1 REINFORCED CONCRETE STRUCTURES
2 Topic Overview
Concrete and reinforcement behavior
Reference standards
Requirements by Seismic Design Category
Moment resisting frames
Shear walls
Other topics
Design Examples
3 Topic Overview
Concrete and reinforcement behavior
Reference standards
Requirements by Seismic Design Category
Moment resisting frames
Shear walls
Other topics
Design Examples
4 Unconfined Concrete Stress-Strain Behavior
5 Confinement by Spirals or Hoops
6 Confinement
7 Confined Concrete
Stress-Strain Behavior
8 Idealized Stress-Strain Behavior of Confined Concrete
9 Reinforcing Steel Stress-Strain Behavior
10 Reinforced Concrete Behavior
11 Behavior Up to First Yield of Steel
12 Behavior at Concrete Crushing
Mn = Asfyjd
13 Typical Moment Curvature Diagram
14 Influence of Reinforcement Ratio
15 Influence of Compression Reinforcement
16 Moment-Curvature
with Confined Concrete
17 Moment-Curvature with Confined Concrete
18 Plastic Hinging
19 Strategies to Improve Ductility
Use low flexural reinforcement ratio
Add compression reinforcement
Add confining reinforcement
20 Other Functions of Confining Steel
Acts as shear reinforcement
Prevents buckling of longitudinal reinforcement
Prevents bond splitting failures
21 Structural Behavior
Frames
22 Story Mechanism
23 Structural Behavior - Walls
24 Structural Behavior - Columns
25 Influence of Hoops on Axial Strength
26 Column with Inadequate Ties
27 Well Confined Column
28 Hysteretic Behavior of Well Confined Column
29 Structural Behavior
Columns
30 Column Shear Failure
31 Structural Behavior
Joints
32 Hysteretic Behavior of Joint with Hoops
33 Hysteretic Behavior of
Joint without Hoops
34 Joint Failure No Shear Reinforcing
35 Anchorage Failure in
Column/Footing Joint
36 Summary of Concrete Behavior
Compressive Ductility
Strong in compression but brittle
Confinement improves ductility by
Maintaining concrete core integrity
Preventing longitudinal bar buckling
Flexural Ductility
Longitudinal steel provides monotonic ductility at low reinforcement ratios
Transverse steel needed to maintain ductility through reverse cycles and at very high strains (hinge development)
37 Summary of Concrete Behavior
Damping
Well cracked: moderately high damping
Uncracked (e.g. prestressed): low damping
Potential Problems
Shear failures are brittle and abrupt and must be avoided
Degrading strength/stiffness with repeat cycles
Limit degradation through adequate hinge development
38 Topic Overview
Concrete and reinforcement behavior
Reference standards
Requirements by Seismic Design Category
Moment resisting frames
Shear walls
Other topics
Design Examples
39 Reference Standards
40 Modifications to Reference Standards
41 Context in NEHRP Recommended Provisions
Provisions ==> ASCE 7-05 ==> ACI 318-08
ASCE 7-05 for Concrete
Structural design criteria: Chap. 12
Structural analysis procedures: Chap. 12
Design of concrete structures: Sec. 14.2
Provisions modifications to ASCE 7
ASCE 7 modifications to ACI 318
42 Reference Standards
ASCE 7:
Defines systems and classifications
Provides design coefficients
ACI 318:
Provides system design and detailing requirements consistent with ASCE 7 system criteria
Modified by both ASCE 7 and the
Provisions
43 Seismic-Force-Resisting Systems
Moment Frames Cast-in-Place Special Intermediate Ordinary
Precast Special Shear walls
Cast-in-Place Special Ordinary Detailed plain Ordinary plain Precast Intermediate Ordinary
Dual Systems
44 Use of Reference Standards
ACI 318
Chapter 21, Earthquake-Resistant Structures
ASCE 7 Section 14.2
Modifications to ACI 318
Detailing requirements for concrete piles
Provisions Section 14.2
Modifications to ACI 318
Detailing requirements for concrete piles
Validation testing for special precast structural walls
Provisions supersede ASCE 7 modifications
45 Detailed Modifications to ACI 318
Wall piers and wall segments
Members not designated as part of the LRFS
Columns supporting discontinuous walls
Intermediate precast walls
Plain concrete structures
Anchoring to concrete
Foundations
Acceptance criteria for validation testing of special precast walls
46 Topic Overview
Concrete and reinforcement behavior
Reference standards
Requirements by Seismic Design Category
Moment resisting frames
Shear walls
Other topics
Design Examples
47 Design Coefficients
Moment Resisting Frames
48 Design Coefficients
Shear Walls (Bearing Systems)
49 Design Coefficients
Shear Walls (Frame Systems)
50 Design Coefficients
Dual Systems with Special Frames
51 General Requirements
52 Moment Frames
53 Reinforced Concrete Shear Walls
54 Precast Concrete Shear Walls
55 Topic Overview
Concrete and reinforcement behavior
Reference standards
Requirements by Seismic Design Category
Moment resisting frames
Shear walls
Other topics
Design Examples
56 Performance Objectives
Special Moment Frames
Strong column
Avoid story mechanism
Hinge development
Confined concrete core
Prevent rebar buckling
Prevent shear failure
Member shear strength
Joint shear strength
Rebar development and splices (confined)
57 Performance Objectives
Intermediate Moment Frames
Avoid shear failures in beams and columns
Plastic hinge development in beams and columns
Toughness requirements for two-way slabs without beams
Ordinary Moment Frames
Minimum ductility and toughness
Continuous top and bottom beam reinforcement
Minimum column shear failure protection
58 Special Moment Frames
General detailing requirements
Beams
Joints
Columns
Example problem
strong column weak beam
60 Required Column Strength
61 Hinge Development
Tightly Spaced Hoops
Provide confinement to increase concrete strength and usable compressive strain
Provide lateral support to compression bars to prevent buckling
Act as shear reinforcement and preclude shear failures
Control splitting cracks from high bar bond stresses
62 Hinge Development
63 Hinge Development
64 ACI 318, Overview of SMF:
Beam Longitudinal Reinforcement
65 ACI 318, Overview of SMF:
Beam Transverse Reinforcement
66 ACI 318, Overview of SMF: Beam Shear Strength
67 ACI 318, Overview of SMF: Beam-Column Joint
68 ACI 318, Overview of SMF: Beam-column Joint
Vn often controls size of columns
Coefficient depends on joint confinement
To reduce shear demand, increase beam depth
Keep column stronger than beam
69 ACI 318, Overview of SMF:
Column Longitudinal Reinforcement
70 ACI 318, Overview of SMF:
Column Transverse Reinforcement at Potential Hinging Region
71 ACI 318, Overview of SMF:
Column Transverse Reinforcement at Potential Hinging Region
72 ACI 318, Overview of SMF: Potential Hinge Region
For columns supporting stiff members such as walls, hoops are required over full height of column if
For shear strength- same rules as beams (concrete shear strength is neglected if axial load is low and earthquake shear is high)
Lap splices are not allowed in potential plastic hinge regions
73 Splice in Hinge Region
74 ACI 318, Overview of SMF: Potential Hinge Region
75 Topic Overview
Concrete and reinforcement behavior
Reference standards
Requirements by Seismic Design Category
Moment resisting frames
Shear walls
Other topics
Design Examples
76 Performance Objectives
Special R/C shear walls
Resist axial forces, flexure and shear
Boundary members
Where compression stress/strain is large, maintain capacity
Development of rebar in panel
Ductile coupling beams
Ordinary R/C shear walls
No seismic requirements, Ch. 21 does not apply
77 Design Philosophy
Flexural yielding will occur in predetermined flexural hinging regions
Brittle failure mechanisms will be precluded
Diagonal tension
Sliding hinges
Local buckling
Shear failures in coupling beams
78 ACI 318, Overview of Special Walls: General Requirements
79 ACI 318, Overview of Special Walls: General Requirements
?? and ?t not less than 0.0025 unless
then per Sec.14.3
Spacing not to exceed 18 in.
Reinforcement contributing to Vn shall be continuous and distributed across the shear plane
80 ACI 318, Overview of Special Walls: General Requirements
Two curtains of reinforcing required if:
Design shear force determined from lateral load analysis
81 ACI 318, Overview of Special Walls: General Requirements
Shear strength:
Walls must have reinforcement in two orthogonal directions
82 ACI 318, Overview of Special Walls: General Requirements
For axial load and flexure, design like a column to determine axial load moment interaction
83 ACI 318, Overview of Special Walls: Boundary Elements
84 ACI 318: Overview of Special Walls
Boundary Elements
Two options for determining need for boundary elements
Strain-based: Determined using wall deflection and associated wall curvature
Stress-based: Determined using maximum extreme fiber compressive
85 ACI 318, Overview of Special Walls: Boundary ElementsStrain
Boundary elements are required if:
?u = Design displacement
c = Depth to neutral axis from strain
compatibility analysis with loads causing ?u
86 ACI 318-05, Overview of Walls: Boundary ElementsStrain
Where required, boundary elements must extend up the wall from the critical section a distance not less than the larger of:
?w or Mu/4Vu
87 ACI 318-05: Overview of Walls
Boundary ElementsStress
Boundary elements are required where the maximum extreme fiber compressive stress
calculated based on factored load effects, linear elastic concrete behavior and gross section properties, exceeds 0.2fc
Boundary element can be discontinued where the compressive stress is less than 0.15fc
88 ACI 318-05: Overview of Walls
Boundary ElementsDetailing
Boundary elements must extend horizontally not less than the larger of c/2 or c-0.1?w
In flanged walls, boundary element must include all of the effective flange width and at
least 12 in. of the web
Transverse reinforcement must extend into the foundation
89 ACI 318-05: Overview of Walls
Coupling Beams
Requirements based on aspect ratio and shear demand
90 Topic Overview
Concrete and reinforcement behavior
Reference standards
Requirements by Seismic Design Category
Moment resisting frames
Shear walls
Other topics
Design Examples
91 Members Not Part of LFRS
In frame members not designated as part of the lateral-force-resisting system in regions of high seismic risk:
Must be able to support gravity loads while subjected to the design displacement
Transverse reinforcement increases depending on: Forces induced by drift
Axial force in member
92 Diaphragms
Check:
Shear strength and reinforcement (min. slab reinf.)
Chords (boundary members)
- Force = M/d Reinforced for tension
(Usually dont require boundary members)
93 Struts and Trusses: Performance Objectives
All members have axial load (not flexure), so ductility is more difficult to achieve
Full length confinement
94 Precast Concrete: Performance Objectives
95
96
97
98
99
100
101
102
103
1 Strong connections
Configure system so that hinges occur in factory cast members away from field splices
2 Ductile connections
Inelastic action at field splice
Quality Assurance: Rebar Inspection
Special inspection
Rebar placement
Prestressing tendon placement, stressing, grouting
Concrete placement
Testing
Rebar (ratio of yield to ultimate)
Concrete
Topic Overview
Concrete and reinforcement behavior
Reference standards
Requirements by Seismic Design Category
Moment resisting frames
Shear walls
Other topics
Design Examples from FEMA P-751
Special Moment Frame Example
Located in Berkeley, California
12-story concrete building
N-S direction: SMF
E-W direction: dual system
Seismic Design Category D
Modal Analysis Procedure
Frame Elevations
Story Shears: E-W Loading
Seismic Analysis: Dual Systems
For dual systems, moment frame must be designed to resist at least 25% of design seismic forces (ASCE 7, Sec. 12.2.5.1)
Layout of Reinforcement
Design Strengths
Bending Moment Envelopes: Frame 1 Beams, 7th Floor
104
Beam Reinforcement: Longitudinal
Maximum negative moment,
Mu = 389 kip-ft at Column A
b = 24 d = 29.5 fc = 4 ksi fy = 60 ksi
Try 4 #8, As = 3.16 in2
? = 0.00446, 0.0033 < ? < 0.025 OK
105
?Mn = 406 kip-ft OK
Beam Reinforcement: Longitudinal (continued)
Positive Mu at face of column = 271 kip-ft
b = 44 in. (beam width plus span/12) Try 3 #8, As = 2.37 in2
? = 0.00335, 0.0033 < ? < 0.025 OK
?Mn = 311 kip-ft OK
Since nearly min ?, 3 #8 are continuous
Check: +Mn > -Mn/2 ==> 311 > 406/2 OK
Mn,min > Mn,max /4 ==> 311 > 406/4 OK
106
107
108
109
110
111
112
113
114
Beam Reinforcement: Layout
Determine Beam Design Shear
Beam Shear
Force
Beam Reinforcement: Transverse
Beam Reinforcement: Transverse
Check maximum spacing of hoops within plastic hinge length (2h)
d/4 = 7.4 in.
8db = 8.0 in.
24dh = 12.0 in.
12 in.
Therefore, 7.0 in. spacing at ends is adequate
At beam rebar splices, s = 4.0 in.
Joint Shear Force Joint Shear Force Joint Shear Force
Frame 1 Column Design
116
117
118
119
120
121
122
Design for strong column based on nominal beam moment strengths
Column Transverse Reinforcement
Column Transverse Reinforcement
Maximum spacing is smallest of:
h/4 = 30/4 = 6.5 in.
6db = 6*1.0 = 6.0 in. (#8 bars)
so calculated as follows:
for 12 #8 vertical bars and #4 hoops,
hx = 8.33 in. and so = 5.72 in.
Next, check confinement requirements
Column Transverse Reinforcement
Therefore, use #4 bar hoops with 4 legs
Ash = 0.80 in2
Determine Column Shear
Based on probable moment strength of columns
and can be limited by probable moment strength of beams
Column Shear Design
Column Shear Design
Assume 6 in. max hoop spacing at mid-height of column
Column Reinforcement
Confinement length, lo, greater of:
h = 30 in.
Hc/6 = (156-32)/6 = 20.7 in.
18 in.
Therefore, use 30 in.
123
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125
126
127
128
129
Intermediate Moment Frames
Beams
Columns
Shear Frame Example
Same building as moment frame example
12-story concrete building
N-S direction: SMF
E-W direction: dual system
Seismic Design Category D
Modal Analysis Procedure
Shear Wall
Story Shears: E-W Loading
Shear Wall Loading
At ground floor: shear and moment determined from the lateral analysis and axial load from gravity load run down.
All are factored forces.
Vu = 663 kips
Mu = 30,511 kip-ft
Pu,max = 5,425 kips
Pu,min = 2,413 kips
Shear Panel Reinforcement
Vu = 663 kips (below level 2)
fc = 5,000 psi, fy = 60 ksi
? = 2.0
? = 0.6 (per ACI 9.3.4(a))
Reqd rt = 0.0019
Min r? (and rt) = 0.0025
Use #5 @ 15 o.c. each face:
rt= 0.0026 and ?Vn = 768 kips
Axial-Flexural Design
At ground floor: shear and moment determined from the lateral analysis and axial load from gravity load run down.
All are factored forces.
Mu = 30,511 kip-ft
Pu,max = 5,425 kips
130
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134
135
136
137
138
u,max
Pu,min = 2,413 kips
Axial and Flexural Design
P-M interaction
Wall reinforcement: #5 @15 o.c. Boundary reinforcement: 12 #9 each end
Boundary Element Check
Use stress-based procedure (ACI 21.9.6.3).
Boundary Elements required if max stress > 0.2fc
Ground level axial load and moment are determined based on factored forces.
Boundary Element Length
Length = larger of c/2 or c-0.1Lw
From P-M interaction, max c = 75.3 in. So, c/2 = 37.7 and c-0.1Lw = 43.8 in
Since length > column dimension, either
Extend boundary into wall panel
Increase fc = reduce boundary element length
For this example, assume fc = 7,000 psi,
Then reqd boundary element length is 26.9 in.
Boundary Element Confinement
Transverse reinforcement in boundary elements is to be designed essentially like column transverse reinforcement.
Assume #5 ties and 4 in. spacing
Shear Wall Reinforcement
ACI 318, Overview of IMF:
Beam Longitudinal Reinforcement
ACI 318, Overview of IMF:
Beam Transverse Reinforcement
ACI 318, Overview of IMF: Beam Shear Strength
Two options:
Same as Special Moment Frames
Design load combinations with 2x earthquake shear
ACI 318, Overview of IMF:
Column Transverse Reinforcement
Hoops at both ends of column: spacing so over length lo
Outside length lo, transverse reinforcement per Ch. 7 & 11
Column shear strength reqts same as beams
139
140
Summary of Seismic Detailing for Frames
Questions
This topic is the seismic design of reinforced concrete structure. During this
presentation you will learn the basics of seismic design of reinforced concrete
buildings.
The examples in this topic draw heavily on the examples in the FEMA P-752 Design
Examples CD.
Reinforced Concrete -1
This slide provides the outline of this presentation.
The first part addresses general behavior of reinforced concrete both individual
members and systems, in particular as it relates to earthquake loading and ductility.
This section does not directly relate to the Provisions can be shortened or
eliminated based on the length or focus of the presentation.
The second and third parts cover the requirements for concrete structures based on
the Provisions, ASCE 7, and primarily ACI 318-08.
The fourth part covers the requirements for concrete moment frames, especially
Special moment frames, and includes the ACI 318 requirements use the concrete
example problem to illustrate the concepts.
The fifth part covers the requirements for concrete shear walls, in particular special
shear walls. The concrete example problem is again used to illustrate the main
design features.
The final section addresses other design and construction topics including
diaphragms and quality assurance.
Reinforced Concrete -2
This slide provides the outline of this presentation.
The first part addresses general behavior of reinforced concrete both individual
members and systems, in particular as it relates to earthquake loading and ductility.
This section does not directly relate to the Provisions can be shortened or
eliminated based on the length or focus of the presentation.
The second and third parts cover the requirements for concrete structures based on
the Provisions, ASCE 7, and primarily ACI 318-08.
The fourth part covers the requirements for concrete moment frames, especially
Special moment frames, and includes the ACI 318 requirements use the concrete
example problem to illustrate the concepts.
The fifth part covers the requirements for concrete shear walls, in particular special
shear walls. The concrete example problem is again used to illustrate the main
design features.
The final section addresses other design and construction topics including
diaphragms and quality assurance.
Reinforced Concrete -3
This slide presents stress-strain diagrams for unreinforced, unconfined concrete in
compression. Behavior is relatively linear up to about one-half of the maximum
compressive stress. Concrete exhibits no precise yield point. Strain at maximum
strength is close to 0.002 regardless of maximum stress. Lower strength concrete
can have strains at crushing that exceed 0.004, however a typical design value is
0.003 at crushing. Stronger concretes are more brittle.
Reinforced Concrete -4
Confining reinforcing can improve concrete behavior in two ways. First it can
enhance strength by restraining lateral strains. Second it can increase the usable
concrete compressive strain well beyond the typical value of 0.003.
This slide shows confinement in practical structural sections. Confinement is
typically provided by spirals, circular hoops, or square hoops. The hatched areas in
the figures may spall. Confining steel is in tension (hoop stress effect) because,
due to Poissons effect, as the concrete is compressed in one direction, it expands
in the orthogonal directions. This is shown in the center illustration. Note that
hoops are not as efficient as spirals in confining concrete because the sides of the
hoop can flex outward as the confined concrete expands outward. For this reason,
cross ties are usually require at hoops.
Reinforced Concrete -5
This slide shows confinement for a square column, which can be provided by
transverse and longitudinal bars. The hatched areas may spall.
Reinforced Concrete -6
This slide shows the benefits of confinement on concrete behavior. Presented are
stress-strain diagrams for confined concrete in compression. The specimens were
6 in. by 12 in. cylinders. Confinement was provided by spiral reinforcement.
Reducing spiral pitch (or hoop spacing) increases maximum concrete stress and
strain capacity (ductility).
Reinforced Concrete -7
This slide shows the idealized stress-strain behavior of confined concrete proposed
by Kent and Park. Note that the model reflects the additional strain, but not the
additional strength, provided by the confinement. Another model that reflects both
strength and strain gain is Scott, Park, and Priestley. This type of model can be
used with the strain compatability method to predict the behavior of confined
reinforced concrete.
Reinforced Concrete -8
This slide shows typical stress-strain behavior of common grades of reinforcing
steel. The most commonly used is Grade 60 which shows a distinct yield plateau
and strain hardening at between 0.5% and 1% elongation. For common analysis of
reinforced concrete behavior, strain hardening is ignored. For seismic design, it is
important that the actual yield strain of the steel is not significantly higher than the
value used in design.
Reinforced Concrete -9
This slide shows stages of behavior of a reinforced concrete beam. At low loads the
section is uncracked and an analysis using uncracked-transformed section
properties can be used to predict behavior. After the concrete cracks, the concrete
on the tension side of the beam is neglected, and a cracked-transformed section
analysis can be used to predict behavior. However, this method is only valid as long
as both the steel and the concrete stress-strain behaviors are linear. Concrete can
be assumed to have a linear stress-strain behavior up to approximately 50% of
maximum concrete stress (fc).
After the concrete stress exceeds about 50%fc, a strain compatibility approach can
be used, using a realistic concrete stress-strain model. After the steel yields, there
is typically an extended plateau in which the displacement increases significantly
with very little increase in applied load. A commonly used indicator of member
ductility is the ratio of the displacement at ultimate to the displacement at first yield.
This is known at the displacement ductility, and for seismic design in particular,
bigger is better.
Reinforced Concrete -10
To characterize section behavior, moment-curvature (M-.) diagrams are often
employed. This slide shows the type of strain compatibility approach that would be
used to locate points on the curve up until first yield of the steel. To locate a point,
first a concrete strain is selected. Then an iterative method is used in which the
depth to the neutral axis is assumed and modified until internal equilibrium is
achieved. The tension force is equal to the strain (based on the strain diagram with
the selected concrete strain and neutral axis depth) times the area and the modulus
of elasticity of the steel. The compression force is determined by integrating under
the stress-position curve from the neutral axis to the extreme compression fiber, and
multiplying by the width of the beam. The value of c is adjusted until C = T. Then
the curvature is calculated as the concrete strain divided by the neutral axis depth,
and the moment is the force (T or C) times the distance between the forces. This
can be repeated for several selected concrete strains to determine points on the M
.
diagram.
Reinforced Concrete -11
After yield but before the onset of strain hardening, the same method as presented
on the previous slide can be used; however, the force in the steel will be Asfy. This
method can be used for points up to the concrete crushing strain of 0.003. The
Whitney stress block method is a good method to calculate the final point on the
moment curvature diagram, but cannot be used for other points. Typically strain
hardening is not considered in design.
Reinforced Concrete -12
This slide shows moment-curvature diagrams for a rectangular section in flexure.
Strain hardening in the tension steel increases the final strength. A concrete strain
of 0.003 corresponds to maximum strength.
Reinforced Concrete -13
This slide shows moment-curvature diagrams for various amounts of tension
reinforcement. As the steel percentage increases, the moment capacity also
increases, but the curvature at ultimate moment capacity is decreased (less
ductility). Ductile behavior is very desirable in seismic force resisting systems. A
common measure of ductility is the ratio of curvature at first yield to curvature at
ultimate. This is known as curvature ductility.
Reinforced Concrete -14
This slide shows moment-curvature diagrams for various amounts of tension and
compression reinforcement. An increase in the compression reinforcement ratio
only slightly increases moment capacity but significantly increases curvature at
ultimate moment capacity (more ductility). This is because when the tension force
does not change (.
is constant) and neither does the compression force. With
larger amounts of compression reinforcement the steel carries more of the
compression, so the concrete carries less. This means the depth to the neutral axis
is more shallow, so the curvature at ultimate (0.003/c) is larger. However, since C
and T do not change and there is only a slight increase in the moment arm, the
moment capacity only increases slightly. (Note: Curve 7 stops at about 0.025; Curve
6 continues off the graph.)
Reinforced Concrete -15
The presence of confining reinforcement can significantly increase the maximum
achievable curvature. After the strain on the compression face exceeds 0.003, the
cover over the confining steel will spall, however the concrete within the core will
remain intact. A model such as the Kent and Park model presented earlier can be
used with the strain compatibility method to calculate moments and corresponding
curvatures.
Reinforced Concrete -16
This slide presents the results of the analysis of a beam, whose dimensions and
reinforcing details are given on the slide. As you can see, the addition of the
confining reinforcing increases the usable curvature from just under 500 microstrain
per inch to just over 1600. The Scott, Park, and Preistley model was used to model
the behavior of the confined concrete. This model accounts for the increase in
concrete compressive strength. In addition the compression steel was able to yield,
and strain hardening was considered in the tension steel. These three factors
combined to result in an increase in moment capacity from the confining steel, even
though the cover concrete was lost.
Reinforced Concrete -17
This slide shows how spreading plasticity can significantly increase plastic rotation
and displacements. The curvature diagram shows a region of very high curvatures
(beyond the yield curvature, .y) at maximum moment and elastic response in other
regions. The region of curvatures past yield curvature is known as the plastic hinge
region. The irregular curvature on the actual curve is due to cracking.
The plastic rotation and the tip displacement can be calculated from the actual
curvature diagram, or from the idealized curvature diagram. The idealized diagram
is based on a bi-linear approximation of the moment-curvature diagram and an
assumed length of the plastic hinge, lp.
Reinforced Concrete -18
The previous discussion presented three strategies for improving ductility. These
are summarized in this slide.
Reinforced Concrete -19
Confining reinforcing also has other useful functions that are presented in this slide.
Reinforced Concrete -20
With an understanding of reinforced concrete member behavior, reinforced concrete
systems can be designed to ensure acceptable behavior in a seismic event. We will
now discuss desirable system behaviors.
The goal in design of structural frames is to size and reinforce members such that
when subjected to large lateral displacements the hinges form in the beams
adjacent to the columns, but the columns remain relatively undamaged. This is
known as the strong column-weak beam approach that is illustrated in the right
frame in this slide. A weak column-strong beam design can result in the
undesirable story mechanism, also known as a soft story, that is shown in the left
illustration.
Reinforced Concrete -21
This slide illustrates a story mechanism.
Reinforced Concrete -22
This figure shows types of failures in shear walls. The left figure shows a flexural
failure with a plastic hinge zone at the base of the wall. The second figure shows
that severe cracking necessitates that web reinforcement carries the horizontal
shear force. The last two figures show types of sliding failures: sliding along full
depth flexural cracks or along construction joints. The most desirable is the flexural
failure with other modes precluded. With proper detailing, the wall can exhibit good
strength and ductility without excessive drift or collapse.
Reinforced Concrete -23
In strong column-weak beam design, undesirable failures in the columns must be
precluded through proper design and detailing. This slide presents the P-M curve
on the left and the P-curvature curve on the right. Note that the presence of large
axial loads reduces the curvature at ultimate. Axial loads above the balanced point
reduce ductility of beam-columns since the reinforcing steel on the tension side of
the column never yields. Confinement reinforcement improves axial ductility, but
this plot shows curvature ductility, which is more important in frames. The strong
column-weak beam design approach ensures that failure will initiate in ductile
beams rather than in brittle columns.
Reinforced Concrete -24
The strength of an unconfined concrete column is the gross area times the
unconfined compressive strength. After the concrete outside the spiral, hoops or
ties has spalled, the strength of the column is the core area times the enhanced
compressive strength. Work done in the 1920s by Richart et al. indicated that
confined concrete strength is roughly the unconfined strength plus 4 times the
confining pressure, flat. The goal in designing the hoops is to ensure that the
strength after cover spalling is not less than the strength before spalling.
Reinforced Concrete -25
This photo shows a column with inadequate ties which provided almost no
confinement. Olive View Hospital after the 1971 San Fernando earthquake.
Reinforced Concrete -26
This slide shows a column with an adequate amount of spiral confinement. After
the cover spalled, the well confined core remains intact and able to carry axial
loads. Olive View Hospital after the 1971 San Fernando earthquake.
Reinforced Concrete -27
This type of hysteresis loop shows good performance of a column with generous
confinement reinforcement. The preferred type of hysteresis loop shows only small
degradation of moment strength with increased imposed drift. Also the loops remain
fat which indicates good energy dissipation.
Reinforced Concrete -28
To ensure strong column-weak beam behavior, shear failures of columns must also
be precluded. Shear is maximum in a column when the moments at each end are
at their maximum, also known as the probable moment. The moment capacity of a
column depends on the magnitude of the axial load. To avoid shear failures, the
design should focus on the axial load that produces the largest moment capacity.
The P-M interaction diagram shows this range of axial loads for an example column.
Reinforced Concrete -29
This photo shows a shear failure of a bridge pier after the 1971 San Fernando
earthquake.
Reinforced Concrete -30
Another location in frames where premature failures must be precluded is the beam-
column joints. This slide shows joint actions. The left figure shows forces
(stresses) imposed on a typical exterior joint, and the right shows cracks. Upon
reversal of direction, perpendicular cracks form. The anchorage of the
reinforcement can be compromised. The important aspects of joint design are
ensuring proper bar development and precluding shear failures in the joint. This
can be accomplished through proper detailing of hoop reinforcement and bar hooks.
Reinforced Concrete -31
This slide shows a typical hysteresis loop for a joint with hoops. The joint shows
good performance under repeated reversed loads.
Reinforced Concrete -32
This slide shows a typical hysteresis loop of a joint without confining hoops. Note
the rapid deterioration of the joint.
Reinforced Concrete -33
This photo is of a joint failure in shear (1971 San Fernando earthquake). Note that
there is NO shear reinforcement in the joint and the joint is too small. The joint can
no longer transmit moments.
Reinforced Concrete -34
Another type of failure which must be prevented in order to ensure ductile frame
behavior is the failure of the joint between the column and the footing. This slide
shows an anchorage failure of a bridge column (1971 San Fernando earthquake).
Reinforced Concrete -35
We will now review reinforced concrete behavior.
Concrete is strong in compression but brittle. Confinement improves compressive
ductility by limiting transverse expansion in the concrete. As the transverse steel
ties take the strain in tension, the concrete core maintains its integrity. Closely
spacing the ties will limit longitudinal bar buckling and thus contribute to improved
compressive ductility. Longitudinal steel provides flexural ductility at low
reinforcement ratios for a single overload. Transverse steel is needed to maintain
integrity of the concrete core (which carries compression and shear), and prevent
longitudinal bar buckling after the cover has spalled and crossing cracks form. A
relative balance of tension and compression steel aids flexural ductility. The amount
of longitudinal tension steel must be limited to insure a tension-type failure mode.
Reinforced Concrete -36
The level of damping in concrete structures depends on the amount of cracking. It
is important to avoid potential problems in concrete structures: Shear failures in
concrete are brittle and abrupt and must be avoided; repeated loadings degrade
strength and stiffness as concrete cracks and steel yields. Degradation can be
limited by assuring adequate hinge development.
Reinforced Concrete -37
This slide provides the outline of this presentation.
The first part addresses general behavior of reinforced concrete both individual
members and systems, in particular as it relates to earthquake loading and ductility.
This section does not directly relate to the Provisions can be shortened or
eliminated based on the length or focus of the presentation.
The second and third parts cover the requirements for concrete structures based on
the Provisions, ASCE 7, and primarily ACI 318-08.
The fourth part covers the requirements for concrete moment frames, especially
Special moment frames, and includes the ACI 318 requirements use the concrete
example problem to illustrate the concepts.
The fifth part covers the requirements for concrete shear walls, in particular special
shear walls. The concrete example problem is again used to illustrate the main
design features.
The final section addresses other design and construction topics including
diaphragms and quality assurance.
Reinforced Concrete -38
Slide shows photos of the covers of reference standards ASCE 7-05 and ACI 31808
Reinforced Concrete -39
Slide shows cover of FEMA P-750 and proposed modifications to ACI 318 Section
14.2.2.
Reinforced Concrete -40
The 2009 NEHRP Recommended Provisions uses ASCE 7-05 as its primary
reference standard for seismic loads and design criteria. ASCE 7-05 in turn
references ACI 318-08 for concrete structures. Required strength (demand) is
determined from ASCE 7 Chapter 12, and provided strength (capacity) is calculated
using ASCE 7 Section 14.2 which references ACI 318.
ASCE 7 makes modifications to ACI 318, and the Provisions makes modifications to
ASCE 7 including some of the ASCE 7 modifications to ACI 318. Therefore, the
Provisions and ASCE 7 modifications to ACI 318 need to be considered.
Reinforced Concrete -41
This slide provides summary of the scope of the two main reference standards
Reinforced Concrete -42
The two common seismic-force-resisting systems using reinforced concrete are
moment frames and shear walls. A combination of shear walls and moment frames
can be considered a dual system when certain criteria are met.
ASCE 7 Section 12.2 presents design coefficients and system limitations for various
Seismic Design Categories. Precast walls can be used, however they will not be
addressed in detail in this session.
The system classifications relate to detailing requirements and associated the
ductility of the structural systems. The system ductility relates to the basic
reinforced concrete behavior covered previously.
Reinforced Concrete -43
ACI 318-08 Chapter 21 contains all the design provisions for earthquake-resistant
structures. Provisions and ASCE 7 Section 14.2 presents some modifications to
ACI 318 Chapter 21 as well as some additional reinforced concrete structure
requirements. This presentation will not cover the precast concrete provisions in
any detail.
Reinforced Concrete -44
This list includes the main modifications to ACI 318 that are contained in the
Provisions and ASCE 7. Most of these are not addressed in more detail in this
session.
Reinforced Concrete -45
This slide provides the outline of this presentation.
The first part addresses general behavior of reinforced concrete both individual
members and systems, in particular as it relates to earthquake loading and ductility.
This section does not directly relate to the Provisions can be shortened or
eliminated based on the length or focus of the presentation.
The second and third parts cover the requirements for concrete structures based on
the Provisions, ASCE 7, and primarily ACI 318-08.
The fourth part covers the requirements for concrete moment frames, especially
Special moment frames, and includes the ACI 318 requirements use the concrete
example problem to illustrate the concepts.
The fifth part covers the requirements for concrete shear walls, in particular special
shear walls. The concrete example problem is again used to illustrate the main
design features.
The final section addresses other design and construction topics including
diaphragms and quality assurance.
Reinforced Concrete -46
This slide presents the design coefficients presented ASCE 7-05 Table 12.2-1.
These tables also present system limitations and height limits by Seismic Design
Category (not shown in slides).
Reinforced Concrete -47
This slide presents the coefficients for shear walls that are part of a bearing wall
system.
Reinforced Concrete -48
This slide presents the coefficients for shear walls that are part of a building frame
system.
Reinforced Concrete -49
This slide presents the coefficients for dual systems that include a special moment
resisting frame.
Reinforced Concrete -50
This slide illustrates some general requirements for concrete buildings based on
Seismic Design Category and independent of specific lateral force resisting system.
Consistent throughout the Provisions the design scope is more detailed for higher
Categories.
Reinforced Concrete -51
The Provisions define three types of frames: ordinary, intermediate, and special.
Ordinary moment frames have very few requirements in ACI 318 Chapter 21. For
the most part, they are designed in accordance with the non-seismic chapters of
ACI 318. Intermediate moment frames must meet requirements of ACI 318 section
21.3 which are more stringent detailing than for ordinary frames but less severe
than for special frames). The overall level of ductility is between Ordinary and
Special.
Special moment frames must meet detailed requirements contained in various
sections of ACI 318, Chapter 21, including detailing to ensure ductility, stability, and
minimum degradation of strength during cyclic loading. A review of ASCE 7 Table
21.2-1 (excerpts shown on the previous slides) shows that the values of R and Cd
reflect the expected behavior of the various types of moment frames. The Seismic
Design Category (SDC) dictates what type of frame may be used. In SDC B,
ordinary frames may be used. Intermediate frames are required (at a minimum) in
SDC C (although a special frame may be more economical because the higher R
will mean lower design forces). For SDCs D, E and F, frames must be special.
There are exceptions to the limitations on type of frame, especially for nonbuilding
structures of limited height.
Reinforced Concrete -52
For reinforced concrete shear walls there are just two main types: Ordinary (not
Chapter 21) and Special (Chapter 21). Plain concrete walls, designed per Chapter
22, are permitted in SDC B for some circumstances.
Reinforced Concrete -53
Precast shear walls are also allowed to be part of the seismic force resisting
system. The intent for special precast walls is that they qualify for the same design
parameters as the special cast-in-place wall. Unlike cast-in-place concrete walls,
there is an Intermediate classification for precast concrete walls.
ACI 318-05 contains a section on special precast walls (Section 21.10); however,
the system is not presented in ASCE 7 Table 12.2-1. There is a large section in
Section 14.2 of the Provisions, that presents acceptance criteria for special precast
structural walls based on validation testing. This presentation does not include
detailed information on precast walls.
Reinforced Concrete -54
This slide provides the outline of this presentation.
The first part addresses general behavior of reinforced concrete both individual
members and systems, in particular as it relates to earthquake loading and ductility.
This section does not directly relate to the Provisions can be shortened or
eliminated based on the length or focus of the presentation.
The second and third parts cover the requirements for concrete structures based on
the Provisions, ASCE 7, and primarily ACI 318-08.
The fourth part covers the requirements for concrete moment frames, especially
Special moment frames, and includes the ACI 318 requirements use the concrete
example problem to illustrate the concepts.
The fifth part covers the requirements for concrete shear walls, in particular special
shear walls. The concrete example problem is again used to illustrate the main
design features.
The final section addresses other design and construction topics including
diaphragms and quality assurance.
Reinforced Concrete -55
The requirements of Special Moment Frames in ACI 318 Chapter 21 are intended to
ensure the performance objectives listed on this slide. The strong column-weak
beam design avoids forming a mechanism in a single story (the story mechanism
presented earlier). Adequate hinge development is needed for ductility and is
accomplished by the use of transverse reinforcement which confines the concrete
core and prevents rebar buckling. Shear strength must be adequate to avoid abrupt
failures in members and joints. Requirements for rebar anchorage and splicing
(such as 135 degree hooks) are intended to maintain the integrity of the design.
Reinforced Concrete -56
Intermediate frames have less ductility, with detailing requirements to prevent the
most significant types of failures, namely shear failures, and they requirements
provide a moderate level of ductility and toughness.
Ordinary moment frames have very few detailing requirements, only those
associated with minimal ductility.
Reinforced Concrete -57
This slide provides a summary of the design features of Special moment frames
that will be covered in this section.
Reinforced Concrete -58
As discussed previously, strong column-weak beam design is required for special
moment frames. This slide reiterates the advantages. For a system with weak
columns, a mechanism is created when the columns of only one story reach their
flexural capacities (less dissipation of seismic energy prior to collapse). For a
system with strong columns and weak beams, a mechanism is created when ALL
beams on ALL stories yield (much more seismic energy dissipated prior to collapse).
Reinforced Concrete -59
To ensure that the beams develop plastic hinges before the columns, the sum of the
flexural strengths of the columns at a joint must exceed 120% of the sum of the
flexural strengths of the beams. This requirement protects against premature
development of a story mechanism, but due to the realities of dynamic response, it
does not assure a full building mechanism.
Reinforced Concrete -60
It is also important in this type of system to ensure proper hinge development. The
hinges must be able to form and then undergo large rotations and load reversals
without significant reduction in strength. In this way, plasticity and hinging will be
able to spread throughout the frame. Tightly spaced hoops are required to ensure
proper hinge development and behavior. Some of the functions of the hoops are
presented in this slide.
Reinforced Concrete -61
This slide presents some of the mechanics of hinge development. Prior to spalling,
the familiar stress diagram is present, with tension in the bottom steel, compression
in a roughly parabolic distribution in the concrete, and some compressive stress in
the top steel. Upon spalling, the stress distribution changes, The compression
block of the concrete moves lower in the cross section, and the stresses in the
compression steel are greatly increased. To maintain section integrity, material
component failures must be avoided. Concrete crushing and compression bar
buckling can be prevented by transverse reinforcement. Closely spaced hoop steel
limits lateral strain in the concrete and allows greater useful strains in the concrete
and hence improved ductility. Proper spacing of hoops also prevents longitudinal
bar buckling.
Reinforced Concrete -62
Under reverse load applications, hinge development affects both the top and bottom
faces of beams. This leads to bidirectional cracking and spalling of cover on the top
and bottom of the beam.
Reinforced Concrete -63
This slide presents the beam longitudinal reinforcement requirements per ACI 318.
The reinforcement ratio limits insure a tension controlled failure mode in bending
and reduce congestion of reinforcing steel. Continuous bars in the top and bottom
are required due to reversal of seismic motions and variable live load. Splice
locations and transverse reinforcement are specified because lap splices are
unreliable and cover concrete will spall.
Reinforced Concrete -64
This slide shows additional beam longitudinal reinforcement requirements per ACI
318. Seismic hooks have special detailing requirements to ensure that the hoops
do not open after the cover spalls. The maximum hoop spacings ensure adequate
confinement of the concrete core and adequate lateral support of the compression
reinforcing bars. However, maximum spacing may be dictated by shear design. To
prevent longitudinal bar buckling, the requirements for tying compression reinforcing
steel also apply to the bars in the expected plastic hinge region (over a distance
equal to twice the beam depth from the face of the support).
Reinforced Concrete -65
This slide presents the beam shear strength requirements per ACI 318. Shear
demand is based on the maximum probable flexural strength of the beam. The
probable flexural strength is based on the assumption that the flexural reinforcement
will achieve a stress of 1.25 times yield. To determine the expected shear from
seismic effects, the probable moment strength is applied at each end of the beam
and the resulting shear is calculated. This shear demand is added to the demand
from gravity loads. For beams (small axial load), concrete shear strength is
neglected when the earthquake-induced shear force ((Mpr1+Mpr2)/.n) represents one-
half or more of the design shear strength of the beam.
Reinforced Concrete -66
The design shear for joints is determined from the maximum probable flexural
capacities of the beams framing into the joint and the shear in the columns. The
column shear is also based on the maximum probable flexural strength of the
beams. In this way, the joint shear is directly related to the amount of reinforcement
in the beams framing into the joints.
Reinforced Concrete -67
Joint shear strength is based on the area of the joint, which is usually the area of
the column. Nominal joint shear stress is a function of confinement. More
confinement implies higher permissible shear stress. The joint shear strength often
controls the sizes of the framing members. If additional joint shear strength is
required, usually the column size is increased. If beam depth is increased to reduce
joint shear, care must be taken to maintain the strong column-weak beam design.
Reinforced Concrete -68
This slide presents the column longitudinal reinforcement requirements per ACI 318.
The limits on reinforcement ratio provide a sizeable difference between cracking
and yielding moments and prevent steel congestion. When fulfilling the strong
column-weak beam rule, recognize that moment capacity varies with axial load.
Reinforced Concrete -69
This slide presents the column transverse reinforcement requirements per ACI 318.
The minima for the area of transverse reinforcement is based on providing adequate
confinement of the core concrete to ensure that the strength of the column after the
cover has spalled equals or exceeds the strength of the column prior to cover loss.
The second equations for the spiral reinforcement ratio or the area of hoops
typically govern for large columns.
Reinforced Concrete -70
Spacing of the transverse reinforcement (so) is limited to prevent longitudinal bar
buckling. The distance between the legs of rectangular hoops (hx) is limited
because the hoops try to become circular (bend outward due to lateral expansion of
confined concrete) after the concrete cover spalls.
Reinforced Concrete -71
This slide presents other requirements for columns per ACI 318. Columns under
discontinued stiff members tend to develop considerable inelastic response (thus
more transverse reinforcement is required). The shear design is similar to that for
beams with the demand calculated based on the maximum probable strengths of
the beams framing into the columns; shear strength of concrete is neglected if axial
load is low and earthquake-induced shear is more than 50% of the maximum
required shear strength within the plastic hinge region.
Reinforced Concrete -72
This slide shows a failure at the base of a column that had splices in the hinge
region. (Building C, Adapazari, Turkey, 1999 Izmit earthquake.)
Reinforced Concrete -73
This slide presents the definition of the potential hinge region, where the highest
level of confinement is required for columns per ACI 318. The hinge region is not to
be assumed less that the largest of the three values.
Reinforced Concrete -74
This slide provides the outline of this presentation.
The first part addresses general behavior of reinforced concrete both individual
members and systems, in particular as it relates to earthquake loading and ductility.
This section does not directly relate to the Provisions can be shortened or
eliminated based on the length or focus of the presentation.
The second and third parts cover the requirements for concrete structures based on
the Provisions, ASCE 7, and primarily ACI 318-08.
The fourth part covers the requirements for concrete moment frames, especially
Special moment frames, and includes the ACI 318 requirements use the concrete
example problem to illustrate the concepts.
The fifth part covers the requirements for concrete shear walls, in particular special
shear walls. The concrete example problem is again used to illustrate the main
design features.
The final section addresses other design and construction topics including
diaphragms and quality assurance.
Reinforced Concrete -75
Design of shear walls for seismic resistance includes designing to resist axial
forces, flexure, and shear. Special boundary confinement is required at the ends of
walls where the maximum compressive stress associated with flexural and axial
loads are high.
In additional to shear walls, ACI 318 provides detailing requirements for coupling
beams.
Since ACI 318 Chapter 21 does not have any seismic provisions for Ordinary shear
walls, they are not covered in this presentation.
Reinforced Concrete -76
The design philosophy for walls is to ensure a ductile, flexural failure mechanism
and preclude all brittle mechanisms.
Reinforced Concrete -77
This slide presents some of the ACI 318 notation for dimensions and reinforcing
ratios in special shear walls.
Reinforced Concrete -78
This slide presents some of the minimum reinforcing requirements for special shear
walls.
Reinforced Concrete -79
This slide presents more requirements for special shear walls.
Reinforced Concrete -80
The equation for shear strength of walls recognizes the higher shear strength of
walls with high shear-to-moment ratios. For stout walls, ..
shall not be less than .t.
Reinforced Concrete -81
To determine the required longitudinal reinforcement, the wall is treated like a
column. An interaction diagram can be developed for the selected reinforcing
layout, and checked against combinations of axial load and moment as determined
from analysis.
Reinforced Concrete -82
If there is a high compressive strains or stresses at the ends of the shear wall,
special boundary element detailing is required. A boundary element is a portion of
the wall which is well confined. Widening of the wall is not required, though it can
be beneficial, especially in reducing the length of the boundary element or reducing
the vertical extent of the boundary element. More on this later
.
Reinforced Concrete -83
This slide presents the two possible methods for checking if boundary elements are
required. There is a strain-based method and a stress-based method. Both are
described in the following slides.
Reinforced Concrete -84
This slide presents one of the two methods ACI 318 presents to check if boundary
elements are required. This method uses strains associated with shear wall
curvature to determine if boundary element confinement is required.
Reinforced Concrete -85
If the strain-based method is used to determine if a boundary element is required,
the method presented on this slide is used to determine at what height up the wall
the boundary element can be terminated.
Reinforced Concrete -86
This slide presents the second possible method for checking if boundary elements
are requiredthe stress-based method. This method has a different way to
determine at what point on the wall the boundary element can be discontinued.
Reinforced Concrete -87
Regardless of method used to determine where boundary elements are required,
the detailing is the same as indicated on this slide. The factor c is the maximum
depth to the neutral axis using any of the governing load combinations.
Reinforced Concrete -88
This slide illustrates the basic design of coupling beams in accordance with ACI
318. Beams with higher aspect rations can be designed as standard ductile
beams. However, if the aspect ratio is smaller and shear demand high, the beam
must be reinforced with diagonal bars.
Reinforced Concrete -89
This slide provides the outline of this presentation.
The first part addresses general behavior of reinforced concrete both individual
members and systems, in particular as it relates to earthquake loading and ductility.
This section does not directly relate to the Provisions can be shortened or
eliminated based on the length or focus of the presentation.
The second and third parts cover the requirements for concrete structures based on
the Provisions, ASCE 7, and primarily ACI 318-08.
The fourth part covers the requirements for concrete moment frames, especially
Special moment frames, and includes the ACI 318 requirements use the concrete
example problem to illustrate the concepts.
The fifth part covers the requirements for concrete shear walls, in particular special
shear walls. The concrete example problem is again used to illustrate the main
design features.
The final section addresses other design and construction topics including
diaphragms and quality assurance.
Reinforced Concrete -90
ACI 318 has provisions to ensure that gravity members can accommodate the
expected seismic drift while maintaining their ability to support the design gravity
loads.
Reinforced Concrete -91
This slide shows some aspects of diaphragm design. The slide shows where
collectors might be needed to transfer forces from a long diaphragm into a narrow
shear wall. The design load is to be from seismic analysis in accordance with the
design load combinations. Slab reinforcement is based on shear stress or slab
reinforcement minima (same as for slender structural walls). The chord (boundary
element) of a diaphragm is designed to resist tension and compression of M/d.
Diaphragms rarely require confined chords. There are also special considerations
for topped and untopped precast diaphragms.
Reinforced Concrete -92
Truss systems of reinforced concrete are rarely used. Ductility, usually developed in
flexure, is difficult to achieve. Every member in a truss is axially loaded; therefore,
every member is designed and reinforced as a column. Full height confinement is
used in all members. Anchorage is extremely important to assure adequate post
yield response.
Reinforced Concrete -93
Frames can be based on one of two basic modes of behavior in precast buildings:
Precast that emulates monolithic construction used for frames (strong
connections). For this type of system, field connections are made at points of low
stress, and the hinges will occur in factory cast members, not field splices.
Jointed precast with ductile connections. For this type of system, yielding occurs
in the field connections.
In the NEHRP Provisions, acceptance of special precast structural walls is based on
validation testing.
Reinforced Concrete -94
Quality assurance is covered in ASCE 7 Chapter 11A. However, this chapter is
oftne not adopted by the local building code, so the QA requirements are often
those contained in the model building code.
A quality assurance plan is generally required for most seismic force resisting
systems.
This slide contains a general list of the types of testing and inspection required for
concrete buildings.
Reinforced Concrete -95
This slide provides the outline of this presentation.
The first part addresses general behavior of reinforced concrete both individual
members and systems, in particular as it relates to earthquake loading and ductility.
This section does not directly relate to the Provisions can be shortened or
eliminated based on the length or focus of the presentation.
The second and third parts cover the requirements for concrete structures based on
the Provisions, ASCE 7, and primarily ACI 318-08.
The fourth part covers the requirements for concrete moment frames, especially
Special moment frames, and includes the ACI 318 requirements use the concrete
example problem to illustrate the concepts.
The fifth part covers the requirements for concrete shear walls, in particular special
shear walls. The concrete example problem is again used to illustrate the main
design features.
The final section addresses other design and construction topics including
diaphragms and quality assurance.
Reinforced Concrete -96
We will now work through a design example. This moment frame example is found
in Chapter 7 of the NEHRP Recommended Provisions: Design Examples (FEMA
P-751). In the North-South direction, the seismic force resisting system is a special
moment frame. In the East-West direction, it is a dual system with moment resisting
frames on Column Lines 1, 2, 7, and 8, and shear walls between Column Lines B
and C along Lines 3-6. Note that Column Lines 1 and 8 have 6 columns while
Column Lines 2 and 7 have only 4 columns. The example will focus on beams,
columns and joints in the frame on Column Line 1.
Reinforced Concrete -97
This slide shows the elevation views of the frames on Column Lines 2 and 3. Note
the shear wall on Column Lines 3 to 6.
The concrete used in the majority of the building is normal-weight concrete with fc =
5,000 psi. To perform the analysis, initial member sizes were estimated then
adjusted as the design process required.
Reinforced Concrete -98
This slide presents the story shears on Frames Lines 1, 2, and 3. All of the shear
wall lines (grid 3-6 are similar to grid 3). Note the locations where story shears are
negative for Frames 2 and 3. Also note that the frame line with the shear wall
attracts the greatest portion of the seismic shear.
Note also that the story shears are the greatest at Frame 1 at Level 7 due to the
interaction between the frames and walls. Therefore, this example focuses on the
elements at Level 7.
Reinforced Concrete -99
ASCE 7 Section 12.2.5.1 requires that for dual systems the moment frame without
walls must be capable of resisting at least 25% of the design forces. The building
was reanalyzed with the walls removed and 25% of the equivalent seismic forces
applied. This slide compares story shears from the original analysis with the 25%
rule. Note that this rule controls the design for the ground level frames.
Reinforced Concrete -100
The typical beams are 24 inches wide by 32 inches deep.
This slide shows the layout of reinforcement for beams intersecting at Column Line
4 for Frame 1. Note the different values of d for beams in each direction.
Reinforced Concrete -101
This slide reviews how strengths are calculated for various aspects of design.
Maximum probable strength is used when a higher strength than the design
strength causes more severe effects. Column strength is modified by the strong
column-weak beam rule.
Reinforced Concrete -102
This slide shows the bending moment envelopes for beams in Frame 1 at Level 7.
The structure and the moment envelopes are symmetric about the centerline.
The combinations are:
1.2D + 1.6L
1.2D + 1.0E + 0.5L
0.9D + 1.0E
With E defined as .QE ± 0.2SDSD with SDS=1.1 and .=1.0. QE is the effect from
horizontal seismic forces.
Reinforced Concrete -103
First the beam longitudinal (top) reinforcement is calculated. We will provide three
(must be at least two) continuous bars top and bottom. Additional top bars are
provided as necessary for moment capacity. The reinforcement ratio is checked
against the ACI 318 limits for maximum and minimum
Reinforced Concrete -104
Next the reinforcement for positive moment at the face of the column is determined.
Note that the calculated positive moment demand is greater than half of the
negative moment demand. The larger of these two values governs design. For
calculation of positive moment capacity the effective width of the beam, since the
compression block is within the slab, includes one twelfth of the span length. This is
from the effective flange width provisions of ACI 318 Section 8.10.3. In this case
the minimum reinforcement is adequate.
Reinforced Concrete -105
The other beams can be checked in a similar manner.
This slide presents the beam reinforcement layout for Frame 1,
Reinforced Concrete -106
Next we will determine the design shear forces for the beams. These shears are
based on the illustrated hinging mechanism in which the maximum probable
negative moment is developed at one end of the beam and the maximum probable
positive moment is developed at the other end. The shears from the probable
moments are then combined with the gravity shear to determine the total design
shear.
Reinforced Concrete -107
This slide shows the beam shear forces. The design shear is the gravity plus the
seismic shear. Seismic shear is computed based on the flexural strength (Mpr) of
the beams based on an assumed hinging pattern.
Reinforced Concrete -108
This slide presents the calculation of the beam transverse reinforcement. Note that
Vc is taken as 0. #4 hoops are selected for the calculations, then the maximum
spacing of hoops within the potential hinging region is determined as shown.
Reinforced Concrete -109
After calculating the required spacing to provide adequate shear strength, the
spacing is checked against the maximum allowable spacing as shown in this slide.
In this case the required spacing for shear strength governs.
Reinforced Concrete -110
The design shear for joints is determined from the maximum probable flexural
capacities of the beams framing into the joint and the shear in the columns. In this
way, the joint shear is directly related to the amount of reinforcement in the beams
framing into the joints. But how is the column shear computed in this limit state
analysis?
Reinforced Concrete -111
The column shear can be computed using a free-body diagram and the probable
moment strengths of the beams at the face of column.
Reinforced Concrete -112
Once the column shears are determined, the joint shear force and stress can be
calculated as shown in this slide. The joint shear force is based on the same
mechanism and moments shown on the previous slide. The joint area is the same
as the column area (30 in. x 30 in.). The computed joint shear strength is then
compared to the factored shear in the joint. If the joint shear strength were
computed as less than the factored demand, the area of flexural steel, the beam
depth, or the column size can be modified to remedy the problem.
Reinforced Concrete -113
Finally, we will consider the design of a representative column, in this case the
Frame 1 column on grid A just below the 7th floor. Recall that ACI considers a
member to be a column where the factored axial demand exceeds 0.1Agfc. The
column design is based on a P-M analysis and the sum of the column moment
capacities must exceed the beam moment capacities at each joint.
Reinforced Concrete -114
This slide shows the calculation of the column design moments from beam flexural
capacities and strong column-weak beam rule. This method assumes an inflection
point at midheight of the column which is reasonable in most cases for regular
frame layouts.
Reinforced Concrete -115
Next the necessary column transverse reinforcement to provide confinement of the
concrete core is calculated. The equation on the slide that results in the larger
amount of confining steel will govern.
Reinforced Concrete -116
This slide presents the rules to calculate maximum hoop spacing within the potential
hinge region.
Reinforced Concrete -117
For most columns in Special moment frames, 4 inch hoop spacing is a reasonable
assumption, so we start there.
Reinforced Concrete -118
The seismic shear in the columns can based on the probable flexural strength of the
columns themselves or by the probably flexural strength of the beams that frame
into the column at the top and the bottom.
Using the column moment strengths is conservative, but if the amount of shear
reinforcement is governed by the confinement requirements, there may be adequate
shear capacity for the conservative but more simple method.
If the probable moments in the beams are used, the column moments above and
below the joint are determined based on their relative flexibilities. Then the shear in
the column is calculated based on the moments at the top and the bottom of the
column and the column clear height.
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In this slide the shear demand in the column is calculated based on the column
moment strengths.
Note that since there is significant axial compression in the column, concrete shear
strength may be used.
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This slide shows the calculation of the concrete contribution to column shear
strength. Then the required shear strength to be provided by the steel is
determined. The shear strength provided by the hoops spaced at 6 inches in the
middle of the column (4 inch spacing is required spacing for confinement at the
column ends) is shown to be more than adequate. Therefore, the final hoop layout
within the plastic hinge lengths at the tops and bottoms of the columns is set.
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This slide shows the final column reinforcing layout. Outside of the plastic hinge
length, the spacing of the hoops can be increased to 6 inches.
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Next, the design and detailing requirements for Intermediate moment frames are
covered. While not addressed in this presentation, the Example Problems contains
the detailed design of the example building as an intermediate moment frame as
well as a special moment frame.
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The same example problem used to illustrate the moment frame design will now be
used to illustrate the concepts for Special shear walls. Recall that in the east-west
direction, the building is a dual system with special moment frames on grids 1, 2, 7
and 8 and special shear walls on grids 3-6.
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We will look at the wall at grid line 3 as shown in the left figure. The right side of the
slide shows the plan section at the shear wall. The columns at the ends of the wall
also serve as part of the north-south moment frame.
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This slide shows the story shears for East-West load application. Note that Frame 3
includes the shear wall. Typical for cantilevered shear wall systems, the maximum
shear and moment are at the base of the wall.
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This slide provides the design loads at the base of the wall on grid 3 The moment
and shear come from the lateral analysis and gravity load comes from the load rundown
and the worst case load combinations.
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First, the vertical and horizontal reinforcement required in the shear panel can be
calculated.. The lower phi factor for shear wall shear is used because we will not
provide enough shear reinforcement to enable the wall to develop its full flexural
strength without a shear failure. This is permitted by the Provisions however, it is
often preferable to ensure that the wall is flexure-controlled where practical. In
some cases that is not practical.
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The axial and flexural (P-M) analysis is done using the loads provided previously.
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With the boundary column reinforcement assumed and the shear panel
reinforcement selected, a column interaction curve can be generated and compared
against the factored combinations of axial load and moment (using appropriate phi
factors). In this case, the wall is more than adequate for the first two levels. The
design could be further optimized to reduce boundary column reinforcing
congestion, except that as noted previously, the column is part of the north-south
moment frames.
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We will check whether a boundary member is required based on the stress-based
procedure of ACI 318. The axial load and moment come from the lateral and gravity
load analysis of the building and the worst case load combination. The gross
section properties are calculated, using the cross-section shown previously. Since a
fairly large compressive stress is present, a boundary element is needed up thru the
8th floor.
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This slide illustrates the procedure for determining the extent of the boundary
element confinement. Since the length exceeds the column dimension, a higher
strength concrete will be used in order to avoid having to confine the shear wall
panel beyond the column.
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The confinement is designed essentially like column confinement. For a hoop
spacing of 4 in., 4 legs of #5 bar are required.
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This slide shows a summary of the reinforcement for shear wall boundary members
and panels.
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This slide presents the beam longitudinal reinforcement requirements per ACI 318.
Continuous bars in the top and bottom are required due to reversal of seismic
motions and variable live load. Unlike Special moment frames, there are no specific
requirements for reinforcing ratios or for splices.
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The hoop requirements for intermediate moment frame beams are similar to those
of special moment frame beams.
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For beam shear strength, the method for special moment frames can be used
(shear based on probable moment strength. Or, the design shear can be based on
the analysis using twice the earthquake shear in the load combinations.
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The spacing of column hoops at the ends of intermediate frames is similar to that of
special moment frames.
For shear design, columns are treated the same as intermediate moment frame
beams, namely that the design shear can be taken from the analysis using twice the
earthquake shear.
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This slide summarizes the differences in detailing requirements for the three types
of moment frames. Special moment frames require special attention to each of the
performance objectives. Intermediate frames have less strict requirements on all
counts. Ordinary frames have very few requirements beyond those of gravity
frames designed using ACI 318. Note that the detailing to avoid rebar congestion is
important in special moment frames (use scaled drawings of joints for this task).
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Slide to prompt questions from participants.
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