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Seismic response of steel buckling restrained knee braced truss moment frames
By Yuanjie Li
Supervised By Prof. Yang
University of British Columbia
Buckling restrained knee braces + Truss
Structural “Fuse”
Buckling restrained knee braces special truss moment frames (BRKB-TMF)
Design Procedure
Traditional code design approach?
design for the forcescheck for the drifts
Iteration
Facing two problems?
unpreditable damage locationsuncontrollable damage effect
Design Procedure
1. Performance based plastic design procedure (PBPD) method
(Yang et al. 2013)
2. Energy equation for BRBs and input earthquake
3. Capacity design for truss and columns
OpenSees Navigator ModelRigid diaphragm assumption
Fiber section force beam column element
Truss element
Calibrated BRB (truss element with steel 02 material)
Truss pin connection
Fix support
BRB Calibration
(Black et al. 2004)
EQ scaling (UC – Berkely 2 % in 50 yr)
The ground motions obtained from PEER (2010) were scaled such that the mean spectrum of the set do not fall below the target spectrum by 10% within the period range from 0.2T to 1.5T.
Different BRB Angles for archetype building
304563
80
90
9030
Design Results based on PBPD
BRB Angles Period(s) FloorBRB Strength
(kips)
Columns
Exterior Interior
90˚ 1.0
4 294W24x229 W24x279
3 450
2 547W24x279 W24x306
1 596
80˚ 0.9
4 221W24x229 W24x250
3 338
2 411W24x279 W24x279
1 447
63˚ 0.8
4 165W24x207 W24x207
3 252
2 306W24x250 W24x229
1 333
45˚ 0.9
4 139W24x162 W24x131
3 212
2 258W24x192 W24x207
1 281
30˚ 1.0
4 132W24x131 W24x117
3 202
2 245W24x162 W24x207
1 267
Truss Member Sizes
Floor Chord Diagonal Vertical Ext. Vertical
4 2MC8x18.7 2MC6x12 L3.5x3.5x5/16 2L3.5x3.5x5/16
3 2MC10x25 2MC6x15.3 L3.5x3.5x5/16 2L3.5x3.5x5/16
2 2MC10x28.5 2MC6x15.3 L3.5x3.5x5/16 2L3.5x3.5x5/16
1 2MC10x28.5 2MC8x18.7 L3.5x3.5x5/16 2L3.5x3.5x5/16
Structural Behavior
1
2
3
4
5
1.00 1.50 2.00 2.50
Flo
or
Acceleration (g)
Median
30 Deg45 Deg63 Deg80 Deg90 Deg
1
2
3
4
5
0.00 0.20 0.40 0.60 0.80 1.00 1.20
Flo
or
Acceleration (g)
Coefficient of Variance
30 Deg
45 Deg
63 Deg
80 Deg
90 Deg
1
2
3
4
0.00% 2.00% 4.00%
Flo
or
Inter-story Drift
Median
30 Deg
45 Deg
63 Deg
80 Deg
90 Deg1
2
3
4
0.10 0.20 0.30 0.40F
loor
Inter-story Drift
Coefficient of Variance
30 Deg45 Deg63 Deg80 Deg90 Deg
BRB impact from Angle
30 40 50 60 70 80 900
0.5
1
1.5
2
2.5
3
BR
B S
tra
in (
%)
BRB Angles (Degree)
θp=0.5%
θp=1.5%
θp=2.5%
θp=3.5%
α
0 1
2
0
( / tan( )) sind pD l l
l
Total Repair Cost Study
Define performance group (structural or non-structural component)
Calculate Engineering Demand Parameter (Interstory drift and floor accleration)
Defined potential damaged items and obtain corresponding fragility curves and unit cost
Calculate life cycle repair cost
Referred to Yang et al. 2009
0 1 2 3 4 5 6 70
0.2
0.4
0.6
0.8
1
EDP - du1
P(D
S<
=D
Si)
Fragility Curves for BRBs
Cumulative Distributed Function
0 2 4 6 8 10 12
x 106
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
P(To
tal R
epai
r Cos
t <=
$C)
$C (dollar)
90o
80o
63o
45o
30o
Parameter study 2 - Comparison Study for Spans
N
6 bays @ 30'=180'
Pin
MomentConnection
Connection
TMF/MF
4 b
ays @
30
'=1
20'
6 bays @ 30'=180'
60 Gravity TrussTMF/MF30 Gravity Truss/Beam
E
D
C
B
A
3@
13'=
39'
14'
6 bays @ 30'=180'
3 bays @ 60'=180'
16
.5'
3@
15
.5'=
46
.5'
30 ft. Span: Typical office building60 ft. Span: Conference room or dining hall
-Truss Moment Frame-Traditional Moment Frame
Parameter study 2 - Comparison Study for Spans
N
6 bays @ 30'=180'
Pin
MomentConnection
Connection
TMF/MF
4 b
ays @
30
'=1
20'
6 bays @ 30'=180'
60 Gravity TrussTMF/MF30 Gravity Truss/Beam
E
D
C
B
A
30 ft. Span: Typical office building60 ft. Span: Conference room or dining hall
-Truss Moment Frame-Traditional Moment Frame
3@
13'=
39'
14'
6 bays @ 30'=180'
W24X68
W27X94
W30X108
W30X116
W40X215W44X290
W40X215W44X290
W36X150W40X215
W36X150W40X215
3 bays @ 60'=180'
15
'3
@1
4'=
42
'
W 30X99
W 33X169
W 36X135
W 36X135
W 40X431W 40X503
W 40X431W 40X503
W 40X183W 40X215
W 40X183W 40X215
Parameter study 2 - Comparison Study for Spans
3@
13'=
39'
14'
6 bays @ 30'=180'
W24X68
W27X94
W30X108
W30X116
W40X215W44X290
W40X215W44X290
W36X150W40X215
W36X150W40X215
3 bays @ 60'=180'
15
'3
@1
4'=
42
'
W 30X99
W 33X169
W 36X135
W 36X135
W 40X431W 40X503
W 40X431W 40X503
W 40X183W 40X215
W 40X183W 40X215
3@
13'=
39'
14
'
6 bays @ 30'=180' 3 bays @ 60'=180'
16
.5'
3@
15
.5'=
46
.5'
Structural Behavior
1
2
3
4
1.00% 2.00% 3.00% 4.00%
Flo
or
Interstory Drift
30 ft Truss MF
60 ft Truss MF
30 ft Typical MF
60 ft Typical MF
1
2
3
4
5
0.00 1.00 2.00
Flo
or
Acceleration (g)
30 ft Truss MF
60 ft Truss MF
30 ft Typical MF
60 ft Typical MF
Cost Comparison
$-
$1,000,000
$2,000,000
$3,000,000
$4,000,000
$5,000,000
$6,000,000
$7,000,000
$8,000,000
30 ft. TMF 60 ft. TMF 30 ft. MF 60 ft. MF
Initia
l S
tru
ctu
ral C
ost
Slab
Gravity Columns
Gravity Truss/Beams
Seismic Columns
Seismic Truss/Beams
BRB
Initial Structural Cost Life Cycle Repair Cost
$0
$1,000,000
$2,000,000
$3,000,000
$4,000,000
$5,000,000
$6,000,000
30 ft.TMF
60 ft.TMF
30 ft.MF
60 ft.MF
Rep
air C
ost
Equipment
Contents
Int. Non-Structural Acc.Sensitive
Int. Non-Structural DriftSensitive
Ext. Non-Structural
Structural Lateral Comp.*
Conclusion
From angle parameter study:
1) The proposed PBPD procedure is an efficient and straight forward design procedure to select the
member sizes.
2) The structural response was not significantly affected by the orientation of the BRB.
3) As the orientation of the BRB became more horizontal, the BRBs were able to tolerate higher drift
demand, hence produced lower repair cost during the maximum credible earthquake shaking.
From span parameter study:
1) The larger truss span could create more flexible and attractive architectural usage for the BRKBTMF
and it costs less compared with traditional moment frame.
2) The structural behavior with different span systems is similar in BRKBTMF, quite different in
traditional moment frame.
Acknowledgement:
Thank you for your invitation and attention.
Prof. T. Y. Yang from University of British ColumbiaProf. S.C. Goel from University of MichiganProf. S. Leelataviwat from King Mongkut’s University of TechnologyMr. John D. Hooper from MKAMr. David MacKinnon from SSEFFunding from Natural Sciences and Engineering Research Council of Canada (NSERC) and Steel Strcutres Education Foundation (SSEF)
Contact information:Yuanjie [email protected]
Appendix
Optimal Truss Depth for Gravity Truss and BRB Truss
5 10 15 20 252
4
6
8
Depth (ft)
Ste
el U
sag
e (
ft3)
BRB = 200 kips
BRB = 300 kips
BRB = 400 kips
G G G G G
Span
Dep
th
G G G G G
Span
Dep
th
BRB BRB
LD 6.12.1
LD
D)6.12.1(
(1 )D
/ 240Limit L
