Promoting preventive mitigation of buildings against hurricanes

PROMOTING PREVENTIVE MITIGATIONS OF
BUILDINGS AGAINST HURRICANES THROUGH
ENHANCED RISK-ASSESSMENT AND DECISION
MAKING
FLORIDA SEA GRANT PROJECT R-CS-60
Sungmoon Jung (Principle Investigator)
Arda Vanli (Co-Principle Investigator)
Bejoy P. Alduse (Research Assistant)
Spandan Mishra (Research Assistant)

Overview
2FLORIDA SEA GRANT PROJECT R-CS-60
1. Background and Proposed Tasks
2. Tasks Completed
A. Compile Experimental Data
B. Deterministic Model for Capacity
C. Capacity Prediction Model
 Conventional capacity model
 Capacity Update Model ( Considering the deterministic model)
 Statistical Pooled Model (Without considering the deterministic model)
D. Fragility analysis
 Conventional
 Proposed
E. Comparison of Fragility Results
3. Summary
4. Future Tasks
5. Questions and Comments

1. Background Proposed Tasks
Background
Insured value of coastal
counties approach $3
trillion (AIR Worldwide
2013)
Mitigation (Ex: Improved
Roof to Wall Connections)
results in financial benefits
and improved resilience
However, uncertainties
exist about cost-benefit
analysis of different RTW
connections.
Motivation
Uncertainties exist in
performance of the
common RTW connections
- Hurricane clips.
Address uncertainties in
capacities systematically
Improve cost-benefit
knowledge by addressing
the uncertainties in
performance.
a. Address uncertainties in
building components before and
after mitigation
1. Develop Fragility
formulations
2. Calibrate Fragility
formulations

4
A.
Compile
Experimental
Data
B.
Deterministic
Model for
Capacity
C.
Capacity
Prediction
Model
D.
Fragility
analysis
E.
Comparison
of results
2. Tasks Completed

• 6 different sources - 1 PhD. Diss., 2 M. Thesis, 2 J. Publ., 1 T.
Report
• Results of component level testing
• Categorized results based on number of clips and wood type
Ex: Ahmed et al.(2011)
• Capacity depends on mode of failure which in turn depends on
combination of number of clips and wood type.
FLORIDA SEA GRANT PROJECT R-CS-60 5

Ahmed et al. (2011) - H2.5A clips on (SPF,SYP and DF)
6
a) Nail pull out b) Clip tearing c) Wood splitting
Capacity in lbs – Mean and
(Standard deviation)
Woodtype
Number of clips
1 2 4
SPF (2 “ x 4 “) 436.6 591.4 887.4
(51.9) (68.3) (70.5)
SYP (2 “ x 4 “) 459 711.4 931.2
(29.6) (65.8) (85.3)
DF (2 “ x 6 “) 640.2 753.2
(53.1) (65.5)
Observed Modes of failure
Woodtype
Number of clips
1 2 4
SPF (2 “ x 4 “) Nail pull out Wood split Wood split
SYP (2 “ x 4 “) Nail pull out Wood split Wood split
DF (2 “ x 6 “)
Clip
deformation Clip tearing

a) Nail pull out strength (N)
1800 G(5/2)D L
G – Specific gravity of wood
D – Dia. of nail and
L – Length of Nail
b) Tearing of the clip (C)
c/s Area of clip x Yield stress
c) Wood rupture strength (W)
Area of wood x Rupture stress
Deterministic capacity = Minimum (N,C,W)
B. Deterministic Model for Capacity
Deterministic Capacity in lbs
Woodtype
Number of clips
1 2 4
SPF (2 “ x 4 “) 441.4 882.8 1200
SYP (2 “ x 4 “) 554.1 1108.2 1500
DF (2 “ x 6 “) 682.5 1365.1 1950

→ Conventional Capacity Model
• The capacity follows a log-normal distribution
𝐶𝐶𝑐𝑐 = 𝐿𝐿𝐿𝐿(µ, σ)
• 𝐶𝐶𝑐𝑐 Conventional capacity value
• µ Mean value of capacity from experiments
• σ Standard deviation of capacity from experiments

→ Capacity Update Model
• The polynomial model for bias correction is as follows
𝐶𝐶𝑢𝑢 𝑥𝑥 = 𝜌𝜌 𝑥𝑥 𝐶𝐶𝑝𝑝 𝑥𝑥 + 𝛿𝛿 𝑥𝑥 + ε
• 𝐶𝐶𝑢𝑢 Updated capacity value
• 𝜌𝜌 Scale correction function
• 𝐶𝐶𝑝𝑝 Deterministic capacity
• 𝛿𝛿 Bias correction function (𝛿𝛿0+𝛿𝛿1 𝑥𝑥1+𝛿𝛿11 𝑥𝑥1
2+𝛿𝛿2 𝑥𝑥2+𝛿𝛿3 𝑥𝑥3)
• 𝑥𝑥1 Number of clips
• 𝑥𝑥2 , 𝑥𝑥3 Indicator variables for wood type.
• ε Random model error

Statistical pooled model based on number of connection and wood type:
𝐶𝐶𝑒𝑒 𝑥𝑥 = 𝛿𝛿 𝑥𝑥 + ε
𝛿𝛿 Bias correction function (𝛿𝛿0+𝛿𝛿1 𝑥𝑥1+𝛿𝛿11 𝑥𝑥1
2+𝛿𝛿2 𝑥𝑥2+𝛿𝛿3 𝑥𝑥3)
𝑥𝑥1 Number of clips
𝑥𝑥2 , 𝑥𝑥3 Indicator variables for wood type.
ε Random model error
C. Capacity prediction model
→ Statistical Pooled Model

Example
• Residential building – Wood, Gable
roof (Cope, 2004)
• Rigid, Fully enclosed, Exposure B
• Length 56’, Breadth 44’, Wall height
10’, Roof slope 5:12 (θ =22.6°)
• Eave overhang 2’, Truss spacing 2’
• 1 and 2, H2.5A clips at each
connection.
• SPF 2” x 4”
56’
44’
10’
9.2’
44’
Truss
Top plate
Column 11FLORIDA SEA GRANT PROJECT R-CS-60
D. Fragility Analysis

Example
• Wind parallel to ridge
• Region 3 and 4
• Cpi = 0.18, Cp = -0.9, Cpov = 0.8
• Force per connection
=0.00256 x kz x kzt x kd x V2
x ( (Cp- Cpi)x(44/2)x2 + Cpov x 2 x 2 )
3
4

→ Conventional
• SPF, 1 H2.5A clip
• Mean capacity = 436.6 lb
• Std. deviation = 51.89 lb
• SPF, 2 H2.5A clip
• Mean capacity = 591.4 lb
• Std. deviation = 68.34 lb






Φ=
ζ
µ)/ln(
)(
D
vF𝐶𝐶𝑐𝑐 = 𝐿𝐿𝐿𝐿(µ, σ)

Log transformation
• Quantile Quantile-plot of
regression model residuals
and lognormal distribution
• Lognormal distribution is an
adequate fit for model
random errors
• Use logarithmic capacity
values in the model
-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5
-3
-2
-1
0
1
2
3
Quantiles of normal Distribution
QuantilesofInputSample
QQ Plot of Sample Data versus Distribution

𝑃𝑃 𝐶𝐶𝑢𝑢 𝑋𝑋, 𝑥𝑥 = 𝑡𝑡𝜈𝜈
�𝑏𝑏′ 𝑥𝑥, 𝑠𝑠2(1 + 𝑥𝑥𝑥 𝑋𝑋𝑋𝑋𝑋 −1 𝑥𝑥)
𝑥𝑥 Regressor vector 𝐶𝐶𝑝𝑝 1 𝑥𝑥1 𝑥𝑥2 𝑥𝑥1
2
𝐶𝐶𝑝𝑝 Computer prediction of capacity
�𝑏𝑏 Coefficient vector 𝑋𝑋𝑋𝑋𝑋 −1 𝑋𝑋′ 𝑦𝑦
𝑠𝑠2 Error variance 𝑁𝑁 − 𝑑𝑑 −1 𝐶𝐶𝑒𝑒 − 𝑋𝑋�𝑏𝑏
′
𝐶𝐶𝑒𝑒 − 𝑋𝑋�𝑏𝑏
𝜈𝜈 𝑁𝑁 − 𝑑𝑑
𝐶𝐶𝑒𝑒 Vector of capacity observations
𝑋𝑋 Matrix of regressor observations 15
→ Proposed
Posterior predictive distribution of updated capacity model

Updated capacity distribution
• For a given number of clips
the predictive distribution of
the capacity is a lognormal
distribution.
• We calculate the probability
of failure from these
distributions.
→ Proposed

17
→ Proposed
Updated Model and Statistical Pooled Model

Assume 𝐷𝐷 is the wind-load effect, then the limit state due to wind failure is given
𝑔𝑔 𝛽𝛽, 𝑣𝑣 = 𝐶𝐶𝑢𝑢 𝑥𝑥, 𝛽𝛽 − 𝐷𝐷(𝑣𝑣) ≤ 0
The probability of failure at a given wind speed 𝑣𝑣 is found by integrating the
predictive distribution:
𝑃𝑃𝑓𝑓𝑓𝑓 = 𝑃𝑃 𝑔𝑔 𝛽𝛽, 𝑣𝑣 ≤ 0 = �
−∞
𝐷𝐷
𝑃𝑃 𝐶𝐶𝑢𝑢 𝑋𝑋, 𝑥𝑥
→ Proposed
Failure Probability

→ Proposed
Results

Proposed approach Conventional approach
E. Comparison of Fragility Results

Bounds on wind speed at 0.50
failure probability
• Bayesian approach allows us to
quantify the confidence in
predictions of updated and
statistical model.
• Computer updated model is
not markedly improved than
the statistical model for
prediction uncertainty.
E. Comparison of fragility results

3. Summary
Bayesian based approaches in capacity prediction were studied
Fragility curves were obtained using predicted capacities.
Fragility curves from different approaches were compared

4. Future tasks
Demand uncertainty
Improve the deterministic capacity model
Improve the Bayesian model fit.
Improve bound estimation
Extreme value prediction
What EQECAT wants us to do ?

Questions and Comments
?

References
• S.S., Ahmed, I., Canino, A.G., Chowdhury, A., Mirmiran, N., Suksawang. (2011). “Study of the Capability of Multiple
Mechanical Fasteners in Roof-to-Wall Connections of Timber Residential Buildings.” Practice Periodical on Structural Design
and Construction, 16, 2-9.
• K. G., Tyner, (1996).”Uplift capacity of rafter-to-wall connections in light-frame construction,” MS thesis, Dept. of Civil
Engineering, Clemson University, Clemson, S.C.
• T.D., Reed (1997). “Wind resistance of roof systems in light-frame construction.” MS thesis, Dept. of Civil Engineering,
Clemson University, Clemson, S.C.
• B., Shanmugam, (2011). “Probabilistic assessment of roof uplift capacities in low-rise residential construction” Doctoral
dissertation, Dept. of Civil Engineering, Clemson University, Clemson, S.C.
• L.R., Canfield, S.H. Niu, H. Liu (1991). “Uplift resistance of various rafter-wall connections.” Forest Products Journal, 41, 27-
34.
• J. Cheng (2004). “Testing and analysis of the toe-nail connection in the residential roof-to-wall system.” Forest Products
Journal, 54, 58-65.
• P. Gardoni, A.D., Kiureghian, K. M. Mosalam (2002). “Probabilistic capacity models and fragility estimates for reinforced
concrete columns based on experimental observations.” Journal of Engineering Mechanics, 128, 1024-1038.
• M. A. Riley, F., Sadek (2003). “Experimental testing roof to wall connections in wood frame houses.” Building and Fire
Research Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, USA.

Back up slides

Wind load estimation (Ch 27, ASCE - 07)
• V – Basic wind speed
• Kz = 0.61 (velocity pressure
exposure coefficient)
• Kzt = 1 (topographic constant)
• Kd = 0.85 (Wind directionality
factor)

Wind load estimation
– Parallel to ridge
• q = qi = 0.00256*Kz*Kzt*Kd*V2
• Self weight = 17 psf.
• Cpi = +0.18,-0.18 (Internal pressure
coefficient) Figure 26.11-1
• Cp (External pressure coefficient)
Figure 27.4-1.
• Design wind pressure = qGCp - qiGCpi
• Force on the sheathing = Area *(
Wind pressure – self wt. )
• Fconnection =.00256 x kz x kzt x kd x V2 x
( (Cp- Cpi)x(44/2)x2 + Cpoverhang x 2
x2 )
3
4
5
6

1 1.5 2 2.5 3 3.5 4
6
6.2
6.4
6.6
6.8
7
7.2
7.4
x, Number of Connections
y(x),Capacity
SPF - updated model
Pure Model Output
Experimental data
Pred of Updated
95% PIof updated
1 1.5 2 2.5 3 3.5 4
6
6.2
6.4
6.6
6.8
7
7.2
7.4
x, Number of Connections
y(x),Capacity
SPF - statistical pooled model
Pure Comp Model
Experimental data
Pred of Statistical
95% PIof statistical

1 1.5 2 2.5 3 3.5 4
6
6.2
6.4
6.6
6.8
7
7.2
7.4
x
y(x)
SPY-updated model
Pure Comp Model Output
Bias/Scale Corrected
Experimental data
1 1.5 2 2.5 3 3.5 4
6
6.2
6.4
6.6
6.8
7
7.2
7.4
x
y(x)
SPY - statistical model
Pure Comp Model
Experimental data
95% PI of statistical

1 1.2 1.4 1.6 1.8 2
6
6.5
7
7.5
x
y(x) DYI-updated model
Pure Comp Model Output
Experimental data
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
6
6.5
7
7.5
x
y(x)
DYI-statistical model
Experimental data

60 80 100 120 140 160 180
0
0.2
0.4
0.6
0.8
1
wind speed (mph)
F(v)
Fragility curve for SPF with confidence bounds- Updated Model
2 connection
1 connection
60 80 100 120 140 160 180
0
0.2
0.4
0.6
0.8
1
wind speed (mph)
F(v)
Fragility curve for SPF with confidence bounds - Pooled Stat Mode
2 connection
1 connection

60 80 100 120 140 160 180
0
0.2
0.4
0.6
0.8
1
wind speed (mph)
F(v)
Fragility curve for SPY with confidence bounds- Updated Model
2 connection
1 connection
60 80 100 120 140 160 180
0
0.2
0.4
0.6
0.8
1
wind speed (mph)
F(v)
Fragility curve for SPY with confidence bounds - Pooled Stat Mode
2 connection
1 connection

60 80 100 120 140 160 180
0
0.2
0.4
0.6
0.8
1
wind speed (mph)
F(v)Fragility curve for DYI with confidence bounds- Updated Model
2 connection
1 connection
60 80 100 120 140 160 180
0
0.2
0.4
0.6
0.8
1
wind speed (mph)
F(v)
Fragility curve for DYI with confidence bounds - Pooled Stat Mode
2 connection
1 connection

SPF
0.5 1 1.5 2 2.5
130
140
150
160
170
180
model
windspeed,mph
wind speed for 50% failure prob. 1: updated, 2: stat,
1 connect 2 connect 4 connect

SPY
0.5 1 1.5 2 2.5
130
140
150
160
170
180
model
windspeed,mph
1 connect 2 connect 4 connect

DYI
0.5 1 1.5 2 2.5
140
145
150
155
160
165
model
windspeed,mph
1 connect 2 connect

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