Section 2 Bending moment at fixed end of stiffener
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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 2 Bending moment at fixed end of stiffener

Section 2 Bending moment at fixed end of stiffener

2.1 The generalised stress equation is:

The ultimate material properties may be found from Table 3.1.1 Mechanical properties for chopped strand mat (CSM) glass reinforced polyester resin laminates and Table 3.1.2 Mechanical properties for woven roving (WR) and cross-plied (CP) glass reinforced polyester resin laminates at 0/90° degree orientation in Pt 8, Ch 3 of the Rules for Special Service Craft and the limiting stress fractions from Table 7.3.1 Limiting stress criteria for local loading in Pt 8, Ch 3 of the Rules for Special Service Craft.

2.2 Consider the crown of the stiffener:

  1. Consider the WR (G c = 0,5) in compression:

    E c = 14000 N/mm2
    y i = 85,305 – 22,44
    = 62,865 mm
    σWR comp = 66,8 x 10–6 x 14000 x 62,865
    = 58,8 N/mm2
    σWR ucs = 147 N/mm2

    Stress fraction = 58,8/147 = 0,40 hence reject.

  2. Consider the UDT (G c = 0,54) in compression:

    E c = 20748 N/mm2
    y i = 85,305 – 22,44 – (2 x 0,979)
    = 60,907 mm
    σUDT comp = 66,8 x 10–6 x 20748 x 60,907
    = 84,4 N/mm2
    σUDT ucs = 279 N/mm2

    Stress fraction = 84,4/279 = 0,303 hence acceptable.

  3. Consider the CSM (G c = 0,33) over the stiffener former in compression:

    E c = 7200 N/mm2
    y i = (85,305 – 22,44) – (4 x 0,979) – (2 x 0,66)
    = 57,629 mm
    σCSM comp = 66,8 x 10–6 x 7200 x 57,629
    = 27,7 N/mm2
    σCSM ucs = 122 N/mm2

    Stress fraction = 27,7/122 = 0,227 hence acceptable.

2.3 Consider the loaded face of the shell:

  1. Consider the wet surface CSM (G c = 0,286) in tension:

    E t = 6290 N/mm2
    y i = 22,44 mm
    σCSM tension = 66,8 x 10–6 x 6290 x 22,44
    = 9,4 N/mm2
    σCSM uts = 91 N/mm2

    Stress fraction = 9,4/91 = 0,10 hence acceptable.

    Due to such a low stress fraction the adjacent CSM (G c = 0,33) will also be acceptable.

  2. Consider the WR (G c = 0,5) in tension:

    E t = 14500 N/mm2
    y i = 22,44 – 1,112 – 0,625
    = 20,703 mm
    σWR tension = 66,8 x 10–6 x 14500 x 20,703
    = 20,05 N/mm2
    σWR uts = 190 N/mm2

    Stress fraction = 20,05/190 = 0,105 hence acceptable.

2.4 However, the conclusion is that the compressive stress fraction in the WR in the crown of the stiffener is unacceptable. A number of options exist, which include:

  1. The use of higher strength materials such as carbon fibre or aramid reinforcements.

  2. Add UDT reinforcements in the crown of the stiffener.

  3. Laminate local collars at the end of the stiffeners to increase the section stiffness. This is usually labour intensive and not weight efficient.

2.5 Logically, for this example, the easiest solution is to add UDT reinforcements in the crown of the stiffener. Two additional UDT reinforcements have been included in the revised arrangement. The effect on the section stiffness of the revised schedule is shown in Table 5.2.1 Revised tabulation of 'top-hat' stiffener calculations including additional uni-directional reinforcements.

2.6 Recalculation of stress in the WR reinforcement in the stiffener crown using the revised section stiffness of 5200996 Ncm/mm2:

Consider the WR (G c = 0,5) in the crown of the stiffener in compression:

E c = 14000 N/mm2
y i = 86,625 – 24,926
= 61,7 mm
σWR comp = 56,09 x 10–6 x 14000 x 61,7
= 48,4 N/mm2
σWR ucs = 147 N/mm2

Stress fraction = 48,4/147 = 0,329 hence acceptable.

2.7 Re-consider the outermost UDT (G c = 0,54) in compression:

E c = 20748 N/mm2
y i = 86,625 – 24,926 – 0,979
= 60,720 mm
σUDT comp = 56,07 x 10–6 x 20748 x 60,720
= 70,66 N/mm2
σUDT ucs = 279 N/mm2

Stress fraction = 70,66/279 = 0,25 hence acceptable.

Table 5.2.1 Revised tabulation of 'top-hat' stiffener calculations including additional uni-directional reinforcements

  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 86,136 14000 78,32 1096480 94445853 581087,7 8135228350
  2 UDT 0,54 600 0,660 80 85,316 20748 52,80 1095494 93463200 384323,6 7973946157
  3 WR 0,5 600 0,979 80 84,497 14000 78,32 1096480 92648722 559184,3 7828580341
  4 UDT 0,54 600 0,660 80 83,677 20748 52,80 1095494 91667685 369699,1 7670516637
  5 UDT 0,54 600 0,660 80 83,017 20748 52,80 1095494 90944659 363890,1 7549992490
  6 WR 0,5 800 0,979 80 82,198 14000 78,32 1096480 90127915 529169,8 7408376853
  7 UDT 0,54 600 0,660 80 81,378 20748 52,80 1095494 89149143 349663,5 7254818749
  8 WR 0,5 800 0,979 80 80,559 14000 78,32 1096480 88330784 508277,4 7115883045
  9 CSM 0,33 450 0,937 80 79,601 7200 74,96 539712 42961345 474970,0 3419784035
  10 web 0,5 – 66,850 9,706 45,707 12687 648,85 8231910 376255932 1597160,7 20263177372
  11 bonding 0,5 – 3,150 170,000 10,707 14500 535,50 7764750 83137178 61832,4 896570245
  12 WR 0,5 800 0,979 302 8,643 14500 295,66 4287041 37050752 22107,1 320553529
  13 CSM 0,33 300 0,625 302 7,840 6950 188,75 1311813 10285266 11609,3 80684330
  14 WR 0,5 800 0,979 302 7,039 14500 295,66 4287041 30174338 14670,7 212724485
  15 CSM 0,33 300 0,625 302 6,236 6950 188,75 1311813 8181119 7347,4 51064249
  16 WR 0,5 800 0,979 302 5,435 14500 295,66 4287041 23297924 8755,5 126954976
  17 CSM 0,33 300 0,625 302 4,632 6950 188,75 1311813 6076971 4056,7 28194272
  18 WR 0,5 800 0,979 302 3,831 14500 295,66 4287041 16421511 4361,7 63245002
  19 CSM 0,33 300 0,625 302 3,028 6950 188,75 1311813 3972824 1737,3 12074400
  20 WR 0,5 800 0,979 302 2,227 14500 295,66 4287041 9545097 1489,3 21594564
21 CSM 0,33 300 0,625 302 1,424 6950 188,75 1311813 1868677 389,2 2704632
Wet
see Note 		22 CSM 0,286 450 1,112 302 0,556 6290 335,82 2112333 1174457 138,4 870664
TOTALS         86,625       4541,65 55410871 1381181352   86437539378

Note ‘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. Consider the crown of the stiffener in compression.

Note Position of neutral axis above base 24,926 mm above base Tensile modulus of elasticity of section 12201 N/mm2

Note Stiffness EI of section about NA = 5200996 N cm4/mm2

2.8 The example demonstrates that the additional two UDT’s in the crown increases the section stiffness by 19 per cent and is accompanied by a movement in the neutral axis from 22,44 – 24,926 mm above the base. The stress fraction in the woven roving in the crown is reduced from 0,4 to 0,329 and meets the Rule requirement of 0,33.

2.9 Considerable care must be exercised when additional material radically affects the position of the neutral axis. For this reason the stress in the outermost UDT’s has also been re-calculated and found to be satisfactory.

2.10 Where aramid reinforcements are being used then special consideration must be given to the compressive properties. For comparison purposes aramid reinforcements, at a fibre content of 0,45, typically have the following properties:

  Tension Compression
Ultimate strength (N/mm2) 300 100
Elastic modulus (N/mm2) 21000 17000

2.11 The radical reduction in ultimate compressive strength may prove to be unsuitable in the crown of the stiffener at the end or in the panel at mid span. Designs which feature aramid fibres in the outer plies of the panel, in an attempt to make use of the superior impact properties, must be checked at mid span for compression in the individual layers. This also applies to hybrid reinforcements containing aramid fibres. These reinforcements have one off properties of higher than one of the constituent fibres however, in service the individual allowable strains for each fibre reinforcement should not be exceeded.

2.12 In accordance with Pt 8, Ch 3, 1 General of the Rules for Special Service Craft, it is of paramount importance that the strain compatibility of the component materials is carefully considered.

2.13 Consider typical values of apparent strain, ∊a' at failure for the following materials in laminate form:

  Tension Compression
‘E’ glass 1,3% 1,05%
Carbon fibre 0,9% 0,55%
Aramid fibre 1,3% 0,60%

2.14 The actual strain permissible is controlled by the material with the lowest apparent strain. The level of strain depends upon whether the reinforcements are in tension or compression and depends on their relative positions within the laminate. Consequently if, for example, a carbon fibre reinforcement is used in the crown of the stiffener then the compression strain must be constrained to a maximum of 0,33 x 0,55 per cent, i.e. 0,297 per cent. Therefore, the corresponding allowable stress in the other reinforcements must be related to the strain in the reinforcement relative to its position away from the neutral axis and that of the carbon fibre reinforcement, e.g.:

2.15 Other materials incoporated into stiffening members requiring strain compability consideration are plywoods, timbers, etc. which have very differing strains at failure dependent upon the direction of the grain.

Parent topic: Chapter 5 Design of Stiffening Members
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