Instrumentation needs for PBEE

W
Shared by:
Categories
Tags
-
Stats
views:
0
posted:
6/7/2012
language:
pages:
16
Document Sample

```							Quantifying risk by performance-
based earthquake engineering, Cont’d

Greg Deierlein
Stanford University

…with contributions by many

2006 IRCC Workshop on Use of
Risk in Regulation
PBEE Assessment Components
Decision     DV: COLLAPSE
Variable

Damage       DM: Non-simulated failure,
Measure
e.g., Loss of Vertical
Engineering       Carrying Capacity (LVCC)
Demand      EDP: Interstory Drift Ratio
Parameter

Intensity    IM: Sa(T1) + Ground Motions
Measure
Deterioration Modes & Collapse Scenarios

A
A
E               D
F                                            C

B
E

1. Deterioration Modes of RC Elements
- Simulation vs. Fragility Models
2. Building System Collapse Scenarios
- Sidesway Collapse (SC)
- Loss in Vertical Load Carrying Capacity (LVCC)
3. Likelihood of Collapse Scenarios
- Existing vs. New Construction
- “Ordinary” versus “Special” seismic design
Realistic RC Component Simulation
QCap,pl
M

My

Ke                                                                        Ke

Qy                                                                               Q

1.5                                                                                             200
Experimental Results
Non-Deteriorated                                      Model Prediction
Backbone                                150
1
Normalized Moment (M/My)

100

0.5
50

Shear Force (kN)
0
0

-50                                                        Test 19 (kN, mm, rad):
-0.5
Ke = 3.1779e+007
Kinit = 7.4024e+007
s = 0.02
-100
c = -0.04 (ND = 1)
-1                                                                                                                                                          y = 0.0091
cap,pl = 0.069 (LB = 1)
u,mono,pl = 0.116 (LB = 1)
-150
 = 85, c = 1.20
isPDeltaRemoved = 1
-1.5
-8   -6   -4      -2      0       2       4        6             8                       -200
-100              -50               0              50                    100            150
Chord Rotation (radians)                                                                               Column Top Horizontal Deflection (mm)
Example: Criteria for RC Beams (FEMA 273)
Sidesway Collapse Modes - SMF
11151, Sa: Sa:
EQ: EQ: 11021,2.51g2.52g             EQ: Sa: 2.26g
EQ: 11152, 11022, Sa: 2.12g

EQ: 11091, Sa: 2.19g             EQ: 11092, Sa: 3.06g
EQ: 11131, Sa: 2.19g          EQ: 11132, Sa: 2.12g

EQ: 11122, Sa: 2.32g        EQ: 11141, Sa: 1.79g          EQ
40% of collapses           27% of collapses

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

EQ: 11101, Sa: 1.52g
EQ: 11141, Sa: 1.79g              11142, Sa: Sa:
EQ: EQ: 11102,1.32g1.06g
17% of collapses            12% of collapses

5% of collapses             2% of collapses
Incremental Dynamic Analysis – Collapse
4

3.5
GROUND MOTION INTENSITY

3
Sag.m.(T=1.0s)[g]

2.5                            Mediancol = 2.2g
σLN, col = 0.36g
2

1.5

1

0.5

0
0           0.05                       0.1       0.15
Maximum Interstory Drift Ratio
STRUCTURAL RESPONSE (DRIFT)
7
Uncertainty – Plastic Rotation Capacity
1.2                                                                                                   1.2

1.0                                                                                                   1.0
Normalized Moment (M/My)

Normalized Moment (M/My)
0.8                                                                                                   0.8

Mean (m) Plastic
0.6                                                                                                   0.6

Reduced (m-s)
Mean minus standard
deviation (lognormal)

Rotation Capacity
0.4                                                                                                   0.4                    for both plastic

Plastic Rot. Cap.
rotation capacity and
post-capping stiffness
0.2                                                                                                   0.2

0.0                                                                                                   0.0
0.00         0.02         0.04         0.06          0.08     0.10                                   0.00         0.02             0.04      0.06         0.08     0.10

1.4

1.2                                                                                                1.2

1                                                                                                  1

Sacomp(T=2.0s)[g]
Sacomp(T=2.0s)[g]

0.8                                                                                                0.8

0.6                                                                                                0.6

0.4                                                                                                0.4

0.2                                                                                                0.2

0                                                                                                  0
0             0.05                   0.1           0.15                                            0               0.05                    0.1          0.15
Maximum Interstory Drift Ratio                                                                       Maximum Interstory Drift Ratio

8
Correlation of Component Variabilities
Type A: Correlation
of parameters                                                                                                Type B: Correlation
within an element                                                                                            between parameters
of different elements

Type B Correlations - Between Parameters of Elementi and Elementj

σLN, modeling                     Full Correlation
Partial (ρij = 0.5) -
No Correlation
approx. method
Different Parameters of the Same
Type A Correlations - Between

Full Correlation        1.12                     0.89                    0.63
Full Correlation
Element

between Variables
Expected to be          0.63                     0.50                    0.33
Correlated

No Correlation          0.43                     0.34                    0.23
9
Collapse Capacity – with Modeling Uncert.
1
Median = 2.2g
0.9
sLN, Total = 0.36
Cummulative Probability of Collapse

0.8
σLN, Total = 0.64 w/mod.
0.7

0.6
Margin 2.7x
0.5

0.4

0.3
P[collapse |Sa = 0.82g] = 5%
0.2

Empirical CDF
0.1                                         Lognormal CDF (RTR Var.)
5%                                                                                Lognormal CDF (RTR + Modeling Var.)
0
0       0.5     1      1.5     2    2.5      3      3.5       4      4.5        5
MCE          Sag.m.(T=1.0s) [g]
2% in 50 yrs GROUND MOTION INTENSITY                                       10
Mean Annual Frequency of Collapse
1

0.9

Collapse Performance
Cummulative Probability of Collapse

Collapse
0.8

0.7

0.6       CDF                                                                                  Margin: Sa,collapse = 2.7 MCE
0.5

0.4

0.3                                                                                            Probability of collapse under
design MCE = 5%
0.2

Empirical CDF
0.1                                    Lognormal CDF (RTR Var.)
Lognormal CDF (RTR + Modeling Var.)
0
0     0.5   1   1.5   2       2.5         3    3.5       4      4.5        5

0.0020
Sag.m.(T=1.0s) [g]
   MAFcol = 1.0 x 10-4 (about ¼
of the MCE 2% in 50 year
MAF of Excedance (Poisson rate)

0.0018

Hazard
0.0016

0.0014                                                                                                                                         ground motion)
0.0012                                                                                 Curve
0.0010

0.0008

0.0006

0.0004
2/50
0.0002

0.0000
0                       0.5     1   1.5       2         2.5       3        3.5         4           4.5   5

Sa at First Mode Period (g)
11
Benchmarking Archetype Studies

…                  …

DV’s:
Facility                                                      p(collapse)
Definition
p(\$ > X)
p(D.T. > Y)
2003 Code Compliant
- Strength
- Stiffness
PBEE
- Capacity Design     multiple realizations   Assessment
- Detailing           “design uncertainty” IM-EDP-DM-DV
30 Archetype Realizations

• Height: 1, 2, 4, 8, 12 and 20 stories
• Bay Width: 6 & 9 meters
• Space vs. Perimeter Frame (Atrib/A = 0.1 to 0.2)

Space Frame           Perimeter Frame
(Atrib/Atotal = 1.0)   (Atrib/Atotal = 0.16)

• Strength/Stiffness Distribution
(A) step sizes per typical practice
(B) weak story (1st or 1st-2nd stories)
Likelihood & Mode of Collapse
30

25                           Perimeter                       Mean Annual
Frames
collapse[10-4] -4

Frequency (MAF)
MAF x 10

20

15
of collapse:
Space                                 5 to 25 x 10-4
10
Frames
5
Space Frames
Perimeter Frames
0
0        5          10           15                 20
Number of Stories

1 story                      2 stories            4 stories                  8 stories    12 stories   20 stories
Relative Risk Levels
Gravity & Wind
7x10-4
(LRFD limit state)
Earthquake
1 x 10-4
(collapse, new RC)
Nuclear Reactor
1 x 10-5
(earthquake hazard)
Fire
1 x 10-6
(flashover, 100m2 office)
Fire + (1.0D + 0.5L)
1 x 10-7
(flashover, 100m2 office)
Concluding Remarks
• PB Methods == Means of Quantifying Performance
scientific models and data
role of judgment
probabilistic vs. scenarios assumptions

• Performance Targets
minimum life safety
minimum “convenience” (societal value - cost/benefit)
enhanced performance (cost-benefit)

• Implementation
explicit assessment
prescriptive methods (calibrated to performance targets)

• Consensus Guidelines and Standards
design professionals, societal representatives, and stakeholders

```
Related docs
Other docs by b7CWM77
EP ack Presentation