Sudhakar final sem 2

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CHAPTER 1

INTRODUCTION

1.1 GENERAL

Shell structures find application in many fields of engineering, notably civil,

mechanical and aeronautical disciplines. In the past 100 years, considerable effort

has been expended on the development of rigorous theories both general and

specialist-to describe the behavior of shells in the elastic range as realistically as

possible.

1.2 BEHAVIOUR OF SHELL

1.2.1 Membrane Behaviour of Shell

The membrane behavior of shell structures refers to the general state of stress

in a shell element that consists of in-plane normal and shear stress resultants which

transfer loads to the supports. In thin shells, the component of stress normal to the

shell surface is negligible in comparison to the other internal stress components and

therefore neglected in classical thin shell theories. The initial curvature of shell

surface enables shell to carry even load perpendicular to the surface by in-plane

stresses only.

The carrying of load only by in-plane extensional stresses is closely related to

the way in which membranes carry their load. Because of the flexural rigidity is

much smaller than the extensional rigidity, a membrane under external load mainly

produces in-plane stresses. In case of shells, the external load also causes stretching

or contraction of the shell as a membrane, without producing significant bending or

local curvature changes. Hence, there is referred to the membrane behavior of shells,

described by the membrane theory.

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Carrying the load by in-plane membranes stresses is far more efficient than

the mechanism of bending which is often seen by other structural elements such as

beams. Consequently, it is possible to construct very thin shell structures. Thin shell

structures are unable to resist significant bending moments and, therefore, their

design must allow and aim for a predominant membrane state. Bending stresses

eventually arise when the membrane stress field is insufficient to satisfy specific

equilibrium or deflection requirements.

1.2.2 Bending Behaviour

In regions where the membrane solution is not sufficient for describing the

equilibrium and deformations requirements, bending moments arise to compensate

for the shortcoming of the membrane behavior. For example at the supports, by local

concentrated (thin shell structures are exceptionally suited to carrying distributed

loads, however, they are unsuited to carrying concentrated loads) or a sudden change

in geometry the membrane state is distributed causing bending action. Bending

moments only compensate the membrane solution and do not carry loads. Hence

there is often referred to compatibility moments. Due to their compensating

character, bending moments are confined to a small region; the major part of the

shell still behaves as a true membrane. It is the salient feature of shells and that is

responsible for the most profound and efficient structural performance.

The performance for membrane action arises as a consequence of being thin.

In thicker shell the preference is not so notorious and eventually it may reverse.

Shells can be categorization into membrane-dominated, bending-dominated, and

mixed shell problems. The category can be made more specific by considering the

asymptotic behavior of shells.

1.2.3 Material Effect

Reinforced concrete shells have complicated nonlinear material behavior with

strong influence on the structural behavior. Significant tensile stresses in the shell

will cause cracking and with that weakening of cross-section. Micro-cracking at the

surface is caused by the evaporation of water. Due to high amount of surface exposed

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the micro-cracking in the shell surface may exceed the allowable value. Furthermore,

creep of concrete will cause flattening of the shell surface, resulting in less curvature

and possible bending stresses to occur. Additionally shrinkage may lead to unwanted

residual stresses.

1.3 CLASSIFICATION OF SHELL SURFACES

The spatially curved surface of shell structures can be classified in several

ways. For shell structures it is convenient to make a classification according to

Gaussian curvature. The Gaussian curvature of a three dimensional surface is the

product of principal curvatures, which are defined as the maximum and minimum

curvature of a certain surface. The principal curvatures can be found by intersecting

shell by an infinite number of planes normal to the shell surface at an arbitrary point

and determining the two planes for which the secant with the surface has a maximum

curvature and a minimum curvature. The principal curvatures are, by definition,

orthogonal to each other. The product of the principal curvatures is either positive,

zero or negative. Classification in Gaussian curvature therefore means a

classification in surfaces with positive Gaussian curvature (synclastic), zero Gaussian

curvature (monoclastic) or negative Gaussian curvature (anticlastic).

1.3.1 Synclastic

The Gaussian curvature of synclastic shell is positive and both principal

curvatures have the same sign. A synclastic surface is a non-developable. A shell is

either developable or non-developable. If it is possible to develop a surface it can, in

contrast with non-developable surfaces, be changed into a plane form without cutting

or stretching the middle surface. Therefore, surface which are non-developable are

stronger .An example of a synclastic structure is the dome. Synclastic surface carry

their load by meridional and circumferential in-plane stresses. Except for elpar

(hemisphere sliced to a square base shape) which carries forces with in-plane shear.

1.3.2 Monoclastic

An example of a developable surface is a monoclastic surface. The Gaussian

curvature of monoclastic surface equals zero. Zero Gaussian curvature refers also to

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structures with zero curvature in both directions, as plates; however, these structures

are named as zeroclastic. Monoclastic shells do have curvature in one direction but

zero in the orthogonal direction. An example of monoclastic surfaces are cylindrical

shells such as barrel vaults. Cylindrical shells, probably the most used form of

concrete shells, are widely used to cover e.g. airplane hangars or train stations. The

membrane behavior of cylindrical shells loaded perpendicular to their surface

consists of an interaction of two behavioural components such as beam action and

arch action. Whether the cylindrical shell has mostly the beam action or the arch

action depends on the shell geometry and the edge conditions. Long cylindrical shells

resting on end supports act like simply supported beams.

1.3.3 Anticlastic

A surface with negative Gaussian curvature is called anticlastic and is, like

synclastic surfaces, non-developable. The two principal curvatures have opposite

signs, which make the product negative. The characteristic feature of having a

positive curvature in one direction and a negative curvature in the perpendicular

direction makes the shell act as a combination of a compression and tension arch

when loaded perpendicular to its surface . Example of anticlastic shell are the

hyperbolic paraboloid (hypar) shells of Felix Candela. The hyper carries forces with

in-plane shear like elpar shells.

1.4 TERMINOLOGY

Asymmetrical Cylindrical Shells- Cylindrical shells which are asymmetrical about

the crown.

Chord Width – The chord width is the horizontal projection of the arc of the

cylindrical shell.

Continuous Cylindrical Shells – Cylindrical shells which are longitudinally

continuous over the traverses.

Cylindrical Shells – Shells in which either the directrix or generatrix is a straight

line.

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Edge Member – A member provided at the edge of a shell.

End Frames or Traverses – End frames or traverses are structures provided to

support and preserve the geometry of the shell.

Folded Plates - Folded plates consist of a series of thin plates, usually rectangular,

joined monolithically along their common edges and supported on diaphragms. They

are also known as hipped plates.

Generatrix,Directrix – A curve which moves parallel to itself over a stationary

curve generates a surface. The moving curve is called the generatrix and the

stationary curve the diectrix. One of them may be straight line.

Junction Member – The common edge member at the junction of two adjacent

shell.

Multiple Cylindrical Shells – A series of parallel cylindrical shell which are

transversely continuous.

North-Light Shells – Cylindrical shells with two springing at different levels and

having provisions for north-light glazing.

Radius – Radius at any point of the shell in one of the two principal directions.

Rise – The vertical distance between the apex of the curve representing the center

line of the shell and the lower most springing.

Ruled Surfaces – Surfaces which can be generated entirely by straight lines. The

surface is said to be ‘singly ruled’ if at every point, a single straight line can be ruled

and ‘doubly ruled’ if at every point, two straight lines can be ruled. Cylindrical

shells, conical shells and conoids are examples of singly ruled surfaces; hyperbolic

paraboloids and hyperboloids of revolution of one sheet are examples of doubly

ruled surfaces.

Semi-Central Angle – Half the angle subtended by the arc of a symmetrical circular

shell at the center.

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Shells – Thin shells are those in which the radius to thickness ratio should not be

more than 20.

Shells of Translation – Shells which are obtained when the plane of the generatrix

and the directory are at right angles. Examples are cylindrical shells, elliptic

paraboloids, hyperbolic paraboloids.

Shells of Revolution – Shells which are obtained when a plane curve is rotated about

the axis of symmetry. Examples are segmental domes, cones, paraboloids of

revolution, hyperboloids of revolution, etc.

1.5 OBJECTIVE

(i) To model the cylindrical shells with and without GFRP and determine the

ultimate load carrying capacity and deflection .

1.6 SCOPE

(i) To study the behavior of cylindrical shell when it is subjected to

compressive load on in plan and in plane surfaces.

(ii) To find the ultimate load carrying capacity of the cylindrical shells for

various heights ,with and without GFRP.

(iii) To study the deflection characteristics with respect to various height of the

cylindrical concrete shells with and without GFRP.

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CHAPTER 2

LITERATURE REVIEW

2.1 GENERAL

The previous work on thin cylindrical shells are studied and most of the

literatures are analytical. Some of the literature reviews are collected and they are

listed below.

2.2 LITERATURES

Chryssanthopoulos, et al. (1995), There are number of difficulties in

calculating design buckling loads for shells based only on numerical analysis. In

many cases there is lack of experimental data. These papers has concentrated on

presenting methods for estimating knockdown factors based on probabilistic

imperfection modelling and finite element analysis.

Venkata Narayana Yenugula, et al. (2013), The linear and nonlinear

buckling of composite cylindrical shell were performed using generalized finite

element program ANSYS. The cylindrical shell specimens were manufactured using

filament winding machine and these samples were tested under compressive loads.

The experimental results were compared with general purpose finite element

program. Limited point loads evaluated for geometric imperfection magnitudes

shows an excellent agreement with experimental results which clearly indicates the

confidence gained on the numerical results presented.

Zingoni,et al. (2013), They have been investigated the buckling behaviour of

vertical concrete arch dams which are curved in plan. A number of significant

observations were made. The actual mathematical shape of the arch does not have

significant effect on the buckling strength. But other geometric properties (such as

shell thickness t, rise ratio h/a and aspect ratio b/a) have a far greater effect. The

buckling pressures are seen to decrease sharply with increasing relative depth (i.e.

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aspect ratio) of the arch dam, the rate of decrease becoming slower as b/a gets larger.

The shell rise ratio has a particularly strong influence on the buckling strength of the

dam and therefore it can be used as a tool for enhancing the buckling strength of an

arch of given dimensions without having to increase the shell thickness, thus saving

on the volume of material used in the construction.

Diederik Veenendaal, et al. (2014), The field of fabric formwork represents

over a century of exciting inventions and discoveries, yet provides many

opportunities still. A historical overview of flexibility formed shell structures and

prototypes, often hypars, has been presented, many of which were constructed with

comparable goals to the present work. The solution has been developed to allow

large-span formworks with little or no falsework and enable a wider range of

anticlastic shapes than those possible through traditional means. The first proto type

presented here is the first cable-net and second is fabric formwork. It is clear that

much work needs to be done for the further development of this construction. Future

work will focus on improving the optimization procedure and tackling the challenges

associated with scaling up the construction method.

Rigoberto Burgueno, et al. (2014), The buckling of cylindrical shells has

long been regarded as an undesirable phenomenon, but increasing interests on the

development of active and controllable structures open new opportunities to utilize

such unstable behaviour. In this paper, approaches for modifying and controlling the

elastic response of axially compressed laminated composite cylindrical shells in the

far post buckling regime are presented and evaluated. Three methods are explored (i)

varying ply orientation and laminate stacking sequence (ii) introducing patterned

material stiffness distributions (iii) providing internal lateral constraints.

Experimental data and numerical results show that the static and kinematic response

of unstable mode branch switching during post buckling response can be modified

and potentially tailored.

2.3 SUMMARY OF REVIEW OF LITERATURE

Knockdown factor can be determined based on imperfection modelling and

finite element analysis. The linear and non-linear buckling of composite cylindrical

shell were performed by analytical and compared with experimental results. The

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comparative study of cable net and fabric formwork of hyperbolic shell structure that

needs further development of this construction.

2.4 NEED FOR THE RESEARCH

The underground structure need to withstand in buckling behaviour using

different composite material with concrete. To avoid the sudden collapse, GFRP will

be used as reinforcement in thin cylindrical shell. And need to compare with normal

reinforcement as well as GFRP.

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CHAPTER 3

MATERIALS AND METHODOLOGY

3.1 MATERIALS

3.1.1 Cement

Ordinary Portland Cement of 53 grade is used for the investigation which is

conforming to IS:12269(1987).The following Table 3.1 gives the properties of

cement.

Table 3.1 Properties of Cement

PROPERTY VALUE

Specific gravity of cement 3.1

Fineness of cement 5 %

Normal consistency of cement 35 %

Initial setting time of cement 32 minutes

3.1.2 Fine Aggregate

The sand is used as fine aggregate and it is collected from nearby area. The

sand has been sieved in 4.75 mm sieve. The following Table 3.2 gives the properties

of fine aggregate and Table 3.3 gives the sieve analysis of fine aggregate.

Table 3.2 Properties of Fine Aggregate

PROPERTY VALUE

Specific gravity of fine aggregate 2.68

Fineness modulus of fine aggregate 2.78

According to IS 383-1970 ZONE II

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Table 3.3 Sieve Analysis of Fine Aggregate

IS SIEVE SIZE CUMULATIVE %

PASSING

GRADING ZONE II

ACCORDING TO

IS 383- 1970

4.75 mm 100 90-100

2.36 mm 96.08 85-100

1.18 mm 67.2 75-100

600 µ 46.21 60-79

300 µ 11.56 12-40

150 µ 1.34 0-15

Passed 0 -

3.1.3 Coarse Aggregate

Locally available coarse aggregates are taken and sieved to the required

quantity of volume to the maximum nominal size of 10 mm. Care is taken to arrive

the size of coarse aggregate ranging from 4.75 mm to the maximum nominal size of

10 mm.

Table 3.4 Properties of Coarse Aggregate

PROPERTY VALUE

Specific gravity of coarse aggregate 2.74

Fineness modulus of coarse aggregate 6 %

3.1.4 Water

Potable water available in Concrete and highway laboratory of department of

civil engineering was used for mixing the concrete and curing the specimens. pH

value of water is 7.

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3.2 METHODOLOGY

The following Fig. 3.1 shows the methodology.

Review of Literature

Preliminary test of material

Mix Design

Preliminary Test on hardened concrete

Creating different size of mould

Casting of thin cylindrical shell

With and without GFRP

Testing the shell specimens

Comparing the Result

Fig 3.1 Methodology

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CHAPTER 4

EXPERIMENTAL WORK AND TEST RESULTS

4.1 SPECIMEN DETAILS

4.1.1 Cube Specimens

Cube of size 100 × 100 × 100 mm is used for making conventional concrete

Specimens.

4.1.2 Cylinder Specimens

Cylinders of 100 mm in diameter and 200 mm in height is used for making

conventional concrete Specimens.

4.1.3 Cylindrical Shell Trial Specimens

Cylinders shell is having outer diameter of 160 mm and inner diameter of

90mm, so the shell is having 30 mm thickness. The following Fig.4.1 has shown the

testing of cylindrical shell.

Fig 4.1 Trial Specimen of Cylindrical shell

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4.1.4 Mix Proportion

Design of mix proportion is given in Appendix A. The proportion of each

ingredient of concrete used are,

(i) Cement = 557 kg/m3

(ii) Water = 250 lit/m3

(iii) Fine Aggregate = 1058.94 kg/m3

(iv) Coarse Aggregate = 418.28 kg/m3

(v) Water Cement Ratio = 0.45

Mix proportion - C : F A : C A

1 : 1.9 : 0.76

4.2 SPECIMEN TESTS

4.2.1 Compression test

Concrete is primarily meant to withstand compressive stresses. Cubes are

casted and cured for 7 days and for 28 days. After curing, compressive strength is

tested in a Compression Testing Machine (CTM) according to IS 14858:2000. The

compressive strength of concrete are given in Table 4.2.

Compression Strength of concrete = Load applied on the cube specimen …(4.1)

Cross Section area of the cube

Table 4.1 Compressive Strength of Conventional concrete

DURATION COMPRESSIVE STRENGTH

( N/mm2)

7 days 23.1

28 days 30.1

4.2.2 Young’s Modulus Test

Initially it is assumed that concrete is elastic, isotropic, homogeneous and it

conforms to Hook’s law. Actually none of these assumptions are strictly true and

concrete is not a perfectly elastic material. Concrete deforms when load is applied

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but this deformation does not follow any simple rule. The deformation depends upon

the magnitude of the load, the rate at which the load is applied and the elapsed time

after which the observation is made.

4.2.3 Cylindrical Shell Specimens

Cylinders shell is having outer diameter of 300 mm and inner diameter of 240

mm, so the shell is having 30 mm thickness and height of 200mm, 400mm, 600mm.

The following Fig. 4.2 shows the specimen of cylindrical shell.

Fig. 4.2 Specimen after casting and demoulding

4.2.4 Axial Compression Test on Cylindrical Shell

Axial compression on cylindrical shell is same as loading the cylinder axially

on top and bottom of shell. A deflectometer is placed to take the deflection of

cylindrical shell. Two steel rings are attached at top and bottom of the specimens.

Strain gauges are attached on four sides of specimen to measure the lateral deflection

using strain indicator. The Fig. 4.3 shows the testing of specimen.

Fig. 4.3 Testing of Specimens

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4.2.5 Specimen Details of Cylindrical Shell

The following Table 4.2 shows the specimen details of cylindrical specimens.

Table 4.2 Specimen Details of cylindrical shell

SPECIMEN

DETAILS

HEIGHT

(mm)

DIAMETER

(mm)

THICKNESS

(mm)

Specimen 1 200 300 30

Specimen 2 400 300 30

Specimen 3 600 300 30

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CHAPTER 5

RESULTS AND DISCUSSION

5.1 YOUNG’S MODULUS

The modulus of elasticity is determined by subjecting a cylinder specimen to

uniaxial compression and measuring the deformations by means of dial gauges fixed

between certain gauge length. Dial gauge reading divided by gauge length would

give the strain and load applied divided by area of cross-section would give the

stress. A series of readings were taken and the stress-strain relationship was

established.

After 28 days of curing, the cylinders are tested in a Compression Testing

Machine (CTM). The following equation is given by the following equation(5.1)

Modulus of Elasticity = Linear Stress ………..(5.1)

Linear Strain

The following Fig. 5.1, Fig. 5.2, Fig. 5.3 and Fig. 5.4 shows the stress vs

strain graph for various cylindrical specimens.

Fig. 5.1 Stress vs Strain for Specimen 1 at 7 days

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The size of the aggregate used for making the cylinder is 4.75 mm. Because

of that smaller size of aggregate, it was effected in the linear strain. So the Young’s

modulus for 7 days resulted as 17207 MPa and 15901 MPa.



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Table 5.1 Young’s Modulus of Conventional concrete

DURATION Young’s modulus (N/mm2)

SPECIMEN 1 SPECIMEN 2

7 days 17207 15901

28 days 20167 22329

The above Table 5.1 shows the young’s modulus of concrete for 7 days and

28 days. Since the young’s modulus is directly proportional compressive strength, as

the strength increase, E value is also increased. Young’s modulus of 28 days is 0.85

times increased from 7 days value.

5.2 AXIAL COMPRESSION TEST ON TRAIL CYLINDRICAL SHELLS



cylindrical shell. The means of applying the load shall provide for the load to be

applied either with the specimen in direct contact with the machine platens, or

spacing blocks, or with auxiliary platens interposed between each machine platen, or

spacing block, and the specimen. The following Fig. 5.5 and Fig. 5.6 shows the load

vs deflection graph for various specimens.

Fig. 5.5 Load vs Deflection for Trail Specimen 1

The above Fig. 5.5 shows the load vs deflection curve of cylindrical shell

specimen 1 of size 160 mm in outer diameter and 30 mm thickness with height 300

mm. The ultimate load carrying capacity of this specimen is 190 kN. During the

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ultimate load crack was formed and sudden failure of concrete was observed at one

edge.

Fig. 5.6 Load vs Deflection for Trail Specimen 2


specimen 2 of size 160 mm in outer diameter and 30 mm thickness with height

600mm. The ultimate load carrying capacity of this specimen is 220 kN. During the

ultimate the crack was formed and sudden failure of concrete was observed at one

edge and the reinforcement was buckled.

5.3 AXIAL COMPRESSION TEST ON CYLINDRICAL SHELL SPECIMENS



cylindrical shell. Two steel rings are attached at top and bottom of the specimens to

avoid the direct contacts of machine platens with specimen. Strain gauges are

attached on four sides of specimen to measure the longitudinal deflection. The

following Fig. 5.7, Fig. 5.8 and Fig. 5.9 shows the load vs deflection graph for

various specimens.

Fig. 5.7 Load vs Deflection for Specimen 1

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200 mm. The ultimate load carrying capacity of this specimen is 650 kN and 350 kN.

During the ultimate load crack was formed throughout the height of specimen in

without GFRP specimen and there is crushing of concrete at one end and the

specimen was buckled at center. There is no crack present outside the GFRP while

using it.


. The above Fig. 5.8 shows the load vs deflection curve of cylindrical shell

specimen 2 of size 300 mm in outer diameter and 30mm thickness with height


During the ultimate load crack was formed from top end and extended to some

distance. Spalling of concrete was observed in the specimens of without GFRP and

buckling of specimen at above the center on one side and there is no crack outside

the GFRP.


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specimen 3 of size 300 mm in outer diameter and 30mm thickness with height


During the ultimate load crack was formed from top end to bottom and was observed

of in without GFRP and there is damage in GFRP at bottom of specimen. There

was no crack outside the GFRP.

5.4 SIMPLY SUPPORTED TEST ON CYLINDRICAL SHELL

Specimen is placed in compression machine as simply supported and load

was applied as point load at center along its length. A deflectometer is placed to take

the deflection at center of cylindrical shell.The support is adjustable, so it can be

tested in different size of specimen. The following Fig. 5.10 shows the testing of

various specimens. The following Fig. 5.11, Fig. 5.12 and Fig. 5.13 shows the load

vs deflection graph for various specimen 1, 2, and 3.

Fig. 5.10 Testing of Specimens


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200 mm. The ultimate load carrying capacity of this specimen is 0.6 kN without

GFRP and 1.2 kN with GFRP. During the ultimate load crack was formed

throughout the length of specimen in without GFRP and there was crack and no

sudden failure while using GFRP .




400 mm. The ultimate load carrying capacity of this specimen is 1.4 kN

without and 1.7 kN with GFRP. During the ultimate load crack was formed and

sudden failure in without GFRP and there was no sudden failure while using GFRP

was observed.




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600 mm. The ultimate load carrying capacity of this specimen is 1.6 kN

without GFRP and 2.4 kN with GFRP. During the ultimate load crack was formed

and sudden failure in the specimen of without GFRP and there was no sudden failure

while using GFRP was observed. The Table 5.2 shows the maximum deflection of

axial compression test.

Table 5.2 Deflection of axial compression test of specimens

MAXIMUM

DEFLECTION(mm)

EXPERIMENTAL

VALUE

THEORITICAL

VALUE

WITHOUT

GFRP

WITH

GFRP

WITHOUT

GFRP

WITH

GFRP

Specimen 1 3.975 5.838 1.28 2.37

Specimen 2 3.432 4.368 1.09 1.6

Specimen 3 6.201 8.919 1.53 1.9

The above Table 5.1 shows the maximum deflection of experimental value as

3.975 mm and theoretical value is 1.28 mm of deflection. The theoretical deflection

is decreased to 3.1 times of experimental , because when the specimen is subjected to

axial compression, it behave like hollow cylinder rather than shell. The Table 5.2

shows the maximum deflection of axial compression test.

Table 5.3 Ultimate load of axial compression test of specimens

ULTIMATE LOAD

(kN)

WITHOUT GFRP WITH GFRP

Specimen 1 350 650

Specimen 2 300 440

Specimen 3 420 520

The ultimate load carrying capacity is increased by 33% when GFRP is used.

The bonding between the GFRP and concrete gives the good results. The Table 5.4

shows the maximum deflection of simply supported point load test.

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Table 5.4 Maximum deflection of the specimens placed as simply supported

MAXIMUM

DEFLECTION (mm)

EXPERIMENTAL

VALUE

THEORITICAL

VALUE

WITHOUT

GFRP

WITH

GFRP

WITHOUT

GFRP

WITH

GFRP

Specimen 1 1 0.95 2.45 4.90

Specimen 2 3 2 5.72 8.17

Specimen 3 2 1.2 6.54 9.81

The above Table 5.4 shows the maximum deflection of different specimen

and theoretical value of deflection. The theoretical deflection increased to 1.45 times

of experimental value, because the specimen in axial compression act as shell

behaviour. The Table 5.5 shows the ultimate load carrying capacity of simply

supported point load test.

Table 5.5 Ultimate load of simply supported and concentric load at center

ULTIMATE LOAD(kN) WITHOUT GFRP WITH GFRP

Specimen 1 0.6 1.2

Specimen 2 1.4 1.7

Specimen 3 1.6 2.4

The ultimate load carrying capacity is increased when GFRP is used. The

bonding of GFRP with concrete is good but when loading at center the specimen

tends to bend inwards .

26

CHAPTER 6

CONCLUSION

6.1 GENERAL

From both axial compression and simply supported test the results

were concluded and they are given below. The future scope of the project also given.

6.1 CONCLUSION

(i) In axial compression test the ultimate load carrying capacity is 300 kN

without GFRP and 440 kN with GFRP, the load has been increased

by 46.67% .

(ii) Deflection in axial compression is increased to the maximum by 0.46

times, when using the GFRP.

(iii) In axial compression test the experimental value is 3.975 mm and in

theoretical value is 1.28 mm, theoretical value is reduced 0.67 times

than experimental value. This is due to specimen behaves like a

cylinder not like a shell.

(iv) In simply supported the ultimate load carrying capacity is 1.4 kN

without GFRP and 1.7 kN with GFRP. Because of using GFRP the

load has been increased 0.2 times.

(v) Deflection in simply support test is decreased 0.67 times eventhough

if the GFRP is used.

(vi) In simply supported test, the deflection by experiment value is 1 mm

and in the theoretical value is 2.45 mm. Deflection is increased for

theoretical value is 0.40 times then experimental value. This is due to

the specimen acted as a cylindrical shell.

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6.3 FUTURE SCOPE

(i) In the forthcoming researches, it is better to reduce the thickness of

shell, so that the behaviour will be purely like thin shell.

(ii) Different types of boundary conditions can be applied on cylindrical

shells.

(iii) Either the GFRP can be wrapped inside or both sides of cylindrical

shells.

(iv) By above steps and changing the parameters the characteristics of

cylindrical shell can be analysed.

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APPENDIX A

MIX DESIGN AS PER ACI 211.1

Target mean strength = fmin +ks

= 30 + 1.64 x 4

= 36.56 MPa

From Table A1.5.3.4(a) of ACI 211.1

Water/cement ratio =0.45

From Table A1.5.3.3 of ACI 211.1

Water for given slump = 250.69/.45 = 557.09 kg/m3


Volume of coarse aggregate = 0.2614 x 1600

= 418.28 kg/m3


For 5mm aggregate = 2285 kg/m3

Weight of Fine aggregate =2285-(250.69+557.09+418.28)

=1058.94 kg/m3

Absolute volume of all ingredients

Cement = 557.09 x 1000 = 179.92 x 103 cm

3

3.1

Water = 250.69 x 1000 = 250.69 x 103 cm

3

1

Coarse aggregate = 418.28 x 1000 = 152.65 x 103 cm

3

2.74

583.09 x 103 cm

3

Absolute volume of fine aggregate =1000-583.09

= 416.96 x 2.68

= 1117.45 kg/m3

29

Estimated Quantities of materials per cubic meter of concrete

Cement = 557.09 kg

Fine aggregate = 1117.45 kg

Coarse aggregate = 418.28 kg

W/C = 0.45

Mix Proportion - Cement : F.A : C.A

1 : 1.9 : 0.76

30

APPENDIX B

MAXIMUM DEFLECTION

Wmax= P

8×β4×D

Where, β4= 3×(1-µ

2)

a2 ×h

2

Thickness, h = 30 mm

Internal Radius, a = 120 mm

Poisson’s ratio µ = 0.3

Internal Diameter D = 240 mm

β4= (3×(1-0.3

2))

1202×30

2

β = 0.5

(i) Specimen 1

Load = 588.6 N

Wmax = 588.6

8×0.53×240

= 2.45 mm.

(ii) Specimen 2

Load = 1569.6 N

Wmax = 1569.6

8×0.53×240

= 6.54 mm.

(iii) Specimen 3

Load = 1373.4 N

Wmax = 1373.4

8×0.53×240

= 5.72 mm.

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REFERENCES

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