1. Section 2.1 Overview Types of NL Models Inelastic Model Attributes
Energy Dissipation and Damping
Gravity Loading
Acceptance Limit States

2. Notes for PEER-SCEC TBI Meeting
Greg Deierlein
Stanford University
January 17, 2008

3. 2.1 NL Analysis & Behavioral Effects
IDEALLY
- NL analysis simulates directly ALL significant modes of deformation & deterioration
PRACTICAL REALITY
Some behavioral effects are simulated directly
Other effects are not simulated and are checked using appropriate limit state criteria
GENERAL MODELING GUIDELINES
Specify model parameters based on AVERAGE (MEAN) properties
Specification of acceptance criteria will depend on how uncertainties are considered elsewhere in the analysis/assessment method
e.g., Should check of wall shear strength be based on “median”, “average”, or “median + sigma” shear force demands? What should be the corresponding capacity (“average” or “expected”; “nominal”)?

4. Types of Models
Choice of model will dictate how modeling guidelines and acceptance criteria are expressed
FEMA 356/ASCE 41 tends towards “concentrated spring” models, although “fiber-type” models are common for RC walls

5. Component Attributes
Idealized “Backbone” Curve for Spring-Type Model
elastic, hardening, peak, and post-peak(?) response
is degradation captured in cyclic model?
- “modified backbone curve” (FEMA 356/ASCE 41)
calibrate properties to average (mean) values

6. 2.1.3 Energy Dissipation & Damping
definition of “damping” depends how it is modeled
Hysteretic versus Viscous
Type of Analysis Model (physical vs. phenomenological)
amplitude dependent
- service versus DBE and MCE
unique characteristics of tall buildings (vs. low-rise)
less damping induced by soil-structure interaction
unique characteristics of cladding, partitions, etc.

7. 2.1.4 Gravity Loading Mean (Expected) Values of Gravity Loading
1.0D + 0.2L
1.0D + 0.5L (for non-reduceable LL)
Same values used for gravity load and seismic mass

8. 2.1.5 Acceptance Criteria Serviceability
- onset of significant structural damage
- check using elastic analysis
- assess based on mean of component criteria
MCE Level (or Collapse Prevention)
- onset of significant degradation
- check of component criteria if degradation is not modeled in analysis
- suggested drift requirements
IDR < 0.03 (mean of 7 records)
IDR < (maximum of 7 records)

9. 2.4 Damping in NLTH Analysis
Definition: reduction in dynamic building response due to energy dissipation of structural and nonstructural components of the building, its foundation, and the underlying soil/rock materials
Complicating Factors: The interpretation and representation of damping is complicated by –
relationship of mathematical representation of damping to the physical sources of damping, e.g., (1) artificial distinctions between energy dissipation of structural components that is modeled by nonlinear hysteretic response versus equivalent viscous damping, (2) modification of input motions to account for reduction in response due to SSI effects
amplitude dependency (displacement, velocity, acceleration) of damping effects and its effect on building performance for different overall intensity of building response, and (b) different effects for alternative vibration modes.

10. 2.4.1 Physical Sources of Damping
SUPERSTRUCTURE – STRUCTURAL:
Primary Structural Components whose nonlinear behavior may be explicitly modeled in the analysis (e.g., walls, beams, columns, …)
“Secondary” Structural Components that contribute to response but whose energy absorbing characteristics may not be modeled explicitly (e.g., energy dissipation provided gravity framing, deformations to floor slab at slab-wall connections, etc).
SUPERSTRUCTURE – “NONSTRUCTURAL”
Exterior Cladding – a likely source of considerable damping, depending on the material, method of attachment, expansion joints.
Interior Wall Partitions and Finishes (issues – materials, method of attachment of finishes to structural walls/braces/columns, method of attachment of partitions to slabs, “density” of partitions – i.e., open office versus partitioned residential)
Mech/Electrical - piping, electrical conduit, HVAC risers, elevator rails and cables, stairs, etc.
 SUBSTRUCTURE – FOUNDATION & SITE
Energy dissipation at soil-foundation interface (e.g, soil yielding and gapping)) and in surrounding soil deforms due to building motion

11. 2.4.2 Survey of Practice Wind Engineering Earthquake Engineering
Occupant comfort: % steel, % RC
Strength design: % steel, % RC
Earthquake Engineering
Elastic vs. Inelastic Analysis (e.g., LATBC % for DBE, % at MCE)
SAC Steel Project 2%
SF AB083 <5%
CTBUH – Japan: 2% steel, 3% RC
CTBUH 2-5% steel, 5% RC
China (Li et al.) 3%

12. 2.4.3 Measurements Goel/Chopra
Recorded during earthquakes
(peak IDR = 0.5 to 1%)
Range of Values
< 30 stories: 2% to 12%
> 30 stories: 2% to 4%
No clear trend in amplitude differences with building height or damping differences with roof drift ratios

13. 2.4.2 Measurements Satake et al.
Mostly forced vibration , a few ambient & strong ground shaking
(peak RDR = 0.002% ?)
Range of Values (generally smaller than Goel/Chopra):
< 30 stories: <4% steel, < 8% RC
> 30 stories: <2%
Attribute major differences to less soil-structure interaction in tall buildings

14. 2.4.2 Measurements in Wind Storms
Mostly forced vibration , a few ambient & strong ground shaking
(peak RDR = 0.002% ?)
Range of Values (generally smaller than Goel/Chopra):
< 30 stories: <4% steel, < 8% RC
> 30 stories: <2%
Attribute major differences to less soil-structure interaction in tall buildings

15. 2.4.2 Measurements in Wind Storms

16. 2.4.4 How is Damping Represented
Explicit modeling of nonlinear hysteretic respond of structural components
Equivalent viscous (velocity proportional) damping, i.e., [C]
Modification of input ground motion by filtering or scaling to damped hazard levels
NOTE – scaling 5% GM spectra to 5% damped spectrum does NOT result in a reduction in ground motions

17. 2.4.4 Viscous Damping with NLTH Analysis
Raleigh (proportional) Damping:
a and b are usually set to provide some level of “critical damping” in certain modes, but for nonlinear analysis the meaning of this is less clear
mathematical conveniences of Raleigh damping do not apply for NL analysis
Explicit Damping Elements (more transparent?)
[c]i configured to represent likely sources of viscous and other incidental damping.
[c]i

18. 2.4.4 Raleigh Damping Coefficients

19. 2.4.4 Issue with Raleigh (Prop.) Damping
Fixed or Variable [C]: Should [C] be varied during the analysis, either as a function of [Kt] or other parameters?
Studies suggest that [C] should be varied (reduced) as function of the reduced [Kt] so as not to over-damp the yielded structure.
Take care if artificial “rigid-plastic” springs are introduced into the model, lest they lead to generation of very large damping forces, which may lead to large equilibrium violations for the yielded structure.

20. 2.4.5 Damping Recommendations
D (% critical) = a/N (for IDR = 0.5% to 1.0%)
(30 ST – 2.7% to 70 ST – 1.1%)

21. Section 3.1 Characterizing NL Properties
Key Parameters (MEAN values)
Pre-Yield Stiffness
Yield and Maximum Strength
Deformations (capping point, post-capping)

22. Section 3.2 Statistical Uncertainties
Characterization of Variability
Statistics from Tests
Judgments
Other modes of failure
Lab tests versus real conditions
Typical COVs (std(ln))
Well defined & understood 0.2 to 0.3
Not well defined or measured 0.5 to 0.6

23. Section 3.5 Modeling & Criteria for RC Frames
(Conforming Beam-Columns & B-C Joints)

24. RC Column Simulation Model Calibration
ATC 63 PRP Meeting
March 19, 2007
RC Column Simulation Model Calibration
Key Parameters:
strength
initial stiffness
post-yield stiffness
plastic rotation (capping) capacity
post-capping slope
cyclic deterioration rate
Calibration Process:
250+ columns (PEER database)
flexure & flexure-shear dominant
calibrated to median (characteristic) values
RC Index Archetypes

25. RC Beam-Column Initial Stiffness
P/Po
0.3
0.8
0.4Py (EI/EIg)
0.30
0.60
0.80
Py (EI/EIg)
0.20
0.35
Haselton, Lange, Liel, Deierlein (2008)
ASCE 41 (Elwood et al., 2007)
YIELD: EI/EIg = 0.3 to 0.7

26. RC Beam-Column Parameters
EERI Seminar
RC Beam-Column Parameters
Qcap
Semi-Empirical -- calibrated from tests, fiber analyses, and basic mechanics:
Secant Stiffness (EIeff)
Yield Strength (My)
Hardening Stiffness
Empirical - calibrated from tests:
Capping (peak) point
Post-peak unloading (strain softening) stiffness
Hysteretic stiffness/strength degradation
Deierlein

27. Structural Modeling: Model Calibrations
EERI Seminar
Structural Modeling: Model Calibrations
Equation for plastic rotation capacity:
Bond-slip contributes 35% of element plastic rotation capacity.
Deierlein

28. ASCE 41 (Conforming, Flexural Failure)
Haselton et al., Qpl = 0.02 to 0.08 for p”=0.0075

29. RC Beam-Column Joint Model
ASCE 41 – Modeling Recommendations

30. EERI Technical Seminar
Idealized Joint Model
Beam-end zone
Panel zone
Column-end zone
Column Spring
Joint Panel Spring
Beam Spring
Spring Response Models
Flexural Hinging – beam & column springs
Joint Shear Distortion – joint panel spring
Bond Slip – beam, column & joint panel springs
1.5
The connectivity to adjacent frame elements
Nodes
Springs
Combination of nodes, multi-point constraints 1
0.5
Component Force (M or V)
-0.5 -1
-1.5 -8 -6 -4 -2 2 4 6 8
Deformation (Q or g)
Deierlein - NHTH Analysis