MCR1135
-
Upload
pradeepjoshi007 -
Category
Documents
-
view
14 -
download
2
description
Transcript of MCR1135
Reinforced concrete edge beam–column–slab
connections subjected to earthquake loading
M. Shin* and J. M. LaFave*
University of Illinois at Urbana-Champaign
Four two-thirds-scale reinforced concrete edge beam–column–slab subassemblies (two concentric and two ec-
centric connections) were tested under quasi-static cyclic lateral loading. Each subassembly represented a cruci-
form connection in an exterior moment-resisting frame with a monolithic floor slab on one side only, loaded in the
longitudinal direction of the edge-beams. The tests explored the effect of eccentricity between beam and column
centrelines, and the effect of floor slabs, on the structural performance of edge beam–column–slab connections
subjected to earthquake loading. Performance of the specimens was evaluated in terms of overall strength and
stiffness, energy dissipation, beam plastic hinge development, joint shear deformation, and joint shear strength. All
specimens underwent some beam hinging at the beam/column interfaces. However, both eccentric specimens, and
one concentric specimen with a heavily reinforced floor slab, eventually failed as a result of joint shear, whereas
the other concentric specimen exhibited more ductile load–displacement response. The eccentric specimens (with
different eccentricities and edge-beam widths) underwent similar behaviour before they started to break down, and
they also reached similar joint shear strengths. Slab participation was evaluated using slab bar strain gauge data
with respect to storey drift. Actual effective slab widths were much larger than the ones typically used in design,
especially for the specimens with a column wider than the edge-beams. Finally, floor slabs imposed significant joint
shear demand, but they also increased joint shear capacity by expanding effective joint width.
Notation
bb beam width
bc column width
bj,318, bj,352 effective joint width computed per
ACI 318-02 and ACI 352R-02
bj,exp and b9j,exp effective joint width estimated using
experimental maximum joint shear
force
bj,RW effective joint width computed per an
equation suggested by Raffaelle and
Wight
dt vertical distance between longitudinal
slab bars and centroid of a transverse
beam
e eccentricity between edge-beam and
column centrelines
f 9c concrete compressive strength
fy steel yield strength
hb beam depth
hc column depth
hph vertical distance between gauges on
top and bottom of an edge-beam
jd1, jd2 assumed moment arms at east and
west beam/column interfaces
lb beam pin-to-pin span length
lc column pin-to-pin storey height
Mnþ, Mn
� beam positive and negative nominal
moment strengths
Mr column-to-beam moment strength
ratio
V1, V2 measured reaction forces in east and
west beam-end supports
Vc storey (column) shear force
Vc,m(cal) predicted storey strength
Vc,m(exp) measured storey strength (maximum
storey shear force)
Vj horizontal joint shear force
Magazine of Concrete Research, 2004, 55, No. 6, June, 273–291
273
0024-9831 # 2004 Thomas Telford Ltd
* University of Illinois at Urbana-Champaign, Department of Civil
and Environmental Engineering, 3108 Newmark Civil Engineering
Laboratory, MC-250, 205 North Mathews Avenue, Urbana, IL 61801,
USA.
(MCR 1135) Paper received 29 April 2003; last revised 14 October
2003; accepted 13 November 2003
Vj,m experimental maximum joint shear
force
Vj,u design ultimate joint shear force
˜bot average of relative displacements
measured by two gauges on bottom of
an edge-beam
˜top average of relative displacements
measured by two gauges on top of an
edge-beam
ª joint shear deformation (at exterior
face of joint)
ªd design joint shear stress level
ªm maximum joint shear stress level
ªn nominal joint shear stress level
Łph beam rotation near beam/column
interface
�eq equivalent viscous damping
Introduction and background
The vulnerability of reinforced concrete (RC) beam–
column connections in moment-resisting frames has
been identified from structural damage investigations
after many past earthquakes.1,2
Since the mid-1960s,
numerous experimental studies have been conducted to
investigate the behaviour of RC beam–column connec-
tions subjected to earthquake loading. However, few
tests on edge beam–column–slab connections (cruci-
form connections in exterior frames with floor slabs on
one side only) have been reported in the literature to
date. This paper presents experimental and analytical
results for RC edge beam–column–slab connections
loaded in the longitudinal direction of the edge-beams.
The research specifically explored the effect of eccen-
tricity between beam and column centrelines, as well as
the effect of floor slabs, on the structural performance
of edge connections subjected to earthquake loading.
Key previous research on these two subjects is briefly
summarised below.
When a beam–column connection is subjected to
lateral loading, the beam top and bottom forces from
bending are transmitted to the column at the beam/
column interfaces, producing large joint shear forces.
In many edge connections the exterior faces of the
columns are flush with the exterior faces of the edge-
beams (Fig. 1). The columns are often wider than the
edge-beams, resulting in an offset between the beam
and column centrelines. This kind of connection is
classified as an eccentric connection. Owing to the
eccentricity between beam and column centrelines, the
transmitted beam forces may also induce torsion in the
joint region, which will produce additional joint shear
stresses. A few RC eccentric beam–column connec-
tions have been tested without floor slabs,3–8
but more
research is needed to clarify the extent to which the
presence of eccentricity between beam and column
centrelines affects the behaviour of eccentric connec-
tions, particularly when floor slabs are present. In this
study, two eccentric edge connections were tested, as
well as two concentric edge connections, all with floor
slabs.
Lawrance et al.3
tested one cruciform eccentric
beam–column connection. Eccentricity between beam
and column centrelines did not affect the global
strength of the specimen, but strength degradation
occurred at lower displacement ductility than in compa-
nion concentric specimens. Although the column-
Centroidal axisof column
Torsionaleffect
C
T
T
C
T
C
C
T
Forces transferredfrom edge-beams
Assumedcontra-flexurepositions
Directionof motion
Fig. 1. Eccentric beam–column connections in an exterior frame
Shin and LaFave
274 Magazine of Concrete Research, 2004, 55, No. 6
to-beam moment strength ratio was high (roughly 2),
some column longitudinal bars at the flush side experi-
enced local yielding, due possibly to torsion from the
eccentricity. Joh et al.4tested six cruciform beam–
column connections, including two eccentric connec-
tions. The displacement ductility of specimens with
eccentricity was only from 2.5 to 5, whereas specimens
without eccentricity had displacement ductility ranging
from 4 to 8. In their specimen with a flush face of the
column and eccentric beams, joint shear deformations
on the flush side of the joint were four to five times
larger than those on the offset side of the joint.
Raffaelle and Wight5tested four cruciform eccentric
beam–column connections. Inclined (torsional) cracks
were observed on the joint faces adjoining the beams.
Strains in joint hoop reinforcement on the flush side
were larger than those on the offset side, which was
attributed to additional shear stress from torsion. The
researchers suggested that joint shear strengths of ec-
centric beam–column connections were overestimated
by American Concrete Institute (ACI) design recom-
mendations in existence at the time,9but that this could
be rectified by using a proposed equation for reduced
effective joint width. Teng and Zhou6tested six cruci-
form beam–column connections, including two con-
centric, two medium eccentric, and two one-sided
eccentric connections. The researchers formulated joint
shear strength recommendations for eccentric connec-
tions by limiting the allowable shear deformation in an
eccentric joint to the magnitude of shear deformation
in a companion concentric joint at 2% storey drift.
Chen and Chen7
tested six corner beam–column
connections, including one concentric connection, one
conventional eccentric connection, and four eccentric
connections with spread-ended (tapered width) beams
covering the entire column width at the beam/column
interface. The researchers concluded that eccentric cor-
ner connections with spread-ended beams showed
superior seismic performance to conventional eccentric
corner connections, in terms of displacement ductility,
energy-dissipating capacity, and joint shear deforma-
tion. Finally, Vollum and Newman8tested 10 corner
beam–column connections; each consisted of a column
and two perpendicular (one concentric and one ec-
centric) beams. Various load paths were tested to inves-
tigate the behaviour of the connections. Performance
improved significantly (in terms of both strength and
crack control) with reduction in connection eccentri-
city.
For approximately the past 15 years, various investi-
gators have evaluated the effect of floor slabs on the
seismic response of RC moment frames. According to
Pantazopoulou and French,10
who discussed results of
the previous studies and consequent code amendments,
most of the research focused on investigating how
much a floor slab contributed to beam flexural strength
(reducing the column-to-beam moment strength ratio)
when the slab was in the tension zone of the beam
section. However, limited research was concerned with
the effect of floor slabs on joint shear behaviour,
although some researchers did indicate that floor slabs
could impose additional shear demands on joints. Floor
slabs may increase joint shear capacity by expanding
effective joint width and/or by providing some confine-
ment to joints (along with transverse beams). For ec-
centric connections, floor slabs may also reduce joint
torsional demand by shifting the acting line of the
resultant force of the beam top and slab reinforcement.
In this paper, the slab effect on joint shear demand is
evaluated by inspecting slab strain gauge data at var-
ious storey drifts to compute joint shear forces. Then
the slab effect on joint shear capacity is also evaluated,
by estimating the effective joint widths of the test
specimens and comparing them with other specimens
without floor slabs reported in the literature.
Experimental programme
This study investigated the effect of eccentricity be-
tween beam and column centrelines, as well as the
effect of floor slabs, on the seismic performance of RC
edge beam–column–slab connections. Four beam–
column–slab subassemblies (two concentric and two
eccentric connections) were tested. Each subassembly
represented an edge connection subjected to lateral
earthquake loading, isolated at inflection points be-
tween floors and between column lines. Considering a
prototype structure with a storey height of 4.5 m and a
span length of 7.5 m, the specimens represent approxi-
mately two-thirds-scale models; the scale factor is large
enough to simulate the behaviour of the prototype RC
structure.11
Design of test specimens
The specimens were designed and detailed in confor-
mance with ACI requirements and recommendations
for RC structures in high seismic zones. In particular,
ACI 318-02 (Building Code Requirements for Structur-
al Concrete)12
and ACI 352R-02 (Recommendations
for Design of Beam–Column Connections in Mono-
lithic Reinforced Concrete Structures)13
were strictly
adhered to, except for a few design parameters that
were specifically the subject of this investigation.
Each specimen consisted of a column, two edge-
beams framing into the column on opposite sides, and
a transverse beam and floor slab on one side only. Fig.
2 shows plan views around the joints (floor slabs are
not shown for clarity), and Fig. 3 illustrates reinforcing
details in the specimens. In specimens 1, 2 and 3 all
design details were identical except for the edge-beams,
so the parameters varied in the first three specimens
were the eccentricity (e) between the edge-beam and
column centrelines, and the edge-beam width. (In parti-
cular, the connection geometry of specimen 1 was quite
similar to that found in a nine-storey building that
RC edge beam–column–slab connections subjected to earthquake loading
Magazine of Concrete Research, 2004, 55, No. 6 275
Transversebeam
Columncentroid
Edgebeam
West East
330
457
279
(a)
457 279
330
(c)
457
178
330
279
(b)
279 279
368
(d)
Fig. 2. Plan views around joints (units: mm): (a) specimen 1 (e ¼ 89 mm); (b) specimen 2 (e ¼ 140 mm); (c) specimen 3 (e ¼0 mm); (d) specimen 4 (e ¼ 0 mm)
8-#6
457
330
#3@83
#3@83
4-#5
2-#5
#3@254
406
279
102 #3@305
#3@83
330
2-#6
2-#5
#3@305
406
(c)(b)(a)
368
4-#7 at cor.4-#6 at mid.
#3@83
279
(d)
#3@83
178
4-#5
2-#5
#3@254
406
(e)
#3@83
279
2-#6
2-#5
#3@305
406
#3@305
(f)
(S4: #4@127)
Fig. 3. Reinforcing details (units: mm): (a) column (specimens 1, 2 and 3); (b) edge-beam (specimens 1, 3 and 4); (c) transverse
beam (specimens 1, 2 and 3); (d ) column (specimen 4); (e) edge-beam (specimen 2); ( f ) transverse beam (specimen 4). See
Table 3 for bar size designations
Shin and LaFave
276 Magazine of Concrete Research, 2004, 55, No. 6
exhibited noticeable joint damage associated with a
recent strong earthquake.2) Specimen 2 had the largest
eccentricity and the narrowest edge-beam width. In
specimen 4 there were many different design details in
comparison with the other specimens. The most impor-
tant difference between the first three specimens and
specimen 4 was the reinforcement ratio of longitudinal
slab bars. In addition, each of the three beams framing
into the column in specimen 4 covered more than
three-quarters of the corresponding column face,
whereas only the transverse beam did so in the first
three specimens, with possible confinement implica-
tions.
The edge-beams of all specimens were reinforced
with the same number and size of reinforcing bars, to
achieve similar beam moment strengths. All floor slabs
were 1220 mm wide (including the edge-beam width)
and 102 mm thick, reinforced with a single layer of
reinforcing bars in each direction. All longitudinal
beam, column and slab reinforcement was continuous
through the connection, except for transverse beam and
slab bars, which were terminated with standard hooks
within the column and edge-beams respectively. A
minimum concrete clear cover of 25 mm was provided
in all members.
Table 1 summarises the main design parameters and
other important values that are generally considered to
govern the behaviour of RC beam–column connections.
When calculating the design column-to-beam moment
strength ratios (Mr), beam moment strengths were com-
puted considering a slab contribution within the effec-
tive slab width defined in ACI 318-02, for both slab in
compression and slab in tension. (The effective over-
hanging slab width for beams with a slab on one side
only is taken as the smallest of one-twelfth the span
length of the beam, six times the slab thickness, or
one-half the clear distance to the next beam.) The total
ACI effective slab width (including edge-beam width)
was then 69 cm in specimens 1, 3 and 4, and 59 cm in
specimen 2. The normalised design joint shear stress
levels (ªd) listed first and second were computed fol-
lowing ACI 318-02 and ACI 352R-02 respectively.
When computing the ªd values, longitudinal slab bars
within the effective slab width (two bars for specimens
1, 2 and 3, and three bars for specimen 4) were
included, as well as all top and bottom beam bars, per
ACI 352R-02, but not per ACI 318-02. The ªd values
would be limited to 1.00 in the first three specimens
and to 1.25 in specimen 4 by both ACI 318-02 and
ACI 352R-02, based on the joint confinement level
from adjoining members. The Mr and ªd values were
computed using design material properties. All speci-
mens were reinforced with three layers of horizontal
joint reinforcement; each layer consisted of a No. 3
hoop and two No. 3 cross-ties (nominal diameters of all
bars used are provided in Table 3). This is approxi-
mately the minimum amount of joint reinforcement
prescribed by ACI 318-02 and ACI 352R-02 for the
first three specimens, and about 1.5 times the minimum
amount for specimen 4.
Construction of test specimens
For each subassembly, all members except the upper
column were cast at one time; the upper column was
typically cast one week later. Concrete with a maxi-
mum aggregate size of 10 mm and a slump of 125 mm
was used to accommodate any steel congestion in the
joint region and the small minimum clear cover of
25 mm. The design compressive strength of concrete
was 28 MPa, and the design yield strength of reinfor-
cing steel (ASTM standard reinforcing bars12) was
420 MPa.
Table 2 summarises the actual compressive strength
of concrete on the day of subassembly testing. At least
six concrete cylinders were cast for each placement of
concrete, with three of them tested at 28 days for
reference and the others tested on the day of the sub-
assembly test. Table 3 lists the actual yield strength
Table 1. Main design parameters and important values
Specimen 1 2 3 4
Eccentricity, e (mm) 89 140 0 0
Edge-beam width, bb (mm) 279 178 279 279
Longitudinal slab steel ratio (%) 0.28 0.28 0.28 1.0
Moment strength ratio, Mr* 1.31 1.41 1.31 1.35
Joint shear stress level, ªd 1.14†/1.08‡ 1.80†/1.58‡ 0.70†/0.96‡ 1.02†/1.34‡
Joint reinforcement, Ash§ (mm2) 213@83 mm 213@83 mm 213@83 mm 213@83 mm
Member depth to bar
diameter
hb/db(col)¶ 21.3 21.3 21.3 18.3
hc/db(bm)¶ 20.8 20.8 20.8 23.2
*Mr ¼ �Mn(columns)/�Mn(beams).
†,‡ ªd ¼ Vj,u(N)=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffif 9c(MPa)
p� bj(mm) � hc(mm), Vj,u ¼ design ultimate joint shear force.
† In ACI 318-02, bj ¼ bb + 2x, x ¼ smaller distance between beam and column edges.
‡ In ACI 352R-02, bj ¼ bb + �mhc/2, m ¼ 0.3 when e . bc/8, otherwise m ¼ 0.5.
§ Ash ¼ total area of horizontal joint reinforcement within a layer (in the longitudinal direction.)
¶ db(col) and db(bm) ¼ maximum diameter of longitudinal bars used in column and edge-beam.
RC edge beam–column–slab connections subjected to earthquake loading
Magazine of Concrete Research, 2004, 55, No. 6 277
( fy), yield strain (�y), ultimate strength ( f u), and strain
at the onset of strain-hardening (�sh) for flexural rein-
forcing bars and column hoops. Three reinforcing steel
coupons were tested for each bar size to get the average
properties listed in the table. The stress–strain relation-
ship of column hoops did not have a well-defined yield
plateau, but rather exhibited gradually decreasing stiff-
ness, so their ‘yield’ properties were determined using
the 0.2% offset method.
Test set-up and loading sequence
Figure 4 shows a picture of the test set-up with the
specimen supports and other key components labelled.
Table 2. Compressive strength of concrete on the day of the
subassembly test (MPa)
Specimen 1 2 3 4
Except upper column 29.9 36.2 47.4 31.2
Upper column 35.8 40.7 45.4 31.5
Driftreferenceframe
Reaction frame Actuator
(�)(�)
Out-of-planetranslationconstraint
Hinge
Pin
Pin
Pin
Beam-endsupportwith loadcell (typ.)
Pin
Fig. 4. Test set-up (specimen 4 in testing rig, looking south)
Table 3. Properties of reinforcing bars
Specimens 1 and 2
Bar size No. 3 No. 5 No. 6 Column hoop
fy (MPa) 448 506 539 466
�y 0.0022 0.0027 0.0026 0.0045
�sh 0.008 0.017 0.016 n.a
fu (MPa) 703 662 690 715
Specimens 3 and 4
Bar size No. 3 No. 4 No. 5 No. 6 No. 7 Col. hoop, S3/S4
fy (MPa) 424 555 512 521 506 552/580
�y 0.0021 0.0030 0.0027 0.0025 0.0024 0.0044/0.0044
�sh 0.004 0.017 0.017 0.016 0.008 n.a./n.a.
fu (MPa) 696 676 634 655 717 696/731
Diameter (mm) of bars: No. 3 – 9.5, No. 4 – 12.7, No. 5 – 15.9, No. 6 – 19.1, No. 7 – 22.2.
Shin and LaFave
278 Magazine of Concrete Research, 2004, 55, No. 6
The specimens were tested in their upright position.
The column was linked to a universal hinge connector
at the bottom and to a hydraulic actuator (with a swivel
connector) at the top. The end of each edge-beam was
linked to the strong floor by a pinned-end axial support.
Thus the two ends of the edge-beams and the top and
bottom of the column were all pin-connected in the
loading plane, to simulate inflection points of a frame
structure subjected to lateral earthquake loading. The
column pin-to-pin storey height (lc) was 3.0 m, and the
beam pin-to-pin span length (lb) was 5.0 m. The inter-
ior edge of the floor slab was left free (unsupported),
which neglected any possible effect of slab membrane
action that might have provided additional confinement
to the joint region. (Such compressive membrane forces
were observed and credited for some strength enhance-
ment in slab–column connection tests where the slabs
extended to the centrelines between columns in the
transverse direction and rotation of the slab edges was
restrained.14)
Uniaxial storey shear was statically applied at the top
of the column (parallel to the longitudinal direction of
the edge-beams) by a hydraulic actuator with a 450 kN
loading capacity and a �250 mm linear range. (Positive
(eastward) and negative (westward) loading directions
are indicated in Fig. 4.) No external column axial load
was applied, conservatively in accordance with results
of previous studies that found the presence of column
compression could either slightly improve joint shear
strength13
or have no apparent influence on joint shear
strength.15,16
The transverse beam and floor slab were
not directly loaded. Because the specimens were not
symmetric about the loading direction, a slotted steel
bracket was installed near the top of the column in
order to guide specimen displacements along the long-
itudinal direction only. Twist of the column about its
longitudinal axis was not restrained by any of the
external column supports (the actuator, the slotted steel
bracket, or the universal hinge connector). Column tor-
sion was not a topic investigated in this study, and it
should not considerably affect joint behaviour. (Further-
more, severe column damage from torsion has not been
reported even for eccentric connection tests where col-
umn twist was restrained.4) Any unbalanced torsional
moments in the specimens were resisted by combina-
tions of horizontal forces in the transverse direction at
the beam-end supports and at the ends of the column.
Instrumentation used in each specimen was as fol-
lows. Roughly 60 electrical resistance strain gauges
were mounted on reinforcing bars at key locations in
and around the connection. Eight cable-extension
gauges were installed on the top and bottom of the
edge-beams to estimate beam rotations in the vicinity
of the beam/column interfaces. Five linear variable
differential transformers (LVDTs) were used on the
exterior face of the joint to examine overall joint shear
deformations. Finally, each beam-end support was
equipped with a load cell to monitor the reaction forces
generated in the support.
Figure 5 shows the pattern of cyclic lateral displace-
ments applied by the actuator during each test. A total
of 22 displacement cycles were statically applied up to
6% storey drift. (The maximum drift of specimen 1
was limited to about 5.5% owing to misalignment of
the specimen.) Consecutive same-drift cycles were
tested to examine strength degradation, and 1% drift
cycles were inserted between other cycles to investigate
stiffness degradation.
Experimental results
Load–displacement response
Figures 6(a) and 6(b) show the hysteretic loops of
storey shear against storey drift (load against displace-
ment) for specimens 2 and 3 respectively. They were
typical in that they exhibited pinching (the middle part
of each hysteretic loop was relatively narrow), as well
as stiffness and strength degradation during repeat
same-drift cycles. These were attributed to reinforce-
ment bond slip through the joint region, concrete crack-
ing, and/or reinforcement yielding. Fig. 6(c) compares
the envelope curves of load against displacement for all
four specimens, from connecting the peak drift point of
each cycle. (Maximum loads for the specimens
are summarised later in Table 6.) Among the first
three specimens (with the same slab reinforcement),
specimen 3 reached slightly larger maximum loads in
both loading directions; this was attributed primarily to
a difference in concrete compressive strength. Speci-
men 3 also exhibited higher stiffness than specimens 1
and 2 at the beginning of the test owing to high con-
crete strength. Consequently, the load–displacement re-
sponse of specimen 3 got flat slightly earlier (between
2% and 2.5% drift cycles) than the others (between
2.5% and 3% drift cycles). Specimen 4 reached the
largest maximum load (20–30% higher than the other
specimens), primarily because its floor slab was much
more heavily reinforced.
Yield points of the specimens are not easily deter-
0 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 221 2 3 4Cycle number
�6�5�4�3�2�1
0123456
Sto
rey
drift
: %
Fig. 5. Pattern of cyclic lateral displacements
RC edge beam–column–slab connections subjected to earthquake loading
Magazine of Concrete Research, 2004, 55, No. 6 279
mined from the load–displacement curves because the
reinforcement layout of the edge-beam and slab was
not symmetric about the centreline of the beam, and
because of slab reinforcement ‘shear lag’ effects.
Therefore yielding of individual bars in each edge-
beam and slab was examined. Bottom beam bars typi-
cally underwent faster strain increases and consequently
yielded earlier than top beam bars. Fig. 7 summarises
the subassembly storey drift applied when each long-
itudinal beam bar yielded at beam/column interfaces;
strain gauge data were compared with yield strains of
the reinforcing bars. (Yielding of slab bars will be
discussed in detail later.) First yielding of bottom beam
bars occurred during 1.5% or 2% drift cycles in all
specimens. (Therefore all specimens were eventually
tested to a displacement ductility of almost 4.) In the
first three specimens all beam and slab bars yielded by
3% drift cycles, whereas some slab bars in Specimen 4
did not yield by the end of the test. In all specimens
beam bar yielding spread to half an effective beam
depth away from the interfaces by 3% drift cycles,
meaning that beam hinging developed adjacent to
beam/column interfaces.
Table 4 summarises storey shear forces at various
drifts as a percentage of the maximum storey shear
force reached in each specimen. (The table also indi-
cates (by ‘100’) that the specimens reached their maxi-
mum storey shear forces during 3% or 4% drift cycles.)
Specimens 1, 2 and 4 underwent larger strength drops
Table 4. Storey shear forces divided by maximum story shear
forces (%)
Storey drift (%) S1 S2 S3 S4
+3/�3 100/100 99/99 99/100 96/97
+4/�4 100/100 100/100 100/99 100/100
+5/�5 96/95 92/95 97/95 94/96
+6/�6 85/85 83/88 94/90 83/86
100
75
50
25
0
�25
�50
�75
�100�8 �6 �4 �2 0 2 4 6 8
100
75
50
25
0
�25
�50
�75
�100�8 �6 �4 �2 0 2 4 6 8
100
75
50
25
0
�25
�50
�75
�100�8 �6 �4 �2 0 2 4 6 8
Storey drift: %(a)
Sto
rey
shea
r: k
N
Storey drift: %(b)
Sto
rey
shea
r: k
N
Storey drift: %
Sto
rey
shea
r: k
N
(c)S1 S2 S3 S4
Fig. 6. Load against displacement response: (a) specimen 2;
(b) specimen 3; (c) envelope curves (S1 ¼ specimen 1)
2·5 2·5 2·5 2·5
1·5 1·5
2·5 2·5
1·5 1·5
2 2
(a)
(c)
Ext.edge
Int.edge
Ext.edge
Int.edge
2·5
1·5 1·5
2·5 2·5 2·52
22
2 2·5
2·5
(b)
(d)
Ext.edge
Int.edge
Ext.edge
Int.edge
Fig. 7. Storey drift (%) at onset of beam bar yielding at
beam/column interfaces: (a) specimen 1; (b) specimen 2; (c)
specimen 3; (d) specimen 4
Shin and LaFave
280 Magazine of Concrete Research, 2004, 55, No. 6
than specimen 3, approximately 15% (an average for
both directions) by the 6% drift cycle, whereas speci-
men 3 exhibited the most ductile load–displacement
behaviour. Considering that beam hinging typically
does not cause large strength drops, some other failure
mechanism probably developed, leading to the break-
down of specimens 1, 2 and 4. However, neither col-
umn hinging nor severe anchorage failure was observed
throughout the tests. (With the ratio of column depth to
beam bar diameter slighty greater than 20, the speci-
mens did exhibit some beam bar slippage through the
joint, as has been reported previously for other similar
connections.13) Therefore it was concluded that speci-
mens 1, 2 and 4 failed as a result of joint shear (similar
to previous studies, where it was also observed that
beam–column connections can fail from joint shear,
although they undergo some beam hinging16,17
); this
conclusion is strengthened in later sections.
Strength degradation of the specimens was further
examined by comparing storey shear forces of consecu-
tive same-drift cycles (reduction in storey shear force
during the second (repeat) cycle with respect to the
first cycle). In all specimens strength degradation re-
mained low (roughly 5%) until the 2% or 3% drift
cycles, but it increased up to 13%, 19%, 12% and 18%
in specimens 1–4 respectively, during the 5% drift
cycle. Specimen 3 generally showed the smallest
strength degradation throughout.
Overall stiffness of a specimen for a particular load-
ing cycle was defined as an average of the storey shear
divided by the storey displacement at the positive and
negative peak drifts of the cycle. In each specimen
stiffness degradation continued throughout the test, and
exceeded 80% of the first-cycle stiffness by the end of
the test (the first-cycle stiffness was 25.0 kN/cm,
27.3 kN/cm, 39.3 kN/cm and 29.6 kN/cm in specimens
1–4 respectively). Stiffness degradation was faster be-
fore about 1% drift in all specimens, possibly because
most of the concrete cracking and bond slip initiation
occurred during the early stages of the tests.
Energy dissipation
The amount of energy dissipated during a loading
cycle was calculated as the area enclosed by the corre-
sponding load–displacement hysteretic loop, presented
in Fig. 8. In each specimen the energy dissipated during
the 4% drift cycle was roughly twice that during the
3% drift cycle, even though storey shear barely in-
creased between 3% and 4% drift. However, the rate of
increase in energy dissipated per cycle (with respect to
storey drift) quickly reduced during the 5% drift cycle,
although strengths of the specimens did not drop by
much.
The table within Fig. 8 contains equivalent viscous
damping (�eq) values for various drift cycles of each
specimen, computed following standard procedures de-
scribed elsewhere.18
(For comparison, �eq values for an
elastic-perfectly plastic system with no pinching would
be 0%, 21% and 25% at displacement ductilities of 1, 2
and 3 respectively.) The specimens exhibited similar
patterns of equivalent viscous damping throughout the
tests. In particular, �eq values decreased after the 4%
drift cycle in the first three specimens. Although speci-
men 4 showed a slightly different pattern, the variation
between �eq values of all specimens for each cycle was
negligible. Thus it may be concluded that the energy-
dissipating capacity of these edge connections was very
similar, whether they were eccentric or concentric, and
regardless of their failure modes (even though speci-
mens 1, 2 and 4 had some joint shear breakdown, their
energy dissipation performance was similar to that of
specimen 3).
Plastic hinge development
The rotational behaviour of the edge-beams near
beam/column interfaces was investigated to examine
the development of beam plastic hinges. In each speci-
men, eight cable-extension gauges were used to esti-
mate beam rotations in the vicinity of the beam/column
interfaces. The gauges were installed on top and bottom
of the edge-beams (two gauges at each location), ap-
proximately one effective beam depth (355 mm) away
from the column faces, to where a plastic hinge region
might extend (see Fig. 11). Each gauge monitored the
relative displacement between the column face and the
section where the gauge was mounted; the values meas-
ured by the two gauges at a location were averaged.
Beam rotations in the plastic hinge regions (Łph) werecomputed by:
Łph ¼˜bot � ˜top
hphor
˜top � ˜bot
hph(1)
Here hph is the vertical distance between gauges on the
top and bottom of the edge-beam, ˜bot is an average of
the relative displacements measured by the two gauges
on the bottom of the edge-beam, and ˜top is an average
of the relative displacements measured by the two
gauges on the top of the edge-beam. Beam rotations
were considered positive when the specimen was
loaded in the positive direction. The estimated beam
Drift (%)Equiv. viscous damping (%)
8
7
8
12
10
8
8
6
8
12
11
10
8
7
8
11
11
9
7
7
7
10
10
11
1
2
3
4
5
6
0 1 2 3 4 5 6 7Storey drift: %
S1 S2 S3 S4
0
2
4
6
8
10
12
Ene
rgy
diss
ipat
ed p
er c
ycle
: kN
m
S1 S2 S3 S4
Fig. 8. Energy dissipated per cycle
RC edge beam–column–slab connections subjected to earthquake loading
Magazine of Concrete Research, 2004, 55, No. 6 281
rotation comprised both plastic hinge rotation and rigid
beam-end rotation. Plastic hinge rotation was due to
yielding of longitudinal beam bars near the interfaces
after concrete cracking. Rigid beam-end rotation was
attributed to bond slip of reinforcing bars and opening
of large flexural cracks at the interfaces.
Figure 9(a) compares the envelope curves of storey
shear against beam rotation in the two eccentric speci-
mens, from connecting the peak drift point of each
cycle. In the figure, ‘E’ and ‘W’ stand for the east and
west beams respectively. In general, all edge-beams in
both specimens showed similar beam rotations through-
out testing (up to rotational ductility of about 8). The
rate of increase in beam rotation (with respect to storey
drift) got higher during the 2.5% and 3% drift cycles,
because all longitudinal beam and slab bars yielded by
that cycle. Also, beam rotation increased whereas stor-
ey shear did not increase (or even decreased) during
higher drift cycles (in other words, beam moments at
the beam/column interfaces did not increase). These
observations imply that beam hinging had developed in
the plastic hinge regions.
Figure 9(b) compares the envelope curves of storey
shear against beam rotation in the two concentric speci-
mens. Specimen 3 underwent beam hinging in the
plastic hinge regions and generally had larger beam
rotations (up to a rotational ductility of about 10) than
the eccentric specimens and specimen 4. In specimen 3
the increment in beam rotation from 2% to 3% drift
was roughly twice that from 1% to 2% drift. Also,
beam rotation increased whereas storey shear barely
increased from the 2.5% drift cycle onward. Specimen
4 generally exhibited the smallest beam rotations out of
all four specimens (up to a rotational ductility of about
6). In specimen 4 the rate of increase in beam rotation
(with respect to storey drift) rose somewhat during the
3% drift cycle; however, it dropped after the 4% drift
cycle as the specimen started to break down because of
joint shear.
Slab bar strains
The first three specimens had four longitudinal slab
bars (at the same floor slab locations), whereas speci-
men 4 was reinforced with seven longitudinal slab bars.
Each longitudinal slab bar was instrumented with a
strain gauge located crossing the west beam/column
interface. Fig. 10 illustrates the strain profiles of long-
itudinal slab bars in a section crossing the west beam/
column interface at peak drift points of various cycles.
(The top of the west beam/column interface was in
tension when the specimen was loaded in the positive
direction.) All longitudinal slab bars experienced con-
tinuous strain increases before yielding, as storey drift
got larger. Therefore it was clear that slab participation
(to beam moment strengths and joint shear demands)
got larger as each specimen was subjected to larger
storey drifts. The slab bar nearest to the edge-beams
generally underwent the fastest strain increase, except
in specimen 2.
Onset of slab bar yielding occurred during the 1.5%,
1% and 2% drift cycles in specimens 1, 2 and 3
respectively, and all longitudinal slab bars yielded by
3% drift in the first three specimens. Specimens 1 and
2 showed larger slab bar strains than specimen 3, possi-
bly because the longitudinal slab bars were located
closer to the column in the first two specimens. How-
ever, in specimen 4 only the two slab bars nearest the
edge-beam underwent yielding by the end of the test.
(The slab bar nearest the edge-beam underwent yield-
ing during the positive 4% drift cycle, and then the
strain quickly dropped, possibly as a result of partial
de-bonding of the strain gauge.) Lower slab bar strains
in specimen 4 were partly attributed to its column and
transverse beam, which were narrower than in the other
specimens, and also to torsional distress in the trans-
verse beam at the column face. These issues will be
explored further in later sections.
Joint shear deformation
Initial joint shear cracks were observed during the
0.75% drift cycle in all four specimens. The cracks
were diagonally inclined and intersected one another,
owing to the reversed loading. Some joint concrete
spalled off from the exterior joint face after extensive
cracking at higher storey drifts. Specimens 3 and 4
underwent the least and the most joint concrete crack-
90
60
30
0
�30
�60
�90�0·05 �0·03 �0·01 0·01 0·03 0·05
Beam rotation: rad
Sto
rey
shea
r: k
N
S1-W S1-E S2-W S2-E(a)
120
80
40
0
�40
�80
�120�0·05 �0·03 �0·01 0·01 0·03 0·05
Beam rotation: rad
Sto
rey
shea
r: k
N
S3-W S3-E S4-W S4-E(b)
�6 �5 �4 �3 �2 �1S1S2
1 2 3 4 5 6
S2
S1
Storey drift: %
�6 �5 �4 �3 �2 �1
S3
S41 2 3 4 5 6
S3
S4Storey drift: %
Fig. 9. Envelope curves of storey shear against beam rota-
tion: (a) specimens 1 and 2; (b) specimens 3 and 4
Shin and LaFave
282 Magazine of Concrete Research, 2004, 55, No. 6
ing and spalling respectively. To monitor overall joint
shear deformation in an average sense, five LVDTs
were installed at the exterior face of the joint in each
specimen (see Fig. 11). Considering the two triangles
formed by the LVDTs, angular changes at the 908
angles were computed for each measuring step. Then
the average of the two angular changes was defined as
the joint shear deformation (ª) at the exterior face of
the joint, as explained in Fig. 11.
Figure 12 shows the envelope curves of storey shear
against joint shear deformation, from connecting the
peak drift point of each cycle. The eccentric connec-
tions (specimens 1 and 2) exhibited similar joint shear
deformations at a relatively slow rate of increase during
5000
4000
3000
2000
1000
0
�10000 20 40 60 80 100 120
Distance from exterior face of slab: cm(a)
Mic
rost
rain
(S
1)0·51·01·52·02·53·04·05·0
Column width
Beam width
Yield
5000
4000
3000
2000
1000
0
�10000 20 40 60 80 100 120
Distance from exterior face of slab: cm(b)
Mic
rost
rain
(S
2)
0·51·01·52·02·53·04·15·1
Column width
Beam width
Yield
5000
4000
3000
2000
1000
0
�10000 20 40 60 80 100 120
Distance from exterior face of slab: cm(c)
Mic
rost
rain
(S
3)
0·51·01·52·02·53·04·05·0
Column width
Beam width
Yield
5000
4000
3000
2000
1000
0
�10000 20 40 60 80 100 120
Distance from exterior face of slab: cm(d)
Mic
rost
rain
(S
4)
0·51·01·52·02·53·04·04·9
Column width� Beam width
Yield
Fig. 10. Slab bar strain profiles across west beam/column interface (storey drift (%) in legend): (a) specimen 1; (b) specimen 2;
(c) specimen 3; (d) specimen 4
LVDTs
2 Cable extensiongauges at a location
γ1
Joint γ2
36 cm
28 cm
γ � (γ1 � γ2)/2
Undeformed LVDTs
Deformed LVDTs
Fig. 11. Eight cable-extension gauges and five LVDTs
RC edge beam–column–slab connections subjected to earthquake loading
Magazine of Concrete Research, 2004, 55, No. 6 283
the early stages of the tests. However, the rate of in-
crease in joint shear deformation (with respect to storey
drift) became higher during the 2.5% and 3% drift
cycles. This fast increase occurred without considerable
rises (or even with drops) of storey shear in these speci-
mens. This resulted from cracking, crushing and/or
spalling of some joint concrete because of joint shear.
Specimen 2 eventually underwent larger joint shear
deformations than specimen 1, during the negative 5%
and 6% drift cycles. The joint shear deformations ex-
hibited by these two specimens (roughly 0.03–0.04
radians maximum) were similar to or larger than those
in other eccentric connections found in the literature
that failed by joint shear.3,5,6
Specimen 3 exhibited very small joint shear defor-
mations (less than 0.007 radians maximum). This may
be partly because the joint shear deformations were
measured at the exterior face of the joint (over 85 mm
away from the exterior face of the edge-beams), so they
did not necessarily represent joint shear deformations
in the joint core. However, it was unlikely that speci-
men 3 underwent joint shear deformations as large as
the other specimens anyway because it exhibited rela-
tively moderate joint cracking damage and showed the
most ductile overall load–displacement behaviour. (For
comparison, all eight cruciform concentric connections
tested by Joh et al.19
underwent beam hinging without
joint shear failure, and they exhibited joint shear defor-
mations of less than 0.004 radians by 5% drift.) Speci-
men 4 had the largest joint shear deformations among
all four specimens (especially in the positive direction),
and the rate of increase got higher from the 2.5% drift
cycle, without considerable rises (or even with drops)
in storey shear.
The rapid increases in joint shear deformation oc-
curred after exceeding approximately 0.01 radians in
specimens 1, 2 and 4. (For these specimens, a joint
shear deformation of 0.01 radians by itself produces
roughly 0.8% drift, as will be described below in more
detail.) The above observations support the conclusion
that specimens 1, 2 and 4 started to break down as a
result of joint shear during the tests.
The portion of storey displacement due to joint shear
deformation was computed using the joint shear defor-
mations measured at the exterior face of the joint,
assuming the column and the edge-beams remained
rigid (and assuming the measured joint shear deforma-
tions were representative of the values through the
joint). The table within Fig. 12 presents the percentage
contribution of joint shear deformation to the applied
storey displacement (at the top of the column); each
number is an average for both loading directions at the
indicated storey drift. By the end of the tests, the joint
shear deformation contribution to overall drift was
42%, 53% and 58% in specimens 1, 2 and 4 respec-
tively. The joint shear deformation contribution was
also significant (greater than 25%) within the cracked
elastic range of behaviour (for instance, even at 1%
drift). Specimen 3 showed smaller joint shear deforma-
tion contributions to drift than the other specimens,
which agrees with the observation that it experienced
larger beam rotations than the other specimens.
Joint hoop strains
In each specimen, three layers of horizontal joint
reinforcement (each consisting of a hoop and two
cross-ties) were equally spaced at 83 mm between the
top and bottom longitudinal beam bars. Each joint hoop
was instrumented with two strain gauges, one near the
centre along each of the legs parallel to the loading
direction, to monitor strain at the exterior and interior
sides of the joint. Fig. 13 shows the envelope curves of
joint hoop strain against storey drift in all specimens,
from connecting the peak drift point of each cycle. In
the figure the three joint hoops are referred to as
‘bottom’, ‘middle’ and ‘top’ according to vertical posi-
tion, and an arrow indicates that a strain gauge was
broken after the specified cycle.
In general, joint hoop strains at the exterior side of
the joint were larger than those at the interior side for
both eccentric and concentric specimens, in part be-
cause the transverse beam and floor slab provided some
confinement to the interior side of the joint. There are
additional possible reasons for this phenomenon in the
eccentric specimens. From the standpoint of eccentric
joint capacity, the interior (offset) side could be less
effective than the exterior (flush) side in resisting joint
shear forces. From the standpoint of eccentric joint
demand, eccentricity between the beam and column
centrelines could induce torsion in the joint region,
resulting in an increase in net shear stress near the flush
side. However, a big difference was not found between
the joint hoop strains of specimens 1 and 3 (eccentric
and concentric specimens with identical edge-beam
width), suggesting that these latter two effects were not
very significant, probably because the floor slabs ex-
panded effective joint width and reduced joint torsional
demand by shifting the acting line of the resultant force
from top beam and slab reinforcement. The eccentric
connections with floor slabs and transverse beams in
120
90
60
30
0
�30
�60
�90
�120�0·06 �0·04 �0·02 0 0·02 0·04 0·06
Joint shear deformation: rad
Sto
rey
shea
r: k
N
S1 S2 S3 S4
Joint contribution to storey displ. (%)Drift (%)
1
2
3
4
5
6
26
29
33
36
38
42
24
26
35
41
51
53
10
12
10
8
8
8
24
27
34
39
49
58
S1 S2 S3 S4
Fig. 12. Envelope curves of storey shear against joint shear
deformation
Shin and LaFave
284 Magazine of Concrete Research, 2004, 55, No. 6
this study showed more uniform strain distributions
across the joint than did other eccentric connections
(without slabs and transverse beams) reported in the
literature,3,5,6
where joint hoop strains at the flush side
were much larger (two or three times) than those at the
offset side.
In all specimens, joint hoop strains started to rise
after several small drift cycles, and they increased even
7000
6000
5000
4000
3000
2000
1000
0
�1000�6 �4 �2 0 2 4 6
Storey drift: %
Bottom Middle Top
Mic
rost
rain
at i
nt. s
ide
(S1)
7000
6000
5000
4000
3000
2000
1000
0
�1000�6 �4 �2 0 2 4 6
Storey drift: %
Bottom Middle Top
Mic
rost
rain
at e
xt. s
ide
(S1)
7000
6000
5000
4000
3000
2000
1000
0
�1000�6 �4 �2 0 2 4 6
Storey drift: %
Bottom Middle Top
Mic
rost
rain
at i
nt. s
ide
(S2)
7000
6000
5000
4000
3000
2000
1000
0
�1000�6 �4 �2 0 2 4 6
Storey drift: %
Bottom Middle Top
Mic
rost
rain
at e
xt. s
ide
(S2)
7000
6000
5000
4000
3000
2000
1000
0
�1000�6 �4 �2 0 2 4 6
Storey drift: %
Bottom Middle Top
Mic
rost
rain
at i
nt. s
ide
(S3)
7000
6000
5000
4000
3000
2000
1000
0
�1000�6 �4 �2 0 2 4 6
Storey drift: %
Bottom Middle Top
Mic
rost
rain
at e
xt. s
ide
(S3)
7000
6000
5000
4000
3000
2000
1000
0
�1000�6 �4 �2 0 2 4 6
Storey drift: %
Bottom Middle Top
Mic
rost
rain
at i
nt. s
ide
(S4)
7000
6000
5000
4000
3000
2000
1000
0
�1000�6 �4 �2 0 2 4 6
Storey drift: %
Bottom Middle Top
Mic
rost
rain
at e
xt. s
ide
(S4)
Fig. 13. Envelope curves of joint hoop strain against storey drift (int. ¼ interior, ext. ¼ exterior) (S1 = specimen 1)
RC edge beam–column–slab connections subjected to earthquake loading
Magazine of Concrete Research, 2004, 55, No. 6 285
while storey shear decreased during 5% and 6% drift
cycles, although the rate of increase in strain got lower
at high storey drifts. Specimens 2 and 4 generally
exhibited larger joint hoop strains than specimens 1
and 3, which was consistent with the observation that
specimens 2 and 4 underwent larger joint shear defor-
mations. Comparing the two eccentric specimens, spe-
cimen 2 exhibited larger increments in joint hoop strain
than specimen 1 at high storey drifts, which agreed
with the fact that specimen 2 underwent larger joint
shear deformations after starting to break down. Com-
paring specimens with the same edge-beam width,
specimen 4 underwent larger joint hoop strains than
specimens 1 and 3, because specimen 4 had the smal-
lest effective joint area and was subjected to the largest
joint shear force due to the heavily reinforced slab.
Yielding of joint reinforcement was investigated
based on the yield strain of the joint hoops determined
by the 0.2% offset method. (The yield strain was about
0.0045 in all tests, with the stress–strain proportional
limit occurring at a strain of approximately 0.003.)
Only the middle joint hoop of specimen 4 yielded
(during the negative 5% drift cycle) at the interior side
of the joint; however, many joint hoops yielded or
approached yielding during 4% or 5% drift cycles at
the exterior sides of the joints. (For some joint hoops, it
was not possible to distinguish whether they yielded or
not, because their strain gauges broke during the tests.)
In particular, the middle joint hoops of specimens 2
and 4 saw very large strains of nearly 0.007.
Analysis of test results
Effective slab width contribution (to beam flexural
strength and joint shear)
The concept of an effective slab width is generally
used to incorporate floor slab contributions (to beam
moment strength and joint shear demand) in RC design.
It is well known that the slab contribution depends
strongly on imposed lateral drift level. In this study the
number of effective slab bars at a particular storey drift
was defined, considering slab in tension, as the sum of
forces in all longitudinal slab bars (at the storey drift)
divided by the product of actual yield strength and area
of the bars. To compute this, first the strain in each
longitudinal slab bar (plotted in Fig. 10) was divided by
the yield strain of the bar; one (1.0) was assigned if this
strain ratio was larger than unity. Then the number of
effective slab bars was computed by adding the strain
ratios of all longitudinal slab bars, and the correspond-
ing effective slab width was estimated considering the
locations of the slab bars. Table 5 lists the number of
effective slab bars and the effective slab width at var-
ious storey drifts. When each specimen reached its
maximum storey shear force, the number of effective
slab bars (and corresponding effective slab width) com-
puted in this way was 4.0 (122 cm), 4.0 (122 cm), 3.9
(119 cm) and 4.0 (77 cm) in specimens 1–4 respec-
tively. These numbers of effective slab bars will be
used to estimate maximum joint shear demands of the
specimens in a later section. (The maximum effective
slab width of specimen 3 could have been larger if a
wider slab had been tested, as all longitudinal slab bars
yielded and the specimen did not experience joint shear
failure.)
The maximum effective slab width that can poten-
tially contribute to beam flexural capacity may not be
fully activated when a connection fails in part due to
other modes before complete beam hinging; this may
have occurred in specimens 1, 2 and 4. The maximum
effective slab width in specimen 4 seems to have also
been limited by the torsional strength of the transverse
beam, which was subjected to large torsional moments
near the column face, where concrete cracking and spal-
ling damage occurred as shown in Fig. 15. The torsional
moments were generated as a result of the vertical dis-
tance (dt) between longitudinal slab bars and the cen-
troid of the transverse beam. At positive 4% drift, for
instance, tensile forces in all longitudinal slab bars at the
west beam/column interface can be computed using
strain gauge data from Fig. 10. Considering only the
tensile slab bar forces, without taking into account any
concrete or slab bar forces at the east beam/column
interface, the possible torsional moment applied at the
column face adjacent to the transverse beam in speci-
men 4 is equal to the sum of the slab bar forces times dt,
or 46.8 kNm. (Some portion of the slab bar forces may
Table 5. Number of effective slab bars and corresponding effective slab width
Drift (%) Number of effective slab bars Effective slab width (cm)
S1 S2 S3 S4 S1 S2 S3 S4
1 2.3 2.6 1.5 0.8 79 86 58 37
1.5 3.0 3.1 2.2 1.4 97 99 76 44
2 3.5 3.4 2.7 2.0 109 107 89 52
2.5 3.9 3.8 3.4 2.6 119 117 107 60
3 4.0 4.0 3.7 3.2 122 122 114 67
4 4.0 4.0 3.9 4.0 122 122 119 77
5 4.0 4.0 4.0 4.2 122 122 122 80
6 n.a. 4.0 3.5 4.1 n.a. 122 109 79
Shin and LaFave
286 Magazine of Concrete Research, 2004, 55, No. 6
enter into the joint by means of diagonal compression in
the slab panel and/or weak axis bending of the trans-
verse beam, as well as torsion of the transverse beam.10)
This torsional moment is equal to 80% of the torsional
strength of the transverse beam, computed based on the
thin-walled tube (space truss) analogy per ACI 318-02.
The transverse beam in specimen 4 was also under con-
siderable horizontal shear from the four slab bars,
286 kN, which is 80% of the shear strength of the
transverse beam, also computed per ACI 318-02. There-
fore it was judged that the transverse beam in specimen
4 suffered distress due to a combination of torsion and
shear, thereby limiting the amount of slab participation.
On the other hand, the transverse beams in the first three
specimens did not experience much distress; they only
reached less than 35% of their torsional strengths and
35% of their shear strengths.
The ACI effective slab width for design would be
69 cm for specimens 1, 3 and 4, and 59 cm for speci-
men 2, which encompasses two, two, two and three
longitudinal slab bars in specimens 1–4 respectively.
(According to ACI 318-02, a single effective slab width
for design is used regardless of positive or negative
bending, or of the magnitude of imposed lateral drift.)
The number of effective slab bars determined above
(when each specimen reached its maximum storey
shear force) was more than the number of slab bars
included within the ACI effective slab width, particu-
larly in specimens 1–3. In other words, the effective
slab width estimated based on slab bar strains was 1.7–
2.0 times larger than the ACI effective slab width in
the first three specimens, but similar to the ACI value
in specimen 4 (with a narrower column and a trans-
verse beam that suffered some deterioration). The ac-
tual effective slab width when each specimen reached
its maximum storey shear force was roughly equal to
the column width plus two times the transverse beam
width for these test specimens.
Chapter 21 of ACI 318-02 comments that the ACI
effective slab width is reasonable for estimating beam
negative moment strengths of interior connections at
roughly 2% drift. In this study the effective slab width
estimated at 2% drift was 109 cm, 107 cm, 89 cm and
52 cm in specimens 1–4 respectively; these values are
also substantially larger than the ACI effective slab
widths in the first three specimens, and somewhat
smaller in specimen 4. (In fact, laboratory experiments
on edge connections with floor slabs on one side only,
loaded in the longitudinal direction of the edge-beams,
have not previously been reported in the literature and
would therefore not be the basis for current ACI proce-
dures to estimate effective slab width.) This is of parti-
cular importance because a smaller effective slab width
is not conservative for estimating joint shear demand or
column-to-beam moment strength ratio.
Because all specimens underwent beam hinging near
beam/column interfaces, the predicted storey strength
(Vc,m(cal)) of each specimen may be computed assuming
the edge-beams reached their nominal moment
strengths at the beam/column interfaces:
Vc,m(cal) ¼(Mþ
n þ M�n )
lc� lb
(lb � hc)(2)
Here Mþn and M�
n are beam positive and negative
nominal moment strengths, computed using the ACI
318-02 nominal moment strength calculation method
(equivalent rectangular stress block concept) with ac-
tual material properties. These beam nominal moment
strengths depend on the amount of slab participation.
Table 6 compares the predicted storey strength
(Vc,m(cal)), computed using the number of effective slab
bars (about four in each specimen) and corresponding
effective slab width when each specimen reached its
maximum storey shear force, with the measured storey
strength (Vc,m(exp)), which is the maximum storey shear
force. The Vc,m(cal) values are 6%, 11%, 4% and 1%
higher than the Vc,m(exp) values in specimens 1–4 re-
spectively. (Vc,m(exp) values for positive loading were
used for this comparison because the specimens under-
went some damage after being loaded first in the posi-
tive direction.) In other words, the beam–slab moment
strengths in specimens 1–3 are slightly overestimated
considering the effective slab bars computed based on
slab bar strains. This is because some concrete at the
bottom of these edge-beams near beam/column inter-
faces started to spall off at about 2.5% drift, which
reduced beam sectional moment arms, leading to smal-
ler actual storey strengths than the computed values (in
specimen 4, concrete spalling did not occur at the
bottom of the edge-beams).
Slab effect on joint shear demand
Considering horizontal force equilibrium of an RC
joint free body diagram, and moment equilibrium of
Table 6. Measured and predicted storey strengths
Specimen 1 2 3 4
Vc,m(exp) (kN) (+) loading 88.1 83.4 92.7 109.1
(�) loading 81.1 80.5 90.9 109.6
Vc,m(cal) (kN) No. of included slab bars 2 83.8 82.6 87.1 90.9
3 88.9 88.2 92.6 101.4
4 93.7 92.9 96.5 109.7
5 – – – 117.9
RC edge beam–column–slab connections subjected to earthquake loading
Magazine of Concrete Research, 2004, 55, No. 6 287
the edge-beams, the horizontal joint shear force (Vj) at
mid-height of the joint during a test can be computed
as explained in Fig. 14. Here V1 and V2 are the edge-
beam end shears, which are simply the axial forces
measured in the east and west beam-end supports re-
spectively, and Vc is the applied storey shear force.
Also, jd1 and jd2 are the beam moment arms at the east
and west beam/column interfaces, which were assumed
to be 355 mm for sagging (positive) moments, and
330 mm (305 mm in specimen 2) for hogging (nega-
tive) moments. (These assumed moment arms were the
ones determined above when calculating the nominal
moment strengths of the edge-beams.) Using this meth-
od, the maximum joint shear force was computed to be
631 kN, 670 kN and 793 kN in specimens 2, 3 and
4 respectively. (This method could not be used in
specimen 1 because the load cells in the beam-end
supports did not operate.)
The maximum joint shear force can also be deter-
mined using an alternative method. All beam longitudi-
nal bars yielded at beam/column interfaces before each
specimen reached its maximum storey shear force, but
no longitudinal beam or slab bars underwent strain-
hardening during testing. Therefore the maximum joint
shear force (Vj,m) can be estimated at the storey drift
when each specimen reached its maximum storey shear
force as:
Vj,m ¼X
As f y � Vc,m(exp) (3)
Here As is the area of each reinforcing bar, fy is the
actual yield strength of each reinforcing bar, and
Vc,m(exp) is the maximum storey shear force measured at
the column top. The summation term includes all (top
and bottom) longitudinal beam bars, as well as the four
effective slab bars for each specimen (as determined
above). Using this equation, the Vj,m value was 647 kN,
651 kN, 643 kN and 792 kN in specimens 1–4 respec-
tively. Maximum joint shear forces estimated with the
two methods are in good agreement, with a discrepancy
of less than 5%. However, the latter method was con-
sidered to estimate maximum joint shear forces better,
because the former method was based on assumed
beam moment arms.
As mentioned earlier, ACI 318-02 does not consider
slab participation in joint shear demand design calcula-
tions, whereas ACI 352R-02 recommends including
slab reinforcement within the ACI effective slab width.
The experimental maximum joint shear forces (Vj,m)
exceeded the values computed per ACI 318-02 by
roughly 25% in the first three specimens and 55% in
specimen 4, and they also exceeded the values com-
puted per ACI 352R-02 by roughly 10% in all four
specimens. Specimen 4 probably would not have under-
gone joint shear failure if it had been reinforced with a
lower slab steel ratio similar to that of the other speci-
mens.
Slab effect on joint shear capacity
The effect of floor slabs (and transverse beams) on
RC joint shear capacity was evaluated by estimating
effective joint widths of the eccentric specimens in this
study and comparing them with other eccentric speci-
mens without slabs found in the literature. For a speci-
men that failed due to joint shear, its joint shear
strength can be considered equal to the maximum joint
shear force (Vj,m) applied during the test, and thus an
effective joint width (bj,exp) for the specimen may be
estimated by:
bj,exp(mm) ¼ Vj,m(N)
ªnffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffif 9c(MPa)
p� hc(mm)
(4)
Here ªn is the nominal joint shear stress level specified
by ACI 318-02 and ACI 352R-02, to place eccentric
connections on an equal basis for comparison with
similar concentric connections. Table 7 summarises the
maximum joint shear forces (Vj,m) and the estimated
effective joint widths (bj,exp) of eccentric specimens
(from this testing programme and from the literature)
that were judged to fail because of joint shear (ªn is
1.00 for all specimens in the table).
To appreciate the effect of the floor slabs, the bj,expvalues were normalised using an equation suggested by
Raffaelle and Wight:5
bj,RW ¼ bc
1þ 3e=xc(5)
Here e is the eccentricity between beam and column
V1 East edge-beam
(lb � hc)/2
jd1
Cb1
Tb1
Cb1
Tb1
jd1 Vj Vj
Vc
jd2
Tb2
Cb2
Vc
Joint
Vj � Cb1 � Tb2 � Vc
Cb1 � V1(lb � hc)/2jd1
Tb2 � V2(lb � hc)/2jd2
Fig. 14. Edge-beam and joint free body diagrams
Fig. 15. Torsional damage of transverse beam in specimen 4
Shin and LaFave
288 Magazine of Concrete Research, 2004, 55, No. 6
centrelines, and xc is equal to the smaller of bc or hc.
This equation was derived taking into account the addi-
tional stresses due to torsion in the joint, but without
considering the effect of floor slabs. The bj,exp to bj,RWratios are generally higher in the specimens with floor
slabs than in those without floor slabs. Therefore it
may be concluded that the floor slabs (and transverse
beams) improved the joint shear capacity of eccentric
connections. This was partially because joint shear
forces applied at the top of the joint were distributed
across the entire column width by means of the floor
slabs, so the effective joint width was enlarged when
compared with the case without slabs.
The table also contains ratios of the estimated effec-
tive joint width (bj,exp) to the effective joint widths
computed following ACI 318-02 (bj,318) and ACI 352R-
02 (bj,352) (see Table 1 for details). It is clear that ACI
318-02 greatly underestimates the joint shear strength
of eccentric connections, particularly in cases with
floor slabs. For the one-sided (flush) eccentric connec-
tions, the bj,318 values are simply equal to the edge-
beam widths. Therefore all the eccentric connections in
Table 7 could just be considered as concentric connec-
tions with imaginary (reduced) column widths equal to
the edge-beam widths, a case where ªn is 1.25. The
b9j,exp values used in Table 7 were computed by equation
(4) with ªn ¼ 1.25, and they were closer to the bj,318values than the bj,exp values were. In summary, it ap-
pears to be more reasonable to apply ªn ¼ 1.25 when
using bj,318 values for the joint shear strength of one-
sided (flush) eccentric connections.
Finally, the joint shear strength of the two eccentric
specimens with floor slabs reported herein was well
estimated using the effective joint width currently de-
fined for concentric connections in ACI 352R-02,
namely bj ¼ (bb + bc)/2, as listed in Table 7. However,
bj ¼ (bb + bc)/2 was not conservative for some pre-
viously tested eccentric connections without slabs, as
would probably also be the case for eccentric connec-
tions with slabs where the interior faces of columns are
flush with the interior faces of beams.
In Table 8, the maximum joint shear stress level (ªm)actually reached in specimen 4 was computed using the
experimental maximum joint shear force (Vj,m) and
compared with other concentric connections found in
the literature that failed because of joint shear. To
Table 7. Estimation of effective joint width for eccentric connections
Specimen Vj,m(kN)
bb(mm)
bc(mm)
bj,exp(mm)
bj,exp/bj,RW bj,exp/bj,318 bj,exp/bj,352 b9j,exp/bj,318 bj,exp/
(bb+bc)/2
Authors 1 647 279 457 359 1.42 1.29 1.09 1.03 0.97
2 651 178 457 329 1.63 1.85 1.45 1.48 1.04
Joh et al.4
JX0-B5 294 150 300 204 1.19 1.36 1.05 1.09 0.91
Raffaelle & Wight5
1 650 254 356 343 1.38 1.35 1.12 1.08 1.12
2 421 178 356 229 1.13 1.29 0.99 1.03 0.86
3 472 191 356 217 1.03 1.14 0.89 0.91 0.79
4 413 191 356 265 1.26 1.39 1.09 1.11 0.97
Teng & Zhou6
S3 716 200 400 405 2.02 2.02 1.64 1.61 1.34
S6 391 200 400 318 1.95 1.56 1.36 1.25 1.04
Note: ªn ¼ 1.00 for bj,exp (ªn ¼ 1.25 for b9j,exp).
Table 8. Maximum joint shear stress level for concentric connections (ªn ¼ 1.25)
Specimen Vj,m (kN) ªm (1) ªm (2) (1)/ªn (2)/ªn
Authors 4 793 1.38 1.38 1.10 1.10
Leon21
BCJ2 341 1.01 1.12 0.81 0.90
BCJ3 412 1.02 1.13 0.82 0.90
Durrani & Wight22
X1 689 0.90 1.02 0.72 0.82
X2 701 0.93 1.04 0.74 0.83
X3 533 0.73 0.83 0.58 0.66
Park et al.23
Interior 966 1.34 1.53 1.07 1.22
Meinheit & Jirsa15
1 841 1.09 1.18 0.87 0.94
2 1248 1.28 1.39 1.02 1.11
3 945 1.22 1.32 0.98 1.06
4 1099 1.22 1.29 0.98 1.03
5 1179 1.31 1.42 1.05 1.14
6 1292 1.42 1.53 1.14 1.22
7 1110 1.21 1.28 0.97 1.02
12 1458 1.63 1.77 1.30 1.42
13 1169 1.21 1.31 0.97 1.05
14 1148 1.33 1.40 1.06 1.12
Note: (1) ¼ Vj,m=ffiffiffiffiffif 9c
p� bj,318 � hc and (2) ¼ Vj,m=
ffiffiffiffiffif 9c
p� bj,352 � hc.
RC edge beam–column–slab connections subjected to earthquake loading
Magazine of Concrete Research, 2004, 55, No. 6 289
identify the effect of the slab (and transverse beam),
only cruciform connections (without transverse beams
and slabs) whose beams covered more than three-quar-
ters of their column faces (ªn ¼ 1.25) were selected.
(Other important variables, such as joint shear reinfor-
cement and bond condition, were not necessarily the
same in all of these specimens.) In general, specimen 4
reached a slightly higher ªm than the other concentric
connections. This was probably limited because the
transverse beam suffered concrete cracking and spalling
near the column face, so it could neither resist joint
shear forces as an extended part of the joint, nor effec-
tively confine the joint. It is also interesting to note that
the maximum joint shear stress level (ªm) reached in
many of the other concentric connections was smaller
than the nominal joint shear stress level (ªn ¼ 1.25).
Conclusions
In this study, the seismic performance of RC edge
beam–column–slab connections was experimentally
evaluated by testing four large-scale subassemblies
(two eccentric and two concentric connections) sub-
jected to simulated lateral earthquake loading. The
main design variables in the specimens were the eccen-
tricity between beam and column centrelines, the edge-
beam width, and the reinforcement ratio of longitudinal
slab bars. A summary of the experimental results and
related conclusions is as follows:
(a) All four edge connections exhibited similar overall
load–displacement behaviour, stiffness degrada-
tion, and energy dissipation. First yield of beam
flexural reinforcement occurred during the 1.5% or
2% drift cycle in all specimens, and each sub-
assembly reached its maximum storey shear force
during the 3% or 4% drift cycle. Strength degrada-
tion was greatest in the three specimens (both
eccentric connections and one concentric connec-
tion) that ultimately failed because of joint shear.
(b) Joint shear deformations were largest in the three
specimens that ultimately failed because of joint
shear (after some beam hinging); the magnitude of
joint shear deformation in these three specimens
was similar to that in other connections found in
the literature that had joint shear failures. In these
three specimens, the rate of increase in joint shear
deformation got higher at about 2.5% drift, and
joint shear deformations were eventually responsi-
ble for about half of the overall subassembly storey
displacements.
(c) In all cases, strains measured in joint hoop reinfor-
cement near the exterior face of a joint were some-
what larger than those measured near the interior
face of the joint. The distribution in joint hoop
strain across the joint was not much different be-
tween the eccentric and concentric connections
tested, and it was much more uniform than in other
eccentric connections (without floor slabs and
transverse beams) reported in the literature, indi-
cating that the floor slabs may have expanded the
effective joint width and reduced joint torsional
demand by shifting the acting line of the resultant
force coming from top beam and slab reinforce-
ment.
(d) Slab participation contributions to beam moment
strength, joint shear demand and transverse beam
torsional demand played an important role in the
behaviour of the connections, particularly with in-
creasing drift. Effective slab widths in tension ob-
served in this study were greater than those
commonly recommended for use in design of edge
connections, and slab effects on joint shear demand
were particularly pronounced.
(e) The joint shear capacity of the two eccentric con-
nections tested was greater than that of most simi-
lar eccentric connections without floor slabs or
transverse beams reported in the literature. Some
effective joint widths commonly recommended for
use in design seem to be ill suited for application
to eccentric connections, whereas others work
fairly well for eccentric connections with or with-
out floor slabs. Finally, the joint shear capacity of
the concentric connection in this study that failed
in joint shear was slightly higher than that ob-
served in other similar concentric connections
(without floor slabs and transverse beams) found in
the literature.
References
1. Youd T. L., Bardet J. and Bray J. D. 1999 Kocaeli, Turkey,
Earthquake Reconnaissance Report. EERI, Oakland, California,
2000.
2. Hirosawa M., Akiyama T., Kondo T. and Zhou J. Damages
to beam-to-column joint panels of RC buildings caused by the
1995 Hyogo-ken Nanbu earthquake and the analysis. Proceed-
ings of the 12th World Conference on Earthquake Engineering,
Auckland, New Zealand, 2000, 1321.
3. Lawrance G. M., Beattie G. J. and Jacks D. H. The Cyclic
Load Performance of an Eccentric Beam–Column Joint. Central
Laboratories, Lower Hutt, New Zealand, 1991, Central Labora-
tories Report 91-25126.
4. Joh O., Goto Y. and Shibata T. Behavior of reinforced con-
crete beam–column joints with eccentricity. In Design of
Beam–Column Joints for Seismic Resistance, American Con-
crete Institute, Detroit, Michigan, 1991, SP-123, pp. 317–357.
5. Raffaelle G. S. and Wight J. K. Reinforced concrete ec-
centric beam–column connections subjected to earthquake-type
loading. ACI Structural Journal, 1995, 92, No. 1, 45–55.
6. Teng S. and Zhou H. Eccentric reinforced concrete beam–
column joints subjected to cyclic loading. ACI Structural Jour-
nal, 2003, 100, No. 2, 139–148.
7. Chen C. C. and Chen G. K. Cyclic behavior of reinforced
concrete eccentric beam–column corner joints connecting
spread-ended beams. ACI Structural Journal, 1999, 96, No. 3,
443–449.
8. Vollum R. L. and Newman J. B. Towards the design of
Shin and LaFave
290 Magazine of Concrete Research, 2004, 55, No. 6
reinforced concrete eccentric beam–column joints. Magazine of
Concrete Research, 1999, 51, No. 6, 397–407.
9. ACI-ASCE Committee 352. Recommendations for Design of
Beam–Column Joints in Monolithic Reinforced Concrete
Structures. American Concrete Institute, Detroit, Michigan,
1985, ACI 352R-85.
10. Pantazopoulou S. J. and French C. W. Slab participation in
practical earthquake design of reinforced concrete frames. ACI
Structural Journal, 2001, 98, No. 4, 479–489.
11. Abrams D. P. Scale relations for reinforced concrete beam–
column joints. ACI Structural Journal, 1987, 54, No. 6, 502–
512.
12. ACI Committee 318. Building Code Requirements for
Reinforced Concrete; Commentary. American Concrete Institute,
Michigan, 2002, ACI 318-02, ACI 318R-02.
13. ACI-ASCE Committee 352. Recommendations for Design of
Beam–Column Connections in Monolithic Reinforced Concrete
Structures. American Concrete Institute, Farmington Hills,
Michigan, 2002, ACI 352R-02.
14. Long A. E., Cleland D. J. and Kirk D. W. Moment transfer
and the ultimate capacity of slab column structures. The Struc-
tural Engineer, 1978, 56A, No. 4, 95–102.
15. Meinheit D. F. and Jirsa J. O. Shear strength of RC beam–
column connections. ASCE Journal of the Structural Division,
1981, 107, No. ST11, 2227–2244.
16. Bonacci J. and Pantazopoulou S. Parametric investigation of
joint mechanics. ACI Structural Journal, 1993, 90, No. 1, 61–71.
17. Hwang S. J. and Lee H. J. Analytical model for predicting
shear strengths of interior reinforced concrete beam–column
joints for seismic resistance. ACI Structural Journal, 2000, 97,
No. 1, 35–44.
18. Chopra A. K. Dynamics of Structures: Theory and Applica-
tions to Earthquake Engineering. Prentice Hall, Upper Saddle
River, New Jersey, 2000.
19. Joh O., Goto Y. and Shibata T. Influence of transverse joint
and beam reinforcement and relocation of plastic hinge region
on beam–column joint stiffness deterioration. In Design of
Beam–Column Joints for Seismic Resistance. American Con-
crete Institute, Detroit, Michigan, 1991, SP-123, pp. 187–223.
20. French C. W. and Moehle J. P. Effect of floor slab on behav-
ior of slab–beam–column connections. In Design of Beam–
Column Joints for Seismic Resistance. American Concrete
Institute, Michigan, 1991, SP-123, pp. 225–258.
21. Leon R. T. Shear strength and hysteretic behavior of interior
beam–column joints. ACI Structural Journal, 1990, 87, No. 1,
3–11.
22. Durrani A. J. andWight J. K. Behavior of interior beam-to-
column connections under earthquake-type loading. ACI Jour-
nal, 1985, 82, No. 3, 343–349.
23. Park R., Gaerty L. and Stevenson E. C. Tests on an interior
reinforced concrete beam–column joint. Bulletin of the New
Zealand National Society for Earthquake Engineering, 1981,
14, No. 2, 81–92.
Discussion contributions on this paper should reach the editor by
1 January 2005
RC edge beam–column–slab connections subjected to earthquake loading
Magazine of Concrete Research, 2004, 55, No. 6 291