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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)