Department of Naval Architecture & Ocean Engg, IMU , M.
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MIDSHIP SECTION
INTRODUCTION
Midship section design is in accordance with Part 4, Chapter 9 of Lloyds Register,
Rules and Regulations for Classification of Ships, which has been revised to include requirements
for Double Hull Oil Tankers. These requirements reflect regulation 13F of Annex I of MARPOL
73/78 with the other features. Fig.1 is a typical midship section of a double skin tanker.
Figure 1 - Typical midship section of a double skin tanker
1.1. Definitions
(1)
Rule length, in m, is the distance, in meters, on the summer load water line
from the forward side of the stem to the after side of the rudderpost or to
the center of the rudder stock, if there is no rudder post. L is neither to be
less than 96% nor to be greater than 97% of the extreme length on the
summer load water line.
97% of extreme length of LWL = 229.89m
(2)
Breadth at amidships or greatest breadth, in meters.
B = 42.0 m
(3) D
Depth is measured, in meters, at the middle of the length L, from top of the keel
to top of the deck beam at side on the uppermost continuous deck.
(4)
= 22.0 m
= 14 m
T is the summer load draught in m, measured from top of keel.
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(5)
LPP
Distance
in
on
the
summer
LWL
from
foreside
of
the
stem
to
after
side
of rudder post, or to the center of the rudder stock, if there is no rudder post.
(6)
LPP
= 233 m
CB
Moulded
block
coefficient
at
draught
corresponding
to
summer
waterline, based on rule length L and moulded breadth B, as follows:
moulded displacement (m3) at draught T
CB
=
L.B.T
(7)
The
width
of
plating
supported
by
the
primary
member
or
secondary
member in m or mm respectively.
(8)
be
The effective width, in m, of end brackets.
(9)
bI
The
minimum
longitudinal
distance
bulkhead
from
measured
side
shell
to
inboard
at
right
the
inner
angles
hull
to
the
or
outer
centre
line
at summer load water line, in m
(10)
le
Effective
length,
in
m,
of
the
primary
or
secondary
member,
cargo
tank
boundary
and
measured
between effective span points.
(11)
ds
The
distance,
in
m,
between
the
the
moulded
line of the side shell plating.
(12)
The load height applied to the item under consideration, in m.
(13)
db
The
distance,
moulded
line
in
of
m,
the
between
bottom
the
shell
bottom
plating
of
the
measured
cargo
at
tanks
right
angles
and
the
to
the
bottom shell plating.
(14)
kL, k :
Higher tensile steel factors. For mild steel, kL, k may be taken as 1.
(15)
Moment
of
inertia,
in
cm3,
of
the
primary
or
secondary
member,
in
primary
or
secondary
member,
in
association with an effective width of attached plating.
(16)
Spacing of secondary members, in mm.
(17)
Overall span of frame, in mm
(18)
Thickness of plating, in mm.
(19)
Section
modulus,
in
cm3,
of
the
association with an effective width of attached plating.
(20)
L1
Length of ship in meters, but need not be greater than 190m.
(21)
CW
Wave head, in m.
(22)
RB
Bilge radius, in mm.
Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I
(23)
FD,FB :
Local
scantling
respectively.
reduction
factor
above
neutral
axis
FD
= 0.67, for plating and 0.75, for longitudinals
FB
= 0.67, for plating and 0.75, for longitudinals
(24)
Specified minimum yield stress, in N/mm2
(25)
Maximum compressive hull vertical bending stress, in N/mm2
(26)
T1
T but to be taken not less than 0.05L m
and
below
neutral
axis
= 11.495 m
(27)
hT1
T + CW m but need not be taken greater than 1.36 T
(28)
hT2
T + 0.5CW m but need not be taken greater than 1.2 T
(29)
c1
60 / (225 165 FD) at deck; 1.0 at D/2; 75 / (225 150FB) at base `
line
of ship
(30)
c2
165 / (345 180FB) at deck; 1.0 at D/2;
165/(345 180FB) at base line of
ship
(31)
sin, where is the roll angle in degrees
sin
R
(32)
D1
= (0.45+0.1 L/B)(0.54 L/1270)
=0 .358
D, in m, but is to be taken not < 10 and need not be taken >16
D1 = 16m
sin = (0.45 + 0.1L/B)(0.54 L / 1270 )
R = 0.358
(33) dDB
Rule depth of center girder, in mm
(34)
SS
Span of the vertical web, in m
(35)
tW
Thickness of web, in mm
(36)
tB :
Thickness of end bracket plating, in mm
1.1.2. Class Notation
Vessel is designed to be classed as +100 A1 Double Hull Oil Tanker ESP. ESP means
Enhanced Survey Program. This is for seagoing tanker having integral cargo tanks for carriage of oil
having flash point > 60o C.
1.1.3. Cargo Tank Boundary Requirements
Minimum double side width (ds) in m
Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I
ds
0.5 + (dwt/20,000) or ds = 2.0 m
whichever is lesser. But ds should not be less than 1 m.
ds
0.5+(95,000/20,000) = 5.25 m
Double side width is taken as 2.0 m to get the required ballast volume.
ds
2.0 m
Minimum double bottom depth (dB)
dB
B/15 or dB = 2.0 m
whichever is lesser
dB
= 42/15 = 2.8
A double bottom height of 2.0 m is provided to get the required ballast volume.
dB
2.0 m
Structural configuration adopted has a single centerline longitudinal bulkhead. According
to Maritime Law of India (Appendix V111:63, Regulation 24), Length of cargo hold shall not exceed
10m or (0.25bi /B +0.15) x LL (for longitudinal bulkhead provided at centerline), whichever is greater.
[LRS Part 4, Chapter 9, Section 1.3.9]
(0.25bi /B +0.15) LL
35.85 m
For length of cargo tanks and tank boundaries refer General Arrangement Plan.
Type Of Framing System
The bottom shell, inner bottom and deck are longitudinally framed (for L > 75m). The
side shell, inner hull bulkheads and long bulkheads are also longitudinally framed (L > 150m). When
the side shell in long framed, the inner hull bulkhead is also to be framed longitudinally. Primary
members are defined as girders, floors, transverses and other supporting members.
LONGITUDINAL STRENGTH
Design vertical wave bending moment
(P3, C4, S5.2)
The appropriate hogging or sagging design hull vertical wave bending moment at
amidships is given by the following:
Mw
Where,
f1 f2 Mwo
Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I
M wo
0.1C1 C2 L2 B (C b + 0,7) kN m
Cb is to be taken not less than 0,60
C1 is given in Table 4.5.1 = 10.163
C2
1, (also defined in 5.2.2 at other positions along the length L)
f1
ship service factor. For unrestricted sea-going service f 1 = 1,0
f2
1,1 for sagging (negative) moment
f2
for hogging (positive) moment
1.025
0.110.1631(229.89) 242(.825+0.7)
3440180.424 KNm
1-1.13440180.424 =-3784198.47
11.0253440180.424 =3526184.935
1.9C b
M wo
Mw
(C b + 0.7)
(sagging)
(hogging)
Permissible Still water Bending Moment
Ms
fsnCwL2B(CB+0.7) KNm
fsn
0.072
Cw
10.75-{(300-L)/100}3/2
Ms
0.07210.163(229.89)242(0.825+0.7)
247692.991 KNm
for sagging bending moment
Hull Moment of Inertia
(P3, C4, S5. 8)
(| M s + M w |)
Imin
3L
139.373 m4
kL
10 5 m4
Minimum Hull Section Modulus [LRS Part 3, Chapter 4, Section 5]
The hull midship section modulus about the transverse neutral axis, at the deck or keel is
to be not less than
Z min
f1KL C1L2B (CB + 0.7) x 10-6 m3
Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I
f1
ships
the
service
service
factor.
restriction
T
and
be
in
any
specially
event
For unrestricted sea going service f1 = 1.0
f1 taken as 1
For M.S; KL
1 [Part 3 Chap.2 Sec 1.2]
C1
10.75 [(300-L)/100] 1.5 for 90<L<300m
10.163
CB
Block Coefficient = 0.825
Zmin
34.4018 m3
Hull Envelope Plating
Itemization of parts is shown in figure 8.2.
Fig.2
For longitudinally framed system [LRS Part 4, Chapter 9, Section 4]
O/C = 235/175 = 1.34
1720.5{(1-1/)/O} for < 2
56.53
s/J + 2.0
spacing of deck longitudinals = 850 mm
56.53
1) Deck plating
considered
should
not
depending
be
less
than
upon
0.5.
Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I
17 mm
2) Sheer strake
The greatest of the following is to be taken:
a)
0.0042 s hT1k
spacing of longitudinals = 700 mm
hT1
1.36T = 19.04
1, for mild steel
15.17 mm
s/J + 2 = 17 mm
17 mm
Selected t
17 mm
or
b)
3) Side shell above mid-depth
The greatest of the following is to be taken:
a)
0.001s(0.059L1 + 7) FD/ kL
spacing of side shell longitudinals = 700 mm
FD
0.67 (refer DEFINITIONS)
L1
190 m (refer DEFINITIONS)
kL
1 (refer DEFINITIONS)
12.67 mm
0.0042 s hT1k, whichever is greater
hT1
19.04 m, as shown in pervious sections
1 (refer DEFINITIONS)
15.18 m
Selected t
16 mm
or
b)
4) Side shell below mid-depth
The greatest of the following is to be taken:
Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I
a)
0.001s (0.059L1 + 7) FB/kL
12.67 mm
0.0042 s hT1k
spacing of shell longitudinals = 850mm
15.18 mm
Selected t
16 mm
But not less than
5) Bottom shell and bilge
The greatest of the following is to be taken:
a)
b)
s/J + 2.0
spacing of bottom and bilge longitudinals = 850 mm
56.53
17 mm
0.0052s
hT2
1.8-FB
T + 0.5CW m but need not be taken greater than 1.2T
16.52
FB
0.67 (refer DEFINITIONS)
1 (refer DEFINITIONS)
16.61 mm
Selected t
17 mm
hT2k
6) Keel Plating
Keel plating should be equal to thickness of bottom shell + 2 mm
t
but need not exceed t
Selected t
19 mm,
25 k = 25 mm
19 mm
Width of keel plate is to be not less than 70B mm, but need not exceed 1800 mm and is
to be not less than 750 mm. ( LRS part 4, chapter1,table 1.5.1)
70B
2940mm
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1800 mm
t0 / 2-FB
t0
0.005s kh1
spacing of inner bottom longitudinals = 850mm
distance in m, from the plate in consideration to the highest
7) Inner bottom Plating
point of the tank, excluding hatchway.
t0
0.72 (h+Rbi)
19.4
0.36 (refer previous sections)
b1
B/2 = 21 m
18 mm
8) Inner hull plating
same as outer shell,t = 18mm
Hull Framing [LRS Part 4, Chapter 9, Section 5]
1) Bottom Longitudinals
The section modulus of bottom longitudinals within the cargo tank region is not to be
less than greater of the following:
a)
Z = 0.056kh1sle2F1FS cm3
K
1 (refer DEFINITIONS)
h1
(h0
(0.00L1
D1/8),
+
but
0.7)
in
m,
no
case
whichever
be
is
taken
greater
less
&
than
need
L 1/56
not
be
or
taken
greater than (0.75 D + D1/8), for bottom longitudinals.
h0
distance
in
m,
from
the
midpoint
highest point of tank, excluding hatchway.
=
22 m
D1
16 m (refer DEFINITIONS)
h1
18.5 m
of
span
of
stiffener
to
Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I
s
le
spacing of bottom longitudinals = 850 mm
s,
where
le
effective
span
of
longitudinals
assumed to be supported by web frames spaced at 5s, where s
spacing in midship region = 850 mm
b)
le
4.25 m
F1
Dc1/(25D-20h)
c1
75/(225 150FB), at base line of ship.
FB
0.75 (refer DEFINITIONS)
c1
0.667
distance of longitudinal below deck at side, in meters
22 m
22m (refer DEFINITIONS)
F1
0.1334
FS
1, at upper deck at side and at the base line
2121.84 cm3
0.0051kh3sle2F2 cm3
1 (refer DEFINITIONS)
h3
ho+ Rbi
b1
21 m
(0.45+0.1 L/B)(0.54 L/1270) = 0. 358
22 m
h3
29.52
but not greater than or equal to,0.75D+Rbi
= 24.02
Therefore h3 = 24.02
Z
1880.79 cm3
Greater of the two is to be taken, i.e. Z = 2121.84 cm3
Selected Half bulb section of scantling 430x21 .
2) Deck Longitudinals
which
basic
are
frame
Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I
The modulus of deck longitudinals within the cargo tank region is not to be less than
greater of the following:
a)
0.056kh1sl2eF1FS cm3 ( LRS, part 4,chapter 9,5.3.1)
1 (refer DEFINITIONS)
h1
(h0
h0
0 ( for deck longitudinals)
L1
190 m
D1
16
L1/56
3.39
h1
L1/56
850 mm
le
4.25m
F1
Dc1 / (4D + 20h)
0 (for deck longitudinals)
c1
60 / (225 165FD) at deck
FD
0.75 (refer DEFINITIONS)
c1
0.593
F1
0.1475
Fs
1, at upper deck at side and at baseline of ship
429.9 cm3
0.36
bi
B/2
21m
h3
h0 + Rbi
7.56 m
850 mm
le
4.25m
F2
Dc2 / (D + 2.18h)
c2
165 / (345 180FD)
FD
0.75
c2
0.785
F2
0.785
(h0 + D1/8)
D1/8),
but
in
no
case
be
3.39
b) Z = 0.0051kh3sl2eF2 cm3
(refer DEFINITIONS)
taken
less
than
L 1/56
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464.7 cm3
Greatest of the two is to be taken, i.e. Z = 464.7 cm3
Taken half bulb section of scantling 260x12.
3) Side Shell Longitudinals
( LRS part 4, chapter 9,5.3.1)
From standardization point of view the side shell is divided into longitudinal fields as
shown in fig 8.2. Design of the longitudinals for each field is done using the information for the
lowest longitudinal in each field.
Fig. 1.3 Plate fields for the determination of side,
inner hull and CL bulkhead longitudinals
The modulus of side shell longitudinals within the cargo tank region is not to be less than
greater of the following:
a)
0.056kh1sle2F1Fs cm3
b)
0.0051kh3sle2F2 cm3
h1
(h0
850 mm
le
4.25m
FD
0.75
D1
16
L1
190m
L1/56
3.39
where,
+
D1/8),
but
in
no
case
be
taken
less
than
L 1/56
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distance of longitudinal below deck at side, in meters
h3
h0 + 2xRb1
For side longitudinals above D/2,
F1
Dc1 / (4D + 20h)
F2
Dc2 / (D + 2.18h)
For side longitudinals below D/2,
F1
Dc1/(25D-20h)
F2
Dc2/(3.18D-2.18h)
Table 1.1 Determination of scantlings of side longitudinals
Item
REG 1
REG 2
REG 3
REG 4
ho
10
15
20
D1
16
16
16
16
h1= h0+D1/8
12
17
22
h3
20.12
25.12
30.12
35.12
F1
0.12
0.12
0.12
0.12
F2
0.73
0.73
0.73
0.73
Fs
a) Z
722.211
1238.076
1650.768
2063.46
b) Z
1141.82
1427.62
1656.25
1884.89
Taken Z
1141.82
1427.62
1656.25
2063.46
Section
Half bulb
Half bulb
Half bulb
Half bulb
Scantling
370x13
400x14
430x15
430x21
Z of taken section
1150
1450
1800
2150
1.2.4.
Inner Hull, Inner Bottom And Longitudinal Bulkheads
The inner hull, inner bottom and longitudinal bulkheads are longitudinally framed.
The symbols used in this section are defined as follows:
b1
the greatest distance in meters, from the centre of the plate panel
or midpoint of the stiffener span, to the corners at top of the tank
on either side.
c1
60 / (225 165FD) at deck
1.0 at D/2
75/(225 150FB), at base line of ship
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c2
h
(a)
165/(345 180FB) at deck
1.0 at D/2
165/(345 180FD) at baseline of ship
load height, in meters measured vertically asfollows:
for bulkhead plating the distance from a point one third of the height of the plate panel above its lower edge to the
highest point of the tank, excluding hatchway
(b)
for bulkhead stiffeners or corrugations, the distance from the midpoint of span of the stiffener or corrugation to the
highest point of the tank, excluding hatchway
h1
(h + D1/8), but not less than 0.72(h + Rb1)
h2
(h + D1/8), in meters, but in no case be taken less than L1/56 m .
h3
distance of longitudinal below deck at side, in meters, but is not to
be less than 0
h4
h + Rb1
h5
h2 but is not to be less than 0.55h4
t0
0.005s kh1
t1
t0(0.84 + 0.16(tm/t0)2)
tm
minimum value of t0 within 0.4D each side of mid depth of
bulkhead
1) Longitudinal Bulkhead Plating
For the determination of scantlings of longitudinal bulkhead plating [16, Part 4, Chapter
9], the fields in fig. 1.2 are assumed.
Region1
b1
21 m
3.33
h1
5.33
t0
0.005s kh1
11.85 mm
10.27 mm
but not less than t1
t0
2-FB
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t0 (0.84+0.16(tm / t0 )2
11.85 mm
b1
21 m
6.66
h1
10.18
t0
13.56
t1
t0 (0.84+0.16(tm / t0 )2
13.56 mm
t1
( Selected 12 mm)
Region2
( Selected 14mm)
Region3
b1
21 m
9.33
h1
11.33
t0
11.38t1 = t0 (0.84+0.16(tm / t0 )2
14.78 mm
12.81 mm
t1
14.78 mm (selected 15mm)
b1
21 m
12
h1
14
t0
15.91
13.79 mm
t1
t0 (084+0.16(tm / t0 )2
15.91 mm (Selected 16mm)
Region4
2) C.L Longitudinal Bulk Head Longitudinals and Inner Hull Longitudinals
Inner hull and longitudinal bulkheads are to be horizontally stiffened. The modulus of
longitudinals is not to be less than greater of the following:
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(a)
Z = 0.056kh2sl2eF1 cm3
(b)
Z = 0.0051kh4sl2eF2 cm3
The inner hull and bulkhead plating is divided into various strakes for the determination
of center line bulkhead longitudinals and inner hull longitudinals.
L1/56
3.39
850 mm
le
4.25m
Table 1.2 Determination of scantlings of CL longitudinal bulkhead
longitudinals .
Region 1
Region 2
Region 3
Region 4
b1
21
21
21
21
10
14
18
h2
12
16
20
h4
12.488
17.488
21.488
25.488
F1
0.12
0.12
0.12
0.12
F2
0.73
0.73
0.73
0.73
Z1
722.211
1238.076
1650.768
2063.46
Z2
713.81
999.6
1228.24
1456.88
Taken Z
722.211
1238.076
1650.768
2063.46
Section
Half bulb
Half bulb
Half bulb
Half bulb
Scantling
300x14
370x16
430x15
430x21
Z of taken section
740
1300
1800
2150
Table 1.3 Determination of scantlings of inner hull longitudinals
Region 1
Region 2
Region 3
Region 4
b1
21
21
21
21
10
14
18
h2
12
16
20
h4
18.536
23.536
27.536
31.536
F1
0.12
0.12
0.12
0.12
F2
0.73
0.73
0.73
0.73
Z1
722.211
1238.076
1650.768
2063.46
Z2
1059.51
1345.31
1573.94
1802.58
Taken Z
1059.51
1345.31
1650.768
2063.46
Section
Half bulb
Half bulb
Half bulb
Half bulb
Scantling
370x13
400x14
430x15
430x21
Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I
Z of taken section
1150
1450
1800
2150
3) Inner Bottom Plating and Longitudinals
The inner bottom is to be longitudinally framed and the inner bottom plating thickness is
to be
t
t0 / 2-FB
t0
0.005s kh1
20 m
D1
16
0.36
h1
h + D1/8 = 22m
t0
20mm
18.12 mm
Selected t
18 mm
The modulus of longitudinals is not to be less than greater of the following:
(a)
(b)
0.056kh2sl2eF1 cm3
20 m
D1
16 m
h2
h + D1 / 8 =
c1
0.667
F1
0.095
2063.46 cm3
0.0051kh4sl2eF2 cm3
h4
h + Rbi = 31.536m
c2
0.785
F2
0.64
but minimum value of F2 = 0.73
Z
2063.46 cm3
22 m
Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I
. Hence, Half bulb section of scantling 430x21 is taken having section modulus of 2150
cm3.
1.2.5. Primary Members Supporting the Hull Longitudinal Framing
1) Centre girder
(LRS part 4 chapter 1,8.3.1)
(a) Minimum depth of centre girder
dDB
28B + 205 T mm
dDB
1943.04 mm
Given 2.0m.
(b)
Minimum thickness of centre girder( LRS, part 4, chapter 9,14.2.5)
t
Given thickness
(0.008 dDB + 1) k
17 mm
17 mm
2) Floors and Side Girders ( LRS part 4, chapter 9,14.2.5)
=
(0.007dDB + 1) k
15 mm
but not to exceed 12 k
12 mm
given thickness
12 mm
12 mm
3) Deck Transverses
Section modulus of deck transverses is not to be less than
Z
53.75 (0.0269sL + 0.8) (ST + 1.83)k cm3
4.25 m
233 m
ST
span of transverse
13.3 m
53.75 (0.269 4.25 233+ 0.8) (13.3 + 1.83) 1
22313.4 cm3
The section selected is a T-section with scantlings as follows
Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I
1500X25 web and 300X25 flange with the section modulus as 25400 cm3
4) Vertical web on centerline longitudinal bulkhead
Section modulus of vertical web is to be not less than
Z
K3shsSs2k (sm3)
K3
1.88
4.25
hs
distance
between
the
lower
span
point
of
the
vertical
is
to
be
web
and the moulded deckline at centreline, in meters
Ss
18 m
span
of
vertical
web,
in
meters,
between end span points.
13 m
24575.64 cm3
Taken 1500x 300x 25/25, with Z = 25400 cm3
1.2.6. Primary Members End Connections [LRS Part 3, Chapter 10, Section 3]
The following relations govern the scantlings of bracket:
(a + b) 2l
a
0.8 l
0.8 l
90
(14 +Z Z)- 1
mm
1) Bracket connecting deck transverse and inner hull
l
(14 +Z Z) - 1
90
mm
90 { 2 ( 25400 / [ 14 + 25400]) 1}
2088.0 mm
a 0.8l
1670.4 mm
b 0.8l
1670.4 mm
and
measured
Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I
Given a
2300 mm and b = 2000 mm
thickness of web itself
= 21 mm
Flange breadth to be not less than
bf
40 (1 + Z / 1000) mm, but not less than 50mm
40 (1 + 25400 / 1000 )
1056 mm
2) Bracket connecting deck transverse and center line bulkhead web
l
(14 +Z Z) - 1
90
mm
90 { 2 ( 25400 / [ 14 + 25400]) 1}
2088.0 mm
a 0.8l
1670.4 mm
b 0.8l
1670.4 mm
Given a
2300 mm and b = 2000 mm
thickness of web itself = 21 mm
Flange breadth to be not less than
bf
40 (1 + Z / 1000) mm, but not less than 50mm
40 (1 + 25400 / 1000 )
1056 mm
3) Bracket connecting center line vertical web and inner bottom plating
l
90
90 { 2 ( 25400 / [ 14 + 25400]) 1}
2088 mm
1670.4 mm
b 0.8l
1670.4 mm
Given a
2300 mm and b = 2000 mm.
tb
thickness of web itself = 15 mm
0.8l
(14 +Z Z)- 1
Flange breadth to be not less than
mm
Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I
bf
40 (1 + Z / 1000) mm, but not less than 50mm
40 (1 + 25400 / 1000 )
1056 mm
1.2.7. Section Modulus Calculation
Table 1.4 Section Modulus Calculation
AREA(m2)
20
20
N
O:
2
2
AL
A L2
I own(m4)
0.924
0.374
LEVE
R
22
15.25
19.404
5.2734
0
0.818
0.323
6.75
1.938
17
0.56695
0.008
2635
17
0.08959
1.15
2365
3600
18000
2800
20
19
18
18
2
1
2
2
0.10406
0.0684
0.648
0.1008
21
0
12
3.71
INN BOT PLATE
CENTRE GIRDER
SIDE GIRDER
CL BKD reg 1
CL BKD reg 2
CL BKD reg 3
CL BKD reg 4
WING TANK HORI.GIRDER 1
WING TANK HORI.GIRDER 2
WING TANK HORI.GIRDER 3
17000
2000
2000
5000
5000
5000
5000
370*13
400*14
430*15
18
17
12
12
14
15
16
2
1
6
1
1
1
1
2
2
2
0.612
0.034
0.144
0.06
0.07
0.075
0.08
0.0139
0.0162
0.0188
2
1
1
19.5
14.5
9.5
4.5
9
14
20
0.118482
8
45.89046
0
93.312
1.387421
3
2.448
0.034
0.144
22.815
14.7175
6.76875
1.62
1.1259
3.1752
7.52
SHEERSTRAKE PLATE
KEEL PLATE
INN HULL PLATE
MARGIN PLATE
0.00453
6
0.10302
9
2.18526
0
6.48
0.37396
8
1.224
0.034
0.144
1.17
1.015
0.7125
0.36
0.125
0.227
0.376
447.216
86.97837
5
14.71668
8
3.628E-05
8500
19
BOTTOM SHELL PLATE
16675
BOTTOM BILGE PLATE
DECK LONGITUDINALS
260*12
50
0.2065
21.87
4.13
98.76831
INNER HULL LONGITUDINALS
IH 1
IH 2
IH 3
IH 4
IH 5
IH 6
IH 7
IH 8
IH 9
2
2
2
2
2
2
2
2
2
0.01392
0.01392
0.01392
0.01392
0.01392
0.01628
0.01628
0.01628
0.01628
19.15
18.3
17.45
16.6
15.75
14.9
14.05
13.2
12.35
0.266568
0.254
0.242
0.231
0.219
0.242
0.228
0.214
0.201
5.104
4.661
4.238
3.835
3.453
3.614
3.213
2.836
2.483
ITEMS
L(mm)
B(mm)
DECK PLATE
SIDE SHELLPLATE
21000
8500
SIDE SHELLPLATE
370*13
370*13
370*13
370*13
370*13
400*14
400*14
400*14
400*14
0.818
0
0.0082
0
5.46
0.029
0
0.011
0.008
0.125
0.146
0.15625
0.1666
0
0
0
Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I
IH 10
IH 11
IH 12
IH 13
IH 14
IH 15
IH 16
IH 17
IH 18
IH 19
400*14
430*15
430*15
430*15
430*15
430*21
430*21
430*21
430*21
430*21
2
2
2
2
2
2
2
2
2
2
0.01628
0.01882
0.01882
0.01882
0.01882
0.024
0.024
0.024
0.024
0.024
11.5
10.65
9.8
8.95
8.1
7.25
6.4
5.55
4.7
3.85
0.187
0.2
0.184
0.168
0.152
0.174
0.153
0.133
0.112
0.092
2.153
2.134
1.807
1.507
1.234
1.261
0.983
0.739
0.53
0.355
BOTTOM LONGITUDINALS
430*21
40
0.444
INNER BOTTOM
LONGITUDINALS
430*21
34
0.408
0.816
1.632
S1
S2
S3
S4
S5
S6
S7
S8
S9
S 10
S 11
S 12
S 13
S 14
S 15
S 16
S 17
S 18
S 19
S 20
S 21
370*13
370*13
370*13
370*13
370*13
400*14
400*14
400*14
400*14
400*14
430*15
430*15
430*15
430*15
430*21
430*21
430*21
430*21
430*21
430*21
430*21
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
2
0.01392
0.01392
0.01392
0.01392
0.01392
0.01628
0.01628
0.01628
0.01628
0.01628
0.01882
0.01882
0.01882
0.01882
0.024
0.024
0.024
0.024
0.024
0.024
0.024
19.15
18.3
17.45
16.6
15.75
14.9
14.05
13.2
12.35
11.5
10.65
9.8
8.95
8.1
7.25
6.4
5.55
4.7
3.85
3
2.15
0.266
0.254
0.242
0.231
0.219
0.242
0.228
0.214
0.201
0.187
0.2
0.184
0.168
0.152
0.174
0.153
0.133
0.112
0.092
0.072
0.051
5.104
4.661
4.238
3.835
3.453
3.614
3.213
2.836
2.483
2.153
2.134
1.807
1.507
1.234
1.261
0.983
0.739
0.53
0.355
0.216
0.11
BKD 1
BKD 2
BKD 3
BKD 4
BKD 5
BKD 6
BKD 7
BKD 8
BKD 9
BKD
10
BKD
300*14
300*14
300*14
300*14
300*14
370*16
370*16
370*16
370*16
370*16
1
1
1
1
1
1
1
1
1
1
0.0058
0.0058
0.0058
0.0058
0.0058
0.00807
0.00807
0.00807
0.00807
0.00807
19.15
18.3
17.45
16.6
15.75
14.9
14.05
13.2
12.35
11.5
0.111
0.106
0.101
0.096
0.091
0.12
0.113
0.106
0.099
0.092
2.126
1.942
1.766
1.598
1.438
1.791
1.593
1.406
1.23
1.067
370*16
0.00807
10.65
0.085
0.915
SIDE LONGITUDINALS
BULKHEAD LONGITUDINALS
Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I
11
BKD
12
BKD
13
BKD
14
BKD
15
BKD
16
BKD
17
BKD
18
BKD
19
BKD
20
BKD
21
430*15
0.00941
9.8
0.092
0.903
430*15
0.00941
8.95
0.084
0.753
430*15
0.00941
8.1
0.076
0.617
430*15
0.00941
7.25
0.068
0.494
430*15
0.00941
6.4
0.06
0.385
430*21
0.024
5.55
0.133
0.739
430*21
0.024
4.7
0.112
0.53
430*21
0.024
3.85
0.092
0.355
430*21
0.024
0.072
0.216
430*21
0.024
2.15
0.051
0.11
53.0416
912.233
6.239
Height of the neutral axis, hNA
AL
A
53.042
6.239
8.502 m from base line
Ah2 + IXX
912.233 + 7.371
919.604 m4
I KEEL - A x (hNA)2
919.604- 6.239x (8.502)2
468.65 m4
Moment about keel,
I KEEL
Moment about neutral axis,
I NA
Section modulus about deck,
INA
ZDECK
=
=
=
Section modulus about keel,
h DECK
468.65
21-8.71
37.788m3
7.3708
Department of Naval Architecture & Ocean Engg, IMU , M.Tech(NA&OE), Batch- I
ZKEEL
=
=
Required section modulus, ZMIN
INA
hNA
468.65
8.507
55.124m3
34.402 m3
Here ZDECK and ZKEEL are getting more than the minimum section modulus required. So the design is
satisfactory.
The maximum hull vertical bending stresses at deck, DECK, and keel, KEEL, are given by the
following, using the appropriate combination of bending moments to give sagging and hogging
stresses:
DECK =( |Ms+Mw|x 103) / ZDECK N/mm2
= 94.347 N/mm2
KEEL = (|Ms+Mw|x 103 )/ ZKEEL N/mm2
= 67.271 N/mm2
