Modeling s Cbf

Modeling SCB frames using beam-column elements

Vesna Terzic UC Berkeley

January 2013

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

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.

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

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)

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

Analytical Predictions

Uritz & Mahin, 2008 Hsiao et al., 2012

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.

Buckling of HSS braces

Hsiao et al. 2013

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

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.

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]

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

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

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

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

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

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.

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

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

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

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)

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

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

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

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

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)

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