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ACI Structural Journal/September-October 2011 581

Title no. 108-S55

ACI STRUCTURAL JOURNAL TECHNICAL PAPER

ACI Structural Journal, V. 108, No. 5, September-October 2011.MS No. S-2009-398.R3 received July 29, 2010, and reviewed under Institute

publication policies. Copyright © 2011, 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 July-August 2012 ACI Structural Journal if the discussion is received by March 1, 2012.

Punching Shear of Thick Plates with and without Shear Reinforcementby E. Rizk, H. Marzouk, and A. Hussein

Thick concrete plates are currently used for offshore and nuclear containment concrete walls. In this research, five thick concrete slabs with a total thickness of 300 to 400 mm (12 to 16 in.) were tested under concentric punching loading. Four specimens had no shear reinforcement, whereas the remaining one included T-headed shear reinforcement consisting of vertical bars mechanically anchored at the top and bottom by welded anchor plates. The main focus of this research was to investigate the influence of the size effect on the punching shear strength of thick high-strength concrete plates. All tests without shear reinforcement exhibited brittle shear failures. The addition of T-headed shear reinforcement with a shear reinforcement ratio of approximately 0.68% by volume changed the failure mode to ductile flexural failure. The test results revealed that increasing the total thickness from 350 to 400 mm (14 to 16 in.) resulted in increased punching capacity and at the same time resulted in a small increase in ductility characteristics. An equation based on fracture mechanics principles is recommended to account for the size effect factor. The proposed equation is verified using the test results and is compared with the predictions of different design codes.

Keywords: punching; shear reinforcement; size effect; thick plates.

INTRODUCTIONNorth American design codes such as ACI 318-081 and

CSA A23.3-042 provide practical equations to design flat plates subjected to punching loads. The design requirements provided by the ACI code1 do not account for the size effect factor. At the same time, the size effect factor provided by the Canadian standard2 is empirical and does not apply to slabs having an effective depth less than 300 mm (12 in.). The main reason for disregarding the size effect is the lack of enough experimental tests, especially for thick high-strength concrete slabs. North American design codes also do not have provisions for minimum shear reinforcement requirements for thick slabs over 300 mm (12 in.) in thickness; these provisions could be required to prevent the brittle shear failure behavior of thick plates due to size effect. One more reason to provide shear reinforcement requirements is to allow the use of a slab with a large amount of the flexural reinforcement ratio. Increasing the flexural reinforcement ratio increases the punching capacity but strongly decreases the deformation capacity of the slab. The focus of this research is to experimentally investigate the influence of size effect on the punching shear strength of thick high-strength concrete plates to better understand the punching mechanism of thick plates.

RESEARCH SIGNIFICANCERational models and design formulae for punching shear

are based on the results of experimental tests performed mostly on thin slabs. Design codes, however, are also used in the design of thick plates and footings. The few available tests performed on thick slabs exhibit a notable size effect.

As a consequence, there is a need for a rational model that correctly describes and accounts for size effect. This paper presents an experimental investigation. Five thick plates with different flexural reinforcement ratios were tested to examine the accuracy of available design equations. A simplified practical punching shear equation that accounts for the size effect factor is proposed. The proposed equation is verified using experimental test results and is compared with the predictions of different design codes.

PREVIOUS RESEARCHAlthough extensive research has been done on the punching

shear strength of slabs, to date there is still no generally applicable rational theory. There is also great discrepancy between different design codes. Some of these codes, such as ACI 318-08,1 do not even account for basic and proven factors affecting the shear capacity of concrete members, such as reinforcement ratio and size effect. The analysis of databases available from the literature indicates a lack of experimental data regarding member size.3 The testing of thick slabs represents a great challenge to many researchers due to expensive test setups compared to limited research budgets and limited lab spaces.

Richart4 presented the results of a number of reinforced concrete footing tests. The researcher reported that high tensile stresses in the flexural reinforcement led to extensive cracking in the footings. This cracking reduced the ability of the section to resist shear, resulting in the footings failing at lower shearing stresses than expected. The maximum shearing stresses, computed at the conventional critical section, varied considerably with the effective depth of the footing, being larger for the thinner footings.

Based on the results of a finite element parametric study on 81 slabs by Marzouk et al.,5 the authors recommended a nontraditional expression for shear strength for high-strength concrete application as follows

0.4

30.88 chu t

lCv fd h

− = r (1)

where ft is the direct tensile strength of concrete; C is the column side length; d is the slab depth; lch is the characteristic

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582 ACI Structural Journal/September-October 2011

length, which is described later in the paper; and h is the slab thickness.

The punching shear behavior of interior slab-column connections was investigated by Kevin.6 The response of six two-way slab specimens, which were designed such that they would fail in punching shear, was examined. The overall thickness h of the slabs varied from 135 to 550 mm (5.3 to 21.6 in.). The results showed a strong size effect with deeper members having smaller shear stresses at failure than shallow ones. It was also concluded that there is a significant size effect for effective depths greater than approximately 200 mm (8 in.).

Regan and Braestrup7 studied the effect of the shear span-depth ratio (a/d) on the shear strength. Although the data in this area are limited, it could be concluded that the shear strength rises quite sharply when the a/d is less than approximately 1.5 but is relatively constant for larger values of the ratio. For very short shear spans a, the support location significantly interferes with the failure surface. According to Hallgren,8 slender slabs are those slabs with a/d of more than 3 to 4. This ratio could be used to distinguish between thick and thin slabs.

Experimental investigations on the punching behavior of reinforced concrete footing were conducted recently by Hegger et al.9,10 A total of 22 reinforced concrete footings were tested to investigate the punching shear behavior of footings. The test parameters were a/d, concrete strength, and punching shear reinforcement. The experimental investigation indicated that for the footings without shear reinforcement, the inclination of the failure shear crack seems to be mainly influenced by a/d and not by the concrete strength. The observed inclinations of the failure crack were approximately 45 degrees for the compact footings (a/d = 1.25) and less

than 35 degrees for the more slender footings (a/d = 2.0). This failure angle seems to be steeper than that for a flat slab. Furthermore, the a/d significantly affected the punching shear capacity.

Birkle and Dilger11 studied the influence of slab thickness on punching shear strength. A total of nine slab-column assemblies were tested. It was concluded that without shear reinforcement, a slab of 230 mm (9.1 in.) thickness may not have a sufficient factor of safety if designed in accordance with ACI 318-08.1

One of the effective solutions to the problem of size effect for thick plates is to include provisions for shear reinforcement (for example, shear studs). The extensive investigations that were conducted by different researchers12-14 on full-size slab-column connections verified that stud-type reinforcement can substantially increase the strength and prevent brittle failure of thick plates. Berner et al.15 developed T-headed bars as shear reinforcement for thick flat plates. The advantage of this type is the ability to replace conventional stirrups and hence facilitate concrete placement and vibration.

Different codes and design guidelines allow the use of shear reinforcement for thick plates. Nonetheless, there is no accepted code-based formula to provide minimum shear reinforcement requirements for thick plates. The only exception is for the Eurocode 2,16 which requires that where shear reinforcement is required in reinforced concrete slabs, the minimum area of shear reinforcement must be equal to that needed for the same cross section that is to be designed as a beam.

EXPERIMENTAL INVESTIGATIONThe main variables in the experimental investigation were

the reinforcement ratio, concrete strength, and slab effective depth. A total of five thick concrete plates were tested. One normal-strength concrete (NSC) plate and four high-strength concrete (HSC) plates were selected, as detailed in Table 1. In numbering the specimens, an extra “S” was used to represent the size effect parameter and was added to the specimens’ numbers. This was done to distinguish between specimens in this research and previous specimens tested and published by the authors.17 In this research, the thicknesses ranged from 300 to 400 mm (12 to 16 in.). The specimens were designed to examine the effect of depth on the structural behavior of thick concrete plates. The slabs had an a/d of 3.33 to 4.8. The details of a typical test specimen are shown in Fig. 1.

All the specimens were designed to fail under punching failure except Specimen HSS1, which was designed to fail under flexure. Specimen HSS2 included T-headed shear stud reinforcement and was designed to examine the effect of shear reinforcement on the structural behavior of thick concrete plates. The shear reinforcement consisted of vertical bars with a diameter of 15 mm (No. 5) and a specified yield

E. Rizk is a PhD Candidate and Research Assistant at Memorial University of Newfoundland, St. John’s, Newfoundland, Canada, and is an Assistant Lecturer at Menoufia University, Shebin El-Kom, Egypt. He received his BSc and MSc from Menoufia University in 1999 and 2005, respectively. His research interests include cracking of offshore structures and shear strength of two-way slabs.

ACI member H. Marzouk is the Chair of the Civil Engineering Department at Ryerson University, Toronto, ON, Canada. He received his BSc from Cairo University, Giza, Egypt, and his MSc and PhD from the University of Saskatchewan, SK, Canada. He is a member of ACI Committees 209, Creep and Shrinkage in Concrete, and 213, Lightweight Aggregate and Concrete. His research interests include structural and material properties of high-strength concrete, lightweight high strength, creep, fracture mechanics, and finite element analysis.

ACI member A. Hussein is an Associate Professor of civil engineering at Memorial University of Newfoundland. He received his BSc from Ain-Shams University, Cairo, Egypt, in 1984, and his MEng and PhD from Memorial University of Newfoundland in 1990 and 1998, respectively. His research interests include the use of fiber-reinforced polymer in concrete, the mechanical and structural behavior of high-strength concrete, and nonlinear finite element analysis of concrete structures.

Slab no.*Compressive

strength fc′, MPa Bar size, mmBar spacing,

mmConcrete cover

Cc, mmSlab thickness,

mm Depth, mmFlexural reinforcement

ratio r, %Shear reinforcement

ratio rz , %

HSS1 76 25 368 70 350 267.5 0.50 —

HSS2 79 25 195 70 300 217.5 1.42 0.68

HSS3 65 35 289 70 350 262.5 1.42 —

NSS1 40 35 217 70 400 312.5 1.58 —

HSS4 60 35 217 70 400 312.5 1.58 —*NS is normal-strength slabs; HS is high-strength slabs.Notes: 1 MPa = 145 psi; 1 mm = 0.0394 in.

Table 1—Details of test specimens


strength of 400 MPa (58 ksi). The bars were anchored at the top and bottom by welded anchor plates. The layout of the shear reinforcement is shown in Fig. 2.

MaterialsType 10 SF cement blended with silica fume was used for

all the mixtures. Local fine aggregate that had a composition similar to that of the coarse aggregate was used. Crushed sandstone fine aggregate and crushed sandstone with a coarse aggregate of 19 mm (0.75 in.) maximum nominal size were used. Two concrete mixtures with a compressive strength of 35 and 70 MPa (5076 and 10,152 psi) after 28 days were used. The water-cement ratio (w/c) was 0.55 and 0.29 for the NSC and HSC mixtures, respectively. A non-chloride water-reducing agent of polycarboxlate base and a retarder of organic base conforming to ASTM C494 Types C and D was adopted. Three 150 x 300 mm (6 x 12 in.) cylinders were cast from each batch and used to determine the concrete compressive strength. Reinforcing bars consisting of Grade 400 steel—conforming to CSA standards with an actual tested yield strength of 460 MPa (67 ksi)—and a yield strain of approximately 2250 µε were used.

Test specimensThe test slabs had a side dimension of 2650 mm (106 in.)

in both directions. The test specimens were simply supported along all four edges with the corners free to lift. A concentric load was applied on the slabs through a 400 x 400 mm (16 x 16 in.) column stub. The specimen represents the region of negative bending moment around an interior column and the simply supported edges simulate the lines of contra-flexure. Reinforcement ratios of 0.50, 1.42, and 1.58% were selected for flexural reinforcement. The compression reinforcement ratios were selected to satisfy ACI 318-081 for the minimum reinforcement ratio to control shrinkage. The T-headed shear reinforcement consisted of a 15 mm (No. 5) bar as a stem and two 30 x 70 mm (1.2 x 2.8 in.) steel plates individually welded to both ends as anchor plates. A total of 40 T-headed studs were placed in Specimen HSS2, as shown in Fig. 2. The rectangular plate anchors had an area that was at least 10 times the area of the stem.12 The stud spacing s was chosen to be 0.5d as the lower of two spacings recommended by Joint ACI-ASCE Committee 421.18 The shear studs were extended to approximately 2d from the column faces as recommended by Marzouk and Jiang.14 The distance between the first row of studs and the column face so was taken as 0.4d to avoid shear failure between the column and the first row of shear studs.

Test setup A new test setup was designed and fabricated in

the structural laboratory of Memorial University of Newfoundland (MUN). The main function of this setup is to apply direct transverse load through a hydraulic jack. The test setup consists of four retaining walls; two of them were used for supporting steel beams. The beams act as a support for the test slab. The steel beams were anchored to the retaining walls. The walls were anchored to the 1 m (3.28 ft) thick structural floor. The third and fourth retaining walls were used to support the hydraulic jack that applied the load directly on the column stub. The retaining wall units were restrained at the top and lower edges by self-supporting closed rigid steel frames. The function of the frames was to minimize the lateral displacement of the supporting retaining

walls and to ensure that the test setup would act as a rigid self-supporting unit. A picture of the test setup is shown in Fig. 3(a). A hydraulic jack was used to apply a concentric load on the column stub in a horizontal position. The jack was a hydraulic jack cylinder with a maximum capacity of 3110 kN (700 kips) and a maximum displacement of 300 mm (12 in.).

Test procedureThe test slabs were placed in the frame in a vertical position.

The slabs were simply supported along all four edges with the corners free to lift. The test specimens were instrumented to measure the applied load, central deflection, strains in concrete, and rein forcement. The load was applied at a selected load increment of 44.0 kN (10 kips). The load-deflection curves were obtained using the linear variable

Fig. 1—Dimensions and reinforcement details of Specimen HSS2 with T-headed shear reinforcement. (Note: Dimensions in mm; 1 mm = 0.0394 in.)

Fig. 2—Arrangement of T-headed shear reinforcement in Specimen HSS2 (h = 300 mm [12 in.]). (Note: Dimensions in mm; 1 mm = 0.0394 in.)


locations on the compression faces of the concrete slabs. The concrete strains were measured with electrical 50 mm (2 in.) strain gauges, as shown in Fig. 3(d).

The cracks were marked manually and the maximum visible crack width was measured using CDTs. The gauges

differential transformer’s (LVDT’s) measurements at four predetermined locations on the tension surface, as shown in Fig. 3(b). The slabs were carefully inspected at the end of each load step. Steel strains at five locations were monitored, as shown in Fig. 3(c). Concrete strains were recorded at eight

(a) (b)

(c) (d)

(e) (f)

Fig. 3—Test setup: (a) photograph; (b) arrangement of LVDTs; (c) locations of steel strain gauges; (d) locations of concrete strain gauges; (e) crack displacement transducer (CDT); and (f) typical specimen indicates size effect challenge. (Note: Dimensions in mm; 1 mm = 0.0394 in.)


slab. In all the test slabs, the initial observed cracks were first formed tangentially under the edge of the column stub, followed by radial cracking extending from the column edge toward the edge of the slab. As the load increased, the tension reinforcement yielded, which resulted in a significant in-crease in the crack width and deflection. It was noted that the ratio of the yield load to the cracking load increased with increasing the reinforcement ratio.

Load-deflection characteristicsThe applied load versus the de flection at the center of the

slab for the different specimens is shown in Fig. 4. The yield displacement is calculated at the first yield of reinforcement bars. The first yielding of the bottom reinforcement is indicated by a circle on each curve. Table 2 presents the measured deflection at first crack, at first yield of tension steel, at ultimate load, and at post-ultimate load. It should be noted that the load-deflection curves can be used in classifying failure type.17 Post-ultimate loading capacity refers to slab capacity at ultimate deflection. Also, post-ultimate deflection is commonly defined as the deflection in the post-peak load range and when approximately 20% of the peak load is lost (that is, deflection when the load is 80% of the peak value). For slabs failing in punching, there could be a complete loss of load-carrying capacity for some slabs that failed in punching. Hence, a descending portion of the load-deflection curve would not be obtained in that case. As a result, it may not be possible to apply the common definition of post-ultimate deflection.

The load-deflection curve of Specimen HSS1 indicated that it failed in flexure. The slab reached the state of steadily increasing deflection at constant load. Thus, it displayed ductile behavior characterized by a continuously increasing capacity with increasing deflection after overall yield of the flexural reinforcement. This is a normal charac teristic for a lightly reinforced concrete specimen experiencing flexural failure. Specimen HSS2 failed in flexure failure, as indicated by its load-deflection curve. Specimens HSS3, NSS1, and HSS4 failed in punching; this is characterized by a sudden drop in the load-deflection curve.

The inclusion of T-headed shear reinforcement (Specimen HSS2) improved the ultimate load capacity as compared to that of Specimen HSS3 without shear reinforcement. The provision of shear enhancement also provided a post-ultimate behavior after the ultimate loading ca pacity was reached and eliminated the so-called punching shear failure. On the other hand, the punching

were mounted at the concrete surface cracks to measure the crack opening displacement, as shown in Fig. 3(e). The crack displacement transducer is a waterproof-enabled gauge with a length of 64 mm (2.6 in.). The range of the gauge is between ±2 to ±5 mm (±0.08 to ±0.2 in.). The accuracy of the measurements improved as the cracks started to widen. The testing of thick specimens posed some challenge, as shown in Fig. 3(f). The data from the transducers were measured using a high-speed data acquisition system and were stored on a personal computer. All tests were terminated after punching occurred and the load dropped considerably.

Test resultsThe first crack in each specimen was visually inspected

and the corresponding load was recorded. The yield steel strain was assumed to occur at 2000 με, which produced a stress in the steel reinforcing bar equal to 400 MPa (58 ksi). The yield strain was measured first at the center of the

Fig. 4—Load-deflection characteristics at center span of test slabs: (a) Specimens HSS1, HSS2, and HSS3; and (b) Specimens HSS1 and HSS4. (Note: Dimensions in mm; 1 mm = 0.0394 in.; 1 kN = 0.2248 kips.)

Slab no.

Concrete steel strength

fc′, MPa

Flexural reinforcement ratio

r, %First crack load, kN

First crack deflection, mm

Yield load Py, kN

Yield load deflection Dy,

mm

Ultimate load Pu,

kN

Ultimate load deflection DPu,

mmPost-ultimate load PDu, kN

Post-ultimate load deflection Du, mm

HSS1 76 0.50 312 5.9 790 7.3 1722 22.5 360 32.0

HSS2 79 1.42 320 5.7 1219 18.9 2172 35.5 1067 43.5

HSS3 65 1.42 258 7.0 1381 17.3 2090 24.1 617 35.1

NSS1 40 1.58 276 4.1 2094 11.5 2234 13.1 549 24.6

HSS4 60 1.58 317 4.4 2081 9.4 2513 13.1 507 25.7

Notes: 1 MPa = 145 psi; 1 mm = 0.0394 in.; 1 kN = 0.2248 kips.

Table 2—Deflection characteristics of test slabs


failure occurred and no post-ultimate loading capacity was observed for Specimen HSS3.

Ductility and energy absorption characteristicsDuctility is a term that reflects the deformation capacity

of a structural member before failure. Ductility U is defined as the ratio of the post-ultimate deflection ΔU to the deflection at first yield Δy. The energy-absorption capacity is defined as the area under the load-deflection curve. The ductility at failure and the energy-absorption capacity of all test slabs, as de fined previously, are given in Table 3. The test results indicated that as the steel reinforcement increased, the ductil ity decreased. For example, increasing the reinforce ment ratio from 0.50 to 1.42% de creased the ductility by more than 50%. The test results revealed that as the depth of the slab increased, the ductility decreased. HSC Specimen HSS3 had almost the same reinforcement ratio and concrete strength compared to Specimen HSS4. The results showed that the ductility and energy absorption capacity of Specimens HSS3 and HSS4 were almost the same; this could indicate that after a certain depth limit (d = 260 mm [10.4 in.]), increasing the effective depth resulted in increasing the punching capacity but at the same time did not result in a significant increase in ductility and energy absorption. In addition, by increasing the slab effective depth, the structural behavior became more brittle. This is known as the size effect.

The ductility of Specimen HSS2 was almost the same as the ductility of Specimen HSS4. At the same time, the energy absorption capacity of Specimen HSS4 was approximately 80% of Specimen HSS2. This reflected the enhanced structural behavior of Specimen HSS2 by using shear reinforcement. The brittle structural behavior of Specimen HSS4 can be transformed to ductile structural behavior by using shear reinforcement. Adding shear reinforcement ensures using the full benefit due to increasing the slab effective depth. The test results indicated that increasing the slab thickness from 350 to 400 mm (14 to 16 in.) resulted in increased punching capacity and at the same time resulted in only a 25% increase in ductility characteristics. The possible explanation for the slight increase in the ductility ratio for Specimen HSS4 compared to Specimen HSS3 is the increase in brittleness of Specimen HSS4; this is due to the size effect factor.

Flexural reinforcement alone cannot provide adequate ductility of slab-column connections, especially when deformations are large (for example, during seismic events). Adding shear reinforcement to the slabs at the column area can substantially increase the punching shear capacity and ductility, which was shown by several researchers (Dilger and Ghali13 and Megally and Ghali19).

Concrete strainsFor all the test slabs, measurements were made to

determine the distribution of the concrete strain along a radius of the slab. Figure 5 shows the load-concrete strain for a typical test specimen. None of the concrete strains in the tangential or the radial directions reached a limiting value of 3000 με for any of the test slabs, except for Specimen HSS2. The concrete strains for Specimen HSS2 reached a value of almost 3000 με at a distance equal to 100 mm (4 in.) from the column face. The load-concrete strain curves for Specimens HSS1, HSS3, NSS1, and HSS4 were linear until the first cracking load.

Slab no.

Concrete strength fc′,

MPa

Flexural reinforcement

ratio r, %Ductility,

Du/Dy

Energy absorption capacity, kN.mm × 103

HSS1 76 0.50 4.38 33.44

HSS2 79 1.42 2.30 50.00

HSS3 65 1.42 2.03 35.19

NSS1 40 1.58 2.14 29.98

HSS4 60 1.58 2.73 39.53

Notes: 1 MPa = 145 psi; 1 kN.mm = 0.00886 kip.in.

Table 3—Observed ductility and energy absorption

Fig. 5—Load-concrete strain for typical test Specimen HSS2. (Note: Dimensions in kN; 1 kN = 0.2248 kips.)

Fig. 6—Load-steel strain for test slabs: (a) Specimens HSS1, HSS2, and HSS3; and (b) Specimens NSS1 and HSS4. (Note: Dimensions in kN; 1 kN = 0.2248 kips.)


tangential crack; orthogonal cracking was the most dominant crack pattern (Fig. 8).

For Specimen HSS2, inclined shear cracks were observed beyond a distance 2d from the column face. From the test observations, flexural cracking occurred first, and it advanced roughly from the column outlines towards the slab edges parallel to flexural reinforcement. Subsequently, tangential cracks developed around the vicinity of the column outline. In terms of inclined cracking, the T-headed shear studs were not intersected by the inclined shear cracks. The final failure progressed with most of the reinforcement pulling out of the outer part of the slab. Quite large areas enveloped by outmost tangential cracks were observed on the tension face of the slab. In that case, the punching shear failure was eliminated, and the failure transformed into a ductile flexure one.

Crack spacing Numerous cracks were developed on the tension face of

the slab at the time of failure. It was found that, for all the specimens, the first crack formed along the reinforcing bar passing through the slab center or close to the slab center. The second crack formed along the similar reinforcing bar in the other direction. CDTs were mounted on the concrete surface of the first, second, and third visible cracks to measure the crack-opening displacement. The corresponding load at which each crack occurred was recorded. The cracks formed at this stage had no effect on the characteristics of the crack pattern and primarily depended on the concrete strength. One parameter—namely, the bar spacing—was examined to investigate its effect on crack spacing and crack width.

All slabs, except Specimen HSS1, exhibited an orthogonal crack pattern that formed along the direction of the reinforcement. The orthogonal cracks were a function of the bar spacing as it was noticed for Specimens HSS2, HSS3, NSS1, and HSS4. Once the bar spacing was increased, the average orthogonal crack spacing was increased. For Specimens HSS1, HSS3, and HSS4, the average crack spacing was less than the bar spacing (Table 4). In

Steel strainsMeasurements were made to determine the strain

distribution along a radius for all test slabs. The measured steel strains are shown in Fig. 6. For all slabs, the tension reinforcement yielded before punching occurred. The degree to which yielding spread in the tension steel varied as the reinforce ment ratio changed. For high reinforcement levels, the yielding of the tension reinforcement occurred at higher applied loads and was localized around the column stub. For the lightly reinforced Specimen HSS1, yielding initiated at the column stub and gradually progressed throughout the whole tension reinforcement. Moreover, Specimen HSS1 reached the state of steady steel strains at a constant load, which is a normal behavior of slabs failing in flexure. The highest strain and consequently initial yielding occurred below the stub column. Specimen HSS2 experienced flexure failure, with the slab failing at 100% of the flexure strength. For both Specimens HSS1 and HSS2, which used full flexural capacity, the yielding of flexural reinforcement occurred at almost 50% of the failure load. Specimens HSS3, NSS1, and HSS4 experienced punching failure. The yielding of the flexural reinforcement occurred at almost 75 to 85% of the ultimate load. In general, the slope of the load-strain curve was almost the same for HSC and NSC slabs that failed in shear. Regarding the T-headed shear studs, none of the shear studs reached yielding. The contribution of the shear reinforcement did not take place before the slab reached 60% of the ultimate load. The slope of the load-strain curve for shear studs was small and gradual.

Cracking and failure characteristicsFor the slab failing in flexure (Specimen HSS1), the crack

pattern observed prior to punching consisted of one tangential crack, roughly at the column outline, followed by radial cracking that extended from the col umn. Flexure yield lines were well developed (Fig. 7). This failure can be classified as flexure failure. For the slabs failing by punching, the crack pattern observed prior to punching consisted of almost no

Fig. 7—Crack pattern of test Specimen HSS1 (radial crack pattern.)

Fig. 8—Crack pattern of test Specimen HSS4 (orthogonal crack pattern.)


thick concrete cover. At sections between successive cracks, some tensile stress is retained in the concrete around steel bars due to the action of bond, contributing to the bending stiffness of the member; this is reflected by a reduction in tensile strain in the reinforcement. This is called the tension-stiffening effect. The crack width can be calculated by multiplying the crack spacing by the average steel strain after reducing the crack width due to tension stiffening. The steel strain can be determined at any loading by determining the neutral axis and assuming linear strain distribution.

Effectiveness of shear reinforcementThe shear reinforcement has little effect before the

occurrence of the inclined shear cracks inside the slab. After the development of the inclined shear cracks, however, shear reinforcement transfers most of the forces across the shear crack and delays the further widening of the shear crack, thus increasing the punching shear capacity and ductility of the slab. To achieve this, the reinforcement needs to be well anchored and have enough ductility to allow the mobilization of many legs of the reinforcement. In the case of Specimen HSS2 with T-headed shear reinforcement, none of the shear studs were intersected by inclined shear cracks. The existence of T-headed shear reinforcement forced the shear crack to develop outside the shear reinforcement zone, resulting in increasing the punching perimeter, and this resulted in increasing the ultimate load capacity. At the same time, the existence of T-headed shear reinforcement did not result in increasing the ductility of Specimen HSS2 because the shear studs were not intersected by inclined shear cracks. A possible reason for the low ductility of Specimen HSS2 is the wide (large) coverage area of T-headed shear stud reinforcement, the coverage zone extended to more than 2d from the column face, as shown in Fig. 2, and this did not give the chance for flexure reinforcement to be fully mobilized after the occurrence of the shear crack. As a result, the failure mode was less ductile, as indicated by the load-deflection curve (Fig. 4(b)). The structural behavior of Specimen HSS2 could be enhanced by either increasing the flexure reinforcement development length or decreasing the shear reinforcement ratio to force the shear crack to develop inside the shear reinforcement zone.

Code requirements for two-way shearModern European codes of practice treat punching shear

in terms of shear stresses calculated at control perimeters located at relatively large distances from the column or loaded area. In the CEB-FIP 1990 model code,20 the distance is 2d. In BS 8110-97,21 it is 1.5d, but the perimeter has square corners as compared with CEB-FIP20 rounded corners. In North American codes such as ACI 318-081 and CSA A23.3-04,2 the control punching shear perimeter is only 0.5d away from the loaded area. ACI 318-081 does not

Specimen HSS1, the crack pattern was radial, which is a normal behavior of a slab having a small reinforcement ratio and exhibiting large deflections. Most of the slabs that failed in punching exhibited a large radius of punching cone on the tension face of the slab.

Crack widthThe crack width was measured at each load stage. Figure 9

shows the crack opening displacement versus the steel strain for a typical test slab. The crack width increased as the applied load increased; however, this increase was not very smooth, as concrete is not a homogenous material. It was noticed that the crack width versus the steel strain can be represented by one straight line up to a value approximately equal to 2000 µε of steel strain (yield strain), except for Specimen HSS3. In most of the slabs, the crack width versus the steel strain curve tended to behave nonlinearly after the steel strain reached the yield strain. In Specimen HSS1, the crack width continued to increase after the steel strain reached the yield point, which is an expected behavior for a slab that failed in flexure.

All measurements reported in Table 4 were taken at a steel stress level of 267 MPa (38.7 ksi), which corresponded to approximately 0.67fy. The results showed that the maximum crack width can be influenced by as much as 50% when the bar spacing was increased from 217 to 368 mm (8.5 to 14.5 in.). This means that for the same concrete cover, increasing the bar spacing by approximately 70% resulted in increasing the crack width by approximately 50%. The test slabs included two specimens, Specimens NSS1 and HSS4, reinforced with a high reinforcement ratio of 1.58%. The two specimens had the same bar spacing of 217 mm (8.5 in.). The test results revealed that crack control (crack width) can still be achieved by limiting the spacing of the reinforcing steel despite using a

Fig. 9—Steel strain versus crack width for typical test Specimen HSS2. (Note: Dimensions in mm; 1 mm = 0.0394 in.)

Slab no. Concrete cover Cc, mm Slab thickness h, mm Bar spacing s, mm fc′, MPa Average crack spacing Sm, mm Maximum crack width wk, mm

HSS1 70 350 368 76 221 0.581

HSS2 70 300 217 79 228 0.876

HSS3 70 350 289 65 264 0.435

NSS1 70 400 217 40 250 0.439

HSS4 70 400 217 60 210 0.469

Notes: 1 MPa = 145 psi; 1 mm = 0.0394 in.

Table 4—Measured crack spacing and crack width


The punching resistance according to BS 8110-9721 is

(6a)Vf

d udBSc=′

0 79 1000 78

25400

1 3

1 4..

( )

/

/ρ (SI units)

Vf

d udBSc=′

4 08 1000 78

2516

1 3

1 4..

( )

/

/ρ (U.S. units) (6b)

where 4 400 d is a size effect factor; u is the length of a square perimeter at 1.5d from the loaded area for both circular and square loaded areas; and r is the flexural reinforcement ratio.

Size effectFor design engineers, the size effect is a useful concept

that is based on fracture mechanics. The size of the fracture process zone is represented by a material property called the characteristic length lch. It relates the fracture properties of the concrete, such as the modulus of elasticity Ec, the fracture energy Gf, and the tensile strength ft and is calculated as

2c f

cht

E Gl

f= (7)

where Gf is defined as the amount of energy required to cause one unit area of a crack; hence, it can be obtained as the area under the load-crack width opening curve. A higher value of lch reflects that the material is less brittle and a smaller value means that the material is more brittle. In an earlier investigation by Marzouk and Chen,22 the fracture energy Gf was determined experimentally for HSC to be 160 N/m (11 lb/ft) compared to 110 N/m (7.5 lb/ft) for NSC. The character istic length lch was estimated to have an average value of 500 and 250 mm (20 and 10 in.) for NSC and HSC, respectively.

Proposed change for size effectThis section presents a proposal to modify the ACI 318-081

equation by the inclusion of the brittleness ratio h/lch to account for the size effect factor as proposed earlier in Eq. (1) by Marzouk et al.5 However, it should be noted that any size effect factor that is derived using linear elastic fracture mechanics (LEFM) could be applied. It is also proposed that punching shear strength is proportional to the reinforcement ratio to the power of 0.33, as given by most European codes.16,20,21

Nominal shear strength in the proposed equation for punching has been evaluated using the control perimeter, concrete strength, reinforcement ratio, and brittleness ratio h/lch. In this case, it is proposed that the punching shear strength is proportional to the ratio of lch/h to the power

include the influence of either the flexural reinforcement or the size effect on the limiting shear stress.

The test results are compared to the predictions of ACI 318-08,1 CSA A23.3-04,2 Eurocode 2,16 CEB-FIP,20 and BS 8110-97.21 ACI 318-081 requires that the ultimate shear resistance for slabs Vc is the smallest of

(2)

V f b d

V f b d

c c o

c c o

= +

′

= +

′

0 17 12

24

.β

λ

βλ

(SI units)

or ((U.S. units)

where b is the ratio of long side to short side of the column, concentrated load, or reaction area;

(3)V

d

bf b d

Vd

b

cs

oc o

cs

o

= +

′

= +

0 083 2

2

.α

λ

α

(SI units)

or λλ f b dc o′ (U.S. units)

where αs is 40 for interior columns, 30 for edge columns, 20 for corner columns; and

(4)V f b d

V f b d

c c o

c c o

= ′

= ′

0 33

4

. λ

λ

(SI units)

or (U.S. units)

where bo is the perimeter of critical section for shear in slabs and footings; d is the slab effective depth; fc′ is the cylinder compressive strength of concrete; and l is the modification factor reflecting the reduced mechanical properties of lightweight concrete. CSA A23.3-042 accounts for the slab effective depth. If the effective depth d used in two-way shear calculations exceeds 300 mm (12 in.), the value of punching shear resistance Vc shall be multiplied by 1300/(1000 + d). Fracture mechanics concepts suggest that the size effect factor is not related to the member thickness only but must be related to the concrete strength as well.

In CEB-FIP,20 the punching shear resistance VCEB is assumed to be proportional to (fck)1/3, where fck is the characteristic compressive strength of concrete. The influences of reinforcement and slab depth are also considered in this design code. The punching resistance according to CEB-FIP20 is

V fd

u dCEB ck= +

0 18 100 1

2003

1. ρ (SI units) (5a)

V fd

u dCEB ck= +

0 93 100 1

83

1. ρ (U.S. units) (5b)

where ( )1 200 d+ is a size effect factor; u1 is the length of the control perimeter at 2d from the column; and r is the flexural reinforcement ratio.


ratio and were designed to fail under punching shear. This confirms that the size effect factor cannot be taken as a constant number related to the member depth but it must also be related to the mechanical properties of concrete.

3. The enhanced structural behavior of Specimen HSS2 (300 mm [12 in.]) with T-headed studs reflects the benefit of using shear reinforcement. The structural behavior of Specimen HSS4 (400 mm [16.0 in.]) could be enhanced by adding shear reinforcement. Adding shear reinforcement will ensure using the full benefit due to the increasing slab effective depth. The test results revealed a reduced ductility and energy absorption capacity despite increasing the effective depth. The addition of shear reinforcement with a reinforcement ratio of approximately 0.68% by volume changed the punching failure mode to a ductile flexure failure.

4. A size effect factor is recommended based on the thickness of the slab and fracture mechanics material property represented by the brittleness factor known as the characteristic length lch.

ACKNOWLEDGMENTSThe authors are grateful to the Natural Sciences and Engineering Research

Council of Canada (NSERC) for providing the funds for the project. Sincere thanks are due to M. Curtis, S. Organ, D. Pike, and the technical staff of the Structural Engineering Laboratory of Memorial University of Newfoundland for their assistance during the preparation of the specimens and during testing. Sincere thanks are extended to Capital Ready Mix Ltd., Newfoundland, Canada, for providing the concrete for this project.

NOTATIONbo = perimeter of critical section for shear in slabs and footingsC = side length of square columnd = slab effective depthfc′ = uniaxial compressive strength of concrete (cylinder strength)fck = characteristic compressive strength of concrete in MPaft = uniaxial tensile strength of concretefy = yield stress of reinforcementGf = fracture energyh = slab thicknesslch = characteristic lengths = spacing between peripheral lines of shear reinforcementu = length of control perimeter at distance equal to 1.5d from loaded areau1 = length of control perimeter at distance equal to 2d from loaded areaVc = nominal shear strength provided by concreteas = constant used to compute Vc in slabs and footingsDU = post-ultimate deflectionDy = deflection at first yieldl = modification factor reflecting reduced mechanical properties of lightweight concreter = flexural reinforcement ratio

of 0.33. Based on the previous assumptions, the following equation is recommended

(8a)V fl

hb dc eq c

cho− = ′

( )0 33 1000 33

0 33.

..ρ (SI units)

(8b)V fl

hb dc eq c

cho− = ′

( )4 1000 33

0 33.

.ρ (U.S. units)

where bo is the critical shear control perimeter calculated at a distance equal to 0.5d from the support face.

Test results versus code predictionsThe ultimate recorded test loads versus the code predictions

are given in Table 5, together with the estimated values by the proposed equation. The nominal shear stress presented in Table 5 is defined as v = Pu/bod√fc′. The nominal shear stress at failure of Specimen HSS4 is lower than the nominal shear stress at failure of Specimen NSS1. Both slabs have the same thickness and the same reinforcement ratio and were designed to fail under punching shear. This confirms that the size effect factor cannot be taken as a constant number related to the member depth but it must be related to the concrete strength as well. It should be noted that the proposed equation does not cover the effect of shear enhancement for T-headed reinforcement. It is clear from Table 5 that ACI 318-081 underesti mated the punching shear capacity of all specimens with the exception of Specimen HSS1. For example, in the case of Specimen NSS1, ACI 318-081 underestimated the punching capacity by 17%, whereas in the case of Specimen HSS1, which has the minimum amount of flexural reinforcement ratio, ACI 318-081 overestimated the punching capacity by 19%. ACI 318-081 is applied with the omission of the capacity reduction factor. The most accurate ultimate load predictions for the size effect were given by the CEB-FIP20 equation.

CONCLUSIONS1. North American design codes do not provide guidance

for thick plates over 250 mm (10 in.) and do not account for the size effect factor.

2. The nominal shear stress at failure of Specimen HSS4 (400 mm [16.0 in.]) is lower than the nominal shear stress at the failure of Specimen NSS1 (400 mm [16 in.]). Both slabs have the same thickness and the same reinforcement

Slab no. Ultimate load Pu, kNNominal shear stress

v = Pu/bod√fc′

Pcode/Pu

Pu/PflexBS 8110-9721 CEB-FIP20 ACI 318-081 Eurocode 216 CSA A23.3-042 Eq. (8)

HSS1 1722 0.28 0.85 0.89 1.19 0.89 1.37 0.90 1.25

HSS2 2172 0.46 0.96 1.08 0.91 1.06 1.15 0.93 0.99

HSS3 2090 0.37 0.88 0.93 0.89 0.93 1.02 0.94 0.64

NSS1 2234 0.40 0.92 0.98 0.83 0.98 0.95 0.92 0.46

HSS4 2513 0.36 0.94 1.00 0.91 1.00 1.03 0.96 0.50

Average 0.91 0.98 0.95 0.97 1.10 0.93

Standard deviation 0.04 0.07 0.14 0.07 0.17 0.02

Coefficient of variation 0.05 0.07 0.15 0.07 0.15 0.02

Notes: 1 MPa = 145 psi; 1 kN = 0.2248 kips.

Table 5—Comparison of code predictions with test results


12. Elgabry, A., and Ghali, A., “Design of Stud-Shear Reinforcement for Slabs,” ACI Structural Journal, V. 87, No. 3, May-June 1990, pp. 350-361.

13. Dilger, W., and Ghali, A., “Shear Reinforcement for Concrete Slabs,” Journal of the Structural Division, ASCE, V. 107, No. 12, 1981, pp. 2403-2420.

14. Marzouk, H., and Jiang, D., “Experimental Investigation on Shear Enhancement Types for High-Strength Concrete Plates,” ACI Structural Journal, V. 93, No. 1, Jan.-Feb. 1997, pp. 49-58.

15. Berner, D.; Gerwick, B.; and Hoff, G., “T-Headed Stirrup Bars,” Concrete International, V. 13, No. 5, May 1991, pp. 49-53.

16. BS EN 1992-1-2, “Eurocode 2: Design of Concrete Structures—Part 1-1: General Rules and Rules for Buildings,” Brussels, Belgium, 2004, 230 pp.

17. Marzouk, H., and Hussein, A., “Experimental Investigation on the Behavior of High-Strength Concrete Slabs,” ACI Structural Journal, V. 88, No. 6, Nov.-Dec. 1991, pp. 701-713.

18. Joint ACI-ASCE Committee 421, “Shear Reinforcement for Slabs (ACI 421.1R-08),” American Concrete Institute, Farmington Hills, MI, 2008, 15 pp.

19. Megally, S., and Ghali, A., “Seismic Behavior of Edge Slab-Column Connections with Stud Shear Reinforcement,” ACI Structural Journal, V. 97, No. 1, Jan.-Feb. 2000, pp. 53-60.

20. Comité Euro-International du Béton-Fédération de la Précontrainte (CEB-FIP), Model Code 1990, Bulletin d’information No. 203-305, Lausanne, Switzerland, 1990, 462 pp.

21. BS 8110, “Structural Use of Concrete, Part 1: Code of Practice for Design and Construction,” British Standards Institution, London, UK, 1997, 117 pp.

22. Marzouk, H., and Chen, Z., “Fracture Energy and Tension Properties of High-Strength Concrete,” Journal of Materials in Civil Engineering, ASCE, V. 7, No. 2, 1995, pp. 108-116.

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

Concrete (ACI 318-08) and Commentary,” American Concrete Institute, Farmington Hills, MI, 2008, 473 pp.

2. CSA A23.3-04, “Design of Concrete Structures for Buildings,” Canadian Standards Association, Rexdale, ON, Canada, 2004, 258 pp.

3. Comité Euro-International du Béton-Fédération de la Précontrainte (CEB-FIP), “Punching of Structural Concrete Slabs,” Bulletin No. 12, Lausanne, Switzerland, 2001, 307 pp.

4. Richart, F., “Reinforced Concrete Wall and Column Footings,” ACI JOURNAL, Proceedings V. 45, No. 2 and 3, 1948, pp. 97-127 and 237-260.

5. Marzouk, H.; Emam, M.; and Hilal, M., “Sensitivity of Shear Strength to Fracture Energy of High-Strength Concrete Slabs,” Canadian Journal of Civil Engineering, V. 25, No. 1, 1998, pp. 40-50.

6. Kevin, K., “Influence of Size on Punching Shear Strength of Concrete Slabs,” master’s thesis, McGill University, Montreal, QC, Canada, 2000, 92 pp.

7. Regan, P., and Braestrup, M., “Punching Shear in Reinforced Concrete: A State of Art Report,” Bulletin d’information No. 168, Comité Euro-International du Beton, Lausanne, Switzerland, 1985, 232 pp.

8. Hallgren, M., “Punching Shear Capacity of Reinforced High Strength Concrete Slabs,” doctoral thesis, Department of Structural Engineering, Royal Institute of Technology, Stockholm, Sweden, 1996, 206 pp.

9. Hegger, J.; Sherif, A.; and Ricker, M., “Experimental Investigations on Punching Behavior of Reinforced Concrete Footings,” ACI Structural Journal, V. 104, No. 3, May-June 2006, pp. 604-613.

10. Hegger, J.; Ricker, M.; and Sherif, A., “Punching Strength of Reinforced Concrete Footings,” ACI Structural Journal, V. 106, No. 5, Sept.-Oct. 2009, pp. 706-716.

11. Birkle, G., and Dilger, W., “Influence of Slab Thickness on Punching Shear Strength,” ACI Structural Journal, V. 105, No. 2, Mar.-Apr. 2008, pp. 180-188.

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