Design Theories of Ship and Offshore Plant

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1 7-6-6 Lecture Note o Design Theories o Ship and Oshore Plant Design Theories o Ship and Oshore Plant Part I. Ship Design Ch. 6 Structural Design Fall 6 yung-il Roh Department o Naval Architecture and Ocean Engineering Seoul National University Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh Contents Ch. Introduction to Ship Design Ch. Introduction to Oshore Plant Design Ch. 3 Hull Form Design Ch. 4 General Arrangement Design Ch. 5 Naval Architectural Calculation Ch. 6 Structural Design Ch. 7 Outitting Design Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh

2 7-6-6 Ch. 6 Structural Design 6. Generals & aterials 6. Global Hull Girder Strength (Longitudinal Strength) 6.3 Local Strength (Local Scantling) 6.4 Buckling Strength 6.5 Structural Design o idship Section o a 3,7 TEU Container Ship Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 3 6. Generals & aterials () Stress Transmission () Principal Dimensions (3) Criteria or the Selection o Plate Thickness, Grouping o Longitudinal Stiener (4) aterial Factors Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 4

3 7-6-6 () Stress Transmission Inner Bottom Plate Load Longitudinals Side Girder Center Girder Web rame Plate Longi. Web rame Girder : Stress Transmission Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 5 () Principal Dimensions DNV Rules, Jan. 4,Pt. 3 Ch. Sec. The ollowing principal dimensions are used in accordance with DNV rule. ) Rule length (L or L s ) : Length o a ship used or rule scantling procedure.96 L L.97 L WL Distance on the summer load waterline (L WL ) rom the ore side o the stem to the ais o the rudder stock Not to be taken less than 96%, and need not be taken greater than 97%, o the etreme length on the summer load waterline (L WL ) ) Breadth Eample o the calculation o rule length L BP L WL.96 L WL.97 L WL L : Greatest moulded breadth in [m], measured at the summer load waterline WL Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 6 3

4 7-6-6 () Principal Dimensions DNV Rules, Jan. 4,Pt. 3 Ch. Sec. 3) Depth (D) : oulded depth deined as the vertical distance in [m] rom baseline to moulded deck line at the uppermost continuous deck measured amidships 4) Drat (T) : ean moulded summer drat (scantling drat) in [m] 5) Block coeicient (C B ) : To be calculated based on the rule length C B.5LBT, ( : oulded displacement in sea water on drat T) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 7 (3) Criteria or the Selection o Plate Thickness, Grouping o Longitudinal Stiener ) Criteria or the selection o plate thickness DNV Rules, Jan. 4,Pt. 3 Ch. Sec. When selecting plate thickness, use the provided plate thickness. ().5 mm interval () Above.5 mm:.5 mm (3) Below.5 mm:. mm E) 5.75 mm 6. mm 5.74 mm 5.5 mm ) Grouping o longitudinal stiener For the eiciency o productivity, each member is arranged by grouping longitudinal stieners. The grouping members should satisy the ollowing rule. Average value but not to be taken less than 9% o the largest individual requirement (DNV). E) The longitudinal stieners have design thickness o, 9, 8, 7, 6 mm. The average thickness is given by 8 mm 5. However, the average value is less than mm 9% = 9 mm o the largest individual requirement, mm. Thereore, the average value should be taken 9 mm 5. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 8 4

5 7-6-6 (4) aterial Factors ) DNV Rules, Jan. 4, Pt. 3 Ch. Sec. ) James. Gere, echanics o aterials 7th Edition, Thomson, Chap., pp.5~6 The material actor is included in the various ormulae or scantlings and in epressions giving allowable stresses. ) aterial Designation Yield Stress (N/mm ) aterial Factor ( ) NV-NS 35 35/35 =.. NV /35 =.3.8 NV /35 =.34.8 NV NS NV /35 =.5.39 NV /35 = * Yield Stress (σ y ) [N/mm ] or [Pa]: The magnitude o the load required to cause yielding in the beam. ) * NV-NS: Normal Strength Steel (ild Steel) * NV-XX: High Tensile Steel * High tensile steel: A type o alloy steel that provides better mechanical properties or greater resistance to corrosion than carbon steel. They have a carbon content between.5-.5% to retain ormability and weldability, including up to.% manganese, and other elements are added or strengthening purposes. * A: A grade Normal Strength Steel * AH: A grade High Tensile Steel Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 9 6. Global Hull Girder Strength (Longitudinal Strength) () Generals () Still Water Bending oment (s) (3) Vertical Wave Bending oment (w) (4) Section odulus Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 5

7-6-6 () Generals Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh Interest o Ship Structural Design Ship Structural Design What is designer s major interest?

6 7-6-6 () Generals Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh Interest o Ship Structural Design Ship Structural Design What is designer s major interest? Saety: Won t it ail under the load? a ship a stiener a plate global local Let s consider the saety o the ship rom the point o global strength irst. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 6

7 7-6-6 Dominant Forces Acting on a Ship What are dominant orces acting on a ship in view o the longi. strength? w ( ) z w():weight weight o light ship, weight o cargo, and consumables z b ( ) b():buoyancy hydrostatic orce (buoyancy) on the submerged hull hydrodynamic orce induced by the wave What is the direction o the dominant orces? The orces act in vertical (lateral) direction along the ship s length. AP FP Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 3 Longitudinal Strength : Overall strength o ship s hull which resists the bending moment, shear orce, and torsional moment acting on a hull girder. Longitudinal strength loads : Load concerning the overall strength o the ship s hull, such as the bending moment, shear orce, and torsional moment acting on a hull girder Static longitudinal loads z Loads are caused by dierences between weight and buoyancy in longitudinal direction in the still water condition Hydrodynamic longitudinal loads z Loads are induced by waves ) Okumoto,Y., Design o Ship Hull Structures, Springers, 9, P.7 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 4 7

8 7-6-6 Idealization o the Ship Hull Girder Structure How can we idealize a ship as a structural member? Structural member according to the types o loads Aially loaded bar: structural member which supports orces directed along the ais o the bar Bar in torsion: structural member which supports torques (or couples) having their moment about the longitudinal ais 3 Beam: structural members subjected to lateral loads, that is, orces or moments perpendicular to the ais o the bar Since a ship has a slender shape and subject to lateral loads, it will behave like a beam rom the point view o structural member. y w Ship is regarded as a beam. AP FP RA RB Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 5 Applying Beam Theory to a Ship y RA y w w RB AP FP V( ) R A R B V ( ) ( ) ( ) y ( ) I there are supports at the ends, delection and slope o the beam occur. * James. Gere, echanics o aterials, 6 th Edition, Thomson, Ch. 4, p. 9 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh y Idealize AP FP Actually, there are no supports at the ends o the ship. However, the delection and slope could occur due to inequality o the buoyancy and the weight o a ship. For this problem, we assume that there are simple supports at the A.P and the F.P. L 6 8

7-6-6 Correction o a Bending oment Curve Beore correction ( ) Ater correction AP What i the

Thus, we correct the bending moment curve to have at AP and FP. - = FP * James.

9 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 7 Actual Stress Allowable Stress

l : Largest SWB among all loading conditions and class rule S : Calculated by class rule or

9 7-6-6 Correction o a Bending oment Curve Beore correction ( ) Ater correction AP What i the bending moment is not zero at FP? The delection and slope o the beam occur at FP. Thus, we correct the bending moment curve to have at AP and FP. - = FP * James. Gere, echanics o aterials, 6 th Edition, Thomson, Ch. 4, p. 9 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 7 Actual Stress Allowable Stress - Bending Stress and Allowable Bending Stress ) DNV Rules, Pt. 3 Ch. Sec. 5, Jan. 4 The actual bending stress ( act. ) shall not be greater than the allowable bending stress ( l ). kg cm S W 3 act. [ / ] act. l : Largest SWB among all loading conditions and class rule S : Calculated by class rule or direct calculation W (DNV Pt. 3 Ch. Sec. 5 C33) l allow N mm 75 [ / ] within.4l amidship 5 [ N / mm ] within.l rom A.P. or F.P. ( : aterial actor. E. ild steel., HT-3.8, HT-36.39) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 8 9

10 7-6-6 Criteria o Structural Design (/) Ship Structural Design z y a ship L The actual bending stress ( act. ) shall not be greater than the allowable bending stress ( l ). act. l, σ act. S W : Largest SWB among all loading conditions and class rule S W : calculated by class rule or direct calculation l : allowable stress For instance, allowable bending stresses by DNV rule are given as ollows: l 75 [ N / mm ] within.4l amidship 5 [ N / mm ] within.l rom A.P. or F.P., Ton m Eample o bending moment curve o container carrier 5 Light ship 5 Ballast dep. Ballast arr. 5 Homo t dep. Homo t arr. 5 Homo 8t dep. Homo t arr. 5 5 AP F. P Actual bending moments at at and orward area are smaller than that at the midship. What is, then, the? Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 9 Criteria o Structural Design (/) act. l σ act. S W () Still Water Bending oment (s) () Vertical Wave Bending oment (w) (3) Section odulus () Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh

11 7-6-6 () Still Water Bending oment (s) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh Still Water Bending oment (s) act. l, σ act. S W, S : Still water bending moment W : Vertical wave bending moment Hydrostatic loads along ship s length caused by the weight & the buoyancy S ( ) : distributed loads in longitudinal direction in still water buoyancy VS ( ) : still water shear orce VS( ) S( ) d S ( ) : still water bending moment S( ) VS( ) d weight Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh

7-6-6 Distributed Loads in Longitudinal Direction ( ) ( ) ( ) S W (): Distributed loads in longitudinal direction S (): Static longitudinal loads in longitudinal direction W (): Hydrodynamic

12 7-6-6 Distributed Loads in Longitudinal Direction ( ) ( ) ( ) S W (): Distributed loads in longitudinal direction S (): Static longitudinal loads in longitudinal direction W (): Hydrodynamic longitudinal loads induced by wave In still water z ( ) ( ) ( ) S b w w ( ) b ( ) z z w() : weight b() : buoyancy b(): Distributed buoyancy in longitudinal direction w() = LWT() + DWT() - w(): Weight distribution in longitudinal direction - LWT(): Lightweight distribution - DWT(): Deadweight distribution S z S () = b() + w() : Load Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 3 Distributed Loads in Still Water Eample o a 3,7 TEU Container Ship in Homogeneous ton Scantling Condition - Principal Dimensions & Plans Principal dimension Proile & plan Load Curve, S () Weight, w() Buoyancy, b() Actual Still Water Shear Force, V S () V ( ) ( ) d S S S idship section Actual Still Water Bending oment, S () ( ) VS( ) d - Loading Condition: Homogeneous ton Scantling Condition (Sailing state) * Frame space: 8mm Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 4

7-6-6 Distributed Loads in Still Water - Lightweight Eample o a 3,7 TEU Container Ship Load Curve, S () Weight, w() Buoyancy, b() Actual Still Water Shear Force, V

P LIGHTWEIGHT DISTRIBUTION DIAGRA Engine Crane FP Bow Thruster Emergency Pump 5 5 74 99 5 5 75 6 5 76 3 36 FR. NO F.

homogenous ton scantling condition Load Curve, S () Weight, w() Buoyancy, b() Actual Still Water Shear Force, V S () V ( ) ( ) d S Actual Still Water Bending oment,

13 7-6-6 Distributed Loads in Still Water - Lightweight Eample o a 3,7 TEU Container Ship Load Curve, S () Weight, w() Buoyancy, b() Actual Still Water Shear Force, V S () V ( ) ( ) d S Actual Still Water Bending oment, S () S S ( ) VS( ) d E/R TONNES AP A.P LIGHTWEIGHT DISTRIBUTION DIAGRA Engine Crane FP Bow Thruster Emergency Pump FR. NO F.P Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 5 Distributed Loads in Still Water - Deadweight Eample o a 3,7 TEU Container Ship -Loading plan in homogenous ton scantling condition Load Curve, S () Weight, w() Buoyancy, b() Actual Still Water Shear Force, V S () V ( ) ( ) d S Actual Still Water Bending oment, S () S S ( ) VS( ) d Deadweight distribution in longitudinal direction in homogenous ton scantling condition -Deadweight distribution curve in homogenous ton scantling condition A.P FR.Space : 8 mm Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh F.P 6 3

7-6-6 Distributed Loads in Still Water - Buoyancy Curve Load Curve, S () Weight, w() Buoyancy, b() Actual Still Water Shear Force, V S () Actual Still Water Bending oment, S () VS( ) S( ) d S( ) V S(

P FR. No () Integration o sectional area over the ship s length A Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 7 Distributed Loads in Still Water -Load Curve Load Curve S =

14 7-6-6 Distributed Loads in Still Water - Buoyancy Curve Load Curve, S () Weight, w() Buoyancy, b() Actual Still Water Shear Force, V S () Actual Still Water Bending oment, S () VS( ) S( ) d S( ) V S( ) d Eample o a 3,7 TEU Container Ship Calculation o buoyancy Buoyancy curve in homogeneous ton scantling condition ton () Calculation o sectional area below waterline z ' y ' A.P FR. Space: 8 mm F.P FR. No () Integration o sectional area over the ship s length A Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 7 Distributed Loads in Still Water -Load Curve Load Curve S = Lightweight Weight Curve + Deadweight in homogenous ton scantling condition Load Curve, S () Weight, w() Buoyancy, b() ( ) : Loads Curve = Weight + Buoyancy Lightweight Distribution Curve Actual Still Water Actual Still Water Shear Force, V S () Bending oment, S () VS( ) ( ) S d S( ) V ( ) S d Deadweight Distribution Curve in homogenous ton scantling condition TONNES 4. LIGHTWEIGHT DISTRIBUTION DIAGRA A.P Buoyancy Curve in homogenous ton scantling condition ton F.P. A.P. F.P FR. NO A.P FR.Space : 8 mm F.P Load Curve = Weight w() + Buoyancy b() in homogenous ton scantling condition A.P F.P A.P FR.Space: 8 mm F.P FR.No FR.No Actual Still Water Shear Force Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 8 4

15 7-6-6 Actual Still Water Shear Force & Actual Still Water Bending oment Load Curve, S () Weight, w() Buoyancy, b() Actual Still Water Actual Still Water Shear Force, V S () Bending oment, S () VS( ) ( ) S d S( ) V ( ) S d Eample o a 3,7TEU Container Ship Load Curve ( ) b( ) w( ) S Actual Still Water Shear Force VS( ) S( ) d Actual still water shear orce Design still water shear orce Actual Still Water Bending oment S( ) VS( ) d Actual still water bending moment Design still water bending moment Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 9 Rule Still Water Bending oment by the Classiication Rule Recently, actual still water bending moment based on the loading conditions is used or still water bending moment, because the rule still water bending moment is only or the tanker. The design still water bending moments amidships are not to be taken less than SO [ knm] S.65C WU SO L B( C B.7) (.5.5 ) [knm] in sagging CWU L B C [knm] in hogging B : Wave coeicient or unrestricted service (DNV Pt. 3 Ch. Sec. 5 A5) The still water bending moment shall not be less than the large o: the largest actual still water bending moment based on the loading conditions and the rule still water bending moment. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 3 5

16 7-6-6 Rule Still Water Shear Force by the Classiication Rule The design values o still water shear orces along the length o the ship are normally not to be taken less than Q S Q k sq Q SO (kn) SO 5 ( kn) L k sq = at A.P. and F.P. =. between.5l and.3l rom A.P. =.8 between.4l and.6l rom A.P. =. between.7l and.85l rom A.P. SO.65CWU L B( CB.7) [knm] in sagging SO C L B(.5.5 ) [knm] in hogging WU C B (Dnv Pt.3 Ch. Sec. 5 B7) : wave coeicient or unrestricted service The still water shear orce shall not be less than the large o: the largest actual still water shear orces based on loading conditions and the rule still water shear orce. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 3 (3) Vertical Wave Bending oment (w) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 3 6

diraction orce + added mass orce + damping orce ( ) r F ( Body Force) ( Surace Force) Fgravity () r FFluid (,,) rrr Fgravity FBuoyancy () r FF.

17 7-6-6 Vertical Wave Bending oment (w) act. l, σ act. S W, S : Still water bending moment W : Vertical wave bending moment Hydrodynamic loads induced by waves along ship s length W VW W ( ) : distributed loads induced by waves = Froude-Krylov orce + diraction orce + added mass orce + damping orce ( ) r F ( Body Force) ( Surace Force) Fgravity () r FFluid (,,) rrr Fgravity FBuoyancy () r FF. K () r FD () r F (,) r r F (,) r r : vertical wave shear orce VW ( ) W ( ) d ( ) : vertical wave bending moment W ( ) VW ( ) d R, Damping R, ass added mass diraction damping FK. mass inertia Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 33 Dynamic Longitudinal Loads In still water z ( ) ( ) ( ) S b w (): Distributed loads in longitudinal direction S (): Static longitudinal loads in longitudinal direction W (): Hydrodynamic longitudinal loads induced by wave S z S ()= b() w(): Load In wave z Dynamic longitudinal loads : Loads are induced by waves Vertical bending due to waves Ship in oblique waves Hogging Sagging Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 34 7

18 7-6-6 Dynamic Longitudinal Loads - Direct Calculation o Dynamic Longitudinal Loads (/) In still water z In wave z ( ) ( ) ( ) S b w (): Distributed loads in longitudinal direction S (): Static longitudinal loads in longitudinal direction W (): Hydrodynamic longitudinal loads induced by wave Dynamic longitudinal loads : Loads are induced by waves () W Direct calculation o dynamic longitudinal loads rom 6DOF motion o ship T XYT,,,,, S z z? S ()= b() w(): Load Re.> 6 DOF motion o ship Yaw Heave T Pitch y O z ( ) ( ) S W b ( ) w ( ) ( ) ( ) ( ) where, D F. K R ( ) ( ) ( ) R a b Roll D (): Diraction orce at R (): Radiation orce at by damping and added mass Design Theories o Ship and Oshore Plant, Fall 6, F.K (): Froude-Krylov orce at yung-il Roh additional loads in wave 35 Dynamic Longitudinal Loads - Direct Calculation o Dynamic Longitudinal Loads (/) In wave z Direct calculation o dynamic longitudinal loads Load induced by Wave ( ) ( ) ( ) ( ) W D F. K R where, ( ) ( ) ( ) R a b Actual Vertical Wave Shear Force QW( ) W( ) d Actual Vertical Wave Bending oment W( ) QW( ) d Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 36 8

19 7-6-6 Rule Values o Vertical Wave Bending oments Direct calculation o dynamic longitudinal loads Loads are induced by waves Actual Vertical Wave Shear Force QW( ) W( ) d Actual Vertical Wave Bending oment W( ) Q ( ) W d Recently, rule values o vertical wave moments are used, because o the uncertainty o the direct calculation values o vertical wave bending moments. The rule vertical wave bending moments amidships are given by:.c WO.9 [ knm] W W L B( C B WO.7) [knm] in sagging CW L BC B [knm] in hogging α=.or seagoing condition L L 3 3 L 35 L L =.5 or harbor and sheltered water conditions (enclosed iords, lakes, rivers) C W : wave coeicient C B : block coeicient, not be taken less than.6 L (DNV Pt.3 Ch. Sec.5 B) C W (3 ) / 3 /.75 L ( L 35) /5 3/ Direct calculation values o vertical wave bending moments can be used or vertical wave bending moment instead o the rule values o vertical wave moments, i the value o the direct calculation is smaller than that o the rule value. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 37 Rule Values o Vertical Wave Shear Forces Direct calculation o dynamic longitudinal loads Loads are induced by waves Load induced by Wave ( ) ( ) ( ) ( ) W D F. K R where, ( ) a( ) b( ) R Actual Vertical Wave Shear Force QW( ) W( ) d The rule values o vertical wave shear orces along the length o the ship are given by: Positive shear orce: (DNV Pt.3 Ch. Sec.5 B3) β: coeicient according QWP.3k wqpcw LB( CB.7) to operating condition Negative shear orce: QWN.3k wqncw LB( CB.7) k wqp, k wqn : coeicients according to location in lengthwise C W : wave coeicient Direct calculation values o vertical wave shear orces can be used or vertical wave shear orce instead o the rule values o vertical shear orces, i the value o the direct calculation is smaller than that o the rule value. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 38 9

20 7-6-6 [Eample] Rule Values o Still Water Bending oments (s) and Vertical Wave Bending oment (w) Calculate L S, C B,SCANT, and vertical wave bending moment at amidships (.5L) o a ship in hogging condition or sea going condition. Dimension : L 33. m, L 37. m, L 3.85 m, B 43. m, T 4.5m OA BP EXT s Displacement tonatts 4,96 ton (Sol.) Ls.97LEXT ,96 CB, SCANT /.5Ls BTs , or sea going condition, CW.75, i 3 L 35 (wave coeicient). between.4l and.65 L rom A.P(=.) and F.P kwm.9 C L BC knm WO W B, SCANT ,66,33 knm at.5l, kwm.. W WO S SO (knm) SO.65 CWU L B( CB.7), in sagging CWU L B(.5.5 CB ), inhogging w WO (knm) WO. CW L B( CB.7), insagging.9 CWL BCB, inhogging So,. 6,66,33 knm W WO ) DSE, Ship Structural Design, 5- Load on Hull Structure, Eample 4, 5 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 39 Still Water Bending oment Curve (T&S Booklet) 4 3 Design SWB Hogging SWB(ton-m) Design SWB Sagging (m ) LC LC3 LC4 LC5 LC6 LC7 LC8 LC9 LC LC LC LC3 LC4 LC5 LC6 LC7 LC8 LC9 LC LC LC LC3 LC4 LC5 LC6 LC7 LC8 LC9 LC3 LC3 LC3 LC33 LC34 LC35 LC36 LC37 LC38 LC39 LC4 LC4 LC4 LC43 LC44 LC45 LC46 LC47 LC49 LC5 LC5 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 4

21 7-6-6 Total Bending oment Curve Total Bending oment Hogging = Design SWB + VWB 8 6 Design SWB Hogging VWB Hogging Bending oment(ton-m) Total -8 Bending oment Sagging = Design SWB + VWB Design SWB Sagging (m) VWB Sagging T/S ma. T/S in. B/E a. B.E in. Design SWB Hog. Design SWB Sag. VWB Hog. VWB Sag. Total B Hog. Total B Sag. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 4 (4) Section odulus Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 4

22 7-6-6 Eample o idship Section o a 3,7 TEU Container Ship ) First, determine the dimensions o the longitudinal structural members such as longitudinal plates and longitudinal stieners by rule local scantling. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 43 Vertical Location o Neutral Ais about Baseline ) Second, calculate the moment o sectional area about the base line. hi Ai h i : vertical center o structural member A i : area o structural member 3) Vertical location o neutral ais rom base line ( h ) is, then, calculated by dividing the moment o area by the total sectional area. h ha i A i <idship section> Upper Deck h : vertical location o neutral ais A: total area y D y B h i A i h N.A. B.L. By deinition, neutral ais pass through the centroid o the cross section. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 44

23 7-6-6 idship Section oment o Inertia about N.A - The midship section moment o inertia about base line (I B.L ) I I A h BL. N. A. - then calculate the midship section moment o inertia about neutral ais (I N.A ) using I B.L. I I A h NA.. BL. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 45 Calculation o Section odulus and Actual Stress at Deck and Bottom y <idship section> y D y B Upper Deck N.A. B.L. :bending stress T :Total bending moment A:Total Area IN. A. : Inertia moment o the midship section area about neutral ais (N.A.) B.L : Base Line Section modulus D I y NA.., D B I N y. A. B Calculation o Actual Stress at Deck and Bottom Deck Bottom D B I I y NA. / NA. / D y B l, σ I / y N. A Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 46 3

24 7-6-6 Global Hull Girder Strength (Longitudinal Strength) - Deinition o the Longitudinal Strength embers Eample o Requirement or Longitudinal Structural ember DNV Rules or Classiication o Ships Part 3 Chapter HULL STRUCTUREALDESIGN SHIPS WITH LENGTH ETERS AND ABOVE Sec. 5 Longitudinal Strength C 3 Section modulus 3 The requirements given in 3 and 33 will normally be satisied when calculated or the midship section only, provided the ollowing rules or tapering are complied with: a) Scantlings o all continuous longitudinal strength members shall be maintained within.4 L amidships. b) Scantlings outside.4 L amidships are gradually reduced to the local requirements at the ends, and the same material strength group is applied over the ull length o the ship. The section modulus at other positions along the length o the ship may have to be specially considered or ships with small block coeicient, high speed and large lare in the ore body or when considered necessary due to structural arrangement, see A6. Application o hull girder load eects * Hughes, Ship Structural Design, John Wiley & Sons, 983 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 47 The inimum Required idship Section odulus and Inertia oment by DNV Rule DNV Rules, Jan. 4, Pt. 3 Ch. Sec. 5 The midship section modulus about the transverse neutral ais shall not be less than: (Pt.3 Ch. Sec.5 C3) O C WO L B( C.7) [cm ] 3 B C WO : wave coeicient L L 3 3 L 35 L 35 C WO (3 ) / 3 /.75 L ( L 35) /5 3/ C B is in this case not to be taken less than.6. The midship section moment o inertia about the transverse neutral ais shall not be less than: (Pt.3 Ch. Sec.5 C4) I C L B C cm 3 4 ship 3 W ( B.7) [ ] * DNV Rules, Jan. 4, Pt. 3 Ch. Sec. 5 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 48 4

25 7-6-6 aterial Factors ( ) ) DNV Rules, Jan. 4,Pt. 3 Ch. Sec. ) James. Gere, echanics o aterials 7th Edition, Thomson, Chap., pp.5~6 The material actor is included in the various ormulae or scantlings and in epressions giving allowable stresses. ) aterial Designation Yield Stress (N/mm ) NV NS aterial Factor ( ) NV-NS 35 35/35 =.. NV /35 =.3.8 NV /35 =.34.8 NV /35 =.5.39 NV /35 = * Yield Stress (σ y ) [N/mm ] or [Pa]: The magnitude o the load required to cause yielding in the beam. ) * NV-NS: Normal Strength Steel (ild Steel) * NV-XX: High Tensile Steel * High tensile steel: A type o alloy steel that provides better mechanical properties or greater resistance to corrosion than carbon steel. They have a carbon content between.5-.5% to retain ormability and weldability, including up to.% manganese, and other elements are added or strengthening purposes. * A: A grade Normal Strength Steel * AH: A grade High Tensile Steel Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 49 Summary o Longitudinal Strength l, σ I / y N. A Calculation o hull girder total shear orce & bending moment Still water shear orces Q S Still water bending moments S (Q S, S ) based on the loading conditions. Weight curve W (). Buoyancy curve B() 3. Load curve ( ) W( ) B( ) S 4. Shear orce curve Qs S d 5. Bending moment curve S Qd s (Q S, S ) in. rule requirements Larger value shall be used or the still water bending moment between the largest actual still water bending moment based on loading conditions and design still water bending moment by rule. Wave shear orce Q W Wave bending moment W Direct calculation (Q W, W ). Wave Load curve ( ) ( ) ( ) ( ) W D F. K R. Vertical Wave Shear orce curve QW Wd 3. Vertical Wave Bending moment curve W QWd Class rule (Q W, W ) Direct calculation values can be used or wave shear orce and wave bending moment. Calculation o section modulus (Local scantling) Actual bending stress Allowable bending stress Yes End o design o longitudinal strength Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh No odiy longitudinal structural members 5 5

26 Local Strength (Local Scantling) () Procedure o Local Scantling () Local Strength & Allowable Stress (3) Design Loads (4) Scantling o Plates (5) Scantling o Stieners (6) Sectional Properties o Steel Sections Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 5 Local Scantling Ship structure members are designed to endure the loads acting on the ship structure such as hydrostatic and hydrodynamic loads ). ) For instance, the structural member is subjected to: Hydrostatic pressure due to surrounding water Internal loading due to sel weight and cargo weight Hydrodynamic load due to waves Inertia orce o cargo or ballast due to ship motion ) Okumoto, Y., Takeda, Y., ano,., Design o Ship Hull Structures - a Practical Guide or Engineers, Springer, pp. 7-3, 9 ) ansour, A., Liu, D., The Principles o Naval Architecture Series Strength o Ships and Ocean Structures, The Society o Naval Architects and arine Engineers, 8 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 5 6

27 7-6-6 () Procedure o Local Scantling Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 53 Procedure o Local Scantling - Design Procedure o Structures Estimation o design bending moment ain data, geometry and arrangement idship section arrangement Local scantling As-built ship midship section modulus Ship structure design is carried out in accordance with the procedure shown in the igure. Calculation o stress actor Local scantling Calculation o actual section modulus Assumption o initial midship section modulus Given by the rule requirement Each member is adjusted to have enough local strength given by the rule o Classiication Societies based on the mechanics o materials. No Required section modulus Actual section modulus Longitudinal strength check This is called the local scantling. Yes Rule scantling end Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 54 7

7-6-6 Design Procedure o Structures - Stress Factor Why iteration is needed or the calculation o local scantling? The actual midship section modulus at bottom or deck is needed.

Thereore, the actual section modulus is calculated to be equal to the assumed section modulus by the iteration.

28 7-6-6 Design Procedure o Structures - Stress Factor Why iteration is needed or the calculation o local scantling? The actual midship section modulus at bottom or deck is needed. However, the section modulus can be calculated ater the scantlings o the members are determined. Assumption! Thereore, the actual section modulus is calculated to be equal to the assumed section modulus by the iteration. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 55 Design Procedure o Structures - Stress Factor ) DNV Rules, Pt. 3 Ch. Sec. 6 C8, Jan. 4 Why iteration is needed or the calculation o local scantling? Eample) Inner bottom longitudinals ) inimum longi. stiener section modulus 83lspw k 3 ( cm ) l: Stiener span in m s: Stiener spacing in m p: Design loads w k: Section modulus corrosion actor in tanks, Sec.3 C4 σ db: ean double bottom stress at plate langes, normally not to be taken less than = or cargo holds in general cargo vessel = 5 or holds or ballast = 85 b/b or tanks or liquid cargo Where, 5.7 b : aterial actor as deined in DNV Rules Pt. 3 Ch. Sec. db : Allowable stress o this structural part b,d 5.7( S W ) b, d S : Largest design SWB ) [kn m] W : VWB by class rule or direct calculation in [kn m] ) Largest SWB among all loading conditions and class rule Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh b : stress actor Required midship section modulus [cm 3 ] at bottom or deck Actual midship section modulus [cm 3 ] at bottom or deck as-built The actual midship section modulus at bottom or deck is needed. However, the section modulus can be calculated ater the scantlings o the members are determined. Assumption! Thereore, the actual section modulus is calculated to be equal to the assumed section modulus by the iteration. 56 8

29 7-6-6 () Local Strength & Allowable Stress Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 57 Local Strength & Allowable Stresses - Allowable Stress or Local Strength Deck Relationship between load and stress ) Longitudinal load induced by waves (Hogging or Sagging) BHD BHD Bottom Longitudinal girder local etc Longitudinal ) Cargo load BHD BHD a. 9 a. 5 girder ( db ) a. 45 In the igure above, the meaning o the coeicients o the maimum allowable stresses is as ollows: 45 : aimum Yield Stress 35 : Proportional Limit 3) Ballasting load local BHD Transverse Web BHD 5 : The maimum allowable stress or the local strength uses the value less than the maimum yield stress. In other words, 5 is used or the yield stress, ecept or the other eects. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 58 9

30 7-6-6 Local Strength & Allowable Stresses Longitudinal girder ( db ) local Primary, secondary, and tertiary structure * ansour, A., Liu, D., The Principles o Naval Architecture Series Strength o Ships and Ocean Structures, The Society o Naval Architects and arine Engineers, 8 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 59 Allowable Stresses - Allowable Stress or Local Strength Deck Another interpretation o the igure Eample) Inner bottom longitudinals ) Bottom Longitudinal girder local etc a. 9 a. 5 a. 45 The section modulus requirement is given by: 83 l spwk ( cm 3 ) where, p is the local pressure on bottom structure. The nominal allowable bending stress due to lateral pressure is used ecept or the longitudinal stress and the double bottom stress. 5 b. 7 The longitudinal stress is given by the stress actor. And the double bottom stress is given by: db σ db : ean double bottom stress at plate langes, normally not to be taken less than = or cargo holds in general cargo vessel = 5 or holds or ballast = 85 b/b or tanks or liquid cargo ) DNV Rules, Pt. 3 Ch. Sec. 6 C8, Jan. 4 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 6 3

31 7-6-6 DNV Rules, Pt. 3 Ch. Sec. 6, 7, 8, 9, Jan. 4 Allowable Stresses ( ) l or Bottom Plating, Deck Plating, Bulkhead Plating, Side Plating Strength deck (Pt. 3 Ch. Sec. 8 C) Strength deck N.A. 6 4 CL : material actor Bottom 4 Inner Bottom Plating (Pt. 3 Ch. Sec. 6 C4) 3 Longi. Girder Plating (Pt. 3 Ch. Sec. 6 C5) Bottom Plating (Pt. 3 Ch. Sec. 6 C3) Allowable stress at the neutral ais (N.A.) is largest. And the allowable stress decreases proportionally rom the neutral ais (N.A) to the deck and bottom o the section. Because actual bending stress is smallest at the neutral ais (N.A.), the allowable stress increases proportionally rom N.A to the deck and bottom o the section. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 6 DNV Rules, Pt. 3 Ch. Sec. 6, 7, 8, 9, Jan. 4 Allowable Stresses ( l ) or Longitudinal Stieners N.A. On Decks (Pt. 3 Ch. Sec. 8 C3) 5 3,ma 6 d : Strength deck Longitudinal z z 5 3,ma 6 n a d zn Longitudinal On Inner Bottom (Pt. 3 Ch. Sec. 6 C8) 5.7,ma 6 b db : Continuous decks below strength deck b,d CL Longitudinal On Double Bottom Girders (Pt. 3 Ch. Sec. 6 C9) 5 b, ma 6 On Double Bottom (Pt. 3 Ch. Sec. 6 C7) Longitudinal 3 b.7 db σ db : ean double bottom stress at plate langes, normally not to be taken less than = Longitudinal or cargo holds in general cargo vessel = 5 or holds or ballast 5 5.7( S W ) b, d Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh S : Largest design SWB [kn m] W : Rule VWB in [kn m] b, d : idship section modulus [cm 3 ] at bottom or deck as-built ( b : Pt. 3 Ch. Sec. 6 A) = 85 b/b or tanks or liquid cargo n : vertical distance in [m] rom the base line or deck line to the neutral ais o the hull girder, whichever is relevant a : vertical distance in [m] rom the base line or deck line to the point in question below or above the neutral ais, respectively 6 3

32 7-6-6 Allowable Stresses - Longitudinal Stieners (/6) DNV Rules, Pt. 3 Ch. Sec. 6, 7, 8, 9, Jan. 4 3 cm req. DSE, DNV Rule Commentary Book, l spwk l Calculation o b,d 5.7( S W ) b, d b,d S : Largest design SWB [kn m] W : Rule VWB in [kn m] b,d : idship section modulus [cm 3 ] at bottom or deck as-built N.A.( Longitudinal ) For eample, 3,7 TEU Container Carrier: I.343e cm 4 CL Bottom: Deck: yb B yd D 9.8 e cm.595e cm e cm.345e cm 7 3 b d 5.7( S W).3 b 5.7( S W).4 d Section modulus o bottom is larger than that o deck, and thus the stress actor b is smaller than d. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 63 Allowable Stresses - Longitudinal Stieners (/6) DNV Rules, Pt. 3 Ch. Sec. 6, 7, 8, 9, Jan. 4 DSE, DNV Rule Commentary Book, 99.8 req. 83l spwk l 3 cm Calculation o z a z, z n a n : Vertical distance in [m] rom the base line or deck line to the neutral ais o the hull girder, whichever is relevant z n N.A. ( Longitudinal ) a : Vertical distance in [m] rom the base line or deck line to the point in question below or above the neutral ais z n z a CL b,d 5.7( S W ) b, d S : Largest design SWB [kn m] W : Rule VWB in [kn m] b,d : idship section modulus [cm 3 ] at bottom or deck as-built Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 64 3

33 7-6-6 Allowable Stresses - Longitudinal Stieners (3/6) On Decks (Pt. 3 Ch. Sec. 8 C3) DNV Rules, Pt. 3 Ch. Sec. 6, 7, 8, 9, Jan. 4 DSE, DNV Rule Commentary Book, k zn za l 5 3 d z req. l s p w l n 3 cm Actual.8 Assumption:.8 For eample, 3,7 TEU Container Carrier: Longitudinal d.4 zn za zn.7, za., z l 39.8 [ Pa] n zn za zn.7, za , 3.3 [ ] z l Pa Actual. n N.A. Actual. zn za zn.7, za , z n l [ Pa] 6 [ Pa] (aimum: 6) b,d CL 5.7( S W ) b, d S : Largest design SWB [kn m] W : Rule VWB in [kn m] b,d : idship section modulus [cm 3 ] at bottom or deck as-built n : Vertical distance in m rom the base line or deck line to the neutral ais o the hull girder, whichever is relevant a : Vertical distance in m rom the baseline or deck line to the point in question below or above the neutral ais Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 65 Allowable Stresses - Longitudinal Stieners (4/6) On Decks (Pt. 3 Ch. Sec. 8 C3) 5 3 DNV Rules, Pt. 3 Ch. Sec. 6, 7, 8, 9, Jan. 4 DSE, DNV Rule Commentary Book, 99.8 d zn za z n req. l s p w 83 k l 3 cm b,d CL b, d N.A. 5.7( S W ) S : Largest design SWB [kn m] W : Rule VWB in [kn m] b,d : idship section modulus [cm 3 ] at bottom or deck as-built n : vertical distance in m rom the base line or deck line to the neutral ais o the hull girder, whichever is relevant a : vertical distance in m rom the base line or deck line to the point in question below or above the neutral ais σ db : mean double bottom stress at plate langes, normally not to be taken less than = or cargo holds in general cargo vessel = 5 or holds or ballast = 85 Design Theories b/b or tanks or liquid cargo o Ship and Oshore Plant, Fall 6, yung-il Roh For eample, 3,7 TEU Container Carrier:.8 d.4 zn za zn.7, za., 39.8[ ] z l Pa On Double Bottom (Pt. 3 Ch. Sec. 6 C7) 5 3 b.7 db For eample, 3,7 TEU Container Carrier, Assumption: db =.8 b.3 zn za zn 9.8, za., 54.[ ] z l Pa n Allowable stresses at deck are smaller than those at bottom, because the distance rom N.A to deck is longer than N.A to bottom. I the mean double bottom stress ( db ) is considered as, l 5 3 b.7 db [ Pa] n 66 33

34 7-6-6 Allowable Stresses - Longitudinal Stieners (5/6) DNV Rules, Pt. 3 Ch. Sec. 6, 7, 8, 9, Jan. 4 DSE, DNV Rule Commentary Book, 99.8 req. l s p w 83 k l 3 cm z a On Side Shell (Pt. 3 Ch. Sec. 7 C3) 5 3 zn za z n N.A. ( L ) z n 3 which is lesser. Longitudinal z n z a CL a 3 5 b,d 5.7( S W ) b, d S : Largest design SWB [kn m] W : Rule VWB in [kn m] b,d : idship section modulus [cm 3 ] at bottom or deck as-built n : Vertical distance in m rom the base line or deck line to the neutral ais o the hull girder, whichever is relevant a : Vertical distance in m rom the baseline or deck line to the point in question below or above the neutral ais Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 67 Allowable Stresses - Longitudinal Stieners (6/6) DNV Rules, Pt. 3 Ch. Sec. 6, 7, 8, 9, Jan. 4 DSE, DNV Rule Commentary Book, 99.8 req. l s p w 83 k l 3 cm z a On Longitudinal Bulkhead (Pt. 3 Ch. Sec. 9 C) 5 3 zn za z n ( ) N.A. L z n 6 which is lesser. Longitudinal z n z a CL a 6 5 b,d 5.7( S W ) b, d S : Largest design SWB [kn m] W : Rule VWB in [kn m] b,d : idship section modulus [cm 3 ] at bottom or deck as-built n : Vertical distance in m rom the base line or deck line to the neutral ais o the hull girder, whichever is relevant a : Vertical distance in m rom the baseline or deck line to the point in question below or above the neutral ais Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 68 34

35 7-6-6 (3) Design Loads Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 69 Contents Ship otion and Acceleration Combined Acceleration Design Probability Level Load Point Pressure & Force Sea Pressure Liquid Tank Pressure Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 7 35

36 7-6-6 [Review] Loads in Wave In still water z ( ) ( ) ( ) S b w (): Distributed loads in longitudinal direction S (): Static longitudinal loads in longitudinal direction W (): Hydrodynamic longitudinal loads induced by wave S z S ()= b() w(): Load In wave z Dynamic longitudinal loads : Loads are induced by waves () W Direct calculation o dynamic longitudinal loads z? rom 6DOF motion o ship T XYT,,,,, Re.> 6 DOF motion o ship Yaw Heave T Pitch y O z ( ) ( ) S W b ( ) w ( ) ( ) ( ) ( ) where, D F. K R ( ) ( ) ( ) R a b Roll D (): Diraction orce at R (): Radiation orce at by damping and added mass Design Theories o Ship and Oshore Plant, Fall 6, F.K (): Froude-Krylov orce at yung-il Roh additional loads in wave 7 [Review] 6 DOF Equation o otion o Ship, How to know? By solving equations o motion, we can get the velocities and accelerations. Pressure acting on hull Linearized PFluid ρgz Bernoulli Eq. t I ρgz t Fluid orce acting on hull I D R FFluid PndS ρgz ds ( ) ds S n B S B SB t t t F FF. K FD FR Static t D t R F F.K : Froude-Krylov orce F D : Diraction orce F R : Radiation orce : Incident wave velocity potential I : Diraction wave velocity potential D : Radiation wave velocity potential R A : 66 added mass matri B :66 damping coe. matri C : 66 restoring coe. matri 6 D.O.F equations o motion o a ship in waves Newton s nd Pressure orce acting as surace orce on hull Law F F Body + F Surace F Body orce Surace orce F Gravity F F F F FRestoring Gravity Static F. K D R F F R A B Wave eciting ( F F ) F A B F F Gravity Static Wave eciting Eternal, dynamic Eternal, static Linearization,( F ( F F ) C) Restoring Gravity Static Added mass A B CF F, F, Damping Coeicient Wave eciting Eternal dynamic Eternal static F Eternal Eternal orce ecluding wave eciting orce (e. control orce) Eternal, dynamic Eternal, static By solving equations o motion, we can get the velocities and accelerations o the ship! 7 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh F Fluid F F 36

37 7-6-6 () Ship otion and Acceleration - Empirical Formula o DNV Rule Common Acceleration Parameter Surge Acceleration Combined Sway/Yaw Acceleration Heave Acceleration Tangential Roll Acceleration Tangential Pitch Acceleration a 3C L w C C v v a.ga C b a y.3g a.7 az g Cb a ar Rr T r a p T p g : standard acceleration o gravity =9.8m/s R p Re. 6 DOF motion o ship Yaw Heave T Common Acceleration Parameter, a L CV,maimum. 5 V CV, minimum.8 L DNV Rules, Pt. 3 Ch. Sec. 4, Jan. 4 Pitch O z C W Wave coeicient L y Roll C W L.79 L L 3.75 (3 L)/ 3/ 3 L L ( L 35) /5 3 / Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 73 () Ship otions and Accelerations - Roll Angle & Roll Period DNV Rules, Pt. 3 Ch. Sec. 4, Jan. 4 Roll angle Pitch angle Roll period Pitch period k r =.39B or ships with even transverse distribution o mass =.35B or tankers in ballast =.5B or ships loaded with ore between longitudinal bulkheads G=.7B in general =.B or tankers and bulk carriers g : standard acceleration o gravity =9.8m/s Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 74 37

38 7-6-6 () Combined Acceleration - Combined Vertical Acceleration (a v ) The acceleration along the ship s vertical ais considering combined eect o heave, pitch & roll motion ) k g a v o av C K v Acceleration distribution actor along thelength o vessel.7 between.3land.6lrom A.P. a Common Acceleration Parameter <Section View> LC Design Theories o Ship and Oshore Plant, Fall O6, yz yung-il Roh b z O o a v a ma a a, z Heave C Acceleration 4) b Vertical component o tangential roll acceleration cos a a.7g z ) DNV Rules, Pt. 3 Ch. Sec. 4 B6, Jan. 4 ) DNV Rules, Pt. 3 Ch. Sec. 4 B4, Jan. 4 3) DNV Rules, Pt. 3 Ch. Sec. 4 B4, Jan. 4 4) DNV Rules, Pt. 3 Ch. Sec. 4 B33, Jan. 4 rz a z a pz Vertical component o tangential pitch acceleration rz a r A z cos( t) a T r R A cos( t) TR TR ar Rr a r : tangential roll acceleration A R r : distance in m rom the center o the mass R r Rr to the ais o rotation T y r : angle o center o mass about,o the body ied coordinate system y : roll angle A ) : roll angleamplitude 3) T R : period o roll O yz: Space ied coordinate system g : standard acceleration o gravity : Body ied coordinate system =9.8m/s 75 () Combined Acceleration - Combined Vertical Acceleration (a v ) The acceleration along the ship s vertical ais considering combined eect o heave, pitch & roll motion ) k g a v o av C K v Acceleration distribution actor along thelength o vessel.7 between.3land.6lrom A.P. a Common Acceleration Parameter <Elevation View> b o z z O O ap v a pz a p a ma Heave a a, acceleration 4) Vertical component o tangential roll acceleration a az.7g Cb z cos acceleration A cos( t) T A cos( t) TP TP ap Rr Rp A Rr TP ) DNV Rules, Pt. 3 Ch. Sec. 4 B6, Jan. 4 ) DNV Rules, Pt. 3 Ch. Sec. 4 B4, Jan. 4 3) DNV Rules, Pt. 3 Ch. Sec. 4 B4, Jan. 4 4) DNV Rules, Pt. 3 Ch. Sec. 4 B33, Jan. 4 rz a z P a pz Vertical component o tangential pitch O yz: Space ied coordinate system O yz : Body ied coordinate system Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh a P : tangential pitch acceleration A ) : pitch angleamplitude) : pitch angle 3) T P : period o pitch R P : distance in m rom the center o the mass to the ais o rotation : angle o center o mass about the body ied coordinate system 76 38

39 7-6-6 () Combined Acceleration - Combined Transverse Acceleration (a t ) The acceleration along the ship s transverse ais considering combined eect o sway, yaw & roll motion ) Combined sway & yaw acceleration a. g a y 3 a a g sin a t y o ry ) DNV Rules, Pt. 3 Ch. Sec. 4 B7, Jan. 4 Transverse component o the tangential roll acceleration Transverse component o acceleration o gravity by roll angle <Section View> z z ar a a sin ry r A ar Rr Tr : tangential roll acceleration a r R r : distance in m rom the center o the mass to the ais o rotation : roll angle g LC Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh R r sin g y y A : roll angleamplitude 3) T R : period o roll g : standard acceleration o gravity =9.8m/s O yz: Space ied coordinate system O yz : Body ied coordinate system 77 () Combined Acceleration - Combined Longitudinal Acceleration (a l ) The acceleration along the ship s longitudinal ais considering combined eect o surge & pitch motion ) a a g sin a l o p ) DNV Rules, Pt. 3 Ch. Sec. 4 B8, Jan. 4 Surge acceleration a.ga C b Longitudinal component o the pitch acceleration Longitudinal component o gravitational acceleration by pitch angle <Elevation View> z z a py a p a pz A ap Rr TP O yz: Space ied coordinate system O yz : Body ied coordinate system Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh g sin g : tangential pitch acceleration a P R P : distance in m rom the center o the mass to the ais o rotation : pitch angle A ) : pitch angleamplitude 3) T P : period o pitch g : standard acceleration o gravity =9.8m/s 78 39

40 7-6-6 () Combined Acceleration - [Eample] Vertical Acceleration (Eample) Calculate the vertical acceleration o a given ship at.5l (amidships) by DNV Rule. [Dimension] L s =35.79 m, V=5.5 knots, C B =.83 k g a v o av C b o K Acceleration distribution actor along the length o vessel a v.7 between.3l and.6l rom A.P. Common Acceleration Parameter g Standard acceleration o gravity (=9.8m/sec ) (Sol.) a k g a C v v B / / m / sec where, kv.7 at mid ship a 3 CW / LCvCv 3.75/ Cv L / / or a.. =..5.5 Cv V / L =5.5/ =.87 or in..8 =.87 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 79 (3) Design Probability Level ) DNV, Fatigue Assessment o Ship Structures, p.8, 3 Probability Level ) d Etreme values Once 5 years Once a day N Q Hull girder strength Buckling strength Local scantlings Fatigue strength Local strength o container supports Design Probability Level ) Number o waves that the ship eperiences during the ship s lie (or 5 years): about 8 The ship is designed to endure the etreme wave ( -8 probability) which the ship encounters once or 5 years. (Etreme condition: Ship motion, acceleration is given as etreme value.) In case o design pressure, use the reduced value o -4 (Reduction value =.5 Etreme value) E) Liquid Tank Pressure: Pressure, P, considering vertical acceleration p g.5a o v s h log n Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 8 4

41 7-6-6 (4) Load Point - Horizontally Stiened Plate DNV Rules, Pt. 3 Ch. Sec. 4 A, Jan. 4 p g hs b H bt.67. o T L GR L L3 SP SP SP 3 s The pressure at the load point is considered as uniorm load o unit strip Deinition o load point. General : idpoint o stiened plate ield. Seam & butt (In case two plates are welded) ) When considered plate includes the midpoint o stiened plate ield : idpoint o stiened plate ield ) When considered plate does not include the midpoint o stiened plate ield : Nearest seam or butt line rom midpoint Load point o sea pressure acting on the side plate L GR L SP L4 Unit strip L3 SP L5 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh s : longi.spacing L4 L5 SP 3 : Load point 8 (4) Load Point - Longitudinal Stieners (/) DNV Rules, Pt. 3 Ch. Sec. 4 A, Jan. 4 T The pressure at the load point is considered as uniorm load Deinition o load point. In vertical direction : The point o intersection between a plate and a stiener L GR L SP l SP s. In longitudinal direction : idpoint o span Load point o sea pressure acting on the side plate - In vertical direction GR L L L3 SP 3 L3 L4 L5 s : longi.spacing l : longi.span L4 L5 : Load point Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 8 4

42 7-6-6 (4) Load Point - Longitudinal Stieners (/) GR L L L3 L4 SP Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh T p3 g.67 hs l. H lt o * Pressure distribution can be changed in longitudinal direction l SP SP 3 s : longi.spacing l : longi.span s Deinition o load point. In vertical direction : The point o intersection between a plate and a stiener. In longitudinal direction : idpoint o span L DNV Rules, Pt. 3 Ch. Sec. 4 A, Jan. 4 The pressure at the load point is considered as uniorm load Load point o sea pressure acting on the side plate - In longitudinal direction l l s : Load point 83 (5) Pressure and Force - Sea Pressure DNV Rules, Pt. 3 Ch. Sec. 4 C, Jan. 4 Sea pressures = Static sea pressure + Dynamic sea pressure P P s P d H : Always positive h h T T T P s gh h Static Sea Pressure Pd p dp Dynamic Sea Pressure Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 84 4

43 7-6-6 (5) Pressure and Force - Liquid Tank Pressure (/7) DNV Rules, Pt. 3 Ch. Sec. 4 C3, Jan. 4 The pressure in ull tanks shall be taken as the greater o p ~ p 5 ) p go.5av hs p g o.67 hs b. H bt p3 g h l H l p g h P 4 5 o.67 s. t.67 o p dyn p g h p o s o P : Considering vertical acceleration P : Considering rolling motion P 3 : Considering pitching motion P 4 : Considering overlow P 5 : Considering tank test pressure aimum pressure is dierent depending on locations (3) () (3) ( ) () (3) (5) () (5) a v : Vertical acceleration : Roll angle b : The largest athwart ship distance in [m] orm the load point to the tank corner at top o tank bt & l : Breadth and length in [m] o t top o tank : Density o liquid cargo h s : Vertical distance rom the load point to tank top in tank h p : Vertical distance rom the load point to the top o air pipe p : 5 kn/m general : Calculated pressure drop p dyn (5) (5) (5) (5) ( ) () () (4) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 85 (5) Pressure and Force - Liquid Tank Pressure (/7) p go.5av hs p go.67hs b. H bt p3 go.67hs l. H lt p4.67 g h P o p dyn p g h p 5 o s o P : Considering vertical acceleration P : Considering rolling motion P 3 : Considering pitching motion P 4 : Considering overlow P 5 : Considering tank test pressure Design pressure P considering vertical acceleration (General) P ghs. 5a h v s Static Pressure Dynamic Pressure h s Reduced value o -4 by probability level is used. (Reduction value=.5 Etreme value) p ( g.5a ) h v s a v : Vertical acceleration h s : virtical distancein m rom load point to top o tank Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 86 43

44 7-6-6 (5) Pressure and Force - Liquid Tank Pressure (3/7) p go.5av hs p go.67hs b. H bt p3 go.67hs l. H lt p4.67 g h P o p dyn p g h p 5 o s o P : Considering vertical acceleration P : Considering rolling motion P 3 : Considering pitching motion P 4 : Considering overlow P 5 : Considering tank test pressure Design pressure P considering vertical acceleration (In case o side shell) In case o side shell, the eect o sea pressure is considered. P ghs.5avhs hb hs T Static Pressure Dynamic Pressure Sea Pressure T h b When we consider the design pressure, the largest value shall be applied. The liquid cargo pressure acting on the side shell is the highest when the sea pressure is the lowest, i.e. in case o minimum drat. p ( g.5a ) h h v s b h b : vertical distance in m rom load point to minimum design drat = +.L or Tanker =.35 T or Dry Cargo (T: Rule Drat) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 87 (5) Pressure and Force - Liquid Tank Pressure (4/7) p go.5av hs p go.67hs b. H bt p3 go.67hs l. H lt p4.67 g h P o p dyn p g h p 5 o s o P : Considering vertical acceleration P : Considering rolling motion P 3 : Considering pitching motion P 4 : Considering overlow P 5 : Considering tank test pressure Design pressure P considering vertical acceleration (In case o bottom shell) In case o bottom shell, the eect o sea pressure is considered P gh.5ah T s v s h s Static Pressure Dynamic Pressure Sea Pressure h s T When we consider the design pressure, the largest value shall be applied. The liquid cargo pressure acting on the bottom shell is the highest when the sea pressure is the lowest, i.e. in case o minimum drat. p ( g.5a ) h T T : vertical distance in m rom load point to minimum design drat v s = +.L or Tanker =.35 T or Dry Cargo (T: Rule Drat) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 88 44

45 7-6-6 (5) Pressure and Force - Eample) Calculation o P Pressure (Eample) When the tank is illed up, calculate the P pressure o inner bottom and deck by using vertical acceleration (a v =.86 m/s ) and dimensions o tank which is given below. [Dimension] Inner bottom height: 3. m, Deck height: 3.m, ρ =.5 ton/m 3 (Sol.) P g.5a v h s a.86 m/s v Inner Bottom 3 density ton/m a Vertical acceleration hs m P g.5av hs kn / m v g Standard acceleration o gravity (=9.8m/sec ) h s : virtical distancein m romload point to topo tank Deck hs DNV Rules, Pt. 3 Ch. Sec. 4 B8, Jan m P g.5av hs kn / m Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 89 (5) Pressure and Force - Liquid Tank Pressure (5/7) Design pressure P considering the rolling motion h s b p Air pipe Load point h h h s g [.67( h p go.5av hs p go.67hs b. H bt p3 go.67hs l. H lt p4.67 g h P o p dyn p g h p When the ship is rolling, the higher static pressure is applied. h h s cos h s h bsin b h s h h h b b). s Hb ] s t 5 o s o Assumption: << P : Considering vertical acceleration P : Considering rolling motion P 3 : Considering pitching motion P 4 : Considering overlow P 5 : Considering tank test pressure DSE, 선박구조설계 5-3 DNV Rules, Pt. 3 Ch. Sec. 4, Jan. 4 H: Height in m o the tank b t : Breadth in m o top o tank Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh In case o rolling o a ship, two third (=.67) o actual pressure is applied considering pressure drop by overlow. The illing ratio o the most tank is about 98%. That (about %) is considered. 9 45

46 7-6-6 (5) Pressure and Force - Liquid Tank Pressure (6/7) Design pressure P 4 considering the tank overlow p go.5av hs p go.67hs b. H bt p3 go.67hs l. H lt p4.67 g h P o p dyn p g h p 5 o s o P : Considering vertical acceleration P : Considering rolling motion P 3 : Considering pitching motion P 4 : Considering overlow P 5 : Considering tank test pressure DSE, 선박구조설계 5-3 DNV Rules, Pt. 3 Ch. Sec. 4, Jan. 4 Air pipe h s h p Load point The liquid o tank is illed up to air pipe in case o tank overlow. So, h p is used or calculating static pressure. verticaldistancein m rom the load point h p to the top o air pipe b p g h P.67 p dyn Calculated pressure drop Generally, 5kN/m In case o rolling o a ship, two third (=.67) o actual pressure is applied considering pressure drop by overlow. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 9 (5) Pressure and Force - Liquid Tank Pressure (7/7) p go.5av hs p go.67hs b. H bt p3 go.67hs l. H lt p4.67 g h P o p dyn p g h p Design pressure P 5 considering the tank test pressure 5 o s o P : Considering vertical acceleration P : Considering rolling motion P 3 : Considering pitching motion P 4 : Considering overlow P 5 : Considering tank test pressure DSE, 선박구조설계 5-3 DNV Rules, Pt. 3 Ch. Sec. 4, Jan. 4 h s T Over-pressure is applied in order to have the water head o tank height +.5 [m] in case o tank test or leakage. (Water head o over-pressure o tank test:.5m) p g h p s o T p o g.5.5 5kN / m Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 9 46

47 7-6-6 (4) Scantling o Plates Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 93 Scantling o Plates (/3) Use o eccentric beam element (a) Beams attached to plating (b) Structural model using eccentric beam element Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 94 47

7-6-6 Scantling o Plates (/3) p : pressure on the load point or the stiener idship Secton Longitudinals Side Girder Web Frame Bottom plate Unit Strip plate S S Bottom plate Design Theories o Ship and

48 7-6-6 Scantling o Plates (/3) p : pressure on the load point or the stiener idship Secton Longitudinals Side Girder Web Frame Bottom plate Unit Strip plate S S Bottom plate Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 95 Scantling o Plates (3/3) idship Secton Side Girder Longitudinals Web Frame Bottom plate Unit Strip plate S Unit Strip plate Longitudinals y p : pressure on the load point or the stiener s : Longitudinals span Bottom plate s t t : Plate thickness N.A. : Neutral Ais t N.A. Bottom plate ied p ied Assumption. Cut o the unit strip plate supported by the longitudinals or girder. And consider the unit strip plate as a ied-end beam which has a span s, thickness t. Assumption. Consider the lateral load o the beam as a uniormly distributed load. (Assume the pressure on the load point as an intensity o uniormly distributed load.) Assumption 3. The design o plates is based on the plastic design. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 96 48

49 7-6-6 Comparison between Stiener and Plate p : pressure on the load point or the stiener T l s s Unit strip s : Stiener spacing l: Stiener span s : Stiener spacing Longitudinal stiener attached to the plate l t : Stiener span s : Stiener spacing Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh l s ps l Unit strip plate Longitudinals Bottom plate s : Stiener spacing : Unit length o strip s t N.A.: Neutral Ais t N.A. P ps 6 97 Comparison o the Elastic and Plastic Design o the Plate -Overview Fleure ormula I/ y Substituting ormula: 5.8ka s p treq. tk ( mm) l Plastic Design Plastic moment ( p ) p s p 6 Plastic section modulus ( p ) t t p 4 4 p ps s p ps s p, t, t p 4t t assumption: l assumption: l ka correction actor or aspect ratio o plate ield.4 ka s p treq. tk ( mm) tk Substituting ormula: corrosion addition l Elastic Design Elastic moment () p s Elastic section modulus () t t 6 6 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 98 49

50 7-6-6 Comparison o the Elastic and Plastic Design - [Eample] Thickness Requirements Plastic moment ( p ) p ps 6 Plastic section modulus ( p ) p t 4 t 4 Elastic moment () p s Elastic section modulus () t t 6 6 A mild steel plate carries the uniorm pressure o kn/m on a span length o 8 mm. Compare the thickness requirement depending on the plastic design and elastic design. 5.8ks a p.4ks t t a req. req. plastic l elastic mm.69 mm The thickness requirement o the plate o plastic design is smaller than that o the elastic design at the same pressure and on the same span. correction actor or aspect ratio o plate ield k a l p Longitudinals Bottom plate P s L V / L / L L t t Vma ps p ps 6 p ps 6 N.A. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 99 Comparison o the Elastic and Plastic Design - [Eample] Design Pressure Plastic moment ( p ) p ps 6 Plastic section modulus ( p ) p t 4 t 4 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh Elastic moment () p s Elastic section modulus () t t 6 6 Longitudinals Bottom plate V A mild steel plate has a thickness o mm on a span p ps L 6 length o 8 mm. L / p ps Compare the design pressure that the maimum stresses o 6 the plate reaches the yield stress depending on the plastic design and elastic design. t l t l pplastic p elastic 5.8 s.4 s [ kn / m ] 73 [ kn / m ] The design pressure o plastic design that reaches the yield stress, is higher than that o the elastic design on the same span with the same thickness. P s L / L t t Vma ps N.A. 5

7-6-6 (5) Scantling o Stieners Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh Scantling o Stieners (/3) p : pressure on the load point or the stiener Longitudinals Side Girder Web Frame

51 7-6-6 (5) Scantling o Stieners Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh Scantling o Stieners (/3) p : pressure on the load point or the stiener Longitudinals Side Girder Web Frame Bottom plate s : longi.spacing l : longi.span l s b e b e : eective breadth * Okumoto, Y., Takeda, Y., ano,., Design o Ship Hull Structures - a Practical Guide or Engineers, Springer, pp. 7-3, 9 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 5

7-6-6 Scantling o Stieners (/3) p : pressure on the load point or the stiener Longitudinals Side Girder Web Frame t l s Bottom plate s : longi.spacing l : longi.

Sectional properties o stiener are calculated including attached plate. Assumption. Consider the stiener and attached plate as a ied-end beam supported by the web rames. Assumption 3.

52 7-6-6 Scantling o Stieners (/3) p : pressure on the load point or the stiener Longitudinals Side Girder Web Frame t l s Bottom plate s : longi.spacing l : longi.span Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh l s Assumption. Cut o the stiener and attached plate with eective breadth. Sectional properties o stiener are calculated including attached plate. Assumption. Consider the stiener and attached plate as a ied-end beam supported by the web rames. Assumption 3. Consider the lateral load o the beam as a uniormly distributed load. (Assume the pressure on the load point as an intensity o uniormly distributed load.) Assumption 4. The design o stiener is based on the elastic design (when the load is removed, the material returns to its original dimensions) p L V L / / Vma psl L psl L 4 ma psl 3 Scantling o Stieners (3/3) p : pressure on the load point or the stiener Longitudinals Side Girder t s Web Frame l Bottom plate s : longi.spacing l : longi.span Shear orce wl wl L/ l s L P L / V L / Bending moment wl 4 L/ Vma psl L psl L 4 ma psl L wl Relation between p s and w p: pressure (load per unit area) p s: distributed load (load per unit length) = w: distributed load (load per unit length) wl w p s L l psl Same! Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 4 5

53 7-6-6 (6) Sectional Properties o Steel Sections Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 5 Sectional Properties o Steel Sections or Ship Building ) (/) <Sectional properties o steel sections including attached plate> (Base plate dimension : b p t p = 4 8) b p t p b p = breadth o plate (mm) t w t p = thickness o plate (mm) d t w d A I A I A I A I A I A I A I t w A = Area including plate(cm ) = Section modulus including plate (cm 3 ) I = oment o inertia o area including plate(cm 4 ) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh d A I A I A I A I A I A I A I A = 4*.8 + 5*.4 = [cm ] Top = [cm 3 ] Bottom = 97. [cm 3 ] ) 조선설계편람, 제 4 판 ( 일본어 ), 일본관서조선협회,

54 7-6-6 Sectional Properties o Steel Sections or Ship Building ) (/) <Sectional properties o steel sections including attached plate> - Use the standard dimension o plate depending on a (b p t p ) => (a 75 : 4 8, 75<a<5 : 6, 5 a : 6 5) Dimension Area Including plate Symbol a b t t r r A I Unit mm cm cm 4 cm 3 Equal angle ) 조선설계편람, 제 4 판 ( 일본어 ), 일본관서조선협회, t p b p Unequal angle Design Theories o Ship and Oshore Plant, Fall 56, yung-il 9 Roh Sectional Properties o Steel Sections or Ship Building ) (3/) Dimension Area Including plate Symbol a b t t r r A I Unit mm cm cm 4 cm 3 Unequal angle Channels Bulb lats Design Theories o Ship and Oshore 5Plant, Fall 456, yung-il Roh ) 조선설계편람, 제 4 판 ( 일본어 ), 일본관서조선협회, 996 <Sectional properties o steel sections including attached plate> - Use the standard dimension o plate depending on a (b p t p ) => (a 75 : 4 8, 75<a<5 : 6, 5 a : 6 5) t p b e t p b e t p b e 8 54

modulus including plate (cm 3 ) I: oment o inertia including plate (cm 4 ) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 9 Sectional

55 7-6-6 Sectional Properties o Steel Sections or Ship Building ) (4/) <Sectional properties o steel sections including attached plate> (Base plate dimension: b p t p = 6 5) ) 조선설계편람, 제 4 판 ( 일본어 ), 일본관서조선협회, 996 Unit: mm A : Sectional area (cm ) A: Sectional area including plate (cm ) : Section modulus including plate (cm 3 ) I: oment o inertia including plate (cm 4 ) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 9 Sectional Properties o Steel Sections or Ship Building ) (5/) ) 조선설계편람, 제 4 판 ( 일본어 ), 일본관서조선협회, 996 Section shape A I e P Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 55

56 7-6-6 Sectional Properties o Steel Sections or Ship Building ) (6/) ) 조선설계편람, 제 4 판 ( 일본어 ), 일본관서조선협회, 996 Section shape A I e P Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh Sectional Properties o Steel Sections or Ship Building ) (7/) ) 조선설계편람, 제 4 판 ( 일본어 ), 일본관서조선협회, 996 Section shape A I e P Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 56

57 7-6-6 Sectional Properties o Steel Sections or Ship Building ) (8/) ) 조선설계편람, 제 4 판 ( 일본어 ), 일본관서조선협회, 996 Section shape A I e P Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 3 Sectional Properties o Steel Sections or Ship Building ) (9/) ) 조선설계편람, 제 4 판 ( 일본어 ), 일본관서조선협회, 996 Section shape A I e P Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 4 57

58 7-6-6 Sectional Properties o Steel Sections or Ship Building ) (/) ) 조선설계편람, 제 4 판 ( 일본어 ), 일본관서조선협회, 996 Section shape A I e P Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 5 Sectional Properties o Steel Sections or Ship Building ) (/) ) 조선설계편람, 제 4 판 ( 일본어 ), 일본관서조선협회, 996 Section shape and distribution o shear orce Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 6 58

59 7-6-6 Sectional Properties o Steel Sections or Ship Building ) (/) ) 조선설계편람, 제 4 판 ( 일본어 ), 일본관서조선협회, 996 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh Buckling Strength () Column Buckling () Buckling Strength o Stiener (3) Buckling Strength o Plate (4) Buckling Strength by DNV Rule (5) Buckling Strength o Stiener by DNV Rule (6) Buckling Strength o Plate by DNV Rule Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 8 59

60 7-6-6 Buckling James. Gere, echanics o aterials 6 th Edition, Thomson, pp Rules or classiication o ships, Det Norske Veritas, January 4, Pt. 3 Ch. Sec. 3 Deinition: The phenomenon where lateral delection may arise in the athwart direction* against the aial working load * 선측 ( 船側 ) 에서선측으로선체를가로지르는 This section covers buckling control or plate and longitudinal stiener. Fleural buckling o stieners plus plating Plate alone buckles between stieners * ansour, A., Liu, D., The Principles o Naval Architecture Series Strength o Ships and Ocean Structures, The Society o Naval Architects and arine Engineers, 8 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 9 () Column Buckling - The Equation o the Delection Curve Dierential equation or column buckling: Using the notation k, y k y EI General solution o the equation: P y C sin kc cos k Boundary conditions: y( ) C y(), y( l) yl () CsinkL ) I C =, y = (trivial solution). ) I sinkl =, (sinkl =: buckling equation) James. Gere, echanics o aterials 6 th Edition, Thomson, pp. 748~76 EIy Py Ikl =, y = (trivial solution). n Ikl = nπ (n=,, 3) or P EI, it is nontrivial solution. l E = modulus o elasticity n y Csin kcsin, n,,3... L y P B A L y P k EI P B A y, n k l I = nd moment o the section area EI = leural rigidity P = aial load v = delection o column L = length o column y A P y Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 6

61 7-6-6 [Eample] ode Shapes o a Cantilevered I-beam Lateral bending (st mode) Torsional bending (st mode) Vertical bending (st mode) Lateral bending (nd mode) Torsional bending (nd mode) Vertical bending (nd mode) * Reerence: Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh () Column Buckling - Critical Stress James. Gere, echanics o aterials 6th Edition, Thomson, pp. 748~76 Dierential equation or column buckling : The equation o the delection curve : The critical loads : y C sin EIy Py nπ, n,, 3... L P P B B y A P y y L n P k EI EI L The lowest critical load (n=) : P n k,k EI l y A y A EI Pcr EI L L The corresponding critical stress : cr Pcr EI A AL Euler s ormula Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh E = modulus o elasticity I = nd moment o area EI = leural rigidity P = aial load v = delection o column A = area o column L = length o column 6

62 7-6-6 () Column Buckling -Critical Load James. Gere, echanics o aterials 6 th Edition, Thomson, pp. 748~76 Dierential equation or column buckling : The equation o the delection curve : y () C sin( n / L) n y y, y(), yl ( ), where P / EI P L The critical loads : Pn n EI L n /,,,3... L y The lowest critical load (n=) : Pcr P EI/ L E = modulus o elasticity I = nd moment o area EI = leural rigidity P = aial load y = delection o column A = area o column L = length o column Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 3 () Column Buckling - Critical Buckling Stress A critical buckling stress is oten used instead o a buckling load and it can be derived by dividing P cr by A, the cross sectional area o the column. Euler s ormula E = modulus o elasticity P I = cr cr nd moment o area The corresponding critical stress : EI = leural rigidity A P = aial load EI y = delection o column A =area o column Al l = length o column k E l, where kk I / A is the radius o gyration ) o the section o the column. The ratio (l/k), oten called the slenderness ratio, is the main actor which governs the critical stress For large value o l/k the critical stress tends toward zero, and at small values o l/k it tends to ininity. In Euler s ormula, the buckling stress may become ininite or a small value o l/k, however, buckling stress never goes up above the yield stress o the material in actual conditions, because the material would ail i the stress eceeded the yield stress. ) The radius o gyration describes a circular ring whose area is the same as the area o interest. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 4 6

63 7-6-6 () Column Buckling - Curve o Buckling Stress by theoretical consideration, a horizontal line o yield stress connected to Euler buckling stress is speciied as an upper limit o Euler s buckling curve. l cr ab k l cr ab k a cr bl / k Tetmayer s ormula Johnson s ormula Rankine s ormula For eample, one o the Classiication Societies, ABS (American Bureau o Shipping) speciies the permissible load o a pillar or strut o mild steel material in the ollowing equation: l cr.3.45 [ ton / cm ] k From the above equation, we can see that the ABS ormula is theoretically based on Tetmayer s eperimental result. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 5 () Column Buckling - Buckling o Thin Vertical Column Embedded at Its Base and Free at Its Top (/) Suppose that a tin vertical homogeneous column is embedded at its base (=) and ree at its top (=L) and that a constant aial load P is applied to its ree end. The load either causes a small delection, or does not cause such a delection. In either case the dierential equation or the delection y() is d y d y EI P y EI Py P () d d P P y () What is the predicted delection when? L - The general solution o the dierential equation () is P P y ccos csin EI EI L - The boundary conditions o the dierential equation () are y() y'() - I, this implies that c c and y ( ). That is, there is no delection. * ill, D.G., Advanced Engineering athematics, 3rd edition, pp.66-74, 6 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 6 63

64 7-6-6 () Column Buckling - Buckling o Thin Vertical Column Embedded at Its Base and Free at Its Top (/) Suppose that a tin vertical homogeneous column is embedded at its base (=) and ree at its top (=L) and that a constant aial load P is applied to its ree end. The load either causes a small delection, or does not cause such a delection. In either case the dierential equation or the delection y() is d y d y EI P y d () When, show that the Euler load or this column is one-ourth o the Euler load or the hinged column? - I, the boundary conditions give, in turn, c, c. Then P y cos EI - In order to satisy the boundary condition yl ( ), we must have P cos L EI Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh EI Py P () d P cos L P EI L n EI - The smallest value o Pn, the Euler load, is then P L or P * ill, D.G., Advanced Engineering athematics, 3rd edition, pp.66-74, 6 EI 4 L L P P y EI L Euler load One-ourth o the Euler load 7 () Buckling Strength o Stiener P Longitudinals Side Girder Web Frame Bottom plate s : longi.spacing l : longi.span l s It is assumed that the stiener is a ied-end column supported by the web rames. Hull girder bending moment is acting on the cross section o the ship as moment rom the point view o global deormation. And it is acting on the each stiener as aial load rom the point view o local deormation. y what is our interest? The actual compressive stress ( a ) shall not be great than the critical Saety: buckling stress ( cr ) Won t it ail under the, where a load? a cr I. y NA, ( y) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 8 64

65 7-6-6 (3) Buckling Strength o Plate (/7) Longitudinals Side Girder Web Frame Web Frame Longitudinals Bottom plate s : longi.spacing l : longi.span l s y thickness : t A ship hull is a stiened-plate structure, the plating supported by a system o transverse or longitudinal stieners. For practical design purpose, it is oten assumed that the plate is simply supported at the all edges, since it gives the least critical stress and is on the sae side. a b Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 9 (3) Buckling Strength o Plate (/7) Let us consider the rectangular plate with only supported edges as shown in this igure. y thickness : t a The equation o elastic buckling stress o the plate under uni-aial compressive stress: Et w w w w t 4 4 () ( v ) y y b σ : the uni-aial compressive stress ν : Poisson's ratio E : odulus o elasticity a : plate length b : plate width t : thickness o the plate where, w w(, y) : delection o the plate * Okumoto, Y., Design o Ship Hull Structures, pp.57-6, 9 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 3 65

66 7-6-6 (3) Buckling Strength o Plate (3/7) The equation o elastic buckling stress o the plate under uni-aial compressive stress: Et w w w w t 4 4 ( v ) y y () y thickness : t where, w w(, y) : delection o the plate a b σ : the uni-aial compressive stress ν : Poisson's ratio E : odulus o elasticity a: plate length b : plate width t : thickness o the plate Because all our edges are simply supported, the boundary condition can be epressed in the orm: w(, y) w( a, y) deormation at the edges are zero w (,) wb (, ) Let us assume the ollowing ormula or the solution o the equation (), so that the solution satisies the boundary conditions. m n y w sin sin () a b where, m, n are integers presenting the number o hal-wave o buckles. * Okumoto, Y., Design o Ship Hull Structures, pp.57-6, 9 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 3 (3) Buckling Strength o Plate (4/7) The equation o elastic buckling stress o the plate under uni-aial compressive stress: Et w w w w t 4 4 () ( v ) y y Substituting the ormula () into the equation (), m n y w sin sin () a b y thickness : t where, w w(, y) : delection o the plate a b σ : the uni-aial compressive stress ν : Poisson's ratio E : odulus o elasticity a : plate length b : plate width t : thickness o the plate 3 Et m n ( v ) b t m (3) a where, b Elastic buckling stress is a minimum critical stress, thereore, we put n= in the equation (3), Ideal elastic (Euler) compressive buckling stress: E t el K ( v ) b * Okumoto, Y., Design o Ship Hull Structures, pp.57-6, 9 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh m where, K inimum value o k, k m 3 66

67 7-6-6 (3) Buckling Strength o Plate (5/7) Ideal elastic (Euler) compressive buckling stress: E t where, K inimum value o k el K m ( v ) b k, m a b y thickness : t a b σ : the uni-aial compressive stress ν : Poisson's ratio E : odulus o elasticity a : plate length b : plate width t : thickness o the plate For the small b in comparison with t, the elastic buckling stress becomes more than the yield stress o the plate material. Thereore, it is usual to use Johnson s modiication actor p and the critical buckling stress or the ull range o value o t/b as ollows: c Bryan s ormula ) c E t el K b p Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh y,when el p y y y p,when el el 4 el σ y = upper yield stress in [N/mm ] σ c : the critical compressive buckling stress σ el : the ideal elastic(euler) compressive buckling stress K : plate actor (corresponding to the boundary conditions and a/b) η p : plasticity reduction actor e) Coeicient K when all our edges are simply supported K 4. a/ b. K a/ bb/ a, a/ b. ) DSE, 선박구조설계 3-8 Buckling, (3) Buckling Strength o Plate (6/7) - Buckling Strength o Web Plate Web plate o stiener have to be checked about buckling. In case o T-bar, it is assumed that the web plate o stiener is the plate simply supported by lange and attached plate. E t d c el K p d t w EK v, (Bryan s ormula), K = 4. el ) DSE, Ship Structural Design, 3-8 Buckling, 5.8 t w lange d web plate attached plate σ cr : the critical compressive buckling stress σ el : the ideal elastic(euler) compressive buckling stress ν : Poisson s ratio K : Plate actor (corresponding to the boundary conditions and a/b) d : depth o web plate t : thickness o web plate E : odulus o elasticity Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 34 67

68 7-6-6 (3) Buckling Strength o Plate (7/7) - Buckling Strength o Flange Plate Flange o stiener have to be checked about buckling. It is assumed that the lange o stiener is the rectangular plate simply supported on one end by web plate. c el K p E t b b K E t v, (Bryan s ormula), K =.5 el ) DSE, Ship Structural Design, 3-8 Buckling, 5.8 b lange t web plate attached plate In general, b/t does not eceed 5. σ c : the critical compressive buckling stress σ el : the ideal elastic(euler) compressive buckling stress ν : Poisson s ratio K : Plate actor (corresponding to the boundary conditions and a/b) b : breadth o lange plate t : thickness o lange plate E : odulus o elasticity Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 35 (4) Buckling Strength by DNV Rule Criteria or buckling strength a c ) Rules or Classiication o Ships, DNV, Pt. 3 Ch. Sec. 3, pp.9~93, January 4 σ c = critical buckling stress in N/mm σ a = calculated actual stress in N/mm η = usage actor Critical buckling stress σ c Calculated actual stress σ a σ is yield stress o material in N/mm c el, when el ( ),when el 4 el σ a is calculated actual stress in general In plate panels subject to longitudinal stress, σ a is given by s w z z N mm 5, / a n a I NA.. minimum 3 N/mm at side y <idship section> Upper Deck y i N.A.,( y) y i B.L. σ el or Plate in uni-aial compression ) Plate t tk el.9 ke( ) s Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh σ el or stiener in uni-aial compression ) el tw tk 3.8 E ( ) h Stiener σ el or stiener in lateral buckling mode I el.e Al A W consider each dierent stress according to location S : still water bending moment as given in Sec. 5 W : wave bending moment as given in Sec. 5 I NA : moment o inertia in cm 4 o the hull girder σ el : ideal compressive buckling stress σ el is determined according to speciic load. σ c : critical buckling stress σ : upper yield stress in [N/mm ] t : thickness in [mm] t k : corrosion addition t w : web thickness, h w : web height E : modulus o elasticity s : stiener spacing in [m] I A : moment o inertia in [cm 4 ] about the ais perpendicular to the epected direction o buckling A : cross-sectional area in [cm ] l : length o member in [m] 36 68

69 7-6-6 (5) Buckling Strength o Stiener by DNV Rule - Stiener in Uni-aial Compression (/) Criteria or Buckling Strength (in the same way o plate) a c ) Rules or Classiication o Ships, DNV, Pt. 3 Ch. Sec. 3, pp.9~93, January 4 σ c : critical buckling stress in [N/mm ] σ a : calculated actual compressive stress in [N/mm ] η : usage actor Usage Factor () =. Deck, Single bottom & Side shell (long sti) =.9 Bottom, Inner bottom & Side shell (trans sti) =. Etreme loads (Q = -8 ) =.8 Normal loads (Q = -4 ) Critical buckling stress σ c c el, when el ( ),when el 4 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh el σ el : ideal compressive buckling stress σ el is determined according to speciic load. σ : yield stress o material in N/mm Calculated actual stress σ a (Uni-aial compression) σ a is calculated actual compressive stress in general In plate panels subject to longitudinal stress, σ a is given by s w z z N mm 5, / a n a I NA.. minimum 3 N/mm at side ( Hull girder bending moment is acting on the cross section o the ship as moment rom the point view o global deormation. And it is acting on the each stiener as aial load rom the point view o local deormation.) S = still water bending moment as given in Sec. 5 W = wave bending moment as given in Sec. 5 I N = moment o inertia in cm 4 o the hull girder 37 (5) Buckling Strength o Stiener by DNV Rule - Stiener in Uni-aial Compression (/) Critical buckling stress σ c c el, when el ( ),when el 4 el σ el is determined according to speciic load. ) Rules or Classiication o Ships, DNV, Pt. 3 Ch. Sec. 3, pp.9~93, January 4 σ : yield stress o material in [N/mm ] Ideal compressive buckling stress σ el o stiener in uni-aial compression ) tw tk el 3.8 E ( ) h W Derivation o the coeicient 3.8 cr E t From Bryan s ormula e, K b.938(. 9) And substituting K=4(or simply supported plate), the coeicient is approimately equal to 3.8. σ el : ideal compressive buckling stress σ c : critical buckling stress σ s : minimum upper yield stress t w : web thickness, h w : web height E : modulus o elasticity s : stiener spacing (m) Design Theories ν : o.3 Ship (Poisson's and Oshore ratio Plant, o steel) Fall 6, yung-il Roh Ideal compressive buckling stress σ el o stiener in lateral buckling mode I el. E A l A Derivation o the coeicient. 4 EI N / mm cm From Euler s ormula cr, Al cm m 4 4 N / mm cm N / mm ( mm) cm m ( mm) ( mm). N/mm Thickness o lange For langes on angles and T-sections o longitudinals and other highly compressed stieners, the thickness shall not be less than t.b t mm k b = lange width in mm or angles, hal the lange width or T-Section(m) t k = corrosion addition(dnv Rule : Pt. 3 Ch. Sec. Page5) 38 69

70 7-6-6 (6) Buckling Strength o Plate by DNV Rule - Plate Panel in Uni-aial Compression (/4) Criteria or buckling strength a c ) Rules or Classiication o Ships, DNV, Pt. 3 Ch. Sec. 3, pp.9~93, January 4 σ c : critical buckling stress in [N/mm ] σ a : calculated actual compressive stress in [N/mm ] η : usage actor Usage Factor () =.: Deck, Single bottom & Side shell (longi. sti) =.9: Bottom, Inner bottom & Side shell (trans. sti) =.: Etreme loads (Q = -8 ) =.8: Normal loads (Q = -4 ) Critical buckling stress σ c c el, when el ( ),when el 4 el σ el : ideal compressive buckling stress σ el is determined according to speciic load. σ : upper yield stress in [N/mm ] From Bryan s ormula, c E t el K b p when el, p c p el c el when el, p el 4 el c pel c 4 el Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 39 (6) Buckling Strength o Plate by DNV Rule - Plate Panel in Uni-aial Compression (/4) Criteria or buckling strength a c ) Rules or Classiication o Ships, DNV, Pt. 3 Ch. Sec. 3, pp.9~93, January 4 σ c : critical buckling stress in [N/mm ] σ a : calculated actual compressive stress in [N/mm ] η : usage actor Usage Factor () =.: Deck, Single bottom & Side shell (long sti) =.9: Bottom, Inner bottom & Side shell (trans sti) =.: Etreme loads (Q = -8 ) =.8: Normal loads (Q = -4 ) Critical buckling stress σ c c el, when el ( ),when el 4 el σ el : ideal compressive buckling stress σ el is determined according to speciic load. σ : upper yield stress in [N/mm ] Calculated actual stress σ a (Uni-aial compression) σ a is calculated actual compressive stress in general In plate panels subject to longitudinal stress, σ a is given by s w z z N mm 5, / a n a I NA.. minimum 3 N/mm at side ( Hull girder bending moment is acting on the cross section o the ship as moment rom the point view o global deormation. And it is acting on the each plate as aial load rom the point view o local deormation.) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh S : still water bending moment as given in Sec. 5 W : wave bending moment as given in Sec. 5 I N : moment o inertia in cm 4 o the hull girder 4 7

71 7-6-6 (6) Buckling Strength o Plate by DNV Rule - Plate Panel in Uni-aial Compression (3/4) Critical buckling stress σ c c el, when el ( ),when el 4 el ) Rules or Classiication o Ships, DNV, Pt. 3 Ch. Sec. 3, pp.9~93, January 4 σ : minimum upper yield stress o material in [N/mm ] Ideal compressive buckling stress σ el in uni-aial compression ) t tk el.9 ke ( ) s Derivation o the coeicient.9 cr E t From Bryan s ormula e K, b (..3 9) σ el : ideal compressive buckling stress σ c : critical buckling stress σ : upper yield stress in N/mm t : thickness (mm) t k : corrosion addition E : modulus o elasticity s : stiener spacing (m) ν :.3 (Poisson's ratio o steel) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh σ el is determined according to speciic load. actor k For plating with longitudinal stieners (in direction o compression stress): 8.4 k k l. For plating with transverse stieners (perpendicular to compression stress): k k s s. c l. ψ = ratio between the smaller and the larger compressive stress (positive value) c =. when stieners are angles or T sections =. when stieners are bulb lats =.5 when stieners are lat bars =.3 when plating is supported by deep girders s l s l 4 (6) Buckling Strength o Plate by DNV Rule - Plate Panel in Uni-aial Compression (4/4) Critical buckling stress σ c Ideal compressive buckling stress σ el in uni-aial compression ) t tk el.9 ke ( ) s Derivation o the coeicient.9 cr E t From Bryan s ormula e K, b (..3 9) σ el : ideal compressive buckling stress σ c : critical buckling stress σ : upper yield stress in N/mm t : thickness (mm) t k : corrosion addition E : modulus o elasticity s : stiener spacing (m) ν :.3 (Poisson's ratio o steel) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh c el, when el ( ),when el 4 el σ el is determined according to speciic load. actor k σ : minimum upper yield stress o material in [N/mm ] For plating with longitudinal stieners (in direction o compression stress): 8.4 k k l. For plating with transverse stieners (perpendicular to compression stress): s. k ks c l. Eample) I., c.5, s/ l / 8.4 k k l 4.. s k ks c l ) Rules or Classiication o Ships, DNV, Pt. 3 Ch. Sec. 3, pp.9~93, January Thus, the plate with longitudinal stieners can endure much stress than the plate with transverse stieners 4 7

72 Structural Design o idship Section o a 3,7 TEU Container Ship () Data or Structural Design () Longitudinal Strength (3) Local Strength (4) Buckling Strength Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 43 () Data or Structural Design Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 44 7

73 7-6-6 idship Section or 3,7 TEU Container Ship Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 45 Design Still Water Bending oment or Ballast Arrival Condition Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh S 4,994[ ton m] 46 73

74 7-6-6 Design Still Water Bending oment From ballast arrival condition, 4,994[ ton m] S By calculating the section modulus and stress actor o the basis ship, we can assume the stress actor or the design ship. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 47 () Longitudinal Strength Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 48 74

7-6-6 Eample o idship Scantling - idship Scantling or 3,7 TEU Container Ship <Calculation o Design Bending oment (Hogging)> Still water bending moment - Larger value shall be used or still water

75 7-6-6 Eample o idship Scantling - idship Scantling or 3,7 TEU Container Ship <Calculation o Design Bending oment (Hogging)> Still water bending moment - Larger value shall be used or still water bending moment between the largest actual still water bending moment based on loading conditions and design still water bending moment by rule. Design still water bending moment by rule ) CWU CW 3/.75 [(3 L) /].75 [( ) /].37 SO CWU L B(.5.5 CB ) ( ),364,7.77 ( kn m) S ksmso.,364,7.77,364,7.77 ( kn m) W Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 3/ Largest actual still water bending moment based on the loading conditions - At ballast arrival condition S,9, 9( kn m) 4,994( tonm),364,7.77( knm) S ) DNV Rules, Pt. 3 Ch. Sec. 5 B, Jan. 4 ) DNV Rules, Pt. 3 Ch. Sec. 5 B, Jan. 4 Wave bending moment ).9 C L BC,56,48.9( kn m) WO WU B W kwmwo.,56,48.9,56,48.9( kn m) S W,364,7.77,56, ,94, ( kn m) <Calculation o Design Bending oment (Sagging)> Design bending moment at sagging condition is calculated in the same way. S,87,679.5( kn m) S W 3,59,49.6( kn m),87, ,59,49.6 4,866,88.( kn m) 49 Eample o idship Scantling - idship Scantling or 3,7 TEU Container Ship Plates at Bottom Structure IBP area =34X.35=459 cm IBP (inner bottom plate) area (A) = Width o IBP X Thickness o IBP E. Area o IBP cm st moment o IBP area about base line = Area o IBP (A) X Vertical center o IBP (b) E. st moment o Area o IBP ,3 cm nd moment o IBP area about base line = Area o IBP (A) X Vertical center o IBP (b) nd nd E. nd moment o Area o IBP e cm oment o inertia o IBP area (I ) E. oment o inertia o IBP area L B 3 3 LB e cm 4 oment o inertia o IBP area about base line (I ) is obtained by using the parallel-ais theorem. I I b A Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 5 75

7-6-6 Eample o idship Scantling - idship Scantling or 3,7 TEU Container Ship Stieners at Bottom Structure nd IBP area =34X.

55 [ cm] 7,59 5 Eample o idship Scantling - idship Scantling or 3,7 TEU Container Ship Calculation o moment o inertia o sectional area rom neutral ais Area, neutral ais, st moment & nd moment about

rom baseline ( h ) is calculated by using the above table. h Total st moment o area about baseline / Total area 7.583e 873.

76 7-6-6 Eample o idship Scantling - idship Scantling or 3,7 TEU Container Ship Stieners at Bottom Structure nd IBP area =34X.35=459 cm nd nd For convenience o calculation o moment o inertia o the stiener area about base line, we consider that the stiener is actually composed o lange and web plate and thus the stiener is assumed as the lange and web plate. Flange Web plate nd Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh Neutral ais o bottom structure = Total st moment o area about base line / Total area 59, [ cm] 7,59 5 Eample o idship Scantling - idship Scantling or 3,7 TEU Container Ship Calculation o moment o inertia o sectional area rom neutral ais Area, neutral ais, st moment & nd moment about baseline, and moment o inertia o side structu re, bulkhead structure, deck structure are calculated in the same way and the results are as ollows: Vertical location o neutral ais o midship section rom baseline ( h ) is calculated by using the above table. h Total st moment o area about baseline / Total area 7.583e 873.[ cm] 8,7 oment o inertia o area about neutral ais o midship section:,, IBase, Total IN. A., Total h Ai IN. A., Total IBase, Total h Ai (Parallel-ais theorem) I Ah h A I I Ah i i Base, Total Local, i 3 I NA..: moment o inertia o midship section area about neutral ais (cm ) 3 IBase : moment o inertia o midship section area about base line (cm ) hi : verticalcenter o structural member (cm) A i : area o structuralmember (cm) Local i i i i I Ah h A Local i i i i ,7.34 [ ] e e e cm Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 5 76

77 7-6-6 Eample o idship Scantling - idship Scantling or 3,7 TEU Container Ship b,d 5.7( S W ) b, d Assume section modulus Bottom stress actor o the basis ship B.595e cm 7 3,.3 b Deck stress actor o the basis ship D e cm d,.4 Actual section modulus Deck section modulus D I / yd (port & starboard) Bottom section modulus.34 e /,6.8 B I / y (port & starboard) B e /873.. e [ cm ] e [ cm ] (y B : Vertical distance rom N.A to bottom = 873.cm) Because the section modulus at bottom is larger than that o the basis ship, the stress actor should be decreased. Bottom Stress Factor 5.7( S W) b B 5.7 4,94, e 3 Because the stress actor ( b ) is decreased, the allowable stress is increased b db e.g., Allowable stress or longitudinals at inner bottom Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh (y D : Vertical distance rom N.A to deck= =,6.8 cm) Because the section modulus at deck is smaller than that o the basis ship, the stress actor will be increased. However, i HT-36 is used, then the stress actor can be decreased. Deck Stress Factor 5.7( S W) d D 5.7 4,94, e 4 Because the allowable stress is increased, the required section modulus is decreased. So, we can reduce the size o the structure member. 83lspw k 3 e.g., Required section modulus [ cm ] or longitudinals at inner bottom 53 Eample o idship Scantling - idship Scantling or 3,7 TEU Container Ship Estimation o design bending moment ain data, geometry, and arrangement idship section arrangement Local scantling The local scantling is determined assuming that initial midship section modulus o the design ship is equal to that o the basis ship. Calculation o stress actor Local scantling As-built ship midship section modulus Assumption o initial midship section modulus According to the rule requirement The midship section modulus o the basis ship: B.595e cm e cm D 7 3 b.3 d.4 Calculation o actual section modulus No Required section modulus Actual section modulus Longitudinal strength check The actual bending stress ( act. ) shall not be greater than the allowable bending stress ( l ). Yes Rule scantling end Thereore, we have to repeat the calculation. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 54 77

7-6-6 (3) Local Strength Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 55 Eample o idship Scantling - idship Scantling or 3,7 TEU Container Ship In this eample, we consider the midship

78 7-6-6 (3) Local Strength Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 55 Eample o idship Scantling - idship Scantling or 3,7 TEU Container Ship In this eample, we consider the midship section is composed o bottom structure, side structure, bulkhead structure, and deck structure. Bottom Structure Side Structure Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh Bulkhead Structure Deck Structure 56 78

79 7-6-6 Eample o Local Scantling Outer Bottom & Bilge plate Outer Bottom Longitudinals Inner Bottom Plate Inner Bottom Longitudinals Side Shell Plate Side Shell Longitudinals Deck Plate Deck Longitudinals Longitudinal Bulkhead Plate Longitudinal Bulkhead Longitudinals Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 57 Outer Bottom & Bilge Plate ain particulars o design ship LOA (m) LBP (m) L_scant (m) B (m) 3. D (m) 9.3 Td (m) Ts (m).6 Vs (knots) 4.5 C b.6563 S : The largest SWB among all loading conditions and class rule W : calculated by class rule or direct calculation It is assume that the initial stress actor is equal to the stress actor o basis ship. BP3 BP BP KP e cm B [ ] e cm D [ ] b.3.4 d Design KP: Keel Theories plate, o Ship BPn: and n-th Oshore Outer Plant, Bottom Fall Plate 6, yung-il Roh Seam line 58 79

80 7-6-6 Keel Plate (KP) (/) 3 KP :Load point Design Load Structure Outer bottom Load Type Sea pressure DNV Rules, Pt. 3 Ch. Sec. 6 Table B, Jan. 4 p T p ( kn / m ) : Design load acting on the keel plate is only the sea pressure. Design load (p) acting on the unit strip o keel plate p dp Keel plate is composed o the three unit strips. Load point o the unit strip:, : idpoint 3: Point nearest the midpoint Calculate the required thickness o each unit strip. And the thickest value shall be used or thickness o the plate. The material o keel plate o basis ship (NV-3) is used or that o design ship. ( =.8) p pdp pl ks.l~.7l rom A.P. ks= Cw.343 < L < 3,.75 - [(3-L)/]^(3/) 6.7 k y 8.5 z = vertical distance rom the waterline to the top o the ship s side at transverse section considered, maimum.8*cw (m) pl ( ks CW k )(.8.5V / L ) horizontal distance in m rom the ship s center line to the load point, minimum B/4(m)=8.5 vertical distance in m rom the ship s baseline to the load point, maimum T(m) p p 35 y.( T z ) ( kn / m ) dp l B 75 p T The design loads o the unit strip and 3 are calculated in the same way. Unit strip : p = (kn/m ) Unit strip 3: p = (kn/m ) p dp Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 59 Keel Plate (KP) (/) Required Thickness 5.8k as p t tk ( mm) T p aimum Design Load Allowable Stress or Bottom Plate Required thickness o the unit strip o the keel plate k a (.. 5s / l), maimum. or s/l =.4 ka. minimum.7 or s/l = - s.74 stiener spacing in m.8 aterial actor =.8 or NV-3 σ 53.6 tk.5 Corrosion addition ka s p t tk ( mm) The required thickness o the unit strip and 3 are calculated in the same way. Unit strip : t = 3.4 (mm ) Unit strip 3 : t = 4.63 (mm ) 3 inimum Thickness. 5L t 7. tk ( mm) t L 45. in (L, 3) (m).8 aterial actor =.8 or NV-3 tk.5 Corrosion addition 9.33 c) inimum Breadth b 8 5L(mm ) b KP. 5L t 7. tk ( mm) Rule,5.566 Arr. 354 Breadth o keel plate Rule is satisied. 3 :Load point 4 t ma( t, t ) [ mm] Unit strip 9.33 Unit strip 9.33 Unit strip The thickest value between the thickness o unit strips shall be used or thickness o keel plate. t [ mm] Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 6 8

81 7-6-6 Longitudinals at Keel Plate (L) (/) Design Load DNV Rules, Pt. 3 Ch. Sec. 6 Table B, Jan. 4 Structure Load Type p ( kn / m ) L KP :Load point Outer bottom Sea pressure Design load (p) acting on the L p T : Design load acting on the keel plate is only the sea pressure. p dp Load point : idpoint The material o L o basis ship (NV- 3) is used or that o design ship. ( =.8) p pdp pl ks.l~.7l rom A.P. ks= Cw.343 < L < 3,.75 - [(3-L)/]^(3/) 6.7 = vertical distance rom the waterline to the top o the k ship s side at transverse section considered, maimum.8*cw 6.7 (m) pl ( ks CW k )(.8.5V / L ) y 8.5 horizontal distance in m rom the ship s centre line to the load point, minimum B/4(m)=8.5 z vertical distance in m rom the ship s baseline to the load point, maimum T(m) p p 35 y.( T z ) ( kn / m ) dp l B 75 p T p dp Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 6 Longitudinals at Keel Plate (L) (/) Required Section odulus Allowable Stress 83 l spwk ( cm 3 ) σ 5 3 b. 7 le.96 Distance between web rame (3.6m) -. m(braket) s.74 stiener spacing in m p aimum Design Load tkw. Corrosion addition wk tk. Corrosion addition.5. 5( tkw tk )or langed section.8 aterial actor =.8 or NV-3 b.4 It is obtained rom the section modulus o the basis ship. σdb 5.6 in general db b l spwk ( cm 3 ) db L KP :Load point 3 inimum Thickness o Web and Flange k h t 5. tk ( mm), t tk ( mm) g k 4.9. L.8 aterial actor =.8 or NV-3 t tk. Corrosion addition.83 k t 5. tk ( mm) h 4 Proile height in m g 7 7 or langed proile webs t tk. Corrosion addition 7. h t tk (mm) g t ma( ) t, t t 4 Select the longitudinal whose section modulus is larger than the required section modulus rom the table. 조선설계편람, 제 4 판 ( 일본어 ), 일본관서조선협회, 996 a b t t r r A I mm cm cm 4 cm ,, Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 6 8

7-6-6 Inner Bottom Plate ain particulars o design ship LOA (m) 59.64 LBP (m) 47.64 L_scant (m) 45.38 B (m) 3. D (m) 9.3 Td (m) Ts (m).6 Vs (knots) 4.5 C b.

to the stress actor o basis ship. e cm B D 7 3.

82 7-6-6 Inner Bottom Plate ain particulars o design ship LOA (m) LBP (m) L_scant (m) B (m) 3. D (m) 9.3 Td (m) Ts (m).6 Vs (knots) 4.5 C b.6563 S : The largest SWB among all loading conditions and class rule W : Calculated by class rule or direct calculation IBP4 IBP3 IBP IBP Seam line It is assume that the initial stress actor is equal to the stress actor o basis ship. e cm B D [ ] e cm [ ] b.3.4 d Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 63 Inner Bottom Plate (IBP4) (/3) Design Load IBP4 Structure Inner bottom Inner Bottom, loors and girders Load Type Dry cargo in cargo holds Pressure on tank boundary in double bottom inimum pressure p ( g. 5a V ) H p ( h p p dyn p 4 h s p p 5 T C ) 4 3 Design load (p4, p3) acting on the unit strip o IBP4 :Load point Inner bottom plate 4 (IBP4) is composed o the our unit strips. Load point o the unit strip:,, 3, 4: idpoint Calculate the required thickness o each unit strip. And thickest value shall be used or thickness o the plate. The material o inner bottom plate o basis ship (NV-3) is used or that o design ship. ( =.8) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh Dry cargo in cargo holds Container is considered as a light cargo, so load by container can be negligible during local scantling. (Opinion by epert in structural design, p 4 = ) Design load acting on the inner bottom plate considering the overlow o the cargo tank. p 3 Δpdyn 5 5 in general hp vertical distance in m rom the load point to the top o air pipe (Air pipe is located on.76 m above the second deck) 4.89 P3.67( gh p Pdyn ) The design loads o the unit strip, 3, and 4 are equal to that o the unit strip. 64 8

83 7-6-6 Inner Bottom Plate (IBP4) (/3) Design load acting on the inner bottom plate considering the static pressure on the tank. Design load (p4, p5) acting on the unit strip o IBP4 p 4 h s vertical distance in m rom the load point to top o tank (= ) p 5 5 in ballast hold o dry cargo vessels 5 p4 hs p Design loads acting on the unit strip, 3 and 4 are calculated in the same way. Unit strip : p 4 = 53.88(kN/m ) Unit strip 3: p 4 = 53.88(kN/m ) h s 3. 88m Unit strip 4: p 4 = 53.88(kN/m ), (h s o the unit strip, 3, 4 is dierent rom that o the unit strip.) Design load acting on the inner bottom plate considering the damaged condition. p 5 6 p5 T The design loads o the unit strip, 3, and 4 are equal to that o the unit strip. Largest value between p 3, p 4, and p 5 shall be used or pressure acting the unit strip. p ma( p, p, p [ kn / m ] ) Unit strip : p = p 5 = 6 Unit strip : p = p 4 = Unit strip 3: p = p 4 = Unit strip 4: p = p 4 = Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 65 Inner Bottom Plate (IBP4) (3/3) Required Thickness 5.8k as p t tk ( mm) Allowable Stress or Inner Bottom Plate 4 3 inimum Thickness. 3L t t t k ( mm) Required thickness o the unit strip o the inner bottom plate t p 6 aimum Design Load k a (.. 5s / l), maimum. or s/l =.4 ka. minimum.7 or s/l = - s.84 stiener spacing in m.8 aterial actor =.8 or NV-3 σ tk Corrosion addition.4 5.8ka s p t tk ( mm) The required thicknesses o the unit strip and 3 are calculated in the same way. Unit strip : t = 3.3 [mm] Unit strip 3: t = 3.3 [mm] Unit strip 4: t = 3.3 [mm] Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 4 t t in general L 45. in (L, 3) (m).8 aterial actor =.8 or NV-3 tk Corrosion addition.5 t ma( t, t ) [ mm] Unit strip.5 Unit strip 3.3 Unit Strip The thickest value between the thickness o unit strips shall be used or thickness o inner bottom plate. t.5.5 [ mm] 66 83

84 7-6-6 Longitudinals at Inner Bottom (L) (/) Design Load IBP4 L3 L :Load point Structure Inner bottom Inner Bottom, loors and girders Load Type Dry cargo in cargo holds Pressure on tank boundary in double bottom inimum pressure Design load (p4) acting on the L p ( g. 5a V ) H p ( h p p dyn p 4 h s p p 5 T C ) Load point: idpoint The materials o L and L3 o basis ship (NV-3) are used or those o design ship. ( =.8) Design load acting on the longitudinals at inner bottom is equal to that on the inner bottom plate. L4 : p = p 4 =53.88 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 67 Longitudinals at Inner Bottom (L) (/) Required Section odulus 83 l spwk ( cm 3 ) Allowable Stress 5 b. 7 le.96 Distance between web rame (3.6m) -. m(braket) s.84 stiener spacing in m p aimum Design Load wk σ tkw. Corrosion addition tk. Corrosion addition.. 5( tkw tk )or langed section.8 aterial actor =.8 or NV-3 b.4 It is obtained rom the section modulus o the basis ship. σd b 5.6 in general b. 7 db l spwk ( cm 3 ) db 3 inimum Thickness o Web and Flange k h t 5. tk ( mm), t tk ( mm) g k 4.9. L.8 aterial actor =.8 or NV-3 t tk. Corrosion addition.33 k t 5. tk ( mm) h 3 Proile height in m g 7 7 or langed proile webs t tk. Corrosion addition 5.9 h t tk (mm) g t ma( ) t, t t 4 Select the longitudinal whose section modulus is larger than the required section modulus rom the table. 조선설계편람, 제 4판 ( 일본어 ), 일본관서조선협회, 996 Section modulus whose longitudinal involves the plate. ) a b t t r r A I mm cm cm 4 cm ,4 68 ) When the section modulus is calculated, standard breadth depending on a is used or eective breadth or simplicity. But eective breadth Design Theories o Ship and Oshore in Plant, accordance Fall 6, with rule yung-il should Roh be used in actual calculation. (b p t p ) => (a 75 : 4 8, 75<a<5 : 6, 5 a : 6 5) 68 84

85 7-6-6 Side Shell Plate SP5 SP4 SP3 ain particulars o design ship LOA(m) LBP(m) L_scant(m) B(m) 3. D(m) 9.3 Td(m) Ts(m).6 Vs(knt) 4.5 C b.6563 SP SP S W : The largest SWB among all loading conditions and class rule : Calculated by class rule or direct calculation It is assume that the initial stress actor is equal to the stress actor o basis ship. 7 3 B.595e cm b e cm.4 D d SP: Side shell Plate Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 69 Side Shell Plate (SP5 - Side Plating) (/3) Design Load & Load Point SP 5 :Load point Side shell plate (SP5) is composed o the two unit strips. Load point o the unit strip:, : idpoint Calculate the required thickness o each unit strip. And thickest value shall be used or thickness o the plate (SP5). The material o SP5 o basis ship (NV- 3) is used or that o design ship. ( =.8) Because SP5 is a side plate and a shear strake at strength deck, the required thickness o SP5 considering both the required side plating and strength deck plating is as ollows. (DNV Rules, Jan. 4,Pt. 3 Ch. Sec. 7 C) t t t [ mm] t : required side plating in mm t : strength deck plating in mm t shall not be taken less than t. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 7 85

7-6-6 Side Shell Plate (SP5 - Side Plating) (/3) SP 5 Structure Eternal Load Type Sea pressure above summer load waterline DNV Rules, Pt. 3 Ch. Sec. 7 Table B, Jan. 4 p p ( kn / m ) pdp 4.

86 7-6-6 Side Shell Plate (SP5 - Side Plating) (/3) SP 5 Structure Eternal Load Type Sea pressure above summer load waterline DNV Rules, Pt. 3 Ch. Sec. 7 Table B, Jan. 4 p p ( kn / m ) pdp 4.ks ) ( h : Design load acting on the SP5 is only the sea pressure. Design load (p) acting on the unit strip o SP5 :Load point ks.l~.7l rom A.P. ks= Cw.343 < L < 3,.75 - [(3-L)/]^(3/) Side plate (SP5) is composed o the two unit strips. Load point o the unit strip:, : idpoint Calculate the required thickness o each unit strip. And thickest value shall be used or thickness o the plate (SP5). p pdp pl 6.7 k y 6. z h 5.63 = vertical distance rom the waterline to the top o the ship s side at transverse section considered, maimum.8*cw (m) pl ( ks CW k )(.8.5V / L ) horizontal distance in m rom the ship s centre line to the load point, minimum B/4(m)=8.5 vertical distance in m rom the ship s baseline to the load point, maimum T(m)) p p 35 y.( T z ) ( kn / m ) dp l B 75 vertical distance in m rom the waterline considered to the load point p pdp ( 4.k ) h The material o SP5 o basis ship (NVs 3) is used or that o design ship. ( =.8) The design loads o the unit strip is calculated in the same way. Unit strip : p =.558(kN/m ) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 7 Side Shell Plate (SP5 - Side Plating) (3/3) SP5 Required Thickness 5.8kas p t tk ( mm) Allowable stress or Side Shell Plate 4 at N.A. σ shall be reduced linearly. 3 inimum Thickness kl t 5. tk ( mm) :Load point Required thickness o the unit strip o the SP5 t _ p aimum Design Load k a (.. 5s / l), maimum. or s/l =.4 ka. minimum.7 or s/l = - s.87 stiener spacing in m.8 aterial actor =.8 or NV-3 N.A(4)~ deck(4), It shall be reduced sigma linearly. tk 3 Corrosion addition ka s p t tk ( mm) The required thickness o the unit strip is calculated in the same way. Unit strip : t = (mm) 4 t ma( t, t ) [ mm] Unit strip 4.5 Unit strip 4.5 t _ k.3 in (L, 3) (m) L 45. in (L, 3) (m).8 aterial actor =.8 or NV-3 tk 3 Corrosion addition 4.5 c) inimum Breadth b 8 5L(mm ) b kl t 5. tk ( mm) Rule Arr. 354 Breadth o side shell plate 5 The thickest value between the thickness o unit strips shall be used or thickness o SP5. t 4.5[ mm] Rule is satisied. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 7 86

87 7-6-6 Side Shell Plate (SP5 - Shear Strake at Strength Deck) (/3) SP 5 :Load point Shear strake at strength deck (SP5) is composed o the two unit strips. Load point o the unit strip:, : idpoint Calculate the required thickness o each unit strip. And thickest value shall be used or thickness o the plate (SP5). The material o SP5 o basis ship (NV- 3) is used or that o design ship. ( =.8) Structure Weather deck p pdp Sea pressure pl DNV Rules, Pt. 3 Ch. Sec. 7 Table B, Jan. 4 Load Type p ( kn / m ) p a( pdp (4.ks ) h ) : Design load acting on the SP5 is only the sea pressure. Design load (p) acting on the unit strip o SP5 ks.l~.7l rom A.P. ks= Cw.343 < L < 3,.75 - [(3-L)/]^(3/) 6.7 k y 6. = vertical distance rom the waterline to the top o the ship s side at transverse section considered, maimum.8*cw (m) horizontal distance in m rom the ship s centre line to the load point, minimum B/4(m)=8.5 z.6 vertical distance in m rom the ship s baseline to the load point, maimum T(m) pdp p 35 y.( T z ) ( kn / m ) l B 75 a.8. or weather decks orward o.5l rom FP, or orward o deckhouse ront, whichever is the oremost position or.8 or weather decks elsewhere h pl ( ks CW k )(.8.5V / L ) Unit strip : p =5.743(kN/m ) vertical distance in m rom the waterline considered to the load point p a( pdp (4.ks ) h ) The design loads o the unit strip is calculated in the same way. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 73 Side Shell Plate (SP5 - Shear Strake at Strength Deck) (/3) SP5 Required Thickness 5.8kas p t tk ( mm) t _ 4 p aimum Design Load k a (.. 5s / l), maimum. or s/l =.4 ka. minimum.7 or s/l = - s.87 stiener spacing in m.8 aterial actor =.8 or NV-3 sigma 53.6 tk 3 Corrosion addition ka s p t tk ( mm) Allowable stress or Side Shell Plate at N.A. σ shall be reduced linearly. Required thickness o the unit strip o the SP5 The required thickness o the unit strip is calculated in the same way. Unit strip : t _ =8.574 (mm) 3 inimum Thickness t _ kl t t tk ( mm) t or unsheathed weather and cargo deck k.. in vessels with single continuous deck L 45. in (L, 3) (m).8 aterial actor =.8 or NV-3 tk 3 Corrosion addition.883 kl t t tk ( mm) c) inimum Breadth b 8 5L(mm ) b Rule Arr. 354 Breadth o shear strake :Load point Rule is satisied. 4 t ma( t_, t_ ) [ mm] Unit strip.883 Unit strip The thickest value between the thickness o unit strips shall be used or thickness o SP5. t [ mm] Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 74 87

88 7-6-6 Side Shell Plate (SP5 - Shear Strake at Strength Deck) (3/3) SP5 Side shell plate(sp5) t t t [ mm] t : required side plating in mm t : strength deck plating in mm t 4.5 t 3. t shall not be taken less than t. t 4. 5 t t t 4.5[ mm] :Load point Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 75 Longitudinals at Side Shell Plate (L38 - Deck Structure) (/4) SP 5 L38 :Load point Structure Eternal DNV Rules, Pt. 3 Ch. Sec. 7 Table B, Jan. 4 Load Type p ( kn / m ) Sea pressure above summer load waterline ks.l~.7l rom A.P. ks= p pdp 4.ks ) ( h : Design load acting on the L 38 is only the sea pressure. Design load (p) acting on the L 38 o the SP5 Load point: idpoint The material o L38 o basis ship (NV- 3) is used or that o design ship. ( =.8) L38 to be considered is the longitudinals located between the side structure and deck structure. p pdp pl Cw.343 < L < 3,.75 - [(3-L)/]^(3/) 6.7 k y 6. z h = vertical distance rom the waterline to the top o the ship s side at transverse section considered, maimum.8*cw (m) pl ( ks CW k )(.8.5V / L ) horizontal distance in m rom the ship s centre line to the load point, minimum B/4(m)=8.5 vertical distance in m rom the ship s baseline to the load point, maimum T(m)) p p 35 y.( T z ) ( kn / m ) dp l B 75 vertical distance in m rom the waterline considered to the load point p pdp 4.ks ) ( h Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 76 88

7-6-6 Longitudinals at Side Shell Plate (L38 - Deck Structure) (/4) SP5 L38 Required Section odulus 83 l spwk ( cm 3 ) _ Allowable stress zn za 5 3 z le.96 Distance between web rame (3.6m) -.

89 7-6-6 Longitudinals at Side Shell Plate (L38 - Deck Structure) (/4) SP5 L38 Required Section odulus 83 l spwk ( cm 3 ) _ Allowable stress zn za 5 3 z le.96 Distance between web rame (3.6m) -. m(braket) s.986 = (.87+. )/, stiener spacing in m p aimum Design Load wk σ tkw 3 Corrosion addition tk 3 Corrosion addition.3.5( tkw tk )or langed section.8 aterial actor =.8 or NV-3.9 It is obtained rom the section modulus o the basis ship. = , vertical distance in m rom the neutral.7 zn ais to the deck za. vertical distance in m rom the deck to the load point zn za zn ( ) l spwk cm 3 n 3 inimum Thickness o Web and Flange k h t 5. tk ( mm), t tk ( mm) g k 4.9. L.8 aterial actor =.8 or NV-3 t_ tk 3 Corrosion addition.33 k t 5. tk ( mm) h Proile height in m g or plat bar proile t_ tk 3 Corrosion addition 3 h t tk (mm) g t ma( t, t ) t _ :Load point [ cm ], t 3 [ mm] 3 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 77 Longitudinals at Side Shell Plate (L38 - Deck Structure) (3/4) SP 5 L38 Load point: idpoint :Load point The material o L38 o basis ship (NV- 3) is used or that o design ship. ( =.8) L38 to be considered is the longitudinals located between the side structure and deck structure. Structure Weather deck p pdp Sea pressure pl DNV Rules, Pt. 3 Ch. Sec. 7 Table B, Jan. 4 Load Type p ( kn / m ) p a( pdp (4.ks ) h ) : Design load acting on the L 38 is only the sea pressure. Design load (p) acting on the L 38 o the SP5 ks.l~.7l rom A.P. ks= Cw.343 < L < 3,.75 - [(3-L)/]^(3/) 6.7 k y 6. = vertical distance rom the waterline to the top o the ship s side at transverse section considered, maimum.8*cw (m) horizontal distance in m rom the ship s centre line to the load point, minimum B/4(m)=8.5 z.6 vertical distance in m rom the ship s baseline to the load point, maimum T(m)) pdp p 35 y.( T z ) ( kn / m ) l B 75 a.8. or weather decks orward o.5l rom FP, or orward o deckhouse ront, whichever is the oremost position or.8 or weather decks elsewhere h pl ( ks CW k )(.8.5V / L ) vertical distance in m rom the waterline considered to the load point p a( pdp (4.ks ) h ) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 78 89

90 7-6-6 Longitudinals at Side Shell Plate (L38 - Deck Structure) (4/4) SP5 L38 Required Section odulus 83 l spwk ( cm 3 ) _ Allowable stress zn z 5 3 d z le.96 Distance between web rame (3.6m) -. m(braket) s.986 = (.87+. )/, stiener spacing in m p 5.37 aimum Design Load wk σ tkw 3 Corrosion addition tk 3 Corrosion addition.3.5( tkw tk )or langed section.8 aterial actor =.8 or NV-3 d.9 It is obtained rom the section modulus o the basis ship. = , vertical distance in m rom the neutral.7 zn ais to the deck za. vertical distance in m rom the deck to the load point zn za 5 3 d zn l spwk ( cm 3 ) n a 3 inimum Thickness o Web and Flange k h t 5. tk ( mm), t tk ( mm) g k 4.9. L.8 aterial actor =.8 or NV-3 t _ tk 3 Corrosion addition.33 k t 5. tk ( mm) h Proile height in m g or plat bar proile t _ tk 3 Corrosion addition 3 h t tk (mm) g t ma( t, t ) t _ :Load point [ cm ], t 3 [ mm] 3 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 79 Longitudinals at Side Shell Plate (L38 - Side Structure & Deck Structure) SP5 L38 Side structure: Deck structure: cm, t 3 mm cm, t 3 mm Side structure & Deck structure ma( t ma( t 3, ) , t ) mm cm 3 :Load point 조선설계편람, 제 4 판 ( 일본어 ), 일본관서조선협회, Select the longitudinal whose section modulus is larger than the required section modulus rom the table. Section modulus o lange whose longitudinal involves the plate. ) d tw A I Section o web plate modulus whose longitudinal involves the plate. d tw A I ) When the section modulus is calculated, standard breadth depending on a is used or eective breadth or simplicity. But eective breadth in accordance with rule should be used in actual calculation. (b p t p ) => (a 75 : 4 8, 75<a<5 : 6, 5 a : 6 5) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 8 9

91 7-6-6 Deck Plate DP DP ain particulars o design ship LOA(m) LBP(m) L_scant(m) B(m) 3. D(m) 9.3 Td(m) Ts(m).6 Vs(knt) 4.5 C b.6563 DP3 DP4 DP5 S W It is assume that the initial stress actor is equal to the stress actor o basis ship. 7 3 B.595e cm b e cm d.4 D : The largest SWB among all loading conditions and class rule : Calculated by class rule or direct calculation DP: Deck Plate Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 8 Deck Plate (/) DP 3 Structure Weather deck Sea pressure Load Type DNV Rules, Jan. 4,Pt. 3 Ch. Sec. 7 Table B p ( kn / m ) p a( pdp (4.ks ) h ) : Design load acting on the DP is only the sea pressure. Design load (p) acting on the unit strip 3 o DP :Load point Deck plate (DP) is composed o the three unit strips. Load point o the unit strip:,, 3: idpoint Calculate the required thickness o each unit strip. And thickest value shall be used or thickness o the plate (DP). The material o DP o basis ship (NV- 3) is used or that o design ship. ( =.8) p pdp pl ks.l~.7l rom A.P. ks= Cw.343 < L < 3,.75 - [(3-L)/]^(3/) 6.7 k y 5.85 z a.8 h = vertical distance rom the waterline to the top o the ship s side at transverse section considered, maimum.8*cw (m) pl ( ks CW k )(.8.5V / L ) horizontal distance in m rom the ship s centre line to the load point, minimum B/4(m)=8.5 vertical distance in m rom the ship s baseline to the load point, maimum T(m)) p p 35 y.( T z) ( kn / m ) dp l B 75. or weather decks orward o.5l rom FP, or orward o deckhouse ront, whichever is the oremost position or.8 or weather decks elsewhere vertical distance in m rom the waterline considered to the load point p a( pdp (4.ks ) h ) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 8 9

92 7-6-6 Deck Plate (/) DP 3 Required Thickness 5.8kas p t tk ( mm) Allowable stress or Side shell Plate 3 inimum Thickness kl t t tk ( mm) :Load point Required thickness o the unit strip 3 o the DP t p aimum Design Load k a (.. 5s / l), maimum. or s/l =.4 ka. minimum.7 or s/l = - s.765 = ( )/, stiener spacing in m.8 aterial actor =.8 or NV-3 sigma 53.6 tk 3 Corrosion addition 5.8ka s p 6.6 t tk ( mm) The required thicknesses o the unit strip and are calculated in the same way. Unit strip : t = 6.45 (mm) Unit strip : t = (mm) 4 t ma( t, t ) [ mm] Unit strip.883 Unit strip.883 t t or unsheathed weather and cargo deck k.. in vessels with single continuous deck L 45. in (L, 3) (m).8 aterial actor =.8 or NV-3 tk 3 Corrosion addition.883 kl t t tk ( mm) c) inimum Breadth b 8 5L(mm ) b Rule Arr. 354 Breadth o side deck plate 5 The thickest value between the thickness o unit strips shall be used or thickness o DP. t [ mm] Rule is satisied. Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 83 Longitudinals at Deck Plate (/) DP L L Load point: idpoint :Load point The materials o L, L o basis ship (NV-3) are used or that o design ship. ( =.8) Structure Weather deck p pdp Sea pressure pl Load Type DNV Rules, Jan. 4,Pt. 3 Ch. Sec. 7 Table B p ( kn / m ) p a( pdp (4.ks ) h ) : Design load acting on the L, L is only the sea pressure. Design load (p) acting on the L and L ks.l~.7l rom A.P. ks= Cw.343 < L < 3,.75 - [(3-L)/]^(3/) 6.7 k y 5.55 z a.8 h = vertical distance rom the waterline to the top o the ship s side at transverse section considered, maimum.8*cw (m) pl ( ks CW k )(.8.5V / L ) horizontal distance in m rom the ship s centre line to the load point, minimum B/4(m)=8.5 vertical distance in m rom the ship s baseline to the load point, maimum T(m) p p 35 y.( T z) ( kn / m ) dp l B 75. or weather decks orward o.5l rom FP, or orward o deckhouse ront, whichever is the oremost position or.8 or weather decks elsewhere vertical distance in m rom the waterline considered to the load point p a( pdp (4.ks ) h ) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 84 9

93 7-6-6 Longitudinals at Deck Plate (/) Required Section odulus 83 l spwk ( cm 3 ) Allowable stress zn z 5 3 d z le.96 Distance between web rame (3.6m) -. m(braket) s.695 = ( )/, stiener spacing in m p aimum Design Load wk σ tkw 3 Corrosion addition tk 3 Corrosion addition.3.8 aterial actor =.8 or NV-3 d.9 It is obtained rom the section modulus o the basis ship. = , vertical distance in m rom the neutral.7 zn ais to the deck za vertical distance in m rom the deck to the load point ( tkw tk )or langed section ) When the section modulus is calculated, standard breadth depending on a is used or eective breadth or simplicity. But eective breadth in accordance with rule should be used in actual calculation. (b 85 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh p t p ) => (a 75 : 4 8, 75<a<5 : 6, 5 a : 6 5) n a 3 inimum Thickness o Web and Flange k h t 5. tk ( mm), t tk ( mm) g d tw zn za A d zn l spwk 65. ( cm 3 ) I t t_ DP L L k 4.9. L :Load point.8 aterial actor =.8 or NV-3 tk 3 Corrosion addition k.33 t 5. tk ( mm) h 5 Proile height in m g or plat bar proile tk 3 Corrosion addition.5 h t tk (mm) g t ma( t, t) 4 Select the longitudinal whose section modulus is larger than the required section modulus rom the table. 조선설계편람, 제 4판 ( 일본어 ), 일본관서조선협회, 996 Section modulus o lange whose longitudinal involves the plate. ) t Longitudinal Bulkhead Plate LBP6 LBP5 LBP4 ain particulars o design ship LOA(m) LBP(m) L_scant(m) B(m) 3. D(m) 9.3 Td(m) Ts(m).6 Vs(knt) 4.5 C b.6563 LBP3 LBP LBP S : The largest SWB among all loading conditions and class rule W : Calculated by class rule or direct calculation It is assume that the initial stress actor is equal to the stress actor o basis ship..595e cm B e cm D 7 3 b.3 d.4 LBP: Longitudinal Bulkhead Plate Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 86 93

94 7-6-6 Longitudinal Bulkhead Plate (LBP4) (/3) LBP4 :Load point Longitudinal bulkhead plate (LBP4) is composed o the ive unit strips. Load point o the unit strip: : Point nearest the midpoint, 3, 4, 5: idpoint Calculate the required thickness o each unit strip. And thickest value shall be used or thickness o the plate (LBP4). The material o LBP4 o basis ship (NV- NS) is used or that o design ship. ( =.) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh Design Load Structure Watertight bulkheads ` Tank bulkheads in general DNV Rules, Jan. 4,Pt. 3 Ch. Sec. 6 Table B Load Type p ( kn / m ) Sea pressure when looded or general dry p h b cargo minimum P3 ( g. 5a V ) h s P4. 67( gh p Pdyn) P g h 5 s p Design load (p) acting on the unit strip o LBP4 Watertight decks submerged in damaged condition p hb 3.75 vertical distance in metres rom the load point to the deepest equilibrium waterline in damaged condition obtained rom applicable damage stability calculations. The deepest equilibrium waterline in damaged condition should be indicated on the drawing o the deck in question p hb The design loads o the unit strip, 3, 4, and 5 are calculated in the same way. Unit strip : p = 3.3(kN/m ) Unit strip 3: p =.63(kN/m ) Unit strip 4: p =.93(kN/m ) Unit strip 5: p = 4.9(kN/m ) 87 Longitudinal Bulkhead Plate (LBP4) (/3) Considering vertical acceleration (P 3 ) p 3 Design load (p3, p4, p5) acting on the unit strip o LBP4 av Cw.34 < L < 3,.75 - [(3-L)/]^(3/) Cv. C V L / 5, ma. a Cv.56 C V V / L, ma a 3C / L CV C W V kv.7.7 between.3l and.6l rom A.P a v kv g a / CB hb vertical distance in metres rom the load point to the deepest equilibrium waterline in damaged condition obtained rom applicable damage stability calculations. The deepest equilibrium waterline in damaged condition should be indicated on the drawing o the bulkhead in question. p h 3 ( g. 5av ) hs The design loads o the unit strip, 3, 4, and 5 are calculated in the same way. Unit strip : p = 3.3(kN/m ) Unit strip 3: p =.63(kN/m ) Unit strip 4: p =.93(kN/m ) Unit strip 5: p = 4.9(kN/m ) Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh b LBP4 :Load point Considering the tank overlow (P 4 ) p 4 Δpdyn 5 5 in general hp vertical distance in m rom the load point to the top o air pipe P4. 67( gh p Pdyn ) The design loads o the unit strip, 3, 4, and 5 are calculated in the same way. Unit strip : p4 = 4.9(kN/m ) Unit strip3 : p4 = 36.44(kN/m ) Unit strip4 : p4 = 3.58(kN/m ) Unit strip5 : p4 = 4.76(kN/m ) Considering tank test pressure (P 5 ) p 5 P 5 5 in general Hs 3.75 vertical distance in m rom the load point to the top o tank or hatchway ecluding smaller hatchways 5.46 P 5 gh s p The design loads o the unit strip, 3, 4, and 5 are calculated in the same way. Unit strip : p5 = 45.48(kN/m ) Unit strip 3: p5 = 36.75(kN/m ) P 5 gh s p Unit strip 4: p5 = 8.(kN/m ) Unit strip 5: p5 = 9.3(kN/m ) Largest value between p, p 3, p 4 and p 5 shall be used or pressure acting the unit strip. p ma( p, p, p, p ) [ kn / m ] Unit strip : p = p 5 = 5.46 Unit strip : p = p 5 = Unit strip3 : p = p 5 =36.74 Unit strip4 : p = p 4 = 3.58 Unit strip5 : p = p 4 =

95 7-6-6 Longitudinal Bulkhead Plate (LBP4) (3/3) Required Thickness 5.8k as p t tk ( mm) t p 5.46 aimum Design Load Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh Allowable Stress or Longitudinal Bulkhead Plate 6 at N.A. σ shall be reduced linearly. Required thickness o the unit strip o the LBP4 k a (.. 5s / l), maimum. or s/l =.4 ka. minimum.7 or s/l = - s.87 stiener spacing in m aterial actor =. or NV-NS σ tk 3 Corrosion addition ka s p t tk ( mm) The required thickness o the unit strip, 3, 4, and 5 are calculated in the same way. Unit strip : t =.99 (mm) Unit strip 3: t =.6 (mm) Unit strip 4: t = 9.67 (mm) Unit strip 5: t = 8.96 (mm) 3 inimum Thickness k L t 5. tk ( mm) 4 t t ma( t, t ) [ mm] Unit strip.59 Unit strip.99 Unit strip 3.6 Unit strip Unit strip t [ mm] L 45. in (L, 3) (m). aterial actor =. or NV-NS Tk 3 Corrosion addition k.. or other bulkheads k L 8 t 5. tk ( mm) LBP4 :Load point 5 The thickest value between the thickness o unit strips shall be used or thickness o LBP4. 89 Longitudinals at Longitudinal Bulkhead Plate (LBP4) (/3) L34 L33 LBP4 L3 L3 :Load point Design Load Structure Watertight bulkheads Tank bulkheads in general Load Type Sea pressure when looded or general dry cargo minimum Design load (p) acting on the L3 DNV Rules, Jan. 4,Pt. 3 Ch. Sec. 6 Table B p h b p ( kn / m ) P3 ( g. 5a V ) h s P4. 67( gh p Pdyn) P g h 5 s p Load point: idpoint The material o LBP4 o basis ship (NV- NS) is used or that o design ship. ( =.) Considering the sea pressure at damaged condition (P) p hb vertical distance in metres rom the load point to the deepest equilibrium waterline in damaged condition obtained rom applicable damage stability calculations. The deepest equilibrium waterline in damaged condition should be indicated on the drawing o the deck in question p hb Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 9 95

96 7-6-6 Longitudinals at Longitudinal Bulkhead Plate (LBP4) (/3) Design load (p3, p4, p5) acting on the L3 Considering vertical acceleration (P 3 ) p 3 p 5 av Cw.34 < L < 3,.75 - [(3-L)/]^(3/) Cv. C V L / 5, ma. a Cv.56 C V V / L, ma a 3CW / L CV CV kv.7.7 between.3l and.6l rom A.P a v kv g a / CB hb P 5 5 in general vertical distance in metres rom the load point to the deepest equilibrium waterline in damaged condition obtained rom applicable damage stability calculations. The deepest equilibrium waterline in damaged condition should be indicated on the drawing o the bulkhead in question. p ( g. 5a ) h h 3 v s Considering tank test pressure (P 5 ) Hs vertical distance in m rom the load point to the top o tank or hatchway ecluding smaller hatchways P 5 gh s p b Considering the tank overlow (P 4 ) p 4 Δpdyn 5 5 in general hp 4.4 vertical distance in m rom the load point to the top o air pipe 45. P4. 67( gh p Pdyn ) Largest value between p, p 3, p 4 and p 5 shall be used or pressure acting the unit strip. p ma( p, p3, p4, p5) [ kn / m ] p = p 5 = Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 9 Longitudinals at Longitudinal Bulkhead Plate (LBP4) (3/3) Required Section odulus Allowable stress 83 l spwk ( cm 3 ) zn za 5 3 z le.96 Distance between web rame (3.6m) -. m(braket) s.87 stiener spacing in m p aimum Design Load tkw.5 Corrosion addition wk tk.5 Corrosion addition.5. 5( tkw tk )or langed section σ l spwk ( cm 3 ) n 3 inimum Thickness o Web and Flange k h t 5. tk ( mm), t tk ( mm) g k 4.9.L. aterial actor =. or NV-NS t tk.5 Corrosion addition 8.95 k t 5. tk ( mm) h 34 Proile height in m g 7 7 or langed proile webs t tk.5 Corrosion addition 4.36 h t tk (mm) g t ma( ) t, t t 4 Select the longitudinal whose section modulus is larger than the required section modulus rom the table. b e 조선설계편람, 제 4 판 ( 일본어 ), 일본관서조선협회, 996 a b t t r r A I mm cm cm 4 cm ,87 34 Section modulus whose longitudinal involves the plate. ) ) When the section modulus is calculated, standard breadth depending on a is used or eective breadth or simplicity. But eective breadth Design Theories o Ship and Oshore in Plant, accordance Fall 6, with rule yung-il should Roh be used in actual calculation. (b p t p ) => (a 75 : 4 8, 75<a<5 : 6, 5 a : 6 5) 9 96

97 7-6-6 (4) Buckling Strength Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 93 Eample o Buckling Check by DNV Rule ) Basis ship: 3,7TEU Container Carrier Arrangement o structure member, longi. spacing, seam line o design ship are same with those o basis ship. ) Rules or Classiication o Ships, DNV, Pt. 3 Ch. Sec. 3, pp.9-98, Jan. 4 idship section o 37TEU container carrier Design ship in this eample is the same with the ship considered in the eample o local scantling. ain particulars o design ship LOA (m) LBP (m) Ls (m) B (m) 3. D (m) 9.3 Td (m) Ts (m).6 Vs (knots) 4.5 C b.6563 Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 94 97

7-6-6 Eample o Buckling Check by DNV Rule - idship Section idship Section Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 95 Eample o Buckling Check by DNV Rule - Bottom Plate (/4) BP5

98 7-6-6 Eample o Buckling Check by DNV Rule - idship Section idship Section Design Theories o Ship and Oshore Plant, Fall 6, yung-il Roh 95 Eample o Buckling Check by DNV Rule - Bottom Plate (/4) BP5 KP BP BP BP3 BP4 Calculation o elastic buckling stress Name Because el or all bottom plates, critical buckling stress is calculated as ollows: c 4 el c el when el c when el 4 el c critical buckling stress minimum yield stress 35 N / mm or mild steel 35 N / mm or AH, DH, EH steel 355 N / mm or AH36, DH 36, EH36 steel el elastic buckling stress t tk.9 ke s ( N / mm ) E.6 N / mm k kl. or ( ) s: shortest side o plate panel in m Ψ : the ratio between the smaller and the larger compressive stress assuming linear variation In this eample, Ψ at bottom and deck are assumed as, Ψ at side plate is assumed as.97. ) Design Rules Theories or Classiication o Ship and Oshore o Ships, Plant, Det Fall Norske 6, yung-il Veritas, Roh Pt. 3 Ch. Sec. 3, pp.9-98, January

7-6-6 Eample o Buckling Check by DNV Rule - Bottom Plate (/4) BP5 KP BP BP BP3 BP4 Calculation o elastic buckling stress Because el or all bottom plates, critical buckling stress is calculated as

buckling stress t tk.9 ke ( N / mm ) s 5 E.6 N / mm 8.4 k kl or ( ).

99 7-6-6 Eample o Buckling Check by DNV Rule - Bottom Plate (/4) BP5 KP BP BP BP3 BP4 Calculation o elastic buckling stress Because el or all bottom plates, critical buckling stress is calculated as ollows: c 4 el Name c el when el c when el 4 el c critical buckling stress minimum yield stress el 35 / N mm or mild steel N mm or AH DH EH steel 35 /,, 355 N / mm or AH 36, DH 36, EH36 steel elastic buckling stress t tk.9 ke ( N / mm ) s 5 E.6 N / mm 8.4 k kl or ( ). s: shortest side o plate panel in m Ψ : the ratio between the smaller and the larger compressive stress assuming linear variation In this eample, Ψ at bottom and deck are assumed as, Ψ at side plate is assumed as.97. ) Design Rules Theories or Classiication o Ship and Oshore o Ships, Plant, Det Fall Norske 6, yung-il Veritas, Roh Pt. 3 Ch. Sec. 3, pp.9-98, January 4 97 Eample o Buckling Check by DNV Rule - Bottom Plate (3/4) BP5 KP BP BP BP3 BP4 Comparison between critical buckling stress and actual stress a c Name min. a c z z N mm al I ( ) ( / ) S W 5 a n a N minimum 3 N / mm at side or mild steel 3 N / mm or AH, DH, EH 38.4 N / mm or AH36, DH 36, EH N / mm In this eample, buckling check or BP~BP3 are not satisied. To satisy that, the change such as increase o plate thickness or change o material rom mild to high tensile steel is needed. ) Design Rules Theories or Classiication o Ship and Oshore o Ships, Plant, Det Fall Norske 6, yung-il Veritas, Roh Pt. 3 Ch. Sec. 3, pp.9-98, January 4. or deck, single bottom, longitudinally stiened side plating.9 or bottom, inner bottom, transversely stiened side plating. or local plate panels where an etreme load level is applied. (e.g impact pressures).8 or local plate panels where an normal load level is applied. z n : vertical distance in m rom the baseline or deck line to the neutral ais o the hull girder, whichever is relevant z a : vertical distance in m rom the baseline or deck line to the point in question below or above the neutral ais, Respectively I: oment o Inertia (cm4) s,w: Still water bending moment, vertical wave bending moment( knm) 98 99

7-6-6 Eample o Buckling Check by DNV Rule - Bottom Plate (4/4) BP5 KP BP BP BP3 BP4 Determination o the way o buckling reinorcement a c a S c a al I N ( z n z a) ( N / mm ) W 5 minimum 3 N / mm at

100 7-6-6 Eample o Buckling Check by DNV Rule - Bottom Plate (4/4) BP5 KP BP BP BP3 BP4 Determination o the way o buckling reinorcement a c a S c a al I N ( z n z a) ( N / mm ) W 5 minimum 3 N / mm at side Name or mild steel 3 N / mm or AH, DH, EH 38.4 N / mm or AH36, DH 36, EH N / mm In this eample, we increase the thickness o plate. ) Design Rules Theories or Classiication o Ship and Oshore o Ships, Plant, Det Fall Norske 6, yung-il Veritas, Roh Pt. 3 Ch. Sec. 3, pp.9-98, January 4. or deck, single bottom, longitudinally stiened side plating.9 or bottom, inner bottom, transversely stiened side plating. or local plate panels where an etreme load level is applied. (e.g impact pressures).8 or local plate panels where an normal load level is applied. z n : vertical distance in m rom the baseline or deck line to the neutral ais o the hull girder, whichever is relevant z a : vertical distance in m rom the baseline or deck line to the point in question below or above the neutral ais, Respectively I: oment o Inertia (cm4) s,w: Still water bending moment, vertical wave bending moment( knm) 99

Evaluation of Scantlings of Corrugated Transverse Watertight Bulkheads in Non-CSR Bulk Carriers Considering Hold Flooding

Evaluation of Scantlings of Corrugated Transverse Watertight Bulkheads in Non-CSR Bulk Carriers Considering Hold Flooding (1997) (Rev.1 1997) (Rev.1.1 Mar 1998 /Corr.1) (Rev. Sept 000) (Rev.3 eb 001) (Rev.4 Nov 001) (Rev.5 July 003) (Rev.6 July 004) (Rev.7 eb 006) (Corr.1 Oct 009) (Rev.8 May 010) (Rev.9 Apr 014) Evaluation