Proyecto de un puente empujado y estudio mediante análisis no lineal del comportamiento diferido y en estado límite último

PORTADA PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 1 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. Trabajo Final de Máster Por: Wilfer de Jesús Arango Restrepo Tutor: Antonio Marí Bernat Barcelona, Febrero 2012 MEMORIA PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 2 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 3 AGRADECIMIENTOS Deseo expresar mis más sinceros agradecimientos al profesor Dr. Antonio Marí Bernat y su asistente Noemí Duarte, tutores de este trabajo final de Máster, por su colaboración y la oportunidad de realizar un trabajo bajo su consejo y asesoría. Agradezco también a toda mi familia, y especialmente a mí Madre recientemente fallecida, el apoyo la comprensión y el cariño que me han dado durante todo el Máster. Gracias de nuevo esperando que este trabajo no sea más que un nuevo comienzo. Barcelona, Febrero de 2012 Wilfer de J. Arango Restrepo PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 4 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 5 RESUMEN El proceso de construcción por empuje de puentes de hormigón pretensado da lugar a una solución industrializada muy competitiva en determinados rangos de luces y geometría. Aún así, existen algunos aspectos que, debido al carácter altamente evolutivo de la construcción, hacen que el comportamiento diferido y en ELU de flexión sean poco conocidos y requieran estudios más precisos que los habituales, a fin de evaluar cómo influye la velocidad de construcción en el comportamiento a largo plazo y en la resistencia del puente. En este trabajo se pretende proyectar totalmente un puente empujado de 8 vanos con luces de 50 m, analizando en detalle el proceso de construcción por empuje. Se pretende así mismo estudiar, mediante un modelo de análisis no lineal evolutivo, el comportamiento en servicio y en rotura a corto y largo plazo, a fin de extraer conclusiones de cara a proyecto y ejecución de este tipo de puentes. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 6 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 7 SUMMARY The construction process by incremental launching prestressed concrete bridge results in a very competitive solution in selected industrialized ranges of lights and geometry. However, there are some aspects that in case of highly evolutionary construction make the deferred behavior and flexural ELU are poorly understood and require more precise studies than usual to assess how it influences the speed of construction long-term performance and resistance of the bridge. In this thesis aims to project a the construction process by incremental launching bridge completely the 8 bays with lights 50 m. analyzing in detail the construction process thrust. The aim is to study it through a nonlinear analytical model of evolution the service performance and failure in the short and long term, in order to draw conclusions for the design and construction of such bridges. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 14 1.1.2. EMPUJE COMPLETO. Figura 2. Esquema general. Figura 3. Detalle de la fabricación. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 15 1.1.3. GIRO COMPLETO. Figura 4. Detalle de la colocación. 1.1.4. TRASLACIÓN TRANSVERSAL. Figura 5. Planta empuje transversal. Figura 6. Sección empuje transversal. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 16 2. MÉTODO DE EMPUJE POR SEGMENTOS. La fabricación de puentes de hormigón mediante este procedimiento requiere de los componentes siguientes: • Planta de fabricación del tablero: Consta fundamentalmente del taller de ferralla, encofrado y planta de hormigonado. Suele estar protegido de la intemperie. • Pico de lanzamiento: Su misión es disminuir el peso del puente en el proceso de lanzamiento. Es una estructura metálica conectada a la sección transversal frontal del puente. • Pilas auxiliares: Si resulta necesario, y en general para vanos superiores a los 40 ó 50 m., se disponen unas pilas provisionales a fin de acortar los vanos de mayor longitud. • Apoyos de neopreno-teflón: Facilitan el proceso de lanzamiento debido a su reducido coeficiente de rozamiento. • Dispositivos del empuje: Proporcionan la fuerza de arrastre o de empuje para mover el puente en cada fase del empuje. Foto 2. Vista del conjunto. Foto 3. Fabricación del tablero. Foto 4. Pico de lanzamiento. Foto 5. Pilas auxiliares. Foto 6. Apoyos de neopreno-teflón. Foto 7. Dispositivos de empuje. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 17 2.1. FABRICACIÓN DEL TABLERO. 2.1.1. Preparación de la ferralla: La armadura pasiva se prepara con antelación habitualmente en talleres de ferralla en elementos de la misma longitud que el segmento de puente que se va a hormigonar. Foto 8. Ferrallado. Foto 9. Protección del parque de prefabricación. 2.1.2. Sistemas de encofrado: El encofrado suele ser metálico y está soportado exteriormente e interiormente por estructuras auxiliares que deben permitir el proceso de separación de los moldes en la etapa de desencofrado. El hormigonado se realiza habitualmente en dos fases con una junta en la losa inferior, en el centro de las caras laterales o en la losa superior. Las juntas suelen estar situadas al lado de la zona de diafragmas y en ellos el encofrado interior es diferente que en el resto del tablero. Figura 7. Sección encofrado. Foto 10. Detalle del encofrado. Foto 11. Deslizamiento del encofrado. Foto 12. Encofrado losa superior. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 18 Figura 8. Encofrado en la zona de diafragma. 2.1.3. Separación de moldes: En el encofrado exterior se lleva a cabo por separación hacia fuera de los moldes o por giro desde unas articulaciones situadas en las esquinas inferiores. Los moldes interiores se separan retirando los burlones y los perfiles metálicos de apoyo. Figura 9. Separación de moldes. 2.2. PICO METÁLICO. Figura 10. Planta y alzados. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 19 Foto 13. Pico metálico. Foto 14. Pico metálico vista lateral. Figura 11. Dispositivos de anclaje en la sección. Foto 15. Conexión entre pico y sección. 2.3. EMPUJE RIGIDIZADO CON TIRANTES. Figura 12. Atirantamiento temporal. Figura 13. Fases de la de construcción. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 20 Foto 16. Detalle de atirantamiento. 2.3.1. TÉCNICAS DE EMPUJE. Figura 14. Arrastre mediante cordones. Figura 15. Detalle del dispositivo. Figura 16. Empuje dorsal. Foto 17. Detalle del empuje. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 21 Figura 17. E. por rozamiento mecánico. Figura 18. Empuje por presión hidráulica. Figura 19 y foto 18. Arrastre con elevación del tablero. Figura 20. Sistema híbrido de arrastre y empuje. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 22 3. ESQUEMAS DE POSTENSADO En los puentes empujados hay dos tipos fundamentales de postensado: el que se lleva a cabo durante la construcción del puente con las sucesivas fases de lanzamiento y el que se realiza una vez que el puente ya está situado en su posición final. Las misiones de cada uno de ellos son: 3.1 Postensado durante el empuje: La misión de estos tendones es soportar el peso propio de la estructura. Ya que durante el lanzamiento el momento flector cambia de valor, e incluso de signo, en cada sección transversal, el objetivo de este postensado es mantener el puente en compresión compuesta. Figura 21. Postensado en fase de construcción. 3.2 Postensado final: Una vez concluido el empuje del puente los tendones de postensado instalados permiten soportar no solo la carga permanente, sino una parte de la sobrecarga de uso, usualmente no mayor del 50%. Para soportar la parte restante se añaden otros cables de postensado. Figura 22. Postensado en fase de servicio. Figura 23. Acopladores durante el empuje. Figura 24. Avance durante el empuje. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 23 Foto 19. Acopladores del tendón, anclaje armadura activa. Figura 25. Tendones rectos interiores solapados. Figura 26. Tendones externos rectos. Foto 20. Tendones externos. Figura 27. Postensado final. Figura 28. Postensado final, acopladores. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 30 M−estribo= 9,94 ∗25 ∗18 ∗ 18 2=40257 KN_M < 78050 KN_M. Cumple! 5. APARATOS DE APOYO. En este apartado dimensionaremos los aparatos de apoyo utilizando la normativa (SETRA; B.T #4); [2] 5.1. Cargas; 𝑃𝑃= 9,94𝑚2∗25 𝐾𝑁 𝑚3=248,5 𝐾𝑁 𝑚→𝐶𝑃=37,5 𝐾𝑁 𝑚→𝑆𝐶= 4 𝐾𝑁 𝑚2∗12,5𝑚=50 𝐾𝑁 𝑚→𝑄=600𝐾𝑁 5.2. Propiedades mecánicas de la sección; Hormigón; HP45/B/12/IIb. 𝐼𝑐=16,05 𝑚4 𝐸𝑐=𝐾∗(𝑓𝑐𝑚)1 3 𝑀𝑝𝑎, Con K=4000 para cargas de larga duración y K=8500 para cargas instantáneas. 𝑓𝑐𝑚=𝑓𝑐𝑘+ 8 𝑀𝑝𝑎→𝐸𝑐(28)=8500 ∗(45 + 8)1 3=31928,43 𝑀𝑝𝑎, (𝐼𝑛𝑠. ) 𝐸𝑐(∞)=4000 ∗(45 + 8)1 3=15025,14 𝑀𝑝𝑎, (𝐷𝑒 𝑙𝑎𝑟𝑔𝑎 𝑑𝑢𝑟𝑎𝑐𝑖ó𝑛) 𝐸𝑐𝐼𝑐=15025,14 𝑁 𝑚𝑚2∗16,05 𝑚4∗1𝐾 103∗10002 𝑚𝑚2 1𝑚2=241153545,4 𝐾𝑁∗𝑚2 5.3. Reacciones y giros; Figura 42. Reacción máxima en estribos. Figura 43. Reacción mínima en estribos. 𝑅𝑚á𝑥.(𝐸1)=5372 𝐾𝑁 𝑅𝑚í𝑛.(𝐸1)=3617,61 𝐾𝑁 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 31 Figura 44. Giro máximo en estribos. 𝐻𝑖𝑝. 1 →𝜃𝑀á𝑥= 0,00174 𝑟𝑎𝑑 𝐻𝑖𝑝. 2 →𝜃𝑀á𝑥= 0,0009 𝑟𝑎𝑑 Figura 45. Reacciones máxima y mínima en pilas 1 y 2. 𝑅𝑚á𝑥.(𝑃1,2)=17140,61 𝐾𝑁 𝑅𝑚í𝑛.(𝑃1,2)=13558,48 𝐾𝑁 Figura 46. Giro máximo en pilas 1 y 2. 𝐻𝑖𝑝. 1 →𝜃𝑀á𝑥= 0,00079 𝑟𝑎𝑑 𝐻𝑖𝑝. 2 →𝜃𝑀á𝑥= 0,00012 𝑟𝑎𝑑 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 32 Figura 47. Reacciones máxima y mínima en pilas 3 y 4. 𝑅𝑚á𝑥.(𝑃3,4)=17924,64 𝐾𝑁 𝑅𝑚í𝑛.(𝑃3,4)=14002,24 𝐾𝑁 Figura 48. Giro máximo y mínimo en pilas 3 y 4. 𝐻𝑖𝑝. 1 →𝜃𝑀á𝑥= 0,00056 𝑟𝑎𝑑 𝐻𝑖𝑝. 2 →𝜃𝑀á𝑥= 0,00061 𝑟𝑎𝑑 Figura 49. Reacciones máxima y mínima en pilas 5 y 6. 𝑅𝑚á𝑥.(𝑃5,6)=17788,74 𝐾𝑁 𝑅𝑚í𝑛.(𝑃5,6)=13748,02 𝐾𝑁 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 33 Figura 50. Giro máximo y mínimo en pilas 5 y 6. 𝐻𝑖𝑝. 1 →𝜃𝑀á𝑥= 0,00069 𝑟𝑎𝑑 𝐻𝑖𝑝. 2 →𝜃𝑀á𝑥= 0,00055 𝑟𝑎𝑑 Figura 51. Reacciones máxima y mínima en la pila 7. 𝑅𝑚á𝑥.(𝑃7)=17866,38 𝐾𝑁 𝑅𝑚í𝑛.(𝑃7)=13800,67 𝐾𝑁 Figura 52. Giro máximo y mínimo en la pila 7. 𝐻𝑖𝑝. 1 →𝜃𝑀á𝑥= 0,00068 𝑟𝑎𝑑 𝐻𝑖𝑝. 2 →𝜃𝑀á𝑥= 0,00057 𝑟𝑎𝑑 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 34 5.4. Tabla resumen; Apoyos Reacción máxima (KN) Reacción mínima (KN) Giro máximo (rad) E1-E2 5372 3617,61 -0,00174 P1-P2 17140,61 13558,48 -0,00012 P3-P4 17924,64 14002,24 -0,00061 P5-P6 17788,74 13748,02 -0,00069 P7 17866,38 13800,67 -0,00068 5.5. Predimensionamiento de los aparatos de apoyo; (colocaremos 2 aparatos de apoyo por cada sección); 5.5.1. E1-E2. En planta; Compresión admisible; 𝜎𝑎𝑑𝑚.=150 𝐾𝑝 𝑐𝑚2→𝐴≥ 5372 𝐾𝑁 2∗150 𝐾𝑝 𝑐𝑚2∗ 103 1𝐾∗1𝐾𝑝 10 𝑁=1790,67 𝑐𝑚2 𝑎∗𝑏=40 ∗50 𝑐𝑚2 (2000 𝑐𝑚2) 5.5.2. Predimensionamiento en espesor; 𝑡𝑔𝛾=𝑈𝑥,1 𝑛∗𝑒 ≤0,5; Supondremos el punto fijo en el centro del puente; 𝑈𝑥,1→∆𝑇=35°𝐶→∝= 1,2 ∗10−5°𝐶−1 5.5.3. Deformación longitudinal (ɛ); ɛ=∝∗∆𝑇= 1,2 ∗10−5°𝐶−1∗35°𝐶= 4,2 ∗10−4 5.5.4. Punto fijo en el centro del puente; 𝑈𝐸,1=ɛ∗187,5 𝑚. = 4,2 ∗10−4∗187,5 = 78,75 𝑚𝑚=−𝑈𝐸,2 5.5.5. Espesor; 𝑡𝑔𝛾=78,75 𝑛∗𝑒 ≤0,5 →𝑛∗𝑒=157,5 𝑚𝑚≅160 𝑚𝑚 𝑒=10 𝑚𝑚;𝑒𝑠𝑝𝑒𝑠𝑜𝑟 𝑑𝑒 𝑢𝑛𝑎 𝑐𝑎𝑝𝑎 𝑑𝑒 𝑛𝑒𝑜𝑝𝑟𝑒𝑛𝑜. 𝑛=16 ;𝑛ú𝑚𝑒𝑟𝑜 𝑑𝑒 𝑐𝑎𝑝𝑎𝑠. 5.5.6. Estabilidad; 𝑎 𝑛∗𝑒≥5→𝑎≥5∗𝑛∗𝑒→𝑎≥5∗160 →𝑎𝑚í𝑛.=800 𝑚𝑚>400𝑚𝑚 Tomaremos; 800 ∗800 ∗16(10 + 2)→𝑎∗𝑏∗𝑛(𝑒+𝑡𝑠) (800 ∗800)→𝑃𝑙𝑎𝑛𝑡𝑎. 16 →𝑁ú𝑚𝑒𝑟𝑜 𝑑𝑒 𝑐𝑎𝑝𝑎𝑠. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 35 10 →𝐸𝑠𝑝𝑒𝑠𝑜𝑟 𝑑𝑒𝑙 𝑒𝑙𝑎𝑠𝑡ó𝑚𝑒𝑟𝑜 𝑒𝑛 𝑚𝑚. 2→𝐸𝑠𝑝𝑒𝑠𝑜𝑟 𝑎𝑐𝑒𝑟𝑜 𝑧𝑢𝑛𝑐ℎ𝑎𝑑𝑜. 5.5.7. Pilares; 𝐴≥𝑅𝑚á𝑥. 𝜎𝑎𝑑𝑚. =17924,64 𝐾𝑁 2∗150 𝐾𝑝 𝑐𝑚2∗103 1𝐾∗1𝐾𝑝 10 𝑁=5974,88 𝑐𝑚2 𝑎∗𝑏=80 ∗80 𝑐𝑚2 (6400 𝑐𝑚2) 5.5.8. Espesor; 𝑡𝑔𝛾=𝑈𝑥,1 𝑛∗𝑒 ≤0,5; Supondremos el punto fijo en el centro del puente; 𝑈𝑥,1→∆𝑇=35°𝐶→∝= 1,2 ∗10−5°𝐶−1 5.5.9. Deformación longitudinal (ɛ); ɛ=∝∗∆𝑇= 1,2 ∗10−5°𝐶−1∗35°𝐶= 4,2 ∗10−4 5.5.10. Punto fijo en el centro del puente; 𝑈𝑃,1=ɛ∗150 𝑚. = 4,2 ∗10−4∗150 =63 𝑚𝑚=−𝑈𝐸,2 𝑡𝑔𝛾=63 𝑚𝑚 𝑛∗𝑒 ≤0,5 →𝑛∗𝑒=126 𝑚𝑚≅130 𝑚𝑚 5.5.11. Estabilidad; 𝑎 𝑛∗𝑒≥5→𝑎≥5∗𝑛∗𝑒→𝑎≥5∗130 →𝑎𝑚í𝑛.=630 𝑚𝑚→(𝑎=8000 𝑚𝑚) 𝑛∗𝑒≤800 5=160 →𝑛=160 10 =16 𝑐𝑎𝑝𝑎𝑠. 𝑆=𝑎∗𝑏 2(𝑎+𝑏)𝑒=800 ∗800 2(800 +800)10 =20 5.5.12. Rotación admisible; ∝𝑎𝑑𝑚.= 3 ∗𝑛∗�𝑒𝑎�2= 3 ∗16 ∗�10 800�2= 7,5 ∗10−3 n 16 17 e 10 10 S 20 20 𝝈𝒂𝒅𝒎. 32 32 ∝𝒂𝒅𝒎. 7,5 ∗10−3 8∗10−3 Tenemos; 𝜃𝑚á𝑥.= 6,1 ∗10−3→∝𝒂𝒅𝒎.= 8 ∗10−3 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 36 𝜎𝑎𝑑𝑚.≤2∗𝐺𝐿∗𝑆≤2∗0,8 ∗20 =32 𝑀𝑝𝑎. 𝐺𝐿= 8 𝐾𝑝 𝑐𝑚2= 0,8 𝑀𝑝𝑎. ∝𝑎𝑑𝑚.= 3 ∗𝑛∗�𝑒𝑎�2= 3 ∗17 ∗�10 800�2= 8 ∗10−3 Tomaremos; 800 ∗800 ∗16(10 + 2)→𝑎∗𝑏∗𝑛(𝑒+𝑡𝑠) 5.6. Verificación aparatos de apoyo en los estribos; 800 ∗800 ∗16(10 + 2) 5.6.1. Compresión máxima; 𝜎𝑚á𝑥.=5372 𝐾𝑁 (0,80 ∗0,80)𝑚2∗103 1𝐾∗1𝑀 106= 8,39 𝑀𝑝𝑎. 𝜎𝑎𝑑𝑚.=32 𝑀𝑝𝑎. > 𝜎𝑚á𝑥.→𝑂.𝐾! 5.6.2. Compresión mínima; 𝜎𝑚í𝑛.=3617,61 𝐾𝑁 (0,80 ∗0,80)𝑚2∗103 1𝐾∗1𝑀 106= 5,65 𝑀𝑝𝑎. 5.6.3. Seguridad frente al deslizamiento; 𝜎𝑚í𝑛.𝑑𝑒𝑠𝑙𝑖𝑧. = 3 𝑀𝑝𝑎.→𝜎𝑚í𝑛.=𝑅𝑚í𝑛. 𝑎∗𝑏≥3 𝑀𝑝𝑎→5,65 ≥3→𝑂.𝐾! 5.7. Posición del punto fijo; 𝑋0=∑𝐾𝑖𝐿𝑋𝑖 ∑𝐾𝑖𝐿 𝐾𝑎𝑝𝑜𝑦𝑜→𝐹 𝜇=𝑎∗𝑏∗𝐺 𝑛∗𝑒 𝐾𝐸1,2=2∗800 𝑚𝑚∗800 𝑚𝑚∗0,8 𝑀𝑝𝑎 (16 ∗10)𝑚𝑚 ∗106 1𝑀∗𝑁 𝑚2∗1𝑚2 10002𝑚𝑚2=6400 𝑁 𝑚𝑚 5.7.1. Predimensionamiento de las pilas; tendrán sección rectangular constante de dimensiones (5,00 ∗1,20)𝑚. y el hormigón será HA-30. Pilas Altura (h=metros) P1 y P2 7,50 P3 y P4 7,50 P5 y P6 7,50 P7 7,50 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 37 𝐾𝑃1,2=1 1 𝐾𝑃𝑖𝑙𝑎1,2+1 𝐾𝑎𝑝1,2 𝐾𝑃1,2=3𝐸𝐼 ℎ3 𝐼𝑃1,2=5∗1,203 12 = 0,72 𝑚4 𝐸𝑐(∞)=4000 ∗(30 + 8)1 3=13447,90 𝑀𝑝𝑎, (𝐷𝑒 𝑙𝑎𝑟𝑔𝑎 𝑑𝑢𝑟𝑎𝑐𝑖ó𝑛) 𝐾𝑃1,2=3∗1,345 ∗107 7,53∗𝑚3∗𝐾𝑁 𝑚2∗0,72𝑚4=68864,00 𝐾𝑁 𝑚 𝐾𝑎𝑝1,2=2∗800 ∗800 ∗0,8 17 ∗10 =6023,53 𝑁 𝑚𝑚 𝐾𝑃1,2=1 1 68864,00+1 6023,53=5539,03 𝑁 𝑚𝑚=𝐾𝑃3,4,5,6,7 Punto fijo; 𝑋0=∑𝐾𝑖𝐿𝑋𝑖 ∑𝐾𝑖𝐿 =(5539,03 ∗37,5)+(5539,03 ∗87,5)+(5539,03 ∗137,5)+(5539,03 ∗187,5)+(5539,03 ∗237,5)+(5539,03 ∗287,5)+(5539,03 ∗337,5)+ (6400 ∗375) (2∗6400)+(5539,03 ∗6)+5539,03 𝑋0=187,5 →Debido a la simetría en altura y distribución longitudinal de los pilares el punto fijo está situado en el eje del puente. 5.8. Determinación de la fuerza de frenado (IAP); 𝐹𝐹=1 20 ∗�4𝐾𝑁 𝑚2∗11 𝑚.∗375 𝑚. +600 𝐾𝑁�=855 𝐾𝑁 [3] 𝐹𝐹.𝑚í𝑛=20 ∗𝑏=20 ∗11 =220 𝐾𝑁 𝐹𝐹.𝑚á𝑥=60 ∗𝑏=60 ∗11 =660 𝐾𝑁 𝐹𝐹.𝑚á𝑥=60 ∗𝑏≤720 𝐾𝑁 No cumple la normativa para frenado y arranque por lo que aumentaremos la dimensión de los andenes laterales (b=9,00 m.); 𝐹𝐹=1 20 ∗(4∗9∗375 + 600 )=705 𝐾𝑁→𝑂.𝐾! 5.9. Nuevas rigideces para fuerzas instantáneas; 𝐺𝑖= 2 ∗𝐺 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 38 𝐾𝐸1,2= 2 ∗6400 𝑁 𝑚𝑚=12800 𝑁 𝑚𝑚 →𝐾𝑃1,2=1 1 𝐾𝑃𝑖𝑙𝑎1,2+1 𝐾𝑎𝑝1,2 𝐾𝑃1,2=3𝐸𝐼 ℎ3→𝐼𝑃1,2=5∗1,203 12 = 0,72 𝑚4 𝐸𝑐(28)=10000 ∗(30 + 8)1 3= 3,362 ∗107 𝐾𝑁 𝑚2, (𝑖𝑛𝑠𝑡𝑎𝑛𝑡á𝑛𝑒𝑎𝑠) 𝐾𝑃1,2=3∗3,362 ∗107 7,53∗𝑚3∗𝐾𝑁 𝑚2∗0,72𝑚4=172134,40 𝐾𝑁 𝑚 𝐾𝑃1,2=1 1 172134,40+1 12047,06=11259,08 𝑁 𝑚𝑚=𝐾𝑃3,4,5,6,7 5.9.1. Desplazamiento; 𝑢=𝐹𝐹 ∑𝐾𝑖=705 𝐾𝑁 (2∗12800)+ (11259,08 ∗7) = 6,752 ∗10−3𝑚. 5.9.2. Fuerzas de frenado en estribos y pilas; Fuerzas Valor Cantidad Total (KN) 𝐹𝐹𝐸1,2 12800𝐾𝑁 𝑚∗6,752 ∗10−3=86,43 𝐾𝑁 2 172,85 𝐹𝐹𝑃1,2 11259,08𝐾𝑁 𝑚∗6,752 ∗10−3=76,02 𝐾𝑁 2 152,04 𝐹𝐹𝑃3,4 11259,08𝐾𝑁 𝑚∗6,752 ∗10−3=76,02 𝐾𝑁 2 152,04 𝐹𝐹𝑃5,6 11259,08𝐾𝑁 𝑚∗6,752 ∗10−3=76,02 𝐾𝑁 2 152,04 𝐹𝐹𝑃7 11259,08𝐾𝑁 𝑚∗6,752 ∗10−3=76,02 𝐾𝑁 1 76,02 �𝐹𝐹 705 5.10. Continuación con la verificación aparatos de apoyo; 𝑢=ɛ∗𝑋0= 4,2 ∗10−4∗187,5 𝑚. = 0,07875 𝑚. 5.10.1. Distorsión admisible; 0,5 ≥𝑡𝑔𝛾𝐿=78,75 𝑚𝑚 16 ∗10 = 0,492 < 0,5 →𝑂.𝐾! 0,7 ≥𝑡𝑔𝛾𝐿+𝛾𝑔𝑖=86,43 𝐾𝑁 2∗(80 ∗80)𝑐𝑚∗8𝐾𝑝 𝑐𝑚2∗2∗1𝐾𝑝 10𝑁∗103 1𝐾+ 0,492 = 0,534 < 0,7 →𝑂.𝐾! 5.10.2. Rotación admisible; ∝𝑎𝑑𝑚.= 3 ∗𝑛∗(𝑒𝑎)2= 3 ∗16 ∗(10 800)2= 7,5 ∗10−3>> 0,00174 →𝐺𝑖𝑟𝑜 𝑚á𝑥.𝑒𝑠𝑡𝑟𝑖𝑏𝑜→𝑂.𝐾! PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 39 5.10.3. Inestabilidad; 𝑎 𝑛∗𝑒=800 16 ∗10 = 5 →𝑂.𝐾! 5.10.4. Placas de acero zunchado; 𝑡𝑠≥𝑎𝑆∗𝜎𝑚 𝜎𝑒→𝑡𝑠= 2 𝑚𝑚. 𝑆=𝑎∗𝑏 2(𝑎+𝑏)𝑒=20 𝜎𝑚á𝑥.=𝑅𝑚á𝑥. (𝑎𝑏)= 8,39 𝑀𝑝𝑎. 𝜎𝑒=𝐿.𝑒𝑙á𝑠𝑡𝑖𝑐𝑜 𝑑𝑒𝑙 𝐴𝑐𝑒𝑟𝑜=275 𝑀𝑝𝑎. 𝑡𝑠≥𝑎𝑆∗𝜎𝑚 𝜎𝑒=800 20 ∗11,76 275 = 1,71 𝑚𝑚.→ 𝑡𝑠= 2 𝑚𝑚.→𝑂.𝐾! Aparatos de apoyo de los estribos verificados; 2𝑁𝑍 800 ∗800 ∗16(10 + 2) 𝑎 ∗ 𝑏 ∗ 𝑛 (𝑒+𝑡𝑠) 5.11. Verificación aparatos de apoyo en pilas; 800 ∗800 ∗16(10 + 2) 5.11.1. Compresión máxima; 𝜎𝑚á𝑥.=17924,64 𝐾𝑁 (0,80 ∗0,80)𝑚2∗103 1𝐾∗1𝑀 106=28,01 𝑀𝑝𝑎. 𝜎𝑎𝑑𝑚.=32 𝑀𝑝𝑎. > 𝜎𝑚á𝑥.→𝑂.𝐾! 5.11.2. Compresión mínima; 𝜎𝑚í𝑛.=14002,24 𝐾𝑁 (0,80 ∗0,80)𝑚2∗103 1𝐾∗1𝑀 106=21,88 𝑀𝑝𝑎. 5.11.3. Seguridad frente al deslizamiento; 𝜎𝑚í𝑛.𝑑𝑒𝑠𝑙𝑖𝑧. = 3 𝑀𝑝𝑎.→𝜎𝑚í𝑛.=𝑅𝑚í𝑛. 𝑎∗𝑏≥3 𝑀𝑝𝑎→21,88 ≥3→𝑂.𝐾! 𝑢=ɛ∗𝑋0= 4,2 ∗10−4∗150 𝑚. = 0,0630 𝑚. 5.11.4. Distorsión admisible; 0,5 ≥𝑡𝑔𝛾𝐿=63,00 𝑚𝑚 17 ∗10 = 0,371 < 0,5 →𝑂.𝐾! PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 46 6.4.2 Compresión cordón superior. Servicio. (𝑃𝐾∞); 𝜎𝑠𝑢𝑝.=−0,9(𝑃𝐾∞+𝑃𝐾𝑖) 𝐴𝑐−�𝑀𝑔+𝜓𝑀𝑞+ 0,68𝑃𝐾∞�∗𝑣 𝐼𝑐−0,9𝑃𝐾∞∗𝑒∗𝑣 𝐼𝑐≥−0,6 𝑓𝑐𝑘 −0,9[−11776,68 + (71432,09 ∗0,75)] 9,94 −[31392,09 +(0,6 ∗10345,12)+ (0,68 ∗−11776,68)]∗1,33 16,05 −0,9(−11776,68)(−1,92)1,33 16,05 ≥−27000 −3784,47 −2452,09 −1686,33 ≥−27000 →−7922,89 ≥−27000 →𝑂.𝐾! 6.4.3 Tracción cordón superior. Vacio. (𝑃𝐾𝑖); 𝑃𝐾𝑖=0,9 0,8 𝑃𝐾∞= 1,125∗(−11776,68)=−13248,77𝐾𝑁 −1,1 ∗(−13248,77) 9,94 −27276 ∗1,33 16,05 −1,1 ∗(−13248,77)∗(−1,92)∗1,33 16,05 ≤2660 1466,16 −2260,25 −2318,71 ≤2660 →−3112,80 ≤2660 →𝑂.𝐾! 6.4.4 Compresión cordón inferior. Vacio. (𝑃𝐾𝑖); −1,1 ∗(−13248,77) 9,94 −27276 ∗(−2,07) 16,05 −1,1 ∗(−13248,77)∗(−1,92)∗(−2,07) 16,05 ≥−27000 1466,16 +3517,84 +3608,82 ≥−27000 →8592,82 ≥−27000 →𝑂.𝐾! 6.4.5 Tracción cordón superior. Servicio. (PK∞) (En el apoyo); 𝜎𝑠𝑢𝑝.=−0,9(𝑃𝐾∞+𝑃𝐾𝑖) 𝐴𝑐−�𝑀𝑔+𝜓𝑀𝑞−0,68𝑃𝐾∞�∗𝑣 𝐼𝑐−0,9𝑃𝐾∞∗𝑒∗𝑣 𝐼𝑐≤ 𝑓𝑐𝑡,𝑘 −0,9[𝑃𝐾∞+ (71432,09 ∗0,75)] 9,94 −[(−60747,09) + (0,6 ∗−12822,96)−(0,68𝑃𝐾∞)]∗1,33 16,05 −0,9𝑃𝐾∞∗1,18 ∗1,33 16,05 =2660 −0,091𝑃𝐾∞−4850,77 +5671,42 + 0,056𝑃𝐾∞−0,088𝑃𝐾∞=2660 →𝑃𝐾∞=1839,35 −0,123 =−14953,61 𝐾𝑁 6.4.6 Compresión cordón inferior. Servicio. (PK∞); 𝜎𝑖𝑛𝑓.=−0,9(𝑃𝐾∞+𝑃𝐾𝑖) 𝐴𝑐−�𝑀𝑔+𝜓𝑀𝑞−0,68𝑃𝐾∞�∗𝑣´ 𝐼𝑐−0,9𝑃𝐾∞∗𝑒∗𝑣´ 𝐼𝑐≥−27000 −0,9[−14953,61 + (71432,09 ∗0,75)] 9,94 −[(−60747,09) + (0,6 ∗−12822,96)−(0,68 ∗−14953,61)]∗(−2,07) 16,05 −0,9 ∗−14953,61 ∗1,18 ∗(−2,07) 16,05 ≥−27000 −3496,82 −7515,51 −2048,17 ≥−27000 →−13060,50 ≥−27000 →𝑂.𝐾! 6.4.7 Tracción cordón inferior. Vacio. (PKi); 𝑃𝐾𝑖=0,9 0,8 𝑃𝐾∞= 1,125 ∗(−14953,61 )=−16822,81𝐾𝑁 −1,1 ∗(−16822,81) 9,94 −(−52782)∗(−2,07) 16,05 −1,1 ∗(−16822,81)∗1,18 ∗(−2,07) 16,05 ≤2660 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 47 1861,68 −6807,40 −2816,23 ≤2660 →−7761,95 ≤2660 →𝑂.𝐾! 6.4.8 Compresión cordón superior. Vacio. (PKi); −1,1 ∗(−16822,81) 9,94 −(−52782)∗1,33 16,05 −1,1 ∗(−16822,81)∗1,18 ∗1,33 16,05 ≥−27000 1861,68 +4373,84 +1809,46 ≥−27000 →8044,98 ≥−27000 →𝑂.𝐾! 6.5. Comprobación de la sección a fisuración en el momento de la construcción cuando se está realizando el empuje del puente; 6.5.1. Tracción cordón inferior. Vacio. (𝑃𝐾i)(En el vano); [6] 𝑃𝐾𝑖= 0,75𝑃0→𝑃0𝑇𝑜𝑡.=30 ∗18 ∗1400 ∗140 =105840𝐾𝑁 𝑃𝐾𝑖= 0,75 ∗105840 =79380𝐾𝑁 −0,9 ∗79380 9,94 −36513 ∗(−2.07) 16,05 −0,9 ∗79380 ∗(−2.07)∗(−1,92) 16,05 ≤2660 −7187,32 +4709,15 −17690,91 ≤2660 →−20169,08 ≤2660 →𝑂.𝐾! 6.5.2. Compresión cordón superior. Vacio. (PKi); −0,9 ∗79380 9,94 −36513 ∗1,33 16,05 −0,9 ∗79380 ∗1,33 ∗1,18 16,05 ≥−27000 −7187,32 −3025,69 −6985,74 ≥−27000 →−17198,75 ≥−27000 →𝑂.𝐾! 6.5.3. Tracción cordón inferior. Vacio. (PKi)(En el apoyo); −0,9 ∗79380 9,94 −(−78050)∗(−2,07) 16,05 −0,9 ∗79380 ∗(−1,92)∗(−2,07) 16,05 ≤2660 −7187,32 −10066,26 −17690,91 ≤2660 →−34944,49 ≤2660 →𝑂.𝐾! PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 48 6.5.4. Compresión cordón superior. Vacio. (PKi); −0,9 ∗79380 9,94 −(−78050)∗1,33 16,05 −0,9 ∗79380 ∗1,33 ∗1,18 16,05 ≥−27000 −7187,32 +6467,69 −6985,74 ≥−27000 →−7705,37 ≥−27000 →𝑂.𝐾! 6.6. Pérdidas de pretensado; El pretensado continuo de extremo a extremo en longitudes tan grandes (L>150 m.) presenta ΔP excesivas; Figura 64. Pérdidas a lo largo del trazado. [2] Propondremos un trazado con anclajes intermedios, es decir 50% de los cordones acoplados y el otro 50% alternado; Figura 65. Trazado del cable por tramos. [2] 6.7. Diseño de la armadura activa; 𝑃𝐾∞(𝑣𝑎𝑛𝑜)=−11776,68𝐾𝑁 (𝐸𝑠𝑡𝑖𝑚𝑎𝑑𝑜)→𝑃𝐾𝑖(𝑣𝑎𝑛𝑜)=−13248,77 𝐾𝑁 (𝐸𝑠𝑡𝑖𝑚𝑎𝑑𝑜) Lo cual quiere decir que la sección está comprimida y en un principio no necesitaría más armadura activa. Falta restar las pérdidas instantáneas y las diferidas. Con lo cual, asumiremos y siempre del lado de la seguridad 2T 18c ɸ0,6”; Para aceros Y1860S7, la tensión máxima será; 𝜎𝑚á𝑥.= 0,75 ∗1860 =1395 ≅1400 𝑁 𝑚𝑚2 [2] 𝐴𝑝.𝑚í𝑛.=18 ∗2∗140 =5040 𝑚𝑚2 𝑑𝑒 𝑎𝑟𝑚𝑎𝑑𝑢𝑟𝑎 𝑎𝑐𝑡𝑖𝑣𝑎. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 49 Se tiene 2T 18c ɸ0,6” ; AP.tendón=140 𝑚𝑚2∗18 →2520 𝑚𝑚2→AP.total=5040 𝑚𝑚2 P0.tendón=3528 KN →P0.total=36 ∗1400 ∗140 =7056 𝐾𝑁 Figura 66. Posición de los cables. 6.8. Cálculo de pérdidas; [6] 6.8.1. Pérdidas instantáneas. Rozamiento; (ΔP1) (En un tendón.); ∆P1=7056� 1 −e−(0,22∗0,954+0,0025∗25)�=1682,40 𝐾𝑁 2=841,20 𝐾𝑁 (𝑉𝑎𝑛𝑜) ∆P1=7056� 1 −e−(0,22∗1,908+0,0025∗50)�=2963,65 𝐾𝑁 2=1481,83 𝐾𝑁 (𝐴𝑝𝑜𝑦𝑜) 6.8.2. Pérdidas instantáneas. Penetración de cuñas; (ΔP2) (En un tendón.); la = 5∗1,9 ∗105∗2520 3528 ∗103−3528 ∗103∗e−�0,22∗0,954+2,5∗10−6 0,22 ∗la� Si; la = 25 m.→la = 3,580 m. Si; la = 24 m.→la = 3,580 m. La serie parece converger para valores menores de (la = 25,00 m.), por lo que en la sección considerada ya no hay pérdidas por penetración de cuñas. 6.8.3. Pérdidas instantáneas. Acortamiento elástico; (Δ P3) (En toda la sección.); ∆P3=σcp∗n−1 2n ∗Ap∗Ep Ecj →σcp→P0−∆P1−∆P2=7056 −1682,40 =5373,60 KN (Vano) P0−∆P1−∆P2=7056 −2963,65 =4092,35 KN (Apoyo) σcp(vano)=5373,60 9,94 +27276 ∗(−1,92) 16,05 +5373,60 ∗(−1,92)∗(−1,92) 16,05 =−1488,10KN m2 ∆P3(vano)=−1,49 ∗1 4∗5040 ∗190000 31928,43 =−11,17 KN PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 50 σcp(apoyo)=4092,35 9,94 +(−52782)∗1,18 16,05 +4092,35 ∗1,18 ∗1,18 16,05 =−3113,81 KN m2 ∆P3(apoyo)=−3,11 ∗1 4∗5040 ∗190000 31928,43 =−23,32 KN 6.8.4. Pérdidas diferidas; (Δ P.dif.); ∆Pdif.(vano)=n∗φ(t,t0)∗σcp+ Ep∗εcs(t,t0)+χ∗∆σcpr 1 + n ∗Ap Ac∗�1 + Ac∗yp2 Ic�∗(1 + χ∗φ(t,t0))∗Ap=118,73 1,030 ∗5040 =580,97KN ∆Pd.(apoyo)=n∗φ(t,t0)∗σcp+ Ep∗εcs(t,t0)+χ∗∆σcpr 1 + n ∗Ap Ac∗�1 + Ac∗yp2 Ic�∗(1 + χ∗φ(t,t0))∗Ap=77,02 1,017 ∗5040 =381,69KN n = Ep Ecj=190000 31928,43 = 5,95 →φ= 2,50 →εcj= 4,2 ∗10−4→χ= 0,8 →ρf= 8% ∆σcpr=ρf∗Pkj Ap= 0,08 ∗5384,77 5040 ∗103=85,47 (vano)→∆σcpr=65,33 (apoyo) Pkj(vano)= P0−∆P1−∆P2−∆P3=5373,60 +11,17 =5384,77 KN PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 51 Pkj(apoyo)= P0−∆P1−∆P2−∆P3=4092,35 +23,32 =4115,67 KN σcp(vano)=5384,77 9,94 +31392,07 ∗(−1,92) 16,05 +5384,77 ∗(−1,92)∗(−1,92) 16,05 =−1976,79 KN m2 P = P0−Pinst.→M→Peso Propio +Cargas Permanentes σcp(apoyo)=4115,67 9,94 +(−60747,07)∗1,18 16,05 +4115,67 ∗1,18 ∗1,18 16,05 =−3695,04 KN m2 Resumen de pérdidas; Instantáneas ∆P1 1682,40 KN (vano) 23,84 % ∆P1 2963,65 KN (apoyo) 42 % ∆P2 0 0 % ∆P3 -11,17 KN (vano) -0,16 % ∆P3 -23,32 KN (apoyo) -0,33 % Diferidas ∆Pdif. 580,97 KN (vano) 8,23 % ∆Pdif. 381,69 KN (apoyo) 5,41 % Pki= P0−∆P1−∆P2−∆P3=5384,77 KN (vano) Pki= P0−∆P1−∆P2−∆P3=4115,67 KN (apoyo) Pk∞= P0−∆P1−∆P2−∆P3−∆Pdif.=4803,80 KN (vano) Pk∞= P0−∆P1−∆P2−∆P3−∆Pdif.=3733,98 KN (apoyo) 6.8.5. Comprobación de la sección a fisuración; [6] 6.8.5.1. Comprobación cordón inferior. Servicio. (PK∞) (En vano); −0,9 ∗4803,80 9,94 −29591,02 ∗(−2,07) 16,05 −0,9 ∗4803,80 ∗(−1,92)∗(−2,07) 16,05 ≤3795 −434,95 +3816,41 −1070,59 ≤2660 →2310,87 ≤2660 →𝑂.𝐾! 6.8.5.2. Comprobación cordón superior. Servicio. (PK∞); −0,9 ∗4803,80 9,94 −29591,02 ∗1,33 16,05 −0,9 ∗4803,80 ∗(−1,92)∗1,33 16,05 ≥−27000 −434,95 −2452,09 +687,87 ≥−27000 →−2199,17 ≥−27000 →𝑂.𝐾! 6.8.5.3. Comprobación cordón superior. vacio. (PKi); −1,1 ∗5384,77 9,94 −27276 ∗1,33 16,05 −1,1 ∗5384,77 ∗1,33 ∗(−1,92) 16,05 ≤2660 −595,90 −2260,25 +942,41 ≤2660 →−1913,74 ≤2660 →𝑂.𝐾! 6.8.5.4. Comprobación cordón inferior. vacio. (PKi); −1,1 ∗5384,77 9,94 −27276 ∗(−2,07) 16,05 −1,1 ∗5384,77 ∗(−2,07)∗(−1,92) 16,05 ≥−27000 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 52 −595,90 +3517,84 −1466,75 ≥−27000 →1455,19 ≥−27000 →𝑂.𝐾! 6.8.5.5. Comprobación cordón superior. Servicio. (PK∞) (En apoyo); −0,9 ∗3733,98 9,94 −(−58272,41)∗1,33 16,05 −0,9 ∗3733,98 ∗1,33 ∗1,18 16,05 ≤2660 −338,09 +4828,80 −328,60 ≤2660 →4162,11 ≤2660 →𝑁𝑜 𝑐𝑢𝑚𝑝𝑙𝑒! Aunque no cumple hemos sido muy conservadores en algunas cosas como por ejemplo; 𝑓𝑐𝑡,𝑘= 0,7 ∗𝑓𝑐𝑡,𝑚= 2,66 𝑀𝑝𝑎. Así que podemos tomar 𝑓𝑐𝑡,𝑘=𝑓𝑐𝑡,𝑚= 3,80 𝑀𝑝𝑎. ó disminuir un poco el número de cordones por tendón para descomprimir un poco más la sección y así evitar la microfisuración por compresión excesiva. 6.8.5.6. Comprobación cordón inferior. Servicio. (PK∞); −0,9 ∗3733,98 9,94 −(−58272,41)∗(−2,07) 16,05 −0,9 ∗3733,98 ∗(−2,07)∗1,18 16,05 ≥−27000 −338,09 −7515,51 +511,44 ≥−27000 →−7342,16 ≥−27000 →𝑂.𝐾! 6.8.5.7. Comprobación cordón inferior. vacio. (PKi); −1,1 ∗4115,67 9,94 −(−52782)∗(−2,07) 16,05 −1,1 ∗4115,67 ∗1,18 ∗(−2,07) 16,05 ≤2660 −455,46 −6807,40 +688,99 ≤2660 →−6573,87 ≤2660 →𝑂.𝐾! 6.8.5.8. Comprobación cordón superior. vacio. (PKi); −1,1 ∗4115,67 9,94 −(−52782)∗1,33 16,05 −1,1 ∗4115,67 ∗1,18 ∗1,33 16,05 ≥−27000 −455,46 +4373,84 −442,68 ≥−27000 →3475,70 ≥−27000 →𝑂.𝐾! 7. DISEÑO DE LA ARMADURA PASIVA. FLEXIÓN. 7.1. Valores de cálculo de los esfuerzos y resistencias; [7] 𝑀𝑑(𝑣𝑎𝑛𝑜)= 1,35(𝑀𝑝𝑝+𝑀𝑐𝑝) + 1,5�𝑀𝑠𝑐+𝑀𝑄�= 1,35 ∗31392,09 + 1,5 ∗10345,12 =57897 𝐾𝑁.𝑀 𝑀𝑑(𝑎𝑝𝑜𝑦𝑜)= 1,35(𝑀𝑝𝑝+𝑀𝑐𝑝) + 1,5�𝑀𝑠𝑐+𝑀𝑄�= 1,35 ∗60747,09 + 1,5 ∗12822,96 =101243 𝐾𝑁.𝑀 7.2. Valores de cálculo de los esfuerzos y resistencias; 𝑓𝑐𝑑=45 1,5 =30 𝑁 𝑚𝑚2(𝐻𝑜𝑟𝑚𝑖𝑔ó𝑛)→𝑓𝑝𝑦𝑑=0,9 ∗1860 1,15 =1455,65 𝑁 𝑚𝑚2(𝑎.𝑎𝑐𝑡𝑖𝑣𝑎)→𝑓𝑦𝑑=500 𝑁 𝑚𝑚2(𝑎.𝑝𝑎𝑠𝑖𝑣𝑎) PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 53 7.3. Comprobación de la sección por rotura dúctil; [7] 7.3.1. Axil de tracción último de la armadura activa; En el vano tenemos; Figura 67. Área de hormigón comprimido. Suponiendo que la rotura será dúctil y que las compresiones se reparten en la losa superior; Se tiene; 𝑓𝑐𝑑∗𝑏∗𝑥=𝐴𝑝𝑓𝑝𝑦𝑑→𝑥=(252 ∗140 ∗1455,65) 30 ∗12,5 ∗103=136,95𝑚𝑚.→𝑥= 0,8𝑦→𝑦= 0,171 𝑚. Con lo que la cabeza de compresiones no sobrepasa la losa superior. 7.3.2. Momento último (vano); 𝑀𝑢=𝐴𝑝𝑓𝑝𝑦𝑑�𝑑−𝑦 2�=51355�3,25 −0,171 2�=162509 𝐾𝑁.𝑚→𝑀𝑑(𝑣𝑎𝑛𝑜)<𝑀𝑢→𝑂.𝐾! Por lo que no haría falta más refuerzos en la sección analizada que el armado mínimo. En la sección de apoyo tenemos; Se tiene; 𝑓𝑐𝑑∗𝑏∗𝑥=𝐴𝑝𝑓𝑝𝑦𝑑→𝑥=(360 ∗140 ∗1455,65) 30 ∗5∗103=489,10𝑚𝑚.→𝑥= 0,8𝑦→𝑦= 0,611 𝑚. Con lo que la cabeza de compresiones no sobrepasa la losa inferior. 7.3.3. Momento último (apoyo); 𝑀𝑢=𝐴𝑝𝑓𝑝𝑦𝑑�𝑑−𝑦 2�=73365�3,25 −0,611 2�=216023 𝐾𝑁.𝑚→𝑀𝑑(𝑎𝑝𝑜𝑦𝑜)<𝑀𝑢→𝑂.𝐾! Por lo que no haría falta más refuerzo en la sección analizada que el armado mínimo. 7.3.4. Dimensionamiento armadura mínima; Tomaremos; As.mín.= 0,0028 ∗𝐴𝑐→As`.mín.=30 10 ∗0,0028 ∗𝐴𝑐→𝐴𝑐= 9,94 𝑚2 [4] PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 54 Por lo tanto; As.mín.= 0,0028 ∗9,94 =278,32 𝑐𝑚2→As`.mín.=30 10 ∗0,0028 ∗9,94 =83,49 𝑐𝑚2 Optaremos por colocar barras de 20 mm. de diámetro alrededor de toda la sección, separadas cada 25 cm. una de otra, tanto en el perímetro exterior como en el interior. 7.4. Verificación de la hipótesis de rotura dúctil; 𝜀𝑝0+∆𝜀𝑝≥𝜀𝑝𝑦→∆𝜀𝑝 𝑑−𝑥=0,0035 𝑥→∆𝜀𝑝= 0,0035 ∗3,25 −0,214 0,214 = 0,0497 𝜀𝑝∞=𝜎𝑝∞ 𝐸𝑝=0,75 ∗1400 190000 = 0,0055 →𝜀𝑝𝑦=𝑓𝑝𝑦𝑑 𝐸𝑝=1455,65 190000 = 0,0078 𝜀𝑝=𝜀𝑝∞+∆𝜀𝑝= 0,0055 + 0,0497 = 0,0552 > 0,0078 =𝜀𝑝𝑦→𝑂.𝐾! 𝜀𝑝0+∆𝜀𝑝≥𝜀𝑝𝑦→∆𝜀𝑝 𝑑−𝑥=0,0035 𝑥→∆𝜀𝑝= 0,0035 ∗3,25 −0,764 0,764 = 0,0114 𝜀𝑝∞=𝜎𝑝∞ 𝐸𝑝=0,75 ∗1400 190000 = 0,0055 →𝜀𝑝𝑦=𝑓𝑝𝑦𝑑 𝐸𝑝=1455,65 190000 = 0,0078 𝜀𝑝=𝜀𝑝∞+∆𝜀𝑝= 0,0055 + 0,0114 = 0,0169 > 0,0078 =𝜀𝑝𝑦→𝑂.𝐾! Ambos comportamientos son dúctiles. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 55 8. DISEÑO DE LA ARMADURA PASIVA. CORTANTE. 8.1. Valores de cálculo de los esfuerzos y resistencias; [4] Se comprobará el cortante en la sección de apoyo de la viga; Por peso propio; PP = 9,94 ∗25 =248,5 𝐾𝑁 𝑚.𝑙→VPP.máx.(x=87,5_287,5)=12546,34 𝐾𝑁 Por cargas permanentes; CP =37,5 𝐾𝑁 𝑚.𝑙→VCP.máx.(x=87,5_287,5)=1893,31 𝐾𝑁 Por sobrecarga de uso; SC = 4 𝐾𝑁 𝑚2∗12,5 𝑚=50 𝐾𝑁 𝑚.𝑙→VSC.máx.(x=87,5_287,5)=2524,41 𝐾𝑁 Por carga móvil; En posición infinitamente próxima al apoyo; VQ.(x=87,5_287,5)=600 𝐾𝑁 Cortante debido al postensado; Figura 68. Cortante en el apoyo. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 62 𝐴𝑠=829 ∗1,15 ∗10 500 =19,06 𝑐𝑚2 𝑚.𝑙 Colocaremos ɸ25 cada 25 cm.; 𝐴𝑠=19,64 𝑐𝑚2 𝑚.𝑙 Para (𝑀𝑑+); 𝑌𝐿𝑖𝑚.=�1−�1−2𝑀𝑑+ 𝑈0𝑑�∗𝑑= 0,0284 𝑚.→𝑍=𝑑− 𝑌𝐿𝑖𝑚. 2= 0,3608 𝑚. 𝑈𝑠1=𝑀𝑑+ 𝑍=724 𝐾𝑁 𝑚.𝑙→𝐴𝑠=16,65 𝑐𝑚2 𝑚.𝑙 Colocaremos ɸ20 cada 16 cm.; 𝐴𝑠=18,84 𝑐𝑚2 𝑚.𝑙 Dispondremos superiormente corrida la armadura determinada para el ala (ɸ25 cada 16 cm), una barra de las dobles. En la parte inferior colocaremos ɸ20 cada 16 cm. Figura 72. Esquema de armaduras. 8.7. Dimensionamiento a torsión; [9] Según el artículo 45.2.1 E.H.E, el espesor eficaz (he) de la pared de la sección de cálculo es; 𝐴= 5,54 ∗3,4 = 18,82 𝑚2→𝑢= 2(5,54 + 3,4)=17,88 𝑚.→ℎ𝑒≤𝐴 𝑢=18,82 17,88 = 1,05 𝑚. ℎ0= 0,40 𝑚. Como ℎ𝑒>ℎ0; el valor real del espesor mínimo de la pared que se adopta ℎ𝑒=ℎ0= 0,4𝑚 Según el artículo 45.2 E.H.E; 𝑇𝑢1=𝛼∗𝑓1𝑐𝑑∗𝐴𝑒∗ℎ𝑒∗ 𝑐𝑜𝑡𝜃 1 + 𝑐𝑜𝑡2𝜃→𝑓1𝑐𝑑= 0,6 ∗𝑓𝑐𝑑= 0,6 ∗45 1,5 =18 𝑁 𝑚𝑚2 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 63 𝛼= 1,5 →𝐴𝑟𝑚𝑎𝑑𝑢𝑟𝑎 𝑒𝑛 𝑙𝑎𝑠 𝑑𝑜𝑠 𝑐𝑎𝑟𝑎𝑠,𝑒𝑥𝑡𝑒𝑟𝑖𝑜𝑟 𝑒 𝑖𝑛𝑡𝑒𝑟𝑖𝑜𝑟 𝑑𝑒 𝑙𝑎𝑠 𝑝𝑎𝑟𝑒𝑑𝑒𝑠. 𝜃; es el ángulo entre las bielas de compresión del hormigón y el eje de la pieza. Se adoptará el valor que cumpliese; 0,4 ≤𝑐𝑜𝑡𝜃≤2,5 → 𝑐𝑜𝑡𝜃=�1−𝜎𝑥𝑑 𝑓𝑐𝑡𝑚→𝑓𝑐𝑡𝑚= 0,3 ∗(452)1 3= 3,8 𝑁 𝑚𝑚2 𝜎𝑥𝑑=−𝑃𝑘∞ 𝐴𝑐=−7675,74 𝐾𝑁 9,94 𝑚2∗103 1𝐾∗1𝑚2 10002𝑚𝑚2=−0,77 𝑁 𝑚𝑚2 𝑐𝑜𝑡𝜃=�1 + 0,77 3,8 = 1,097 →ℎ𝑒= 0,40 𝑚.→𝐴𝑒= 5 ∗3 = 15 𝑚2 𝑇𝑢1= 1,5 ∗18 ∗15 ∗106∗400 ∗ 1,097 1 + 1,0972=80654,11 𝐾𝑁.𝑚 8.7.1. Esfuerzos de cálculo; en este caso solo provocan esfuerzos de torsión las cargas que pueden ser excéntricas respecto del plano medio de la sección; sobrecarga repartida y carga puntual. El coeficiente de seguridad que se considera es 𝛾𝑄= 1,5. Figura 73. Torsión en estribos y pilas. [7] 𝑇𝑆𝐶=25 𝐾𝑁 𝑚∗6,25 𝑚∗0,90 𝑚=140,63 𝐾𝑁.𝑚→𝑇𝑄=600 𝐾𝑁∗0,90 𝑚=540 𝐾𝑁.𝑚 𝑇𝑑= 1,5(140,63 +540)=1020,95 𝐾𝑁.𝑚<< 𝑇𝑢1,𝑝𝑜𝑟 𝑙𝑜 𝑞𝑢𝑒 𝑛𝑜 𝑎𝑔𝑜𝑡𝑎 𝑙𝑎 𝑠𝑒𝑐𝑐𝑖ó𝑛. 8.7.2. Dimensionamiento de las armaduras transversales; ℎ𝑒= 0,40 𝑚.→𝐴𝑒= 5 ∗3 = 15 𝑚2→𝑢𝑒=17,88 𝑚. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 64 El dimensionamiento se lleva a cabo imponiendo que el esfuerzo de agotamiento por tracción de la armadura transversal sea igual al esfuerzo torsor de cálculo; 𝑇𝑑=𝑇𝑢2=2∗𝐴𝑒∗𝐴𝑡 𝑆𝑡∗𝑓𝑦𝑡,𝑑∗𝑐𝑜𝑡𝜃 𝐴𝑡 𝑆𝑡=𝑇𝑑 2∗𝐴𝑒∗𝑓𝑦𝑡,𝑑∗𝑐𝑜𝑡𝜃=1020,95 2∗15000000 ∗400 ∗𝑐𝑜𝑡𝜃= 0,78 𝑐𝑚2 𝑚.𝑙 Colocaremos ɸ8 a 50 cm.; 𝐴𝑠= 1 𝑐𝑚2 𝑚.𝑙 Figura 74. Armadura transversal por torsión. [7] 8.7.3. Dimensionamiento de la armadura longitudinal; [9] 𝑇𝑑=𝑇𝑢3=2∗𝐴𝑒∗𝐴1 𝑢𝑒∗𝑓𝑦1,𝑑∗𝑡𝑎𝑛𝜃 𝐴1=𝑇𝑑∗𝑢𝑒∗𝑐𝑜𝑡𝜃 2∗𝐴𝑒∗𝑓𝑦1,𝑑=1020,95 ∗17880 ∗1,097 2∗15000000 ∗400 =16,69 𝑐𝑚2 𝑚.𝑙 Esta armadura ya está cubierta por la armadura de piel puesta anteriormente; ɸ20 a 25 cm. 8.8. Interacción cortante-torsión; [9] Se considera que no produce agotamiento por interacción cortante-torsión en las bielas comprimidas si se satisface; �𝑇𝑑 𝑇𝑢1�𝛽+�𝑉𝑟𝑑 𝑉𝑢1�𝛽≤1→𝛽= 2 ∗�1−ℎ𝑒 𝑏�= 2 ∗�1−400 5000�= 1,84 𝑇𝑑,𝑉𝑟𝑑; son respectivamente los esfuerzos torsor y cortante efectivo de cálculo que actúan de forma concomitante. En los apoyos (x=87,5 m. ó x=287,5 m.) la situación pésima se produce con la siguiente combinación de acciones; Figura 75. Acciones por torsión. [7] PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 65 Que provoca los siguientes valores de cálculo; 𝑃𝑃=25 𝐾𝑁 𝑚3∗9,94 𝑚2=248,5 𝐾𝑁 𝑚→𝐶𝑃= 3 𝐾𝑁 𝑚2∗12,5 𝑚=37,5 𝐾𝑁 𝑚 𝑆𝐶= 4 𝐾𝑁 𝑚2∗6,25 𝑚=25 𝐾𝑁 𝑚 𝑇𝑃𝑃+𝐶𝑃=143 𝐾𝑁 𝑚∗6,25 ∗0,90 = 804,38𝐾𝑁.𝑚→𝑇𝑆𝐶=140,63𝐾𝑁.𝑚→𝑇𝑄=540𝐾𝑁.𝑚 𝑇𝑑= 1,5(804,38 + 140,63 +540)=2227,51𝐾𝑁.𝑚→𝑉𝑟𝑑=12055,23 𝐾𝑁 �2227,51 80654,11�1,84+�12055,23 13770 �1,84= 0,78 ≤1 No se produce agotamiento por compresión oblicua del hormigón bajo solicitaciones tangentes, verificándose por tanto el estado límite último. 9. DISEÑO DEL DIAFRAGMA. Estos elementos se apoyarán en los estribos y en las pilas. La dimensionaremos como una viga de gran canto, aunque la E.H.E defina viga de gran canto a los elementos de sección generalmente uniformes ó constantes (Regiones D. Método de bielas y tirantes); Figura 76. Diafragma en los apoyos. [10] 9.1. Cargas; 𝑃𝑃=25 𝐾𝑁 𝑚3∗21,29 𝑚2=532,25 𝐾𝑁 𝑚→𝐶𝑃= 3 𝐾𝑁 𝑚2∗12,5 𝑚=37,5 𝐾𝑁 𝑚 𝑆𝐶= 4 𝐾𝑁 𝑚2∗12,5 𝑚=50𝐾𝑁 𝑚→𝑄=600 𝐾𝑁 12,5 𝑚=48𝐾𝑁 𝑚 𝑃𝑑= 1,5(667,75)=1001,63 𝐾𝑁 𝑚.𝑙 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 66 9.2. Anchura mínima; [10] Esta viene condicionada por el agotamiento en compresión de los nudos y bielas; 𝜎𝑐,𝑚á𝑥.=𝑅𝑑 𝑎0∗𝑏0→𝑅𝑑= 0,5 ∗𝑃𝑑∗𝐿= 0,5 ∗1001,63 ∗4,20 =2103,41 𝐾𝑁 𝜎𝑐,𝑚á𝑥.=2103,41 0,8 ∗𝑏0→𝑅𝑑 𝑎0∗𝑏0≤𝑓1𝑐𝑑= 0,70𝑓𝑐𝑑= 0,7 ∗30 =21000 𝐾𝑁 𝑚2 𝑏𝑖≥2103,41 0,8 ∗21000 =125 𝑚𝑚. Imponiendo que la esbeltez geométrica, entendida como el cociente entre la longitud de pandeo y el ancho de la viga, sea menor que 12, se obtiene el ancho de la viga que evita la comprobación del pandeo fuera del plano de la viga (𝑏>𝑙0 12) ; Donde 𝑙0 es la longitud de pandeo. Al tratarse de un modelo formado por barras articuladas, este valor coincide con la longitud de la biela, que en este caso alcanza su máximo en 3280 mm.; 𝑏>3280 12 =273 𝑚𝑚→𝑇𝑜𝑚𝑎𝑟𝑒𝑚𝑜𝑠 𝑏= 0,30 𝑚. 9.3. Armadura; 𝑈𝑠= 0,20 ∗𝑃𝑑∗𝐿= 0,20 ∗1001,63 ∗4,20 =841 𝐾𝑁 𝐴𝑠∗𝑓𝑦𝑑=𝑇=841 →𝐴𝑠=841000 ∗1,15 400 = 24,17 𝑐𝑚2 𝑚.𝑙 Colocaremos 8ɸ 20 �𝐴𝑠=25,12 𝑐𝑚2 𝑚.𝑙� Figura 77. Diafragma en los apoyos, separación entre barras. [8] Se ha de disponer de una armadura mínima de 0,01 % de cuantía en cada dirección y cada cara del elemento (armadura secundaria); 𝐴𝑠𝑒𝑐.= 0,001 ∗300 ∗1000 = 3 𝑐𝑚2 𝑚.𝑙 [10] Colocaremos ɸ 10 a 25 cm. �𝐴𝑠= 3,16 𝑐𝑚2 𝑚.𝑙� PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 67 En las zonas de apoyo de acuerdo al artículo 61 de la E.H.E, cargas concentradas sobre macizos, si no se dispone de armadura de confinamiento la fuerza máxima de compresión será el menor de los siguientes valores; 𝑁𝑢=𝐴𝑐1∗𝑓2𝑐𝑑=𝐴𝑐1∗0,7 ∗𝑓𝑐𝑑=800 ∗300 ∗0,7 ∗30 =5040 𝐾𝑁 𝑁𝑢=𝐴𝑐1∗𝑓1𝑐𝑑=𝐴𝑐1∗0,85 ∗�1−𝑓𝑐𝑘 250�∗𝑓𝑐𝑑=800 ∗300 ∗0,85 ∗�1−45 250�∗30 =5018,41 𝐾𝑁 𝑁𝑢 es superior en cualquier caso a la reacción máxima en apoyos (1001,63 KN). Por lo tanto no es necesario reforzar esta zona de apoyos. Figura 78. Diafragma en los apoyos, armadura de piel, abertura de paso. 10. PREDIMENSIONAMIENTO DE LAS PILAS. Figura 79. Acciones a considerar. [11] PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 68 Figura 80. Altura de la pila. [11] 10.1. Criterios de diseño; 𝑒= 1,20 𝑚.→(𝐴𝑠𝑢𝑚𝑖𝑑𝑜)→𝑏= 5,00 𝑚.(𝐴𝑠𝑢𝑚𝑖𝑑𝑜=𝑎𝑛𝑐ℎ𝑜 𝑖𝑛𝑓𝑒𝑟𝑖𝑜𝑟 𝑑𝑒 𝑙𝑎 𝑣𝑖𝑔𝑎) 𝐴=𝑏∗𝑒≥𝑁𝑚á𝑥. 𝜎𝑎𝑑𝑚.→𝐴= 1,20 ∗5,00 = 6 𝑚2→𝑁𝑚á𝑥.=17924,64 𝐾𝑁 Hormigón (HA-30); 𝑓𝑐𝑑.=30 1,5 =20 𝑁 𝑚𝑚2→17924,64 0,7 ∗20 = 1,28 𝑚2<< 𝐴→𝑂.𝐾! 10.2. Reacciones de apoyo. Esfuerzos; • Fuerzas verticales debidas a todas las cargas. • Fuerzas horizontales; viento, tráfico (frenado, aceleración), resistencias a la deformación, sismo. • Momentos flexores. 10.3. Desplazamientos relativos de la pila; Figura 81. Desplazamiento de la pila. [11] PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 69 𝛿=𝛿𝑐+𝛿𝑃+𝛿𝑎.𝑝 𝛿𝑐= desplazamiento debido al giro y traslación de la cimentación. 𝛿𝑃= desplazamiento debido a la deformabilidad de la pila. 𝛿𝑎.𝑝= desplazamiento debido a la deformabilidad del apoyo. 10.3.1. Desplazamiento debido a la pila; 𝛿𝑃=𝐹 𝐾𝑝→𝑎𝑛á𝑙𝑖𝑠𝑖𝑠 𝑟𝑒𝑎𝑙𝑖𝑧𝑎𝑑𝑜 𝑒𝑛 𝑙𝑜𝑠 𝑎𝑝𝑎𝑟𝑎𝑡𝑜𝑠 𝑑𝑒 𝑎𝑝𝑜𝑦𝑜. Resumen (𝛿𝑃) en pilas; 𝐹𝐹.𝑃𝑖𝑙𝑎𝑠=76,02 𝐾𝑁→𝛿𝑃=76,02 11259,08 = 0,00675 𝑚. = 6,75 𝑚𝑚→�𝐿 1111,11�→𝑂.𝐾! 10.4. Inestabilidad de la pila (Pandeo); Consideramos la viga pared empotrada en su base y con el movimiento horizontal impedido en el extremo de unión con la viga (unión trabada). A este esquema estático le corresponde un 𝛼= 0,7; por lo tanto; 𝑙0=𝛼∗𝑙= 0,7 ∗7,5𝑚. = 5,25 𝑚. 𝑖𝑐=�𝐼𝐴=�5∗1,203 12 ∗5∗1,2 = 0,346 𝑚.→𝜆=5,25 0,346 =15,17 (𝑒𝑠𝑏𝑒𝑙𝑡𝑒𝑧 𝑚𝑒𝑐á𝑛𝑖𝑐𝑎). La estructura es intraslacional ya que bajo solicitaciones de cálculo presenta desplazamientos transversales cuyos efectos pueden ser despreciados desde el punto de vista de la estabilidad del conjunto. 11. ANÁLISIS NO LINEAL DEL PUENTE EMPUJADO. 11.1. Descripción del modelo numérico CONS. Antes que nada mencionar la enorme dificultad de simular el proceso de empuje con el programa CONS, (es decir en el momento de la construcción) y solo se ha considerado el puente construido simultáneamente para hacer el análisis no lineal diferido. Por otra parte, la duración del empuje no es muy grande, y los efectos diferidos son limitados. Por último, la retracción apenas producirá curvaturas, ya que toda la sección esta comprimida uniformemente. El modelo numérico CONS desarrollado por Marí [12] está basado en una idealización de las estructuras mediante elementos lineales tipo barra con 6 grados de libertad por nodo, discretizando la sección transversal en filamentos. Permite considerar el comportamiento no lineal de los materiales y la geometría, así como el comportamiento diferido y el proceso evolutivo de construcción. Asume que la hipótesis de planeidad de las secciones y no considera las deformaciones producidas por cortante. La no linealidad de los materiales por fisuración y plastificación, así como los efectos estructurales producidos por las deformaciones diferidas, son considerados en el análisis estructural. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 70 La deformación total en cualquier punto de la estructura ε(t) es suma de las deformaciones de tipo mecánico y no mecánico: Las tensiones de tipo mecánico son las directamente producidas por cargas aplicadas, mientras que en las deformaciones de tipo no mecánico se engloban las producidas por las deformaciones diferidas de retracción εsh(t) y fluencia εcr(t) así como las deformaciones térmicas εT(t) y las aging strain εa(t). El diagrama de tensión-deformación del hormigón considerado es el que se muestra en la siguiente figura; Figura 82. Diagrama tensión-deformación del hormigón adoptado en el CONS. El diagrama tensión-deformación para la rama negativa (tracciones en hormigón) se modifica para considerar la tensión stiffening. La evolución de las propiedades mecánicas del hormigón con el tiempo, envejecimiento, se considera siguiendo lo establecido por el MC-90. Para el acero de armar, se considera una relación de tensión-deformación de tipo bilineal. Para el acero activo se utiliza una ecuación constitutiva a partir de un gráfico multilineal, asumiendo siempre que la descarga y la recarga ocurren con el módulo de deformación inicial. De manera habitual se adopta dos puntos para definir dicho diagrama: el asociado al límite elástico del acero activo y el correspondiente a fpu (tensión máxima en rotura). Para la determinación de la deformación de fluencia del hormigón, el programa de acuerdo al principio de superposición de las acciones, debería resolver la integral de la expresión 3, integral de Volterra. Siendo ),( ττ −tc la función de fluencia reducida, función de la edad de carga τ , y siendo )( τσ la tensión en el hormigón en el instante de evaluación. () () () m nm ttt εε ε = + [12] () () () () () a nm cr sh T t t ttt ε ε ε εε = + ++ [12] () () (, ) t cr o t ct d στ ε ττ τ τ ∂ = −⋅ ∂ ∫ [13] PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 71 En la resolución de un problema estructural general, no es posible conocer a “priori” la historia de tensiones (o deformaciones) en cada punto de la estructura, por lo que el análisis numérico debe realizarse discretizando el tiempo en intervalos ∆t, en los que se producen incrementos o decrementos de tensión. Cualquiera que sea la función de la integral de la ecuación 4, se puede transformar en una relación incremental utilizando fórmulas de cuadratura de diferentes niveles. La función de fluencia reducida es aproximada en CONS por una serie de Dirichlet: Siendo los valores m , i λ and )( τ i a coeficientes que deben ser ajustados a partir de ensayos. Los coeficientes )( τ i a son parámetros de envejecimiento que dependen de la edad del hormigón en el instante de aplicación de la carga. Los parámetros son coeficientes que gobiernan la forma de la función mientras que los valores de m indican el número de términos de la serie. En éste trabajo se considera que usando tres términos de la serie (m=3) y λi = 10-i la precisión de la respuesta es suficiente. Los modelos de retracción y fluencia adoptados son los incluidos en el CEB-FIP Model Code de 1990 [13]. La utilización de series de Dirichlet permite obtener los incrementos de deformación de fluencia en un instante de tiempo dado, a partir de los datos almacenados del instante anterior, no siendo necesario almacenar todo el historial de tensiones y deformaciones. A nivel numérico se traduce en una solución a los problemas de almacenaje de datos. El cálculo estructural se realiza mediante un análisis paso a paso en el tiempo. El dominio temporal se divide en intervalos de tiempo y se realiza un proceso de avance paso a paso en el que los incrementos de desplazamientos y deformaciones se van acumulando sobre los obtenidos en escalones anteriores. En cada escalón de tiempo se actualizan las propiedades de los materiales, la matriz de rigidez y el vector de cargas, a la vez que se evalúan los incrementos de deformaciones diferidas que han tenido lugar durante el más reciente intervalo de tiempo. Métodos iterativos como Newton-Raphson o Newton-Raphson Modificado o control de desplazamientos, combinado con análisis de tipo incremental son las herramientas implementadas para abordar la solución del problema no-lineal. El modelo permite obtener desplazamientos en nodos, fuerzas internas en elementos, tensiones y deformaciones en cada filamento en que se descompone la sección, reacciones etc. El análisis exclusivamente seccional se realiza mediante un elemento ménsula de longitud unidad sometido a flexión en su extremo libre. El modelo descrito ha sido comprobado experimentalmente por Marí y Valdés [14], y ha servido como herramienta de cálculo en el análisis de puentes y pilas esbeltas por Marí [15] y [16] y Chacón et. al [17]. Para poder reproducir el comportamiento de sección fisurada aislada el programa CONS ha sido modificado para no considerar la resistencia a tracción del hormigón así como el fenómeno de tension stiffening. El programa modificado ha sido la herramienta utilizada en el estudio paramétrico de tipo seccional que se describe a modo de conclusiones en el capítulo 3.1. [ ] )t( m 1i i i e1)(a)t,(c τ−λ− = −τ=τ−τ ∑ [13] PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 78 Figura 90. Leyes de momentos bajo cargas permanentes y bajo cargas de cálculo en la hipótesis de máximos momentos positivos. Figura 91. Curva factor de sobrecarga-desplazamiento a corto plazo, hipótesis de máximo momento positivo. 0 100 200 300 400 Distancia al origen -150000 -100000 -50000 0 50000 100000 Momento flector (kNxm) Leyes de Momentos Flectores Bajo cargas permanentes CP + 1,50 Sobrecarga Max positivos -0.30-0.25-0.20-0.15-0.10-0.050.00 Desplazamiento (m) 0 2 4 6 8 10 12 Factor de sobrecarga Curva P-delta bajo carga creciente Máximo Mom-Positivo Factor de sobrecarga-Desplazamiento Desplazamiento centro vano central PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 79 Figura 92. Curva factor de sobrecarga a los 10000 días-desplazamiento. Hipótesis de máximo momento positivo. Figura 93. Curva Factor de sobrecarga-desplazamiento a corto plazo, hipótesis de máximo momento negativo. -0.30-0.25-0.20-0.15-0.10-0.050.00 Desplazamiento (m) 0 2 4 6 8 10 12 Factor de sobrecarga Paso de tiempo hasta 10000 dias Máximo Mom-Positivo Factor de sobrecarga-Desplazamiento Desplazamiento centro vano central -0.30-0.25-0.20-0.15-0.10-0.050.00 Desplazamiento (m) 0 2 4 6 8 10 12 Factor de sobrecarga Curva P-delta bajo carga creciente Máximo Momento negativo Factor de sobrecarga-Desplazamiento Desplazamiento centro vano central PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 80 Figura 94. Evolución de las tensiones en los tendones de pretensado con el tiempo. Figura 95. Tensiones en las armaduras pasivas superior e inferior. Figura 96. Tensiones en el hormigón, en la fibra superior del vano central. 0 2000 4000 6000 8000 10000 Tiempo (días) 1100 1200 1300 1400 Tensión en el pretensado superior (N/mm2) Evolucion de las tensiones del pretensado con el tiempo Tendones de construcción Tendones de servicio 0 2000 4000 6000 8000 10000 Tiempo (días) -160 -140 -120 -100 -80 -60 Tensión (N/mm2) Evolucion de las tensiones en las armaduras pasivas con el tiempo Armadura superior vano central Armadura inferior vano central 0 2000 4000 6000 8000 10000 Tiempo (días) -7.00 -6.00 -5.00 Tensión (N/mm2) Evolucion de las tensiones en el hormigón comprimido con el tiempo Fibra superior vano central PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 81 12. CONCLUSIONES. En esta tesina se ha realizado un estudio sobre puentes empujados, con dos partes claramente diferenciadas., una orientada proyectar el puente con todo detalle y otra orientada analizar su comportamiento no lineal y diferido. En la primera parte se ha proyectado completamente un puente empujado de 8 vanos, los 6 vanos centrales de 50 m y los extremos de 37,5 m; se ha diseñado el pretensado necesario para la construcción, a partir de los esfuerzos obtenidos de la consideración de todas las fases constructivas. El diseño ha incluido el predimensionamiento de la sección transversal, la decisión sobre la longitud del tramo en cada fase de empuje y de la nariz, los aparatos de apoyo sobre las pilas y el dimensionado de estas y de la cimentación, entre otros muchos detalles constructivos. En la segunda parte, partiendo de los datos del puente proyectado, se ha realizado un análisis no lineal, instantáneo y diferido, para conocer la influencia del paso del tiempo en los estados tensionales y en la capacidad última de la estructura. Se ha considerando así mismo el comportamiento no lineal de los materiales y su influencia en las distribuciones de esfuerzos y otros aspectos, conforme se va aumentando la carga hasta la rotura de la estructura. Las conclusiones más importantes del trabajo son las siguientes; En cuanto a la fase de diseño del puente; • El proceso constructivo por empuje da lugar a que todas las secciones del puente pasen alternativamente por esfuerzos de ambos signos, lo que requiere un pretensado centrado para contrarrestar las tracciones en las fibras superiores e inferiores de todas las secciones. • Igualmente, el proceso constructivo es determinante en el canto, área e inercia de la sección del puente, pues da lugar a solicitaciones más desfavorables durante la construcción que las de servicio. Ello hace que el canto del puente daba ser mayor que con otros tipos de construcción. En este caso el canto, de 3,40m., resulta ser aproximadamente L/15, muy superior al canto típico de un puente continuo de sección cajón construido vano a vano que podría ser alrededor de L/20 ó L/25. • El fuerte pretensado necesario y las dimensiones de la sección transversal hacen que no sea necesaria armadura de cortante, habiendo dispuesto la mínima. • La longitud de la nariz de empuje diseñada ha sido de 30,00m., valor al que se ha llegado tras un estudio que ha permitido equilibrar la reducción de esfuerzos (y de coste) en el tablero de hormigón con el coste de la nariz. • Los aparatos de apoyo son del tipo neopreno zunchado con las siguientes características; 2𝑁𝑍 800 ∗800 ∗16(20 + 4). • La fuerza de empuje analizada es la correspondiente a la fuerza de frenado y su efecto directo sobre las pilas al imprimir en ellas desplazamientos relativos estudiados en detalle en el apartado correspondiente a los aparatos de apoyo y predimensionamiento de la pila. En cuanto al análisis y comportamiento no lineal del puente; • Debido a la enorme dificultad de simular el proceso de empuje con el programa CONS, se ha considerado el puente construido simultáneamente para hacer el análisis no lineal diferido. Ello se justifica en base a la siguiente consideración teórica: Cada sección del puente se ve sometida a variaciones continuas de esfuerzos durante el empuje, cambiando de signo a lo largo del mismo. Ello hace que la fluencia debida a las tensiones de un signo se compense parcialmente con PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 82 la debida a tensiones del signo opuesto. Por otra parte, la duración del empuje no es muy grande, con lo que los efectos diferidos son limitados. Por último, la retracción apenas producirá curvaturas, ya que toda la sección esta comprimida uniformemente. • Los diagramas Momento-curvatura ponen de manifiesto que la sección fisura para momentos próximos a la plastificación de las armaduras (del orden del 75% o más), lo cual es debido a la gran cantidad de fuerza de pretensado requerida para la fase constructiva. • Igualmente, el diagrama Momento-Curvatura pone de manifiesto que al fisurar la sección se produce una reducción muy importante de la rigidez, lo que ha debido ser tratado con especial cuidado para evitar problemas numéricos de divergencia. Para ello en el proceso de análisis no lineal se ha utilizado una estrategia de control de desplazamiento y también una reducción de los esfuerzos desequilibrados a introducir en cada iteración. • Mediante un dimensionamiento adecuado y el uso de materiales apropiados es posible conseguir estructuras de hormigón armado y pretensado suficientemente dúctiles y capaces de redistribuir las leyes de esfuerzos durante el comportamiento no-lineal antes de la rotura. • Se observa que el puente tiene una seguridad a rotura, bajo sobrecarga, enorme, debido al gran pretensado necesario para la construcción. La carga última es 1,35 (PP*CP) +11,7 SC+Q). • Se observa que apenas varía la capacidad última con el paso del tiempo. Es decir las deformaciones de fluencia y retracción y la relajación del acero no afectan a la capacidad resistente. El puente sigue teniendo una seguridad a rotura bajo sobrecargas enorme, debido al gran pretensado necesario para la construcción. La carga última es 1,35 (PP*CP) +11,5 SC+Q). • Se observa prácticamente la misma carga última que bajo la hipótesis de máximo momento positivo. • Se observan las pérdidas diferidas, que a los 10000 días son del 15,7% de la tensión inicial (y siguen aumentando). Ello concuerda bastante con el cálculo de perdidas realizado manualmente para la verificación de tensiones. • Las tensiones en las armaduras pasivas superior e inferior, se observan que aumentan por efecto de la fluencia, en mayor cuantía en la armadura superior, en la zona comprimida. • Se observa que por efecto de la fluencia se relajan las tensiones en un 20% aproximadamente. 13. RECOMENDACIONES A continuación se ofrecen algunas recomendaciones para futuros trabajos; • Sería deseable verificar si la hipótesis realizada sobre la escasa influencia del proceso constructivo en el comportamiento diferido es correcta. Ello conllevaría un ingente trabajo de modelización numérica a través del programa CONS o de un programa comercial, que no ha podido hacerse en este trabajo. • Sería deseable realizar un estudio de optimización de los parámetros clave, como son la longitud de la nariz, la longitud de los tramos a empujar y las dimensiones de la sección, que permitiera obtener la solución de menor coste global. En este coste podrían incluirse el coste del tablero, del parque de fabricación, del proceso de empuje, de las pilas y aparatos de apoyo, del tiempo de duración de la construcción y de la nariz de empuje. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 83 14. REFERENCIAS BIBLIOGRÁFICAS. [1] PDF página en internet “Palabra clave; PDF Incremental Launching Bridge”, Octubre 2011, 106 páginas. http://onlinepubs.trb.org/onlinepubs/archive/NotesDocs/20-07(229)_FR.pdf [2] A.C. Aparicio y J.R. Casas. “Puentes”. Tomo I y II. Escuela Técnica Superior de Ingenieros de Caminos Canales y Puertos de Barcelona. Publicaciones http://cpet.upc.es, Ref; cc701. [3] Instrucción I.A.P_98. Orden de 12 de febrero. 1998. “Proyecto de puentes de carretera.” [4] Instrucción de Hormigón estructural E.H.E-08. Documento base para la realización de este trabajo. Real decreto 1247/2008, de 18 de julio. 2008. [5] Marí Bernat, Antonio R. Aguado de Cea, Antonio. Agulló, L. Martínez, F. Cobo, D. “Hormigón armado y pretensado.” Ejercicios. Ediciones UPC. Pág. 109-114. Barcelona 1999. [6] Marí Bernat, Antonio R. “Fundamentos del proyecto de estructuras. Hormigón pretensado.” PDF documento de clase. Octubre de 2009. [7] Marí Bernat, Antonio R. Aguado de Cea, Antonio. Agulló, L. Martínez, F. Cobo, D. “Hormigón armado y pretensado.” Ejercicios. Ediciones UPC. Pág. 199-222. Barcelona 1999. [8] PDF. “MK4 innovative solutions” Pdf pág. Internet. Sistema MK4, 28 Pág. Barcelona. [email protected] [9] Marí Bernat, Antonio R. Aguado de Cea, Antonio. Agulló, L. Martínez, F. Cobo, D. “Hormigón armado y pretensado.” Ejercicios. Ediciones UPC. Pág. 257-264. Barcelona 1999. [9] Marí Bernat, Antonio R. Aguado de Cea, Antonio. Agulló, L. Martínez, F. Cobo, D. “Hormigón armado y pretensado.” Ejercicios. Ediciones UPC. Pág. 243-251. Barcelona 1999. [10] Jiménez Montoya, Pedro. García Meseguer, Alvaro. Morán Cabré, Francisco. “Hormigón armado.”14 edición basada en la E.H.E. Pág. 470-488. Barcelona 2004. [11] Manterola, Javier. “Puentes, tomo IV” Libro base. Escuela Técnica Superior de Ingenieros de Caminos, Canales y Puertos de Madrid. Capítulos 13 y 15. [12] Marí A., Nonlinear geometric, material and time dependent analysis of three dimensional reinforced and prestressed concrete frames, in Structural Engineering and Structural Mechanics. 1984, Department of Civil Engineering. University of California. Berkeley, California. [12] Marí Bernat, Antonio R. Bairan, JM. “Análisis y comportamiento no lineal de estructuras de hormigón y acero”. PDF, documento de la asignatura de hormigón no lineal. Barcelona 2010. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 84 [12] Marí Bernat, Antonio R. “Análisis y comportamiento no lineal de estructuras de hormigón armado”. PDF, documento de la asignatura de hormigón no lineal. Barcelona 2010. [12] Marí Bernat, Antonio R. “Para el análisis no lineal en el tiempo de estructuras de hormigón estructural construidas evolutivamente”. Ejercicios resueltos para el programa CONS. Barcelona, abril de 2005. [13] CEB-FIP, CEB-FIP Model Code 90. Telford, ed. B.d.I. nº213/214. London, 1993. [14] Marí A.R. and Valdes M., Long-Term behaviour of continuos precast concrete girder bridge model. ASCE J. Bridge Eng, 2000. 5(1): p. 22-30. [15] Marí A.R. and Montaner J., Continuous Precast Concrete Girder and Slab Bridge Decks, Proc. ICE-Strucs. and Buildings, 2000(140): p. 195-207. [16] Marí A.R., Mirambell E., and Estrada I., Effects of construction process and slab prestessing on the serviceability behaviour of composite bridges. J.Cont.Steel Res, 2000. 59: p. 135- 163. [17] Chacón R., Mirambell E., and Marí A., Long-term response of concrete-encased composite columns, Proc. ICE-Strucs. and Buildings, 2000(160): p. 273-285. [-] Marí Bernat, Antonio R. Molins Borrell, Climent. “Formigó armat i pretensat.” Exercicis. Libro base. Ediciones UPC. Barcelona Septiembre 2006. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 85 15. ANEJO 1. PLANOS. Figura 97. Trazado del cable armadura activa, tramos de 37,5 m. Figura 98. Trazado del cable armadura activa, tramos de 50 m. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 86 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 87 Figura 99. Armadura vano (centro luz). Figura 100. Armadura apoyo (pila). Figura 101. Diafragma en los apoyos (pilas y estribos). Figura 102. Sección transversal. Figura 103. Armadura por torsión. Figura 104. Armadura en zonas de anclaje de armadura activa. PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 94 27 30 0 1.0 1.000 0.5000 0.5 0.5 28 30 0 1.0 1.000 0.5000 0.5 0.5 29 30 0 1.0 1.000 0.5000 0.5 0.5 30 30 0 1.0 1.000 0.5000 0.5 0.5 31 30 0 1.0 1.000 0.5000 0.5 0.5 32 30 0 1.0 1.000 0.5000 0.5 0.5 33 30 0 1.0 1.000 0.5000 0.5 0.5 34 30 0 1.0 1.000 0.5000 0.5 0.5 35 30 0 1.0 1.000 0.5000 0.5 0.5 36 30 0 1.0 1.000 0.5000 0.5 0.5 37 30 0 1.0 1.000 0.5000 0.5 0.5 38 30 0 1.0 1.000 0.5000 0.5 0.5 39 30 0 1.0 1.000 0.5000 0.5 0.5 40 30 0 1.0 1.000 0.5000 0.5 0.5 41 30 0 1.0 1.000 0.5000 0.5 0.5 42 30 0 1.0 1.000 0.5000 0.5 0.5 43 30 0 1.0 1.000 0.5000 0.5 0.5 44 30 0 1.0 1.000 0.5000 0.5 0.5 45 30 0 1.0 1.000 0.5000 0.5 0.5 46 30 0 1.0 1.000 0.5000 0.5 0.5 47 30 0 1.0 1.000 0.5000 0.5 0.5 48 30 0 1.0 1.000 0.5000 0.5 0.5 49 30 0 1.0 1.000 0.5000 0.5 0.5 50 30 0 1.0 1.000 0.5000 0.5 0.5 16.2. Modelo introducido en CONS en servicio, paso del tiempo con sobrecarga hasta rotura bajo momentos positivos máximos; PET Puente empujado de 37.5+50+50+50+50+50+50+37.5 de sección cajón. Paso tiempo. Sobrecarga máximos positivos y carga hasta rotura 151 9 150 1 1 1 1 1 1 0 3 8 1 1 1 0 0 1 0 0 0 16 37.5 0 0 36 87.5 0 0 76 187.5 0 0 96 237.5 0 0 116 287.5 0 0 136 337.5 0 0 151 375.0 0 0 1 16 36 56 76 96 116 136 151 1 24 10 1 -6.25 1.33 2 -3.03 1.33 3 -2.48 1.33 4 2.48 1.33 5 3.03 1.33 6 6.25 1.33 7 -6.25 1.08 8 -3.03 0.88 9 -2.48 0.88 10 2.48 0.88 11 3.03 0.88 12 6.25 1.08 13 -2.65 -1.24 14 -2.09 -1.24 15 2.09 -1.24 16 2.65 -1.24 17 -1.25 -1.67 18 1.25 -1.67 19 -2.50 -2.07 20 -2.09 -2.07 21 -1.25 -2.07 22 1.25 -2.07 20 2.09 -2.07 24 2.50 -2.07 1 1 2 8 7 1 1 6 2 2 5 11 8 1 1 6 3 5 6 12 11 1 1 6 4 8 9 14 13 1 1 8 5 10 11 16 15 1 1 8 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 95 6 13 14 20 19 1 1 8 7 14 17 21 20 1 1 8 8 17 18 22 21 1 1 8 9 18 15 23 22 1 1 8 10 15 16 24 23 1 1 8 1 2 1 0.01 0 1.28 0 50000 1 0.01 0 -2.02 0 50000 10000.00 20000.00 0.0100 0.2000 0.10000 1 1 2 1 1 1 0 0 50000 0 0 100 2 2 3 1 1 1 0 0 50000 0 0 100 3 3 4 1 1 1 0 0 50000 0 0 100 4 4 5 1 1 1 0 0 50000 0 0 100 5 5 6 1 1 1 0 0 50000 0 0 100 6 6 7 1 1 1 0 0 50000 0 0 100 7 7 8 1 1 1 0 0 50000 0 0 100 8 8 9 1 1 1 0 0 50000 0 0 100 9 9 10 1 1 1 0 0 50000 0 0 100 10 10 11 1 1 1 0 0 50000 0 0 100 11 11 12 1 1 1 0 0 50000 0 0 100 12 12 13 1 1 1 0 0 50000 0 0 100 13 13 14 1 1 1 0 0 50000 0 0 100 14 14 15 1 1 1 0 0 50000 0 0 100 15 15 16 1 1 1 0 0 50000 0 0 100 16 16 17 1 1 1 0 0 50000 0 0 100 17 17 18 1 1 1 0 0 50000 0 0 100 18 18 19 1 1 1 0 0 50000 0 0 100 19 19 20 1 1 1 0 0 50000 0 0 100 20 20 21 1 1 1 0 0 50000 0 0 100 21 21 22 1 1 1 0 0 50000 0 0 100 22 22 23 1 1 1 0 0 50000 0 0 100 23 23 24 1 1 1 0 0 50000 0 0 100 24 24 25 1 1 1 0 0 50000 0 0 100 25 25 26 1 1 1 0 0 50000 0 0 100 26 26 27 1 1 1 0 0 50000 0 0 100 27 27 28 1 1 1 0 0 50000 0 0 100 28 28 29 1 1 1 0 0 50000 0 0 100 29 29 30 1 1 1 0 0 50000 0 0 100 30 30 31 1 1 1 0 0 50000 0 0 100 31 31 32 1 1 1 0 0 50000 0 0 100 32 32 33 1 1 1 0 0 50000 0 0 100 33 33 34 1 1 1 0 0 50000 0 0 100 34 34 35 1 1 1 0 0 50000 0 0 100 35 35 36 1 1 1 0 0 50000 0 0 100 36 36 37 1 1 1 0 0 50000 0 0 100 37 37 38 1 1 1 0 0 50000 0 0 100 38 38 39 1 1 1 0 0 50000 0 0 100 39 39 40 1 1 1 0 0 50000 0 0 100 40 40 41 1 1 1 0 0 50000 0 0 100 41 41 42 1 1 1 0 0 50000 0 0 100 42 42 43 1 1 1 0 0 50000 0 0 100 43 43 44 1 1 1 0 0 50000 0 0 100 44 44 45 1 1 1 0 0 50000 0 0 100 45 45 46 1 1 1 0 0 50000 0 0 100 46 46 47 1 1 1 0 0 50000 0 0 100 47 47 48 1 1 1 0 0 50000 0 0 100 48 48 49 1 1 1 0 0 50000 0 0 100 49 49 50 1 1 1 0 0 50000 0 0 100 50 50 51 1 1 1 0 0 50000 0 0 100 51 51 52 1 1 1 0 0 50000 0 0 100 52 52 53 1 1 1 0 0 50000 0 0 100 53 53 54 1 1 1 0 0 50000 0 0 100 54 54 55 1 1 1 0 0 50000 0 0 100 55 55 56 1 1 1 0 0 50000 0 0 100 56 56 57 1 1 1 0 0 50000 0 0 100 57 57 58 1 1 1 0 0 50000 0 0 100 58 58 59 1 1 1 0 0 50000 0 0 100 59 59 60 1 1 1 0 0 50000 0 0 100 60 60 61 1 1 1 0 0 50000 0 0 100 61 61 62 1 1 1 0 0 50000 0 0 100 62 62 63 1 1 1 0 0 50000 0 0 100 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 96 63 63 64 1 1 1 0 0 50000 0 0 100 64 64 65 1 1 1 0 0 50000 0 0 100 65 65 66 1 1 1 0 0 50000 0 0 100 66 66 67 1 1 1 0 0 50000 0 0 100 67 67 68 1 1 1 0 0 50000 0 0 100 68 68 69 1 1 1 0 0 50000 0 0 100 69 69 70 1 1 1 0 0 50000 0 0 100 70 70 71 1 1 1 0 0 50000 0 0 100 71 71 72 1 1 1 0 0 50000 0 0 100 72 72 73 1 1 1 0 0 50000 0 0 100 73 73 74 1 1 1 0 0 50000 0 0 100 74 74 75 1 1 1 0 0 50000 0 0 100 75 75 76 1 1 1 0 0 50000 0 0 100 76 76 77 1 1 1 0 0 50000 0 0 100 77 77 78 1 1 1 0 0 50000 0 0 100 78 78 79 1 1 1 0 0 50000 0 0 100 79 79 80 1 1 1 0 0 50000 0 0 100 80 80 81 1 1 1 0 0 50000 0 0 100 81 81 82 1 1 1 0 0 50000 0 0 100 82 82 83 1 1 1 0 0 50000 0 0 100 83 83 84 1 1 1 0 0 50000 0 0 100 84 84 85 1 1 1 0 0 50000 0 0 100 85 85 86 1 1 1 0 0 50000 0 0 100 86 86 87 1 1 1 0 0 50000 0 0 100 87 87 88 1 1 1 0 0 50000 0 0 100 88 88 89 1 1 1 0 0 50000 0 0 100 89 89 90 1 1 1 0 0 50000 0 0 100 90 90 91 1 1 1 0 0 50000 0 0 100 91 91 92 1 1 1 0 0 50000 0 0 100 92 92 93 1 1 1 0 0 50000 0 0 100 93 93 94 1 1 1 0 0 50000 0 0 100 94 94 95 1 1 1 0 0 50000 0 0 100 95 95 96 1 1 1 0 0 50000 0 0 100 96 96 97 1 1 1 0 0 50000 0 0 100 97 97 98 1 1 1 0 0 50000 0 0 100 98 98 99 1 1 1 0 0 50000 0 0 100 99 99 100 1 1 1 0 0 50000 0 0 100 100 100 101 1 1 1 0 0 50000 0 0 100 101 101 102 1 1 1 0 0 50000 0 0 100 102 102 103 1 1 1 0 0 50000 0 0 100 103 103 104 1 1 1 0 0 50000 0 0 100 104 104 105 1 1 1 0 0 50000 0 0 100 105 105 106 1 1 1 0 0 50000 0 0 100 106 106 107 1 1 1 0 0 50000 0 0 100 107 107 108 1 1 1 0 0 50000 0 0 100 108 108 109 1 1 1 0 0 50000 0 0 100 109 109 110 1 1 1 0 0 50000 0 0 100 110 110 111 1 1 1 0 0 50000 0 0 100 111 111 112 1 1 1 0 0 50000 0 0 100 112 112 113 1 1 1 0 0 50000 0 0 100 113 113 114 1 1 1 0 0 50000 0 0 100 114 114 115 1 1 1 0 0 50000 0 0 100 115 115 116 1 1 1 0 0 50000 0 0 100 116 116 117 1 1 1 0 0 50000 0 0 100 117 117 118 1 1 1 0 0 50000 0 0 100 118 118 119 1 1 1 0 0 50000 0 0 100 119 119 120 1 1 1 0 0 50000 0 0 100 120 120 121 1 1 1 0 0 50000 0 0 100 121 121 122 1 1 1 0 0 50000 0 0 100 122 122 123 1 1 1 0 0 50000 0 0 100 123 123 124 1 1 1 0 0 50000 0 0 100 124 124 125 1 1 1 0 0 50000 0 0 100 125 125 126 1 1 1 0 0 50000 0 0 100 126 126 127 1 1 1 0 0 50000 0 0 100 127 127 128 1 1 1 0 0 50000 0 0 100 128 128 129 1 1 1 0 0 50000 0 0 100 129 129 130 1 1 1 0 0 50000 0 0 100 130 130 131 1 1 1 0 0 50000 0 0 100 131 131 132 1 1 1 0 0 50000 0 0 100 132 132 133 1 1 1 0 0 50000 0 0 100 133 133 134 1 1 1 0 0 50000 0 0 100 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 97 134 134 135 1 1 1 0 0 50000 0 0 100 135 135 136 1 1 1 0 0 50000 0 0 100 136 136 137 1 1 1 0 0 50000 0 0 100 137 137 138 1 1 1 0 0 50000 0 0 100 138 138 139 1 1 1 0 0 50000 0 0 100 139 139 140 1 1 1 0 0 50000 0 0 100 140 140 141 1 1 1 0 0 50000 0 0 100 141 141 142 1 1 1 0 0 50000 0 0 100 142 142 143 1 1 1 0 0 50000 0 0 100 143 143 144 1 1 1 0 0 50000 0 0 100 144 144 145 1 1 1 0 0 50000 0 0 100 145 145 146 1 1 1 0 0 50000 0 0 100 146 146 147 1 1 1 0 0 50000 0 0 100 147 147 148 1 1 1 0 0 50000 0 0 100 148 148 149 1 1 1 0 0 50000 0 0 100 149 149 150 1 1 1 0 0 50000 0 0 100 150 150 151 1 1 1 0 0 50000 0 0 100 3 2 0 0 145210 0.00764 161700 0.02000 1 1 1 150 0.04564 28. 1 1 150 0 187.5 375 0 0 0 1.18 1.18 1.18 2 1 1 150 0.02800 28. 1 1 150 0 187.5 375 0 0 0 -1.92 -1.92 -1.92 3 1 1 150 0.00504 105. 15 1 12 0 15.00 30.0 0. 0. 0. 0.00 -1.92 0.00 13 18 30.0 37.50 45.0 0 0 0 0.00 1.18 0.00 19 32 45. 62.5 80.0 0 0 0 0.00 -1.92 0.00 33 38 80.0 87.50 95.0 0 0 0 0.00 1.18 0.00 39 52 95. 112.5 130.0 0 0 0 0.00 -1.92 0.00 53 58 130.0 137.50 145.0 0 0 0 0.00 1.18 0.00 59 72 145. 162.5 180.0 0 0 0 0.00 -1.92 0.00 73 78 180.0 187.50 195.0 0 0 0 0.00 1.18 0.00 79 92 195. 212.5 230.0 0 0 0 0.00 -1.92 0.00 93 98 230.0 237.50 245.0 0 0 0 0.00 1.18 0.00 99 112 245. 262.5 280.0 0 0 0 0.00 -1.92 0.00 113 118 280.0 287.50 295.0 0 0 0 0.00 1.18 0.00 119 132 295. 312.50 330.0 0 0 0 0.00 -1.92 0.00 133 138 330.0 337.50 345.0 0 0 0 0.00 1.18 0.00 139 150 345. 360.0 375.0 0 0 0 0.00 -1.92 0.00 3000 0 50000 9.94 30.46 70 1 1 20000000 10000 43500 0.01 0.1 0.1 0.1 100 100 1 1 0.01 1 9 2 2 2 4 66 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 9 3 66 5 76 5 66 116 76 1 66 2 76 1 66 2 66 3 76 1 76 3 8 ETAPA1.Peso propio de todo el puente y activación pretensado construcción 1 105 1 1 0 2 0 0 2 1 0 1 1.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 98 16 0.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 36 0.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 56 0.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 76 0.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 96 0.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 116 0.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 136 0.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 151 0.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 66 76 1 2 6391 6391 0 2 2 3927 3927 0 1 150 1 0 0 0 0 0 0 0 0 0 1 10 0 1.00 1.000 1.000 1 1 ETAPA2.Paso del tiempo de 30 dias 1 30. 0 1 0 2 0 1 0 0 0 66 76 1 0 0 0 0 0 0 0 0 0 1 10 0 1.000 1.000 1.000 1 1 ETAPA3.Pretensado de servicio 1 0 0 1 0 2 0 0 1 0 0 66 76 3 3 705 705 0 1 0 0 0 0 0 0 0 0 0 1 10 0 1.000 1.000 1.000 1 1 ETAPA4.Paso del tiempo de 30 dias 1 30. 0 1 0 2 0 1 0 0 0 66 76 1 0 0 0 0 0 0 0 0 0 1 10 0 1.000 1.000 1.000 1 1 ETAPA5.Disposición de la carga muerta de -37.5 kN/ml 1 0 0 1 0 2 0 0 0 0 1 66 76 1 150 0 0 -3.75 0 0 0 1 0 0 0 0 0 0 0 0 0 1 10 0 1.000 1.000 1.000 1 1 ETAPA6.Paso del tiempo de hasta 10000 dias 20 9835. 0 1 0 2 0 1 0 0 0 66 76 1 0 0 0 0 0 0 0 0 0 1 10 0 1.000 1.000 1.000 0.5 0.5 ETAPA7.Incremento de carga permanente un 0.35*(24.85 + 3.75) 1 0 0 1 0 2 0 0 0 0 1 66 76 1 150 0 0 -10.01 0 0 0 4 0 0 0 0 0 0 0 0 0 1 10 0 0.25 1.000 1.000 0.8 0.8 2 10 0 0.25 1.000 1.000 0.8 0.8 3 10 0 0.25 1.000 1.000 0.8 0.8 4 10 0 0.25 1.000 1.000 0.8 0.8 ETAPA8.Incremento de sobrecarga uniformemente para configuracion max pos hasta rotura 1 0 0 1 0 2 0 0 0 0 4 66 76 15 35 0 0 -5 0 0 0 56 75 0 0 -5 0 0 0 96 115 0 0 -5 0 0 0 136 150 0 0 -5 0 0 0 50 3 0 1 66 3 -0.010 0 0 0 65 0 0 -20 0 0 0 66 0 0 -20 0 0 0 67 0 0 -20 0 0 0 1 30 0 1.0 1.000 2.0000 0.5 0.5 2 30 0 1.0 1.000 0.8500 0.5 0.5 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 99 3 30 0 1.0 1.000 1.1500 0.5 0.5 4 30 0 1.0 1.000 1.0000 0.5 0.5 5 30 0 1.0 1.000 1.0000 0.5 0.5 6 30 0 1.0 1.000 1.0000 0.5 0.5 7 30 0 1.0 1.000 1.0000 0.5 0.5 8 30 0 1.0 1.000 0.5000 0.5 0.5 9 30 0 1.0 1.000 0.5000 0.5 0.5 10 30 0 1.0 1.000 0.5000 0.5 0.5 11 30 0 1.0 1.000 0.5000 0.5 0.5 12 30 0 1.0 1.000 0.5000 0.5 0.5 13 30 0 1.0 1.000 0.5000 0.5 0.5 14 30 0 1.0 1.000 0.5000 0.5 0.5 15 30 0 1.0 1.000 0.5000 0.5 0.5 16 30 0 1.0 1.000 0.5000 0.5 0.5 17 30 0 1.0 1.000 0.5000 0.5 0.5 18 30 0 1.0 1.000 0.5000 0.5 0.5 19 30 0 1.0 1.000 0.5000 0.5 0.5 20 30 0 1.0 1.000 0.5000 0.5 0.5 21 30 0 1.0 1.000 0.5000 0.5 0.5 22 30 0 1.0 1.000 0.5000 0.5 0.5 23 30 0 1.0 1.000 0.5000 0.5 0.5 24 30 0 1.0 1.000 0.5000 0.5 0.5 25 30 0 1.0 1.000 0.5000 0.5 0.5 26 30 0 1.0 1.000 0.5000 0.5 0.5 27 30 0 1.0 1.000 0.5000 0.5 0.5 28 30 0 1.0 1.000 0.5000 0.5 0.5 29 30 0 1.0 1.000 0.5000 0.5 0.5 30 30 0 1.0 1.000 0.5000 0.5 0.5 31 30 0 1.0 1.000 0.5000 0.5 0.5 32 30 0 1.0 1.000 0.5000 0.5 0.5 33 30 0 1.0 1.000 0.5000 0.5 0.5 34 30 0 1.0 1.000 0.5000 0.5 0.5 35 30 0 1.0 1.000 0.5000 0.5 0.5 36 30 0 1.0 1.000 0.5000 0.5 0.5 37 30 0 1.0 1.000 0.5000 0.5 0.5 38 30 0 1.0 1.000 0.5000 0.5 0.5 39 30 0 1.0 1.000 0.5000 0.5 0.5 40 30 0 1.0 1.000 0.5000 0.5 0.5 41 30 0 1.0 1.000 0.5000 0.5 0.5 42 30 0 1.0 1.000 0.5000 0.5 0.5 43 30 0 1.0 1.000 0.5000 0.5 0.5 44 30 0 1.0 1.000 0.5000 0.5 0.5 45 30 0 1.0 1.000 0.5000 0.5 0.5 46 30 0 1.0 1.000 0.5000 0.5 0.5 47 30 0 1.0 1.000 0.5000 0.5 0.5 48 30 0 1.0 1.000 0.5000 0.5 0.5 49 30 0 1.0 1.000 0.5000 0.5 0.5 50 30 0 1.0 1.000 0.5000 0.5 0.5 16.3. Modelo introducido en CONS en servicio con carga hasta rotura bajo momentos positivos máximos; PE6 Puente empujado de 37.5+50+50+50+50+50+50+37.5 de sección cajón. Sobrecarga máximos positivos y carga hasta rotura 151 9 150 1 1 1 1 1 1 0 3 8 1 1 1 0 0 1 0 0 0 16 37.5 0 0 36 87.5 0 0 76 187.5 0 0 96 237.5 0 0 116 287.5 0 0 136 337.5 0 0 151 375.0 0 0 1 16 36 56 76 96 116 136 151 1 24 10 1 -6.25 1.33 2 -3.03 1.33 3 -2.48 1.33 4 2.48 1.33 5 3.03 1.33 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 100 6 6.25 1.33 7 -6.25 1.08 8 -3.03 0.88 9 -2.48 0.88 10 2.48 0.88 11 3.03 0.88 12 6.25 1.08 13 -2.65 -1.24 14 -2.09 -1.24 15 2.09 -1.24 16 2.65 -1.24 17 -1.25 -1.67 18 1.25 -1.67 19 -2.50 -2.07 20 -2.09 -2.07 21 -1.25 -2.07 22 1.25 -2.07 20 2.09 -2.07 24 2.50 -2.07 1 1 2 8 7 1 1 6 2 2 5 11 8 1 1 6 3 5 6 12 11 1 1 6 4 8 9 14 13 1 1 8 5 10 11 16 15 1 1 8 6 13 14 20 19 1 1 8 7 14 17 21 20 1 1 8 8 17 18 22 21 1 1 8 9 18 15 23 22 1 1 8 10 15 16 24 23 1 1 8 1 2 1 0.01 0 1.28 0 50000 1 0.01 0 -2.02 0 50000 10000.00 20000.00 0.0100 0.2000 0.10000 1 1 2 1 1 1 0 0 50000 0 0 100 2 2 3 1 1 1 0 0 50000 0 0 100 3 3 4 1 1 1 0 0 50000 0 0 100 4 4 5 1 1 1 0 0 50000 0 0 100 5 5 6 1 1 1 0 0 50000 0 0 100 6 6 7 1 1 1 0 0 50000 0 0 100 7 7 8 1 1 1 0 0 50000 0 0 100 8 8 9 1 1 1 0 0 50000 0 0 100 9 9 10 1 1 1 0 0 50000 0 0 100 10 10 11 1 1 1 0 0 50000 0 0 100 11 11 12 1 1 1 0 0 50000 0 0 100 12 12 13 1 1 1 0 0 50000 0 0 100 13 13 14 1 1 1 0 0 50000 0 0 100 14 14 15 1 1 1 0 0 50000 0 0 100 15 15 16 1 1 1 0 0 50000 0 0 100 16 16 17 1 1 1 0 0 50000 0 0 100 17 17 18 1 1 1 0 0 50000 0 0 100 18 18 19 1 1 1 0 0 50000 0 0 100 19 19 20 1 1 1 0 0 50000 0 0 100 20 20 21 1 1 1 0 0 50000 0 0 100 21 21 22 1 1 1 0 0 50000 0 0 100 22 22 23 1 1 1 0 0 50000 0 0 100 23 23 24 1 1 1 0 0 50000 0 0 100 24 24 25 1 1 1 0 0 50000 0 0 100 25 25 26 1 1 1 0 0 50000 0 0 100 26 26 27 1 1 1 0 0 50000 0 0 100 27 27 28 1 1 1 0 0 50000 0 0 100 28 28 29 1 1 1 0 0 50000 0 0 100 29 29 30 1 1 1 0 0 50000 0 0 100 30 30 31 1 1 1 0 0 50000 0 0 100 31 31 32 1 1 1 0 0 50000 0 0 100 32 32 33 1 1 1 0 0 50000 0 0 100 33 33 34 1 1 1 0 0 50000 0 0 100 34 34 35 1 1 1 0 0 50000 0 0 100 35 35 36 1 1 1 0 0 50000 0 0 100 36 36 37 1 1 1 0 0 50000 0 0 100 37 37 38 1 1 1 0 0 50000 0 0 100 38 38 39 1 1 1 0 0 50000 0 0 100 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 101 39 39 40 1 1 1 0 0 50000 0 0 100 40 40 41 1 1 1 0 0 50000 0 0 100 41 41 42 1 1 1 0 0 50000 0 0 100 42 42 43 1 1 1 0 0 50000 0 0 100 43 43 44 1 1 1 0 0 50000 0 0 100 44 44 45 1 1 1 0 0 50000 0 0 100 45 45 46 1 1 1 0 0 50000 0 0 100 46 46 47 1 1 1 0 0 50000 0 0 100 47 47 48 1 1 1 0 0 50000 0 0 100 48 48 49 1 1 1 0 0 50000 0 0 100 49 49 50 1 1 1 0 0 50000 0 0 100 50 50 51 1 1 1 0 0 50000 0 0 100 51 51 52 1 1 1 0 0 50000 0 0 100 52 52 53 1 1 1 0 0 50000 0 0 100 53 53 54 1 1 1 0 0 50000 0 0 100 54 54 55 1 1 1 0 0 50000 0 0 100 55 55 56 1 1 1 0 0 50000 0 0 100 56 56 57 1 1 1 0 0 50000 0 0 100 57 57 58 1 1 1 0 0 50000 0 0 100 58 58 59 1 1 1 0 0 50000 0 0 100 59 59 60 1 1 1 0 0 50000 0 0 100 60 60 61 1 1 1 0 0 50000 0 0 100 61 61 62 1 1 1 0 0 50000 0 0 100 62 62 63 1 1 1 0 0 50000 0 0 100 63 63 64 1 1 1 0 0 50000 0 0 100 64 64 65 1 1 1 0 0 50000 0 0 100 65 65 66 1 1 1 0 0 50000 0 0 100 66 66 67 1 1 1 0 0 50000 0 0 100 67 67 68 1 1 1 0 0 50000 0 0 100 68 68 69 1 1 1 0 0 50000 0 0 100 69 69 70 1 1 1 0 0 50000 0 0 100 70 70 71 1 1 1 0 0 50000 0 0 100 71 71 72 1 1 1 0 0 50000 0 0 100 72 72 73 1 1 1 0 0 50000 0 0 100 73 73 74 1 1 1 0 0 50000 0 0 100 74 74 75 1 1 1 0 0 50000 0 0 100 75 75 76 1 1 1 0 0 50000 0 0 100 76 76 77 1 1 1 0 0 50000 0 0 100 77 77 78 1 1 1 0 0 50000 0 0 100 78 78 79 1 1 1 0 0 50000 0 0 100 79 79 80 1 1 1 0 0 50000 0 0 100 80 80 81 1 1 1 0 0 50000 0 0 100 81 81 82 1 1 1 0 0 50000 0 0 100 82 82 83 1 1 1 0 0 50000 0 0 100 83 83 84 1 1 1 0 0 50000 0 0 100 84 84 85 1 1 1 0 0 50000 0 0 100 85 85 86 1 1 1 0 0 50000 0 0 100 86 86 87 1 1 1 0 0 50000 0 0 100 87 87 88 1 1 1 0 0 50000 0 0 100 88 88 89 1 1 1 0 0 50000 0 0 100 89 89 90 1 1 1 0 0 50000 0 0 100 90 90 91 1 1 1 0 0 50000 0 0 100 91 91 92 1 1 1 0 0 50000 0 0 100 92 92 93 1 1 1 0 0 50000 0 0 100 93 93 94 1 1 1 0 0 50000 0 0 100 94 94 95 1 1 1 0 0 50000 0 0 100 95 95 96 1 1 1 0 0 50000 0 0 100 96 96 97 1 1 1 0 0 50000 0 0 100 97 97 98 1 1 1 0 0 50000 0 0 100 98 98 99 1 1 1 0 0 50000 0 0 100 99 99 100 1 1 1 0 0 50000 0 0 100 100 100 101 1 1 1 0 0 50000 0 0 100 101 101 102 1 1 1 0 0 50000 0 0 100 102 102 103 1 1 1 0 0 50000 0 0 100 103 103 104 1 1 1 0 0 50000 0 0 100 104 104 105 1 1 1 0 0 50000 0 0 100 105 105 106 1 1 1 0 0 50000 0 0 100 106 106 107 1 1 1 0 0 50000 0 0 100 107 107 108 1 1 1 0 0 50000 0 0 100 108 108 109 1 1 1 0 0 50000 0 0 100 109 109 110 1 1 1 0 0 50000 0 0 100 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 102 110 110 111 1 1 1 0 0 50000 0 0 100 111 111 112 1 1 1 0 0 50000 0 0 100 112 112 113 1 1 1 0 0 50000 0 0 100 113 113 114 1 1 1 0 0 50000 0 0 100 114 114 115 1 1 1 0 0 50000 0 0 100 115 115 116 1 1 1 0 0 50000 0 0 100 116 116 117 1 1 1 0 0 50000 0 0 100 117 117 118 1 1 1 0 0 50000 0 0 100 118 118 119 1 1 1 0 0 50000 0 0 100 119 119 120 1 1 1 0 0 50000 0 0 100 120 120 121 1 1 1 0 0 50000 0 0 100 121 121 122 1 1 1 0 0 50000 0 0 100 122 122 123 1 1 1 0 0 50000 0 0 100 123 123 124 1 1 1 0 0 50000 0 0 100 124 124 125 1 1 1 0 0 50000 0 0 100 125 125 126 1 1 1 0 0 50000 0 0 100 126 126 127 1 1 1 0 0 50000 0 0 100 127 127 128 1 1 1 0 0 50000 0 0 100 128 128 129 1 1 1 0 0 50000 0 0 100 129 129 130 1 1 1 0 0 50000 0 0 100 130 130 131 1 1 1 0 0 50000 0 0 100 131 131 132 1 1 1 0 0 50000 0 0 100 132 132 133 1 1 1 0 0 50000 0 0 100 133 133 134 1 1 1 0 0 50000 0 0 100 134 134 135 1 1 1 0 0 50000 0 0 100 135 135 136 1 1 1 0 0 50000 0 0 100 136 136 137 1 1 1 0 0 50000 0 0 100 137 137 138 1 1 1 0 0 50000 0 0 100 138 138 139 1 1 1 0 0 50000 0 0 100 139 139 140 1 1 1 0 0 50000 0 0 100 140 140 141 1 1 1 0 0 50000 0 0 100 141 141 142 1 1 1 0 0 50000 0 0 100 142 142 143 1 1 1 0 0 50000 0 0 100 143 143 144 1 1 1 0 0 50000 0 0 100 144 144 145 1 1 1 0 0 50000 0 0 100 145 145 146 1 1 1 0 0 50000 0 0 100 146 146 147 1 1 1 0 0 50000 0 0 100 147 147 148 1 1 1 0 0 50000 0 0 100 148 148 149 1 1 1 0 0 50000 0 0 100 149 149 150 1 1 1 0 0 50000 0 0 100 150 150 151 1 1 1 0 0 50000 0 0 100 3 2 0 0 145210 0.00764 161700 0.02000 1 1 1 150 0.04564 28. 1 1 150 0 187.5 375 0 0 0 1.18 1.18 1.18 2 1 1 150 0.02800 28. 1 1 150 0 187.5 375 0 0 0 -1.92 -1.92 -1.92 3 1 1 150 0.00504 105. 15 1 12 0 15.00 30.0 0. 0. 0. 0.00 -1.92 0.00 13 18 30.0 37.50 45.0 0 0 0 0.00 1.18 0.00 19 32 45. 62.5 80.0 0 0 0 0.00 -1.92 0.00 33 38 80.0 87.50 95.0 0 0 0 0.00 1.18 0.00 39 52 95. 112.5 130.0 0 0 0 0.00 -1.92 0.00 53 58 130.0 137.50 145.0 0 0 0 0.00 1.18 0.00 59 72 145. 162.5 180.0 0 0 0 0.00 -1.92 0.00 73 78 180.0 187.50 195.0 0 0 0 0.00 1.18 0.00 79 92 195. 212.5 230.0 0 0 0 0.00 -1.92 0.00 93 98 230.0 237.50 245.0 0 0 0 0.00 1.18 0.00 99 112 PROYECTO DE UN PUENTE EMPUJADO Y ESTUDIO MEDIANTE ANÁLISIS NO LINEAL DEL COMPORTAMIENTO DIFERIDO Y EN ESTADO LÍMITE ÚLTIMO. 103 245. 262.5 280.0 0 0 0 0.00 -1.92 0.00 113 118 280.0 287.50 295.0 0 0 0 0.00 1.18 0.00 119 132 295. 312.50 330.0 0 0 0 0.00 -1.92 0.00 133 138 330.0 337.50 345.0 0 0 0 0.00 1.18 0.00 139 150 345. 360.0 375.0 0 0 0 0.00 -1.92 0.00 3000 0 50000 9.94 30.46 70 1 1 20000000 10000 43500 0.01 0.1 0.1 0.1 100 100 1 1 0.01 1 9 2 2 2 4 66 3 1 3 2 3 3 3 4 3 5 3 6 3 7 3 8 3 9 3 66 5 76 5 66 116 76 1 66 2 76 1 66 2 66 3 76 1 76 3 8 ETAPA1.Peso propio de todo el puente y activación pretensado construcción 1 105 1 1 0 2 0 0 2 1 0 1 1.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 16 0.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 36 0.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 56 0.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 76 0.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 96 0.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 116 0.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 136 0.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 151 0.0000E+20 1.0000E+20 1.0000E+20 1.0000E+20 0.0000E+20 1.0000E+20 66 76 1 2 6391 6391 0 2 2 3927 3927 0 1 150 1 0 0 0 0 0 0 0 0 0 1 10 0 1.00 1.000 1.000 1 1 ETAPA2.Paso del tiempo de 30 dias 1 30. 0 1 0 2 0 1 0 0 0 66 76 1 0 0 0 0 0 0 0 0 0 1 10 0 1.000 1.000 1.000 1 1 ETAPA3.Pretensado de servicio 1 0 0 1 0 2 0 0 1 0 0 66 76 3 3 705 705 0 1 0 0 0 0 0 0 0 0 0 1 10 0 1.000 1.000 1.000 1 1 ETAPA4.Paso del tiempo de 30 dias 1 30. 0 1 0 2 0 1 0 0 0 66 76 1 0 0 0 0 0 0 0 0 0 1 10 0 1.000 1.000 1.000 1 1 ETAPA5.Disposición de la carga muerta de -37.5 kN/ml 1 0 0 1 0 2 0 0 0 0 1 66 76 1 150 0 0 -3.75 0 0 0 1 0 0 0 0 0 0 0 0 0 1 10 0 1.000 1.000 1.000 1 1 ETAPA6.Paso del tiempo de 30 dias 1 30. 0 1 0 2 0 1 0 0 0 66 76 1 0 0 0 0 0 0 0 0 0 1 10 0 1.000 1.000 1.000 1 1 ETAPA7.Incremento de carga permanente un 0.35*(24.85 + 3.75) LANZAMIENTO POR SEGMENTOS LANZAMIENTO COMPLETO. Esquema general. LANZAMIENTO COMPLETO. Detalle de la fabricación. GIRO COMPLETO. TRASLACIÓN TRANSVERSAL MÉTODO DE LANZAMIENTO POR SEGMENTOS La fabricación de puentes de hormigón mediante este procedimiento requiere de los componentes siguientes: 1) Planta de fabricación del tablero: Consta fundamentalmente del taller de ferralla, encofrado y planta de hormigonado. Suele estar protegido de la intemperie. 2) Pico de lanzamiento: Su misión es disminuir el peso del puente en el proceso de lanzamiento. Es una estructura metálica conectada a la sección transversal frontal del puente. 3) Pilas auxiliares: Si resulta necesario, y en general para vanos superiores a los 40 ó 50 m., se disponen unas pilas provisionales a fin de acortar los vanos de mayor longitúd. 4) Apoyos de neopreno-teflón: Facilitan el proceso de lanzamiento debido a su reducido coeficiente de rozamiento. 5) Dispositivos de lanzamiento: Proporcionan la fuerza de arrastre o de empuje para mover el puente en cada fase de lanzamiento. FASES DEL PROCESO VISTA DEL CONJUNTO DE LOS ELEMENTOS PLANTA DE FABRICACIÓN DEL TABLERO PICO DE LANZAMIENTO PILAS AUXILIARES APOYOS DE NEOPRENO-TEFLÓN DISPOSITIVOS DE LANZAMIENTO Separación de moldes: En el encofrado exterior se lleva a cabo por separación hacia fuera de los moldes o por giro desde unas articulaciones situadas en las esquinas inferiores. Los moldes interiores se separan retirando los burlones y los perfiles metálicos de apoyo. PICO DE LANZAMIENTO Planta y alzados. PICO DE LANZAMIENTO (cont.). Conexión entre pico y sección transversal. Dispositivos de anclaje en la sección. Vista compuesta LANZAMIENTO RIGIDIZADO CON TIRANTES Esquema del atirantamiento temporal. LANZAMIENTO RIGIDIZADO CON TIRANTES Fases del proceso de construcción. Arrastre con elevación del tablero Sistema híbrido de arrastre y empuje. ESQUEMAS DE POSTENSADO En los puentes lanzados hay dos tipos fundamentales de postensado: el que se lleva a cabo durante la construcción del puente con las sucesivas fases de lanzamiento y el que se realiza una vez que el puente ya está situado en su posición final. Las misiones de cada uno de ellos son: Postensado durante el lanzamiento: La misión de estos tendones es soportar el peso propio de la estructura. Ya que durante el lanzamiento el momento flector cambia de valor, e incluso de signo, en cada sección transversal, el objetivo de este postensado es mantener el puente en compresión compuesta. Postensado final: Una vez concluido el lanzamiento del puente los tendones de postensado instalados permiten soportar no solo la carga permanente, sino una parte de la sobrecarga de uso, usualmente no mayor del 50%. Para soportar la parte restante se añaden otros cables de postensado. POSTENSADO DURANTE EL LANZAMIENTO Tendones rectos interiores acoplados. Tendones rectos interiores solapados Tendones externos rectos. POSTENSADO FINAL Postensado interior. Postensado exterior. Geometrías de los cables. Postensado exterior. Esquema de desviadores. 56 interest among state DOT engineers. These presentations include the following: o A series of “brown bag” presentations was delivered to the Utah and Oregon DOT bridge engineering staff o An eight hour seminar devoted exclusively to bridge construction by incremental launching was presented at an ASCE conference in Sacramento in September 2007. o A presentation entitled “Incremental Launching of Bridges in Europe” was delivered at the Western Bridge Engineers Seminar in Boise, ID in September, 2007 o The design and construction of the innovative curved steel girder Kicking Horse Canyon Bridge was presented at the World Steel Bridge Symposium in December 2007 • Secure the assistance of specialty equipment manufacturers such as Hilman, VSL, Freyssinet, Enerpac and others to provide additional examples, details and technical assistance to support the use of incremental launching for appropriate project locations. • Promote cross-collaboration between concurrent and closely related research projects. The research team for the current study has recently been contracted through the Strategic Highway Research Program to serve as co-investigators on project R04 Innovative Bridge Designs for Rapid Renewal. During this study, additional investigation of accelerated bridge construction techniques will be performed with the intent of developing design specifications for rapidly constructed bridges. • Assist interested state DOT bridge owners in applying for funding for innovative bridge construction methods through the FHWA Innovative Bridge Research and Deployment program. This program has been established with the expressed intent of directing discretionary funding to projects which will yield tangible transportation and safety benefits. It is anticipated that a combination of these efforts, as well as the publication of a technical paper based on the results of the current study will be effective in generating interest within the US bridge community to consider the incremental launching method for appropriate project sites. 57 REFERENCES Baur, Willi, “Bridge Erection by Launching is Fast, Safe and Efficient”, Civil Engineering – ASCE, Vol. 47, No. 3, March 1977. Bergeron, J. and Laurie Sawicki, “The incremental adaptation of the Clifford Hollow Bridge”, Structural Engineer, May 2002. Bennett, M. and Taylor, A., “Woronoroa River Bridge, Sydney”, Structural Engineering International, Vol. 12, No. 1, February 2002. Durkee, Jackson L., “Railway Box-Girder Bridge Erected by Launching”, Journal of the Structural Division, ASCE, Vol. 98, No. ST7, Proc. Paper 9028, July, 1972, pp. 1443-1463. Durkee, Jackson, “Steel Bridge Construction”, pgs 45-58, Bridge Engineering Handbook, CRC Press, 2000. Engineering News Record, “Span Launched over Deep Gap”, Engineering News Record, Vol. 241, No. 22, December 14, 1998. Favre, R., Badoux, M., Burdet, O., Laurencet, P., “Incremental Launching fo the Ile Falcon Bridge”, Concrete International, Vol. 21, Issue 2, February 1999. Favre, R., Badoux, M., Burdet, O., Laurencet, P., “Design of a Curved Incrementally Launched Bridge”, Structural Engineering International, Vol. 9, Issue 2, May 1999. Gohler, Bernhard and Pearson, P., Incrementally Launched Bridges Design and Construction, Ernst and Sohn, Berlin, 2000. Granath, P., “Distribution of support reaction against a steel girder on a launching shoe.” Journal of Constructional Steel Research, Vol. 47, No. 3, pp. 245-270, 1998. Granath, P., “Serviceability limit state of I-shaped steel girders subjected to patch loading”, Journal of Constructional Steel Research, Vol. 54, No. 3/2000(A), pp. 387-408. Granath, P., Anders Thorsson, and Bo Edlund, “I-shaped steel girder subjected to bending moment and travelling path loading”, Journal of Constructional Steel Research, Vol. 54, No. 3, June 2000(B), pp. 409-421. Hewson, N. and Hodgkinson, A., “Incremental Launch of Brides Glen Bridge, Ireland”, Concrete, Vol. 38, Issue 7, 2004 LaViolette, M., “Pushing”, Structural Engineer, May 2003. 58 LaViolette, M., McDonald, D., “Landmark Launch”, Modern Steel Construction, February 2004. Lebet, J., “Composite Construction in Steel and Concrete V”, Proceedings of the 5th International Conference, July 2006. Llombart, J. A.and Jordi Revoltos, “Petra Tou Romiou Viaduct, Cyprus”, Journal of Structural Engineering International, Vol. 10, No. 4, pp. 233-234, November 2000. Malite, M., Takeya, T., Goncalves, R. and Jairo de Sales, J., “Monitoring of the Parana River Bridge During Construction”, Structural Engineering International, March 2000, pg. 193-196. Marzouk, Mohamed, Hisham Zein El-Dein and moheeb El-Said, “Application of computer simulation to construction of incrementally launching bridges”, Journal of Civil Engineering and Management, Vol. 13, No. 1, 2007, pp. 27-36. McGarth, R., “Concrete Thinking in Engineered Structures Stoney Trail Bow river Bridge”, Cement Association of Canada, 2002. McLaughlin, Mike., "The practical and portable British Bailey Bridge helped Allied troops remain on the march." Military Heritage Presents: WWII History, pp. 10-15, 76, 2005. Monsarrat, C.N., “Erection of French River Bridge – Canadian Pacific Railway”, The Canadian Engineer, June 5, 1908, pg. 400-404. Nader, M., Manzanarez, R., Lopez-Jara, J., De La Mora, C., “Launching of the San Cristobal Bridge”, Proceedings from the Transportation Research Board, 2007 Nahawi, K., and Banchik, C., “North Halawa Valley Viaduct Design and Construction”, Journal of Concrete International, Vol. 16, No. 2, pp. 39-43, February 1994. Paul, Alistair, “Large and Small Incrementally Launched Structures”, Transportation Research Record 1696, Paper No. 5B0060, Transportation Research Board, Washington D.C., 2000. Podolny, Walter and Jean M. Muller, Construction and Design of Prestressed Concrete Segmental Bridges, John Wiley and Sons, 1982. Ramakrishna, A. and Sankaralingam, C., “Panval Nadhi Viaduct, India”, Structural Engineering International, Vol. 7, No. 3, August 1997. Reina, P., “London Crews Launch Spans over Tracks with Little Room”, Engineering News Record, Vol. 255, No. 2, July 18, 2005. Rogowski, D., “Green Giant”, Bridge Builder, January-March 2003. Rosignoli, M., “Creep Effects During Launch of the Serio River Bridge”, Concrete International, Vol. 22, Issue 3, March 2000 59 Rosignoli, Marco, Launched Bridges: Prestressed Concrete Bridges Built on the Ground and Launched into Their Final Position, ASCE Press, 1998(A). Rosignoli, M., “Site Restrictions Challenge Bridge Design”, Concrete International, Vol. 20, No. 8, August 1998(B). Rosignoli, M. “Presizing of Prestressed Concrete Launched Bridges”. ACI Structural Journal, Title No. 96-S77, Vol. 96, No. 5, Sept-Oct 1999(A), pp. 705-711. Rosignoli, M. “Nose-Deck Interaction in Launched Prestressed Concrete Bridges”. Journal of Bridge Engineering, February 1998(C). pp. 21-27. Rosignoli, M. “Reduced-Transfer-Matrix Method of Analysis of Launched Bridges”. ACI Structural Journal, Vol. 96, No. 4. July-August 1999(B). pp. 603-608. Rosignoli, M.,“Monolithic Launch of the Reggiolo Overpass”, Concrete International, Vol. 29, No. 2, February 2001. Rosignoli, Marco. Bridge Launching. Thomas Telford Ltd, Parma, Italy, 2002. Rosignoli, M. and Rosignoli, C., “Launch and Shift of the Tiziano Bridge”, Concrete International, American Concrete Institute, October 2007, pp. 44-49. Saje, F. and Markelj, V., “Bandera Bridge, Slovenia”, Structural Engineering International, Vol. 7, No. 1, February 1997. Skeet, J., Lester, W., McClary, C., “Incremental Launch: The Stoney Trail Bridge:, Concrete International, Vol. 20, Issue 2, February 1998. Svensson, H.S., “Incremental Launching of Steel Bridges”, paper presented at World Steel Bridge Symposium, Chicago, IL, 2001. Swanson, David T, “Launching a Concrete Bridge Saves $200,000”, Concrete International, Vol. 1, Issue 4, April 1979. VSL Technical Report, ‘The Incremental Launching Method in Prestressed Concrete Bridge Construction”, April 1977, VSL International Ltd., Berne, Switzerland. Wipf, T.J., B.M. Phares, R.E. Abendroth, B. Chang and S. Abraham, “Monitoring of the Launched Girder Bridge over the Iowa River on US 20”, Final Report CTRE Project 01-108, Center for Transportation Research and Education, Iowa State University, Ames, IA 50010, March 2004. Zhuravov, L.N., O.I. Chemerinsky and V.A. Seliverstov, “Launching Steel Bridges in Russia”, Journal of International Association for Bridge and Structural Engineering (IABSE), Vol. 6, No. 3, 1996, pp. 183-186. A-1 APPENDIX A Database of Incrementally Launched Bridges Table A.1 provides an information summary of the bridges that have been previously described within this report in both the literature review and the case study sections. Following Table A.1 is information regarding an online database for launched bridges from around the world that will provide additional information. A-2 Table A.1. Launched bridge information Name Location Year Built Featured Crossed Superstructure Type Function / Usage Contractor Designer Owner U.S. 20 Iowa River Bridge Steamboat Rock, Hardin County, Iowa U.S.A. 2002 Iowa River Valley Steel I-girder Road bridge Jensen Construction HNTB Corporation Iowa Department of Transportation Stoney Trail Bridge Calgary, Alberta, Canada 1997 Bow River Double-celled concrete box girder Road bridge Walter & SCI Construction (Canada) Ltd. J.R. Spronken & Associates Ltd. City of Calgary Brides Glen Bridge Dublin, Ireland 2003 Brides Glen Valley 2-Post-tensioned concrete box girders Road bridge Main contr: ASCON; Subcontr: VSL Systems (U.K.) Ltd. and Tony Gee and Partners Roughan and O'Donovan; Tony Gee and Partners N/A Vaux Viaduct A1 Highway; Vaud, Switzerland 1999 Vaux Valley 2-Steel-concrete composite girder bridges Road bridge Steel: Zwahlen & Mayr SA; Prestressing: VSL International; Pot bearings and expansion joints: Mageba SA Giacomini & Joliet; Realin & Bader SA Etat de Vaud Serio River Bridge Bergamo, Italy N/A Serio River Double-cell precast box girder N/A N/A N/A N/A Woronora River Bridge New South Wales, Australia 2001 Woronora River Single-cell prestressed concrete box girder Road bridge Contr: Barclay Mowlem Pty. Ltd; Launching: Leonhardt Andra & Partner Structural: RTA & Taylor & Herbert Consultants Pty. Ltd.; Field: PERI Australia Roads and Traffic Authority of New South Wales Bandera Bridge Ljubljana-Trieste Highway, Slovenia 1995 Natural valley 2-Externally prestressed concrete box girder2 Road bridge SGP Primorje; Ajdovscina Viktor Markelj, Ponting Inc., Maribor Republic of Slovenia N/A= Information not available A-2 A-3 Table A.1 (continued). Launched bridge information Name Location Year Built Featured Crossed Superstructure Type Function / Usage Contractor Designer Owner San Cristobal Bridge Chiapas, Mexico 2006 Chentic Creek Canyon Curved steel composite and orthotropic box girder Road bridge Final Contr: Ingenieros Civiles Asociados Final Designer: T.Y. Lin International Mexican Secretary of Communication and Transportation Ile Falcon Bridge Valais, Switzerland 1998 & 1999 Rhone River 2-Curved prestressed concrete box girders Road bridge Ambrosetti & Zschokke; Freyssinet SA SD Ingenierie Deneriaz & Pralong Sion; Bureau d'ingenieurs SA; Andenmatten SA N/A Panval Nadhi Viaduct Konkan Railway, western India 1995 Panval Nadia Valley Prestressed concrete box girder Railway bridge Larson & Toubro Ltd. ECC Group; Wayss & Freytag AG, Germany Shrish Patel & Assoc. Ltd. Konkan Railway Corporation Ltd. Wabash River Bridge Covington, Indiana, U.S.A. 1977 Wabash River Double-cell prestressed concrete box girder Road bridge Roger Construction Co.; Weddle Brothers Construction Co. VSL Corporation, Los Gatos, Calif. Indiana Department of Transportation Clifford Hollow Bridge Moorefield, West Virginia N/A N/A Steel I-girder bridge Road bridge Dick Corporation Parsons; HDR Engineering West Virginia Department of Transportation Palizzi Overpass Milan, Italy N/A Six-lane railway Prestressed concrete box girder Road & tramway bridge Bonatti SpA. Marco Rosignoli Milan Underground Railway Authority Parana River Bridge Brazil N/A Parana River Two welded truss beams w/box cross sections Road & railway bridge N/A N/A N/A Reggiolo Overpass Reggiolo, Italy 2003 Verona- Mantua railway Multi-cellular prestressed concrete plate girder Road bridge N/A N/A N/A N/A= Information not available A-3 A-4 Table A.1 (continued). Launched bridge information Name Location Year Built Featured Crossed Superstructure Type Function/ Usage Contractor Designer Owner Petra Tou Romiou Viaduct Limassol-Paphos Highway, Cyprus 2001 Natural valley 2-Post-tensioned mono-cellular concrete box girders Road bridge China Wanbao Eng. Corp. Beijing; MeKano4, Barcelona EIPSA, Madrid Republic of Cyprus, Public Works Department Easton Bridge Cascade Mountains, Washington, U.S.A. N/A Yakima River & Hall Creek Steel I-girder Pedestria n & biking bridge Main contr: Boss Construction Co.; Subcontr: Engineered Transport and Lifting Co. N/A N/A Paddington Bridge London, England (U.K.) N/A Railway & subway Steel girder w/composite deck Road bridge Hochtief Construction Ltd. (U.K.) Cass Hayward Ltd., Chepstow Westminster City Ravensbosch Viaduct Maastricht and Heerlen Motorway, Netherlands N/A Valley of Strabekerv -loedgraaf 2-Single-cell post-tensioned concrete box girders Road bridge Internationale Gewapend Betonbouw; Societe Belge des Betons Bouvy, van der Vlugt, van der Niet, Scheveningen Provinciale Waterstaat Limburg Maastricht Port Wakefeild Road South Australia, Australia N/A Major highway 2-Single-cell prestressed concrete box girders Road bridge N/A N/A N/A Blanchetown Bridge Blanchetown, South Australia, Australia N/A Murray River Single-cell posttensioned concrete box girder Road bridge N/A N/A N/A N/A= Information not available A-4 A-5 During the completion of this work a comprehensive database related to bridge construction was identified. This database contains a specific subcategory of bridge construction related to launching bridges. The public database is located at http://en.structurae.de/structures/mtype/index.cfm?ID=3001. Several screen captures from the database are shown in Figures A.1 and A.2. To view project information, the database is setup to allow a user to browse by 1) name; 2) structural type; 3) function; 4) construction method; 5) geographic location; and 6) year of completion. The projects summarized in this report that were not previously contained in the Structurae database have been submitted to the webmaster for their entry into the database. A bridge owner/designer/contractor can contribute to the Structurae database by following the instructions on the website and filling out electronic submission forms or by sending pertinent data via email. The website does not accept anonymous submissions. Presented below is a list of bridges that were not described within this report due to insufficient information and were not found within the existing database. The bridges were, however, briefly mentioned by several references (Rosignoli, 1998(A), Rosignoli 2002, and Gohler, 2000). The bridges are as follows: • Ager Bridge, Austria • Amiens Viaduct, France • Boivre Viaduct, France • Boivre Bridge, Poitou-Charente, France • Bubiyan Bridge, Kuwait • Canyon Creek, Idaho, USA (2006) • Charix Viaduct, Rhone-Alpes, France • Charolles Bridge, Charolles, France • Dal Bridge, Avesta, Sweden • Hamburg Bridge, Utrecht, Netherlands • Juneau River, Juneau Alaska, USA (1999) • Kicking Horse Canyon Bridge, Canada • Kufstein Bridge, Germany • Lawyers Creek, Idaho, USA • Neckarburg Bridge, Baden-Württemberg, Germany • Queets River Bridge, Washington State, USA (1991) • Rio Caroni Bridge, Venezuela • Sathorn Viaduct, Bangkok, Thailand • Schnaittach Bridge, Germany • Schrotetal Bridge, Germany • Skye Bridge, Scotland • Val Restel Bridge, Italy • Veitschochheim Bridge, Bavaria, Germany • Wandre Bridge, Belgium A-6 • Yakima River Bridge, Washington State, USA (1999) • Zilwaukee River, Michigan, USA(1984) Lastly, a brief list of noteworthy bridges from other sources is presented, but again, insufficient information was found for report summaries. The bridges are as follows: • Chiapas I Bridge, Chiapas, Mexico • Damsumlo Bridge over Skeena River, Hazelton, British Columbia, Canada • North Halawa Valley Bridge, Oahu Island, Hawaii • Tai Po Bypass, Hong Kong Figure A.1. Partial list of database projects B-6 B-7 B-8 C-1 APPENDIX C Details of Incremental Launching Systems The selected sheets include examples provided by Hilman from previous projects along with a sheet on their jack/roller bridge launching unit. This unit combines both vertical lift capabilities (e.g. for jacking up the girders to insert permanent bearings) along with horizontal thrust to provide launching force component. This information is provided at the risk of appearing to endorse a commercial product, which is not the case. The fact is that they are THE heavy moving specialists for this kind of application and have many rollers that have been widely used and proven over time. C-2 C-3 C-4 C-5 C-6 C-7 D-6 D-7 D-8 D-9 D-10 D-11 D-12 D-13 D-14 E-1 APPENDIX E Example Specifications for Steel Erection by Launching The following example Special Provision is from the U.S. 20 Iowa River Bridge incremental launching project in Iowa. The specification is for erection of the steel superstructure by launching. This specification is provided as an example which may be useful to owners considering a special erection process and addresses the types of information the contractor may be required to submit in support of his erection engineering proposal. Incremental Launching Challenges on Mount Henry Bridge, Wenham Page 3 of 10 lower cantilevers of the two bridges would be approximately 185mm for the entire length of the bridge. Extensive survey was carried out to ensure these clearances could be achieved for launching the new bridge along a circular curve. A number of factors influenced the final shape of the cross section, including functional requirements for the deck and a lower level shared path, aesthetic requirements, structural design requirements, and construction requirements. The existing Mount Henry Bridge is considered to be an important Perth landmark because of its location and unique aesthetic qualities which meant the architectural requirement for the new bridge to complement the existing bridge was of utmost importance. The final structural form was heavily influenced by Leighton Contractors’ architect, Parry & Rosenthall Architects, in combination with Main Roads’ architect. The Leighton Contractors team had a two year contract to carry out the Package E works which included the design and construction of the new Mount Henry Bridge as well as strengthening of the existing bridge. To minimise impact on the heavily trafficked Freeway, the northbound carriageway had to be moved to the new bridge before the majority of the modification works to the existing bridge could be carried out, hence both lots of work could not be carried out concurrently which put additional pressure on the already tight schedule. From the outset, the realisation was that the timeframe for the project was exceptionally tight and this factor guided a lot of the decision making throughout the job. 3. CONSTRUCTION METHOD Initially a number of construction methods were put forward for consideration. These included incremental launching, segmental balanced cantilever, and segmental spanby-span. The original Mount Henry Bridge was constructed using a segmental spanby-span approach. However in the case of the new bridge, segmental methods were not preferred because of the difficulty in handling and placing segments to fit around the old bridge. Other reasons for not using segmental construction included: the additional prestress resulting from the requirement for net compression across segment joints; and more importantly, incremental launching was considered to be a quicker construction method for the size of the project. Once incremental launching was selected as the preferred construction method, the next decision to be made was whether or not to utilise temporary intermediate supports during the launch. Launching unsupported over 76m spans with a 4m deep section was outside the known experience of the team so relatively early it was decided that temporary piers were required. By using temporary intermediate supports to achieve 38m launched span lengths, Leighton Contractors was able to re-use an existing launch nose, albeit with some modification. This not only saved money on the launch nose, but also reduced setup time. The use of temporary supports also gave the construction team tighter control over displacements during launching which was critical in ensuring the new bridge would not contact the old bridge during construction. In addition, the shorter spans required less concentric prestress which had cost and time benefits, as discussed later. For Leighton Contractors in this case, the benefits of adopting the shorter spans were significant. Incremental Launching Challenges on Mount Henry Bridge, Wenham Page 4 of 10 4. TEMPORARY PIERS 4.1 Piles A major challenge that faced the team was to design a temporary pier system that was cost effective and would not delay the works with deck construction expected to closely trail the pier construction. The preference was to use similar steel pile sections used for the permanent piers as they could be procured relatively quickly. Two similar thin walled circular hollow section sections were available, the larger of which was a 660mm diameter pipe with a wall thickness of 11.6mm fabricated from steel with a yield strength of 448MPa. Geotechnical investigation by Coffey (Package E Design Reports) confirmed previous test results and showed there was a layer of weak Swan River Alluvium, up to 25m deep, overlying a strong South Perth Siltstone. The soft alluvium layer was expected to provide little lateral restraint to the piles, which meant the most critical temporary pier piles would be effectively unsupported for almost 30m from the top of the siltstone to the underside of the headstock beams. Buckling analysis of the pier frame, using lateral soil spring values provided by Coffey, revealed that the alluvium layer did in fact provide some restraint against buckling, however the effective length (Le) of the piles was in the order of 23m (refer Figure 2). The modified member slenderness (λn) of the piles was calculated to be 135, hence the section would be only about 35% efficient for pure compression. Based on this assessment, a minimum of seven piles was required at each temporary pier just to carry the vertical loads during launching and even more to resist the longitudinal bearing friction forces. Propped Le = 12m Free Standing Le = 23m Figure 2: Temporary pier buckling modes (frame model with soil springs) Incremental Launching Challenges on Mount Henry Bridge, Wenham Page 5 of 10 A number of pile options were considered, including the use of raking piles and bracing between the piles, but for all cases a minimum of seven piles was required. To meet the construction schedule, six piles was considered to be a realistically achievable upper limit. A significant structural improvement could be made by propping the top of the temporary piers in the longitudinal and transverse directions thus halving the effective length of the piles (Le = 12m) and doubling the effective member capacity to almost 70 percent of the section capacity (again refer Figure 2). In addition to improving the buckling behaviour, propping also meant the temporary piers were not required to resist the longitudinal bearing friction loads. One option for propping the temporary piers that was considered was to connect them to the existing bridge. However connecting the two structures raised the concern that a potential failure of the temporary piers could occur with expansion or contraction movement of the existing bridge which would drag the attached temporary piers with it, thereby putting bending moments into the piles caused by forced displacement and second order effects. 4.2 Bracing The final solution to the temporary pier problem was unusual, but suited this particular situation. It involved connecting the temporary piers in the transverse direction to the existing bridge using a flexible prop system capable of accommodating the longitudinal movements, and in the longitudinal direction to the permanent piers. Longitudinal connection was made by running prestress strands between the temporary and permanent piers so that each temporary pier was tied to both adjacent permanent piers. By bracing in this way, each temporary pier was able to be constructed with just four piles. Figure 3 shows the temporary pier arrangement with cable bracing to the permanent piers and lateral prop to the existing bridge. Although bracing dramatically improved the performance of the temporary piers, the safety of the system was still reliant on the soft soil providing some lateral restraint to the piles. A simple test procedure was developed to assess the actual insitu restraint conditions. The test, carried out at three of the critical temporary piers, involved strapping two piles together near the top of the piles and pulling them towards each other to simulate lateral loading on the individual piles. Measurements taken for increasing levels of loading and sustained loading were used to assess the immediate and long term soil restraint respectively. The results for each test showed that the short term stiffness of the soil was considerably higher than the long term stiffness due to creep effects but also proved that the actual lateral restraint of the piles in the long term was safely higher than the original design predictions. This gave the design team considerable confidence to proceed with the four pile arrangement. To ensure each temporary pier would stand vertical with the strands tensioned to a relatively uniform stress, a sequence had to be derived for stressing the cable bracing at each temporary pier. This calculation required an estimate of the effective Incremental Launching Challenges on Mount Henry Bridge, Wenham Page 6 of 10 stiffness of the pier, including interaction with the soil, for loading in the longitudinal direction which was then modified for the stiffness of the other connected piers and for each strand as it was added. The stiffness interaction model was used to predict the stress in the strands and the movement of the temporary piers during each stage of stressing but was sensitive to the geotechnical assessment of the lateral soil spring values. Figure 3: Temporary pier with cable bracing to adjacent permanent piers The movements of each temporary pier were measured during stressing of the cables which provided additional confirmation of the soil stiffness values and enabled further calibration of the temporary pier models, carried out as the stressing operation proceeded. The piers were stressed from alternating sides hence stressing for each stage pulled the temporary pier in one direction while the subsequent stage pulled it back in the opposite direction. For each temporary pier, movement from the first stage of stressing was recorded and reported back to the designer who used the information to reassess the effective pier stiffness, which was then fed back into the model to generate a revised stressing sequence. In all cases, the results again confirmed that the geotechnical engineer’s estimate of the lateral soil stiffness values was safely conservative. 4.3 Presetting the Supports With propping at the top, the temporary piers would theoretically work, but only marginally and it was critical that the soft alluvium stratum provided sufficient lateral restraint. To improve the safety of the system, it was decided to relieve load from the temporary piers during launching. This was achieved by setting the launching bearings on the temporary piers so that when fully loaded, they would sit lower than the adjacent permanent pier supports. Effectively, the deck support level at the permanent piers would be on the theoretical circular launch line, while the support level at the temporary piers would be a nominal 15mm below the theoretical launch line. Because the temporary piers, comprising four piles, were considerably less stiff Incremental Launching Challenges on Mount Henry Bridge, Wenham Page 7 of 10 vertically than the permanent piers, comprising between 14 and 18 piles, the temporary pier supports were initially set 5mm above the line of the permanent pier supports to end up slightly below as required. The relative displacement between the supports meant that additional bending moments were imposed on the deck, which had to be designed for. Modelling also had to include the effects of presetting the supports and the relative movement of the supports at all stages of launching allowing for the differential vertical stiffness of the permanent and temporary piers. During launching, the settlements at all supports were monitored with periodic survey. The results were reported to the designer who used them to calibrate the design models, adjust subsequent vertical preset values, and carry out structural checks for various stages of construction. Shim plates provided a mechanism for adjusting the height of the temporary bearings up or down if required. In this way it was possible to ensure the structure was operating within safe ranges during the entire launch. 5. BRIDGE DECK 5.1 Two Part Construction Staging With the substructure designed, the challenge then was to optimise the deck construction. Each incremental segment length was 25.4m, which allowed manageable concrete pour sizes and optimal speed of construction. The segment length, being one third of the main span length, also allowed the section to be changed to incorporate thicker webs over the permanent piers, which meant the section could be kept relatively light within the spans. Bottom flange and webs constructed in back half of casting bed Top flange constructed in front half of casting bed Figure 4: Staging of deck construction in casting bed Incremental Launching Challenges on Mount Henry Bridge, Wenham Page 8 of 10 The segment length was also selected to achieve a two part construction staging of the section within the available area at the launching end. The casting bed was two segments in length to allow for simultaneous work on two fronts. The bottom flange and webs were cast in the back half of the casting bed. Once completed, the deck was launched thereby shifting the partially completed section to the front of the casting bed. While the top flange of the segment was being completed in the front half of the casting bed, the bottom flange and webs of the next segment were being constructed in the back half (refer Figure 4). 5.2 Concentric Prestress To further improve the speed of construction, Leighton Contractors sought to minimise the launching prestress operations. This was achieved by running each concentric prestress cable for three segment lengths equal to one main span length (76m). Hence for the construction of each segment only one third of the concentric prestress had to be applied. This meant that the completed section had just one third of the full concentric prestress when launched from the casting bed and did not have the full prestress until the two subsequent segments had been constructed and stressed. Analysis showed that the section could carry the loads from the first two launches without the full concentric prestress. Again, modelling included the presetting and subsequent settlement of the supports as the bridge was launched over. The use of temporary piers facilitated the concentric prestress arrangement by reducing the total prestress required and lowering the stresses in the deck over the length without full prestress. 6. COMPLETION OF NEW BRIDGE With launching completed and the bridge securely anchored in position, a number of finishing works were still required to make the bridge operational. Included in these were: • Bearing changeover at permanent piers. This operation required the bridge to be jacked off the launching bearings and lowered onto the permanent bearings. • Application of continuity prestress. The effect of applying the continuity prestress was to lift the bridge at the temporary pier supports thus reducing the load at these supports and shifting load to the permanent piers. • Lowering of temporary piers, transferring all load to the permanent piers. • Deck works such as construction of barriers and asphalting applying additional load to the structure. Careful analysis of these works was required to ensure the bridge was not overstressed and the temporary piers were not overloaded during the process. However it was important not to place too many restrictions on the staging of the works to facilitate construction on a number of simultaneous fronts to meet the schedule. So as not to overload the launching bearings at the permanent piers, the bearing changeover at each pier was required to be carried out prior to applying any of the continuity prestress in the spans adjacent to the pier. However, with only concentric prestress applied and with the permanent pier supports already preset higher than Incremental Launching Challenges on Mount Henry Bridge, Wenham Page 9 of 10 the temporary piers, a limit had to be set on the jacking height to ensure the bridge capacity was not exceeded. The continuity prestress was applied in stages after the permanent bearings in the adjacent piers had been installed and before the temporary piers could be lowered. To ensure the final deck works were not adversely affected by subsequent deck displacements, particularly the barriers, a restriction was put in place which limited deck works to at least one span away from any temporary piers still supporting the deck. Figure 5 shows the bridge site before, during and after construction of the new Mount Henry Bridge which was opened to traffic in January 2006. Note that the temporary piers are still in place but are not supporting the bridge deck in the final photo. Old Mount Henry Bridge Mount Henry Bridge During Launching Completed Mount Henry Bridge Figure 5: Before, during and after construction of new Mount Henry Bridge Incremental Launching Challenges on Mount Henry Bridge, Wenham Page 10 of 10 7. CONCLUSION Although incremental launching is not a new technology in bridge construction, each job has its own challenges and launching the New Mount Henry Bridge was no exception. The positioning of the new bridge partially overhanging the old bridge necessitated the use of temporary piers to control deflections. Due to the slenderness of the piles in the soft river alluvium, the temporary piers required a unique bracing system which utilised the reserve strength of the permanent piers and the adjacent bridge. Continuous monitoring during construction helped to confirm the design assumptions and improve predictions of structural behaviour for subsequent construction phases. Testing and monitoring of the insitu lateral temporary pier behaviour enabled a firmer understanding of the soil properties, and recording the vertical pier movements enabled the designer to continuously check that the piers and deck were not overloaded. The efficient design of the temporary piers, the two part construction staging of the deck, and the concentric prestress arrangement all contributed to the swift construction of the new Mount Henry Bridge, which was opened to traffic two years after the design and construct contract was let. ACKNOWLEDGMENTS The author and Wyche Consulting would like to acknowledge the efforts of the new Southern Suburbs Railway Package E team including: • Leighton Contractors (principal contractor); • Coffey Geosciences (geotechnical consultant); • GHD (civil/structural engineering consultant); • Hawkins Engineering (construction consultant); • Parry & Rosenthal Architects (civil/structural architect); and • Main Roads Major Projects. IMPLEMENTATION OF INCREMENTAL LAUNCHING IMPLEMENTATION OF INCREMENTAL LAUNCHING ANALYSIS IN ANALYSIS IN GT GT STRUDL STRUDL USING THE USING THE PARAMETERIZATION PARAMETERIZATION Dmitry Maslov Dmitry Maslov Institute Giprostroymost Saint Institute Giprostroymost Saint- -Petersburg, Petersburg, Russian Federation Russian Federation http://www.gpsm.ru http://www.gpsm.ru Incremental Launching is the most commonly used method Incremental Launching is the most commonly used method for bridge erection in Russia. for bridge erection in Russia. Cantilever and floating methods are used for large Cantilever and floating methods are used for large structures like cable structures like cable- -stayed or arch bridges but they are stayed or arch bridges but they are rarely build nowadays. rarely build nowadays. Thus, almost every project of a bridge involves the analysis Thus, almost every project of a bridge involves the analysis of incremental launching process. of incremental launching process. 2 2 9 9 There are many ways to calculate the necessary data. For There are many ways to calculate the necessary data. For example we drew piers and beam in AutoCAD, then moving example we drew piers and beam in AutoCAD, then moving the the “ “beam beam” ”along the along the “ “piers piers” ”we found required coordinates. we found required coordinates. The same operation The same operation could be easily could be easily performed in Excel. performed in Excel. It does not seem a It does not seem a hard problem if we hard problem if we have enough time to have enough time to solve it. solve it. 10 10 There was a bridge being launched over a river near the city There was a bridge being launched over a river near the city of Vologda. 105 meters long central span and a temporary of Vologda. 105 meters long central span and a temporary pier decreasing the span to 97 meters promised no troubles. pier decreasing the span to 97 meters promised no troubles. But the surveying monitoring reported that the launching But the surveying monitoring reported that the launching nose had approached the temporary pier one meter higher nose had approached the temporary pier one meter higher than it was supposed to. than it was supposed to. One meter, whereas One meter, whereas we could allow no we could allow no more than 25 cm, or more than 25 cm, or we would start we would start developing a project developing a project for cleanup the river for cleanup the river- - bed from the bridge bed from the bridge wreckage. wreckage. 11 11 For three days we tried to figure out whether our For three days we tried to figure out whether our “ “patient patient” ” was alive rather than dead, or dead rather than alive. was alive rather than dead, or dead rather than alive. For three days we considered how to proceed with the For three days we considered how to proceed with the launching. launching. For three days the cantilever was wobbling with the wind, and For three days the cantilever was wobbling with the wind, and the stresses were very close to the ultimate critical value. the stresses were very close to the ultimate critical value. 12 12 Finally we managed to discover that the builders had Finally we managed to discover that the builders had bolted the nose to the span incorrectly and it was bolted the nose to the span incorrectly and it was possible to go on after raising the top of temporary pier. possible to go on after raising the top of temporary pier. 13 13 We built a bridge with 147 meter long central span over the We built a bridge with 147 meter long central span over the main navigable channel connecting the basin of the Volga main navigable channel connecting the basin of the Volga river with the White and Baltic seas. river with the White and Baltic seas. Because of that no temporary pier was allowed within the Because of that no temporary pier was allowed within the central span. As it was prohibited inside, we placed central span. As it was prohibited inside, we placed temporary piers outside the central span and put the temporary piers outside the central span and put the receiving beam on them. receiving beam on them. 14 14 The structure behavior after the connection was strictly The structure behavior after the connection was strictly dependent on the angle with which the nose would be dependent on the angle with which the nose would be bolted to the receiving beam. bolted to the receiving beam. It so happened that the cantilever displacements did not It so happened that the cantilever displacements did not match their theoretical values. match their theoretical values. At each move we stopped At each move we stopped launching to perform analysis launching to perform analysis for the current situation. for the current situation. Each step took about an hour Each step took about an hour to analyze with drawing to analyze with drawing scheme and transferring data scheme and transferring data from one application to from one application to another. another. 15 15 At that time the builders were tossing stones into the At that time the builders were tossing stones into the water and watching the spreading circles. water and watching the spreading circles. The difference between the theory and the practice grew The difference between the theory and the practice grew larger from one move to another until we found out that a larger from one move to another until we found out that a cradle was dangling right at the launching nose tip. cradle was dangling right at the launching nose tip. When it was removed all the coordinates became exactly as When it was removed all the coordinates became exactly as predicted. predicted. 16 16 We figured out that we had to improve the process in order We figured out that we had to improve the process in order to decrease time needed to complete the calculations, to decrease time needed to complete the calculations, especially for a bridge being monitored during the especially for a bridge being monitored during the launching. launching. We decided to apply a We decided to apply a technique called technique called “ “parameterization parameterization” ” that we successfully that we successfully used for solving other used for solving other problems. problems. 17 17 status support status support - - #for var s = 0 to #for var s = 0 to NumPier NumPier - -1 1 #if ( #if (sn[s sn[s] == ] == - -1) or ( 1) or (sty[s sty[s] == 0) ] == 0) then continue then continue ' 'N N%&d %&d 1000+sm[s]% 1000+sm[s]%' ' - - #next #next #back 1 #back 1 joint releases joint releases #var Flag = true #var Flag = true #for var s = 0 to #for var s = 0 to NumPier NumPier - -1 1 #if ( #if (sn[s sn[s] == ] == - -1) or 1) or \ \ ( (sty[s sty[s] == 0) then continue ] == 0) then continue #if Flag then #if Flag then ' 'N N%&d %&d 1000+sm[s]% 1000+sm[s]%' mom z ' mom z #Flag = false #Flag = false #continue #continue #endif #endif ' 'N N%&d %&d 1000+sm[s]% 1000+sm[s]%' for x mom z ' for x mom z #next #next status support status support - - 'N1228' 'N1228' - - 'N1246' 'N1246' - - 'N1194' 'N1194' joint releases joint releases 'N1228' mom z 'N1228' mom z 'N1246' for x mom z 'N1246' for x mom z 'N1194' for x mom z 'N1194' for x mom z Î Î What is parameterization? What is parameterization? It is nothing but a facility of It is nothing but a facility of using mathematical using mathematical expressions as well as expressions as well as numeric constants in numeric constants in analytical model. analytical model. It is nothing but a facility of It is nothing but a facility of using programming using programming statements such as loops statements such as loops and conditionals as well as and conditionals as well as commands of GT commands of GT STRUDL STRUDL problem oriented language. problem oriented language. 18 18 We developed an application We developed an application to extend the command to extend the command language, to turn the making language, to turn the making of an analytical model a bit of an analytical model a bit into the programming. into the programming. The program has a script The program has a script language with built language with built- -in features in features as befit a programming as befit a programming language. language. So we are able to prepare a So we are able to prepare a model and, when necessary, to model and, when necessary, to modify it easily changing only modify it easily changing only a few parameters instead of a few parameters instead of altering the entire model. altering the entire model. In other words we developed a tool to make In other words we developed a tool to make “ “custom wizards custom wizards” ”. . 25 25 There was something which suspended the analysis: we had There was something which suspended the analysis: we had to deal with pier detachments manually because it is to deal with pier detachments manually because it is impossible to use absolutely rigid unilateral supports. impossible to use absolutely rigid unilateral supports. When we found a negative support reaction we excluded the When we found a negative support reaction we excluded the pier from the model and repeated analysis watching for pier from the model and repeated analysis watching for negative joint displacement which was the sign that the pier negative joint displacement which was the sign that the pier was really attached. was really attached. And so on and on and on, until the process converged. And so on and on and on, until the process converged. 26 26 This winter, during the launching of a bridge over a river in This winter, during the launching of a bridge over a river in Western Siberia, 114 meter long cantilever collapsed and lay Western Siberia, 114 meter long cantilever collapsed and lay on the pier it had been hanging above. on the pier it had been hanging above. The steel samples taken near the breach proved that the The steel samples taken near the breach proved that the material conformed to all the requirements. The Institute material conformed to all the requirements. The Institute Giprostroymost was commissioned to make expert Giprostroymost was commissioned to make expert examination and inquire whether the accident had occurred examination and inquire whether the accident had occurred due to some calculation incorrectness. due to some calculation incorrectness. 27 27 We applied our We applied our “ “launching wizard launching wizard” ”and managed to confirm and managed to confirm all analytical statements and perform complete analysis for all analytical statements and perform complete analysis for further launching after mending the breach. It took two further launching after mending the breach. It took two weeks as scheduled. weeks as scheduled. Actually there were no analytical errors and the bridge Actually there were no analytical errors and the bridge crashed because of stress concentration after violation of crashed because of stress concentration after violation of welding technologies. welding technologies. 28 28 The second problem of incremental launching arises when the The second problem of incremental launching arises when the analysis is completed. How should we work up megabytes of analysis is completed. How should we work up megabytes of the results? We need the envelope for forces, moments, and the results? We need the envelope for forces, moments, and reactions. Also we need joint coordinates in deformed reactions. Also we need joint coordinates in deformed configuration at every step. configuration at every step. We developed a post We developed a post- -processing application to deal with the processing application to deal with the results taken from the text files created by COUTPUT command. results taken from the text files created by COUTPUT command. The program reads data from a group of text files and transmits The program reads data from a group of text files and transmits to Excel the information in the proper form. to Excel the information in the proper form. 29 29 In order to feed the post In order to feed the post- -processor with necessary information processor with necessary information the the “ “launching wizard launching wizard” ”writes to the resulting files the output writes to the resulting files the output of MEMBER FORCES, LIST DISPLACEMENTS, and LIST of MEMBER FORCES, LIST DISPLACEMENTS, and LIST REACTION commands. Also it writes additional information: REACTION commands. Also it writes additional information: correspondence between pier numbers and supported joint correspondence between pier numbers and supported joint identifiers, joint coordinates in non identifiers, joint coordinates in non- -deformed configuration, deformed configuration, and section modulus (to build stress envelopes). and section modulus (to build stress envelopes). The program works very The program works very fast and delivers from fast and delivers from possible errors which possible errors which might occur during the might occur during the manual data transferring. manual data transferring. 30 30 The technique we invented allows us to dramatically improve The technique we invented allows us to dramatically improve the performance of incremental launching analysis. the performance of incremental launching analysis. It can be applied to any bridge, even for spatial models It can be applied to any bridge, even for spatial models including plate finite elements. including plate finite elements. There are no limits but engineering mind and experience. There are no limits but engineering mind and experience. 31 31 A language to describe an analytical model is a great feature. A language to describe an analytical model is a great feature. A language like GT A language like GT STRUDL STRUDL’ ’s sis a greater feature. And a language is a greater feature. And a language with parameterization is one of the greatest facilities which with parameterization is one of the greatest facilities which expand the class of problems to be solved with a program. expand the class of problems to be solved with a program. Unfortunately there are not so many programs having Unfortunately there are not so many programs having parameterization (or what it parameterization (or what it’ ’s called) as a built s called) as a built- -in feature. And in feature. And their price grows more than a hundred thousand dollars and more. their price grows more than a hundred thousand dollars and more. The parameterization is a useful and convenient tool for us. And The parameterization is a useful and convenient tool for us. And we think it could be useful for other GT we think it could be useful for other GT STRUDL users. STRUDL users. Of course, the creation of parameterized analytical models Of course, the creation of parameterized analytical models demands a more competent engineer. But the skill comes quickly demands a more competent engineer. But the skill comes quickly because the parameterization language is much easier than because the parameterization language is much easier than BASIC. Anyone who knows what BASIC. Anyone who knows what ‘ ‘variable variable’ ’means, anyone who is means, anyone who is able to input a formula, is able to use the parameterization. able to input a formula, is able to use the parameterization. 32 32 Our recommendations for future GT Our recommendations for future GT STRUDL development: STRUDL development: 1. 1. GENERATE and REPEAT commands to create a group of rigid bodies a GENERATE and REPEAT commands to create a group of rigid bodies as s well as finite elements. well as finite elements. 2. 2. ACTIVE and INACTIVE commands for rigid bodies. ACTIVE and INACTIVE commands for rigid bodies. 3. 3. Drawing rigid bodies as lines from the master joint to the slave Drawing rigid bodies as lines from the master joint to the slaves. (!) s. (!) 4. 4. Keeping SLAVE RELEASES information while saving the text in Keeping SLAVE RELEASES information while saving the text in GT GT MENU. (!) MENU. (!) 5. 5. A command like A command like LOAD LIST MEMBER LOAD LIST MEMBER ‘ ‘M1 M1’ ’MAX FORCE X MAX FORCE X that that means means “ “find the loading in which axial force of member find the loading in which axial force of member ‘ ‘M1 M1’ ’is is maximal and make that loading active for the results output. maximal and make that loading active for the results output. 6. 6. A command like A command like LIST ENVELOPE MIN MOMENT Z <members> LIST ENVELOPE MIN MOMENT Z <members> that means that means “ “print member forces for loadings in which bending print member forces for loadings in which bending moments along Z moments along Z- -axis are minimal axis are minimal” ”. . 7. 7. Displaying the directions of element principal stresses in GT Displaying the directions of element principal stresses in GT MENU. MENU. 8. 8. UNDO and REDO in GT UNDO and REDO in GT MENU. (!) MENU. (!) 9. 9. More than 8 character long identifiers. (!) More than 8 character long identifiers. (!) 33 33 Our recommendations for future GT Our recommendations for future GT STRUDL development (cont): STRUDL development (cont): 10. 10. Writing animation into a sequence of bitmap files. Writing animation into a sequence of bitmap files. 11. 11. SELF WEIGHT command for finite elements in Command Mode which SELF WEIGHT command for finite elements in Command Mode which generates joint loads (as GT generates joint loads (as GT MENU does). (!) MENU does). (!) 12. 12. Subtraction of different sign loads rather than composition of Subtraction of different sign loads rather than composition of them at them at the creation of masses for dynamic analysis. the creation of masses for dynamic analysis. 13. 13. TERMINATE command to quit GT TERMINATE command to quit GT STRUDL immediately with no STRUDL immediately with no question dialog boxes. (!) question dialog boxes. (!) 14. 14. Axial local loads for truss members. Axial local loads for truss members. 15. 15. Allowing MEMBER RELEASES in stability analysis. Allowing MEMBER RELEASES in stability analysis. Stability analysis Stability analysis for plane models. (!) for plane models. (!) 16. 16. LIST DISPLACEMENT command which does not pick out supported LIST DISPLACEMENT command which does not pick out supported joints. joints. 17. 17. Improving text selection in Command Mode and developing Improving text selection in Command Mode and developing rectangular selection facility. (!) rectangular selection facility. (!) 18. 18. “ “Automatic groups Automatic groups” ”: all objects with the same prefix in identifier : all objects with the same prefix in identifier being an implicitly defined group named as the prefix. being an implicitly defined group named as the prefix. VSL THE INCREMENTAL LAUNCHING METHOD IN PRESTRESSED CONCRETE BRIDGE CONSTRUCTION APRIL 1977 VSL INTERNATIONAL LTD. Berne / switzerland The length of one increment depends firstly upon this programme and secondly upon design and cost considerations. From the design viewpoint it is desirable for the construction joints to be located at sections of low stress, that is near the points of zero moment. This means, however, that the pier diaphragms must be installed later. If this is to be avoided, the subdividing of the units must be done in such a way that each pier diaphragm is located at the front of the increment to be concreted. This however involves a departure from the principle of locating the joints in lightly stressed cross-sections. To use the repetition effect to maximum advantage, a whole number of increments should fall in one span. The length of a unit is finally influenced also by the costs, since the total costs of formwork and forward jacking should be a minimum; this is the case when the equation B = Kv .Kb-1.L is satisfied, in which B = length of formwork in m, Kv = cost for one forward jacking (including the costs for hire and operation of equipment, operation of temporary bearings, joint forming, couplers for the central prestressing tendons and stressing of them), Kb = cost per metre run of formwork (including costs for foundations, formwork facing, supporting structures and pulling strands), L = total length of bridge to be constructed. The satisfying of all these conditions often results in the length of a unit being a half-span; depending upon the size of cross-section and length of span, it may be necessary to choose an increment smaller than this (for example 1/3 or 1/4 of span). In the normal case, the length of an increment is from 15 to 25 m. 3.4. Prestressing It has already been mentioned that we must distinguish between central prestressing and continuity prestressing. 3.4.1. Central prestressing The tendons for central prestress are usually located in the deck slab and bottom slab (or in double T-beams at the bottom of the web) in a quantity inversely proportional to the distances between centroid of tendons and centroid of section. The prestressing tendons are usually made up of small units, of up to about 1000 ki`I (100 t) working load (that is up to VSL 5-7), since the dimensions of the two slabs permit only small anchorages to be used. The tendons in the upper slab are coupled and stressed only in each alternate unit and those in the lower slab in every third (possibily every second) unit alternately, which results in an economic sequence of work for the stressing team, resulting in reduced costs. The assembled tendons for the upper slab may be reeled onto drums and the drums suspended from a trestle (fig. 11), to enable other operations to continue unimpeded. Fig. 11: Trestle for tendons for deck slab 6 Fig. 10: Cable arrangement (central and continuity prestressing) In the past, bar systems have often been used instead of cables for the central prestress. The bars were then lengthened at each unit by couplers; they were stressed, however, only at every second or third increment. In exceptional cases, the central prestress is provided by cables which are not concreted in but are located outside the concrete cross-section. Anchoring buttresses are then used as the stressing points. This arrangement is adopted when it is necessary to remove the cables for the completed state, to prevent the stresses becoming too high. This case can arise with large spans and a relatively shallow bridge superstructure. 3.4.2. Continuity prestressing The continuity tendons, which are normally located in the webs and terminate at anchoring buttresses on their inner faces, are plulled or pushed through later and are not stressed until the bridge has been completely launched. These cables are larger units and usually have stressing anchorages (in the VSL system: type E) at both ends. This does not however mean that they must be stressed at both ends, since single-end stressing may be sufficient depending upon the friction conditions. For the latter case, the VSL prestressing system offers an alternative solution by the use of the dead-end anchorage type H (fig. 12): The strands of the continuity tendons are pushed through one by one from the stressing anchorage, as soon as the unit in which the H-anchorages are situated is in the formwork. The dead-end anchorage is formed insitu and concreted in. Since stressing cannot be carried out until some time later, temporary corrosion protection is necessary. 3.4.3. General remarks With the incremental launching method, the total quantity of prestressing steel is in general some 40 to 60 0/o higher than for bridges constructed on falsework, due to the provision of both central and continuity prestressing. The resultant additional costs are, however, more than compensated by savings in formwork and labour costs. Double T-beam bridges require more prestressing steel than boxsection bridges, but are very simple to construct. In addition to the longitudinal prestressing, transverse and vertical prestressing may also be necessary. Prestressed cables are also used for attaching the temporary nose. 3.5. Auxiliary equipment Various auxiliary equipment and components are necessary for the incremental launching method. A pulling device rather than a pushing device is more sui- Fig. 13: VSL-jacks with suporting structure Fig. 12: Continuity tendons with H-anchorages table for applying the forward movement; this principle is used, for instance, in the VSL system (see also fig. 3). The VSL jacks bear against a steel support structure, which in turn is anchored to the abutment (fig. 13). Before each forward movement, a further auxiliary structure of steel beams (termed pick-up beams) is placed at the end of the just completed unit, to which the strand cables are attached. At the abutment the cables pass through the centrehole jacks and can be easily withdrawn after each launching operation. The speed of forward movement depends upon the types of jacks and pumps used and is from 3 to 6 m/h. Further auxiliary components include the temporary sliding bearings (or special sliding surfaces on the permanent bearings) and the lateral guides (fig. 14). Fig. 14: Temporary sliding bearing with lateral guide The temporary bearings usually consist of a high-quality concrete block covered with a stressed chrome-steel plate. The surface of the block must be of such a shape that the sliding plates can be inserted without difficulty. It must be remembered that the sliding plates, which are of steel-reinforced neoprene with a teflon coating on one face, become slightly compressed under the load. In order to remove the temporary bearings when transferring the bridge onto the permanent bearings or in order to remove the sliding plates and chrome-steel plate (when the bridge is launched over the permanent bearings), jacks are used. The jacks are positioned alongside the temporary bearings beneath the webs or beneath the pier diaphragm, depending upon which of these locations will provide sufficient space for the jacks and the necessary operating access to them. 7 The forward end of the temporary nose is so designed that, in spite of the deflection, it can ride gently and reliably onto the pier. Either the underside bearing surface is rounded vertically at the forward end or there is an upward hinging end piece which, when the nose meets the pier, is pressed into the horizontal position by jacks. Even when the cantilever moment is relieved by mast guying, a short nose with a rounded running surface is fitted to the forward end of the structure to ensure that it lands without difficulty on the pier. The design of the temporary piers will of course depend upon their height, but the principal factor influencing it is whether they are to be completely demolished when removed or whether they are so designed that most of their component parts can be reused. Short supports of relatively small dimensions can be easily removed. If they are of steel, then some parts can certainly be used again; if they are of reinforced concrete, they are demolished after use. High temporary piers can with advantage be built up from prefabricated components, and their subsequent removal therefore presents no special problems. This also permits a certain amount of reuse. Some examples of auxiliary pier designs may be seen in fig. 15. The auxiliary supports are automatically relieved of load when the continuity tendons are stressed and the temporary bearings can be removed and the piers dismantled. The guying or staying of piers and auxiliary supports, that is anchoring back of the heads of the piers, can be carried out by two basic methods: by inclined guys or, where the spans and length of bridge are small, by horizontal anchoring back (fig. 16). In both cases, these guys can be constituted of individual prestressing strands or of complete prestressing cables. The method which uses horizontal anchoring to the abutment has the advantage that the abutment is relieved of load by the tying-back forces. Each pier head must, however, be tied back individually, since otherwise the pier deformations would be cumulative and become too large. Inclined guys are anchored either in the base of the adjacent pier or directly to the ground by ground anchors. 4. VSL service range 4.1. Extent The VSL Organisations can offer a comprehensive service for a bridge to be constructed by incremental launching; the extent of the tender will depend upon the particular circumstances. The VSL services consist essentially of: - the drawing up of a preliminary scheme for a bridge not originally designed for incremental launching, - the supply, placing, stressing and grouting of the prestressing tendons (central and continuity prestressing), - hiring and operating of the horizontal jacking equipment, - supply of pulling cables, - design and supply of the auxiliary structures, - design and supply of the temporary sliding bearings (including sliding plates), - design and supply of the steel or prestressed concrete nose or mast guying system, - hiring and operating of jacks for transferring the bridge from the temporary to the permanent bearings, - design and supply of any necessary pier guys. Some of the VSL Organisations are also able to offer the slipform for the piers as well as bridge bearings and expansion joints. Fig. 15: Auxiliary piers Fig. 15: Auxiliary piers 4.2. Personnel requirements The prestressing and incremental launching operations are provided as a combined tender wherever possible. By using VSL personnel for both classes of work appreciable savings in cost can be achieved since the crew can be kept continuously employed. During the launching operations, the main contractor is asked to provide a crew for manning the sliding bearings, since these people would hardly have any other work to do during this period. 4.3. Preparation of a tender Detailed drawings and specifications are an essential basis for a tender. In addition discussion between the main contractor and the VSL Organisations is desirable, in order to clarify the possibilities and extent of the VSL services. The tender for the incremental launching operations comprises the transporting, installation, provision and hiring, dismantling and operating of the equipment and auxiliary components. A drawing indicating the detailed constructional arrangements is also included with the tender. 8 5. Examples of completed structures 5.1. Ravensbosch Viaduct, Netherlands Client: Provinciale Waterstaat Limburg, Maastricht Engineers: Bouvy, van der Vlugt, van der Niet, Scheveningen Contractor: Joint Venture Internationale Gewapend Betonbouw (IGB), Breda Societe Belge des Betons (SBB), Brussels Post-tensioning: Civielco B. V., Leiden Launching: VSL INTERNATIONAL LTD., Berne Introduction The Ravensbosch Viaduct forms part of the motorway linking Maastricht and Heerlen in Southern Netherlands. It spans the valley of the Strabekervloedgraaf near Valkenburg at a height of about 25 m. The structure consists of two parallel box girders topped by a common deck slab of 37.77 m width. Its length of 420 m is divided into eight spans of 42, 6 x 56 and 42 m. The viaduct is uniformly curved with a 2000 m radius. Choice of the Construction Method Due to the importance of the structure and in order to find the most economical construction method, three different designs were prepared for tender: - The basic design with spans of 42, 6 x 56 and 42 m to be executed according to the (Incremental Launching Method», - Alternative I with spans of 45, 5 x 66 and 45 m to be carried out with prefabricated segments, - Alternative II with spans of 35, 7 x 50 and 35 m to be conventionally built. Additionally the contractors had the opportunity of tendering with a design of their own. Eleven prequalified contractors (six Dutch and five from abroad) were invited to tender. After a period of three months eighteen offers were received, i. e. ten for the basic design, two for alternative I, four for alternative II and two for other designs. The joint venture IGB/SBB offered the lowest bid with its price for the basic design and it was awarded the contract worth nearly 7.5 million Dutch Florin. The time for the execution of the viaduct - the first in the Netherlands built according to the Incremental Launching Method - was limited to 26 months. 9 The Structure in Detail The main dimensions of the structure are given in the preceding figure. The lay-out of the section was, of course, specially adapted to the use of the Incremental Launching Method and some typical details show that: The height of the box girder corresponds to about 1/17th of the main spans whereas this ratio normally is 1/20th or less. The aim was to reduce the quantity of post-tensionihg cables to be installed and to increase the stiffness of the superstructure. This second point was important as during construction no previous compensations for longterm deformations were possible. The thickness of the bottom slab is also greater than usual; it was governed on the one hand by the dimensions of the anchorages of the tendons incorporated, on the other hand by the weight transferred by the inside shuttering when the deck slab was concreted. Finally it should be noted that the dimensions of the whole section are constant throughout the length of the bridge whereas normally the thickness of the webs at least is increased near the supports. But here this was not possible because the shuttering was of steel and could not be adapted to different sections. Construction Sequence The construction yard of the Ravensbosch Viaduct was located behind the eastern abutment. This side was chosen in view of the launching operations as the viaduct has a downward inclination towards the west of 1 0% .Thus the friction was accordingly reduced. For the construction yard an aera 75 m long and 25 m wide was necessary. This gave room for two casting yards, a storage area for reinforcing and prestressing steel, a runway with a tower crane and a concrete mixing unit. The casting and storage yards were protected by a roof. The increments of about 19 m length were executed in three stages. In the first casting yard the bottom slab was built. Then the webs were cast in the second yard, followed by the deck slab. By this method the bottom slab had an age of one week when it came into the second yard. It was therefore capable of supporting the inside shuttering and the weight of the concrete of the top slab. The construction cycle for one segment was as follows: Monday morning: stressing of the cables of the segment cast the week before Monday afternoon: launching Tuesday: construction of the bottom slab Wednesday: construction of the webs Construction of the webs Placing of transverse cables Thursday and Friday: construction of the deck slab Saturday and Sunday: hardening of the concrete Special attention had to be given to the accuracy of the shuttering. Indeed a deviation of 1 mm at one end of the 19 m segment would have resulted in a cumulated error of 100 mm over the total length of the bridge. It was, however, possible to install the shuttering with a precision of 1/10 mm! Prestressing In the case of the Ravensbosch Viaduct the central prestressing consists of tendons of 828 kN ultimate capacity; eight cables are arranged in the bottom slab, eighteen in the deck. They induce a central stress in the concrete of about 1.5 N/mm2. Temporary piers helped to keep the central prestress small. In front of the structure a steel truss of 15 m length and 20 tonnes weight was installed. How much it reduced the cantilever moment can be seen by the weight of a corresponding part of the superstructure which was about 375 tonnes for a 15 m legth. Continuity cables are made of VSL tendons EE 6-12 (ultimate capacity 3100 kN). Each web contains a group of six cables arranged in such a way that over the supports the groups of two adjacent spans overlap. Thus on each side of a pier diaphragm six cables are anchored in block-outs at the top of the web. The cables were pulled into the ducts only after completion of launching and then fully stressed. The deck of the viaduct is also post-tensioned. VSL cables 6-4 at 330 mm c/c are used for this purpose. One cable in four has a fixed anchorage type U at one end and was Launching For the execution of the launching the VSL strand system was used. Two jacks SLU-330 were fixed to steel girders placed in front of the eastern abutment. Each jack pulled a cable 6-31 (breaking load approx. 8000 kN) anchored to a pair of steel girders specially installed at the end of every increment. The total weight to be launched near the end of the operation was about 11 500 tonnes. The stroke of the jacks being 200 mm, launching over a distance of 19 m - the length of a segment - took about six hours. During the construction stage all permanent and tem 10 porary piers were provided with special bearings consisting of a block of concrete Grade 60 (60 N/m m2 at 28 days) covered with a stressed sheet of chrome steel. In order to keep the friction as low as possible steel/ neoprene/teflon plates were introduced between the advancing box girder and these bearings. The same method was used to guide the bridge laterally. Lateral guides were placed on both sides at every permanent pier and on the inner side only at the temporary piers. After completion of launching the special bearings were replaced by permanent ones. The friction was recorded at each jacking operation; as can be seen from the figure on the right, it was rather high at the beginning but then became constant at about 5 %. This value corresponded to the assumption made at the design stage. Client: State of Bavaria, Road Construction Office of Weilheim Engineer: Bung Consultants, Memmingen Contractor: Joint venture Bilfinger+Berger, Munich Wayss & Freytag, Augsburg Prestressing: VSL GmbH, Garching-Hochbruck Introduction To bypass Landsberg, about 60 km to the west of Munich, the Federal Highway B 12 was moved to the northern perimeter of the town and designed as a portion 5.2 Highway bridge over the Lech at Landsberg, Federal Rapublic of Germany of the future highway from Munich to Lindau (Lake Constance). This work required the construction of a new bridge over the Lech. The structure, 264 m in length and 30 m wide, crosses the river at a height of about 30 m and has a curvature of 20,800 m radius in the vertical plane and 1,687 m radius horizontally. Its maximum longitudinal gradient is 3.3 0/o. The structure The bridge had originally been intended as a steel bridge with three clear spans of 88 m each. In 1972, construction of the corresponding abutments and piers was 11 commenced. Difficulties then arose in connection with the constructional activities for the Olympic Games at Munich, so that construction of the bridge was temporarily stopped. As a consequence of the increase in steel prices which occurred at this period, the project was finally dropped and a new design was prepared, providing for a superstructure of prestressed concrete. The already existing abutments and piers were retained, with the spans of 88 m. The structure was now designed as two box-section girders of 4.50 m depth, connected together by a common deck slab. In view of the possibility of flooding of the Lech and the height of the superstructure above the river, the incremental launching method was selected for construction. Construction The following are some of the special features of the construction of the bridge, partly as a result of these circumstances: It was neccessary to construct the formwork, which was of timber, for the 17.60 m long increments in front of the lower (west) abutment, instead of in the more usual position behind the abutment. Since the intermediate piers had been constructed as central, round supports of 6 m diameter, it was necessary to build special temporary structures of concrete-filled steel tubes for the launching condition. During the construction stage, it was obviously not possible to bridge the gaps of 88 m without intermediate support; auxiliary supports of reinforced concrete were therefore provided in the centre of each span and additionally in the upper end span 11.60 m in front of the abutment. A steel nose was fitted to the forward end of the superstructure, to reduce the bending moments. The two box-section girders were slid forward in succession, since as usual only one formwork unit was used; the southern box section was first constructed, followed by the northern section. After launching of both bridge halves, the two parts were joined together by a 7.10 m wide central strip of the deck slab. The support diaphragms and end diaphragms also provide a crossconnection. After a commencement period, in which two weeks were necessary for the construction of an increment, it was possible to construct one increment per week. Each of the girders was subdivided into 15 increments. Erection of the bridge had commenced in December 1975 and the work was substantially completed in March 1977. The VSL prestressing For the transverse and continuity prestressing the VSL system was employed. The transverse prestressing comprises the cables in the deck slab and also the tendons in the support and end diaphragms. For the deck slab, 361 kN (36.8 t)-cables of type VSL EE 5-4 were used, all 29.30 m long and at an average spacing of 0.49 m. When the two box-section girders were erected, only the empty cable ducts were built in. The cables were not installed until the central strip had been concreted. They were installed strand by strand using the VSL push-through machine, which was operated for this purpose on the north side of the bridge from an overhanging platform. The cables were stressed at one end only, but alternately VSL push-through machine The eccentric or continuity prestressing consists of VSL tendons EE 5-16. Some of these are in the webs and some in the bottom slab (the span cables). A certain number of web cables terminate at stressing buttresses, which had been concreted later onto the webs. All the tendons (244 in total) were pushed into the ducts strand by strand using the push-through machine after the incremental launching had been completed. The longest tendons, which are located in the central span and extend at both ends beyond the supports, are 124.3 m in length. The majority of longitudinal cables had to be stressed at both ends, in order to keep the friction losses due to cable curvature as low as possible. For the central prestressing of the first flour increments, in addition to the small prestressing tendons, VSLcables 5-16 were also incorporated in the webs and bottom slab, to keep the stresses at the cantilever end during launching within the acceptable limits. 12 5.3. Highway bridges Bonn-Ramersdorf, Federal Republic of Germany Client: Landschaftsverband Rheinland, Highway Construction Office, Bonn Engineer: Wayss & Freytag, Cologne/Frankfurt Contractor: Joint venture Wayss & Freytag, Cologne Beton- and Monierbau, Cologne Prestressing: VSL GmbH, Garching-Hochbruck Introduction Between the highway intersection Bonn-Ramersdorf and the Konrad-Adenauer-Rhine Bridge, two parallel bridges carry the A 56 over the tracks of the Bonn Suburban Tramway (Siebengebirgsbahn) and over the Konigswinterer Hauptstrasse (B 42). Both structures are about 145 m long and 19.28 m wide. In the region of the bridges, the line of the highway is at a maximum gradient of 1.9 0/o and a curve of 2,400 m radius, also with a vertical curve (radius 39,000 m). Each half bridge has seven spans ranging between about 15 and 22 m. Details of the bridges Each half bridge consists of a double T-beam, without diaphragms, of 1.80 m total depth, with a distance between web centre lines of 11 m. The webs rest on circular individual piers of 4 to 6 m height and 1.10 m diameter, founded upon large piles. The cross-section of the superstructure was adopted from a special proposal of the contractor, who bid on the basis of the incremental launching method. It should be noted in this connection that only a few double T-beam bridges have so far been erected by this method. It is for bridges of relatively shallow depth, however, that double T-beam sections are simpler than box-sections and the formwork is therefore less costly. Erection Each half bridge was constructed in nine sections of 13.65 to 16.20 m length in a wooden form. The form was erected behind the upper abutment. After a somewhat slower initial period, the construction of one increment required one week, so that forward jacking could be carried out each Monday. To permit sliding over the individual piers, the bearings were constructed in such a manner that they could be used as sliding bearings during erection and as permanent bearings in the completed state. Each pier on the inner side of the curve was equipped with a temporary guide device in addition. A steel nose was fitted to the cantilever end of the bridge structure the bridge structure in the usual way. In this case, it was possible to use an existing nose from an earlier site, adapting it by means of a few new parts to the changed conditions. The two parts of the bridge were constructed one after the other, commencing with the north structure. The erection period lasted from September 1976 to May 1977. The VSL prestressing In bridges constructed by incremental launching, three types of prestressing are usually found: the central, the eccentric and the transverse prestressing. On this project, the cables of the second and third groups were by the VSL system. For the continuity prestressing, only the empty ducts (80/85 mm diameter) were laid during construction. After the bridges had been completely launched, the strands were pushed in with a pushthrough machine, from one end over the entire length of 145 metres. In each web, there are four cables of type VSL EE 5-16 which, on account of their length and in view of the fact that they extend over seven spans, had to be stressed at both ends. For the tranverse tendons, VSL cables of type EH 5-4, of 17.30 to 19.50 m length, were used. They were made up directly on the site and installed as complete, ducted cables. In total, 1,158 transverse tendons had to be manufactured, laid at an average spacing of 0.24 m. To ensure symmetry, the stressing anchorage was alternately at the left and right edge of the slab. At the abutments, the two bridge structures were closed by prestressed end diaphragms, which had been concreted against the bridge structure afterwards. Bearing with sliding plates Fixed anchorage type HI of transverse cables 13 Client: Indiana State Highway Commission Engineer: VSL Corporation, Los Gatos, California Contractor: Joint venture Weddle Brothers Construction Co., Rogers Construction Co., both of Bloomington, Indiana Prestressing and launching: VSL Corporation, Los Gatos, California Introduction This is the first bridge built by incremental launching in the USA. It carries the re-located US road number 136 over the Wabash river in the vicinity of Covington, Indiana. The structure is straight both in elevation and in plan and without any gradient. Its length is 285 m with a width of 14.17 m, and it spans the river at about 11 m above the mean water level. When in spate, however, the Wabash River rises considerably, so that construction of the bridge on falsework was out of the question. The Tender In the tender documents it had been envisaged that the superstructure would be built of prefabricated segments by the cantilever method. This would have necessitated the use of mobile and floating cranes, to enable the elements to be placed. The Client, however, permitted alternative proposals, on the condition that the superstructure cross-section and arrangement of supports would be retained. This led the VSL Corporation to offer a variant, in the incremental launching method, to interested contractors. In fact, this bridge presented ideal circumstances for the use of this method, possibly with the exception of the double-cell box-section. The latter circumstance, however, presented no obstacle, since double-cell box-section bridges had already been erected by the incremental launching method. The Weddle/Rogers joint venture, which had submitted the cheapest bid and obtained the contract on that basis, decided in the middle of October 1976 to adopt the proposal of the VSL Corporation and to entrust this Corporation with the redesign of the bridge and the provision of the launching equipment, the steel nose, the temporary sliding bearings and the reinforcing steel, and also with the execution of the prestressing operations. Details of the bridge The superstructure of the Wabash River bridge is 2.50 m in depth and is subdivided into four central spans of 57 m and two end spans each of 28.50 m. It rests on solid-wall piers of 6.10 m width and 1.52 m thickness. They are founded directly on the solid rock and are at an angle of 80° to the axis of the bridge, since the bridge does not cross the river at right angles. The abutments, however, are orthogonal. Erection The superstructure was constructed in 20 increments each 14.25 m in length. Each section was built in two steps, the bottom slab being first constructed, followed by the webs and deck slab. Two forms were therefore necessary, a rear form for the bottom slab and a forward form for the remainder of the cross-section. Using this method, one section could be constructed every week and forward jacking could be carried out every Monday. Two 3000 kN (300 t)-jacks were used for the forward jacking. These were, however, not VSL jacks of the SLU range but a sliding equipment differing from the VSL system and already used a number of times in Europe; this equipment is shown below: 5.4. Bridge over the Wabash River, USA This type of sliding equipment can be used where the applied force is sufficiently large in relation to the sliding force required. The principle of operation is as follows: the horizontal (sliding) jack is fully retracted before sliding commences. Then the vertical jack is extended and the superstructure is slightly lifted. The sliding jack then pushes forward the vertical jack, which rests on a special sliding bearing, and with it the entire superstructure, by the length of one piston stroke. The vertical jack is then released, the piston of the sliding jack is retracted and the cycle commences again (with the lifting of the superstructure), and is continued until the superstructure has bee-n advanced by the length of one increment. 14 Ravensbosch viaduct, Netherlands Bridge of the Maastricht-Heerlen Motorway, executed 1972/74 Owner Provinciale Waterstaat Limburg, Maastricht Engineer Bouvy, van der Vlugt, van der Niet, Scheveningen Contractor Joint Venture IGB, Breda/SBB, Brussels Post-tensioning Civielco B. V., Leiden Launching VSL INTERNATIONAL LTD., Berne Total length 420 m, Alignment: horizontal radius 2000 m, slope 1% Spans 42/6 x 56/42 m (auxiliary piers during construction) Width 37,77 m (2 box girders) Depth 3,30 m Pier heights 6,50 to 23,50 m Tendons longitudinally 192 cables EE 6-12 transversally 1152 cables EE/EU 6-4 Launching equipment 2 SLU-330 with 2 cables 6-31 Horomoi bridge, Japan Highway bridge near Muroran (Hokkaido), executed 1973 Owner Hokkaido Prefecture Engineer Osaka Consultant, Osaka Contractor Taisei Corporation, Tokyo Post-tensioning Total length 170 m, Alignment: straight, horizontal Spans 52,50/63,00/52,50 m (auxiliary piers during construction) Width 10,00 m (1 box girder) Depth 3,00 m Pier height 38,5 m Tendons 8 cables EE 5-31 I = 172,5 m An insert possessing a high coefficient of friction is placed between the piston of the vertical jack and the superstructure, thus ensuring that no relative movement between the piston and superstructure can occur. In order to limit the bending moments in the superstructure during the erection stage, auxiliary supports of steel were installed between the permanent piers. Since these temporary supports were relatively light, they had to be anchored back by VSL cables type 5- 4 to the rearward main piers. The lower slab of the superstructure, with its width of 7.62 m, is wider than the piers, so that here again auxiliary structures had to be provided, capable of carrying the temporary sliding bearings. A steel nose, 17.70 m in length, consisting of two cross-braced solid-web girders, was fixed to the cantilever end of the superstructure to reduce the bending moments. After launching had been completed, the bridge was transferred from the temporary bearings to the permanent bearings. The prestressing Both the central and the eccentric prestressing consists of VSL tendons. For the central prestressing, 16 cables 5-12 were used; contrary to the usual practice, however, these tendons were placed in the webs. Six each of these tendons were placed in the outer webs and four in the middle web. They were stressed when the concrete had reached a minimum strength of 24 N/mmz (245 kg/cmz). The tendons of the eccentric prestressing are of type 5-4 with a flat duct and cast-iron anchorage. They are located exclusively in the bottom slab (in the span region) and in the deck slab (over the supports). The use of flat ducts enabled bundles of two or three superimposed tendons to be formed. The tendons terminate at small buttresses on the lower and upper side respectively of the slabs. They were stressed strand by strand. The unusual arrangement of the cables was due to the constraint that the cross-section dimensions of the original design had to be retained. The use of small cables for the eccentric prestressing had, however, the advantage that the stressing buttresses were very small and a small, light jack, very easy to use for overhead work, could be used for stressing. In addition, VSL tendons were also used for the prestressing of the 1.77 m wide support diaphragms, for anchoring the temporary structures to the piers and for attaching the temporary nose. 6. Representative list of incrementally launched bridges post-tensioned and/or launched with the VSL-system Pipeline bridge SNAM across the Po River, Italy Bridge for oil pipelines near Pavia, executed 1968/69 Owner SNAM S. p. A. Engineer Dr. Giancarlo Giuliani, Milan Contractor Presspali S. p. A. and EDIM SRL, Milan Post-tensioning } VSL Italia S. p. A., Milan Launching (formerly Beton Precompresso S. p. A.) Total length 1362 m (6 parts: 4 x 215 m and 2 x 251 m) Alignment: straight, slope 0.3 °/o Spans 38 x 35,84 m Width 4,60 m (U-shaped section) Depth 2,12 m Pier heights 10 to 15 m Tendons temporary (central) 156 cables EE 5-12 final (eccentric) 152 cables EU 5-7 12 cables EU 5-3 Launching equipment 6 VSL-Monojacks Dal bridge Avesta, Sweden Bridge of the National Highway No. 70 over the Dal River, executed 1972 Owner Statens Vagverk Engineer ELU-Consult, Stockholm Contractor Nya Asfalt AB, Stockholm Post-tensioning Internordisk Spannarmering, Stockholm Total length 350 m, Alignment: horizontal radius 3500 m, vertical radius 25'000 m, max. slope 2,9 °/a Spans 40/6 x 45/40 m Width 16,50 m (1 box girder) Depth 3,20 m Pier heights 15,80 to 24,80 m Tendons 48 cables EE 5-12 1 = 56,7 to 77,1 m 15