Method for strengthening cable anchorage of a bridge

Abstract

The invention concerns method for strengthening cable-to-girder connection in cable-stayed bridges. The system is particularly suitable for retrofitting cable-to-girder connections that exhibited design deficiencies and / or have already undergone significant service induced deterioration.

Description

[0001] The invention refers to method for strengthening the anchorages of a bridge - cable stayed-bridge - for strengthening the cable-to-girder connection of a cable stayed - underslung bridge. The method is particularly useful for upgrading cable-to-girder connections that suffer from design flaws and / or have already undergone significant service-induced deteriorations.

[0002] A stay-cable can be connected to a steel bridge deck in several ways. Typical components and arrangements of such systems are described in ei, X., Xiao, L., & Wang, Z. (2018). Full-Scale Specimen Testing and Parametric Studies on Tensile-Plate Cable-Girder Anchorages in Cable-Stayed Bridges with Steel Girders. Journal of Bridge Engineering, 23 (4), 04018006. https: / / doi.org / 10.1061 / (ASCE)BE.1943-5592.0001193

[0003] Known strengthening options include: a) vertical plate welded to a strengthened upper flange or to an extended girder web, to which the cable anchoring head is rigidly attached (welded); b) a vertical plate welded to a strengthened upper flange or to an extended girder web, to which the cable anchoring head is attached by a pin joint; c) an anchor pipe passing through the girder web and welded thereto.

[0004] The aforementioned solutions are discussed for example in: Chen, H., Zhuo, Y., Jiao, Y., & Bao, W. (2023). Fatigue Assessment of Cable-Girder Anchorage Zone in a Low Ambient Temperature Environment Based on Extended Finite Element Method. Applied Sciences, 13 (17), 9990. https: / / doi.org / 10.3390 / app13179990 Li, D., & Jiang, X. (2020). Fatigue Stress Analysis of Key Nodes in Cable-Girder Anchorage Zone of Long-Span Cable-Stayed Bridge. IOP Conference Series: Earth and Environmental Science, 531 (1), 012057. https: / / doi.org / 10.1088 / 1755-1315 / 531 / 1 / 012057 Tsakopoulos, P. A., & Fisher, J. W. (2005). Full-Scale Fatigue Tests of Steel Orthotropic Deck Panel for the Bronx-Whitestone Bridge Rehabilitation. Bridge Structures, 1 (1), 55-66. https: / / doi.org / 10.1080 / 15732480412331294704 Wang, H., Wu, H., Hu, L., & Zhang, C. (2023). Analysis and Predictive Evaluation of Mechanical Properties of Steel Anchor Box for High-Speed-Railway Cable-Stayed Bridge. Applied Sciences, 13 (9), 5575. https: / / doi.orq / 10.3390 / app13095575 Li, G., Xiao, L., Huang, Q., Pu, L., & Wei, X. (2023). Experimental Investigation on the Performance of Cable-Girder Anchorage Structure of Hybrid Cable-Stayed Suspension Bridges. Structures, 56, 104911. https: / / doi.org / 10.1016 / j.istruc.2023.104911

[0005] The cited works focus on material fatigue or on how cable-to-girder connections geometries affect stress distribution within this vulnerable zone of a bridge. Existing strengthening proposals are adequate only when the eccentricity between the cable axis and the girder axis is small, leaving no practical means to enhance load capacity of the cable-to-girder connection when this eccentricity is large.

[0006] Accordingly, there is a need for providing a solution capable of enhancing the load capacity of a cable-to-girder connection - anchorage, which cannot be improved by means of the aforementioned standard solutions.

[0007] Known solutions, for reinforcing the cable-to-girder connections - anchorages - of bridges, are described, for example, in the technical report Concept for Strengthening Stay-Cable Anchorage Nodes in the Deck of the Bridge over the Brda River on the University Route in Bydgoszcz (Consulting Design Office Krzysztof Zó ttowski, January 2021). However, this report presents only a traditional methodology, in which the cable-to-girder connections are strengthened by:welding additional steel ribs and diaphragms to the existing structure, placing new stiffeners both outside and inside the main deck girder, creating all new elements from 40 mm plates, joined to the existing ones by full-penetration welds, de-tensioning the cable stays before the works begin, supporting the deck on temporary piers during the works, and re-tensioning the cables once the repair works are finished.

[0008] Typical elements of cable-to-girder connections repaired in this traditional way include a bearing plate, a guide anchoring pipe, gusset plate and stems, and a side plate.

[0009] Drawbacks of the known solutions is need of use of temporary piers is required when cable forces are partly reduced and the deck must be supported for a certain period of time. The known inventions required to make ;extensive full-penetration welds have to be created inside confined space of the deck girder. All use needed elements impact on high total cost arises from the labor-intensive welding and additional works - temporary supports.

[0010] The goal of the invention was to provide method for strengthening of anchorages in cable-stayed bridge that efficiently redistributes forces in cable-to-girder connection even when there is a substantial eccentricity (up to several decimeters) between the anchorage axis and the deck-girder axis - axis of girder of bridge. In addition the goal was to provide method for strengthening cable-to-girder anchorages in order to restores and improves insufficient design load-carrying capacity of the cable-to-girder connection and to ensure that the structure is according to standards - rules and able of withstanding increased design loads during the use of the facility.. In addition the goal was to simplifies the repair methods of anchorages in cable-stayed bridge by eliminating temporary supports, and the need for cable de-tensioning and re-tensioning, as well as does not require creation of large numbers of full-penetration welds in extremely unfavorable working conditions.

[0011] The invention is intended to strengthen of anchorages - existing underslung cable stay-cable - cable to girder connections of cable stayed bridges. According to the invention, the anchorage pipe - guide - anchor piper, the pipe into which the multi-strand stay-cable is anchored by means of a stressing head, is connected - fixed permanently, e.g. by welding, to a side plate arranged parallel to the webs of the deck girders. Steel sheet - steel ribs that surrounds the additional (extension) pipe is connected the deck - bridge girders by means of webs located on the extension of the bridge crossbeam. The dimensions of steel elements - sheet are depended on the type of structural steel to be used during the repair - making anchorages. The additional goal in providing the effected possible strengthening method was to minimize the number of new strengthening elements necessary (including the length and number of welds - seams to be made in-situ) and to simplify the repair procedure while ensuring that the reinforced anchorages could withstand extreme standard design loads. Moreover post-tensioned bars are added that stabilize the cable-to-girder connection, ease the repair procedure and increase the load-bearing capacity of the connection even more.

[0012] The aim was also to minimize: the number of new strengthening components, the total length of in-situ welds the complexity of the repair procedure and range or repair works.

[0013] The proposed strengthening method of anchorage of bridge - method of strengthening the cable-to-girder connection is based on the following assumptions and boundary conditions: 1. as a result of carrying out the works in accordance with the presented concept, there will be no change in the existing bridge gradeline so the finished works shall not alter the existing deck grade line; 2. the strengthening can be mounted without directly unloading the bridge, namely no de-tensioning of the cable-stays before repair works are started is needed; 3. the main girder structure shall not be cut or weakened; 4. the scope of work should not disturb the arrangement of the wedges anchoring the cable strands - the wedge-type anchoring cones of the stay strands shall remain intact; 5. the scope of work should not create the need to carry out welding work within the limited space of the main girders so no welding operations shall be required inside the confined space of the main girders; 6. the reinforcement design should minimize the length and thickness of in-situ welds, which generate undesirable high heat input leading to increased post-weld stresses so the in-situ welds introduced by the strengthening should be as short and as thin as possible, so heat input and the resulting post-weld residual stresses can be controlled and significantly reduced; 7. reinforcement - anchorage construction should avoid locating a large number of welds in the areas of highest stress in the existing anchorage detail so new welds should be located away from regions that have been already subjected to highest stresses.

[0014] During providing of the methods according to invention it was determined that the adopted concept can be realized by adding post-tensioned bars, appropriate tensioned. Experimental work has shown that the addition of these bars causes a favorable redistribution of internal forces in the detail and stabilizes it. Post-tensioned bars shall be attached to the existing cable-to-girder connection. The implementation of the realization of goal was achieved by using additional ribbing together with the extension of the steel guide (casing) pipe. The method of strengthening does not require the operation of relieving the force in the cable and therefore the use of temporary supports. Not only bars are added, but also supplementary stiffening plates are mounted and the steel guide (anchorage) pipe is extended. In consequence, specifically because the bars are installed, it is not required to de-tension stay-cables before the repair works begin and re-tension them after works are finished. Moreover, temporary supports of the deck do not have to be built in bridgeand therefore the use of temporary supports. The whole system enables for a safe repair.

[0015] According to the state of the art, the following anchoring elements of the active ropes suspending the platform are made and attached to the bridge structure - A: retaining plate and anchoring system cable-to-girder connections' components A - bearing plate and anchoring device, B - guide anchor pipe, C gusset plates, D - side plate - closing sheet metal, E - upper flange of the deck girder, F existing rib of the cross-beam box.

[0016] However, due to design errors or increased loads during bridge operation, these components- elements may not provide adequate load-bearing capacity for the cable-stayed bridge connection to the deck. In the event of a failure caused by for example design flaw, manufacturing error or unexpected accident, the load bearing capacity of a cable-to-girder connection may become insufficient.

[0017] Therefore, the anchorage reinforcement method, according to the invention, includes the following components of the system described below is being mounted to the existed anchorage of in following steps.

[0018] In the first step to the existed anchorage of bridge - to shroud of bridge the first and the second post-tensioned bar 1 is attached to the flanges of the down - lower strip - deck girder - lower flange G of girder and the second post-tensioned bar is added to the upper strip- deck girder = upper flange E and to the already installed side plate - sheet metal D). Based on the producers guidelines, in order to activate, the anchorage is reinforced with post-tensioned bars configured and tensioned so that the minimum tensile strength - force in the each bar not less than 10 % GUTS (Guaranteed Ultimate Tensile Strength) and not greater than 45 % GUTS. Do both bars are tensioned in controlled way in order to activate it and redistribute stresses within the cable-to-girder connection.

[0019] For a preliminary determination of the required pipe extension length ΔL of the anchor - guide pipe according the invention the following relationship is met: ΔL = N_perm + live / N_perm × L × γ × k where N_perm+live - stay cable force under characteristic permanent and live loads, N_perm - stay cable force under characteristic permanent loads only, L - original length of the guide (anchorage) pipe, γ - safety factor specified by the relevant design code, k - correction factor established by Finite Element Analysis (FEA) and validation (minimum 0.6).

[0020] Thanks to this, the entire anchorage (elements A-D) is stabilized and the negative effects caused by its excessive bending strain are reduced.

[0021] In the next step an additional pipe segment - anchorage pipe 3 is welded to the existing guide pipe B - anchor pipe - is permanently connected so the pipe 3 of anchorage B is added e.g. by welding which transfers the forces - loads are transmitted from this anchorage pipe segment through the connector plate 4 and the oblique stiffener plate 5 the diagonal stabilizing rib 5 - oblique rib - stiffener, in the form of sheet metal directly to the upper flange E of the deck girder and to the cross beam rib F. Plate 4 and rib 5 are connected to the existing anchorage and the upper flange E of the girder by welding. The dimensions of plate 4 are fitted in order to this dimensions are suitable for connecting the anchorage pipe extension 3 and the upper flange E. The size and thickness of stiffener 5 are to be established by Finite Element Simulations (FEM). In line with this, the plate 4 has dimensions that are suitable for connecting the anchorage pipe extension 3 and the upper flange E. The size and thickness of stiffener 5 are to be established by Finite Element Simulations (FEM).

[0022] The metal sheet - connector plate 4 and rib 5 are welded to the existing elements of the cable-to-girder connection and the upper flange E of the deck girder.

[0023] When applying this invention to other cable stayed bridges, individual FEAs have be carried out in order to select appropriate plate thicknesses and post-tensioning forces in the bars. The features provided in the description of the invention are enough and can be easily used by a person skilled in the art it is possible to provide appropriate strengthening of anchorage of bridge - cable-to-girder connections. According to the invention, it was chosen that the thickness and size of the sheet metal 4 should be analogous to the sheets used in the reinforced structural solution. The minimum tensile strength - force in the each bar shall be not less than 10 % GUTS (Guaranteed Ultimate Tensile Strength) and not greater than 45 % GUTS.

[0024] For a preliminary determination of the required pipe extension length ΔL of the anchor - guide pipe according the invention the following relationship is met: ΔL = N_perm + live / N_perm × L × γ × k where N_perm+live - stay cable force under characteristic permanent and live loads, N_perm - stay cable force under characteristic permanent loads only, L - original length of the guide (anchorage) pipe, γ - safety factor specified by the relevant design code, k - correction factor established by Finite Element Analysis (FEA) and validation (minimum 0.6).

[0025] This data was provided based on the experimental study to obtain the best results of the invention.

[0026] In line with this, the system is added - mounted to the anchorage in order to intensify - strengthen it.

[0027] The system that is mounted comprises the first post-tensioned bar (1) is anchored to the lower flange (G) of the deck girder and the anchorage gusset plate (D), while the second post-tensioned bar (2) is anchored to the upper flange (E) of the deck girder and to the gusset plate (D). the system comprises an additional guiding - anchor pipe (3) that extends coaxially the existing guide - anchor pipe one (B) by the length of ΔL (described below). A steel plate (4) connects this additional pipe to the upper flange. The plate is positioned horizontally. The system comprises an additional rib (5) - oblique that make sheet metal connects the upper flange E of girder, the plate (4) - sheet metal and the extension of guide pipe (3). Its role is to stabilize the system and prevent the plate (4) from buckling.

[0028] The system configured in the way described above is employed to strengthen the anchorage.

[0029] In accordance with the manufacturers' guidelines the force in each bar was set as follow : the minimum force in post-tensioned bar is not less than 10 % of the Guaranteed Ultimate Tensile Strength (GUTS); and and not greater than 45 % of GUTS.

[0030] For a preliminary sizing of the required extension of the guide - anchor pipe ΔL by additional guide - anchor pipe according to , the invention the following relationship is met: ΔL = N_perm + live / N_perm × L × γ × k where N_perm+live - stay cable force arising from characteristic permanent and live loads; N_perm - stay cable force arising from characteristic permanent loads only; L - original length of the guide (anchorage) pipe; γ - safety factor prescribed by the applicable design standard; and k - calibration factor determined by FEA and validation (k ≥ 0.6).

[0031] When the bars are post-tensioned in this way the entire cable-to-girder connection - anchorage (components A-D) is stabilized and negative bending effects ssociated with its excessive bending strain are minimized. Thus, the extensive rotational motion of the faulty cable-to-girder connection that was observed when there was no strengthening is stopped.

[0032] According to the invention, plate - sheet metal thicknesses and overall dimensions are kept similar to those already present in the anchorage. Stresses in the bars post-tensioned bars - shall conform to the manufacturer's specifications and according to the invention, it was developed that the minimum value of the force in the tendon shall be not less than 10% of GUTS (Guaranteed Ultimate Tensile Strength) and the maximum value was not greater than 45% of GUTS. To initially determine the required increase - extension of the guide (casing) pipe length using an additional pipe, the following relationship was established: ΔL = N_perm + live / N_perm × L × γ × k where N_perm+live - stay-cable force arising from characteristic permanent and live loads; N_perm - stay-cable force arising from characteristic permanent loads only; L - original length of the guide (anchorage) pipe; γ - safety factor prescribed by the applicable design standard; and k - calibration factor determined by FEA and validation (k ≥ 0.6).

[0033] Experimental investigations confirmed that the inventive combination of plates and post-tensioned bars produces a significant redistribution of internal forces, enabling effective repair and strengthening even when the anchorage has experienced plastic deformations of the plates. The use of the method according to the invention, i.e., additional plates - additional guiding - anchor pipe and post-tensioned bars - tendons, significantly redistributes internal forces within the anchorage. As a result, it is possible to effectively repair and strengthen damaged anchorages, even those showing signs of overloading, revealed by excessive plate deformation (min. 0.6).

[0034] The proposed method is economically superior to traditional methods involving additional ribs and diaphragms. It does not require de-tensioning of the stays. The activation of the new components is achieved solely by adding post-tensioned bars that clamp the anchorage side plate to the deck girder.

[0035] During execution no temporary supports are needed, and welding inside plasticized zones of the closed girder box is avoided, thereby minimizing residual stresses.

[0036] The presented invention does not interfere in any way with the anchoring elements (sheets) that have been overloaded (or plasticized). Welding in plasticized zones within the bridge deck box is avoided, as this would require limited movement of the welders and could be inaccurate. Furthermore, post-weld deformations and stresses are not introduced into critical areas of the detail. The proposed repair concept does not require relieving the cables or introducing temporary support for the entire structure. The additional elements mentioned above can be prefabricated, simplifying repair work. The invention concerns strengthening the active cable anchorage in a cable-stayed bridge deck by adding a system of tendons and additional reinforcing elements, which increases its load-bearing capacity and ensures the structure's full capacity to withstand standard design loads throughout the entire service life of the structure. Reinforcing the anchorage zones according to the presented concept significantly simplifies the repair process, as it eliminates the need to install additional ribs inside the main girder box of the bridge, relieve the stay cables, or use additional temporary supports. Additional elements that need to be introduced into the node for reinforcement can be prefabricated, simplifying repair work.

[0037] The invention thus increases the load carrying capacity of the cable-to-girder connection and restores full design performance which is needed throughout the bridge's service life.

[0038] The invention was developed using inventors' analyses and Finite Element Analysis - continuum mechanics based FEAs during the response analysis of the University Bridge in Bydgoszcz. Although a different, traditional repair was ultimately implemented there, the present invention offers a simpler and more cost effective alternative.

[0039] The invention is illustrated in the accompanying drawings listed below. Fig. 1. Visualization of the cable-to-girder connection in a cable stayed bridge for which the proposed strengthening method is effective. Fig. 2. Visualization of the strengthened cable-to-girder connection - view 1. Fig. 3. Visualization of the strengthened cable-to-girder connection - view 2. Fig. 4. Visualization of the strengthened cable-to-girder connection - view 3. Figs. 5-6. Illustrations showing the originally designed cable-to-girder connection elements denoted by letters A-E as well as the strengthening, which elements are denoted by numbers 1-5. Fig. 7. General view of the main river bridge span together with the approach viaducts. Fig. 8. Representative cable-to-girder connection of the University Bridge over the Brda River in Bydgoszcz - view 1. Fig. 9. Representative cable-to-girder connection of the University Bridge over the Brda River in Bydgoszcz - view 2. Fig. 10. Control point at which the horizontal displacement of the side plate was recorded during the five step analysis of the cable-to-girder connection repair. Fig. 11. Equilibrium path of the cable-to-girder connection before and after it is repaired using two post-tensioned bars, stiffening plates and a guide pipe extension. Figures 7-11 present visualizations of the cable-to-girder connection after strengthening in accordance with the developed concept and serve as an example for evaluating the effectiveness of the invention.

[0040] List of reference symbols - invention - the elements added according to the invention - method 1 - additional 1 5t< post-tensioned bar - flexible connector, tie rod 2 - additional 2 nd< post-tensioned bar - flexible connector, tie rod 3 - additional anchorage pipe also known as additional guiding - anchor pipe - extension of the pipe B 4 - plate - metal sheet connecting the additional guide pipe 3 - stabilizing plate 5 - oblique - diagonal stiffener plate - diagonal rib stabilizing the connector plate Example 1

[0041] As shown in Figs. 5 and 6, the originally designed components that are added, of the cable-to-girder connection, denoted by the letters A-E, are supplemented by the new system components, denoted with the numbers 1-5. This is done to strengthen the existing cable-to-girder connection and enable it to carry loads much greater than those assumed at the design stage. The post-tensioned bars based concept is also illustrated in Figs. 1-4.

[0042] In the first step, two high strength steel bars are installed within the existing cable-to-girder connection. Bar no. 1 is fixed between the lower flange G of the deck girder and the anchorage gusset plate D. Its length is approximately 2.1 m. Bar no. 2 is fixed between the upper flange E of the deck girder and the same gusset plate D. Its length is likewise about 2.1 m. Both bars are post-tensioned in a controlled manner so they are able to redistribute the stress state within the cable-to-girder connection in a favorable way.

[0043] In this example each bar is stressed to 900 kN, corresponding to 45 % of the Guaranteed Ultimate Tensile Strength (GUTS). As a result, the entire cable-to-girder connection (components A-D) is stabilized and the unfavorable bending effects, causing rotation of the whole original cable-to-girder connection are minimized. In effect, when the bars are added, the rotational motion of the detail without strengthening is stopped.

[0044] In the next step an additional pipe segment 3, having a length of ΔL = 2.25 m, is welded to the existing anchorage pipe B. From now on, service loads are transmitted from this segment through 20 mm thick plates (nos. 4 and 5) directly to the upper flange E of the deck girder and the cross beam rib F. Plates 4 and 5 are both welded to the existing cable-to-girder connection and to the upper flange E.

[0045] The Plate 4 has dimensions that are suitable for connecting the pipe extension 3 and the upper flange E, while the size and thickness of the stiffener 5 are established by FEA. In this example both plates are 20 mm thick and fabricated from S355 steel.

[0046] The parameters adopted for this example are summarized below: ΔL = 2.25 m according to the relationship ΔL = (N_perm+live / N_perm) × L × γ × k N_perm+live = 11 073 kN (cable force under characteristic permanent and live loads) N_perm = 10 440 kN (cable force under characteristic permanent loads) L = 2.30 m (original anchorage pipe length) γ = 1.15 (code safety factor) k = 0.79 (finite element calibration factor, k ≥ 0.6)

[0047] The pipe extension (having a thickness of 20 mm and made of S355 structural steel) is welded to the existing cable-to-girder connection and to the upper flange of the deck girder via plates 4 and 5 (each 20 mm thick and made of S355 steel). For the cable-to-girder connection no. 2201 of the University Bridge, the dimensions of the plate 4 are 1.45 m by 1.35 m. These were selected to allow for an easy oval cut out through which the plate can be welded to the inclined anchorage pipe extension 3. The dimensions of the stiffener 5, has been determined in the course of FEA. The stiffener is 1.63 m long and 1.16 m wide.

[0048] The University Bridge is a single pylon cable-stayed structure located along the Ogi skiego Street over the Brda River in Bydgoszcz (Fig. 7). It has a main river span of 110 m and a floodplain span of 90 m, which are separated by the pylon axis. The bridge was opened for traffic in 2013 and operated without restrictions until July 2020, when deformations of the side plates were observed indicating overloading of the cable-to-girder connection.

[0049] To verify the effectiveness of the proposed strengthening, a numerical simulation of a representative cable-to-girder connection was carried out. A five stage, materially and geometrically non-linear static analysis was performed. The stages of the analysis are listed below. I. recreation of normal force in the cable arising due to the dead loads and post-tensioning (g + n); II. application of test loads during acceptance trials (g+n) + (p); III. removal of the test loads (g+n) + (p) - (p); IV. installation and post-tensioning of the additional bars (g+n) + (p) - (p) + (C); V. re-application of service loads with unlimited scaling (g+n) + (p) - (p) + (C) + α × p.

[0050] After Stage IV the stress and strain state was saved and the invented strengthening was added to the numerical model. Then Stage V calculations were executed. The strengthened cable-to-girder connection was able to sustain increasing force in the stay cable to the moment when new plastic strains (PEEQ) started to appear, which was treated as the moment when the analysis should be stopped, as no more plastic deformations can be allowed after the repair is finished for safety reasons. In this case the ultimate capacity of the cable-to-girder connection reached approximately 15200 kN, i.e. about 50 % more than cable-to-girder connection was able to sustain before the repair (~10 MN). This result has been achieved using a validated model and without any de-tensioning of the stay-cable.

[0051] The equilibrium path, plotted as force in the cable stay versus displacement of the control point shown in Fig. 10, is given in Fig. 11. Comparison of the paths confirms that the strengthening increased the anchorage capacity by roughly 50 %. For clarity the graph is expressed in physical quantities (cable forces and displacements), omitting the dimensionless load scaling parameter α.

[0052] In summary, the strengthening system with post-tensioned bars and additional steel plates offers an economical alternative to the traditional strengthening method, mainly because it does not use internal ribs and diaphragms, it requires no temporary supports or cable de-tensioning, and can be prefabricated outside the site prior to installation.

Claims

1. Method for strengthening cable anchorages of a cable stayed bridge is characterized in that, - in the first step to the anchorage the first and the second post-tensioned bar 1 is attached to the installed lower flanges of flange (G) of girder and the second post-tensioned bar (2) is added to the upper flange (E) and to side plate (D) of girder wherein the first post-tensioned bar (1) and the second post-tensioned bar (2) are tensioned so that the minimum tensile force in the bar is not less than 10 % GUTS (Guaranteed Ultimate Tensile Strength) and not greater than 45 % GUTS, - In the next step, the length of installed pape (B) is extended by an additional anchorage pipe (3) that is permanently connected so that the anchorage pipe (3) transfers the forces from this anchorage pipe (3) through the plate (4) and the diagonal rib (5) that stabilize the plate (4) directly to the upper flange (E) of girder and to the cross beam rib (F) so that the length ΔL of anchor pipe (3) extending the installed guide pipe (B) is according to the following formula: ΔL = N_perm + live / N_perm × L × γ × k where: • N_perm+live is the stay-cable force generated by characteristic permanent and live loads, • N_perm is the stay-cable force generated by characteristic permanent loads, • L is the original length of the guide (anchorage) pipe, • γ is the safety factor stipulated by the relevant standard, and • k is a correction factor determined by FEA and validation (k ≥ 0.6); and in the following step the plate (4) and rib (5) are connected to the anchorage and the upper flange (E) of girder and the size and thickness of rib (5) are to be established by Finite Element Simulations (FEM).

2. The method according to claim 1, wherein bars are tension so that post-tensioning force of bar is 900kN, which corresponds to 45 % GUTS.

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