Birkle, Dilger - 2008

180 ACI Structural Journal/March-April 2008

ACI Structural Journal, V. 105, No. 2, March-April 2008.MS No. S-2006-405.R2 received October 31, 2006, and reviewed under Institute

publication policies. Copyright © 2008, American Concrete Institute. All rights reserved,including the making of copies unless permission is obtained from the copyright proprietors.Pertinent discussion including author’s closure, if any, will be published in the January-February 2009 ACI Structural Journal if the discussion is received by September 1, 2008.

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

Tests to study the influence of slab thickness on the punching shearstrength of flat slabs clearly demonstrate the significant effect ofsize on the shear stress resistance, particularly for tests withoutshear reinforcement. New tests in which the slab thickness variedbetween 160 and 300 mm (6.3 and 11.8 in.) and tests by otherswith slabs up to 500 mm (19.7 in.) thick indicate that slabs withoutshear reinforcement thicker than approximately 260 mm (10.2 in.)may not have a high factor of safety if designed according toACI 318-05. For thick slabs with shear reinforcement, the shearstress resistance provided by concrete is also reduced but to alesser degree.

Keywords: flat slab; punching shear; reinforcement; shear; stud.

INTRODUCTIONThe design of slab-column connections according to

ACI 318-051 is simple and thus practical. It was developedin the 1960s and was primarily based on work by Moe2 andJoint ACI-ASCE Committee 326.3 No considerable changeshave been made to the punching provisions since. Nevertheless,this empirical design procedure has several shortcomings,one of them being the neglect of size effects.4-9 The mainreason for the disregard of the size effect is the lack ofconclusive experimental evidence. This lack of experimentaldata has triggered the main test series presented herein. Atotal of nine slab-column connections were tested, with theslab thickness as their main variable. Slabs with and withoutshear stud reinforcement designed to fail inside and outsidethe shear-reinforced zone were investigated.

RESEARCH SIGNIFICANCEThe lack of a factor for size effect in the ACI 318-05

equations for the punching shear strength provided byconcrete in slabs is a limitation of the code. Addressing thisquestion is very timely in view of the current discussions inJoint ACI-ASCE Committee 445, Shear and Torsion, on sizeeffect on beam shear. The evidence presented in this paperdemonstrates conclusively that a size factor is urgentlyneeded for the safe design of slabs with an effective depth largerthan approximately 220 mm (8.7 in.).

BACKGROUNDThe design for shear in two-way slabs according to

ACI 318-05 is based on the concept of limiting the shearforce that can be resisted along a defined failure surface. Thedesign capacity of the connection, that is, the factorednominal shear resistance φVn , shall not be less than the shearforce due to factored loads Vu. The nominal shear resistanceVn is the sum of the nominal shear capacities provided by theconcrete and the shear reinforcement. In this paper, the slabthickness is one of the main variables. It is therefore moreexpedient to express the shear resistance in terms of stressesrather than forces; this facilitates direct comparison of thetest results. The nominal shear stress resistance can be

calculated by dividing the nominal shear resistance by bod,where bo is the perimeter of the critical section at d/2 fromthe face of the support and d is the average effective depth.It can be expressed as

vn = vc + vs with (1)

where vc and vs are the shear stress resistances provided bythe concrete and the steel, respectively, and s is the spacingof the shear studs. When headed studs are used as shearreinforcement, ACI 421.1R-9910 limits the nominal shearstress resistance vn, depending on the stud spacing s.

For the tests reported in this paper, the nominal shearstress resistance of concrete without shear reinforcement isdefined as

vc = 0.33 (2)

where fc′ is the specified concrete strength in MPa. For themajority of slab-column connections encountered in practice,Eq. (2) governs the design.

For slab-column connections with shear reinforcement,the contribution of the concrete to the shear strength is basedon an expression similar to Eq. (2); however, the constant0.33 is reduced to 0.17 for slabs with conventional shearreinforcement. For slabs reinforced with shear studs, thefollowing value is proposed in ACI 421.1R-99

vc = 0.25 (3)

The reason for the higher value for slabs with shear studsis the slip-free anchorage of the headed studs. For the criticalsection at d/2 outside the shear-reinforced zone, thefollowing equation applies

vc = 0.17 (4)

The contribution of the shear reinforcement to the nominalshear stress resistance is expressed as

(5)

vn 0.50 fc′ when s 0.50d≤≤

vn 0.67 fc′ when s 0.75d≤≤

fc′

fc′

fc′

vsAv fyv

bos------------=

Title no. 105-S19

Influence of Slab Thickness on Punching Shear Strengthby Gerd Birkle and Walter H. Dilger

181ACI Structural Journal/March-April 2008

In Eq. (5), Av is the cross-sectional area of all vertical legsof shear reinforcement on a peripheral line parallel to thecolumn perimeter; fyv is the specified yield strength of theshear reinforcement; and s is the spacing of the shearelements in the direction perpendicular to the critical section.

The effect of the slab thickness on the punching shearresistance had been recognized as early as 1938 by Graf11

who reported that the shear strength at punching found in a500 mm (19.7 in.) thick slab is more or less the same as theshear strength of beams failing in shear, which is approxi-mately half the punching shear strength of a two-way slabwith a slab thickness of 150 mm (6.3 in.). In 1948, Richart12

came to the conclusion that the shear stress at failuredecreases considerably with increasing effective depth of thetested footings. Recent experiments by Guandalini andMuttoni13 confirm this trend. An investigation into the sizeeffect was also recently reported by Li.14 Unfortunately, thesetests had small span-depth ratios that were further reduced forthe thicker slab. Therefore, the results of this test series onlyallow for limited conclusions in regard to a size factor.

An explanation for the lack of recognition for this importantparameter in ACI 318-05 is, perhaps, the fact that mostexperimental studies of the last 50 years were conducted onslabs with a thickness of approximately 150 mm (6 in.). Thismeans that experimental evidence for the size effect in slabsis rather scarce.

EXPERIMENTAL PROGRAMTest parameters

A total of nine slab-column assemblies were tested toinvestigate the influence of the slab thickness on the shearstrength of slab-column connections in three series.• Series 1: Slabs without shear reinforcement;• Series 2: Slabs with shear reinforcement designed to

fail inside the shear-reinforced zone; and• Series 3: Slabs with shear reinforcement designed to

fail outside the shear-reinforced zone.Each of the three test series had slabs with thicknesses of

160, 230, and 300 mm (6.3, 9.1, and 11.8 in.). The main testparameters are defined in Fig. 1 and summarized in Table 1.

The tests of Series 1 (Specimens 1, 7, and 10) weredesigned to investigate the size effect on slabs without shearreinforcement.

The specimens of Series 2 (Specimens 2, 9, and 12) weredesigned to fail in punching with the punching coneexpected to develop inside the shear reinforced zone. Toensure shear failure in the vicinity of the column, the studspacing s was chosen to be 0.75d, the upper limit for s, andthe shear studs were extended to approximately 4d from thecolumn faces. The distance between the first row of studsand the column face so was taken as 0.5s to avoid shearfailure between the column and the first row of shear studs.

The tests of Series 3 (Specimens 4, 8, and 11) weredesigned to fail outside the shear-reinforced zone. Therefore,

a tighter stud spacing s = 0.5d was chosen with the studsextending to approximately 2.3d from the column faces.

Test specimensThe shape of all test specimens was octagonal, which is a

compromise between a square specimen being the mostconvenient to fabricate and a circular one that can be assumedto represent the line of contraflexure around the column for atwo-way slab with equal spans in both directions.

The size of the square column c and the radius Bc, definingthe position of the supports of the octagonal slabs, werevaried linearly with the slab thickness. This variation waschosen because the slab thickness is usually selected byminimum thickness requirements that are linearly related tothe clear span in most major design codes. The reinforcementratio was slightly decreased for increasing slab thickness tokeep the ratio between the predicted shear capacity (accordingto ACI 318-05) and the flexural capacity (established by yield-line theory) of the specimens constant. This approach waschosen over keeping a constant reinforcement ratio becausethe main influence of the reinforcement ratio on the punchingcapacity is to control cracking; hence, it is desirable to be at asimilar level of flexural capacity when punching occurs.This can only be achieved by a reduction in reinforcementratio for an increase in slab thickness. The yield line patternused in the design was derived from a standard yield linepattern for a circular specimen of radius Bc, with a circularcolumn with the circumference of the circular columnreplaced by the circumference of the square column

(6)Vflex 2πBc

Bc cc–----------------mave 2π

Bc

Bc 2 cx cy+( ) π⁄–-------------------------------------------mave⇒=

Gerd Birkle is a Structural Engineer with Stantec Consulting Ltd., Calgary, AB,Canada. He received his Dipl-Ing degree in civil engineering from the University ofStuttgart, Stuttgart, Germany, and his PhD from the University of Calgary, Calgary,AB, Canada, in 2004.

Walter H. Dilger, FACI, is Professor Emeritus in the Department of Civil Engineering,University of Calgary. He is a member of ACI Committee 209, Creep and Shrinkage inConcrete, and Joint ACI-ASCE Committee 445, Shear and Torsion. His researchinterests include creep of plain and structural concrete and reinforced andprestressed concrete.

Table 1—Test parameters

Testc,

mmh,

mmdave, mm

Bc, mm

fc′ ,*

MPaf ′c_test ,

†

MPa ρave,%fy,

MPa Studs

1

250 160 124 1000

33.1 36.2

1.54 488

No

2 27.7 29.0 Yes

4 36.1 38.0 Yes

7

300 230 190 1500

33.5 35.0

1.30 531

No

8 35.0 35.0 Yes

9 36.1 35.2 Yes

10

350 300 260 1900

31.0 31.4

1.10 524

No

11 30.0 30.0 Yes

12 33.8 33.5 Yes

Ref. 13 520 200 464 2145 — 32.4 0.32 550 No*Twenty-eight-day cylinder strength (100 x 200 mm cylinders).†Cylinder strength at day of testing (100 x 200 mm cylinders).Note: 1 MPa = 145 psi; 25.4 mm = 1 in.

Fig. 1—Definition of specimen variables. (Note: 25.4 mm =1 in.)


where mave can be calculated as

mave = ρavedavefy (7)

where ρave is the average flexural reinforcement ratio, dave isthe average effective depth, fy is the yield strength of theflexural reinforcement, and α1 is the stress block factor, thatis, the ratio of average stress in the rectangular stress blockto the specified concrete strength. It is recognized that theassumed simple yield pattern and Eq. (6) give an approximateupper bound of Vflex.

Concrete strengthThe target strength of the concrete at 28 days fc′ was 30 MPa

(4350 psi). Three 100 x 200 mm (4 x 8 in.) cylinders weretested at 28 days and three on the days of the experiments. Themaximum coarse aggregate size was 14 mm (0.55 in.) for the160 mm (6.3 in.) slabs and 20 mm (0.79 in.) for the thickerslabs. The proportions of the concrete mixtures are summarizedin Table 2.

daveρavedave fy

2α1fc′------------------------–⎝ ⎠

⎛ ⎞

Flexural reinforcementThe flexural reinforcement layout is shown in Fig. 2 and

all flexural reinforcement had a 180-degree hook at bothends to ensure proper anchorage. The concrete cover was20 mm (0.79 in.). The reinforcing bars had a specified yieldstrength of 400 MPa (58.0 ksi). The 15M and 20M barsshown in Fig. 2 have a cross-sectional area Ab = 200 and300 mm2 (0.310 and 0.465 in.2), respectively. The bottomreinforcement (compression zone) comprised 10M bars witha cross-sectional area Ab = 100 mm2 (0.155 in.2) spaced at200 mm (7.87 in.). Each series of specimens had reinforcementfrom the same heat. Testing was done according to ASTMA370-05.15 The yield strength, fy , listed in Table 1 was takenas the average of three tension tests at a 2% offset.

Shear reinforcementIn Test Series 2 and 3, shear reinforcement in the form of

shear studs was installed. The shear studs were double-headstuds tack-welded to a steel rail to ensure proper spacing andaccurate installation (refer to Fig. 3). The shear stud param-eters are summarized in Table 3 and the layout of the studsis illustrated in Fig. 4.

Test setupThe testing of specimens with different dimensions requires

a flexible test setup. This was achieved by supporting the slabsby means of eight high-strength bars anchored in the strongfloor and by placing the actuator between the specimen andthe strong floor (refer to Fig. 5). Depending on the size of thespecimens, the high-strength bars were supported eitherdirectly through the strong floor or by steel yokes. Bothsupporting systems were engineered to have similar stiff-nesses so that all eight bars were more or less equally stressedduring testing. To monitor the bar forces, measurements weremade by strain gauges fitted to opposing sides on the high-strength bars. The bar forces were transferred to the concreteslab by 200 mm (8 in.) diameter spherical seats to allow slabdisplacements to develop without bending the rods. The testsetup is described in more detail by Birkle.9

Table 2—Concrete mixture proportions

SpecimensWater,kg/m3

Cement (Type GU),

kg/m3

Fineaggregate,

kg/m3

Coarse aggregate,

kg/m3 w/c

1 to 6 195 300 870 1085 0.65

7 to 12 180 288 885 1193 0.63

Note: 1 kg/m3 = 1.68 lb/yd3.

Table 3—Summary of stud parameters forSeries 2 and 3

Test

Stud dimensions Layout parameters

Diameter, mm

Area, mm2

Height, mm

fyv, MPa

dave, mm so s Extent

49.5 71 120

465124

0.25d 0.50d 2.2d

2 393 0.38d 0.75d 4.0d

89.5 71 190 460 190

0.25d 0.50d 2.4d

9 0.38d 0.75d 4.3d

1112.7 127 260 409 260

0.25d 0.50d 2.2d

12 0.38d 0.75d 4.1d

Note: 25.4 mm = 1 in.; 1 MPa = 145 psi.

Fig. 2—Flexural reinforcement layout. (Note: 25.4 mm = 1 in.)

Fig. 3—Stud rails. (Note: 25 mm = 1 in.)

Fig. 4—Stud layout for Test Series 2 and 3. (Note: 25 mm =1 in.)

ACI Structural Journal/March-April 2008 183

MeasurementsThe applied load was recorded using a calibrated load cell

or, in the case of the 300 mm (11.8 in.) thick specimens, bya pressure transducer that had been calibrated before eachtest. The applied load includes the self-weight of the specimens.Displacements of the specimens were measured at the fivepoints shown in Fig. 6 using linear variable displacementtransducers (LVDTs).

To locate the position of the shear cracks within the slabdepth, the transverse expansion of the slab was measured onSpecimens 7 to 12 by means of dial gauges at the eight locationsshown in Fig. 7(a). The dial gauges were attached to thinmetal rods placed through small sleeves in the slab andanchored by 180-degree hooks at the bottom (refer to Fig. 7(b)).

Steel strains were monitored on the flexural reinforcementas well as the studs in one quadrant of the slab (refer to Fig. 8(a)and (b)). For the 160 mm (6.3 in.) thick specimens, flexuralstrain measurements were taken on each bar, whereas on allthe other specimens, the measurements were taken on alternatebars. Strains on studs were measured at midheight of thestem of the stud. Measurements were taken on two studrailsadjacent to one corner of the column.

The load was applied in steps of 50, 75, and 100 kN (11.2,16.9, and 22.5 kips) to the slabs of thickness 160, 230, and300 mm (6.3, 9.1, and 11.8 in.), respectively. At each loadstep, cracks were marked with a different color on the white-washed surface and slab expansions were recorded. The

duration of the tests depended on the number of load stepsand the extent of cracking and took up to 3 hours. All testswere terminated after punching had occurred and the loadhad dropped considerably.

TEST RESULTS AND THEIR INTERPRETATIONFailure loads

With the exception of Specimen 4, all tests failed at d/2from the column face. The recorded failure loads and thelocation of the punching cone are summarized in Table 4.This table also lists other important test parameters: slabthickness h; average effective depth dave; concrete strengthf ′c_test at the time of testing; extent of the shear reinforcementfrom the column faces; percentage of shear reinforcementρv, calculated as the total area of shear reinforcement alongthe perimeter Av divided by the critical section bo and thespacing of shear reinforcement s; location of the punchingfailure (inside meaning inside the shear-reinforced zone);and shear stress at failure vu inside or outside the shear rein-forced zone.

Fig. 5—Test setup (arrangement used for Specimens 1 to 6).

Fig. 6—Location of displacement transducers. (Note:25.4 mm = 1 in.)

Fig. 7—Location of expansion dial gauges. (Note: 25.4 mm =1 in.)

Fig. 8—Location of strain measurements on reinforcement.

Table 4—Summary of test results

Testh,

mmdave, mm

bo , mm

f ′c_test ,MPa Extent ρv, % s

Failure location

vu, MPa

1

160 124 1496

36.2 — — — — 2.60

4 38.0 2.2d 0.63 0.50d Outside 3.42

2 29.0 4.0d 0.42 0.75d Inside 3.09

7

230 190 1960

35.0 — 0.00 — — 2.22

8 35.0 2.4d 0.29 0.50d Inside 2.82

9 35.2 4.3d 0.19 0.75d Inside 2.93

10

300 260 2440

31.4 — — — — 1.65

11 30.0 2.2d 0.32 0.50d Inside 2.55

12 33.5 4.1d 0.21 0.75d Inside 2.40

Ref. 13 500 464 3936 32.4 — — — — 1.18

Note: 25.4 mm = 1 in.; 1 kip = 4.45 kN.


Effect of slab thicknessSlabs without shear reinforcement—A very alarming

finding of the test results listed in Table 4 is the rapiddecrease of the shear stress resistance vu at the criticalsection d/2 from the column with increasing slab thickness.The nominal shear stress resistance of 0.33( fc′ )

1/2 (refer toEq. (4)) for slabs without shear reinforcement was onlyachieved by the 160 and 230 mm (6.3 and 9.1 in.) thick slabs(Specimens 1 and 7). The decrease of shear stress resistanceat failure with increasing effective depth is shown in Fig. 9in terms of the ratio vu/vn. The continued decrease of theshear stress resistance is confirmed by a recent test byGuandalini and Muttoni13 on a 500 mm (19.7 in.) thick slabthe result of which is added to the authors’ tests in Fig. 9. Thedata of this test is also added to Tables 1 and 4. Examining

Fig. 9 shows that for slabs without shear reinforcement, thestresses at failure for the 300 and 500 mm (11.8 and 19.7 in.)thick slabs are only 89% and 63% of the ACI 318-05 nominalfailure stress, respectively. The relative values of vu/vn for160, 230, 300, and 500 mm (6.3, 9.1, 11.8, and 19.7 in.) slabsare: 1.00, 0.87, 0.68, and 0.48. Note that the influence of themaximum aggregate size on the punching capacity was notconsidered in this study but should be expected to havelimited influence on the findings of this study.

Slabs with shear reinforcement—The failure loads of theslabs with shear reinforcement are listed in Table 4 and theevaluation is presented in Table 5. Table 5 lists the shearstresses at failure, vu_in and vu_out, the nominal shear stressesvn = vc + vs, as well as the upper allowable limit of vn and theratios vu/vn inside and outside the shear reinforced zones.The controlling values that are the values reflecting theactual failure location are printed in bold.

Specimen 4 (s = 0.5d extending ~ 2.4d) failed—asintended—outside the shear-reinforced zone under a load of634 kN (143 kips). The corresponding shear stress resistanceis 1.78 MPa (258 psi) (refer to Table 5, Column 10), whichis 69% higher than the permissible value at d/2 outside theshear reinforced zone vc = 0.17 = 1.05 MPa (152 psi)(refer to Columns 11 and 12). At failure, the steel stresses inthe studs were well below yield.

Specimen 2 with s = 0.75d failed—as expected—insidethe shear-reinforced zone under a load of 574 kN (129 kips).The corresponding shear stress resistance (3.09 MPa [448 psi])was higher than both the stress vc + vs (3.00 MPa [435 psi]),and the maximum shear stress allowed for slabs with s =0.75d, (2.69 MPa [390 psi]), the latter being the controllingvalue for this test. The studs had reached yield at failure.

Specimen 8 (h = 230 mm [9.1 in.]) failed inside the shearreinforced zone under a load of 1050 kN (236 kips) eventhough the shear stress outside the shear reinforced zone(1.29 MPa [187 psi]) was well above the allowable value of1.01 MPa (146 psi) (refer to Table 5, Columns 10 and 11).Punching shear failure in Specimen 8 occurred after theshear reinforcement had reached yield at exactly the nominalstrength (refer to Table 5, Column 8) before reaching themaximum allowable shear stress.

Specimen 9 also failed by punching inside the shear-reinforced zone under 1091 kN (245 kips), at a slightlyhigher load than Specimen 8, even though it had less shearreinforcement. The shear stress at failure vu was 24% higher

fc′

Fig. 9—Influence of slab thickness on failure stress in slabswithout shear reinforcement. (Note: 25.4 mm = 1 in.)

Fig. 10—Location of failure crack of Specimen 11.

Table 5—Evaluation of test results1 2 3 4 5 6 7 8 9 10 11 12

Inside shear-reinforced zone Outside shear-reinforced zone

Test Vu, kN vu,in, MPa vc ,* MPa vs, MPa vn = vc + vs, MPa vmax ,† MPa vu/(vc + vs) vu /vmax vu,out, MPa vc = vn, MPa vu/vc

1 483 2.60 1.99 — 1.99 — 1.31 — — — —

4‡ 634 3.42 1.54 2.94 4.48 4.13 0.76 0.83 1.78 1.05 1.70

2 574 3.09 1.35 1.66 3.00 2.69 1.03 1.15 1.12 0.92 1.22

7 825 2.22 1.95 — 1.95 — 1.13 — — — —

8 1050 2.82 1.48 1.33 2.81 2.96 1.00 0.95 1.29 1.01 1.28

9 1091 2.93 1.48 0.89 2.37 2.97 1.24 0.99 0.90 1.01 0.89

10 1046 1.65 1.85 — 1.85 — 0.89 — — — —

11 1620 2.55 1.37 1.31 2.68 3.67 0.95 0.70 1.14 0.93 1.23

12 1520 2.40 1.45 0.87 2.32 2.89 1.03 0.83 0.71 0.98 0.73*For slabs without reinforcement: vc = vn = 0.33√f ′c_test ; for slabs with stud shear reinforcement: vc = 0.25√f ′c_test .†For slabs with shear reinforcement and s ≤ 0.5d: vmax = 0.67√f ′c_test ; when 0.5d ≥ s ≤ 0.75d: vmax = 0.50√f ′c_test .‡Shear reinforcement in Specimen 4 did not reach yield.Note: 1 MPa = 145 psi; 1 kip = 4.45 kN.


than the calculated nominal shear stress resistance vn (referto Table 5, Column 8).

Specimen 11 (h = 300 mm [11.8 in.]) failed inside theshear-reinforced zone under a load of 1620 kN (364 kips).The location of the failure cone was confirmed by cutting theslab after the completion of the test (refer to Fig. 10). Theshear stress reached outside the shear reinforced zone was23% higher than the allowable value (Table 5, Column 12).On the other hand, the shear stress resistance at d/2 reachedonly 95% of (vc + vs) after the studs had yielded (Table 5,Column 8). Calculating the contribution of the concrete tothe shear stress resistance by rearranging Eq. (1) and puttingvn = vu, we find that vc reached only 90% of the value calcu-lated according to Eq. (2). This percentage is similar to thatreached in Specimen 10 (h = 300 mm [11.8 in.]) withoutshear reinforcement and leads to the conclusion that a sizeeffect also exists for slabs with shear reinforcement.

Specimen 12 failed at d/2 from the column at a load of1520 kN (342 kips), corresponding to 1.03 times thepredicted failure load (Table 5, Column 8). The studs hadyielded before failure.

Plotting the results of the tests that failed within theshear reinforcement in Fig. 11 indicates a decreasing trendwith increasing slab depth. It is to be noted, however, thatSpecimen 4 failed outside the shear-reinforced zone and thatthe somewhat inconsistent ratios vu/vn do not necessarilyallow definitive conclusions regarding the size effect forslabs with shear reinforcement.

Effect of shear reinforcement and stud strainsThere are several observations that can be made looking at

the test results summarized in Table 5. One of the moreobvious ones is that for all slab thicknesses, the shear stressresistance of the connection was increased considerably byproviding shear reinforcement. The increase was up to 31%,32%, and 55% for specimens with a thickness of 160, 230,and 300 mm (6.3, 9.1, and 11.8 in.), respectively. Theincreased effectiveness of the shear reinforcement for the300 mm (11.8 in.) specimens can be explained by thereduced shear stress resistance of the concrete at failure, thusincreasing the relative contribution of the shear reinforcementto the total shear capacity of the connections. Anotherdistinct benefit of the shear stud reinforcement is thesubstantial increase in ductility and post-failure capacity.The load deflection curves for the three test series shown in

Fig. 12 illustrate the increased ductility by a plateau in theload deflection curve. The increase in post-failure capacitycan be concluded from the gradual decline of the load withthe applied displacements (displacement-controlled test setup).

The steel strains in the studs are plotted in Fig. 13 to 16.Figure 13 shows that the studs of Specimen 2 just reachedyield at failure, whereas Fig. 14 clearly demonstrates that thestud strains in Specimen 4 were well below yielding whenpunching occurred outside the shear-reinforced zone. Thefour shear-reinforced specimens of the other two seriesreached yield before failure as indicated in Fig. 15 and 16 forSpecimens 9 and 12, respectively. From these figures, it isevident that yielding developed only in the studs closest tothe column and that the punching cone developed in theregion between the column face and SG3 because Studs SG1through SG3 exhibit large strains.

Transverse slab expansionThe transverse slab expansion measured in Specimens 7 to

12 indicate the demand for shear reinforcement to prevent

Fig. 11—Influence of slab thickness on shear stress resistancein slabs with shear reinforcement. (Note: 25.4 mm = 1 in.)

Fig. 12—Load-deflection curves. (Note: 25.4 mm = 1 in.;4.45 kN = 1 kip).

Fig. 13—Strains in shear studs for Specimen 2. (Note:4.45 kN = 1 kip.)



failure. Comparing measurements for slabs with and withoutshear reinforcement in Fig. 17(a) and (b) shows that thetransverse slab expansion of the two specimens was similarup to the failure of the slab without shear reinforcement(825 kN [185 kips]). Beyond this load, however, the trans-verse displacements of the slab with shear reinforcementincreases significantly and exceeds 1.5 mm (0.059 in.) atpunching failure. Note that Gauges 1 to 4 in Fig. 17(a) and(b) are located on diagonal lines at an angle 45 degrees to thecolumn faces (refer to Fig. 7) and that Gauge 1 is the gaugefurthest away from the column. Figure 17 shows that thedemand for shear reinforcement is very small up to a loadthat creates a substantial shear crack that leads to failure inthe specimen without shear reinforcement. This observationis confirmed by looking at the stud strains in Fig. 15.

Strains in flexural reinforcementA typical plot of steel strain in the flexural reinforcement

versus applied load is presented in Fig. 18 for Specimens 8and 11. This figure indicates that the bars in the vicinity ofthe column reached yield first and that even though thereinforcement ratio for the thicker slabs was reduced, theamount of yielding in the thinner slabs was higher. The flexuralfailure load according to the yield line theory was notreached in any of the tests9 confirming that all tests failedin shear.

DeflectionsThe load deflection curves for all three tests series

presented in Fig. 12 illustrate the difference between slabswith and without shear reinforcement. The deflectionspresented in Fig. 12 are the measured center deflectionsminus the deflections at the supports. Specimens 1, 7, and 10exhibit sudden brittle failure typical for slabs without shearreinforcement. The slabs with shear reinforcement (2, 4, 8, 9,11, and 12) develop a small yield plateau and a gradualfailure with some residual strength after yielding of the shear

reinforcement. Note that the LVDT in Specimen 4 failedbefore the test was completed.

PROPOSED CODE CHANGESThe influence of the slab thickness on the punching shear

capacity has been recognized in many codes of practice. Sizeeffects in major design codes are as follows (d in mm)

CSA A32.3-0416: (8)

EC217/DIN 1045-118: (9)

BS 8110-9719: (10)

The Canadian Standard16 differs from ACI only in that itincludes the size factor of Eq. (9). To compare these differentapproaches with the size effect, Eq. (10) was altered bydividing both sides by 2. The size factors as well as the ratiosof recorded ultimate shear stress resistances to nominal shearstress resistances vu/vn for the tests of slabs without shearreinforcement are plotted in Fig. 19. From this figure, it isobvious that the slope of all three codes is too shallow incomparison with the test results and that both CSA and BSstart to account for the size effect at slab thicknesses that aretoo high, namely, at an effective depth of 300 and 400 mm (11.8and 15.7 in.), respectively, whereas the ratio vu/vn suggests that asize factor should come into effect at an effective depth ofapproximately 220 mm (8.6 in.). The nominal shear stressresistances vn were calculated according to ACI 318-05.

To reflect the steep descent of the experimental curve ofFig. 19, the size factor can be approximated by

(11)

13001000 d+--------------------- 1≤

1 200d

--------- 2≤+

400d

--------- 1≤4

kd200d

--------- 0.5≥=



Fig. 17—Slab expansions for Specimens 7 and 8. (Note:25.4 mm = 1 in.; 4.45 kN = 1 kip.)

Fig. 18—Strains in flexural reinforcement. (Note: 4.45 kN =1 kip.)


Using this size factor in combination with Eq. (2) yieldsthe broken line in Fig. 19.

It is well known,4-9 however, that the punching shearstrength not only depends on the concrete strength and the slabthickness but also on the flexural reinforcement ratio ρ. BothBS and EC2 include ρ in their punching shear strength equationsin the form of ρ1/3. Based on statistical evaluations, Birkle9

proposed the following expression for the nominal stressresistance of slabs without shear reinforcement

(12)

where fc′ is the specified compressive strength of theconcrete in MPa, ρ is the reinforcement ratio, and d the effectivedepth in mm. In Imperial units, the constant changes to 150.The minimum reinforcement ratio in Eq. (12) is 0.5% and thelower limit of Eq. (12) should be 0.17 . The comparison ofEq. (12) with the test results in Fig. 20 shows good agreement.

For slabs with shear reinforcement, the concrete componentof the shear capacity is reduced relative to that of slabswithout shear reinforcement. As mentioned in the discussionof the test results, there is evidence that the reduction of theshear stress resistance of the concrete of the 300 mm (11.8 in.)thick slab (Specimen 11) is similar to that of the slab without

vn 16fc′ ρ⋅

d-------------⎝ ⎠⎛ ⎞

1 3⁄

=

fc′

shear reinforcement (Specimen 10). A single test, however,does not provide enough evidence to draw definite conclusions.

SUMMARY AND CONCLUSIONSTests on slabs with thicknesses between 160 and 300 mm

(6.3 and 11.8 in.) with and without shear reinforcement(shear studs) are presented. One tests series was designedto fail inside, and another one to fail outside, the shearreinforced zone.

The most important conclusions from these experiments are:1. There is a significant decrease of the shear stress resis-

tance with increasing slab thickness. For a slab thickness of300 mm (11.8 in.), only 89% of the nominal shear resistanceof ACI 318-05 was reached. In a recent test by Guandaliniand Muttoni13 on a 500 mm (19.7 in.) thick slab, only 63%of the code value was reached. This low shear strengthnecessitates a consideration of the size effect. Slabs withshear reinforcement showed a small decrease of the shearresistance with increasing slab depth;

2. Slabs with shear reinforcement showed a small decreaseof the shear resistance with increasing slab depth;

3. Slabs with shear reinforcement resulted in significantincreases in shear capacity and ductility compared with slabswithout shear reinforcement;

4. For the test results presented, size factors suggested inCSA A23.3-0416 underestimate the influence of the effectivedepth on the punching shear capacity;

5. Considering the size factors presented in EC217 andBS8110-9719 in isolation, that is, not considering the effectof the reinforcement ratio ρ also underestimate the size factor;

6. Based on the statistical evaluations by Birkle,9 thefollowing equation is proposed for the nominal shear stressresistance of concrete in slabs without shear reinforcement

In the U.S. Standard system of units

; and

7. For slabs with shear reinforcement, the data available isinsufficient to propose an equation for the shear stress resis-tance of the concrete for thick slabs. Research on this topicis urgently required.

ACKNOWLEDGMENTSThis research was supported by the Natural Science and Engineering

Research Council of Canada, which is gratefully acknowledged. Thedouble-headed studs with forged heads were provided by DECON ofBrampton, ON, Canada. The flexural reinforcement and the concrete weredonated by Harris Rebar, Calgary, AB, Canada, and Lafarge, Calgary,respectively, which is highly appreciated.

NOTATIONAb = area of reinforcement barAv = total area of shear reinforcement perpendicular to critical sectionBc = radius of round slab specimen (at supports)bo = perimeter of critical sectionc = length of column side for square columncc = diameter of circular columncx = length of column side in x-directioncy = length of the column side in y-directiond = effective depth

vn 16fc′ ρ⋅

d-------------⎝ ⎠⎛ ⎞

1 3⁄

0.17 fc′ (MPa)≥=

vn 150fc′ ρ⋅

d-------------⎝ ⎠⎛ ⎞

1 3⁄

2 fc′ (psi)≥=

Fig. 19—Comparison of code provisions for size effect andtest results.

Fig. 20—Influence of slab thickness using size factor. (Note:25.4 mm = 1 in.)


dave = average of effective depth in two directions of slabfc′ = concrete design strength based on 100 x 200 mm (4 x 8 in.)

cylinderfc_test = concrete cylinder strength at time of testingfy = specified yield strength of flexural reinforcement fyv = specified yield strength of shear studsh = thickness of slabmave = average moment capacity per unit widths = distance of shear elements perpendicular to column sidesso = distance of first shear element to face of columnVfex = flexural strength of slab-column connection (yield-line theory)Vn = nominal shear resistance of slab-column connectionVu = ultimate shear force applied to slab-column connectionvc = shear stress resistance provided by concretevmax = shear stress limitvn = nominal shear stress resistancevs = shear stress resistance provided by shear reinforcementvu = shear stress on critical section at ultimate loadsvu,in = shear stress on the critical section inside shear-reinforced zone

at ultimate loadsvu,out = shear stress on the critical section outside shear-reinforced zone

at ultimate loadsx = distance between deflection transducersα1 = ratio of average stress in rectangular compression block to

specified concrete strengthαs = factor that adjusts shear capacity for column locationβ = ratio of long side to short side of columnεy = yield strain of reinforcementφ = global resistance factor for slab column connectionρave = average percentage of reinforcement ratio in two directions of slabρv = percentage of shear reinforcement

REFERENCES1. ACI Committee 318, “Building Code Requirements for Structural

Concrete (ACI 318-05) and Commentary (318R-05),” American ConcreteInstitute, Farmington Hills, MI, 2005, 430 pp.

2. Moe, J., “Shearing Strength of Reinforced Concrete Slabs and FootingsUnder Concentrated Loads,” Bulletin No. D47, Journal of the PortlandCement Association, Research and Development Laboratories, Apr. 1961,130 pp.

3. Joint ACI-ASCE Committee 326, “Shear and Diagonal Torsion,” ACIStructural Journal, V. 85, No. 6, Nov.-Dec. 1988, pp. 675-696.

4. Regan, P. E., and Bræstrup, M. W., “Punching Shear in ReinforcedConcrete,” Bulletin d’Information No. 168, Comité Euro-International duBéton, Jan. 1985, 232 pp.

5. Regan, P. E., “Symmetric Punching of Reinforced Concrete Slabs,”Magazine of Concrete Research, V. 38, No. 136, Sept. 1986, pp. 115-128.

6. Bažant, Z. P., and Cao, Z., “Size Effect in Punching Shear Failure ofSlabs,” ACI Structural Journal, V. 84, No. 6, Jan.-Feb. 1987, pp. 44-53.

7. Gardner, N. J., “Punching Shear Provisions for Reinforced andPrestressed Concrete Flat Slabs,” Canadian Journal of Civil Engineering,V. 23, 1996, pp. 502-510.

8. Sherif, A.G., and Dilger, W. H., “Critical Review of the CSA A23.3-94Punching Shear Provisions for Interior Columns,” Canadian Journal ofCivil Engineering, V. 23, No. 5, 1996, pp. 998-1011.

9. Birkle, G., “Punching of Flat Slabs: The Influence of Slab Thicknessand Stud Layout,” PhD thesis, University of Calgary, Calgary, AB, Canada,2004, 152 pp.

10. ACI Committee 421, “Shear Reinforcement for Slabs (ACI 421.1R-99),”American Concrete Institute, Farmington Hills, MI, 15 pp.

11. Graf, O., “Versuche über die Widerstandsfähigkeit von allseitigaufliegenden dicken Eisenbetonplatten unter Einzellasten,” DeutscherAusschuß für Eisenbeton, Heft 88, Berlin, Germany, 1938, 22 pp.

12. Richart, F. E., “Reinforced Concrete Wall and Column Footings,”ACI JOURNAL, Proceedings V. 45, No. 2, Oct. 1948, pp. 97-127.

13. Guandalini, S., and Muttoni, A., “Punching Tests on Concrete Slabswithout Shear Reinforcement,” Swiss Federal Institute of Technology,Lausanne, Switzerland, 2004, 129 pp.

14. Li, K. K. L., “Influence of Size on Punching Shear Strength ofConcrete Slabs,” MSc thesis, McGill University, Montreal, QC, Canada,2000, 65 pp.

15. ASTM A370-05, “Standard Test Methods and Definitions forMechanical Testing of Steel Products,” ASTM International, West Consho-hocken, PA, 2003, 49 pp.

16. CSA Standard A23.3-04, “Design of Concrete Structures,” CanadianPortland Cement Association, Rexdale, ON, Canada, 2004, 167 pp.

17. Eurocode 2, “Planung von Stahlbeton- und Spannbetontragwerken,”DIN V 18932 (10.91), DIN ENV 1992-1-1 (06.92), 1992, 171 pp.

18. DIN 1045-1, “Tragwerke aus Beton, Stahlbeton und Spannbeton;Teil 1: Bemessung und Konstruktion,” DIN—Deutsches Institut fürNormung, Berlin, July 2001, 148 pp.

19. BS 8110-97, “Structural Use of Concrete, Part 1: Code of Practicefor Design and Construction,” British Standard Institute, London, UK,1997, 117 pp.

Documents

Birkle, Dilger - 2008