Authors: Daniel Cantero & Dr. Arturo González (University College Dublin)

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

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Introduction

Vehicle/Bridge Interaction

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Maximum Stress not necessarily at mid-span

P-load

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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

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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

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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

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P-load

FDAF DAF

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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 %

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Speed Influence

DynamicAmplification

DAF & FDAF

γ valuesCOP

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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)

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Monte Carlo

COP

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γ values

Monte Carlo

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Monte Carlo

Mean Values

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Conclusions

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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

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