Civil Engineering Reference
In-Depth Information
point in time. Subtracting the signals, time shifted by the interval between axle arrivals, has the effect of removing most of
the influence of the road profile. This is a key feature of this approach and is the reason why the results are better than in
simpler drive-by monitoring concepts. The vehicle is simulated crossing different paths through the road profile to assess
sensitivity to transverse position of the vehicle on the bridge.
10.2 Vehicle-Bridge Interaction Model
The truck-trailer model can be seen in Fig.
10.1
. The truck is a three axle, five-degree-of-freedom rigid vehicle. The five
degrees-of-freedom account for the axle hop displacements of each of the three axles,
y
u;i
ð
i
¼
1
;
2
;
3
Þ
, sprung mass bounce
displacement,
y
s;
1
, and sprung mass pitch rotation,
θ
s;
1
. The body of the vehicle is represented by the sprung mass,
m
s;
1
, and
the axle components are represented by the unsprung masses,
m
u;
1
,m
u;
2
and
m
u;
3
respectively. The axle masses connect to
the road surface via springs of stiffness
K
t,
1
,
K
t,
2
and
K
t,
3
, while the body mass is connected to the tires by springs of stiffness
K
s,
1
,K
s,
2
and
K
s,
3
with viscous dampers of value
C
s,
1
,C
s,
2
and
C
s,
3
. This combination represents the suspension of the truck
system.
The trailer is a two axle, four-degree-of-freedom half-car suspension model. The four degrees-of-freedom account for axle
hop displacements of each of the two axles,
y
u;i
ð
i
¼
4
;
5
Þ
, sprung mass bounce displacement,
y
s;
2
and sprung mass pitch
rotation,
θ
s;
2
. The body of the vehicle is represented by the sprung mass,
m
s;
2
, and the axle components are represented by the
unsprung masses,
m
u;
4
and
m
u;
5
. The suspension springs have stiffness
K
t,4
and
K
t,5
, while the tires springs have stiffness
K
s,4
and
K
s,5
. The viscous dampers have coefficients,
C
s,4
and
C
s,5
. Tire damping is assumed to be negligible here for both the
tractor and trailer and is thus omitted. The model also accounts for the sprung mass moments of inertia
I
s;
1
and
I
s;
2
for the truck
and trailer respectively. The center of gravity of the truck is taken to be at two thirds the wheel base length from the front axle,
and the center of gravity of the trailer is taken to be central between the axles. The truck and trailer vehicle properties are
gathered from the literature [
16
-
18
] and presented in Table
10.1
. The geometry and mass of the truck are obtained from a
manufacturer specification for a 30 t three-axle truck [
19
].
The equations of motion of the vehicle are obtained by imposing equilibrium of all forces and moments acting on the
vehicle and expressing them in terms of the degrees of freedom. They are given by
M
v
€
C
v
_
y
v
þ
y
v
þ
K
v
y
v
¼
f
v
(10.1)
where
M
v
,
C
v
and
K
v
are the mass, damping and stiffness matrices of the vehicle respectively. The (
n
1) vectors
y
v
,
y
v
_
and
y
v
contain the of vehicle displacements, their velocities and accelerations respectively. The vector
f
v
contains the time
varying interaction forces applied by the vehicle to the bridge:
€
Fig. 10.1
Truck-trailer model
