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1Robert TremblayPolytechnique Montreal, QC Canada
Universidad Tecnica Federico Santa Maria Valparaiso, March 2014
Seismic Design and Global Stability Requirements for Steel Building
Structures in Canada and the U.S.
Part I
Seismic Design
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2 Introduction
Seismic Loading and Analysis(ASCE 7-10 vs NBCC & NCh codes)
Seismic Design of Steel Structures(AISC 341-10 vs CSA S16 & NCh codes)
Plan
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Introduction
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3h
h
W
T = 0.38 s5% damping
Elastic
0.0 10.0 20.0 30.0 40.0Time (s)
-0.5
0.0
0.5
ag (g)
-1.0
0.0
1.0
/ h (%)
Horizontal 90 deg.
0.0126 h-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
V / W
1.28 W
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
/ h (%)
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
V / W
High ground motion levels considered for design can impose large force demands on structures:
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0.0 0.5 1.0 1.5 2.0 2.5 3.0Period, T (s)
0.0
0.5
1.0
1.5
2.0
2.5
S a (g
) M 7.0-7.510-20 km
0.0 0.5 1.0 1.5 2.0 2.5 3.0Period, T (s)
0.0
0.5
1.0
1.5
Sa
(g)
M 7.0-7.530-50 km
0.0 0.5 1.0 1.5 2.0 2.5 3.0Period, T (s)
0.0
0.4
0.8
1.2
1.6
2.0
Sa
(g) M 6.5-7.0
10-20 km
0.0 0.5 1.0 1.5 2.0 2.5 3.0Period, T (s)
0.0
0.5
1.0
S a (g
)
M 6.5-7.030-50 km
0.0 0.5 1.0 1.5 2.0 2.5 3.0Period, T (s)
0.0
0.5
1.0
S a (g
)
M 6.5-7.070-100 km
0.0 0.5 1.0 1.5 2.0 2.5 3.0Period, T (s)
0.0
0.5
1.0
S a (g
) M 6.0-6.530-50 km
Earthquakes in California Site Class B 5% damping
Ground motions may be caused by different earthquake scenarios and have difference characteristics
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4Steel is a ductile material and this characteristic can be exploited by allowing structures to deform in the nonlinear range under rare, large seismic events
FF
Fracture,instability,etc.
Ductileresponse
y
u
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0.0 10.0 20.0 30.0 40.0Time (s)
-0.5
0.0
0.5
ag (g)
-1.0
0.0
1.0
/ h (%)
Horizontal 90 deg.
0.0126 h-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
V / W
1.28 W
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
/ h (%)
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
V / W
-1.0
0.0
1.0
/ h (%)
-0.017 h
-1.0
-0.5
0.0
0.5
1.0
V / W
0.33 W
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
/ h (%)
-1.0
-0.5
0.0
0.5
1.0
V /
W
h
h
h
W
T = 0.38 s5% damping
Vy = 0.25 W
Elastic
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5-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06Plastic Rotation (rad.)
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
M /
Mpr
M. Englehardt Ecole Polytechnique of Montreal, 1996
Ecole Polytechnique of Montreal, 1996
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-8 -4 0 4 8
/ y-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
P / Py
HSS 102x76x6.4 - KL/r = 112
Tensionyielding (typ.)
Inelastic bucklingwith plastic hinge (typ.)
PPPlastic
Hinge
+
-
+
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6h
h
W
T = 0.38 s5% damping
Vy = 0.25 W
0.0 10.0 20.0 30.0 40.0Time (s)
-0.5
0.0
0.5
ag (g)
-1.0
0.0
1.0
/ h (%)
Horizontal 90 deg.
0.018 h-0.4
-0.2
0.0
0.2
0.4
V / W
-0.36 W -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0/ h (%)
-0.4
-0.2
0.0
0.2
0.4
V / W
-1.0
0.0
1.0
/ h (%)
-0.017 h
-0.4
-0.2
0.0
0.2
0.4
V / W
0.33 W
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
/ h (%)
-0.4
-0.2
0.0
0.2
0.4
V / W
h
Vy = 0.25 W
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0.0 0.5 1.0 1.5 2.0 2.5 3.0Period, T (s)
0.0
0.4
0.8
1.2
1.6
2.0
S a (g
)
Los Angeles AreaSite Class B
M6.0 - M7.5Dist. = 10-100 km
0.0 0.5 1.0 1.5 2.0 2.5 3.0Period, T (s)
0.0
0.4
0.8
1.2
1.6
S a (g
), C
s
Los Angeles AreaSite Class B
Sa (Elastic)Cs (OCBF - R = 6.0)
x 1/R
Resistance to seismic ground motions through inelastic deformations can represent an effective strategy :
Design forces can be reduced; Structure response, including forces, can be better
controlled.This approach has been adopted in codes. Design must however be performed to achieve the intended ductile response.
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7R. Tremblay, Polytechnique Montreal, Canada 13
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8Grav.
Grav.
C
C' T
u
u y
Grav.
E
> E
> E
Grav.
Grav.
Grav.
Column designed for gravity plus expected brace tensilestrength
Gusset plates designed incompression for the expectedbrace compressive strength
2. Design other elements :
1. Select Braces:
Design for gravity + ECheck KL/r, b/t, etc. for ductile response
Gusset plate designed in tensionfor the expected brace tensilestrength
Two-Step Capacity Design Procedure (CBF example):
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AISC 360-10
ASCE 7-10AISC 341-10
United StatesR. Tremblay, Polytechnique Montreal, Canada 16
9NBCC 2010
CSA S16-09
Canada
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Seismic Force Resisting Systems
Plastic Hinge (typ.)
Shearyielding
Plastic Hinge (typ.)
Tensionyielding
Plastic HingeTension
yielding
Tensionyielding
Compressionyielding e
Plastic Hinge (typ.)
Plastic Hinge
End-plateBending
Shearyielding
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10
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11
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NCh2369 (2003)
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12
Structural damage & residual deformations are expected when applying this design strategy
Kobe, 1995 Kobe, 1995
C.-M. Uang, UCSDR. Tremblay, Polytechnique Montreal, Canada 23
Variability & Uncertainty
in Demand & Response
0 4 8 12 16Number of Storeys
0.0
1.0
2.0
3.0
4.0
/ h
s (%
)
84th percentile50th percentilePredictedIndividual Record
0.0 1.0 2.0 3.0 4.0Period (s)
0.0
0.5
1.0
1.5
S a (g
)
Historical Records
Ground MotionsDesign Spectrum
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13
Bruneau, M., Sabelli, R., and Uang C.-M. (2003) Ductile Design of Steel Structures, 2nded., Wiley
AISC. (2013) Seismic Design Manual, 2nd ed., AISC
Filiatrault, A., Tremblay, R., Christopoulos, C., Foltz, B., and Pettinga, D. (2013)Elements of Earthquake Engineering and Structural Dynamics, 3rd ed.,Presses Internationales Polytechnique (PIP)
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Seismic Loading and Analysis(ASCE 7-10 vs NBCC & NCh codes)
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14
0.0 0.5 1.0 1.5 2.0 2.5 3.0Period, T (s)
0.0
0.4
0.8
1.2
1.6
2.0
S a (g
)
0.53 g
1.22 g
0.23 g
T = 1.0 s
T = 0.2 s
Absolute AccelerationResponse Spectrum
(5% damping)
T = 2.0 s
0.0 10.0 20.0 30.0 40.0Time (s)
-0.4
-0.2
0.0
0.2
0.4
ag (g)
-0.4-0.20.00.20.4
a (g)
-1.2-1.0-0.8-0.6-0.4-0.20.00.20.40.60.81.01.2
a (g)
0.53
1.22
0.57
-0.4
-0.2
0.0
0.2
0.4
a (g)
- 0.23
M6.7 1994 NorthridgeCastaic - Old Ridge Route St. 90o
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Required Seismic Data
(from maps or GS websites)
MCER Spectral Valuesfor Site Class B:
SS (0.2s)
S1 (1.0s)
Long-period transition period:
TL
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15
http://earthquake.usgs.gov/hazards/designmaps/usdesign.php
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http://earthquake.usgs.gov/designmaps/us/application.php
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16
http://earthquake.usgs.gov/designmaps/us/application.php
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http://earthquake.usgs.gov/designmaps/us/application.php
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17
http://earthquake.usgs.gov/hazards/designmaps/usdesign.php
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http://www.earthquakescanada.nrcan.gc.ca/hazard-alea/zoning-zonage/NBCC2010maps-eng.php
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18
http://www.earthquakescanada.nrcan.gc.ca/hazard-alea/interpolat/index_2010-eng.php
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19
MCER SS & S1 Spectral Valuesfor Site Class B
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20
Importance Factor, IeDepends on the Occupancy Category:
I. Buildings that represent low hazardto human life in the event of failure
II. All buildings except those listed inOccupancy Categories I, III & IV
III. Buildings that represent substantial hazardto human life in the event of failure
IV. Essential facilities
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21
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22
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23
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T from: - T = Ta ; or- Dynamic analysis; except that T < CuTa for strength design
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24
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FF
VMx
i
xxhx hxh i
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25
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26
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27
= redundancy factorEarthquake Effects:
Load combinations including E:
When combining the two above:
Amplified Earthquake Loads
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P- effects can be neglected if < 0.1 Earthquake effects x 1/(1-) Nonlinear static or dynamic analysis
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28
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29
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2011 Decreto
2011 Decreto
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30
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Fk
Zk
h
2011 Decreto
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31
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RASCE/SEI 7-10
3-1/468
3-1/24-1/2
87
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32
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Seismic Design of Steel Structuresin accordance with AISC 341-10
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33
Inelastic response of framesPlastic
Hinge (typ.)Shearyielding
Plastic Hinge (typ.)
Tensionyielding
Plastic HingeTension
yielding
Tensionyielding
Compressionyielding e
Plastic Hinge (typ.)
Plastic Hinge
End-plateBending
Shearyielding
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16 seismic forceresisting systemsdetailed for ductileseismic response
+
SFRS not specificallydetailed for seismic resistance
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34
VeR
V =
Perimetermembers
RoofDiaphragm
Braceconnections
Bracingmembers
Anchor rods
Foundations
V V
Capacity DesignPoutrelle(typ.) Poutre de toit
(typ.)
Poteau(typ.)
Feuille de tablier mtall ique
typ.)
Contreventement (typ.)
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Control ofLocal Buckling
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35
Expected (probable)material strength
Liu, J. et al. (2007). AISC Eng.
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Concentrically Braced Frames (SCBFs)
Energy dissipated in bracing members through tensile yielding and flexural hinging
Connections and other members expected to remain essentially elastic
Tensionyielding (typ.)
Inelastic bucklingwith plastic hinge (typ.)
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36
Kobe 1995
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37
Uriz and Mahin (2004) Univ. of California, Berkeley
Fracture in1st cycle at1 2% hs1
2
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Northridge 1994Photos from Peter Maranian, Brandow and Associates (P. Uriz Thesis, 2005)
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38
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
/ LH (%)-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
P /
AgF
y
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 / hs (%)
HSS 254 x 254 x 12b/t = 18, KL/r = 42
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39
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-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
/ LH (%)-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
P /
Py
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 / hs (%)
RHS-4KL/r = 40b0/t = 17
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
/ LH (%)-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 / hs (%)
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
/ LH (%)-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 / hs (%)
RHS-2KL/r = 40b0/t = 13
RHS-19KL/r = 60b0/t = 13
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
/ LH (%)-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
P /
Py
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 / hs (%)
CHS-1KL/r = 42b0/t = 30
-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
/ LH (%)-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
-3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 / hs (%)
-3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0
/ LH (%)-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
-4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 4.0 / hs (%)
CHS-2KL/r = 62b0/t = 31
W-6KL/r = 67b0/t = 5.9
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40
W4
W6
W4 W660004000
2000
0
2000
4000
6000
3 2 1 0 1 2 3
Interstorey Drift Angle (%)P
(kN)
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0.0 0.5 1.0 1.5 2.0 2.5
Brace Slenderness, = (Fy / Fe)0.50
5
10
15
20
25
Duc
tility
at F
ract
ure,
f
f = 2.4 + 8.3
y
-6 -4 -2 0 2 4 6
-10 -8 -6 -4 -2 0 2 4 6 8 10
.
KL/r = 93HSS 127x76x4.8
KL/r = 142HSS 76x76x4.8
f f
yy
-6 -4 -2 0 2 4 6
-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
P /
A gF y
KL/r = 42HSS 254x254x12
f
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41
Design Bracing Configuration Along any braced line, between 30% & 70% of lateral
load is resisted by tension braces Tension-only braced frames not permitted K-bracing not permitted
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42
Design Bracing Members Braces must resist gravity + lateral loads Pn in tension and compression as per AISC 360-10 KL/r < 200 Section must meet seismic hd limits For built-up sections, individual components must
meet KL/r limits and stitch subjected to shear under buckling must meet minimum shear strength
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L
L
H
N
KLout 0.9 LHKLin 0.5 LN
KLout 0.5 LHKLin 0.5 LN
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43
Bracing ConfigurationTension-only braced frames permitted
Bracing MembersSection must meets b/t limits that vary with KL/r
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Cexp
Cexp
Design Expected Brace Strengths
P/P
y
Texp
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44
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0.0 0.5 1.0 1.5 2.0 2.5
0.0
0.2
0.4
0.6
0.8
1.0
1.2
Cu
/ AgF
y
Cu (S16-01, n = 1.34)Cu (AISC 1999)
0 50 100 150 200KL/r
0.0 0.5 1.0 1.5 2.0 2.50.0
0.2
0.4
0.6
0.8
1.0
C' u
/ A
gFy
(Duc
tility
= 1
.0)
Cu (S16-01, n = 1.34)
0 50 100 150 200KL/r
0.0 0.5 1.0 1.5 2.0 2.50.0
0.2
0.4
0.6
0.8
1.0
C' u
/ A
gFy
(Duc
tily
= 3.
0)
Cu (S16-01, n = 1.34)C'u (mean)
0.0 0.5 1.0 1.5 2.0 2.50.0
0.2
0.4
0.6
0.8
1.0
C' u
/ A
gFy
(Duc
tility
= 5
.0)
Cu (S16-01, n = 1.34)C'u (mean)
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Texp = A RyFy
Cexp = A (1.12 Fcr) where Fcre = Fcr with RyFy< A RyFy
Cexp = 0.3 Cexp
Cexp
Cexp
Texp
45
Texp = A RyFyCexp = A (1.12 Fcr) ,Fcre = Fcr with RyFy
< A RyFyCexp = 0.3 Cexp
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Schimdt and Bratlett (2002)
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46
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Design Brace ConnectionMust resist brace Texp & 1.1 Cexp
Must allow for ductile rotational behavior or resist 1.1 x brace expected flexural strength
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Net Section Fracture(HSS Braces)
Kobe 1995
Archambault et al. (1995)Tremblay and Bolduc (2002)
cole Polytechnique,Montreal
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Kobe1995
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48
Yang and Mahin (2004) Univ. of California, Berkeley
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Kanwinde and Fell (2005) Univ. of California, Berkeley
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49
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50
Sabelli (2003) Sabelli (2005)
Sabelli (2003)
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Prototype Test Specimen
Attachment toload frame:
LW
LW
LC-C
LTS
2 t 2 t g g
Gussetplate
Gussetplate
35O
Coverplate
Coverplate
5182
(min
) @
793
7 (m
ax)
102
290
35O
Elevation
Specimen
End Restraint
Side View
EndHinge
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Design Columns and BeamsMust resist gravity loads plus two brace force scenarios:
Upon first buckling & yielding (Texp & Cexp) In post-buckling range (Texp & Cexp)
Beams in V and inverted-V bracing must be continuous between columns
Column sections must meet hdBeam sections must meet md
52
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At Buckling Post-Buckling
T T
T T
T T CC
CC
CCexp,1 exp,1
exp,2 exp,2
exp,3 exp,3 exp,3exp,3
exp,2exp,2
exp,1exp,1
F3 F3F3
F2 F2F2
F1 F1F1
W W WW W WW W W
Brace force scenarios for columns:
Northridge 1994Photos from Finley 1999(P. Uriz Thesis, 2005)
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53
Taiwan 1999
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54
MRF
(typ
.)
BF (typ.)
5 @ 9000 = 45 000
[mm]PLAN
300(slab edge)
5 @
900
0 =
45 0
00
Gravity loads: Roof: Dead = 3.2 kPa Live = 1.0 kPa Floor: Dead = 3.5 kPa Partitions = 1.0 kPa Live = 3.8 kPa Exterior walls = 1.5 kPa
Seismic Load Data (NCh433): Zone 2 Soil Type C A= 0.30 g In-plane torsion omitted
Load Combinations: 1.2D + 1.6L 1.2D + 1.0L + 1.4E 0.9D + 1.4E
Seismic weight: P = 7720 kN (Level 9) 12635 kN (Levels 2-8) 12840 kN (Level 1)
Steel: BRB cores: Fyc = 260-290 MPa Other members: Fy = 345 MPa
Note: Redundancy factor, ,and seismic load effectswith overstrength factor, 0,are not considered.
SCBF
5500
EBF BRBF
4 @
400
0=
16 0
00
[mm]ELEVATIONS
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55
Static method of analysis
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SAP2000Analysis
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Brace Design
Brace Expected Strengths
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At Buckling
Column Design
1103
4890
4092 47492492
7916 791625914437
+ 1.2 x 644 (D)+ 1.0 x 372 (L)= 5893
-0.9 x 644 (D)= 1913
1103
4092
2001 4890
29072907
70077007
599
169 169169
599599 599
1692001
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57
Post-Buckling
Column Design
1103
4890
1227 5136662
6085 60867774437
+ 1.2 x 644 (D)+ 1.0 x 372 (L)= 6280
-0.9 x 644 (D)= 82
331
1227
600 4890
29072907
70077007
856
812 812812
856856 856
812600
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Column Design
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58
At Buckling Post-Buckling
Beam Design
1103 331
4092 1227
2001 600
2001 600
1103 331
1498 1210
939 556
1498 1210
939 556
1077 842
2907 2907
7007 7007
4890 4890
4890 4890
2907 2907
-1498 -1210
-939 -556
-2800 -2565
M = 243 M = 243
M = 759 M = 3896
M = 2785 M = 3939
1498 1210
939 556
1077 842
1.2 w + 1.0 w = 8.71
1.2 w + 1.0 w = 24.0
1.2 w + 1.0 w = 24.0
1.2 w + 1.0 w = 8.71
1.2 w + 1.0 w = 24.0
1.2 w + 1.0 w = 24.0
D
D
D
u u
u u
u u
D
D
D
L
L
L
L
L
L
[kN,m]
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Beam Design
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Next Steps:
Verify drifts and P-delta effectsPerform 3D analysis for in-plane torsionDesign connections
59
9000
O41.6 W610 Beam
Bolted EndPlate Connection
750 +
/-
4500 +
/-602
1
Hinge
4000
Once member sizes are known, more realistic, shorter, brace effective lengths can be used to assess brace resistances. Brace sizes may be reduced, which would diminish the force demand on beams and columns and, possibly, member sizes.
Period T* will increase if member sizes are reduced, which may lead to lower seismic loads and allow further reduction in member sizes.
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SCBF
5500
2 @ 4000= 8000
For this example:
T* = 0.55 s -> 0.65 sC = 0.119 -> 0.093 (22% reduction)
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Assignment no. 1
Redo the design of the braced frameconsidering that KL for braces are 5600 mm at Level 1
and 4500 mm at levels 2&3.
You may use/refer to the SAP2000 model & the spreadsheet that were used in the preliminary design
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Moment Resisting FramesEnergy dissipated by plastic hinging in beams and limited shear yielding in column panel zones. Plastic hinging in columns permitted at the base and in single-storey structures.
Connections and other members expected to remain essentially elastic
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61
Section must meet hdMust resist expected shear demand upon hingingMust be laterally braced
Design Beams
L'
L
L' = L - 2 x - d c
wpb
1.1 R My pb
1.1 R My pb
V = wL' / 2 + 2.2 R M / L'h y pb
Vh Vh
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Section must meet hdMust satisfy weak beam-strong column criteriaexcept for:
Columns with Puc < 0.3 AcFy in single-storey buildings or at the top storey of multi-storey buildings;Columns with Puc < 0.3 AcFy when their total shear contribution < 20% of total storey shear resistance and 33% of storey shear resistance along their MF line; orColumns that have shear capacity to demand ratio 50% gretaer than in the storey above.
Design Columns
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62
L'
L
L' = L - 2 x - d c x + d /2c x + d /2c
ww w
1.1 R My pb
1.1 R My pb
1.1 R My pb
1.1 R My pb
V = wL' / 2 + 2.2 R M / L'h y pb
Vh Vh
Vh
Vh
M'rc, i+1
M'rc, iCf, i
Cf, i+1
Weak beam-strong column criteria:
M*: projected at membercenter lines
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Member forcesupon beam hinging:
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x + d /2c x + d /2c
1.1 R My pb
1.1 R My pb Vh
Vh
V
V
Must meet: t > (dz + wz)/90Shear strength, Rn:
Design Column panel zone
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64
Design Beam-to-column connections
Must accommodate 4% storey drift angleMeasured flexural resistance at column face (Mcf) at 4% storey drift angle > 80% MpbPerformance considered as demonstrated if pre-qualified connections are used; otherwise must be demonstrated through physical cyclic testing:
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http://www.aisc.org
Design requirements
Welding requirements
Bolting requirements
Requirements for 6pre-qualified connections
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Welded Unreinforced FlangeWelded Web
Bolted End Plate
Kaiser Bolted Bracket
Bolted Flange PlateReduced Beam Section
Conxtech Conxl
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MRF
Example
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From analysis:
b) Moments from response spectrum analysis
c) Maximum probable bending moments and shear forces at plastic hinge locations
d) Beam induced forces imposed at column faces
e) Beam induced forces at column centerlines
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RBS:
> 682 kN-m => OK!
> 442 kN => OK!
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At Level 1:
M*pb = 656 + 738 = 1394 kN-m
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371 kN & 354 kNshears in columns (see above)
1992 kN force from Mcf = 1319 kN-m :1992 = 1319/(678-16.3)
17 kN force induced by floor diaphragm (from equilibrium of the two column shears)
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