Designing Hollow-Core Slabs for Continuity

82

Kiang-Hwee Tan Dr.Eng., P.Eng. (S)

Senior Lecturer Department of Civil Engineering National University of Singapore

Singapore

Lian-Xiang Zheng, Ph.D. Former Research Scientist Department of Civil Engineering National University of Singapore Singapore

P. Paramasivam Ph.D., P.Eng. (S)

Professor Department of Civil Engineering National University of Singapore

Singapore

Precast, prestressed hollow-core slabs are usually used as part of a simple span system. However, in a multispan floor slab system, designing for continuity over supports leads to increased span capacity, improved structural integrity and savings in materials. In this paper, formulas relating the fractional increase in span capacity, percentage of moment redistribution from supports and design midspan and support moments of hollow-core slabs are derived theoretically. These relations are put in a graphical form to facilitate the design of connections in continuous hollow-core slabs, the use of which is illustrated by several examples. To demonstrate the development of full continuity at the supports, three specimens, each consisting of two hollow-core slab components on a supporting beam element and connected by in-situ structural concrete topping, were tested under three-point loading to simulate the portion of a continuous span under hogging bending. The test results show that the specimens did achieve the ultimate load-carrying capacities calculated using conventional reinforced concrete theory. Under heavy shear conditions, vertical links placed in the cut-open cores were found to be effective in improving the shear behavior of the specimens.

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ULTIMATE BENDING MOMENT FOR SIMPLY SUPPORTED SLAB

L;

Lo

ULTIMATE BENDING MOMENT FOR CONTINUOUS SLAB

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

P recast, prestressed hollow-core slabs are the most common ly used precast concrete compo­

nents in low and high rise building construction. They are usually used as simply supported elements with struc­tural topping concrete provided over supports to serve as structural integrity ties and diaphragm connections.'

In the past two decades, a significant amount of research has been carried out to investigate the shear resistance of hollow-core slabs, 2.3 special rein­forcement for end supports ,' slab re­sponse to concentrated load,5·

6 behavior under edge loads,7 and composite ac­tion with topping concrete.8 However, very Little published information exists on continuity in hollow-core slabs and this information was limited to the use of separate dowel bars grouted into drilled holes in precast slabs,9 and the use of prestressing strands in the cores filled with concrete.'"

Although the PCI Hollow-Core De­sign Manual ' acknowledges that continu­ity over supports results in better control of superimposed load deflections and a lower requirement for positive moment capacity, this is usually not exploited in hollow-core slab design, mainly because of the lack of design aids.

The main objective of this study is to develop charts for the design of connec­tions in continuous hollow-core slab construction. A set of formulas relating the increase in span capacity of hollow-

January-February 1996

core slabs , moment redistribution al­lowed at supports, and the design midspan and support moments of the slab, is first derived theoretically. These relations are then shown in a graphical form to facilitate the design process.

Several examples are given to illus­trate the use of the design charts for both one-end and two-end continuous slab construction. Also, tests were car­ried out on three specimens simulating connections over supports to demon­strate the development of moment continuity and to study the effect of shear force due to increased span.

BASIS FOR DESIGN CHARTS

As indicated earlier, two major bene­fits result from designing for moment continuity over supports in hollow-core slab construction . First, this practice leads to an increase in the span capacity of hollow-core slabs for a given design load. Second, it helps to reduce the de­flections of the slabs. The first aspect is employed in the development of design charts for the design of moment conti­nuity over supports as follows.

Design for Two-End Continuous Span

Fractional Increase in Span Ca­pacity - In hollow-core slab design, the span capacity, L0 , corresponding to

a safe superimposed load is usually specified by the manufacturers or in handbooks for simply supported end conditions . Given the self-weight of the slab, the design uniform load, W, on the slab can be established and the nominal moment capacity, M5 , of the slab corresponding to the span is :

M =l_WL2

s 8 0 (1)

Suppose that the same slab was de­signed as a two-end continuous slab with ultimate support moment Me at each end (see Fig. 1) and midspan mo­ment aM5 , where a is the ratio of the design midspan moment to the nomi­nal moment capacity of the hollow­core slab. Here, the coefficient a de­notes the degree to which the nominal moment capacity of the slab is being utilized in continuous construction and has a value between 0 and 1 inclusive. For the same design uniform load W, the continuous slab would be able to span a length L; given by:

1 2 aMs +Me = g WL; (2)

Introducing {3 = Me!Ms and eliminat­ing W from Eqs. (1) and (2) leads to:

(3)

It is seen from Eq. (3) that if a+ {3 > 1, L; will be Larger than L0 ; and an in­crease in span is achieved.

Under e lastic conditions , however, the fixed end moments wou ld have been M1 where:

Thus, the moment M1 at the support has been assumed to be redistributed at ultimate such that:

where R is the percentage of moment redistribution from the supports , of which a value of up to 30 percent is usually allowed in design.

Substituting Eqs. (4) and (5) into Eq. (2) and rearranging for L; gives:

L = 24aMS I (1+2R)W

(6)

83

0.90

" :;. ·o ~ 0.80 rl c " E ~ 0.70 ;;; c: E 0

5 0.60 iii E 0 E lij 0.50 g. " ~

0.40

0%

0.8

0.6

5% 10% 15% 20% 25% 30%

Moment Redistribution from Supports(%)

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

1.3 1.2

1.0

" iE 0.90 u .. a. .. u

c 0.9

" E 0.80 0

E Iii c: ·e 0.8 0 z c 0.70

" E 0 E p =0.7 c: .. a. .. 0.60 " i

5% 10% 15% 20% 25% 30%

Moment Redistribution from Support, R(%)

Fig. 3. Design chart for one-end continuous span.

From Eq. (1):

L = ~ 8Ms 0 w (7)

Hence, the fractional increase in span capacity can be expressed as:

84

24aM5

_dL = _L,_: -_L_o = -'-'-(l-==+=2=R=-) W _ _ 1 L Lo ~8~s

_ ~ 3a _ 1 1+2R

(8)

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

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

M = 2(1- R)aMS c 1+2R

or, noting that f3 = MJ M,:

f3 = 2(1- R) a (I+ 2R)

(9)

(10)

Eqs . (8) and (10), which respec-

tively relate the fractional increase in span dL/L and the ratio f3 to the per­centage of moment redistribution from supports R and the ratio a , are ex­pressed graphically in Fig . 2. The chain lines and solid lines shown in the figure indicate combinations of R and a for specified values of dLIL and {3, respectively.

For the case w here a = 1 and R ~ 0.3, it is seen from Fig. 2 that the span capacity of hollow-core slabs can be increased by between 37 and 70 percent. If the full positive moment capacity of slab is not used (that is, a < 1), then the fractiona l increase in span capacity due to the provision of continuity at the supports would be correspondingly less.

Design for One-End Continuous Span

It can be shown in a similar manner that if the slab is designed as a one­end continuous s lab , the increased span capacity, L;, would be given by:

ll= ~a+/3 (11 ) L

0 2

where L 0 is the span capacity for a simple-support slab design, and a and f3 are the ratios of the design midspan moment and support moment at the continuous end , respectively , to the value of M 5 , which, as defined earlier, is the nominal moment capacity with respect to L0 .

The fractional increase in span ca­pacity, dLIL, and the value of f3 can be shown to be related to a and R by:

dL _ L;-L0 -~a l ------ ---L L

0 l+R

( 12)

and

f3 = 2(1- R) a (1+R) (1

3)

Eqs. (12) and (13) are depicted graphically in Fig. 3. An increase in span capacity is achieved only if a > ( I + R)/2 . For the case where a = 1 and R ~ 30 percent, the increase in span capacity varies from 24 percent to 41 percent.

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Use of Design Charts

The design charts given in Figs. 2 and 3 allow the value of f3 and, hence, the required moment resistance Me at the connection and the corresponding increase in span capacity of the slab to be determined from specified values of Rand a. Once the value of Me is determined, the required reinforce­ment ratio, A,fbd, at the connections over the supports can be worked out from conventional section analysis or from design aids for flexure .

The obtained section should be checked for rotational capacity or duc­tility (as required for moment redistri­bution) in the usual manner. Accord­ing to BS 8110" and ACI, '2 this is satisfied, respectively, by ensuring that the limit on the neutral axis depth at ultimate or the reinforcing index is not violated.

Other Considerations

Deflections- In general, the provi­sion of moment resistant connections at supports leads to reduction in de­flections of hollow-core slabs, as is evident from the bending moment dia­gram shown in Fig. 1. The reduction in deflections due to service loads is even more significant, as can be de­duced from the bending moment dia­gram illustrated in Fig. 4 for the case of a two-end continuous span.

Both the BS 8110'' and ACI '2 allow deflections to be checked using span­to-depth ratios in lieu of deflection calculations. The allowable ratio is 20 for simply supported slabs. The BS 811 0" specifies a ratio of 26 for con­tinuous slabs , while according to ACI, 12 the allowable span-to-depth ratio is 28 for two-end conti nuous slabs and 24 for one-end continuous slabs. Thus, it appears that deflection would not pose a problem if the frac­tional increase in span is less than 0.4 in the case of two-end continuous span and 0.2 in the case of one-end continu­ous span.

Effect of shear - The increase in span capacity of the hollow-core slab by providing moment continuity at supports would be accompanied by an increase in applied shear near the sup­ports, given the same design uniform

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\ ~

SERVICE BENDING MOMENT FOR CONTINUOUS SL AB

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

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

load. This may become critical , partic­ularly in cases where the design super­imposed live load is high or when the fractional increase in span capacity is unduly large. To overcome this, shear links can be placed in cut-open cores near the supports to enhance the shear capacity of the slabs, as demonstrated in the test program reported herein.

NUMERICAL EXAMPLES Fig. 5 shows the cross section of a

typical 215 mm (8.5 in.) hollow-core slab [50 N/mm2 (7250 psi) concrete]. The slab is 1.2 m (3.94 ft) wide and is reinforced with seven prestressing strands, each with a diameter of 12.9 mm Ch in.) and a concrete cover of 40 mm (1.6 in.). The elastic modulus of the strands is 195 kN/mm2 (28.3 ksi) and the initial prestressing force is 846.3 kN (190 kips), about 65 percent of the ulti­mate tensile strength of the strands.

The self-weight of the slab includ­ing a 65 mm (2.6 in.) structural con­crete topping is 5.56 kN/m (381 lbs per ft). According to manufacturer's specifications, the slab can be simply supported over a span L 0 of 9 m (29.5 ft) for a design superimposed dead load of 1.5 kN/m2 (31.3 psf) and a su­perimposed live load of 4.0 kN/m 2

(83.5 psf) . Following the British Stan­dard BS 8110, " the nominal moment capacity, M5 , would be [1.4(5.56 + 1.5 X 1.2) + 1.6(4 X 1.2)) X 9 X 9/8 = 182 kN-m (134ft-kips).

Example 1

The hollow-core slab shown in Fig. 5 is to be designed as two-end continu­ous. Find the span capacity and the re­quired moment resistance at supports if a 15 percent moment redistribution is allowed. Assume a design midspan moment to reach 70 percent of the

85

• GAUGE ON CONCRETE 0 GUAGED BARS

SECTION A-A

( lN TEST POSITION, ALL UNITS IN MM 1 PRESTRESSING STRANDS NOT SHOWN)

Fig . 6. Test setup and main instrumentation.

rS_HEAR LINK R6·150MM

8 IOMESH\ 2TIO';~ ;'2TIO

5 '} t< 5 - '- r <: - ~ '-- - -,: ;:-:· 2

.A .A

I 1200 I

I IN CAST POSITION, ALL UNITS IN MM, PRESTRESSING STRANDS NOT SHOWN)

Fig. 7. Shear reinforcement in Specimen 3.

Table 1. Reinforcement details in the specimens.

Specimen number Longitudinal reinforcement Shear reinforcement 1--- -

I B785 mesh, A, = 943 mm' No -

2 B785 mesh+ 4TIO, A, = 1256 mm' I No -

3 B785mesh+4TIO, A, = 1256mm' I 4R6 at 150 mm

Note: I mm = 0.0394 in. ; I mm2 = 0.00155 sq in .

nominal moment capacity Ms for a sim­ple support design (that is, a= 0.7).

Solution - From Fig. 2, the values of dL/L and f3 corresponding toR= 15 percent and a= 0.7 are dL/L = 0.27 and f3 = 0.92. Thus, the span capacity of the slab is increased by 27 percent to (9 + 0.27 x 9) = 11.4 m (37 .5 ft). The required moment of resistance at the connections is 0.92 x 182 = 167 kN-m (123 ft-kips).

Example 2

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

86

supports is restricted to 20 percent, find the minimum moment of resis­tance required of the connections.

Solution- For a value of dL/L = ( I 0 - 9)/9 = 0.11 , Fig. 2 indicates that the minimum value of f3 is obtained when R = 20 percent. That is, f3min = 0.66 and the corresponding value of a is 0.58 (< 1). Therefore, the minimum moment of resistance to be provided by the connections is 0.66 x 182 = 120 kN-m (88ft-kips).

Example 3

If the moment of resistance that can be developed at the supports is re­stricted to 142 kN-m (105 ft-kips) ,

find the maximum span capacity of the hollow-core slab shown in Fig. 5, designed as two-end continuous over the supports.

Solution - The va lue of f3 is 142/182 or 0 .78 . From Fig. 2, the maximum value of dL/L is obtained when R = 30 percent. That is , (dLIL)max = 0.29 and a= 0.89 (< 1). Hence, the maximum span capacity of the continuous slab is (I + 0.29) x 9 = 11 .6 m (38. 1 ft) .

Example 4

Suppose that the hollow-core slab is to span 10 m (32.8 ft) and the moment redistribution from the support is re­stricted to 20 percent as in Example 2, but it is to be designed as one-end con­tinuous. Find the minimum moment of resistance required at the support.

Solution - As in Example 2, the minimum value of f3 is obtained when R is maximum. For a value of dLIL = 0.11 and R = 20 percent, Fig. 3 gives f3 = 0.99 and a= 0.74 (< 1). Thus, the minimum moment of resistance re­quired at the support is 0.99 x 182 = 180 kN-m (133ft-kips).

DEVELOPMENT OF MOMENT CONTINUITY

AND EFFECT OF SHEAR

Moment continuity can be realized by providing longitudinal steel rein­forcement over the supports while the shear capacity of the hollow-core slabs can be enhanced by placing shear links in cut-open cores near the con­nections. These aspects are examined in a test program on the deformation characteristics and ultimate load ca­pacity of connection specimens.

Test Program

Full size, Grade 50 (7252 psi) hol­low-core slab components were used to make the connection specimens that simulate the hogging region over the supports of a continuous slab. The components are 215 mm thick, 1.2 m wide and 1.8 m long (8.5 in. , 3.9 ft, and 5.9 ft), with cross-sectional details as shown in Fig. 5.

For each specimen, two such slab components were rested on a beam el-

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ement with a bearing width of I 00 mm (4 in.). Reinforcement was then placed on top of the hollow-core slabs and thi s was followed by the casting of Grade 45 (6530 psi) topping concrete, with a maximum aggregate size of 10 mm (0.4 in .).

Fig. 6 shows a specimen in its test position . The specimens were cast in the inverted position. A total of three specimens were prepared. Specimen 1 was designed to carry an ultimate mo­ment of 145 kN-m (107 ft-kips) (as wou ld be req uired in Examp le 3) whi le Specimens 2 and 3 were de­signed for an ultimate moment of 190 kN-m (140ft-kips) (as would be re­qu ired in Example 4).

A layer of steel mesh (8785) with 10 and 8 mm e ts and 5/ 16 in .) high yield steel bars welded in a grid with spacing of 100 and 200 mm (3 .9 and 7.8 in.), respectively, was provided in Specimen 1. The 8 785 mesh and an additional 4Tl0 bars [4 number of 3/s in. (9 mm) deformed high yield bars] were used in Specimen 2.

The longitudinal steel in the topping concrete of Specimen 3 was the same as in Specimen 2, but shear reinforce­ment consisting of 6 mm Cl4 in .) diam­eter mild steel closed links at 150 mm (6 in.) spacing was also provided in two rows of cores that were cut open and later filled with concrete , as shown in Fig. 7. Reinforcement detai ls in the specimens are summarized in Table 1. The concrete cover to the main reinforcement was 25 mm (1 in.) in all specimens.

The specimens were tested under three-point loading, as shown in Fig. 6. This test setup closely represents the portion of a continuous span under hogging bending. To study the effect of shear, the shear span was decreased from 1.70 m (5.58 ft) in Specimen 1 to 1.26 m ( 4.13 ft) to induce high shear force in Specimens 2 and 3.

Strains in the mesh reinforcement were measured using 10 mm (0.4 in.) electrical strain gauges. Strain gauges of 60 mm (2.4 in.) in length were also placed on the concrete surface. Linear variable displacement transducers (L VDTs) were used to measure de­flections of the specimens. The loca­tions of the key instrumentation on the specimens are shown in Fig. 6.

January-February 1996

(a) Specimen 1

(b) Specimen 2

(c) Specimen 3

Fig. 8. Specimens after test.

Table 2. Ultimate load of the specimens.

Concrete strength Maximum I Ultimate Ultimate (N/mm') applied moment moment

'----Specimen Day of load Mtest Meal. M test

--number 28 days test (kN) (kN-m) (kN-m) M eal.

-

I 46.5 46.3 185.5 148.9 144.5 1.03

2 44. 1 42. 1 359.3 207.7 190.3 1.09

3 44.9 47.0 35 1.9 203 .9 190.3 1.07

Note: I N/mm' = 145 ps1; I kN = 224.8 lbs; I kN-m = 0.73753 ft-k1ps.

Test Results and Discussion

Mode of Failure - In Specimen 1, which was tested under a shear span of 1.70 m (5.58 ft), the shear stress was

relatively small and failure was caused by bending moments. Fig. 8(a) shows Specimen 1 after failure.

The shear span was reduced to 1.26 m ( 4.13 ft) for Specimen 2 in order to

87

400

~ z 300 6 • % • "0 t1l LVDT .3 200 "0 ~ 0. ~ 100 first cracking load,

90.4 kN

0 0 10 20 30 40

Displacement (mm)

(a) Specimen 1

400

z 300 6 "0 t1l .Q 200 "0 ~ :.___sz_ first cracking load, 0. ~ 100 130.1 kN

0 0 10 20 30 40

Displacement (mm)

(b) Specimen 2

400 ~------------------------------------------~

z 300 6 ~ .Q 200 "0 .(}1 0. ~ 100

'V first cracking load, -- 135.1 kN

0 ~----------~----------~----------~--------~ 0 10 20

Displacement (mm)

(c) Specimen 3

30 40

Fig . 9. Load-displacement relations.

introduce high shear. When the ap­plied load reached 302 kN (67.9 kips), diagonal cracks occurred suddenly. At this juncture, damage to the concrete caused by the cracks was quite severe. As the cracks widened, the app lied load started to drop. However, the specimen did not fail immediately.

88

The diagonal cracks stopped open­ing up upon reaching the location of the steel reinforcement. Thereafter, the applied load picked up again and the flexural cracks at the interface be­tween the precast slab components and the supporting beam started to widen excessively. The specimen fi -

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

Specimen 3 was tested under the same test setup as Specimen 2. Unlike Specimen 2, diagonal cracks did not occur in Specimen 3, indicating that the shear links provided were effective in resisting shear stress. The final fail­ure was caused by the applied bending moments. Fig. 8(c) shows Specimen 3 after the test.

Load vs. displacement relations - Displacements at the center of the specimens were obtained from LVDT readings and the relationships be­tween the applied loads and displace­ments are shown in Figs. 9(a), (b) and (c) for Specimens 1, 2 and 3, respec­tively. The relationships show that before cracking , displacements in­creased nearly linearly with an in­crease in load . After cracking has occurred, the slope of the load­displacement curve decreases and the curve flattens out just before reaching the ultimate load.

During the testing of Specimen 2, when diagonal cracks opened at the load level of 302 kN (67.9 kips), there was a sudden drop in the applied load. Although the applied load could be increased further before Specimen 2 collapsed, the increase in load was not significant.

Load vs. steel strain relations -Strains of steel reinforcements were measured at Section 1 (refer to Fig. 6) close to the section of maximum bending moment. There were three gauges from which the strains were obtained and plotted against the ap­plied moments at the section in Figs. lO(a), (b) and (c) for Specimens 1, 2 and 3, respectively . The measured strains obtained from the three gauges in each specimen were very close to each other.

Before cracking, the relations were nearly linear. The strains increased further as cracks developed with rela­tively small load increases and this was followed by a hardening phase in which the strains increased almost linearly with the applied load until near to failure. The specimens even­tually collapsed when the reinforce­ment fractured .

Load vs. concrete compressive

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strain relations - Concrete strains were measured on the extreme com­pressive surface at Section l (refer to Fig. 6). Three gauges were used for Specimen l and five gauges for the others. Figs. ll(a), (b) and (c) show the relations between the applied loads and the measured strains for Speci­mens l , 2 and 3, respectively.

The load vs . concrete strain curves of Specimens 1 and 3 show a linear re­lation at the beginning until cracking occurred . This was followed by a curved portion in which the strains in­creased with a small increase in load, and a hardening phase in which the strains increased again in an approxi­mately linear manner with load.

The load vs . concrete strain relation of Specimen 2 is different from those of Specimens 1 and 3 at the high load range prior to fai lure . In this speci­men, diagonal cracks appeared and widened quickly when the app lied load reached 302 kN (67.9 kips), cor­responding to a bending moment of about 150 kN-m (110.6 ft-kips) at Sec­tion 1. When the load was further in­creased, the strain gauges registered a reduction in concrete compressive strain. This was probably caused by a change from a force transfer path dominated by bending to one domi­nated by shear.

When the diagonal cracks devel­oped further, the dowel action of the reinforcement in the specimens con­tributed to shear resistance. The re­quired shear force for the specimen to break off along the diagonal crack was too high and the bending capacity was reached first instead.

Ultimate moment capacity -The ultimate loads and moments at which the specimens failed are listed in Table 2. The measured ultimate bending moments are those for the critical section at the hollow-core slab and beam interface. Topping concrete strengths at 28 days and on the day of testing are also given in Table 2. They were average values obtained from three 100 mm (4 in .) cubes.

The ultimate moment capacities of the specimens were calculated using conventional reinforced concrete the­ory with the strain profile of the criti­cal section and the corresponding sim-

January-February 1996

400r------------------------------------------,

z 300 ::::. "0 (I)

.Q 200 "0 -~ 0. c. c( 100

t~ q I gauge klcatkm

&~..,g,~!IPO o gauge 1 + gauge 2 t; gauge 3 = first cracking

load, 90.4 kN

2000 4000 6000 8000 1 0000 12000 Strain in continuity steel (x 1 o·6 mm/mm)

(a) Specimen 1

400.--------------------------------------------,

o gauge 1

+ gauge 2

t; gauge 3

0~----~------~------._----~------~----~ 0 2000 4000 6000 8000 1 0000 12000

Strain in continuity steel (x 1 o·~ mm/mm)

(b) Specimen 2

400.---------------------------------------------~

z 300 ::::. "0 (I)

.Q 200 "0 S! 0. c. c( 100

first cracking load, 135.1 kN

o gauge 1

+ gauge 2

t; gauge 3

om-------~------~------~------~------~------~ 0 2000 4000 6000 8000 10000 12000

Strain in continuity steel (x1 o·6 mm/mm)

(c) Specimen 3

Fig . 10. Load-steel strain relations.

plified stress block as shown in Fig. 12. An average tensile strength of 634 Nlmm' (92 ksi) for the longitudinal re­inforcement and a concrete cube strength of 45 N/mm' (6530 psi) were assumed in the calculations.

The calculated ultimate load capaci­ties are compared to observed values in Table 2. In general , the calculated values, M eat• are very close to the mea­sured values, Mtest·

Effect of shear - In practice, the

89

400r----------------------------------------------,

........ 300 z ~ "'0

~ 200 "'0 ~ a. < 100

-e- gauge 10 B gauge 11 -er gauge 12

first cracking load, 90.4 kN

0 ~------~--------~--------~--------~--~~ -2500 -2000 -1500 -1 000 -500

........ 300 z ~ "'0 t1l

.Q 200 "'0 .!!l a. a. < 100

Concrete compressive strain (x 1 o·6 mm/mm)

(a) Specimen 1

first cracking load, 130.1 kN sz

-er gauge 7 -0- gauge 8 B gauge 9 *gauge 10 + gauge 11

0

0~------_. ________ ._ ______ _. ________ ~--------

-2500 -2000 -1500 -1000 -500 0 Concrete compressive strain (X 1 0"6 mm/mm)

(b) Specimen 2

400r---------------------------------------------·

........ 300

! -g ..Q 200

~ a. a. < 100

first cracking load, 135.1 kN

-er gauge 7 -e- gauge 8 B gauge 9 * gauge 10 + gauge 11 0 L-------~~------~--------_. ________ _. ________ ~ -2500 -2000 -1500 -1000 -500 0

Concrete compressive strain (x 1 o·6 mm/mm)

(c) Specimen 3

Fig. 11 . Load-concrete strain relations.

effect of shear may become critical at the support if the superimposed load is heavy and the span increase caused by providing continuity is large.

Consider the case where the design live load is 10 kN/m2 (208.8 psf) and

90

the superimposed dead load is 1.5 kN/m2 (3 1.3 psf) in addition to a dead load due to self-weight of 5.56 kN/m (381 lb/ft). These would give a fac­tored uniform load of W = 29.5 kN/m (2.02 kips/ft) according to BS 811 0. "

With a nominal moment capacity, M5 ,

of 182 kN-m (134ft-kips) , the 215 mm (8.5 in .) prestressed hollow-core slab shown in Fig. 5 would be able to span a maximum of 7.0 m (23.0 ft) when considering simply supported conditions.

If moment resistan t connections with a design capacity of 190 kN-m (140ft-kips) as provided in Specimens 2 and 3 are introduced at both ends of the slab (that is, f3 = 190/182 = 1.04) and assuming a midspan moment equal to M 5 (that is, a = 1 ), Fig. 2 gives the percentage of moment redis­tribution as 23.6 percent and the frac­tiona l increase in span capacity as 0.43. This translates to a span capac­ity, L;, of 10.0 m (32.8 ft).

Under the above conditions, the shear force at the supports would be WL/2 or 148 kN (33.2 kips) . Thus, the moment-to-shear ratio at the sup­ports would be 190/148 or 1.28 m ( 4 .21 ft) . The test arrangement for Specimens 2 and 3 approximated thi s situation.

The nominal shear capacity of Spec­imen 2 based on an average web width of 688 mm (27 .1 in .), a longitudinal stee l reinforcement provided in the topping concrete, A" of 1256 mm2

(1.95 sq in.), an effective depth to re­inforcement, d, of 250 mm (9.8 in .), and a maximum concrete strength of 40 N/mm2 (5800 psi) , is 161 kN (36.2 kips) according to BS811 0.'' This is only slightly less than the theoretical shear force of 190/ 1.16 or 164 kN (36.8 kips) that would result in a flex­ural fail ure of Specimen 2 at the criti­cal section.

It was therefore expected that Speci­men 2 would suffer shear distress . In the test, the shear force that resulted in extensive shear cracking was 151 kN (34.0 kips) . The specimen, however, fi nally fai led in flexure under a shear force of 180 kN (40.5 kips).

To enhance shear capacity , rein­forceme nt consisting of two 6 mm (114 in .) diameter mild steel closed links at 150 mm (6 in.) spacing was provided in Specimen 3. This specimen did not experience any diagonal cracking and fai led directly under bending, indicat­ing that the method used was effective in improving the shear behavior at the connection.

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f~ o.9{Q-c LJNEUTRAL AXiSI-­

...i+T=Asfy Es

STRAIN PROFILE SIMPLIFIED STRESS BLOCK

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

CONCLUSIONS In this study, charts for the design of

one- and two-end continuous hollow­core slabs were developed. These charts enable the required moment ca­pacity at supports and the moment re­distribution from supports to be deter­mined for a desired increase in span capacity . Tests were carried out to demonstrate the effectiveness of con­nections in resisting bending moment and shear force.

Within the scope of the study, it can be concluded that:

1. Designing for continuity leads to an increase in span capacity of hol­low-core slabs with reduced deflec­tions in general.

2. Moment continuity can be effec­tively provided by placing longitudi­nal steel reinforcement in the topping concrete over the connection.

3. Shear distress at connections can be effectively arrested by providing shear links in cut-open cores of the slabs.

ACKNOWLEDGMENT L & M Precast Pte. Ltd. (Singapore)

kindly donated the hollow-core slab components for the experiments. The tests were carried out in the Structural Engineering Laboratory of the Na­tional University of Singapore. The authors wish to thank all the techni­cians for their assistance in the work.

January-February 1996

REFERENCES 1. PC/ Manual for the Design of Hollow­

Core Slabs, Precast/Prestressed Con­crete Institute , Chicago, IL, 1988, 174 pp.

2. Pisanty, A., "Shear Strength of Ex­truded Hollow-Core Slabs," Materials and Structures, Research and Testing (RILEM, Paris), V. 25, No. 148, May 1992, pp. 224-230.

3. Ueda , T. , and Stitmannaithum, B. , "Shear Strength of Precast Prestressed Hollow Slabs With Concrete Top­ping," AC! Structural Journal, V. 88, No.4, July-August 1991, pp. 402-410.

4. Mejia-McMaster, J. C. , and Park, R. , "Tests on Special Reinforcement for the End Support of Hollow-Core Slabs," PCI JOURNAL, V. 39, No. 5, September-October 1994, pp. 90-105.

5. Stanton, J. F. , "Proposed Design Rules for Load Distribution in Precast Con­crete Decks," AC! Structural Journal, V. 84 , No. 5, September-October 1987, pp. 371-382.

6. Stanton, J. F. , "Response of Hollow­Core Slab Floors to Concentrated Loads," PCI JOURNAL, Y. 37, No.4, July-August 1992, pp. 98-113.

7. Aswad, A., and Jacques, F. J. , "Behav­ior of Hollow-Core Slabs Subject to Edge Loads," PCI JOURNAL, V. 37, No.2, March-April 1992, pp. 72-84.

8. Scott, N. L. , "Performance of Precast Prestressed Hollow-Core Slab With Composite Concrete Topping ," PCI JOURNAL, Y. 18, No.2, March-April 1973, pp. 64-77.

9. Rosenthal , I. , "Full Scale Test of Con­tinuous Prestressed Hollow-Core Slab," PCI JOURNAL, Y. 23, No. 6, May-June 1978, pp. 74-81.

10. "Ductility of Tie Connections for Con­crete Components in Precast Struc­tures," FIP Technical Report, Federa­tion Intemationale de Ia Precontrainte, London, October 1992.

11. "British Standard , Structural Use of Concrete, Part I - Code of Practice for Design and Construction," British Standards Institution, BS811 0: Part I: 1985, Issue 2, London, May 1989.

12. ACI Comrrtittee 318, "Building Code Requirements for Reinforced Concrete (ACI 318-89) and Commentary ," American Concrete Institute, Detroit, Ml, 1989.

APPENDIX - NOTATION

As = area of longitudinal tensile re­inforcement

b = width of member

d = effective depth to longitudinal reinforcement

dL/L = fractional increase in maxi­mum span capacity

h = overall depth of member

L0 =maximum span capacity of uniformly loaded hollow-core slabs , assuming simply sup­ported conditions

L; =maximum span capacity of uniformly loaded hollow-core slabs, assuming continuity over supports

Me = design support moment M1 = fixed end moment, assuming

elastic conditions

M5 = nominal moment capacity of hollow-core slabs

R = degree of moment redistribu­tion from supports

W = design uniform load

a= ratio of design midspan mo­ment to nominal moment ca­pacity of hollow-core slab

f3 = ratio of design support moment to nominal moment capacity of hollow-core slab

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