FINITE ELEMENT STUDY ON FLEXURAL BEHAVIOR OF …bi-axial system and originally used for slab system. This type of void former has the same concept of bubble-deck systemwhich is to

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International Journal of Civil Engineering and Technology (IJCIET)

Volume 9, Issue 10, October 2018, pp. 123–138, Article ID: IJCIET_09_10_014

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 FLEXURAL

BEHAVIOR OF VOIDED CONCRETE BEAMS

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 flexural behavior of

voided concrete beams using ABAQUS (6.14-4) computer program. Six different beam

specimens were modeled to study the effect of certain parameters on the flexural

behavior of the beams. The parameters included the effect of void formers and their

locations. Also, for further study of the effect of the void formers the modified

specimens made by increase and decrease the effective depth of the beams were used.

In these models a nonlinear materials behavior for concrete beam and steel

reinforcement was simulated using appropriate constitutive model. The analytical

results showed that the ultimate load carrying capacity of the solid beam is greater

than the voided beam ranged from (5.12 %) at the failure point of solid beam to (0.4

%) at the failure of the voided beam. While using the same amount of concrete as in

solid beam for voided beam specimen and make modified voided beam with larger

effective depth than voided beam, increases its ultimate load capacity from (20.52 %)

at the failure point of modified voided beam to (16.64 %) at the failure point of solid

beam. Also, for solid beam with same amount of concrete as in voided beam (MSB)

the ultimate load capacity decreases from (27 %) at the failure point of voided beam

to (17.14 %) at failure point of modified solid beam.Furthermore, omitting void

formers from the two ends of the voided beam (VB1) causes slight increase in ultimate

load by (1.86 %) and omitting void formers from the mid span section of the voided

beam (VB2) causes decrease in ultimate load by (0.35 %)due to decrease in its

ductility, comparing to voided beam with void formers distributed at all areas.

Key words: Finite Element Modeling, Flexural Behavior, Voided Concrete Beams,

Cobiax Void Formers.

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

Behavior of Voided Concrete Beams, International Journal of Civil Engineering and

Technology (IJCIET) 9(10), 2018, pp. 123–138.

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



1. INTRODUCTION

In order to achieve some structural and or some architectural requirement like large spans for

beams without making additional columns the beam's effective depth should be increased to

resist extra applied loads and avoid large deflections. So, the beam will be heavier and needed

larger column and foundation. Thus, the consumption of the building materials like concrete

and steel reinforcement will increase and will cause more cost (J.H.Chung et. al. 2009) [1].

So, to avoid the extra weight of the additional depth of the beam the voided beam method can

be used.

The Cobiax system which is used in this study as a void formers is a Swiss made special

bi-axial system and originally used for slab system. This type of void former has the same

concept of bubble-deck systemwhich is to omit the non- working concrete from the member

(extra un-required load). The difference between the Cobiax and babbles is the shape of the

void former which for the Cobiax system is quasi-spherical shape also the mobility of the

Cobiax void formers is easier than bubbles where the Cobiax can be transported in halves and

combined together at the site.

There are numerous benefits of using void formers in the concrete as general, which are:

1) Flexibility in design which can easily adapts to irregular and curved plan layouts,longer

spans and fewer supports (Nasvik J. 2011) [2].

2) Reducing overall costs: The material consumption will reduced and constructionwill be

faster (Nasvik J. 2011) [2].

3) Reduced dead weight by about 35% which allows smaller foundation sizes (Mohammad R.

2017) [3].

4) Longer spans between columns: Up to 50% further than traditional structures.

5) Reduced foundation sizes: There is up to 50% less structural dead-weight.

6) Reduced concrete usage: 1 kg of recycled plastic replaces 100 kg of concrete.

7) Environmentally Green and Sustainable: Reduced energy & carbon emissions. 8%of global

CO2 emissions are due to cement production (A. Churakov 2014) [4].

8) Use of recycled materials.

2. SPECIMENS DESCRIPTION

This paper represents an analytical study on flexural behavior of voided concrete beams made

by using Cobiax which are quasi-spherical plastic void formers. The total number of six

concrete beams were tested.The used beam specimens have different properties which are:

Voided and normal beams.

Voided beams with void formers at different locations.

Modified voided and normal beams

The detail of the test specimens is shown in Figure (1) and listed in Table (1):

a) Voided Beam with Void Formers at All Area (VBA).

Finite Element Study on Flexural Behavior of Voided Concrete Beams


b) Solid Beam with Null Void Formers (SB).

c) Voided Beam with Void Formers at Two Ends of the Beam (VB2).

d) Voided Beam with Void Formers at Beam's Mid Span (VB1).

e) Modified Voided Beam with Void Formers at All Area (MVB).

f) Modified Solid Beam with Null Void Formers (MSB).



Figure 1 Schematic Representation of Test Specimens.

As it can be seen from the Figure (1), all of the beam specimens have the same length of

4500 mm.The selection of cross section dimensions have some requirement to be considered:

All of the beam specimens have the same width of 250 mm which is a normal width for beams

in building with loaded break walls.

The height of the beam (Section A-A) is considered to be as minimum as440 mm, due to

minimum cover of 50 mm and the size of Cobiax void formers.

The height of the beam (Section B-B) remain as in (Section A-A) due to comparison between

voided beams and solid beams.

The height of the beam (Section C-C) is increased by 84 mm. This increase in height was

measured by calculating the volume of the Cobiax void former by using volume revolution

integration method, then multiply it by its number to find the total volume of the voids in the

beam. After that find the equivalent height by dividing the total volume of the voids by beams

length and beams width.

The height of the beam (Section D-D) is decreased by 84 mm by the same method used in

(Section C-C).

Table 1 Specimens Identification.

Beam

No.

Beam

Symbol

Length

(mm)

Width

(mm)

Height

(mm)

Void Formers

Position

1 VBA 4500 250 440 all

2 SB 4500 250 440 null

3 VB2 4500 250 440 two ends

4 VB1 4500 250 440 mid span

5 MVB 4500 250 524 all

6 MSB 4500 250 356 null



It is worth noting that the spacing between the Cobiax void formers was selected so that

the void formers start and end at the effective depth of the beams.

3. FINITE ELEMENT MODELING OF THE SPECIMENS

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[9].

3.1. Modeling of Voided Concrete Beam

3.1.1. Voided Concrete Beam Sketch

The beam parts have been sketched and their characteristics have been selected to obtain the

most reliable simulation of the voided concrete beam. First, the concrete beam structure was

created by selecting the solid extrusion shape, deformable type and 3D space modeling, as

shown in Figure (2). The dimensions of the beam's cross section and its lengthselected as

described earlier. Also, to simulate the Cobiax void former, 3D modeling space, deformable

type and solid shape revolution was selected to create a solid sphere, as shown in Figure (3).

Figure 2 Modeling of Solid Concrete Beam.

Figure 3 Modeling of Cobiax Void Formers.

Finally to achieve the voided beam, the solid void former is subtracted from the solid

beam part as shown in Figure (4).



Figure 4 Modeling of Voided Concrete Beam.

To create steel reinforcing bars, 3D modeling space, deformable type and wire shape

planar was selected, and arranged as it was illustrated in Figure (1). Figure (5) shows the

modeling of steel reinforcement.

Figure 5 Reinforced Steel Bars Sketch and Arrangement.

3.1.2. Selecting Element Type

In this study a 10-node standard 3D stress modified quadratic tetrahedron elements

(C3D10M) with 6 degree of freedom at each node is adopted to represent the voided concrete

beam. Also, the steel reinforcing bars are represented by using 2-node standard 3D stress

linear geometric order (T3D2) and embedded representation (Truss element in

ABAQUS).The element is defined by two nodes, the cross-sectional area and the material

properties. Figures (6,7) show the adapted elements for voided concrete beam and

steel reinforcing bars, respectively.



Figure 6 10-Node Quadratic Tetrahedron Element (C3D10M) [5].

Figure 7 Truss Element Geometry [5].

The mesh density for the voided beam is selected so that each element has 5 cm length.

Then the beam will have 5 element in width and 280 element in length. Figure (8) shows the

meshed shape of the voided beam.

a) Shaded Render View.



b) Wireframe Render View.

Figure 8 Meshed Shape of Voided Beam Model.

3.1.3. Material Properties and Constitutive Models

3.1.3.1. Constitutive Model of Ordinary Concrete

In the present study, the concrete is assumed to be homogeneous and initially isotropic, the

adopted stress-strain relation is shown in Figure (9). The compressive uniaxial stress-strain

relationship for concrete model was obtained by using the following equations to compute the

multilinear isotropic stress-strain curve for the concrete.

(1)

(

) (2)

(3)

(4)

(5)

where:

= stress at any strain ε

ε = strain at stress

εo= strain at ultimate compressive stress

Ec = concrete elastic modulus

The simplified stress-strain curve for concrete model is constructed from six points

connected by straight lines. The curve starts at zero stress and strain. Point number 1,at 0.3 ,

is calculated for the stress-strain relationship of the concrete in the linear range Equations (1).

Point numbers 2, 3, and 4 are obtained from Equation (2), in which εo is calculated from

Equation (5). Point number 5 is at εo and .



Figure 9 Idealized Uniaxial Stress-Strain Curve For Concrete [6].

Also, in the present study the behavior of the concrete was assumed to be perfectly plastic

after point number 5.

The ACI committee 318M-95(55) [7] states that the modulus of elasticity Ec for normal

strength concrete (NSC) can be determined from the compressive strength of concrete using

the formula:

√ ( ) (6)

The concrete parameters which are used in this study are shown in Table (2):

Table 2 Concrete Material Properties.

3.1.3.2. Constitutive Model of Steel

The adapted stress-strain relation for steel reinforcing barsin this study is shown in Figure

(10), 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 Misses yielding

criterion.

Figure 10 Stress-Strain Curve for Steel [8].

fc' (MPa) Ec (MPa) υ

33 25743 0.2



During the elastic-plastic stage (a-b), by increase inapplied 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):

( )

( ) (7)

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):

( )

( ) (8)

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

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

Table 3 Steel Material Properties.

3.2. Modeling of Other Types of Beam

To model other beam cases like solid beam and beams with void formers at certain locations

as well as modified voided beam and modified solid beam, the similar voided concrete model

that was used in the voided concrete beam with void formers at all area was used. But, there

was no void formers in concrete for solid beam and for other cases the void formers were

eliminated at certain points. Also, the total depth along with effective depth was increased for

modified voided beam and was decreased for modified solid beam. Figure (11) illustrates the

other beam cases.

fy (MPa) Es (MPa) υ

253 200,000 0.3



Figure 11 Representation of Solid Beam (SB), Voided Beams (VB2 and VB1), Modified Beams

(MVB and MSB).

4. BOUNDARY CONDITIONS

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

concrete beams the boundary conditions at beam edges are needed. In the present study the

voided concrete beams are considered to have fixed support at each end of the beams. Figure

(12) shows the simulation of the fix support at beam's ends.

Figure 12 Modeling of the Fixed Support at Beam's Ends.

5. LOADING SYSTEM

In the finite element modeling, the applied load on the beam specimens was modeled by using

mechanical pressure type of loading acting on top surface of the beam as shown in Figure

(13).

Figure 13 Modeling of Loading Pressure on Top Surface of the Beam Specimen.



The applied pressure is distributed evenly at all surface area and increases linearly up to

failure of the specimen.

6. LOAD-MID SPAN DEFLECTIONCURVES

Deflection for the concrete beam specimens is measured at mid-span for the lowest nodal

point selected from the beam meshed shape element.

Figure (14) shows the comparison for load- midspan deflection curves between voided

concrete beam with void formers at all area (VBA) and solid beam without void formers (SB).

Figure 14 Comparison of Load-Deflection Curves between (VBA) and (SB).

As it can be seen from Figure (14) the (SB) specimen has more strength than (VBA)

specimen from the beginning of the curve until its failure. However, this strength is very

smallat the beginning of the curve and becomes greater by increasing the applied load. The

ultimate load carrying capacity for (SB) specimen isgreater than strength of (VBA) specimen

by (5.12 %) at the (SB) specimen central deflection failure point.

But the (VBA) specimen curve shows more ductility than the solid specimen due to the

existence of the void formers and by increasing the maximum central deflection for (VBA)

specimenits ultimate load increases as well and the difference of maximum load between two

specimens decreases to be only about (0.4 %).

Figure (15) shows the comparison for load- mid span deflection curves between(VBA),

voided beam with void formers at mid span (VB1) and voided beam with void formers at two

ends of the beam (VB2).

As it can be seen from Figure (15) all of the beam specimens have nearly same flexural

behavior since the only difference between the specimens is omitting the void formers from

center of the beam for (VB2) and from two ends of the beam (VB1). Although, the beams

with more solid area at the center (VB2) has slightly more strength than the other beams due

to strength of solid concrete section. At the failure stage of (VB2) specimen it has greater

ultimate load capacity than (VBA) and (VB1) by about (2.51 %) and (0.29 %), respectively.

Also, in here the specimens (VBA) and (VB1) have more ductility than (VB2) specimen

which causes the increase in the central deflection of these specimens and it leads to increase

in ultimate load carrying capacity of these specimens. This increase in ductility shows to be

more effective for (VB1) specimen and make it to have greater strength than (VB2) specimen

by about (2.22 %) at the same time the greater ductility for (VBA) than (VB2) also make

(VBA) specimen stronger than (VB2) but only for (0.35 %).



Figure 15 Comparison of Load-Deflection Curves between (VBA), (VB1) and (VB2).

Figure (16) shows the comparison for load- mid span deflection curves between(SB) and

modified voided beam (MVB).

Figure 16 Comparison of Load-Deflection Curves between (SB) and (MVB).

As it can be seen from Figure (16), by increasing the effective depth of the (VBA) to have

the same amount of concrete as in (SB), the load carrying capacity of the (MVB) increased

significantly by about (20.52%) compared to (SB) at the failure point for (MVB). However,

the smaller effective depth for (SB) causes increase in beam's ductility and make the beam to

experience more mid span deflection before the failure that causes an increases in its strength

and decreases the difference in strength between (SB) and (MVB) to be (16.64 %).

Figure (17) shows the comparison for load- mid span deflection curves between(VBA)

and modified solid beam (MSB).

As it can be seen from Figure (17), at the failure point of the (VBA) specimen the ultimate

load carrying capacity is greater than (MSB) by (27 %) due to higher effective depth than

(MSB) specimen. As it was explained previously the (MSB) is obtained by decreasing the

effective depth of (SB) to make both beams have same amount of concrete. In hear also the

beam with less depth experiences more central deflection and increase its strength to be less

than (VBA) by (17.14 %) at the failure point of (MSB).



Figure 17 Comparison of Load-Deflection Curves between (VBA) and (MSB).

The Finite Element Method (FEM) analysis results for the ultimate load capacity and the

maximum mid-span deflection are shown in Table (4):

Table 4 FEM Test Results.

7. SPECIMENS DEFORMED SHAPE

The following figures illustrate the deformed shape of the analytically tested voided beams

due to the distributed load applied on top surface of the beams in finite element analysis

model.

By comparing the models deformed shapes hown in Figures (18-20), it can be seen that

the deformed shape of these models are generally very similar, however as it can be seen the

stress distribution in the beams without the void formers is very smooth without any

disturbance like in beams with void formers.

Figure 18 The Deformed Shape for FEM Tested Specimens (VBS, SB), Respectively.

Beam

No.

Beam

Symbol Wmax (KN/m) Δmax (mm)

1 VBA 17.15 39.11

2 SB 17.22 33.73

3 VB2 17.09 35.79

4 VB1 17.47 39.6795

5 MVB 20.08 29.5649

6 MSB 14.64 50.613



Figure 19 The Deformed Shape for FEM Tested Specimens (VB1, VB2), Respectively.

Figure 20 The Deformed Shape for FEM Tested Specimens (MVB, MSB), Respectively.

8. CONCLUSIONS

In this study, an analytical investigation on flexural behavior of voided concrete beamsis

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

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

conclusions can be obtained:

1) The ultimate load carrying capacity for the solid beam is greater than the voided beam from

the beginning of the loading process and increased by increasing the applied load. However,

at the failure point of the two beams the difference of ultimate load between the two curves

become very small.

2) By omitting the void formers from the center of the beam (VB2) and make it to be solid

concrete section gave the beam greater strength than (VB1) and (VBA). However, the greater

ductility of (VB1) and (VBA) make it possible for these beam to carry more applied load than

(VB2) at their failure point.

3) As it can be predicted by using the same amount of concrete used in (SB)for (VBA) and

increase its total depth, the new beam (MVB) show greater ultimate load carrying capacity

than (SB). However, the obtained results show that the larger the section is the less ductility it

has before the failure. Thus, the ultimate load capacity difference between the two beams

become smaller at the failure point of (SB)

4) Also, decreasing the solid beam depth to make it has the same amount of concrete as in

(VBA), the new beam (MSB) has significantly less strength than (VBA) although they both

used the same amount of concrete.



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[2] Nasvik J. (2011), On the bubble: Placing concrete around plastic voids increases

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[3] Mohammad Redha K. Mahmood, and Mustafa B. Dawood (2017), "Punching Shear

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[4] A. Churakov (2014), "biaxial hollow slab with innovative types of voids", Saint-Petersburg

Polytechnical University, Russia.

[5] Abaqus (6.14-4), "Analysis User's Manual", U.S.A. (2014).

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[8] F. W. Lu, S. P. Li and Guojun Sun, "Nonlinear Equivalent Simulation of Mechanical

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Documents

FINITE ELEMENT STUDY ON FLEXURAL BEHAVIOR OF …bi-axial system and originally used for slab system. This type of void former has the same concept of bubble-deck systemwhich is to