Jordan Yerbury
Lightness structure
LIGHTNESS STRUCTURE
by Jordan Yerbury
Student number: 4327535
Email: yerbury@gmail.com
Delft University of Technology, Department of Architecture
Graduation Lab Architectural Engineering
May 12, 2015
Carbon Fiber Reinforced Polymer (CFRP) truss, cables and plates
Structural components with high specific strength
Jordan Yerbury
Email : j.yerbury@student.tudelft.nl
Delft University of Technology, Department of Architecture
Graduation Lab Architectural Engineering
Abstract – The choices of materials for building light structures in the construction industry are often made
based on market-driven concerns. These market-driven choices have been informed by developments in material
applications over the past one hundred and fifty years (Beukers and van Hinte, 2001). Since the eighteen
hundreds, the most significant new materials used in the construction industry are steel, aluminum, titanium,
synthetic polymers, and artificial ceramics (Beukers and van Hinte, 2001). This list continues to evolve, as the
choice of materials are still made with the intention of reducing costs, using less energy, and meeting safety
standards. New production methods and fabrication techniques may lead to reduced costs in the future, as has
been the case with steel, for example.
Two technologies will be examined in this paper. The first is a carbon fibre-reinforced polymer “strip”
(CFRP strip) used for repairing existing concrete structures. The second is a CFRP lattice component used in
a truss. Both the CFRP strips and CFRP lattices are used for their lightweight, specific strength, and particuar
manner of resisting a variety of forces. The strips can also, hypothetically, be used to make connections when
structurally repurposeing an existing building, and the lattices can be used for parts of a building that should be
thin, light and stiff. Key words – Lightweight structure; building on rooftops; building on exsiting buildings; composite materials;
carbon fibre reinforced polymers (CFRP); carbon fibre truss; IsoTruss™; future technology.
Total primary energy to produce steel has reduced over time
20%
To produce 1.5 GT of steel in 1900, it took 20% of the total primary energy supply
(TPES).
TPES 44 exajoules
6.6%
To produce 1.5 GT of steel in 2010, it took 6.6% of the total energy.
(Harvard Buisness Review, March 2015)
TPES 544 exajoules
(Source: Harvard Buisness Review, March 2015)
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Jordan Yerbury
Lightness structure
Introduction - The objective of this paper is to
explain how a lightweight structure can be built on an
existing concrete parking garage to accomodate both
housing and hotel rooms for the city of Utrecht.
2. Method - The method of design will analyzed
in terms of basic properties of polymers, fibers,
production and processing, and ways to recycle carbon
fibre at end-of-life.
Lightweight materials are currently used as
a retrofitting and repairing tool in the construction
industry, albeit, in a mostly limited way because it is still
a relatively expensive material to produce. Since the
1960s, major developments in carbon fibre production
have drastically increased the potential for applications
in the construction industry, however since the
limitations of carbon fibre reinforced polymers (CFRP),
for large scale construction is currently prohibitive, the
material is only used in certain special circumstances.
3. Results- The result of a CFRP in terms of mechanical
properties, building physics properties, permeability to
light and heat and the environmental impact.
4. Conclusions - The conclusion, which is a comparative
presentation that covers structural forces and the
resulting form of the structural members.
There are many CFRP plane-truss pedestrian
bridges, such as those designed by Strongwell and
Wheeler Lumber Corp. While bridges are increasingly
being made out of composites, the materials have only
been used in the structural design of buildings in very
few cases such as the BMW Pavilion by Atelier Bow
Wow.
CFRP material will be analyzed in four phases
with the assumption that it will be used both as a
component that connects the new structure to the
exitsting structure, and as a lightweight component of
a truss. Combined, these two features will both reduce
the overall weight of the entire structure and transmitt
an aesthetic sense of lightness.
1. Background - A description of the CFRP material; its
current applications will be described and the reason
for choosing the material will be explained.
CLASSIFICATION OF TYPES OF FIBERS
2
Natural fibres
Flax
Sisal
Hemp
Jute
Ramie
Banana
Asbestos
Organic fibres
Polyethylene (PE)
Polyethylene terephthalate (PET)
Polyamide (PA)
Polyimide (PI)
Polyacrylonitrile (PAN)
Polytetrafluoroethylene (PTFE)
Aramid
Metal fibres
Steel
Aluminium
Copper
Inorganic fibres
Glass
Carbon
Basalt
Ceramic
(Knippers et al., 2011)
Research tools
The research for this paper includes reference
literature, and testing virtual models by comparitive
analysis .
Prior to the analysis, the literature is referenced
from a variety of sources, including text books, scientific
journals, academic publications, museum publications,
reputable industry-specific websites of companies who
manufacture materials in the construction industry.
Virtual models will be tested, in a comparative
manner, using Scan & Solve®, Karamba® with MatProps,
and Grevit® softwares for Rhinocerous 3D® . In order
to elaborate the potential of a complete structural
system, which include the combination of two CFRP
technologies.
1. Background - Lightness is the combination of
lower mass (kg), thinness (mm), and being part of a
system that appears visually light, such as transparency
(+/-). The essential qualities of lightness are innate to
CFRP materials, yet expressing these qualities requires
assembling a variety of ideas into a composition.
CFRP “strips” (kg)
CFRP “strips”, commonly used to repair concrete, is
the inspiration for replacing angled steel plates. Not
only does this invention offer a reduction in mass, less
damage will be caused when the strips are screwed
into the existing concrete. By gluing the strips to the
concrete, lighter screws are needed to connect the
CFRP angled strips to the slab.
CFRP lattice (mm)
Using CFRP lattice components to replace existing
structural components, withh up to a twenty percent
reduction in mass per elelment, the entire system will
be lighter.
Jordan Yerbury
Lightness structure
Breaking Lengths
Breaking lengths is the distance that a fiber can be
suspended in the air before it breaks under it’s own
weight.
COMPARING THE APPROXIMATE
“BREAKING LENGTHS” OF FIBERS
(distrances are in km)
5000
Carbon Fiber is very rigid
Exposed carbon fibres are brittle, therefore, a coat of
epoxy resin protects them from buckling. Rigidity or
stiffness of a material is measured by its Young Modulus
of elasticity (E) and implies how much a material
deflects under stress. Carbon fiber reinforced plastic
is over four times stiffer than glass reinforced plastic,
almost twenty times more than pine, and two times
greater than aluminum. A carbon fibers modulus of
elasticity is categorized in three forms, either:
1. High tensile strength (HT);
2. High material stiffness (HM);
3. Intermediate tensile strength and stiffness (IM)
500
STRAIN VERSUS (%) VERSUS NORMAL
STRESS (N/mm2) IN VARIOUS
MATERIALS
Carbon Properties (in the direction of
the fibers)
Tensile
Strength
(103/mm2)
Elastic
modulus
(103/mm2)
Elongation
at failure
(%)
Density
(g/cm3)
HT
3-5
200-250 1.2-1.4 1.75-1.80-1.00
17
IM
4-5
250-350 1.1-1.9 1.73-1.80-1.20
7-9
HM
2-4
350-450 0.4-0.8 1.79-1.91-1.30
7-9
115
7-9
(Knippers et al., 2011)
Carbon
fibers
5000
Fiber
diamter
(µm)
σσ (N/mm2)
Specifica-
Coeff.
Thermal
thermal
conductivity
expansion (W/mK)
(10-6/K)
CARBON NANOTUBES
ALUMINUM
25
CARBON FIBER
Dynamic properties of carbon fiber
Carbon fiber is a high performance material for
certain applications due to the rigidity, low self-weight,
extremely high resistance to corrosion thanks to
chemical stability and virtually no “cold flow” (creep).
Creep is the permanent deformation of a material
under particular stresses.
Tensile fatigue
This effect is observed as a reduction in stiffness with
larger numbers of stress cycles. When the temperature
is high, however, this reduction in stiffness happens in
a different manner. Failure is unlikely to be a problem
when cyclic stresses coincide with the fibre directions.
GLASS FIBER
Currrent uses of the material
Carbon fibre reinforced polymers are most often
used in the construction industry for retrofitting
compromised structures and in other related industries
such as cycling, motor vehicles and furniture.
Resistance to fatigue
Despite its amazing properties, when carbon fibre
fails, it usually fails catastrophically. There is often
no indication of fatigue before collapse, unlike with
metals that may show significant deformation before a
structure comes apart.
COTTON
Transparency (+/-)
The light strips combined with the thin lattice members
are part of a light system that gives the illusion of
transparency.
4000
PE
3000
E glass
Aramid
fibers
2000
1000
PET fibres
0
0
1
2
3
4
ɛ (%)
5
6
3
Lightness structure
This is similar to the fibres in a material like bamboo.,
for instance.
The orientation of the fibres, in a woven sheet,
and the several layers with crossing orientations, have a
great deal of influence on how a CFRP component will
resist fatigue. The type of forces applied also results in
different types of failures. Tension, compression or sheer
forces all result in very different failure results.
Anisotropic properties
1. Both stiffness and strength of carbon fibre are low in
the transverse direction to the fiber.
2. The coefficient of thermal expansion is negative along
the length, and positive in the transverse direction.
3. Carbon fibers therefore become shorter as they
become warmer.
Resistance to corrosion
Although carbon fibres themselves do not deteriorate,
epoxy resin is sensitive to sunlight. Measures can be
taken to protect the epoxy, though this may have
effects on the material performance. There may be
other improved alternatives to epoxy resin, yet these
matrices might also be unpredictably reactive, so more
studies need to be made to ensure safety standards.
Carbon fiber is electrically Conductive
Depending on where it is used, this impressive
feature of the material can be a hazard. Aluminum
has a comparable advantage/shortcoming and special
considerations should be made even when using
certain materials together. For example, galvanic
corrosion occurs by conductive materials long after
installation. Fiber particles in a fabrication shop,
for instance, may cause circuits in appliances and
equipment to short.
Tensile strength (ultimate strength)
Tensile strength is called ultimate strength. Ultimate
strength is the maximum stress a material can
undertake as it is being stretched. As it is pulled, the
force per unit area can be measured. As carbon fibre
is brittle, failure does not always occur at the same
measured stress levels. It is the internal flaws which
lead to different types of failures and this is difficult to
predict. Small strains cause failure and there is virtually
no bending or stretching prior to catastrophic failure as
a warning sign.
Material strength (specific strength)
The specific strength is a material’s strength (force
per unit area at failure) divided by its density. It is also
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Jordan Yerbury
known as the strength-to-weight ratio or strength/
weight ratio. The SI unit for specific strength is Pa/(kg/
m3).
Coefficient of thermal expansion “alphaT” (1/ºC)
Materials can expand or shorten depending on changes
in temperature. The increase in stress or strain is
dynamically displayed as a change in the strain per
degree Celsius for an unrestrained component. Steel,
for example has the value 1.0E - 5 (1.0E -5 = 1.0 -5
= .00001). An 1000mm rod made of steel increases
by 1mm if the temperature is increased by 10ºC. This
characteristic is calculate when loads are applied to the
structure in the model.
Yield stress fy (kN/cm2)
The yield stress is the strength of the material or
the force per unit area before the material fails. The
stresses within a composite are a function of the
material properties of the materials, the geometry,
and the loading condition.. Using BeamView alows this
characteristic to be displayed as the ratio of actual
stress and yield stress. The yield strength is the stress
above which a material will remain permanently
deformed even when the applied load is removed, so
this does not apply for carbon fiber.
Low thermal conductivity
The negative coeeficient of thermal expansion of
carbon fiber implies that along the length of the fiber,
when it is heated, the fiber becomes shorter. The fibers
are not highly susceptible to change under seasonal
weather variations and this means that the material is
well suited to outdoor applications.
Environmental impact of polymers
Despite the natural occurance of carbon in chrystaline
form (graphite and diamonds), these materials can
not be processed to make fibers at the present
time. Polyacrylonitrile (PAN) is composed of various
elements and these are removed to retain only the
carbon molecules as much as possible.
Customizing fibre and resin types
The strength and stiffness of the structure can be
tailored by combinations of additives and the number
of tows/rovings. It is currently possible to create thicker
or thinner elements and hybrid geometries are even
possible yet hardly explored. Using a custom made
script for optimizing the geometry of the Isotruss, a
taylor-made geometry can be designed to suit specific
applications. For example certain cases call for a
Lightness structure
Jordan Yerbury
solution that maximizes axial strength for asymmetrical
bending loads. Since there may be more load in one
direction most of the time, an elliptical cross-sections
may be appropriate. Furthermore, if the loading of a
certain member creates high compressive forces at a
particular location of a component, that area can be
designed thicker to resist the stress.
Torsion
Helical members take the majority of the load. The
radial symmetry distributes the load and resists buckling
equally around the central axis. With the loading along
the fibre axis, which is the most efficient orientation
possible, this exploits the unique properties of the
material.
Since the fibers are usually uniaxial, Isotruss distributes
multi directional loads to fibres aligned in the
appropriate directions. IsoTruss is limited currently to
6 to 12 nodes, but the script designed for this project
allows endless combinations of nodes and geometries
Carbon fibre is used to repair cracks and damaged concrete in buildings and
bridges. The tensile properties of the material resist against the forces that
pull the concrete apart and could eventually lead to failure.
to be analyzed in detail. Pyramidal configurations made
of an eight-node structure are more efficient in bending
and resists buckling better because the longitudinal
members are further away from the neutral axis. By
increasing the moment of inertia and stiffness, less
material can be used to achieve desired effects with
reduced material.
Using advanced visualization techniques, the
effects of various configurations can be compared
quickly in order to optimize the nodal configuration of
carbon fiber lattices and essentially tailor the geometry
to any type of loading necessary.
Hooke’s Law and the Parallel Axis theorem
Since the overall diameter should grow larger to
increase the moment of inertia, or structural stiffness,
according to an engineer at IsoTruss, a regular tube
is more likely to buckle. With the CFRP lattice, the
forces are evenly distributed throughout the helictical
segments, and into the base segments. This means that
the lattice works more efficiently with less material than
a solid tube of the same material.
Carbon fibers are woven into a network of isosceles triangles in this
example by Delta7. Triangles join together to form pyramid-shaped trusses,
which provide huge structural support with less material, simply by using a
more efficient geomtry.
Mechanical properties to compare materials
By comparing steel, aluminum, and carbon fiber
tubes in different geometric configurations, a
virtual comparative analysis is possible. Using the
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Lightness structure
Jordan Yerbury
MatProps component of Karamba for Grasshopper
in Rhinocerous 3D, various configurations and
modifications of a Delta7 carbon fiber Isotruss can be
tested for performance as individual members and as a
2D or 3D structural system. The objective is to achieve
the lightest structure. The following characteristics are
used to compare the materials for the initial testing:
Young’s Modulus “E” (kN/cm2)
A measure of the stiffness of a material, defined as
the axial stress divided by the axial strain. Materials
with higher modulus are stiffer. Also known as Young’s
Modulus.
Westraven P + R, Utrecht. This parking garage is ideally located to
develop the transferium into a welcoming gateway into the city.
Shear modulus “G” (kN/cm2)
Defined as the shear stress divided by the shear strain.
Also known as the Modulus of Rigidity. The shear
stress is the component of stress parallel to the crosssectional face of a material, and the shear strain is the
deformation of a material caused by a shear stress. A
shear strain causes skewing of a material element.
Specific weight “gamma” (kN/m3)
This is a force per unit of volume. Due to Earths
gravitational acceleration and according to Newtons
law (f = ma) a mass m of one kilogram acts downwards
with a force of f = 9.81N. For calculating reactions
of structures the assumption of f = 10N is accurate
enough.
Some examples of specific weights of materials:
Steel 78.5
Aluminum 27.0
Reinforced concrete 25.0
Glass 25.0
Carbon fiber 16.0
Water 10.0
Snow wet 9.0
Wood 3.2
Snow loose 1.2
Specific weights of building materials loads (kN/m2)
Live load in dwellings 3.0
Live load in offices 4.0
Snow on horizontal plane 1.0
Cars on parking lot (no trucks) 2.5
Trucks on bridge 16.7
6
Parking garages are designed to hold cars weighing aproximately 25kN.
Each car parking space is 5.0m x 2.5m. The total weight that can be
added to the parking garage, including live and dead loads should not
exceed 2.5kN/m2.
2. Method
Jordan Yerbury
Transparency and lightness
Carbon fibres are black and opaque with a crystaline
structure. These mechanical properties carbon fibre
to be used in such a way that much less material can
provide the same duties as metals and other materials.
By using the lattice grid as the geometrical
foundation for the design of members made of carbon
fibre, a sense of visual lightness can also be exgeratted
with transparent or translucent materials which appear
light .
Lightness structure
Fabrication. While the current manufacturing method is adequate for larger
structures, cost and productivity limitations complicate smaller diameter
structures. A continuous automated process will reduce production costs.
(Source: Isotruss)
Concept for the CFRP
“Strips”. This invention
could significantly reduce
the damage caused when
connections are made between
new and old structure.
Specific technologies: CFRP strip angled plate
According to research published in International
Journal of the Physical Sciences, “CFRP has high tensile
strength,and it is installed on the tensile region to
improve the load bearingcapacity of structures.” If a
CFRP strip is used as a pin connection angled plate,
it may served the dual purpose of supporting a new
superstructure and reinforcing the existing structure
upon which the superstructure is being built.
Summary of the invention: CFRP strip angled plate
A structural member with enhanced performance is
glued to the existing concrete slab and connected with
glue. Once the top and bottom plates are connected,
they are bolted to the slab for additional security.
7
1
6
5
5
1. CFRP lattice
2
3
2. CFRP “strip” with angled
bracket
3. Existing beam
4
Existing concrete topping
4. Steel anchor screw
5. CFRP strip
6. New structure for housing
7. Steel cable
7
Lightness structure
Specific technologies: CFRP lattice truss
IsoTruss™ Structures Inc. (Brigham City, Utah) initially
developed and tested a filament-wound, open tubular
lattice. This novel structural component is made of a
series of intersecting triangles and pyramids. Despite
IsoTruss™ Structures having exclusive rights on the
technology in the U.S, the potential for developing
various geometries according to each project is
presently achievable.
Some specific examples are a beam-like
composite truss with a triangular cross-section and a
length of 6 m that was then subjected to a three-point
bending test. Furthermore, an all-composite space truss
unit composed of GFRP profiles was tested.
Summary of the inventions: lattice truss
A structural member with enhanced performance
characteristics in terms of strength and reduced weight
is sought in the bicycle industry. The invention of the
IsoTruss for Delta7 is a three dimensional structural
member that includes:
1) minimum two helical components;
2) at least one “reverse” helical component attached
to two helical components;
3) a common longitudinal axis shared by the helical
and reverse helical components. These components
also have opposing angular orientations about the
axis.
One example of this type of composite lattice design
tubes has 13% of the weight of a similar steel tube in
bending applications, compared on an equal-load basis.
(http://www.compositesworld.com/)
Material selection and lattice shape can improve
strength and stiffness and an open structure with lower
material content makes IsoTruss™ competitive with
metals and even carbon fiber tubes because it uses so
much less material and performs so well.
Basic design features
Unidirectional fiber tows called rovings are wound
over a mandrel. Helical and longitudinal fibers are then
interwoven and compacted on the metallic mandrel,
and strong, integrated nodal joints are formed.
Bending, buckling, axial, torsion, combined loads Isotruss is suited for loads at multiple locations
around the center axis or along its length. “In effect, it
8
Jordan Yerbury
is analogous to the geometry of an I-beam, with the
longitudinal elements functioning like the flanges of the
beam, moved outward from the neutral centerline tube
axis.” (Livingston)
3. Results
Comparative presentation
Using a steel bridge deck with steel and aluminium
truss as the starting point, the members were replaced
with lattice members and the mass of the trusses were
compared.
Tension and compression
With the Grasshopper plugin Karamba, accurate
predictions were analyzed based on the confiurations
of the nodes, helixes and moment of inertia. The
compression and tension are mde visible and the
intensity of compression or tension can be displaced
to different segments of member by changing different
parameters related to the geometry.
Form-finding based on forces
A lattice design is usually selected for
elecommunication towers and other similar structures
because it uses less material and thus is about half the
weight of a solid tube. An open structure also creates
less resistance to wind loads and appears visually lighter.
On-site ssembly and fastening contributes significantly
to the cost of any construction, and therefore the
more a project can be manufactured and assembled
automatically, the less costs will be associated with onsite labour.
Scalable
The results from the virtual models and research have
indicated that replacing certain members of truss
with a lattice grid made of carbon fibre can reduce
the entire weight of the structure by approximately
20%. Furthermore, as indicated by the company that
currently produces Isotruss, the system is scalelable.
Restrained forms
The trend in furniture and car design using CFRP tends
to focus on formal strudies that utilized the material
properties and simultaneously express the plastic
nature of the mouldable fabric.
Since the intention of this research is lightness,
shells, domes and more amorphic forms were
purposefully avoided, in order not to cause distractions
from the essential qualities of lightness and thinness.
Jordan Yerbury
Lightness structure
4. Conclusion and discussion
Not only can certain parts of a truss can be replaced
with carbon fibre and use significantly less material than
carbon fibre tubes, but also that this script for vizualizing
the forces in of the lattice truss members can be used
to change the size and geometry of the system on both
the component level and the larger spatial scale.
I-beams are either AC or BD. If these components are made of carbon
fibre (instead of steel or aluminium) the essential advantages of CFRP
would be wasted. The entire geometry needs to be altered to see
noticeable savings in material and cost.
1.2 m
0.8 m
Joints and connections
The connections between carbon fibre components
and steel are perhaps the most difficult technical
problem to resolve. Unlike a welded steel connection,
the connection between the CFRP lattice and a steel
pin is difficult to connect chemically, and mechanical
connection is unavoidable at the present time.
1.2 m
Dimensions of this truss are based on the trussed members and their
cross sections (dimensions in mm) according to the research based on
experiments done by D. Zhang et al. / Composite Structures 108 (2014)
600–615
12 m
This changeable structure includes at least two helical components and at least
one reverse helical component all attached at nodes. The structure can include
at least two rotated helical components and at least one rotated reverse helical
component which are rotated with respect to the helical and reverse helical
components forming a second square cross section, rotated with respect to the
first.
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Lightness structure
Jordan Yerbury
Existing
Aluminum 'EN AW-6061 T4'
F
G
E:7000[kN/cm2]
G:2700[kN/cm2]
gamma:27[kN/m3]
alphaT:2.4E-5[1/C°]
fy:11[kN/cm2]
F
G
Trussed members F Diagonal
web member(aluminum) will be
systematically replace with isotruss
configurations to determine the
savings in mass and visual lightness
for each configuration.
G
G
G
G
E
Trussed members:
E Lower chord member(HFRP)
F Diagonal web member(aluminium)
G Vertical web member(aluminum)
E
F
G
Lattice truss components
F
G
Material: 'Carbon fibre
E:18000 kN/cm2
G:8000 kN/cm2
gamma:16 kN/m3
alphaT:-1.0E-5 1/C°
fy:23.5 kN/cm2
F
G
G
G
G
E
Trussed members:
E Lower chord member(CFRP)
F Diagonal web member(CFRP)
G Vertical web member (CFRP)
10
G
Tension
Compresion
Conceptual images of truss
components. Comparing
different geometries, radius of
carbon fiber lattice strands and
other properties may lead to
material savings and improved
specific strength.
Jordan Yerbury
Lightness structure
Aluminium cross
members
Closeup of aluminium cross
member of the truss. The
level of stress is indicated by
a gradient. By replacing the
aluminum member with a new
type of lightweight carbon fibre
truss member, the overall weight
of the structure will be reduced
significantly.
2.7 kN
Total mass: 12 800 kg
2.7 kN
2.7 kN
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Jordan Yerbury
Lightness structure
4 helixes
Total mass: 9 120 kg
8 helixes
Total mass: 9 500 kg
12 helixes
Total mass: 9 880 kg
With lighter components, truss an be suspended by cables from a super
structure and this will futher emphasize the affect of lightness. Pathways
and pedestrian bridges will seem to over in the spaces above, and
without heavy columns, movement will be facilitated and the spatial
emphasis will be on thiness and lightness.
16 helixes
Total mass: 10 260 kg
8 nodes
improves the
even distribution
of forces to the
nodes
With a combination of carbon fibre components, the overall affect of the
entire structure will markedly transformed from something that might
have appeared mechanical and heavy, to a building that appears light
and thin.
16 nodes
distributes the
forces even better
when compressed
12
Schematic section of a possible cross-member lattice column connected
by an angled pin joint attatched to a CFRP strip. The strip is then bolted
throught the concrete topping to another strip which is fastened to the
underside of the beam.
Jordan Yerbury
Lightness structure
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