modeling s cbf
DESCRIPTION
modeling scbf using openseesTRANSCRIPT
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