Recent UBC Researchon the Seismic Design ofConcrete Shear Wall Buildings:towards the 2014 Canadian Code
Perry Adebar Professor of Structural EngineeringThe University of British Columbia, Vancouver, BC, Canada
August 19 – 21, 2013
Background:
Significant changes to
Clause 21 – Seismic Design
of 2014 CSA A23.3 Design of Concrete Structures.
Presentation:
Briefly highlight some CSRN sponsored research done at UBC that informed the changes.
2
Outline of Presentation:
1. Effective Stiffness of Concrete Walls
2. Thin Concrete Walls
3. Flexural Yielding at Mid-Height
4. Design Shear Force
5. Gravity-load Frames
6. Foundation Movements
3
1. Effective Flexural Rigidity of Concrete Shear Walls
4
Current CSA A23.3 Clause 21
Typical value: αw = 0.70
5
Δ
V
Vn/ki ΔyUB ΔyLB
Vcc
Vco
Vn
ks1
1
kiA
B
C
D
E
F
B
C
E
F
A
D
: Upper bound loading
: unloading (prior to yield)
: mid-cycle reloading
: unloading (after yield)
: residual displacement
: Lower bound loading
Loading curves after wall severely cracked
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 2 4 6 8 10
Dki/Vn
V/V
n
W-L2-R3
W-L2-R2
W-L2-R1
W-L4-R4
W-L4-R2
W-L4-R1
W-L5-R3
W-L5-R2
W-L5-R1
W-L6-R3
W-L6-R2
W-L6-R1
W-L8-R2
High Compression
Low Compression
7
Δ
V
Vn/ki ΔyUB ΔyLB
Vcc
Vco
Vn
ks1
1
kiA
B
C
D
E
F
B
C
E
F
A
D
: Upper bound loading
: unloading (prior to yield)
: mid-cycle reloading
: unloading (after yield)
: residual displacement
: Lower bound loadingHigh Compression
Low Compression
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0
Ratio of elastic force demand to strength R
ke/k
g
W-L2-R3
W-L2-R2
W-L2-R1
W-L4-R4
W-L4-R2
W-L4-R1
W-L5-R3
W-L5-R2
W-L5-R1
W-L6-R3
W-L6-R3
W-L6-R2
W-L8-R2Ti = 3.0
Wall with largest compression
Each point average of 40 ground motions
Initial period of SDOF “building” = 3.0 s
Results from SDOF model of “building” for one Ti
9
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1 1.5 2 2.5 3 3.5 4
EI e
/ E
I g
Force reduction factor R
10 stories
20 story
30 stories
40 story
50 stories
= 1.4-0.4R 0.5
Results from nonlinear analysis of full buildings
Force ratio R
0.5
From E. Dezhdar, 2012
10
CSA A23.3 – 2014:
The effective stiffness of a concrete wall to be
used in a linear seismic analysis depends on
the ratio of elastic force demand to strength.
11
New typical values:
Rd = 2.0 αw = 0.65
Rd = 3.5 αw = 0.50
Generally larger design displacements! 12
2. Thin Concrete Walls
13
Feb. 2010 M8.8 Maule Earthquake Chile
14
15
16
17
18
Recent UBC tests inspired by shear wall failures in 2010 Chile Earthquake
19
20
0 0.5 1 1.5 2 2.5 3 3.5 4
x 10-3
0
5
10
15
20
25
30
35
Strain
Str
ess (
MP
a)
Average (LP1,LP2)
21
0 0.5 1 1.5 2 2.5 3 3.5 4
x 10-3
0
5
10
15
20
25
30
Strain
Str
ess (
MP
a)
Average Value (LP1,LP2)
22
Loaded to here
23
24
25
26
0 0.5 1 1.5 2 2.5 3 3.5 4
x 10-3
0
5
10
15
20
25
30
Strain
Str
ess (
MP
a)
Average Value (LP1,LP2)
27
Compression strain capacity = 0.0015
Compression strain capacity = 0.00125
28
29
Experimental study on gravity-load columns:
Cross section of four gravity columns tested in current study.
P = 0.33 fc′ Ag
From: Helen Chin, 2012
30
Results of gravity-load column test:Photographs of 27.5 x 55 cm column after test showing height of damaged zone – column had much more ductility than expected.
From: Helen Chin, 2012 31
32
33
Complete collapse of wall specimen
34
Changes to CSA A23.3:
1. Reduce axial compression applied to thin columns and walls (Clause 10).
2. Limit compression strain depth in all shear walls to ensure yielding of vertical reinf. in tension prior to concrete crushing in Clause 14 – over full height (next topic).
3. Account for unexpected strong axis bending of long thin bearing walls.
35
3. Flexural Yielding at Mid-Height of Cantilever Shear Walls
36
Traditional design approach
for cantilever shear walls
37
0
18.9
37.8
56.7
75.6
0 400,000 800,000 1,200,000 1,600,000 2,000,000
M (kN.m)
H (
m)
C1
C2
C3
C4
C5
C6
C7
S1
S2
S3
Average
Bending moment envelopes: nonlinear elements only at base of wall
38
Simple EPP model of shear wall
Actual shear wall
39
0
10
20
30
40
50
60
70
80
90
0 0.2 0.4 0.6 0.8 1 1.2
Hei
ght
(m)
Curvature (rad/km)
EPP, 0.5EIg
Trilinear
EPP yield curvature
Trilinear yield curvature
40
From E. Dezhdar, 2012
Influence of nonlinear model
0
10
20
30
40
50
60
70
80
90
0 0.1 0.2 0.3 0.4 0.5
Heig
ht
(m)
Curvature (rad/km)
matched to UHS
CMS at T1
Historical records
Selected records
FEMA records
Yield curvature
R = 1.5
41
From E. Dezhdar, 2012
Influence of ground motion selection and scaling
Mid-height Curvatures: results from appropriate NLA
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0 0.5 1 1.5 2 2.5
Mid
he
igh
t c
urv
atu
rex
wa
ll l
en
gth
Roof displacement / wall height * 100
10story,R=3.2
20story,R=2.7
30story,R=3.1
40story,R=3.6
50story,R=3.7
Wall R µ µ+σ
1.7 0.0018 0.0035
2.3 0.002 0.0037
3.2 0.0021 0.0037
20 story 2.7 0.0023 0.0042
1.4 0.0014 0.0027
2 0.002 0.0039
2.3 0.0019 0.0032
3.1 0.0021 0.0037
40 story 3.6 0.0018 0.0033
1.3 0.0015 0.0027
1.8 0.0018 0.0029
2 0.0019 0.0025
3.7 0.0023 0.004
Average 0.0019 0.0034
f mid . l w
10 story
30 story
50 story
Mid-height curvature is less than commonly assumed yield curvature 42
From E. Dezhdar, 2012
Summary:
• Need to design wall for nominal yielding at mid-height
• Most important issue –prevent compression failure of wall (relates to thin walls)
• Some advocate adding vertical reinforcement at mid-height to reduce (or even eliminate) yielding
43
4. Design Shear Forces
44
Same force reduction
factors as used for bending
Amplification for flexural overstrength
“Dynamic Magnification of Shear”
45
Many existing recommendations for Dynamic Magnification Factor based on:
• improperly selected and scaled ground motions
and/or
• nonlinear models that do not account for highly
nonlinear moment-curvature response due to flexural
cracking.
46
0
1
2
3
4
5
6
7
8
9
0 10 20 30 40 50 60 70
Sh
ear
Am
pli
ficati
on
Facto
r (R
d =
3.5
)
Number of Storeys
NZ/SEAOC
Rutenberg (Van)
Rutenberg (Mont)
Ghosh (Van)
Ghosh (Mont)
Keintzel (Van)
Keintzel (Mont)
Priestly (2003, Van)
Priestly (2003, Mont)
Priestly (2006, Van)
Priestly (2006, Mont)
From J. Yathon, 2011
47
0
10
20
30
40
50
60
70
80
90
0 5000 10000 15000 20000 25000 30000 35000 40000
He
igh
t
Shear kN
Ehsan
EPP
RSA
Trilinear
From E. Dezhdar, 2012
48
Influence of nonlinear model
0.0
0.5
1.0
1.5
2.0
2.5
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Sh
ea
r a
mp
lifi
ca
tio
n fa
cto
r
Force reduction factor R (0.5EIg)
10 story
20 story
30 story
40 story
50 story
Force ratio R (0.5 EIg)
From E. Dezhdar, 2012
49
Results from appropriate NLA
Dezhdar, 2012
50
Reasons to use a low shear magnification factor:
• Very few wall shear failures outside the laboratory,
• Higher mode shear forces exist for a very short time,
• Nonlinear analysis has shown that walls have shear ductility –
horizontal reinforcement yields,
• Max. base shear force does not occur at same time as
maximum base rotation.
• The largest shear force demand occurs during one cycle
• …
51
5. Design of Gravity-load Frames
… for Seismic Deformations
Largest change in CSA A23.3 – 2014
52
53
CTV Building (built 1986)
Courtesy Ken Elwood
BeforeChristchurch
Earthquake2011
54
Courtesy Ken Elwood
AfterShear wall
Gravity-load frame
55
Interstory Drift Demands - Shear Wall Buildings
• Important in order to evaluate demands on gravity
frame members such as slab-column connections and
gravity-load columns.
• Nonlinear interstory drift envelope different than
determined from linear analysis for same top wall disp.
• Currently no simplified approach to estimate nonlinear
interstory drift envelope.
56
0
20
40
60
80
100
120
0 0.2 0.4 0.6 0.8 1 1.2 1.4
He
igh
t (m
)
Interstory drift (%)
40 story, R = 3.6
RSA
THA,
THA, +σ
Model
Example Results:
From: E. Dezhdar, 2012
Need to account for drift due to shear strain in hinge region
57
CSA A23.3 – 2014 Clause 21.11.2.2 Simplified analysis of shear wall buildings
The shear force and bending moments induced in members of a gravity-load frame shall be determined at each level by subjecting the frame to the interstory drift given in Fig. 21-1 for that level. …
58
Fig. 21-1
59
21.11.2.2 Simplified analysis of shear wall buildings…The deflection demand used to calculate the global drift Δ/hw in Fig. 21-1 shall be design lateral deflection at top of gravity-load frame determined from an analysis incorporating the effects of torsion, including accidental torsional moments and including foundation movements.
60
6. Foundation Movements
61
Overturning Resistance of Foundation
Capacity protected
Not capacity protected“ROCKING”
Results of nonlinear analysis by P. Bazargani, 2013
62
Each point is average result from 10 ground motions on a shear wall building with given foundation size and soil type
CSA A23.3 – 2014 Clause 21.10.3.3 Foundation movements
The increased displacements due to movements of foundations shall be accounted for in design of SFRS and design of members not considered part of SFRS (i.e., the gravity-load frame).
(similar requirement in Draft 2015 NBCC)
63
Movements of capacity-protected foundations
… may be calculated using a static analysis that accounts for assumed bearing stress distribution in soil or rock and stiffness of soil or rock.
64
Footing rotation may be estimated from:
Where:
as = length of uniform bearing stress in soil or rock;
qs = uniform bearing stress in soil or rock;
Gs = effective Shear Modulus of soil or rock, which may
be estimated from 0.2γsVs2 (γs = density of soil or
rock,Vs = shear wave velocity measured in soil or
rock immediately below foundation)
lf = length of footing (perpendicular to axis of rotation).
𝜃 = 0.3𝑞𝑠𝐺𝑠
𝑙𝑓
a𝑠
65
Movements of not capacity-protected (“Rocking”) foundations
… shall be determined using a dynamic analysis that accounts for the reduced rotational stiffness of footing due to footing uplift and soil deformation.
66
In lieu of a dynamic analysis…
interstorey drift shall be increased at every level, including immediately above footing,
by an interstorey drift ratio equal to 50% of displacement at top of SFRS divided by height above footing;
but shall be increased by not less than an interstorey drift ratio equal to 0.005.
67
The End
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