ultimate load test of a segmentally … · of a segmentally constructed prestressed concrete i-beam...

ULTIMATE LOAD TESTOF A SEGMENTALLYCONSTRUCTED PRESTRESSEDCONCRETE I-BEAM

Saad E. MoustafaManager, Engineering MechanicsConcrete Technology CorporationTacoma, Washington

Test results of a segmentally constructed prestressedconcrete bridge I-beam are presented. The testgirder was manufactured from short precast segmentswhich were joined together and post-tensioned, afterwhich a deck slab was cast on the top. The girder,92 ft long, was cast in eleven segments: 9 segmentsof 8 ft each and two end blocks of 10 ft each. Theassembled girder was then post-tensioned using two

bonded tendons. The girder was made composite

with a 6-in. thick, 6-ft t wide, cast-in-place deck slab.

The composite girder was then load tested,predominantly in flexure and its behavior, underworking, cracking, and ultimate loads is reported.It is concluded that the performance of thesegmentally constructed girder, under service as well

as ultimate load, is comparable to that of a

monolithic girder.

54

Spans of precast prestressed concretebridge girders have been limited by themaximum transportable weights and/orlengths, rather than their capacities.When delivered over highways, thelength of precast girders is usually lim-ited to 100 ft maximum.

However, span capabilities of up to250 ft can be achieved with existingstandard cross sections.' Through seg-mental construction techniques, onecan overcome existing limitations ofweight and length and make possiblemore efficient use of the material.

Precast concrete segmental box gird-er bridges, with spans up to 300 ft,have been built; and spans of 750 ft canbe constructed. 2 Glaidesville bridge,Sydney, Australia, is a segmental pre-cast concrete post-tensioned archbridge of 1000 ft span.

Segmental bridge construction in-volves the manufacture of precast con-crete elements which are assembled atthe job site. These units are joined to-gether, end to end, and post-tensionedto form complete spans.

The length and weight of the seg-ments are chosen so as to be most suit-able for transportation and erection.Box girder and I-beam shapes havebeen used successfully. Efficient pre-casting techniques have been devel-oped to produce elements with precisedimensions, well adapted to field as-sembly and jointing.

Very satisfactory joints between ele-ments have been obtained by the use ofepoxy resin as well as cement mortarand cast-in-place concrete. With epoxyjoints, precision is obtained by match-casting the segments, one against theother.

Although a relatively large numberof prestressed concrete bridges havebeen built by the segmental method,little has been published concerning thestructural behavior of segmental gird-ers, especially under cracking and un-der ultimate load conditions .3

Saad E. Moustafa

SCOPE

This investigation was carried out forthe purpose of reaching a better under-standing of the behavior of segmentallyconstructed precast post-tensioned gird-ers.

To achieve this objective, an experi-mental investigation was carried out asfollows:

A bridge I-beam was cast in 11 seg-ments. The segments were glued endto end. The assembled beam was thenpost-tensioned and the tendons grout-ed. Later, a deck slab was cast compos-ite with the beam. The composite sec-tion was then load tested to failure.Elastic, as well as nonelastic, behaviorof the beam was observed.

CROSS, SECTION

The beam cross section at ,midspan,shown in Fig. 1-a, is known as theWSHD* Standard 100-ft Series. In

° Washington State Highway Department.

PCI Journal/July-August 1974 55

5 ILHJJ5ҟ30.1

58 42ҟC.G.

27.9

6

24

CROSS-SECTION AREA =ҟ546 IN2MOMENT OF INERTIA = 249,000 IN`}

Fig. Ia. Typical cross section.

5 SPACES ® 1'-5 "= 7'-I"ҟ5_

'rST

*4

Fig. lb Reinforcing details of typical segment.

practice, this beam is used for highwaybridges in which a cast-in-place con-crete deck is assumed to act compositewith the beams for live loads.

The experimental girder was de-signed to satisfy AASHOt specifica-tions4 for prestressed concrete bridges

t American Association of State Highway 0111.vials.

carrying HS 20-44 loading, and re-quired twenty-four 0.5-in. diameter,270-kip post-tensioned bonded strands.

Two draped tendons of twelve 1/2-in.,270-kip strands each were used. Fig. 2shows an elevation of the completedgirder.

The overall length was 92 ft com-posed of 11 segments. Nine segments,

56

IҟI T6L I T5L I T4L I T3L T2L Iҟ!TI I T2R I T3R I T4R I T5R I T6R IҟIJI J2 J3 J4 J5 J6 J7 J8 J8 JIO

10'-O"_4_ 9 SPACES( 8'-0"' 72-092!-0"

A. ELEVATION

TENDONS' 12-1/2 0STRANDS EACH

B. TENDONS' PROFILE

Fig. 2. Assembled girder.

8 ft each, were typical in cross section.Each segment was reinforced longitudi-nally with two No. 6 deformed bars inthe bottom flange to minimize crackingunder load in the segments and to forcecracks to occur at the joints (see Fig.1-b).

The webs of the two end segmentswere thickened to accommodate thepost-tensioning anchors. Design calcu-lations are presented in the Appendix.

FABRICATION ANDMATERIALS OF SEGMENTS

A 20-ft steel form was used for cast-ing the nine typical segments. The mid-span segment T 1 was cast first and lat-er moved to the left end of the form.Next, Segment T 2R was cast againstthe right end of Segment T 1.

This process was repeated with each

FIRSTT2L .TI . OPERATION'

II-

I

JOINT

SECONDT3L T2L •TI T2R T3R OPERATION,

3- JOINTS

THIRDT5L T4L T3L T2L iTI T2R T3R T4R T5R OPERATION

4- JOINTS

FOURTHT2L .TI T2R T3R T4R T5R T6R OPERATION'

2- JOINTS

Fig. 3. Sequence of assembly.


Fig. 4. Epoxy application. Fig. 5. First joint completed.

successive segment match-cast againstits neighbor. A water-soluble form oilwas used as a bond breaker, both on thesurface of the form and on the end ofeach segment.

Both ends of each segment were pre-pared for gluing by sandblasting andcleaning any traces of form oil or looseparticles. The 28-day cylinder strengthof the concrete averaged 7500 psi.

ASSEMBLY OF SEGMENTSIn order to test the joint itself with-

out any help from shear keys or align-ment pins, the segments were cast withflat smooth ends. The segments wereplaced on a level base to assure properalignment during the epoxy gluing op-eration. See Figs. 3 through 5, whichillustrate the assembly procedure.

Manufacturer's data indicated thatthe pot life of the epoxy was 25 min-utes. A layer of epoxy-sand mortar,about 1/is to 1/8 in. thick, was applied oneach of the mating surfaces.

When segments were forced togeth-er, mortar oozed out along the perime-ter, insuring the absence of air voids inthe joint. Temporary external prestress-ing of about 100 psi was applied imme-diately after each gluing operation andthen released after 24 hours.

It should be noted that the elimina-tion of shear keys and alignment pins

did not affect the gluing operations,since each segment was resting onbunks. However, in the case of canti-lever type of construction, where theuse of aligning jigs is impossible, it isfelt that shear keys should be provided.

To determine the shear strength ofepoxy joints, small test beams madefrom 6-in, cubes, as shown schemati-cally in Fig. 6, were prepared in thesame way as the segmental girder.

The loading was applied in such away as to force a failure in pure shearat the joints. Failure always occurredin the concrete layer adjacent to theepoxy.

As can be seen from Fig. 6, the shearstrength increased from 1130 to 1900psi when the normal prestress was in-creased from zero to 400 psi. Fromthese results, it was concluded that thetensile strength of the joint is morecritical than the shear strength.

POST-TENSIONINGAfter the last epoxy joint was 24

hours old, the temporary clamping ca-bles were removed, and the tendons,each consisting of twelve 0.5 in. diame-ter 270-kip strands, were threadedthrough the ducts inside the assembledgirder. A jacking force of 372 kips wasapplied at one end of each tendon.

The final elongation of the strands

58

O.IP 0.4P o.4P 0.IP4" 4–-4I _4 x'

2000 '^ NORMAL

UNIFORMPRESTRESS

1800 O5 0.5P5.2n 76° 5.2"

N

°v 1600 SWEAR DIAL.

MAX. SHEARZҟ @ JOINT

1400BENDING/tf .NT DIAL.

N 1200ZEf.O MOMENT (G JOINT

I000 NORMAL PRESTRESS (PSI)0 100 200 300 400

Fig. 6. Shear strength of epoxy mortar joints.

after seating the anchor was 7.0 in.Based on the jacking load and mea-sured elongation, coefficients of wobbleand friction were determined to bek = 0.0002 and la. = 0.20, respectively.

Based on these friction loss coeffi-cients, the effective prestress forcetransmitted at midspan was 653.5 kips.The measured instantaneous camber, atmidspan, was 0.74 in.

Immediately after completion of thepost-tensioning operation, the tendonswere grouted using a neat cement mor-tar. Two days later, the girder wasplaced in its final position on the sup-ports, where neoprene bearing padswere used.

DECK SLABS

The deck slab formwork was boltedto the girder. The dead weight of thedeck slab was carried by the bare girdersection alone. Interface shear betweenthe girder and the deck slab was devel-

oped by projecting steel from the girderweb and anchoring it into the slab.

The deck concrete had a 28-day cyl-inder strength of 5500 psi.

CAMBER HISTORY

The deck slab was cast 8 days afterpost-tensioning and grouting. Duringthis time, the camber in the girder in-creased by 0.06 in., i.e., a total camberof 0.8 in. was measured prior to casting.

Immediately after casting, the girderdeflected downward 0.42 in. under thedead weight of the wet concrete. Threehours after placing the deck concrete,the girder camber gradually increaseduntil it stabilized after 12 hours. Short-ly thereafter, the girder started to de-crease its camber.

This phenomenon becomes intelligi-ble if one realizes that the heat of hy-dration generated in the deck slabwould raise the temperature of the topflange and cause upward deflection. Af-


nAe.r nr . eI Ao

— 0.6z

Z Q50I-C)W 0.4U-w0

03

0.2

0.1

0 2 4 6 8 10 12 14 15 19 34 ob oa wU

aneT True.nw.

0.8

0.7

TIME (DAYS)

Fig. 7. Camber history.

ter the heat of hydration subsided, thegirder deflected downward again.

Later, shrinkage of the newly castconcrete, which was partially restrainedby the girder, caused additional down-ward deflection. Fig. 7 shows the his-tory of camber in the beam up to thestart of the test.

TEST PROCEDURE ANDINSTRUMENTATION

The load test program consisted ofthe following four phases:

1. Evaluation of elastic constants.2. Study of elastic behavior under

service load.3. Study of post-cracking nonelastic

behavior under several levels of over-load.

4. Evaluation of ultimate strength.The live load on the beam simulated

three concentrated axle loads from anAASHO HS 20-44 truck and trailer.

The girder live load, plus impact, wasapplied by hydraulic jacks (see Fig. 8).The dead overload was simulated by4300-lb concrete blocks.

One side of the girder was sprayedwith a white latex paint to facilitate ob-servation and recording of crack pat-terns. As each crack developed, it wasmarked in black.

Strains were measured mechanically,using an extensometer having an 8-in.gage length, and electrically, using SR-4 electric resistance bonded gages of t-in. gage length.

Deflections were measured at eachsupport, at midspan, and at one-quarterspan. Deflections were measured bydial gages under the soffit and also by aprecision level.

Crack widths were measured using aBausch and Lomb 7-power microscope.Beam end rotation was measured by aninclinometer, which indicated angle ro-tations to the nearest 0.001 radians.

60

STRAN

1/2" 0270 K

Fig. 8. Loading system detail.

TEST RESULTSAND DISCUSSION

Phase I

In order to evaluate the elastic con-stants, the girder was subjected to fiveincrements of loading. Each load incre-ment consisted of a concrete blockweighing about 4300 lbs. Blocks wereplaced in the sequence and locationsshown in Fig. 9.

The theoretical deflection was com-puted in terms of E (modulus of elas-ticity) for each load increment. Fig. 10shows the computed values of E 8 ver-sus the measured values of S. Using theleast squares method, a value of Eequal to 6480 ksi was obtained.

Phase II

The , second phase loading consistedof two parts, a dead load and a liveload part. The dead load represented

4ҟ12 5

37' ^4' LW 1 41 W I 37' 1rҟI I 111

Fig. 9. Phase I loading sequence.


1400

1200

1000Z

a_Y 800

W 600

400

200

SLOPE' E% 6,480

`W—ҟ0.1 0.2

MEASURED S (IN.)

Fig. 10. Computed modulus of elasticity times deflection ver-sus measured deflection.

4.3K 2.3K 2.3K 2.3K 4.3K

LONG. BLOCK JACK JACK JACK CONC. BLOCK

15' 16' 14' 14' 16' 15'

Fig. 11. Additional dead load.

Vҟ---'I ҟIt

Fig. 12. Live load and impact factor.

62

I.0 5 19.11

4

12

6ҟ8,10,10.2ҟ0.4ҟ0.6ҟ0.6ҟ1.0

MEASURED DEFLECTION (IN.)

Fig. 13. Load versus midspan deflection.

0.8

N

0.6U-0

z00.4

U-

0.2

the beam's share of the dead weight ofthe curbs, railings, diaphragms, and as-phalt surface.

This additional dead load amountedto 15.5 kips, and was applied by twoconcrete blocks and hydraulic jacks, asshown in Fig. 11.

The live load which represented thebeam's share of AASHO HS 20-44truck load plus impact was applied byhydraulic rams, as shown in Fig. 8.

In order to produce the maximumlive load bending moment in the beamat midspan, axle loads with locationsand magnitudes shown in Fig. 12 wereused. This load was applied in fourequal increments and then removed.

Following this, the full load was ap-plied and removed three times, and theload-deflection relations are plotted onFig. 13.

The value of E obtained from thelast three load cycles was 6050 ksi.

The computed neutral axis locationand composite section properties as-suming Egtab /E9ti,5er = 0.80 are:

Yb=42.0in.,Yt=22in.

• 1= 453,500 in.4

Zt = 453,500_ 25,750 in.3(22)(0.80)

Zb = 453,2

00 = 10,800 in.3

The computed fiber stresses underfull live load, plus impact, are as fol-lows:

M_fr = Zt -

10,83025,750 = 0.42 ksi (comp)

_M11)=

10,830= = 1.00 ksi (ten)10,800

Fig. 14 shows the strain distributionmeasured at, midspan under full liveload plus impact. The observed neutral


M

0.75JU-0

0 0.50

UQ

Lj 0.25

NFl V11VA1. WAAM100ҟ200ҟ300ҟ0ҟ100ҟ200ҟ300

STRAIN X106

0¢i0

170x106

Fig. 14. Strain distribution at midspan under full design load.

axis location is about 1.5 in. above thatcomputed.

Assuming the idealized strain distri-bution represented by the broken line,the following values of the moduli ofelasticity for the girder and the slabare obtained:

Egirder'— 170 X10-6 = 5880 ksi

E —_ 0.42 = 4670 ksislab 90 X 10-6

The rotation of the ends of the girderwas measured using the inclinometer.

Fig. 15. Load versus strain across the joints.

64

J4

i

1.4J

J5

1.2

1.0

a 43

01)4

v J5

.6 O 46

X J7

.4

.2

O_wvҟcwҟouuҟquoҟ5OO 600

STRAIN X 106

Fig, 16. Load versus strain across the joints (first cracking).

"-'N"J

2OHU

U-

Under full live load plus impact, theangle of rotation was 0.015 radians,which indicated a value of E of 5716ksi.

Fig. 15 shows the strains measuredacross the joints under load. An averagevalue of E of 5800 ksi was calculatedfrom these readings.

Comparing the three values of E ob-tained from three different types ofmeasurement, a range of 5.5 percentwas obtained.

Phase IIIIn this phase, the behavior of the

girder under moderate overloads wasstudied. The live load was applied tothe girder in increments until severalcracks appeared in the bottom flange.

Cracks were detected at Joints 4, 5,and 6. The load, which reached 1.6 (L+ I), was then removed. Strains mea-sured across Joints 3, 4, 5, 6, and 7 areshown in Fig. 16.

The cracking load is obtained by in-terpolation, as shown in Fig. 16. Cracksdeveloped at Joints 5, 6, and 4 under1.39, 1.4, and 1.55 times (L + I), re-spectively. It was noticed that thesecracks occurred in the concrete layeradjacent to the epoxy.

The live load was applied again inincrements until the cracks at Joints 4,5, and 6 reopened. The load, whichreached 1.4 (L + I), was then re-moved. Measured strains across Jointsnumber 3, 4, 5, 6, and 7 are shown inFig. 17. The load corresponding to the


J4 r

J6 / o J3

O J4

eJ50 J6x J7

100ҟ200ҟ300ҟ400ҟ500ҟ600STRAIN X 106

Fig. 17. Load versus strain across the joints (crack reopen-ing).

1.6

1.4

1.2

I.0r+J

Z 0.60HU

u.. 0.6

0.4

0.:

00

reopening of each crack was deter-mined by interpolation, as shown inFig. 17.

Cracks reopened at Joints 6, 5, and 4under 0.93, 0.94, 1.10 times (L + 1),respectively. At the instant of reopen-ing of the cracks, the stress at the bot-tom fibers of the beam is zero.

Since the external loads are known,the amount of prestress left in the beamcan be computed from equations ofequilibrium and the condition of zerostress at the bottom fibers. Subtractingthis force from the initial prestressforce, the prestress loss can be estimat-ed. The average prestress loss calculat-ed from the above results was 9.3 ksi.

The bottom fiber stress incrementcorresponding to the difference be-tween the loads causing initial crackingand those causing reopening of thecracks equals the tensile strength of thejoint. The average value of the tensilestrength obtained from the above re-sults was 421 psi which correspondedto the tensile strength of the concreteadjacent to the joints.

Fig. 18 shows the load versus mid-span deflection under these two loadcycles. The occurrence and the reopen-ing of the cracks can be seen from thisfigure. Note that the sensitivity of de-flection to cracking is less than that ofthe strain across the joints.

66

6 10

1.4ҟ 9ҟ14

2 8ҟ13

0 3,5,7 1

4.J

0.8ZO_

U-

0.6ҟ_70.4

0.2

14,61115ҟ0.2ҟ0.4ҟ0.6ҟO_eҟ1nMIDSPAN DEFLECTION (IN.)


2.4

2.0

rr1.6

ZOHUҟ1.2

LL

0.8

Q4

I 14

8

5

4ҟ12'16

3

2ҟII

'ҟ7

1ҟ151.0ҟ2.0ҟ3.0ҟ4.0ҟ5.0

MIDSPAN DEFLECTION (IN.)


After completion of the cracking load its own weight.cycles, the beam was subjected to load Fig. 19 shows the load versus mid-cycles up to [1.25D + 2.2 (L + I)], span deflections. Worth noting is theequivalent to 2.65 (L + I) in excess of nearly complete recovery of deflection


H ^

Jz0

HU

C

2.5

2.0

1.5jJ

zO_I-0• 1.0U-tL

0.5

0.05 U.IVҟVJUҟ020

CRACK WIDTH (IN.)

Fig. 20. Load versus crack width at J6.

.2

.8

.4

.0

.6

1.2

).8 /

L4 /

__I//iiiiEiII0 2 4 6ҟe w ^^ •^ ._

MIDSPAN DEFLECTION (IN.)


0

Fig. 22. Load test, August 1971.

after load removal, even under thesehigh overloads. Fig. 20 shows load ver-sus crack width across Joint 6.

Phase IVTest of August 1971 —The last load-

ing phase was concerned with the ulti-mate strength of the girder. The addi-tional dead load simulating the curb,railings, diaphragms, and asphalt sur-face, and 50 percent of all dead loadwere applied first in the form of con-crete blocks. A total of 16 concreteblocks, each weighing 4.3 kips, wasused.

The live load was applied by hydrau-lic jacks exactly in the same manner de-scribed in Phase III. It was planned toincrease the live load monotonically un-til failure. However, when the totalload reached [1.5D + 3.0 (L + I)],

the deflection reached 18.5 in., whichwas the maximum possible under thetest arrangement.

Upon release of the applied test load,the beam deflection recovered 13.5 in.,leaving a residual deflection of 5 in., asshown plotted in Fig. 21. The beamwas then stored for 2 years, duringwhich time the deflection gradually de-creased from 5 to 2 in.

Fig. 22 shows the beam during theprogress of the test where it can be seenthat cracks were localized at the joints.Consistently each crack progressedalong the joint all the way up to the topflange in what can be described as flex-ural type cracking.

However, between one-half to two-thirds up the web height, shear flexuralinclined cracks branched out from ver-tical cracks at joints near beam ends


70

r

ti

'I r/t L` l'

J6 J7 J8

Fig. 23. Crack pattern.

(e.g., Joints 3 and 8). On the otherhand, cracks near midspan at Joints 4,5, 6, and 7 were more or less symmetri-cal in a tree-like pattern (see Fig. 23).

At maximum load level, the maxi-mum crack width at Joint 6 was 1.5 in.and it could be seen propagating into

the lower zones of the deck slab. Thisbehavior indicated a tendency to con-centrate the curvature and yielding oftendons at joint locations.

The amount of reinforcing steel inthe bottom flange of each segment wasinsufficient to resist these high moments

Fig. 24. Load test, September 1973.

without causing flexural cracking of theconcrete in the lower flange. Conse-quently, the absence of this crackingindicated some loss of bond betweenthe tendons and the bottom flange con-crete. A computed curvature of 0.025radians corresponded to a crack widthof 1.5 in. and a neutral axis location 4in. below the top of the deck.

If the curvatures were concentratedwithin the immediate vicinity of thejoint, a compression failure in the flange

would have occurred at an earlier stageof loading. The fact that the beam sur-vived the load test intact can be ex-plained by the spreading of the verticalcrack into many branches (resemblinga tree), as shown in Fig. 23.

The crack at Joint 6 (nearest mid-span) ran upward to midheight of theweb, and at a loading of [1.25D + 2.2(L + I)] the crack width reached 0.18in. As the loading increased, twobranches emerged from the single


crack, and subsequently spread into thetree-like pattern of Fig. 23. Obviously,the proliferation of cracks in the upperregion of the beam caused a redistribu-t=on of curvature along the top flange.

It is believed that, while the place-ment of mild steel inside the bottomflange of the segments forced the crack-ing to take place at the joints, and thesubsequent loss of bond between theprestressing tendons and the concreteprevented the initiation of new cracksin between, the continuous mild steel inthe cast-in-place deck slab promotedthe redistribution of strains and the de-velopment of the tree-like pattern ofcracking. Therefore, the cast-in-placedeck slab should be credited for theconsiderable ductility of the beam.

Test of September 1973—After 2years of storage, the beam was againload tested, this time to destruction.The loading system consisted of twoconcentrated loads, one at midspan andthe other 7 ft away. The ultimate loadwas reached when the top flangecrushed.

A maximum concentrated load of 93kips was reached at each load point be-fore failure. This load exceeded thepredicted value of 84.3 kips based onthe procedure for calculating ultimatestrength as given in Section 1.6.9 of theAASHD specifications.

The calculated procedure indicated amaximum tension stress in the prestress-ing tendons of 264 ksi at ultimate. Fig.24 shows the beam during the progressof loading up to destruction.

The maximum load produced abending moment corresponding to[1.0D + 4.3 (L + I)], or [1.3D +3.9 (L + I)] loading.

A computed prestressing steel stressof 275.0 ksi corresponded to this load.A maximum compression strain of0.0028 was measured in the top fibersbefore failure.

The exact location of the neutral axisat the instant of failure was not known;

however, it is believed that a compres-sion block of not more than 2 in. deepexisted when the maximum load wasacting on the beam, resulting in an av-erage concrete stress of 7100 psi. Themaximum recorded deflection beforefailure was 24 in.

CONCLUSIONS

Based on the observations and resultsobtained from this investigation, thefollowing conclusions can be drawn:

1. Cracks occurred at the joints, asanticipated, due to the lack of any mildsteel reinforcing bars in the joints be-tween the segments.

2. Cracks at the joints occurred inthe concrete adjacent to the epoxy mor-tar and the tensile strength of the epoxyexceeded that of the concrete.

3. Because the initial cracks wereconcentrated in the joints between thesegments, one would assume some lossof ductility in the beam due to exces-sive hinging action of the top flangeabove the joint. However, the spread-ing of branch cracks in the webs at mid-height caused a very favorable redistri-bution of compression along the topflange, resulting in ductile behavior atultimate load.

4. The performance of the segmen-tal beam exceeded the ultimate loadcriteria specified by AASHO for mono-1 tis c -restressed concrete construction.The concept of match-cast segments,glued together and post-tensioned isnot only practical, but more than satis-fies the technical requirements for high-way bridges.

ACKNOWLEDGMENT

This investigation is part of a com-prehensive research program on longspan prestressed concrete bridges spon-sored by Concrete Technology Corpo-ration. The author gratefully acknowl-edges the guidance and technical assis-

72

tance of Dr. Arthur R. Anderson andRobert W. LaFraugh of Concrete Tech-nology Corporation, Tacoma, Washing-ton.

REFERENCES

1. Anderson, A. R., "Stretched-OutAASHO-PCI Beams, Types III andIV for Longer Span HighwayBridges," PCI JOURNAL, Vol. 18,No. 5, September-October 1973,pp. 32-49.

2a. Lee, D. J., "The Design of Bridgesof Precast Segmental Construc-tion," Table 1, Technical Paper,SfB Df(91), UDC 624.21:012.36,PCS 10, The Concrete SocietyLimited, Terminal House, Grosve-nor Gardens, London SW1W oAU.

2b Lee, D. J., "Prestressed ConcreteElevated Roads in Britain," Tech-nical Paper SfB (91), UDC 652.-74.012.46 (41-4), PCS 12, TheConcrete Society Limited, Termi-nal House, Grosvenor Gardens,London SW1W oAU.

2c. "Prestressed Viaducts Sweep PastLake Geneva Hardly Harming aTree," Engineering News-Record,January 8, 1970, p. 24.

2d. Lacey, G. C., and Breen, J. E.,"Long-Span Prestressed ConcreteBridges of Segmental Construc-tion, State of the Art," Research

Report No. 121-1, The Texas High-way Department by Center forHighway Research, the Universityof Texas at Austin, May 1969.

3a. Somerville, G., and Caldwell, J.A. D., "Tests on a One-TwelfthScale Model of the MancunianWay," Technical Report SfB Ba4.-Ab5, UDC 624.74(427.2).001.5,TRA/394, Cement and ConcreteAssociation, 52 Grosvenor Gardens,London SW1W oAU, December1965,

3b. Leonhardt, Fritz, and Baur, Willi,"Die Agerbrucke eine aus Gros-Fertigteilen ZusammengesetzteSpannbetonbrucke," Die Bautech-nik, Verlag von Wilhelm Ernst &Sohn, 1 Berlin 31, Hohenzollern-damm 169, July 1963.

3c. Hoving, H. T., Krijn, A. C., andvan Loenen, J. H., "The BridgeOver the Oosterschelde," SfB(91)Dug, UDC 624.2.012.46 (492.6),Cement and Concrete Association,52 Grosvenor Gardens, LondonSW1W oAU.

3d. Muller, Jean, "Precast SegmentalBridges Conception and DesignFundamentals," (Preprint), PCIAnnual Convention (Chicago),September 23-27, 1973.

4. Standard Specification for High-way Bridges adopted by the Amer-ican Association of State HighwayOfficials, Eleventh Edition, 1973.

APPENDIX-DESIGN CALCULATIONS OF TEST BEAM

The following design was performed inthe summer of 1971, and, therefore, re-flects the old AASHO Specifications loadfactors.

It should be pointed out, also, that thedesign is the same as that for monolithiccontruction. No special reinforcement orprestressing is needed to account forstresses introduced during fabrication andassembly as is the case for cantilever con-struction.

1. Section PropertiesGirder Composite

A = 546 sq in. Y'b = 42 in.Y b — 27.9 in. I,, = 453,500 in .4I = 249,000 in .4 Z`, = 25,750 in .3Z, = 8272 in . 3 Zr.F. = 28,344 in.-Zb — 8925 in.' Z`b = 10,800 in.'

2. LoadsGirder:w = (546/144) (160) = 607 lb/ftM — (0.607) (90)2 (1.5) = 7375 in.-kips


Slab:

w = (1) (6/12) (6.0) (150) = 450 lb/ftM = (0.45) (90) 2 (1.5) = 5470 in.-kipsAsphalt, diaphragms, curb, and railing:w (assumed) = 200 lb/ftM = (0.2) (90) 2 (1.5) = 2400 in.-kipsLive load (AASHO, HS 20-44):Impact factor = 50/(125 + 90) = 0.23Live moment - 1345 ft.-kipsGirder moment plus impact =ML +r = (1345) (12) ( r/) (6/5.5) (1.23)

= 10,830 in.-kips

3. Estimate of required prestressMoment acting on bare girder section =

7375 + 5470 = 12,845 in.-kipsMoment acting on composite section =

2400 + 10,830 = 13,230 in.-kipsBottom fiber stress =fL = (12,845/8925) + (13,230/10,800)

= 2.67 ksi (tension)Allowing no tension stress under full de-sign load, then:P[(1/A) + (elZb)] = fbAssume e = 27.9 - 4.25 = 23.65 in.Hence:P [(1/546) + (23.65/8925)] =2.67from which P = 596 kipsTry two 12 -1/2 in. diameter 270-kip strandtendons.

4. Friction loss calculationAssume the tendons have a parabolic pro-file and let the distance from the soffit tothe center of gravity of the tendons be X.X at midspan = 4.25 in.X at end = 29.25 in.Xe„a - X.nidsPan = 29.25 - 4.25 = 25 in.Angle a = (25) (8)/(90) (12)

= 0.185 radians.Assume a friction coefficient p = 0.2.Also, assume a wobble coefficient

K = 0.0002 for semi-rigid smooth duct.(KL + µ a) _ (90) (0.0002) + (0.2) (0.185)

= 0.055fdead end = Backing end e - (KL + µ a^

= /.,. e-o.uss = 0.947 f.,.f' ,. e . = (0.75) (270) = 202.5 ksifd.e. = (0.947) (202.5) = 192 ksiAssume anchorage seating loss = 0.75 in.Distance affected by seating loss:

X - \' (0.75) (90) (12) (28,000)- (202.5 - 192)= 122 ft (> 90 ft)

Avg Af = (0.75) (28,000)(90) (12)

= 19.4 ksi

Therefore, Qf,. e. = 19.4 + 10.5 = 29.9 ksiand Qfd.e.= 19.4-10.5=8.9ksi

The effective prestress at mid-span equalsf;.,. minus the friction and seating loss forthe half-span minus the creep and shrink-age losses (25 ksi). Thus:fa ir=202.5-(10.5/2)- 19.4-25

= 153 ksiandPa» = (153) (0.153) (24) = 561 kips

(< 596 kips required)However, since the beam will be tested a

relatively short time after post-tensioning,only one-half of the losses due to shrinkageand creep will be considered. Therefore,

ferr= 153+12.5=165.5ksiand

Pe rr = (165.5) (0.153) (24) = 608 kips[> 596 kips (ok)]

5. Tendon elongationBefore seating loss =

(202.5 + 192) (90) (12)(2) (28,000)

= 7.61 in.

After seating loss = 7.61 - 0.75 = 6.86 in.

6. Stress reviewA summary of the working load stresses

is given in Table 1.

Note: "c" denotes compression."t" denotes tension.

7. Ultimate strength checkA1,, (req) =1.5D+2.5 (L+I)

= 1.5 (7375 + 5470 + 2400)+ 2.5 (10,830)

= 49,943 in.-kipsM„ (prow) = Aafea d (l - 0.6 pf8„/f e)

Now:fs = 270 [1 - (0.5) (0.00085) (270)/(5)]

= 263.8 ksiTherefore:M„ (prov) = (0.153) (24) (263.8) (59.75) X

[1 - (0.6) (0.00085) (263.8)/(5)]= 56,320 in.-kips

[> 49,943 in.-kips (ok)]

74

Table 1. Summary of Working Load Stresses.

Top BottomStress conditions fiber nterface fiber

P/A = 608/546 1.11c 1.11c

Pe/Z —_ (608) (23.65)8272 & 8925 1.74t 1.61c

Mg ^, d ^ r /Z — 7375 0.89c 0.83t8272&8925

M,5/Z=5470 0.66c 0.6'lt8272 & 8925

M—,b, ../Z = 2400 0.09c 0.08c 0.22t25750 & 28344 & 10800

0.09c 1.00c 1.06cService, dead load =

Mr _ 10,830 0.42c 0.38c 1.00t25750 & 28344 & 10800

Service, full load = 0.51c 1.38c 0.06c

Note: "c" denotes compression."t" denotes tension.

8. Shear design

A, _ (V, — V`) S 0.0025b's2 Lid

V, 0.06 f', b' id 180b'jdInvestigate shear at L /4:V„ at L/4 = (1.5) (90/4) (0.607 + 0.45 +

0.2) + (2.5) (31.2) = 121 kipsV, — (0.18) (5) (0.8) (59.75) = 43 kips

A„.__(121-43)(1)(2) (40) (0.8) (59.75)

= 0.0204 in 2/in.

Use two No. 4 stirrups at 1 ft 7 in, fulllength.

9. Camber prediction

Prestress before creep and shrinkage losses= (0.153) (24) (178) = 654 kips

Moment due to post-tensioning at midspan= (654) (23.65) .= 15,460 in.-kips

Eccentricity at end is practically zero.

E, = 33w' S Vf',= (33) (160)' ” \/7500 = 5,784,000 psi

Camber after post-tensioning =

(5) (15460 — 7375) (90)2 (12)2(48) (5784) (249,000)

= 0.68 in. (up)

Discussion of this paper is invited.Please forward your discussion to PCI Headquartersby December 1, 1974, to permit publication in theJanuary-February 1975 PCI JOURNAL.


ultimate load test of a segmentally … · of a segmentally constructed prestressed concrete i-beam...

Documents