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COURSEENGI -8700
Confederation Bridge
CIVIL
Design Project
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
TOPIC
Lecture
Monte Carlo simulation
Case Study for
REFERENCES.
Case Study for cost and load estimating
FILES
WEB
http://www.engr.mun.ca/~sbruneau/teaching/8700project
http://www.confederationbridge.com/en/about_the_bridge/bridge_faqs.php
COURSEENGI -8700
CIVIL
Design Project
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
TOPIC
Lecture
Monte Carlo simulation
Case Study forConfed Bridge
REFERENCES.
Case Study for cost and load estimating
Confed Bridge
Case Study
S Bruneau
FILES
S.Bruneau
Records
WEB
http://www.engr.mun.ca/~sbruneau/teaching/8700project
COURSEENGI -8700
Class Study in Monte Carlo Simulation for Probabilistic Load Estimating . . .
Case Study: Confederation Bridge, PEI, NB
CIVIL
Design Project
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
Ice Loading on Pier Diameter
TOPIC
Lecture
Monte Carlo simulation
Case Study forThickness
REFERENCES.
Case Study for cost and load estimating
Simplified Assumptions for Illustrative Purposes
FILES
A 100 year design load for pier stability required by developer. Models suggest:
1) Pier Force = Lesser of Ice Crushing or Driving Force
2) Ice Crush Resist = Ice Thickness * constantsWEB
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2) Ice Crush Resist Ice Thickness constants
3) Driving Force = Floe Diameter * Wind * constants
4) Ice thickness is independent of floe size is independent of wind
COURSEENGI -8700
start
Input data
Monte Carlo Simulation for Bridge Ice Loads
CIVIL
Design Project
Ice Thick, Floe diameter, Wind
Simulation: random number for each p d f to get a simulated value for each
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
p.d.f. to get a simulated value for each parameter (thick, diameter, wind)
C t f iRepeat for No of
Repeat for No of floes per year
TOPIC
Lecture
Monte Carlo simulation
Case Study for
Compute force on pier
Sort forces into f
years of Simulation
REFERENCES.
Case Study for cost and load estimating
frequency intervals track
years also
FILES
Prob(x) = Freq(x)/ No. simulations
Cumulative(x) = sum of prob up to Freq(x)
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Tabulate data
Plot Data
End
COURSEENGI -8700
Simplified Assumptions for Illustrative Purposes
F(pier) = lesser of F(thick), F(diameter, wind)Th th f t t llCIVIL
Design Project
diameter
wind thickness
These three factors are naturally random independent variables that affect loading every time a collision occurs – perhaps millions f ti th lif f th
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected] We must research and judge what the best representative probability
distributions are that will provide the best long term estimates for each In this
diameter of times over the life of the structure, therefore. . .
TOPIC
Lecture
Monte Carlo simulation
Case Study for
distributions are that will provide the best long term estimates for each. In this case study lets assume that a triangular probability distribution is sufficient.
The Triangular Distribution is typically used in cases where the relationship between variables is known but data is scarce (possibly because of the
REFERENCES.
Case Study for cost and load estimating
between variables is known but data is scarce (possibly because of the high cost of collection). It is based on a knowledge of the minimum and maximum and an "inspired guess" as to the modal value. the triangular distribution is a continuous probability distribution with lower limit a, mode c and upper limit b
FILES
c and upper limit b
2/(b-a)
WEB
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x
(height of triangle)
COURSEENGI -8700
Simplified Assumptions for Illustrative Purposes
Therefore, we define the triangular probability density functions for our random variables with estimates for a, b and c. For example:
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Design Project
random variables with estimates for a, b and c. For example:
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
TOPIC
Lecture
Monte Carlo simulation
Case Study for Now, what do we know: For ice Thickness
REFERENCES.
Case Study for cost and load estimating
1.01. The area under a probability density function is
equal to 1.0 (triangular included)
2. The random variable (thickness etc) always has a
For ice Thickness
FILES 0 20.5
value somewhere between a and b
3. For each collision in a monte carlo simulation we need a value for the random variable that is between a and b and weighted towards c in
WEB
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between a and b and weighted towards c in accordance with the probability function.
We get this random value each time using the following …
COURSEENGI -8700
Simplified Assumptions for Illustrative Purposes
Density function for CIVIL
Design Project
yIce Thickness
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
TOPIC
Lecture
Monte Carlo simulation
Case Study for
Probability of Thickness (l) = P
REFERENCES.
Case Study for cost and load estimating
Thickness at Probability P = (l)
FILESProbability of Thickness (n) = P
Thickness at Probability P = (n)
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So, a random number generator is used to give a value for P between 0 and 1, thus a value of l or n is computed with the formulas above, giving. . .
COURSEENGI -8700
A value for thickness, diameter and wind. We then use the deterministic formulas that we know about for Ice Cruching Force and Driving forces to get a force on the pier , ie. . .
CIVIL
Design Project
Monte Carlo Simulation
F(pier) = lesser of F(thick), F(diameter, wind)
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
TOPIC
Lecture
Monte Carlo simulation
Case Study for
So we end up with this after many, many collisions are modeled in the simulation
REFERENCES.
Case Study for cost and load estimating
simulation
urre
nce
FILES
babi
lity
of O
ccu
WEB
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Force in MN
Pro
0 5 10 15 20 25 30
COURSEENGI -8700
Simplified Assumptions for Illustrative Purposes
So from this figure we can get the probability of exceedance for e
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p yany risk level over the period of the simulation.
y of
Occ
urre
nce
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
F i MN
Pro
babi
lity
So, if you want a design load value that will not be exceeded
th i 10 0000 5 10 15 20 25 30
TOPIC
Lecture
Monte Carlo simulation
Case Study for
Force in MN
eede
nce
more than once in a 10,000 years99.99%
REFERENCES.
Case Study for cost and load estimating
obab
ility
of E
xce
FILESPr
oForce in MN
Here’s your number!
24 MN0 5 10 15 20 25 30
WEB
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COURSEENGI -8700
Fixed Link and the Confederation Bridge
CIVIL
Design Project
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
TOPIC
Lecture
Monte Carlo simulation
Case Study for
REFERENCES.
Case Study for cost and load estimating
FILES
WEB
http://www.engr.mun.ca/~sbruneau/teaching/8700project
COURSEENGI -8700
Getting Ice Floe Thicknesses
CIVIL
Design Project
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
TOPIC
Lecture
Monte Carlo simulation
Case Study for
REFERENCES.
Case Study for cost and load estimating
FILES
WEB
http://www.engr.mun.ca/~sbruneau/teaching/8700project
COURSEENGI -8700
CIVIL
Design Project
Testing Ridge Keel Stength
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
TOPIC
Lecture
Monte Carlo simulation
Case Study forConfed Bridge
REFERENCES.
Case Study for cost and load estimating
Confed Bridge
Case Study
S Bruneau
FILES
S.Bruneau
Records
WEB
http://www.engr.mun.ca/~sbruneau/teaching/8700project
COURSEENGI -8700
Primary Document for
CIVIL
Design Project
Document for Bridge Design
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
TOPIC
Lecture
Monte Carlo simulation
Case Study forDesign Case
REFERENCES.
Case Study for cost and load estimating
Design Case Studies
Professor’s Sources,
FILES
Professor s Sources, Reports, Commercial Investigations, WWW
WEB
http://www.engr.mun.ca/~sbruneau/teaching/8700project
COURSEENGI -8700
Primary Document for
CIVIL
Design Project
Document for Bridge Design
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
TOPIC
Lecture
Monte Carlo simulation
Case Study forDesign Case
REFERENCES.
Case Study for cost and load estimating
Design Case Studies
Professor’s Sources,
FILES
Professor s Sources, Reports, Commercial Investigations, WWW
WEB
http://www.engr.mun.ca/~sbruneau/teaching/8700project
COURSEENGI -8700
Probabilistic Estimating:
CIVIL
Design Project
Estimating: Cost example
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
TOPIC
Lecture
Monte Carlo simulation
Case Study forDesign Case
REFERENCES.
Case Study for cost and load estimating
Design Case Studies
Professor’s Sources,
FILES
Professor s Sources, Reports, Commercial Investigations, WWW
WEB
http://www.engr.mun.ca/~sbruneau/teaching/8700project
COURSEENGI -8700
Probabilistic Estimating:
CIVIL
Design Project
Estimating: Cost example
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
TOPIC
Lecture
Monte Carlo simulation
Case Study forDesign Case
REFERENCES.
Case Study for cost and load estimating
Design Case Studies
Professor’s Sources,
FILES
Professor s Sources, Reports, Commercial Investigations, WWW
WEB
http://www.engr.mun.ca/~sbruneau/teaching/8700project
COURSEENGI -8700
Primary Document for
CIVIL
Design Project
Document for Bridge Design
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
TOPIC
Lecture
Monte Carlo simulation
Case Study forDesign Case
REFERENCES.
Case Study for cost and load estimating
Design Case Studies
Professor’s Sources,
FILES
Professor s Sources, Reports, Commercial Investigations, WWW
WEB
http://www.engr.mun.ca/~sbruneau/teaching/8700project
COURSEENGI -8700
Primary Document for
CIVIL
Design ProjectBridge Design
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
TOPIC
Lecture
Monte Carlo simulation
Case Study for
We were right!
REFERENCES.
Case Study for cost and load estimating
FILES
WEB
http://www.engr.mun.ca/~sbruneau/teaching/8700project
COURSEENGI -8700
Class example using excel Filename: monte carlo simulation xnew.xlsx
CIVIL
Design Project
INSTRUCTORDr. Steve Bruneau EN.4013Ph 8642119 [email protected]
TOPIC
Lecture
Monte Carlo simulation
Case Study for
REFERENCES.
Case Study for cost and load estimating
FILES
WEB
http://www.engr.mun.ca/~sbruneau/teaching/8700project