STRENGTHENING OF RC BEAMS USING FRP SHEET

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International Journal of Research and Innovation (IJRI)

International Journal of Research and Innovation (IJRI)STRENGTHENING OF RC BEAMS USING FRP SHEET

Ketepalli Sravani 1, K. Mythili2, G.Venkat Ratnam3

1 Research Scholar, Department Of Civil Engineering, Aurora's Scientific Technological & Research Academy, Hyderabad, India2 Associate Professor, Department Of Civil Engineering, Aurora's Scientific Technological & Research Academy,Hyderabad, India3 Associate Professor, Department Of Civil Engineering, Aurora's Scientific Technological & Research Academy, Hyderabad, India

*Corresponding Author: Ketepalli Sravani, Research Scholar, Department of CIVIL Engineering, Aurora's Scientific Technological & Research Academy, Hyderabad, India Published: October 27, 2014Review Type: peer reviewedVolume: I, Issue : II

Citation:Ketepalli Sravani,(2014)STRENGTHENING OF RC BEAMS USING FRP SHEET

INTRODUCTION

General

To keep a structure at the same performance level, it needs to be maintained at predestined time inter-vals. Ifthe lack of maintenance has lowered the per-formance level of the structures, the need to repair up to the original performance level is required. In case, when higher performance levels are needed, upgrading of the structure is necessary. Perfor-mance level means load carrying capacity, durabil-ity and function. Upgrading refers to strengthening, increased durability and change of function.

The fundamental aim of this work is to give clear guidelines for the process of strengthening rein-

forced concrete beams using FRP materials. Types and methods of FRP construction are described in general. FRP properties and their effect on strength-ening are illustrated. External plate bonding is a method of strengthening which involves adhering additional reinforcement to the external faces of a structural member. The suc-cess of this technique relies heavily on the physical properties of the material used and on the quality of the adhesive, generally an epoxy resin, which is used to transfer the stresses between the flexural element and the attached reinforcement. The first reported case strengthened by this technique was in 1964. Epoxy-bonded mild steel plates were applied to load bearing beams in the basement.

Frp Strengthening Of Beam:

Many existing buildings and bridges are in need of repair or upgrade. A crumbling infrastructure is areality that all communities are dealing with. Existing beam members that are deficient with re-spect toflexural capacity are costly to demolish and reconstruct. An efficient, cost-effective means of-strengthening existing concrete beams is needed so an unsafe or unuseable structure can once again beutilized.The method of epoxy-bonding steel plates and fiberglass reinforced plastics to the tensile face

Abstract

Strengthening structures via external bonding of advanced fibre reinforced polymer (FRP) composite is becoming very popular worldwide during the past decade because it provides a more economical and technically superior alternative to the traditional techniques in many situations as it offers high strength, low weight, corrosion resistance, high fatigue resistance, easy and rapid installation and minimal change in structural geometry. Although many in-situ RC beams are continuous in construction, there has been very limited research work in the area of FRP strengthening of continu-ous beams.

In the present study an experimental investigation is carried out to study the behavior of continuous RC beams under static loading. The beams are strengthened with externally bonded glass fibre reinforced polymer (GFRP) sheets. Differ-ent scheme of strengthening have been employed. The program consists of fourteen continuous (two-span) beams with overall dimensions equal to (150×200×2300) mm. The beams are grouped into two series labeled S1 and S2 and each series have different percentage of steel reinforcement. One beam from each series (S1 and S2) was not strengthened and was considered as a control beam, whereas all other beams from both the series were strengthened in various patterns with externally bonded GFRP sheets. The present study examines the responses of RC continuous beams, in terms of failure modes, enhancement of load capacity and load deflection analysis. The results indicate that the flexural strength of RC beams can be significantly increased by gluing GFRP sheets to the tension face. In addition, the epoxy bonded sheets improved the cracking behaviour of the beams by delaying the formation of visible cracks and reducing crack widths at higher load levels. The experimental results were validated by using finite element method.

KEYWORDS: continuous beam; flexural strengthening; GFRP; premature failure;

1401-1402

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ofreinforced concrete beams has been studied ex-tensively as a method to strengthen existing rein-forcedconcrete structures. Experimental results have proven that these techniques can be an effec-tive means ofincreasing a beam’s flexural capacity and stiffness. However, a problem that has been encounteredduring the testing of reinforced beams with epoxy-bonded plates is separation of the plate from the beamat the plate termination prior to con-crete compression failure. Furthermore, there is some question as tothe loss of the ductile failure mode usually associated with reinforced concrete failure when carbon fibersheets and plates are used for external reinforcement. The use of expansion anchors has been examinedas a method of elimi-nating epoxy-bonded plate tear off at termination.

Bonding of steel and fiber-reinforced plastics is the most popular means of reinforcing existingconcrete beams. However, applying epoxy can be a delicate process requiring near perfect workingconditions. The beam must be properly prepared for epoxy ap-plication (smooth, flat, sandblasted, dustfree,clean surface), and the thickness of the epoxy layer must be uniform. Perfect conditions are not thenorm when one is working in the field. This procedure can be successful, but the quality controlmeasures can be extreme. A solution to this problem is to take advantage of the fact that bolts have beensuccessful in stopping plate tear-off, and go one step further and use anchor bolts as the main system ofanchor-ing supplemental external steel reinforcement to the beam. This method can be used underfrequently encountered field conditions since the work envi-ronment need not be ideal and prep work formount-ing the reinforcement is minimal (aside from drilling holes into the flexural member).

In the 1980s, fiber reinforced polymer (FRP) materi-als began being used in civil engineering applica-tions. The external strengthening of reinforced con-crete members was an ideal use for preformed FRP strips, which are lighter and easier to install than steel strips. FRP strips do not rust when exposed to moist environments as do steel strips. Currently FRP strips are bonded to the concrete surface in the same manner as the steel strips, and the concrete substrate requires similar preparation as it would for the bonding of a steel plate. The adhesive layer between the concrete and strip can present prob-lems for the behaviour of the strengthened flexural member. Peeling stresses are induced in the ends of the strip, which tend to pull the strip away from the concrete. If these peeling stresses are larger than the strength of the adhesive, the strip will peel away from the beam suddenly. This results in the beam losing the increase in strength provided by the strip, and may cause a sudden and catastrophic failure.

Flexural members with attached steel strips often have large anchor bolts on the ends of the strips. These anchor bolts are provided to keep the steel plate from falling and damaging people or prop-erty in case the adhesive layer fails. Recently end

anchorages have been examined for use with FRP strips as well.

Many researchers have been argued that the bond is significantly affected by surface preparation and general concrete quality, the degree and type of external anchorage was found to be important in maintaining the composite behaviour. This moti-vates researches to find a more sustainable method to bond CFRP and GFRP laminates with concrete substrate using mechanical techniques.

A method of flexural strengthening reinforced con-crete members with mechanically steel bolts is de-veloped in this research study instead of an adhe-sive to attach a specially designed FRP strip to the concrete. This new technique has a potentially fast-er installation time and a potentially more ductile failure structural response than the sudden failure of conventional bonded method with epoxy.

Fibre-Reinforced Plastic (FRP):

(also fibre-reinforced polymer) is a composite mate-rial made of a polymer matrix reinforced with fibres. The fibres are usually glass, carbon, basalt orara-mid, although other fibres such as paper or wood or asbestos have been sometimes used. The polymer is usually an epoxy, vinyl ester or polyester thermo-setting plastic, andphenol formaldehyde resins are still in use.

Fibre Types:

Different types of fibres can be used in manufactur-ing the FRP materials such as the following (Kend-all, 1999):

E-Glass: The most common reinforcing fibre is E-Glass, which derives its name from its electrical resist-ance. E-glass is available in a variety of forms such as continuous rovings, woven rovings, stitched fab-rics, unidirectional tapes and chopped fibre mats or Chopped Strand Mat (CSM) as it is commonly known. The fibre is very economical and of moder-ate strength but low modulus (stiffness).

C, R and S Glass: C glass is a chemical resistant grade mainly used in the production of surface tissues to protect the surface of a laminate. R glass and S glass are high strength grades. Aramid Aramid, or Polyaramid fi-bres such as Kevlar 49 are man-made organic fibres offering very high tensile strengths and low density. Aramid fabrics are very soft and easy to handle.

Carbon:Carbon fibre is the most expensive of the more common reinforcements, but due to its very high strength and stiffness it is the most commonly used fibre.

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Advantages Of Fibre-Reinforced Plastics:

Fibreglass and other fibre-reinforced plastics (FRP), such as carbon fibre and Kevlar, have many advan-tages:

Low weight: even the cheapest fibreglass is much less dense and therefore lighter than the equivalent volume of steel or aluminium.

Mechanical strength: fibreglass is so strong and stiff for its weight, it can out-perform most other materials including steel, aluminium and timber. Carbon-fibre and Kevlar can be used to make items even lighter. The strength and stiffness per weight of these exotic materials exceeds that of all known materials.

High impact strength: in contrast to most metals, fibreglass does not change shape even when it is ruptured.

Resiliance: fibreglass products have a hard finish. The gelcoat which covers and colours finished fi-breglass products can be tailored to provide greater hardness or more resiliance.

Formability: fibreglass can be moulded to almost any desired shape. We can create or copy most shapes with ease. Fibreglass moulds are cheap to make compared with those for metal or plastic. It is quite easy to change the weight and strength of a product without having to make a new mould.

Chemical resistance: fibreglass is minimally re-active, making it ideal as a protective covering for surfaces where chemical spillages might occur. It is useful in the construction of tanks, hoods, cov-ers, pipes, ducts and other structures in the paper, chemical, water treatment and petroleum indus-tries.

Corrosion resistance: unlike metal, fibreglass does not rust away and it can be used to make long-last-ing structures.

Weatherproof: the chemical and corrosion resist-ance of fibreglass combined with the gelcoat finish on most products make fibreglass ideal for using outdoors. If necessary, chemicals can be added to provide additional protection against UV light.

Electrically insulating: for those working in the power industry, materials such as fibreglass which do not conduct electricity are essential for safety. However, if required, we can adapt our fibreglass to become electrically conductive.

Thermally insulating: fibreglass is not only long lasting but maintains its temperature, thus reduc-ing heating and cooling costs. The fibreglass sur-face remains comfortable to touch, being neither hot nor cold.Fire resistance: by the addition of special addi-

tives, fibreglass can be made fire resistant to meet most fire codes. The resins used conform to BS476 or ASTM-E-84.

Low thermal expansion: minimally affected by changes in external temperature, fibreglass is ideal for situations where temperatures fluctuate.

Anti-magnetic, no sparks: making it super safe for the power industry, fibreglass has no magnetic field and resists electrical sparks.

Low maintenance: once installed, fibreglass prod-ucts require minimal maintenance.

Durable custom colours: fibreglass can be col-oured, shiny or dull. We can even add patterns if you wish. Your production costs are reduced as our gelcoated products don't need further painting or finishing. With care, the gelcoat finish on our auto-motive parts can last for up to 20 years.

Long life: our fibreglass products are built to last. Fibreglass has high resistance to fatigue and has shown excellent durability over the last 50 years.

Structural Applications Of FRP:

FRP can be applied to strengthen the beams, col-umns, and slabs of buildings and bridges. It is pos-sible to increase the strength of structural members even after they have been severely damaged due to loading conditions. In the case of damaged rein-forced concrete members, this would first require the repair of the member by removing loose debris and filling in cavities and cracks with mortar or epoxy resin. Once the member is repaired, strength-ening can be achieved through wet, hand lay-up of impregnating the fibre sheets with epoxy resin then applying them to the cleaned and prepared surfaces of the member. Two techniques are typically adopted for the strengthening of beams, relating to the strength en-hancement desired: flexural strengthening or shear strengthening. In many cases it may be necessary to provide both strength enhancements. For the flex-ural strengthening of a beam, FRP sheets or plates are applied to the tension face of the member (the bottom face for a simply supported member with applied top loading or gravity loading). Principal tensile fibres are oriented in the beam longitudinal axis, similar to its internal flexural steel reinforce-ment. This increases the beam strength and its stiff-ness (load required to cause unit deflection), how-ever decreases the deflection capacity and ductility.

Disadvantages Of FRP:

The main disadvantage of externally strengthening structures with fibre composite materials is the risk of fire, vandalism or accidental damage, unless the strengthening is protected. A particular concern for bridges over roads is the risk of soffit reinforcement

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being hit by over-height vehicles.

A perceived disadvantage of using FRP for strength-ening is the relatively high cost of the materials. However, comparisons should be made on the basis of the complete strengthening exercise; in certain cases the costs can be less than that of steel plate bonding. A disadvantage in the eyes of many clients will be the lack of experience of the techniques and suitably qualified staff to carry out the work. Final-ly, a significant disadvantage is the lack of accepted design standards.

Experimental Study

Experimental Program:

A total of six rectangular beams were tested to find the effectiveness of the strengthening process us-ing GFRP laminates. Two beams were tested as con-trolled beams for flexure, while the remaining four beams were strengthened using GFRP mats and tested with the goal of increasing their flexural ca-pacities. The concept is based on the fact that the force developed in the GFRP mat is due to contact between the materials because of the bond which is responsible for the increase in flexural capacities.This paper provides information regarding(i)Deformation characteristics of load versus deflec-tion(ii)Ductile capacity of composite beams.

Casting Of Specimen:

For conducting experiment, the proportion of 1: 1.9: 3.91 is taken for cement, fine aggregate and course aggregate. The mixing is done by using concrete mixture. The beams are cured for 28 days. For each beam six concrete cube specimens were made at the time of casting and were kept for curing. The uni-axial compressive tests on produced concrete (150 × 150 × 150 mm concrete cube) were performed and the average concrete compressive strength (fcu) af-ter 28 days for each beam is shown in tables.

Descrip-tion Cement

Sand (FineAggregate)

CourseAggregate Water

Mix Pro-portion

(by weight)1 1.9 3.91 0.51

Quantities of materi-

als213 404.7 832.83 108.63

Materials For Casting:

Cement :

Portland Slag Cement (PSC) (Brand: Konark) is used for the experiment. It is tested forits physical prop-erties in accordance with Indian Standard specifica-tions. It is having a specific gravity of 2.96.(i)Specific gravity : 2.96 (ii)Normal Consistency : 32%

(iii)Setting Times : Initial : 105 minutes Final : 535 minutes.(iv)Soundness : 2 mm expansion (v)Fineness : 1 gm retained in 90 micron sieve.

Fine Aggregate:

The fine aggregate passing through 4.75 mm sieve and having a specific gravity of 2.67are used. The grading zone of fine aggregate is zone III as per In-dian Standard specifications.

Coarse Aggregate: The coarse aggregates of two grades are used one retained on 10 mm size sieve and another grade contained aggregates retained on 20 mm sieve. It is having a specific gravity of 2.72.

Water:

Ordinary tap water is used for concrete mixing in all the mix. Test Specimens:

All the six cast test specimens are rectangular RC beamsof cross section 220mmx250mm and length 2000mm.six numbers of beams were tested for flex-ure. It consists of two numbers of 10mmdiameter and one number of 12mm diameter bars whichare used in compression and tension sides. The ver-ticalstirrups are provided with 6mm diameter bar at aspacing of 225mm c/c as shown in Figure. Thesebeams were designed to fail by flexure. Out of sixbeams, two were used as control beams and remainingfour were strengthened using GFRP mats. The designmix adopted for all beams were 1: 1.9: 3.91 and watercement ratio of 0.51. The test speci-mens were cured for28 days and they were tested.

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GFRP Composites:

E-Glass fiber in the form of woven fabric of600gm/sq.m is used for strengthening purposes. Forbond-ing these fabric mats with RC beams, 45% byweight of general purpose Iso resin is used.

Strengthening Configurations:

Two strengthening configurations were adopted us-ingGFRP mats for flexure beams which are shown in figure. Externally they are wrapped by a (i) Sin-glelayer at two vertical sides, and tension bottom face(GFRP1) and (ii) Double layer at two vertical sides andtension bottom face(GFRP2).

ReinforcementOf Beam

Strengthening Of Gfrp Beams

Testing Arrangements:

The beams were tested in a steel loading frame ca-pacityof 500kN. The arrangement is shown in Fig-ure. Forgetting moment effect of the beam, an ex-perimentalsetup has been arranged as shown in Figure. Thesupport points were provided with a hinge support atboth ends of steel rod welded to the base plate. The loadwas applied by means of 500kN capacity hydraulic jackpowered by hand operat-ed hydraulic pump. The systematic Figure clearly shows the loadingarrangement for getting the mo-ment effect of the beam.

Deflections measured at important points. Three number of dial gauges have used for recording the deflection ofthe beams. One dial gauge has placed just below thecenter of the beam and the remaining two dial gaugeshave placed just near the middle of the beam to measuredeflections as shown in Figure. The cracking patternwas also marked by drawing lines along the crack. The tests are carried out till the ultimate failure.

FABRICATION OF GFRP PLATE:

There are two basic processes for moulding: hand lay-up and spray-up. The hand lay-up process is the oldest and simplest fabrication method. The process is most common in FRP marine construc-tion. In hand lay-up process, liquid resin is placed along with FRP against finished surface. Chemi-cal reaction of the resin hardens the material to a strong light weight product. The resin serves as the matrix for glass fiber as concrete acts for the steel reinforcing rods.The following constituent materials were used for fabricating plates:

1.Glass Fiber2.Epoxy as resin 3.Diamine as hardener as (catalyst) 4.Polyvinyl alcohol as a releasing agent

A plastic sheet was kept on the plywood platform

Loading frame

Loading System

Shear Force Diagram

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Bending Moment Diagram

Flexural Zone

and a thin film of polyvinyl alcohol was applied as a releasing agent by the use of spray gun. Laminating starts with the application of a gel coat (epoxy and hardener) deposited in the mould by brush, whose main purpose was to provide a smooth external sur-face and to protect fibers from direct exposure from the environment. Steel roller was applied to remove the air bubbles. Layers of reinforcement were ap-plied and gel coat was applied by brush. Process of hand lay-up is the continuation of the above process before gel coat is hardened. Again a plas-tic sheet was applied by applying polyvinyl alcohol inside the sheet as releasing agent. Then a heavy flat metal rigid platform was kept top of the plate for compressing purpose. The plates were left for mini-mum 48 hours before transported and cut to exact shape for testing.

Determination Of Ultimate Stress, Ultimate Laod And Young’smodulus:

The ultimate stress, ultimate load and young’s mod-ulus was determined experimentally by performing unidirectional tensile test on the specimens cut in longitudinal and transverse direction. The speci-mens were cut from the plates by diamond cutter or by hex saw. After cutting by hex saw, it was pol-ished in the polishing machine.

For measuring the young’s modulus, the specimen is loaded in INSTRON 1195 universal tensile test machine to failure with a recommended rate of ex-tension. Specimens were gripped in the upper jaw first and then gripped in the movable lower jaw. Gripping of the specimen should be proper to pre-

vent slippage. Here, it is taken as 50 mm from each side. Initially, the stain is kept zero. The load as well as extension was recorded digitally with the help of the load cell and an extensometer respectively. From these data, stress versus stain graph was plotted, the initial slope of which gives the Young’s modulus. The ultimate stress and the ultimate load were

Bonding epoxy

Universal Testing Machine

obtained at the failure of the specimen. The average value of each layer of the specimens is given.

TESTING OF BEAMS:

All the six beams are tested one by one. All of them are tested in the above arrangement. The gradual increase in load and the deformation in the dial gauge reading are taken throughout the test. The load at which the first visible crack is developed is recorded as cracking load. Then the load is applied till the ultimate failure of the beam. The deflections at midpoint of each span are taken for all beams with and without GFRP and are recorded with re-spect to increase of load. The data furnished in this chapter have been interpreted and discussed in the next chapter to obtain a conclusion.

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Test Resultsand Discussions

Failure Modes Of Beams:

Peeling Failure:

The application of the GFRP fabrics to the soffit of the concrete beam introduces shear transfer to the concrete/epoxy interface. At the termination of the GFRP fabric, a change in stiffness and discontinuity of beam curvature creates a stress concentration in the concrete, often initiating cracks that can lead to debonding. Based on the experimental observations, the mech-anism of peeling failure can be described in the following sequences: 1) uniformly spaced cracks developed in the con-stant bending moment zone and some small cracks in the shear span 2) as a result of shear stress and normal stress con-centrations at the GFRP fabric end, the concrete rupture strength was exceeded at this point and a crack formed near the fabric end. This end Debond-ing propagation to the CFRP fabric endDebond-ingstarted here Loading point crack widened with increasing load and propagated to the level of the internal steel reinforcement3) individual concrete cover blocks were formed be-tween two adjacent cracks;4) the end concrete cover block peeled away as the load increased 5) This process continued sequentially for the rest of the blocksDue to the dowel action of the stirrups, the weakest plane forms right under the longitudinal steel rein-forcement, thus, the peeling failure always started from the end of the plates and propagated along the concrete cover parallel to the longitudinal steel re-inforcing bars.

Debonding Failure

The beams with FRP fabric extending all the way to the support are subjected to lower stress concentra-tions at the FRP cutoff points and shear crack may not developed at these points. On the other hand, within the shear span, the shear stress concentra-tion around the flexural or shear crack mouth dis-placements may also lead to the local debonding of the fabric along concrete-fabric interface.

Flexural cracks, located in regions of the beam with large moment, can initiate interfacial fracture which propagates between the concrete and FRP interface. Crack mouths located in regions of the beam with mixed shear and moments can subject an interfa-cial crack to mixed mode loading. For beam with a long fabric covering almost the whole length of span, the debonding started at one of the flexural cracks in vicinity of the point load. The debonding propagated towards the sheet end until total delamination occurred.

In general, peeling of the concrete cover at the level of internal steel reinforcement occurred in beams with shorter fabric length where significant shear cracks were formed, indicating that significant stress con-centration can occur at the sheet anchorage zone. Debonding failure between FRP fabric and concrete occurred due to susceptibility of the interface rela-tive to vertical displacements of shear cracks in the concrete beam.

BEAM SHEAR FAILURE MODES:

Three distinct modes of shear failure are observed, which describe the manner inwhich concrete fails:• Diagonal tension failure• Shear compression failure• Shear tension failure

DIAGONAL TENSION FAILURE:

This type of failure is usually a flexure-shear crack. The diagonal crack starts from the last flexural crack at mid span, where it follows direction of the bond reinforcing steel and the concrete at the sup-port. After that, few more diagonal cracks develop with further load, the tension crack will extend gradually until it reaches its critical point where it will fail without warning. This type of shear failure is always in the shear-span when the a/d ratio is in the range of 2.5 to 6. Such beams fail either in shear or in flexure.

Failure Plane

SHEAR COMPRESSION FAILURE:

This type of failure is common in short beams with a/d ratio between 1 and 2.5. It’s called a web shear crack, it’s crushing the concrete in the compression zone due to vertical compressive stresses developed in the vicinity of the load.

Compression Failure

SHEAR TENSION FAILURE:

This type of failure is also common in short beams and it is similar to diagonal tension failure. First

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we can see a shear crack that is similar to the di-agonal crack that goes through the beam; the crack extends toward the longitudinal reinforcement and then propagates along the reinforcement that re-sults in the failure of the beam.

Shear Torsion Failure

RESULTS OF EXPERIMENTS:

FAILURE PATTERN OF CONTROL BEAM:

The beam was so designed that it fails by flexure. The beam was tested up to 42kN. The yield of steel was found at 37kN. With further increase in the load, regularly spaced flexure and shear cracks were observed and they extended from the bottom of the specimen towards the top fiber as shown in figure.

Failure Pattern OfControl Beam

FAILURE PATTERN FOR STRENGTHENING BEAM:

The beam was strengthened with one layer of GFRP1 laminate on the bottom face and two vertical sides completely. The ultimate load carrying capacity of the beam was 66kN. The yield load was 57kN. The load carrying capacity of this beam was increased by 55%when compared to control beam as shown in Figure. The failure was initiated by the stretching of fiber wrap at the bottom in the flexure zone followed by the crushing of concrete in compression zone as shown in figure.

Failure Pattern Of Single Layer GFRP1 Beam

Failure Pattern OfDouble Layer GFRP2Beam

The beam was strengthened with two layers of GFRP2 laminate on the bottom face and two verti-cal sides completely. The ultimate load carrying ca-pacity of the beam was 92kN. The yield load was 78kN. The load carrying capacity of this beam was increased by 120% when compared to control beam as shown in Figure. The failure was initiated by the stretching of fibre wrap at the bottom in the flexure zone followed by the crushing of concrete in com-pression zone as shown in Figure.

Designationof Beams Failure Mode Pu(KN) λ=Pu(strengthened beam)

Pu(Control beam)

Control beam Flexure failure 42 1

Single layer GFRP1

Debonding failure without concrete

cover66 1.57

Double layer GFRP2 Tensile rupture 92 2.19

LOAD DEFLECTION AND LOAD CARRYING CAPACITY:

The GFRP strengthened beams and the control beams are tested to find out their ultimate load carrying capacity. The deflection of each beam un-der the load point i.e. at the midpoint of each span position is analyzed. Mid-span deflections of each strengthened beam are compared with the control beam. It is noted that the behavior of the flexure deficient beams when bonded with GFRP sheets are better than the control beams. The mid-span deflec-tions of the beams are lower when bonded externally with GFRP sheets. The stiffness of the strengthened beams was higher than that of the control beams. Increasing the numbers of GFRP layers generally reduced the mid span deflection and increased the beam stiffness for the same value of applied load. The use of GFRP sheet had effect in delaying the growth of crack formation.

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Ductility:

A qualitative measure of ductility has to be with reference to a load – deformation response. A duc-tileresponse would be reflected in the deformation-increasing at nearly constant load. The ratio of theultimate deformation to the deformation at the-beginning of the horizontal path can give a measure ofductility.

Ductility has generally been measured by a ratio calledthe ductility index or factor (μ). The ductil-ity index isusually expressed as a ratio of rotation (θ), curvature(φ), deflection (displacement) (M), and absorbed energy(E) at failure (peak load) divided by the correspondingproperty when the steel starts yielding. In the presentstudy, ductility was obtained based on displacement and absorbed energy meth-ods.

Displacement Ductility:

Figure shows the response of a strengthened RC-beam. Point A corresponds to initial concrete cracking,point B to the first steel yielding, and point C to failure.Based on Figure , the displacement duc-tility index is defined by Eq. Where Mu is the mid span deflection at ultimate beamload and My is the mid span deflection at yielding loadof the tensile steel reinforcement at the central support.

Table shows the experimental values of (Mu), (My),the displacement ductility index value of (μM), and percentage of increase of displacement ductility in theBC. It can be seen that increasing the num-ber of GFRPsheet layers led to increased mid span deflection at yieldload level and ultimate load level.

Finite Element Analysis

Finite element method (FEM) is a numerical meth-od for solving a differential or integral equation. It has been applied to a number of physical problems, where the governing differential equations are avail-able. The method essentially consists of assuming the piecewise continuous function for the solution and obtaining the parameters of the functions in a manner that reduces the error in the solution.

Formulation:The governing equation for beam is given in Equa-tion 5.1. d2 y M = EI d x2 The displacement field v(x) assumed for the beam element should be such that it takes on the

values of deflection and the slope at either end as given by the nodal values

The v(x) can be given by, v(x) = c0 + c1x + c2 x2 +c3x3

Type Of Beam

(∆u) (∆y) (µ∆) Increase (Eu) (Ey) (µE) Increase

overthe control beam(%)

overthe control beam(%)

(mm) (mm) By Eq.(1)

kN kN By Eq.(2)

Control beam

20 8 2.5 - 42 37 1.13 -

Sin-glelayr GFRP1

29 9.5 3.05 22 66 57 1.16 3

Double layer GFRP2

38 11 3.45 38 92 78 1.18 5

In solving the differential equations through integra-tion, there will be constants of integration that must be evaluated by using the boundary and continu-ity conditions. The variables whose values are to be determined are approximated by piecewise continu-ous polynomials. The coefficients of these polynomi-als are obtained by minimizing the total potential energy of the system. In FEM, usually, these coef-ficients are expressed in terms of unknown values of primary variables. Thus, if an element has got n nodes, the displacement field u can be approxi

Where ui are the nodal displacements in x-direction and Ni are the shape functions, which are functions of coordinates.Shape functions or interpolation functions Ni are used in the finite element analysis to interpolate the nodal displacements of any element to any point within each element.The beam element has modulus of elasticity E, mo-ment of inertia I, and length L. Each beam element has two nodes and is assumed to be horizontal as shown in Figure. The element stiffness matrix is giv-en by the following matrix, assuming axial deforma-tion is neglected.

VALIDATION OF EXPERIMENTAL VALUE:

In the experimental work, the tested beams consist of two spans of each 1000 mm as shown in Figure is discritized as shown in Figure.

Test Beam

Finite Element Model

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Beam Element Forces

The following sign convention is considered for the deflection calculation.

(a)x is +ve towards right

(b)y is +ve upwards

(c)Anticlockwise slopes are +ve

(d)Sagging BM are +ve

Three element mesh is taken as shown in Figure. Subdividing the span AD into three elements with a node at the load point has the advantage that, the nodal forces can be specified very easily. The meshing has also ensured that all elements are of uniform size, for easy hand calculation. Following the standard procedure, the global stiffness matrix and force vector is obtained as below,{K}8x8{U}8x1 = {F}8x1

Since there are four nodes and two d.o.f. per node, the global stiffness matrix is of size (8x8) and {F} is a column vector of size (8×1). The boundary condi-tions stipulate that the vertical deflection be zero at node 2 and 4.

Boundary conditions are the known values of de-flection and slope at specified values of x. Here the following boundary conditions are used for the ex-act analysis of the beam.

At x =L/2; y=0 At x= 3L/2; y= 0

Thus reduced set of equations involving unknown nodal d.o.f. is obtained in matrix form as, {f}6x1 = [k]6x6 [u]6x1

Solving the Equation, the nodal displacement is found out.

The Numerical and Experimental results are found to be very near. The trend of the loads varying with the deflection presents that the linear elastic state exits in the structure, when the loads are equivalent to about 48 KN.

CONCLUSIONS

Based on the Investigation the Following Conclu-sions were made:

1.The provision in the ACI code can be used as guidelines for the use of FRP in the repair and reha-bilitation of structures.

2.Maximum percentage of increase in ultimate strength was 55% for single layer GFRP and 120% for double layer GFRP.

3.By the use of GFRP wrapping in the beams, the initial cracks are formed at higher loads than in their respective control beams. This shows that the use of GFRP wrapping is more efficient in the case of strengthening of shear and flexure.

4.The increase in the strength of the beam depends upon the increasing number of laminates provided to the beam.

5.The presence of GFRP laminate beam inhibits the development of the diagonal cracks. There is a sig-nificant difference in the load which causes this ini-tial crack. The load –deflection behaviour was better for beams retrofitted with GFRP laminate beams.

6.For the beams laminated with GFRP flexural fail-ure was more prominent than shear failure.

7.When compared to control beams, displacement ductility index of the strengthened beams is in-creased by 22%, and 38% for Single layer of GFRP1 and Double layer of GFRP2 respectively.

8.The energy ductility index is increased by 3% and 5% for Single layer of GFRP1 and Double layer of GFRP2 respectively, when compared to control beams.

9.In lower range of load values the deflection ob-tained using Finite Element models are in good agreement with the experimental results. For higher load values there is a deviation with the experimen-tal results because linear FEM has been adopted.

Scope Of The Future Work

It promises a great scope for future studies. Follow-ing areas are considered for future research:

a.Experimental study of continuous beams with opening

b.Non linear analysis of RC continuous beam

c.FEM modeling of unanchored U-wrap

d.FEM modeling of anchored U-wrap

37


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AUTHOR

Ketepalli SravaniResearch Scholar, Department Of Civil Engineering,Aurora's Scientific Technological & Research Academy, Hyderabad, India

K. MythiliAssociate Professor, Department Of Civil Engineer-ing, Aurora's Scientific Technological & Research Academy,Hyderabad, India

G.Venkat RatnamAssociate Professor, Department Of Civil Engineer-ing, Aurora's Scientific Technological & Research Academy,Hyderabad, India