Detailed analysis of Railway Bridge Connection Details
M.J. Ing1, R. Pan1
1 Opus International Consultants Pty Ltd NSW, Australia
Abstract A significant number of railway bridges within New South Wales are constructed from steel and have riveted connections which are forced to flex when transmitting loads through the structure. These connections are typically considered to have only a nominal moment resisting capacity and therefore are predominately designed for shear. Further, these connections are subject to significant dynamic loads, but do not have an appropriate fatigue detail category, which caters for out-of-plane bending. Failure of such connections due to an insufficient allowance for moment, and or short fatigue lives, can have significant consequences as there is typically little redundancy within these simple structures. This paper focuses on angle cleat connections between stringers and cross girders on a number of typical railway structures, which have been subject to a detailed finite element examination of their performance. The study follows work to strengthen the structures and the effect of the ensuing changes in behaviour, as a result of increased stiffness, on the connection details’ moment resisting capacity and fatigue life. The paper outlines the finite element models used to develop a deeper understanding of the behaviour and forces within the angles, such that bolt size and arrangements can be optimized to maximize capacity and fatigue life. The findings of the study highlight the need for designers to consider in more detail the complex behaviour of angle cleat connections, and how limitations imposed when modifying existing structures, need to be examined and understood to ensure that a robust design can be achieved.
Introduction
A significant number of railway bridges within New South Wales are constructed from steel and have riveted connections which need to flex in order to transmit loads through the structure. These structures are nearing 100 years in age and over their life have been exposed to axle and gross masses far in excess of their original design loadings. Additionally, with the increase in freight volumes by rail, these bridges are seeing an increase in train frequency, which in combination with
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higher axle loads, can have significant effects on the residual fatigue life of the structure. At the time of original design and construction, it is perceivable that the fatigue life of such structures was not given much attention, and even today, the simple angle cleat connection of the stringers to the cross girder can easily be overlooked as a simple connection. However, most of the fatigue damage reported on riveted structures has been reported on the riveted connections between the stringers and cross girders, largely attributed to secondary effects, in particular out-of-plane bending [1][2][3]. These connections, whilst appearing simple, often undergo complex deformations to transmit loads, and as loadings increase, and angles and stringers are replaced, more attention is required during design of structural retrofitting to ensure that the connection arrangement is optimized for fatigue performance.
Simple Connections
Figure 1 illustrates a typical railway bridge on part of the New South Wales rail network. These structures generally consist of through girder main beams, connected together with cross girders at regular intervals. The track is usually supported on timber transoms connected to two stringer girders which span between cross beams. The stringers are notionally simply supported, and connected to the cross girder by riveted angle cleats (Figure 2). The stringers are usually placed on a seating angle, although these components do not contribute to the behavior of the connection. (a) (b)
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(c) Figure. 1a Typical Steel Through Girder Span Bridge and Stringer Connection, b Typical underside showing cross girders and stringers, c Typical Angle Cleat Connection
The angle cleats are designed to be nominally pinned, thus transfer the vertical shear action only (often there is a physical gap between the stringer flanges and the cross girder, which would prevent any appreciable transfer of moment). In reality, deflection of the stringers under loading will cause the ends of the girders to rotate, thus deformation of the angle cleats is required to prevent any appreciable build up of moment. In static circumstances, any rigidity provided by the angle cleats could be viewed as advantageous, as the ultimate bending capacity of the member would be increased (up to 50% for a fully rigid connection). However, in a rail environment, subjected to frequent, heavy axle loads, such dynamic effects are likely to (and have been reported to) result in fatigue cracking of the connection if the detail is too stiff and incorrectly designed. Cracking can occur in various places in the connection detail due to the complex stress concentrations, however it will usually occur in the area which exhibits the highest degree of flexing, or around bolt holes. Following cracking of riveted angle cleat connections, studies were made by Wilson[4][5] who recommended minimum gauge lengths to provide adequate flexibility and a reduction in stress ranges, thus improving the fatigue life of the connections. This rule has since been adopted by AS5100 (2004) Clause 3.9.7, as Equation 1:
(1)
Where: g = gauge of the fasteners in the outstanding legs of the upper third of a
member depth
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L = Span length t = connection angle thickness This rule enables designers to follow simple rules-of-thumb guidelines when designing angle cleat connections, thus avoiding difficult and complex analysis to determine joint ductility and stress ranges. However, the consequence of failure of angles could be severe, with little redundancy being a typical feature of these structures. Consequently recent work, undertaken by Opus International Consultants, investigated the stress concentrations within angle cleats as a result of dynamic train loads, and considered the optimal bolt arrangement for maximizing fatigue life, yet maintaining static capability. The study involved modelling angle cleat connections in finite element software to obtain a deeper understanding of the component behaviour and stresses as part of a bridge refurbishment commission for a rail owner/operator, and investigated how to determine an appropriate fatigue life.
Case Study – Retrofit of a Through Girder Bridge
This case study involved the upgrade of an existing through girder structure to accommodate 300LA loading (as per AS5100), located in New South Wales. The structure was approximately 20m long, and carried a single standard gauge main line track, supported on two lines of stringers, each with a span length of 2.5m. A rating analysis of the existing structure confirmed that the through girders and cross girders were adequate for the proposed loading, however the stringers were insufficient and required upgrading. A sensitivity analysis was run to determine the most efficient size of stringers required to carry the new load. This analysis quickly identified the sensitivity of the structure to larger stringers, such that the stiffer members altered the behavior of the structure, attracting load away from the through girders into the stringers. This effect resulted in little negative moment at the cross girders and significantly larger mid-span bending moments in proportion to the previous stringers. The new stringers were to have a significantly thicker web, and thus the gauge of the new angle cleats (if the existing holes in the cross girder were to be utilized), would marginally not comply with Clause 3.9.7, thus the connection would need to be designed to take 50% of the new, higher, midspan bending moment, unless a second column of bolts was installed.
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Two design options were considered. The first design involved installing a second column of bolts to achieve the minimum gauge distance over the top and bottom third of the connection detail. This enabled the connection detail to be designed for only 33% of the mid-span bending moment. However, adding an extra column of bolts provided additional difficulties on site in terms of drilling and fixing, and achieving 50% moment under ULS. As the non compliance with Clause 3.9.7 was only marginal, the adequacy of a 33% moment in this array was investigated, together with the effects of the non-compliance gauge on fatigue life. This solution was compared with adding a new column of bolts and complying with Clause 3.9.7. It should also be noted that achieving the 33% moment at ULS was generally straight forward, however achieving 33% moment capacity at SLS, assuming compliance is based on the non slip capacity of the high strength friction grip bolts, was more challenging. It is not explicit in AS5100 if the requirement for 33% / 50% moment applies for both ULS and SLS, however BS5400, which is operating under a similar philosophy, suggests that meeting this demand is only a requirement at ULS. This would make sense given that the requirement is based around research undertaken 70 years ago, prior to the introduction of HSFG bolts. If the latter is to be followed, there is then no firm guidance on the requirements for SLS design of these connections in the current code.
Modeling the Angle Cleats
The analysis of the two angle cleat options began with developing a finite element model of the connections, as shown in Figure 2 for a typical detail. The models, which were created in SAP2000, modelled the connection of the angles to the cross girder as spring supports, and connection to the stringer as fixed, as it was assumed that under the applied serviceability loads slip did not occur (this was checked later). The high strength friction grip bolts were modelled on the cross girder side only and were pretensioned to enable the influence of the compressive effects on the stresses in the angle leg to be investigated.
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Figure. 2. Typical Connection Model
Once the model was working, an estimate of the serviceability moments and co-existing shear forces needed to be derived, to enable the stress ranges within the angle to be determined. This was achieved by determining the stiffness of the connection through applying a series of increasing moments and then measuring the ensuing rotation. A typical moment / rotation plot is presented in Figure 3a and 3b for the two angle types, where it should be noted that the linear response is due to only linear analysis being undertaken. For flexible connections, a non linear response should be expected with the gradient dramatically reducing with moment, as shown in Figure 4. Assuming a linear response was considered conservative, although the degree of conservativeness varies depending upon the overall stiffness.
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Figure. 3a. Bending Moment – Rotation angle Curve for 1 Column Bolts Connection
Figure. 3b. Bending Moment – Rotation angle Curve for 2 Column Bolts Connection
Rotation ∅ (rad)
Rotation for simply supported beam
Beam lineEnd moment
for fixed beamIncreasing connection stiffness
End moment
Figure. 4. General Bending Moment – Rotation Angle Curve
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A screenshot of the typical deflection recorded in the Finite Element Analysis (FEA) is given in Figure 5. This Figure demonstrates the behavior of the model with two columns of bolts under an applied moment, and confirms that the behavior of the angles corresponds to the distortion theory surrounding the behavior of these joints. The stiffness of the joints with a single and double column of bolts, is presented in Figure 3a and 3b respectively. The single column was determined to have a rotational stiffness of 27000kNm/rad and 8900kNm/rad for the double. This range corresponds well with the suggestions provided in BS5400.3 (1982), which gives a range of 0.5x10-10rad/Nmm (20000kNm/rad) for similar joint types. These rotational stiffness were then entered into a line-beam model of the structure as a joint release and the analysis re-run for 300LA to provide a bending moment at the end of each stringer for each detail. The corresponding moments were compared with the mid-span bending moment of a stringer with full moment release.
Figure. 5. Angle cleat Deformed Shape
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The line-beam analysis indicated that for a stiffness of 27000kNm/rad, the single column joint was attracting approximately 18% of the mid span bending moment and for 8900kNm/rad approximately 8%. These moments were significantly less than the 33% and 50% moments respectively, required by the code, and are also lower than the SLS capacity of the proposed designs, therefore validating the non-slip assumption in the FEA analysis. The analysis was re-run, introducing 8% and 18% of the midspan moments, and co-existent shears into the model to determine the stress ranges under the fatigue loading for both details.
Fatigue Analysis
Figure 6 illustrates the stress concentrations under dynamic loading in the leg connected to the cross girder. The concentrations are consistent with research of others which indicates that the top and bottom bolts, and fillet are subjected to the highest stress concentrations. The concentrations around the lower bolt hole are taken from the rear face of the angle (i.e. the face nearest the cross girder) and are a result of in and out of plane bending due to the angle distorting under negative moment, restraint provided by the HSFG bolt and local stress concentrations due to the bolt holes. These secondary distortional and geometrical effects, makes fatigue analysis in accordance with A5100 difficult to apply. BS5400 Part 10 is clear in that it states stress concentrations should be ignored. AS5100, provides a lower fatigue classification for plates containing bolt holes / stress concentrations, however both codes consider in-plane bending only, with a principal stress direction aligned with the main axis of the material, therefore direct application to these complex geometries is questionable.
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Single column of bolts two columns of bolts
Stress range: MPa
Figure. 6. Stress Distribution in angle cleats
If the concentrations around the bolt holes are considered first, AS5100 and BS5400 suggests using nominal stresses to calculate fatigue life, in conjunction with a lower fatigue classification. In this instance, the nominal stresses away from concentrations should be considered. In this example, this position (albeit relatively arbitrary), could be taken as the bottom edge of the angle cleat. The nominal stresses (derived from averaging the principal stress concentrations), were determined to be 154MPa for the single column connection and 26MPa for the double column connection. This gave a fatigue life of 0.8yrs and 100yrs respectively based on AS5100.6-2004. An alternative approach could be to record the principal peak stress in the concentration, and using the magnification factor due to concentrations (taken to be 2.4), determine the nominal ‘background’ stress. This stress value would be used in conjunction with the higher fatigue classification as the effect of the stress concentration is being directly assessed in the FEA. This calculation gave 106Mpa and 75Mpa of the single and double column connections respectively. Both these approaches gave very different fatigue life estimates. The third approach considered the significance of the location of the stress concentration: while cracking around bolt holes was a concern, the cracks, once initiated may not lead to instability of the connection per se. Of more concern was the potential for cracking in the internal angle which is also required to transfer shear. Using the peak stresses within the corner to calculate fatigue life, in conjunction with the
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higher fatigue classification of 160, the predicted fatigue lives were 2.1 years for the single column connection and 100 years for the double column connection. These results support the findings of Wilson, that increasing the gauge length lowers the peak stresses and increases the fatigue life. The analysis identified that utilizing existing holes (in a like-for-like replacement) was not feasible as the geometry of the connection had marginally altered in terms of an increased stringer web thickness. The analysis also highlighted the difficulties of determining fatigue life in complex distortional modes in accordance with the codes which currently only consider normal stresses and shear stresses.
Conclusions
The analysis of angle cleat connections for fatigue life is complex and to date the design codes for cleat flexible connections are based around empirical testing and analysis. Furthermore the current fatigue codes do not lend themselves well to addressing stress concentrations as a result of secondary distortional effects which involves out-of-plane bending. FEA modelling of the angle cleat connections enabled a detailed examination of their performance to be ascertained, and fatigue findings compared well with the code guidance on gauge lengths. While both designs suggested a much lower moment transfer than that allowed for in the code, there were significant differences in calculated fatigue life, supporting compliance with the code in terms of gauge length rather than assuming using the existing holes would suffice. The study also found that while the connections can be relatively easily designed for 33% moment at ULS, achieving 33% moment capability at SLS is more challenging. However, based on the rotational stiffness’s implied by the FEA model, the flexibility of the connection (moments developed at the stringer connection) may be significantly lower than the 33% value and confirmed that moments are generated in these simple connections. The investigation highlighted the need to accommodate the code to ensure that a 100 year fatigue life can be met. Where compromises in the gauge length are required, it is recommended that a detailed fatigue assessment is undertaken.
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References
[1] Righiniotis TD, Imam BM, Chryssanthopoulos MK. (2008) Fatigue analysis of riveted railway bridge connections using the theory of critical distances. Engineering Structures, 30 (10), pp. 2707-2715
[2] Imam BM, Righiniotis TD, Chryssanthopoulos MK. (2008) Probabilistic fatigue evaluation of riveted railway bridges. Journal of Bridge Engineering, 13 (3), pp. 237-244
[3] Imam BM, Righiniotis TD, Chryssanthopoulos MK.(2007) Numerical modelling of riveted railway bridge connections for fatigue evaluation. Engineering Structures, 29 (11), pp. 3071-3081
[4] Wilson, W.M. (1940) Design of Connection Angles for Stringers of Railway Bridges. University of Illinois
[5] Wilson, W.M., and Coombe, J.V. (1939) Fatigue Tests of Connection Angles. Engineering Experiment Station Bulletion Series No.317, University of Illinois
