DOI : 10.17577/IJERTV10IS060008
- Open Access
- Authors : Rohit Kurlapkar , Amruta Patil
- Paper ID : IJERTV10IS060008
- Volume & Issue : Volume 10, Issue 06 (June 2021)
- Published (First Online): 09-06-2021
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
Optimization of Various Parameters of Castellated Beam Containing Sinusoidal Openings
Rohit Kurlapkar
Annasaheb Dange College of Engineering and Technology Ashta, India
Amruta Patil
Annasaheb Dange College of Engineering and Technology Ashta, India
Abstract: This paper discusses optimization of the size of opening i.e. depth and width of opening of castellated steel beam containing sinusoidal openings. Optimization of opening of sinusoidal shape was performed using finite element method (FEM). The results of FEM analysis are verified by implementing laboratory testing of 150 mm height castellated beam specimen. All the castellated beam specimens were modified from 100 mm I beam. Optimum results from FEM analysis was a castellated beam with sinusoidal openings having opening size 0.62 times its overall depth with S/D0 ratio 1.4 and D/D0 1.61 From laboratory testing results and FEM analysis it is observed that, the deflection obtained from FEM result is 1.170 mm. While deflection from experiment results is 1.172 mm. Percentage variation in above case is almost negligible, that is 0.18 percent.
Keywords: Castellated beam, sinusoidal openings, finite element analysis, steel beam
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INTRODUCTION
Castellated name come from the Latin word whose meaning is to structurally fortify. Before castellated beams, I-beams were used in construction because they are strong and solid way of supporting houses and other industrial structures. Castellated beams were developed as structural channels to increase the beams depth of parent I-beam and strength without adding additional material causing no change in weight. Since 1950, because of shortage of steel and increase in cost of steel, castellated beams gets started to be used in the construction. Castellated beams were advanced in Europe to overcome the steel shortages and high cost of steel.
Castellated beams are the beams having different geometrical shape perforations in the web of beam. The different shapes such as hexagonal, circular, rectangular, diamond, sinusoidal etc. are used in castellated steel beams. These shapes are constructed with the help of computer controlled cutting torch to cut the section according to given geometry.
Castellated beams are produced in two steps. In first step the beam is cut in required pattern. In second step both top and bottom parts are welded together to create deeper section. Construction of castellated beam is very efficient process as most of the work is done by automated plasma torch cutting. In order to reduce the man power time and cost on the site, the beams can be constructed with connection points already manufactured into the beam.
The principle advantage of castellated beam is we can
increase the depth of beam to increase its strength without Adding its weight. Hence castellated beams are high efficient when it come to load carrying capacity. Many investigators related with behavior of castellated I beam was carried out by [7]-[8] Few researcher [4]-[5] were also carried out research related with behavior of cellular beam with sinusoidal openings. So far there was less research related with optimized depth and length of opening.
This paper explains the results of research for obtaining the optimum size of sinusoidal opening within castellated beam. The aim of this research are (1) examining the result obtained from FEM analysis by conducting laboratory test of castellated steel beam;(2) identifying the maximum stress, of castellated beam containing sinusoidal opening by conducting finite element method; and (3) finding the optimum size of opening of sinusoidal opening within castellated beam .
-
RESEARCH METHOD
-
General
The procedure used in the project was divided into three steps. First step is related with software analysis in computer. Method used for analysis of castellated beam with sinusoidal opening was finite element method. Deflection was computed from software analysis which is then verified by performing the second step which is laboratory tested of castellated beam. In third step after comparing the result parametric study was conducted for optimization of depth of opening and width of opening. For laboratory testing two point loading test is preferred, whose schematic representation is shown below.
Fig1. Two point loading system in castellated steel beam model
-
Guidelines for perforation in web
The openings made in the web of beam greatly affect the
structural performance of the beam. And hence it is essential to make some logical and practical considerations while providing openings in the web of beam. Following are the general guidelines which given by the euro code and some of them are assumed on field considerations.
These guidelines for opening in the web of beam can be changed or altered without affecting the structural performance of beam [11]. These guidelines are as below
Fig 2. Typical Castellated Beam with its Cross Section
1. 1.08 < S/< 1.5
2. 1.25 < D/< 1.75
3. < 0.8 D
4. e >0.4
5. Width of end post > 0.5
Where,
0 = Depth of opening
D = Overall depth of opening
S = Centre to Centre spacing between the two opening e = Clear distance between two opening
-
Criteria for Failure
In order to identify the failure of beam in Abaqus, a von mises failure criterion is used to determine the failure condition of ductile material [10]. Von mises stress is defined as uniaxial tensile stress that creates the same distortional energy as any actual combination of applied stress. Failure occurs when the von mises stress value increases beyond the yield stress value of material. In this project work material used for analysis of beam is steel whose yield stress is 250 MPa. The load that produces stress below 250 MPa is taken as permissible load.
-
Laboratory Testing Setup
Laboratory test was carried out using simple support system beam and subjected with two point loading system. Effective length of beam was 900 mm, depth of opening 110 mm, total depth of beam 150 mm and thickness of beam 3.5mm.
Fig3. Laboratory testing setup
-
Selection of parameters for parametric study on beam with sinusoidal shaped openings
Considering the limitations of perforation in the web of beam given by euro code different dimensions of web perforations are selected. The criterion such as S/D0 and D/Do ratio of the opening are considered for the study. These different parameters and their respective cross sectional dimensions are given in table No 1. For beam with sinusoidal openings. All the castellated beams have been derived from 100 mm depth I beam. All the beams were analyzed by using finite element software and optimize section for depth of opening and width of opening has been found. For castellated beam,
First S/D0 ratio (i.e. 1.4) is kept constant while D/D0 ratios have been varied from 1.25 to 1.75. After this same process we have repeated for other S/D0 ratios. i.e. (1.3 and 1.2).
-
-
RESULTS AND DISCUSSION
-
Comparative analysis results between software results with laboratory results
The finite element analysis results are verified by using laboratory tests. Purpose of this laboratory test is to check the correlation between software model and real model. Verification was conducted based on the maximum load given by software to the corresponding deflection of castellated beam having sinusoidal opening. Model used for laboratory test was having depth of 150 mm and of opening depth of 10 mm.
Sr. No.
D0
D
D/D0
S/D0
S
e
1
130
165
1.26
1.4
182
52
2
120
160
1.33
1.4
168
48
3
110
155
1.40
1.4
154
44
4
100
150
1.50
1.4
140
40
5
90
145
1.61
1.4
126
36
6
80
140
1.75
1.4
112
32
7
130
165
1.26
1.3
169
52
8
120
160
1.33
1.3
156
48
9
110
155
1.40
1.3
143
44
10
100
150
1.50
1.3
130
40
11
90
145
1.61
1.3
117
36
12
80
140
1.75
1.3
104
32
13
130
165
1.26
1.2
156
52
14
120
160
1.33
1.2
144
48
15
110
155
1.40
1.2
132
44
16
100
150
1.50
1.2
120
40
17
90
145
1.61
1.2
108
36
18
80
140
1.75
1.2
96
32
Sr. No.
D0
D
D/D0
S/D0
S
e
1
130
165
1.26
1.4
182
52
2
120
160
1.33
1.4
168
48
3
110
155
1.40
1.4
154
44
4
100
150
1.50
1.4
140
40
5
90
145
1.61
1.4
126
36
6
80
140
1.75
1.4
112
32
7
130
165
1.26
1.3
169
52
8
120
160
1.33
1.3
156
48
9
110
155
1.40
1.3
143
44
10
100
150
1.50
1.3
130
40
11
90
145
1.61
1.3
117
36
12
80
140
1.75
1.3
104
32
13
130
165
1.26
1.2
156
52
14
120
160
1.33
1.2
144
48
15
110
155
1.40
1.2
132
44
16
100
150
1.50
1.2
120
40
17
90
145
1.61
1.2
108
36
18
80
140
1.75
1.2
96
32
Table I. Parameters considered for sinusoidal opening
10
100
150
1.50
1.3
90
32
246
11
90
145
1.61
1.3
81
34
250
12
80
140
1.75
1.3
72
32
247
13
130
165
1.26
1.2
104
22
249
14
120
160
1.33
1.2
96
24
246
15
110
155
1.40
1.2
88
34
247
16
100
150
1.50
1.2
80
29
247
17
90
145
1.61
1.2
72
29
245
18
80
140
1.75
1.2
64
32
245
10
100
150
1.50
1.3
90
32
246
11
90
145
1.61
1.3
81
34
250
12
80
140
1.75
1.3
72
32
247
13
130
165
1.26
1.2
104
22
249
14
120
160
1.33
1.2
96
24
246
15
110
155
1.40
1.2
88
34
247
16
100
150
1.50
1.2
80
29
247
17
90
145
1.61
1.2
72
29
245
18
80
140
1.75
1.2
64
32
245
Table II. Comparison between FEM analysis results and laboratory testing results
Sr.No.
Load (kN)
Deflection by software in mm
Deflection by experiment in mm
1
5
0.29
0.15
2
10
0.58
0.52
3
15
0.87
0.85
4
20
1.17
1.17
5
25
1.46
1.53
6
30
1.75
1.72
7
35
2.05
2.24
8
40
2.34
2.68
9
45
2.69
3.36
10
50
2.93
3.84
11
55
3.22
4.18
Sr.No.
Load (kN)
Deflection by software in mm
Deflection by experiment in mm
1
5
0.29
0.15
2
10
0.58
0.52
3
15
0.87
0.85
4
20
1.17
1.17
5
25
1.46
1.53
6
30
1.75
1.72
7
35
2.05
2.24
8
40
2.34
2.68
9
45
2.69
3.36
10
50
2.93
3.84
11
55
3.22
4.18
Fig 4. Comparison between FEM analysis results and laboratory testing
results
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Finite element analysis of castellated beam to optimize depth of opening and width of opening
After verifying the finite element model with software model, parametric studies were conducted on the castellated beams. The aim of parametric study is to examine the depth and width of opening which carries the maximum load without failure. The parameters, which are selected for this study, include depth of opening and width of opening. All other dimensions such as depth of parent I beam, thickness of web and flange were kept constant. Finite element analysis was performed for eighteen castellated beams for optimizing depth of opening. Then from that, optimized depth width of opening was optimized. Each study was carried out by varying one parameter while keeping other parameter constant. It should be noted that while doing analysis, the loading condition and support condition were kept same as those adopted for experimentally tested castellated beam
Sr No
D0
D
D/D0
S/D0
Length of opening
Load at yield
Stress (N/mm2)
1
130
165
1.26
1.4
130
25
240
2
120
160
1.33
1.4
120
26
245
3
110
155
1.40
1.4
110
27
258
4
100
150
1.50
1.4
100
30
259
5
90
145
1.61
1.4
90
38
244
6
80
140
1.75
1.4
80
36
246
7
130
165
1.26
1.3
117
22
257
8
120
160
1.33
1.3
108
23
251
9
110
155
1.40
1.3
99
25
259
Sr No
D0
D
D/D0
S/D0
Length of opening
Load at yield
Stress (N/mm2)
1
130
165
1.26
1.4
130
25
240
2
120
160
1.33
1.4
120
26
245
3
110
155
1.40
1.4
110
27
258
4
100
150
1.50
1.4
100
30
259
5
90
145
1.61
1.4
90
38
244
6
80
140
1.75
1.4
80
36
246
7
130
165
1.26
1.3
117
22
257
8
120
160
1.33
1.3
108
23
251
9
110
155
1.40
1.3
99
25
259
Table III. Results of FEM analysis of castellated beam to optimize depth of opening
Fig5. Variation in yield load for different S/D0 and D/D0 for castellated beam
Beam with D/D0 ratio equal to 1.611 and S/D0 ratio equal to
-
takes the maximum load of 38 kN After optimization of depth of opening, Width of opening has been optimized. To optimize whole opening of sinusoidal shape, optimized depth has been taken and width of opening has been varied
Table IV. Results of FEM analysis of castellated beam to optimize width of opening
Sr No
D0
D
D/D0
S/D0
Length of opening
Load at yield
Stress (N/mm2)
1
90
145
1.61
1.4
90
38
244
2
90
145
1.61
1.3
81
34
244.2
3
90
145
1.61
1.2
72
29
244.6
After analysis it is observed that, D/D0 ratio equal to 1.61 and S/D0 ratio equal to 1.4 takes the maximum load of 38 kN. i.e. beam with depth of opening 90mm , overall depth 145mm, length of opening 90 and center to center spacing 126mm takes the maximum load .
-
-
CONCLUSION
Based on analysis of castellated beam with Finite element method and laboratory test, it can be concluded that
-
From laboratory testing results and FEM analysis it is observed that, the deflection obtained from FEM result is 1.170 mm. While deflection from experiment results is 1.172 mm Percentage variation in above case is almost negligible, that is
0.18 percent. The method used for analysis of castellated beam was valid.
-
The optimum condition is obtained at castellated beam with sinusoidal openings with opening size
0.62 times its overall depth with S/D0 ratio 1.4 and D/D0 1.61.
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