seismic design and detailing of reinforced concrete...
TRANSCRIPT
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Seismic Design and Detailing of
Reinforced Concrete Structures
Based on CSA A23.3 - 2004
Murat Saatcioglu PhD,P.Eng.
Professor and University Research Chair
Department of Civil Engineering
The University of Ottawa
Ottawa, ON
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Reinforced concrete structures are designed to
dissipate seismic induced energy through
inelastic deformations
Basic Principles of Design
Ve = S(Ta) Mv IE W / (Rd Ro) Ve
Ve /Rd Ro
Ve /Rd
∆∆∆∆
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Basic Principles of Design
Inelasticity results softening in the structure,
elongating structural period
S(T)
T T1 T2
S1
S2
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Basic Principles of Design
Capacity ≥≥≥≥ Demand
It is a good practice to reduce seismic
demands, to the extent possible4.
This can be done at the conceptual stage
by selecting a suitable structural system.
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To reduce seismic demands4
� Select a suitable site with favorable soil conditions
� Avoid using unnecessary mass
� Use a simple structural layout with minimum
torsional effects
� Avoid strength and stiffness taper along the height
� Avoid soft storeys
� Provide sufficient lateral bracing and drift control by
using concrete structural walls
� Isolate non-structural elements
![Page 6: Seismic Design and Detailing of Reinforced Concrete …libvolume3.xyz/civil/btech/semester6/designdrawingofrc... · · 2014-12-30Reinforced Concrete Structures Based on CSA A23.3](https://reader034.vdocuments.mx/reader034/viewer/2022050720/5accc80e7f8b9a6a678cae37/html5/thumbnails/6.jpg)
Seismic Amplification due to Soft Soil
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Liquefaction
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Liquefaction
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Liquefaction
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To reduce seismic demands4
� Select a suitable site with favorable soil conditions
� Avoid using unnecessary mass
� Use a simple structural layout with minimum
torsional effects
� Avoid strength and stiffness taper along the height
� Avoid soft storeys
� Provide sufficient lateral bracing and drift control by
using concrete structural walls
� Isolate non-structural elements
![Page 11: Seismic Design and Detailing of Reinforced Concrete …libvolume3.xyz/civil/btech/semester6/designdrawingofrc... · · 2014-12-30Reinforced Concrete Structures Based on CSA A23.3](https://reader034.vdocuments.mx/reader034/viewer/2022050720/5accc80e7f8b9a6a678cae37/html5/thumbnails/11.jpg)
Use of Unnecessary Mass
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Use of Unnecessary Mass
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Use of Unnecessary Mass
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Use of Unnecessary Mass
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To reduce seismic demands4
� Select a suitable site with favorable soil conditions
� Avoid using unnecessary mass
� Use a simple structural layout with minimum
torsional effects
� Avoid strength and stiffness taper along the height
� Avoid soft storeys
� Provide sufficient lateral bracing and drift control by
using concrete structural walls
� Isolate non-structural elements
![Page 16: Seismic Design and Detailing of Reinforced Concrete …libvolume3.xyz/civil/btech/semester6/designdrawingofrc... · · 2014-12-30Reinforced Concrete Structures Based on CSA A23.3](https://reader034.vdocuments.mx/reader034/viewer/2022050720/5accc80e7f8b9a6a678cae37/html5/thumbnails/16.jpg)
Effect of Torsion
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Effect of Torsion
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Effect of Torsion
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Effect of Torsion
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Effect of Torsion
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Effect of Torsion
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Effect of Torsion
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Effect of Torsion
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To reduce seismic demands4
� Select a suitable site with favorable soil conditions
� Avoid using unnecessary mass
� Use a simple structural layout with minimum
torsional effects
� Avoid strength and stiffness taper along the height
� Avoid soft storeys
� Provide sufficient lateral bracing and drift control by
using concrete structural walls
� Isolate non-structural elements
![Page 25: Seismic Design and Detailing of Reinforced Concrete …libvolume3.xyz/civil/btech/semester6/designdrawingofrc... · · 2014-12-30Reinforced Concrete Structures Based on CSA A23.3](https://reader034.vdocuments.mx/reader034/viewer/2022050720/5accc80e7f8b9a6a678cae37/html5/thumbnails/25.jpg)
Effect of Vertical Discontinuity
![Page 26: Seismic Design and Detailing of Reinforced Concrete …libvolume3.xyz/civil/btech/semester6/designdrawingofrc... · · 2014-12-30Reinforced Concrete Structures Based on CSA A23.3](https://reader034.vdocuments.mx/reader034/viewer/2022050720/5accc80e7f8b9a6a678cae37/html5/thumbnails/26.jpg)
Effect of Vertical Discontinuity
![Page 27: Seismic Design and Detailing of Reinforced Concrete …libvolume3.xyz/civil/btech/semester6/designdrawingofrc... · · 2014-12-30Reinforced Concrete Structures Based on CSA A23.3](https://reader034.vdocuments.mx/reader034/viewer/2022050720/5accc80e7f8b9a6a678cae37/html5/thumbnails/27.jpg)
To reduce seismic demands4
� Select a suitable site with favorable soil conditions
� Avoid using unnecessary mass
� Use a simple structural layout with minimum
torsional effects
� Avoid strength and stiffness taper along the height
� Avoid soft storeys
� Provide sufficient lateral bracing and drift control by
using concrete structural walls
� Isolate non-structural elements
![Page 28: Seismic Design and Detailing of Reinforced Concrete …libvolume3.xyz/civil/btech/semester6/designdrawingofrc... · · 2014-12-30Reinforced Concrete Structures Based on CSA A23.3](https://reader034.vdocuments.mx/reader034/viewer/2022050720/5accc80e7f8b9a6a678cae37/html5/thumbnails/28.jpg)
Effect of Soft Storey
![Page 29: Seismic Design and Detailing of Reinforced Concrete …libvolume3.xyz/civil/btech/semester6/designdrawingofrc... · · 2014-12-30Reinforced Concrete Structures Based on CSA A23.3](https://reader034.vdocuments.mx/reader034/viewer/2022050720/5accc80e7f8b9a6a678cae37/html5/thumbnails/29.jpg)
Effect of Soft Storey
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Effect of Soft Storey
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Effect of Soft Storey
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To reduce seismic demands4
� Select a suitable site with favorable soil conditions
� Avoid using unnecessary mass
� Use a simple structural layout with minimum
torsional effects
� Avoid strength and stiffness taper along the height
� Avoid soft storeys
� Provide sufficient lateral bracing and drift control by
using concrete structural walls
� Isolate non-structural elements
![Page 33: Seismic Design and Detailing of Reinforced Concrete …libvolume3.xyz/civil/btech/semester6/designdrawingofrc... · · 2014-12-30Reinforced Concrete Structures Based on CSA A23.3](https://reader034.vdocuments.mx/reader034/viewer/2022050720/5accc80e7f8b9a6a678cae37/html5/thumbnails/33.jpg)
R/C Frame Buildings without Drift Control
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Buildings Stiffened by Structural Walls
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To reduce seismic demands4
� Select a suitable site with favorable soil conditions
� Avoid using unnecessary mass
� Use a simple structural layout with minimum
torsional effects
� Avoid strength and stiffness taper along the height
� Avoid soft storeys
� Provide sufficient lateral bracing and drift control by
using concrete structural walls
� Isolate non-structural elements
![Page 36: Seismic Design and Detailing of Reinforced Concrete …libvolume3.xyz/civil/btech/semester6/designdrawingofrc... · · 2014-12-30Reinforced Concrete Structures Based on CSA A23.3](https://reader034.vdocuments.mx/reader034/viewer/2022050720/5accc80e7f8b9a6a678cae37/html5/thumbnails/36.jpg)
Short Column Effect
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Short Column Effect
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Seismic Design Requirements of
CSA A23.3 - 2004
Capacity design is employed4..
Selected elements are designed to yield
while critical elements remain elastic
Design for
Strength and Deformability
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Principal loads: 1.0D + 1.0E
And either of the following: 1) For storage occupancies, equipment areas and
service rooms: 1.0D + 1.0E + 1.0L + 0.25S 2) For other occupancies: 1.0D + 1.0E + 0.5L + 0.25S
Load Combinations
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Stiffness Properties for Analysis
� Concrete cracks under own weight of structure
� If concrete is not cracked, then the structure is not reinforced concrete (plain concrete)
� Hence it is important to account for the softening of structures due to cracking
� Correct assessment of effective member stiffness is essential for improved accuracy in establishing the distribution of design forces among members, as well as in computing the period of the structure.
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Flexural Behaviour of R/C
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Flexural Behaviour of R/C
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Section Properties for Analysis as
per CSA A23.3-04 Beams Ie = 0.40 Ig
Columns Ie = ααααcIg
Coupling Beams
without diagonal reinforcement Ave = 0.15Ag
Ie = 0.40 Ig
with diagonal reinforcement Ave = 0.45Ag
Ie = 0.25 Ig
Slab-Frame Element Ie = 0.20 Ig
Walls Axe = ααααwAg
Ie = ααααw Ig
1.0
1.0
1.0
1.0
AAAAffffPPPP0
.6
0.6
0.6
0.6
0.5
0.5
0.5
0.5
ααααgggg
''''cccc
sssscccc ≤≤≤≤++++====
1.0
1.0
1.0
1.0
AAAAffffPPPP0
.6
0.6
0.6
0.6
ααααgggg
''''cccc
sssswwww ≤≤≤≤++++====
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Seismic Design Requirements of
CSA A23.3 - 2004
Chapter 21 covers:
� Ductile Moment Resisting Frames (MRF)
� Moderately Ductile MRF
� Ductile Shear Walls
� Ductile Coupled Shear Walls
� Ductile Partially Coupled Shear Walls
� Moderately Ductile Shear Walls
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Ductile Moment Resisting Frame
Members Subjected to Flexure Rd = 4.0 Pf ≤ Agf’c /10
h0.3bw ≥
mm250bw
≥
d4n ≥l
yxcb 2w ++≤
h3/4x ≤
h3/4y ≤
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Beam Longitudinal Reinforcement
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Beam Transverse Reinforcement
nnnnl
2/ds2 ≤≤≤≤
4/ds1 ≤≤≤≤
mm300s1 ≤≤≤≤
bar.longb1 )d(8s ≤≤≤≤
hoopb1 )d(24s ≤≤≤≤
No lap splicing within
this region
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Formation of Plastic Hinges
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Beam Shear Strength
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Beam Shear Strength
� The factored shear need not exceed that
obtained from structural analysis under
factored load combinations with RdRo = 1.0
� The values of θθθθ = 45o and ββββ = 0 shall be used
in shear design within plastic hinge regions
� The transverse reinforcement shall be
seismic hoops
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Ductile Moment Resisting Frame
Members Subjected to Flexure and
Significant Axial Load
Rd = 4.0 Pf > Agf’c /10
hshort ≥ 300 mm D ≥ 300 mm
hshort / hlong ≥ 0.4
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Longitudinal Reinforcement
ρρρρ min = 1% ρρρρ max = 6%
Design for factored axial forces
and moments using Interaction
Diagrams
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Strong Beam-Weak Column Design
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Strong Beam-Weak Column Design
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Strong Column-Weak Beam Design
∑∑∑∑ ∑∑∑∑≥≥≥≥pbnc
MM
Nominal moment
resistance of columns
under factored axial loads
Probable moment
resistance of beams
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Column Confinement
Reinforcement
lo ≥ 1.5h
lo ≥ 1/6 of clear col. height
If Pf ≤ 0.5 φφφφc f’c Ag ;
lo ≥ 2.0h If Pf > 0.5 φφφφc f’c Ag ;
Columns will be confined for improved
inelastic deformability
lo
lo
Columns connected to rigid members such as
foundations and discontinuous walls, or columns
at the base will be confined along the entire height
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Poorly Confined Columns
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Poorly Confined Columns
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Well-Confined
Column
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Column Confinement Reinforcement
yh
cps
f
f'0.4kρ ====
o
fp
P
Pk ====
yh
c
c
g
sf
f'1)
A
A0.45(ρ −−−−≥≥≥≥
Circular Spirals
MPa500≤≤≤≤yhf
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Column Confinement Reinforcement
c
ch
gsh
A
A
yh
cpnsh
f
f'k0.2kA ====
o
fp
P
Pk ====
cshyh
csh
f
f'0.09A ====
Rectilinear Ties
MPa500≤≤≤≤yhf
)2n/(n −−−−====llnk
ln : No. of laterally supported bars
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Spacing of Confinement
Reinforcement
� ¼ of minimum member dimension
� 6 x smallest long. bar diameter
� sx = 100 + (350 – hx) / 3
Spacing of laterally supported longitudinal
bars, hx ≤ 200 mm or 1/3 hc
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Column Shear
Strength
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Column Shear Strength
� The factored shear need not exceed that
obtained from structural analysis under
factored load combinations with RdRo = 1.0
� The values of θθθθ ≥ 45o and ββββ ≤ 0.10 shall be
used in shear design in regions where the
confinement reinforcement is needed
� The transverse reinforcement shall be
seismic hoops
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Shear Deficient Columns
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Shear Deficient Columns
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Beam-Column Joints
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Poor Joint Performance
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Computation of Joint Shear
Vx-x ≤ that obtained from frame analysis using RdRo = 1.0
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jccj A'f2.2V φφφφλλλλ====
jccj A'f6.1V φφφφλλλλ====
jccj A'f3.1V φφφφλλλλ====
Shear Resistance of Joints
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� Continue column confinement
reinforcement into the joint
� If the joint is fully confined by four
beams framing from all four sides,
then eliminate every other hoop. At
these locations sx = 150 mm
Transverse Reinforcement in Joints
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Design Example
Six-Storey Ductile Moment Resisting Frame in Vancouver
Chapter 11
By D. Mitchell and P. Paultre
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•Rd = 4.0 and Ro = 1.7
•Site Classification C
(Fa & Fv = 1.0)
Interior columns: 500 x 500 mm
Exterior columns: 450 x 450 mm
Slab: 110 mm thick
Beams (1-3rd floors): 400 x 600 mm
Beams (4-6th floors): 400 x 550 mm
Six-Storey Ductile Moment Resisting Frame in Vancouver
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Material Properties
Concrete: normal density concrete with 30 MPa
Reinforcement: 400 MPa
Live loads
Floor live loads:
2.4 kN/m2 on typical office floors
4.8 kN/m2 on 6 m wide corridor bay
Roof load
2.2 kN/m2 snow load, accounting for parapets
and equipment projections
1.6 kN/m2 mechanical services loading in 6 m
wide strip over corridor bay
Dead loads
self-weight of reinforced concrete members
calculated as 24 kN/m3
1.0 kN/m2 partition loading on all floors
0.5 kN/m2 mechanical services loading on all
floors
0.5 kN/m2 roofing
Wind loading
1.84 kN/m2 net lateral pressure for top 4 storeys
1.75 kN/m2 net lateral pressure for bottom 2
storeys
The fire-resistance rating of the building is
assumed to be 1 hour.
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Gravity Loading
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Design Spectral Response
Acceleration E-W Direction
Empirical: Ta = 0.075 (hn)3/4 = 0.76 s
Dynamic: T = 1.35 s but not greater than 1.5Ta = 1.14s
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Design of Ductile Beam
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Design of Ductile Beam
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Design of Ductile Beam
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Design of Ductile Beam
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Design of Ductile Beam
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Design of Ductile Beam
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Design of Ductile Interior Column
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Design of Ductile Interior Column
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Design of Ductile Interior Column
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Design of Ductile Interior Column
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Design of Ductile Interior Column
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Design of Ductile Interior Column
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Design of Interior Beam-Column Joint
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Design of Interior Beam-Column Joint
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Design of Interior Beam-Column Joint
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ℓw
hw
Plastic
Hinge
Length
Ductile Shear Walls
Rd = 3.5 or 4.0 if hw / ℓw ≤ 2.0; Rd = 2.0
SFRS without irregularities:
Plastic hinge length:1.5 ℓw
� Flexural and shear reinforcement
required for the critical section
will be maintained within the
hinging region
� For elevations above the plastic
hinge region, design values will be
increased by Mr/Mf at the top of
hinging region
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ℓw
hw
Plastic
Hinge
Length
Ductile Shear Walls
Wall thickness in the plastic hinge:
tw ≥ ℓu / 14 but may be limited to
ℓu / 10 in high compression regions
tw
ℓu
Because walls are relatively thin
members, care must be taken to
prevent possible instability in
plastic hinge regions
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Ductile Shear Walls
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Ductile Shear Walls
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Ductile Shear Walls
ℓf
Effective flange width:
ℓf ≤ ½ distance to adjacent wall web
ℓf ≤ ¼ of wall height above the section
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Wall
Reinforcement
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Distributed Reinforcement in Each Direction
Amount ρρρρ ≥ 0.0025 ρρρρ ≥ 0.0025
Spacing ≤ 300 mm ≤ 450 mm
Concentrated Reinforcement
Where @ends and
corners
@ends
Amount
(at least 4 bars)
ΑΑΑΑs ≥ 0.015 bwlw
ΑΑΑΑs ≤ 0.06 (A)be
ΑΑΑΑs ≥ 0.001 bwlw
ΑΑΑΑs ≤ 0.06 (A)be
Hoops Confine like
columns
Like non-
seismic
columns
Plastic Hinges Other Regions
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Ductile Shear Walls
� Vertical reinforcement outside the plastic
hinge region will be tied as specified in
7.6.5 if the area of steel is more than
0.005Ag and the maximum bar size is #20
and smaller
� Vertical reinforcement in plastic hinge
regions will be tied as specified in 21.6.6.9 if
the area of steel is more than 0.005Ag and
the maximum bar size is #15 and smaller
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Ductile Shear Walls
� At least two curtains of reinforcement will
be used in plastic hinge regions, if:
cv
'
ccf Af18.0V λφλφλφλφ>>>>Where;
Acv : Net area of concrete section bounded by
web thickness and length of section in the
direction of lateral force
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Ductile Shear Walls
For buckling prevention, ties shall be provided
in the form of hoops, with spacing not to
exceed:
� 6 longitudinal bar diameters
� 24 tie diameters
� ½ of the least dimension of of the member
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Ductility of Ductile Shear Walls
Rotational Capacity, θθθθic> Inelastic Demand, θθθθid
004.0
2h
RR
ww
wfdofid ≥≥≥≥
−−−−
∆∆∆∆−−−−∆∆∆∆====
l
γγγγθθθθ
ℓw
hw
φφφφy φφφφcu
ℓw/2 025.0002.0
c2
wcuic ≤≤≤≤
−−−−====
lεεεεθθθθ
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Ductility of Ductile
Shear Walls
004.0
2h
RR
ww
wfdofid ≥≥≥≥
−−−−
∆∆∆∆−−−−∆∆∆∆====
l
γγγγθθθθ
025.0002.0c2
wcuic ≤≤≤≤
−−−−====
lεεεεθθθθ
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Ductility of Ductile Shear Walls
w
'
cc11
f
'
cc1nsns
bf
AfPPPc
φφφφββββααααφφφφαααα−−−−++++++++
====
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x P P
E.Q.
M2 M1
Mtotal = M1 + M2 + P x
If P x ≥≥≥≥ 2/3Mtotal
Coupled Wall
If P x < 2/3Mtotal
Partially
Coupled Wall
Ductile Coupled Walls
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Ductility of Ductile Coupled
Walls Rotational Capacity, θθθθ ic> Inelastic Demand, θθθθ id
004.0h
RR
w
dof
id≥≥≥≥
∆∆∆∆====θθθθ
025.0002.0c2
wcu
ic ≤≤≤≤
−−−−====
lεεεεθθθθ
ℓw: Length of the coupled wall system
ℓw: Lengths of the individual wall segments
for partially coupled walls
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Ductility of Coupling Beams
Rotational Capacity, θθθθic> Inelastic Demand, θθθθid
u
cg
w
dofid
h
RR
l
l
∆∆∆∆====θθθθ
θθθθic = 0.04 for coupling
beams with diagonal
reinforcement as per
21.6.8.7
θθθθic = 0.02 for coupling beams without
diagonal reinforcement as per 21.6.8.6
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Coupling Beams with Diagonal
Reinforcement
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Wall Capacity @ Ends of Coupling
Beams
� Walls at each end of a coupling beam shall be
designed so that the factored wall moment
resistance at wall centroid exceeds the
moment resulting from the nominal moment
resistance of the coupling beam.
� If the above can not be achieved, the walls
develop plastic hinges at beam levels. This
requires design and detailing of walls at
coupling beam locations as plastic hinge
regions.
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Shear Design of Ductile Walls
Design shear forces shall not be less than;
� Shear corresponding to the development of
probable moment capacity of the wall or the
wall system
� Shear resulting from design load combinations
with RdRo = 1.0
� Shear associated with higher mode effects
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Shear Design of Ductile Walls
Shear design will conform to the requirements of
Clause 11. In addition, for plastic hinge regions;
� If θθθθid ≥ 0.015 Vf ≤ 0.10φφφφc f’cbwdv
� If θθθθid = 0.005 Vf ≤ 0.15φφφφc f’cbwdv
� For θθθθid between the above two values, linear
interpolation may be used
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Shear Design of Ductile Walls
� If θθθθid ≥ 0.015 β = 0β = 0β = 0β = 0
� If θθθθid ≤ 0.005 β β β β ≤ 0.180.180.180.18
� For θθθθid between the above two values, linear
interpolation may be used
For plastic hinge regions:
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Shear Design of Ductile Walls
� If (Ps + Pp) ≤ 0.1 f’cAg θ = 45θ = 45θ = 45θ = 45οοοο
� If (Ps + Pp) ≥ 0.2 f’cAg θ θ θ θ ≥ 35353535οοοο
� For axial compression between the above
two values, linear interpolation may be
used
For plastic hinge regions:
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Moderately Ductile Moment
Resistant Frame Beams
(Rd = 2.5)
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nnnnl
2/2hs ≤
4/ds1 ≤≤≤≤
mm300s1 ≤≤≤≤
bar.longb1 )d(8s ≤≤≤≤
hoopb1)d(24s ≤≤≤≤
Moderately Ductile Moment
Resistant Frame Beams
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∑ ∑≥ nbrc MM
Factored moment
resistance of columns
Nominal moment
resistance of beams
Moderately Ductile Moment
Resistant Frame Columns
Column design forces
need not exceed those
determined from factored
load combinations using
RdRo = 1.0
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lo ≥ h
lo ≥ 1/6 of clear col. height
lo ≥ 450 mm
Columns will be confined for improved
inelastic deformability
lo
lo
Moderately Ductile Moment
Resistant Frame Columns
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Spacing of Confinement
Reinforcement
� 1/2 of minimum column dimension
� 8 x long. bar diameter
� 24 x tie diameters
Crossties or legs of overlapping hoops shall
not have centre-to-centre spacing exceeding
350 mm
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Column Confinement Reinforcement
yh
cps
f
f'0.3kρ ====
o
fp
P
Pk ====
yh
c
c
g
sf
f'1)
A
A0.45(ρ −−−−≥≥≥≥
Circular Hoops
MPa500≤≤≤≤yhf
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Column Confinement Reinforcement
c
ch
gsh
A
A
yh
cpnsh
f
f'k0.15kA ====
o
fp
P
Pk ====
cshyh
csh
f
f'0.09A ====
Rectilinear Ties
MPa500≤≤≤≤yhf
)2n/(n −−−−====llnk
ln : No. of laterally supported bars
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Beam Shear Strength
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The factored shear need not exceed
that obtained from structural analysis
under factored load combinations with
RdRo = 1.0
Beam Shear Strength
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Computation of Joint Shear
Joint shear
associated with
nominal resistance
of beams
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�Joint shear associated with nominal
resistances of the beams and the
columns will be computed and the
smaller of the two values will be used
�The joint shear need not exceed that
obtained from structural analysis under
factored load combinations with
RdRo = 1.0
Joint Shear
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jccj A'f2.2V φφφφλλλλ====
jccj A'f6.1V φφφφλλλλ====
jccj A'f3.1V φφφφλλλλ====
Shear Resistance of Joints in
Moderately Ductile Frames
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� Longitudinal reinforcement shall have a
centre-to-centre distance not exceeding
300 mm and shall not be cranked within
the joint
� Transverse reinforcement shall be
provided with a maximum spacing of 150
mm
Transverse Reinforcement in Joints
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Moderately Ductile Shear Walls
� Wall thicknesses will be similar to those of
ductile shear walls, except;
ℓu / 10 ℓu / 14 ℓu / 14 ℓu / 20
� Ductility limitation will be similar to that
for ductile walls with minimum rotational
demand as 0.003.
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Moderately Ductile Shear Walls
� Distributed horizontal reinforcement ratio
shall not be less than 0.0025 in the vertical
and horizontal directions
� Concentrated reinforcement in plastic
hinge regions shall be the same as that for
ductile walls, except the tie requirements
are relaxed to those in Chapter 7
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Shear Design of Moderately Ductile
Walls
Design shear forces shall not be less than the
smaller of;
� Shear corresponding to the development of
nominal moment capacity of the wall or the
wall system
� Shear resulting from design load combinations
with RdRo = 1.0
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Shear Design of Moderately Ductile
Walls
� Vf ≤ 0.1 φφφφcf’cbwdv
� β = 0.1β = 0.1β = 0.1β = 0.1
� θθθθ = 45o
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Design Example
Ductile Core-Wall Structure in Montreal
Chapter 11
By D. Mitchell and P. Paultre
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Twelve-Storey Ductile
Core Wall Structure
in Montreal
•E-W: Rd = 4.0 and Ro = 1.7
•N-S: Rd = 3.5 and Ro = 1.6
•Site Classification D
(Fa = 1.124 & Fv = 1.360)
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Design Spectral Response
Acceleration N-S Direction
Empirical: Ta = 0.05 (hn)3/4 = 0.87 s
Dynamic:
T = 1.83 s but not greater than 2Ta = 1.74s
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Torsion of Core Wall
Max BNS = 1.80
Max BEW = 1.66
Max B > 1.7
irregularity
type 7
avemaxx/B ∂∂=
Torsional Sensitivity
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Seismic and Wind Loading
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Diagonally Reinforced Coupling Beam
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Wall Reinforcement Details
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Factored Moment Resistance E-W
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Factored Moment Resistance N-S
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Squat Shear Walls
hw / ℓw ≤ 2.0; Rd = 2.0
� The foundation and diaphragm components
of the SFRS shall have factored resistances
greater than the nominal wall capacity.
� The walls will dissipate energy either;
� through flexural mechanism, i.e., V @
Mn is less than Vr,
� or, through shear mechanism, i.e., V @
Mn is more than Vr.
In this case: vwcr dbf'0.2V ≥
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Squat Shear Walls
The distributed reinforcement:
� ρρρρh ≥ 0.003 ρρρρv ≥ 0.003
� Use two curtains of reinforcement if
� At least 4 vertical bars will be tied with
seismic hooks and placed at the ends
and at junctions of intersecting walls
over 300 mm wall length with ρρρρ ≥ 0.005.
vwccf dbf'φ0.18λV >
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Squat Shear Walls
Shear Design
� Vf ≤ 0.15 φφφφc f’cbwdv
� ββββ = 0 θθθθ = 300 to 450
� Vertical reinforcement required for shear:
where; ρρρρh : required horizontal steel
gys
s2
hvAfφ
Pθcotρρ −=
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Conventional Construction Rd = 1.5
Buildings with Rd = 1.5 can be designed as
conventional buildings. However, detailing
required for nominally ductile columns will be
used unless;
� Factored resistances of columns are more
than those for framing beams
� Factored resistances of columns are greater
than factored loads based on RdRo =1.0
� IEFaSa(0.2) < 0.2
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Walls of Conventional Construction
Walls can be designed as conventional walls.
However, the shear resistance will be greater
than the smaller of;
� the shear corresponding to factored
moment resistance,
� the shear computed from factored loads
based on RdRo =1.0.
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Frame Members not Considered Part
of the SFRS
Frames that are not part of SFRS, but “go for
the ride” during an earthquake shall be
designed to accommodate forces and
deformations resulting from seismic
deformations.
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Thank You4..
Questions or Comments?