Estudio Del Comportamiento de Columnas de Hormigon Pretensado

7/28/2019 Estudio Del Comportamiento de Columnas de Hormigon Pretensado

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Robert L. YuanDepartment of Civil

EngineeringUn iversity of Texas

at Arlington

Arlington, Texas

Mohsen IssaDepartm ent of Civil

EngineeringUniversity of Illinois

at ChicagoCh icago, Illinois

Prestressed Concrete

Colum n Behavior

P restressed concrete columns havebeen used in the construction in-dustry as precast compression members

for more than 15 years. Although theprestressing force in the column reduces

a small percentage of the concrete's

compressive strength, the effective pre-stress level has been proven to be bene-ficial to the column's load resistantcapacity when the eccentric loads in-duce high bending moment on the com-pression member. Field experience alsoindicates that there are few significantproblems during construction with re-gard to fabrication, transportation, erec-

tion, and serviceability of prestressedconcrete columns.

Many research projects have beendone on prestressed concrete compres-sion members since the late 'SOs. Someefforts were directed toward developingrational methods for predicting the ul-timate load capacity;'- 4 others concen-trated on evaluating the effects of slen-

derness, eccentricity, prestress leveland material properties on the strength

of prestressed concrete columns.5-8However, research has not yet come tothe point where the influence and con-tribution of lateral reinforcement re-

garding its type, size, and percentage ofreinforcement is fully understood.The returned questionnaire surveysfrom the precast concrete industry 9 alsoindicated a need for better assessment ofthe effectiveness of lateral reinforce-ment.

In 1968, the first tentative recommen-dations for the design of prestressedconcrete columns were made by the PCICommittee on Prestressed ConcreteColumns. 1 0 Those recommendationswere revised in 1976 1 1 and again in1987; 1 2 they were presented in codelanguage and were based on the designprovisions created for reinforced con-crete columns from the ACI BuildingCode.

PCI JOURNAL/Novem ber-Decem ber1989 51


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RESEARC H SIGNIFICAN CEThe objectives of this study were (1)

to evaluate the need for and influence ofindividual tie and continuous lateralreinforcement on prestressed concretecolumns, (2) to determine if continuoussquare lateral reinforcement of small di-

ameter is an acceptable alternative, and(3) to study the effect of slenderness onthe strength and stability of prestressed

concrete columns.

The parameters in the investigationincluded (a) types of lateral reinforce-ment, (b) pitch spacing, (c) prestressinglevel, (d) diameter of lateral reinforce-ment, (e) concrete strength, (f) eccen-tricity of applied load, and (g) slender-ness ratio.

A total of 53 prestressed concrete col-umns were tested. During the experi-mental investigation, the ultimate loadand lateral deflection were measured. Inaddition, strains on lateral reinforce-ments, prestressing strands, and con-crete surface were also recorded. Ex-perimental results were compared withcomputational analyses for ultimateloads and lateral deflections.

EXPERIMENTAL P ROGRAM

Test SpecimensAll prestressed concrete columns

were fabricated and tested in the struc-tural laboratory at the University ofTexas at Arlington. Conventional prod-uction techniques and commerciallyavailable materials were used. Thenormal weight concrete contained natu-ral sand, crushed limestone, and TypeIII portland cement. Specified concretecompressive strengths, as obtained from

4 x 8 in. (102 x 204 mm) cylinders, were

7000 and 10,000 psi (48 and 69 MPa) atthe time of column testing.

Thirty relatively short, prestressedconcrete columns were tested underconcentric load. These columns had across section of 6 x 6 in. (152 x 152 mm)

and a height of 8 ft (2.4 m). The corre-sponding slenderness ratio was kllr =56. The test matrix of these short col-

umns is shown in Table 1.Twenty-three intermediate and long

prestressed concrete columns weretested under concentric and eccentricloads. The columns had a cross sectionof 8 x 8 in. (204 x 204 mm) with variable

heights of 12, 16, and 19 ft 3 in. (3.6, 4.8and 5.8 m). The corresponding slen-derness ratios kl/r were 62, 83, and 100,

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Table 1. Test matrix and results of prestressed concrete columns (6 x 6 in. cross section).

Group Spacing Pre- Ulti- Ulti- A ver- A ver- Concre t eand Type of or stress mate mate age age cyl indercolumn la tera l p itch level load stress load stress strengthnumber r e in fo rcemen t (in .) (p si) (kip s) (p s i) (kips) (ps i) (psi)

GR1C1 Plain 237 6583 7160G R 1 C 2 concre te 240 6 6 6 7 238.5 6625 8 2 5 0G R 1 C 3 column 187.5 5208 8250

Prestressed colum n

GR2C1 1000 210 5833 7320

G R 2 C 2 N o 1000 20 0 5 5 . 5 5 7350G R 2 C 3 lateral 1000 202 5611 204.6 5683 7400G R 2 C 4 reinforcement 1000 204 5 6 6 7 7380G R 2 C 5 1000 20 7 5750 7360

GR3C1 6 1000 210 5833 7350G R 3 C 2 Ties 6 1000 210 5833 206.6 5740 7340G R 3 C 3 6 1000 20 0 5 5 5 5 7320

GR4C1 6 1000 237 6 5 8 3 7160G R 4 C 2 Square spiral 6 1000 215 5972 220.6 6 129 7240

G R 4 C 3 6 1000 210 58 33 7120G R 5 C 1 6 1000 224 6222 7350G R 5 C 2 Round sp ira l 6 1000 210 5833 216.3 6 0 0 9 7320G R 5 C 3 6 1000 215 5972 7400

G R 6 C 1 Ties 3 1000 210 5833 7310G R 6 C 2 Ties 3 1000 220 6111 215 5972 7330

GR7CI 3 1000 218 6055 7320G R 7 C 2 Square spiral 3 1000 220 6111 219 6083 7437G R 7 C 3 3 1000 2 0 0 * 5 5 5 5 7343

G R 8 C 1 Round sp ira l 3 1000 220 6111 7320G R 8 C 2 Round sp ira l 3 1000 217 6027 218.5 6069 7315

GR9C1 Square spiral 1 1000 235 6527 7335

GR1OC1 Round sp i ra l 1 1000 238 6611 7344

GR11Cl Square spiral 6 1000 28 5 7916 9440GR11C2 Square spiral 6 1000 295 8194 290 8055 9909

GR12C1 Square spiral 3 1000 26 7 7416 9079GR12C2 Square spiral 3 1000 270 7500 268.5 7458 9252

All columns w ere subjected to concentric loads (e = 0 ).* Columns failed at the ends.M aterial failure occurred for all 6 x 6 in. x 8 ft columns.Note: 1 psi = 6.895 kPa; 1 kip = 4.45 kN.

PCI JOURNAL/November-December 1989 53


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Table 2. Test matrix and results of p restressed concrete columns (8 x 8 in. cross section).

Series Square sp ira l Pre- C on cre teand la tera l stress Failure cyl inder

column r e in fo rcemen t Pitch level load strength Mode ofn u m b e r diameter(in.) (in.) P . (psi) Llr eld (kips) (psi) failure

S1C1 0 . 1 3 5 - 0 3 0 0 1 0 0 1 3 0 . 5 7 1 3 3 Instabil i tyS 2 C 1 0 . 1 3 5 9 0 . 0 1 3 0 0 1 0 0 1 2 7 . 5 7 1 4 6 Instabil i tyS 3 C 1 0 . 1 3 5 6 0 . 0 0 1 5 5 3 0 0 1 0 0 1 2 8 6 7 0 0 Instabil i tyS 4 C 1 0 . 1 3 5 3 0 . 0 0 3 1 3 0 0 1 0 0 1 3 1 7 3 6 5 Instabil i tyS 4 C 2 0 . 1 3 5 3 0 . 0 0 3 1 3 0 0 1 0 0 1 2 8 6 8 0 0 Instabil i tyS 5 C 1 0 . 1 3 5 4 . 5 0 . 0 0 2 0 7 3 0 0 1 0 0 1 3 0 . 5 7 1 8 6 Instabil i tyS 6 C 1 R C 0 . 1 3 5 3 0 . 0 0 3 1 - 1 0 0 1 2 8 7 1 0 0 Instabil i tyS 7 C 1 0 . 2 1 9 4 0 . 0 0 6 3 0 0 1 0 0 0 2 8 5 7 2 0 0 M ate ri a lS 7 C 2 0 . 2 1 9 4 0 . 0 0 6 3 0 0 1 0 0 0 . 2 5 9 2 7 2 0 0 Instabil i tyS 7 C 3 0 . 2 1 9 4 0 . 0 0 6 3 0 0 1 0 0 0 . 5 4 5 7 2 0 0 Instabil i tyS 7 C 4 0 . 2 1 9 4 0 . 0 0 6 3 0 0 1 0 0 1 3 0 7 2 0 0 Instabil i tyS 7 C 5 0 . 2 1 9 4 0 . 0 0 6 6 0 0 1 0 0 1 3 0 7 2 0 0 Instabil i tyS 8 C 1 0 . 2 1 9 4 0 . 0 0 6 3 0 0 9 5 1 3 0 7 2 0 0 Instabil i ty

S 9 C 1 0 . 2 1 9 4 0 . 0 0 6 3 0 0 8 3 0 2 9 5 7 2 0 0 M ate ri a lS 9 C 2 0 . 2 1 9 4 0 . 0 0 6 3 0 0 8 3 0 . 2 5 1 0 5 7 2 0 0 Instabil i tyS 9 C 3 0 . 2 1 9 4 0 . 0 0 6 3 0 0 8 3 0 . 5 6 0 7 2 0 0 Instabil i tyS 9 C 4 0 . 2 1 9 4 0 . 0 0 6 3 0 0 8 3 1 3 2 . 5 7 2 0 0 Instabil i tyS 9 C 5 0 . 2 1 9 4 0 . 0 0 6 6 0 0 8 3 1 3 6 . 0 7 2 0 0 Instabil i ty

S10C1 0 . 2 1 9 4 0 . 0 0 6 3 0 0 6 2 0 3 2 0 * 7 1 8 0 M ate ri a lS I O C 2 0 . 2 1 9 4 0 . 0 0 6 3 0 0 6 2 0 . 2 5 1 2 5 * 7 1 8 0 Instabil i tyS 1 O C 3 0 . 2 1 9 4 0 . 0 0 6 3 0 0 6 2 0 . 5 0 7 7 . 5 7 1 8 0 Instabil i tyS 1 O C 4 0 . 2 1 9 4 0 . 0 0 6 3 0 0 6 2 1 3 8 . 0 7 1 8 0 Instabil i tyS I 0 0 5 0 . 2 1 9 4 0 . 0 0 6 6 0 0 6 2 1 4 6 7 1 8 0 Instabil i ty

p g = rat io of lateral s teel reinforceme nt.* Colum ns fai led at the ends.Note : 1 ps i = 6 .895 kPa; 1 k ip = 4 .45 kN.

respectively. The test matrix of the in-termediate and long columns is shownin Table 2.

Prestressing StrandsThe seven-wire stress-relieved

strands, with Grade 270, have a diame-ter of 3/8 in. (9.5 mm) for short columnsand '/2 in. (13 mm) for intermediate andlong columns.

Strands in the column were tensionedindividually by using a center-pullstressing ram. Prestress levels at a given

column cross section were 1000 psi (6.9MPa) for short columns, 300 and 600 psi

(2.1 and 9.2 MPa) for intermediate and

long columns. Strain gauges weremounted on the individual strands atpredetermined locations in order tomeasure prestressing force, prestressing

loss, and the change of strains.

Lateral Reinforcem entIndividual tie and continuous lateral

reinforcements were fabricated fromplain round steel wires of two differentsizes. The wire with a diameter of 0.135in. (3.4 mm) had a yield strength of 77ksi (531 MPa) and an ultimate strengthof 108 ksi (745 MPa). The wire with adiameter of 0.219 in. (5.6 mm) had ayield strength of 43 ksi (296 MPa) and an

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(a) Tie lateral reinforcement (b) Continuous sq uare lateral reinforcement

Fig. 1. Three typ es of lateral reinforcement.

ultimate strength of 58 ksi (400 MPa).The configurations of lateral reinforce-ment are shown in Fig. 1.

Test ProceduresAll columns were tested in a vertical

position as shown in Figs. 2 and 3. Assoon as a column was aligned in thereaction frame with roller supports atboth ends, a hydraulic ram was operated

from the top to keep the column in

place. The column was then loadedeither in concentric or eccentric mono-tonic compression.

One direct current differential trans-ducer (DCDT) was placed on the topplate and one on the bottom plate tomeasure the longitudinal deformation of

the column and the rotations at the ends.

Mechanical dial gauges were placed at (c) Continuous round lateral reinforcement



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Fig. 2. Short column under concentric load. Fig. 3. Long colum n under eccentric load.(Column testing in a vertical position.) (Column testing in a vertical position.)

the quarter points of the column heightto measure lateral deflections of shortcolumns; transits and theodolites werealso used to record lateral deflec-tions of long columns. A high speed,

automatic, data acquisition system wasused to collect the load and strain read-ings.13

EXPERIMENTAL RESULTS

Effect of C oncrete Strength

All prestressed concrete columns inthis investigation had the same concretemix proportion. The average cylinderstrength reached about 4000 psi (28MPa) at 24 hours, 7000 psi (48 MPa) at 3

days, and 10,000 psi (69 MPa) at 28 days.The test results in Table 2 indicate thatthe ultimate load of prestressed concretecolumns increases with an increase in

concrete strength.

Everything else being equal, for con-crete strength f, = 7200 psi (50 MPa),the ultimate load of a prestressed con-crete column, with a cross section of 6 x

6 in. (152 x 152 mm) and a height of 96in. (2.4 m), is 220 kips (979 kN); for con-crete strength that increases to f, = 9700psi (67 MPa), the ultimate strength is290 kips (1.3 MN). The increase of 30percent in column ultimate strength isdue to an increase in the same order ofconcrete strength.

Effect on Lateral Reinforcemen tThe test results for short columns are

presented in Table 2. For plain concretecolumns, the average ultimate load is239 kips (1.1 MN). For prestressed con-crete columns without lateral rein-forcement, the average ultimate load is205 kips (912 kN). The reduction of 34

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C.

LATERAL REINFORCEMENT O.2I9"6x 6"COLUMN CROSS SECTION

PITCH SPACING = 3 IN.

6

5

4 } ^E

3-

/LATERAL DEFLECTION AT 160 KIPS

2 +-SQUARE SPIRAL PC COLUMN

*- ROUND SPIRAL PC COLUMN

0- TIED PC COLUMN

0 .125 .2 5 .375 .5 .625 .75 .875

LATERAL DEFLECTION (IN.)

Fig. 4. Deflection configuration of prestressed concrete columns (6 x 6 in.).Note: 1 ft = 0.305 m ; 1 in. = 25.4 mm .

www

z

J0vw0II-zwJ

kips (151 kN) of ultimate load capacity in

prestressed concrete columns is primar-

ily due to the prestress 1000 psi (6.9MPa) or the preloading 36 kips (160 kN)on the columns.

For prestressed concrete columns

with lateral reinforcements, the averageultimate load is 215 kips (956 kN) in 6 in.

(152 mm) pitch spacing, 218 kips (970kN) in 3 in. (76 mm) pitch spacing, and237 kips (1.1 MN) in 1 in. (25 mm) pitchspacing. Thus, the ultimate loads of theprestressed concrete columns with lat-eral reinforcements of 1 in. (25 mm)pitch spacing are 10 percent higher than

that of columns with 3 in. (76 mm) or 6in. (152 mm) pitch spacing lateral rein-forcement, and 15 percent higher thanthat of columns without lateral rein-forcement.

For a given pitch spacing, the average

ultimate loads of prestressed concretecolumns with continuous lateral rein-forcements are 6 percent higher thanthat of columns with tie lateral rein-forcement.

The results tend to indicate that, for agiven concrete strength, there is no sig-nificant difference in ultimate loadcapacity between columns with 3 and 6

PCI JOURNAUNovember-December 1989 57


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CONTINUOUS SQUARE SPIRAL LATERALREINFORCEMENT 0.135 IN. DIAMETER

f =7200 PSI

IiL/r = 100

35 PL = 300 PSI

e/d= i

25

1 5

J p-NO LATERAL REINFORCEMENT1 0 *PITCH SPACING= 9 IN

--PITCH SPACING = 6 IN.X-PITCH SPACING= 4.5 IN.

5 $-PITCH SPACING = 31N.

0 I 2 3 4 5 6 7 8CENTRAL DEFLECTION (IN.)

Fig. 6. Load -deflection curves of p restressed columns (8 x 8 in.) w ith different

p itch spacing of lateral reinforcem ent. Note: 1 kip = 4 .45 kN; 1 in. = 25.4 m m.

a--

0J

The test results of long columns arepresented in Table 2. For a prestressedconcrete column with a slendernessratio hr = 100 and loading eccentricityeld = 1, the ultimate loads are about the

same for columns with and without lat-eral reinforcements. Apparently, insta-bility dominates the critical load.

The effects of lateral reinforcement onlong column deflection are shown inFigs. 5 and 6. The lateral deflection ofthe column decreases with a decrease in

pitch spacing; in a column with a pitchspacing less than 4.5 in. (114 mm), de-

flection is significantly smaller than de-flection of a column with a pitch spacing

larger than 6 in. (152 mm).

Effect of S lenderness RatioTypical load-deflection curves of pre-

stressed concrete columns with variousslenderness ratios are shown in Fig. 7.For a given eccentricity ratio, the ulti-mate loads decrease with an increase inslenderness ratio, while the lateral de-flections increase with an increase inslenderness ratio.



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50e/d = 0.25

40 O- L/r = 100'JE L/r= 83

30 H +-L/r= 62

120 }

110

jF r

00^

90

80 ^F

70

i

^F

60 I50 I '

IIIPL = 300 Psi

40

30

20

1 0

0 0:

I 2iii 111111111111

3 4 S


Fig. 7. Load-deflection curves of prestressed co ncrete column s w ith different

slenderness ratios (eld = 0.25). Note: 1 kip = 4.45 kN; 1 in. = 25.4 mm.

U)a .

0J

The results indicate that, for highslenderness ratio (hr = 100) and largeeccentricity (eld = 1), the ultimate loadsof prestressed columns are about thesame regardless of pitch spacing and di-ameter of lateral reinforcements.

Effects of Eccentricity RatioThe effects of the eccentricity ratio on

lateral deflection are represented by thecurves in Fig. 8. The results indicatethat, for a given slenderness ratio, thedeflectional stiffness and ultimate load

of prestressed concrete columns de-

crease with an increase in the eccen-tricity ratio. The effect of eccentricityratio on the ultimate load appears to bemore significant than that of slendernessrat io.

Effects of P restress LevelThe effects of prestress level on

load-deflection curves are representedby the curves in Fig. 9. For eccentricityratio eld = 1, the results indicate thatthere is no effect of prestress level ondeflectional stiffness before the eccen-tric load reaches about 15 kips (67 kN) or

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30L /r =83

20 +- e /d = 0 .25-e /d= 0 .50

0 D- e / d = 1 . 0l

00 +/

90

80

70 %

i6

50

40 I30/!

20PL=300 PSI

10

0 0 I 2 3 4 5 6


Fig. 8. Load-deflection curves of p restressed columns w ith different eccentricity

ratios (L/r = 83). Note: 1 kip = 4.45 kN; 1 in. = 25.4 mm .

U)

OJ

induced column stress of 235 psi (1.62MPa). Beyond that point, the ultimateload and deflectional stiffness increasewith an increase in prestress level.The effects of prestress level on ultimateload and deflectional stiffness are more

significant in a relatively short columnunder an eccentric load than in a long

slender column.

Column Load -Strain Relations

Typical axial load-strain relation forconfined short prestressed concrete col-umn is shown in Fig. 10. The prestress

level in the column was 1000 psi (6.9MPa); the initial compressive strain onthe concrete surface was 0.00025; theinitial tensile strain on the prestressingstrands was 0.003. Prior to column fail-ure, the compressive strain on the con-

crete surface was in the range of 0.0013to 0.002 for unconfined columns and0.002 to 0.003 for confined columns; thetensile strain on the steel was in ther a n g e o f 0 . 0 0 0 5 t o 0 .0 0 1 5 .

Typical eccentric load-strain relationfor confined long columns is shown inFig. 11. The initial concrete compres-sive strains were 0.00012 and 0.0022 for



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f 'C =7200 PSI

L/r= 100

e/d=1.o

100-EXPERIMENTAL DATA PL=300 PSI

1 - -EXPERIMENTAL DATA PL=600 PSI

0 I 2 3 4 5 6 7 8 9 1 0


Fig. 9. Load- deflection curves of prestressed concrete columns with different prestresslevels (L/r = 100). Note: 1 kip = 4.45 kN; 1 in. = 25.4 mm.

35r

a _

0OJ

prestress levels of 300 and 600 psi (2.1and 4.2 MPa), respectively. When theeccentric load increased, the strain onthe compression surface of the concreteincreased; the strain on the tension sur-face decreased and changed from com-pressive strain to tensile strain. Prior tocolumn failure, the compressive strainon the compression face of the columnreached a value of 0.0025 to 0.0038,while the strain on the tension face ofthe column developed tensile strain of0 . 0 0 2 5 .

The initial tensile strains on pre-

stressing steel were 0.0011 and 0.0022,corresponding to prestress levels of 300and 600 psi (2.1 and 4.2 MPa), respec-tively. When the eccentric load in-creased, the tensile strain on the steel in

the tension side increased, while thetensile strain on the steel in the com-pression side decreased. Prior to failure,the tensile strain was in the range of0.004 to 0.008, which was below theyield point strain of the prestressingsteel; while the strands in the compres-

sion side were about to change from ten-sion to compression.

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30LATERAL REINFORCEMENT 0 =0.219 IN,

SQUARE SPIRAL PC COLUMNPITCH SPACING= 6 IN.

ULTIMATE LOAD= 237 KIPSULTIMATE STRESS=6583 PSI

225

200

U)175

0 150JJa 125x

L.J

75F- // STRAIN GAGES ON:

0-CONCRETE SURFACE*-PRESTRESSING STEEL

50

25

500 1000 1500 2000 2500 3000

CHANGE OF STRAIN (MICRO IN./IN.)

Fig. 10. Load-strain curves of prestressed column 6 x 6 in. at midheight (with I lateralreinforcement, (A = 0.219 in., S = 6 in.). Note: 1 kip = 4.45 kN; 1 in. = 25.4 imm.

Percentage of LateralReinforcement

The percentage of lateral reinforce-ment, p, is defined as the ratio of thevolume of continuous lateral reinforce-

ment in one loop to the volume of con-

crete core. The calculated values areshown in Table 3.

The experimental results indicatethat, with continuous square lateral re-inforcement, the percentage of steel p =0.0124 for a 6 x 6 in. (152 x 152 mm)column and p = 0.006 for a 8 x 8 in. (203

x 203 mm) column were considered ade-quate for confinement and deflectionalstiffness. According to ACI Code 318,the minimum percentage of continuoussquare lateral reinforcement with a di-ameter d = 0.219 in. (5.6 mm) shall be p

= 0.1107 for a 6 x 6 in. (152 x 152 mm)column and p = 0.1122 for a 8 x 8 in. (203x 203 mm) column; these figures implythat the pitch spacing of lateral rein-forcement shall be reduced to less than1 in. (25 mm) for the size of columntested. It is apparent that the ACI re-quirement for lateral reinforcement is



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Tab le 3 . Tes t m a t r ix o f the p e rcen tage o f the con t inuous l a t e ra lr e in fo rcemen t .

Column and la te ra lP i tch spac ing

9 in. 6 in. 4.5 in. 4 in. 3 in. 1 in.e in fo rcemen t

(A) 6 x 6 in. cross sect ion(i) Square la teral

re inforcement ,4) = 0.219 in. , p value 0.0062 0.0124 0.0372

( ii ) Rou nd la tera lre inforcement ,

= 0 .219 in., p value 0.0048 0.0095 0.0285

(B) 8 x 8 in. cross section(i) Square lateral

re inforcement ,4) = 0.219 in. , p value 0.0040 0 .0060 0.0080

(ii) Square lateralre inforcement , = 0 .135 in. , p value 0.0010 0.0015 0.0021 0.0031

Note: 1 in. = 25.4 m m.

f 'c =7200 PSI

L /r= 100

PL=600 PSI

e/d= I3

a -

0J 7

0-COMPRESSION FACE Q *1-10 TENSION FACE

-5000 -4000 -3000 -2000 -1000 0 1000 2000 3000 4000 5000COMPRESSION TENSION

CONCRETE STRAIN (MICRO IN./IN.)

Fig . 11 . Load-s t r a in cu rves o f p res t r e s sed conc re t e co lum n 8 x 8 in . a t m idhe igh t (Lh =100). Note: 1 kip = 4.45 kN; 1 in. = 25.4 mm.

6 4


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Tab le 4 . Com par i son o f expe r im en ta l r e su l ts andcom puta t iona l an a lys is fo r p re s tr e s sed conc re t e co lumn s(ult ima te load , kips) .

C o l u m n

N o. efd L ir

Tes t

results

Nathan'scomputa t iona l

results

UTA'scomputa t iona l

results

S1C1 1 .0 10 0 3 0 . 0 28.5 29.0

S2C1 1 . 0 100 2 7 . 5 28.5 29.0

S3C1 1 . 0 100 28.0 27.5 28.5

S4C1 1 . 0 100 31.0 28.5 29.5S4C2 1 . 0 100 28.0 28.0 28.5

S5C1 1 . 0 10 0 3 0 . 5 28.5 29.0

S6C1* 1 . 0 100 28.0

S7C1 0 . 0 10 0 285.0 249.0 254.0S7C2 0.25 100 92.0 7 7 . 5 8 1 . 0S 7 C 3 0.50 10 0 45.0 44.0 42.5S7C4 1 . 0 100 30.0 28.5 29.0S7C5 1 . 0 10 0 30.0 30.5 31.5

S8Ci 1 . 0 90 30.0

S9C1 0 . 0 80 295.0 308.0 303.0S9C2 0.25 80 105.0 99.0 101.5S9C3 0.50 80 60.0 54.5 54.0S9C4 1 . 0 80 3 2 . 5 34.0 35.0S9C5 1 . 0 80 3 6 . 0 36.0 37.0

S10C1 0 . 0 60 3 2 0 . O t 385.0 371.0S1OC2 0 . 2 5 60 1 2 5 . O t 139.0 137.5SIOC3 0 . 5 0 60 7 7 . 5 74.0 7 3 . 5STOC4 1 . 0 60 38.0 41.5 44.0S 1005 1 . 0 60 46.0 43.5 46.0

* S6C1 is a reinforced concrete column.t Columns failed at the ends.Note: 1 kip= 4.45 kN.

considerably higher than the lateral re-inforcement used in this research pro-

gram; the p value specified in the ACICode seems to be impractical for the ar-rangement of lateral reinforcement.

Com parison Between Experimentaland C om putational Results

A comparison was made on the ulti-

mate load and lateral deflection of pre-stressed concrete columns between the

experimental data and computationalresults from the finite element pro-gram 1 4 and from Professor Nathan'sanalysis.' The procedure of nonlinearfinite element analysis is capable of es-tablishing the equilibrium position atdiscrete load steps through the elastic,inelastic, and ultimate load ranges. Both



16/17

50

7200 PSI

PL=600 PSI45

L/r = 1 O0 e/d= 1.0

40

35

30

25

20

IS

q -TEST DATA UTA*-COMPUTATIONAL DATA UTA10+-COMPUTATIONAL DATA NATHAN

5

I III Iii ill III liii II I I0 ILI I.;t II till lii1 2 3 4 5 6 R a n

CENTRAL DEFLECTION (IN.)

Fig. 12. Com p arison of p restressed concrete column load-deflection relationsfrom experimental results and computational analysis (PL = 600 psi, L/r = 100).Note: 1 kip = 4.45 kN; 1 in. = 25.4 m m.

a

0

0J

material and geometric nonlinearitiesand the effect of progressive cracking onthe structural stiffness are considered.Nathan's theory was developed byequating the external and internal mo-ments, where the external moment atany point in beam-column was givenby a primary moment plus the secondarymoment.

The comparison of the ultimate loads

is presented in Table 4. A comparison ofload-deflection curves is shown in Fig.12. In general, the experimental resultsare in close agreement with the compu-tational data. They indicate that both the

finite element program and Nathan'scomputer program are reasonably accu-rate in predicting ultimate loads.

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SU MMARY AND CO NCLU SIONS

The following conclusions can bemade as a result of this investigation on

prestressed concrete columns:

1 . The ultimate load capacity of a pre-stressed concrete (PC) column increaseswith a decrease in the pitch spacing oflateral reinforcement. If the pitch spac-ing is small, the ultimate load capacity ofa PC column with lateral reinforcement

is greater than that of a PC column with-out lateral reinforcement. If the pitchspacing is large, there is no significantdifference in the ultimate load between

PC columns with and without lateralreinforcement.

2 . For a given load, deflectional stiff-ness of the PC column increases signifi-cantly with a decrease in pitch spacingof lateral reinforcement.

3 . The ultimate load capacity of a PCcolumn with continuous lateral rein-forcement is slightly higher than that of

a PC column with tie lateral reinforce-ment. Continuous lateral reinforcementappears to be more effective in con-fining concrete than tie lateral rein-forcement. Continuous square lateralreinforcement is as effective in con-finement as continuous round lateralreinforcement. A decrease in pitchspacing of lateral reinforcement would

increase the effectiveness of core con-finement.

4 . The stress and strain on the lateralreinforcement with a diameter d = 0.219

in. (5.6 mm) are small compared to mate-rial's yield strength and yield strain.Thus, the steel wire with such a small

diameter can be used for continuous lat-eral reinforcement of large size PC col-u m n s .

5 .The test results of long, intermedi-

ate, and short columns have indicatedthat the percentage of continuous lateralreinforcement specified in the ACICode seems too high, and is not appro-priate for application to PC columns.Rather, the pitch spacing should be con-sidered in the arrangement of lateralreinforcement.

6 . Based upon the experimental andtheoretical analyses, the pitch spacing oflateral reinforcement is recommendedto be one-half of the least core dimen-sion of the PC column as far as confine-ment and deflectional stiffness are con-

cerned.

7 . For a PC column under eccentricload, both ultimate load and deflectionalstiffness increase with an increase in

prestress level. The effect of prestresslevel is more significant in the relativelyshort column with a larger eccentricitythan in a long slender column under ec-centric load.

8 . The ultimate load of the PC col-umn decreases with an increase in slen-derness ratio. For the PC column with aslenderness ratio larger than 81), insta-

bility dominates the mode of failure.9 . The computational results indicatethat both Nathan's computer programand UTA's finite element program arereasonably accurate in predicting ulti-mate loads and lateral deflections of PCcolumns.

PC I JOURNAL/November-December 1989 67

Estudio Del Comportamiento de Columnas de Hormigon Pretensado

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