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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."

Cambridge Shake Table Results

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Page 1: Cambridge Shake Table Results

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."

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The Experimental Seismic Testing of Hypar Shells Daniel Balding, St Catharine’s College

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Table of Contents

1 Introduction ........................................................................................................................ 2

Project Proposal........................................................................................................... 2 1.1

Motivation for the Hypar Roof.................................................................................... 2 1.2

Motivation and Objective ............................................................................................ 3 1.3

2 Hypar Roof Design ............................................................................................................ 3

Hypar Shape and Background ..................................................................................... 3 2.1

Current Uses of Hypar Roofs ...................................................................................... 5 2.2

Previous Testing .......................................................................................................... 6 2.3

3 Procedure and Methodology .............................................................................................. 7

Materials to be used..................................................................................................... 7 3.1

Shell Properties ........................................................................................................... 8 3.2

Hypar Properties .......................................................................................................... 9 3.3

4 Materials testing ................................................................................................................. 9

Reinforcement Mesh ................................................................................................... 9 4.1

Latex Modified Concrete ............................................................................................ 9 4.2

Fibreglass Mesh Reinforced Latex Modified Concrete ............................................ 10 4.3

Results ....................................................................................................................... 13 4.4

Implications for Full Structure .................................................................................. 19 4.5

5 Hypar Test and Results .................................................................................................... 21

The Structure to be Built, Scaling and Post Loading of Structure ............................ 21 5.1

Construction .............................................................................................................. 22 5.2

Experimental Equipment ........................................................................................... 25 5.3

Experimental Procedure ............................................................................................ 26 5.4

Predictions ................................................................................................................. 28 5.5

Results ....................................................................................................................... 28 5.6

Discussion and Implications...................................................................................... 36 5.7

6 Conclusions ...................................................................................................................... 41

General Implications of Research ............................................................................. 41 6.1

Specific Conclusions ................................................................................................. 42 6.2

Further Testing .......................................................................................................... 43 6.3

7 References ........................................................................................................................ 44

8 Appendix .......................................................................................................................... 45

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1 Introduction

Project Proposal 1.1

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 Roof 1.2

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 Objective 1.3

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 Background 2.1

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

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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

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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 Roofs 2.2

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 Testing 2.3

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

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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 Used 3.1

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.

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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 Properties 3.2

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.

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Hypar Properties 3.3

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 Mesh 4.1

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 Concrete 4.2

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

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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 Concrete 4.3

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 19

0C, 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

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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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Results 4.4

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

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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

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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

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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

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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.

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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 15mm Sample 25mm Sample 35mm Sample 45mm 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 110mm Sample 210mm Sample 310mm Sample 410mm Sample 5

Figure 4.13 – Four point bend results of 10mm thick sample

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Implications for Full Structure 4.5

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

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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.

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5 Hypar Test and Results

The Structure to be Built, Scaling and Post Loading of Structure 5.1

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

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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)

Construction 5.2

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

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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

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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

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Experimental Equipment 5.3

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

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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 Procedure 5.4

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

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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.

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Predictions 5.5

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.

Results 5.6

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

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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.

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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

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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

Acc

eler

atio

n (

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

Acc

ele

rati

on

(g)

Acceleration on SledAcceleration at ApexAcceleration at Face0.3g

-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

Acc

eler

atio

n (

g)

Acceleration on SledAcceleration at Apex0.3g

Figure 5.14 – Acceleration of Face, Apex and Sled – Kobe - Magnitude 0.3g

Time (s)

Time (s)

Time (s)

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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

Acc

eler

atio

n (

g)

Acceleration of Sled0.3g

-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

Acc

eler

atio

n (

g)

Acceleration of SledAcceleration at Apex0.3g

-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

Acc

eler

atio

n (

g)

Acceleration of SledAcceleration at ApexAcceleration at Face0.3g

Time (s)

Time (s)

Time (s)

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Time (s)

-9-8-7-6-5-4-3-2-101234567

0 1 2 3 4 5 6 7 8 9 10

Acc

eler

atio

n (

g)

Acceleration on SledAcceleration at ApexAcceleration at Face2.1g

-3

-2

-1

0

1

2

3

4

5

0 1 2 3 4 5 6 7 8 9 10

Acc

eler

atio

n (

g)

Acceleration on Sled2.1g

-3

-2

-1

0

1

2

3

4

5

0 1 2 3 4 5 6 7 8 9 10

Acc

eler

atio

n (

g)

Acceleration on SledAcceleration at Apex2.1g

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)

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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

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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

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Discussion and Implications 5.7

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

Acc

eler

atio

n (

g)

Time (secs)

Acceleration on SledAcceleration at ApexAcceleration at Face

Figure 5.27 – Acceleration of Sled, Apex and Face – 10Hz Sinusoid

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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

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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

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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

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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

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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 Research 6.1

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.

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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 Conclusions 6.2

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.

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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 Testing 6.3

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.

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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

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[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 Retrospective 8.1

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.

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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.