 Open Access
 Total Downloads : 252
 Authors : Riyas Pr, Dr. G. Arunkumar
 Paper ID : IJERTV6IS020239
 Volume & Issue : Volume 06, Issue 02 (February 2017)
 DOI : http://dx.doi.org/10.17577/IJERTV6IS020239
 Published (First Online): 23022017
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Investigation of Cold – Formed I – Section Castellated Beam with Cellular Openings
Riyas PR1
1PG Scholar Depatment of Civil Engineering
Government College of Engineering Salem11,Tamil Nadu, India
Dr. G. Arunkumar2
2Assistant Professor
Depatment of Civil Engineering Government College of Engineering Salem Salem11,Tamil Nadu, India
AbstractThe cold formed steel structural members are made through cold forming a thin plate which is normally from 1.2 mm to 3 mm and has a section shape with the right purpose. One of the advantages of cold formed steels is that the strength to weight ratio is much higher than that of common hot rolled shapes, thus it can reduce the total weight of structures. Lots of study has been done in optimizing sizes of castellated beams with hexagonal openings, and hence there is need to optimize the beams with other shaped openings. While the local failure associated with the castellated beam can be minimized by providing other shaped openings like circular, diamond shapes etc. Investigation of cold formed I section castellated beam with cellular 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 S700:2007, 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. Results showed that, the beam gives better strength results for cellular shaped opening with opening size of 0.4 times the overall depth of the beam. It is also observed that, castellated beams are mostly tends to fail in their local modes of failure.
Keywords Castellated beam, Cellular web opening, Cellular beam, Finite Element Analysis, ABAQUS 6.13, Optimization.

INTRODUCTION
Castellated beam is a name commonly used for a type of expanded beam. It is made by expanding a standard rolled shape in a manner which creates a regular pattern of holes in the web. The name is derived from this pattern of web holes, because castellated means "built like a castle, having battlements, or regular holes in the walls, like a castle".
It is made by separating a standard rolled shape into two halves by cutting the web in a regular alternating pattern as shown. The halves are rejoined by welding, after offsetting one portion so that the high points of the web pattern come into contact. Some design conditions make it advantageous to increase the depth even more. This is done by adding web plates between high points of the tee sections. These added plates are called "increment plates".

REVIEW OF PREVIOUS STUDIES
In recent times, a lot of research work has been carried out for analysis and design of castellated beams, especially with hexagonal openings. There is no universally accepted design
method for castellated beam because of complexity in geometry accompanied by complex mode of failure. At present, there are possibly six failure modes of castellated beam namely, formation of flexure mechanism, lateral torsional buckling, formation of Vierendeel mechanism, rupture of welded joint, shear buckling of web post and compression buckling of web post. Various research studies carried out for analysis and design of castellated beams are presented in the following section.

Erdal F. and Saka M. P [04]
The authors have studied the load carrying capacity of optimally designed castellated beam with various numbers of holes and spacing. Finite element analysis of same beams is also carried out under the application of centrally applied point load and failure patterns are studied and verified using ANSYS. Study shows that, even though the members are relatively of shorter spans, lateral supports are governing factor for the analysis of beams due to torsional buckling. It is concluded that, the beam fails in Vierendeel mode when the load is applied above the openings while it fails in web post buckling when load is applied in between space of the openings.

Jamadar A. M. and Kumbhar P.D [09]
They carried out experimentally as well as analytically using Abaqus (CAE 6.13) of castellated beams provided with circular and diamond shaped openings by following the guidelines given in EUROCODE 3. The software results were validated by comparing it with experimental results. The result indicates that the castellated beam with diamond shaped opening suffers least amount of local failure as more shear transfer area is available as compared to the castellated beams with circular opening. Also load carrying capacity is greater for diamond shape than circular opening.

Ehab Ellobody [10]
The author analyzed the castellated beam with circular openings by nonlinear analysis, where the combined modes of buckling of these beams were considered. The behavior was checked for high strength of beam by considering the parameters like imperfection of geometry, remaining stresses and also nonlinear material properties of material were considered. The nonlinear finite element method helped in predicting deflection, failure modes and also the loads causing failure. The result of parametric study shows the cellular beam fails because of combined action of web distortional as well as due to web post buckling mode which
shows considerably decrease in failure load. Lateral torsional buckling was observed in cellular beams with normal strength while distortion of web and also the web post buckling was observed in cellular with high strength.

Wakchaure M.R., Sagade A.V. and Auti V. A [02]
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.

B. Anupriya and Dr. K. Jagadeesan [13]
They studied the 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).


PARAMETERS OF THE SPECIMEN
Nine different castellated beams with cellular openings were selected by varying depth of openings and the spacings of openings as shown in Table I.
TABLE I. PARAMETERS CONSIDERED FOR CELLULER SHAPED OPENINGS
S Spacing of openings L Span of the Beam
Fig. 1. Geometry of Castellated beam with cellular openings

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, shallbe 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
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
Where,
D Depth of the specimen Do Depth of openings
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. Ly Unbraced length of member for bending about y axis.


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
– 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,
Mne = a value defined in session (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

For d > 0.673

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.
i. For b 0.60,
Mc = My
ii. For 0.60< b < 1.336,
iii. 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,
My – a value defined in section (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
Where,
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 togethr 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 points, 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 processor 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 cellular openings in the web are estimated by theoretical investigations and numerical analyses were discussed here. 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.
TABLE II. RESULTHS OF THEORETICAL AND NUMERICAL INVESTIGATION
Sp.
No.
MAISI
KNm
MAUS/NZ
kNm
MABAQUS
kNm
1
9.579
10.620
14.649
1.529
1.379
2
9.579
11.352
14.551
1.519
1.282
3
9.579
11.889
14.598
1.524
1.228
4
7.725
9.488
13.715
1.775
1.446
5
7.725
8.824
12.160
1.574
1.378
6
7.725
9.376
13.238
1.714
1.412
7
5.962
8.354
10.582
1.775
1.267
8
5.962
6.496
12.423
2.084
1.912
9
5.962
7.089
11.872
1.991
1.675
Mean
1.701
1.442
Standard Deviation
0.500
0.473
MAISI AISI S1002007 MAUS/NZS AS/NZS 4600:2005
MABAQUS Numerical Analysis by ABAQUS 6.13 The load carrying capacities of cold formed
castellated beam with cellular openings are estimated by theoretical investigations and numerical analyses were discussed here. Chart 1 show the various moment of resistance obtained by the numerical and theoretical analysis.
Chart. 1. Various moment of resistance obtained by the numerical and theoretical analysis.

CONCLUSION

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 1.442.

It also shows that the standard deviation which was obtained holds good between
MABAQUS/MAISI and MABAQUS/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., Specimen number 1, 2 and 3 with spacing of 0.8, 1.0 and 1.5 times the overall depth of beam respectively); it shows that specimen number 1 gives the result.

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

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

In overall comparison of all the nine specimens, Specimen number 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) gives the better result.
REFERENCES

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.

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. 2153 2160, 2012.

Soltani M. R., BouchaÃ¯r A. and Mimoune M., Nonlinear FE analysis of the ultimate behavior of steel castellated beams, Journal of Constructional Steel Research, Vol. 70, pp. 101114, 2011.

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 32033215. 1991.

Sung C. Lee, M. ASCE; Chai H. Yoo and Dong Y. Yoon, Behavior of Intermediate Transverse Stiffeners Attached on Web Panels, Journal of Structural Engineering, Vol. 128, pp 337345. 2002.

Ehab Ellobody, Interaction of Buckling Modes in Castellated Steel Beams, Journal of constructional steel research, Vol. 67, pp 814825. 2011.

Konstantinos Daniel Tsavdaridis and Cedric DMello, Web Buckling Study of the Behavior and Strength of Perforated Steel Beams with Different Novel Web Opening Shapes, Journal of Constructional Steel Research, vol.67, pp 16051620. 2011.

Jamadar A. M. and Kumbhar P.D., Parametric Study of Castellated Beam with Circular and Diamond Shaped Openings, International Research Journal of Engineering and Technology, Vol.02, pp 715722. 2015.

Ehab Ellobody, Nonlinear analysis of cellular steel beams under combined buckling modes, Thin walled structures, Vol. 52, pp 6679. 2012.

B. Anupriya and Dr. K. Jagadeesan, Strength Study on Castellated Beam, International Journal on Engineering Research & Technology, Vol.2, pp 38533859. 2013.

Delphine Sonck and Jan Belis, Lateraltorsional buckling resistance of cellular beams, Journal of Constructional Steel Research, vol.105, pp 119128. 2015.

Ajim S. Shaikh and Harshal R. Aher, Structural Aanalysis of Castellated Beam, International Journal on Recent Technologies in Mechanical and Electrical Engineering, Vol.2, pp 081084. 2015.

Konstantinos Daniel Tsavdaridis and Grigorios Galiatsatos, Assesment of Cellular Beams with Transverse Stiffeners and Closely Spaced Web Openings, ThinWalled Structures, vol.94, pp 636650. 2015.