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Location and Evaluation of Maximum Dynamic Effects on a Simply Supported Beam due to a Quarter-Car Model. Authors: Daniel Cantero & Dr. Arturo González (University College Dublin). 1. 2. 3. 4. 5. Overview. 1) Introduction. 2) P-load. 3) Speed Influence. 4) Monte Carlo. 5) Conclusions. - PowerPoint PPT Presentation
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Location and Evaluation of Maximum Dynamic Effects on a Simply Supported
Beam due to a Quarter-Car Model
Authors:
Daniel Cantero & Dr. Arturo González(University College Dublin)
Overview
1) Introduction
2) P-load
3) Speed Influence
4) Monte Carlo
5) Conclusions
1 2 3 4 5
Introduction
Vehicle/Bridge Interaction
1 2 3 4 5
Maximum Stress not necessarily at mid-span
P-load
1 2 3 4 5
Euler-Bernoulli beam
Constant vertical force at constant speed
Span = 25m Speed = 25 m/s Load = 10 KN
0 5 10 15 20 25
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Vehicle position (m)
Nor
mal
ized
Ben
ding
Mom
ent
P-load
Static Bending Moment at mid-span
1 2 3 4 5
0 5 10 15 20 25
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Vehicle position (m)
Nor
mal
ized
Ben
ding
Mom
ent
P-load
Total Bending Moment at mid-span(Static + Dynamic)
DAF = 0.9959
1 2 3 4 5
Observation point (m)
Veh
icle
pos
ition
(m
)
0 5 10 15 20 250
5
10
15
20
25
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Observation point (m)
Veh
icle
pos
ition
(m
)
0 5 10 15 20 250
5
10
15
20
25
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
P-load
Total Bending Moment(Static + Dynamic)
FDAF = 1.0648
COP = 11 m
1 2 3 4 5
P-load
FDAF DAF
1 2 3 4 5
FDAF = ( 1 + γ ) · DAF
P-load
Dynamic Amplification Factor DAF = 0.9959
Full length Dynamic Amplification Factor FDAF = 1.0648
γ = 6.92 %
Critical Observation PointCOP = 11 m
COP = 44 %
1 2 3 4 5
Speed Influence
DynamicAmplification
DAF & FDAF
γ valuesCOP
1 2 3 4 5
Monte Carlo
Vehicle parameters ( Speed, Masses, Suspension stiffness and damping, Tyre stiffness)
Bridge lengths ( 8 different spans between 17 and 31 m)
Road profile ( ISO Class A, B and C profiles)
1 2 3 4 5
Monte Carlo
COP
1 2 3 4 5
γ values
Monte Carlo
1 2 3 4 5
Monte Carlo
Mean Values
1 2 3 4 5
Conclusions
1 2 3 4 5
1) Maximum stress can be significantly higher than mid-span stress
2) Maximum stresses occur in between 30 % and 70 % of bridge span
3) Road roughness has big influence
Acknowledgments
Assessment and Rehabilitation of Central European Highway Structures
1 2 3 4 5
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