Evaluation of fatigue cracking at cross diaphragms of a multigirder steel bridge

J. Construct. Steel Research 9 (1988) 95-110

Evaluation of Fatigue Cracking at Cross Diaphragms of a Multigirder Steel Bridge

C . A . C a s t i g l i o n i , * J. W . F i s h e r , t a n d B . T . Y e n t *Structural Engineering Department, Politecnico di Milano, Milano, Italy +Fritz Laboratory, Lehigh University, Bethlehem, PA, USA

SYNOPSIS A numerical study has been performed, in order to investigate the behavior of web gaps subjected to out-of-plane displacements in multi-girder steel bridges. Some results are presented attd discussed, focusing the attention on the eJ]ects of a variation of the ratio g/tw of the gap length g to the web thickness tw.

By varying the web thickness tw in a finite elements numerical model, it was possible to get some indication of the local behavior of the girder web in the gaps, and o f the stresses induced by out-of-plane displacements. The results show that the presence of web gaps causes concentrated distortions to take place in the gap area. The web in the gap is subjected to double curvature and, under different loading conditions, to a reversal in the sign o f the induced transversal displacements. Varying the gap length seems not to influence the transversal displacements magnitude. The horizontal and vertical components of the diaphragm member ~brces are not much influenced by variations o]" the web thickness and gap length, but they sharply increase if the connection plate is tightly fitted to the tension flange.

1 INTRODUCTION In a b r i d g e s t r u c t u r e , the interaction a m o n g longitudinal a n d t r a n s v e r s a l m e m b e r s d o e s n o t heavily influence the global b e h a v i o r o f the s t r u c t u r e , a n d This paper was originally presented at the International Conference on Steel Structures. Budva, Yugoslavia, 28 September-I October 1986. 95 J. Construct. Steel Research 0143-974X/88/$03.50 6-~ 1988 Elsevier Applied Science Publishers Ltd, England. Printed in Great Britain

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designing single members for in-plane action and bending seems to be adequate. Sometimes, however, relevant damage (growing in time) can be caused by localized distortions induced by that interaction. The transversal distribution of the loads causes, in fact, relative displacements (and/or rotations) between the longitudinal girders; the effect of the presence of the transversal secondary members is a reduction of these relative displacements. As a consequence, a stress state is induced at the principal-to-secondary members' connections, whose effect may be locally amplified by sudden variations of the stiffness of the connected members (Fig. 1).

Fatigue cracking at cross diaphragms of a multigirder bridge

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Web gaps between tension flange and cut-short stiffeners (Fig. la, b), sharp variations of the cross-sectional properties (Fig. lc), design and/or accidental eccentricities, web gaps between transversal stiffeners and gusset plates (Fig. ld) are typical details where fatigue fractures can develop. In fact, because of the sharp variation in the connected members' stiffness, these locations represent weakness areas in the joint; as a consequence, localized strains take place (Fig. 2) that induce relevant stress concentration, and cracking under cyclic loading.

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This kind of fracture was detected in bridges of different typoiogies; 1 fractures were more frequent in welded structures, where the presence of the welds in zones of relevant stress concentration made crack initiation easier. The same problem was also detected in riveted and/or bolted structures, but in this case, because of the smaller mechanical imperfections and the greater adaptability of the connections, cracks grew more slowly. Fractures were found in skewed bridges, as well as in curved or straight structures, in single-span as well as in continuous girder bridges. O n the basis of the previous experience (with riveted and/or bolted structures) out-of-plane and/or secondary stress-induced cracking could not be predicted, and were unexpected by both designers and constructors; it was not until the late 1970s that the phenomenon was taken into consideration.2,3,'*. 7 The problem was first looked at by Fisher in 1974; 5 later, a more exhaustive paper was published, 6 which gave the first directions for avoiding, or at least reducing, cracking induced by out-of-plane displacements.

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C. A. Castiglioni, J. W. Fisher, B. T. Yen

Multigirder steel bridges are one of the most common type of highway bridges today. In these bridges diaphragm members are used extensively to assist in erection, and to transversally distribute the vertical loads among the longitudinal girders, as well as to distribute wind loads laterally. Usually these diaphragm members are connected to the steel girders through connection plates welded to the web, sometimes welded to the compression flange and often cut short of the tension flange. There are two main reasons to cut short the connection plate at the tension flange: one is easy fabrication, since in this way the tolerance on the connection plate height is increased. The second is to avoid transverse welds on tension flanges, which could reduce the fatigue strength of the girders. Since the early 1970s fatigue cracking was reported in several bridges at the web gaps left at the end of intermediate diaphragm connection plates cut short from the tension flange. Despite the large nun~ber of cracks found, relatively little analytical and experimental study was performed to understand the behavior of web gaps in order to evaluate causes and effects of their cracking. To the authors' knowledge, there is only one published laboratory test program concerning the out-of-plane displacement-induced fatigue cracking. 7 Tests are currently being carried out at Lehigh University at Bethlehem, Pennsylvania, USA on a N C H R P Project, taking into account also the effects of random loading. A n analytical study of a single-span, four-girder highway bridge was reported by Fisher. s In this investigation, a typical bridge from the US Steel Highway Structures Design Handbook was used. The diaphragm connection plate gap region was analyzed by finite element modelling. The bridge was not an actual structure, hence no verification of the analytical results through field measurements could be made. A n analytical study and field measurements of a single-span multigirder mass transit bridge was presented by Mertz 9 who performed a finite element modelling using a 'zooming method' by substructuring. Recently, some work on the topic was performed in Japan by Maeda and O k u r a 1°'I1 who considered also the second-order effects in plate girders under bending and shear. In a study, presently nearing completion, in cooperation between the Structural Engineering Department of the Politecnico di Milano, Milano, Italy and the Fritz Laboratory, Lehigh University, Bethlehem, Pa., USA, attention was focused on the negative moment region of a five-continuousgirders four-span bridge; experimental results were available to the authors, who collected them during a field inspection in the summer of 1984.12.~3 A n u m b e r of numerical models were set up, which allowed a correct finite element simulation of the structural behavior. 12.13,14

Fatigue cracking at cross diaphragms of a multigirder bridge

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By use of these models, a parametric study was performed, encompassing the variation of dimensions of the girder dimensions and of the web gap. 15 In this paper, some results of this parametric study, highlighting the web gaps behavior, are presented and discussed.

2 NUMERICAL RESULTS Using the finite element code SAP V, and with reference to the Beaver C r e e k Bridge, ~2'z3 a numerical model was set up, ~4 which, by means of a 'zooming method', allowed a fairly good simulation of the behavior of the whole structure. In o r d e r to cut the costs of this lengthy procedure, a second finite element model was set up, which still allowed a satisfactory simulation of the structure and its details, but avoided the substructuring technique. The different models are presented and discussed in Reference 15. Using the second model, a small portion of the structure, 10.20 meters long, spanning from an intermediate pier, was studied in the parametric study. The finite element mesh is presented in Fig. 3, while the dimensions of the cross-section are shown in Fig. 4. Considering the geometrical symmetries, the structure restraint conditions are those of a cantilever. T h r e e cross diaphragms are present (Fig. 3), one at the pier (C.D. 0), a second one at 5 meters from the pier (C.D. 1), and one at 10 meters from the pier (C.D. 2). Five loading conditions were taken into account: - - l o a d i n g condition 1 refers to a single concentrated vertical load of 500 kN applied at the free edge of girder G 1 - - l o a d i n g condition 2 refers to a single concentrated vertical load of 500 kN applied at the free edge of girder G2

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- - l o a d i n g condition 3 refers to a single concentrated vertical load of 500 kN applied at the free edge of girder G3 - - l o a d i n g condition 4 refers to two concentrated vertical loads of 250 kN each, applied at the free edges of girders G 1 and G2 - - l o a d i n g condition 5 refers to two concentrated vertical loads of 25() kN each, applied at the free edges of girders G2 and G3. Figure 5 shows the deformed shapes of the cross-section at transversal diaphragm 2 in the case of a web gap length G = 100 mm (Figs 5a and 5b), and G = 5 0 m m (Figs 5c and 5d) and G - - 0 m m (Figs 5e and 5f) respectively under loading 1 (Figs 5a, 5c and 5e) and loading 3 (Figs 5b, 5d and 5f). By examining Fig. 5, it appears clearly that the presence of a web gap (independently from its length and from the loading condition) causes concentrated deformations to take place in the web, in the gap area (Figs 5a, 5b, 5c and 5d). When there is no gap (G -- 0), then nearly no concentrated deformation can be noticed (Figs 5e and 5f). The transversal distribution of the vertical loads among the girders may generate, however, a reversal in the sign of the deformations induced on the same girder, in the different loading conditions. U n d e r cyclic loading, this sign reversal will lead to fatigue crack growth. By keeping the global bending stiffness of the structure as a constant, the thickness of the web was varied; the three following values were considered: tw = 7.6 mm, tw = 9-5 mm and tw = 14.25 mm. Corresponding to these values, small variations of the flange widthJw were required in order to keep constant the moment of inertia of the girder: values offw of 418 mm, 400 mm and 354 mm, respectively, were considered. Figures 6a, 6b and 6c show (respectively for loading conditions 1, 2 and 3) a comparison of the transversal web displacements at the transversal diaphragms, for different values of the gap length (G = 50 mm and G = 100 mm), and for different values of the web thickness tw. It will be noticed that varying the gap length from G = 50ram to G = 100mm does not influence the magnitude of the transversal displacements, which remain practically constant. The magnitudes of the

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Figure 8 shows, for different values of tw, and for G = I(X)mm and G = 50 ram, the variation of the bending moment in the web. It can be seen that there is a change in the sign of the moment when passing from the top to the bottom of the gap. This is in agreement with the already observed double curvature of the deformed shape of the web gap. Figure 9 shows a comparison among the influence lines of the horizontal c o m p o n e n t s of the diaphragm members' actions that were drawn for different values of tw and of G. Only small variations can be noticed when changing the web thickness; the global behavior of the structure, in fact, is not influenced by varying a local parameter. The same considerations hold when varying the gap length from G = 100 mm to G = 50 ram. On the contrary, if the gap is eliminated (G = 0), a significant increase in the diaphragm member forces can be noticed. The same is not true for the vertical c o m p o n e n t s of the diaphragm member forces, which remain nearly constant, not being heavily influenced by either the gap length G or the web thickness t+, but rather by the vertical deflection of the girder.

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3 SUMMARY AND CONCLUSIONS A numerical study was performed for assessing the behavior of web gaps in order to evaluate fatigue cracking at cross diaphragm connection plates in multigirder steel bridges. Some results are presented showing the following features: h t h e presence of web gaps causes concentrated deformations to take place in the gap area - - t h e web in the gap is subjected to double curvature and, under different loading conditions, to reversal of the sign of the induced transversal displacements

Fatigue cracking at cross diaphragms ota multigirder bridge

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- - v a r y i n g the gap length seems not to influence the transversal displacements' magnitude which remains constant - - t h e horizontal components of the diaphragm m e m b e r forces are not influenced much by variations of web thickness and gap length, but they sharply increase if the gap length is cut to zero.

ACKNOWLEDGEMENTS Financial aid for this research was supplied by the Italian National Council of Research, Structural Engineering Division (CNR-GIS). The numerical work was carried out within the computing facilities of the Structural Engineering Department of the Politecnico di Milano, Milan, Italy.

REFERENCES 1. Fisher, J. W., Fatigue attd Fracture in Steel Bridges, Case Studies, New York, John Wiley & Sons, 1984. 2. Fisher, J. W., Fatigue cracking in bridges from out-of-plane displacements. Canadian Journal of Civil Engineering, 5, No. 4 (1978) 542-56. 3. Fisher, J. W., Inspecting Steel Bridgesjor Fatigue Damage, Fritz Lab. Report 386-16, Lehigh University, 1981. 4. Fisher, J. W., Fisher, T. A. and Kostem, C. N., Displacement induced fatigue cracks, Engineering Structures, 1 (October 1979)252-7. 5. AISC, Guide to the 1974 A A S H T O Fatigue Specifications New York, 1974. 6. Fisher, J. W., Bridge Fatigue Guide: Design and Details, New York, American Institute of Steel Construction, 1977. 7. Fisher, J. W.~ Hausammann, H., Sullivan, M. D. and Pense, A. W., Detection attd repair OEf'atigue damage in wehted highway bridges, TRB-NCHRP Report 206, Washington D.C., 1979. 8. Fisher, T. A. and Kostem, C. N., The interaction oJprimary and secondary members in multigirder composite bridges using finite elements, Fritz Lab. Report 432.5, Lehigh University, June 1979. 9. Mertz, D. R., "Displacement-induced fatigue cracking in welded steel bridges', PhD Thesis, Lehigh University, April 1984. 10. Okura, I. and Maeda, Y., Analysis of deformation-induced fatigue of thinwalled plate girder in shear, Proc. Jap. Soc. ('it'. Engrs, JSCE, 2, no. 2 (October 1985). 11. Maeda, Y. and Okura, I., Fatigue strength of plate girder in bending considering out-of-plane deformation of web, Proc. JSCE, I, no. 2 (October 1984). 12. Lee, J. J., Castiglioni, C. A., Yen, B. T. and Fisher, J. W., "Forces and Displacements of Diaphragm Members in Multigirder Steel Bridges', Proc. 2nd International Bridge Conf., Pittsburgh, June 1985. 13. Lee, J. J,, Castiglioni, C. A., Fisher, J. W., Kostem, C. N. and Yen, B. T.,

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Displacement induced stresses in rnultigirder steel bridges, Fritz Lab. Report 500-1, Lehigh University, 1985. 14. Castiglioni, C. A., Analisi sperimentale e modellazione numerica di un ponte a travata soggetto a f e n o m e n i di fatica, Proc. X CTA Congress, Montecatini, Italy, October 1985. 15. Castiglioni, C. A., Fatigue cracking in multigirder steel bridges: effects of web thickness on local stresses and displacements in web gaps, Costruziotti Metalliche, 1 (1987), 2-27.