Original Article
Nonlinear finite element
analysis of thermoplastic
railroad bridge
Journal of Thermoplastic Composite
Materials
2016, Vol. 29(6) 850–866
ª The Author(s) 2016
Reprints and permissions:
sagepub.co.uk/journalsPermissions.nav
DOI: 10.1177/0892705716632859
jtc.sagepub.com
Rajai Z Al-Rousan1,2, Nadim I Shbeeb1
and Rund Al-Masri1
Abstract
Due to the environmental and financial benefits of thermoplastic materials as mentioned in
literature and being a viable green solution, a nonlinear finite element analysis was conducted
to study the behavior of thermoplastic materials of the No. 3 Fort Eustis railroad bridge
using ABAQUS in terms of deflection, stress, and vertical forces at critical locations. Six
models were simulated. These models were evaluated under GE 80-Ton switcher at 8 km/h
(kph) speed and GP 16-120 Ton locomotives at speeds of 8, 24, 40, 56, and 80 kph. The
models were validated against experimental results available in the literature. The models
studied the effect of train speed on the deflection profile, flexural stress profile, vertical force
profile, and stress profile along the bridge as well as the stress profile along the section. Based
on the simulated models, it is clearly shown that the thermoplastic material has lower
deflection and stress than wood; higher speeds resulted in lower stress and deflection. Based
on this study, thermoplastic material can be considered as a good alternative because of its
performance in terms of stress, vertical force, and corresponding deflection.
Keywords
Nonlinear finite element analysis, thermoplastic, railroad, simulated, bridge, deflection,
stress, vertical force
Introduction
The loss of structural integrity of existing steel, timber, and reinforced concrete bridges
due to corrosion and biodegradation has been a major issue in the world. The estimated
1
Department of Civil Engineering, Jordan University of Science and Technology, Irbid, Jordan
Department of Civil and Infrastructure Engineering, American University of Ras Al Khaimah, Ras Al Khaimah,
UAE
2
Corresponding author:
Rajai Z Al-Rousan Jordan University of Science and Technology, Ar Ramtha, Irbid 22110, Jordan.
Email: [email protected]
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Al-Rousan et al.
851
cost of repair and replacement in the United States alone is estimated to be around
US$300 billion per year.1 Every year about 10–15 million wood railroad crossties are
replaced as they do not perform well in a wet environment.2 Moreover, the prices of
wood will rise due to the laws and policies that protect trees and forests.3 The need for
new advanced materials has become a necessity. This new material when compared to
conventional materials such as steel, concrete, and wood should be more durable, sustainable, should accelerate construction, and be environmentally friendly. Such a
material is enhanced reinforced structural plastic composite (RSPC). RSPC is an
immiscible polymer blend (IMPB) with reinforcing agents such as polypropylene- or
polystyrene-coated glassed fiber merged within the recycled plastic lumber matrix and it
is made of nearly 100% recycled postconsumer and industrial plastics. RSPC is maintenance free (corrosion, insect, and rot resistant) for at least 50 years.4
It is environmentally friendly as it does not leach toxin chemicals into soil or water
and reduces deforestation and green house gases. It has high-energy absorption capacity
and is recyclable.5,6 These prefabricated light-weight materials can be molded in any
shape and readily transported to construction sites, thus expediting the construction
time.7 In May 1997, The Facility for Accelerated Service Testing (FAST) track at the
American Association of Railroads (AAR) and Transportation Technology Center in
Pueblo, Colorado, installed 24 plastic/composite crossties. In February 1998, a second
batch of 24 plastic/composite crossties were installed in Fast track. By April 1999, the
first batch of crossties was subjected to 182 million gross tons (MGT) and the second
batch was subjected to 108 MGT. After visual inspection at that time, no deterioration
was observed.8 AAR (December, 1998) constructed plastic ties in No. 10 turnout
(switch) at Naval Surface Warefare Center in Crane, Indiana, USA. This was the first
project to utilize plastic ties in turnout.9 New York City Department of General
Devices constructed the first plastic lumber civil structure of major significance, the
Tiffany Street pier, located at the end of Tiffany Street in the Bronx in New York City,
USA. The recreation pier is 125 m long and 15 m wide. This structure includes plastic
lumber pilings, timber joists, and railings.10 United State Army (1998) constructed the
first thermoplastic (PS/HDPE) vehicular bridge at Fort Leonard, Missouri, USA, the
24-foot span bridge was designed by M. G. McLaren Consulting Engineers, with
maximum load capacity of 29,430 kg. The decadent deck was replaced by a new
thermoplastic deck with rectangular cross section supported by the existing steel girders; it shows no sign for degeneration and requires no maintenance even after
13 years. The bridge was built with initial high cost, which was recovered within the
first 8 years of its life.11
United State Army (2010) decided to replace two railroad timber bridges at Fort
Eustis, Virginia, USA, to be the world’s first thermoplastic railroad bridges. All the
components of both bridges including girders, pier caps, pilings, and crossties are made
from thermoplastic (FRPP/HDPE) material, but for economic reasons the existing
abutments were retained. Bridge No. 3 consists of four spans with 11.73 m total length
and bridge No. 7 consists of eight spans with approximately 25.6 m total length, designed
to carry the Cooper E60 load and the 1156 kN alternate live load on four axles to have a
maximum load capacity of 127,530 kg. Live load testing was carried out on the bridge
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Journal of Thermoplastic Composite Materials 29(6)
using several railway vehicles and speeds, including a GE 80-Ton (72,574.8 kg) switcher
and a GP 16-120 Ton (117,000 kg) locomotives. The vehicles passed over the bridges
back and forth with speed ranging from 8 km/h (kph) to 40 kph. The speed was limited
to 40 kph due to the curved tracks close to the bridge. The maximum deflection
recorded was 5.33 mm compared to the allowable deflection of 5.5 mm (The US Army
chose to limit the deflection to L/60012). Also estimation for deflection was conducted
using the LARSA program that is an advanced structural analysis program that is
capable of performing moving loads.12 Recently, the US Army Engineer Research and
Development Center conducted a load test on a thermoplastic composite bridge located
on Tuckers Road in North Carolina, USA. The bridge was made with 94% recycled
high-density polyethylene. The finite element analysis performed on the bridge based
on the test data proved that the bridge exceeded design specifications.13 Another study
tackled the strengthening of concrete column stubs by using resin-infused composite
wraps. The study showed that the use of the composite wraps substantially increased
both the load carrying capacity and deformation capability of the stubs.14 Other
researcher focused on understanding the flexural behavior of thermoplastic beams,
in which the ultimate strength design procedure was developed for thermoplastic
beams.15
Nonlinear finite element analysis
Six models were simulated using ABAQUS16 using two types of materials (thermoplastic and wood). These models were evaluated under GE 80-Tons switcher (GE80) at
8 kph speed and GP 16 120-Ton (GP16) locomotive with speeds of 8, 24, 40, 56, and
80 kph. The first stage aimed at validating the model by comparing the simulated models
against the experimental results reported by Kim et al.12 Then the analysis was expanded
to include the effect at higher speeds. Although the experimental study was limited to
40 kph due to the curved tracks close to the bridge, no such restrictions are present in the
simulated models. Only one speed of 40 kph was chosen for the wood model for
comparison with the thermoplastic material.
Description of the bridge
Figure 1(a) depicts the cross section of the bridge used in the models (Fort Eustis Bridge
No. 3). The bridge consists of pile caps, bearing stiffeners, clusters of three 460 I-beams
reinforced with horizontal and vertical stiffeners, block shears, a deck located above the
460 I beams, and crossties (Parsons Brinckerhoff 2011). Two rails are used with the
inside distance between them equal to 1440 mm according American Railway Engineering
and Maintenance-of-way Association (AREMA, 2014).17 The crossties dimensions were
250 250 mm2.
Material parameters
Two types of material are used in the models for comparison reasons.
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Al-Rousan et al.
853
Figure 1. Cross-section and 3-D view of the model: (a) Cross-section of the model, all dimensions
in millimeters; (b) Plan view of bridge, all dimensions in meter; (c) Fort-Eustis’ Railroad Bridge;12
and (d) 3-D model.
3-D: three-dimensional.
Thermoplastic material. Thermoplastic is a viscoelastic material. The mechanical
properties are listed in Table 1.18 The stress–strain relationship, stress relaxation data, and
normalized shear modulus versus time are shown in Figure 2.2 The stress relaxation test
data (shown in Figure 2(b)) were used to estimate the shear modulus (G(t)) and the normalized shear modulus (shown in Figure 2(c), calculated at 40 h intervals). The normalized
shear modulus, which is used in ABAQUS, is implemented through the use of Prony
series. The instantaneous modulus G0 and bulk modulus K0 are determined from the
modulus of elasticity and poison ratio provided in Table 1.18 The shear long-term modulus
was assumed to be the one at the end of the shear modulus curve at time equal to 2160 h.
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Journal of Thermoplastic Composite Materials 29(6)
Table 1. Mechanical properties of thermoplastic material.18
Mechanical properties
0.85–0.90
2413.2 MPa
4.14 MPa (ultimate ¼
4.14 MPa (ultimate ¼
4.14 MPa (ultimate ¼
2.41 MPa (ultimate ¼
0.0000282 in/in/deg F
881 kg/m3
0.35
35
3.2
30
2.8
25
Stress (MPa)
Stress (MPa)
Specific gravity (ASTM D6111)
Elastic modulus (ASTM D6108)
Allowable tensile stress (ASTM D638)
Allowable flexural stress (ASTM D6109)
Allowable compressive stress (ASTM D695)
Allowable shear stress (ASTM D6109)
Coefficient of thermal expansion (ASTM D696)
Density
Poisson’s ratio
20
15
10
2.4
2.0
1.6
1.2
5
0
0.0
20.68 MPa)
17.24 MPa)
17.24–29.6 MPa)
10.34 MPa)
(b) Experimental relaxation stress–time (90 days)
(a) Stress–strain relationship [2]
2.5
5.0
7.5
10.0
Strain (%)
12.5
0.8
15.0
0
240 480 720 960 1200 1440 1680 1920 2160
Time (h)
Normalized shear modulus
1.2
1.0
0.8
0.6
0.4
0.2
(c) Viscoelastic parameters
0.0
0
240
480
720
960 1200 1440 1680 1920 2160
Time (h)
Figure 2. Mechanical properties of thermoplastic material.
Wood material. Wood (White oak) was modeled as an orthotropic material. The
mechanical properties are listed in Table 2.19
Assembly of model
Figure 1 represents Fort-Eustis’s No. 3 railroad bridge that consists of four spans with a
total length equal to 11.43 m.12 All parts of the bridge except the rails are made of
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Al-Rousan et al.
855
Table 2. Wood material’s twelve constant.19
Constant
Elastic modulus
Shear modulus
Poisson’s ratio
Value
E1
E2
E3
G12
G13
G23
12
13
23
0.369
0.428
0.618
13,500 MPa
2200 MPa
972 MPa
1161 MPa
1094 MPa
284 MPa
21
31
32
0.0601
0.031
0.273
thermoplastic material. The model was built as shown in Figure 1(a). The different parts
(mentioned in the description of the model earlier) were connected together through the
tie constraint feature in ABAQUS. The tie constraint feature allows for the fusion of two
regions together despite the fact that the meshes created on the surface of the different
parts are dissimilar. Only half the bridge was modeled making us of symmetry along the
longitudinal direction (z axis; Figure 1(d)). A quarter model could not be used due to the
loading arrangement of the locomotives.
Each pile cap of the Fort-Eustis’s No. 3 railroad bridge is supported by six piles. The
piles were not modeled in this study, instead and due to symmetry, three circular
partitions were created at the bottom of each cap and treated as fixed boundary condition. Two types of trains were used as loads in the analysis, GE80 and GP16. The
GE80 switcher is a diesel–electric locomotive model built by GE Transportation
Systems. It is classified as a B-B–type wheel arrangement locomotive, meaning four
wheels on each side with a diameter of 1.0-m the distance between the wheels (center
to center) is 2.14 m. The distance between the centers of the wheel bases is 6.71 m. It
was designed for industrial and light switching duties around railheads and ports with
weight equal to 80 short tons. The GP16 is a series of rebuilt diesel–electric locomotives, a result of a remanufacturing program initiated by the Seaboard Coast Line
Railroad in an effort to spare the cost of purchasing new motive power in the late
1970s. The GP16 is also classified as a B-B–type wheel arrangement locomotive with
four wheels on each side with a diameter of 1.0 m, the distance between the wheels
(center to center) is 2.74 m. The distance between the centers of the last wheel to the
first wheel is 6.71 m. The GE80 locomotive loads were modeled as four blocks that
simulate the wheels of the train (Figure 1(d)). The dimensions of the block were 1.0 m
in length and 0.5 m in height with a width equal to 0.25 m less than the width of the rail
(0.3 m) to avoid any stress concentrations at the edges. The GP16 locomotive loads were
modeled as two blocks (same dimensions as the GE80 blocks) that simulate the wheels of
the train (Figure 1(d)). Only two wheels were needed for the GP16 since it’s longer than
the bridge (17 m), as the last wheel of the front axle leaves the bridge the first wheel of the
back axle enters. The rails were extended beyond the bridge to accommodate the length of
the trains. Fixed boundary conditions were used for the extended rails. The surface to
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Journal of Thermoplastic Composite Materials 29(6)
6.0
Deflection (mm)
5.5
5.0
4.5
4.0
50 × 103 100 × 103 150 × 103 200 × 103 250 × 103 300 × 103
Number of elements
Figure 3. Convergence study.
surface interaction feature in ABAQUS was used to simulate the contact between the
blocks (wheels) and ties.
The element type selected for the analysis was an eight-node linear brick incompatible mode element (designated in ABAQUS as C3D8I). This type of element is suited
for flexural analysis and eliminates the development of any artificial energy. ABAQUS/
Explicit was used for the analysis. Several convergence studies were conducted for the
different speeds and materials. The optimum mesh was based on the thermoplastic
material as it needed more elements for convergence than wood. At the end, 35,335
elements were selected for all the models. Figure 3 shows one of the convergence
studies, while Figure 1(d) shows the mesh of the model.
Results and discussion
Validation of NLFEA results
The nonlinear finite element analysis (NLFEA) results were validated with the
experimental test results reported by Kim et al.12 The maximum deflection obtained
from the NLFEA and the experimental test results were in good agreement as shown in
Table 3. The maximum error is equal to 7.0% for the GP16 train at a speed of 40 kph,
while the minimum error of 0.3% was for the GE80 train at a speed of 8 kph. It should
be pointed out that the piles were not modeled and considered as fixed-boundary
condition, thus any axial deformation in the piles were not accounted for. It is also
observed that the insensitivity of the LARSA results to speed since it does not count for
the effect of speed.
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Al-Rousan et al.
857
Table 3. Validation of NLFEA results.
Model
GE80 (8 kph)
GP16 120 (8 kph)
GP16 120 (24 kph)
GP16 120 (40 kph)
GP16 120 (56 kph)
GP16 120 (80 kph)
NLFA max (mm) Experiment max (mm) LARSA max (mm) %Error
4.483
5.752
5.401
5.354
4.791
4.579
4.496
5.410
5.055
5.004
–
–
6.401
6.401
6.401
6.401
–
–
0.295
6.322
6.845
6.994
–
–
max: maximum deflection (mm).
Figure 4. Position of the wheels for the GP16 from the beginning of the bridge.
Deflection profile along the bridge
Figures 4 and 5 show the wheel locations and naming convention at which the results
were taken for the GP16 and GE80 locomotives, that is, F1-GP16 is when the front wheel
of the GP16 locomotive is at a distance 1.90 m from the start of the bridge (at the middle
of the first span). Figure 6(a) to (d) illustrates the deflection profile along the bridge for
the GP16 locomotive at speeds of 8, 24, 40, 56, and 80 kph. It is evident that the
deflection decreases with the increase of the speed and it’s more distinct at higher speeds.
For safety reasons and other dynamic effects, this phenomenon is neglected by the
AREMA codes. Figure 6(e) shows the deflection profile along the bridge for the GE80 at
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Journal of Thermoplastic Composite Materials 29(6)
Figure 5. Position of the wheels for the GE80 from the beginning of the bridge.
a speed of 8 kph for different positions of the front wheel. The maximum deflection is
attained when the front wheel is at a distance 12.40 m from the start of the bridge.
Load profile along the bridge
The effect of train speed on the load profile of GP16 locomotive is shown in Figure 7(a)
to (d). It can be seen that for all the simulated thermoplastic bridges, the ultimate load
consistently decreased with the increase of train speed. Also, the difference in stress
between bridges with train speed of 8 and 24 kph was significantly larger than the
difference between the train speed of 24 and 40 kph, such behavior was expected because
large speeds become less effective with the increase of speed rate. Figure 7(e) shows the
load profile for GE80 locomotive. Inspection of Figure 7(e) reveals that the lower bound
was for the F1 location and the upper bound was for the F5 location.
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(a)
F1-GP16
Allowable Deflection [12]
0
Vertical displacement (mm)
8 kph
24 kph
40 kph
56 kph
80 kph
Vertical displacement (mm)
0.5
0.0
–0.5
–1.0
–1.5
–2.0
–2.5
–3.0
–3.5
–4.0
–4.5
–5.0
–5.5
–6.0
859
0.5
0.0
–0.5
–1.0
–1.5
–2.0
–2.5
–3.0
–3.5
–4.0
–4.5
–5.0
–5.5
–6.0
1
2
3
4
5
6
7
8
Bridge length (m)
9
10
11
8 kph
24 kph
40 kph
56 kph
80 kph
(c)
F3-GP16
Allowable Deflection [12]
1
2
3
4
5
6
7
8
Bridge length (m)
Vertical displacement (mm)
0
0.5
0.0
–0.5
–1.0
–1.5
–2.0
–2.5
–3.0
–3.5
–4.0
–4.5
–5.0
–5.5
–6.0
9
10
11
0.5
0.0
–0.5
–1.0
–1.5
–2.0
–2.5
–3.0
–3.5
–4.0
–4.5
–5.0
–5.5
–6.0
8 kph
24 kph
40 kph
56 kph
80 kph
(b)
F2-GP16
Allowable Deflection [12]
0
Vertical displacement (mm)
Vertical displacement (mm)
Al-Rousan et al.
0.5
0.0
–0.5
–1.0
–1.5
–2.0
–2.5
–3.0
–3.5
–4.0
–4.5
–5.0
–5.5
–6.0
1
2
3
4
5
6
7
8
Bridge length (m)
9
10
11
9
10
11
8 kph
24 kph
40 kph
56 kph
80 kph
(d)
F4-GP16
Allowable Deflection [12]
0
1
2
3
4
5
6
7
8
Bridge length (m)
F1-GE80
F2-GE80
F3-GE80
F4-GE80
F5-GE80
(e)
8 kph
Allowable Deflection [12]
0
1
2
3
4
5
6
7
8
Bridge length (m)
9
10
11
Figure 6. Effect of train speed on the deflection profile of thermoplastic bridge.
Stress profile along the bridge
Figure 8(a) to (d) shows the flexural stress profile along the bridge for the GP16 locomotive at speeds of 8, 24, 40, 56, and 80 kph. Negative stress indicates compressive
stress. It is observed that the effect of train speed on the flexural stress is not pronounced
as in the deflection. Although the trend is toward the decrease of stresses with increase of
speed (talk about lumping of speeds). Figure 8(e) and (f) shows the flexural stress profile
along the bridge for the GE80 locomotive at speed of 8 kph. Inspection of Figure 8(e)
and (f) reveals that the GE80 locomotive had uniform distribution of stresses along the
bridge.
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Journal of Thermoplastic Composite Materials 29(6)
50
0
0
–50
–50
Vertical force (kN)
Vertical force (kN)
50
–100
–150
–200
–250
8 kph
24 kph
40 kph
56 kph
80 kph
(a)
–300
F1-GP16
–100
–150
–200
–250
–300
–350
8 kph
24 kph
40 kph
56 kph
80 kph
(b)
F2-GP16
–350
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
Bridge length (m)
50
6
7
8
9
10
11
8
9
10
11
50
0
0
–50
–50
–100
Vertical force (kN)
Vertical force (kN)
5
Bridge length (m)
8 kph
24 kph
40 kph
56 kph
80 kph
–150
–200
–250
(c)
–300
–100
8 kph
24 kph
40 kph
56 kph
80 kph
–150
–200
–250
(d)
–300
F3-GP16
–350
F4-GP16
–350
0
1
2
3
4
5
6
7
8
9
10
11
0
1
2
3
4
Bridge length (m)
5
6
7
Bridge length (m)
50
Vertical force (kN)
0
–50
–100
–150
–200
–250
F1-GE80
F2-GE80
F3-GE80
F4-GE80
F5-GE80
(e)
–300
8 kph
–350
0
1
2
3
4
5
6
7
8
9
10
11
Bridge length (m)
Figure 7. Effect of train speed on the load profile of thermoplastic bridge.
Stress profile along the depth
Figure 9 shows the stress profile along the section for F2-GP16 at a speed of 56 kph.
Inspection of Figure 9 reveals that the fibers on the upper section are subject to compression stress of 0.883 MPa (negative stress) while the fibers on the lower section are
subject to tension of 0.911 MPa (positive stress) for F2-GP16 at a speed of 56 kph. Since
there is compression on the top of the section and tension on the bottom, there must be a
transition point between the two where there is no stress at all at a distance of 0.2286 m
from the top fiber of the section, which is equal to half of the section depth. Therefore,
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Al-Rousan et al.
861
1.5
1.5
Allowable stress = 4.14 MPa [18]
Allowable stress = 4.14 MPa [18]
1.0
0.5
0.0
8 kph
24 kph
40 kph
56 kph
80 kph
–0.5
(a)
–1.0
F1-GP16
–1.5
0
1
2
3
4
5
6
7
8
9
10
Flextural stress (MPa)
Flextural stress (MPa)
1.0
0.5
0.0
8 kph
24 kph
40 kph
56 kph
80 kph
–0.5
(b)
–1.0
F2-GP16
–1.5
11
0
1
2
3
Bridge length (m)
7
8
9
10
11
0.0
–0.5
(c)
0.5
0.0
–0.5
(d)
–1.0
F3-GP16
0
1
2
Allowable stress = 4.14 MPa [18]
8 kph
24 kph
40 kph
56 kph
80 kph
1.0
Flextural stress (MPa)
Flextural stress (MPa)
0.5
–1.0
F4-GP16
3
4
5
6
7
8
9
10
–1.5
11
0
1
2
3
Bridge length (m)
4
5
6
7
8
9
10
11
Bridge length (m)
1.5
1.5
Allowable stress = 4.14 MPa [18]
Allowable stress = 4.14 MPa [18]
1.0
0.5
0.0
–0.5
F1-GE80
F2-GE80
F3-GE80
(e)
–1.0
8 kph
0
1
2
3
4
5
6
7
Bridge length (m)
8
9
10
11
Flextural stress (MPa)
1.0
Flextural stress (MPa)
6
1.5
Allowable stress = 4.14 MPa [18]
8 kph
24 kph
40 kph
56 kph
80 kph
1.0
–1.5
5
Bridge length (m)
1.5
–1.5
4
0.5
0.0
–0.5
(f)
–1.0
F4-GE80
F5-GE80
8 kph
–1.5
0
1
2
3
4
5
6
7
8
9
10
11
Bridge length (m)
Figure 8. Effect of train speed on the flexural stress profile of thermoplastic bridge.
the stress over the cross section produced force equilibrium in the horizontal direction in
which the area under the tension is significantly equal the under compression.
Effect of train type
Figure 10 shows the effect of train type on the deflection and flexural stress profile for
F2-location at a speed of 8 kph. Inspection of Figure 10 reveals that the GE80 locomotive
had feeble impact on deflection and strong impact on flexural stress profile than GP16.
The maximum deflection due to GP16 is about 5.51 mm, which is equal to 130% of the
deflection of GE80. Also, the area under the deflection profile of the GE80 is equal to
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Journal of Thermoplastic Composite Materials 29(6)
0.0
Depth (mm)
–0.1
–0.2
–0.3
F2-GB16
(56 kph)
–1.0
–0.4
–0.5
0.0
0.5
1.0
Stress (MPa)
1.5
0.5
0.0
–0.5
–1.0
–1.5
–2.0
–2.5
–3.0
–3.5
–4.0
–4.5
–5.0
–5.5
–6.0
Area under the
curve = 15.7 m2
Flextural stress (MPa)
Vertical displacement (mm)
Figure 9. Stress profile along the section for F2-GP16 at 56 kph. kph: km/h
Area under the
curve = 21.5 m2
(37% wrt GE80)
4.23 mm
30% wrt GE80
5.51 mm
F2-(8 kph)
GP16
GE80
1.0
63% wrt GE80
1.03 MPa
0.5
0.63 MPa
Area under the
curve = 5.0 MPa m
(43% wrt GE80)
Area under the
curve = 3.5 MPa m
0.0
–0.5
–1.0
GP16
GE80
F2-(8 kph)
–1.5
0
1
2
3
4
5
6
7
Bridge length (m)
8
9
10
11
0
1
2
3
4
5
6
7
8
9
10
11
Bridge length (m)
Figure 10. Effect of train type on the deflection and flexural stress profile for F2-location.
137% of the area of GP16. Whereas, the maximum flexural stress due to GP16 is about
1.03 MPa, which is equal to 163% of the flexural stress of GE80 and this value is
equivalent to 25% of the allowable compressive stress of 4.14 MPa. Finally, the area
under the flexural stress profile followed similar general trend as the area under the
deflection profile.
Effect of train speed
Figure 11 shows the effect of GP16 train speed on the deflection, vertical force, and
flexural stress for F3-location. It is obvious from the Figure 11 that the vertical force and
displacement decrease with the increase of train speed but the flexural stress decreased
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Al-Rousan et al.
863
4.0
240
–3%
–12%
3.5
220
–16%
Vertical force (kN)
Vertical displacement (mm)
0%
–18%
3.0
40 kph is the optimum
train speed
2.5
0%
–5%
200
–14%
180
–19%
–23%
160
40 kph is the optimum
train speed
140
120
GP16
2.0
GP16
100
0
20
40
60
80
100
0
20
40
Train speed (kph)
60
80
100
Train speed (kph)
1.2
Flexural stress (MPa)
1.1
0%
1.0
–14%
0.9
–15%
–13%
–12%
0.8
40 kph is the optimum
train speed
0.7
GP16
0.6
0
20
40
60
80
100
Train speed (kph)
Figure 11. Effect of train speed on the deflection, vertical force, and flexural stress for
F3-location.
with the increase of train speed up to 40 kph and then flexural stress started to increase
slightly with the increase of train speed. Inspection of Figure 11 reveals that the peak
deflection for bridge with train speeds of 8, 24, 40, 56, and 80 kph is decreased with
percentages of 0%, 3%, 12%, 16%, and 18% with respect to deflection of the train speed
of 8 kph, respectively. Also, the peak vertical force followed similar general trend as the
peak deflection but with higher percentage reduction of 0%, 5%, 14%, 19%, and 23%
with respect to deflection of the train speed of 8 kph, respectively. Also, the results in
Figure 11 show that as the minimum flexural stresses occurred at a train speed of 40 kph.
Finally, inspection of Figure 11 reveals that the deflection and vertical force versus train
speed can be divided into three stages. In the first stage, the vertical force and deflection
decreased rapidly up to the train speed of 40 kph followed by a moderate decrease up to
overlay train speed of 56 kph, which characterize as second stage. After that, the
deflection and vertical force started to decrease slightly as shown in the third stage.
Effect of material type
Figure 12 shows the effect of material type on the deflection and flexural stress profile
for F2-GP16 at a speed of 40 kph. Inspection of Figure 12 reveals that the wood material
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864
Journal of Thermoplastic Composite Materials 29(6)
3
Bridge length (m)
10.11 mm
8
9
10
11
Flextural stress (MPa)
5.33 mm
90% wrt
Thermoplastic
Area under the curve = 1.86 MPa m
(155% wrt Thermoplastic)
2.20 MPa
2
Vertical displacement (mm)
2
1
Thermoplastic
Wood
0
–1
Area under the
–2
curve = 23.9 m2
–3
Area under the
–4
2
curve = 49.9 m
–5
(110% wrt
–6 thermoplastic)
–7
–8
–9
F3-GP16
–10
(40 kph)
–11
–12
0
1
2
3
4
5
6
7
170% wrt
thermoplastic
1
Area under the
curve = 4.80 MPa m
0.82 MPa
0
–1
–1.10 MPa
–2
–3
F3-GP16
(40 kph)
0
1
2
175% wrt
Thermoplastic
Thermoplastic
Wood
–3.00 MPa
3
4
5
6
7
8
9
10
11
Bridge length (m)
Figure 12. Effect of material type on the deflection and flexural stress profile for F3-GP16 at
40 kph.
had strong impact on deflection and flexural stress profile than thermoplastic. The
maximum deflection due to wood bridge is about 10.11 mm, which is equal to 190% of
the deflection of thermoplastic. Also, the area under the deflection profile of the wood
bridge is equal to 210% of the area of thermoplastic. On the other hand, the maximum
flexural stress due to wood bridge is about 3 MPa, which is equal to 275% of the flexural
stress of thermoplastic bridge that reflects the advantage of thermoplastic to sustain more
stress and strain before failure. In both cases, the predicted stress levels did not exceed
50% of the allowable stresses. For wood, it’s about 37.5% and 26.5% for the thermoplastic material. Finally, the area under the flexural stress profile followed similar
general trend as the area under the deflection profile. Therefore, thermoplastic material is
a good alternative because of its performance, environmental, and financial benefits. The
following are advantages of using thermoplastic material: thermoplastic is a green
solution since it is made of plastic stream lying in landfills and can be recycled after its
lifetime, can be molded in any shape to optimize performance since it is a fabricated
material, can be effectively used in wet environment with no need to add chemicals and
retains its mechanical properties in such environments, can be used in structural application due to its mechanical behavior; and despite thermoplastic’s high initial cost, it
pays for it during its expected lifetime of 50 years.
Conclusions
Repair and replacement of crossties has been a troubling issue for the people involved in
this industry since it is a highly priced process. Moreover, some of the materials used for
treatment such as creosote has some toxic properties; in addition to the deforestation
polices of wood leading to limited supplies of wood, thus increasing the price of wood.
Therefore, thermoplastic (RSPC) was the alternative solution to benefit from plastics
stream lying in landfills. The nonlinear finite element model, developed in the present
work, predicted vertical load capacity, deflection, and stress in models very well as
concluded from comparisons with experimental data.
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Al-Rousan et al.
865
The GP16 had a strong impact on deflection and strong impact on flexural stress
profile than GE80. The increasing of train speed decreased the flexural stresses, vertical
force capacity, and deflection, which indicate a considerable decrease in the structural
ductility. The wood material had the strongest impact on the characteristic of bridge
behavior, which had the highest flexural stress and the deflection. However, the thermoplastic material had an excellent impact on deflection, which offered a strong and
ductile structure. Based on this study thermoplastic material can be considered as a good
alternative because of its performance in terms of stress, vertical force, and corresponding deflection.
Acknowledgment
The authors acknowledge the technical support provided by Jordan University of Science and Technology.
Declaration of Conflicting Interests
The author(s) declared no potential conflicts of interest with respect to the research,
authorship, and/or publication of this article.
Funding
The author(s) received no financial support for the research, authorship, and/or publication of this article.
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