Load Models for Bridges

Outline Dead load Live load Extreme load events Load combinations

Andrzej S. NowakUniversity of MichiganAnn Arbor, Michigan

Load Models

For each load component: Bias factor, = mean/nominal Coefficient of variation, V = /mean Cumulative distribution function

(CDF) Time variation: return period,

duration

Statistical Data Base Load surveys (e.g. weigh-in-motion

truck measurement) Load distribution (load effect per

component) Simulations (e.g. Monte Carlo) Finite element analysis Boundary conditions (field tests)

Examples of Load Parameters

Dead load for bridges = 1.03-1.05

V = 0.08-0.10 Live load parameters for bridges

(AASHTO LRFD Code) = 1.25-1.35

V = 0.12

No. 4 Stanley Road over I-75in Flint (S11-25032)

Examples of Bias Factors

Two bridge design codes are considered: AASHTO Standard Specifications (1996) AASHTO LRFD Code (1998)For the first one, denoted by HS20, bias factor is non-uniform, so design load in LRFD Code was changed, and the result is much better.

Two trucks side-by-side

Bias Factor for Load Effect Bias factors shown previously were

for lane load (bridge live load) For components (bridge girders),

bias factor can be very different

Girder Distribution Factors

What is the percentage of lane load per girder?

Is the actual distribution the same as specified by the design code?

What are the maximum strains? What is the load distribution factor

for one lane traffic and for two lanes

Code-Specified GDF -AASHTO Standard (1996)Steel and prestressed concrete girders One lane of traffic

Two lanes of traffic

S = girder spacing (m)3.36

SGDF

4.27S

GDF

Code-specified GDF -AASHTO LRFD (1998)

1.51

0.1

3s

g0.30.4

tanθc1Lt

K

LS

4300S

0.06GDF

1.51

0.1

3s

g0.20.6

tanθc1Lt

K

LS

2900S

0.075GDF

0.50.25

3s

g1 L

SLt

K0.25c

)AeI(nK 2

gg

One lane

Two lanes

Dynamic Load

Roughness of the road surface (pavement)

Bridge as a dynamic system (natural frequency of vibration)

Dynamic parameters of the vehicle (suspension system, shock absorbers)

Dynamic Load Factor (DLF)

Static strain or deflection (at crawling speed)

Maximum strain or deflection (normal speed)

Dynamic strain or deflection = maximum - static

DLF = dynamic / static

Code Specified Dynamic Load Factor

AASHTO Standard (1996)

  

AASHTO LRFD (1998) 0.33 of truck effect, no dynamic load for the uniform loading

3.012528.3

50

L

I

0 20 40 60 80 100 1200.0

0.2

0.4

0.6

0.8

1.0

Static StrainDynamic Strain

Strain

Dyn

amic

Loa

d F

acto

r

  

  

 

0 50 100 150 2000.0

0.2

0.4

0.6

0.8

1.0

Static StrainDynamic Strain

Strain

Dyn

amic

Loa

d F

acto

r

0 50 100 150 2000.0

0.2

0.4

0.6

0.8

1.0

Static StrainDynamic Strain

Strain

Dyn

amic

Loa

d F

acto

r

0 20 40 60 80 100 1200.0

0.2

0.4

0.6

0.8

1.0

Static StrainDynamic Strain

Strain

Dyn

amic

Loa

d F

acto

r

0 50 100 150 200 250 300 350 4000.0

0.2

0.4

0.6

0.8

1.0

Static StrainDynamic Strain

Strain

Dyn

amic

Loa

d F

acto

r

0 20 40 60 80 100 1200.0

0.2

0.4

0.6

0.8

1.0

Static StrainDynamic Strain

Strain

Dyn

amic

Loa

d F

acto

r

0 20 40 60 80 100 1200.0

0.2

0.4

0.6

0.8

1.0

Static StrainDynamic Strain

Strain

Dyn

amic

Loa

d F

acto

r

Load Combinations Load combination factors can be

determined by considering the reduced probability for a simultaneous occurrence of time-varying load components

So called Turkstra’s rule can be applied

Turkstra’s Rule Consider a combination of uncorrelated,

time-varying load components Q = A + B + C

For each load component consider two values: maximum and average. Then,

Qmax = maximum of the following:(Amax + Bave + Cave)

(Aave + Bmax + Cave)

(Aave + Bave + Cmax)