Articles Rolando Chacn* Marina Bock Enrique Mirambell Esther Real

DOI: 10.1002/stco.201200001

Hybrid steel plate girders subjected to patch loading

Hybrid girders represent an economical alternative to homogeneous girders because they achieve greater flexural capacity with less material. One of the potential applications of hybrid steel plate girders is their use in bridges. One potential method of construction for these bridges is the push launch method in which patch loading may affect the design. The aim of this paper is to present the advanced conclusions of research work dealing with these two fields simultaneously: hybrid steel plate girders subjected to the particular case of patch loading. It is shown that, contrary to the EN 1993-1-5 formulation, the influence of the fyf /fyw ratio (namely, the hybrid grade) is negligible for both unstiffened and longitudinally stiffened girders according to the EN 1993-1-5 assumptions. Suggestions for considering these findings in design codes are provided at the end of the paper. with a homogeneous girder, greater flexural capacity is obtained at lower cost and weight [78]. Extensive experimental, theoretical and numerical research on hybrid design can be found in the literature [913]. Patch loading phenomena has been widely analysed since the early 1960s. Experimental and theoretical analyses have pinpointed the failure mechanisms of girders subjected to patch loading and, consequently, ultimate load predictions have been provided [1420]. Despite the vast amount of research devoted to hybrid girders and patch loading separately, research work covering both subjects is rather scant. Schilling [21] presented the first publication related to hybrid steel girders dealing explicitly with concentrated loading. Moreover, when studying the behaviour of slender girders subjected to patch loading, Granath [22] reached conclusions about the influence of the moment capacity of the flanges on the bearing capacity of plate girders subjected to concentrated loads. Following this thread, the authors of this paper subsequently presented several research works [35].

1 Introduction
The collapse behaviour of patch-loaded homogeneous plate girders has been widely reported [1, 2]. Researchers have proposed several expressions for the elastic critical loads and physical models which, referring to these expressions, accurately reproduce the limit state of the plates at ultimate load. Most of these approaches agree with a vast number of experimental results obtained from various sources. However, it has been pointed out that the vast majority of these studies only deal with the resistance of homogeneous plate girders [36]. The resistance of both unstiffened and longitudinally stiffened hybrid steel plate girders subjected to patch loading is studied in this work. The paper is based on the conclusions previously given in [36]. Such works demonstrate that, contrary to the EN 1993-1-5 provisions, the varying yield strength of the flange fyf (and hence the hybrid grade) does not play any role in the resistance of girders subjected to concentrated loading. Highlights concerning this proposal are presented at the end of the paper.

3 EN 1993-1-5
Verification of patch loading according to EN 1993-1-5 FRd is based on simplifications of the procedures provided in [1] and [2]. The general approach currently included in EN 1993-1-5 is based on a plastic resistance Fy which is partially reduced by means of the resistance function (Eq. (1)). The plastic resistance includes the key length parameter ly, which is the yield-prone effectively loaded length. This length can be calculated from the geometrical and mechanical properties of the girders using Eqs. (2) and (3). More details concerning the EN 1993-1-5 formulation are given in a companion paper [23].

FRd = 2 Review of earlier work

A steel girder is deemed as being hybrid when it is fabricated with different steel strengths for the flange and web panels. This type of girder is popular because compared
* Corresponding author: e-mail rolando.chacon@upc.edu

F Fy M1

F fyw l y t w M1

F fyw a t w M1

(1)

l y = ss + 2 t f 1 + m1 + m 2 a m1 = fyf bf fyw t w h m 2 = 0.02 w tf

2

(2)

(3)

Ernst & Sohn Verlag fr Architektur und technische Wissenschaften GmbH & Co. KG, Berlin Steel Construction 5 (2012), No. 1

R. Chacn/M. Bock/E. Mirambell/E. Real Hybrid steel plate girders subjected to patch loading

4 Numerical study
A numerical study was carried out using the FE-based software Abaqus-Simulia [24]. The software was used as a simulation tool and therefore numerical databases of unstiffened and longitudinally stiffened steel plate girders subjected to patch loading could be modelled and constructed. Details of those models can be found in [6].

Table 1. Numerical database of unstiffened girders

Numerical database variations Web yield strength fyw (N/mm2) Flange yield strength fyf (N/mm2) hw (mm) a (mm) Group U0 235 235 275 355 460 1000 1000 2000 3000 tw (mm) ss (mm) Flange dimensions (mm2) Stiffener thickness (mm) Girders per group Total number of numerical simulations 8 12 250 500 800 60 40 48 UI 235 235 275 355 460 2000 2000 4000 6000 12 20 500 1000 900 80 60 48 UII 235 235 275 355 460 3000 3000 6000 9000 15 25 750 1500 UIII 235 235 275 355 460 4000 4000 8000 12000 15 30 1000 2000

4.1 Unstiffened girders

The simulations were performed on a single panel centrically loaded with a patch as sketched in Fig. 1a. The numerical database was constructed by varying the parameters depicted in Table 1, which resulted in 192 specimens.

4.2 Longitudinally stiffened girders 4.2.1 Open stiffeners

The simulations were performed on a single panel centrically loaded with a patch as sketched in Fig. 1b. The numerical database was constructed by varying the parameters given in Table 2. Other parameters such as the distance between transverse stiffeners (a= 9000 mm), the web yield strength (fyw = 235 N/mm2), the web depth (hw = 3000 mm), the flange dimensions (80 900 mm), the transverse stiffener dimensions tst bf (30 900 mm), the longitudinal stiffener width (bsl = 300 mm) and the stiff bearing length (ss = 2250 mm) were kept constant. Table 2 summarizes the set of variations.

1000 80 1200 100 60 48 80 48

192

4.2.2 Trapezoidal closed stiffeners

Several girders were provided with a closed, trapezoidal longitudinal stiffener (Fig. 1c). In this case, both the position and the stiffener rigidity were kept constant. Other parameters such as the distance between transverse stiffeners (a = 9000 mm), the web yield strength fyw =
Table 2. Numerical database of longitudinally stiffened girders, open stiffeners
Dimensions hw (mm) tw (mm) fyf (N/mm2) LS0 3000 10 235 355 460 300 b1 (mm) 600 900 1200 10 tsl (mm) 20 30 40 LSI 3000 15 235 355 460 300 600 900 1200 10 20 30 40 LSII 3000 20 235 355 460 300 600 900 1200 10 20 30 40 LSIII 3000 25 235 355 460 300 600 900 1200 10 20 30 40 LSIV 3000 30 235 355 460 300 600 900 1200 10 20 30 40

Fig. 1. Geometry of the modelled prototypes

235 N/mm2, the web depth hw = 3000 mm, the flange dimensions (80 900 mm), the transverse stiffener dimensions (30 900 mm) and the stiff bearing length ss = 2250 mm were kept constant as well. Table 3 gives the geometrical data of the specimens tested numerically. It is worth pointing out that for all cases, the longitudinal stiffener has the same thickness tsl as the web plate tw. Fig. 2 shows the geometrical proportions of the closed longitudinal stiffener.

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R. Chacn/M. Bock/E. Mirambell/E. Real Hybrid steel plate girders subjected to patch loading

Table 3. Numerical database of longitudinally stiffened girders, closed stiffeners

Dimensions hw (mm) tsl = tw (mm) fyf (N/mm2) b1 (mm) LSa 3000 8 235 355 460 900 LSb 3000 10 235 355 460 900 LSc 3000 12 235 355 460 900 LSd 3000 15 235 355 460 900 LSe 3000 20 235 355 460 900

All results are located above the EN 1993-1-5 (on the safe side). Generally, the results follow a typical Eulerian hyperbolic shape. Some girders highlighted in Fig. 4a show anomalous results. Their geometrical proportions are such that the EN 1993-1-5 formulation must be modified slightly and therefore these girders do not follow the same trends.

Web folding of the loaded panel

Web folding of both loaded panels Fig. 2. Geometric proportions of the closed longitudinal stiffener Fig. 3. Typical failure modes

5 Numerical results
Results in the form of ultimate load capacity Fu, load-displacement plots, load-stress plots and thorough comparisons with EN 1993-1-5 are widely available in previously published papers from the authors [35]. Tables with precise data concerning each numerically simulated prototype as well as several plots and contours of the simulations are also provided. In this paper, and for the sake of conciseness, only the key results are displayed. These results aim at show the most remarkable findings of the present research work.

5.1 Ultimate load capacity

The ultimate load capacity of the steel plate girders subjected to patch loading has been obtained as the maximum load the prototype is able to carry in an incremental process. The observed failure modes are in accordance with the typical failure modes associated with patch loading. Slender girders tend to fail by local instability, whereas stocky girders tend to fail by an intertwined local yieldingbuckling mode. Fig. 3 shows a qualitative plot in which local folding of the loaded panel is noticeable. Moreover, numerical results for Fu are illustrated graphically in Fig. 4a for unstiffened girders and Fig. 4b for longitudinally stiffened girders. These results are plotted on the - space for comparison purposes. It is possible to draw the following conclusions from these plots:

Fig. 4. Ultimate load capacity of the numerical prototypes

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R. Chacn/M. Bock/E. Mirambell/E. Real Hybrid steel plate girders subjected to patch loading

These girders have closely spaced transverse stiffeners (in these cases, the effectively loaded length ly is greater than the distance between transverse stiffeners a, i.e. ly > a) and their failure modes do not fully match with patch loading. Additional research concerning this topic has been addressed by the authors [25].

5.2 Load-deflection plots

Load-deflection plots characterize the response of the steel plate girders subjected to patch loading. In a hypothetical incremental process, the applied load is plotted against the vertical displacement of a point located on the loaded flange. The response is initially linear but becomes gradually non-linear until the load reaches a maximum. From this maximum load onwards, a softening branch is recorded and the deformation increases sharply. Fig. 5 shows four load-deflection plots of selected prototypes from the numerical database of unstiffened

girders. The main varying parameter between the four plots is the web depth of the specimens and therefore the web slenderness hw/tw. Fig. 5a represents the stockiest girders, whereas Fig. 5d represents the most slender prototypes. Within each plot, load-displacement curves as well as values of Fu are shown for girders with a varying hybrid grade fyf/fyw. The following features can be gleaned from these plots: Irrespective of the web slenderness, all load-displacement curves are identical because the fyf/fyw ratio is varied. The response of the girders does not depend on the variation of the flange yield strength. Irrespective of the web slenderness, the ultimate load capacities Fu are identical because the fyf/fyw ratio is varied. Fu is not dependent on the flange yield strength either. Stocky girders present a quite marked linear branch, whereas in slender prototypes the curves are non-linear from low levels of load onwards.

Fig. 5. Load displacement plots for unstiffened girders

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R. Chacn/M. Bock/E. Mirambell/E. Real Hybrid steel plate girders subjected to patch loading

On the other hand, Fig. 6 shows four load-deflection plots of selected prototypes from the numerical database of longitudinally stiffened girders. The main varying parameter between the four plots is the position of the longitudinal stiffened b1 and therefore the b1/hw ratio. Fig. 6a represents the longitudinal stiffener closest to the loaded flange (b1/hw = 0.1), whereas Fig. 6d represents the longitudinal stiffener with a relative position b1/hw = 0.4. Within each plot, load-displacement curves as well as values of Fu are shown for girders with varying hybrid grade fyf/fyw. The following features should be pointed out: Irrespective of the position of the longitudinal stiffener, all load-displacement curves are identical because the fyf/fyw ratio is varied. The response of the girders does not depend on the variation of the flange yield strength. Irrespective of the position of the longitudinal stiffener, the ultimate load capacities Fu are identical because the fyf/fyw ratio is varied. Fu is not dependent on the flange yield strength either.

5.3 Hybrid vs. homogeneous prototypes numerical and EN 1993-1-5 results

The ultimate load capacity Fu of a given hybrid girder Fu,hyb can be compared with the ultimate load capacity Fu of its equivalent homogeneous girder Fu,hom. If Fu depends on fyf/fyw, then Fu,hyb should differ from Fu,hom. Fig. 7 shows the ratio Fu,hyb/Fu,hom as fyf/fyw is varied for unstiffened girders (Fig. 7a) and longitudinally stiffened girders (Fig. 7b). Numerical as well as EN 1993-1-5 results are included in each plot. From these figures, the following features should be pointed out: For both unstiffened and longitudinally stiffened girders, the numerical results show very little dependency on fyf/fyw. The Fu,hyb/Fu,hom ratios vary, ranging from Fu,hyb/Fu,hom = 1.00 to 1.02 (variation that might arguably be attributed to numerical reasons). For both unstiffened and longitudinally stiffened girders, the EN 1993-1-5 results show a significantly strong dependency on fyf/fyw. The Fu,hyb/Fu,hom ratios vary,

Fig. 6. Load displacement plots for longitudinally stiffened girders

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R. Chacn/M. Bock/E. Mirambell/E. Real Hybrid steel plate girders subjected to patch loading

7 Conclusions
A vast numerical study of more than 800 hybrid and homogeneous steel plate girders has been presented in this paper. The numerical study is based on girders with geometrically realistic proportions. The parametric variation of the most relevant variables influencing the resistance of girders to patch loading is quite profuse, although the particular emphasis was on the hybrid grade fyf/fyw. The numerical results presented for both transversally and longitudinally stiffened girders do not agree with the results provided by EN 1993-1-5 when the focus is on the effect of the flange yield strength (and therefore the hybrid parameter fyf/fyw). Numerically, it is predicted that for girders with widely spaced transverse stiffeners (ly < a), fyf/fyw has no influence on the ultimate load capacity of patch-loaded girders. The current formulation of EN 19931-5 takes this ratio into account in such a way that the greater the ratio fyf/fyw, the higher is the ultimate load capacity of the girders. It is worth pointing out that this parameter appears explicitly in the term m1. The current formulation of EN 1993-1-5 leads to structurally unsafe results. An attempt to correct this anomaly involves making the fyf/fyw ratio equal to 1.0 in the current expressions for FRd. This attempt leads to reshaping the effectively loaded length ly in Eq. (4), in which m1 is replaced by m*. This proposal has been tested both struc1 turally and statistically in [35]. For reliability purposes, further research concerning the recalibration of the resistance function and the partial safety factor is addressed in a companion paper [23].
Fig. 7. Fu,hyb/Fu,hom

Acknowledgements
The authors gratefully acknowledge the financial support provided by the Ministerio de Ciencia e Innovacin as part of research project BIA-2008-01897 as well as the scholarship provided by AGAUR to Ms Bock.
References

ranging from Fu,hyb/Fu,hom = 1.02 to 1.14. This anomaly is structurally unsafe and should be corrected in the formulation.

6 Design proposal
The results obtained suggest that the patch loading resistance should not depend on the hybrid parameter fyf/fyw to any extent because the flange yield resistance does not seem to play any role in the development of the collapse mechanism. For the sake of correcting the aforementioned anomaly, a modification to the current EN 1993-1-5 formulation that enhances the results quite satisfactorily is provided. Readably, it is proposed that the m1 coefficient in Eq. (3) be replaced by m*, see Eq. (4): 1
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l y = ss + 2 t f 1 +

2 h bf + 0,02 w tw tf

* m1 =

bf tw

(4)

This proposal has been tested both structurally and statistically. The results lead to a satisfactory improvement of the formulation. The results obtained with the up* graded coefficient m1 are structurally sound and on the safe side.

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R. Chacn/M. Bock/E. Mirambell/E. Real Hybrid steel plate girders subjected to patch loading

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Authors:
Dipl.-Ing. Marina Bock Dr.-Ing. Rolando Chacn Prof. Dr.-Ing Enrique Mirambell Assoc. Prof. Dr.-Ing Esther Real Construction Engineering Department, Universitat Politcnica de Catalunya, C/Jordi Girona (Campus Nord), 1-3, C1 Building, 08034 Barcelona, Spain

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