PERFORMANCE OF PRECASTPRESTRESSED HOLLOW CORESLAB WITH COMPOSITECONCRETE TOPPINGNorman L. ScottPresidentThe Consulting Engineers Group, Inc.Glenview, Illinois

This load test of a machine-made hollow-core slabwith composite topping verified a number ofaccepted industry design and fabrication practices,specifically the following:

1. Impact test hammer data taken on the sideof the member provided an accurate assessmentof concrete strength as determined by uncrackeddeflection behavior and ultimate moment capacity.

2. The observed ultimate moment was about10 percent greater than calculations based onEq.(18-3) in ACI 318-71 but nearly identical tocalculations based on strain compatibility byFig. 5.2.5 in the PCI Design Handbook.

3. The bilinear concept for predicting thedeflection of cracked prestressed members wasconservative well beyond a nominal bottom fibertensile stress of 12i,/ f'c.

4. Composite action between the precast andcast-in place portions was evident up to ultimateload. The top surface of the precast slab was a smooth,even, machine cast finish and did not comply withSection 17.7 of ACI 318-71. There was noreinforcing steel projecting from the precast slabinto the topping concrete.

5. A shear failure did not occur even though theultimate shear stress vu was 1.75 times vc as computedin accordance with ACI 318-71.

64

I--ҟ600

WZJW 500a-U)a]J

400

0Jaw0 300a_Mo:wa(n 200

0w_J

a 100

InitiaV 1^loading

22.625ҟ3000 psi—ҟtopping

.0.0.0. 6700 psiprecast

23.875

5 layers conc. blks = 540 plf

^4 layers conc.blks = 432 plf

.Initial loading

3 layers conc blks = 324 plf

Reloading

/ I /2 layers conc. blks = 216 pif

Unloading

layer conc. blks = 108 plf

Reloading

+ Iҟ-1" -2 -3" -4 -5' -6 -7" -8 -9" -10 -II"-12 -13"-14-15"

CAMBER

ҟ

ҟ DEFLECTION

Fig. 1. Load-deflection curves

At this time in the development of pre-stressed concrete it does not seem nec-essary to perform a load test of a wide-ly used pretensioned member. But aconscientious producer of Spiroll hol-low core slabs in La Crosse, Wisconsin(Hemstock Prestressed Inc.) asked fora load test just to confirm that theywere still producing a quality product.

The resulting load test was routineand the slab performed as expected butit also verified a number of design prac-tices and provisions of the 1971 ACIBuilding Code (ACI 318-71).

The test member was an 8 in. deep24 in. wide machine made hollow coreslab with a 2 in. concrete topping (seeFig. 1). The precast pretensioned slab

PCI Journal/March-April 1973ҟ 65

C)Table 1. Comparison of observed and calculated deflections for various loading stages

Load stageCalculated bottom

fiber stress, psiCalculated

deflection frominitial camber, in.

Calculateddeflection from

level, in.

Observeddeflection from

level, in.Remarks

No load 650 (compression) 0 -0.67* 0.661 layer of concrete block

108 lb per ft 75 (compression) —0.36 +0.31 t +0.282 layers of concrete block

216 lb per ft —499 (tension) —0.71 —0.04t —0.093 layers of concrete block Cracking occurred

324 lb per ft —1074 (tension) —1.07 —0.40t —1.72 while placing thislayer of block

No load 650 (compression) 0 +0.67* 0.40$1 layer of concrete block

108 lb per ft 75 (compression) —0.36 +0.31 t —0.152 layers of concrete block Cracks reopened

216 lb per ft —499 (tension) —0.71 +0.04t —0.60 while placing3 layers of concrete block this layer of block

324 lb per ft —1074 (tension) —1.07 —0.40t —1.72

4 layers of concrete block Further flexural432 lb per ft —1649 (tension) —1.42 —0.76t —4.97 cracking but no

shear cracks5 layers of concrete block

540 lb per ft —2224 (tension) —1.78 —1.11t —15.35 Slab graduallysettled to floor

* Camber calculated with elastic materials properties indicated 0.62 in. Value here is obtained using multipliers to account for creep and prestress losses. See com-puter output in the Appendix.

Values calculated are based on gross section properties. Cracking occurred when the net tensile stress in the bottom fiber was near 619 psi or 7.5 -\/t'. After crack-0

ing, section properties are greatly reduced and observed deflection values are accordingly larger than calculated. See the deflection calculations in the Appendix andFig 2.

$ Slab returned to within 0,26 in. of cambered position. Some creep set apparently occurred. With more time part of this set would probably have disappeared.

was taken from stock and consequentlythere was no opportunity to determinethe concrete properties at time of mix-ing or the stressing provisions. Similar-ly, the concrete topping was cast with-out concrete cylinders so compressiontests could not be used to verify thestrength of the topping.

Such a situation would seriouslyhandicap any serious research study butthis problem is typically encountered inthe load testing of existing structures.A straight strand pretensioned floorslab can be easily checked after castingfor dimensions, section properties, num-ber, location, and size of strands. Theconcrete properties were determinedwith a concrete impact hammer. Thedimensional measurements and the im-pact hammer data were sufficient toaccurately determine the structural be-havior and strength of the slab.

It is unfortunate that we encounterso much suspicion and mistrust of theconcrete impact hammer (Swiss ham-mer) within the engineering profession.Frequently we find engineers who willput almost blind faith in concrete testcylinders as representing the concretein a structural member but will rejectimpact values taken directly on themember. Cores taken from concretemembers frequently furnish erratic re-sults but these too are usually givenmore credibility than impact values.The impact hammer is a practical meth-od for determining the concretestrength of machine-made slabs andconsiderably more accurate than testcylinders. This is because the compac-tion of the machine cannot be accurate-ly duplicated in making the cylinders.In my opinion the concrete impacthammer should be the standard methodfor determining compressive strength inmachine-made slabs.

The hollow core slab tested was pre-stressed with four 1/z in. diameterstrands having an ultimate catalogstrength of 250,000 psi. The precast

member is made with normal weightconcrete consisting of limestone coarseaggregate and natural sand fine aggre-gate. At the time of the test the precastslab had reached a compressivestrength of 6700 psi and the topping,3000 psi. Both of these strength valueswere obtained by a concrete impacttest hammer. An average of 8 readingswere taken on the slab and 11 readingson the topping.

It should be noted that the impacthammer readings were taken on theside of the floor member with the in-strument in the horizontal position. Thecorrelation to 6 x 12 in. compressioncylinder strengths was made with theuse of curves printed on a plate at-tached to the instrument. Obviously, itwould have been better to have a cor-relation curve based on concretes mixedfrom local materials but such data werenot available. Impact readings taken onhollow core floor and roof assemblieswith the instrument in the vertical posi-tion are not as reliable as horizontalreadings because of the presence of thecores. The cores tend to "soften" thehammer impact and hence indicatelower than actual compressivestrengths. Again, this is a serious handi-cap in evaluating the strength of hol-low core members in place on a build-ing but with a single slab we had nodifficulty obtaining reliable values fromthe sides of the slab.

DESCRIPTION OF TEST

The hollow core floor assembly was33 ft long and the slab was placed onsupports to provide a 31.5 ft clear span.One end of the slab was placed on asteel roller to eliminate the effects ofhorizontal friction which would be in-duced on a rigid support as the slabdeflects. If these frictional forces arenot eliminated, a negative moment isinduced at the supports and can affectthe results of the test. The roller end

PCI Journal/March-April 1973 67

support consisted of two plates with a1½ in. steel rod sandwiched between.The lower plate was supported by 6 x 8in. solid concrete blocks stacked twohigh such that the support was about15 in. above the floor. Deflection read-ings were taken with the aid of a transitlocked in the horizontal position and alevel rod reading in feet, inches, andeighths of an inch. Prior to the test,readings were taken at each end of theslab and in the center.

TEST LOADSBefore commencing the test it was

determined that the slab would proba-bly take about 500 lb per linear ft atfailure. This determination was quicklymade by a time-sharing computer. Thedata obtained from measurements onthe test slab were telephoned to our of-fice and the computer results were tele-phoned back within a half hour. Beforethe availability of the computer it wasoften not possible to compare actual re-sults with analytical values until some-time after the test. In this case we couldmake comparisons as the test pro-gressed. It was decided to load the slabin five increments and these loadswould be applied using solid concreteblocks. The blocks were 55/s x 75/s x155/8 in. (nominal 6 x 8 x 16 in.). Tenblocks were weighed and the averagewas 541/s lb per block. It was thereforeassumed that each block would weighan even 54 lb each. The test slab wasmarked off with 21 equal spaces, 11/z

ft long over the 31V2 ft span. Since theslab was nominally 2 ft wide, each ofthe 21 rectangles represented 3 sq ft.By placing three 6 x 8 in. blocks in eachof these rectangles, each block repre-sented the load applied per square foot.In other words, one layer of blockplaced on the slab within these rectan-gles would represent 54 lb per sq ft or108 lb per linear ft. After each layer ofblock was placed on the slab, deflectionreadings were taken.

TEST RESULTSTable 1 shows the results of the five-

stage load test. The slab was first load-ed up to Stage 3 which consisted of 324lb per linear ft and the blocks were re-moved to determine the recovery. Thereason for this step is that ACI 318-71provides for a procedure to evaluate thestrength of existing structures. Part 6 ofthe ACI Building Code specifies thatthe structure shall be subjected to aload consisting of 0.85 (1.4D + 1.7L).This load is to be left on the structurefor 24 hours and the deflection readingstaken. If the measured maximum de-flection of a prestressed member ex-ceeds 12/20,000h, the deflection re-covery within 24 hours after the remov-al of the test load shall be at least 80percent. In this case the 12/20,000hequals 0.715 in. It will be noted fromTable I that under the third stage loadour deflection was —1.72 + 0.66 =2.38 in. from the cambered positionwhich exceeds the value specified bythe ACI Code. Although it was notpractical to hold the load on for 24hours in this case, the recovery wasnevertheless observed. It can be seenfrom Table 1 that the member wentback to within 0.26 in. of its originalcambered position. This is an 89 per-cent recovery.

Table 1 shows that the slab initiallyhad 0.66 in. of camber under its owndead load. The calculated camber valueas shown on the computer sheets in-cluded in the Appendix was 0.67 in.(0.68 in. at erection, 0.66 in. final).For the first two load stages the com-puter output shows that the bottom fi-ber stress would be less than the modu-lus of rupture (7.5Vf',) and thereforeelastic deflection behavior could be ex-pected. The member performed almostexactly as calculated, as can be seenfrom Table 1. Under the first load stageit was anticipated that 0.36 in. of de-flection would occur from the cambered

68

Load stage 5 540 plf

Load stage 4 432 plf

/<-Cracked I deflection

Load stage 3 324 plf

J Load stage 2 216 plf

/ҟGross I deflectio

Load1

stage I 108 plf

o-

0I-I-0Ɂ-1649mzI)

wa -1074r

I2 fr-997wJU,z 7.5ҟ-.619-UHɁ6 - 499'I-wzJҟ0z_ҟ+75—M0z

+650 1

+ Iҟ-I' -2 -3" -4 -5" -6 -7"-8 -9"-10 -I I°-12 -13°-14 -15"

CAMBERҟ DEFLECTION

Fig. 2. Tensile stress-deflection curve

position, leaving a net camber of 0.31in. The observed data show that theslab had a camber of 0.28 in. at thisload stage. The calculations furthershow that under the second load stagethe member would have a net deflec-tion of 0.04 in. and the actual measure-ment was 0.09 in. This agreement be-tween calculated and test results is verygood, and confirms that the commonlyused equation E = 33w 1 • 5Vf', incorpo-rating values for f' taken by impacthammer will provide accurate results inpredicting deflections. It was antici-pated that during the third load stage,

cracking would occur and the deflec-tion would increase substantially. It canhe seen from the load-deflection curve(see Fig. 1) that this did happen andthe curve breaks over between LoadStages 2 and 3. Fig. 2 shows the samecurve but relating net bottom tensilestress to deflection. The break in thecurve would appear to come close tothe load associated with a net tensilestress in the bottom of about 7.5-'./f' or619 psi, which is the value given inSection 9.5.2.2 of the ACI BuildingCode. Although this section of theCode pertains to reinforced concrete,

PCI Journal/March-April 1973ҟ 69

the 7.5\/j' value seems reliable whenapplied to this type of prestressed mem-ber. After removal of the concreteblocks for the third load stage, the slabwas reloaded for Stages 1, 2, and 3.Since the slab had cracked during thefirst loading it could be expected thatthe cracks would reopen when the nettensile stress in the bottom became ze-ro. Computer calculations in the Ap-pendix show that this net tensile stressin the bottom corresponds to a super-imposed load of about 122 lb per linearft. It can be noted from Fig. 1 that thereloading curve begins to break awayfrom the straight line at about 122 lbper linear ft. When the third layer ofblocks was applied, the slab returnedexactly to the position that was ob-served for the first loading. This be-havior is consistant with the results ofmany other load tests involving the re-loading of previously cracked pre-stressed members. The next two layersof block were added with the results asshown in Table 1. Further flexuralcracking occurred during both of thesestages but there was no evidence ofshear cracking or separation of the com-posite slab from the precast portion ofthe member. Failure of the slab oc-curred very near the time when the lastblock was applied near midspan for thefifth load stage. The failure was gradualand was the result of yielding of theprestressing strand. Following this ten-sile failure the topping buckled at mid-span and separated from the precastslab about 6 ft each side of the center-line.

As can be seen from the ultimatemoment calculations, the observed ulti-mate moment is first determined andthen the ultimate moment is calculatedbased on the two methods prescribedby ACI 318-71. The first calculations,based on Eq. (18-3) for fr,s, the steelstress at ultimate, underestimates theobserved ultimate moment. The secondcalculation, based on strain compatibil-

ity making use of the design aid in thePCI Design Handbook (Fig. 5.2.5),shows much better agreement with theobserved ultimate moment. The deflec-tion behavior and ultimate flexuralstrength clearly demonstrated that fullcomposite action was present up to theultimate load. The precast slab had asmooth top surface finished by the vi-brating screed that is part of the Spirollmachine. The surface obviously did notcomply with the surface roughness re-quirements of Section 17.7 in ACI 318-71. It is not practical to provide pro-jecting steel from a machine cast slaband of course none was provided.

From the computer output in theAppendix, it should be noted that atthe final load stage (540 lb per linearft) the shear stresses were very highyet no shear distress occurred. It can benoted from the output that at a pointapproximately 3 ft from a support theshear stress in the member was 137 psiover the value specified for plain con-crete. This is considerably in excess ofwhat the ACI Code allows for beamswithout the use of reinforcing steel. Forbeams without stirrups, Section 11.1 ofthe ACT Code says that v,2, must be lessthan one-half v, but slabs and footingsare exempted from minimum shearsteel requirements. In this test v,, was1.75 v0 at ultimate load. The load testproved that the code exemption forslabs is justified and applicable to ma-chine made hollow core slabs. In de-signing machine made slab floor sys-tems with high shear stresses it shouldbe recognized that accidential crackingor web tearing could be present andcould reduce the shear strength. Thetest, nevertheless, shows that theseslabs do possess a substantial shear re-sistance without web reinforcement.

DEFLECTIONThe deflection calculations relate to

Load Stages 2 and 3. The computer

70

output sheets also calculate deflectionsbut these computations are alwaysbased on the assumption of a gross sec-tion. Up to cracking this procedure isaccurate as can be seen from Table 1.After cracking, the moment of inertiais substantially reduced and deflectioncalculations based on the gross momentof inertia will be unconservative as canhe seen from Table 1.

The ACI Building Code in Section1.8.4.2(c) states that when the net ten-sile stress is 12Vf', a bilinear momentdeflection relation must be used to cal-culate deflections. This relation isshown in the Appendix as well as inFig. 2. The actual moment-deflection(or load-deflection or bottom fiberstress-deflection) diagram is approxi-mated by two straight lines. The firstline has a slope proportional to thegross moment of inertia Ig and the slopeof the second line is proportional to thecracked moment of inertia I,, the twolines joining at the point correspondingto a net tensile stress of 7.5^/f',. Thisbilinear approximation was first devel-oped by the PCI Committee on Allow-able Stresses and adopted for the ACIBuilding Code.

The calculations show that with thisprocedure the deflection at Load Stage3 would be —2.32 in. The observed de-flection was —1.72 in. so the bilinearmethod overestimates deflection at thisstress level (-1074 psi or 13Vr) andhence is conservative. At Load Stage 4(bottom fiber stress —1649 psi or 20i/)the calculated deflection is —4.84 in.and the observed deflection was —4.97in. Above this load or tensile stress levelthe bilinear method would greatly un-derestimate the actual deflection. Thebilinear method is apparently satisfac-tory for predicting deflections for thisproduct within the service load range.In my opinion it is just as simple andmore useful to calculate cracked de-flection using the two-step approach

rather than the effective moment of in-ertia method proposed in the ACI Com-mentary and presented in the PCI De-sign Handbook.

CONCLUSIONS

The results of this test reemphasizethat the ultimate flexural capacity ofprestressed members can be predictedvery precisely using the provisions ofthe ACI Building Code. The slab testedon a 31.5 ft span carried 270 lb per sqft (540 lb per linear ft) at flexural fail-ure. At service load, cracking will notoccur and the behavior can be judgedfrom Table 1 for Stages 1 and 2 loadingconditions. The test further demon-strated substantial shear strength capa-bilities for this member when used inconjunction with a 2 in. concrete top-ping of modest strength. Additionally,the test confirms that the bilinear meth-od of predicting deflection behavior inthe cracked range is conservative up to12\/f', and beyond. In all respects, themember exhibited a behavior that is invery close agreement with the resultsexpected from calculations.

APPENDIX

Ultimate moment calculations

The ultimate moment observed is:

Mu = 1.5(wn + wsz)L2= 1.5(160 + 540) (31.5)2= 1,040,000 in.-lb

To compute the ultimate momentcalculated use Eq. (18-3) of ACI 318-71. For bonded members:

fps„=fpu-0.5pl,fr, U l

fps _ Aps fluPe f', bd •f0

_ 4(0.144) 250— (22.625)(8.56) • 3 = 0.25

PCI Journal/March-April 1973 71

LOAD OR

MOMENT OR

BOTTOMFIBER

STRESS

12ҟ THIS SLOPE ISA FUNCTION OFCRACKED MOMENTOF INERTIA

CHANGE OCCURS WHEN BOTTOMFIBER STRESS REACHES NETTENSILE STRESS = 7.5 /C

THIS SLOPE IS A FUNCTION OFGROSS MOMENT OF INERTIA

DEFLECTION

Fig. Al. Bilinear moment-deflection diagram

The ultimate steel stress is

fps = 250 [1-0.5(0.25)]

= 219 ksi

To determine the true ultimate mo-ment, the 0 factor must be ignored.

M,, = Apsd(1-0.59Wr)

A, fps^p = bd f,

_ 4(0.144) 21922.625(8.56) 3

= 0.22

M,, = 4(0.144)(219)(8.56) x

[1 — 0.59(0.22)]

= 940,000 in.-lb

From the PCI Design Handbook(Fig. 5.2.5) determine fps by straincompatibility.

W,- bd . f'u -0.25

Now C = 1 for 3000-psi concreteand therefore Ca 0.25.

From the chart (bottom of Fig. 5.2.5),

fps/fpu = 0.93.

fps = 0.93(250) = 235 ksi

M,, = 4(0.144)(235)(8.56) X

[1 — 0.59(0.235)]

= 1,000,000 in.-lb

Thus, the ultimate moment usingthe strain compatibility method closelymatches the observed ultimate moment.

Deflection calculations

Calculate the deflection using thebilinear moment- deflection relation (seeFig. Al), as specified in Section18.4.2(c) of ACI 318-71.

Use the PCI Design Handbook tocalculate Icracked-

_ E g 29,000,000= 6.15

^aE 4,716,000

_ Aps _ 4(0.144)- 0.003

Pp bd 22.625(8.563)

72

npp = 6.15(0.003) = 0.0185

From Fig. 5.2.27, C = 0.17.

bd3'cracked = C 12

_ 0.17(22. 625) (8.563)312

= 201 in.4

7.5 /6700=219 psi

Find the load at 619 psi by averag-ing the conditions at Load Stages 2and 3.

Stage 2—Tensile stress = 499 psi

2161b L,499 psi 619

L1 = 187 Ib

Stage 3—Tensile stress = 1074 psi

324 lb _ L21074 psi 619

L2= 268 lbz

The average of these two conditionsis 228 lb.

5wL4^l 384EIy

5(228)(31.5)4(1728)384(4,716,000)(1427)

= 0.75 in.

From this deflection deduct the ini-tial camber (calculated) of 0.67 in.

Therefore, the net deflection is 0.08in.

Next, (calculate the deflection at

Load Stage 3 (f b = 1074 psi, tension).The applied load after cracking is:

324 — 228 = 96 lb per ft

5wL4

384EIer¢cked

5(96)(31.5)4(1728)384(4,716,000)(201)

= 2.24 in.

To this deflection add i = 0.08 in.

Thus, the total calculated deflectionis 2.32 in.

From Table 1, the observed deflec-tion is 1.72 in.

But, the allowable stress is 12Vf'e= 997 psi.

Therefore, the bilinear method isconservative at this level.

Finally, calculate the deflection atLoad Stage 4 (fn = —1469 psi, tension).

The applied load after cracking is:432 — 228 = 204 lb per ft

_ 5(204)(31.5)4( 1728)384(4,716,000)(201)

= 4.77 in.

To this deflection add A 1 = 0.08 in.

Thus, the total deflection —is 4.85 in.

From Table 1 the observed deflec-tion equals 4.97 in.

Therefore, the bilinear method isvery close at this stress level on thisfloor system.

(See pp. 74-77 for typical computer output.)

Discussion of this paper is invited.Please forward your discussion to PCI Headquarters by August 1, 1973, topermit publication in the September-October 1973 issue of the PCI JOURNAL.

PCI Journal/March-April 1973 73

Table Al. Typical computer output

THE CONSULTING ENGINEERS GROUPi INC.

PRESTRESSED CONCRETE MEMBER DESIGN--PAGE 1

PROJECT;

ḏ

ḏ DESIGNER:DATE:

SECTION:

WIDTH(B)= 24.00 DEPTH(H) =ḏ8.00 WEB(8W) =ḏ6.00TOPPING WIDTH= 22.63ḏTHICKNESS= 2.00

SECTION PROPERTIES

PLAINḏCOMPOSITE*A= 107ḏSO.IN. 137 SO.1N.I= 832 IN.4TH 1427 IN.4THY8= 4.00 IN 5.10 1NYT= 4.00 IN 4.90 1NZ8= 208 1N.3RD 280 IN.3RDL1= 208 IN.3RD 291 1N.3RDW= 108 PLF 153 PLF*DIFFERENCE 1N MODULUS OF'ELASTICITY OF TOPPING INCLUDED

CONCRETE STRANDWT=ḏ145 PCF AREA=ḏ.144 SC IN PER STRANDFC=ḏ6700 PSI FPU=ḏ250 KSIEC=ḏ4716 KSI NO. OFḏSTRAND=ḏ4FCI= 3500 PSI INITIAL LOSS=ḏ10 PCTEC1= 3409 KSI FINAL LOSS=ḏ20 PCT

P1=ḏ101ḏKIPSTOPPING Pu=ḏ91ḏKIPS

WT=ḏ145 PCF P=ḏ81ḏKIPSFC= 3000 PSI END ECCENTRICITY=ḏ2.56 INEC= 3156 KSI CTR ECCENTRICITY=ḏ2.56ḏIN

ECC• AT 0.4L=ḏ2.56ḏ1N

LOAD STAGE 1

SERVICE DEAD LOAD=ḏ0 PSFḏ0 PLF EXCLUDING TOPPINGLIVE LOAD=ḏ57 PSFḏ108 PLFSPAN= 31.50 Fl

SERVICE LOAD MOMENTS

MIDSPAN 0.4LMDL= 160 K-IN 154 K-iNMSDL= 0 K-1N 0 K-INMTOP= 68 K-IN 65 K-iNTOIL= 228 K-IN 219 K-INMLL= 161 K-IN 154 K-INTOIL= 389 K-1N 373 K-1N

74

Table Al (cont.). Typical computer output

STRESSES

RELEASEEND MIDSPAN

FB FT FB FTP/A 848 848 848 848PE/Z 1117 -1117 1117 -1117MDL/Z -771 771(MTOP+MSDL)/ZMLL/ZTOTAL 1964 -269 1193 502ALLOWABLE 2100 -177 2100 2100

CAMBER

SERVICE LOADSMIDSPAN 0.4L

FB FT FB FT

754 754 754 754

992 -992 992 -992

-771 771 -740 740

-326 326 -313 313

-575 552 -552 529

74 1410 141 1344

3015 3015 3015 3015

RELEASE MULT ERECTION MULL FINALPRESTRESS 1.46 1.65 2.41 2.20 3.22MEMBER WT -.84 1.75 -1.47 2.50 -2.10

NET .62 .94 1.11SERVICE DL -.26 1.75 -.45

NET .68 .66SERVICE'LL -.36

NET .31

SHEARLOCAT10N VU VC VU-VC (VU-VC)BW

•00 143.7 409.3 -265.6 -15941.58 129.3 349.5 -220.2 -13213.15 114.9 190.0 -75.1 -4504.72 100.6 163.7 -63.1 -3796.30 86.2 163.7 -77.5 -4657.87 71.8 163.7 -91.9 -5519.45 57.5 163.7 -106.2 -63711.03 43.1 163.7 -120.6 -72412.60 28.7 163.7 -135.0 -81014.47 14.4 163.7 -149.3 -89615.75 .0 163.7 -163.7 -982

LOAD TO PRODUCE ZERO BOTTOM FIBER STRESS

SERVICE DEAD LOAD= 0 PSF .0 PLF EXCLUDING TOPPINGLIVE LOAD= 65 PSF 122 PLFSPAN= 31.50 FT

SERVICE LOAD MOMENTS

MJDSPAN 0.4LMDL= 160 K-1N 154 K-1NMSDL= 0 K-IN 0 K-INMTBP= 68 K-1N 65 K-INTOTL= 228 K-1N 219 K-iNMLL= 182 K-IN 174 K-1NTDTL- 410 K-1N 393 K-IN

PCI Journal/March-April 1973 75

Table Al (cont.). Typical computer output

STRESSES

RELEASE SERVICE LOADSEND MIDSPAN MIDSPAN 0.4L

FB FT FB FT FB FT FB FTP/A 848 648 848 848 754 754 754 754PE/Z 1117 -1117 1117 -1117 992 -992 992 -992MDL/Z -771 771 -771 771 -740 740(MTOP+MSDL)/L -326 326 -313 313MLL/Z -649 623 -623 598TOTAL 1964 -269 1193 502 0 1481 70 1412ALLOWABLE 2100 -177 2100 2100 -962 3015 3015 3015

CAMBER

RELEASE MULT ERECTION MULT FINALPRESTRESS 1.46 1.65 2.41 2.20 3.22MEMBER WT -.84 1.75 -1.47 2.50 -2.10

NET .62 .94 1.11SERVICE DL -.26 1.75 -.45

NET .68 .66SERVICE LL -.40

NET •26

SHEARLOCATION VU VC VU-VC (VU-VC)BW

.00 152.3 409.3 -257.0 -15421.58 137.0 349.5 -212.4 -12753.15 121.8 190.0 -68.2 -4094.72 106.6 163.7 -57.1 -3436.30 91.4 163.7 -72.3 -4347.87 76.1 163.7 -67.6 -5259.45 60.9 163.7 -102.8 -61711.03 45.7 163.7 -116.0 -70812.60 30.5 163.7 -133.3 -80014.17 15.2 163.7 -148.5 -69115.75 .0 163.7 -163.7 -982

LOAD STAGE 5 - ULTIMATE LOAD

SERVICE DEAD LOAD= 0 PSF 0 PLF EXCLUDING TOPPING

LIVE LOAD= 286 PSF 540 PLFSPAN= 31.50 FT

SERVICE LOAD MOMENTS

MIDSPAN 0.4LMDL= 160 K-IN 154 K-INMSDL= 0 K-1N 0 K-INMTOP= 68 K-1N 65 K-INIOTL= 228 K-IN 219 K-IN

MLL= 804 K-1N 772 K-1N

101L= 1032 K-1N 991 K-1N

76

Table Al (cont.). Typical computer output

STRESSES

RELEASE SERVICE LOADSEND MIDSPAN MIDSPAN 0.4L

F8 FT FB FT FB FT FB FTP/A 848 848 848 848 754 754 754 754PE/Z 1117 -1117 1117 -1117 992 -992 992 -992MDL/Z -771 771 -771 771 -740 740(MI©P+MSDL)/Z -326 326 -313 313MLL/L -2874 2758 -2759 2647TOTAL 1964 -269 1193 502 -2225 3616 -2066 3462ALLOWABLE 2100 -177 2100 2100 -982 3015 -962 3015

CAMBER

RELEASE MOLT ERECTION MULT FINALPRESTRESS 1.46 1.65 2.41 2.20 3.22MEMBER WT -.84 1.75 -1.47 2.50 -2.10

NET .62 .94 1.11SERVICE DL -.26 1.75 -.45

NET .68 .66SERVICE LL -1.78

NET -1.11

SHEARLOCATION VU VC VU-VC (VU-VC)BW

•00 408.6 409.3 -.6 -41.58 367.8 349.5 18.3 1103.15 326.9 190.0 136.9 8214.72 286.0 163.7 122.3 7346.30 245.2 163.7 81.5 4897,87 204.3 163.7 40.6 2449.45 163.5 163.7 -.3 -211.03 122.6 163.7 -41.1 -24712.60 81.7 163.7 -82.0 -49214.17 40.9 163.7 -122.8 -73715.75 .0 163.7 -163.7 -982

PCI Journal/March-April 1973ҟ 77