Dynamic Behavior and Reliability Assessment of a CFTA ...

Steel Structures 8 (2008) 315-324 www.ijoss.org

Dynamic Behavior and Reliability Assessment of a CFTA girder

subjected to Truck Collision

Trinh Thai Trung1, Jung Hoon Kim1, Kyung Hoon Park2, and Jung Sik Kong1*

1Department of Civil, Environmental and Architectural Engineering, Korea University, Seoul, Korea2Korea Institute of Construction Technology, 2311, Daehwa-dong, Ilsanseo-gu, Goyang, Korea

Abstract

One of the principle aims of engineering design is the assurance of the system performance within the constraint of economy.Indeed, the assurance of performance, including safety, is primarily the responsibility of engineers. In this study, the impactdynamic behavior of an innovative girder entitled the Concrete-Filled and Tied steel Tubular Arch or CFTA girder was studied.The girder consists of a steel plate frame, arch concrete and outside tendons. A CFTA girder has several advantages comparedto conventional types of girders such as buckling prevention by concrete filling, an increase in the stiffness and durability ofconcrete due to the confinement effect and aesthetic and economical matters due to arch concrete. In this study, impact dynamicsimulation and analysis were performed to investigate the dynamic responses of the girder. Furthermore, the reliabilityassessment developed for a CFTA girder will facilitate the intuitive sense in the design, and the evaluation of the performanceof bridges.

Keywords: CFTA girder, Dynamic Behavior, Collision, Reliability

1. Introduction

1.1. Overview of Composite girders

Innovative structures using new materials are essential

for the development of the construction field. In order for

them to be widely and intensively applied, research needs

to be carried out on these structures, and they need to be

carefully analyzed and optimized. Nowadays, a great deal

of research related to superstructures of bridge engineering

are being performed to develop a more effective design,

to make full use of the material properties and finally to

create a more economical application. A number of

innovative typical structures that maximize the merits of

concrete, steel and strands include CFT (Concrete Filled

Steel Tube) or SCP (Steel Confinement Pre-stressed)

girders. This paper proposes a new type of girder entitled

the Concrete Filled and Tied Steel Tubular Arch (CFTA).

CFTA has many advantages compared to the current

structure because it makes use of almost all the prominent

characteristics of each material and of its structural

design, including buckling prevention by concrete filling,

a higher stiffness and durability due to the confinement

effect, a longer span and lighter structures due to

prestressed tendons, as well as the pleasing aesthetics of

an arch shape (Lee et al., 2008).

1.2. Impact problem

In advanced structural engineering, attention has been

paid to impact analysis. Through experimental, theoretical

and numerical calculations, a number of studies (Sherif et

al., 2005; Kong et al., 2006; Itoh et al., 2007; Zeinoddini

et al., 2007) have accounted for the collision issue in

various fields such as industrial engineering, civil engineering

and transportation, etc. Since bridges are one of the main

components of the transportation system, accidental collisions

involving transport vehicles and bridges would probably

induce catastrophic consequences (Itoh et al., 2007;

Zineddin & Krauthamer, 2007). Therefore, serious and

rigorous studies on impact issues, especially in terms of

the use of innovative structures such as CFTA, are

necessary and valuable.

Because CFTA typically carries its service loads

(almost dead loads and truck live loads), a collision can

be very dangerous, especially when there is lateral impact

to the structure. A CFTA comprises of steel plates,

concrete components and outside prestressed tendons.

These tendons resist only the tensile forces and cannot

sustain a lateral load. Hence, when an impact is generated

between an object and a tendon, the tendon will lose its

stability and working capacity. This may affect the

behavior of the overall structure, partly or entirely

damaging the structure. Thus, researching the lateral

impact dynamic behavior of CFTA, an innovative girder,

Note.-Discussion open until May 1, 2009. This manuscript for thispaper was submitted for review and possible publication on October15, 2008; approved on December 1, 2008

*Corresponding authorTel: +82-2-3290-3323; Fax: +82-2-928-7656E-mail: [email protected]

316 Trinh Thai Trung et al.

is useful for the prediction of the experimental results as

well as suggesting some technical data or limitations in

calibrating this structure in the future. The resulting data

is used to support the next experimental program, which

will be carried out after these results are finalized.

2. Physical Background of the Research

2.1. The concept of collision theory

The collision concept is described by using the

conservation of momentum. If it is considered to be an

elastic collision the conservation of energy will also be

used and when it is an inelastic collision, the kinetic

energy will be lost and transferred to some other forms of

energy. Collisions will produce changes in momentum

equivalent to the impulse of force.

A perfectly elastic collision is defined as one in which

there is no loss of kinetic energy in the collision. This

type of collision usually occurs in perfect conditions. An

inelastic collision is one in which part of the kinetic

energy is changed to some other form of energy. Impact

load, momentum and energy can be summarized using

the equations formulated by Zukas (1990):

(1)

(2)

where ρ=material density; V=volume; F=force; m=mass;

v=velocity; E=internal energy; i=initial condition and f=

final condition. Hence, elementary impulsive plays an

important role in impact:

(3)

where τ=impulsive load; and F=impact load density.

In an elastic collision, both conservation of momentum

and conservation of kinetic energy are observed. This

implies that there is no dissipative force acting during the

collision and that all of the kinetic energy of the objects

before the collision is still in the form of kinetic energy

afterwards. Macroscopic collisions are generally inelastic

and do not conserve kinetic energy, though of course the

total energy is conserved. The extreme inelastic collision

is one in which the colliding objects stick together after

the collision, and this case may be analyzed in general

terms:

Before impact, the colliding object has a momentum of

m1v1 and 0.5m1v1 of kinetic energy. After object m1

impacts object m2 and two objects stick together, the

momentum becomes (m1+m2)v2 and the kinetic energy is

0.5(m1+m2)v2. From the conservation of momentum, we

have:

(4)

The ratio of kinetic energies before and after the

collision is:

(5)

and the fraction of kinetic energy lost in the collision is:

(6)

2.2. Analysis methods for Impact problem

To compute the nonlinear behavior of CFTA girder by

impact the ABAQUS finite element program was used in

this study. ABAQUS can carry out many different types

of simulations, including two of the most common: static

and dynamic stress analyses. In a static analysis, the long-

term response of the structure to the applied loads is

obtained. In other cases, the dynamic response of a

structure to the loads may be of interest: for example the

effect of a sudden load on a component, such as occurs

during an impact, or the response of a building in an

earthquake. The explicit dynamics procedure performs a

large number of small time increments efficiently. An

explicit central-difference time integration rule is used;

each increment is relatively inexpensive (compared to the

direct-integration dynamic analysis procedure available in

ABAQUS/Standard) because there is no solution for a set

of simultaneous equations. In this research, the Explicit

dynamic analysis was used for the impact problem

because it is computationally efficient for the analysis of

large models with relatively short dynamic response times

and for the analysis of extreme discontinuous events. By

default, an important difference between implicit and

explicit module of ABAQUS during computation is that

implicit (or standard) assumes small deformations, while

Explicit assumes large deformations.

The explicit central-difference operator satisfies the

dynamic equilibrium equations at the beginning of the

increment, t; the accelerations calculated at time t are

used to advance the velocity solution to time t+∆t/2 and

the displacement solution to time t+∆t. This explicit

analysis is based on the implementation of an explicit

integration rule together with the use of diagonal or

“lumped” element mass matrices. The equations of

motion for the body are integrated using the explicit

central difference integration rule:

(7)

(8)

ρ Vd∫ Const=

F mdv

dt----- Fi∑→

1

2--- ρvi

2

∑+ Ef∑1

2--- ρvf

2

∑+= =

τ F td

t0

t1

∫=

m1v1

m1m

2+( )v

2v2

⇒m

1

m1m

2+

-----------------v1

= =

KEf

KEi

--------

1

2--- m

1m

2+( )

m1

m1m

2+

-----------------v1

2

1

2---m

1v1

2

-----------------------------------------------------m

1

m1m

2+

-----------------= =

KEi KEf–

KEi

---------------------

1m

1

m1m

2+

-----------------– KEi

KEi

--------------------------------------m

2

m1m

2+

-----------------=

u'

i1

2---+⎝ ⎠

⎛ ⎞

u'

i1

2---–⎝ ⎠

⎛ ⎞

=∆t

i 1+( )∆t

i+

2-------------------------u''

i( )+

ui 1+( )

ui( )∆t

i 1+( )u'

i1

2---+⎝ ⎠

⎛ ⎞

+=

Dynamic Behavior and Reliability Assessment of a CFTA girder subjected to Truck Collision 317

where u'=the velocity; and u''=acceleration. The superscript

(i) refers to the increment number.

The explicit procedure integrates through time by using

many small time increments. The central difference

operator is conditionally stable, and the stability limit for

the operator is given in terms of the highest eigenvalue in

the system as no damping and with damping, respectively:

(9)

(10)

where ξ is the fraction of critical damping in the highest

mode (Hibbitt, Karlson & Sorensen, Inc ABAQUS).

2.3. Overview of reliability analysis

The main objective of design specifications and codes

is to protect public life and safety by preventing structural

collapse or failure during rare events in a building’s

lifetime. However, common design theory now does not

perfectly describe the performance of the structure due to

natural disasters or extreme events such as transport

accidents, tsunami, flood, etc. Performance-Based Design

(PBD) was therefore proposed which aims at satisfying

the specific performance criteria under hazard levels. This

research focuses on the behavior of CFTA during an

impact event which is considered to be rare and dangerous

for the safety of the structure. Consequently, applying

Performance Based Design and its tools will consolidate

the reliability for the structure. The basic concept of

performance-based design is to design a structure so that

it will perform in a specified manner when subjected to

various loading scenarios. Hence, the engineers can

design structures that are capable of providing reasonable

levels of protection against various hazard levels. The

performance-based design approach particularly allows for

the selection of specific performance objectives based on

various parameters, including the owner’s requirements,

the functional utility of the structure, and potential

economic losses. One of its applications is to derive the

probabilistic measure of assurance of the hazards, known

as reliability.

The problems of reliability can be seen essentially as a

problem of supply versus demand. In reality, the available

supply and actual demand cannot be determined precisely;

they may be described as belonging to the respective

ranges of possible supply (X) and demand (Y), which may

be modeled as random variables. The objective of reliability

analysis is to insure the event (X>Y) throughout the

useful life or some specified life of the system. This

assurance is possible only in terms of the probability

P(X>Y). Conversely, the probability of the complimentary

event (X<Y) is the measure of unreliability or failure.

Assume that the necessary probability distributions of

X and Y are available, that is, that FX(x) or fX(x) and FY(y)

or fY(y) are known. The required probability may then be

formulated as (Kyung Ho Lee & David V. Rosowsky.

2005):

(11)

where Y=a random demand on the system such as the

truck’s velocity or the flood level. For continuous X and

Y, (11) becomes

(12)

The probability of non-failure or safety is therefore:

pS=1−pF (13)

3. Numerical simulation of the collision

between an ideal truck and the tendons of

CFTA

3.1. Characteristic of CFTA girder

The research and development of a bridge involves the

process of an initial sketch of the ideal design to a

structural design, by concentrating attention on both high

performance and aesthetics, together with applying new

materials. Even though there has been a great deal of

research carried out on this structure, the application of

the new developed type by using new materials or composite

materials to an actual construction is still problematic.

For example, with the mid-long span bridge, although

there is no safety issues, several problems emerge as the

size increases, such as the inefficiency of the process or

disharmony with the surroundings. Therefore, it is

necessary to develop a structure that is capable of not

only maximizing most of the advantages of materials but

also exhibits aesthetic harmony with the environment.

Among these innovative structures, the CFTA girder is

one example which shows the effective combination of

using innovative materials and structures. These are the

concrete filled steel tubular (CFST) arch and the prestressed

tendon structure. Using CFST, we can utilize the high

tensile strength and ductility of the steel component with

the advantages of compressive strength and stiffness of

concrete. In terms of the working behavior, by transferring

the weight of the girder and its loads into a horizontal

direction, the applied loads are transformed into axial

compression and the over girder moment is reduced,

which is the advantage of the arch structure. One of the

characteristics of prestressing structures is that they

improve the performance of other members by including

the initial deformation and stress which tend to counteract

the service loads. It can be applied to larger spans and

lighter structures, and can improve recovery after overload,

improve strength in shear and tension and improve

fatigue resistance. By applying all these characteristics to

the CFTA, we can achieve an efficient use of the sections,

a complementary effect between the steel plate and

∆t2

wmax

-----------≤

∆t2

wmax

-----------≤ 1 ξ2

+ ξ–( )

pF P X Y<( ) P X Y< Y y=[ ]

all y

∑ P Y y=[ ]= =

pF FX y( )fY y( ) yd

0

∞

∫=


concrete, prevent buckling of the steel tube, increase the

internal force and ductility, maximize the economical

efficiency by reducing the process of fabrication work

and enhance the aesthetics of the bridge with a broad and

visually pleasing shape.

3.2. Numerical Model of CFTA and colliding truck

The numerical method has been an effective tool in

modeling and simulating the problem before executing

the experimental program. In this research, a CFTA girder

and the truck were modeled using the finite element

method to simulate the collision process.

3.2.1. Object model

Consider that, in the transportation system, there has

been a sudden accident between the vehicles. Because of

the collision, one of the vehicles (a truck for example)

transporting cargo impacts the CFTA girder at the tendon

position, which is considered to be the most vulnerable

component of the CFTA. The authors chose a middle

light truck, which is very popular in Korea, to be the

sample for the simulation. The vehicle weighs 8,536 kg,

including the truck self-weight and the cargo inside. Its

dimensions are as follows: Height 2.26 m×Width 2.4 m×

Length 5.9 m. Figures 1 & 2 shows the image of the truck

and the ideal FE model.

By consulting the Korean Expressway Corporation

(KEC. 2007) that gives the standard of the speed limit for

all the vehicles travelling in Korea, the authors chose the

average speed of 60 km/hour for the truck. The numerical

model of the truck is shown in Fig. 2. Because the impact

problem involves very large mesh distortions (large-strain

analysis), it is better to use fine mesh of linear, reduced

integration elements. Referring to the technical documents

of the mechanical manufacturer, the various thicknesses

for the truck frame are 6.35 mm (1/4''), 7.9375mm (5/16'')

and 9.525 mm (3/8''). Thus, an 8 mm thickness shell

element was modeled, with a 4-node doubly curved thin

shell, reduced integration, hourglass control and finite

membrane strains. An 8-node brick, with reduced

integration with hourglass control, was applied to model

the engine of the truck and the cargo inside.

3.2.2. CFTA girder model

The CFTA has an overall length of 25m. The numerical

model of the CFTA comprises four main components: the

concrete slab and its rebar; the concrete used for

confinement; the steel frame girder; and the tendons. The

slab is meshed by 18816 solid elements; type C3D8R,

reduced integration with hourglass control, has been

applied. 30 reinforcing bars were also embedded in the

slab and modeled as the truss elements, with a 2-node

linear 3D truss; type T3D2 was available in ABAQUS, to

mesh the reinforcing bar (Fig. 3). The concrete block was

created by pumping and confining it into the steel frame,

which is an arch form. A block of 25576×1476×1480

mm3 of 12096 solid elements was simulated.

Enclosing the concrete block, the steel part performed

the task of protecting the concrete block as well as

forming the CFTA girder shape (Fig. 4). The steel shape

was modeled with a shell element (type 04) and

homogeneous steel sections with 10, 12, and 22 mm shell

thicknesses. Inside the steel block was a hollow space

holding the concrete, creating a very efficient composite

section. In order to simulate the simultaneous working

between the steel part and the concrete part, constraint

contact was applied because the clearance (the distance

separating two surfaces), between concrete and steel must

be zero. The composite section uses tie constraints (type

Figure 1 & 2. Actual middle truck and its numerical model..

Figure 3. Numerical model of rebar and concrete slab.

Figure 4. Numerical Model of arch concrete and steelframe girder.


07) to tie together two surfaces for the duration of a

simulation, using the surface-to-surface constraint

enforcement method in which steel plates will be the

master surfaces while concrete will be the slave surfaces.

The fourth part of the model is the prestressed tendons,

with a length of 25,576 mm and a cross sectional area of

1,664.4 mm2 or a diameter of 46 mm (Fig. 5). The

prestressed strength will be retrieved from the static

analysis considering construction steps, which is discussed

in Sec 3.2.4, with 883.61 MPa for the two inside tendons

and 443.82 MPa for the two outside tendons. It is

possible to simulate the tendons of the truss or beam

element using the T3D2 element. The two ends of all 4

tendons were constrained in the composite CFTA

surfaces by the kinematic coupling type, with constrained

U1, U2 and U3 degrees of freedom. All four parts

described above integrate to form the CFTA girder with

its prominent advantages (Fig. 5). Table 1 shows a

summary of the numerical simulation of the CFTA girder.

3.2.3. Material properties

The linear mechanical properties of all materials used

in the simulation are shown in table 2. Taking account of

the strain rate-dependent plastic behavior of the structural

steel, the isotropic strain hardening is input, and the yield

stress σ0=392.4 Mpa, with σu=539.55 Mpa for the ultimate

stress (Table 3).

Table 3 shows the nonlinear mechanical properties of

the tendons. The tendons were made of high tensile steel

with a yield stress σy=1,700 Mpa and σu=2,150 Mpa for

Table 1. Summary of the properties of CFTA components

Component Element Type Number Dimensions (mm) Note

Concrete slab C3D8R 18816 25,576×3,500×240 Solid

Rebar T3D2 166 8 in radius Truss

Concrete block C3D8R 120096 25,576×1,476×1,480 Solid

Steel block S4R 8256 25,576×1,476×1,480 Shell

Tendon T3D2 17025,576 in length

46 in radiusTruss

Figure 5. CFTA numerical simulation.

Table 2. Linear Mechanical Properties of materials

Material/Component Density (kg/m3) Young’s Modulus (Mpa) Poisson’s Ratio

Concrete for slab 2500 21,500 0.167

Concrete block 2500 29,885 0.167

Steel 7850 210,000 0.3

Tendon 8000 210,000 0.3

Table 3. Nonlinear mechanical properties of steel and tendons

MaterialYield stress σy

(Mpa)Plastic strain εy

Steel392.4392.4

0539.55

00.01803920.167304

Tendon

17001920205021002150

00.002140670.009551480.019296600390418

Table 4. Concrete Damaged Plasticity Properties

Material/Compo-

nent

Compressive Behavior Tensile Behavior

Yield stress σy (Mpa)

Inelastic strain εy

Yield stress σy (Mpa)

Cracking strain εcr

Concrete on slab

15.340426.441629.562

0.00000.002240.000445

2.08230.04164

00.003

30.680729.8659

0.0007570.001087

27.249715.3404

0.0014970.002619

2.270350.40231

0.0052080.010292

Concrete on arch block

22.58538.060543.128145.170144.244340.987122.5852.134230.349808

00.0001610.0003430.0006390.0008930.0012360.002370.0051420.01021

2.534690.050694

00.003


the ultimate stress when the strain values ranged from

0.000214 to 0.03904.

For slabs and concrete blocks, normal concrete is used

for materials. The nonlinear material properties for

concrete are shown in Table 4, where the concrete density

γ=2.5×10−9 kg/mm3, Young’s modulus E=29885.3 Mpa

and ν=0.167. Table 4 also gives the damaged plasticity

parameters for concrete, including plasticity figures,

compressive behavior and tensile behavior properties.

3.2.4. Construction step analysis

The working pre-stressed values of the tendon will

differ from its initial values depending on the installation

steps. These figures will be used as the initial stresses of

the impact model. The first step of the procedure was to

pump concrete into the steel frame. The first two inside

tendons were then installed and a prestressing force of

973.564 Mpa was imported. This prestressed force shows

deformation and stress that tend to counteract the dead

load of concrete and steel. Consequently, the two tendons

and the prestressing forces were both 855.853 Mpa at that

stage. In step 3, the behavior of the girder was observed

when resisting a hypothesis force equal the concrete slab

weight, and the real slab was then imbedded onto the

upper side of the steel block. The final step involved

setting up the two outside tendons with a prestressing

force of 540.728 Mpa to create the complete model of the

CFTA. At this stage, the girder only resists its self-weight.

The calculated prestressing forces are 883.61 Mpa and

443.818 Mpa for the two inside and two outside tendons,

respectively. All these parameters and figures were input

into the impact dynamic analysis step as initial conditions.

When a collision occurs between an object and one

tendon, the tendon may be in local buckling. This leads to

the instability condition of the overall girder. This

modeling and its results will be discussed in the following

section. The full numerical simulation of the CFTA and

ideal truck are shown below (Fig. 6).

3.3. Impact dynamic algorithm

When two objects collide, contact stresses are transmitted

through their common interfaces. If the contact surfaces

are smooth, only normal stresses are transmitted. With

rough surface contact, a limited amount of shear stress

can also be transferred due to frictional forces. In the

problem of an impact phenomenon, the contact area must

be defined and the stress transmitted through the contact

should be calculated. Contact problems can be simulated

through contact elements. There are various types of

contact element definitions, for instance, GAP elements

for point to point contact, INTER element for small

sliding/ geometry linear contacts, IRS elements for large

sliding/rigid body-deformable body nonlinear contacts,

and ISL elements for large sliding/two deformable bodies

in nonlinear contacts. In the advanced numerical programs

used today, it is no longer necessary to define contact

elements. Instead, the master and slave surfaces or first

and second surfaces acquainted and the properties of

contact interaction are defined. We can create the contact

interaction properties of two objects with finite sliding,

small sliding, or with friction depending on which model

more closely approximates the real situation.

Contact pair interactions in ABAQUS/Explicit are used

in this research to describe the contact between two

deformable surfaces, or between a set of nodes and a

deformable surface (Hibbitt, Karlson & Sorensen, Inc

ABAQUS). In this study, the surface to surface contact

algorithm is used, in which the head of the truck was

assigned as the first surface and the nodes region on

tendon as the second or slave surface. The contact first

surface and second surface have allowed a finite sliding

type of interaction between the truck and the tendons.

The time incrementation scheme in ABAQUS/Explicit is

fully automatic and requires no user intervention.

ABAQUS/Explicit uses an adaptive algorithm to determine

Figure 6. Finite Element Model of CFTA and truck.

Figure 7. Interaction properties of the impact simulation.

Figure 8. Initial 60km/h velocity of colliding truck.


conservative bounds for the highest element frequency.

An estimate of the highest eigenvalue in the system can

be obtained by determining the maximum element

dilatational mode of the mesh. Dynamic impact response

is usually associated with severely discontinuous nonlinear

behavior and can be considered to be an intermediate

dynamic event.

3.4. Reliability analysis

Since the impact phenomenon is a hazardous event, it

is necessary to evaluate the reliability level of our system.

When the collision occurs, the most vulnerable component

of the structure is definitely all four tendons. They may

exceed their stress limit and therefore become ruptured

due to the event. The performance function is the

relationship between the stress capacities and the stress

demand which was derived from the finite element

analysis:

(MPa) (14)

Here, the g<0 occurs when the stress exceeds the

strength and the variable σfe will depend on the output of

the ABAQUS analysis,

(15)

where vtruck, atendon

and mtruck are the random variables of

the truck velocity, the actual area of the tendons, and the

mass of the truck, respectively.

Probabilistic finite element analysis provides a means

to quantify the reliability of complex systems. However,

since the structural analysis prophecies often rely on the

results of finite element (FEM) programs such as ABAQUS,

LSDYNA, MSC/NASTRAN, probabilistic analysis methods

must be interfaced to such programs to achieve more

consistent results. The NESSUS (SwRI v8.30) probabilistic

analysis software can be used to merge the probabilistic

algorithms with FEM packages to compute the probabilistic

response and the reliability of engineering structures.

NESSUS can be used to simulate uncertainties in loads,

geometry, material behavior, and other user-defined

uncertainties (D. S. Riha et al., 2000). The function “fe”

will be defined under response models.

4. Numerical Results Assessment

4.1. Impact Simulation results

The truck model is simulated to impact the outside

tendons of the CFTA girder in a head-on mode in the

transverse direction to the longitudinal axis of the girder.

Based on the previous research, a coefficient of friction of

0.45 is assigned for the dynamic friction with penalty

formulation and a slight damping is entered. In this

analysis, the impact event is simulated for a period of 2s

using an automatic time step and a 9.8µs average time

increment. A significant amount of output data is extracted

from the numerical results including stress and strain

values, critical components deformation, energy diagrams,

etc. Fig 9 shows various views of the model and impact

event at various times.

The truck is placed at a distance of 2.5 m toward the

CFTA girder. With the velocity of 60 km/h, the impact

will begin at the time of 0.21 s and last for about 0.5 s

when the truck rebounded at 0.7 s. The energy quantities

derived from the numerical analysis ensured the precision

of the conservation of energy. The initial kinetic energy of

the vehicle must be completely transformed into residual

kinetic energy, energy lost to friction and internal energy

stored in the deforming vehicle components and girder

members (Fig 10).

We observe that the tendons were violently influenced

by the head of the truck. The authors examined the

behavior of the tendons to determine whether they were

ruptured or had only deformed under the effect of impact.

One of these responses involves investigating the strain of

the tendons and comparing them to the ultimate strain (at

rupture level) in the numerical analysis records. Fig. 11

gives the nonlinear numerical response of the stress

versus strain; it shows that the stress and strain of the

tendon increased rapidly during the impact event. Tendon

04 is the outmost tendon, colliding with the truck first.

g 2150 σfe–=

σfe fe vtruck atendon mtruck, ,( )=

Figure 9. Progress of collision between object and CFTA.


Checking the strain rates at several positions in the

tendons has revealed that quite high levels of strain rate

could occur in the tendons in the surrounding area of the

tendons. Figure 13 presents the numerical time histories

of strain at the most critical points on the tendons.

It can be seen that the strains in tendon 04, which is the

first tendon to collide, and tendon 02, which has the

higher prestressed input, are the highest. Although all

four tendons are deformed during the impact period, the

results show that they are within the plastic range and are

not ruptured by the crash. Table 5 and table 6 show the

comparison data between numerical analysis and the

ultimate strength records.

Observing other critical parts of the CFTA girder,

including the displacement of the concrete slab, the stress

of the steel frame and the strain of the concrete arch

block, the results reveal the high safety values of these

components during the impact.

4.2. Reliability assessment

For any probabilistic analysis, several ingredients are

required including performance function (g-function),

random variables definitions and solution options. A random

variable is typically defined by a probability density

function characterized by a mean value, a standard

deviation and a distribution type. Normal and lognormal

distributions are commonly used in the structural field. In

this study, since the impact event directly influenced the

tendons, the actual area of tendons will be set as random

variables. Moreover, the velocity of the truck and its self

weight will also contribute as two main factors in the

probability of the impact result.

Variations in the area of tendons have previously been

studied by a number of researchers (Barakat et al.,

Figure 10. Various Curves of energy versus time quantities.

Figure 11. Stress strain relationship of tendon 04.

Figure 12. Stress strain relationship of tendon 01.

Figure 13. Strain-Time relationship of 04 tendons

Table 5. Tendons strain rate comparison

Tendon No Numerical strain ε Ultimate strain εu Time (s)

01 0.002066 0.0390418 0.37501

02 0.003211 0.0390418 0.400002

03 0.001065 0.0390418 0.400002

04 0.003002 0.0390418 0.37501

Table 6. Tendons stress rate comparison

Tendon No Numerical stress σUltimate stress σu

Time (s)

01 974.543 2150 0.37501

02 1660.18 2150 0.400002

03 1209.5 2150 0.400002

04 1171.08 2150 0.375001


Ellingwood, 1977). Taking these studies into account, the

area of tendons is assumed to be a normal distribution

with a mean value µ=1664.4 mm2 and a coefficient of

variation of δ=4%. With velocity, the mean and COV are

µ=16.67 m/s and δ=0.2, respectively (Fig. 14) and for

the self weight of the truck, its mean value µ=8.536 Ton

and COV δ=0.25 were appointed. NESSUS is used (Sec

3.4) since it can combine the probabilistic algorithms and

numerical packages. Although Monte Carlo is the traditional

method, this approach generally requires a large number

of simulations to compute the probability and is impractical

when each simulation involves extensive finite element

computations i.e. the CFTA impact model.

As a result, approximate fast probability integration

(FPI) is demonstrated to be more effective than Monte

Carlo simulation and may afford sufficient accuracy for

the structural problem. The advanced mean value (AMV)

procedure, based on FPI, is applied in this study, which is

suitable for a complex CFTA model with relatively few

response calculations. The analysis type here involves the

specification of performance levels of the g-function in

order to compute the reliability of the system. The authors

executed two of the most probable cases; 60 km/h and 90

km/h for the truck velocity. The results derived from the

probability analysis program are as follows (Fig. 15):

Table 7 shows the reliability index as well as the

probability of failure of the CFTA girder due to the

uncertainty of the truck’s velocity. The reliability index

decreases when the velocity increases and this correctly

reflected the simulation. The output shows that the

structure may be in danger after approximately 15000

cases for the colliding truck with 90 km/h velocity.

These normalized sensitivities shown in Fig. 16 will

allow the designer to evaluate the effect of the probability

of failure with any changes in the design parameters.

Concerning the probabilistic sensitivity factors, less

importance is observed on the area tendons and the

standard self weight of the truck, compared to the

velocity variable. This may suggest that the tendon

manufacturing process needs to be changed in order to

reduce the cost and to be considered for safety velocity

specification in the transportation system.

5. Conclusions

The performance of a Concrete-Filled and Tied steel

Tubular Arch or CFTA girder subjected to lateral impact

has been numerically studied by the authors. The

Figure 14. Tendon area and velocity density functions.

Figure 15. Integrate Abaqus and Nessus to run the probability.

Table 7. Reliability output from the analysis

Truck velocity(km/h)

Index β Pf

6090

5.00003.8187

0.2871047945E-060.6708851639E-04

Figure 16-1. Probabilistic sensitivity factors of randomvariables for case truck 60 km/h.

Figure 16-2. Probabilistic sensitivity factors of randomvariables for case truck 90 km/h


numerical simulation results will be used in the near

future as the database for the experimental analysis. The

common middle truck has been considered as the

colliding object, which crashed into the CFTA girder at

the weakest point, where the prestressed tendons are in

the normal direction. The finite element analysis was

carefully studied and modified, and many previous studies

were analyzed.

It was discovered that tendon behavior could be

convincingly well predicted by the numerical analysis.

The results show that the tendons were immediately

deformed but were not ruptured or damaged by the

accident.

Due to the uncertainties in the parameters as well as the

current necessity of applying the performance-based

design theory, probabilistic analysis was also evaluated in

order to ensure the safety measure of the structure. This

analysis uses the maximum tendon stress as the

performance function with the area of the tendon, the self

weight and the velocity of the truck as the random

variables.

The simulation presented in this paper reveals that

finite element analysis could be a reliable tool to

scrutinize the vulnerability of the impact event. However,

this numerical simulation incorporated a number of

limited material properties, colliding object, velocities

and impact directions as well as positions. The authors

are currently continuing this project by adding more

parameters i.e. other vehicles and damage scenarios, a

more developed vehicles model as well as different

colliding objects. Probabilistic analysis will be studied

more profoundly with the upgrading of the g-function and

random variables, in order to perform the fragility

assessment.

Acknowledgment

This paper is a part of the result from the

“Standardization of Construction Specifications and Design

Criteria on Performance (’06~’11)”, the “Construction &

Transportation R&D Policy and Infrastructure Project”

and was partially supported also by the Korea Institute of

Construction Technology (KICT) through the project

“Assessment of safety and economical efficiency of

CFTA girder (06D14). The supports received are

gratefully acknowledged.

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