Experimental Study on Post Buckling Behaviour of Steel Plate Girder

Transcription

1 GRD Journals- Global Research and Development Journal for Engineering Volume 1 Issue 8 July 2016 ISSN: Experimental Study on Post Buckling Behaviour of Steel Plate Girder Rohit V. Khobaragade Department of Civil Engineering Kavikulguru Institute Of Technology and science,ramtek , Nagpur University P. D. Ramteke Department of Civil Engineering Kavikulguru Institute Of Technology and science,ramtek , Nagpur University Abstract This paper describes three tests on small scale, transversely stiffened plate girder. The objective of the test was to observe collapse mechanism and to study post buckling behavior i.e.in particular to investigate the behavior of the transverse web stiffeners. A problem was selected to choose the dimensions and loads of the plate girder and design can be solved according to clauses of Indian Standers Model analysis technique was used to reduce the dimensions and loads of actual structure. Accordingly three small scale plate girder models were constructed with varying number of stiffeners and with constant dimensions of web, flange and stiffeners. The main objective of this experimental study was to study post buckling behavior. The observation given should facilitate future development of improved method of stiffeners. Keywords- Longitudinal deflection, lateral deflection, web buckling, web crippling, tension field stress I. INTRODUCTION Plate girder is basically an I shape beam constructed from plates using riveting or welding. It is a deep flexural member used to carry loads that cannot be economically carried by rolled beams. Generally rolled beams are used for general structure but in situation where the load is heavier and span is large the plate girder is generally used. The designer has choice to choose component of convenient sizes therefore plate girder offer unique flexibility in fabrication and the cross- section can be uniform or non-uniform along the section. Plate girder provides maximum flexibility and economy in the design of plate girder. For the short span (< 10 m) plate girder are uneconomical due to higher connection cost and hence rolled I-section is generally preferred but the span (> 10 m) and up to the span of 35 m plate girder are economical and used in the railway bridges of span 15 to 40 m and in highway bridges of span 24 to 46 m and also used in building when it is required to support heavy concentrated load exlarge hall. Plate girder are generally composed of compact flanges, slender webs, transverse and longitudinal stiffeners. For efficiency, most plate-girder cross sections are built geometrically similar to wide-flange steel beams, i.e., with top and bottom flanges to resist normal stresses associated with bending moment and a deep web plate to resist resulting shearing forces. The transverse stiffeners are provided vertically and closed to support to increase the bearing resistance and to improve shear capacity. The longitudinal stiffeners provided in horizontal direction to increases the buckling resistance of the web against bending. Rode [1916] developed the first physical explanation for very high shearing capacities of slender plate girder webs. Wagner [1931] developed the theory of uniform diagonal tension field. Basler [1950] was the first to develop a successful plate girder model for tension field action of the type used in civil engineering structure. Wilson [1986] was the first to discover the post buckling behavior of plate girder web panels by studying the slender aluminium shear panels with rigid boundary elements utilized in aircraft structures. Galmbos [1998] developed many theories for the ultimate shear capacity of plate girder. Porter et al introduced Cardiff model in which collapse of girders was related with the emergence of plastic hinges in flanges. Cardiff model was later adopted into the British Standards. Hoglund proposed a simplified rotating stress field theory to simulate stiffened and unstiffened web plates and his theory later introduced into the Eurocode 3. II. DESIGN OF PLATE GIRDER A simply supported welded plate girder having span of 30 m and udl of 30 kn/m and two concentrated load of 150 kn. Each acting at 10 m from both end and having load factor of 1.5, yield stress f y =250 MPa.is selected and design can be solved according to clauses of IS The values obtained from selected problem given below- 1) Maximum bending moment = kn/m 2) Maximum shear force= 990 kn 3) Required flange area = mm 2 4) Assume flange width = 550 mm. 5) Thickness of flange = 40 mm. 6) Section of the flange = mm. 7) Total depth of girder =1680 mm 8) Assume thickness of web = 20 mm. All rights reserved by 32

2 III. MODEL ANALYSIS As the selected span of the model was 30 m and such a large span of structure was not able to test in laboratory. So to reduce the dimensions and loads of actual design structure model analysis technique was used. Generally this technique was used in important problem such as design of long span bridges. The main objective to use this technique was determination of stress value (bending moment, shear force, deflection) and to determine the critical or buckling load and determination of stress distribution, stress pattern in structure. Generally there are two types of model analysis 1) direct model analysis 2) indirect model analysis. In this study direct analysis study was used to scale down the actual structure. The values obtained after scale down the actual structure are given below- By assuming span of the model is 1.5 m. Scale for length k = (L S / L m ) = (30 / 1.5) = 20 A. Selection of Section 1) Approximate depth of girder = 80 mm 2) Required flange area = mm 2 3) Required flange width = 27.5 mm 4) Required thickness of flange =2 mm 5) Section of the flange model is mm 6) Thickness of web = 1 mm B. Factored Load 1) Udl / m = kn/m 2) 1 st concentrated load = kn 3) 2 nd concentrated load = kn 4) Maximum moment = kn/m 5) Maximum shear force = 2.07 kn Fig. 1: Cross section of plate girder model IV. FABRICATION OF MODEL An intermittent fillet weld of thickness 2 to 3 mm and length 40 mm was provided throughtout the length of the girder to join the symmetrical flange plate of thickness 2 mm and web plate of thickness 1 mm. So that whole section can be act as a one unit. Mild Steel plate of thickness 2 mm and depth 80 mm was used as bearing stiffeners and intermediate transverse stiffeners. All rights reserved by 33

3 A. Model 1 st Fig. 2: Plate girder model with intermediate transverse stiffeners at spacing 250 mm B. Model 2 nd - Fig. 3: Plate girder model with alternate intermediate stiffeners at spacing c=d (80 mm) C. Model 3 rd Fig. 4: Plate girder model with intermediate stiffeners at spacing c=d (80 mm) on both side of web V. EXPERIMENTAL TEST ON PLATE GIRDER MODEL The same experimental procedure was applied for model-1,model-2, model-3 i.e. with intermediate transverse stiffeners at spacing 250 mm, alternate intermediate transverse stiffeners at spacing c=d (80 mm) and with intermediate transverse stiffeners at spacing c=d (80mm). A. Longitudinal Deflection 1) One Point Loading It was assumed that the compression flange not moving laterally. To observe the deflection at L/3, 2L/3, L/2 so load was applied centrally and 25 mm dial gauge was attached to below the center of weight hanger. One 10 mm dial gauge was placed at a distance L/3 and attached to bottom width of flange. Second 10 mm dial gauge was placed at a distance 2L/3 and also attached to bottom width of flange. All rights reserved by 34

4 Fig. 5: Experimental setup for one point loading 2) Two Point Loading It was assumed that compression flange not moving laterally. To observes the deflection at L/3, L/2, 2L/3 so loads was applied at a distance of L/3 and 2L/3. One 10 mm dial gauge was placed at distance of L/3 and second at distance 2L/3 and attached to below the center of weight hanger. 25 mm dial gauge was placed at a distance 2L/3 and connected to bottom width of flange. B. Lateral Deflection Fig. 6: Experimental setup for two point loading 1) Flange Displacement It was assumed compression flange moving laterally. In this case load was applied centrally. 25 mm dial gauge was placed at a distance of L /2 and attached to center of upper flange plate thickness. One 10 mm dial gauge was placed at a distance of 650 mm and attached to the center of flange plate thickness and second 10 mm dial gauge was attached exactly opposite of first 10 mm dial gauge. Fig. 7: Experimental setup for flange displacement C. Web crippling It was assumed that compression flange moving laterally. In this case load was applied centrally and 25 mm dial gauge was placed at a distance L/2 and attached at distance of 30 mm from the upper end of web plate. One 10 mm dial gauge was attached at a distance of 15 mm from upper end of web plate and placed just left to center. Second 10 mm dial gauge was attached at a distance of 40 mm from bottom end of web plate and placed just right to the center. All rights reserved by 35

5 Fig. 8: Experimental setup for web crippling D. Web buckling It was assumed that compression flange moving laterally. In this case load was applied centrally and 25 mm dial gauge was placed at a distance of L/2 and attached to center of web plate. One 10 mm dial gauge was placed at one end and attached at a distance of 46 mm from the upper end of web plate. Second 10 mm dial gauge was placed at other end and attached at a distance of 46 mm from lower end of web plate. Fig. 9: Experimental setup for web crippling VI. RESULT AND DISCUSSION When the 1st plate girder model ie intermediate transverse stiffeners at spacing 250 mm was subjected to under transverse loading it can be observed that at the load of 68 kg (0.68 kn) the buckling of web panel near support and under the transverse load was observed. And also the small buckling in the intermediate stiffeners was observed. This is due to the diagonal compression which cause web to buckle. This condition is the pre buckling stage of the girder which indicates the tension field start to develop in the web of the panel. In the pre-buckling stage the web plate developed diagonal tension and diagonal compression, where diagonal tension does not cause any problem but diagonal compression cause to buckle web in a direction perpendicular to its action. As the spacing of the stiffeners was large so the tension field cannot developed fully in web plate and to resist this diagonal compression the stiffeners was provided at spacing of c=d in model-2. Fig. 10: Pre-buckling position of stiffener Fig. 11: Mechanism in panel All rights reserved by 36

6 When 2nd plate girder model i.e. alternate intermediate transverse stiffeners at spacing c=d (80 mm) was subjected to transverse loading the failure of all intermediate stiffeners was observed except the stiffeners at support. Also the failure of compression flange was observed at the load of 75 kg (0.75 kn).this failure of stiffeners and compression flange was due to the tension field stresses developed in the web panel. This tensile membrane stresses exert the pull on the tension and compression flange and causes failure of flange plate. Fig. 12: Failure of compression flange Due to this failure of compression flange the plastic moment capacity of the flanges would be reduced and all the tensional field stress was supported entirely by intermediate stiffeners. This is the post- buckling stage. In which horizontal component of tensional field stress act directly on top and bottom portion of stiffeners. The horizontal component which act on top pull the stiffener one side and component act bottom pull the stiffeners another side. Due to this horizontal component of tensional field stresses the intermediate transverse stiffeners losses its rigidity and hence failure of stiffeners in each panel was observed. Fig. 13: Failure of stiffeners Fig. 14: Mechanism of tension field stress Also during the transverse loading it can be observed that as the intermediate stiffeners was fail but the end bearing stiffeners still remain straight. This is due to mechanism that tension field in panel CD was balanced by tension field in panel BC. Therefore the interior panels are anchored by the neighboring panels. The end panels have no anchorage and hence tensional field stress was not developed in the end panel and end bearing stiffeners remain straight. Fig. 15: Mechanism of tension field in end panel When 3rd plate girder model i.e. with intermediate transverse stiffeners at c=d (80 mm) on both side of web was subjected to transverse loading it was observed that as load was continuously increases up to 82 kg (0.82 kn) this stiffeners still remain straight i.e. this newly attached stiffeners not losses its rigidity. Therefore failure not takes places. This means that newly All rights reserved by 37

7 provided stiffeners plays a very critical role in achieving the ultimate load capacity of girder and it increases the web buckling stresses, support tension field in the web in the post buckling stages and finally prevent the flanges from failure. Graph was plotted from the obtained dial gauge reading which showing comparison of longitudinal deflection, lateral deflection, web crippling and web buckling shown below. From the graph it was observed that as no of stiffeners increases the deflection, lateral movement, crippling and buckling in girder was reduced. Also from the dial gauge reading it was observed that the web crippling was takes place girder at a distance of 30 mm from bottom of web plate and this crippling dial gauge values were compared with the web buckling values from that it was observed that web crippling was more critical as compared to web buckling. Fig. 16: Comparison on one Point Loading Fig. 17: Comparison on Two Point Loading Fig. 18: Comparison on Flange Displacement Fig. 19: Comparison on Web Crippling Fig. 20: Comparison on Web Bucklng Value All rights reserved by 38

8 VII. CONCLUSION The results obtained from these three tests on small- scale girder enables the following conclusion to be drawn 1) Under the transverse load bending takes places in the plane of the loading. 2) Under transverse load lateral torsional buckling occur which reduce the bending capacity of the girder. 3) Under transverse load compressive stresses are formed which reduced the shear capacity of the web. 4) Under the transverse load bending stresses are formed which reduced plastic moment resistance of flange. 5) Under transverse load diagonal compressive stresses are formed which cause buckling of web panel at support and under transverse load. 6) Under transverse load tension field stresses are formed in web panel to cause failure of flange which reduced plastic moment resistance. 7) Under transverse load tension field stress act directly on the stiffeners which cause reduce the rigidity of stiffeners. REFERENCES [1] Alinia M. M., Gheitasi A. and Shakiba M. (2011). Post buckling and ultimate state of stresses in steel plate girder, Thin-walled structures 49, Science Direct, [2] De Bejar L. A. and Younis M. A. (1991). Shear strength of open-web plate girders with inclined tension bars, Journal of Engineering Mechanics, ASCE (26398), [3] Franc S. (2013). Moment-shear interaction of stiffened plate girder Test and numerical model verification, journals of constructional steel research 85, Science Direct, [4] Graciano C. and Uribe-Henao A.F. (2014). Strength of steel I-girder subjected to eccentric patch loading, journals of engineering structure 79, Science Direct, [5] Hassanein M. F. and Kharoob O. F. (2013). Shear capacity of stiffened plate girder with compression tubular flanges and slender webs, Thin-wall structure 70, Science Direct, [6] Hwang S. C., Kyou H. and Tagawa Y. (2004). Study on elastic rigidity of composite girder in steel structure, 13World Conference on Earthquake Engineering, Canada, 400. [7] Linzell D. G. and Geschwindner L.F.(2013). Computational studies of horizontally curved, longitudinally stiffened, plate girder web in flexure, journals of constructional structure 93, Science Direct, [8] Lucic D. (2003). Experimental research on I-girders subjected to eccentric patch loading, Journal of Constructional Steel Research 59, Science Direct, [9] Tang K. H. and Evans H. R. (1984). Transverse stiffeners for plate girder webs-an experimental study, Journal of Constructional Steel Research 4, [10] Chacon R., Serrat M.and Real E. (2012). The influence of structural imperfections on the resistance of plate girders to patch loading, Thin-walled structures 53, Science Direct, [11] IS 800: 2007 General construction in steel-code of practice (Third Revision). All rights reserved by 39