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Introduction
J. Gerritsma
Modern composites for marine application
G.W. Mull 1
Results and analysis of the Delft Systematic Series II Yacht Hull form experiences
J. Gerritsma, J.A. Keuning, R. Onnink 38
Amsterdam is building a Dutch-East-Indiaman
H.J. Wimmers 69
Multi-stage waterjets for over 40 knot craft
G.H. Davison 86
Rig load measurements and comparison with calculations
P.J. Keuning, T.F. van der Werff 101
Safety aspects in yacht construction with reference to international standards
F. Hartz 129
The use of low temperature curing prepregs for the fabrication of large composite structures
C. O'Connell 148
The V.O.C. ship "Amsterdam": A velocity prediction
A.H. Hubregtse 160
Computer aided yacht design and its application in the yacht building industry
H.R.F. Ktirner 200
The international measurements system: A description
of the new international rating system
Introduction
The 11th International Symposium on developments of interest to yacht architecture and yachtbuilding has been organized under the auspices of the RAI Exhibition Centre and the HISWA -- National Association of Watersports Industries in the Netherlands, in co-operation with the Delft University of Technology.
This meeting reflects modern trends in yachtbuilding with regard to construction, material, strength and production, as well as
full-scale measurements to validate calculation methods and performance predictions.
With regard to developments in the EEC the important subject of the unification of national rules and regulations of scantlings and safety requirements will be treated. In contrast, some
aspects of the construction and the performance of an 18th Century V.O.C.-ship will be discussed.
In the past 20 years these symposia have attracted interest from
abroad. Also this time the organizing committee aims at a
fruitful international exchange and discussion of expert knowledge on design, manufacture and use of pleasure craft.
J.11Gerritsma
MODERN COMPOSITES for MARINE APPLICATIONS Gary W. Mull
Gary W. Mull, Naval Architects 6671 Gunn Drive
Oakland, California 94611 USA
INTRODUCTIOX
Fiber reinforced plastic composites have advanced over the past
45 years. From early composites making use of organic fibers such as
cotton, through ordinary E-Glass fibers, to a variety of other types of glass fibers, as well as aramid, carbon, boron, and polyethylene fibers, industry now makes available a dizzying choice of
reinforcements. Add to this the variety of formats from chopped
strand mat to cloth, woven roving, unidirectional roving,
unidirectional tape, and u.d. tows, not to mention biaxial and
triaxial stitched knits and even three dimensional weaves, and it is
not surprising that designers and builders cannot know how best to utilize this new capability.
Ever since he first dropped or, more probably, fell out of a tree into the water, there to clutch gratefully to a log floating by, man has sought to build stronger and more seaworthy vessels from a
variety of materials. The earliest vessels were simply logs reshaped
a bit to make them easier to push through the water and, hopefully,
more comfortable to ride. It took quite a few centuries for man to
attempt to build a vessel from constituent pieces. The bound papyrus
reed vessels of the Egyptians and the very similarly bound reed vessels of South America were fairly logical attempts at alternate
boatbuilding systems. Somewhat later, boats with internal framing
and exterior skins were produced, imitating the bone and skin
structural system, an obvious favorite of the Master Architect. A
good deal later, the navies and merchantmen of most of the world had pretty well settled on the continued use of the skeleton and skin
concept, and the methods for determining scantlings had become
dependable enough to support international commerce and exploration. Looking back now at those early attempts to rationalize scantling systems, it is easy enough to scoff at their unscientific rules of thumb, but it wasn't only Helen's face that launched a thousand ships
and far more than a thousand ships were launched. Kingdoms were
founded and lost, continents were stumbled upon, and mankind was
enabled to continue its fungus-like growth covering the planet. Ship structures continued to make use exclusively of organic materials and retained their anthropomorphic characteristics in
structural system for centuries. It wasn't until relatively recently
that man developed the ability to produce sufficient quantities and sizes of metal plates to consider building vessels with metal
structure. Of course the beginning, at least in the terms we
consider here, of the use of metals was in hand forged stiffeners,
in a more or less common direction. Somewhat later, industry became capable of producing fairly large metal plates from which first,
armor, and, later, shell plating was made. It was at this point in
the history of shipbuilding that shipbuilders and, in fact,
structural engineers in other disciplines as well, began to lose
their intuitive ability to deal with anisotropic materials. Whereas
previously the loads on a frame were understood to be composed
principally of bending stresses, matched quite naturally by the grain
structure of a bent frame, frames and shell plating of steel could be
fabricated with total ignorance of material orientation. This, of
course, simplified the engineer's task immeasurably, making all of those simple loaded beam diagrams and equations in textbooks quite accurate reflections of design problems in the real world.
Composite structures are generally considered today to be a
fairly recent and highly technical development. In truth, Mexicans
have been building houses and cathedrals of composite (clay + straw = adobe) for a couple of centuries, And Nervi in Italy showed the world
that ferrocement, in the hands of the truly talented, can produce as
beautiful a structure as exists anywhere in the world.
However, it is not the point of this paper to analyze the structural characteristics of an adobe Formula One offshore
powerboat, nor a ferrocement America's Cup challenger. Composites as
treated here will be considered to be that group of materials
consisting of high strength and modulus reinforcing fibers carried in
a polymer matrix having lower mechanical properties. Most
importantly, they are differentiated by the anisotropic nature of
their properties and the absolute necessity for accounting for their
anisotropic behavior in the proper design of a composite structure.
If there is one point that this paper intends to make, it is that composite structures cannot be adequately analyzed with simple
methods intended for use with isotropic materials. Our grandfathers
and great grandfathers well understood, albeit intuitively, that the run of the grain in a frame or hanging knee was a major factor to
consider in its
ability to meet the loads imposed upon it.
Through
years of use of metal plate and extruded shapes, this has been lost and unfortunately, altogether too many designers and builders have failed to come to grips with the reintroduction of "grain" as a major factor in the design and construction of composite vessels.
Lest the naval architect or shipbuilder begin to develop a sense of inferiority in comparison with their supposedly higher tech cousins in the aerospace field, let me assure them that the "quasi-isotropic" ply stack is a common and broadly used design feature in
much of the composites work in commercial aviation. Even there,
however, while the use of a quasi-isotropic ply stack is still fairly common, it is becoming better understood that a careful analysis of the effects of individual ply orientations and load paths must be undertaken to avoid "surprises" such as first ply failure occuring
well below expected levels of stress. Worse yet, this can occur to
an internal ply, and lead to reduced stiffness of a structure without external evidence of the failure to alert the user to the need for repair or reinforcement.
1. EFFECTS OF ORTEOTROPY
Although we live in a three dimensional world, and as designers and builders of marine craft we are accustomed to working in three dimensions, we generally tend to try to simplify our structural
problems into two dimensions. A shell plating panel, except on the
most slab sided barge, will usually be a curved surface in all three
dimensions. Unless the curvature is very large, we will simplify our
problem by assuming a flat plate and making a "correction" for
curvature. In practice, many designers and engineers will assume a
flat plate if there is not much curvature and not make use of a
"correction factor", knowing that this errs on the conservative side. Where the curvature is more substantial, "curvature factors" can be applied which themselves still err on the conservative side and, even more conservatively, have established limits beyond which they should
not be applied. While these curvature factors themselves seem very
simple in form, they do have a fundamental technical basis and, perhaps even more importantly, have proven themselves in general
application. One such curvature factor is that used by ABS and is
shown below in Figure 1.
ABS CURVATURE CORRECTION FACTOR FOR PLATING
Figure 1
Although deck beams are almost always cambered, they are today
ordinarily analyzed as straight beams. Certainly frames are most
usually curved. Here again, they are ordinarily analyzed on the
basis of straight beam theory, sometimes with another "correction"
factor for curvature. In fact, there are very few structural members
on any vessel from an Optimist pram on upward that are not curved in
at least one plane, and more usually two or three. Nevertheless, a
trained engineer should have no problem making the appropriate choices and simplifications to allow the structure to be analyzed without resorting to the extremely complex computations involved in
c = 1a/s
0.70 c = CURVATURE FACTOR a = DEPTH OF CURVATURE s = SHORT SIDE tc= c*t
tc= CORRECTED THICKNESSof finite element analysis, such work was reserved for doctoral theses and seldom, if ever, made its way out of academia into the practical
engineering world.
However, while it is perfectly acceptable and eminently practical to simplify structures from their real three dimensional geometry to a more practically handled two dimensional geometry, it
is by no means acceptable and in fact can be quite dangerous to assume the same sort of simplifications apply to the properties of
structural materials themselves.
With the advent of metal shipbuilding came the assumption of
isotropic building materials. As a working definition of an
isotropic material, I simply mean that all mechanical properties are
independent of axis or orientation. Metals, for instance, are
isotropic, except for minor variations due to the rolling process. It must, however, be very clearly qnderstood that fiber
reinforcements are NOT isotropic at all. Even the ubiquitous chopped
strand mat is not isotropic. Testing has shown that there can be up
to a ten percent difference in properties between the warp and weft direction, owing to the manufacturing process, and of course there is a larger difference between the in plane and z axis properties for the same reason.
Graphs such as the one shown below in Figure 2 are quite common
for many woven reinforcements. They invariably show that, even in a
"balanced weave", the off-axis properties are substantially below those on the major axis, and quite clearly a designer must be certain that stress levels in any given direction do not exceed material
properties in the same orientation.
90
40,000
30,000
20,000
10,000
FLEXURAL STRENGTH OF WOVEN ROVING vs
ANGLE OF WEAVE
Figure 2
Using all chopped strand mat reinforcement, as was common not too many years ago, designers were not too far in error in assuming uniform in-plane material properties, regardless of orientation. With the advent of the use of woven rovings in combination, usually with alternate layers of chopped strand mat, designers, builders, and
the major scantling societies continued to treat laminates as having
the same in-plane properties in all directions. While technically
this was known to be in error, it didn't really make too much difference since the major scantling societies assumed mechanical properties for woven rovings that were not very much higher than
chopped strand mat! As can be seen in Fig. 3 below, the alternate
mat and woven roving laminate is certainly not isotropic, though the
addition of chopped strand mat to a woven roving ply mitigates this
problem to some extent.
M M 40,000
/
60 / 30,000 20,000 10,0M/
'N
45\
30 0FLEXURAL STRENGTH OF CSM + WOVEN ROVING
vs
ANGLE OF WEAVE
Figure 3
Now compare the information shown in Fig. 4 below. Obviously
the old "rules of thumb" can lead to serious errors in assessing modern laminates!
It is unfortunately still the case today that one of the major yachting periodicals in the world still insists on describing
laminate structures for hulls in terms of ounces of reinforcement per square foot, regardless of type or orientation of reinforcement.
Unfortunately, this has the ridiculous consequence of leading a reader to believe that laminate and reinforcement details make no
difference and, for instance, 24 ounces of chopped strand mat are the
structural equivalent of 24 ounces of carefully oriented
unidirectional or cross-plied preforms.
60,000 50,000 40,000 30,000 20,000
/
/
X . 10,000 75 60EGlass U.D. Tape
15 / ---- -... / 45
/
---...,/ N/
///
N.\
/
N/
\
/\
30/N
-/
\
/
\ ./
/ \
\
\ 0TENSILE STRENGTH OF EGLASS U.D. TAPE
VS
PLY DIRECTION
Figure 4
Chopped strand mat and woven roving are still perfectly
suitable materials for marine construction and are today used quite effectively on everything from small dinghies to major warships and
submarines. However, it is the unidirectional and stitch knit
reinforcement formats that are usually referred to as modern
composites. The use of unidirectional reinforcements to achieve high
strength or stiffness in a single direction is obvious.
Unfortunately, such simple structural problems occur very rarely as a
practical matter. As a consequence, it is a common laminate design
technique to use multiple plies of unidirectional reinforcement oriented specifically to meet design loads.
Happily, we live in an orthotropic world and most load
systems can be resolved into three mutually right angled axes. This,
of course, lends itself very nicely to reinforcements oriented in a 0/90 manner, and is one of the reasons why cloth and woven roving
enjoy their continuing popularity. However, for a given amount of
reinforcement, a 0/90 cross ply of unidirectional tape will exhibit substantially higher properties than either cloth or woven roving.
The reasons for this are obvious. In a woven preform, the fiber
distribution is less uniform and twist and crimp induce stress risers while forcing the fiber orientations away from the major axes of the
fabric. Taken together, these reductions in properties as compared
to a similar amount of unidirectional reinforcement are usually
called "knockdowns". Depending on the material, weave pattern, etc., knockdowns can account for losses of up to 15 percent or more which
in many cases is not acceptable. Lest it be assumed that, except for
aerospace projects, such a small savings in weight should be
considered insignificant, it is well to remember that the savings in
Another advantage of the newer stitch knit unidirectionals is that their texture requires much less filler and fairing compound for surface finish on a male plug construction, and requires much less chopped strand mat behind the gel coat to avoid roving print-through on production boats built in female moulds.
The disadvantage to using stitch knit reinforcements is that only through a detailed engineering analysis can a laminate be
optimized. In point of fact, without a proper engineering analysis
and design of the laminate, it is quite possible to produce a
laminate with properties dangerously below those required. In the
simplest case, it should be obvious that unidirectional
reinforcements not aligned with major stresses might not be suitable. It was not that many years ago that a number of highly regarded
designers and boatyards produced rudder posts built of unidirectional
carbon fiber oriented parallel to the rudder post axis. Making the
very erroneous assumption that the carbon fiber tubular posts could be sized on the basis of the ratio of the tensile strength of carbon
fiber versus the tensile strength of stainless steel, dozens of these very expensive, supposedly aerospace, rudder posts snapped like
carrots, and all because an engineering analysis utilizing Mohr's Circle and taking into account torsional stresses to properly align
the reinforcing carbon fibers was left undone. More recently, a very
large powerboat developed a crack in the bottom laminate running
through several compartments. A quick look at the bottom laminate
showed that the majority of reinforcements ran fore and aft, while
the bottom panels were also oriented fore and aft. With the
principal stresses running at 90 degrees to the major axis of the reinforcements, it is not surprising that a structural failure occurred.
Both of the above failures, as well as numerous others, have occurred either through a lack of any engineering at all or through a poor understanding of the consequences of using isotropic engineering
principles to deal with orthotropic materials. It is the intention
of this paper to reinforce the necessity of using the more complex analytical procedures needed to fully understand anisotropic
structures and, in some small way, to contribute to the introduction of some of the basic principles involved.
2.
BASIC MATERIALSThe basic concept of composite structures is simplicity itself.
A relatively weak and elastic plastic matrix is reinforced with a
much stronger and stiffer fiber. In very broad terms, steel
reinforced concrete is on a macro scale quite analagous to a
composite laminate on a micro scale. It is important to develop a
conceptual understanding of the significance of this model. Just as
the tensile strength of a steel reinforced concrete structure is
dominated by the strength and amount of steel in the mix, so the
tensile properties of a laminate are dominated by fiber properties.
Just as the properties of concrete gain significance when considering
a steel reinforced concrete structure in compression, so too do the
characteristics of the plastic matrix gain significance in the design
of a laminate intended to carry compressive loads. It is important
It would be impossible here to provide a detailed explanation of the failure mechanism theories which form the basis of modern
laminate design. Two very good texts are References 8 and 9. For
our purposes here, it is helpful to keep in mind the relationship between stress and strain which mandates that the stiffest materials
carry the greatest loads. A simple way to visualize this is to
imagine a piano wire in a piece of bubble gum. It is not hard to see
that, when loaded in tension, the wire will take virtually all of the load, and so it is in laminates that the stresses in the various
constituents are proportional to the modulii in the appropriate
directions. It is all well and good, and in fact often extremely
effective, to use a hybrid reinforcement with one type or amount of reinforcement in the warp direction, and another type or amount of
reinforcement in the fill direction. In fact, complete
characterization of the laminate for an orthotropic plate is based on
this concept. However, there are a great many reinforcements
currently available which utilize combinations of fiber types in both
warp and fill directions which must be more carefully considered. As
an example, take a hypothetical fabric with fifty percent E-glass and fifty percent Kevlar 49 (fiber volume fraction) in both warp and fill
directions. The schoolboy's approach to a resolution of properties
assuming a rule of mixtures would lead one to conclude, quite
erroneously, that the tensile strength for the hybrid would be the average of the two constituent tensile strengths (ignoring matrix).
In fact, because the tensile modulus of Kevlar is nearly twice that of E-glass while the tensile strengths are nearly equal, if the designer is not careful, a laminate could be designed which would begin to fail at a much lower tensile strength than predicted by this method, since the Kevlar will take the greater proportion of the
loading up to the point where it would strain to failure, thereby
reducing the overall laminate to that of E-glass. The correct
resolution of the tensile strength of a hybrid laminate must take
into consideration the relative modulii of the constituents. This,
of course, presupposes that the matrix has sufficient adhesion to carry both fibers to equal strain under a given load.
Table 1
SOME IMPORTANT PROPERTIES OF A FEW STANDARD FIBERS
E-Glass - Borosilicate glass. The most common reinforcement used
today. The designation "E" comes from electrical, owing to its high
resistivity.
S.G. = 2.58; tensile strength = 3450 MPa = 500 ksi; tensile modulus = 72.5 GPa = 10.5 msi.
8-Glass (or 82-Glass) - magnesia-alumina-silicate glass. Designed to
provide very high tensile strength filaments.
S.G. = 2.48; tensile strength = 4590 MPa = 665 ksi; tensile modulus = 86.0 GPa = 12.5 msi.
Arid (Caviar 49) - An organic polymer or aramid fiber designed to have high tensile strength and low density.
S.G. = 1.44; tensile strength = 3620 MPa = 525 ksi; tensile modulus = 124.0 GPa = 18.0 msi.
A84 Carbon Fiber - One of the most common carbon reinforcing fibers
in the U.S. Available in a variety of forms.
S.G. = 1.80; tensile strength = 3795 MPa = 550 ksi; tensile modulus = 235.0 GPa = 34.0 msi.
7-300 Carbon Fiber - Another very common carbon reinforcing fiber. Also available in a variety of forms.
S.G. = 1.76; tensile strength = 3450 MPa = 500 ksi; tensile modulus = 228.0 GPa = 33.5 msi.
Spectra 1000 - A polyethylene fiber having very high tensile strength
and very low weight. Requires experience to achieve good lamination.
Plasma treatment of the fibers enhances laminate adhesion. Available
in a variety of forms.
S.G. = 0.97; tensile strength = 3210 MPa = 435 ksi; tensile modulus = 116.0 GPa = 17.0 msi.
Table 2
SOME IMPORTANT PROPERTIES OF A FEW STANDARD RESINS
One of the most difficult tasks facing the composites engineer is the simple accumulation of information regarding the mechanical
properties of some of the basic reinforcements available. Table 3
gives the mechanical properties for a fairly broad spectrum of
reinforcements which the author has used for the design of a number
of projects. It must be noted that the properties given here are by
no means guaranteed. The only sure way to be confident of mechanical
properties of laminates is to have test specimens realistically produced and carefully tested and to utilize reasonable methods for
developing design allowables. Design allowables are not simply
average values from a few mechanical tests, but are developed by
statistical weighting of not only the test results but the spread of
test results in order to assure the designer that the mechanical properties used for a particular design reflect achievable properties
within the design failure boundary under consideration. These are
normally divided into four bases - an (a) allowable, being the mechanical property value above which at least 99 percent of the population of values is expected to fail with a confidence of 95 percent; the (b) basis, being the value above which at least 90
percent of the population of values is expected to fail, with a
confidence at 95 percent; the (s) basis, which is a minimum value
specified by a governmental or regulatory limit such as we are
familiar with from Lloyd's, ABS, Det Norske Veritas, etc.; and,
finally, the "typical" basis, which is the simple average value with
no statistical assurance associated with it. An excellent review of
the methodology used to develop design allowables can be found in
RESIN TENSILE STRENGTH
ksi TENSILE MODULUS msi STRAIN S.G. Polyester 6 - 13 .3 - .64 1.1 - 1.5 1.75 Vinylester 7 - 11 .44 - .6 2.0 - 5.5 1.80 Epoxy 8 - 15 5.0 - 7.0 1.85 PEEK 10.2 - 15 1.30 PPS 9.5 .48 1.0 - 2.0 1.30
Table 3
MECHANICAL PROPERTIES FOR A FEW SELECTED THERMOSET REINFORCEMENTS NOTE: The following data should NOT be used for design purposes without confirmation by testing.
3. THERMOPLASTICS
Heretofore, at least in yacht and ship building, the terms "composites" or "frp" have generally assumed the broad branch of
polymers known as thermosets. These polymers have the characteristic
that, in their room temperature "uncured" state, they are liquid and can be caused to cure or harden through some catalytic process,
usually involving heat, chemicals, or light. The usual boat and ship
building resins fall into this category. There is, of course,
another family of polymers called thermoplastics.
These polymers
have the characteristic of being solid at room temperature or other service temperatures, but can be melted at elevated temperatures to
allow them to be formed using suitable tooling. Unlike thermoset
plastics, thermoplastics have virtually unlimited shelf life and
require no refrigeration or other special storage techniques. They
can also be reheated and reprocessed without loss of mechanical
properties. Their principal engineering advantages are that they are
usually tougher than thermosets and have generally higher service
temperatures. Their main commercial advantage is that they lend
themselves to dramatically reduced production times.
The part shown below, a vertical stabilizer fairing for an Apache helicopter, was originally designed in Revlar-49/epoxy and carried with it 3-1/2 man hours of labor for the laminating cycle. The photograph shows the same part made in Revlar-49/PPS and was
produced in 92 seconds. The thermoset laminating cycle consisted of
laying down the requisite number of plies of R-49/epoxy prepreg over
a male tool, following which several bleeder plies were laid down,
followed again by the application of a vacuum bag including
appropriate suction hoses, etc. The part was then wheeled into an
Material Weight Oz/yd^2 Vf% Poisn Patio Str. Comp. 0 Deg psi Mod. Comp. 0 Deg msi Str. Comp. 90 Deg psi Mod. Comp. 90 Deg ms1 Str. Tens. 0 Deg psi Mod. Tens. 0 Deg msi Str. Tens. 90 Deg psi Mod. Tens. 90 Deg msi Str. Shear psi Mod. Shear msi 1 o. CSM 9.00 13.0% 0.300 20400 1.060 20400 1.060 10500 0.870 10500 0.870 11000 0.500 E Cloth 1.00 29.3% 0.107 24459 2.050 24459 2.050 27500 1.625 27500 1.625 8500 0.518 S Cloth 1.00 29.3% 0.107 25787 2.494 25787 2.494 53873 1.869 53873 1.869 9000 0.548 K49 Cloth 1.00 29.3% 0.107 18000 2.300 18000 2.300 49000 2.750 49000 2.750 4000 0.500 G Cloth 1.00 29.3% 0.107 26770 4.210 26770 4.210 48580 4.810 48580 4.810 15000 0.800 E-Uni 1.00 29.3% 0.300 54000 3.000 16000 1.600 62000 3.410 2500 0.650 8500 0.518 S-Uni 1.00 29.3% 0.300 53120 3.520 21140 2.080 121500 4.020 3380 0.650 9000 0.548 K49-Uni 1.00 29.3% 0.350 24820 5.340 10890 0.670 11700 5.900 670 0.660 4000 0.500 G-450-Uni 4.75 35.0% 0.250 97000 9.800 10000 0.900 135000 12.500 8000 1.500 15000 0.800 18 oz MR 18.02 29.3% 0.107 26300 2.200 26300 2.200 29600 1.960 27500 1.540 14500 0.518 C0120 12.00 29.3% 0.198 28070 2.311 28070 2.311 32230 2.043 32230 2.043 8500 0.518 08120 12.11 29.3% 0.523 31900 1.256 31900 1.256 5200 1.181 5200 1.181 10000 0.500 C1M1808 24.69 31.6% 0.173 21040 1.732 21040 1.732 18120 1.501 18120 1.501 13000 0.051 K49/095 9.52 40.0% 0.300 19000 3.300 15000 3.000 65000 3.400 60000 3.200 15000 0.340 E-7781-PP 8.92 70.0% 0.107 70000 4.000 70000 4.000 80000 4.000 80000 4.000 10000 0.500 S-4522 3.70 29.3% 0.107 25787 2.494 25787 2.494 53873 1.869 53873 1.869 8600 0.580
autoclave and cured under appropriate temperature and pressure, and then removed from the autoclave, at which time the vacuum bag and bleeder plies could be removed and the part finally removed from the
male tool. All told, 3-1/2 hours of fully burdened labor.
Figure 5
Kevlar/PPS Apache Helicopter Fairing
The thermoplastic production cycle is nearly fully automatic.
The appropriate number of plies of thermoplastic, in this case
Quadrax Biaxial Tape K-49/PPS, are loaded into a transport tray.
Since they are at room temperature, these prepreg plies are quite dry
and relatively stiff, rather like veneers of wood. The cycle starts
at the press of a button when the transport tray runs under a bank of
infrared heaters in the heating section of the thermoformer. At
about 55 seconds, the plies noticeably "slump", showing that the
thermoplastic has melted. At this point, the plies are transported
into the forming bay between a male tool and what I call a "very
nearly matched die" female tool, consisting of a female tool lined with high temperature silicon rubber which, because of its rubbery
consistency, performs the job of a matched die without the necessity
for extremely high accuracy. The hot prepregs are pressed between
the tools for approximately 30 seconds for a cool down and
solidification process, and at approximately 92 seconds total the
finished laminated part is delivered, ready for trimming.
While the production cycle just described obviously depends
upon the use of a rather expensive automatic thermoforming machine,
the overall cost of this part dropped from $1495 in thermoset to $600
in thermoplastic. Thermoforming machines cost approximately US
been processed using heated tools and vacuum bags, avoiding the use of an autoclave with its inherent high cost and very low production
cycling.
Obviously, the likelihood of thermoforming the major components of a vessel such as the hull, deck, or main superstructure is
unlikely at present owing to the high cost of capital equipment of
the size needed to do that sort of job. However, both Baltek and
Hexcel Corporations are currently involved in the development of
thermoplastic sandwich panels with view toward reduction of
production times through the use of automatic thermoplastic
processing, thus bringing down the cost of sandwich panels to the point where their use may no longer be restricted to expensive
leading edge racing vessels only. Other potential uses of reinforced
thermoplastics in the field of yachts and small vessels include scores of smaller high production run items such as hatches, hatch covers, hatch hoods, other various watertight closures, and, in fact, any part where lightweight high strength composites might be
currently precluded because of their high manufacturing costs.
The field of thermoplastics is very much in the mid-development
stage, and is not as mature an industry as thermosets. Nevertheless,
the development of high end reinforced thermoplastics has received sufficient attention over the past ten years to be able to produce very dependable mechanical properties for many of the polymers
available. Basically, reinforced thermoplastics can make use of any
reinforcing fiber currently in use in thermosets, providing, of
course, that the processing temperature for the particular polymer is
not too high to affect the reinforcing fiber. The author has had
good experience with a number of high end reinforced thermoplastics and offers the following set of mechanical properties for review. The data for AS-4 carbon fiber/PEEK (polyether etherketone),
designated APC-2, is from a very extensive series of tests run by the owner at Boeing Technology Services for Quadrax Advanced Materials Corporation.
Table 4
MECHANICAL PROPERTIES FOR A FEW SELECTED THERMOPLASTIC REINFORCEMENTS NOTE: The following data should NOT be used for design purposes without confirmation by testing.
Str. mod. Ste-. Mod. Str. Mod. Str. Mod. Str. Mod.
Tens. T
Material Weight Vf% Poisn Comp. Comp. Comp. Comp. Tens. Tens. ens. Shear Shear
0./yd^2 Ratio 0 Deg 0 Deg 90 Deg 90 Dag 0 Deg 0 Deg 90 Deg 90 Deg
psi msi psi msi psi msi psi msi psi msi
E/PPS Uni 7.67 53.0% 0.300 161000 6.000 53000 1.800162000 6.300 6700 2.000 8900 0.800
A54/PPS Uni 3.50 52.4% 0.010 124530 17.280 62265 8.640 219412 17.280 N.I. N.I. 9705 0.310
K49/PPS Uni 3.50 55.0% 0.040 49888 8.660 N.I. N.I. 104466 8.660
4.011 N.I. N.I. 7208 0.190 83310 4.268 83310 E/PPS OBT 15.34 53.0% 0.300 107000 4.011 107000 4.260 19500 2.100 AS4/PPS QBT 7.00 52.4% 0.010 62265 8.640 62265 8.640 10970624944 4.330 109706 8.640 9705 0.310 :.::: K49/PPS QBT 7.00 55.0% 0.040 24944 4.330 52233 52233 4.330 7208 0.190
E/PPS Uni is a prepreg unidirectional tape of E-Glass and Polyphenylene Sulfide which processes at approximately 550 F under pressures varying from 1 to 20 atmospheres depending on thickness.
AS4/PPS Uni is a prepreg unidirectional tape of AS4 Carbon fiber and Polyphenylene Sulfide which processes at approximately 550 F under pressures varying from 1 to 20 atmospheres depending on thickness.
K49/PPS Uni Is a prepreg unidirectional tape of Kevlar-49 and Polyphenylene Sulfide which processes at approximately 550 F under pressures varying from 1 to 20 atmospheres on thickness.
APC-2 is ICI trade name for AS4 Carbon Fiber in PEEK (polyether etherketone) thermoplastic polymer at 61% fiber volume.
QOT is Quadrax Advanced Materials Corporation tradename for specially formatted U.D. tape reinforcement in a
balanced 0/90 5-harness satin weave. All panels were manufacture from a single batch of ICl/Fiberite APC-2
(AS4/PEEK) unidirectional tape. QUADRA% Corp. interlaced 3/16" slit ribbons into a 7 ft. wide format from which
all QBT panels were produced. Cross-plied tape control panels (XP) were produced directly from the U.D.
tape.Test panels were stacked and vacuum bagged on a flat steel Pool and consolidated as follows, Vacuum was maintained throughout the cycle.
Autoclave pressure - 130 psi (9 Bar)
Part temperature 740 +/- 10 F (395 +/- 6 C)
Dwell time at temperature 30 Min.
Cool-down rate to R.T. 10-13 F per Min. (5-7 C)
Vacuum and autoclave pressure maintained through cool-down.
All panels were consolidated by Boeing Technology Services and 100% inspected for porosity and delaminations
using TTU methods. TTU scans on all panels were free from high porosity areas, debonds, or voids, indicating
complete consolidation.
4. LOAD PREDICTION METHODS
It is unfortunate that strain gauging is so expensive and time
consuming since, were the truth to be known, we have very little hard
information regarding the actual lqads imposed on small boats and
ships. It is all well and good to become deeply involved in the
detailed analysis of a structure, but without the key ingredient of a
good working knowledge of the loads imposed, it must be admitted that
at times the analytical power brought to bear on these problems is
most analagous to performing brain surgery with a fire axe.
Naval APC-2 QUADRAX ----Table 5 U.D. TAPE ---- X-Ply ----COMPARISON OF PROPERTIES QBT vs. CROSS PLIED QBT
----PROPERTY %45 Str Mod. Poisson Str Mod. Poisson
Plies ksi msi Ratio ksi msi Ratio
UN-NOTCHED 0% 125.4 9.79 0.0396 120.2 9.79 0.0357 TENSION 20% 101.5 9.00 0.1365 R.T. Dry 50% 103.8 7.17 0.2958 101.4 7.16 0.3226 80% 60.7 4.77 0.5075 UN-NOTCHED 0% 119.1 9.91 0.0401 120.2 9.84 0.0343 TENSION 20% 121.7 8.97 0.1350 180 Wet 50% 98.2 6.82 0.3152 98.4 6.95 0.3649 80% 56.4 4.62 0.4997 UN-NOTCHED 0% 95.3 9.03 0.0375 100.3 8.97 0.0377 COMPRESSION 20% 101.6 8.25 0.1284 R.T. Dry 50% 78.6 6.79 0.2958 76.9 6.76 0.3332 80% 58.8 4.79 0.4974 UN-NOTCHED 0% 86.9 8.89 0.0366 82.6 8.97 0.0408 COMPRESSION 20% 83.9 7.97 0.1222 180 Wet 50% 69.3 6.56 0.2905 67.9 6.73 0.2810 80% 50.5 4.57 0.5130
a number of very careful studies published which give extremely useful information regarding loadings which can be used with a high degree
of confidence for a small vessel structure. Foremost among the
definitive papers dealing with the issue of bottom pressure loadings and distribution is Heller and Jasper, Reference 30, which has been broadly accepted and which has formed the base for a great many
governmental and scantling society requirements. Undoubtedly the
most well known of all the results reported in that original paper is
the curve relating impact reduction factors versus length. See
Figure 6 below.
PRESSURE = 13.43 psi
38 Ft. HIGH SPEED RACING POWER BOAT
PRESSURE = 10.74 psi
Ft FAST MOTOR YACHT
HELLER & JASPER BOTTOM PRESSURES
Figure 6
Here, a 38 foot racing powerboat and a 47 foot fast motoryacht are shown rescaled so that their overall lengths are equal and curves
for the bottom pressures of the two boats are shown scaled
proportional to each boat's length overall (LOA). By inspection, the
relative magnitudes of the two bottom pressures seem reasonable in
consideration of the boat types. It should be noted, however, that
the Savitsky and Brown/Heller and Jasper methods are extremely
dependent on a realistic assessment of the sea conditions in which
the vessel will be operated at maximum speed.
Heller and Jasper's work defined a maximum impact pressure
which their study predicted would be found over approximately 25% of
the length of the vessel, fore and aft of which pressures were
predicted to reduce in a linear fashion. Also included in their
study is a prediction of pressure for transverse members, including
plating, as a function of half-girth, as well as a method to predict
longitudinal load distribution as a function of location, based on
statistical probabilities. The transverse factor is not always taken
structure to optimize around this parameter can be needlessly
expensive. It is also well to remember that the reductions based on
this factor are usually not very large in any case.
A careful reading of the original Heller and Jasper paper has led a number of researchers to suggest that the data collected and statistical analysis of that data might be more accurately
interpreted to suggest that the transverse and longitudinal reduction
factors be interchanged. It is the author's opinion that the
transverse reduction factor can be ignored in many cases, or at least reduced in power by approximately 50%, not only for the practical reason given above, but, more importantly, in consideration of the fact that it presupposes that the vessel will run at 0 roll, whereas in the real world in heavy seas, wave induced roll and pitch will most assuredly negate the mathematical niceties necessary to justify the use of the transverse reduction factor.
Below are shown the results of a number of methods commonly in
use for predicting bottom pressure for powerboats. It is instructive
to note both the similarities as well as the disparities. It should
be noted that the Savitsy and Brown method for predicting
acceleration at LCG has been used assuming an average for tenth
highest waves. In addition, the safety factors recommended for each
of the methods has been included to derive a design pressure for each
of the methods. A review of the results of these calculations would
seem to lead to the conclusion that the reason most of these methods seem to work is that they employ safety factors which virtually bury any engineering niceties.
COMPARISON OF BOTTOM PRESSURE PREDICTIONS FOR POWER VESSELS 47 Foot Fast Motor Yacht
LOA = 47 Ft. DWL= 43.17 Ft. L = 45.09 Ft. V/L= 2.5
Bmax = 17.58 Ft. BWL = 15.25 Ft. G = 7.88 Ft. V = 16.79
D=
5.00 Ft. d = 2.00 Ft. Beta= 14.70 Trim = 2Displ = 41000 Lbs. 2.00
Savitsky & Brown - Acceleration @ c.g., n = 0.42 g's
Note: This is for average of 1/10th highest waves.
Heller & Jasper - Basic Bottom Pressure - Phj
Poi = 5.11 psi Dyn. Load Factor = 1.1
Phj = 6.51 psi Max Impact Factor= 1
Pdhj = 9.77 psi Safety Factor = 1.5 On Ult. Wet Str.
(Safety factor originally 1.1 on welded yield)
Gibbs & Cox - Basic Bottom Pressure - Des. Pgc
Pgc = (19.7 x V"2 + 10.1 x V x L".5 +116.8) x 10-3 psi
Pgc = 11.96 psi Safety Factor = 1.5 On Ult. Wet Str.
Pdgc = 17.93 psi
Spaulding & Silvia - Basic bottom pressure - Pss
.625 x V psi
10.49 psi Safety Factor =
15.74 psi
1.5 Assumed
Pss =
Pss =
Danahy - Basic Bottom pressure - Pdh
Pdh = .02 x VA2 psi
Pdh = 5.64 psi Safety Factor = 2 Assumed
Pddh = 11.27 psi
ABS Proposed Fast Motor Boat Rule - Basic Bottom Pressure - Pabs
Pabs =
Max(.06875xDispl/(LxB) x (1 + n)
, 3.29xnxd
Pabs = 5.04 psi Safety Factor = 2.5 On Ult. Wet Str.
Pdabs = 12.61 psi
Below is a printout of the prediction of maximum hull bottom
loading for a 38 foot racing powerboat. As can be seen, the major
factor driving hull bottom pressures is the application of impact loading derived from an estimate of speed and vertical acceleration
at LCG. Since bottom pressures are assumed to vary linearly with
acceleration, it is important to get this right. In much of the
literature, it is assumed that, for reasons of human practicality,
accelerations much above 3 G's are highly unlikely. This comes from
studies of military craft and for such boats this is probably true. On the other hand, modern offshore racing powerboats with seats or cockpits specially designed with spring and shock absorber systems are pushing this limit severely, and a number of unconfirmed reports of accelerations in the neighborhood of 5 and even 6 G's have been heard.
With accelerations due to impact of such magnitude, it is some concern whether the static structural analysis currently in use can
accurately cope with the problem. This is of particular concern in
sandwich structures where the constituents have significantly different stiffnesses and may have even more significant time
response mechanisms to contend with. Several interesting studies
have been undertaken in this area. The reader is referred to
References 21 and 35.
For powerboats, there are so many combinations of longitudinal and transverse reduction factors involved that our calculations end
at the development of the maximum design pressure. From this point,
a second program, ORTHOPNL (Pg XXX), is used to compute shell
thicknesses, section modulii, and moments of inertia to both surfaces of the shell, taking into consideration panel geometry and the
orthotropic properties of the material involved.
ACCELERATION @ C.G. AND BASIC BOTTOM PRESSURE PER SAVITSKY & BROWN + HELLER & JASPER
38 Foot High Speed Racing Powerboat
LOA = 37.45 Ft. DWL = 37.45 Ft. L = 37.45 Ft. V/L= 6.55
Bmax = 8.00 Ft. BWL = 8.00 Ft. G = 4.37 Ft. V = 40.08
D=
5.00 Ft. d = 1.75 Ft. Beta = 23.63 Trim = 2Displ = 10000 Lbs.
Savitsky & Brown - Acceleration @ c.g., n = 2.89 g's
Note: This is for average of 1/10th highest waves. Heller & Jasper - Basic Bottom Pressure
Poi = Pmax = Ph = %LOA 7.43 8.17 0.78 Fi psi Usually 1 or 1.1 psi
psi Base Bottom pressure = Pb = Pmax * Fl
*** IMPACT FACTORS *** Pb %LoA Fi Pb psi psi 0% 0.50 4.08 55% 0.93 7.56 5% 0.60 4.90 60% 0.85 6.94 10% 0.70 5.72 65% 0.78 6.33 15% 0.80 6.54 70% 0.70 5.72 20% 0.90 7.35 75% 0.63 5.11 25% 1.00 8.17 80% 0.55 4.49 30% 1.00 8.17 85% 0.48 3.88 35% 1.00 8.17 90% 0.40 3.27 40% 1.00 8.17 95% 0.33 2.66 45% 1.00 8.17 100% 0.25 2.04 50% 1.00 8.17 %G or L Ft
*** TRANSVERSE & LONGL FACTORS ***
Fl %G or L Ft Fl 0% 1.000 0.750 55% 0.760 0.475 5% 0.963 0.723 60% 0.751 0.475 10% 0.927 0.695 65% 0.741 0.475 15% 0.890 0.668 70% 0.732 0.475 20% 0.854 0.640 75% 0.722 0.475 25% 0.817 0.613 80% 0.713 0.475 30% 0.808 0.585 85% 0.703 0.475 35% 0.798 0.558 90% 0.694 0.475 40% 0.789 0.530 95% 0.684 0.475 45% 0.779 0.503 100% 0.675 0.475 50% 0.770 0.475 Design Pressure P=Pb*Ft*Fl+Ph Pb = 8.17 Fl = 1.00 Ft = 1.00
Design Pressure P= 8.95 psi (Note: No safety factor included!)
ACCELERATION @ C.G. AND BASIC BOTTOM PRESSURE PER SAVITSKY & BROWN + HELLER & JASPER
47 Foot Fast Motor Yacht
LOA = 47.00 Ft. DWL = 43.17 Ft.
L =
45.09
Ft. V/L=2.5
Bmax = 17.58 Ft. BWL = 15.25 Ft. G = 7.88 Ft. V = 16.79
D = 5.00 Ft. d = 2.00 Ft. Beta = 14.70 Trim = 2
Displ = 41000 Lbs.
Savitsky & Brown - Acceleration @ c.g., n = 0.42 g's
Note: This is for average of 1/10th highest waves. Heller & Jasper - Basic Bottom Pressure
Po = 161.22 lbs./in. Dynamic Load Factor = 1.1
Poi = 5.11 psi Usually 1 or 1.1
Pmax = 5.62 psi
%LoA Fi *** Pb psi IMPACT FACTORS *** %LOA Fi Pb psi 0% 0.50 2.81 55% 0.93 5.20 5% 0.60 3.37 60% 0.85 4.78 10% 0.70 3.94 65% 0.78 4.36 15% 0.80 4.50 70% 0.70 3.94 20% 0.90 5.06 75% 0.63 3.52 25% 1.00 5.62 80% 0.55 3.09 30% 1.00 5.62 85% 0.48 2.67 35% 1.00 5.62 90% 0.40 2.25 40% 1.00 5.62 95% 0.33 1.83 45% 1.00 5.62 100% 0.25 1.41 50% 1.00 5.62 0% 1.000 0.750 55% 0.760 0.475 5% 0.963 0.723 60% 0.751 0.475 10% 0.927 0.695 65% 0.741 0.475 15% 0.890 0.668 70% 0.732 0.475 20% 0.854 0.640 75% 0.722 0.475 25% 0.817 0.613 80% 0.713 0.475 30% 0.808 0.585 85% 0.703 0.475 35% 0.798 0.558 90% 0.694 0.475 40% 0.789 0.530 95% 0.684 0.475 45% 0.779 0.503 100% 0.675 0.475 50% 0.770 0.475
*** TRANSVERSE & LONGL FACTORS ***
%G or L Ft Fl %G or L Ft Fl
Design Pressure P=Pb*Ft*Fl+Ph Pb = 5.62 Fl = 1.00
Ft = 1.00
Design Pressure P= 6.51 psi (Note: No safety factor included!)
While Silvia, Reference 31, and others may suggest that a
careful analysis of Heller and Jasper might lead to interchanging the two curves, it is important to point out that thousands upon
thousands of vessels have been designed and built based on analyses relying on Heller and Jasper, and to date no major calamities seem to
have occurred as a consequence. So broadly accepted is the concept
of a pressure reduction field based on a function of length that no serious engineering analysis could ignore it.
The hull design heads which form the basis of analysis for the American Bureau of Shipping's Scantling Guide for Offshore Racing
Yachts is but one derivative of the Heller and Jasper curve. See
Figure 7 below.
The most broadly used method for developing design pressures for sailboats is that found in the American Bureau of Shipping's
Scantling Guide for Offshore Racing Yachts. The basic hull bottom
design pressure formula contains three factors. The first factor
calculates the hydraulic head from the static waterline to the
deepest point of the hull. The second factor is a function of length
which may be thought of as containing both speed and sea state
adjustments. The third factor is a second hydraulic head which is
independent of geometry and has the effect of increasing design pressures for smaller boats more powerfully than for larger ones.
While difficult to support directly on the basis of first principles, its use is a reasonable approximation of the effects of a given sea
state on boats of varying sizes. It is readily noted that the ABS
rule modifies this basic head by a load factor very similar to that of Heller and Jasper, but which runs from 80 percent at the bow
through 120 percent in the area most likely to sustain impact damage,
and thence to 70 percent at the stern. ABS chose not to implement a
specific factor for impact. This seems quite reasonable, since even
the very fastest sailboats raced offshore seldom approach
speed/length ratios greater than 1, except off the wind surfing where impact is not a significant threat..
In Figure 7 below, are shown the design bottom pressures
produced by the ABS rules for a moderate displacement 45 footer and a
27 foot ULDB. The hulls have been rescaled to a common length, and
pressures are shown proportional to LOA. As before, the design
pressures for these two boats, considering the two types, appear to be reasonable. T PRESSURE = 9.38 psi 7' -I
-FREEDOM 45-
PRESSURE = 5.71 psi I '127 Ft. FAST MORC RACER
ABS OFFSHORE RACING YACT BOTTOM PRESSURES
Figure 7
A comparison of these two methods for developing pressure
curves is instructive, partially owing to a comparison of the
magnitudes and reductions but, just as importantly, to compare how
the two curves deal with overhangs. It can be seen that the original
Heller and Jasper curve ignored overhang and was based on length
overall. This was undoubtedly a practical matter as they were
testing a World War II PT boat (PT-'8), but also owing to the
fact
that bow profiles and forward overhangs as a percentage of length for
high speed power boats did not vary to a very great extent when these
first tests were run. Therefore, relating impact effects to
differences in locations on a fast power boat of that day. Sailboats, on the other hand, have both bow and stern overhangs which vary
tremendously from type to type and, as a consequence, the location of the high impact area as a function of load waterline must be a more
accurate representation of full scale load conditions. The fact that
both the original Heller and Jasper as well as the ABS Scantling Guide for Offshore Racing Yachts can be called curves only in the strictest mathematical sense brings the question to mind as to whether or not these straight line curves with very sharp corners would not more accurately represent nature if the corners were
rounded a bit In fact, there is probably some continuous
mathematical ;unction which might more elegantly describe the impact area as a function of length, but as a practical matter good
engineering practice involving continuity of structure makes this
point moot. Such curves would probably not produce structures
greatly different from those produced from the original curves, but being continuous functions they would lend themselves to computer analysis more easily.
One final comment on the use of the Heller and Jasper curves is
appropriate. Purcel, Reference 33, notes that, strictly speaking,
the Heller and Jasper curve is appropriate only for hard chine
planing vessels, but found in his analysis of the Island Class patrol boats that there appeared to be no glaring problem with using the
curve for round bilged vessels as well. The author would note here
that reduction of the transverse load reduction factor is additional insurance that application of the fore and aft impact reduction
factor curve to round bilged vessels is a reasonable practice.
Impact or design pressure reduction curves are useful only in combination with dependable methods for developing basic design pressures. Erbil' first principles, the total pressure at any given point must be a combination of hydraulic head, velocity induced
pressure, and impact. In quite a number of simplistic analyses,
hydraulic head is taken simply as the depth below static load waterline, while velocity induced pressure and impact effects are ignored, and the entire matter is buried under an enormous safety
factor. This sort of practice masqueraded as engineering for many
years in the pleasure boat field. The fact that so many thousands of
boats were designed and built in this manner without more loss of life is proof only that the Lord takes care of fools and little children.
Below are the computer printouts for the bottom pressures for
the two sailing vessels shown above. In the case of sailing vessels,
base design head is developed from ABS and, using material properties for a standard laminate (18 ounce 0/90 UD E-Glass/polyester), shell thickness to meet strength and stiffness criteria as well as moment
of inertia and stiffness El are derived. At this point, information
from a laminate analysis package, PBJ, is introduced and comparison made between the required bending moment and El versus the bending
moment and El properties of the specific laminate analyzed. Finally,
core shear for the candidate laminate is calculated and compared to
the core shearlproperties. As a final calculation, the analysis of
basic stiffeners is produced as a guide to final structural design. Examples of two boats are shown below.
OFFSHORE RACING YACHTS
LAMINATE PROPERTIES MIMIMUM FLEX. STRENGTH MINIMUM TENS. STRENGTH MINIMUM COMP. STRENGTH MINIMUM FLEX. MODULUS MINIMUM TENS. MODULUS MINIMUM COMP. MODULUS
PLATING PANEL ANALYSIS
PANEL LOCATION: STATION 1.7 - BOTTOM VCP to BL 0.00 FT.
LOCL PANEL Fl,F2 = 1.2 (FROM ABOVE)
DESIGN HEAD: H = 21.11 FT.
PANEL SIZE: S = 30.00 IN. x L = 60.00 IN.
PANEL CURV: DEPTH= 2.00 IN.
DESIGN HEAD RED. FACTOR F = 0.613 CF = 0.419
PANEL CURVATURE FACTOR: C = 0.967 NOTE! MINIMUM VALUE = 0.70
PANEL ASP. RAT. FACTOR: k = 0.495 FOR STRENGTH
PANEL ASP. RAT. FACTOR: kl= 0.028 FOR STIFFNESS
SINGLE SKIN CONSTRUCTION
REQ'D PLATE THICKNESS: T = 0.418 IN. (FOR STRENGTH)***GRP***
REQ'D PLATE THICKNESS: T = 0.451 IN. (FOR STIFFNESS)
SANDWICH CONSTRUCTION
REQ'D SECTN. MOD. TO OUTSIDE SKIN = 0.024 INA3
REQ'D SECTN. MOD. TO INSIDE SKIN = 0.027 INA3
REQ'D MOMENT OF INERTIA = 0.0071 IN','
REQ'D MIN. BEND. MOM. of SANDWICH = 789.65 IN*LB
REQ'D SANDWICH STIFFNESS "El" = 16116.45 LB*INA2
18 oz 0/90 U.D. E-Glass from PBJ
27114 psi 27114 33545 psi 33545 = 29215 psi 29215 = 2108000 psi 2108000 = 2126000 psi 2126000 = 2405000 psi 2405000
BASIC DESIGN HEADS - ABS
45 Foot Sailing Yacht for FREEDOM YACHTS
LOA = 44.75 FT. DWL = 34.375 FT. L = 39.56 FT.
Bmax = 13.49 FT. D = 6.2 FT. d = 2.25 FT.
BASE HEAD, H = 17.59 FT.
STATION BOTTOM BOTTOM SIDE STATION BOTTOM BOTTOM SIDE
Fl HEAD F2 Fl HEAD F2 STEM 0.80 14.07 0.70 4 1.17 20.58 1.05 -1 0.80 14.07 0.70 5 1.10 19.35 0.99 0 0.93 16.36 0.95 6 1.03 18.12 0.93 .5 1.07 18.82 1.08 7 0.97 17.06 0.87 1 1.20 21.11 1.08 8 0.90 15.83 0.81 2 1.20 21.11 1.08 9 0.83 14.60 0.75 3 1.20 21.11 1.08 10 0.77 13.54 0.69 3.5 1.20 21.11 1.08 11 0.70 12.31 0.63 TRANSOM 0.70 12.31 0.63
Hd = Uncorrected Deck Plating Head -= 8.58 Ft.
3/4 oz CSM CDM 1808 CDM 1808 3/4 oz CSM Core Balsa 3/4 oz CSM CDM 1808 CDM 1808 Strength Margi Core Shear = 0.026 in. 0.059 in. 0.059 0.026 0.500 in. 0.026 0.059 in. 0.059 in. 1.17 Stiffness Margin = 119.77 psi
STIFFENER ANALYSIS per ABS
STIFFENER LENGTH = 5.00 FT. STIFNR SPACNG =
STIFNR HEAD RED. FACTOR F = 0.258 CF
LOCL PANEL F1,F2 = 1.20 (FROM ABOVE)
LOCAL PL DES. HD = 21.11 FT.
STIFNR DES. HEAD = 5.44 FT.
REQ'D MOM - FLOORS @ CL =95866.65 in*lbs
REQ'D MOM - FLOORS @ ARMS =43544.82 in*lbs REQ'D MOM - FRS & LONGLS =43544.82 in*lbs
1.85
2.50 FT. 1.048
REQ'D EI=9.06E+06 lb*in-2 REQ'D EI=4.12E+06 lb*in-2 REQ'D EI=4.12E+06 lb*in-2
BASIC DESIGN HEADS PER ABS and MATERIAL PROPERTIES 27 Foot U.L.D.B. for MIKE HALE
LOA = 27.43 FT. DWL = 24.07 FT. L = 25.75 FT.
Bmax = 10.05 FT.
D=
3.16 FT.d=
0.6 FT.BASE HEAD, H = 10.71 FT.
STATION BOTT M BOTTOM SIDE STATION BOTTOM BOTTOM SIDE
Fl HEAD F2 Fl HEAD F2 STEM 0.80 8.56 0.70 4 1.17 12.52 1.05 -1 0.180 8.56 0.70
1.10
11.78
0.99 0 0.13 9.96 0.95 6 1.03 11.03 0.93 .5 1.07 11.45 1.08 7 0.97 10.38 0.87 1 1.20 12.85 1.0g a 0.90 9.63 0.81 2 1.20 12.85 1.08 9 0.83 8.89 0.75 3 1.20 12.85 1.08 10 0.77 8.24 0.69 3.5 1.20 12.85 1.08 11 0.70 7.49 0.63 TRANSOM 0.70 7.49 0.63Hd = Uncorrected Deck Plating Head = 8.03
Hh = Uncorrected House Plating Head= 6.50
Ft. Ft.
LAMINATE PROPERTIES 18 oz 0/90 U.D. E-Glass from PBJ
MIMIMUM FLEX. STRENGTH 27114 psi 27114
MINIMUM TENS. STRENGTH 33545 psi 33545
MINIMUM COMP. STRENGTH = 29215 psi 29215
MINIMUM FLEX. MODULUS = 2108000 psi 2108000
MINIMUM TENS. MODULUS = 2126000 psi 2126000
MINIMUM COMP. MODULUS = 2405000 psi 2405000
Laminate from BJ:
Thick = 0.815 in
Wt. = 0.863 lb/ft-2
Mom = 923 in*lbs
PLATING PANEL ANALYSIS
REQ'D SECTN. MOD. TO OUTSIDE SKIN =
REQ'D SECTN. MOD. TO INSIDE SKIN =
REQ'D MOMENT OF INERTIA
REQ'D MIN. BEND. MOM. of SANDWICH = REQ'D SANDWICH STIFFNESS "El" = Laminate from PBJ: 12 oz E-Glass 0/90 12 oz E-Glass 0/90 Core Div H45 12 oz E-Glass 0/90 12 oz E-Glass 0/90 Strength Margin = Core Shear = 0.021 in. 0.021 in. 0.750 in. 0.021 in. 0.021 in.
STIFFENER ANALYSIS per ABS
STIFFENER LENGTH = 3.08 FT. STIFNR SPACNG = 2.00 FT.
STIFNR HEAD RED. FACTOR F = 0.353 CF 0.697
LOCL PANEL F1,F2 = 1.20 (FROM ABOVE)
LOCAL PL DES. HD = 12.85 FT.
STIFNR DES. HEAD = 4.53 FT.
REQ'D MOM - FLOORS @ CL =24284.1e in*lbs REQ'D EI=1.41E+06 lb*in-2
REQ'D MOM - FLOORS @ ARMS =11030.42 in*lbs REQ'D EI=6.43E+05 1b*in-2
REQ'D MOM - FRS & LONGLS =11030.42 in*lbs REQ'D EI=6.43E+05 1b*in-2
The following is a printout of a program which is used to analyze a panel under uniform normal pressure load based on the geometry of the panel and taking into account a material with different mechanical
properites in the 0 and 90 (long and short panel directions. It is
based on work by Bob Curry of ABS (See Reference 35), and one of my professors in Naval Architecture at the University of California at Berkeley, Dr. Henry Schade (Reference 5).
0.010 IN-3 0.012 IN-3 0.0024 IN-4 340.67 IN*LB 5493.79 LB*IN-2
PANEL LOCATION: STATION 1.7 - BOTTOM VCP to BL 0.00 FT.
LOCL PANEL F1,F2 = 1.2 (FROM ABOVE)
DESIGN HEAD: H = 12.85 FT.
PANEL SIZE: S = 24.00 IN. x L = 37.00 IN.
PANEL CURV: DEPTH= 0.00 IN.
DESIGN HEAD RED. FACTOR F = 0.657 CF = 0.361
PANEL CURVATURE FACTOR: C = 1.000 NOTE! MINIMUM VALUE = 0.70
PANEL ASP. RAT. FACTOR: k = 0.478 FOR STRENGTH
PANEL ASP. RAT. FACTOR: kl= 0.026 FOR STIFFNESS
SINGLE SKIN CONSTRUCTION
REQ'D PLATE THICKNESS: T = 0.275 IN. (FOR STRENGTH)***GRP***
REQ'D PLATE THICKNESS: T = 0.315 IN. (FOR STIFFNESS)
SANDWICH CONSTRUCTION Thick = 0.834 in Wt. = 0.863 lb/ft-2 Mom = 923 in*lbs El = 29781 lb*in-2 2.71 Stiffness Margin = 5.42 53.84 psi
Short Dim. s = Long Dim. 1. = Panel Curve Ce = Panel Curve Cl = Allw. Defl. d = Base Pres. Impact Fact. Pi = Curve Fact. Fcs = Curve Fact. Fcl = Des. Pres. P = Safety Fact. = Allw. Defl. ; Corrected Ks = Corrected K1 = Corrected K1e = Corrected K1 (s) = (1) = (s) = (1) =
OR HOTROPIC PLATES w/ SANDWICH CONSTRUCTION PLATE i1IMENSIONS:
=
*** For Strength ***
0.24 Inches Mom.(s) = 284.78 in.*lbs.
0.165 Inches Mom. (1) = 298.75 in.*lbs.
*** For Stiffness ***
0.21 Inches E*I (s) = 3501.81 in.*lbs.
0.231 Inches E*I (1) = 3576.36 in.*lbs.
*** Sandwich Shell Section Properties (I & Z) Required (Fixed Edges) *** Req'd Z to Outside Skin (s) =
Req'd Z to Outside Skin (1) = Req'd Z to Inside Skin (s) = Req'd Z to Insidle Skin (1) = Req'd I to Outside Skin (s) = Req'd I to Outside Skin (1) = Req'd I to Inside Skin (s) =
rItReq'd
I to Insid Skin
Cl) =
5.
DESIGN MINIM
ell Thicknesses (t) Required (Fixed Edges) ****
It is unfortunate that not all of the problems in a structural analysis can be reduced to the simple solution of a rectangular plate
with all fixed edges. Judgment based on solid experience and an
engineering background helps to understand why panels bounded by a chine
or the deck edge should be considered as pin edged on that boundary. In
fact, a panel may have a variety of boundary
conditions.
References 5and 34 go into this in some detail. In particular, when using composite
materials, the effects of orthotropy must be understood and considered. Below are printouts of a PBJ sandwich analysis examining a standard
0.0137 in-3/in 0.0001
in-3/in
0.0040 in-3/in 0.0183 in"3/in 0.0011 in-4/in 0.0010 in-4/in 0.0009in-4/in
0.0011 in"4/in 20.00 30.00 1.00 1.00 Inches Inches Inches Inches MATERIAL:K49-095 *** Properties *** *** From PBJ ***2.00% Span Flex. Str. (Strs)= 15828 psi
5.00 psi Flex. Str. (Str1)= 19718 psi
1.00 Tens. Str. (Strs)= 65451 psi
0.950 Tens. Str. (Str1)= 70905 psi
0.967 Comp. Str. (Strs)= 16363 psi
4.75 psi Comp. Str. (Str1)= 20726 psi
2.00 Flex. Mod. (Efs) = 3161000 psi
0.40 Inches Flex. Mod. (Efl) =3.42E+06 psi
0.473 Tens. Mod. (Ets) =3.49E+06 psi
0.475 Tens. Mod. (Etl) =3.71E+06 psi
0.025 Comp. Mod. (Ecs) =3.27E+06 psi
Kevlar laminate, first in the 0 and then in the 90 degree direction. As
can be seen, bending strength is 25 percent better in the 0 direction,
while bending stiffness is only 8 percent better. Tensile strength is
also approximately 8 percent better, while compression strength is 27
percent better. These sorts of variations in properties due to
orientation affect a variety of design details. Clearly, joining of a
bulkhead to a hull by tabbing will be greatly improved using a bias
material. Ordinarily, a +/-45 bias tape will resist shear loading at
the joint much better than a 0/90. References 21 and 35 offer excellent
information in this area.
6. DEALING WITH ORTHOTROPY
P8.) SANDWICH ANALYSIS Gary W. Mull - Naval Architects Marine Engineers
10-01-1990 HISWA ORTHO PLATE
LAMINATE 1 K49-095 0 0 Dog.
90 deg. strain 0
Engineering properties of composites are highly dependent on shop environment and methods. Results from this program are based on published data. The only sure way to determine the strength of a part is to build and test it.
LAMINATE IN BENDING ************************************************************************** LOAD IN PLANE STRENGTH with core w/o core STIFFNESS with core w/o core
1st layer Skin Skin Core shear
0.0444 in.
1
failure failure 1 wrinkling failure
from top
Z (in"3) St (psi) Sf (psi)
0.0013 19718 17012 0.0013 19718 17012 I (in-4) 0.0001 0.0001 Sf (psi) 19718 19718 Ef (psi) 3.422E+06 3.422E+06 A (in"2) St (psi) 0.0882 70905 0.0882 70905 A (in-2) Et (psi) 0.0882 3.709E+06 0.0882 3.709E+06 TENSION COMPRESSION
1st lyr Ultimate 1st lyr Ultimate
St (psi) 70905 70905 Et (psi) 3.709E+06 3.709E+06 Sf (psi) N/A N/A Sc (psi) Sc (psi) 20726 20726 20726 20726 Ec (psi) Ec (psi) 3.600E+06 3.600E+06 3.600E+06 3.600E+06
IS MAT'L LOADING Fv Fmax Fist
(in.) (psi) (10-6) (in.) (in.) (lb.) (lb.)
1 K49-095 O COMP 0.40 0.022 20726 3.60 0.0334 0.0444 457 344
2 K49-095 O COMP 0.40 0.022 20726 3.60 0.0113 0.0224 457 117
3 K49-095 O FLEX 0.40 0.022
4 K49-095 O TENS 0.40 0.022 70905 3.71 0.0328 0.04,38 1564 348
0.088 N.A. shift 0.0107 460
Ef (psi)
Shear basis:
3.422E+06 Beam length 53.0 in.
3.422E+06 Beam ends - pinned
Fail EIo 1st EIo fall
(lb.) (in"2 lb) (1,1'2 lb) 344 88 88 117 10 10 348 aa 68 460 196 196 BENDING N.Axis STRENGTH with core *w/o core STIFFNESS with core w/o core
************************************************************************** BENDING STRENGTH: Mnt. (in lb) STIFFNESS:EI (in-2 lb) ************************************************************************** IN PLANE STRENGTH (lb) STIFFNESS (lb @ e=.01) **************************************************************************
published data. The only sure Hayto determine the strength of a part is to build and
iff NAT'L LOADING Fv
(in.) 1 K49-095 90 COMP 0.40 0.022 2 K49-095 90 COMP 0.40 0.022 3 K49-095 90 FLEX 0.40 0.022 4 K49-095 90 TENS 0.40 0.022 STIFFNESS with core w/o core LOAD IN PLANE STRENGTH with core w/o core BENDING LAMINATE IN I (in-4) 0.0001 0.0001 A (in-2) 0.0882 0.0882 STRENGTH: Mnt. (in lb) STIFFNESS:EI (in-2 lb) BENDING 1st layer failure 25 196 Laminate in tension 1st layer maximum 6257 6257 3273 3273 1st layer failure Sf (psi) 15828 15828 Ef (psi) 3.161E+06 3.161E+06 St (psi) 65451 65451 Et (psi) 3.491E+06 3.491E+06 1st layer failure 20 181 Skin failure 25 196 65451 3.49 0.0325 0.0435 1444 Skin failure Sf (psi) 15828 15828 Ef (psi) 3.161E+06 3.161E+06 TENSION 1st lyr Ultimate St (psi) 65451 65451 Et (psi) 3.491E+06 3.491E+06 Skin failure 20 181 0.088 NA.. shift 0.0104 366 Skin wrinkling N/A (no core) Laminate in compression 1st layer maximum 1829 1829 3177 3177 366 181 181 ************************************************************************** Skin wrinkling Sf (psi) 16116 16116 Sc (psi) 16363 16363 Ec (psi) 3.273E+06 3.273E+06 Skin wrinkling N/A (no core) Interlam'r shear (psi) 34.73 n=53.0 Pin Core shear failure Sf (psi) N/A N/A Shear basis:
Beam length 53.0 in. Beam ends - pinned
COMPRESSION 1st lyr Ultimate Sc (psi) 16363 16363 Ec (psi) 3.273E+06 3.273E+06 Interlam'r shear (psi) 27.63 @L=53.0 Pin STIFFNESS A (in-2) with core 0.0882 w/o core 0.0882 ************************************************************************** BENDING N.Axis 0.0448 in. from top STRENGTH Z (in-3) with core 0.0013 w/o core 0.0013 tst it.
PBJ SANDWICH ANALYSIS Gary W. Mull - Naval Architects Marine Engineers
10-01-1990 HISWA ORTHO PLATE
LAMINATE 2 K49-095 Rotated 90 degrees
90 deg. strain 0
Engineering properties of composites are highly dependent on shop environment and methods. Results from this program are based on
Fist Fail EIo 1st EIo fail
(lb.) (lb.) (in"2 lb) (1n"2 lb)
272 272 82 82
94 94 10 10
279 279 81 81
Fmax
(psi) (10"6) (in.) (in.) (lb.)
16363 3.27 0.0337 0.0448 361
************************************************************************** Laminate in compression 1st layer maximum 1444 1444 2888 2888 **************************************************************************
7. COMPUTER AIDED REGIMMER1MG AND DESIGN ((!AED)
It goes without saying that the professions of design and
engineering have changed dramatically over the past decade or so.
Not too many years ago, the author produced a number of successful designs with paper, pencil, slide rule, and a few splines and
weights. Today, these have been replaced almost totally by keyboard,
screen, and plotter. Unfortunately, just as the shift from wood to
metal costs the designer and builder an intuitive sense of "grain", the changeover from calculation pad to computer printout tends to separate the designer and engineer from a close and intuitive
connection with the problem at hand. Whereas ten or fifteen years
ago it was clearly understood that paper, pencil, and calculator were
mere tools to use to solve problems, too often today computers are
seen as inherently containing the solution with only minimal input or
fundamental knowledge on the part of the operator.
It is quite common nowadays to pick up any of the various trade
or technical journals catering to the marine field to see software
advertised as though the mere purchase of a few 5-1/4 inch computer
disks is a reasonable substitute for a university degree in naval
architecture and marine engineering. A great many CAD and CAE
programs are available, but none of them can substitute or even be
used dependably and accurately without the fundamental engineering
background intrinsic to a degree in engineering. In fact, the only
thing that can be predicted from use of a good CAD package is that the lettering will at least be legible - accuracy is another thing entirely!
Having said the above, it is still considered worthwhile to review the CAD/CAE system currently at use at Gary W. Mull, Naval Architects, as a guide for use by other naval architects for
implementation in their own offices.
OPERATING SYSTEMS: It is not intended here to go into a
detailed description of computer operating systems. Basically, there
are three main operating systems current in the world, being IBM
compatible MS-DOS, Apple MacIntosh, and various versions of UNIX. It
is easy to become embroiled in an emotional discussion of the various operating systems, but looking at computers strictly as tools, the obvious choice is to go with whatever system provides the most available software addressing the specific problems you wish to
solve. One operating system may claim to be easier or more enjoyable
to use, another operating system may claim to be more scientific, but at the present time there is simply no question that the amount of
quality of software written for general engineering and the
marine engineering fields in IBM-compatible MS-DOS makes it an obvious and
overwhelming choice. There are, of course, other systems developed
IN PLANE Laminate in tension
1st layer maximum
STRENGTH (lb) 5776 5776
