1. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
Seismic Design Chapter 1
General Requirements
Requirements
in ACI 318-08 Modifications in
By: Scope
Luis Enrique García
President American Concrete Institute – ACI – 2008-2009 Terminology
Partner Proyectos y Diseños Ltda. Consulting Engineers
Professor Universidad de los Andes
Bogotá, Colombia
R1.1.9 – Provisions for
R1.1.9 – Provisions for earthquake resistance
earthquake resistance
In this version of ACI 318 (2008), for the first
time, earthquake resistance requirements are
Commentary was expanded to: defined in function of the Seismic Design
Category — SDC required for the structure and
not directly associated with the seismic risk
zone.
Explain changes in terminology used
Simplify adoption and interaction of The minimum SDC to use is governed by the
ACI 318-08 with model codes and other legally adopted general building code of which
documents ACI 318 forms a part.
4
1
2. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
TABLE R1.1.9.1 — CORRELATION BETWEEN SEISMIC-RELATED
TERMINOLOGY IN MODEL CODES Chapter 2
Code, standard, or resource
document and edition
Level of seismic risk or assigned seismic
performance or design categories as
Notation and Definitions
defined in the Code
ACI 318-08; IBC 2000, 2003; 2006;
NFPA 5000, 2003, 2006; ASCE 7- SCD* SCS SCD There were important changes in
98, 7-02, 7-05; NEHRP 1997, 2000, A, B C D, E, F notation of the whole document and all
2003
individual Chapter notation was moved
BOCA National Building Code
to Chapter 2.
1993, 1996, 1999; Standard
SPC† SPC SPC
Building Code 1994, 1997, 1999;
A, B C D; E
ASCE 7-93, 7-95; NEHRP 1991,
7 93, 7 95;
1994
There are a few new definitions related
to Chapter 21. All definitions, old and
Uniform Building Code 1991, Seismic Zone Seismic Zone Seismic Zone new, were moved to Chapter 2.
1994, 1997 0, 1 2 3, 4
*SDC = Seismic Design Category as defined in code, standard, or resource document.
†SPC = Seismic Performance Category as defined in code, standard, or resource document
5
Chapter 21 Seismic Design Category and
Energy Dissipation Capacity
Earthquake-resistant
structures
SDC Denomination
Must comply with in
Seismic D i
S i i Design (Energy di i ti
(E dissipation
ACI 318-08
Category capacity)
Chapter 21 was reorganized in function of A Chapters 1 to 19 and 22
Seismic Design Categories (SDC) A, B, C,
and D, E, and F in incremental order from Ordinary
ordinary to special: B Chapters 1 to 19, 22,
and 21.2
Chapters 1 to 19, 22,
A → B → C → D, E, F C Intermediate and 21.3 y 21.4
Chapters 1 to 19, 22,
D, E, F Special And 21.5 to 21.13
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3. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
ACI 318-08 – Chapter 21
Earthquake-resistant structures 21.1 – General requirements
Content Scope
21.1 – General requirements
21.2
21 2 – Ordinary moment frames B
21.3 – Intermediate moment frames
C Chapter 21 contains provisions considered
21.4 – Intermediate precast structural walls
21.5 – Flexural members of special moment frames
to be the minimum requirements for a
21.6 – Special moment frame members subjected to bending and
cast-in-place or precast concrete
axial load structure capable of sustaining a series of
21.7 – Joints of special moment frames D
oscillations into the inelastic range of
21.8 – Special moment frames constructed using precast concrete response without critical deterioration in
21.9 – Special structural walls and coupling beams
E
g
strength.
21.10 – Special structural walls constructed using precast
concrete
21.11 – Structural diaphragms and trusses F Therefore, the objective is to provide energy
21.12 – Foundations
21.13 – Members not designated as part of the seismic-force-
dissipation capacity in the nonlinear
resisting system
range of response.
TABLE R21.1.1 — SECTIONS OF CHAPTER 21 TO BE SATISFIED IN TYPICAL APPLICATIONS
Component resisting Seismic Design Category (SDC)
Global Energy Dissipation Capacity
earthquake effect,
unless A B C D
(none) (21.1.1.4) (21.1.1.5) (21.1.1.6)
Force elastic
otherwise noted
Maximum elastic maximum elastic
Analysis and design Fe
21.1.2 21.1.2 21.1.2, 21.1.3 force demand displacement demand
requirements
Materials None None 21.1.4 21.1.7 nonlinear
21.5, 21.6,
Frame members 21.2 21.3
21.7, 21.8
Maximum nonlinear
Structural walls and Yield strength displacement demand
coupling beams
None None 21.9 Fy
Precast structural walls None 21.4 21.4,† 21.10
None
Structural diaphragms and
None None 21.11
trusses uy ue um Displacement
Foundations None None 21.12
Frame members not In several earthquake resistance Fe u
proportioned
to resist forces induced by
None None 21.13 regulations this is defined through R = = e
earthquake motions parameter R Fy uy
Anclajes None 21.1.8 21.1.8
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4. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
Elastic vs. Nonlinear Demand Current seismic design strategy
20 linear elastic
nonlinear Given an energy dissipation capacity for the structural
10 material and structural system, defined through an R
u
0 value depending of the detailing scheme the design
(cm) horizontal seismic force is obtained from:
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
-10
-20 time (s) Fe
0.8 Fy =
0.6
linear elastic R
0.4 nonlinear
force 0 2
0.2 and the maximum elastic force demand is in turn
0 obtained using Newton’s 2nd Law:
(1/W)
-0.2 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
-0.4
-0.6
Fe = m a s s × S a (T , ξ ) Acceleration response spectrum
from the general building code
-0.8 time (s)
What would happen if
energy dissipation
capacity is not
available?
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5. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
C.21.1 – General Requirements
Nonstructural wall
panel in contact
Compressive strength of concrete fc′ ≥ 21 MPa
with the structure column
Specified compressi e strength of light eight
compressive lightweight
Nonstructural wall concrete ≤ 35 MPa
panel separated h
from the structure For computing the amount of confinement
reinforcement fyt ≤ 700 MPa (= 100,000 psi = 7000
kgf/cm2)
ACI 318-08 requires (21.1.2) that interaction between structural and
Reinforcing steel must meet ASTM A706. If ASTM
nonstructural elements that may a ect t e response du g t e ea t qua e
o st uctu a e e e ts t at ay affect the espo se during the earthquake A615 is used, it must meet:
Must be taken into account. The actual yield strength based on mill tests does not
Rigid members assumed not to be a part of the seismic-force-resisting exceed fy by more than 125 MPa.
system are permitted provided their effect on the response of the system is The ratio of the actual tensile strength to the actual yield
considered and accommodated in the structural design. strength is not less than1.25
Consequences of failure of structural and nonstructural members that are
not a part of the seismic-force-resisting system shall be considered.
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6. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
Reinforcing steel 21.2 – Ordinary moment frames
σ
stress
MPa
actual tensile strength Corresponds to SDC B
σu Beams must have at least two continuous
longitudinal bars along both top and bottom
σy failure faces. These bars shall be developed at the
face of support. c1
c2
actual yield strength Columns having clear
height less than or equal to
E maximum elongation five times the dimension c1
1 yield elongation must be designed for shear in
accordance with 21.3.3.
(shear requirements for intermediate SDC C)
O ε
εy strain ε
max
21.3 - Intermediate moment frames 21.3 - Intermediate moment frames
Requirements for this Section are equivalent to the
rest of Chapter 21, but are less strict and have a Reinforcement details in a frame member
lesser scope.
p shall satisfy beam requirements if the
y q
factored axial compressive load, Pu , d
f d i l i l d does
Two alternatives are presented for shear design of not exceed Ag fc′ 10 .
beams and columns:
Obtain design shear forces as function of When Pu is greater reinforcing details must
nominal end moments as done for special meet column requirements.
elements, or
use twice the shear from analysis This is
analysis.
equivalent to using the following load When a slab-column system without beams
combinations: is part of the seismic-force-resisting
U = 1.2D + 1.0L + (1.0E)x2.0
system, reinforcement details in any span
resisting moments caused by E must
U = 0.9D + (1.0E)x2.0 satisfy 21.3.6.
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7. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
21.3 - Intermediate moment frames 21.3 - Intermediate moment frames
For beams:
For beams:
Moment strength must comply with:
g py At both ends of the beam, hoops shall be provided over
lengths not less than 2h measured from the face of the
supporting member toward midspan. The first hoop shall
− be located not more than 50 mm from the face of the
Mn −
Mn supporting member. Spacing of hoops shall not exceed the
1 smallest of d/4, 8db of the smaller longitudinal bar, 24db
Mn ≥ ⋅ ( Mn )max .face of hoop, or 300 mm. Stirrups shall be spaced not more
5
than d/2 throughout the length of the beam.
+ 1 −
Mn ≥ Mn 2h @d/2 2h
3
21.3 - Intermediate moment frames 21.3 - Intermediate moment frames
For columns
Two-way slabs without beams (slab-column frames)
At both ends of the column, hoops
shall be provided at spacing so over Reinforcement provided to resist Mslab shall be placed
a length 0 measured from the joint within th column strip.
ithi the l ti
face. Spacing so shall not exceed the
smallest of 1/2 of the smallest Not less than 50% of the reinforcement in the column
cross-sectional dimension of the strip at supports shall be placed within the effective
column, 8db of the smallest slab width defined by lines drawn parallel to the span at
1.5 slab depths from the column face .
longitudinal bar enclosed, 24db of
the hoop bar, or 300 mm. Outside
this length spacing must be the one Continuous bottom reinforcement in the column strip
shall be not less than 33% of the top reinforcement at
defined in Chapters 7 and 11.
11 the
th support in the column strip.
t i th l ti
Length 0 shall not be less than the
largest of the maximum cross- Not less than 25% of the top reinforcement at the
sectional dimension of the column;, support in the column strip shall be continuous
1/6 of the clear span of the column, throughout the span.
or 450 mm.
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8. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
21.3 - Intermediate moment frames 21.3 - Intermediate moment frames
Two-way slabs without beams (slab-column frames)
At the critical sections for punching shear, shear
caused by factored gravity loads shall not exceed,
0.4φVc where Vc must be calculated as defined in
Chapter 11 for prestressed and non prestressed
slabs.
This requirement may be waived if the slab
complies with 21.13.6
21.4 — Intermediate precast structural walls 21.5 — Flexural members of special
moment frames
Requirements of 21.4 apply to intermediate
precast structural walls forming part of the
t t t l ll f i t f th A i l force Pu must not exceed 0 10fc′ Ag
Axial f t t d 0.10
seismic-force resisting systems.
Clear span of element n must be larger
In connections between wall panels, or than 4d
between wall panels and the foundation,
yielding must be restricted to steel elements Ratio bw/h > 0.3
or reinforcement..
Width bw must comply with:
Elements of the connection that are not
designed to yield must develop at least 1.5Sy. bw > 250 mm
larger than the width of the supporting
element plus 3h/4 at each side
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9. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
21.5 — Flexural members of special 21.5 — Flexural members of special
moment frames moment frames
Longitudinal reinforcement
Steel ratio for negative and positive
reinforcement must not be less than:
fc′ 1.4
ρ≥ ≥
4 ⋅ fy fy
but:
ρ ≤ 0.025
At least two bars continuous top and bottom.
21.5 — Flexural members of special 21.5 — Flexural members of special
moment frames moment frames
Longitudinal reinforcement Longitudinal reinforcement
Moment strength at each section must be at least:
Lap splices are permitted if hoops are provided
−
Mn −
Mn throughout the splice length. Maximum hoop
spacing must not exceed d/4 or 100 mm.
Mn ≥ 0.25 ⋅ ( Mn )max .face No lap splices are permitted in joints or within 2h
of column face or where inelastic action is
expected.
t d
+ −
Mn ≥ 0.5Mn
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10. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
21.5 — Flexural members of special 21.5 — Flexural members of special
moment frames moment frames
Hoops must be provided:
Shear design:
ΔV
Δ e
50 mm 50 mm −
s ≤d/2 M pr n
+
M pr
(M )
+
pr
izq .
(
−
+ M pr ) der .
(M )
−
pr izq .
(
+
+ M pr ) der .
ΔVe = ΔVe =
n n
2h 2h
confinement Mpr computed using fypr = 1.25 fy and φ = 1.0
zones
21.5 — Flexural members of special
21.6 — Special moment frame members
moment frames
(Vu)vert. left (Vu)ver. right subjected to bending and axial load
Pu1 Wu Pu2
General
Vu(x)
(Vu)ver. left + ΔVe ⎡( V ) − P ⎤
⎢ u ver.izq. ( u ) ver.der. ∑ u ⎥ n
1 1
+ V
⎣ ⎦ Axial force greater than 0.10 ⋅ fc′ ⋅ Ag
(Vu)ver. left- ΔVe
x The least section dimension that passes
(Vu)vert. right - ΔVe through the centroid must be greater than
th h th t id tb t th
shear
envelope
300 mm.
(Vu)ver. right+ ΔVe
For design, Vc = 0 if ΔVe is more than 50% Ratio b/h > 0.4
of required shear strength, or axial force is less than 0.05f’cAg
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11. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
21.6 — Special moment frame members 21.6 — Special moment frame members
subjected to bending and axial load subjected to bending and axial load
Transverse reinforcement in confining zones must comply
g py
Column flexural strength must comply with:
with: Spiral columns: f′
ρ s = 0.12 ⋅ c
fyt
∑ Mnc ≥ 1.2∑ Mnb Columns with hoops:
Mnc Mnc Mnc 0.3 ⋅ s ⋅ bc ⋅ fc′ ⎡⎛ Ag ⎞ ⎤
Mnb Mnb Mnb Mnc Ash = ⋅ ⎢⎜ ⎟ − 1⎥
fyt ⎢⎝ Ach ⎠ ⎥
⎣ ⎦
Mnb Mnb Mnc Mnc Mnb Mnc Mnb Mnc Mnb
Mnc Mnc 0.09 ⋅ s ⋅ bc ⋅ fc′
(a) (b) (c) Ash =
fyt
21.6 — Special moment frame members 21.6 — Special moment frame members
subjected to bending and axial load subjected to bending and axial load
hx ≤ 350 mm Shear design Mpr
(M ) ( )
hx hx hx joint transverse
+ M pr
reinforcement as
i f t
required by 21.7
50 mm pr arriba abajo
0
Ve =
hx b
⎧b / 4
hn
⎪ Ve
confinement lap splices in s ≤ ⎨6d b long. hn
zones central zone ⎪s Mpr corresponds to the maximum moment
hc ⎩ 0
⎧h
strength for the axial load range on the
⎪ element (1.25fy and φ=1). Ve cannot be
≤ ⎨ hn 6 ⎧6d b long .
⎧ ⎛ 350 hx ⎞
350-h
0
⎪ 450 mm s≤⎨ less than the one obtained from analysis.
⎪100 + ⎜ ⎩ ⎩150 mm
⎪ ⎝ 3 ⎟ ⎠ 0
50 mm
s0 = ⎨ For design Vc = 0 if Ve is more than 50%
⎪ ≤ 150 mm joint transverse
of the required shear or the axial force
⎪ ≥ 100 mm
⎩
reinforcement as
required by 21.7 is less than 0.05f’cAg
Mpr
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12. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
21.7 — Joints of special moment frames 21.7 — Joints of special moment frames
Computation of the shear demand on the joint:
General requirements Ve-col
plane to evaluate M pr-c
shear Vu column
When computing shear strength within the joint in
Ts′ = 1.25fy As
′ Cc = Ts = 1.25fy As
special frames all longitudinal reinforcement must be
presumed to be stressed at 1.25fy.
Longitudinal reinforcement terminating at a joint must
Cc = Ts′ = 1.25fy As
′ ′ Ts = 1.25fy As
be extended to the far face of the column confined core
and anchored in tension. beam
When th beam l
Wh the b longitudinal reinforcement passes
it di l i f t Mpr-c Ve-col
through the joint , the column dimension parallel to the Beam in both sides: Beam in one side:
reinforcement cannot be less than 20db largest ⎧1.25fy ( As )viga − (Ve )col
longitudinal bar, for normal weight concrete and 26db Vu = 1.25fy ( As + As )viga − (Ve )col
′ ⎪
⎪
Vu ≥ ⎨
for lightweight concrete. ⎪
⎪1.25fy ( As )viga − (Ve )col
⎩
′
21.7 — Joints of special moment frames 21.7 — Joints of special moment frames
Definition of Aj
Shear strength
Joints confined in all four faces
φ ⋅ Vn = φ ⋅ 1.70 ⋅ fc′ ⋅ A j
Joints confined in three faces or in opposite faces h
Aj
bw
φ ⋅ Vn = φ ⋅ 1.25 ⋅ fc′ ⋅ A j bw
Other joints
h
Aj
φ ⋅ Vn = φ ⋅ 1.00 ⋅ fc′ ⋅ A j bw
x
⎧ bw + 2 x
≤⎨
⎩ bw + h
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13. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
21.7 — Joints of special moment frames 21.8 — Special moment frames
constructed using precast concrete
Development for hooks embedded in the The requirements of 21.8 apply for special
q pp y p
confined core moment frames built using precast
critical
concrete forming part of the seismic-force-
section resistant system.
dh The detailing provisions in 21.8.2 and
21.8.3 are intended to produce frames that
fy ⋅ d b db
respond to design displacements
dh = esse t a y e o o t c special o e t
essentially like monolithic spec a moment
5.4 fc′ frames.
The provisions of 21.8.4 indicate that when
not satisfying 21.8.2 or 21.8.3 they must
satisfy the requirements of ACI 374.1
21.8 — Special moment frames 21.9 — Special structural walls
constructed using precast concrete and coupling beams
Special precast moment frames with ductile Terminology
connections must comply with all
ti t l ith ll
requirements for special cast-in-place frames
and Vn should not be less than 2Ve.
h
Special precast moment frames with strong
connections are intended to experience
flexural yielding outside the connections
connections.
hw
These requirements are applicable
independently of any of these two situations. w
Vu
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14. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
21.9 — Special structural walls and 21.9 — Special structural walls
coupling beams – General requirements and coupling beams
Cover Flexure design
20 mm
Design for flexure and flexure and axial load for
structural walls must be performed using the
requirements of Chapter 10.
Maximum s h
reinforcement spacing s
s
s
Concrete and developed longitudinal reinforcement
within effective flange widths boundary elements,
widths, elements
s ≤ 3h and the wall web shall be considered effective.
s ≤ 450 mm
s The effects of openings shall be considered.
s
21.9 - Special structural walls and 21.9 - Special structural walls and
coupling beams coupling beams
Flexure design 21.9.2
21 9 2 – Reinforcement
Unless a more detailed analysis is performed, The distributed web reinforcement ratios, ρt
effective flange widths of flanged sections ( I, L, C and ρ , for structural walls shall not be less
or T) may be supposed to extend from the face of than 0.0025, except that if Vu does not exceed
the web a distance equal to the smaller of: 0.083A cv λ fc′ (MPa) = 0.27A cv λ fc′ (kgf/cm2),
ρt and ρ , may be reduced to the values given
(a) 1/2 the distance to an adjacent wall web, in14.3.
and Separation of reinforcement must not exceed
(b) 25 percent of the total wall height. 450 mm
14
15. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
Minimum steel ratio
Difference between wall
14.3.2 – Minimum steel ratio of vertical reinforcement ρ
computed over gross section is:
and column
0.0012
0 0012 for
f deformed bars not larger than Nº 5 ( / ) ó 16M
f º (5/8”)
(16 mm), with fy not less than 420 MPa. 14.3.6 — Vertical reinforcement
0.0015 for other deformed bars. need not be enclosed by lateral ties
0.0012 for welded wire reinforcement with diameter not if vertical reinforcement area is not
larger than16 mm.
14.3.3 - Minimum ratio of horizontal reinforcement area to
greater than 0.01 times gross
gross concrete area, ρt: concrete area, or where vertical
0.0020 for deformed bars not larger than Nº 5 (5/8”) ó 16M reinforcement is not required as
(16 mm), with fy not less than 420 MPa.
compression reinforcement.
0.0025 for other deformed bars.
0.0020 for welded wire reinforcement with diameter not
larger than16 mm.
21.9 - Special structural walls and 21.9 - Special structural walls and
coupling beams coupling beams
Nominal shear st e gt must not exceed:
o a s ea strength ust ot e ceed
At least two curtains of reinforcement
l tt t i f i f t
Vn = Acv ⎡α c λ fc′ + ρ n fy ⎤
⎣ ⎦
must be used in a wall if Vu exceeds
αc
0.17λ A cv fc′ (MPa) = 0.53λ A cv fc′ where αc is:
0.25
0.17
(kgf/cm2)
hw
0 0.5 1.0 1.5 2.0 2.5 w
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16. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
Wall boundary elements Displacement-based boundary element
Boundary elements must be placed at edges and
procedure in ACI 318 (21.9.6.2)
around openings when inelastic response is This procedure is based on the compressive
expected.
expected ACI 318-08 gives two alternatives to strain demand at edges of wall when the wall is
define if boundary elements are needed: deformed under the maximum expected lateral
1) Section 21.9.6.2 presents a displacement- displacement caused by the design earthquake
based procedure. Boundary elements are ground motion.
needed or not depending on the compressive Section 21.9.6.2 is based on the assumption that
strain at the edge of wall caused by the inelastic response of the wall is dominated by
seismic lateral deflection, or flexural action at a critical, yielding section.
2) Section 21.9.6.3 requires boundary elements The wall should be proportioned so that the
when the compressive stress at the edge of critical section occurs at the base of the wall and
wall caused by the seismic forces exceeds a is applicable only to walls continuous from base
threshold value. to top of the structure.
Displacement-based boundary element Nonlinear response of a wall
procedure in ACI 318 (21.9.6.2)
P δ
The wall should have a single critical
section under flexure and axial load at the
base of the wall.
The zones of the wall in compression must
be provided with specially reinforced
boundary elements when the depth of the θ p
neutral axis at nominal strength, c, is greater
than:
c≥ w and δu Plastification
≥ 0.007 p length
⎛ δu ⎞ hw
600 ⋅ ⎜ ⎟
0 0
Wall Mu My Mcr φu φ y φcr
⎝ hw ⎠ section Moment Curvature
16
17. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
Nonlinear response of wall Nonlinear wall deflection
Using Moment-area theorems it is possible to show that the Curvature Deflection Nonlinear Nonlinear
lateral deflection caused by curvature up to yield (green at yield at yield curvature deflection
(δu−δy)
w
zone) is: δy
b
hw
and the additional deflection caused by nonlinear
rotation (orange zone) is:
p θp
φy (φu − φy)
The total deflection is:
Total lateral deflection is then: p
φ a
(φu− φy) φy We can solve for the ultimate curvature
demand and obtain:
φu
Moment-curvature diagram for wall section What happens at section?
M Ultimate curvature
demand
Mn At level of εcu
displacement
φu
demand
Strain
At level of εc = 0.003
nominal εs > εy φn
strength c
εc < 0.003
εs = εy φy
At level of cy
Mcr yield in
tension of
extreme h
0 φ reinforcement
φcr φy φn φu w
17
18. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
Equation (21-8) deduction Equation (21-8) deduction
The rotation at the plastic hinge when the displacement
The concrete strain at the extreme fiber in compression
demand (δu) takes place is:
at ultimate is:
We can then obtain the strain at ultimate for the
With a plastic hinge length equal to half the wall horizontal displacement demand:
length:
and
Then the curvature at the wall base when the displacement
demand occurs is:
The value of c for a ultimate strain of εcu = 0.003 is:
Equation (21-8) deduction Need for boundary elements in
If a 600 value parameter is used instead of 666 in last equation displacement-based procedure
ε ε
and it is solved for cu a value of cu = 0.0033 is obtained,
If equation (21-8) indicates that the value
which in turn leads to the following equation:
of c is exceeded this is a symptom that
exceeded,
strains greater than εcu = 0.0033 must be
expected and the need to confine the
edge of the wall is warranted in order to
If the maximum strain at the extreme compression fiber exceeds prevent spalling of the concrete there.
εcu = 0.0033 then the value of c obtained from last equation
would be exceeded. Thus the form ACI 318 presents it:
exceeded
In that case ACI 318 prescribes the same
If c is greater than the value obtained type and amount of confining transverse
boundary elements must be placed reinforcement that for columns.
along the length where it is exceeded and
a little more.
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19. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
Boundary elements Displacement-based boundary element
displacement-base procedure procedure in ACI 318 (21.9.6.32
Boundary elements must be placed
Mn from the critical section up for a
εcu distance not less than the larger of w o
εs 0.003
Mu/(4Vu).
The evaluation is performed for the wall
c when subjected to the nonlinear
Region where horizontal design displacements
boundary corresponding to the design
elements must
be provided
earthquake.
The value of δu corresponds to the
nonlinear roof horizontal displacement.
Stress-based boundary element
procedure in ACI 318 (21.9.6.3)
Stress-based boundary
Boundary elements must be provided at edges element procedure in
and around openings of walls when the maximum
p g ACI 318 (21 9 6 3)
(21.9.6.3) Pu
stress at the extreme fiber in compression
caused by factored loads that include seismic Mu
effects exceeds 0.2 fc′ unless that whole wall is Pu Mu
confined as a column. Ptu =
Pu
−
Ag (
Mu
− 300 mm )
≤0 Pcu = +
2 ( w − 300 mm )
w
Pu M u ⋅ w
fcu = + > 0.2 ⋅ fc′ This procedure had been part of ACI 318 since
Ag Iw ⋅ 2 the 1971 version.
version
In the 1999 version of 318 a modification was
The boundary elements can be discontinued introduced in which the need to resist all flexural
when the compression stress is less than 0.15 fc′ forces from seismic effects with just the
boundary elements was suppressed.
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20. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
21.9 - Special structural walls and
Old (pre-1999) procedure coupling beams
Boundary elements – Both procedures
Boundary elements w
resisting all flexural
i ti ll fl l When boundary elements are needed (under any of the two
procedures) these boundary elements must extend
effect that include horizontally from the maximum compression fiber a
heb
seismic forces distance equal to the greater of : c-0.1 w or c/2.
In section with flanges the boundary element must include
Pu the effective flange width and must extend at least 300 mm
into the web.
Transverse reinforcement must be that required for column,
Mu but there is no need to comply with equation 21-3.
py q
P Mu Pu Mu
Ptu = u − ≤0 Pcu = + Special transverse reinforcement in the boundary element
Ag ( 2 ( − heb )
w − h eb ) w must extend into the foundation element supporting the
wall.
φ ⋅ P0n = φ ⋅ [0.85 ⋅ fc′ ⋅ (A g − Ast ) + A st ⋅ f y ] Wall horizontal transverse reinforcement must be anchored
φ ⋅ Ptn = φ ⋅ A st ⋅ f y into the confined boundary element core.
φ ⋅ Pn(max) ≤ 0.80 ⋅ φ ⋅ P0n
21.9 - Special structural walls and
coupling beams Coupling beams
In ACI 318-08, there are modifications in
the requirements for coupling beams in
walls.
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21. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
21.10 — Special structural walls
constructed using precast concrete
Scope— These requirements apply to special
structural walls constructed using precast
t t l ll t t d i t
concrete forming part of the seismic-force-
resisting system.
Special structural walls constructed using
precast concrete shall satisfy all requirements
of special cast-in-place structural walls plus
those of section 21.10.
Special structural walls constructed using
precast concrete and unbonded post-
tensioning tendons and not satisfying the
requirements of 21.10.2 are permitted provided
they satisfy the requirements of ACI ITG-5.1.
21.11 — Structural diaphragms and trusses 21.11 — Structural diaphragms and trusses
This section contains:
prescribed
horizontal Requirements for slabs-on-grade , floor and roof slabs
forces when they are part of the seismic-force-resisting system
must comply with this section.
Minimum thickness for diaphragms are given.
Gives minimum reinforcement for diaphragms.
floor Indicates shear strength for these elements
diaphragm
Defines when boundary elements must be used in
diaphragms.
Includes requirements for construction joints within the
diaphragm.
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22. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
21.12 — Foundations 21.13 — Members not designated as part of
the seismic-force-resisting system
This section contains:
This section is a response to the extended practice by
21.12.1 — Scope - Foundations resisting earthquake structural designers of designating arbitrarily some of the
induced forces or transferring earthquake-induced
i d df f i h k i d d structural elements as being parte of the seismic-force-
forces between structure and ground. resisting system and part not. Northridge Earthquake
21.12.2 — Footings, foundation mats, and pile caps – affecting the City of Los Angeles in 1994 pointed out great
Gives requirements for the anchoring of reinforcement deficiencies in this practice. In ACI 318-95 this section was
in vertical elements of the seismic-force-resisting totally revised and it was updated in 1999, 2002, 2005 , and
system to these foundation elements. now in 2008.
21.12.3 — Grade beams and slabs-on-ground – Sets
minimum dimension s and minimum reinforcement for
u d e so a d u e o ce e t o In essence it is a call to the designer to check the
these elements, deformation levels that so called “non participating”
21.12.4 — Piles, piers, and caissons – Indicates the type elements are subjected and the minimum reinforcement
of effects to take into account in design and the they should comply with.
minimum reinforcement allowable for these elements.
21.13 — Members not designated as part of 21.13 — Members not designated as part of
the seismic-force-resisting system the seismic-force-resisting system
This Section contains two procedures to check non-
p
participating elements that are not part of the seismic-
This section includes new requirements for slab-
column frames that are not part of the seismic-
force-resisting system: force-resisting system.
• When the forces induced by the design displacement Slab-column frames have shown repeatedly their
combined with the gravity forces do not exceed the vulnerability under seismic demands. This
design strength of the elements, this section indicates vulnerability is specially associated with the
the minimum reinforcement to use. punching shear strength of the slab-column joint.
• If the strength is exceeded the sections of Chapter 21 The new procedure in ACI 318-08 (Section
that are mandatory for these elements are indicated. 21.13.6) indicates when shear reinforcement
must be provided in the slab-column joint as a
function of the story drift.
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23. ACI 318-08 - Seismic Requirements -- Luis E. Garcia
21.13 — Members not designated as part of 21.13 — Members not designated as part of
the seismic-force-resisting system the seismic-force-resisting system
Story drift cannot exceed the larger of:
0.005
or
⎛ Vug ⎞
⎜ 0.035 − 0.05 ⎟
⎝ φVc ⎠
where Vug is the factored gravity punching
shear demand and Vc is the punching shear
strength.
The End
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