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IBRACON Structures and Materials Journal • 2012 • vol. 5 • nº 5
P. V. P. SACRAMENTO | M. P. FERREIRA | D. R. C. OLIVEIRA | G. S. S. A. MELO
Some criteria were established in order to evaluate results ob-
tained with the theoretical methods used in comparison with the
experimental results. In general, it is expected that theoretical me-
thods meet two basic principles: safety and precision. Primarily, it
is desirable that, within a representative range of the design varia-
bles of flat slabs or slabs with the loads applied in small areas, the
methods are able to provide safety results, with a minimum of fra-
gile results (unsafe). In this regard, it was established that no more
than 5% of unsafe results would be ideal. The accuracy of obtained
results was evaluated according to the average of the ratio
P
u
/
V
calc
,
were
P
u
is the experimental failure load and
V
calc
is the theoretical
resistance
estimated by each method. For the average, it was esta-
blished that: the method presents a high level of precision if 1.0
≤
P
u
/
V
calc
<1.10; for to values of 1.10
≤
P
u
/
V
calc
≤ 1.30
the method has
a satisfactory level of precision; and for
P
u
/
V
calc
> 1.30 the method
is conservative. The coefficient of variation (COV) was also used
to evaluate the precision of the methods, but without establishing
ranges for the ideal values of the coefficient of variation, with these
results used only in a qualitative way.
Figure 11 shows a comparison between the experimental results
with theoretical results obtained with the recommendations of ACI
318 [7]. The solid line in the figures represents the level of the
nominal strength and the dotted line represents the level of the de-
sign strength. By varying the parameters
f
c
(compressive strength
of concrete) and
B
/
d
(equivalent diameter of the column
u
0
/π
divi-
ded by the effective depth
d
of slab) it is observed that only 5% of
Tabl� � � Charact�r�st�cs of slabs �� th� databas� (co�t�)
Author
Slab r
s
(mm)
r
q
(mm)
h
(mm)
d
(mm)
C
(mm)
f
c
(MPa)
f
ys
(MPa)
E
s,f
(GPa)
d
g
(mm)
P
u
(kN)
HS2
850
750
120
95
0.007
150 S
70.0
490
200
20
249
HS3
850
750
120
95
0.012
150 S
69.0
490
200
20
356
HS4
850
750
120
90
0.021
150 S
66.0
490
200
20
418
HS7
850
750
120
95
0.009
150 S
74.0
490
200
20
356
HS8
850
750
150
120
0.010
150 S
69.0
490
200
20
436
HS9
850
750
150
120
0.015
150 S
74.0
490
200
20
543
HS10
850
750
150
120
0.021
150 S
80.0
490
200
20
645
HS11
850
750
90
70
0.007
150 S
70.0
490
200
20
196
HS12
850
750
90
70
0.012
150 S
75.0
490
200
20
258
HS13
850
750
90
70
0.016
150 S
68.0
490
200
20
267
HS14
850
750
120
95
0.012
220 S
72.0
490
200
20
498
HS15
850
750
120
95
0.012
300 S
71.0
490
200
20
560
NS1
850
750
120
95
0.012
150 S
42.0
490
200
20
320
65-1-1
1,500
1,250
320
275
0.015
200 S
64.3
500
200
16 2,050
65-2-1
1,300
1,100
240
200
0.017
150 S
70.2
500
200
16 1,200
95-1-1
1,500
1,250
320
275
0.015
200 S
83.7
500
200
16 2,250
95-1-3
1,500
1,250
320
275
0.025
200 S
89.9
500
200
16 2,400
95-2-1
1,300
1,100
240
200
0.017
150 S
88.2
500
200
16 1,100
95-2-1D
1,300
1,100
240
200
0.017
150 S
86.7
500
200
16 1,300
95-2-3
1,300
1,100
240
200
0.026
150 S
89.5
500
200
16 1,450
95-2-3D
1,300
1,100
240
200
0.026
150 S
80.3
500
200
16 1,250
95-2-3D+
1,300
1,100
240
200
0.026
150 S
98.0
500
200
16 1,450
95-3-1
750
550
120
88
0.018
100 S
85.1
500
200
16
330
115-1-1
1,500
1,250
320
275
0.015
200 S
112.0
500
200
16 2,450
115-2-1
1,300
1,100
240
200
0.017
150 S
119.0
500
200
16 1,400
115-2-3
1,300
1,100
240
200
0.026
150 S
108.1
500
200
16 1,550
HSC 1
1,270
1,200
245
200
0.008
250 C
91.3
627
200
18
1021,
HSC 2
1,270
1,200
240
194
0.008
250 C
85.7
620
200
18
889
HSC 4
1,270
1,200
240
200
0.012
250 C
91.6
596
195
18
1,041
HSC 6
1,270
1,200
239
201
0.006
250 C
108.8
633
210
18
960
N/HSC 8
1,270
1,200
242
198
0.008
250 C
94.9
631
213
18
944
HSC 9
1,270
1,200
239
202
0.003
250 C
84.1
634
231
18
565
Marzouk and
Hussein [18]
Hallgren [17]
Tomaszewicz [34]