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Section Iv - : Longitudinal Strength Calculation

The document summarizes the calculation of the minimum required longitudinal strength and section modulus for a vessel over 61m in length according to ABS rules. It involves calculating the still water bending moment, wave induced bending moment, and total bending moment. It then calculates the required section modulus using the total bending moment and permissible stress. The minimum required section modulus is 4,061,802.34 cm3. The actual installed section modulus is 3,517,185.295 cm3, which provides a safety factor of over 69%.

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Mikhail Roy Dela Cruz
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649 views5 pages

Section Iv - : Longitudinal Strength Calculation

The document summarizes the calculation of the minimum required longitudinal strength and section modulus for a vessel over 61m in length according to ABS rules. It involves calculating the still water bending moment, wave induced bending moment, and total bending moment. It then calculates the required section modulus using the total bending moment and permissible stress. The minimum required section modulus is 4,061,802.34 cm3. The actual installed section modulus is 3,517,185.295 cm3, which provides a safety factor of over 69%.

Uploaded by

Mikhail Roy Dela Cruz
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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SECTION IV - LONGITUDINAL STRENGTH CALCULATION

ABS 3.3 Longitudinal Strength for Vessels 61 m (200 ft) in Length and Over
ABS 3.7 Bending Strength

3.7.1 Hull Girder Section Modulus 3.7.1

(a) Section Modulus. The required hull girder section modulus for 0.4L amidships is to be
the greater of the values obtained from the following equation or 3-2-1/3.7.1 (b)

SM = Mt/fp cm3
where:

Mt = total bending moment, as obtained below


fp = nominal permissible bending stress in metric ton / cm2

240−L t
= 1.663− [ ]
1620 cm2

The total bending moment, Mt, is to be considered as the maximum algebraic sum of still-
water bending moment and wave-induced bending moment, as follows:

Total Bending Moment (Mt) = Ms + Mws + Mwh

where:

Ms = still-water bending moment in kN-m (ton-m) as obtained per actual load

Mws = wave-induced bending moment in kN-m (ton-m) in sagging condition


per actual load.
Mwh = wave-induced bending moment in kN-m (ton-m) in hogging condition
A-1 - MINIMUM SECTION MODULUS REQUIREMENT BASED ON ABS RULES

A-1-1 Still Water Bending Moment

Ms = Cst x (L)2.5 x B x (Cb+ 0.5)

Where

110−L
[
Cst = 0.618+
462 ]
x 10−2

110−105.58
[
Cst = 0.618+
462
x 10−2 ]
= 0.0062757

Cb = 0.876; L = 105.58 m; B = 27.80 m

Ms = 0.0062757 x (105.58)2.5 x 27.80 x (0.632 + 0.5)

Ms = 27496.5 tonne-m

A-1-2 Wave Induced Bending Moment

Mw = C 2 x L 2 x B x H x K b

where;

Cb = 0.876; L = 105.58 m; B = 27.80 m

−2
C2 = [ 2.34 x C b +0.2 ] x 10

= [ 2.34 x 0. 876+ 0.2 ] x 10−2

C2 = 0.0224984
Kb = 1.4 – 0.5 x Cb

= 1.4 – 0.5 x 0.876

Kb = 0.962

H = 0.0172 x L + 3.653

= 0.0172 x 105.58 + 3.653

H = 5.468976

Mw = 0.0224984 x 105.582 x 27.8 x 5.468976 x 0.962

Mw = 36680.97194 tonne-m

A-1-3 Total Bending Moment

MT = M S + M W

= 22620.77821 + 36680.97194

MT = 64177.4798 tonne-m

fp = nominal permissible bending stress in metric ton / cm 2

240−L t
= 1.663− [ ]
1620 cm2

240−105.58 t
= 1.663− [ 1620 cm 2 ]
t
= 1.663− [ 0. 08296 ]
cm2
t
= 1.5800
cm2

A-1-4 Section Modulus Requirement

SM = MT / fp

64177.4798 metric ton−meter 100 cm


SM = x
1.5 8 meteric ton /cm 2 m

SM = 4,061,802.34 cm3

As Installed Minimum Section Modulus (from the bottom)

Sm = 3,517,185.295 cm3 . . . . . . compliant

42,430.53
Safety Factor =100% -
140,203.08

= +69.74%
TABLE 1 - CALCULATION OF EQUIVALENT SECTION MODULUS OF THE MIDSHIP SECTION
USING AUTOCAD PROGRAM “MASSPROP”
Note : Measurement are in centimeters

Neutral axis from keel 320.1713 cm


Moment of inertia at the neutral axis 1,126,101,788.3859 cm^4
Section modulus from the top 3,520,952.899 cm^3
Section modulus from the bottom 3,517,185.295 cm^3

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