FOR THE CALCULATION OF STILL WATER BENDING MOMENT OF SELF-PROPELLED INLAND CARGO CARRIERS

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1 E. T. S. Ingeniería Naval y Oceánica Final Project: DEVELOPMENT OF EMPIRICAL FORMULAE FOR THE CALCULATION OF STILL WATER BENDING MOMENT OF SELF-PROPELLED INLAND CARGO CARRIERS Titulación: INGENIERÍA NAVAL Y OCEÁNICA Departamento: TECNOLOGÍA NAVAL Tutor de proyecto: GERMÁN ROMERO VALIENTE Alumna: TANIA SÁNCHEZ MACIÁ Publicación: CARTAGENA 2013 Project: : Development of empirical formulas for Still Water Bending Moment. TANIA SÁNCHEZ MACIÁ 1

2 Acknowledgment I would like to thank to Germán Romero Valiente (my project manager), for his attention and help. Also express my special acknowledgement to the Classification Society Bureau Veritas, ( in particular to the Inland Navigation Management, Antwerpen) for the opportunity of develop my master thesis with their collaboration. To highlight the help and dedication given by Mr Nzengu and Mr Tri, my daily project managers and constants sufferers of my questions for the resolution of the problems encountered during the development of the project. And acknowledge the support and confidence of all the other employees, who in one way or another have helped me to do this thesis. That although not explicitly mentioned, I can't deny a sincere thanks. Moreover, I would like to give my sincere thanks to Professor Mr Philippe Rigo, of the Université de Liège, for all his attention. And note that without him this project would not have taken place since he was the person who put me in contact with Bureau Veritas company. Finally, I can't finish without mention the support of my family and friends, and especially my parents and brother, whose have always been there when I needed. To all of them, THANK YOU VERY MUCH. TANIA SÁNCHEZ MACIÁ 2

3 Abstract Still water bending moment is function of the longitudinal distribution of weights and the hull geometry (buoyancy distribution). While buoyancy distribution is known from an early stage of the vessel design, weight distribution is completely defined only at the end of construction. Therefore, values of still water bending moments derived from empirical formulae developed on the basis of statistical analysis are often used at the preliminary design stage. The study to be performed within the scope of this thesis aims to develop empirical formulae giving the maximum still water bending moments in sagging and hogging conditions applicable to inland self-propelled cargo carrier vessels. The formulae of still water bending moments are based on standard light weights and weight distribution of the following items: -Lightship weight Hull Cargo hold / Cargo tank Deckhouse Main Machinery Aft Machinery Installations Aft Machinery Fore Machinery Installations Fore Aft auxiliary machinery Fore auxiliary machinery Piping system Anchor equipment and gear fore Anchor equipment and gear aft -Cargo weight -Ballast and supplies weight TANIA SÁNCHEZ MACIÁ 3

4 ABSTRACT Where the weights and /or weight distribution present a deviation from standard values, corrections are to be brought using adequate correction formulas (Mc). The study methodology for the development of the empirical formulae for still water bending moment has been done as following: 1. Collection of sample vessels (46 different cargo carrier vessels) 2. Study of the weight and weight distribution. 3. Modelling of operating conditions Navigation: lightship and fully loaded vessel Harbour: transitory conditions (loading in 1R and 2R) 4. Direct Calculation of the still water bending moments in different operating conditions, for each loading case (we will use ARGOS program as a tool) 5. Collection of maximum bending moment values in hogging and sagging conditions 6. Development of the equation of the standard maximum bending moment values using curve fitting (we will use Datafit program as a tool). 7. Validation of the developed formulas. TANIA SÁNCHEZ MACIÁ 4

5 Summary BOOKLET 0: PROJECT OVERVIEW (Spanish)...11 BOOKLET I: HULL GIRDER LOADS Introduction Loads applied to a ship structure Longitudinal Strength Loads Transverse Strength Loads Local Strength Loads Still water global loads Direct evaluation of still water global loads Application of Beam Theory Characteristics of the Shear force and Bending moment Curves Uncertainties in the evaluation Bibliography...62 BOOKLET II: SCOPE OF THE STUDY. INLAND NAVIGATION VESSELS Scope of the Study Inland Waterways Inland Vessels Inland Cargo Carriers Inland Vessels Types Cargo Vessels Bulk Cargo Vessels Container Vessels General Cargo Vessels Roro Cargo Vessels Tank Vessels Tank Type G Tank Type C Tank Type N Passenger Vessels Vessels for dredging activities Dredger Hopper Barge Split Hopper Barge...79 TANIA SÁNCHEZ MACIÁ 5

6 SUMMARY Hopper Dredge Split Hopper Dredge Working Units Launch Pontoon Pusher Tug Bibliography...83 BOOKLET III: PUBLICATION REVIEW Symbols and definitions Symbols Definitions Estimated Still Water Bending Moments Estimated design bending moments Range of application Standard weights and weight distribution for self-propelled cargo carriers Standard light vessel weights and weight distribution Standard cargo weight and cargo distribution Values of estimated still water bending moments Correction bending moment Wave Bending Moments Total vertical Bending Moments...96 BOOKLET IV: STUDIED VESSELS. RANGE OF PARAMETERS Investigated vessels Studied Parameters and Range of Application Studied Parameters Range of Application Ships for validation BOOKLET V: INVESTIGATION OF THE WEIGHT AND WEIGHT DISTRIBUTION Introduction Light Ship Weight TANIA SÁNCHEZ MACIÁ 6

7 SUMMARY 2.1 Symbols and Units Definitions Reference Co-ordinate System Studied Vessels List Structural weight Central part Cargo hold/tank Total hull weight Deckhouse 2.6 Machinery weight Main machinery Main machinery installations Fore machinery Fore machinery installations Auxiliary machinery (fore and aft) Cargo piping system (tank vessels) 2.7 Fittings Anchor equipment and gear fore Anchor equipment and gear aft 2.8 Deck equipment Light ship weight comparison Self-propelled cargo carriers. Standard weights and weight distribution. Summary table Coherence with non propelled cargo carriers Supplies Ballast Cargo weight Self-propelled cargo carriers Coherence with non propelled cargo carriers Standard Hold/Tank length Container vessels Tank vessels BOOKLET VI: STANDARD LOADING CONDITION Standard Loading Conditions Standard Loading Conditions Lightship Fully Loaded Transitory conditions 2. Loading Cases inducing Maximum Still Water Bending Moments Taking into account distances and weights Influence line diagram TANIA SÁNCHEZ MACIÁ 7

8 SUMMARY BOOKLET VII: DIRECT CALCULATION OF THE STILL WATER BENDING MOMENT Overview of the used tool (ARGOS) Aplication Input data Limitations Direct calculation of the Still Water Bending Moment (SWBM) Direct calculation of the bending moment (Argos) Main Particulars Lightship distribution Loading conditions Summary of the Load Cases where the Maximum Still Water Bending Moment occurs Loading in one run: Maximum hogging moment Loading in one run: Maximum sagging moment Loading in two runs: Maximum hogging moment Loading in two runs: Maximum sagging moment BOOKLET VIII: DEVELOPMENT OF THE NEW STILL WATER BENDING MOMENT FORMULA Used methodology Non-Linear Regressing (Used tool Datafit) Methods for evaluate the results Influence line diagram Symbols and definitions Studied Vessels Summary table of the influence line diagram parameters in hogging condition Summary table of the influence line diagram parameters in sagging condition Summary table coefficients Ki Principle of calculation using formulae Symbols Design Bending Moments Estimated Still Water Bending Moments Navigation in light ship, hogging condition (Mo) Development of the formula structure Methods to analyze the results Comparison with other formulae TANIA SÁNCHEZ MACIÁ 8

9 SUMMARY Validation of the formulae Navigation in fully loaded, sagging condition (Mso) Development of the formula structure Methods to analyze the results Comparison with other formulae Validation of the formulae Harbour 1R in hogging condition (Mh1) Development of the formula structure Methods to analyze the results Comparison with other formulae Validation of the formulae Harbour 2R in hogging condition (Mh1) Development of the formula structure Methods to analyze the results Comparison with other formulae Validation of the formulae Harbour 1R in sagging condition (Ms1) Development of the formula structure Methods to analyze the results Comparison with other formulae Validation of the formulae Harbour 2R in sagging condition (Ms1) Development of the formula structure Methods to analyze the results Comparison with other formulae Validation of the formulae Correction formulae (Mc) Comparison of the results using the correction Mc 3.4. Conclusions of the new estimated SWBM formulas New studies proposed Summary of Developed Formulae Symbols Design Bending Moments Estimated still water bending moments General Standard weights and weight distribution for self-propelled cargo carriers Standard light vessel weight and weight distribution Standard cargo weight and cargo distribution Values of estimated still water bending moments Correction bending moment Total vertical bending moment TANIA SÁNCHEZ MACIÁ 9

10 SUMMARY BOOKLET IX APPENDIX Appendix I: Approximated Methods of Weight Distribution Appendix II: Investigation of Weight and Weight Distribution Details of Calculation Appendix III: Cargo Weight Formula Analysis Appendix IV: Marine Container Types Appendix V: Vessel's standard holds. Loaded with standard cargo weight Appendix VI: Vessel's standard holds. Vessels for validation. Loaded with standard cargo weight Appendix VII: Vessel's standard holds. Loaded with actual cargo weight Appendix VIII: Standard weight and weight distribution Appendix IX: Loading cases Inducing Maximum Still Water Bending Moment Appendix X: Summary table of the Bending Moments Results Appendix XI: Influence Line Diagram Calculations Appendix XII: Correction Bending Moment (Mc) TANIA SÁNCHEZ MACIÁ 10

11 Booklet 0: Project Overview (Spanish) TANIA SÁNCHEZ MACIÁ 11

12 Booklet 0: Project Overview I. INTRODUCCIÓN De acuerdo con su propia definición, un proyecto es un conjunto de cálculos y dibujos que se hacen para tener una idea de cómo será y lo que debe costar una obra de arquitectura o ingeniería. Esta definición puede ser completamente aplicada a la ingeniería naval. A pesar de que el procedimiento de diseño de un buque puede diferir de país a país, de astillero en astillero y entre los diferentes tipos de buques (buques de guerra, comerciales, de pasaje, de gran velocidad...)de forma general, se puede afirmar que el proyecto comienza con la fase de diseño o idea preliminar. Donde son definidas las dimensiones y formas principales del casco, la ubicación de los mamparos longitudinales y los transversales, el máximo momento de flector del buque en aguas tranquilas, etc, asumiendo valores coherentes, para satisfacer las necesidades del armador, tales como peso muerto y la velocidad del buque. Durante el desarrollo del proyecto, las conversaciones con el propietario del buque van progresando por lo que cada vez se refinan más los datos. Por lo que, se puede decir que el proyecto habitual de un buque tiene dos características principales: Es cíclico. lo que significa que el proceso que conduce a la descripción detallada de la embarcación se desarrolla mediante ciclos cuyo grado de definición es cada vez mayor. Es iterativo. lo que significa que en cada ciclo, el proyecto sigue un proceso de prueba y error. Ambas características se pueden mostrar en la espiral de diseño del buque. Que es la representación esquemática de los diversos cálculos y decisiones de cada ciclo o fase de proyecto y los controles o revisiones al final de cada ciclo. Espiral de Diseño del buque Un ejemplo de una metodología viable del procedimiento de diseño estructural para un buque de carga, puede ser: Recibir el plano de disposición general realizado por los encargados del diseño básico Definir la disposición estructural basado en el plano de disposición general TANIA SÁNCHEZ MACIÁ 12

13 Booklet 0: Project Overview Determinar el escantillón inicial de los miembros estructurales acorde a los criterios de diseño (basado en los reglamentos). Este escantillonado está basado en normas que son función del máximo momento flector que el buque puede soportar Comprobar la resistencia longitudinal y transversal Cambiar la disposición estructural o escantillón (si es necesario) Transferir la disposición estructural y los escantillones al grupo de diseño de producción Por lo tanto, como resultado de esta breve introducción sobre el diseño de los buques, se puede ver la gran influencia e importancia de hacer una buena estimación del momento de flector en aguas tranquilas. Dado que cuanto mejor sea la estimación inicial, más rápido serán las iteraciones para alcanzar los resultados óptimos. Ahorro de tiempo y esfuerzo, y por lo tanto dinero. El objetivo de esta tesis es desarrollar nuevas fórmulas empíricas que nos permitan estimar el valor del máximo momento flector en aguas tranquilas para buques de carga autopropulsados de navegación interior. Una fórmula empírica es una expresión derivada sobre la base de los datos experimentales o numérica de los buques. Por lo tanto, este tipo de fórmulas puede proporcionar soluciones razonables para los cascos convencionales, pero no se puede utilizar para los buques con el diseño inusual o los buques cuyos parámetros son diferentes al rango de parámetros que se definirán durante el estudio. No podemos olvidar que las fórmulas que vamos a obtener proporcionan unos valores estimados. No valores reales. Y como por lo general los fórmulas se van a utilizar para comprobar el momento de flexión mínimo durante las etapas preliminares del proyecto y en estas etapas no sabemos todos los parámetros del buque, las fórmulas deberán ser lo más simples posibles. La metodología a seguir en el estudio del desarrollo de las nuevas fórmulas empíricas del momento flector en aguas tranquilas será de la siguiente forma: 1. Recolección de los barcos a utilizar (46 diferentes buques de carga) 2. Estudio del peso y distribución de pesos. El momento flector de un buque en aguas tranquilas es función de la distribución longitudinal de pesos y de la geometría del casco (la distribución del empuje). Mientras que la geometría del casco es conocida desde las etapas iniciales de diseño, la distribución de pesos se define completamente solamente al final de la construcción. Donde pesos y/o la distribución de pesos reales presentan una desviación de los valores estándares, habrá que corregir aplicando la correspondiente fórmula de corrección (Mc). 3. Modelización de las condiciones de operación Navegación: buque en rosca y completamente cargado Puerto: condiciones transitorias (cargando en 1R o 2R) 4. Cálculo directo del momento flector en aguas tranquilas en las diferentes condiciones de operación para cada caso de carga (se usará el programa ARGOS como ayuda) 5.Recolección de los valores máximos de los momentos flectores en las condiciones de arrufo y quebranto. TANIA SÁNCHEZ MACIÁ 13

14 Booklet 0: Project Overview 6. Desarrollo de la ecuación de los máximos momentos flectores estándares usando el ajuste de curvas (se usará el programa Datafit como ayuda) 7. Validación de las fórmulas desarrolladas. I. CARGAS APLICADAS A LA ESTRUCTURA DEL BUQUE Durante toda su vida, un buque está sometido a muchos tipos diferentes de cargas que causan deformaciones en su estructura, así como tensiones. Los diferentes tipos de cargas que se pueden aplicar a la estructura de un casco se transmiten poco a poco y de forma continua desde un miembro estructural local al elemento de soporte adyacente más grande. Por lo que se pueden definir los siguientes tipos de cargas: Cargas de resistencia longitudinal Cargas de resistencia transversal Cargas de resistencia local Cargas de resistencia longitudinal Las cargas de resistencia longitudinal se pueden dividir en dos categorías: las cargas longitudinales estáticas y dinámicas. Cargas estáticas longitudinales son inducidas por las desigualdades locales de peso y empuje en la condición de aguas tranquilas, que causan un momento estático flector y una fuerza de cizallamiento. Las desigualdades locales de peso y empuje asimétricas, pueden causar un momento de torsión. En nuestro estudio vamos a suponer una secuencia de carga simétrica, por lo que no vamos a tener influencia del momento de torsión. Un buque tiene dos posibles condiciones de carga según esté sometido a unas u otras tensiones: son quebranto y arrufo. -Quebranto (hogging) ocurre cuando el buque tiene demasiado peso en la proa y en la popa y la cresta de la ola está en el centro del buque. El resultado estructural es tener sometida la cubierta a tracción y la quilla a compresión. Condición de Quebranto TANIA SÁNCHEZ MACIÁ 14

15 Booklet 0: Project Overview -Arrufo (sagging) ocurre cuando el buque tiene demasiado peso en su zona central, y la proa y la popa está en la cresta de dos olas sucesivas. El resultado estructural es tener sometida la cubierta a compresión y la quilla a tracción. Condición de arrufo Cargas longitudinales dinámicas están inducidas por las olas. Las olas producen fuerzas horizontales y verticales que actúan sobre forro del costado, por lo que pueden inducir un momento de flexión en el plano horizontal y vertical al mismo tiempo, si por ejemplo, el buque está navegando diagonalmente a través de una onda regular (como se muestra en la figura. I.1.3 ); Buque en olas oblicuas Por otra parte, las ondas también pueden crear un momento de torsión debido a la variación de la superficie de ola en diferentes secciones a lo largo de la eslora del buque. Sin embargo, como nuestro objetivo es desarrollar las fórmulas empíricas del momento de flexión en aguas tranquilas, el efecto de las olas están fuera de alcance de nuestro estudio. Por lo tanto, no vamos a estudiar cualquier carga dinámica aplicada en un barco. Pero si queremos saber el momento de flexión total durante la navegación, se deberá añadir el momento de flexión debido a las olas al momento de flexión en aguas tranquilas que vamos a calcular. Cargas de resistencia transversal Las cargas de resistencia transversal son aquellas que actúan sobre los miembros transversales y causan una distorsión estructural en la sección transversal. En este tipo de cargas se incluyen: TANIA SÁNCHEZ MACIÁ 15

16 Booklet 0: Project Overview - Presión hidrostática e hidrodinámica sobre el forro del casco - Peso estructural y peso de la carga sobre la estructura del fondo - Fuerza de inercia de la carga o el lastre debido al movimiento del buque, por lo que inducen deformación de los tanques - Las cargas de impacto (slamming and sloshing) Como ya hemos explicado, nuestro estudio se va a desarrollar en aguas tranquilas, por lo que de la lista anterior, sólo vamos a tener en cuenta (a) la presión hidrostática y (b) la carga interna debido a peso propio y el peso de la carga. Así, por ejemplo, imaginemos una sección transversal de un buque flotando en aguas tranquilas, como se ilustra en la figura. Ejemplo de deformación de una sección debido a cargas transversales Ambas cargas no siempre son iguales entre sí en cada punto, por consiguiente, las cargas que trabajen sobre los miembros transversales producirán una distorsión transversal como se muestra en la línea discontinua. Desde el punto de vista de análisis de la resistencia del buque, cuando se consideran cargas transversales y longitudinales, es importante saber que: "La distorsión debida a las cargas longitudinales no afecta a la deformación de la sección transversal." Por ejemplo, el momento de flexión longitudinal no tiene ninguna influencia en la distorsión de la sección transversal. Por lo tanto, la deformación transversal de la estructura del casco debida a las cargas transversales se considerará independiente de la deformación producida por la carga longitudinal. Como el momento de flexión longitudinal no se ve afectado por la distorsión de la sección transversal, no vamos a tener en cuenta las cargas transversales durante nuestro estudio. Cargas de resistencia Local Las cargas de resistencia local incluyen cargas que afectan a los miembros de resistencia locales, tales como paneles del forro, refuerzos y estructuras de conexión entre refuerzos. Una carga que actúa sobre la estructura puede ser tratada de forma independiente teniendo en cuenta la transferencia de carga a partir de una estructura local a una estructura más grande. Por ejemplo, consideremos el caso en que el diseñador comienza el diseño de una estructura inferior como se muestra en la figura. TANIA SÁNCHEZ MACIÁ 16

17 Booklet 0: Project Overview Estructura del fondo sometida a la presión del agua En primer lugar, la fuerza de las tracas del forro del fondo debe ser determinada en función de la presión hidrostática. Después se debe evaluar la resistencia de los refuerzos longitudinales que soportan las tracas. A continuación, la resistencia de las cuadernas transversales que sostienen los refuerzos y, finalmente, la fuerza global de la estructura del fondo debe ser evaluada. Las investigaciones se pueden realizar por separado para cada miembro teniendo en cuenta las magnitudes de las cargas que se transmiten en cada miembro. A pesar de que las cargas locales pueden jugar un rol importante en el cálculo de la respuesta global, con el fin de simplificar nuestro trabajo, durante el estudio no se van a estudiar las cargas locales, sino simplemente las cargas globales o longitudinales. Es decir, las cargas que actúan sobre el buque en su conjunto, considerado como una viga (vigacasco). CARGAS GLOBALES EN AGUAS TRANQUILAS En el nivel de respuesta global del buque (respuesta primaria) podemos hacer las siguientes simplificaciones / aproximaciones: La viga-casco actúa de acuerdo con la teoría de viga simple. Las acciones sobre el casco-viga, se describen sólo en términos de las fuerzas y momentos que actúan en las secciones transversales y aplicadas sobre el eje longitudinal. Por lo tanto, sólo hay una variable independiente, la posición longitudinal y las cargas y deflexiones tienen un sólo valor en cualquier sección transversal. La viga-casco permanece elástica, sus deformaciones son pequeñas, y la deformación longitudinal debido a la flexión varía linealmente sobre la sección transversal, sobre un eje transversal de deformación cero (eje neutro). Los efectos dinámicos se desprecian. Dado que la deformación por flexión es lineal, la flexión producida horizontal y verticalmente de la viga-casco, se podrán tratar por separado y superponerse. Como el momento flector vertical es mucho mayor que el horizontal, nos ocuparemos principalmente de él (como ya hemos dicho en el punto anterior). TANIA SÁNCHEZ MACIÁ 17

18 Booklet 0: Project Overview Por lo tanto, en el buque-viga podemos suponer que en cada sección se aplican tres componentes diferentes: Una fuerza resultante a lo largo del eje vertical de la sección (contenida en el plano de simetría), indicada como fuerza vertical resultante qv Una fuerza en la dirección normal, (eje horizontal local), denominada fuerza horizontal resultante qh Un momento alrededor del eje x. Todas estas acciones se distribuyen a lo largo del eje longitudinal x. Fig. I, 3.1. Fuerzas y momentos en una sección Por lo que, cinco componentes principales (ecuaciones de la 1 a la 5) son generadas a lo largo de la viga relacionados a las fuerzas y momentos seccionales mencionados anteriormente. - Fuerza Vertical Resultante - Momento resultante Vertical - Fuerza resultante Horizontal - Momento resultante Horizontal = = = = [1] [2] [3] [4] - Momento de torsión = [5] Debido al equilibrio total de una viga en condiciones de extremos libres, todas las características de las cargas tienen cero en los extremos: 0 = = 0 = = 0 0 = = 0 = = 0 [6] 0 = = 0 TANIA SÁNCHEZ MACIÁ 18

19 Booklet 0: Project Overview De acuerdo con el punto anterior, las principales fuerzas aplicadas a un buque flotando en aguas tranquilas son: Peso en rosca (peso estructural, motores...) Peso muerto y carga, los suministros, el lastre... Empuje, el cual está determinado por la forma del casco y la ubicación de la embarcación en el agua (calado y asiento). Por lo tanto, esto significa que: No hay componentes horizontales de las fuerzas seccionales y en consecuencia ninguna componente de cizalladura horizontal y momento de flexión. (ecuación 3 y 4 son iguales a cero). Por lo general, las cargas anteriores tienen el plano de simetría normal a la superficie del agua. En esta condición, sólo una distribución simétrica de la presión hidrostática actúa sobre cada sección, junto con las fuerzas gravitatorias verticales. Si estos últimos no son simétricas, (x) se genera un par de torsión del eje en sección alrededor. Sin embargo, en nuestro estudio, vamos a suponer que son simétricos. Así que para nosotros, la ecuación 5 es igual a cero. Por último sólo tenemos en cuenta la vertical de la fuerza resultante V v (x), que es la suma de toda la carga vertical q sv (x)a lo largo de la longitud del buque. Obtenido q sv (x) como una diferencia entre el empluje b (x) y el peso w (x), como se muestra en la ecuación 7. = = [7 ] Donde: A I = área transversal inmersa. Por lo tanto, las componentes de momento de flexión se pueden derivar de acuerdo con las ecuaciones 1 y 2, (que se explica en el cálculo directo del momento flector de un buque en aguas tranquilas). TANIA SÁNCHEZ MACIÁ 19

20 Booklet 0: Project Overview II. BUQUES ESTUDIADOS (RANGO DE PARÁMETROS) El ámbito de estudio del presente proyecto son los buques de navegación interior autopropulsados, con maquinaria a popa. Los buques de navegación interior son buques destinados a navegar en las vías navegables interiores. Estando incluidos en ellas los ríos, afluentes, canales y lagos. Dentro de toda la gama de buques de navegación interior (explicada en el booklet II), nuestro estudio se centra en buques de carga. Como son: Buques de Carga Buques de carga a granel Portacontenedores Buques de carga general Buques tanque Tanques Tipo G Tanques Tipo C Tanques Tipo N Para ver una descripción de cada uno de ellos, véase el "Booklet II: Scope of the Study. Inland Navigation Vessels". En la siguiente tabla se pueden observar las características de los 46 buques estudiados. N Tipo de buque L (m) B (m) D (m) T (m) Loa (m) 1 Carga General 49,45 11,40 5,55 3,17 51,20 9,55 7,40 0,872 9,81 3,63 0,657 2 Portacontenedor 131,55 14,50 5,70 3,60 134,24 17,60 10,45 0,903 12,88 6,36 0,787 3 Portacontenedor 133,90 11,40 3,90 3,80 135,00 17,90 16,50 0,926 10,14 3,85 0,743 4 Portacontenedor 97,77 11,20 3,00 2,20 100,20 13,80 9,67 0,908 9,95 3,00 0,760 5 Portacontenedor 106,30 17,10 5,68 4,50 110,00 13,50 9,30 0,854 10,00 6,68 0,786 6 Portacontenedor 108,15 11,45 3,65 3,55 110,00 17,40 10,25 0,895 10,09 4,83 0,744 7 Portacontenedor 84,50 14,15 5,00 4,50 86,00 1,50 8,47 0,935 12,55 5,50 0,882 8 Portacontenedor 133,00 11,45 3,90 2,80 135,00 17,00 9,00 0,896 10,18 3,98 0, Portacontenedor 132,92 11,40 3,50 3,49 134,97 17,25 9,70 0,917 10,13 2,90 0, Tanque Tipo N 108,50 11,41 4,99 3,65 110,00 19,00 12,10 0,902 9,77 4,44 0, Tanque Tipo N 103,20 10,45 3,80 2,90 105,00 15,60 10,38 0,873 9,15 3,10 0, Tanque Tipo N 107,57 10,45 4,00 3,31 109,92 15,85 9,50 0,892 9,15 3,32 0, Tanque Tipo N 108,78 11,40 4,30 3,35 109,98 17,40 9,78 0,901 9,96 3,59 0, Tanque Tipo N 108,18 11,35 4,00 2,85 109,80 17,68 11,30 0,873 9,92 3,23 0, Tanque Tipo N 84,05 10,95 4,60 2,80 85,95 17,30 9,15 0,853 9,33 3,85 0, Tanque Tipo N 53,50 11,50 4,60 3,30 55,42 13,65 4,65 0,829 9,90 3,80 0, Tanque Tipo N 107,86 10,95 3,50 3,46 109,96 16,40 9,96 0,887 8,84 2,54 0, Tanque Tipo N 33,70 6,40 3,55 2,50 35,00 9,60 6,10 0,835 0, Tanque Tipo N 84,03 9,00 3,58 2,61 85,95 11,10 7,08 0,938 7,00 2,78 0, Tanque Tipo G 92,30 11,40 5,70 2,80 95,04 15,16 9,71 0,882 9,60 4,80 0, Tanque Tipo G 103,60 11,36 5,32 2,80 106,00 16,81 9,93 0,885 9,00 4,50 0, Tanque Tipo G 106,25 11,35 5,20 2,50 108,50 18,46 7,41 0,877 8,85 4,43 0, Tanque Tipo C 108,37 11,40 5,40 3,86 110,00 16,10 9,77 0,898 9,78 4,65 0,761 dar (m) TANIA SÁNCHEZ MACIÁ 20 dav( m) Cb Bc (m) Dc (m) R

21 Booklet 0: Project Overview 30 Tanque Tipo C 107,84 13,50 5,32 4,00 110,00 16,25 10,59 0,877 11,88 4,54 0, Tanque Tipo C 133,65 16,80 5,75 4,95 135,00 22,25 13,15 0,892 15,20 4,93 0, Tanque Tipo C 107,95 11,45 5,32 3,60 110,00 15,60 10,65 0,883 9,85 4,58 0, Tanque Tipo C 108,00 11,45 4,67 3,20 110,00 17,30 9,19 0,882 9,85 3,88 0, Tanque Tipo C 122,00 11,40 6,00 4,05 125,00 19,48 10,98 0,687 9,38 5,17 0, Tanque Tipo C 107,95 11,40 5,32 3,80 110,00 15,60 10,65 0,885 9,79 4,53 0, Tanque Tipo C 83,05 9,56 4,70 3,60 84,30 14,30 9,57 0,921 7,96 4,00 0, Tanque Tipo C 84,47 9,60 4,70 3,35 85,96 16,05 10,46 0,881 8,00 3,95 0, Tanque Tipo C 118,36 11,40 6,00 4,30 121,16 15,30 10,06 0,898 9,38 5,17 0, Tanque Tipo C 83,63 10,50 5,10 3,60 85,00 16,05 10,43 0,878 8,90 4,34 0, Tanque Tipo C 132,00 11,40 5,34 4,00 135,00 18,81 9,80 0,928 9,78 4,64 0, Tanque Tipo C 107,20 11,40 5,40 3,76 110,00 16,00 8,70 0,894 9,90 4,65 0, Tanque Tipo C 108,41 11,40 5,30 3,40 110,00 18,50 10,71 0,896 9,80 4,60 0, Tanque Tipo C 83,75 9,50 4,25 2,80 86,00 15,48 9,22 0,909 7,50 3,40 0, Tanque Tipo C 82,95 9,46 4,75 3,07 85,95 16,15 9,03 0,875 7,86 4,00 0, Tanque Tipo C 128,10 11,45 5,70 4,10 130,00 15,80 10,80 0,935 9,85 4,88 0, Tanque Tipo C 107,99 13,50 5,32 4,20 109,99 16,30 10,69 0,875 11,90 4,58 0, Tanque Tipo C 65,95 10,50 5,10 3,45 66,00 15,60 12,25 0,821 8,90 4,00 0, Tanque Tipo C 133,25 15,00 5,39 4,31 135,00 16,50 10,55 0,913 13,40 4,59 0, Tanque Tipo C 106,55 13,50 5,32 4,20 110,00 14,90 10,65 0,880 11,90 4,55 0, Tanque Tipo C 98,00 11,45 5,00 3,20 100,00 16,01 9,00 0,865 9,40 4,25 0, Tanque Tipo C 131,86 22,80 6,36 5,20 134,95 17,00 12,30 0,909 20,80 0,85 0, Tanque Tipo N 108,35 10,45 4,60 3,20 110,00 15,65 10,33 0,894 9,15 3,85 0,760 Lista de barcos estudiados PARÁMETROS ESTUDIADOS A continuación se encuentra una lista de los parámetros que han sido estudiados para cada uno de los barcos. a) Eslora de la normativa, en m : < L < b) Manga, en m : 9 < B < 22.8 c) Calado máximo T, en m d) Puntal D, in m e) Coeficiente de bloque Cb, correspondiente al calado máximo: < Cb < f) R ( coeficiente del espacio de carga) : < R < De la lista anterior se han eliminado, de nuestro estudio, los siguientes buques debido a que sus parámetros exceden del rango que queremos estudiar: Buque N º 7: porque tiene una "dar" muy pequeña. Es un diseño de situación extraña o inusual en el que el buque se carga detrás de la cabina de mando, lo que produce una gran TANIA SÁNCHEZ MACIÁ 21

22 Booklet 0: Project Overview R. Es una construcción no usual, por lo que no se usará para la base de barcos utilizados para el cálculo del momento flector para los buques convencionales. Buque N º 21: porque tiene un eslora muy pequeña, y R está fuera de nuestro rango al ser muy pequeña. Buque N º 35: porque tiene el coeficiente de bloque fuera de nuestro rango de estudio. Las fórmulas del momento flector que vamos a obtener son muy sensibles a los valores del coeficiente de bloque. RANGO DE APLICACIÓN Por lo que ya podemos adelantar que las fórmulas a obtener tienen un rango de aplicación para buques de carga de navegación interior autopropulsados con maquinaria a popa y: 0.58 R 0.82 y 0.80 Cb < 0.94 Y no serán aplicables en los siguientes casos: a) Los buques con características diferentes de las descritas anteriormente b) Los buques de diseño inusual c) Los buques con otras condiciones de carga no homogéneas descritas en las condiciones de carga estándar del booklet VI. d) los buques de más de 135m de eslora e) Los buques con una desviación mayor del 20% entre el desplazamiento en rosca real y el valor estándar obtenido como se indica en el booklet V. BUQUES PARA LA VALIDACIÓN DE LAS FÓRMULAS La siguiente tabla contiene las características principales de los 12 buques de carga autopropulsados con maquinaria a popa que se usarán para la validación de las fórmulas: N Tipo de buque L (m) B (m) D (m) T (m) 57 Tanque Tipo C 84,59 9,48 5 3, ,12 9,67 0,886 7,840 4,100 0, Carga a granel 38 5,06 3 2,5 38,5 6 5,25 0,907 0,000 0,000 0,704 9 Portacontenedor ,41 5 3, ,5 10,1 0,922 10,12 4,600 0,785 l 8 Tanque Tipo C 132,75 11,4 6 3, ,95 9,8 0,914 9,400 5,150 0,791 Loa (m) 32 Tanque Tipo C 123,24 11,41 5 3,2 125 dar (m) 27,20 5 Dav (m) 10,34 5 Cb Bc (m) Dc (m) R 0,907 9,400 4,600 0, Tanque Tipo C 108,25 11,35 6 3, ,45 8,693 0,891 9,350 4,823 0, Tanque Tipo C ,4 6 4, ,55 11,11 0,894 9,956 4,870 0, Tanque Tipo C 107,85 11,41 5 3, ,6 10,55 0,881 9,810 4,620 0,758 11,88 56 Tanque Tipo C 107,75 13, ,75 0,871 4,537 0, Tanque Tipo C 106,85 11,4 5 3, ,8 9,55 0,912 9,786 4,230 0, Tanque Tipo C 92,98 11,34 5 3, ,6 5,38 0,922 9, ,742 Tanque Tipo 15 53,2 9,5 4 2, ,2 5,6 0,832 7,900 2,820 0,647 Ncerrado Lista de buques para validación TANIA SÁNCHEZ MACIÁ 22

23 Booklet 0: Project Overview III. ESTUDIO DEL PESO Y DE LA DISTRIBUCIÓN DE PESOS Como ya se ha mencionado anteriormente, el momento flector en aguas tranquilas viene determinado por: El peso y la distribución longitudinal de pesos del buque Peso de la carga y su distribución Peso del lastre y los suministros, y sus distribuciones Geometría y dimensión del casco Sabiendo la gran importancia que tiene considerar correctamente los pesos y sus distribuciones longitudinales sobre el buque, el primer objetivo en el que se centrará el presente estudio será desarrollar fórmulas para la estimación de los pesos y sus distribuciones. Con estas fórmulas se van a modelizar unos pesos estándares, con los que definiremos nuestros buques estándares ( los cuales serán empleados en la determinación de las fórmulas a desarrollar). Para conservar la misma estructura empleada actualmente por B.V., vamos a estudiar separadamente el peso en rosca, el peso del lastre, de suministros y de carga de los siguientes 12 buques. La suma de todos los estos elementos será el desplazamiento del buque. Nº Tipo de buque 6 Portacon tenedor 23 Tanque Tipo G 24 Tanque Tipo G 26 Tanque Tipo C 31 Tanque Tipo C 33 Tanque Tipo C 36 Tanque Tipo C 37 Tanque Tipo C 47 Tanque Tipo C 48 Tanque Tipo C 50 Tanque Tipo C 51 Tanque Tipo C L (m) B (m) D (m) T (m) Loa (m) dar (m) dav (m) Cb Bc (m) Dc (m) 108,15 11,45 3,65 3,55 110,00 17,40 10,25 0,895 10,09 4,83 0,744 92,30 11,40 5,70 2,80 95,04 15,16 9,71 0,882 9,60 4,80 0, ,60 11,36 5,32 2,80 106,00 16,81 9,93 0,885 9,00 4,50 0, ,37 11,40 5,40 3,86 110,00 16,10 9,77 0,898 9,78 4,65 0, ,65 16,80 5,75 4,95 135,00 22,25 13,15 0,892 15,20 4,93 0, ,95 11,45 5,32 3,60 110,00 15,60 10,65 0,883 9,85 4,58 0, ,95 11,40 5,32 3,80 110,00 15,60 10,65 0,885 9,79 4,53 0,757 83,05 9,56 4,70 3,60 84,30 14,30 9,57 0,921 7,96 4,00 0,713 82,95 9,46 4,75 3,07 85,95 16,15 9,03 0,875 7,86 4,00 0, ,10 11,45 5,70 4,10 130,00 15,80 10,80 0,935 9,85 4,88 0,792 65,95 10,50 5,10 3,45 66,00 15,60 12,25 0,821 8,90 4,00 0, ,25 15,00 5,39 4,31 135,00 16,50 10,55 0,913 13,40 4,59 0,797 Lista de barcos estudiados para el peso y distribución de peso R Para ver los detalles de los cálculos por favor véase el AppendixIII: Investigation of Weight and Weight Distribution. Details of Calculation y el Booklet V: Investigation of weight and weight distribution TANIA SÁNCHEZ MACIÁ 23

24 Booklet 0: Project Overview PESO EN ROSCA Para el análisis del peso en rosca del buque se han estudiado los siguientes elementos: -Casco - Tanque o bodega de carga - Caseta -Maquinaria principal a popa -Instalaciones de la maquinaria principal a popa -Maquinaria de proa -Instalaciones de la maquinaria de proa -Maquinaria auxiliar a popa -Maquinaria auxiliar a proa -Sistema de tuberías de carga -Equipo de fondeo y engranajes de proa -Equipo de fondeo y engranajes de popa El resultado final del estudio del peso en rosca se resume en la siguiente tabla: Elemento Peso Po, en t Centro de gravedad Xo desde AE, en m Ubicación desde AE, en m X 01 X 02 Casco D 3.7 m D > 3.7 m LBD LBD 0 L Bodega/tanque de carga (*) 0.03 L C B C D C d AR L d AV Caseta D 3.7 m D > 3.7 m LBD LBD 0 d AR Maquinaria Principal (**) Instalaciones de la maquinaria (**) Maquinaria a proa (**) Instalaciones de la maquinaria a proa (**) Maquinaria auxiliar a popa (**) Maquinaria auxiliar de proa (**) Sistema de tuberías (***) Equipamiento de anclaje a proa P C 0 (2/3)* d AR P C 0 d AR P C L- d AV / P C L - d AV L P C 0 d AR P C L - d AV L 0.01 LBT d AR L - d AV T (LB) 0.5 L- d AV /3 TANIA SÁNCHEZ MACIÁ 24

25 Booklet 0: Project Overview Elemento Equipamiento de anclaje a popa Peso Po, en t Centro de gravedad Xo desde AE, en m T (LB) Ubicación desde AE, en m X 01 X 02 Tabla resumen. Pesos y distribución de pesos estándar. (*) Se aplica en buques de carga de casco doble (**) En barcos, como por ejemplo los buques tanque tipo G, donde la relación entre la potencia y el peso muerto del buque es 1,de deberá aplicar factor corrector de 2. (***) Se aplica solamente en buques tanque PESO DE LOS SUMINISTROS Y PESO DEL LASTRE La cantidad de los suministros depende de las condiciones de operación de cada embarcación, como puede ser la distancia del viaje, si el barco navega en un río o canal, el tamaño de los buques, la capacidad de carga... por lo que es difícil definir un valor o fórmula que se adapte a todos los tipos y condiciones de los buques. Por lo que es necesario definir unos valores estándar. El peso del lastre también depende de las condiciones de operación de cada embarcación. Se utiliza para: Mejorar la estabilidad, el aumento del peso en la parte inferior del buque con el fin de bajar su centro de gravedad. Controlar el trimado Controlar el calado y la altura total del buque. Por ejemplo en la navegación interior a veces se necesita reducir la altura total del buque para pasar a través de puentes. Controlar los esfuerzos del buque cuando no se carga completamente. Mejora de la eficiencia de la hélice, para evitar que la hélice trabaje fuera del agua. Por lo que es difícil definir un valor o fórmula que se adapte a todos los tipos y condiciones de los buques. Por lo que es necesario definir unos valores estándar. Las ubicaciones de los suministros y del lastre se seleccionan con el fin de considerar la condición de carga más severa en la operación del buque: La posición longitudinal de ambos pesos se va a considerar en el punto medio de la parte de popa y proa. Y para la estimación del peso a considerar, se irá cambiando el porcentaje de llenado de los tanques con el fin de inducir arrufo o quebranto, según nos convenga. Vamos a mantener las fórmulas estándar que hoy en día utiliza BV para estimar ambos pesos: TANIA SÁNCHEZ MACIÁ 25

26 Booklet 0: Project Overview Elemento Peso Po, en t Centro de gravedad Xo desde AE, en m Suministros (proa) α 1 LBT L - d AV/2 Suministros (popa) α 1 LBT d AR /2 Lastre (proa) D 3.7 m D > 3.7 m Lastre (popa) D 3.7 m D > 3.7 m α 2 LBD α 2 LBD L - d AV / α 2 LBD α 2 LBD d AR /2 Peso estándar de lastre y suministros Donde, los valores de los coeficientes α 1 (suministros) y α2 (lastre) son: Condiciones de Carga α 1 α 2 Peso en Rosca Completamente cargado Condiciones transitorias Hogging 0 Sagging 0 PESO DE CARGA Al igual que en el estudio de peso en rosca del buque, se ha considerado que las fórmulas utilizadas actualmente por B.V. tienen una buena precisión para buques de casco sencillo. La fórmula usada actualmente es: P C = 0.85 LBT Cb Por lo que nuestro objetivo en esta sección es mejorar la estimación para buques de casco doble. Una evidencia de la necesidad de mejora se puede ver en el Appendix V: Cargo Weight formula analysis, donde se comprueba que el peso de la carga está sobreestimado. Para mantener una coherencia en nuestro estudio, la mejora se ha propuesto hacerla con los conceptos de peso de bodega / tanque y el peso del sistema de tuberías (solo para los buques tanque) por lo que la nueva fórmula a considerar será: P C = 0.85 LBT Cb X Y Asumiendo que la carga está distribuida en la zona central del buque, consideraremos: X 01 = d AR + X AR X 02 = L - d AV - X AV TANIA SÁNCHEZ MACIÁ 26

27 Booklet 0: Project Overview IV. CONDICIONES DE CARGA ESTÁNDAR. Hay muchas formas diferentes de distribuir la carga de un barco y a menudo algunas distribuciones o combinaciones pueden causar excesivos valores de momento de flexión en el buque. Por lo tanto, nuestro estudio debe centrarse en unas condiciones de carga generales o estándar, donde se incluyan las condiciones de carga más severas previstas para la explotación de este tipo los buques. (Utilizaremos las mismas que Bureau Veritas) PESO EN ROSCA Suministros 100% Lastre 50% Suponemos que en la condición de navegación en rosca, el buque está en quebranto (hogging). Como los suministros y lastre estándares considerados se encuentran en los extremos del barco, considerando esta condición estándar de carga se inducirá la condición más severa. COMPLETAMENTE CARGADO Suministros 10% Lastre 0% El barco se considera cargado uniformemente con su máximo calado. En esta situación el buque estará navegando en condición de arrufo (sagging), por lo que se considerará el mínimo peso de suministros y lastre, ya que estos están situados en los extremos del buque. Así se inducirá la condición más severa. CONDICIONES TRANSITORIAS En condición de quebranto (hogging): Suministros 100% y lastre 0% En condición de arrufo (sagging): Suministros 10% y lastre 0% Estas condiciones ocurren en puerto, cuando el buque está siendo cargado (1R o 2R). La razón de considerar estos porcentajes es la misma explicada anteriormente en las condiciones de buque en rosca y/o cargado completamente. V. CÁLCULO DIRECTO DEL MOMENTO FLECTOR DE UN BUQUE EN AGUAS TRANQUILAS APLICACIÓN DE LA THEORÍA DE UNA VIGA Una pequeña deformación de una viga, en estado elástico, viene gobernada por la ecuación del momento flector M (x) igual a: = donde f(x) es la carga aplicada de forma distribuida sobre la viga. La solución de M(x) requiere dos integraciones a lo largo de la eslora del buque. A continuación se explican los pasos a seguir: TANIA SÁNCHEZ MACIÁ 27

28 Booklet 0: Project Overview En primer lugar tenemos que obtener la fuerza vertical resultante neta, como ya hemos explicado anteriormente. Vamos a considerar el peso en rosca y de carga positivo w (x) y negativo de la fuerza de empuje b (x), (7 eq). En segundo lugar se obtiene la fuerza de corte Q (x) como la integral de la curva de fuerzas resultante. Se obtiene mediante la imposición de equilibrio de fuerzas de cizallamiento vertical de un elemento diferencial considerado como un cuerpo libre: Q+ f dx - Q - dq = 0 or = = + Recordemos que la viga buque se considera como una viga con extremos libres, por lo que tendrá esfuerzo cortante cero en los extremos. Ecuación 6 : Vv(0)= Q(0)=0 Finalmente se obtiene el momento flector: + + = 0 or = Donde C=0 por la misma explicación que en el esfuerzo cortante. = + El convenio de signos tomado se puede observar en la fotografía siguiente. - Esfuerzo cortante en cualquier punto es positivo si la integración, o acumulación neta, de la carga hasta el punto considerado es positivo. Si se define una "cara positiva", como la sección transversal que se muestra, cuando se mira en la dirección "x" positiva, la fuerza de corte es positiva hacia arriba cuando actúa sobre una cara negativa. -El momento de flexión en cualquier punto es positivo si la integración, o acumulación neta, de la fuerza de cizallamiento hasta el punto de que es positivo. Se puede demostrar fácilmente que con esta definición, el momento flector positivo corresponde a la curvatura del haz que es convexa hacia arriba (Hogging = quebranto). Y el estado opuesto, cóncava hacia arriba, se conoce como el arrufo. TANIA SÁNCHEZ MACIÁ 28

29 Booklet 0: Project Overview Resumen del momento flector de la viga casco De aquí en adelante, el momento de flexión aguas tranquilas es, conceptualmente, una tarea sencilla pero tediosa: Es simplemente una doble integración de la suma de la fuerza de empuje y el peso. Dado que esta es una parte básica de los cálculos hidrostáticos, utilizaremos el programa ARGOS para el cálculo de la fuerza de corte y el momento flector a lo largo de la eslora del buque en función de los pesos estándares que nosotros introduciremos. Para ver cómo se introducirán las cargas y como se calculará el momento flector, véase el capítulo 2 "Direct calculation of the Still Water Bending Moment" del Booklet VII: Direct Calculation of SWBM. Y para ver los resultados obtenidos, por favor véase el Appendix X: Summary table of the Bending moments results. TANIA SÁNCHEZ MACIÁ 29

30 Booklet 0: Project Overview Después de analizar los resultados obtenidos del máximo momento flector para cada condición y buque, se puede decir que las condiciones de carga donde ocurren los máximos momentos flectores son las siguientes: Cargando en 1R: Máximo momento en quebranto (hogging) Cargando en 1R: Máximo momento en arrufo (sagging) Cargando en 2R: Máximo momento en quebranto (hogging) Cargando en 2R: Máximo momento en arrufo (sagging) Analizando estas figuras, vemos que los máximos momentos flectores ocurren en puerto durante la carga/descarga del buque y no durante la navegación. El máximo hogging se obtiene cuando se empieza a cargar de proa hacia popa. Y en cambio, para el sagging se consigue cuando se empieza a cargar de popa hacia proa. Además, es importante señalar que el momento de flexión máximo, por lo general, se produce cuando las dos/tres bodegas/tanques estándar están cargados / descargados y las restantes bodegas/tanques están vacías / llenas (esto se produce tanto en las condiciones de carga, 1R y 2R), lo que significa que el momento de flexión debido al peso de la carga (ML) durante condiciones transitorias (Puerto), están asociadas a la misma ley. Este concepto se va a utilizar para desarrollar las nuevas fórmulas. VI. DESARROLLO DE LAS NUEVAS FÓRMULAS PARA EL CÁLCULO DEL MOMENTO FLECTOR EN AGUAS TRANQUILAS Para conocer las publicaciones previas a este proyecto referidas a fórmulas empíricas para el cálculo del momento de flector de un buque de carga de navegación interior, autopropulsado y en aguas tranquilas, véase el Booklet III: Publication review (BV Inland Rules Pt B, Ch 3, Sec 1-2). SÍMBOLOS M H: Momento flector de diseño en condición de quebranto en aguas tranquilas, en kn m M S: Momento flector de diseño en condición de arrufo en aguas tranquilas, en kn m TANIA SÁNCHEZ MACIÁ 30

31 Booklet 0: Project Overview M HO: : Momento flector en quebranto en aguas tranquilas (buque en rosca), en kn m M SO: : Momento flector en arrufo en aguas tranquilas (cargado completamente), en kn m M H1: : Momento flector en quebranto en aguas tranquilas durante carga/descarga, en kn m M S1: : Momento flector en arrufo en aguas tranquilas durante carga/descarga, en kn m M TH: : Momento flector vertical total en condición de quebranto, en kn m M TS: : Momento flector vertical total en condición de arrufo, en kn m M W: Momento flector de la ola, en kn m M C: Correción del momento flector, en kn m L: Eslora del reglamento, en m B: Manga, en m D: Puntal, en m Loa: Eslora total, en m Lwl: Eslora en la flotación, en m Δ: Desplazamiento, en ton, al calado T Cb: Coeficiente de bloque ρ: Densidad, en t/m^3 F: Factoer de carga: F = P/ P T 0.8 F 1 P : Peso de la carga real, en t P T : Peso de la carga, en ton, correspondiente al máximo calado T d AR: Distancia desde el final de popa AE hasta el mamparo de la bodega/tanque más a popa, en m d AV: Distancia desde el inicio de proa FE hasta el mamparo de la bodega/tanque más a proa, en m X AR: Distancia de la carga más a popa al mamparo de la bodega/tanque más a popa,en m X AV: Distancia de la carga más a proa al mamparo de la bodega/tanque más a proa,en m L AR: : Distancia de la carga al final de popa AE, en m : = + L AV: : Distancia de la carga al inicio de la proa FE, en m : = + R : Coeficiente tomado igual a: Project: : Development of empirical formulas for Still Water Bending Moment. TANIA SÁNCHEZ MACIÁ 31

32 Booklet 0: Project Overview ki : Coeficientes definidos como: = Buques Condición k 1 K 2 K 3 K 4 Autopropulsados Quebranto (hogging) Arrufo (Sagging) M L : Momento flector debido a la carga, en kn*m: Quebranto (Hogging) Condición Arrufo (Sagging) = = P L : Coeficiente de carga igual a: Quebranto (Hogging) Condición Arrufo (Sagging) = = L 1i : Coefficient taken equal to: Quebranto (Hogging) Condición Arrufo (Sagging) = 0.36 = = = = = X oi : Coeficiente tomado igual a: = = TANIA SÁNCHEZ MACIÁ 32

33 Booklet 0: Project Overview = METODOLOGÍA Como ya sabemos, el momento flector está en función del peso y la distribución de pesos. Y como para la estimación de pesos hemos usado fórmulas simples (las cuales eran función de las principales dimensiones del buque L,B, D, Cb..). Para estar en coherencia y como las fórmulas que estamos buscando son estimaciones para las etapas iniciales del proyecto en donde muchos datos son todavía desconocidos, es lógico pensar que necesitamos fórmulas simples que sean función también de L, B, D, Cb,... Si consideramos el momento flector como función de múltiples variables como son L, B, D..., es evidente que no podremos usar un modelo lineal para estimarlo. Por esta razón utilizaremos el programa Datafit como herramienta para resolver las regresiones no lineales necesarias. Una regresión no lineal es una evaluación para un modelo de tipo y = f (x, Ө) + ξ, basado en data multidimensional x,y donde "f" es una función no lineal referida a un parámetro Ө desconocido. El propósito es obtener valores de los parámetros que mejor se ajustan (normalmente usando el método de los mínimos cuadrados). MÉTODOS PARA EVALUAR LOS RESULTADOS Para cada condición de carga estudiaremos qué factores tienen influencia y propondremos la estructura de cada fórmula, con varias variables independientes y varios grados de libertad. Introduciremos todos los datos en el programa Datafit, y él nos dará los resultados de la regresión. Pero para saber si los resultados obtenidos los podemos considerar como válidos o no, estudiaremos los siguientes aspectos: Relación de los parámetros Dividiremos el valor del momento flector obtenido utilizando las nuevas fórmulas entre el valor obtenido por cálculo directo usando el peso y distribución de peso estándar. Los resultados serán aceptables si la relación es igual o mayor que 1. Lo que significará que las nuevas fórmulas dan valores más conservativos a los obtenidos por cálculo directo utilizando pesos estándar. Estudio de la relación entre la correlación de los datos experimentales y los puntos obtenidos con el ajuste de la curva (R 2 ): El factor de correlación R 2 entre el ajuste de la curva y los datos experimentales nos da información precisa acerca de cómo será el modelo. En nuestro estudio hacemos una gráfica con los valores experimentales (aquellos obtenidos mediante el cálculo directo del momento de flector) en el eje Y, y los valores obtenidos usando las nuevas fórmulas en el eje X. En esa gráfica dibujaremos la línea de tendencia y el factor R 2. R 2 es un índice estandarizado con un intervalo de 0 a 1. Se considera que el ajuste de la curva es bueno cuando R 2 es 1 o está cerca de 1. Un valor de R 2 cercano a 0 significará que los datos no se ajustan correctamente. TANIA SÁNCHEZ MACIÁ 33

34 Booklet 0: Project Overview - R 2 = 1, la línea de tendencia tiene un ajuste muy bueno a los puntos, lo que significa que la nueva fórmula es fiable o segura. - If R 2 1, (R 2 = ), significa que la flínea de tendencia no se ajusta a los puntos considerados. Método de los mínimos cuadrados Se trata de minimizar la suma de cuadrados de las diferencias en el eje de ordenadas (llamado residuos) entre los puntos generados por la función de valores de los datos seleccionados. Formulación dimensional del problema: Siendo, una serie de n puntos en el espacio rela, y una serie de m independientes funciones lineales en un espacio de funciones. Nosotros queremos encontrar una función f(x) la cual sea una combinación lineal de las funciones base, por lo que, lo que implica:. El objetivo es encontrar los m coeficientes cj que proporcionen el mejor ajuste de la función f(x) a los puntos dados (xk, yk). El criterio para considerar el mejor ajuste puede variar, pero en general está basado en minimizar la acumulación del error individual en cada punto simple referido al conjunto global. El error global se muestra como el método de la raíz cuadrada: La aproximación por mínimos cuadrados se basa en minimizar el error cuadrático medio o, de manera equivalente, en la minimización del error del radicando, llamado error al cuadrado, (Para ser capaz de aceptar la nueva fórmula, el error medio cuadrado debe ser pequeño) Project: : Development of empirical formulas for Still Water Bending Moment. TANIA SÁNCHEZ MACIÁ 34

35 Booklet 0: Project Overview LÍNEA DE INFLUENCIA Debido a la amplia variedad de posibles condiciones de carga, el barco rara vez estará en las mismas condiciones que hemos supuesto para los cálculos del momento de flexión. Por lo tanto, es importante ser capaz de calcular, lo más sencillamente posible, el efecto sobre el momento flector de la adición o eliminación de peso de la carga sobre la viga-casco. Una técnica útil para esto es la construcción de un diagrama de línea de influencia. Una línea de influencia muestra el efecto en el momento de flexión máximo de la adición de una unidad de peso en cualquier posición x a lo largo de la longitud del buque. La altura de la línea en la x representa el efecto sobre Mmáx de la adición de una unidad de peso en x. Dos líneas de influencia se dibujan normalmente, uno en condición de quebranto y otra para la condición de arrufo. Para los cálculos, véase el Appendix XI: Influence line diagram calculations. La línea de tendencia, en cada condición de carga (quebranto o arrufo) se va a dividir en dos partes: Parte de popa X X m BM = k x + k L Parte de proa X > X m BM = k x + k L Diagrama de la línea de influencia. Momento flector inducido añadiendo (quitando) 1ton Siendo, K 1L= Altura del punto intersección de la línea de influencia (parte de proa) con el eje Y. K 2 = pendiente de la línea de influencia en la parte de proa K 3L= Altura del punto intersección de la línea de influencia (parte de popa) con el eje Y. K 4 = pendiente de la línea de influencia en la parte de proa Centroide: puntos donde el momento inducido por añadir/eliminar 1 ton es cero. TANIA SÁNCHEZ MACIÁ 35

36 Booklet 0: Project Overview X 02 = posición longitudinal del centroide 1. X 04 = posición longitudinal del centroide 2. 0 = k x + k L = 0 = k x + k L = X m= posición longitudinal de la intersección de ambas líneas de influencia (proa y popa) ΔBM = ΔBM k x + k L = k x + k L = MOMENTOS FLECTORES DE DISEÑO Los momentos flectores estimados M H and M S, no se deben tomar inferiores a: Condición de carga Quebranto (Hogging) Arrufo (Sagging) Navegación Puerto = + = + = + = + Momentos flectores de diseño MOMENTOS FLECTORES ESTIMADOS EN AGUAS TRANQUILAS - NAVEGACIÓN EN ROSCA, CONDICIÓN DE QUEBRANTO (HOOGING)(Mo) - DESARROLO DE LA ESTRUCTURA DE LA FÓRMULA En esta situación, los pesos que influyen son: Empuje Δ = ρ V C 1 LBDC b Peso en rosca estándar C 2LBD Peso estándar de los suministros C 3LBD Peso estándar del lastre C 4 LBD TANIA SÁNCHEZ MACIÁ 36

37 Booklet 0: Project Overview Tomando momentos desde AE: BM = - C 1 LBDC b *L/2 + C 2LBD * L/2 + C 3LBD * (L- dav/2) + C 4 LBD * (L- dav/2) + C 3LBD * dar/2 + C 4 LBD * dar/2 L BM = LBD C 2 C L C 2 + C L dav 2 + C L dav 2 + C dar 2 + C dar 2 BM = a LBD L 2 b C + c L dav dar + d 2 2 BM = a L BD b C + c L dav L 2 + d dar L 2 Esta estructura puede ser introducida en el programa Datafit para obtener las constantes de la ecuación. Pero como nuestra intención es obtener fórmulas que sean lo más simples posible y teniendo en cuenta que los pesos de los suministros y el lastre se pueden despreciar en comparación con el peso en rosca del buque, se ha propuesto la siguiente estructura, con los grados de libertad a,b,c,d : BM = a L B D d C Utilizando el programa Datafit para resolver las regresiones no lineales, obtenemos unos valores de: a = ; b=1.430; c= 0.236; d = Por lo que la nueva fórmula propuesta será: =.... *Para ver los resultados del cálulo del momento flector véase el Appendix X: Summary table of the Bending moment results. -ANÁLISIS DE LOS RESULTADOS Método del mínimo cuadrado: el error global error es = , el cual comparado con las grandes magnitudes con las que estamos trabajando, se considera aceptable. Relación de los parámetros: La media es 1.04 >1, por lo que la nueva fórmula proporciona valores más conservativos. Ok! Factor de correlación (R 2 ): R 2 = Como este valor es cercano a 1, eso significa que la línea de tendencia se ajusta muy bien a los puntos. Consideramos la fórmula como válida! TANIA SÁNCHEZ MACIÁ 37

38 Booklet 0: Project Overview -NAVEGACIÓN A PLENA CARGA, CONDICIÓN DE ARRUFO (SAGGING) (Mso) - DESARROLLO DE LA ESTRUCTURA DE LA FÓRMULA Los pesos a tener en cuenta en esta condición son: el peso estándar del barco, el peso estándar de la carga y el peso estándar de los suministros. En este caso vamos a conservar la estructura utilizada hoy en día en BV: Siendo, M = F M M M HS : condición de carga del peso en rosca estándar y el peso estándar de los suministros (10%). Como ya hemos analizado previamente, el buque en rosca se supone en una condición de quebranto (por eso aparece en negativo en la fórmula anterior) con la siguiente estructura en la fórmula de estimación del momento flector: M = a L B D d C F Factor de carga igual a: F = P/ P T ; 0.8 F 1. Como el buque se considera con plena carga, en este caso F= 1. Mcs momento flector debido a la carga (la cual está distribuida a lo largo de la zona central produciendo una condición de arrufo). El peso de la carga se propone como "LBTCb". Como ya hemos estudiado en el estudio de las líneas de influencia, añadir o quitar un peso tiene diferente influencia en el momento flector del buque dependiendo de la situación longitudinal donde se produzca, por lo que en la estructura de Mcs tendremos en cuenta las ecuaciones de las lineas de influencia en arrufo de la siguiente manera: M = a LBTC [ k R L + K L X d ] + [ k L + K L L d d ] L = X d + d 2 = 0.5 d + X L = L = L d X + X 2 = 0.5 L d + X L Finalmente la estructura de la fórmula para Mso se propone con los siguientes grados de libertad: "a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q". TANIA SÁNCHEZ MACIÁ 38

39 Booklet 0: Project Overview L M = F a L B D C L L L e k 0.5 f d + g K K K K L + h K L i K K K K L d + j k L d + k K K K K L + l K L L d m K K K K L n L B D q C Utilizando el programa Datafit para calcular las regresiones no lineales obtenemos: a= 0.877; b=-0.077; c= 1.104; d = 0.366; e=5.647; f=0.211 g= 1.020; h =0.98; i=1.201; j=0.486; k=0.962; l=1.013 m=1.306; n=2.9262; o=1.125; p=0.042; q=1.079 Por lo que la nueva fórmula propuesta para el cálculo del momento flector de un buque en plena carga navegando en aguas tranquilas, en knm, será: = =..... [ +.. ] + [ +.. ] =.. +. =. +. = =.... Es importante resaltar que estas fórmulas dan los valores sin signo. *Para ver los resultados del cálulo del momento flector véase el Appendix X: Summary table of the Bending moment results. -ANÁLISIS DE LOS RESULTADOS Método del mínimo cuadrado: el error global error es = , el cual comparado con las grandes magnitudes con las que estamos trabajando, se considera aceptable. Relación de los parámetros: La media es 1.01 >1, por lo que la nueva fórmula proporciona valores más conservativos. Ok! TANIA SÁNCHEZ MACIÁ 39

40 Booklet 0: Project Overview Factor de correlación (R 2 ): R 2 = Como este valor es cercano a 1, eso significa que la línea de tendencia se ajusta muy bien a los puntos. Consideramos la fórmula como válida! - PUERTO, EN CONDICIÓN DE QUEBRANTO CARGANDO EN 1R (Mh1) - DESARROLLO DE LA ESTRUCTURA DE LA FÓRMULA Al igual que ocurre con la estructura de un buque en plena carga, en este caso también conservaremos la estructura actual de BV: M = M + M M HH = Peso en rosca estándar + 100% peso estándar de los suministros En este caso se propone la misma estructura ya explicada anteriormente pero con diferente cantidad de suministros, por lo que el resultado es: =.... M L = Máximo momento flector debido al peso de la carga durante las condiciones transitorias de carga y descarga en puerto Como ya sabemos el máximo momento flector ocurre cuando 2 o 3 bodegas/ tanques estándares están cargados / descargados (P L) y el resto permanece vacío/lleno. Por lo que para el cálculo de M L nos ayudaremos de la línea de influencia. M = P K X + K L Donde, X es la posición longitudinal del centro de gravedad del peso P L. = 6 2 P L es el peso de carga que induce el máximo momento flector TANIA SÁNCHEZ MACIÁ 40

41 Booklet 0: Project Overview P = a LBTC L L L 6 n n = número de bodegas/tanques cargados cuando ocurre el máximo momento flector n = L X d 6 Por lo que, para condición de quebranto, M H1 tomará la siguiente estructura: M = L B. D C + K a LBTC L b L L L 6 K L d 6 L d d K K L ck L d ek L Utilizando el programa Datafit para calcular las regresiones, obtenemos: a= 0.389; b=0.36; c= ; d = 0.966; e= Por lo que la fórmula propuesta para estimar el momento flector en aguas tranquilas en quebranto para la carga en 1R, en knm, es: = + =.... =. +. =. =. = +. *Para ver los resultados del cálulo del momento flector véase el Appendix X: Summary table of the Bending moment results. -ANÁLISIS DE LOS RESULTADOS Método del mínimo cuadrado: el error global error es = , el cual comparado con las grandes magnitudes con las que estamos trabajando, se considera aceptable. Relación de los parámetros: La media es >1, por lo que la nueva fórmula proporciona valores más conservativos. Ok! TANIA SÁNCHEZ MACIÁ 41

42 Booklet 0: Project Overview Factor de correlación (R 2 ): R 2 = Como este valor es cercano a 1, eso significa que la línea de tendencia se ajusta muy bien a los puntos. Consideramos la fórmula como válida! - PUERTO, EN CONDICIÓN DE QUEBRANTO CARGANDO EN 2R (Mh1) - DESARROLLO DE LA ESTRUCTURA DE LA FÓRMULA Al igual que ocurre con la estructura de un buque en plena carga, en este caso también conservaremos la estructura actual de BV: M = M M *Para ver los resultados del cálulo del momento flector véase el Appendix X: Summary table of the Bending moment results. -ANÁLISIS DE LOS RESULTADOS Método del mínimo cuadrado: el error global error es = , el cual comparado con las grandes magnitudes con las que estamos trabajando, se considera aceptable. Relación de los parámetros: La media es >1, por lo que la nueva fórmula proporciona valores más conservativos. Ok! Factor de correlación (R 2 ): R 2 = Como este valor es cercano a 1, eso significa que la línea de tendencia se ajusta muy bien a los puntos. Consideramos la fórmula como válida! - PUERTO, EN CONDICIÓN DE ARRUFO CARGANDO EN 1R (Ms1) - DESARROLLO DE LA ESTRUCTURA DE LA FÓRMULA Al igual que ocurre con la estructura de un buque en plena carga, en este caso también conservaremos la estructura actual de BV: M M + M M S0 = Máximo momento flector a plena carga (calculado anteriormente) M L = Máximo momento flector debido al peso de la carga Seguimos el mismo procedimiento ya explicado en condición de quebranto, solo varían los valores. Por lo que la fórmula propuesta para estimar el momento flector en puerto en condición de arrufo cargando en 1R, en knm, es: TANIA SÁNCHEZ MACIÁ 42

43 Booklet 0: Project Overview = + = =..... [ +.. ] + [ +.. ] =.. +. =. +. =.... = =. +. =. =. = +. *Para ver los resultados del cálulo del momento flector véase el Appendix X: Summary table of the Bending moment results. -ANÁLISIS DE LOS RESULTADOS Método del mínimo cuadrado: el error global error es = , el cual comparado con las grandes magnitudes con las que estamos trabajando, se considera aceptable. Relación de los parámetros: La media es 1.02 >1, por lo que la nueva fórmula proporciona valores más conservativos. Ok! Factor de correlación (R 2 ): R 2 = Como este valor es cercano a 1, eso significa que la línea de tendencia se ajusta muy bien a los puntos. Consideramos la fórmula como válida! TANIA SÁNCHEZ MACIÁ 43

44 Booklet 0: Project Overview - PUERTO, EN CONDICIÓN DE ARRUFO CARGANDO EN 2R (Ms1) - DESARROLLO DE LA ESTRUCTURA DE LA FÓRMULA Al igual que ocurre con la estructura de un buque en plena carga, en este caso también conservaremos la estructura actual de BV: M = M M *Para ver los resultados del cálulo del momento flector véase el Appendix X: Summary table of the Bending moment results. -ANÁLISIS DE LOS RESULTADOS Método del mínimo cuadrado: el error global error es = , el cual comparado con las grandes magnitudes con las que estamos trabajando, se considera aceptable. Relación de los parámetros: La media es 1.02 >1, por lo que la nueva fórmula proporciona valores más conservativos. Ok! Factor de correlación (R 2 ): R 2 = Como este valor es cercano a 1, eso significa que la línea de tendencia se ajusta muy bien a los puntos. Consideramos la fórmula como válida! TABLA RESUMEN DE LOS MOMENTOS FLECTORES ESTIMADOS PARA AGUAS TRANQUILAS Condición de carga Quebranto (Hogging) Arrufo (Sagging) Navegación Puerto 2R R + + Note 1: [ ] TANIA SÁNCHEZ MACIÁ 44

45 Booklet 0: Project Overview CORRECCIÓN DE LAS FÓRMULAS (M C) La corrección de fórmulas se usa para determinar el valor del momento flector correspondiente a los pesos y distribución de pesos real del barco, ya que hasta ahora hemos trabajado siempre con pesos estándar. La corrección M C es la suma de cada corrección individual del momento flector Mc para cada element, de la forma definida a continuación: Xg Xm BM = k x + k L Xg Xm BM = k x + k L Donde, ki coeficientes tomarán los valores: Buques Condición k 1 K 2 K 3 K 4 Autopropulsados Quebranto (Hogging) Arrufo (Sagging) Donde el peso o la posición del centro de gravedad de un elemento presenta una desviación mayor del 10% con respecto al valor estándar, se debe usar la corrección Mc dada anteriormente. Sin embargo, como la fórmula de Mc ha sido obtenida utilizando la línea de influencia, se debe tener en cuenta que está destinada para cambios pequeños de peso ( no más del 20% de discrepancia del desplazamiento) *Para ver los cálculos de Mc véase el Appendix XII: Correction bending moment (Mc). TANIA SÁNCHEZ MACIÁ 45

46 Booklet 0: Project Overview MOMENTO FLECTOR VERTICAL TOTAL Condición de carga Estado límite Quebranto (Hogging) Arrufo(Sagging) Navegación Rendimiento de la viga casco = + = + Otros estados límites = + ɤ = + ɤ Puerto Todos los estados límites = = TANIA SÁNCHEZ MACIÁ 46

47 Booklet I: Hull Girderr Loads TANIA SÁNCHEZ MACIÁ 47

48 Summary Booklet I 1. Introduction Loads applied to a ship structure Longitudinal Strength Loads Transverse Strength Loads Local Strength Loads Still water global loads Direct evaluation of still water global loads Application of Beam Theory Characteristics of the Shear force and Bending moment Curves Uncertainties in the evaluation Bibliography...62 TANIA SÁNCHEZ MACIÁ 48

49 CHAPTER 1: Introduction Accordingly with his own definition, a project is a set of calculations and drawings that are made to give an idea of how to be and what it must cost a work of architecture or engineering. The above definition can be fully applied to marine engineering. So, the documentation of the project should cover three key areas: 1. Economic 2. Technical 3. Commercial These aspects are nested, which means that changing any of the points, inevitably affects at least one other if not, the two remaining aspects. On the other hand, an usual ship project has two main features: It is cyclical. which means that the process leading to the detailed description of the vessel is always in cycles whose degree of definition is growing. It is iterative. which means that in each cycle, the project follows a process of trial and error. In fact, this cyclical and iterative process can be shown in the ship design spiral, schematic representation of the various calculations and decisions of each cycle or stage of project and checks at the end of each cycle, also known as project reviews. Fig I.1.1. Ship Design Spiral Nevertheless the design procedures differ from country to country, from shipyard to shipyard and differ between naval ships, commercial ships and high-speed passenger vessels. TANIA SÁNCHEZ MACIÁ 49

50 Booklet I: Hull Girder Loads 1. INTRODUCTION In a general way, we can say that the project starts with the basic design stage or preliminary idea. Where principal dimensions, hull forms, location of longitudinal bulkheads and transverse bulkheads, maximum still water bending moment, etc. are determined, assuming coherent values, to meet the owner's requirements such as deadweight and ship's speed. In addition, an example of one feasible methodology of the structural design procedure for commercial vessel such as tanker, container, can be: Receive general arrangement from the basic design group, Define structural arrangement based on the general arrangement, Determine initial scantling of structural members within design criteria (rulebased). This scantling based on rules is function of the maximum still water bending moment that the ship has to support. Check longitudinal and transverse strength, Change the structural arrangement or scantling (if it is necessary) Transfer the structural arrangement and scantling to the production design group. During project development, discussions with the ship owner are progressing and the project is fitting more and more, so that more and more refined data is being produced. Therefore, as a result of this brief introduction about ship design, we can see the great influence and importance of do a good estimation of the still water bending moment. Since as better the initial estimation be, faster will be the iterations to reach optimal results. Saving time and effort, and consequently money. The aim of this thesis is to develop new empirical formulas to estimate the maximum still water bending moment in sagging and hogging condition applicable to inland selfpropelled cargo carrier vessels. An empirical formula is an expression derived on the basis of experimental or numerical data of ships. So, this type of formulas may provide reasonable solutions for conventional hulls, but we can't use them for vessels with unusual design or vessels whose parameters are different of the range of parameters that we will define during this study. We cannot forget that the formulas that we are going to improve give us approximately values. They are an estimation, not actual values. And as usually the formulas are to be used for checking the minimum bending moment or during preliminary stages of the project and in these stages we don't know all the parameters of the ship, so they should be as simple as we will could obtain them. TANIA SÁNCHEZ MACIÁ 50

51 CHAPTER 2: Loads Applied to a Ship Structure A sailing ship is subjected to various load patterns with many magnitudes which cause deformation in her structure, as well as stresses. The structural designer needs to know the hull structure load features as accurately as possible. During the first design step, as we are already explained in the previous introduction, it is assumed exact loads acting on the structure, in order to estimate the structural strength in a reasonable way and consequently to develop the design. Hereunder is explained, in a general way, the classification and features of typical loads which can be applied to a hull structure. When considering the load features where the load is transmitted gradually and continuously from a local structural member to an adjacent bigger supporting member, the best way to categorize loads on the hull structure is as follows: Longitudinal strength loads Transverse strength loads Local strength loads 2.1. Longitudinal Strength Loads Longitudinal strength load means the load concerning the overall strength of the ship s hull, such as the bending moment, shear force and torque acting on a hull girder. Since a ship has a slender shape, it will behave like a beam, from the point of view of global deformation. (It will be discussed in the chapter 3 "Still water global loads"). The longitudinal strength loads may be divided into two categories: static longitudinal loads and dynamic longitudinal loads. Static longitudinal loads are induced by the local inequalities of weight and buoyancy in the still water condition. For instance, differences between weight and buoyancy in longitudinal direction cause a static bending moment and a static shear force, and asymmetrical cargo loading causes in a static torsional moment. As we are going to suppose a symmetrical cargo loading, and in still water we have a symmetric distribution of hydrostatic pressure acting on each section, we will not have torsional moment influence in our study. For a ship there are two possible longitudinal stresses situations due to the static bending moment: hogging and sagging condition. TANIA SÁNCHEZ MACIÁ 51

52 Booklet I: Hull Girder Loads 2. LOADS APPLIED TO A SHIP STRUCTURE Hogging occurs when the vessel has too much weight at her bow and stern and the crest of the wave is amidships with troughs on both ends of the vessel. The result of hogging is to put the deck under tensile strength and keel into compression. Fig I.2.1 Hogging Condition. Sagging may occur when the vessel has too much weight amidships with her bow and stern on the crest of two successive waves and the wave trough at the middle of the hull. The result of sagging is to put the deck under compression strength and keel into tensile. Fig I.2.2 Sagging Condition Dynamic longitudinal loads are induced by waves. Waves produce horizontal and vertical forces acting on side shell, so they can induce bending moment working in the horizontal and vertical plane at the same moment, if for example the ship is sailing diagonally across a regular wave (as shown in Fig. I.1.3); Fig. I.2.3 Ship in oblique waves TANIA SÁNCHEZ MACIÁ 52

53 Booklet I: Hull Girder Loads 2. LOADS APPLIED TO A SHIP STRUCTURE On the other hand, waves can also create a torsional moment due to variation of the wave surface at different sections along the ship's length. Nevertheless, as our aims is to develop the empirical formulae of still water bending moment, waves are out of range in our study. So, we will not study any dynamic load applied in a ship. But if we want to know the bending moment during navigation, we must add the bending moment due to waves to the still water bending moment that we are going to calculate Transverse Strength Loads The transverse strength loads represent the loads which act on transverse members and cause structural distortion of a cross section. Transverse strength loads include: - Hydrostatic and hydrodynamic pressure on the outer shell - Structural weight and cargo weight working on the bottom structure - Inertia force of cargo or ballast due to ship motion, so they induce deformation of the ballast or cargo tanks - Impact loads (slamming and sloshing) As we have already explained, our study is going to be developed in still water, from the above list, we are only going to take into account (a) the hydrostatic pressure due to the surrounding water and (b) the internal loading due to self weight and cargo weight. So, for instance, let s imagine a transverse section of a ship floating in still water as illustrated in Fig. I.2.4 Fig. I.2.4 Example of deformation due to transverse strength loads These loads are not always equal to each other at every point, consequently loads working on transverse members will produce transverse distortion as shown by the broken line. From the strength analysis point of view, when there is considered transverse loads and longitudinal loads, it is important to know that: "The distortion due to longitudinal loads does not affect the deformation of the transverse section." For example, the longitudinal bending moment or shear force can never have an influence on the distortion of the cross section. It is therefore necessary to consider the transverse deformation of the ship structure due to the transverse load, independently from the deformation induced by a longitudinal load. TANIA SÁNCHEZ MACIÁ 53

54 Booklet I: Hull Girder Loads 2. LOADS APPLIED TO A SHIP STRUCTURE As the longitudinal bending moment is not affected with the distortion of the cross section, we will not take into account transverse loads during our study Local Strength Loads The local strength loads include loads which affect the local strength members such as shell panels, stiffeners and connecting constructions between stiffeners. A load acting on the structure can be treated independently by considering the load transferring from a local structure to a bigger structure. For example, let s consider the case where the designer commences the design of a bottom structure as shown in Fig. I.2.5. Fig. I.1.5. Bottom structure under water pressure Firstly, the strength of bottom shell panels must be determined regarding lateral water pressure. Secondly, the strength of longitudinal stiffeners, which support the subject panels, must be evaluated. Thirdly, the strength of transverse webs holding stiffeners at their ends must be estimated and finally, the global strength of the bottom structure must be discussed. Investigations can be done separately for each member by only considering the magnitudes of the loads which are transmitted by each member. This is a convenient concept. However, time-dependent relations between those simplified loads have been intentionally omitted. Despite the phase of the loads can play an important roll when calculating the overall response, in order to make easier our study we are not going to talk about local loads, we are going to study the global ones. Which means, loads acting on the ship as a whole, considered as a beam (hull girder) in order to study the ship structural primary response. TANIA SÁNCHEZ MACIÁ 54

55 CHAPTER 3: Still Water Global Loads As it was said previously, longitudinal strength loads are loads which affect the overall strength of a ship (primary level of ship structural loading response), in which she is idealized as a hollow thin-wall box beam; referred to as the hull girder. At this level (primary) we can make several simplifying assumptions and approximations: The hull girder acts in accordance with simple beam theory. Actions on the beam are described, as usual with this scheme, only in terms of forces and moments acting in the transverse sections and applied on the longitudinal axis. So, there is only one independent variable, longitudinal position, and loads and deflections have only a single value at any cross section. The hull girder remains elastic, its deflections are small, and the longitudinal strain due to bending varies linearly over the cross section, about a transverse axis of zero strain (neutral axis). Dynamic effects may be either neglected. Since the bending strain is linear, the horizontal and vertical bending of the hull girder may be dealt with separately and superimposed. Since vertical bending predominates, we shall deal mainly with it (as we have already said in the previous point). So, we can assume that in longitudinal strength three components can act on each section: A resultant force along the vertical axis of the section (contained in the plane of symmetry), indicated as vertical resultant force q v A force in normal direction, (local horizontal axis), termed horizontal resultant force q H A moment about the x axis. All these actions are distributed along the longitudinal axis x. Fig. I, 3.1. Sectional Forces and Moment Therefore, in a general way, five main load components are accordingly generated along the beam, related to sectional forces and moment through equation 1 to 5: TANIA SÁNCHEZ MACIÁ 55

56 Booklet I: Hull Girder Loads 3. STILL WATER GLOBAL LOADS - Vertical resultant force - Vertical resultant moment - Horizontal resultant force - Horizontal resultant moment = = = = [1] [2] [3] [4] - Torque = [5] Due to total equilibrium, for a beam in free-free conditions (no constraints at ends) all load characteristics have zero values at ends: 0 = = 0 = = 0 0 = = 0 = = 0 [6] 0 = = 0 Global loads for the verification of the hull girder are obtained with a linear superimposition of still water and wave-induced global loads. According with the previous point, the main still water loads applied on the ship floating in calm water are: Lightship (structural weight., engines...) Dead weight and cargo load, supplies, ballast Buoyancy. These forces are determined by the shape of the hull and the location of the vessel in the water ( draft and trim). So, that means: There are no horizontal components of sectional forces and accordingly no components of horizontal shear and bending moment. (equation 3 and 4 are equal to zero). Usually the above loads have the plane of symmetry normal to the still water surface. In this condition, only a symmetric distribution of hydrostatic pressure acts on each section, together with vertical gravitational forces. If the latter ones TANIA SÁNCHEZ MACIÁ 56

57 Booklet I: Hull Girder Loads 3. STILL WATER GLOBAL LOADS are not symmetric, a sectional torque around (x) axis is generated. But in our study we will suppose that they are symmetrical. So for us, equation 5 is equal to zero. Finally we only consider the vertical resultant force V v (x), which is the sum of all the vertical load q sv (x)along the ship length. Obtained q sv (x) as a difference between buoyancy b(x) and weight w(x), as shown in equation 7. = = [7 ] Where: A I = transversal immersed area. So, components of vertical shear and vertical bending moment can be derived according to equations 1 and 2, as application of beam theory, which is explained in the next point. TANIA SÁNCHEZ MACIÁ 57

58 CHAPTER 4: Direct evaluation of Still Water Global Loads 4.1. Application of Beam Theory Direct evaluation of still water global loads are based in the beam theory. Following we are going to explain this theory, and later we will say how it is applied in a practical way. In elastic, a small-deflection beam theory the governing equation for the bending moment M(x) is: = in which the right hand side, f(x), is the loading on the beam expressed as distributed vertical force. The solution of M (x) requires two integrations along the length of the ship. Following is explained the steps that we must follow: Firstly we need to obtain the net resultant vertical force, as we have already explained in the previous point. As in early times forces were taken as positive download, we are going to consider positive the weight force w(x) and negative the buoyancy force b(x), (eq 7). Secondly we obtain the shear force Q(x) as the integral of the resultant forces curve. It is obtained by imposing vertical shear force equilibrium of a differential element considered as a free body: Q+ f dx - Q - dq = 0 or = = + We remember that for ships the constant of integration is always zero because the hull girder is a "free-free" beam, with zero shear force at the ends. Equation 6: Vv(0)= Q(0)=0 And finally to obtain the bending moment (say, about the right hand end of the element, and positive clockwise) yields: + + = 0 or = = + Where C=0 (for the same explanation than the shear force). TANIA SÁNCHEZ MACIÁ 58

59 Booklet I: Hull Girder Loads 4. DIRECT EVALUATION OF S.W. GLOBAL LOADS Fig I, 4.1. Summary of hull girder bending The sign conventions that is has been taken for shear force and bending moment are shown in the fig I, Shear force at any point is positive if the integral, or net accumulation, of load up to that point is positive. If we define a "positive face" as the cross section that one sees when looking in the positive x-direction, then the shear force is positive upward when acting on a negative face. -The bending moment at any point is positive if the integral, or net accumulation, of shear force up to that point is positive. It can easily be shown that with this definition, TANIA SÁNCHEZ MACIÁ 59

60 Booklet I: Hull Girder Loads 4. DIRECT EVALUATION OF S.W. GLOBAL LOADS positive bending moment corresponds to beam curvature that is convex upward (Hogging). And the opposite state, concave upward, is referred to as sagging Characteristics of the Shear force and Bending moment Curves If we tried to study the above graphics, we can define the following characteristics of the Shear force and Bending Moment curves: As we have seen, both the shear force and the bending moment must be zero at the ends. Since the load is the derivative of the shear force Q, a point of zero load corresponds to a local maximum or minimum value of Q, as shown in Fig I.4.1. If the loading is approximately similar forward and aft of amidships, the shear force is approximately asymmetric, passing through zero somewhere near amidships and having maximum values, positive and negative, near the quarter points. Since the shear force and the bending moment are related by Q=dM/dx, a point of zero Q corresponds to a local maximum or minimum value of bending moment, as shown by the dashed lines joining Fig I,4.1.e and f. If the loading is symmetric, the bending moment will be a maximum, positive or negative, near amidships. Since shear force is zero at both ends, the bending moment curve will have zero slope at both ends, and its value will be small forward and aft of the quarter points Uncertainties in the evaluation On the other hand, applying the explained theory to an actual ship, we know that the direct evaluation procedure requires, for a given load condition, a derivation, section by section, of vertical resultants forces, applied along the longitudinal axis x of the ship. To obtain the weight distribution w(x), there are some ways: Dividing the ship length into portions: for each of them, the total weight and center of gravity is determined summing up contributions from all items present on board between two bounding sections. Apply separately the procedure for different types of weight items, grouping together the weights of the ship in for example, lightweight conditions, cargo, ballast, consumables... However, as weight distribution is not completely defined until the end of the construction, in the early design stages, a significant contribution to uncertainties in the TANIA SÁNCHEZ MACIÁ 60

61 Booklet I: Hull Girder Loads 4. DIRECT EVALUATION OF S.W. GLOBAL LOADS evaluation of still water loads comes from the inputs to the procedure, in particular those related to quantification and location on board of weight items. Ship types like bulk carriers are more exposed to uncertainties on the actual distribution of cargo weight than, for example, container ships, where actual weights of single containers are kept under close control during operation. As we can see, the problem of the weight distribution is very important. For that, we will discuss widely in booklet V. In addition, model uncertainties arise from neglecting the longitudinal components of the hydrostatic pressure, which generate an axial compressive force on the hull girder. As the resultant of such components is generally below the neutral axis of the hull girder, it leads also to an additional hogging moment. Fig I.4.2. Longitudinal Component of Pressure All these compression and bending effects are neglected in the hull beam model, which accounts only for forces and moments acting in the transverse plane. Another approximation is represented by the fact that buoyancy and weight are assumed in a direction normal to the horizontal longitudinal axis, while they are actually oriented along the true vertical. TANIA SÁNCHEZ MACIÁ 61

62 CHAPTER 5: Bibliography Ship Structural Analysis and Design. By Owen F. Hughes and Jeom Kee Paik, with Dominique Bélghin, John B.Cqldwell, Hans G.Payer and Thomas E.Schellin. Published by The Society of Naval Architects and Marine Engineers. Analysis and Design of Ship Structure. By Philippe Rigo and Enrico Rizzuto Design of Ship Hull Structures. By M. Mano. Springer-Verlag Berlin Heidelberg Cálculo de Estructuras de Buques. By Ricardo Martin Dominguez. Escuela Técnica Superior de Ingenieros Navales, Sección de publicaciones año El proyecto de un buque mercante book-fbll01.1.odt.asignatura de Proyectos (E.T.S. Ingenieros Navales y Oceánicos). Impartida por los profesores D. Domingo García López y D. Francisco Blasco Lloret. Ship Structures I. E6002. By C.G. Daley Ship Global Response in Still Water. By Giles Thomas Tecnología de la Construcción del Buque. By Francisco Gonzales de Lema Martínez. Servicio de Publicaciones de la Universidad da Coruña. Mayo Inglés Técnico Naval. 3ºEdición By Elena Lopez, José M. Spiegelberg and Francisco Carrillo. Ship Structural Design. A rationally-based, Computer-Aided, Optimization Approach. By Owen F. Huges TANIA SÁNCHEZ MACIÁ 62

63 Booklet II: Scope of the study Inland Navigation Vessels TANIA SÁNCHEZ MACIÁ 63

64 Summary Booklet II 1. Scope of the Study Inland Waterways Inland Vessels Inland Cargo Carriers Inland Vessels Types Cargo Vessels Bulk Cargo Vessels Container Vessels General Cargo Vessels Roro Cargo Vessels Tank Vessels Tank Type G Tank Type C Tank Type N Passenger Vessels Vessels for dredging activities Dredger Hopper Barge Split Hopper Barge Hopper Dredge Split Hopper Dredge Working Units Launch Pontoon Pusher Tug Bibliography...83 TANIA SÁNCHEZ MACIÁ 64

65 CHAPTER 1: Scope of the Study The scope of the present study is inland navigation vessels. Inland navigation vessels are vessels intended for operation in inland waterways. So, the first idea that should be clear is what the waterways term includes. 1.1 Inland Waterways Inland waterway includes rivers, tributaries, canals and lakes. Inland navigation completes and extends maritime navigation and constitute the most economical means of transport on medium and long distances, namely for liquid and dry bulk cargoes. In developing countries, waterway is the most practical way to reach different areas in case of lack of infrastructure. The major assets of inland waterway transport can be: Effectiveness Inland waterway transport is particularly effective and energy-efficient ; its energy consumption per ton-kilometre of transported goods corresponds to 1/6 of the consumption on the road and to half of that of rail transport. Environmental impacts Its noise and gaseous emissions are modest. According to recent studies, the total external costs of inland navigation (in terms of accidents, congestion, noise emissions, air pollution and other environmental impacts) are 7 times lower than those of road transport. Reliability Compared to other modes which are often confronted with congestion and capacity problems, inland waterway transport is characterized by its reliability and has a major unexploited capacity. Safety Inland waterway transport ensures a high degree of safety, in particular when it comes to the transport of dangerous goods. Finally it contributes to the decongestion of the overloaded road network in densely populated regions. A close dependence of inland vessels on the infrastructure of the waterway network they are intended to operate should be noted. Making economic choice of inland waterway infrastructure is the most important problem to which government have to face up in order to reduce the transport cost per ton/km. TANIA SÁNCHEZ MACIÁ 65

66 Booklet II: Scope of the Study. Inland Navigation Vessels 1. SCOPE OF THE STUDY Several studies aiming to optimize the use of inland waterway are carried out all over the world. For instance: Use of one big deep lock instead of successive locks fitted for small difference of levels in order to save time of passing through locks Increase of power applied to gates and pumps for the reason given here above Optimization of lock number and dimensions to suit intended traffic Inland Vessels As we have said previously, the primary purpose of inland vessels is the transport of goods or passengers on rivers, canals or lakes. So, inland vessels are considerably affected by physical conditions in rivers and canals. Depending of the waterways features, the most important limitations are the following: Maximum draught and head room, because sometimes the ship may have to pass through bridges along the route. Length and witdth Radius of curvature in way of meanders Current velocity Ice, etc. We want to remark some differences between seagoing vessels and inland vessels: Environment Besides the vessel mission, operating environment determines the vessel design (geometry, lines and scantlings). Seagoing vessels are subjected to more severe environmental conditions than inland vessels (wave, corrosion). Lines and geometry Adapted to operating conditions: a) Vessel speed b) Seakeeping Parameters such as waterline length, draught, bow shape (U or V), etc, have an important effect on seakeeping, e.g.: -longer is better from seakeeping viewpoint -forward draught is very important in considering slamming -shape of forebody sections: V-shape is advantageous in considering slamming. c) Vessel stiffeness The length-to-depth ratio is a rough measure of the stiffness of the vessel and, of course, for a given set of scantlings, a deeper hull will provide equal longitudinal strength with less weight. The extreme value of L/D for sea going vessels is around 15. For inland vessels this ratio is held to a maximum of 25, for estuary navigation and to 35 for other ranges of navigation. TANIA SÁNCHEZ MACIÁ 66

67 Booklet II: Scope of the Study. Inland Navigation Vessels 1. SCOPE OF THE STUDY Applicable Rules and Regulations Statutory Rules applicable to seagoing vessels are worldwide Regulations, whilst most of statutory Rules applicable to inland vessels are local Regulations Inland Cargo Carriers Within the entire range of inland navigation vessels (which it is explained into the next chapter), we will focus this study into the following Cargo Carrier vessels: Cargo Vessels Bulk Cargo Vessels Container Vessels General Cargo Vessels Tank Vessels Tank Type G Tank Type C Tank Type N TANIA SÁNCHEZ MACIÁ 67

68 CHAPTER 2: Inland Vessels Types Ships are difficult to classify, mainly because there are so many criteria to base the classification on. As for example : Inland navigation or sea navigation. The shape, size and function or use. The number of hulls : monohull, catamaran, trimaran.. The hull material : steel, aluminum, wood, fiberglass and plastic. Type of propulsion system used : sailing ship, motorship, steamship.. The manufacturer, series or class. Following we are going to explain the different inland vessels types according to their purpose: 2.1 Cargo Vessels Bulk Cargo Vessels Container Vessels General Cargo Vessels Roro Cargo Vessels 2.2. Tank Vessels Tank Type G Tank Type C Tank Type N 2.3. Passenger Vessels 2.4. Vessels for dredging Activities Dredger Hopper Barge Split Hopper Barge Hopper Dredge Split Hopper Dredge 2.5. Working Units Launch Pontoon Pusher Tug TANIA SÁNCHEZ MACIÁ 68

69 Booklet II: Scope of the Study. Inland Navigation Vessels 2.INLAND VESSEL TYPES 2.1 Cargo Vessels Bulk Cargo Vessel Bulk cargo vessels are vessels, self-propelled or non-propelled, intended to carriage of dry bulk cargo in bulk, such coal, ores, phosphates, fertilizers, sand, gravel, feed, etc. They are provided with long hatches to facilitate grab discharge; they are also have strong holds and they have no derricks or cranes as the bulk cargoes are usually loaded by means of conveyor belts, spouts and other equipment installed on shore; however, some bulk carriers are designed with appropriate handling equipment for rapid loading and unloading of their particular cargo, or are self-unloading by means of conveyor belts. These ships can be loaded without having to trim their cargo by means of sloping sides, so this helps in a easy unloading by grabs or other systems. They are provided with ample ballast tanks. Following is shown a picture of an example of general arrangement drawing of this kind of ships. Hereafter, we can see an example of bulk cargo sailing in a river. This type of ships has to comply with PtD, Ch1, Sec 2 of BV rules. TANIA SÁNCHEZ MACIÁ 69

70 Booklet II: Scope of the Study. Inland Navigation Vessels 2.INLAND VESSEL TYPES Container Vessel. Container vessels are vessels, self-propelled or non-propelled, designed to transport containers. The hull is divided into cells accessible through large hatches in the main deck, and when the hatches are closed, more layers of containers are loaded on deck. Loading and unloading takes place at special berths equipped with giant travelling gantry cranes. Some of these ships are also fitted with gantry cranes. The loading of containers can create many problems, as the vessel has to be properly trimmed and leveled at all stages, in order that containers can be easily lowered into the cell guides; so these ships are equipped with sophisticated systems for pumping water ballast from one side of the ship to the other. Although there are different sizes of containers, the International Standards Organization (I.S.O.) has regulated standard dimensions for the containers, which are known as I.S.O. containers. The most usually containers have a length of 20 or 40. In the Appendix I we can see the Marine Container Types. When we describe the capacity of a container vessel, we mention the number of containers that she can carry, using the abbreviation teu. For example a 932 teu vessel means a container vessel that can carry 932 containers, each of 20 length. Following is shown a picture of an example of general arrangement drawing of this kind of ships. In this second picture we can see a typical inland container vessel. This type of ship has to comply with Pt D, Ch 1, Sec4 of BV rules. Project: : Development of empirical formulas for Still Water Bending Moment. TANIA SÁNCHEZ MACIÁ 70

71 Booklet II: Scope of the Study. Inland Navigation Vessels 2.INLAND VESSEL TYPES General Cargo Vessel General cargo vessels are vessels,, self-propelled or non-propelled, designed to transport general cargo, dry bulk cargo of density 1t/m^3 included. This type of ship has to comply with Pt D, Ch 1, Sec Roro Cargo Vessel Roro cargo vessels are vessels, self-propelled or non-propelled, intended for the carriage of : Vehicles which embark or disembark on their own wheels and/or goods in or on pallets or containers which can be loaded and unloaded by means of wheeled vehicles. Vehicles may be also embarked or disembarked by lift-on / lift-off methods. Railway cars, on fixed rails, which embark or disembark on their own wheels. They are usually equipped with bow and stern openings from which ramps can be extended to the quay; within the ship other ramps are provided for distributing the vehicles over the various decks. This type of ships has to comply with Pt D, Ch 1, Sec 5. Following is shown a picture of an example of general arrangement drawing of this kind of ships. TANIA SÁNCHEZ MACIÁ 71

72 Booklet II: Scope of the Study. Inland Navigation Vessels 2.INLAND VESSEL TYPES And in this second picture we can see a typical inland Ro-Ro vessel. Project: : Development of empirical formulas for Still Water Bending Moment. TANIA SÁNCHEZ MACIÁ 72

73 Booklet II: Scope of the Study. Inland Navigation Vessels 2.INLAND VESSEL TYPES 2.2.Tank vessels Tank vessels are vessels, self-propelled or non-propelled, designed for carry liquid or gaseous cargo in bulk. This type of ships has to comply with Pt D, Ch 1, Sec 3 of BV rules. The list of cargoes the tanker is allowed to carry will be issued by the Society, in the case of transport of dangerous goods (see Pt D, Ch 3, Sec 1). Except tankers type G, which tanks are cylindrical, the remaining type of tankers use to have a general arrangement similar to the following picture: Tanker Type G Type G applies to a tanker built and equipped for the carriage of gases under pressure or under refrigeration. The vessel shall be designed so as to prevent gases from penetrating into the accommodation and the service spaces. Outside the cargo area, the lower edges of door openings in the sidewalls of superstructures and the coamings of access hatches to under-deck spaces shall have a height of not less than 0.50 m above the deck. This requirement need not be complied with if the wall of the superstructures facing the cargo area extends from one side of the vessel to the other and has doors the sills of which have a height of not less than 0.50 m. The height of this wall shall not be less than 2.00 m. In this case, the lower edges of dooropenings in the sidewalls of superstructure and the coamings of access hatches behind this wall shall have a height of not less than 0.10 m. The sills of engine room doors and the coamings of its access hatches shall, however, always have a height of not less than 0.50 m. In the cargo area, the lower edges of door-openings in the sidewalls of superstructures hall have a height of not less than 0.50 m above the deck and the sills of hatches and ventilation openings of premises located under the deck shall have a height of not less than 0.50 m above the deck. This requirement does not apply to access openings to double-hull and double bottom spaces. TANIA SÁNCHEZ MACIÁ 73

74 Booklet II: Scope of the Study. Inland Navigation Vessels 2.INLAND VESSEL TYPES The bulwarks, foot-rails, etc shall be provided with sufficiently large openings which are located directly above the deck. This type of ships has to comply the requirements of Pt D, Ch3, Sec 3 of BV rules. Following is shown a picture of an example of general arrangement drawing of this kind of ships Tanker Type C Type C applies to a tanker built and equipped for the carriage of liquids. The vessel shall be of the flush deck type and double hull type with double hull spaces, double bottoms, but without trunk. The cargo tanks may be formed by the vessel s inner hull or may be installed in the hold spaces as independent tanks. The vessel shall be designed so as to prevent gases from penetrating into the accommodation and the service spaces. Outside the cargo area, the lower edges of door openings in the sidewalls of superstructures and the coamings of access hatches to under-deck spaces shall have a height of not less than 0.50 m above the deck. This requirement need not be complied with if the wall of the superstructures facing the cargo area extends from one side of the ship to the other and has doors the sills of which have a height of not less than 0.50 m. The height of this wall shall not be less than 2.00 m. In this case, the lower edges of door-openings in the sidewalls of superstructures and of coamings of access hatches behind this wall shall have a height of not less than 0.10 m. The sills of engine room doors and the coamings of its access hatches shall, however, always have a height of not less than 0.50 m. In the cargo area, the lower edges of door-openings in the sidewalls of superstructures shall have a height of not less than 0.50 m above the deck and the sills of hatches and ventilation openings of premises located under the deck shall have a height of not less than 0.50 m above the deck. This requirement does not apply to access openings to double-hull and double bottom spaces. The bulwarks, foot-rails, etc shall be provided with sufficiently large openings which are located directly above the deck. TANIA SÁNCHEZ MACIÁ 74

75 Booklet II: Scope of the Study. Inland Navigation Vessels 2.INLAND VESSEL TYPES This type of ships has to be comply with the requirements fo Pt D, Ch 3, Sec3 of BV rules Tanker Type N Type N applies to a tanker built and equipped for the carriage of liquids in accordance with the applicable BV rule requirements stated under Pt D, Ch3, Sec4. The vessel shall be designed so as to prevent gases from penetrating into the accommodation and the service spaces. Outside the cargo area, the lower edges of door openings in the sidewalls of superstructures and the coamings of access hatches to under-deck spaces shall have a height of not less than 0.50 m above the deck. This requirement need not be complied with if the wall of the superstructures facing the cargo area extends from one side of the ship to the other and has doors the sills of which have a height of not less than 0.50 m. The height of this wall shall not be less than 2.00 m. In this case, the lower edges of door-openings in the sidewalls of superstructures and of coamings of access hatches behind this wall shall have a height of not less than 0.10 m. The sills of engine room doors and the coamings of its access hatches shall, however, always have a height of not less than 0.50 m. In the cargo area, the lower edges of door-openings in the sidewalls of superstructures shall have a height of not less than 0.50 m above the deck and the sills of hatches and ventilation openings of premises located under the deck shall have a height of not less than 0.50 m above the deck. This requirement does not apply to access openings to double- hull and double bottom spaces. The bulwarks, foot-rails, etc. shall be provided with sufficiently large openings which are located directly above the deck. There are two types: tanker type N closed and Tanker typer N open: TANIA SÁNCHEZ MACIÁ 75

76 Booklet II: Scope of the Study. Inland Navigation Vessels 2.INLAND VESSEL TYPES Tanker Type N Closed Tanker Type N Open TANIA SÁNCHEZ MACIÁ 76

77 Booklet II: Scope of the Study. Inland Navigation Vessels 2.INLAND VESSEL TYPES 2.3. Passenger Vessels Passenger vessels are vessels, self-propelled or non-propelled, designed to transport passengers. They are usually provided with bow thruster to assist in maneuvering when docking or undocking. Following is shown a picture of an example of general arrangement drawing of this kind of ships. And in this second picture we can see a typical inland passenger vessel sailing. Project: : Development of empirical formulas for Still Water Bending Moment. TANIA SÁNCHEZ MACIÁ 77

78 Booklet II: Scope of the Study. Inland Navigation Vessels 2.INLAND VESSEL TYPES 2.4. Vessels for dredging activities There are different type and service notations Dredger The aims the dredgers are excavate, transport and dispose soil lying underwater. Dredgers are employed to maintain ports, canals and estuaries at desired water depth, as well as preparation of new sites. Typically, soil is removed, transported/pumped to holds within the dredger, stored (as a soil-water mixtures), and discharged at another side. There are two basic techniques for dredgers: -Hydraulic using erosion by waterjet and pumping (cohesionless soil such as silt, sand and gravel). -Mechanic using cutting tools and conveyor belts or grabs (cohesive soils). Normally both transverse and longitudinal stability is evaluated for at least four operational conditions (departure fully loaded, arrival fully loaded, departure in ballast condition, arrival in ballast condition). Special attention must be paid to free-surface effects due to the water-soil mixture in the tanks. Intermediate filling conditions may be most critical and different intermediate conditions should be analyzed. The type and service notation Dredger, applies to vessels specially equipped only for dredging activities (excluding carrying dredged material), complying with applicable requirements stated under Pt D, Ch 1, Sec 9. TANIA SÁNCHEZ MACIÁ 78

79 Booklet II: Scope of the Study. Inland Navigation Vessels 2.INLAND VESSEL TYPES Hopper barge The type and service notation Hopper barge, applies to vessels specially equipped for carrying spoils or dredged material only, complying with applicable requirements stated under Pt D, Ch 1, Sec Split hopper barge The type and service notation Split hopper barge, applies to vessels specially equipped for carrying spoils or dredged material only, an d which open longitudinally around hinges in compliance with Pt D, Ch 1, Sec 9. TANIA SÁNCHEZ MACIÁ 79

80 Booklet II: Scope of the Study. Inland Navigation Vessels 2.INLAND VESSEL TYPES Hopper dredger The type and service notation Hopper dredger, applies to vessels specially equipped for dredging activities and carrying spoils or dredged material, complying with applicable requirements stated under Pt D, Ch 1, Sec Split hopper dredger The type and service notation Split hopper dredger applies to vessels specially equipped for dredging activities and carrying spoils or dredged material, which open longitudinally around hinges, complying with Pt D, Ch 1, Sec 9. TANIA SÁNCHEZ MACIÁ 80

81 Booklet II: Scope of the Study. Inland Navigation Vessels 2.INLAND VESSEL TYPES 2.5. Working Units There are different type and service notations: Launch The type and service notation Launch is assigned to small vessels which are used to provide facilities and assistance for the performance of specified activities, complying with the requirements stated under Pt D, Ch 1, Sec Pontoon The type and service notation Pontoon is assigned to non-propelled units intended to carry cargo and/or equipment on deck only, complying with the requirements stated under Pt D, Ch 1, Sec 8. When a crane is permanently fitted on board, the crane is to be certified and the type and service notation Pontoon -crane is granted Pusher The type and service notation Pusher, applies to vessels specially equipped for pushing, complying with applicable requirements stated under Pt D, Ch 1, Sec 7. TANIA SÁNCHEZ MACIÁ 81

82 Booklet II: Scope of the Study. Inland Navigation Vessels 2.INLAND VESSEL TYPES Tug The type and service notation Tug, applies to vessels specially equipped for towing. In general, towing hooks and winches are arranged in way of the vessel s centerline, in such a position as to minimize heeling moments in normal working conditions. This type of vessels has to comply with applicable requirements stated under PtD, Ch1,Sec 7. TANIA SÁNCHEZ MACIÁ 82

83 CHAPTER 3: Bibliography Class Rules.DNI Training Material November Bureau Veritas BV. Rules for the Classification of Inland Navigation Vessels. November 2011 Ship Design. Ship Types. Introduction to Inland Rules. DNI Training Material November Website: TANIA SÁNCHEZ MACIÁ 83

84 Booklet III: Publication review (B.V. Inland Rules Pt B,Ch3, Sec1-2) Sec1 TANIA SÁNCHEZ MACIÁ 84

85 Summary Booklet III 1.Symbols and definitions Symbols Definitions Estimated Still Water Bending Moments Estimated design bending moments Range of application Standard weights and weight distribution for self-propelled cargo carriers Standard light vessel weights and weight distribution Standard cargo weight and cargo distribution Values of estimated still water bending moments Correction bending moment Wave Bending Moments Total vertical Bending Moments...96 TANIA SÁNCHEZ MACIÁ 85

86 CHAPTER 1: Symbols and Definitions 1.1. Symbols Following we are going to explain all the symbols that are used in the B.V. Rules Pt B, Ch 3, Sec 2 to obtain the estimated bending moments. M H: : Design still water bending moment in hogging condition, in kn m M S: : Design still water bending moment in sagging condition, in kn m M HO: : Still water bending moment in hogging condition, in kn m M SO: : Still water bending moment in sagging condition, in kn m M H1: : Still water bending moment in hogging condition while loading/ unloading, in kn m M S1: : Still water bending moment in sagging condition while loading/ unloading, in kn m M TH: Total vertical bending moment in hogging condition, in kn m M TS: : Total vertical bending moment in sagging condition, in kn m M W: Wave bending moment,, in kn m M C: Correction bending moment, in kn m L: Rule length, in m B: Breadth, in m D: Depth, in m Loa: Length overall, in m Lwl: Length of waterline, in m Δ: Displacement, in tons, at draught T Cb: Block Coefficient ρ: Density, in t/m^3 F: Loading factor equal to: F = P/ P T 0.8 F 1 P : Actual cargo weight, in t P T : Cargo weight, in t, corresponding to the maximum vessel draught T n : Navigation coefficient, taken as: n = 0.85 H TANIA SÁNCHEZ MACIÁ 86

87 Booklet III: Publication Review 2. ESTIMATED STILL WATER BENDING MOMENT H : Wave height C : Wave parameter, taken equal to : = < = ɤ w : Coefficient, taken equal to: ɤ w = 1.00 for n < 1.02 ɤ w = 0.72 for n d AR: Distance of aftmost cargo hold/tank bulkhead from aft end (AE), in m d AV: Distance of foremost cargo hold/tank bulkhead from fore end (FE), in m X AR: Distance of aftmost cargo edge to aftmost cargo hold/tank bulkhead, in m X AV: Distance of foremost cargo edge to foremost cargo hold/tank bulkhead, in m L AR: Distance of cargo from aft end, in m, taken equal to: = + L AV: Distance of cargo from fore end, in m, taken equal to: R : Coefficient taken equal to: l i : Coefficient taken equal to: ki : Coefficients defined in table 6 L i : Coefficients taken equal to: = + = = = = 0.5 TANIA SÁNCHEZ MACIÁ 87

88 Booklet III: Publication Review 2. ESTIMATED STILL WATER BENDING MOMENT = 0.5 = P L : Coefficients taken equal to: = 0.77 M L : Bending moment, in kn m, taken equal to: = + R ij : Coefficients taken equal to: = 0.5 = 0.5 = 0.5 = Definitions Rule length (L) The rule length L is the distance, in m, measured on the load waterline from the fore side of the stem to the after side of the rudder post, or to the centre of the rudder stock where there is no rudder post. L is to be not less than 96% of the extreme length on the load waterline. In case of vessels having neither a rudder post (e.g. vessels fitted with azimuth thrusters) nor a rudder (e.g. pushed barges) the rule length L is to be taken equal to the length of the load waterline. In vessels with unusual stem or stern arrangements, the rule length L is to be considered on a case by case basis. Hereafter, whenever we say length L, we will refer to the rule length. Ends of rule length and midship The fore end (FE) of the rule length L, is the perpendicular to the load waterline at the forward side of the stem. TANIA SÁNCHEZ MACIÁ 88

89 Booklet III: Publication Review 2. ESTIMATED STILL WATER BENDING MOMENT The aft end (AE) of the rule length L, is the perpendicular to the waterline at a distance L aft of the fore end. The midship is the perpendicular to the waterline at a distance 0.5L aft of the fore end. Breadth (B) The breath B is the greatest moulded breadth, measured amidships below the weather deck. Depth (D) The depth D is the distance, in m, measured vertically on the midship transverse section, from the moulded base line to the top of the deck beam at side on the uppermost continuous deck. In the case of a vessel with a solid bar keel, the moulded base line is to be taken at the intersection between the upper face of the bottom plating with the solid bar keel. Draught (T) The draught T is the distance, in m, measured vertically on the midship transverse section, from the moulded base line to the load line. In case of vessels with a solid bar keel, the moulded base line is to be taken as defined before in the section of the depth. Length overall (Loa) The length overall is the extreme length of the vessel, in m, measured from the foremost point of the stem to the aftermost part of the stern. Illustration of some parameters In order to clarify a little bit the meaning of some parameters we show this picture. But as in our formulas we will not use all of this parameters, we don't explain the meaning now, we will do it later with our final parameters. Because this latest are the important ones for us. TANIA SÁNCHEZ MACIÁ 89

90 CHAPTER 2: Estimated Still Water Bending Moments 2.1. Estimated Still Water Bending Moments The values of design still water bending moments M H and M S, are to be provided by the designer, for all load cases considered. Al calculation documents are to be submitted to the Society. If the values of design still water bending moments are not provided thy the designer, they are not to be taken less than those derived from the following table III.1: Load case Hogging Sagging Navigation = + = + Harbour (1) = + = + (1) Applies only to cargo carriers Note1: For application of, see 2.5 Table III.2.1: Estimated design bending moments 2.2. Range of application The requirements of this Article (BV Inland rules Pt B, Ch 3, Sec2 ) apply to vessels of types and characteristics listed hereafter: Self-propelled cargo carriers with machinery aft with: 0.60 R Cb < 0.95 We are not to mention the requirements of non-propellers or passenger ships because they are out of our aims. The formulae given hereafter are not applicable to following types of vessels: Vessels of types other than those covered above Vessels of unusual design Vessels with any non-homogeneous loading conditions other than standard loading conditions which we will described it in Ch 3 Sec1. TANIA SÁNCHEZ MACIÁ 90

91 Booklet III: Publication Review 2. ESTIMATED STILL WATER BENDING MOMENT Vessels greater than 135m in length Vessels with actual lightship displacement showing at least 20% deviation from standard value derived from the next point Standard weights and weight distribution for self-propelled cargo carriers Standard light vessel weights and weight distribution The formulae of estimated still water bending moments are based on standard weights and weight distribution defined in table III.2. Item Weight Po, in t Centre of gravity Xo from AE, in m Location from AE, in m X 01 X 02 Hull D 3.7 m D > 3.7 m LBD LBD 0 L Deckhouse D 3.7 m D > 3.7 m LBD LBD 0 d AR Main Machinery LBT d AR /2 Machinery Installations LBT 0 d AR Piping System (1) 0.005LBT d AR L - d AV Anchor equipme nt and Gear LBT L- d AV /3 Supplies (fore) Supplies (aft) Ballast (fore) D 3.7 m D > 3.7 m Ballast (aft) D 3.7 m D > 3.7 m 0.005α 1LBT 0.005α 1LBT 0.010α 2LBD 0.003α 2LBD 0.010α 2LBD 0.003α 2LBD (1) Application for tank vessels only Note 1: α 1, α 2. Coefficients defined in Table III.3 L- d AV /2 L- d AR /2 L- d AV /2 d AR /2 Table III. 2.2 : Self-propelled cargo carriers standard weights and weight distribution TANIA SÁNCHEZ MACIÁ 91

92 Booklet III: Publication Review 2. ESTIMATED STILL WATER BENDING MOMENT Loading Conditions α 1 α 2 Lightship Fully loaded vessel Transitory conditions Hogging Sagging Table III. 2.3 : Values of coefficients α1 and α Standard cargo weight and cargo distribution The cargo weight is assumed to be uniformly distributed on the cargo space, and is taken equal to, in t: Po= 0.85 LBT Cb The standard weight of items not covered in or is to be taken equal to: Po= Values of estimated still water bending moments For self-propelled cargo carriers the hogging and sagging bending moments in still water conditions are to be obtained, in, kn m, from formulae given in table III. 4 Load Case Hogging Sagging Navigation = = Harbour 2R = = R = + = Note 1: = = = [ ] Table III. 2.4 : Estimated still water bending moments of self-propelled cargo carriers TANIA SÁNCHEZ MACIÁ 92

93 2.5. Correction bending moment The correction bending moment applies only to cargo carriers whose still water bending moment is calculated with the formulae derived from the table III.4. The correction bending moment Mc is the sum of each individual correction bending moment Mc of each individual item as defined in Tab III. 5 and is to be considered for both hogging and sagging conditions. Where the weight or location of the centre of gravity of a lightship item or cargo item presents a deviation greater than 10% with respect to the standard value defined 2.2 and 23, as applicable, the design bending moment is to be corrected using correction bending moment Mc given in table III. 5. Item Location X L/2 X > L/2 Self-propelled cargo carriers Hull weight (1) Concentrated weights or loads Distributed weights or loads = = + + = + + (1) Uniform weight distribution Note 1: = = ki= Coefficients defined in table III. 6 d= Actual distance from midship as shown in fig III.1,in m, of centre of gravity of concentrated weights or loads (d 0): d= L/2 - x for x L/2 d=x- L/2 for x > L/2 d 0= Standard distance from midship, in m, of centre of gravity of concentrated weights or loads (d 0) d 1,d 2 = Distances measured from midship, in m, defining the extent of actual distributed weight or load d 01,d 02 = Distances measured from midship, in m, defining the extent of standard distributed weight or load Table III.2. 5 : Correction bending moment Mc TANIA SÁNCHEZ MACIÁ 93

94 Booklet III: Publication Review 2. ESTIMATED STILL WATER BENDING MOMENT Vessels Conditions k 1 K 2 K 3 K 4 Self- Propelled Hogging Sagging Table III. 2.6 : Coefficinets ki Figure III : Definition of distances d, d1 and d2 TANIA SÁNCHEZ MACIÁ 94

95 CHAPTER 3: Waves Bending Moments Waves bending moments are out of our aims has we are already explained in previous booklets. Nevertheless as to obtain the total estimation of the vertical bending moment of a ship when she's sailing, is needed to superimpose the effect of the still water bending moment and bending moment induced by waves, we are going to explain the formulas that B. V. Inland Rules uses actually. An additional wave bending moment taking into account the stream and water conditions in the navigation zone is to be considered, except for range of navigation IN(0). For range of navigation IN(0.6), the absolute value of the additional bending moment amidships is to be obtained, in kn m, from the following formula: Mw= L 2 B Cb For range of navigaton IN (1.2 x 2), the absolute value of the wave-induced bending moment amidships is to be obtained, in kn m, from the following formula: Mw = n C L 2 B ( Cb + 0.7) TANIA SÁNCHEZ MACIÁ 95

96 CHAPTER 4: Total Vertical Bending Moment The total vertical bending moments are to be determined as specified in table III.7 Load Case Limit State Hogging Sagging Navigation Hull girder yielding = + = + Other limit states = + ɤ = + ɤ Harbour All limit states = = Table III. 4.1 : Total vertical bending moments TANIA SÁNCHEZ MACIÁ 96

97 Booklet IV: Studied Vessels (Range of parameters) TANIA SÁNCHEZ MACIÁ 97

98 Summary Booklet IV 1. Investigated vessels Studied Parameters and Range of Application Studied Parameters Range of Application Ships for validation TANIA SÁNCHEZ MACIÁ 98

99 Booklet IV: Studied Vessels 1. INVESTIGATED VESSELS CHAPTER 1: Investigated vessels N All the studied vessels are inland self-propelled cargo carriers with machinery aft and double hull. The following table contains the particulars of the forty-six investigated vessels: Cargo Carrier Type L (m) B (m) D (m) T (m) Loa (m) Cargo 1 49,45 11,40 5,55 3,17 51,20 9,55 7,40 0,872 9,81 3,63 0,657 Vessel 2 Container 131,55 14,50 5,70 3,60 134,24 17,60 10,45 0,903 12,88 6,36 0,787 3 Container 133,90 11,40 3,90 3,80 135,00 17,90 16,50 0,926 10,14 3,85 0,743 4 Container 97,77 11,20 3,00 2,20 100,20 13,80 9,67 0,908 9,95 3,00 0,760 5 Container 106,30 17,10 5,68 4,50 110,00 13,50 9,30 0,854 10,00 6,68 0,786 6 Container 108,15 11,45 3,65 3,55 110,00 17,40 10,25 0,895 10,09 4,83 0,744 7 Container 84,50 14,15 5,00 4,50 86,00 1,50 8,47 0,935 12,55 5,50 0,882 8 Container 133,00 11,45 3,90 2,80 135,00 17,00 9,00 0,896 10,18 3,98 0, Container 132,92 11,40 3,50 3,49 134,97 17,25 9,70 0,917 10,13 2,90 0, Tanker Type N 108,50 11,41 4,99 3,65 110,00 19,00 12,10 0,902 9,77 4,44 0, Tanker Type N 103,20 10,45 3,80 2,90 105,00 15,60 10,38 0,873 9,15 3,10 0, Tanker Type N 107,57 10,45 4,00 3,31 109,92 15,85 9,50 0,892 9,15 3,32 0, Tanker Type N 108,78 11,40 4,30 3,35 109,98 17,40 9,78 0,901 9,96 3,59 0, Tanker Type N 108,18 11,35 4,00 2,85 109,80 17,68 11,30 0,873 9,92 3,23 0, Tanker Type N 84,05 10,95 4,60 2,80 85,95 17,30 9,15 0,853 9,33 3,85 0, Tanker Type N 53,50 11,50 4,60 3,30 55,42 13,65 4,65 0,829 9,90 3,80 0, Tanker Type N 107,86 10,95 3,50 3,46 109,96 16,40 9,96 0,887 8,84 2,54 0, Tanker Type N 33,70 6,40 3,55 2,50 35,00 9,60 6,10 0,835 0, Tanker Type N 84,03 9,00 3,58 2,61 85,95 11,10 7,08 0,938 7,00 2,78 0, Tanker Type G 92,30 11,40 5,70 2,80 95,04 15,16 9,71 0,882 9,60 4,80 0, Tanker Type G 103,60 11,36 5,32 2,80 106,00 16,81 9,93 0,885 9,00 4,50 0, Tanker Type G 106,25 11,35 5,20 2,50 108,50 18,46 7,41 0,877 8,85 4,43 0, Tanker Type C 108,37 11,40 5,40 3,86 110,00 16,10 9,77 0,898 9,78 4,65 0,761 dar (m) dav( m) Cb Bc (m) Dc (m) R TANIA SÁNCHEZ MACIÁ 99

100 Booklet IV: Studied Vessels 2. STUDIED PARAMETERS AND RANGE OF APPLICATION N Cargo Carrier Type Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type N L (m) B (m) D (m) T (m) Loa (m) dar (m) dav( m) Cb Bc (m) Dc (m) 107,84 13,50 5,32 4,00 110,00 16,25 10,59 0,877 11,88 4,54 0, ,65 16,80 5,75 4,95 135,00 22,25 13,15 0,892 15,20 4,93 0, ,95 11,45 5,32 3,60 110,00 15,60 10,65 0,883 9,85 4,58 0, ,00 11,45 4,67 3,20 110,00 17,30 9,19 0,882 9,85 3,88 0, ,00 11,40 6,00 4,05 125,00 19,48 10,98 0,687 9,38 5,17 0, ,95 11,40 5,32 3,80 110,00 15,60 10,65 0,885 9,79 4,53 0,757 83,05 9,56 4,70 3,60 84,30 14,30 9,57 0,921 7,96 4,00 0,713 84,47 9,60 4,70 3,35 85,96 16,05 10,46 0,881 8,00 3,95 0, ,36 11,40 6,00 4,30 121,16 15,30 10,06 0,898 9,38 5,17 0,786 83,63 10,50 5,10 3,60 85,00 16,05 10,43 0,878 8,90 4,34 0, ,00 11,40 5,34 4,00 135,00 18,81 9,80 0,928 9,78 4,64 0, ,20 11,40 5,40 3,76 110,00 16,00 8,70 0,894 9,90 4,65 0, ,41 11,40 5,30 3,40 110,00 18,50 10,71 0,896 9,80 4,60 0,731 83,75 9,50 4,25 2,80 86,00 15,48 9,22 0,909 7,50 3,40 0,705 82,95 9,46 4,75 3,07 85,95 16,15 9,03 0,875 7,86 4,00 0, ,10 11,45 5,70 4,10 130,00 15,80 10,80 0,935 9,85 4,88 0, ,99 13,50 5,32 4,20 109,99 16,30 10,69 0,875 11,90 4,58 0,750 65,95 10,50 5,10 3,45 66,00 15,60 12,25 0,821 8,90 4,00 0, ,25 15,00 5,39 4,31 135,00 16,50 10,55 0,913 13,40 4,59 0, ,55 13,50 5,32 4,20 110,00 14,90 10,65 0,880 11,90 4,55 0,760 98,00 11,45 5,00 3,20 100,00 16,01 9,00 0,865 9,40 4,25 0, ,86 22,80 6,36 5,20 134,95 17,00 12,30 0,909 20,80 0,85 0, ,35 10,45 4,60 3,20 110,00 15,65 10,33 0,894 9,15 3,85 0,760 R Table IV.1.1 : Investigated vessels list TANIA SÁNCHEZ MACIÁ 100

101 CHAPTER 2: Studied Parameters and Range of Application 1. Studied Parameters are: Therefore we can summarize and say that the parameters which have been studied g) Rule length, in m : < L < h) Breadth, in m : 9 < B < 22.8 i) Maximum draught T, in m j) Depth D, in m k) Block coefficient Cb, corresponding to the maximum draught: < Cb < l) R (cargo space coefficient) : < R < The above summary is done deducting the following vessels because their parameters exceeds from the range that we want to study. And in order to. This vessels are: Vessel Nº 7: because she has a very small "dar". It's a strange situation or unusual design in which the vessel is load behind the wheelhouse, which produces a very big R. And consequently results no goods in the bending moment for standard ships. Vessel Nº 21: because she has a very small rule length, and R is out our range because it is so small. Vessel Nº 35: because she has block coefficient out of our range, and the formulas of bending moment that we are going to obtain are too sensitive to the values of block coefficient. TANIA SÁNCHEZ MACIÁ 101

102 Booklet IV: Studied Vessels 2. STUDIED PARAMETERS AND RANGE OF APPLICATION 2. Range of Application We can advance that the formulae that we are going to propose can be applicable to selfpropelled cargo carriers with machinery aft with: 0.58 R Cb < 0.94 And it will not be applicable to the following type of vessels: a) Vessels of types other than those covered in the previous point b) Vessels of unusual design c) Vessels with any non-homogeneous loading conditions other than standard loading conditions which we will described it in the booklet VI. d) Vessels greater than 135m in length e) Vessels with actual lightship displacement showing at least 20% deviation from standard value derived from the next booklet (booklet V). TANIA SÁNCHEZ MACIÁ 102

103 CHAPTER 3: Ships for Validation All the ships used for the validation of the new formulae are inland self-propelled cargo carriers with machinery aft. The following table contains the particulars of the twelve used vessels: N l Cargo Carrie r Type Tanker Type C Bulk carrier Contai ner Tanker Type C Tanker Type C Tanker Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type C Tanker Type N closed L (m) B (m) D (m) T (m) Loa (m) dar (m) Dav (m) Cb Bc (m) Dc (m) R 84,59 9,48 5 3, ,12 9,67 0,886 7,840 4,100 0, ,06 3 2,5 38,5 6 5,25 0,907 0,000 0,000 0, ,41 5 3, ,5 10,1 0,922 10,120 4,600 0, ,75 11,4 6 3, ,95 9,8 0,914 9,400 5,150 0, ,24 11,41 5 3, , ,34 5 0,907 9,400 4,600 0, ,25 11,35 6 3, ,45 8,693 0,891 9,350 4,823 0, ,4 6 4, ,55 11,11 0,894 9,956 4,870 0, ,85 11,41 5 3, ,6 10,55 0,881 9,810 4,620 0, ,75 13, ,75 0,871 11,884 4,537 0, ,85 11,4 5 3, ,8 9,55 0,912 9,786 4,230 0,772 92,98 11,34 5 3, ,6 5,38 0,922 9, ,742 53,2 9,5 4 2, ,2 5,6 0,832 7,900 2,820 0,647 Table IV.3.1 : Validation vessels list TANIA SÁNCHEZ MACIÁ 103

104 Booklet V: Investigation Investigat ion of Weight and Weight Distribution TANIA SÁNCHEZ MACIÁ 104

105 Summary Booklet V 1.Introduction Light Ship Weight Symbols and Units Definitions Reference Co-ordinate System Studied Vessels List Structural weight Central part Cargo hold/tank Total hull weight Deckhouse 2.6 Machinery weight Main machinery Main machinery installations Fore machinery Fore machinery installations Auxiliary machinery (fore and aft) Cargo piping system (tank vessels) 2.7 Fittings Anchor equipment and gear fore Anchor equipment and gear aft 2.8 Deck equipment Light ship weight comparison Self-propelled cargo carriers. Standard weights and weight distribution. Summary table Coherence with non propelled cargo carriers Supplies Ballast Cargo weight Self-propelled cargo carriers Coherence with non propelled cargo carriers Standard Hold/Tank length Container vessels Tank vessels TANIA SÁNCHEZ MACIÁ 105

106 CHAPTER1: Introduction As we already know, still water bending moment is determined by: Weight and weight distribution of the vessel Cargo weight and cargo distribution Weights of ballast and supplies, and their distribution Hull dimensions and geometry This is the reason for which we consider the investigation of the weight and weight distribution as an important task to perform. The approximation quality of the weight and center of gravity will be crucial for the success of the estimation of the bending moment, and consequently the scantling of the structure and finally the success of the project. Due to the amount of labor involved in the weight estimation, approximation methods for distribution hull weight have been proposed over the years. Hull weight is traditionally defined as lightship minus the weight of the anchor, chain, anchor handling gear, steering gear and main propulsion machinery. Determination of the breakdown of hull weight is made based on the relative density of the object in question. Items left out of hull weight are independently distributed as rectangles or trapezoids and combined with the hull weight distribution to determine the total weight distribution for the ship. Most approximation methods are based on combinations of a midship rectangle with forward and after trapezoids. More sophisticated methods base a portion of the weight curve on the ship's buoyancy curve. In the Appendix II Approximate Methods of Weight Distribution we can see details and equations of Comstock, Hughes, Prohaska... methods. It's necessary to say that these approximations are general and appropriate only for initial stage design due to their low fidelity. B.V. estimate the ship weight with the sum of different standard weights of some items (hull, deckhouse, main machinery, machinery installations, piping and anchor equipment), as we already have seen in booklet III. So knowing the importance of the weight and weight distribution, our first aim will be focus into check the empirical formulas which are currently used by Bureau Veritas rules and try to improve they and/or develop new formulas for the items that currently are not being taking into account. In order to follow the same structure that B.V. rules use, we are going to study on the one hand the lightship weight and separately the cargo, ballast and supplies weight. The sum of all items will be the displacement of the vessel. TANIA SÁNCHEZ MACIÁ 106

107 Booklet V: Investigation of weight and weight distribution 1.INTRODUCTION It is necessary to say that these standard weights (weights of different items obtained with the empirical formulae ) will help us to define standard vessels. And for the determination of the bending moment formulae we will use these standards vessels in different loading conditions. The reason of use standard weights instead of actual ones is in order to simplify calculations. Because each ship has many different items with different weights and positions. And make a study of forty-six vessels, and for each vessel study the weight distribution item by item, it would be a very difficult and hard work. And other reason is because in early stages of the project the actual ship weight and her distribution is unknown and the bending moment must be estimated. So, it is clearly that we need to define a standard ships using standard weights. And the formulae to estimate the standard weights must be as simple as possible (in the early stages of the project there is not much information). For the weight and weight distribution study we have selected twelve ships of our data base. TANIA SÁNCHEZ MACIÁ 107

108 CHAPTER 2: Light Ship Weight 2.1 SYMBOLS AND UNITS We are going to keep the same symbols (L, B, D, T, Cb, etc.) which B.V. rules are currently using, and which we have already explained in booklet III, Point 1, Section 1. But we are going to add the following ones: X: Standard Cargo Hold/Tank Weight, in ton Y: Standard Piping System Weight of Tanker Vessels, in ton Pc: Standard Cargo Weight, in ton Pw: Standard engine power, in Hp E: Standard engine weight, in ton Pa: Required bow anchor mass, in Kg Lc : Cargo length, in m. Where, Lc = L -dar-dav Bc : Cargo hold/tank breadth, in m Dc : Cargo hold/tank depth, in m 2.2 DEFINITIONS Cargo hold/tank Cargo hold or cargo tank means a hold or tank which is permanently attached to the vessel and the boundaries of which are either formed by the hull itself or by walls separate from the hull and which is intended for the carriage of goods. Independent cargo hold/tank Independent cargo hold or cargo tank means a hold or tank which is permanently built in, but which is independent of the vessel s structure. Cargo hold breadth and cargo hold /tank depth (Bc, Dc) Cargo hold/tank depth (Dc) is the depth of the cargo hold or cargo tank, in m. Cargo hold/tank breadth (Bc) is the total breadth of the cargo hold or cargo tank. It means that if we have two hold/tanks along the Y axis direction, Bc is the sum of the breadth of each cargo hold/tank. TANIA SÁNCHEZ MACIÁ 108

109 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT In order to clarify these two new concepts, we are going to use the following pictures. Double hull vessels Bc Bc Dc Dc Independent hold/tank vessels Bc Dc Bc/2 Dc *Bc/2 because there are two different tanks. The total Bc is the sum of both tanks. 2.3 REFERENCE CO-ORDINATE SYSTEM The vessel s geometry, weight and loads are defined with respect to the following right-hand co-ordinate system. Origin: at the intersection among the longitudinal plane of symmetry of vessel, the aft end of L and the baseline. X axis: longitudinal axis, positive forwards Y axis: transverse axis, positive towards portside Z axis: vertical axis, positive upwards TANIA SÁNCHEZ MACIÁ 109

110 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT 2.4 STUDIED VESSELS LIST Table V.1 shows the particulars of the twelve double hull self-propelled cargo carriers with machinery aft selected for the weight and weight distribution study. Nº Cargo Carrier Type L (m) B (m) D (m) T (m) Loa (m) 6 Contain. 108,15 11,45 3,65 3,55 110,00 17,40 10,25 0,895 10,09 4,83 0, Tanker Type G 24 Tanker Type G 26 Tanker Type C 31 Tanker Type C 33 Tanker Type C 36 Tanker Type C 37 Tanker Type C 47 Tanker Type C 48 Tanker Type C 50 Tanker Type C 51 Tanker Type C dar (m) dav (m) Cb Bc (m) Dc (m) 92,30 11,40 5,70 2,80 95,04 15,16 9,71 0,882 9,60 4,80 0, ,60 11,36 5,32 2,80 106,00 16,81 9,93 0,885 9,00 4,50 0, ,37 11,40 5,40 3,86 110,00 16,10 9,77 0,898 9,78 4,65 0, ,65 16,80 5,75 4,95 135,00 22,25 13,15 0,892 15,20 4,93 0, ,95 11,45 5,32 3,60 110,00 15,60 10,65 0,883 9,85 4,58 0, ,95 11,40 5,32 3,80 110,00 15,60 10,65 0,885 9,79 4,53 0,757 83,05 9,56 4,70 3,60 84,30 14,30 9,57 0,921 7,96 4,00 0,713 82,95 9,46 4,75 3,07 85,95 16,15 9,03 0,875 7,86 4,00 0, ,10 11,45 5,70 4,10 130,00 15,80 10,80 0,935 9,85 4,88 0,792 65,95 10,50 5,10 3,45 66,00 15,60 12,25 0,821 8,90 4,00 0, ,25 15,00 5,39 4,31 135,00 16,50 10,55 0,913 13,40 4,59 0,797 R Table V.2.1 : Weight and weight distribution. Studied vessels list. Please find calculation's details in the Appendix III: Investigation of Weight and Weight Distribution. Details of Calculation. 2.5 STRUCTURAL WEIGHT In order to make easier the investigation of the weight and weight distribution of the structural weight, the vessel is considered divided into three parts: hull, cargo hold and deckhouse. HULL, in order to define easily the items that they are going to be taken into account, the hull is going to be divided into three different portions: aft, central and fore portion. Aft portion, which includes the structures located aft of the after peak bulkhead. We mean, the hull shell structures, but for example the bulwark too. TANIA SÁNCHEZ MACIÁ 110

111 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT Central portion, which includes the structures related to the out shell hull located between the fore part and the aft part. Remarking that in this part we are going to take into account the weight of the hatches, manholes, entrance of cofferdams, guard rail Fore portion, which includes the structures of the stems and those: - Located in the part before the cargo zone in the case of vessels with a separated cargo zone ( separated by bulkheads) - Located in the part extending over 0.1 L behind the stem in all other cases unless otherwise mentioned. We mean, the hull shell structures, but for example the bulwark too. DEKCHOUSE. It is a decked structure other than a superstructure, located on the strength deck or above. Where the strength deck (main deck) is the uppermost continuous deck contributing to the hull girder longitudinal strength. CARGO HOLD/TANK, which includes the structures of the inner hull, cargo holds or independent tanks situated between the aft part and the fore part. It's important to remark that hereafter when we talk about the structure weight of a part, we are including the weight of the followings items too: - Weld. Adding the appropriate weight of each part. Usually welding weight is around 3% of the total weight of the structure. - Paint. Adding the appropriate weight of each part. The paint weight that is used to protect against corrosion can be deducted because comparing it with the weight of the structure it is so small. The reason of this big difference is because the density of the paint is lower than the density of the steel. We start assuming that the Standard Hull Weight BV formulas are very accurate for single hull vessels. This is the reason for we keep the same formulas for the hull structure weight, as a distributed weight along the length. And we center our efforts into adapt or improve it for double hull vessels. As the bigger difference between a single hull vessel and a double hull vessel is located on the central part of the ship, our study related with the hull part will be focus on the central portion of the vessel. TANIA SÁNCHEZ MACIÁ 111

112 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT Central part Estimating the central part weight of the hull with the BV formulae, D 3.7 m LBD D > 3.7 m LBD we obtain the following results: Central Part Weight (t) Vessel Number BV Rules Actual Deviation % 6 504, ,114 3, , ,430 1, , ,059 2, , ,748-23, , ,256-26, , ,116-19, , ,869-18, , ,940-23, , ,698-24, , ,548-29, , ,811-55, , ,013-19,15 Table V.2.2 : Central Part Weight. Comparison BV formulae - Actual values. As we can see in most of the results the individual deviation is negative. That means usually the actual value of the weight of the central part is bigger than the estimated BV value. So, assuming that BV formulas are accurate for single hull vessels, we must increase the weight in the central part for double hull vessels. Our solution is to use a new concept, which is the weight of the cargo hold/tank. Therefore, we will estimate the weight of the central part as the sum of the Hull Structure approximation using formulae of BV and the cargo hold/ tank weight (formula explained in the next paragraph). Cargo hold/tank For estimate the cargo hold/tank weight we think that the formula should to be a simple formula whose variables depend of the size of the holds or tanks. = TANIA SÁNCHEZ MACIÁ 112

113 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT For estimate the value of the constant α, we made the average of the results of solving the following equation en each ship: Actual Weight in Central part = BV formula in central part + Cargo Hold/tank Weight We obtained a value of α = 0.03 Finally we propose the Cargo hold/tank Weight formula as: = 0.03 The improvement in the weight estimation of the central part can be seen clearly in the following table: Total Central Part (ton) Vessel Number New formulae=bv+cargo Deviation % 6 581,402 16, ,454 19, ,912 18, ,426-0, ,028-3, ,179 1, ,285 2, ,458-2, ,105-2, ,807-6, ,195-28, ,585 2,99 Table V.2.3 : Central Part Weight. Comparison New formulae - Actual values. Using the new concept of cargo hold/tank we see that the standard weight of the most vessels is closer to the actual one. And although the results of the three first ships get worse, the greatest deviation, %, is lower than the greatest one using BV formulae, %. So we consider valid the new cargo hold/tank concept. Total Hull Weight As we have realized before, double hull vessels needed the addition of the " Cargo hold/tank Weight" concept to approximate more the standard values to the actual ones. So, let see the influence of this new parameter in the estimation of the entire hull weight. TANIA SÁNCHEZ MACIÁ 113

114 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT Nº BV Rules Actual HULL STRUCTURE WEIGHT (ton) Deviation BV-Actual % New formulae Deviation New formulae -Actual % 6 677, ,888-0,28 733,317 7, , ,384-66,30 692,994-43, , ,794-48,50 719,497-29, , ,444-20,13 779,681-2, , ,753-23, ,944-5, , ,852-12,51 768,078 3, , ,129-11,67 763,486 4, , ,301-22,55 429,693-6, , ,360-24,05 427,229-8, , ,123-37,45 982,412-16, , ,752-35,28 397,332-20, , ,880-14, ,284 3,09 Table V.2.4 : Hull Structure Weight. Comparison different formulae We consider the results as good because the most standard weights results are closer to the actual ones. And neglecting the worst result, which we can consider that is an exception ship, all the remaining results have a deviation acceptable. The standard hull structure weight is supposed to be a distributed load all over the rule length (L), in m. Deckhouse Regarding the deckhouse, it is missing information concerning some ships of our study. As for example the vessel with a deviation of 94.02% of BV standard values (please see below table), which is a negligible value because it is obviously the lack of information. On the one hand we don't have all the actual values and on the other hand, it the standard BV values aren t so bad. So it is decided to keep the current formula and the standard location. It is important to know that this standard weight is a structural weight, so it doesn t take into account the equipment weight. And it is supposed to be a distributed load between the aft perpendicular and the location of dar, in m. Deckhouse standard weight: D 3.7 m LBD D > 3.7 m LBD TANIA SÁNCHEZ MACIÁ 114

115 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT DECK HOUSE WEIGHT (t) Nº BV Rules = New formulae Actual Deviation % 6 45,199 43,690 3, ,986 39,074-8, ,567 49,299-31, ,028 49,453-23, ,464 78,259-1, ,454 47,477-20, ,282 45,010-14, ,390 29,993-33, ,364 21,829 2, ,163 3,000 94, ,190 34,850-64, ,640 67,106-3,82 Table V.2.5 : Deckhouse Weight. Comparison different formulae. 2.6 MACHINERY WEIGHT Main Machinery When BV formulas are applied and in comparison with the actual values, we can see that in most of the cases BV formulas give results higher than the actual ones. So nowadays the weight of the main machinery is overestimated. The formula used by BV is 0.005LBT and it is supposed to be a concentrate weight in the longitudinal position of d AV/2 from the AE. MAIN MACHINERY WEIGHT (ton) Vessel Number BV Rules Actual Deviation % 6 21,980 15,4 29, ,731 18,532-25, ,477 27,818-68, ,844 9,907 58, ,572 34,600 37, ,248 17,120 23, ,382 16,116 31, ,291 10,150 28, ,045 6,915 42, ,068 25,000 16, ,945 9,130 23, ,073 40,130 6,83 Table V.2.6 : Main Machinery Weight. Comparison BV formulae. In order to improve the above results, it is proposed to suppose that the weight of the main machinery is function of the weight of the following items: a) Engine Weight b)reduction Gear Weight TANIA SÁNCHEZ MACIÁ 115

116 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT c) Shaft Weight d)propeller Weight Our first goal in this section is to standardize the weights of the above items. In order to perform it easier, it was proposed to standardize the engine weight and consider the remaining items as a percentage of it. Please find hereafter the procedure which has been taken: Usually the weight of the engine is function of the installed power in the ship: Engine Weight = f (Power) And the installed power is function of the dead weight which is the vessel destined to carry: Power = f (Dead weight) In order to find a way to define a formula for estimate the dead weight, and consequently estimate the power and finally the engine weight, we are going to suppose that the dead weight is equal to the cargo weight. So we are assuming that the weight of supplies, crew, etc is a small value in comparison with the dead weight, and we neglect them. The standard cargo weight has the following formula, (we will describe the process to obtain it in the chapter 5 "Cargo weight") Pc = (0.85*LBT C b X Y) Assuming that the power is a directly function of the deadweight, it is proposed to standardize the power using the standard cargo weight formula multiplied by a factor called " β " Pw = (0.85*LBT C b X Y)*β And using the same argumentation, we say that the standard engine weight formula takes the following structure, being "ϒ" the coefficient which link the standard power with the standard engine weight. E = (0.85*LBT C b X Y)*β*ϒ In order to know the values of the constants β and ϒ it has been used the actual values to be more accurate. We obtain the value of β doing the average between the division of the actual total power and the actual dead weight. Please see Table V.7: β and γ Calculation. Obtaining a result of β= It is important to remark that in the average calculation it has not been taken into account the values of the vessels Nº23 and Nº 24, which are tankers type G, because they have a very different results of the rest of vessels. TANIA SÁNCHEZ MACIÁ 116

117 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT This difference is because the standard engine weight is function of the deadweight, and usually in most of cargo carriers, the deadweight and the installed power have a ratio approximate of : 2ton of cargo 1HP power. But in tankers type G, whose load is a little bit special, the deadweight and the power have a relationship of: 1ton cargo 1HP power. Please see Table V.7: β and γ Calculation. So, in order to take into account this difference, all the formulas that we are going to develop in function of the standard engine weight, we will apply a correction coefficient of 2 in all vessels, like tankers type G, where the ratio between the power and the deadweight is 1. And we obtain the value of ϒ doing the average between the division of the actual engine weight into the actual power. Please see Table V.7: β and γ Calculation. Obtaining a result of ϒ = Vessel Number TOTAL POWER (HP) Actual Dead Weight (t) β Standard Power (Hp) Actual Engine Weight (t) , ,28 7,85 0, , ,150 6,4 0, , ,359 10,5 0, , ,967 6,832 0, , ,574 20,6 0, , ,474 7,5 0, , ,610 7,195 0, , ,774 6,4 0, , ,973 5,1 0, , , , , ,157 5,6 0, , , ,006 γ Table V.2.7: β and γ Calculation. Substituting the values of β and ϒ in the previous equations we can estimate the Standard Engine Weight as: a) Engine Weight E = Pc To know the percentage of the shaft, the propeller and the reduction gear, we divide the actual weight of each item into the actual engine weight. And we make the average. So finally we conclude with the following results: b) Reduction gear weight= 35% Engine weight c) Shaft weight= 29% Engine weight d) Propeller weight= 13% Engine weight TANIA SÁNCHEZ MACIÁ 117

118 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT We conclude proposing the main machinery standard weight, in ton, as the weight of the engine plus 77% of the engine weight too. We mean, Main Machinery Standard Weight= Pc, in ton *We remember that we must apply a correct factor of 2 for tankers type G, because the ratio of the power and the dead weight is different of the remaining vessels. On the other hand, we propose to change the distribution location, because as we consider that the main machinery is composed by (engine, shaft, propeller and reduction gear). It s obviously that it isn t a concentrate weight. For us it will be a improvement to take into account as a distributed weight, with the following location: X 01as the initial point of the length rules. So X 01= 0 m X 02 as the engine longitudinal position, which normally is situated at (2/3) d AR Finally our results are: MAIN MACHINERY WEIGHT (ton) New Vessel Number BV Rules Actual Deviation % Deviation% formulae 6 21,980 15,400 29,94 16,666 7, ,731 18,532-25,80 21,278 12, ,477 27,818-68,83 23,999-15, ,844 9,907 58,45 17,778 44, ,572 34,600 37,74 41,269 16, ,248 17,120 23,05 16,238-5, ,382 16,116 31,08 17,148 6, ,291 10,150 28,98 10,979 7, ,045 6,915 42,59 8,735 20, ,068 25,000 16,86 23,324-7, ,945 9,130 23,57 8,158-11, ,073 40,130 6,83 33,645-19,28 Table V.2.8 : Main Machinery Weight. Comparison different formulae. Main Machinery Installation We consider as main machinery installations all the items needed for a proper operation of the main machinery, so they should have a direct connection to the main machinery. We mean, hull reinforcement, machinery foundations, piping, fittings (like pumps), etc. BV estimation consider the weight of the main installations as two times the standard main machinery weight. But as we can see in the below table, the estimated values are always bigger than the actual ones. TANIA SÁNCHEZ MACIÁ 118

119 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT We propose to take the main installations weight as 50% of the main machinery weight. So, the new formula proposed is Main Machinery Installations = Pc We keep the distribution of the weight with the longitudinal location from AE of X 01=0m and X 02= d AR Please find hereafter the obtained results: MAIN INSTALLATIONS AFT (ton) Vessel Number BV Rules Actual Deviation % New formulae Deviation % 6 43,960 5,475 87,55 8,333 34, ,462 12,325 58,17 10,639-15, ,953 13,750 58,27 11,999-14, ,687 7,950 83,33 8,889 10, ,143 13,500 87,85 20,635 34, ,497 10,517 76,37 8,119-29, ,764 12,482 73,31 8,574-45, ,582 7,600 73,41 5,489-38, ,091 8,790 63,51 4, , ,137 8,065 86,59 11,662 30, ,890 4,200 82,42 4,079-2, ,146 12,954 84,96 16,822 22,99 Table V.2.9 : Main Installations Aft Weight. Comparison different formulae. Fore Machinery Nowadays there isn t any formula to calculate a standard fore machinery weight. As fore machinery we refer to the bow thruster. Studying the actual values of this group and their relationship with the standard dead weight, it is proposed to estimate the weight of this group as the 20% of the weight of the main machinery, considering it as a concentrate weight in a longitudinal position of L-d AV/2. Fore machinery weight = Pc Please find hereafter the obtained results: TANIA SÁNCHEZ MACIÁ 119

120 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT MACHINERY FORE (ton) Vessel Number Actual New formulae Deviation % 6 4 3,268-22, ,8 4,172 8, ,85 4,706 60, ,569 3,486-31, ,96 8,092 13, ,2 3,184-63, ,64 3,362-8, ,2 2,153-48, ,2 1, , ,1 4,573-33, , , ,2 6,597-54,62 Table V.2.10 : Fore Machinery Weight. Comparison with actual values. If we deducted the results of the vessels numbers 47 and 50, which are obviously wrong values, this estimation can be considered as acceptable. Fore Machinery Installation We consider as fore machinery installations all the items needed for a proper operation of the fore machinery with a direct connection to it. We mean, hull reinforcement, machinery foundations, piping, fittings (like pumps),etc. Nowadays there is no formula to calculate a standard fore machinery installation weight. Studying the actual values of this group and they relationship with the standard dead weight, we propose to estimate the weight of this group as the 85% of the weight of the main machinery installations, considering it as a distributed weight with the locations from aft end (AF) in meters, X 01= L-d AV and X 02= L Fore machinery installations weight = Pc Please find hereafter the obtained results: FORE MACHINERY INSTALLATIONS (ton) Vessel Number Actual New formulae Deviation % 6 9,135 7,091-28, ,732 9,054 36, ,186 10,211 19, ,605 7,564-53, ,400 17,560 74, ,904 6,909 33, ,684 7,296 4, ,590 4,671-11, ,389 3,717 2,06 TANIA SÁNCHEZ MACIÁ 120

121 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT Vessel Number Actual New formulae Deviation % 48 5,455 9,924 67, ,000 3,471-21, ,004 14,316 57,39 Table V.2.11 : Fore Machinery Installations Weight. Comparison with actual values. Like in the standard fore machinery weight formulas, if we deducted the results of the vessels numbers 31 and 48, which are the biggest ones, we can consider that the estimation can be acceptable. Auxiliary Machinery Nowadays, as occurs with fore machinery and fore machinery installations, there is no formula to estimate the standard auxiliary machinery weight. So, in order to standardize it, we are going to divide this group into two different subgroups: Auxiliary Machinery aft and Auxiliary Machinery Fore. Each subgroup comprises the auxiliary machinery (generators) and auxiliary machinery installations (pipes, fittings, hull reinforcement, etc). We suppose that both groups (auxiliary aft and fore) have uniform distribution along each part: -In aft part, from aft perpendicular to dar location -In fore part, from L-dav to L Auxiliary Machinery Fore It is proposed to estimate the weight of this group as the 80% of the weight of the machinery installations fore. Fore auxiliary machinery weight = Pc Please find hereafter the obtained results, we would want to remark that despite the individual deviation seems a little high, it is due to weights are so small and a little difference in this case it seems bigger than it is. So for us, deducting the two highest values that are obviously wrong, the reaming results are acceptable. AUXILIARY MACHINERY FORE (ton) Vessel Number Actual New formulae Deviation % 6 3,20 5,926 46, ,05 7,093 0, ,80 8,000-72, ,27 5,926-22,63 TANIA SÁNCHEZ MACIÁ 121

122 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT Vessel Number Actual New formulae Deviation % 31 1,01 13,756 92, ,75 5, , ,92 5, , ,50 3,660 31, ,85 2, , ,45 7,775-21, ,719-10, ,045 11,215-34,15 Table V.2.12 : Fore Auxiliary Machinery Weight. Comparison with actual values. Auxiliary Machinery Aft It is proposed to estimate the weight of this group as the 40% of the weight of the main machinery. Aft auxiliary machinery weight = Pc Please find hereafter the obtained results. As in the previous subgroup, it is important to remark that despite the individual deviation seems a little high, it is due to weights are so small and a little difference in this case it seems bigger than it is. So for us, deducting the two highest values that are obviously wrong, the reaming results are acceptable. AUXILIARY MACHINERY AFT (ton) Vessel Number Actual New formulae Deviation % 6 2,27 6,97 67, ,84 8,34-89, ,35 9,41 43, ,21 6,97 25, ,84 16,18-72, ,02 6,37 21, ,55 6,72-12, ,06 4,31 5, ,60 3,43-180, ,99 9,15 56, ,5 3,20 53, ,07 13,19 61,54 Table V.2.13 : Aft Auxiliary Machinery Weight. Comparison with actual values. Cargo Piping System = Y (Tank Vessel) First of all, it's important to remark that cargo piping system has to be applied only in tank vessels. The standard values of BV formula and the new ones refer only to the pipes, pumps and fittings which are needed to load the ship. We mean, ballast piping isn t included in this TANIA SÁNCHEZ MACIÁ 122

123 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT section. We suppose a linear distribution along the central part of the ship ( from the longitudinal position dar to L-dav. As it is shown in the below table, BV value's underestimate the actual ones. The formula used for standard BV values is: 0.005LBT. CARGO PIPING SYSTEM (ton) Vessel Number BV Rules Actual Deviation % New formulae Deviation % 6 She is a container vessel 23 14,731 28,264-91,866 29,462 4, ,477 8,815 46,500 32,953 73, ,844 37,906-58,978 47,687 20, , ,301-94, ,143 2, ,248 42,334-90,278 44,497 4, ,382 44,220-89,120 46,764 5, ,291 18,057-26,347 28,582 36, ,045 21,850-81,399 24,091 9, ,068 45,300-50,657 60,137 24, ,945 18,225-52,570 23,890 23, ,073 59,003-36,984 86,146 31,51 Table V.2.14 : Cargo Piping Weight. Comparison different formulae. We divide the standard BV values into the actual ones in order to know approximately the ratio of both values, and we realize that if we increase two times the coefficient of that the standard BV rules used, the new standard values are more accurate. Although now the new standard values are higher than the actual ones, so we are more conservative, we accept this formula because the deviation average is lower. So we propose the new formula for the piping system weight, in tons, as: Y = 0.01 LBT 2.7 FITTINGS The weight of this group is very difficult to standardize as a whole because it is form of very different items without any relationship between them. We identify as fittings the bollards, beats, mooring cables, anchors, chains, cables, stairs, ladders, rudder, steering mechanism, etc. Within this big group we are going to separate the items related with the anchor equipment and gear fore and aft, and we are going to standardize them. But the remaining items that don t form part of these two groups, we won t take into account in our light ship weight estimation. TANIA SÁNCHEZ MACIÁ 123

124 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT Anchor Equipment and Gear Fore Analyzing the results of applying the standard BV formulas, we can see that always BV formulas give results higher than the actual ones. The formula used by BV is 0.005LBT. Regarding it as a concentrate weight in the longitudinal position L- d AV /3 from AE, in m. ANCHOR EQUIPMENT AND GEAR FORE (ton) Vessel Number BV Rules Actual Deviation % New formulae Deviation % 6 21,98 12,35 43,81 11,73-5, ,73 8,194 44,38 7,86-4, ,47 9,261 43,79 8,31-11, ,84 12,24 48,67 11,74-4, ,57 16,00 71,21 20,29 21, ,24 11,84 46,76 10,95-8, ,38 7,09 69,65 11,53 38, ,29 10,75 24,78 8,77-22, ,04 9,63 20,03 7,44-29, ,06 13,30 55,77 13,58 2, ,94 7,50 37,21 7,85 4, ,07 13,80 67,96 16,67 17,20 Table V.2.15 : Anchor Equipment and gear fore Weight. Comparison different formulae. Following it is proposed to improve the formulae keeping the weight as a concentrate weight in the same longitudinal position described before. The weight of this group is going to be divided into the following items: a) Anchor Weight b) Chain/cable Weight c) Winch Weight First of all, the anchor weight is going to be standardized and later on the chain/cable and winch are going to be a percentage of this one. It is similar to the procedure used to obtain the standard machinery weight. To find the standard formula of the weight of the anchor, we start using the formula of bow anchors for cargo carriers given by BV in the Pt B, Ch 7, Sec 4. Which give us the total mass Pa of the bow anchors: P = k BT Where, =. *K = c for pushed barges Lm = maximum length of the hull, in m, excluding rudder and bowsprit. In our study we are going to consider this length the same as the rule length L. TANIA SÁNCHEZ MACIÁ 124

125 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT c = coefficient defined in the following table. Dead weight Coefficient c 400t 45 >400t 600t 55 >600t 1000t 65 >1000t 70 So, assuming that all ships have a deadweight bigger than 1000t, we consider c = 70. And substituting this value in the above equation and calculating the equivalence in tons, we obtain the following standard anchor weight formula: We remark some aspects: = We consider a standard/normal anchor, not special one. So we don t apply any reduction factor. Anchors must be of an approved type. The requirements provide the equipment in anchors for ranges of navigation IN(0), IN (0.6) and IN(1.2 x 2) without any reduction weight for lower speed. Cast iron anchors shall not be permitted. The above formula is used for ships with deadweight bigger than 1000t. The following step is to define the percentage of the chain/cables and winch. To define it, we have studied these items of the eleven vessels and we conclude that approximately the total weight of the anchor equipment and gear fore is 3.5 times the standard anchor weight. So, it is propose the formula: =.. The study performed is attached in the Appendix II: Investigation of Weight and Weight Distribution Details of Calculation. Anchor Equipment and Gear Aft We consider the same items than in the anchor equipment and gear fore. We mean, that in this group comprise the weight anchor, chain and winch aft. Using the actual values, we realize that in the most cases the weight anchor equipment aft is 44% of the anchor equipment fore. So we propose the formula: TANIA SÁNCHEZ MACIÁ 125

126 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT =.. We propose to regard it as a concentrate weight in the aft end (AE). Please find hereafter the obtained results: ANCHOR EQUIPMENT AND GEAR AFT (ton) Vessel Number Actual New formulae Deviation % 6 4,35 5, ,194 3, , ,9 3,650-6, ,27 5,156-2, ,913 55, ,865 4,810 19, ,48 5,066 31, , , ,436 3,268-35, ,6 5,967 22, ,450 13, , ,322 25,85 Table V.2.16 : Anchor Equipment and gear aft Weight. Comparison with actual values. Deducting the two highest values that are obviously is missing information regarding the actual ship, the reaming results are acceptable. 2.8 DECK EQUIPMENT The weight of this group is very difficult to standardize because it depends to the requirements and the operational conditions of each vessel. So as it doesn't follow a common rule in all of the vessels, we are not going to try to standardize it. Items like cranes, winches, masts, etc. form part of this group. It is important to remark that the windlass weight (which can be considered as a deck equipment) has been taken into account in the group of anchor equipment and gear. 2.9 LIGHT SHIP WEIGHT COMPARISON Doing the sum of the standard structure, machinery and fittings weight explained before, we can obtain the final standard light ship weight. Please find below the summary table with the comparison of the obtained values. Finally we can agree to accept the previous formulae, due that the final deviation is lower. TANIA SÁNCHEZ MACIÁ 126

127 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT TOTAL LIGHT WEIGHT (t) N Actual %Deviation New formulae %Deviation ,910-68,86 830,330-44, ,292-56,19 871,254-33, ,799-20,62 934,901-6, ,100-30, ,249-16, ,896-21,73 914,018-7, ,946-21,47 914,948-7, ,622-27,97 524,551-13, ,406-31,86 509,260-17, ,248-28, ,665-12, ,952-43,05 476,940-30, ,340-17, ,849-3,40 Table V.2.17 : Total Light Ship Weight. Comparison different formuale. It is important to remark that BV formulae underestimate the light ship, but as we will see in the point 5, the cargo weight is overestimate. So, it was compensated. Now the new formulae propose a higher value for the light ship weight (more items has been taken into account) and as we will see later, the standard cargo weight estimation is going to need a reduction. TANIA SÁNCHEZ MACIÁ 127

128 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT 2.10 SELF-PROPELLED CARGO CARRIERS. STANDARD WEIGHTS AND WEIGHT DISTRIBUTION. SUMMARY TABLE Item Weight Po, in t Centre of gravity Xo from AE, in m Location from AE, in m X 01 X 02 Hull D 3.7 m D > 3.7 m LBD LBD 0 L Cargo Hold/ Cargo Tank (*) 0.03 L C B C D C d AR L d AV Deckhouse D 3.7 m D > 3.7 m LBD LBD 0 d AR Main Machinery (**) Machinery Installations (**) Machinery Fore (**) Machinery Installations Fore (**) Aft Auxiliary Machinery (**) Fore Auxiliary Machinery (**) Piping System (***) Anchor equipment and Gear Fore Anchor equipment and Gear Aft P C 0 (2/3)* d AR P C 0 d AR P C L- d AV / P C L - d AV L P C 0 d AR P C L - d AV L 0.01 LBT d AR L - d AV T (LB) 0.5 L- d AV / T (LB) Table V.2.18 : Self-propelled cargo carriers. Standard Weights and weight distribution. Summary table (*) Application for double hull cargo carriers (**) For vessels, like tankers type G, where the ratio between the power and the dead weight is 1, we apply a correct factor of 2. (***) Application for tank vessels only TANIA SÁNCHEZ MACIÁ 128

129 Booklet V: Investigation of weight and weight distribution 2. LIGHT SHIP WEIGHT 2.11 COHERENCE WITH NON PROPELLED CARGO CARRIERS As we expect our formulas will be applied in the future by inland BV rules, they must be in coherence with non propelled cargo carriers vessels. So the first step is to suppose that the BV rules are accurate for single hull vessels. And, as we have already done in self-propelled vessels, we need to apply the correction of the cargo hold/tank weight (x) in the central part of the ship of double hull non propelled vessels too. And for tankers we add the cargo piping system (Y) in the central part too. Being the formula with the following structure: P C = 0.12 LBD + X + Y for D < 3.7 m P C = 0.10 LBD + X+ Y for D 3.7 m Please find below the summary table: Item Hull D < 3.7 m D 3.7 m Weight Po, in t LBD LBD Location from AE, in m X 01 X 02 0 L Cargo Hold/ Cargo Tank (*) 0.03 L C B C D C d AR L d AV Piping System (**) 0.01 LBT d AR L d AV Table V.2.19 : Non-propelled cargo carriers. Standard Weights and weight distribution. Summary table (*) Application for double hull cargo carriers (**) Application for tank vessels only TANIA SÁNCHEZ MACIÁ 129

130 CHAPTER 3: SUPPLIES The amount of supplies depends on the operation conditions of each vessel. As it can be the distance of the trip, if the ship sails in a canal or river, the vessel size, the cargo capacity So it s difficult to define a value o formula which fits all vessel types and conditions. This is the main reason for which we need to define standard values. The locations of supplies are selected in order to envisage the most severe loading condition in the vessel operation. So we are going to locate the supplies into the midpoint of the aft and fore part. And changing the percentage of it we are going to induce hogging or sagging condition, as it suits us. We are going to keep the standard formulas that nowadays BV is using to estimate the weight of the supplies. Please find below the summary table: Item Weight Po, in t Centre of gravity Xo from AE, in m Supplies (fore) Supplies (aft) α 1 LBT α 1 LBT L - d AV/2 d AR /2 Table V.3.1: Standard supplies formulae Where, the values of coefficients α 1 (supplies) are: Loading Conditions α 1 Lightship 1.0 Fully loaded vessel 0.1 Transitory conditions Hogging 1.0 Sagging 0.1 *The standard loading conditions are defined in the booklet number VI. TANIA SÁNCHEZ MACIÁ 130

131 CHAPTER 4: BALLAST to: The amount of ballast depends on the operation conditions of each vessel. Ballast is used Improve stability, increasing the weight in the bottom of the ship in order to lower her centre of gravity. Control factors as trim or list Control draught and the total height of the ship. For example in inland navigation sometimes is needed to reduce the height to permit the ship pass through bridges. Control the efforts of the ship when the ship was not fully loaded. Improve the efficiency of the propeller, to avoid the propeller works in the air and not into the water. So it s difficult to define a value o formula which fits all vessel types and all the situations. This is the main reason for which we need to define standard values. The locations of ballast, as for the supplies, are selected in order to envisage the most severe loading condition in the vessel operation. So we are going to locate the ballast into the midpoint of the aft and fore part. And changing the percentage of it we are going to induce hogging or sagging condition, as it suits us. We are going to keep the standard formulas that nowadays BV is using to estimate the weight of the supplies. Please find below the summary table: Item Weight Po, in t Centre of gravity Xo from AE, in m Ballast (fore) D 3.7 m D > 3.7 m Ballast (aft) D 3.7 m D > 3.7 m α 2 LBD α 2 LBD α 2 LBD α 2 LBD L - d AV /2 d AR /2 Table V.4.1 :. Standard ballast formulae TANIA SÁNCHEZ MACIÁ 131

132 Where, the values of coefficients α2 (ballast) are: Loading Conditions α 2 Lightship 0.5 Fully loaded vessel 0 Transitory conditions Hogging 0 Sagging 0 *The standard loading conditions are defined in the booklet number VI. TANIA SÁNCHEZ MACIÁ 132

133 CHAPTER 5: CARGO WEIGHT 5.1 SELF-PROPELLED CARGO CARRIERS As in the light ship weight study performed before, we are going to assume that the standard cargo weight formula of BV is accurate for single hull vessels. The current formula is: P C = 0.85 LBT Cb Therefore our goal is improve it for double hull vessels. One evidence for the needed for improvement in this formula for double hull vessels is attached in the Appendix V: Cargo Weight formula analysis. Where with the studied vessels we divide the actual dead weight into the actual displacement for the maximum draught and we obtain a constant of approximately 0.74 and no So clearly, we must to think in a way to decrease the value of the standard cargo weight. If we remember the standard light ship formulas of BV, they gave us values lowers than the actual ones, so we used the new concept of cargo hold/tank to increase the weight of the central of double hull vessels. Now, we realize that using the coefficient 0.85 the standard cargo weight is overestimate. It is proposed to correct the formula using the cargo hold/tank concept and the piping system (only for tank vessels). P C = 0.85 LBT Cb X Y Please find hereafter the obtained results, which we can consider more accurate that the previous ones. N BV rules (t) Pc= 0.85LBTCb Actual Deadweight %Deviation New formulae Pc=0.85LBTCb-X-Y %Deviation , , ,894 9, , , ,087 30, , , ,835 23, , , ,796 2, , , ,025 13, , , ,957 6, , , ,262 5, , , ,708 23, , , ,738-7, , , ,359 7, , , ,537 15, , , ,027 4,43 Table V.5.1 : Comparison Cargo Weight. Different formulae. TANIA SÁNCHEZ MACIÁ 133

134 Booklet V: Investigation of weight and weight distribution 5. CARGO WEIGHT Regarding the location to be considered, it is proposed to assume the standard cargo weight as a distributed load along the cargo space. That means: X 01 = d AR + X AR X 02 = L - d AV - X AV 5.2 COHERENCE WITH NON PROPELLED CARGO CARRIERS For non-propelled cargo carriers we follow the same methodology. We assume that the standard cargo weight formula of BV is accurate for single hull vessels. The formula used is: P C = 0.90 LBT Cb So our goal is improve it for double hull vessels. So, we propose to correct the formula using the cargo hold/tank concept and the piping system (this last only for tank vessels). P C = 0.90 LBT Cb X Y 5.3 STANDARD HOLD/TANK LENGTH As we know cargo carriers comprises very different type of ships (containers, tankers, bulkcarriers), with holds/tanks sizes different. We need to standardize the length of the cargo hold/tank, because the accuracy of the bending moment during loading/unloading depends of it. We are going to study the following type of vessels: Container vessels A container is a recipient for the multimodal transportation (air, sea, river, ground...). The container dimensions are standardized, by ISO 6346 to facilitate handling. There are containers with different measures, changing the height and length. - Width is fixed: 8 ft. - Height changes between: 8 ft and 6 inches (2.59m) and 9 ft and 6 inches (2.90m). - Length changes between: 8 ft (2.44m), 10ft (3.05m), 20ft (6.058m), 40ft (12.19m), 45ft (13.72m), 48ft (14.63m) y 53ft(16.15m). The most widespread throughout the world are the containers of 20 and 40 feet. We attached in the Appendix V: Marine Container Types. As the worse condition we select the 20ft container (length= 6.058m). TANIA SÁNCHEZ MACIÁ 134

135 Booklet V: Investigation of weight and weight distribution 5. CARGO WEIGHT Tank vessels In order to define the standard tank length, we use the concept of maximum permissible capacity of a cargo tank for the carriage of dangerous goods. The reason is because our study comprises tankers type C, G and N. So, going to the Pt D, Ch3, Sec1 of the BV rules, we can see that the maximum permissible capacity of a cargo tank for single hull tank vessels, double hull tank vessels and vessels with tank independent of the hull shall be in accordance with the following formula: Loa B D, in m^3 Maximum permissible capacity of a cargo tank, in m^3 < Loa B D From 600 to ( LoaB D-600)* > Using the above formula of maximum permissible capacity cargo tank, and knowing Bc and Dc, we can obtain the maximum individual cargo hold/tank length (L h/t), in m. And the length tank has to comply too: For vessels with a length not more than 50m, the length of a cargo tank shall not exceed 10m. For vessels with a length of more than 50m, the length of a cargo tank shall not exceed 0.2L. This provision does not apply to vessels with independent built-in cylindrical tanks having a length to diameter ratio 7. As all of our studied vessels have a length bigger than 50m, they must to satisfy the second requirement. The following table show the results: N Loa (m) L (m) B (m) D (m) LoaBD (m^3) Maximum Capacity (m^3) Bc (m) Dc (m) L h/t (m) Shall not to exceed (m) Table V.5.2 : Standard tank length TANIA SÁNCHEZ MACIÁ 135

136 Booklet V: Investigation of weight and weight distribution 5. CARGO WEIGHT As we can see any cargo length (L h/t ) exceeds of the maximum required by the BV rules. We are going to select the minimum value as the worse condition, so in containers vessels the minimum value is L h/t = 6.058m. And in tank vessels is L h/t =5.071m. We are going to make an approximation and propose: Standard cargo hold/tank length as L h/t =6 m. Which means than in our study we are going to load and unload the ship with ideal holds / tanks of 6m length. In this way we are going to be able to see more accurately the variation of the bending moment in each condition. Please find in the Appendix V: Vessel's Standard Holds Loaded with Standard Cargo Weight and Appendix VI: Vessel's Standard Holds Loaded with Actual Cargo Weight, how we have distributed each ship. TANIA SÁNCHEZ MACIÁ 136

137 Booklet VI: Standard Loading Conditions TANIA SÁNCHEZ MACIÁ 137

138 Summary Booklet VI 1.Standard Loading Conditions Standard Loading Conditions Lightship Fully Loaded Transitory conditions 2. Loading Cases inducing Maximum Still Water Bending Moments Taking into account distances and weights Influence line diagram TANIA SÁNCHEZ MACIÁ 138

139 CHAPTER 1: Standard Loading Conditions Because the cargo is the largest item to the weight and because there are so many possible variations in its distribution, there are often some distributions and combinations that would cause excessive values of bending moment and that therefore must be avoided. This is particularly the case with bulk carriers in which, for various reasons (e.g. tank cleaning, avoidance of free surface or the shifting of dry bulk cargo, very dense cargo such as iron ore) it is preferable to have the cargo holds or tanks either completely full or completely empty. Given such extreme differences it is important that they be spread out and interspersed, rather than grouped together, because the latter would give excessive shear force and/or bending moment, So, we need to consider a general or standard loading conditions in which focus our study. Our study should cover the most severe loading conditions for the structural elements under investigation, with a view to maximizing the stresses in the primary supporting members. These loading conditions are to be selected among those envisaged for the vessel operation. 1. STANDARD LOADING CONDITIONS LIGHTSHIP For non-propelled cargo vessels and tank vessels, the vessel is assumed empty, without supplies nor ballast. For self-propelled cargo vessels and tank vessels, the light standard loading conditions are: o Supplies: 100% o Ballast: 50% We suppose that hogging is the usual condition of a ship in navigation with lightship load condition. Taking into account this quantity of supplies and ballast, as they are located into the fore and aft part, we are inducing the most severe loading condition. FULLY LOADED For non-propelled cargo vessels and tank vessels, the vessel is considered to be homogeneously loaded at its maximum draught, without supplies nor ballast. For self-propelled cargo vessels and tank vessels, the vessel is considered to be homogeneously loaded at its maximum draught with 10% of supplies (without ballast). We suppose that sagging is the usual condition of a ship in navigation in fully load condition. Taking into account zero ballast and a small value of supplies, as they are located into the fore and aft part, we are inducing the most severe loading condition. TANIA SÁNCHEZ MACIÁ 139

140 Booklet VI : Standard Loading Conditions 1.STANDARD LOADING CONDITIONS TRANSITORY CONDITIONS Transitory conditions occurred in harbour condition while the ship is being loaded or unloaded. The different type of way for loading/unloading are: Loading/ unloading in two runs (2R) Loading and unloading are performed uniformly in two runs of almost equal masses, starting from one end of the cargo space, progressing towards the opposite end. Loading/ unloading in one run (1R) Loading and unloading are performed uniformly in one run, starting from one end of the cargo space, progressing towards the opposite end. Loading/ unloading for liquid cargoes Loading and unloading for liquid cargoes are assumed to be performed in two runs, unless otherwise specified. The standard loading conditions in transitory conditions are: For non-propelled cargo vessels and tank vessels, the vessel is assumed without supplies nor ballast. For self-propelled cargo vessels and tank vessels, the vessel without ballast, is assumed to carry following amount of supplies: o o In hogging condition: 100% of supplies In sagging condition: 10% of supplies The reason to take these values are the same that we have explained before. In hogging condition we try to increase the weight in the extreme parts of the ship and in sagging condition we try to decrease the weight in the extreme parts of the ship in order to study the most severe loading condition. A summary table is considering α 1 as the percentage of supplies and α 2 as the percentage of ballast): Loading Conditions α 1 α 2 Lightship Fully loaded vessel Transitory conditions Hogging Sagging TANIA SÁNCHEZ MACIÁ 140

141 CHAPTER 2: Loading Cases inducing Maximum Still Water Bending Moments As we can see in the Appendix IX: Loading cases inducing Maximum Still Water Bending Moments, the loading condition in which appears the maximum bending moments is always during loading/ unloading, (which means in harbour condition) and no when the ship if fully loaded (navigation load case). BV rules NR217 (November 2011) is not mentioned from which end to which end you should start loading to obtain the maximum bending moment during loading condition. Indeed the definitions are: Loading / unloading in two runs (2R): Loading and unloading are performed uniformily in two runs of almost equal masses, starting from one end of the cargo space, progressing towards the opposite end. Loading/ unloading in one run (1R): Loading and unloading are performed uniformily in one run, starting from one end of the cargo space, progressing towards the opposite end. In order to know from which end to which end we should load the vessels to obtain the highest BM values, (so which one will be the worst loading condition which we must to take into account) we will study the situation from two different view of points: taking into account the distances and weights and in the other hand, using the influence line diagram. As we will see hereafter both concepts will conclude with the same idea. 2.1.TAKING INTO ACCOUNT DISTANCES AND WEIGHTS: When a standard cargo hold/tank is going to be loaded with the same standard cargo weight (starting from the aft part or for the fore part of the ship), in order to know which situation will induce higher values of bending moment, we have to look in the distances: - For hogging condition: Normally dar > dav, so, when we start the loading sequence from the fore part, we are going to load a bigger distance from the centre of gravity of the ship. Consequently we are going to increase the hogging bending moment (we are in worse condition loading from the fore part to the aft, than starting from the aft part and going to the fore one). -For sagging condition: in 1R, as the studied vessels are with machinery aft, the machinery weight aft is bigger than the fore machinery weight, and additionally dar > dav, so it is obviously that if we start the loading sequence from the aft part of the ship and we progress towards the fore part, we will obtain higher sagging bending moment results (we are in a TANIA SÁNCHEZ MACIÁ 141

142 Booklet VI : Standard Loading Conditions 2.LOAD CASES INDUCING MAXIMUM BM worse condition starting from the aft part and progressing to the fore part, than starting for the fore part and progressing to the aft one) INFLUENCE LINE DIAGRAM After the influence line diagram study done in the Booklet VIII: Development of the new Still Water Bending Moment Formula, Chapter 2"Influence line diagram". We can see that normally X 02 < L - X 04 and X m < L/2, too. Analizing that results, we conclude that: -For hogging condition: if X 02 < L - X 04 it means that if we start loading from the fore part progressing up to the aft part we will be able to load a bigger longitudinal distance which his influence will be to induce hogging condition. So, the worse hogging condition during the transitory conditions (harbour) will occur loading from the fore part an progressing to the aft part of the ship. -For the sagging condition. X 02 < L - X 04 indicates that it will be necessary to load a small longitudinal distance to start o inducing sagging condition if you start loading from the aft part to the ship and progressing to the fore part. And X m < L/2, means that the longitudinal position where an addition/remove has the biggest influence before the midship. So starting loading from the aft part of the ship will be the worse condition to be taken into account due that we will arrive earlier to higger values of sagging influence that if we start loading from the fore part. TANIA SÁNCHEZ MACIÁ 142

143 Booklet VII: VI Direct Calculation of the Still Water Bending Moment TANIA SÁNCHEZ MACIÁ 143

144 Summary Booklet VII 1. Overview of the used tool (ARGOS) Aplication Input data Limitations Direct calculation of the Still Water Bending Moment (SWBM) Direct calculation of the bending moment (Argos) Main Particulars Lightship distribution Loading conditions Summary of the Load Cases where the Maximum Still Water Bending Moment occurs Loading in one run: Maximum hogging moment Loading in one run: Maximum sagging moment Loading in two runs: Maximum hogging moment Loading in two runs: Maximum sagging moment TANIA SÁNCHEZ MACIÁ 144

145 CHAPTER 1: Overview of the used tool (ARGOS) 1.1. APPLICATION ARGOS is a modular program with an integrated date file management. The user selects the different options by menus and may choose how to work. The file management releases him from file problems (name, version, device, capacity...) and enables to store easily several ships and types of data on the same cartridge or disc. Two types of modules may be distinguished: Definition, correction and intermediate calculations converting data of the first level in more elaborate data. Calculation: -Longitudinal strength distribution -Maximum permissible KG -Maximum permissible grain shifting moment -Intact stability 1.2. INPUT DATA 2.1. Basic ship data -Ship identification -Main particulars -Hull frame definition 2.2. Body plan -Main characteristics (appendages, camber, sheer...) -Spacing of sections -Definition of sections (from keyboard) 2.3. Hydrostatic particulars and righting levers can be directly entered from the keyboard or calculated from the body plan Capacity plan. For each capacity, following data must be entered: -Name -Volume and longitudinal location -Free surface moment -Cargo specific gravity 2.5. Lightship: for each item, following data must be entered: TANIA SÁNCHEZ MACIÁ 145

146 Booklet VII : Direct Calculation of SWBM 1.OVERVIEW OF THE USED TOOL (ARGOS) -Weight and longitudinal distribution -Position of the centre of gravity 2.6. Loading conditions: loading conditions may be defined in two different ways: -Total displacement and position of the centre of gravity -Combination of elementary loads (individual weights and capacity loads) with the location of their centre of gravity LIMITATIONS -Maximum number of sections: 60. -Maximum number of offsets per section: 23. -Maximum number of loading conditions: Maximum number of capacities: Maximum number of individual weights per loading condition: 25. When hydrostatic particulars and righting levers are entered from the keyboard, following limitations are considered: -Hydrostatic particulars: maximum number of drafts (15) -Righting levers: maximum number of heel angles (9) and maximum number of displacements (15). TANIA SÁNCHEZ MACIÁ 146

147 CHAPTER 2: Direct Calculation of the Still Water Bending Moment (SWBM) From the foregoing discussion, is clear that the calculation of the still water bending moment is, conceptually, a straightforward task. It is simply a double integration of the sum of the buoyancy force and the weight force. The calculations are straightforward but tedious. Since this is a basic part of the hydrostatic calculations, we will use ARGOS for calculating the shear force and bending moment distributions along the ship length in function of the loads that we will entered. The aim of this chapter is to obtain the maximum bending moment (Mmax) by direct calculation. From experience we know that the maximum bending moment does not always occur amidships. Some typical cases are : 1. Vessels with unusual internal arrangements (e.g. combination of oil cargo and ordinary cargo, as in a naval replenishment ship). 2. Tankers and bulk carriers with some empty cargo holds. For example, in tankers with empty spaces amidships Mo may be quite small and there may be two peak values of bending moment, at or near the two quarter points. Also, with a heavy cargo such as iron ore, a bulk carrier may be loaded in alternate holds, and in this case there is a peak value of bending moment in the way of each alternate hold. Moreover, with bulk carriers, the shear force Q can be quite significant and it will have several peak values. Therefore, even in preliminary design it is best to calculate the shear force (Q) and the bending moment (M) over the full length of the vessel DIRECT CALCULATION OF THE BENDING MOMENT (ARGOS) Hereafter is described the procedure to follow in argos to calculate the still water bending moment. As example it is explained for the ship Nº 26, but it has to be done for all the 46 studied vessels MAIN PARTICULARS As it was said before, the first step is to introduce the main particulars of the ship. TANIA SÁNCHEZ MACIÁ 147

148 Booklet VII : Direct Calculation of SWBM 2. DIRECT CALCULATION SWBM LIGHT SHIP DISTRIBUTION Lightship module allows to define the light ship weight distribution by a set of load located all along the ship. Each item of load may be defined as: CONCENTRATE WEIGHT, by a weight in ton (P) applied in a point (Lcg) LOCALIZED WEIGHT, by a weight in ton (P) with the longitudinal centre of gravity in (Lcg), but being the weight distributed between two longitudinal coordinates: -X1(m): distance from AE to the start of the distribution of the weight. -X2 (m): distance from AE to the end of the distribution of the weight. DISTRIBUTED WEIGHT, by a longitudinal extent and the values of a linear weight distribution (W1, W2) in (ton/m). For all the studied vessels (46) it is necessary to define the standard light ship, using the items (hull, cargo hold/cargo tank, deckhouse, main machinery, main machinery installations, etc) described in the Booklet V : Investigation of the weight and weight distribution. The standard definition of each vessel can be found in the Appendix VIII: Standard weights and weight distribution. Additionally, for the vessels for which we have the actual distribution of the weight (vessels used for the study of the weight and weight distribution) it is necessary to create both versions of light ship in argos: standard light ship and actual light ship. We will calculate the bending moment in both cases to be able to compare the results. * SHIP Nº26. STANDARD LIGHT SHIP VERSION TANIA SÁNCHEZ MACIÁ 148

149 Booklet VII : Direct Calculation of SWBM 2. DIRECT CALCULATION SWBM * SHIP Nº26. ACTUAL LIGHT SHIP VERSION TANIA SÁNCHEZ MACIÁ 149

150 Booklet VII : Direct Calculation of SWBM 2. DIRECT CALCULATION SWBM TANIA SÁNCHEZ MACIÁ 150

151 Booklet VII : Direct Calculation of SWBM 2. DIRECT CALCULATION SWBM TANIA SÁNCHEZ MACIÁ 151

152 Booklet VII : Direct Calculation of SWBM 2. DIRECT CALCULATION SWBM LOADING CONDITION In the loading condition module we are going to select the "detailed loading condition" and we are going to enter individual weights to define it. As elementary loading conditions we are going to define the quantity of supplies and ballast that we assumed in each condition (navigation and harbour). This loadings conditions are already defined in the Booklet VI: Standard Loading Conditions. TANIA SÁNCHEZ MACIÁ 152

153 Booklet VII : Direct Calculation of SWBM 2. DIRECT CALCULATION SWBM STANDARD ELEMENTARY LOADING CONDITIONS Lightship, the standard loading conditions are: supplies 100% and ballast 50% Transitory hogging condition, the standard loading conditions are: supplies 100% and ballast 0% TANIA SÁNCHEZ MACIÁ 153

154 Booklet VII : Direct Calculation of SWBM 2. DIRECT CALCULATION SWBM Transitory sagging condition. Standard loading conditions are: supplies 10% and ballast 0% Fully loaded condition. Standard loading conditions are: supplies 10% and ballast 0% ACTUAL ELEMENTARY LOADING CONDITIONS To define the actual loading conditions, we will use the same % in each elementary loading condition than those already used defining the standard conditions. The only difference is that in this case, instead to define the loading conditions as individual weight, we will use the capacities, entering the % of filling in each case. Hereafter is shown how is filled in light ship condition. The same procedure needs to be applied in the others loading conditions, just changing the % of filling accordingly. TANIA SÁNCHEZ MACIÁ 154

155 Booklet VII : Direct Calculation of SWBM 2. DIRECT CALCULATION SWBM TANIA SÁNCHEZ MACIÁ 155

156 Booklet VII : Direct Calculation of SWBM 2. DIRECT CALCULATION SWBM Once defined all the elementary conditions, the following step to be performed is enter the normal conditions (load each standard cargo tank with the cargo weights). To see how many standard hold has each vessel and with which weight we are going to load it, please see Appendix V: Vessel's Standard holds. Loaded with standard cargo weight. or Appendix VII: Vessel's standard holds. Loaded with actual cargo weight. The vessel Nº26, which we are using as example, has 13 standard holds. And we have to define the loading sequence in 1R and 2R. So we will have to define the following loading condition (first with standard values, and later on with the actual ones): TANIA SÁNCHEZ MACIÁ 156

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