Innovative Steel Plate Girders With Corrugated Webs

Girders with corrugated steel webs represent a new innovative system which has emerged in the past decade. These girders have thinner webs, higher fatigue resistance, and are more economical, easier to fabricate, more aesthetic, and provide faster construction compared to ordinary plate girders with stiffeners or reinforced concrete beams. They have been adopted in several countries for construction of a variety of structures; however, the current Indian code on steel structures does not contain provisions for their design. In this article, Dr. N. Subramanian provides some in-depth information and references for designing these innovative girders as an alternative to RC bridges and girders.

To increase the shear capacity of large steel plate girders, shaped webs may be used; in this situation, the web plate is first cold-formed with waves or corrugations usually parallel to the web depth and then welded to the flanges. Although many types of corrugations are possible, trapezoidal and sinusoidal corrugations have received the most attention.

Girders fitted with corrugated webs tend to be most used in the construction of industrial buildings in Sweden, Germany, and other European countries (Subramanian, 2011). Figure 1 shows some examples from Germany. Corrugated webs, though not yet commonly used for highway bridges in India and North America, have been incorporated into several highway bridges constructed in Europe and Japan.


Similar webs with reinforced and/or pre-stressed concrete flanges have been used for bridges in France. The first pre-stressed hybrid box girder bridge was the Cognac Bridge, constructed in France in 1986. It is a three-span continuous box girder bridge with a total length of 105m and a maximum span of 43m (Fan et al., 2006). More recently the Shinkai and Hondani bridges have been constructed in Japan (Fan et al. 2006). A summary of the research and development in beams and girders with corrugated webs was reported by Elgaaly and Dagher, 1990.

Many types of corrugations are possible such as rectangular, trapezoidal, and sinusoidal. The sinusoidal corrugations generally prevent failure due to loss of stability before it reaches the plastic limit loading. Sinusoidal corrugations may also eliminate the problem of local buckling of the web. This aspect is considered advantageous as compared to the trapezoidal corrugations, where the web may fail due to local buckling, as it consists of a number of flat sections. A typical profile of a corrugated web is shown in Fig. 2.

The corrugated webs are usually welded to the top and bottom flanges of the girders using computer controlled equipment that minimizes all costly and time consuming pre-assembly and welding processes through automation, as shown in Fig. 3.


Advantages of Corrugated Webs in Bridge Girders

• Compared to the flat steel web, the corrugated steel web has higher out-of-plane stiffness and shear buckling resistance even without additional stiffeners, which considerably reduces the material and labor costs of fabricating superstructures.
• The results of studies on girders with corrugated webs indicate that the fatigue strength of these girders can be 50% higher compared to girders with flat stiffened webs (Machacek & Tuma 2006).
• In addition to the improved fatigue life, these girders could be 30 to 60% lighter than the girders with flat webs and have the same capacity (Elgaaly & Dagher 1990). Thus, larger spans can be achieved with less weight.
• Compared to the concrete web, the lighter corrugated steel web leads to reduced seismic forces and smaller substructures, thereby reducing the construction cost of the bridge.
• Moreover, corrugated webs improve the aesthetics of the structure.
• The manufacture of a bridge with corrugated webs emits 20% less carbon dioxide than a steel bridge and concrete bridge. Hence a bridge with corrugated webs is eco-friendly.
• In the case of prestressed concrete bridge girders, the ‘accordion effect’ of the corrugated web (which has a higher resistance to shear buckling) enables the upper and lower decks of the girder to be prestressed efficiently (See Fig. 4). Hence the loss of prestressing is reduced considerably compared to conventional box girder bridges.
• Box girder bridges with corrugated steel webs are economic and competitive for spans exceeding 100 m.

Beams used in Germany for buildings have web thicknesses that vary between 2 and 5 mm and the corresponding web height-to-thickness ratios vary between 150 and 260 mm. The corrugated webs of two bridges built in France were 8 mm thick and the web height-to-thickness ratio was in the range of 220 to 375 mm.

Design of Girders With Corrugated Webs
While designing girders with corrugated webs, the following points should be kept in mind (Maquoi, 1992).

• When the axis of the corrugations is perpendicular to the girder’s longitudinal axis, the web cannot sustain significant levels of longitudinal direct stress; with the result that only the flanges can be mobilized for the girder’s bending resistance. Thus, the shear strength can be determined without consideration of moment–shear interaction. Hence design is carried out by assuming all the shear forces are resisted by corrugated webs. The ultimate moment capacity can be calculated based on the flange yielding, ignoring any contribution from the web.
• The enhancement of shear strength is mainly due to an increase in the plate critical shear buckling stress, as a result of the corrugations; once the web buckles, large displacements and distortions occur and hence the post-buckling strength cannot be relied upon.
• Compared to a plain web, a corrugated web with identical thickness can only be economical when its critical shear buckling load exceeds the ultimate shear load of the plain web. Fabrication costs, however, must be considered.

The corrugations increase the out-of-plane stiffness of the web and eliminate the use of vertical stiffeners. From experimental results, it was found that failure in shear is usually due to the buckling of the web and the failure in bending is due to the yielding of the compression flange and vertical buckling into the web (Elgaaly et al. 1996; Elgaaly et al. 1997). The failure is sudden with no appreciable residual strength.

Corrugated webs have been found to fail in shear by instability, and both local and global buckling modes have been observed experimentally. In theory, local buckling involves a single flat panel or ‘fold’, whereas global buckling involves multiple folds, with buckles that extend diagonally over the entire depth of the web. Global buckling may be predominant for dense corrugation and local buckling for course corrugation. In experiments, however, failure modes that appear to have characteristics of both local and global buckling have been observed (Driver et al. 2006).

Plate stability theory can be used to predict the local shear buckling of corrugated webs (Lindner & Huang, 1995; Lindner, 1988). A given fold (longitudinal or inclined) is assumed to be supported by adjacent folds along its vertical edges and by the flanges along its horizontal edges. Design rules for girders with trapezoidal and sinusoidal corrugations are provided in Annex D of Eurocode 3, EN 1993-1-5:2006. See also the commentary by Johansson et al., 2007. In Annex D of EC3-1.5, bending resistance of a corrugated beam is given as the minimum of the tension or compression flange resistances multiplied by the section height and no contribution of the web is taken into account. On the other hand, shear action is assumed to be carried by the web alone.

As per EN 1993-1-5:2006, the moment of resistance due to bending should be taken as the minimum of the following:


Where f_yf,r is the yield stress reduced due to transverse moment in the flange and equals f_yf f_T, γ_mo (=1.10) and γm1 (=1.25) are partial safety factors against yield stress and buckling and against ultimate stress respectively. b₁, t₁ are the breadth and thickness of compression (top) flange and b₂, t₂ are the breadth and thickness of tension (bottom) flange, ψ is the reduction factor for out-of-plane buckling according to 6.3 of EN I993-1-1:2005 (same as given in Clause 7.1.2.1 of IS 800:2007), h_w is the height of the web, f_T the reduction of the bending resistance is given by:


For sinusoidally corrugated webs, the factor f_T can be taken as 1.0.

Shear Resistance of Corrugated Webs
Notations for the corrugated web are shown in Fig. 2. For the sinusoidally corrugated web the measures a3 and 2w are relevant and the developed length of one full wave is denoted 2s. For the trapezoidal web, the following relations are used.

a₂ = a₃/sinα     (2a)

a₄ = a₃cotα     (2b)

w = a₁ + a₄     (2c)

s = a₁ + a₂     (2d)

t_w = thickness of web

h_w = depth of web

a_max = max(a₁,a₂)

There are two shear buckling modes; one local governed by the largest flat panel and one global involving one or more corrugations. The critical stress for local buckling is taken as that for a long plate, which can be written as


For a sinusoidally corrugated web the local buckling is less likely to occur. A formula for critical shear stress for local buckling of webs has been derived for girders with corrugations as used in Austria by Pasternak and Hannebauer (2004) (See the sinusoidal corrugation profile shown in Fig. 2), as below:


where, E = Young’s modulus of elasticity, N/mm², μ = the Poisson’s ratio.

But this equation (4) was found to give large errors, if the dimensions are different than those manufactured in Austria. For this reason, Johansson et al., 2007 suggest that the sinusoidally corrugated webs have to be designed by testing with regard to local shear buckling. The critical shear stresses for local buckling can also be found by using with FEM and used with the design rules given here.

The critical stress for global buckling is given by (Peterson and Card, 1960)


Where, I_z is the second moment of area of one corrugation of length w. The first versions of the formulae (5b) and (5c) are relevant for sinusoidally corrugated webs. The second versions are relevant for trapezoidally corrugated webs.

The shear resistance of the corrugated web may be determined by


The critical stress for local and global buckling, τ_cr,l and τ_cr,g have already been defined in Equations (4) and (5) respectively.

Other Practical Issues
A small value of β (= a₁/a₂) may lead to an uneconomical design due to a large amount of web material required when the corrugations are deep. A large value of β may result in low global buckling strength. Values of β normally range between 1 and 2. The value of α is normally taken as 30° or 45°. Lindner and Huang (1995) suggest that the value of α should not be less than 30° for the corrugation folds so as to provide adequate support to one another along the fold lines in order to mobilize the full shear capacity. The parameter α not only influences the shear strength but also fabrication and fatigue life.

Under static loading, the common practice of fillet welding the web to the flanges from one side only, was found to be adequate. The use of single sided welds is not recommended for bridges as it would cause problems with the corrosion protection and the fatigue resistance is not documented (Johansson et al., 2007). Lindner (1988) also studied the lateral torsional behavior of girders with corrugated webs and found that the torsional section constant J for a beam with corrugated web does not differ from that of a beam with flat web, but the warping section constant C_w is different. Elgaaly et al., 1997 discuss the lateral-torsional buckling of girders with corrugated web. Elgaaly and Seshadri, 1997 provide information on the behaviour of these girders under partial compressive edge loading. Based on eight large-scale tests, Sause et al., 2006 found that plate girders with corrugated webs {having HPs 485 W steel and welded by gas-metal-arc (GMAW) fillet welding} exhibit a fatigue life that is longer than that of conventional plate girders with transverse stiffeners.

Openings in Corrugated Webs
Prathebha and Jane Helena, 2020 carried out experimental and numerical investigations to investigate the influence of circular-shaped cutouts in corrugated web steel girders. They found that for small diameter cutouts (≤0.15a), the shear stress increases for higher web slenderness, and this increase in shear stress is due to the buckling capacity of the web. Whereas, when the diameter of the cutout is greater than 30% of the fold length of the corrugated web, the decrease in shear capacity cannot be neglected and must be included in the design criteria. Beams with cutouts fail mainly by global and interactive shear buckling, whereas beams without cutouts fail in interactive shear buckling. Corrugated web girder with cutout does not lose its shear capacity even if the web depth is increased. Kiymaz et al., 2010 conducted a numerical parametric study, using a general purpose finite element program (ABAQUS), on the behaviour of simply supported corrugated web beams of 2 m length and with web openings at quarter span points. They found that the web opening causes strength reductions between15% to 50%, depending on the size of openings.

Both Lindner and Uuang (1994) and Romeijn et al. (2009) predicted that the buckling coefficient is linearly dependent on the diameter of the cutout. The linear equation proposed by them is found to underestimate the experimental values by a margin of 10 to 15% (Prathebha and Jane Helena, 2020).

Summary and Conclusions
Girders with corrugated steel webs represent a new innovative system which has emerged in the past decade. In this system, corrugated steel plates are used in the web(s) and either steel or reinforced/prestressed concrete slabs could be used in the flanges. The entire flexural strength of the girder is assumed to be provided by the flanges of the girder and the entire shear capacity is assumed to be provided by the corrugated web. Thus, the corrugated web is subjected to an ‘almost’ pure shear stress state. The girders with corrugated webs will have thinner webs (as their resistant to buckling is increased due to the corrugations/folds), higher fatigue resistance, and are economical than girders with flat webs. They are also more aesthetic and provide faster construction than ordinary plate girders with stiffeners or reinforced concrete beams. With the use of modern automatic welding processes, the corrugated webs can be fabricated with much ease. These innovative girders have been adopted in several countries for the construction of a variety of structures.

Failure of a corrugated steel web plate may occur by the classical steel yielding of the web under a pure shear stress state. It may also occur by web buckling due to either local instability of any ‘panel’ between two folds or overall instability of the web over two or more panels. An interactive failure mode between these different failure criteria represents another possibility of failure. Researchers in the past have done extensive research on all these aspects and have provided solutions, which have been verified by experimental research. Based on these solutions, provisions have been included in the Eurocode 3 for the design of these innovative systems. The current Indian code on steel structures does not contain provisions for their design and the information and references provided here, may be quite useful in designing such innovative girders as an alternative to RC bridges and girders.

References

1. Driver, R.G., Abbas, H.H., and Sause, R.(2006) Shear behavior of corrugated web bridge girders, Journal of Structural Engineering, ASCE, Vol. 132, No. 2, Feb., pp. 195-203.
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About the Author
Dr. N. Subramanian, Ph.D., FNAE, is an award-winning author and consultant, based in Maryland, USA. He is former chief executive of Computer Design Consultants, India. He holds a doctorate from IITM and has worked with the TU Berlin and the University of Bundeswehr, Munich. He has authored 25 books and 300 technical papers and served as a past vice president of ICI and the ACCE (I). Awards won include the ICI - L&T Life-Time Achievement award (2013), Tamil Nadu scientist award (2001), Gourav Award of the ACCE(I) (2021), and the ACCE(I)-Nagadi best book awards.