However, it
should
be have
clearly
understood
that
a
pragmatic solution only is being sought here. A number of commentators
already expressed concerns
regarding the level of complexity of the ISO draft scantling standard [1]. It is not being suggested that the ‘derivations’ above are very theoretically rigorous - merely that they provide a platform for comparison against real test data.
2.4 USE OF THREE-POINT BEND TEST DATA FOR DESIGN OF SINGLE SKIN PANELS
Of course, the discussion so far glosses over the whole issue as to whether three-point bending tests on small coupons (or indeed tensile/compressive tests) are particularly relevant to the design of marine structures. The arguments for testing at ‘panel’ size are well rehearsed in the public literature. While the three-point bending test is a simple method of producing flexural properties, it does not represent even design (let alone real-life) loads either in terms of loading type, duration or boundary conditions. Panel design tends to be based on uniformly distributed pressure loads with built-in as the most commonly adopted edge boundary condition. However, this is too big a question to be addressed here. The fact is that such test data are accepted in most classification society rules and the ISO standard.
However as an aside, it is interesting to compare the proportion of the total sample which is stressed at various levels of the maximum stress. A comparison of three and four point bending (load at one-third span points) against distributed loads, simple support and built-in ends for a single ply (i.e. fixed distance from the neutral axis) is shown in Figure 1 (see back of paper).
The four point bending test gives a similar representation of non-uniform stress distribution to that of a uniformly loaded simply supported coupon. Since four-point bending produces the maximum stress throughout the centre section, the ratio of flexural strength to tensile will be lower than for three-point bending since the smaller the volume under the peak stress, the higher will be the localized strength (i.e. lower probability of weak and highly stressed zones coinciding).
According to [7, 8], the ratio for four-point bending for quarter span points is:
ff tt
{4( 1) (2)
2
V V
1/ (8)
This would give flexural strengths obtained from 4-point bending about 10% below those obtained from three point bending.
Comparison of figure 1 suggests that data from three- point
bending may be used conservatively for
applications with high aspect ratio, built-in panels as the volume of highly stressed material is lower for the built-
© 2008: Royal Institution of Naval Architects
in uniformly loaded beam than for the three-point bending case.
As an aside, the fact that only a tiny
proportion of a built-in panel is experiencing anything like the maximum moment is probably the single most likely reason why simple marine design codes work so well (i.e. are conservative). This is particularly so when the code gives no credit for the effect of stiffener bonding angles in increasing the nominal panel thickness as per [1].
3. EXPERIMENTAL RESULTS
In order to ascertain whether the foregoing apparent ply strain values have any basis in reality, fifteen panels (approximately 300mm x 300mm) were wet-laid/hand consolidated using nominal 300 gsm E-glass, carbon and aramid (all 0/90) in epoxy at a fibre volume fraction of about 34%.
3.1 FIBRE CONTENT BY MASS:
The resin density was measured and found to closely agree with the manufacturers’ value. Fibre content by mass was principally obtained by direct measurement (i.e. known fibre mass/measured laminate mass) of a large number of coupons as well as of the larger panels prior to cutting. The ‘loss on ignition’ (ashing) method [10] was also employed for glass which gave a fibre content by mass within 1.7% of the direct measurement value for the five coupons which were ‘ashed’ and within 3% of the direct measurement average for 30+ coupons. A separate test on fibre alone confirmed that the glass fibre loss of ignition was less than 1%. The results are shown in Table 3.
Fibre content by mass Fibre
E-glass Carbon Aramid
Target Direct measure
0.500 0.526 0.540 0.444 0.449 0.400 0.392
n/a n/a
CoV direct measurement (all fibres) 2.2%
Table 3: Experimental determination of fibre content by mass
Acid ingestion was not carried for carbon or aramid coupons, since the close agreement of fibre content between ashing and direct measurement test for glass was taken as confirmation that direct measurement results were reasonably accurate. without its problems.
3.2 PRESENTATION OF LAMINATE STACK STRENGTH AND STIFFNESS
Quoted values in this paper are characteristic strength values (Sk) calculated according to:
Sk = Smean (1 – kn. CoV) (9) Ignition
Acid ingestion is not
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