Literature_Study_Itza_Perez_Gomez.
DynamicBehaviourofLarge
HydraulicStructuresinFRP
“A look into the dynamic behaviour of a lift gate made in FRP
for guard lock Limmel in Maastricht”
I.C. Pérez Gómez
February 2014
MSc Thesis Literature Study
Dynamic Behaviour of Large Hydraulic Structures in FRP
“A look into the dynamic behaviour of a lift gate made in FRP for guard lock
Limmel in Maastricht”
I.C. Pé rez Gó mez
Submitted to:
Department of Structural Engineering
Technical University of Delft
Version 2
5 February 2014
Title
Dynamic Behaviour of Large Hydraulic Structures in FRP
Subtitle
A look into the dynamic behaviour of a lift gate made in FRP for guard lock Limmel in
Maastricht.
Student
Name:
Student nr.:
Address:
Mobile Phone:
e-mail:
Study:
MSc. Track:
Itza C. Perez Gomez
4093887
Rijswijkseweg 340-45
2516 HM Den Haag
06-46644636
[email protected]
Civil Engineering, Technical University of Delft
Structural Engineering
Study
Technical University of Delft
Faculty of Civil Engineering and Geosciences
Section of Structural engineering
Specialisation Hydraulic Structures
Graduate company
Iv-Infra
Trapezium 322
3364 DL Sliedrecht
Graduation committee
Prof. ir. F.S.K Bijlaard (Chairman)
TU delft CiTG, Department of Steel, Hybrid and Composite Structures
Ir. A. van der Toorn
CiTG, Department of Hydraulic Structures
Dr. M.H. Kolstein
CiTG, Department of Structural and Building Engineering, Steel Structures
Ir. J.R. Augustijn
Iv-Infra, Senior project manager
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TABLE OF CONTENTS
1. Introduction ............................................................................................................................................... 1
2. Lock gates................................................................................................................................................... 2
2.1. Types ................................................................................................................................................... 2
2.1.1. Mitre gates ................................................................................................................................... 2
2.1.2. Single leaf gate.............................................................................................................................. 3
2.1.3. Lift gate ........................................................................................................................................ 4
2.1.4. Rolling or sliding gate .................................................................................................................... 6
2.1.5. Radial gate .................................................................................................................................... 7
2.2. Choice of gate ...................................................................................................................................... 9
2.3. Lift gates .............................................................................................................................................. 9
2.3.1. Gate guides................................................................................................................................... 9
2.3.2. Lifting mechanism ......................................................................................................................... 9
3. Fibre reinforced polymers ......................................................................................................................... 10
3.1 History ................................................................................................................................................ 10
3.2. General characteristics of FRP ............................................................................................................ 13
3.3. Materials ........................................................................................................................................... 15
3.3.1. Reinforcement ............................................................................................................................ 15
3.3.2. Resins ......................................................................................................................................... 21
3.3.3. Cores .......................................................................................................................................... 22
3.4. Moulding processes/Manufacturing processes .................................................................................. 23
3.4.1. Open mould ................................................................................................................................ 23
3.4.2. Closed mould .............................................................................................................................. 25
3.4.3. Continuous Processes ................................................................................................................. 28
4. Material properties of FRP ........................................................................................................................ 30
4.1. Mechanical properties ....................................................................................................................... 30
4.1.1. Fibre/Resin ratio ......................................................................................................................... 30
4.1.2. Stiffness analysis ......................................................................................................................... 31
4.1.3. Laminate theory.......................................................................................................................... 34
4.1.4. Strength analysis ......................................................................................................................... 38
4.2. Durability ........................................................................................................................................... 38
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4.2.1. Water degradation...................................................................................................................... 39
4.2.2. UV resistance .............................................................................................................................. 40
4.3. Fatigue .............................................................................................................................................. 41
5. FRP connections ....................................................................................................................................... 43
5.1. Mechanical connections .................................................................................................................... 43
5.2. Bonded connections .......................................................................................................................... 44
5.3. Combined connections ...................................................................................................................... 47
6. Dynamics .................................................................................................................................................. 48
6.1. Excitation sources .............................................................................................................................. 48
6.1.1. Flow-induced: Excitation due to turbulence ................................................................................ 49
6.1.2. Excitation due to flow instability ................................................................................................. 49
6.1.3. Self-excitation ............................................................................................................................. 50
6.1.4. Amplification of the excitation due to fluid resonance................................................................. 50
6.1.5. Self-excitation in case of fluid oscillations.................................................................................... 50
6.1.6. Waves......................................................................................................................................... 51
6.2. Dynamics of structures in water ......................................................................................................... 53
6.2.1. Mass-spring- damper system equations ...................................................................................... 53
6.2.2. Added water forces..................................................................................................................... 54
7. FRP in structural applications .................................................................................................................... 56
7.1. Examples ........................................................................................................................................... 56
7.1.1. Pedestrian and cyclist bridge at Kolding in Denmark.................................................................... 56
7.1.2. Bridge-in-a-Backpack .................................................................................................................. 57
7.1.3. Bus station ‘The Giant Whale Jaw’............................................................................................... 58
7.1.4. Column mould parking garage Amsterdam.................................................................................. 58
7.1.5. Façade ‘Building X’ Windesheim University in Zwolle .................................................................. 59
7.2. Examples of hydraulic structures in FRP ............................................................................................. 60
7.2.1. Valves in the Kreekraksluizen ...................................................................................................... 60
7.2.2. Spieringsluis ................................................................................................................................ 61
7.2.3. Golbey gate replacement, France ................................................................................................ 62
7.2.4. Erica-Ter Apel lock gates ............................................................................................................. 63
7.2.5. Wilhelminakanaal gates in Tilburg ............................................................................................... 64
7.2.6. Composite vertical lift arch gates research in France ................................................................... 65
Bibliography ................................................................................................................................................. 66
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1. INTRODUCTION
Thequestionforthereductionofmaintenanceofstructuresespeciallythoseinmarine
environmentsisincreasingandmoreisaskedofstructuresintermsofdurabilityandcapacity.
Fibrereinforcedpolymerscanbeagoodalternativestocurrentmaterialstofulfilthesedemands.
Sinceitsuseinothermarkets/industryhasprovedthatitisahighlyresistantmaterial.Butdueto
thefactthatthematerialisrelativelynewinthecivilengineeringmarket,thereisstillmuchtobe
researchedinorderforittobecomeanacceptedstructuralmaterial.
InthepastyearssomeFRPlockgateshavebeencarriedoutintheNetherlands.Theselockgatesare
relativelysmallmitregatesthathavebeenmadeinthismaterialtoreducemaintenance.Forthis
typeofgatestheadvantageswhenlookingatthestructuralbehaviourislessfrictionduetothelight
weight.
Oneofthemainreasonswhythismaterialisn’tbeingusedmorefrequentlyisthelackofdesign
knowledgeandexperienceworkingwiththismaterial,andalsotheuncertaintyregardingits
durability.Manyresearchesonthedurabilityandsustainabilityofithavebeencarriedoutthough
theyarebasedonacceleratedlaboratorytests,inrealitythebehaviourmaybesignificantly
different.Becauseofthisnodefinitiveconclusioncanbedrawn.Althoughduetotheresistanceand
durabilityithasprovedtohaveinotherindustryliketheaerospaceindustry,marineindustryand
thechemicalindustryitisexpecteddurabilitynottobeaproblem.
Inthisliteraturestudywasdonetoobtainknowledgeregardingthismaterialandotherinformation
neededinordertostartthemainpartofthethesisresearch.Theoutlineofthisreportisasfollows:
Inchapter2ashortdescriptionisgivenaboutlockgates,thetypesandthechoicemadeforthe
mainresearchisexplain.Inchapter3,4,and5anoverviewofdifferentaspectsoffibrereinforced
polymersisgiven.FirstthematerialsfromwhichFRPcanbemadeandthemanufacturing
processesavailablearedescribed.Thenthematerialproperties,i.e.determiningmechanical
properties,durabilityofFRPandfatiguearedescribed,followedbyadescriptionofthetypesof
connectionsavailable.Inchapter6thedynamicsarestudied,inthischapteranoverviewwillbe
givenofthedifferenttypesofdynamicloadingforstructuresinwaterandwhatthismeansforthe
basiccalculations.Finallyinchapter7examplesofprojectwhereFRPgateshaveorwillbe
implementedarepresented.
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2. LOCK GATES
At first lock gates were made of wood and they were limited to small gates, because of the
limitations of allowable stresses of the wood, the lack of power needed to open large gates and the
costs. With the new developments in mechanical power and material knowledge larger lock gates
are possible. Nowadays most lock gates are constructed of steel. However a drawback of steel is
that it requires to be conserved to avoid corrosion, thus a lot of maintenance is needed.
In this chapter the most common types of gates will be described of these a choice is then made
regarding the type of gate that will be developed in the case study. This has been a lift gate, reasons
are the possibility to open it under a differential head and the clear advantage it would have
regarding the lightweight of FRP. Lift gates will then be further described in greater detail.
Based on: (Molenaar, 2011), (Vrijburcht, 2000)
2.1. Types
There are different types of gates each having different features and characteristics in this chapter a
short description of some of the most important types of gates will be giving.
2.1.1. Mitre gates
Mitre gates are flat gates consisting of two leaves, that when closed lean against each other pointing
in upstream direction (see fig. 2.1).
The gates rotate around their vertical axis, transferring forces through the pivots to the chamber
walls. The axis of rotation at the recess is eccentric, to guarantee room between the gate and the
lock chamber when opening the gate, and when closed this space should be as small as possible to
retain water.
They are only intended for one-sided water retention and can retain a limited negative head when
hydraulic cylinders are used. This type of gate is not applicable when there are high water currents
or wave action, like is the case for flood gates or weirs. The limited width of mitre gates is
approximately 20-25 metres, which is 10-12.5 metres per door. Of great importance is the
height/width ratio, when it is smaller than 1 the forces on the pivot points are relatively large.
Figure 2.1: Mitre gate (Molenaar, 2011, page 93)
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Advantages
• No limitations regarding vertical clearance
• Functions as a three pivot girder, resulting in relatively light gate structures
• Shallow gate recess
• Simple operating mechanism
• The mechanism doesn’t have to carry the weight of the gate
Disadvantages
• Length of the lock chamber, because of the way the gate opens.
• Exact dimensions (accurate mounting and frequently checking of the contact points of load
transmission is necessary).
• Sensitivity to waste and ice, it may get trapped in between the gates stopping them from
closing properly.
• They cannot be opened or closed under a head differential.
• Possibility of collision is greater because of the shape of the gate, it points to the outside.
2.1.2. Single leaf gate
A single leaf gate is a flat single pivot gate, similar to half a mitre gate (see fig. 2.2). Unlike a mitre
gate where forces are mostly transferred by horizontal forces, for a single leaf gate the transfer of
forces is mostly by bending moments.
Advantages:
• Simple construction and operation, suitable for small locks
• No limitations regarding vertical clearance
• Retention in both directions when gate is lock at the free end
• Forces are transferred parallel to the lock wall (when closed gate is perpendicular to the
lock axis
Disadvantages:
• Recesses are longer than for mitre gates.
• Opening and closing of the gate results and a lot of water displacement
• More rigid and those heavy construction needed for the pivots, socket and collar strap
• Sensitivity to waste and ice
• Not suitable for wide locks because the supports (pivot points/hinges) would have to be
very heavy.
Figure 2.2: Single leaf gate (Molenaar, 2011, page 93)
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2.1.3. Lift gate
Lift gates are lifted along guide towers to open the lock (see fig. 2.3). Guide towers are required to
guide the door into position. The weight of the gate can be balanced by counterweights to reduce
the operating forces of the lifting mechanism.
Advantages:
• Little space is needed for the lock head, enabling the total lock length to be reduced
• Short heads
• Possibility of water retention in both direction
• Possibility to open the gate under a head difference, because the force directions are in a
different plane
• Good inspection and maintenance possibilities
• Little sensitivity to waste and ice
Disadvantages:
• Limited vertical clearance
• Complicated gate guides and operating system
• Large, heavy and expensive superstructure
• Lifting the whole gate under differential head results in very strong underflow
• Spillage of water on vessels passing the gate
• Difficulties with the roller tracks because of the deflection of the gates when under full head
• Balancing the gate can be complicated and expensive. When opening floating debris or ice
as well as ice frozen to the gate can increase its weight and negatively influence the balance
with the counterweights. Also risk of debris falling on ships when passing underneath gate.
Figure 2.3: Lift gate (Molenaar, 2011, page 95)
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2.1.4. Submersible gate
Submersible gates, like lift gates, move vertically with the exception that submergible gates move
downward when opening. They are often used as upstream gate in very high head locks, where the
sill of the lock is so high that there is no need to for a recess in the bottom lock chamber. When a
recess is needed major excavation would be required, limiting their application for larger locks.
(Doeksen, 2012)
There are two types of submersible gates: single leaf and multiple leaf gates.
The double leaf gate is the most commonly used. This gate is composed of a down-stream leaf used
for normal lock operation and an upstream leaf used as a movable sill or as an operating leaf in case
of an emergency, also referred to as an emergency leaf. (See figure 2.4).
This type of gate is useful for skimming ice and drift from the lock approaches when necessary or to
regulate the flow of flood water by opening the gates. (USACE [1], [2])
Advantages:
• No limitations in vertical clearance
• Possibility to open the gate under a (large) head difference, because the force directions are
in a different plane
• Little space is needed for the lock head, enabling the total lock length to be reduced
Disadvantages:
• Large excavation needed for gate recess.
• Sedimentation and erosion at the bottom of the sill may create problems, e.g. impediment in
the movement of the gate and gate not closing properly.
• Maintenance of the gates is difficult since they are always under the (upstream) water level.
Figure 2.4: Schematization of a double leaf
submersible gate, (USACE [2], 2013, page 3.4)
Figure 2.5: Lift gate (USACE [1], 2013, page 7.3)
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2.1.5. Rolling or sliding gate
Rolling gates are preferred where large widths are required, without limiting the vertical clearance.
They close the passage perpendicularly and when opened they are stored in a deep gate chamber at
one of the chamber walls, on the other chamber wall there is a gate recess. Because of this it can
only be applied where sufficient space besides the lock is available (see fig. 2.4).
The gate rests on two roller carriages, each fitted with four wheels that are guided along rails by
means of flanges on the wheels or by means of roller guides or guide blocks. For sliding doors the
roller carriages are replaced by hydrostatic slide bearings.
Usually the gate is equipped with float control chambers, which result in a decrease of the weight
and frictional forces on the roller carriages as well as reducing wear and tear. When the gate is
closed these chambers can be filled, serving as ballast tanks, ensuring the necessary contact
pressure.
During opening the upper corner of the gate is unsupported when a force is on this area the gate
may become unstable. Forces on this area can be a result of e.g. a remaining water level difference
or a large flow. To provide stability a certain gate thickness is required.
Advantages:
• Water retention in both directions
• Possibility for two sided turning
• Light operating mechanism
Disadvantages:
• Expensive, deep gate recess
• Expensive guiding system
• Large area needed for storage of the gate when open
• The minor overweight requirement could make the gate sensitive to waves during
movement of the gate
• The gate can be obstructed due to accumulation of sediment or debris on the tracks
Figure 2.6: Rolling gate (Molenaar, 2011, page 96)
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2.1.6. Radial gate
2.1.6.1. Sector gate (Rotation about the vertical axis)
Sector gates have curved shaped skin plates that are stiffened in order to resist the hydrostatic
water pressures. The skin plate is supported both vertically and horizontally by arms, triangular
shape trusses in the horizontal plane. Upper and lower arms are connected by braces to provide the
required vertical stiffness (see fig. 2.5).
Generally two gates are used, one on each side with a rotation point on the chamber wall, along
which the forces are transferred. Sector gates can be pushed into movement mechanically or
hydraulically like mitre gates. But unlike the mitre gates, that have to push the water in front of the
gate, the sector gate cuts through the water. Therefore the driving mechanism can be designed
relatively lighter.
Another option, instead of a mechanical operating mechanism, is to use the hydrostatic water
pressure difference due to differing water levels on either side of the gate.
First the recesses are closed off and the water level is raised by letting water in through culverts.
Because the water level is then higher in the recesses the gate is pushed out, vice versa if water is
let out of the recesses and the water level in the lock would be higher than in the recess the gate
will move into the recess.
Advantages:
• Can retain water on two sides
• Possibility to close under flow conditions
• Can move under water pressure
• Light operating mechanism
• Statically determinate
• Can be operated when there is a water head
• Can resist negative heads
• Unlimited vertical clearance
• Opening and closing of the gates can be done in a short time
Disadvantages:
• Expensive gates, large amount of material
• Large area needed for gate recesses
• The gates are heavier than mitre gates, making them more expensive
• Sensitivity to debris and ice
Figure 2.7: Sector gate (Molenaar, 2011, page 93)
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2.1.6.2. Tainter gate (Rotation about the horizontal axis)
These types of radial gates also have a circular cross section. On the chamber walls short arms are
positioned that go through pivoting points that coincide with the centre of the circle (see fig. 2.6).
If counterweights are present they are applied on the opposite side of the extended arms. The arms
rotate on rotation points positioned about halfway of the water depth. Sometimes the gates are not
balanced by counterweights, in that case the arms are longer.
The gate can be dropped to the bottom of the lock by turning downwards into a slot in the bottom
or into a stilling chamber. Or it can be turned up, but this results in a limited clearance.
The gate is mostly applied, when there is a very high lift, in combination with an energy dissipation
chamber.
Advantages:
• Short, shallow gate chambers
• Water retention on both sides
Disadvantages:
• Recess on the bottom of the lock head, as a result a deeper foundation is needed. This
increases the costs
• Entire weight of the gate has to be carried by the equipment unless counterweights or
floating elements are used.
Figure 2.8: Tainter gate (Molenaar, 2011, page 94)
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2.2. Choice of gate
For the location Limmel it was decided that the most attractive type of gate to design in FRP would
be a lift gate, because of its lightweight the moving mechanism of the gate could be designed much
lighter. This does not mean that the application of FRP in other types of gates does not have
advantages. For example when applying mitre gates or rolling gates in FRP the supports and hinges
have to carry less weight resulting in less abrasion, thus making the gates more durable.
Since the choice has been for lift gates other types of gates will not be discussed any further.
2.3. Lift gates
Lift gates are lifted vertically out of the lock chamber allowing ships to pass underneath. Therefore
they can only be applied when the height limitation for passage is not too grand. And they are
commonly selected when there isn’t the required space for other door types.
2.3.1. Gate guides
Usually the gates are lifted through sliding or rolling guides. They function as tracks, supports at the
end position, and as the sealing. Guides are placed at both sides of the gate to avoid that the gate
start running next to the rails. They required extra tensile force in the hoisting direction because of
the load against the lift gate during movement. During loading, extra weight may be required to
drop the gate.
Gates experiencing heavier loads often have rolling guide systems. Rolling guides require less
tensile force, because of their lower friction. However the rotating parts under water require more
attention and maintenance and they tend to be more expensive and heavier. The weight to be
balanced is therefore heavier and deeper recesses are required.
2.3.2. Lifting mechanism
In order to lift the gate it is partly balanced by counterweights used to limit the weight on the winch
gear. The winch gear is positioned in the towers on both sides of the lock chamber and connected to
the lifting cables and to the counterweight. Usually more than one lifting cable is used in order to
limit the size of the winch gear, this way the needed machine room is smaller. However this
requires extra provision to ensure that the load is distributed equally over the cables (as much as
possible).
The gate has to be heavier than the counterweights and the upward force, to ensure that there will
be no leakage at the bottom edge of the gate. Overweight is also needed to surmount the resistance
of the gate guides, the upward force of the gate under water and the resistance against the bending
of the cables around the drums and pulleys.
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3. FIBRE REINFORCED POLYMERS
In this chapter we will focus on Fibre Reinforced Polymers (FRP), to gain a better understanding of
FRP as a building material. First the history of FRP and the uses at has in different industries will be
shortly described in chapter 3.1. In chapter 3.2 the main characteristics of FRP will be given and in
chapter 3.3 the materials used to make FRP composites are described. The materials described in
this chapter are the reinforcement, namely: glass, polyaramid and carbon fibres; the matrix:
polyester, vinyl ester and epoxy resin; and cores that may be used for the manufacturing of
sandwich panel. Then the different manufacturing processes with which FRP elements can be made
are given in chapter 3.5.
3.1. History
Composites have been around for many centuries; however composites consisting of polymers have
a starting point with the introduction of phenolic in the beginning of the 20th century. But the birth
of polymer composites was in 1935 when Owens Corning introduced the first glass fibre,
Fiberglas®.
It was in the 1940’s with the development of polyester resins that the industry of polymer matrix
composites had a rapid development and has been growing ever since. During the Second World
War the need for strong and lightweight materials for aircraft first arose, resulting in the discovery
that FRP wasn’t only strong and lightweight but that it also was transparent for radio frequencies
and it was soon used in the development of so called radomes (protective domes for electronic
radar equipment). By 1944 the first boat hull in glass fibre reinforced polymer (GFRP), was made
and in 1946 more everyday products were been made in GFRP, e.g. fishing rods and serving trays.
[(Kolstein, 2008), (Chlosta, 2012)]
Nowadays it is used in a variety of different applications, from applications in the sport sector to the
aerospace industry. An example is the automotive industry where, like the example in figure 3.1,
composites are not only used in interior component, but also to build the car’s body. Another
industry it is often used is in the energy sector where e.g. pipes are made of composite.
Figure 3.1: ‘superbus’ a project by Wubbo Ockels in cooperation with the TU Delft. (Nedcam)
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Primary and secondary structure
for the Boeing 777, an example of
1990s commercial application of
composites (15-30% made in
composites)
Projections for composites used
in the Boeing 787 (50%),
Currently the usage is
approaching 70% on the
‘Eurofighter’ and other advanced
aircraft, with entire airframes
and support structures being
constructed of PMC’s (polymer
matrix composites)
Figure 3.2: The figure above shows how fast the use of FRP in the aviation industry has increased in the
last two decades. (Committee on Durability and Life Prediction of Polymer Matrix Composites in Extreme
Environments, National Research Council, 2005)
Figure 3.3: Filament Wound Boeing 787 Fuselage (Groh, 2012)
These figures give an idea how fast the growth that composites have had over the last 2 centuries
within the aviation industry.
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Figure 3.4: View of wind turbines equipped with FRP rotor
Figure 3.5: Rotor blade of wind turbines
blades (Solico)
made of FRP, made by Fiberline (Fiberline
[1])
Figure 3.6 & 3.7: Van Dutch project, yacht build out of FRP composites (Nedcam)
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3.2. General characteristics of FRP
FRP has certain properties that cannot be achieved by other materials, this is one of the reasons its
use has grown so rapidly in the last 50 years. Some of these properties are mentioned below:
• Easily formed into shapes.
• Ability to make large sections.
• Lightweight.
• Good environmental resistance.
• Corrosion resistance.
• Lower life cycle costs, because of the good environmental and chemical resistance it is
expected that composites require less maintenance and thus have lower life cycle costs
(though this is still an area of uncertainty).
• Low thermal conductivity, it is a good thermal insulator strains due to temperature
fluctuations are controlled.
• High tensile strength and compressive strength of the fibres at a relatively low weight.
(Resin serves to: bond all fibres together, the loads can be spread to all fibres; provide
protection to the fibres from impact loading and to provide chemical resistance).
• Improved strength-to-weight ratios, high stiffness-to-weight ratios.
Possibility to consider new design concepts, where larger spans can be achieved and lighter
more cost efficient foundations and substructures can be build.
• Low tooling costs.
• It is possible to design sections to have the required properties in the required direction,
making it more efficient and economic by the placing direction of the fibres.
• Longer fatigue life. Unlike other materials FRP can exhibit gradual softening and loss of
stiffness when subjected to cyclic loading due to microscopic damage before visible cracks
appear.
• It has non-Magnetic properties, unlike steel members that are prone to caused interference
under electromagnetic properties, which is often a problem where radar or other sensitive
electronic equipment is housed.
• Possibility for parts integration. Larger sections can be made reducing the number of joints
and increasing the overall safety.
• Faster field installation, because of their lightweight large composites sections can be
fabricated off site, making the construction on site faster. Fabrication off site means also
that construction is not dependent on seasonal changes, making it possible for year-round
installation. Though attention should still be paid to the joining of the structural
components.
(Lopez-Anido, 2000), (Kolstein, 2008)
However one of the main drawbacks is that the properties of FRP are highly dependent on the
manufacturing process and the environment. These properties can therefore not be guaranteed,
unless the composite is produced under a controlled environment and by skilled personnel.
Other disadvantages that can affect the composite are:
• Higher initial material cost
Composite materials are more expensive per unit of weight than other conventional
materials. However these costs should be looked at more closely since strength-to-weight
and stiffness-to-weight ratios of composites are higher than that of other materials, and so
less material is needed. Also composites can be fabricated with processes that minimize the
labour and thus minimizing the costs of production.
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•
•
•
•
•
MSc Thesis Literature Study
Poor ductility, especially those made of a thermoset.
However some components can be developed to exhibit damage before failure.
Thermoplastic based materials have limited recycling ability.
Lack of design experience
Due to the differing properties in different directions the standardizing of the material
properties is not possible. Also the dependency of the properties on weaknesses that may
occur during manufacturing (e.g. voids) makes it difficult to make a structural design.
Lack of knowledge on design of composite structures.
Unlike with conventional materials both the geometry of the structure and the material has
to be designed. This can be a hindrance to use composites.
Lack of comprehensive standards and design guidelines.
(Lopez-Anido, 2000), (Kolstein, 2008)
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3.3. Materials
Composites consist of at least two materials a bulk material and reinforcing material and can be
divided into 3 main groups, namely:
• Polymer Matrix Composites (PMC’s) or Fibre Reinforced Polymers (FRP);
• Metal Matrix Composites (MMC’s);
• Ceramic Matrix Composites (CMC’s).
Fibre reinforced polymers consist of two materials: reinforcing fibres and a matrix (in this case a
polymer resin). Fibres act as reinforcement providing the strength and stiffness of the FRP. While
the matrix both forms a solid material from the fibres making it possible to transfer loads between
the fibres, and protects them from environmental influences. To ensure collaboration between
these two components the bond and interaction between the two is of great importance.
Next to these to materials also additives are used such as curing agents (e.g. hardeners and binders)
and fillers. They serve to control and aid the reaction of the matrix in order to get the desired
consistency of the resin and the required material properties.
In the following paragraphs the most often used reinforcing fibres and resins will be discussed.
Other components like gel coats and additives will not be discussed further, since they have little or
no influence on the materials characteristics as long as they are added properly. They only
influence the appearance, though in some cases they may also improve the fire/chemical resistance
of the composite.
Based on: (Weatherhead, 1980), (Hancox, 1981), (Kolstein, 2008), (Chlosta, 2012)
3.3.1. Reinforcement
Fibres give the composite the main bearing capacity, strength and stiffness. Due to their high
strength and light weight, composites have a good strength to weight ratio that is superior to that of
steel. The mechanical properties of the fibres within the matrix are determined by the type,
thickness, length, and form and orientation of the fibres.
First the different types of fibres, namely glass, poly aramid, carbon and natural fibres used in
industrial applications will be looked at followed by the different forms in which these fibres are
available.
3.3.1.1. Glass fibre reinforcement
Glass fibres as reinforcement where first introduced in the 1950’s, although they were being
produced commercially before that. They are the most commonly used type of reinforcement, due
to its lower cost. In comparison with other fibre types they have higher elongation to failure but a
lower strength and moduli. Glass fibres come in a variety of forms and compositions.
The compositions used in composites are:
• A-glass: Alkali glass, once widely used has been replaced by E-glass in many applications.
• C-glass: Chemical resistant glass used mostly as surface tissue because of its superior
resistance to environmental conditions, impact and abrasion.
• D-glass: Mainly used in electronics industry due to its good dielectric properties.
• E-glass: Electrical grade glass (low alkali content borosilicate glass, good electrical,
mechanical and chemical properties).
• R- and S-glass: High strength glasses used mostly for aerospace applications.
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E-glass is the most often used type of reinforcement because of its good strength and stiffness
properties at low costs. Despite of this E-glass is susceptible to chemical corrosion. It is therefore
mostly protected by applying a resin surface layer with C-glass reinforcements.
Because of this a new type of fibre glass has been developed, the so-called E-CR glass, which has
high resistant against chemical attack and similar properties to E-glass.
In the table below the main properties of the different types of glass are giving. It can be seen that
the high strength glass gives the best performance and that the most commercially used E-glass has
good properties in comparison with the other types of glasses.
Table 3.1: Material properties of different types of glass reinforcements
Property
A-glass C-glass D-glass E-glass R-glass S-glass E-CR glass
Specific gravity
2.68 c
2.5 a
2.16 b
2.45 a
2.53 c
2.49 b
2.71 a
Tensile strength [GPa]
- Filament (not
3.1 d
3.0 a
2.4 b
3.4 a
4.4 d
4.6 b
3.3 a
coated)
- Roving (coated)
2.76 d
2.35 d
2.4 d
3.1 d
3.91 d
c
a
b
a
d
b
Tensile modulus [GPa]
73
69
52
72
85
86
72 a
c
a
b
a
c
b
Fracture strain [%]
4.4
4.8
4.7
4.8
4.8
5.4
4.8 a
Softening point [°C]
773 c
700 d
850 d
990 d
882 c
Table sources: a: (Clarke, 1996; page 56), b: (Nijhof, 1981; page 2.2), c: (Chlosta, 2012, page 28), d:
(Weatherhead, 1980; page 47)
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Figure 3.15: Illustration of production of glass fibres (Chlosta, 2013, page 27)
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3.3.1.2. Carbon fibre reinforcement
Carbon fibres have been known for many years, in the 1880’s they were used by Thomas Edison in
incandescent lamps, which was later replaced by tungsten. But it was in the 1960’s with the need
for high strength, lightweight and thermally stable materials for the aerospace industry that the
development of the carbon fibres known today took flight.
The production of carbon fibres takes place by a controlled oxidation and carbonization of the
precursor material at temperatures of up to 2600°C. When increased to 3000°C carbon fibres are
converted to high modulus graphite fibres. Materials used to obtain carbon fibres (precursor
materials) are:
• Cellulose fibre
• Polyacrylonitrile (PAN) fibre (thermoplastic)
• Lignin
• Hydrocarbon pitch
Properties of fibres resulting from these precursors are given in the table 3.2.
Table 3.2: Material properties of different types of carbon fibre reinforcements
Property
PAN
PAN
Cellulose
Lignin*
Hydrocarbon pitch*
Fibre type
Graphite
Carbon
Carbon
Carbon
Carbon
Diameter [µm]
8
8
6.6
10-15
10.5
Specific gravity
1.87
1.76
1.67
1.5
1.6
Tensile strength [GPa] 2.4
3.2
2
0.6
1.03
Tensile modulus [GPa] 330
230
390
Elongation [%]
0.74
1.34
0.6
1.5
2.5
*Lignin and Hydrocarbon pitch precursors produce lower strength fibres
Table sources: (Weatherhead, 1980)
Carbon reinforcing fibres are commonly used despite of their high cost, this due to their high
strength properties. However a disadvantage of carbon fibres is that their smooth surface gives low
bonding strength between the fibre and the matrix. In order to improve the bonding carbon fibres
are surface treated. They are also often sized with a resin to improve handling and to prevent
damage during processing.
3.3.1.3. Polyaramid fibre reinforcement
Polyaramid fibres, shortly known as aramid fibres, are man-made organic fibres. They were mostly
known under their trade name KEVLAR by DuPont in the 1970’s, because they were one of the first
to developed aramid fibres, but this changed with the production of other aramid fibres.
Their main feature is high tensile strength with low density. Some other advantages are:
• Strength and stiffness/weight ratio: 30% weight saving over glass and 50% over aluminium
alloys, although lower compression strength
• Good thermal stability
• High impact resistance
• Good fatigue resistance and good vibration damping
• Superior insulating properties to glass
• Fracture in ductile manner unlike glass and carbon fibres
• However they have a lower compressive strength and are therefore more susceptible to
fibre breaking in bending by a compressive mode
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A disadvantage of aramid fibres is the low compression strength. Fibres under compressive
stresses break at an elongation of about 0.5%.
3.3.1.4. Other reinforcing fibres
Glass, carbon and aramid fibres are the mostly used for FRP. However other less known fibres
existed usually used in applications. Some examples are:
• Polyester fibres are of low cost, high impact, chemical and abrasion resistance but with
low modulus. Often used in surfacing tissue.
• Nylon fibres are used to reinforce epoxy resin, they also have high impact, chemical and
abrasion resistance
• Boron fibres are used in epoxy resins, with much better properties than other fibres but
very expensive, for this reason they are currently used in specialized aerospace applications
only.
• Ceramic fibres have high chemical and abrasion resistance, and high temperature stability.
Often used where high temperature resistance is required. Often associated with metal
alloys instead of polymer matrices.
• Natural fibres are mostly used in surfacing tissue and rarely as reinforcement, only in ‘lowtech’ applications.
In the following paragraph a short elaboration follows on the types of natural fibres used in many
fibre reinforced polymers.
Based on: (FAO, 2009), (Kolstein 2008)
Natural fibres can be divided in plant fibres, animal fibres and mineral fibres. Animal fibres are
mostly used in the textile industry. Those used for industrial and structural purposes are plant
fibres, especially those made from the stem and leaves of plants.
Plant fibres include seed hairs (trichome) such as cotton, stem fibres, leafs fibres, and husk fibres
such as coconut.
Some of the natural fibres used are:
• Abaca: Abaca is made from the leaves of the abaca plant also called Manila hemp (Musa
Textilis).
• Coir: Obtained from the tissue surrounding the seed of the coconut palm.
• Sisal: Inexpensive natural fibres used in phenolic based matrix but rarely with polyester or
epoxy. Produced from the leaves of the agave plant (Agave Sisalana)
• Jute: Naturally occurring cheap fibres used in mostly in third world countries. Advised not
to use in thermoplastic resin due to its low bonding strength properties. Extracted from the
bark of the white jute plant (Corchorus Capsularis).
• Hemp: Obtained from the stem of the Cannabis Sativa plant
• Flax: Obtained from the stem of the (Litnum Usitatissimum) plant.
• Ramie: Made from the bark of the commonly known China grass (Boehmeria Nivea).
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3.3.1.5. Application of reinforcements
Reinforcement can be applied in different forms. Each form can provide the composite with
different mechanical properties. Some of these forms are:
• Continuous filament roving. Spool of filament made of consistent parallel strands.
• Chopped strands are mostly used for coating to give a more equal surface to the composite
using a spray lay-up method (by hand or with the use of automotive machines).
• Chopped strand mat [CSM], also known as needle mat, consists of chopped rovings spread
uniformly and bonded together to form a mat. In order to bond the rovings together two
types of binders can be used, namely powder or liquid. Examples are polyvinyl acetate
emulsion (liquid) and bi-phenol polyester (powder). Usually the binder content is between
3-6%
CSM’s have good wet-out characteristics. They are compatible with polyester resins, though
not with epoxy resins except for mats with powder binders.
• Continuous strand mat/Continuous filament mat [CFM] consists of multiple layers of
continuous glass fibres randomly deposited in a swirl-like pattern. The fibres are bonded in
a similar way as with CSM.
• Woven fabrics can be divided into two classes, one made by rovings and the other made
from yarn. Yarn is made twisting sized continuous filament.
Woven fabrics are available in different weaves, see figures 3.16 to 3.21:
Fig. 3.16: Plain weave
(Gurit, 2013, page 35)
Fig. 3.17: Twill weave
(Gurit, 2013, page 35)
Fig. 3.18: Satin weave
(Gurit, 2013, page 36)
Fig. 3.19: Leno weave
(Gurit, 2013, page 36)
Fig. 3.20: Mock leno weave
(Gurit, 2013, page 36)
Fig. 3.21: Unidirectional weave
(Kolstein, 2008, page 3.7)
If woven mats are used alone there is a tendency for delamination, to prevent this chopped strand
mats are laid in between the each layer. This is especially done when the composite is thick.
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3.3.2. Resins
Resins are used to bind the fibres into a single unit providing the mechanical properties and
preventing the fibres to buckle under compression. They also serve as protection against chemical
and environmental agents. Two types of resins can be distinguished: thermosets and
thermoplastics.
Thermoplastics soften every time they’re heated, that is why curing needs to be done at higher
temperatures. Thermosets permanently set after curing and do not soften or dissolve afterwards,
so they can be cured at room temperature. This is one of the main reasons they are used in Civil
Engineering. Because of the size of the structures it would be difficult to cure them at high
temperatures, however, there is also a growing interest because of their toughness, resilience and
corrosion resistance.
3.3.2.1. Unsaturated polyester resins
Unsaturated polyester resins, also known as polyester resins, are the most often used type of resin.
They are especially used in the marine industry because of their good water resistance properties
and they are also easily available, and economical.
Polyester resins are polymer chains dissolved in a reactive solvent (such as styrene), a catalyst and
accelerator are added to form a solid. The addition of styrene reduces the viscosity of the resin
making it easier to handle. It also allows the resin to cure without the use of high pressure
equipment. Therefore they are referred to as low density resins. Mainly two types of polyester
resins are used:
• Ortho-phthalate polyester is standard economic resin used by many people
• Iso-phthalate polyester resin is now becoming preferred due to its superior water
resistance.
Other polyester resins have been developed, such as bi-phenol, with improved mechanical and
chemical properties.
3.3.2.2. Vinyl ester resins
Vinyl esters are similar to polyester resins that were especially developed for the manufacture of
plastic components in corrosive environments. They have a higher chemical resistance, high
resilience and toughness, and a uniformed cured structure with reduced internal stresses. The
reason for this is that they have less ‘ester-groups’, which are the parts that couple to each other
through the styrene. Due to a better water and chemical resistance it is sometimes used as a
protective coat for polyester laminates. In order to achieve a tougher material it has to be postcured at a higher temperature.
3.3.2.3. Epoxy resins
One of the main advantages over polyester resins are: higher mechanical properties, resistance to
environmental degradation, and low shrinkage during cure. Shrinkage during curing is about 1-2%
but can be reduced to virtually zero by adding fillers. Another advantage is that they can be
obtained from a wide range of components giving them great versatility.
A cured epoxy is resistant to moisture and chemicals, has good insulating properties, and when
cured above service temperature better properties can be reached. A disadvantage of this type of
resin is their higher viscosity which makes them harder to apply.
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3.3.2.4. Other Thermosetting resins
• Polyimide resins
Best thermally stable organic resin, low chemical resistance and high water absorption.
Post-cured at 400C° to obtain thermal stability. Condensation during curing makes them
difficult to process, they are brittle after curing and are extremely costly.
• Phenolic resins
Have high fire resistance performance, good thermal stability, acceptable electrical
properties, and good water and chemical resistance except for alkalis. Condensation during
curing can lead to inclusion of voids and surface defects. No high mechanical properties and
brittle behaviour. Frequently used in laminating applications.
• Furane resins
Have exceptional chemical resistance except in oxidizing conditions. Requires acidic catalyst
to cure like phenolic resins.
• Silicone resins
Based on inorganic material, silicon. They have outstanding thermal stability and good
electrical properties. Though compared to other resins they have poor mechanical strength,
poor chemical resistance, and higher costs.
3.3.3. Cores
Sandwich constructions are often used to improve the structural efficiency of composites. Core
materials can provide stiffness, thermal insulation, and light weight properties to composite
structures.
Cores come in different types and can be made out of different materials.
3.3.3.1. Solid cores
Lightweight materials such as balsawood and cedar are often used.
3.3.3.2. Foams
Foams are often used is core material because of their lightweight. They are mostly made of plastics
such as PVC and PVDC (polyvinyl chloride and polyvinylidene chloride). Foams can divided into
three types
• Non-structural foams have low density and can be applied where no/low compression and
shear rigidity is required.
• Structural foams consist of full density skins and cellular cores, thus have good
compression and shear rigidity.
• Reinforced foams are usually reinforced with short glass fibres, applied to increase
stiffness of the foam.
3.3.3.3. Honeycombs
Honeycombs can be made from paper, glass fibre laminate, metal, or other thin sheet material. They
are made in the shape of ‘honeycombs’, which provides high structural performance in direct
compression and shear.
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3.4. Manufacturing processes
The end properties of a composite are not only a function of the properties of the individual
materials that form the composite, but also of the design of the material and the manufacturing
process used.
Based on: (Weatherhead, 1980), (Hancox, 1981), (Kolstein, 2008)
3.4.1. Open mould
3.4.1.1. Contact moulding
Hand lay-up
Initially a gel coat is laid on the mould, it is then left to gelatinise. Alternative layer of resin and
reinforcement are then laid by hand. Fibres are laid and impregnated with resin by hand. Although
low in productivity and little control of the thickness uniformity over the area this method is widely
used because of the flexibility and the low cost of the needed tools.
Figure 3.22: Hand lay-up (Gurit, 2013, page 49)
Spray lay-up
Chopped fibres and resin are sprayed onto the mould with a spray gun. The spray gun can be man
or machine operative. Like with hand lay-up tooling is rather inexpensive and there is little control
over the uniformity of the laminate. Although if spray gun is machine operated the process can be
quite fast. Also uniformity in the thickness and a more controlled composition of the resin/fibres
mixture of the laminate can be achieved.
Disadvantages are that it consists of short fibres and a high resin concentration with low viscosity
limiting the mechanical properties.
Figure 3.23: Spray lay-up (Gurit, 2013, page 48)
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3.4.1.2. Saturation
Saturation is similar to hand lay-up, the difference is that in this case the resin is not applied by
pouring it on to the mould but by making use of a spray gun. The resin and the catalyst are mixed in
the gun, making it only possible to use low viscosity resins. An advantage, above the hand lay-up
process, is a better resin control.
3.4.1.3. Filament winding
Filament windings are feed through a resin bath, the excess resin is removed by nip rollers and then
they are wraps around a rotating mould (mandrel). The properties the section will have are
controlled by orientation of the fibres, the speed of the fibre feeding mechanism, and the rotation
rate of the mandrel. The orientation of the fibres gives the laminate certain structural properties, so
that the fibres can be laid to match the applied loads/ the needed properties.
This manufacturing process is used for hollow, circular or oval sections e.g. pipes.
Figure 3.24: Filament winding (Schumacher, 2009)
Figure 3.25: FRP pipe production, by filament winding (Fibrex)
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3.4.1.4. Spray winding
This method combines both spray lay-up and filament winding. Alternating layers of chopped fibre
and continuous fibre strands wound on to a rotating former. It is more costs effective than filament
winding, though the chopped fibre components have lower strength than continuous strands
components.
3.4.1.5. Centrifugal moulding
Used to produce hollow sections, resin and fibres are sprayed onto the moulding while it rotates at
high speed. The centrifugal acceleration forces the material onto the mould resulting in dense
material, the fibres, to concentrate at the outer surface, making the inner part resin rich.
Figure 3.26: Centrifugal moulding (Kolstein, 2008, page 4.8)
3.4.2. Closed mould
3.4.2.1. Vacuum bag moulding
This can be considered an extension of the hand laminating process. After laminate is done a
release film followed by a bag is placed over the mould clamped at both sides. The air is then
pumped out of the area between the mould and the bag creating a vacuum, consolidating the
laminate. Rolling on the outside of the bag will give a better consolidation. However, atmospheric
pressure is not sufficient to distribute the resin and impregnate the fibres, so a good hand lay-up
needs to be performed. Another advantage is that emissions during curing are reduced.
Figure 3.27: Vacuum bag moulding (Kolstein, 2008, page 4.10)
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3.4.2.2. Pressure bag moulding
Similar to vacuum moulding, only in this case more pressure is applied providing a better
consolidation and fibre content of the laminate. Although because of the higher pressure the mould
must be stronger. This method also allows for the use of prepreg (pre-impregnated) systems.
Figure 3.28: Pressure bag moulding (Kolstein, 2008, page 4.11)
3.4.2.3. Autoclave
The autoclave process is a combination of both vacuum and pressure bag moulding, exclusively
used with prepreg systems. The laminate is build out of prepreg fibres, which are placed on the
mould. Then a vacuum bag is placed over the mould and is partially vacuumed. The mould is then
placed in a vacuum, pressurized and heated in a chamber to speed up curing. This method ensures
that no air remains in the laminate. An advantage is that mould is not subjected to large pressures.
Figure 3.29: Autoclave (Kolstein, 2008, page 4.12)
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3.4.2.4. Resin injection or resin transfer moulding (RTM)
Dry fibres are loaded on to the mould, the mould is then closed and resin is pumped in between the
mould. Vacuum may be applied to help the resin to better penetrate the fibres and make the resin
injection faster. This method is also called vacuum assisted resin injection (VARI).
Can also be done by vacuum bagging an open mould, this is called vacuum impregnation/injection.
Figure 3.30: Resin injection moulding (Kolstein, 2008, page 4.18)
3.4.2.5. Leaky mould
The fibres and resin are placed in the female part of a mould by hand laminating. The male part is
then pressed onto the female part. The mould is clamped together and let to cure. This method
gives accurate dimensions and a good and smooth finish on both sides of the laminate.
3.4.2.6. Cold press moulding
Dry fibres are loaded on to the mould and the required amount of resin is poured on the mould, the
mould is then closed and pressure is applied. After curing, the mould is opened and the parts are
taken out. Cold press moulding allows for two smooth sides and requires the set of mould to it
properly.
Figure 3.31: Cold/Hot press moulding (Kolstein, 2008, page 4.14)
3.4.2.7. Hot press/matched metal moulding
Hot press moulding can be carried out as cold press moulding with dry fibres and liquid resin or
with preperg systems. The added temperature makes the curing process faster.
3.4.2.8. Injection moulding
Usually used with thermoplastic resins, could be adapted for the use of thermosets. When making a
composite, the fibre and resin mixture is loaded into the hopper and forced into the mould by a
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piston. This may cause degradation of the fibres. Another disadvantage is that the orientation of the
fibres cannot be controlled.
Figure 3.32: Injection moulding (Kolstein, 2008, page 4.21)
3.4.3. Continuous Processes
3.4.3.1. Continuous sheet manufacture
Impregnated fibres between two layers of release film are pulled through needing rollers into a
curing oven and as they emerge from the oven the release film is pulled off and the laminate is cut
to the desired length. This process can be cost attractive, due to the continuous process, although
only simple shapes are possible.
Figure 3.33: Continuous sheet manufacture (Kolstein, 2008, page 4.23)
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3.4.3.2. Pultrusion
Fibres are pulled through a resin bath into a heated die. In the die the fibres are cured into the final
shape. The tension imposed on the fibres gives good longitudinal properties, where transverse
strength is required woven fabrics or mechanically bound mats can be incorporated. Because of the
continuous pulling of the fibres through the die, only constant cross-sections can be made.
Manufacturing costs can be low.
Figure 3.34: Pultrusion (Schumacher, 2009)
3.4.3.3. Continuous filament winding
Like described under filament winding, continuous filaments are wound-up around a rotating
mandrel. In this case the mandrel continuously collapses at the end of the process, after emerging
from a curing oven, and reform at the beginning of the process into a cylindrical form.
Figure 3.35: Continuous filament winding (ZCT)
Figure 3.36: Schematization Continuous filament
winding (Chlosta, 2012, page 70)
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4. MATERIAL PROPERTIES OF FRP
4.1. Mechanical properties
Based on: (Clarke, 1996), (Nijhof, 2004), (Chlosta, 2012), (CUR, 2009), (Zenkert, 1995), (Gurit, 2013)
FRP is anisotropic this means that the properties of the material are different in every direction,
and they are also heterogeneous. However commonly in calculations the material is assumed to be
homogeneous, not taking into account the effects of load variations. Due to the fact that they have a
small effect on the mechanical properties, the assumption that for design purposes the laminate can
be seen as homogeneous is quite accurate. (For the dynamic behaviour this could be of importance
because the effects of loading variations on the material properties also alter the eigen frequencies
of the gate.)
Although the material properties are different in every direction the assumption is made, to
simplify the calculations, by assuming an orthotropic (with different properties in only 2
directions) material. This means that there are two principle directions where the material
properties vary.
Mechanical properties are determined by:
• The properties of the fibre
• The properties of the resin
• The ratio fibre to resin (FVF – Fibre Volume Fraction)
The FVF is mostly determined by the manufacturing process, in the boat-building industry
FVF values of 30-40% can be reached and in the aerospace industry where better
manufacturing processes have been developed FVF values of up to 70% can be achieved.
• The geometry and the orientation of the fibres
The highest mechanical properties are parallel to the fibres.
4.1.1. Fibre/Resin ratio
Prior to the prediction of the elastic properties the volume fractions have to be determinate.
Based on: (Clarke, 1996), (Nijhof, 2004), (Chlosta, 2012), (CUR, 2009), (Zenkert, 1995) and (Gurit, 2013)
Weight fractions:
w + w = 1(4.01)
W
W
(4.02)&(4.03)
w =
;
W
W
W + W V ∙ ρ + V ∙ ρ
ρ=
=
(4.04)
V + V
V + V
w =
ρ = v ∙ ρ + v ∙ ρ (4.05)
W
ρ
w ∙ ρ
v =
=
W W w ∙ ρ + w ∙ ρ
ρ + ρ
;
v =
W
ρ
W W
ρ + ρ
=
ρ
w ∙ ρ + w ∙ ρ
(4.06)&(4.07)
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w =
W V ∙ ρ ρ
=
= ∙ v
W
V∙ρ
ρ
;
w =
W V ∙ ρ
ρ
=
=
∙ v
W
V∙ρ
ρ
MSc Thesis Literature Study
(4.08)&(4.09)
1 v + v m m
=
=
+
(4.10)
ρ
ρ
ρ
ρ
Volume fractions:
v + v = 1(4.11)
A
A
v =
v =
;
(4.12)&(4.13)
A
A
With: A = A + A(4.14)
4.1.2. Stiffness analysis
Assumption of material behaviour is that for short term loading material behaves linear elastic to
ultimate failure. And under long term loading the material is linear viscoelastic with recovery on
removal of load, providing the strain does not cause permanent material deterioration.
(Clarke, 1996)
In this chapter the models for the determination of properties of unidirectional composites will be
given.
Unidirectional composites have a principal direction, the longitudinal direction (giving by a
subscript L), and the transverse direction (giving by a subscript T). For more than two components
the expressions below can be extended.
Definition unidirectional continuous lamina: (EUROCOMP, page 99)
• Has higher stiffness and strength in the direction of the fibre
• Stiffness and strength dominating by the matrix properties in the transverse direction
• Idealised as orthotropic
4.1.2.1. Lamina stiffness
Several methods exist to predict the elastic properties of unidirectional reinforced composites.
Some of the most commonly used methods will be described below.
(The properties of the fibre and the matrix are indicated by a subscript f and m respectively.)
RoM method [(Gurit, 2013) and (Nijhof, 2004)]
The Rule of Mixtures method is based on the assumptions that there are no voids or imperfections,
that there is a uniform stress and strain distribution and it can only be used for determining the
upper and lower bounds. The method doesn’t contain geometric terms (fibre spacing, fibre shape,
packing geometry, etc.) or the degree of bonding, which due influence the properties of the
laminates but it is conservative method, values will always be higher.
In longitudinal direction the strain of both components is equal. ε = ε = ε
Average stress in the longitudinal direction, when subjected to a force P:
P
σ ∙ A + σ ∙ A
σ = = E ∙ ε =
= v ∙ σ + v ∙ σ = v ∙ E ∙ ε + v ∙ E ∙ ε (4.15)
A
A
With:
σ
E =
= v ∙ E + v ∙ E (4.16)
ε
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Figure 4.1: Schematization of RoM model for longitudinal properties (Gurit, 2013, page 13)
In transverse direction the elastic modulus is as follow:
1
ε! v ∙ ε v ∙ ε v ∙ ε v ∙ ε v v
4.17
E! σ!
σ!
σ
σ
E E
E! E ∙ E
E ∙ E
4.18
v ∙ E v ∙ E v ∙ E 1 " v ∙ E
Figure 4.2: Schematization of RoM model for transverse properties (Gurit, 2013, page 13)
Longitudinal-transverse Poisson ratio:
#! = v ∙ # v ∙ # 4.19
Transverse Poisson ratio:
E! ∙ #!
#! =
4.20
E
Shear modulus:
G =
E
;
2 ∙ 1 # G! =
E!
4.21&4.22
2 ∙ 1 #! 32
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Halpin-Tsai method (Nijhof, 2004)
With this method the properties of the lamina are expressed in terms of the properties of the
components with the use of only one formula.
P=
P ∙ [P + ξ ∙ P + ξ ∙ v ∙ (P − P )]
(4.23)
[P + ξ ∙ P − v ∙ (P − P )
P: property
ξ: reinforcing efficiency parameter of the composite material, the extent to which the load is
transmitted to the reinforcing phase. Expressed differently depending on the property to be
calculated (see table 4.1)
Table 4.1: (Nijhof, 2004, page 92)
P
Pf
Pm
ξ
*
E,
E
E
2∙
d
#!
E!
#!,
E!,
#!,
E!,
G!!
G!!,
G!!,
G!
G!,
G!,
∞(forfilaments)
∞
a
2∙
b
a √;
8 9
b
k=
k = + 2 ∙ G!!,
ξ=
1
(forisotropicmatrix)
3 − 4 ∙ #
k: compression modulus
As a simplification it can be assumed that the components are isotropic, the formulas of Halpin and
Tsai then become:
E = v ∙ E + v ∙ E = v ∙ E + (1 − v ) ∙ E (4.24)
#! = v ∙ # + v ∙ # (4.25)
E! = E ∙
E + 2(v ∙ E + v ∙ E )
(4.26)
v ∙ E + v ∙ E + 2E
G! G ∙
G!! G ∙
G v ∙ G v ∙ G
4.27)
v ∙ G v ∙ G G
(3 − 4# )G v ∙ G v ∙ G
4.28)
3 " 4# ) ∙ (v ∙ G v ∙ G G
Other methods are: the Tsai-Hahn method, Hashin and Shtrikman method and Puck’s Empirical
formulas. For an elaborated description of these and other method reference is made to (Clarke,
1996), (Nijhof, 2004) and (CUR, 2009).
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4.1.2.2. Laminate stiffness
The stiffness is then determined for the laminate making use of the laminate theory.
With the laminate theory the strength and stiffness properties of the laminate (in this case the
composite) can be determined.
4.1.3. Laminate theory
Properties of laminate are determined by the properties of the laminas that compose it.
Here it is assumed that the laminas are orthotropic and under a plane, that they have a constant
thickness, and there is no shift between the laminas. The laminate works as a whole.
The analysis has its basis on the (orthotropic) plate theory which states that for a thin plate the
shear/normal forces in the z-direction in the plate are negligible, because it has a negligible bending
stiffness through the thickness. (σz = τxz = τyz=0)
Based on: (Nijhof, 2004)
Figure 4.3: Schematization forces acting on plate element (Nijhof, 2004, page168)
E
G
F
NB = C σB dz ;
E
H G
F
E
G
F
MB = C σB ∙ zdz ;
E
H G
F
E
G
F
NI = C σI dz ;
E
H G
F
E
G
F
MI = C σI ∙ zdz;
E
H G
F
E
G
F
NBI = C τBI dz
E
H G
F
(4.29 " 4.34
E
G
F
MBI = C τBI ∙ zdz
E
H G
F
Laminas can be regarded as homogeneous and anisotropic. Because of this the stresses in the
laminas will be linear. With Hooke’s law and these properties the relation between the strains and
stresses can be determined.
Strains and stresses:
1
σ E ∙ ε → ε ∙ σ4.35
E
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1
∙ τ4.36
G
duP
duI
εP (4.37 " 4.39
εI dz
dy ;
τ = G ∙ γ → γ εB duB
dx
;
γBI = γIB =
duB duI
dy
dx
;
γBP = γPB =
duB duP
dz
dx
;
γIP = γPI =
duI duP
dz
dy
(4.40
−(4.42
Relation between the strains and the stresses:
1/EB
εB
ε
"#
Q I R S BI /EI
γBI
0
"#IB /EB
1/EI
0
Stiffness matrix
EB
σB
1
σ
#
Q IR S BI ∙ EI
1 " #BI ∙ #IB
τBI
0
0
σB
0 U Q σI R4.43
1/GBI τBI
#IB ∙ EB
EI
0
0
εB
ε
0
U Q I R4.44
GBI 1 " #BI ∙ #IB γBI
Compliances matrix
Figure 4.4: Strains present in a plate element (Nijhof, 2004, page 27)
The matrices can then be transformed from the local to the global coordinate system through the
transformation matrix [T].
[T] = [T]
HE
cosF θ
sinF θ
2 sin θ cos θ
cF sF
F
F
= W sin θ
cos θ
"2 sin θ cos θ Y W s F c F
" sin θ cos θ sin θ cos θ cosF θ " sinF θ
"sc sc
2sc
"2sc Y4.45
cF " sF
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Where θ is the angle of the fibres relative to the main direction within the global coordinate system
(the x-direction).
The transformation of the strains and stresses from the local to the global coordinate system is:
σB
σ
Q IR
τBI
c F sF
W sF cF
−sc sc
Z[\]
εB
Q εI R
γBI
cF sF
W sF cF
−sc sc
Z[\]
Curvatures:
∂F w
κB = − F
∂x
;
σB
2sc
σ
4.46)
−2sc Y Q I R
c F − sF τBI ^]Z_\]
εB
2sc
ε
IR
Y
4.47)
Q
−2sc
F
F
γ
BI
c −s
^]Z_\]
κI = −
∂F w
∂y F
;
κBI = −2
∂F w
∂x ∂y
(4.48) − (4.50)
Depending on the position and the thickness of each lamina there contribution to the laminate
stiffness is determined. Using the relations given in equations (4.29) to (4.34) and the stress-strain
relations in equations (4.43) and (4.44) a matrix can be derived for the relation between forces and
bending moments to strains and curvatures.
This relation is then used to determine the deformations of the laminate with respect to the global
coordinate. Then the can be transformed with the transformation matrix [T] and checked against
the failure criteria.
In the chart below (figure 4.5) an overview is given of the steps to be taken when designing a
laminate with the laminate theory. First the properties of each lamina are derived, depending on
their composition and fibre orientation. Then the properties of the laminate are determined for a
chosen configuration of the laminas that form the laminate, deriving the stiffness matrix and then
the compliances matrix. From which the strains and stresses in the laminate can be derived.
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Lamina stiffness
WRT the lamina’s main direction
Orientation of laminas
Lamina stiffness
WRT the laminate’s main direction
Laminate configuration
Laminate stiffness
WRT the laminate’s main direction
Laminate compliances
WRT the laminate’s main direction
Laminate deformations
WRT the laminate’s main direction
Loading
WRT the laminate’s
main direction
Lamina deformations
WRT the laminate’s main direction
Laminate deformations
WRT the lamina’s main direction
Laminate stresses
WRT the lamina’s main direction
Failure criterion
deformations
Failure criterion
stresses
First ply failure (lamina failure)
Failure laminate
Figure 4.5: Flow chart for stiffness and strength analysis of a laminate with the use of the Laminate Theory.
(Nijhof, 2004, page 177)
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4.1.4. Strength analysis
Strength analysis can also be done with the use of the laminate theory. After determining the
laminate stresses, see figure 46, the laminate can be check with the use of failure criteria.
Some of these failure mechanisms will be described below.
Tsai-Wu (Nijhof, 2004)
The Tsai-Wu failure mechanism makes a global analysis of the structural system by using the
interaction between the various strength components.
The criterion for the plan stresses is given by:
F
F
F
cE,h,i
cF,h,i
jEF,i
1
1
1
1
+
+
−
+ F
g ∙ cE,h,i + b
g ∙ cF,h,i −
b
cE,d,e ∙ cE,f,e cF,d,e ∙ cF,f,e jEF,e
cE,d,e cE,f,e
cF,d,e cF,f,e
1
F
∙c
∙c
1
2 E,h,i F,h,i
−
≤b
g (4.51)
m= ∙ mn ∙ mf
kcE,d,e ∙ cE,f,e ∙ cF,d,e ∙ jF,f,e
Formula (4.51) considers interaction between the various stress components and requires prior
knowledge of the lamina’s longitudinal tension and compression strength, and transverse tension
and compression strengths and shear strengths in the longitudinal-transverse plane.
For multiple ply laminates it should be evaluated for both stress components parallel to and
perpendicular to the fibre directions, for each lamina.
Hart-Smith (EUROCOMP, 1996)
This theory considers multiple failure modes by superposition in contrast to Tsai-Wu where there
is assumed there is interaction between the various stress components.
In case of laminate design the stresses in plane are typically zero and can thus be neglected, the
maximum-shear-stress criterion imposes a limit in the remaining two principal stresses.
The maximum-shear-stress criterion states that yield occurs whenever the maximum shear stress,
reaches a critical point.
The failure envelope can be adjusted with different Poisson’s ratios for an orthotropic material.
Failure envelope of laminate is constructed by superimposing the failure envelopes of the lamina.
First ply failure criterion (Nijhof, 2004)
The strength of the laminate is related to the manner of loading. To make a stress analysis first the
stiffness analysis has to be done per lamina (w.r.t. the main direction of the lamina) for a given load.
These results are then compared with the result obtained from the calculation of the failure criteria
on the level of the lamina.
Because the relations given in the laminate theory are linear, it is sufficient to apply a unity load to
reach the ultimate strength criterion of the lamina. The smallest factor determines the loading at
which the first lamina will fail, the so-called ‘first ply failure’ (F.P.F.) load. The load at which the
laminate fails is also the load at which the lamina fails.
Although in reality the laminate doesn’t always fail at this load, but the other laminas can take up
the additional load. To calculate the ultimate strength if this load can be exceeded, the strength
analysis is carried out again but this time assuming that the strength of the lamina that fail is equal
to zero.
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4.2. Durability
The durability of FRP composites is assumed to be high due to its use in the aerospace industry,
where FRP components are subjected to high stresses and tough environmental conditions e.g. high
temperatures, UV radiation, and humidity. Also their use in the chemical industry where they
endure corrosive/acrid chemicals, have proven FRP to be quite resistant. The high resistance of this
material can also be seen in the marine industry where FRP composites have been successfully
used for many centuries.
Despite of this the limited experience with this material means that the durability in the long term
is not yet fully known, because it has only been used for about 60 years. Besides the fibre reinforced
polymers used in other markets varies from those for structural use. FRP has only been used in civil
engineering for the last 20 years, thus substantiated data of the long term durability of FRP
structures is unavailable.
One of the degradation agents that have a great effect on FRP is water, especially water vapour. In
wet conditions the rate of growth of fatigue cracks in cyclic loading accelerates. Other factors that
contribute to degradation of FRP are: oxidation, UV radiation, frost, thermal aging/cycling,
exposure to high temperatures, fatigue resistance, creep and relaxation, and chemical attack.
(Hancox, 1981)
Because lock gates are constantly in a wet environment the focus in this chapter will be on the
degradation due to water and UV-radiation will also be discussed.
Based on: (Gurit, 2013), (Clarke, 1996), (Walter, 1982), (Campbell 2010), (Weatherhead, 1980) and
(Karbhari, 2003)
4.2.1. Water degradation
All laminates in a wet environment will permit low quantities of water to pass through them in
vapour form. Water absorption leads to an increase in weight and a decrease in stiffness, and in
time this also affects the ultimate mechanical properties of the FRP. Water absorption can
especially be a problem for polyester based resins.
Degradation can happen at different levels of a composite, at different rates, and having different
consequences.
At the resin level properties of the matrix are affected in several ways:
• Water absorption causes the composite to swell, producing strains in the through-thickness
direction.
• Plasticization can be beneficial to a certain point because it makes the resin more ductile.
• If water is trapped in micro-cracks or delamination, when the water freezes it expands
causing extra pressure, leading to larger cracks or delamination.
• On the other hand when exposed to high temperatures, e.g. for high temperature repairs,
the water in the composite will vaporize increasing the pressure also leading to cracks and
delamination. This leads to more water absorption. Therefore one has to be careful, when
repairing FRP composites with bonded adhesives, that the composite is properly dried.
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Another mechanism is osmosis. Water passing through the composite reacts with any
hydrolysable (that can be dissolved in water) components that can be present inside the
laminate, forming tiny cells of concentrated solution.
During the cycle of osmosis more water is drawn in to dilute this solution, increasing the
water pressure in the cell. Eventually causing the laminate or gel coat to distort and even
burst. Some hydrolysable components are dirt and debris that has been trapped during
manufacturing, but also the ester linkages in cured polyester and to a lesser extent vinyl
ester.
Between the resin and the fibres, at the fibre-matrix interface water intrusion can cause loss of
integrity of the bond, which can have consequences for the mechanical properties of the laminate.
In a carbon fibre reinforced composite the fibre-matrix interface is usually relatively stable.
At the fibre level the effect of moisture is highly dependent on the fibre type applied. Carbon fibres
are generally unaffected by most moisture conditions, while moisture and chemicals have shown
that in the case of aramid and glass fibres they cause degradation at the fibre level. In glass fibres
the effects are mostly on the surface.
The effects of water degradation can be minimized in sometimes avoided by applying a resin with a
low water transmission rate and high resistance against water, reinforcements with similar
resistant surface treatment and laminated to a very high standard, and through the selection of
appropriate resin systems, processing conditions, and the application of gel coats and protective
coatings.
4.2.2. UV resistance
UV radiation has wavelength from 290-400nm at this range polymers have bond dissociation
energies, bond dissociation energy is the energy that is required to break a molecule of the bond,
decomposing it into atoms, because of this they are greatly affected by it. This damage is generally
limited to darkening of the resin at the surface layer. In general polyester resins are more resistant
to UV radiation than epoxies. The great danger with UV-radiation is that in affected areas the
moisture ingress increases. This can lead to loss in mechanical properties. (See chapter 4.2.1.)
To prevent UV damage standard marine paint, pigmented gel coatings, and poly-urethanes has been
used. However, it must be noted that the use of polymeric protective coating does not prevent UVinduced damage from occurring, but rather serves as a “self-sacrificing” layer to prevent the FRP
composite from being directly exposed to UV radiation. This protective coating will eventually
degrade and will have to be maintained.
Another method that has been used in the past to overcome degradation due to exposure to
sunlight is adding up to 1% UV light stabiliser to the resin system. The compounds used for this
purpose are hydroxybenzophenone derivatives such as 2-hydroxy-4-methoxybenzophenone,
phenyl salicylate and acetylsalicylic acid. These compounds may be used in combination with
thriethyl phosphite and epoxidised oils.
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4.2.3. Fatigue
Fatigue is the degradation on mechanical properties due to cyclic stresses, much lower than the
stress required to cause failure during a single application. Cyclic stresses are stresses that fluctuate
in time. These stresses lead to cracking of the material, the number of cracks and their size
increases in time, eventually leading to failure.
Factors needed to cause fatigue are:
• A maximum stress of sufficiently high value.
• A large enough fluctuation in the applied stress.
• A sufficiently large amount of cycles of the applied stress.
There are three types of fluctuating stresses:
• Fully reversed stress cycle; applied where maximum and minimum stresses are equal.
• Repeated stress cycle; a mean stress applied on top of the max and min stresses.
• Random or spectrum stress cycle; subjected to random loads.
In comparison with metals FRP composites exhibit better fatigue resistance due to their high
fatigue limit. Fatigue limit is the stress amplitude below which failure doesn’t occur even after large
numbers of cycles. This limit is found to be around 107 cycles in comparison with metal which is 106
cycles.
Fatigue failure mechanisms in composites are different from those in metals. In metals a single
crack appears and continues to grow until it becomes so long that the remaining section cannot
support the load. While in composites different kinds of damage occur at different locations and
eventually link up causing failure.
There are 5 main failure mechanism, namely matrix cracking, fibre fracture, crack coupling,
delamination initiation, delamination growth and fracture. These failure mechanisms are divided
under three phases of damage progression:
• Phase 1: Matrix cracks develop due to tension loads in the off-axis plies until they reach a
steady state, this steady state is a function of the lamina/ply thickness and the material
properties. These cracks can be a source of moisture ingression, which accelerates the
failure process.
• Phase 2: Fibre fracture is initiated by high concentration stresses caused by the matrix
cracks in the off-axis laminas reaching the zero-degree lamina, which stop the cracks and
leads to high stress concentrations. This also induces longitudinal cracks running parallel to
the fibres and perpendicular to the matrix cracks. The combination of longitudinal and
matrix cracks is called crack coupling. Later on in phase 2 large interlaminar stresses at the
intersection between longitudinal and matrix cracks develop due to crack coupling, leading
to initiation of delamination.
• Phase 3: Delamination start growing between the lamina interfaces, eventually leading to
isolation and eventually failure of the zero-degree lamina, and failure of the composite.
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Figure 4.6: Progressive fatigue failure. (Campbell, 2010, page 386)
In conclusion fatigue behaviour is difficult to predict, because of the limited data available and the
complex interaction of the loading conditions (e.g. type of matrix and reinforcement, nature of
fatigue loading and its frequency, and the environment) under consideration.
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5. FRP CONNECTIONS
Based on: (Mosallam, 2011), (Campbell, 2010), (Kolstein, 2008)
Connections are critical parts of a structure where high stress concentrations occur and are avoided
wherever possible. They may be needed because of limitations in material size, due to
manufacturing or transportation, to provide access, or to link sub-assemblies.
Efficiency of the joints depends on:
• Type of adhesive
• Surface preparation
• Curing process
• Surrounding environment
• Applied torque
• Edge distance
• And other geometrical ratios.
For composites the same types of connections are used as those in steel structures, namely: bolted
connections, adhesively bonded connections, combined connections, and welded connections.
Welded connections are only applicable for thermoplastics and are therefore not discussed here.
5.1. Mechanical connections
Mechanically fastened connections are difficult to design for strength greater than 50% of that of
the composite. To obtain acceptable efficiency, local reinforcement may be needed, because of the
high concentration stresses occurring at the position of the fastener.
Advantages:
• Straightforward method, less dependence on pre-treatment of the adherents and less
affected by environmental exposure.
• Less sensitive to peel off stresses or residual-stress effects.
• Disassembly is possible.
• Repair of these joints is easier because they required no specific environmental conditions,
like the curing of adhesives, which is difficult to achieve on site.
Disadvantages:
• Lower joint efficiency (strength to stress concentrations), about 50% of laminate strength.
• Lower bearing capacity of composites in comparison to the fasteners causes elongation of
holes and can result in delamination.
• Assembly can be time consuming
• Corrosion and wear of the connection can be a problem. Also metal parts are susceptible to
fatigue cracking.
• Galvanic corrosion may occur at the interface between the composite and the fastener when
using Carbon fibre reinforcement, use of sealant or corrosion protection is recommended.
(Galvanic corrosion is the corrosion resulting from contact between two metals or alloys.)
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Failure modes
The emphasis here will be on connections subjected to tensile stresses, the reason for this is that
composite connections subjected to compressive loading are less sensitive to joint geometry and
are generally stronger than those subjected to tensile loading.
• Bearing failure: Characteristic by localized damage, e.g. delamination and hairline cracks
of the matrix around the hole. Localized compression leads to buckling of the fibres
followed by crushing of the matrix.
• Shear-out failure: As a result from insufficient edge distance or because of having too
many laminas oriented in the load direction.
• Net tension failure: Caused by insufficient width or by having too many laminas oriented
in the load direction.
• Cleavage tension failure (tension and shear out failure): Due to insufficient edge
distance and width or insufficient number of cross-plies.
• Bolt/Fastener failure: Happens when the fastener is too small relative to the laminate
thickness, unshimmed or improperly shimmed gaps or if there is insufficient fastener
clamp-up.
• Punching failure: Can occur when countersink is too deep or when a shear head fastener is
used.
Of these failure modes the most significant is the tension failure.
Figure 5.1: Possible failure mechanism of bolted connections (Campbell, 2010, page 451)
5.2. Bonded connections
Bonded connections can be considered the most ‘natural’, because they are made like FRP’s matrix
from resin. Examples of adhesive used are: epoxies, polyurethane adhesives, cyanoacrylates (socalled ‘super glues’), methacrylate, solvent cements.
Some advantages are:
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•
•
•
•
•
•
•
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Ease to make aesthetic joints.
Strength may be greater for some adhesive than when using mechanical connections.
Fluid and weather tightness.
Weight saving
More uniform stress distribution, leading to better fatigue life.
Can provide connections with better vibration and damping capability.
Rigid/stiff connection.
However, some disadvantages are:
• Adhesives tend to be brittle, giving a brittle failure or creep related problems when using a
more ductile adhesive.
• Disassembly not possible.
• Pre-treatment and adequate environmental conditions are needed for a good joint
assembly.
• Susceptibility to environmental degradation.
• The use is limited because of lack of analysis methods, reliable material properties and
knowledge of long-term joint behaviour.
Figure 5.2: Basic joint types for bonded connections (Campbell, 2010, page 469)
In bonded connections load transfer occurs by shear between the laminates to be connected. Thus
bonded connections should be designed so that they are primarily stressed in shear or compression
since they can take up shear and compression better than tensile stresses. Therefore one should
avoid high tensile stresses, where this is not possible these connections should be carefully
evaluated.
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Failure modes
Failure can occur in the adherent by tensile or transverse failure, or in the adhesive through
interlaminar or cohesive failure as illustrated in figure 5.3.
Cohesive failure (i.e. within the adhesive) occurs by brittle fracture or rubbery tearing depending
on the type of adhesive used. Interlaminar failure may be caused by poor processing, voids,
delamination, or thermal stresses. And by in plane through-the-thickness stresses. Adhesive failure
will be in shear or peel.
Figure 5.3: Possible failure mechanisms of bonded connections (Kolstein, 2008, page 6.7)
To achieve a satisfactory bonded joint a carefully developed fabrication process is needed,
providing:
• Proper selection of an adhesive
• Proper surface preparation
• Proper conditions of temperature and humidity control
• A curing process as recommended by the adhesive supplier, to ensure that they provide the
required properties when in service.
• Also of great importance are the overlap length of the joint and the thickness of the
adherent.
Bonded joint configurations
The weakest type of joint configuration is the unsupported single lap joint and the strongest and
most complicated is the stepped lap joint.
Figure 5.4: Influence of member size on selection of optimum joint configuration (Mosallam, 2011, 162)
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5.3. Combined connections
In combined connections both adhesives and mechanical fasteners are used. The used of both
provides a joint with greater capacity and more reliability, acting as a fail save system. The adhesive
is usually stronger than the adherents. Therefore no significant loads are expected to develop in the
fasteners until the failure of the bond line. The reason for this is that the connection through the
fastener is much less stiff than that through the adhesive. Therefore combined connections are only
applied when redundancy is needed or to prevent peel stresses. Only when dealing with and
adhesive with lower modulus, which allows for load sharing between adhesive and the bolt, one
may have better strength, stiffness, and fatigue life in comparison to bonded connections.
Combined connections can also offer advantages during erection: fastener can provide the needed
pressure needed for curing the adhesive and the adhesive serves as a means to maintain alignment
for the mechanical fastener.
The analysis of combined connections is really complex and requires the use of non-linear
techniques. Also the load transfer is complicated due to the difference in stiffness.
Because of the lack of information and the complexity of the design analysis, it is recommended to
design these joints taking into account only one type of connection and regard the other only as an
additional benefit.
Which type of connection it should be designed as is still ambiguous. In the ‘Design guide for FRP
Composite Connections’ (Mosallam, 2011) it is recommended to design them as bolted-only, since
on-site the curing condition for the adhesives cannot properly be controlled. Hence, based on the
inherent brittle failure behaviour of the bond lines, it is better to design the composite connection
as bolted-only. And in the ‘EUROCOMP design code’ (Clarke, 1996) the recommendation is to design
them as being adhesively bonded connections, because the adhesive takes up the loads in first
instance.
A better understanding of these types of connections is needed to take advantages of the better
performance they may offer.
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6. DYNAMICS
In the main thesis research the focus will be on the dynamic behaviour of a lift gate. In order to
achieve a better understand on this subject. This chapter of the literature study will shortly
described what the different sources of dynamic loading can be and how to take into account the
surrounding water into the calculations.
6.1. Excitation sources
There are different sources that can cause vibration in gates:
1. Flow- induced: Initial turbulence and turbulence in the wake including vortex trail behind
the structure.
2. Flow instability resulting from separation of flow, separation point thus shape of structure
is important.
3. Self-excitation, movement induced vibrations/ self-excitation is smaller the stiffer structure.
4. Amplification of the excitation due to the resonant rise of the water.
5. Fluid resonance due to self-excitation
6. Waves: oscillations of waves and wave impact
Figure 6.1: Possible causes of excitation. (Kolkman [Part A], 2007, page 13)
When dealing with the dynamic loading caused by these sources important are the magnitude of
the pressure fluctuations and if the dominant frequency is close to the resonance frequency of the
structure.
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6.1.1. Flow-induced: Excitation due to turbulence
Excitation due to turbulence may be caused by turbulence in the approach flow, or by what
happens around the part of the structure concerned. In case of gates, the excitation due to
turbulence usually is of little significance, because as a rule the resonance frequency of the gate is
high in relation to the frequency of the flow-induced excitation and because the excitation is spread
out across a wider frequency band.
For the description of excitation due to turbulence, two characteristic values are important: the
Strouhal number and the ‘dynamic force coefficient’. The dynamic force coefficient relates to the
amplitude of the dynamic load and the Strouhal number is a measure for the excitation frequency. It
can be defined as:
fL
S = (6.01)
V
In this equation f is the excitation frequency due to the flow, L is a measure for the size of the gate
or the component of the gate that experiences the excitation, and V is the approach flow velocity.
6.1.2. Excitation due to flow instability
Flow-instability is related to the separation of the flow and when the flow attaches further on.
Where this happens is coupled to the specific shape of the object. In case of round shapes the
separation point is undefined, causing the flow to be very instable. Also, a vibration of the structure
may cause the point of separation to shift periodically, generating a change of force, which is
triggered exactly at the point of the resonance frequency.
The zone between the point of separation and the point of attachment may be governed by an
under-pressure, creating great force fluctuations when these points alternate. This means that the
periodic shift of these the point of separation and the point of attachment due to the movement of
the structure results in periodic excitation.
Flow instability generates a strong periodic excitation, in case of gates this occurs in the following
cases:
1. if the point of separation is not fixed by a sharp edge, but consists of a rounded shape;
2. if, after release, the flow attaches again (further down) against a wall of the structure, in
which the point of attachment is not fixed;
3. if the flow attaches again and the location of this is fixed, then a free boundary layer with
undulations is generated. Periodic pressure fluctuations with discrete frequencies are
generated within the enclosed vortices;
4. at a gate, in case of overflow, and a flow pattern that is between a situation of ‘diving nappe’
and a situation of ‘nappe deflected toward the water surface’;
5. at a gate with an overflowing nappe, beneath which there is an enclosed volume of air.
A small gate vibration may be, under certain conditions, already sufficient to cause the separation of
the flow or the periodic attachment to vary with the frequency of the gate vibration.
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6.1.3. Self-excitation
Self-excitation occurs in case both the vibration of the structure or the fluid, e.g. standing wave, and
the exciting force are harmonic. And the magnitude of the frequency of the exciting force is coupled
with the vibration. This excitation is referred to as ‘movement-induced excitation’, or also as
feedback vibration, self-excitation vibration or negative damping.
Self-excitation at a structure occurs when the excitation force is caused by the movement of the
structure itself. An initial vibration can become gradually stronger since the stronger the
movement the more amplification there is. This is also true in case of a standing wave, only in case
of great amplitude damping forces are generated.
In case of movement-induced vibrations, both the amplitude of the vibration and the excitation
coupled to it, grow exponentially, until a boundary is reached, as an example, when the flow pattern
changes.
Because this type of vibration may reach very high amplitudes, the prevention of self-excitation
vibrations is the first requirement when designing a structure.
6.1.4. Amplification of the excitation due to fluid resonance
Amplification of the excitation may be caused when the water has a clear resonance frequency.
In case of communicating vessels (this includes a surge shaft together with the outer water), a
standing wave, an air bubble enclosed in water, again and again there is an inertia and a stiffness
component of the water (or of the air bubble) and during the amplification, kinetic energy is
alternatingly converted into potential energy and vice versa.
When this fluid resonance system is periodically loaded in the resonance frequency, strong
oscillations may be caused that generate yet more load on the structure.
An example is when enclosed air, combined with a culvert of a finite length filled with water, causes
the water-air system to have a resonance frequency. Because of this or because of the vibration, the
turbulence downstream of the gate may cause amplification when frequencies approach each other.
6.1.5. Self-excitation in case of fluid oscillations
“A fluid oscillator is here defined as a limited fluid area, in which a resonant rise or a standing wave
may occur, without kinetic or potential energy radiating outward from that oscillation or being
added externally.” Kolkman [Part A] (2007).
Fluid oscillations are only dampened due to damping factors within the system itself. Depending on
the number of degrees of freedom, an oscillator may resonate in different frequencies. These fluid
resonances reside in the structure. Despite of this the resonance is completely determined by the
natural period of the resonant rise of the fluid, which may be the period of a standing wave or the
period of the resonance of communicating vessels.
Instable fluid resonances can occur when two preconditions are met:
• Precondition 1
The situation needs to be such, that a low-damped resonance of a fluid oscillator or of a
standing wave is possible.
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Precondition 2
In case of increased pressure, the floating gate generates an extra discharge in the direction
of the basin or the pipe in which the standing wave may be caused. In reality this means
that, when the basin is situated upstream of a gate, the gate discharge decreases in case of a
pressure increase upstream. If the basin is situated downstream of the gate, instability
occurs when the gate discharge increases in case of a pressure increase downstream of the
gate.
6.1.6. Waves
Waves impacting a structure cause loads that vary in time, the magnitude of these loads is
dependent on wave height, wave period and wave direction, and the dimensions of the surface of
the structure on which these loads operates. Also the shape and the surface properties of the
structure, the foreland geometry and the presence of other structures play a role in this (in relation
to reflection, diffraction and refraction, wave overtopping and the dissipation of wave energy).
Wave loads may be differentiated into quasi-static loads and wave impact loads.
6.1.6.1. Quasi-Static wave load
Quasi-static loads are loads that move with the same period as the waves themselves.
6.1.6.2. Wave impact
Wave impacts occur when a wave is suddenly blocked. The momentum in the water is then
cancelled out, converting it into energy. The structure should provide the strength to dissipate this
energy. Depending on the stiffness the structure will be distorted to some extent, causing the
structure in some cases to displace. However in practice the water may run off sideways and part of
the momentum takes on a different direction. If the water cannot run off sideways, high pressures
are generated. The magnitude of these pressures is dependent on the elastic elements present, i.e.:
• The compressibility of the water itself;
• This compressibility increases when there are air bubbles in the water;
• Air pockets enclosed between the water front and the structure operate as an elastic
element;
• The elasticity of the structure.
The weakest element determines the magnitude of the impact pressure.
Another significant fact is that a structure isn’t always hit simultaneously across the whole surface
area, therefore a spreading of the impact occurs over time, which results in a longer impact
duration and a lower peak pressure. The distortion of the structure may therefore influence the
magnitude of the impact pressure. This distortion (i.e. the response of the structure) is also
dependent on the elastic properties of the structure, thus resulting in an interaction between the
generated wave loads and the structure (response).
Figure 6.2: Schematic of wave impact on structure. (Kolkman [Part B], 2007, page 31)
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There are many factors that influence the occurrence of wave impacts, the magnitude of impact
pressures, and the progress of the impact in time and space. Some of these factors are:
Geometric factors:
• The shape of the structure (with reference to air enclosures, the possibility of water flowing
away sideways, the dimension of the affected surface area);
• The angle with and the position in relation to the average water surface (as an example,
components that protrude over the water surface, levee slopes, walls);
• The depth and the course of the foreland (with reference to the propagation of the waves,
refraction and breaking).
Factors in relation to rigidity:
• The elasticity of the structure and the compressibility of the water;
• The presence of air pockets between the water surface and the structure or the presence of
air bubbles in the water.
Factors in relation to the incoming wave:
• The wave height and the wave period (the greater the wave height and the shorter the wave
period, the higher the velocity of the water surface);
• The wave direction (the greater the angle between the normal on the structure and the
wave direction, the smaller the probability of wave impacts);
• Wave directional dispersion;
• The shape of the local wave, which is co-determined by preceding waves travelling back.
Factors in relation to the water:
• The salinity of the water (the salinity influences the size and the distribution of air bubbles
in the water and thereby the celerity of shock waves; also the density depends on the
salinity);
• Flow of the water (flow influences the wave field, but also the waves that are locally present
at the structure);
• The water level.
Different types of wave impacts can be differentiated:
• Hammer shocks
Incoming water runs parallel to the surface of the structure in which the water cannot run
off sideways. And there is little or no air inclusion between the water and the structure.
• Ventilated shocks
Air may escape from between the water surface and the structure and water can run off
sideways. This phenomenon is predominantly determined by inertia forces and gravity.
• Compression shocks
Air is enclosed and compressed between the water front and the structure. This air bubble
later oscillates generating an oscillating pressure distribution in the downward flank of the
wave impact. The maximum pressure is however, smaller than that of the hammer and
ventilated shocks.
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6.2. Dynamics of structures in water
6.2.1. Mass-spring- damper system equations
The classic equation for a (1 dimensional) mass-spring-damper system is:
dF y
dy
m F c ky Ft6.02
dt
dt
Here the y is the displacement of the mass from a reference point, m is the mass, c is the damping, k
is the stiffness, and F is defined as the external force(s).
The terms on the left are called the inertia term, the damping term and the stiffness term
respectively, while on the right there is the external force that here does not depend on the
movement of the structure.
Figure 6.3 is a schematic representation of an elastically suspended gate in a flowing fluid,
illustrating the symbols used. The most basic assumption is that the flowing water causes the
external force.
Figure 6.3: Schematization of a gate in flowing fluid. (Kolkman [Part A], 2007, page 16)
The damping force (in which c is positive) is in anti-phase to the vibration velocity, dy/dt; in
magnitude it is proportional to this velocity, but it operates in the opposite direction. When a force
like this operates in-phase with the vibration velocity, then the term negative damping is used (c is
negative in that case). In that case, a vibration is generated with ever increasing amplitude, which is
also referred to as self-excitation. Negative damping can only occur if a source is included in the
system that produces energy.
For a system in water the mass spring system, in equation (6.02) changes into:
dF y
dy
dy dF y
(m mr F c cr k k r y FE,r t FF,r by, , F g6.03
dt
dt
dt dt
The index w indicates that the magnitude concerned relates to the water.
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On the right, sometimes the term F1,w(t) may be distinguished for those forces that are not coupled
to the movement of the mass. While the other term, F2,w(y, dy/dt, d2y/dt2), represent coupled forces
for as far as these are non-linear.
On the left the mw is the so-called added water mass, cw is the added water damping and kw is the
added spring stiffness. These are the passive forces influencing the dynamic behaviour of a
structure in water. Each of these magnitudes can be frequency dependent and may be either
positive or negative. In the following chapter these added terms are further discussed.
6.2.2. Added water forces
6.2.2.1. Added water mass
The added water mass is the water that moves along with the structure. This definition is simplified
by Kolkman et al.[Part A] (2007) taking as an example a piston in a cylindrical vessel, in figure 6.4,
the added water mass in that case is the water on top of the piston. If the piston moves the water
has to move along, as it is locked in sideways, and the acceleration forces results in an extra
pressure on the piston surface.
Figure 6.4: Added water mass in case of a
piston. (Kolkman [Part A], 2007, page 53)
Figure 6.5: Potential flow in case of a vibrating
strip. (Kolkman [Part A], 2007, page 54)
In case of an infinitely long strip, see figure 6.5, the added water mass equals the mass of water in
the imaginary surrounding circular cylinder of the strip. This is a different situation from the one of
the vibrating piston. The contribution of the kinetic energy is proportional to the square of the flow
velocities. These flow velocities are, due to the flow pattern, smaller further away from the strip.
The extra kinetic energy determines the magnitude of the added water mass. This magnitude can
also be determined by considering the pressures at the surface of the strip in relation to its
acceleration. The added water length, Lw, depends on the vibration direction, and is always coupled
to the dimensions of the vibrating body, varying across the width of the strip.
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6.2.2.2. Added stiffness
Added stiffness can be divided into three types. These are the stiffness due to immersion, the
stiffness due to quasi-stationary flow forces and the stiffness that is generated when an object
suddenly experiences a change of position (the so-called sudden stiffness).
Stiffness due to immersion
The stiffness of an object that is vertically immersed may be described as:
Kw,float =ρ·g· Across-section.
The surface of the cross-section with the free water level is normative for this stiffness.
Stiffness due to flow
The flow force (i.e. the force coefficient) may vary relative to the position.
The flow stiffness is generally proportional to the squared flow velocity or, in case of gates (where
the flow velocity is proportional to the root of the hydraulic head), proportional to the hydraulic
head.
Sudden stiffness
The so-called sudden stiffness is a stiffness that only occurs at gates, particularly at culvert gates,
where the discharge in the culvert has such inertia, that it does not immediately adapt to the
changed position of the gate.
6.2.2.3. Added damping
Added damping is mainly caused by the flow. Flow induced added damping can include:
• Added damping due to flow in case of an object vibrating in flow direction
The flow forces, that are square with the flow velocity, change due to the velocity of
movement of the vibrating structure. As a consequence of this vibration velocity, both the
magnitude of the relative approach flow velocity and the angle of approach change.
• Added damping due to flow in case of the vibration direction differs from the flow
direction
In case of a circular cylinder or a sphere, the damping may also be calculated when the
vibration direction is not the same as the flow direction.
However for gates, the quantified positive water damping is of little significance, because strong
vibrations only occur when the water damping is negative.
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7. FRP IN STRUCTURAL APPLICATIONS
7.1. Examples of FRP structures
In the late 20th century FRP started being used in infrastructures. In the 1970’s the first bridges
incorporating composite elements were constructed, although it was in the 1990’s that the use of
FRP in structural applications really started.
Below some examples of infrastructure build in FRP or with FRP components (e.g. cables, structural
profiles, bridge decks, etc.) are presented.
7.1.1. Pedestrian and cyclist bridge at Kolding in Denmark
This bridge was developed by Fiberline and opened in 1997. It is made out of glass fibre reinforced
polyester (GFRP) profiles, except for the bolds and abutments which were made of stainless steel. It
has a width of 3.2m and a span of 40m divided over 2 sections one of 27m and the other of 13m.
(Fiberline [2], s.d.)
Figure 3.8: Pedestrian and Cyclist Bridge at Kolding in Denmark. (Fiberline [2])
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7.1.2. Bridge-in-a-Backpack
“The Bridge-in-a-Backpack is a lightweight, corrosion resistant system for short to medium span bridge
construction using FRP composite arch tubes that act as reinforcement and formwork for cast-in-place
concrete. The arches are easily transportable, rapidly deployable and do not require the heavy
equipment or large crews needed to handle the weight of traditional construction materials”.
Citation from University of Maine website.
This system was developed by the Advanced Structures and Composites Centre at the University of
Maine and patented by Advanced Infrastructure
Technologies (AIT).
Figure 3.9 (above):
Illustration of the ‘Bridge-in-a-Backpack’ system. (AIT)
Figures 3.10 and 3.11 (right):
The McGee Bridge Arch build with the so-called ‘Bridge-in-aBackpack’ system in Maine, USA. (GCE)
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7.1.3. Bus station ‘The Giant Whale Jaw’
This is a bus station in Hoofddorp build in FRP. The bus station is 50 m long, 10m wide and 5m tall
and is made out of one single piece. Build on site with blocks of polystyrene foam, most commonly
known as Styrofoam, and coated with a 6mm thick glass reinforced polyester using the spray-up
method.
Figure 3.12: Bus station 'The Giant Whale Jaw'. (Poly Products)
7.1.4. Column mould parking garage Amsterdam
Developed for by Nedcam for the columns (see figure 3.13) in a parking garage under the
Oosterdokseiland in Amsterdam, showing the ease in forming different shape in FRP. The moulds
were made of a polystyrene foam (Styrofoam) core with a reinforced polyester resin.
Figure 3.13: Columns in a parking garage under Oosterdokseiland in Amsterdam. (Nedcam)
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7.1.5. Façade ‘Building X’ Windesheim University in Zwolle
This façade consists of 50 % glass, made out of triangular glass sections glued to a sandwich
structure. The sandwich structure has dimensions of 12.5 by 3.5 m and a thickness of 300mm.
Figure 3.14: Façade Windesheim University as viewed from the inside. (Hollands Composites)
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7.2. Examples of hydraulic structures in FRP
7.2.1. Valves in the Kreekraksluizen
The Kreekraksluizen had a fresh-salt water separation system consisting of 256 steel valves, with
dimensions 1.8 by 0.8 metres. One of these steel slides was replaced by a composite one from 1993
until the closure of this water separation system.
The slide was designed for a head level of 3.2m when closed and 0.3m when opening. To ensure
water tightness the deflection of the slide had to be limited to 0.1mm when closed and while
moving 8mm. They were designed with a service life of 50 years.
It was made of glass fibre reinforcement with a matrix vinyl ester resin, and stiffened on the outside
edge using a core made of polymer concrete. As seen in figure below.
The manufacturing process used was RTM-resin transfer moulding, with an applied pressure of 15
to 20bar. (Honselaar, 1999)
Figure 7.1: Composite steel slide in the Kreekraksluizen (1993-1997). (Honselaar, 1999, page 9)
Figure 7.2: Cross-section of stiffeners applied on the edge of the valve. (Honselaar, 1999, page 9)
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7.2.2. Spieringsluis
The “Spieringsluis” dates back to 1953, it forms a connection between the “Nieuwe Merwede” and
the “Biesbosch”in Noord Brabant in the Netherlands. In 2000 the timber mitre gates were replaced
by composite ones, they were chosen to try to suppress the costs of maintenance. It was the first
time in the Netherlands that FRP gates where used.
Laminates for these gates were build-out of E-glass fibres and an iso-phthalics polyester resin,
which has better resistance to wet conditions.
The GFRP gates are chosen with a configuration of [0/90/+45/-45] with 55% of fibres in the main
direction and 15% in the other directions. The laminates where made by hand lamination and
weighs 5100 kilos, which is less than the replaced timber ones (14000 kilos). (Nagtegaal, 2001)
Figure 7.3: Lock gates Spieringsluis. (Nagtegaal, 2001)
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7.2.3. Golbey gate replacement, France
Located in the Canal des Voges in France, in a lock dating back to 1925, the Golbey gates originally
build of steel where replace in 2000 by composite mitre gates. The composite gates are composed
of circular shaped skin plates made out of glass fibre reinforced polymer (GFRP) stiffened by blocks
of sandwiched glass fibre and foam. The gates are hinged to the old masonry with an adjustable
stainless steel U- shaped frame. (InCom, 2009)
Figure 7.4: right, the lock dating from the origin of the channel (1853) and now abandoned. Left the lock
built in 1925 and equipped with composite doors in 2000. (Website: Bord à Bord asbl)
Figure 7.5: Composite gate with visible hinges
(Website: Bord à Bord asbl)
Figure 7.6: Adjustment of composite gates
downstream (InCom, 2009, page 18)
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7.2.4. Erica-Ter Apel lock gates
The Erica-Ter Apel lock gates are situated in the Erica-Ter Apel canal in the vicinity of Emmen in
the Netherlands. They were placed in March of 2012.
This project was an assignment from the provinces of Drenthe and Groningen. The gates, 4 in total,
were designed and fabricated by FiberCore Europe. They are 5 meters tall by 3.6 meters wide and
made with InfraCore® Inside (patented by FiberCore Europe). They are dimensioned so that the
specific weight corresponds to the buoyancy force of the water, this way the driving mechanism is
loaded as little as possible. (Visser, 2012), (FiberCore [1])
Figure 7.7: Placing of the Erica-Ter Apel gates (FiberCore [1])
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7.2.5. Wilhelminakanaal gates in Tilburg
Plans are being made for the biggest FRP gates yet to be build it will be situated in the
Wilhelminakanaal in Tilburg in the Netherlands, being 12.5 meters tall and having 6.2 meters in
wide. The gates will be a design of FiberCore and will be placed by Heijmans, who together with
Boskalis will develop the entire canal and the lock. This would be the third project in the
Netherlands where composite gates will be used. The production of the gates is plant to start in
2014 and are planned to be put into their final place by mid-2015.
The composite gates will consist of a foam core with 30mm thick skins made out of glass fibre
reinforced polyester, this will be done using the InfraCore® Inside-technology patented by
FiberCore. The gates will be provided a beige/yellow gel coat.
(FiberCore [2])
Figure 7.8: Illustration of the gates for the Wilhelmina canal. (FiberCore [2])
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7.2.6. Composite vertical lift arch gates research in France
CETMEF (France) has studied an arched vertical lift gate made out of composite materials.
The downstream gate is divided into 3 identical monolithic sections, In order to make the
manufacture, transport and installation of the gate easier. Each section is reinforced on the
downstream side with two horizontal stiffeners, 600mm in height. Consisting of an omega shaped
skin made out of CVR composite, with a thickness of 30 to 40mm, and filled with foam.
The sections are connected on site. With all sections connected the gate’s height is 12.4m in height.
The gate is placed in a lock with a width of 12m.
Due to its cylindrical shape the structure transmits most of the thrust stress, load from the
differential head, as compression.
The hydrostatic load reaches 20000kN. The weight of the gate (composite part only) is 400kN and
totally equipped (with steel devices and cylinder) the weight to be lifted is 600kN with friction
forces. The gate is guided by the sliding of the arches extremities on fixed parts.
(InCom, 2009)
Figure 7.9: Composite vertical lift gate. (InCom, 2009, page 135)
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Internet sites
AIT (Advanced Infrastructure Technologies):
http://www.aitbridges.com/compositebridgesystem/
Bord à Bord asbl:
http://bordabord.org/news/ecluse-de-laneuveville-devant-nancy-indisponible-1
Fiberline [1]:
http://www.fiberline.dk/
Fiberline [2]:
http://www.fiberline.com/structures/profiles-and-decks-bridges/profiles-footbridgesand-cycle-bridges/case-stories-footbridge/fiberline-bridge-kolding
Fibrex:
http://www.fibrex.com/industries-served/other-frp-pipe-production/
GCE (Gardeners Construction Enterprises):
http://gardnerconstructionenterprises.com/composite.asp
Hollands Composites: http://www.hollandcomposites.nl/
Nedcam:
http://www.nedcam.com/index.php
Poly Products:
http://www.polyproducts.nl/bijzondere_bouwelementen/busstation-hoofddorp.htm
Solico:
http://www.solico.nl/
University of Maine, The Advanced Structures and Composite Center:
http://www2.umaine.edu/aewc/content/view/185/71/
ZCT:
http://zct.ru/en/katalog
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