DOI : 10.17577/IJERTCONV4IS30016
- Open Access
- Total Downloads : 10
- Authors : Mayuri Patil, Vidhi Janbandhu
- Paper ID : IJERTCONV4IS30016
- Volume & Issue : IC-QUEST – 2016 (Volume 4 – Issue 30)
- Published (First Online): 24-04-2018
- ISSN (Online) : 2278-0181
- Publisher Name : IJERT
- License:
This work is licensed under a Creative Commons Attribution 4.0 International License
CFSM and GBT: Elastic Buckling Behaviour and Capacity of CFS Purlins and Girts Under Uplift Loading Condition
Mayuri Patil1
1Post Graduate persuingStudent,
Department of Civil Engineering,G.H. Raisoni College of Engineering, (An autonomous institute).
Vidhi Janbandhu2
2Post Graduate persuingStudent,
Department of Civil Engineering,G.H. Raisoni College of Engineering, (An autonomous institute).
Abstract:- Objective of this work is to study the elastic buckling behavior and load carrying capacity of purlins and girts. 30 specimens including both C and Z sections are chosen from literature survey especially from research work of TianGao. For these sections buckling behavior is studied using CUFSM and GBTUL software and load factor is compared with that obtained from experimental study of TianGao. Lateral restraint of sheeting is introduced as springs in analytical study and behavior observed. For purlins author did not included orientation of purlin as criteria, in this study orientation of purlin also included as prime factor. Based on CUFSM and GBTUL analytical result design capacity of purlins and girts are obtained and compared with experimental studies from literature.
Keywords: CUFSM, GBTUL, failure modes, rotational restraint, purlin orientation
-
INTRODUCTION
Cold formed steel sections are thin sections made out of thin sheets of steel by rolling or press braking method in cold state. These sections are having uniform thickness. These sections are also called Light Gauge Steel Sections or Cold Rolled Steel Sections. Cold formed steel is used as secondary structural members like purlins and girts.Cold formed steel sections are thin in cross section and fails by buckling prior to yielding. Different modes of failure are observed in cold formed steel like local buckling, distortional buckling and lateral distortional buckling. [1]
1.1. FOCUS ON STUDY
The main aim is to study the behaviour of purlins and girts under uplift condition in metal roof construction with considering rotational restraint due to roof covering sheet profile. An extension of research work by TianGao. [4][5]
1.1.1. Rotational Restraint
Roof covering sheets creates restraint to compression flange of purlin and cladding provides restraint to flanges of girts. Rotational restraint creates behaviour differ both in purlins and girts as mode of failure changes. In AISI method rotational restraint is not taken in to consideration for design purpose. TianGao initiated research in considering rotational restraint in metal roof construction. Shear flow generated because of major axis bending causes the section to rotate. TianGao conducted experiments [4] to predict R factor to determine yield moment in AISI method and found experimental results comes nearer to predicted result. Predicted stiffness value is based on considering rotation of specimen as deflection of cantilever beam. Flange connecting with roof covering sheet becomes fixed end and another flange is free end. TianGao also conducted flexural experiment to estimate the strength of purlins and girts and also to examine failure modes like failure of screw and failure of cladding sheet by creating suction pressure as uniform load.
-
METHODOLOGY
From the experimental study conducted by TianGao [4][5] 30 specimens were chosen to conduct parametric study. As initial part of study 10specimens were taken and studied their parameters using CUFSM and GBTUL Software. CUFSM software is based on Finite Strip Method (FSM). The best known of numerical methods developed for analyzing cold formed steel sections based on the separation of variables is perhaps the Finite Strip Method. Finite Strip Method is quite economical with respect to the computational efficiency. The Finite Strip Method can be considered as a specialization of FEM. Unfortunate
Table I Section Properties Zed profile
S.NO
Test Name
CROSS SECTION – Zed Profile
fy (N/sq.m
m)
COMPRESSION FLANGE
TENSION FLANGE
B (mm)
D
(mm)
(deg.)
(deg.)
B
(mm)
D
(mm)
(deg.)
(deg.)
H (mm)
r (mm)
t (mm)
1
Z200D-2
68.4
26.4
92
47
72.5
27.5
92
53
202
6.6
2.59
420
2
Z250B-1
71.7
21.1
91
55
72.9
22.1
90
47
253
5.9
1.51
401
3
Z200D-R100-1
67.9
25.2
90
48
67.9
27.6
90
53
205
5.7
2.54
428
4
Z200D-TH25-2
66.1
26.3
90
47
69.4
26.3
89
53
205
6.3
2.54
418
5
Z250B-TH100-1
68
18
90
53
72.9
20
88
45
254
5.1
1.52
388
Table II Section Properties Zed profile
S.NO
Test Name
CROSS SECTION – Channel Profile
fy (N/sq.m
m)
COMPRESSION FLANGE
TENSION FLANGE
B (mm)
D
(mm)
(deg.)
(deg.)
B
(mm)
D
(mm)
(deg.)
(deg.)
H (mm)
r (mm)
t (mm)
1
C200D-1
65.2
21.3
92
90
65
21.7
92
90
203
5.1
2.57
522
2
C200D-TH25-1
63.8
21
93
90
64.5
21
93
90
203
4.8
2.57
525
3
C200D-TH50-1
61.5
21.2
91
90
62.8
20.2
91
90
203
4
2.58
514
4
C250D-TH25-1
63.1
21.2
89
90
63.2
20.9
89
90
254
4.3
1.49
411
5 C250D-TH100-1
64.1
19.7
90
89
65.2
18.9
90
89
254
4.4
1.5
417
the applicability of the FSM to various geometries or boundary loading conditions introduced is weak. In the buckling analysis of thin walled beams using the FSM difficulties are experienced for example when dealing with non-periodic buckling modes or shapes with high gradients. The Finite Strip Method is so named, because only a single element (strip) is used to model the longitudinal direction.
S.No
Test Name
Stiffness value K Nmm/rad/mm
1
Z200D-2
1339
2
Z250B-1
1342
3
Z200D-R100-1
994
4
Z200D-TH25-2
1339
5
Z250B-TH100-1
1342
6
C200D-1
941
7
C200D-TH25-1
941
8
C200D-TH50-1
941
9
C250D-TH25-1
1151
10
C250D-TH100-1
1151
[3] GBTUL is based on Generalized Beam Theory. Generalized Beam Theory is an extension to conventional engineering beam theory that allows cross-section distortion to be considered. Stability analysis of thin-walled members may also be performed using GBT. GBT was originally developed by Schardt in Germany, then extended by Davies. Currently, no code exists in the public domain for the application of GBT. However, Camotim and Silvestre have recently supplied code focusing on distortional buckling of C and Z sections common in cold- formed steel. A particular advantage of this implementation is the ability to consider the impact of different end conditions.[2]Both considering rotational restraint and neglecting rotational restraint were taken different cases of main study. As TianGao not extended research up to analytical study but limited to experimental study, here analytical studies were focused. TianGao not considered the roof angle while studying purlin parameters which also considered here.S.No
Test Name
Stiffness value K Nmm/rad/mm
1
Z200D-2
1339
2
Z250B-1
1342
3
Z200D-R100-1
994
4
Z200D-TH25-2
1339
5
Z250B-TH100-1
1342
6
C200D-1
941
7
C200D-TH25-1
941
8
C200D-TH50-1
941
9
C250D-TH25-1
1151
10
C250D-TH100-1
1151
Table III Stiffness value
Table IV Section Properties and Yield Moment
Test Name
Area A
mm2
Section Modulus Z mm3
1
Z200D-2
1112.70
68497.92
2
Z250B-1
721.54
86445.04
3
Z200D-R100-1
1066.77
69431.99
4
Z200D-TH25-2
1072.57
69571.28
5
Z250B-TH100-1
693.54
84093.49
6
C200D-1
1034.83
68768.31
7
C200D-TH25-1
1023.09
68694.57
8
C200D-TH50-1
1002.38
68155.43
9
C250D-TH25-1
664.45
84678.51
10
C250D-TH100-1
669.15
84855.49
Table V CUFSM Girts and Purlins Zed and Channel profile with roof angle as zero without rotational restraint
S.
No
Test Name
Crippling Moment McrKNm
Local
Distort ional
Glob al
1
Z200D-2
35.09
16.68
1.72
2
Z250B-1
15.25
8.31
0.34
3
Z200D-R100-1
38.33
17.83
0.29
4
Z200D-TH25-2
38.67
16.86
0.29
5
Z250B-TH100-1
16.31
7.83
0.32
6
C200D-1
48.45
25.84
0.35
7
C200D-TH25-1
50.84
27.04
0.36
8
C200D-TH50-1
55.35
29.42
0.35
9
C250D-TH25-1
21.22
17.05
0.34
10
C250D-TH100-1
21.93
16.27
0.35
Table VI CUFSM Girts and Purlins Zed and Channel profile with roof angle as zero with rotational restraint
S.
No
Test Name
Crippling Moment McrKNm
Local
Distort ional
Global
1
Z200D-2
35.09
16.68
12.94
2
Z250B-1
15.25
8.66
10.05
3
Z200D-R100-1
38.33
18.12
13.67
4
Z200D-TH25-2
38.67
17.15
13.66
5
Z250B-TH100-1
16.31
8.15
7.83
6
C200D-1
48.45
26.19
19.73
7
C200D-TH25-1
50.84
27.40
19.83
8
C200D-TH50-1
55.34
29.42
19.61
9
C250D-TH25-1
21.22
17.40
10.78
10
C250D-TH100-1
21.93
16.27
10.61
Figure 1: Z200D2 Local Buckling without restraint
S.
No
Test Name
Crippling Moment McrKNm
Local
Distort ional
Global
1
Z200D-2
45.16
28.19
0.28
2
Z250B-1
14.90
14.21
<>0.34 3
Z200D-R100-1
46.66
29.42
0.29
4
Z200D-TH25-2
47.69
27.91
0.29
5
Z250B-TH100-1
15.33
12.72
0.32
6
C200D-1
67.83
27.99
0.35
7
C200D-TH25-1
70.32
28.48
0.36
8
C200D-TH50-1
74.26
30.12
0.35
9
C250D-TH25-1
22.27
16.74
0.34
10
C250D-TH100-1
22.28
15.92
0.35
Table VII CUFSM Purlins Zed and Channel profile with roof angle as 10 degrees without rotational restraint
Table VIII CUFSM Purlins Zed and Channel profile with roof angle as 10 degrees with rotational restraint
S.
No
Test Name
Crippling Moment McrKNm
Local
Distort ional
Global
1
Z200D-2
45.16
28.77
12.08
2
Z250B-1
14.90
14.55
7.97
3
Z200D-R100-1
46.66
30.01
11.88
4
Z200D-TH25-2
47.69
28.49
12.50
5
Z250B-TH100-1
15.33
13.04
6.52
6
C200D-1
67.83
27.99
16.51
7
C200D-TH25-1
70.32
28.48
16.22
8
C200D-TH50-1
74.26
30.47
16.11
9
C250D-TH25-1
22.27
17.05
8.35
10
C250D-TH100-1
22.28
16.27
8.13
Figure 2: Z200D2 Distortional Buckling without restraint
Table IX CUFSM Purlins Zed and Channel profile with roof angle as 15 degrees without rotational restraint
S.
No
Test Name
Crippling MomentMcrKNm
Local
Distort ional
Global
1
Z200D-2
45.45
28.48
0.86
2
Z250B-1
13.86
14.21
0.35
3
Z200D-R100-1
45.47
30.31
0.29
4
Z200D-TH25-2
45.36
28.78
0.29
5
Z250B-TH100-1
15.00
13.04
0.32
6
C200D-1
66.03
29.07
0.35
7
C200D-TH25-1
67.79
29.20
0.36
8
C200D-TH50-1
70.06
29.07
0.35
9
C250D-TH25-1
19.14
16.70
0.34
10
C250D-TH100-1
22.64
15.92
0.35
S.
No
Test Name
Crippling MomentMcrKNm
Local
Distorti onal
Global
1
Z200D-2
45.45
29.05
12.65
2
Z250B-1
13.86
14.21
7.62
3
Z200D-R100-1
45.47
30.91
11.88
4
Z200D-TH25-2
45.36
29.37
11.62
5
Z250B-TH100-1
15.00
13.37
6.85
6
C200D-1
66.03
29.42
16.15
7
C200D-TH25-1
67.79
29.56
16.22
8
C200D-TH50-1
70.06
29.42
15.76
9
C250D-TH25-1
19.14
16.70
8.00
10
C250D-TH100-1
22.64
16.27
8.49
S.
No
Test Name
Crippling MomentMcrKNm
Local
Distorti onal
Global
1
Z200D-2
45.45
29.05
12.65
2
Z250B-1
13.86
14.21
7.62
3
Z200D-R100-1
45.47
30.91
11.88
4
Z200D-TH25-2
45.36
29.37
11.62
5
Z250B-TH100-1
15.00
13.37
6.85
6
C200D-1
66.03
29.42
16.15
7
C200D-TH25-1
67.79
29.56
16.22
8
C200D-TH50-1
70.06
29.42
15.76
9
C250D-TH25-1
19.14
16.70
8.00
10
C250D-TH100-1
22.64
16.27
8.49
Table X CUFSM Purlins Zed and Channel profile with roof angle as 15 degrees with rotational restraint
Figure 3: Z200D2 Global Buckling without restraint
Table XI GBTUL Girts and Purlins Zed and Channel profile with roof angle as zero without rotational restraint
S.
No
Test Name
Crippling Moment McrKNm
Local
Distorti onal
Global
1
Z200D-2
16.58
10.44
1.8
2
Z250B-1
54.37
8.94
3.53
3
Z200D-R100-1
15.94
10.43
0.50
4
Z200D-TH25-2
17.87
8.94
3.53
5
Z250B-TH100-1
73.90
8.94
3.53
6
C200D-1
8.47
5.16
0.69
7
C200D-TH25-1
17.87
8.94
3.53
8
C200D-TH50-1
26.38
9.32
0.35
9
C250D-TH25-1
5.13
3.29
0.11
10
C250D-TH100-1
5.60
2.79
0.12
Table XII GBTUL Girts and Purlins Zed and Channel profile with roof angle as 10 degrees without rotational restraint
S.
No
Test Name
Crippling Moment McrKNm
Local
Distorti onal
Global
1
Z200D-2
15.80
10.04
0.54
2
Z250B-1
2.82
2.82
0.40
3
Z200D-R100-1
16.14
10.51
0.50
4
Z200D-TH25-2
16.79
9.50
0.49
5
Z250B-TH100-1
2.98
2.33
0.23
6
C200D-1
25.68
8.42
0.37
7
C200D-TH25-1
26.21
8.41
0.36
8
C200D-TH50-1
26.55
8.82
0.35
9
C250D-TH25-1
4.90
2.98
0.11
10
C250D-TH100-1
5.33
2.79
0.12
Figure 4: Z200D2 Local buckling with restraint
Table XIII GBTUL Girts and Purlins Zed and Channel profile with roof angle as 15 degrees without rotational restraint
S.
No
Test Name
Crippling Moment McrKNm
Local
Distorti onal
Global
1
Z200D-2
17.17
10.38
0.54
2
Z250B-1
2.83
2.75
0.24
3
Z200D-R100-1
15.74
10.70
0.50
4
Z200D-TH25-2
17.02
9.73
0.49
5
Z250B-TH100-1
2.98
2.33
0.23
6
C200D-1
24.69
8.49
0.37
7
C200D-TH25-1
25.84
8.77
0.36
8
C200D-TH50-1
27.53
8.33
0.35
9
C250D-TH25-1
4.99
2.85
0.11
10
C250D-TH100-1
5.31
2.77
0.12
Figure 5: Z200D2Distortional Buckling with restraint
Figure 6: Z200D2 Global buckling with restraint
Figure 7: Z200D2 Buckling curve with rotational spring and excluding rotational spring
Figure 8: Z200D2 Buckling curve-GBTUL
Figure 9: Z200D2 Modal Participation Diagram-GBTUL
-
RESULTS AND DISCUSSION
As from the analytical study it is evident that inclusion of rotational restraint resulted in increase of section capacity for the same cross section and orientation. For girts, the half wave length obtained from CUFSM used to interpolate buckling load from GBTUL in order to correlate the buckling behaviour at same length. Including rotational restraint in girts results in increase of strength in global buckling mode almost several folds of rotationally
unrestrained girt sections. Section Z200D2 shown capacity increase of global buckling strength from 1.74KNm to 16.42KNm. Most of the girt section showed enhanced strength. In case of purlins orientation of purlins included as a prime factor for analytical study and roof angle range fixed from practical existing structures from 10 degrees to 26 degree 30minutes. In this parametric study 10 degree and 15 degree were taken as orientation of purlins and showed enhanced strength compared to flat placed purlin section. As purlins are generally placed inclined based on roof angle which also changes based on type of truss, it is found orientation also influence capacity and buckling mode of purlin sections. From the analytical result capacity of sections increase by 20% when orientation changes positive in CUFSM and strength not enhanced in GBTUL. Orientation changes in purlin specimens while analyzing in GBTUL some sections showed local buckling in top flange instead bottom causing strength reduction.
-
FUTURE WORK
As of now 10 specimens were analyzed using CUFSM and GBTUL software for Behaviour study under influence of rotational restraint on capacity of cold formed steel purlins and girts and influence of roof angle. In further work another 20 specimens with different boundary condition are to be analyzed and conclusion to be arrived after comparing analytical results with values from experimental study and codal provisions as well.
REFERENCES
-
Ãdány S, Silvestre N, Schafer B.W. andCamotim D. GBT AND cFSM: Two Modal Approaches To The Buckling Analysis Of Unbranched Thin-walled Members Advanced Steel Construction Vol. 5, No. 2, pp. 195-223 (2009)
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Pedro Natario, NunoSilvestre, Dinar Camotim Localized web buckling analysis of beams subjected to concentrated loads using GBT, Thin-Walled Structures 61 (2012) 2741
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Schafer BW, Adany S. Buckling analysis of cold-formed steel members using CUFSM: conventional and constrained finite strip methods. In: Eighteenth International Specialty Conference on Cold-Formed Steel Structures, Orlando, Florida; 2006
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TianGao , Cristopher D. Moen Flexural strength experiments on exterior metal building wall assemblies with rigid insulation,
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TianGao, Cristopher D.Moen, Predicting rotational restraint provided to wall girts and roof purlins by through-fastened metal panels Thin-Walled Structures 61 (2012) 145153