Hybrid simulation evaluation of the suspended zipper braced frame

Transcription

1 Hybrid simulation evaluation of the suspended zipper braced frame Tony Yang Post-doctoral scholar University of California, Berkeley Acknowledgements: Andreas Schellenberg, Bozidar Stojadinovic, Jack Moehle Georgia Institute of Technology, University at Buffalo, University of Colorado, Boulder, Florida A&M University Inverted-V braced frame 2 1

2 Suspended zipper braced frame 3 Shaking table test UB 4 2

3 Quasi-static test Analytical simulation Experimental testing GT 5 Hybrid simulation test Advantages: Numerical hard to model. New systems. Economical. Test structure to extreme states. Collapse. Geographically distributed tests. Share resources. Larger and complex structures. UCB and CUB 6 3

4 Scope of the test Develop an analytical brace model Simulate the brace buckling response. Quasi-static test of the brace sub-assembly Verify the analytical brace force-deformation hysteretic response. Hybrid simulation test of the suspended zipper braced frame Model the system response using both analytical elements and physical elements in the laboratory. 7 Modeling of analytical brace material: σ ε section: M κ component: F Δ 8 4

5 Modeling of analytical brace Displacement-based nonlinear beam column element v 2 v 3 v 1 Force-based nonlinear beam column element qv 3 qv 2 qv 1 9 Modeling of analytical brace Brace behavior under cyclic displacement loading Rotational spring Mid node Rotational spring Force-based NL BC element Force-based NL BC element Uriz and Yang 1 5

6 Hysteretic response of analytical brace Axial force [kips] Axial deformation [in.] 11 Scope of the test Develop an analytical brace model Simulate the brace buckling response. Quasi-static test of the brace sub-assembly Verify the analytical brace force-deformation hysteretic response. Hybrid simulation test of the suspended zipper braced frame Model the system response using both analytical elements and physical elements in the laboratory. 12 6

7 Test setup 1/3 -scale 13 Instrumentation 14 7

8 Instrumentation 15 Instrumentation 16 8

9 Quasi-static test Displacement

10 Photograph of damaged specimen 19 Out-of-plane buckling of the braces 2 1

11 Out-of-plane buckling of the gusset plate 21 Brace deformation 5% 5% 22 11

12 Axial forces of the braces 6 4 Brace 1 Brace 2 Brace axial forces [kips] Time [sec].75 % interstory drift ratio 23 Unbalanced forces Unbalanced vertical force [kips] Time [sec] Unbalanced out-of-plane force [kips] Time [sec] 24 12

13 Rotation of the supporting beam 3 Beam out-of-plane rotation [deg] Time [sec] 25 Finite element model Force-based BC element Force-based BC element Force-based BC element Force-based BC element 26 13

14 Normalized axial forces [%] Hysteretic response of the braces Experiment Analytical Brace 1 Normalized axial forces [%] Normalized axial deformations [%] Brace 2 Experiment Analytical Normalized axial deformations [%] 27 Scope of the test Develop an analytical brace model Simulate the brace buckling response. Quasi-static test of the brace sub-assembly Verify the analytical brace force-deformation hysteretic response. Hybrid simulation test of the suspended zipper braced frame Model the system response using both analytical elements and physical elements in the laboratory

15 Equations of motion ( ) M u + Cu + P u, u = P n n r n n n Dynamic Loading Seismic Wind Blast/Impact Wave Traffic analytical model of structural energy dissipation and inertia physical model of structural resistance 29 Integration algorithm Newmark average acceleration integration method 2 u ( ) n+ 1 = un+ hu n + h u n + u n+ 1 /4 ( ) un+ 1 = un + h un + un+ 1 /2 No added numerical damping and unconditionally stable. Form equilibrium equations at next time step ( ) M u + Cu + P u, u = P n+ 1 n+ 1 r n+ 1 n+ 1 n F ( u) = M 2 ( u un) u n u n + C ( u un) u n h h h + P ( uu,, u, u ) P + = r n n n n

16 Experimental testing architecture Simulation PC Finite element model Physical specimen(s) Dsp Real time PC P-C program Random Force time interval Model complexity. Processor speed. Communication delay. Force Dsp Force Test PC Dsp Fixed time interval 124 Hz) Servo-control Program 31 Transformation of displacement dof 32 16

17 Transformation of force dof Measured forces Feedback forces to finite element model Equation 3 33 Movie 1% Kobe Earthquake 34 17

18 Movie 2% Kobe Earthquake 35 Out-of-plane buckling of the braces 36 18

19 Hysteric responses of the braces 5 3 rd story left brace 5 3 rd story right brace Brace axial forces [kips] nd story left brace 2 nd story right brace st story left brace 1 st story right brace Brace axial deformations [in.] 37 Hysteric responses of the zipper columns 3 rd story zipper column Axial force [kips] nd story zipper column Axial force [kips] Axial deformations [in.] 38 19

20 Hysteric responses of the columns 3 rd story left column 3 rd story right column 5 5 Axial forces [kips] nd story left column st story left column Axial deformation [in.] nd story right column st story right column Axial deformation [in.] 39 Analytical verification roof drift ratio.8.6 Experiment Analytical.4 Roof drift ratio [%] Time [sec] 4 2

21 Analytical verification brace axial forces Brace axial forces [kips] 5 3 rd story left brace nd story left brace st story left brace rd story right brace nd story right brace st story right brace 5 Experiment Analytical Time [sec] Time [sec] 41 Analytical verification - ZC axial forces Axial forces [kips] Axial forces [kips] rd story zipper column Experiment Analytical nd story zipper column Experiment Analytical Time [sec] 42 21

22 Geographically distributed test University of California, Berkeley University of Colorado, Boulder 43 Test setup at Colorado University Boulder 44 22

23 Transformation of displacement dof 45 Transformation of force dof 46 23

24 Input ground motions Kobe (8% - 1%) Ground accelerations [g] Time [sec] 47 Hysteric responses of the braces 5 3 rd story left brace 5 3 rd story right brace Brace axial forces [kips] nd story left brace st story left brace nd story right brace st story right brace Brace axial deformation [in.] 48 24

25 Hysteric responses of the zipper columns Axial Force [kips] 3 rd story zipper column Axial Force [kips] nd story zipper column Axial deformation [in.] 49 Hysteric responses of the columns 3 rd story left column 3 rd story right column 5 5 Axial forces [kips] nd story left column st story left column nd story right column st story right column Axial deformation [in.] 5 25

26 Summary Conduct a system evaluation of the suspended zipper braced frame. Develop an analytical brace model Simulate the brace buckling response. Quasi-static test of the brace sub-assembly Verify the analytical brace force-deformation hysteretic response. Hybrid simulation test of the suspended zipper braced frame Model the system response using both analytical elements and physical elements in the laboratory. 51 Conclusions Behavior of the suspended zipper braced frame Behave as intended. Many redundancies. Braces buckled out of plane. Zipper columns are effective in transferring unbalanced vertical forces. Beams are rotated out of plane, needed to be braced. Plastic hinges developed at the column base. Base plate of the column bases need to be designed for the ultimate strength of the column

27 Conclusions (cont.) Results of the hybrid simulation test First hybrid simulation test to combine complex analytical and experimental elements. Excellent match between the hybrid and analytical simulation results. This shows the analytical brace model, solution algorithm and experimental testing architecture works. Application of hybrid simulation test Can be used to test multiple sub-assemblies. Larger and more complex structural system. More extreme loading. Can test the structure to extreme states. 53 Thank Question? you! This work was supported in part by the National Science Foundation under a pre-nees award number CMS Any opinions, findings, and conclusions or recommendations expressed in this document are those of the authors and do not necessarily reflect those of the National Science Foundation. Resource: 27