Dimensionamento Estrutural de uma Ponte Canal. Structural Design of a Canal Bridge. Francisco Barbosa Alves de Moura. Introduction

Transcription

1 Dimensionamento Estrutural de uma Ponte Canal Structural Design of a Canal Bridge Francisco Barbosa Alves de Moura IST, Technical University of Lisbon, Portugal Key Words: Structural Design, Canal Bridge, Reinforced Concrete, Eurocodes Introduction October 2014 This dissertation presents the structural design of a reinforced concrete canal bridge, according to the standards of structural safety, actions and design criteria established in Eurocodes. In this context, it is studied the behaviour in service of the following elements: bridge deck, bearings, piers and foundations. In Portugal, the canal bridges are mainly used in water supply and distribution systems, establishing links between water canals by the crossing of valleys. Although it may seem that these type of structures have a minor importance, they are vital in the supporting of major water storage constructions. The structural solution of the projected construction might be considered as a reinforced concrete bridge portico, with a total length of 54.4 m, comprising two side spans and three central spans of 9.2 m and 12.0 m, respectively, guaranteeing an outflow cross section of 9 m!. The bridge, which has a U shape cross section deck, is monolithically connected to the central piers and solely supported in the abutments and side piers. In these elastomeric bearings are used. The piers have a portico configuration and are oriented transversely to the axis of the deck. Given the good characteristics of the ground foundations (rocky soil), the piers supports are implemented through direct foundations and complemented by the application of soil nails. So as, to obtain the elements stresses, both analytical processes and 2D and 3D automatic calculi models, created with SAP2000 program, are used. The structural elements are analysed through the characterization of (i) the project constrains, (ii) the overall designed solution, (iii) the actions to which the structure is subjected, (iv) the general design criteria and (v) through the verification of the elements structural safety, considering the Ultimate Limit States (ULS) and the Service Limit States (SLS), according to the Eurocodes. Thus, the main objectives of this project are identified as the following: 1. To conceive and design the structure, taking into account the constraints of a similar structure; 2. To quantify the actions and design criteria, using as project standards the Eurocodes; 3. To verify the structural safety of the various reinforced concrete elements that make up the structure and design the deck elastomeric bearings; 4. To verify in detail the structural safety of the piers towards the seismic action, analysing how different modelling hypothesis of their behaviour, influence this verification. As for the design and study of the piers behaviour, when these are submitted to the seismic action, it is taken in consideration the influence of the elements cracking, the hydrodynamic overpressures and the rigidity level of the piers structural nodes. Finally, a measurement of the structure is made and the project drawings are presented. Conception of the studied solution The bridge deck has a maximum height of 16 m, which varies significantly along the transverse direction to the axis of the deck, due to the irregular topography. The foundation ground is composed by a low fractured rock mass, which is assumed to be 1

2 capable of a 3000 kn m! resistant capacity [Gomes e Vinagre, 1997]. As for the structural materials, it is stipulated the use of a C30/37 concrete and a A500NR steel reinforcement rebar. In order to define a simple and efficient cross section for the canal, it s defined the U shape frame displayed in Fig.1, which demonstrates a reasonable ratio between the section area and its inertia. For a better performance of the frame corners, gussets are implemented through the interior of the canal. Figure 2 Piers type module configuration. A single pier solution wasn t adopted as it wasn t thought to be a better solution neither for aesthetics nor for structural reasons. Although this solution would facilitate the execution of the element, comparing to the configuration adopted, the chosen one provides a rigidity increase for the columns alignment, for the same value of the cross section area. Each columns alignment have two independent direct foundations, rectangular and of equal dimensions, in which are inserted soil nails constituted by 32 reinforcement bars, inserted in holes made in the ground and sealed by cement grout injection. Thus, it is assumed in all analytical and numerical models of the structure created that the piers are completely fixed in the base. Figure 1 Cross Section of the Canal. Due to the irregular topography of the construction location, all piers have different heights, being the central ones higher than the lateral. The first have a width of 0.75 m and the second have 0.50 m, since during the seismic analysis of the structure it was found to be necessary to increase the rigidity of the central piers. An example of the configuration adopted for the piers is shown in Fig.2. The geometry adopted for the abutments is merely representative, as these structures correspond to the hydraulic structures of reception and output of the water flow of the canal, and their conception and design are not part of this study. For the connection system between the substructure and the superstructure are studied three different solutions, in which the deck is: 1. Fixed to one of the abutments; 2. Monolithically attached to one of the side piers and to both central piers, with the remaining support sections being simply supported on elastomeric bearings; 3. Monolithically attached to both central piers, with the remaining support sections being simply supported on elastomeric bearings. From the three hypotheses, the last was the chosen as it verifies the non- cracking of the reinforced concrete sections in the base of the piers. For the execution of this verification are used the length variations of the bridge deck, in service limit states, due to the effects of the uniform temperature contraction component together with the shrinkage of the concrete. 2

3 The elastomeric bearings mentioned are placed between the bridge deck and the piers/abutments. The structural design of these elements is made together with the previous verifications, for which are respected the maximum displacements obtained for each support section of the bridge deck, as well as the maximum distortions and compression stresses. The performed calculations take in consideration the equivalent horizontal stiffness of the assemblies pier plus bearing. Different solutions are used for the side piers bearings and the abutments bearings. Actions and Design Criteria In the design of the stated structural elements are analysed the effects of the structure s self- weight (pp), the hydrostatic pressures, the uniform ( T! ) and the difference ( T! ) components of the temperature actions, the shrinkage of concrete, the wind action (F! ), the seismic global action and the local hydrodynamic overpressures on the walls and bottom slab of the canal. Regarding of the joint action of the uniform temperature component and the shrinkage of concrete, two different calculation hypotheses are defined, to adjust the effects resulting from the uniform temperature component. This amendment is made since it is considered unrealistic the value obtained for T!,!"#., in the situation in which the canal is full, as the mass of water contained in it gives an elevated thermal inertia to the structure, when facing temperature variation. Thereby: 1ª hypothesis: It s considered that the waterway is empty, with T!,!". = 44.5 ( T!,!"#. = 21.5 ); 2ª hypothesis: It s stated that the waterway is full, with T!,!". = 33 ( T! = 10 ). Similarly to these hypotheses, and for the same reasons mentioned above, another two hypotheses are defined, for consideration of the temperature difference components: 1ª hypothesis: It s considered T!! = ±2, for when the waterway is full; 2ª hypothesis: It s defined T!! = +10, for a situation in which the waterway is filled to 10% of its capacity. As for the seismic action, the projected bridge is characterized for a limited ductile seismic behaviour, as it is localized in a low seismicity zone (NA (4), NP EN ). The behaviour coefficient q must be inferior to 1.5 ( (1), NP EN ). The stresses, due to combinations of horizontal components of the seismic action, are calculated by means of the two next combinations, for each one of the seismic action types. E!"# "+" 0.30 E!"# 0.30 E!"# "+" E!"# The structural safety verifications in service are executed using the fundamental and the seismic combination for the Ultimate Limit States (ULS) and trough the characteristic combination for the Service Limit States (SLS). The main design criteria defined is the cracking control of the bridge deck elements, in which it must be guaranteed an appropriate level of tightness, translating this assurance by the control of the cracked elements width (w! ). It s attributed to the structure a Tightness Class 2, limiting it to a value of 0.10 mm. Structural Analysis and Design Verification Bridge s Deck Transversal Analysis The transversal analysis of the bridge deck is executed through manual calculations, since the equivalent structural model of the bridge s deck cross section, is isostatic. There are considered two distinct sets of loads, one including the hydrostatic pressures that act in the interior of the canal, the other containing the wind action that act on the exterior of the canal s walls. Design verifications for bending and shear ULS are performed, as well for structure s SLS. The resultant quantities of the necessary section s steel reinforcements are not defined at this stage, as they will need to be added/compared with the results 3

4 from the shear design of the bridge s deck longitudinal analysis. In the design for SLS, is indicated the need to calculate the cracks width in the canal bottom slab sections, near the gussets. The control of cracking is performed through direct calculation, being it represented by the expression: To assess the level of rigidity that the nodes of the piers frame grant to the structure, two different models are created for comparison: one with "rigid" nodes (in which the elements that constitute the nodes are infinitely rigid); and another one with "flexible" nodes (in which the elements that constitute the nodes have the same rigidity has the elements next to them) (Fig.3). w! = s!,!á! ε!" ε!" Bridge s Deck Longitudinal Analysis For the longitudinal analysis of the bridge deck is used a 2D automatic model of a structural portico equivalent to the projected structure, in which it is not considered, in the supported sections of the deck, the characteristics of the existent elastomeric bearings. The connections with the piers in those sections are defined as simply supported. The establishment of a continuous beam model for the bridge deck is not appropriate for calculating the deck s longitudinal stresses, because of the actual axial deformations of the piers. In the performed calculations aren t considered any losses for the pier s elements stiffness. In accordance with the hypotheses established for the temperature difference component, are defined the following action combinations: Figure 3 Analytical model. In the analysis of the hydrodynamic overpressures caused by the self- oscillation of the water mass inside the canal, is created a model with two masses of water, one oscillatory and another "inert", based on the fundamentals of elevated tanks. In Fig.4 it s displayed schematically the calculation model that represents the revealed behaviour. Comb. 1 pp + p! + T!! + F!,! ; Comb. 2 pp p! + T!! + F!,!. Considering these combinations, design verifications for bending and shear ULS are performed, as well for structure s SLS. In the structure s design for SLS, is indicated the need to calculate the cracks in some of the inside support sections of the deck. The control of cracking is again performed through direct calculation. Are also calculated in this chapter de the minimum amounts of steel reinforcement, needed along the cross section of the bridge deck. Piers Analysis To study the influence of the piers characteristics (mentioned above) in their behaviour, different 3D automatic models are created. The piers are analysed for the wind and seismic actions. Figure 4 Calculation model. These three models are only analysed for the seismic action, being for all of them accounted the full amount of water that the canal is able to lodge, without being applied any enhancement factors. From the modal information of these models it s perceptible that the vibration modes are correspondent from one model to next one and that the obtained frequencies values are also proportional. 4

5 The wind action loads are applied has linear and nodal loads, in a model similar to the rigid nodes model. To evaluate the influence of the piers elements cracking state in the structure behaviour, it s created another model similar to the rigid nodes model, in which the elements now have half of the rigidity that was assigned to them in the past models (non- cracked rigidity), in order to simulate the piers cracking. In the design verifications for bending ULS is used an elastic- plastic analysis, considering the piers elements subjected to bending with axial force and second order effects, as also considering the resistant capacity of the elements associated to the their rebar detailing, defined according to the next expressions. M! = μ! b h! f!" 1 M! = M! + P w!,! 1 P P!",! P!",! = π! EI! l!! M! = EI! R! EI! = M! R! Tables 1 and 2 show an example of one element s design. For the ULS are also performed the shear design verifications of the piers elements and the interface connections between the central piers and the bridge deck. In the structure s SLS design are calculated the seismic deflections that affect the support bearings, permitting to recalculate the first choices made for these components and allowing to define the expansion joints that must be applied between the deck s ends and the abutments. Foundations Design Foundations design is executed independently for each bending direction of the piers, considering the stresses combinations of all models created for the piers analysis. Numerical models are used, created specifically for the projected situation, which define different type cases of the foundations behaviour. For all cases it s considered a linear elastic distribution of the soil compressions, given the good characteristics it presents. For the cases with higher solicitations it is projected the application of soil nails, as have been indicated before. In the ULS design verifications are defined the foundations dimensions and the number and length of the soil nails to fix to each direct foundation. The dimensions of the side piers foundations are m and for the central piers foundations are m. Conclusions Regarding the longitudinal alignment, it s noted that the geometric shape defined for the cross section of the bridge deck should be such that the positive and negative cracking moments were closer to each other, in absolute value, as the SLS acting moments values are. For the transversal behaviour of the bridge deck, it should be elaborated a more thorough study of the frame corners behaviour, or could be considered alternatives to the section of the canal, which also might solve the cracking of the bottom slab sections. As it was indicated for the bridge deck cross section, the piers frame nodes behaviour should also be analysed in more detail, in terms of the reinforcement detailing to use and concerning the non- linear effects that they can be subject to. Table 1 Design of the element P 1 d 0, for y pier bending direction. P kn M! knm ω!"! ν μ! M! knm M! M! A!",!"! cm! % % Table 2 Design of the element P 1 d 0, for z pier bending direction. P kn M! knm ω!"! ν μ! M! knm

6 It was showed that the elastomeric bearings had some difficulty responding to the design seismic deflections, being noted that in the event of a seismic occurrence it could needed the replacement of some of these components or, alternatively, the choice of the bearings should take into account the displacements produced by the seismic action. Analysing the results of the piers design, for each model, it was concluded that the Rigid Nodes Model presented the most conditioning results, regarding the seismic action, although some elements design have been limited by the results due to wind action. This aspect proves that the wind action should not be neglected for bridges located in areas of low seismicity. Regarding the foundations design, it s noted that it was considered an admissible compression stress of the soil of 3000 kpa, being suggested that further studies on the real capacity of the soil are however necessary. The projected solution of soil nails for the structure foundations also requires further detail for a execution project phase. As further development to this project it s proposed an additionally study that considerate the effects of the hydraulic forces imposed upon the structure by the movement of the water inside the canal, as well as the design of the input and output flow structures of the bridge. Figure 5 Longitudinal alignment of the canal bridge. 6