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International Journal of Civil Engineering and Technology (IJCIET)

Volume 9, Issue 10, October 2018, pp. 139–152, Article ID: IJCIET_09_10_015

Available online at http://www.iaeme.com/ijciet/issues.asp?JType=IJCIET&VType=9&IType=10

ISSN Print: 0976-6308 and ISSN Online: 0976-6316

©IAEME Publication Scopus Indexed

FINITE ELEMENT STUDY ON HOLLOW

CORRUGATED STEEL BEAMS UNDER IMPACT

LOADING

Mohammad R.K.M. Al-Badkubi

Building and Construction Technical Engineering Department,

College of Technical Engineering, the Islamic University, Najaf, Iraq

ABSTRACT

This paper presents a nonlinear finite element analysis on the behavior of

corrugated steel beams subjected to impact load using ABAQUS (6.14-4) computer

program. Six corrugated steel beams with length 1.8 m and three unit profile of

corrugated steel for each side of the square cross section rested on fixed steel blocks

at the ends were modeled. The parametric study was made on the corrugated steel

plate thickness and the magnitude of the total impact force. The adopted model was

validated by using data from experimental test. In these models a nonlinear materials

behavior for steel plate was simulated using appropriate constitutive model. The

results showed that the general behavior of the finite element models represented by

the mid span deflection - time history curves, maximum mid span deflection, vibration

time of the beams, and residual impact deformation show good agreement with the

experimentally tested specimen. After analyzing the models it was found that by

increasing the thickness of the corrugated steel plate the mid span deflection along

with vibration time will decreases up to (29.3 %) and (45.9 %), respectively. Also,

reduction in total impact force causes the decrease in mid span deflection and

vibration time up to (32.6 %) and (46.12 %), respectively.

Key words: Finite Element Modeling, Corrugated Steel Beams, Impact Load, and

Residual Impact Deformation.

Cite this Article: Mohammad R.K.M. Al-Badkubi, Finite Element Study on Hollow

Corrugated Steel Beams under Impact Loading, International Journal of Civil

Engineering and Technology (IJCIET) 9(10), 2018, pp. 139–152.

http://www.iaeme.com/IJCIET/issues.asp?JType=IJCIET&VType=9&IType=10

1. INTRODUCTION

Nowadays almost all industries are redirecting their strategic plans on developing

environmentally friendly products that building and construction industry is not an exempt.

Although numerous research is being conducted to commercialize incorporation of novel

materials in infrastructures applications, structural elements made from steel alloys are yet the

most common ones. This popularity can be due to the high strength to weight ratio attributes

and remarkable fabrication versatility of steel material [1].



Corrugated sheets and plates have been used in lots of engineering fields. They have a

several advantages like lightweight, economical, self-strengthen, and easy shipping and

storage process. Hitherto have attracted researcher's interests to broaden their applications,

since they were introduced for the first time.

The corrugated shape provides continuous stiffening for the sheets similar to stiffened

panels, but allows using thinner plates. They can be bent in one direction easily while it

retains its rigidity in the other direction. Furthermore, the fabrication cost of elements with

corrugated panels are normally lower than those with stiffened plates [2-4].

The use of fabricated hollow sections built up from corrugated plates was introduced by

Nassirnia et al. [5] for the first time. The idea was further developed by implementing in

concrete-filled double skin columns [6] and combining with ultra-high strength steel tubes

[7]. Also, the performance of new sections under uniaxial loading was investigated.

During the lifetime of a structure, in addition to bearing quasi-static loads induced by live

and dead loads, it may inevitably suffer from various natural hazards such as impact loads,

earthquakes, and fire [8].

Thus, in this study, A theoretical analysis was performed to predict the behavior

(deflection and impact deformation) of corrugated beams subjected to impact load by using a

nonlinear finite element program (Abaqus 6.14-4). The validity of analytical test results are

compared with experimental test results [1].

2. SPECIMENS DESCRIPTION

This paper represents an analytical study on the behavior of the corrugated steel beams under

impact load. The total number of six corrugated steel beams were tested. The parameters

which are studied are the thickness of the corrugated steel beam and the magnitude of the total

impact force applied on the beams. The detail of the test specimens is shown in Table (1):

Table 1 Specimens Identification.

It is worth noting that the analytical tests are verifying due to comparison of experimental

results and analytical results for beam (CB31), after which the remaining specimens were

tested using the same calibrated model.

3. FINITE ELEMENT MODELING OF THE SPECIMENS

3.1. Modeling of Corrugated Steel Beam

The first step involved in the finite element analysis method consists of building the model. In

this step, the structure is created and then divided intofinite elements connected together at

their nodes. In building a finite element model, it is necessary to define the geometry of the

model, element type and material properties.

Beam

No.

Beam

Symbol

Thickness t

(mm)

Impact force

Factor

1 CB31 3 1

2 CB41 4 1

3 CB61 6 1

4 CB30.5 3 0.5

5 CB40.5 4 0.5

6 CB60.5 6 0.5

Finite Element Study on Hollow Corrugated Steel Beams under Impact Loading


3.1.1. Selecting Geometry

Generally, a corrugated plates are formed by repeating identical unit profile. The number of

units depends on the application and the target size. In this study, three units (n = 3) are

considered [1]. Also, there are several type of unit corrugation profiles for various

applications. In this study, trapezoidal corrugated unit as shown in Figure (1) is chosen to be

studied [1].

Figure 1 A Trapezoidal Corrugated Unit Profile.

Since unit geometrical dimensions could affect the overall performance of corrugated

beams, the unit profile dimensions are shown in Table (2).

Table 2 Corrugated Unit Profile Dimensions [3].

All of the beam specimens in this study are 1.8 m long and Figure (2) illustrates the

generated finite element model for the corrugated steel beam.

Figure 2 Modeling of Corrugated Steel Beam.

3.1.2. Selecting Element Type

A 4-node shell element S4R (4-node doubly curved general-purpose shell, reduced

integration) is adapted in this study to represent the corrugated steel beam. The shell element

which has displacement and rotation degrees of freedom (6 D.O.F) at each node is shown in

Figure (3). Also, Figure (4) shows the meshed shape of the corrugated steel member.

α (o) a (mm) b (mm) h (mm) d (mm) L (mm) Drawing

45 20 10 15 15 70



Figure 3 Two Dimensional 4-Node Conventional Shell Element [9].

Figure 4 Meshed Shape of Corrugated Steel Beam Model.

3.1.3. Constitutive Model of Steel

The adapted stress-strain relation for structural steel in this study is shown in Figure (5),

where fp , fy and fu are proportional limit, yield stress and ultimate stress of steel respectively.

The plastic deformation of steel in this work is described using the Von Mises yielding

criterion.

Figure 5 Stress-Strain Curve for Steel [10].

During the elastic-plastic stage (a-b), by increase in applied stress, the tangent modulus of

elasticity for steel (Est) decreases from Young’s modulus (Es) to zero (during the yielding



stage b-c).Hence, the calculation of (Est) is done by using the formula which proposed by

Bleich in (1952):

(1)

where (σs) is the stress in the steel. Furthermore, the change in steel response to the

applied stresses the Poisson's ratio (µs) also changes by increase of stress at the elastic-

plasticstage. Hence, the Poisson's ratio in this stage is calculated using the following formula

which was proposed by Han in (2004):

(2)

It should be noted that the steel was assumed to have identical properties in tension and

compression. The steel parameters which used in this study are shown in Table (3):

Table 3:Steel Material Properties.

4. BOUNDARY CONDITIONS

In order to obtain a unique solution in analyzing the deformation displacement for the

corrugated steel beams the boundary conditions at beam edges are needed. To make sure that

the FEM model acts similar to the experimental specimen's condition, the boundary

conditions were applied at two edges of the beam[11].

In the experimental system all of the specimens were placed on a supporting steel section

frame as shown in Figure (6). Then the specimens were fastened with bolts inside the frame to

obtain fixed support as much as possible. Also, this configuration of the boundary conditions

restrained any outward deformation. However, any inward deformation could happen since

the specimens have hollow section.

Figure 6 Experimentally applied Boundary Condition [1].

In the analytical system, the experimental boundary conditions was simulated by resting

and bounding the specimens inside a blocked steel section frame. In finite element model a

20-node standard 3D stress reduced integration quadratic hexahedral (brick) element

(C3D20R) was used to represent the steel frame elements. The geometry and node locations

fy (MPa) Es (MPa)

252 200,000



for the element type are shown in Figure (7). The original shape of blocked steel section

frame and the meshed shape of the frame is shown in Figure (8).

Figure 7 20-Node Quadratic Brick Element (C3D20R) [9].

Figure 8 Original and Meshed Shape of Blocked Steel Frame.

The blocked steel frame considered to has fixed supports at its outer surfaces, as shown in

Figure (9). Also, the contact between the specimens and the steel frame was simulated by

using surface to surface contact interaction which defined the inner faces of the frame as

master surface and the outer most surface of the corrugated beam as slave surface with finite

sliding formulation and the contact property was considered to have rough friction

formulation in tangential behavior which do not allow any slip to occur once points are in

contact along with hard contact property that will allow separation of the beams from the

frame when the deformation occurs.

Figure 9 Modeling of the Boundary Condition of the Specimens.



5. LOADING SYSTEM

In the finite element modeling, the impact force was modeled by using a steel plate to

simulate the dropped steel hammer. A 20-node quadratic, reduced integration, hexahedral

(brick) element with linear elastic properties for steel material was used to represent the steel

plate. The used element is shown in Figure (7), and the steel plate model is shown in Figure

(10).

Figure 10 Steel Plate Modeling.

To simulate the impact force resulting from modeled steel plate there are two different

approaches which are as following:

1) Subjecting the steel plate to gravitational acceleration during the solution in order to leave

the weight to fall freely. This method recommended to save analysis time by starting at small

distance from the top of steel beam and apply initial velocity according to the shifted distance

[9].

2) Simulating the impact force by a pulse such a rectangular or triangular load function, the

magnitude of maximum impact force and its duration time has to be taken from the

experimental results [9].

In the present study the second method is adopted to simulate the impact force. The

magnitude of impact force and its duration has taken from experimentally tested specimen [1]

and illustrated as a rectangular pulse shown in Figure (11):

Figure 11 Impact Force and Its Magnitude Simulation.

So, for both hammer weight the impact force duration has taken to be (0.03 s) and its

magnitude taken as (1486 KN) and (1243 KN) for normal weight and half weight hammer,

respectively.

The kinetic impact energy was calculated by using the following equation:



(3)

Where (m) is the steel plate (steel hammer) mass (Kg) and (v) is the velocity of drop steel

hammer which is calculated based on the governing velocity formula of a falling object which

is defined as:

(4)

Where (g) is the gravitational acceleration which is about (9.81 m/sce2) and (t) is the

travelling time for dropped steel hammer from the starting height of the fall to impact with the

steel beam.

Also, this time of travel can be calculated if the height of the drop (h) is known using the

following formula:

(

)

(5)

Table (4) shows the kinetic energy calculation results for specimens (1-6):

Table 4 Impact Test Level Definition

6. TIME-DEFORMATIONCURVES

Deformations are measured at mid-span from the upper face of the beam to the lowest

location of the deformed beam.

By comparing the analytical result curve and experimental result curve as shown in Figure

(12), it can be seen that the adapted finite element model is in good agreement with the

experimental results. This good agreement shows that the model can be utilized for some

other cases other than this experimental case. So, the analytical cases mentioned previously

were considered to be investigated.

Figure 12 Comparison of Mid Span Deformation History for FEM CB31 Model and Experimental

Test.

Test No. h (m) m (kg) t (s) v

(m/s)

KE

(kJ)

1-3 7 266.5 1.194 11.7 18.24

6-4 7 133.25 1.194 11.7 9.12



From the Figure (12) it can be seen that the finite element deflection curve have about

four pulses of vibration which is more than that obtained from the experimental curve which

leave the beam at rest after about two pulses of vibration. This response of the beam in FEM

shows that in the FEM the computer program can observe the deformation of the model more

adequately from the experimental specimens in this very small time interval. Also, it is may

be due to the other factors which affect the experimental work more than that in the FEM,

such as human error, equipment efficiency, corrugated steel beam making process, etc.

Figure (13) shows the comparison between mid-span deformation history curves for FEM

models with different corrugated steel thicknesses.

Figure 13 Comparison between Mid-Span Deformation History Curves for FEM CB31, CB41 and

CB61 Models.

As it can be seen from Figure (13) by increasing the corrugated steel beam thickness the

mid-span deflection decreases as well as the time period between each pulse ofvibration

decreases that will lead to make the beam at rest much sooner than the beam with smaller

thickness. Furthermore, it shows that the thinner plates response to vibration more than those

of thicker plates which tend to be more resistance to vibration effects.

As it was mentioned previously another factor which investigated in this study is the mass

of the impact force. By reducing the falling steel hammer weight to half the respond of the

corrugated steel beam to this new impact force is shown in following figures.

Figure (14): Comparison between Mid-Span Deformation History Curves for FEM CB31

and CB30.5 Models.



Figure 15 Comparison between Mid-Span Deformation History Curves for FEM CB41 and CB40.5

Models.

Figure 16 Comparison between Mid-Span Deformation History Curves for FEM CB61 and CB60.5

Models.

From Figures (14, 15 and 16) it can be seen that by decreasing the steel hammer weight to

its half original weight, the corrugated steel beams show smaller deflection as mid span as

well as smaller time of vibration which leads the beam to be at rest in shorter time compare to

beams respond to original hammer weight.

As it can be seen from Figure (17) the behavior of steel beams subjected to half weight of

original hammer weight is similar to behavior of the beams subjected to original hammer

weight which is by increasing the corrugated steel beam thickness the mid-span deflection

decreases as well as the time period between each pulse of vibration decreases that will lead

to make the beam at rest in shorter timecompared tothinner steel beams.



Figure 17 Comparison between Mid-Span Deformation History Curves for FEM CB30.5, CB40.5 and

CB60.5 Models.

The Finite Element Method (FEM) analysis results for maximum mid-span deflection and

the impact vibration time are shown in Table (5):

Table 5 FEM Test Results.

7. FAILURE DEFORMATION

Figures (18-24)illustrate the corrugated steel beam deformation shape due to the application

of the impact load for tested beams in finite element analysis model as well as experimentally

tested beam.

Figure 18 Residual Failure Deformation for Experimentally Tested CB31 [1].

Beam

No.

Beam

Symbol Δmax (mm)

Vibration Time

(s)

1 CB31 195 0.093

2 CB41 168.87 0.074

3 CB61 137.86 0.0594

4 CB30.5 131.43 0.0592

5 CB40.5 119 0.041

6 CB60.5 105.5 0.032



Figure 19 Residual Failure Deformation for FEM Tested CB31.



Figure 22 Residual Failure Deformation for FEM Tested CB30.5.





By comparing the experimental failure shape with finite element failure shape Figures

(18) and (19), it can be seen that the local deformation of the beam due to the applied load as

well as global bent in the beam are very similar. Also, by comparing failure shape of Figures

(19) to (24), it can be seen that when the corrugated steel beam thickness increases the overall

behavior of the beam enhanced due to the increase in steel section strength. This enhancement

make it possible for the beam to utilizes the strength of the whole beam in resisting the

applied impact load and make the load distributed in the whole section rather than just little

area around and under the impact load steel hammer.

8. CONCLUSIONS

In this paper, an analytical study on hollow corrugated steel beams under impact loading is

performed by using a nonlinear finite element computer program (Abaqus).

Based on the results obtained by testing simulated steel beam models, the following

conclusions can be obtained:

1. The general behavior of the finite element models represented by the mid span deflection -

time history curves show good agreement with the experimentally tested result curve.

However, the finite element models tend to be slightly stiffer than the experimental beam in

the linear stage of respond.

2.for normal weight steel hammer by increasing the corrugated steel beam thicknesses from (3

mm) to (4 mm) and (6 mm), the maximum mid-span deflection decreases about (13.4 %) and

(29.3 %), respectively.Also, the vibration time decreases about (20.4 %) and (36.12 %) for

(4mm) and (6mm) respectively compared to (3 mm) beam thickness.

3. for half weight steel hammer by increasing the corrugated steel beam thicknesses from (3

mm) to (4 mm) and (6 mm), the maximum mid-span deflection decreases about (9.4 %) and



(19.72 %), respectively. Also, the vibration time decreases about (30.7 %) and (45.9 %) for

(4mm) and (6mm) respectively compared to (3 mm) beam thickness.

4. By using half weight steel hammer there is reduction in maximum mid span deflection and

vibration time about (32.6 %) and (36.34 %) for beam thickness (3 mm) and about (29.5 %)

and (44.6 %) for beam thickness (4 mm) and about (23.4 %) and (46.12 %) for beam

thickness (6 mm), respectively.

CONFLICT OF INTEREST SATEMENT

On behalf of all authors, the corresponding author states that there is no conflict of interest.

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FINITE ELEMENT STUDY ON HOLLOW CORRUGATED STEEL … · the mid span deflection - time history curves, maximum mid span deflection, vibration ... This popularity can be due to the