 Open Access
 Authors : Ali S. Ngab, Md. Saifuddin Shahin
 Paper ID : IJERTV10IS030270
 Volume & Issue : Volume 10, Issue 03 (March 2021)
 Published (First Online): 15042021
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
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 flatplate slabcolumn 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 31814, Eurocode 2, CSA14 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; highstrength concrete; interior column; building codes.

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 slabcolumn 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 31814 [5], Eurocode 2 [6], CSA A23.314 [7], IS4562000 [8] for interior slab column connections without shear reinforcement.

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), ElGamal and Benmokrane (2004), Ali S. Abdul Jabbar et. al (2012), Elsanadedy, H.M., AlSalloum, 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
ElGamal 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

DATA COLLECTION
Punching shear tests can be done on either a multipanel structure or on isolated slab column connections. Multipanel 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 columnslab 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 Ã— 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 bestfit equation is as follows.
represent connections in a continuous structure and the moment
= 1.5 () (3
) (
Ã— ) (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 multistory 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 highstrength 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 19562012. Table 3 presenting some of the details of NSC data from 243 samples. 
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] nd9511
3000
200
S
275
83.7
500
1.42
2250
P
18
[15] nd9513
3000
200
S
275
89.9/p>
500
2.43
2400
P
19
[15] nd11511
3000
200
S
275
112
500
1.42
2450
P
20
[15] nd6521
2200
150
S
200
70.2
500
1.66
1200
P
21
[15] nd9521
2600
150
S
200
88.2
500
1.66
1100
P
22
[15] nd9521d
2600
150
S
200
87
500
1.75
1300
P
23
[15] nd9523
2600
150
S
200
90
500
2.49
1450
P
24
[15] nd9523d
2600
150
S
200
80
500
2.62
1250
P
25
[15] nd9523d+
2600
150
S
200
98
500
2.62
1450
P
26
[15] nd11521
2600
150
S
200
119
500
1.66
1400
P
27
[15] nd11523
2600
150
S
200
108.1
500
2.49
1550
P
28
[15] nd9531
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] S11090
2200
200
S
117
112
537
0.9
438.6
P
38
[19] S11139
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
PG1
3000
260
S
210
27.6
573
1.5
1023
P
31
2009
PG6
1500
130
S
96
34.7
526
1.5
238
P
32
2009
PG7
1500
130
S
100
34.7
550
0.75
241
P
33
2009
PG11
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 31814
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 A23.314
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 ACI31814 code
3
= 1.5() Ã— ( 0 Ã— )
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
nd9511
83.7
2250
1577
1919
1816
1793
1736
1.43
1.17
1.24
1.26
1.30
18
nd9513
89.9
2400
1635
2351
1883
1858
2152
1.47
1.02
1.27
1.29
1.12
19
nd11511
112
2450
1825
2115
2101
2074
2009
1.34
1.16
1.17
1.18
1.22
20
nd6521
70.2
1200
774
1095
891
880
898
1.55
1.10
1.35
1.36
1.34
21
nd9521
88.2
1100
868
1181
999
986
1006
1.27
0.93
1.10
1.12
1.09
22
nd9521d
87
1300
862
1197
992
979
1017
1.51
1.09
1.31
1.33
1.28
23
nd9523
90
1450
877
1362
1009
996
1164
1.65
1.06
1.44
1.46
1.25
24
nd9523d
80
1250
826
1332
952
939
1116
1.51
0.94
1.31
1.33
1.12
25
nd9523d+
98
1450
915
1425
1053
1039
1235
1.59
1.02
1.38
1.39
1.17
26
nd11521
119
1400
1008
1305
1161
1145
1169
1.39
1.07
1.21
1.22
1.20
27
nd11523
108.1
1550
961
1447
1106
1092
1275
1.61
1.07
1.40
1.42
1.22
28
nd9531
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
S11090
112
438.6
518
513
597
589
490
0.85
0.85
0.74
0.74
0.90
38
S11139
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
PG1
27.6
1023
684
951
788
778
767
1.49
1.08
1.30
1.32
1.33
31
PG6
34.7
238
169
272
194
192
189
1.41
0.87
1.23
1.24
1.26
32
PG7
34.7
241
179
229
206
203
159
1.35
1.05
1.17
1.19
1.51
33
PG11
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 experimentaltopredicted 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 31814, Eurocode 2, CSA A23.314, 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 31814
EC2
CSA A23.314
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 31814
EC2
CSA A23.314
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 31814
EC2
CSA A23.314
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

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 slabcolumn connection of HSC flat plates could be defined as below:
() (3100) ( Ã— )
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 31814 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 A23.314 and IS 456:2000.
In case, using NSC the ACI 31814 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 31814 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 31814 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 slabcolumn 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 31814 is conservative and with large scatter compared with Euro02 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 31814, CSA A23.314 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.

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 31814 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 Ã— ) ( )
100
the compressive strength;
3. The American code, CSA
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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.

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