The Distortion Effect of Thin-walled Wide Hollow PC Beam Under
Bridge Deck Pavement
Houxuan Wu
1
, Juanyan Li
2
and Hanbin Yi
3
1
Jiangxi Ganyue Expressway CO.,LTD,, Nanchang, Jiangxi, China
2
Jiangxi transportation vocational technical institute, Nanchang,Jiangxi, China
3
Jiangxi transportation institute, Nanchang, Jiangxi, China
Keywords: PC wide open hollow plate, distortion effect, elastic foundation beam analogy method, finite element
method, bridge deck pavement.
Abstract: The distortion stress of thin wall hollow slab is solved by using elastic foundation beam analogy method and
finite element method. The influence of the structure distortion effect on 10cm thick concrete pavement was
considered. The results show that the numerical solution and the finite element method are consistent, and
the finite element method is simpler and more efficient. The transverse tensile stress of calculation point 1
and 2 decreased by 13.2% and 13.6% respectively when considering the effect of deck pavement. The
distortion effect causes a large transverse tensile stress on the bottom plate.
1 INTRODUCTION
Thin-walled PC wide open hollow plate has been
widely used in highway Bridges in the 1990s due to
its characteristics such as large hollowing-out rate,
thick wall thickness, structural economy and light
weight. Due to the thin wall thickness of hollow
wall, the effect of transverse tensile stress caused by
the distortion cannot be ignored. At present, the
scholars all over the world have focused on the study
of distortion effect mainly in the steel box girder.
The theoretical calculation methods mainly include
the method of substitute the beam, the Kupfer
method and the generalized coordinate method. In
this paper, an example of thin-walled PC wide slabs
is given based on an expressway bridge, the elastic
foundation beam analogy method and the finite
element method were used respectively to calculate
the distortion of the hollow slab stress, the torsional
effect and the influence of Poisson effect on
structure horizontal stress is analysed. In addition,
the influence of concrete pavement on the stress of
structural distortion is considered.
The superstructure of bridge is constructed of a
20-meter PC wide open hollow slab and a total
length of 9.1 km. There are 8 hollow plates in each
transverse section, with height of 0.9 m, width 1.55
m, bottom and top plate 10cm thick, and the web
thickness is 11cm, as shown in Fig.1. Each board
has 15 ASTMA416-90a270 (0.6 inch diameter) steel
hinge lines.
The lateral layout of the deck is: 0.5m guardrail
+11.5m carriageway +0.5m guardrail +2m central
divider with +0.5m guardrail +11.5m carriageway
+0.5m guardrail (total 27m). Design load of the
bridge: car - super 20 level; Trailer - 120; the crowd
- 3.5 KN/m
2
.
7.5 7.5
21.5 21.55×21.4
150
155
90
5 17.5 2×22.5 22.5
14×10
Figure 1: the transverse section of thin wall hollow slab
(unit: cm)
Wu, H., Li, J. and Yi, H.
The Distortion Effect of Thin-walled Wide Hollow PC Beam Under Bridge Deck Pavement.
In 3rd International Conference on Electromechanical Control Technology and Transportation (ICECTT 2018), pages 271-275
ISBN: 978-989-758-312-4
Copyright © 2018 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
271

2 THE CALCULATION OF THE
LATERAL FORCE OF
DISTORTION
2.1 The calculation of torsional load of
single hollow plate
The transverse distribution coefficient of the load of
hollow slab is calculated using the hinged plate
method, the influence line of torque’s horizontal
distribution of 1-4 beam is shown in Fig. 2.
1#
2# 3# 4# 5# 6# 7# 8#
1# 2#
3# 4# 5# 6# 7# 8#
1# 2# 3#
4# 5# 6# 7# 8#
1# 2# 3#
4# 5# 6# 7# 8#
1.317
0.182
0.035
0.920
1.006
0.403
0.118
0.639
0.849
0.699
0.521
0.199
0.439
0.595
0.306
1#
2#
3#
4#
Figure 2: the influence line of torque’s horizontal
distribution
The influence line is loaded and calculated, and
the results show that the horizontal distribution
coefficients of the 4# hollow plates with the load of
trailer-120 load and car-20 load are the largest, and
the results are listed in table 1. According to the
cross-medium torque influence line and load lateral
distribution coefficient, the torque of 4# hollow slab
is obtained. Then the torsion and distortion load are
solved, as shown in Fig. 3.
T=189.2kN.m
PP
equivalent
P=131.1kN
H
d
=Pb/2h=120.4kN
V
d
H
d
V
d
=P/2=65.7kN
H
d
V
d
H
d
V
d
P=131.1kN
144cm
75cm
Figure 3: the distortion load of wide hollow plate
Table 1 The torque horizontal distribution coefficient of No 1-4 hollow plate
Load type 1# hollow slab 2# hollow slab 3# hollow slab 4# hollow slab
car-20 0.300 0.643 0.696 0.852
trailer-120 0.165 0.312 0.545 0.622
2.2 Analytical method
The lateral internal force generated under the
deformation load is calculated based on the beam
ratio method of elastic foundation. The calculation
steps are as follows:
ICECTT 2018 - 3rd International Conference on Electromechanical Control Technology and Transportation
272

IV
bd
E
IKV ωω +=
(1)
There into:
00
0
32( )
6
bc
aa aa
EI EJ
aa
μ
μ
μ
+++⋅
=⋅
++
(2)
2
0
00
2
96
1
23
1
+6
c
c
cc
EI
K
II
b
bh
hI
II II
b
I
Ih
μ
μμ
=⋅
+
+
+
+⋅
⋅
(3)
According to the dimensions shown in Fig. 4, the
symbols in the above formula are explained.
t c
t
0
t
u
h
h
0
b
b u
b 0
b c
h
0
h
c
1
2
a)
V
d
V
d
H
d
H
d
w
b)
A
B
D
C
M A
M B
M C
M D
c)
A
B
C
D
d)
Figure 4: Distortion deformation, lateral bending
moment and warping stress diagram
00
0
()
c
bbt
a
bht
=
；
()
c
bbt
a
bht
μμ
μ
=
(4)
3
2
12(1 )
i
i
t
I
μ
=
−
(0 )ic μ = ，，
(5)
The above varieties:
E
，
μ
are the elastic
modulus and Poisson ratio respectively,
K
is the
rigidity of the anti-distortion frame,
ω
is the vertical
deflection of the distortion load,
d
V
,
d
H
are the
vertical and horizontal component of the distortion
load respectively.
According to the similarity relation between
bending of elastic foundation girder and box beam
distortion (
Xiang H.F. 2013), the above parameter
values are calculated.
7.24k
A
M
Nm=⋅
，
5.47k
B
M
Nm=⋅
.
After find the transverse bending moment of the
bottom plate
B
M
， It is calculated by linear
interpolation
,1
B
M
and
,2B
M
,The transverse tensile
stress is calculated according to the material formula
,1
B
σ
，
,2
B
σ
.
,1
,1
2
,1
=
1
6
B
B
B
M
tB
σ
⋅⋅
；
,2
,2
2
,2
=
1
6
B
B
B
M
tB
σ
⋅⋅
Of which
,1
B
t
is thickness of the bottom plate at
1,
,2
B
t
is thickness of the bottom plate at 2,
B
is
width per meter,
B
equal to1m.
It can be solved that：
,1
=0.76
B
M
Pa σ
,2
=2.58
B
M
Pa σ
Considering the distortion transverse tensile
stress calculation of deck pavement, the calculation
formula is still based on the above calculation
formula. The deck pavement is regarded as the joint
force of the PC wide hollow plate. Obtain
8.17k
A
M
Nm=⋅
,
4.74k
B
M
Nm=⋅
，The transverse
tensile stress of calculation point 1 and 2
,1
0.66
B
M
Pa σ =
,
,2
2.23
B
M
Pa σ =
.
2.3 Finite element method
In order to verify the results of the theoretical
solution, ANSYS was used to analyse the distortion
effect of the finite element model. The key in
numerical simulation is the imposition of the
distortion load. In this paper, the surf154 surface
unit is given on solid65 entity unit, and the uniform
force is applied on the surface unit to achieve the
distortion load. The calculation model and the
distortion load are shown in Fig.5. The results of
finite element numerical analysis are listed in table
2. The distortion tensile stress at the hollow corner
The Distortion Effect of Thin-walled Wide Hollow PC Beam Under Bridge Deck Pavement
273

of the hollow corner is 2.58MPa and 2.69 MPa
respectively using analytical method and finite
element method. The tensile strength of C40
concrete has been exceeded. Considering the effect
of 12cm thick bridge deck pavement, the distortion
tensile stress generated by the analytical method and
finite element method is 2.23MPa and 2.35MPa less
than C40 concrete. The numerical simulation
method is more convenient to solve the distortion
strain of the structure, and the calculation results of
the two calculation methods are more consistent.
a) Calculation model b) The distortion load
Figure 5 Numerical calculation model
Table 2: The results of lateral stress calculation under the influence of car-20
Calculation
method
Lateral stress
at point 1
(MPa)
Lateral stress at point
1 that consider the
deck pavement(MPa)
Lateral stress at
point 2 (MPa)
Lateral stress at point
2 that consider the
deck pavement(MPa)
Elastic foundation
beam similarity method
0.76 0.66 2.58 2.23
FEM 0.83 0.73 2.69 2.35
According to the discussion in the previous
section, torque is finally decomposed into distortion
load and torsional load, and the distortion effect and
torsion effect are common.
In the above analysis, the transverse tensile stress
of 2# is obtained under the distortion load effect,
while the thin wall hollow slab can produce
transverse stress under the torsion effect and Poisson
effect. Therefore, the lateral stress of the wide
hollow plate under the torsion and Poisson effect is
calculated by ANSYS.
The lateral stress of the corner under the torsion
effect and Poisson effect is calculated, as shown in
Fig. 6. The calculation results are shown in table 4.
The results show that the distortion effect is the main
factor causing the transverse tensile stress,
accounting for 96% and 97% of the total stress
respectively.
a) Lateral stress caused by torsional effect b) Lateral stress caused by poisson effect
Figure 6. The lateral stress of thin wall hollow is generated by torsion effect and Poisson effect
ICECTT 2018 - 3rd International Conference on Electromechanical Control Technology and Transportation
274

Table 3: Lateral stress caused by various effects
Type
Lateral stress at
point 2(MPa)
Lateral stress at point 2 that
consider the deck pavement(MPa)
Distortion effect（1） 2.69 2.35
Torsional effect（2） -0.13 -0.17
Poisson effect（3） 0.24 0.24
TOTAL=（1）+（2）+（3） 2.80 2.42
3 CONCLUSIONS
Based on the thin wall hollow beam widely used in
medium and small span Bridges, the distortion stress
of the hollow slab is calculated by using the elastic
foundation beam analogy method and the finite
element method respectively, the following main
conclusions:
(1) The numerical solution and the finite element
method are consistent, however the finite element
method is more simple and efficient. Considering
the effect of deck pavement, the transverse tensile
stress of calculation point 1 and 2 decreased by
13.2% and 13.6% respectively.
(2) The distortion effect is the main factor that
causes the transverse tensile stress, which accounts
for 96% and 97% of the total transverse tensile
stress, and the tensile stress is larger.
Therefore, the design and use of this type of
beam should pay attention to the influence of
distortion effect in the future, the thin and thick of
hollow slab inappropriate transition reduction.
ACKNOWLEDGEMENTS
The authors would like to acknowledge the financial
support provided by Transportation Science and
Technology Project of Jiangxi Provincial [Grant
2014C0001].
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