ship project a report3 hull jle - aalto

Kul-‐24.4110: Ship project A

Arctic Bulk Carrier

Assignment 3: Hull Structures

20.10.2014

Markus Mälkki, 84343C

Jesse Lehtonen, 84692L

CONTENTS 1 Introduction .......................................................................................................................................... 1

2 Loads ..................................................................................................................................................... 2

2.1 Rule design loads ............................................................................................................................ 2

2.1.1 Still water bending moment and shear force .......................................................................... 2

2.1.2 Wave bending moment and shear force ................................................................................. 4

2.2 NAPA design loads ......................................................................................................................... 5

2.3 Design pressures ............................................................................................................................ 7

2.3.1 Sea pressures .......................................................................................................................... 7

2.3.2 Deck pressures ........................................................................................................................ 7

2.3.3 Bulkhead pressures ................................................................................................................. 8

2.3.4 Ice pressures ........................................................................................................................... 8

3 Local strength ........................................................................................................................................ 9

3.1 Section modulus using analytical beam theory .............................................................................. 9

3.2 Structural spacing ........................................................................................................................... 9

3.3 Beam end supporting ..................................................................................................................... 9

3.4 Pressures into line loads .............................................................................................................. 10

3.5 Beam end supporting ................................................................................................................... 10

3.5.1 Effective breadth ................................................................................................................... 10

3.5.2 Analytical section modulus ................................................................................................... 11

3.6 Plating .......................................................................................................................................... 12

3.6.1 Corrosion addition ................................................................................................................ 12

3.6.2 Bottom plating ...................................................................................................................... 13

3.6.3 Side plating ............................................................................................................................ 14

3.6.4 Deck plating ........................................................................................................................... 14

3.7 Stiffeners ...................................................................................................................................... 15

3.7.1 Section moduli ...................................................................................................................... 15

3.7.2 Bottom longitudinals ............................................................................................................. 15

3.7.3 Side longitudinals .................................................................................................................. 15

3.7.4 Strength deck longitudinals ................................................................................................... 15

3.7.5 Side girders ............................................................................................................................ 15

Kul-‐24.4110: Ship Project A Markus Mälkki, 84343C Assignment 2: GA Jesse Lehtonen, 84692L

20.10.2014 iii

3.7.6 Deckhouse Deck Longitudinals .............................................................................................. 15

3.7.7 Machinery Deck Longitudinals .............................................................................................. 16

4 Response ............................................................................................................................................. 17

4.1 Normal stress ............................................................................................................................... 17

4.2 Shear stress .................................................................................................................................. 18

4.3 Torsion ......................................................................................................................................... 19

5 Buckling ............................................................................................................................................... 20

5.1 Stiffeners and girders ................................................................................................................... 20

5.2 Plating .......................................................................................................................................... 20

5.3 Maximum allowable hull girder bending ..................................................................................... 21

6 Fatigue ................................................................................................................................................. 23

7 Vibrations ............................................................................................................................................ 24

7.1 Beams ........................................................................................................................................... 24

7.2 Plates ............................................................................................................................................ 25

8 Ultimate strength ................................................................................................................................ 26

9 Optimization ....................................................................................................................................... 28

9.1 Reliability analysis ........................................................................................................................ 28

9.2 Optimization of structures ........................................................................................................... 28

References ................................................................................................................................................. 29

Appendix A: MATLAB -‐ Shear Stress Calculation ....................................................................................... 30

Appendix B: Stiffener, Girder and Plate Properties ................................................................................... 31

Appendix C: Mid-‐Ship Section ................................................................................................................... 33

Appendix D: Engine Room Section ............................................................................................................ 34


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1 INTRODUCTION The ship will be operating in extremely cold temperatures, which needs to be taken into account when selecting material grades for the hull structures. As the temperature in the arctic can drop below -‐30°C, the design temperature for the material properties is assumed to be -‐40°C.

Due to the arctic climate, the hull needs to be designed to withstand extremely high ice pressures on the sides, bow and stern. The long parallel mid-‐ship section of the ship with vertical sides is especially vulnerable to compressive ice fields. This needs to be compensated by strengthening the ice belt sufficiently. As the ship is carrying heavy bulk cargo, especially the bending of the hull girder and more locally bending of the double bottom below the cargo holds needs to be analysed.

The ship has following class notations:

Bulk Carrier ESP

POLAR-‐10

The ship has a mixed framing system, which means that the sides have transversal frames known to be better for ice loads. Rest of the hull is longitudinally stiffened, which is considered better especially in the double bottom for long ships [DNV Pt.3 Ch.1 Sec.6 A402].

Cargo holds are separated from each other by transversal self-‐stiffened corrugated bulkheads. Collision bulkhead and machinery space bulkheads are vertically stiffened. Locations of different bulkheads are presented in Figure 1.

Figure 1 Locations of bulkheads. Corrugated bulkheads are shown in red and vertically stiffened bulkheads in green.


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2 LOADS

2.1 RULE DESIGN LOADS Classification society (DNV) gives bending moment and shear force values in still water and wave conditions that are to be treated as the upper limits with respect to hull girder strength. The sign conventions of vertical bending moments and shear forces at any ship transverse section are shown in Figure 2.

Figure 2 Sign conventions for shear forces and bending moments

The vertical bending moments MS are positive when they induce tensile stresses in the strength deck (hogging bending moment) and are negative in the opposite case (sagging bending moment) the vertical shear forces QS positive in the case of downward resulting forces preceding and upward resulting forces following the ship transverse section under consideration, and is negative in the opposite case. Effects of horizontal bending moments are not considered at this design stage.

2.1.1 Still water bending moment and shear force According to DNV Pt.3 Ch.1 Sec.5 B, the design still water bending moments amidship are not to be taken less than:

MS = MSO (kNm)

MSO = – 0.065 CWU L2B (CB + 0.7) (kNm) in sagging

= CWU L2B (0.1225 – 0.015 CB) (kNm) in hogging

Where Cwu = 9.20 is the wave coefficient for the project ship according to DNV Pt.3 Ch.1 Sec.4 B.


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When required in connection with stress analysis or buckling control, the stillwater bending moments at arbitrary positions along the length of the ship are normally not to be taken less than:

MS = ksm MSO (kNm)

ksm = 1.0 within 0.4 L amidships

= 0.15 at 0.1 L from A.P. or F.P.

= 0.0 at A.P. and F.P

Between specified positions ksm shall be varied linearly. Calculated still water bending moments in hogging and sagging are shown in Figure 3.

Figure 3 Design still water bending moment distribution

DNV states in Pt.3 Ch.1 Sec.5 B that design values for stillwater shear forces along the length of the ship shall not be less than:

QS = ksq QSO (kN)

QSO = 5 MSO/L (kN)

Where

MSO =design stillwater bending moments (sagging or hogging).

ksq = 0 at A.P. and F.P.

= 1.0 between 0.15 L and 0.3 L from A.P.



Between specified positions ksq shall be varied linearly. Calculated still water shear force in hogging and sagging are shown in Figure 4.

0

100

200

300

400

500

600

700

800

0,0 0,2 0,4 0,6 0,8 1,0

Ben

ding m

omen

t [MNm]

L from A.P.

SLll water bending moment

Sagging

Hogging


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Figure 4 Design wave shear force distribution

2.1.2 Wave bending moment and shear force Vertical wave bending moments at arbitrary positions along the length of the ship are normally not to be taken less than:

MW = MWO (kNm)

MWO = – 0.11 α CW L2 B (CB + 0.7) (kNm) in sagging

= 0.19 α CW L2 B CB (kNm) in hogging

α = 1.0 for seagoing conditions

Calculated wave bending moment in hogging and sagging are shown in Figure 5.

Figure 5 Design wave bending moment distribution

0

5

10

15

20

25

0,0 0,2 0,4 0,6 0,8 1,0

Shear force [M

N]

L from A.P.

SLll water shear force

Sagging

Hogging

0

200

400

600

800

1000

1200

0,0 0,2 0,4 0,6 0,8 1,0

Ben

ding m

omen

t [MNm]

L from A.P.

Wave bending moment

Sagging

Hogging


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The rule value of vertical wave shear force is given in DNV Pt.3 Ch.1 Sec.5 B by:

QWV = 30 FQ fp Cw L B (CB +0.7) 10-2

Where FQ is a distribution factor defined in DNV Pt.8 Ch 4 Sec.3. The shear force will get a positive value when there is a surplus of buoyancy forward of section considered, and negative value when there is a surplus of weight. Calculated wave shear force distribution is shown in Figure 6.

Figure 6 Design wave shear force distribution

2.2 NAPA DESIGN LOADS As the rules don’t take the lightweight distribution or different loading conditions into account, still water bending moment and shear force distributions are also calculated using NAPA. Strength curves are plotted using same lightweight distribution and loading conditions as in the earlier stability check. Figures Figure 7 to Figure 9 show bending moment and shear force along the length of the ship.

0

5

10

15

20

0,0 0,2 0,4 0,6 0,8 1,0

Shear force [M

N]

L from A.P.

Wave shear force

Posilve

Negalve


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Figure 7 Load curves in full cargo loading condition

Figure 8 Load curves in ballast condition 1


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Figure 9 Load curves in ballast condition 2


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Table 1 shows maximum values of shear forces and bending moments in different loading conditions. As can be seen, these values are slightly lower than those given by the classification rules. However, at this design stage rule values are to be used as the lightweight distribution and cog are very preliminary estimations.


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Table 1 Maximum load values in different loading conditions

Cargo Ballast 1 Ballast 2 Shear force min (MN) -‐12.14 -‐14.31 -‐17.99 Shear force max (MN) 14.00 14.43 14.60 Sagging moment (MNm) -‐353.20 -‐481.87 -‐584.01 Hogging moment (MNm) 84.80 148.86 30.73

2.3 DESIGN PRESSURES

2.3.1 Sea pressures External sea pressures for mid-‐ship section are calculated with equations in DNV pt. 3 Ch. 1 Sec. 4. Pressures are evaluated at five points around the mid-‐ship hull: weather deck, top of the side, side at the design waterline, bilge and bottom of the ship. The resulting pressure distributions are presented in the mid-‐ship section figure in Appendix C.

2.3.2 Deck pressures Pressures acting on decks are mainly caused by iron ore cargo in the holds and water inside the ballast tanks. Design loads for upper and lower ballast water tank bottoms as well as cargo holds' bottom are calculated according to DNV pt. 3 ch. 1 sec. 6 B. For dry cargo in cargo holds:

!!"#!" = !!"#$% ! + 0,5!! !! ≈ !"#.! !"#,

where ρcargo = 2,5 t/m3 for crushed iron ore, HC = 10m is the loading height of the cargo hold and av is combined vertical acceleration

!! =!!!!!!!

≈ 2.67 !!! ,

where kv = 0,7 between 0.3L and 0.6L from AP and ao is common acceleration parameter

!! =!!!!+ !

!"≈ 0.299

As a small bulldozer (Liebherr 724) has a track pressure of about 60 kN/m2, a small bulldozer can easily operate in the cargo hold without having to strengthen the cargo hold floor.

For ballast tank bottoms the same equation is applied. Ballast water density is the same as sea water’s so ρbw = 1,025 t/m3 and the height of BW tanks in the double sides hbw = 6 m. Maximum pressure on the tank bottom when ballast tanks are full is

!!"# = !!" ! + 0.5!! ℎ!" ≈ !".! !"# .

Pressure decreases linearly from its peak value on the bottom to 0 on the tank top.

DNV Pt.3 Ch.1 Sec.8 defines the minimum for accommodation deck thickness to be 5 mm. The design load per square meter is to be 0.35 tons, which gives the design pressure based on the following equation

!!""#$"% = 0.35 ! + 0.5 ∙ !! = !.! !"#

where av= 5.4 m/s2 is the vertical acceleration due to the ship motions at the aft ship based on DNV Pt.3 Ch.1 Sec.4.


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The design pressure of one engine is calculated based on weight of one engine and the base area of the engine with the following equation

!!"#$!%& =89 t

5.5 m ∙ 2 m! + 0.5 ∙ !! = !"" !"#

2.3.3 Bulkhead pressures On ballast water tank bulkheads the value of pressure decreases from its maximum value on the bottom to zero on tank top. Maximum value is pbw = 68.5 kN/m2 as calculated in the decks section. Ballast tanks will be arranged with overflow pipes, so Δpdyn = 0. All the ballast tanks are rectangular shaped, which means b = bt and l = lt. In this phase of design the roll and pitch angles are considered to be 0.

Angle of repose for iron ore is 35 degrees [1]. Pressures acting on cargo hold bulkheads are calculated with equation for p2 presented in appendix 3. Parameters for the pressure on the bottom of the vertical part of the bulkhead are the height HC = 9 m and angle α1 = 90° between the panel and horizontal plane. Maximum value of the pressure on the bottom of the vertical part is 306 kN/m2. Pressure value decreases linearly as a function of distance from the cargo hold bottom. Pressure acting on the inclined bottom part of the hold is calculated in the same way with an angle α1 = 45° and HC = 11 m.

2.3.4 Ice pressures The basic ice pressures for the midship section are calculated according to the selected POLAR-‐10 notation by DNV. The design pressure is in general pice = 4.2 MPa for midship and 2.8 MPa for lower transition area according to DNV Pt.5 Ch.1 Sec.4 Critical width of the contact area is at this state of design assumed to be w = 600mm, which is the transversal frame spacing.


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3 LOCAL STRENGTH 3.1 SECTION MODULUS USING ANALYTICAL BEAM THEORY The effects of various pressures on the stiffeners, girders and web frames are taken into account by approximating pressures as constant line loads. Line load q is calculated by multiplying the pressure p in question with the spacing s between the corresponding structural members.

3.2 STRUCTURAL SPACING Spacing of the structures is defined based on the initial designs done on the Conceptual Design course. All the stiffeners are bulb flats and web frames and girders are T-‐ or I-‐beams. Mixed framing system is used in the side plating. Web frame spacing in the sides is 2400 mm and for stiffeners a third of that resulting in 600 mm. Close spacing is used because of the expected heavy ice loads on side plating. Spacing for the longitudinal side girders at the ice belt region is 2000 mm.

The decks between the BW tanks and the weather deck are longitudinally stiffened with spacing of 800 mm. Longitudinal stiffening is used to improve the total longitudinal stiffness of the ship. While the length-‐height ratio of the ship is small, the importance of longitudinal stiffness is pronounced. If the size of the stiffeners is getting too big when trying to achieve the desired section modulus, few bigger girders are applied to make the structure stiffer. Same stiffening system is used in the longitudinal bulkheads.

Both inner and outer part of the double bottom is stiffened with spacing of 700 mm. Double bottom includes longitudinal bulkheads and they are considered as I-‐beam girders with the height of double bottom and spacing of 1500 -‐ 2000 mm. Same system is applied in the higher central part of the double bottom. One part of the cargo hold bottom is inclined, but it is considered as a flat area to simplify calculations. The inclined part makes the structure stiffer than an even deck so the structure will in reality be stronger than the calculated approximation. Inclined cargo hold bottom parts are longitudinally stiffened with spacing of 700 mm.

3.3 BEAM END SUPPORTING To simplify calculations it is assumed that the beams are either simply supported or clamped. In reality the cases are something in between those two situations. For instance a simple support with some kind of spring attached to it. However, in this phase of design defining the spring constants would just be waste of time, while the structure isn’t final. All the deck and bottom beams and stiffeners are clamped on both ends, while the load acting on them is near to constant on each sides of limiting bulkheads and crossing frames when the holds and tanks are full. Thus they will have same deformations and the ends of the beams will have zero rotation.

On the side plating loadings over the whole height aren’t close to constant by nature. That’s why the transversal side stiffeners and beams of the lower BW tank are assumed to be clamped on the lower end, which is connected to the double bottom, and simply supported on the upper end. The transversal beams in the side of upper BW tanks are simply supported on both ends. Longitudinal stiffeners and girders are assumed as clamped on both ends, because the loading is more constant in that direction.


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3.4 PRESSURES INTO LINE LOADS Pressures are calculated in the Design loads section. Hydrostatic and other linearly varying pressures in on the hull sides, BW tanks and cargo hold sides are approximated to be uniform with the maximum magnitude over the entire length of the structure. Structure will become heavier that way, but approximation simplifies and makes the calculations faster at this stage. Changes to the structures can be made later on when the design gets more precise and the overall loads are better known. Ice load is taken into account on ice belt region as an additional loading. Plate and stiffener thicknesses shall be greater due to extra loading. The extent of ice loading will be between next longitudinal girders above and below the ice belt area.

3.5 BEAM END SUPPORTING To simplify calculations it is assumed that the beams are either simply supported or clamped. In reality the cases are something in between those two situations. For instance a simple support with some kind of spring attached to it. However, in this phase of design, the definition of the spring constants would be just a waste of time, while the structure isn’t final. All the deck and bottom beams and stiffeners are clamped on both ends, while the load acting on them is near to constant on each sides of limiting bulkheads and crossing frames when the holds and tanks are full. Thus they will have same deformations and the ends of the beams will have zero rotation.

On the side plating loadings over the whole height are not close to constant by nature. That’s why the transversal side stiffeners and beams of the lower BW tank are assumed to be clamped on the lower end, which is connected to the double bottom, and simply supported on the upper end. The transversal beams in the side of upper BW tanks are simply supported on both ends. Longitudinal stiffeners and girders are assumed as clamped on both ends, because the loading is more constant in that direction.

3.5.1 Effective breadth

Figure 10 Effective breadth coefficient C

From lecture slides of the structural design course is gotten a simplified approach of DNV for evaluating the effective breadth. It is calculated with a simple equation

!! = ! ∙ !


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where b is web frame, stiffener or girder spacing and C is defined from Figure 10 with distance a between the zero values at bending moment diagram and r which is the number of point loads acting on the structural member. In all of our cases loads are distributed line loads so r -‐> ∞ which is clearly greater than 6 so the curve used for the definition of C is the uppermost. For defining a, equations for moment distributions of clamped and half clamped beams loaded with distributed load are used.

For clamped beam:

!!"#!"#$ ! =!2(!" − !! −

!!

6)

!!"#$%&' ! = 0,

when ! = !!3 ± 3 !,

where can be calculated that !!"#$%&' =!!3!

For half clamped beam:

!!!"#$" ! =3!"8! −

!2!!

!!!"#$" ! = 0,

when x = 0 and x = 3/4L

where is gotten:

!!!"#$" =!!!.

After the C values are defined, the section modulus for different structural parts can be calculated.

3.5.2 Analytical section modulus For section modulus calculation also equations for 1st area moment SZ, 2nd moment of inertia IZ and Steiner inertia moment Is are needed.

For 1st area moment

!! = !!!

where A is the area of the structural member and ey is the centre of mass in y-‐direction from the top of the plating. For 2nd moment of inertia

!! =!!!ℎ!

12

where n is the number of the structural elements, be is the effective breadth and h is the structural member height. For Steiner inertia moment

!! = !!!!

The moment of inertia around the neutral axis

!! = !! + !!

The moment of inertia around the zero-‐plane (plate top)


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! = !! − !.!.!∙ !

where N.A. is the location of bending neutral axis from the plate surface. Finally section modulus Z is gotten

! =!!

where c is the distance of N.A from either top or bottom of the structural element. Z values are calculated with both distance from top and bottom. Whichever value is smaller is used as a design value.

3.6 PLATING

3.6.1 Corrosion addition In ballast water tanks, cargo holds and hull exteriors the plates, stiffeners and girders shall have a corrosion addition thickness tt as specified in DNV Pt.3 Ch.1 Sec.2 D. Total corrosion addition t'k = tk + tc can be calculated from Table 2 and Table 3.

Table 2 Corrosion additions for plating


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Table 3 Corrosion addition

3.6.2 Bottom plating Plate thicknesses for the double bottom are defined in DNV Pt.3 Ch.1 Sec.6. For the keel plating that shall extend over the complete length of the ship, the minimum thickness is:

where L1 is the length of the ship, f1 material factor and tk corrosion addition. Thickness requirement for the bottom and bilge plating is given by:

For the inner bottom plating, the thickness shall not be less than:

where t0 = 7.0 in cargo holds and 5.0 elsewhere. For the plating in double bottom floors and longitudinal girders, the plate thickness shall not be less than:

where k = 0.04L for centre girder and 0.02L for other girders and floors. The resulting requirements are presented in Table 4.


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3.6.3 Side plating Plate thickness for the side structures is mainly determined by the ice class rules and the lateral pressure caused by the iron ore cargo on the cargo hold sides. For the cargo hold side plating, the minimum thickness is given in DNV Pt.3 Ch.1 Sec.7:

where ! = 140f1 within 0.4L amidship and ka = (1.1 -‐ 0.25 s/l)2 is a correction factor for aspect ratio of plate field.

Vertical extent for the ice-‐reinforced areas is from the upper ice waterline (UIWL) to the lower ice waterline (LIWL) and the additional extent required by the ice class notation. For the midship section the required vertical extend is from T = 12.6m to T = 2.6m. When considering the plate division, this basically means that the whole vertical side of the midship has to be ice-‐reinforced.

The thickness of plating directly exposed to local ice pressure is generally not to be less than:

where h = 0.4 hice = 0.8m,

kw = influence factor for narrow strip of load = 0.87,

mp = bending moment factor = 2.68.

3.6.4 Deck plating Thickness of the strength deck plating is given in DNV Pt.3 Ch.1 Sec.8. The thickness shall not be less than:

where t0 = 5.5 for unsheathed weather deck and k = 0.02 in vessels with single continuous deck.

Table 4 Plate thicknesses calculated from DNV rules.

Plating Material Required t [mm] Selected t [mm] Keel plating NV-‐NS, E 14,9 20,0 Bottom plating NV-‐NS, E 11,3 20,0 Bilge plating NV-‐NS, E 11,3 20,0 Cargo hold bottom plating NV-‐27, EH 12,5 20,0 Upper BW bottom NV-‐NS, E 12,7 15,0 Lower BW bottom NV-‐NS, E 11,7 20,0 Weather deck plating NV-‐NS, E 9,6 25,0 Outer shell plating, Ice belt region NV-‐36, EH 31,0 32,0 Outer shell plating, Outside Ice belt NV-‐NS E 26,6 27,0


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3.7 STIFFENERS

3.7.1 Section moduli Section moduli are first calculated for the structural locations with analytical equations from basic beam theory. Then the values required by DNV are evaluated with the equations from rules. The two values are then compared. Analytical value should exceed the value from the rules.

3.7.2 Bottom longitudinals The section modulus required for the bottom longitudinals is given in DNV Pt.3 Ch.1 Sec.6 by:

where ! = maximum allowable stress = 160f1 and section modulus corrosion factor wk=1. Inner bottom longitudinals have similar requirements.

3.7.3 Side longitudinals Side longitudinals in longitudinal bulkheads between the cargo hold and water ballast tanks have a section modulus requirement of:

Thicknesses of web and flange have similar requirements as for bottom longitudinals.

3.7.4 Strength deck longitudinals

where ! = maximum allowable stress = 160f1.

3.7.5 Side girders Longitudinal girders that support transversal stiffeners in ice strengthened sides have section modulus requirement given by Pt.3 Ch.1 Sec.7 D for simple girders:

where S is girder spacing.

Achieved section modulus values and plate thicknesses are presented in table 3. Required Z is calculated from DNV rules and after that the structure is designed so that the final section modulus exceeds the requirement.

3.7.6 Deckhouse Deck Longitudinals The design pressure of 4.4 kPa calculated in the previous section results in section modulus requirement with the following equation from DNV Pt.3 Ch.1 Sec.8


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!!""#$"% =83 !! ! !!""#$"%

160= 11.8 !"!

where l = 2.4 m is the stiffener span s = 0.9 m is the stiffener spacing and 160 is the maximum allowable stress for normal grade steel. Minimum requirement by DNV is 15 cm3, which is used because the result from the equation is smaller than the minimum requirement. Some extra capacity is reserved and a combined section modulus of Z = 36.3 cm3 is acquired by using the required 5 mm plate and B*100*5 stiffeners.

3.7.7 Machinery Deck Longitudinals The deck thickness of 15 mm for the engine room deck is taken from the Wärtsilä Project Guide [2].

Based on the design pressure calculated in the previous section the required section modulus is gotten

!!"#$!%& =83 !! ! !!"#$!%&

160= 272 !"!

This value is greater than 15 cm3 so it is used. Again some reserve is taken into account and a section modulus Z = 344.6 cm3 is acquired, with B*220*10 stiffeners with spacing s = 0.9 m and span l = 2.4 m.

All the calculated stiffener requirements are presented in Table 5. Full spreadsheet of the cross-‐section calculations is presented in Appendix B.

Table 5 Section moduli of the stiffeners and double bottom girders

Stiffener type Material Required Z [cm3] Achieved [cm3]

Bottom longitudinals B*180*8 NV-‐NS, E 171,4 196,3 Keel longitudnials B*180*8 NV-‐NS, E 171,4 196,3 In BW bottom long B*140*8 NV-‐NS, E 99,5 108,2 In cargo bottom long B*240*12 NV-‐NS, E 444,5 1199,27 Strength deck long B*200*12 NV-‐NS, E 20,6 399,1 Upper BW bottom B*140*8 NV-‐NS, E 99,5 99,5 Side longitudinals B*140*8 NV-‐NS, E 99,5 99,5 Longitudinal girders I*15*2000*15*2000 NV-‐NS, E 21350,0 28499,1


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4 RESPONSE 4.1 NORMAL STRESS In last section the local cross-‐section values were calculated for different structural parts separately. Those values were used to calculate same values for the whole mid-‐ship section. Deck values were easy to apply for the bending around the transversal axis, while all the neutral axes of the stiffeners are at the same height from the baseline. However, on the longitudinal bulkheads and side plating the case is a bit more complicated, while each stiffener and girder is at different heights and therefore affect the bending differently. With the longitudinal bulkheads and side plating some simplifications were made to ease the calculations. Longitudinal stiffeners were taken into calculations as an added thickness on the plating. Equation for equivalent thickness is

!!" =!!

where A is the cross sectional area of the stiffener or girder and s is the spacing between corresponding beams. Assumption may cause some error into the calculated values. Longitudinal stiffeners on a longitudinal bulkhead are wide but low and thus the effect in bending is somewhat smaller than when they would be melted onto the plate and the height-‐width-‐relation changes, as in the made simplification. Error caused is however considered small enough to be made. Locations of the stiffeners and girders are not yet final so some error would be made that way in any case.

After calculating the cross sectional values for different members separately, they were multiplied by the number of corresponding parts and then summed to get the total values for the mid ship section. The distance of the horizontal neutral axis from the baseline was evaluated with equation

!.!.=!!!!

= 5.91 !

where ST is the total 1st are moment for the mid ship and AT is the total mid ship cross section area. The 2nd moment of inertia I could then be calculated.

! = !! + !! − !.!.! !! = 69.3 !!

where Is is the total Steiner moment of inertia and IZ is the sum of local second moments of inertia. As I and N.A. are known, the section moduli for the mid ship section are gotten.

!!"#$ =!

! − !.!= 8.57 !!

!!"##"$ =!

!.!.= 11.73 !!

where D is the total height of the ship. Smaller of the values is just above the value that DNV rules require. DNV Pt. 3 Ch. 1 Sec. 5 offers two equations for minimum value of mid-‐ship section modulus. One of them is based on main dimensions of the ship and the other is based on the still water and wave bending moments. They give us

!! =!!"

!!!!! !! + 0.7 = 8.52 !!

!! =|!! +!!|

!10!! = 8.51 !!


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where CWO = 9.04 is the wave coefficient and f1 = 1 is the material factor. Both Z values are almost the same perhaps mostly because also the bending moment values are calculated with DNV equations based on main dimensions.

Total bending moment MT acting on the main frame can be calculated by summing up still water and wave bending moments MT = Mw + Ms. Normal stress acting on the mainframe can then be calculated from basic beam theory:

!! = !!

!=!!!!

where z is distance from the neutral axis and I the second moment of inertia of the cross-‐section. This will assume that the normal stress changes linearly along the height of the cross-‐section. This is not exactly the case in reality, but corresponds pretty well to normal stress distribution in simple cross-‐sections with few decks and no superstructure. Vertical normal stress distributions for sagging and hogging are presented in Figure 11.

Figure 11 Normal stress distribution across the mid-‐ship cross-‐section

As can be seen, normal stresses caused by bending moment have maximum values far from the neutral axis. This should be taken into account by adding more material to double bottom and strength deck.

4.2 SHEAR STRESS Shear stress distribution of the main frame cross-‐section is based on the design shear forces calculated earlier for the still water and wave conditions. Total maximum shear force is taken as the sum of maximum still water and maximum wave shear forces.

The main frame is simplified to be a box shaped thin-‐walled section with same dimensions as the mainframe. Static moments are calculated first to get the shear stresses for each side of the cross-‐section. As the horizontal members have constant distance to neutral axis, the static moment is increasing linearly towards the edge of the section. More detailed calculations are presented in Appendix A. At the sides the static moment is parabolic and the maximum is at neutral axis.

0

2

4

6

8

10

12

14

-‐160 -‐110 -‐60 -‐10 40 90 140

DISTAN

CE FOR BA

SELINE [M

]

NORMAL STRESS [KPA]

NORMAL STRESS Sagging Hogging


20.10.2014 21

Shear stresses can be calculated from the static moments with following formula:

! = ! !! ! ,

where S is static moment, Q is shear force, t is plate thickness and I is second moment of inertia of the cross-‐section. Calculated shear stress distribution is presented in Figure 12.

Figure 12 Shear stress distribution across the mainframe cross-‐section

4.3 TORSION Pressure variation around the hull can cause torsional moment to the hull girder. It can cause significant normal and shear stresses. Transversal bulkheads restrict the “warping“ or out-‐of-‐plane deformation during torsion loading. This will produce additional normal stresses on the structure, but also makes it more resistant against the torsion.

Because of the large openings on the deck, the torsion rigidity is significantly decreased compared to the case where hatch covers could also carry loads. However, the closed side structures greatly contribute to torsional stiffness of the cross section. Upper ballast water tanks will act as closed “torsion boxes” that compensate the openings in the weather deck. These tanks will have increased plate thicknesses to make them carry more loads, especially in torsion. However more detailed torsion calculations are ignored in this work.


20.10.2014 22

5 BUCKLING 5.1 STIFFENERS AND GIRDERS For longitudinal girders and stiffeners the critical buckling loads are calculated with equations from DNV Pt. 3 Ch. 1 Sec. 13 C. Critical buckling load σc, including the ideal Euler buckling and plasticity correction, is evaluated from DNV equations and is the stress value that causes the structural part to buckle. Required minimum buckling stress value σcreq is the minimum value of critical buckling stress the classification society requires for the structure in order to have a safe structure under design load conditions. It is calculated by dividing the design normal stress value by a usage factor η given for various locations in DNV Pt. 3 Ch. 1 Sec. 13. σc is the value when the structural part buckles. So σc

should be greater than σcreq to have a safe structure.

Equations are based on the main dimensions, calculated normal stresses in corresponding locations and 2nd moment of inertia of the beams. The values for these are calculated in the structural response part. Required critical buckling loads for longitudinal bulkhead stiffeners and side plating girders are calculated only for the uppermost members. That is because the compressive normal stress caused by total bending moment is there at its maximum value as the distance from the neutral axis of bending is the greatest and thus the risk of buckling is the greatest. Buckling can occur only in case of compressive normal stress. Evaluated values for critical buckling loads σc and the required minimum values are presented in Table 6.

Table 6 Buckling stress values for stiffeners and side girders

Beam σc σc,req Safety

N/mm2 N/mm2 factor

Weatherdeck stiff 255,29 158,46 1,90 Bottom side stiff 247,90 143,15 2,04

Keel stiff 247,90 143,15 2,04 Inner bottom center stiff 262,26 73,41 4,20 Inner bottom side stiff 228,98 96,66 2,79

BW tanktop stiff 233,61 37,22 7,38 Long bh stiff 223,93 158,46 1,66

Side long beam 264,87 158,46 1,97

5.2 PLATING Critical buckling stresses for plates are calculated with equations from DNV pt. 3 ch. 1 sec. 13B. Same approximation for longitudinal bulkhead and girders is applied as in the calculations for beam buckling: values are calculated for uppermost parts only. Evaluated values for plate buckling are presented in Table 7.


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Table 7 Critical buckling stresses for plate sections

Plating σc σc,req Safety N/mm2 N/mm2 factor

Keel 212,19 135,20 1,74 Bottom side 212,19 135,20 1,74 Inner bottom center 232,87 69,33 3,73 Inner bottom side 206,84 91,29 2,52 BW tanktop 152,26 39,55 4,81 Maindeck 214,31 168,36 1,59 Long bh (uppermost part) 211,58 134,69 1,57 Side (uppermost part) 324,66 134,69 2,41

All the critical buckling values presented in table two fulfill the required value, so the design is good enough from that point of view.

5.3 MAXIMUM ALLOWABLE HULL GIRDER BENDING The maximum value for the hull girder bending can be evaluated by first checking the most critical part of the ship considering normal stresses. As the biggest value of normal stress is located in the uppermost part of the ship or on the main deck, the critical buckling stress there should be taken as the limiting parameter. Buckling stress value and the location of uppermost part of the longitudinal bulkhead are used when calculating maximum bending moment as an example. The moment needed to achieve the critical stress on the main deck is calculated using backwards the equation for σa and using the critical stress at longitudinal bulkhead as the stress value.

!!"#$ = !!"#$ +!!"#$ =!!"!!!

= 2,03 ∙ 10! !"#

where IN is the 2nd moment of inertia of the mid-‐section and z is the vertical distance from the neutral axis to the load point. The total hogging moment is MT = 1.295 ·∙ 106 kNm so the difference to the maximum is 735·∙103 kNm.

In the same manner as above, hull girder moment values for all the other buckling cases are calculated and presented in table 6 in ascending order of hull girder bending moments. As can be seen, the order of buckling is right as plates buckle at lower bending moment values as the corresponding stiffeners. It can be seen also that the longitudinal bulkhead plate is the first one to buckle in excessive sagging situation and the bottom side plate in case of hogging. The smallest critical bending moments are about 1.5 times the total wave and still water bending moments combined. That should be enough.


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Table 8 Critical hull girder moments

Structural member Hull girder bending moment Inner bottom center stiffener -‐6,26E+06 kNm

Inner bottom center plate -‐5,56E+06 kNm Inner bottom side stiffener -‐4,15E+06 kNm Inner bottom side plate -‐3,75E+06 kNm Bottom side stiffener -‐3,04E+06 kNm Keel stiffener -‐3,04E+06 kNm Keel plate -‐2,60E+06 kNm Bottom side plate -‐2,60E+06 kNm Long bulkhead plate (uppermost part) 2,03E+06 kNm Main deck plate 2,06E+06 kNm Longitudinal bulkhead stiffener (uppermost) 2,15E+06 kNm Main deck stiffener 2,46E+06 kNm Side plate (uppermost part) 3,12E+06 kNm Side longitudinal girder (uppermost) 3,42E+06 kNm BW tank top plate 6,23E+06 kNm BW tank top stiffener 9,56E+06 kNm


20.10.2014 25

6 FATIGUE Fatigue stress levels are checked for weather deck and bottom longitudinals using simplified fatigue calculations by DNV. It is considered sufficient to only inspect those structural details as those locations have the highest stresses. Also, bottom or deck plating will fail when the stiffener fails. When a one-‐slope S-‐N curve is used, the fatigue damage D can be calculated with the following formula:

Where a and m are S-‐N parameters that are gotten for base materials for corrosive environment. η is a usage factor that is not to exceed 1.0. This kind of S-‐N curve based fatigue design is based on 97.6% probability of survival. Td = 20 years is the design lifetime of the ship and p is a fraction of design life in each load condition. In this case it is assumed to be 1.0 as only dynamic wave bending moment is considered. Δσ0 is the stress range from minimum to maximum stress in the specific stress condition. In a case of wave bending, this means the sum of absolute stresses in hogging and sagging. Resulting fatigue damages are D = 0.39 for deck longitudinals and D = 0.15 for bottom longitudinals. They are both well below the maximum allowed value of 1.0, so there should be no fatigue issues in the hull girder. The values for the fatigue calculations are presented in Table 9.

Table 9 Fatigue calculations

Fatigue calculations Length L 157,00

Depth D 14 Draught T 10 Design lifetime T 9,46E+08 Zero-‐crossing frequency v0 0,11 Deck longitudinals

Bottom longitudinals S-‐N parameter a 5,46E+12

S-‐N parameter a 5,46E+12

S-‐N parameter m 3,00

S-‐N parameter m 3,00 fraction p 1,00

fraction p 1,00

stress range scale q 15,33

stress range scale q 11,19 no of cycles n 8,31E+09

no of cycles n 8,31E+09

stress range σ 325,12

stress range σ 237,43 shape parameter h0 1,02

shape parameter h0 1,02

gamma function

5,49

gamma function

5,49 Fatigue damage D 0,39

Fatigue damage D 0,15


20.10.2014 26

7 VIBRATIONS Main sources of vibration are the main engines, propulsion and different wave-‐induced loads like slamming. In this study the focus is on controlling vibrations caused by the engines and propulsion system. Speed of the main engine is 750 rpm or 12.5 Hz. Four bladed propeller speed is about 150 rpm, which means that the frequency of pressure shocks when a blade is in uppermost position is 10 Hz.

All plates, stiffeners and web frames should be designed so that their eigen frequencies are above the frequencies of engines and propeller to avoid resonance.

7.1 BEAMS For beam is gotten

! = !!"!

where λ = π/L is the first root of the characteristic equation for simply supported beam and m is the weight of the beam of length of one meter. Only first or smallest natural frequencies were calculated, because they are the most critical when considering resonance. Vibration wake frequencies should be below those. Calculated angular frequency values for beams are presented in Table 10.

Table 10 Beam eigen frequencies

It can be seen that the lowest eigen frequency of 34 Hz is for the stiffener of longitudinal bulkheads. This value is well above the frequencies of the main vibration sources. It also has to be taken into account that these frequencies are calculated for the beam members only and the plate hasn’t been taken in consideration. In reality the frequency will be higher as the beams are welded on plates.

Beams E I m L n λr ω f[Pa] [m^4] [kg/m] [m] nπ/L [rad/s] [Hz]

Bottom, side, stiff 2,10E+11 1,27E-‐04 86 2,4 1 1,31 729 116Bottom, side, gird 2,10E+11 1,00E-‐02 384 2,4 1 1,31 3061 487Bottom, keel, stiff 2,10E+11 8,59E-‐05 79 2,4 1 1,31 624 99Bottom, cent, gird 2,10E+11 7,65E-‐02 511 2,4 1 1,31 7339 1168Bottom, keel, gird 2,10E+11 7,65E-‐02 511 2,4 1 1,31 7339 1168Inner bottom, cent, stiff 2,10E+11 8,70E-‐05 76 2,4 1 1,31 643 102Inner bottom, side, stiff 2,10E+11 1,26E-‐05 57 2,4 1 1,31 282 45Long bulk, stiff 2,10E+11 1,29E-‐05 102 2,4 1 1,31 213 34Side, stiff 2,10E+11 4,24E-‐05 164 2 1 1,57 366 58Side, gird 2,10E+11 1,93E-‐02 451 2,4 1 1,31 3924 625Tank top, stiff 2,10E+11 1,27E-‐05 62 2,4 1 1,31 272 43Main deck, stiff 2,10E+11 3,14E-‐04 132 2,4 1 1,31 925 147


20.10.2014 27

7.2 PLATES For plates is gotten

where L is the longitudinal side of the plate in question, v = 0.3 is the Poisson ratio for steel and ρ is the area mass of the plate. λ is a coefficient based on the W/L relationship and the plates’ boundary conditions [3]. It is assumed that the plates are clamped at all ends as the flexibility of the welds and connections with the stiffeners is assumed to be very stiff. An additional 2000 kg/m3 is taken into account to the steel density as the plates are in most cases surrounded by water, which acts as added mass and thus reduces the frequency. Calculated eigen frequencies for plates are presented in Table 11.

Table 11 Plate eigen frequencies

From table 9 it is seen that all the eigen frequencies are above the wake frequencies from the engines and propulsion. The most critical is the accommodation deck with frequency of 29 Hz but there should not be problems related to vibrations with these eigen frequencies.

Plates t L W Ea W/L λ^2 ν f[m] [m] [m] [Pa] -‐ -‐ -‐ [Hz]

Keel 2,00E-‐02 2,4 0,6 2,10E+11 0,25 23,65 0,3 174Bottom, side 2,00E-‐02 2,4 0,6 2,10E+11 0,25 23,65 0,3 174Inner bottom, center 1,50E-‐02 2,4 0,6 2,10E+11 0,25 23,65 0,3 130Inner bottom, side 1,50E-‐02 2,4 0,6 2,10E+11 0,25 23,65 0,3 130Long bulkhead 1,50E-‐02 2,4 0,8 2,10E+11 0,33 23,65 0,3 98Side 4,00E-‐02 2 0,6 2,10E+11 0,30 23,65 0,3 348Tank top 1,50E-‐02 2,4 0,8 2,10E+11 0,33 23,65 0,3 98Main deck 2,00E-‐02 2,4 0,8 2,10E+11 0,33 23,65 0,3 130Accommodation decks 5,00E-‐03 2,4 0,9 2,10E+11 0,38 23,65 0,3 29Engine room deck 1,50E-‐02 2,4 0,9 2,10E+11 0,38 23,65 0,3 87


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8 ULTIMATE STRENGTH Ultimate strength of the hull girder is determined by comparing the plastic moment with the yield moment, elastic moment or buckling moment. The plastic moment can be calculated from basic beam theory with the following formula:

!! = !!!2(!! + !!)

Where σy is the yield stress, A is the total area of the cross section. y1 and y2 are the distances of the upper and lower cross sections’ center of gravities to the plastic neutral axis that splits the cross section horizontally into two equally large areas so A1 and A2 are defined so that A = A1 + A2.

Elastic moment ME can also be derived from the basic beam theory:

!! = σ!!!

where I is the second moment of inertia of the cross section and z the distance of neutral axis from the deck or bottom. Safety ratio ϕ is calculated by dividing the plastic moment with the smaller of the elastic moments. As elastic moments are used the smallest value of buckling moments and elastic moments calculated with the equation for ME above. Values for the elastic and plastic moments are presented in Table 12.

Table 12 Calculated elastic and plastic moment values

σy 2,35E+08 Pa Mp 2,68E+09 Nm Me (bottom) 2,60E+09 Nm Me (deck) 2,03E+09 Nm ɸ 1,32

The value for the Mp/Me ratio ϕ should be around 1.5. Our value is a bit smaller and thus some arrangements to make should be done. However, the most important issue concerning the ME values is that MP value is always bigger. That requirement is fulfilled. Sketch of the ultimate strength curve based on the first fiber yield is presented in Figure 13 Sketch of the ultimate strength curve. Strain values in Figure 13 are calculated with basic strength of materials equation

! =!!

Strain values are calculated at mid-‐ship area from zero moment to the elastic moments in both sagging and hogging. After that the values are approximated so that the curve shows a sketch of how the curve would continue after the first fiber yield.


20.10.2014 29

Figure 13 Sketch of the ultimate strength curve

As can be seen from figure 13, the elastic moment value in sagging conditions is quite close to the plastic moment. That is however not a huge problem as the moment values are at a safe distance from the design moment values.

-‐3,0E+09

-‐2,0E+09

-‐1,0E+09

0,0E+00

1,0E+09

2,0E+09

3,0E+09

-‐0,12 -‐0,07 -‐0,02 0,03 0,08 0,13

Hull girder ben

ding m

omen

t [Nm]

deflecLon at midship

Ullmate strength

Sagging Hogging Mt,hog Mt,sag

Mp Mp Me, bo|om Me, deck


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9 OPTIMIZATION

9.1 RELIABILITY ANALYSIS Reliability of the structure is defined with safety factors, which define the difference between the critical and design loadings. They are calculated by dividing the critical loading by the design value of the loading for the corresponding structural member.

Safety factors are in this case chosen to be at least 1.5 for all structural parts. That is to have an adequate safety marginal between the critical loading of the structure and still to not have too heavy and expensive structure. The existence of the safety margin improves structure’s capabilities of tolerance in case the design loadings are exceeded. As the defining values for the safety factor, critical buckling loads are used, while they are smaller than those of yielding, and are thus more critical when concerning hull rigidity and endurance. Calculated safety factor values after optimization for different structural members are presented in Table 13.

9.2 OPTIMIZATION OF STRUCTURES The main frame is optimized in such a way that plate thicknesses and stiffener dimensions are varied to get the minimum total area for the cross section. Total area is chosen to be the minimized value, because it is proportional to the total weight and cost of the structure. Plate thicknesses are constrained by the minimum thicknesses given by the classification rules and minimum safety factors. Minimum safety factor for buckling case is 1.5 for all structural members. New plate thicknesses and stiffener dimensions are then checked that they fulfil also minimum requirements for section moduli. New plate thicknesses will be then rounded up to the nearest producible plate thickness, and stiffeners profiles will be selected to be the closest available profile in stock. Stiffener dimensions for the calculations are also constrained to be realistic. Calculations done by the Microsoft Excel Solver–tool are presented in Table 13.

Table 13 Optimized dimensions for plates and stiffeners

t bstiff hstiff ф

Structural member mm mm mm Keel plate 15,00 8 280 1,54

Bottom side 14,18 11 317 1,50 Cargo bottom 13,00 8 252 2,84 Inner bottom side 12,00 8 139 1,68 Tanktop 13,00 8 138 3,58 Main deck 22,25 12 400 1,50 Long bulkhead 23,73 8 128 1,50

Microsoft Excel solver can be used to minimize or maximize desired cell values by giving certain boundary conditions. Boundary conditions in this case are the rule-‐based minimum values for plate thicknesses and frame cross-‐sections.


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REFERENCES [1] Bulk material chart,

http://www.unionironworks.com/engineering_calculator_detail.aspx?x=wZWr/QqjPORgDQ4VPL%2Bqn07XK8X1uqUw, [17.10.2014]

[2] Wärtsilä 32, Product Guide, Vaasa, Finland, 2013

[3] Spijkers J.M.J et al., Structural Dynamics Part 1 – Structural Vibrations, Delft University of Technology, the Netherlands, January 2005


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APPENDIX A: MATLAB -‐ SHEAR STRESS CALCULATION function [taud, taumax, taub, taubs, tauds] = shearstress

b = 13;

I = 75.42;

Qw = 15000*10^3;

Qs = 20000*10^3;

Q = Qw + Qs;

td = 25*10^-3;

ts = 40*10^-3;

tb = 20*10^-3;

h1 = 6.13;

h2 = 7.87;

Sd = h2*td*b;

Sb = h1*tb*b;

Ssmax = Sd+0.5*h2^2*ts;

taud = (Sd*Q)/(I*td);

taub = (Sb*Q)/(I*tb);

tauds = (Sd*Q)/(I*ts);

taubs = (Sb*Q)/(I*ts);

taumax = (Ssmax*Q)/(I*ts);


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APPENDIX B: STIFFENER, GIRDER AND PLATE PROPERTIES

Part No. Parts Young's modulus True breadth Eff breadth Height N.A Area 1. Area moment Local I Steinern E b beff h e_y A Sz = A*e_y Iz = n*b*h^3/12 Is = A*e_y^2

-‐ -‐ [Gpa] [mm] [mm] [mm] [mm] [mm^2] [mm^3] [mm^4] [mm^4]

Outer bottom side -‐ B*180*8 & 20 mm platePlate 1 210 700 469 14,1802225 7,09011123 6,65E+03 4,72E+04 1,11E+05 3,34E+05Stiffener web 1 210 11 11,0338395 291 159,917299 3,22E+03 5,14E+05 2,28E+07 8,22E+07Stiffener flange 1 210 33 33 25,5 318,404376 8,42E+02 2,68E+05 4,56E+04 8,53E+07

Total 331,154376 1,0708E+04 8,29E+05 2,29E+07 1,68E+08Eref 210 GpaN.A, bending 7,75E+01 mm from deck L B a a/b r CElement Iz 2,29E+07 mm^4 2400 700 1385,6 1,979486637 > 6 0,67Element Is 1,68E+08 mm^4I_n 1,91E+08 mm^4 around deckI 1,27E+08 mm^4 around N.A. Achieved Z 498,93 cm^3Z_top 4,99E+05 mm^3 = 498,93 cm^3 Required Z 171,395 cm^3Z_bottom 1,63E+06 mm^3 = 1634,22 cm^3 Difference 327,54 cm^3ωn 7,29E+02 rad/sfn 1,16E+02 Hz

Outer bottom keel -‐ B*180*8 & 20 mm platePlate 1 210 700 469 15 7,5 7,04E+03 5,28E+04 1,32E+05 3,96E+05Stiffener web 1 210 8 8 255 142,274045 2,04E+03 2,90E+05 1,10E+07 4,12E+07Stiffener flange 1 210 33 33 25,5 282,29809 8,42E+02 2,38E+05 4,56E+04 6,71E+07


Inner bottom side -‐ B*140*8 & 15 mm platePlate 1 210 700 469 12 6 5,63E+03 3,38E+04 6,75E+04 2,03E+05Stiffener web 1 210 8 8 120 71,816242 9,57E+02 6,87E+04 1,14E+06 4,94E+06Stiffener flange 1 210 27 27 19,7 141,482484 5,32E+02 7,53E+04 1,72E+04 1,06E+07

Total 151,332484 7,1170E+03 1,78E+05 1,23E+06 1,58E+07Eref 210 GpaN.A, bending 2,50E+01 m from deck L B a a/b r CElement Iz 1,23E+06 mm^4 2400 700 1385,6 1,979486637 > 6 0,67Element Is 1,58E+07 mm^4I_n 1,70E+07 mm^4 around deckI 1,26E+07 mm^4 around N.A. Achieved Z 99,50 cm^3Z_top 9,95E+04 mm^3 = 99,50 cm^3 Required Z 99,5 cm^3Z_bottom 5,03E+05 mm^3 = 503,38 cm^3 Difference 0,00 cm^3ωn 2,82E+02 rad/sfn 4,49E+01 Hz

Inner bottom center -‐ B*240*12 & 15 mm platePlate 1 210 700 469 13 6,5 6,10E+03 3,96E+04 8,59E+04 2,58E+05Stiffener web 1 210 8 8 216 121,06119 1,73E+03 2,09E+05 6,73E+06 2,53E+07Stiffener flange 1 210 46 46 35,4 246,82238 1,63E+03 4,02E+05 1,70E+05 9,92E+07

Total 264,52238 9,4544E+03 6,51E+05 6,99E+06 1,25E+08Eref 210 GpaN.A, bending 6,88E+01 m from deck L B a a/b r CElement Iz 6,99E+06 mm^4 2400 700 1385,6 1,979486637 > 6 0,67Element Is 1,25E+08 mm^4I_n 1,32E+08 mm^4 around deckI 8,70E+07 mm^4 around N.A. Achieved Z 444,50 cm^3Z_top 4,45E+05 mm^3 = 444,50 cm^3 Required Z 444,5 cm^3Z_bottom 1,26E+06 mm^3 = 1263,45 cm^3 Difference 0,00 cm^3ωn 6,43E+02 rad/sfn 1,02E+02 Hz

Inclined cargo bottom -‐ B*240*12 & 15 mm platePlate 1 210 700 469 15 7,5 7,04E+03 5,28E+04 1,32E+05 3,96E+05Stiffener web 1 210 12 12 204,6 117,3 2,46E+03 2,88E+05 8,56E+06 3,38E+07Stiffener flange 1 210 46 46 35,4 237,3 1,63E+03 3,86E+05 1,70E+05 9,17E+07

Total 255 1,11E+04 7,27E+05 8,87E+06 1,26E+08Eref 210 GpaN.A, bending 6,54E+01 m from deck L B a a/b r CElement Iz 8,87E+06 mm^4 2400 700 1385,6 1,979486637 > 6 0,67Element Is 1,26E+08 mm^4I_n 1,35E+08 mm^4 around deckI 8,72E+07 mm^4 around N.A. Achieved Z 459,83 cm^3Z_top 4,60E+05 mm^3 = 459,83 cm^3 Required Z 444,5 cm^3Z_bottom 1,33E+06 mm^3 = 1333,03 cm^3 Difference 15,33 cm^3ωn 6,43E+02 rad/sfn 1,02E+02 Hz

Side long girder -‐ T*1400*16*500*20 & 40 mm platePlate 1 210 2000 600 40 20 2,40E+04 4,80E+05 3,20E+06 9,60E+06Web 1 210 16 16 1400 740 2,24E+04 1,66E+07 3,66E+09 1,23E+10Flange 1 210 500 500 20 1450 1,00E+04 1,45E+07 3,33E+05 2,10E+10

Total 1460 5,64E+04 3,16E+07 3,66E+09 3,33E+10Eref 210 GpaN.A, bending 5,60E+02 mm from deck L B a a/b r CElement Iz 3,66E+09 mm^4 2400 2000 1385,6 0,7 > 6 0,3Element Is 3,33E+10 mm^4I_n 3,70E+10 mm^4 around deckI 1,93E+10 mm^4 around N.A. Achieved Z 21440,78 cm^3Z_top 2,14E+07 mm^3 = 21440,78 cm^3 Required Z 21350 cm^3Z_bottom 3,45E+07 mm^3 = 34508,00 cm^3 Difference 90,78 cm^3ωn 3,92E+03 rad/sfn 6,25E+02 Hz

Girders bottom center side -‐ I*15*3000*20*1500Plate 1 210 1500 540 15 7,5 8,10E+03 6,08E+04 1,52E+05 4,56E+05Web 1 210 15 15 3000 1515 4,50E+04 6,82E+07 3,38E+10 1,03E+11Flange 1 210 46 540 20 3025 1,08E+04 3,27E+07 3,60E+05 9,88E+10

Total 3035 6,3900E+04 1,01E+08 3,38E+10 2,02E+11Eref 210 GpaN.A, bending 1,58E+03 mm from deck L B a a/b r CElement Iz 3,38E+10 mm^4 2400 1500 1385,6 0,9 > 6 0,36Element Is 2,02E+11 mm^4I_n 2,36E+11 mm^4 around deckI 7,65E+10 mm^4 around N.A. Achieved Z 48457,75 cm^3Z_top 5,26E+07 mm^3 = 52559,67 cm^3 Required Z cm^3Z_bottom 4,85E+07 mm^3 = 48457,75 cm^3 Difference 48457,75 cm^3ωn 7,34E+03 rad/sfn 1,17E+03 Hz


20.10.2014 34

Part No. Parts Young's modulus True breadth Eff breadth Height N.A Area 1. Area moment Local I Steinern E b beff h e_y A Sz = A*e_y Iz = n*b*h^3/12 Is = A*e_y^2

-‐ -‐ [Gpa] [mm] [mm] [mm] [mm] [mm^2] [mm^3] [mm^4] [mm^4]

Center girder -‐ I*15*3000*20*1500Plate 1 210 1500 540 15 7,5 8,10E+03 6,08E+04 1,52E+05 4,56E+05Web 1 210 15 15 3000 1515 4,50E+04 6,82E+07 3,38E+10 1,03E+11Flange 1 210 540 20 3025 1,08E+04 3,27E+07 3,60E+05 9,88E+10


Bottom side girder -‐ I*15*2000*15*2000Plate 1 210 2000 600 15 7,5 9,00E+03 6,75E+04 1,69E+05 5,06E+05Web 1 210 15 15 2000 1015 3,00E+04 3,05E+07 1,00E+10 3,09E+10Flange 1 210 600 15 2022,5 9,00E+03 1,82E+07 1,69E+05 3,68E+10


Long bulkhead stiff -‐ B*140*8 & 15 mm platePlate 1 210 800 480 23,7300525 11,8650263 1,14E+04 1,35E+05 5,35E+05 1,60E+06Stiffener web 1 210 8 8 108 77,9398808 8,67E+02 6,76E+04 8,50E+05 5,27E+06Stiffener flange 1 210 27 27 19,7 141,999709 5,32E+02 7,55E+04 1,72E+04 1,07E+07


Tank top stiff -‐ B*140*8 & 15 mm platePlate 1 210 800 480 13 6,5 6,24E+03 4,06E+04 8,79E+04 2,64E+05Stiffener web 1 210 8 8 119 72,2966927 9,49E+02 6,86E+04 1,11E+06 4,96E+06Stiffener flange 1 210 27 27 19,7 141,443385 5,32E+02 7,52E+04 1,72E+04 1,06E+07


Main deck stiff -‐ B*200*12 & 20 mm platePlate 1 210 800 480 22,2541539 11,1270769 1,07E+04 1,19E+05 4,41E+05 1,32E+06Stiffener web 1 210 12 12 368 206,204154 4,41E+03 9,10E+05 4,98E+07 1,88E+08Stiffener flange 1 210 43 43 32,1 406,204154 1,38E+03 5,61E+05 1,19E+05 2,28E+08


Side trans stiff -‐ B*180*8 & 40 mm platePlate 1 210 600 462 40 20 1,85E+04 3,70E+05 2,46E+06 7,39E+06Stiffener web 1 210 8 8 154,5 117,25 1,24E+03 1,45E+05 2,46E+06 1,70E+07Stiffener flange 1 210 33 33 25,5 207,25 8,42E+02 1,74E+05 4,56E+04 3,61E+07

Total 220 2,0558E+04 6,89E+05 4,97E+06 6,05E+07Eref 210 GpaN.A, bending 3,35E+01 mm from deck L B a a/b r CElement Iz 4,97E+06 mm^4 2000 600 1500,0 2,5 > 6 0,77Element Is 6,05E+07 mm^4I_n 6,55E+07 mm^4 around deckI 4,24E+07 mm^4 around N.A. Achieved Z 227,41 cm^3Z_top 2,27E+05 mm^3 = 227,41 cm^3 Required Z cm^3Z_bottom 1,27E+06 mm^3 = 1265,51 cm^3 Difference 227,41 cm^3ωn 365,54 rad/sfn 5,82E+01 Hz

Accommodation Decks -‐ B*100*5 & 5 mm platePlate 1 210 900 495 5 2,5 2,48E+03 6,19E+03 5,16E+03 1,55E+04Stiffener web 1 210 5 5 85 47,5 4,25E+02 2,02E+04 2,56E+05 9,59E+05Stiffener flange 1 210 20,5 20,5 15 97,5 3,08E+02 3,00E+04 5,77E+03 2,92E+06

Total 105 3,2075E+03 5,64E+04 2,67E+05 3,90E+06Eref 210 GpaN.A, bending 1,76E+01 mm from deck L B a a/b r CElement Iz 2,67E+05 mm^4 2400 900 1385,6 1,539600718 > 6 0,55Element Is 3,90E+06 mm^4I_n 4,16E+06 mm^4 around deckI 3,17E+06 mm^4 around N.A. Achieved Z 36,31 cm^3Z_top 3,63E+04 mm^3 = 36,31 cm^3 Required Z 15 cm^3Z_bottom 1,81E+05 mm^3 = 180,66 cm^3 Difference 21,31 cm^3

Machinery Deck -‐ B*220*10 & 15 mm platePlate 1 210 900 495 15 7,5 7,43E+03 5,57E+04 1,39E+05 4,18E+05Stiffener web 1 210 10 10 188 109 1,88E+03 2,05E+05 5,54E+06 2,23E+07Stiffener flange 1 210 41 41 32 219 1,31E+03 2,87E+05 1,12E+05 6,29E+07

Total 235 1,0617E+04 5,48E+05 5,79E+06 8,57E+07Eref 210 GpaN.A, bending 5,16E+01 mm from deck L B a a/b r CElement Iz 5,79E+06 mm^4 2400 900 1385,6 1,539600718 > 6 0,55Element Is 8,57E+07 mm^4I_n 9,15E+07 mm^4 around deckI 6,32E+07 mm^4 around N.A. Achieved Z 344,56 cm^3Z_top 3,45E+05 mm^3 = 344,56 cm^3 Required Z 15 cm^3Z_bottom 1,22E+06 mm^3 = 1224,37 cm^3 Difference 329,56 cm^3


20.10.2014 35

APPENDIX C: MID-‐SHIP SECTION


20.10.2014 36

APPENDIX D: ENGINE ROOM SECTION

ship project a report3 hull jle - aalto

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