Modeling Steel Moment Resisting Frames with OpenSeesopensees.berkeley.edu/.../SteelMomentFrames.pdf · 2014-10-01 · ... Modeling Steel Moment-Resisting Frames with ... 4-story building

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!


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!


(Images courtesy of Prof. M. Engelhardt) !

Steel Components for Nonlinear Modeling in MRFs!


(Image courtesy of Prof. M. Engelhardt) !

Steel Components for Nonlinear Modeling in MRFs!

Beam (Flexural Yielding)

Panel Zone (Shear Yielding)

Column (Flexural & Axial

Yielding)


(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


(Image courtesy of Prof. M. Engelhardt) !

Steel Components for Nonlinear Modeling in MRFs!-Panel Zone Shear Yielding!


(Image from Suzuki and Lignos 2014)!

Steel Components for Nonlinear Modeling in MRFs!-Column Plastic Hinging!


Image Source: NIST GSR 10-917-5!

Simulation Approach!



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)!



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!


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


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


Steel Material Models Available in OpenSees!

Steel01-Simple Bilinear! Steel02-Giuffre Menegotto-Pinto Model with Isotropic Strain Hardening!


Steel Material Models Available in OpenSees!Utilization of Steel01 for Modeling of Steel Components!


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!


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)!


Steel2.tcl – FiberSteelWsection2d!


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.!


Steel2.tcl – Procedure: ForceBeamWSection2d!

àUses forceBeamColumn element!


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!


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!


Procedure for Modeling Panel Zones!-Available from OpenSees Examples Posted by Dr. L. Eads!


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!


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!


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!


4-Story SMF – Concentrated Plasticity Approach!From Steel2d.tcl: Procedure to Create Elastic Beam-Column Element!

àLook for Procedure! ElasticBeamSection2d!


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 !


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)!


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!


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 !


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!


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


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


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)!


Utilizing the Modified IMK Model in OpenSees!Visit: dimitrios.lignos.research.mcgill.ca/databases/component/!


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!


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!


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


0 0.05 0.11

2

3

4

Roof

Story Drift Ratio, SDR [rad]Fl

oor


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!


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!


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!


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!


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.!

!


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.!

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Modeling Steel Moment Resisting Frames with OpenSeesopensees.berkeley.edu/.../SteelMomentFrames.pdf · 2014-10-01 · ... Modeling Steel Moment-Resisting Frames with ... 4-story building