Assessing Effectiveness of Building Code Provisions Greg Deierlein & Abbie Liel Stanford University...

Assessing Effectiveness of Building Code Provisions

Greg Deierlein & Abbie LielStanford University

Curt Haselton Chico State University

… other contributors (PEER TA I & ATC 63)

EQ: 11111, Sa: 2.06g EQ: 11112, Sa: 2.19g

EQ: 11121, Sa: 2.86g EQ: 11122, Sa: 2.32g

PEER 2007 Annual Meeting

2

PBEE: Collapse (SAFETY) Assessment

Decision Variable

Decision Variable

Intensity Measure

Intensity Measure

Damage Measure

Damage Measure

Engineering Demand

Parameter

Engineering Demand

Parameter

DV: COLLAPSE

DM: Loss of Vertical Carrying Capacity (LVCC)

EDP: Interstory Drift Ratio

IM: Sa(T1) + Ground Motions

EDPs: Deformations & Forces

3

Illustration – 4 Story SMF Building

Office occupancy

Los Angeles Basin

Design Code: 2003 IBC / 2002 ACI / ASCE7-02

Perimeter Frame System

Maximum considered EQ demands:

Ss = 1.5g; S1 = 0.9g

Sa(2% in 50 yr) = 0.82g

Design V/W of 0.094g

Maximum inelastic design drift of 1.9% (2% limit)

Typical Perimeter Frame Members

Beams: 32” to 40” deep

Columns: 24”x28” to 30”x40”

Governing Design Parameters

- Beams: minimum strength

- Column size: joint strength

- Column strength: SCWB

- Drift: just meets limit

8 inch PT slab

4

Nonlinear Analysis & Calibration

-1.5

-1

-0.5

0

0.5

1

1.5

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

Chord Rotation (radians)

No

rma

lize

d M

om

en

t (M

/My)

Non-Deteriorated Backbone

-150 -100 -50 0 50 100 150-250

-200

-150

-100

-50

0

50

100

150

200

250

She

ar F

orce

(kN

)

Column Top Horizontal Deflection (mm)

Experimental ResultsModel Prediction

EQ: 11111, Sa: 2.06g EQ: 11112, Sa: 2.19g

EQ: 11121, Sa: 2.86g EQ: 11122, Sa: 2.32g

5

0 0.05 0.1 0.150

0.5

1

1.5

2

2.5

3

3.5

4

Sa g.

m.(T

=1

.0s)

[g]

Maximum Interstory Drift Ratio

0.82g is 2% in 50 year motion

Capacity Stats.:Median = 2.2gσLN = 0.36

Incremental Dynamic Analysis – Collapse

2% in 50 year = 0.82g

IDRcol = 7-12%

Mediancol = 2.2g

σLN, col = 0.36g

Simulation Results: Collapse Modes

EQ: 11111, Sa: 2.06g EQ: 11112, Sa: 2.19g

EQ: 11121, Sa: 2.86g EQ: 11122, Sa: 2.32g

EQ: 11011, Sa: 4.39g EQ: 11012, Sa: 2.66g

EQ: 11021, Sa: 2.52g EQ: 11022, Sa: 2.12g

EQ: 11151, Sa: 2.51g EQ: 11152, Sa: 2.26g

EQ: 11161, Sa: 0.66g EQ: 11162, Sa: 0.72g

EQ: 11131, Sa: 2.19g EQ: 11132, Sa: 2.12g

EQ: 11141, Sa: 1.79g EQ: 11142, Sa: 1.32g

EQ: 11091, Sa: 2.19g EQ: 11092, Sa: 3.06g

EQ: 11101, Sa: 1.52g EQ: 11102, Sa: 1.06g

EQ: 11131, Sa: 2.19g EQ: 11132, Sa: 2.12g

EQ: 11141, Sa: 1.79g EQ: 11142, Sa: 1.32g

40% of collapses 27% of collapses

17% of collapses

**Predicted by Static Pushover

12% of collapses

5% of collapses 2% of collapses

0 0.05 0.1 0.150

0.5

1

1.5

2

2.5

3

3.5

4

Sa

g.m

.(T=1

.0s)

[g]


Incremental Dynamic Analysis

Collapse Fragility Curve

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sag.m.

(T=1.0s) [g]

Cum

mul

ativ

e P

roba

bilit

y of

Col

laps

e

Empirical CDFLognormal CDF (RTR Var.)Lognormal CDF (RTR + Modeling Var.)

Median = 2.2g

LN, Total = 0.36 0 0.05 0.1 0.15

0

0.5

1

1.5

2

2.5

3

3.5

4

Sa

g.m

.(T=1

.0s)

[g]


Incremental Dynamic Analysis

8

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.02 0.04 0.06 0.08 0.10

Total Chord Rotation (radians)

No

rmali

zed

Mo

me

nt

(M/M

y)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0.00 0.02 0.04 0.06 0.08 0.10

Total Chord Rotation (radians)

No

rmali

zed

Mo

men

t (M

/My)

Mean minus standard deviation (lognormal)

for both plastic rotation capacity and post-capping stiffness

0 0.05 0.1 0.150

0.2

0.4

0.6

0.8

1

1.2

1.4

Sa co

mp(T

=2

.0s)

[g]

Maximum Interstory Drift Ratio0 0.05 0.1 0.15

0

0.2

0.4

0.6

0.8

1

1.2

Sa co

mp(T

=2

.0s)

[g]


Uncertainty – Plastic Rotation Capacity

Mean () Plastic Rotation Capacity

Reduced ( Plastic Rot.

Cap.

9

Correlation of Model Uncertainties

Type A: Parameters within one element

Type B: Between parameters of different elements

-1.5

-1

-0.5

0

0.5

1

1.5

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

Θ, Chord Rotation

M, C

olum

n B

ase

Mom

ent

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sag.m.

(T=1.0s) [g]

Cu

mm

ula

tive

Pro

ba

bili

ty o

f C

olla

pse


Collapse Capacity – with Modeling Uncert.

Median = 2.2g

LN, RTR = 0.36

σLN, Total = 0.64 w/mod.

0.82g2% in 50 yrs

P[collapse |Sa = 0.82g] = 5%

5%

Margin 2.7x

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Sag.m.

(T=1.0s) [g]

Cu

mm

ula

tive

Pro

ba

bili

ty o

f C

olla

pse


0.0000

0.0002

0.0004

0.0006

0.0008

0.0010

0.0012

0.0014

0.0016

0.0018

0.0020

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Sa at First Mode Period (g)

MA

F o

f Exc

ed

an

ce (

Po

isso

n r

ate

)Mean Annual Frequency of Collapse

Collapse CDF

Hazard Curve

Margin: Sa,collapse = 2.7 MCE

5% Probability of collapse

under design MCE = 5%

MAFcol = 1.0 x 10-4

(0.5% in 50 years)

2.7

Collapse Performance

5%

2/50

The 2% in 50 year ground motion

Illustration:

Site dominated by single event (M 6.9, R 14 km) -- return period of 200 years (MAF 25% in 50 yr)

Boore-Joyner (BJ) attenuation function

Sa (25/50) -- median of BJ. At T=1 sec., Sa = 0.28g

Sa (2/50) -- +1.5 of BJ. At T=1 sec., Sa = 0.56g.

Mean Annual Freq. = (Probability of Sa > Sa*, given EQ) x (MAF of EQ)

Ground motion selection (+effect

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Sa co

mpo

nent

[g]

Period [seconds]

BJF Prediction: MedianBJF Prediction: Median +/- 1.0 sigmaBJF Prediction: Median +/- 1.0 sigmaBJF Prediction: Median +/- 2.0 sigmaBJF Prediction: Median +/- 2.0 sigmaObserved Sa - Loma Prieta (ID 11022)

+1.7 at T = 1.0 sec.

-0.3 at T = 0.45 sec.

Consider the Loma Prieta (11022 record):

• Close match to characteristic event [M 6.9, R 14, Sa(T=1) = 0.65g]

• Epsilon: +1.7 at T=1 sec; -0.3 at T = 0.45 sec

• General trend for +epsilon records to peak at the +e periods and drop off elsewhere

14

Effect of Spectral Shape () on collapse capacity

-2 -1 0 1 2

-1

-0.5

0

0.5 Best-Fit: LN(Sa) = -0.3481 + 0.311p-value = 4.716e-010

error = 0.331 (LN units)

LN[S

aco

l(T1=

1.71

s)]

(T1=1.71s)

ObservationOutlierRegression5/95% CIs on Mean

0 0.5 1 1.5 2 2.50

0.2

0.4

0.6

0.8

1

Sa(T=1.71s) [g]

P[c

olla

pse]

Empirical CDF with no adjustment

Lognormal CDF with no adjustment

Lognormal CDF after adjustment

+ +

Seismic Region T1 < 0.6s T1 > 1.4s T1 < 0.6s T1 > 1.4s T1 < 0.6s T1 > 1.4s

California High Seismic Region 1.30 1.50 1.25 1.15 1.00 1.00

Other Regions of Continental U.S. 1.00 1.15 1.00 1.10 1.00 1.00

SSF

* Baker (2005) found that the use of ε is not appropriate for pulse-type ground motions, so SSF should be used when these motions are expected (i.e. R < 10km).

High Deformation Capacity

Moderate Deformation Capacity

Brittle

Structural System Inelastic Deformation Capacity and Fundamental Period

1967 and 2003 Design Comparisons

Space Frame1967 UBC, Zone 4Design V/W: 0.068 gMember sizes

Col. 20x20 to 24x24 Beam depth 20 to

26

No SCWB, no joint check, non-conforming ties

1967 Design 2003 Design

Perimeter Frame2003 UBC/2002 ACIDesign V/W: 0.094 gMember sizes

Col. 24x28 to 30x40 Beam depth 32 to 42

Fully conforming design

Comparison of 1967 vs. 2003 Designs

Column Hinge Backbone Parameters

p,cap : 1967 = 0.02 rad (COV 50%)

2003 = 0.06 rad

Kc/Ke: 1967 = -0.22 (COV 60%)

2003 = -0.08

Static Pushover Response

u : 1967 = 2.4

2003 = 2.7

u: 1967 = 1.5% roof drift ratio

2003 = 5.0%FEMA 356 p limits:

1967 = 0.006 rad 2003 = 0.015 rad

Incremental Dynamic Analysis – Sidesway Collapse

0 0.05 0.1 0.150

0.5

1

1.5

2

2.5

3

3.5

4

Sag.

m.

(T=1

.0s)

[g]


IDRcol = 7-12%

0 0.05 0.1 0.150

0.5

1

1.5

2

2.5Incremental Dynamic Analysis, Controlling Component, 1967 Analysis Model

Sa

(T=

1.0s

) [g

]


col = 0 g

Median Sa = 2.2g

Median Sa = 1.0 g

IDRcol = 3-6%

1967 DesignStrength: Median Sa = 1.0g, COV = 30%

Deformation: IDRmax = 3 to 6%

2003 DesignStrength: Median Sa = 2.2g, COV = 36%

Deformation: IDRmax = 7 to 12%

0 1 2 3 4 5 60

0.25

0.5

0.75

1

Collapse Sa / MCE

P[C

olla

pse

]

1967, 4-Story2003, 4-Story

Simulated (sidesway) collapse fragility: 4-story building

FACTORS CONSIDERED• Beams & Cols: flexure-shear • B-C Joints: shear/bond • Modeling Uncertainty• Spectral Shape ()

Margins (collapse/MCE)

• 2003: 2.7

• 1967: 1.0

P[C/MCE]

• 2003: 4%

• 1967: 50%

2.71.0

50%

4%

1967 Sidesway and Vertical Collapse (4-story)

Total Collapse Probability

Sidesway Collapse Probability at IMi

Probability of LVCC (given drift ratio)

= + X Probability of No SS Collapse at IMi

Per Elwood/Moehle & Aslani/Miranda:

• Column Shear Failure:

Column IDR = 0.024 (mean)

• Column Axial Failure:

Column IDR = 0.056 (mean)

Recall – Sidesway collapse occurs at peak drift ratios of 0.03 to 0.06.

0 1 2 3 40

0.25

0.5

0.75

1

Collapse Sa / MCE

P[C

olla

pse

]

1967, 4-story1967, 4-story, incl. column shear failure1967, 4-story, incl. col. loss of vertical capacity

Shear failure reduces median capacity by

about 15%

RC Building Archetype Study

beam-column joint

column

beam

foundation

MWtrib

Wlean

bay size

H1st

-sto

ryn

-sto

rie

s a

t H

leaning (P-)

column

• Archetype Design Space & Parameters

heights & configurations

seismic design shears

capacity design/detailing

• Archetype Analysis Model3-Bay Multistory

Interior/Exterior Joints

Deterioration, P-

• Archetype Index BuildingsHeights: 1, 4, 8, 12, 20

Space & Perimeter

Perimeter Frame (Atrib/Atotal = 0.16)

Space Frame (Atrib/Atotal = 1.0)

0 1 2 3 4 5 60

0.25

0.5

0.75

1

Collapse Sa / MCE

P[C

olla

pse

]

1967, 4-Story2003, 8-Story2003, 12-Story1967, 8-Story1967, 12-Story2003, 4-Story

Effects of Codes (’67 vs ’03) and Building Heights

Normalized Sidesway Collapse

Fragilities

1967:

8 – 12 – 4 stories

2003:

12 – 8 – 4 stories

0 1 2 3 40

0.25

0.5

0.75

1

Collapse Sa / MCE

P[C

olla

pse

]

1967, 8-story, w/shear1967, 8-story, w/ LVCC1967, 8-story

1967 Sidesway and Vertical Collapse: 8-story

Total Collapse Probability

Sidesway Collapse Probability at IMi

Probability of LVCC (given drift ratio)

= + X Probability of No SS Collapse at IMi

From Elwood/Moehle & Aslani/Miranda:

• Column Shear Failure:

Column IDR = 0.022 (avg.)

= 0.014 (1st-story)

• Column Axial Failure:

Column IDR = 0.050 (avg) = 0.025 (1st-

story)

Sidesway collapse occurs at peak (median) drift ratio of 0.038.

AXIAL collapse reduces median by ~

40%

SUMMARY – Key Collapse Results

Simulated Sidesway Collapse Statistics

Including Shear-to-Axial Column Failure for 1967 Designs:

• 4-story building: little change

• 8-story building: significant change (column IDR = 0.025)

MAF,collapse = 190 x 10-4 c/yr (35x rate of 2003 design)

5 to 12x 10 to 30x

2003 1967 2003 1967 2003 1967

4-Story 4% 50% 3 30 0.083 0.038

8-Story Space 7% 80% 5 150 0.068 0.038

12-Story Perimeter 14% 67% 11 100 0.053 0.035

P[Collapse|MCE] MAF (x10-4) IDR,ult

Comments on Collapse Assessment

Accuracy of Assessment Procedure stiffness/strength degrading models characterization of ground hazard (spectral shape effect) modeling uncertainties ..

Comparison of 1960-70’s versus modern frames “regular” frames have 10 to 30x collapse risk what about irregular frames? validation & corroboration of results appropriate level of safety?

Interpretations and Implications communicating risks in consistent & meaningful ways providing tools and engineering solutions (new buildings & retrofit) action/implementation strategies

Assessing Effectiveness of Building Code Provisions Greg Deierlein & Abbie Liel Stanford University...

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