A Simple Equation for Predicting the Punching Shear Capacity of Normal and High Strength Concrete Flat Plates

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A Simple Equation for Predicting the Punching Shear Capacity of Normal and High Strength Concrete Flat Plates

Ali S. Ngab

Civil Engineering Department University of Tripoli

Tripoli, Libya

Md. Saifuddin Shahin

Civil Engineering Department University of Tripoli

Tripoli, Libya

AbstractThe aim of this research is to propose a new simple equation that can predict the punching shear strength of normal and high strength concrete flat plates. In this work test data for interior flat-plate slab-column connections subjected to concentric gravity loads were collected from literature and compared with the proposed equation. From test data available in the literature, a new simple equation for punching shear capacity due to gravity load as a function of concrete strength, slab reinforcement ratio, slab effective depth and the critical perimeter was developed. The punching shear resistance strength was evaluated using ACI 318-14, Eurocode 2, CSA-14 and the IS456 design code equations. The new equation was checked and compared with the known approaches to predict the punching shear for normal as well as high strength concretes by using the tests in the data bank available and it gave good correlation with reasonable standards of deviation and small coefficient of variation.

Keywords Punching shear strength; flat plates; high-strength concrete; interior column; building codes.

  1. INTRODUCTION

    Flat plate construction is very common in parking, office, and apartment buildings. Exclusion of the beams, drop panels, or column capitals in the structural system optimizes the story height, formwork, labour, construction time, and the interior space of the building. This makes flat plate construction a very desirable structural system in view of economy, construction, and architectural desires. However, from structural point of view, supporting a relatively thin plate directly on a column is significantly problematic due to the structural discontinuity. [1]

    Punching shear failure disasters have occurred several times in the last decades. This type of failure is extremely dangerous and should be prevented. In 1995 June 30th a five story Sampoong department store in South Korea collapsed due to this sudden brittle failure. Where more than 500 people were killed and nearly 1000 were injured [2]. Also Pipers Row Multi- Story Car Park which was built in 1965 collapsed during the night of 1997 March 20th. Initial reports identified some of the factors which contributed to cause punching shear failure which is developed into a progressive collapse [3].

    There are significant variations in the approaches used to assess shear resistance of reinforced concrete slab-column connections in the current major codes. Generally, all design codes adopt the simple shear on certain critical perimeter approach and involve only the most important parameters. The critical section for checking punching shear is usually situated a distance between 0.5 to 2.0 times the effective depth (d) from

    the edge of the loaded area [4].( 0.5d for ACI, CSA, IS456 and 2d in EC 2)

    The other important difference amongst codes is in the way they represent the effect of concrete compressive strength (fc) on punching shear capacity. Generally, these codes expressed this effect in terms of (fc)n, where (n) varies from (1/2) in the ACI code to (1/3) in the European code. The further complication is the definition of the concrete compressive strength. The ACI and CSA codes use specified concrete strength fc. while the European and Indian codes use characteristic strength fck. Punching shear provisions of current major codes are illustrated in Table 4.

    The main purpose of this study was to propose a new simple punching shear equation for both normal strength concrete (NSC) and also for high strength concrete (HSC) flat plates and to compare the proposed equation with the shear strength provisions of ACI 318-14 [5], Eurocode 2 [6], CSA A23.3-14 [7], IS456-2000 [8] for interior slab column connections without shear reinforcement.

  2. RESEARCH SIGNIFICANCE

    Punching shear is a very important issue specially in flat plate slabs. Errors in predicting the punching shear have shown to lead to catastrophic failure [9]. Different codes have discussed the punching shear provisions with great importance. In recent years the use of high strength concrete (HSC) is becoming more and more popular. Increase uses of HSC is faster than the development of appropriate design code and recommendations. Several recent studies showed that HSC have different characteristics than NSC. As the use of HSC is becoming more popular, the importance of research on

    punching shear provisions for HSC is increased.

    Even for NSC, to calculate the punching shear capacity according to most of the major codes, it is required to use several equations and need to deal with various factors. Thus, a simple equation is needed to predict the punching shear for both, the NSC and HSC.

    Although some researchers including Rankin (1987, 2003), Sherif and Dilger (1996), Gardner and Shao (1996), El-Gamal and Benmokrane (2004), Ali S. Abdul Jabbar et. al (2012), Elsanadedy, H.M., Al-Salloum, Y.A. and Alsayed, S.H. (2013) proposed their own equations to predict punching shear as shown in Table 1 [4,10,11,19]. However, these equations are not studied in this research.

    TABLE I. FORMULAS PROPOSED BY OTHER RESEARCHERS FOR CONCRETE PUNCHING SHEAR CAPACITY OF HSC FLAT PLATES [4,10,11,19]

    Researcher

    Concrete Punching shear Capacity (Units: N and mm)

    Modified Rankin (1987; 2003)

    = 0.783 4100

    0

    Sherif and Dilger (1996)

    = 0.73 3100

    0

    Gardner and Shao (1996)

    200

    = 0.793 3 1 +

    0 0

    El-Gamal and Benmokrane (2004)

    8

    = 0.333 [0.53 (1 + )] .

    0 0

    where E= modulus of elasticity of reinforcing

    material (MPa)

    Ali S. Abdul Jabbar et. al (2012)

    3 . 4 200

    = 0.9 0

    0

    Elsanadedy, H.M. et al. (2013)

    8 125

    = 0.13 (1 + ) (1 + ) .

    0 0

  3. DATA COLLECTION

    Punching shear tests can be done on either a multi-panel structure or on isolated slab column connections. Multi-panel tests are time consuming, expensive and it is difficult to determine experimentally the shear and moments applied in individual connections. Isolated slab column connection tests have the problem that the boundary conditions may not

    equals to 1. It is generally accepted that the punching shear capacity of slab column connections results from concrete contribution and the contribution from shear reinforcement, if present. However, this study is limited for symmetrical flat slabs without shear reinforcement and connected to square or circular columns which means the aspect ratio is neglected and all other factors is taken to 1.0 for comparison reasons as noted before. So, to make the comparisons easier the provisions for the nominal concrete shear capacity Vc can be summarized in Table 4.

    Eviews 10 statistic program is used to get the equation to predict the punching shear strength of interior column-slab connection of HSC flat plates. HSC specimens from literature conducted by different researcher [13,14,15,16,17,18,19] were selected for the rgression analysis given earlier in Table 2. Investigations showed that the main variables affecting punching shear strength are: Concrete compressive strength (fc), Flexural Reinforcement ratio (), Average effective depth (d), Column geometry (Critical perimeter b0) [20]. These declared four variables have the most significant effect on flat plates without shear reinforcement.

    Accordingly, the concrete punching shear strength can be expressed as follows:

    Vc= C1(fc)C2(/100)C3(b0 × d)C4 (1)

    In the above equation C1, C2, C3, C4 are constants to be determined from the regression analysis. From the Regression analysis using Eviews 10 program, after cycles of iterations, it is found that C1=1.5, C2=0.5, C3=1/3, C4=1.0. The best-fit equation is as follows.

    represent connections in a continuous structure and the moment

    = 1.5 () (3

    ) (

    × ) (2)

    redistribution cannot occur in an isolated connection test. [12]

    0

    0

    100

    All comparisons in this study are with the results from tests on isolated specimens. Flat plates are widely used for floor construction in multi-story buildings, as such a significant amount of experimental research work has been done on the punching shear failure of concrete flat plates.

    A review of the literature revealed that only a few experimental studies are available on punching shear strength of high-strength slabs. The specimens data was collected from the previous test results of isolated specimens conducted by Hallgren and Kinunen (1996) [13], Marzouk and Hussein (1991) [14], Tomaszewricz (1993) [15], Osman et al. (2000)

    [16], Ramdane (1996) [17], Ozden et al (2006) [18], Susanto T. et al. (2018) [19] with a total number of 38 specimens. These selected specimen samples for this study have compressive strength ranging between 70 to 119MPa. The reinforcement ratios were between 0.33 to 2.62 %. The effective depth ranged between 70 to 275mm. Table 2 presents details of HSC data. A large number of normal strength concrete specimens (243 specimen) test data are collected from literature (Susanto T. et al. (2018)) [19] where these data from 1956-2012. Table 3 presenting some of the details of NSC data from 243 samples.

  4. ANALYSIS OF DATA

    In this study for the purpose of comparing code provisions safety factors have been removed from the equations. It might be important to note that this comparison is held between code provisions of interior circular or square columns of c1/c2 ratio

    Where, Vc = predicted nominal punching shear stress (N)

    fc = Concrete compressive strength (MPa)

    d = average effective depth (mm)

    = flexural reinforcement ratio (%) b0 = critical perimeter at distance d/2 from column face b0 = 4(c+d) for square column

    and (c+d) for circular column

    c = column diameter or width (mm) The above equation has R2 = 0.98. It should be illustrated that in the proposed equation, the critical section was assumed to be at a distance of d/2 from the column face because this value has been used to define the critical section in the ACI code since the 1960s. Therefore, the critical perimeter (b0) is equal to 4(c + d) for square columns and (c + d) for circular

    columns.

    It is important to emphasize that the suggested equation was concluded using punching shear strength testing database with specific physical and geometrical limits of the following: circular and rectangular columns with (c1/c2) ratio equals to 1.

    TABLE II. DETAILS OF HSC SPECIMENS FROM LITERATURE CONDUCTED BY DIFFERENT RESEARCHER

    No.

    Ref. [No.]

    Slab ID

    L

    (mm)

    c (mm)

    Column Shape

    d (mm)

    fc

    (MPa)

    fy

    (MPa)

    (%)

    Vexp (kN)

    Failure mode

    1

    [13]

    HSC0

    2540

    250

    C

    200

    90.3

    643

    0.8

    965

    P

    2

    [13]

    HSC1

    2540

    250

    C

    200

    91

    627

    0.8

    1021

    P

    3

    [13]

    HSC2

    2540

    250

    C

    194

    85.7

    620

    0.82

    889

    P

    4

    [13]

    HSC4

    2540

    250

    C

    200

    91.6

    596

    1.2

    1041

    P

    5

    [13]

    HSC6

    2540

    250

    C

    201

    108.8

    633

    0.6

    960

    P

    6

    [13]

    HSC8

    2540

    250

    C

    198

    95

    634

    0.8

    944

    P

    7

    [13]

    HSC9

    2540

    250

    C

    202

    84.1

    631

    0.33

    565

    FP

    8

    [14]

    HS2

    1700

    150

    S

    95

    70.2

    490

    0.84

    249

    P

    9

    [14]

    HS6

    1700

    150

    S

    120

    70

    490

    0.944

    489

    P

    10

    [14]

    HS7

    1700

    150

    S

    95

    73.8

    490

    1.19

    356

    P

    11

    [14]

    HS9

    1700

    150

    S

    120

    74

    490

    1.611

    543

    P

    12

    [14]

    HS10

    1700

    150

    S

    120

    80

    490

    2.333

    645

    P

    13

    [14]

    HS11

    1700

    150

    S

    70

    70

    490

    0.95

    196

    P

    14

    [14]

    HS12

    1700

    150

    S

    70

    75

    490

    1.524

    258

    P

    15

    [14]

    HS14

    1700

    220

    S

    95

    72

    490

    1.473

    498

    P

    16

    [14]

    HS15

    1700

    300

    S

    95

    71

    490

    1.473

    560

    P

    17

    [15]

    nd95-1-1

    3000

    200

    S

    275

    83.7

    500

    1.42

    2250

    P

    18

    [15]

    nd95-1-3

    3000

    200

    S

    275

    89.9/p>

    500

    2.43

    2400

    P

    19

    [15]

    nd115-1-1

    3000

    200

    S

    275

    112

    500

    1.42

    2450

    P

    20

    [15]

    nd65-2-1

    2200

    150

    S

    200

    70.2

    500

    1.66

    1200

    P

    21

    [15]

    nd95-2-1

    2600

    150

    S

    200

    88.2

    500

    1.66

    1100

    P

    22

    [15]

    nd95-2-1d

    2600

    150

    S

    200

    87

    500

    1.75

    1300

    P

    23

    [15]

    nd95-2-3

    2600

    150

    S

    200

    90

    500

    2.49

    1450

    P

    24

    [15]

    nd95-2-3d

    2600

    150

    S

    200

    80

    500

    2.62

    1250

    P

    25

    [15]

    nd95-2-3d+

    2600

    150

    S

    200

    98

    500

    2.62

    1450

    P

    26

    [15]

    nd115-2-1

    2600

    150

    S

    200

    119

    500

    1.66

    1400

    P

    27

    [15]

    nd115-2-3

    2600

    150

    S

    200

    108.1

    500

    2.49

    1550

    P

    28

    [15]

    nd95-3-1

    1500

    100

    S

    88

    85.1

    500

    1.72

    330

    P

    29

    [16]

    HSLW 1.0 P

    1900

    250

    S

    115

    73.4

    435

    1

    473.5

    P

    30

    [16]

    HSLW 1.5 P

    1900

    250

    S

    115

    75.5

    435

    1.5

    538.5

    P

    31

    [16]

    HSLW 2.0 P

    1900

    250

    S

    115

    74

    435

    2

    613.4

    P

    32

    [17]

    16

    1700

    150

    C

    95

    99.2

    650

    1.28

    362

    FP

    33

    [17]

    22

    1700

    150

    C

    98

    84.24

    650

    1.28

    405

    P

    34

    [18]

    HR1E0F0

    1500

    200

    S

    100

    70.3

    471

    1.49

    331

    P

    35

    [18]

    HR1E0F0r

    1500

    200

    S

    100

    71.3

    471

    1.49

    371

    P

    36

    [18]

    HR2E0F0r

    1500

    200

    S

    100

    71

    471

    2.26

    489

    P

    37

    [19]

    S11-090

    2200

    200

    S

    117

    112

    537

    0.9

    438.6

    P

    38

    [19]

    S11-139

    2200

    200

    S

    114

    112

    501

    1.39

    453.6

    P

    Where, L = slab width or diameter (mm), c = column width or diameter (mm), d = average effective depth (mm), Column shape: S = Square; C = Circular, Failure mode: P = Punching failure; F = Flexural failure

    TABLE III. DETAILS OF NSC SPECIMENS FROM LITERATURE CONDUCTED BY DIFFERENT RESEARCHER

    2000

    No.

    Year

    Slab ID

    L

    (mm)

    c (mm)

    Column Shape

    d (mm)

    fc

    (MPa)

    fy

    (MPa)

    (%)

    Vexp

    (kN)

    Failure mode

    1

    1997

    L5

    1970

    399

    C

    172

    31.1

    612

    0.66

    696

    P

    2

    1997

    L6

    1970

    406

    C

    175

    31.1

    612

    0.65

    799

    P

    3

    1997

    L7

    1970

    201

    C

    177

    22.9

    586

    0.64

    478

    P

    4

    1997

    L8

    2470

    899

    C

    174

    22.9

    576

    1.16

    1111

    P

    5

    1997

    L9

    2470

    897

    C

    172

    22.9

    576

    1.17

    1107

    P

    6

    1997

    L10

    2470

    901

    C

    173

    22.9

    576

    1.16

    1079

    P

    7

    1998

    H.H.Z.S.1.0

    1900

    250

    S

    119

    67.2

    460

    1

    511.5

    P

    8

    2000

    9

    2600

    250

    S

    150

    26.9

    500

    0.52

    408

    P

    9

    2000

    9a

    2600

    250

    S

    150

    21

    500

    0.52

    360

    P

    10

    2000

    NU

    2300

    225

    S

    110

    30

    444

    1.11

    306

    P

    11

    2000

    NB

    2300

    225

    S

    110

    30

    444

    2.15

    349

    P

    12

    P100

    925

    201

    S

    99

    39.3

    488

    0.97

    330

    P

    13

    2000

    P150

    1190

    201

    S

    150

    39.3

    464

    0.9

    582.7

    P

    14

    2000

    P200

    1450

    201

    S

    201

    39.3

    464

    0.83

    902.9

    P

    15

    2000

    P300

    1975

    201

    S

    300

    39.3

    468

    0.76

    1378.9

    P

    16

    2000

    P400

    1975

    300

    S

    399

    39.3

    468

    0.76

    2224

    P

    17

    2000

    1

    2400

    120

    S

    93

    60.9

    695

    1.5

    270

    P

    18

    2000

    2

    1700

    120

    S

    97

    62.9

    695

    1.4

    335

    P

    19

    2004

    L1b

    1680

    120

    S

    108

    59

    749

    1.08

    322.4

    P

    20

    2004

    L1c

    1680

    120

    S

    107

    59

    749

    1.09

    318

    P

    21

    2004

    OC11

    2200

    200

    S

    105

    36

    461

    1.81

    423

    P

    22

    2006

    NR1E0F0

    1500

    200

    S

    100

    20.5

    507

    0.73

    188

    P

    23

    2006

    NR2E0F0

    1500

    200

    S

    100

    19

    507

    1.09

    202

    P

    24

    2006

    HR2E0F0

    1500

    200

    S

    100

    60.5

    471

    2.26

    405

    P

    25

    2008

    1

    2400

    250

    S

    124

    36.2

    488

    1.54

    483

    P

    26

    2008

    7

    3400

    300

    S

    190

    35

    531

    1.3

    825

    P

    27

    2008

    30U

    2300

    225

    S

    110

    30

    434

    1.11

    306

    P

    28

    2008

    30B

    2300

    225

    S

    110

    30

    434

    2.15

    349

    P

    29

    2008

    65U

    2300

    225

    S

    110

    67.1

    445

    1.18

    443

    P

    30

    2009

    PG-1

    3000

    260

    S

    210

    27.6

    573

    1.5

    1023

    P

    31

    2009

    PG-6

    1500

    130

    S

    96

    34.7

    526

    1.5

    238

    P

    32

    2009

    PG-7

    1500

    130

    S

    100

    34.7

    550

    0.75

    241

    P

    33

    2009

    PG-11

    3000

    260

    S

    210

    31.5

    570

    0.75

    763

    P

    34

    2010

    S1

    1500

    152

    S

    127

    47.7

    471

    0.83

    433

    P

    35

    2010

    S2

    1500

    152

    S

    127

    47.7

    471

    0.56

    379

    P

    36

    2012

    A0

    1050

    200

    S

    105

    21.7

    492

    0.66

    284

    P

    37

    2012

    B0

    1350

    200

    S

    105

    21.7

    492

    0.75

    275

    P

    38

    2012

    C0

    1650

    200

    S

    105

    21.7

    492

    0.7

    264

    P

    Where, L = slab width or diameter (mm), c = column width or diameter (mm), d = average effective depth (mm), Column shape: S = Square; C = Circular, Failure mode: P = Punching failure; F = Flexural failure

    TABLE IV. SUMMARY OF CODE PROVISION WITH PROPOSED EQUATION

    Code

    Critical Perimeter

    Nominal Shear Capacity

    ACI 318-14

    Located at 0.5d from the columns face

    b0 = 4(c + d) for square column b0 = (c + d) for circular column

    0.33

    0

    0.17 (1 + 2)

    = min 0

    0.083 ( + 2)

    { 0 0

    Eurocode 2

    Located at 2d from the columns face b0 = 4(c + d) for square column b0 = (c + 4d) for circular column

    0.18 1

    = (100)30

    200

    = 1 + 2.0

    CSA A23.3-14

    Located at 0.5d from the columns face

    b0 = 4(c + d) for square column b0 = (c + d) for circular column

    1 + 2

    0.19 ( )

    0

    = min ( + 0.19)

    0 0

    { 0.38

    0

    IS 456

    Located at 0.5d from the columns face

    b0 = 4(c + d) for square column b0 = (c + d) for circular column

    Vc = c b0 d

    = (0.25)

    ks = 0.5 + c 1.0

    Author s Proposed equation

    Similar to ACI318-14 code

    3

    = 1.5() × ( 0 × )

    100

    TABLE V. THE COMPARISON OF THE PROPOSED METHOD, ACI, EC 2, CSA AND IS 456 EQUATIONS WITH HSC EXPERIMENTAL DATA FOR THE SECIMENS

    Ref

    No.

    Specimen

    f'c (MPa)

    Exp. (kN)

    ACI (kN)

    Euro (kN)

    Canadian (kN)

    Indian (kN)

    Proposed (kN)

    V(exp)/V(pred)

    ACI

    EC2

    CSA

    IS

    Proposed

    [13]

    1

    HSC0

    90.3

    965

    887

    989

    1021

    1008

    806

    1.09

    0.98

    0.95

    0.96

    1.20

    2

    HSC1

    91

    1021

    890

    992

    1025

    1011

    809

    1.15

    1.03

    1.00

    1.01

    1.26

    3

    HSC2

    85.7

    889

    827

    936

    952

    939

    758

    1.08

    0.95

    0.93

    0.95

    1.17

    4

    HSC4

    91.6

    1041

    893

    1138

    1028

    1015

    929

    1.17

    0.91

    1.01

    1.03

    1.12

    5

    HSC6

    108.8

    960

    980

    964

    1129

    1114

    810

    0.98

    1.00

    0.85

    0.86

    1.19

    6

    HSC8

    95

    944

    896

    991

    1032

    1019

    815

    1.05

    0.95

    0.91

    0.93

    1.16

    7

    HSC9

    84.1

    565

    868

    730

    1000

    986

    587

    0.65

    0.77

    0.57

    0.57

    0.96

    [14]

    8

    HS2

    70.2

    249

    257

    293

    296

    293

    238

    0.97

    0.85

    0.84

    0.85

    1.05

    9

    HS6

    70

    489

    358

    422

    412

    407

    344

    1.37

    1.16

    1.19

    1.20

    1.42

    10

    HS7

    73.8

    356

    264

    334

    304

    300

    274

    1.35

    1.07

    1.17

    1.19

    1.30

    11

    HS9

    74

    543

    368

    513

    424

    418

    422

    1.48

    1.06

    1.28

    1.30

    1.29

    12

    HS10

    80

    645

    383

    596

    440

    435

    497

    1.69

    1.08

    1.46

    1.48

    1.30

    13

    HS11

    70

    196

    170

    203

    196

    193

    164

    1.15

    0.96

    1.00

    1.01

    1.20

    14

    HS12

    75

    258

    176

    243

    203

    200

    198

    1.47

    1.06

    1.27

    1.29

    1.30

    15

    HS14

    72

    498

    335

    411

    386

    381

    373

    1.49

    1.21

    1.29

    1.31

    1.33

    16

    HS15

    71

    560

    417

    473

    481

    474

    465

    1.34

    1.18

    1.17

    1.18

    1.20

    [15]

    17

    nd95-1-1

    83.7

    2250

    1577

    1919

    1816

    1793

    1736

    1.43

    1.17

    1.24

    1.26

    1.30

    18

    nd95-1-3

    89.9

    2400

    1635

    2351

    1883

    1858

    2152

    1.47

    1.02

    1.27

    1.29

    1.12

    19

    nd115-1-1

    112

    2450

    1825

    2115

    2101

    2074

    2009

    1.34

    1.16

    1.17

    1.18

    1.22

    20

    nd65-2-1

    70.2

    1200

    774

    1095

    891

    880

    898

    1.55

    1.10

    1.35

    1.36

    1.34

    21

    nd95-2-1

    88.2

    1100

    868

    1181

    999

    986

    1006

    1.27

    0.93

    1.10

    1.12

    1.09

    22

    nd95-2-1d

    87

    1300

    862

    1197

    992

    979

    1017

    1.51

    1.09

    1.31

    1.33

    1.28

    23

    nd95-2-3

    90

    1450

    877

    1362

    1009

    996

    1164

    1.65

    1.06

    1.44

    1.46

    1.25

    24

    nd95-2-3d

    80

    1250

    826

    1332

    952

    939

    1116

    1.51

    0.94

    1.31

    1.33

    1.12

    25

    nd95-2-3d+

    98

    1450

    915

    1425

    1053

    1039

    1235

    1.59

    1.02

    1.38

    1.39

    1.17

    26

    nd115-2-1

    119

    1400

    1008

    1305

    1161

    1145

    1169

    1.39

    1.07

    1.21

    1.22

    1.20

    27

    nd115-2-3

    108.1

    1550

    961

    1447

    1106

    1092

    1275

    1.61

    1.07

    1.40

    1.42

    1.22

    28

    nd95-3-1

    85.1

    330

    201

    315

    232

    229

    236

    1.64

    1.05

    1.42

    1.44

    1.40

    [16]

    29

    HSLW 1.0 P

    73.4

    473.5

    475

    491

    547

    539

    465

    1.00

    0.96

    0.87

    0.88

    1.02

    30

    HSLW 1.5 P

    75.5

    538.5

    481

    568

    554

    547

    540

    1.12

    0.95

    0.97

    0.98

    1.00

    31

    HSLW 2.0 P

    74

    613.4

    477

    621

    549

    542

    588

    1.29

    0.99

    1.12

    1.13

    1.04

    [17]

    32

    16

    99.2

    362

    240

    351

    277

    273

    256

    1.51

    1.03

    1.31

    1.33

    1.42

    33

    22

    84.24

    405

    231

    347

    266

    263

    246

    1.75

    1.17

    1.52

    1.54

    1.65

    [18]

    34

    HR1E0F0

    70.3

    331

    332

    421

    382

    377

    371

    1.00

    0.79

    0.87

    0.88

    0.89

    35

    HR1E0F0r

    71.3

    371

    334

    423

    385

    380

    374

    1.11

    0.88

    0.96

    0.98

    0.99

    36

    HR2E0F0r

    71

    489

    334

    486

    384

    379

    429

    1.47

    1.01

    1.27

    1.29

    1.14

    [19]

    37

    S11-090

    112

    438.6

    518

    513

    597

    589

    490

    0.85

    0.85

    0.74

    0.74

    0.90

    38

    S11-139

    112

    453.6

    500

    573

    576

    568

    547

    0.91

    0.79

    0.79

    0.80

    0.83

    Mean

    1.30

    1.01

    1.13

    1.14

    1.18

    STD

    0.27

    0.11

    0.23

    0.23

    0.16

    COV

    0.07

    0.01

    0.05

    0.05

    0.03

    TABLE VI. THE COMPARISON OF THE PROPOSED METHOD, ACI, EC 2, CSA AND IS 456 EQUATIONS WITH NSC EXPERIMENTAL DATA FOR THE SPECIMENS

    Ref

    No.

    Specimen

    f'c (MPa)

    Exp. (kN)

    ACI (kN)

    Euro (kN)

    Canadian (kN)

    Indian (kN)

    Proposed (kN)

    V(exp)/V(pred)

    ACI

    EC2

    CSA

    IS

    Proposed

    [19]

    1

    L3

    31.1

    530

    374

    437

    431

    425

    281

    1.42

    1.21

    1.23

    1.25

    1.89

    2

    L4

    31.1

    686

    562

    597

    647

    639

    482

    1.22

    1.15

    1.06

    1.07

    1.42

    3

    L5

    31.1

    696

    568

    602

    654

    645

    484

    1.23

    1.16

    1.06

    1.08

    1.44

    4

    L6

    31.1

    799

    588

    617

    677

    668

    499

    1.36

    1.30

    1.18

    1.20

    1.60

    5

    L7

    22.9

    478

    332

    459

    382

    377

    280

    1.44

    1.04

    1.25

    1.27

    1.71

    6

    L8

    22.9

    1111

    926

    970

    1067

    1053

    953

    1.20

    1.14

    1.04

    1.06

    1.17

    7

    L9

    22.9

    1107

    912

    959

    1050

    1037

    941

    1.21

    1.15

    1.05

    1.07

    1.18

    8

    L10

    22.9

    1079

    922

    965

    1061

    1047

    948

    1.17

    1.12

    1.02

    1.03

    1.14

    9

    H.H.Z.S.1.0

    67.2

    511.5

    475

    499

    547

    540

    465

    1.08

    1.02

    0.93

    0.95

    1.10

    10

    9

    26.9

    408

    411

    404

    473

    467

    323

    0.99

    1.01

    0.86

    0.87

    1.26

    11

    9a

    21

    360

    363

    372

    418

    412

    286

    0.99

    0.97

    0.86

    0.87

    1.26

    12

    NU

    30

    306

    266

    341

    307

    303

    270

    1.15

    0.90

    1.00

    1.01

    1.13

    13

    NB

    30

    349

    266

    426

    307

    303

    337

    1.31

    0.82

    1.14

    1.15

    1.04

    14

    P100

    39.3

    330

    246

    297

    283

    279

    238

    1.34

    1.11

    1.17

    1.18

    1.39

    15

    P150

    39.3

    582.7

    436

    514

    502

    495

    412

    1.34

    1.13

    1.16

    1.18

    1.41

    16

    P200

    39.3

    902.9

    669

    769

    770

    760

    615

    1.35

    1.17

    1.17

    1.19

    1.47

    17

    P300

    39.3

    1378.

    9

    1244

    1392

    1432

    1413

    1112

    1.11

    0.99

    0.96

    0.98

    1.24

    18

    P400

    39.3

    2224

    2308

    2365

    2658

    2623

    2063

    0.96

    0.94

    0.84

    0.85

    1.08

    19

    1

    60.9

    270

    204

    307

    235

    232

    229

    1.32

    0.88

    1.15

    1.16

    1.18

    20

    2

    62.9

    335

    220

    321

    254

    250

    241

    1.52

    1.04

    1.32

    1.34

    1.39

    21

    L1b

    59

    322.4

    250

    337

    287

    284

    251

    1.29

    0.96

    1.12

    1.14

    1.29

    22

    L1c

    59

    318

    246

    333

    284

    280

    248

    1.29

    0.95

    1.12

    1.14

    1.28

    23

    OC11

    36

    423

    254

    384

    292

    288

    303

    1.67

    1.10

    1.45

    1.47

    1.40

    24

    HR2E0F0

    60.5

    405

    308

    460

    355

    350

    396

    1.31

    0.88

    1.14

    1.16

    1.02

    25

    1

    36.2

    483

    368

    495

    424

    419

    417

    1.31

    0.98

    1.14

    1.15

    1.16

    26

    7

    35

    825

    727

    887

    837

    826

    777

    1.13

    0.93

    0.99

    1.00

    1.06

    27

    30U

    30

    306

    266

    341

    307

    303

    270

    1.15

    0.90

    1.00

    1.01

    1.13

    28

    30B

    30

    349

    266

    426

    307

    303

    337

    1.31

    0.82

    1.14

    1.15

    1.04

    29

    65U

    67.1

    443

    398

    456

    459

    453

    412

    1.11

    0.97

    0.97

    0.98

    1.07

    30

    PG-1

    27.6

    1023

    684

    951

    788

    778

    767

    1.49

    1.08

    1.30

    1.32

    1.33

    31

    PG-6

    34.7

    238

    169

    272

    194

    192

    189

    1.41

    0.87

    1.23

    1.24

    1.26

    32

    PG-7

    34.7

    241

    179

    229

    206

    203

    159

    1.35

    1.05

    1.17

    1.19

    1.51

    33

    PG-11

    31.5

    763

    731

    788

    842

    831

    651

    1.04

    0.97

    0.91

    0.92

    1.17

    34

    S1

    47.7

    433

    323

    387

    372

    367

    297

    1.34

    1.12

    1.16

    1.18

    1.46

    35

    S2

    47.7

    379

    323

    340

    372

    367

    261

    1.17

    1.12

    1.02

    1.03

    1.45

    36

    A0

    21.7

    284

    197

    232

    227

    224

    168

    1.44

    1.23

    1.25

    1.27

    1.69

    37

    B0

    21.7

    275

    197

    242

    227

    224

    175

    1.40

    1.14

    1.21

    1.23

    1.57

    38

    C0

    21.7

    264

    197

    236

    227

    224

    171

    1.34

    1.12

    1.16

    1.18

    1.54

    Mean

    1.40

    1.01

    1.22

    1.23

    1.37

    STD

    0.30

    0.21

    0.26

    0.26

    0.21

    COV

    0.088

    0.046

    0.066

    0.068

    0.045

    Therefore, this proposed equation should be updated by the same expert software program Eviws 10 for its application to wide range beyond those mentioned here once testing database on HSC flat plates become available.

    The above suggested formula of Equation was utilized to assess the concrete punching shear capacity for the 38 HSC specimens and the ratios of the experimental-to-predicted punching shear capacity are then calculated and plotted as displayed in Figure (1). Comparison between experimental vs. predicted by the proposed equation for high strength concrete (HSC) specimens is presented in the Figure 1.

    Fig. 1. Comparison of Vexp vs. Vpre for HSCspecimens using proposed equation.

    Fig. 2. Comparison of Vexp vs. Vpre for HSC specimens using proposed equation and different codes.

    Table 5 summarize the comparison of different codes and proposed equation for high strength concrete, Also the

    statistical indicators the mean and standard deviations and the coefficient of variance are presented. Figure 2 showing comparison between experimental vs. predicted by different codes and the proposed equation for high strength concrete (HSC) specimens.

    Fig. 3. Comparison of Vexp vs. Vpre for NSC specimens using proposed equation.

    Fig. 4. Comparison of Vexp vs. Vpre for HSC specimens using proposed equation and different codes.

    Fig. 5. Comparison of Vexp vs. Vpre for HSC and NSC specimens using proposed equation.

    Fig. 6. Comparison of Vexp vs. Vpre for HSC specimens using proposed equation and different code.

    Although, the basis in deriving the proposed equation was estimating the punching shear for high strength concrete flat plates, we might extrapolate it for use with normal or low strength concrete (NSC). Therefore, to evaluate and assess the applicability of this proposed equation for NSC a sample of different slabs tested by different researchers with compressive strength less than 69 MPa were used. The prediction of shear strength for normal strength concrete (NSC) specimens by proposed equation and different codes are calculated and the means, standard deviations and coefficients of variation are

    given in Table 6. The statistic parameters: mean, standard deviation and the coefficient of variation were used for comparing with ACI, EC2, CSA, IS provisions in Table 6. Figure 3 shows a comparison between experimental vs. predicted by the proposed equation for normal strength concrete (NSC) specimens. Also in Figure 4 shows a comparison between experimental vs. predicted by different codes and the proposed equation for normal strength concrete (NSC) specimens.

    281 existing published data for normal and high strength concrete specimens is used to evaluate the accuracies and safety of the ACI 318-14, Eurocode 2, CSA A23.3-14, IS 456 and proposed equation for punching shear. Table 7 shows (mean, standard deviation and coefficient of variation) fot the comparison of the proposed equation and ACI, Eurocode 2, CSA and IS 456. In all cases, test was conducted on square or circular slabs supported by column stubs or loading plates. Figure 5 shows a comparison between experimental vs. predicted by the proposed equation for normal and high strength concrete (NSC and HSC) specimens. Also in Figure 6 shows a comparison between experimental vs. predicted by different codes and the proposed equation for normal and high strength concrete (NSC and HSC) specimens.

    TABLE VII. COMPARISON OF STATISTICAL RESULTS OF DIFFERENT CODES AND PROPOSED EQUATION

    HSC Specimen

    ACI 318-14

    EC2

    CSA A23.3-14

    IS 456:2000

    Proposed Eq.

    Mean

    1.30

    1.01

    1.13

    1.14

    1.18

    STD

    0.27

    0.11

    0.23

    0.23

    0.16

    COV

    0.07

    0.01

    0.05

    0.05

    0.03

    NSC Specimen

    ACI 318-14

    EC2

    CSA A23.3-14

    IS 456:2000

    Proposed Eq.

    Mean

    1.40

    1.01

    1.22

    1.23

    1.37

    STD

    0.30

    0.21

    0.26

    0.26

    0.21

    COV

    0.088

    0.046

    0.066

    0.068

    0.045

    NSC and HSC Specimen

    ACI 318-14

    EC2

    CSA A23.3-14

    IS 456:2000

    Proposed Eq.

    Mean

    1.39

    1.01

    1.21

    1.22

    1.35

    STD

    0.29

    0.20

    0.26

    0.26

    0.22

    COV

    0.087

    0.041

    0.065

    0.067

    0.047

  5. DISCUSSION

    According to above analysis based on the available data of specimens from different experimental studies, the relation between the variables and the punching shear strength of interior slab-column connection of HSC flat plates could be defined as below:

    () (3100) ( × )

    0

    0

    Compared with the given provisions of major codes (ACI, EC2, CSA, IS) this proposed formula based on regression analysis gives good correlation with test results.

    Therefore, the new proposed equation reasonably shows that the punching shear strength in HSC flat plates is proportional to the square root compressive strength but it is also shows that the influence of the flexural reinforcement ratio is proportional to the cubic root. On the other hand, it was found that the punching strength is proportional to the effective depth multiplied by the critical perimeter which is in accordance with the definition on the ACI code.

    In case, using HSC the ACI 318-14 shows the most conservative and scatter results among other design codes as evidenced by the highest mean of 1.30 and standard deviation of 0.27. While EC2 prediction shows the least difference to the experimental values with the lowest mean of 1.01 and least scatter with a standard deviation of 0.11. On the other hand, proposed equation is better than ACI code and close to CSA A23.3-14 and IS 456:2000.

    In case, using NSC the ACI 318-14 shows the most conservative and scatter results among other design codes as evidenced by the highest mean of 1.40 and standard deviation of 0.30. While EC2 prediction shows the least difference to the experimental values with the lowest mean of 1.01 and least scatter with a standard deviation of 0.21. On the other hand, proposed equation is conservative, similar to ACI code with mean of 1.37 and standard deviation of 0.21. Canadian and Indian code with mean 1.22, 1.23 and standard deviation of. 0.26, 0.26 respectively.

    In case, using NSC and HSC together the ACI 318-14 shows the most conservative and scatter results among other design codes as evidenced by the highest mean of 1.39 and standard deviation of 0.29. While EC2 prediction shows the least difference to the experimental values with the lowest mean of 1.01 and least scatter with a standard deviation of 0.20. On the other hand, proposed is conservative similar to ACI code with mean of 1.35 and standard deviation of 0.22. Canadian and Indian code with mean 1.21, 1.22 and standard deviation of. 0.26, 0.26 respectively. The statistical analysis is summarized in Table 7.

    It must be noted that the ACI 318-14 places the upper limit of by 8.33MPa which means it is limited to a concrete with a compressive strength of about 69MPa. This limitation in the American code is due to the fact that these provision developed

    mostly from tests on low and normal strength concrete flat

    plates. Therefore, this study uses 70MPa or more as a HSC flat plate specimens.

    From the previous summary, it is clear that the European design code consider the influence of the flexural reinforcement on the punching capacity of slab-column connections either

    However, the proposed design equation is limited to flat plates with depth not more than 300 mm and concrete compressive strength below 120 MPa. For slabs exceeding these limits, experimental validation is required. The proposed equation is onlymeant for typical interior columns.

    Moreover, the validity of different code approaches to predict the punching shear strength were checked and compared with the new presented formula. It is found that the new proposed equation can be used for high strength or normal strength or both of them with a reasonable accuracy. This equation for all strength levels studied, gave conservative results compared to ACI 318, EC2, CSA and IS456 codes.

    Generally the investigations show that the punching shear predictions of ACI 318-14 is conservative and with large scatter compared with Euro-02 code formula which is more accurate and with smaller coefficients of variation. The CSA and the IS456 code seemed to be in good correlation with experimental results.

    The provisions of North American codes ACI 318-14, CSA A23.3-14 which are based on same expression do not include the influence of flexural reinforcement. The proposed equation which is based on regression analysis by using an expert software program depends on results of specimens from different studies and includes the influence of flexural reinforcement ratio.

  6. CONCLUSIONS

This Parametric study showed that the significant parameters that primarily affect the punching shear behavior of slab- column connection of flat plates are concrete compressive strength, slab effective depth, flexural reinforcement ratio and critical perimeter. Despite being a simple equation, the new proposed equation includes the main four significant parameters (f'c, , d and b0) can predict the punching shear capacity with a conservative and reasonable accuracy compared with other available design codes.

1. The proposed equation is found proportional to one half the square root of the compressive strength and to the cubic root of the reinforced ratio, and to effective depth and assumed that the critical perimeter at a distance 0.5d from the column face as it defined in the ACI 318-14 code. The punching shear strength of plates is a function of the flexural reinforcement ratio, and the investigation shows it is proportional to power 1/3. And a power of 1/2 for f'c. This proposed equation is in good agreement with other code equations yet it has a very simple form and is valid for a wide range of normal as well as high strength concrete flat plates. The proposed equation has the following form;

directly or indirectly, and in most cases it is increased in

3

proportion to the cubic root of the flexural reinforcement ratio. This capacity is also increased in proportion to the cubic root of

= 1.5 () ( ) (0 × ) ( )

100

the compressive strength;

3. The American code, CSA

REFERENCES

standard and IS 456 do not reflect the influence of flexural reinforcement ratio, but the capacity is increased in proportion to square root of the compressive strength; Vc .

In this study the code provisions for punching capacity, all the limitations on the magnitude of concrete compressive strength, flexural reinforcement ratio and size effect are ignored in the comparison given. No distinctions was made between fc and fck.

  1. Fariborz M., Concentric Punching Shear Strength of Reinforced Concrete Flat Plates, Master of Engineering thesis, Swinburne University of Technology, Melbourne, Australia, June 2012

  2. Zhang, X., Punching Shear Failure Analysis of Reinforced Concrete Flat Plates using Simplified UST Failure Criterion M.Sc thesis, Griffith University, Gold coast, Australia, 2002.

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