Seismic Design of Reinforced and Precast Concrete Buildings

Seismic Design of Reinforced and Precast Concrete Buildings
اسم المؤلف
Robert E. Englekirk
التاريخ
28 مايو 2021
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Seismic Design of Reinforced and Precast Concrete Buildings
Robert E. Englekirk
Consulting Structural Engineer and Adjunct Professor
University of California at San Diego
NOMENCLATURE
I have chosen to use both English and metric units so as not to alter the graphic
description of experimental data. The following conversions are standard:
1 m = 39.37 in.
1 kN = 0.2248 kips
1 kN-m = 0.737 ft-kips
1 MPa = 1000 kN/mm2
ADOPTED NOMENCLATURE
A Area, usually subscripted for definition purposes
Aj Effective cross-sectional area within a joint in a plane parallel to plane of
reinforcement generating shear in the joint. The joint depth is the overall
depth of the column. The effective width will depend to a certain extent on
the size of the beams framing into the joint.
A
ps Area of prestressed reinforcement in tension zone
As Area of nonprestressed tension reinforcement
A
s Area of compression reinforcement
Ash Total cross-sectional area of transverse reinforcement (including crossties)
within spacings
Ast Total area of longitudinal reinforcement
A1 Loaded area
xvxvi NOMENCLATURE
A2 The area of the lower base of the largest frustum of a pyramid, cone, or
tapered wedge contained wholly within the support and having for its upper
base the loaded area and having side slopes of 1 vertical to 2 horizontal
C Compressive force—subscripted when qualification is required
Cd Force imposed on the compression diagonal
D Dead loads; depth of frame
DR Drift ratio (x/hx) or (n/H )
E Load effects of seismic forces, or related internal moments and forces;
modulus of elasticity usually subscripted to identify material
EI Flexural stiffness
F Loads attributable to strength of provided reinforcement, usually
subscripted to identify condition
Fy
Yield strength of structural steel
H Overall height of frame
Icr Moment of inertia of cracked section transformed to concrete
Ie
Effective moment of inertia
Ig
Moment of inertia of gross concrete section about centroidal axis,
neglecting reinforcement
L Live loads, or related internal moments and forces
M Moment in member, usually subscripted to identify loading condition,
member, or stress state
M Mass subscripted when appropriate to identify (e) effective or (1)
contributing mode
Mbal Nominal moment strength at balanced conditions of strain
Mcr Cracking moment
Mel Elastic moment
M
pr Probable flexural moment strength of members, with or without axial load,
determined using the probable properties of the constitutive materials
N An integer usually applied to number of bays or number of connectors
P Axial load, usually subscripted to identify load type or strength state
Pb Nominal axial load strength at balanced conditions of strain
Po Nominal axial load strength at zero eccentricity
P
pre Prestressing load applied to a high-strength bolt
Q Stability index for a story—elastic basis (see Section 4.3.1)
Q∗ Stability index for a story—inelastic basis (see Section 4.3.1)
Rˆ Spectral reduction factor
Sa
Spectral acceleration—in./sec
S
ag Spectral acceleration expressed as a percentage of the gravitational force g
Sd Spectral displacement
Sv Spectral velocityNOMENCLATURE xvii
SF Square feet
U Required strength to resist factored loads or related internal moments and
forces
V Shear force usually quantified to describe associated material or
contributing load
Vc Shear strength provided by concrete
Vch Nominal capacity of the concrete strut in a beam-column joint
VN Component of joint shear strength attributed to the axial load imposed on a
column load
Vsh Nominal strength of diagonal compression field
W Wind load
W Weight (mass) tributary to a bracing system
a Depth of equivalent rectangular stress block, acceleration, shear span
b Width of compression face of member
bw Web width
c Distance from extreme compression fiber to neutral axis
cc Clear cover from the nearest surface in tension to the surface of the flexural
tension reinforcement
d Distance from extreme compression fiber to centroid of tension
reinforcement
d Displacement (peak) of the ground
d˙ Velocity (peak) of the ground
d¨ Acceleration (peak) of the ground
d Distance from extreme compression fiber to centroid of compression
reinforcement
db Bar diameter
ds
Distance from extreme compression fiber to centroid of tension conventional
reinforcement
d
ps Distance from extreme compression fiber to centroid of prestressed
reinforcement
dz
Depth of the plate
e Eccentricity of axial load
f Friction factor; measure of stress, usually subscripted to identify condition
of interest
fc Specified compressive strength of concrete
fci Compressive strength of concrete at time of initial prestress
fci Square root of compressive strength of concrete at time of initial prestress
fcr Critical buckling stress
fct Average splitting tensile strength of aggregate concretexviii NOMENCLATURE
fcg Stress in the grout
fpse Effective stress in prestressed reinforcement (after allowance for all
prestress losses)
fpy Specified yield strength of prestressing tendons
fr Modulus of rupture of concrete
fs Calculated stress in reinforcement
fsc Stress in compression steel
fy
Specified yield strength of reinforcement
fyh Specified yield strength in hoop reinforcing
h Overall thickness of member
hc Cross-sectional dimension of column core measured center-to-center of
confining reinforcement
hn Height of the uppermost level of a frame
hw Height of entire wall or of the segment of wall considered
hx Maximum horizontal spacing of hoop or crosstie legs on all faces of the
column; story height
k Effective length factor for compression members; system stiffness usually
subscripted to identify objective
kel Elastic stiffness
ksec Secant stiffness
kd Depth of neutral axis—elastic behavior is assumed
– Span length of beam center to center of supporting column
-c Clear span of beam from face to face of supporting column
-d Development length for a straight bar
-dh Development length for a bar with a standard hook
-w Length of entire wall or of segment of wall considered in direction of shear
force
n An integer usually applied to number of floors
r Radius of gyration of cross section of a compression member
s Spacing of transverse reinforcement
t
g Thickness of grout
w Unit weight
w
z Width of steel plate
yt Distance from centroidal axis of gross section, neglecting reinforcement, to
extreme fiber in tension
α Factor in bar development length evaluation. 1.3 for top bars, 1.0 for bottom
bars. See ACI,[2.6] Eq. 12.2.2
β Coating factor. See ACI,[2.6] Eq. 12.2.2NOMENCLATURE xix
β1 Factor that defines the relationship between the depth of the compressive
stress block and the neutral axis depth, c[2.6]
γp Postyield shearing angle
1 Participation factor
δu Member or component displacement
An increment of force, stress, or strain
n Relative lateral deflection between the uppermost level and base of a
building
x Relative lateral deflection between the top and bottom of a story
ε Strain—usually subscripted to describe material or strain state
ζ Structural damping coefficient expressed as a percentage of critical
damping
ζˆ Total damping coefficient expressed as a percentage of critical damping
θ Rotation
λ Lightweight aggregate concrete factor
λo Component or member overstrength factor that describes overstrength
expected in a member
µ Ductility factor usually subscripted; bond stress; friction factor
µ Displacement ductility factor
µε Strain ductility factor
µθ Rotation ductility factor
µφ Curvature ductility factor
ρ Ratio of nonprestressed tension reinforcement, As/bd
ρ Ratio of nonprestressed compression reinforcement, As/bd
ρb Reinforcement ratio producing balanced strain conditions
ρg Ratio of total reinforcement area to cross-sectional area of column
ρs Ratio of volume of spiral reinforcement to total volume of core (out-to-out
of spirals) of a spirally reinforced compression member
ρv Ratio of area of distributed reinforcement perpendicular to the plane of Acv
to gross concrete area Acv
φ Curvature, rad/in.; capacity-based reduction factor; strength reduction
factor
φe Normalized elastic displacement (i/u)
φk Stiffness reduction factor
φp Probable overstrength of the steel
ω Reinforcement index ρfy/fc
ω Reinforcement index ρfy/fc
ωp
Reinforcement index ρpfps/fc
<o System overstrength factorxx NOMENCLATURE
SPECIAL SUBSCRIPTS
Special subscripts will follow a notational form to the extent possible. Multiple
subscripts will be used where appropriate, and they will be developed as follows:
1. s, u, n, p, pr, y, i, max, and M will be used to describe member strength or deformation state:
s, service or stress limit state (unfactored)
u, ultimate or factored capacity (strength)
n, nominal capacity
p, postyield
pr, probable
i, idealized
y, yield
max, maximum permitted
min, minimum permitted
M, mechanism
2. c, b, s, f , and p will be used to describe a member category or characterize a
system behavior condition:
c, column
b, beam
s, shear component of deformation
f , flexural component of deformation
p, postyield component of deformation
3. e, i will be used to describe a location; i will also be used to identify an idealized
condition such as yield:
e, exterior beam or column
i, interior beam or column
4. L, D, E will be used to describe a load condition:
L, live load
D, dead load
E, earthquake load
5. A, B, C, L, R and 1, 2 will be used to locate an event with reference to a specific
plan grid or point:
L, left
R, right
Example:
Mcui MbCsD MuD
Interior
Ultimate or factored
Column
Dead load
Unfactored
Grid line C
Beam
Dead load
FactoredNOMENCLATURE xxi
6. Capitalized subscripts will be used to describe the stress class and its location:
B, bottom
C, compression
CB, compression bottom
CT, compression top
T, top, tension, transverse
TB, tension bottom
TT, tension top
7. Special subscripts will be used to identify the following:
a, attainable or average
d, design, as in design basis
D, degrading or diaphragm
ed, energy dissipater
g, grout
SDOF, single-degree-of-freedom systemCONTENTS
PREFACE xiii
NOMENCLATURE xv
INTRODUCTION 1
1 BASIC CONCEPTS 7
1.1 Ductility—A System Behavior Enhancer 8
1.1.1 Impact on Behavior 9
1.1.2 Impact of Strength Degradation on Response 13
1.1.3 Quantifying the Response of Structures to Ground
Motion 14
1.1.4 Strength-Based Design 22
1.1.4.1 Identifying a Design Strength Objective 22
1.1.4.2 Creating a Ductile Structure 24
1.1.5 Displacement-Based Design 26
1.1.5.1 Equal Displacement-Based Design 28
1.1.5.2 Direct Displacement-Based Design 31
1.1.6 System Ductility 33
1.1.7 Recommended Displacement-Based Design
Procedure 44
vvi CONTENTS
1.1.8 Selecting Design Strength Objectives 49
1.1.9 Concluding Remarks 51
1.2 Confinement—A Component Behavior Enhancement 54
1.2.1 Impact of Confining Pressure on Strength 54
1.2.2 High-Strength Concrete (HSC) 59
1.2.2.1 Ductility 61
1.2.2.2 High-Strength Ties 62
1.2.2.3 Higher Axial Loads 63
1.3 Shear 64
1.3.1 Shear Strength 65
1.3.2 Shear Transfer across Concrete Discontinuities 82
1.3.3 Passively Activated Shear Transfer Mechanisms 86
Selected References 90
2 COMPONENT BEHAVIOR AND DESIGN 92
2.1 Beams 93
2.1.1 Postyield Behavior—Flexure 95
2.1.1.1 Experimentally Based Conclusions—General
Discussion 95
2.1.1.2 Predicting Postyield Deformation Limit States 107
2.1.1.3 Impact of Shear and Confinement on Behavior 112
2.1.1.4 Importance of Detailing 116
2.1.1.5 Modeling Considerations 120
2.1.2 Designing the Frame Beam 122
2.1.2.1 Beam-Column Joint Considerations 124
2.1.2.2 Reinforcing Details 126
2.1.2.3 Beam Shear Demand 129
2.1.2.4 Column Shear Demand 131
2.1.2.5 Available Ductility 133
2.1.2.6 Design Process Summary 135
2.1.2.7 Example Designs 135CONTENTS vii
2.1.3 Analyzing the Frame Beam 144
2.1.3.1 Analysis Process Summary 146
2.1.3.2 Example Analysis 149
2.1.3.3 Postyield Behavior 163
2.1.4 Precast Concrete Beams 166
2.1.4.1 Moment Transfer 168
2.1.4.2 Shear Transfer 172
2.1.4.3 Composite Systems 173
2.1.4.4 Post-Tensioned Assemblages 185
2.1.4.5 Bolted Assemblages 216
2.1.4.6 Experimental Confirmation 222
2.2 The Beam Column 244
2.2.1 Strength Limit States 245
2.2.1.1 Developing an Interaction Diagram 247
2.2.1.2 Design Relationships 250
2.2.2 Experimentally Based Conclusions 251
2.2.2.1 Strength 251
2.2.2.2 Strain States 255
2.2.2.3 Stiffness 263
2.2.3 Conceptual Design of the Beam Column 264
2.2.3.1 Estimating Probable Levels of Demand 264
2.2.3.2 Sizing the Beam Column 270
2.2.3.3 Story Mechanism Considerations 275
2.2.3.4 Design Process Summary 276
2.2.3.5 Example Designs 278
2.2.4 Analyzing the Beam Column 292
2.3 Beam-Column Joints 296
2.3.1 Behavior Mechanisms 296
2.3.1.1 Bond Stresses 300
2.3.1.2 Biaxially Loaded Joints 301viii CONTENTS
2.3.1.3 Exterior Joints 301
2.3.1.4 Eccentric Beams 301
2.3.2 Experimentally Based Conclusions 302
2.3.3 Impact of High-Strength Concrete 310
2.3.4 Impact of Joint Reinforcing 312
2.3.5 Bond Deterioration within the Beam-Column Joint 314
2.3.6 Design Procedure 314
2.3.7 Design Example 321
2.3.8 Precast Concrete Beam-Column Joints—DDC
Applications 322
2.3.8.1 Experimentally Based Conclusions 322
2.3.8.2 Beam-Column Joint Design Procedures 332
2.3.9 Precast Concrete Beam-Column Joints—Hybrid
System 335
2.3.9.1 Experimentally Based Conclusions—Interior
Beam-Column Joint 335
2.3.9.2 Design Procedures—Interior Beam-Column
Joints 341
2.3.9.3 Design Procedures—Exterior Beam-Column
Joints 344
2.3.9.4 Corner Hybrid Beam-Column Joints 345
2.4 Shear Dominated Systems 348
2.4.1 Tall Thin Walls 349
2.4.1.1 Experimentally Based Conclusions 349
2.4.1.2 Design Procedures 374
2.4.1.3 Design Summary 387
2.4.1.4 Design Example 389
2.4.2 Shear Walls with Openings 402
2.4.2.1 Coupling Beams 402
2.4.2.2 Analytical Modeling of the Coupling Beam 417
2.4.2.3 Design Procedures—Coupling Beams 425CONTENTS ix
2.4.2.4 Coupled Shear Walls with Stacked Openings—
Design Process and Example 437
2.4.2.5 Capped and Belted Shear Walls 455
2.4.2.6 Shear Walls with Randomly Placed Openings 471
2.4.3 Precast Concrete Shear Walls 484
2.4.3.1 Experimental Efforts 485
2.4.3.2 Experimentally Inferred Conclusions—Hybrid
Precast Wall System 514
2.4.3.3 Design Procedures 514
2.4.3.4 Example Design—Ten-Story Shear Wall 519
Selected References 530
3 SYSTEM DESI 533
3.1 Shear Wall Braced Buildings 534
3.1.1 Shear Walls of Equivalent Stiffness 534
3.1.1.1 Alternative Shear Wall Design Procedures 536
3.1.1.2 Analyzing the Design Processes 561
3.1.1.3 Conceptual Design Review 564
3.1.1.4 Summarizing the Design Process 571
3.1.2 Shear Walls of Varying Lengths 576
3.1.2.1 Alternative Design Methodologies 576
3.1.2.2 Suggested Design Approach 593
3.1.3 Coupled Shear Walls—Design Confirmation 597
3.1.4 Precast Concrete Shear Walls 615
3.1.4.1 Hybrid Wall System—Equal Displacement-Based
Design (EBD, Section 3.1.1) 621
3.1.4.2 Hybrid Wall System—Direct Displacement Design
Procedure 639
3.1.4.3 Vertically Jointed Wall Panels 648
3.2 Frame Braced Buildings 662
3.2.1 Design Objectives and Methodologies 662
3.2.1.1 How to Avoid Lower Level Mechanisms 669x CONTENTS
3.2.2 Force- or Strength-Based Design Procedures 669
3.2.3 Displacement-Based Design 680
3.2.3.1 Building Model 680
3.2.3.2 Single-Degree-of-Freedom (SDOF) Model 689
3.2.4 Precast Concrete Frame—Direct Displacement-Based
Design 691
3.2.4.1 DDC Frame 694
3.2.4.2 Hybrid Frame 700
3.2.4.3 Precast Frame Beam Designs 702
3.2.5 Irregular Frames 704
3.2.6 Frame Design Evaluation by Sequential Yield
Analysis 711
3.2.6.1 What Constitutes Good Behavior? 712
3.2.6.2 P Concerns and Modeling Assumptions 713
3.2.6.3 Behavior Review—Frame 3 (Table 3.2.1) 718
3.2.6.4 Frame 3—Consequences of Alternative
Strengths 729
3.2.6.5 Behavior Review—Irregular Frame 734
3.2.6.6 Behavior Review—Precast Frame Systems 736
3.3 Diaphragms 738
3.3.1 Design Approach 738
3.3.2 Estimating Diaphragm Response 740
3.3.3 Establishing the Strength Limit State of a Diaphragm 746
3.3.4 Precast Concrete Diaphragms 753
3.3.4.1 Composite Diaphragms 753
3.3.4.2 Pretopped Precast Concrete Diaphragms 754
3.4 Design Process Overview 757
3.4.1 System Ductility 758
3.4.2 Capacity Considerations 758
3.4.3 Recommended Design Approach 759
Selected References 762CONTENTS xi
4 DESIGN CONFIRMATION 763
4.1 Response of Shear Wall Braced Buildings to Ground Motion 764
4.1.1 Testing the Equal Displacement Hypothesis 768
4.1.2 Impact of Design Strength on Response 776
4.2 Frame Braced Buildings 780
4.2.1 Impact of Design Strength on Performance 780
4.2.2 Impact of Modeling Assumptions 784
4.2.3 Distribution of Postyield Deformations 794
4.2.4 Design/Behavior Reconciliation 797
4.2.5 Postyield Beam Rotations 800
4.2.6 Evaluating Column Behavior 800
4.2.7 Response of Irregular Frame 802
4.2.8 Response of Precast Concrete Frames—DDC 806
4.3 Behavior Imponderables 807
4.3.1 System Stability Considerations 807
4.3.2 Torsion 810
Selected References 814
INDEX 815
815
Index
Index Terms Links
Analysis
analysis process summary 146
analyzing the wall design process 561 562 563 564
beam column 292 293 294 295 296
cast-in-place frame beam 144 145 146
example analysis, cast-in-place frame
beam 149 150 151 152 153
154 155 156 157 158
159 160 161 162 163
objective 147 148
thin shear wall 397
Acceleration
impact of strength on experienced
accelerations 569 570 571
maximum 11
response 12
Base shear
code development basis 375
coefficients 43
comparison of strength and
displacement-based for shear walls 376 377 378 379 380
381 382
impact on drift of frame braced
buildings 782
related to displacement 40
spectrum 21
Beams
cast-in-place frame beams 93–166
behavior idealizations, stiffness 97 98 99 100 101
102 103
curvature, estimated 111 112
curvature, observed 106
depth of the compressive stress
block 96
detailing the plastic hinge region 116 117 118 119 120
156 157 158 159 160
developing a flexural reinforcing
program 153 154 155 156
ductility 103 133 134 135
estimating the probable postyield
concrete strain state 111 112
experimentally based conclusions 95 96 97 98 99
100 101 102 103 104
105 106 107
experimentally deduced concrete
strain limit states 107
general 93816
Index Terms Links
hysteretic behavior 96
idealized yield strength (Pyi ) 98
impact of shear and confinement 112 113 114 115 116
importance of detailing 116 117 118 119 120
inelastic curvature model 101 109
measured curvatures 104 105 106 107
modeling considerations 120 121 122
overstrength factor 98 99
plastic hinge length 107 109
postyield behavior, cast-in place
frame beam 163 164 165 166
postyield behavior, flexure 95
postyield deformation model 109
postyield rotation demand 794
predicting postyield behavior 163 164 165 166
strength 95
strength and stiffness degradation 104
composite beam system, see Composite
frame beams
coupling beams, see Coupling beams
precast concrete beams 166–173 167 168 169 170
171 172 173 185–244
DDC beam, see DDC system
Beams (continued)
general 166 167 168
hybrid beam, see Hybrid beam system
moment transfer mechanism 168 169 170 171 172
shear transfer 172 173
Beam columns 244–296
analyzing the beam column 292 293 294 295 296
balanced axial load 245
balanced moment 248
balanced strain state 245
boundary columns 245 729 730 731 732
733 734 735 736 737
800 801 802
conceptual design 264
concrete strain state, spalling 261
constructability 270
curvature, estimating 293
design relationships 250 251
design process summary 276
details 287
developing an interaction diagram 247 248 249 250
ductile limit state 250 270
effective moment of inertia 264
estimate of reinforcing required 251
estimating probable levels of demand 264 265 266 267 268
269 270
evaluating column behavior 800
example designs 278
experimentally based conclusions 251–263817
Index Terms Links
experimentally determined shear stress
limit state 254
experimentally determined strain states 255
flexural strength demand 244 245
impact of column spacing 268 269 270
impact of high modes 245
interaction diagram 246
observed behavior 257 258
overturning moment 267 268 269 270
postspalling behavior 262
response of irregular frame 802 803 804 805 806
sizing the beam column 270 271 272 273 274
275
sizing the column for axial loads 250
sizing the column for flexural loads 250
story mechanism 265 275
strain limit state confined core 263
strain state, estimating 293 294 295
strength of the confined core 262
strength limit states 245 246 247 248 249
250
transverse reinforcing 280 281 282 283 284
285 286 287 288 289
290 291 292
transverse reinforcing program, base
level 281
Beam-column joints
cast-in-place frames 296–322
behavior mechanisms 296–348
biaxially loaded joints 301
bond considerations 300
bond deterioration 314 315 316 317 318
cast-in-place subassembly 309
conceptual design 124 125 126
design example 321
eccentric beams 301
experimentally based conclusions 302 303 304 305 306
307 308 309 310
exterior joints 301
forces imposed on an interior
beam-column joint 299
impact of axial load 307 308
impact of high-strength concrete 310 311 312
impact of joint reinforcing 312 313
mechanisms of shear transfer,
interior joint 297
minimum joint reinforcement 306
recommended design procedures 314 315 316 317 318
319 320 321
strength limit states, suggested by818
Index Terms Links
others 299
suggested strength limit state 318
precast concrete beam-column joints 322–348
DDC system 322–334
design procedures 332 333 334
experimentally based conclusions
DDC 322–332
hoop tie strains, observed 329 330
hysteretic behavior 325
load flow 326 327 328 329 330
331
strain in ductile rod 326
hybrid system 335–348
bond penetration 336
corner conditions 345 346 347 348
design procedure, exterior
beam-column joint 344 345
design procedure, interior
beam-column joint 341 342 343 344
experimentally based conclusions 335 336 337 338 339
340 341
hysteretic behavior 341
interior beam column joint 335–344
Bolted precast concrete systems 216–244
See also DDC system
Bond
bar development length 241
bond stress in beam-column joint 300
deterioration in a beam-column joint 314
hybrid beam-column joint, debond
length 336
implied bond stress 241
Capacity-based design
of the beam-column joint 296 298 299
definition 52
developed using inelastic time history
analysis 800 801 802
developed using sequential yield
analysis, see Shear walls; Frame
design
example 36
of the frame beam 156 157 158 159 160
of the frame column 270 274 275 283
general 24 25
objective 244
overview 758
Columns, see Beam columns
Composite frame beams 173–185
Compression reinforcing, effectiveness 300 314 315 316 317
connector 175
developing the objective strength 177 178 179 180819
Index Terms Links
hysteretic behavior 325
photo 176
sizing the beam-column joint 180 181
Concrete strain, see also specific system
analytically developed 355 356 357 358 363
cast-in-place walls reported 362
estimating postyield strain state in a
cast-in-place frame beam 111 112
estimating concrete strain in columns 259 260 261 262 263
experimentally determined limit state
cast-in-place beams 107
experimentally determined limit state
columns 255
T wall section 372
Confining pressure
impact of confinement on behavior 112 113 114 115 116
impact on cast-in-place wall strength 370 371
impact on component strain limit state 54 263
impact on component strength 54 116 262
impact on concrete strength 54 55 56 57 58
59
impact on precast wall strength 499 500 501 502 503
504 505
quantification 56 57
Confining reinforcing, see also member
category
codification objectives 55
detailing in cast-in-place wall 396 454
detailing objectives 57 58
detailing in precast walls 489 529
detailing at support of steel coupling
beam 434
developing transverse reinforcing
program 182
high-strength concrete 59 60 61 62 63
64
high-strength reinforcing 62 63
objective 54 55
objective pressures 56 57
Conjugate beam models 107 108 109 110 111
Coupled shear walls, see Shear walls
Coupling beams
analytical models 405–411 417–425
assumed compressive strut width 406
compression diagonal 406
design conclusions 424 425
design procedures 425
diagonally reinforced 426
flexural behavior model 425
steel coupling beams 429
truss reinforced coupling beam 428
detailing steel coupling beams 434 435 436 437820
Index Terms Links
diagonally reinforced coupling beam 407 408 409 410 411
422
effective moment of inertia 420 422 423
diagonally reinforced coupling
beams 422
Coupling beams (continued)
flexural model 420
steel coupling beams 423
example design, steel coupling beam 435 436 437
447 448 449 450 451
452 453 454
flexural behavior model 403 404 405 406 407
general 402 403
limiting the shear stress 420
link beam length 416
modeled using a strut and tie 403 404 405
objective peak shear 407
observed behavior 415 433
shear rotation relationships 408 409 410 412 417
steel coupling beams 414
traditional flexural model 405
truss reinforcing program 410 411 412 413 414
Curvature, see also specific component
experimentally determined
cast-in-place beam 106
experimentally determined in walls 507
precast beams 170 171
Damping 15 16 17 18 19
20
cast-in-place concrete wall 512
equivalent structural 15 16 17 18
hybrid wall system 512
impact on behavior 52
DDC system 216–244
assembling 231
beam flexural reinforcement ratios 239
connection detail 219 235
design procedure 232
detailing the frame beam 240 241 242 243 244
estimating strain in the ductile rod 243 244
example design 233–244
experimental confirmation 222–231
forged ductile rod 218
hardware dimensions 235
isometric view 217
load transfer mechanisms 220 221 222
postyield strain 231
shear capacity development 239 240
test specimen 223 224 225
used in hybrid shear wall 519
vertical orientation 236821
Index Terms Links
Deflection, see also Drift; specific system
experimental limit state, cast-in-place
beam 96 103
predicting limit state in cast-in-place
frame beam 107 108 109 110 111
Design, see also specific component or
system
confirmation 763–807
developing the design moment 148
example designs cast-in-place frame
beams 135–144
impact of dead and live loads 136 137
process overview 757
process summary cast-in-place frame
beams 135
recommended approach 759
Detailing
cast-in-place beam column 287
cast-in-place beams 126 127 128
DDC beam-column joint 323 326
diaphragms 754 755
exterior beam-column joint 302 303
hybrid beam 199 200
hybrid system, corner condition 345 346 347 348
hybrid system, exterior beam-column
joint 345
importance of 116 117 118 119 120
Diaphragm 738–757
alternative load paths in a reinforced
diaphragm 756
composite diaphragms 753
creating a design response spectrum 742
deep beam models 72–82
design approach 738 739
development of diaphragm load paths 751
effective moment of inertia 739
establishing the strength limit state 746
estimating response 740
fundamental frequency 739
load paths 88 89 90
postyield distress in a diaphragm 757
precast concrete diaphragms, general 753
pretopped precast concrete
diaphragms 754
probable maximum inertial force 743
Direct displacement-based design, see also
Displacement-based design
example design, shear wall braced
building 557 558 559 560
Displacement
beam and column subassembly 663
diaphragms 746 747 748 749822
Index Terms Links
single story frame 29
Displacement-based design 26 27 28 29 30
31 32 33
constant spectral velocity method 551 552 553 554 555
definition 52
direct displacement 31 32 33
direct displacement-based design 555 556 557 558 559
560 561
displacement constant region 48
equal displacement 28 29 30 31
equal displacement-based design 539–551
general 9
recommended procedure 44 45 46 47 48
49 571 572 573 574
575 576
Drift
details 235
estimating the drift of frame braced
building 672 673 683 684
estimating the drift of shear wall braced
buildings 391 392 393
objective limits 28
standard forging 218
Ductile rods
assemblies used in composite
construction 175
stress–strain curves 176
Ductility
cast-in-place frame beams 103
general 7
impact on damping 15 16 17 18 19
20
impact on system response 12 20 21 22
member ductility, as related to system
ductility 37 38 39 40
overview 758
reduction factors used in design 40 41 42
related to member stiffnesses 40
rotation demand irregular frames 803 804 805 806
system behavior enhancer 8 9 10 11 12
13 14
system ductility, frame braced
structures 680 681 682
system ductility, general 33–44 52
Dynamic response of
single-degree-of-freedom system 9–22
Dynamic characteristics of a building, see
also specific system
discussion 52 53
Earthquake
ground motions used in analyses 766 767823
Index Terms Links
Elastic
time history analysis, examples 768–807
Energy, see also Damping
design methodologies, general 9
dissipated 17
Equal displacement-based design, see also
Displacement-based design
applied to frame braced buildings 680–691
applied to shear wall braced buildings 539–555
definition 51
recommended procedure 44
single story example 28 29 30 31
testing the equal displacement
hypothesis 768–776
Example designs
cast-in-place frame beam 149–163
concrete coupling beam 449 450
composite beam system 174–185
DDC system 233–244
hybrid beam 196–216
precast hybrid wall system 519–529
shear wall, capped shear wall 456–471
shear wall, coupled shear walls with
stacked openings 437–447
shear wall, thin wall 389–402
shear wall, 12-inch thick wall 379–389
steel coupling beam 435 436 437 447 448
449
Example designs (continued)
unequal spans, cast-in-place system 140 141 142 143 144
Factored dead and live loads 136
Force-based design, see also
Strength-based design
code procedure 22 42
general 8 9
Frame design 662–737
analysis
building model approach 680 681 682 683 684
685 686 687 688 689
consequences of alternative strengths 729
DDC frame 694
design evaluation by sequential yield
analysis 711–737
design objective 662
direct displacement-based design 691 692 693 694 695
696 697 698 699 700
701 702
displacement-based design, see
Displacement-based design
equal displacement-based design 680–691
estimating building period 672
hybrid frame 700824
Index Terms Links
irregular frames 704
behavior 733
subassemblies 706
lower level mechanisms 669
mechanism approach 666
P concerns and modeling
assumptions 713
precast concrete frame 691–704
precast frame beam designs 702
precast frame system behavior 735
postyield drift distribution 680
response to ground motion
design/behavior reconciliation 797
distribution of postyield
deformations 794
elastic/perfectly plastic model 780 781 782 783 784
impact of design strength 780–794
impact of modeling assumptions 784–794
P effects 786
residual drift 782 783 787
response of precast concrete
frames
DDC 806 807
slip control model 785
stiffness degrading model 785
single-degree-of-freedom model
approach 689 690 691
stability 807 808 809 810
stiffness 671 688 690
strength-based design 669–679
strength-based design procedure 669
subassembly stiffness 663
two-story building mechanism 666
what constitutes good behavior 712
Frequency, see Natural frequency
Height
effective, Blue Book development 541 543 545 547
effective, linear mode shape basis 542 543
High-strength concrete 59 60 61 62 63
64
ductility available 61 62 63 64
Hybrid beam system 185–216
analysis 203
balanced moment 209 210 211 212
design procedures, beam-column joints 341 342 343 344 345
346 347 348
design process 195
detailing 199 200
developing a flexural reinforcement
program 205
developing the design moment 203 204 205825
Index Terms Links
estimating steel stresses 188 189 190 191 192
193 194
experimental support 185–195
minimum reinforcing objectives
207 208
overstrength 201
probable strength 194
reinforcement ratios 200 201
stiffness 188 189
strain evaluation 188 189 190 191 192
193 194 214 215 216
Hybrid frame system, see Frame design
Hybrid wall system, see Shear walls;
Precast concrete system
Hysteretic response
DRAIN-2DX model 120 121 122
IDARC2D model 121 122 123
impact on damping 16 17 18
partially full 18
Idealized behavior, see also Shear walls
beam yield 98 99 100 565
frames 716 717 718 719 720
721
SDOF system 25
system behavior 566 716 721 735
Inelastic behavior
impact on system response 20 21 22
inelastic response spectrum 20 21 22
time history examples 768–807
Limit states
cast-in-place concrete 107
experimentally deduced concrete strain
limit states 107
Mass
effective height 542 544
effective height, linear mode shape
basis 544
effective mass 535 542
effective mass, linear mode shape
basis 543
Mechanism
frames 666
impact of dead and live loads 179 180
irregular frame 709
lower level mechanisms, how to avoid 669
most critical mechanism 245
story 275
two-story example 666 667 668 669
use of in design 177 178 179 180
Member behavior826
Index Terms Links
beam column 255 256 257 258
beam-column joint 298 299 300
cast-in-place beam 95–116
Member modeling
considerations 120
first yield of steel 100 101
inelastic curvature model 101 102
modeling considerations 120
Modal analysis
based on linear mode shape 543
elastic mode shape basis 545
inelastic mode shape basis 545
modal analysis 542 543 544 545 546
547
modal mass 542
Modeling
DRAIN-2DX model 120 121 122
hysteretic behavior 790 791
IDARC2D model 121 122 123
Moment of inertia, see also specific
member or system
required/effective 29
Moment redistribution 137 141 142
Moment transfer, precast beams
general 168 169 170 171 172
Natural frequency, see also Period
development; specific system
determining objective 28
ductile structure 32
single-degree-of-freedom system 11
Neutral axis
beam 101
hybrid wall 449–504
wall 362
Nominal strength, see Member category
Overstrength
material 211
member
frame beams 98 99 689
shear walls 352 361 495 566
567 568 569 570
system 25 30
cast-in-place frame 162
walls 352 361
Participation factor 542
linear mode shape 543
P
definition 51
design impact 718 719 720 721 722
723827
Index Terms Links
effect on building response 13 14
impact on system stability 807 808 809 810
modeling considerations, frames 713 714 715 716 717
718
Period development 21 22
capped shear walls 458 459
coupled shear walls 442 443 444 445
Period development (continued)
estimates of 22 42 43
frame braced structure 672
idealized 27
shear wall 391 392 393
Plastic design 177–180 666 667 668 669
see also Mechanism
Plastic hinges
length
cast-in-place beams 107
columns 255 256 257 258
hybrid walls 498 499 514
walls 356 506 507
precast beams 170 171 172
Plastic truss analogy
theory 66
used to develop capacity of a DDC
beam-column joint 331
used to identify shear strength in
cast-in-place beam 113 114 115
Post-tensioned systems, see also Hybrid
beam system; Shear walls, precast
concrete
experimental support 185–195
general 185
hybrid beam system 185–216
Postyield behavior, see specific member
or system
Precast concrete system
beam-column joints 322–348
precast concrete beams 166–244
See also Composite frame beams; DDC
system; Hybrid beam system
precast concrete walls, see Shear
walls
time history response of frames to
ground motion 806 807
PRESSS program 640
shear wall elevation, test building 493
Pushover analysis, see Sequential yield
analysis
Reinforcement
developing a flexural reinforcing
program for the cast-in-place frame
beam 148828
Index Terms Links
developing a transverse reinforcing
program for the cast-in-place frame
beam 148
effectiveness of compression bars 134
hoop ties 119
restraining force 119
spacing 127
stability 116 117 118 119 120
Reinforcement ratio
maximum 133 134 135
Response spectrum 14 15 16 17 18
19 20 21 22
acceleration-displacement response
spectra 548
definition 51
Restoring force impact on response 12
Sequential yield analysis, see also specific
system
coupled shear walls 600 601
frame braced buildings 716 719 720 721 729–738
shear wall braced systems 556 582 585 586 587
Shear
arching action 71 74
beam shear model 65
capacity-based demand beam 129 130 131
compression diagonal modeling 76
demand, columns 131 132 133
deep beams 73
diaphragm load paths 88 89 90
ductility 77 78 79 80 81
82
impact on behavior 112 113 114 115 116
limit states 67 68 69 70
columns 254
need for effective development 7
node development 75 76 754
passively activated shear friction 86 87 754 755 756
plastic truss analogy 66 113 114
pure friction 82 83
shear friction 83 84 85
shear span, impact on strength 71 72
shear strength 65–77
squat shear walls 76 77
transfer across concrete discontinuities 82 83 84 85 86
87 88 86 90 172
173
truss analogy 65
Shear walls
design, general 534–576
constant spectral velocity method 551 552 553 554 555
curvature distribution 507829
Index Terms Links
direct displacement-based design 555 556 557 558 559
560 561
equal displacement-based design 540–555
estimating strain states 355 356 357 358 363
idealized stiffness 536
impact of confined core 370 371 372
impact of system strength 567 568 569 570 571
modal analysis 542 543 544 545 546
547
mode participation 538
modeling shear walls of equivalent
stiffness 534 535 536
period development 391 392 393
preparing alternative designs 561
reported strain states 362
sequential yield analysis examples 565 566 567 568 569
570 571
stability of the compression flange 366 367 368 369 370
T walls 367 368 369
design summary
design objective is to limit building
drift 573
design requires the adoption of a
substitute structure 574
wall characteristics are a
precondition 572
precast concrete 484–529 615–661
base details 489
carbon fiber system 485
concrete strains
estimated 504 505
experimentally inferred 514
reported 492 498
cracking experienced 486
curvature distribution emulative wall 507
design assumptions 506
design procedures, hybrid wall 514 515 516 517 518
519
detailing 524 525 526 527 528
529
emulative system 485
example design, hybrid wall 519–529
experimental efforts 485–514
hybrid T wall design solutions 646
hybrid wall system 615–661
constant velocity equal
displacement 622–639
design procedures 615–661
direct displacement-based 639 640 641 642 643
644 645 646
equal displacement-based 621–639
PRESSS test wall 493830
Index Terms Links
prestressed (only) wall assembly 485 486 487 488 489
490 491 492
reinforced base 487
stiffness 495
structural damping 512
vertically joined wall panels 648–661
response to ground motion, see also
Time history analysis
hysteretic response in the plastic
hinge region 770
impact of design strength on
response 776–784
period shift 778
testing the equal displacement
hypothesis 768–776 782 783 784
shear wall braced buildings 534–661
shear walls with openings 402–484
capped shear wall system 457–468
idealized behavior 469
mechanism shear 460 461 462 463 464
465 466
period development 458 459
probable strain states 466 467 468
coupled shear walls with stacked
openings 437–455
compression side pier 453
coupling beam design 447 448 449 450 451
452 453 454
See also Coupling beams
design confirmation 597–614
design process and example 437 438 439 440 441
442 443 444 445 446
447
estimating the period 601
estimating strain states 608
period development 442 443 444 445
postyield deformation demand 453
postyield rotational demand on
coupling beams 453
sequential yield analysis 600
strength criterion for the shear
piers 450
shear walls of varying lengths 576–597
displacement-based approach 578 579 580 581 582
583 584 585
force-based design procedures 576 577 578
secant stiffness 587
Shear walls (continued)
sequential yield analysis 585–593 586 587 588 589
590 591 592 593
suggested design approach 593
shear walls with randomly placed831
Index Terms Links
openings 471–484
design conclusions 481
design objectives 474
experimental efforts 471–481
multiple openings 481
shear fan development 475
strut and tie model 481 482 483 484
tall thin walls 349–402
code design strength 376 377 378
concrete strain limit states 372
conclusions developed from
experimental efforts 373 374
curvature 362
curvature ductility factor 357 371
design, direct displacementbased
(DBD) 555–561
design, displacement-based
approach 376 377 378 379 380
381 382 383 384 385
386
design, equal displacementbased
(EBD) 540–555
design example 389–402
design procedures 374–387
elastic deflection 356
experimentally based
conclusions 349–374
influence of shear on period 392 393
period determination 379 380
plastic hinge length 356
sequential yield analysis 565 566 567 568 569
570 571
stability limit states 366
stiffness 353 361
stiffness, T walls 369
strain profiles 359 360 361 362
T sections 367
Spectral acceleration 15
Spectral displacement 15 20
Spectral velocity 15 19 20 28 31
Spectrum
base shear 375
creating a design spectrum 14 15 16 20 21
22
design response spectrum 765
matched spectrum 763 764 765 766
scaled ground motion spectra 763 764 765 766
single-degree-of-freedom 375
Stability index 809
Stability832
Index Terms Links
system 13
tall thin walls 366 367 368 369
Steel
ductile rod 218
reinforcement index 212
stress–strain diagram for prestressing
steel and mild steel bar 211
used as coupling beam, see Coupling
beams
Stiffness
columns 263
cast-in-place concrete shear walls 352 361 508
diaphragms 739
effective stiffness of the substitute
structure 644
design
effective height 542
effective height, linear mode shape
basis 544
selecting compatible length of shear
wall 551
determining objective stiffness 28
ductile structure 26
hybrid system 340 341
precast concrete shear walls 495
secant stiffness 587
strength and stiffness degradation
cast-in-place frame beams 104
subassembly 663
subassembly stiffness, cast-in-place
subassembly 340 341
substitute structure 644
T walls 369
Strain
cast-in-place beams 107
columns 255–264
confined core 263
estimating postyield strain states 163 164 165 166
estimating postyield strain state in a
cast-in-place frame beam 111 112
example cast-in-place frame beam 160
experimentally deduced concrete strain
limit states 107
hybrid beams 190 191 192 193 194
213 214 215 216
hybrid walls 498 504 505
postyield behavior cast-in-place frame
beam 163 164 165 166
prestressing strand in shear walls 490
Strength
degradation 13833
Index Terms Links
design 40 46
developable 40
impact on response 567 568 569 570 571
776 777 778 779 780
781 782 783 784
objective 8 22 49
required 30
strength and stiffness degradation
cast-in-place frame beams 104
Strength-based design, see also specific
system
definition 52
example 42
general 22
Structural systems
behavior, see specific system
design, see specific system
response to ground motion 14 15 16 17 18
19 20 21 22
Strut and tie modeling, see also Coupling
beams; Diaphragm; Plastic truss
analogy
beam shear transfer 65 66 67
compressive strut width 406
deep beams 73 74
node development 75 754 755
precast wall panels 77
squat shear walls 76
used to development diaphragm 756
used to estimate shear deformation 77
System behavior
ductile structures 8
elastic, see Time history analysis
idealization 8
inelastic, see Sequential yield analysis;
Time history analysis
System stability 807
Time history analysis 763–807
elastic/inelastic response compared 768 769 772 778 803
807
ground motions 763 764 765 766 767
impact of modeling on response 784–794
impact of strength on response 776–784
inelastic response 782 783 792
modeling hysteretic behavior 790 791
objectives 763
plastic hinge distribution 795 796 797 798 799
800 801 802 803
response of frame braced buildings 780–807
response of shear wall braced 768–780834
Index Terms Links
buildings
testing the equal displacement
hypothesis 768–776 782 783 784
Torsion 810 811 812 813 814
Walls, see Shear walls
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