Pál Vásárhelyi Doctoral School of Civil Engineering and Earth Sciences 

Department of Structural Engineering

Supervisor: Dr. Dunai László

Steel Trapezoidally Corrugated Web Girders – Stability Behavior and Design

Introducing the research area

Due to the improvements in the production technology, in the mathematical background of the numerical simulations and in the hardware capacity new structural layouts can be studied economically without using expensive experimental testing and measurements.

The structural behavior of trapezoidally corrugated web girders significantly differs from the structural behavior of flat web I-girders¹ [1-3] for which the conventional beam theory² is valid. From the point of view of the static system the periodic waving of the web along the girder length (Figure 1) borrows numerous favorable properties [4-6], however, due to the increased design parameters it could not have been studied in detail until now, since the earlier investigation methods do not provide economic solutions and sufficient accuracy. Thus the international literature lacks the investigation of the response of the structure subjected to different internal forces and the combination of different internal forces (combined loading³ situation). As a result, design proposals are not available for structural engineers on several loading conditions and structural layouts. The local and international trends, however, confirm the need for the application of the new structural layouts in design praxis due to material-consumption reasons.

 

a) industrial hall [7]                                                      b) bridge, Japan

Figure 1: Application of steel corrugated webs

 

Brief introduction of the research place

The research work is performed in a research group at the BME Department of Structural Engineering⁴ under the guidance of Dr. László Dunai. The experimental testing was completed in the Structural Laboratory of the Department⁵. The Department participates in the activities of the standardization working groups⁶ being responsible for the development of the new generation European standards for steel structures. Regarding corrugated web girders, two standards are involved: the plated structural elements and the brand new numerical model-based design standard which is being developed under the guidance of Dr. László Dunai. My researches also contribute to the development of the new European standards.

 

History and context of the research

The application of trapezoidally corrugated webs in steel girders raises several questions in the structural engineering praxis. In the case of bridges, the construction method greatly influences the main internal forces in the structure. In the case of incremental launching⁷ of a bridge superstructure and in the case of a continuous beam the girder is subjected to the combination of different internal forces that can lead to stability problems⁸ of slender steel structures. Figure 2 shows the internal forces along the girder length during the critical phase of incremental launching. In this construction phase the girder is just about to reach the next pier and subjected to a large cantilever bending moment (M) with large accompanying shear force (V) and transverse force (F) at the previous pier.

In literature, design proposals are provided only for the determination of the shear buckling [8] and transverse force resistances [9] of trapezoidally corrugated web girders, however, resistance models for the determination of the bending moment and the interaction resistance under the combination of the aforementioned internal forces are not available. In lack of these proposals only girders with stocky plates strengthened by vertical stiffeners can be designed which is unfavorable from point of view of material consumption and direct labor need. Figure 2 presents a Chinese bridge being under construction, where large number of vertical stiffeners is placed against the transverse force caused by the support reaction. For the reduction of the plate thicknesses and the number of stiffeners, a comprehensive research study need to be performed.

 

Figure 2: Incremental launching: a) internal forces and b) strenghtening⁹

 

The research goals, open questions

The purpose of my research work was to understand the structural behavior of trapezoidally corrugated web girders and to develop new applicable design procedures. The European trends in the steel standards improvements involve two directions in the design procedures: (i) conventional, semi-empirical design resistance models and (ii) new, numerical simulation-based design procedures, which are collected in different standards. My research focuses on the development of both – harmonized with each other – European standard conform design procedures. When developing the design procedures, the geometric parameter ranges applied in the praxis and beyond had to be determined first. So a new database containing the geometric parameters of more than 2000 existing bridge and building girders with corrugated webs was developed. The research work had to address the following problem areas:

1)   It is known [10, 11] that the periodic waving of the web panel along the girder length causes additional normal stresses in the flanges that can lead to capacity decrease. Thus, at first, the stress distributions had to be investigated in the elastic state¹⁰ of the girder.

2)    Analysis of the pure bending moment resistance especially for slender flanges where the failure occurs by the buckling of the flange prior to the strength failure of the material [12, 13].

3)  At zones undisturbed from the support reaction (transverse force), the girder is subjected to combined bending moment and shear force for which interaction resistance shall be investigated. Consequently, the amount of decrease in the bending moment and shear buckling resistance shall be determined that is expected if both effects act simultaneously [14, 15].

4)  At the support regions, the girder is subjected to the combination of large bending moment, shear force and transverse force. The extent of the reduction effect of the transverse force on the bending moment and on the shear buckling resistances has to be evaluated.

Figure 3 presents the typical failure modes under different internal forces. From left to right: (a) plate buckling of the compression slender flange under pure bending moment, (b) shear buckling of the corrugated web panel under shear force and (c) web crippling of the corrugated web panel under transverse force.

 

Figure 3: Pure failure modes: a) bending, b) shear and c) transverse force

 

Methods

To achieve the research purposes, experimental testing, numerical simulations¹¹ (virtual testing) and analytical investigations were applied. Numerical simulations significantly reduce the number of experimental test specimens, which makes the research work more efficient. At the same time, a number of experiments is required to provide sufficient test specimens for the determination of production and assembly originated imperfections so that they can implemented into the numerical model. By giving prescriptions for the imperfections, material model and approximations in the mathematical description between the reality and model, a new numerical simulation-based design procedure can be developed. The investigations regarding different loading conditions have been performed according to the developed methodology below:

(i)  Design of the experimental test specimens by preliminary numerical simulations;

(ii) Execution and evaluation of the experimental tests with special focus on the imperfections (geometric and material deviations from production), material properties, structural behavior, performance and failure mode;

(iii) Development of an advanced numerical model with special focus on the application of the real material properties, initial geometric imperfections and residual stresses – from rolling, cutting and welding;

(iv) Development of the numerical simulation-based design procedure considering the imperfections originated from production and assembly and the material and geometric nonlinearities;

(v)  Execution of the numerical study on an extended parameter domain using the advanced numerical model in order to investigate the structural behavior in detail;

(vi) Evaluation of the numerical simulations’ results and development of the new semi-empirical design resistance models, defining the range of applicability based on theoretical considerations.

 

Figure 4: Solution strategy

 

Results

1)  The results of the stress analysis show that due to the web corrugation additional normal stresses arise in the flanges in addition to the stresses appearing in the conventional flat web girders. The alteration of the additional normal stresses follows the corrugation of the web panel. The amplitude of the normal stresses depends on the support conditions, load type and introduction place, the number of corrugations and the lateral supports. The left side of Figure 5 presents an example for the alteration of the additional stresses. Using the results of the experimental and numerical investigations a new mechanical model based design procedure is developed for the determination of the additional normal stresses in the flanges (right side of Figure 5) [s2, s3]. The standardization committee decided to implement the developed mechanical model in the new European standard for plated structural elements.

Figure 5: Additional stresses along the girder length and the developed mechanical model

 

2)  In the case of trapezoidally corrugated web girders with slender flanges the failure mode under pure bending can be the buckling of the flange before the strength failure of the material. Experimental and numerical investigations pointed out that the flange buckling resistance significantly depends on the corrugation profile of the web and on the quality of the web-to-flange junction (left side of Figure 6). Based on the results foremost numerical simulation-based and conventional semi-empirical (right side of Figure 6) design procedures have been developed [s4-s6].

 

Figure 6: Flange buckling analysis and the developed semi-empirical design procedure

 

3)  The experimental and numerical investigations unanimously verified that under the combined bending and shear interaction both, the bending and shear buckling, resistances can be mobilized with their maximum value. The simultaneous effect of the two different internal forces do not result in overall resistance reduction. It could be attributed to the so called accordion effect that the shear force is carried by the corrugated web and the bending moment is carried by the flanges alone, since the web behaves as an accordion to the axial forces and as a stiffened plate to the vertical forces. Left side of Figure 7 presents the stress analysis coupled with capacity analysis and the right side of Figure 7 presents the typical responses of the structure under different bending-shear utilizations. Based on results a numerical simulation-based and a conventional semi-empirical design procedures have been developed [s1, s7, s8] which are implemented into the new European standards for steel structures.

 

Figure 7: Bending-shear interaction analysis

 

4)   The experimental and numerical investigations of the support regions show that the bending and shear buckling resistances are significantly reduced due to the presence of the support reaction (transverse force). It justifies the application of several vertical stiffeners and stocky plates due to the lack of design proposals. Based on the results suggestions are provided for applicable corrugation profiles and plate thicknesses if vertical stiffeners are not used. By these proposals the labor work and material consumption can be significantly reduced. The left side of Figure 8 presents typical combined web crippling and shear buckling failure modes of the web panel. By the results foremost numerical simulation-based and conventional semi-empirical (right side of Figure 8) design procedures have been developed and published for the interaction check [s9-s12].

 

Figure 8: Bending, shear and transverse force interaction analysis and the developed design procedure

 

Expected impact and further research

The extended use of trapezoidally corrugated web girders is promoted by the standardized new design procedures. The abovementioned results have been published and new researches have been started since the previous results verified that by the application of the corrugated web the dead load of the structure can be reduced beside the improvement of the performance of the structure. Currently I am focusing on the investigation of steel-concrete composite and hybrid structures with trapezoidally corrugated web being applicable for small and medium spans (20–100 m) by experimental and numerical background in the frame of an R&D project [s13-s15]. In the case of steel-concrete structures the composition of the two materials having different time-dependent behavior¹² is of high importance. In addition, design method improvements are being focused on the bending-shear interaction behavior of conventional welded I-girders having unstiffened and longitudinally stiffened flat webs [s16-s20].

 

Publications, references, links

Number of publications: 23, cumulated impact factor: 18.95, number of independent citations: 38

 

List of corresponding own publications.

[s1] Kövesdi, B., Jáger, B., Dunai, L., Girders with trapezoidally corrugated webs subjected to combined bending and shear, Report for the ECCS TWG 8.3 meeting, November 8, 2013, Zürich, Switzerland, pp. 1-20. (2013)

[s2]   Kövesdi, B., Jáger, B., Dunai, L., Stress distribution in the flanges of girders with corrugated webs, Journal of Constructional Steel Research, 79, pp. 204-215. (2012)

[s3]    Kövesdi, B., Jáger, B., Dunai, L., Stress distribution in the flanges of corrugated web girders, Report for the ECCS TWG 8.3 meeting, November 11, 2011, Stuttgart, Germany, pp. 1-20. (2011)

[s4]   Jáger, B., Dunai, L., Kövesdi, B., Flange buckling behavior of girders with corrugated web Part I: Experimental study, Thin-Walled Structures, 118, pp. 181-195. (2017)

[s5]    Jáger, B., Dunai, L., Kövesdi, B., Flange buckling behavior of girders with corrugated web Part II: Numerical study and design method development, Thin-Walled Structures, 118, pp. 238-252. (2017)

[s6]    Jáger, B., Kövesdi, B., Dunai, L., Flange buckling resistance of trapezoidal web girders, Experimental and numerical study, Proceedings of the 8^th European Conference on Steel and Composite Structures, EUROSTEEL 2017, September 13-15, 2017, Copenhagen, Denmark, p. 10. (2017)

[s7]    Kövesdi, B., Jáger, B., Dunai, L., Bending and shear interaction behaviour of girders with trapezoidally corrugated webs, Journal of Constructional Steel Research, 121, pp. 383-397. (2016)

[s8]  Jáger, B., Dunai, L., Flange buckling behavior of trapezoidally corrugated web girders subjected to bending and shear interaction, Proceedings of the Annual Stability Conference, April 10-13, 2018, Baltimore, MD, USA, p. 13. (2018)

[s9]  Jáger. B., Dunai, L., Kövesdi, B., Girders with trapezoidally corrugated web subjected by combination of bending, shear and patch loading, Thin-Walled Structures, 96, pp. 227-239. (2015)

[s10] Jáger, B., Kövesdi, B., Dunai, L., Trapézlemez gerincű tartók interakciós viselkedésének vizsgálata, Proceedings of the XII. Hungarian Conference on Mechanics, MAMEK, August 25-27, 2015, Miskolc, Hungary, p. 10. ISBN 978-615-5216-74-9. (2015)

[s11] Jáger, B., Dunai, L., Kövesdi, B., Experimental based numerical modelling of girders with trapezoidally corrugated web subjected to combined loading, Proceedings of the 7^th International Conference on Coupled Instabilities in Metal Structures, CIMS2016, November 7-8, 2016, Baltimore, Maryland, USA, p. 14. (2016)

[s12] Jáger, B., Dunai, L., Kövesdi, B., Experimental investigation of the M-V-F interaction behavior of girders with trapezoidally corrugated web, Engineering Structures, 133, pp. 49-58. (2017)

[s13] Käferné Rácz, A., Jáger, B., Kövesdi, B., Dunai, L., Lateral torsional buckling resistance of trapezoidally corrugated web girders, Proceedings of the 20^th International Conference on Design and Analysis in Structural Engineering, April 19-20, 2018, New York, NY, USA, p. 6. (2018)

[s14] Jáger, B., Németh, G., Kovács, N., Kövesdi, B., Kachichian, M., Push-out tests on embedded shear connections for hybrid girders with trapezoidal web. Proceedings of the 12^th International Conference on Advances in Steel-Concrete Composite Structures, ASCCS 2018, June 27-29, 2018, Universitat Politècnica de València, València, Spain, p. 8. (2018)

[s15] Németh, G., Jáger, B., Kovács, N., Kövesdi, B., Trapézlemez gerincű hibrid tartók beágyazott nyírt kapcsolatának push-out tesztes vizsgálata, Nemzetközi Építéstudományi Konferencia, ÉPKO2018, May 31 – June 3, 2018, Csíksomlyó, Romania, p. 4. (2018)

[s16] Jáger, B., Kövesdi, B., Dunai, L., Vékonygerincű I-tartók M-V kölcsönhatásos viselkedésének vizsgálata – EC3 fejlesztés, A BME Hidak és Szerkezetek Tanszék Tudományos Közleményei: Tassi Géza és Orosz Árpád 90 éves, Budapest, Hungary, pp. 59-66. (2016)

[s17] Jáger, B., Kövesdi, B., Dunai, L., I-girders with unstiffened slender webs subjected by bending and shear interaction, Journal of Constructional Steel Research, 131, pp. 176-188. (2017)

[s18] Jáger, B., Kövesdi, B., Dunai, L., Bending and shear buckling interaction behaviour of I-girders with longitudinally stiffened webs, Journal of Constructional Steel Research, 145, pp. 504-517. (2018)

[s19] Jáger, B., Kövesdi, B., Dunai, L., I-girders with unstiffened slender webs subjected to combined bending and shear, Report for the ECCS TWG 8.3 meeting, February 25, 2016, Stuttgart, Germany, pp. 1-21. (2016)

[s20] Jáger, B., Kövesdi, B., Dunai, L., Bending and shear buckling interaction of I-girders with slender web, Proceedings of the 8th International Conference on Thin-Walled Structures, ICTWS2018, July 24-27, 2018, Lisbon, Portugal, p. 20. (2018)

Table of links.

1.    https://en.wikipedia.org/wiki/I-beam

2.    https://en.wikipedia.org/wiki/Euler%E2%80%93Bernoulli_beam_theory

3.    https://en.wikipedia.org/wiki/Stress_(mechanics)

4.    http://hsz.bme.hu/node/1249?language=en

5.    https://hsz.bme.hu/hsz/labor

6.    https://www.steelconstruct.com//site/

7.    https://en.wikipedia.org/wiki/Incremental_launch

8.   https://en.wikipedia.org/wiki/Buckling

9.    http://pubs.sciepub.com/ajcea/4/1/2/index.html

10.  https://en.wikipedia.org/wiki/Plasticity_(physics)

11.  https://en.wikipedia.org/wiki/Finite_element_method

12.  https://en.wikipedia.org/wiki/Creep_and_shrinkage_of_concrete

 

List of references.

[1]      Aschinger, R., Lindner, J., Zu Besonderheiten bei Trapezstegtragern. Stahlbau, 66, pp. 136-142. (1997)

[2]     Abbas, H.H., Sauce, R., Driver, R.G., Behaviour of corrugated web I-girders under in-plane loads, Journal of Engineering Mechanics, ASCE, 132, pp. 806-814. (2006)

[3]     Huang, L., Hikosaka, H., Komine, K., Simulation of accordion effect in corrugated steel web with concrete flanges, Computers and Structures, 82, pp. 2061-2069. (2004)

[4]     Hannebauer, D., Zur Querschnitts- und Stabtragfähigkeit von Trägern mit profilierten Stegen, PhD dissertation, Brandenburgischen Technischen Universität Cottbus, (2008)

[5]     Hassanein, M.F., Kharoob, G.F., Behaviour of bridge girders with corrugated webs: (I) Real boundary condition at the juncture of the web and flanges, Engineering Structures, 57, pp. 554-564. (2013)

[6]     Sayed-Ahmed, E.Y., Lateral torsion-flexure buckling of corrugated web steel girders, Proceedings of the Institution of Civil Engineers, Structures and Buildings, 158(1), pp. 53-69. (2005)

[7]     Aydin, R., Yuksel, E., Yardimci, N., Gokce, T., Cyclic behaviour of diagonally-stiffened beam-to-column connections of corrugated-web I sections, Engineering Structures, 121, pp. 120-135. (2016)

[8]     EN 1993-1-5:2005, EUROCODE 3: design of steel structures part 1–5: plated structural elements.

[9]     Kövesdi, B., Braun, B., Kuhlmann, U., Dunai, L., Patch loading resistance of girders with corrugated webs, Journal of Constructional Steel Research, 66, pp. 1445-1454. (2010)

[10]   Abbas, H.H., Sauce, R., Driver, R.G., Analysis of flange transverse bending of corrugated web I-girders under in-plane loads, Journal of Structural Engineering, ASCE, 133, pp. 347-355. (2007)

[11]   Abbas, H.H., Sauce, R., Driver, R.G., Simplified analysis of flange transverse bending of corrugated web I-girders under in-plane moment and shear, Engineering Structures, 29, pp. 2816-2824. (2007)

[12]   Watanabe, K., Masahiro, K., In-plane bending capacity of steel girders with corrugated web plates, Journal of Structural Engineering, JSCE, 62, pp. 323-336. (2006)

[13]   Li, G.Q., Jiang, J., Zhu, Q., Local buckling of compression flanges of H-beams with corrugated webs, Journal of Constructional Steel Research, 112, pp. 69-79. (2015)

[14]   Kuchta, K., Zum Einfluss der Interaction von Biegemoment und Querkraft auf das Tragverhalten von Wellstegträgern, Stahlbau, 75(7), pp. 573-577. (2006)

[15]   Hassanein, M.F., Elkawas, A.A., El Hadidy, A.M., Elchalakani M., Shear analysis and design of high-strength steel corrugated web girders for bridge design, Engineering Structures, 146, pp. 18-33. (2017)