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STRENGTH OF EXTERIOR SLAB-COLUMN CONNECTIONS
S. Teng, Nanyang Technological University, SingaporeJ.Z. Geng*, Nanyang Technological University, Singapore
H.K. Cheong, Nanyang Technological University, Singapore
29thConference on OUR WORLD IN CONCRETE & STRUCTURES: 25 - 26 August 2004,Singapore
Article Online Id: 100029069
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29
t
Conference o OUR WORLD IN CONCRETE STRUCTURES: 25
-
26 August 2004 Singapore
STRENGTH OF EXTERIOR SLAB COLUMN CONNECTIONS
S. Teng
Nanyang Technological University, Singapore
J.Z. Geng*,
Nanyang Technological University, Singapore
H.K.
Cheong Nanyang Technological University, Singapore
Abstract
Punching shear strength of exterior slab-column connections, including edge and corner
connections is discussed in detail based on the analysis of available data in t
he
literature
according to the
ACI
318-02. It is found that the interaction between moment and shear for
exterior connections
is not as strong as represented in the ACI 318-02. The interaction is
weak for edge connections,
and
even weaker for corner connections. A reduction f
v
is
proposed based on the analysis. For edge connections, the reduced v is equal to 60
percent of the ACI defined value; for corner connections, it equals
to
10 percent of the ACI
defined value only. Once this reduction of v is considered in the ACI 318-02, the accuracy
of prediction can be improved greatly for the collected data.
Keywords: punching shear strength, slab-column connections, moment transfer, design code.
1. Introduction
The
ACI
318-02
1
presents
an
eccentric shear stress model for predicting punching shear strength
of slab-column connections with moment transfer.
It
assumes that the shear stresses due
to
unbalanced moment can be added directly
to
shear stresses due to shear force. The shear stresses
due
to
unbalanced moment vary linearly along
the
critical section . The interaction between shear and
moment transfer
is
represented by a coefficient Yv which defines the fraction of unbalanced moment
resisted
by
eccentric shear.
This paper begins with a summary of data obtained from numerous experiments
on
exterior slab
column connections, including edge and corner connections. The eccentric shear stress model in the
ACI 318-02
is
reviewed. The predictions according
to
the ACI 318-02 for the collected data are
analyzed and compared with the experimental results. Detailed discussions are provided and the
interaction between shear and moment is studied and emphasized .
2.
Research significance
The present study provides a fresh review of previous experimental data on exterior slab-column
connections, including edge and corner connections. The punching strength of experimental data
is
checked based on the ACI 318-02.
It is
found that the interaction between shear and moment
is
weak
for edge connections, and even weaker for corner connections . Reductions of
y
v are both proposed
based
on
the ACI defined value for edge and corner connections.
3. Review of experimental data
Numerous experimental data
on
slab-column connections are available
in
the literature. Included
in
this study are seventy-four exterior slab-column connections subjected to combined shear and
moment transfer, tested by over 15 research centers around the world. Of the
74
connection
specimens, 46 are edge slab-column connections
and
28 are corner connections. Some details of
each group of specimens are described below.
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Compression surface
Simply supported r . \ i
!
Tension surface
10;10
3 1
Edge slab column connections
Forty-six data involving edge slab-column connections were collected
in
this study. The respective
detailed experimental information can be found in Ref. 2) through [17]. For all included test slabs, the
outer faces of the columns were flush with the slab edge. Most of specimens had columns extended
from
both
above and below the slab, while some other specimens had columns extended from below
the slab
only.
Those data included both isolated single slab-column edge connections (Ref [2] through
[9])
and
non-single specimens (Ref [10] through [17]). The specimens tested by Scavuzzo [10] and
Sherif
and
Dilger [14] comprised both an interior and exterior connections. The specimens tested
by
Regan [11) comprised a slab spanning two edge connections. The subassemblies tested
by
Robertson
and Durrani [15] consisted of two exterior connections and one interior connection each. Falamaki and
Loo [16) tested a series of nine half-scale models representing two adjacent edge and corner panels of
a building floor. Each specimen contained six columns, including three slab-column connections with
spandrel beam or torsion strip. Only the connections without spandrel beam were collected
in
this study.
Typical test specimens are shown
in Fig.1
.
Vertical loads
Roller-supported
edge
Lateral load
Reactions ~
Lateral Load
Restrained against
rotation about edge
t
Reactions
Vertical reaction
a)
Scavuzzo test specimens [10] b)
Specimens tested by Regan [11]
Fig. 1 Typical non-single specimens of edge connections
None of the connections
had
slab shear reinforcement or edge beams, and no moment
transferred parallel
to
the slab edge. The specimens tested
by
Hawkins et
al [5)
were subjected to
inelastic load reversals simulating earthquake effects. The subassemblies tested by Robertson and
Durrani
[15)
were applied cyclic lateral load
on
the top of columns to study the load-drift response and
interaction between interior and exterior connections. All other specimens collected herein were tested
under static loading.
Load
Transverse
Load plate
Reaction
.
Transverse load
(a) Test specimen
by
Zaghlool et
al
[19]
(b) Test specimen by Zaghlool et
al
[22]
Fig. 2 Typical specimens of corner connections
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3.2 Corner slab column connections
Twenty-eight data were collected from the literature (Ref [16], and Ref [19] through [23]) involving
corner slab-column connections. The detailed experimental information can
be
found in the
corresponding references. Normally, gravity-induced biaxial unbalanced moments are transferred from
the
slab
to
the column plus horizontal loads from wind or earthquake forces for corner slab-column
connections. The specimens involved
in
Zaghlool et al [19], Walker and Regan [20], were corner bays
of flat plate floors supported on four corner columns. The specimens tested
by
Ingvarsson [21],
Zaghlool et
al
[22],
and
Hammill
and
Ghali [23], were isolated single corner connections. Typical test
specimens are shown
in
Fig.2.
4
ACI 318 02 for punching strength with moment transfer
According
to
the
ACI
318-02, the punching shear strength of slabs without shear reinforcement
can be
determined from the lowest of the following expressions
in
SI units)
Vc=0.083Xl2+;}f t ; (MPa) (1)
(MPa) (2)
c = 0.083X +
2] Jf7
Vc = 0.083
x
4.JC'
(MPa) (3)
where
f is
the ratio of the longer side
to
the shorter side of the concentrated load (or columns),
a sis 40 for interior column, 30 for edge columns, and
20
for corner columns. b
o
is
the length of critical
shear perimeter taken at a distance of
0 5d
away from the column face
and
has square corners for
square columns and round shapes for circular columns. d is the effective depth of slabs. ( is specific
concrete cylinder strength,
in
MPa unit.
r
2
+O.5d=b
2
1
A
IZ
-
------r-------- C
i g
Column
centroid
Vul
;
t.lM V
g
u u
Critical
section
- _______ 1________
B i .. _C.:..=AB== . : .it--- cC D=---.I
z
I
Fig. 3 Eccentric shear stress model for edge connections
A
Column
centroid
-.2;"
Shear stress
Fig.
4 Eccentric shear stress model for corner connections
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The ACI 318-02 presents an analytical method eccentric shear stress model) to calculate the
shear stress when both shear force and unbalanced moment are transferred. It assumes that the shear
stresses on the critical section due to the direct shear force can be added to the shear stresses on the
same section due to moment transfer. The shear stress due to unbalanced moment
is
distributed
linearly on the critical section.
The critical ratio between measured and computed strength for edge connections is the maximum
value of three ratios : vAB vc VCD / v
c
and 1 Yv XM u- Vug}/M
r
where, v S is the shear stress along
critical section AB as shown in Fig 3;
vCD
is the shear stress along critical section CD;
y
v is the
fraction of unbalanced moment resisted by shear;
(Mu - Vug)
is the ultimate unbalanced moment
acting at the centroid of the slab critical section; g is the distance between centroids of the slab critical
section
and
the column critical section; M
r
is the flexural strength of slab reinforcement with a transfer
width of c
1
+ 3h .
The critical ratio between measured and computed strength for corner connections is the
maximum value of three ratios:
vB/v
e
v c / ve
and flexural strength ratio, similar to that for edge
connections, where,
V
is the shear stress at Point
B;
vc is the shear stress at Point C as shown in
Fig . 4.
5. Data analyses for all collected specimens
5.1 Edge slab column connections:
Table 1 lists the overall prediction for the forty-six collected data. Note that due to the space limit ,
the respective prediction of each specimen collected herein is not listed in this paper. The overall
prediction includes the average strength ratio , the standard deviation Stdev) of the strength ratio, and
the coefficient of variation COV).
Table 1 Overall prediction according to AC1318-02 and that with a reduction of Yv
for edQe connections 46 data)
Method
Minimum of
strength ratio
Maximum of
strength ratio
Average of
strength ratio
Stdev
COV
AC1318-02 0.807 2.546
1.464
0.419 0.286
ACI 318-02 with the
proposed reduction of
y
v
0.750 2.277 1.236 0.293
0.237
According to ACI 318-02, analysis of the data collected reveals that calculated strength is
governed by limiting shear stresses on the slab critical section rather than flexural yield for nearly all the
test specimens, except two specimens Specimen 5A tested by Hall and Rangan [12]. and Specimen C
by Rangan [13]). The calculated strengths of those two specimens are governed by flexural yield .
Calculated strengths are almost in all cases conservative, with ratios between measured and
calculated strengths ranging from 0.807 to 2.546, except four specimens, having a mean of 1.464 and
a coefficient of variation of 0.286. It is interesting to note that even for the two specimens with moment
transfer only Specimen M/E/2 tested by Stamenkovic and Chapmen [3] and Specimen Z-V 4) tested
by Zaghlool [4]) the calculated strengths are still governed by the limiting shear stress on the critical
section, not by the flexural yielding .
Moehle [18] suggested that there is no interaction between shear and moment for edge
connections based
on
the analysis
of
27 data he collected. The strong interaction between shear and
moment embodied in the ACI 318-02 is the coefficient of
Yv
the fraction of unbalanced moment
transferred by shear). Analytical work has been done herein to see how the predictions go by reducing
this coefficient y v step by step. The criterion is the value of COV for the data collected in this study. Fig.
5 shows the relationship between C OV and the percent 0 f yv This figure clearly shows that when
reducing
Yv
from 100 percent of ACI defined value, the value of COV becomes smaller and smaller
until
Yv
was reduced to 60 percent of ACI value. After that, the value of COV becomes larger if we
continue to reduce this
Yv
This behavior suggests that the relationship between shear
and
moment for
edge connections is neither as strong as that represented in the ACI 318-02 100 percent of
yv
should
be used), nor as zero as that proposed by Moehle [18]. A 60 percent of ACI defined Yv value should be
used for edge connections. Table 1 also lists the overall predictions when considering the reduction of
Yv
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0.300
c:
.290
.Q
/
;::
m
0.280
m
>
/
....
0.270
0
C
/
)
0.260
'
(3
/
E
Q
0.250
0
/
.240
....
/
0.230
0.00 0.20
0.40
0.60 0.80 1.00
Percent of y v
Fig . 5 Relationship of value of COY and percent
of
yv for edge connections
It shows that the predictions have been improved much after we use a reduced value of
v
(60
percent of ACI defined value), meaning that a less interaction between shear and moment exists for
edge connections. The average strength ratio is 1.236, having a value of COY of 0.237. Note that there
are nine specimens which had strength ratios less than unity when we reduce this y
v
This problem
can
be
easily solved by using a slightly larger strength reduction factor, which will not
be
discussed in
this paper.
5.2 Corner slab column connections:
Table 2 lists the overall prediction for the twenty-eight collected data. The overall prediction also
includes the average strength ratio, the standard deviation (Stdev) of the strength ratio, and the
coefficient of variation (COV).
Table 2 Overall prediction according to ACI 318-02
and
that with a reduction of
v
for corner connections (28 data
Method
Minimum of
strength ratio
Maximum of
strength ratio
Average of
strength ratio
Stdev
COy
AC13180-02 1.067
3.441
1.901
0.638
0.335
ACI 318-02 with the
proposed reduction of v
0.731 1.687
1.160
0.253 0.218
According to ACI 318-02, analysis of the data collected reveals that calculated strength is
governed by limiting shear stresses on the slab critical section rather than flexural yield for all the test
specimens. Calculated strengths are in all cases conservative, with ratios between measured and
calculated strengths ranging from 1.067 to 3.441, and having a mean of 1.901 and COY of 0.335. The
over-conservativeness and scattered trend of the data in Table 2 occurs in part because the analytical
model assumes a significant interaction between shear and moment as we discussed in the previous
section, which is embodied by the coefficient
Yv as
defined in the ACI 318-02. Analytical work has
been
done similar to that for edge connections
to see
how the predictions go
by
reducing this
coefficient yv step by step. The criterion is still the value of COY for the data collected for corner
connections.
Fig.
6 shows the relationship between COY and the percent of
Yv
This figure obviously
shows that when reducing
yv from 100 percent of ACI value, the value of COY becomes smaller and
smaller until
v
was reduced
to 10
percent of
ACI
value. After that, the value of COY becomes larger if
we continue
to
reduce this Yv This behavior suggests that the relationship between shear and moment
for corner connections
is
even less than that for edge connections. In the previous discussion part for
edge connection ,
v
was reduced
to
60 percent of ACI defined value.
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0.340
/
.320
c:
o
ii 0 300
.;::
rn
/
:: 0.2BO
o
/
0 260
'
(3
/
EO 0.240
( )
o
/
0 220
0.
200
0.00
0.20 0.40
0.60 O.
O
1.00
Percent of Yv
Fig . 6 Relationship of value of COY and percent of Yv for corner connections
The overall predictions following a reduction of Yv (10 percent of
ACI
defined value) are also listed
Table 2. The strength ratio ranges from 0.
731 to
1.687, having a mean of 1.
160
and a value of COY
about 0.218. The accuracy of prediction
is
highly improved by reducing
v
only. However, there are
nine specimens which had strength ratios less than unity, meaning that their strengths are
overestimated. This problem can also be easily solved by applying for a larger strength reduction factor
in the ACI 318-02, which is not discussed in detail in this paper.
6
Conclusions
Based
on the
analysis of available data for exterior connections, including edge and corner
connections, the following conclusions may
be
drawn.
For exterior connections the interaction between shear and moment is not as strong
as
expected.
The interaction between shear and moment
is
even weaker for corner connections than for edge
connections . A
60
percent of ACI defined Yv value should
be
used for edge connections, and 10
percent of that value should
be
used for corner connections only. Once the reduced value of Yv
is
used
in the ACI 318-02, the accuracy of the strength prediction for exterior slab-column connections can be
improved greatly.
7
Acknowledgements
This research is part of the joint BCA-NTU research
on
fiat plate structures. Research grants from
the Building and Construction Authority - Singapore, and the Nanyang Technological University are
gratefully acknowledged.
8 References
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ACI Committee 318, "Building Code Requirements for Structural Concrete (ACI 318-02) and
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[2J
Hanson, N.W. and Hanson, J.M., "Shear and Moment Transfer between Concrete Slabs and
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o
the Research and Development Laboratories Portland Cement Association,
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A
and Chapman, J.
C.,
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in
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to
A
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55