Reinforcing Bar 9tmt Bar ) Analysis in India

7/22/2019 Reinforcing Bar 9tmt Bar ) Analysis in India

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January 2004 * The Indian Concrete Journal 19

Characterisation of steel

reinforcement for RC

structures: An overview andrelated issues

Characterisation of steel reinforcement is as important as thatof concrete ingredients. The paper presents an overview ofcharacterisation along with some related issues. After brieflyhighlighting the mechanics of RC structures, importantcharacteristics of reinforcement, namely, bond with concrete,strength, ductility, resistance to corrosion are discussed. Theeffects of manufacturing process on the rebar characteristicsare then described. Finally, a comparison of specifications ofstandards of different countries dealing with reinforcing steelis presented. The authors have suggested certain modificationsin the Indian specifications IS 1786.

Steel is the time proven match for reinforcing concretestructures. Reinforced concrete structure is designed on theprinciple that steel and concrete act together to withstandinduced forces. The properties of thermal expansion for bothsteel and concrete are approximately the same, this alongwith excellent bendability property makes steel the bestmaterial as reinforcement in concrete structures. Anotherreason steel works effectively as reinforcement is that it bondswell with concrete. When passive reinforcement (steel bars)is employed, the structure is known as reinforced concrete(RC) structure. In prestressed concrete structure, thereinforcement (steel wire) is stressed prior to subjecting thestructure to loading, which may be viewed as active

reinforcement. Passive steel reinforcing bars, also known asrebars, should necessarily be strong in tension and, at thesame time, be ductile enough to be shaped or bent.

Rebars are rolled from billets that are obtained from afurnace. Billets can be produced either from iron-ore throughthe blast furnace converter route, or by melting scraps andrefining the same in the furnace. When billets are producedfrom scrap, they are known as re-rollables. IS : 17861allowsmanufacture of billets for reinforcing steel by open hearth,

electric, duplex, basic-oxygen or a combination of theseprocesses. Higher strength is imparted to rebars either bypost rolling process or by adopting additional measuresduring manufacturing of billets. Rebars are generally rolledin round section. Ribs are indented on the surface of thedeformed rebars or wires during the process of rolling. Theprime objective of such deformation is the enhancement of

bonding with concrete by mechanical interlocking.

In India, construction of reinforced concrete structuresstarted about 100 years back. Plain mild steel (MS) rebars ofgrade Fe-250 were used widely till about 1967. Square twisted

bars (deformed bars) were first introduced in India in 1965.But this was phased out due to their inherent inadequacies.

The high yield strength was first imparted to the rebarsby raising carbon as well as manganese contents, and to agreat extent, by cold twisting. The cold twisted deformed(CTD) bars are produced by cold working process, which is

basically a mechanical process. It involves stretching andtwisting of mild steel, beyond the yield plateau, andsubsequently releasing the load. CTD round rebars havingyield strength in the range of 405 MPa (Grade 40) wereintroduced in 1967. Since then, there has been an increasingdemand for high strength deformed bars.

Thermomechanically treated (TMT) bars were introduced

in India during 1980-1985. Thermo mechanical treatment isan advanced heat treatment process in which hot bars comingout of last rolling mill stand are rapidly quenched through aseries of water jets. Rapid quenching provides intensivecooling of surface resulting in the bars having hardenedsurface with hot core. The rebars are then allowed to cool inambient conditions. During the course of such slow cooling,the heat released from core tempers the hardened surfacewhile core is turned in to ferrite-pearlite aggregatecomposition. TMT process thus changes the structure of

Prabir C. Basu, Shylamoni PPrabir C. Basu, Shylamoni PPrabir C. Basu, Shylamoni PPrabir C. Basu, Shylamoni PPrabir C. Basu, Shylamoni P. and Roshan A. D.. and Roshan A. D.. and Roshan A. D.. and Roshan A. D.. and Roshan A. D.


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The Indian Concrete Journal * January 200420

material to ac o m p o s i t estructure ofductile ferrite-p e a r l i t ecomposition withtough surface rimof tempered

m a r t e n s i t eproviding ano p t i m u mcombination of

high strength, ductility, bendability and other desirableproperties. TMT bars of grade Fe415, Fe500 and Fe550 arenow available in India.

Now-a-days, alloy steels are also being introduced asreinforcing steel. Microalloying is found to be an efficientway to improve the properties of steel for rebars.

Three grades of rebar are presently available in India forstructural use. The rebars are graded according to theirspecified yield strength. These are Fe415, Fe500 and Fe550.CTD rebars of grade more than Fe415 are scarcely availablein market. However, TMT rebars of Fe500 grade are easilyavailable in the market. Fe250 grade mild steel rebars arealso available, but these are presently used generally assecondary reinforcement such as distribution steel in slabs,stirrups in beams and column ties.

Typical cross sections of MS, CTD and TMT rebars areshown in Fig1. For engineering a sound and durable concretestructure, it is essential to use reinforcement of appropriatecharacteristics and quality. Characterisation is a process tocontrol and ensure the quality of a material. Principal objectiveof characterisation of a material is to ensure that it possessesthe requisite properties necessary for its intended engineeringusage. Properties of rebars are influenced by the chemical

composition of the steel from which it is manufactured.Table1 shows the influence of different chemical ingredientsof steel on the properties of rebar.

Characterisation is generally performed by checking thechemical composition and certain specified physicalproperties. The particular chemical ingredients and physicalproperties, which are selected for characterisation, againdepend on the attributes of the material that are importantfor its specified application. A summary of specifications forrebar characterisations as per Indian standards is given inTable2.

Characterisation of steel rebars is as important as that ofconcrete for a sound RC structure of desired strength. Presentpaper tries to address the various aspects of characterisationof reinforcement and also related issues, which are importantfor design. Only passive reinforcement bars falls within thescope of the paper. Clear understanding of mechanics ofreinforced concrete structures helps in understanding theintricacy involved with the characterisation of rebars.

Moreover, basic knowledge onmanufacturing process of steelhelps in appreciating various facetsof the characterisation. These twoaspects are also discussed brieflyin the paper along with issuesrelated to characteristics of rebarsvis-a-vis performance of RCstructure. A comparative study ofthe national standards of a fewcountries is presented followed byconcluding remarks.

Brief overview ofmechanics of RCstructures

Reactions are induced withinstructural elements under theaction of applied forces. In three-dimensional cartesian co-ordinatesystems, these reactions are

translational forces along the threecoordinate axes (axial and twoshear forces) and moments aboutthese three axes (twisting momentand bending moments). Structuresmay fail in many ways due to theaction of these induced forces. Outof which, three types of failures,namely, stability failure, strengthfailure and serviceability failure are

Table 1: Influence of different chemical ingredients in steel on properties of rebars

No Chemicals Effects on rebars

C on troll in g Actual effect

proper ty

1 Carbon (C) Hardness, Higher carbon contributes to the tensile strength of steel, that is, higher load

strength, bearing capacity and vice versa. Lower carbon content less than 0.1 percent

weldabili ty and will reduce the strength. Higher carbon content of 0.3 percent and above

brittleness makes the steel bar unweldable and brittle.

2 Manganese Strength and The manganese content in steel is not specified as per IS: 1786.

(Mn) yield strength However higher manganese content in steel increases the tensile strength

and also the carbon equivalent property.

3 Sulphur (S) Present as an Presence of sulphur should be limited as per IS:1786. Presence of higher

impurity in sulphur makes the bar brittle during twisting, as higher sulphur content

steel which brings the hot shot problem during rolling.

increases its

brittleness.

4 Phosphorus Present as an Higher phosphorus content contributes to the increase in strength and

(P) impurity which corrosion resistance properties but brings britt leness due to the formation

increases of low euctoid phosphicles in the grain boundary. Also lowers the impact

strength and value at sub zero temperature level (transition temperature).

brittleness

5 Copper (Cu) Strength and Being a pearlite stabiliser, it increases the strength and corrosion resistance

corrosion property

resistanceproperties

6 Chromium Weldability Present as an impurity from the scrap and influences carbon equivalent;

(Cr) and corrosion weldabi li ty and inc reases co rrosion resistance p roperty.

resistance

7 Carbon Hardness, Th is proper ty i s requi red to set the coo ling paramete rs in TMT processEquivalent tensile strength and a slight variation in carbon equivalent may alter the physical

(CE or Ceq) and weldability properties. In case of CTD bars, carbon equivalent has a maximum limit

of 0.42 percent but there is no lower limit prescribed. As such, as long as the

chemical composition and physical properties of raw materials are within

specified limits, the variation in carbon equivalent as in the case of TMT

bars.


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important in most of the design cases. Stability failure usuallyrelates to overall structural systems, whereas strength failurerelates to elements of a structure. Serviceability failure isrelated to both overall structures as well as to individualelement. Reinforcement plays a key role in the design andconstruction of sound and durable structures for strengthand serviceability.

Failure modes of RC structural elements due to theinduced forces (six degrees of freedom) are generallycategorized in two groups for the design:

axial force and flexure

torsion and shear.

For the design of RC structural elements subjected to bi-axial bending or shear force (along two axes), bi-axialmoments or shear forces (along two axes) are decoupled touniaxial moments or shear forces along each axis and thedesign is performed separately for each uniaxial forces alongwith corresponding moments. Adequacy of reinforcementas well as strength of elements against the effect of combined

biaxial moments or forces is checked by satisfying interaction

equations.

For flexure design of the concrete structural elements, itis desirable to have enough warning time before failure.Concrete itself cannot provide such warning. It is theproperties of steel reinforcement as well as judicious selectionof its type/quantity, which contribute this attribute to thedesigned section. Under-reinforced designof section for

bending moment is important in this respect2,3

. The ultimatestrength of under reinforced beams is computed on the basis

that tensile steel provided is so low in quantity that the neutralaxis is close to the mid-depth of the rectangular beam (nearerto the compression edge), such that the maximum concretestrain, !cu, is attained simultaneously when the tensile rebar isyielded

3,4. The concept of under reinforced design of beam of

singly reinforced section is explained in Fig2. The maximumallowable strain in concrete, !cu, under flexure is limited to0.0035 as per IS 456 : 2000

5. Strain in rebar at the limit state of

collapse could be more and there is no restriction on itsmaximum value. This implies that the reinforcing steel shouldhave high capability of elongation after yielding. This is avery important characteristic of reinforcing steel for under-reinforced design.

The concept of under-reinforced section is important forachieving ductile design of structure. One of the importantapplications of ductile design is the aseismic design of thestructures

6. Structures are expected to experience more severe

ground motion than the one specified in codes for design.Utilising ductile behaviour of the structure is therefore mostdesirable as this enables the structure to withstand highershocks without collapse. Considering this, IS 1893, has laid

down regulations so that the structure shall suffer only adesired level of damage during earthquake of all magnitudes7.Rather, the objective is to ensure that, as far as possible,structures are able to respond without much structuraldamage to shocks of moderate intensities, and withoutcollapse to shocks of high intensities.

Shear failure is a brittle type of failure and occurs withoutwarning. Such type of failure should be avoided as far aspossible by appropriate design measures. In the shear design,reinforcement is restrained from yielding.

The basic principle behind the design of a RC structure isto achieve ductile rather than brittle failure of the structure.Ductility refers to a structures ability to undergo large

deformation before failure and dissipate more energy. Thismeans that the structure will not fail without sufficient priorwarning, and will be capable of large plastic deformations atnear maximum load-carrying capacity. Concrete is

Table 2: Summary of specifications for rebar characterisation

No Characteri stic s Spec ification

1. Chemical composi tion

(a) Mild steel IS 202614

(i) Carbon

Dia"20mmDia > 20mm

(ii) Sulfur

(iii) Phosphorus

(b) High strength deformed bars IS 1786

1

(i) Carbon

(ii) Sulfur

(iii) Phosphorus

2. Mechanical propert ie s

(a) Mild steel IS 43215

/IS 202614

(i) Ultimate tensile strength

(ii) Yield stress

Dia"20mmDia > 20mm

(iii) Elongation

(b) High strength deformed bars IS 17861

(i) 0.2 percent proof stress

(ii) Ultimate strength(iii) Elongation gauge length 5.65 #A

3. Bendability IS 17861/ IS 432

15

4. Tolerance of nominal mass

Dia "10mm 7 percent per metre run

10 "Dia "16 5 percent per metre runDia > 16mm 3 percent per meter run

5. Ribs of high strength deformed bars IS 17861

Note:Sampling for quality control should satisfy the requirements of IS 10790


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comparatively brittle material. It is the steel reinforcementwhose ductile property is the main contributor to the overallductile behaviour of designed section of a RC structuralelement.

IS 456 allows re-distribution of moments for the design ofstructural elements, such as slabs and beams, supporting

gravity loads. Studies established that ductility of rebarenhances the available capacity of concrete section of suchelements for moment re-distribution

8, 9.

Important characteristics of reinforcement

Good strength, bond with concrete, thermal expansioncharacteristics (similar to concrete) and bendability are primeattributes which make steel rebars most effective reinforcingmaterial for engineering of RC structures. Besides strength,the durability of the structure depends upon rebar quality.Durability is the ability of the structure to maintain safetyand serviceability criteria during its design life. Durability isdependent on the condition of concrete and reinforcement.

Corrosion of reinforcement is one of the main factors thatcould impair durability. Corrosion can be either due to chlorideintrusion or due to the effect of carbonation. Chemicalcomposition of reinforcement plays an important role in thisrespect.

Two characteristics of rebars bendability andweldability are important for construction. Bendability isessential from giving requisite shape to the rebar to suit thedemand of the structures. Sometimes, welding of highdiameter rebars is resorted to reduce congestion. Weldability

of rebar is also an important factor forfixing embedded parts in the concrete

before pouring.

To summarise, attributes ofreinforcements that are important forengineering of sound and durable RCstructures are:

bond with concrete

strength

ductility

resistance against corrosion.

Enhancement of strength by coldworking process or by changingchemical composition (for exampleincrease in carbon content) hasconflicting effect in the ductility andweldability. Therefore, balancing of

conflicting requirements is required infixing the characteristics of rebar tostrike an optimum balance betweenstrength, ductility, durability and cost.

Bond with concrete

The bond between rebar and concretedepends upon many factors, such as

shape, geometry of ribs. Steel rebars are generally round incross section. To restrict longitudinal movement of the barsrelative to the surrounding concrete, lugs or protrusions calleddeformations or ribs are rolled on to the bar surface. Forappropriate bond strength, the deformations of ribs of rebarshould satisfy certain specifications

1.

Strength

Typical stress strain curve of monotonically loaded (tension)mild steel rebar is shown in Fig3(a). The curves exhibit aninitial elastic portion, a yield plateau (that is, a yield point

beyond which the strain increases with little or no increase instress), a strain hardening range in which stress again increaseswith strain, and finally a range in which the stress drops offuntil fracture occurs. The slope of the linear elastic portion ofthe curve represents the modulus of elasticity of steel. Thestress at the yield point, referred as the yield strength, is avery important property of steel reinforcement.Reinforcement is generally characterized by its yield strength.

Stress-strain curves of the steel in compression andtension are considered to be the same. In case of mild steel,yielding sometimes is accompanied by an abrupt decrease instress, and the stress-strain diagram has two stress (yield)levels, which are marked as A and B in Fig3(a). Points A andB are referred as upper and lower yield strengths respectively.The position of the upper yield point depends on the speedof testing, the shape of the section and the form of thespecimen. The lower yield strength is usually considered asthe true characteristic of the material and simply referred asyield strength, which is around 250 MPa for mild steel rebars.


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In cold working (stretching and twisting) process, the mildsteel bar is subjected to repeated loading. the steel will followa similar linear elastic path, as that of original mild steel till itreaches the point where unloading started, which becomesthe new yield point, Fig3(b). The cold working of steel cancause the shortening of the yield plateau or even eliminatingit completely. Desired increase in yield strength is achieved

by appr opri ate se lect ion of unloading po int

Fig3(b). This is why high strength bars generally do notexhibit definite yield strength as that in case of mild steel.Fig3(c) presents a typical stress strain curve of cold twistedhigh strength rebar. Cold working process is simple, reliableas well as cost effective, but reduces elongation of rebarcompared to mild steel. In India most of the high strengthdeformed bars are manufactured by cold working process.CTD bars does not exhibit specific yield point and 0.2 percentproof stress is taken as yield strength, Fig3(c).

Stress-strain curve of TMT bars is similar to that for MSbars, Fig3(d). But in case of TMT bars, there are no distinctyield plateau and two yield points.

The actual yield strength of the rebar is usually somewhathigher than that considered in design. The specified yieldstrength normally refers to a guaranteed minimum value ofthe yield strength lower yield strength in case of mild steelrebar. Fatigue strength of reinforcement depends on its yieldstrength and rebars having higher fatigue strength have

better capability of withstanding dynamic loads.

Bond strength signifies its ability for holding concretearound it. It depends on the reinforcing properties of the

bars, such as yield strength, adhesion with concrete matrix,indentation (configuration of deformed shape).

Ductility

During initial period of reinforced concrete construction,

requirement of ductility was considered synonymous withbendability. However, ductility of reinforcement has beenfound to have far reaching effects on the safety and durabilityof the structure. The physical property of rebar, which isresponsible for ductility, is its elongation. As discussed earlier,ductility refers to ability of dissipating energy and largedeformation. Ductility of a beam under flexure, $f, is given

by,

f$ =y

u

%

%(1)

Where, %uand %y are the curvature of the section at collapseand yield state respectively. Ductility of rebar, which hassignificant influence on $f,is expressed as the ratio of ultimatedeformation at collapse to deformation at yielding. Referringto Fig 3(a), the ductility of a mild steel rebar under themonotonic tensile loading is given by

$ =y

u

!

!(2)

Where $, !uand !yare ductility factor, ultimate strain andyield strain of the rebars respectively. In CTD bars, !y refers

to the strain corresponding to 0.2 percent proof stress. For agiven value of !y, $increases with !u,which increases withelongation of rebars. This makes elongation a good indicatorof ductility and is used as a parameter to characterise therebar for ductility.

Under the repetitive loading when the load is releasedbefore failure, the specimen will recover along a stress-strainpath that is parallel to the original curve,Fig3(b), with perhapsa small hysteresis and/or strain-hardening effect. The virgincurve is then closely followed, as if unloading had notoccurred. Hence, the monotonic stress-strain curve gives agood idealization for the envelope curve of rebar underrepeated loading of the same sign

2.


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Requirement of ductility is more important where thestructure is subjected to cyclic loading (for example,earthquake load) or impact. If axial loading of cyclic nature(tension-compression) is applied to a mild steel specimen inthe yield range, a stress-strain curve of the type presented in

Fig 4 is obtained. Due to Bauschinger effect, that is, strainsoftening that takes place under reversed loading, the stress-strain curve becomes nonlinear at a stress much lower thanthe initial yield strength

2. This behaviour of steel bars is

strongly influenced by previous strain history; time andtemperature also have an effect. The unloading path followsthe initial elastic slope.

An idealisation by Kato et al22, based on observation ofexperimental stress-strain data, obtains the stress-strain curvefor reversed loading from the monotonic curves for tensionand compression in the manner illustrated in Fig 5. Thereversed load diagram (Fig 5(a)) is divided in curvescorresponding to loadings attained for the first time,

unloading branches (straight lines), and loadings attained inprevious cycles (softened curves due to the Bauschingereffect). The parts of the diagram of the same sign can beplotted in sequence, as in Fig 5(b). Connecting the segmentsof the first loading branches end for end (Fig 5(c)) leads to adiagram similar to the monotonic curves. A difference existsat the initial part of the curve in compression, which isconsiderably curved, compared with the monotonic curve.

The above discussion essentiallyindicates that the behaviour with respectto ductility of rebar, against monotonic,repetitive and cyclic loading can becharacterised by means of ultimatestrain at fracture or total elongation. Therequirement of minimum strain atfracture or minimum elongation isspecified in codes. Such specification isessential for the safety of the structureand in order to ensure that the steel isductile enough to undergo largedeformations before fracture. It may benoted that CTD bar has lesser elongation

before fracture than the mild steels.

Resistance against corrosion

Resistance of rebars against corrosion depends upon itschemical composition. Corrosion of rebars in reinforcedconcrete structure is a complex phenomenon. Corrosion ofsteel occurs due to a number of initiating causes that exposethe rebars to moisture and oxygen either by carbonation orchloride intrusion. During the process of cement hydration,

a thin protective alkaline passive film is formed around rebars.Corrosion process is initiated when this protective film isbroken. Though good quality concrete is a pre-requisite forthe corrosion resistance of RC structure, the quality of rebarshas also a significant influence on it.

No carbon steel reinforcement bar could be termed ascorrosion resistant steel; one type may have lower corrosionpotential than the other. Experience shows that MS rebarsare more corrosion resistant than CTD bars. Possible reasonsfor higher corrosion resistance of MS reinforcement barscompared to that of CTD and also of TMT rebar are listed

below.

(i) In the manufacture of MS bars, a thin film is formed

around the bars during cooling operation, and thisfilm acts as a barrier. This barrier retards the initiationof corrosion in MS bars. In the case of TMT bars thisfilm almost does not exist, while for CTD bars thethin film is lost during the twisting process.

(ii) During the cold twisting process a part of residualstrain is withheld in the periphery of the CTD bars.This locked-in strain initiates the corrosion processfaster.

(iii) The level of induced stresses in CTD and TMT rebarsare much higher than those in MS bars which againenhances the potential of initiating corrosion .

Effect of manufacturing process on rebarcharacteristics

Production of high-strength CTD bars are achieved throughthree stages:

(i) manufacturing of billets

(ii) rolling of billets into rebars, and


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(iii) process to impart further strength.

Production of TMT rebars involves only the first twoprocesses. All the stages have significant influence on thecharacteristics of rebars. In general, both the quality of basicmaterials used in rolling the rebars and its manufacturingprocess are important. Quality of metal scrap has utmostimpact on the performance of rebars when re-rollables are

used. Kaushik and Singh discussed in detail the influence ofmanufacturing process on the quality of rebars11

.

The so called mild steel rebars are rolled from generalcarbon steel billet without adopting any special measures orimparting further strength. In India, more than 50percent ofthe rebars are manufactured from the re-rollablesmanufactured from the scrap materials such as scrap rails,automobile scrap, defense scrap, defectives from steel plants,and scrap generated from ship breaking or discardedstructures. Composition of scrap steel was fixed based on thepurpose of original usage from which the scrap is generated.Such composition may not always be suitable formanufacturing of rebars having required characteristics.

It is necessary to refine the molten scrap to control thecontents of carbon, sulphur, phosphorus etc. to desired levels.Though lower carbon content reduces the strength of steel,higher value makes steel brittle and unweldable. Highersulphur and phosphorus content makes the steel brittle, eventhough higher phosphorus content may have beneficial effectlike increasing strength and corrosion resistance. All theseconflicting aspects indicate that certain level of refinement ofthe composition of steel is necessary. The desired refinementcan be suitably achieved with the use of an electric arc furnace,which unfortunately is not being employed now-a-days dueto prohibitive cost of production. Induction furnace is mostlyused in India for manufacturing of rebars from scraps. It iswell known that induction furnace cannot yield sufficient

refinement of molten scrap to produce billets of desiredquality.

Enhancement of rebar strength is generally achieved bythree processes:

(i) cold working,

(ii) thermo mechanical treatment (TMT), and

(iii) micro alloying.

The first process may be viewed as post rolling processwhile the second one is a part of rolling process and the thirdone is associated with the billet production process.

The technology of producing CTD bars had beenintroduced in mechanised cooling bed across the country fora long time. Proper equipment, manpower and overall goodquality of raw material are necessary for achievingappropriate quality of CTD bars. The effects of processparameters are established. For example, tensile strengthcan be controlled by pitch of the twist. The limitation of theprocess is that it cannot produce bars below 8 mm diameter.

For the TMT process, rolling mill with automatic coolingbed is essential. Proper control during cooling of the rebars is

essential to ensure the quality of the finished products. Goodquality of raw material (billet) and skilled manpower are ofcourse the prerequisites for producing TMT bars of desiredquality. The effect of process parameters on its characteristicsare yet to be established. Corrosion resistance of TMT bars isclaimed to be better than that of the CTD bars but certainlynot better than MS bars. TMT rebars are more ductile andhave better capability to withstand dynamic loading as their

elongation is expected to be better at higher strengths.However, their fire resistance property is still in experimentalstage.

In micro alloying process, strengthening micro alloys likeNiobium (Nb), Vanadium (V), Boron (B) and Titanium (Ti)are added during the production of billet. When individualingredient or combination does not exceed 0.3percent, thestrength of rebars is increased. Other properties depend onother ingredients as usual. This is an expensive process andgenerally not employed in India.

Performance by RC structures greatly depends on thequality of rebars; this need not require any emphasis. Thedanger is due to defective and/or substandard rebars foundoccasionally in the market. Defective or substandard rebarsare produced due to several reasons: lack of quality controlin the basic material used in the billet production process,rolling process and post rolling process. Defective bars arethose that can be detected by visual inspection. However, onmany occasions, visual inspection fails to identify substandard

bars, which are generally identified by testing mechanicaltests to determine strength and stress-strain curve are veryuseful tools for this purpose. Substandard bars are moredangerous than the defective ones, as they cannot be detectedvisually by the users, especially in smaller projects.

Fig6 contains stress-strain curves of three samples ofcommercially-procured TMT rebars marketed as Fe 415 grade

steel. Stress-strain curve of Fe415-CTD bar, as given in SP16is also plotted in Fig 6. The difference between the three barsare obvious from this figure. Yield strength of sample-1 wastested as 511 MPa and its elongation is quite high, this sampleis acceptable as per IS I786

1. Yield strength of sample-2 is

acceptable but its elongation is low and hence is liable to berejected. Sample-3 was not acceptable as its yield strengthwas 380 MPa lower than the specified value.

Performance of these three rebars in design is illustratedwith an example illustrated in Fig7. The section was designedfor the induced moments and shear force using Fe415 gradeCTD rebars following the provision of IS 456 and IS 13920

12.

Moment curvature (M-%) diagram of this section is evaluated

for the design stress-strain curve given in SP 164

for CTDrebar of grade Fe415 and those given in Fig 6. It may bementioned that there is no design stress-strain curvesspecified by Bureau of Indian Standards for TMT either in IS456 or SP 16 or IS 13920, though IS 13920 explicitly allows theusage of TMT bars. These M-%curves are plotted in Fig 8.The curve evaluated using sample-1 is almost similar withthat evaluated using CTD bars specified in SP-16 in linearzone and higher in nonlinear zone. M-%curve using sample-3 always falls below the curve determined using CTD rebar


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specified in SP16. The ultimate moment of the section islower even though the curvature is higher in case of sample-3. Similar trend is observed for CTD bars of SP16. But in caseof samples-1 and 2, while the ultimate moment is higher, thecurvature at failure is lower indicating low ductility of thesection. It is evident from Fig 8 that yielding of tension steeloccurs in sample-3 and CTD bars of SP16 whereas the ultimatemoment in sample 1 and 2 are achieved when concretecrushes. The moment-curvature diagrams of sample-3 andCTD bars of SP16 indicate well defined points for yield andultimate curvatures and the curvature ductility factor is around1.8. For samples 1 and 2, though their yield stresses are aboveacceptable limits, the moment curvature diagrams arecharacterised by a lack of well spaced points for yield andultimate curvature of the specimens. Both the specimens showalmost a linear behaviour before sudden failure.

Variability of properties of rebars have very significantinfluence on the safety of structure. The variability can beminimised if the desired level of quality control in each phase

of production is strictly adhered to. Statistical analysis of thetest results of strength of about 500 samples were carried outfor rebars designated as Grade-415 and the results are as

below.

Yield strength Ultimate strength

Mean value 509.8 MPa 620.68 MPa

Standard deviation 43 43.61

Coefficient of variation 8.93 7.02

The coefficient of variation of the yield strength, in theopinion of the authors, is on the higher side; it should bewithin 5percent.

Comparison of specifications of differentcountries

Practices followed in different countries, for characterisationof rebars are outlined in the specifications published by therespective national bodies. A comparison of specifications ofdifferent countries would help to understand the status of ISspecification vis--vis practices followed in other countries.Specifications followed in the USA, European nations (EN),Australia/New Zealand and Russian Federation (RF) were

studied along with Indian Standard specifications. Threegrades of rebar; Fe415, Fe500 and Fe550 or their equivalentare taken for this exercise and the equivalent grades adoptedin the USA, European nations, Australia/New Zealand andRussian Federation are given in Table3. Different grades ofreinforcement, which are commonly used, are clustered infour groups. It is noted that there is only one grade of ASTMA706/A706M rebar available, which is Grade-420

recommended for earthquake resistant design. Australian/New Zealand specification allows three categories of rebarsof Grade-500: Class L (low ductility) 500L, Class N (normalductility) 500N, and Class E (high ductility for earthquakeprone region) 500E. Similar observation can be made onEurocode.

From sustainability view point, the use of steel from scrapis inevitable now-a-days. In the USA and Europe, systemsexist for quality control of scrap to be used for steel making

11.

Example of such systems are: Institution of Scrap Iron andSteel (ISIS), which provides code numbers that relate to 29different types of scrap in the USA, and similar system by theCommittee of National Scrap Federations and Association ofthe Common Market (COFENAF) in Europe. Unfortunately,

no such system exists in India for controlling the scrap usedin steel making.

There exists a high risk in using rebars, re-rolled fromscrap materials that do not adhere to the quality requirementof basic material in line with the relevant nationalspecifications. Again, it may not always be possible for smallusers of rebars to institute quality control measures beforeprocurement. Branding system is useful in this respect.American Society of Testing Materials (ASTM) has establisheda standard for branding of deformed reinforcing bars. The

branding system consists of marking the following on thereinforcing bars,

Manufacturers identity mark Bar size

Type of steel: new billet (-N-), rolled rail steel (-I-) orrolled axle steel (-A-)

Bureau of Indian Standards (BIS) has not specified anysuch system. The branding system may not be a full proofsystem. But, this is an effective system for a reasonable levelof control, under the action of market dynamics, in selecting

Table 3: Grades of rebar considered in the comparative study

Group India USA Russian Australian / EuropeanNew Zealand

1_

Grade-300b _ _ _

2 Fe415a

Grade-420b

A III Graded

430f

B450Cg

Grade-420c

3 Fe500a

Grade-520b

A 500 S Gradee

500 Lf

B500Ag

500 Nf

B500Bg

500 Ef

4 Fe550a _ _ _

-

Notes: a - Rebar conforming to IS 17861; b - Rebar conforming to ASTM A 615/A

615M17

; c - Rebar conforming to ASTM A 706/A 706M18

; d - Rebar conforming to

GOST 578116

; e - Rebar conforming to STAOCHEM19

; f - Rebar conforming to AS/

NZS 467120

; g - Rebar conforming to prEN 10080-1 -199913


9/12


requisite quality of steel depending on their usage, especiallyfor small users.

Rebars falling under groups 1 and 4, Table3, are no longerused in India now, while those under groups-2 and 3 arepredominantly used. Findings of comparative study of thesegroups, 2 and 3, are discussed in thepresent paper. Comparison of chemicalcomposition and mechanical propertiesspecified in IS 1786, ASTM A615/A615M, ASTM A706/A706M, Russianand European standards of these twogroups are given in Tables 4 to 7. Thecomparison of chemical composition

indicates that limits on the carboncontent is in general lower in Russianand European specifications incomparison to IS 1786, though the limitspecified in ASTM A706M is similar tothat of IS 1786. Allowing high carboncontent implies Indian rebars have therisk of possessing lesser ductility incomparison to that of other countries.Limits on the sulphur and phosphorus

contents is in general higher in IS 1786 thanthose in ASTM A615M and 706M, Russian andEuropean specifications. This also increases therisk of higher brittleness of Indian rebars. IS1786 and ASTM A615/A615M do not putlimitation on the carbon equivalent, whileASTM A706/A706M and European codespecify such limitation. However, IS 1786

specifies limits on variation over specifiedmaximum limits of carbon, sulphur andphosphorus. It also limits the quantity of microalloying elements.

The mechanical properties of rebars,whose minimum values are generally givenin most of the specifications, are yield strength(0.2percent proof stress in case of CTD bars),ultimate strength (or maximum tensilestrength) and elongation as parameters forcharacterisation. Following observations could

be made from the comparative study.

Ratio of ultimate strength (tensilestrength) to yield strength decreaseswith increase in yield strength in IS1786. Similar observation is made fromthe specifications of other countries.

Differences between the specifiedvalues of minimum tensile strength andminimum yield strength of IS 1786 arelower than those of ASTM, AS/NZS,GOST and STOACHEM forcorresponding grades of rebar.

ASTM A706/A706M and AS/NZS 4671specifies both minimum and maximumyield strengths.

Table 5: Mechanical properties of group-2 rebar (grade: 415 to 430)

Att rib ute s IS 1786 ASTM Australian / Rus sia n Europe an

615M 706M New Zealand

Tensile 10 percent more 620 550(a)

Rat io of ul timate 585 Ratio of ul timate

strength than the actual tensile strength to tensile strength to yieldyield stress but not yield strength should strength should be &less than 485 MPa be &1.15 and "1.50 1.15 and "1.35

Yield 415 420 420 &410 395 450Strength,

minmum

Yield

Strength, - - 540 "520 - -maximum

Elongation 14.5 For bar # 10 9 14 &10 14 7.5For bar # 13, 16 9 14

For bar # 19 9 14

For bar # 22, 25 8 12

For ba r # 29, 32 , 36 7 12

For bar # 43, 57 7 10

Table 4: Chemical composition of group-2 rebar (grade: 415 to 430)

Item IS 1786(a,b)

ASTM Russian Europe an

Percentage Variation over 615M(c)

706M

maximum specified percentage by percentage

maximum manufacturer by purchaser

limit, percentage,

maximum

Carbon 0.30 0.02 - 0.30 0.33 0.2-0.29 0.22

Sulphur 0.060 0.005 - 0.045 0.053 0.05 0.05

Phosphorus 0.060 0.005 0.06 0.035 0.043 0.045 0.05

Sulphur and 0.11 0.010 - - - - -

Phosphorus

Manganese - - - 1.50 1.56 1.2-1.6 -

Silicon - - - 0.50 0.55 0.6-0.9 -

Nitogen - - - - - - 0.012

Carbon - - - 0.55(d)

- - 0.5(e)

equivalent

Nickel - - --

- 0.3 -

Copper - - - - - 0.3 -

Chromium - - - - - 0.3 -

Notes:

(a): For guaranteed weldability, the percentage of carbon shall be restricted to 0.25 percent maximum.

(b): Addition of micro alloying elements is not mandatory for any of the above grades. When strengthening

elements like Nb (Niobium), V (Vanadium), B (Boron) and Ti (Titanium) are used individually or incombination, the total contents shall not exceed 0.30 percent; in such case manufacturer shall supply

the purchaser or his authorized representative a certificate stating that the total contents of strengthening

elements in the steel do not exceed the specified limit.

(c): (i) An analysis of each heat of steel shall be made by the manufacturer from test samples taken preferably

during the pouring of the heats. The percentage of carbon, manganese, phosphorus, and sulphur

shall be determined. The phosphorus content thus determined shall not exceed 0.06 percent.

(ii) An analysis may be made by the purchaser from finished bars. The phosphorus content thus

determined shall not exceed by more than 25 percent of above value.

(d): Carbon equivalent, CE, shall be calculated using the following formula:

10

%

50

%

10

%

20

%

40

%

6

%%

VMCNCMCCE

oriun ''(((()

(e): Carbon equivalent, Ceq, shall be calculated using the following formula:

1556

uiorneq

CNVMCMCC

((

(((()

Specified value of minimum elongation generallydecreases with the increase of steel grade.

Minimum elongations specified for Fe 415, Fe 500, Fe550 grade rebars in IS 1786, Grade 420 rebars in ASTMA706/A706M; and Grade 500E and 430 in AS/NZS


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4671 are higher than those specified for correspondingrebars in ASTM A615/A615M; and Grade 500L and500N of AS/NZS 4671.

Requirements of minimum elongation and that of tensilestrength or ultimate strength shall not be less than 1.25 timesthe actual yield strength in case of ASTM A706/A706M en-sure adequate inelastic deformability of the reinforcement,

which then translates into inelastic deformability of structur-al members. The tensile strength of grades 500E and 430rebars by AS/NZS 4671 is specified to fall within 1.15 to 1.4(for 500E grade) or 1.5 (for 430 grade) times the characteris-tics yield strength, which is used in design. Minimum elonga-tion is required to be more than or equal to 10 percent toensure inelastic deformability of the structural members. The

requirements of minimum elongation and ultimate and yieldstrengths specified in GOST, STOACHEM and European stand-ards also ensure inelastic deformability of the structural mem-

bers.

As per ACI 31822, rebar complying with ASTM A706/A706M is to be used in earthquake-resistant design of concretestructures. In Australia and New Zealand, rebars of grade500E and 430 of AS/NZS 4761 are used for earthquake-resistant design. In earthquake-resistant design where ductile

behaviour of structure is required (for example, designagainst the earthquake forces), it is undesirable to have actualyield strength much higher than its minimum specified valuethat is considered in design. This is because higher the actualyield strength of rebars, higher would be the ultimate momentcapacity of a RC section. Again, increase in flexural strengthof a member will enhance the shear demand on the memberunder seismic loads. Fig 9 shows the increase in shear demandwith the increase in yield strength for the RC beam section of

Fig 7. This scenarios could lead to higher risk of brittle shearfailure of the member rather than a ductile flexure failure,which is against the spirit of safe aseismic design criteria ofRC section. From this consideration, specification of bothminimum and maximum yield strengths in ASTM A706/A706M and AS/NZS 4671 (for rebars to be used in seismic

Table 6: Chemical composition of group-3 rebar (grade: 500 to 520)

Item IS 1786(a,b)

ASTM 615(c)

Rus sian Europe an

Carbon 0.30 - 0.22 0.22

Sulphur 0.055 - 0.05 0.05

Phosphorus 0.055 0.06 0.05 0.05

Sulphur and 0.105 - -

Phosphorus

Manganese - - 1.6 -

Silicon - - 0.9 -

Nitrogen - - 0.012 0.012

Carbon equivalentCequiv - - 0.50 0.50

(d)

Nickel - - - -Copper - - - -

Chromium - - - -

Notes:(a):For guaranteed weldability, the percentage of carbon shall be restricted to 0.25

percent maximum.

(b):Addition of micro alloying elements is not mandatory for any of the above grades.

When strengthening elements like Nb (Niobium), V (Vanadium), B (Boron) and

Ti (Titanium) are used individually or in combination, the total contents shall

not exceed 0.30 percent; in such case manufacturer shall supply the purchaser or

his authorized representative a certificate stating that the total contents of

strengthening elements in the steel do not exceed the specified limit.

(c): (i) An analysis of each heat of steel shall be made by the manufacturer from test

samples taken preferably during the pouring of the heats. The percentage of

carbon, manganese, phosphorus, and sulphur shall be determined. The

phosphorus content thus determined shall not exceed 0.06 percent.

(ii) An analysis may be made by the purchaser from finished bars. The phosphorus

content thus determined shall not exceed by more than 25 percent of above

value.

(d):Carbon equivalen, Ceq, shall be calculated using the following formula:

1556

uiorneq

CNVMCMCC

((

(((()

Table 7: Mechanical properties of group-3 rebar (Grade: 500 to 520)

Att rib ute s IS 1786 ASTM 615 M Australian/ New Zealand Rus sian European

500L 500N 500E B500A B500B

Tensile 8 percent more than 690 Ratio of ultimate Ratio of ultimate Ratio of ultimate 600 Ratio of ultimate Ratio of ultimate

strength the actual yield tensile strength tensile strength tensile strength to yield tensile strength to tensile strength to

stress but not less to yield strength to yield strength strength should be & y iel d st ren gt h y iel d s tr en gt hthan 545 MPa should be &1.03 should be &1.08 1.15 but "1.40 should be &1.05 should be &1.08

Yield 500 520 &500 &500 &500 500 500 500strength,

minimum

Yield - - "750 "650 "600 - - -strength,

maximum

Elongation 12 For bar # 10 - &1.5 &5.0 &10.0 14 2.5 5.0For bar # 13, 16 -

For bar # 19 7

For bar # 22, 25 7

For bar # 29, 32, 36 6

For bar # 43, 57 6


11/12


design) is effective. This important aspect is missing in IS1786.

It is not possible for direct comparison on elongation asdifferent countries have different specifications for testingelongation. However, the requirements of elongationspecified in IS 1786 is in line with other internationalspecifications for Fe 415 and Fe 500 grades from ductility

consideration. Fe 550 grade steel falls short of it. IS 1786 doesnot guarantee the requirement of minimum ratio of tensilestrength to minimum yield strength for inelastic deformabilityas are the cases of ASTM A706/A706M. Moreover, IS1786does not specify both the minimum and maximum yieldstrengths for safeguarding against brittle shear failure.

Specification of IS 1786 seems to be somewhatconservative as far as design for ductility of rebars is required.Specifications of Fe 415 grade may guarantee the attributesof ductility. But, this cannot be stated for other grades,particularly for Fe 550. Detailed study is required for usingthis grade of rebars in the design requiring ductility. Cautiousapproach may be solicited before using Fe 550 grade steel inthe design of earthquake-resistant design followingstipulations of IS189319.

No codes specifies any limitation on the statisticalparameters of the reinforcement properties such as yieldstrength. It was seen in the discussion of preceding sectionthat coefficient of variation of yield strength could increasedue to variability in the production process. The safety indesign is adversely affected with the increase in coefficient ofvariation of yield strength. This calls for a need in specifyingcoefficient of variation on the yield strength of rebars, atleast, for projects of higher importance.

Concluding remarks

Characterisation of steel reinforcement is as important asthat of concrete ingredients for engineering sound and durableconcrete structures. Manufacturing process, designrequirements and construction method have significantimpact on characterisation of rebars. Chemical compositionand mechanical properties like yield strength, ultimatestrength and elongation are generally considered forcharacterisation of rebars. The ribs on the surface of thedeformed bars also need to be characterised.

Strength, ductility and corrosion resistant properties ofrebars are important from design considerations. Fromconstruction point of view, bendability and weldability ofrebar are two important characteristics. The required ductilityof rebars could be guaranteed against all type of loadings,

that is, monotonic, repetitive and reversed loading byelongation.

It is inevitable to re-roll rebars from metal scraps bothfrom the sustainability and economic angles. A degree ofcontrol on scrap metal is necessary to manufacture requisitequality of rebars. Well-defined systems exist in the USA andEurope for this purpose but, not in India. Similar system isnecessary to implement requisite control, especially in thepresent free market regime. In addition, branding system to

identify whether the rebar is manufactured from new steelor scrap is needed. This will help the small users, as a mean ofpreliminary quality control.

A maximum limit for yield strength is desirable to bespecified in standards used for earthquake-resistant design.The absence of such a maximum limit may lead to brittlefailure (shear) of the structure. Requirements specified in IS

1786 for Fe 415 grade rebars are in line with the requirementsof other countries for ductile design. However, this does nothold good for rebars of grade Fe 550 as per IS 1786. Cautiousapproach should be adopted in using rebar grades higherthan Fe 415, especially Fe 550 grade, where ductility of rebarsis necessary for inelastic deformation of structural membersas demanded by design philosophies. Such design cases areearthquake-resistant design, design for impact load, designof slabs/beams, with adjustment of support moments/load,against gravity load, etc.

TMT bars are used presently in India for construction ofconcrete structure. Neither IS 456 nor SP 16 provides designstress strain curve of TMT rebar. Use of the design curve ofCTD bar is not correct. BIS should come out with designstress-strain curve and design value of the yield strength ofTMT bars.

A limitation on coefficient of variation on yield strengthof rebars is desirable for the project of higher importance.

Acknowledgement

Authors thankfully acknowledge the help and cooperationrendered by Dr C. S. Viswanatha of Torsteel ResearchFoundation, Bangalore in preparation of the paper.

References

1. ______Indian standard specification for high strength deformed steel bars andwires for concrete reinforcement (Third Revision), IS 1786 : 1985, Bureau of Indian

Standards, New Delhi2. PARK, R. and PAULAY, T. Reinforced Concrete Structures, John Willey & Sons,

1975, New York.

3. PURUSHOTHAMAN, P. Reinforced Concrete Structural Elements Behaviour,

Analysis and Design, Tata McGraw-Hill Publishing Company Ltd, 1984, NewDelhi.

4. ______Design aids for reinforced concrete to IS 456 : 1978, SP 16, Bureau ofIndian Standards, New Delhi.

5. ______Plain and reinforced concrete Code of practice, IS 456, Fourth revision,

September 2000, Bureau of Indian Standards, New Delhi.

6. BASU, PRABIRC. Seismic upgradation of buildings: An overview, The Indian

Concrete Journal, Mumbai, August 2002, Vol 76, No 8, pp. 461-475.

7. ______Criteria for earthquake resistant design of structures, Part 1 General

provisions and Buildings, IS 1893, 2002, Bureau of Indian Standards, New Delhi

8. GRAVINA, R.J. and WARNER, R.F. Moment re-distribution in indeterminate RCbeams and slabs constructed with 500 MPa Grade, Class L and Class Nreinforcing steels, Proceedings of the Concrete Institute of Australiaconference,

2001.

9. GILBERT, R.I. The impact of 500 MPa reinforcement on the ductility of concretestructures Revision of AS 3600, Proceedings of the Concrete Institute ofAustralia Conference , 2001.

10. BISHNOI, L. R. and BASU, PRABIRC., Methodology for rehabilitation of agednuclear safety related concrete structures, Proceedings of first national


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symposium on ageing management of nuclear facilities (AMNF-94), January 13-15, 1994, BARC, Mumbai.

11. KAUSHIK, S.K. and SINGH, B. Influence of steel-making processes on the quality

of reinforcement, The Indian Concrete Journal, July 2002, Vol. 76 , No 7,

pp. 407-412.

12. ______Ductile detailing of reinforced concrete structures subjected to seismic

forces - Code of practice, IS 13920 : 1993, Bureau of Indian Standards, New

Delhi.

13. ______European standard on steel for the reinforcement of concrete- weldable

reinforcing steel, prEN 10080-1, 1999, European Committee for

Standardization, Brussels.

14. __________ Indian standard specification steel for general structural purposes

(Fourth Revision), IS 2026: 1985, Bureau of Indian Standards, New Delhi.

15. ______Indian standard for mild steel and medium tensile steel bars and hard-

drawn steel wire for concrete reinforcement (Third Revision) , IS 432 (part 1):

1982, Bureau of Indian Standards, New Delhi

16. ______USSR standard of hot rolled steel for reinforcement of ferro concrete

structure, GOST 5781-83, 1983, Moscow, Russian Federation.

17. ______Standard specification for deformed and plain billet-steel bars for concrete

reinforcement, ASTM A 615/A 615M, American Society of Testing Materials,

USA.

18. ______Standard specification for low-alloy steel deformed and plain bars for concrete

reinforcement , ASTM A 706/A 706M-01, American Society of Testing

Materials, USA.

19. ______Rolled material of periodic profile of reinforcement steel, STOACHEM 7-

93, 1993, Moscow, Russian Federation, USA.

20. ______Steel reinforcing materials, AS/NZS 4671: 2001, Standards Association

of New Zealand.

21. ______Building code requirements for reinforced concrete , ACI-318, 1999,

American Concrete Institute, USA.

22. KATO. B, AKIYAMA, H. and YAMANOUCHI, Y. Predictable properties of material

under incremental cyclic loading, Sympoisum on resistance and ultimate

deformability of structures acted on by well-defined repeated loads, Reports of

working commissions, Vol 13, International Association for Bridge and

Structural Engineering, Lisbon, 1973, pp 119-124.

Dr Prabir C. Basu is presently the director, civil andstructural engineering division of Atomic EnergyRegulatory Board (AERB), Mumbai. He graduatedfrom the Bengal Engineering College, Shibpore,Howrah and obtained his M-Tech degree from theIndian Institute of Technology, Kanpur. He wasawarded the Commonwealth Scholarship for research

at Liverpool University, UK which led him to his PhD degree.Before joining AERB, Dr Basu worked with DevelopmentConsultants Ltd and M.N. Dastur and Company, Calcutta wherehe had commendable achievements to his credit in design andproject engineering of high-tech projects in the strategic sectors.Dr Basu has made significant contribution in the development ofhigh performance concrete (HPC) and preparation of specificationsfor the construction of the primary containment dome of theNuclear Power Plant at Kaiga using HPC. His work in thedevelopment and preparation of codes and guides of nuclearpower plant structures is outstanding. A fellow of Institution ofEngineers (India), Dr Basu has authored about 50 technical papers.His current interest in research is in the field of HPC andearthquake engineering. He was awarded the ICI-Fosroc awardfor Outstanding Concrete Technologist, 2003.

Ms Shylamoni P. is presently working as scientificofficer (D) in civil & structural engineering division

of AERB, Mumbai. She obtained her B.Tech fromT.K.M. College of Engineering, Kollam, Kerala. Sheworked with Uhde India Ltd and Bhagwati DesignsPvt Ltd, Mumbai where she was associated withanalysis and design of multi stored industrial

structures. Her areas of interest include analysis and design ofsteel structures.

Mr Roshan A. D. is presently working as scientificofficer (D) in civil & structural engineering divisionof AERB, Mumbai. He obtained his B.Tech fromRegional Engineering College, Calicut and M.Tech instructural engineering from Indian Institute ofTechnology, Kanpur. He has also completed a one-year orientation course in nuclear science and

engineering conducted by Bhabha Atomic Research Centre. His

areas of interest include seismic analysis, design and non linearfinite element analysis of concrete structures.

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Reinforcing Bar 9tmt Bar ) Analysis in India