THE BEHAVIOUR OF REINFORCED r.ONCRETEThis project investigates the behaviour of reinforced...
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THE BEHAVIOUR OF REINFORCED r.ONCRETE :BEAM-coLUMN ·JOlNTS UNDER OYCLIC A thesis .submitted for the degree of Master of Engineering in Civil Engineering in the University of. Canterbury, Christchurch, New Zealand. by G.W. RENTON 1972 .•
Transcript of THE BEHAVIOUR OF REINFORCED r.ONCRETEThis project investigates the behaviour of reinforced...
THE BEHAVIOUR OF REINFORCED r.ONCRETE
:BEAM-coLUMN ·JOlNTS UNDER
OYCLIC LOADmG~
A thesis .submitted for the degree of
Master of Engineering in Civil Engineering
in the University of. Canterbury,
Christchurch, New Zealand.
by
G.W. RENTON
1972 .•
ENGINEERING lllli\A~Y i
l'rr:;, .l :}
I.\
ABSTRACT
This project investigates the behaviour of reinforced concrete· beam-
column joints under the application of high intensity cyclic loading.
The experiments, wbicb were carried o~t on specimens with a beam
framing in on only one side of the joint, were conducted to investigate
the amount of transverse reinforcement re(}.uired for confinement and shear
resistance in the joint and column regions, in order to establish the
ductility available in the column, when subjected to simulated seismic
loading.
Four units were tested during the experimental program, the design
parameters being:-
(i) tbe amount of transverse reinforcement in the joint.
( ii) the method of anchol'ing the beam flexural steel in the joint.
(iii) the amount of transverse reinforcement in the column.
The type of failure mechanism, and the cause of degradation in stiff-
ness in the post-elastic range, is examined for eacr specimen leading to
a critical appraisal of the joint detail.
Frorn the results obtained during testing, recommendations rave been
suggested for the design of reinforced concrete joints, including ways in
wl'dcb detailing could be improved to enable t11e load resisting capacity to
be sust~ined durine post-elastic cycles.
I gratefully acknowledge the assistance given by members of the
academic and technical staff of the Civil Engineering Department, and
extend my thanks to the following people:
Professol~ H.J. Hopldns, Head o.f the Civil Engineering Dept., under
whose overall guidance this study was performedJ
Professor R. Park, supervisor of this project, for hhJ guidance and
assistance during the experimental work and in the preparation of this
thesis;
Dr. T. Paul.9.y, supervisor of this project, for his constructive
suggestions and ei'lcouragement throughout this study;
Messrs H .T. Watson and P.C; Dawson, Technioal Officers, for co
ordination of the testing programme;
Mr N.W. Prebble, Senior Tecrnician, for his technical advice and
practical belp throughout the preparation and testing of the specimens;
Messrs J.N. Byers, Senior Technician, J.M. Adams and S.R. Robinson,
Technicians, for their valuable assistance during tasting;
Mr II. Patterson for photographic work;
Mr R.W.G. Blakeley for the design of the test rig;
Mr s. J. Dawson for his tireles'a efforts tracil1g diagrams;
Mrs N.J. Robinson for typing the manuscript;
I also r:r;ratefully acknowledge the financial aid from my parents and
the University of Canterbury.
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TABLE OF CONTENTS.
ABSTRACT.
ACKNO\r.LEDGEMENTS.
TABLE OF r.ONTENTS,
LIST OF FIGURES.
LIST OF TABLES.
NOTATION.
CHAPTER ONE - INTRODUCTION.
1. 1 General.
1.2 Behaviour of Reinforced Concrete Frames.
1.3 Scope of this Research.
CHAPTER TWO - THE STATE OF THE ART.
2.1 Present Design Procedures.
2.2 Review of Previous Work.
CHAPTER THREE - TEST SPECIMENS.
3.1 Introduction.
3. 2 Design
3. 2.1
3.2.2
3.2.3
of Specimen.
Overall Specifications.
Size and Flexural Reinforcement
3. 2. 2. 1 Column.
3.2.2.2 Beam.
Transverse Reinforcement.
3.2.3.1 Joint Ties,
3.2.3.2 Column Ties.
3.2.3.3 Beam Stirrups.
3. 3. Theoretical Behaviour,
3.3.1 Elastic Range.
3.3.1.1 Flexural Cracking.
of Members.
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3.3.1.2 Yield Load.
3.3.1.3 Rotations and Deflections.
3.3.1.4 Steel Strains.
3.3.2 Post Elastic Range.
3.3.2.1 Ultimate Load.
3.3.2.2 Rotational Ductility.
3.4 Earthquake Loading Representation.
3.4.1 Load Application.
3.4.2 Loading Sequence.
~IIAPTER FOUR - UNIT 1 •
4.1 Introduction.
4.2 Detail of Reinforcement.
4.3 General Performance.
4.4 Behaviour of Flexural Reinforcement.
4. 4. 1 Column Bars.
4.4.2 Beam Bars.
4.5 Behaviour of Transverse Reinforcement.
4.5.1 Column Ties.
4. 5. 2 Joint Ties.
4.5.3 Beam Stirrups~
4.6 De forma tiona.
4. 6. 1 Deflections.
4.6.2 Moment-Rotation
4.6.3 Load-Deflection
4.7 Cracking.
4.8 The Failure Mechanism.
F:HAPTER FIVl~ - UN IT 2.
5. 1 Introducti.on.
Relationships.
Re la ti on ship:
5. 2 Detail of Reinforcement.
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5.3 General Performance.
5.4 Behaviour of Flexural Reinforcement.
5.4.1 Column Bars.
. 5. 4. 2 Beam Bars.
5.5 Bel;aviour of TranAverse Re i.nforc.3m~nt.
5.5.1 Column Ties.
5.5.2 Joint Ties.
5.6 Deformations.
5.6.1 Deflections.
5.6.2 Moment-Rotation
5. 6. 3 ·Load-Deflection
5.7 Cracking.
5.8 The Failure Mechan:i.sm.
r;HAPTER SIX - IDTIT 3.
6.1 Introduction.
Relationships.
Relationship.
6, 2 Detail of Reinforc~tilt.·mt.
6. 3 General Performance.·
6. 4 Behaviour of Flexural ~einforcement.
6.4.1 Column Bars.
6.4.2 Beam Bars.
6, 5 Dehaviour of Transverse Reinforcement.
6, 5.1 Oolumn Ties.
6.5.2 Joint Ties.
6.6 Deformations.
6.6.1 Deflections.
6,6.2 Moment-Rotation Relationships.
6.6.3 Load-Deflection Relationship.
6.7 Cracking.
6. 8 The Fapure Mechanism.
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CHAPTER SEVEN - UlilT 4.
7.1 Introduction.
7. 2 Detail of. Reinforcement.
7.3 General Performance,
7.4 Behaviour of FJexur&l Reinforcem(·mt.
'7. 4. 1 Colu:nn Bars.
'7.4.2 Beam Bars.
7.5 Behaviour· of Transverse Reinforcement.
7.5.1 Column Ties,
7.5.2 Joint Ties.
7.6 Deformations.
7.6.1 Deflections.
7.6.2 Moment-Rotation Relationships.
7.6.3 Load-Deflection Relationship.
7. 7 Cracking.
'7. 8 The Failure Mechanism.
CHAPTER EIGHT - DISCUSSIOl; MlD CON•-,LUSIONS.
8.1 Comparison of Specimens.
8.2 Criticism of Detail.
8.3 Recommendations.
;p:rENDIX A.
A. 1. Materials.
A. 2. Fabrication of Specimen~
A. 3. Test Rig.
A.4. Application of Load.
A. 5. Instrumentation.
A. 5. 1.. Load Measurement.
A.5.2 . Rotstions.
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1.34
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A.5.3 Deflections,
A.5.4 Strain Measurements.
A.5.4.1 DEMEC Gauges,
A.5.4.2 Electric Resistance Strain Gauges.
APPENDIX B.
B.1 Design Calculations.
B.1.1 Column Reinforcement.
B.1.2 Balanced Load of Column.
B.1.3 Ultimate Moment Capacity of Column.
B.1.4 Beam Reinforcement.
B. 1.5 Anchorage Requiremen:ts,
B. 1.6 Analysis of U- type Anchorage Detail.
B.1.7 Joint Hoops for Confinement.
B.1.8 Joint Ties for Sh8ar,
B: 1, 9 Column Ties for Shear,
B.1.10 Confinement of the Column.
"B.1, 11 Shear in the Beam.
B,2 Theoretical Predictions.
B.2.1 Cracking.
B. 2. 1. 1 Beam.
B.2.1.2 Column.
B.2.2 Yield Load.
B.2.3 Rotations.
B.2.4 Deflections.
B,2.'5 Ultimate Moment of the Column.
B,2,6 Rotational Ductility.
B.2.7 Tbeoretlcal Steel Strains.
B.2.7.1 ~earn Steel,
B.2.7.2 Colu~1 Steel.
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B.2.8 Ultimate Moment Capacity of the Column Core of UNIT 4. 159
B.2.9 Bond Stress Developed in Beam Flexural BarG. 159
APPENDIX C - BIBLIOGRAPHY. 161
LIST OF FIGURES.
Figure.
1.1 Response of Framed Struct'..lre to Lateral Load.
1.2 Test Specimen.
3.1 Forces on Test Specimen.
3.2 Loading Sequence.
4. 1 Reinforcing Detail for UNIT 1.
4. 2 The Distribution of Steel Strains in Column Flexur~~l Bars
4.3
4.4
4.5
4.6
4.7
4.8
in UNIT 1.
(a) For Downward Load Runs.
(b) For Upward Load Runs.
The Distribution of Steel Strains in
UNIT 1.
(a) For Downward Load Runs.
(b) For Upward Load Runs.
IDliT 1 on Load Run 6.
Buckling of Column Flexural Bars.
The Distribution of Joint Tie Strains
(a) At Back of Column.
(b) At Side of Column.
(a) The Strain Distribution on Back
(b) The Strain Distribution on Side I
Beam Flexural Bars in
in UNIT 1.
of Joint Ties in UNIT
of Joint Ties in UNIT
The Load-Strain Relationship for Joint Ties in UNIT 1.
(a) Back of Ties.
(b) Side of Ties.
1.
1.
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4. 9 Deflected Shapes of UNIT 1 at Peaks of El!.:.stic Load Runs. 35
4.10 Moment-Rotation Relationshi-ps for UNIT 1;
(a) Col\..unn Above the Joint.
('b) Colur.m Below the Joint.
4.11 Load-Deflection Relationship for illiiT 1.
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4.12 UNIT 1 on Load Run 1.
4.13 Back of Joint· in UNIT 1 on Load Run 6.
4.14 ill~IT 1 on Load Run 4.
4.15 mriT 1 at Failure on Load Run 7.
4.16 Failure Mechanism of UNIT 1. •,
5.1 Reinforcing Detail for ffi~IT 2.
5. 2 UNIT 2 on Load Run 3.
5.3 UNIT 2 on Load Run 4.
5.4 ill~IT 2 Showing Secondary Vertical Crack at Failure.
5.5 The Distribution of Steel Strains in Column Flexural Bars
in UNIT 2.
(a) For Downard Load.
(b) For Upward Load.
5.6 The Distribution of Steel Strains in Beam Flexural Bars in
UNIT 2.
(a) For Downward Load.
(b) For Upward Load.
5.7 The Distribution of Joint Tie Strains in ill~IT 2.
(a) At Back of Column.
(b) At Side of Column.
5.8 (a) The Strain Distribution on Back of Joint Ties
(b) 'l1he Strain Distribution on Side of Joint Ties
in UNIT
in UNI'r
2.
2.
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5. 9 Back of Joint Showing Vertical Splitting Crach in illHT 2. 57
5.10 The toad-Strain Relationship for Joint Ties in WHT 2.
(a) Back of Ties.
(b) Side of Ties.
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5. 11 Deflected Shapes of UNIT 2 at Peaks of Elastic Load Runs. 60
5.12 Moment-Rotation Relationships 'for UNIT 2.
(a) Column Above the Joint.
(b) Cplumn Below the Joint.
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5.13 Load-Deflection Relationship for UNIT 2.
9.14 UNIT 2 on Load Run 5.
5.15 Crushing of Concrete in Column of UNIT 2 Immediately
Above Beam-Column Junction.
5. 16 UlHT 2 at Failure.
5.17 Failure Mechanism of UNIT 2.
6.1 Reinforcing Detail for UNIT 3.
6.2 UNIT 3 on Load Run 3.
6. 3 UNIT 3 on Load Run 4.
6.4 .UNIT ·3 on Load Run 9.
6.5 The Distribution of Steel Strains in Column Flexural Bars
in UNIT 3.
(a) F0r Downward .Load Runs.
(b) For Upward Load Runs.
6. 6 The Distribution of Steel St1•ains in Beam Flexural Bars in
UNIT 3.
6.7
6.8
(a) For Downward Load Runs.
(b) For Upward Load Runs.
The History of Strain for the Beam li'lexural Bars in UNIT 3.
The Distribution of Joint Tie Strains in UNIT 3.
(a) At Back of Column (DEMEO and Electric Resistance Strain
Gauges).
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(b) At Side of Column (DEMEO Gauges). 79
(c) At Side of Column (Electric Resistance Strain Gauges). 80
6, 9 (a) The Strain Distribution on Back of Joint Ties in
illHT 3.
(b) The Strain Distribution on Side o~ Joint Ties in
UNIT 3.
6.10 The Load-Strain Relationship for Joint Ties in UNIT 3.
(a) Bp.ck of Ties ( DENIEC and Electric Resistance Strain
Gauges).
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(b) Side of Ties ( DEMEC Gauges).
(c) Side of Ties (Electric Resistance Strain Gauges).
(d) Inside of Ties (Electric Resistbnce Strain Gauges).
6.11 Deflected Shapes of UNIT 3 and Peaks of Elastic Load Runs.
6.12 Moment-Rotation Relationships for UNIT 3.
(a) Column Above the Joint.
(b) Column Below the Joint.
6.13 Load-Deflection Relationship for UNIT 3.
6.14 UNIT 3 on Load Run 1.
6.15 UNIT 3 at Failure.
7. 1 Reinf::1rcing Detail for UNIT 4.
7.2 UNIT 4 on Load Run 3.
7.3 illfiT 4 on Load Run 8.
7.4 The Distribution of Steel Strains in Column-Flexural Bars in
UNIT 4.
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90
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(a) For Downward Load. 99
(b) For Upward Load. 100
7.5 The Distribution of Steel Strains in Beam Flexural Bars in
UNIT 4.
(a) For Downward Load. 102
(b) For Upward Load. 103
7. 6 End of Top Beam Flexural Bar Lifted off Bearing Surface. 98
7.7 The Distribution of Steel Strains on Column Ties of UhiT 4. 105
;.8 The Distribution of Joint Tie Strains in UNIT 4.
(a) At Back of Column. 106
(b) At Side of Column. 107
7.9 Th,e Load-strain Relationship for Joint Ties in UNIT 4.
(a) Back of Ties.
(b) Side of Ties.
7. 1.,; Deflected Shapes of UNIT 4 at Peaks of Elastic Load Runs.
108
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111
7. 11 Moment-Rotation Relationships for UNIT 4.
(a) Column Above the Joint.
(b) Column Below the Joint.
7.12 Load-Deflection Relationship for UNIT 4. -~
7.13 UNIT 4 on Load Run 4.
7.14 UlHT 4 on Load Run 5.
7. 15 UNIT 4 on Load Run 8.
7.16 UNIT 4 at Failure.
7.17 UNIT 4 at Failure.
8.1 Distribution of Internal Forces.
8.2 Forces on Joint of UNIT 4 (Run 1)·
8.3 Pressure on One Leg of Tie.
8.4 Dimensions of Specimen.
A. 1 Reinforcing Cage of UNIT 1.
A.2 Reinforcing Cage Positioned in Mould.
A.3 Joint of UNIT 1 Showing Demeo Studs.
A.4 (a) Test Rig and Specimen.
(b) Beam Loading Frame.
A.5 Specimen Prepared for Testing.
A.6 Rotation and Deflection Recording Apparatus.
A.7 Bowing of Joint Ties Due to Bursting Pressure of Column
Core.
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A.8 Shape of Back of Tie Due to Internal Pressure. 138
A.9 Joint of Reinforcing Cage of UNIT 4 Positioned in Mould. 140
LIST OF TABLES.
Table,
4. 1 Performance of UNIT Durins Load Cycling.
5. 1 Performance of UNIT 2 During Load r.ycling.
6. 1 Performance of ill~ IT 3 During Load Cycling.
7. 1 J:'erformance of UNIT 4 During Load Cycling.
8. 1
8,2
8.3
Bond Stress Developed in Beam F1e:wral Bars.
Comparison of Theoretical
Comparison of Theoretical
Deflections.
3.4 Joint Shear Reinforcement.
A.1 Material Properties.
B.1 Beam Cracking Loads.
B.2 Column Cracking Loads.
B.3 Theoretical Yield Loads.
and Actual Loads,
and Actual Rotations
B.4 Load-Rotation Relationships for the Golurm.
B, 5 Load-Deflection Relationships for the Beam.
B.6 Theoretical Ultimate Moments for the Column.
B,7 Moment-StTess Relations~ips for Beam Steel.
B, 8 Stress in ~olumn Bars.
and
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XV
NOTATION.
A = area of core of reinforced column, measured to the outside of the c
transverse reinforcement.
gross area o£ section.
= Ag + (n - 1) Ast' the equivalent concrete area of a section.
area of tension reinforcement,
A' s ""
:::
=
=
=
area of compression reinforcement.
area of transverse hoop bar (one leg).
area of structural steel in a composite
depth of equivalent rectangular stress
deptb of equivalent rectangular stress
conditions.
a = area of individual reinforcing bar. s
av = area of transverse tie (one leg)
b
0
0 s
c
c b
=
-
=
=
width of compression face of member.
concrete compressive force.
steel compressive force.
distance from extreme compression fibre
distance from extreme compression fibre
balanced load conditions.
D = nominal diameter of reinforcing bar.
section.
block.
block under balanced load
to neutral axis.
to neutral axis under
d = distance from extreme compression fibre to centroid of tension
reinforcement.
d' = distance from extreme compression fibre to centroid of compression
E c
E s
e c
e cu
= ,:::::
:::
:::
reinforcement.
modulus of elasticity of concrete.
modulus of eb.stici ty of steel.
concrete strain.
limiting concrete strain.
a = steel strain in tension reinforcement. s
e' = steel strain in compression reinforcement. s
e = yield strain in reinforcement. y
e* = difference in strain readings from DEMEC gaugeA and electric
f
f c
f' c
g
H
resistance gauges at same gauge locations.
= compressive stress.
= concrete compressive stress.
= concrete cylinder compressive strength.
= tensile stress developed by a standard hook.
= steel tensile stress.
= steel compressive stress. I
= tensile strength of concrete.
= yield stress in reinforcement.
= parameter in equation 'of parabola (Section A.5.4.1).
= horizontal reaction at top and bottom of column.
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h' = maximum unsupported length of rectangular hoop measured between
perpendicular legs of the hoop or supplementary cross-ties.
= moment of inertia of beam.
= moment of inertia of column:
k ratio of distance from extreme compression fibre to the neutral
axis/d.
L = anchorage length of reinforcing bar.
Ld = computed development length.
L = equivalent embedment length. e
M' = modified bending moment.
Mb "' bending moment applied to beam.
M ~ bending moment-applied to column. c
M = moment at first cracking. or
Mub = ultimate moment capacity of the beam.
M = ultimate moment capacity of the column. uc
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M = theoretical moment strength of a section. uo
m = number of ties in the joint.
N = column axial load.
Nb = axial load on column to produce balanced load conditions.
N = column axial load at the ultimate strength of the column. u
n ratio of modulus of elasticity of steel to that of concrete.
p load applied at the end of the beam.
P = load on beam at first cracking. cr.
P = the maximum load applied to the beam either during.one load run max.
or over the whole test.
P* = the load on the beam at which theoretical ultimate capacity of the u
specimen is attained.
P* = the load on the beam·at which first yield of the flexural rain-y
foroement should theoretically occur.
p = tension steel area ratio, As/ bd.
p' = compression steel area ratio, A~/bd.
pb = steel area ratio to produce balanced load conditions.
p' = ratio of volume of transverse reinforcement to total volume of s
core (out to out of ties) of a reinforced concrete column.
Pt = total steel area ratio, Ast/bd.
r = length of demec studs.
s = spacing of transverse reinforcement.
T = steel tensile force.
t = overall depth of section •.
u = bond stress.
umax = maximum bond stress developed.
uu = ultimate bond stress.
V0
= shear force carried by concrete.
vj = shear force applied to the joint.
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V = shear force carried by reinforcement. s
V = ultimate shear force. u
v = shear etress.
v = shear stress carried by concrete. c
w = density of concrete.
x,y = co-ordinates of parabolic equation {section A.5.4.1).
= distance from centroid to extreme tension fibre.
= general angles defined in text.
= deflection.
6u = lateral displacement of centre of gravity of a building at ultimate.
A = deflection at end of beam due to rotation of the column. Ov1
6v2 = deflection at end of beam due to bending of beam.
lly = lateral displacement of centre of gravity of a. building at first
yt~l.d,~ ·',
b = movement at end of demec stud due to bending of reinforcing bar.
¢ = rotation of column.
¢u = ultimate curvature.
¢y = curvature at first yield.
f'lliAPTER ONE.
INTRODUCTION
1.1 GENERAL:
The task of designing earthquake resistant structures has come under
close scrutiny during the last decade as the effects of earthquake loading
on stru~tural behaviour becomes more apparent. Recent observations1' 2 have
shown that many buildings, even though they have not been designed for the
purpose, have the ability to resist earthquakes without undereoing any rne.jor
structural damage due to the interent safety incorporated in tradi tiotlal
design mathods. How~ve1· 1 the fa~lure of many other huildines subjected to
Geismic excj_t.ation, and tl·e increase in construction of high-rise building$,
r,as lead to a demand for increased knowledee of the e;nthquake behaviour
of such structures in o~der to establish adequate seismic design criteria.
Prior to this, the design of structures insured tbat allowable stresses
were not exceeded in the elastic 1·ange. However, modern earthquake - r·esistant
structures are designed on the assumption that, although the large Jateral
forces induced by a major earthquake in the post-elastic range may cause
loc8.l overstressing, adequate ductility is available to dissipate the energy
of the earthquake motions. Thus it is the aim of the more recent design
methods to ensure t.hat sufficient post-elastic deformation can take place
to enable the structure to survive without collapse.
The concept of ductility in reinforced concrete entails much revjsion
of tl:e tredi tional design procedures wr·icr basically depended on conr:rete
for its 'strengtr·. It does r·owever, lead to more effird.etlt and economical
use of construction rna terials, and increased confidelJCe by engineers in tt>eir
ability to design structures able to resist tbe large post-elastic deform-
ations imposed by a severe earthquake.
1
1. 2 BEHAVIOUR OF REINFORCED t:!ONCRETE FRAMES:
The recommendations pertaining to ductility in reinforced concrete
structures were first proposed by Blume, Newmark, and Corning in 1961, 1
which eventually lead to a section in the S.E.A.o.c. 1968 Revision of
"Recommended Lateral Force Requirements" which states3 "•••••••••buildings
more than 160 ft. in height shall have ductile moment-resisting space
frames ••••••••• The necessary ductility shall be provided by a frame of
. II structural steel ••••••••• or by a reinforced concrete frame ••••••••••
Consequently the behaviour of reinforced concrete frames has been a topic
of considerable interest.
Reinforced concrete frames designed as ductile moment-resisting space
frames may, depending on tbe intensity of the earthquake, be subjected to
several post-elastic cycles throughout its duration. With each cycle, the
accumulation of damage in the failure region means a degradation in stiffness,
and since ductility is determined by the ratio of deflection at ultimate to
the deflection at first yield ~/Ay), this loss of stiffness tends to
increase the apparent ductility of. the structure. However the ability for
energy absorption, as indicated by the area under the load-deflection curve,
is generally not enhanced due to a loss in load-resisting capacity. Convent-
ional theories based on maintaining the ultimate strength of the structure
cannot, therefore, be forgotten in the need to satisfy ductility requirements.
Since energy absorption in reinforced concrete is best acheived by
yielding of the flexural reinforcement, care must be taken to ensure that
other stress requirements are not underestimated. If a "brittleu failure
occurs - that is, one due primarily to bond, shear or compression - little
or no ductility is available for post-elastic deformations and collapse of
the structure is a l:l.kely outcome. The beam-column joint is a region wher.e
shear and bond stresses are critical, and since the strengtr. and ductility
2
of the members cannot be achieved without an adequate connecting detail,
the performance of this reeion can be a decisive factor in determining tte
overall behaviour of the structure.
When a reinforced concrete frame is subjected to earthquake motions
it will deform as shown in Fig. 1. 1. Considering the region surrounding an
exterior beam-column joint (circled) as a free body, the forces required to
establish equilibrium are shown in Fig. 1.2 {a). If the assembly is rotated
through the angle a, then the specimen i.s located conveniently for testing
purposes, Fig. 1.2 {b).
1.3 SCOPE OF THIS PROJECT:
The original purpose of this series of tests was to determine the amount
of transverse reinforcement necessary to provide sufficient ductility and
energy absorption in the column region immediately adjacent to the joint,
by subjecting different specimens to high intensity cyclic loading. For
this reason it was necessary to absorb tl:e energy by yielding of the column
flexural steel, and therefore the ultimate flexural capacity of the beam was
designed to be greater than that of the column, but other requirements for
shear, bond and confinement as specified by the code were considered in tre
design.
The intention was to test specimens with differing amounts of trans-
verse reinforcement in the column, increasing the steel content from nominal \
ties until the required ductility was acheived. As results obtained during
the testing programme indicated that the joint was prone to fail before the
ultimate moment of the column could be attained, it became increasingly
obvious'that little satisfactory information concerning column ductility
could be derived from the tests until an adequate joint detail could be ~·
designed.
3
--1 I I I I r--t------+---........... ---.__;~...........,j..._.__-+---, I I I
~~~--~~--~~~~~~~ I I I I
~~------~r-~----~~~--~~~,
FIG. 1.1 RESPONSE OF FRAMED STRUCTURE TO LATERAL FORCE.·
H 0111111
p
\ (a) {b)
FIG. 1.2 TEST SPECIMEN
I I
4
+ EO
The emphasis of the test programme, therefore, shifted from invest
igating column ductility to endeavouring to detail a joint with the strength
to enforce yielding of the flexural bare. Obviously muoh of the difficulty
arose from testing specimens with joints unconfined by spandrel beams.
However, although exterior· joints such as these are not often used in actual
construction, the tests revealed weaknesses in the detail and gave indications
of stress distributions, which would not have been .apparent had the specimens
consisted of other than an isolated joint deta.il.
5
CHAPTER TWO
THE STATE OF THE ART
2. 1 PRESENT DESIGN PROCEDURES:
The concept of designing for ductility in reinforced concrete structures
was initiated by Blume, Newmark and Corning1 and its acceptance was such
that it is now a basic design procedure incorporated in the design codes
of the majority of earthquake prone countries. It is .well recognised 1 '4
that, should failure occur, the flexural yielding should preferably be
enforced in the horizont~l-rather than the vertical members. Therefore
it is stipulated5 that th~ ultimate moment capacity of the column must be
greater than that of the beam, where they frame into the same joint.
However even though the column is designed to be stronger than the
beam there are factors which in practice can greatly influence the relative
strengths of the members. The most significant of these is when the
direction of the earthquake is at 45° to the axes of the building. At
any beam-column joint the column is subjected to the full earthquake
effect while the beams need only resist the component of the earthquake
along their· longitudinal ·axes. This means that the column must be designed
more than 4o% stronger than tbe beams. If, in addition to this, the
variability in material strengths of both concrete and steel in the members
combine unfavourably, then it is obviously impractical to design the
column stronger than the beam for every situation. Therefore it is specif-
ied that,although the column should not attain its ultimate flexural
strength, it shall be provided with sufficient transverse reinforcement
so that if it does so, it will have adequate ductility to survive the
earthquake.
The importance of joint integrity during earthquake response is
basic. Should a joint fail, the capacity of all members framing into the
joint is reduced or eliminated.
2 .. 2 REVIEW OF PREVIOUS WORK.
The analysis and design of structures has become increasingly theoretical
due presumably to the continued sophistication of the· electronic computer,
the speed and accuracy of which is unattainabl~ by the usual design procedures.
However, owing to the assumptions and simplifications which must be imposed
to enable the program to be adaptable, the accuracy of the results obtainable
are .limited by the applicability of these restrictions. Because the pro-
parties of many structural materials,. particularly reinforced concrete, are
unpredictable. to the required degree of accuracy, there is a need for ex
perimental work t? be performed ·whereby the structure, or a model thereof,
is subjected to forces from a simulated earthquake in order to understand
the bebaviour of the actual structure8 Since much of the information re-
vealed by tests of this sort are obtained in the post-elastic range it is
impractical to perfor-m any experiments on existing structures.
The recommendations developed from the results of tests on small scale
specimens are not in many cases applicable to large building members6·
Therefore the need for tests on full scale component parts of structures
becomes evident and may, in some circumstances, provide the only reliable
source of information.
Mucr.. of the reeearcb wtich has been done on tbe ductility of columns
has involved testing of members subjected to flexure and axial load7. When
laree srear forces are also present the problem becomes more acute. This
is the situation at a beam-column joint where these three forces are all
present. Tbe work which has been done to determine the bel>.aviour of interior
beam column joints8 cannot be extended to apply to exterior joints because
of the special provisions re~uired -·in particular where no spandrel beams
7
frame into the joint to provide extra confinement.
The most significant work on exterior joints to be attempted was per
formed in the P.O.A. laboratories, a review of which is published by the
A.s.c.E.9. Results from this paper indicate that for the identical specimens
III and IV, which were designed with the column weaker than the beam, with
different column axial loads; the greater column load was more favourable
for attainment of the theoretical ultimate moment capacity. Even so the
ability·of the specimen to maintain its.ultimate capacity was diminished
signifi'oantly after the first post-elastic cycle. The fact that the results
from these two specimens did not appear to affect the conclusions to any
extent, even though specimen .IV did not at any stage attail'l its theoretical
ultimate capacity, indicates that the authors placed little emphasis on the
performance of these specimens. The otr.er test specimens and subsequent
tests10 showed that the code requirements for these beam-column joints are
conservative with regard to transverse reinforcement. It is apparent that
a joint, detailed according to accepted design practice, will provide
sufficient ductility and energy absorption to survive a series of post-elastic
load cycles.
Megget 11 developed the work on exterior joints further when he tested
three specimens with different beam anchorage reinforcement in the joint.
However the transverse joint reinforcement was insufficient to maintain the
integrity of the joint and brittle failures occurred in all three specimens.
Therefore it is obvious that much work is yet to be done in this field
to establish an adequate mechanism for resistance in exterior joints and it
is with this purpose that tre experiments reviewed herein have been under-
taken.
8
CHAPTER THREE
TEST SPEr,n/IENS.
3.1 INTRODUCTION;
The pl:ilosophy behind the design of ·the specimens is described in this
chaptar. Restrictions from c.ode requirements are outlined in an attempt
to srow the reasons upon wbicr m~ny of the decisions are based.
Theoretical predictions of t'be beh:9.viour of the specimens are also
formulated so tha·t, subsequently, a comparison can bE1 made with the actual
behaviour.
3. 2 DESIOJil OF SPliiCIMEN:
3.2.1 Overall Specifications:
The specimen represented an e:<terior beam column assembly with
only one beam framin,q; into the joint. Al tho'..tgh the dimensions of the assembly
.were determined to some extent by tre si.ze and load capacity of the existing
test rig12 ' it was considered necess':lry to test a full scale specimen to avoid
tre possibility of sr.ale effects6· Trerefore tl:e dimensions of tre structural
comvonents were a~ lare;e as possible wi t 1.• in the limi tatiorw o.f t 1·e apparatus.
As well as designing a speci(tlr;m in whin'' the ultimate moments of re-
sist3nce of tre ~olumns were less t~an that of tre beam, as dis~ussed in
section 1. 3, the detail reflected current trend in construdion in an attemrt
to provide information directly a:rplicahle to practical conditions.
The strength properties of the matt'3rials used throughout tl-e design
were:-
9
concrete f' = c 4,000 psi
steel fy = 45,000 psi
.3. 2. 2 Size and Flexural Reinforcement of Membertu
3. 2. 2. 1 · Column:
The dimensions of the column were the most important criteria when
selecting representative sizes and a 15" x 15" square column was considered
to be the optimum size.
The restrictions on flexural reinforcement in columns13 stipulates
t:':lere must be at least four bars for tied columna so that
o. 01 <Pt< o.o8
Taking this into account, the column was 15" x 15", with four 1-! in.
diameter bars symmetrically placed, giving p = 0.0206.
For t}lis column
= .370 kips.
The earthquake provisions for lateral confining steel5' apply only to
columns where
Nu > o. 4Nb == 148 kips.
Therefore the load N = 148 kips was the minimum load on the column through-
out the test.
The test specimen with applied loads is shown in Fig. 3.1.
However, with the intended load arrangements, since the horizontal ¢
reactions, H, must be equal, only equal moments could be generated in the
column. That is, from Appendix B,
10
11
12
t t 0
$ failure
" 6 1-0 +-' u cu
LL 8 10 >- 2 Load
+-' Runs -u
:::1 0 2 9 11 ....... ltl c 0 - 6 ttl -0 0::
l to failure
12
FIG. 3.2 LOADING SE QU.ENCE
=· M uc2 = M uc 1875 kip-in.
It was decided that the beam.should have an ultim~te moment
of resistance 20% greater than that of tr.e columns to allow for variations
in material strengths.
Required Mub 1.20 x 2 Muc
= 4, 500 kip-in.
The reinforcing ratio, p, was restricted13 by
~00 < p <0.50 pb y
o.005<P < 0.023
The beam width was 12 in. and the flexural reinforcement, both top and
bottom, consisted of four 1t in. diameter bars in a single layer. The depth
of the beam was determined by the required moment capaoi ty. Assuming a
steel couple to produce Mub = 4500 kip-in
M' "' A f (d-d') ub s y
d-d' = 4200 = 20.35 in. 4.92 X 45
t = 24.6 il)..
D:i.mensions of the beam were 12" x 25"~ witb four 1! in. diameter bars,
top Jnd bottom, giving p = p' = 0.018.
Anchorage requirements5 (calculated in Appendix B), indicate that an
ancrorage lengtr. of 32 in. is requj.red of eaor bar measured from the face
of the colurpn. However, problems arise in tr.e joint with separate nnchorages
for thei top and bottom bars, with 0ongestion in the joint and interlacing
of the bars. Altroueh these were by no means insurmountable problems, H
was decided· t'ha t l'unning the top :.md bottom steel in a continuous U t'hrough
the joint would provide the best solution and also test
12
the capability of a detail commonly used in N.z. construction. The anchor-
age length of the bars must transfer to the concrete both the tensile and
compressive forces from the top and bottom beam bars. In this specimen, from
the details given in Appendix B, the maximum expected bond stress, u, is
given by:
u ( f + f' ) D "" s s . 4L
= 1.378 X 41,800 X 1,22 4 X 40
= 450 psi.
A bond stress of this magnitude should be easily attainable in a well
confined joint. However, tbis anchorage detail was four1d to be one of tbe
reasons for deterioration in t·he joint during testing, and':'for · UNIT· 4 separc. te
anchorages for top and bottom bars were used.
3.2.3 Transverse Reinforcement:
3.2.3.1 Joint Ties:
The transverse reinforcement in the joint is provided to
resist both bursting forces from the concrete and shear forces.
Using i in. diameter hoops, five were required for confinement within
the joint. (see calculations in Appendix B). I
From standard design procedure for joint detailh1g 10914, six ~ in.
diameter joint ties are required to resist the shear forces. However because
of Ue conservative nature of joint srear requirements as evidenced by
previou~ tests9 ' 10 ' UNIT 1 was provided wi tb five i· in. di9meter ,joint ties
to determine tre validity of these ~onclusions. Trese ties were insufficient
to prevent deterioration of tre joint of UNIT 1, and so for UNIT 2 seven
~ in. diameter ties were proviiled, which represented 25% more transverse
13
reinforcement than was theoretically required. Because of the inadequacy,
also, of these ties, UNITS 3 and 4 bad nine i in. diameter ties which more
than satisfied the more conservative code requirements outlined in Section
8. 1.
3.2.3.2 Column Tiest
The original intention of the research was to provide only ' '
suffi0ient column ties to resist the shear force, and to increase the
number of ties in succeeding specimens until adequate ductility was obtained
from, the plastic hinges.
Sinoethe concrete was capable of resisting the applied shear force
only nominal ties were required,in the column. These consisted of* in.
diameter ties at 12 in. spacing. This reinforcement was provided for both
UlliTS 1 and 2. For mnTS 3 and 4 additional confinement was provided by
i· in. diameter ties at 2 in. spacing adjacent to the joint. The spacing
increased to 4 in. and eventually 8 in., further away from the joint, as
shown in Figs. 6.1 and 7.1.
3.2.3.3 Beam Stirrups:
The minimum shear reinforcement in flexural members means i in.
diameter stirrups must be provided at 6 in. spacing. In all specimens,
stirrQps were provided at 4 in~ spa~ing close to the joint, to fit con-
veniently between the demec studs on the flexural bars. The spacing in-
creased to the maximum spacing of 11 in. beyond the demec studs.
3.3 THEORETICAL BEHAVIOUR:
3.3.1 Elastic Range:
Much of tte infonnation concerning behaviour of the specimens in
14
the elastic range is determined from equilibrium artd strain compatibility
after the material properties have been established. The calculations are
presented in Appendix B with the spe~ific results for eacr specimen included
in the relevant chapter.
3.3.1.1 Flexural Crackings
Cracking first occurs in the beam then in the column. The
loads at which cracking should theoretically occur are calculated and the
effects are shown on the load-deflection relationships.
3.3.1.2 Yield Load:
Once f' had been. established for each specimen, the load at 0
which first yield should occur was determined. In fact, yield,whioh occurs
in the column flexural bars, was observed only in UNIT 4. The theoretical
yield load is tabulated for each specimen in Table 8.1 along witr the actual
loads obtained.
3.3.1.3 Rotations and Deflections:
The elastic rotation of the column is calculated for both the
uncracked and cracked sections and compared in Table 8.3. Deflection at
the end of the beam is :considered to be contributed to by rotation of the I
I
columrl and bending of the beam. This is shown on the load-deflection re-
la tionsh ips.
The theoretical deflected shapes at the peaks of the elastic load runs
are shown diagrammatically in each chapter and compared with the actual i
shapes obtained. Joint distortion, which can have a considerable effect on
the deflection of the structure was not considered in the theoretical pre-
dictions. Its effent then becomes apparent when theoretical and actual
values of deflection are compared.
15
3.3.).3 Steel Strains:
The strains in the flexural reinforcement are calculated by
elastic theory for the first run of loading in each direction and compared
with the recorded strains on the figures of strain distribution in each
chapter.
3.3.2 Post-Elastic Range •
.Although UNITS 1 , .2, and 3 do not yield in flexure, the response
to the applied load is similar to what would be expected and althougt not
strictly correct it is oon'venient to refer to the "elastic" and -"post-elastic"
portion of each load run.
3.3.2.1 Ultimate Load:
16
The ultimate loads for each specimen are calculated in Appendix
B, and tabulated in Table 8.2 for comparison witp actual maximum loads obtained.
3.3.2.2 Rotational Ductility:
For the design specimen the ductility available can be deter
mined from consideration of the rotations at ultimate and at first yield.
It has been suggested 1 that although the ultimate concrete strain is gen
erally taken as 0.003, for confined concrete a more realistic figure would
be 0.01. This means that provided the concrete is well confined the theoret
ical maximum rotational ductility fGctor attainable is giv~n, by .Appendix
B, as
However tre performance of the specimens, witt the exception of UNIT 4,
sl'owed that this 'is not aprJicable if the concrete is not sufficiently
confined. The ductility factors for post-elastic load runs are computed
using the method outlined by Bennett el al 15 and tabulated in each chapter.
3.4 EARTHQUAKE LOADING REPRESENTATIOK&
3.4.1 Rate of Load Application:
Statio cyclic loading was applied to the end of the beam by means
of screw jacks to simulate the high intensity reversals imposed by an 'earth-
quake. Although earthquake loadings are dynamic in character, it has been
shown16 that the strength and energy absorption characteriestics of reinforced
concrete members are increased witb increased speed of loading, and, i7 that
static tests can satisfactorily predict the structural response of reinforced
concrete structures to earthquakes. Consequently it appears conservative
to use static loading as a basis for testing seismic specimens.
3.4.2 Loading Sequence:
The load sequence applied was adjusted slightly depending on the
performance of the individual specimens. However the sequence took tte
gen~ral form as shown in Fig. 3.2. The initial runs 1,2, and 3 were to
establish the stiffness of the structure. in its uncracked and cracked states.
Runs 4 and 5 subjected the specimen to deformations which would be expected
during a major earthquake, which were followed by two elastic runs to deter-
mine the stiffness and general performance after the earthquake. The remain-
ing cycles were to demonstrate the response and ductility of tre structure
durinp a second major earthquake.
17
CHAPTER FOUR
UNIT 1
4.1 INTRODUCTION3
The overall performance of the first specimen is described in this
chapter and account is given of the behaviour and stress distribution of
reinforcing components of the structure. The way in whiob the stiffness
deteriorated under continued load applica·tion leading to eventual failure
of the specimen is also described.
4. 2 DETAIL OF REINFORCEMENTs
This specimen, desie;ned as described in section 3.1, had reinforcement
details as shown in Fig. 4.1.
The joint hoops were sufficient for confinement according to ACI
318 - 71 and were theoretically capable of resisting 83~ of the joint shear
force at theoretical ultimate. The column had only nominal ties outside
the joint region.
4. 3 GE}I'ERAL .PERFORMAN.CE:
The cracks in the joint, wlci~r appeared early in the loading sequence,
widened considerably, indicating large stresses in tre joint ties, even
during tl~e ini ti3l elastic cycles. Tbe widU and number of cranks increased
during subsequent cycles until eventually the cover concrete became ineffect-
ive.
Most of the joint ties reached yield stress during Run 2 and were
obviouBly inadequate to resist both the shear forces in the joint and burst-.
ing forces from the column core. Failure ~ubsequently occurred primarily
'18
! ·~
•
FIG. 4.1
A
I
SECTION C-C
v ~~·-o·-
SECTION A-A
1 ... -~
1
...
1---•'·0"
_oo~
... ~•h otirru o
4 ~0 baro
SECTION B-B
J---t'·t'
/.,0 ~··· _, tioo
P. /..-QA
(/ // h t-
r-1" l
") l'"n ' ]'4 olle baro ., 3 otirrupo
SECTION D-D
REINFORCING DETAIL FOR UNIT 1
19
in the joint regiono The inadequate joint shear :reinforcement allowed tbe
diagonal tension cracks to widen, leading to degradation in tr.e joint stiff-
ness and the moment :resisting capacity. This premature failure meant that
t~e flexural bars did not yield and the specimen attained only 71% of its
computed theoretical ultimate flexural capacity.
The distressed nature of the joint after Run 5 indicated t'tat little
infonnation would be provided from application of further elastic cycles and
so, during Runs 6 and 7, tr.e specimen was taken to its maximum deflection
in eaor direction before the test was terminated.·
4.4 BEHAVIOUR OF FLEXURAL REINFORCEMENT:
All strain measurements were taken by DEI\IEC gauges as explained in
Appendix A.
4.4.1 Column Bars:
Apart from inconsistencie$ resulting from the effects described
in section A. 5. 4, the recorded strains in the bR.rs were generally consist-
ent with theoretical predictions for cyclic loading (see Figs. 4.2 (a) and
4. 2 (b)).
Strain readings on tre more reliable outer column bars (the two furthest
from tbe beam) indicated stresses of approximately 35 ksi in eac~ bar at
maximu:n load. This stress must be dissipated within the ,jo.int, by bond with
tre concrete, over a distance of about 12 in., representing a bond stress,
u, .r>;iven by Df s u = 4L
= 1. 12~ X 32000,
4 X 12
= 820 psi
20
-- t- f --, I I I I 13 ;-
\
t ·-· t I. i
' i
I I . l I
I !
I ' I -t- ..
29-
:
:»
-ey~ comju·euion
-tooo 1000 microstrains
13
17 18
21 22 I
25 26 l 29 :r 33
I -+
strain gauge location
-f •
1 ·-I
_,. -o -a -+
14
·-Run 1 "-Run 2 o-Run 3 &-Run 4 +-Run 5
beam flexural
. . I .
21
. I . I bll:ll'lll .
. . I . , ·-___ .~.,...._ -I I
t
t~nsion 'e 2000
FIG. 4·2 (a) THE DISTRIBUTION OF STEEL STRAINS IN COLUMbl FLEXURAL BARS IN UNIT 1 (FOR DOWNWARD LOAD RUNSJ
For strain gouge locations see Fig. 4. 2(a)
I
i· I I + . -· L--
• i I
~---
-!-I i-- ;--'
-~----+- --1
-t I
1' l
-L ---; I t--: . i
j_ i I 1
+ I l : -eul . 1. ,
I _J_
!
"; compressaon tensaon · ......-t-r ---1000+1 -+1 --+--·-t---r,doo--+--
microstrains
-~---+--1 I
18-+ -+-
22
FIG .4.2(b) THE DISTRIBUTION OF STEEL STRAINS IN COLUMN FLEXURAL BARS IN UNIT 1 (FOR UPWARD LOAD RUNS]
The maximum bond otress s·: ecified by the M:I for ultimate atrength design . 13 is 800 psi ' which is not difficult to acheive in a region which is well
confined. However, these bars were not adequately confined to witrstand
tr.e S)litting stresses induced by the cyclic loading, and vertical cracks
down the back sides of the column during Run 4 gave evidence of parti3l
bond fan ure.
4.4.2 Beam Bars:
The strain distributions for these bars, shown in Figs. 4.3 (a)
and 4.3 (b) were as expected with the steel providing the tensile force
and the majority of the compressive force beinc ·resisted by the concrete.
The readings of strain taken in the column at gauge locations 37 and
42 were obtained from i in. diameter studs 3 in. long, which were too
flexible to produce consistently accurate results as is evident from tre
distributions shown at these locations.
4.5 BEHAVIOUR OF TRANSVERSB REINF'tlR~MENT:
Strain measurements were again taken by DE~AE~ gauges on tre ties, Y>ow-
eve:r only a genernl idea of tre be'~-.aviour of the ties ~ould be deduced since
tbe aecuracy of tre strain readings was influenced by tr.e bowing of tr.e ties,
as explained in section A. 5. 4. 1.
4.5.1 ~olumn Ties:
The ! in. diameter ttes provided only minimal resistance in shear
and confinement, however for the msjority of the test when the failure was
confined to t.he joint, they were rwt required since the concrete resisted
all the :Jl:ear. Once cracking exte11ded ouhdde the joint region, the
irJade,luacy of tr~ese ties was clearly demonstrated. Tbe level of strain
mainly reflected the diversification of cracking :i.r1 the column, since
23
37 38 39 40 41 42 -· . ·-Run 1 strain -~~ oc-Run 2 gauge -o o-Run 3
location -a &-Run 4 43 44 45 46 47 48 -+ +-Run 5
37 38 40 42
column beam
-.500
- -- r---- -1000
FIG. 4.3(a) THE DISTRIBUTION OF STEEL STRAINS IN BEAM
FLEXURAL BARS IN UNIT 1 [FOR DOWNWARD LOAD RUNS]
24
25
For strain gauge locations see Fig . 4. 3 (a)
# Top 10. Bars d--.'--·-- c
.2 -500 Ill Ill
- . ===-=-. ~ t
~ 0 u
37 38 3~ 40 41 -42 Ill c::
column I beam ·e .... Ill
43 ,.
44 45 46 47 48 e .~ E
I I c::
-~ Ill c:: 4.1 +'
500
1000
FlO . 4 . 3(bl THE DISTRIBUTION OF STEEL STRAINS IN BEAM FLEXURAL BARS IN UNIT 1 (FOR UPWARD LOAD RUNS]
26
FIG. 4.4 UNIT 1 ON LOAD RUN 6
FIG.4.5 BUCKLING OF COLUMN FLEXURAL BARS
tl-e readin&; generall;y sYowed at least yieJ d strain wrerever a cr·ack crossed
the gauge location on a tie.
The inability of ttese ties to prevent buckling of tbe column f1exural
bars in tte compression region, As s~own by Figs. 4.4 and 4.5, indicated
that they would be tmsatisfactory if required as lateral confining steel
in the column.
4.5.2 Joint Ties:
The strain readings on ttese ties did.not reflect the situation
for individual ties to any decree of accuracy becaune of bowing of the ties.
Tbe relative Ilarticipation of eacl1 tie c!m be determined, 1-·owever, from
tr.e measured strair:s crown in Figs, 4.6 (a) :md 4.6 (b). Tl-e strair, diE<.-
tributions indicate that the ties do not all resist the bursting and s~ear
forces equaJ ly. The eenero.l trewl oF' tbe upper ties beix1g subjected to a
C D I I 1
I 2
I 3
I _.
strain gauge locations on joint-· ties
-·---·-Run 1 -~---~-Run 2 -o---o- Run 3 -A- --A- Run 4 -+- _;_._ Run 5
Average· of Readings C · and D
I .
27
I 5 ---------------
Back of Column 1000 3000
mic:rostrains
1000 2000 3000
.ey I
4000
-4000
I I -------- ----+i _, ____ _ ------· ------·--t··-.
. I I \ . I '
I
--+---i-- 0 ---0- ---~-
--+-;}49 ~\t---·-0/-+ , ___ --~----~ I ----- ----~
I
5000
Load) Up
FIG. 4.6(a) THE DISTRIBUTION OF JOINT TIE STRAINS AT BACK OF COLUMN IN UNIT 1
6000
Readings A
I s --- ! ____ --tp ---· -a{.- --- - -- . ----, ,, I /P,• \
~ ' I '\j·\~:-u J -..... I -~ -- • . --\- I ---- ~V '\.A -~
I ~, i'h l I ...._ • '\ " - -
' - i ~A--j ~~1~1- I ~~-- I /,. iE?:9 l I 1 I _ f
r "' i II I I I -6 -· ~ - ----- ~-- - jl ·"f_,·'{\ i
. ... \ I
-- ·--+- ___ 'X -·- .... - - .. ---- --4 I .
I -------.
I I 2
I I 3
I I 4
I I 5
4000 3000 2000 1000
microstrai IU Side of Column
3000 2000 1000
&y. I
-0 J -0·
I I. 1' l·l -\- l+2 2
\ - \ i .. . i -~--+ . ) - I 4-3 3
. I I I
~f ~~ ~+4 4 !
-! _i..,, · : .L. -1 +s 5 I I l
I " '&. I' "t. I '0. L~
"l--~-~~~- ~-l-). + -
I U __ . L ... {~/1 ______ L
1000 2000-
microstrains
1000
ley
I \ I_-+.o . -0---
2000
1 \ -l~'-" i -- - \ ' . - ' I , --%tc·,T·J·-
I 'I ' . ' /rt®l- ~--~- I I !
i I ! I . - -f·-I . I f. -0--- t·-o -- -+ -- - I 1+- i •
I
Loa~~ Down
Loa~ Up)
FIG. 4. 6 (b) THE DISTRIBUTION OF JOINT TIE STRAINS AT SIDE OF COLUMN IN UNIT 1
tv 00
greater amount of bending,. for downward load, than tbe lower ties would I
be due to them either resisting a la;rger force or having less restraint for
the imposed force. This is caused by the type of failure which occurred in
this opecimen, and results in the opposite distribution for upward load runs.
r;.'he actual strain rendings at the back of the ties, as srown in Fig.
4. 7 (a) demonstrate tbe symmetrical curvature of each tie caused by tl1e
interr;al forces in tre column core~ The strain along the sides of the ties,
shown in Fig. 4. 7 (h) indicat.e a difference. in curvature, as explained in
section A.5.4, rather than a non-uniform stress along the tie.
Figs. 4.8 (a) and 4.8 (b) show how the strain in tbe ties increases
witb increase in applied load. for each load run. The effect that the bow-
ing of the ties has on the readings is clearly shown in Run 1. At 40%
of the theoretical ultimate load tbe bowinr- of the ties appeared to be
negligible, the strain readings being caused by minor diagonal tension
cracking in tt.e joint. As. tbe cracks openr::~, the ties picked up more strain
untH eventually, due to a combination of >1; 1·ds, and internal cracking caus-
ine, expansion of the column core, tbe strdn readir;i?.'S increased considerably.
4.5.3 Beam Stirrups:
Al trough tl,ese were instrumented in this specimen, only minor
flexural cracks formed .in t'be beam resul tin-s in the beam stirrups being
virtually unstressed.
4. 6 DEFORII'u\TIONS:
Deflections and rotations were measured by means of. dial gauges as
described in Appendix A.
Load\ Down~
--=:-l--- ---t.~----· ...........
I ................... _
- ~-*~ ................ ·---·~----: . ----x---·-i -·-·-·-
I f= -- ---+-------·-----------·----·--)(----x-
-·-·-·-·--
! I ---:-------
->t--~- -.. _ _ --; * ::::n ::...~------' -><-
I
-~· """""',..._.,.,....·~·-____ ..,_ . ---~-.k~-
1
9 10
li)
c cu L. +" li)
0 L. u
E
-·---·-Run 1 -.:---)(-Run 2 -o-- -o- Run 3
3000.
2000
1000
3000
2000
1000
3000
2000
1000
3000
2000
tOOO
Load
-·-·-·~~---- -r-----r---- -1 . ----r---,---~--4-..::-
-. ·-r·-·-l-·-~ -- i -. - . ---j - -
I
---· ·- ---l----·-·--r·-·--- I
. ~, ___ _ I
-------t----+--1 ---1~--=+~-
_- ·-+·--· _!_-.-_ -t----i- .
9 10
FIG. 4.7 (a) THE DISTRIBUTION OF STEEL STRAINS ON BACK OF JOINT TIES IN UNIT 1
30
-~1-------c--· -+,, '
. . ' I -'- [ ___ ' I
. ! ' I
-~-::::-·~1-·----- ~- --~-...:;:..:::4~ ...... , -- .
-~--=-.:: =F
II)
c ·-ro L. +' II)
0 L. u
E
3000
2000
1000
3000
:woo
1000
5 6
3000
2000 ---~+------+-----~ -·-t-·-·-·1-·-__ :_t---: ~-=- ~t::: __ i- ---1-
3000
I
2000
1000
··-...... ~,, ..
-·+·-,-1 ' ! I
FIG. 4. 7 (b) THE DISTRIBUTION OF STEEL STRAINS 0N SIDE OF JOINT TIES IN UNIT 1
31
32
I I'
t, Run 1 I'·
('·
;;'" ',,,''"'-,
ey -·1 :~.~ ·,, '· ' .....:.. . . ..,....,..."-_ ·-
t' " ',, ', ·<:Y
'~"' ·, . ..,_
~.,:;<<'" i'-<Y
-~"\: ~~~ i:--yy ~· '7p~
Back of Column _,
0.2 0..4 1.0 0.6 0.8
. Range of Average C and D Readings
0 J 1-I
Run 3 ;"' 0
!;'' ' ' ~y .A." _.., 0 ', "
f<>~</' 0 /..' r:··<·,"
~"· ~~ ey t0-.:~ ... -·-._, ~· -· t-·- ·-"<">"~ <~~~
0 ...... ' ~y
0
'%· Pu
~--~r---~F-----~----~~~100
I
. -·---~-j------J---------<-~-4 50
~J I
Q2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 0.8 1.0
FIG. 4. 8 (a) T,HE LOAD-STRAIN
IN UNIT 1 AT
RELATIONSHIP FOR JOINT TIES
BACK OF COLUMN
.. -· .. -----/'------A 8
Side of Column
0.2 0.4 0.6
33
2000~--~~---+-----+-;~-r----~
~ 15 F~~·=·=-4· ----'·---· -+-----~_,___-+--·- 00
0.2 0.4 0.6 0.8 1.0
Range of Readings A and B
fiG. 4.8 (b) THE LOAD-STRAIN RELATIONSHIP FOR JOINT TIES IN UN IT 1 AT SIDE OF COLUMN
4.6.1 Deflections:
The deflected shapes of the specimen at the peaks of the elastic
runs are shown :i.n Fig. 4. 9 and compared with the theoretical deflected shapes.
The column does not deform symmetrically about its centre~line because of
the difference in stiffness of the upper and lower columns caused by more
cr·ackn forming in tl:e regj_on of lower axial load.
4.6.2 Moment-Rotation Relationships:
The moment-rotation relationships for tte column, both above and
below the joint, are plotted in Figs. 4.10 (a) and 4.10 (b). The rotations
were measured over a length of 15 in. from the face of the beam.
Fig. 4.10 shows the rotational ductility achieved during each cycle.
However because otter components of tr~e structure, such as the joint and
the beam, also contribute to the deformation of the specimen, this re
lationstip cannot be used as a measure of overall ductility.
The rotation recording apparatus had to be removed after Run 5 due
to e:x:ce ss i ve deformation of the frames arou.nd the column, and therefore
the rotation could not be determined during Runs 6 and 7.
~. 6. 3 Load-Deflection Relatiom3h ip.:
Tbe load-deflection relationship ~ts shown in Fig. 4. 11, gives a
truer representation of the du~tility and energy absorbing capacity of the
strunture. Since tt':e deflection was measured at the end of the beam,
deformations caused by beam and colu:nr1 rotations and joint distortion v1ere
all taker; into account. The ductility factor obtained during each load run
is shown in 'l1able 4. 1.
The loss of, stiffness of the f>>ecimen due to crackilig, and bond failure
34
35
1.6
1.2
----theoretical 1.0
---actual 0.8
~---------------------------------4~- ~
0.2 0.2
Deflec:tion ( in5.)
FIG. 4.9 DEFLECTED SHAPES OF ELASTIC LOAD
OF UNIT 1 RUNS
., II
'
0.8
1.0
1.2
1.4
1.6
1.8
2.0
AT
.... \J 0
~ Q
PEAKS
-·Ill
I .. ><
-: 1500
I :I
--· ·- ~>1000 -
]
Rota tiM IR ado.l
,!'--l-~·-+ ... ~. ~I
-----..
(II) COLUMN ABOVE THE JOINT
FIG. 4.10
~ r-----
Rota1ion 1Rod:1 ~ -·03 -.02 -.01
I
I +------- -1000 ~
li .. ·----+-
-~- -----+ -j-1500! I ·--c
-Mu 1 l ; ....._ 1- - - - - !- -- - - Ill
I - - --- -2ooo
-+--·
lbl COLUMN BELOW THE JOINT
THE MOMENT-ROTATION RELATIONSHIPS FOR UNIT I
I
·r-1
36
"' "'
"' "j ( sd!)i l peo1 p
JeMd
n
~ 7
-t-
-t-
1 --ti-+-i --+~+--i' -------+-1 -
:' \
\ \
:. ! '
: I '\.
! ~
I i
i I
I I
I i
II I
; I
! -;; "t-l--.J-""c-~---lf---...... :--.~ +
-+
-+
+---t-!I -
-+
:
i I
! ,
.!: , ~r-r--
~--+---~~---r---+----+---+' ;f+---+---~~~f-------1~~~--~
t-; +
I l ~ ! ~-i J Y
i-
1---i +-
. . l
i ..
" -j
f ---+ ~
~~~· -----· : -~-·-
~ j
T
i !
L--+------, i--
-~ .• _
_
.. . +
J__ +-----1--l
a: 0 LL.
a. J: If)
z 0 1-
<
...J U
J a:
z 0 1-
u UJ
...J LL. U
J 0 0 <
0 ...J 37
of the flexural bars, is demonatrat.ed J.n Fig. 4.11 after application of
R.un 4, the first run into the post...-elastic~ range. The load resisted during
Run 6 represents a loss of more than 40% of the load resisted during Run 4.
The theoretical bilinear load-deflection curve is shown for comparison
in Fig. 4.11 an~ the effect of stiffness degradation is tabulated in Table
4. 1.
TARLE 4. 1 Performance of illHT 1 During Load Cycling •
Run· Maximum Tin ax Ductility . Average Load ~X 100 Factor % t Pmax. Pu·' Stiffness
(kips) (%)
1 23.9 69.7 - 47.8 2 24.3· 70.8 - 54.9 3 20.9 61.0 - 35.9 4 24.0 70.0 7.0 36. 1 5 18.8 54.8 9.0 1.9 6 14.0 40.8 13.7 4.6 7 13.6 39.7 15. 5 4.3
t Expressed as % of the theoretical stiffness.
4. 7 CRACKD\'0:
Flexural cracks first appeared in the beam as :predided by t1•eory at
* P = o. 25 P • However, a:part from tl,e cracl< at tl:e .iunotion of t1·e beam wi tb u
tl:e column, Uese remained minor cra<:'ks influenced onJ.y by tte strain in tbe
beam flexural bars, generally closin.'~ on reversal of loading. Cracks in the
tension regions of the column above and below the joint became visible at
* 1) = 0 • .40 P u. More than 5o% of tl::e tLeoretical ultimate load had been applied
before diagonal tension cracks formed in th:: joint region. To some extent
the configuration of tr..e cracks was influenced by tbe holes arourHl tbe studs
for gauge points on the reinforcement. However the general angle of diagonal
t · k ho by F' ~ 1° is steeper than 45° due to the pre-enslon crac.s, ass. vm 1g. t• ... _,
senoe of axial compression affectin(: the direction of principal tension.
38
It\· 1,
) I;~
• I ~-j·,r")t
FIG. 4.12 UNIT 1 ON LOAD RUN 1
FIG. 4.13 BACK OF JOINT IN UNIT 1 ON LOAD RUN 6
FIG. 4.14 UNIT 1 ON LOAD RUN 4
39
Vertical cracks down the line of the outer column bars both at the back,
Fig, 4.13, and sides of the colum1 indicated the tigh splitting stresses
in this region. The cracks in the side of the column which followed the
line of these bars eventually connected with tbe diagonal tension cracks
to form tbe main failure cracks 3cross tr:e joint, as shown in Fig. 4.14.
4.8 THE FAILURE MECHANISM.
From the observations made during the load sequence and from the
apvearance of the specimen at failure, Fig. 4.15, it is apparent that the
joint ties were insufficient to provide both adequate confinement and
shear resistance.
The strain readings in the.steel, and the crack pattern, indicated that
tba beam was attempting to rotate independently of the column, the joint
ties being the conn0cting links. On downward cycles tre beam appears to
rotate about the base of tre beam-column junction, pullir1g out at the top,
therefore subjecting the. upper ties to a e:reater strain than tbe lower ties.
The reverse is tYe case for upward loading, t'rereby fiving tr'e strain dis
tribution in tr.e ties as shown in Fig. 4.6 (b).
Breaking up of the concrete in the joint lowered its ability to resist
the applied shear force, which meant that tle joint ties were then expected
to take a larger proportion of the joint srear. However tl:e distribution
40
of strain in the joint ties shows trat not. :1ll the ties work effectively
during eaob load run. This led to yielding of the ties which allowed cracks
to widen in the joint region. The diagonal tension cracks opened sufficiently
to promote a shear failure across the joint as represented diagrammatically
in Fig •. 4. 16.
0 () ('
0
0
r\ \ \~\
0
\ /
FIG. 4.15 UNIT 1 AT FAILURE ON LOAD RUN 7
F-= _:::_::.::::-= = = J
·.~::->--
cot umn bars--buck ted in compression
-~ 2 joint ties crossing crack
~~major shear crack
FIG. 4.16 FAILURE MECHANISM OF UNIT 1
41
CHAPTER FIVE
UNIT 2.
5.1 INTRODUCTION:
The behaviour of the second specimen is described in this chapter with
particular reference to the strength of the joint itself, and the improve-
ments shown over the strength of UNIT .1.
The majority of the results are presented in the form of graphs, to
facilitate comparison of responses at different load levels.
5. 2 DETAIL OF REINFORCEMENT:
To improve both the confining capability and the shear resistance of
the joint, seven ~- in. diameter ties were ~1rovided within this critical
region, in an attempt to alleviate the stress in each tie, caused by the
tendency for unequal stress distribution during different cycles, This
represents 25% more transverse reinforcement than is theoretically required,
The otrer reinforcing details remained as specified in section 3.1,
and are shovm in Fig. 5. 1.
5. 3 GElf.ER.AL PERFORMANCE :
During the initial elastic cycles the behaviour of this specimen showed
similar tendencies to UNIT 1, except that tr,e less intense diagonal tension
cracking in t1.,e joint, Fig. 5.2, indicated the effect of the increase in the
amount of transverse reinforcement. Less strain in the joint ties supported ' .
the belief that the specimen was resisting the applied load more effectively
than its predecessor, however the fact that the majority of the cracking was
-:lonfined to the ,joint region indicated that this was again going to be the
43
l I I 'I
cV .; \lc .t!2!.!:..: c:oveir = 1-a to <all main stc~l
.i B • A
I I 10' -e.!t'
~ ~ 2 otirruM . d>• ,;,,.~ •• 11"<-<.
~ L
or~ -~ D
' ---,-
L 1---1'-3' ~ A
J L....ee--1·· o·-·--:' --t'·O~
b. ~ -~ ~ ~ -..r--.4 *to bare
po~ "-....4 litto boru
"' ... I r---eolumn
I beyond
I I I ~ ' I
::: ~3 otirrup& ;. I I ;. '--<1'3 otirru •
4 '*to baro 4 ¢4'10 barB
SECTION EH3
SECTION A -A
j _,
J~~~~ SECTION C -C SECTION D-D
FIG. 5.1 REINFORCING DETAIL FOR UNIT 2
FIG. 5. 2 UN IT 2 ON LOAD RUN 3
FIG. 5.3 UNIT 2 ON LOAD RUN 4
FIG. 5.4 UNIT 2 SHOWING SEC. VERTICAL CRACK AT FAILURE
44
weakest component of the structure.
Most of the deterioration of the joint, botr visually and structurally,
became apparent during Run .4, the first j)Ost-elastic run, following similar
lines to UNIT 1. The vertical cracks connected with the diagonal tension
cracks in the joint, to form the major failure cracks. Cover concrete was
forced off, particularly around the joint, providing negligible load resist-
ance after the elastic cycles.
Although the specimen exhibited better resiliei:lCe than UNIT 1, by
sustaining its load over a greater number of cycles, the maximum load re-
sisted was still only 75~ of the theoretical ultimate load - an insit,.rnificant
improvement over UNIT 1. A bond failure of the beam flexural bars in the
column appeared to be the main cause of the loss in load resisting capacity.
Runs 6 and 7 were imposed on this spe~imen in an attempt to attain
* 0.75 Pu' ratl:'ler than a ductility factor of 0.75. It was soon realised that
this could not be achieved. The test was terminated after Run 9 when the
specimen could not resist a significant prcportion of the treoretical
ultimate load.
5. 4 BEllA VI OUR OF FLEXURAL REINFORCEMENT:
5.4.1 Column Bars:
Apart from the occasional inaccurate reading, strains were generally
consistent with theoretical predictions. The distribution of strain in the
column bars is shown in Figs. 5.5 (a) and 5.5 (b). At low beam loads the
bars 1n the column may be in compression over their whole lengtr., indicating
the effect of axial column load.
Vertical cracks down the side of the column on the line of the outer
culunm bars again indicated tl::e imrninence of bond failure, which became
45
15 16
19 2
23 24
27 28
31 32
strain gauge location
.
-j--
46
·-Run 1 _,. ~~.-Run 2 -o o-Run 3 -A tt.-Run 4 -+ +-Run 5
lhl·~· 'i'~·72\ .... ~~~~----,~ ~r \~~ -~-r -
7 &· 1.1 I(. . /J.
. I beam
bars;; .1
flexural
. 'L ;;----+ ---
I I I
--~-r--~-4!--~i--~~~y 1000
compression 1.Gnslon
-1000 1000 mlcrostralns microstralns
FIG. 5.5 (a)
FLEXURAL THE DISTRIBUTlON OF STEEL STRAINS IN COLUMN
BARS IN UNIT 2 [FOR DOWNWARD LOAD RUNS]
47
For strain gauge locations see Fig . 5. 5(a)
~+
FIG . 5. 5 (b) THE DISTRIBUTION OF STEEL STRAINS IN COLUMN FLEXURAL BARS IN UNIT 2 (FOR UPWARD LOAD RUNS)
apparent as early as Runs 3 and 4 in the load sequence. From observation
of the nature of the bond failure it was evident that although the bond
stress was reasonably large, it was the application of reversed loading
whiob was detrimental to bond performance. The slip between the concrete
and steel during Run 5 was large enough for the concrete to be forced
against the demec studs, so tbat readings of strain intbe outer column
bars were not meaningful.
Eventually, once the cover concrete bad been dislodged, the column
bars buckled in compression in the region above the joint due to inadequate
restraint from tre transverse reinforcement.
5.4.2 Beam Bars:
The strain in tbese bars showed a reasonably consistent trend
at the various load levels for different cycles, as shown in Figs. 5.6 (a)
and 5.6 (b), where variations in strain at different locations show
the effect of cracking in tbe particular region. Although the readings
from the demec studs in the column (locations 77 and 85) are obviously
suspect, there appears to be a tendency for the stress to be dissipated
from the point where the bar enters the column.
The increase in strain during the post-elastic range of Run 4 is pre
sumably ·caused by the greater deflection·ar-plied at tte end of tre beam.
The increased stress in the bars did not, ~'owever, produce a greater moment
of resistance in tr.e beam since tPe measured load is virtually unchanged in
this ;range.
The anc1-.orage of the beam b:trs in tte column was inadeq_uate for tl,is
specimen once the joint began to deteriorate, and at failure, wr:en the
cover concrete rad been dislode;ed, it was obvious that bond failure had
occurred around ~he outside of the bend of the beam flexural bars in the
48
strain gauge
location
/
' .__.j.
77
column
v
77 78
e 86
v
beam
79 80 81 82
-ff1 88 89 90
79 80
Bottom
-· ·- Run 1 -~ x- Run 2 -o-o- Run 3 -4 &-Run 4 --+ +- Run 5
1000
500
Ill c:
81 82 I'll c.. .... Ill 0 L.
89 90 u
E
I I ll c: ~ I 0
--==lf Ill =: ll Ill
-=>} 4J )( L.
J __ -- -- .. .! a. E -500 0 u
#10 Bars
I i --··r . ·-+ ---·--+····-·-------·---- -1000
' FIG. 5.6 (a) THE DISTRIBUTION OF STEEL STRAINS IN BEAM
FLEXURAL BARS IN UNIT 2 (FOR DOWNWARD LOAD RUNS].
49
For strain gauge locations see Fig; 5.4(a)
--+-'-------t-------1-~---+-1---t--l -+- -1000
Top · ~~' 10 Bars
c: ·-f-----+---·2 -500
Ul
column beam 85 86 87 · ee 90
I Bottom ~~'10 Bars
- -. ::::::::::--. ..:::::::.-. ---+-----+-=._.- . =f.- ~=t== ~=
~ Cl. e 0 u
e
1000
1500
Ill c: ·~ Ill 0 .... v .E
FlO. 5.6(b) THE DISTRIBUTION OF STEEL STRAINS IN BEAM FLEXURAL BARS IN UNIT 2 [FOR UPWARD LOAD RUNS]
50
joint (see Fig. 5.16).
5.5 BEHAVIOUR OF TRANSVERSE REINFORCEMENT:
5.5.1 Column Ties:
Again tre column ties proved to be inadequate. During the elastic
cycles when shear was the major consideration and the extent of cracking
was as stown in Fig. 5. 2, the strain readings indicated a maximum stress in
the ties of 30,000 psi. However when Run 4 was applied the cracking pro
pagated above the joint region (see Fig. 5.3) and the strain in the ties in
this region increased by 50~ into .the yield range. The ties below the
joint yielded on Run 5.
A vertical crack down the centre of the column, shown in Fig. 5.4,which
opened during the post-elastic cycles gave further evidence of the inability
of these ties to restrain lateral expansion of the column.
5.5.2 Joint Ties:
Tl-·e effee'lt trat bowing of the ties had on tre strain readings
was not realised until after tr.e testing of UNIT 2 and trerefore the DEMEC
strain gauge readings are subject to .the S<t:ne inaccuracies as UNIT 1.
Considering the strain distribution on the back of the ties, as shown
in Fig. 5.7 (a), the vast difference between the strain readings in the
elastic and post-elastic cycles suggests that the expansion of the joint
concrete really takes effect after the elastic range, with very little
expansion before then. The readings at the same load for successive cycles
show consistently higrer values, inC:icatine; some permanent strain in the
hoops or, possibly, a small amount of permanent bending. The trend for ·
the upver ties sr;owing larger readings on downward load runs was again
tLe case.
51
strain gauge locations on joint ties
-·---·-Run 1 _,. ___ ,._Run 2
.....,o---o- Run 3 -A---t.- Run 4 -+---+-Run 5
52
Average of Readings C and D
c D '1
2
J
-4
1
- -- ____1\,r----...L
Back of Column
1
2
3
5
s 7
I
1000 3000
2000
-I I I .J I
1 1 1 r,b1~--Load \ : i , I , · Down~ , 1 _! 1 ~
I I ' I ..+-
1 I iL@-i -·I --"' ?t./ .
~, ~ - :::-~ ---+t." I J-- ' I I
-A -1 : I I ' j I '
5000 7000 9000 11000 13000
microstrains
FIG. 5. 7 (a) THE DLSTRIBUTION OF JOINT TIE STRAINS AT BACK OF COLUMN IN UNIT 2
Readings A I I ~I . .
- I i ; I I ! I ! I -==---~: : i ~p,· I .1 I J ~ ----~----'--- _ ____ ~ u I , ~r b~ ~ l I ,.._- - - -- -- - I . \ ' 38, ____ _;__- l-- _-:---L- r--- i ,- --r·-------~·72-~-. ' ' - - . ---f.;- -- - - -- - I . I I\.'\]\~\ . ~-- ! ---~+' _: -4- : - ;- ·: ~- ~-~1~~-, . ; I _..t. . \\ \
-+--- -t------t--_;__--r-----,------, ~ ........ -r ! +I . - I •'ii\\ --+---~~ _ : ~,"" . T- --+ 1 ~ ~~~· ! i - ~-~-+-a1-=----+--~-- -- I i L·,ji\'\ -t •-~-t ; • · i T --t ----.---r-. __lUlU , i ; I ! [ ! I f.7.i'i:J1il
l : 1 ' i ' l I~~~~~ I I ' ' I
1 I .J.IIlit
I i I i l I I : 1
1
i . ! I I I I I i I I '
13000 11000 9000 7000 5000 3000
microstrains
14000 12000 10000 8000. 6000 -4000 2000
1 1e . ')/ i I • :
l' L I __ l_0-0 · -- ---- f I I
. @I,~~; ·,~ ·=:r-="'~=--=-==--~=o.::e+~~ I I _L -----r-fi \\ I - i I
' I I ! I • • c +' ' ' ' - --1'-· ·-- ' ' ; " + - - --L ~·- --.., __ . -- ' . -0~ + 1=--1=- ------r. -- I-- --~- -+-:.::l::..:::."'t.+-J-::::+-+-·-. , I - --~ ; : it' -I :::f---~.:::-~ I I l 8 ~ I ; ' ' t -- -..- ' I . -~-' I I ------r------j- • _ -r ..... r--, , m' ___ L __ -·-'----------- . : : . __.....,.. ---~ --- --, I . H t --· I : > - +-1:;,.+ : !
! i . ..;..+"'"""--=F---. -- ..,- ..,_.! 1 -· ~ - --+-- ' 1 ' ··"·-J-' . - -+--•-- , , , iJ I ~..:::--1- ' . ....,---k-+ , . ' I I 1 • -o-' -; ' -' ---· _ _,- ; ' ' . ----+ ---,+- I ;.-- --+--- -t---- . - ' - I ' _J_ ___ c -- -- : , I , :-- i : _.._.. - ' --- ---t--- . I I 'I • I
1 _!_--~'"----~ +-t"-- T- r i ! 1 : , 1 1 -+- +--r----r ! : I I I I I . I i ' I I I I • ' I
I ' I I I l I '
Readings B
A B I I . . I I 2
,_ ~ 3
I 1 4 II ----:- v
I I 5_ .----.~
I I § • • J. 7 .----~
microstrains
2000
2
i J J]';m;:[TI LoaD ·3
Up ' . ! w- 9 'llll~
5
6
:'! _.j_..._ __ ..._---~~1-&.~lt'!\-o --·
FIG.·-5. 7 (b) THE Dl STRI BUT ION OF JOINT Tl E STRAINS AT SIDE OF COLUMN UNIT 2
01 w
The strain readings from the side of the ties, shown in Fig. 5.7 (b),
demonstrated good performance in t~e elastic range, as expected, since
tre ties are here mainly concerned with srear resi.starice.
Vertical cracks down the back of the column became apparent during
Run 3 and by the onset of tre post-elasti~·range of Run 4 tre cracks
were fully developed down tre joint whicl': coincided wi tb the dramatic
strain increase shown in Fig. 5.7 (b). The distribution of strain during
Run 5 is consistent with the theory, explained in section 3.5.2.
Fig. 5.8 (a) shows the consistency and symmetry ofthe readings on
the back of the joint ties. The inorea.ee in readings at the same load
level for successive cycles can be easily seen, and in this case, is pro
bably due to a permanent bend le:ft in the ties from the previous cycle.
Fig. 5.8 (b), apart from the two upper ties, shows remarkably con
sistent readings along each tie, consider:i.ng t}:e unsymmetrical nature of
the diagona) tension cracking. · The top two ties may have been subject~d
to some bursting pressure before the lower ties, since the vertical crack
at the back of· the column extends from abov·e the joint, Fig. 5. 9, trereby
affecting the readings on these ties.
The development of stress in tl1e ties can be seen from Figs. 5.10 (a)
and 5.10 (b) whare ti.o.e recovery of strain from a previous cyr:Jle can be
easily extrapolated, The readings on the :·:ide of tbe ties show very little
permanent strain, indicating that tbe higbor readings for successive cycles
may be due more to degradation in joint sti.ffness rather than a permanent
strain from the previous cycle.
From the higher readings on the 'back c·f the ties, compared with the
side readings, it appears that this region is subjected to considerably •"
wore bursting pressure than the side of thf:; ties.
54
-·---·-Run 1 -i4---x- Run 2 -o---o- Run 3 -~>---~-Run 4
3000 ~ Load +-2ooo - Up -
1000 =~- _:..- _ ... T_ ----~-
2 i -- I - - -r--~y=-;T-- --- _,._
3:14 -.A--- -A-
2000
1000
3 4
I I ----!f--·~-·~·--t--- _,_ ----_:.--- .... -t-------=f-- -1~
2000
1000 -·f·-·-+·-
-o- ...:'?""'
II)
c ·-co :woo t.. +-' II)
0 1000 t.. u
=3-~ -J_/®·~ -o- "' I I -o~-----o
I E 7
I ~ -·+·-· .:..--A----2000
1000
I
s 10 9 10
-.t._,j,_ t----A-- I 1000
·-·E-·=t·-=--o----
I I -~--- -~-
11 12 11
2000
1000 -o- _..,......,-o-
1 I --o- -- -o-
13 14 13 14
FIG. 5.8 (a) THE DISTRIBUTION OF STEEL STRAINS ON BACK OF JOINT TIES IN UNIT 2
55
yield strain, e.. -·- ... -·-·~
Loa~ Down)
-·- ·-·-·-!-·-
-·+·-·-·-·-1 --- --.:::: :::: ..._ ::.=, ..... .-...,..IWl;:::: -----~=
11 12
---·- ·- ··-·-·-·-·--+--
13 14
tn c
2000
1000
2000
1000
~ ,.woo ci 1000
L. u
E 2000
1000
12000
1000
:woo 1000
1 2 3 4
1 '
3 4
-· --. -· -· --·--
1 e
----~---- -cp--
10
i ,, 12
13 14 <'
FIG. 5. 8 (b) THE DISTRIBUTION OF STEEL STRAINS ON SIDE OF JOINT TIES IN UNIT 2
56
57
FIG. 5.9
BACK OF JOINT SHOWING VERTICAL SPLITTING CRACK IN UN IT 2
The over~ll performance of the ties appeared to be adeQuate in the
elastic range, roweve:r, from tlle rapid deterioration of the joint during
Run 4 it was obvious that the ties were insufficient for ~0nfinement of
t~e joint under post-clastic cyclic loading conditions.
5.6 DEFORMATIO:NS:
5.6.1 Deflections:
The deflected shapes of the specimen at the peaks of the elastic
runs are shown in Fig. 5.11 and compared with the theoretical sbapes. It
is apparent from the shape of tbe column that H did not rotate freely about
t:-1e base llinge, thereby upsetting some of the theoretico.l assumptions of
erp1i Ubrium of the specimen, although this did not affect the outcome of
the test.
- --- (\ . -
c-~
·3
7·
58
Ill .: 15Ga===~==~=.:..:=~~=F--===-+,. t.. ... 1ft e 1 cnn~----t- ----:;;s,.JP.~~+c-"""'-"---+---+u
•b
E
P/ • /Pu
Back of Column
3000
Run 4
500
FIG. 5. 10(a)
Range of Average C and D Readings
-~
Run 5 -
Range of Readings: 10000 -25000 mjs
---f----
------ ~--
1-()
THE LOAD-STRAIN RELATIONSHIP FOR JOINT TfES IN UNIT .2 AT BACK OF COLUMN
A
2
3
Side of Column
Run
0.2 0..4 0.6 0.8
59
0.6 0.8 t.O
Range of Readings A and 8
- -----+--1
t.O
Run 5 --- t
Range of Readings:
A: 3000-25000 mjs. ··· 8: -2000-5000 mjs r
I
L---+---+-----1--f---J.
FIG.5.10(b) THE LOAD-STRAIN RELATIONSHIP FOR JOINT TIES IN UNIT 2 AT SIDE OF COLUMN
1.2
----theoretical· o""' 1.0
---actual· 0.8
0.6
OA
..... VI c: ·-.... c: 0
+' v v ... u 0
0.8
1.0 ., 1.2
n, 1.4
0.2 0.2
Deflection (ins.)
FIG. 5.11 DEFLECTED SHAPES OF UNIT 2 AT PEAKS OF ELASTIC LOAD RUNS
60
61
5.6.2 Moment-Rotation Relationship~:
These are shown plotted in Fig. 5.12. The column exhibited a greater
stiffness tran did UNIT 1, presumably becnuse of the reduction in the amount
of crar,king extending outside the joint region, during the initial elastic
cycles. However the loss of stiffness of the column iurine subsequent
cycles is clearly demonstrated.
5.6.3 Load-Deflection Relationship:
As shown in Fig. 5. 13, the specimen exhibits a greater st:iffness
than UNIT 1 and also, althougl1 not providing sufficient ductility for the
applied cyclic load sequence, does show a marked improvement in resilience
under repeated load. The load capacity of Run 6 represents a 25% decrease
in the maximum load resisted by Run 4.
The due til i ty factor and stiffness of the specimen during eacr'. load
run can be obtained from Table 5.1.
TABLE 5. 1. Performance of UN IT 2 During Load C~1cl in g.
Run Maximum T' Ductility Average ~,oad
'max 100 Factor ct.
~ ,o t max p Stiffness
(kips) u (%)
1 24.0 66.9 - 69.1 2 26.3 73.3 .. 72.2 3 22.7 63.2 ~ 50.8 4 27. 1 75.5 7.2 48.6 5 22.9 63.8 9.3 9.8 6 20.3 56.6 9.7 7.9 7 18.7 52.1 8.0 6. 5 8 18.8 52.4 12.3 7.0 9 17.7 49.3 14.4 4.5
t Expressed as % of thA theoretical stiffness.
b. ;;:
-.-·-- - 1500 I <= I "' E
I . -· __ :~. 1000
I I t-·· :
Ia) COLUMN ABOVE THE JOINT
-·l
J - .o~ - .o3
I
-I I
I +---~-L
------- I -- I . r~ I I
___ J_ ----- -- ~-
- 2000 t! ., ... ;;:
p - . - 1500 l l
- - --=-- -rM~~ un
I ___ L __
Q
.~ I ...
ii: -1000-
-1500
-2000
~ E 0 l[
l!' :;; c ~
I b) COLUMN BELOW THE JOINT
-/~ I
I I
+
FIG. 5.12 THE MOMENT- ROTATION RELATIONSHIPS FOR UNIT 2
62
I I
r----
--r----+---m
--l---+
----
-----
---
: i
I 1 i
--+
---·
1-~-;
-r-· -r--------+ -. -i -
.,__ +
-II
I .. .
I I
~~----~--~-----+t-'---=~---==---+--~--+----+ ... ---~-------
-----~----
r----t---+
I .,~
--!
~R-, I
1 I
I I
I I
I I
I I
I
I ~ J
I i I
+----+
----
I I
I i
I I
I I
I I
a: 0 1.1..
a.. :X: 1
/}
z 0 1-
<
_J
IJJ a:
z 0 1-
u IJJ _
J
1.1.. IJJ 0 0 <
0 _
J
IJJ :r 1
-
63
5. 7 nRA~KING:
The pattern of cracking was similar to UNIT 1 initially but wi tl' fewer
d.ia.:ronal tension ~racks in t11e ,joint. The major diagonal tension craoks and
vertical cracks down the line of the outer column bars combined on reversal
of load to form a semi-circular cracl: following tre line of tre beam flexural
bars in the column (see Fie;, 5.14). The subsequent deterioration followed
similar lines to UNIT 1, with the cover concrete being dislodged and diA.gonal
tension cracks widening and extending outside the joint r.ee;ion. Trere was
local evidence of crushing and tension cracking both above and below the
joint, see Fig. 5. 15, bowevAr the tendency for the beam to pull out of the
column caused a secondary vertical creek to form up the centre of the column
necessitating the termim.t tion of the test. Tl:e crack can be seen clearly
:i.n Fig. 5. 4.
From observed behaviour of the specimen and strain readings taken dur
ing the test, it was apparent that the .joint was sufficiently confined to
withstand a number of reversed cycles in tl~e elastic range. However the
strengtr of tre specimen was not appreciably increased over ill!IT 1. From
strain readings on the joint ties botr at t~e side and back of the ioint~
t1 e ties really began to bow as tJoe maximum load was attained on Run 4.
This suggests that the expansion wrich is then allowed to occur is directly
responsible for the reduction in load resisting capacity, by facilitating
bond failure of tre flexural bars. This bond failure, shown in Fir. 5.16,
results in the loss of stiffness of the specimen, since the beam te11ds to
act independently of tl1e column, as shown diagrammatically in Fig. 5. 17.
This rnecl1anism causes the vertical crack to form up the centre of ti'e column
because of lack of resistance from tl'e ()Olumn ties.
64
UNIT 2 ON LOAD RUN 5
,FIG. 2.j~ CRUSHING OF CONCRETE IN COLUMN OF UNIT 2 IMMEDIATELY ABOVE BEAM-COLUMN JUNCTION
65
FIG. 5.17
FIG. 5.16 UNIT 2
secondary vertical crack
well-confined concrete
beam rotating about fulcrum
AT FAILURE
FAILURE MECHANISM OF UNIT 2
66
67
CHAPTER SIX.
UNIT 3.
6.1 INTRODU~TION:
This chapter. deals with the performance of tl:e third specimen through-
out tl1e cyclic loading-;sequence, and the deterioration of tre specimen as
a load resisting structure leading to failure. The.description is part-
icularly concerned with the influence which the increase in the number of
joint ties have on the behaviour of the specimen in comparison with UNITS
1 and 2.
6.2 DETAIL OF REINFORCEMENT:
From the results obtained from tnHT 2, further confinement is obviously
required in the joint region. Although the performance of UNIT 2 indicated
that the seven joint ties were adequate to resist the applied shear force
during the elastic cycles, they did,not impose the necessary confinement to i
prevent deterioration of the joint under the application of the ·post-elastic
reversed cycles.
At this stage the emphasis was on providing a joint witr the necessary
strengtr to ensure that full flexural strength of the column can be attained.
The natural progression for T.n~IT 3 was to provide furtter confinement re-
inforcement in the joint. However, from tre results of UNITS 1 and 2, the
column ties were obviously inaderwate and little improvement had been observed
:from the increase in transverse reinforcement in the joint. Therefore it
was decided the best solution would be to fully reinforce both refions of
tre column and joint, thereby hoping to show the need for, pri:narily, an
improved anchorage detail.
~ -91 ~ ---i I i \1
Note: I ~
covt:r :: 1 -a to <~.II moain stee I
; k
!.~ ~ ~-; L{:::==t I -~~ r• r-------~----- to'-o.lf·
_!;.! .P3 llllrruno at " · j)3 titirruna at II"
B r I Mlj or~:· U=:::t
" --t·-o·~ v.
/
L f---1'-3" L A
A B
v r--r-o·~ 1--t'-0'--
--
~ ~ ~ ...__l--4 '~~to bore uu~ ~4 *to baro
I I I i I I !--column
I beyortd
- I I I I -· I N I I I _,
I I I I ~ f 3 utirrupi ... - <1>3 storrupi
I I I I I I I I I I I I
H Hb I r--1----- 4 '~~to baro _...__. 4 ~I 0 ban
b Q__Q_ 0 c
·•
-
SECTION B-B
SECT ION A-.A t'- 3'
1 .:_
I ...-----4 !lg baro
. L----J
-1'J tieo 1 L..-lls tieo
/*to baro
::::>, Of' r-- I-
( § r-- I-
- r-- 1-: ~ r--- 1--
1---- 1--r-- I-
l ~I "' *9 ~ l &tirrups bar a
SECTION c-c SECTION 0-0
FIG. 6.1 REINFORCING DETAIL FOR UNIT 3
68
The outcome of 'this decision, as shown in Fig. 6.1, was nine c~ in.
diameter ties in the joint and i in. diameter ties, at spacings varying
from 2 in. to 8 in. , in the column.
6 • .3 GENERAL PERFORMANCE:
As a load resisting stru~ture, this specimen appeared to rave very few
advantages over UNIT 2. The performance of ·the specimen was simiLr to
UNITS 1 and 2 with vertinal cracks at Ue sides of tte column connenting
with the diagonal tension cracks in the joint (see Fig. 6. 2) wricl~ widened
under the application of the cyclic loading (see Fig. 6. 3), indicating the
commencement of joint failure. However on subsequent cycles, evidence of
crushing of tte concrete outside .tYe joint region, Fig. 6.4, showed the
tendency for the failure to be propagated in the column. The breakdown of
the cover concrete on the back and sides of the joint is unavoidable once
69
the cracks open, and tree bond between the steel and the concrete is diminished.
However it appears that, provided the confinement is adequate, this does
not. have a significant effect on the structural performance.
In terms of theoretical ultimate capacity based on tre actual materials
used, UNIT 3 resisted 72% of l.ts ultimate load, whi~h was less than the
percentage for UNIT 2. It is expected that the crushing strength of the
concrete bad a greater effect on the strength of t~ese specimens than would
be accounted for by t·heory, since the failures are attrillutable to cracking
in tre joint resulting in bond failure, ratl~.er than flexural yielding of
the steel. However, the increase in the number of ties meant t1,at U;e load
was resisted effectively over a greater number of reversed cycles,
Tt~ load sequence for this specimen.included elastic cycles after t~e
first post-EJlastic cycles 4 and 5, s'"owing tbe loss of stiffness of tt,e
specimen, followed by two more post-elastic cynles in whic~ the beam was
taLon to maximum deflection and tr..e test terminated.
Fl G. 6. 2 UNIT 3 ON LOAD RUN 3
/0
FIG. 6.3 UNIT 3 ON LOAD RUN 4
FIG. 6.4 UNIT 3 ON
LOAD RUN 9
The difficulty in preventing the cover concrete from spalling
means tl1aJr. i-t is cHft:i.eul t to obtain the Tequired bond Ertx·ess of tho column
flexural bars as long as tbe jo:int conth.tv.es to l1e -Gb0 failure 1"(3eion. Even
tl~ough the 6onfinemcmt of t11e joint. for this specimon was improved over
UNIT 2 1 bond failure of flexural barr-3 was. still ap})a:i~E.m.'G. 'l'he breaking up
of surface concrete round the outer column ba:rs, l"ig. 6. 3, meant tl-:a t the
DEMEC readil1gs were unreliable during Run 5 ::md could not be re~·o:r:ded, How-·
ever, the strain distributions shown in Fig, 6.5 (a) and 6,5 (b) wer~ con
sistent with t~o expected t~eor~tical distribution. The critical readings
on the inner column 1Jars are affected to a larger extent 'Nl'ere the tensile
beam flexural barFJ entor tlJe column, rat\~er t'nan wrere the compressive
bars enter because Of 'G]iG larger bond forces wricl~ must be developed.
The strain gauge readiJ'lgs are shovvn in Figs. 6, 6 (a) and 6. 6 (b)
and, as for Uli!ITS 1 and 2, indicate tl-.e valuos of tensile st:rain greator
tJ-,an would be expected for tbe load which is resisted. Fig, 6. 6 (a) shows
a trend in tl':e strain :cel'tdings which makes it apparent tr1at the:re is a
local l'igh reading of strain on the first gauge location .in t}'e beam
(location 70). Since, f:eom J1'ig. 6. 2 1 trere:J is no crack crossing trc f.Sauge
lengt}~ to provide t1,e large str:dn; t'l,is in·i:~cates t>,nt t'"ere <:ould l1e a
sl:irr,}~t benging of tl'e.bay·s at tris section.
Fi~. 6.7 indicates tro influence o~ t~a position of t~e bar on its
)•erformance u11der cyclic~ loading. 'ln'ile tbe inner two bars s~ov1 good
re~overy of strain, indicating efficient bond, tte strain in tro outer
b~r~ s~ows a deterioration in bond performance. This would be due to the
?'l
72
11 12
Run 1 -· ~ ·-Run 2 -x-x-Run 3 -o-o-
23
Run 4-A-A-Run 5-+-+- 27 28
31 32
11
5train gauge location
15
mic rostrai ns microstrains
FlO. 6.5(a) THE DISTRIBUTION OF STEEL STRAINS IN COLUMN FLEXURAL BARS IN UNIT 3 [FOR DOWNWARD LOAD RUNS]
73
For strain gauge locations see Fig . 6 . 5(a)
-1000 mic::r03tr'oins
FIG. 6.5(b) , THE DISTRIBUTION OF STEEL STRAINS IN ·COLUMN FLEXURAL BARS IN UNIT 3 f.l=OR UPWARD LOAD RUNS]
69 70 71 72 73 74 -·-·-Run 1 . strain _,._,._Run 2 gauge -o-o-Run 3
location · -A~A-RUn 4 77 78 79 80 81 82 -+-+-Run 5
----t-- -----··--- -· 500
i I I
Ill c
69 70 71 72 73 74 :! column beam
.... Ill 0 !..
78 81 82 u ·e c 0
Ill ·Ill 4.1 1.. Q.
E -500 0
i u
I
I I
I I I I ! I i i
--j 1--- - I t .. .I -1000
FIG. 6.6 (a) THE DISTRIBUTION OF STEEL STRAINS IN BEAM
FLEXURAL BARS IN UNIT 3 [FOR DOWNWARD LOAD RUNS]
74
75
For strain gouge locations see Fig. 6.6(a)
-- ~-'•
~~ "' Pu To~ 10 Bars
·+ c:
~~ ·a+
-·l __ Ill
~theoretical 4J 1.. Q.
:~------ E I . t -= 0
u
J---' J . @ . i
b-69 70 1'1 72 74
column · beam
77 78 75 8 81
---+-----+---- - 1000
1500
FlO . 6. 6(b) THE DISTRIBUTION OF STEEL STRAINS IN BEAM FLEXURAL BARS IN UNIT 3 (FOR UPWARD LOAD RUNS]
strain gauges
76
-c--o- Inner 2 Bars
-)(-.c- Outer 2 Bars
+-+- I ,---500 __ T ____ --· -J_ X
·t :,· . ' j
---- M- r· 4 0 0 en
I \: ~ ' \ i - 3oo ~ I
~-~ ,u" •. ~ Run/ ",, 1 "" :
'\' . ' - 200
FIG. 6.7
0 '~
-30 -20 Upward Load
I I
-10 (Kips}.
30 Load (1'\i ps)
I
THE HISTORY OF STRAIN FOR THE BEAM FLEXURAL BARS IN UNIT 3
~.Hfferen t depth of cover· to the bars from the sides of the column which has
been shown18 to influence the bond perfonnance significantly. The strain
developed in the bars at the mid point of the anchorage, shows that the
anchorage length is insufficient for tbe tensile force in the bars to be
dissipated.
6.5 BEHAVIOUR OF TRANSVERSE REINFORCEMENT:
6.5.1 Column Ties:
Again, due to the tendency for the cracking and breaking up to
be confined to the joint region, little interest was generated in the per-
fo~mance of tre column ties, except for their ability to prevent a second-
ary failure being prppagated outside the joint region once the joint .had
deteriorated sufficiently to allow it. The absence of a splitting crack
up t~e column and the prevention from.buckling of the column flexural bars
testified to the adequacy of tre column ties.
6.5.2 Joint Ties:
All the DEMEC readings on these ties were duplicated in this
specimen by having electric resistance strain gauges p1aoed on the ties
between \each pair of demeo~ studs. The strain readings from bot1·, sournes,
as shown in Figs. 6.8 (a), 6._8 (b) and 6.8 (c), verified the effect that
bowing of the ties had on the strain readings. For the strain readings on
the back of tr.e ties, no DEMEC readings •!iere recorded during Run 1, but the
comparison of DEMEl': and electric resistance strain gauge readings for sub-
sequent cycles shows the extent to which bowing of tre ties affects the read-;
ings. It is obvious trat even from the first cycle tre DEMEC readings are
unreliable, but tJoe electric resistance strain g~uge readings stow trat the
use of nine ties.in the joint is sufficient to prevent yielding at t~e back
/7
DEMEC Gauges
Run 1-·---·.Run 2-><- --~~Run 3-o-- -oRun 4-t.~ -- ~o- · Run 5-+-- -+-
c I
D 1 I
I :t
I 7
I e
-----· ·-- -- \-------· Back of Column
5
7
Electric Resistance Strain Gauges
-·-e-Run 1 -><-><-Run 2 -o-o-Run 3 -A-A-RUn 4 -+-+-Run 5
Average of Readings C and D
1000 3000 5000
m ic:rostrains
2000 4000
700
6000
Load\ Down)
Loa~ Up)
FIG. 6. 8 (a) THE DISTRIBUTION. OF JOINT TIE STRAINS AT BACK OF COLUMN IN UNIT 3
78
-.-- I B
I I A B 1 !'-~---+-+-~
I I I 3
JL__ I 5 -~...t-.:1=---+--+---t- L8;-e~ ' -------. 7
-+----!
'
' I ' ., ' I I I i 7000 5000 3000 1000
I 1 9 ~! ----,/'---- 1000 3000 5000
microstrairts Side- of Column micro strains
6000 4000 2000 2000 4000
1
3 3
5 5
7 7
s 9
FIG. 6.8 (b) THE DISTRIBUTION OF JOINT TIE STRAINS AT SIDE OF COLU [DEMEC GAUGES]
·sooo
UNIT 3
....... (.()
Readings A
I
3000 1000
4000 2000
A I
B I
7
Side of Column
7
microstr:ii ns
80
-Load\ Down;
Load'\ Up)
FIG. 6.8 (c) THE DISTRIBUTION OF JOINT TIE STRAINS AT SIDE OF COLUMN IN UNIT 3 [ELECTRIC RESISTANCE STRAIN GAUGES]
0f the ties during the application of the five instrumented cycles,
Strain readings on tl:e side of the joint ties from both sources are
shown in Figs. 6.8 (b) and 6.8 (c) for comparison, and the distribution
of strains in the ties generally bear little relationship to each other.
·The D3MEC readings are similar in many respects to previous results with
the majority of the bowing seemingly.occurring in the·post-elastic·-ranges
of Runs 4 and 5. It is apparent that the two sources show comparable
distributions during 'Runs 1, 2 and 3, however the tensile strains become
ne-gligible once bowing of the ties occurs, and the DEME~ distributions sub
sequently give meaningless results.
As Fig. 6.8 (c) shows, o~ the downward load runs it is the top ties
w"ich are more righly stressed, with t'be lower ties being subjected to very
little tensile. s~ress. On the upward load cycles the situation is reversed.
The strain distributions on each tie are sr..own in Figs. 6.9 (a) and
6.9 (b) where tre electric resistance strain gauge readings only have been
recorded. The symmetrical nature of the stress at the back of tre ties is
contrasted with the distributions on the sides of the ties where the readings
A are consistently great.er thim the readinr,s B except for the tie 3, which
lends credence to the belief that this electric resistance strain gauge
failed after Run 4.
The lo.01d strain relationships for gauges on all four sides of the ties
are shown in Figs. 6.10 (a), 6.10 (b), 6.10 (c) and 6.10 (d). These show
how the stress is developed during each run and the full effect of the ties
is not imposert until the latter part of eacr run. The effect that bowing
of the ties ras on the D:!i!MEr: readings is sr·own by not only resulting in
ri~her rendings but also a gre~ter variation. ··The relationsrip s~own in
Fig. 6.10 (d) s'"OWf.l how t,e bu-rstivg effent of the column is ::·resent even
at the inside of ,tre column wrere tbe restr'cining effect of the beam would
-· yield strain, ey -;-r -K
-·-·~·- ·- -n-t t
-o
-ll. - -+ 9 10
strain location
2000
1000 .
=E=~=·-2000
+- 1000 ~~
~,~,~ 3 4
II) c: ·- 2000 <U r.. ..... II)
.0 1000
= f.. u
5 6 E
1000
----+-=-!= -·+·-· ·-. - -r --· t:::-•i ~
2000
2000
1000
·-Run 1 ,._Run 2 o- Run 3 A- Run 4 +-Run 5
Loa~ Up .
=1~-·-r S3
~ +~ ~ f• . i 2{§
-f=--=r-= -··~ ----~ll!
3 4
I . -·t-·-·=4·-_.,.,.,
~--i- -.:;:-\) I -o <?-
5 6
7 8
+-1 +--10
FIG. 6.9 (a) THE DISTRIBUTION OF STEEL STRAINS ON BACK OF JOINT TIES IN UNIT 3 [ELECTRIC RESISTANCE STRAIN GAUGES)
82
_.. -I
2
"'"'tT ! ~ A t
""T'1'""
§~ strain
location 2000
1000
3000
2000
1000
II) 3000 c
. ~ 2000
.... II)
0 1000 ·g_
u
E 3000
2000
-·-·-Run -K---IC- Run -o--o- Run -6--A- Run -+ Run
-·-f--·-·- ·-1000
7
3000
2000
1000
---1 t-9 10
Fl G. 6. 9 (b) THE DISTRIBUTION OF STEEL STRAINS ON S I DE 0 F J 0 IN T T IE S IN U N I T 3
(ELECTRIC . RESISTANCE STRAIN GAUGES]
83
~ DEMEC Gaugu
84
-~---t-:\:_r~-----r---
1
"' ·~ 1500 F'-"==F=· -=-=·-=-~=·-' -=-=·~==F""~=:::t--.50() ~=.:::::f:_:_::;;;~~~~~~~=-:=t=-' ... ... Ill ~ 1000- Run 1 u ·e 5001-~
1·0 0.4 0.6
. 3000
c D .1
Range of 3
Average
C and D 5
Readings· 7
!!)
Back of Column
-4000 -
~ 1------,--r---+--
0.2 0.4 0.6 0.8 1.0 0.2 0.6 o.e
FIG.6.10(a) THE LOAD-STRAIN RELATIONSHIP FOR JOINT TIES IN UNIT 3 AT BACK OF COLUMN
1.0
+----l-4000 1-----1-
ey f=-'-=~'-'-===-=-j=="-===f~=--'-===f:---'-=~=1-1500 -.- .
Run 2 000
B ~
FA· Pu 0·4 o.& o.a 1.0 0.2
A
3
7
0·4 o.s 0·8
o.e
Range of Readings A and B
Ill c:
Side of Column
::! 2000 ----- --------\------:r~-~-1'----+ ... Ill o ey .~ 1500 =-~:- ::.=.:_ __ =-;·~~t.;;t:;;¥-AP:o;
E
~ 1------ :·-1
500 i~- --------~~~,~~--+
L 0.2 0.4 0.6 0.8 1.0 0.2 0.4 0.6 o.e
85
~J 1·0
1.0
1.0
FIG . 6 .10 (b) THE LOAD -STRAIN RELATIONSHIP FOR JOINT TIES IN UNIT 3 AT Sl DE OF COLUMN [DEMEC GAUGES]
~ 1500 -~ .... ~ 1000 1.. v
E500
e~
Run 1 ·-
A [A'
~A -~~ B
-- -0.8
II.'IJOO
ey 1 500 ·-·-·-·-·
Run 2 ·-""""' 500
~u~~~ o .. 2 0.8
86
~Pu 1.0
2000 1-----t---+---+---+----i-
ey __ _ -~ 1500 F-'-'=-'==t:...:.=:::....:....::=J'-'=====f..'-:===1==-'=-'-==l-~ Run 3 .... :s 1000 1---l-- ----J.----l-1.. \J
E 500 f---'---+----+,..~¥¥-'l'------+
·-- --··----\,.----'- 0.2 0.4 o.G 0.8
Side of Column
Range of Readings A and B
2~f--------J.---+--~--~---~
2000 1"-----+----+--
~~~ ey .s 1!500 ·--= . ~ .~:..:.·: -:=:-::...:'--=J=--'-=...:.='F-'--"=;p.;:.:....=::f:....:.=::..:...==l--1
~ Run 4 ... ~ 1000 --------1------+-----=~"*~/>.,------+----i 1000 !... v 'f: 500
~-Pu ~[ ____ 0.2 0.4 o.G 08 1.0 0·2 0.4 O.G 0.8
,!%. Pu
1.0
FIG . 6 . 10 {c) THE LOAD- STRAIN RELATIONSHIP FOR JOINT TIES IN UNIT 3 AT SIDE OF COLUMN [ELECTRIC RESISTANCE STRAIN GAUGES)
outline ot
beam
---\---------, I E 1 I I I I 3 I I 5 I I 7 I I I I ~ I '---· ___ j
_.__ ___ jlr---·-
lnside of Column
87
. 500 1------1
~J o.~ 1.0
Range of Readings E
FIG. 6.10 (d) THE LOAD- STRAIN RELATIONSHIP FOR JOINT TIES IN UNIT 3 AT INSIDE OF COLUMN
88
seem to be considerable.
6. 6 DEFORMATIONS:
6.6.1 Deflections:
The deflected sl•apes of the specimen at the peaks of Runs 1, 2 and
3 are sl,own in Fig. 6. 11, and ~ompared wi tb t~e tneoret ically predicted
s~apes. The increased r~sponse of this specimen when subjected to similar
' loads to UNIT 2 indicates the effect that the concrete strength has on the
deflection of the structure in the elastic range. The concrete strength
has a considerable effe<"lt on t'l'e extent of flexural cracking and on dis-
tortion of the joint due to diar.onul tension .~cra"lting, which results in the
larger deflections.
6. 6. 2 Moment"':"Rotation Relationships:
The relationships, shown in Fig. 6.12, indicate that tbe column
was not as Rtiff in this sper:1imen as in ijNIT 2, during the elastic cycleE'i.
This was rrobably due to the reduction in concrete strengt~, w~ich enabled
cr.1cks to form at lower loads. The increac,ed ,joint confinement causes
cracks to be propaegted from tre ,joint into the column region, lowering
the stiffness of t'he column, acnountin!?' for tre swiden degradation in
stiffnef!s near t'he peo.k of' Run 1. The perm3nent rot"ltion of the sections
of the column is demonstrated by the bias each curve gets to one side of
tre origin,
6.6.3 Load-Deflection Relationsh~:
The relationship is sho\'m in Fig. 6. 13. The loss of stiffness
of the spen-imen after Runs 4 and 5 is shown by the resr,onse of the specimen
\:~ul:i.t.g 0la.s"tic R~ns 6 and 7 when onl;y 10% of the theoretical ultimate load
89
1.6
c/'' 1.4
U!
----theoretical ---actual 1.0
·0.8
c::
~------------~---------------------+-+-0
-u 0
-0.4
1.0
1.2 0.2 0.2 Deflection (ins)
FIG. 6.11
1.4
1.S
1.8
2.0
DEFLECTED SHAPES OF UNIT 3 AT PEAKS OF ELASTIC LOAD RUNS
--J,Jo.r.:.., -~-1000 "-1---~ I
·-M 1- u......._ __
I
:II
-~- -15001
"' ---- -2000 -
-+ I
Cal COLUMN AI!OVE THE JOINT
' I t-
1
- f I
Rotation
--~-
-"'-....~
Mu
- ;j2000 'j = ~- ~
.!!
"' -l~--,-=1
· Mu 1
--+-~~~-+--~~--+=--~~~~~~-,4J~~---4--~~-+-04 - ·0)
·02
-+--
---~1-----~----1 -- - -- ---
lbl COLUMN B€LOW IHE JOINT
FIG. 6.12 THE MOMENT- ROTATION RELATIONSHIPS FOR UNIT 3
90
~---+ I
-+----~ -
I I I
~- __ _;__+-! .
,_ -- ~-. -
' I _, , -n· I -,• -;:I : I. -- - i 0 :
7 ' (ins}
8 9
0 -
1
- ' --
+
:
-- ~ - -+ j t -
I I ' -j 1- - -----T _____ _;.
! I --i----t
-+--
f1G.G.13 THE LOAD DEFLECTION RELATIONSHIP FOR UNIT 3 (() .......
is resisted at an equivalent deflection tc· the initial elastic o.vcles.
Tbe resilience of the speoimen showed a sligh·t improvement over UlHT 2 9
with the maximum load resisted durir1g Run 8 being 22% less than that of
Run 4.
Table 6.1 indicates tbe stiffness of the speeim~n and t~a ductility
factors obtai.ned·during each load run.
TABLE 6. 1 Performance of UNr.r 3 During Load Cycling.
Run Maximum p Duotili ty Average ~oad ~X 100 Factor % t * max p Stiffness
(kips) u ( ;t)
...
1 22.0 64.4 - 42~4 2 22.9 67.0 - 50.9 .3 19.7 57.6 ao . 29.3 4 24.7 72.2 5.2 32.4 5 21.6 63.2 8.9 11. 3 6 3.2 9.4 - 3.2 7 1. 2 3.5 - 2.3 8 19.0 55.6 11. 3 7. 6 9 15.6 45.6 17. '1 2.9
. .
t Bxpressed as fa of "the tbeoreticA.l stiffness.
6.7 CRA'%ING;
The cre.cking showed <.1 very similar pattern to tr'e previous two specimenn,
wi tb diagonal tension crac~<s being confined generally to the joint. Large
bond stress and bond failure of the flexural bars was indicated by tbe cracks
fol1owing the lines of both the column and beam flexural bars. Vertical
cracks down the bctck of the column, Fig. 6.14, indicated column expansion
as early as Run 1. '1.1he low concrete tensile strength coulct be the reason
for· th~ exr,<msion of the ~olumn being· initiated so early in the load sequence,
and tbis could be an impor·tant factor wl1en determining column burntine; forces.
92
UNIT 3 ON LOAD RUN 1
FIG. 6.15 UNIT 3 AT FAILURE
93
There was more evidence of concrete out~?ide the joint region spalling
in this specimen, due to crushing and cracking of the concrete, than had
been observed in previous specimens.
6.8 THE FAILURE MECHANISM:
The loss of stiffness and subsequent det~rior5tion of the joint due
to diagonal tension cracking indica ted tre gra,dual approach of fai1ure,
The nine joint ties enabled the specimen to w~thstand tte load cycling
without the diagonal tension cracks widening s,ufficiently to cause shear
failure in tl:.e joint. However, al tbougr: the core was well confined the
concrete in tt.e core appeared to be crushed by the diagonal compression
forces. This weakened tr_e bond strength of the beam flexural bars which
meant that the joint could not be maintained as an integrul unit. The joint
degradation caused by bond failure of the flexural bars lead to a failure
similar to UNIT 2. Fig. 6.15 shows the specimen at failure.
94
CHAPTER~·
7.1 INTRODUCTIONt
Tbe change in the reinforcing·detail and its effect on the behaviour
of UlHT 4 are descr·ibed in this chapter in an attempt to determine the
reasons for ~he improvement in its performance compared with the p:r·(wious
specimens.
7.2 DETAIL OF REINFOR~EMEl~T:
Since little improvement in· load capacity had been achi~ved in the
previous ttree specimens, it was apparent ttat a radical change of the
joint detail was rec1uired. The inability of the flexural bars to develop
the required bond strength was a fundamental cause of these premature
failures and indicated the rc.ecessi ty for improved bond performance. This
can be achieved eitter by ensuring more favourable bond conditions or by
reducing the required bond stress. The first method has been attempted in
UNITS 2 and 3 by increasirJ,~ the confinement. To investigate the effeet of
the second method the continuous arrangement of beam flexur&l bars has
been dispensed with in lJNI'l1 4, the beam flexural steel consisting of separate
top and bottom bars, t~ereby providing increased aDchorago length in the
column.
In order to determine the problems directly attributable to the con
tinuous arrangement, the reinforcement detail, as shown in Fig. 7.1, was
unc'banged otr:erwise from UHIT 3.
7. 3 GEliE;RAL PERFDRMANCE.
It was obvious from tte be~aviour of this specimen, even during the
95
u
u
] .:_
FIG. 7.1
L A
.1 N
i----1'·3"
--
p /' ~---~
v n (?
~1'·3"'--~
A
L
~~ R ~ ~ ~ ~~---4 *10 bnro
''1\~1 I I'll! II ,: I I I I 11 II I 1 Jl I I ...__column I I II II I jl I I bel ond
3 tie6
I d II II 'I' II ,, I I 1 Jill 11 ::::Oflotirrul>"
,l ,, Jl " 11 11 I! :1 h ~ II 11
t! 8_1 i b ~f---4*10 bm
I 'I I I I I I
SECTION A-A
)
4 #"g bare
)
B
1'-3'
. ·' "'
J--1'· 0"-----
p Q ~ ~4'i>IObm
1--<1>3 '''""'"'
SECTION B-B
l / >lho bars 1/~5 ti .. or . I
1-- - r-
§I 1-- - r-1-- - 1-:: 1-- - r-1-- - r-1-- - r-
r::ll ''\.
* 4 9 baro (> 3 6tirrupu
SECTION c-c SECTION D-D
REINFORCING DETAIL FOR UNIT 4
96
elastic cycles, that there was a vast improvement in performance over the
previous specimens.
Although ·diagonal tension cracks formed during Runs 1, 2 and 3 trey
did not widen perceptibl~r and the joint was still intact, as shown in Fie;.
7.2, prior to the application of the post-elastic cycles. The major diagonal
tension eracks, running between opposite corners of the joint, opened dur~
ing Runs 4 and 5, however, evidence of concrete crushing and tension cracks
outside the joint region indicated flexural yielding of the steel in the
column on both upward and dovmward runs.
The appearance of the specimen at the peak of Run 8, shown in E'ig.
7.3, demonstrates how the cover concrete remained on tre joint over a far
greater proportion of the load sequence tr.an it did for tJ·e previous speci
mens. The increased confinement in the joint reduced the tendency for bond
failure of either column or beam flexural bars and substantially improved
the resilience of the specimen.
However, the most interesting facet of the behaviour of UNIT 4 was
tr.at it resisted 9Cf'/o of its theoretical ultimate capacity, substantially
more than any of the previous three specimex;ts.
7. 4 B.B;HAVIOUR OF' FLEXURAL REI1'FORCEJVIENT:
7.4.1 Column Bars:
The strain distributions sbovm in Fig. 7.4 (a) and 7.4 (b) show
yielding which occurred in the column bars during both upward and down~
ward load runs. T},e inner column bars are, as predicted for thb situation,
the only bars which yield since trey are in tension in tre critical region
for botr directions of loading.
97
FIG. 7. 2 UNIT 4 ON LOAD RUN 3
98
FIGfl UNIT 4 ON LOAD RUN 8
.EJQJ'. 6 END OF TOP BEAM FLEXURAL BAR LIFTED OFF BEARING SURFACE
13 16 . '-------l
19 20
23
41 42
'
-r----~-1 I
-· -M
-o
-b.
-+
--r···- t· -
·-><-
o-
A-
+-
strain gauge_-i-location '
I -e c:omprossion tons ion tQnsion
-1000 . 1000 m1c.rostralns
-1000 1000 microstrai ns
Run 1 Run 2 Run 3 Run 4 Run 5
e 2000
FIG. 7.4 (a) THE DISTRIBUTION OF STEEL STRAINS IN COLUMN FLEXURAL BARS IN UNIT 4 [FOR DOWNWARD LOAD RUNS]
99
For strain . gauge locations see Fig . 7. 4 (a)
-r I
··~
-+--&--!---~-+----- I I
1000
mic:rostrains mic:rostrains
100
2000
J i \
FIG . 7. 4(b) THE DISTRIBUTtON OF STEEL STRAINS IN COLUMN FLEXURAL BARS IN UNIT 4 (FOR UPWARD LOAD RUNS)
Some of tr,e strain readings on tte outer column bars during Run 5 indir.·
ate a distribution inconsistent with wl:at would be expected. This is in the
region where the top beam flexural bars terminate, and since, on upward
load runs tl::ese bars are in compression the bearing stress at tr.e ends of
the bars could cause lateral bowing of the column bars thereby infJ uencing,
tbe strain readings.
101
Even tl_,ough the strain at different load increments indicates a higher
stress than had been recorded for previous specimens, the absence rf splitting
cracks, Fig. 7.2, means that the efficiency of the bond must have l.Jeen
substantially improved.
7.4.2 Beam Bars:
:B'mm the strain distributions sbown in Figs. 7.5 (a) and 7.5 (b)
the ancl:orage lengtl: appears adequate for downward load during the elastic
cycles, however subsequent deterioration in bond during the post-elastic
cycles resulted in bond failure of the top bars, as indicated by the strain
distribution shown in Fig. 7.5 (a) for Rilll 8. A similar pattern was evident
for the bottom bars on upward load runs except trat there appeared to be a
residual stress at the end of tl:e bars. However, the strain distribution,
shown in Fig. 7. 5 (b) suggests tta t tl-.ere was an anomaly between the readings
of gauges 7* and 8*.
The residual stress at the end of the bars, when they are subject to
a compression stress, is due to the bearinc pressure of the end of tbe bar
on the concrete. The effect is shown in Fig. 7.6, which is a detail taken
from the circled ctrea of Fig. 7. 16. where tr,e beam flexural bar, now in
tension; has lifted off the concrete bearing surface.
In many cases the stress in the tensile bars is greater inside tre column
tl·an in the beam., Theoretically t'··e maximu:n stress should be at the inter
GE:ction of the inner column IJars, since this is wl:ere the column tensile
x---x
r.--o
C.--A
+--+ E!'---<!l
/]
Run 1 Run 2 Run 3 Run 4 Run 5 Run 8
43 44 45
2
3
5"' 4S 47 48
l_, • 'v
strain gauge locations
s*
*electrical resistance strain gauge
----~-+--------~~---------~~----+-------~---+~
--------~------------~----------r-----~~-------------=~~~~~~4=~~~~~~,~ #
Top 10 Bars
~ -----~ I 1000
:7"' I , , ., _...,.lr I J7 /'l I =.;.;.=-- ...........-- , ----
1
I i 1500 c .2 Ill c ~ ... ~
41! 4"
1* 43 44 -45
column beam 7* ~ 48
-----....__-
--~-r---;-th .. orc;;t i cal Bottom 10
------ --- j
FiG . 7. 5(a) THE DISTRIBUTION OF STEEL STRAINS BEAA1 FLEXURAL BARS IN UNIT 4 [FOR [)()YINIA!ARO lOAD RUNS]
... c: .f
~ 1.1 ·e
-a. 0 1\)
t--~~--·- ·-t~~~ < ;;---, 1 .2 # .72). ' ::1
Top 10 Bars-~p-~:~~ k ~-- I /~ ~ '@~ i ~ th~or~tical I 1 -~ : "
43
+
a* 48
---- --I
- "'-?> I
-+-----------
\ j 500
-+------+-----+---+ 1000
For strain gauge locations ~ i see Fig. 7. 5(a) j l
·-·-·-=F- -=t=-·-·- ' . I
I I
Bars
\ / I FIG. 7. 5(b) THE DISTRIBUTION OF S"flC'....EL STRAiNS BE.Aiv'i F--LEXURAL BARS 4 lfOR :JfWARD lOAD RUNS]
... IC
1 ~
_... 0 w
1U4
force is introduced.
7. 5 BEHAVIOUR OF TRA11 S VERSE REINFORCEMENT:
7.5.1 Column Ties:
The strain distributions on the column ties above and below the
joint are shown in Fig. 7.7. These regions were subjected to greater
rotations and more flexural cracking than in any of the previous specimens,
however as can be seen from the strain· distributions, it was still only
the ties closest to the joint which were significantly affected. These
are also most prone to bowing, being near the area of internal cracking,
which casts doubt on the accuracy of the DEMEO readings. However, because
of tbe failure being mainly confined to the joint region. the actual stress
in the ties was considered secondary to their ability to prevent a brittle
column failure.
7.5.2 Joint Ties:
This was the first specimen to be subjected to a post~elastic
cycle withou·t any of the joint ties yielding. The strain distributions
are shown in Figs. 7.8 (a) and 7.8 (b).
The strain readings on the back of the joint ties show an apparently
random distribution, with aLi. the ties working effectively and being
subjected to similar stresses.
The distribution of strain at the side of the ties, in comparison with
the bar'k, shows definite tendencies for the stress in a particular tie to '
be depondent on tJ-e direction of loading. Por this specimen, tre bigl:er
stress oc~urs in tbe lower ties during dowmvard load runs and in the upper
105
-r 125
11
-x-x- Run 2 -.~>-to.- Run 4.
1 -"~-·-Run 3 ..__. ,_...,...-~--1----,lL- - +-~+- Run 5
~ Down
7
I I 14 15
Ill c
HIOOO u
E 2000
1000
-------J 0 IN T
32
I __ ._(.
~;;: 36
FIG. 7. 7 THE THE
-r-37
·-Ill L. ... Ill 0 1..
2000
1000
·~ 11000
i'ooo
DISTRIBUTION OF COLUMN TIES OF
-·-·-i ~ ~ -~ ··-~-----I I
~- ---=~
14 15
I 32
JG
STEEL U Nl T
~ ..
37
STRAINS 4
IN
p cl ·-Run 1 A orB -· ·-Run 2 -o o- Run 3
c -b. a- Run 4 -+ +-Run 5 -$ $-Run a
~ Aor 8 ~ -® ®-Run 9 I
strain gauge locations on joint ties
c
- Ba-c-k ·~-lu_m_n~ 1000 :woo 3000 4000 5000
microstrains
FIG. 7. a (a)
2
3
<4
5
6
7
a
THE AT
DISTRIBUTION OF BACK OF COLUMN
4000 5000
JOINT TIE STRAINS IN UNIT 4
106
Loa~ u·r;)
Readings A
--- + ------
4000 3000 2000 1000
microstra i :os
4000 3000 2000
i ' ley 1 )
_--I--9w.V T .~~~~,--0 ~* ~~ \
Pu . ~ /i ----~~K\\ Ji• :Jr. ·• t +~~~·
I ! 1
rr- I A B '
2
3
4
_5 0
6
7
8
~
l
I
I
Readings I
B
I ---~ -1 --
1
__ J 1____.....1 "• .
Side of ~Column 1ooo 20oo 30oo micros trains
1000 2000 3000 4000
1
3
5
7
9
2
I
ey ' . i I '! i I I . I
nrrnn· · 1 ,
. l I I -+----~-o ;-----t- I I / I
"I I L+~·- u -I--
[!JL14 L--L-@J Lo~~) \~ \ \ l\ ~®L _________ -- -·--0 -<>---+----+l~--+-1 '
! •
4
6
al
FIG. 7. 8 (b) THE DISTRIBUTION OF .JOINT TIE STRAINS AT SIDE OF COLUMN IN U T 4
...... 0 -....!
Oo2 0.4 OoS
------~-
c
--~
Back. of Column
Oo2 OA OoS
108
I --- I o - o j ·-'--· .•cod~ -~
---- ~- . I . -. -~ - --- -I
---+ ~00 ---- -- -------! i --- ·j
~~ 1.0 Oo8
I
LL~~o~ Oo4 00 s 0.,
FYpu 0.2 1o0.
Range of Readings C
T
I
~~~~:±:~C- -~l e.= -+~---,-0.8 100 Oo2 0.4 O.G 0. 8 100
FIG. 7.9 (a) THE
IN
LOAD-STRAIN RELATIONSHIP FOR JOINT TIES
UNIT 4 AT BACK OF COLUMN
~,. ey ·=;;u:- ;=t·-. .!:; 1000 --+-------j'-----~----t~~--+ Ill 0 1..
-~ 5001----~-+----+---
0.2 0.4 0.1
A B 1
3
I 1 5
6
7
s
-·--+-Side of Column
0.8 1.0 0.2 0.4
02 0.-4
Range of Readings A and B
3000
I 2500 --r--200 Run
~1500 "ii 1.. .... ~ 100 L.
-~ E 500
0.2 0.4 0.6 0.8 1.0 0.2 0.4
109
0.6 0.8 1.0
0.6 0.8 1.0
I i
--t I
·-· -~ i I
~j ' FYpJ
0.6 0.8 1.0
FIG. 7.9{b) THE LOAD -STRAIN RELATIONSHIP FOR JOINT TIES
IN UNIT 4 AT Sl DE OF COLUMN
. ties on the upward load runs. Ttis is the:· opposite effect to what ·Nas
observed in tbe previous specimens and suggests that this joint has a
completely different load resisting mechanism for this reinforcement detail.
rrhere is also a distinct similarity between the distribution of readings
A and B on each tie, indicating that they are to some extent dependent on
each other, the bond stress along ·the tie not being significant.
The development of strain in the ties is shown in Figs. 7. 9 (a) and
7.9 (b). The inclusion of the nir1e ties in the joint ensures that tbe
stresses are kept low during elastic cycles, when _shear resistance appears
to be tre major function of t'be tie.s. However wl-":en bursting forces are
exerted during post-elastic eycles the effect can be clearly seen from tl:e
load-strain relationships.
Althougl1 the 'ties were only fully effective for one post-elastic cycle
before they yielded, from a practical point of view, nine ties would seem
to be a maxiwum amount of transverse reinforcement for this particular joint.
7. 6 DEFORMA'riONS:
7.6.1 Deflections:
The deflected shapes of the specimen at the peaks of the elastic
cycles are shovm in Fig. 7. :0 and compared wi.tl1 tbe theoretical sl:.apes.
'Pho observed behaviour of tbe specimen acting more as an integrGl unit in
tr:e joint region would account for .tr'e better correlation between t'heoretica1
and actual defleeted shapes for this specimen.
·7.6.2 Moment-Rotation Relationsrips:
The relationships, shown in Fig. 7.11, emphasise tte extent to
wlr:i.ch the rotation oceurs in the region of lower axial load. The column
was obviously much stiffer than for UNIT 3 ·Nhich suggests that it is affected
110
111
o.e "----theoretical
actual ~o""'
·~ ~ 0 ~~
·0.6
0.4
-0.8
1.0
~·--~-.~-...-
0.2 0.2 Deflection <ins)
FIG. 7.10 DEFLECTED SHAPES OF UNIT 4 AT PEAKS
OF ELASTIC LOAD RUNS
"\J.___.~ - -:;+:.--r.cc-_ -r~M·-I I I _.----, I
--- :r.woo ~~~., ~--
1 i!' 11 -I --------------l----------,L..\-..
1 __ J~~ --- ___ .;; soo
-.02
,QJ~_.~ R-lll11.~1 y
-t=-T ~-----~------~------------~------ ~
-
Col COLUMN ACIIOVE Til€ JOINT
1
Rotollon C Rode.l
I m M U_:::--,.__- - i ~~~-. ~-
Cbl COLUMN BELOW THE JOINT
FIG. 7.11 THE MOMENT-ROTATION RELATIONSHIPS FOR UNIT 4
112
113
by the overall stiffness of the specimen rather than the extent of cracking
in the column itself.
7.6.3 Load~Deflection Relationship:
The improved load resisting characteristics and resilience are
amply demonstrated by the relationship shown in Fig. 7.12. Adequate stiff~
ness of the specimen was sustained up to Run 8, after which the stiffness
degradation and loss of load capacity became apparent, as shown in Table 7. 1.
The increased resilience of the specimen over UNIT 3 is emprasised
by the fact that the maximum load capacity of the specimen was acbeived
during Run 8.
TABLE 1.1. Performance of U}JIT 4 During Load Cycling.
Run Maximum F Duotili ty Average ~oad
max: 100 Factor % ~ t max p Stiffness (kips) u
(%)
1 23.2 66.3 - 76.2 2 23.6 67.4 - 92.0 3 20.3 58.0 - 81.7 4 31.0 88.7 4.0 53.7 5 28.4 81. 1 4.6 33.7 6 1.9 22.6 - 17.0 1 4.9 14.0 - 18.2 8 31.3 89.6 10.7 18.0 9 22.2 63.5 16.0 6.5
10 22.G 64.6 21.8 3.6 '11 13.8 39.4 19.0 2.2
t E~pressed as % of the theoretical stiffness.
7. 7 CR.J\CKING:
'l'he development of the diagonal tension cracks sbown in Fig. 7. 2
eventually lead to a major crack. runninr, between OJ!posite corners of the
I r I
t:t I tt-·tt:l I I 7~· ~~~ I .
-I -9
-I
I
' ' -r·- --
· -r --- T rq . -+- >>
> --+
'
i
Deflection · (ins)'-" -6-- o-=s -4
-- ·--r--r I_-··.
-3
I ~ I i
c: ;;: 15 0 0
9
I
-----I r ·------
' II I 20; --t- tJ . ·
~-~--rt=t===Tl ; --+---l---t-~+~-1---i i~:1--+- L +-----~-r~~~r_ FiG. 7.12 THE LOAD DEFLECTION RELATIONSHIP FOR UNIT 4 ....lo
....lo
~
joint. Figs. 7.13 and 7.14 show the specimen at tbe peaks of Runs 4 and 5
respectively where it is shown that not only the diagonal tension cracks
were widening, but also flexural cracks at the junction of the beam and
column. Fig. 7.15 stows the specimen at the peak of Run 8, when flexural
yielding of both tbe beam and column bars has occurred and the cover con
crete is being forced off the back and sides of the joint. The cover
concrete was eventually completely removed from the joint, as shown by
Fig. 7 .16.
7.8 FAILURE MECHANISM:
The increase in load capacity of this specimen over the previous three
was primarily attributable to the increase in anchorage length of the beam
flexural bars.
115
At this stage it should be noted that the joint ties were more regularly
spia.0ed than they were for UNIT 3. However since this may have affected
the confinement slightly it would be more likely to improve the resilience
rather than the load capacity.
Because of the increased ancrorage length of the beam flexural bars
the tendency for bond failure was minimised, Until the repetitive load
cycling reduced the bond sufficiently to allow differential movement.
Since the anchorage length was not enough to dissipate the tensile stress
in the top beam bars durinc Run 4, the first post-elastic run, a further
increase in the length of the bars would possibly enable the theoretical
ultimate capacity of the specimen to be attained. The movement of the
flexural steel in_the joint is the prime cause of load capacity reduction
and initiates the joint deterioration by breaking the cohesion within the
joint.
\
,\ \ I
FIG. 7.13 UNIT 4 ON LOAD RUN 4 FIG. 7.14 UNIT 4 ON LOAD RUN 5
FIG. 7.15 UNIT 4 ON LOAD RUN 8
116
UNIT 4 FAILURE
117
Detail Shown in Fig.7.6
Although bond failure eventually dominated the stiffness degradation
and overall performance of the specimen, yielding of the flexural steel
did occur and would also bave influenced the behaviour to some extent.
Fig. 7.17 shows the specimen at the peak of cycle 11 where it is obvious
that the joint is still well confined by the ties, and the majority of
rotation is provided by the column outside the joint region.
118
CHAPTER EI GUT.
DISCUSSION AND CONCLUSIONS.
8.1 .COMPARISON OF SPECIMENS:
The beam-column joint is generally considered to provide its load
resis-tance by a type o:f truss mechanism, where the joint ties and the
concrete provide the tension and compression struts respectively. Two
alternative methods of distributing the forces on downward load runs are
shown in Figs. 8.1 (a) and 8.1 (b). Each of these would have a charact-
eristic crack pattern determined by the fact that compression cannot be
carried across an open crack. Fig. 8.2 shows the forces imposed on the
joint o:f UNIT 4 and the crack pattern at the peak of Run 1. Since the
cracking does not correspond to either of the distributions shown in Fig.
8.1, it is probable that the actual mechanism is some combination of these
distributions. However, to be effective both these systems require the joint
to perform as an integral unit. Because of the tendency for bond failure
of the flexural bars in the first three specimens, the force in the outer
column bars could not be distributed, since they were virtually separated
from the majority of the joint. Therefore th~ effectiveness of the truss
mechanism was significantly reduced.
The initial elastic cycles served to break up the joint sufficiently
so that the load capacity of the: first three specimens was limited by
the bond stress which could be developed between the beam flexural bars '
and the cracked concrete in the 1joint. Table 8.1 compares the bond stress
TABLE 8.1 Bond'Stress Developed in Beam Flexural Bars.
Unit F M • f f + f' urnax. u max; max. s s s ~·
(kips) (kip-in) (ksi) (ksi) (psi) f' 0
1 24.3 2960 29.4 40.5 317 5.2 2 27.3 3330• 33.0 44.6 350 4.7 3 24.8 3020 ·30.0 41.9 32-3 5.6 4 31.3 ·3820 37.9 - 377 5.8
11Q
' >4IIIS' ( '-. '\
~ ", \ '
111119.' '.., ''a-\ ' \\ '.
~. "<it
--~ ~ ">'(~
' ' .. \
" Ccb '"""1 ' '
--~ .. ~ Ts fcc
(a) (b)
FIG. 8.1 DISTRIBUTION OF INTERNAL FORCES
t39K 140K
}\ a--
fl-._
~ () ....____
~23K 0 0
0
( J!• •' '
172Kf 36K
FIG. 8.2 FORCES ON JOINT OF UNIT 4 (RUN 1)
developed in tbe beam flexural bars for each of the specimens, although the
value given for UNIT 4 does not represent the ultimate bond stress. The
recommendation by ACI 318 - 63 is given as
u u
However, from Table 8.1, no specimen attained this level. A more realistic
figure for this situation would be that specified for top bars
u u
§_J_ = D
which would represent the maximum obtainable bond stress unless the concrete
is more adequately confined as in UNIT 4. The anchorage length required
in UNIT 4 on the ACI 318 - 63 recommendation is ·
L ·. fA . i!s
= 7.6 ~lTD .. 45000 x(5
7.6 X 63 X 16
= 28.5 in.
In UNIT 4, 32 in. of anchorage was provided, which should therefore have
been adequate to develop t~e required bond stress.
Since the failures were always concrete failures tre .maximum loads
resisted by the specimens were largely dependent on the tensile and cn1shing
strength of the.concrete. This was shovm to be the case particularly for
the first three specimens. The maximum loads obtained and the tbeoretical
ultimate and yield loa,ds for each specimen are shown in Table 8.2 for com-
pari son.
TABLE 8.2 .Comparison of Theoretical and Actual Loads.
'UNIT f' tre6retical actual theoretical Fffiax -c yield load ultimate load 100 (ksi) · · maximum 1 oad ~X
P; (kips) Ttnax· (kips) P~ (kips) u '/o
1 3. 73, 32.7 24.3 34.3 71% 2 5.57 35.2 27.0 35.9 75% 3 3.44 32.3 24.7 34.2 72% 4 4.22 33.3 31.3 35.0 90%
121
The maximum column moment ar.rieved in UNI~ 4 was
M = 1690 kip-in, e
whic~ is lower tran the theoret1cal moment at fi~st yield of the tension
steel, for a col1imn of this size. Therefore if the column had been behav-
ing as a composite structural roGmb.er the flexural steel would not have
,yielded, 'l'he far.t that the steel did yieJ d suggests that only tre r.olunm
core was t'ne effective structural member. By nep;lectine; tr,e structural
action of the cover concrete the ultimate moment c:J.padty of the column
core, of dimension~ 13.5" x 13.5" is
M 1760 kip-in. uc
However this moment capacity was not acrieved due to tre rremature ,ioint
failure,
The diffe~ence in stiffness of the specimens was •1ui te apro.rent r:1u~ing
testinp and Table 8.3 tabfilates the deflection crara~teristics for com-
11arison, Tre theoretical rotation of tne column .:md be.:~m '~-ave been r'leter-
mined for bot~ unnran~ed and crJcked sections And ~ompare~ wit~ t~e a~tual
values obtained in RunE> 1, 2 and 3.
The column rotation is predi~te<.1 re':tson,~1bl:r ncr:urately in most cases
by the theory o~ a cracked concrete section, , However the deflection ~t the
122
end of the beam is, in all cases, gre~J.ter thun t'reoretically preriictecJ. Tri:·
is du8 to joint distortion not being taken into account w~en comrutin~ the
theoretical roto.tions an~ deflections. It can be seen from Table 8,3 t~at
~oint diAtortion c9n have a conAidersbla effect on the de¥lectirm of tte
beqm, ex:peci'll Jy in TJNJT 3 where the l0w c0ncrete Rtren,s-tn means t'bat joint
distortion acM•mb ·for more tn:m riO';'t of t'"e totnl. deflectjon of the beRm,
The extr2. rot0.tion o~ t'he ,i0i:nt .111:',0 ,<>ffef'!ts the deflection of
123
'.:'/1BLE 8 .. 1 ,.,ornparison of Tl--eoreticJ.l ·.md A"tnal Rotn.t.ions ann Deflections.
. TJI\ IT- ·-~u~ ·~il-B-.X-.i-m_u_m..,...~~t·-h-e-or.-.·e_t_.J-.. c-a_l_....,fTtr-l-te-o~'etical actual ~_.,-1
CO
r Load uncracked cl·a_c_k_e_d_...,.. __ +------r---tij;;x max. r1. 6. ¢ ~ ¢ 6. '/o
(kips) 'f uncr. 0 uncr. cr·, 1 cr.
3
23.9 24.3 20.9
radP x 1CL (in) rads x 10'· (in)
.13
.13 • 11
• 38 • 39 • 33
.22
.23 • 20
• 61 • 62 • 54
~.,
x··:1ds X 1C (in)
• 30 • 34 .26
1. 28 1. 50 1. 15
48~{, 411· 47{i,
1----+-~f----+-----+--+·-----+---lr----···-~---~---~---1
2 1 2 3
24,C 26.3 22.7
• 11 .12 • 12
.33 .20 ·55
.36 .21 .61 • 36 • 21 • 58
.18
.25 • 16
0.80 69% .,. 01 61% ·J. 83 7o%·
r-----;---~~-----~+---------+----+----------+---~r-~-------~--_.--------~
3 1 2
22,0 22.9 19,7
• 12 .13 • 11
• 36 • 21' • 58 . 33 1. 37 • 3 7 . 22 . 60 • 41 1. 66 .31 .19 .51 .25 1.18
~----~----~-------~---------+~---+~--------+-----r.-·--~--------~---------·~
4 ,.., L
3
23.2 23~6 20.3
• 12 • 12 • :11
• 35 .36 • 31
. 21
. 21
. 18
• 58 • 17 • 7 6 .59 .18 .oo ,51 .13 .63
~-----~----~------d----------~-----L----~--- ------~---------L--~6-----~
A comparison can be made between the shear roini:orcement provided in
the joint of caob. ~3pecimen and the tJ-,eoretical re<}uirements,
T;:, ble 8, 4 compares t}1e amount of shear reinforcement by vario•Js U ff'eren t
metbods. Methods A and B are commonl;y used h1 desi,ct1 and are tbose recommended c:;
by the 11Cl-'. Metbod C is the most conserva.,ive met\ od, not c:;,l1owin:, f(_;r s.ny
.Jrear resi3taune from tbe concrete. The shear reir1:norcement for these tr:ree
10U:ode i:~ provided on tr·e basis of 45° craf'k.:ing. Eethodr; D,E, and F differ
from Uese in the way in wbich shear reinfo1·cernent is computed. The basis '
be\d_nd tte tl;eor:y is that tbe major ohe:.1r cr·ack runs betweer! oprosi te corners
0f the joint, and t~e ties are provided to rrevent the joint from sep1rating
.tlonr; ttis cr·ack.
T~BLE 8._1: Joint Shear Reinforcement.
-Ul~IT Numl1er Ratio: shear reinf,.>rcement prov~
of x·er1ui:red Ties A B c ( m)
1 h. 0.83 0.67 ·0.52 2 7 1. 25 0.91 0.70 3 9 1. 48 1. 20 0.94 ~f 9 1. 50 1.17 0.91
v c = 3.5 bd Jf' (1 + o.oo2 N;, );
C A
v d v
c bd ( 1 o 9 ~ f ~ + 2 500p W .~ 1 ) ;
C: 0;
D: V as for A; ~
E: V as for B; ()
F: v <)
0;
8. 2 ,.~BITit;n~.~,~ OF THE m~TAIL:
.1·
g
sl'. Jar D
I. 34 2.02 ). 38 :?.42
v s
v s
reinforcement H: ""
1. 07 1. 47 1, 93 1. !';9
A f v y
F
.o •. S4 1. 12 1. 51 1. 47
A f d/s v y
A f v y
V == m2a f s v y
v s m2a.f v y
m2a f v y
0 The 45 crack theory 1•as bGen developed from she:u tests on reinforced
concrete flexural members. However wren tbe member is subjected to a com-
rressi ve stress, suer; as a column under axial load, the angle of cracking ' .
is af·r'ected. :B'or example using the si tua t: on srown ln Fi[t:. 8, 2, for any
elemerJt witl:in the joiil.t:
sbear stress, v = 1~0 ::: 623 psi 15 X 15
compressive stress, f 148 658 psi == 15 15 -X
Tl1e direction of maximum diagonal tension is found from
tan o< 2v 1. 89 ::t
f :=
:.:: 31°
The ar;gle of the rnain crack s'bown in Fig. 8. 2 is 3Jr) to t"'e vertical. T1;ere-
fore it is ap:rarent that the preserJt recomtnendati<)rJS for design of r:;he:s.r
reinforcement in joints is based on an inv1lid assumption.
The formula used to determine the arno'.mt of transverse confining steel
required is based on maintaining the original strength of the column when
tr.e cover concrete has 1Jeen removed, howevGr it would seem more appropriate
to provide this reinforcement on a basis of achieving adec1uate ductility.
These tests have shown that cover concrete ·provides minimal structural
resistance during post-elastic load cycles, and therefore it would seem
desirable to consider the column core as tr.e structural member. Then tr.e
Ag/A ratio is meaningless, and only serves to introduce a highly variable c
facto1• wben considering different size columns.
be more dependent on the l~/A ratio and prob.s.bly c
The bursting pressure should
on the value of f' c· The
restr.:dning effect of the hoops is dependent on fy' Ash' sand h'. How
ever as shown in Fig. 8.3 the Festraint provided by the hoops relies on the
flexural resistance of one leg of the hoop between its two supports. Since
2 the s't1·ess on the bar is dependent on ( h') , more emphasis should be placed
on reducing the value of h' as much as possible. Since only four column
flexural bars were provided the legs of each tie were unrestrained over a
distance of more tban 12 in. This was shown to be particularly unfavourable
for confinement but generalJ.y, with a e;reater number of bars in tr.e column
the problem is not as critical as it was here.
~he major downfall of the detail was caused by the rnet}'od of anol:oring
tbe b~3am bar·::: in t1:.e column in the continuous form. As shown in Section
8, 1 tl:e bond stress required to attain .theoretical ultimate load was greater
than could be developed, due partly to the lack of confinement \':hich meant
that tre only efficient bond was on tbe inside of the anchorage hooks. The
0imensions of the joint meant that the horizontal length of anchorage before
the hook, which provides the most efficient anchorage for the beam bars, was
small enough to allow rotation of the beam bars within the column once .the
l1om1 was weakened. UNIT 4 showed 'tbnt adeq .. wte anchorage could be provided
if detailed properly.
I h'
t t t t t assumed uniform
pressure
.FIG. 8.3 PRESSURE ON ONE LEG OF TIE
H
T 51~''
t ~ ·-t 25"
-
t .. -·~
i 122" I
54"
j_ . H t
FIG: 8.4 DIMENSIONS OF SPECIMEN
127
The original analysis, based on centre-line dimensions indicated that
the beam was 20% stronger than tbe column. However, if the analysis was
done accour1ting for the actual size of. members this was not the case. Fig.
8.4 shows the load situation. At theoretical ultimate of tr·e column
M = · 1875 kip ... in. uc
~ := 122 p = 122 X 1~15 Since P ::::: H.
= 4230 kip-in.
Mub ·.12QQ 1. 07 Mb
::::
4230 =
Due to this oversight tbe beam would actually be on the point «>f yield-
ing which was not anticipated. However it did not affect the outcome of
the results significantly since the theoretical ultimate load was not attained
during testing.
8. 3 RECOMMENDATIOl~S:
These recommendations apply only to isolated joints, since if beams
frame in on an;;r of the other three sides of the joint they would act as
efficient confinement for the colunm core, and also keep the joint intact,
providing more favourable bond and shear conditions. Special provisions
also apply because of the cyclic load imposed. It was apparent during
testing that many of the regions, which would have adequately withstood
a direct load application, gradually deteriorated under tre reversed load-
ing, thereby reducing the load capacity. When designing for ductility it
is obvious tl-at code requirements must be adhered to, wit'\: particular
emphasis being placed on ·the strength of the joint.
The anchorage lengths, particularly for the beam flexural bars, must
at least comply with the requirements of ACI 318 - 7"1. The theory which was
the basis of t~e 'continuous arrangement in UNITS 1, 2, and 3 is therefore
not applicable. In fact an anchorage length of 50 in. is required (see
Appendix B), which would mean carrying the beam flexural bars through the
joint, necessitating a stub at the back of the column. The sepa~ate anchor-
ages appeared to give sufficient development length in UNIT 4. An increase
in anchorage length would ensure the maximum load capacity was retained over
a greater number of load cycles. Construction techniques require a con
struction joint in the column just below the level of the beam, and there~
128
fore, for ease of construction, the anchorage length of the top beam flexural
bars should not protrude below this level. This is the reason for the
popularity of the continuous arrangement. If necessary the size of the
bars can be reduced and the number of bars increased in order to reduce
the required development length.
The design of the joint reinforcement is a critical factor in determin-
ing the strength of the joint. From the results obtained the diagonal
tension cracks run between opposite corners of the joint. Therefore, all
the joint ties cross the major crack, although on each load run not all
the ties work efficiently. It can be assumed that a certain percentage
of the ties work to their full capacity on each load run, neglecting the
remaining ties. For example, if 75% of the ties are effective, then for
the joint design:
= o. 75 m 2a f v y
v =0 c 171.3 = 0.75 m 2 X 0.31 X 45
number of ties, m ::: 8.2
Nine joint ties would be req_uired. For this type of mechanism the shear
resistance of the concrete should be neglected.
Tests could be carried out on joints of both narrow and wide columns
to investigate the thebry of corner-to-corner cracking and also to deter
mine to what extent the configuration of the anchorage detail in the joint
affects the bond strength of the beam flexural bars.
In order to improve the confinement within the joint of these specimens,
the reduot.ion in.the unrestrained length of the legs of the ties could only
be aohieve·d by cross-ties, laterally restraining the legs of each tie. The
.effect of reducing the unrestrained length needs to be investigated in
greater detail. However it is obvious from the bowing of the ties in these
tests that there should be an ·upper limit on the value of h'. This is
particularly so when large shear forces are imposed, since it is apparent
that once the steel has yielded its effectiveness as confining reinforce
ment is significantly reduced.
APrENDIX A.
A. 1 MATERIALS.
The ready mixed concrete was brought to the laboratory by agitator
truck from the plant. Concrete with a cement content of 390 lb/yd3 and
water: cement ratio of 0.701 was specified. This gave a certified crush-
ing strengt}! of 2,500 psi at 28 days and a 3 in. slump. Actual concrete
crusting strengths at the time of testing were found from compression
te'sts on standard cylinders, 12 in, Yi~jh by 6in. diiimeter. Tests were also
performed on 3" x 3" x 12" prisms to determine the tensile st:rene;th of the
concrete. The average of four compressive tests and three tensile tests
for each specimen are given in Table A.1.
TABLE A. 1. Material Properties.
130
UNIT ,Concrete # 10 beam # 9 column ¢5 joint ¢3 beam column flexural steel flexural' steel ties stirrups ties *
f' ft f f f f f f f f f f c y u y u y u y u y u (psi) v . ) (k.si) (k.si) (ksi) (ksi) (ksi) (ksi) (ksi) (ksi) (ksi) (ksi) psJ.
1 3730 610 43.1 66.8 44.7 68.7 45.1 72.8 43.6 69.6 48.6 75.3 2 5570 770 42.2 66.6 45.3 69.6 46.7 72.6 44.1 69.9 46.2 73.2 3 3440 550 41.9 66.6 45.2 69.0 45.4 72. 3 43. 3 68.9 46.4 71,6 4 4220 640 43.7 63.1 45.4 69.7 45.4 72.3 43.5 69.3 46.8 71. 6
* ¢2 ties in illUTS 1 and 2; ¢3 ties in illUTS 3 a.nd 4.
The mild steel reinfordng bars used tr·rougrout t'be testing had n
guaranteed minimum yield strength of 40,000 psi. Deformed bar was used as
longitudinal steel and plain bars as transverse steel, T~e average yield
and ultimate tensile strengths for all the bn.rs are given in Table A, 1.
A. 2 l~'ABRIC:l TIOl~ OF SrE~IMbK.
The reinforcing bars were cut to length and cold bent to form the
components of the structure. Then the strain measuring devices, either
demec studs or electric resistance strain gauges, were placed in position
/
131
FIG· A.1
REINFORCING CAGE OF UNI
1T 1
FIG. A.2
REINFORCING CAGE POSITIONED IN MOULD
FIG. A.3
JOINT OF UNIT 1 SHOWING DEMEC STUDS
before the reinforcing cage was put tag~ther~ The transverse and longitud
inai bars were tied tqgether with tie~w~re to form the reinforcing cage,
as shown in Fig. A. 1, except at the.extrem~ties of the beam and column where
th~ bars were .tack .welded in order to pos~tipn trem accurately. Then the
cage was lowered into posi t:ton in the b.eam ... oolumn mould, .as shown in Figs.
A.2 and A.3 •.
Tbe mould itself, shown in Fig. A.~ 1 consisted of Mreboard sl'·eets
bolted to a steel framework. This rested on adjustable legs which l'lould
be raised or lo•••ered. to minin~ise defleotior>. of the base. The sides of the !
mould were steel channel sections which ensu:red the dimensi.onal accuracy of
the members. These were bolted to the base of the mould and could be easily
removed when stripping·the specimen,
When the concrete arrived it w~~ plaoeq ev~nly over the reinforcing and
vibrated with a. spud vibrator. The oon'orete~ waa then covered and moist cured
for seven days before the mould was ertr~·pped and the speoime~ prepared for
testing'.
A. 3 TEST RIG.
The test rig had been desi@.~ed and useq for teatin~ ~reatressed con
C'rete frameo 12 and minor modifioations ~o tre' capacity and the beam l·oading
apparatun ·enabled it to be sui ta.hle for teating tl·ese reinforced concrete
beam-column joints. Th'l test rig apd specimen are ahown in Fig. A .. 4. The
1 oading r1ead above tr:e ~liYdraulic ram at the top of the o61umn transfers
tl'.e load to the laboratory floor by means of an A-frame arrangement in tl;le
plane perpendicular to the diagram'. The rollers at the top and bottom of
the ~olumn enable the column to t'otate as ringed supports.; The available I
def1 ections were Hi" in the upwa:rd direct. ion and tO" in the downward dir-
ection for t.J1IT9 1 and 2. The "step" at the end of t~e beam in UNITS 3
and 4 ~}:;own in F!l.g·s. 6. 1 anc~ 7. 1 t.mil ple the a van able downwa:r-d deflection
to be inorea('led also to 16",
132
~ ,_
rae..-
FIG. A.4 (a) TEST G 0 SPECIMEN
~ 1J D J!l -strain eel.l fer ~ mea~ring loCCI
(b) BEAM LOADING FRAME
_,. w w
A.4
The colu~J load was applied by means of a 100 ton capacity hydraulic
ram at tbe JGop· of th(coJ cJOlumn, read:!.ly adjustabh) by a l1and pump. 1.l'r1e
minimum column load of 148 kips remained (:onstant o:n downward load rur1s 9
however the load at the top of the column varied on upward load runs.
Occasional adjustment of the; load was necessary at times to alJ ow for
movement of the column.
The end beam load was apr;lied hy means of screw ,jacks as sl'OWD i:n li'ig.
A. 4. 'l1he screw jacks allow for a.pplication of measured displacements whieh
is desirable when loading into the post~elastic range. The posHion of the
apparatus in F'ig. A. 4 is as it would be for a downward load :rw;1. On reversal
of load the load cell is ·trc·rwferred to the upper screw jack and ·tl'e load
applied.
111he hydraulic ram a·t the top of the column was ~omJE~e·ted. in
r)arallel wi tr. anot~'er 100 ton mtpaoi ty hydrClulic ram and 100 ton 1oar1 con
wl':lr~h wore braced against tre loading bead of a test mac1'ine, Sinee tl~e
}JYdrauJ.ic.pressure in bo"tJo hOB8S was tl'e same, tr·G lo.Jd nell (;';avi? a l!l8CltlUJ:'e
of the load bein~ applied at the top of the coluom.
rl'be 20 ton load cell shown in Fig. A, 4 vns u~1ed to ii18Llf:J\U'Il thG load
on the end of the beam.
Both of t:1ese load cells were calibrated on an Avery 250,000 llJ Untversal
TeGting l1lachine v1.i th a Budd Strain Bridee.
Tl•o olectric .resistance strain gauges on the ·1 in. diameter J-,igb
strengt1~ tension rods, show:n in Fig. A.4 (b) gave an alternative! measure~·
ment of thEl beam load. 11wo aoti ve and rt;wo compenenting gauges on each
bar ensured that the results were accurate even if bending of the bars
occurred.
'rbese strain gauges were calibrated against the 20 ton load cel1 and
recorded direc-tly by the movement of tbe pens or1 tbe Y - axes of two X ~· Y
plotters connected in series (see section A.5.2).
A.5.2 Rotations.
Frames were connected to tl--e colunm above and bolow ·the joint at
distances of 7L in. and 15 in. from tl:e bear1, as sbovm h1 F'ig, A, 5. Dial
gauge:1 were attached to the frames to record the column rotation over the
.15 in, immediately adjacent to the joint. However the majority of the
rotation occurred between the beam face and the first gauge frame, a dis~
tance of 7i in. This region, which represents a distance of t/2, generally
provided greater than 80}s of the total column rotation. Fig. A.6 shows the
1 in6 capacity, 0.001 in. Mercer dial gauges attached to the frames above
the J;int at the ·back of the column.
Linear variable displo.cement transducers were .also connected between
tl:le first frawe and the beam ac sllovm in Fig. A. 6, T'hese gave a m0asure
of tt-n "'.lll.lfm1 rc)tation as a movement of the pens on the X ~ axes of trJE3
;z - Y plo-tters One X - Y plotter recorded t~e colunm rotOl tio:n above the
joint 1 an<l tl'e otrer recorded t1~e column rotation below the joint. Wben
combined wit~ the load measurement as described in section A.5.1 1 the X- Y
'Plotters gave a direct ';)lot of tr.e Joad-ro-tation relationsbips for eacr;
r8gion durin;~ tr1e test. Tr~e linear variable rlisplacement transducers were
co.libra•ted against a micrometer VJrich r.ould be rend directly to 0.001 in.
Dial gauges were positioned on the svec~nen to record the deflect-
~135
FIG.A.5 SPECIMEN PREPARED FOR TESTING
I -., i \
~-
!'0 (t.
i . ' (t
FIG A.6 ROTATION AND DEFLECTION RECORDING APPARATUS
136
lons of the l)eam and column so that defleded shapes could be obtained.
'.l.'hese were 2 in. capacity 0.001 in. Mercer dial gauges, one of wh:ich can
be seen in Fig. A. 6 NJoording the column deflection.
For deflections at the end of the beam a graduated scale was attached
'1
to tLe beam loading frame and a pointer on the beam gave deflc'lct:i.on readings 7
once the dia1 gauge had exceeded the li.mi t of i.tFJ traveL
To reoord the movement of the test rig a steel rule was attached to
tre lorizontal reaction frame at tbe top of the column whict was read tbrough
a fixed theodolite. Adjustments were made to the deflection readings to
oompensate for tbis movement.
A. 5. 4 s·train Measurements.
A. 5. 4. 1 DEMEO Gauges.
These were used to record the strain readings on all the re
inforaing steel for UNITS ·1 and 2. The advantage of this method is that the
readings give a continuous distribution of strain along the rE)inforcing bar"
Each reading, on the side of the specimen was duplicated with a reading on
the opposite side. The mean of tl1ese readings was plotted in the r:rtra111
distribution diagrams provided each reading dB no·t vary by more than 10;~
from the mean. 'Phe demec s·tuds on which the readings are taken can be
seen nlearly in Fig. A.3. The most apparent inaccuracy in these readings
occur:3 wren the reinforcing bar is bent, ra tl"'er tl."an being subjected to a
direct tensile, or compressive strain. This was the case wi tr tl1e joint
ties in tbese speo~mens when ttey bowed outwards due to the bursting pressure
from tbe columr) core, From tho re~orded strain readings it is apparent that
t1~,e ties· bowed as shown in Fig. A. 7, due to the configuration of tbe cracks.
To determine the effect thaJj l10wing of the ties ra'J on tl;e strain readings,
c ~~\
1 internal
D '=f_---~. . cracks I . I . . -----:~
FIG. A. 7 BOWING OF .JOINT TIES DUE TO BURSTING PRESSURE OF COLUMN CORE
(a) <b> FIG. A. S SHAPE OF BAC~ OF TIE DUE TO INTERNAL PRESSURE
f
139
assume as in Figs. A.8 (a) and (b) that the curve at the back of the column
resembles a parabola.
Then·
where r = i in. for i in. diameter joint ties
but 6 = 4~* x 10-6 in.
where e* is the difference between the DEMEO reading and the actual strain,
in miorostrains. . -6
8.e* x 10 rads. __ (A.1).
from Fig. A.8 (b)
at y "' 4:
2 Y = 4g X
g
X "": .1 g
cot6 = tan ~
cote
= 4g.6
= ~ A
= r.f6 = d X 7.56
=~ ___ (A.2).
A relationship can be established between equations (A.1) and (A.2) to
deterraine the difference in strain readings.
For example, when A = 0 •. 01 in.
from Eqn. A.2 cote. = 378.
i.e. e = 00 9'
= 2.62 x 10-3 rads.
fro.m ~qn. A. 1 e* = 330 microstrains.
For low values of Q, this will be a linear relationsr.ip. From this it can
be seen that the tie only has to bow outwards a very small amount to produce
a substantial inaccuracy in the strain readings from the DEMEC gauge.
The colurm bars are also prone to local bending, producing tbe same
inaccuracies, when tr.ey are not adequately confined. This effect can be
seen on the strain distribution diagrams in the region where the beam tensile
bars enter the. column.
To check on the theory of the joint ties bowing and givinr, false DEMEO
strain readings, electric resistance strain gauges were placed between the
demec studs on the joint ties of UNIT 3.
A.5.4.2 Electric Resistance Strain Gauges.
The gauges used were KYOWA type l<F - 10 - C8 - 11 of length
10 mm. and 120 ohm resistance. Trese were attacred to tre reinforcing bars
with JTiastman 910 adhesive 'Phich, in :Preliminary calibration tests,gave
satisfactory results right up to·:fracture of the test bar. The gauges
used on tbe test s:recimens were waterproofed with sealing wax and water-
proof Den so Tape. However tbis was inadequate, and in some cases w.':!s
fou11d to contribute to failure of the gauges. Fig. A.9 shows the electric
rE3sistance strain gauges positioned on the joint ties, covered with the
waterproof tape.
FlO. A. 9 JOINT OF REINFORCING CAGE OF UNIT 3 POSITIONED IN MOULD
140
The strain g-c1uge readings are shown for UNITS 3 and 4 in Chapters 6
and 7 and the distribution of strain in the joint ties verifies that the
bowing of these ties affects the DEMEO readings to a marked degree. This
means tr.at the DEMEO readings on the joint ties of UNIT 1 and 2 are not
repre::1entative of the tensile s.train in the steel. However they give an
indication of the bowing of the ties, and have been shown as dashed lines
on the strain distribution diagrams.
141
B. 1 DESIGN CAL,ULATIONS.
B.1..1 Column Reinforcement:
bd
APT'ENDIX B.
4 = 15 X 12.94 ·
= 0.0206
B.1.2 Balanced Load of Column:
e = ~:2000 6 = 0.00155 y 29 X 10
cb = 0.003 d 0.003 + ey
ob :::: 0.003 X 12.2~
0.00455
::: 8.55 in.
ab == 0.85 x 8.55 "' 7.26 in.
(e' = 0.003 X cb - 2.1
0.0023, compression = s cb
yielding).
N -b = 0.85 f~ ~ b
steel
= 0.85 X 4000 X 7.26 X 15
::: 370,000 lbs.
D.1.3 Ultimate Moment Capacity of the Column.
at ultimate a N = o.85 r• o c
142
is also
= 148 0.85 X 4000 X 15
== 2. 90 in.
M = 0 85 f' ab (.i- ~) +A f (d - t) + A'f (i- d') uc • c (2 ~ 8 y 2 s y 2 .
= 0.85 X 4 X 2.9 X 15 (7.5 - ~.45) + 2 X 96 X 5.44
= 895 + 980
= 1875 kip-in.
B.1.4 Beam Reinforcement:.
A AI 4 1 23 -- ,Ao92 ~, 2 • s= s"" x • + ......
bd = 12 X 22.9
p = p' = 4.92 12 X 22.9
= 0.018
B. 1,5 Annhorage Requirements from A. C. I, 318- 71.
::: 34.9 in,
(0.004 Df = 0.004 x 1.25 x 45,000 = 22 in). y
from 12. 5. 1 ( d) 1.1M
reduction factor of uc 1. 2 M uc
is applied since Muo
= 32.0 in.
from 12.8 using a standard hook
90° bend + 12 D = 15~.
= 1. 2 M u
fh = 360 J 4000 ~ 22,800
143
increase of 30-j, is allowed for confinement
22,800 X 1.3
29, 6oo psi.
. gs___ 29600 0.04 X ~X 4000 ·
= 23 in.
Therefore 9 in. must be provided apart from tbe standard hook, measured
from the column face.
B.1e6 Analysis of U-type Anchorage Detail.
Since the beam was expected to remain in tt.e elastic range, when
one set of bars is at maximum stress in tension the stress in the opposing
bars can be found from equilibrium and strain compatibility.
k =Jn2 (p' + p) 2 + 2n (p' ~ + p) - n (p' + p).
p = p' = 0.018
d1 ~ 2.1 = 0.092 J 22.9
k = 0.628- 0.286
= 0.342
kd = 7.8 in.
f' ::;: f kd - 2.1 s s 22.9 - kd
== 1tr fs
= 0.378 f s
From code requirements, the anchorage length of bars in compression is
obtair~ed from 12. 6.1, ACI 318 - 71, where
Ld = 0.02 fy D
:::
Jf!:"" c
0.02 X 45000 X 1.25
J4000
17.8 in,
144
T'ltal length of ancrorage for tne bars would be
32 + 18.
50 in.
However, this is assuming that the bars are stressed to their yield stress.
\'Jnen the bars are kept at a lower stress then, theoretically, t!ey req_uire
less anohorage length. The anchorage length required in compression would
·be
== 6. 7 in.
Total length of anchorage required would then be
= 39 in.
The U-type of anchorage detai1 tn this heam provides 40 in. of anchorage
between column facss.
bond strength U: ( f
8 + f~) 41T D2
= 41T D X L X 4 ( f + f 9 ) D ::: s s
=
41 1.378 fs D
41
To determine the steel stress in the bars, f , at maximum load: s
M_ = A f (d- kd) - A'f' (d' - kd) -~ s s . 3 s s 3
= 4.92 f (20.3) - 4.92 X 0.378 s
= 101 f s
M bmax. ::= 4230 kip-in (section 8. 2).
f = Mb s TOT
= 41 ,800 psi
f ( o. 5). s
145
B.1.7 Joint Hoops for Confinement from A.C.T. 318- 71.
from A,6,4,3 A "' s ..
wl:ere from 1 o. 9. ~:·: p! ,_,
= h'p' s s 2
U "'4nu ii. • -·-~ b a 1.n, diameter hoops: ·
p' s
s
4000 = 0.45 (0.28) 45000
f' f'; ::: 0.126 c >0.12 c f - y f y
"" 0.0112
= 2 Ash
h'p' s
o. 612 "" 12.625 X 0,0112
4.3 in.
but the maximum al1mm1)]e spacing is 4 in.
Tl,erefore five hoops are rerptll ~d 1n t'oe space cf' i;he joint,
B. 1. 8, Joint Ties . for Shf ~ir:
maximum force expec'Gi;d for the design spe~imen.
T 41.8 X 4.92
::: 206 kips.
= .1.[Zj,
54 nolumn shear .. H
:::: 34.7 kips.
joint shear force vj "" T - H,
- 171.3 kips.
fTom 11.4.3, ACI 3i8- 71:
'11h8 n.• i;] .)d Ut>Eld fe-r UlJI'rS awl 2 was:-
v Li. c
t -N';-3.5 bd Jf~ 1 + o.oo~ · A g
146
. 1 !\ ~- )-3.5 X 15 X 12.94 ~4000 (1 + 0,002 X 0'<-~ '-•
v s
from a v
65. 3 kips.
v' -· v J c
= 106 kips.
v s s
2fi 106 X 20.8
2 X 45 X 12.94
f P, ' Ol' 8 1n. diameter.· ties:
numt)8T of ties,
a v
m
.0 :: o. 307 in.._.
106 X 20.8 2 X 45 X 12.94 X 0.307
::::: 6. 1
Fl.ve joint ties were used in Ul-IT 1, Lind seven in UNI'l1 2.
Tbe 11ore oonserv3.tive method from ACI 318- 71, 11.4.3, gives v d
v = v ba ,._ bd ( 1. 9 ffT + 2500 p .1 -~ ) c c 'd .L (', 11
M' =c M _ N (4t - d) u u 8
--60 1 ') 9-4 . 127 5 ~ ·t48 ( - ri '- • - )
-- 1005 kip-in,
v :-.":
c 15 X 12.9,~ (1.S' ''"20 J4ooo + 2500 x o~o2oG .x ~;05 )
44 • .3 kip::~.
rJ == 171.3 - 44.3 s
127 kips.
rnunlH:'ll' of ties, 127 X 2C.8 tit "' r,
X 45 X 12.94 X o. 307 ,_
:= 7.4
Tl'erefore the nir,e joint ties, used in both UNITS 3 and 4, more them s:1 tis:i.fu 1
In ordet to compare the use of the different methods shovm in Table 8. 4, actu?..l
1ll:l terial prorcrtien for eanh Sl~ecimen were inoer·ted in the above eci.l\ations,
~. 1. 9 Column Ties for Shear.
vu = ll
nominal t in, diameter ties only are re1luired at tl't) le•ast spacir1g of~
16 D = 16 X 1i = 18 in.
48 D = 48 x t =· 12 in.
or 15 in.
Therefore column ties were !"diameter at 12 in. spacing, in UNITS 1 and 2.
B.1.10 Confinement of the Column:
using ~ in.· diameter ties:
A c
p' s
s
=
-
"'
=
12.7511 i 12.7511 a 162.5
o.45 (0 • .385) Sc i~ggo
0.0153
2 X 0. 11 0.0153 X 12.375
1. 2 in.
2 in •
:Because of the unlikel:Lll<>n(l <jf' a failure outside the joint region the
·E· Jn. cUamet(:Jr t:tes were at 2 in. spacing, in the region immediately adjacent
to the joint.
B.1.11 Shear in the Beam:
p 34.7 kips. max,
v :::: v bd "' 2 m bd c c c ..
"' 2 hooo x 12 X 22.9
= 35 kips.
nominal stirrups only rertuired in the beam.
B. 2 THEORETICAL rREDICTIOlJS.
B, 2. 1 Cracking. I
i4B
B.2.1.1 ~:
When the beam is on the point of cr~cking.
from equilibrium and similar triangles
kd 12.5 in.
M = l fcbkd ( 23. X 25) + f A (20.8). s s
f kd - 2.1
f = f' = n t x kd s s
= 0.83 nft
M ~ 6 ft X 12 X 12.5 X !2 + 4.92 X 20.8 X 0.83 nft
~ (1250 + 85 n) ft
The loads at which cracking is predicted to occur in the beam are given in
Table B. 1.
TABLE B. 1. Beam Cracking Loads.
tnUT f' (psi) l1 ft (psi) M (kip-in) p (kips) c cr. 0r
1 3730 8.3 610 1190 9.8 2 5570 5.8 770 1410 11. 6 3 3440 8.7 550 1090 8.9 4 4220 7.8 640 1220 10.0
-
Where n
B. 2. 1. 2 Column.
f N Mi = r + I n c
A == A + (n - 1) Ast n g
= 225 + 4 (n - 1)
-y :::: 7.5 in.
149
I ::::: bt3 + A t (n -. 1) ct- d'>2 .c 12. s
. . 3 (5.44) 2
= 15 x1,15) + 4 (n _ 1)
= 4220 + 118 (n - 1)
When the concrete is at its ultimate tensile strength in the tension
fibre:
lT = r .±.
n
M -cr,y 1 c
Table B.2 gives the predicted c:racking loads for the column.
TABLE B. 2 Column Cracking Lo.ads •.
illTIT n-1 ¥-(psi) ft (psi) I (in4) M . (kip-in) p (kips)
1 2 3 4
n c or.
7.3 583 610: 5081 809 5.8 597 770 4905 895 7.7 578 550 51.29 771 6.8 587 640 5023 823
----~-._..,c,,
n.2.2 Yield Load:
At first yield of the column flexura.l steel:
f' r• "
= c - d' f d - c y
= a _; o. 85d' f o.B5d - a y
= a-1.75x 4'l 11,0-a ~
and N ~ 0.85 f'ab + A'f' - A ~ c s s s y
cr.
15.0 16.6 14.3 15.2
0 8 f ' a - 1.75 = o 5 X 15a + 2 X 11 O c • - a 148 X 45 - 2 X 45
= 12.75 f' a + 90 (2a - 12.75) 0 11.0- a
150
a2
- c~1· 1 + 11.0) a + 2~7· 5 = 0 __ (B.1)
c c
151
from tris equatior1 ~:md
M 0 85 f' b (t a) + A1 f 1 (i- d') +A f (d..: l) · "' • · oa .2·- 2 e e 2 a y 2
.= 12.75,f~a (7.5- ;) + 10.9 (f~ + fy)
the moment and therefore the load, at wh:i.~h first yield of the column
fle:rura 1 steel should theoretically oocur7 can be determined. The.se are
given in Table B.3 for eao~' specimen.
!_ABLE B.J Theoretical Yield Loads.
UNIT f' a f' M c e . (kai). (in) {ksi) l?=ip-in
1 3. 73 4. 28. 16.9 1766 2 5.57 3.14 8.0 1900. 3 3.44 4.55 19.5 1745 4 4.22 3 .. 92 13.8 1808
~rhr;) :co·i;a tion of Ue colu:mn can be. ~o~d ,by the moment-area method. . .. • ·'. C•
M .21 5~x2 _1, = E I X 2 X 3 X 54 0 c
¢
and M = 54 I'
¢ :~ 9E!,. E I
0 G···.
•ubox·e E ,.. w 1• 5 33 1fT c ~Io
TABLE B-'_4 Load-Rotation Relationships :t:pr the Column •
. ~,-·-~ U:ncracked Section CrF.l.oked Seci.ion
Ul~IT E I ¢ 8 1 9l 8 0 -6 0 04
(psi :x 10 ) (in4) {rads x 10 ) (in ) ( I'D.d S X 1 0 )
1 ' 3.48 5081 5.49 p 2966 9.42 r 2 4.25 4905 4.66 p ?806 8.15 p 3 3. 34 5129 5. 67 p 3020 9.64 p
I
4 3. 70 5023' 5.23 p 2909 9. 04 I)
The 1 oad rota t:ion rela tio:ns'rlip i[; given in Table B. 4 for ·tr:e column ill the
uncracked and cracked condi tiona.
When the column ie c1·acked, the .extent of 'cranking depends on the
magnitude of P. However thir3 was found to have a negligible effect on
tJ·,e vnlue of I , for the range considered. c
152
I :::. b(kd)3
+ bkd (.i.:. k<i) 2 +A (n- 1) (d -1) 2 +A' (n- 1) (t- d') 2 c '12 2 2 s ' 2 s 2
b(kd) 3 t kd 2 ' ' 2 =. - 12- + bkd (2- 2) + A
8t (:n.- 1) (5.44)
= 1.25 (kd) 3 + 15 kd (7.5- ~) 2 + 118 (n ~ 1)
The value of kd is found from th~ relationshir: der:i.ved in section
B. 2. 7.
'B.2.4 Deflections:
The deflections caused by cohlUU:l rota,tion and bending. of the beam
c::rEI fJ(n•ivad and shown in Tal1le: :B,, 5. IJ.1he effect of joint distortion on the
overu.1l deflection for each specimen can be obtained fror.1 Table 8. 3 •
.6.v1 "' 129 ¢
before cracking:
Ib "' ~~3 + A6 (n - 1) ( d - ~) 2 + A~ (r1 - 1) ( ~ - d')
2
= bt3 +A (n- 1) (10.4) 2 12 s
= 15625 + 1063 (:n - 1)
after crackir.g¥
b(kd) 3 (t kd 2 ( ( )2 Ib = -12- + bkd 2- 2-) + 2 A9
n- 1) 10.4
3 kd,. .. = (kd) + 12 kd (12. 5 ·2)~ + 1063 (n - 1)
Th;, derivation of kd for c:nch specimen is given in section B.2.7.
T).EIE B= 5 Load -De-:-lc :;-:icr: Re lc:. tiorlsl·~ir;s fo:- t!!e Beame
-Uncracked Sectior:
UlGT E l:lv~ I-,., 6...,2 / 6v 6v1 c
• I 6 (~4) (in X 10b) (in X 106) .' . -6, \:il: X 10 ) =l:lv1 +~ - \IS~ X 10 _)
1 3.48 7 .. 08 p 23,390 8.81 p 15.9 p 12.15 p ,.. 4.25 6.01 :2 21,800 7. 73 p 13.7 p 10.51 p c. "" 3.34 7732 p 23,800 9.02 p 16.3 p. 12 .. 44 p .)
4 3. 70 6., 75 p 2:?,860 8.47 p 15.2 p 11.65 p
Cracked Section
Ib 6v
(in4) 2 6
(in x 10 )
15170 13.58 p 13480 12.51 F 15620 13 .. 73 F 14590 13.28 p
llv
=6Y1 ~v2
- 25.7 p 23.0 p 26.2 p 24.9 p
I
~
Ul w
B.2.5 Ultimate Moment of tbe Column.
From the formulae.
N ~ 0.85 f'ab c
and M "'0 85 f'ab (l- a) +A f (d - 1) + A1 f (1- d') u, • 0 2 2 s y 2 s y 2
the theoretical ultimate loads are found and are given in 'J}able B. 6 •
M uc
a . N
o.85 f~b
= - 14_8-0.85 X f' X 15 c
::c 1L6 f'
Q
t ''l "'0.85 f'ab (-2 - ~2) + 2 A f (5.44). c s y
'!'ABLE B. 6 Theoretical Ultimate Moments for the Column.
·~'"'""-""-' ~·--·-··"""--~~ -~~-"--
01llT i'' a f M c y uc (lmi) (in) (ksi) (kip-in)
1 3 .. '73 3. 11 44.7 1251 2 5.57 2.08 45.3 1940 3 .3. 44 3.36 45.2 18.43 4 4.22 2. 75 45.4 1892
154
This theory does not apply to these tests since no 8pecimen actually
attained its theoretical ultimate load. Hov1ever the theoretical rotational
ductility available in the design specimen is given by
¢u/¢ where y,
¢u
¢y
·=
""
e at ultimate. ~ c
e at first yield c -c of tre flexural steel.
at first yield: as given by Equation B.1 in·seotion B.2.2,
2 - ( 2".J.. 11) lli.:-2. 0 a f' + a + f' = • c c
for tr..e design Bpecimen f' c "" 4 ksi.
d.t
a2 - 17.42 a + 5.44
ultimate: as given in
a
c
e c
secti.-'n
a
c
¢u
¢\}.; ¢ y
= o.
"" 4 •. 06 in.
"' 4.77 in,
f :::; c X_JL
d - 0 E 8
f = (d
JL - c) E
s
- 42QOO s·.11 x 29 X
;;: 1. 90 X 10-4
B. 2. 5.
- 1h.§. f'
c
"" 2.90 in.
-· 3.41 in.
0,01 "" 3. 41
"" 2.93 X 10-3
_1
- 2.93 X w.) 1. ()0 X 10-4
::: 15.4
B.2.7 Theor0tical Steel Strains:
B.2.7. 1 ~eam Steel.
10b
rads.
rads.
By assuming that, t'r:e beam remains in the eLtstic range, the
s-ter:il str·ess can be n~lated dire~tly to the apr-lied momeni. dfJ shown below.
155
The x-elationships are given in Table B. 7.
I 2 · 2 '' k = ~ n ( p' + p) + 2n ( p' ~ + p) -· n ( p' + p)
f' = s
M
f kd- 2.1 8 22.9 - kd
Af._f;3 (d - ¥)
TABLE B.J Moment-Stress Relation:.>hips for Beam Steel.
~~ ~·~-- -· -~
Ul~IT · n k kd f' M./ f (in)
s s ( in3)
1 8.3 0.343 7.85 0.378 f '100. 6 2 6. 8 0.326 7.46 6.350 fs 100.9 3 8.7 0.348 7.97 o. 396
8 . 100.5 f 4 7.8 o. 337 7. 72 0.368 fs 100.7 s
B.2.7•2 Column Steel.
In the colurrm~ t:'"' :Jttlel stresses must be computed individ-
ually for each value of applied moment. 'rhe stee1 strains are calculated
for the peaks of load runs 1 ontl 3 for ecch srenimen. To.ble B. 8 t."lbuJ.ates
the steel stress. The different values of column load refE:r to tJ-,o fact that
tt·e load :1t tte top and bottorn of tbe column differ'S on any l)artinul<:lr in--
crernent. The larger load has been ar1proximated to 170 kips for convenience.
156
f' s f kd - 2.1 11 o kd -- ___ , B.2)
from (B. 4) M·
f s
M
nf 12.9 - kd c kd
C· + C - T s
~ ~ f bkd + A'f' 6.1 c s 8
7.5 f0kd + 2 (f~ ~ f
8)
c (~- -· kd) + s 44 ( c + r:L') 2 3 ~· 8
10.8 2 X f ·· ~.lo·~
___ ,B. 3)
___ ,B.4)
f c 56.25(kd)
the assumption that n = 8 has a negligible effe~t on the results and sim-
plifies the calculations.
2kd - 11) N = ( 7. 5 ·kd + 2n icr---) f'
0
= (7.5 kd + 2n 2kdk~ 15) 56.25 (kd) - 2.5 (kd) + 943
when N = 148 kips.
(kd)3- (kd) 2 (22.5- 0.0203 M) + 0.0865 Mkd- 0.649 M- 377 "'O.
When :N ;= 170 kips: ·
(kd) 3 - (kd) 2 (22.5 ;_ o.on6 M) + o.o754 Mkd. - o.s6s M - 377 ::: o.
157
UNIT 'i.UN kd (in)
1 1 6. 69 3 7.27
1 6.68 2 3 7.05
3 1 7.00 3 7.51
4 1 6~80 3 7-39
TABLE B.3 Stress in Column Bars.
~olumn Load = 148 kips Column Load = 17C kips
fc (rsi) f 1 (psi) If (psi) . s ' s kd (in) fc (psi) f~ (psi)
3185 18130 24540 7.26 3180 18750 2765 19670 21400 7.99 2750 i6820
3200 14920 20240 7 .. 24 3190 15390 2900 13840 •:6360 7.75 2890 14320
2920 17780 2 400 7.70 2910 18400 2630 16490 ' 0 8.28 2610 16930
c :
3090 16660 2i620 7.40 3000 17200 2690 15020 15660 8.22 2680 15580
f (psi) 1 s I
20500 14020
16940 I I
13060
17100 . 12630
17840 11910
-a. Ui (X)
'l'he stresses are ther1 convertHd to strains from
e s
and plotted on the str~in diagrams.
'rhe stress in the b<~rs due to axiul load only is follnd fror:1:
when N = 148 kips:
f c
when N = 170 kips:
f ~
= f (221 + 32). c
253 f. c
148,000 ~ 585. P.si 253
170000 "' 253 633 psi
Strain in t1·,e column bars is obtained from:
nf. e s c r
'Plwse v;~lues al'e plotted at the top and bottom of the column bars on the
strain distributions.
, B. 2. 8 Ultimate Moman t Capacit;y of the Column Core of UJHT 4.
The dimensions of the column core, out-to-out of the ·~ in.
diameter column ties are Ui:" x 13~".
148 O.B5 X 4.22 X 13.5 3. 05 in.
M uc 148 (6.75 - 1.52) + 2 X 90,8 X 5.44.
~ 1760 kip-in •
. [
B.2.9 Bond Stress Developed in Beam Flexural Bars.
The stress oan be determined from section £.2. 7.1. '.l:lrer, for
~1'. I'l'S 1 , 2 and 3 ~
159
u
for UNIT 4:
u
A f + A'f' 8 s s s
4lfDL
4.92 (f + f') s s lf X 5 X 40
= 0.0784 (f8
+ f~)
= A f s s 411'DL
4.92 f s Trx 5 x .32. 0,
= 0.0979 f s
A comparison of tbe maximum bond stress developed by tbe bars is given in
Table 8.1.
160
APPENDIX C.
BIBLIOGRAPHY.
1.. BLUME J. A., NEWMARK N. M., and f'10RNING L. H., 11Dasign of Multi-
story Reinforced Concrete Buildings for·Earthquake Motions", Portland
Cement Association, Stokie, Illinois, 1961.
2. WFliQEL R. L. et. al •. ( 1970) 11Earthqua.ke Engineering " Prentice-Hall,
Inc., New Jersey.
3,. ST':ISMOLOGY COMMITTEE OF THE STRUCTURAL ·ENGINEERS ASSOCIATION OF
CALIFORNIA (1968). "Recommended Lateral Force Requirements", San
Francisco. ·
4.. PARK, ~. · ( 1968) "Ductility of Reinforced Concrete Frames UrJder
Sei.smic Loading" New Zealand Engineering,, Vol., 23, No. 11, pp
427 - 35.
5.. ACI COMMITTEE 318 (1970) "~reposed Revision of ACI 318- 63:
Building Code Requirements for Reinforced Concrete" Journal of
the ACI., Vol. 67, No. 2, pp 77 - 186.
6. McKENZIE G.H.F. (1969) "A Critical Look at the Design of Reinforced
Concrete foi' Duotili ty". Bull. N.Z. Soc. Earthquake Eng. Vol. 2
No. 3, pp 29.5 - 307.
7. ,Il0011ESTAD l~. , ( 1951) "A Study of Combined Bending and Axial Load in
Reinforced Concrete Members" University of. Illinois Engineering
Experimental Station B~.,tlletin No.· 399.
161
8. CORLEY a., and HANSON·N.W., (1969) "nesign of Beam-Column Joints
for Seismic Resistant Reinforced. Concrete Frames". Proc. 4th World
Conference on Earthquake Engineering, Santiago.
162
9. HANSON N.W., and noNNOR H.W., (1967) "Seismic Resistance of Reinforced
Concrete Beam-Column Joints 11• Proc. A.s.c.E. 93, ST5 (October) pp
533 - 560.
10. HANSOlT N. W., ( 1971) "Seismic Resistance of Concrete Frames with
Grade 60 Reinforcement".· Proc., A.s.c.E •. 97, ST6 (June) pp 1685-
1700.
11. MEGGET, L.M. (1971)': "Ancborage of Beam Reinforcement in Seismic
Resistant Reinforced Concrete Frames" •. Unpublished M.E. Report
University of Canterbury, New Zealand~
12. BLAKELEY R.W.G., (1971) "Ductility of Prestressed Concrete Frames
Under Seismic Loading". Ph. n.· Thesis in Civil Engineering University
of Canterbury, l.ll'ew Zealand.
13. AMERICAl~ CONCRETE DlSTITUTE ( 1963): "ACI 318 - 63 Building ~ode
Requirements for Reinforced Concrete", Detroit.
14. PARK R., and PAULAY T., (1970) "Ultimate Strength Design of Re
inforced Concrete Structures". Printed for a Seminar Arranged
by DepA.rtments of ~:ivil Er1gineering and Extension Studies, University
of Canterbury, Vol. 1.
15. BEla\lETT 'N.B., PARME A.L., HANSON N. W., SBAROUliiS J.A., ( 1965)
"LaboratOf:'Y Investigation of Reinforced Concrete Beam-Column
Connections Under Lateral Loads". Proc. 34th Annual Convention
·s.E.A.o.c., Coronado.
16. ATCHLEY 'N.L., and FURR H.L., (1967) nstrength and Energy Absorption
Capabilities of Plain Concrete Under Dynamic arid Static Loadings".
Journal of the ACI, Vol. 64, No. 1.1' pp 745 - 56.
11q TAKEDA T., SOZEN M.A., and NEILSON :tr~N", · ( 1970) "Reinforced Concrete
Response to Simulated Earthquakes" Proc. A. s. 0.-E. 96 ST 12 (December)
PP 2557 ... 257 3. ·
18. ------ ( 1964) "An Investigation of the Bond of Deformed
Steel Bars with Concrete·". Translation No. 112, Cement and· Concrete
Association.
163
