ductiity and seismic behaviour

7/27/2019 ductiity and seismic behaviour

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8 Ductility andseismicbehaviorS KGhoshandMuratSaatcioglu8.1 ntroductionIt has been shown for quite some time that concrete becomes lessdeformableormore brittleas itscompressive strength increases. Figure8.1showsahigh-strength concrete cylinder beingtested incompression. Thefailure isobviously explosive, indicating that th e material isbrittle. Thesame fact is depicted in a different way by Fig.8.21 which shows the

Fig.8.1 Testingof ahigh-strengthconcrete cylinder


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Fig.8 .2 Completeaxialstressversu s axial strain curve s fornormalweightconcretesofdifferent strengths1axial stress-strain curvesandaxial-lateral strains curvesincompressionofnormal weight concretes having dif ferent strength levels. Low-strengthconcrete obviouslycandevelop onlyamodest stress level,but it cansustainthatstress overasignificantrangeofstrains. High-strength concrete attainsamuch higher stress level,but then cannot sustainitover any mean ingfu lrangeof strains. Theload-carrying capacity drops precipitously beyond thepeakof the stress-strain relationship.

Figure8.31showsthestress-strain curvesoflightweight concretes havingdifferent compressive strengths. Thesecurves were obtained byAhmad inan investigation on mechanical properties of high strength lightweight

U n i t w e i g h t - 1 5 0 . 7 5 I b s / f t3S t r a i n r a t e = 1 0 ( a e / s e c J 1 ( k s i )

Stesk

L a t e r a ls t r a i n ,8 2 = S 3 ( i n / i n )

A x i a l s t ra i n ,S 1 ( i n / i n )

f c ( k s i )

L i g h t w e i g h t P e a k

I n f l e c t i o np o i n t

D a t a p o i n t s

StrainFig.8.3 S tress-straincurvesoflightweightconcretesofdifferent strengths1

Ste

k


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Strain i g 8 4 Comparisonofstress-strain curvesofnormalweight and lightweightconcretes1aggregate concrete which was conducted at North Carolina State Univer-sity. In Fig.8.4,1 a selected comparison is made between the stress-straincurves ofnormal weight and lightweight concretes having essentially th esame compressive strengths of about 4000 and 12,000psi (27.6 and82.8MPa). It can be seen that for similar strengths, lightweight concreteexhibits a steeper drop of the descending part of the stress-strain curvethan normal weight concrete. In other words, lightweight concrete is amore brittle material than normal weight concrete of the same strength.

The lack of deformability of high-strengthconcrete doesnot necessarilyresult in a lack of deformability of high-strength concrete members thatcombine this relatively brittle material with reinforcing steel. This interest-ing and important aspect is discussed in detail in this chapter. Theapplication of high-strength concrete in regions of high seismicity isdiscussed at the end of the chapter. Such application depends, of course,on adequate inelastic deformability of high-strength concrete structuralmembers under reversed cyclic loading of the type induced by earthquakeexcitation.8.2 Deformabilityof high strengthconcretebeamsNormalw eightconcrete beam sunder m onotonicloadingPerhaps the earliest investigation on the deformability of high-strengthconcrete beams was carried out by Leslie, Rajagopalan and Everard.2They tested 12 under-reinforced rectangular beams with fc ' rangingbetween 9300 and ll,800psi (64 and 81MPa). The specimen details areshowninFig.8.5 andTable8.1.It wasobserved thatas thereinforcementratio p increased, the 'maximum ultimate deflection' decreased, and the

N o r m a lw e ig h tL i g h t w e i g h t

N o r m a l w e ig h t

L i g h t w e i g h tD a t a p o in t s

Stesk


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F i g 8.5 Detailsof specim enstestedbyLeslieetal.2duct i l i ty index J J L (the ratio ofmaximum ultimate deflection to the deflec-tion at the end of the initial linear portion of the load-deflection curve)decreased drastically. It is evident from Table8.1that the ductility indexdrops to quite low values for p /pb =0.69, whereas a ratio of up to 0.75 isallowedby the ACI Code.

3However, this observation probably requiressome qualif icat ion. Table8.2 from Leslieetal.2liststhe average ductility

indices forincreasing valuesofp .Also listedin thetableareaverage valuesofultimate deflectionandyielddeflect ion.First, neitherofthese termswasclearlydef ined inLeslieetal.2Secondly,as can beseen,the ducti l i tyindexdecreased with increasing p not so much because the ultimate deflectiondecreased asbecause the yield deflection increased. Thus, without know-ingpreciselyhow theyield deflectionwasdetermined,it isdifficult totellifthisinvestigationwas indicativeof any lackof inelastic deformabilityonthe part of high-strength concrete beams containing moderately highamounts of tension reinforcement (above1.5%). It should be noted fromTable8.1that ^ x values variedwid ely for thebeams havingth esame tensionreinforcement ratio, and that there was no correlation between thisvar ia t ionand thevariationinconcrete strength.

A comprehensive investigation on the deformability of high-strengthconcrete beamswascarriedout byPastoretal.4Twoseriesoftests,A andB,were conducted.

Series A consisted of fourbeams of high-strength concrete (HSC), oneof medium strength concrete (MSC) and one of low-strength concrete(LSC). The scopewaslimitedto singlyreinforced,unconf inedrectangularmembers subjecttoshort-term1/3point loading. Beam SeriesAdetailsaregivenin Fig.8.6andTable 8.3.Concrete compressive strength, fc ' (at thetime of testing), and the tensile steel ratio, p, were the experimentalvariables.

Thescopeof Series B was limited to high-strength concrete rectangular

N O T E D I M E N S I O N S O N S E C T I O N A R ET O T H E C E N T E R L I N E O FT H E S T I R R U P . L E O S .

S T I R R U P S P A C I N QS P A C E S A T 3 2 - 3F O R 3 ( 7 6 ) ( 6 9 )S T I R R U P S R A C I N QS P A C E S A T g 2 ' - IF O R 1 % , I . 5 V . J 2\ Z B JS U R T S U P P O R T


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Table8.1 S pecimen detailsanddu ctil i ty indices2

Specimen(a)7.5-18.0-19.0-17.5-1.58.0-1.59.0-1.57.5-28.0-29.0-27.5-38.0-39.0-3

fc ,PS i(MPa)9310(64.1)10,660(73.5)10,620(73.2)9720(67.0)11,400(78.6)11,630(80.2)10,850(748)10,610(73.1)11,780(81.2)11,650(80.3)11,730(80.9)11,210(77.3)

b,in.( m m )8.25(210)8.25(210)8.25(210)8.00(203)8.13(207)8.50(216)8.50(216)7.88(200)8.13(207)8.38(213)8.25(210)8.25(210)

d,in.( mm)10.63(270)10.63(270)10.63(270)10.56(268)10.56(268)10.56(268)10.50(267)10.50(267)10.50(267)10.50(267)10.50(267)10.50(267)

A (b )2#62#62#62#72#72#72#82#82#83#83#83#8

P0.010.010.010.0140.0140.0130.0180.0190.0190.0270.0270.027

P b0.00450.0460.0450.0510.0510.0510.0400.0400.0390.0390.0390.039

P / P b0.300.260.270.440.310.306.690.630.560.820.710.77

5.98.04.34.52.54.23.22.42.71.92.11.5

(a)Thefirstnum ber indicates cement content insacks/cu.yd.Thesecond numberindicatesthenom inal percentage oflongitudinal re inforcem ent.(b)Theyield strengths for No. 6, No. 7 and N o. 8 bars were 60.22 ksi(415 MPa),55.83 ksi(385 MPa)and 66.88 ksi(461 MPa),respectively.members, confined and doubly reinforced, under short-term 1/3 pointloading. No low-strength concrete or medium strength concrete beamswere tested. Beams in this series were modeled after beam A-4 of Series Ato establish a basis for comparison between the behavior of unconfinedsingly reinforced, and confined doubly reinforced beams. Beam Series BdetailsaregiveninFig.8.7 andTable 8.4. Compressive steel ratio, p',andlateral reinforcement ratio, ps, were the controlled variables. Concretestrength was kept around 8500psi (58.7 MPa), except for B-2a which hadTable 8.2 Com parison of du ctility indice s2Reinforcementratiop0.010.0140.0190.027

Deflectionat the endofinitialstrengthport ion,i n.(mm)0.28 (71)0.32 (81)0.36 (91)0.55(140)

Ultimatedeflection,in .(mm)1.70(432)1.18(300)1.05(267)1.00(254)

Duct i l i tyindex6.03.72.91.8


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Table8.3 Beam SeriesAdetails4

1 in. =2 5 . 4 m m1000 psi=6.895MPa

Tenestregion dimensionsReb,in.,in.z , in.Age at test,days

Compressivestrengthattest,psieam2#63#62#63#73#86#7

10.6910.6310.6510.5610.509.75

7.347.227.137.386.566.94

12.0712.0112.0312.0012.0012.00

951137122122137

370065009284853592648755

A-IA-2A-3aA-4A-5A-6a


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N o t e N o m in a l c r o s s - s e c t io n : 7 x 1 2A c t u a l te s t r e g i o n d im e n s io n s h ,b a n d d g i v e n i n T a b le 3 . 6

SectionA -A Section B- BFig. 8.6 Details of Series A beams tested by Pastoretal.4fc =9284psi (64.1 MPa), while the amount of tensile steel was the samefo r all beams and consisted of three No. 7 (22mm diameter) deformedbars.Tofacil i tatethe evaluation of the moment-curvature and load-deflectiondata, experimental curvesare represented asshowninFig.8.8(SeriesA)and Fig. 8.9 (Series B). Key load-deformation values, identified in each

N o t e N o m in a l c r o s s - s e c t i o n : 7 x 1 2A c t u a l t e s t r e g io n d im e n s io n s h , b , d , d ' g i v e n i n T a b le 3 . 7

i g 8.7 Details of Series B beams tested by Pastoretal.4

L o a d p o in tT o p l a y e ri n A 6 ( a )

S u p p o r t S t ir ru p s p a c in g :

L o a d p o in t

S t ir ru p s p a c i n g :S u p p o r t H o o p s p a c in g :

H o o p d e ta i le c t i o n B -B2 a ,B 4 , B 6B 1 . B 3 , B 5( t y p . )

s t i r r u p


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Table8 .4 Beam SeriesBdetails4

(a)Yield strength = 51 ksi1 in. = 25.4mm1000 psi= 6.895MPa

ensile steelestregion dim ensions plpb /,,ksiin .2/i, in. ^, in. d, in. d'7 in.

Ageattest,days

Compressivestrengthattest,psieam0.024 0.430.023 0.310.024 0.460.025 0.360.024 0.430.025 0.36

6260

3#7 62(1.80) 62

6262

12.13 6.94 10.69 1.7612.25 7.19 10.81 1.7012.25 6.88 10.81 1.8812.19 6.69 10.75 1.8812.06 7.00 10.63 1.6912.06 6.88 10.63 1.75

1867

189186194190

853492848578847885168468

B-IB-2aB-3B-4B-5B-6


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DeformationFig 8.8 Idealizationo fbeam SeriesA load-deformation curves4experimental figure, are listed inTable8.5 (moment-curvature data) andTable8.6 (load-deflection data). Included in these tables are the corres-ponding values of the curvature ( J J L C ) and displacement ( J J L ^ ) ductilityindices.

Curvatureanddisplacement ductility indicesofSeriesAbeams, aslisted

P r e - c r a c k i n gp o r t i o n P r e - y ie l d in g s ta g e P o s t - y i e l d i n g s t a g eF a i l u r eo s t - c r a c k i n gp o r t i o n

Y ie l d in g o f te n s i le s te e l

C r a c k i n g o f te n s ile c o n c r e t e

L

DeformationFig.8.9 Idealizationo fbeam SeriesBload-deformationcurves4

P o s t - c r a c k i n gp o r t i o nP r e - y i e l d i n gs t a g eP r e - c r a c k i n gp o r t i o n '

S p a l l i n gp o r t i o nP o s t - y i e l d i n g s t a g eP r e - s p a l l i n g p o r tio n P o s t - s p a l lin g p o r t io n

F a i l u r eL o s s o fc o n c r e te c o v e rY i e l d i n g o ft e n s i le s te e l

C r a c k i n g o f t e n s i le c o n c r e t e

L


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Table8.5 Moment-curvaturedataand curvatureductilityindices forSeriesA and Bbeams4

(a)S eeFigs.8.8and8 .9ford efinitionof symbols(b)Extrapolated(c)Fromex trapolated value s(d)Failed prematurely

urva tures 4 > x1(T6(in. 1)omentsM(ft-kips),,>43 ycru43c ream 1409

1293 (33941060673630

NotApplic-able

j > 3 = ( J )4350388373390424427

502017302535

50.075.056.0100.0119.0142.0

NotApplic-ableM3=M,43.068.545.695.0112.2124.0

8.010.27.212.212.615.0

A-IA-2A-3aA-4A-5A-6a

144671482732444828713463

144643961225170019812130

118125581182145011791431

396513259357410439

452530173050

84.0116.097.2119.0101.0110.0

84.0108.094.097.094.097.0

96.0106.0100.0103.097.097.0

85.088.185.085.085.085.0

15.013.015.07.610.014.4

B -IB-2aB-3B-4< d>B-5(d)B-6(d)


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Table8 6 Load-deflection dataandd isplaceme nt duct i l i ty indicesforS eriesA and BBeam

(a)SeeFigs. 8.8 and 8.9 for definitio n of symbols(b)Ex trapolated(c)From extrapolated values(d)Failed prem ature ly

eflectionsA(in.)oads P(kips).43,c,u3yereams 3.502.503.631.881.211.20

N otapplic-ableA3 =A,

0.950.940.711.051.050.95

0.120.060.050.080.080.08

25.037.528.050.059.571.0

Notapplic-ablePs= Pu

23.534.224.047.556.164.0

4.05.13.66.16.37.5

A-IA-2A-3aA-4A-5A-6a1.955.634.047.104.365.38

1.954.552.603.152.953.13

1.753.002.482.631.952.16

0.830.790.890.840.790.86

0.100.080.110.040.070.09

42.058.048.659.550.555.0

42.054.047.048.547.048.5

48.053.050.051.548.548.5

42.543.843.542.544.242.5

7.56.57.53.85.07.2

B-IB-2aB-3B-4 (d >B - 5 < d >B-6^


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inTables 8.8 and 8.6, are plotted as functions of the tensile steel ratio p inFig. 8.10. Results show an overall reduction in both j m c and \Ld withincreasing p. Thelossofductility with increasingp i sassociated mainly witha decrease in the ultimate deformation of the member. In turn, ultimatedeformat ionsare inversely proportional to the neutral axis depth at fa i lure .

Figure8.11plotstheinverseof theSeriesAneutral axis depthsatfailureas a funct ion of p. Since c values reflect the inf luence of fundamentalmater ia l properties such as fc ' and f y , the behavior shown in Fig. 8.11provides abasic explanationto that shown inFig. 8.10. Forhigh-strengthconcrete beams, therefore, lossofductility with increasingp can be tracedback to the fact that cincreases with increasing valuesof p.

Consider the upper half of Fig. 8.10. Points corresponding to thelow-strength and medium strength concrete beams lie below the curvedef ined by the high-strength concrete data. When all other variables areheld constant, J J L C clearly increases with/c'.Tognon et al.5 arrived at the same conclusion from tests on singlyreinforced model beams of every high-strength concrete. Reinforcedconcrete beams (4in.x8in.x6.5ft or 100mmx200mmx2m) weremanufac tu r edusing very high-strength concrete (VHSC,fc' =23,484psi or162 MPa) and an ordinary concrete (LSC, fc ' =5797psi or 40MPa) as areference. The reinforcement consisted of three or six longitudinal steel

K e yL S C ( fc- 3.7 k s i )M S C ( fc- 6.5 k s i )H S C ( 8 . 5 fc 9.3 k s i )

p- A s / b dFig 8 10 Beam SeriesAcurvatureanddisplacementdu cti l i tyindices versus tensile steelratio4

^

4

AuAy


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1/c,nr

K e yL S C (fi- 3.7 k s i )M S C ( fc- 6.5 k s i )H S C ( 8 . 5 ^ f J s =9 .3 k s i )

p =A s / b d i g 8 11 Inversevalues ofbeam SeriesAneu t ralaxisdepthsatfailureversustensi lesteelratio4

bars in the tensile zone with a concrete cover of approximately0.4in. or10 mm. Theamountoftransverse reinforcement providedin thepartof thebeam subjected to variable moment was sufficient to prevent shearcracking.

To emphasize the different behavior of the two concretes with low,medium andhigh percentagesofreinforcement, reinforced concrete beamswere prepared with 0.87, 1.97 and 4.61% tension steel. 8.88% steel wasalso used for the very high-strength concrete. Balanced steel percentageswere 3.85 and 13.49 for the ordinary and very high-strength concretes,respectively.

Ductility was represented by the ratio of ultimate curvature to yieldcurvature. The yield curvature was def ined as corresponding to a tensilesteel strain of 0.2%, and the ultimate curvature to a tensile steel strain of0.1%or a compressive concrete strain of0.35%.

Figure 8.12 shows that the beams made with VHSC are more ductilethan those made with LSC when the reinforcement is about or over 1%.Moreover, the ductility of the beams made with LSC quickly decreases asthe reinforcement ratio increases, whereas that of the beams made withVHSC declines gently up to a reinforcement ratio of about5%.It isworth noting that the curvature ductilityof allheavily reinforcedsections (p>p6) theoretically approaches unity regardless of concretestrength,fc ' . This suggests that th e increase in J J L C with/c'tends todecreasewith p.Thereseems to be, therefore, a limiting tensile steel ratio beyondwhich J J L C valuesare practicallyth e same regardless of f c r .Results shownin the lowerhalf ofFig. 8.10 pertainingto \Ldexhibit thesame general characteristics previously described for J U L C . Differences

1/c,mm1


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ReinforcementpercentageFig.8.12 Curva tureduc ti l i tyversusreinforceme ntpercentagefor LSC andVHSCbeams5

between \id values due to differencesin fcr are,however, much smaller,mainly because th e expected reduction from \ L C to J J L ^ is greater for thel ightly to moderately reinforced HSC beams than for the LSC and MSCmembers.This suggests that th e hypotheticalplimit beyond which \Ldis nolonger inf luenced by/c ' iscomparatively smaller than that for J U L C . In anycase, it seems reasonable to assume that J J L ^ increases with// , althoughmuchless significantly than J J L C .The above conclusion emphasizes the difference between material,sectional and member ductility.The ductilityof concrete as a materialdepends on the post-peak deformation of its stress-strain response, aproperty inf luenced primarily byfc'. The ductilityof asingly reinforcedconcrete section, on the other hand, depends on the post-yield deforma-tion of its momentum-curvature response. Similarly, the ductility of asingly reinforced beam as a structural unit depends on the post-yielddeformat ion of itsload-deflection response. The two latter characteristicsare associated withthe position of the neutral axisat fai lure , a propertyinf luenced notonlyby/c ' ,but alsoby pand/^.As shown inFig. 8.11, neutral axis depths at fai lure for the LSC andMSC beams are greater than the corresponding HSC values. It follows,therefore,that the decrease incwith//more than compensates for the lossof material ductility in the HSC range, and helps explain the observedincreaseinsectionalandmember ductilitywith// forconstantpand/^.

Consider Fig. 8.134 where J J L C and \Ld are plotted versus p/p^ . It isinterestingtonote that differences betweenLSC,MS C and HS C J J L C valuesshown inFig. 8.13are greatly reduced compared to those observed in theupper half of Fig. 8.10. This can be explained in terms of the inverseproportionality that exists between p/p^and// . In effect, everythingelsebeing equal, pb willbehigherfor abeam withhigher//.Therefore,abeamof low//with the same p/p^ ratio as that of a higher strength membernecessarilyhasless areaofsteel.Lesstensileateel areaimpliesashallowerneutral axis depth at failure. Consequently, the difference in ultimate

S 1000

S400Ducy


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P / P b ig 8.13 Beam SeriesAcurvatureanddisplacement ductility indices versus tensile steelratioexpressedas afraction ofbalanced steelratio4curvaturesandthereforeincurvature ductility indicesdue todifferencesinfc decreases, which is precisely what is illustrated in the upper half ofF i g . 8.13.

Results shown in the lower half of Fig. 8.13 for p/p^= 0.45 indicate ageneral tendency for J U L ^ to decrease with increasing/c', although thedifference betweenthevaluesfor MSC and HSC isinsignific ant.Insofarasthe behavior suggested by the LSC and the corresponding HSCvalues,theobserved decrease in J J L ^ withfc ' agrees with results reported by Leslie etal.2 For reasons previously mentioned while discussing the relationshipbetween \Ld and/c ' ,differences between LSC and HSC \^dvalues shoulddecrease with increasing valuesof p/p^ .

Inaccuracies in linear voltage differential transducer (LVDT) measure-ments introduced by the relatively large rotations of doubly reinforcedbeams at loads approaching ultimate resulted inerratic < j > M values whichinturn resulted inunreliable jxc values that exhibited large scatter. Conse-quently, curvature ductility indicesforSeriesBbeams, listedinTable8.5,were not included in fur ther analyses. On the other hand, data fromrelated Cornell tests by Fajardo4were included to compensate for the lossofSeries B data due to the premature failures of B-4, B-5, and B-6.Eachofthese beams had faileddue to rupture of the tensil steel at the first stirrupweld outside the central test region (stirrups were spot welded to thelongi tud inal rebars). Although in all cases the tensile steel had already

K e yL S C ( fj=3 .7 k s i)M S C ( fj = 6 . 5 k s i)H S C ( 8 . 5 s s fc s c 9 .3 k s i )

N o t e p b a c c o r d in g t oe q u a t i o n 5 .1

=

d=AU/Ay


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yie lded when failure occurred and in some cases measured strains werewellin thestrain hardening portionof thesteel stress-straincurve,this typeof failurewasconsidered premature. Full detailsof theFajardo beams aregiveninTable 8.7.Consider Fig. 8.14where displacement duct i l i ty indices J L J L ^ ) of nine

d oub ly reinforced conf ined HSC beams and one singlyreinforced uncon-fined HSC member (beam A-4) are plotted versusthe quantityp ////c .The symbol fc is the yield strength of the lateral steel, fc ' is thecompressive strength of the concrete, and p is the combined volumetricratioofcompressiveand lateral reinforcement,def ined as follows:

9 =9s+ As'lb d (8.1)where p5=volumetric ratiooflateral reinforcement

= 2(b + d )As /b d sA S area oflongitudinal compressive steelAs = areaoflateraltiesteelb = width (outside-to-outside of tie steel vertical legs) of the

d confined core5 - = depth (outside-to-outside of tie steel horizontal legs) of theconfined core

=spacing (center-to-center)of tiesteelThe best-fit linear regression curves shown interpolating the plotted datain Fig.8.14intersect at a p ////c' value of about 0.11. They define twodistinctlyd if ferent modesofbehavior thatare briefly discussed below.Therelativelyflatslopeof the lineto the left indicates that beams with

P a s to r , N i ls o n a n d S la t e ( a v e r a g e f = 8 .8 k s i)F a j a r d o ( a v e r a g e f = 1 2 .6 k s i)

A 4 ( u n c o n f in e d s in g ly r e in f o r c e d )

P W ig 8 14 Influenceofcompressionan dtransversereinforceme nton thedisplacem entducti l i tyofdoublyreinforced confined HS Cbeams4

=AuAy


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Table8 .7 Propertiesofbeams testedbyFajardo4

1 in. = 2 5 . 4mm1000psi=6.895MPa

AinP ,O//OAin/


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p fy '7fc '


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increasing th e post-yie ld deformat ionso fbeams as they are , for example ,in increasing th e post-peak deformat ions of concentr ical ly loaded mem-bers. This is m ainly becau se late ral de form ations in beam s tend to be largeat the extrem e com pression fiber, and prac tical ly non-e xistent at theneu t ra laxis location. Con seq u ently , lateralconfining stressesareune ve n l yandtherefore inefficiently distributed across the depth of the compressionzone.On the other hand, the presence of properly restrained cxompressionsteel al lows the member to behave (after loss of cover) much l ike atwo-flanged stee l beam (particularly whe n A5' =A5), the core concreteacting in this case as the connecting web. Consequently, significantinelasticde format ionsand large J J L ^ can be obta ined . For such behavior tooccur, however, the compression steel must remain stable in the strainharden ing range . The stabil i ty of the compression bars is inf luencedstrongly by the lateral restraint provided by the transverse t ies.Hence, itm aybe reasonable to think that the prim ary role of the transverse steel inincreasing beam duct i l i tyis not as aprovider ofconcrete conf inement , bu trather as a lateral support m echan ism for the long itud inal steel . Re du cin gth e spacingof the ties d id not, therefore, increase th e conf inementof theconcrete core as much as i t reduced the unsupported length of thecompression bars.

Summariz ing , th e addit ion oflong itud inal com pression steel and lateralt ie steel increases the displacem ent d uc ti l i ty of singly re inforced HSCbeams ( the former more efficiently than the latter) , provided that there inforcement index p ////c' is gre ater than 0.11. Beam s w ith p ///fc 0.11, apractical lyl inear \Ldp fy /fc 'relationship develops in which J J L ^ increases noticeablyfor re lat ive ly smal l valuesof p fy '7 fc'.Swartz etal.6 tested four beams ( fc f =11,500psi or 79 M P a for the firsttwo, and 12,300psi or 85 MP a for the other two) w ith long itud inalreinforcing varyingfrom 0.5p to 1.5p& based on an assumed t r iangularstress block (p/pfc ratios would be somewhat lower, based on the ACIrectangular stress block). The amount of shear reinforcement also variedfrom zero to 100% based on ACI 318-83.3 These designs are shown inFig. 8.16. Load versus midspan displacement is plotted for each beam inFig . 8.17. The beams with l i t t le or no shear re inforcement and also theover-reinforced beam exhibited v ery l i tt le du cti l i ty. No d etai l other thanthat shownonFig.8.17wasavailable.The flexural ducti l i ty of ultra-hig h-streng th concrete m em bers (concretestrength ran gin g up to 15 ksi or 103.4 MP a) u nd er m onotonic load ing wasinvestigated by Shin.79 All specimens were 6in . (150mm)X 1 2in.(300mm) in cross-section, and 10ft (3m) long (Fig.8.18). Three sets oftwelve specimens each were manufactured, using concrete compressivestrengthsof 4 ksi (27.6 MP a), 15 ksi(103.4M P a )and 12 ksi(82.7 M P a) forsets A, B and C, respectively. There were six groups of two identical


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ig 8.16 Detailsofspecimens testedbySwartzetal .6

F o i l g a u g e sF o i l g a u g e s( b o t h s i d e s ) 3 , # 7 b a r s

W h i t t m o r e g a u g e s( b o t h s i d e s )

3 s t i rr u p s a t11 c /c7 b a r s

f ;=1 1 , 5 0 0 p s i ( 7 9 M P a )a t 6 0 d a y sc o v e r

2 b a r # 3 s t i r r u p sa t11 c / c b a r s

f ; = 1 2 , 3 1 0 p s i ( 8 5 M P a )a t 6 0 d a y s

3 s t i r r u p s a t 4 c / cb a r s

c o v e r

fi= 1 2 ,3 1 0 p s i( 8 5 M P a )a t 6 0 d a y s

s t i r r u p s a t 3 c / cb a r s

c o v e r

b a r 4 s t i rr u p s a t 3 c / c b a r s in tw o r o w s

s t i r r u p s a t


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Deflection, i n .Fig.8.17 Load versus midspandisplacement ofbeams testedbyS wartzetal.6

specimens in eachset,two groups containingfourNo.3 (10 mm diameter)bars, twomore groups havingfourNo. 5 (16mm diameter) bars, and thelasttwogroups being reinforced withfourNo. 9 (29 mmdiameter) barsatthe fourcorners.Thedifference between twogroupsofspecimens withthesame concrete strengthandlongitudinal reinforcementwas in the spacing

Fig. 8.18 Specimensandsetup- Shinetal.19

B e a m 5 D

B e a m 5 CB e a m 5 B

B e a m 5 A

L

kps

T e n s i o nr e i n f o r c e m e n t

C o m p r e s s i o nr e i n f o r c e m e n t

D i a l g a u g eD . C . D . T .


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of No. 3 (10mmdiam ete r) t ies which w as either 3in . (75m m ) or 6in .(150mm) .The specimens were reinforcedas ifthey were colu m ns. They we re casthorizontally u nd er field conditions, and we re also cured un de r f ieldcondit ions. Each specime n w as tested un de r two-point loading , whichsubjected a considerable portion of the specimen to pure flexure. Thelongitudinal reinforcementwasdivided equ ally into tensionand compress-ion reinforceme ntareas.W hile the tension reinforcem ent always yielded atadvanced load stages, the compression reinforcement quite often de-velope d only small stresses all the w ay up tobeam fai lure .Member duct i l i tywas firstdef inedas:

, X O = Ao/A (8.2)where A0is m em ber deflection corresponding to the m axim um load on them e m b e r , and A ^ is member def lect ion at first yield ing of the tensionre inforcement .In view of the fact that the beams continued to sustain substantial loadswell beyond th e peak of the load-deflection diagram (theload -carryingcapacityofheavily reinforced beam s temp orari ly dropped offimm ediate lyfollowing the peak , bu t then picking up again), a second definition ofducti l i tywas also considered:

M/=VA y (8-3)where Ay is the 'final' deflection corresponding to 80% of the max i mu mload along the descending branch of the load-deflection curve. Since theconcept of duc tility is related to the ability to sustain inelastic de form ationswithout a substantial decrease in the load-carrying capacity, the definitionof ductilityasgivenbyEqu ation (8.2)wasfelt to be logical and practical.The ratio p/pb turn ed out to be the most dom inant factor influencing th emagni tudes of the du ctility indices. For a dou bly reinforced section inwhich the compression reinforcement does not yield at the ultimate stage(definedby theex trem e compression fiber concrete strain attainingavalueof 0.3%), pb isgivenby the following equ ation:

Pb= to f> (fb /fy) (8-4)where pb =M3(fc '/f y)[E szu/(E s eu+f y )] (8.5)isthe balanced reinfo rce m ent ratio for the corresponding singly reinforce dsection, andwhere fb'= Eseu-(d'/d)(Eszu+fy)^fy (8.6)is the stress in the compression reinforcement at balanced strain condi-tions.Plots of J U L 0 versus p/pb and J J L ^ versus p/pb are presented in Figs.8.19and8.20, respectively. The figures clearly show that for the same concretestrength, the du ctility indices decrease rathe r d rastically as the ratio p/pbincreases. However, even at the large p/pb ratio of0.8,(jy, which probably


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p / p b ig 8.19 Flexuralducti l i ty,asdefined byEquation (8.2), under monotonicloading7^ 9isamore practical measure ofductilityforbeams tested than J J L O , hasrathersubstantial values.

Figures 8.19 and8.20 generally show that the same amountsoflongitu-dinal and confinement reinforcement, the ductility indices rise sharply astheconcrete strength increases from4 ksi(27.6MPa) to 12 ksi(82.7 MPa)(nominal values),but then decrease somewhatas/c'increases further from12ksi(82.7 MPa) to 15 ksi(103.4MPa).

The confinement reinforcement spacing, within the range studied, did

fc , p s i ( M P a )4 2 5 0 ( 2 9 . 3 )1 2 2 0 0 ( 8 4 . 1 )1 5 0 0 0 ( 1 0 3 . 4 )

DucyndexJ0=A0/Ay

Duc

yndexf=AfAy

P / P bFig. 8.20 Flexuralducti l i ty,asdefined byEquation (8.3), under monotonicloading7'9

4 2 5 0 ( 2 9 .3 )1 2 2 0 0 ( 8 4 . 1 )

1 5 0 0 ( 1 0 3 . 4 )

t;,psi ( M P a )


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D is t r ib u t io n o f lo n g i t u d i n a l a n d c o n f in e m e n t re i n fo r c e m e n tF ig . 8 . 2 1 S p e c im e n s a nd s e t u p - Kam ara e ta l 9 '1 0not haveanappreciable effect on member ductility,forreasons discussedearlier and inShin etal.8

Normalw eightconcrete beams under reversedcyclicloadingShin8 and Kamara9'10 investigated the flexural duct i l i ty ofultra-high-strength concrete members (concrete strength ranging up to 15 ksi or103.4 MPa) underfullyreversed cyclic loading.

All specimens (Fig. 8.21) were 4.5in. (112.5mm) x 9 in. (225mm) incross-section, and 10ft (3m) long. Four sets of sixspecimens each weremanufactured, usingconcrete compressive strengths of 5 ksi (34.5MPa),11 ksi(75.9 MPa), and 15 ksi(103.4 MPa)forsetsA, B, and C,respective-ly . Set D was a duplicate of set C. In each set there were two beamsreinforced with four No. 3(10mm diameter) bars, two beams reinforcedwithfourNo. 4 (13 mm diameter) bars and two beams reinforced withfourNo. 6 (19 mm diameter) bars. The difference between two specimens withthe same concrete strength and longitudinal reinforcement was in thespacing ofNo.2 (6 mm diameter) ties whichwaseither 3 in. (75 mm) or6in. (150mm).

The specimens, reinforced like columns, were cast horizontally underfieldconditions,andwere also cured underfieldconditions.Thespecimenswere tested under two-point loading which subjected a considerableportion of the specimens to pure flexure. The applied cyclic loadingfol lowedthe displacement controlled schedule shown in Fig. 8.22.

The measured hysteretic load-deflection curves for the twenty-fourbeams tested have been presented inKamara.10A sampleisillustratedinFig. 8.23. The envelopes of the hysteretic load-deflection curves for thebeams were also included inKamara.10It was observed that the envelopeofthe load-deflection curves for a cyclically loaded beam showed the same

T h e be a m s p e c i m e nD e t a i ls o f b e a m s e c t io n

D 5 a t 6 fo r D 1 c o n f i n e m e n tD 5 a t 3 fo r D 2 c o n f in e m e n t


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Fig. 8.22 Deformat ionsequenceforreversedcyclicloading testsbyKa ma raetal .y-10features as the load-deflection curve for a comparable monotonicallyloaded beam.

Member ductility,as def ined by Equation (8.3), wasinvestigated.Thefinal deflection Ay was considered to be 2.4in. (61mm) which was thedeflection at the end of cycling. The value of the applied load at thatdeflect ion wasfound to beequalto orslightly larger thantheconservativeva lue of the calculated ultimate load. Theductility ratios fordownwardand upward load cycles are plotted in Figs. 8.24 and8.25,respectively.

In view of previous research work and building codes, a deflectionducti l i ty of 4 appears to represent a reasonably conservative minimumrequirement for members subjected to gravity plus wind or moderateseismic loads. This requirement was more than met by all the specimenstested inKamara's program. Thusit wasconcluded that,in theabsenceofaxial loads acting simultaneously with f lexure , high-strength reinforcedconcrete members subjected to reversed cyclic loading possess as much

Fig. 8.23 Hystereticload-deflectioncurveofspecimen tested under reversedcyclicloading9 '10

L o a dc y c l e

L o a di n c r e m e n t

D e f l e c t i o n ,i n .fi= 1 5 . 6 ksi( 1 0 7 .6 M P a )N o . 4 ( 1 3 m m d ia . ) b a rsN o . 2 ( 6 m m d i a . ) t ie sa t 3 i n . (7 6 m m ) s p a c in g

Loadkps


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p / p bFig. 8.24 Flexuralducti l i ty,asdefinedinEquation(8.3),under reversedcyclicloading-upward def lect ion9 '10ducti l i tyas is likely to be required of them in practicalsituations.It shouldbe remembered, however, that the specimens tested in the course ofKamara's investigation were under zero axial load.

For the same amounts of longitudinal reinforcement and confinementreinforcement, the ductility ratios were found to increase with increasingconcrete strength. For the same concrete strength, the ductility ratiodecreased with increasing amounts of longitudinal reinforcement. Withintherange studied inKamara's work,thespacing between ties appeared tohave virtually no effect on the ductility of the tested specimens.

f ips i

P / P bFig. 8.25 Flexuralducti l i ty,asdefinedin Equation(8.3),under reversedcyclicloading-downward deflection9 '10

Ducyndex=AfAy

Ducyndexf=AfAy


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Lightweightconcrete beams under monotonic loadingAhmad and Barker11 reported limited experimental data on the flexuralbehavior of high-strength lightweight concrete beams. Flexural tests wereconducted on sixsinglyreinforced beams. Experimental variables were thecompressive strength of concrete (5200


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Table8.8 Testprogram11

Ecksi(MPa) 0psi(MPa)

/c,(b)psi (MP a)

Age attesting,daysd,in .(m m )fc,in .( m m )b,in .( m m )eam(a)3500 (2415)3520 (2429)3760 (259 4)3750 (2588)4410 (3043)4770 (3291)

5200(35.9)5410(37.3)8330(57.5)8120 (56.0)10980 (75.8)11010(76.0)

5470(37.7)5690 (39.3)8770 (60.5)8550 (59.0)11560(79.8)11590(80.0)

22554949

10.25 (260)9.25 (235)10.19(259)9.13(231)10.13(257)9.00 (229)

12.0(304.8)12.0 (304.8)12.0 (304.8)12.0 (304.8)12.0 (304.8)12.0(304.8)

6.0(152.4)6.0(152.4)6.0(152.4)6.0(152.4)6.0(152.4)6.0(152.4)

LR5-19LR5-41LR8-22LR8-51LRl1-24LR11-54(a )Beamnom enc lature: for Beam LR5-19,'5'indicates the approxim ate concrete compressive streng th (b)Basedon 4 x8-in. c yl inde r strength(c)Using equ ivalent6 x12-in. cylinder strength, assumedto be 95 percentof 4 x8-in. cyl inder strength


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P / P bFig 8.27 Effect of the re inforceme ntratio,p/p6 ,on thedisplacementdu ctil ityofsinglyreinforced lightweightconcrete beams testedb yAhmada ndBarker11deflection ductility J J L ^ becomes essentially independent of concretestrength, as suggested earlier byPastorandNilson.4Figure 8.28 shows theeffect ofconcretestrength on \Ld fo rbeams with different values of p/p6.The comparison ofdeflection ductilitiesforlightweightand normal weighthigh-strength concrete beams Fig. 8.29 from Ahmad and Barker11)

L R 5 - 1 9

L R 8 - 2 2 f = 5 k s ifi= 8 ks i

L R 1 1 - 2 4 L R 5 - 4 1fi=11ks i

L R 8 - 5 1L R 1 1 - 5 4

d

Ud

0 . 1 9 < p / p b < 0 . 2 40 . 4 1 < p / p b < 0.54

L R 5 - 1 9L R 8 - 2 2

L R 1 1 - 2 4L R 5 - 4 1

L R 8 - 5 1L R 1 1 - 5 4

f cFig 8.28 Effect of theconcrete strength,fc ' fg on the displacementdu ctility ofsinglyreinforcedlightweight concrete beams testedbyAhmadandBarker


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P f cFig. 8.29 Comparisonofducti l i t iesoflightweightand norm alweight high-strengthsinglyreinforced l ightweightconcrete beams testedbyAhmadand B arker1 1indicatesthat p has asimilarinfluence on J U L ^ fo rbeams made ofboth typesof concrete. The \Ldvalues obtained inAhmad's study

11were lower thanthose reported by Pastor and Nilson4 for reinforced normal weighthigh-strength concrete beams.

Ahmad andBaits12 developed limited experimental dataon the flexuralbehavior of doubly reinforced high-strength lightweight concrete beamswith web reinforcement. Flexural tests were conducted on six doublyre inforced beams. Experimental variables were the compressive strengthof concrete (6700


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Table 8 9 Testprogram12ensile steelestregion dim ensions

A9, in .2 p', i n .,in.,in.z , in.fc'


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PFig. 8.30 Effect ofre inforceme ntratio,p, on thedisplacem ent du ct i l i tyofd oubly reinforced(p '~0.5p)lightweightconcrete be ams tested by Ahm ad andBatts12

1 C i g 8 31 Effect ofconcrete stre ngthon thed isplacem ent du ct i l i tyofdoubly reinforced(p '~0.5p)lightweightconcrete beam s tested by Ahm ad andB atts12

P / P bFig. 8.32 Effect of there inforcem ent rat io , p /pb , on thedisplaceme nt duc t i l i tyofdoub l yreinforced (p'~0.5p)l ightweig ht concrete beams tested by Ahm ad andBatts12

d(R =0 . 8 8 )L J - 6 - 1 6L J - 7 - 3 1

L J - 8 - 2 1L J - 1 1 - 2 2 L J - 8 - 4 4 L J - 1 1 - 4 7L J - 7 - 3 1 , d a t a n o t u s e d in t h e r e g r e s s i o n

L J - 6 - 1 6L J - 7 - 3 1

L J - 8 - 2 1L J - 8 - 4 4L J - 1 1 - 4 7

L J - 1 1 - 2 2

0 . 1 6 < p / p b < 0 . 2 20 . 3 1 < p / p b < 0 . 4 7

L J - 6 - 1 6 f ^ = 6 . 7 k s iL J - 7 - 3 1

L J - 8 - 2 1

L J - 1 1 - 2 2f = 8 k s i L J - 8 - 4 4

f j = 11 ksi L J - 1 1 - 4 7

d

d

d


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p f cFig.8.33 Displacementdu cti l i tyversusp/r'fo rdou bly re inforced (p'0.5p)l ightweightconcretebeams testedbyAhmadan dBatts12

inFigs.8.30-8.33clearly shows that the addition of compression reinforce-ment equal to approximately half the amount of tension reinforcement hadadistinctly beneficialeffect ondeflection ductility.Lightweightconcrete beams under reversed cyclic loadingGhosh etal.

13conducted an experimental investigation aimed at gatheringinformat ion on the f lexuralproperties, including ductility,ofhigh-strengthl ightweightconcrete members (concrete with a dry unit weight of approx-imate ly120 pcf and with compressive strength approaching 9 ksi at 56 days)

under reversed cyclic loading.Two sets of six specimens each were manufactured using lightweight

aggregate concrete having compressive strengths of 5 ksi(34.5 MPa)at 28daysand 9 ksi (62MPa)at 56days. The test variables were the concretestrength, the amount of longitudinal reinforcement, and the spacing of ties.The test results, including hysteretic load-deflection curves, for the speci-mens representing columns under zero axial load are reported in Ghoshetal.13

The specimen dimensions, test procedure and loading history wereidenticaltothose used earlier byKamara.9'10 Allspecimensofeach serieswere castat thesame time.

Exceptfor one specimen that failedinshear, themoderate - aswellashigh-strength lightweightconcrete specimens exhibited stable hystereticbehavior all the way up to the limiting stroke of the testing machine.Flexure-dominated behavior could be ensured by supplying design shearstrength in excess of the shear corresponding to the probable flexuralstrength.

The maximum deflection that could be imposed on the lightweightconcrete beams of this investigation and on the normal weight concretebeams tested under reversed cyclic loading in the previous investigation byKamara9'10was limited by the maximum stroke of the testing machine, so

L J - 6 - 1 6o L J - 7 - 3 1

2 0 1 8= 7o - (R = 0 - 9 4 )P C

L J - 8 - 2 1L J - 1 1 - 2 2 L J - 8 - 4 4 L J - 1 1 - 4 7L J - 7 - 3 1 , d a ta n o t u s e d in t h e r e g r e s s io n

^d


34/37

that full potential values of the ducti l i ty index J U L /(Equ at ion (8.3)) couldnot be m easure d. The du cti l i ty indices of the l ightwe ight concrete beam swe re lower than those of the corresponding norm al w eigh t concretebeams.The reason isthat,because of the low er m od ulu s of elasticity of lightw eigh tconcrete, the ne utral axis de pth at yield in a l ightwe ight concrete beam w aslarger than that in a corresponding normal weight concrete beam. Thismade the yieldcurvature ,and consequently the yielddeflection, A7 , largerin the l ightweight beam. In terms of the drop in maximum load carryingcapacity at the maximum deflect ion that could be imposed, there was nosignificant difference between l ightweight and normal weight concretebeams having the same longi tudinal re inforcement and comparablecon-crete streng ths, if the she ar-dom inated l ightweight beam were exclud edfrom consideration.

The ratio p/pb once again turned out to be the most dominant factorinfluencing the magni tudes of the ductility indices. Plots of J J L O versus p/pband \ L f versus p/pb are presented in Figs. 8.34and 8.35,respectively. Thefigures clearly show that for the same concrete strength, the ductilityindices decrease rather drastically as the ratio p/pb increases. However, allspecimens, with the exception of the one that failed in shear, developedrather substantial valuesof j u y ,whichi sprobably a more practical measureof ducti l i ty for the specimens tested than J J L O . It needs to be pointed outagain that the values of J J L / i nFig. 8.35are the largest value s that cou ld bemeasured ,and not the largest values that couldbe at ta ined.Figures 8.34and 8.35 general ly show that the same amount oflongi tu-dinal reinforc em ent, du cti l i ty increases w ith increasing concrete strength.T he confinement reinforcement spacing, within the range studied, d idnot have an appreciable effect on m em ber du cti l i ty, as is to be expected inview of earlier discussions.

ConclusionsThe fol lowing conclusions can be draw n with respect to the de formab il i tyof high-strength concrete beams:

1 Althoug h high-strength concrete is a less deformable material thanlower strength concrete, the curvature duct i l i ty , J J L C , of a singlyreinforced concrete section increases with/,'for the same valueof thereinforcement rat io, p =As/bd. This isbecause th eneutral axis depthc decreases with increasing concrete strength, and the decrease in cwith// more than compensates for the lossofm aterial du cti l i tyin theHS C range. For the same//, J U L C decreases with increasing p, becauseth e neutral axisdepth, c increases with increasing valuesof p.2 The curvature duct i l i ty of all heavily reinforced sections ( p > p ^ )theoretically approaches u ni ty regardless of concrete stren gth, fc ' .Thus , the increase in |J L C with fc' tends to decrease with p. There


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p / p b( b )

ig 8.34 Duc t i l ity index J U L O versusp/pb fo rdoubly reinforced (p = p ')lightweightconcreteb e a m s13appearsto be alimiting tensile steel ratio beyond which J J L C values arepractically thesame regardlessof fc'.3 The curvature ductility, J J L C , decreases with increasing values of thereinforcement ratio, p/p^ . At the same p/p/,, the differences betweenLSC, MSC and HSC curvature ductility (u ,c) values are greatlyreduced compared to those observedfor aconstant valueof p.Thisis

U p w a r df c p s iMPa)

D o w n w a r df c p s i MPa)

Ducyndex0

Ducyndex0

P / P b(a )


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p / p b(b )

Fig. 8.35 Du ctil ity index ( j yversusp/pfefo rdoublyreinforced (p = p') lightweightconcretebeams13

because the value of pb increases with greater concrete strengths. Fora constant value of p /p^ , a beam with a higher strength concretecontains more steel thanonewith lower strength concrete.4 The member deflection ductility, J U L ^ , decreases with increasingvalues of p. For the same value of p, J J L J increases with increasing

U p w a r dfips iMPa)

P / P b(a )

f t p s i MPa)

Ducyndexfa

WxepujjprQ


37/37

concrete strength,fc ' . How eve r, the m agn itud e of the increase is lessthan in the case of J J L C .5 The deflect ion duct i l i ty , J J L ^ , also decreases with increasing valuesofp/p^ . For the same p /p^ , depending on that value of p /p^ , J J L ^ m aydecrease with increasing concrete strength. The differences be tweenLSC and HSC \Ldvaluesdecreasew ith increasing value sof p /ph .6 The p l imit beyond which J J L ^ is no longer influenced by fcr iscomparat ivelysmaller than that for u,c.7 The add it ion of long itud inal compression steel and lateral t ie steelincreases the displacem ent du cti l i ty of singly reinforced HS C beam s(the former more efficiently than the latter) , provided that there inforcement index p fy / fc ' isgreater than ace rtain cri tical valu e.8 For low value s of the above reinforc em ent ind ex , beam s fail amostimmedia te ly after losing their concrete cover. Sincesignificant inelas-ticd i latancyof the compression zone concrete occu rs onlyafter lossofth e cover concrete, th e presence of longitudinal compression andlateral ti e steel hasl i t tle influenc eon the duct i l i tyofthese m em bers .9 For m ode rate to larger values of the index p /y //c'', displacementducti l i ty is influenced significantly by the presence of long i tud ina lcompressive and lateral tie steel, because the post-spalling lateralexpenasion of thecompressed concrete isrestrained by the compress-ion zone re inforcem ent .10 La teral ties are not as efficient in increasing the post-yield deforma-tionsofbeams astheyare inincreasingthepost-peak de format ionsofconcentrical ly loaded members. This is because lateral confiningstresses are unevenly and inefficiently distributed across the beamcompressionzone.Thep rim ary roleof the transverse steel inincreas-ing beam duct i l i tyis not as a provider of concrete confinement ,bu trather as a lateral support m echan ism for the lo ng itud inal steel .11 The above conclusions draw n from tests on normal weight concretebeams under monotonic loading also apply, from all indications, tol ightweight concrete beams under monotonic loading, except that ,allother variables being the same, ductility is l ikely to be lower for thel ightweight beam thanfor the corresponding normal weight member.12 In the absence of axial loads acting sim u ltaneo u sly w ith flexure,high-strength re inforced concrete members subjected to reversedcyclic loading possess as much duct i l i tyas is l ikely to be required ofthem in practical si tuations. Un de r the same loadin g, the du cti l i tyindices of l ightwe ight concrete beams are lower than those of thecorresponding normal weight concrete beams. The reason is that ,because of the lower m odulusofelasticityofl ightweightconcrete, thene utral axis dep th at yield is a l ightwe ight concrete beam is larger thanthat in a corresponding norm al we ight concrete beam . This mak es the

ductiity and seismic behaviour

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