Analysis and verification of stresses in reinforced concrete bridge projects of the box type with sequential application of prestress based on the successive advancement method

Given the importance of road bridge systems for the development of a country, rigor in the design process becomes extremely essential in order to meet all requirements related to their functionality. One of the challenging aspects of avoiding possible collapse problems at the beginning or during the construction phase of the project is the selection of the construction process. In this context, the criteria for defining the construction process to be adopted is intrinsically linked to cost, ease of execution, and safety during the creation of the work of art, construction time and the technical capacity of the construction professionals. In this study, deformation analyses and the evolution of efforts in the upper fibers of a bridge were carried out based on conventional construction methods, taking into account the application of pre-stress during construction, aiming to compare the results. Highlighting that the critical tensions were overcome with the help of applying pre-stress in a phased and/or sequential manner. The structural system in question is a single-cell box bridge made of pre-stressed concrete with variable height, measuring 2.50 m in the middle of the span and 4.70 m at the supports. The computational numerical modelling was developed based on the use of finite element programs CSiBridge v.20 and Robot Structural, considering bar and plate/shell/shell elements. Using the method of successive symmetric advances, a longitudinal, linear-static analysis was carried out (neglecting dynamic effects), taking into account the zero, corresponding and closing staves with length measurements of 6.40 m, 4.20 m and 3.00 m, respectively. The results were compared, where it was concluded that the efforts obtained in the construction phase after closing the consoles turned out to be relatively lower due to the redistribution of efforts, taking into account the change in the structural system from isostatic to hyperstatic. With this change, tensile stresses appeared in the lower fibers (this during the construction phase), increasing by 92.10% during the operation phase. The tensile efforts of the upper fibers in the support area increased by 85.6% from the construction phase to the operation phase. Regarding the pre-stressing strength of the concrete, it was applied in order to guarantee reduced losses resulting in values lower than 15%.


Introduction
Regarding studies and/or developments in different locations, bridges have always been assumed as indicators for economic development.As we know, for its correct design, even taking into account the economic aspects, it is necessary that the requirements related to functionality (traffic) are met or fulfilled, ensuring that the constituent materials resist the stresses requested (ensuring safety), as well as correct structural behaviour, taking into account, above all, vibrations due to the passage of vehicles (in the particular case of bus stations) so that the structural system meets the useful life predicted in its design phase.
To this end, it is important that the structural parts that make up the system are rigorously defined.
Even though construction processes have achieved significant advances over the years, it appears that most bridge structure collapses occur during the construction phase (Almeida, 2016;Barbaros et al., 2022;Briseghella at al., 2021;Cardoso, 2014 andCardoso, 2015).Therefore, there is a strict need to adopt carefully developed study criteria to mitigate known problems in the bridge sector.
Various scholars have carried out numerous studies on the effects of optimizing construction taking into account stresses in the structural system.It is important to note that Davide et al. (2022) compared four methods when applied to analyse the impact of loading on deformations and stresses of bridge structures.In the case of authors Chen et al. (2017), they proposed the force balance method to determine the initial stresses in reinforced concrete decks subjected to different loads, resulting in a reasonable distribution of bending moments (under the deck).Huang et al. (2019) studied the (long-term) performance of bridges built based on different methods affected by reinforced concrete shrinkage and creep.
As discussed above, decision-making on which construction method to adopt results from an in-depth analysis of several conditioning factors, such as: ease of execution (technical feasibility), cost, safety (during the process and/or carrying out of the bridge), construction time, technical capacity of professionals and others (Quissanga et al., 2021;2022;Reis and Peres, 2016;Zhou at al., 2019).
In this context, in the case of reinforced concrete bridges with considerably large spans, these should be designed based on the most viable execution solutions, among which is the (quite efficient) solution that consists of adopting a box-beam section of one or more cells.The solution in question provides numerous benefits in the execution process, such as high rigidity, high resistance to bending and torsion, durability and ease in the process of future maintenance and/or inspections (Da Silva et al, 2023;Paixão, 2015;Motter et al., 2018;Fatemi et al. 2016;Davide et al., 2022).
The method of successive advances is quite advantageous compared to the others, due to the fact that it provides speed in the execution process and the possibility of eliminating false work supported on the ground, also giving the possibility of crossing large valleys and lakes with high depths without the need to interrupt traffic or navigation during the construction phase (Chai et al., 2019).However, the method in question makes it possible to carry out several or different work fronts (several spans simultaneously) to at the end or later join the referred spans (closing of consoles), thus making a much more economical and less time-consuming work carried out in a very short time, however demanding a rigorously specialized workforce, so that the cantilevers of the different spans are on the same alignment at the time of joining.However, it is also important to mention that due to the existence of several actors involved in the construction process, it is often difficult to collect all the information produced and analyse the results obtained in the different phases of the project, therefore not becoming possible to draw conclusions about the differences in the results obtained and which reveal the evolution of the process, namely about the quantification and accounting of the requesting actions, the characteristics of construction materials, and also about the evolution of the calculation models used, thus evaluating, the differences and draw the appropriate conclusions.
Reinforced concrete bridges constructed using this method are typically constructed using a single-segment construction sequence, which involves first one or two segments being lifted and then the remaining segments installed also by lifting one at a time.Therefore, the present research work is intended to analyse and evaluate the structural stresses following (or in the process of) the application of pre-stresses during the construction of a reinforced concrete bridge with a box girder section, based on the use of the methodology of successive advances, which will be presented as a proposal for the bridge to be built on the Congo River or also called the Zaire River located in the north of Angola.
The computational numerical model investigated corresponds to a road structure with a deck and single-cell box beam with variable height of reinforced concrete in a parabolic shape, with a straight axis presenting 5 continuous spans (free spans) of 40.0 m at the ends, 55.0 m intermediate spans and a central span of 85.0 m, thus adding up to a 275.0 m bridge length.It is important to note that in this work, the usual mesh refinement techniques presented in simulations carried out with the aid of the finite element method implemented in the CSiBridge v.20 and Robot Structural software's were adopted.
The results of the analyses are presented with the aim of verifying the deformations generated through the application of pre-stresses in a sequenced manner during the construction process.Therefore, the main conclusions of the study in question are intended to alert structural engineers about one of the most viable and recommended methodologies for the construction of bridges with large spans subjected to load actions.

Methodology
This research work was prepared through a comparative analysis of a computational numerical study, using the qualitative method, which helps to better understand phenomena rigorously studied in isolation.As for the theoretical foundation, it was structured based on technical regulations for the design of reinforced concrete bridges and viaducts (Eurocode 1, 2010; NBR 7188: ABNT, 2021).It is important to note that in addition to the concepts focused on cantilever bridge analysis methods formulated by Bakht & Jaeger (1985), the updates developed by the authors Bakht e Mufti (2015) were also taken into account.
As already mentioned, the numerical models were developed and simulated with the aid of CSiBridge v.20 and Robot Structural software in order to streamline the comparison and facilitate the extraction of the set of results for each case analysed.
The comparison of the results of the numerical models used in this research are illustrated in item 5. Noting that the process of organization and understanding of this study occurs through the comparative analysis of the results obtained in the simulation of bridge slabs taking into account the staves and the pre-effort with the help of the aforementioned software; which are programs based on the finite element method.However, to obtain and organize the calculation results for the bridge slabs, the different thickness ratios of the deck structures were considered.In other words, based on the results obtained, the analyses were presented, comparative discussions were inferred and finally the conclusions and recommendations of the study, according to the flowchart presented in Figure 1.

Coffin Type Bridges
The structural model of the reinforced concrete bridge investigated corresponds to a typical system composed of a deck and box beam with a straight axis (continuous), with a variable height of 2.50 m in the middle of the span and 4.70 m at the supports, with the main span of 275.0 m, and with span arrangements of 40.0 + 55.0 + 85.0 + 55.0 + 40.0 m, respectively.As can be seen in Figure 2, the bridge's structural system has a symmetrical arrangement of four pillars.The bridge deck has a total width of 12.50 m, with a bidirectional transverse slope of the slab of 2.5%.The characteristics of the materials used in the bridge in question are described in Table 1 below.

Two Numerical Models
Two numerical models were developed, the first of which was intended for the construction phase of the bridge, where stresses were analysed in the sequence of all phases.The second (model) was intended for structural analysis during the operational phase of the bridge in question.As an illustration for better understanding, Figure 3 shows the longitudinal profile, as well as all current staves measuring 4.20 m each; the zero staves measuring 6.40 m and the closing staves measuring 3.0 m.As can be seen in the figure above (Figure 3), the staves are highlighted with the numbers 0 to 9, which in turn corresponds to each construction phase.In the case of the segment "F" (in the middle of the span of the bridge) it represents the closure of the pairs of cantilevers.It can also be seen that the bridge will be built on two work fronts, with pairs of consoles being built symmetrically from the two central pillars.Then, in Table 2, the main parameters that constitute the materials used in the global model of the bridge are shown in detail below.High strength prestress steel tensioner with 1,860.00MPa tensile strength (similar to ASTM A416/A416M).

Reinforced Concrete Bridge Structural Project
The cross-section of the artwork was pre-dimensioned based on the Schlaich proposal (Morim, 2008 andChai et al., 2019).Next, the dimensions of the box section of the bridge beam are shown in Figure 2. Highlighting that the height of the box beam section (at the supports) in the case study is determined according to the mathematical formulation expressed in Equation 1 (Morim, 2008).
As can be seen, the webs of the box beam were assumed to be maintained at a constant inclination and with a consequent variation in the width of the lower chord depending on the height.The inclination decision was adopted with the aim of providing less self-weight by reducing the width of the lower flange and a smaller transverse span in the section, thus favouring its rigidity.
Table 3 shows the cross-sectional dimensions of each stave that makes up the bridge.

Quantification of the Actions Considered
The actions were considered to be those of a permanent nature (self-weight of the staves and other fixed components of the bridge, as well as the own weight of the assembly aid equipment) and of a variable nature, which in this case are road overloads and wind action.
Permanent loads were calculated by multiplying the cross-sectional area of the element by the specific weight of the respective material that constitutes it.Table 4 presents some geometric properties and self-weight of the bridge staves.The weight of the remaining pressing loads (asphalt, curb, border beam and guardrails) were calculated taking into account the respective cross-sectional areas and multiplied by two, in order to mirror their existence on both sides of the section.
Table 5 shows the values of the areas, as well as the remaining permanent loads.The bridge's road overloads were quantified according to Eurocode 1part 2 (2010).They were defined by the application of two uniformly distributed loads: 9.0 kN/m 2 on the first lane and 2.5 kN/m 2 on the remaining lanes, and concentrated loads spaced 2.0 m apart, 300 kN and 200 kN for the first and the second track respectively.A crowd load of 5.0 kN/m 2 was considered, taking into account that when producing vibrations with a frequency equal to that of the bridge, they can lead to structural collapse.
In the construction phase, overloads arising from the weight of all auxiliary equipment for the execution of the deck were considered.However, a mobile load with a total weight of 500.0 kN was defined, lower than the weight of the closing rod (563.43 kN) according to the recommended weight value.The remaining equipment is given by an evenly distributed overload of 0.50 kN/m 2 .As for the wind action, it was quantified based on the European standard Eurocode 1part 4 (2010), having obtained the loads in each direction, being 11.528 kN/m, 2.882 kN/m and 11.277 kN/m, in the X, Y, Z directions respectively, as presented in Table 6.Furthermore, the combination and reduction factors considered in the variable actions are presented in the same table.For the operational phase, three combinations were defined for checking the Ultimate Limit State ("ELU") and another three for the Service Limit State ("ELS"), with the vehicle overload being the most variable and influential action, taken with greater attention, as shown in Table 7.The combinations for "ELU" and "ELS" are expressed mathematically according to Equations 1 and 2, respectively (EC1 -part 4, 2010).It is worth highlighting that, in the case of "ELS", quasi-permanent combinations were taken into account (long-term limit stateswith a probability of occurrence greater than 50% of the structure's useful life), as were also the frequent combinations (short-term limit stateswith a probability of occurrence greater than or equal to 5% of the structure's useful life) and the rare combinations (limit state of very short duration -with probability of occurrence; a few hours of the structure's useful life), respectively.The nomenclatures of the equations were considered based (2)

Finite element model
The computational numerical model (see Figure 4) developed in the CSiBridge program to evaluate the stresses and deformations (linear-static) of the reinforced concrete bridge adopted the usual mesh refinement techniques present in finite element method simulations implemented by others using this same software as well as in the Robot Structural 2018 program.
The box beam and deck were modelled and simulated with area or shell finite elements.The pillars were simulated by bar-type elements.The global (final) model adopted used 17,261 elements, 18,453 nodes, resulting, therefore, in a numerical model with 91,082 Degrees of Freedom (GL).As for the damping rate, it was adopted as recommended in the standard EN 1991EN -2 (2003) ) for concrete bridges.Next, Figure 5 illustrates the different views of the model in order to illustrate its details.Source: Authors.

Model Used in the Construction Phase of the Bridge
As previously discussed, the CSiBridge program v.20 was adopted for the longitudinal analysis of the deck, taking into account the influence of the construction process and structural behaviour.In other words, two numerical models were developed; the first for the construction phase, as shown in Figure 6, and the second, intended for structural analysis during the operational phase of the bridge in question.
This first model was simplified to a single pair of consoles built symmetrically from a central pillar, reflecting the behaviour of the two work fronts, which will later be connected by closing staves.During the analysis of this construction process, the effects of creep, shrinkage, aging of the concrete, as well as the relaxation of the structural steel were taken into account.
6 -First numerical model -Used for the analysis during the construction phase.
The set of cables, which can also be called a family of pre-stressing cables defined to link each current stave, is made up of internal cables adherent to the concrete, with horizontal and straight lines, applied to the upper fibers of the section, as it is the zone where tensile stresses occur most frequently during the construction phase of the bridge.
And in the case of consoles, the family of continuity cables were defined as internal prestress cables that adhere to the concrete, but with parabolic layouts, ensuring the connection between the two work fronts and introduced into the lower fibers of the section in order to overcome the tensile stresses that arise in this area, resulting from the redistribution of efforts, resulting from the change in the structural system, initially isostatic and then becoming a hyperstatic structural system.

Numerical Model Used in the Bridge Operation Phase
In the case of the second model developed, as illustrated in Figure 7, it was intended for carrying out structural analyses during the operational phase of the bridge in question.In this second model, with the closure of all pairs of cantilevers, their 5 respective spans were considered, this being the numerical model (hyperstatic) adopted for the analysis and used for the operational phase of the bridge.It is important to highlight that, as in the first model, in this second model the curvature of the lower flange was defined parametrically, so as to obey a parabolic shape with specific heights for each stave.In the analysis process, geometric nonlinearity as well as material non-linearity were taken into account.As for the effects of temperature and the effects of earthquakes or seismology, these were not considered, as they were not within the delimitation and/or objectives of the present research work.

Transverse Numerical of the Bridge Deck
A detailed analysis was necessarily carried out for the transverse direction of the deck, to determine an optimal sequence of application of the pre-stressing cables, in each of the phases, since the sequence in question consists of a process that influences and/or has a considerable impact on its stability, to the point that in some cases it generates excessive displacements and rotations when not applied judiciously, thus causing additional efforts in the structural system.
In this way, carrying out the transverse analysis on the deck makes it possible to assess whether or not it is necessary to apply a transverse prestress, depending on the efforts that will arise in the structure.To this end, the cross-section model in the support region was developed based on the aid of the finite element software Robot Structural Analysis, using bar elements.It is worth highlighting that the support regions are those where the greatest efforts arise or are perceived during the construction phase.
As expected, in the analysis process, the loads displayed in the model are related to the fixed elements which contribute to the permanent loads in the section.Therefore, the concentrated loads located at the ends, corresponding to 6.07 kN (Fz) reflect the border beams with the guardrails.The concentrated loads of 3.19 kN (Fz), located in the innermost area of the console, mirror the curb; and in the case of the uniformly distributed load in a linear way corresponding to 4.75 kN/m (Pz), these reflect the weights of the sidewalks (on both sides of the bridge), and the load of 1.25 kN/m (Pz) reflects the weight of the bituminous material, which is also known as asphalt.

Results and Discussion
The results were obtained for both the construction phase and the operational phase.Next, the maximum internal design forces obtained for the bridge deck in each phase are presented in Table 8.The values were taken from the most highly tensioned area (specifically in stave zero), for the application sequence of the prestress cables so they become structurally more efficient.It can be seen that with the application of the pre-stress, the internal stresses are considerably reduced due to the opposite deformation imposed on the structure, but with the exception of the axial effort which increases, since the pre-stress contributes to the compression of the structure.
It is important to highlight that, after closing the two pairs of consoles (phase "F"), there was a redistribution of efforts, changing the maximum bending moment from a value of -46365.51kN.m to a value of -29611, 65 kN.m, this is due to the change in the structural system, which was initially isostatic and became hyperstatic, consequently generating, in the middle span, a bending moment with a value of 7129.03 kN.m, after the removal of the assembly equipment, even before taking into account the actions of the operational phase of the bridge.

Evolution of Internal Efforts
As can be seen, Figures 8, 9 and 10 present the results of the internal sizing efforts (bending moment, transverse effort and axial effort), obtained during the construction phase.It can be seen that the values in question grew in accordance with an approximate mathematical function, as the length of the cantilever pair increased (until reaching their maximum values in the phase prior to the closing of the staves).Source: Authors.
In Figure 8, it can be seen from the bending moments graph (construction phase), that the values, represented by a fifthdegree polynomial, increase until the end of the construction phase.After the closure of the two pairs of consoles, there is a redistribution of efforts resulting from this new phase of the project.In this context, the evolution of the bending moment in the construction phase follows an increasing average rate per 4.2 m of 1920.46 kN.m.
In the case of the growth of the transverse effort (shear force shown in Figure 9) in the phase in question, the values can be represented by a third-degree polynomial.These are greatly influenced by the curvature of the lower flange and the reduction of the sections along the consoles (reduction of self-weight).The curvature of the lower flange considerably alleviates the effect of transverse stress due to the vertical component of the concrete stress.
In the case of the axial force results illustrated in Figure 10, these grow almost linearly during the construction phase, compressing mainly the upper fibers of the section, since the pre-stressing cables were introduced at the upper flange (consolidation cables) until shortly before closing the consoles (continuity cableslower flange).

Pressurising Results Based on the Number of Cables
In Table 9, the values determined for the prestress based on the family of internal cables adherent to the concrete with straight lines are presented.It is highlighted that, for the continuity cables of the consoles, a family of internal cables adhering to the concrete was used, but with parabolic layouts, consisting of cords, each of them having 7 wires with nominal diameters of 15.0 mm and an area of 1.40 cm 2 as recommended by ASTM -American Society for Testing and Materials (ASTM, 1998), having, however, a total area of 9.80 cm2 subject to a tension of 1,860 MPa.As can be seen in the previous table (Table 9), the construction of stave zero was carried out with 4 cables, and the others were built by successively adding 4 new cables (respectively).As for the force applied to the pre-stress, it increases with each new construction phase, thus following the growth of internal efforts.The way in which the application force increases depending on the construction of the consoles (staves), as well as the behaviour of the bridge in terms of displacements, is then presented in graphic form in Figure 11.
As can be seen, the pre-stress force increases linearly until the phase prior to the closing of the cantilever pairs.However, based on the increase in tensile stresses, there is obviously a need to increase the number of cables, in order to guarantee a larger pre-stress area, thus reducing possible prestress losses.The decay seen during the stave closing phase is due to the fact that, at this stage, the pre-stress cables to be applied are those of continuity, that is, in the lower fibers, in order to overcome the tensions that arise there as a consequence of the redistribution of efforts also ensuring continuity between consoles.These tensions, in turn, are smaller compared to those that arise in the upper fibers, hence the need to apply a lower prestress force.Regarding the application of pre-stress cables in the structural system, it is highlighted that three different application sequences of pre-stress cables were considered and carried out in order to verify their efficiency and influence on the structural behaviour in terms of displacements and deck rotations, as well as internal sizing efforts.In this context, the results presented in this research are only those that demonstrate the best cable application sequences and consequently greater efficiency regarding the behaviour of the bridge, considering that the cable sequence in question is managed to generate smaller deformations and, consequently lower internal efforts.Figure 12 then illustrates the sequence of application of the staves and their respective deformations.Figure 13, finally illustrates the deformed state of the bridge deck; and below, the displacements and rotations of the deck during the construction of the bridge are illustrated in Figure 14, in a graphical form.As discussed, the displacements in the three sequences gradually increase, resulting in a sudden change in the "Closing" phase of the consoles, as a result of the increase in internal efforts, caused by the redistribution of forces resulting from the change in the structural system.And in the case of rotations, with oscillatory behaviour, these had little influence at a structural level, since their values are very close to zero, which translates into good transverse stability in the defined section and in the way in which the prestressing cables were applied.Considering the structural behaviour, it can be clearly observed (see Figure 14) that the results defined by the third sequence of cables are predominantly lower than the results of the first sequence.This efficiency is due to the alternating application and concentration of cables from the initial and final phases (0, 1 and 9) in areas of greater cross-sectional effort (inclined webs), which are also, in turn, the areas that give it greater rigidity.

Results of Internal Efforts in the Operational Phase
In addition to the loads applied during the construction phase of the bridge (the actions of the self-weight of the staves and the remaining permanent loads), the road overloads in accordance with the Eurocode, the wind forces in the three directions ("X", "Y" and "Z") and the vehicle type loads and the prestress were applied during the operational phase.It should be noted that the results in question, based on the use of the CSiBridge v.20 software, were obtained in the areas/regions of the internal supports, at the end supports and in the middle of each span as well, as these are the most highly tensioned areas.As expected, the efforts in question are greater than those obtained in the construction phase (after the redistribution of the efforts), due to the influence of all the operational loadings.Source: Authors.
As can be seen, combinations 2 and 6 (COMB_2 and COMB_6) highlighted the largest and smallest efforts in the longitudinal direction ''Z''.Therefore, it is concluded that the most unfavourable efforts are provided in the COMB_2 combination.In the transverse direction, based on the application of the Robot Structural software, the most critical values were obtained, resulting in: -733.76 kN.m and 562.14 kN.m (bending moments); -49.06 kN and 531.64 kN (shearing/transverse forces); 0.0 kN and 635.88 kN (normal efforts), minimum and maximum, respectively.

Results of Deck Deformations in the Operational Phase
The results of the maximum and minimum deformations of the deck in the operational phase, taking into account the most critical/unfavourable combinations (COMB_2 and COMB_6), are presented in Table 11.Next, the deformed states of the deck in the direction "Z".

Results of Prestress Losses
As for the results referring to pre-stress losses in areas with higher tensile stresses (the middle of each span) taking into account the combinations that provide the greatest efforts, these (results) are presented in detail in Table 12.
In this context, the loads identified as Pmin (in Table 12) correspond to the minimum loads which guarantee no decompression in the section where the pre-stress is applied.The Papl value corresponds to the load that will be applied, which must always exceed Pmin.According to the regulatory technical recommendations this value, even after all the losses (immediate and deferred), must still be larger than Pmin.It can be seen from the table in question that the greatest prestressing losses are acceptable since they add up to less than the 15%, which were considered in the design.As can be seen in Figure 17, the pre-stress losses due to friction develop linearly, following a growth rate of around 6.48% of the initial value, which occurs mainly in longer cables, specifically and or above all, in the middle of the central span of the bridge.

Figure 1 -
Figure 1 -Flowchart of activities developed during the preparation of the research.

•Figure 2 -
Figure 2 -Layout and dimensions of the bridge: (a) Longitudinal view of the bridge, b) Cross section of 1/2 of the bridge's main beam and (c) schematic diagram of precast segments of the main span.(Unit: mm).

Figure 3 -
Figure 3 -Longitudinal profile and distribution of spans with respective dimensions (Unit: mm).

Figure 4 -Figure 5 -
Figure 4 -Overall model of the bridge highlighting the interior prestress cables adherent to the concrete.

Figure 7 -
Figure 7 -Second numerical model -Analysis during the bridge operational phase.

Figure 8 -Figure 9 -
Figure 8 -Evolution of the bending moment effort in the upper fibers of stave zero.

Figure 10 -
Figure 10 -Evolution of the axial compression force in the structure.

Figure 11 -
Figure 11 -Evolution of the axial compression force in the structure.

Figure 12 -
Figure 12 -Evolution of the axial compression force in the structure.

Figure 13 -
Figure 13 -Evolution of the axial compression force in the structure.

Figure 14 -
Figure 14 -Evolution of displacements and rotations of the bridge deck; a) displacements; b) rotations.

Figure 17 -
Figure 17 -Friction losses in the domain of distances in meters.

Table 1 -
Geometric and physical characteristics of the investigated reinforced concrete bridge.

Table 2 -
Main material parameters.

Table 3 -
Dimensions of the cross-section of each stave that make up the bridge.
h -Section height; i -Inclination of web.Source: Authors.

Table 4 -
Properties and self-weight of the bridge staves.

Table 6 -
Wind actions in each direction and combination factors, and the reduction of variable actions.
Sb_v, Sb_M -Action due to road overload of vehicles and crowds; Vx, Vy e Vz -Action due to the force of the wind.Source: Authors.

Table 7 -
Multiplicity factors of variable actions.
AVB -Base variable action taken in each combination; PP -Action due to own weight; CM -Action due to the weight of the moving load; Rcp -Action due to remaining permanent loads; PE -Action due to prestress.Source: Authors.

Table 8 -
Maximum values of bridge design efforts.

Table 9 -
Efforts determined for pre-stress.
Table 10 presents the internal forces obtained during the operational phase of the bridge, taking into account the most critical/unfavourable combinations, both from the point of view of checking the Ultimate Limit State (ELU) and the Service Limit State (ELS), described in the table as COMB_2 and COMB_6, respectively.

Table 10 -
Internal efforts obtained in the operational phase of the bridge -CSiBridge v.20.

Table 11 -
Maximum and minimum deformations in the operational phase.

Table 12 -
Prestressing losses due to friction taking into account eccentricity.