Workshop Nonlinear Dynamic Analysis in SAP2000 Manish Kumar Post-doctoral Associate Civil, Structural and Environmental Engineering University at Buffalo, State University of New York (SUNY) EERI Engineering Workshop Manish Kumar
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Outline • • • • •
Nonlinearity Modal analysis Pushover analysis Response spectrum analysis Response history analysis
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Geometric nonlinearity
Source: wiki.csiamerica.com
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Geometric nonlinearity • P-Delta – Geometric stiffness matrix formulated at beginning – Computational efficient – Appropriate when vertical loads do not vary substantially during analysis
• P-Delta + large deformations – Stiffness matrix updated at each step – Computationally expensive – Appropriate when vertical loads vary substantially during analysis
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Geometric nonlinearity • Two ways to include P-Delta effects – Create static nonlinear case for each load combination • Only for static analysis
– Create initial P-Delta for anticipated gravity loads • Use modified stiffness from this for all analysis • Can be used for modal, static, and dynamic analysis
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Material nonlinearity • Concentrated yield – Appropriate for frame members – Assign at the member ends – Discretize members using “hinge overwrites to get better convergence
• Distributed plasticity – Computationally expensive EERI Engineering Workshop Manish Kumar
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Modal analysis • Eigen vectors • Ritz vectors – For dynamic analysis – More accurate
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Pushover analysis Create the computational model
Define a nonlinear static load case
Run the analysis
Review results
• Create SAP2000 model • Define hinge properties and assign it to frame elements • Define load pattern applied during pushover analysis
• Define nonlinear static load case in the desired direction • Define nonlinear analysis option through "other parameters"
• Run the analysis for modal, DL, LL, and pushover case
• Review pushover curve • Review individual hinge results • Review sequence of hinge formation in the structure EERI Engineering Workshop Manish Kumar
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Time-history analysis • Modal
• Direct integration
– Linear & nonlinear
• Modal nonlinear analysis
– Also called fast nonlinear analysis (FNA) – Appropriate for limited nonlinear in members at concentrated locations (e.g, structures with dampers and baseisolators)
– Linear & nonlinear – Appropriate to capture large nonlinear response of structures (e.g, collapse simulation)
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Time-history analysis • Modal
• Direct integration
– Linear & nonlinear
• Modal nonlinear analysis
– Also called fast nonlinear analysis (FNA) – Appropriate for limited nonlinear in members at concentrated locations (e.g, structures with dampers and baseisolators)
– Linear & nonlinear – Appropriate to capture large nonlinear response of structures (e.g, collapse simulation)
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Local axis • Local axis 1 is always the longitudinal axis • The default orientation of the local 2 and 3 axes is determined by the relationship between the local 1 axis and the global Z axis:
– The local 1-2 plane is taken to be vertical, i.e., parallel to the Z axis – The local 2 axis is taken to have an upward (+Z) sense unless the element is vertical, in which case the local 2 axis is taken to be horizontal along the global +X direction – The local 3 axis is always horizontal, i.e., it lies in the X-Y plane EERI Engineering Workshop Manish Kumar
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Thank You! Questions?
[email protected] www.manishkumar.org
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