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


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.



( 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


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



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


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



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


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



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


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)



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


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



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


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.



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.

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Discussion contributions on this paper should reach the editor by

1 January 2005



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