Behavior and Design of High-Strength Prestressed Concrete Girders

8/11/2019 Behavior and Design of High-Strength Prestressed Concrete Girders

1/16SeptemberOctober 2008 | PCI Journal

Editors quick points

n This paper proposes provisions to extend the application ofcurrent American Association of State Highway and Transporta-tion Ofcials AASHTO LRFD Bridge Design Specications tohigh-strength concrete (HSC) girders.

n The proposed design provisions are for predicting the ultimateexural strength of prestressed concrete girders with concretecompressive strengths up to 18 ksi (124 MPa) to include com-posite action with normal-strength concrete (NSC) deck slabs.

n The experimental program investigated the failure modes ofthree different types of compression zones: one with NSC only,

one with HSC only, and one with both NSC and HSC.

Behaviorand design of

high-strengthprestressedconcretegirders

Wonchang Choi,Sami Rizkalla,Paul Zia,and Amir Mirmiran

Although a number of state departments of transportationhave successfully used high-strength concrete (HSC) gird-ers as part of Federal Highway Administration (FHWA)demonstration projects, the current American Associationof State Highway and Transportation Officials AASHTO

LRFD Bridge Design Specifications 1 are limited to ap-plications where concrete compressive strengths are 10 ksi(69 MPa) or less.

Concrete with compressive strengths greater than 10 ksi(69 MPa) is now available commercially as a result of im-provements in concrete admixtures and the quality controlprocess in plants. Many researchers have shown that by us-ing HSC, engineers are able to design bridges with longerspans for a given girder cross section or reduce the numberof girders by increasing the girder spacing. Adelman andCousins 2 showed that increasing the concrete design com-pressive strength from 6000 psi to 8000 psi (42 MPa to55 MPa) resulted in an average 10% increase in span capa-bility for prestressed girders used in routine bridge design.

Due to these advantages, it is likely that the use of HSC inthe design of prestressed girders will continue to increase.However, the uncertainty regarding the applicability of de-sign provisions causes reluctance on the part of designersto use HSC for highway bridge construction. 3 Therefore, aneed exists for reassessment of the material properties andthe design provisions for the analysis of HSC girders. Thisneed to expand the applicability of the AASHTO LRFDspecifications to HSC has been addressed by a series ofprojects under the direction of the National CooperativeHighway Research Program (NCHRP). The goal of one ofthese projects, NCHRP project 12-64, was to expand the

use of the AASHTO LRFD specifications to reinforced

54


2/1655PCI Journal | SeptemberOctober 2008

the girder designs required sixteen to twenty in.(13 mm), grade 270 (1860 MPa), 7-wire strands. Eachstrand was tensioned to 75% of its ultimate strength, or 31kip (138 kN). All strands were straight and fully bondedover their entire lengths. Figure 1 shows strand configura-tions for the three design concrete compressive strengths.After concrete was placed in the girders for each design

concrete compressive strength, the concrete was moist-cured until it reached the required releasing strength. Afterrelease of the prestressing strands, the concrete girderswere air-cured in the prestressing plant until they weredelivered to the laboratory.

For each HSC test girder, fifteen 4 in. 8 in. (100 mm 200 mm) cylinders and nine 6 in. 6 in. 20 in.(150 mm 150 mm 500 mm) prisms were made foreach casting to determine the HSCs elastic modulus andmodulus of rupture, respectively. The cylinder and prismspecimens were cured with the test girders and under thesame conditions.

After the girders were delivered to the laboratory, a 5-ft-wide (1.5 m) deck slab was cast on one of the three gird-ers, a 1-ft-wide (0.3 m) deck slab was cast on the secondgirder, and the third girder was left without a deck slabfor each of the target concrete compressive strengths.Figure 1 shows the final cross sections for each specimengroup.

A local ready-mix concrete producer supplied theconcrete used to cast the 8-in.-thick (200 mm) deckslabs. The average 28-day compressive strengths ofthe concrete used for the 5-ft- and 1-ft-wide (1.5 m and0.3 m) deck slabs were 4.1 ksi and 5.6 ksi (28 MPa and38 MPa), respectively.

and prestressed concrete members with 18 ksi (124 MPa)compressive strength in flexure and compression.

As a part of NCHRP project 12-64, research was conductedto examine the validity of the current analytical methodsused to determine the flexural behavior of typical AASHTOType II prestressed HSC girders with and without a cast-

in-place normal-strength concrete (NSC) deck. The ex-perimental program validated the stress block parameterscurrently used to determine the flexural resistance of flangedsections made with HSC. It also addressed the cases wherethe compression zone was composed of NSC deck and HSCgirder in composite action. Test results were used to evaluatethe AASHTO LRFD specifications equations to predict theelastic modulus and modulus of rupture for HSC.

Experimental program

Nine 40-ft-long (12 m) AASHTO Type II prestressed HSCgirders were designed and tested to evaluate their flex-ural responses. They were tested under a static load usingfour-point bending. The concretes used for the girders weredesigned to achieve target compressive strengths of 10ksi, 14 ksi, and 18 ksi (69 MPa, 97 MPa, and 124 MPa).Table 1 shows the mixture proportions of the concretes.All girders were designed based on the AASHTO LRFDspecifications. However, several design details were modi-fied to prevent premature failure in shear or bond slippageprior to flexural failure. Shear reinforcement consisted ofno. 4 (13M) stirrups at a spacing of 3 in. (75 mm) near theend blocks and 6 in. (150 mm) along the rest of the girder.More detailed information about the test girders can befound in Choi. 4

Standard Concrete Products in Savannah, Ga., producedthe girder specimens. The three concrete strengths used for

Table 1. Mixture properties for prestressed, AASHTO Type II high-strength concrete girders

Target compressive strength 10 ksi 14 ksi 18 ksi

Cement, lb/yd3 670.0 703.0 890.0

Fly ash, lb/yd3 150.0 192.0 180.0

Microsilica, lb/yd3

50.0 75.0 75.0No. 67 granite, lb/yd3 1727.0 1700.0 1700.0

Sand (river), lb/yd3 1100.0 1098.0 917.0

Water, lb/yd3 280.0 250.0 265.0

Recover hydration stabilizer, oz/yd3 26.0 50.0 50.0

Waterreducing admixture, oz/yd3 98.0 125.0 135.0

Watercementitious materials ratio 0.32 0.26 0.23

Source explanation for no. 67: American Society for Testing and Materials (ASTM). 2007.Standard Specication for Concrete Aggregate . ASTM C33-07.

West Conshohocken, PA: ASTM.Note: 1 ksi = 6.895 MPa; 1 lb/yd 3 = 0.5933 kg/m 3; 1 oz/yd3 = 38.7 mL/m 3.



Figure 1. These diagrams illustrate the strand congurations for 18 ksi, 14 ksi, and 10 ksi design concrete compressive strengths and the cross sections for an 18 ksihigh-strength concrete girder with different deck-slab congurations. Note: HSC = high-strength concrete. 1 in. = 25.4 mm; 1 ft = 0.3048 m; 1 ksi = 6.895 MPa.



statistical analysis are presented in previous studies. 4,8

E c = 310,000 K 1wc2.5 f c

' 0.33 (1)

where

K 1 = correction factor to account for aggregate source

wc = density of concrete

f c

' = specified design compressive strength of concrete

The correction factor K 1 is typically assumed to be 1.0unless determined by physical testing and as approved bythe authority of jurisdiction. The results indicated that theAASHTO LRFD specifications overestimate the elasticmodulus determined from HSC cylinder tests, while theproposed equation provides a closer prediction.

Figure 5 shows the average moduli of rupture f r obtainedfrom the two control specimens for each of the nine girderspecimens. Predictions of the modulus of rupture using thetwo expressions given by the AASHTO LRFD speci-fications are also plotted in the same figure. One of the

AASHTO expressions is used for computing cracking mo-ment under service limit load combination ( f r = 0.24 f c

' [in ksi]), while the other is used for determining minimumreinforcement ( f r = 0.37 f c

' [in ksi]). Test results con-firmed that the current equations of the AASHTO LRFDspecifications overestimated the modulus of rupture forHSC. Equation (2), which is from ACI 318-05, is thereforerecommended to estimate the modulus of rupture for HSCup to 18 ksi (124 MPa):

f r = 0.19 f c' (in ksi) (2)

Five or six characters identify each girder specimen. Thefirst two numbers represent the design concrete compres-sive strength of the girders, followed by the uppercaseletters PS , which stands for prestressed concrete girder.The final one or two characters following the hyphenshow the dimensions of the deck slab, using a number torepresent the deck width, with either an uppercase letter S

to representslab

or an uppercase letter N

to representno

slab . For example, 10PS-5S represents a prestressed girdermade with 10 ksi design concrete compressive strength anda 5-ft-wide (1.5 m) deck slab.

Load cells monitored the prestressing force in each girderfrom the start of fabrication to the time immediatelybefore the transfer of prestress. The prestressing force waschecked against the elongation of selected strands at thetime of jacking. Prior to placing the concrete, two straingauges were welded (using low voltage) to two strandsat the bottom row of each girder to measure the strainchanges in the prestressing strands due to elastic shorten-ing, prestress losses, and strains in prestressing strandsduring load tests. Figure 2 shows an installed strain gauge.

Figure 3 shows a schematic view of the test setup and aphoto of the typical instrumentation layout. Potentiometersmeasured the deflections at midspan, loading points, andquarter points along the girder and at the supports. Loadwas applied in displacement control at a rate of0.1 in./min (2.5 mm/min) in order to observe crack initia-tion in the girder. The loading rate was increased to 0.25in./min (6.3 mm/min) after the prestressing strands yielded.Visual inspection and mapping of the cracks were per-formed throughout the tests. A high-speed data acquisitionsystem was used to record data from the potentiometersand strain gauges. Tests were terminated after crushing ofconcrete occurred in the constant-moment region.

Material propertiesand early-age behavior

Table 2 lists the measured material properties of theconcrete on the test day for each girder and deck slab. Alltests for material properties conformed with ASTM speci-fications (ASTM C39, 5 ASTM C469, 6 and ASTM C78 7).

Except for concrete used for girder 18PS-1S, all specimensachieved their design compressive strengths.

Table 2 also lists the average elastic moduli obtained fromthe three control cylinders for each of the nine prestressedAASHTO girders tested for this project. Figure 4 showsthe predicted values using the AASHTO LRFD specifica-tions as well as the predictions according to Eq. (1) using149 lb/ft 3 (2387 kg/m 3) as the measured density of the con-crete. Equation (1) is the proposed formula 4,8 to determinethe elastic modulus E c for HSC with strengths ranging from10 ksi to 18 ksi (69 MPa to 124MPa). It was obtained by a

statistical analysis of over 4000 test results. Details of the

Figure 2. The photo shows an example of the strain gauges that were weldedto two of the bottom strands in each girder to measure the strain changes in theprestressing strands due to elastic shortening, prestress losses, and strains inprestressing strands during load tests.



where

E p = modulus of elasticity of strand

= strand end slippage

f pi = initial prestress of the strand just before detensioning

Transfer length

To determine the transfer lengths, the end slippages of sixpreselected strands were measured using a tape measure-ment before and after prestress transfer. Equation (3) 9 wasthen used to determine the transfer lengths lt .

l t =2 E

f

p

pi

(3)

Figure 3. Shown are a schematic view of the test setup and an instrumentation layout and a photo of the test setup for a girder with a 5-ft-wide deck slab.Note: CFL = Constructed Facilities Laboratory. 1 ft = 0.3048 m.



Girder tests

Load-deflection responseand failure mode

Figure 6 presents the load-deflection responses at themidspans of the three girders with 5-ft-wide (1.5 m) deckslabs. The figure shows that the initial flexural stiffnessesof all three composite girders were practically the sameprior to cracking. Also, the flexural stiffnesses were notaffected by the compressive strength of concrete becausethere were only small differences in the elastic moduliof the three different concretes. In addition, Fig. 6 showsthe predicted load-deflection responses using a sectionanalysis program, RESPONSE. 10 The predicted responses

agree with the measured responses for the flexural stiffnessinitially and at ultimate load, while the measured deflec-tion after yielding of prestressing strands is slightly lessthan the predicted deflection, possibly due to the variationof prestrain for input data. Figure 6 shows that the failureof test specimens occurred gradually due to crushing ofconcrete within the NSC deck slab.

Figure 7 shows the measured and predicted load-deflection responses of the three composite girders with1-ft-wide (0.3 m) deck slabs. A similar behavior among thethree girders was observed prior to the initiation of cracks.

The measured responses reflected a small drop in load-

Table 3 lists the calculated transfer lengths of the girderspecimens. The range of the measured transfer lengthsvaried from 21 in. to 34 in. (525 mm to 850 mm). Basedon these data, it appears that the predicted value of 30 in.(750 mm) for -in.-diameter (13 mm) strand by AASHTOLRFD specifications section 5.11.4.1 is reasonable forconcrete compressive strengths up to 18 ksi (124 MPa).

Elastic shortening

Table 4 compares the measured and calculated losses dueto elastic shortening at the bottom level of prestressingstrands. The calculated values were based on the AASHTOLRFD specifications Eq. (5.9.5.2.3a-1) with the elasticmodulus specified by the current AASHTO LRFD specifi-

cations, as well as the proposed Eq. (1).

The table indicates that the average loss due to elasticshortening at the bottom level of strands was 7.7%, whichis close to the predicted values using the current AASHTOLRFD specifications as well as Eq. (1).

Table 2. Material properties of test specimens

Specimen Specimen type Age, days f c(test) , ksi E , ksi f r , ksi

10PS-5SGirder 120 11.49 5360 0.768

Deck 29 3.78 2690

14PS-5SGirder 143 16.16 5560 0.711

Deck 43 5.34 3300

18PS-5SGirder 175 18.06 5970 0.872

Deck 67 3.99 2660

10PS-1SGirder 189 13.19 5630 0.820

Deck 77 5.04 2770

14PS-1SGirder 184 15.53 5440 0.751

Deck 70 5.04 2770

18PS-1SGirder 199 14.49 5150 0.680

Deck 84 5.04 2770

10PS-N Girder 222 11.81 5540 0.820

14PS-N Girder 228 15.66 5330 0.717

18PS-N Girder 232 18.11 6020 0.706

Note: 1 ksi = 6.895 MPa.



Figure 5. This graph plots the concrete compressive strength versus the modulus of rupture to compare the average moduli of rupture f r obtained from the two control

specimens for each of the nine girder specimens with the predictions from the two expressions given by the American Association of State Highway and TransportationOfcials AASHTO LRFD Bridge Design Specications . Note: Equations are in English units.1 ksi = 6.895 MPa.

Figure 4. This graph plots the concrete compressive strength versus the elastic modulus to compare the research results with the predicted values using the American

Association of State Highway and Transportation Ofcials AASHTO LRFD Bridge Design Specications and the proposed equation E c = 310,000 K 1w c 2.5 f ' c 0.33 .Note: Equations are in English units. 1 kip-ft = 1.356 kN-m; 1 ksi = 6.895 MPa.



carrying capacity near failure due to complete crushing ofthe NSC deck slab followed by crushing of a portion ofthe HSC girder flange. Failure of test specimens occurredsuddenly after crushing of the deck slab followed by crush-ing of the top flange of the HSC girder. Figure 7 shows thebuckling of the longitudinal reinforcement and prestressingstrand in the compression zone.

Figure 8 shows the measured and predicted load-deflection responses of the three girders without a deckslab. The three girders without a deck slab exhibited simi-lar behavior to that of the composite HSC girders exceptthat the failure mode was more brittle. For the girderswithout a deck slab, Fig. 8 shows that the failure occurredsuddenly, followed by the buckling of prestressing strandin the compression zone. In two of the three casesgirderwithout a deck slab and girder with a 1-ft-wide (0.3 m)deck slabthe sudden crushing of the compression zonealso led to immediate crushing of concrete in the web.

Cracking moment

Table 5 compares the measured cracking moments M cr ofthe nine girders with the calculated values using Eq. (4).

M cr = S bc( f r + f ce - f d / nc) (4)

where

S bc = composite section modulus

f ce = compressive stress due to effective prestress only atthe bottom fibers

f d / nc = stress due to non-composite dead loads at the sameload level

When predicting the cracking moment, two different valueswere used for f r : that specified by the current AASHTOLRFD specifications article 5.4.2.6 and the one recommend-ed in Eq. (2). The predicted cracking moment depends onthe modulus of rupture. For all girder specimens, the results

continued on page 65

Table 3. End slippage and transfer lengths of test specimens

Specimen , in. l t , in.

18PS-1S 0.10 29.0

18PS-5S 0.08 23.0

18PS-N 0.04 12.0

Average 0.07 21.314PS-1S 0.08 22.0

14PS-5S 0.10 29.0

14PS-N 0.13 36.0

Average 0.10 29.0

10PS-1S 0.10 30.0

10PS-5S 0.20 58.0

10PS-N 0.05 15.0

Average 0.12 34.3

Note: 1 in. = 25.4 mm.

Table 4. Elastic shortening loss at the bottom-level strands of test specimens

Specimen Initial strain, Average measured losses

Calculated losses from elastic modulus, %

AASHTO LRFD BridgeDesign Specications

Proposed equationE c = 310,000 K 1w c 2.5 f ' c 0.33 %

18PS-1S 6282 613 9.8 7.9 7.9

18PS-5S 6149 329 5.3 7.8 7.9

18PS-N 5786 401 6.9 7.6 7.7

14PS-1S 6189 495 8.0 7.7 7.5

14PS-5S 6282 448 7.1 8.2 7.9

14PS-N 5579 482 8.6 8.2 7.9

10PS-1S 6373 522 8.2 6.8 6.6

10PS-5S 6333 532 8.4 6.8 6.6

10PS-N 6477 472 7.3 6.7 6.6

Average 6161 477 7.7 7.5 7.4



Figure 6. The graph plots the load-deection responses, and the photo shows a typical failure mode of the three girders with 5-ft-wide deck slabs. Note: 1 ft = 0.3048 m.



Figure 7. The graph plots the load-deection responses, and the photo shows a typical failure mode for the three girders with 1-ft-wide deck slabs. Note: 1 ft = 0.3048 m.



Figure 8. The graph plots the load-deection responses, and the photo shows a typical failure mode for the three girders without deck slabs.



the short-term prestress losses occurring from the time ofrelease to the time of testing and do not include the long-term prestress losses of the nine girder specimens.

Flexural strength

The flexural strengths of all girder specimens werecalculated using three different approaches. In the first ap-proach, the AASHTO LRFD specifications Eq. (5.7.3.2.2-1) was used with the current values of 1 and 1 in thespecification. In the second approach, Eq. (5) and (6) wereused to determine 1 and 1 as the new recommendedrelationships. 8,11,12

1 =0.85 for f c

' 10 ksi

0.85 0.02 f c' 10( ) 0.75 for f c' 10 ksi

(5)

continued from page 61

in Table 5 indicate that the predicted cracking moment usingthe proposed modulus of rupture produced conservativeresults. The results suggest that the recommended Eq. (2) forthe modulus of rupture is more appropriate to determine thecracking moment of prestressed HSC girders.

After initial cracking was observed, each test girder wasunloaded. On the girders second loading, the moment thatcaused the crack to reopen was recorded. Based on thesetwo moment measurements and the rupture modulus, theloss of prestress at the time of test was calculated. 8 Thecalculated prestress loss varied from 7.3% to 13.9% for thenine test girders, with an average of 11%. This loss com-pares with an average of 15.1% based on AASHTO LRFDspecifications and an average of 14.9% based on Eq. (2)for the rupture modulus. 8 These loss values represent only

Table 5. Summary of measured and predicted cracking moments of test specimens

Specimen

Measuredcracking moment

Predicted cracking moment

AASHTO LRFD Bridge Design Specications Proposed equation E c = 310,000 K 1w c 2.5 f ' c 0.33

kip-ft kip-ftMeasuredPredicted

kip-ftMeasuredPredicted

10PS-5S 1097 1123 0.98 1061 1.03

14PS-5S 1267 1314 0.96 1244 1.02

18PS-5S 1377 1436 0.96 1373 1.00

10PS-1S 935 974 0.96 922 1.01

14PS-1S 1054 1084 0.97 1034 1.02

18PS-1S 1131 1183 0.96 1130 1.00

10PS-N 799 751 1.06 708 1.13

14PS-N 867 843 1.03 796 1.09

18PS-N 918 964 0.95 908 1.01

Note: 1 kip-ft = 1.356 kN-m.

Table 6. Flexural strength of girders with a 5-ft-wide deck

Specimen

Measuredmoment

Flexural strength

AASHTO LRFD Bridge DesignSpecications

Proposed equationE c = 310,000 K 1w c 2.5 f ' c 0.33

Strain compatibility




10PS-5S 2123 1904 1.12 1904 1.12 1977 1.07

14PS-5S 2349 2181 1.08 2181 1.08 2246 1.05

18PS-5S 2543 2344 1.08 2344 1.08 2445 1.04

Note: 1 ft = 0.3048 m; 1 kip-ft = 1.356 kN-m.



LRFD specifications can be used to predict the flexuralstrength when the compression zone is within the NSCdeck slab.

For the composite girders with the 1-ft-wide (0.3 m) deckslabs, the current AASHTO LRFD specifications do notprovide clear recommendations on how to determine theflexural strength of a section when the compression zoneincludes two different concrete compressive strengths.Because the neutral axis was located below the deck, thecompression zone required two different concrete stress-strain distributions. However, for simplicity, the stressdistribution in the compression zone may be assumedconservatively using the stress-strain relationship of NSC.Therefore, the equivalent rectangular stress block can bedetermined with the recommended method.

The computed flexural strengths using the recommendedmethod were about 12% to 14% less than the measuredflexural resistance. These results in Table 7 indicated thatthis method can be used to safely determine the nomi-nal flexural strength M n. The predicted nominal flexuralstrength based on the strain compatibility with the mea-sured material properties showed more accurate resultswithin a 1% difference of the measured flexural strength.

Table 8 gives the measured and predicted ultimate flexuralstrengths using the proposed 1 and 1 and the straincompatibility for the girders without a deck slab. This table

1 =0.85 for f c

' 4 ks i

0.85 0.05 f c' 4( ) 0.65 for f c' 4 ksi

(6)

where

f c

' is in ksi

1 = stress-block parameter


The third approach was based on strain compatibility, forceequilibrium, and the actual stress-strain relationship of theconcrete obtained from tests of control cylinders.

For the composite girders with the 5-ft-wide (1.5 m) deckslabs, the flexural strength depended on whether the neu-tral axis was located in the flange or in the girder. Becausethe neutral-axis depth c was located in the deck concrete,the composite girder behaved as a rectangular section. Thestress-block parameters for computing the flexural strengthof the composite HSC girders could be determined usingthe current AASHTO LRFD specifications. Table 6 showsthe comparisons between the measured and predicted val-ues of flexural strength of the three girders with 5-ft-widedeck slabs using the three approaches mentioned previ-ously. The comparisons indicate that the current AASHTO

Table 7. Flexural strengths of girders with a 1-ft-wide deck

Specimen

Measured momentFlexural strength

Proposed equation E c = 310,000 K 1w c 2.5 f ' c 0.33 Strain compatibility



10PS-1S 1752 1558 1.12 1735 1.01

14PS-1S 1941 1706 1.14 1928 1.01

18PS-1S 2083 1830 1.14 2107 0.99

Note: 1 ft = 0.3048 m; 1 kip-ft = 1.356 kN-m.

Table 8. Flexural strengths of girders without deck slab

Specimen

Measured momentFlexural strength

Proposed equation E c = 310,000 K 1w c 2.5 f ' c 0.33 Strain compatibility



10PS-N 1465 1324 1.11 1433 1.02

14PS-N 1688 1519 1.11 1623 1.04

18PS-N 1808 1692 1.07 1813 1.00

Note: 1 kip-ft = 1.356 kN-m.



References

1. American Association of State Highway and Trans-portation Officials (AASHTO). 2004. AASHTO

LRFD Bridge Design Specifications . 3rd ed. Wash-ington, DC: AASHTO.

2. Adelman, D., and T. E. Cousins. 1990. Evaluation ofthe Use of High Strength Concrete Bridge Girders inLouisiana. PCI Journal, V. 35, No. 5 (SeptemberOctober): pp. 7078.

3. Roller, J. J., B. T. Martin, H. G. Russell, and R.N. Bruce. 1993. Performance of Prestressed HighStrength Concrete Bridge Girders. PCI Journal , V.38, No. 3 (MayJune): pp. 3445.

4. Choi, W. C. 2006. Flexural Behavior of PrestressedGirder with High Strength Concrete. PhD thesis.Department of Civil, Construction, and Environmen-tal Engineering, North Carolina State University,Raleigh, NC.

5. American Society for Testing and Materials (ASTM).2005. Standard Test Method for CompressiveStrength of Cylindrical Concrete Specimens . ASTMC39/C39M-05e1. West Conshohocken, PA: ASTM.

6. ASTM. 2002. Standard Test Method for Static Modu-lus of Elasticity and Poissons Ratio of Concrete inCompression . ASTM C469-02e1. West Conshohock-en, PA: ASTM.

7. ASTM. 2008. Standard Test Method for FlexuralStrength of Concrete (Using Simple Beam with Third-Point Loading) . ASTM C78-08. West Conshohocken,PA: ASTM.

8. Rizkalla, S., A. Mirmiran, P. Zia, H. Russell, and R.Mast. 2007. Application of the LRFD Bridge DesignSpecifications to High-Strength Structural Concrete:Flexure and Compression Provisions . NCHRP report595. Washington, DC: Transportation ResearchBoard, the National Academies.

9. Oh, B. H., and E. S. Kim. 2000. Realistic Evaluationof Transfer Lengths in Pretensioned Prestressed Con-crete Members. ACI Structural Journal , V. 97, No. 6(NovemberDecember): pp. 821830.

10. Bentz, E. C. 2000. Sectional Analysis of ReinforcedConcrete Members. PhD thesis. Department of CivilEngineering, University of Toronto, Toronto, ON.

11. Mertol, H. C. 2006. Characteristics of High StrengthConcrete for Combined Flexure and Axial Compres-

sion Members. PhD thesis. Department of Civil,

indicates that it is satisfactory to use the proposed parame-ters 1 and 1 to predict the flexural strength of prestressedgirders with concrete strengths up to 18 ksi (124 MPa).

Conclusion

The flexural behaviors of prestressed HSC girders with and

without deck slabs were investigated, including the materialproperties and their early-age behaviors. Based on the ex-perimental results, the following conclusions were drawn:

The current AASHTO LRFD specifications equation

for the elastic modulus of concrete may overestimatemeasured values. Based on the results from this study,the recommended equation provides better agreementwith the measured values for HSC girders with con-crete compressive strengths up to 18 ksi (124 MPa).

Based on the findings of this study, Eq. (2), which is

the ACI 318-05 calculation for the modulus of rupture,provides a better estimate of the cracking moment forprestressed HSC girders with concrete compressivestrengths up to 18 ksi (124 MPa) than the equationprovided by the AASHTO LRFD specifications.

The transfer-length equation of the AASHTO LRFD

specifications provides a reasonable estimate forprestressed HSC girders with concrete compressivestrengths up to 18 ksi (124 MPa).

For a composite HSC girder with NSC deck slab, if

the compression zone occurs in both HSC and NSC, aconservative estimate of the nominal flexural strengthcan be determined based on the concrete compressivestrength of the NSC deck with reasonable accuracy.

When the compression zone occurs only in HSC, the

nominal flexural strength can be determined using theAASHTO LRFD specifications with the recommendedvalues of 1 and 1 for HSC girders with concretecompressive strengths up to 18 ksi (124 MPa).

Acknowledgments

The authors acknowledge the support of NCHRP project12-64 and the senior program officer, David Beal. Theyare also grateful for the contributions of Henry Russellof Henry Russell Inc. and Robert Mast of Berger/ABAMEngineers Inc., both of whom served as consultants for theproject. The cooperation of Standard Concrete Productsin Savannah, Ga., and the personnel of the ConstructedFacilities Laboratory are greatly appreciated. The authorsare responsible exclusively for the findings and opinionsexpressed in this paper.



Construction, and Environmental Engineering, NorthCarolina State University, Raleigh, NC.

12. Mertol, H. C., S. Rizkalla, P. Zia, and A. Mirmiran.2008. Characteristics of Compressive Stress Distri-bution in High-Strength Concrete. ACI Structural

Journal (under review) .

Notation

c = depth at neutral axis

E c = modulus of elasticity of concrete

E p = modulus of elasticity of strand

f c

' = specified compressive strength of concrete

f ce = compressive stress due to effective prestress only atthe bottom fibers

f d / nc = stress due to non-composite dead loads at the sameload level

f pi = initial prestress of the strand just before detensioning

f r = modulus of rupture

K 1 = the correction factor to account for aggregate source

lt = transfer length

M cr = cracking moment

M n = nominal flexural strength

S bc = composite section modulus

wc = density of concrete



= strand end slippage


16/16

About the authors

Wonchang Choi, PhD, is an

adjunct assistant professor ofCivil, Construction, andEnvironmental Engineering atNorth Carolina State Universityin Raleigh, N.C.

Sami Rizkalla, PhD, P.Eng., is aDistinguished Professor of Civil,Construction, and EnvironmentalEngineering and director of theConstructed Facilities Labora-tory at North Carolina StateUniversity.

Paul Zia, PhD, P.E., FPCI, is aDistinguished University Profes-sor Emeritus at North CarolinaState University.

Amir Mirmiran, PhD, P.E., is aprofessor and interim dean forthe College of Engineering andComputing at Florida Interna-tional University in Miami, Fla.

Synopsis

This paper proposes provisions to extend the currentAmerican Association of State Highway and Trans-portation Officials AASHTO LRFD Bridge DesignSpecifications to include prediction of the ultimateflexural strength of prestressed concrete girderswith concrete compressive strengths up to 18 ksi(124 MPa). The proposed design provisions include

composite action of a high-strength concrete (HSC)girder with normal-strength concrete (NSC) deckslab.

Nine 40-ft-long (12 m) AASHTO Type II HSC gird-ers were tested with and without cast-in-place NSCdecks of differing widths to achieve various possiblemodes of failure. The concrete used for the girderwas designed for three target compressive strengthsof 10 ksi, 14 ksi, and 18 ksi (69 MPa, 97 MPa, and124 MPa).

The experimental program investigated failure modesof three different types of compression zones: onewith NSC only, one with HSC only, and one withboth NSC and HSC. All girders were tested to failureunder static loading to study the different limit-statebehaviors, including prestress losses, initiation ofcracking, yielding, and final failure mode.

Keywords

Bridge girder, cracking strength, elastic shortening,flexural strength, high-strength concrete, prestressloss, transfer length.

Review policy

This paper was reviewed in accordance with thePrecast/Prestressed Concrete Institutes peer-reviewprocess.

Reader comments

Please address any reader comments to PCI Journal editor-in-chief Emily Lorenz at [email protected] Precast/Prestressed Concrete Institute, c/o PCI

Journal , 209 W. Jackson Blvd., Suite 500, Chicago,IL 60606. J

Documents

Behavior and Design of High-Strength Prestressed Concrete Girders