Experimental Seismic Testing of Hypar Shell Structures

The Experimental Seismic
Testing of Hypar Shells
by
Daniel Balding (CTH)
Fourth-year undergraduate project
Group D, 2012/2013
"I hereby declare that, except where specifically indicated, the work submitted herein
is my own original work."

The Experimental Seismic Testing of Hypar Shells
Daniel Balding, St Catharine’s College
1
Table of Contents
1 Introduction........................................................................................................................2
Project Proposal...........................................................................................................21.1
Motivation for the Hypar Roof....................................................................................21.2
Motivation and Objective............................................................................................31.3
2 Hypar Roof Design ............................................................................................................3
Hypar Shape and Background.....................................................................................32.1
Current Uses of Hypar Roofs......................................................................................52.2
Previous Testing..........................................................................................................62.3
3 Procedure and Methodology..............................................................................................7
Materials to be used.....................................................................................................73.1
Shell Properties ...........................................................................................................83.2
Hypar Properties..........................................................................................................93.3
4 Materials testing.................................................................................................................9
Reinforcement Mesh ...................................................................................................94.1
Latex Modified Concrete ............................................................................................94.2
Fibreglass Mesh Reinforced Latex Modified Concrete ............................................104.3
Results.......................................................................................................................134.4
Implications for Full Structure ..................................................................................194.5
5 Hypar Test and Results....................................................................................................21
The Structure to be Built, Scaling and Post Loading of Structure ............................215.1
Construction ..............................................................................................................225.2
Experimental Equipment...........................................................................................255.3
Experimental Procedure............................................................................................265.4
Predictions.................................................................................................................285.5
Results.......................................................................................................................285.6
Discussion and Implications......................................................................................365.7
6 Conclusions......................................................................................................................41
General Implications of Research .............................................................................416.1
Specific Conclusions.................................................................................................426.2
Further Testing..........................................................................................................436.3
7 References........................................................................................................................44
8 Appendix..........................................................................................................................45

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1 Introduction
Project Proposal1.1
TSC Global is a charity organisation that works to develop a sustainable form of housing in
countries where living conditions are poor, either through the effects of a natural disaster or
economic hardship. For several years now they have been utilising hypar roofs - whose name
originates from the hyperbolic paraboloid shape of the surface - to provide the basis of this
housing, however recent work in seismically active areas has prompted concern for the
resilience of the structure to dynamic loading. For this reason it was decided to attempt to
further determine the strength of the structure to help justify its continued use.
Motivation for the Hypar Roof1.2
TSC Global promote the development ethic of roof first housing, and see this as the quickest
and most sustainable method of delivering shelter to many in a short amount of time. This
concept works by building simple roof structures and supporting them on basic corner posts,
before any other building work takes place. This gives the inhabitants immediate shelter from
rain and intense sun, and allows them to use local techniques to construct temporary and then
permanent none load bearing wall structures as and when required.
The desirable attributes of the roof can be linked directly to the conditions in which the
structures are to be implemented. In general the economic climate will be poor - a key reason
for the requirements of the houses - either through lack of state support or natural disaster.
There will also be little or no construction equipment or training for the work force for
similar reasons, thus requiring a simple, cheap and repeatable solution. Further to the local
conditions, for the roof first method to be effective the roofs themselves must be quick to
construct, as the key benefit is the speed at which shelter can be delivered. The structure must
also be light, allowing for them to be constructed on the ground, and manually lifted onto
simple, small foundation supports. Finally the roofs must be strong and durable to provide a
protective and sustainable solution which must be a considerable improvement to living
conditions before. The thin shelled hypar roof structure is a good fit to the above
requirements with its simple construction sequence and use of readily available materials.

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Motivation and Objective1.3
TSC Global have utilised the hypar design in many projects around the world including cases
of resettlement after natural disasters. A recent case of this is the resettlement of communities
following the Haiti earthquake in 2010 and due to the nature of the disaster, further
requirements of the construction were to have resilience to any future earthquakes. Whilst the
original designers of the hypar roof claimed that the shell would perform well under dynamic
loading, this has never been tested or quantified, and the failure mechanisms of the roof
structure were unknown. The primary objective of this project is thus:
To determine the resilience of a typical hypar roof to seismic loads, and to determine the
failure modes of the structure when a critical dynamic load is reached.
This will be done firstly by finding the material properties of key materials used in
construction, including analysis of how the concrete shell of the structure could fail. A half
scale hypar roof will then be excited using real earthquake records until failure occurs.
Specific objectives are to:
 Identify typical failure mechanisms in the material used for the roofs shell
 Find what peak ground acceleration causes first and final failure of the hypar
 Identify the fundamental mode and frequency of the hypar
 Quantify the dangers faced to the structures inhabitants should an earthquake occur
2 Hypar Roof Design
Hypar Shape and Background2.1
The word hypar was first used by Heino Engel in his 1967 book “Structure Systems” [1] and
originates from the roofs shape – a hyperbolic paraboloid – which is formed when a square
frame covered with a flexible fabric is twisted from two opposing sides. This results in a
doubly curved surface, with parabolas being created in both diagonal directions. A specific
property of the hypar shape is that a line on the surface of the fabric between equal points on
two opposing edges of the structure will remain perfectly straight, regardless of the extent to
which the frame is twisted. This can be seen in Figure 2.1 and allows the shape to be created

4
by completely rigid members spanning in two directions – a feature which is utilised in the
construction of the structure. A typical roof is formed by four hypar surfaces constructed onto
a square based frame creating a curved pyramid structure with side lengths ranging between
three and eight metres.
The first noted use of a structure based on the hyperbolic paraboloid was by Felix Candela, a
Spanish Engineer who worked with concrete shell structures predominantly in Mexico in the
1950’s [2]. His work on doubly curved surfaces or saddles was based on the principle of
tension and compression cables and arches, removing the need for bending capacity in thin
walled shells. Whilst this effect can be generated using a variety of shell shapes and
geometries, it was identified by Candela that the hyperbolic paraboloid provided by far the
easiest and most practical construction method. This is due to the straight lines inherent in the
shape, allowing simple and rigid formwork to be made from straight members as can be seen
in Figure 2.2. Examples of Candelas early work utilising hyperbolic paraboloids are the El
Altillo Chapel in Mexico City, and Rio’s Warehouse which utilises a typical hypar form
upside down as an ‘umbrella’ also in Mexico City [2].
The first evidence of the use of a hypar form as housing comes from George Nez, an
American urban planner who pioneered the ‘roof first’ resettlement strategy. The first case of
this methodology utilised normal metal roof construction in the relocation of villages from
the Volta reservoir region in Ghana. He worked on the design of a thin shelled hypar
structure for relocation as it was seen as a cheaper and quicker alternative to building metal
truss roofs, and could be fabricated on site from raw materials without the need for factory or
pre-casting procedures. A series of hypar surfaces and roofs were constructed in 1984 in
Mclean, Virginia [3] and subsequently tested for strength to justify the structure suggested by
Nez. Following the results of this testing, further structures were built using the same
construction methods, including an example at the University of Colorado, Boulder [4].
The construction of these hypar structures begins with a square based pyramid wooden frame
as seen in Figure 2.3a). A reinforcing material, most commonly a fibreglass mesh is then
attached in strips onto a face and layered in alternating directions. This utilises the shape
property specific to the hypar that it can be formed by straight rigid members in two
directions and thus these mesh strips remain straight and taught in all directions. Finally a
latex modified concrete is painted onto the reinforcing mesh in a series of layers, until the

5
thickness reaches roughly 10mm. The latex admixture in the concrete improves the roof
structure in several ways. The admixture is known to increase the tensile strength of the
concrete allowing the shell to be more ductile, and it also gives the concrete shell additional
waterproofing properties. The latex also gives the concrete mix added viscosity, such that it
can be painted onto a reinforcing mesh and will hold the mesh during the first layer of
concrete application. A completed structure can be seen in Figure 2.3b).
Current Uses of Hypar Roofs2.2
Over the past ten years, the roofs have been utilised by a range of organisations in a variety of
places around the world including Afghanistan (for an NGO by George Nez), Romania, Peru,
Tanzania and Kenya (TSC Global). The wide variety of locations in which the structures
have been used has led to significant variations in construction sizes and materials, however
the construction method and face shape have stayed relatively constant.
Figure 2.3 – Hypar roof structure in Haiti for BBBC expositions a) Hypar roof frame with
fibreglass mesh being applied b) Complete hypar roof structure (Images courtesy of TSC
Global)
Figure 2.2 –Sketch of formwork for Candela’s
Rio Warehouse [13]
Figure 2.1- Hyperbolic paraboloid
formed by square grid [14]

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The first aspect of the roof which has seen significant variation is the wooden frame on which
the shell is supported. Whilst typical design would utilise sawn timber, the economic
conditions of the area and the availability of cheap and local materials often results in
alternatives being used. In areas of natural disaster, it has been preferred to recycle wooden
members of varying shapes and sizes from damaged and collapsed structures, whilst in other
cases, local bamboo has been used to construct the frame [5].
The typical material used to reinforce the concrete shell is a fibreglass render mesh however
in many locations this is not widely available. The material used must be flexible in order to
take the shape of the hypar and have sufficient tensile strength to provide reinforcement. In
certain cases, rolls of chicken wire have been used where fibreglass mesh is unavailable and a
cotton cloth is then sewn to the wire in order to hold the first layer of concrete.
The mix design for the concrete to be applied also has had significant variation. All mixes
have contained a latex additive, however the form of the latex and the proportions have
significantly varied, with both powdered and liquid latex additives, and even a latex based
paint used. The concrete mix itself is very difficult to control with many types of cement and
sand available in different areas. The water content of each mix is also dependant on the
desired workability and thus can vary dramatically between projects.
Previous Testing2.3
As mentioned previously, a limited amount of testing has been completed of the hypar roof
design to indicate the strength of the structure. The main bulk of this was conducted at the
Fairbanks-Turner Highway Research Centre of the Federal Highway Administration in
McLean, Virginia, and was conducted by Evan Curtis [3]. The tests to be done were on a
single specimen equivalent to a single face of a 6mx6mx1.3m tall hypar with shell thickness
of 25mm. The structure was loaded equally across its surface with sandbags, and eventually
failed in shear at a pressure of 4.7kPa [3].The implications of this test were that the roof shell
was suitably strong for all applications as it was very unlikely to experience this load in the
field.
In parallel to this project, Seth Carlton, a Masters student from the University of Oklahoma is
also completing work on hypar roof design. In particular, Seth is looking at the effects of the
proportions of latex admixture to the strength of the concrete in the hypar and aiming to

7
optimise the mix design to reduce the raw material cost whilst maintaining sufficient strength.
Whilst the results from this work will not be published until after the completion of this
project, assistance in the material choice and hypar fabrication has been sought as referenced.
3 Procedure and Methodology
In order for the results of experiments conducted to be relevant and comparable with the vast
range of hypar designs currently in existence, the specifications of the structure and its
materials were found and documented. This will enable the comparison of both current
structures and future design proposals to be put in context with the results generated. For this
reason, design decisions were made as typical as possible and the implications of these made
clear.
Materials to be Used3.1
3.1.1 Concrete
As with most hypar roofs, a normal concrete mix was supplemented with a latex additive to
enable the mix to be painted onto the reinforcement material whilst providing further strength
and waterproofing properties as mentioned in section 2. It was decided to use a liquid latex
produced by the Wykamol group [6], which is generally available as a typical bonding agent
and admixture for portland cement mortars and concrete. The product data sheet for this
material can be found in the Appendix. The admixture contains 25% latex solids with the
remaining 75% water [7], and these proportions were taken into account when creating a mix
by weight of 1:0.5:0.1 – Water: Cement: Latex. This mix design was found using a
combination of information from previous work done by TSC Global, advice from Seth
Carlton, and small test samples applied to the reinforcement mesh. (Note: at the time this
decision was taken, work by Seth Carlton was at a preliminary stage.)
The cement product used was a type II ordinary portland cement. This is readily available
throughout the world and a common base for previous hypar roofs. The rapid hardening
nature of type II portland cement means that the time allowed for drying between application
layers of the mix must be small. This is to ensure that there can be sufficient chemical
bonding between layers preventing possible delamination during loading of the thin shell. In
this process a maximum time lag between layers of 24 hours was used.

8
3.1.2 Aggregate
Due to the thickness required for the shell, a maximum aggregate size of 0.6mm was used
such that the aggregate will not span the full depth of any layer preventing a good bond being
created. The sand used was well graded to give strong interlocking within the concrete, and
will be added only to the central layers of the mix, ensuring a smooth finish both on the
internal and external faces. The larger particles of sand will also provide sufficient
interlocking between layers to create a cohesive material and facilitate interlayer bonding.
3.1.3 Reinforcement
The most representative and common type of reinforcement material is a fibre glass mesh,
which gives good strength properties and does not require an additional sheet material in
order to hold the first layer of concrete such as would be the case if chicken wire was used.
The Textile Technologies product used was a typical external render reinforcement fibreglass
mesh with an aperture of 4mmx4mm. The strength properties for this mesh are relatively
unknown and thus basic materials testing will be carried out in order to quantify its strength,
and stiffness. The data sheet provided with the reinforcement can be found in the Appendix.
3.1.4 Frame
The frame structure is most typically built with any available timber given in the region and
thus would normally be of average to poor quality. For this reason a rough sawn standard
joinery redwood was used. This was acquired at a nominal size of 25mmx75mm section
which relates to half the dimensions commonly used for a full scale structure for reasons to
be discussed later [5].
Shell Properties3.2
Considering the above material specifications, a prediction could have been made on the
performance of the shell in simple loading cases. However, due to the relatively unknown
behaviour of the mesh reinforcement within a concrete structure, the small depth of the shell
being used, and the unusual staggered method of applying the concrete, the behaviour of the
material under loading needed to be considered more accurately. For this reason, testing of
the material properties of the shell particularly in bending was completed using the same
construction method for the samples as was used for the final structure.

9
Hypar Properties3.3
With a sound understanding of the materials being used, and their performance relative to
alternative hypar construction methods now gained, a full test was carried out on a square
based hypar roof by exciting it dynamically from its base. The testing was to continue until
complete failure occurred, allowing for the mode of failure of the structure due to dynamic
excitation to be found. The frame design and dimensions of the roof were in accordance with
the guidance from TSC Global on the construction around a typical wooden frame as given in
the Appendix, as this provides a good match both to current hypar structures and to future
design specifications. The roof structure was securely connected to a testing sled at each of
the four mid-spans as this represents the most typical load bearing system in design. This
supporting case also gives the least resistance to overall deformation of the roof, ensuring the
fundamental collapse mode could be found during testing.
Due to limitations in the size of testing equipment and the laboratory space, the testing was
completed on a half scale model of a full hypar roof, with each length scale reduced
accordingly. Adjustments were made to the loading cases exerted on the structure in order
for the results to be equivalent to that of a full scale hypar roof as discussed later.
4 Materials Testing
Reinforcement Mesh4.1
In order to test the tensile strength of the fibreglass reinforcement, samples of one, five and
twenty strands of the mesh were clamped at either end, and extended using a constant
displacement rate testing sequence on an Instron testing machine. Samples were tested at
constant initial length of 180mm and extended at 5mm/min, with the twenty strand sample
being folded in four to fit in the testing apparatus. The mesh itself has a different structure in
orthogonal directions, and thus the test was carried out in both directions, referred to as
length and width meaning along the length of the roll that the mesh is supplied on and across
the 1m width of the role respectively. The testing apparatus can be seen in Figure 4.1.
Latex Modified Concrete4.2
The compressive strength of the composite material can be assumed to come from the latex
modified concrete alone. Cubes were poured of concrete both with and without added

10
aggregate. This is done to account for the first and final layer of the concrete which are
applied with no aggregate. These cubes were then tested in compression after 28days using a
constant load rate testing procedure. The cubes had edge length 50mm, and were tested at a
compression rate of 900N/s [8].
Fibreglass Mesh Reinforced Latex Modified Concrete4.3
4.3.1 Fabrication of Samples
For the testing of the final shell material, two thicknesses of sample were created. The first
was 10mm in thickness as suggested by TSC Global for a full scale roof [5], and the second
at half this thickness (5mm), equivalent to that which will be used in the half scale model.
This allowed the comparison of how a normal shell thickness would perform compared to the
half scale shell which will be used in later tests. The results of this can then be used to justify
the results of the final roof test in regards to previous and future structures.
When creating the required samples for testing, a similar procedure to the final roof must be
followed for forming the concrete. To do this, two wooden frames were constructed and the
fibreglass mesh stretched across the frame in orthogonal directions. The mesh was then
stapled at regular intervals to the underside of the wooden frame, during which care was
taken to ensure that each stand of the mesh was suitably taught to keep the mesh flat against
the surrounding strips. For the full scale 10mm thick concrete sample, four layers of mesh
were created (strips overlapped by 50% on both sides effectively doubling thickness of mesh)
whilst only two layers were used for the half scale model (strips only overlapped by 10mm).
As with the final structure this was applied in alternating direction strips creating a weaving
pattern to hold the layers of mesh together.
Figure 4.1 – Testing apparatus for fibreglass mesh tensile test

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The first layer of concrete was then made up using the ratio of 1:0.5:0.1- Cement: Water:
Latex by weight with no aggregate, and applied to the mesh using a brush onto both the top
and bottom surface. This first layer was to hold to the mesh, bridging most of the holes in the
fibreglass, however there is often considerable waste of material at this point. A relatively
smooth finish was obtained particularly on the bottom surface, with any drips that began to
form removed.
Sufficient time was given to allow the first layer to dry, however this must be less than 24
hours to prevent a cold joint forming between layers where there is insufficient bonding. The
process is then repeated for each layer up to layer five with the material ratios used as
depicted in Figure 4.2. The time gaps actually left between each layer ranged between 7 and
18 hours. Small amounts of layer two were applied to the bottom surface to ensure all gaps in
the mesh were filled and a smooth surface was achieved but all other layers were built up on
the top surface only. After layer five, the thickness of the shell was measured to ensure the
desired thickness had been achieved. If either sample (either 5mm or 10mm thick sample)
was still too thin after five layers, the fifth mixture could be repeated until the desired depth is
achieved, with layer six applied to smooth of the surface and cover all aggregate. In this case,
layer five was repeated for both thickness samples and a note made to apply more concrete
per layer in the final structure. The temperature that each layer was applied and set at was
held relatively constant between 140
and 190
C, and the humidity was typical for Cambridge
in a dry November.
After the samples had been left to cure for 28 days, they were cut into individual beam
samples. This was done using a high pressure water jet cutter, utilising a CAD file detailing
the size and shape of required samples.
4.3.2 Testing of Samples
The key property required of the shell material is its flexural strength. This is found using the
standard test method for flexural properties utilising four point bending [9] in both hogging
and sagging modes. This was again done using a constant deflection rate test method as
detailed by the standard, with a deflection rate of 7.5mm/min. The rig itself utilised an Instron
machine with layout as depicted in Figure 4.6. The distance between supports in the 10mm
thickness case was 300mm with a separation of 150mm for the loading bars. These

12
measurements were halved for the 5mm thick sample to mirror the final half scale model and
to keep deflections of the sample reasonable. The advantage of the four point bend test is the
creation of a constant moment region in the central span where no shear force is present. This
enables failure to occur by pure bending, allowing accurate calculation of the section
properties of the material.
Layer
Water by
weight
(kg)
Latex by
weight
(kg)
Cement
by weight
(kg)
Sand
weight
(Kg)
1 0.5 0.1 1 0
2 0.5 0.1 1 0.3
3 0.5 0.1 1 0.8
4 0.5 0.1 1 1
5 0.5 0.1 1 1
6 0.5 0.1 1 0
Figure 4.2 – Material ratios for concrete layers as recommended by TSC Global (see
Appendix)
Figure 4.3 - Test sample with first layers of
fibreglass mesh
Figure 4.4 - Test sample during application
of first layer
Figure 4.5 – Test samples cut from frames Figure 4.6 – Test rig for 4 point bend

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Results4.4
4.4.1 Reinforcement Mesh
The results for the tensile testing of the strands in the reinforcement mesh can be found in
Figures 4.9, 4.10 and 4.11. The single strand data gives a good indication of the stiffness of
the mesh with the average gradient of length strands of 26.1 N/mm and width strands of 38.6
N/mm. The results for multiple strand tests are largely influenced by the number of strands
engaged in tension during a given stage of the test. This leads to a large variety of perceived
stiffness values as well as a large range in ultimate load. Width strands tested in fives
consistently achieved above 500N of load before total failure, however tests on the individual
strands did not consistently reach 100N which would equate to the equivalent stress across
the samples. Results on samples of twenty strands are equally varied and visual observations
during testing show that the gripping procedure was not appropriate for the larger sample
size.
The gripping procedure at either end of the test sample involved the tight compression of
metal plates against the fibreglass mesh. Most failures during the tests occurred at this
location suggesting the contacts were causing a weakening or pinching of material at this
Figure 4.7 – Final cut out 5mm test sample
Figure 4.8 – Final 5mm test sample section

14
point. This is particularly prevalent with only one fibreglass strand due to the pressure
required to restrain the sample. As mentioned previously, the best results were obtained
during the five strand experiment where a high proportion of the sample was engaged in the
test, and the weakening effects of the grips were reduced. The average load which can be
carried by each strand is therefore assumed to be 100N in the width direction and 40N in the
length direction, however it is envisaged that the actual load which could be carried within a
concrete substrate may be considerably more.
0
20
40
60
80
100
120
140
0 1 2 3 4 5 6 7 8 9
Load (N)
Displacement (mm)
Length tests
Width tests
Figure 4.9 – Fibreglass mesh tensile test – single strand
0
100
200
300
400
500
600
700
800
0 2 4 6 8 10
Load (N)
Displacement (mm)
5 Strands - Length
5 Strands - Width
Figure 4.10 –Fibreglass mesh tensile test – 5 strands

15
4.4.2 Cube Test
The compressive cube strength of the latex modified concrete with sand aggregate was found
to be fcu = 31.9Mpa and the samples made with no aggregate found as fcu = 38.41Mpa. The
mean 28 days strength given for type II portland cement with no aggregate by the portland
cement association is 42.1Mpa [10] thus making the results obtained reasonable in
comparison as the latex additive is not expected to have a considerable effect on the
compressive strength of the concrete. The samples with no aggregate yield a higher
compressive strength than those with aggregate, however the thickness of this layer within
the shell is small compared to the overall section. The average cube strength will thus be
assumed equal to the sample with aggregate as this provides a conservative estimate of
compressive strength.
4.4.3 Predictions for Flexural Properties
In order to estimate the ultimate moment capacity of the sample, it is assumed that the
concrete in compression will be fully yielded and that the effective depth to the centre of
reinforcement is 0.9d as seen in figure 4.12. The maximum moment capacity of the two
samples is thus:
0
500
1000
1500
2000
2500
3000
3500
0 5 10 15 20
20 Strands - Length
20 Strands - Width
Displacement (mm)
Load (N)
Figure 4.11 – Fibreglass mesh tensile test – 20 strands

16
10mm Thick Sample
Compression zone = 0.45d = 4.5mm
Width of samples = 50mm
Load carried in compression = A.0.6fcu = 0.45x10x50x0.6x31.9 = 4306.5N
Distance between compression and tension centres = (0.45+0.45/2)d = 6.75mm
Maximum moment capacity =Load x Distance = 29.1Nm
5mm Thick Sample
Maximum moment capacity = 7.27Nm
4.4.4 Flexural Results and Discussion
The 10mm thick samples extended a considerable distance under loading before failure
occurred at the values indicated in Figure 4.13. The eventual failure mode was of shear
failure at 450
to the horizontal, combined with separation of the concrete and reinforcing
mesh at this point as can be seen in Figure 4.15b). This is believed to occur by firstly the
tension at the bottom of the sample straining the reinforcement mesh, and this tensile load
causing micro-cracking in the concrete. This can be seen in the load extension curve by a
change in gradient occurring at roughly 150N load and is supported by the hogging test
completed on the sample (as discussed later) which gave failure in tension of the concrete at
147.7N. These micro cracks grow as the sample is further loaded and begin to contribute to
the delamination of the reinforcement. Finally the load increases close to the shear capacity
of the sample, and the presence of the micro cracks facilitate the total shear failure of the
sample by extending diagonally across the sample in one location. During this, the
reinforcing mesh completely delaminates from the concrete locally around the failure site.
The average max load resisted by the samples that failed in shear is 931.7N giving a
maximum shear force through the sample of 465.9N. This corresponds to a moment of
34.9Nm which is larger than that predicted in section 4.4.3, despite failure not occurring in a
typical bending mode.
Figure 4.12 – Section properties of sample

17
The 5mm sample also showed considerable deflection during loading with final failure due to
local crushing of the concrete in the compression layer combined with a separation of the
reinforcement mesh in the tensile layer as seen in figure 4.16. Whilst no visible change in the
force extension graph indicates the onset of micro cracking as with the thicker section, the
moment induced in the sample indicates that the concrete surrounding the reinforcement
mesh should have failed in tension which would lead to such cracking. Final failure occurred
between 198N and 286N in the same mode for each sample tested, with an average moment
at failure of 6.1Nm. The separation of reinforcement at the bottom of the sample is only
evident for one of the two mesh layers. This suggests that the bottom layer does not
contribute to the strength of the sample due to insufficient cover and that the tensile bending
force is only taken through one mesh layer. If this were the case, using an assumption from
4.4.1 that each strand of mesh could hold 100N, failure in bending would occur by the
snapping or yielding of the tensile reinforcement at 4.6Nm. As both the crushing of concrete
in the compression layer, and a failure in the tensile reinforcement may lead to the other
failure occurring when the sample finally breaks, it is difficult to judge to actual failure
mechanism of the sample, however, it is clearly caused by the bending load and not a shear
failure as in the 10mm sample.
The deflections of both samples before failure were considerable as shown in Figure 4.17 and
many samples showed considerable ductility in failure. The deflections of the 5mm sample
were such that the points of loading changed considerably due to the rounded loading device.
The effects of this are considered negligible as the samples had reached plateau before the
magnitude of this change would affect the moment being applied significantly. As expected
the beam showed considerably smaller resistance in hogging due to the poor performance of
concrete in tension, with the average moment resisted by the 10mm sample being 5.54Nm.
Using the sample section properties, this indicates that the concrete failed at a tensile strength
of 6.65Mpa.

18
0
50
100
150
200
250
300
350
0 5 10 15 20 25 30 35 40 45 50
Load (N)
Displacement (mm)
5mm Sample 1
5mm Sample 2
5mm Sample 3
5mm Sample 4
5mm Sample 5
Figure 4.14 – Four point bend results of 5mm thick sample
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30 35 40 45
Load (N)
Displacement (mm)
10mm Sample 1
10mm Sample 2
10mm Sample 3
10mm Sample 4
10mm Sample 5
Figure 4.13 – Four point bend results of 10mm thick sample

19
Implications for Full Structure4.5
The results of these material tests will ensure that the full hypar test results can be quantified
against current and future uses of the hypar roof. The compressive strength of the Latex
modified concrete is typical for most cases due to basic cement being readily available
Figure 4.15 a) and b) - 10mm sample failure by four point bend
Figure 4.16 a) and b) – 5mm sample failure by four point bend
Figure 4.17- Deflections during testing before failure a) 10mm sample b) 5mm sample

20
around the world, whilst the tensile results of the reinforcement mesh should provide easy
comparison with other materials available.
The Large deflections experienced during testing and the considerable ductility of the
samples is a positive result, suggesting that the final structure could sustain significant
displacements in a given mode shape before complete failure of the shell will occur.
Furthermore the relatively low stiffness of the material may lend itself to increased overall
strength of the shell due to the resistance of loads under deformed shapes as utilised by
tensile structures.
The final indication this testing gives us is the relationship between the behaviour of the full
and half scale shell thicknesses. The prediction for the reduction in bending moment gives a
fourfold reduction in maximum capacity, with test results giving the factor between the
average peak moment capacity of 5.16 (31.6Nm/6.1Nm). The reason for this greater disparity
is assumed to be due to the lower capacity of the half scale samples than predicted which
could be caused by the magnification of irregularities in the sample due to the smaller overall
thickness. For example, if the variation in thickness of the sample is 0.5mm due to the
fabrication technique, then this represents an error of +/-10% for the half scale model, and
only a +/-5% error in the full scale sample. This effect would be further heightened when
considering moment capacity, as the peak capacity is dependent upon the square of depth
when failure is assumed in crushing of the compression concrete. A further reason for the
reduced capacity could be the greater effect of local load concentrations on the thinner
sample. This occurs at the points of loading, where due to the small area of load application, a
build-up in stress may occur in the concrete on the top surface. As the sample is half the
thickness, this zone may take up a greater proportion of the sample section, causing a greater
reduction in capacity relative to a full scale sample. This is supported by the fact that failure
in the 5mm samples occurred close to or at the point of load application.
The effect of this disparity between the half scale model and its full scale equivalent may be
reduced in the full structure due to the lack of direct load application points, however any
effects upon the final results will give a conservative estimate for the final failure load, and as
such can be tolerated.

21
5 Hypar Test and Results
The Structure to be Built, Scaling and Post Loading of Structure5.1
For the final test, the structure was built to the specifications from TSC Global as shown in
the Appendix which has been used to create hypar roofs most recently in Bangladesh. The
frame structure is designed to be very robust with significant amounts of bracing to the roof
base as can be seen in the Appendix, which is often utilised to create a second story within
the hypar roof. The 6m square frame was reduced to a 3m square frame creating a half scale
structure and the vertical height of the Apex reduced from 3m to 1.5m.
In order for the results from the half scale structure to be equivalent to that of a full scale
hypar, the loading conditions for the test were increased. The failure of the structure is caused
by stresses induced within the shell and these stresses scale with area (normally measured in
N/m2
). As the dimensions of the structure will be reduced in three dimensions, this will
change the loading conditions caused only by self-weight in proportion to a volume. This
disparity means that the loading conditions on the final test structure should be doubled. The
justification for this can be found by considering a simple beam in bending, and is considered
in the Appendix.
For this reason, a method was required to either double the density of the shell, or apply a
load equal to the mass of the structure equally over the roof. Doubling the density of the
structure would clearly have involved a change to the material properties of the shell and thus
this was ruled out. Important considerations for the final method to be used were that any
applied masses should be well distributed across the surface of the structure to ensure that
there was no consequential effect on the mode shapes. Further to this, there must be
significant gaps between any applied loads, such that any cracking failure in the shell can
occur without being prevented by strengthening due to stiff masses applied over large surface
areas.
A variety of solutions to this were considered and assessed for their viability and effects on
the performance of the structure. One suggestion was for steel ball bearings or similar small
masses to be imbedded into the final layer of the structure providing very good control over
equal distribution of the load across the shell. Another method considered was for additional
concrete to be poured into a grid mesh on the surface of the hypar, thus adding mass whilst

22
allowing failure of the shell to occur where the grid has prevented concrete from being
applied. These methods along with others were rejected due to insufficient connection and
stability of ball bearings, and the difficulty in fitting a grid onto the hyperbolic shaped roof
respectively.
The final solution reached was to attach full or part household bricks to the surface using a
combination of brick mortar and tile adhesive. This method was simple to execute and
allowed sufficient control of the equal distribution of load over the surface, whilst providing
large enough gaps in between bricks for full failure of the shell to occur. The attachment of
the bricks to the surface was designed to be strong enough such that the bricks will not break
of during dynamic loading, and was a major concern for the health and safety assessment for
the final test.
As only one hypar roof was built, and the testing rig only allows excitation of the structure in
one axis, a decision was required as to which orientation the roof should be tested. If the
hypar was excited perpendicular to one edge of the square base, each face of the structure
would be at 450
to the axis of excitation and would act in a combination of shear and bending.
If the hypar was excited parallel to a diagonal of the base, two faces would be loaded in
shear, and two faces would be excited in bending. As failure is predicted to occur in bending
of the structure, the structure was aligned along a diagonal of the base such that the
fundamental mode shape of the face in bending will be directly excited. This can be seen in
figure 5.1a)
Construction5.2
In order to create a final structure which was representative of previous structures constructed
and in line with future designs, help was provided by Seth Carlton to ensure details in
construction techniques and tolerances could be followed. The frame structure was built as
close to specification as possible, with further details of joint fabrication where required
sought from an experienced carpenter. Where design details were still unknown, such as the
connection design of the frame apex, sensible layouts were proposed to ensure the strength of
the frame. These can be seen in Figure 5.1 b) and c).
Due to the nature of the hypar frame shape, the reinforcement mesh strips had to have an
increasing overlap between the slanted frame units and the base as seen in figure 5.2a). This

23
overlap was kept consistent with each strip, to provide a uniform reinforcement across the
full structure. The nature of this increasing overlap means that there was additional mesh
reinforcement in the lower sections of the hypar.
During the application of the first concrete layer, much of the mix was pushed straight
through the mesh material and thus application was done from both sides of the mesh. Large
amounts of material were lost during this initial process, and thus care was taken to apply the
concrete in a way in which it held the mesh and filled as many of the gaps as possible. This
problem was particularly distinct as only two layers of mesh were present due to the reduced
scale, whereas in full structures, four layers of mesh would be used resulting in significantly
less wasted material. The second layer was applied after roughly fifteen hours, and filled all
remaining holes in the shell by application on both sides where necessary, whilst also
beginning to build up the thickness of the shell. Layers three to five were where the main
bulk of material was applied to the structure, facilitated by the first two layers having gained
sufficient strength to hold the hypar shape provided by the reinforcement mesh. The final
layer provided a smooth finish and took the shell to 5mm thickness or above. The concrete
was mixed in a maximum batch size of around seven or eight kilograms, and was applied
within fifteen minutes of mixing. This was to ensure a good and equal consistency of material
was applied, as aggregate was likely to settle in the relatively fluid mix as well as to prevent
the concrete beginning to set creating a thick and unworkable mix.
After 28 days of curing, additional loads could be added to the structure in order to account
for the scaling of the hypar as mentioned in 5.1. The household bricks acquired were secured
using a normal brick mortar to the lower regions where the bond strength needed was small.
As the tests will use earthquakes up to a maximum of 2.1g, the peak lateral load on a
particular brick will be 2.1g times the mass of the brick, and thus should not require
significant bond strength. For the upper regions of the hypar, a more expensive tile adhesive
was used in order to hold the bricks to the shell surface, which had a considerably shorter
hardening time, thus allowing the bricks to be fixed to the near vertical surface without
sliding off. The total mass of the structure was first estimated by summing the mass of the
concrete applied to the shell, and confirmed by balancing the structure on just two supports
and mounting a load cell under one of these. The total mass of the structure was found to
measure 167.5kg, and subtracting the mass of the wooden base of the frame (as this would

24
not contribute to the loading of the shell of the structure) the final shell mass was found to be
120.8kg. As such 40.2kg of bricks were distributed equally over each face of the structure.
Figure 5.1 a), b) and c) - Frame construction
Figure 5.2 a) and b) – Reinforcement mesh construction
Figure 5.3 a), b) and c) – First layer of concrete

25
Experimental Equipment5.3
The hypar itself was mounted on a sled which rolled smoothly on single axis bearings. The
sled was made up of two channel sections welded onto a rectangular steel frame. At each end
of the channel sections, thick steel angle connection brackets were fitted corresponding to the
four mid edge joints of the hypar as shown in both Figure 5.1 and 5.8 and located such that
the structure was restrained tightly in each lateral direction. The wooden frame was then
bolted to the angle sections through pre-drilled holes, and secured using fabricated plate
washers, thus preventing any vertical movement of the structure and further fixing it to the
sled. The strength of these connections along with the overall stability of the structure under
testing is considered in the appendix.
The hydraulic jack which was used to excite the sled is linked to a servo hydraulic pump and
controlled using a computer running lab view software. The pump is calibrated to take an
input between 0-5V and is controlled using displacement feedback from a laser transducer.
Figure 5.4 – Part dry after third layer Figure 5.5 - Complete hypar roof
Figure 5.6 – Hypar with brick loading

26
The jack is rated at a maximum dynamic load of 18.9kN and has a maximum stroke of
150mm. The servo hydraulic pump has a maximum working pressure of 3500psi (~240bar)
and is able to deliver fluid at a maximum rate of 33.3litres/minute. The implications of these
limits will be considered later.
Experimental Procedure5.4
The final testing of the hypar roof was through progressive incrementing of earthquake tests
until total failure occurred. Three test earthquakes were prepared using recordings from real
earthquakes namely Kobe 1995, Imperial Valley 2010 and North Ridge 1994 [11]. These
records were then scaled in the time domain such that the displacements could be reduced by
a half to yield the same accelerations as the initial earthquake. The displacements were then
scaled to give earthquakes with peak accelerations at intervals of 0.1g. As the accelerations
applied to the structure increased, the earthquake files became limited by the stroke of the
jack. For this reason, the records were further reduced in the time domain to increase the
accelerations for given displacements, allowing results up to roughly 2g to be generated.
Should the structure withstand excitation by earthquake records at 2g, the fundamental
frequency of the structure was to be found, and the structure excited by a sinusoid function at
this frequency. For this test, depending upon the value of the fundamental frequency, the
volume flow rate of hydraulic fluid would become the limiting factor as the short time period
requires high jack velocity. For this reason, the largest amplitude sinusoid that could be
accommodated by the pump and jack system was to be used as this will yield the highest
acceleration.
Figure 5.7 – Arrangement of Jack Figure 5.8 – Connection detials

27
Initial testing was carried out on the sled before the structure was attached and loading
equivalent to the full structure was applied to the sled in order to assess the ability of the jack
to produce the required earthquake motion. For this test the displacement and acceleration of
the sled were monitored and compared directly with the earthquake records. The results from
these tests highlighted two issues with the instrument set up. Firstly, when initialising a test,
the jack jumped to the test start value rapidly, causing accelerations of around 1g to be
experienced by the sled. With only one test structure available and its resilience to ground
accelerations unknown at this point, this spike could potentially have caused failure before
the first test was implemented at 0.1g. To counteract this effect, a programme was created to
move the jack slowly to the starting voltage before the test was ran. Further to this the
programme was prevented from running if the variation between initial jack position and
record start value was greater than 0.1V which corresponded to 3mm of jack movement. The
second issue raised was that the sled did not follow the input displacement to the desired
accuracy, such that there was an overshoot by the sled and the correction takes a number of
cycles of a set frequency to reduce the error to zero. This could also be seen as a juddering of
the jack system as it corrected to the desired displacement. To solve this issue, a recalibration
of the signal amplifier was required, with the settings of the gain and integral optimised to
ensure the movement of the sled accurately resembled that of the earthquake record.
In order to identify and analyse the failure modes and key features of the structures behaviour
such as the fundamental frequency, monitoring was conducted for the duration of the tests.
This was done visually by three video cameras, recording a view from both parallel and
perpendicular to the axis of excitation, as well as one view from above and at 450
to the shake
axis to view the movements of the structure overall. As in the sled testing sequence above,
the acceleration and displacement of the sled was also recorded, and logged on a separate
computer to that controlling the sled. Finally, three-axis accelerometers were placed on both
the top apex of the structure, and on the face perpendicular to axis acceleration. This was
mainly to pick up the behaviour and fundamental frequency of both the structure as a whole,
and of the face in bending. The position of the accelerometer on the face of the structure was
also adjusted as and when the face began to show deformation due to dynamic excitation
such that it was positioned on the point of largest deflection.

28
Predictions5.5
Previous to the main testing, small impulses were applied to the structure by gently sliding
the sled into a stiff stopper and by the tapping the shell with a hammer. Results from the
accelerometer on the face of the structure indicated a number of resonant frequencies with the
accelerometer placed at the centre of the face as can be seen in Figure 5.9. This suggests the
fundamental frequency was roughly 20Hz, however this is larger than would be expected for
a structure with a relatively low stiffness shell.
From the ductile nature of failure in materials testing, it was expected that the structure may
have large deformations, but will not fail catastrophically. This is supported by the relative
strength and rigidity of the underlying frame structure.
Results5.6
Early testing of the structure from ground accelerations of 0.3g and upward resulted in visible
deflections upon the faces excited in bending. The mode shape visible was the bulging of the
upper third of the face, combined with the downward bending of the tip of the structure and
vice versa. A diagrammatic of this can be seen in Figure 5.11a) with 5.11b) identifying the
regions in which deflections were occurring. For these lower early records the acceleration of
the apex of the structure is consistently larger than the acceleration of the sled itself and
moves in phase with the sled as seen in Figures 5.12 and 5.13. The acceleration of the face of
the structure is considerably higher than that of the sled, with peaks of above 1.5g for a 0.3g
ground movement as shown in Figure 5.14. The response spectra of both the apex and the
face show considerable spikes at 10Hz whilst the input ground motion has no particular peak
Figure 5.9 – Response Spectra of face due to impulse response from hammer

29
at this frequency. There is no visible damage caused to the structure for these lower
acceleration earthquakes.
Of the three earthquakes tested, there was no significant variation in the results seen at similar
ground acceleration values. The Imperial Valley earthquake had a considerably longer
duration, and thus often greater build up in the deflections was identified, however the most
damage occurred when the peak ground acceleration of each record occurred.
For the subsequent tests, the visible deflections for the mode shape described above increased
becoming more violent with increased acceleration. Small cracks became visible from tests of
1.2g onward at the edges of the faces in bending, particularly in the upper third where the
largest deflections were occurring. The acceleration at the face also increased with larger
ground accelerations reaching +/- 6g for a ground acceleration of 2.1g whilst acceleration of
the apex continued to follow that of the sled.
At earthquake tests of 2.0g and upward, the accelerations of the face began to cause bricks
which had been mortared to the surface to detach and slide away. During a test at 2.1g the
concrete underneath a brick located at a site of peak displacement delaminated just above the
reinforcement layer, and detached completely from the structure as seen in Figure 5.10c).
Delamination also occurred at a site of severe cracking at the edge of a face in bending
leaving the reinforcement layer completely exposed as seen in Figure 5.10a) and b). Cracks
also appeared radially from bricks in the top third of the faces particularly those located in
areas of maximum displacement.
Having identified the frequency of the fundamental mode shape at 10 Hz the structure was
then excited initially at 5 Hz and then at 10Hz using the maximum stroke available given the
testing equipment. This resulted in violent excitation of the mode shape to the extent that the
structure and sled began to bounce on its bearings. Further cracking was seen across the
faces, and a large amount of the bricks attached to the surface became loose and slid off the
structure. Following testing, the regions in which large displacement had occurred had lost
significant amounts of their stiffness due to the cracking of the concrete, however only at two
locations has significant delamination occurred and thus the functionality of the roof been
compromised.

30
Figure 5.11 a) and b) – Fundamental mode shape sketches
Initial Hypar shape
Deformed Hypar shape
Figure 5.10 a) and b) - Cracking and delamination following testing at 2.1g
c) Delamination under a brick at a location of high displacement

31
Figure 5.12 – Acceleration of Sled – Kobe - Magnitude 0.3g
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
0 2 4 6 8 10 12 14 16 18 20
Acceleration(g)
Acceleration on Sled
0.3g
Figure 5.13 – Acceleration of Apex and Sled – Kobe - Magnitude 0.3g
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
0 2 4 6 8 10 12 14 16 18 20
Acceleration(g)
Acceleration at Apex
Acceleration at Face
0.3g
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
0 2 4 6 8 10 12 14 16 18 20
Acceleration(g)
0.3g
Figure 5.14 – Acceleration of Face, Apex and Sled – Kobe - Magnitude 0.3g
Time (s)
Time (s)
Time (s)

32
Figure 5.17 – Acceleration of Face, Apex and Sled – Imperial Valley - Magnitude 0.3g
Figure 5.16 – Acceleration of Apex and Sled – Imperial Valley - Magnitude 0.3g
Figure 5.15 – Acceleration of Sled – Imperial Valley - Magnitude 0.3g
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
0 1 2 3 4 5 6 7 8 9 10
Acceleration(g)
Acceleration of Sled
0.3g
-1
-0.75
-0.5
-0.25
0
0.25
0.5
0.75
1
0 1 2 3 4 5 6 7 8 9 10
Acceleration(g)
0.3g
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5
0 1 2 3 4 5 6 7 8 9 10
Acceleration(g)
0.3g
Time (s)
Time (s)
Time (s)

33
Time (s)
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
0 1 2 3 4 5 6 7 8 9 10
Acceleration(g)
2.1g
-3
-2
-1
0
1
2
3
4
5
0 1 2 3 4 5 6 7 8 9 10
Acceleration(g) Acceleration on Sled
2.1g
-3
-2
-1
0
1
2
3
4
5
0 1 2 3 4 5 6 7 8 9 10
Acceleration(g)
2.1g
Figure 5.18 – Acceleration on Sled – Kobe 2.1g
Figure 5.19 – Acceleration on Apex and Sled – Kobe 2.1g
Figure 5.20 – Acceleration on Face Apex and Sled – Kobe 2.1g
Time (s)
Time (s)
Time (s)

34
Figure 5.23 – Response Spectrum of Face for Kobe 0.3g
Figure 5.22 – Response Spectrum of Apex for Kobe 0.3g
Figure 5.21 - Response Spectrum of Kobe Earthquake

35
Figure 5.26 – Response Spectra at Face for Kobe 2.1g
Figure 5.25 – Response Spectra of Apex for Kobe 2.1g
Figure 5.24 – Response Spectra of Kobe earthquake using time step equivalent of 2.1g

36
Discussion and Implications5.7
The testing of the full hypar roof indicated that the structure has a considerable resilience to
earthquake loading, and fails in a progressive and none catastrophic manor. The fundamental
failure mode was seen in the two faces in bending, and occurred at a frequency of 10Hz. This
frequency was not picked up in preliminary testing as the accelerometer used was been
placed on a node of the fundamental mode shape.
5.7.1 Structure Accelerations
During initial small acceleration testing, the acceleration of the apex of the structure matched
very closely with the input acceleration of the sled, with the apex generally accelerating at a
slightly higher rate. This is caused by the deflections in the apex being larger than that of the
sled due to the elastic leaning of the structure as the sled moves. The implications of this is a
general sway of the structure on top of the sled, however the magnitude of this is fairly small.
The accelerations of the face of the structure were considerably higher than that of the input
acceleration and this is due to the excitation of the fundamental mode of the face of the
structure. This can be seen very clearly in the response spectra of the face in Figure 5.23, with
a significant spike in the frequency response at 10 Hz. It is deemed that this mode is
-8
-6
-4
-2
0
2
4
6
8
10
18.3 18.35 18.4 18.45 18.5 18.55 18.6
Acceleration(g)
Time (secs)
Figure 5.27 – Acceleration of Sled, Apex and Face – 10Hz Sinusoid

37
predominantly a mode shape of the face of the structure and not a full structure mode as there
is no significant increase in the acceleration response at the apex of the structure. A spike in
the response spectra at the apex of 10Hz is also present, however this is deemed to be caused
by the face driving the frame of the structure, with the apex responding elastically to this
driving force.
A spike is also present at 10Hz on the response spectra of the sled, and this is also believed to
be from the fundamental frequency of the structure driving the sled and piston, but at an
amplitude which has no effect on the testing procedure. It was also considered that this
frequency spike could have been caused by the amplifier which controls the displacement of
the jack and would correct the displacement at a specific frequency. This is proved not to be
the case by a preliminary test conducted whereby the sled was loaded with an equivalent
mass and each earthquake ran through the system. Results indicate no spike in frequency
other than those found in the response spectra of the earthquake, and thus this effect can be
deemed negligible.
5.7.2 Structural Damage
As the input ground acceleration increased the accelerations of the face of the structure also
increased with the magnitude of the deflection due to the fundamental mode visibly
increasing. This increase in the deflection can be attributed to the increase in peak excitation
acceleration, but may also be due to the progressive cracking and weakening of the face. As
the displacements in the mode shape increase, the curvatures in the shell during peak
deflection increase, causing cracking of the concrete, particularly in hogging of the shell as
the concrete has relatively low tensile strength. This cracking will present a weakening of the
concrete in that mode, and thus less resistance to deflection in this mode shape will be
provided. This was particularly noticeable following completion of all testing, as the concrete
would deflect easily when pressed or pulled by hand – behaviour which was not evident
before testing.
In higher acceleration cases the regions of the face subject to high displacements began to
show significant cracking, particularly at the face edges and in some cases, delamination
occurred of the concrete from the reinforcement mesh. This failure mode is similar to that
seen in the failure of 10mm samples during materials testing, and may be a result of shear

38
forces generated during deflection. As before this occurs when micro cracking along the
tensile mesh begins to isolate the concrete from the reinforcement. As the section is then
loaded in shear, the concrete has no tensile restraint locally and thus does not have sufficient
strength to resist the shear load. A micro crack propagates up from the reinforcement layer
before becoming a shear crack at 450
to the horizontal. When this failure spreads, large areas
of concrete become separated from the mesh leading to delamination.
A further case of delamination of the structure is seen where a brick is forced away from the
shell. This occurs in a large displacement region, whereby the acceleration of the brick on the
surface results in a pull away force of the concrete surface. As the accelerations of the face
peak at above 6g, and the mass of the brick is significant compared to that of the shell, this
force can be over 100N (assuming brick mass of 2kg). This load is resisted by shear in the
concrete section at the perimeter of the brick and by the concrete to mesh bonding strength
over the area of the brick. This resistive force was insufficient in one location causing the pull
off of a brick during testing as seen in Figure 6.10 c). Further cases of brick pull off resulted
in local damage to the structure, but with delamination occurring within the concrete section,
where the bond between application layers of concrete had been insufficient to resist the pull
off force. In this case there is little contribution from the concrete in shear at the perimeter of
the brick due to the shallow depth of failure.
5.7.3 Testing Procedure Implications
As mentioned previously there was a weakening of the fundamental mode of the structure
through the repetitive loading nature of the test. The process of cracking of the structure will
dissipate energy during an earthquake, and thus a smaller response may be recorded if an un-
cracked structure was tested under large ground accelerations. This would be particularly
prevalent with a short duration earthquake, in which only one or two cycles at high ground
acceleration were present. This dissipation of energy is a method commonly used in
earthquake resistant building design, however design utilises the yielding of steel members
and not the cracking of concrete which would dissipate considerably more energy, and thus
this effect may be negligible.
The detachment of bricks from the surface of the structure during the final high acceleration
earthquake testing and the large amplitude sinusoidal testing caused a reduction in the

39
loading of the surface. This means that whilst the structure is being excited at large ground
accelerations, the loading is no longer equivalent to that of a full scale structure, and thus its
resilience for the largest ground acceleration is still in doubt. Despite this, the majority of
loading on the structure was still in place for the first test at 2.1g, and thus these results still
remain valid.
5.7.4 Scale Implications
During a considerable portion of the testing, the full additional loading provided by the
household bricks was applied to the structure. This identified the key fundamental frequency
of the structure and caused large amounts of the cracking and delamination. Implications of
the materials tests indicate that the half thickness shell failed before the full thickness would
have done when scaling is taken into account, and thus the scaling provides a conservative
estimate of the failure modes and stresses of the structure. It can thus be assumed that the
behaviour of the half scale model matches that of a full scale roof, and therefore the results
can be directly compared.
5.7.5 Ultimate and Serviceability Failure
The results from the hypar testing indicate that the structure tested remained structurally
sound against ultimate failure up to earthquakes of 2.1g peak ground accelerations. Even
under direct excitation of the fundamental mode shape, the structure showed no signs of
catastrophic collapse, with failure only occurring in cracking or delaminating of small
sections of the shell. Following the testing, the structure was suitably sound to bear
reasonable loads as no critical damage had occurred to the flexible mesh and a significant
amount of the concrete was unaffected by the failure mode.
In terms of serviceability of the structure due to a range of earthquake loading, the excitation
of the mode shape above 1.2g created visible cracks in the structure particularly at the face
edges. These would affect the deflections of the roof, should it be subject to static or dynamic
loading (wind, snow, storage etc.) particularly when the concrete is stressed in a hogging
mode. The presence of cracking also makes the structure susceptible to further deterioration
due to the ingress of water into the surface. Processes such as freeze thaw weathering or
chemical attack of the concrete could lead to spalling of layers of concrete. This deterioration
was seen in a hypar structure in Franktown Colorado [5], whereby cracking caused by poor

40
construction practice, lead to the ingress of water, and full delamination of the lower regions
of the hypar occurred. The delamination and complete separation of the concrete seen in tests
at 2.1g resulted in the exposure of the reinforcement mesh at one location. This could lead to
the structure being no longer water tight and possibly result in the roof being no longer fit for
purpose.
5.7.6 Material Implications
When considering the implication of this test on both planned and existing hypars, the
differences between the real and test structures must be considered. During analysis, there
was very little deflection in the frame of the structure, and its effect on the failure of the face
was minimal. The structures which are built with slightly weaker frames including those
made of locally sourced bamboo (often a stronger material with weaker connections) can thus
be considered to behave in a similar fashion to the test structure.
The effects of the reinforcement mesh in the structure had a greater impact on the overall
failure of the shell, and thus each individual case of reinforcement should be compared to that
of the test for validity. The first key consideration when considering the effectiveness of the
mesh is the predicted bonding of the reinforcement to the layers of concrete. As seen in the
failure of the full hypar, significant deflections in the shell cause large bending strains, and if
the bond between the reinforcement layer and the concrete is weaker than that of the testing
completed, this failure is likely to occur sooner and at lower loads. This bond strength will
also be linked to the cover provided below the reinforcement as the separation of the lower
layers of mesh could have been avoided if the cover was increased. Failure of the
reinforcement itself only occurred in one 5mm test sample, and thus the implications of the
tensile strength of the mesh are unknown. The alternative materials used such as chicken
wire, if sufficiently bonded should provide sufficient reinforcement strength, as the tensile
capacity would be higher than that of the fibreglass mesh.
The strength of the concrete mix will clearly have a large effect upon when failure will occur.
The variation in latex admixture used including quantity and form could have adverse effects
on the increase in tensile strength and ductility which the admixture provides. This may
result in the cracking of the structure at a lower load, possibly leading to serviceability
failure, and the ingress of water into the structure. Further concrete factors such as the cement

41
quality or the water cement ratio will also have implications on the final shell strength of the
structure. Work being done by Seth Carlton on the mix design of concrete used in hypar roofs
should give an indication of the effect of variations in the concrete and thus should be
consulted when considering the strength of any given structure.
The connection conditions used in the test were chosen to provide the most representative and
most conservative estimates of the failure stresses and modes of the structure. By only
supporting the structure at the four mid-spans, deflections in all other frame locations were
permitted. Many roof structures, however, are secured around full sections of the frame or
around the complete perimeter of the hypar and this would lead to a different failure mode of
the structure. In these cases, the corners of the frame would be restricted from moving and
thus the fundamental mode shape found would have been damped or prevented completely.
This would result in a different fundamental mode shape with a higher resonant frequency
and could involve the whole of a face to be engaged in the mode shape. A typical earthquake
often has peak response below 10 Hz, and thus as the fundamental frequency of the structure
increases this will mean the fundamental mode will be excited less, causing less damage to
the structure and thus the effects of this increase in supporting conditions will only provide a
safer roof.
It is important to note that the testing conducted focused purely on the resilience of the roof
structure to dynamic loading, assuming it was rigidly connected to the ground. Current
hypars and those to be designed for future construction will not have completely rigid and
robust connections between the supporting structure and the roof itself. Failure of each hypar
must also thus consider the strength of these connections particularly in shear. Further
consideration must also be given to the effect of an earthquake on the combined structure, in
particular by considering the roof structure as a mass fixed onto a sway frame, however this
is outside the scope of the work completed above.
6 Conclusions
General Implications of Research6.1
The resilience of the hypar roof structure to seismic loading has been shown to be very good
with very large peak ground accelerations required to cause only small amounts of damage.

42
The failure mode is progressive and never complete or catastrophic thus presenting no threat
to human life due to the collapse of the structure. Following the largest earthquake tested, the
structure would still be functional to provide shelter against both sun and rain in the short
term, with further long term deterioration only leading to shell delamination and possible
serviceability failure.
Whilst the hypar roof itself can be deemed as very resilient to earthquake loading, its use in a
seismic zone within the ‘roof first’ policy of TSC Global is highly dependent upon the
structure it is supported upon. Further work is required on how best to support this roof such
that it would not fall or topple when an earthquake hits. This currently provides the greatest
risk to human occupants, as whilst the structure is deemed ‘light’, a full sized roof would
weigh in the order of 800kg.
Whilst the shape of the hypar frame tested is very typical in terms of hypars constructed, the
strength and resilience of the structure has led to suggestions that the height of the structure
could be reduced, thus creating a lower profile, saving material and reducing weight. The
effects of this would be a reduction in curvature of the arch and cable structure, thus reducing
their capacity particularly in static loading cases, however, in locations of reduced loading
(areas of low winds, no snow and low seismic activity) this could reduce the costs of the
structure allowing more roofs to be built for a community.
Specific Conclusions6.2
From the testing completed both during materials testing and upon the half scale hypar
structure, the following conclusions can be drawn;
 During bending of the composite shell, micro cracking occurs along the reinforcement
mesh leading to disengagement between the reinforcement and the concrete.
 Micro cracking in the tensile layer reduces the capacity of the sample to shear
loading.
 Due to the fabrication technique, there is often insufficient cover of concrete for the
bottom layer of reinforcement to engage in the section, and thus provide tensile
reinforcement.
 Thinner shell thicknesses are susceptible to local crushing under loading, leading to
weaker section properties.

43
 The fundamental frequency of a typical 6mx6mx3m hypar will be around 10Hz, and
will consist of deflections in the face of the roof.
 Initial failure of the roof under dynamic loading will be by cracking of the shell
followed by delamination caused by large deflections and shear forces.
Further Testing6.3
As mentioned previously, the stability of the structure is dependent upon its supporting
conditions. Further testing could include an analysis of the typical shear strength provided by
supports and connections currently used in the roof first programme. Consideration should
also be given to the fundamental frequency of the combined roof and supports and how this
may behave and fail under dynamic ground movements. For the roof first approach where the
roof is supported by simple columns, this could be done by considering the structure as a
mass on a single storey sway frame. The implications this test has on the foundations of the
supports should also be considered, particularly if they are considered to be fully built in.
As development of the hypar shape and roof continues, further shapes of building and roofs
are being considered. The resilience shown by this hypar has led to the suggestion that the
pitch of the roof could be lowered. This would reduce the surface area and thus the amount of
raw materials required, however the shallower curvatures would decrease the compression
arch and tensile cable effect with implications on overall strength. Further testing could
include the optimisation of the height for different loading conditions. Further suggestions of
alterations to the shape of the roof include suggestions from TSC Global of a cross gable
structure as seen in Figure 6.1. Whilst aspects of the design are similar to that of the square
based hypar, each development of shape should be considered individually for its stability
under earthquake loading and further scaled testing completed.
A further loading condition on the hypar roof not considered is that of impact testing. This
could be caused by debris from other failed structures hitting the roof surface due to storm
winds or an earthquake in built up areas. This could be tested by fabricating one face of the
structure or just a sample of the shell material itself.

44
The repeated result of disengagement of the lower layers of reinforcing mesh leads to a
suggestion that the cover of concrete below the reinforcement could be increased. This could
be done by applying a further layer of concrete with no aggregate to the underside of the
structure, thus improving the reinforcement bond. Testing on samples of the shell material
particularly in bending with this variation in fabrication technique could lead to improved
material properties.
7 References
[1]
H. Engel, Structure Systems (p215), Hatje Cantze, 1967.
[2]
M. E. Moreyra Garlock and D. P. Billington, Felix Candela, Engineer, Builder,
Structural Artist, Princeton University Art Museum, 2008.
[3]
P. P. Evan H. Curtis, “Hypars Test Out,” U.S. National Park Service, Denver Service
Center, Falls Church, Va..
[4]
S. Carlton, Interviewee, University of Oklahoma, Information shared in colloaboration
of work. [Interview]. January 2013.
[5] “Information provided in correspondance with TSC Global through working documents,
email correspodance and meetings.,” [Online]. Available: www.tscglobal.org.
Figure 6.1- Further suggested roof shapes courtesy of TSC Global

45
[6]
“Wykamol group website,” [Online]. Available:
http://www.wykamol.com/services/damp-proofing/waterproofers-and-
additives/wykamol-sbr-latex.html.
[7]
“Email Correspondance with Wykamol Group - See Appendix”.
[8]
Standard Test Method for Compressive Strength of Hydraulic Cement Mortars, ASTM
International standard C109.
[9]
A. International, “Standard Test Method for Flexural Properties of Unreinforced and
Reinforced Plastics and Electrical Insulating Materials by Four Point Bending,” DOI:
10.1520/D6272-10, April 2010.
[10]
“Portland Cement Assosciation - Portland Cement Characteristics 1998,” [Online].
Available: http://www.cement.org/tech/pdfs/pl992.pdf.
[11]
Records supplied by M J DeJong, Cambridge University 2013.
[12]
Dr George Nez, Michael H. Barrett P.E. and Dr Albert Knott P.E., “Design and
Construction of Acrylic Concrete Structures,” April 26, 2003.
[13]
J.Hindle, after Fabre, “ Candela: The Shell Builder, 92”.
[14]
Garlock, M after Faber, C, Candela : The Shell Builder p226, New York 1963.
8 Appendix
Risk Assessment Retrospective8.1
When considering the potential hazards of testing a hypar structure, there were several key
aspects which were considered. The first is the use of cement which is a hazardous material
itself. Necessary precautions in regards to the handling of the substance were set out from the
beginning, and preventative measures including protective clothing, eyewear and breathing
apparatus were used where appropriate.

46
The second main hazard came from the final testing of the structure, as a large sled driven by
a servo hydraulic pump was being used. This too was identified from the outset, and the
implications of its use were discussed extensively with both the project supervisor and the
chief technician of the lab. Precautionary measures including emergency stop procedures,
exclusion zones and an established communication sequence for testing were put in place and
adhered to.
A hazard which could not have been predicted at the beginning of the project was the method
used to add mass to the structure for final testing. The bricks which were mortared to the
surface of the structure presented a hazard, as the bond strength was relatively unknown.
‘Worst case scenario analysis was conducted’ assuming a brick had come free and was then
structure by the structure at maximum velocity. The implications of this analysis led only to
further exclusion zones of one metre around the full perimeter of the structure, as the
maximum distance the bricks could be projected was under 0.5m.

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