 Open Access
 Total Downloads : 243
 Authors : K. M. Karthick, Dr. G. Arunkumar
 Paper ID : IJERTV6IS030215
 Volume & Issue : Volume 06, Issue 03 (March 2017)
 DOI : http://dx.doi.org/10.17577/IJERTV6IS030215
 Published (First Online): 20032017
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Theoretical and Numerical Investigation of Cold Formed I Section Castellated Beam with Hexagonal Openings
K. M. Karthick 1,
1PG Scholar, Department of Civil Engineering,
Government College of Engineering, Salem11, Tamil Nadu, India.
Abstract – The use of cold formed steel structures is increasing throughout the world as they are efficient in terms of stiffness and strength. The main aim of introducing the concept of cold formed thin section is to reduce the cost to strength ratio of the building components and to reduce the overall cost of construction besides making the structure light in weight. Castellated beams are becoming very popular now a day due to its advantageous structural applications. The advantage of using such beams is that it causes reduction in total weight of the structure and hence requires less quantity of steel .Investigation of cold formed I section castellated beam with hexagonal openings is carried out by varying the size of openings and the spacing between openings. The performance is analyzed using ABAQUS 6.13 by keeping the depth and width of the sections constant. Theoretical investigation is carried out by using North American specification for the design for cold formed steel AISI S 700:2007, Australian/New Zealand design code for cold formed steel AS/NZS 4600:2005. The results predicted using numerical analysis and theoretical analysis are compared and presented.
Keywords Castellated beam , Hexagonal Opening, I Section , ABAQUS 6.13, AISI S 700:2007, AS/NZS 4600:2005

INTRODUCTION
Use of steel for structural purpose in structure is rapidly gaining interest these days. In steel structures the concept of preengineered building (PEB) is most popular due to its ease and simplicity in the construction. Pre engineered buildings have very large spans but comparatively less loading. Generally, steel sections satisfy strength requirement, the difficulty is that, section have to satisfy serviceability requirement i.e. deflection criteria in safety check. This necessitates the use of beams with greater depth to satisfy this requirement. Use of castellated beams is the best solution to overcome this difficulty. The castellated or perforated web beam is the beam which has perforation or openings in its web portion. Generally, the openings are with hexagonal or square or circular in shapes.Use of castellated beam with hexagonal opening is very common in recent years because of the simplicity in its fabrication. Castellated beams are fabricated by cutting flange of a hot rolled steel I beam along its centerline and then welding the two halves so that the overall beam depth gets increased for more efficient structural performance against bending.
Dr.G.Arunkumar2
2Assistant Professor, Department of Civil Engineering, Government College of Engineering
Salem11, Tamil Nadu, India.
Hot rolled and cold formed members are the two main families of structural members in steel construction. Even though cold formed structural members are less familiar of the two, they have a growing importance relative to the traditional heavier hotrolled structural members. Cold formed steel members are made at room temperature using rolling or pressing thin flat steel sheet to get a desired shape that will support more load than the flat sheet itself.

REVIEW OF PREVIOUS STUDIES

Salokhe S.A and Patil P. S
It can be interpreted that the cold formed steel sections shows 17.37 % more load carrying capacity as compared to hot rolled sections and it gives 33% lesser lateral deformation as compared to hot rolled section. It also shows little variation in axial deflection of both cold formed steel section and hot rolled steel section. The stress distribution of hot rolled steel section is much uniform throughout the length, on the contrary cold formed steel section shows distinct variation in stress distribution. The finite element software ABAQUS gives results nearer to experimental results up to 0.6 % for load carrying capacity calculation. While comparing failure pattern, hot rolled steel member shows bending failure and cold formed steel shows distortional local buckling failure

Benediktas Dervinis and Audronis Kazimieras Kvedaras
An analysis of perforated beams with a hexagonal form of perforations by finite element method is accomplished in this paper. Some conclusions may be drawn:

A nontraditional method for selecting castellated beams has been proposed.

The proposed method may be adopted and used for design in future works.

The charts determining the behaviour of beam failure may be drawn.

Data received are only valid for beams with the condition mentioned above.

With some coefficients, the curves used in charts can be adopted for beams of different lengths.

It can be seen from calculation data that the higher the web, the more efficiently the beam material is used.
However, the bigger the web slenderness, the more critical influence has local buckling on the beams carrying capacity. That is why it is very important to find such dimensions of the beam which in the moment of failure would ensure maximal stresses in the section.


B.Anupriya and Dr. K. Jagadeesan
Studied analytically shear strength and deflection properties of castellated beams with hexagonal openings using ANSYS14. Study shows that, as the depth of castellated beam increases, the stress concentration at corners as well as at the loading point increases. In order to avoid this, study was also carried out by provision of diagonal stiffeners and also with diagonal and vertical stiffeners (i.e. combined form) in the openings. The results indicate that minimum deflections occur in the castellated beam provided with diagonal and vertical stiffeners (combined form).

Sagade A.V. and Auti V. A
The authors have experimentally studied the behavior of simply supported castellated beams under two point loading (four point bending) by varying the depth of hexagonal openings (and hence the overall depth). Modes of failure of the castellated were examined for different depths of openings. From the experimentation, researchers conclude that the castellated beam behaves satisfactorily up to a maximum depth of 0.6 times the depth of opening (0.6D). Investigators recommend for providing reinforcement (stiffeners) in order to avoid Vierendeel effects caused due to openings.


SPECIMEN SPECIFICATIONS
Nine different castellated beams with hexagonal openings were selected by varying depth of openings and the spacings of openings are shown in Table I.
Sp.
No.
D
mm
Do mm
S
mm
D/Do Ratio
S/D Ratio
L
mm
1
300
120
240
0.4
0.8
1800
2
300
120
300
0.4
1.0
1980
3
300
120
450
0.4
1.5
1860
4
300
150
240
0.5
0.8
1920
5
300
150
300
0.5
1.0
2100
6
300
150
450
0.5
1.5
1950
7
300
180
240
0.6
0.8
1620
8
300
180
300
0.6
1.0
2220
9
300
180
450
0.6
1.5
2040
TABLE I: Details of the Specimen
Fig I: Details of the specimen

THEORETICAL INVESTIGATION

Design as per North American Specification of Cold formed Steel (AISI S 100:2007)

Nominal flexural section strength
The nominal flexural strength (resistance) Mn, shall be minimum of lateral torsional buckling strength Mne, local buckling strength Mnl, distortional buckling Mnd.
Effective initial yield moment, My = Se X Fy Where, Se = Effective section modulus
Fy = yield stress

Lateral Torsional buckling strength
The nominal flexural strength (resistance) Mne, for lateraltorsional buckling shall be calculated in accordance with the following:

For Mcre > 2.78 My
Mne = My
(No lateral buckling at bending moments less than or equal to My)

For 2.78 My Mcre 0.56 My

For Mcre < 0.56 My
Mne = Mcre Where,
Where,
Cb – conservatively taken as unity for all cases d – Depth of section.
Iyc – Moment of inertia of compression portion of section about centroidal axis of entire section parallel to web, using full unreduced section.
Sf – Elastic section modulus of full unreduced section relative to extreme compression fibre.
Ky Effective length factor for bending about y axis
b. For d > 0.673
Where,
My – a value defined in section 6.1.3
Mcrd – critical elastic distortional buckling moment determined by following method
Mcrd = Sf x Fd
Sf – Elastic section modulus of full unreduced section relative to extreme compression fiber.
Fd – Elastic distortional buckling stress
.


Local buckling strength
The nominal flexural strength (resistance) Mnl, for local buckling shall be calculated in accordance with the following

For l 0.776
Mnl = Mne

For l > 0.776
Where,
Mne = a value defined in session 6.1.2
Mcrl = critical elastic local buckling moment determined by following method.
Where,
E – Youngs modulus
Âµ – poisons ratio
t – Thickness of element Wplate width of element
K – Element (plate) buckling coefficient K = 4 for flange and web
K = 0.43 for lip
Mcrl = fcrl X Se


Distortional buckling strength
The nominal flexural strength (resistance) Mnd, for distortional buckling shall be calculated in accordance with the following

For d 0.673
Mnd = My
Where,
– A value accounting for moment gradient, which is permitted to be conservatively taken as 1.0



Design as per Australian/New Zealand Specification of Cold formed steel (AS/NZ 4600:2005)

Nominal section moment capacity (Ms)
Based on initiation of yielding (Ms) = Ze x fy

Nominal member moment capacity (Mb)
The nominal member moment capacity (Mb) shall be lesser of nominal section moment capacity (Ms), and the values calculated by the following methods.

Local bucking moment of resistance
Mb= Zc x fc
Where,
Zc = effective section modulus calculated as a stress fc in the extreme compression fibre.
fc = Mc/ Zf
Where,
Zf = full unreduced section modulus for extreme compression fibre
Mc= critical moment calculated as following condition.
a) For b 0.60
Mc = My
b) For 0.60< b < 1.336
c) For b 1.336,
Where,
b = non dimensional ratio used to determine critical moment
Where,
Mo = elastic buckling moment

Distortional buckling moment of resistance


Mb = Zc x fc
Where,
Zc = effective section modulus calculated as a stress fc in the extreme compression fibre.
fc = Mc/ Zf
Zf = full unreduced section modulus for extreme compression fibre.
Mc = critical moment calculated as following
condition.

For d 0.674
Mc = My

For d > 0.674,
Where,
d = non dimensional ratio used to determine critical moment


FINITE ELEMENT ANALYSIS
The finite element method is a numerical analysis technique for obtaining approximate solutions to wide variety of Engineering problems. Most of the engineering problems today make it necessary to obtain approximate numerical solutions to problems rather than exact closed form solutions. The basic concept behind the finite element analysis is that structure is divided into a finite number of elements having finite dimensions and reducing the structure having infinite degrees of freedom to finite degrees of freedom. The original body of structure is then considered as an assemblage of these elements connected at a finite number of joints called Nodes or Nodal points. This method of analysis has an advantage of that it can take care of any boundary and loading conditions. An engineering problem can be solved in four phases.

Preprocessing

Solid Modelling
The geometric Modeling is done using ABAQUS
6.13. The connectivity between web and flanges for spot welding constrain is done. The dimensions of the created solid model are same as the dimensions of the specimen used in the experimental test. Fig 2 shows the Perspective view of the specimen.
Fig 2: Perspective view of the specimen

Element Type
The type of element chosen for finite element model idealization plays an important role in the prediction of actual behavior of the structure. From the finite element behavior study it is finalized that element 3D DEFORMABLE SHELL is used. Each element are created by individual parts then assembled together.

Material Properties
The elastic properties of the material were assigned to the created model of castellated cold formed steel beam. The value of Youngs modulus E is given as 2 x 105 N/mm2. The Poissons ratio is given as = 0.33. The yield stress of the material is 250 Mpa. Thickness of section is assigned to 2 mm.

Meshing
The construction of a 3D Finite element model usually requires a variety of mesh generation techniques. In our case global meshing size of 25mm meshing is done. Depending upon the range of fine and coarse meshing the computer time varies to run the process. This figure represents the modeling of the specimen number 1 with meshing size 25 mm and the parts are connected using tie constraint. Fig 3 shows the perspective view of the specimen with meshing.
Fig 3: Perspective View of specimen with meshing

Interaction of Elements
Top and bottom flange and web with circular openings are created by separate parts; those parts are welded together by means of tie constraint. The nodes are selected and tie connections are applied.

Applying Boundary Condition
Boundary conditions imposed on a finite element solid model is usually given in ABAQUS by specifying the nodal point index and then restraining the necessary displacement component. Here in our problem the castellated beam is analyzed by simply supported end condition. So that displacement components Ux, Uy, and Uz are restrained at one end and displacement components Ux and Uy are restrained at another end.

Applying Loads
Loads can be applied to the finite element model in various forms such as applying loads to the key poins, lines, areas, elements and at the nodes. For our problem the analysis is carried out for the two points loading on castellated beam. Loads are applied at one third from the both end of the span of beam.


Linear Analysis
Linear analysis is based on the following assumptions that stress and strain follows Hookes Law (i.e. linear relationship between stress and strain), deformations are covered by small deflection theory (i.e. small geometric difference between the initial and deformed shape) and other material properties are constant. In this stage problem is subjected to static linear analysis. The errors and warnings are identified at this stage. After nullifying those errors the solution process gets completed and the various deformations are studied. Fig 4 shows the distortional failure of specimen.
Fig 4: Distortional failure of specimen

NonLinear Analysis
Nonlinear analysis is based on the following assumptions that stress and strain does not follow Hookes Law (i.e. nonlinear relationship between stressstrain due to material plasticity), deformations are covered by large deflection theory (i.e. large geometric difference between the initial and deformed shape) and material properties that are temperature dependent.
Any reason causing a variation in stiffness of the assembly being analyzed is potentially a source of non linearity and therefore requires a nonlinear analysis to be captured. It is widely accepted that the three main sources of nonlinearity are;

Plasticity of material (variation of the material Young's modulus will cause the stiffness of the structure to change).

Large displacements (Stiffness varies as a result of large geometric difference between the initial and deformed shape).

Contact: if two parts or bodies of the assembly come into contact, or lose contact, or the extent of their contact patch changes, then the stiffness of the assembly also varies.


Post Processing
Post processing helps us to view the results obtained from the analysis. The results obtained as nodal solution may be viewed in the tables form or contour plots. These plots are very much useful for us to identify the results such as displacements stresses and strains and also their maximum and minimum values.


COMPARISON OF RESULTS
The moment carrying capacities of castellated beam I section with hexagonal openings in the web are estimated by theoretical investigations and numerical analyses were discussed here.

Comparision of Theoretical Results
The ultimate moment Mu obtained by the two code books AISI S100:2007and AS/NZS 4600:2005 were compared in Table 2. It shows that the moment values obtained by AS/NZS 4600:2005 is higher compared to the other
TABLE II: Comparison of Theoretical Results
Specimen
AISI S100:2007
Mu (kNm)
AS/NZS 4600:2005
Mu (kNm)
1
9.579
11.268
2
9.579
10.203
3
9.579
11.352
4
7.725
8.954
5
7.725
8.035
6
7.725
8.984
7
5.962
6.817
8
5.962
6.111
9
5.962
6.905
VARIOUS MOMENT OF RESISTANCE
12
10
8
6
4
2
0
CBHCBHCBHCBHCBHCBHCBHCBHCBH 1 2 3 4 5 6 7 8 9
SPECIMEN
AISI S100:2007 Mu (kNm)
AS/NZS 4600:2005 Mu (kNm)
VARIOUS MOMENT OF RESISTANCE
16
14
12
10
8
6
4
2
0
CBH CBH CBH CBH CBH CBH CBH CBH CBH 1 2 3 4 5 6 7 8 9
SPECIMEN
AISI S100:2007 Mu (kNm) AS/NZS 4600:2005 Mu (kNm) ABAQUS (kNm)
MOMENT
CARRYING
CAPACITY
MOMENT CARRYING CAPACITY
Chart 1: Various Moment of Resistance Obtained By AISI S100:2007and AS/NZS 4600:2005

Comparisons of Theoretical results and Numerical results
The ultimate moment Mu obtained by the two code books AISI S100:2007 and AS/NZS 4600:2005 were compared with the ultimate moment obtained from the numerical analyses by ABAQUS. Table 2 shows the results of Theoretical and Numerical investigation.
MAISI AISI S1002007 MAUS/NZS AS/NZS 4600:2005
MABAQUS Numerical Analysis by ABAQUS 6.13
S
no
MAISI
kNm
MAUS/NZ
KNm
MABAQUS
kNm
MABAQUS/M
AISI
MABAQUS/M
AUS/NZ
1
9.579
11.268
13.535
1.412
1.201
2
9.579
10.203
12.543
1.309
1.326
3
9.579
11.352
14.487
1.875
1.512
4
7.725
8.954
12.442
1.610
1.389
5
7.725
8.035
11.897
1.540
1.480
6
7.725
8.984
12.735
1.648
1.417
7
5.962
6.817
10.735
1.800
1.574
8
5.962
6.111
11.132
1.867
1.821
9
5.962
6.905
10.660
1.649
1.543
MEAN
1.701
1.473
STANDARD DEVIATION
0.472
0.351
TABLEIII: Results of Theoretical and Numerical investigation
Chart 2: Various Moment of Resistance Obtained by Theoretical and Numerical investigation


CONCLUSION

The theoretical and numerical results obtained from ABAQUS 6.13 shows that the specimen with minimum opening and maximum spacing between the hexagonal openings provide better moment of resistance when compared to other specimens.

The moment of resistance value obatained from AS/NZS 4600:2005 is higher when compared to AISI S1002007 values due to the fact that length is not a factor for calculation as per AISI S1002007.

ABAQUS 6.13 provides greater moment of resistance when compared with the values from the AISI S100 2007 and AS/NZS 4600:2005 codes.

The ratio of strength predicted using Numerical to Theoretical AISIS100:2007 for all beams put together was found to have mean 1.701.

The ratio of strength predicted using Numerical to Theoretical AS/NZS 4600:2005 for all beams put together was found to have mean 1.473.

It also shows that the standard deviation which was obtained holds good between
MABAQUS / MAISI and
ABAQUS / MAUS/NZS ratios.

Within the parametric study, it was observed that the theoretical investigation AISI S100:2007 and AS/NZS 4600:2005 holds in good agreement with numerical investigation.

Comparing the specimens with openings of 0.4 times the overall depth of the beam (i.e., CBH 1, CBH 2and CBH 3 with spacing of 0.8, 1.0 and 1.5 times the overall depth of beam respectively); it shows that CBH 3 shows the result.

Comparingthe specimens with openings of 0.5 times the overall depth of the beam (i.e., CBH 4, CBH 5 and CBH 6with spacing of 0.8, 1.0 and 1.5 times the overall depth of beam respectively); it shows that CBH 6 shows the result.

Comparing the specimens with openings of 0.6 times the overall depth of the beam (i.e., CBH 7, CBH 8 and CBH 9 with spacing of 0.8, 1.0 and 1.5 times the overall depth of beam respectively); it shows that CBH 8 shows the result.

In overall comparison of all the nine specimens, CBH 3 1 (i.e., openings with 0.4 times the overall depth of the beam and spacing of 0.8 times the overall depth of the beam) shows the better result.

Codes and Guidelines
REFERENCES

AISIS100:2007, North American Specification for the Design of ColdFormed Steel Structural members Specifications.

AS/NZS 4600:2005, Australian / New Zealand Standard Cold Formed Steel Structures.


Journal Articles

J. P. BOYER Castellated Beam A New Development (AISC National Engineering Conference, Omaha, Nebr., in May, 1964)

Richard Redwoodland Sevak Demirdjian Castellated Beam Web Buckling In Shear Journal of Structural Engineering 1october 1998/1207

Wakchaure M.R., Sagade A.V. and Auti V. A., Parametric study of castellated beam with varying depth of web opening, International Journal of Scientific and Research Publication, Vol. 2,No.8, pp. 21532160, 2012.

Wakchaure M.R. and Sagade A.V., Finite element analysis of castellated steel beam, International Journal of Engineering and Innovative Technology,Vol.2, No. 1, pp. 37443755, 2012.

Tadeh Zirakian, Hossein Showkati Distortional Buckling of Castellated Beams (Journal of Constructional Steel Research 62, pp. 863871, 2006

Nikos D. Lagaros, Lemonis D. Psarras, Manolis Papadrakakis, Giannis Panagiotou Optimum Design of Steel Structures with Web Openings Engineering Structures 30, pp. 25282537, 2008.

H. R. Kazemi Nia Korrani1, M. Z. Kabir, S. Molanaei Lateral Torsional Buckling of Castellated Beams Under End Moments International J. of Recent Trends in Engineering and Technology, Vol. 3, No. 5, May 2010.

M.R. Soltani, A. BouchaÃ¯r , Nonlinear FE analysis of the ultimate behavior of steel castellated beamsJournal of Constructional Steel Research 70 (2012), pp. 101114

Ehab Ellobody Nonlinear Analysis of Cellulars Steel Beams Under Combined Buckling Modes (ThinWalled Structures 52 (2012), pp. 6679).

Wakchaure M.R. and Sagade A.V., Finite element analysis of castellated steel beam, International Journal of Engineering and Innovative Technology, Vol.2, No. 1, pp. 37443755, 2012.

Erdal F. and Saka M. P., Ultimate load carrying capacity of optimally designed steel cellular beams, Journal of Constructional Steel Research, Vol. 80, pp. 355368, 2013.

Hideo Takabatake, Shigeru Kusumoto and Tomitaka Inoue, Lateral Buckling Behavior of I Beams Stiffened With Stiffeners, Journal of Structural Engineer, Vol.117, pp 3203 3215. 1991.
