Modeling s Cbf

28
Modeling SCB frames using beam-column elements Vesna Terzic UC Berkeley January 2013

description

modeling scbf using opensees

Transcript of Modeling s Cbf

Page 1: Modeling s Cbf

Modeling SCB frames using beam-column elements

Vesna Terzic UC Berkeley

January 2013

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Agenda

•  Different modeling approaches of SCBFs •  Line-element model of SCBF

•  3 different models of gusset plate connections will be considered and demonstrated on an example

•  Comparison of seismic responses of a SCBF considering different gusset plate connection models

•  Sensitivity of the model to geometric imperfection of the brace and the number of elements used to model the brace

•  Consideration of further simplifications of the model (demonstrated on an example)

•  Conclusions and summary •  Q & A with web participants

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Introduction

•  Special Concentrically Braced Frames (SCBF) are commonly used as the seismic resisting system in buildings.

•  During large seismic events they may experience buckling of the braces.

•  Inelastic deformation of the braces place inelastic deformation demands on beams, columns and connections.

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Modeling approaches for SCBF

§  Continuum models (shell or brick elements) •  Accurate •  Computationally expensive

§  Line-element models (beam-column elements and zero-length elements) •  Simple = Computation time significantly

reduced •  Accurate simulation of global behavior •  Reasonable predictions of many local

behaviors

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OpenSees elements used in Line-element models

•  Braces, beams and columns can be modeled with force-based (FB) fiber beam-column elements.

•  Rigidity of the gusset, gusset-to-beam, and gusset-to-column connections can be modeled with rigid elastic elements.

•  Beam-column connections of shear tab type can be modeled with zero-length rotational spring model (Liu & Astaneh-Asl, 2004)

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OpenSees elements used in Line-element models

Gusset plates (GP) connection can be modeled in two ways:

1.  Force-based fiber elements (Uriz & Mahin, 2008)

2.  Rotational hinge (Hsiao et al., 2012)

Lavg=(L1+L2+L3)/3

FBE

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Analytical Predictions

Uritz & Mahin, 2008 Hsiao et al., 2012

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Example

•  One story-one bay SCBF with chevron configuration of braces

•  Beams: W27x84 •  Columns: W14x176 •  Braces:HSS10x10x0.625 •  Gusset plate: tapered plate with t=1.375 in •  Beam-column connections are shear tab

connections (not designed for the purpose of this example)

360 in.

180

in.

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Buckling of HSS braces

Hsiao et al. 2013

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OpenSees model – 3D model

1 2

12

3

133101

31

321

322421

522422

432

4

431

233201

21

51

5521

3201+#El3101+#El

X

Y

Nonlinear FB elements Rigid elastic elements Nodes Pinned connection

Gusset plate connection modeled in following ways: 1.  FB element 2.  Out-of-plane

rotational spring 3.  Pin

Braces are modeled: •  with 10 FB elements. •  Corotational geometric

transformation. •  Quadratic out-of-plane

imperfection (Leff/1000)

Shear-tab connections are modeled as pins

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OpenSees model

§  All nonlinear elements are modeled using Steel02 wrapped with Fatigue material •  3 integration points (IP) are used for braces and

beams and 4 IPs are used for columns §  Nonlinear rotational spring is modeled using

zero-length element and Steel02 material assigned to it.

§  All rigid elements are modeled with elastic beam-column elements with 10 times bigger A and I than that of the corresponding element.

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OpenSees model - loads

§  Loads: •  Gravity •  Ground motion with its two components

(horizontal and vertical)

0 5 10 15 20 25 301.5

1

0.5

0

0.5

1

1.5

Time [sec]

Ground motion [g]

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Seismic performance of SCBF with different gusset plate connections

1 0.5 0 0.5 1

1500

1000

500

0

500

1000

1500

Disp. [in]

Force [kip]

SpringFBEpin

1 0.5 0 0.5 1

1500

1000

500

0

500

1000

1500

Disp. [in]

Force [kip]

SpringFBE

Base shear vs. displacement

Note: period is ~ the same for all three types of models: T=0.156 sec

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Story drift

0 5 10 15 20 25 30

0.6

0.4

0.2

0

0.2

0.4

0.6

Time [sec]

Story Drift [%]

SpringFBE

0 5 10 15 20 25 30

0.6

0.4

0.2

0

0.2

0.4

0.6

Time [sec]

Story Drift [%]

SpringFBEpin

Seismic performance of SCBF with different gusset plate connections

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0 5 10 15 20 25 30

1.5

1

0.5

0

0.5

1

1.5

Time [sec]

Floor acceleration [g]

FBESpring

Floor acceleration

0 5 10 15 20 25 30

1.5

1

0.5

0

0.5

1

1.5

Time [sec]

Floor acceleration [g]

FBESpringpin

Seismic performance of SCBF with different gusset plate connections

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Axial force – deformation at the middle of the left brace

0.02 0.01 0 0.01

1000

500

0

500

1000

Axial Strain [in/in]

Axial Force [kip]

left brace

SpringFBE

0.02 0.01 0 0.01

1000

500

0

500

1000

Axial Strain [in/in]

Axial Force [kip]

left brace

SpringFBEpin

Seismic performance of SCBF with different gusset plate connections

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Stress-strain of a fiber at the midd cross-section of the left brace

0.04 0.02 0 0.0260

40

20

0

20

40

60

Strain [in/in]

Stre

ss [

ksi]

left brace

SpringFBE

0.04 0.02 0 0.0260

40

20

0

20

40

60

Strain [in/in]

Stre

ss [

ksi]

left brace

SpringFBEpin

Seismic performance of SCBF with different gusset plate connections

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Summary

§  GP connections modeled with either FBE or rotational spring provide similar global and local responses of the system.

§  FBE element is simpler to model (input information are t, Ww) than rotational spring (input information are t, Ww and Lavg)

§  Pinned GP connection results in great loss of accuracy and is not recommended for estimating a seismic performance of SCBF under large earthquakes that can induce the buckling of the braces.

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Effect of initial imperfection on the results – GPC = FBE

Geometric imperfection

Max. Drift [%]

Max. Acc. [g]

1%Leff 0.62 1.33 0.2%Leff 0.59 1.56 0.1%Leff 0.54 1.59 0.05%Leff 0.52 1.61

1 0.5 0 0.5 1

1500

1000

500

0

500

1000

1500

Disp. [in]

Force [kip]

p=1%Leffp=0.2%Leffp=0.1%Leffp=0.05%Leff

Global responses

Note: compression elements usually have constriction tolerance of 0.1%Leff

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Effect of initial imperfection on the results – GPC = FBE

Local responses

0.025 0.02 0.015 0.01 0.005 0 0.005

1000

500

0

500

1000

Axial Strain [in/in]

Axial Force [kip]

left brace

p=1%Leffp=0.2%Leffp=0.1%Leffp=0.05%Leff

0.025 0.02 0.015 0.01 0.005 0 0.005

1000

500

0

500

1000

Axial Strain [in/in]

Axial Force [kip]

right brace

p=1%Leffp=0.2%Leffp=0.1%Leffp=0.05%Leff

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Number of elements

Max. Drift [%]

Max. Acc. [g]

2 0.55 1.59 4 0.54 1.59 8 0.54 1.59 16 0.54 1.59

Global responses

Effect of number of FBE used to model the brace – GPC = FBE

1 0.5 0 0.5 1

1500

1000

500

0

500

1000

1500

Disp. [in]

Force [kip]

noEle=2noEle=4noEle=8noEle=16

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Effect of number of FBE used to model the brace – GPC = FBE

Local responses

0.03 0.02 0.01 0

1000

500

0

500

1000

Axial Strain [in/in]

Axial Force [kip]

left brace

noEle=2noEle=4noEle=8noEle=16

0.03 0.02 0.01 0

1000

500

0

500

1000

Axial Strain [in/in]

Axial Force [kip]

right brace

noEle=2noEle=4noEle=8noEle=16

To capture failure of the brace it is suggested to use 10-20 elements (Uriz & Mahin 2008)

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Spatial dimension

Max. Drift [%]

Max. Acc. [g]

2D 0.591 1.569 3D 0.586 1.554

Global responses

3D vs. 2D frame – GP connection modeled with rotational spring

1 0.5 0 0.5 1

1500

1000

500

0

500

1000

1500

Disp. [in]

Force [kip]

2D3D

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3D vs. 2D frame – GP connection modeled with rotational spring

Local responses

0.025 0.02 0.015 0.01 0.005 0 0.005

1000

500

0

500

1000

Axial Strain [in/in]

Axial Force [kip]

left brace

2D3D

0.025 0.02 0.015 0.01 0.005 0 0.005

1000

500

0

500

1000

Axial Strain [in/in]

Axial Force [kip]

right brace

2D3D

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Spatial dimension

Max. Drift [%]

Max. Acc. [g]

2D 0.58 1.60 3D 0.54 1.60

Global responses

3D vs. 2D frame – GP connection modeled with FBE

1 0.5 0 0.5 1

1500

1000

500

0

500

1000

1500

Disp. [in]

Force [kip]

2D3D

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3D vs. 2D frame – GP connection modeled with rotational spring

Local responses

0.025 0.02 0.015 0.01 0.005 0 0.005

1000

500

0

500

1000

Axial Strain [in/in]

Axial Force [kip]

left brace

2D3D

0.025 0.02 0.015 0.01 0.005 0 0.005

1000

500

0

500

1000

Axial Strain [in/in]

Axial Force [kip]

right brace

2D3D

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Summary and conclusions §  GP connections modeled with either FBE or rotational spring

provide similar both global and local responses of the system. §  GP connections should not be modeled as pinned if buckling of

the braces is expected. §  Global and local responses are sensitive to the value of the

geometric imperfection at the middle of the brace •  AISC specifies construction tolerance of steel elements under

compression to Leff/1000 (design documents) §  Local response of the system is sensitive to the number of FB

elements used to model the brace. •  To capture the fracture of the brace it is recommended to use

10-20 elements §  3D frame models can be replaced with 2D models without

compromising the accuracy of the results (especially in the case of GP connections modeled with rotational springs)

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References

1.  Patxi Uriz, and Stephen A. Mahin, (2008), “Toward Earthquake-Resistant Design of Concentrically Braced Steel-Frame Structures”, PEER report 2008/08.

2.  Po-Chien Hsiao, Dawn E. Lehman, and Charles W. Roeder, (2012), "Improved analytical model for special concentrically braced frames", Journal of Constructional Steel Research 73 (21012) 80-94.

3.  Liu J, and Astaneh-Asl A, (2004), “Moment-Rotation Parameters for Composite Shear Tab Connections,” Journal of structural engineering, ASCE 2004;130(9).

4.  Po-Chien Hsiao, Dawn E. Lehman, and Charles W. Roeder, (2013), “A model to simulate special concentrically braced frames beyond brace fracture,” Earthquake Engng Struct. Dyn. 2013; 42:183–200