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SEISMIC RESPONSE OF HIGH-STRENGTH CONCRETE BEAM-COLUMN-SLAB SPECIMENS
by
Pierre-Alexandre Koch
November 1998
Department of Civil Engineering and Applied Mechanics
McGill University
Montréal, Canada
A thesis subm itted to the Faculty of Graduate Studies
and Research in partial fulfilrnent of the requirements
for the degree of Master of Engineering
O Pierre-Alexandre Koch, 1998
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SEISMIC RESPONSE OF HIGH-STRENGTH CONCRETE BEAM-COLUMN-SLAB SPECIMENS
ABSTRACT
The effects of high-strength concrete on the seismic performance of reinforced concrete
exterior beam-column-slab subassemblages were investigated by comparing the behaviour of
three full-scale specimens. Two specimens. one constructed with normal-strength concrete and
one constructed with high-strength concrete. were designed with square columns- The specimen
tested in this thesis was constructed with high-stren-d concrete and designed with a circular
column. All the specimens were designed as ductile moment-resisting frames and tested under
reversed-cycl ic loading.
The Canadian Standard, CSA A23.3-94, lirnits the concrete compressive strength used in
seismic design to 55 MPa. Tlie applicability of the cuvent design specifications, developed for
normal-strengtli concrete. were investigated when applied to ductile beam-colurnn joints made
witli liigher strength concrete. The reduced amount of confinement reinforcement permitted by
the New Zealand Standard is also investigated. AI1 specimens in the study were instrumented to
allow for detailed strain, load and deflection measurements to be monitored during testing
process. Tlie hysteretic behaviour of each specimen was analysed in order to investigate energy
dissipating characteristics as well as attainable ductility levels. Strains in the slab bars were used
to determine the amount of effective slab reinforcement which contributes to the negative
f iesurd capacity of the main beam. Deflection and strain measurements were used to determine
the full torsional response of the spandrel beams. Non-linear dynamic analyses were also
performed to compare the predicted seismic performance of normal-strength concrete and high-
strength concrete prototype structures.
COMPORTEMENT SISMIQUE D'ASSEMBLAGES COLONNE-POUTRE-DALLE CONSTRUITS EN SÉTON A HAUTE RESISTANCE
Trois spécimens en grandeur réel le d'un assemblage externe colonne-poutre-dalle ont été
évalués afin d'étudier la performance du béton à haute résistance sous charges renversées. Deux
des spécimens, l'un en béton normal et l'autre en béton à haute résistance, ont été construits avec
des colonnes carrées. Le spécimen testé dans cette thèse était en béton à haute résistance avec
une colonne ronde. Les trois spécimens ont été dimensionnés pour un cadre rigide ductile.
Selon le Code Canadien (CSA A23.3-94), la résistance maximale en compression du
béton permise pour la conception sismique est limitée à 55 MPa. L'application des normes du
code du bâtiment en vigueur pour les joints extérieurs construits en béton normal est évaluée
pour le béton à haute résistance. Le nombre réduit de linteaux en acier dans les colonnes permis
par le Code Néo-zélandais, est aussi évalué. Les trois spécimens ont été instrumentés afin
d'obtenir des mesures détaillées sur les déformations unitaires, les charges et les déflections
durant les tests. L'hystérésis de chaque spécimen a été analysé afin de caractériser la dissipation
d'énergie et les niveaux de ductilité atteins. Les déformations unitaires dans l'armature de la
dalle sont utilisées pour déterminer la contribution de la dalle à la capacité de la poutre en
flexion négative. Les déformations unitaires et les déflections sont aussi uliiisés pour démontrer
le comportement en torsion de la poutre de rive. Une analyse dynamique non-linéaire est aussi
utilisée pour comparer le comportement des trois structures prototypes.
ACKNOWLEDGEMENTS
The author would like to sincerely thank Professor Denis Mitchell for his guidance and
encouragement throughout the course of this research programme. The patience and invaluable
assistance of both Dr. William D. Cook and Stuart Bristowe is also tremendously appreciated. In
addition the author expresses his gratitude to Suzanne Rattray and Glenn Marquis for the testing
of Specimens R4 and R4H, respectively.
The research presented in this thesis was carried out in the Jarnieson Structures
Laboratory at McGiII University. The author would like to extend special thanks to Ron
Sheppard, Marek Przykorski, John Bartczak, and Damon Kiperchuk for their assistance in the
laboratory. Special thanks is also extended to Bryce Tupper, Emmet Poon, Carla Ghannoum,
Wassim Ghannoum, Jay McHarg, Hanaa Issa, Glenn Marquis, David Dunwoodie, Pedro Da
Silva, Kevin Li and Robert Zsigo for their assistance during this study.
The completion of this project would not have been possible without the patience and
valuable help of the secretaries of the Civil Engineering Department, particularly Lilly Nardini,
Sandy Schewchuk-Boyd, Ann Bless, and Donna Sears.
Finally, the author would like to thank his famiiy and friends, and especially Samantha
Jones, for their incredible support and understanding throughout his stay at McGill University.
Pierre Alexandre-Koch Novem ber, 1998
iii
TABLE OF CONTENTS
ABSTRACT ......................................................................................................................... i . . RÉsm .............................................................................................................................. i i ... ................................................................................................ ACKNOWLEDGEMENTS i i i
LIST OF FIGURES .......................................................................................................... vii LIST OF TABLES .................... .. ..................................................................................... x LIST OF SYMBOLS ................ .... ................................................................................ xi
C W T E R 1 : INTRODUCTION .................................................................................. 1
1 . 1 Design Criteria for Ductile Moment-Resisting Frames ................................... 1 1.2 Need for Research on High-Strength Concrete Subjected to Reversed-
.............................................. ........................................... Cyclic Loading ... 4 ...................... 1.3 Brief Summary of Previous Research .................................... .... 5
1 -4 Summary of Previous Experiments on High-Strength Concrete Specimens Su bjected to Reversed-Cyclic Loading .......................................... 7
1.5 Research Objectives ..................... .. ............................................................... 10
CHAPTER 2: EXPERIMENTAL PROGRAM .............................................................. 12
Description of Prototype Structures ................................................................. 12 2 . I - 1 Building Descriptions ...................................................................... 12 2.1 -2 Loading and Analysis Assumptions ................................................. 14
Specimen Dimensions ...................................................................................... 15 Design and Detailing of the Test Specimens .................................................... 18
2.3.1 Reinforcement Details for Specimen R4 ......................................... 21 2.3.2 Reinforcement Details for Specimen R4H ....................................... 24 2.3.3 Reinforcement Details for Specimen R4HC ..................................... 27
............................................................................................ Material Properties 30 2.4.1 Reinforcing Steel ............................................................................... 30 2.4.2 Concrete ........................................................................................... 32
.......................................................................................................... Test Setup 35 ............................................................. .......................... Instrumentation ..... -38
2.6.1 Load Measurements .......................................................................... 38 2.6.2 Deflection Measurements ................................................................. 38
......................................................................... 2.6.3 Strain Measurements 39 .............................................................................................. Testing Procedure 42
CHAPTER 3: REVERSED-CYCLIC LOADING TEST RESULTS ............................ 44
3.1 Specimen R4HC ................................................................................................ 44 3.1 - 1 Load-Deflection Response ......................... ...... ............................. 44 3.1.2 Beam Behaviour ................................................................................ 47 3.1.3 Slab Behaviour .................................................................................. 51
................................................................. 3.1.4 Spandre! Beam Behaviour 53 3.1 -5 Coiumn Behaviour ............................................................................ 54 3.1.6 Joint Behaviour ................................................................................. 56
Specimen R4H ................................................................................................... 58 ................................................................ 3.2.1 Load-Deflection Response 58
3.2.2 Beam Behaviour ...................... ... ................................................... 60 3.2.3 Slab Behaviour .................... .... ........................................................ 64 3.2.4 Spandret Beam Behaviour ................................................................. 66 3.2.5 Column Behaviour ............................................................................ 67 3.2.6 Joint Behaviour ................................................................................. 68
Specimen R4 ..................................................................................................... 59 3.3.1 Load-Deflection Response ................................................................ 59 3.3.2 Bearn Behaviour ................................................................................ 71
........................ 3.3.3 Slab Behaviour ... ................................................... 75 ................................................................. 3.3.4 Spandrel Beam Behaviour 76
3 3 -5 Column Behaviour ............................................................................ 77 3.3.6 Joint Behaviour ................................................................................. 77
..................... CHAPTER 4: ANALY SIS AND COMPAIUSON O F TEST RESULTS -78
.............................................................................. Load-Deflection Responses 78 .................................................... Tip Deflection Components .................... .. 82
.......................................................................... Hysteretic Loading Behaviour 86 ............................................................................ 4.3.1 Energy Dissipation 86
..................................................................... 4.3 -2 Displacement Ductility 89 ...................................................................... 4.3.3 Damping and Stiffness 90
................................................ Moment-Curvature Responses and Predictions 91 ..................................... 4.4.1 Moment-Curvature Response of the Beams 91 .................................. 4.4.2 Moment-Curvature Response of the Columns 95
Role of the Spandrel Beam ..................... .. ................................................... 97 4.5.1 Measured and Predicted Torsional Response of the
Spandrel Beams ................... .... .................................................... 99 Role of the Slab ................................................................................................. 103
4.6.1 Strut and Tie Mechanism for Transfemng Forces from Slab Bars .................................................................................. 103
........................................................... 4.6.2 Effective Slab Reinforcement 104 4.6.3 Determination of Effective Slab Reinforcement ............................. 106 4.6.4 Simplified Detemination of Effective Slab Reinforcement ............. 108
..................................................................... 4.6.5 Flexural Strength Ratio 1 1 1
C H m E R 5: NON-LINEAR ANALYSIS ...................................................................... 113
..................................................................... 5.1 Hysteresis Rule Used in Analysis 113 5.2 Ground Motion Records Used for Analysis ............................... .. ............ I I5 5.3 Roof Displacement Time Histories ............. ... .......................................... 115 5.4 Plastic Hinge Locations ..................................................................................... 117 5.5 Envelopes of Lateral Displacements ................................................................. 119
......................................................... 5.6 lnterstorey Drifts a d Damage Estimates 119 .............................................................................................. 5.7 Ductility Demand 122
CHAPTER 6: RECOMMENDATIONS AND CONCLUSIONS .................................. 124
6.1 Conclusions ..................................................................................................... 124 6.2 Future Rescarch Recommendations .................................................................. 125
.................................................................................................................. REFERENCES 126
....................................... APPENDIX A: Calculations for the Design o f Specimen R4HC 131
Determination of Design Forces for Prototype Structure ................................ 132 Beam Design .................................................................................................. 136 Column Design ................................................................................................. 140 Joint Design ...................................................................................................... 145
LIST OF FIGURES
Chapter 1
Chapter 2
C hapter 3
Summary of the 1994 CSA detailing requirements for beams and columns .... 2 ..................................... Different hinge mechanisms for fiames (CPCA. 1995) 3
Plan and elevation view of prototype structure (Paultre. 1 987) ......................... 13 Location of full-scaie specimen ......................................................................... 16 Dimensions of Specimen R4 ............................................................................ 17 Dimensions of Specimen R4H ........................................................................... 17 Dimensions of Specimen R4HC ........................................................................ 18 Reinforcement details for Specimen R4 ............................................................. 22 Photographs of reinforcing cage of Specimen R4 .............................................. 23 Rein forcement details for Specimen R4H ......................................................... 25 Photographs of reinforcing cage of Specimen R4H ........................................... 26 Reinforcement details for Specimen R4HC ...................................................... 28 Photographs of reinforcing cage of Specimen R4HC ........................................ 29
....................... ............ Stress-strain responses for reinforcing bars of R4HC .. -31 ............................... Compressive stress-strain response for concrete of R4HC 3 4
Shrinkage strains measured in concrete prisms for concrete of R4HC ............ 3 4 Photograph of test setup ..................................................................................... 3 6
............................................................................................. Details of test setup 37 ............................................................................................ Location of LVDT's 40
................................................................. Location of mechanical strain targets 41 Locations of electrical resistance strain gauges ................................................. 42 Loading sequence for specimens ........................................................................ 4 3
Load versus tip deflection response for Specimen R4HC ................................. 4 5 Photographs of Specimen R4HC at various stages of testing ............................ 4 8 Photograph of darnage near the joint of Specimen R4HC ................................ 49
........................................................ Curvaîure and shear strain plots for R4HC 50 Crack patterns in slab of Specimen R4HC ......................................................... 51 Distribution of strain in slab longitudinal bars for Specimen R4HC ................. 52 Photograph of spandrel bearn of Specimen R4HC at the 8" positive
.......................................................................................................... cycle (8A,.+) 53 Torsional response of spandrei beam for Specimen R4HC ............................... 5 4
................ Strains in vertical column bars of Specimen R4HC ... ................... 56 Distribution of strain in colurnn hoops of Specimen R4HC .............................. 57
.................................. Load versus tip deflection response for Specimen R4H -58 Photographs of Specimen R4H at various stages of testing .............................. 61
...................... Photopph of beam damage near the joint of Specimen R4H -62 ........................................................... Curvature and shear strain plots for R4H 63
Crack patterns in slab of Specimen R4H ............................................................ 64
vii
Chapter 4
Chapter 5
Distribution of strain in slab longitudinal ban for Specimen R4H ................... 65 Photograph of spandrel bearn of Specimen R4H at the 6h positive
.......................................................................................................... cycle (44+) 66 Strains in vertical column bars of Specimen R4H ............................................. 67 Distribution of strain in column hoops of Specimen R4H ................................. 68 Load versus tip deflection response for Specimen R4 ...................................... 69 Photographs o f Specimen R4 at various stages of testing ................................ 72 Photograph of bearn damage near the joint of Specimen R4 ............................. 73 Curvature and shear strain plots for R4 .............................................................. 74 Distribution of strain in slab longitudinal bars for Specimen R4 ...................... 75 Photograph of spandrel b a r n of Specimen R4 at the 1 oh loading
........................................................................................................... cycle (74.) 76
Applied load venus tip deflection response for Specimen R4HC .................... 80 Applied load versus tip deflection response for Specimen R4H ....................... 80 Applied load versus tip deflection response for Specimen R4 .......................... 81 Load versus deflection envelopes for the three specimens ................................ 81 . . ............................................................................................. Determination of Ar 83
........................................ Determination of 4 83
............................................................................................. Determination o f A, 84 Predicted and measured tipdeflection components for Specimen R4HC ........ 85
........... Predicted and measured tipdeflection components for Specimen R4H 85 Predicted and measured tipdeflection components for Specimen R4 .............. 86 . . . Energy dissipation of the specimens ............ .. ................................................. 87 Stiffness degradation of the specimens .............................................................. 90 Variation of strain across the T-section .............................................................. 92 Accounting for strain variation across the flange of the T-bearns ..................... 93 Moment-curvature responses for the beam of Specimen R4HC ....................... 94 Moment-curvature responses for the beam of Specimen R4H .......................... 94 Moment-curvature responses for the beam of Specimen R4 ............................. 95 Moment-curvature response for the column of R4HC ....................................... 96
......................... Moment-curvature respnse for the column of R4H .... ..... 96 Role of spandrel beam ...... .. ...... .. ......................................................................... 97 Measured strain distributions in the slab bars at slab-spandrel beam
............................................................................. ..................... interfaces ..... 98 ............................................ Spandrel beam deformations for Specimen R4HC 102
............................... Torsional response of spandrel beam for Specimen R4HC 103 ldealized strut and tie mode1 for the specimens ........................................... 104
..... Determination of slab bar forces from torsional strength of spandrel bearn 107 ................................................. Stmt and tie model showing forces in slab bars 108
Torsion induced by slab bars ......................... .. ................................................ 109 ............................................................................ Simpiified stmt and tie mode1 110
5.1 Modi fied Takeda mode1 (Otani. 1974) .............................................................. 114 5.2 Roof displacement time histories ........................................................................ I l6 5 -3 Summary of hinge locations during entire time history responses .................... 118
viii
5.4 Envelopes of lateral displacements .................................................................. 120 5.5 Interstorey drifis .................................................................................................. 121
................................ 5.6 Estirnated curvature ductilities and plastic hinge rotations 123
Appendix A
......... A . 1 Unfactored loading cases used for the design o f a typical interior fiame 134 A.2 Layout o f longitudinal reinforcernent ............................................................... 137 A.3 Shear reinforcernent details in the beam ............................................................ 139 A.4 Trial column reinforcement details .................................................................... 140
........................................... A S Determination of design shear force in the column 141 ......................................................... A.6 Shear reinforcement details of the column 144
............................................................................. A.7 Details of joint reinforcement 146
LIST OF TABLES
Chapter 2
. ............................................................................ 2 I Properties of reinforcing steel 30 2.2 Mix proportions for concrete of Specimen R4HC ............................................. 33 2.3 Concrete properties ................... ... ................................................................... 33
Chapter 3
3.1 Applied loads and tip deflections at cycle peaks for Specimen R4HC ............. 46 ................ 3.2 Applied Ioads and tip deflections at cycle peaks for Specimen R4H 59
3.3 Applied loads and tip deflections at cycle peaks for Specimen R4 ................... 70
Chapter 4
...... ....................... Cornparison of failure mode and key response parameters .. 78 ...................... Energy dissipation for Specimen R4HC .. ................................. 87
............................................................... Energy dissipation for Specimen R4H 88 .................................................................. Energy dissipation for Specirnen R4 89
....................... Maximum moments and curvature ductilities of the specimens 91 ..................... Effective slab widths used in current design codes .... ........... 105
................... Predicted and experimentally determined number of yielded bars 106 ................................................. Simplified determination of effective slab bars 1 1 1
........................................... Flexural strength ratio for varying effective widths 112 Actual flexural strength ratios ......................................................................... 112
Chapter 5
5.1 Ground motion parameters ................................................................................. 115 ........................................ 5.2 Predicted periods and maximum roof displacements 117
5 -3 Darnage estimates ................................................................................................ 122
Appendix A
..................................................... A . 1 Lateral load calculations for each floor levei 133 ............................................................. A 2 Design seismic lateral loads on frarne 2 135
.................... A.3 Beam moments at znd b e l exterior column (afier redistribution) 136
LIST OF SYMBOLS
As As*
AS.",
depth of equivalent rectangular stress block area of spandrel beam cross-section area of confined core gross area of concrete column total effective transverse reinforcement in the joint area enclosed by torsional shear flow path area enclosed by centreline of closed transverse torsion rein forcement area of longitudinal reinforcement area of slab bars within the distance s s total cross sectional area of transverse rein forcement within spacing, s, and perpendicular to dimension, hc area of slab reinforcement contributing to the negative flexural capacity of the beam ma,ximum permitted longitudinal reinforcement minimum permitted longitudinal rein forcement area of column vertical reinforcement area of one leg of the closed hoop rein forcement effective area of transverse reinforcement effective width of T-beam in negative bending width between corner longitudinal bars of the spandrel beam niinimum effective width in shear size of rectangular or equivalent rectangular column distance from extreme compression fibre to centroid of tension reinf. diameter of concrete core nominal diameter of hoop rein forcement
d" the to e
nominal diameter of longitudinal rein forcement distance between the resultants of tensile and compressive forces due flexure eccentricity of slab rein forcement about the centre of twist of the spandrel beam specifled compressive strength of concrete magnification factor splitting strength of concrete modulus of rupture specified yield strength of reinforcement yield strength of transverse rein forcement yield strength of spiral ultimate strength of reinforcement foundation factor of a structure force in slab bars at cracking acceleration due to gravity cross-sectional dimension of column core thickness of the slab total height of a structure height between corner longitudinal bars of the spandrel beam importance factor of a structure moment lever a m stiffness at a deflection of A, stiffness at a deflection of A, distance from loading point to the column face length of clear span f,p.asf; cracking moment factored moment maximum moment obtained in the beam nominal flexural resistance of a beam negative probable moment in the beam
T,. Tcr
U
factored moment resistance positive moment resistance negative moment resistance fiexural strength ratio factored flexural resistance of a column number of effective slab bars number of storeys in a structure design axial load at ultimate limit state outside perimeter of concrete cross- section perimeter of the centreline of the closed transverse hoop rein forcement mial load on column factored axial load resistance of a rnem ber applied load corresponding to the peak of the cycle maximum factored axial load resistance o f a column applied load corresponding to Au applied load corresponding to Ai force modification factor spacing of transverse rein forcement ma~ imum stirrup spacing for shear spacing between slab bars seismic response factor of a structure fundamental period of vibration of a structure yield torque of a beam cracking torque of a beam calibration factor of a structure zona1 velocity ratio seismic base shear of a structure factored shear resistance provided the concrete factored shear resistance net horizontal joint shear factored shear resistance provided the steel factored shear resistance of a mem ber yieid force dead load o f a structure plus 25% of design snow load effective width of the slab
Ptm
Ptmi
acceleration-related seismic zone velocity-related seismic zone component of beam tip deflection due to flexure component of beam tip deflection due to bond slip and joint shear deformation cycle peak tip deflection component of beam tip deflection due to shear beam tip deflection maximum recorded tip deflection deflection at general yielding deflection at general yielding in the positive direction deflection at general yielding in the negative direction concrete strain corresponding to f,' strain in reinforcement yield strain of reinforcement resistance factor for concrete resistance factor for reinforcement shear strain in the beam joint shear factor beam curvature ultimate curvature of beam yield curvature of beam factor to account for density o f concrete shear stress cracking shear stress of beam shear stress due to torsion in the beam shear stress due to shearing in the beam joint shear stress angle of principal compression rotation ofjoint due to bond slip rotation of joint due to shear ratio of spiral reinforcement shear reinforcement ratio ratio of non prestressed longitudinal column reinforcemnet modi fied transverse rein forcement ratio modified and increased rein forcement ratio
xii
CHAPTER 1
INTRODUCTION
The behaviour of concrete structures under seismic loading is king increasingly studied
in an attempt to prevent loss of Iife and to minimize darnage in füture eanhquakes. The 1995
National Building Code of Canada (NBCC, 1995) contains detailed provisions for the earthquake
resistant design of structures. The intent of these provisions is to prevent major faiture and loss
of life. As stated in Commentary J of the 1995 NBCC; "structures designed in conformance with
these provisions shoufd be able to resist moderate earthquakes without significant damage and
major earthquakes without collapse." In order to distinguish between structures with differing
Ievels of ductility, the NBCC introduces a force modification factor, R. This factor reflects the
capability of a structure to dissipate energy through inelastic behaviour and ranges fiom 1 .O for
unreinforced masonry construction. to 4.0 for ductile moment-resisting space frarnes. The
Canadian Standards Association A23.3-94, Design of Concrete Structures (CSA, 1994), sets out
design and detailing requirernents for achieving the levels of R required by the NBCC. Some of
the detailing requirements for R equal to 4.0,2.0 and 1.5 are given in Fig. 1.1.
1.1 Design Criteria for Ductile Moment-Resisting Frames
In order for a ductile moment-resisting frame to resist significant seismic actions, it must
posses a high level of ductility in specified members. These ductile mernbers will allow the fiame
to dissipate an adequate arnount of the seismic energy through inelastic actions. In order to ensure
this behaviour, the CSA Standard (CSA, 1994) requires that ductile structures (R=4) have the
fol lowing characteristics:
(i) The ability to exhibit large displacements without significant strength loss,
(ii) A desirable hierarchy of yielding of the members,
(iii) Adequate confinement in regions expected to undergo inelastic action.
(iv) Avoidance of undesirable, brittle modes of failure such as shear,
(v) Reinforcement detailed such that it is effective, even afier severe distress (e-g., cover
spalling).
srnallest of:
-1 &-:= 1
I d . 0
SECTION 1-1 SECTION 2-2
R = 1.5
greater of: *sCs
greatcr of:
- .
SECTION 1-1 SECTION 2-2 SECTION 1-1 SECTION 2-2
R = 2.0 R = 4.0
Figure 1.1: Summary of the 1994 CSA detailing requirements for beams and columns
The importance of achieving a desirable hierarchy of yielding in frame members is
illustrated in Fig. 1.2. Figure 1 . 2 ~ shows the "column sidesway mechanism" which would oçcur if
the columns in the structure had !ower flexural capacities than the beams. This mechanism is very
undesirable, resulting in "soti-storeys" and potential structural failure without significant amounts
of energy absorption. In order to avoid these types of actions, a "strong column-weak beam" design
approach is usually adopted. This design philosophy will create for a "beam sidesway mechanism"
(Fig. 1.2b) which will allow for greater ductility and energy absorption. To ensure the desired
hierarchy of yielding, the 1994 CSA Standard requires that the sum of factored flexural resistance
of the column above and below the joint be greater than 1.1 times the sum of the nominal flexural
resistances of the beams h i n g into it. The ratio of nominal strength to factored strength for a
column subjected to low axial loads is about 1.2 (Le., 1/$,). This results in a minimum ratio of the
nominal flexural strength of the column to the nominal flexural strength of the beam, called the
nominal strength ratio, MR, of 1.1 x 1.2 =1.33. The 1995 AC1 Building Code (ACI, 1995) specifies
the same nominal strength ratio where the factors 1/$ x 6/5 = 1.33. The 1995 New Zealand Code
( N Z S , 1995) specifies a slightly larger nominal strength ratio of 1.25/0.85 = 1.47 (where the
overstrength of the steel is taken as 1.25 f;. and the strength reduction factor is 0.85). This higher
nominal flexural strength ratio was chosen partly to counteract the less stringent transverse
reinforcernent spacing limits. These minimum required flexural strength ratios in design are aimed
at ensuring that plastic hinging occurs in the beam, and not in the cofumns.
(a) Seismic Forces (b) Beam-sidesway mechanism (c) Column-sidesway mechanism (desira ble) (undesirable)
Figure 1.2: Difietent hinge mechanisms for frames (CPCA, 1995)
In order to ensure that these strength limits are respected, it is crucial to determine the
fiesural strength of the beams accurately. In order to achieve this, it is necessary to estimate the
contribution of the slab reinforcement in negative bending. The 1994 CSA Standard currently
specifies that any slab steel within an effective slab width of three times the slab thickness on either
side of the barn (3 hf) wil l contribute to the negative flexurai resistance of the beam.
The amount of slab reinforcement in the effective slab width also affects the design of the
joint since the forces in these slab bars will be transferred through the joint. In design, these bars
are computed to have a strength of 1.25 times their yield strength to account for the possibility of
higher yield stresses as well as strain hardening. In order to avoid yielding, the transverse
reinforcement within the joint must be designed such that it can transfer the design joint shear from
the slab and beam bars. The reinforcement must also provide sufflcient confinement to the
concrete core and the longitudinal column bars.
In order for plastic hinging to occur in the barns, the 1994 CSA Standard specifies that the
beams must have sufficient shear strength in order to permit the development of significant flexural
Iiinging. This is done by providing factored shear resistance corresponding to the development of
the probable flexural resistance in the beam and by limiting the transverse reinforcement spacing in
tlie region where hinging is expected (hinge let@).
Apart from satisfying the minimum flexural strength ratio MR, the columns must be
adequately detailed so tliat they can e.xhibit significant ductility and avoid brittle failure modes.
Slirar failures are prevented by providing suficient factored shear resistance corresponding to the
development of the probable flexural resistances in the beams. Transverse rein forcement, in the
fonn of closed hoops must provide adequate confinement of the column core and must restrain the
vertical bars from buckling (see Fig. 1. l c).
1.2 Need for Research on High-Strength Concrete Subjected to Reversed Cyclic Loadiog
The use of high-strength concrete (HSC) and high-performance concrete (HPC) has gained
popularity in recent years due to not only its increased strength but also its increased durability.
With tlie use of Iiigher and Iiigher strength concrete, it becomes critical to assess whether the design
requirements developed for normal-strength concrete are applicable to high-strengtii concrete.
Tliere has k e n some concern in the case of ductile moment resisting frames as to whether the same
levels of ductility can be attained for the typically more brittle high-strength concrete. A number of
national-scale research programs have been established to investigate the use of HSC including the
Center for Science and Technology for Advanced Cernent-Based Materials (ACBM - United
States). the Strategic Highway Research Program (SHRP - United States). Concrete Canada a
Network of Centres of Excellence @CE) Program, the Royal Nonvegian Council for Scientific and
lndustrial Research Program, the Swedish National Program on HPC. the French National Program
called "New Ways for Concrete" and the Japanese New Concrete Program. There lias also been a
considerable amount of research on tlie seismic response of HSC king conducted at the University
of Canterbury in New Zealand. by the Concrete Canada Program and by the Japanese New
Concrete Program.
Since research on the performance of HSC is coiitinuing, some codes of practice have
lim ited the compressive strength of concrete for seisrnic design of ductile elements. The 1994 CSA
Standard is rather stringent. limiting the concrete compressive strength to 55 MPa. The New
Zealand Standard (NZS. 1995) has a specified lirnit of 70 MPa, while the AC1 Code does not
currently speciw an upper limit.
1.3 Brief Summary of Previous Research
This section briefly reviews some of the research which has k e n previously conducted on
beam-column subassemblages. It focuses on the research which has had an impact on design
practice and that is particularly relevant to this research program.
Blume et al. (1961) were responsible for some of the first tests on beam-column
connections. Their research which was conducted at the University of Illinois for the Portland
Cernent Association showed the benefits of joint confinement on the hysteretic behaviour of beams.
l t did not however, provide a clear understanding of joint behaviour due to lack of shear transfer
simulation during the tests.
Hanson and Conner (1967) were the first to publish studies done on beam-column
subassemblages. They showed through a series of tests, that joints could undergo reversed cyclic
loading without significant loss of strength, given proper detailing. They suggested that adequate
closed hoops be provided throughout the joint to increase the shear strength and confinement.
Ma et al. (1976), and Bertero and Popov (1977) tested nine beam-column subassemblages,
some of which included slabs, at the University of California at Berkeley. They observed that the
presence of slabs in the subassemblages increased the negative moment capacity of the beam and
increased the amount of energy dissipated. However, it was noticed that the increased moment
capacity resulted in early buckling of the bottom longitudinal bars in the beams and increased shear
degradation across f b l l depth cracks in the beams. In order to control these effects, the authors
suggested the use of additional transverse reinforcement in critical regions. Their tests also showed
that the amount of compressive reinforcement in the bearns had a significant effect on their energy
dissipating capabilities. Due to this, they concluded that the ratio of area of bottom to top
longitudinal reinforcement in the bearns be not less than 0.75.
Park and Paulay (1975) and Park (1977) presented an excellent summary of the
bchavioural aspects of beam-column joints. Paulay et al. (1978) tested the joint shear resistance
contributed by joint shear reinforcement as well as inclined concrete compressive struts. It was
suggested that the contribution of the concrete be neglected due to the yield penetration into the
joint under cyclic toading. They also suggested a limit in the diameter of longitudinal bars passing
through the joint to limit bond deterioration.
Much research has been conducted on the contribution of slab steel to the negative moment
capacity of beams. Park and Paulay (1975) suggested that the design width within which the slab
steel would be effective should be 4 times the slab thickness on either side of the bearn. Ehsani and
Wight ( 1982. 1 %sa) tested many beam-column-slab subassernblages which also contained
spandrel beams. They had originally designed the specimens assuming that only the first set of slab
bars adjacent to the beam would contribute to the negative flexural strength. They noticed
liowever, that the reinforcement across the full width of the slab had yielded in tension. They
suggested an effective width at least equal to the width of the bearn on either side of the column, be
included. They also suggested a minimum flexural strength ratio. MR. of 1.4. Durrani and Zerk
(1985) obsewed that the presence of the longitudinal slab steel in beam-column-slab
subassemblages could increase the negative flexural capacity by as much as 70%. From this. they
suggested tliat the effective slab width be taken as the width of the column plus twice the depth of
tlie spandrel beam.
In 1 986. a research program began at McGil l University (Rattray. 1986. Paultre. 1987,
Paultre er al.. 1989. DiFranco. 1993, and Marquis, 1997) involving the testing of full-scale, exterior
beam-column-slab subassemblages. The focus was on the design and detailing requirements for
ductile and nominally ductile frame members to be used in the development of the 1994 CSA
Standard. Tliey also investigated the rote of the spandrel beam in controlling the effective width of
tlie slab. In these cases. the torsional resistance of the spandrel beam was found to limit the extent
of yielding in the longitudinal sIab bars. They found tliat the effective width of the slab was
sigificantly larger than that specified by the CSA Standard ( 1984) at the time. of three times the
slab tliickness on either side of the main beam. They concluded that the significant contribution of
the slab bars to tlie beam strength could result in overestimating tlie flexural stren-s$h ratio and
possibl) lcad to an undesirable " weak-column - strong beam" failure mechanism.
Clieung el ui. ( 199 1 ) tested beam-column-slab subassemblages subject to bi-directional
loading wliicli simulated earthquake actions dong a line skewed from the frame Iine. This meant
tliat loads were applied not only to the main beam but also to the spandrel beam. They found that
tlie loaded transverse bearns displayed earlier yielding and stiffness loss than those not loaded
directly, leading to a reduced slab contribution to the strength of the beams. However. they found
tliat even with this reduced slab contribution, the effective width was still greater than twice the slab
width on eitlier side of the column as suggested by the New Zealand Standard 3 10 1 ( N Z S , 1982).
Fro~n their research, they concluded that the effective width of slabs at exterior joints be taken as
tlie lesser of: one quarter of the span of the transverse edge beam on each side of the colurnn
centreline; or one quarter of the span of the main beam taken on each side of the column centreline.
1.4 Summary o f PreMous Experiments on High-Strength Concrete Specimens Su bjected to Reversed-Cyclic Loading
Little research has k e n done to date into the use of high-strength concrete in beam-column
connections subjected to reversed cyclic loading. The first study was conducted by Ehsani el al.
(1987). The research consisted of testing four high-strength concrete beam-column
subassem blages and com par ing the results with similar normal-strength specimens tested by Ehsani
and Wight (1985b). The study focused mainly on the actions in the joint region. The auîhors
concIuded that properly detailed connections made with high-strength concrete exhi bited similar
hysteretic behaviour to their normal-strength counterparts. They also suggested that the concrete
compressive strength should be considered when defining the maximum permissible joint shear
stress.
Ehsani and Alameddine (1991 ) tested twelve beam-column corner connections subjected to
cyclic loading. These specimens had varying compressive sîrengths (55.8 MPa to 93.8 MPa),
varying joint shear stresses (7.6 MPa to 9.7 MPa) and varying degrees of joint confinement. The
researchers found that many of the iimits set by the ACI-ASCE Cornmittee 352 (1995) regarding
bearn-column connections should be altered to accommodate high-strength concrete. They found
tl-iat the limit recommended for joint shear stress is unconservative for concrete strengths above 4 1
MPa, The current limit is:
where, f,' = concrete compressive strength (MPa)
vj = joint shear stress (MPa)
y, =joint shear factor (dependant on the joint type and joint geometric classification)
The new limit proposed by the authors for the shear in connections with concrete strength above
41 MPa is:
The authors also found that the methods used in the AC1 Code (1995) for calculating total
cross-sectional area of shear reinforcement, required in joints, give very large values when
high-strength concrete is used. The current code requirements (ACI, 1995 and CSA, 1994) for
confinement reinforcement is:
but not less than:
Where. ACh = area of the confined core
A, = gross area of the column
f?h = yield strength of the transverse reinforcement
11, = cross-sectional dimension of column core
s = spacing of transverse reinforcement aiong the longitudinal a..is of the column
As can be seen from Eq. 1-3. the area of confinement reinforcement required is directly
proportional to the concrete compressive strength. It was found that although there should be an
increase in confinement reinforcement Eq. 1-3 overestimates the required arnount. Ehsani and
Alarneddine also found that there should not be a linear relationship between the yield strength of
the reinforcement. f,+,. and the spacing required S. They recommended a new method to detennine
the transverse reinforcement ratio wliicfi takes into account the concrete compressive strength. the
joint shear stress and the flexural strength ratio. Their recommendation is as follows:
wliere.
for f i < 41.3 MPa
f, = magnification factor = for f; 2 4 1.3 M Pa
p,, = modified transverse reinforcement ratio = 1 .O, 0.50 or 0.25 depending on the joint
shear stress factor and the flesural strength ratio.
p,,, = modified and increased reinforcement ratio.
Tlie actual reinforcement ratio is related to the modified and increased ratio by:
Tlie area of shear reinfairement can then be calculated as:
Ash = -Psh ( 1 - 6 )
Shin et al. (1992) conducted a similar program which compared normal-strength to hi&-
strength concrete half-scale bearn-column joint specimens. The tests involved specimens with
varying concrete compressive strengths (30.2 MPa to 78.5 MPa), joint confinement, loading type
(rnonotonic or reversed cyclic), flexural strength ratios (1.4 to 2.0), and number of bent-up bars
(longitudinal beam bars which are angled from top to bottom of the joint) in the joint. The study
gave the following concIusions:
(i) The hi&-strength concrete specimens, which were loaded monotonically, tended to fail
in bending while those undergoing cyclic loading failed in combined shear and flexure.
(ii) The high-strength concrete specirnens wh ich were detailed with iarger hoop spacing
than that recommended by the ACI-ASCE 352 (1985) displayed failure in the beam-
column joint core which contradicted the findings of Ehsani and Alarneddine (1991).
(iii) The specimens which had bat-up bars within the joint core displayed shear dominated
hysteretic load-displacement loops that were severely pinched. This suggested high stress
concentration at the beam-coiumn joint face.
(iv) Increasing the flexural strength ratio between the colurnn and the beam increased the
energy dissipating capacity of the specimens. It was thetefore suggested that the lower
limit value of MR be increased from 1.4 to 1.6.
In 1996, two independent studies were conducted on the influence of high-strength
concrete on the seismic behaviour of columns. Légeron and Paultre (1996) conducted tests on six
high-strength concrete columns and concluded that the flexural behaviour was greatly influenced by
the tie spacing and the axial load level. Zhu et al (1996) conducted similar studies on columns with
varying axial loads, varying amounts and configurations of transverse reinforcement and varying
ratios of concrete core to gross section. Both studies concluded that with properly detailed
transverse reinforcement and limited axial load, high-strength concrete columns could be designed
to behave in a ductile manner.
Bristowe, Cook and Mitchell (1996) perforrned tests to determine the potential ductility of
high-strength concrete specimens. This study consisted of testing a series of full-scale high-
strength concrete coupling beams under reversed-cyclic loading. The bearns had concrete
compressive strengths of 30 MPa and 70 MPa and also varied in detailing requirements (ductile and
nominally ductile moment resisting fiames). The study found that the high-strength concrete
coupling beams exhibited higher levels of ductility, with better energy absorption and increased
initial stiffness than the normal-strength specirnens.
Research on the influence of high-strength concrete on siesrnic response was also
conducted by Marquis (1997) at McGill University. The research involved the testing a full-
scale Iiigh-strength concrete exterior beam-column-s!ab subassemblages under reversed cyclic
loading. The study found that the current CSA ( 1995) provisions for ductile moment resisting
frames are suited for the use of high-strength concrete. The HSC specirnen displayed ductile
114.steric behaviour with good energy dissipation capabilities, comparable with a normal-strength
specimen. I t was found however. that tlie current confinement lirnits when used with high-
strengtii concrete result in excessive amounts of transverse reinforcement especially in the
columns and joints.
1.5 Research Objectives
Tlic main objective of tliis study is to investigate the ef-rects of high-strength concrete on
tlie behaviour of ductile moment-resisting frames subjected to reversed cyclic loading. It also
examines the potential of allowing for reduced transverse reinforcement in columns if subjected to
small axial loads.
The test specimen consists of a full-scale high-strength concrete (f: =70MPa)
subassemblage with a transverse spandrel beam and a circular column. Tiie components of the
specimen were designed and detailed as a ductile moment resisting frame as specified in the 1994
CSA Standard. However, the transverse reinforcement lirnits used in the design of the column i e r e
as specified by New Zealand (NZS. 1995) Code. This allowed for smaller amounts of confinement
reinforcernent in the column and less congestion in the joint region. The results are compared with
two similar specimens with square columns, one made of high-strength concrete and tested by
Marquis (1997) and one of normal-strength concrete (f: =30 MPa) tested by Rattray (1986) and
reported by Paultre ( 1987). Tliese specimens were completely detailed according to the 1994 CSA
Standard as ductile moment resisting frames. The intent is to compare the response of the high-
strengli specimens with that of the normal-strength specimen. Afl specimens were instrurnented in
order to determine certain beliaviounl aspects including:
(i) Load versus deflection responses
(ii) Moment versus curvature responses
(iii) Strain distribution in the slab reinforcernent
(iv) Effective slab widths
(v) Curvatures and shear strains in the beams
(vi) Tip deflection components
(vii) Energy dissipation characteristics
Non-linear analysis is also included to determine the effects of concrete compressive
strength on the seismic performance of a prototype structure. The final purpose of this study is to
extend the current CSA Standard (CSA, 1994) to allow design of ductile frame members with
concrete compressive strengths above 55 MPa and to study ways of reducing the amounts of
transverse reinforcernent required in the columns.
CHAPTER 2
EXPERIIMENTAL PROGRAM
2.1 Description of Prototype Structures
This study is part of an ongoing research program investigating the seismic response o f
reinforced concrete exterior bearn-cotumn-slab subassemblages. As such, each specimen in the
program has been designed using the same prototype structure (same overall dimensions and
loads) in order to allow for proper comparison. The structure is a six-storey reinforced concrete
office building situated in Montreal. Previous research has included tests on specimens made
with normal-strength concrete (f: =30 MPa) carried out by Rattray (1986), Paultre (1987),
Castele (1988) and DiFranco (1993). These tests assessed the influence of design and detailing
as well as the influence of slabs on the seismic performance of reinforced concrete structures in
Canada. The specimen reported in this test program, d o n g with that tested by Marquis (1997),
involves assessing the usability of high-strength concrete (fi=70 MPa) in order to reduce the
dimensions o f the normal-strength concrete structural components while maintaining similar
flexural strengths and ductilities. This report compares the performance of three specimens, one
made of normal-strength concrete and two made of high-strength concrete. Al1 three specimens
were designed as ductile moment-resisting fiames in accordance with the National Building
Code of Canada.
2.1.1 Building Description
The rectangular 42 rn by 24 m layout o f the prototype structure consists of seven equal - 6 rn bays in the N-S direction and two - 9 m bays separated by a 6 m wide corridor in the E-W
direction as seen in Fig 2.1. The building is 23.1 m high with a ground level storey height of
4.85 m and subsequent storey heights of 3.65 m. The structural components were originally
designed with normal-strength concrete. The original column dimensions are 500 mm x 500 mm
for interior columns and 450 mm x 450 mm for excerior columns. The main beams spanning
between the columns are 400 mm wide x 600 mm deep for the first 3 storeys and 400 mm wide x
550 mm deep for the remaining storeys. The 1 10 mm thick siab is supported by 300 mm wide x
350 mm deep secondary beams spanning between the main beams in the N-S direction.
(a) Plan View
(b) Section A-A
Figure 2.1: Plan and elevation view of prototype structure (Paultre, 1987)
2.1.2 Loading and Analysis Assumptions
The design loads for the prototype structure are as specified by the 1995 NBCC. The
original loads were established by Paultre (1987) using the 1985 NBCC which included base
shear equations which used a K-factor to speciQ ductility. The 1985 NBCC used a K-factor of
0.7 for ductile structures while the 1995 NBCC uses a force modification factor, R, of 4 in the
base shear equations. However, the base shear equations and the resulting design forces are
alrnost identical. Another slight modification in these codes is in the calculation of the
fundamental period, T. The equation used in previous codes (NBCC, 1985-90) specified the
period for al1 frame structures as k ing T=O. IN, where N represents the total number of storeys
in the structure. The equation used in the new code (NBCC, 1995) is T= 0.075 hn3'4, where h.
represents the total height of the structure. Neither of these changes significantly effects the
loading patterns or load magnitudes and hence a direct cornparison between al1 specimens is still
valid. The design parameters specified by the 1995 NBCC are as foHows:
Floor live load: 2.4 4.8
Roof load: 2.2 1.6
Dead loads:
Wind loading
Seismic loading:
kN/m2 on typical office floon kN/m2 on 6 m wide corridor bay
kN/m2 full snow load kN/m2 mechanical services loading in 6 m wide strip over corridor bay
kN/m3 self weight of concrete memben kN/m2 partition loading on al1 floors kN/m2 mechanical service loading on al1 floors kN/m2 roof insulation
kN/m2 net lateral pressure for top four floors kN/m2 net lateral pressure for bottom two floors
2, = acceleration-related seismic zone = 4 2, = velocity-related seismic zone = 2 v = zona1 velocity ratio = 0.1
314 - T = fundamental period = 0.075 h, - 0.79 S.
S = seismic response factor = 1.5 /fi = 1.68 1 = importance factor, taken as 1 .O for an office building F = foundation factor, taken as 1 .O U = calibration factor specified as 0.6 W = dead load plus 25% of design snow load
Hence the seismic base shear. V, is :
The complete design calculations can be found in Appendix A-
The structure was analysed using the linear elastic analysis program, ETABS
(Habibullah, 1989). In order to simpliQ the lateral load anatysis, the floor slab system was
assumed to act as a rigid diaphragm. This allows the system to be reduced to a single two
dimensional Crame. It was aIso assumed that the centre of stiflness coincides with the centre of
mass of each floor thereby giving a torsional eccentricity of zero. The NBCC requires however,
that a accidental torsional eccentricity o f 2 4.2 m (+ 0.1 D,.J be added to the lateral loads in the
E-W direction. The critical frarne for analysis was determined to be ftame 2 due to the
significant eccentricity effects and since the gravity loads on this fiame are larger than on frame
1. This frame was therefore used in the design of the test specimens. A reduction in gross
member stiffnesses was also assumed in order to obtain more realistic results due to cracking.
This involved reducing the uncracked stiffness in the beams by 50% and in the columns by 20%.
2.2 Specimen Dimensions
This research program focuses on a beam-column-slab subassemblage taken fiom the
prototype structure. Through analysis o f the structure, it was found that the critical section for
study was an exterior joint connection situated at the second storey as seen in Fig 2.2. Al1
specimens described in this study comprise four main components; an exterior column, a main
beam, a spandrel beam and a slab.
The overall dimensions of the specimens were Iimited by both physical and design limits.
The column height of 3 m was chosen such that the ends represent points of countraflexure in the
prototype structure. All beams were 600 mm deep which includes a 1 10 mm thick slab. This
means that the column extends 1.2 m above and below the joint region. The width of the slab and
spandrel beam was limited to 1900 mm due to the dimensions of the universal testing machine.
The length of the main beam was such that it extended 2200 m m fiom the centreline of the column.
This allowed for adequate loading distance as well as for some addîtional strength and confinement
around the loading points.
Figure 2.2: Location of full-scale specimen
The R4, normal-strength concrete specimen, was designed with details corresponding to a
force modification factor, R, o f 4.0 with a square 450 mm x 450 mm column, 400 mm wide by 600
mm deep bearns and a 1 I O mm thick slab (Fig. 2.3). The high-strength specimens, R4H and R4HC,
were designed in order to produce similar flexural and compressive strengths as those obtained in
the normal-strength specimer?. This allowed reduction o f the bearn size to 350 mm wide by 600
mm deep. It also allowed for a reduction in the cross-sectional area of the columns. Specimen R4H
was designed with a 350 mm x 350 mm square column (Fig. 2.4). Specimen R4HC was designed
with a circular column in order to take advantage o f the increased effectiveness of spiral
reinforcement in providing confinement. In order to obtain similar compressive strengths in both
high-strength concrete columns, their cross-sectional areas were chosen to be equal. This resulted
in a 400 mm diameter column for specimen R4HC.
Al1 specimens were designed so that the loading point be exactly 2000 mm fkom the centre
of the column. Due to varying column sizes, this results in slightly different moment lever amis for
each specirnen.
Special consideration had to be given when designing the specimen with the circular
column due to its complicated formwork at the beam-column joint. An additional 25 mm of cover
was added to the outside face of the spandrel beam so that this face matches the outside of the
coiumn. This resulted in an actual spandrel beam width of 375 mm as seen in Fig 2.5.
Elevation View
Figure 2.3: Dimensions of Specimeo R4
Elevation View
Plan View
Plan View
Figure 2.4: Dimensions of Specimen R4H
Elevation View Plan view
Figure 2.5: Dimensions of Specimen R4HC
2.3 Design and Detailing of the Test Specimens
The seismic design of concrete structures is govemed by the 1994 CSA Standard in
Canada. The Standard specifies that a certain level of energy dissipation in the non-linear range be
attainable for highly ductile (R = 4) earthquake resistant structures. The 1994 CSA Standard states
that .'in the capacity design of structures, energy dissipating elements or mechanisrns are chosen
and suitably designed and detailed, and al1 other structural elements are then provided with
su fficient reserve capacity to ensure that the chosen energy-dissipating mechanisms are maintained
throughout the defomations that may occur". Currentiy, due to lack of experimental evidence of
the seisrnic behaviour of high-strength concrete elements, the code limits the concrete strength used
in design to 55 MPa. The code also permits a 20% moment redistribution in ductile moment
resisting frames as specified by Clause 2 1.
The beam-slab component of the h e must be designed in order to maintain a high levei
of ductility. The Standard specifies a maximum and minimum amount of longitudinal steel
permitted in the beam (Clause 2 1.3.2.1). It also specifies that for negative bending, the slab bars
within a distance of 3hf fiom the sides of the beam be considered effective and that the positive
moment resistance, M,' ,at the face of the column be at least one half of the negative moment
resistance, M i .
In order to develop plastic flexuraI hinging at the ends of the beams, the code specifies
strict transverse reinforcement spacing limits within a distance 2d from the face of the columns.
Within this region, the spacing of the closed hoops is limited by the smaller of d14, 8 dbI, 24 dbh, or
300 mm (Clause 21 -3.3.3). The transverse reinforcement outside this region is controlled by the
minimum shear reinforcement specified by Clause 1 1.
In order to ensure a proper hierarchy of yielding in the frame members and hence to avoid
undesirable modes of faiiure such as column hinging, the code specifies a "strong-cohmn - weak
beam" philosophy. Hinging in the beams rather than the columns allows for greater rotations and
hence greater energy dissipation while maintaining a stable overall structure. In order to achieve
this mechanism, the code specifies that the total factored resistance of the column be at least 10%
greater than the sum of the nominal tesistances of the beams M i n g into it. that is:
The 1994 CSA Standard requires a minimum arnount of confinement reinforcement in the critical
region of the column. For square columns, this is catculated as:
but not less than:
Where, ACh = area of the confined core
A, = gross area of the column
f,, = yield strength of the transverse reinforcement
s = spacing of transverse reinforcement along the longitudinal axis of the column
For circular columns, the CSA Standard specifies a minimum volumetric ratio of spiral or circular
hoop reinforcement, p, of:
but shall not be taken less than
The code also states a minimum amount of transverse reinforcement
(2-5)
necessary to prevent
the buckling of the longitudinal bars. Clause 21.4.4.3 states that the hoop spacing not exceed the
smaller of 114 the minimum member dimension, 100 mm, 6 times the dimension of the smallest
longitudinal bar, or the requirements of Clause 7.6. This spacing shall be continued over a length
on either side of the joint no less than the depth of the member at the face of the joint, one-si-xth of
the clear span of the member, or 450 mm. Outside this region, the transverse reinforcement spacing
is govemed by the limits set in Clauses 1 1.
The limits set by the 1994 CSA Standard can lead to congestion in the reinforcing cages
when using high-strength concrete. The New Zealand Code (NZS, 1995), however, rnakes
allowances for columns subjected to varying levels of axial load. The minimum amount of
transverse reinforcement for a circular column specified by the NZS 1995 Code is the greater of:
where A$A, shall not be taken less than 1.2 and p,m shall not be taken greater than 0.4 or:
Where, A,= area of confined core measured to outside of spiral or hoop
A,= gross area of section
A,,= total area of longitudinal reinforcement
d" = diameter of concrete core of measured to outside of spiral or circular hoop
Cr,= yield strength of spiral rein forcement
m = f,/ (0.85 fi)
N* = design axial load at ultimate limit state
p, = ratio of non-prestressed longitudinal column reinforcement
In the joint, the amount of transverse steel provided for confinement and shear resistance
is specified in Clause 2 1.6.2.1 which cites that joints not confined on al1 four sides must provide
transverse hoop reinforcement as determined by Eq. 2-3 (Clause 21.4.4). The anchorage of beam
reinforcement within the joint is determined from Clauses 2 1.6.1.3 and 2 1.6.5.
The reinforcing steel used must be weldable grade in conformance with CSA Standard
G3O. 18 (CSA, 1992). Ail hoops must be closed in plastic hinge regions and have seismic hooks.
These hooks must be anchored with at least 135 degree bends with extensions of at l es t 6 bar
diameters but not less than 100 mm. The seismic hook must engage the longitudinal bar and be
anchored in the con fined core (Clause 2 1.1 ).
2.3.1 Reinforcement Details for Specimen R4
Specimen R4 was designed in accordance with the 1984 CSA Standard. The beams were
reinforced with 4 No. 20 longitudinat bars on both the top and the bottom. The concrete cover on
al1 sides of both the main beam and the spandrel beam was 40 mm resulting in an effective depth
d= 540 mm. The shear reinforcement in the plastic hinge region was provided by No. 10 closed
hoops with a spacing of 1 30 mm on centres. This spacing was govemed by the dl4 spacing limit as
described above. Each set of hoops includes a fidl seismic hoop enclosing the four corner bars and
an inner U-stirmp hooked around the four inner bars. This configuration allows 4 legs of
reinforcement to resist shear forces. The plastic hinge region extended a distance 2d (1052 mm)
from the face of the column, outside of which the shear reinforcement was lessened to 6 sets of
double U-stimps spaced at 130 mm on centre.
The slab reinforcement consisted of two mats of No. 10 bars spaced at 300 mm in both
directions. The longitudinal slab bars were anchored into the core of the spandrel beam by standard
90 degree hooks with free end extensions of 12 db (120 mm).
The column longitudinal reinforcement consisted of 8 No. 20 bars. The shear and
confinement reinforcement in the column was provided by square perimeter hoops as well as
diamond shaped inner hoops. A spacing of 80 mm was used for these hoops in the potential hinge
region which extended 600 mm above and below the joint. Outside this hinge region, the spacing
was increased to 190 mm. Within the joint, the same configuration of transverse reinforcement was
used with a spacing of 70 mm. The cover on the column hoops was 40 mm.
40 mm clear cover - 4
2sek0fN0.10 -
closed hoops
8 - No.20 bars --
s - .A-- O
SECTION 1-1
I l Omm
3 sets @ 19Omm
7 sets @ 80mm
6 sets @ 70 mm
7 sets @ 80mm
3 sets @ 190mm
No.10 hmp - , , 1 - 4 N ~ . Z O
_ - 1 ... - * . _ -_ _ _ _ 20 mm clear - ,-,--,- ,..:o:,;~
I 1 - 4 No.20 bars
N0.10@300mm A
both diredians
SECTION 3-3
1 i ' +
- 4 No.20 bars
9 sets of hoops with 6 sets of double U-stimps @ 130mm U-stirmps @ 130mm
Figure 2.6: Reinforcement details o f Specimen R4
(a) View of reinforcing cage
(b) Back view of cage showing spandrel beam and joint det;
Figure 2.7: Pbotographs of reinforcing cage of Specimen
23
2.3.2 Reinforcement Details for Specimen R4H
Specimen R4H was designed in accordance with the 1994 CSA Standard. The beams
were reinforced with 3 No. 25 longitudinal bars on both the top and on the bottom. The concrete
cover on al1 sides of both the main beam and the spandrel barn was 30 mm resulting in an effective
depth, d, of 548 mm, The shear reinforcement in the plastic hinge region was provided by No. 10
closed hoops with a spacing of 135 mm. This spacing was governed by the d/4 spacing limit
specified as above. Each set of hoops includes a hli seismic hoop enclosing the four corner bars
and a single cross-tie hooked around the two middle bars. This configuration allows 3 legs of
reinforcement to resist shear forces. The plastic hinge region extended a distance 2d (1096 mm)
from the face of the column outside of which the shear reinforcement was lessened to 4 sets of U-
stirnips with cross ties spaced at 200 mm on centre.
The slab reinforcement consisted of two mats of No. 10 bars spaced at 300 mm in both
directions. The longitudinal slab bars were anchored into the cote of the spandrel beam by standard
90 degree hooks with free end extensions of 12 db (1 20 mm). The clear cover to the slab bars was
20 mm.
The column longitudinal reinforcement consisted of 12 No. 20 bars. The shear and
confinement reinforcement in the column was provided by 3 sets of closed hoops arranged such
that there were 4 legs of a No. 10 bar contributing to the effective area of transverse reinforcement.
A spacing of 65 mm was provided for these hoops in the potential hinge region which extended 5 18
mm above and below of the joint. I t is noted that the hoops had a yield stress of 648 MPa in order
to permit larger spacing for confinement. Outside this hinge region, the spacing was increased to
120 mm. Within the joint, the same configuration of transverse reinforcement was used with a
spacing of 65 mm. The cover on the column hoops was 40 mm.
Additional considerations were made due to limitations in specimen size and loading
method. These included welded plates on the free ends of the longitudinal spandrel beam bars in
order to fully develop the steel as well as additional transverse slab reinforcement bars on either
side of the loading points in order to limit cracking.
30 mm clear caver
C 4
3 sets of No.10 dosed hoops al
12 - No.20 bars - -
5 sets @ 120mm
9 sets @ 65mm
7 sets @ 65 mm
9 sets @ 65mm
5 sets @ 120mm
SECTION 1-1
No.10@300mm -
both directions 1 I - 3 - No.25 bars
No.1 O ~ O O P -- 3 - No.25 bars
No. 10 tie --
A* cover SECTION 2-2
~ 0 . 1 0 stimp - 1 - 1 3 - No.25 bars
No. 10 tie --- - -1 -
SECTION 3-3
4 --- 2- . 34 - ------- ---- - - --- C
9 sets of hmps wtth 4 sets of U-stimps with single tie @ 135mm single ties @ 2OOmm
Figure 2.8: Reinforcement details of Specimen R4H
(a) View of reinforcing cage and base connection
(b) Back view of cage showing spandrel beam and joint details
Figure 2.9: Photographs of reinforcing cage of Specimen R4H
2 3 3 Rein forcement details for Specimen R4HC
The beams and slab of Specimen R4HC were designed and detailed according to the 1994
CSA Standard and were identical to those used in Specimen R4H. The beams are reinforced with 3
No. 25 longitudinal bars on the top and bottom. The stirrup cover on al1 sides of the main beam is
30 mm which gives an effective depth of 548 mm. The spandrel beam has the same effective depth
and cover on ail sides although an extra 25 mm of concrete was added to the back face in order to
facilitate the construction of the fonnwork at the column-beam interface. The shear reinforcement
in the plastic hinge region is provided by No. 10 closed seismic hoops spaced at 135 mm. This
spacing b a s governed by the dl4 spacing limit. Each set of hoops includes a full seismic hoop
enclosing the four corner bars and a single crosstie hooked around the two middle bars. This
configuration allowed three legs of steel to resist the shear forces. The plastic hinge region extends
a distance 2d (1096 mm) from the face of the column outside of which the shear reinforcement
comprised of U-stinups and a cross tie.
The slab reinforcement consists of two mats of No. 10 bars spaced at 300 mm in both
directions. The longitudinal slab bars were anchored into the core of the spandrel beam by standard
90 degree hooks with free end extensions of 12 db (120 mm). The cover on the slab bars was 20
mm.
The column longitudinal reinforcement consists of 8 No. 25 bars spaced evenly around a
circle. The size and orientation of these bars was govemed not only by the code requirements but
by the placement of the longitudinal beam bars which extend through the column. The shear and
confinement reinforcement in the column was provided by a continuous 10 mm diameter spiral
with seismic hooks at both ends. The spacing of the turns of the spiral was chosen in coordinance
with the New Sealand Code (NZS, 1995). The spacing in the potential hinge region, which extends
400 mm above and below the joink is 100 mm as govemed by the 114 column diameter criteria
(Clause 8.5.4.3, NZS, 1995). Outside this hinge region, the spacing was increased to 130 mm as
governed by the 113 column diameter criterion (Clause 8.5.4.3, NZS, 1995). The cover on the
column spiral is 40 mm as specified for a column with exterior exposure.
Additional considerations were made due to limitations in specimen size and loading
method. These included welded plates on the free ends of the longitudinal spandrel beam bars in
order to fully develop the steel as well as additional transverse slab bars on either side of the
loading points in order to Iimit cracking.
40 mm clear -ver
Continous Spirat
8 - No.25 bars
SECTION 1-1
Spiral @ s=130 mm
Spiral @ s=lOO mm
Spiral @ s=130 mm
I 3 - N a 2 5 bars
3 - No.25 bars No. 10 tie - -
A mver -
SECTION 2-2
I 1 - 3 - No.25 ban
~ 0 . 1 0 s t i ~ ~ [ r 1 - 3 - No.25 bars
No. 10 tie -- a--*-/
- -
SECTION 3-3
24 -- a - - -- -- ---
34 C
9 sets of hoops with 4 sets of U-stimps with single tie @ 135mm single ties @ 2OOmm
Figure 2.10: Reinforcement details for Specimen R4HC
View of reinforcing cage and base connection
(b) Back view of cage showing spandrel beam and joint details
Figure 2.11: Photograpbs of reinforcing cage of Specimen R4HC
2.4 Material Properties
2.4.1 Reinforcing Steel
All reinforcing steel used in Specimens R4 and R4HC were weldable, Grade 400 steel as
specified by CSA G30.18 (CSA, 1994). Specimen R4H used Grade 600 steel for the transverse
reinforcernent of the column in an attempt to alleviate some of the congestion within the joint
region. The mechanical properties of the steel reinforcement used in these specimens can be found
in Table 2.1. The stress-strain curves for the steel used in Specimen R4HC are illustrated in Fig.
2.1 2. Three sampIes were tested for each bar size.
Table 2.1: Pmperties of reinforcing steel
- - - --
II Specimen r Bar DeSCCiption 1 f, (MPa) 1 E, If, (MPa:
11 1 No.10 column hoop 1 518 1 0.0026 1 701.68 II 1 std. deviation 1 10.0 1 0.00005 1 4.16 All other No. 10 bars 428 0.0023 587
std. deviation 11.3 0.0001 6 6.5 No.25 433 0.0023 592
std.deviation 1.9 0.0001 3 0.3 No.10 column hoop 647.7 0.0052 672.00
std. deviation 2.52 0.00026 5.3 All other No. 10 bars 602.7 0.0053 636.3
std. deviation 11.0 0.0001 5.5 No.20 468 0.0028 618.0
II 1 std. deviation 1 1.3 1 0.00013 1 0.9
fy=433 MPa - 500
600
fy=51 8 MPa -
500
_*-----.---...-.--.--..--.----
- No25 bars ----.- No.10 bars
..--
puge kngth = 200 mm fw No. 25 gaqp bngm = M mm for No. 10
O 50 100 150 200 200
Strain (xloJ mmlmm)
- No.10 bars - column spirals
50 mm gauge length
- 0.002 offset
15 20 25
Stnin (x1 O~ mmlmm)
Figure 2.12: Stress - strain responses for reinforcing bars of R4HC
2.42 Concrete
The 28 day concrete compressive strengths specified for Specimens R4. R4H and R4HC
were 30 MPa, 70 MPa and 70 MPa, respectively. The concrete was ordered from the same batch
plant in al1 cases and was manually placed into the formwork. The normal-strength concrete had a
maximum aggregate size of 20 mm and minimum slump of 100 mm. In order to properly
consoIidate the high-strength concrete around the highty congested reinforcing cage, the aggregate
size used in the high-strength mix was Iimited to 10 mm and the slump to a minimum of 200 mm.
Each specimen was cast in two separate stages. The first included the beams, the slab, and
the column, up to the top of the slab. The top column was cast only after hardening of the slab, and
hence resulted in a cold joint between the top column and the slab as is usuafly found in practice.
The concrete was cured in the foms for approximately I O days.
Each cast included a series of concrete cylinders and beams which were tested for various
properties in conjunction with the testing of the main specimens. These tests included compression
tests to determine compressive strength, f: , split cylinder tests to determine tensile splitting
strength, f,,. and flexural beam tests to detemine the modulus of rupture of the concrete. The
cylinders used for the compressive testing and split cyIinder testing were 150 mm in diameter by
300 mm long. The flexural beam specimens had a cross section of 100 x 100 mm and had a total
length of 400 mm. Four-point bending testing was perfonned on the beams. A sumrnary of these
tests along with typicaf stress-strain curves for the concrete of Specimen R4HC can be found in
Table 2.3 and Fig. 2.13 respectively. Three specimens were tested for each property determined.
Shrinkage measurements were also taken for both casts of Specimen R4HC. These
measurements were taken on 2 - IO0 x 100 x 400 mm concrete prisms which were cast and cured
under the same conditions as the full scale specimen. The average shrinkage measurements are
shown in Fig. 2.14.
Table 2.2: Mir proportions for concrete of Specimen R4HC
1 ~ y p e - 1 OSF Cernent (kg/rn3i 1 480 1
A Water (Un3) I 735 1 # Water-Cernent ratio 1 0.28 1
803
1059
-
II Water Raducing Agent (L/m3' 1 1.502 1
Fine Aggregate (kg/m3)
) Superplasticizer (L/m3) 1 13.0 1
10mm Coarse Aggregate
Slump (mm) 1 50
Air Content 1.5%
11 Density (kg/m3)
Table 23: Concrete properties
Specimen Cast No. fC G fw ft
(MPa) (rnm/mm) (MPa) (MPa) ------ 1 76.52 0.0027 4.18 6.05
R4HC std. deviation 0.864 O. 00006 0.35 0.07 2 67.1 O. 0029 4.09 6.3
std. deviation 0.9 0.0001 4 0.39 0.34 1 80.0 0.0030 5.50 8.00
R4H std. deviation 1.95 0.00004 0.74 0.60 2 87.5 0.0023 6.70 8.40
std. deviation 1.93 0.00004 1.29 0.20
R4 1 40.4 - 2.60 - 2 36.2 - 2.60 -
---* /-- .\
\
\ \
Cast #l - Lower Column. Bearns, Slab /BI--._\ Cast wt2 - Upper column
Figure 2.13: Compressive stress-strain response for concrete of R4HC
------ ------------ -/- /-
- Câst #1 - Lower Cdumn. Beams, Slab - - - Cast #2 - Upper column
-- 200 mm gauge kngth
Figure 2.14: Shrinhge strains measured in concrete prisms for concrete of R4HC
2.5 Test Set-up
Al l specimens were tested in the Jarnieson Structures Laboratory at McGi l t University,
The same set-up was used in ail cases in order to ensure compatibility of results. Figures 2.15 and
2.16 illustrate the test set-up.
The specimen was constnicted and tested in place, under the universal testing machine.
During testing, the specimens were fixed in place only at the top and bottom of the columns. The
top and bottom connections of the column were designed to simulate points of contra-flexure in the
columns. This was don: by connecting the top and bottom of the column to thin steel plates which
Lvere tlien bmced against the sides of the machine in order to prevent lateral movement. The plates
were tliin enoush to allow rotation of the ends in order to sirnulate a pin connection. The axial load
was applied by the universal testing machine through 75 mm diarneter rollers at the top and bottorn
of tlie colurnn. The axial load applied simulated 90% of the gravity load of the prototype structure
in the second storey column which was equivalent to 1076 kN. This load was kept constant during
testing.
The reversed cyclic loading of the specirnens was simulated using hydraulic Ioading jacks.
Four jacks were used to apply tlie loads at a distance of 2000 mm frorn the centre of the column.
Two jacks were used simultaneously in each direction. The two jacks situated under the reaction
floor were used to apply load in the positive direction through two 32 mm high-strength threaded
rods anchored in a reaction beam on top of the slab. The negative loading was simulated by
applying an upwards load through a 50 mm diameter roller reacting against a plate on the bottom of
tlie beam.
Figure 2-15: Pbotograph of test set-up
36
- axial load applied by 1 universal testing machine
hinge connection
A
A 1 mr - load ceII , ,
steel reaction beam --
A - 32mm high-streng th threaded r d - -- 150mm sboke loading jacks
., q? 1- .. (upwards direction) b 3 -+J4 .. load cel!
250mm stroke ioading jacks (downwards direction)
Elevation View Profile View
(a) Details of Loading Mechanism.
-- head of universal testing machine
75mm + rolier 2 - 25mm distribution plates
2 channels providing lateral restraint bearing against the frame of the testing machine
(b) Details of Hinge Connection.
- 6mm flexible plate
._ 6mm capping plate, welded to the longitudinal calumn bars
Figure 2.16: Details of test setup
2.6 Instrumentation
The performance of each specimen was monitored continually during the test by both
electronic and mechanical instrumentation. These included linear voltage differentiai tramducers
(LVDT's) to measure external deflections, electrical resistance strain gauges to measure strains in
the reinforcing steel, load cells to measure applied loads and mechanical targets to measure strains
on the concrete surface. All electronic readings were taken at small intervals throughout the test by
rneans of a computerised data acquisition system. The mechanical readings were taken manually at
the peak of each load stage as well as at zero load-
2.6.1 Load Measurements
Load cells were used to measure the applied load during the test. The simuiated earthquake
loads were measured by 350 kN load cells which were in direct contact with the loading jacks as
seen in Fig. 2.16. Two load celis were used for the upwards loading and two were used for the
downwards loading. The axial load which was applied to the column was monitored by the load
cell connected to the universal testing machine.
2.6.2 Deflectioa Measurernents
The specimen was instrumented with numerous LVDTs in order to investigate the relative
movements of each member. The vertical tip deflection of the main bearn-slab at the point of
applied load was measured using two LVDTs mounted on a aluminium frame as seen in Fig. 2.17.
This frame was attached to the column in order to measure tip deflection of die main beam relative
to the column. Each LVDT was used to measure one loading direction.
The twist of the spandrel beam was detennined from measured horizontal deflections using
two pairs of horizontal LVDTs attached to the back face of the spandrel beam. The ends of these
LVDTs were glued directly to the core of the spandrel through drilied holes in order to obtain
measurements even afker concrete spalling. Four LVDT's were attached vertically on the back of
the spandrel beam to detennine the strains of the outside legs of the hoop reinforcement in the
beam. Two vertical LVDTs measured the relative movement across the joints between the column
and the spandrel beam.
Finally, the relative movement of the slab with respect to the upper column was measured
by two LVDTs, one horizontai and one vertical, connected to the aluminium frame on the top
column. A similar set-up was used to mesure the relative movement between the lower column
and the main beam. See Fig. 2.17 for the location of the LVDTs for Specimen R4HC.
2.6.3 Strain Measurements
Strains were measured using both electrical resistance strain gauges and dernountable
mechanical strain gauges. The electrical gauges were giued to the reinforcing steel and monitored
local stnins in the bars. The gauges were placed in critical locations throughout the specimen as
illustrated in Fig. 2.19. Four of the longitudinal colurnn bars were instrumented with gauges at the
level of the top of the slab as well as at the bottom of the beam. The four corner main beam bars
were instrumented at the face of the column and two gauges were attached to the top back
longitudinal spandrel beam bar at the column interface. Four gauges were also glued to the spiral
reinforcement in the joint region to determine the strains reached in the spirals. All electrical
resistance strain gauges had a gauge length of 5 mm except those on the spiral which had a length
of 2 mm.
The mechanical targets were glued to the surface of the concrete (Fig. 2.18) and their
readings taken using a manual extensometer with a precision of measuring strain of 1 x 1 O-*. Six sets
of targets were glued to the top surface of the slab along the longitudinal slab bars. These were
used to determine both the strains in the slab bars and the effective slab width. A row of five sets of
targets was also glued to the top of the slab along the length of the main beam. An identical row of
targets was placed on the side of the beam at the height of the bottom longitudinal reinforcement.
Together, these readings were used to determine the curvature of the main beam and hence allow an
estimation of the contribution of the flexural deformations to the tip deflection of the main beam.
Mechanical strain targets glued in the form of five rosettes were also placed aiong the length of the
main beam at mid height. These readings enable the calculation of shear strains, principal strains
and the direction of principal strains. These values can then be used to estimate the contribution of
sliear deformations to the total tip deflections of the main bearn. All mechanical targets were
identical and were placed to provide a gauge length of 200 mm.
Vertical LVDT to rneasure tip deflection of main beam relative to the coiurnn
(a) Elevation View
2 LVDTs to measure bond slip. joint sepaabon and joint shear 2 LVDTs to measure distortion (similady arranged spandrel bearn rotation undemeath at the main beam
- and lover column inteffaœ)
4ûûmm
2 LVDTs to mersuru culumn rotation
4 LVOTs to measure strain in the spandrel 2 LVDrs to measure hoops joint movemnt
I
(b) View of Exterior of Spandrel Beam
Figure 2.17: Location of LVDT's
. - 5 strain rasenes at mid4epth (urge& spaœd @ 200mm)
lûOmm
U 4 @ 260mm * ---- 5 sels at level of longitudinal * - beam steel (targets spaced
@ 2 0 M m )
(a) Elevation View
* - : +-4
. - longirudinal targets (@ 2Wmrn) along slab steel
---*----*---.-.--.-....-------.-.....---.--.--.*---*-.**- . - longitudinal rargets (@ 2OOmm)
along k a m steel . * * e-.----*-+---. ,._.__._...-..-.___....*-.--..__--*-----------*.----~-.-. - - - * -. P Note: al1 mechanial stnin targets weie
glued to the cancrete surface
Figure 2.18:
(b) Plan View
Location of mechanical strain targets
4 gauges on beam corner . - - I ban (top and bottom)
2 gauges on evîerior top - i . '
. . . . . . . m e r spandrel bar . : -
eu : : .
4 gauges on sefected column spirals
(a) Side View (b) Exterior View
* - - .
-
-- - - - - - -
Figure 2.19: Locations of electrical resistance strain gauges
8 gauges on column corner bars (at dab level and al kvel of bonom of main &am)
2.7 Testing Procedure
A general testing procedure was followed for al1 tests, although this was altered slightly
depending on the individual specimen.
The test began by applying a constant compressive axial load to the column. This load of
1076 kN represents approximately 90% of the structure dead load in the second storey level
exterior column. Then, reversed cyclic loading was simulated by applying downwards and
upwards loads to the end of the main beam. Each cycle consisted of one downwards (positive)
loading sequence and one upward (negative) loading sequence. The downwards loads produced
negative moments in the main beam and were labelled the "A" half cycles.
The peaks of the first two cycles were governed by calculated loads. The first cycle peak
was at a load creating a moment in the main beam 1.2 times that which produced first cracking.
This represents the full service moment. The peak of the second cycle was at the first yielding of
the longitudinal beam reinforcement as monitored by the electrical resistance strain gauges. The
peak of the third cycle corresponded to the overall or general yield of the bearn as observed by a
significant reduction in the loading stif iess. This could be seen on îhe Joad versus deflection
response of the main bearn. Subsequent cycle peaks were taken as multiples of the deflection at
general yielding. Figure 2.20 illustrates the ideal loading sequence for the specimens.
The performance of the specimens was monitored throughout the test. Electronic
resistrince strain gauge readings as well as LVDT readings were taken at small intervals of load and
deflection by the computerised data acquisition system. Manual target readings were taken at the
peaks of each cycle as well as between cycles (zero load). Other information such as crack patterns
and widths as well as photographs were taken at the cycle peaks.
positive loading sequences
negative loading sequences
C
numkr
indiates where manual readings wen taken
I
Figure 2.20: Loading sequence for specimens
CHAPTER 3
REVERSED-CYCLIC LOADING TEST RESULTS
The applied load versus tip deflection response of the main beam was used to monitor the
overail performance o f each specimen during testing. AI1 loads were applied to the end o f the main
beam at a distance of 2000 mm fiom the centre of the column. Each specimen had a different
moment lever arm fiom the loading point to the face of the column. These were 1.800 m, 1.825 m
and 1.775 m for Specimens R4HC, R4H and R4, respectively. In each case, the self weight of the
beam and slab, as well as the weight of the loading apparatus was taken into account in calculating
the moments. ïhese additional moments were equal to 22.1 kN m for Specimens R4HC and R4H
and to 23.6 kN m for Specimen R4. The total moments at the face of the column were obtained by
multipiying the applied load by the lever arm and adding the dead load moment.
3.1 Specimen R4HC
3.1.1 Load-Deflection Response
The applied load versus tip deflection response for the main beam o f Specimen R4HC is
sliown in Fig. 3.1. The peak loads for each half-cycle and the corresponding tip deflections are
s h o w in Table 3.1. Each cycle started with a downwards or positive applied load, causing
negative bending in the main beam. The first cycle was meant to simulate the "service l o a d
moment in both directions. First cracking in the main beam occurred at a downwards (positive)
load of 1 15.5 kN. This load corresponded to a beam tip deflection of 2.9 mm and resutted in a
negative cracking moment, Mc;, of 230 kN m. Assuming the service load to be equal to 1.2 Mc-,
the peak of half-cycle 1A was taken to an applied load of 138.4 kN and a corresponding
deflection of 5.4 mm. This caused a moment of -271 kNm in the main beam. In the first
downwards half-cycle (1 B), first cracking occurred at an upwards load of -61.1 kN. This C
corresponded to a tip deflection of 2.5 mm and resulted in a positive cracking moment, Mc, . of
88 kN m. The peak o f cycle I B \vas reached at a service moment, 1.2 Mc,, of
occurred at a load o f -70.8 kN and deflection of -3.3 mm.
105 m m . This
- . - - . - . - - -
first yielding and general yielding
Figure 3.1: Load versus tip deflection response for Specimen R4HC
The peaks of the second cycle (2A-2B) reached first yielding of the longitudinal steel in
the main beam. The strains in the longitudinal steel were monitored using electrical resistance
strain gauges glued to the beam bars. The first yielding of the longitudinal bars in negative
bending was reached at an applied load of 275.2 kN which corresponds to a moment o f 51 7
kN m. The predicted yield moment was 473 kN m. At this stage, there was a noticeable decrease
in the loading stiffness o f the main beam. Due to this, it was judged that the peak o f cycle 2A
represented both first yielding as well as general yielding of the main beam. The tip deflection at
this srage was 19.9 mm. This value represented the deflection ( A , ) corresponding to a ductility
leve! of 1 .O. A similar situation occurred at the peak of half-cycle 2B. The first yield and
general yield of the beam occurred almost simultaneously at a load of -1 87.7 kN and moment of
3 16 kN m. The negative yield deflection, &, was -12.6 mm. The remaining cycle peaks were
chosen as multiples of the yield deflections found during the second cycle.
In the positive direction. the maximum load was reached at a deflection of 60.1 mm
representing a ductility level of 3 4 . The maximum applied load of 323.0 kN resulted in a
maximum negative moment in the main beam of -605 kNm. In the negative direction, the
maximum load was reached at a ductility level of 4 4 . The load of -225.3 kN resulted in a
mavimum positive moment in the barn of 387 m'm.
The maximum ductility levels reached during the test were 104 (200.3 mm) in the positive
direction and 8A, (-103.7 mm) in the negative direction. The test was stopped at these maximum
deflections due to limitations in the testing apparatus. The hysteritic loops of Specirnen R4HC
show good energy dissipation characteristics, although there is some pinching of the loops at
higher ductility levels. This is consistent with some shear distress in the joint. At maximum
deflection, the load carrying capacity of the specimen was only reduced to 83% of the yield ioad.
Table 3.1: Applied loads and tip deflections at cycle peaks for Specimen R4HC
Cycle Oescription Tip Defiedior I 16 -70.81 -3.25 2A First Yield and 275.21 19.88 28 General Yield -1 87.67 -1 2.57 3A 1 302.92 29.32 38 1 SAy- -1 99.36 -1 9.02 4A ?Ay) 31 3.98 40.15 48 2 4 - -205.98 -25.46 SA 3 d ~ y 322.96 60.08 5B 3Ay -21 6.57 -38.4 6A
+ 4AY - 314.97 80.12
68 4Ay -225.26 -51 -36 7A 6 ~ , * 316.02 120.3
3.1.2 Beam Bebaviour
First cracking of the main beam occuned during the first positive half-cycle. At this stage,
hvo cracks formed, extending fiom the top of the slab and continuing to half the depth of the beam.
The cracks were located 120 mm and 325 mm fiom the face of the spandret bearn and had a
maximum width of O. 15 mm. Two cracks also formed during the first negative half cycle. The two
cracks, located 30 mm and 200 mm from the face of the spandrel bearn, began on the bottom of the
beam and extended half way up the depth of the main beam. The cracks had a maximum width of
0.2 mm and their location corresponded with the placement of the transverse beam reinforcement.
Four new cracks formed on the top of the main beam during the second positive half-cycle.
These cracks had a maximum width of 0.3 mm and tended to be more inclined the further they
occurred from the face of the spandrel bearn. This was due to increased shear forces. Eight new
cracks formed during the second negative half-cycle. These coincided perfectly with the spacing
and location of the beam hoops and ranged in size from 0.1 5 mm to 0.3 mm. At this stage, the
largest crack was along the bottom beam-column interface and had a width of 1 mm (see Fig- 3-2
(a)). Following these first two cycles, few new cracks appeared in the beam; the existing cracks
only Iengthened and widened.
At the maximum positive applied load (peak of cycle SA), the largest crack was located at
the top column-beam interface and measured 1.7 mm in width. At the maximum negative applied
load (peak of cycle 7B), the largest crack was situated on the bottom of the beam at the face of the
column and had a width of 6 mm. Overall, the main beam remained in good condition during the
entire test with little concrete crushing or spalling.
The curvatures and shear strain distributions along the main beam are plotted in Fig. 3.4.
The maximum curvature and shear strain at the positive peak of the yielding and general yielding
Iialf-cycle was 5.32 x IO-^ rad/m and 3.47 x 1 0 - ~ rad respectively. The maximum recorded
çurvature was 35.87 x 10') radm during the seventh loading stage while the maximum recorded
shear strain was 3.89 x IO-) rad which occurred during the tifth cycle. Discontinuities in the plots
of Fis. 3.4 are Iikely attributed to the discrete nature of the cracks.
(a) Firçt yielding and general yielding, P = 275.2 kN
(b) 1.5 %', P = 302.9 kN
(c) Maximum applied load, P = 323.0 kN
Figure 3.2: Photograpbs of Specimen R4HC at various stages of testing
Figure 33: Pbotograph of damage near the joint of Specimen R4HC
(a) First Cracking
4.0
S O - (b) First Yielding and
General Yielding
(d) Maximum Load (cl 1.5 4
Figure 3.4: Curvature and shear strain plois for R4HC
3.13 Slab Behaviour
Cracking in the slab first occurred during the first positive half-cycle and subsequently only
occurred during positive loadings. During cycle 1 A, five cracks formed in the slab, with the largest
located at the face of the column and measuring 0.3 mm. One crack extended the full width of the
slab at a distance of 400 mm from the face of the column. This crack coincided with the location of
the transverse slab reinforcement.
During the second positive half cycle, three cracks extended the f i i l l width of the slab; their
location coinciding with the placement of the transverse slab reinforcement- These cracks ranged
in size from 0 2 mm to 0.4 mm. Two torsional cracks also formed, starting at the inside face of the
column and extending towards the exterior of the spandrel beam as c m be seen in Fig. 3.5. By the
third positive cycle, the crack located at the face of the column was 3 mm wide. It was observed
that this crack extended down into the slab to the junction of the main beam and column
longitudinal bars; the crack was then transferred through the spandrel beam. The location of this
crack could be due to the geometry of the round column-spandrel beam interface. Cracks starkd
forming around the loading beam during cycle 4A. By stage 8A, the crack at the face of the column
was 15 mm wide and the longitudinal beam and column steel could be clearly seen.
(a) Cycle 2A (b) Cycle 7A
Figure 3.5: Crack patterns in slab of Specimen R4HC
Figure 3.6 shows the strain distributions in the longitudinal slab steel for Specimen R4HC.
Tiiese strains were measured using two rows of mechanical targets with a gauge length of 200 mm.
The shaded area on the plots represents the yield strain of the longitudinal No. 10 slab bars (E, =
0.0023). It is interesting to note that at first yield and general yield of the main beam, oniy the inner
most slab bars have yielded; those being inside the effective slab width. However, by the
mâuirnum load at a ductility level of 34.. al1 longitudinal slab bars have yielded.
-- 1.2 M u - - first YÎelding and ;
Geneml Yelding i - r.s+ - 2 % - 3 4
Figure 3.6: Distribution of strain in slab longitudinal bars for Specimen R4HC
3.1.4 Spandrel Beam Bebaviour
The first noticeable distress in the spandrel beam occurred during cycle 1A. A torsional
crack formed in the top east corner of the top column-spandrel beam interface and propagated down
to the bottom face of the spandrel bearn, 200 mm fiom the column face. On the first negative cycle,
this crack completely closed. During the second positive half-cycle, a second torsional crack
formed on the West side. which mirrored the first crack. The maximum width of these two torsional
cracks was 1 mm. Two splitting cracks also formed along the two back longitudinal column bars.
ïiiese cracks only measured between 0.05 mm and 0.2 mm in width. A new torsional crack formed
during the fourth positive half-cycle which started on the east side, approximately 150 mm fiom the
top column face and extended downwards at 45 degrees into the spandrel bearn.
During the sixth positive cycle, some crushing was evident at the top column-spandrel
beam interface. At this stage, lateral movement of about 3 mm could be seen along the torsional
cracks (see Fig. 3.7). The sixth negative cycle produced the first positive torsional cracking with
two cracks beginning on either side of the bottom column and extending upwards at 45 degrees.
Crushing was also evident at the north face of the bottom column just below the main beam. By the
8th positive cycle, the lateral movement between the two ends of the spandrel bearn and the centre
reçion measured as much as 1 1 mm causing some concrete to spall off. By the final toad stage, al1
of the cover had been effectively dislodged fiom the joint region of the spandrel beam.
Figure 3.7: Pbotograpb ofspaadrel beam of Specimea R4HC at tbe positive cycle (M,*)
Figure 3.8 shows the torque venus twist response for the spandrel beam of Specimen
R4HC. The experimental torque was detennined from the forces in the slab bars corresponding
to the measured strains. These forces were then rnultiplied by their eccentricity about the centre
of rotation of the spandrel beam to obtain a torque. For a more detaifed description of these
calculations see Section 4.5.
C
E - t A governed by slrut and tic rncchanism ; govemed by torsional sirengîh of w
1 the spandnl k a m
O 40 a -- - - - . --
A ..T " C F 1 = 245 mm
- 3 - No.25 bars top and bottom
---- - No. 1 O haop
--- No. 10 tie
O 0.001 0.002 0.003 0.004 Twist ( -dm)
Figure 3.8: Torsional response of spandrel beam for Specimen R4HC
3.1.5 Columa Behaviour
The first cracks in the column appeared during the second positive half-cycle. Three
cracks formed on the south face of the bottom column, spaced at 150 mm, 270 mm, and 380 mm
from the bottom of the bearn. These cracks ranged from hair-line to 0.1 mm in width. There were
also 4 cracks on the north face of the top column at distances of IO0 mm, 3 10 mm, 395 mm and
540 mm from the top of the slab. These cracks ranged in width fiom 0.25 mm near the slab to 0.05
mm at the top of the column. Few other horizontal cracks fonned in the column during the
remainder of the test and the maiuimum crack width was consistent at approximately 0.25 mm.
Minor crushing at the column-beam interface started in the third positive half-cycle. Signs
of crushing and splitting cracks were observed on the top south face of the column, during the fiAh
positive cycle. Spalling associated with crushing of the concrete also occurred on the bottom north
face, the top south face, and the bottom south face during the remainder of the test.
Figure 3.9 shows the strains in the longitudinal column bars which occumd during testing
of Specimen R4HC. From Fig. 3.9 it c m be seen that the first yielding of a column longitudinal bar
(top NW bar) occurred at the peak of the third positive haIf-cycle at a deflection of 1-54. and a load
of 302.9 kN. The maximum moment carried by the column was 335 kN m during the fifth positive
half-cycle (34). This maximum applied moment is very near the maximum calculated moment
capacity in the column of 338 kN m. From Fig. 3.9 it can be seen that at maximum load, the north
longitudinal coIumn bars both yielded in tension in the top column but the south bars did not yield.
In the bottom column, only one bar had yielded in compression. The smaller strains at the bottom
of the joint may be due to the higher compressive strength of the concrete in the bottom column,
and also due to the fact that the bottom column has a higher compressive load than the upper
column.
TOP 0 N W gauge
x NE auge
SWgaugc r SE gauge
.- top s h i n gauge . i -;-
' a - s r
bollom sttain gauge
Figure 3.9: Strains in vertical column bars of Specimea R4HC
3.1.6 Joint Behaviour
The joint behaviour was monitored by 4 electrical resistance strain gauges glued to the
spiral reinforcement. The strains at these locations in the joint are plotted in Fig. 3.10. It can be
seen that yielding of the transverse reinforcement in the joint was never reached during the test.
The maximum strain reached was 1.2 x 1 05. There was m e evidence, however, that the pitch of
the spiral reinforcement may have been too large to provide complete confinement of the concrete
core. It was observed that some spalling extended into the concrete core between the spirals.
stain gauge
STRAIN (xl O")
0.00 0.50 1.00 1.50 2.00 2.50
Note: For me aolumn hoops. &, = 2.6 x 10'
Figure 3.10: Distribution of strains in column spiral of Specimen R4HC
The deformations of the joint were measured by two pairs of LVDTs as described in
Section 2.6.2. These LVDTs were used to indicate bond slip and calculate the extent that the joint
shear defonnation contributed to the overall tip deflection of the beam.
3.2 Specimen R4H
Specimen R4H was tested at McGill University by G. Marquis (1997). It was designed and
constructed in high-strength concrete with a 350 mm by 350 mm square column, and is used for a
cornparison of responses with Specimen R4HC.
3.2.1 Load-Defiection Response
The applied load versus tip deflection response for the main bearn of Specimen R4H is
s hown in Fig. 3.1 1 . The peak loads for each ha1 f-cycle and the corresponding tip deflections are
shown in Table 3.2. The first cycle was meant to simulate the "service load" moment in both
directions. Assuming the service load moment to be equal to 1.2 Ma, the peak of half-cycle 1A
was taken to an applied load of 136.4 kN and a corresponding deflection of 4.4 mm. This caused a
moment of -271 lcNm in the beam. In the first downwards half-cycle (IB), the service load
moment was reached at a load of -72.6 kN and a tip detiection of -0.8 mm. This represents a
service load moment, 1.2 Mc,, of 1 10 kN m.
Tip Defiaction (mm)
Figure 3.11: Load versus tip deflection response for Specimen R4H
The peaks of the second loading cycle (2A-2B) reached first yielding of the longitudinal
steel in the main beam. In the positive loading direction, first yield occurred at a load of 306.1 I<N
and at a karn tip deflection of 22.9 mm. In the negative loading direction, first yield occurred at a
Ioad of -185.4 kN and a beam tip deflection of -7.8 mm. It was later judged by reviewing the
hysteretic behaviour of the specimen, that a sipificant reduction in the loading stifhess had taken
place by this load stage, and that these peaks also represented the general yielding of the main
bearn. Hence, the yield deflectbns for the main bearn of Specimen R4H were taken as 4+ = 22.9
mm and &- = 7.8 mm. The remaining cycle peaks were chosen as multiples of the general yieid
deflections found during the second cycle.
Table 3.2: Applied loads and tip deflections at cycle peaks tor Specimen R4H
cyc* 1 cydcOac.iprn
1.2 M,
2A First Yield and 26 1 General Yield
(mm) 4.4 -0.8
In the positive direction, the maximum load was reached at a deflection of 95.9 mm
representing a ductility level of 4 4 . This maximum load of 412.5 kN resulted in a maximum
negative moment in the main beam of -775 M ' m . In the negative direction, the maximum load was
reached at a ductility level of 8 4 . The load of -255.2 kN resulted in a maximum positive moment
in the main bearn of 443 kN m.
Tiiere was a sudden drop in the load carrying capacity of specimen R4H during the
seventh positive half-cycle. At this stage, ten of the nvelve longitudinal bars in the slab ruptured.
This was attributed to the fact that the slab bars were high-strength, No. 1 O cold-rolled reinforcing
bars with limited ductility. Testing was stopped during the ninth positive half-cycle when one of
the three top No. 25 longitudinal bars in the bearn ruptured. The maximum ductility levels reached
during the test were 84 . (1 90.8 mm) in the positive direction and 104. (-8 1.4 mm) in the negative
direction. The hysteretic loops of specimen R4H show good energy dissipation characterktics,
witli large energy absorption and relatively little pinching of the load versus deflection loops until
the rupturing of the slab bars.
3.2.2 Beam Bebaviour
First cracking of the main bearn occurred during the first positive half-cycle. At this stage.
a single crack fonned, extending vertically from the top of the slab and continuing to just below
Iialf the depth of the main h m . This hairline crack was located 165 mm from the face of the
spandrel beam. Two hairline cracks also formed during the first negative half-cycle. The two
cracks. located 85 mm and 190 mm from the face of the spandrel bearn. began on the bottom o f the
beam and extended approxirnately 100 mm up the face of the main bearn.
Four new cracks formed on the top of the main bearn during the second positive half-cycle.
These cracks Iiad a maximum width of 0.4 mm and tended to be more inclined as they occurred
fiirther from the face of the spandrel beam. This was due to increased shear forces. Sevenl new
cracks formed during the second negative half-cycle. The location o f ail theses cracks tended to
coincided with the spacing and location of the transverse beam reinforcement. Following these first
two cycles. few new cracks appeared in the beam: the existing cracks only lengthened and
~videned.
During the third loading cycle, the mâuirnum crack width in negative bending was 0.6 mm
and in positive bending it was 1-25 mm. At the maximum positive applied load (peak of cycle 6A),
the largest recorded crack width in the main beam was 2.0 mm. At the maximum negative applied
load (peak of cycle 7B), the largest crack had a width o f 5.0 mm. During the seventh positive half-
cycle, crushing of the concrete on the bonom of the beam was noticed. The crushing was followed
by the rupturing o f several of the longitudinal slab bars. Eventually, the additional stress caused to
the main bearn by the loss of negative flexural strength in the slab. resulted in the rupture o f one o f
(a) First yielding and general yielding, P = 306.1 kN
(b) 1.5 4, P = 354.8 kN
(c) Maximum applied load, P = 41 2.5 kN
Figure 3.12: Photograpbs of Specimen R4H at vanous stages o f testing
the top longitudinal beam bars during the ninth positive half-cycle. The bottom longitudinal beam
bars also started to buckle during the eighth cycle.
The curvatures and shear strain distributions along the main bearn of Specimen R4H are
plotted in Fig. 3.14. The maximum curvature and shear strain at the positive peak of the yielding
and general yielding half-cycle was 5.89 x 1 o5 r a d h and 3.17 x 10" rad respectively. The
maximum recorded curvature was 24.83 x IO-' rad/m d u h g the sixth load stage while the
maximum recorded shear strain was 16.4 1 x lo5 rad which occurred during the seventh cycle.
Discontinuities in the plots of Fig. 3.14 are likely attributed to the discrete nature of the cracks.
Figure 3.13: Photograpb of beam damage no i r the joint ofspecimen R4H
1.0 ! 1.5 ; 2.0 : 2.5 3.0 ; 3.5 i 4.0 f 4.5 i 5.0 :
(a) First Cracking
3.5 i 4.0 j 4.5 i 5.0 -
(b) First Yielding and General Yielding
(CI 1.5 4, (d) Maximum Load
Figure 3.14: Curvature and shear strain plots for R4H
3.2.3 Slab Bebaviour
Cracking in the slab fim occurred dunng the fim positive half-cycle and subsequently only
occurred dunng positive loadings. During cycle I A, one flexural crack fomed on the top of the
slab at a distance of 180 mm from the face of the column. The crack extended the full width of the
slab. During the second positive half-cycle, several fiexural cracks formed which extended the full
width of the slab. The location of the flexural cracks coincided with the transverse siab
reinforcement. The largest of these cracks measured 1.0 mm and was located at the face of the
column. Torsional cracks also formed during cycle 2A, starting at the inside face of the column
and extending towards the exterior of the spandrel beam as seen in Fig 3.15.
Dunng the seventh positive half-cycle, ten of the twelve longitudinal slab ban ruptured
creating a very large crack along the face of the column which extended across the entire width of
the slab. Only the two western-most bars did not rupture which caused a sort of wedge effect
across the slab. The width of this crack ranged from 1.5 mm on the west side to 27 mm on the east
side where no slab bars remained effective. The nipturing of the slab bars also affected the
subsequent loading cycles since a very large torsional eccentricity was created, adding twist to the
specimen. The width of this crack reached 95 mm by the end of testing.
-
(a) Cycie 2A (b) Cycle 7A
Figure 3.15: Crack patterns in slab of Specimen R4H
Figure 3.16 shows the strain distributions in the longitudinal slab steel for Specimen R4H.
These strains were measured using two rows of mechanical targets with a gauge length of 200 mm.
The shaded area on the plots represents the yield strain of the longitudinal No. 10 slab bars (E, =
0,0053). Figure 3.16 if lustrates that at general beam yielding, none of the longitudinal slab bars had
reached yield strain. This was attributed to the unexpected strength increase of the cold roIled No.
10 bars.
- - 1.2 Mcr .- First Yœlding and ;
General Yielding i - lSb,
- 2 4 , - 3 4 -- Near Siab Bar Rubture !
STRAIN
0.000
0.005
0.010
0.075
0.020
0.025
0.030
0.035
0.010
0.045
Figure 3.16: Distribution of strain in slab longitudinal ban for Specimen R4H
-
3.2.4 Spandrel Beam Behaviour
The first noticeable distress in the spandrel beam occurred during the second positive half-
cycle. Two torsional cracks formed on either side of the top column and propagated approximately
three-quarters of the way down to the face of the spandrel beam at 45 degrees. Two vertical
splitting cracks also formed in the spandrel beam along the back corner longitudinal column bars.
These cracks had a maximum crack width of 0.50 mm. Small inclined cracks also formed on the
inside north face of the spandrel beam, under the slab.
Two new torsional cracks formed on the back West side of the spandrel barn during half-
cycle 3A. The maximum width of the torsional cracks at this stage was 0.6 mm. There was also a
large, 2 mm wide crack along the slab-spandrel beam interface on the north side.
At maximum applied load, some crushing was observed on the exterior face of the spandrel
beam near the construction joint between the upper column and the spandrel beam (see Fig. 3-17).
At this stage, twisting of the spandrel beam was visible. Progressive damage to the spandrel beam
significantly diminished subsequent to the rupturing of the slab bars. Following this event, the
twisting of the spandrel beam becarne less significant and the crack widths ceased to increase.
Figure 3.17: Photagmph of spnidrel bean o f Specimea R4H at the 6<' positive cycle (4~;)
3.2.5 Column Bebaviour
The first cracks in the column appeared during the second positive half-cycle. Three
flexural cracks formed on the north face of the top column, spaced at 255 mm, 380 mm, and 495
mm from the top of the slab. There were also 2 flexural cracks on the south face of the bottom
column at distances of 170 mm, and 355 mm fiom the bottom of the beam. These cracks ranged in
width from 0.10 mm to 0.1 5 mm. Few other horizontal cracks formed in the column during the
remainder of the test and the maximum crack width reached was 2.0 mm. During the final loading
cycle, a splitting crack formed on the interior face of the lower column. At this stage, there was
also some spalling at the bottom column-joint interface.
Figure 3.18 shows the strains in the longitudinat column bars which occurred during testing
of Specimen R4H. First yielding of a column longitudinal bar occurred at the peak o f the third
positive half-cycle at a deflection of 1 SA,. and a load of 352 W. The maximum moment carried by
the column was 387 kNm during the sixth positive half-cycle (4&). The electrical strain gauges on
the column longitudinal bars showed significant yielding during the later stages o f the test as seen
in Fig. 3.18. This may be attributed to the higher negative moment capacity of the bearn resulting
from the use o f high-strength, cold-rolled No. 10 bars in the slab.
- .- bonom strain gauge
-0.003 -0.002 4.001 0.000 0.001 0.002 0.003 0.001 Stnin, E,
Figure 3.18: Strains in vertical column bars of Specimen R4H
3.2.6 Joint Behaviour
The joint behaviour was monitored by 4 electrical resistance strain gauges glued to the
transverse reinforcement. The strains at these locations in the joint are plotted in Fig. 3.19. It can
be seen that yielding of the transverse reinforcement in the joint was never reached during the test.
The maximum strain reached was 1.9 x IO-' while the yield m i n of the hoops w s 5.2 x l ~ - ~ .
From this data as well as physical performance, it is evident that there was suficient joint shear
reinforcement provided.
strain gauge
'2% P
1
I - - 1.2 MU - - Firsl Yielding and Genenl Yelding
I
., . :. .', *. .. 1.5%
- 2 4 - 3 4 - - ARer Siab Bar Rupture
Note: For the column hoops. E, = 5.20 x to4
Figure 3.19: Distribution of strain in column hoops of Specimen R4H
The deformations of the joint were measured by two pairs of LVDTs as described in Section 2.6.2.
These LVDTs were used to indicate bond slip and the arnount that the joint shear deformation
contributed to the overall tip deflection of the bearn.
3.3 Specimen R4
Specimen R4 was tested at McGill University by S. Rattray (1986). It was designed and
constmcted in normal-strength concrete with a 400 mm by 400 mm square column, and is used for
a cornparison of responses with Specimen R4HC.
3.3.1 Load-Deflection Response
The applied load versus tip deflection response for the main beam of Specimen R4 is
shown in Fig. 3.20. The peak loads for each half-cycle and the conesponding tip deflections are
show in Table 3.3. The first cycle was meant to simulate the "service load" moment in both
directions. Assuming the service load moment to be equal to 1.2 Ma, the peak of half-cycle IA
was taken to an applied load of 101 -7 kN and a corresponding deflection of 2.9 mm. This caused a
moment of -203 kNm in the beam. In the first downwards half-cycle ( 1 B), the service load
moment was reached at a load of -79.9 kN and a tip deflection of -1 -5 mm. This represents a
maximum moment, 1.2 Mc,, of 1 19 kN m.
400 - O first yielding O general yielding
Figure 3.20: Load venus tip deflection response for Specimen R4
The peaks of the second loading cycle (2A-2B) were reached at first yielding of the
longitudinal steel in the main beam. In the positive direction, first yield occurred at a load of 2 18.6
kN and at a bearn tip deflection of 1 1.4 mm. In the negative loading direction, first yield occurred
at a load of - 140 kN and a beam tip deflection of -6.6 mm.
Table 33: Applied loads and tip defieetions at cycle peaks for Specimen R4
The peaks of the third loading cycle (3A-3B) were reached upon general yielding of the
main beam as observed by a reduction in rnember stiffness. In the positive direction, this occurred
at a load of 27 1.6 kN and a beam tip deflection of 16.6 mm. In the negative direction, this occurred
at a load of - 1 75.9 kN and a beam tip deflection of -9.4 mm. The remaining cycle peaks were
c~de
1A 1B
chosen as multiples of the general yield deflections found during the third cycle.
Cyde Desdpaotr
1.2 M,
A p O î i i Load (W) 101.7 -79.9
fip DefWüon (mm) 2.9 -1 -5
In the positive direction. the maximum load was reached at a deflection of 75.8 mm
representing a ductility level of 54. . This maximum load of 360.5 kN resulted in a maximum
negative moment in the main beam of -662.0 kN m. In the negative direction. the mavimum load
was reached at a ductility level of 8 4 . . The load of -242.9 kN resulted in a mavirnum positive
moment in the main beam of 309 kN m.
The maximum ductility levels reaclied during the testing of Specimen R4 were 94. ( 1 76.4
nim) in the positive direction and 8 4 . (-76.7 mm) in the negative direction. Testing was stopped at
tliese deflections due to limitations in the testing apparatus. The hysteretic ptots for specimen R4
show good energy dissipation characteristics, with large energy absorption and relatively M e
pinching of the loops. At maximum deflections. the load carrying capacity of the specimen was
only reduced to 90% of the maximum load capacity.
3.3.2 Beam Behaviour
First cracking of the main beam occurred during the first positive half-cycle. At this stage,
two flexural cracks formed. extending from the top of the slab and continuing into the bearn. The
cracks were located 80 mm and 360 mm from the face of the spandrel beam and had a maximum
width of O. 1 mm. Two cracks also formed during the first negative haif-cycle. The first crack was
located at the face of the column and the other at a distance of 200 mm from the face of the
spandrel beam.
Three new cracks formed at tlie top of the main beam during the second positive half-cycle.
Tliese cracks had a maximum width of 0.5 mm. Six new cracks formed during the second negative
Iial f-cycle. Ttiese cracks were inclined at 45 degrees and coincided perfectly with the spacing ( 130
mm apart) and location of the beam hoops. The cracks which appeared in subsequent cycles tended
to follow the same trends as those previously described.
Local crushing of the concrete on the bottom of the beam started during the sixth positive
loading cycle. The load of 339.0 kN at this stage also caused splitting cracks at the level of the
bottom longitudinal reinforcement in the main beam, near the joint.
At the maximum positive applied Ioad (peak of cycle 8A), there was obvious crushing and
spal ling of the concrete outside the joint region. During the 8th negative half-cycle. severe spalling
of the concrete occurred on the bottom of the beam. The bottom 40 mm barn cover was lost over a
(a) First yielding, P = 218.6 kN
(b) General yielding, P = 271.6 kN
(c) Maximum applied load, P = 360.5 kN
Figure 3.21: Photograpbs of Specimen R4 at various stages of testing
distance of 180 mm, exposing the bearn reinforcement. Further spalling occurred in the remainder
of the test and eventually, ail four bottom bars buckled at a ductility of 8 4 .
The curvatures and shem strain distributions along the main beam of Specimen R4 are
plotted in Fig. 3.23. The maximum curvature and shear strain at the positive peak of the general
yielding half-cycle wru 3.9 x 10" radlm and 2.4 x lo5 rad, respectively. The maximum recorded
curvature was 50.8 x 10" radlm during the ninth load stage while the maximum recorded shear
strain was 1 1.6 x 10;' rad which occurred during the fifth cycle. From the measured curvatures, it
was estimated that the hinge region extended approximately 400 mm fiom the column face.
Discontinuities in the plots of Fig. 3.23 are likely attributed to the discrete nature of the cracks-
Figure 3.22: Photograph of beam damage near the joint of Specimea R4
(a) First Cracking
P = 271.6 kN
(c) General Yielding
Ê :-- 3 l o i
(b) First Yielding
(dl "Near" Ultimate Load
Figure 3.23: Curvature and shear straia plots for R4
74
3.3.3 Slab Bebaviour
Cracking in the siab first occurred during the first positive half-cycle and subsequently only
occurred during positive loadings. During cycle 1 A, two flexural cracks formed on the top of the
slab. Their location coincided with the first two transverse slab bars fiom the face of the column.
Both cracks extended the full width of the slab. During the second positive half-cycle, there were
four cracks which extended the full width of the slab. The location of the cracks coincided with the
transverse slab reinforcement. The largest of these cracks measured 0.3 mm in width. During the
third positive half-cycle, the largest crack had a width of 0.5 mm. Torsional cracks also formed
during cycle 2A, starting at the inside face of the column and extending back towards the face of
the spandrel beam. During the tenth cycle, crushing of the slab surface around the column was
noted.
Figure 3.24 shows the strain distributions in the longitudinal slab steel for Specimen R4.
These strains were measured using two rows of mechanical targets with a gauge length of 200 mm.
The shaded area on the plots represents the yield strain of the longitudinal No. 10 slab bars (E, =
0.0024). It is interesting to note that at general yield of the main beam, the k t two sets of top
longitudinal slab bars on either side of the bearn had yielded. This conformed with the design
effective slab width of 4hF However, by the maximum load, al1 of the slab bars had yielded.
- Fint Cracking i - - Fimt Yelding i -. Genenl Yelding i -. Ultimate Load :
Figure 3.24: Distribution of strain in the slab longitudinal bars for Specimen R4
75
3.3.4 Spaadrel Beam Behaviour
The first noticeable damage to the spandrel bearn occumd during the second positive half-
cycle. Two torsional cracks formed on either side of the top column and propagated half way down
the face of the spandrel bearn. These cracks were angled at approximately 45 degrees and
measured beîsveen 0.05 mm and 0.25 mm in width. During the second negative half-cycle. these
cracks completely closed. Two splitting cracks also formed during the second cycle, along the
spandrel beam-column interface. These cracks had a maximum width of 0.5 mm.
During the fourth positive half-cycle, the torsional cracks extended the full depth of the
spandref beam. At this stage, the maximum measured crack width was 1.4 mm. The torsional
cracks increased in site to a maximum width of 6.0 mm during the sixth positive loading cycle. At
this time, it was observed that the spandrel beam and the slab had separated across the entire width
of the specimen. During the tenth positive half-cycle, there was cmshing and spalling of the
concrete along the two main torsional cracks on the back face of the spandrel beam as seen in Fig.
3.25.
Figure 3.25: Pbotograph of spandrel beam of Specimen R4 at the 10" loading cycle (7Ay)
3.3.5 Column Behaviour
The first crack in the column appeared only during the third positive half-cycle. This was a
0.2 mm wide flexural crack located on the extetior face of the bottom column near the spandrel
beam. Severaf more flexural cracks developed in the column during the fourth positive loading
stage. Three cracks formed on the north face of the top column, al1 spaced equally over a distance
of 500 mm. A second crack also fonned along the south face of the bottom column. No additional
cracks fonned during the remainder of the test, the existing cracks sirnply opening and closing upon
load reversal.
The maximum moment carried by the column was 331 kN'm during the eighth positive
half-cycle (54,). At this stage, the maximum crack width in the colurnn was 0.6 mm. Crushing
and spalling of the concrete on the north face of the bottom column also began at this stage and
continued for the remainder of the test.
3.3.6 Joint Behaviour
It was hard to determine the condition of the joint during the test due to the fact that the
spandrel bearn and main b a n covered three sides of the joint. The contribution of the joint shear
deformation to the tip deflection was measured by a dial gauge placed 85 mm from the top of the
slab. This deformation was measured at 9.8 mm at a peak load of 292.8 kN and a ductility level of
1.5 A,. The maximum deflection reached was 38.1 mm at a ductility level of 4 4. From the
overall behaviour, it was concluded that no significant distress took place in the joint region during
the testing, hence leading to the conclusion that the joint hoop reinforcement was adequate.
CHAPTER 4
ANALYSIS AND COMPAREON OF TEST FtESULTS
This chapter presents the analysis of the test results and compares the performance of
Specirnen R4HC tested in this research project with the performance of Specimen R4H tested by
Marquis ( 1997). and Specimen R4 tested by Rattray ( 1986) and reported by Paultre ( 1987).
4.1 Load - Deflection Responses
Table 4.1 lists some of tlie key response parameters for specimens R4HC. R4H and R4.
The ratio of the maximum recorded positive tip deflection. A, , and the displacernent at positive
çeneral yield, A'. represents the displacement ductility for each specimen. The n t i o of the applied
load at maximum deflection and the load at general yield, P JP?. is a measure of the ability of the
specinien to maintain load afier genenl yielding. The third parameter k,/k,. provides a measure of
tlie change in loading stiffness undergone by each specimen during testing. The stiffness
panmeters. k, and Cc,. are the dopes obtained by joining the peak positive and peak negative load-
displacement values at general yielding and at the final load stage respectively.
Table 4.1: Cornparison of failure mode and key rcsponse parametcm
R4HC 1 severe spalling affecting I I I II
The applied load versus tip deflection plots for al1 three specimens are shown in Figs.
4.1.4.2 and 4.3. Figure 4.1 shows the hysteretic behaviour of specimen R4HC. This plot shows
R4H
column and joint
Beam flexural hinging and 8.33 0.54 0.10
very good load carrying capacities at high levels of ductility. The specimen maintained near-
maximum load to a ductility of 6Ay which satisfies the ductility requirements for an R of 4
structure. The energy dissipation characteristics o f Specimen R4HC were very good in both the
positive and negative loading directions, up to a deflection of 4&. At greater deflections, the
hysteretic loops show some signs of pinching between half cycles. This can be attributed to the
presence of some shear distress in the joint region. The test was stopped due to limitations in
the testing apparatus. however it can be seen that even at a ductility level of IOAy, the specimen
maintained 83% of its load carrying capacity at yield.
Figure 4.2 shows the applied load versus tip deflection plots for Specimen R4H. These
Iiysteretic loops show very good energy dissipation. in both the positive and negative directions,
throughout the test. The load carrying capacity of the specimen was consistently greater than the
yield Ioad until the rupture of the slab bars during the seventh positive cycle. Following this
event, there was a significant drop in the load carrying capacity of the specimen. Figure 4.3
shows the hysteretic behaviour o f Specimen R4. This specimen showed ideal behaviour
throughout the test both in load carrying capacity at high levels of ductility as well as energy
dissipation. As with Specirnen R4HC, the testing of Specimen R4 was stopped due to
displacernent limitations in the testing apparatus, even though the specimen was likely capable of
reaching higher levels o f ductility.
Figure 4.4 compares the load-deflection response envelopes of the three specimens. It
should be mentioned that althougli Specimens R4HC and R4H were constructed with high-
strength concrete, their smaller member dimensions allows for a direct response comparison with
Specirnen R4. These specimens were al1 designed to have the same yield moment in the beams.
however high-strength slab bars provided in Specimen R4H resulted in a higher moment
capacity in the beam. From Fig. 4.4, it can be seen that Specimen R4H reached the highest
applied load in the positive direction while Specimens R4HC and R4 reached similar loads. This
can be attributed to the extra strength supplied in negative bending by the cold rolled high-
strength slab bars of Specimen R4H. The peak loads attained in the negative direction were
sirnilar for ail specimens. Al1 specimens showed good energy dissipation with only Specimen
R4HC exhibiting some pinching at ductility levels above 6 4 . All specimens also exhibited good
load can-ying capacities well into the non-linear range and only Specimen R4H exhibited actual
failurz by the end o f the test. Specimen R4 exhibited a slightly larger loading stiffness than the
two high-strength specimens, presumabiy due to the larger member dimensions. The
performance of al1 three specimens was consistent with R of 4 ductile structures.
mfirst yielding and general yielding
-1 00 -50 O 50 100 150 200 fip hflection (mm)
Figure 4.1: Appüed load venus tip deîlection response for Specimen R4HC
- first yielding and general yielding
-1 00 -50 O 50 1GU 150 200
Tip üefkction (mm)
Figure 4.2: Appücd load versus tip deflection response for Specimen R4H
Tip Ikfkcb'on (mm)
Figure 4.3: Applied load versus tip deflection response for Specimen R4
4.2 Tip Deflectioa Components
The tip deflections which have k e n previously referred to in this thesis have been those
rneasured by a pair of LVDT's located at the tip of the main beam. These deflections consist of
different displacement components. There is a beam displacement component which consists of
deflections due to flexural defonnations as well as shear deformations. There is also a joint
displacement component which consists of both the shear distortion and the bond slip of the bars
within the joint region. The displacement component from the column was assumed to be
elirninated as described in Section 2.6.2. Al1 components were estimated fiom the measurements
taken during the testing o f the specimens.
The following equation can be used to calculate the bearn tip deflection from the
components mentioned above:
Atip = Af + 4 + Aj
where, Ali, is the total estimated beam tip deflection
Af is the component due to beam flexure
4 is the component due to beam shear
A, is the component due to joint shear and bond slip
The calculation of the beam flexure component, Ar, was calculated using the equation in
Fig. 4.5. This is equivalent to applying the first moment-area theorem to the measured curvature
distributions pIotted in Figs. 3 .4,3.14 and 3.23, assuming a rigid joint. In this equation, cp is the
beam curvature and x is the distance from the loading point to the centroid o f a small element of
area, <ph.
Figure 4.5: Determination of A,
The shear component, 4. is calculated using the equation in Fig. 4.6, This equation gives
the area under the measured shear strain distributions, y, in the beams plotted in Figs. 3.4, 3.14,
and 3.23.
500 :
Figure 4.6: Determination of A,
The displacement component caused by joint shear distortion and bond-slip, Aj7 was
determined using the equations in Fig. 4.7. As can be seen, Ai is the surn of a shear component
and a bond slip component. The deflection and curvatures used in these calculations were taken
from the LVDT measurements recorded during the test.
A , = ejb
(a) Joint deformation due to shear (b) Joint deformation due to bond slip
A , = A,,. + A j b
Figure 4.7: Determination of A,
Figures 4.8, 4.9 and 4. I O show both the actual beam tip deflection measured during the
test, and the beam tip deflection calculated as the sum of individual component deformations. It
can be seen that the calculated tip deflection coincides closely with the total measured
deflection. Tlie total calculated tip deflections for Specimens R4HC and R4H are slightly less
than those measured. This can be attributed to the discrete nature of the crack patterns, where
some large cracks formed very close to the column, outside of the range of the strain targets.
The measured beam flexural component and beam shear component were very similar for a11
specimens with the shear component being very smali in ail cases. The beam flexural
component was however slightly larger in Specimen R4, which is consistent with the significant
beam flexural hinging observed during the test. As can be seen in the figures, the joint
distortions contributed greatly to the over-al1 deflection of the main beam, particuiarly for
Specimens R4HC and R4H. This indicates that there was some bond deterioration and/or joint
distortion afier yielding of the main beam. It can also be seen that the loading stiffness is smaller
in the high-strength specimens probably due to the smaller member dimensions.
Deflecüon (mm)
h
5 250 - u 8 200 A
Figure 4.8: Predicted and measured tip-deflection components for Specimen R4HC
.. . . b
b calculaied tip defledion
- measured tip defledion
b calculated tip deflection
measured tip deflection
O 10 20 30 40 50 60 70 80 90 100 Oeflection (mm)
Figure 4.9: Predicted and measured tip-deflection components for Specimen R4H
calculated tip deflection 2% - measured tip deflection
0 10 20 30 40 50 60 70 80 90 100 Deflection (mm)
Figure 4.10: Predicted and measu red tip-deflection components for Specimen R4
4.3 Hysteretic Loading Behaviour
1.3.1 Energy Dissipation
The arnount of energy dissipated by each specimen during each loading cycle can be
caiculated as the area enclosed by each loop of the load-deflection curves. As the ductility levels
increase, the hysteretic loops get wider and more energy is dissipated. Tables 4.2,4.3 and 4.4 give
the arnot.int of energy dissipated during each half-cycle by Specimens R4HC, R4H and R4
respectively. The total energy dissipated in negative bending was very high for al1 thtee specimens.
The total energy dissipated for each specimen was 140 kNm for Specimen RQHC, 2 13 kN-m for
Specimen R4H, and 195 kN'm for Specimen R4. Specimen R4HC dissipated less energy due to
some shear distress in the joint which caused pinching of the hysteretic loops. It should be noted
that alîhough these values represent very good energy dissipation, the values cannot be directly
compared due to the different loading histories. For example, Specimen R4 underwent two more
cycles than Specimens R4H and R4HC. Figure 4.1 1 shows the plots of cumulative energy versus
ductility ratio and cumulative energy versus tip deflection for each specimen.
40 60 80 100 120 140 160 180 200 Tip Deflection (mm)
(a) Cumulative energy versus ductility ratio (b) Cumulative energy versus tip defi ection
Figure 4.11: Energy dissipation of the specimens
Table 4.2: Energy dissipation for Specimen R4HC
16 75.2 1 First Yield and 1 .O0 2227.0 1 .O0
l I 1 1 I I 1 Total 1 139708.9 1
1 2B 3A
General Yield 1 S A y 1.47
1090.3 2826.0 1.10
Table 4.3: Energy dissipation for Specimen R4H
Cy- Cy- 444 mw P&Y Description positivecydes Di-pated posibivecydes
(Mm) 1A 1.2 M, 0.19 245.9 - 16 68.2 2A First Yield and 1 .O0 4925.0 1.00 26 General Yield 241 7.9 3A 1.54' 1.39 2526.1 1.16 36 1572.2 4A 2 ~ + 2.08 6503.9 1.27 4 6 34- 1 4060.0 5A 3 4 * 2.78 9988.2 1.31 56 4 4 - 6323.7 6A Ii4' 4.18 1 19296.3 1.35
A Total 1 212557.8 11
Table 4.4: Energy dissipation for Specimen R4
4.3.2 Displacement Ductility
Tables 4.2, 4.3 and 4.4 also give the displacement ductilities of each specimen; the
displacement ductility k i n g the ratio o f the maximum displacement reached at a certain point,
A*, divided by the displacement at general yielding, 4. Both Specimens R4HC and R4 reached a
displacement ductility of 10 in the positive direction and 8 in the negative direction. Both
specimens showed signs of k i n g able to reach higher levels of ductility but were limited by the
testing apparatus. Specimen R4H reached a displacement ductility of 7 in the positive direction and
10 in the negative direction. These were the maximum safe Ievels attainable due to the rupture of
ten slab bars and one longitudinal main beam bar.
4.3.3 Damping and Stiffness
The hysteretic performance of each specirnen can be illustrated through two key
parameters; the specimen's ability to dissipate energy and it's ability to maintain stifiess. The
ability to maintain stiffhess is represented by the loading stifiess parameter k. As shown in Fig.
4.12, this factor represents the siope of the line joining the peak load and peak deflection values in
the positive and negative loading directions. These values are plotted against the ductility ratio and
the tip deflection in Fig. 4.1 2. The plots show similar stiffness degradation for al1 three specimens
although Specimen R4 displayed a siightly higher stiffness versus ductility ratio response. This
could be attributed to the larger rnember dimensions for the specirnen,
Loading stiffness, k
1 2 3 4 5 6 7 8 9 1 0 1 1 1 2 O 20 40 60 80 100 120 140 160
A**/& Tip Deflection (mm) (a) Loading stiffness versus ductility ratio (b) Loading stiffness versus tip deflection
Figure 4.12: Stiffness degradation of the specimens
4.4 Moment - Cuwature Responses and Predictions
4.4.1 Moment - Curvature Response of the Beams
Significant ductility of a structure can only occur if a sufïkient amount of rotational
ductility is exhibited in those members expected to undergo plastic hinging. The "curvature
ductility" of the sections of members is measured as the ratio of the maximum curvature attainable
before significant drop in load canying capacity, <pu, over the yield curvature, 9,. Table 4.5
summarises the maximuin moments and curvature ductilities determined for each specimen from
the test results.
Table 4.5: Maximum moments and curvature ductilities of the specimens
Specimen M- '4. (pu Q&
(k~.rn) (XI O= radim) (xl O= rad/m)
The effective slab width assumed in design has a significant impact on the negative
bending moment-curvature responses of the beams. The moment-curvature responses for each
specimen considering various effective slab widths were predicted using the program RESPONSE
(Collins and Mitchell, 1997). The sections analysed were:
(i) A rectangular beam with no flanges having cross-sectional dimensions of
350 x 600 mm for Specimens R4HC and R4H, and 400 x 600 mm for Specimen
R4.
(ii) A T-beam with an effective slab width of 3hr on each side of the beam.
This resulted in an effective slab width, b, = 1010 mm for Specimens R4HC and
R4H, and b, = 1060 mm for Specimen R4, with 4 No. 10 stab bars within this
width.
(iii) A T-beam with an effective slab width o f 4hr on each side of the beam.
This resulted in an effective slab width, b, = 1230 mm for Specimens R4HC and
R4H. and b, = 1280 mm for Specimen R4, with 8 No. 10 slab bars within this
width.
(iv) A T-beam including the entire width of the slab, b, = 1900 mm for
Specimens R4HC, R4H and R4, with 12 No. 10 slab bars within this width.
(v) A T-bearn including the entire slab width and considering a non-linear
distribution of strains across the slab.
The prediction for case (v) was made using the actual strains measured in the slab bars
during the test at maximum load as outlined in Figs. 4.13 and 4.14. The moment-curvature
responses for the five cases are s h o w in Figs. 4.15, 4.16 and 4.1 7. These are compared with the
experimentally determined response for each specimen. It is noted that the plot for the varying
strain distribution model displays a more rounded curve than those predictions assuming a unifonn
strain. This is due to the sequential yielding of the slab bars in the tension flange. The distribution
of strains in the tension flange of the beam is a function of the torsional stiffiess and strength o f the
spandrel bearn (DiFranco, 1993, Marquis, 1997). The larger and stiffer the spandrel beam, the
more linear the strain distribution across the slab, and the more bars would tend to yield
simultaneously as assurned in cases (i) to (iv). From the moment-curvature plots we can see that al1
experimentai results reached moment curvature responses resembling those of cases (iv) and (v).
This suggests that the 1994 CSA Standard recommended effective slab width limits of 3hr on either
side of the beam to be considered for flexural strength ratios, may be underestimated.
Figure 4.13: Variation of strain across the T-section
15.0 . mcuureâ shear . 12.5 . disaibution
. - ideaiid $min 10.0 distribution
+ i . i l
7.5 - ! ,, . - . . 5.0 . '4
3 - No.25 bars bath direetions
N0.10 h m - - 3 - N0.25 bars
(a) Specimen R4HC
- - 3 - N0.25 bars
- 3 - No.25 ban
25.0 .
22.5 . ~ 7 1 . .
20.0 . i . , 17.5 . i i 15.0
12.5 10.0 . 7- . i , .
i i 7.5 . ;
t i 5.0 . ; I I 'd-
l .
2.5 i 1 01
No.10 hoop --- fi* j 1 -- 4 N0.20 Ban
(c) Specimen R4
(b) Specimen R4H
Figure 4.14: Accounting for strain variation across the flange of the T-beams
*- 1900 0
constant smin
simin
Figure 4.15: Moment-curvature responses for the beam of Specimen R4HC
constînt simin variable -
Figure 4.16: Moment-curvature mponses for the beam of Specimen R4H
strain - U! variable 7 -
4th 0 - 4 . ---
~min
Figure 1.17: Moment-curvature responses for the beam of Specimen R4
4.4.2 Moment - Curvature Response of the Columns
The curvature of the column was measured during the test using two sets of LVDTs placed
vertically at the column-joint interfaces on both the north and south face of the column, and also by
the strain gauges glued on the column longitudinal steel. Figure 4.18 shows the experimental
results as weil as two predicted moment-curvature responses. The first prediction was made
excluding the effects of confinement, while the second prediction assumes a theoretical stress-strain
mode1 which accounts for the effects of confinement on the concrete core (Mander et al., 1988). As
can be seen, the confinement greatly increases the ability of the column to maintain loads at higher
curvatures- The experimental moment-curvature response foliows the sarne shape and maximum
moments as the predicted responses although there is slightly iess curvature present. This may be
due to a significant arnount of curvature occurring very close to the face of the column, outside the
mechanical targets.
Figure 4.19 shows similar responses for Specimen R4H. We cm see that the experimental
column response in this case closely followed the predicted response including the effects of
confinement. Because of the presence of the hi&-strength, cold-rolled bars in the slab, significant
yielding took place in the column. The response of Specimen R4 showed a very ductile behaviour
with significant yielding in the main bem, and less moment k i n g piaced on the column.
prediction (induding confinement)
/-
1 prediction (exduding confinement)
r test resufts
Figure 4.18: Moment-curvature response for the column of R4HC
400 4
a - w prediction
(inciuding confinement)
prediction \ (crduding confinement)
test results
Figure 4.19: Moment-cuwature response for the column of R4H
4.5 Role of the Spandrel Beam
When the main beam undergoes negative bending, there are torsional moments which are
created in the spandrel bearn. This is due to the eccentricity between the line of action of the forces
in the slab bars and the centroid of the spandrel beam. Figure 4.20 depicts a fke body diagram of
the subassemblage showing the flow of forces which take place in the hinge region and the spandrel
beam when the main bearn is subjected to negative bending. As the moments increase in the main
beam, larger strains are created in the slab bars and the greater the torsional effect in the spandrel
bearn. Torsional cracking in the spandrel barn greatly reduces its torsional stiffness and torsional
yielding of the spandrel beam limits the strain that cm develop in the slab bars. Torsion in the
spandrel beam causes the side faces of the joint region to be subjected to both direct shear and
torsional shear flow. Hence, the size and strength of the spandrel bearn plays a large role in
determining the strain distribution in the slab bars. The greater the torsional stiffness and torsional
yielding moment of the spandrel beam, the more unifonn and constant the strain distribution in the
slab bars across the width of the slab.
-- - -+
net shear from beam bars. -4
slab bars and calurnn shear -- -+ shear due to the torsional shear flow
Figure 4.20: Role of spandrel beam (DiFranco et al., 1995)
Figure 4.2 1 shows the experimental strain distributions at peak load across the slab bars for
al1 three specimens. This figure shows that in each case, at maximum load, ail twelve No. 10
longitudinal slab bars had yielded. Specimen R4HC displayed smaller strains in the slab due to the
fact that the major cracks at the bearn-column interface did not cross the mechanical targets. The
distribution of strains in the slab bars for Specimens R4H and R4 are very similar.
a m
0-
O O10
O 015
0020
O a 5
O M O
O b 3 5
0010
O M 5
(a) Strain distribution at maximum load for SpeUmen R4HC (b) Strain diçtribubon at maximum load for Specimen R4H
(c) Strain distribution at maximum load for Specimen R4
Figure 4.21: Measured strain distributions in the slab bars at slab-spandrel beam intedaces
4.5.1 Measured and Predicted Torsional Response of tbe Spandrel Beams
The experimental torsional response of the spandrel beam was measured by two pairs of
LVDTs on the back (south) face of the spandrel as described in Section 2.6. Each pair consisted of
one LVDT placed 100 mm from the bottom of the spandrel and another LVDT placed 400 mm
directly above it. One pair was located along the column with the other pair situated 825 mm away
from the column, near the end of the spandrel beam. From these LVDT measurements, the
rotation as well as the horizontal deformation of the spandrel beam could be calculated as seen in
Fig. 4.22.
Figure 4.22a shows the rotation or twist of the spandrel beam at the peaks of the positive
loading cycles. These values are obtained by subtracting the deflection measured by the botîom
LVDT from the deflection measured by the top LVDT and dividing by the distance between them
of 400 mm (see Fig. 4.22a). Figure 4.22b shows the horizontal deformations in the spandrel beam
at the peaks of the positive half-cycles. These deflections are obtained by taking an average
deflection for each pair of LVDTs.
Figure 4.23 shows the torsional response of the spandrei bearn for Specimen R4HC during
testing. The torque in the spandrel barn was calculated using the strains in the slab steel to
determine the forces in the slab bars. The sum of forces in the slab bars was then multiplied by the
eccentricity to the centre of the spandrel beam to obtain a torque. The twist of the spandrel beam
\vas obtained from the difference between the measured rotation at the column and the measured
rotation 825 mm away (see Fig.4.22a and b). From this figure, the cracking torque is
approximately 17.5 kN m with a twist of 0.0002 rad. The pure torsional cracking moment, Tm, can
be calculated by the equation:
where. A, = area enclosed by outside perimeter of concrete cross section
p, = outside perimeter of the concrete cross section
This equation greatly overestirnates the cracking torque because it oniy takes into account
the torsional efTects and neglects the shear involved. In order to properly estimate the cracking
torque, the interaction between the shear and torsion must be considered as in the equation:
033 J m = (F,, x e) x 2(350+600)
i- Fcr (350 x 6 0 0 ) ~ 600 x 293.5
where, b, = minimum effective width in shear
d = effective depth in shear
e = eccentricity of slab bars from the centre of twist of the spandrel beam = 245 mm
Fcr = force in slab bars at cracking
Tc, = cracking torque induced by slab bars = Fcr x e
Solving Equation 4-3 gives a cracking torque of 43.6 kN.m for Specimen R4HC, 44.5
kN rn for Specirnen R4H, and 38.8 kN.m for Specimen R4. These values are very close to those
attained for Specimens R4H and R4 but much greater for Specimen R4HC. This is due to the fact
that high-strength concrete tends to be more sensitive to shrinkage and thermal effects duting
curing and can crack at Iower stress levels than normal-strength concrete.
From Fig. 4.23, it can be seen that the torque at maximum applied load for Specirnen
R4HC was 64 kN m with a twist of 0.0028 rad. The graph also shows a predicted yield torque of
49. i kN m. This value was determined using the compression field theory, taking into account the
effects of both shear and torsion. The yield torque, T,, can be easily calculated if the shear eflects
are ignored, This can be done with the following equation (Mitchell and Collins, 1974, and
Collins and Mitchell, 199 1):
where, A, = area enclosed by torsional shear flow path
A, = area of one leg of the closed hoop reinforcement
f,, = yield stress of hoop reinforcement
8 = angle of principai compression measured from the horizontal axis of the beam
s = spacing of shear or torsion reinforcement measured parallel to the longitudinal axis
This gives a predicted torsional yield moment, T,, of 1 03.5 kN-m for Specimen R4HC, 145.7 kN.m
for Specimen R4H and 121.4 kN.m for Specimen R4. In order to account for both shear and
torsion, the yield shear force in the stirrups must be determined by:
where, A, = area of shear reinforcement
d = effective depth
. = yield strength of rein forcement
Vy = yield force
Cornbining both the torsionat effect and shear effect gives:
where, F, = force in slab bars when yielding of spandrel beam occurs.
In order to detennine 0 the combined shear stress for a solid section is needed and can be
determined from the following expression (Mitchell and Collins, 1974 and Collins and Mitchell,
where, AOh = area enclosed by centreline of closed transverse torsion reinforcement
b , = minimum effective width
d,. = distance, measured perpendicular to the neutral axis, between the resultants of the
tensile and compressive forces due to flexure
e = eccentricity of slab bars from the centre of twist of the spandrel beam
ph = perimeter of the centreline of the closed transverse torsion reinforcement
T = torsion induced by slab bars = F x e
V = transverse shear = F,
v = shear stress
The yielding torques are determined by using an iterative approach with Equations 4-6 and
4-7 and using the limits for 8 from the modified compression field theory. Using this method. the
yield torques were calculated as 49.1 kN.m, 52.3 kN.m and 50.6 kN.m for Specimens R4HC, R4H,
and R4 respectiveiy.
The torsional strength of the spandrel beam governs the contribution of the slab bars to the
nesative flexural strength of the beam only until yielding of the spandrel bearn occurs. AAer this,
the contribution of the slab bars can be determined by a strut and tie mechanism as described in the
next section.
undeformad shape
Rotation (r10 rad)
Elevation view of defonned spandrel beam Rotation of spandrel beam
(a) Vertical deformation of spandrel beam
undeiomied shape defonned shape - . . - .- - - - - -
P -- 1 3 8 4 k N f i 275.2 kN
- 302.9 LN 1 1 314 O LN
A -C-H . 1 0 323.0 kN
825 mm T \ - > - . , -- --- --- - - --- ---.
7 L- O 5 10 1s 20 Honzonîal Deformations (mm)
Plan view of deformed spandrel beam Horizontal deformation of spandrel beam
(b) Horizontal deformation of spandrel beam
Figure 4.22: Spandrel beam deformations for Specimen R4HC
l' . -- A No. 10 tie
O 0.001 0.002 0.003 0.004 Twist (radlm)
Figure 4.23: Torsional response of spandrel beam for Specimen R4HC
4.6 Role of the Slab
4.6.1 Strut and Tie Mechanism for Transferring Forces from Slab Bars
Once yielding has occurred in the spandrel beam, the mechanism by which the slab forces
are transferred into the joint region can be visualised by a stmt and tie model. Figure 4.24 shows a
diagram of the "disturbed regions" around the column. These disturbed regions can be idealised by
discrete flows of tensile and compressive forces making up a strut and tie model. Figure 4.24 b)
shows a plan view of al1 three slabs with their stmt and tie models, assuming that the slab bars are
anchored near the outer edge of the spandrel bearn. In these models, the back longitudinal bars in
the spandrel beam act as the tension chord white the top horizontal legs of the closed hoops in the
spandret beam provide tension members. The tensile forces in the slab bars can be determined
using these strut and tie models, provided that the forces in the tension ties are limited to their yield
values. The tensile forces in the slab bars can then be determined fiom the geometry of the
spandrel barn and the size, spacing and yield stress of the reinforcing bars.
unâefonncd shape defomwd shape
(a) Disturûed region of the specimens
r r . .
. . - . . '
* c
Specimen R4HC
Specimen R4
(b) Flow of forces in the disturbed region
Figure 4.24: Idealized strut and tie mode1 for the specimens
4.6.2 Effective Slab Reinforcement
n i e effective slab width and hence the effective area of slab reinforcernent considered to
contribute to the negative flexural capacity of a beam can geatly affect the ductility levels and the
hierarchy of yielding between the beams and the columns. I f the slab bar contributions are
underestimated, the flexural strength ratio between the column and the beam can be significantly
lower than that specified by the codes. The actual number of bars which can develop is govemed
by either the torsional strength of the spandrel beam or by the capacity of the stnrt and tie
mechanism in the top of the spandrel beam. Table 4.6 summarises the effective slab widths # recornmended by the Canadian, Arnerican and New Zealand design codes for exterior joint
connections. Many tests, including the ones described in this thesis, have showvn that yielding of
the longitudinal slab bars actually occurs over a greater width than that which is recommended by
the codes.
Table 4.6: Effective slab widths useà in current design codes
Standard
CSA Standard (CSA. 1994)
- --
AC1 Code (AC!, 1995)
New Zealand Standard (NZS, 1995)
' E f k t h Sbb \lllSdthm in Tension
Clause 21.4.2.2 specifies that slab reinforcernent within a width of 3hf from the side faces of the beam be considered effective.
Chapter 21 which contains the special provisions for seismic design does not specify an effective width. Section 8.10, however, specifies that the effective width of T-beam flanges must be less than 114 of the span of the beam, and the effective overhang flange must be less than: (a) 8th (b) 112 clear span to next web
Clause 8.5.3.3 specifies that for an exterior joint with a transverse beam the slab reinforcement within a width defined as the lesser of the following should be considered effective: (a) 114 of the span of the beam, extending on each side from the centre of the beam. (b) 112 of the span of the slab, transverse to the beam, extending on each side from the centre of the beam (c) 1/4 of the span of the transverse edge beam extending on each side from the centre of the beam.
4.63 Determination of Effective Slab Reinforcement
A summary of the number of slab bars which contribute to the negative flexural capacity
of the beam can be found in Table 4.7. Here, the experimental values determined using
compression field theory, strut and tie models, and experimental data are compared. The larger
nurnber of bars from the torsional and strut and tie mode1 analysis is also given as the final
prediction. The number of bars specified in the table represents the number of effective slab bars
in one half of the effective siab width of the specimen. In these cases, the maximum possible
number of effective slab bars is six. The experimental results were taken from the strains
measured in the slab bars at maximum appiied positive load.
Table 4.7: Predicted and experimeatally determiad aumber of yielded bars
1 R4 74.2' 1 6.0' 1 50 -6 1 4.2 1 5.4 1 5.4 1 * these values were limited by the size of the slab used for the experiments. If a wider slab had
Specimen and
Researcher R4HC
been provided, thus more slab bars would have been present, then it is predicted that these values may have been higher.
The number of effective slab bars predicted to be effective using the rnodified
compression field theory can be determined by dividing the predicted yield torque in the
spandrel beam by the eccentricity of the slab bar forces as shown in Fig. 4.25. Once the force in
the slab bars is known, the area of steel which has yielded can be calculated by dividing the force
by the yield stress of the slab bars. For instance, for Specimen R4HC, the predicted spandrel
beam yield torque was calculated from Eqs. 4-2 and 4-3 to be 49.1 kNm. If this torque is
divided by the an eccentricity, e = 245 mm, we get a tensile force of 200.4 kN in the slab bars.
Dividing this force by the yield stress of the slab bars gives an effective area As = F / f , = 200.4 x
1 O00 / 428 = 468.2 mm2. Since the area of a No. 1 O bar is 100 mm2, this represents 4.7 slab bars
Experimental values
i
yielding on either side of the main beam.
Toque (kN-m)
63.2'
Number of Bars
6.0'
Preâ i in from m o d i compression field theory
Prediction from stnrt and
biemodel
Number of 6ars
6.0
Predicted f0rque (Mm 49.1
Final Predic-
. tion
Number of Bars
6.0
Number of Bars
4.7
,predicted using modified compression field theory (see Section 4.5.1 )
centre of twist . .. ., F = l y - . * . . e
Figure 4.25: Determination of slab bar forces from torsionai strength of spandrel beam
The number o f slab bars predicted to be effective using the strut and tie model can be
detennined through simple statics, assuming that the maximum values of the tensile and
compressive forces are limited by the yieid strength o f the reinforcing steel and the compressive
strength of the concrete, respectively. Figure 4.26 shows the maximum forces which can be
attained in the tension stmts o f the three specimens. The maximum stresses in the longitudinal
slab reinforcement was taken as f,. since the steel experienced M e strain hardening. The arnount
of spandrel beam longitudinal reinforcernent considered to be effective in calculating the tension
resultant in the strut and tie model was 1.5 No. 25 longitudinal bars for Specimens R4HC and
R4H. and 2.0 No. 15 longitudinal bars for Specimen R4. The limiting factor in Specimens R4H
and R4 was the ultimate stress allowable in the spandrel beam reinforcement which was taken as
1.25 K.. For example, in Specimen R4H, the two inner slab bars had yielded and the two outside
bars reached a force o f 116.4 kN when the ultimate force o f 442.4 kN was reached in the
spandrel tension chord. Dividing the sum o f the forces reached in the slab bars by their yield
stress gives (120.5 t 120.5 +1 16.4) x 1000 / 602.7 = 593 mm'. This represents 5.93 effective
slab bars on either side o f the spandrel beam. AI1 six slab bars o f Specimen R4HC yielded due to
their lower yield stress. It is evident, using the stnit and tie model, that more than the slab bars
within a distance of 3hf are predicted to be effective in negative bending of the main beam. The
node where the compressive struts intersect in the model was assumed to be located a distance
equal to 0.8 times the column size, c, that is, 0 . 8 ~ from the tension resultant.
(a) Specimen R4HC
(b) Specimen R4H
(c) Specimen R4
Figure 4.26: Strut and tic modek showing forces in slab bars
46.4 Simplifed Determination of Effective Slab Reinforcement
A simplified method for detemining the effective slab reinforcement was developed by
DiFranco et of. (1993). This method uses Eq. 4-4 (Collins and Mitchell, 1974) for determining
the torsional strength and assumes that the angle of principal compression acts at 45 degrees,
thus:
when equated to the induced torque created from the slab bars:
where ho and bo are the dimensions between the corner longitudinal bars in the spandrel beam as
shown in Fig. 4.27 and n is the number of effective slab bars. Solving for n, gives:
If the area of the longitudinal slab bars is the same as that of the closed hoops in
beam. as is often the case, Eq. 4-10 can be further reduced to:
The number of effective slab bars estimated using this equation are listed in Table
(4 - 10)
the spandrel
(4- 11 )
4.8 for each
specimen. It is noted that
shear to the yielding of the
these values may be slightly overestimated, since the contribution of
spandrel beam in torsion is ignored in this simplifled method.
centre of twist . .*. ...$ ' At
Figure 4.27: Torsion induced by slab bars
The strut and tie model calculations used in determining the effective number of slab
bars can also be sirnplified by noting that the limiting parameter is the magnitude of the tensile
forces in the longitudinal bars at the back face of the spandrei beam. In the strut and tie model,
the resisting moment is provided by the force in the longitudinal spandrel bearn bars multiplied
by a lever a m assumed to be 0.8 times the column dimension (Fig. 4.28). Taking moments
about this nodal point as shown in Fig. 4.28 gives:
A: f, x -.- = A,, f, (0.8 C) ss 2
where, Ad= the area of slab bars within the distance s,
A,, = the area of top longitudinal steel in the outer half of the spandrel beam
x = effective width of the slab
'd2 = the lever a m to the resultant of the slab bars
s, = spacing behveen the slab bars (see Fig. 4.28)
nodal point
Figure 4.28: Simplified strut and tie mode1
Solving Eq. 4- 12 for the effective width, x, gives:
The number of slab bars expected to yield, n, is therefore the total number of bars within the
distance x. The values obtained using this simplified method are summarised in Table 4.8.
Table 4.8: Simplified determination of effective slab bars
Specimen
II R4HC - this study 1 8.3' I 5.7
/ R4H - Marquis (1997) 8.3' 5-3 a6.0 t 1 (1 R4 - Rattray (1 986) 1 9.9' 1 4.4
* - controlling number of effective bars
4.6.5 Flexural Strength Ratio
The flexural strength ratio, MR, is the ratio of the total nominal flexural strength of the
columns to the sum of the nominal flexural strengths of the beams. The greater the contribution
of the longitudinal slab steel to the negative flexural strength of the bearn. the smaller the
flexural strength ratio. As discussed in Section 1.2, the current Canadian Standard (CSA, 1994)
specifies a minimum flexural strength ratio, MR, of 1.33. This limit is aimed at ensuring the
proper hierarchy of yielding in the structure. Table 4.9 gives the calculated flexural strength
ratios during design for vawing effective widths as discussed in Section 4.4.
Comparing the predicted flexural strength ratio using an effective slab width of 3hf on
either side of the main beam, to the actual flexural strength ratios, shows that significantly lower
flexural strength ratios were attained than were predicted. This is mostly due to the larger
contribution of the slab bars to the negative flexural strength of the bearn. In al1 three specimens,
al1 twelve slab bars had yielded at the maximum applied load showing that the effective slab
width was actually greater than a distance of 3hfon either side if the bearn.
Table 4.10 shows the actual flexural strength ratios of the specimens based on the
recorded yield stresses of the reinforcement, compressive strengths of the concrete, and the
amount of slab steel which was actually effective.
Specimen R4H had an actual flexural strength ratio very close to 1 due to the use of the
high-strength, cold-rolled slab bars. Specimen R4HC also had a low experimental flexural
strength ratio due to some shear distress in the joint region.
Table 4.9: Flexural streneh ratio for varying effative widths
Effective Siab \1\1Sdai S m m R4 Spacimen R4H Specimen R4HC
Mri MR
i) beam only, no slab bars effective 1 2.80 1 2.01 1 1.79 1 ii) 3 h,, 4 slab bars effective 2.13 1.61 1.43
iii) 4 h,, 8 slab bars effective 1.73 1.34 1.20
iv) full width of slab effective. 12 slab bars 1 1.45 1 1.15 1 7 - 0 4
Table 4.10: Actual flexural strength ratios
NON-LINEAR DYNAMIC ANALYSES
This chapter presents the results of non-linear analyses performed on three prototype
structures located in Vancouver. The three structures analysed include one constructed with
normal-strength concrete, displaying similar response characteristics to Specimen R4, one
constructed with hi@-strength concrete displaying similar response characteristics to Specimen
R4H, and one const~cted of high-strength concrete displaying similar response characteristics
to Specimen R4HC. Each building was subjected to three accelerograrns scaled to an ultirnate
peak ground acceleration level of 0.3 15g.
The prototype structures representing Specimens R4 and R4H were analysed by H. Issa
( 1997) using the computer program RUAUMOKO (Cam, 1996). A cornparison will be made
behveen these results and the results obtained for the prototype structure representing Specimen
R4HC.
5.1 Hysteresis Rule Used in Analysis
The analysis program RUAUMOKO requires that a specific hysteresis model be chosen
to represent the response of each structure. The model used in this analysis was developed by
Takeda et al. (1970), at the University of Illinois and later modified by Otani and Sozen (1972)
and Litton (1975). The model includes considerations for stiffness change at flexural yielding,
strain hardening past flexural yielding, an unloading stiffness which reduces by an amount
wtiich depends on the largest previous hinge rotation and a reloading stiffness which accounts for
past loading histories. The Modified Takeda mode1 is shown in Fig 5.1. Figure 5.1 also shows
the specific shapes of the hysteretic models used for each structure. The model used for the
R4HC structure attempts to account for greater stiffhess degradation and lower energy
dissipation which was observed during the testing of Specimen R4HC.
Modified TAKEDA H y s t e r e s i s Rule
a) Model for R4 and R 4 H structures b) Model for R4HC structure
Figure 5.1 : Modified Takeda mode1 (Otani 1974)
5.2 Ground Motion Records Used for Analysis
Three separate accelerograms were used for the non-linear dynamic analysis. in order to
adequately assess the performance of each structure. The three ground motion records selected
as being representative of expected ground motions for Vancouver were:
i ) May 18, 1940 imperial Valley. El Centro NS record provided in the cornputer
program RUAUMOKO (Cam, 1996),
i i ) October 17. f 989 Loma Prieta N-S record (National Geophysical Data Centre. 1996),
i i i ) January 17. 1994 Northridge N-S record (National Geophysical Data Centre, 1996).
The acceleration and velocity characteristics for these earthquake records as well as the
cliaracteristics specified for Vancouver in the 1995 NBCC (probability of exceedance of 10% in
50 years) are show in Table 5.1.
Table 5.1: Ground motion parameters (uoscaled values)
NBCC 1 El Centro Loma Prieta Northridge
The respective ground motions for each earthquake were scaled in order to produce the
desired maximum peak ground acceleration value of 0.3 15 g representing the "ultimate" motions
for the Vancouver area. Tliese motions were assumed to be those caused by earthquakes having
a probability of exceedence of about 5% in 50 years (1 000-year retum period).
More details on the analysis procedures are given by Issa (1997).
1 1 1
I
5.3 Roof Displacement Time Histories
The roof displacement time histories of each structure subjected to each of the three
earthquakes are presented in Fig. 5.2. Table 5.2 lists the maximum predicted roof displacements
as well as the estimated fundamental periods for each structure.
O. 1 03 I 1 .O50 PHV. m/s I 0.2 1 O I 0.334
I . - '-: - high-strength R4HC
- high-strength R4H
1940 N S El Centro ground motion ---- normal-strength R4
time. seconds
O 2 4 6 8 10 12 14 16 18 20
time, seconds
- high-strength R4HC , - - high-strength R4H
1994 N-S Northridge ground motion ---- nomal-strength R4 O
. O 2 4 6 8 10 12 14 16 18 20
time, seconds
Figure 5.2: Roof displacement time histories
Table 5.2: Predicted periods and maximum roof disphcements
- -
R4 Structure 0.3 15 1 .O38 125
R4H Structure 0.3 15 1.185 136
R4HC Structure 0.3 15 1.185 134
As illustrated in Fig. 5.2, the high-strength concrete structures exhibited over-ail higher
roof displacements than did the normal-strength concrete structure. This can be attributed to the
fact that the member sizes for the high-strength concrete structures are smaller than those for the
normal-strength concrete structure and therefore have a lower moment of inertia, This results in
the high-strength concrete structures having a iarger period of vibration as seen in Table 5.2. The
hiçh-strength concrete structures are therefore more flexible and display larger roof
displacements. The displacements exhibited by the two high-strength structures are very similar
for al1 three earthquakes. This may be due to limitations set by the hysteresis mode1 in
distinguishing between the two experimental loading responses. It can also be seen from Fig 5.2
that the 1940 N-S El Centro ground motion governs the predicted responses.
5.4 Plastic Hinge Locations
Figure. 5.3 shows the locations of al1 the plastic hinges which formed in the structures
when analysed with the most critical ground motions. It can be seen that al1 structures satisfied
the desired "weak beam-strong column" criteria in that ail inelastic action took place in the
beams and at the base of the ground floor columns, rather than in the upper storey columns. The
inelastic actions in both the normal-strength concrete structure and the high-strength concrete
structures favour good energy dissipation and high levels of ductility. Only the normal-strength
concrete structure exhibited hinging at the bottom of the first storey columns.
a moment hinging
a) Normal-strength concrete fiame
- -- --
b) High-strength concrete tiarne (R4HC)
c) High-strength concrete frame (R4H)
26 beam hinges
4 column hinges
25 beam hinges
O column hinges
26 beam hinges
O column hinges
Figure 5.3 Summary of hinge locations dunng entire time history responses
5.5 Envelopes of Lateral Displacements
The envelopes of lateral displacements for each structure and ground motion are shown
in Fig. 5.4. Once again. it can be seen that boîh the high-strength concrete specimens undenvent
similar displacements. It can be seen from Fig 5.4 that the displacement response of the
structure depends strongly on the ground motion characteristics. The displacement envelopes are
very similar in shape for each structure, given a specific ground motion, but these differ greatly
when subjected to a different ground motion. For exarnple, given the higher frequency content
of the Northridge earthquake, the normal-strength concrete structure rather than the high-strength
concrete structure undenvent the largest deformations. This is consistent with observations made
by Powell and Row ( 1 976) and Biggs, Hansen and Holley (1 977) who stated that the seismic
responses of structures Vary greatly for different ground motions, even if those ground motions
have similar characteristics. Figure 5.4 also highlights the fact that the displacements in the
lower storeys are nearly identical for al1 three structures, diverging only at the upper levels.
5.6 Interstorey Drifts and Damage Estimates
The envelopes of interstorey drifis for each structure are shown in Fig. 5.5. It can be
seen thar the interstorey drifts Vary greatly depending on the ground motion. The interstorey
drifts for a specific ground motion, however. were very similar for each structure regardless of
concrete strength. In al1 cases the interstorey drift increased towards the base of the structure
wliich is consistent with the flexural response of a ductile moment-resisting frame.
The maximum drifts occurred with the 1940 El Centro ground motion and had a
maximum value for al1 structures of approximateiy 40 mm. The 1995 NBCC Iimits the
allowable interstorey drifi to 0.02 times the height of the storey in question. For the prototype
structure, this gives a maximum allowable interstorey drifi of 73 mm, which is greater than the
values pred icted.
roof
ground
T
/ /A''
- hig h-strength R4HC - -- high-strength R4H
---- normal-strength R4
displacement, mm
a) 1940 N S El Centro ground motion
displacement, mm
roof .
b) 1989 N-S Loma Prieta ground motion
6 . .' /'-
.J'
O 20 40 60 80 100 120 140 displacement. mm
:."' ,/ /'*
- high-strength R4HC - high-strength R4H ---- normal-strength R4
roof - .-.
c) 1994 N-S Northridge ground motion
6 ,
5 .
Figure 5.4 Envelopes of Iateral displacements
.: r ,s
i , i. .i' ,'
.i' ; r' ; f . : . = ,
= 3 .
- high-sttength R4HC - - high-strength R4H ---- normal-strength R4
ground
displacement, mm
a) 1940 N-S El Centro ground motion
roof - 6
5
- - a _ _ _ _ - , - - - - high-strength R4HC
. - - -' - -- - . . hgh-strength R4H I i : I ---- : i
normal-strength R4
Y.'- - .
ground 1 O 5 10 15 20 25 30 35 40 45
displacement, mm
b) 1989 N-S Loma Prieta ground motion
displacement, mm
c) 1994 N-S Northndge ground motion
Figure 5.5: Interstorey drifts
The darnage sustained to a structure during a given earthquake can be estimated using
damage indices. One such darnage index is calculated as the ratio of the maximum ductility
reached in the response to the ultimate ductility attainable in the structure as specified for the
mem ber actions. TabIe 5.3 presents both the maximum damage indices and average damage
indices for each structure.
Table 53: Damage estimates
According to Carr (1993), a damage index of 0.4 represents the limit of repairable
damage to a structure and any damage index above 1.0 represents failure of the structure.
According to this, al1 three structures failed under the "ultimate" 1940 El Centro Earthquake
ground motion. The R4HC structure exhibited the largest maximum damage index due to the
extra stiffness degredation specified in the hysteresis model. It should be noted that under
"design" earthquake ground motions, the structures experience repairable darnage (Issa, 1997).
The "design" earthquake ground motions are more consistent with the motions which may occur
severai times over the life of a structure.
5.7 Ductility Demand
Figure 5.6 gives the maximum predicted curvature ductilities and plastic hinge rotations
for the beams o f the three structures. The predicted ductility demands, defined as the ratios of
the ultimate beam curvature to the curvature a t first yield, show significant yielding o f the beams
at al1 storey Ievels, but particularly in the bottom storeys.
Figure 5.6 shows that the high-strength concrete structures displayed lower overall
ductility demands than did the normal-strength concrete structure. This is consistent with the
hysteresis models used, where the high-strength structures had larger curvature at first yield.
roof
6
5
tc 4
e
3
2
ground
O 2 4 6 8 10 ductility demand
roof
6
5
5 4 c
3
2
ground
. , . - . . .,: . - >--. ' ,. .. : -. ' . . . . ..
, . . . . . . -
' - . . .-. . . . I f - ' . .
O 1 2 3 4 5 6
hinge rotation, 1 0.' rad
Figure 5.6: Estimated curvature ductiütics and plastic hinge rotations
CHAPTER 6
RECOMMENDATIONS AND CONCLUSIONS
6.1 Conclusions
This experimental program investigated the response of a full-scale high-strength
concrete column-beam-slab subassemblage subjected to reversed cyclic loading. The response
of this specimen was compared to the responses of a similar high-strength concrete specimen
with a square column and a normal-strength concrete subassemblage. All three specimens were
designed and detailed as ductile moment-resisting frames with a force modification factor, R, of
4.0 as specified by the National Building Code of Canada (NBCC, 1995).
The main objective of this research prograrn was to investigate the influence of high-
strength concrete on the seismic performance of ductile moment-resisting frarnes. There has
been sorne concern in the case of ductile moment-resisting frames as to whether the same levels
of ductility reached using normal-strength concrete can be attained using the typically more
brittle high-strength concrete. Due to this, the 1994 CSA Standard (CSA, 1994) limits the
concrete compressive strength to be used for the seismic design of ductile elements to 55 MPa.
Through this study, it was shown that the performance of high-strength concrete frarnes under
reversed-cyclic loading is very similar to that of the normal-strength concrete frames. It is
concluded that high-strength concrete ductiIe members designed using the current CSA
provisions displayed excellent energy dissipation characteristics and reached high levels of
ductility.
The confinement reinforcement requirements for columns in the 1994 CSA Standard and
in the 1995 New Zealand Standard were investigated. The Canadian Standard specifies an
amount of confinement reinforcement which is proponional to the concrete compressive
strength. When high-strengîh concrete is used in design, the code limits provide an excessive
amount of confinement reinforcement. The New Zealand Standard specifies an amount of
confinement reinforcement expressed as a function of the axial load. It is concluded that the
circular column designed using the New Zealand Standard had far less confinement
reinforcement and yet displayed adequate confinement of the column.
The arnount of slab reinforcement which contributes to the negative flexural capacity of
the main beam was also investigated. It was concluded that the amount of effective slab bars
was significantly above that suggested by current design codes. An accurate estimate of the
number of effective slab bars is essential in order to ensure that the columns are stronger than the
beams and that a proper hierarchy of yielding of the members dcvelops. The 1994 CSA Standard
requires that the steel within an effective width of three times the slab thickness on either side of
the main bearn be considered in design. This results in four bars being considered effective,
while tests showed that al1 twelve slab bars in the specimens were actually effective. It is
suggested that the effective width specified by the 1994 CSA Standard, be increased in order to
properly determine the fiexural strength ratios for ductile moment-resisting frames.
The dynamic non-linear analysis conducted in this thesis showed that both the normal-
strength concrete and the high-strength concrete prototype structures displayed similar
responses. The smaller column dimensions for the high-strength structures resulted in higher
periods of vibration, but the amount of inelastic action and the roof deformations were very
similar for al1 three prototypes.
5.2 Future Researcb Recommendations
It is suggested that the following aspects of high-strength concrete bearn-column-slab
su bassem blages be further investigated:
( i ) The effect of high-strength concrete on the seismic response of interior joint
connections.
(ii) The revetsed cyclic loading response of a subassemblage which has k e n designed
with the full width of the slab being considered effective.
(iii) The possibility of adapting current design codes to take into account of axial load
levels when determining the amount of confinement reinforcement in colurnns. This
aspect needs further study.
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Calculations for the Design of Specimen R4HC (Sections A. 1 and A.2 fiom G. Marquis, 1997)
A.l DETERMINATION OF DESIGN FORCES FOR PROTOTYPE STRUCTURE:
a ) Building Description
The building has 7 identical bays in the N-S direction spanning 6.0 m and 3 bays in the
E-W direction which consist of 2 - 9.0 m bays and a central 6.0 m wide corridor bay. The
interior columns al1 measure 400 x 400 mm while the exterior columns are 350 x 350 mm. The
one-way floor systern consists of a 110 mm thick slab spanning in the E-W direction supported
by beams in the N-S direction. The secondary beams supporting the slab are 250 mm wide x 350
mm deep (measured fi-om the top of the slab to the bottom of the bearn). The beams of both
directions are 350 mm wide x 600 mm deep for the first three storeys and 350 x 550 mm for the
top three.
b ) Material Properries
The material properties for the structure are:
Concrete: high-strength concrete with f,'= 70 MPa
Reinforcement: f . = 400 MPa
c ) Gravity and Wind Loadings
Floor Live Load: 2 -4 4.8
Roof Load: 2.2 1 -6
Dead Loads:
Wind Loading
kN/m2 on typical office floon k ~ / r n ' on 6 rn wide corridor bay
k ~ l r n ' full snow load k ~ l r n ~ rnechanical services loading in 6 m wide strip over corridor bay
k ~ l r n ' self weight of concrete mem bers kWm2 partition loading on al1 floor k ~ l m ' rnechanical services loading on al1 floors k ~ l r n ~ roof insulation
k ~ l r n ~ net lateral pressure for top four floors kN/rn2 net laieral pressure for bottom hvo floors
d) Seisrnic Loading
For this structure, located in Montreal, the acceleration-related seismic zone, Z,, is 4,
the velocity-related seismic zone, Z,, is 2 and the zona1 velocity ratio, v, is 0.10. Other relevant
variables required in the determination of seismic Iateral loads are:
314 - T = fiindamental period = 0.075 h, - 0.79 S.
S = seisrnic response factor = 1.5 /fi = 1.68
1 = importance factor, taken as 1 .O for an office building
F = foundation factor, taken as 1 .O for a building on rock
Hence the seismic base shear, V. is :
The calcufations of the seismic lateral loads at each floor are summarized in Table A. 1.
Table A.l: Lateral load calculations for each floor level
2
Total 1' The analysis of the structure was carried out using a linear elastic plane frame program.
It was assumed, in the analysis of lateral forces in the E-W direction, that the floor slab system
would act as a rigid diaphragm allowing each frarne to be subjected to one-eighth of the lateral
Ioad. in order to make allowances for cracking the gross member stiffnesses were reduced to
50% of EI in the beam members and 80% of ET in the columns. The mode1 used in the analysis
and the lateral forces appiied to frame 2 are shown in Fig. A. 1.
r --------Tt npid '1
- offset mernbe~. r - - - 1
t-- baamnoda 1 - at face of
column
Model For Frame Analysis
93 kN each
101 kN each
102 kN each
Total Lateral Seismic Loads
4 b ' 4- L -- + S... A L-
- - - Dead toads
83 kN each
76 kN each
77 kN each
40 kN each 43 kN each 58 kN each
Lateral Wind Loads
- - - - Live Loads
26 kN each
Figure A.1: Unfactored loading cases used for the design of a typical interior frame
f) Accounfing for Torsional Eccentriciîy
The analysis of the structure for lateral forces was carried out in the E-W direction. For
this building, the masses and stiffnesses at each level are symmetrically distributed producing an
eccentricity, ex, between the centre of mass and the centre of rigidity of zero. The applied
torsional moment, T,, at each level can therefore be found using:
Tx=Fx(+O.l D,)
where F, is the lateral force applied at level x and D,, is the plan dimension of the building in
the direction of the computed eccentricity. The eight frames in the N-S direction have the same
stiffness therefore the torsion induced shears in these frames will be proportional to their
distance from the centre of stiffness. The analysis will be carried out for frame 2, hence F2,, =
( 1 1 ) . From statics the shear induced by torsion in frame 1 at level x is Tx/72. The
calculations of the additional lateral loads due to torsion are summarized in Table A.2.
Table A.2: Design seismic Iateral ioads on Crame 2
Total m
A.2 BEAM DESIGN
For the purpose of this research program the design will concern itself with a typical
esterior column at the second storey level.
a ) Determination of Design Moments
The unfactored beam moments in a bearn at the face of a typical second level exterior
column located in Frame 2 are sumrnarized in Table A.3. The table also gives the fzctored
moment combinations which need to be considered in the design.
Table A.3: &am moments i t 2.d level exterior column (dter redistribution)
b ) Design of Flexural Rein forcernenr
The critical factored negative design moment in the main beam at the face of a second
storey exterior column was found from frame analysis to be Mf = - 25 1.7 kN'm.
Assuming a flexural lever arm of O.Xh = 0.75 x 600 = 450 mm, we obtain a preliminary
area of steel:
Ml- - A s = - - 251.7 x 1000 = 1645 mm' + fy jd 0.85 x 400 x 0.450
Clause 21.4.2.2 suggests that slab reinforcement within a distance 3 hf from the sides of
the beam are to be considered effective. Assuming that 4 No.10 slab bars fall within this
distance, an additional 1245 mm* of reinforcement is required. Try 3 No. 25 bars as shown in
Fig. A.2. Also, it must be kept in mind that Clause 21.3.2.2 specifies that the positive moment
resistance be at least one-half o f the negative moment resistance, therefore try 3 No. 25 bars as
bottom rein forcement as well.
slab bars effective in tension over this width ( - -- - ------- w
, No.10 @ 300 - 3 No. 25 both diredons
No. 1 O stirrups Clear cover to hoops = 30mm 7.
Figure A.2: Layout of longitudinal reinforcement
Assuming that the compression steel yields, the depth of the compression block, c, is
found to be equal to 60.56 mm and the factored negative moment capacity is found from:
Using the above equation the factored negative moment resistance was calculated to be
M; = 34 1.5 kN-m. Hence, the moment capacity is satisfactory. This capacity was verified using
the program RESPONSE (Collins and Mitchell, 1997) which gave a value of 338 kN-m for M;.
The positive moment capacity was found in a similar manner to be M," = 267.1 kN-m.
RESPONSE (Collins and Mitchell, 1997) gave a value of 283.6 kN-m. This value is greater than
1 /2 M; = 1 7 1 kN-m . Therefore the requirement of Clause 2 1 -3 -2.2 is satisfied.
The minimum top and bottom reinforcement, ASqmi,, specified by clause 2 i -3.2.1 is:
The maximum reinforcement permitted, A,,,, speciEed by clause 2 1.3.2.1 is:
A ,,, = 0 . 0 2 5 b , d = 0 . 0 2 5 ~ 3 5 0 ~ 5 4 8 = 4 7 9 1 ~ 1900mm2 O.K.
c ) Design of Transverse Reinforcernent
The shear requirements in the beam are designed based on the shear corresponding to
the probable moment in the bearn. This can be accurately estimated in beams by multiplying M, by the ratio 1.2S/O.85 = 1.47. Hence w e obtain M, = 1.47 x 34 1.5 = 502 kN-m giving a design
shear, V, o f 502/1.825 = 275.1 kN.
i ) Determine the factored shear and spacing for shear:
The design shear, V = 275.1 kN, Using the simplified method o f shear design
with V,=O gives:
Using 3 legs of No. 10 bars for transverse reinforcement near the column face gives an
A, = 300 mm2. Hence the spacing required for shear is:
ii) Check maximum shear (Clause 1 1.3.6.6.):
= 0 . 8 ~ 0 . 6 ~ f i x 3 5 O x 5 4 8 / 1000
= 769.6 > 275.1 O.K.
iii) Check minimum shear requirements (Clause 1 1.2.8.4):
iv) Check spacing limits (Clause 1 1.2.1 1):
Therefore s,, = 600 mm o r 0.7d = 0.7 x 548 = 383 mm.
Thus the spacing of 203 mm controls.
v) "Anti-buckling" and confinement requirements (Clause 2 1.3.3):
Hoops must be provided to prevent buckling of the beam longitudinal steel over
a length of 2d from the face of the column and the spacing shall not exceed:
a) d/4 = 548/4 = 137 mm
b) 8 db (smallest bar diameter) = 8 x 25 = 200 mm
c) 24 db (hoop) = 24 x 10 = 240 mm
d) 300 mm
Note that the 3 legged arrangement satisfies the requirements of Clause 2 1.3.3.4. Thus
hoops are provided at a spacing of 135 mm over a distance of 2d = 1096 mm from the column
face. Outside this region the spacing for shear is as previously calculated at 203 mm. Three
legged s t imps will therefore be spaced at 200 mm for the remainder of the beam's length. This
spacing confonns with Clause 2 1 -3.3.4 which States that in regions where hoops are not required
a spacing of no more than d 2 = 271 mm will be used. Figure A.3 shows reinforcing details in
the beam.
- .- -- - w
9 sets of hoops with 4 sets of U-stirrups I single :ie @135rnrn with single ties @200mm
N0.10 h ~ p -3-No.25bars No. 10 tie - - O --L
SECTION 1-1
No. lOst imp- -1 - - 3 - No.25 bars
No. 10 tie 3 - No.25 bars
SECTION 2-2
Figure A3: Shear reinforcement details in the beam
A.3 COLUMN DESIGN
The design axial load for this experiment is Pr = 1 O76 kN. The fotlowing arrangement of
cohmn reinforcement will be attempted:
40 mm dear Cover
D'a
Spiral 400 mm
8 - No.25 bars
400 mm
Figure Al: M a l column reinforcement detaüs
a ) Design of Longitudinal Reinforcement
i) Veri* if Clause 2 1.4 applies:
Clause 21.4 applies to ductile frame mernbers that are included as part of the
lateral force resisting system, and are subjected to an axial compressive force which
exceeds:
Since Pf > 879.6, therefore the requirements o f this clause apply.
From Ciause 2 1.4.3.1, the minimum area of longitudinal reinforcement, A, ,in =
0.01 x A, = 0.01 x (n x 2 0 0 ~ ) = 1257 mm2 and the maximum area of longitudinal
reinforcement, A,,, = 0.06 x A, = 0.06 x (n x 2003 = 7540 mm2. Since the area of
longitudinal steel in the trial section is A, = 8 x 500 = 4000 mm2, this clause is satistied.
ii) Check column capacity:
From the program RESPONSE (Collins and Mitchell, 1997), for an axial load of 1076
kN the factored moment resistance of the column is M,, = 272 kN-m.
i i i ) VeriQ "Strong Column - Weak Beam" requirement:
Clause 2 1.4.2.2 requires that the flexural capacity of the columns exceeds the
nominal flexural resistance of the bearns such that:
CM,, 2 I . E M , b
CM,, = 272 + 272 = 544 kN-rn
Mn,, = 1.2Mr = 1.2x341.5 = 409.8kN-m
1.1 Mnb = 1.1 ~409 .8 = 450.8 kN-m
Since 544 kN-m > 450.8 kN-m this requirement is satisfied. This arrangement of
longitudinal steel is satisfactory.
b ) Design of Transverse Reinforcement in Cofumn:
The design shear force for the column is determined from statics considering the
development of the probable moment in the beam. Figure A S demonstrates this calculation.
1076 kN
Figure AS: Determination of design shear force in the column
i) Determine the spacing for shear:
From clause 21.7.3.1 the shear carried by the concrete is equai to that
determined by the following equation:
The required V, is equal to:
Using an area of shear reinforcement, A, = 200 mm2. as seen in Fig. A.4, and assurning
that the yield strength of the shear reinforcement, f,, = 400 MPa, the required stirrup
spacing is determined as (Clause 1 1.3.7):
Since V, = 209.2 kN < 0.1 x 0.6 x 70 x 400 x 350 x 10-3 = 588 kN then from
Clause 1 1.2.1 1, the mâuimum spacing of shear reinforcernent is 0.7d = 0.7 x 350 = 245
mm.
The minimum shear requirements specified by Clause 1 1.2.8.4 give a maximum spacing
of the spiral hoops:
Thus, a shear spacing of 245 mm governs.
i i ) Check confinement requirements ( from NZS, 1995):
In accordance with Clause 8.5.4.3 of the 1995 NZS, confining spirals must be
provided in the potential hinge region (as defined by Clause 8.5.4.1) as follows:
but not less than:
- A,, f~ 1 P s - --- 1lOd" fy, d b
Hence a spiral with a pitch of 128.7 mm shouid be provided in the region as
specified by Clause 8.5.4-1. This region is denoted, $, and it extends from the face of
each joint and on both sides of any section where flexural yielding may occur in
connection with inelastic laterai displacements of the frame. For an axial load of IO76
kN c 0.25 x 0.85 x 70 x n 200' = 1869 kN, the length. /,, shali not be less than:
a) d=400mm
b) where the moment exceeds 0.8 of the maximum moment = 240 mm
Clause 8.5.4.3 states that the spacing of the spiral shall not exceed:
Thus. the confinement requirements govern. The spiral will be provided at a pitch of
100 mm over a length of 400 mm on either side of the joint. Outside this region the spacing is
governed by Clause 8.5.4.3 which requires that transverse reinforcement outside the region
previously specified shall not exceed 1/3d = 133 mm or 10db = 250 mm. Therefore, outside the
400 mm hinge region, the spiral will have a pitch of 130 mm. Figure A.6 shows the layout of
transverse reinforcement in the column.
s = 1M) mm over 400 mm
s= lWmrn over 400 mm
s = 13ôrnrn over 775 mm
Figure A.6: Shear reinforcement detaiis of the column
A.4 JOINT DESIGN
a) Capaciv Design (fiom tVZS 1 995)
The probable tensile force in the beam reinforcement is 1 -25 Asfy = 1 -25 x 1900 x 400 =
950 kN. To determine the corresponding shear, V,,,, assume that the flexural hinging occurs in
the beam (development of the probable moment in the beam). The factored shear in the colurnn,
V,,,, corresponding to Mp; in the beam is as previously calculated at 209 kN. This produces a
shear in the joint, Vj = 950 - 209 = 74 1 kN. If the shear resisted by the concrete is neglected, the
total effective transverse reinforcement required in the joint from Clause 1 1.4.4.1 is::
CjN As
fc
Gv j h but the terni - 2 0.85
Clause f 1.4.4.1 also States that
vjh 74 1 000 3 A jh 2 0.4 - = 0.4 = 741.0 mm'
f~ h 400
Tlierefore the total area of transverse reinforcement required is 74 1 mm' over the length of the
joint so that the spacing required is 600 x 200/741 = 150 mm. However, 8.5.4.3 limits the
spacing to 1/4d =100
b) C'heck Factored Sheur Resisrance of ihe Joint
For joints confined on three faces, such as the exterior joint being designed, Clause
2 1 -6.4.1 specifies that the factored shear resistance of the joint shall not exceed:
V, = I . 8 A $ c J f i ~ j = 1 . 8 ~ 1 x 0 . 6 x ~ x n x 2 0 0 ~ x 1 0 - ~ = 1135kN
Since, Vj = 74 1 kN < 1 135 kN, the shear resistance of the joint is adequate.
145
c ) Check Confinement Reinforcemen Required in the Joint @on NZS: 1995)
From Clause 11.4.4.5, the spacing of the spiral need not exceed the smaller of the
requirements of Clause 8.5.4.3 = 129 mm. 10 x the smallest column bar = 250 mm, or 200 mm.
Hence, transverse reinforcement will be spaced at 100 mm within the joint.
d) Anchorage of Beam Reinforcement
Both top and bottorn bearn longitudinal reinforcement must be anchored in tension
within the joint as specified by Clause 21.6.5. From Clause 21.6.5.2, for a bar with a standard
900 hook, the development length, ld,, shall not be less than the greatest of:
i) 8db=8x25=200mm
ii) 150 mm
iii) 0.2 =,O mm
However, Clause 2 1.6.1.3 requires that any b a r n longitudinal reinforcement that teminates
within the column shall be extended to the far face of the confined column core. Therefore, ldh =
400 - 40 - IO = 350 mm for the top tension steel and ldh = 350 - 25 = 325 mm for the bottom
compression steel. The free end will extend, in accordance with Clause 21 -6.5, a length equal to
12 d, = 12 x 25 = 300 mm. Figure A.7 shows the layout of reinforcement within the joint.
Figure A.7: Details of joint reinforcement
