Análisis del ciclo de vida de puentes carreteros convencionales con diversas soluciones de proyecto

Trabajo realizado por: Dirigido por: Grado en: Barcelona, Departamento de TR A BA JO FINAL DE GRA DO Análisis del ciclo de vida de puentes carreteros convencionales con diversas soluciones de proyecto Julio Fernández de Betoño Villanueva Jesús Miguel Bairán García Bachelor degree in civil engineering 19 de junio de 2024 Ingeniería Civil y Ambiental Summary In this final degree project it has been tried to analyze the environmental implications generated by the different materials and processes in the execution of a civil works infrastructure. The two most common materials in structures in this field are concrete and steel. Concrete primarily provides compressive strength and steel primarily provides tensile strength. Both materials are necessary for the execution of beams, pillars or plates. Steel has a much more harmful environmental impact than concrete but much smaller quantities are required in volume. In the introduction the environmental impact of both materials has been further developed. Subsequently, a practical case has been executed. Firstly, the limiting conditions of a specific project, a bridge that must cross a highway, have been exposed. Secondly, a design of a possible deck for that case has been developed, arguing the choice of said solution and the main geometries. The deck is composed of 6 precast prestressed concrete beams under a concrete top slab. The deck is simply supported on the two abutments and on an intermediate pillar. Thirdly, the calculation of the loads affecting a highway bridge of those dimensions has been carried out and the effects of said loads have been calculated using the SAP2000 software. In addition, the necessary steel reinforcement has been designed to withstand the forces calculated in SAP2000 throughout the deck. The prestress, the prestress losses, the shear reinforcement of the beams and the reinforcement of the upper slab have been calculated. On the other hand, once the entire reinforcement calculation was carried out, it was possible to obtain the total mass of steel, the total volume of concrete and the surface area required for the formwork. All of this has been necessary for the life cycle analysis carried out with the SimaPro software. It has also been necessary to estimate the transportation processes from the raw material production factories to the construction site as well as the machinery required on site. Once all this data has been defined, the SimaPro software has developed in different categories the impacts on the environment that would be caused by the execution of this project. Finally, to contrast the SimaPro analysis, the equivalent CO2 emissions have been compared with cases of similar projects, seeking the most useful comparative unit when comparing. Being two other projects of concrete bridge decks for other geometric conditions, the equivalent CO2 emissions produced by each bridge for each square meter of deck surface have been compared. 2 Resumen En este trabajo de fin de grado se ha pretendido analizar las implicaciones ambientales que generan los diferentes materiales y procesos en la ejecución de una infraestructura de obra civil. Los dos materiales más habituales en estructuras de este campo son el hormigón y el acero. El hormigón proporciona principalmente resistencia a la compresión y el acero proporciona principalmente resistencia a la tracción. Ambos materiales son necesarios para la ejecución de vigas, pilares o placas. El acero tiene un impacto medioambiental mucho más perjudicial que el hormigón, pero se requieren cantidades mucho menores en volumen. En la introducción se ha desarrollado más a fondo el impacto medioambiental de ambos materiales. Posteriormente se ha ejecutado un caso práctico. En primer lugar, se han expuesto las condiciones limitantes de un proyecto concreto, un puente que debe cruzar una carretera. En segundo lugar se ha desarrollado un diseño de un posible tablero para dicho caso, argumentando la elección de dicha solución y las principales geometrías. El tablero está compuesto por 6 vigas prefabricadas de hormigón pretensado bajo losa superior de hormigón. El tablero se apoya simplemente sobre los dos estribos y sobre un pilar intermedio. En tercer lugar se ha realizado el cálculo de las cargas que afectan a un puente carretero de esas dimensiones y se han calculado los efectos de dichas cargas mediante el software SAP2000. Además, se ha diseñado el refuerzo de acero necesario para soportar los esfuerzos calculados en SAP2000 en todo el tablero. Se han calculado el pretensado, las pérdidas de pretensado, el refuerzo a cortante de las vigas y el refuerzo de la losa superior. Por otro lado, una vez realizado todo el cálculo de armaduras se pudo obtener la masa total de acero, el volumen total de hormigón y la superficie requerida para el encofrado. Todo ello ha sido necesario para el análisis del ciclo de vida realizado con el software SimaPro. También ha sido necesario estimar los procesos de transporte desde las fábricas de producción de materia prima hasta la obra, así como la maquinaria necesaria en la obra. Una vez definidos todos estos datos, el software SimaPro ha desarrollado en diferentes categorías los impactos al medio ambiente que provocaría la ejecución de este proyecto. Finalmente, para contrastar el análisis de SimaPro, se han comparado las emisiones de CO2 equivalentes con casos de proyectos similares, buscando la unidad comparativa más útil a la hora de comparar. Al tratarse de otros dos proyectos de tableros de puentes de hormigón para otras condiciones geométricas, se han comparado las emisiones de CO2 equivalentes que produce cada puente por cada metro cuadrado de superficie del tablero. 3 Resum En aquest treball de fi de grau s'han pretès analitzar les implicacions ambientals que generen els diferents materials i processos en l'execució d'una infraestructura d'obra civil. Els dos materials més habituals en estructures del camp són el formigó i l'acer. El formigó proporciona principalment resistència a la compressió i l'acer proporciona principalment resistència a la tracció. Tots dos materials són necessaris per a l'execució de bigues, pilars o plaques. L'acer té un impacte mediambiental molt més perjudicial que el formigó, però calen quantitats molt menors en volum. A la introducció s'ha desenvolupat més a fons l'impacte mediambiental dels dos materials. Posteriorment, s'ha executat un cas pràctic. En primer lloc, s'han exposat les condicions limitants d’un projecte concret, un pont que ha de creuar una carretera. En segon lloc, s'ha desenvolupat un disseny d'un possible tauler per a aquest cas, argumentant l'elecció d'aquesta solució i les geometries principals. El tauler està compost per 6 bigues prefabricades de formigó pretesat sota llosa superior de formigó. El tauler es recolza simplement sobre els dos estreps i sobre un pilar intermedi. En tercer lloc, s'ha realitzat el càlcul de les càrregues que afecten un pont carreter d'aquestes dimensions i s'han calculat els efectes de les càrregues esmentades mitjançant el programari SAP2000. A més, s'ha dissenyat el reforç d'acer necessari per suportar els esforços calculats a SAP2000 a tot el tauler. S'han calculat el pretesat, les pèrdues de pretesat, el reforç a tallant de les bigues i el reforç de la llosa superior. D'altra banda, un cop realitzat tot el càlcul d'armadures, es va poder obtenir la massa total d'acer, el volum total de formigó i la superfície requerida per a l'encofrat. Tot això ha calgut per a l'anàlisi del cicle de vida realitzat amb el programari SimaPro. També ha calgut estimar els processos de transport des de les fàbriques de producció de matèria primera fins a l'obra, així com la maquinària necessària a l'obra. Un cop definides totes aquestes dades, el programari SimaPro ha desenvolupat en diferents categories els impactes al medi ambient que provocaria l'execució d'aquest projecte. Finalment, per contrastar l'anàlisi de SimaPro, s'han comparat les emissions de CO2 equivalents amb casos de projectes similars, cercant la unitat comparativa més útil a l'hora de comparar. Com que es tracta de dos projectes més de taulers de ponts de formigó per a altres condicions geomètriques, s'han comparat les emissions de CO2 equivalents que produeix cada pont per cada metre quadrat de superfície del tauler. 4 Index 1 - Introduction……………………………………………………………………………………………………………...…8 1.1 - Description and properties of concrete………………………………………………………..…………...8 1.2 - Ecological impact and sustainability challenges of concrete…………………………………………….9 1.3 - Description and properties of steel as concrete reinforcement…………..……………………………11 1.4 - Ecological impact and sustainability challenges of steel…………………….…………………………12 2 - Global design of the bridge deck and its constraints……………………………….……………………………..…13 2.1 - Applied type of solution for the challenge.………………………………….…………………………….13 2.2 - Definition of the geometry of the precast beams and the top slab………….…………………………14 2.3 - Determination of material conditions and solutions……………………………………………………..17 2.3.1 - Type of concrete application.………………………………………………………………….17 2.3.2 - Class of concrete.………………………………………………………………………………17 2.3.3 - Minimum cover of the steel and steel class.…………………………….…………………..19 2.4 - Applied loads.……………………………………………………………………….……………………….20 2.4.1 - Selfweight loads………………………………………………………………………………..20 2.4.2 - Paviment loads…………………………………………………………………………………20 2.4.3 - Traffic loads.…………………………………………………………………………………….20 2.4.3.1 - Division of the carriageway and notional lanes.……………….……………….20 2.4.3.2 - Static load models for vertical loads - LM1 and LM2………………………….21 2.5 - Applied model for the analysis of the resistance of the prefabricated girder bridge: grid method……………………………………………………………………………………………………………..22 2.5.1 - Application of the grid method for the analysis of decks formed by 'T' or double 'T' beams….………………………………………………………………………………………………..23 2.5.2 - Longitudinal beams and bars.…………………………………………………………………24 2.5.3 - Beams and cross bars.……………………………………………...…………………………24 2.5.4 - Application of the grid method to our specific case…………………….…………………..25 2.5.5 - SAP200 software.………………………………………………………………………………26 2.6 - SAP2000 analysis and obtained results…………………………………………………………………27 3 - Steel reinforcement design of the double T beams.………………………………………………………………….28 3.1 - Longitudinal reinforcement………………………………………………………………………………...28 3.1.1 - Moments to apply………………………………………………………………………………28 3.1.2 - Properties to apply……………………………………………………………………………..29 3.1.3 - Admissible stresses……………………………………………………………………………29 3.1.4 - Calculus of the longitudinal prestressing of double T beams……………………………..29 3.1.5 - Calculus of the prestressing losses of double T beams ……………………..……………31 3.2 - Shear resistance analysis and shear armor design of each double T beam.…………..…………….33 4 - Steel reinforcement calculus and design at the top slab………………………………………….…………………37 4.1 - Bending moment resistance analysis of the top span in the transversal section.……………………38 4.2 - Shear resistance analysis of the top span in the transversal section…………………………………39 5 - Summary of the total reinforcement of the bridge deck.………………………………………..……………………41 6 - Designed bridge deck life cycle analysis (LCA)………………………………………………………………………43 6.1 - Life cycle analysis and SimaPro software……………………………………………..…………………43 6.2 - Values to take into account for LCA.………………………………………………………………………44 6.3 - Obtained results of the LCA.……………………………………………………………….………………46 6.4 - Comparison of the obtained results with other projects……………………………………..………48 6.4.1 - Extradosed bridge alternative…………………………………………………...……………49 6.4.2 - Continuous beam alternative.…………………………………………………………………50 6.4.3 - Comparison of the different alternatives.……………………………….……………………50 7 - Conclusions………………………………………………………………………………………………………..……..52 8 - Bibliography.………………………………………………………………………………………………………..…….53 5 Index of figures Figure 2.1 - Geometrical constraints of the bridge……………………………………………………………………….13 Figure 2.2 - Obras de paso de nueva construcción. Conceptos generales - Rango de utilización más frecuente de tipos de obras de paso según su tipología y luz. Fig 3.……………………………………………………………….14 Figure 2.3 - Transversal cross section of the bridge………………………………………………………………….....16 Figure 2.4 - Transversal cross section of one beam and the top slab...……………………………………………….17 Figure 2.5 - EN1991-2: Fig. 4.1 - Example of the Lane Numbering in the most general case…………………...…21 Figure 2.6 - EN1991-2: Fig. 4.2a - Application of load Model 1.……………………………………………………..…22 Figure 2.7 - At the right side, scheme of the position of the tandem of punctual loads at LM1. At the left side, scheme of the position of one punctual load at LM2…………………………………………………………………….22 Figure 2.8 - Notes of the subject Bridges of the Master in Civil Engineering of the UPC…………………………...23 Figure 2.9 - Notes of the subject Bridges of the Master in Civil Engineering of the UPC……………………………24 Figure 2.10 - Cross section corresponding to a longitudinal bar in SAP2000 model………………………………...25 Figure 2.11 - Obtained SAP2000 model…………………………………………………………………….…………….26 Figure 2.12 - Resulting deformations scheme of the deck.…………………………………….……………………….27 Figure 2.13 - Resulting bending moment scheme of the deck..………………………………..………………………27 Figure 2.14 - Resulting shear scheme of the deck..……………………………………………….…………………….27 Figure 3.1 - Prestressing force losses results graph…………………………………………………………………….32 Figure 5.1 - Longitudinal view of the ending of the beam……………………………………….………………………41 Figure 5.2 - Longitudinal view of the beam……………………………………………………………………..………...41 Figure 5.3 - Cross section views of a beam and the top slab in different longitudinal points……………………….42 Figure 5.4 - Cross section views of the deck.………………………………………………………………..…………..42 Figure 6.1 - Introduced data in the software for the Case 1………………………………………………….…………45 Figure 6.2 - Introduced data in the software for the Case 2………………………………………………….…………46 Figure 6.3 - Case 1 obtained results..………………………………………………………………………………….….47 Figure 6.4 - Case 2 obtained results..………………………………………………………………………………….….48 Figure 6.5 - Longitudinal view of the project corresponding to the extradosed bridge solution (Brignardelli, 2015)....................................................................………………………………………………………………............49 Figure 6.6 - Longitudinal view of the project corresponding to the beam bridge solution (ADIF, 2006)..................49 Figure 7.1 - Percentage of impact of the formwork in each category.………………………………………………….53 6 Index of tables Table 2.1 - Geometry dimensions of the deck……………………………………………………………………..……..16 Table 2.2 - EN1992-1 - Tab. 4.1: Exposure classes related to environmental conditions in accordance with EN 206-1………………………………………………………………….………………………………………………………18 Table 2.3 - EN1992-1 - Tab. E.1N: Indicative minimum strength class……………………………………………..…18 Table 2.4 - EN1992-1 - Tab. 4.3N: Recommended structural classification…………………………………………..19 Table 2.5 - EN1992-1 - Tab. 4.4N: Values of minimum cover, Cmin,dur requirements with regard to durability for reinforcement steel………………………………………………………………………………………………………….19 Table 2.6 - EN1992-1 - Tab. 4.5N: Values of minimum cover, Cmin,dur requirements with regard to durability for prestressing steel……………………………………………….……………………………………………….…………..19 Table 2.7 - EN1991-2: Tab. 4.2 - Load model 1 : characteristic values………………………………………………..21 Table 3.1 - Selweight, frequent and characteristic maximum longitudinal moments…………………………………28 Table 3.2 - Additional geometrical considerations……………………………………………………………………….29 Table 3.3 - Maximum admissible tension and compression stresses………………………………………………….29 Table 3.4 - Prestressing force losses calculation parameters and results…………………………………………….31 Table 3.5 - Prestressing force losses results table………………………………………………………………………33 Table 3.6 - Shear calculations table……………………………………………………………………………………….36 Table 4.1 - ULS design calculations for top slab.………………….……………………………………………………..37 Table 4.2 - EHE08 - Tab. 42.3.5: Minimum reinforcement quantities………………………………………………….38 Table 4.3 - Reinforcement bars comparison..…………………………………………………………………………….39 Table 6.1 - Case 1 obtained results.……………………………………………………………………………………....46 Table 6.2 - Case 2 obtained results.……………………………………………………………..………………………..47 Table 6.3 - Global analysis of emissions comparison……………………………..………………………………….…51 Table 6.4 - Deck analysis of emissions comparison……………………………………………………………………..51 7 1 - Introduction Following the United Nations webpage explanation 1, the Sustainable Development Goals are a call for action by all countries – poor, rich and middle-income – to promote prosperity while protecting the planet. They recognize that ending poverty must go hand-in-hand with strategies that build economic growth and address a range of social needs including education, health, social protection, and job opportunities, while tackling climate change and environmental protection. These objectives range from the search for an end to poverty to climate action, including gender equality, peace, justice or quality education. The ninth objective refers to industries, innovation and infrastructure 2. From the point of view of Civil Engineering, this is the point that affects us the most. In particular, point 9.4 says “By 2030, upgrade infrastructure and retrofit industries to make them sustainable, with increased resource-use efficiency and greater adoption of clean and environmentally sound technologies and industrial processes, with all countries taking action in accordance with their respective capabilities.”, in this project this point of the Sustainable Development Goals for the year 2030 will be followed in a particular case related to the Civil Engineering and infrastructures. The most used materials in civil works infrastructures are concrete and steel. In this project we are going to focus on these materials, its impact on the environment - from the beginning of its manufacturing process to its placement on the site passing through the transportation processes and maintenance processes-. The aim of reaching a lower environmental impact in an infrastructure project is becoming increasingly important; however, it should not be forgotten that an infrastructure project is still a business for some design and execution companies and every business must be economically viable. In this project, a concrete bridge deck will be designed by the traditional way, by the use of steel as the reinforcement, for some limiting conditions. After that calculation process of the geometry of the deck and the required quantity of concrete and steel reinforcement, a life cycle analysis will be carried out. 1.1 - Description and properties of concrete Concrete is a construction material widely used in architecture and engineering projects around the world. It has been used, at least, since the Greek empire and Romans developed many constructions with it 3, some still standing today. It is mainly composed of water, aggregates (sand and gravel) and binding (cement). It can also have optional chemical additives. It is distinguished by its consistency, economic affordability and ability to set quickly. As we can read in the webpage of one of the biggest construction companies in Spain and in the World, Ferrovial 4, concrete is one of the most used materials in construction because it is considered one of the most advantageous of the market. Here are the main advantages: - It is easy to access thanks to the commonality of its components, its components are not difficult to reach all around the world. - It is quick to adapt according to its structural purposes. It can be casted and molded into many different shapes. 8 - It is economical. - Low permeability risks. - It has long durability, thanks to the quality of its properties. - It is resistant to heat and, therefore, to deformation or collapse. - It has high resistance to compression, bending, cutting and traction, making it a very safe material. - Requires little maintenance. In the same page of Ferrovial, they have also analyzed the sustainability fact: it is a 100% recyclable material, it contributes to the energy efficiency of buildings, reduces CO2 emission and temperature in urban environments. - Concrete has the ability to absorb carbon from the atmosphere and reduce the amount of CO2 in the air. This is called the CO2 sink effect, which makes it a star resource in terms of sustainability. - Contribution to global energy efficiency: concrete has the quality of being a thermal insulator, which allows energy consumption to be reduced as a result of temperature peaks, minimizing the energy cost of buildings, as well as collaborating in the reduction of greenhouse gases involved in energy production. - High resistance: concrete gives buildings and bridges a lot of strength against fire or natural phenomena such as earthquakes, improving the service of the structures and their level of social security. - Guarantee of quality of life for citizens: concrete has the quality of providing high durability to infrastructure, allowing its conservation with few maintenance costs. 1.2 - Ecological impact and sustainability challenges of concrete However, we must also know that more than 4 billion tons of cement are produced every year, representing around 8% of global CO2 emissions. Compared to plastic production, 8 billion tons of plastic have been produced in the last 60 years. To this we must add the forecast for the future: the demand for cement will grow in relation to the growth and development of new urban and interurban infrastructures in all those areas of the world that are developing as well as Southeast Asia, Australia, Africa or South America 5. Although some of the largest cement companies have reduced the carbon intensity of their products by investing in more fuel-efficient kilns, most of the improvements achieved have been eclipsed by the massive increase in global cement and concrete production. In addition, cement production needs clinker that is made from burned limestone and clay in furnaces. This is the most contaminant element of the cement production process. Three main points are the causes of the CO2 emissions of the concrete, taking into account all its process of production, transportation and placement 6. 9 is 20 cm since it is necessary for the correct placement of the reinforcement and the conservation of the coatings. 𝑆𝑏𝑒𝑎𝑚𝑠=1. 666 𝑚 (𝑒𝑞. 2.7) 𝑆𝑏𝑒𝑎𝑚𝑠 20 ; 20 𝑐𝑚≤ℎ𝑢𝑝𝑝𝑒𝑟 𝑠𝑙𝑎𝑏≤𝑆𝑏𝑒𝑎𝑚𝑠 20 (𝑒𝑞. 2.8) ℎ𝑢𝑝𝑝𝑒𝑟 𝑠𝑙𝑎𝑏=20 𝑐𝑚 (𝑒𝑞. 2. 9) In the following table you can see the geometric dimensions of both the board as well as the upper slab and the beams. Element Nomenclature Unit Quanity Total length of the deck TL m 47,46 Length of each span L m 23,73 Width of the upper slab W slab m 10 Height of the upper slab H slab mm 200 Number of beams N 6 Height of the beam H beam mm 1250 Geometry of each beam Height of the top flange of the beam h top f mm 150 Height of the web of the beam h w mm 600 Height of the bottom flange of the beam h bot. f mm 500 Width of the top flange of the beam w top f mm 1200 Width of the web of the beam w w mm 200 Width of the bottom flange of the beam w bot. f mm 500 Table 2.1 - Geometry dimensions of the deck Figure 2.3 - Transversal cross section of the bridge 16 Figure 2.4 - Transversal cross section of one beam and the top slab 2.3 - Determination of material conditions and solutions 2.3.1 - Type of concrete application For lights smaller than 15 meters it is not strictly necessary, in any case, it has been planned to apply prestressed concrete. In this way we will favor bending behavior and we will control the cracking of the concrete. 2.3.2 - Class of concrete The location studied is far from the coast. For this reason, it is not considered that the environment is harmful. It is considered that it will be exposed to chlorides of non-marine origin. According to the following table 4.1 of the Euro-code, an exposure of type XD3 is assumed: a cyclic wet and dry environment. 17 Table 2.2 - EN1992-1 - Tab. 4.1: Exposure classes related to environmental conditions in accordance with EN 206-1 Table 2.3 - EN1992-1 - Tab. E.1N: Indicative minimum strength class 18 Table 2.4 - EN1992-1 - Tab. 4.3N: Recommended structural classification In conclusion, as can be seen in the previous tables, the minimum class of concrete must be C35/45. For the central pillars it will be applied a concrete of 35 MPa and for the longitudinal beams it will be applied a concrete of 40 MPa. The structural class for the beams is S6 and for the columns S5. 2.3.3 - Minimum cover of the steel and steel class As can be seen in the following tables, we will have a cover of 60 - 65 mm with a tolerance of 5 mm. The concrete minimum cover would be 70 mm. In relation to steel, class C500 is expected for passive reinforcement and 0.6" cords are expected (140 mm2) for prestressing reinforcement. f puk = 1850 MPa; f pyk = 1690 MPa. Table 2.5 - EN1992-1 - Tab. 4.4N: Values of minimum cover, Cmin,dur requirements with regard to durability for reinforcement steel Table 2.6 - EN1992-1 - Tab. 4.5N: Values of minimum cover, Cmin,dur requirements with regard to durability for prestressing steel 19 2.4 - Applied loads Once all the geometrical and material characteristics have been defined, the next step is to analyze the applied loads. 2.4.1 - Selfweight loads For the self weight load calculation, the cross section area of the beams plus the top slab must be defined: 𝐴𝐶𝑆(𝑏𝑒𝑎𝑚𝑠+𝑠𝑝𝑎𝑛)=(0.55 𝑚2·6 𝑏𝑒𝑎𝑚𝑠)+ 10 𝑚·0.2 𝑚( )=5. 3 𝑚2 (𝑒𝑞. 2.10) Once this area is clear, the structure selfweight load can be computed. This is the selfweight of the deck for one longitudinal meter: 𝑄𝑆𝑊 /𝑚=𝐴𝐶𝑆(𝑏𝑒𝑎𝑚𝑠+𝑠𝑝𝑎𝑛)·γ𝑅𝐶 (𝑒𝑞. 2. 11) 𝑄𝑆𝑊 /𝑚=5.3 𝑚2·25𝑘𝑁 𝑚3=132.5𝑘𝑁 𝑚 (𝑒𝑞. 2.12) 2.4.2 - Paviment loads This is the pavement load applied in the deck for one longitudinal meter: 𝑞𝑃𝐴𝑉 =2𝑘𝑁 𝑚2·10 𝑚=20𝑘𝑁 𝑚 (𝑒𝑞. 2.13) 2.4.3 - Traffic loads Traffic loads are surface loads that can be applied in different ways, the static load models applied in EN 1991-2 will be followed. 2.4.3.1 - Division of the carriageway and notional lanes The first point is to divide the carriageway in notional lanes and a remaining area. All of the physical lanes marked on the road surface, in addition to the hard shoulders, hard strips, and marker strips, are part of the carriageway. The usual lane width is a 3 m width. In this case, the carriageway width is 10 m width, so: there will be assumed 3 lanes of 3 m width and the remaining area will have 1 m width. Typically, the notional lane with the most significant impact is designated as lane n. 1 and so forth, in descending order of severity. 20 Figure 2.5 - EN1991-2: Fig. 4.1 - Example of the Lane Numbering in the most general case 2.4.3.2 - Static load models for vertical loads - LM1 and LM2 In EN1991-2 there are four static load models for vertical loads analysis. LM1 and LM2 are going to be applied. LM3 is applied if there is required a special vehicles analysis in a transient design situation, in this case this situation is not fulfilled. LM4 is the application of a crowd loading, it is particularly significant for bridges situated in urban areas, in this case this situation is not fulfilled. Load model number 1, referred to as LM1, primarily replicates traffic-related influences that need to be considered for both global and local assessments. It consists of concentrated and uniformly distributed loads, involving a pair of concentrated axle loads, one for each notional lane denoted as i. Tandem system Uniformly distributed load Axle load Qik qik Unit kN kN/m2 Notional lane 1 300 9 Notional lane 2 200 2,5 Notional lane 3 100 2,5 Other notional lanes 0 2,5 Remaining area 0 2,5 Table 2.7 - EN1991-2: Tab. 4.2 - Load model 1 : characteristic values Load model number 2, referred to as LM2, reproduces traffic effects on short structural members. LM2, designed exclusively for local checks, should be assessed independently while positioned singularly on the bridge, moving along the longitudinal axis of the bridge, in its most disadvantageous orientation. In unfavorable scenarios, consideration should be given to only one wheel. The local applied loads must be of 400 kN. 21 Figure 2.6 - EN1991-2: Fig. 4.2a - Application of load Model 1 In the following figure, schemes of the punctual loads applications in LM1 and LM2 can be seen. Figure 2.7 - At the right side, scheme of the position of the tandem of punctual loads at LM1. At the left side, scheme of the position of one punctual load at LM2. 2.5 - Applied model for the analysis of the resistance of the prefabricated girder bridge: grid method Through the use of the grid method, a real deck of beams, slabs or box section is assimilated to a model of bars (flat or in space) in order to obtain a response to the different load scenarios: self-weight, permanent or for use. The grid method is a numerical method that enables the reproduction and analysis of a three-dimensional structure's behavior by assembling straight frames (1D elements). Despite the existence of many numerical methods, such as spatial grillage and solid FEM, the simplicity of definition and broad range of applications make plane grillage a particularly appealing choice. 22 Figure 2.8 - Notes of the subject Bridges of the Master in Civil Engineering of the UPC The gridding method is very appropriate to easily accommodate variable conditions in plan, straight, curved, oblique deck to variable conditions in the distribution of thicknesses, constant or variable edges of the beams that make up the deck and to links between sections of simple support or continuity. There are behaviors that are well reproduced as well as bending and twisting of real linear elements through this method. The most superficial behaviors can have some more complications depending on the type of acting action. A weak point in this analysis model is that of point charges. For example, when a point load acts on the deck slab, its effect will be correctly determined if a mesh has been carefully created in the zone of action of the point load. A normal discretization of deck bars does not capture the local effect of point loads well, however it does capture the longitudinal response of the deck well. If you want to obtain the local response with more precision, you only have to make a model of the area of action of the loads with a very refined mesh. 2.5.1 - Application of the grid method for the analysis of decks formed by 'T' or double 'T' beams. As is this project case, to reproduce the resistant behavior of a deck, supported or continuous, with a constant or variable depth, made up of a series of longitudinal double "T" beams and an upper slab -in some cases there could also be brace beams, more or less spaced-, we can make several approximations by means of a grid of beams. Each one of the longitudinal beams of the deck is reproduced by a longitudinal beam of the griddle. In the event that there are cross beams, each of them must also be reproduced by a cross bar. The rest of the cross bars reproduce segments of the upper slab. The number and spacing between the cross bars depends on several factors. In principle it is necessary to place one bar at each end of the deck, on the supports, and make intermediate divisions depending on the number of transversal beams, each one corresponding to an area of slab that will be replaced by a transversal bar. In the event that there are intermediate brace beams, these must necessarily coincide with one of these divisions. 23 Figure 2.9 - Notes of the subject Bridges of the Master in Civil Engineering of the UPC These are the main factors when the grid method is applied to a deck formed by 'T' or double 'T' beams under a top slab. - One longitudinal bar per beam. - Transversal bars in the supports and in the center of the span. - Stransversal/Slongitudinal = 1-2. - If the bridge deck consists of 9 or more beams (either a wide deck or beams that are highly concentrated), it is possible to group up to two beams per frame. While this simplification is not strictly necessary given today's computational capabilities, it can be useful for reducing the volume of output results. 2.5.2 - Longitudinal beams and bars The inertia of the longitudinal beams of the grid will be that of the double 'T' framed between the midpoints of separation between beams. A point that should be considered especially, is the width of the compression head that should be used in the determination of the longitudinal inertia. The previous criterion is valid when the separation between the beams is not very large. Otherwise, the participation of the entire upper slab is doubtful due to the loss of effectiveness of the most remote areas as a consequence of deformation due to shear stress. 2.5.3 - Beams and cross bars As in the case of the longitudinal beams, care must be taken that the width of the compression head is not excessive, as then an overestimation of the flexural stiffness of said beams will occur. It is assumed that the center of gravity of all the transversal beams is located in a single plane that coincides with that considered for the general grid, which is that of the centers of gravity of the longitudinal beams. 24 The stiffness values obtained in this way correspond to a perfectly elastic behavior of the deck. However, the behavior in service may not be the same as regards the longitudinal and transverse beams. It is common for the longitudinal beams to be prestressed and the upper slab only reinforced. This causes the fact that in service the upper slab can crack in the longitudinal direction, as corresponds to some transverse bending moments, and not crack in the transverse direction because it is compressed by the longitudinal bending. 2.5.4 - Application of the grid method to our specific case First of all, the geometric and material conditions of the longitudinal bars must be clearly defined, each bar will be centered on a double 'T' beam. Therefore, the cross section of that bar will have to be defined. This section will contain the cross section of the beam and of a part of the upper slab of both concrete and asphalt. Each of these bars will represent 1.666 m of the total width of the bridge (10 m) since there are 6 bars. As explained above, the longitudinal double 'T' beams have a depth of 1.25 m, to which should be added the depth of 0.2 m for the concrete slab. Figure 2.10 - Cross section corresponding to a longitudinal bar in SAP2000 model Secondly, the geometric and material conditions of the crossbars must be defined. In this case, there will be 9 crossbars with a rectangular section 2.373 m wide and 0.2 m high. Under the eleventh crossbar the central pillars will be located. Since the cross bars are rectangular sections, the center of mass of these sections will be the center of said rectangle. Finally, the geometric and material conditions of the edge bars must be defined. There will be 2 edge bars with a rectangular section 2.35 m wide and 0.2 m high. These edge bars are parallel to the cross bars but are the bars located at the first and last support of the bridge. As in the previous case, since the border bars are rectangular sections, the center of mass of these sections will be the center of said rectangle. 25 Obtained prestressing force short and long term losses in comparison with the initial prestressing force can be shown in the following figure. Figure 3.1 - Prestressing force losses results graph 32 Table 3.5 - Prestressing force losses results table 33 x e(x) P0-∆P1(x)‐∆P2(x) Mg(x) σcp(x) ∆P3(x) P0 -∆P1(x) ‐∆P2(x) ‐∆P3(x) ∆P4(x) M quasi σ c quasi(x) ∆P5(x) ∆P6(x) ∆P delay(x) Ptot P0 [m] [m] [kN] [kN m] [MPa] [kN] [kN] [kN] [kN m] [kN/m2] [kN] [kN] [kN] [kN] [kN] 0 0,42 0 0 0,00 0,02 -0,02 0 0 -0,09 -0,005 -0,001 -0,005 -0,02 5821,14 1,02 0,42 5721,39 291,70 9,18 256,14 5465,25 2,71E+02 421,51 17828,62 994,40 262,33 1,17E+03 4,29E+03 5821,14 2,37 0,42 5721,39 633,50 7,75 216,31 5505,07 2,71E+02 927,68 15856,47 884,41 264,24 1,09E+03 4,42E+03 5821,14 4,74 0,42 5721,39 1126, 5,69 158,90 5562,49 2,71E+02 1648,44 13050,77 727,91 266,99 9,63E+02 4,60E+03 5821,14 7,11 0,42 5721,39 1478,17 4,22 117,89 5603,50 2,71E+02 2150,04 11101,98 619,22 268,96 8,78E+02 4,73E+03 5821,14 9,49 0,42 5721,39 1689,33 3,34 93,28 5628,10 2,71E+02 2450,64 9934,22 554,09 270,14 8,27E+02 4,80E+03 5821,14 11,86 0,42 5721,39 1759,72 3,05 85,08 5636,30 2,71E+02 2542,51 9579,74 534,31 270,54 8,11E+02 4,83E+03 5821,14 14,23 0,42 5721,39 1689,33 3,34 93,28 5628,10 2,71E+02 2449,64 9938,41 554,32 270,14 8,27E+02 4,80E+03 5821,14 16,61 0,42 5721,39 1478,17 4,22 117,89 5603,50 2,71E+02 2154,88 11081,76 618,09 268,96 8,77E+02 4,73E+03 5821,14 18,98 0,42 5721,39 1126,22 5,69 158,90 5562,49 2,71E+02 1646,52 13058,82 728,36 266,99 9,63E+02 4,60E+03 5821,14 21,35 0,42 5721,39 633,50 7,75 216,31 5505,07 2,71E+02 935,35 15824,42 882,62 264,24 1,08E+03 4,42E+03 5821,14 22,70 0,42 5721,39 291,70 9,18 256,14 5465,25 2,71E+02 446,15 17725,66 988,66 262,33 1,17E+03 4,30E+03 5821,14 23,73 0,42 0 0 0,00 0,02 -0,02 0 0 -0,09 -0,005 -0,001 -0,005 -0,02 5821,14 3.2 - Shear resistance analysis and shear armor design of each double T beam 𝐶𝑅𝑑=0.18 γ𝐶=0.18 1.5 =0. 12 (𝑒𝑞. 3.32) 𝑘=1+ 200 𝑑 [𝑑 𝑖𝑛 𝑚𝑚]=1+ 200 1325 =1. 3885 (𝑒𝑞. 3.33) 𝑘1=0. 15 (𝑒𝑞. 3.34) 𝑏𝑤=200 𝑚𝑚 (𝑒𝑞. 3. 35) 𝑓𝑐𝑘=40 𝑀𝑃𝑎 ; 𝑓𝑐𝑑=26.67 𝑀𝑃𝑎 (𝑒𝑞. 3. 36) 𝑓𝑦𝑘=500 𝑀𝑃𝑎 ; 𝑓𝑦𝑤𝑑=400 𝑀𝑃𝑎 (𝑒𝑞. 3.37) 𝑓𝑐𝑡𝑚=0.33𝑓𝑐𝑘2 (𝑒𝑞. 3.38) 𝑓𝑐𝑡𝑚=0.33402=3. 508 (𝑒𝑞. 3.39) 𝑓𝑐𝑘=40 𝑀𝑃𝑎 ≤60 𝑀𝑃𝑎 ; 𝑣1=0.6 (𝑒𝑞. 3.40) 𝑧=0.9·𝑑 (𝑒𝑞. 3.41) 𝑧=0.9·1, 325 𝑚𝑚=1, 192.5 𝑚𝑚 (𝑒𝑞. 3.42) σ𝑐𝑝=𝑃+𝑁 𝐴𝑐≤0.20·𝑓𝑐𝑑 (𝑒𝑞. 3.43) σ𝑐𝑝=5821144.939 𝑁+0 883,333.2 𝑚𝑚2=6.5899≤0. 20·26. 67=5. 334 (𝑒𝑞. 3.44) ρ𝑙=𝐴𝑆,𝑙𝑜𝑛+𝐴𝑃 𝑏𝑤·𝑑 ≤0. 02 (𝑒𝑞. 3.45) ρ𝑙=0+4,200 200·1,325 =0. 015≤0.02 (𝑒𝑞. 3.46) 𝑉𝑅𝑑,𝑚𝑖𝑛= 0.035· 𝑘3·𝑓𝑐𝑘+𝑘1·σ𝑐𝑝 ( ) ·𝑏𝑤·𝑑 (𝑒𝑞. 3.47) 𝑉𝑅𝑑,𝑚𝑖𝑛=307, 977.5082 𝑁 (𝑒𝑞. 3.48) 𝑉𝑅𝑑,𝐶= 𝐶𝑅𝐷·𝑘·3100·ρ𝑙·𝑓𝑐𝑘+𝑘1·σ𝑐𝑝 ( ) ·𝑏𝑤·𝑑≥𝑉𝑅𝑑,𝑚𝑖𝑛 (𝑒𝑞. 3. 49) 𝑉𝑅𝑑,𝐶=388, 061.8632 𝑁≥𝑉𝑅𝑑,𝑚𝑖𝑛=307, 977.5082 𝑁 (𝑒𝑞. 3.50) 𝑉𝐷𝑚𝑎𝑥=1225. 584 𝑘𝑁 (𝑒𝑞. 3.51) 34 𝑉𝑅𝑑,𝐶=502. 028 𝑘𝑁≤1225.584 𝑘𝑁=𝑉𝐷𝑚𝑎𝑥 (𝑒𝑞. 3.52) Following calculations depend on the obtained maximum ULS shear in each longitudinal point of the beam. These calculations are going to be shown in the following table. 𝑣= 𝑉𝑑 α𝑐𝑤·𝑣1·𝑓𝑐𝑑·𝑏𝑤·𝑧 (𝑒𝑞. 3.53) 𝑐𝑜𝑡θ≤1+ 1 − 4 · 𝑣2 2 · 𝑣 ≤2. 5 (𝑒𝑞. 3.54) 𝑐𝑜𝑡θ=2.5 (𝑒𝑞. 3. 55) 𝐴𝑆𝑊 𝑠≥𝑉𝑑 𝑓𝑦𝑤𝑑 · 𝑧 · 𝑐𝑜𝑡θ (𝑒𝑞. 3.56) It should be taken into account the reinforcement requirements in linear elements checking. These requirements will also be attended in the cases where the obtained reinforcement are smaller: 𝐴𝑆𝑊 𝑠≥𝐴𝑆𝑊 𝑠 ( ) 𝑚𝑖𝑛=0.08· 𝑓𝑐𝑘 𝑓𝑦𝑤𝑑 ·𝑏𝑤 (𝑒𝑞. 3.57) 𝐴𝑆𝑊 𝑠≥𝐴𝑆𝑊 𝑠 ( ) 𝑚𝑖𝑛=𝑓𝑐𝑡𝑚 7.5 · 𝑓𝑦𝑑 ·𝑏𝑤 (𝑒𝑞. 3.58) Another point to be careful with is the maximum longitudinal spacing and maximum transversal spacing along the width of the web. Transversal reinforcement bars should satisfy that maximum longitudinal spacing is the following one: 𝑠𝑙, 𝑚𝑎𝑥≤0. 75·𝑑 (𝑒𝑞. 3. 59) 𝑠𝑙, 𝑚𝑎𝑥≤0. 75·1, 325=993.75 𝑚𝑚 (𝑒𝑞. 3.60) And maximum transversal spacing along the width of the web: 𝑠𝑡, 𝑚𝑎𝑥≤𝑤𝑤𝑒𝑏−2·𝑐𝑜𝑣𝑒𝑟 (𝑒𝑞. 3.61) 𝑠𝑡, 𝑚𝑎𝑥≤200−2·70=60 𝑚𝑚 (𝑒𝑞. 3.62) In conclusion, these are the obtained shear stirrups reinforcement. Bars with a diameter of 12 mm have been considered applying two different separations depending on the part of the beam. The initial and final parts of the beam, with a higher shear requirement, have a separation of 200 mm between stirrups and the rest of the stirrups, the central part of the beam, have a 300 mm separation. 0−4.74]𝑈[18. 98−23.73[ ] ϕ12 𝑚𝑚@200 𝑚𝑚 (𝑒𝑞. 3.63) 4.74−9. 49]𝑈[14.23−18. 98[ ] ϕ12 𝑚𝑚@300 𝑚𝑚 (𝑒𝑞. 3.64) 35 Table 3.6 - Shear calculations table 36 X V (ULS) v (<=0,5) cotθ Asw / s (calc) Asw / s (min) Asw / s Φ12 (Ast / St) Φ12 (Ast / 200) Φ12 (Ast / 300) [m] [kN] mm2/mm mm2/mm mm2/mm mm2/mm mm2/mm mm2/mm 0 1081,14 0,28 2,5 0,90 0,25 0,90 0,28 0,50 0,78 2,37 905,75 0,23 2,5 0,75 0,25 0,75 0,28 0,50 0,78 4,74 720,58 0,18 2,5 0,60 0,25 0,60 0,28 0,50 0,78 7,11 543,82 0,14 2,5 0,45 0,25 0,45 0,28 0,50 0,78 9,49 376,77 0,09 2,5 0,31 0,25 0,31 0,28 0,50 0,78 11,27 0 0 0 0,25 0,25 0,28 0,50 0,78 11,86 205,22 0,05 2,5 0,17 0,25 0,25 0,28 0,50 0,78 14,23 376,77 0,09 2,5 0,31 0,25 0,31 0,28 0,50 0,78 16,61 543,82 0,14 2,5 0,45 0,25 0,45 0,28 0,50 0,78 18,98 720,58 0,18 2,5 0,60 0,25 0,60 0,28 0,50 0,78 21,35 905,75 0,23 2,5 0,75 0,25 0,75 0,28 0,50 0,78 23,73 1081,1 0,28 2,5 0,90 0,25 0,90 0,28 0,50 0,78 4 - Steel reinforcement calculus and design at the top slab For the analysis of the bending and shear resistance of the top slab in the transversal section, these are the main geometrical factors. 𝐿=1.666 𝑚 ; 𝑏=2.373 𝑚 ; ℎ𝑠𝑙𝑎𝑏=0. 20 𝑚 ; 𝑑=0. 9ℎ=180 𝑚𝑚 (𝑒𝑞. 4.1) The permanent loads of the slab (the slab has a thickness of 20 cm) and the traffic loads with the application of the security factors of the ULS are going to be applied in the scheme of a simply embedded beam with uniform loading throughout the span. 𝑀𝑚𝑎𝑥=𝑞 · 𝐿2 24 𝑎𝑡 𝑥=𝐿/2 (𝑒𝑞. 4.2) 𝑉𝑚𝑎𝑥=𝑞 · 𝐿 2 𝑎𝑡 𝑥=𝐿; 𝑥=0 (𝑒𝑞. 4.3) δ𝑚𝑎𝑥=𝑞 · 𝐿4 384 · 𝐸 · 𝐼 𝑎𝑡 𝑥=𝐿/2 (𝑒𝑞. 4.4) Description Nomenclature Unit Quantity Transversal cross section: central joist of the second longitudinal interbeam space Maximum positive moment of the traffic envelope M+ traffic env [kN m] 35,81 Maximum negative moment of the traffic envelope Mtraffic env [kN m] -27,63 Maximum shear of the traffic envelope V traffic env [kN] 152,36 Transversal cross section: border joist of the second longitudinal interbeam space Maximum positive moment of the traffic envelope M+ traffic env [kN m] 30,04 Maximum negative moment of the traffic envelope Mtraffic env [kN m] -26,17 Maximum shear of the traffic envelope V traffic env [kN] 168,34 Permanent loads: selfweight, pavement and rails Permanent loads g [kN] 16,61 Maximum positive moment due to permanent loads M+ g [kN m] 1,92 Maximum negative moment due to permanent loads Mg [kN m] -3,84 Maximum shear due to permanent loads V g [kN] 13,84 Ultimate limit state ULS maximum positive moment M+ d [kN m] 56,31 ULS maximum negative moment Md [kN m] -46,65 ULS maximum shear V d [kN] 271,20 Table 4.1 - ULS design calculations for top slab 37 4.1 - Bending moment resistance analysis of the top slab in the transversal section 𝑀𝑑=56. 31 𝑘𝑁𝑚 (𝑒𝑞. 4.5) λ=0.8 ; η=1 ; ε𝑐𝑢=0.0035 (𝑒𝑞. 4.6) 𝑓𝑐𝑘=40 𝑀𝑃𝑎 ; 𝑓𝑐𝑑=26.67 𝑀𝑃𝑎 (𝑒𝑞. 4. 7) 𝑓𝑦𝑘=500 𝑀𝑃𝑎 ; 𝑓𝑦𝑑=400 𝑀𝑃𝑎 (𝑒𝑞. 4.8) 𝐴𝑠=0 𝑚𝑚2; 𝐴'𝑠=0 𝑚𝑚2 (𝑒𝑞. 4.9) 𝑦=𝑑 1− 1−2𝑀𝑑 + 𝐴𝑝·𝑓𝑝𝑦𝑑(𝑑−𝑑𝑝) [ ] η·𝑓𝑐𝑑·𝑏·𝑑2 ⎰ ⎱⎱ ⎰ (𝑒𝑞. 4.10) 𝑦=5.0138 𝑚𝑚 (𝑒𝑞. 4. 11) 𝑥=𝑦λ=5.0138 0.8 =6. 2673 𝑚𝑚 (𝑒𝑞. 4.12) ξ𝑙𝑖𝑚=ε𝑐𝑢 ε𝑐𝑢+ε𝑠𝑦 ∼0.6≥𝑥𝑑=0.034 ⇒ 𝑑𝑢𝑐𝑡𝑖𝑙𝑒 𝑓𝑎𝑖𝑙𝑢𝑟𝑒 (𝑒𝑞. 4. 13) 𝐴'𝑆=0 (𝑒𝑞. 4.14) 𝐴𝑆=η𝑓𝑐𝑑 𝑓𝑦𝑑 𝑏𝑦 (𝑒𝑞. 4.15) 𝐴𝑆 =793.1910 𝑚𝑚2/2.373 𝑚=334 𝑚𝑚2/𝑚 (𝑒𝑞. 4. 16) Before deciding the bars spacing and diameters, the minimum required steel reinforcement should be consulted. In this case, the calculated reinforcement area for the resistance against the design bending moment of the top slab is lower than the minimum required steel reinforcement of the normatives, so, this second area will be applied: Table 4.2 - EHE08 - Tab. 42.3.5: Minimum reinforcement quantities 38 𝐴𝑆 (𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑)=0. 002·200·1000=400 𝑚𝑚2/𝑚 (𝑒𝑞. 4.17) 𝐴𝑆 (𝑚𝑖𝑛𝑖𝑚𝑢𝑚 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑)=400 𝑚𝑚2/𝑚>334 𝑚𝑚2/𝑚 (𝑒𝑞. 4.18) After analyzing different steel bars diameters and cross section areas the following selection has been made optimizing the steel excess of each case: Diameter N of bars Separation Excedure Steel area mm mm mm2 mm2 6 15 66,66 24,116 424,11 8 8 125 2,1248 402,12 10 6 166,66 71,24 471,24 12 4 250 52,39 452,39 16 2 500 2,12 402,12 20 2 500 228,32 628,32 Table 4.3 - Reinforcement bars comparison 4ϕ12 𝑚𝑚 @250 𝑚𝑚 (𝑒𝑞. 4.19) 𝐴𝑆=454. 39 𝑚𝑚2/𝑚 (𝑒𝑞. 4.20) This reinforcement will be applied in the longitudinal and in the transversal directions of the top slab. 4.2 - Shear resistance analysis of the top slab in the transversal section 𝐶𝑅𝑑=0.18 γ𝐶=0.18 1.5 =0. 12 (𝑒𝑞. 4.21) 𝑘=1+ 200 𝑑 [𝑑 𝑖𝑛 𝑚𝑚]=1+ 200 180 =2. 054 (𝑒𝑞. 4.22) 𝑘1=0. 15 (𝑒𝑞. 4.23) 𝑓𝑐𝑘=40 𝑀𝑃𝑎 ; 𝑓𝑐𝑑=26.67 𝑀𝑃𝑎 (𝑒𝑞. 4. 24) 𝑓𝑦𝑘=500 𝑀𝑃𝑎 ; 𝑓𝑦𝑤𝑑=400 𝑀𝑃𝑎 (𝑒𝑞. 4.25) 𝑓𝑐𝑡𝑚=0.33𝑓𝑐𝑘2 (𝑒𝑞. 4.26) 𝑓𝑐𝑡𝑚=0.33402=3. 508 (𝑒𝑞. 4.27) 𝑓𝑐𝑘=40 𝑀𝑃𝑎 ≤60 𝑀𝑃𝑎 ; 𝑣1=0.6 (𝑒𝑞. 4.28) 39 𝑧=0.9·𝑑 (𝑒𝑞. 4.29) 𝑧=0.9·180 𝑚𝑚=162 𝑚𝑚 (𝑒𝑞. 4.30) 𝑉𝑑𝑐𝑝=𝑃+𝑁 𝐴𝑐≤0.20·𝑓𝑐𝑑 (𝑒𝑞. 4.31) σ𝑐𝑝=0+0 474,600 𝑚𝑚2=0≤0. 20·26. 67=5.334 (𝑒𝑞. 4.32) ρ𝑙=𝐴𝑆,𝑙𝑜𝑛+𝐴𝑃 𝑏𝑤·𝑑 ≤0. 02 (𝑒𝑞. 4.33) ρ𝑙=804.24+0 2,373 · 180 =0. 003≤0. 02 (𝑒𝑞. 4.34) 𝑉𝑅𝑑,𝑚𝑖𝑛= 0.035· 𝑘3·𝑓𝑐𝑘+𝑘1·σ𝑐𝑝 ( ) ·𝑏𝑤·𝑑 (𝑒𝑞. 4.35) 𝑉𝑅𝑑,𝑚𝑖𝑛=620. 066 𝑘𝑁 (𝑒𝑞. 4.36) 𝑉𝑅𝑑,𝐶= 𝐶𝑅𝐷·𝑘·3100·ρ𝑙·𝑓𝑐𝑘+𝑘1·σ𝑐𝑝 ( ) ·𝑏𝑤·𝑑≥𝑉𝑅𝑑,𝑚𝑖𝑛 (𝑒𝑞. 4. 37) 𝑉𝑅𝑑,𝐶=795. 376 𝑘𝑁≥𝑉𝑅𝑑,𝑚𝑖𝑛=620.066 𝑘𝑁 (𝑒𝑞. 4.38) 𝑉𝑑=271. 207 𝑘𝑁 (𝑒𝑞. 4.39) 𝑉𝑅𝑑,𝐶=795. 376 𝑘𝑁≥271.207 𝑘𝑁=𝑉𝐷𝑚𝑎𝑥 (𝑒𝑞. 4.40) No shear steel armor reinforcement is required for the top slab. 40 5 - Summary of the total reinforcement of the bridge deck First of all, this is the longitudinal prestressing reinforcement of one beam of the bridge deck: 30 𝑐𝑜𝑟𝑑𝑠 ϕ140 𝑚𝑚 (𝑒𝑞. 5.1) 𝐴𝑝=4, 200 𝑚𝑚2 (𝑒𝑞. 5.2) In addition, these are the shear stirrups designed for each beam: 0−4.74]𝑈[18. 98−23.73[ ] ϕ12 𝑚𝑚@200 𝑚𝑚 (𝑒𝑞. 5.3) 4.74−9. 49]𝑈[14.23−18. 98[ ] ϕ12 𝑚𝑚@300 𝑚𝑚 (𝑒𝑞. 5.4) The reinforcement bars that will be applied in the longitudinal and in the transversal directions of the top slab are the following ones: 4ϕ12 𝑚𝑚 @250 𝑚𝑚 (𝑒𝑞. 5.5) 𝐴𝑆=454. 39 𝑚𝑚2/𝑚 (𝑒𝑞. 5.6) In the following figures the total reinforcement of the bridge deck can be seen. Firstly, in the first two figures, the longitudinal section of one of the six beams with the upper slab and each reinforcement represented in a different color can be seen. The longitudinal and transverse reinforcement of the upper slab can be seen marked in green, the prestressed longitudinal reinforcement of the beams can be seen marked in red, and the shear reinforcement of the beams can be seen marked in blue and orange. The shear reinforcements of the blue beams are those positioned at the beginning and end of the beam, with a smaller separation: 200 mm compared to 300 mm in the central part. Figure 5.1 - Longitudinal view of the ending of the beam Figure 5.2 - Longitudinal view of the beam Secondly, in the following figures, the transversal section of the six beams with the upper slab and each reinforcement represented in a different color can be seen. 41 Figure 6.4 - Case 2 obtained results The main conclusions obtained from these results will be stated below: - Impact of the volume of concrete applied. In most cases, concrete is the cause of the highest percentage of conditions in the different categories; something expected since it is the material with the greatest volume. To reduce the impact of the volume of concrete applied, an optimization of the bridge design could be studied in order to reduce the volume of this material. - Impact of the applied formwork. Because the formwork used for the production of the beams or for the in-situ construction of the top slab is made of steel, this has been a very polluting part compared to the volume of concrete. Formwork outperforms steel in all categories. To reduce the environmental impact of this category it could be considered that the formwork plates used for the beams could be reused in other similar projects; In that case the environmental impact of the formwork would be reduced in relation to the number of uses and the results obtained could be drastically improved. - Variation of the distance to be covered by transport depending on the case. An increase is made in all categories in relation to the increase in 50 km between case 1 and case 2. Logical results. 6.4 - Comparison of the obtained results with other projects To contrast the results obtained after carrying out an analysis, it is always good to rely on other similar projects carried out in the same area. In this case, a final master's project from 48 the UPC Master's Degree in Camins Canals i Ports Engineering carried out by Iván Herrera de Argila in June 2020 and titled Study of different typologies of bridges from the point of view of their sustainability 23. It studies the sustainability of three bridge models for a real case, the execution of the Fluviá viaduct, corresponding to the “Madrid - Zaragoza - Barcelona - French border” high-speed railway line. The typologies of bridges analyzed are: extradosed bridge, arch bridge and beam bridge. The beam bridge was the alternative chosen for the actual bridge project already executed while the other two alternatives were discarded. Only the results obtained in relation to the CO2 equivalent will be compared. It has been decided to eliminate the arch bridge from the comparative analysis since the deck of this bridge is composite and the other two proposals are concrete, as is our case. In this case CEEQUAL is used as a sustainable certification for application in civil engineering. It should be taken into account that unlike the designed deck project where the study has focused on the deck, in this project all the elements of the bridge are analyzed; However, we will focus on the part of the analysis dedicated to the study of the deck of each bridge since the rest of the elements have not been studied in our analysis. 6.4.1 - Extradosed bridge alternative The extradosed bridge alternative has a total length of 816 meters between abutments and has 11 spans. The distribution of the lights is as follows: 45 + 2x60 + 45 + 108 + 180 + 108 + 45 + 2x60 + 45 meters. The entire deck is designed with HP-45 prestressed concrete and the bridge is divided into two zones. The first area is the central section of the viaduct, which covers three central spans: one of 180 meters and two of 108 meters. This section crosses the riverbed and is designed as an extradosed bridge. Its cross section consists of a two-celled box 17 meters wide and a constant height of 4.50 meters. However, because this height is not sufficient for a span of 180 meters, an extradorsal bracing system is incorporated. The stays, made up of 15 mm diameter cords, are anchored to the deck every 3.5 meters, with a distance of 35 meters between the axis of the pile and the nearest stay. The furthest beam from the tower is 77 meters from it. The second zone corresponds to the lateral sections of the viaduct, which are the access viaducts. These sections are continuous and are composed of two central spans of 60 meters and compensation spans of 45 meters. This area is designed as beam bridges with continuous spans and does not have extradorsal stays. The cross section of this zone deck is a gullwing box section of width 14m instead of 17m. Figure 6.5 - Longitudinal view of the project corresponding to the extradosed bridge solution (Brignardelli, 2015) 49 6.4.2 - Continuous beam alternative The solution used in the execution of the real project, corresponding to the beam bridge alternative, has a total length of 835 meters and consists of 14 spans with the following spans: 45 + 10x60 + 2x70 + 50 meters. The cross section of the deck is designed as a gull-wing box with a total width of 14 meters, of which 3.50 meters corresponds to each wing and 7.0 meters to the width of the upper slab, while the lower slab It has a width of 5.60 meters. The depth of the deck is constant throughout the entire bridge, with a height of 4.00 meters, except in the areas of piers P11, P12 and P13 (70 meter spans), where it increases to 5.00 meters. .50 meters. In the areas of piles P1 to P10, the thickness of the bottom board is increased from 0.25 meters to 0.60 meters. The entire deck is projected with HP-45 prestressed concrete. Figure 6.6 - Longitudinal view of the project corresponding to the beam bridge solution (ADIF, 2006) 6.4.3 - Comparison of the different alternatives In this case, four alternatives will be compared: the two alternatives defined in this project (Case 1 and Case 2) and the two alternatives (extradosed bridge alternative and continuous beam alternative) of the Fluviá viaduct, discarding the mixed concrete and steel deck alternative. The unit of measurement to carry out the comparison will be the CO2 equivalent emitted. Two aspects must be taken into account: - The case of the Fluviá viaduct is a case of a railway bridge on a high-speed line. Therefore, the loads in this case are greater than those of a highway bridge and this aspect implies larger cross sections with greater depths and a box-section type of cross section. - In the case of the Fluviá, much longer spans are proposed, consequently the edges are larger and the types of cross sections are box section and in the case of the extradosed bridge, stays are added to support the deck of the longer spans. - Transportation process is similar in both cases. In the Fluviá case, three suppliers have been considered: one supplier 105 km away, another 99 km away and the third one 139 km away. Once these considerations have been made, the following table shows the total CO2 equivalent emission obtained in each alternative, the most indicative data of each alternative in general to contextualize the comparison and finally the relationships between CO2 equivalent emissions and the total cubic meters of concrete required for each case, obtaining an estimate of the emissions for each cubic meter of concrete. This last result may 50 not be adequate since neither abutments nor pillars have been included in the first two alternatives, in the table 6.4, a more accurate comparison is made. Global analysis Unit Case 1 Case 2 Extradosed Cont. beam CO2 total emissions t CO2 eq 68,91 70,8 30018,18 18982,9 Production process t CO2 eq 59,28 59,28 27234,73 17372,39 Transportation process t CO2 eq 1,9 3,79 1454,43 797,84 Construction process t CO2 eq 7,73 7,73 1329,02 812,67 Volume of concrete m3 176,11 176,11 51431,03 27229,69 Total length m 47,46 47,46 816 835 Maximum span m 23,73 23,73 180 70 Minimum span m 23,73 23,73 45 45 Number of spans 2 2 11 14 CO2 emissions/Vconcrete t CO2 eq/m3 0,39 0,40 0,58 0,69 Table 6.3 - Global analysis of emissions comparison In the table defined below, the study will focus on the part of the deck, differentiating the part of the emissions specifically referring to this part of each project. Finally, the emissions will be divided by each square meter of the top surface of the deck to compensate for the differences in the longitudinal and transverse axis. Deck analysis Unit Case 1 Case 2 Extradosed Cont. beam Cross section width m 10 10 14-17 14 Cross section depth m 1,45 1,45 4,5 4 - 5,5 Concrete production t CO2 eq 44000 44000 5428,52 2719,07 Steel production t CO2 eq 15280 15280 5437,41 3676,24 Production process t CO2 eq 59280 59280 10865,93 6395,31 Transportation process t CO2 eq 1900 3790 612,04 322,51 Construction process t CO2 eq 7730 7730 664,51 406,33 Emissions/total deck t CO2 eq 68,91 70,8 12142,48 7124,16 Emissions/longitudinal m t CO2 eq/ml 0,14 1,49 14,88 8,53 Emissions/top area t CO2 eq/m2 0,0061 0,0062 0,0048 0,0087 Table 6.4 - Deck analysis of emissions comparison Once the results obtained for each deck have been seen, it can be considered that the estimate in relation to CO2 emissions through SimaPro made for our bridge can be considered reliable. The CO2 emissions per square meter of surface of the upper slab in the case of the extradosed bridge and the continuous girder bridge are lower and higher than our case despite the differences in the approaches and requirements of each alternative as explained above. 51 7 - Conclusions The Sustainable Development Goals (SDGs) call for global action to foster prosperity while safeguarding the planet. Among these goals, SDG 9, which focuses on industries, innovation, and infrastructure, is particularly relevant to civil engineering. Specifically, SDG 9.4 emphasizes upgrading infrastructure and retrofitting industries to enhance sustainability through resource efficiency and environmentally sound technologies. Concrete and steel are pivotal materials in civil infrastructure. This project centers on their environmental impacts from production to placement and maintenance. It acknowledges the importance of minimizing environmental impact without compromising the economic viability of infrastructure projects. Concrete is a widely used, versatile, and durable construction material with several advantages, including affordability, adaptability, and low maintenance. It also has environmental benefits, such as being recyclable and contributing to energy efficiency and CO2 reduction. However, the concrete industry is a significant source of CO2 emissions, primarily from cement production. Efforts to mitigate these emissions include developing energy-efficient kilns, using CO2 capture systems, and optimizing the use of clinker. Additionally, designing structures to use less concrete can further reduce emissions. Steel, essential for reinforcing concrete, has superior tensile strength and ductility but poses challenges due to corrosion and fire resistance. The steel industry also significantly contributes to global CO2 emissions. Although recycling steel through the Electric Arc Furnace (EAF) process is more sustainable than the Blast Furnace-Basic Oxygen Furnace (BF-BOF) process, the majority of steel production still relies on the latter. Transitioning to 100% recycled steel production could drastically reduce CO2 emissions, energy consumption, and environmental pollution. In this project, a concrete bridge deck has been designed for certain conditions after having argued the choice. Regarding the design, the chosen dimensions have also been argued supporting on Javier Manterola tips. Subsequently, the design of the prestressed and ordinary reinforcement of both the prefabricated beams and the upper slab has been carried out and finally the prestress losses have been calculated; previously, the loads of a highway bridge have been analyzed through the SAP2000 software. Subsequently, the life cycle analysis was carried out through the SimaPro software. In this way it has been possible to see the effects in terms of different categories that would occur in the case of building this bridge. The conclusions obtained in relation to these results have been the following. - The parts of the structure produced by steel have much more harmful effects than concrete if you look at the relationship between each volume dedicated to each material. Looking for alternative solutions to improve in this sense can be very interesting. 52 - The use of prefabricated beams can be very ecologically positive if it is carried out in an industrialized way by repeatedly reusing the same formwork created for one beam. In this project the effects of the formwork have been very harmful in percentage terms, it is also true that a metal formwork has been assumed. In the category that the formwork has had the most impact has been that of freshwater aquatic ecotoxicity with an impact of 46.82-47.13% in relation to the rest of the materials and processes. In the following figure you can see the percentage of impact that the formwork represents in each of the environmental impact categories for each case. In other words, a percentage of emissions could be considered to be reduced to zero if the formwork panels were used infinitely for other projects. Figure 7.1 - Percentage of impact of the formwork in each category Finally the equivalent CO2 emissions were compared with those of other projects in the same field to consolidate the validity of the obtained results. In this sense, since the projects with which the equivalent CO2 emissions obtained have been compared were different in terms of the geometric requirements of the width of the deck, in terms of the spans required to be covered or in terms of the type of deck designed, it has been looked for a common comparison unit and this has been the emissions per square meter of deck top surface. Consequently, the two results obtained with the proposal described above have been among the other two results analyzed from other external projects. 𝐸𝑥𝑡𝑟𝑎𝑑𝑜𝑠𝑒𝑑 𝑏𝑟𝑖𝑑𝑔𝑒 𝑑𝑒𝑐𝑘 𝐶𝑂2 𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛𝑠 = 0. 0048 𝑘𝑔 𝐶𝑂2 𝑒𝑞./𝑚2 (𝑒𝑞. 7.1) 𝐶𝑎𝑠𝑒 1 𝑏𝑟𝑖𝑑𝑔𝑒 𝑑𝑒𝑐𝑘 𝐶𝑂2 𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛𝑠= 0. 0061 𝑘𝑔 𝐶𝑂2 𝑒𝑞./𝑚2 (𝑒𝑞. 7. 2) 𝐶𝑎𝑠𝑒 2 𝑏𝑟𝑖𝑑𝑔𝑒 𝑑𝑒𝑐𝑘 𝐶𝑂2 𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛𝑠 =0. 0062 𝑘𝑔 𝐶𝑂2 𝑒𝑞./𝑚2 (𝑒𝑞. 7. 3) 𝐶𝑜𝑛𝑡. 𝑏𝑒𝑎𝑚 𝑏𝑟𝑖𝑑𝑔𝑒 𝑑𝑒𝑐𝑘 𝐶𝑂2 𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛𝑠 = 0. 0087 𝑘𝑔 𝐶𝑂2 𝑒𝑞./𝑚2 (𝑒𝑞. 7.4) Conclusions obtained from this result: - Based on this comparison, it can be concluded that the results obtained in relation to the emissions of our project fall within a logical range. It should also be added that the case with the lowest resulting emissions, the case of the extradosed bridge, is the only one in which there are stays supporting the deck and its loads from some of the pillars. The existence of stays allows the depth of the deck to be reduced. 53 - This project has been focused around the deck of a bridge and in a comparison with other deck projects, however it could be interesting for future projects to add the effect on emissions of the pillars to the study. Compare different solutions for a longer total span with more or fewer number of columns and larger or shorter spans, which would entail: variation in the heights and section areas of the decks and variation in the number of intermediate columns. It could be concluded that this is a project with different phases in which different technological instruments have been used to help understand what a bridge can generate from a more global perspective. From a more global point of view of the project, an economic analysis of the cost that its execution would entail could be added to round out its analysis around sustainability since this condition also exists in reality. The most appropriate option cannot be chosen from an environmental point of view if the economic cost makes it an unaffordable option from that point of view. 54 8 - Bibliography 1 - United Nations - 17 Goals to Transform Our World, United Nations Sustainable Development Goals. 2 - United Nations - Goal 9: Build resilient infrastructure, promote sustainable industrialization and foster innovation 3 - Jesús Miguel Bairán, Escola de Camins UPC - Introduction to Concrete Structures Subject in the Bachelor Degree of Civil Engineering of the UPC 4 - Ferrovial - Hormigón: qué es, cómo se hace, tipos y beneficios. 5 - Pau Seguí, OVACEN - El hormigón: el material más destructivo de la Tierra. 6 - Johanna Lehne & Felix Preston - Making Concrete Change: Innovation in Low-carbon Cement and Concrete. 7 - Elastic Potential - Grooved Hollowcore with topping. 8 - Taehyoung Kim and Chang U. Chae (13/07/2016) - Evaluation Analysis of the CO2 Emission and Absorption Life Cycle for Precast Concrete in Korea 9 - Jesús Miguel Bairán, Escola de Camins UPC - Materials properties in Concrete Structures Subject in the Bachelor Degree of Civil Engineering of the UPC 10 - Esther Real, Enrique Mirambell, Itsaso Arrayago, Escola de Camins UPC - Introduction to Steel Structures, Subject in the Bachelor Degree of Civil Engineering of the UPC 11 - UPC - Proceso de fabricación del acero 12 - Celsa Group - La cadena de suministro circular más grande de Europa 13 - Ministerio de Fomento, Dirección General de Carreteras (2000) - Obras de paso de nueva construcción, conceptos generales 14 - Javier Manterola - Puentes I. Apuntes para su diseño, cálculo y construcción. 15 - Joan Ramon Casas, Gonzalo Ramos, José Turmo and Magi Domingo, Escola de Camins UPC - Notes of the Bridges subject of the Master in Civil Engineering of the UPC 16 - CSI Spain - Información general, SAP2000 17 - Mireia Roca Garciandia, UPC (06/2014) - TFM: Comparativa de Análisis de Ciclo de Vida de dos tipos de puente de carretera: puente de hormigón y puente metálico. 18 - Vincent Thiebault, Guangli Du & Raid Karoumi, Ice (14/10/2011) - Design of railway bridges considering life-cycle assessment 19 - Thomas Charles Edouard Dequidt, NTNU (06/2012) - Life Cycle Assessment of a Norwegian Bridge 20 - Eadic (18/02/2013) - Puentes de Hormigón: Los Puentes Viga 21 - Jorge Espínola, Curso de puentes 2018, Facultad de Ingeniería UNA - Material apoyo, clase XII, Puente en viga T 22 - Escola de Camins (31/03/2017) - Análisis estructural de un puente de vigas con losa superior por el método de emparrillado plano 55 23 - Iván Herrera de Argila, TFM Màster en Enginyeria de Camins Canals i Ports (30/06/2020) - Estudio de diferentes tipologías de puentes desde el punto de vista de su sostenibilidad 24 - Escola de Camins UPC - Notes of the subject Análisis de Ciclo de Vida y Sostenibilidad of the Master en Ingeniería de Caminos Canales y Puertos 56