Modeling Seismic Isolators in SAP2000 - Manish Kumarmanishkumar.org/docs/ppts/SAP2000_Base_Isolation.pdf · Modeling Seismic Isolators in SAP2000 Manish Kumar, Ph.D., P.E., M.ASCE

Modeling Seismic Isolators in SAP2000

Manish Kumar, Ph.D., P.E., M.ASCEPostdoctoral Associate

Civil, Structural and Environmental Engineering University at Buffalo, State University of New York (SUNY)

1/34Modeling of Seismic Isolators in SAP2000 Manish Kumar

Outline

• Introduction• Isolator Models• Modeling in SAP2000• Example of Base-Isolated Building

– Modeling– Nonlinear time-history analysis


Introduction

Fixed-base

Base-isolated

Seismic isolator(lead-rubber bearing)

Shaking

Shaking


Isolator Models

• Rubber isolator– Low damping rubber (LDR) bearings– Lead-rubber (LR) bearings

• Friction isolator• T/C friction isolator• Triple pendulum isolator

Internal section view of lead-rubber bearing

Friction (single pendulum) isolator


Physical Model

• 2 Node, 12 DOFs• Connected by 6 springs

– Represents mechanical behavior in 6 directions

Physical model Discrete spring model


Define in SAP2000

• Modeled as Link Element in SAP2000– Define>>Section Properties>>Link/Support

Properties>>Add New Property• Mass and moment of inertia of isolators

– Generally assigned zero• Directional properties: U1, U2, U3, R1, R2, R3

– Mechanical behavior in six direction– U1: axial, linear only– U2, U3: shear directions, linear and nonlinear– R1: torsion about U1, linear only– R2, R3: rotations about U2 and U3, linear only


Define in SAP2000

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Axial behavior: rubber isolator

• U1 directional property– Always linear

• Effective stiffness: options• Make it fixed (check fixed box)• Assign a large value

– Note: don’t assign unrealistic large values

• Calculate from bearing properties– 𝐾𝐾𝑣𝑣 = 𝐴𝐴𝐸𝐸𝑐𝑐

𝑇𝑇𝑟𝑟(See Constantinou et al (2007) for details)

• Effective damping– Usually 0% is recommended– 2-3% can be used for natural rubber

Axial behavior

𝐾𝐾𝑣𝑣𝑐𝑐

𝐾𝐾𝑣𝑣𝑓𝑓

AXIAL FORCE

AXIAL DEFORMATION


Axial behavior: friction isolator

• U1 directional property– Always nonlinear– Compression only (gap)

• Effective stiffness: options• Make it fixed (check fixed box)• Assign a large value

– Note: don’t assign unrealistic large values

• Calculate as 𝐾𝐾𝑣𝑣 = 𝐴𝐴𝐸𝐸𝑐𝑐𝐻𝐻

– 𝐴𝐴 =area, 𝐸𝐸𝑐𝑐 = elastic modulus, 𝐻𝐻 = height

Axial behavior


Shear behavior: rubber isolator

• U2, U3 directional properties– Coupled bidirectional Bouc-Wen

• Mechanical properties– Calculate from bearing properties

• See Constantinou et al (2007) for details

• Stiffness = 𝐾𝐾𝑒𝑒𝑒𝑒• Yield strength = 𝐹𝐹𝑌𝑌• Post Yield Stiffness Ratio = 𝐾𝐾𝑑𝑑/𝐾𝐾𝑒𝑒𝑒𝑒

Shear behavior10/34Modeling of Seismic Isolators in SAP2000

Manish Kumar

Shear behavior: friction isolator

• U2, U3 directional properties– Coupled bidirectional Bouc-Wen

• Effective stiffness: options• Calculate from bearing properties

– See Constantinou et al (2007) for details

• Friction can be varied– 𝜇𝜇 = 𝜇𝜇𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 − 𝜇𝜇𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 − 𝜇𝜇𝑓𝑓𝑒𝑒𝑠𝑠𝑠𝑠 𝑒𝑒−𝑟𝑟𝑓𝑓𝑓𝑓𝑒𝑒×�̇�𝑢

– Use same 𝜇𝜇𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 and 𝜇𝜇𝑓𝑓𝑒𝑒𝑠𝑠𝑠𝑠 for no variation


Time-history analysis

• Modal – 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 base-isolators)

• Direct integration– Linear & nonlinear– Appropriate to capture

large nonlinear response of structures (e.g, collapse simulation)


Time-history analysis

• Modal – 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 base-isolators)

• Direct integration– Linear & nonlinear– Appropriate to capture

large nonlinear response of structures (e.g, collapse simulation)


Example: base-isolated building

• Example from SAP2000 manual• Base-isolated building• Rubber isolator• Nonlinear time-history analysis


Building model


Material properties• Steel

– E=29000 ksi, Poissons Ratio = 0.3– Beams: W24x55; Columns: W14x90

• Rubber Isolator Properties– Vertical (axial) stiffness = 10,000 k/in– Initial shear stiffness in each director = 10 k/in– Shear yield force in each direction = 5 kips– Ratio of post yield shear stiffness to initial shear stiffness = 0.2

• Vertical Loading and Mass– Roof: 75 psf DL, 20 psf LL– Floor: 125 psf DL, 100 psf LL

• Time History– Apply ground motion simultaneously in X and Y directions

• Required– Obtain displacement histories at the floor level and the roof in X direction– Plot base-shear history vs displacement in Y direction


Model development

• File>>New Model>>3D Frame


Model development


Define materials

• Define>>Materials– Default concrete and steel– Verify values

Concrete

Steel

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Define frame sections

• Define>>Section Properties>>Frame Sections– I/Wide Flange Sections>>SECTIONS.PRO– Import W24x55 and W14x90 sections by holding

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Define area sections

• Define>>Section Properties>>Area Sections– Shell>>Add New Sections>>Shell-Thin– Define two shell sections (note: change units to Kip, in, F)

• ROOF (membrane: 6”, Bending: 6”)• Floor (membrane: 10”, bending: 10”)


Assign frame sections

• Select all beams and assign section W24x55• Select all columns and assign section W14x90


Assign area sections

• Change to X-Y plane (top view)• Draw>>Quick Draw Area>>

– Click on each quadrant at level 3 of with ROOF section selected– Click on each quadrant at level 2 with Floor section selected


Define Isolators• Define>>Section Properties>>Link/Support Property Data

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Assign Isolators• Draw>>Draw 1 Joint Link

– Select all the nodes at the bottom

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Define Load Patterns

• Define>>Load Patterns>>Add New Load Pattern– Add a LIVE load pattern


Assign Loads• Change units to lb, ft, K• Select all objects at level 2

– Assign>>Area Loads>>Uniform (Shell): 125 DEAD and 100 LIVE in the gravity direction

• Select all objects at level 3 (Roof)– Assign>>Area Loads>>Uniform (Shell): 75 DEAD and 20 LIVE in the gravity direction

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Create Base Floor (level 1)

• Create base floor using Replicate command– Select everything at level 2 to be copied to level 1– Edit>>Replicate– Copies everything: frame, sections, load assignments etc.

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Assign Joint Constraints

• Create and assign 3 Diaphragm constraints for three levels– Select everything at level 1– Assign>>joint>>Constraints>>Add New Constraint (Diaphragm)


Define Ground Motion

• Define>>Functions>>Time History>>>>Add New Function (From File)


Define Load Case• Define>>Load Cases>>

– Modify existing MODAL load case to include ritz vector– Define a nonlinear gravity (GRAV) load case– Define a nonlinear time history (EQ) load case


Run the analysis


Post-processing

• Results can be obtained from DISPLAY menu– Show Response Spectrum Curves– Show Plot Functions

• To obtain time-history of response parameters

– Show Tables• To export data to excel/txt for post-processing

– Save Name Display Set• To obtain custom response parameters


Thank You!Questions?

[email protected]


mailto:[email protected]

http://www.manishkumar.edu/

Documents

Modeling Seismic Isolators in SAP2000 - Manish Kumarmanishkumar.org/docs/ppts/SAP2000_Base_Isolation.pdf · Modeling Seismic Isolators in SAP2000 Manish Kumar, Ph.D., P.E., M.ASCE