nonlinear finite element analysis of thermoplastic railroad...

Original Article

Nonlinear finite elementanalysis of thermoplasticrailroad bridge

Rajai Z Al-Rousan1,2, Nadim I Shbeeb1

and Rund Al-Masri1

AbstractDue to the environmental and financial benefits of thermoplastic materials as mentioned inliterature andbeing a viable green solution, a nonlinear finite element analysis was conductedto study the behavior of thermoplastic materials of the No. 3 Fort Eustis railroad bridgeusing ABAQUS in terms of deflection, stress, and vertical forces at critical locations. Sixmodels 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. Themodels were validated against experimental results available in the literature. The modelsstudied the effectof train speed on the deflection profile, flexural stress profile, vertical forceprofile, and stressprofile along the bridge aswell as the stress profile along the section. Basedon the simulated models, it is clearly shown that the thermoplastic material has lowerdeflectionand stress than wood;higher speeds resulted in lower stress anddeflection. Basedon this study, thermoplastic material can be considered as a good alternative because of itsperformance in terms of stress, vertical force, and corresponding deflection.

KeywordsNonlinear 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, Jordan2 Department of Civil and Infrastructure Engineering, American University of Ras Al Khaimah, Ras Al Khaimah,

UAE

Corresponding author:

Rajai Z Al-Rousan Jordan University of Science and Technology, Ar Ramtha, Irbid 22110, Jordan.

Email: [email protected]

Journal of Thermoplastic Composite

Materials

2016, Vol. 29(6) 850–866

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DOI: 10.1177/0892705716632859

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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, sus-

tainable, 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 main-tenance 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 gir-

ders; 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

Al-Rousan et al. 851


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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% recycledhigh-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 (thermo-

plastic 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.

852 Journal of Thermoplastic Composite Materials 29(6)



Thermoplastic material. Thermoplastic is a viscoelastic material. The mechanicalproperties 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 nor-

malized 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.

Figure 1. Cross-section and 3-D view of the model: (a) Cross-section of the model, all dimensionsin 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.




Wood material. Wood (White oak) was modeled as an orthotropic material. Themechanical 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

Table 1. Mechanical properties of thermoplastic material.18

Mechanical properties

Specific gravity (ASTM D6111) 0.85–0.90Elastic modulus (ASTM D6108) 2413.2 MPaAllowable tensile stress (ASTM D638) 4.14 MPa (ultimate ¼ 20.68 MPa)Allowable flexural stress (ASTM D6109) 4.14 MPa (ultimate ¼ 17.24 MPa)Allowable compressive stress (ASTM D695) 4.14 MPa (ultimate ¼ 17.24–29.6 MPa)Allowable shear stress (ASTM D6109) 2.41 MPa (ultimate ¼ 10.34 MPa)Coefficient of thermal expansion (ASTM D696) 0.0000282 in/in/deg FDensity 881 kg/m3

Poisson’s ratio 0.35

Strain (%)0.0 2.5 5.0 7.5 10.0 12.5 15.0

Stre

ss (M

Pa)

0

5

10

15

20

25

30

35

(a) Stress–strain relationship [2]

Time (h)0 240 480 720 960 1200 1440 1680 1920 2160

Stre

ss (M

Pa)

0.8

1.2

1.6

2.0

2.4

2.8

3.2

(b) Experimental relaxation stress–time (90 days)

Time (h)0 240 480 720 960 1200 1440 1680 1920 2160

Nor

mal

ized

shea

r mod

ulus

0.0

0.2

0.4

0.6

0.8

1.0

1.2

(c) Viscoelastic parameters

Figure 2. Mechanical properties of thermoplastic material.




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 con-

dition. 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 loco-

motives, 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

Table 2. Wood material’s twelve constant.19

Constant Value

Elastic modulus E1 13,500 MPaE2 2200 MPaE3 972 MPa

Shear modulus G12 1161 MPaG13 1094 MPaG23 284 MPa

Poisson’s ratio �12 0.369 �21 0.0601�13 0.428 �31 0.031�23 0.618 �32 0.273




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 incompa-

tible 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 shouldbe 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.

Number of elements50 × 103 100 × 103 150 × 103 200 × 103 250 × 103 300 × 103

Def

lect

ion

(mm

)

4.0

4.5

5.0

5.5

6.0

Figure 3. Convergence study.




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

Table 3. Validation of NLFEA results.

Model NLFA �max (mm) Experiment �max (mm) LARSA �max (mm) %Error

GE80 (8 kph) 4.483 4.496 6.401 0.295GP16 120 (8 kph) 5.752 5.410 6.401 6.322GP16 120 (24 kph) 5.401 5.055 6.401 6.845GP16 120 (40 kph) 5.354 5.004 6.401 6.994GP16 120 (56 kph) 4.791 – – –GP16 120 (80 kph) 4.579 – – –

�max: maximum deflection (mm).

Figure 4. Position of the wheels for the GP16 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.

Figure 5. Position of the wheels for the GE80 from the beginning of the bridge.




Stress profile along the bridge

Figure 8(a) to (d) shows the flexural stress profile along the bridge for the GP16 loco-

motive 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.

Bridge length (m)0 1 2 3 4 5 6 7 8 9 10 11

Ver

tical

dis

plac

emen

t (m

m)

–6.0–5.5–5.0–4.5–4.0–3.5–3.0–2.5–2.0–1.5–1.0–0.50.00.5

8 kph24 kph40 kph56 kph80 kphF1-GP16

(a)

Allowable Deflection [12]

Bridge length (m)0 1 2 3 4 5 6 7 8 9 10 11

Ver

tical

dis

plac

emen

t (m

m)

–6.0–5.5–5.0–4.5–4.0–3.5–3.0–2.5–2.0–1.5–1.0–0.50.00.5


(b)


Bridge length (m)0 1 2 3 4 5 6 7 8 9 10 11

Ver

tical

dis

plac

emen

t (m

m)

–6.0–5.5–5.0–4.5–4.0–3.5–3.0–2.5–2.0–1.5–1.0–0.50.00.5


(c)


Bridge length (m)0 1 2 3 4 5 6 7 8 9 10 11

Ver

tical

dis

plac

emen

t (m

m)

–6.0–5.5–5.0–4.5–4.0–3.5–3.0–2.5–2.0–1.5–1.0–0.50.00.5

8 kph24 kph40 kph56 kph80 kph

F4-GP16(d)


Bridge length (m)0 1 2 3 4 5 6 7 8 9 10 11

Ver

tical

dis

plac

emen

t (m

m)

–6.0–5.5–5.0–4.5–4.0–3.5–3.0–2.5–2.0–1.5–1.0–0.50.00.5

F1-GE80F2-GE80F3-GE80F4-GE80F5-GE808 kph

(e)


Figure 6. Effect of train speed on the deflection 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 com-

pression 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,

Bridge length (m)0 1 2 3 4 5 6 7 8 9 10 11

Ver

tical

forc

e (k

N)

–350

–300

–250

–200

–150

–100

–50

0

50


(a)

Bridge length (m)0 1 2 3 4 5 6 7 8 9 10 11

Ver

tical

forc

e (k

N)

–350

–300

–250

–200

–150

–100

–50

0

50


(b)

Bridge length (m)0 1 2 3 4 5 6 7 8 9 10 11

Ver

tical

forc

e (k

N)

–350

–300

–250

–200

–150

–100

–50

0

50


F3-GP16(c)

Bridge length (m)0 1 2 3 4 5 6 7 8 9 10 11

Ver

tical

forc

e (k

N)

–350

–300

–250

–200

–150

–100

–50

0

50


F4-GP16(d)

Bridge length (m)0 1 2 3 4 5 6 7 8 9 10 11

Ver

tical

forc

e (k

N)

–350

–300

–250

–200

–150

–100

–50

0

50

F1-GE80F2-GE80F3-GE80F4-GE80F5-GE808 kph

(e)

Figure 7. Effect of train speed on the load 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 thedeflection of GE80. Also, the area under the deflection profile of the GE80 is equal to

Bridge length (m)0 1 2 3 4 5 6 7 8 9 10 11

Flex

tura

l stre

ss (M

Pa)

–1.5

–1.0

–0.5

0.0

0.5

1.0

1.5


(a)

Allowable stress = 4.14 MPa [18]

Bridge length (m)0 1 2 3 4 5 6 7 8 9 10 11

Flex

tura

l stre

ss (M

Pa)

–1.5

–1.0

–0.5

0.0

0.5

1.0

1.5


(b)


Bridge length (m)0 1 2 3 4 5 6 7 8 9 10 11

Flex

tura

l stre

ss (M

Pa)

–1.5

–1.0

–0.5

0.0

0.5

1.0

1.58 kph24 kph40 kph56 kph80 kph

F3-GP16(c)


Bridge length (m)0 1 2 3 4 5 6 7 8 9 10 11

Flex

tura

l stre

ss (M

Pa)

–1.5

–1.0

–0.5

0.0

0.5

1.0

1.58 kph24 kph40 kph56 kph80 kph

F4-GP16(d)


Bridge length (m)0 1 2 3 4 5 6 7 8 9 10 11

Flex

tura

l stre

ss (M

Pa)

–1.5

–1.0

–0.5

0.0

0.5

1.0

1.5

F1-GE80F2-GE80F3-GE808 kph

(e)


Bridge length (m)0 1 2 3 4 5 6 7 8 9 10 11

Flex

tura

l stre

ss (M

Pa)

–1.5

–1.0

–0.5

0.0

0.5

1.0

1.5

F4-GE80F5-GE808 kph

(f)


Figure 8. Effect of train speed on the flexural stress profile of thermoplastic bridge.




137% of the area of GP16. Whereas, the maximum flexural stress due to GP16 is about1.03 MPa, which is equal to 163% of the flexural stress of GE80 and this value isequivalent to 25% of the allowable compressive stress of 4.14 MPa. Finally, the areaunder 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

Stress (MPa)–1.0 –0.5 0.0 0.5 1.0

Dep

th (m

m)

–0.4

–0.3

–0.2

–0.1

0.0

F2-GB16(56 kph)

Figure 9. Stress profile along the section for F2-GP16 at 56 kph. kph: km/h

Bridge length (m)

0 1 2 3 4 5 6 7 8 9 10 11

Ver

tical

dis

plac

emen

t (m

m)

–6.0–5.5–5.0–4.5–4.0–3.5–3.0–2.5–2.0–1.5–1.0–0.5

0.00.5

GP16GE80F2-(8 kph)

30% wrt GE80

4.23 mm

5.51 mm

Area under thecurve = 15.7 m2


(37% wrt GE80)

Bridge length (m)

0 1 2 3 4 5 6 7 8 9 10 11

Flex

tura

l stre

ss (M

Pa)

–1.5

–1.0

–0.5

0.0

0.5

1.0

1.5

GP16GE80F2-(8 kph)

63% wrt GE801.03 MPa

0.63 MPa Area under thecurve = 3.5 MPa m

Area under thecurve = 5.0 MPa m(43% wrt GE80)

Figure 10. Effect of train type on the deflection and flexural stress profile for F2-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 speedof 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

Train speed (kph)0 20 40 60 80 100

Ver

tical

dis

plac

emen

t (m

m)

2.0

2.5

3.0

3.5

4.0

GP16

40 kph is the optimumtrain speed

–12%–16% –18%

–3%0%

Train speed (kph)0 20 40 60 80 100

Ver

tical

forc

e (k

N)

100

120

140

160

180

200

220

240

GP16

40 kph is the optimumtrain speed

–14%–19% –23%

–5%0%

Train speed (kph)0 20 40 60 80 100

Flex

ural

stre

ss (M

Pa)

0.6

0.7

0.8

0.9

1.0

1.1

1.2

GP16

40 kph is the optimum train speed

–15% –13% –12%–14%

0%

Figure 11. Effect of train speed on the deflection, vertical force, and flexural stress forF3-location.




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% ofthe 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 maximumflexural stress due to wood bridge is about 3 MPa, which is equal to 275% of the flexuralstress 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 thermo-plastic 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 appli-

cation 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.

Bridge length (m)

0 1 2 3 4 5 6 7 8 9 10 11

Ver

tical

dis

plac

emen

t (m

m)

–12–11–10–9–8–7–6–5–4–3–2–1

012

ThermoplasticWood

F3-GP16(40 kph)

90% wrt Thermoplastic

5.33 mm

10.11 mm


(110% wrt thermoplastic)

Area under the

curve = 23.9 m2

Bridge length (m)

0 1 2 3 4 5 6 7 8 9 10 11

Flex

tura

l stre

ss (M

Pa)

–3

–2

–1

0

1

2

3

ThermoplasticWood

170% wrtthermoplastic

2.20 MPa

0.82 MPa

Area under the curve = 1.86 MPa m(155% wrt Thermoplastic)

Area under thecurve = 4.80 MPa m

F3-GP16(40 kph)

–1.10 MPa

–3.00 MPa

175% wrtThermoplastic

Figure 12. Effect of material type on the deflection and flexural stress profile for F3-GP16 at40 kph.




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 ther-

moplastic 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 corre-

sponding deflection.

Acknowledgment

The authors acknowledge the technical support provided by Jordan University of Sci-

ence 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 publi-

cation of this article.

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