Section 1 Calculation procedure
Clasification Society 2024 - Version 9.40
Clasifications Register Guidance Information - Guidance Notes for the Classification of Special Service Craft – Calculation Procedures for Composite Construction, July 2013 - Chapter 5 Design of Stiffening Members - Section 1 Calculation procedure

Section 1 Calculation procedure

1.1 Assume a design pressure of 70 kN/m2 applied to a fully fixed bottom longitudinal located outside of the slamming zone as shown in Figure 5.1.1 'Top-hat' stiffener example model.

1.2 The bending moment is determined from Pt 8, Ch 3, Pt 8, Ch 3, 1 General of the Rules and Regulations for the Classification of Special Service Craft (hereinafter referred to as the Rules for Special Service Craft). For a fully fixed stiffener the maximum bending moment coefficient from Table 3.1.5 Mechanical properties for woven roving (WR) and cross-plied (CP) aramid reinforced epoxy resin laminates at 0/90° degree orientation in Pt 8, Ch 3 of the Rules for Special Service Craft Rule is 1/12.

Figure 5.1.1 'Top-hat' stiffener example model

1.3 Hence, maximum bending moment, M S' is given by:

Assumed shell laminate:

5 x 800/300 combination mats

G c = 0,5 (WR in combination mat)
tWR = 0,979 mm
E t = 14500 N/mm2
G c = 0,33 (CSM in combination mat)
tCSM = 0,625 mm
E t = 6950 N/mm2

1 x 450 CSM adjacent to gel coat

G c = 0,286
tCSM = 1,112 mm
E t = 6290 N/mm2

Total thickness, t p = 9,132 mm

The effective width of attached plating 2b 1 from Pt 8, Ch 3,1.7.1 of the Rules for Special Service Craft for single skin construction is:

b 1 = 0 . 5b w + 10t ap
= 0,5 x 120 + 10 x 9,132
= 151 mm

Hence, apply 302 mm attached plating.

Consider typical layup over ‘top hat’ stiffener:

450 g/m2 CSM @ G c = 0,33 – first ply over former
800 g/m2 WR @ G c = 0,5
800 g/m2 WR @ G c = 0,5
600 g/m2 UDT @ G c = 0,54
600 g/m2 UDT @ G c = 0,54
800 g/m2 WR @ G c = 0,5
800 g/m2 WR @ G c = 0,5 – top ply

1.4 Consider the idealised section shown in Figure 5.1.2 Idealised section.

Figure 5.1.2 Idealised section

1.5 The stiffener bonding is to be in accordance with Pt 8, Ch 3, 1 General of the Rules for Special Service Craft and a typical arrangement is shown in Figure 5.1.3 Typical stiffener bonding arrange. To simplify the calculation of the stiffness of the overall section the tapered bonding is assumed to be an effective constant thickness.

1.6 The effective thickness of the bonding is calculated as:

The boundary bonding may be approximated to a thickness of 3,15 mm over an (85 x 2) mm width to account for both flanges. The majority of the flange comprises of woven rovings and it may be assumed that the tensile modulus is 145000 N/mm2. The discrepancy is negligible since the element is very close to the neutral axis.

1.7 The effective depth and width of the web used in the idealised section are:

d web = 70 – effective thickness on bonding
= 70 – 3,15
= 66,85 mm
t web = 2 x (0,937 + 4 x 0,979)
= 2 x 4,853
= 9,706 mm

1.8 Now the web consists of two types of reinforcements, namely one ply of CSM and four plies of woven rovings. The majority of the web will be in compression and the overall modulus of elasticity may be calculated in accordance with Pt 8, Ch 3, 1 General of the Rules for Special Service Craft.

The web may now be treated as a single laminate item having an overall compressive modulus, given above.

1.9 The laminate section modulus calculation is shown in Table 5.1.1 Initial tabulation of 'top-hat' stiffener calculations. The tabulation consists of each element having the compressive moduli in the section above the neutral axis and tensile moduli below. The actual breadth of each element must be entered to calculate the overall section properties. The tabulation corresponds to the idealised section in Figure 5.1.2 Idealised section.

Figure 5.1.3 Typical stiffener bonding arrange

1.10 The tabulation considers the entire section and calculates all moments about the base, which is taken to be the outer (wet) surface. The stiffness, EI, of the entire section, about the neutral axis, is determined using the parallel axis theorem:

In general,

I na = I xx – Ay 2
EI sect = ΣEI base – (Σ Etb) x y 2

where

y = distance of neutral axis above the base (mm)

1.11 From the tabulation:

EI sect = 70480944121 – 53219882 x (22,44)2
= 4368304336 Nmm4/mm2
EI sect = 4,368 x 106 Ncm4/mm2

1.12 From Pt 8, Ch 3, 1 General of the Rules for Special Service Craft the individual layer stresses are determined from:

The calculation of the stresses in individual layers becomes:

where

E i = modulus of elasticity of layer (N/mm2)
y i = distance of layer from the neutral axis (mm)

Table 5.1.1 Initial tabulation of 'top-hat' stiffener calculations

  Ply No. Description G c Weight t Breadth, Lever @ E t.b E.t.b E.t.b.x I @ EI @
  (g/m2) (mm) b (mm) base, x (mm) (N/mm2)       base base
Dry
see Note 		1 WR 0,5 800 0,979 80 84,816 14000 78,32 1096480 92998499 563414,4 7887801805
  2 WR 0,5 800 0,979 80 83,837 14000 78,32 1096480 91925046 550483,0 7706761655
  3 UDT 0,54 600 0,660 80 83,017 20748 52,80 1095494 90944659 363890,1 7549992490
  4 UDT 0,54 600 0,660 80 82,357 20748 52,80 1095494 90221632 358127,2 7430422738
  5 WR 0,5 800 0,979 80 81,538 14000 78,32 1096480 89404238 520706,1 7289885632
  6 WR 0,5 800 0,979 80 80,559 14000 78,32 1096480 88330784 508277,4 7115883045
  7 CSM 0,33 450 0,937 80 79,601 7200 74,96 539712 42961345 474970,0 3419784035
  8 Web 0,5 – 66,85 9,706 45,707 12687 648,85 8231910 376255932 1597160,7 20263177372
  9 bonding 0,5 – 3,15 170 10,707 14500 535,50 7764750 83137178 61832,4 896570245
  10 WR 0,5 800 0,979 302 8,643 14500 295,66 4287041 37050752 22107,1 320553529
  11 CSM 0,33 300 0,625 302 7,840 6950 188,75 1311813 10285266 11609,3 80684330
  12 WR 0,5 800 0,979 302 7,039 14500 295,66 4287041 30174338 14670,7 212724485
  13 CSM 0,33 300 0,625 302 6,236 6950 188,75 1311813 8181119 7347,4 51064249
  14 WR 0,5 800 0,979 302 5,435 14500 295,66 4287041 23297924 8755,5 126954976
  15 CSM 0,33 300 0,625 302 4,632 6950 188,75 1311813 6076971 4056,7 28194272
  16 WR 0,5 800 0,979 302 3,831 14500 295,66 4287041 16421511 4361,7 63245002
  17 CSM 0,33 300 0,625 302 3,028 6950 188,75 1311813 3972824 1737,3 12074400
  18 WR 0,5 800 0,979 302 2,227 14500 295,66 4287041 9545097 1489,3 21594564
  19 CSM 0,33 300 0,625 302 1,424 6950 188,75 1311813 1868677 389,2 2704632
Wet
see Note 		20 CSM 0,286 450 1,112 302 0,556 6290 335,82 2112333 1174457 138,4 870664
TOTALS         85,305       4436,05 53219882 1194228249   70480944121

Note The crown of the stiffener is considered to be in compression in this example. ‘Dry’ indicates the face of the stiffener within the hull and ‘wet’ the outside of the shell laminate, see Figure 5.1.4 Regions of tension (T) and compression (C) in example model.

Note Position of neutral axis above base 22,44 mm above base Tensile modulus of elasticity of section 11997 N/mm2

Note Stiffness EI of section about NA = 4368304 N cm4/mm2

Figure 5.1.4 Regions of tension (T) and compression (C) in example model

Parent topic: Chapter 5 Design of Stiffening Members
Copyright 2022 Clasifications Register Group Limited, International Maritime Organization, International Labour Organization or Maritime and Coastguard Agency. All rights reserved. Clasifications Register Group Limited, its affiliates and subsidiaries and their respective officers, employees or agents are, individually and collectively, referred to in this clause as 'Clasifications Register'. Clasifications Register assumes no responsibility and shall not be liable to any person for any loss, damage or expense caused by reliance on the information or advice in this document or howsoever provided, unless that person has signed a contract with the relevant Clasifications Register entity for the provision of this information or advice and in that case any responsibility or liability is exclusively on the terms and conditions set out in that contract.