12-119_ferreira phd thesis

363ACI Structural Journal/March-April 2014

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

Twelve slabs, 11 of which contained double-headed studs as shear reinforcement, were tested supported by central column and loaded concentrically. Their behavior is described in terms of deflections, rotations, strains of the concrete close to the column, strains of the flexural reinforcement across the slab width, and strains of the studs. All failures were by punching, in most cases within the shear reinforced region. The treatments of punching resistance in ACI 318, Eurocode 2 (EC2), and the critical shear crack theory (CSCT) are described, and their predictions are compared with the results of the present tests and 39 others from the literature. The accuracy of predictions improves from ACI 318 to EC2 to CSCTthat is, with increasing complexity. However, the CSCT assumptions about behavior are not well supported by the experimental observations.

Keywords: codes; flat slabs; punching; shear studs.

INTRODUCTIONThere is no generally accepted theoretical treatment of

punching, and design is based on empirical methods given in codes of practice. While there is similarity between them in terms of general approach, there are considerable differences in their assumptions and the resulting equations, which leads to uncertainties about their reliability.

A further cause of uncertainty is the wide variety of types of shear reinforcement, such as stirrups of various forms, bent-up bars, welded fabric, and stud systems. Comparisons of design equations with the results of tests using different types of shear reinforcement can result in a wide scatter, while comparisons of slabs with only one type are often limited by the restricted data available.

This paper presents the results of tests1 of slabs with double-headed studs as shear reinforcement, followed by a short review of the design methods of ACI 318,2 Euro-code 2 (EC2),3 and the critical shear crack theory (CSCT) of Muttoni et al.,4,5 which is the basis of the punching clauses of the fib Model Code 2010 draft.6 The results of the present tests and of others on slabs with double-headed shear rein-forcement are then compared with the three design methods.

RESEARCH SIGNIFICANCEThere are considerable differences between the design

methods for punching in ACI 318, EC2, and the CSCT. The primary objective of the experimental study described in this paper was to assess the realism of the assumptions underlying these design methods. The principal variables in the test series were the sizes and spacings of the studs, and the size and shape of the columns. Extensive measurements were made of slab rotations and strains in the concrete, and flexural and shear reinforcement. Comparisons between

experimental and calculated strengths for the present tests and others are presented to evaluate the accuracies of the methods.

EXPERIMENTAL PROGRAMTwelve tests were made at the University of Brasilia. The

specimens were square slabs 2.5 x 2.5 m (8.2 x 8.2 ft) on plan and 180 mm (7.1 in.) thick supported centrally by circular or square columns (Type C and S slabs, respectively). Equal downward loads were applied at eight points close to the slab edges, as shown in Fig.1.

Title No. 111-S32

Punching of Reinforced Concrete Flat Slabs with Double-Headed Shear Reinforcementby Maurcio P. Ferreira, Guilherme S. Melo, Paul E. Regan, and Robert L. Vollum

ACI Structural Journal, V. 111, No. 2, March-April 2014.MS No. S-2012-119, doi:10.14359.51686535, was received April 4, 2012, and

reviewed under Institute publication policies. Copyright 2014, American Concrete Institute. All rights reserved, including the making of copies unless permission is obtained from the copyright proprietors. Pertinent discussion including authors closure, if any, will be published ten months from this journals date if the discussion is received within four months of the papers print publication.

Fig. 1Test arrangements. (Note: Dimensions in mm; 1 mm = 0.0394 in.)

364 ACI Structural Journal/March-April 2014

The main variables were the shape and size of the column, the amount and distribution of the shear reinforcement, and some details of the main reinforcement.

The concrete was made with ordinary portland cement, natural sand, and crushed limestone aggregate with a maximum size of 9.5 mm (3/8 in.). The concrete strength was determined from 100 x 200 mm (4 x 8 in.) control cylin-ders that were tested at the same time as the slabs.

The arrangement of flexural reinforcement was basically the same in all but two of the specimens (Slabs C5 and C6). The general arrangement of the upper tension reinforcement was 16 mm (No. 5) bars with fy = 540 MPa (78 ksi) and Es = 213 GPa (30,893 ksi) at spacings of 100 mm (4 in.) in the outer layer and 90 mm (3.54 in.) in the inner layer, providing almost equal flexural resistances in two directions. The bottom reinforcement was 8 mm (0.315 in.) bars posi-tioned directly below alternate top bars. At the edges, each top bar was lapped with a 12.5 mm (No. 4) hair-pin shaped bar with 500 mm (20 in.) horizontal legs. Only minor adjust-ments to this arrangement were needed to avoid clashes with shear reinforcement.

In Slab C5, the tension reinforcement in the central parts of the widths was increased to 20 mm (No. 6) bars with fy = 544 MPa (79 ksi) and Es = 208 GPa (30,168 ksi) and that in the outer parts was decreased, to obtain a higher reinforce-ment ratio near the column without significantly altering the flexural capacity. The details of this slab are shown in Fig.2.

As the failures of some of slabs appeared to be influenced by crushing of the soffit near the column, Slab C6 was provided with compression reinforcement comprised of four 16.0 mm (No. 5) bars through the column in each direction, and 12.5 mm (No. 4) bars below all the top bars in the rest of the width.

The shear reinforcement was double-headed studs made of deformed 10 mm (No. 3) bars with fyw = 535 MPa (78 ksi) and Es = 211 GPa (30,603 ksi), or 12.5 mm (No. 4) bars with fyw = 518 MPa (75 ksi) and Es = 204 GPa (29,588 ksi). The heads, with diameters three times the bar size, were welded to the shanks, and the completed studs were spot-welded to nonstructural carrier rails, which were 10 mm (3/8 in.) wide and 3.2 mm (1/8 in.) thick. The shear reinforcement was positioned from above, with the carrier rails sitting on the upper tension bars either directly or via cross rails.

Tests of studs, in which the loading was applied via the heads, showed that the welds between the heads and shanks were able to develop the full strengths of the bars with ductile failures away from the welds.

In all but one of the slabs, the lines of studs ran outward from the columns along equally spaced radial lines (radial arrangement). The exception was Slab C4, where a cruci-form arrangement was used. Typical details are shown in Fig. 3. Table 1 summarizes the characteristics of all slabs.

TEST RESULTS

Deflections and rotationsDeflections of the top surfaces of the slabs were measured

along their centerlines by dial gauges mounted from frames spanning over the slabs and supported on the laboratory

floor. An example of the deflected profiles is shown in Fig. 4, where it can be seen that segments of the slab rotated about axes at or very close to the column face, and the top surfaces remained more or less straight on radial lines. The displacements of the slab very close to the column, visible in Fig. 4, were likely due mostly to movements in the support of the column, and were not deflections of the slab relative to the column.

Figure 5 shows envelopes of the experimental load- rotation relationships, and the theoretical ones according to CSCT. The experimental rotations plotted are the aver-ages of values determined from deflections, measured on the centerline of the slabs at distances 274 and 1049 mm (10.8 and 41.3 in.) from the slab center in the North, South, East, and West directions. The CSCT values have been calculated from Eq. (13) and (14). The correlations between experimental and calculated results are good.

Strains of concreteStrain gauges were used to measure the strains of the

bottom surfaces of the concrete close to the columns. The general responses were similar to those observed by others. At low loads, the compression strains in both directions were similar, and increased with increasing load. As loading continued, the radial strains stabilized and then decreased, sometimes becoming tensile before failure. The tangential compressions increased at progressively higher rates.

At circular columns, the maximum compression strains were from 2.5 to 2.8, where the gauges were 20 mm (0.8 in.) from the column faces, and 3.1 to 3.2, where the gauges were 40 mm (1.6 in.) from the faces. In the slabs with square columns, the maximum compressions recorded were lower, but this was probably due to their being on the slab centerlines, while the greatest strains were likely at the corners of the columns.

Fig. 2Flexural reinforcement of Slab C5. (Note: Dimensions in mm; 1 mm = 0.0394 in.)


The difference in maximum strains at distances of 20 and 40 mm (0.8 and 1.6 in.) points to restraint from the columns, and the strains 40 mm (1.6 in.) from the columns were probably high enough to indicate distress of the concrete due to tangential stresses, except in the one slab without shear reinforcement.

Table 1Characteristics of test slabs

Slab No. Column size*, mm (in.) d, mm (in.) , % fc, MPa (ksi)Shear reinforcement

Studs so, mm (in.) sr, mm (in.)C1 270 (10.6) 143 (5.6) 1.48 47.8 (6.9) 10 10.0 x 6 70 (2.8) 100 (3.9)C2 360 (14.2) 140 (5.5) 1.52 46.9 (6.8) 10 10.0 x 6 70 (2.8) 100 (3.9)C3 450 (17.7) 142 (5.6) 1.49 48.9 (7.1) 10 10.0 x 6 70 (2.8) 100 (3.9)C4 360 (14.2) 140 (5.5) 1.52 47.9 (6.9) 12 10.0 x 6 70 (2.8) 100 (3.9)C5 360 (14.2) 140 (5.5) 2.00 49.7 (7.2) 10 10.0 x 6 70 (2.8) 100 (3.9)C6 360 (14.2) 143 (5.6) 1.48 48.6 (7.0) 10 10.0 x 6 70 (2.8) 100 (3.9)C7 360 (14.2) 144 (5.7) 1.47 49.0 (7.1) 10 10.0 x 7 55 (2.2) 80 (3.1)C8 360 (14.2) 144 (5.7) 1.47 48.1 (7.0) 12 10.0 x 6 70 (2.8) 100 (3.9)S1 300 (11.8) 145 (5.7) 1.46 48.3 (7.0) 12 10.0 x 2 70 (2.8) 100 (3.9)S2 300 (11.8) 143 (5.6) 1.48 49.4 (7.2) 12 10.0 x 4 70 (2.8) 100 (3.9)S5 300 (11.8) 143 (5.6) 1.48 50.5 (7.3) S7 300 (11.8) 143 (5.6) 1.48 48.9 (7.1) 12 12.5 x 4 70 (2.8) 100 (3.9)

*Diameter in Series C, side length in Series S.Calculated as x y . In all slabs except C5, reinforcement distributed uniformly across widths. For C5, 2.00% is ratio in central (c + 6d), and 1.56% is ratio for full width.Number of studs per perimeter, stud size (mm) by number of perimeters.

Fig. 3Shear reinforcement. (Note: Dimensions in mm; 1 mm = 0.0394 in.)

Fig. 4Load-displacement of Slab C3. (Note: 1 mm = 0.0394 in.)


Figure 6 shows the developments of strains measured in Slabs C2 and C6, the former having only nominal bottom steel, and the latter being the slab with considerable compres-sion reinforcement. In C6, the maximum strain of 3.2 was reached at a load equal to the failure load of C2. There-after, the strain in C6 decreased as the load was increased to failure. This suggests that the 12% higher ultimate strength was achieved with the compression reinforcement locally taking over the function of the failing concrete.

Strains of flexural reinforcementStrains of the flexural tension reinforcement were

measured by pairs of strain gauges at opposite ends of diam-eters of the upper bars, at a section just outside the column. The resulting profiles of tangential strains for Slabs C1 through 4 and C8 are shown in Fig. 7. Strains beyond yield were recorded in considerable parts of the slab widths, but the yielding never reached the slab edge, that is, a yield line was never developed.

Strains of shear reinforcementStrains were measured at the midheight of the shear

studs in four lines of the shear reinforcement in all slabs.

The strains were measured in the inner three rings of shear reinforcement in the slabs with circular columns, and at all perimeters for the slabs with square columns. The average stresses (strain Es) in the shear reinforcement are summa-rized in Table 2. Typical profiles of stud stresses along radial lines are shown in Fig. 8. The stud stresses summarized in Table 2 are thought to be reasonably close to the maximum stresses in the studs because the studs were short. The differ-ence between the measured and maximum stress depends on the product of the bond stress and the distance from the shear crack to the midheight of the studs. Allowing for bond along lengths between cracks and strain gauges, it appears that the first perimeter of shear reinforcement is likely to have yielded in all the tests except C6, C7, and S7.

Ultimate loads and modes of failureAll of the slabs failed by punching, and Table 2 gives the

ultimate loads and summarizes data from relevant strain measurements at or close to failure. The slabs with shear reinforcement failed inside the shear reinforced areas in all cases but S1, where there were only two perimeters of studs, and S7, where the diameter of the studs was 12.5 mm (No. 4).

Fig. 5Load-rotation behavior of tested slabs. (Note: 1 kN = 0.2248 kip.) Fig. 6Strains of concrete at soffits of Slabs C2 and C6.

(Note: 1 kN = 0.2248 kip.)


Fig. 7Strains of flexural reinforcement. (Note: 1 mm = 0.0394 in.; 1 kN = 0.2248 kip.) Fig. 8Average stud stresses at Perimeters 1 to 3. (Note:

1 kN = 0.2248 kip; 1 MPa = 0.1450 kip.)


Specimens C2, C5, and C6 (Table 1) were similar apart from the detailing of the flexural reinforcement. Comparison of the shear strengths of C2 and C5 shows that the punching resistance was increased by approximately 15% by concen-trating 60% of the flexural reinforcement into a 1 m (39 in.) wide band centered on the column whilst maintaining the same flexural capacity across the slab width as in the other tests. The shear strength of C6 was increased by approxi-mately 12% relative to C2 through the provision of addi-tional compression steel.

The specimens were saw-cut half width in two orthogonal directions to reveal the failure surfaces. For the inside fail-ures, most of the surfaces ran from the soffit at the column face to reach the level of the top steel at the second perim-eter of studs, but there were exceptions. In both sections of Slab C1 and one of Slab C2, the failure surfaces crossed the inner studs very close to their upper heads. In Slabs C5, C6, and S2, they reached to the level of the top bars at the third or fourth perimeter of studs. In C7, there were multiple cracks reaching the main steel from the third to the fifth perimeter in one section, while in the perpendicular direction, the surface ran just above the lower heads of the studs out to the fourth layer and reached the top steel at the sixth layer. In the outside failures, the surface was entirely outside the studs in S1, but did cross them just above their lower heads in S7. In some slabs, most notably C6, there was spalling of the slab around the column that commenced before failure.

METHODS OF CALCULATIONAll three approaches considered herein take the punching

strength of a slab with shear reinforcement as the least of VR,cs, VR,out, and VR,max, but not less that VR,c, where VR,c is the resistance of an otherwise similar slab without shear rein-forcement; VR,cs is the combined resistance of the concrete and shear reinforcement; VR,out is the resistance from the concrete alone just outside the shear reinforcement; and VR,max is the maximum resistance possible for a given column size, slab effective depth and concrete strength.

These resistances correspond to failures of the types shown in Fig. 9. The calculations are made for perimeters at specified distances from supports: uo is the perimeter at the outline of the support; u1 is the perimeter used in the calcu-lation of VR,c and VR,cs; and uout is the perimeter used in the calculation of VR,out.Fig. 9Types of punching failure.

Table 2Summary of test results

Slab No. c,max*, ry, mm (in.)Average stud stresses, MPa (ksi)

Vu, kN (kip) Failure mode1 2 3C1 2.66 450 (17.7) 535 (77.6) 317 (46.0) 137 (19.9) 858 (192.9) InC2 2.81 550 (21.7) 530 (76.9) 235 (34.1) 121 (17.5) 956 (214.9) InC3 2.54 625 (24.6) 511 (74.1) 362 (52.5) 189 (27.4) 1077 (242.1) InC4 2.28|| 770 (30.3) 535 (77.6) 461 (66.8) 297 (43.1) 1122 (252.2) InC5 3.24 490 (19.3) 504 (73.1) 264 (38.3) 160 (23.2) 1117 (251.1) InC6 3.20 750 (29.5) 479 (69.5) 421 (61.0) 474 (68.7) 1078 (242.3) InC7 3.14 540 (21.3) 386 (56.0) 419 (60.8) 167 (24.2) 1110 (249.5) InC8 3.14 660 (26.0) 535 (77.6) 436 (63.2) 179 (26.0) 1059 (238.1) InS1 2.37 560 (22.0) 535 (77.6) 473 (68.6) 1021 (229.5) OutS2 2.15 570 (22.4) 535 (77.6) 514 (74.5) 216 (31.3) 1127 (253.4) InS5 1.47 130 (5.1) 779 (175.1) S7 2.67 600 (23.6) 238 (34.5) 285 (41.3) 137 (19.9) 1197 (269.1) Out

*c,max is maximum tangential strain of concrete (measured 20 mm from columns in C1 to C4, S1 and S2, and 40 mm from columns in C5 to C8 and S7). For slab Type S, strains measured on centerlines.ry is radius in which tangential strain > y.Averages of Ess fyw in Perimeters 1, 2, and 3.Ultimate shear force including self-weights of slabs and loading system.||Measured at 0.85Vu.


The locations and lengths of u1 and uout vary with the method of calculation.

The symbols used for spacings of shear reinforcement are as follows: so is the distance from column to inner studs; sr is the radial spacing of studs; and st is the tangential spacing of studs at a perimeter. The effective depth d is taken as the average for orthogonal directions, d = (dx + dy)/2. The expressions for punching resistances are given below in SI units (N and mm) without any explicit safety factors. Those from ACI 318 are for nominal resistances, and the others are for characteristic resistances. The perimeters u1 and uout and the detailing requirements, in relation to the spacings of shear reinforcement, are illustrated by Fig. 10, 11, and 12 for ACI 318, EC2, and the CSCT, respectively.

ACI 318-08As double-headed studs are not considered explicitly, the

equations used herein are those for studs with heads at their top ends and bottom anchorages provided by welds to struc-tural rails

VR,c = 13 1

f u dc

(1)

VR,cs = 0.75VR,c + VR,s (2)

VR,s = ds

A fr

sw yw with fyw 414 MPa (60,000 psi) (3)

VR,out = 16

f u dc out

(4)

VR,max = 23 1

f u dc

if sr 0.5d (5a)

VR,max = 12 1

f u dc

if 0.5d sr 0.75d (5b)

fc is limited to 69 MPa (10,000 psi) for calculation purposes.

EC2-04

VR,c = 0.18k(100fc)1/3u1d (6)

k = 1 200+ / d 2 (7)

VR.cs = 0.75VR,c + VR,s (8)

VR,s = 1 5. ,ds

A fr

sw yw ef (9)

fyw,ef = 1.15(250 + 0.25d) fyw 600 MPa (87,000 psi) (10)

VR,out = 0.18k(100fc)1/3uout,efd (11)

VR,max = 0 3 1 250. f f u d

c

c

o

(12)

is the ratio of flexural reinforcement calculated as x y , where x and y are the ratios in orthogonal directions deter-mined for widths equal to those of the column plus 3d to

Fig. 10Detailing and control perimeters: ACI 318.

Fig. 11Detailing and control perimeters: EC2.

Fig. 12Control perimeters: CSCT.


either side. 0.02 for calculation purposes, and the scope of EC2 is limited to fc 90 MPa (13,000 psi).

Critical shear crack theoryIn the CSCT, punching resistances are related to the rota-

tion of the slab, outside a critical crack. Half of this rota-tion is assumed to occur in the critical shear crack and, as the slab rotates, the concrete component of shear resistance at the crack is assumed to decrease, while the component from the shear reinforcement increases up to yield. The rotation is related to the ratio V/Vflex, where V is the acting shear, and Vflex is the shear force corresponding to the flexural capacity, calculated by yield-line theory. Values of VR,c, VR,cs, VR,out, and VR,max can be determined as shown in Fig. 13, by plotting the resistances against and finding their intersections with Eq. (13)

=

1 5

32

.

r

dfE

VV

s y

s flex (13)

where rs is the distance from the column center to the line of radial contraflexure; and is in radians. For typical punching test specimens, rs is the distance from the column center to the slab edge. The flexural failure load Vflex is approximated by5

Vflex = 2pimr

r rR

s

q c

(14)

where mR is the moment resistance per unit length of yield line; rq is the radius at which loading is applied; and rc is the radius of the column and for square columns can be taken as 2c/, where c is the side length of the column.

In the CSCT average method given in Reference 5

VR,c =

0 751 15 16

1.

/ ( )u d f

d dc

g+ + (15)

VR,s = Aswsi() Aswfyw (16)

VR,cs = VR,c + VR,s (17)

VR,out = 0 75

1 15 16.

/ ( )u d fd d

out v c

g+ + (18)

VR,max = 3VR,c (19)

where si is the stress in the i-th perimeter of shear reinforce-ment which is related to the width of the critical shear crack, where it crosses the shear reinforcement.5 The summations Asw and Aswsi() are for all the shear reinforcement within a distance d from the column.

The CSCT average method is intended to give approxi-mately mean strengths. In it, the stresses in studs at different distances (d) from the column are calculated assuming that the width of the critical shear crack increases linearly, from zero at the slab soffit to the width corresponding to a slab rotation and a crack opening angle of 0.5, at the level of the tension reinforcement. The stress in a stud is then obtained by equating the vertical component of the crack opening to the elongation of the stud for a given stress at the crack.

COMPARISONS OF TESTS AND CALCULATIONS

GeneralExperimental strengths from the present tests and from

others reported in the literature have been compared with resistances calculated by the three methods described previ-ously. The shear reinforcement in the tests by Regan,7 Regan and Samadian,8 Beutel,9 and Birkle10 was double-headed studs made from either deformed or plain round bars. In the tests by Gomes and Regan,11 it was slices of steel I-beams with the flanges acting as anchorages. The shear reinforce-ment was positioned radially unless noted as ACI type in Table A1 in Appendix A.

The calculations of punching resistances were made using the expressions given previously, with their limits generally respected. Exceptions to this were as follows.

For ACI 318 and EC2, the limits on so/d and sr/d were given a little tolerance. Values of sr/d up to 0.8 were treated as acceptable, and for EC2 the lower limit so/d < 0.3 was waived with values going down to 0.24. EC2 does not envisage the use of plain round shear reinforcement, but this has been ignored, and lower limits on d for the use of shear reinforcement were ignored. (The least effective depth in the tests used was 124 mm [4.9 in.] in six slabs by Birkle.10)

The CSCT shear strengths were calculated using slab rotations calculated with Eq. (13), in which Vflex was calcu-lated with Eq. (14). The stresses in the shear reinforcement were calculated in accordance with the recommendations in (5). The resulting slab rotations were slightly greater than the measured slab rotations, as illustrated in Fig. 5. The predicted shear strengths typically increase by less than 5% for the slabs tested in this program if measured rotations are used instead of calculated rotations. For the CSCT, there

Fig. 13Punching strengths according to CSCT: Slab C1. (Note: 1 kN = 0.2248 kip.)


are only a few cases in which there were two perimeters of shear reinforcement within a distance d from the support, but there are some where a second layer was not much further out (all of the slabs by Gomes and Regan11 where the distances varied from 1.0d to 1.04d and Slabs 2, 3, 9, and 12 by Birkle10 where the distances were from 1.09d to 1.18d). The second perimeter has been included in Asw, where the distance was less than 1.05d.

Details of the individual slabs and the results obtained are given in Appendix A, while Tables 3 and 4 summarize the results of the comparisons for slabs without and with shear reinforcement.

Although there are only six results in Table 3, it is note-worthy that, for all the methods of calculation, Vu/Vcalc decreases with increasing effective depth. This is not surprising for ACI 318, which has no size factor, or for EC2, where the size factor is constant for d 200 mm (7.9 in.). It is surprising for the CSCT, which includes a size factor taking account of the effective depth and the maximum size of aggregate. The best correlation in the table is that for EC2*, which is the same as EC2, but without the limit on k = 1 + ( / )200 d . With this modification, however, the mean Vu/Vcalc is low, and the coefficient of 0.18 in Eq. (7) would need to be reduced.

Table 4 summarizes the results of the comparisons with the 45 slabs with shear reinforcement, and all three methods of calculation are broadly satisfactory.

The coefficient of variation of Vu/Vcalc decreases with increasing complexity in the method. The ACI method is the simplest and gives a coefficient of variation of 0.162. The EC2 method is slightly more complex, and reduces the coefficient by 0.026, while the CSCT is considerably more complicated, but gives a further reduction of 0.015.

There are no unsafe predictions from ACI 318, but there are four from EC2 and the CSCT, with the lowest values of Vu/Vcalc being 0.88 for EC2, and 0.90 for the CSCT. An overall reduction of Vcalc by 4% would make each of these methods safe in the sense of limiting the probability of an unsafe prediction to 5%, assuming a statistically normal distribution of Vu/Vcalc.

ACI 318 and EC2 are basically empirical, but the CSCT claims a rational basis. Unfortunately, its modeling of slab deformations is incorrect. The rotation is predicted satis-factorily by Eq. (13), but, as can be seen from Fig. 4, it is not divided equally into movements at the column face and in a shear crack. In addition, the surfaces at which failure occurs are not at 45 degrees to the slab plane, but have variable geometries. Refer to the section entitled, Ultimate loads and modes of failure.

In nine tests by Ferreira1 and five by Birkle,10 EC2 predicts outside failures for slabs that actually failed in the shear-re-inforced zones. Its predictions of failure modes in the other series are generally good. The main cause of the problem seems to be the overestimation of VR,cs. For the slabs by Ferreira,1 the mean Vu/VR,cs is 0.98, and the coefficient of variation is 0.061. For Birkles tests,10 the corresponding figures are 0.88 and 0.101, but would be improved if the four slabs with so/d less than 0.3 were excluded. The situ-ation could be improved by either a reduction of VR,c or by interpreting the codes expression for the design value of the stud stress (fywd,ef) as not requiring a safety factor so long as fywd,ef is less than fyw/1.15that is, by taking fyw,ef as (250 + 0.25d) fyw.

The EC2 predictions of VR,out for slabs with radial arrange-ments of shear reinforcement are generally satisfactory, though perhaps over-conservative for the slabs by Gomes and Regan.11 In these slabs, the 0.64d widths of the I-beam flanges reduced the clear tangential spacing of the shear reinforcement. This could be allowed for, and would make Vu/VR,out for these tests similar to those for other series.

The strength of Ferreiras1 Slab C4 with an ACI cross arrangement of studs which failed inside is predicted very conservatively with Vu/VR,out = 1.69. For Birkles10 slabs with the ACI layout, which failed outside, the strengths are well predicted with Vu/VR,out = 1.21. Slab C4 was unrealistic in relation to EC2 design because it had six perimeters of studs, while the same strength would be calculated for a slab with two perimeters of studs. The performance of C4 is in marked

Table 3Comparisons with test results for slabs without shear reinforcement

Slab No. d, mm (in.) , %Vu/Vcalc

ACI 318 EC2 CSCT EC2*

Ferreira1

S5 143 (5.6) 1.48 1.30 1.20 1.24 1.10

Gomes and Regan11

11A

159 (6.3)159 (6.3)

1.271.27

1.161.20

0.961.01

1.001.03

0.890.92

Birkle10

1710

124 (4.9)190 (7.5)260 (10.2)

1.531.291.10

1.301.120.88

1.110.940.78

1.101.020.86

0.960.930.78

Mean 1.16 0.99 1.04 0.93

Coefficient of variation 0.13 0.15 0.12 0.11

*EC2 calculations as for EC2, but with no upper limit on k = 1+(200/d).

Table 4Statistics of Vu/Vcalc for slabs with shear reinforcement

No. oftests

ACI 318 EC2 CSCT

Mean COV Mean COV Mean COVFerreira1

11 1.47 0.148 1.20 0.160 1.23 0.108

Regan7 and Regan and Samadian8

9 1.56 0.100 1.06 0.087 1.05 0.102

Beutel9

6 1.72 0.093 1.34 0.087 1.16 0.101

Gomes and Regan11

10 1.76 0.134 1.28 0.081 1.28 0.083

Birkle10

9 1.35 0.185 1.09 0.105 1.06 0.050

Total

45 1.56 0.162 1.19 0.136 1.16 0.121


contrast to that of slabs by Mokhtar et al.,12 with up to eight perimeters of studs on stud rails. Their strengths are quite well predicted by EC2.

Influence of slab rotation on shear resistance provided by concrete

Unlike ACI 318 and EC2, the CSCT predicts that the shear resistance provided by concrete reduces with slab rotation, which is assumed to be proportional to (V/Vflex)1.5. This has significant implications for design because Vu/Vflex may be close to one for practical slabs. Consequently, the CSCT can require significantly greater areas of shear reinforcement than EC2. The influence of slab rotation on Vu/Vcalc for the CSCT is illustrated by Fig. 14, where the ratio is plotted against the normalized rotation d/(16 + dg), with calcu-lated by Eq. (13). There is a clear tendency for the CSCT to become more conservative with increasing slab rotation, which suggests that Vu is either independent of , or that the CSCT overestimates the influence of rotation. In the case of outside failure, this is to be expected as the rotation develops close to the column and not within a crack outside the shear reinforcement.

Muttoni4 plots Vu/u1d fc against d/(16 + dg) for 99 tests of slabs without shear reinforcement, and shows that exper-imental strengths are close to the predictions of Eq. (15), which may appear to contradict the preceding paragraph. This, however, is not the case. Figure 15 shows Vu/u1d fc plotted against d/(16 + dg) for slabs similar to Ferreiras1 C2, but without shear reinforcement, and with from 0.4 to 4.0%. The values of Vu have been calculated by EC2 and the CSCT, u1 is the CSCT control perimeter, and is the rotation calculated by Eq. (13). It can be seen that the effect shown in Muttonis figure can be accounted for by the EC2 relationship between VR,c and 1/3 without involving in the calculations.

Failure surface and locations of shear reinforcement

ACI 318 and the CSCT assume punching surfaces to be inclined at 45 degrees, while EC2 assumes an inclination of 26.6 degrees. These are simplifications of a reality in which the angle increases with increasing shear reinforcement

(refer to Carvalho et al.13). Reasonable results can, however, be obtained in most instances with fixed angles, provided the expressions for VR,c and VR,s are constructed appropriately.

This seems to be the case with ACI 318 and EC2, with the former considering d/sr perimeters of studs acting at fyw, and the latter assuming 1.5d/sr perimeters acting at fyw,eff, which is typically approximately 0.7fyw for test slabs. The situation is more complex in the CSCT, as its numbers of perimeters depend on the exact distances of studs from the column.

There are cases where the use of different failure surfaces has a significant effect. Slabs 2, 3, 10, and 11 by Gomes and Regan11 are an example. In these slabs so = sr 0.5d, Asw = 226 mm2 (0.36 in.2) in Slabs 2 and 10, and 325 mm2 (0.5 in.2) in Slabs 3 and 11. Slabs 2 and 3 had two perime-ters of shear reinforcement, while Slabs 10 and 11 had three. Thus, for ACI 318, two perimeters are taken into account for all the slabs, while in EC2, two perimeters are active in Slabs 2 and 3, but three are active in Slabs 10 and 11. All four slabs failed inside their shear reinforced zones. The EC2 ratios Vu/VR,cs are 1.26 and 1.21 for Slabs 2 and 3, and 1.28 and 1.31 for Slabs 10 and 11. The ACI ratios are 1.39 and 1.28 for Slabs 2 and 3, and 1.58 and 1.61 for Slabs 10 and 11, showing that the extra perimeter of shear reinforcement had an effect.

The same slabs illustrate a problem with the CSCTs considering the active shear reinforcement to be exactly that within a distance d from a column rather than using an expression in d/sr. Because of variations of effective depths, (so + sr) = 1.05d in three cases instead of the intended 1.0d. This discrepancy has been ignored in the calculations for Table A1, but if the CSCT were applied strictly the ratios Vu/VR,cs, which are already unusually high for Slabs 10 and 11, would be significantly increased.

CONCLUSIONSComparisons have been made between the punching

strengths of 45 slabs with and six slabs without shear reinforce-ment and those predicted by ACI 318, EC2, and the CSCT.

ACI 318 is the simplest method, and gives only one unsafe prediction, which is for a slab without shear reinforcement. Its mean value of Vu/Vcalc for slabs with shear reinforcement is rather high, and the coefficient of variation is 0.162. The

Fig. 14Influence of slab rotation on Vu/Vcalc CSCT.Fig. 15Influence of slab rotation on shear strength.


most apparent weakness is the lack of any treatment of the depth effect in the shear resistance from the concrete.

EC2 is only slightly more complicated, but reduces the coefficient of variation of Vu/Vcalc by 0.026. The mean is also reduced, and there are four unsafe predictions for slabs with and four for slabs without shear reinforcement. The simplest way to obtain a characteristic level of safety would be to reduce the constant in the expression for the concrete component of resistance and extend the range of slab depths affected by the depth factor.

The CSCT is considerably more complex, and reduces the mean and coefficient of variation of Vu/Vcalc, by a further 0.015. There are unsafe predictions for four slabs with and one without shear reinforcement.

The CSCT goes further than the other two approaches in attempting to model the slab behavior. Although its expres-sion for total slab rotation seems good, the assumption that half of this rotation occurs in the critical shear crack is incor-rect, as nearly all of it is at the column face. The assumption that all critical cracks are at 45 degrees to the slab plane is also incorrect.

The relationship assumed between the concrete compo-nent of punching resistance and slab rotation is not confirmed by the test data, and the determination of the area of active shear reinforcement as that crossed by a particular 45 degree surface seems less satisfactory than considering d/sr perimeters.

AUTHOR BIOSACI member Maurcio P. Ferreira is a Lecturer at the Federal Univer-sity of Para, Belem, Brazil. He received his PhD from the University of Braslia, Braslia, Brazil, in 2010. His research interests include ultimate shear design, strut and tie, and nonlinear finite element modeling.

ACI member Guilherme S. Melo is an Associate Professor at the Univer-sity of Brasilia, where he was Head of the Department of Civil and Environ-mental Engineering. He is a member of ACI Committees 440, Fiber-Rein-forced Polymer Reinforcement; and Joint ACI-ASCE Committee 445, Shear and Torsion. His research interests include punching and post-punching of flat plates, the use of fiber-reinforced plastic (FRP) in concrete structures, and strengthening and rehabilitation of structures.

ACI member Paul E. Regan is a Professor Emeritus at the University of Westminster, London, UK, where he was Head of Architecture and Engi-neering. He was Chair of the European Concrete Committee (CEB) commis-sion on member design. His research interests include member design in both reinforced and prestressed concrete, with particular emphasis on problems of punching, shear, and torsion.

ACI member Robert L. Vollum is a Reader in concrete structures at Impe-rial College London, London, UK, where he also received his MSc and PhD. His research interests include design for shear, strut-and-tie modeling, and design for the serviceability limit states of deflection and cracking.

ACKNOWLEDGMENTSThe authors are grateful to the Brazilian Research Funding Agencies

CAPES (Higher Education Co-ordination Agency) and CNPq (National Council for Scientific and Technological Development) for their support throughout this research and to RFA-Tech for their permission to include test results from Reference 7.

NOTATIONAsw = area of shear reinforcement in one perimeter

c = side length of square column or diameter of circular columnd = mean effective depthdg = maximum size of aggregatedv = depth from tension reinforcement to compression zone

anchorage of shear reinforcementEs = modulus of elasticity of reinforcementfc = cylinder compression strength of concretefy = yield stress of flexural reinforcementso = distance from column face to first perimeter of shear

reinforcementsr = radial spacing of shear reinforcementst = tangential spacing of shear reinforcementst,max = maximum value of st (general in outer perimeter of shear

reinforcement)u0 = length of column perimeteru1 = length of control perimeter for calculation of VR,c and VR,csuout = length of control perimeter for calculation of VR,outuout,ef = effective value of uout for calculations by EC2, where st,max > 2dV = applied shear forceVcalc = calculated punching resistanceVflex = flexural strength of slab calculated by yield-line theoryVR,c = punching resistance of slab without shear reinforcementVR,cs = punching resistance within shear reinforced zoneVR,max = maximum punching resistance for given column size, slab effec-

tive depth, and concrete strengthVR,out = punching resistance outside shear reinforced zoneVR,s = contribution of shear reinforcement to punching resistance VR,csVu = experimental punching strength = ratio of flexural reinforcement = x y (calculated for width

of column plus 3d to either side in EC2) = rotation of part of slab outside critical shear crack

REFERENCES1. Ferreira, M. P., Puno em Lajes Lisas de Concreto Armado com

Armaduras de Cisalhamento e Momentos Desbalanceados, PhD thesis, Universidade de Braslia, Braslia, Brazil, 2010, 275 pp. (in Portuguese) available at http://repositorio.bce.unb.br/handle/10482/8965.

2. ACI Committee 318, Building Code Requirements for Structural Concrete (ACI 318-08) and Commentary, American Concrete Institute, Farmington Hills, MI, 2008, 473 pp.

3. Eurocode 2, Design of Concrete Structures Part 1-1: General Rules and Rules for Buildings, CEN, EN 1992-1-1, Brussels, Belgium, 2004, 225 pp.

4. Muttoni, A., Punching Shear Strength of Reinforced Concrete Slabs without Transverse Reinforcement, ACI Structural Journal, V. 105, No. 4, July-Aug. 2008, pp. 440-450.

5. Fernadez-Ruiz, M., and Muttoni, A., Applications of the Critical Shear Crack Theory to Punching of R/C Slabs with Transverse Reinforce-ment, ACI Structural Journal, V. 106, No. 4, July-Aug. 2009, pp. 485-494.

6. Fdration internationale du bton, fib Model Code 2010, First complete draftV. 2, Bulletin 56, fib, Lausanne, Switzerland, Apr. 2010, 288 pp.

7. Regan, P. E., unpublished tests for RFA-TECH at Cambridge Univer-sity, 2009.

8. Regan, P. E., and Samadian, F., Shear Reinforcement against Punching in Reinforced Concrete Flat Slabs, The Structural Engineer, V. 79, No. 10, May 2001, pp. 24-31.

9. Beutel, R., Punching of Flat Slabs with Shear Reinforcement at Inner Columns, Rheinisch-Westflischen Technischen Hochschule Aachen, Aachen, Germany, 2002, 267 pp. (in German)

10. Birkle, G., Punching of Flat Slabs: The Influence of Slab Thickness and Stud Layout, PhD thesis, Department of Civil Engineering, University of Calgary, Calgary, AB, Canada, Mar. 2004, 152 pp.

11. Gomes, R., and Regan, P. E., Punching Strength of Slabs Rein-forced for Shear with Offcuts of Rolled Steel I-Section Beams, Magazine of Concrete Research, V. 51, No. 2, 1999, pp. 121-129.

12. Mokhtar, A. S.; Ghali, A.; and Dilger, W., Stud Shear Reinforce-ment for Flat Concrete Plates, ACI Journal, V. 82, No. 5, Sept.-Oct. 1985, pp. 676-683.

13. Carvalho, A. L.; Melo, G. S.; Gomes, R. B.; and Regan, P. E., Punching Shear in Post-Tensioned Flat Slabs with Stud Rail Shear Reinforcement, ACI Structural Journal, V. 108, No. 5, Sept.-Oct. 2011, pp. 523-531.


APPENDIX ATable A1Comparison between theoretical and experimental results

AuthorSlabNo.

Column size, mm

d,mm , %

fy, MPa

fc, MPa

Shear reinforcementVu, kN

Failure mode

Vu/Vflex

Vu/Vcalc and critical strength

Studsfyw,

MPaso,

mm

sr,

mm

stmax,

mm ACI 318-08 EC2-04CSCT

average

Ferr

eira

1

C1 270 C 143 1.48 540 48 10 10.0 x 6 535 70 100 436 858 In 0.72 1.34 Max 0.96 Out 1.07 InC2 360 C 140 1.52 540 47 10 10.0 x 6 535 70 100 464 956 In 0.78 1.27 Max 1.11 Out 1.12 InC3 450 C 142 1.49 540 49 10 10.0 x 6 535 70 100 491 1077 In 0.82 1.21 Out 1.20 Out 1.15 InC4* 360 C 140 1.52 540 48 12 10.0 x 6 535 70 100 900 1122 In 0.92 1.47 Max 1.69 Out 1.50 OutC5 360 C 140 2.00 544 50 10 10.0 x 6 535 70 100 464 1118 In 0.88 1.44 Max 1.16 Out 1.29 InC6 360 C 143 1.48 540 49 10 10.0 x 6 535 70 100 464 1078 In 0.86 1.36 Max 1.19 Out 1.24 InC7 360 C 144 1.47 540 49 10 10.0 x 7 535 55 80 442 1110 In 0.88 1.39 Max 1.21 Out 1.09 OutC8 360 C 144 1.47 540 48 12 10.0 x 6 535 70 100 388 1059 In 0.84 1.34 Max 1.03 Out 1.14 InS1 300 S 145 1.46 540 48 12 10.0 x 2 535 70 100 177 1022 Out 0.80 1.71 In 1.36 Out 1.37 OutS2 300 S 143 1.48 540 49 12 10.0 x 4 535 70 100 280 1128 In 0.89 1.77 Out 1.12 Out 1.24 OutS5 300 S 143 1.48 540 50 779 P 0.61 1.30 P 1.20 P 1.24 PS7 300 S 143 1.48 540 49 12 12.5 x 4 518 70 100 280 1197 Out 0.94 1.88 Out 1.19 Out 1.32 Out

Reg

an7

1 300 S 150 1.45 550 33 10 10.0 x 4 550 80 120 390 881 0.79 1.45 Out 1.02 Out 1.06 In2 300 S 150 1.76 550 30 12 10.0 x 6 550 60 100 390 1141 0.88 1.71 Out 1.13 Out 1.11 Out3 300 S 150 1.76 550 26 10 12.0 x 5 550 60 120 455 1038 0.83 1.73 Out 1.22 Out 1.09 Out5 240 C 160 1.65 550 62 12 12.0 x 5 550 80 120 352 1268 0.88 1.61 Max 0.88 Out 1.12 In6 240 C 150 1.75 550 42 12 10.0 x 5 550 75 120 349 1074 0.83 1.81 Max 1.04 In 1.24 In

Reg

an a

nd

Sam

adia

n8 R3 200 S 160 1.26 670 33 8 12.0 x 4 442 80 120 413 850 Out 0.63 1.44 Out 1.04 Out 0.90 OutR4 200 S 160 1.26 670 39 8 12.0 x 6 442 80 80 444 950 Out 0.69 1.39 Out 1.10 Out 0.93 OutA1 200 S 160 1.64 570 37 8 10.0 x 6 519 80 80 444 1000 Out 0.67 1.50 Out 1.08 Out 0.98 OutA2 200 S 160 1.64 570 43 8 10.0 x 4 519 80 120 413 950 In 0.62 1.42 Out 1.03 In 1.00 In

Beu

tel9

Z1 200 C 250 0.80 890 25 12 14.0 x 5 580 100 200 518 1323 Max 0.41 1.50 Max 1.26 Max 0.96 InZ2 200 C 250 0.80 890 26 12 14.0 x 5 580 88 200 511 1442 Max 0.44 1.59 Max 1.30 Max 1.08 InZ3 200 C 250 0.80 890 24 12 14.0 x 5 580 95 188 487 1616 Max 0.50 1.86 Max 1.57 Max 1.20 InZ4 200 C 250 0.80 890 32 12 14.0 x 5 580 88 175 459 1646 Max 0.49 1.66 Max 1.27 Max 1.18 InZ5 263 C 250 1.25 562 28 12 16.0 x 5 544 94 188 505 2024 Max 0.41 1.90 Max 1.31 Max 1.28 InZ6 200 C 250 1.25 562 37 12 16.0 x 5 544 94 188 489 1954 Max 0.39 1.81 Max 1.31 Max 1.23 In

Gom

es a

nd R

egan

11

1 200 S 159 1.27 680 40 560 P 0.40 1.16 P 0.94 P 1.00 P1a 200 S 159 1.27 680 41 587 P 0.41 1.20 P 0.98 P 1.03 P2* 200 S 153 1.32 680 34 8 6.0 x 2 430 80 80 255 693 In 0.53 1.64 In 1.26 In 1.12 Out3* 200 S 158 1.27 670 39 8 6.9 x 2 430 80 80 255 773 In 0.57 1.64 In 1.21 In 1.20 Out4* 200 S 159 1.27 670 32 8 8.0 x 3 430 80 80 368 853 Out 0.64 1.98 In 1.27 Out 1.26 Out5* 200 S 159 1.27 670 35 8 10.0 x 4 430 80 80 481 853 Out 0.63 1.77 Out 1.24 Out 1.13 Out6 200 S 159 1.27 670 37 8 10.0 x 4 430 80 80 323 1040 Out 0.76 2.07 Out 1.23 Out 1.34 Out7 200 S 159 1.27 670 34 8 12.0 x 5 430 80 80 385 1120 Out 0.83 2.02 Out 1.38 Out 1.38 Out8 200 S 159 1.27 670 34 8 12.0 x 6 430 80 80 447 1200 Out 0.89 1.90 Out 1.48 Out 1.38 Out9 200 S 159 1.27 670 40 8 12.2 x 9 430 80 80 425 1227 0.89 1.31 Out 1.09 Out 1.26 Max

10 200 S 154 1.31 670 35 8 6.0 x 5 430 80 80 385 800 In 0.61 1.58 In 1.28 In 1.33 In11 200 S 154 1.31 670 35 8 6.9 x 5 430 80 80 385 907 In 0.70 1.68 Out 1.31 In 1.42 In

Birk

le10

1 250 S 124 1.53 488 36 483 P 0.56 1.30 P 1.11 P 1.10 P2* 250 S 124 1.53 488 29 8 9.5 x 6 393 45 90 721 574 In 0.68 1.24 Out 1.19 Out 1.08 Out3 250 S 124 1.53 488 32 8 9.5 x 6 393 45 90 495 572 In 0.67 1.10 Out 1.12 Out 1.02 In4* 250 S 124 1.53 488 38 8 9.5 x 5 465 30 60 403 636 Out 0.73 1.67 In 1.21 Out 1.09 Out5* 250 S 124 1.53 488 36 8 9.5 x 5 465 30 60 403 624 Out 0.72 1.67 In 1.21 Out 1.09 Out6 250 S 124 1.53 488 33 8 9.5 x 5 465 30 60 330 615 Out 0.72 1.67 Out 1.18 Out 1.04 Out7 300 S 190 1.29 531 35 825 P 0.49 1.12 P 0.94 P 1.02 P8* 300 S 190 1.29 531 35 8 9.5 x 5 460 50 100 658 1050 In 0.62 1.29 Out 0.98 Out 0.97 In9* 300 S 190 1.29 531 35 8 9.5 x 6 460 75 150 1188 1091 In 0.64 1.28 In 1.06 In 1.15 In

10* 350 S 260 1.10 524 31 1046 P 0.40 0.88 P 0.78 P 0.86 P11* 350 S 260 1.10 524 30 8 12.7 x 5 409 65 130 856 1620 In 0.63 1.24 Out 1.00 Out 1.02 In12* 350 S 260 1.10 524 34 8 12.7 x 6 409 95 195 1541 1520 In 0.58 1.03 In 0.90 Out 1.08 In

*ACI stud layout. Notes: Vu includes self-weight; Vflex is approximate yield-line capacity from Eq. (14). Shear reinforcement: In References 1 and 7: deformed studs, 3 heads, so as given for all lines; in Reference 8, slabs R, plain studs, 2.5 heads, Slabs A deformed studs, 2.5 heads, so as given for orthogonal lines, so = 40 mm for diagonal lines; in Reference 9, deformed studs, 3 heads, so as given for all lines; in Reference 11, I-beam slices, flange breath 102 mm, web breath 4.7 mm. values in the table are equivalent diameters giving the same areas as the actual web sections. so as given for orthogonal lines, so = 40 mm for diagonal lines; in Reference 10, plain studs with 3.2 heads, so as given for all lines. Birkles Slabs 5 and 6 had 7 perimeters of studs. The outer two, with sr = d, have been ignored. Aggregate (maximum size and type): In Reference 1, 9.5 mm crushed limestone. In References, 7, 8, 9, and 11, 20 mm gravel. In Reference 10, Slabs 1-614 mm; Slabs 7-1220 mm, type unknown. Failure modes: P is punching of slabs without shear reinforcement, In = failure inside shear reinforced zone (VR,cs), Out = failure outside shear reinforced zone (VR,out); Max = inclined compression failure of concrete close to column (VR,max); in Reference 7 and Slab 9 of Reference 10, the concrete soffit around the column crushed and spalled due to tangential compression, the spalling extended and at failure there was inclined cracking starting at the end of the spalled area. 1 mm = 0.03937 in.; 1 kN = 0.225 kip; 1 MPa = 145 psi.

12-119_ferreira phd thesis

Documents