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Adjusted Equivalent Static Wind Loads fornon-Gaussian Linear
Static Analysis
Nicolas Blaise, Vincent Denoël
University of Liège (Belgium)
14th International Conference on Wind Engineering
ICWE 201521-26 June 2015, Porto Alegre
N. Blaise, V. Denoël | Adjusted Equivalent Static Wind Loads
for non-Gaussian linear static analysis | ICWE 2015
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Context
Le Nouveau Vélodrome Marseille Stade de Lille Métropole
→ Equivalent Static Wind Loads ?
N. Blaise, V. Denoël | Adjusted Equivalent Static Wind Loads
for non-Gaussian linear static analysis | ICWE 2015
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Academic Example
Considered frame
36.6 m
57.2
m
Wind
. Well-known wind pressure field [Main 2006]
. Limitations of existing ESWLs
. Linear & static structural behaviour
Non Gaussian pressure field !
N. Blaise, V. Denoël | Adjusted Equivalent Static Wind Loads
for non-Gaussian linear static analysis | ICWE 2015
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Academic Example: Pressure Field
-1.5 -1 -0.5 0 0 0.2 0.4 0.6 0.8 1
-2 -1.5 -1 -0.5 0 0.5 0 2 4 6 8
Mean Cp Standard deviation of Cp
Skewness coefficient of Cp Excess coefficient of Cp
N. Blaise, V. Denoël | Adjusted Equivalent Static Wind Loads
for non-Gaussian linear static analysis | ICWE 2015
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Academic Example: Response in Frame #2
20 kNm
10 kNm
0.6
2
4 61 kNm
Mean Bending Moment
Standard Deviation of Bending Moment Excess of Bending
Moment
Skewness of Bending Moment
Example of Cp
Peak Factor (Nonsymmetric) Extreme/Design valueEnvelope
N. Blaise, V. Denoël | Adjusted Equivalent Static Wind Loads
for non-Gaussian linear static analysis | ICWE 2015
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Equivalent Static Wind Load
. Conditional Sampling technique [Holmes 1988]
Average
Equivalent Static Wind Load
Block 1 Block 2 Block 3 Block 4 Block 5 Block 7Block 6
Bending moment @ left support
Time
0 0.5 1 1.5Cp
Bending moments under ESWL Envelope overshooting
N. Blaise, V. Denoël | Adjusted Equivalent Static Wind Loads
for non-Gaussian linear static analysis | ICWE 2015
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Equivalent Static Wind Load. Load-Response Correlation (LRC)
[Kasperski 1992]
Equivalent Static Wind Load
0 0.5 1 1.5
Bending moments under ESWL Envelope overshooting
Cp
N. Blaise, V. Denoël | Adjusted Equivalent Static Wind Loads
for non-Gaussian linear static analysis | ICWE 2015
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Equivalent Static Wind Load
. Non-Gaussian Load-Response Correlation: a bi-cubic model
, : Two correlated normal R.V.
, , , , , , : 7 parameters
Examples of PDFs generated with the bi-cubic model
N. Blaise, V. Denoël | Adjusted Equivalent Static Wind Loads
for non-Gaussian linear static analysis | ICWE 2015
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Equivalent Static Wind Load: Comparison
Bending Moments under ESWL Envelope overshooting
0 0.5 1 1.5
Equivalent Static Wind Load
Conditional Sampling
Load-Response Correlation
Non Gaussian Load-Response Correlation
• LRC: Severe over-estimation of the envelope• Non-G. LRC:
Slight over-estimation of the envelope
N. Blaise, V. Denoël | Adjusted Equivalent Static Wind Loads
for non-Gaussian linear static analysis | ICWE 2015
-
Two important properties & Adjustment
1. the Envelope value condition... The ESWL associated with a
given response should return thedesign value for that response
...
2. the Non-overestimation condition... The responses under a
given ESWL should not exceed the targetenvelope ...
→ 2-step adjustmentp̃(e) = β◦
(αp(e)
)α: load scaling coefficientβ : local adjustment coefficient
N. Blaise, V. Denoël | Adjusted Equivalent Static Wind Loads
for non-Gaussian linear static analysis | ICWE 2015
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Illustration of Adjustment
α β β ◦ αcp
1.13
a a
1.00
b b
1.1
c
0 0.5 1 1.5 0 0.5 1 1.5
Conditional Sampling
Load-Response Correlation
Non Gaussian Load-Response Correlation
25 %
38 %
39 %
Unadjusted ESWL Scaled ESWL Adjusted ESWL
α β β ◦ αcp
α β β ◦ αcp
• α = 1 for the LRC method• β is obtained with a constrained
optimization algorithm
(as close as 1 as possible)
N. Blaise, V. Denoël | Adjusted Equivalent Static Wind Loads
for non-Gaussian linear static analysis | ICWE 2015
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Envelope Reconstruction
[%]
Design envelope Response under adjusted ESWL
Number of load cases
Enve
lope
reco
nstru
ctio
n
• Adjustment → faster reconstruction• Conditional Sampling, LRC,
nG-LRC perform equally if adjusted
N. Blaise, V. Denoël | Adjusted Equivalent Static Wind Loads
for non-Gaussian linear static analysis | ICWE 2015
-
Perspectives & Conclusions
Proposition of a Non Gaussian version of the LRC. bi-cubic
model. regularly extends the LRC for non Gaussian pressure
field/responses
2-Step Adjustment of Equivalent Static Wind Load to meet:. the
Envelope Value Condition. the Non-Overstimation Condition
N. Blaise, V. Denoël | Adjusted Equivalent Static Wind Loads
for non-Gaussian linear static analysis | ICWE 2015
-
Thank you ...
Vincent Denoël, Université de LiègeStructural &
Stochastic Dynamicswww.ssd.ulg.ac.be
Read more about this topic:I Blaise N., Denoël V. (2013).
Principal static wind loads. Journal of Wind
Engineering and Industrial Aerodynamics 113, 29-39.
I Blaise N., Canor T., Denoël V. (to appear). Reconstruction of
the envelope ofnon-Gaussian structural responses with principal
static wind loads.
I Kasperski M., (1992). Extreme wind load distributions for
linear and nonlineardesign. Engineering Structures 14, 27-34
I Holmes J.D., (1988). Distribution of peak wind loads on a
low-rise building.Journal Of Wind Engineering and Industrial
Aerodynamics 29, 59-67
Available @ www.orbi.ulg.ac.be
N. Blaise, V. Denoël | Adjusted Equivalent Static Wind Loads
for non-Gaussian linear static analysis | ICWE 2015
www.ssd.ulg.ac.bewww.orbi.ulg.ac.be
ContextAppendix
