Designing Hollow-Core Slabsfor Continuity

Kiang-Hwee TanDr.Eng., P.Eng. (S)

Senior LecturerDepartment of Civil EngineeringNational University of Singapore

Singapore

Lian-Xiang Zheng, Ph.D.Former Research Scient istDepartment of Civil EngineeringNational University of SingaporeSingapore

P. ParamasivamPh.D., P.Eng. (S)

ProfessorDepartment of Civil EngineeringNational University of Singapore

Singapore

Precast, prestressed hollow-core slabs areusually used as part of a simple span system.However, in a multispan floor slab system,designing for continuity over supports leads toincreased span capacity, improved structuralintegrity and savings in materials. In thispaper, formulas relating the fractionalincrease in span capacity, percentage ofmoment redistribution from supports anddesign midspan and support moments ofhollow-core slabs are derived theoretically.These relations are put in a graphical formto facilitate the design of connections incontinuous hollow-core slabs, the use ofwhich is illustrated by several examples.To demonstrate the development of fullcontinuity at the supports, three specimens,each consisting of two hollow-core slabcomponents on a supporting beam elementand connected by in-situ structural concretetopping, were tested under three-pointloading to simulate the portion of acontinuous span under hogging bending.The test results show that the specimensdid achieve the ultimate load-carryingcapacities calculated using conventionalreinforced concrete theory. Under heavyshear conditions, vertical links placed inthe cut-open cores were found to be effectivein improving the shear behavior ofthe specimens.

Ll ,

ULTIMATE BENDINGFOR CONTINUOUS S

ULTIMATE BENDING MOMFOR SIMPLY S U P P O R T E D

Fig. 1. Increase in span capacity of hollow-core slabs due to continuity at supports.

P recaht. prehtrecced hollow-core~labr are the most commonlyuxed precast concrete compo-

nents in low and high rise buildingconstruction. They are usually used assimply aupported elements with struc-tural topping concrete provided oversupports to cerve as Wuctural integrityties and diaphragm connections.’

In the past two decades. a significantamount of research has been carriedout to inve$tifate the shear resistanceof hollow-core xlabs.’ ( special rein-forcement for end zupports.’ clab re-sponse to concentrated load.“’ behaviorunder edge loads.’ and composite ac-tion with topping concrete.’ However,ver) little published information existson continuity in hollow-core slabs andthis information was limited to the useof separate dowel bar\ grouted intodrilled holes in precast slab\.” and theuse of prestressing strand\ in the coresfilled with concrete.“’

Although the PCI Hollow-Core De-sign Manual’ acknowled_res that continu-ity over \upporth result\ in better controlof superimposed load deflections and alower requirement for positive momentcapacity. this is usually not exploited inhollow-core clab design. mainly hecau\eof the lath of design aids.

The main ob.jective of this study is todevelop charts for the de+n of co~mec-

tions in continuous hollow-core slabcomtruction. A set of formulas relatingthe increase in span capacity of hollow-

core slabs. moment redistribution al-lowed at supports. and the designmidspan and support moments of theslab, is first derived theoretically. Theserelations are then shown in a graphicalform to facilitate the design process.

Several examples are given to illus-trate the use of the design charts forboth one-end and two-end continuousslab construction. Also. tests were car-ried out on three specimens simulatin:!connections over supports to demon-strate the development of momentcontinuity and to study the effect ofshear force due to increased span.

BASIS FORDESIGN CHARTS

As indicated earlier. two major hene-fits result from designing for momentcontinuity over supports in hol low-coreslab construction. First. this practiceleads to an increase in the span capacityof hollow-core slabs for a given designload, Second. it helps to reduce the de-flections of the slabs. The first aspect iscmploycd in the development of desipncharts for the design of moment conti-nuity over supports as follows.

Design for Two-EndContinuous Span

Fractional Increase in Span Ca-pacity - In hollow-core slab design.the span capacity, L,,, corresponding to

a safe superimposed load is usuallyspecified by the manufacturers or inhandbook\ for simply supported endconditions. Given the self-weight ofthe slab, the design uniform load, W,on the slab can be established and thenominal moment capacity, M,, of theslab corresponding to the span i\:

M, = ;wL;, (1)

Suppose that the same slab was de-signed as a two-end continuous slabwith ultimate support moment M, ateach end (see Fig. I) and midspan mo-ment &II,. where (Y is the ratio of thedesign midspan moment to the nomi-nal moment capacity of the hollow-core slab. Here. the coefficient (Y de-note\ the degree to which the nominalmoment capacity of the slab is beingutilized in continuous construction andhas a value between 0 and I inclusive.For the same design uniform load W.the continuous slab would be able tovpan a length L, given by:

aM,+Mc =$WLf 0)

Introducing /-3 = M, lM, and eliminat-ing W from Eqs. ( I) and (2) leads to:

L _----=,Cr+p4,

(3)

It is seen from Ey. (3) that if cr-e /3>I, L, will be larger than L,,: and an in-crea\e in span is achieved.

Under elastic conditions, however.the fixed end moments would havebeen M, where:

Thu\. the moment M, at the ~pporthas been acsumed to be redistributedat ultimate such that:

M, =( I - R)M, (5)

where R is the percentage of momentredistribution from the supports, ofwhich a value of up to 30 percent isusually allowed in design.

Substitutin:! Eqs. (4) and (5) intoEq. (2) and rearranging for L, gives:

(6)

1 . 0 0

0.80 . 9 0

LIdg0EO 0 . 7

3EEg 070 06i i.r

1 0.60 p 5 0.5

i5 0.50::

s

0 . 4 0

0% 5% 10% 1 5 % 20% 25% 30%

Moment Redistribution fmn SWS W)

Fig. 2. Design chart for two-end continuous span.

1 . 0

0.9

0 . 8

p=07

3. Design chart for one-end continuous span.

From Eq. (1):

L,, = 8M,JrWHence, the fractional increase in

span capacity can be expressed as:

dL-ZZ 4=

L L*

Eq. (8) shows that an increase inspan is possible only if a > (1 + 2R)/3.

Required Moment Resistance atSupports - Substituting Eqs. (4) and(6) into Eq. (5) gives:

or, noting that /?I = MJM,:

p= 20-R)oa (10)Eqs. (8) and (lo), which respec-

tively relate the fractional increase inspan dL/L and the ratio p to the per-centage of moment redistribution fromsupports R and the ratio a, are ex-pressed graphically in Fig. 2. Thechain lines and solid lines shown inthe figure indicate combinations of Rand a for specified values of dL/L and/I, respectively.

For the case where Q: = I andR 5 0.3, it is seen from Fig. 2 that thespan capacity of hollow-core slabs canbe increased by between 37 and 70percent. If the full positive momentcapacity of slab is not used (that is, (r< I), then the fractional increase inspan capacity due to the provision ofcontinuity at the supports would becorrespondingly less.

Design for One-EndContinuous Span

It can be shown in a similar mannerthat if the slab is designed as a one-end continuous slab, the increasedspan capacity, Li, would be given by:

L;=: ,+P4, r-2(11)

where L, is the span capacity for asimple-support slab design, and a andp are the ratios of the design midspanmoment and support moment at thecontinuous end, respectively, to thevalue of M,q, which, as defined earlier,is the nominal moment capacity with

respect to L,.The fractional increase in span ca-

pacity, dL/L, and the value of p can beshown to be related to a and R by:

dL L,= 2a-ZZL 4,

--I (12)l+R

and

p = 20 - RI-jiFy (13)

Eqs. (I 2) and (13) are depictedgraphically in Fig. 3. An increase inspan capacity is achieved only if cx >(1 + R)/2. For the case where a: = 1and R 5 30 percent, the increase inspan capacity varies from 24 percentto 41 percent.

Use of Design Charts

The design charts given in Figs. 2and 3 allow the value of p and, hence,the required moment resistance M,. atthe connection and the correspondingincrease in span capacity of the slab tobe determined from specified valuesof R and a. Once the value of M,. isdetermined, the required reinforce-ment ratio, A,vlbd, at the connectionsover the supports can be worked outfrom conventional section analysis orfrom design aids for flexure.

The obtained section should bechecked for rotational capacity or duc-tility (as required for moment redistri-bution) in the usual manner. Accord-ing to BS 81 10” and ACI,” this issatisfied, respectively, by ensuringthat the limit on the neutral axis depthat ultimate or the reinforcing index isnot violated.

Other Considerations

Deflections - In general, the provi-sion of moment resistant connectionsat supports leads to reduction in de-flections of hollow-core slabs, as isevident from the bending moment dia-gram shown in Fig. I. The reductionin deflections due to service loads iseven more significant, as can be de-duced from the bending moment dia-gram illustrated in Fig. 4 for the caseof a two-end continuous span.

Both the BS 81 IO” and ACI” allowdeflections to be checked using span-to-depth ratios in lieu of deflectioncalculations. The allowable ratio is 20for simply supported slabs. The BS81 IO” specifies a ratio of 26 for con-tinuous slabs, while according toAU,” the allowable span-to-depthratio is 28 for two-end continuousslabs and 24 for one-end continuousslabs. Thus, it appears that deflectionwould not pose a problem if the frac-tional increase in span is less than 0.4in the case of two-end continuous spanand 0.2 in the case of one-end continu-ous span.

Effect of shear - The increase inspan capacity of the hollow-core slabby providing moment continuity atsupports would be accompanied by anincrease in applied shear near the sup-ports, given the same design uniform

,

SERVICE BENDING MOMENTFOR CONTINUOUS SLAB

SERVICE BENDING MOMENT

Fig. 4. Reduction in deflections of hollow-core slabs due to continuity at supports.

7NOSl2.9MM@ / :‘t ’

Fig. 5. Cross section details of typical 215 mm (8.5 in.)hollow-core slab (all dimensions in mm).

load. This may become critical, partic-ularly in cases where the design super-imposed live load is high or when thefractional increase in span capacity isunduly large. To overcome this, shearlinks can be placed in cut-open coresnear the supports to enhance the shearcapacity of the slabs, as demonstratedin the test program reported herein.

NUMERICAL EXAMPLESFig. 5 shows the cross section of a

typical 215 mm (8.5 in.) hollow-coreslab [SO N/mm2 (7250 psi) concrete].Tbe slab is 1.2 m (3.94 ft) wide and isreinforced with seven prestressingstrands, each with a diameter of 12.9mm (‘/2 in.) and a concrete cover of 40mm ( 1.6 in.). The elastic modulus of thestrands is 195 kN/mm’ (28.3 ksi) andthe initial prestressing force is 846.3 kN(190 kips), about 65 percent of the ulti-mate tensile strength of the strands.

The self-weight of the slab includ-ing a 65 mm (2.6 in.) structural con-crete topping is 5.56 kN/m (381 lbsper ft). According to manufacturer’sspecifications, the slab can be simplysupported over a span L, of 9 m (29.5ft) for a design superimposed deadload of I .5 kN/m2 (3 1.3 psf) and a su-perimposed live load of 4.0 kN/m2(83.5 psf). Following the British Stan-dard BS 81 IO,” the nominal momentcapacity, M,, would be [ 1.4(5.56 + 1.5x 1.2) + 1.6(4 x 1.2)] x 9 x 9/8 = 182kN-m (134 ft-kips).

Example 1

The hollow-core slab shown in Fig.5 is to be designed as two-end continu-ous. Find the span capacity and the re-quired moment resistance at supports ifa 15 percent moment redistribution isallowed. Assume a design midspanmoment to reach 70 percent of the

L

Fiig. 0. I esr setup ano maln wxumenrarlon.

APPLIED LOAD

R E I N F O R C E M E N

l GAUGE ON CONCRETE 0 GUAGED BARS

SECTION A-A

(INfESTPOSIT,ON,ALL”IOTSIN MY,PRESTRESSIUQS~NDSNDf SHDWN)

SHEAR LINKR6-150MM

8lOMESH\ 2TIOh

(IN CAST POSITION, ALL UNiTS IN HM,PRESfRESSINO STRANDS NOT SHOWN)

Fig. 7. Shear reinforcement in Specimen 3.

Table 1. Reinforcement details in the specimens.

Specimen number Longitudinal reinforcement Shear reinforcement

I B7XS llle\ll. A, = 94.3 I,,,,, N O

2 B 7X5 tnc4t + -IT IO. A, = I’S6 mm ~ N O

3 B7XS me\h + JTIO. A, = 1256 mm‘ 4R6 31 I SO mm

nominal moment capacity M, for 3 sim-ple support design (that is. LY = 0.7).

Solution - From Fig. 2. the v:duesof (IWL and p corresponding to K = ISpercent and (x = 0.7 ure tlLIL = 0.27and /I = 0.92. Thus, the span capacityof the slab is increased by 27 percentto (9 + 0.27 x 9) = I I.4 m (37.5 ft).The required moment of resistance utthe connections is 0.92 x 182 = I67kN-m (123 ft-kips).

Example 2

The hollow-core slab is to span 10m (32.8 ft) by providing moment con-tinuity over both the end supports. Ifthe moment redistribution from the

supports is restricted to 20 percent.find the minimum moment of resis-tunce required of the connections.

Solution - For ;L value of (IL/L =( 10 - 9)/9 = 0. I I. Fig. 2 indicates thatthe minimum value of p is obtainedwhen R = 20 percent. That is, p ,,,,,, =0.66 and the corresponding value of uis 0.58 (< I). Therefore, the minimummoment of resistance to be providedby the connections is 0.66 x IX2 =I20 kN-m (88 ft-kips).

Example 3

If the moment of resistance that canbe developed at the supports is re-stric’ted to I42 kN-m (IO5 ft-kips).

find the maximum span cttptrcity ofthe hollow-core slab shown in Fig. 5.designed 3s two-end continuous overthe supports.

Solution - The value of b is132/lX2 or 0.78. From Fip. 2, themaximum value of tlL/L is obtainedw h e n R = 3 0 percent. Th:tt i s .

‘WL4,,,., = 0.29 and U = 0.89 t< I ).Hence. the m;\ximum span capacity ofthe continuous slab is ( I + 0.39) Y 9 =I I .6 111 (3X. I ftj.

Example 4

Suppose that the hollow-core slab isto spun IO m (32.X ft) and the momentredistribution from the support is rc-stricted to 20 percent ;IS in Ex:rmple 2.but it is to be designed ;ts one-end con-t inuous. Find the minimum moment ofresistance required at the support.

Solution - As in Ex;unple 2. theminimum value of fi is obtained whenR is maximum. For 3 value of r/I./L =0. I I and H = 20 percent. Fig. 3 gives j= 0.99 and 01 = 0.7-t (< I ). Thus. theminitnum moment of resistance re-quired :tt the support is 0.99 Y I82 =I80 kN-m ( I33 ft-kips).

DEVELOPMENT OFMOMENT CONTINUITY

AND EFFECT OF SHEAR

Moment continuity c;m be realizedby providing longitudinal steel rein-forcement over the supports while theshear capacity of the hollow-core slabscan be enhanced by placing shearlinks in cut-open cores ne;tr the con-nections. These aspects are cxnminedin u test propram on the deformationcharacteristics md ultimute lontl U-pacity of connection specimens.

Test Program

Full size. Crude SO (7252 psi) hol-low-core shtb components were usedto make the connection specimens thatsimulate the hogging region over thesupports of ;t continuous slab. Thecomponents are 215 mm thick. 1.2 mwide and 1.X 111 Ion:! (X.5 in.. 3.9 ft.and 5.9 ft). with cross-scctionul detailsas shown in Fip. 5.

For each specimen, two such slltbcomponents were rested on 3 hrmi el-

ement with a bearing width of 100 mm(4 in.). Reinforcement was then placedon top of the hollow-core slabs andthis was followed by the casting ofGrade 45 (6530 psi) topping concrete,with a maximum aggregate size of10 mm (0.4 in.).

Fig. 6 shows a specimen in its testposition. The specimens were cast inthe inverted position. A total of threespecimens were prepared. Specimen 1was designed to carry an ultimate mo-ment of 145 kN-m (I 07 ft-kips) (aswould be required in Example 3)while Specimens 2 and 3 were de-signed for an ultimate moment of 190kN-m (I 40 ft-kips) (as would be re-quired in Example 4).

A layer of steel mesh (B785) withIO and 8 mm (j/x and ‘l16 in.) highyield steel bars welded in a grid withspacing of 100 and 200 mm (3.9 and7.8 in.), respectively, was provided inSpecimen 1. The B785 mesh and anadditional 4TlO bars [4 number of ‘/xin. (9 mm) deformed high yield bars]were used in Specimen 2.

The longitudinal steel in the toppingconcrete of Specimen 3 was the sameas in Specimen 2, but shear reinforce-ment consisting of 6 mm (‘/a in.) diam-eter mild steel closed links at 150 mm(6 in.) spacing was also provided intwo rows of cores that were cut openand later filled with concrete, asshown in Fig. 7. Reinforcement detailsin the specimens are summarized inTable 1. The concrete cover to themain reinforcement was 25 mm (1 in.)in all specimens.

The specimens were tested underthree-point loading, as shown in Fig.6. This test setup closely representsthe portion of a continuous span underhogging bending. To study the effectof shear, the shear span was decreasedfrom 1.70 m (5.58 ft) in Specimen 1 to1.26 m (4.13 ft) to induce high shearforce in Specimens 2 and 3.

Strains in the mesh reinforcementwere measured using 10 mm (0.4 in.)electrical strain gauges. Strain gaugesof 60 mm (2.4 in.) in length were alsoplaced on the concrete surface. Linear .variable displacement transducers(LVDTs) were used to measure de-flections of the specimens. The loca-tions of the key instrumentation on the

(a) Specimen 1

Fig. 8. Specimens after test.

(c) Specimen 3

Table 2. Ultimate load of the specimens.

~ Concrete strength(Nlmm’) applied

Ultimate I Ultimatemoment moment

i west

;g' ~b;i:

1.09~ +~~-1 9 0 . 3 1.07

Note: I N/mm’= 145 PSI, I kN = 224.8 lb\, I kN-m = 0.71753 if-klp\

Test Results and Discussion relatively small and failure was causedby bending moments. Fig. 8(a) shows

Mode of Failure - In Specimen 1, Specimen 1 after failure.which was tested under a shear span of The shear span was reduced to 1.26

specimens are shown in Fig. 6. 1.70 m (5.58 ft), the shear stress was m (4.13 ft) for Specimen 2 in order to

r

flrst cracking load,

0 I

0 1 0 2 0 3 0 4 0

Displacement (mm)

(a) Specimen 1

1 0 2 0

Displacement (mm)

(b) Specimen 2

3 0 4 0

400 , 1

4 30025

B-0 200

B=Ea 100

0 1 0 2 0

Displacement (mm)

3 0 4 0

(c) Specimen 3

introduce high shear. When the ap- The diagonal cracks stopped. open-plied load reached 302 kN (67.9 kips), ing up upon reaching the location ofdiagonal cracks occurred suddenly. At the steel reinforcement. Thereafter,this juncture, damage to the concrete the applied load picked up again andcaused by the cracks was quite severe, the flexural cracks at the interface be-As the cracks widened, the applied tween the precast slab componentsload started to drop. However, the and the supporting beam started tospecimen did not fail immediately. wid& excessively. The specimen fi-

nally failed in flexure at a higherload. Fig. 8(b) shows Specimen 2after the test.

Specimen 3 was tested under thesame test setup as Specimen 2. UnlikeSpecimen 2, diagonal cracks did notoccur in Specimen 3, indicating thatthe shear links provided were effectivein resisting shear stress. The final fail-ure was caused by the applied bendingmoments. Fig. 8(c) shows Specimen 3after the test.

Load vs. displacement relations- Displacements at the center of thespecimens were obtained from LVDTreadings and the relationships be-tween the applied loads and displace-ments are shown in Figs. 9(a), (b) and(c) for Specimens I, 2 and 3, respec-tively. The relationships show thatbefore cracking, displacements in-creased nearly linearly with an in-crease in load. After cracking hasoccurred, the slope of the load-displacement curve decreases and thecurve flattens out just before reachingthe ultimate load.

During the testing of Specimen 2,when diagonal cracks opened at theload level of 302 kN (67.9 kips), therewas a sudden drop in the applied load.Although the applied load could beincreased further before Specimen 2

collapsed, the increase in load was notsignificant.

Load vs. steel strain relations -Strains of steel reinforcements weremeasured at Section 1 (refer to Fig, 6)close to the section of maximumbending moment. There were threegauges from which the strains wereobtained and plotted against the ap-plied moments at the section in Figs,10(a), (b) and (c) for Specimens 1, 2and 3, respectively. The measuredstrains obtained from the threegauges in each specimen were veryclose to each other.

Before cracking, the relations werenearly linear. The strains increasedfurther as cracks developed with rela-tively small load increases and thiswas followed by a hardening phase inwhich the strains increased almostlinearly with the applied load until

near to failure. The specimens even-tually collapsed when the reinforce-ment fractured.

Load vs. concrete compressive

strain relations - Concrete strainswere measured on the extreme com-pre5sive surface at Section I (refer toFig. 6). Three gauges were used forSpecimen 1 and five gauges for theothers. Figs. I I(a). (b) and (c) showthe relations between the applied loadsand the measured strains for Speci-m e n s I .2 and 3, respectively.

The load vs. concrete strain curvesof Specimens I and 3 show a linear re-lation at the beginning until crackingoccurred. This was followed by acurved portion in which the strains in-creased with a small increase in load,and a hardening phase in which thestrains increased again in an approxi-mately linear manner with load.

The load vs. concrete strain relationof Specimen 2 is different from thoseof Specimens I and 3 at the high loadrange prior to failure. In this speci-men, diagonal cracks appeared andwidened quickly when the appliedload reached 302 kN (67.9 kips), cor-responding to a bending moment ofabout IS0 kN-m ( 1 IO.6 ft-kips) at Sec-tion I. When the load was further in-creased, the strain gauges registered areduction in concrete compressivestrain. This was probably caused by achange from a force transfer pathdominated by bending to one domi-nated by shear.

When the diagonal cracks devel-oped further, the dowel action of thereinforcement in the specimens con-tributed to shear resistance. The re-quired shear force for the specimen tobreak off along the diagonal crack wastoo high and the bending capacity wasreached first instead.

Ultimate moment capacity -The ultimate loads and moments atwhich the specimens failed are listedin Table 2. The measured ultimatebending moments are those for thecritical section at the hollow-coreslab and beam interface. Toppingconcrete strengths at 28 days and onthe day of testing are also given inTable 2. They were average valuesobtained from three 100 mm (4 in.)cubes.

The ultimate moment capacities ofthe specimens were calculated usingconventional reinforced concrete the-ory with the strain profile of the criti-cal section and the corresponding sim-

4 300cz2 200gE4 100

0 gauge1 + gauge2 A gauge3

Strain in continuity steel (x 1 U6 mm/mm)

(a) Specimen 1

4 3 0 025B-0 2 0 0-0g::a 100

Strain in continuity steel (x IO” mm/mm)

(b) Specimen 2

00 2000 4000 6000 6000 10000 12000

Strain in continuity steel (xl C6 mm/mm)

(c) Specimen 3

Fig. 10. Load-steel strain relations.

plified stress block as shown in Fig. The calculated ultimate load capaci-12. An average tensile strength of 634 ties are compared to observed valuesN/mm’ (92 ksi) for the longitudinal re- in Table 2. In general, the calculatedinforcement and a concrete cube values, M,,,,, are very close to the mea-strength of 45 N/mm? (6530 psi) were sured values, M,,,,.assumed in the calculations. Effect of shear - In practice, the

-2500 -2000 -1500 -1000 -500 0

Concrete compressive strain (x 1 D6 mm/mm)

(a) Specimen 1

a 300

E.

B-0 200upB

a

100

16

0-2500

gauge-2000 -1500 -1000 -500

Concrete compressive strain (x 1 rY6 mm/mm)

(b) Spec imen 2

400I

4 300 -

5

x-0 200 -B=Ba 100 -

- & g a u g e 7 egauge8 egauge9 -&gauge10 -tgaugei

-;500 -2000 -1500 -1000 -500 0Concrete compressive strain (x 1 V6 mm/mm)

(c) Specimen 3

Fig. 11. Load-concrete strain relations.

effect of shear may become critical at the superimposed dead load is 1.5the support if the superimposed load is kN/m? (31.3 psf) in addition to a deadheavy and the span increase caused by load due to self-weight of 5.56 kN/mproviding continuity is large. (381 Ib/ft). These would give a fac-

Consider the case where the design toTed uniform load of W = 29.5 kN/mlive load is IO kN/m’ (208.8 psf) and (2.02 kips/ft) according to BS 8 I IO.”

With a nominal moment capacity, My,of I82 kN-m (I 34 ft-kips), the 215mm (8.5 in.) prestressed hollow-coreslab shown in Fig. 5 would be able tospan a maximum of 7.0 m (23.0 ft)when considering simply supportedcondit ions.

If moment resistant connectionswith a design capacity of I90 kN-m(140 ft-kips) as provided in Specimens2 and 3 are introduced at both ends ofthe slab (that is, p = 190/l 82 = I .O4)and assuming a midspan momentequal to M,, (that is, 01 = I). Fig. 2gives the percentage of moment redis-

tribution as 23.6 percent and the frac-tional increase in span capacity as0.43. This translates to a span capac-ity, Li. Of 10.0 m (32.8 ft).

Under the above conditions, theshear force at the supports would beWLi/2 or I48 kN (33.2 kips). Thus,the moment-to-shear ratio at the supports would be lc)O/l48 or I .28 m(4.21 ft). The test arrangement forSpecimens 2 and 3 approximated thissituation.

The nominal shear capacity of Spec-imen 2 based on an average web widthof 688 mm (27.1 in.), a longitudinalsteel reinforcement provided in thetopping concrete. A,. of I256 mm!( I .95 sq in.). an effective depth to re.inforcement. (i. of 250 mm (9.8 in.).and a maximum concrete strength of40 N/mm’ (5800 psi). is I61 kN (36.2kips) according to BSXI IO.” This isonly slightly less than the theoreticalshear force of 19011. I6 or I64 kl$(36.8 kips) that would result in a flex.Ural failure of Specimen 2 at the criti-cal section.

It was therefore expected that Speci.men 2 would suffer shear distress. Inthe test, the shear force that resulted inextensive shear cracking was IS 1 kk(34.0 kips). The specimen, however.finally failed in tlexure under a shearforce of I80 kN (40.5 kips).

To enhance shear capacity, rein.forcement consisting of two 6 mm (‘Iin.) diameter mild steel closed links aiI50 mm (6 in.) spacing was providedin Specimen 3. This specimen did neexperience any diagonal cracking anrfailed directly under bending, indicating that the method used was effectivein improving the shear behavior at thiconnection.

/215MM THICK H/C SLAB ,

OMM

215M

0.0035 0.67 fccu

STRAIN PROFILESIMPLIFIED

S T R E S S B L O C K

Fig. 12. Strain and stress profile for section at ultimate load.

CONCLUSIONS REFERENCESIn this study, charts for the design of

one- and two-end continuous hollow-core slabs were developed. Thesecharts enable the required moment ca-pacity at supports and the moment re-distribution from supports to be deter-mined for a desired increase in spancapacity. Tests were carried out todemonstrate the effectiveness of con-nections in resisting bending momentand shear force.

1. PCI Manual for the Design of Hollow-Core Slabs, Precast/Prestressed Con-crete Institute, Chicago, IL, 1988,174 pp.

2. Pisanty, A., “Shear Strength of Ex-truded Hollow-Core Slabs,” Materialsand Structures, Research and Testing(RILEM, Paris), V. 25, No. 148, May1992, pp. 224-230.

Within the scope of the study, it canhe concluded that:

1. Designing for continuity leads toaa increase in span capacity of hol-low-core slabs with reduced deflec-tions in general.

2. Moment continuity can be effec-tively provided by placing longitudi-nal steel reinforcement in the toppingconcrete over the connection.

3. Shear distress at connections canbe effectively arrested by providingshear links in cut-open cores of theslabs .

3. Ueda, T., and Stitmannaithum, B.,“Shear Strength of Precast PrestressedHollow Slabs With Concrete Top-ping,” ACI Structural Journal, V. 88,No. 4, July-August 199 I, pp. 402-410.

4. Mejia-McMaster, J. C., and Park, R.,“Tests on Special Reinforcement forthe End Support of Hollow-CoreSlabs,” PC1 JOURNAL, V. 39, No. 5,September-October 1994, pp. 90-105.

5. Stanton, J. F., “Proposed Design Rulesfor Load Distribution in Precast Con-crete Decks,” ACI Structural Journal,V. 84, No. 5, September-October1987, pp. 371-382.

ACKNOWLEDGMENT

6. Stanton, J. F., “Response of Hollow-Core Slab Floors to ConcentratedLoads,” PC1 JOURNAL, V. 37, No. 4,July-August 1992, pp. 98- 113.

L & M Precast Pte. Ltd. (Singapore)kindly donated the hollow-core slabcomponents for the experiments. Thetests were carried out in the StructuralEngineering Laboratory of the Na-tional University of Singapore. Theauthors wish to thank all the techni-cians for their assistance in the work.

I. Aswad, A., and Jacques, F. J., “Behav-ior of Hollow-Core Slabs Subject toEdge Loads,” PC1 JOURNAL, V. 37,No. 2, March-April 1992, pp. 72-84.

8. Scott, N. L., “Performance of PrecastPrestressed Hollow-Core Slab WithComposite Concrete Topping,” PC1JOURNAL, V. 18, No. 2, March-April1973, pp. 64-77.

9. Rosenthal, I., “Full Scale Test of Con-tinuous Prestressed Hollow-CoreSlab,” PC1 JOURNAL, V. 23, No. 6,May-June 1978, pp. 74-8 1.

10. “Ductility of Tie Connections for Con-crete Components in Precast Struc-tures,” FIP Technical Report, Fed&a-tion Intemationale de la Precontrainte,London, October 1992.

11. “British Standard, Structural Use ofConcrete, Part 1 - Code of Practicefor Design and Construction,” BritishStandards Institution, BS8110: Part 1:1985, Issue 2, London, May 1989.

12. AC1 Committee 3 18, “Building CodeRequirements for Reinforced Concrete(AC1 3 18-89) and Commentary,”American Concrete Institute, Detroit,MI, 1989.

APPENDIX - NOTATION

A, = area of longitudinal tensile re-inforcement

b = width of member

d = effective depth to longitudinalreinforcement

dL/L= fractional increase in maxi-mum span capacity

h = overall depth of memberL, = maximum span capacity of

uniformly loaded hollow-coreslabs, assuming simply sup-ported conditions

L, = maximum span capacity ofuniformly loaded hollow-coreslabs, assuming continuityover supports

A4, = design support momentMf = fixed end moment, assuming

elastic conditionsM, = nominal moment capacity of

hollow-core slabsR = degree of moment redistribu-

tion from supports

W = design uniform load01= ratio of design midspan mo-

ment to nominal moment ca-pacity of hollow-core slab

/!l= ratio of design support momentto nominal moment capacity ofhollow-core slab