Section 2.1Section 2.1•Overview

•Types of NL Models

•Inelastic Model Attributes

•Energy Dissipation and Damping

•Gravity Loading

•Acceptance Limit States

Notes for PEER-SCEC TBI Notes for PEER-SCEC TBI MeetingMeeting

Greg Deierlein

Stanford University

January 17, 2008

2.1 NL Analysis & Behavioral Effects2.1 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 methode.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”)?

2.1.1 Types of Models2.1.1 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

2.1.2 Component Attributes2.1.2 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

2.1.3 Energy Dissipation & Damping2.1.3 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.

2.1.4 Gravity Loading2.1.4 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

2.1.5 Acceptance Criteria2.1.5 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 < 0.045 (maximum of 7 records)

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.

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

2.4.2 Survey of Practice

Wind Engineering Occupant comfort: 0.5-1.0% steel, 1.0-1.5% RC Strength design: 1.0-1.5% steel, 1.5-2.0% RC

Earthquake Engineering Elastic vs. Inelastic Analysis (e.g., LATBC 5 -

10% for DBE, 7.5-12.0% 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%

x

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

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

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

2.4.2 Measurements in Wind Storms

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

2.4.4 Viscous Damping with NLTH Analysis

PxMxKxCxM g

Raleigh (proportional) Damping:

;KMC nn

n

2

1

2

and 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?)

icC

[c]i configured to represent likely sources of viscous and other incidental damping.

[c]i

2.4.4 Raleigh Damping Coefficients

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?

1. Studies suggest that [C] should be varied (reduced) as function of the reduced [Kt] so as not to over-damp the yielded structure.

2. 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.

;KMC nn

n

2

1

2

2.4.5 Damping Recommendations

D (% critical) = /N (for IDR = 0.5% to 1.0%)

(30 ST – 2.7% to 70 ST – 1.1%)

Section 3.1 Characterizing NL PropertiesSection 3.1 Characterizing NL Properties

• Key Parameters (MEAN values)• Pre-Yield Stiffness• Yield and Maximum Strength• Deformations (capping point, post-capping)

Q

M

My

QCap,pl

Ke

Qy

Ke

Section 3.2 Statistical UncertaintiesSection 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

Section 3.5Section 3.5

Modeling & Criteria for RC Frames

(Conforming Beam-Columns & B-C Joints)

RC Column Simulation Model CalibrationRC Column Simulation Model Calibration

-0.1 -0.05 0 0.05 0.1-300

-200

-100

0

100

200

300

She

ar F

orce

(kN

)

Column Drift (displacement/height)

Experimental ResultsModel Prediction

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

Q

M

My

QCap,pl

Ke

Qy

Ke

RC Beam-Column Initial StiffnessRC Beam-Column Initial Stiffness

0

20

40

60

80

100

120

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014

Chord Rotation (rad)

Fo

rce

(kN

)

θy

Fy

KyKstf

0.4Fy

θstf_40

P/Po 0 0.3 0.8

0.4Py (EI/EIg) 0.30 0.60 0.80

Py (EI/EIg) 0.20 0.35 0.60

Haselton, Lange, Liel, Deierlein (2008)

ASCE 41 (Elwood et al., 2007)

YIELD: EI/EIg = 0.3 to 0.7

RC Beam-Column ParametersRC Beam-Column Parameters

Semi-Empirical -- calibrated from tests, fiber analyses, and basic mechanics:

• Secant Stiffness (EIeff)

• Yield Strength (My)

• Hardening Stiffness

-100 -50 0 50 100 150-200

-150

-100

-50

0

50

100

150

200

Sh

ea

r F

orc

e (

kN)

Column Top Horizontal Deflection (mm)

Test 19 (kN, mm, rad): K

e = 3.1779e+007

Kinit

= 7.4024e+007

s = 0.02

c = -0.04 (ND = 1)

y = 0.0091

cap,pl

= 0.069 (LB = 1)

u,mono,pl = 0.116 (LB = 1)

= 85, c = 1.20 isPDeltaRemoved = 1

Experimental ResultsModel Prediction

Empirical - calibrated from tests:

• Capping (peak) point

• Post-peak unloading (strain softening) stiffness

• Hysteretic stiffness/strength degradation

Qcap

Equation for plastic rotation capacity:

Structural Modeling: Model CalibrationsStructural Modeling: Model Calibrations

0.65 0.01 '

, 0.13 1 0.55 0.13 0.02 40 0.57 units cv c f

cap pl sl sha

0.62LN parameter value θcap,pl

Baselineρsh = 0.0075, f'c = 30 MPa, v = 0.10, αsl = 1

0.071

α sl 0 0.046

0 0.0870.3 0.0470.8 0.017

0.002 0.0330.01 0.0850.02 0.13120 0.07540 0.06780 0.054

θcap,pl

f' c (MPa)

v

ρ sh

ASCE 41 (Conforming, Flexural Failure)ASCE 41 (Conforming, Flexural Failure)

Haselton et al., Qpl = 0.02 to 0.08 for p”=0.0075

RC Beam-Column Joint ModelRC Beam-Column Joint Model

ASCE 41 – Modeling Recommendations

Idealized Joint ModelIdealized Joint Model

Column Spring

Joint Panel Spring

Beam Spring

Beam-end zone

Panel zone

Column-end zone

Spring Response Models

• Flexural Hinging – beam & column springs

• Joint Shear Distortion – joint panel spring

• Bond Slip – beam, column & joint panel springs

-1.5

-1

-0.5

0

0.5

1

1.5

-8 -6 -4 -2 0 2 4 6 8

Deformation (Q or )

Com

pone

nt F

orce

(M o

r V)