.6 299.2 320.3 “C” Strake 82.7 125.4 292.9 286.8 294.2 320.7 “D” Strake 53.2 98.3 291.3 282.8 296.2 320.5 “E” Strake 79.7 123.5 289.6 279.3 293.7 320.5 “F” Strake 170.5 154.2 302.0 299.3 305.6 319.1 a. Deck and strake numbering are shown in Figure 15 on p. 30. b. Buckling failure modes are described in Table 14.
Table 16: Applied stresses and safety factors on buckling failure for selected locations on the amidships cross-section of the ND.
a b Location (MPa) Minimum Safety Factor, / , for Indicated Failure Mode
Weather Deck -114.5 1.66 2.65 2.61 2.67 2.79 No. 2 Deck -69.22 1.23 3.71 3.32 4.01 4.64 No. 3 Deck -24.42 1.56 11.1 10.5 11.9 13.2 “A” Strake -163.3 1.28 1.79 1.77 1.83 1.96 “B” Strake -145.9 1.40 2.00 1.98 2.05 2.20 “C” Strake -85.96 1.80 3.41 3.34 3.42 3.73 “D” Strake -17.6 3.02 16.6 16.1 16.8 18.2 “E” Strake -61.22 1.30 4.73 4.56 4.80 5.24 “F” Strake -105.9 1.61 2.85 2.83 2.89 3.01 a. Deck and strake numbering are shown in Figure 15 on p. 30. b. Maximum compressive normal stress in the indicated deck or strake under hogging or sagging loads, as appropriate.
The maximum shear stresses arising in each deck and strake in the forward and aft quarter sections are listed in Table 17 for comparison against the shear buckling criteria in Table 15. Also listed are the
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minimum safety factors corresponding to each location. Results were determined for the forward and aft quarter sections due to the higher shear stresses at those sections compared to amidships. The scantlings in Figure 16 are used for the forward quarter section. The overall safety margin for shear buckling is 1.37, which occurs in Strake “D,” and which is slightly larger than that obtained for compressive buckling in the amidships section. Thus the overall safety margin on global strength for the design is 1.23.
Table 17: Applied shear stresses and minimum safety factors for shear buckling failure at selected locations in the forward and aft quarter cross-section of the ND.
Locationa Fwd Quarterb Aft Quarter
c c (MPa) / (MPa) / Weather Deck 26.4 5.93 28.1 5.57 No. 2 Deck 11.7 10.74 15.4 8.16 No. 3 Deck 2.1 34.76 2.1 34.76 “A” Strake 23.2 6.85 19.7 8.07 “B” Strake 34.1 4.66 46.0 3.45 “C” Strake 53.5 2.34 53.3 2.35 “D” Strake 68.6 1.43 71.5 1.37 “E” Strake 58.6 2.11 61.2 2.02 “F” Strake 33.4 4.62 32.6 4.73 a. Deck and strake numbering are shown in Figure 15 on p. 30. b. Calculations at the forward quarter section are based on the original design scantlings in Figure 16. c. Maximum shear stress in the indicated deck or strake under the rule minimum positive or negative vertical shear force.
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9 Ultimate strength
The NSR requires for the ESA2 notation that the extreme hull girder strength of the hull be determined at “all critical cross sections,” and be “assessed using elasto-plastic ultimate strength methods … based on nonlinear stress strain curves which include the stress strain relationship in the post buckling phase.” The requirements to be met for extreme bending moment and shear force are as follows:
| | | | (3)
| | | | (4) where and are the extreme rule design bending moment and vertical shear forces, shown in Figure 13 and Figure 14, respectively; and are the ultimate bending moment and vertical shear capacities of the hull structure; and 0.9 is a safety coefficient to account for uncertainties in the assessment methods. Little detail is provided in the NSR on the methods to be followed in evaluating and .
The International Association of Classification Societies’ Common Structural Rules (CSR) for Bulk Carriers and Oil Tankers [18] provide considerable detail on the calculation method for for large vessels. The method described closely follows Smith’s method for progressive collapse of hull girders [12]. By assuming beam-like behaviour of a cross section under pure vertical bending in hog and sag (i.e., plane sections remain plane) the longitudinal strain at each position in the cross section can be determined for a given cross section curvature. Curvature is progressively incremented, and the overall resistance to bending is evaluated for each value of curvature. The peak value of bending moment obtained in this way is the ultimate strength of the cross section. The results of this calculation are normally output as a plot of bending moment versus curvature.
To perform each step of the calculation, the cross section is subdivided into small structural elements that are assumed to act independently of each other when the cross section is subject to pure bending. The majority of structural elements are single longitudinal stiffeners with an attached width of plating. The load vs. longitudinal deformation relationship of each element is used to assess its resistance at a given value of longitudinal strain. This is particularly important for structure in compression, where the load-shortening response will include elasto-plastic buckling between transverse frames, which itself depends on initial imperfections in the structure. Accurately assessing the load-shortening response of stiffened panels, including the post-buckling response, is critical to the ultimate strength calculation.
In the CSR, the load shortening behaviour for interframe collapse is determined using analytical formulas. DRDC’s ULTMAT program [11] is based very closely on the method in the CSR and uses the same analytical formulas for the load-shortening behaviour of longitudinal structure. In addition, ULTMAT can determine load-shortening behaviour by interpolating from a database of pre-calculated load-shortening curves [19]. The database was generated from finite element models of stiffened panels of varying plate and column slenderness, stiffener type and imperfection level.
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9.1 Ultimate bending moment results
The ultimate bending strengths presented here were calculated with ULTMAT, using the load-shortening curve database associated with tee-stiffened panels with an average level of plate and stiffener imperfections. Cross section models similar to those shown in Figure 15 to Figure 18 were developed using the ultimate strength module of the STRUC software [20] for analysis with ULTMAT. Cross section structure that does not fully participate in longitudinall bending is assigned a reduced effectiveness value for the analysis. The treatment of completely or partially ineffective longitudinal structure is described in Section 4.5, starting on p. 14.
The ULTMAT cross section model for the amidships cross section is shown in Figure 22. This shows the three types of structural elements used by ULTMAT, of which the most important is the longitudinal stiffened panel. The structure displayed with broken lines is considered completely ineffective. This includes the central span of No. 1 deck, which is ineffective due to the large openings into the engine rooms, and the longitudinal bulkheads extending between Nos. 1 and 3 deck.
Figure 22: Midships cross section model for ultimate strength analysis.
The ULTMAT cross section model for the forward quarter cross section is shown in Figure 22, showing the range of effectiveness values employed in the model. No. 1 deck is fully effective at this location, while the longitudinal bulkheads extending between Nos. 1 and 3 deck and much of the inner bottom structure are considered fully ineffective. No. 4 deck has an effectiveness oof 0.8 due to the termination of this deck at the boundary of the forward engine room (F25).
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Figure 23: Forward quarter cross section model for ultimate strength analysis, indicating effectiveness of structural elements.
The calculated ultimate strengths and extreme vertical bending moments are listed in Table 18 at the forward quarter point, amidships and the aft quarter point. Ultimate sttrength calculations were also performed at 10 m increments along the middle two-thirds off the ship, in order to ensure that the baseline configuration meets the ESA2 requirements for vertical bending. The calculated ultimate strength values are plotted with the extreme vertical bending moment envvelopes in Figure 24. Twwo sets of strrength calculations are provided forward of F18, one using the design scantlings in Figure 16 and the other using the revised design scantlings in Figure 17. The ultimate strength values listed in Table 18, and shown in Figure 24, have the factor applied to them to allow direct comparison with .
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Table 18: Ultimate strength of the baseline configuration under vertical bending.
Location Hogging Bending Moments Sagging Bendiing Moments (MN-m) (MN-m) a a Fwd quarterb 486.2 1002.33 -475.3 -920.4 Fwd quarterc 486.2 950.6 -475.3 -559.2 Amidships 721.9 1008.1 -653.0 -703.8 Aft quartere 409.0 850.9 -462.9 -755.8 a. Extreme rule bending moment from [1], see Figure 13. b. Calculations for the forward quarter section are based on the original design scantlings in Figure 16. c. Calculations for the forward quarter section are based on the revised design scanntlings in Figure 17.
Figure 24: Comparison of the extreme design vertical bending momeent (VBM) envelope for the baseline configuration and the ultimate strength at selected longitudinal positions.
The ND hull is strongest in hogging forward of amidships, in tthe forward engine room between 50 m (F25) and 60 m (F30). In sagging, the ultimate strength is greatest at the forward quarter point at F16.8 in the stores compartment. Because extreme hogging and sagging bending moments are of similar magnitudes and because the weather deck scantlings are relatively light compared to the deep girders on
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the bottom shell, sagging governs the ultimate strength of the hull at all considered positions. The sagging strength is lowest in the engine rooms, due to the presence of the uptake/intake penettrations, and in the adjacent compartments that are affected by the shadow zones of those openings.
The critical location is the compartment with fuel tanks just aft of the aft engine room, where the magnitude of the applied sagging bending moment is the greatest. The safety margin on ultimate strength at that critical location (F39.5), over and above the safety factoors prescribed by the NSR, is approximately 0.7%. That the ND just meets the NSR requirements for ultimate strengtth is desirable as a pessimistic design case for future damage and residual strength investigations. The critical section for hogging is at the same cross-section; however, the additional safety margiin beyond the Rules safety factors is much greater for hogging, at 18%.
Moment-curvature relationships characterizing the vertical bending response of the hull girder at the three design locations are plotted in Figure 25. The slopes of the linear-elastic portion of the curves are in proportion with the cross-section vertical moments of inertia listed in Table 11.
Figure 25: Moment-curvature relationships for vertical bending of the hull girder at selected cross-sections of the baseline configuration.
The onset of significant nonlinearity, as indicated by a drop in the slope of the moment-curvature relationship to 90% of its initial value, first occurs in hoggging in the aft quarter section, at a bending moment of 636 MNm, followed by the forward quarter of thhe revised design, the forward quarter, and amidships sections. That is as expected considering the relative magnitudes of the vertical section moduli (see Table 11), which are associated with first yielding occurring at the keel. In sagging, onset of
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nonlinearity first occurs in the forward quarter of the revised design, at −220 MNm, followed by the amidships, aft quarter and forward quarter sections. The relative weakness in sagging amidships is due to the loss of structural effectiveness in the weather deck material in way of the uptake openings. The considerable difference in the sagging strength between the original and revised forward quarter section designs is due to the much lighter scantlings in the weather deck and the shear strake in the revised design. This is discussed further in Section 11.
The bending moment interaction curves in Figure 26 show the same trends in ultimate strength under vertical bending. Table 11 shows that the horizontal section modulus is greatest amidships due to the breadth of the hull and the presence of the side stringers in the engine rooms. Despiite that, the hull is strongest under pure horizontal bending at the aft quarter point, followed by the amidships cross-section and then the forward quarter point. The greater strength of the aft quarter point cross-section is likely due to the additional deck material between the longitudinal bulkheads, which is not present amidshipps and may contribute significantly to horizontal ultimate strength after the outboard deck strakes have collapsed. On the other hand, the maximum horizontal ultimate strength is achieved amidships, under a combined hogging and horizontal bending moment. Not surprisingly, the weakest design point for horizontal ultimate strength is the forward quarter point wherre the hull is relatively narrow, and therefore has a smaller section modulus (Table 11).
Figure 26: Bending moment interaction curves at selected cross-sections of the baseline configuration.
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9.2 Extreme shear strength assessment
As was noted earlier, the ultimate strength in shear cannot at present be evaluated as required for the ESA2 assessment. Instead, the ESA1 methodology of the NSR can be used to evaluate the extreme strength in shear based on elastic methods. The ESA1 methodology is in fact identical to that used in the global strength calculation for shear in Section 8.2, except that extreme positive and negative shear forces are applied to the cross sections and the limiting shear stress is increased to 0.9 185 MPa. The results of the ESA1 assessment for the three design cross sections determined using shear flow analysis are summarized in Table 19. The minimum factor of safety from these results is 2.06, which is for the extreme positive shear force applied to the aft quarter section. This compares with the minimum factor of safety in shear of 1.98, which was determined in the global strength calculation in Section 8.2. Thus, it can be concluded with some assurance that hull girder shear strength is not a limiting factor with this design.
Table 19: Maximum shear stresses for the baseline configuration resulting from extreme vertical shear forces.
Location Positive Shear Force Negative Shear Force VSFa (kN) Max Shear Stress VSFa (kN) Max Shear Stress (MPa) (MPa) FWD quarterb 13858.36 74.2 -15956.6 85.4 FWD quarterc 13858.36 66.1 -15956.6 76.1 Amidships 13296.03 73.2 -6904.07 38.0 AFT quarter 14253.85 89.7 -13216.3 83.1 a. Extreme vertical shear force. b. Calculations for the forward quarter section are based on the original design scantlings in Figure 16. c. Calculations for the forward quarter section are based on the revised design scantlings in Figure 17.
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10 Design evolution
In this section, the evolution of the ND scantlings is examined by comparing the structural dimensions required to meet the NSR at key points in the design procedure. By way of example, the evolution of the amidships scantlings throughout the design procedure is shown in Figure 27. The dimensions of the initial scantlings, which were designed to resist local loads only, are shown in normal font. The dimensions of scantlings that were increased to meet global and ultimate strength requirements are shown in italics and bold face font, respectively. For example, the weather deck plating was initially sized at 7 mm for local design considerations. The plate thickness was increased by 2 mm in order to meeet global strength requirements and then increased by an additional 1 mm when ultimate strength was considered. The final design scantlings for a particular structural item are those associateed with the last design stage necessitating modifications.14
Figure 27: Amidships cross-section showing thhe scantlings after designing for local loads, global strength and ultimate strength.
14 The final scantlings are also shown in Figure 15 on p. 30.
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Figure 27 shows that the initial hull envelope scantlings decrease with elevation. This is because the local design pressures are greatest near the keel and smallest at the weather deck.15 As a result, most of the scantling modifications required to meet global and ultimate strength were made to the side shell and weather deck, since the bottom shell scantlings were already quite heavy. The structural items located near the neutral axis for vertical bending were least affected in the design for global and ultimate strength (e.g., the scantlings for Strakes “C” and “D”) due to small global bending stress magnitudes. The primary longitudinal members, which were quite large to begin with, were also mostly unaffected by non-local design considerations.
Structural scantlings at the extreme vertical locations had to be increased to meet global and/or ultimate strength requirements. For example, global strength requirements related to buckling led to increased scantlings for the bottom shell (“B” Strake), No. 2 deck, and the webs of the centreline and inboard girders. The weather deck and upper side shell scantlings (Strakes “E” and “F”) had to be increased, first to meet global strength criteria, and then again when ultimate strength was considered. Those areas were subject to the largest increases in scantlings.
The section properties of a typical weather deck panel at various stages of design give an indication of how much the extreme vertical scantlings were increased to meet global and ultimate strength criteria. A deck panel consists of a single bay of plating and one longitudinal stiffener. After design for local loads, the cross-sectional area and section modulus of a typical panel were 44 cm2 and 16.4 cm3, respectively. The scantlings were increased to meet buckling requirements for global strength, leading to an area of 56 cm2 and section modulus of 28.4 cm3. The scantlings were then increased again for ultimate strength giving a final cross-sectional area of 75 cm2 and section modulus of 164 cm3. In other words, the area of a typical weather deck panel designed against local loads is approximately 60% of the area needed to resist the extreme design bending moment. The section modulus of the final deck panel is an order of magnitude greater than for the initial scantlings; however, that is an indirect outcome of the design for ultimate strength. That is because the section modulus of a panel is primarily a concern when considering interframe bending due to local loads, so that the large section modulus for the final design is mainly a by-product of the need for greater cross-sectional area for ultimate strength.
The properties of the amidships cross-section at each design stage are summarized in Table 20. It can be seen that the section area and the elevation of the vertical neutral axis increase with each stage of the design as material is added to the upper portions of the hull structure. Likewise, the section modulus and moment of inertia are seen to increase as the design matures. The vertical section modulus of the final design is over 50% greater than for the initial cross-section designed against local loads only. The trade-off for that increase in ultimate bending strength is a 25% increase in the amidships structural mass per unit length (5.54 tonnes/m after initial design versus 6.94 tonnes/m for the final design). On the other hand, compared to the intermediate global strength design, which meets only the bare minimum Rules requirements, an increase in unit mass of only approximately 6% was needed to satisfy the ESA2 notation (6.56 tonnes/m after the intermediate design versus 6.94 tonnes/m for the final design).
15 See Figure 8 on p. 23.
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Table 20: Section properties amidships at various stages of the structural design.a
Design Stage Neutral Axisb Section Area Section Modulus (m3) Moment of Inertia (m) (m2) (m4) Horiz. Vert. Horiz. Vert. Local Loads 6.266 0.706 2.799 2.233 26.102 17.375 Global Strength 6.631 0.836 3.431 2.925 32.005 21.695 Ultimate Strength 6.992 0.884 3.693 3.396 34.445 23.963 a. All properties are based on calculations whereby longitudinally ineffective structure has been ignored. b. Vertical position of the neutral axis with respect to the baseline.
The net weight penalty for designing to an ultimate strength criterion is even less when the entire structural mass is considered, since scantlings for transverse structure are governed by local loading considerations. For the ND, an additional 68 tonnes of steel is required in order to meet the ESA2 notation, over and above the 1488 tonnes of structural mass associated with meeting the standard NSR requirements for global strength. Thus, the net weight penalty associated with the ESA2 notation is approximately 4.5%. That estimate does not account for the weight of the superstructure, which would not be affected by scantling enhancements for ultimate strength. That would decrease the percentage weight penalty to 4%, assuming the relative weight of the superstructure compared to the total steel weight is similar to past warship designs.16
Because the initial and intermediate scantlings were enhanced to meet other design requirements later on, the safety margins against local loads and global strength are increased. For example, consider the global strength results presented in Table 16 (p. 42). The smallest safety margins on the critical plate buckling failure mode are associated with structures that were not enhanced significantly for ultimate strength requirements, such as No. 2 deck, “E” strake on the side shell, and the keel plate at “A” strake (see Figure 27). The safety factors in those areas were only slightly greater than unity for the intermediate global strength design; the safety factors increased as more material was added for ultimate strength considerations, thereby reducing the stress levels. The plate buckling safety factors are larger for structure that was enhanced for ultimate strength, like the weather deck and shear strake (“F” strake). Safety factors are even higher for “C” and “D” strake on the side shell near the neutral axis, where local loading was the driving factor in the scantling design. The large safety factors on buckling failure generally resulted from increases in scantlings that are required to meet global and ultimate strength requirements.
The ultimate strengths of the amidships cross-section of the ND at various stages of design are listed in Table 21. Even the lightest scantlings designed solely for local loads are sufficient to meet extreme strength requirements under a hogging bending moment. That is because the design of the bottom shell girders and side stringers, which contribute greatly to the hogging ultimate strength, is generally governed by local hydrostatic and hydrodynamic pressures on the hull envelope. Minimum scantling requirements prescribed by the NSR, such as the minimum depth of the keel girder, are also applied at the local design stage and govern the sizing of the primary members in some cases.
16 The superstructure was assumed to account for approximately 13% of the total steel weight of the ND.
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Table 21: Ultimate strength of the amidships section of the baseline configuration under vertical bending at various stages of design.
Design Stage Hogging Bending Moments Sagging Bending Moments (MN-m) (MN-m) Extremea Ultimate Extremea Ultimate Strengthb Strengthb Local Loads 783.7 -293.0 Global Strength 721.9 947.8 -653.0 -446.3 Ultimate Strength 1008.1 -703.8 a. Extreme rule bending moment [1]. b. Ultimate strength values are the ULTMAT predictions multiplied by the NSR’s safety factor of 0.9.
The extreme bending moment for sagging, on the other hand, is not met by the initial or intermediate design scantlings. The sagging ultimate strength after design for local loads and global strength is only approximately 45% and 68%, respectively, of the minimum required strength for the ESA2 notation. Significant scantling enhancements to the global strength design, especially in the weather deck and shear strake (see Figure 27), were required in order to meet extreme strength requirements.
Moment-curvature relationships associated with the ultimate strength analyses for the incremental amidships designs are shown in Figure 28. The hogging responses are qualitatively similar for all design models, characterized by linear-elastic behaviour for most of the loading regime followed by a relatively sudden onset of nonlinearity and collapse. The differences between the responses are related to lower stiffness in the hull girder at the earlier stages of design due to lighter scantlings in the weather deck and shear strake. That leads to higher compressive stresses in the critical areas at the bottom shell and earlier onset of collapse.
On the other hand, the sagging response of the hull girder exhibits different characteristics depending on the stage of design. The local design scantlings lead to a local limit point in the moment-curvature relationship early on in the loading at a sagging bending moment of approximately 260 MN-m. That is likely caused by collapse of the weather deck and shear strake panels, which have relatively light scantlings after local design. However, the nature of designing for local loads leads to increasingly greater scantlings from top to bottom. Thus, after collapse of the upper portions of the hull girder, even greater compressive loads can be carried by the intact side shell and Nos. 2 and 3 decks. The ultimate sagging strength of the local design is approximately 25% greater than the bending moment associated with initial collapse of the weather deck and shear strake. The behaviour of the final design, whereby the scantlings at the extreme vertical positions are relatively balanced, is characterized by the typical initial linear response followed abruptly by ultimate collapse. The response of the intermediate global strength design exhibits characteristics of both the initial local design and the final design.
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Figure 28: Moment-curvature relationships for vertical bending of the hull girder amidships at various stages of design.
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11 Geometric model and design modifications
Using the dimensions and scantlings determined for the ND in Sections 7 through 9, an initial geometric model of the baseline configuration was created using the PW7600 and the Trident Modeller software. As was noted earlier, the geometric model of the hull was used to create the cross section models that were used in the global strength and ultimate strength analysis described in Seections 8 and 9. In addition, the geometric model allows the generation of other types of advanced analysis models. These include linear and nonlinear finite element analysis of the structural performance, e.g., Extreme Strength Assessment, Level 3 (ESA3) and Residual Strength Assessment (RSA) [1], Structural Design Assessment [16], Fatigue Design Assessment – Level 3 [21], and sea-ice interaction studies [22], [23]). Other assessments that could be conducted using models derived from a geometric model include performance under weapons loads (underwater shock and whipping responsse, external and internal air blast).
Several modifications to this initial model were subsequentlyy made within Trident Modeller to create the model shown in Figure 29. The steps taken in creating this model are listed below:
Figure 29: Trident Modeller model of the baseline configuration of the ND; showing the starboard side of the huull.
1. The hull structure was created in Trident Modeller using the scantlings and dimensions of primary and secondary members, as described in the present work;
2. Lloyd’s ATG replaced the dimensions and scantlings in the model forward of F18 using the results of its forward end design study [3];
3. Openings in No. 1 deck in way of the engine rooms were iintroduced for the intakes and uptakes;
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4. The arrangement of secondary stiffeners were modified to ensure that bulkhead, deck and hull stiffeners are properly connected and terminated, with particular attention to the connections between the transverse bulkheads and the hull; and
5. Longitudinal girders in the aft end were reduced in size to reduce weight while still meeting the stiffness and strength requirements of the NSR. 11.1 Forward end design
The revised design of the forward end structure is shown in Figure 30. Pearson and Abbott [3] provide additional details on the frame and stiffener dimensions. This design was based on the stiffness and strength requirements in the NSR for local loading including impact loads: i.e., global strength was not considered forward of F18. This results in an abrupt transitioon in some of the hull envelope scantlings at F18. For example, in No. 1 deck and in the shear strake, the plate thickness drops from 11 mm, just aft of F18, to 7.5 mm just forward of it. There is a similar abrupt transition in the size of the No. 1 deck longitudinals at F18 (Table 22). This can also be seen by comparing the scantlings at the forward quarter sections in Figure 16 and Figure 17.
Figure 30: Reevised forward end design: hull plate thicknesses in mm (top); internal structural arrangement (botttom).
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Table 22: Dimensions of longitudinal stiffeners in the revised design [3].
Location Aft of F18 Forward of F18 No. 1 deck 140x100x6x10 Tee 80x30x5x10 Tee Shear strake 140x100x6x10 Tee 120x60x4x8 Tee Strake E 120x55x5x7 Tee 120x60x4x8 Tee Strake D 115x55x4x7 Tee 120x80x5x10 Tee Strake C 120x60x4x8 Tee 130x60x7x12 Tee Strake B 135x65x5x8 Tee 140x70x6x9 Tee Strake A 135x65x5x8 Tee 140x70x6x9 Tee
The 11 mm plate thickness and larger deck longitudinals arise from the global bending moment requirements at midships. However, calculations in Sections 8 and 9 showed that the revised design of the forward end with 7.5 mm plate thickness and smaller longitudinals satisfies both the global (rule) and ultimate strength requirements. The 11 mm thickness aft of F18 is therefore larger than necessary to meet global strength requirements.
However, the design for the F11-F18 compartment is still incomplete in that the general arrangements show that the VLS will be placed here. Additional design work is therefore needed to create a perimeter casing structure and reinforcements needed to support this system. Furthermore, because of the large openings that will need to be inserted in Nos. 1, 2 and 3 decks, the remaining structure in this compartment will have to be checked to ensure that global, local strength requirements in the NSR are still met. 11.2 Deck 1 openings
As was noted in Section 7.1, No. 1 deck is discontinuous in way of the engine rooms to accommodate the intakes and uptakes into the engine rooms. These are represented in the geometric model as shown in Figure 31, where separate openings for uptakes and intakes are inserted in the main deck structure above each engine room. These openings are notional, and their actual arrangement would depend on the arrangement of machinery in the engine rooms and the locations of air intakes and funnels in the superstructure, considerations which are left for future work.
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Figure 31: No. 1 deck openings in way of engine rooms.
11.3 Transverse bulkhead modifications
Modifications to the stiffening arrangement were made to the transverse bulkheads and to the hull longitudinals to ensure (a) the spacing of longitudinals is as regular as possible; and (b) that stiffeners on bulkheads are properly connected to the hull longitudinals. The military design provisions of the NSR contain design guidance for hull structure and watertight bulkheads to improve their performance under shock and blast loads.17 Two aspects of this guidance are demonstrated here for the wateertight bulkhead at F32. On the margins of the bulkheads that connect to the side shell and hull bottom, it is required that “all bulkhead stiffeners are to end on longitudinals,” and that they “are to be fitted perpendicular to the shell plating.” Application of this guidance to the F32 bulkhead is shown in Figure 32, where stiffeners have been fitted according to this guidance (c.f. Figure 20). The dimensions and spacing of the stiffeners joining the hull were assumed to be the same as the other secondary stiffeners within the same interdeck region.
17 See Vol. 1, Pt 4, Ch. 2, Section 5.5 of Reference [1].
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Figure 32: Transverse watertight bulkhead at Frame 32 indicating plate thickness in mm.
A further requirement for military design is that a margin strake with increased thickness be fitted to transverse bulkheads. The thickness must be at least 80% of the adjacent hull plate, no less than the thickness of the adjacent longitudinals, and at least 6.5 mm. Also, the margin strake must have a width that is at least 1.5 times the adjacent stiffener spacing. This guidance has been followed for the bulkhead in Figure 32, where a margin plate of width 850 mm has been fitted above No. 3 deck with the thickkness enhancements shown. The margin plate was not needed below No. 3 deck as the existing thicknesses were sufficient to meet the above requirements.
These improvements should significantly strengthen and stiffen the connection between transverse bulkheads and the hull and reduce the occurrence of stress concentrations arising from pressure loads on the hull. They are shown here to demonstrate how the basic design of Sections 7 through 9 can be further improved to meet typical requirements for naval vessels.
Design of the structure for military loads involves many other requirements not touched on in the present work, including resistance of the hull to underwater shock, external air blast, underwater explosion-induced whipping, weapons launching loads; resistance of the hull compartments to internal blast, fragmentation and ballistic penetration; and design of the flight deck for air vehicle operations. One area that will be addressed in a future study is the residual strength of the hull structure following weapons damage.
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11.4 Other modifications
The aft end of the ND was modified to reduce the size of the longitudinal girders in the hull bottom. The sizes of these girders can be decreased by virtue of the lower draft in the aft end. Even with these changes, it was necessary to raise No. 4 deck aft of Bulkhead 53 to 6850 mm above baseline to accommodate the bottom girders. These changes are shown in Figure 33. Many similar kinds of optimizations of the scantlings and dimensions of members could be identified in the structure to save weight and improve the producability of the design.
Figure 33: Modifications to aft end structure.
Other changes to improve producability of the design include rounding plate thicknesses up to the nearest millimetre, and offsetting the plate thickness transitions from other structural junctions and connections. In real vessels, plate thickness transitions in the hull or deck plating do not occur at the junctions with decks and bulkheads, or along connections with frames or longitudinals. Instead plate thickness transitions are offset so as to avoid collocation of weld lines. Determining the location of weld lines in the hull and deck plating would be part of the final straking plan for the deesign, and this is left for future work.
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12 Conclusions
The current work describes the structural design of the Notional Destroyer to LR’s Naval Ship Rules. The application of finite element analysis to the ND, including linear elastic global strength analysis and nonlinear ultimate strength analysis, will be discussed in a separate report.
The current version of the ND represents only the global hull structure, and its use is therefore limited to analyses commensurate with that level of model detail, e.g., global and ultimate strength assessments. However, with additional development in areas such as superstructure design and structural details, the ND could be used to explore a number of other aspects of naval ship design and performance not covered by this report, including: fatigue performance, especially: application of spectral fatigue analysis; connection design; and extended design life (45 years). survivability, including: vulnerability to weapons loads; residual strength; and damaged stability. hydrodynamic and structural performance in ice [22],[23]; prediction of extreme wave loading and structural response based on nonlinear seakeeping analysis and finite element analysis, respectively; structural reliability in intact and damaged conditions; resistance to collision and grounding, and residual strength after damage; and integrated platform systems design in areas such as: superstructure design and its effect on global, ultimate and residual strength; synergy between hull strengthening needed to meet fatigue and residual strength requirements; the interaction between platform signatures and other design requirements; and the effect of hydrodynamic and hydrostatic design requirements on structures.
At the very least, the ND provides a benchmark of comparison for the global and local structural performance of other designs of similar size and tonnage, and for comparing the Naval Ship Rules with other classification society rules and naval design standards.
The structural design process and PW7600 software developed for this work can be readily reconfigured for a vessel of different size and tonnage. It is therefore possible to create alternative structural designs (e.g., for a 5,600 tonne general purpose frigate variant or a 6,500 tonne air-warfare destroyer variant) that
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are compliant with the NSR with much less effort than was needed to create the present design. As the design process is based around a fixed hull shape, redefinition of the hull form would be one of the most time-consuming aspects of such a redesign effort. Similarly, the process of arranging and subdividing tankage cannot easily be automated, and would have to be revisited afresh for each new design variant.
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References
[1] Lloyd’s Register (2012), Rules and Regulations for the Classification of Naval Ships, Lloyd’s Register, London, January 2012.
[2] Canadian Forces (2011), Stability & Buoyancy Requirements for Surface Ships, CFTO C 03 001 024/MS 002, Draft Version, May 2011.
[3] Pearson, D. and Abbott, M. (2016), Notional Vessel Design Improvement, Contract Report, (DRDC-RDDC-2017-C100), Lloyd’s Register Applied Technology Group, Ottawa ON.
[4] DesRochers, C., Norwood, M., Wallace, J., Brennan, D., and Riley, M. (2011), Life-cycle cost implications of naval ship rules fatigue life assessment, Contract Report, (DRDC Atlantic CR 2009-100), Defence R&D Canada – Atlantic.
[5] International Maritime Organization (2002), MARPOL 73/78, Articles, Protocols, Annexes, Unified Interpretations of the International Convention for the Prevention of Pollution from Ships, 1973, as modified by the Protocol of 1978 relating thereto, Consolidated Edition, 2002.
[6] Wall, A.S. (2011), Experimental evaluation of airwake quality on a generic destroyer model considering shipboard helicopter operations, (LTR AL 2011 0007) National Research Council Canada Report.
[7] Schmitke, R. and Murdey, D. (1980), Seakeeping and Resistance Trade-Offs in Frigate Hull Form Design, Proceedings of the Thirteenth Symposium on Naval Hydrodynamics, Tokyo: The Shipbuliding Research Association of Japan, pp. 455–478.
[8] Canadian Forces (1981), Structural Design of Surface Ships, Design Standard DMEM 10, Part I, II and III, Department of National Defence, Canada.
[9] Martec Ltd (2015), SubSAS User’s Guide, Version 1.0, Martec Limited (Lloyd’s Register Applied Technology Group), Halifax, Nova Scotia.
[10] Thompson, I., Stredulinsky, D., Gannon, L., and Oakey, S. (2013), STRUC_R v. 2.4 User’s Manual, External Client Report, (DRDC Atlantic ECR 2013-026), Defence R&D Canada – Atlantic.
[11] Smith, M. (2006), ULTMAT 2.1 User’s Manual, Technical Memorandum, (DRDC Atlantic TM 2006-049), Defence R&D Canada – Atlantic.
[12] Smith, C. (1977) Influence of local compressive failure on ultimate longitudinal strength of a ship’s hull, In Proceedings of 3th international symposium on practical design in shipbuilding, 73–79.
[13] Department of National Defence (2000), Halifax Class General Load Monitor (GLM) Operator Guidance Booklet, Version 3, November 2000, DMSS 2, Department of National Defence, Canada.
[14] Hess, P. (2007), Notional US Navy Destroyer Rev 2, unpublished document, NSWC Carderock, 21 Nov 2007.
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[15] Chalmers, D.W. (1993), Design of Ships’ Structures, London: Her Majesty’s Stationery Office.
[16] Lloyd’s Register (2017), Structural Design Assessment - Primary Structure of Naval Ships under Category NS2, Lloyd’s Register, London, March 2017.
[17] Hu, T. and Heath, D. (1995), EBMS – A Computer Program for Equivalent Beam Modelling of Ship Structures, DREA Technical Memorandum 95/208, Defence Research Establishment Atlantic.
[18] IACS (2017), Common Structural Rules for Bulk Carriers and Oil Tankers, Dated 01 Jan 2017, London UK: International Association of Classification Societies.
[19] Smith, M. (2010), A load shortening curve library for longitudinally stiffened panels, Technical Memorandum, (DRDC Atlantic TM 2010-140), Defence R&D Canada – Atlantic.
[20] Nickerson, J. and Smith, M. (2007), User’s Manual for the Ultimate Strength Application, Technical Memorandum, (DRDC Atlantic TM 2007-291), Defence R&D Canada – Atlantic.
[21] Lloyd’s Register (2004), Fatigue Design Assessment – Level 3 Procedure, Lloyd’s Register, London, May 2004.
[22] Daley, C. (2015), Ice Impact Capability of DRDC Notional Destroyer, Contract Report, Defence Research and Development Canada, (DRDC-RDDC-2015-C202), Daley R&E, St. John’s, NL.
[23] Daley, C., Dolny, J., and Daley, K. (2017), Safe Speed Assessment of DRDC Notional Destroyer in Ice, Contract Report, Defence Research and Development Canada, (DRDC-RDDC-2017-C259), Daley R&E, St. John’s, NL.
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Annex A Frame table
Table A.1: Frame table for the ND.
Frame Position (m) Frame Position (m) Frame Position (m) F-4 -8.000 F5 10.000 F38 76.000 F-3.75 -7.500 F6 12.000 F39 78.000 F-3.5 -7.000 F7 14.000 F40 80.000 F-3.25 -6.500 F8 16.000 F41 82.000 F-3 -6.000 F9 18.000 F42 84.000 F-2.75 -5.500 F10 20.000 F43 86.000 F-2.5 -5.000 F11 22.000 F44 88.000 F-2.25 -4.500 F12 24.000 F45 90.000 F-2 -4.000 F13 26.000 F46 92.000 F-1.75 -3.500 F14 28.000 F47 94.000 F-1.5 -3.000 F15 30.000 F48 96.000 F-1.25 -2.500 F16 32.000 F49 98.000 F-1 -2.000 F17 34.000 F50 100.000 F-0.75 -1.500 F18 36.000 F51 102.000 F-0.5 -1.000 F19 38.000 F52 104.000 F-0.25 -0.500 F20 40.000 F53 106.000 F0 0.000 F21 42.000 F54 108.000 F0.25 0.500 F22 44.000 F55 110.000 F0.5 1.000 F23 46.000 F56 112.000 F0.75 1.500 F24 48.000 F57 114.000 F1 2.000 F25 50.000 F58 116.000 F1.25 2.500 F26 52.000 F59 118.000 F1.5 3.000 F27 54.000 F60 120.000 F1.75 3.500 F28 56.000 F61 122.000 F2 4.000 F29 58.000 F62 124.000 F2.25 4.500 F30 60.000 F63 126.000 F2.5 5.000 F31 62.000 F64 128.000 F2.75 5.500 F32 64.000 F65 130.000 F3 6.000 F33 66.000 F66 132.000 F3.25 6.500 F34 68.000 F67 134.000 F3.5 7.000 F35 70.000 F68 136.000 F3.75 7.500 F36 72.000 F69 138.000 F4 8.000 F37 74.000 F70 140.000 F71 142.000
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List of symbols/abbreviations/acronyms/initialisms
Δ displaced volume, ∆ displacement of the hull density of seawater, taken as 1.025 tonnes/m3 direct stress in local or global x, y or z direction
yield stress
critical buckling stress for a particular failure mode, including the interaction of elastic buckling and plastic collapse; also, the critical buckling stress of a plate panel under uni-axial compression
critical overall buckling stress of a stiffened panel under uni-axial compression
critical torsional buckling stress for a secondary stiffener under uni-axial compression
critical web buckling stress for a secondary stiffener under uni-axial compression
critical flange buckling stress for a secondary stiffener under uni-axial compression
elastic buckling stress for a particular failure mode
maximum permissible normal stress in longitudinally effective structure
normal stress in the longitudinal direction in-plane shear stress
shear strength, √
critical buckling stress of a plate panel under pure shear
maximum permissible shear stress in longitudinally effective structure ATG Applied Technology Group AWD Air-Warfare Destroyer
waterplane area maximum breadth of the hull
the breadth of a stiffener flange
maximum breadth of the hull at the waterline b/w between block coefficient, cm centimetres
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CSR Common Structural Rules waterplane area coefficient, the depth of a stiffener section D overall depth of the hull
the depth of a stiffener web DND Department of National Defence DRDC Defence Research and Development Canada EB NSR military notation for external blast ER Engine Room ES NSR notation for enhanced scantlings ESA Extreme Strength Assessment F Frame FDA Fatigue Design Assessment FE Finite Element FP Forward Perpendicular fwd forward
factor applied to the maximum permissible hull girder normal stress in order to account for the longitudinal position being considered
high tensile steel stress correction factor, 0.919 for high strength steel with a yield stress equal to 355 MPa
safety factor used in the ESA2 requirements for ultimate strength (3),(4), 0.9 GHS General Hydrostatics GPa gigapascals
nominal wave limit height HS Hull Strengthening HSS High-Strength Steel IB NSR military notation for internal blast IMO International Maritime Organization kg kilograms kN kilonewtons kPa kilopascals overall length of the hull
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length of the hull between perpendiculars
Rule length LR Lloyd’s Register
length of the hull along the waterline m metres mm millimetres MN meganewtons MPa megapascals
extreme rule design bending moment
still-water bending moment
ultimate bending moment
wave bending moment
extreme wave bending moment
Ⓜ length constant (circular “M”), Ⓜ √
N newtons ND Notional Destroyer No. number NRC National Research Council of Canada NS2 NSR notation for a frigate or destroyer NSR Naval Ship Rules p. page
nominal local design pressure for the weather deck
hydrostatic pressure
local design pressure due to relative vertical motion between ship and wave
local design pressure due to pitching motion
net local design pressure for the hull envelope
equivalent static pressure due hydrodynamic forces in waves
net local design pressure for the weather deck
extreme rule vertical shear force
still-water shear force
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ultimate vertical shear force
wave shear force
extreme wave shear force RSA Residual Strength Assessment R&D Research and Development SA1 NSR notation for a worldwide service area SDA Structural Design Assessment t metric tonne, 1 t = 1000 kg draft
the thickness of a stiffener flange
the thickness of a stiffener web
Tx design draft at longitudinal position, x VBM Vertical Bending Moment VLS Vertical Launch System WT WaterTight longitudinal position XML eXtensible Markup Language elevation
keel elevation
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DOCUMENT CONTROL DATA *Security markings for the title, authors, abstract and keywords must be entered when the document is sensitive 1. ORIGINATOR (Name and address of the organization preparing the document. 2a. SECURITY MARKING A DRDC Centre sponsoring a contractor's report, or tasking agency, is entered (Overall security marking of the document including in Section 8.) special supplemental markings if applicable.)
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3. TITLE (The document title and sub-title as indicated on the title page.)
Structural design of the DRDC notional destroyer
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MacKay, J. R.; Smith, M. J.; Gannon, L.; Perrault, D.
5. DATE OF PUBLICATION 6a. NO. OF PAGES 6b. NO. OF REFS (Month and year of publication of document.) (Total pages, including (Total references cited.) Annexes, excluding DCD, covering and verso pages.) July 2019 78 23
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Ship Structure; Finite Element Analysis; naval ship rules; warship design
13. ABSTRACT (When available in the document, the French version of the abstract must be included here.)
This report describes the structural design of a generic 7,600 tonne air-warfare destroyer, referred to as the DRDC Notional Destroyer (ND). The intent of the ND is to provide a test-bed for evaluating structural, stability, hydrodynamic and other naval engineering design standards, design concepts, analysis methods, and software. The ND is not based on either existing or future naval platforms. The current work is concerned only with the structural aspects of the ND design, which conforms with Lloyd’s Register’s Naval Ship Rules (NSR) for a worldwide service area. In addition to the standard Rules requirements for structures, the ND was designed against LR’s requirements for an Extreme Strength Assessment, Level 2. That entailed comparing the hull girder’s ultimate strength, as predicted using Smith’s progressive collapse method, against extreme lifetime global loads prescribed by the NSR. This Scientific Report describes the hypothetical performance requirements that drove the ND design, the modelling and analysis tools used, and the bottom-up design procedure employed by DRDC. The outcome of the design process is then presented, including the general arrangement; design loads; the final structural configuration and scantlings; and the results of the global and ultimate strength assessments. The evolution of the scantlings, from those meeting the standard NSR requirements to those meeting global and ultimate strength requirements, is discussed, as are the weight implications associated with meeting those requirements.
Le présent rapport décrit la conception de la structure du contre-torpilleur fictif (CTF) de RDDC, un contre-torpilleur générique de 7 600 tonnes destiné à la guerre aérienne. Le CTF vise à fournir un banc d’essai pour évaluer certaines normes de génie naval, notamment celles relatives à la structure, à la stabilité et aux qualités hydrodynamiques des navires, ainsi que certains concepts pour la conception, certaines méthodes d’analyse et certains logiciels. Le CTF n’est pas lié à une plate-forme navale actuelle ni à aucune future plateforme. Les travaux évoqués dans le présent rapport portent seulement sur les aspects structurels de la conception du CTF, laquelle est conforme aux Naval Ship Rules (NSR) de la Lloyd’s Register (LR) pour une zone de service mondial. En plus de respecter les exigences standard de la LR s’appliquant aux structures, le CTF a été conçu pour satisfaire à ses exigences en matière de résistance extrême (niveau 2). La résistance ultime de la poutre-coque a été évaluée en fonction des prédictions réalisées en appliquant la méthode d’effondrement en cascade de Smith et comparée aux charges globales extrêmes indiquées dans les NSR pour la durée de vie des poutres-coques. Dans le présent rapport scientifique, on décrit les exigences de rendement hypothétiques qui ont guidé la conception du CTF, les outils de modélisation et d’analyse employés et la procédure de conception de bas en haut utilisée par RDDC. On présente ensuite les résultats du processus de conception, y compris la configuration générale du navire, les charges théoriques, la configuration de la structure définitive, l’échantillonnage final ainsi que les résultats des évaluations en matière de résistance ultime et globale. Enfin, on discute de l’évolution des différents échantillonnages, en commençant par ceux qui satisfont aux exigences standard imposées par les NSR et en terminant par ceux qui respectent les normes de résistance ultime et globale, et on décrit les conséquences sur le poids du respect de ces exigences.