The design concept of corrugated web girders in stainless steel has been developed and verified to replace conventional stiffened steel girders. In addition, the Eurocode-based design was updated for the proposed concept, and some existing bridges were redesigned. The results indicated approximately 15 to 30% material savings due to the use of the corrugated web plates in the case studies. In the experimental studies, four full-scale girders were tested to shear. 3D DIC was used to monitor the initial geometry and deformations of the web panel during loading. The applied load, maximum vertical deflection, and the strains were all measured. Based on the conducted tests, a finite element model was developed and validated for use in extensive parametric studies to validate Eurocode shear design models.
Steel-concrete composite bridges have been well established as a sustainable design solution since they efficiently take advantage of each material’s superior properties. However, traditional composite bridges are typically produced of heavily stiffened plate girders in carbon steel. Today, the availability of new types of steel with enhanced performance has made it possible to achieve greater sustainability than conventional designs. Stainless steel is one of the most prominent materials in this respect. The combination of high strength and corrosion resistance in stainless steel can better address construction sustainability than conventional carbon steel.
From Life-cycle point of view, several previous national and international studies have demonstrated the advantages of using stainless steel in bridges [1-6]. Detailed life-cycle cost (LCC) analyses have shown that bridges with stainless steel can give up to 30-40% savings in the life-cycle cost compared to conventional carbon steel over 60 years of service life [4]. Such a saving can reach a value of up to 50% after 100-120 years [2], [7].
Despite the advantages of stainless steel in terms of life-cycle cost, the potential of using stainless steel in bridge construction is still not fully utilized. The collective knowledge in the field clearly shows that the main reason for that is the high material and investment cost for stainless steel bridges [1], [4], [8].
During the last three years, the research group of Lightweight Structures at Chalmers has, together with several industrial partners, evaluated various “innovative” concepts with a focus on reducing the investment cost of composite bridges with stainless steel. In the SUNLIGHT research project, a new bridge concept of combining stiff and effective corrugated web plate with stainless steel has been developed and verified to replace conventional stiffened steel girders. The use of corrugation makes it possible to reduce the thickness of the web plates and eliminate the need for transverse intermediate stiffeners for shear, which reduces the amount of needed material and welds for girders. Moreover, an additional weight saving is made possible by taking advantage of the high strength of stainless steel. Fig. 1 shows one of the corrugated web stainless steel girders produced for the SUNLIGHT testing program during 3D laser scanning before doing the test.
To designing bridges, Krav Brobyggande refers to Eurocodes as the base design code. The standard EN 1993 states the rules for the design of steel structures, and standard EN 1994 contains the rules for composite steel-concrete structures. The rules for designing stainless steel and corrugated web girders are separately given in parts 1993-1-4 and Appendix D of 1993-1-5, respectively.
When it comes to the combination of stainless steel, corrugated web plates, and composite performance, there are no codified rules in Eurocodes. Therefore, updating the design rules provided in Eurocodes was necessary for the combined design concept introduced in the project. Several case studies have been performed in which some existing bridges, which were designed and constructed of flat web carbon steel girders, were redesigned using stainless steel corrugated web girders according to the updated design rules [9-10]. The new design results were compared to the existing bridges from various aspects, including the weight of the material, production cost, and total life-cycle cost which are discussed more in section 3.
Updated design
According to Eurocode, the bending stiffness of members with corrugated webs should be based on the flanges only and webs should be considered to transfer shear and transverse loads. The shear resistance of a flat web girder in carbon steel is calculated according to SS-EN 1993-1-5. The specific regulations for corrugated web girders are provided in Appendix D of the same standard.
Due to higher stiffness against buckling, the shear behavior of a corrugated web girder is different from the behavior of a flat web girder showing a higher shear resistance. According to the existing standard, the buckling of a corrugated web under shear loads might occur in two different main modes; local and global, see Fig. 2. The local buckling mode is primarily dependent on the flat fold length of the corrugation ( in Fig. 3). The global buckling mode mainly depends on the corrugation depth (
in Fig. 3). However, studies have shown that a combination of the two local and global modes, called an interactive buckling mode, may occur, which is not considered in the current regulations. For the design concept proposed in the SUNLIGHT project, a more detailed study of the simultaneous effect of corrugation and stainless steel on the shear behavior has been necessary, and this is one of the main work tasks, a brief report of which is presented in section 4.
When it comes to the calculation of the bending strength, the choice of material and a corrugated web affect the classification of the cross-section. The material reference value for the classification () differs depending on whether stainless steel or carbon steel is used. In girders with a corrugated web, the web has no axial stiffness due to the accordion effect; hence only the flange needs to be classified. The buckling factor (
) is modified in EN 1993-1-5-Appendix D to include the effects of having a corrugated web on the flanges.
Another effect brought by the use of the corrugated web is the lateral bending of the girder (flanges) due to the eccentric shear flow in the web. The effect of such transverse bending moment can be included by reducing the yield strength in the calculations of the bending moment capacity. On the other hand, when calculating the resistance against lateral-torsional buckling for girders with corrugated webs, the contribution from the web is neglected due to lack of axial stiffness, and the buckling curve can be used in the calculations for stainless steel. However, there is no buckling curve specific for the lateral-torsional buckling of a corrugated web stainless steel girder in Eurocode.
Worth discussing, due to the high stiffness of a corrugated web in the out-of-plane direction and depending on the geometry of the corrugation, it can provide extra support to the compression flange against lateral movement. However, this additional support, which can increase the resistance against lateral-torsional buckling, is neglected in the design regulations.
When it comes to the thermal stresses, if stainless steel is used instead of carbon steel, the approximately 30% larger coefficient of thermal expansion for stainless steel than concrete would result in a difference in the thermal strains in concrete and stainless steel. This leads to an increase in thermal stresses in the stainless steel. However, the current design regulations do not consider it due to the assumption of the use of carbon steel and the proximity of thermal coefficients of carbon steel and concrete.
Worth mentioning that there are differences between material properties, including yield strength, ultimate tensile strength, and modulus of elasticity, for stainless steel and carbon steel. Since stainless steel displays a non-linear stress-strain behavior below the yield limit, unlike carbon steel, the same modulus of elasticity cannot be used for design in all limit states. Instead, a secant modulus of elasticity should be calculated depending on the limit state and the current level of stresses.
The choice of corrugated web girders affects the calculations in the serviceability limit state as well. For example, because of the reduction of the vertical stiffness of the girder due to the lack of axial stiffness of the web plate, the vertical deflection of a corrugated web girder will be greater than that of a flat web girder. Furthermore, studies have shown that both corrugated webs and stainless steel can increase the strength in the fatigue limit state. However, according to the current regulations (SS-EN 19931-9), the relevant checks do not differ depending on if stainless steel or carbon steel is used. The only difference is that in the case of calculation for a corrugated web girder, the normal stresses in the web are ignored.
For the sake of brevity, a complete description of the updated design process for corrugated web stainless steel girder composite bridges was avoided here. For more information, refer to the relevant conducted master thesis [9-10]. Therefore, only some of the most critical design differences compared to the conventional design were highlighted.
Case studies
Having the updated design rules, three existing twin-I-girder composite bridges, constructed in recent years, were redesigned based on the proposed new design concept to compare the new concept with the conventional composite bridge concept. All the selected bridges for the case studies had flat web girders in carbon steel, mainly S355. Two of the bridges, cases 1&2, had a span of 51 and 36 meters in length and were simply-supported. The height of these two bridges is 2.37 and 2.16 meters, respectively, and their cross-sectional width is 10 and 6.6 meters. The third bridge, case 3, has two continuous spans of 28.3 meters in length. The bridge height was 1.25 meters, and the width of the bridge cross-section was 9.5 meters. In a fourth case study, the same bridge as in case 3 was redesigned based on a new height of 1.75 meters instead of 1.25 meters for the bridge.
In the redesign, some limitations were considered, including the design of only the main girders and the fact that the height and thickness of the web did not change along the spans outside the scope of the main design. The redesigns were all based on duplex stainless steel grade 1.4162.
The redesign of these bridges showed 23 and 29 percent reductions in steel weight for the first two bridges and 15 and 19 percent reduction for the third and fourth ones. Worth mentioning that the weight reductions mainly come from the main girders, this time being designed corrugated in the web, and a small share from the studs and welds. So, although the price of stainless steel at the time of analysis was approximately three times the price of carbon steel (S355), the cost difference of materials between the two –original and new designs is not that big. Finally, if the production costs are added to the cost of materials, the investment cost of the new design will be quite comparable to the original design and only slightly higher. For example, according to an approximate cost estimate of the new design for the first case study (case 1 above) provided by Stål och Rörmontage AB, the investment cost of the new design at the time of the study was SEK 4.3 million, which is not a significant increase over the investment cost of the original design, which was SEK 3.9 million. It is worth noting that the cost of production with carbon steel is generally higher due to the more time needed for welding, the increase in the labor cost, and the need for painting, which costs more than the cost of pickling stainless steel [9].
The results obtained from these studies indicated the possibility of a significant reduction in material weight and investment cost if the combined concept of design with the use of stainless steel and corrugated web girders is used, which can be an essential step towards removing obstacles to the prosperity of the application. Finally, if the maintenance cost is added to the investment cost (stainless steel requires a minimum of maintenance) the total life-cycle cost of the new design will be lower for the case study bridges than the original designs; see Fig. 4 [10].
Experimental studies
As mentioned, the use of corrugated web plates in steel girders increases the shear strength and, therefore, reduces material consumption. Eurocode currently regulates the shear strength of corrugated girders made of carbon steel. In order to study the applicability of current design models to corrugated girders in stainless steel, SUNLIGHT encompassed a testing program with a focus on the shear strength of these girders.
Four girders with different geometric parameters of the corrugation were fabricated and tested in three-point bending. Lateral restraints were provided to prevent lateral-torsional buckling. The dimensions of the flange plates (250 mm×25) were chosen so as to eliminate the risk of flange buckling and to ensure shear failure occurs in the web before other failure modes. All the girders were made of LDX 2101 stainless steel delivered by Outokumpu. The girders all had an approximate length of 4.0 m and height of 1.45 m. They were simply supported and loaded in the middle of the span. The thickness of the web was different on both sides of the load; 4 mm and 6 mm. Thus, the location of the shear failure was limited to the thinner panel. Stiffeners were provided at the supports and under the point load. Views of the test set-up is shown in Fig. 5.
As mentioned, shear failure of corrugated web girders may occur locally, globally or in an interactive mode, depending on the geometry of the corrugation. Research has shown that initial imperfections can also affect the type of the failure mode to a large extent. For this reason, the full field geometry and deformations of the thinner web panel were monitored by 3D-DIC (Digital Image Correlation) before and during the tests as shown in Fig.6. In addition to this, before testing the entire geometry of all visible parts of the beams were documented by 3D laser scanning as shown in Fig. 1.
During testing, the mid-span deflection of the beam was measured using linear variable displacement transducers (LVDT). Also, strains were measured with general purpose strain gauges at specific points of the web panels, top flange, and bottom flange for the purpose of test validation.
The shear failure of all four tested girders, labeled as 1001, 1002, 1003, and 1004, is shown in Fig. 7. From the observation of the ultimate deformations, it is clear that the buckling modes in 1001, 1002, and 1003 which have lower corrugation depth than 1004, are neither wholly local nor global but rather interactive. This observation can be important when comparing the load-bearing capacity of the test with the capacity calculated based on the Eurocode model, in which interactive modes are not considered.
Fig. 7: ultimate deformation of the four tested girders; 1001-1004.
Finite element studies
Updating and validating the design models for corrugated webs is essential to fully take advantage of stainless steel girders with corrugated web plates. Due to the significant increase in the shear strength of a corrugated web and the associated potential to save more materials, accurate updating of shear design equations based on the conducted tests is one of this project’s essential goals.
In the next step of the studies, having the accurate measured information obtained from the tests performed, the experiments were simulated using ABAQUS finite element software. This work aims to provide a validated FE tool to conduct extensive parametric studies to assess the Eurocode design relationships accurately.
The mid-span vertical deflection is plotted against the applied load and shown in Fig. 8 for 1003 as an example. It is observed that the initial stiffness and the ultimate load obtained from the experiment and simulation comply very well. Also, the similarity of FE and experiment results is confirmed when comparing ultimate deformations, as shown in Fig. 8 to 1003 in Fig. 7. It is worth noting that due to the rapid mode of failure, the deformations after reaching the maximum load in Fig. 8 cannot be monitored in the experiment. The nonlinear FE-model is however capable of tracking the post-buckling path reasonably well.
Conclusions and plans for future studies
So far in the SUNLIGHT research project, the results indicate that it is possible to take advantage of the superior properties of stainless steel without significantly increasing the investment cost in the case of the use of corrugated web girders. Since the main advantage of girders with a corrugated web is high shear strength, in this project, experiments were designed and performed to more accurately investigate the shear behavior of girders made of stainless steel and corrugated web plates. Due to the sensitivity of shear behavior to initial imperfections, corrugation parameters, and other parameters, evaluating the current design models in Eurocode is not possible without extensive parametric studies. According to the validated FE results, which were reported in Section 5 briefly, it can be claimed that a validated finite element tool is in hand for performing extensive parametric studies phase. Next, after comparing parametric studies and design models, the final comment on the current shear design regulations will be possible.
Acknowledgements
The authors would like to acknowledge the financial support provided by Vinnova within the project “SUNLIGHT” and by Trafikverket in the project “Sustainable & Maintenance free bridges”. The contributions of all research and industrial partners in both projects are also gratefully acknowledged.
References
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Författare
Mozhdeh Amani, Chalmers
Mohammad Al-Emrani, Chalmers
