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Mid Ship Section Calculations
                       Principle Particulars
                   Model                        4211W
                   LWL (m)                      121.99 m
                   LBP (m)                      110 m
                  Depth,H                       9.103 m
                  Draft,T                       6.0689 m
                  Breadth                      15.1724m
                  Block Coefficient, Cb         0.65
                  Service coefficient, CRW      1 (for unlimited service range)
                  Distribution factor, CF       1 (for midship)
                  Web frame spacing, e          2m
                  Reduction coefficient, nc     1
                  Material factor, K            0.72
Result:
Double bottom height       1.012m
Center Keelson             T- 1012× 100× 10
Side Keelson               T- 1012× 100× 10
Web Frame                  T- 219x55x5.5
Deck Web                   T- 167x50x5
Bottom Longitudinal        L – 60×40 ×6
Deck Longitudinal          L – 60×40×5
Deck Beam                  L- 80× 65× 8
Deck Girder                T- 167x50x5
Side Stringer              T- 219x55x5.5
Main Frame                 L- 75×50×7
Side Longitudinal          L – 60 × 40 × 5
Shell Thickness            8mm
Deck Thickness             7mm
Bilge Thickness            10mm
Bottom Thickness           9mm
Keel Thickness             11mm
                                                                                                              2
Bottom Shell Plating:
Length coefficient = 1 for L ≥ 90 m
Service coefficient CRW = 1 for unlimited service range
Distribution factor , CF = 1 for midship
Wave coefficient, Co = Wave Coefficient
                                                     1 .5
                                            300− L
                       =
                                [ ( )]
                                10. 75−
                                            100               CRW
                                                       1.5
                                           300−110
                       =
                               [ ( )]
                               10 . 75−
                                           100                    x1
                       = 8.131
nf = 0.83 for longitudinal framing
Probability factor, f = 1 for girders and girder systems of the outer hull (web frames, stringers,
grillage systems)
Po = Basic external dynamic load
   = 2.1(CB+0.7) Co × CL× f
   = 2.1(0.65+0.7) × 8.131 × 1 × 1
   = 23.0513 KN/m2
PB = Load at bottom
       = 10T + Po × CF
       = 10 × 6.0689 + 23.0513 × 1
       = 83.7402KN/m2
Now,
                                                          295
 σ perm  =230/ k KN/m2                     for L≥90m
                                                     & K=
                                                          R EH +60 , where R
                                                                             EH = UTS =335 N/mm²
      =230/0.72
      =319.44 KN/m2
 σ LB = 120/k                     for L≥90m
      =166.77 KN/m2
  σ pl = σ perm2−3 τ L -0.89 σ = ( 319 . 442−3 .(0 )2) -0.89 ×166.67 171.01
              √(                   2
                                       )                      √
                                            LB                      =
N/mm2
Corrosion addition tk = 1.5 mm, for thickness ≤10 mm
                               PB
 tB1= 18.3x nf x a x       √   σ pl + tk = 18.3 x 0.83 x .5 x          √   83. 7402
                                                                           171. 01      + 1.5 =6.814mm≈7 mm
 tB2 =1.21 x a x   √( PB .K )      + tK = 1.21×0.5×         √(83.7402 x0.72)          +1.5=6.198mm
                                                                                              3
again, Minimum bottom plate thickness =       ( L. K )
                                              √          =        √ (110×0.72 )    ≈8.899mm
 So, we accept the bottom plate thickness = 9 mm
Side Plate thickness
Thickness of side shell plating, ts1=18.3 × nf × a ×     √       (Ps / σpl) + tK
                    PB
Ts1= 18.3x nf x a x
      Co
                       √
                     8.131
                            k
                                                   83. 7402
                    σ pl + t = 18.3 x 0.83 x .5 x 171. 01    √+ 1.5 =6.814mm≈7 mm
T + 2 = 6.0689+         2     = 10.1344mm (Plates can be thinner)
Bilge thickness
   h
( 100 + 1) × √ K
   1033
=( 100  + 1) × √ 0.72
=9.61   ¿   10 mm=TB
Flat Keel Plate:
Width Of Keel Plate =800+5L = 1350mm =1.35m
The thickness of flat plate keel should not be less than
tFK =tB+2.0
    =9+2.0=11mm
So we take the thickness of our flat plate keel as tFK=11 mm
Deck Plate:
P = PD = Pressure on ship’s deck
        20×T
 = Po × (10+Z −T )H ×CD = 34.195 KN/m2
tE min= (5.5+0.02xL)√k = 6.8966mm
 we take deck plate thickness = 7mm
Web frame and Side Stringers׃
P=Ps=Load on ship side
                            Z
     = 10(T-Z)+ Po x CF (1+ T )
                                                                                             4
                                                     6.0689¿
                                              5.0575¿ ¿
       = 10(6.0689-5.0575) +23.0513x1× (1+           .¿        )
       = 53.221KN/m2
Where,
 Z = vertical distance of the structure's load centre above base line [m]
  = 0.5(depth- double bottom depth)+ double bottom depth
  = 0.5(9.103 -1.013) +1.38 =5.0575m
T = Draft =6.0689 m
CF = distribution factor=1
Co= Wave Coefficient
                          1 .5
                 300− L
   =
         [ ( )]
         10. 75−
                 100               CRW
                            1. 5
                  300−110
   =
         [ ( )]
         10.75−
                  100               x1
   = 8.131
where,
CRW = service range coefficient
    = 1 for unlimited service range
Po = Basic external dynamic load
   = 2.1(CB+0.7) Co × CL× f
   = 2.1(0.65+0.7) × 8.131× 1 × 0.6
   = 13.831 KN/m2
Where,
CL = Length coefficient
f = Probability factor = 0.6 for girders and girder systems of the outer hull (web frames,
stringers, grillage systems)
Web frame spacing, e = 2 m
l = Length of unsupported span
  = 2.2 m
Section modulus, w = 0.55 × e × l2 × P × nc × K
                                                                                               5
                    = 0.55 × 2 × 2.2²× 61.6962× 1 × 0.72
                    = 246.353 ≈ 250cm3
Where, nc = Reduction coefficient, K = Material factor
Dimension  ׃T- 219x55x5.5
Bottom structure (Keelson) ׃
Depth, hmin = 350 + 45×B
         = 350 + (45×15.1724)
         = 1032.758
         ≈ 1033 mm
         =1.033 m
Again, double bottom depth=B/15 = 15.1724/15= 1.012m
So, we take h= 1.012 m
                  h      h
Thickness, t = ha ( 120 + 3) × √ K             for h>1200
                    1012
             = 1 ( 120     + 3) × √ 0.72
           = 9.7 ≈ 10mm
We took ha=h
Face plate width ≈ 10×10=100 mm
       Dimension ׃T- 1012× 100× 10
Deck Web and Deck Girder׃
Po = Basic external dynamic load
    = 2.1(CB+0.7) Co × CL× f
    = 2.1(0.65+0.7) × 8.131× 1 × 1
    = 23.051385 KN/m2
f = Probability factor = 1 for plate panels of the outer hull (shell plating, weather decks)
P = PD = Pressure on ship’s deck                                      H=depth=9.103, T=draft=6.0689
                                                                      Z=5.0575,
        20×T
                                                                      Cd=0.83 taken (0.80-0.86)
 = Po × (10+Z −T )H ×CD                                               Po=23.0513
             20×6. 0689
 = 23.0513× (10+5 .0575−6 . 0689)×9 .103 ×1 = 34.195 KN/m2
Where,
CD = distribution factor = 1
H = Depth = 9.103 m
Section Modulus, W = c × e × l2 × P × K
                   = 0.75 × 2 × 2.0742 × 34.195× 0.72
                                                                                             6
                       = 158.86 cm3≈160 cm3
Where,
 l = Length of unsupported span = 2.074 m
c = 0.75 for beams, girders and transverses which are simply supported on one or both ends
Dimension ׃T- 167x50x5
Bottom Longitudinal׃
Po = Basic external dynamic load
   = 2.1(CB+0.7) Co × CL× f
   = 2.1(0.65+0.7) × 8.131× 1 ×0 .75
   = 17.288 KN/m2
f = Probability factor = 0.75 for secondary stiffening members
P = PB = Load at bottom
       = 10T + Po × CF
      = 10 × 6.0689+23.0513× 1
      =83.74KN/m2
             a       a               0.5      0.5
ma = 0.204 × l [4– ( l ) ] = 0.204 × 2.1 [4–( 2.1 )2] = 0.191; a = frame spacing
                        2
           l KU                      0.5
mk = 1 – Σ l        × sin α = 1- 4 × 2.1 ×(sin45)2 = 0.524
                         2
 ∴   m = mk2 – ma2 = 0.238
      150
σpr = K      = 208.33
                       83.3
Sectional modulus, W =
                        σ pr        × m × a × l2 × P = 17.58 cm3≈19 cm3
Dimension ׃L – 60×40 ×6
Side Longitudinal׃
P=Ps=Load on ship side
                            Z
     = 10(T-Z)+ Po x CF (1+ T )
                                                                                               7
                                                    6.0689¿
                                             5.0575¿ ¿
      = 10(6.0689-5.0575) +23.0513x1× (1+           .¿        )
      = 53.221KN/m2
                           83.3                          83.3
  ∴   Section Modulus, W = σ pr      × m × a × l2 × Ps = 208 .33   × 0.238×.5×2.212 × 53.221
                                               3
                         = 12.35cm3 ≈ 16 cm
  Dimension ׃L – 60 × 40 × 5
Deck Longitudinal׃
P = PD = Pressure on ship’s deck
         20×T
 = Po × (10+Z −T )H ×CD
              20×6. 0689
 = 23.0513× (10+5 .0575−6 . 0689)×9 .103 ×1 = 34.195 KN/m2
      83.3                     83.3
W = σ pr × m × a × l2 × PD = 208 .33 × 0.238 × 2.0752 ×0.5 × 34.195 = 7.007≈16cm3
 ∴    Dimension: = L – 60×40×5
Main frame:
n = 0.55    for L ¿     100 m
          l KU            l KO        0.5           0.5
 c = 1-( l      + 0.4 × l      ) =1-( 2.1   + 0.4 × 2.1 ) = 0.667
                      2
P = Ps = 53.221KN/m
s = bilge = 2.0531 m
        s
Cr = 1- l × 2 = -0.95 = (-ve)
So, Cr (min) = 0.955
Sectional modulus, Wr = n × c × a × l2 × P × Cr × K = 29.59 cm3 ≈ 30 cm3 ( n= 0.55 for L > 100 m
)
Dimension ׃L- 75×50×7
Deck Beam׃
                                                                                8
P = PD = Pressure on ship’s deck
         20×T
  = Po × (10+Z −T )H ×CD
              20×6. 0689
  = 23.0513× (10+5 .0575−6 . 0689)×9 .103 ×1 = 34.195 KN/m2
c = 0.75 for beam & girders
Sectional modulus, Wd = c × a × l2 × K × P = 49.747≈52cm3
Dimension ׃L- 80× 65× 8
Dimension of Brackets
Here for bottom frames p= p B=83.7402kN /mm 2
n=0.7 , c=1
Unsupported span l=2.1 m
The section modulus of bottom and inner bottom frames should not be less than
W B=n × c × a ×l 2 × p × k
                       2
¿ 0.7 ×1 ×0.5 × ( 2.1 ) × 83.7402× 0.72
¿ 93.062 cm3
For flanged bracket c=0.95
The thickness of the bracket should not be less than
                                                W
          93.062
                                   t=c ×
                                           √
                                           3
                                                   +t
                                               0.72 K
¿ 0.95 ×
¿ 6.30 mm
           √
           3
           0.72
                 +1.5
we take the thickness of the brackets as t a=7 mm
                                                                  t
    6.30
                                                  Now c t =
                                                              √   ta
¿
 √    7
 ¿ 0.94
The arm length of brackets should not be less than
             W
l B =46.2 ×
              k√
               3
                × ct
         3 93.062
¿ 46.2 ×
           √0.72
                  ×0.94
                                       ¿ 219 .57 mm≈ 220mm
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