Behaviour of retrofitted steel structures using cost effective retrofitting techniques

Journal of Constructional Steel Research 131 (2017) 38–50

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Journal of Constructional Steel Research

Behaviour of retrofitted steel structures using cost effective retrofitting techniques Olivia Mirza a,⁎, Sukanta Kumer Shill b, Fidelis Mashiri a, Daniel Schroot c a b c

Department of School of Computing, Engineering & Mathematics, University of Western Sydney, Australia Department of Civil Engineering, Dhaka University of Engineering & Technology (DUET), Gazipur 1700, Bangladesh School of Computing, Engineering & Mathematics, University of Western Sydney, Australia

a r t i c l e

i n f o

Article history: Received 31 August 2016 Received in revised form 15 December 2016 Accepted 31 December 2016 Available online xxxx Keywords: Steel bridge girder Fatigue failure Retrofitting technique

a b s t r a c t Steel structures today are edging towards the end of their design life. Recently, the frequency and magnitude of loadings are becoming significantly greater in comparison to the initial design loads at the time of construction. Deterioration from prolonged exposure to environmental conditions including weathering and climate change, as well as the effects of human error, also influence the design life of these older steel structures. The research focuses on developing a comparison between the fatigue performance of 120 years old and new equivalent steel structures. The fatigue resistance of both the old riveted and new welded steel structures is evaluated by investigating and analysing the stresses at critical locations within the structures. Retrofitting techniques are applied to both the old and new structures and analyzed in terms of their capacity to increase resistance to fatigue failure and extend the design life of steel structures. The research is conducted by performing both experimental study and finite element analysis. The experimental research analyses the performance of an old riveted structure, as well as a new equivalent prefabricated hot rolled section, to determine areas which are highly susceptible to fatigue failure. The numerical analysis using the finite element package ABAQUS is conducted to model both the old and new girder. Retrofitting proposals are introduced into the FE model both with and without the fatigue induced cracking to investigate improvements in the fatigue performance of the old and new girders, as well as techniques of repairing existing damage. The retrofitting techniques are cost effective and practical in engineering today to improve the performance and loading capacities to enhance the design life of steel structures. The retrofitting techniques are innovative, cost effective and practical in engineering today to improve the performance and loading capacities to enhance the design life of steel structures. An overall conclusion determines the extent of increasing design life, enhancing profitable engineering and focus on sustainability, in comparative terms of either retrofitting an old structure or replacing it with a new steel structure. Crown Copyright © 2017 Published by Elsevier Ltd. All rights reserved.

1. Introduction During the late 19th and early 20th centuries, riveted steel construction increased in popularity as a result of rapid development of the transport system. Further developments and reliance on transport, increased the frequency of loading and effects of fatigue on these structures [1]. These riveted structures typically have a design life of 100 years, and are therefore reaching the end of this period and becoming more susceptible to fatigue based failure. Kuhn et al. [1] also identified the popularity of repair and strengthening of these types of structures in order to prevent fatigue failure and extend the design life of the structures. Riveted steel structures maintained their popularity until the middle part of the 20th century, when pre-fabricated steel structures such as welded and hot rolled sections became the dominant product for use in the steel construction industry. Even in today's ⁎ Corresponding author. E-mail address: [email protected] (O. Mirza).

http://dx.doi.org/10.1016/j.jcsr.2016.12.026 0143-974X/Crown Copyright © 2017 Published by Elsevier Ltd. All rights reserved.

society, pre-fabricated steel structures are still the preferred choice of steel product for engineers and designers. These types of structures have not been around long enough to come close to the 100 year design life, however it has been identified that fatigue based damage is occurring to these types of steel structures [1]. Due to technological developments and advancements in engineering knowledge, it can be shown that older bridges are subjected to increased loading conditions in comparison to the initial design loads. Steel bridges today are subjected to much larger magnitude and frequency of loadings compared to those at the time of construction [2]. Fatigue is a key failure component for steel structures that determines the structural performance. Repetitive application of various loadings can cause fatigue damage to continuously accumulate even though the loads may be well below the structural capacity of the steel structure. Understanding the effects of fatigue based damage with particular focus on steel structures such as steel bridges, has become more important as a result of increased magnitude and

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frequency of loadings due to population increases and reliance on and development of transport infrastructure. Sustained increases in fatigue damage (cracking) may lead to progressive failure of the structure [3]. Fatigue is complex and not precisely modelled due to the multitude of factors which control the response to cyclic loading. Therefore, experimental testing and finite element analysis is generally conducted to evaluate the fatigue behaviour of the structural members [4]. Rasidi et al. [5] classified fatigue failure into two types, low cycle fatigue and high cycle fatigue, dependant on the magnitude of the stress/ strain and the number of cycles of the loading. Low cycle fatigue failure occurs when the structure fails after minimal cycles (a few cycles up to a few tens of thousands of cycles) under a large loading. High cycle fatigue failure occurs when the structure fails after a much greater number (several million) of cycles. The fatigue behaviour and failure of a structural element is dependent on a number of factors including the magnitude of the stress, material properties, temperature, surface finishing and the presence of any defects. Rasidi et al. [5] identified two key examples of defects which would indicate the presence of fatigue failure, a plate element with a hole and a notched plate. These two defects are associated with areas of higher stress/strain, therefore the cyclic loading will cause minute cracking to develop and become larger with each cycle, eventually leading to rupture of the steel section. Fig. 1 shows the fatigue cracking due to a plate element with a hole and a notched plate. A typical example of fatigue cracking due to a plate element with a hole is shown in Fig. 2. Fig. 2 shows a small fatigue crack near the hole, which over time has propagated along the direction of the arrows over a larger portion of the section. The most common approach to the visual representation and analysis of a fatigue assessment is to plot an S-N curve, where the total cyclic stress (S) is plotted on the y axis, against the number of cycles to failure (N) on a logarithmic scale on the x-axis. Rasidi et al. [5] recognised that an increase in the stress range of the cyclic loading will reduce the fatigue life of the steel structure. A typical S-N curve is shown in Fig. 3. The point at which the S-N curve flattens off is the fatigue limit. Ideally, if the applied loading is in the range of stress below the fatigue limit, the steel element should never be susceptible to fatigue failure. However, in the real situation, bridges are exposed to various condition which caused fatigue failure, therefore this research herein is looking at the fatigue behaviour of retrofitted steel structures using cost effective materials.

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Fig. 2. Typical fatigue cracking due to plate with a hole. (Dexter & Ocel [10].)

2. Experimental program Static strength tests were conducted on both the new and old girders in the Western Sydney University (WSU) laboratory. Both girders were simply supported with loading at the mid-span. Both girders were preloaded to 100 kN, and the load removed in three cycles before being loaded until failure. 2.1. Installation and test setup All girders are 6477 mm in length, with stiffening plates as per Fig. 4 (Girder diagram showing dimensions, locations of stiffeners, loading and support system), with the dimensions as shown in Fig. 5. The test included the use of the following equipment: 1. 100-t hydraulic press to apply point load at the mid-span of the girders. 2. Roller support systems at each end of the girders. 3. Single and strip strain gauges to measure and record the stresses at the most critical locations within the girders. 4. Linear Variable Displacement Transducers (LVDT) to measure and record the deflection data for the girders under load. The ultimate strength test (static load test) was carried out until failure on one of each of the provided old rivet and new welded steel girders (Table 1). 2.2. Static strength capacities The Australian Standard for Steel Structures, AS4100-2012 (SAI [11]) was used to determine the shear capacity, moment capacity and ultimate applied load capacity of the old and new girders. Theoretically, the 120 year old RMS girder should fail following the application of a 583 kN point load is applied at the mid-span, while to new equivalent girder should fail following the applied load reaching 690 kN. The static

Fig. 1. Fatigue cracking due to stress concentration in plate with a hole and notched plate. (Rasidi et al. [5].)

Fig. 3. Typical S-N curve showing low cycle and high cycle fatigue and endurance.

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O. Mirza et al. / Journal of Constructional Steel Research 131 (2017) 38–50

Fig. 4. Girder diagram showing dimensions, locations of stiffeners, loading and support system.

strength represents a single increasing point load being applied at the mid-span of the girder until failure occurs.

3. Finite element analysis Large bridges often have many design attributes, therefore carrying out an experimental study to determine fatigue damage is difficult. Finite Element Modeling (FEM) is a suitable method of studying a steel structure where experimental testing cannot be conducted [6]. ABAQUS is a finite element analysis software that enables the defining of geometric and material properties, as well as constraint conditions, plastic deformation and element connections [7]. Hot Spot Stress evaluation is a technique used to analyse FEM results [8]. Poutiainen et al. [8] identified three methods for hot spot stress evaluation, focussing on Linear Surface Extrapolation (LSE), Through Thickness at Weld Toe (TTWT) and Dong method. Both the new and old girders were reasonably accurately modelled using the finite element modeling software ABAQUS. The conditions in the experimental test, including boundary conditions, constraints and load application were simulated within the FE model. The sensitivity analysis was undertaken by performing different size mesh. The optimum mesh size was defined through convergence results. The load vs. deflection performance of the girders is investigated along with the stress concentration at various critical locations within the girders. Three-dimensional eight-node reduced integration brick elements (C3D8R) are used to model the steel girder and steel plates. Three-dimensional twenty-node reduced integration brick elements (C3D20R) are used to model the bolts. The brick elements give a solution of

comparable accuracy at a better rate of convergence and less computational time than the other elements. Based on the results of the hotspot analysis of the stresses in each girder, fatigue based cracking is introduced into the model. The fatigue cracks are modelled by inputting a 1 mm wide crack using the cut function in ABAQUS at the most critical locations within the girders. The stress strain behaviour of bolts and steel girders is similar. They behave as linear elastic materials until yielding, followed by plastic behaviour. Material is modelled as elasto-plastic material in FE ABAQUS model. The yield strength of 120 years old steel girder is 220 MPa and the yield strength of additional plate is 340 MPa. The load and deflection data for both the 120 year old RMS girder and new equivalent girder was found by applying a point load in ABAQUS with magnitude well above the ultimate applied load capacity. This corresponded to a load of 750 kN for the 120 year old RMS girder and 1050 kN for the new equivalent girder. These magnitudes ensure that the post-yield performance of the girder is thoroughly investigated. Fatigue analysis of the girders is conducted by assessing the stress at critical points in the girders under a load magnitude within the fatigue or elastic range of the steel [9]. 4. Results and discussions The 120 year old RMS girder experienced local and distortional buckling, significant surface rust, as well as missing rivets, holes in the web. Local buckling occurred in the top flange as a result of compression at the location of the applied point load, as shown in Fig. 6. Distortional buckling also occurred as a result of lateral displacement throughout the application of the point load. Both the flange and web elements underwent distortional buckling, which is shown in Figs. 7 and 8. The new equivalent girder also experienced a similar extent of buckling as the 120 year old RMS girder. Local buckling was observed in the flange due compression caused by the applied point load, while distortional buckling was observed due to twisting from a lack of lateral restrain along the length of the girder. The extent and type of buckling is shown in Figs. 9 and 10. 4.1. 120 year old RMS girder The girder was simulated in ABAQUS according to the yields stress (fy) value of 220 MPa obtained from the steel tensile coupon tests con-

Table 1 Section properties for 120 years old RMS girder and new equivalent girder.

Fig. 5. Cross-sections of girder at the mid-span.

Girder capacity

120 years old RMS girder

New equivalent girder

Shear capacity Moment capacity (major axis bending) Ultimate applied load capacity

636.1 kN 874.5 kN m

1306.9 kN 1118.6 kN m

583 kN

690 kN

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Fig. 6. Local buckling in the flange due to compressive load.

ducted. The model was processed in three stages, including the uncracked, cracked and retrofitted (both uncracked and cracked) girders. Fig. 8. Distortional buckling in the flange.

4.1.1. Uncracked girder The time-step load and deflection data outputs from ABAQUS were combined to produce a load vs. deflection curve for the uncracked 120 year old RMS girder, shown in Fig. 11. As the girder was from a 120 year old railway bridge, it was expected that some substantial degree of fatigue based damage had already occurred prior to conducting the experimental study. In terms of the ultimate applied load capacity of the girder, the maximum load carried by the girder in the FE model was 545 kN, while the result from the experimental study was 501.1 kN, an increase of 8.1%. This is again expected due to the FEA not taking into account the service life history of the girder. The elastic load limit was found to also increase from 375 kN for the experimental study to 481.5 kN for the FE model, or by 28.4%. Again, this can be attributed to the unknown service history of the girder. The girder stiffness during the elastic range of the steel calculated for the FE model was 31.7 kN/mm, while the stiffness calculated for the experimental test was only 26.0 kN/mm. The FE model also showed increased ductility of failure when compared to the experimental study due to the elasto-plastic material model adopted in FE ABAQUS model. Reduced ductility in the experimental test reflects prolonged exposure to loading within the service life of the girder which leads to cumulative fatigue damage. The FE model also showed decreased ductility of failure when compared to the experimental study, which was as expected due to the earlier signs of progressive failure due to prolonged exposure to loading within the service life of the girder which leads to

cumulative fatigue damage. The plastic load range of the steel was found to have decreased from 140.1 kN for the experimental study to 63.5 kN for the FE model, or by 45.5%. The stress distribution output for the uncracked girder is shown in Fig. 12. The stress is displayed by a colour contour system, with the scale ranging from blue for areas of low stress, to red for areas of high stress. Due to the position of the applied loading being at the midspan, the focus area for the stress analysis is also at the mid-span, taken to be the region between the two central stiffening plates. Fig. 12 displays the areas of highest stress as being at the center at the top section of the girder, where the girder is under maximum compression, and at the center at the bottom section of the girder, where the girder is in maximum tension. The areas for maximum compression and tension are associated with the maximum bending moment being located at the mid-span, which is as a result of the roller support systems carrying zero moment at the ends of the girder, and the mid-span load application. As part of the analysis of the fatigue performance of the girder, the distribution of the internal stresses at the critical locations where fatigue cracking will occur, determined to be at the mid-span at the bottom flange due to large concentration of tensile stress, was investigated. The magnitude of the applied load was set to the identified elastic load limit of the girder from the load vs. deflection curve of the FE model, equal to 481.5 kN. The maximum principal stress values at four

Fig. 7. Distortional buckling in the web.

Fig. 9. Local buckling in the flange.

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Fig. 12. Contour plot of internal stress in uncracked 120 year old RMS girder.

Fig. 10. Distortional buckling of the web and flange.

critical points in the bottom flange, as shown in Fig. 13, were found at varying distances from the mid-span, and the stress vs. distance away from the crack location was plotted for the four points, as shown in Fig. 14. Fig. 14 Displays relative uniformity of the internal stresses across the entire area of the bottom flange. As expected, a higher value for the stress is found at the two points on the extreme tensile edge of the flange, due to an increased distance from the girder's neutral axis and therefore increased magnitude of tension due to the moment from the mid-span loading. Also, Fig. 14 displays a constant decrease in the magnitude of the internal stress uniformly across the entire area of the bottom flange as the distance from the mid-span increases. This is due to a reduction in the magnitude of the moment associated with the loading conditions and supports as the distance from the mid-span increases. At the location of the cracking, the value of the internal stress is equal to the yield stress of 220 MPa, which confirms that the value of the applied load (481.5 kN) corresponds to the upper limit of the elastic region of the steel. 4.1.2. Cracked girder Based on the analysis of the uncracked 120 year old RMS girder, it was determined that fatigue cracking will propagate from the bottom flange at the centre location of the girder. The hot spot stress method was used to determine the potential crack locations under cyclic loading. High cycle fatigue behaviour is related to the elastic response region

Fig. 11. Load vs. deflection curve for 120 year old RMS girder.

of the load-deflection curves under static loading. This is due to this area having the highest concentration of tensile stress, which will show the first signs of fatigue damage. The fatigue cracking is modelled in two stages, with the initial crack developing in the bottom flange plate only, and then the crack fully extended through the entire bottom flange, including the horizontal plate in the equal angle section and extreme lower section of the web, as shown in Fig. 15. The time-step load and deflection data outputs from ABAQUS for both stages of fatigue cracking were combined to produce a load vs. deflection curve for the cracked 120 year old RMS girder. The load vs. deflection curve for both the partially and fully cracked models was plotted on the same axis as the load vs. deflection curve for the uncracked model, shown in Fig. 16. Fig. 16 displays that the uncracked and partially cracked girders produced similar performance results in terms of elasticity, ultimate applied load capacity and ductility. Fig. 16 displays similar performance between the uncracked and partially cracked 120 year old RMS girders in terms of the ultimate applied load capacity, with only a small reduction from 545 kN to 535 kN, or by 2% observed. The equal angle section of the girder connecting the bottom flange plate to the web is still totally intact and provides confinement to the fatigue crack as well as provides a load transfer path for the tensile stress to the cracked bottom flange plate. There is still a large cross-sectional area suitable to carry the tensile stresses associated with bending under the applied point load. The partially cracked girder was found to have a reduced range of elasticity compared to the uncracked girder, with the elastic load limit reduced from 481.5 kN to 375 kN, or by 22.1%. The stiffness of the partially cracked girder during the elastic range of the steel was calculated to be 31.3 kN/mm, down from 31.7 kN/mm for the uncracked girder as identified previously. As the elastic load limit is decreased by a significantly greater margin than the ultimate applied load capacity, an increase of the ductility of the failure is achieved. This is further emphasized by the increase in the plastic load range of the steel, with the post yield load range increasing from 63.5 kN to 160 kN, or by 152%. The introduction of fatigue cracking through the entire bottom flange however, significantly impacted on the performance of the 120 year old RMS girder. The ultimate applied load capacity was reduced from 545 kN to 440 kN, or by 19.4%, while the elastic load limit was reduced from 481.5 kN to 245 kN, or by 40.8%. This indicates a substantial degradation in the ongoing performance of the girder, as load magnitudes in the post-elastic range of the steel will lead to permanent damage to the structure. It also indicates that further fatigue damage

Fig. 13. Critical point locations for analysis of internal stresses in 120 year old RMS girder.

O. Mirza et al. / Journal of Constructional Steel Research 131 (2017) 38–50

Fig. 14. Stress vs. distance from crack location curve for critical points in 120 year old RMS girder.

will occur at a lower magnitude for the applied load and a reduced number of cycles when compared to the uncracked and partially cracked girders. The introduction of fatigue cracking through the entire flange was also calculated to further reduce the stiffness of the girder through the elastic range to 29.6 kN/mm. The ductility of the failure is also further increased, with the plastic load range of the girder reaching 195 kN, an increase of 307% over the uncracked girder. The stress distributions for the partially cracked and fully cracked 120 year old RMS girder are shown in Figs. 17 and 18. Fig. 17 shows a similar result in terms of the stress distribution for the partially cracked girder as the uncracked girder, however a small stress increase at the central webflange interface is observed along with a stress reduction at the outer edge of the flange, due to discontinuity within the section as a result of the introduced cracking in the bottom flange plate and load transfer through the equal angle section. The stress distribution is observed to normalise as the distance from the crack location increases along the girder towards the central stiffening plates. Fig. 18 however, displays a transfer of the critical stress locations from the bottom flange upward into the lower section of the web. This is as expected due to the bottom flange plate and equal angle section having significantly reduced capacity to carry the large tensile stresses associated with the mid-span bending moment due to discontinuity as a result of the introduced cracking, and the cracking no longer being contained by structural ties to other elements. The lower section of

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Fig. 16. Load vs. deflection curve for cracked 120 year old RMS girder.

the web is also exposed to larger magnitude tensile stresses, with web buckling contributing to the increased ductility of the failure. An investigation into the stress distribution at the four critical locations identified in Fig. 13 was also conducted for the both the partially cracked and fully cracked 120 year old RMS girder. The magnitude of the applied point load was set to the elastic load limit of the uncracked girder, equal to 481.5 kN. The maximum principal stress values at four critical points in the bottom flange were found at varying distances from the mid-span, and the stress vs. distance away from the crack location was plotted for the four points, as shown in Figs. 19 and 20. Both Figs. 19 and 20 display non-uniformity of the internal stresses at the critical points in the bottom flange. As expected, an increase in total stress is found at the two points at the web-flange interface due to load transfer through the riveted connection between the two plate elements and the equal angle section. The outer edge of the bottom flange experienced a significant decrease in total stress due to the introduced fatigue cracking and an increased distance along the load path from the web element. As expected, a convergence to the relatively uniform stress distribution as observed for the uncracked girder is displayed as the distance from the crack location increases. This occurs at a distance of 250 mm from the location of the crack and at a stress magnitude of approximately 200 MPa for the partially cracked girder and at a distance of 450 mm from the fatigue crack location and at a stress magnitude of approximately 200 MPa. These two distances indicate the critical area which requires structural retrofitting to reduce the influence of the introduced fatigue cracking and re-establish stability of the section. 4.1.3. Retrofitted girder Based on the analysis of the stress distribution in the uncracked and cracked 120 year old RMS girders, it was determined that the critical region for retrofitting was in the bottom flange at the center location of the girder, within 450 mm either side of the mid-span fatigue crack location. This is due to this area having the highest concentration of tension, and the fatigue cracking displaying the largest influence on the girder. The retrofitting proposal includes an additional plate of

Fig. 15. Fatigue crack development in 120 year old RMS girder — Stage 1 (L) and Stage 2 (R).

Fig. 17. Contour plot of internal stress in partially cracked 120 year old RMS girder.

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Fig. 18. Contour plot of internal stress in fully cracked 120 year old RMS girder.

12.6 mm thickness, the same thickness as the existing flange plates, attached to the bottom of the flange by 19 mm diameter Ajax bolts falling into strength group M8.8, which extends between the two center stiffening plates, a distance of 705 mm either side of the fatigue crack location to match the distance between the centre stiffeners. The additional plate has material properties which match the steel of the new equivalent girder (fy = 340 MPa). The use of rivets to construct the I-section prevents the placement of another plate on the top side of the bottom flange due to not allowing a flat contact surface between plates. The bolt layout has been determined by AS4100. The location of the additional plate in the cross-section is as shown in Fig. 21. The bolt layout and extent of the retrofitting plate was modelled in ABAQUS, as shown in Fig. 22. The time-step load and deflection data outputs from ABAQUS for both the model were combined to produce a load vs. deflection curve for the retrofitted 120 year old RMS girder. The load vs. deflection curve for the retrofitted model was plotted on the same graph as the load vs. deflection curve for the standard model, shown in Fig. 23, where both girders are in the uncracked state. Fig. 23 shows that the retrofitted girder has an increased ultimate applied load capacity, as well as an extended elastic range and an increased ductility of the failure mode. The ultimate applied load capacity of the girder increased from 545 kN for the standard girder to 660 kN for the retrofitted girder, or by 21.1%. This represents an increase in the overall design capacity of the girder, which will be useful when identifying if an existing bridge structure is capable of carrying a new loading condition (e.g. a new type of train with increased axle load for a railway bridge) despite being designed for the typical load cases experienced up to or greater than 100 years ago. The upper elastic load limit for the girder is increased from 481.5 kN for the standard girder to 540 kN for the retrofitted girder, or by 12.0%. This represents a significant improvement in the fatigue performance of the girder, as the retrofitted girder can carry the same magnitude of loading as the standard girder at a lower proportion of the elastic load limit, and therefore with an increased number of loading cycles required

Fig. 19. Stress vs. distance from crack location curve for critical points in 120 year old RMS girder (partially cracked).

Fig. 20. Stress vs. distance from crack location curve for critical points in 120 year old RMS girder (fully cracked).

to cause failure by fatigue. This is significantly important when discussing the future design life of the structure. An increased number of cycles for a given loading magnitude will correspond to an extension of the allowable service life of the structure before fatigue based failure will occur. The stiffness of the girder within the elastic range has also increased from 31.7 kN/mm for the standard girder to 33.7 kN/mm for the retrofitted girder, or by 6.3%. This represents the scale of the reduction in total deflection for any given applied load magnitude after the installation of the retrofitting techniques. The load vs. deflection curve for the retrofitted girder also displays an increase in the ductility of the failure modes when compared to the standard girder. The plastic load range of the girder is increased from 63.5 kN for the standard girder to 120 kN, or by 89% for the retrofitted girder. This indicates a more progressive mode of failure, rather than the more sudden failure for the standard girder. The ductility is an important factor to take into account for engineers, as a slow, progressive failure mode can be detected and action taken prior to complete failure, which could cause major safety concerns, particularly when considering the use of the structure as a public utility, in particular a railway bridge,

Fig. 21. Retrofitted 120 year old RMS girder cross-section showing retrofitting plate and bolt location.

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Fig. 22. FE model of retrofitted 120 year old RMS girder showing extent of retrofitting plate and bolt layout.

where sudden failure could have catastrophic consequences. The stress distribution for the retrofitted (uncracked) 120 year old RMS girder is shown in Fig. 24. Fig. 24 shows a relatively uniform stress distribution in the lower section of the web and bottom flange. There is a large concentration of stress in the additional retrofitting plate, as this plate carries the majority of the tension due to being located at the extreme tension edge. There are no evident effects on the stress distribution in the web which could cause local buckling. The stress distribution for the retrofitted (partially cracked) 120 year old RMS girder is shown in Fig. 25. Fig. 25 shows again, a relatively uniform stress distribution in the bottom flange; however a small area of high stress is identified in the very lower section at the web-flange interface as a result of the induced fatigue cracking. There is a large concentration of stress in the additional retrofitting plate, as this plate carries the majority of the tension due to being located at the extreme tension edge. There are no evident effects on the stress distribution in the web which could cause local buckling. The stress distribution for the retrofitted (fully cracked) 120 year old RMS girder is shown in Fig. 26. Fig. 26 shows a non-uniform stress distribution in the lower section of the bottom flange. In close proximity to the induced fatigue cracking (within100mm either side of the crack location) a significant decrease in the internal stress is identified at the outside edge at the top of the bottom flange plate. The stress at the web-flange contact is significantly increased due to the web-flange connection. A large stress concentration is identified in the very lower section of the web as a result of the induced fatigue cracking. There is a large concentration of stress in the additional retrofitting plate, as this plate carries the majority of the tension due to being located at the extreme tension edge. There are no evident effects on the stress distribution in the web which could cause local buckling. In all cases of the retrofitted girder, there is a noticeable concentration of stress at the locations near the bolt holes, which is as expected due to reduction in the cross-section area to carry the tensile stresses as a result of bending.

Fig. 23. Load vs. deflection curve for retrofitted 120 year old RMS girder.

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Fig. 24. Contour plot of internal stress in retrofitted 120 year old RMS girder (uncracked).

An investigation into the stress distribution at the four critical locations identified in Fig. 13 was also conducted for the both the uncracked, partially cracked and fully cracked retrofitted 120 year old RMS girder. The magnitude of the applied load was set to the elastic load limit of the uncracked girder, equal to 481.5 kN. The maximum principal stress values at four critical points in the bottom flange were found at varying distances from the mid-span, and the stress vs. distance away from the crack location was plotted for the four points, as shown in Figs. 27, 28 and 29. The stress distribution curves for all three cases of the retrofitted 120 year old RMS girder present similar results which prove the effectiveness of the retrofitting techniques. The four critical locations in the bottom flange experience considerably greater uniformity in terms of stress values when compared to the relative uncracked, partially cracked and fully cracked girders shown in Figs. 13, 18 and 19. Even when the fatigue cracking was included in the retrofitted girder model, the stress distribution remained relatively uniform across the four locations, due to the confinement and ‘bridging effect’ of the retrofitting plates. A reduction in stress was however observed across the top surface of the bottom flange in the fully cracked state. In all cases, the stress output at any point in the bottom flange was found to be the yield stress of 220 MPa. At the critical mid-span, the maximum stress at any point in the bottom flange for the uncracked girder was reduced from the yield stress of 220 MPa for the standard girder to 136 MPa, a reduction of 38.2%. The maximum stress at any point in the bottom flange at the mid-span for the partially cracked girder was reduced from 270 MPa for the standard girder to 170 MPa, a reduction of 37.0%. The maximum stress at any point in the bottom flange at the mid-span for the fully cracked girder was reduced from 411 MPa for the standard girder to 172 MPa for the retrofitted girder, a reduction of 58.2%. As expected, the holes for the retrofitting bolts also impacted on the stress distribution in the bottom flange. The centres of the bolts were spaced at 200 mm apart, with the first bolt centre 52.5 mm from the crack location. Therefore the bolt hole locations correspond to the distances 52.5 mm, 252.5 mm and 452.5 mm in Figs.s 27, 28 and 29. These locations correspond to local spikes in the magnitude of the stress at the critical locations in the bottom flange, which is consistent across the uncracked, partially cracked and fully cracked cases of the model.

Fig. 25. Contour plot of internal stress in retrofitted 120 year old RMS girder (partially cracked).

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Fig. 26. Contour plot of internal stress in retrofitted 120 year old RMS girder (fully cracked).

The bolt holes however, had a larger impact on the stress at the two points on the outer edge of the flange, which can be attributed to a reduction in net cross-section area at these locations, and prevention of the direct load transfer due to the placement of the holes. The two points at the web-flange interface were less affected due to constraint between the web and flange plate elements by the equal angle section. The stress increase associated with the bolt hole nearest to the crack location (corresponding to the distance 52.5 mm in Figs. 27, 28 and 29) displays a stress value approaching very close to the yield stress of 220 MPa. 4.2. New equivalent girder The girder was simulated in ABAQUS according to the yields stress (fy) value of 340 MPa obtained from the standards. The model was processed in three stages, including the uncracked, cracked and retrofitted girders. 4.2.1. Uncracked girder The time-step load and deflection data outputs from ABAQUS were combined to produce a load (vertical axis) vs. deflection (horizontal axis) curve for the uncracked new equivalent girder, which was plotted on the same axes as the load vs. deflection curve for the experimental analysis, shown in Fig. 30. The resulting load vs. deflection curve from the FE model however, indicates a slightly longer period of elasticity compared to the experimental analysis, as well as a reduced ductility of the failure mode. This can be explained by the lateral buckling experienced in the experimental analysis, which is restricted in ABAQUS. The stiffness of the FE model was calculated as 27.5 kN/mm, while the experimental analysis displayed a stiffness of 28.4 kN/mm. The stress distribution output for the uncracked girder is shown in Fig. 31. The stress distribution displays the locations for the highest total stress as being at the centre at the top section of the girder,

Fig. 27. Stress vs. distance from crack location curve for critical points in retrofitted 120 year old RMS girder (uncracked).

Fig. 28. Stress vs. distance from crack location curve for critical points in retrofitted 120 year old RMS girder (partially cracked).

where the girder is under maximum compression, and at the centre at the bottom section of the girder, where the girder is under maximum tension. The areas for maximum tension and compression are associated with the maximum bending moment being located at the mid-span, which is as a result of the roller support systems carrying zero moment at the ends of the girder, and the mid-span load application. As part of the analysis of the fatigue performance of the girder, the distribution of the internal stresses at the critical locations where fatigue cracking will occur, determined to be at the mid-span at the bottom flange due to large concentration of tensile stress, was investigated. The magnitude of the point load was set to the identified elastic load limit of the girder (600.0 kN). The maximum principal stress values at four critical points in the bottom flange, as shown in Fig. 32, were found at varying distances from the mid-span, and the stress vs. distance away from the crack location curve was plotted for the four points, as shown in Fig. 33. Fig. 33 indicates uniformity of the internal stresses across the entire area of the bottom flange. As expected, a higher value for the stress is found at the two points on the extreme tensile edge of the flange, due to an increased distance from the girder's neutral axis and therefore increased magnitude of tension due to the moment from the mid-span loading. As expected, Fig. 33 displays a constant decrease in the magnitude of the internal stress uniformly across the entire area of the bottom flange. This is due to a reduction in the magnitude of the moment associated with the loading conditions and support set-up as the distance from the mid-span increases. At the location of the cracking, the value of the internal stress is equal to the yield stress (340 MPa), which confirms the value of the applied load (600.0 kN) corresponding to the upper limit of the elastic region of the steel.

Fig. 29. Stress vs. distance from crack location curve for critical points in retrofitted 120 year old RMS girder (fully cracked).

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Fig. 32. Critical point locations for analysis of internal stresses in new equivalent girder.

Fig. 30. Load vs. deflection curve for new equivalent girder (FEA & Experiment).

4.2.2. Cracked girder Based on the above analysis of the uncracked new equivalent girder, it was determined that fatigue cracking is most likely to propagate from the bottom flange at the centre location of the girder. This area is highlighted by the red area in the contour plot of internal stress in Fig. 33. This is due to this area having the highest concentration of tensile stress, which will show the first signs of damage. The fatigue cracking is modelled in only one stage, with the initial crack developing through the full extent of the bottom flange, shown in Fig. 34. The time-step load and deflection data outputs from ABAQUS for the cracked stage were combined to produce a load vs. deflection curve for the cracked new equivalent girder. The load vs. deflection curve for the cracked model was plotted on the same axis as the load vs. deflection curve for the uncracked model, shown in Fig. 35. Fig. 35 displays a significant impact on the elasticity and ultimate applied load capacity of the girder as a result of the introduction of cracking to the model. The ultimate applied load capacity was observed to decrease from 750 kN for the uncracked girder to 604 kN for the cracked girder, or by 19.5%. Fig. 35 also shows a reduction of the elastic load limit of the load from 600 kN for the uncracked girder to 268 kN for the cracked girder, or by 55.3%. The introduction of fatigue cracking was also calculated to reduce the stiffness of the girder through the elastic range to 23.8 kN/mm. The cracked model proved to undergo a more ductile failure however, with the plastic load range increased from 150 kN for the uncracked girder to 336 kN for the cracked girder, or by 124%. The stress distribution output for the cracked girder is shown in Fig. 36. The stress distribution displays an upward shift in the concentration of the highest tensile stresses into the lower section of the web element. This is due to the introduced crack which prevents the bottom flange from carrying the majority of the tensile stress due to disconnection of the section. As a result, the web element is forced to carry the tensile stresses which would have previously been carried by the bottom flange. The stress distribution normalises as the distance from the crack location increases, due to the bottom flange being connected to

Fig. 31. Contour plot of internal stresses in uncracked new equivalent girder.

the remainder of the section by the structural weld, which allows for a load transfer path for the tensile stress. The stress distribution also displays non-uniformity of the internal stress across the width of the bottom flange, with a smaller magnitude of stress found at the outer edges when compared to the web edge. This is also seen to normalise as the distance from the crack location increases to become similar to the stress distribution for the uncracked section. As part of the analysis of the fatigue performance of the girder, the distribution of the internal stresses at the same critical locations as identified previously was investigated. The magnitude of the point load was again set to the identified upper limit of the elastic region of the girder (600 kN). The maximum principal stress values at the four critical points in the bottom flange were found at varying distances from the midspan, and the stress vs. distance away from the crack location curve was plotted for the four points, as shown in Fig. 37. Fig. 37 indicates non-uniformity of the internal stresses across the entire area of the bottom flange. As expected, a higher value for the stress is found at the two points on the internal web edge of the flange, due to the welded connection transferring some of the tensile stresses which are now carried by the web. The two points on the outer edge of the flange experience very low tensile stress in comparison, due to the introduced crack preventing the flange from carrying the tensile stress at the mid-span. As expected, Fig. 37 displays a convergence to a uniform stress distribution across the entire area of the bottom flange as the distance from the crack location increases. This occurs at a distance of 300 mm from the location of the crack and at a stress magnitude of approximately 260 MPa. This indicates the critical area which requires structural retrofitting to reduce the influence of the induced fatigue cracking and re-establish stability of the section. 4.2.3. Retrofitted girder The critical area for the structural retrofitting was found to be 300 mm either side of the mid-span crack location, as identified from Fig. 37. The retrofitting proposal includes two additional plates of 17.3 mm thickness, the same as the existing flange plate element, attached to the top and bottom of the flange by 19 mm diameter Ajax bolts of strength group M8.8, which extends between the two centre

Fig. 33. Stress vs. distance from crack location curve for critical points in new equivalent girder (uncracked).

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Fig. 36. Contour plot of internal stresses in cracked new equivalent girder.

Fig. 34. Fatigue crack development in new equivalent girder.

stiffening plates. The aim of the two additional plates is to contain the crack from spreading and inducing further damage by local buckling under load. The plates will also provide re-connection along the entire length of the bottom flange and allow it to once again carry the majority of the tensile stress associated with bending. The additional plates have material properties which match the steel of the new equivalent girder. The bolt layout has been determined by AS4100. The location of the additional plate in the cross-section is as shown in Fig. 38. The bolt layout and extent of the retrofitting plate was modelled in ABAQUS, as shown in Fig. 39. The time-step load and deflection data outputs from ABAQUS for the model were combined to produce a load vs. deflection curve for the retrofitted new equivalent. The load vs. deflection curve for the retrofitted and standard uncracked versions of the model were plotted on the same axis, shown in Fig. 40. Fig. 40 displays the retrofitted girder has an increased ultimate applied load capacity, from 750 kN for the standard girder to 945 kN for the retrofitted girder, or by 26.0%. The elastic load limit also increases from 600 kN for the standard girder to 680 kN for the retrofitted girder, or by 13.3%. This indicates a significant improvement in fatigue performance, as the retrofitted girder can carry the same magnitude of loading as the standard case, with an increased number of loading cycles required to cause failure by fatigue. This is significantly important when discussing the future design life of the structure. An increased number of cycles for a given loading magnitude will result in an extension of the allowable service life of the structure before fatigue based failure

Fig. 35. Load vs. deflection curve for cracked new equivalent girder.

will occur. The girder stiffness through the elastic range is also increased from 27.5 kN/mm for the standard girder to 32.6 kN/mm for the retrofitted girder. The retrofitted girder also experienced greater ductility of the failure mode when compared with the standard girder, with a plastic load range increased from 150 kN for the standard girder to 265 kN for the retrofitted girder, or by 76.7%. This represents a more progressive mode of failure, rather than the more sudden failure indicated by the load vs. deflection curve for the standard girder. This outcome promotes cost-effective engineering and sustainability by providing an alternative method to replacement of old steel girders with new parts, which is often expensive, time consuming and inconvenient. The proposed method is cost-effective, as it allows construction to take place whilst the structure remains in service and removes the requirements for infrastructure planners developing temporary alternative travel paths during the retrofitting process. Construction times are significantly reduced, and overheads for machinery and equipment are minimised. Sustainability is achieved through extending the life of the original structure, rather than simply replacing with new components. The load vs. deflection curves for both the uncracked and cracked models of the retrofitted girder were plotted on the same axis, shown in Fig. 41. Fig. 41 displays very little difference in terms of the performance of the girder with and without the introduced fatigue crack. This indicates the suitability of the retrofitting proposal to adequately contain the cracking and maintain the original performance of the girder. The key properties for structural performance, elasticity, stiffness, ductility and ultimate applied load capacity have all been maintained at the same level despite the introduction of the cracking. Therefore the retrofitting proposal is suitable for application both before and after fatigue cracking is found to have occurred in the girder, and the same outcomes can be achieved in terms of extending the original design life of the girder. The magnitude of the point load was again set to the identified upper limit of the elastic region of the girder (600 kN). The maximum principal stress values at the four critical points

Fig. 37. Stress vs. distance from crack location curve for critical points in new equivalent girder (cracked).

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Fig. 40. Load vs. deflection curve for uncracked standard and retrofitted new equivalent girder.

the uncracked and cracked versions of the model. The bolt holes however, impacted mainly on the two points on the outer edge of the flange, which is due to a reduction in the overall surface area at these points. The internal web edge was less affected due to load transfer through the web element. Fig. 38. Retrofitted new equivalent girder cross-section showing retrofitting plate and bolt location.

5. Conclusions and further research in the bottom flange were found at varying distances from the midspan, and the stress vs. distance away from the crack location curve was plotted for the four points, as shown in Fig. 42 and Fig. 43 for the respective uncracked and cracked retrofitted girders. The stress distribution curves for both the uncracked and cracked retrofitted girders display similar results which prove the effectiveness of the retrofitting proposal. The four critical locations in the bottom flange displayed considerably more uniform stress values when compared to the standard cracked girder above. Even when cracking is included in the retrofitted girder, the stress distribution is relatively uniform across the four locations, due to the confinement and ‘bridging effect’ of the retrofitting plates. The maximum stress at any point in the bottom flange for the uncracked girders was reduced from the yield stress of 340 MPa for the standard girder to 166 MPa for the retrofitted girder, a reduction of 52.9%. The maximum stress at any point in the bottom flange for the cracked girders was reduced from 735 MPa for the standard girder to 185 MPa, a reduction of 74.8%. As expected, the holes for the retrofitting bolts also impacted on the stress distribution in the bottom flange. The centres of the bolt holes were spaced at 200 mm apart, with the first bolt centre 52.5 mm from the crack location. Therefore the bolt hole locations correspond to the distances 52.5 mm, 252.5 mm, 452.5 mm in Figs. 42 and 43. These locations correspond with local spikes in the magnitude of the stress at the critical locations in the bottom flange, which is consistent across both

Fatigue based cracking was found to be most critical at the mid-span at the bottom flange for both 120 years old RMS girder and new equivalent girder, as this is the area with the highest internal stress which is caused by the mid-span loading and support conditions. In the standard (uncracked) state, both girders displayed uniform stress distribution across the entire bottom flange, with the stress magnitude slowly decreasing as the distance from the mid-span increased (as we move towards the ends of the girder). Fatigue cracking was introduced into the models by imparting a 1 mm wide cut through the entire bottom flange at the mid-span (in two stages for the 120 year old RMS girder due to two bottom flange plates). The applied load was set to the point load which corresponded to the point of first yield of the steel, 481.5 kN for the 120 year old RMS girder and 600 kN for the new equivalent girder, also corresponding the upper limit a the elastic region and fatigue range of the steel. The induced fatigue cracking was found to cause a significant change to the stress distribution across the bottom flange, as the internal edges at the web-flange interface experienced significant increases in total stress over the standard state due to the load transfer through the web-flange connection, while the external edges experience a significant reduction in total stress due to disconnection within the section preventing the transfer of tensile stress.

Fig. 39. FE model of retrofitted new equivalent girder showing extent of retrofitting plates and bolt layout.

Fig. 41. Load vs. deflection curve for uncracked and cracked retrofitted new equivalent girder.

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Fig. 42. Stress vs. distance from crack location curve for critical points in retrofitted new equivalent girder (uncracked).

In both girders, stress normalisation occurred at a length of approximately 400 mm from the central crack location. This was adopted as the critical length for the retrofitting proposal, as the induced fatigue cracking had no effect outside this region due to the load transfer through the web-flange connection. Therefore the retrofitting was concentrated to the mid-span section only, between the internal faces of the two central stiffening plates, a length of 705 mm either side of the crack location. The retrofitting techniques included the placement of an additional plate the bottom flange of both girders which matched the thickness of the existing flange. In the case of the new equivalent girder, an additional plate was placed above the bottom flange to provide further containment of the fatigue crack. This was unable to be done in the 120 year old RMS girder due to the installation of rivets preventing the plate from being placed on a flat surface. The plates were connected by 19 mm diameter M8.8 Ajax bolts placed in 21 mm diameter holes. The centres of the bolt holes were aligned at the centre line of the width of the flange, and with an edge spacing of 52.5 mm from the face of the stiffening plates at the ends and 52.5 mm from the centre of the crack location at the mid-span. The in-between region consisted of bolts spaced at 200 mm centres. A total of 16 bolts were used for the retrofitting of each type of girder. In both cases and for both girder types, the stress distribution was found to normalise back to uniformity across the entire area of the bottom flange, thus the retrofitting techniques had eliminated the effect of the introduced fatigue cracking. As expected, small increases in the stress magnitude was found at the regions close to the bolt holes, which can be attributed to a reduction in the cross-section area available to carry the tensile forces at these locations.

Fig. 43. Stress vs. distance from crack location curve for critical points in retrofitted new equivalent girder (cracked).

The proposed retrofitting techniques meet the initial design criteria of being simple and cost-effective. Installation methods are as simple as drilling and bolting to the existing structure which can be done during service. This reduces the impact on society by maintaining access and functionality of the structure. Time constraints can also be met as the retrofitting can be undertaken in significantly reduced time frame as replacement with new parts. Costs are minimised by removing the requirement for the provision of alternative temporary structures for access, such as alternative transport routes. Labour, material and equipment costs are also reduced by eliminating large scale construction. Further research is proposed as an extension of the experimental study to evaluate the fatigue performance of the two girders (120 years old RMS and new equivalent). Static fatigue tests to evaluate stress concentrations and cyclic fatigue tests to determine fatigue life can be carried out in future studies. This research study has been focussed on the use of 19 mm diameter M8.8 Ajax bolts as the means of connection for the a retrofitting plates. Further research could include investigation into different types of connectors including a range of bolts.

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