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1 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Modeling Steel Moment Resisting Frames with OpenSees!
OpenSees Workshop, University of California, Berkeley!September 26th 2014!
DIMITRIOS G. LIGNOS!ASSISTANT PROFESSOR!
MCGILL UNIVERSITY, MONTREAL CANADA!
With Contributions By: Ahmed Elkady* and Samantha Walker*!*Graduate Students at McGill University!
2 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Agenda!² Nonlinear Modeling of Steel MRFs!
² Steel Components for Nonlinear Modeling!
² Distributed and Concentrated Plasticity!
² Nonlinear Force-Based Elements !
² Zero Length Elements (Concentrated Plasticity) !
² Background on Available Steel Materials in OpenSees!
² Examples and Applications!
² Summary Remarks!
3 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
(Images courtesy of Prof. M. Engelhardt) !
Steel Components for Nonlinear Modeling in MRFs!
4 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
(Image courtesy of Prof. M. Engelhardt) !
Steel Components for Nonlinear Modeling in MRFs!
Beam (Flexural Yielding)
Panel Zone (Shear Yielding)
Column (Flexural & Axial
Yielding)
5 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
(Images courtesy of Prof. M. Engelhardt) !
Steel Components for Nonlinear Modeling in MRFs!-Beam Plastic Hinging!
Local buckling of Beams with RBS
Lateral torsional buckling of Beams with RBS
6 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
(Image courtesy of Prof. M. Engelhardt) !
Steel Components for Nonlinear Modeling in MRFs!-Panel Zone Shear Yielding!
7 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
(Image from Suzuki and Lignos 2014)!
Steel Components for Nonlinear Modeling in MRFs!-Column Plastic Hinging!
8 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Image Source: NIST GSR 10-917-5!
Simulation Approach!
9 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Image Source: NIST GSR 10-917-5!
Concentrated Plasticity Models!
Advantages!² Fairly simple!² Effective for interface effects!² Computationally efficient!
Disadvantages!² Require the moment – rotation relationship !(as opposed to engineering stress-strain)!² They don’t capture P-M interaction !(critical for columns)!
10 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Image Source: NIST GSR 10-917-5!
Distributed Plasticity Models!
Advantages!² Force- and displacement-based
element permits spread of plasticity along the element!
² P-M interaction can be captured!
Disadvantages!² Localization!² Requires fiber section discretization (# fibers
matters)!² Deteriorating phenomena (local buckling)
difficult to capture with available engineering stress-strain models in OpenSees!
11 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Example for Today’s Presentation!
3-bays @ 6.10m
I I I I
I
I
I
I
I
I
I
I
30.5
0 m
42.70 m
I
I
I
I
I
I
I
I
I
I
I
I
I I I I
I
I
I
I
Modeled SMF
² 4-story building with perimeter steel special moment frames (SMFs)!
² Design location Bulk Center Los Angeles, CA!
² Design provisions: ASCE 7-10, AISC 2010!
² Fully-Restrained Beam-to-Column connections with Reduced Beam
Sections (RBS)à See AISC-358-10 or FEMA-350!
² First mode period: 1.51sec! (Source: Elkady and Lignos 2014)!
W21x73
W21x73
W21x57
W21x57
W24
x103
W24
x103
W24
x103
W24
x103H =
16.
60m W
24x6
2
W24
x62
W24
x62
W24
x62
3 bays @ 6.10m
4.6m
4.0m
4.0m
4.0m
Perimeter SMF
Rigid links
Leaning Column
12 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
W21x73
W21x73
W21x57
W21x57
W24
x103
W24
x103
W24
x103
W24
x103H =
16.
60m W
24x6
2
W24
x62
W24
x62
W24
x62
3 bays @ 6.10m
4.6m
4.0m
4.0m
4.0m
Perimeter SMF
Rigid links
Leaning Column
Modeling with Distributed Plasticity!
Node i Node j
Fiber element
Engineering stress-‐strain domain
x z
y
Force-‐ or Displacement-‐Based Element
IntegraNon point
13 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Steel Material Models Available in OpenSees!
Steel01-Simple Bilinear! Steel02-Giuffre Menegotto-Pinto Model with Isotropic Strain Hardening!
14 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Steel Material Models Available in OpenSees!Utilization of Steel01 for Modeling of Steel Components!
15 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Steel Material Models Available in OpenSees!Utilization of Steel02 for Modeling of Steel Components!
ï0.04 ï0.02 0 0.02 0.04ï3000
ï2000
ï1000
0
1000
2000
3000
Chord Rotation e [rad]
Mom
ent [
kNïm
m]
SimulationExperimental Data
From calibraNon
Example – Utilization of Steel02 Material Model!
16 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Number of Fibers for Cross Section Discretization!
W-Shapes: 12 MP gives remarkable accuracy in terms of local response estimates!Biaxial bending and failures associated with weak axis bending: (40MP) 2x8 fibers (Flange) 1x8 fibers (Web)!
àFollow the recommendations by Kostic & Filippou (2012)!
17 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Steel2.tcl – FiberSteelWsection2d!
18 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Nonlinear Beam-Column Elements in OpenSees!-Use of forceBeamColumn element!
Recommendations by Kostic & Filippou (2012)!
Node i Node j
x z
y
Force-‐Based Element
IntegraNon point
Fiber element
• Only one element is adequate!• 5 integration points along the
member length are sufficient most of the times for modeling of steel MRFs!
(Neuenhofer and Filippou 1997) à good discussion why you may want to consider using force based elements over displacement-based ones.!
19 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Steel2.tcl – Procedure: ForceBeamWSection2d!
àUses forceBeamColumn element!
20 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
model Basic –ndm 2 –ndf 3!source Steel2d.tcl!!# set some lists containing floor and column line locations and nodal masses!set floorLocs {0. 204. 384. 564.}; # floor locations in inches!set colLocs {0. 360. 720. 1080. 1440. 1800.}; #column line locations in inches!set massesX {0. 0.419 0.419 0.430}; # mass at nodes on each floor in x dirn!set massesY{0. 0.105 0.105 0.096} ; # “ “ “ “ “ “ in y dirn!!# add nodes at each floor at each column line location & fix nodes if at floor 1! foreach floor {1 2 3 4 5} floorLoc $floorLocs massX $massesX massY $massesY {! foreach colLine {1 2 3 4} colLoc $colLocs {! node $colLine$floor $colLoc $floorLoc -mass $massX $massY 0.! if {$floor == 1} {fix $colLine$floor 1 1 1}! }! }!#uniaxialMaterial Steel02 $tag $Fy $E $b $R0 $cr1 $cr2 $a1 $a2 $a3 $a4!uniaxialMaterial Steel02 1 55.0 29000. 0.02 19.0 0.925 0.15 0.12 0.90 0.18 0.90; # material to be used for steel elements!!# set some list for col and beam sizes!set colSizes {W24x103 W24x103 W24X103 W24x64}; #col sizes stories 1, 2, 3 and 4!set beamSizes {W21x73 W21X73 W21X57 W21x57}; #beams sizes floor 1, 2, 3 and 4!!# add columns at each column line between floors!geomTransf PDelta 1! foreach colLine {1 2 3 4} {! foreach floor1 {1 2 3 } floor2 { 2 3 4 5 } {! set theSection [lindex $colSizes [expr $floor1 -1]]; # obtain section size for column! ForceBeamWSection2d $colLine$floor1$colLine$floor2 $colLine$floor1 $colLine$floor2 $theSection 1 1 –nip 5! }! }!#add beams between column lines at each floor!geomTransf Linear 2!foreach colLine1 {1 2 3} colLine2 {2 3 4} {!foreach floor {2 3 4 5} {! set theSection [lindex $beamSizes [expr $floor -2]]; # obtain section size for floor! ForceBeamWSection2d $colLine1$floor$colLine2$floor $colLine1$floor $colLine2$floor $theSection 1 2!}!}!
MRF1.tcl!Same Model in 35 lines!
(Tcl Code by F. McKenna) !
Selection of material model!
Selection of nonlinear force beamColumn element!
21 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Panel Zone Modeling!
W21x73
W21x73
W21x57
W21x57
W24
x103
W24
x103
W24
x103
W24
x103H =
16.
60m W
24x6
2
W24
x62
W24
x62
W24
x62
3 bays @ 6.10m
4.6m
4.0m
4.0m
4.0m
Perimeter SMF
Rigid links
Leaning Column
db!
dc!How to obtain the input parameters? !
see Gupta and Krawinkler (1999)!
Nonlinear force-beam !column elements!
Elastic beam !column elements!
22 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Procedure for Modeling Panel Zones!-Available from OpenSees Examples Posted by Dr. L. Eads!
23 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
4-Story SMF – Distributed Plasticity Approach!Basic Results – Nonlinear Static Procedure!First Mode Lateral Load Pattern!
0 0.02 0.04 0.060
0.05
0.1
0.15
0.2
0.25
Roof Drift Ratio, 6/H [rad]
Base
She
ar/S
eism
ic W
eigh
t, V/
W
Without P−DeltaWith P−Delta
0 0.02 0.04 0.061
2
3
4
Roof
Floo
r
Normalized Floor Displacement [rad]
6r/H = 1%6r/H = 2%6r/H = 3%6r/H = 4%
Does not capture strength deterioraNon of steel components
Formation of a 3-story mechanism!
Cs!Ω!
24 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
4-Story SMF – Distributed Plasticity Approach!Basic Results – Nonlinear Response History Analysis!
0 0.02 0.041
2
3
4
Roof
Story Drift Ratio, SDR [rad]Fl
oor
SF=1.0SF=1.5
0 2 4 60
0.5
1
1.5
Sa
(T, 5
%) [
g]
T [sec]
Canoga Park Record! Northridge 1994 Earthquake!
Unscaled (SF=1.0)!
Does not include the effect of cyclic deterioration on flexural strength and
stiffness of steel components!
25 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
W21x73
W21x73
W21x57
W21x57
W24
x103
W24
x103
W24
x103
W24
x103H =
16.
60m W
24x6
2
W24
x62
W24
x62
W24
x62
3 bays @ 6.10m
4.6m
4.0m
4.0m
4.0m
Perimeter SMF
Rigid links
Leaning Column
4-Story SMF – Concentrated Plasticity Approach!
Elastic beam-column element!
Zero Length element (rotational springs)!With idealized moment – rotation relationship!
26 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
4-Story SMF – Concentrated Plasticity Approach!From Steel2d.tcl: Procedure to Create Elastic Beam-Column Element!
àLook for Procedure! ElasticBeamSection2d!
27 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Available Steel Material Models for Modeling the Moment – Rotation Relationship of a Steel Component!
² Steel01 (Basic Bilinear)!
² Steel02 (Giuffre Menegotto-Pinto Model with Isotropic Strain
Hardening)!
² Modified Ibarra-Medina-Krawinkler (IMK) Deterioration Model with
Bilinear Hysteretic Response (or Bilin in OpenSees) à Considers
Strength and Stiffness Deterioration of Steel Components !
28 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
The Modified IMK Deterioration Model!-Input Model Parameters!
The deduced moment rotation relationship of the component under consideration is needed for input parameter identification!
(Image Source: Lignos and Krawinkler 2012)!
29 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
The Modified IMK Deterioration Model !-Considering Slab Effects (see Elkady and Lignos 2014)!
-0.12 -0.06 0 0.06 0.12-4500
-2250
0
2250
4500
Chord Rotation (rad)
Mom
ent (
kN-m
)
M+c
Post Cap. Strength Det.
Strength Det.
M+y
θ-u
M-r
Unload. Stiff. Det.
θ+p
Initial Backbone Curve
M-cθ-
pcθ-
pM-
ref.
M-y
The deduced moment rotation relationship of the component under consideration is needed for input parameter identification!
N.A!
30 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Utilizing the Modified IMK Model in OpenSees!Visit: dimitrios.lignos.research.mcgill.ca/databases/steel/!
Contains data from more than 300 experiments from steel beams !
31 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Utilizing the Modified IMK Model in OpenSees!Sample Model Calibrations!
(Sources: Lignos and Krawinkler 2011, 2013)!
Steel Beam (bare) with RBS! Steel Beam (Composite) with RBS!
32 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Utilizing the Modified IMK Model in OpenSees!Visit: dimitrios.lignos.research.mcgill.ca/databases/component/!
3-14 3: Modeling of Frame Components PEER/ATC-72-1
3.2.2.4 Regression Equations for Modeling Parameters
It is understood that the trends alone do not provide sufficient information to fully quantify modeling parameters. Empirical equations based on multi-variate regression analysis that account for combinations of geometric and material parameters in the quantification of modeling parameters are suggested.
Data were exploited to derive regression equations for the modeling parameters �p, �pc, and �. The equations have been derived from the full RBS and non-RBS data sets, using the full range of beam depths available in each set (4 in. � d � 36 in. for non-RBS connections, and 18 in. � d � 36 in. for RBS connections). The following equations are suggested to estimate modeling parameters as a function of geometric and material parameters that were found to be statistically significant.
Pre-capping plastic rotation, �p, for beams with non-RBS connections:
0.14 0.230.365 0.7210.34 2
10.0872 21" 50
f unit yp
w f unit
b c Fh L dt t d c
�� �� �� � � ��� � � �� �� � � � � � � � � � � � �� �
(3-1)
Pre-capping plastic rotation, �p, for beams with RBS connections:
0.10 0.1185 0.070.314 0.760.113 2
10.192 21" 50
f unit ybp
w f y unit
b c FLh L dt t r d c
�� � �� �� � � � � ��� � � �� �� � � � � � � � � � � � � � � �� �
(3-2)
Post-capping rotation, �pc, for beams with non-RBS connections:
0.80 0.430.565 0.28 2
15.702 21" 50
f unit ypc
w f unit
b c Fh dt t c
�� �� �� � � ��� � � �
� � � � � � � � � � �� � (3-3)
Post-capping rotation, �pc, for beams with RBS connections:
0.863 0.108 0.360.513 2
9.622 50
f unit ybpc
w f y
b c FLht t r
�� � �� � � � � � ��� �
� � � � � � � � � � � �� (3-4)
Reference cumulative plastic rotation, �, for beams with non-RBS connections:
��0.595 0.361.34 2
5002 50
f unit yt
y w f
b c FhM t t
� �� � � � ��� ��� � � � � � � � ��
(3-5)
213 protocol [42] (see Fig. 2a and b). The same steel-beam-to-column214 connection is used in both examples (i.e. the set of A and k param-215 eters is identical for both cases). When a symmetric loading proto-216 col with increased inelastic cycles is utilized, the steel component217 fractures at a chord rotation of about 4.4% (see Fig. 2c). In the case
218of the near-fault loading protocol, the same component fractures at219about 8% chord rotation (see Fig. 2d). Due to the small amplitude of220inelastic cycles prior to the main pulse of the near-fault protocol221(see Fig. 2b) the steel component does not dissipate much energy;222thus it does not fracture. The same observation can be seen from
Chord Rotation θ
Mom
ent
My
Mc
θp
θpc
Mr
θu
Ke
Chord Rotation θ
Mom
ent
InitialBackBone Curve
Post Cap. Strength Det.
Strength Det.
Unload.Stiffness Det.
(a) backbone curve (b) basic modes of cyclic deterioration
Fig. 1. Modified Ibarra–Krawinkler deterioration model (Lignos and Krawinkler [39]).
Fig. 2. Effect of loading history on fracture due to low cycle fatigue (a) symmetric loading protocol; (b) near-fault loading protocol; (c) hysteretic response due to symmetricloading protocol; (d) hysteretic response due to near-fault loading protocol; (e) cycles to fracture versus normalized cumulative dissipated energy due to symmetric loadingprotocol; (f) cycles to fracture versus normalized cumulative dissipated energy due to near-fault loading protocol.
D.G. Lignos et al. / Computers and Structures xxx (2011) xxx–xxx 3
CAS 4611 No. of Pages 10, Model 5G
7 February 2011
Please cite this article in press as: Lignos DG et al. Numerical and experimental evaluation of seismic capacity of high-rise steel buildings subjected to longduration earthquakes. Comput Struct (2011), doi:10.1016/j.compstruc.2011.01.017
213 protocol [42] (see Fig. 2a and b). The same steel-beam-to-column214 connection is used in both examples (i.e. the set of A and k param-215 eters is identical for both cases). When a symmetric loading proto-216 col with increased inelastic cycles is utilized, the steel component217 fractures at a chord rotation of about 4.4% (see Fig. 2c). In the case
218of the near-fault loading protocol, the same component fractures at219about 8% chord rotation (see Fig. 2d). Due to the small amplitude of220inelastic cycles prior to the main pulse of the near-fault protocol221(see Fig. 2b) the steel component does not dissipate much energy;222thus it does not fracture. The same observation can be seen from
Chord Rotation θ
Mom
ent
My
Mc
θp
θpc
Mr
θu
Ke
Chord Rotation θM
omen
t
InitialBackBone Curve
Post Cap. Strength Det.
Strength Det.
Unload.Stiffness Det.
(a) backbone curve (b) basic modes of cyclic deterioration
Fig. 1. Modified Ibarra–Krawinkler deterioration model (Lignos and Krawinkler [39]).
Fig. 2. Effect of loading history on fracture due to low cycle fatigue (a) symmetric loading protocol; (b) near-fault loading protocol; (c) hysteretic response due to symmetricloading protocol; (d) hysteretic response due to near-fault loading protocol; (e) cycles to fracture versus normalized cumulative dissipated energy due to symmetric loadingprotocol; (f) cycles to fracture versus normalized cumulative dissipated energy due to near-fault loading protocol.
D.G. Lignos et al. / Computers and Structures xxx (2011) xxx–xxx 3
CAS 4611 No. of Pages 10, Model 5G
7 February 2011
Please cite this article in press as: Lignos DG et al. Numerical and experimental evaluation of seismic capacity of high-rise steel buildings subjected to longduration earthquakes. Comput Struct (2011), doi:10.1016/j.compstruc.2011.01.017
(Sources: Lignos and Krawinkler 2011, 2013)!
33 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Utilizing the Modified IMK Model in OpenSees!Visit: dimitrios.lignos.research.mcgill.ca/databases/component/!
34 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
4-Story – Concentrated Plasticity Approach!Steel2d.tcl: Rotational Spring with SteelWsectionMR!
àLook for SteelWSectionMR!Uses the multivariate-regression equations and utilizes the modified IMK model in OpenSees!
35 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
4-Story SMF – Concentrated Plasticity- Deterioration!Nonlinear Static Analysis – First Mode Lateral Load Pattern!Comparisons with Distributed Plasticity Model!
0 0.02 0.04 0.060
0.05
0.1
0.15
0.2
0.25
Roof Drift Ratio, 6/H [rad]
Base
She
ar/S
eism
ic W
eigh
t, V/
W
Fiber−Based,Steel02Spring−Mod. IMK Model
0 0.02 0.04 0.061
2
3
4
Roof
Floo
r
Normalized Floor Displacement [rad]
Formation of a 3-story mechanism!(Did not change in this case)!
Due to! strength deterioration!
36 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
4-Story SMF – Concentrated Plasticity- Deterioration!Nonlinear Response History Analysis with Canoga Park Record!Comparisons with Distributed Plasticity Model!
0 0.02 0.041
2
3
4
Roof
Story Drift Ratio, SDR [rad]
Floo
r
Fiber−Based,Steel02Spring−Mod. IMK Model
0 0.05 0.11
2
3
4
Roof
Story Drift Ratio, SDR [rad]Fl
oor
Fiber−Based,Steel02Spring−Mod. IMK Model
Canoga Park SF=1.0! Canoga Park SF=1.5!
The effect of cyclic deterioration on the !structural response is minimal for SF = 1.0
(close to design level earthquake)!
The effect of cyclic deterioration on the !structural response is significant!
37 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
4-Story SMF – Concentrated Plasticity- Deterioration!Nonlinear Response History Analysis with Canoga Park Record!Comparisons with Distributed Plasticity Model!
0 0.02 0.04 0.06 0.08 0.1−0.2
−0.15
−0.1
−0.05
0
0.05
0.1
0.15
0.2
1st Story Drift Ratio [rad]
Nor
mal
ized
Bas
e Sh
ear V
1 / W
Spring−Mod. IMK ModelFiber−Based, Steel02
Canoga Park Record SF=1.5!
Due to strength deterioration!
Approaching !dynamic collapse!
38 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Case studies: Archetype office steel buildings with perimeter steel special moment frames designed in Urban California (ASCE 7-10, AISC-2010)!
Source: National Seismic Hazard Map (USGS 2008)!(Sources: Elkady and Lignos 2014)!
4 Story
8 Story
12 Story
20 Story
W21x73 W21x73 W21x73
W21x73 W21x73 W21x73
W21x57 W21x57 W21x57
W21x57 W21x57 W21x57
W24
x103
W24
x103
W24
x103
W24
x103
54’
W24
x62
W24
x62
W24
x62
W24
x62
W27x94 W27x94 W27x94
W24x84 W24x84 W24x84
W24
x131
W24
x131
W24
x131
W24
x131
W24x84 W24x84 W24x84
W21x68 W21x68 W21x68
W24
x94
W24
x94
W24
x94
W24
x94
W30x108 W30x108 W30x108
W30x116 W30x116 W30x116
W30x116 W30x116 W30x116
W27x94 W27x94 W27x94
W24
x146
W24
x192
W24
x192
W24
x146
106’
W
24x1
31
W24
x176
W24
x176
W24
x131
W24x84
W24x84
W24x84
W27x94
W27x94
W27x94
W24x84
W24x84
W24x84
W27x94
W27x94
W27x94
158’
W
24x
162
W24
x20
7
W24
x20
7
W24
x16
2
W24
x13
1
W24
x17
6
W24
x17
6
W24
x13
1
W30x124
W30x124
W30x124
W30x132
W30x132
W30x132
W30x132
W30x132
W30x132
W24
x22
9
W24
x27
9
W24
x27
9
W24
x22
9
W24
x19
2
W24
x25
0
W24
x25
0
W24
x19
2
W30x116
W30x116
W30x116
W30x132
W30x132
W30x132
W30x116
W30x116
W30x116
W30x116
W30x116
W30x116
W30x116
W30x116
W30x116
W24
x13
1 W
24x
84
W24
x13
1
W24
x13
1
W24
x94
W24
x94
W24
x13
1 W
24x
84
W33x152
W33x152
W33x152
W33x152
336’
W
14x4
55
W36
x487
W14
x370
W36
x441
W33x130
W33x130
W33x141
W14
x500
W36
x529
W14
x455
W33x152
W33x141
W33x152
W33x141
W33x141
W14
x370
W
14x3
11
W36
x395
W
36x3
61
W24x68
W33x130
W24x68
W33x130
W33x130
W33x130
W33x152
W33x152
W36
x330
W
36x2
32
W27
x194
W
27x1
29
W14
x283
W
14x2
33
W14
x193
W
14x1
32
W36
x262
Collapse Assessment of Steel SMFs Using Concentrated Plasticity Approach!
39 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
0 0.05 0.1 0.150
0.5
1
1.5
2
2.5
Maximum Story Drift Ratio [rad]
Sa (T
1, 5%
) [g
]
Median Collapse Capacity ŜCT!
Collapse!
Example: Collapse Risk of 4-Story Steel SMF!Incremental Dynamic Analysis – Utilization of 44 Ground Motions!
Source: Elkady and Lignos (2014)!
0 1 2 30
0.2
0.4
0.6
0.8
1
IM = Sa(T1, 5%) [g]Pr
obab
ilty
of C
olla
pse
SCT = 1.030 ` = 0.452
Simulation ResultsLognormal CDF
IDA Curves! Collapse Fragility Curve!
40 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Concluding Remarks!² Modeling Steel Moment Resisting Frames in OpenSees !
Ø You can use a number of readily available tools (procedures in tcl, examples, web-based tools, etc)!
² Steel Components to Consider!ü Steel Beams, Columns and Panel Zones!
² Distributed Versus Concentrated Plasticity Approach!ü For low rise code-compliant steel buildings with perimeter MRFs the
differences should not be large for “design level earthquakes” – Distributed plasticity models capture cyclic hardening, P-M interaction!
² If Performance Evaluation at Large Deformations is the Objective: Component Deterioration Must be Considered!ü Concentrated Plasticity with Degrading Phenomenological Models will do
reasonably well for low- to mid-rise steel MRFs.!
!
41 D. G. Lignos – Modeling Steel Moment-Resisting Frames with OpenSees!
Thank you for your kind attention!!
For more information visit: dimitrios-lignos.research.mcgill.ca!References:!1. Elkady, A., Lignos, D.G. (2014). “Modeling of the Composite Action in Fully Restrained Beam-to-Column
Connections: Implications in the Seismic Design and Collapse Capacity of Steel Special Moment Frames”, Earthquake Engineering and Structural Dynamics, EESD, doi: 10.1002/eqe.2430 (available in early view).!
2. Lignos, D.G., Krawinkler, H. (2013). “Development and Utilization of Structural Component Databases for Performance-Based Earthquake Engineering”, ASCE, Journal of Structural Engineering, Vol. 139 (NEES 2), pp. 1382-1394, doi:10/1061/(ASCE)ST.1943-541X.0000646.!
3. Lignos, D.G., Krawinkler, H. (2011). “Deterioration Modeling of Steel Components in Support to Collapse Prediction of Steel Moment Frames”, ASCE Journal of Structural Engineering, Vol. 137 (11), pp. 1291-1302, doi: 10.1061/(ASCE)ST.1943-541X.0000376.!
4. Lignos, D.G., Krawinkler, H. (2012). “Sidesway Collapse of Deteriorating Structural Systems under Seismic Excitations,” Report No. TB 177, The John A. Blume Earthquake Engineering Center, Stanford, CA.!
5. Ibarra, L., Medina, R., Krawinkler, H. (2005). “Hysteretic Models that Incorate Strength and Stiffness Deterioration”, Earthquake Engineering and Structural Dynamics, EESD, Vol. 34(12), pp. 1489-1511.!