ACI Structural Journal/July-August 2013 1

Title no. 110-S43

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

ACI Structural Journal, V. 110, No. 4, July-August 2013.MS No. S-2010-284.R2 received July 17, 2012, and reviewed under Institute

publication policies. Copyright © 2013, 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 May-June 2014 ACI Structural Journal if the discussion is received by January 1, 2014.

Punching Shear of Reinforced Concrete Flat Plates with Openingsby Liana L. J. Borges, Guilherme S. Melo, and Ronaldo B. Gomes

Punching shear tests were conducted on 13 reinforced concrete flat plates with and without openings or/and shear reinforce-ment. The openings (one or two) were adjacent to the shorter sides of rectangular supports and had widths equal to those of the supports. The methods of calculating punching shear strengths given in ACI 318-11 and MC90/EC2 are reviewed along with some proposed formulations, and their predictions are compared with the test results.

Conclusions are drawn on the influence of plate depth on the unit shear resistance from the concrete; the possibility of using straight projections of openings onto control perimeters, rather than radial ones, to evaluate the effect of openings; and the case for consid-ering eccentricity in a pattern of openings as an influencing factor and the detailing of shear reinforcement.

It is shown that for the relatively small openings considered, the provision of continuous bars adjacent to openings—to replace the areas of reinforcement—seems to be an adequate approach to flexural design. It is suggested that the shear stress used for the concrete in ACI 318-11 could be increased for the assessment of strengths at the edges of zones with shear reinforcement (outer control perimeter).

Keywords: flat plates; openings; punching shear; rectangular columns; shear reinforcement.

INTRODUCTIONAlthough there has been significant experimental

work1-6 on flat plates with openings near columns, the treat-ment of their punching strengths in international codes is still not very comprehensive. This is partly because the experi-mental data are limited with relatively few results available for rectangular columns and for slabs with shear reinforce-ment. It is also partly due to neglecting the effects of the location of openings that are eccentric relative to columns.

The experimental work presented herein seeks to fill some of the gaps in the existing knowledge by testing 13 flat-plate specimens with both symmetrical and nonsymmetrical patterns of openings near rectangular columns. The size of the openings considered can be significant for punching strength. The tests also examined the effects of different arrangements of shear reinforcement for slabs with and without openings.

A review of design methods, which follows this introduc-tion, summarizes the provisions of major international codes and some suggested formulations on their treatment of open-ings. The comparisons between experimental and theoretical results allow conclusions to be drawn on the consistency of strength predictions.

The main work considered herein is a series of tests to study the behavior of slabs with openings adjacent to the short sides of rectangular supports made. Specimens with or without shear reinforcement were tested. Data from smaller scale tests by Silva7 are also included at the Appendix, as they extend the range of column rectangularity for slabs with openings.

RESEARCH SIGNIFICANCEThe research reported provides experimental data on the

effects on punching resistance produced by two patterns of openings—one symmetric and the other nonsymmetric—and on the behavior of slabs with openings and shear reinforcement. Although limited by the scope of the testing, the conclusions drawn should be immediately useful in some cases and probably have more general implications.

CODES AND OTHER RECOMMENDATIONSSlabs without shear reinforcement

To avoid undue complexity in comparisons with test results and to concentrate on the effects of openings in slabs, only two basic treatments of punching are considered: those of ACI 318-118 and MC909/EC2.10 All calculations are made by expressions for unfactored strengths and using actual material properties. At concentrically loaded interior supports, without either openings or shear reinforcement in the slab, punching strengths are calculated as follows in MPa. Equations are also given in the English system of units for completeness. For ACI 318-11,8 the equations are not given, as they are easily obtained by the readers.

MC909/EC210

Vc = vcu1d ≤ Vmax (1)

where vc is given in Eq. (2)

( ) ( )

( ) ( )

31

31

2000.18 100 MPa 1mm

7.87        =  4.97 100 psi 1in.

c c

c

v fd

fd

= ρ +

ρ +

(2)

where u1 is the length of a control perimeter 2d from the support and has rounded corners; ρl is the ratio of flexural reinforcement; and Vmax is given in Eq. (3)

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

MPa0.3 MPa 1 mm mm

250

psi             0.3 psi 1 in. in.

36,250

cmax c o

cc o

fV f u d

ff u d

= −

= −

(3)

2 ACI Structural Journal/July-August 2013

Liana L. J. Borges is a Lecturer at Federal Institute of Goiás, Goiânia, Brazil. She received her MSc and her PhD from University of Brasília, Brasília, Brazil. Her research interests include flat plates.

ACI member Guilherme S. Melo is a Professor at the University of Brasília, where he was the Head of the Department of Civil and Environmental Engineering. He is a member of ACI Committees 440, Fiber Reinforced Polymer Reinforcement, and Joint ACI-ASCE Committee 445, Shear and Torsion. His research interests include punching and post-punching in flat plates and the strengthening of structures.

Ronaldo B. Gomes is a Professor at the Universidade Federal de Goiás, where he was Head of the post-graduate course in civil engineering. His research interests include punching in flat plates and the rehabilitation and strengthening of structures.

where uo is the length of the periphery of the column.In EC2, but not in MC90,

( ) ( )200 7.871 1mm in.d d

+ = +

is limited to a maximum of 2.0, but this precautionary restriction is ignored herein.

To take account of the effects of openings near a support, both ACI 318-11 and MC90 reduce the lengths of their control perimeters by subtracting the lengths between lines radiating from the center of the support and tangent to the extremities of the openings (Fig. 1). In EC2, the approach is similar but, if the dimension of the opening in the radial direction l1 is greater than the dimension l2 in the transversal direction, l2 is replaced by (l1l2)1/2. For both MC90 and EC2, both u1 and uo are reduced by openings.

This radial projection approach is very simple but perhaps not very logical. For a rectangular support, it predicts that an opening of a given size is more harmful if it occurs at the long side of the support rather than at the short one, which seems improbable, as the shear can be expected to concentrate near the short sides. The method also ignores any harmful effects that may arise due to unevenness of shear caused by a lack of symmetry in the pattern of openings.

Various attempts have been made to improve the treatment of openings. Regan11 proposed straight projection with only

the actual widths of openings subtracted from control perim-eters for symmetrical patterns of openings, but with account taken of any lack of symmetry by considering fictitious openings restoring symmetry. A similar approach is given in the handbook12 to the British code, but without the treatment of nonsymmetric openings. In the following two versions of straight projection, SP1 and SP2 are adopted—SP1 denotes the use of actual openings only and SP2 denotes the use of extra fictitious openings to restore symmetry (Fig. 1).

An obvious alternative for the treatment of nonsymmetric openings would be to consider only the actual openings and to take account of eccentricity between the load or reaction and the reduced control perimeter by adopting the approach used for eccentric loading on unperforated slabs. This would have the advantage of consistency in the treatments of the two types of eccentricity and would probably be prefer-able for large openings and for cases where the two types of eccentricity coexist. It is, however, not considered further herein, as it seems unnecessary for openings of the size of those in the present tests with no moments transmitted to the supports. Kuang and Teng5 and Teng at al.6 proposed the system of radial projection that is illustrated in Fig. 1 (bottom right), along with the code methods and the two versions of straight projection (SP1 and SP2). In Teng’s approach, even though all the patterns were eccentric in the tests of References 5 and 6, no explicit account was taken of any effects from eccentricity in the pattern of openings.

Slabs with shear reinforcementFor slabs with shear reinforcement in circumferential

layers of equal steel area at a regular radial spacing, both ACI 318-11 and MC90/EC2 limit punching resistance to the least of:• Vcs—the combined resistance of the concrete and shear

reinforcement calculated for the perimeter u1;• Vout—the resistance of the concrete alone at a perimeter

uout, outside the outermost shear reinforcement; and• Vmax—a maximum shear resistance.

For slabs with vertical shear reinforcement, the relevant expressions are given in Eq. (4) and (5). For ACI 318-11,8 the equations are not given, as is easily obtained by the readers, and both the radial distance from the support to the first layer of shear reinforcement and the radial spacings sr of subse-quent layers are limited to d/2 and the transversal spacing of the elements in the first layer is limited to 2d (Fig. 2)

MC90/EC2

1.50.75cs c sw swr

dV V A fs

= +

(4)

Vout = vcuoutd (5)

where Vmax is as for slabs without shear reinforcement; fsw = 1.15(250 + 0.25d) ≤ fyw in EC2; fsw = 345 MPa (50.0 ksi) ≤ fyw in MC90; and uout is the length of a control perimeter 1.5d outside the outer shear reinforcement in EC2, or 2.0d outside it in MC90.

The radial distance from the support to the first layer of shear reinforcement should be 0.35d to 0.5d, and the radial spacings of subsequent layers should not exceed 0.75d. The circumferential spacing of elements of shear reinforcement is limited to 1.5d in layers within u1 and in the outermost layer it should not exceed 2d, where the part of the perimeter

Fig. 1—Methods of reducing control perimeters u1 to allow for openings (l1 and l2 are opening dimensions).

ACI Structural Journal/July-August 2013 3

in question is included in uout (refer to Fig. 2). Neither code gives any advice on the application of these recommenda-tions to slabs with openings near supports, and this intro-duces some problems.

According to ACI 318-11, “that part of the critical section that is enclosed by straight lines projecting from the centroid of the column...and tangent to the boundaries of the open-ings shall be considered ineffective.” (Item 11.12.5 of ACI 318-118, Fig. 1, top left). The wording of EC2 is similar. If no shear reinforcement was placed in the slab areas between the straight lines, the interpretation of the guidance would be straightforward. However, it would seem natural to provide shear reinforcement adjacent to openings, as it is here that the initial shear stresses are likely to be highest. It is debatable whether such shear reinforcement is meant to be treated as effective. Assuming that it can be, it is unclear what parts of the perimeters u1 and uout should be used in determining the shear concrete resistances.

EXPERIMENTAL WORKIn the main series of the test program,13 the slabs

were 200 mm (7.87 in.) thick and 3.0 m (118.11 in.) square on plan. At their centers, they were supported by a thick steel plate 200 x 600 mm (7.97 x 23.62 in.) on plan. Upward loading was applied by a hydraulic jack below this plate and measured by a load cell between the jack and plate. Loading was applied on a load-controlled basis. Reactions were provided by tie bars 150 mm (5.91 in.) from the slab edges, positioned as shown in Fig. 3. The flexural reinforcement of all the slabs was 16 mm (0.63 in.) bars at 100 mm (3.94 in.) centers both ways in the top, extending full width, with 12.5 mm (0.5 in.) hairpin (U-type) bars extending 675 mm (26.57 in.) horizontally in the top and bottom at the slab edges. At the bottom of all the slabs were 8 mm (0.31 in.) bars at 150 mm (5.91 in.) centers both ways, extending full width. In the slabs with openings, this basic pattern of flex-ural reinforcement was modified locally as described in the following. A top clear cover of 20 mm (0.74 in.) and bottom clear cover of 25 mm (0.98 in.) to the outermost reinforcing steel bars or shear reinforcement were adopted. This resulted in a top clear cover of 20 mm (0.74 in.) to the main flexural bars for Slabs 1, 4, 5, 6, 7, 8, and 9, and a top clear cover of 30 mm (1.18 in.) to the main flexural bars for Slabs 2, 3, 10, 11, 12, and 13. The yield strengths of the reinforce-ment were 541 MPa (78.5 ksi) for the 12.5 mm (0.49 in.)

and 601 MPa (87.2 ksi) for the 16.0 mm (0.63 in.), and the measured stress-strain properties are shown in Fig. 4.

Where shear reinforcement was used, it was in the form of stud rails. The studs were 8 or 10 mm (0.31 or 0.39 in.) diam-eter deformed bars welded to a 40 x 10 mm (1.57 x 0.39 in.) plate rail at the bottom and a 40 x 40 mm (1.57 x 1.57 in.) plates at the top. A typical stud rail is shown in Fig. 5 in rela-tion to the flexural reinforcement, together with an overview of the test setup. The yield strengths of the shear reinforce-ment were 598 MPa (86.7 ksi) for the 8.0 mm (0.31 in.) bars and 593 MPa (86.0 ksi) for the 10.0 mm (0.39 in.) bars.

The main series comprised 13 slabs. Slabs 1 to 3 were without openings. Slab 1 was without shear reinforce-ment, while Slabs 2 and 3 had four and two layers of studs arranged, respectively, as in Fig. 6. The next six slabs were without shear reinforcement. Slabs 4 to 6 each had a single opening 200 x 300 mm (7.87 x 11.81 in.) at one short side

Fig. 2—Perimeter uout according to EC2, MC90, and ACI.

Fig. 3—Typical test slabs (Slab 7). (Note: Dimensions in mm; 1 mm = 0.0394 in.)

4 ACI Structural Journal/July-August 2013

of the support, while Slabs 7 to 9 had pairs of 200 x 300 mm (7.87 x 11.81 in.) openings—one at each short side of the plate. The detailing of the flexural reinforcement near the openings was varied in these tests. In Slabs 4 and 7, where main bars were interrupted by openings, the steel area was made up by additional full-length bars near the open-ings. In Slabs 5 and 8, no continuous bars were added, but

Fig. 4—Measured stress-strain properties for steel used (8, 10, 12.5, and 16 mm). (Note: 1 mm = 0.0394 in.; 1 MPa = 145 psi.)

Fig. 5—Test setup (left) and typical detail of stud rail. (Note: Dimensions in mm; 1 mm = 0.0394 in.)

Fig. 6—Details of shear reinforcement. (Note: Dimensions in mm; 1 mm = 0.0394 in.)

12.5 mm (0.49 in.) U-bars were placed adjacent to the cut bars to provide some anchorage for horizontal tension and some shear reinforcement at the edges of the openings. Slabs 6 and 9 were provided with both additional continuous and U-bars. Figure 7 shows the relevant details for Slabs 4 and 5. Slabs 10 to 13 contained shear reinforcement and addi-tional full-length bars near the openings. Each slab had two symmetrical openings 200 x 300 mm (7.87 x 11.81 in.) as in Slabs 7 to 9. The main steel had the same details as in Slab 7. Details of the shear reinforcement are shown in Fig. 6. Data from the smaller-scale tests by Silva7 are presented in the Appendix.

TEST RESULTSUltimate strengths and failure modes

Table 1 summarizes the test data and results for the main test series and for the tests by Silva.7 All of the slabs of the main series failed by punching at loads below their flexural capacities calculated by the yield-line theory. Note that apart from Slabs 7 and 9, all slabs have the same effective depth d = 154 mm (6.06 in.). Figure 8 shows sketches of the plans of the inclined parts of the failure surfaces and Fig. 9 gives examples of the failure surfaces seen in sections cut through the slabs on their principal axes.

Slabs 8 and 9 developed essentially normal failure surfaces for slabs without shear reinforcement running upward from

ACI Structural Journal/July-August 2013 5

the soffit at the edges of the support and reaching the level of the main steel approximately 2d out in Slab 9 but rising more steeply in Slab 8. Slab 10 failed at a surface that was entirely outside the shear reinforcement, indicating that the shear reinforcement was enough to avoid a failure surface close to the column. In Slab 7, without shear reinforcement, and in Slabs 11, 12, and 13, with shear reinforcement, the inclined parts of the failure surfaces were adjacent to the supports

at their short edges, but were moved outward at their long sides. At the long sides, the cracks were almost horizontal in the bottom cover for 300 to 350 mm (11.81 to 13.78 in.) from the support and then inclined upward reaching the main steel 600 to 650 mm (23.62 to 25.59 in.) out. The overall plan forms of the failure surfaces in these slabs were almost circular. For the remaining slabs, the surface in Slab 6 was symmetrical in spite of there being only one

Table 1—Slab data and test results

Slab Openings Support, mm (in.) x mm (in.)Flexural reinforcement at

openingsShear

reinforcementfc, MPa

(psi)d, mm (in.)

Vu, kN (kip)

Test results

1 — 200 x 600 (7.97 x 23.62) — — 42.0 (6091) 154 (6.06) 843 (190)

2 — 200 x 600 (7.97 x 23.62) — Yes 39.0 (5656) 154 (6.06) 1250 (281)

3 — 200 x 600 (7.97 x 23.62) — Yes 41.1 (5961) 154 (6.06) 1092 (246)

4 1 200 x 600 (7.97 x 23.62) Addit bar — 41.4 (6004) 154 (6.06) 776 (174)

5 1 200 x 600 (7.97 x 23.62) U bar — 40.5 (5874) 154 (6.06) 792 (178)

6 1 200 x 600 (7.97 x 23.62) Addit bar + U bar + U bar — 39.0 (5656) 154 (6.06) 750 (169)

7 2 200 x 600 (7.97 x 23.62) Addit bar — 37.0 (5366) 144 (5.67) 685 (154)

8 2 200 x 600 (7.97 x 23.62) U bar — 41.6 (6033) 154 (6.06) 750 (169)

9 2 200 x 600 (7.97 x 23.62) Addit bar + U bar + U bar — 40.6 (5888) 164 (6.46) 850 (191)

10 2 200 x 600 (7.97 x 23.62) Addit bar Yes 43.8 (6352) 154 (6.06) 1230 (277)

11 2 200 x 600 (7.97 x 23.62) Addit bar Yes 39.4 (5714) 154 (6.06) 1050 (236)

12 2 200 x 600 (7.97 x 23.62) Addit bar Yes 43.2 (6265) 154 (6.06) 885 (199)

13 2 200 x 600 (7.97 x 23.62) Addit bar Yes 40.7 (5903) 154 (6.06) 837 (188)

Silva7

L1 — 150 x 150 (5.91 x 5.91) — — 39.6 (5743) 90 (3.54) 273 (61)

L4 2 150 x 150 (5.91 x 5.91) One cut bar — 39.4 (5714) 90 (3.54) 225 (51)

L5 2 150 x 300 (5.91 x 11.81) One cut bar — 39.6 (5743) 90 (3.54) 350 (79)

L6 2 150 x 450 (5.91 x 17.72) One cut bar — 39.1 (5671) 90 (3.54) 375 (84)

Fig. 7—Details of flexural reinforcement near openings (Slabs 4, 5, and L6). (Note: Dimensions in mm; 1 mm = 0.0394 in.)

Fig. 8—Plan forms of inclined failure surfaces.

6 ACI Structural Journal/July-August 2013

opening, and Slabs 2 and 3, without openings, failed at surfaces that were entirely outside the shear reinforcement, also indicating that the shear reinforcement was enough to avoid a failure surface close to the column. Slab 1, without openings or shear reinforcement, presented, for the two support sides (short and long), the typical punching failure surface: from the base of the support plate, at the bottom to the top of the slab, with an inclination of 25 to 30 degrees (Fig. 9). Slabs 4 and 5, both with one opening and without shear reinforcement, presented basically the same behavior, irrespective of the different detailing close to the opening: on the direction of the long side, the failure crack presented the typical punching failure surface from the base of the support plate, at the bottom of the slab, to the top of the slab with an inclination of 25 to 30 degrees, while for the short side, the punching failure surface went flat from the bottom for 350 to 400 mm (13.78 to 15.75 in.), and then went to the top reinforcement, and hit the surface afterward.

The ultimate loads of the slabs without shear reinforce-ment were reduced by openings. Ignoring any effect from the small variations in concrete strength, single openings reduced the punching capacities by 8% on average, while pairs of openings reduced it by 10%. The minimal differ-ence between these reductions suggests that eccentricity in a pattern of openings should be taken into account. For the same slabs, there is no consistent difference between the strengths of slabs with different details of the flex-ural reinforcement. With sufficient shear reinforcement, the strength of Slab 10, with two openings, was practically equal to that of Slab 2, and both were close to the flexural capacity. Even the very-minimal shear reinforcement of

Slab 13 produced a resistance equal to that of the control slab without openings.

DeflectionsIn all tests, there is a stiff initial response corresponding

to uncracked behavior. In the next phase, the response is still linear but with a much reduced stiffness, only margin-ally affected by the openings. Finally, the deflection rate increases up to failure but without the curves ever becoming horizontal. Figure 10 shows deflected profiles for Slab 4. The profiles at higher loads are practically linear between the reactions and the longer sides of the loading plates, with rotations concentrated to a very limited zone near the plates. This zone did not extend to the eventual failure surfaces. In the other direction, the region of high curvature is some-what extended near the opening. Figure 11 presents the load versus center deflection for all the slabs. As expected, deflec-tions are larger with the openings and smaller with shear reinforcement.

Strains of shear reinforcementStrains of shear reinforcement were measured by pairs of

electrical resistance strain gauges at opposite sides of stud diameters at midheight. Figures 12 and 13 show stresses (σs = Es · εs) obtained from the average strains at the highest loads at which full readings were made. For both slabs without openings, the inclined failure surfaces were entirely outside the shear reinforcement. In spite of this, the strains in most of the studs of Slab 3, with two layers of 8 mm (0.31 in.) studs, were high, giving a mean stress of 422 MPa (61.2 ksi) at 1050 kN (236 kips)—that is, at 0.96Vu. These

Fig. 9—Examples of failure surfaces in sections on principal axes. (Note: Dimensions in mm; 1 mm = 0.0394 in.)

Fig. 10—Deflected profiles of Slab 4. (Note: Dimensions in mm; 1 mm = 0.0394 in.)

ACI Structural Journal/July-August 2013 7

results (steel stresses of the order of 400 MPa [58 ksi]) indi-cate that cracking occurred in this region, even though the failure surface was entirely outside the shear reinforcement. The strains in Slab 2 were much lower, with a mean stress of only 235 MPa (34.1 ksi) at 0.96Vu due to the larger diameter and smaller radial spacing of the studs.

For the case of specimens with openings, Slab 10 with four layers of studs, including lines adjacent to the openings, was the only one in which the failure surfaces were fully outside the shear reinforcement. Nevertheless, the relatively few studs strain measurements for this slab showed high strains for the studs at the sides of the opening. Their mean stress was 444 MPa (64.4 ksi) and was higher than that of the studs in the next line. On both lines, the stresses reduced greatly at the outer edge of the opening. In Slab 11, with three layers of studs on radial lines, the strains were high on the lines perpendicular to the long side of the support and in the line adjacent to the opening, but again lower on the next line. In both of these slabs, with considerable shear reinforcement near the short sides of the supports, the distri-bution of shear around the outside of the shear-reinforced zone appears to have been relatively uniform. In Slab 13, the shear seems to have been fairly uniform and high at the long sides of the supports and to have reduced near the openings.

Part of the measured strains correspond to stresses well above the MC90/EC2 limit and also above that of ACI 318-11. The actual maximum stress of any stud was possibly a little greater than that corresponding from the measured strains, due to bond between the crack and gauge strain locations. Potentially, the stresses might have been higher if the slabs’ failure surfaces had been more within the shear-reinforced zones. There are, however, two points to bear in mind herein. The ratio between the areas of the anchor plates and studs was high—32 for the 8 mm (0.31 in.) studs as compared with a typical ratio of 10 for commercial studs, which are normally of larger diameter. Second, the tops of the anchor plates were above the upper main bars, whereas they commonly have the same cover.

COMPARISONS OF EXPERIMENTAL AND CALCULATED STRENGTHS

The comparisons between experimental and theoretical results are given in Tables 2 to 4. For slabs with openings but without shear reinforcement, Table 2 lists the results of comparisons with calculations to ACI 318-11, MC90, and four different treatments of the effect of openings, all using the basic MC90 treatment of slabs without openings. The variants (Fig. 1) are:

• SP 1—straight projection;• SP2—straight projection with fictitious openings

restoring symmetry;• Teng—radial projection from poles cmin/2 from the ends

of supports; and• EC2—radial projection as in MC90 but with increased

effective widths of openings where l1 > l2.MC90 is used as the base for these variants to minimize

variations and errors from sources other than the treat-ments of openings. The ratio of flexural reinforcement has been taken as the basic one without local variations due to openings.

Fig. 11—Load versus displacements (left) and details of Slab 10 after being sawcut (right).

Fig. 12—Stresses in shear reinforcement: slabs without openings (MPa). (Note: 1 MPa = 145 psi; 1 kip = 4.448 kN.)

Fig. 13—Stresses in shear reinforcement: slabs with open-ings (MPa). (Note: 1 MPa = 145 psi; 1 kip = 4.448 kN.)

8 ACI Structural Journal/July-August 2013

Table 3 presents the mean values of Vu/Vcalc from Table 2 for the different groups of tests and different methods of calcu-lations. For all methods of calculation, the ratios are higher for Silva’s7 130 mm (5.12 in.) slabs than for the 200 mm (7.87 in.) Slabs 4 to 9, but the difference is reduced by MC90’s depth factor, which has been used in all the calcula-tions except those to ACI 318-11. This suggests the possi-bility of a size effect on punching resistance related to the slab’s effective depth, even though some differences could have been expected due to the different arrangements of the supports (rectangular for one test series and circular in the other), and for the different values of the ratio cmax/cmin.

For the approaches using radial projections (ACI 318-11 and MC90), Vu/Vcalc is always higher for the specimens with open-

ings than for the unperforated slabs (Borges’s13 Slab 1 and Silva’s7 Slab L1), showing that radial projection overesti-mates the influence of openings adjacent to supports. The variants of radial projection proposed by Teng et al.6 and EC2 make more conservative estimations than that for the simple method of MC90 and ACI 318-11. Straight projection gives the best consistency across the range of slab types. In overall terms, there is little difference between the results for Methods SP1 and SP2, as can be seen in Table 2, indicating that the two methods can be used for slabs with one hole.

For the calculations of punching resistances of slabs with shear reinforcement, the maximum stud stresses are 414 MPa (60.0 ksi) according to ACI 318-11 and 345 MPa (50.0 ksi) according to MC90. The latter value can also be used for EC2 with very little error for the present slabs. The ACI restriction on the spacing of stud layers has been ignored, as has EC2’s limit on the transversal spacing within u1. EC2’s 2d limit on maximum transversal spacing has been respected (refer to Fig. 2) and applied to all layers.

For all the slabs with openings, various detailed interpre-tations of the codes would be possible. In the following, it has been assumed that:

1. All stud lines were potentially active;2. Where the number of studs per layer varied between the

innermost and second layers, Asw can be taken as the average from layers one and two, but not greater than 1.25 times the area of layer one. This approach is that of the British code,14 which appears to be the only one treating the issue;

3. The concrete punching resistances at the perimeters u1 and uout can be determined for perimeter lengths defined by the following deductions for openings (refer to Fig. 14):

(a) For Slabs 10 and 11, with stud lines adjacent to the openings, the lengths between straight projection lines—that is, 200 mm (7.97 in.) per opening; and(b) For Slabs 12 and 13, without stud lines adjacent to openings, the lengths between radial lines from the centers of the supports to the extreme points of the openings.

The perimeters for MC90/EC2 for Slabs 12 and 13 are shown in Fig. 14. The calculations by EC2 have been made using the Eurocode distance of 1.5d from the outer studs to the perimeter uout, but otherwise follow MC90—that is, no limit has been applied to the depth factor and actual widths of openings have been used in place of (l1l2)1/2. The results obtained are given in Table 4. The comparisons with ACI 318-11 suggest that the shear stress used for the concrete could be increased for the assessment of strengths at the edges of zones with shear reinforcement, even though the ACI 318-11 restriction on the spacing of stud layers has been ignored (with the exception of Slab 2). The results from the MC90 and EC2 estimates are closer to the test

Table 2—Comparisons for slabs with openings and without shear reinforcement

Slabcmax/cmin Openings

Vu/ VACI

Vu/ VMC

Vu/ VSP1

Vu/ VSP2

Vu/ VTeng

Vu/ VEC/MC

1 3.00 — 1.38 1.04 — — — 1.13

4 3.00 1 1.44 1.10 1.04 1.10 1.21 1.13

5 3.00 1 1.49 1.13 1.07 1.13 1.25 1.16

6 3.00 1 1.43 1.09 1.02 1.09 1.20 1.12

7 3.00 2 1.68 1.23 1.08 1.08 1.55 1.31

8 3.00 2 1.59 1.22 1.06 1.06 1.60 1.30

9 3.00 2 1.68 1.22 1.14 1.14 1.67 1.39

Silva7

L1 1.00 — 1.52 1.01 — — — 1.26

L4 1.00 2 2.5 1.67 1.01 1.01 1.67 1.67

L5 2.00 2 2.13 1.61 1.30 1.30 1.93 1.61

L6 3.00 2 2.01 1.34 1.19 1.19 1.65 1.34

Table 3—Slabs without shear reinforcement: means of Vu/Vcalc

Method One opening Two openings Two openings (Silva7)

ACI 318 1.45 1.65 2.21

MC90 1.11 1.22 1.54

SP1 1.04 1.09 1.17

SP2 1.11 1.09 1.17

Teng 1.22 1.61 1.75

EC2 1.14 1.33 1.54

Table 4—Comparisons for slabs with shear reinforcement

Slab Openings Studs per layer sr/d

ACI 318-11 MC90 EC2

Vu/Vcs Vu/Vout Vu/Vcs Vu/Vout Vu/Vcs Vu/Vout

2 — 12 φ 10 0.49 (1.08) 2.02 (0.79) 1.09 (0.70) 1.20

3 — 12 φ 8 0.75 (1.57) 2.06 1.08 (1.07) (1.08) 1.20

10 2 17.5 φ 8 0.75 (1.55) 1.73 1.07 (0.95) 1.07 (1.04)

11 2 17.5 φ 8 0.75 (1.35) 1.97 (0.93) 0.96 (0.93) 1.07

12 2 10 φ 8 0.75 (1.57) 1.88 1.09 (1.05) (1.09) 1.15

13 2 10 φ 8 0.75 (1.60) 2.51 1.04 (1.01) (1.04) 1.17Note: Values in parenthesis not critical.

ACI Structural Journal/July-August 2013 9

results presented. The straight projection approach used for Slabs 10 and 12 produces Vu/Vcalc ratios less than those for the other slabs. This could be reversed by the use of radial projection, but it would be difficult to reconcile such projec-tion with the provision of shear reinforcement adjacent to the openings. Such reinforcement seems to work well (refer to Fig. 13) and the ratios Vu/Vcalc for EC2 are acceptable with the perimeters determined as mentioned previously.

CONCLUSIONSThe following conclusions are drawn from the results of the

tests reported, all of which were on slabs with approximately equal bending resistance in two directions and no moment transfer to the supports. Column size was the same for most slabs (β = 3.0) and tests were made with only two patterns of openings. Although the conclusions may be expected to have a wider significance, their extension to other cases would require careful consideration and verification. More tests are needed on slabs with nonsymmetrical loading and unbalanced moments, with different column sizes and slab thicknesses, and with openings on larger column sizes.

1. The tests results suggest there is some indication of a size effect on punching resistance, which can be related to the slab effective depth, even though some differences could have been expected due to the different arrangements of the supports and for the different values of the ratio cmax/cmin at the tests reported.

2. For the relatively small openings considered, the provision of continuous bars adjacent to openings, to replace the areas of reinforcement, seems to be an adequate approach to flexural design. The addition of hairpin bars at the edges of openings did not offer any consistent improvement.

3. Straight projection of the widths of openings onto the control perimeters to determine the reductions of the concrete contributions to punching resistance gave more consistent predictions of strength than any of the forms of radial projection considered for slabs without shear rein-forcement. Straight projection does, however, probably require consideration of the effects of eccentricity between the residual control perimeter and the support.

4. Codes should be conservative, especially when brittle ruptures are involved, and committees tend to opt for simpler (and probably) more conservative formulas. Nevertheless, for slabs with shear reinforcement, it can be suggested that the shear stress used for the concrete in ACI 318-11 could be increased for the assessment of strengths at the edges of zones with shear reinforcement (outer control perimeter). MC90 and EC2 produce less conservative results compared to ACI 318-11. The use of EC2’s control perimeter 1.5d beyond the outer shear reinforcement appears preferable to MC90’s distance of 2d (although MC90 presented a 4% unconservative estimation for one of the slabs tested).

5. The use of shear reinforcement adjacent to the “radial” sides of openings seems beneficial and this should be further investigated.

ACKNOWLEDGMENTSThe authors wish to express their gratitude to ACI member P. E. Regan,

Emeritus Professor of the University of Westminster, City of London, UK, where he was Head of Architecture and Engineering, for suggesting the subject of this research during his visits to Brazil. The authors also wish to express their gratitude to FURNAS (Aparecida de Goiânia), where the tests were carried out, and to CNPq and CAPES, Brazilian Research Development Agencies.

NOTATIONAsw = area of shear reinforcement in one circumferential layercmax = greater side dimension of rectangular support or loadcmin = lesser side dimension of rectangular support or loadd = mean effective depth of slabfc = cylinder crushing strength of concretefsw = limiting stress for shear reinforcementfu = ultimate stress of reinforcement in generalfy = yield or 0.2% proof stress of reinforcement in generalfyw = yield or 0.2% proof stress of shear reinforcementl1 = radial dimension of openingl2 = transversal dimension of openingsr = radial spacing of layers of shear reinforcementst = transversal spacing of elements of shear reinforcementu1 = perimeter used in calculation of Vc and Vcs

uo = perimeter of support or loaduout = control perimeter outside zone with shear reinforcementVc = punching resistance of slab without shear reinforcementVcs = punching resistance within zone with shear reinforcementVmax = maximum punching resistanceVout = punching resistance at edge of (outside) zone with shear

reinforcementVu = experimental punching resistancevc = shear resistance (stress) for concrete in calculation of Vc

β = cmax/cmin

ρl = ratio of flexural reinforcement

REFERENCES1. Moe, J., “Shearing Strength of Reinforced Concrete Slabs and Footing

under Concentrated Loads,” Development Dept. Bulletin D47, Portland Cement Association, Skokie, IL, 1961, 135 pp.

2. Roll, F.; Zaidi, S. T. H.; Sabnis, G. M.; and Chuang, K. H., “Shear Resistance of Perforated Reinforced Concrete Slabs,” Cracking, Deflection, and Ultimate Load of Concrete Slab Systems, SP-30, E. G. Nawy, ed., American Concrete Institute, Farmington Hills, MI, 1971, pp. 77-101.

3. Gomes, R. B., and Andrade, M. A. S., “Punching in Reinforced Concrete Flat Slabs with Openings,” Developments in Computer Aided Design and Modelling for Structural Engineering, Civil-Comp Press, Edinburgh, UK, 1995, pp. 185-193.

4. Regan, P. E., “Shear Reinforcement of Flat Slabs,” TRITA-BKN Bulletin 57, International Workshop Punching Shear Capacity of RC Slabs, Royal Institute of Technology, Sweden, 2000, pp. 97-107.

5. Kuang, L., and Teng, S., “Punching Shear Strength of Slabs with Openings and Supported on Rectangular Columns,” School of Civil Engineering, Nanyang Technological University, Singapore, 2001, 298 pp.

6. Teng, S.; Cheong, H. K.; and Kuang, K. L., “Punching Shear Strength of Slabs with Openings and Supported on Rectangular Columns,” ACI Structural Journal, V. 101, No. 5, Sept.-Oct. 2004, pp. 678-687.

7. Silva, J. A., “Punching of Flat Slabs; Rectangular Columns, Openings and Shear Reinforcement,” MSc thesis, Universidade Federal de Goiás, Goiás, Brazil, 2003, 171 pp.

8. ACI Committee 318, “Building Code Requirements for Structural Concrete (ACI 318-11) and Commentary,” American Concrete Institute, Farmington Hills, MI, 2011, 503 pp.

9. “CEB-FIP Model Code 90,” Thomas Telford, London, UK, 2003, 328 pp.10. BS EN 1992-1-1, “Eurocode 2: Design of Concrete Structures, Part

1-1: General Rules and Rules for Buildings,” British Standard Institution, London, UK, 2004, 225 pp.

Fig. 14—MC90/EC2 control perimeters for Slabs 10, 11, 12, and 13.

10 ACI Structural Journal/July-August 2013

11. Regan, P. E., “Design for Punching Shear,” Structural Engineer, V. 52, No. 6, 1974, pp. 197-207.

12. Handbook to British Standard, BS 8110:1985, “The Structural Use of Concrete,” Palladian Publications Ltd, London, UK, 1987, pp. 56-57.

13. Borges, L. L. J., “Behavior in Punching Shear of Reinforced Concrete Flat Plates with Rectangular Columns and Openings,” PhD thesis, University of Brasília, Brasília, Brazil, 2004, 362 pp.

14. BS 8110, “Part 1: Structural Use of Concrete—Code of Practice for Design and Construction,” British Standards Institution, London, UK, 1997, 168 pp.

APPENDIX—TESTS BY SILVA7

The slabs tested by Silva7 were 130 mm (5.12 in.) thick and 1.8 m (70.87 in.) square on plan. They were loaded upward at their centers through thick steel plates and reac-tions were provided at eight points equally spaced round a 1.65 m (64.96 in.) diameter circle. The top flexural reinforce-ment was 12.5 mm (0.49 in.) bars at 94 mm (3.70 in.) centers in both directions, with 6.3 mm (0.25 in.) U-bars at the edges. The bottom steel was 6.3 mm (0.25 in.) bars at 163 mm (6.42 in.) centers both ways. The outer main bars were those perpendicular to the long sides of the supports. Where there were openings in the slabs, the spacing of the main bars were increased locally so that there were bars close to the edges of the openings and only one bar was cut

in each direction (Fig. 7 for Slab L6). Slab L4 had then three bars through the column at the direction without openings, while Slabs L5 and L6 had, respectively, five and seven bars through the column at the direction without openings. The yield strengths of the reinforcement were 538 MPa (78.5 ksi) for the 12.5 mm (0.49 in.) bars and 594 MPa (86.1 ksi) for the 6.3 mm (0.25 in.) ones. A top clear cover of 27.5 mm (1.08 in.) and bottom clear cover of 17.5 mm (0.69 in.) to the outermost reinforcing steel bars were adopted. Slabs 2, 4, 5, 6, 8, 11, 12, and 13 were tested 18 days after casting. Slabs 1, 3, 7, and 9 were tested 19 days after casting. Slab 10 was tested 25 days after casting.

The results of these tests resulted in punching failures. Slabs L1 and L4 failed at surfaces running from the edges of the supports to reach the main steel at horizontal distances approximately 1.7d from the edges of the supports. In Slab L6, the inclined failure surfaces sprang from the short edges of the supports, but on the other centerline, their lower ends were almost 2d from the long sides of the supports, producing practically circular shapes on plan as in Fig. 8(c). In Slab L5, the lower end of the inclined surface was at the support on one side, but approximately 1.5d on the other side.