STRUCTURAL CALCULATIONS

(CONTAINER/GENERAL CARGO SHIP)

NAVAL DESIGNS, VANCOUVER,B.C., 2009

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 SHIP HULL STRUCTURE

Ship hull structure is calculated according to the Lloyd’s Rules and Regulations
(1994). This document represents short version of the calculation.

Length, wl LWL = 98.514 m

Length, bp Lpp = 93 m
Breadth, moulded B = 16 m
Depth, moulded to main deck D = 8.5 m
Draught, designed T = 5.432 m
Buoyancy ∇ = 6085.881 m3
Speed, designed v = 14.5 kn
koeficijent punoće broda δ = 0.695

Dimensions important for ship structure:

Spacing of bottom longitudinals 800 mm

Spacing of inner bottom longitudinals 800 mm
Spacing of deck longitudinals 800 mm
Spacing of torsion box longitudinals 700 mm
Spacing of frames 750 mm
Spacing of web frames 3·750 = 2250 mm
Spacing of peak frames 600 mm

Material is ordinary-strenght shipbuilding steel.

Structure description

• Longitudinal framing is to be adopted at double bottom and the deck. The side
shell should be framed transversally. Exceptions are peaks, which will be framed
transversally.
• Longitudinal spacing would be 800 mm in double bottom. On every side of the
center bottom girder would be one side bottom girder.
• Bottom transverses will be fitted under the web frames, except in the double
bottom under the engine room where they would be placed under every second frame
and in peaks where bottom transverse would be under every frame. Between bottom
transverses, on the bilge and on the central girder, brackets would be fitted.
• Whole containers load would be shown as four forces distributed on the reclining
points. On these points, local reinforcement will be fitted.
• Spacing of frames on the side shell would be 750 mm, and every third frame
would be web frame. Double skin side would be used as a ballast tank and as a fuel oil
tank, and it would be built for the purpose.
• Ship deck will be reinforced in way of hatch opening.
• Longitudinal hatchway coamings of the cargo hold will be continuous in order to
increase longitudinal strength.
• Vessel torsion boxes will have longitudinal framing.
• Superstructure along with deckhouses would be built in the way that deck has
longitudinal and side skin transversal framing.

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 • All structural elements are to comply with Lloyd’s Register Rules and
Regulations.

Calculated ship’s length:

L = (0.96 ÷ 0.97)LWL = 0.965·98.514= 95.066 m

L = 95.1 m is taken as calculated ship’s length.

Shell envelope plating

Bottom plating thickness

Table 1.5.2, page 4.1.5.17, formula (1)

The greater of the following:

а) t = 0.001·s1·(0,043L1 + 10)·(FB/kL)1/2
b) t = 0.0052·s1·[(hT2·k)/(1.8 – FB)]1/2

L1 = L = 95.1 m
s1 = 800 mm – spacing of bottom longitudinals, but not less then;
s1 ≥ 470 + L2/0.6 = 628.50 mm
kL = k = 1 – shipbuilding steel factor
FB = 0.77
L2 = L = 95.1 m
hT2 = T + 0.5CW = 7.845 m, but not greater then 1.2T = 6.518 m;
Value taken: hT2 = 6.518 m
CW – wave height (1.5.1)
CW = 7.71·10–2·L·e–0.0044L = 4.825 m
⇒
0.77
a) t = 0.001·800·(0.043·95.1 + 10)· = 9.891 mm
1
6.518 ⋅1
b) t = 0.0052·800· = 10.367 mm
1.8 − 0.77
Value taken t = 11 mm

Bilge plating thickness

Table 1.5.2, page 4.1.5.17, formula (2) (bilge plating is framed)

Bilge plating thickness value would be the same as the bottom plating thickness.

Value taken t = 11 mm

Plate keel calculation

Table 1.5.1, page 4.1.5.16, formula (2)

Plate keel is defined by:
breadth: b = 70B = 70·16= 1120 mm
thickness: t = t1 + 2 = 11 + 2 = 13 mm
t1 – bottom plating thickness
Value taken 1200х13 mm

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Side shell plating

Table 1.5.3, page 4.1.5.18.

Side plating within D/4 from the gunwale – transferse framing

According to formula (1)(а) for transverse framing take the greater of following:

i) t = 0,00085·s1·f1·(0,083L1 + 10)·(FD/kL)1/2
ii) t = 0,0042·s1·(hT1·k)1/2

hT1 = T + CW = 10.257 m, but not greater then 1.36T = 7.388 m;

Value taken 7.388 m
CW = 7.71·10–2·L·e–0.0044L = 4.825 m
s1 = 750 mm – spacing of frames
L1 = L = 95.1 m
FD = 1
k = kL = 1 shipbuilding steel factor
1
f1 = 2
= 0.859
⎛ s1 ⎞
1+ ⎜ ⎟
⎝ 1000S ⎠
s1 = 750 mm – spacing of frames
S = 1.85 m – spacing of primary members (in this case celling and torsion box)
1
i) t = 0.00085·750·0.859·(0.083·95.1 + 10)· = 9.796 mm
1
ii) t = 0.0042·750· 7.388 ⋅1 = 8.562 mm

Value taken t = 10 mm

Side plating above D/2 from base – longitudinal framing

According to formula (1)(а) for longitudinal framing take the greater of following:

i) t = 0.001·s1·(0.059L1 + 7)·(FD/kL)1/2
ii) t = 0.0042·s1·(hT1·k)1/2

hT1 = T + CW = 10.257 m, but not greater then 1,36T = 7.388 m;

Value taken 7.388 m
CW = 7.71·10–2·L·e–0.0044L = 4.825 m
s1 = 700 mm – spacing of longitudinals in the torsion box
L1 = L = 95.1 m
FD = 1
k = kL = 1 shipbuilding steel factor

1
i) t = 0.001·700·(0.059·95.1 + 7)· = 8.828 mm
1

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ii) t = 0.0042·700· 7.388 ⋅1 = 7.990 mm

Value taken t = 9 mm
Side plating within D/4 from mid-depth – transferse framing

According to formula (1)(b) for transverse framing, take the greater of following:

i) t = 0.001·s1·(0.059L1 + 7)·(FМ/k)1/2
ii) t = 0.0051·s1·(hT1·k)1/2

hT1 = T + CW = 10.254 m, but not greater then 1,36T = 7.388 m;

Value taken 7.388 m
CW = 7.71·10–2·L·e–0.0044L = 4.825 m
s1 = 750 mm – spacing of frames
L1 = L = 95.1 m
FМ = 1
k = 1 shipbuilding steel factor
1
i) t = 0.001·750·(0.059·95.1 + 7)· = 9.458 mm
1
ii) t = 0.0051·750· 7.388 ⋅1 = 10.396 mm
Value taken t = 11 mm

Side plating within D/4 from base – transverse framing

According to formula (1)(с) for transverse framing take the greater of following:

i) t = 0.00085·s1·f2·(0.083L1 + 10)·(FB/kL)1/2
ii) t = 0.0056·s1·[(hT2·k)/(1.8 – FB)]1/2

L1 = L = 95.1 m
s1 = 750 mm – spacing of frames
hT2 = T + 0.5CW = 7.845 m, but not greater then 1.2T = 6.518 m;
Value taken hT2 = 6.518 m
CW – wave height (1.5.1)
CW = 7.71·10–2·L·e–0.0044L = 4.825 m
k = kL = 1 shipbuilding steel factor
FB = 0.77
1
f2 = 2
= 0.932
⎛ s1 ⎞
1+ ⎜ ⎟
⎝ 1000S ⎠
s1 = 750 mm – spacing of frames
S = 2.775 m (one stiffener fitted in the middle of cargo hold side plate)

0.77
i) t = 0.00085·750·0.932·(0.083·95.1 + 10)· = 9.328 mm
1
6.518 ⋅1
ii) t = 0.0056·750· = 10.566 mm
1.8 − 0.77

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 Value taken t = 11 mm
Overall side plate thickness t = 11 mm.

Sheerstrake

According to formula (2) for sheerstrake thickness (because of torsion box) take the
greather then:

i) t = 0.001·s1·(0.059L1 + 7)·(FD/kL)1/2
ii) t = 0.00083·s1·(L·k)1/2 + 2.5

s1 = 700 mm – spacing of torsion box longitudinals

L1 = L = 95.1 m
FD = 1
k = kL = 1 shipbuilding steel factor
1
i) t = 0.001·700·(0.059·95.1 + 7)· = 8.828 mm
1
ii) t = 0.00083·700· 95.1 ⋅1 + 2.5 = 8.166 mm

Sheerstrake thickness cannot be lesser then side plate thickness, and according to that
rule, sheerstrake thickness is t = 12 mm.

Height of sheerstrake
Table 2.2.1, page 3.2.2.3. (Note 2.):

h = 800 + 5L = 800 + 5·95.1 = 1275.5 mm, gut not greather then 1800 mm

Sheerstrake dimensions are : 1300x12 mm

Torsion box

Torsion box dimensions:

h ≈ 0.25·(D – dDBA) = 0,25·(8.5 – 1.1) = 1.85 m

Height of torsion box is h = 1.85 m.

Breadth of torsion box is the same as double hull breadth and it is taken to be b = 1.5
m in accordance with containers positions.

Torsion box plate thickness would be the same as sheerstrake thickness, which is:
t = 12 mm.

Inner hull plate

Inner skin plate thickness is calculated according to formula (1) for deep tank (double
hull will be used for ballast tanks) from table 1.9.1. on page 4.1.9.28. :

t = 0.004·s·f·(ρ·h4·k/1.025)1/2 + 2.5

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 s
f = 1.1 − , but not greather then 1
2500 ⋅ S
s = 750 mm
S = 3·0.75 = 2.25 m
ρ = 1.025 t/m3
h4 = max{h0/2; hta} – defined on picture 3.5.2, page 3.3.5.16

Inner hull plate is divided on three parts height 2.467m

Part 1:
f = 0.967
2.467
8.5 − 1.1 − + 0, 76
3 2.467
h4 = max{ ; 8.5 – 1.1 – } = max{3.669; 6.578}
2 3
h4 = 6.578 m
t = 9.938 mm

Part 2:
f = 0.967
2.467
8.5 − 1.1 − 2.467 − + 0, 76
3 2.467
h4 = max { ; 8.5 – 1.1 –2.467 – }=
2 3
= max {2.435; 4.111}
h4 = 4.111 m
t = 8.3799 mm

Part 3:
f = 0.967
2.467
8.5 − 1.1 − 2 ⋅ 2.467 − + 0, 76
3 2.467
h4 = max{ ; 8.5 – 1.1 –2·2.467 – }=
2 3
= max{1.202; 1.644}
h4 = 1.644 m
t = 6.128 mm

Thickness of the plate in the deep tank area for a ship length L < 90 m cannot be less
then 6.5 mm.
Value taken for inner hull plate thickness is t = 10 mm.

Shell framing
Bottom stiffeners

Minimal section modulus for bottom longitudinals is defined in the table 1.6.1 on the
page 4.1.6.20, formula (3):

Z = γ·s·k·hT2·le2·F1 [cm3]
le = 2.25 m – effective length of stiffening member (longitudinals), not to be less then
1.5 m
s = 800 mm – spasing of bottom longitudinals (secondary structure)

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hT2 = 6.518 m
F1 = (D2·C1)/(25D2 – 20h5), for bottom longitudinals, not less then 0,14
h5 = D2, D2 = D = 8.5 m, but not greather then 1,6T = 8.69 m, h5 = D2 = 8.5 m
C1 = 60/(225 – 165·FB), on base line, C1 = 0.613
FB = 0.77
F1 = 0.1226, value taken F1 = 0,14
γ = 0.002·le1 + 0.046 = 0.051
le1 = le, but not less then 2.5 m and not greather then 5 m, le1 = 2.5 m

Z = 0.051·800·1·6.518·2.252·0.14 = 165.066 cm3

Profile taken: HP 180 × 9

Double hull stiffeners

Breadth of the double hull is defined according to the cargo hold and it is 1.5 m.

Side frames

Frame in the cargo hold is defined in the table 1.6.2, page 4.1.6.21, formula (1) take
greater value of two:

а) Z = s·k·T·P·c·f2·10-3
b) Z = 9,1·s·k·D1·f2·10-3

s =750 mm – spacing of frames

D1 = D = 8.5 m, but not greater then 1,6T = 8.69 m
f2 = 1 – for standard brackets
c = 1 – for D ≥ 7,5 m
k = 1 – shipbuilding steel factor
P = (1,77H2 + 0,145K1D12 + 14,5)·(1 – x/1,4D)
H = HMF – vertical framing depth, of primar structure, but not less then 2,5 m
8.5 − 1.1 − 1.85
HMF = = 2,775 m
2
⎧ x ⎫
K1 = max ⎨1 − ; 0,35⎬
⎩ 5q ⎭
xa = dDBA – dDB = 1100 – 925.786= 174.214 mm (frame under the stringer plate)
xb = 2.775 + dDBA– dDB = 2949.213 mm (frame above the stringer plate)

8.3.1, page 4.1.8.25

q = dDB = 28B + 205T1/2, not less then 650 mm
dDB = 925.786 mm

⎧ 174.214 ⎫
K1a = max ⎨1 − ;0.35⎬ = max {0.962; 0.35} = 0.962
⎩ 5 ⋅ 925.786 ⎭
⎧ 2949.213 ⎫
K1b = max ⎨1 − ;0.35⎬ = max {0.363; 0.35} = 0.363
⎩ 5 ⋅ 925.786 ⎭
0.1742
Pa = (1.77·2.7752 + 0.145·0.962·8.52 + 14,5)·(1 – ) = 37.31
1.4 ⋅ 8.5

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 2.949
Pb = (1.77·2.7752 + 0.145·0.363·8.52 + 14.5)·(1 – ) = 23.92
1.4 ⋅ 8.5

a)a Z = 750·1·5.432·37.31·1·1·10-3 = 152.001 cm3

a)b Z = 750·1·5.432·23.92·1·1·10-3 = 97.447 cm3
b) Z = 9.1·750·1·8.5·1·10-3 = 58.012 cm3

Frame under the stringer plate

According to Table 1.6.2, page 4.1.6.21, formula (2), take greater of the following:

а) Z = 1.15Z(1)a
b) Z = 6.7·s·k·h·H2·f2·10-3

H = HMF = 2,775 m, but not less then 2,5 m

h = max{h4; h5}
1 2.775 + 0.5 ⋅ 2.775 + 1.85 + 0, 76
h4 = max{ h0; hta} = { ; 2.775 + 0.5·2.775}
2 2
= {3.386; 4.163}, h4 = 4.163 m
h5 = 2.775 + 0.5·2.775 + 1.85 = 6,01 m
h = 6.01 m
s = 750 mm
f2 = 1
k = 1 – shipbuilding steel factor

a) Z = 1.15·152.001 = 167.201 cm3

b) Z = 6.7·750·1·6.01·2.7752·1·10-3 = 232.658 cm3

Profile taken HP 200 × 11

Frame above the stringer plate

According to Table 1.6.2, page 4.1.6.21, formula (2), take grater of the following:

а) Z = 1.15Z(1)b
b) Z = 6.7·s·k·h·H2·f2·10-3

H = HMF = 2.775 m, but not less then 2.5 m

h = max {h4; h5}
1 0.5 ⋅ 2.775 + 1.85 + 0.76 2.775
h4 = max { h0; hta} = { ; } = {1.999; 1.388},
2 2 2
h4 = 1.999 m
h5 = 0.5·2.775 + 1.85 = 3.238m
h = 3.238 m
s = 750 mm
f2 = 1, k = 1

a) Z = 1.15·97.447 = 107.162 cm3

b) Z = 6.7·750·1·3.238·2.7752·1·10-3 = 125.277 cm3

Profile taken HP 160 × 9

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Inner skin frame

The calculation is the same as calculation for deep tank bulkhead Table 1.9.1, page
4.1.9.28, formula (2):

ρ ⋅ s ⋅ k ⋅ h4 ⋅ le 2
Z=
22 ⋅ γ ⋅ (ω1 + ω 2 + 2)
ω1, ω2 – according to fig. 1.9.1, page 4.1.9.29
γ = 1,4 – for rolled sections
h4 = max {h0/2; hta}

Frame under the stringer plate

le = 2.775 − e2 = 2.775 – 0.1·1 = 2.675 m – effective length of stiffening member

1 2.775 + 0.5 ⋅ 2.775 + 1.85 + 0, 76
h4 = max { h0; hta} = max { ; 2.775 + 0.5·2.775}
2 2
= {3.386; 4.163}, h4 = 4.163 m
ω1 = 0, ω2 = 1
1.025 ⋅ 750 ⋅1 ⋅ 4.163 ⋅ 2.6752
Z= = 247.808 cm3
22 ⋅1.4 ⋅ ( 0 + 1 + 2 )

Profile taken HP 200 × 12

Frame above the stringer plate

le = 2,775 m – effective length of stiffening member

1 0.5 ⋅ 2.775 + 1.85 + 0.76 2.775
h4 = max { h0; hta} = { ; } = {1.999; 1.388},
2 2 2
h4 = 1.999 m
ω1=1, ω2=0
1.025 ⋅ 750 ⋅1⋅1.999 ⋅ 2.7752
Z= = 128.055 cm3
22 ⋅1.4 ⋅ (1 + 0 + 2 )

Profile taken HP 160 × 10

Web frame on the hull side

Web frame in torsion box

The torsion box has longitudinal framing so it is calculated according to Table 1.6.3,
page 4.1.6.23, formula (2) (same formula is used for both plates of the double hull,
inner and outer plate):

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Z = 11.71·ρ·k·S·h4 ·le2

ρ = 1.025 t/m3
S = 2.25 m
0.5 ⋅1.85 + 0.76 1.85
h4 = max {h0/2; hta} = maх { ; } = max {0.843; 0.925},
2 2
h4 = 0.925 m
le= 1.85 m = hTK

Z = 11.71·1.025·1·2.25·0.925·1.85 2 = 85.497 cm3

Chosen built section is 300×10 mm. Section modulus for chosen profile is
significantly greater then it needed, but the height of the profile have to be at least 300
mm and the reason for that is that the torsion box and deck longitudinals have to pass
trough this frame.

Web frame in area between torsion box and double bottom

Table 1.6.3, page 4.1.6.23, formula (3) for transverse framing:

Z determined from calculation based on following assumptions:

(a) fixed ends
(b) point loadings
(c) head h4 or hT1 as applicable
(d) bending stress σ = 93.2/k = 93.2 N/mm2 = 9.32 kN/cm2 N/mm 2
(e) shear stress σ = 83.4/k = 83.4 N/mm2 = 8.34 kN/cm2
(k = 1)

Z = Mmax/σ

Mmax = P·l/8
P = p·A
1
A = H·S
2
H = 8.5 – 1.1 – 1.85 = 5.55 m
S = 2.25 m
A = 6.244 m2
According to Table 3.5.1, page 3.3.5.13 for deep tank:
p = 9.82·h4 /C
C = 0.975
2.775 + 1.85 + 0.76
h4 = max {h0/2; hta} = max{ ; 2.775} = max {2.693; 2.775}
2
h4 = 2,775 m
p = 27.949 kN/m2
P = 174.508 kN
l = H = 5.55 m
Mmax = 174.508·5.55/8 = 121.065 kNm
121065
Z = Mmax/σ = = 1298.98 cm3
93.2

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Built section:

f = 0.3(l/b)2/3
l = 2.775 m – effective length of stiffening member
b = 2.25 m – built area breadth
f = 0.345
A = 10·f·b·tb
tb = 11 mm – side plate thickness
А = 85.392 cm2
Assumed web dimesions: dw = 350 mm, tw = 15 mm
z t d
C= = 0.0435, w w = 0.615 ⇒ a/A = 0.28, a = 23.91 cm2
A ⋅d 100 A
Chosen built section: dw = 350 mm, tw = 15 mm, a = 120×20 (24 cm2)
Z = 1320cm3

Stringers in double hull

Stringers in double hull, for transverse framing, are calculated according to Table
1.6.3, page 4.1.6.23, formula (2):

Z = 11.71·ρ·k·S·h4·le2

ρ = 1.025 t/m3
S = 2.775 m
2.775 + 1.85 + 0.76
h4 = max {h0/2; hta} = max{ ; 2.775} = max {2.693; 2.775}
2
h4 = 2.775 m
le= 2.25 m

Z = 11.71·1.025·1·2.775·2.775·2.252 = 467.920 cm3

Built section:

f = 0.3(l/b)2/3
l = 2.25 m – effective length of stiffening member
b = 2.775 m – built area breadth
f = 0.261
A = 10·f·b·tb
tb = 11 mm – side plate thickness
А = 79.626 cm2
Assumed web dimesions: dw = 220 mm, tw = 10 mm
z t d
C= = 0.0267, w w = 0.276, ⇒ a/A = 0.16, a = 12.74 cm2
A ⋅d 100 A
Chosen built section: dw = 220 mm, tw = 10 mm, a = 95 ×15 (14.25 cm2)
Z = 470.25 cm3

Thickness of brackets

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Brackets are calculated according Table 10.3.1, page 3.10.3.12, and bracket shape is
shown on the Fig.1.6.2, page 4.1.6.22.
Bracket dimensions, acording to section 3.4.1, have to fulfill following conditions:

a) a+b ≥ 2⋅l
b) a ≥ 0.8⋅l
c) b ≥ 0.8⋅l

⎛ Z ⎞
l = 90 ⋅ ⎜⎜ 2 − 1⎟⎟
⎝ 14 + Z ⎠

Z – section modulus of the stiffener on which bracket is welded.

According to section 3.4.2 the length of arm of tank side and hopper side bracket is to
be not less than 20 per cent greater than that required above.

Thickness of the brackets in deep tank is defined by formula (b) in the Table 10.3.1:

t = 4.5 + 0.25·Z1/2, calculated value has to be from 7.5 mm to 13.5 mm

Flange breadth is defined by formula from section 3.4.5:

⎛ Z ⎞
bf = 40 ⎜1 + ⎟ , but not less then 50 mm
⎝ 1000 ⎠

under the stringer plate above stringer plate

Frame
side plate inner skin side plate iner skin
Z [cm3] 232.6575 247.8078 125.277 128.055
t [mm] 8.313 8.435 7.298 7.329
l [mm] 417.627 429.572 311.394 314.830
l + 20%l 501.1528 515.4861 373.673 377.796
bf [mm] 49.3063 49.91231 45.0111 45.1222

Taken values:

t [mm] 9 9 8 8
a = b [mm] 450 450 350 350
bf [mm] 50 50 50 50

Double hull longitudinals in torsion box

Two side plate and two inner skin plate longitudinals will be fited in torsion box.
Calculation are made for upper and lower longitudinals, and the greater value is taken
for Z.

Lower longitudinal is calculated according to Table 1.6.1, page 4.1.6.20, formula (2)
take greater then:

a) Z = 0,056·s·k·hT1·le2·F1·Fs

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b) Z calculated for deep tank bulkhead stiffeners according to Table 1.9.1, page
4.1.9.28, formula (2):
ρ ⋅ s ⋅ k ⋅ h4 ⋅ le 2
Z=
22 ⋅ γ ⋅ (ω1 + ω 2 + 2)
s = 700 mm – spacing of double skin longitudinals
k=1
⎛ h6 ⎞
hT1 = CW· ⎜⎜1 − ⎟⎟ ·Fλ, for longitudinals above the waterline
⎝ D 2 − T ⎠
1 95.1
but no less then L1 = = 1.359 m for vessels type В
70 70
1
not greater then 0,86·(h5 + D1), za F1 ≤ 0,14 i
8
1
not greater then (h5 + D1), za F1 > 0,14
8
D1 = D = 8.5 m, but not less then 10 m and not greater then 16 m
Value taken D1 = D = 10 m
h5 – vertical distance, in meters, from longitudinal to deck at depth, D2

h5 = 2·0.7 – 8.5 + 8.5 = 1.4 m

D2 C1
F1 = , for longitudinals above D2/2
4 D2 + 20h5
D2 = D, but not greater then 1,6Т = 8.691 m, D2 = 8.5 m

С1 is given for three height points which are used to get result by interpolation:

on the deck Dx1 = 8.5 m, C1 = 60/(225–165FD) , FD = 1, C1=1

8.5
on the height D2/2 is C1=1 (Dx2 = = 4.25 m)
2
for Dx = 8.5 – 1.4 = 7.1 m, C1=1

8.5 ⋅1
F1 = = 0,137 ≤ 0,14
4 ⋅ 8.5 + 20 ⋅1.4
1 10
hT1 but not greater then 0,86·(h5 + D1)= 0.86· (1,4 + ) = 2.279 m
8 8
CW = 7.71·10–2·L·e–0.0044L = 4.825 m
h6 = D – h5 – T = 8.5 – 1.4 – 5.432 = 1.668 m
Fλ =1, for L ≤ 200 m
⎛ 1.668 ⎞
hT1 = 4.825 ⋅ ⎜ 1 − ⎟ ⋅1 = 2.202 m
⎝ 8.5 − 5.432 ⎠
1.359 m < hT1 = 2.202 m
hT1 < 2,279 m ⇒ hT1 = 2.202 m

Fs are given for two height points, which are used to get Fs for adequate height by
interpolation.
1.1 ⎛ 2b f ⎞
for 0.6·D2 (Dx1 = 0.6·8.5 = 5.1 m): Fs = ⎜1 − (1 − k) ⎟ = 1.1
k ⎝ Bf ⎠
for D2 (Dx2 = 8.5 m): Fs = 1

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Dx = 8.5 – 1.4 = 7.1 m
1.1 − 1
Fs = ·(8.5 – 7.1) + 1 = 1.041
8.5 − 5.1
ρ = 1.025 t/m3
2 ⋅ 0.7 + 0.76
h4 = max{h0/2; hta} = max{ ; 2·0.7} = {1.08; 1.4} = 1.4 m
2
le = 3·0.75 = 2.25 m – effective length of stiffening member
γ = 1,4 – for rolled sections
ω1, ω2 according to Fig. 1.9.1, page 4.1.9.29
ω1 = 1, ω2 = 1

a) Z = 0,056·700·1·2.202·2.252·0.137·1.041 = 62.371 cm3

1.025 ⋅ 700 ⋅1 ⋅1.4 ⋅ 2.252
b) Z = = 41.277 cm3
22 ⋅1.4 ⋅ (1 + 1 + 2 )

Upper longitudinal:

⎛ h6 ⎞
hT1 = CW· ⎜⎜1 − ⎟⎟ ·Fλ, for longitudinals above the waterline,
⎝ D2 − T ⎠
1 95.1
not less then L1 = = 1.314 m for vessels type В
70 70
1
not greater then 0,86·(h5 + D1), za F1 ≤ 0,14 i
8
1
not greater then (h5 + D1), za F1 > 0,14
8
D1 = D = 8.5 m, fut not less then 10 m and not greater then 16 m
Value taken D1 = D = 10 m
h5 = 0.7 – (8.5 – 8.5) = 0.7 m
D2 C1
F1 = , for longitudinal above D2/2
4 D2 + 20h5
D2 = D, but not greater then 1,6Т = 8.691 m, D2 = 8.5 m

С1 is given for three height points which are used to get result by interpolation:

on the deck Dx1 = 8.5 m, C1 = 60/(225–165FD) , FD = 1, C1=1

8.5
on the height D2/2 je C1=1 (Dx2 = = 4.25 m)
2
for Dx = 8.5 – 0.7 = 7.8 m, C1=1
8.5 ⋅1
F1 = = 0,177 > 0,14
4 ⋅ 8.5 + 20 ⋅ 0.7
1 10
hT1 not greater then (h5 + D1) = (0.7 + ) = 1.95 m
8 8
CW = 7.71·10–2·L·e–0.0044L = 4.825 m
h6 = D – h5 – T = 8.5 – 0.7 – 5.432 = 2.368 m
Fλ =1, for L ≤ 200 m
⎛ 2.368 ⎞
hT1 = 4.825 ⋅ ⎜ 1 − ⎟ ⋅1 = 1.101 m,
⎝ 8.5 − 5.432 ⎠

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1.359 m > hT1 = 1.101 m ⇒ hT1 = 1.359 m

Fs are given for two height points, which are used to get Fs for adequate height by
interpolation.
1.1 ⎛ 2b f ⎞
for 0.6·D2 (Dx1 = 0.6·8.5 = 5.1 m): Fs = ⎜1 − (1 − k) ⎟ = 1.1
k ⎝ Bf ⎠
for D2 (Dx2 = 8.5 m): Fs = 1
Dx = 8.5 – 0.7 = 7.8 m
1 − 1.1
Fs = ·(8.5-7.8) + 1 = 1.021
8.5 − 5.1
0.7 + 0.76
h4 = max{h0/2; hta} = max{ ; 0.7} = {0.73; 0.7} = 0.73 m
2
le = 3·0.75 = 2.25 m – effective length of stiffening member
γ = 1.4 – for rolled sections
ω1, ω2 according to Fig. 1.9.1, page 4.1.9.29
ω1 = 1, ω2 = 1

a) Z = 0.056·700·1·1.359·2.252·0.177·1.021 = 48.726 cm3

1.025 ⋅ 700 ⋅1⋅ 0.73 ⋅ 2.252
b) Z = = 21.523 cm3
22 ⋅1.4 ⋅ (1 + 1 + 2 )

longitudinals are choese according to Z = 62.371 cm3 i t = 12 mm.

HP 120 × 8

Double bottom structure

Center bottom girder

Minimal height and thickness of the center girder are defined in the section 8.3.1,
page 4.1.8.25:

q = dDB = 28·B + 205·T1/2 = 28·16 + 205·5.4321/2 = 625.786 mm,

but not less then 650 mm

Center bottom girder thickness:

t = (0.008·dDB + 4)·k1/2 = 11.406 mm

Chosen dimensions of center bottom girder are 1100x12 mm

Side bottom girders

Number of side bottom girders and their thickness are defined in section 8.3.4, page
4.1.8.25. For vessel breadth of В = 16 m ( 14 m ≤ B = 16 m ≤ 21 m) one pair of side
bottom girders is taken. Their thickness should be greater then:

t = (0.0075·dDB + 1)·k1/2 = 7.943 mm

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 Chosen dimensions of side bottom girders are 1100х8 mm

Floors

Floors are defined in section 8.5.1, page 4.1.8.26. Spacing between them is 2.25 m
(3·0.75 m), and it shouldn’t be less then 3,8 m. Floors thickness is defined as:

t = (0.009·dDB + 1)·k1/2 = 9.332 mm, and it should be between 6 mm and 15 mm

Chosen thickness of floors is t = 10 mm.

Vertical stiffeners are fitted on every pair of longitudinals. Their thickness is equal to
the thickness of the floors, and their breadth is minimum 150 mm. Chosen stiffeners
are ≠ 150×10

Watertight floors

According to 8.5.2, page 4.1.8.26, thickness of the watertight floors should be greater
then:

i) t = (0.008·dDB + 3)·k1/2 = 10.406 mm

ii) t = (0.009·dDB + 1)·k1/2 = 9.332 mm

Chosen thickness of watertight floors is t = 11 mm

Watertight floors stiffeners

Section modulus of watertight floors stiffeners is calculated according to 8.5.4, page

4.1.8.26:

Z = 5,41·dDBA2·hDB·s·k·10–9

dDBA = 1100 mm
hDB = D – dDB + 0.76 = 8.5 – 1.1 + 0.76 = 8.16 m
s = 800 mm
k=1

Z = 5.41·11002·8.16·800·1·10–9 = 42.733 cm3

Chosen stiffeners are ≠ 140×10

Inner bottom thickness

According to 8.4.1, page 4.1.8.26:

t = 0.00136·(s + 660)· 4 k 2 LT = 0.00136·(800 + 660)· 4 12 ⋅ 95.1 ⋅ 5.432 = 9.47 mm

Chosen inner bottom thickness is t = 10 mm

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Inner bottom longitudinals

according to 8.4.5, page 4.1.8.26:

Z = 0.85·Zbottom longitudinals
Z = 0.85·165.066= 140.306 cm3
HP 180 × 8

Weather deck

Weather deck structure

Weather deck thickness outside line of openings

Table 1.4.1, page 4.1.4.4, formula (1), take greater of:

i) t = 0.001·s1·(0.059·L1 + 7)·(FD/k)1/2
ii) t = 0.00083·s1·(L·k)1/2 + 2,5

s1 = s = 800 mm – spacing of the longitudinals, which cannot be less then:

{470 + L/0.6 = 628.5 mm; 700 mm}
1
i) t = 0.001·800·(0.059·95.1 + 7)· = 10.089 mm
1
ii) t = 0.00083·800· 95.1 ⋅1 + 2.5 = 8.975 mm

Chosen weather deck thickness outside line of openings t = 11 mm

Weather deck thickness inside line of openings

Deck breadth cannot be less then:

w = 1000 + 1.5L = 1000 + 1.5·95.1 = 1142.65 mm

Weather deck thickness inside line of openings is defined by section 4.3.2, page
4.8.4.8, as greater then:

a) t = 0.012·s1 = 0.012·800 = 9.6 mm

b) t = 0.00083·s1·(L·k)1/2 + 2.5 = 8.875 mm
c) t = min{10 + 0.01L; 12} = min{10.951; 12} = 10.951 mm

Chosen weather deck thickness inside line of openings t = 11 mm.

Weather deck longitudinals

Table 1.4.3, page 4.1.4.5

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Lonitudinals outside line of openings

Formula (1)(а)

Z = 0,0106·s·k·le2·K

s = 800 mm – spacing of weather deck longitudinals

le = 3·0.8 = 2.4 m – effective length of longitudinals
22.6 ⋅ L1
K= ⋅ c1 , but not less then 1.2·c1
1780 − L1
810
c1 = =1
2450 − 1640 FD
22.6 ⋅ 92
K= ·1 = 1.276 > 1.2·c1
1780 − 92

Z = 0.0106·800·1·2.42·1.232 = 62.306 cm3

HP 120 × 8

Lonitudinals inside line of openings

Formula (1)(b):

Z = s·k·(400·h1 + 0.005(le·L)2)·10-4

L2 = L = 95.1 m, ali ne veće od 215 m

le = 3·0.8 = 2.4 m – effective length of longitudinals
Table 3.5.1, page 3.3.5.12
h1 = 1.2 + 2.04·E
5.2.1, page 3.3.5.16
0.0914 + 0.003L
E= – 0.15 = -0.027, but not less then 0 and not greater then 0.147
D−T
Е=0
h1 = 1.2 + 2.04·0 = 1.2 m

Z = 800·1·(400·1.2 + 0.005·(2.4·95.1)2)·10-4 = 59.237 cm3

HP 120 × 7

Longitudinals on the top and bottom of torsion box

Torsion box is used as ballast tank, so longitudinals on the bottom and top of torsion
box has to be calculated by formula (2):

Z = 0.0113·ρ·s·k·h4·le2/b

ρ = 1.025 t/m3
s = 700 mm
k=1
h4 = 0.5·0.76 = 0.38m

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le = 3·0.75 = 2.25 m
b = 1.4 – for rolled or built section

0.0113 ⋅1.025 ⋅ 700 ⋅1⋅ 0.38 ⋅ 2.252

Z= = 11.14 cm3
1.4

Chosen longitudinals outside line of opening on weather deck can be used as

longitudinals on the top of the torsion box: HP 120 × 8

Longitudinals on the bottom of torsion box:

Z = 0.0113·ρ·s·k·h4·le2/b

1.85 + 0.76
h4 = = 1.305 m
2

0.0113 ⋅1.025 ⋅ 700 ⋅1 ⋅1.305 ⋅ 2.252

Z= = 38.26 cm3
1.4

HP 100 × 7

Cargo hatchways

Cargo hatchway is defined by height and thickness. It height cannot be less then 600
mm. Cargo hatchway thickness is defined by section 4.5.1, page 4.1.4.8, as greater
then:

i) t = 0.008·HC· k + 1 = 0.008·2000· 1 + 1 = 17 mm
ii) t = 11 mm

Chosen hatchway plates thickness is t = 17 mm and height is h = 2000 mm

Cargo hatchways stiffeners

HP 220 × 10

Watertight bulkheads

Thickness of the watertight bulkheads is given in the Table 1.9.1, page 4.1.9.28,
formula (1):

t = 0.004·s·f·(h4·k)1/2, but not less then 5.5 mm

s = 800 mm – spacing of weather deck longitudinals

2
h4 = ·(8.5 – 1.1) + 0.91 = 5.843 m
3
s
f = 1.1 − , but not greater then 1
2500 ⋅ S
S = D – dDB = 8.5 – 1.1 = 7.4 m

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 800
f = 1,1 – = 1.057, f = 1
2500 ⋅ 7.4
t = 0.004·800·1· 5.843 ⋅1 = 7.735 mm

Value taken t = 8 mm
Watertight bulkheads siffeners

According to Table 1.9.1, page 4.1.9.28, formula (2):

s ⋅ k ⋅ h4 ⋅ l e2
Z=
71 ⋅ γ ⋅ (ω 1 + ω 2 + 2)

s = 800mm
k=1
8.5 − 1.1
h4 = + 0.91 = 4.61 mm
2
le = D – dDB – e1 = 8.5 – 1.1 – 0.12 = 7.28 m
γ = 1.4 – for rolled sections
ω1, ω2 according to Fig, 1.9.1, page 4.1.9.29
ω1 = 1, ω2 = 1
800 ⋅1⋅ 4.61⋅ 7.282
Z= = 491.595 cm3
71⋅1.4 ⋅ (1 + 1 + 2 )

HP 260 × 13

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