modeling s cbf
DESCRIPTION
modeling scbf using openseesTRANSCRIPT
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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