From cfcb249e8487fa71720bd90ef249401ab6ea67c2 Mon Sep 17 00:00:00 2001 From: soypat Date: Thu, 20 Feb 2020 12:27:52 -0300 Subject: [PATCH] add instalaciones ind and some econ --- economia/economia_itba.pdf | Bin 60793 -> 178277 bytes economia/economia_itba.tex | 450 +++++++++++- economia/gloss.tex | 41 -- instind/fig/api650materiales.png | Bin 0 -> 49545 bytes instind/fig/cirsoc102nomog1.PNG | Bin 0 -> 140885 bytes instind/fig/cirsoc102tab1b.PNG | Bin 0 -> 26263 bytes instind/fig/cirsoc102tab2a.PNG | Bin 0 -> 55360 bytes instind/fig/cirsoc102tab2b.PNG | Bin 0 -> 42901 bytes instind/fig/cirsoc201tab21.png | Bin 0 -> 119572 bytes instind/fig/cirsoc201tab21c.png | Bin 0 -> 123767 bytes instind/fig/cirsoc201tab22.png | Bin 0 -> 74077 bytes instind/fig/cirsoc201tab23.png | Bin 0 -> 40570 bytes instind/fig/cirsoc201tab25.png | Bin 0 -> 66665 bytes instind/fig/cirsoc201tab27.png | Bin 0 -> 23332 bytes instind/fig/cirsoc201tab39.png | Bin 0 -> 61180 bytes instind/fig/resistchapas.PNG | Bin 0 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zPzF#Gfx;m$7z6^rh(h235QqRt-9im-E^p#$0TPrKhe1fs{)P~5mIEx2a2Sw;|LX#w zkVrTZWC{Aq21ESLV2mZG^y(h_lH+U>FpMtABqOgTRoc#Q)1i!eL0H|Jw$K zBhMxSfuqrX7ee?CBM1cQY$Xr``oF4!LNVyG2|{6z|H8qLD9qW4VMr|ctc?JNqcLY4 z!VwVYS^5zWEcWa&BA_tzS!NJeH2iGENK(I?^@qejp(KBQ@c(yTkP`f_Uim%gf6(gc zY+_??;S9Wa69m?=@v;DsdJn9P$Gd{yqy-@fuYi>uE%Bh=uu~;k$$j7Ik Hp$PmRlw9Vi diff --git a/economia/economia_itba.tex b/economia/economia_itba.tex index 7d7b285..9074c7d 100644 --- a/economia/economia_itba.tex +++ b/economia/economia_itba.tex @@ -1,9 +1,12 @@ +% !TeX spellcheck = es_ES + \documentclass[twocolumn,10pt]{article} \usepackage[utf8x]{inputenc} \usepackage[spanish]{babel} \usepackage[a4paper,top=2cm,bottom=2cm,left=2cm,right=2cm,marginparwidth=1.75cm,headheight=28pt]{geometry} %Letra general \usepackage{mathastext} +\usepackage{IEEEtrantools} \renewcommand{\familydefault}{\sfdefault} \usepackage[scaled=1]{helvet} @@ -13,6 +16,7 @@ \usepackage{color} \usepackage{fontawesome} \usepackage{siunitx} +\usepackage{booktabs,tabularx,makecell,multirow,caption} %Math \usepackage{amsmath} @@ -48,8 +52,18 @@ {\sc \large Patricio Whittingslow\par } \vspace{.4cm} ] +\glossml{A}{Activos.}{Assets} +\glossml{P}{Pasivos.}{Liabilities} + +\glossml{PN}{Patrimonio neto.}{Equity (commonly used for companies) or net worth (individuals)} + +\glossml{V}{Ventas.}{Revenue} + +\glossml{Q}{Cantidad demanda.}{Quantity demanded} + \glossml{VF}{Valor futuro.}{Future value $(FV)$} \glossml{VP}{Valor presente/actual.}{Principal/present value $(PV)$} +\glossml{VA}{Valor actual. Refiere los flujos positivos y negativos a un mismo punto en el tiempo para evaluar la conveniencia del proyecto.}{Present value (PV)} \glossml{VAN}{Valor actual neto}{Net present value $(NPV)$} @@ -66,7 +80,7 @@ \glossml{TEM}{Tasa efectiva mensual.}{Effective monthly interest rate} \glossml{TET}{Tasa efectiva trimestral (cada 3 meses).}{} - +\glossml{PN}{Patrimonio Neto.}{} \glossml{TEA}{Tasa efectiva anual.}{Effective annual interest rate} \glossml{CPI}{}{Consumer price index.} \glossml{\pi=\frac{\di CPI}{\di t}}{Inflación.}{Rate of inflation.} @@ -74,28 +88,444 @@ \glossml{FEE}{Flujo efectivo extraordinario.}{} \glossml{UAIG=UB}{Utilidad antes de impuestos a las ganancias o utilidad bruta.}{Profit before tax $(PBT)$} \glossml{UN}{Utilidad neta o utilidad despues de impuestos a las ganancias.}{Net income, net profit, bottom line or net earnings $(NI)$} -\glossml{G}{Ganancias.}{Earnings} +\glossml{G}{Ganancias o beneficio.}{Earnings} \glossml{IG}{Impuestos a las ganancias.}{Income tax $(IT)$} \glossml{BU}{Bienes de uso.}{Durable goods} \glossml{VL}{Valor en libros.}{Carrying value/amount or book value.} \glossml{K_T}{Capital de trabajo.}{Capital goods} +\glossml{K_S}{Capital Social.}{Social Capital} -\glossml{PN}{Patrimonio neto.}{Equity (commonly used for companies) or net worth (individuals)} - +\glossml{EBT}{Ganancias antes de impuestos.}{Earnings before tax.} \glossml{EBIT}{Ganancias antes de interés y impuestos.}{Earnings before interest \& tax.} \glossml{EBITDA}{Ganancias antes de interés, impuestos, depreciación y amortización.}{Earnings before interest, tax, depraciation \& amortization.} \glossml{CV}{Costos variables.}{Variable costs} \glossml{CF}{Costos fijos.}{Fixed costs} +\glossml{CT}{Costos totales.}{Total costs} +\glossml{CT_{Me}}{Costo total promedio.}{Total cost average} + +\glossml{PER}{Relación precio-beneficio.}{Price to earning ratio.} + + +\newcommand{\fiN}{\ensuremath{f_i^N}} + +\tableofcontents + +\part{Primer Parcial} +\section{Curva de la demanda} + +\begin{description} + \item[Bienes normales] Si la renta aumenta, la demanda aumenta + \item[Bienes inferiores] Si la renta aumenta, la demanda disminuye + \item[Bienes complementarios] La relación entre la demanda del bien $X$ y del precio de $C_X$ es inversa tal que si aumenta el precio del bien complementario $C_X$ de $X$, entonces se reducirá la cantidad demandada de $X$ (Automóvil $X$ vs. gasolina $C_X$) + \item[Bienes sustitutos] Si aumenta el precio del bien sustituto $S_X$ se reduce la cantidad demandada de $S_X$ y por lo tanto aumenta la demanda de $X$. La relación entre la demanda de $X$ y del precio de $S_X$ es directa (Hellmann's vs. Heinz) +\end{description} + +\section{Elasticidad} +La \textbf{elasticidad (de la demanda)} $\eta$ es la variación porcentual de la cantidad demandada sobre la variación porcentual del precio. +\begin{IEEEeqnarray*}{c} +\eta = \left| \frac{\Delta Q / Q}{\Delta P / P} \right|= \left| \frac{P\times \Delta Q}{Q \times \Delta P} \right| +\end{IEEEeqnarray*} +también existe la elasticidad de punto $\eta = \left| \frac{\di Q}{\di P}\cdot\frac{P}{Q} \right|$. Algunas fuentes expresan la elasticidad sin el modulo. + +\begin{description} + \item[$\eta_p> 1$] Demanda elástica + \item[$\eta_p = 1$] Demanda de elasticidad unitaria (ganancia máxima) + \item[$\eta_p < 1$] Demanda inelástica +\end{description} + +\textbf{Elasticidad ingreso} o renta de la demanda $e$ es la variación porcentual de la cantidad demandada sobre el cambio porcentual en la renta o ingreso del consumidor. +\begin{IEEEeqnarray*}{c} +e = \frac{ \Delta Q / Q }{ \Delta Y / Y } +\end{IEEEeqnarray*} + +\begin{description} + \item[$e>1$] Bien de lujo + \item[$01$] Bien inferior +\end{description} + + +Luego se tiene la \textbf{elasticidad cruzada de la demanda} $\eta_{XY}$ que es la variación de la cantidad demandada de $X$ sobre la variación porcentual del precio de $Y$. + +\begin{IEEEeqnarray*}{c} +\eta_{XY} = \frac{\Delta Q_X / Q_X}{\Delta P_Y / P_Y} +\end{IEEEeqnarray*} + +\begin{description} + \item[$e_{XY} > 0$] Bienes sustitutos + \item[$e_{XY} < 0$] Bienes complementarios +\end{description} + + +La \textbf{elasticidad precio de la oferta} $\varepsilon_p$ se calcula como la variación porcentual de la cantidad ofrecida sobre la variación porcentual del precio +\begin{IEEEeqnarray*}{c} + \varepsilon_p = \frac{\Delta \% Q_0}{ \Delta \% P} +\end{IEEEeqnarray*} + +\section{Función de la producción} +La función de la producción usa dos factores (Trabajo $L$ y capital $K$) y puede diferir según el plazo de análisis $\Delta t$. +\[ +Q = f(K,L, \Delta t) +\] + +\begin{description} + \item[Corto plazo] El lapso más largo durante el cual no es posible alterar al menos unos de los factores de producción + \item[Largo plazo] El lapso más corto necesario para alterar todos los factores involucrados en el proceso productivo +\end{description} + +\subsection{Ley de los rendimientos marginales decrecientes} +En el corto plazo hay un factor fijo (suele ser $K$) y uno variable (suele ser $L$). Esta ley establece que a medida que se incorporan unidades del factor variable al factor fijo, el rendimiento de cada unidad adicional es menor a partir de cierta cantidad límite. + + +\section{Mercados} + +\subsection{Competencia perfecta} +En una competencia perfecta se hacen las siguientes suposiciones +\begin{itemize} + \item Productos homogeneos + \item Empresas Precio-aceptantes + \item Información perfecta +\end{itemize} + +El mercado de competencia perfecta está en equilibrio cuando: + +\begin{itemize} + \item El precio de mercado es único + \item La oferta es igual a la demanda + \item Todos los consumidores maximizan la utilidad + \item Todas las empresas maximizan el beneficio +\end{itemize} + +Decisiones de producción: +\begin{itemize} + \item Como ya vimos, los beneficios se maximizan cuando $I_{Mg}=C_{Mg}$ + \item Si el $P>CT_{Me}$, la empresa obtiene beneficios + \item $CV_{Me}nlP&D@kKxyuknf0NAoJpHu+=Bq9I+krxdS 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Cana Inalec} \date{April 2019} \usepackage{siunitx} -\usepackage{graphicx} +\graphicspath{ {fig/} } \usepackage{bm} \newcommand{\glossentry}[2]{$#1$\indent #2 \par \vspace{.4cm} }

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+\renewcommand\theadalign{bc} +\renewcommand\theadfont{\bfseries} +\renewcommand\theadgape{\Gape[4pt]} +\renewcommand\cellgape{\Gape[4pt]} + +%%%%%%%%%% +% MACROS % +%%%%%%%%%% +\newcommand{\adm}{\text{adm}} +\newcommand{\str}{\text{str}} +\newcommand{\Dext}{D_\text{ext}} +\newcommand{\Dint}{D_\text{int}} +\newcommand{\Pext}{P_\text{ext}} +\newcommand{\grad}{\ensuremath{^\circ \textrm{C}}} + +\usepackage[symbol*]{footmisc} +\usepackage{titlesec} +\titleformat*{\section}{\normalfont\large\bfseries} +\titleformat*{\subsection}{\normalfont\normalsize\bfseries} + +\title{Instalaciones Industriales} +\author{Hoja de formulas} +\date{\today} +\begin{document} + \maketitle + + \tableofcontents +%{ \centering \vspace{-1cm}\par +% {\Large Hoja de Formulas \par} +% \vspace{.3cm} +% {Instalaciones industriales\par} +%} +\section{Dise\~no de Ca\~ner\'ias de proceso[ASME B31.3]} +Esta norma es para caños de acero. Para caños de acero inoxidable se puede usar ASME B36.19. Cañerías de potencia ASME B31.1. ASME B16.9 rige para accesorios de cañerías. + +Estimación de schedule: Sch$\approx 1000\cdot \frac{P_d}{S}$ donde $S$ es el basic allowable stress. + +El diámetro se puede calcular con la velocidad $v$ y el caudal deseado $Q$ del flujo interno. + +El espesor mínimo permisible de la pared de un caño: +\[ +t_{\min} = t_n+c +\] +corregido por tolerancias mecánicas del fabricante: +\[ +t_{\text{elegido}} = \frac{t_{\min}}{0,875} = \frac{t_{n} + c}{0,875} +\] + +donde $t_n$ es el espesor nominal calculado por la presión de diseño y $c$ incluye el sobre-espesor por corrosión y suma de geometrías mecánicas como profundidad de rosca. El 0,875 toma en cuenta una variación de 12,5\% de tolerancias mecánicas de fabricante. + +\[ +\text{Para } tS_L +\end{cases} +\] +donde $f = 6\cdot N^{-0,2}\leq f_{\max}$ +\begin{itemize} + \item[$S_c$:] Tensión admisible del material a 21\grad [A-1M] + \item[$S$:] Tensión admisible a temperatura $T_d$ (\textit{Basic allowable stress}) [A-1M] + \item[$S_L$:] Suma de tensiones longitudinales debido a presión, peso y otras cargas sostenidas. Se calcula $S_L$ con espesor nominal sin sobreespesor. + \item[$f_{\max}$:] Valor máximo de $f$. Es 1,2 para materiales ferrosos con tensiones de rotura hasta 517 MPa y hasta 371\grad. Es 1 para el resto de los casos. Para número indefinido de ciclos se usa 0,15. +\end{itemize} + + + +\section{Diseño de recipientes a presión[ASME VIII]} +Al igual que en ASME B31.3 se tienen que considerar sobreespesores por corrosión o erosión que dependen del fluido, material, concentración, la temperatura y otras variables. + +Se suele verificar los recipientes ante el vacío total interno ($\Pext=P_\text{atmosfera}$) según ASME Section II, visto en la sección \ref{sec:asmeii} de este documento. + +$T_d$ (temperatura de diseño) se elige como la presión máxima de trabajo en el interior del recipiente incrementada por un \% como un margen de seguridad. + +La MDMT (temperatura mínima del metal) debe ser la temperatura más baja esperada en servicio. + +Las fallas posibles de recipientes a presión: +\begin{itemize} + \item Deformación elastica excesiva + \item Inestabilidad elastica + \item Inestabilidad plastica + \item Rotura fragil + \item Creep (fluencia lenta) + \item Corrosión +\end{itemize} +\subsection{Diseño de envolvente cilíndrica} + +Para un recipiente a presión cilíndrico se tiene que las tensiones en las juntas longitudinales y circunferenciales definen el espesor nominal permisible para el diseño resistente del mismo. + +Esfuerzo circunferencial (juntas longitudinales) +\[ +t_n = \frac{P_d \cdot R}{SE - 0,6P_d}, \qquad P = \frac{S E t}{R+0,6t} +\] + +Esfuerzo longitudinal (juntas circunferenciales) +\[ +t_n = \frac{P_d \cdot R}{2SE + 0,4P_d}, \qquad P = \frac{2S E t}{R - 0,4t} +\] +\begin{itemize} + \item[$t_n$:] Espesor nominal. Unidades dependen de $R$ + \item[$R$:] Radio interno de recipiente. Si hay corrosión interna se debe restar para llevar $R$ al último día de servicio + \item[$P_d$:] Presión interna de diseño. Mismas unidades que $S$. + \item[$E$:] Eficiencia de junta [UW-12] + \item[$S$:] \textit{Maximum allowable stress} [1A] +\end{itemize} + +Luego el espesor de diseño (el construido) va ser +\[ +t = t_n + c +\] +\begin{itemize} + \item[$c$:] Sobreespesor por corrosion y tolerancias mecánicas +\end{itemize} +\subsection{Elección de cabezal} + +\begin{table}[htb!] + \centering + + \bgroup + \def\arraystretch{1.5} + \begin{tabular}{|c|c|c|} + \hline + Torisféricos& $t_n = \frac{0,885 P_d L}{SE - 0,1P_d}$ & \\ + \hline + Cabezales cónicos& $t_n = \frac{P_d \Dint}{2\cos \alpha (SE - 0,6P_d)}$ & \\ + \hline + Cabezales elípticos& $t_n = \frac{P_d D_{e}}{2SE - 0,2P_d}$ & \\ + \hline + Cabezales hemisféricos& $t_n = \frac{P_d L}{2SE - 0,2P_d}$ & \\ + \hline + \end{tabular} + \egroup +\end{table} + +\begin{itemize} + \item[$L$:] Longitud de envolvente cilíndrica + \item[$\alpha$:] Mitad del ángulo de cono. $\alpha < 30^\circ$ + \item[$\Dint$:] Diámetro interno de la envolvente cilíndrica + \item[$D_e$:] Diámetro interno de la envolvente cilíndrica (para cabezales de relación 2:1) +\end{itemize} + +\subsection{Espesor agregado por viento} + +El momento en la base del recipiente es dado por: +\[ +M = P_w \cdot A \cdot h +\] +\begin{itemize} + \item[$P_w$:] Presión del viento + \item[$A$]: Area enfrentada al viento (no es superficie!) + \item[$h$:] Distancia del centroide de la fuerza aplicada por presión hasta la base del recipiente. Se puede tomar la mitad de la altura del recipiente. +\end{itemize} + +El momento en la costura inferior ($M_T$) es el afecta la \textbf{soldadura longitudinal} (para el caso de un cilindro vertical) +\[ +M_T = M - h_T(V - 0,5P_w \cdot A_T) +\] +\begin{itemize} + \item[$h_T$:] Distancia desde la base del recipiente hasta la soldadura + \item[$A_T$:] Area frontal entre la base y la soldadura + \item[$V$:] Corte total ($V=A\cdot P_w$) +\end{itemize} + +Finalmente se calcula el espesor requerido: +\[ +t_{\text{long}} = \frac{4 M_T}{\pi \Dint^2 S E} +\] +\begin{itemize} + \item[$t_{\text{long}}$:] Espesor agregado por cargas de viento. Se suma al espesor nominal por tensión longitudinal $t_n$ (junta circunferencial). +\end{itemize} + + +Usualmente el espesor de un cabezal hemisferico es mitad del espesor de un cuerpo cilíndrico. + +Elección de Bridas según ASME B16.5 +\section{Verificación ante presión externa[ASME II]} \label{sec:asmeii} +Para verificar presión externa se utiliza \textbf{ASME Section II}. +\begin{enumerate} + \item Calcular razón $\frac{\Dext}{t}$ y $\frac{L}{\Dext}$ para ingresar a la figura G de la parte D. Obtengo factor $A$. + \item Ingresar a figura CS-1 ($S_y<207$ MPa) o CS-2 ($S_y\geq207$ MPa) dependiendo de la mínima tensión de fluencia del material $S_y$\footnote{No es lo mismo que \textit{basic allowable stress.}} [A-1M]. $E$ es el módulo de Young del acero, dependiente de la temperatura de trabajo $T_d$. Si $A>0,1$ considerar proyección horizontal del fin de curva. Si $A<0,0002$ entonces continuar al paso siguiente. Obtengo factor $B$ + \item Calcular la presión máxima exterior admisible $P_a$ y verificar que sea inferior a la presión exterior de trabajo o la atmosférica (vacío en el tubo) dependiendo del caso +\end{enumerate} +\[ +P_a = \begin{dcases} +\frac{4B}{3(\Dext/t)}\qquad 0,0002\leq A<0,1 \\ +\frac{2A\cdot E}{3(\Dext/t)}\qquad A<0,0002 +\end{dcases} +\] +donde $E$ es el módulo de Young. + +\section{Tanques de almacenamiento[API 650]} + +Los tanques de almacenamiento actúan como pulmón entre producción y transporte. Sus otras funciones pueden incluir la sedimentario de agua y barros en la industria petrolera +\begin{description} + \item[API 650] Tanques soldados para almacenamiento de petroleo crudo + \item[API 620] Diseño y construcción de tanques de almacenamiento grandes, soldados a baja presión +\end{description} + +Su característica es que están a presión atmosférica + +Algunos techos para tanques verticales: +\begin{description} + \item[Techo cónico soportado] Bajo costo inicial. Se requieren soportes internos (columnas) + \item[Techo domo] Más costos que el cónico. Mayor facilidad para aplicar revestimientos internos + \item[Techo geodésico] Bajo costo de mantenimiento y excelente durabilidad. Mayor costo inicial + \item[Techo flotante interno] Reduce las pérdidas por evaporación. Excelente para almacenar fluidos volátiles inflamables. Muy delicado. Se combina con uno de los techos anteriores. + \item[Techo flotante externo] Puede ser de simple o doble cubierta. Es necesario contar con un sistema de drenaje para lidiar con agua acumulado sobre el techo flotante. +\end{description} + +Pasos para el diseño de un tanque soldado para petroleo: +\begin{enumerate} + \item Elección de material y los espesores mínimos para las placas del envolvente y piso [tablas 5.2a; 5.1a y sección 5.6.1.1] \footnote{Tener en cuenta que la virolas suelen venderse en largos de 6 y 12 metros.} + \item Se eligen las conexiones y entradas de hombre [5.6a y 5.13a] + \item Anillos rigidizadores para cargas de viento. + \item Cálculo de espesor de envolvente. Para tanques con diámetro mayor a 61m se puede usar la regla del pie\footnote{Se verifica para condiciones de diseño $_d$ y de prueba $_t$ hidrostática}: + \[ + t_d = \frac{4,9D(H-0,3)G}{S_d} + CA + \] + \[ + t_t = \frac{4,9D(H-0,3)}{S_t} + \] + \begin{itemize} + \item[$CA$:] El el sobre-espesor por corrosión (Corrosion allowance), en mm + \item[$D$:] Diámetro nominal del tanque, en m + \item[$t_d$:] Espesor de diseño, en mm + \item[$H$:] Es la altura de diseño del liquido, en m + \item[$G$:] Es la gravedad especifica del liquido + \item[$S_d,S_t$:] Es la tensión admisible para condiciones de diseño y de prueba, en MPa [5.2a] + \end{itemize} +\end{enumerate} + +\begin{figure}[htb!] + \centering + \includegraphics[width=1\linewidth]{fig/api650materiales} + \label{fig:api650materiales} +\end{figure} + +\section{Cálculo de cargas mayoradas} +Una carga mayorada es aquella que se multiplicada por un factor para aumentar su valor. En la ingeniería civil se suele mayorar las cargas según + +\[ +1,2 P_p + S_c + 1,6W +\] +donde $P_p$ es el peso propio de la estructura, $S_c$ es la sobrecarga de uso y $W$ son las cargas dinámicas (viento) + +\section{Estructuras de acero para edificios[CIRSOC 301-2005]} +Este Reglamento es de aplicación a todos los elementos estructurales resistentes de +acero, laminados o armados con perfiles laminados y/o chapas, y sus uniones, que +formen parte de las estructuras de acero de edificios destinados a vivienda, locales +públicos, depósitos e industrias (incluso las que tengan carácter provisorio como +andamios cimbras, puntales, etc.), y que sean necesarias para soportar los efectos de +las acciones actuantes. Se incluyen las vigas carril de puentes grúas, monorrieles y las +estructuras de soporte de instalaciones y cañerías. + +\subsection{Límites de esbeltez[B.7]} +\[ +\text{Esbeltez} = \frac{kL}{r} +\] + +\begin{description} + \item[Barras comprimidas] la esbeltez será menor o igual que 200. En presencia de efectos dinámicos (como viento) se reduce a 150 + \item[Barras traccionadas] la esbeltez será menor o igual que 300. No aplica para cables. En presencia de efectos dinámicos se reduce a 250. +\end{description} + +\subsection{Estabilidad de estructura[C.2]} + +\begin{description} + \item[Estruc. trianguladas interiormente isostaticas] $k = L_1/L$ donde $L_1$ es la distancia entre puntos no desplazables lateralmente por efecto del sistema de arriostramiento lateral, en cm. $L$ es la longitud real de la barra en cm + \item[En pórticos y reticulados] cuya estabilidad lateral es provista por un sistema de + arriostramiento, el factor de longitud efectiva $k$ para barras comprimidas se deberá tomar + igual a la unidad, a menos que un análisis estructural demuestre que se puede adoptar un valor menor. +\end{description} + + +\subsection{Columnas (inestabilidad)[E.1]} +Son elementos sometidos a compresión con excentricidad. + +La resistencia de diseño para pandeo flexional: + +\[ +\phi_c P_n +\] +\begin{itemize} + \item[$\phi_c$] = 0,85 + \item[$P_n$:] resistencia nominal, en kN. $P_{n}=F_{c r} A_{g}\left(10^{-1}\right)$ +\end{itemize} + +\[ +F_{c r}=\begin{cases} +\left(0,658^{\lambda_{c}^{2}}\right) F_{y} & \lambda_c\leq 1,5 \\ +\left( \frac{0,877}{\lambda_{c}^{2} } \right) F_{y} & \lambda_c > 1,5 \\ +\end{cases} +\] +\begin{itemize} + \item[$F_y$:] Tensión de fluencia especificada, en MPa + \item[$A_g$:] Área bruta de barra, en cm$^2$ + \item[$\lambda_c$:] factor de esbeltez adimensional + \[ + \lambda_{c}=\frac{1}{\pi} \frac{k L}{r} \sqrt{\frac{F_{y}}{E}} + \] + \item[$E$:] Módulo de elasticidad longitudinal, en MPa + \item[$k$:] Factor de longitud efectiva calculado según [C.2] + \item[$L$:] Longitud real de la barra, en cm + \item[$r$:] Radio de giro de la sección en cm + \[ + r = \sqrt{ I/A_g } + \] + \item[$I$:] El segundo momento de inercia de la sección bruta, en cm$^4$ +\end{itemize} + +\subsection{Dimensionamiento de vigas al corte[F.2]} +El área del alma $A_w$ será el producto entre altura total de la sección $d$ por el espesor del alma $t_w$. + +La resistencia de diseño al corte de almas no rigidizadas, con $h/t_w \leq 260$, será: +\[ +\phi_v V_n +\] +\begin{itemize} + \item[$\phi_v$] = 0,90 + \item[$V_n$:] La resistencia nominal al corte definido según las siguientes expresiones, en kN: + \[ + \!\!\!\!\!\!\!\!V_n = \begin{dcases} + \arraycolsep=1.4pt\def\arraystretch{2.2} + 0,6F_{yw} A_w (10^{-1}) \\ + \frac{0,6 F_{y w} A_{w}(2,45 \sqrt{E / F_{y w}})\left(10^{-1}\right)}{\left(h / t_{w}\right)} \\ + \frac{4,52 E A_{w}(10)^{-1}}{\left(h / t_{w}\right)^{2}} + \end{dcases} + \] + Para los casos (respectivamente) + \[ + \begin{cases} + + \frac{h}{t_w}\leq 2,45 \sqrt{\frac{E}{F_{yw}}}\\ + 2,45\sqrt{\frac{E}{F_{yw}}}<\frac{h}{t_w}\leq 3,07 \sqrt{\frac{E}{F_{yw}}} \\ + 3,07 \sqrt{\frac{E}{F_{y w}}}<\frac{h}{t_{w}} \leq 260 + \end{cases} + \] + + \item[$F_{yw}$:] Tensión de fluencia, en MPa + \item[$h$:] Distancia libre entre alas, unidades de $t_w$ [K.1.5] +\end{itemize} + +\subsection{Uniones [J]} + +\subsection{Resistencia a la tracción o al corte [J.3.6]} +La resistencia de diseño a la tracción o al corte de los bulones de alta resistencia y de elementos roscados será: +\[ +\phi F_n A_b (10^{-1}) +\] +\begin{itemize} + \item[$\phi$:] el factor de resistencia indicado en la Tabla J.3.2. + \item[$F_n$:] la resistencia nominal a la tracción Ft, o al corte Fv, indicadas en la Tabla J.3.2. , en MPa. + \item[$A_b$:] el área nominal del cuerpo no roscado del bulón o de la parte roscada (para varillas recalcadas, ver la nota (c) al pie de la Tabla J.3.2.). ,en cm2. +\end{itemize} + +\subsubsection{Combinación de tracción y corte en uniones tipo aplastamiento[J.3.7]} +La resistencia de diseño a tracción de un bulón sometido a corte y tracción +combinados será: +\[ +\phi F_t A_b (10^{-1}) +\] + +\begin{itemize} + \item[$\phi$:] = 0,75 + \item[$F_t$:] la resistencia nominal a tracción en términos de tensión calculada con las expresiones de la Tabla J.3.5. como una función de la tensión de corte requerida $f_v$ producida por las cargas mayoradas, en MPa. La tensión de corte requerida $f_v$ será menor o igual que la resistencia de diseño al corte $\phi F_v$ ,indicada en la Tabla J.3.2. +\end{itemize} + +\subsubsection{Bulones de alta resistencia en uniones de deslizamiento crítico[J.3.8]} +La resistencia de diseño al corte de bulones de alta resistencia en uniones de deslizamiento crítico se obtendrá de acuerdo con la Sección J.3.8(a) o J3.8(b). Los bulones así dimensionados se deberán verificar a corte trabajando en uniones tipo aplastamiento con las Secciones J.3.6. y J.3.7. y será verificado el aplastamiento de la chapa de acuerdo con las Secciones J.3.1. y J.3.10.. + +La\textbf{ resistencia de diseño al deslizamiento} $\phi R_\str$, deberá ser mayor o igual que la fuerza requerida debida a las cargas mayoradas, donde: +\[ +R_{\str} = 1,13 \mu T_b N_s +\] + +\begin{itemize} + \item[$R_{\str}$:] la resistencia nominal al deslizamiento, en kN. + \item[$T_b$:] la fuerza de tracción mínima del bulón dada en la Tabla J.3.1., en kN. + \item[$N_s$:] la cantidad de superficies de rozamiento. + \item[$\mu$:] el coeficiente medio de rozamiento para las Clases A, B, o C, según corresponda, o el que surja de ensayos. + \begin{itemize} + \item[(a)] Para superficies Clase A (superficies de acero limpias con cepillo metálico libres de polvo, óxido o cascarillas de laminación y no pintadas, o superficies con recubrimientos Clase A en acero limpiado con chorro de arena), $\mathbf{\mu=0,33}$ + \item[(b)] Para superficies Clase B (superficies de acero limpiadas con chorro de arena y no pintadas o superficies con recubrimiento Clase B en acero limpiado con chorro de arena), $\mathbf{\mu=0,50}$ + \item[(c)] Para superficies Clase C (superficies galvanizadas por inmersión en caliente y con superficies ásperas), $\mathbf{\mu=0,35}$ + \end{itemize} +\item[$\phi$] el factor de resistencia +\begin{itemize} + \item[$\phi=1,0$] Para agujeros normales + \item[$\phi=0,85$] Para agujeros holgados y ovalados cortos + \item[$\phi=0,7$] Para agujeros ovalados largos con eje mayor perpendicular a la dirección de la fuerza + \item[$\phi=0,6$] Para agujeros ovalados largos con eje mayor paralelo a la dirección de la fuerza +\end{itemize} +\end{itemize} + +\subsubsection{Tracción y corte combinados en uniones de deslizamiento crítico[J.3.9]} +Cuando las uniones de deslizamiento crítico estén solicitadas por una fuerza de tracción $T_u$, que reduzca la fuerza de apriete entre las superficies en contacto, la \textbf{resistencia de diseño al rozamiento} $\phi R_\str$ de la Sección J.3.8(a) deberá ser multiplicada por +el siguiente factor, en el cual $T_u$ (kN) es la resistencia a tracción requerida bajo cargas mayoradas: +\[ +[1 - T_u /(1,13 T_b N_b)] +\] +\begin{itemize} + \item[$T_b$:] la fuerza de tracción mínima del bulón dada en la Tabla J.3.1., en kN. + \item[$N_b$:] la cantidad de bulones cargados con la fuerza de tracción $T_u$. +\end{itemize} + +\subsubsection{Resistencia al aplastamiento de la chapa en los agujeros[J.3.10]} +La resistencia al aplastamiento de la chapa será verificada tanto para las uniones tipo aplastamiento como para las tipo deslizamiento crítico. La utilización de agujeros holgados y ovalados cortos y largos con eje mayor paralelo a la dirección de la fuerza se restringe para las uniones de deslizamiento crítico por medio de la Sección J.3.2.. + +La \textbf{resistencia de diseño al aplastamiento de la chapa en los agujeros} será: +\[ +\phi R_n +\] + +\begin{itemize} + \item[$\phi$] = 0,75 + \item[$R_n$:] la resistencia nominal al aplastamiento de la chapa, en kN. +\end{itemize} + +\begin{figure}[htb!] + \centering + \includegraphics[width=1.13\linewidth]{fig/resistchapas.PNG} +\end{figure} + + + + + + + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%55 +%% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{figure}[htb!] + \centering + \includegraphics[width=1.1\linewidth]{fig/tabJ32.PNG} +\end{figure} + +\begin{figure*}[htb!] + \centering + \includegraphics[width=\textwidth]{fig/tabJ33.PNG} +\end{figure*} + +\begin{figure}[htb!] + \centering + \includegraphics[width=1.1\linewidth]{fig/tabJ35.PNG} +\end{figure} + + + + + + + + +\clearpage +\subsection{Uniones [Apéndice J]} +\subsubsection{Resistencia al aplastamiento} +La resistencia de las superficies solicitadas al aplastamiento será: +\[ +\phi R_n +\] +\begin{itemize} + \item[$\phi$] = 0,75 + \item[$R_n$] la resistencia nominal al aplastamiento, en kN +\end{itemize} +donde +\begin{itemize} + \item Para superficies mecanizadas, pernos pasantes en agujeros escariados, taladrados + o punzonados y en los extremos de rigidizadores ajustados trabajando a + aplastamiento: + \[ +R_n = 1,8 F_y A_{pb} (10^{-1}) +\] +\item[$F_y$:] la tensi\'on de fluencia especificada, en MPa +\item[$A_{pb}$:] la proyecci\'on del \'area +\end{itemize} +\subsubsection{Bulones (desl. crítico)} + +\begin{table*}[htb!] + \centering + \caption{\textbf{A-J.3.1.} Resistencia nominal a la tracción ($F_t$), en MPa. Uniones de tipo aplastamiento.} +% \footnotesize + \begin{tabular}{|c|c|c|} + \hline + \thead{Descripción de \\ los bulones} & \thead{Rosca incluída\\ en el + plano\\ de corte} & \thead{Rosca excluída \\ del + plano\\ de corte} \\ + \hline + \thead{Bulones Comunes\\ + Tipo A307, ISO 4.6} & \multicolumn{2}{c|}{$\sqrt{620^{2}-6,25 f_{v}^{2}}$} \\ + \hline + \thead{Bulones + A325,\\ A325M + ISO 8.8} & $\sqrt{620^{2}-6,25 f_{v}^{2}}$ & $\sqrt{620^{2}-4.00f_{v}^{2}}$ \\ + \hline + \thead{Bulones + A490,\\ A490M + ISO 10.9} & $\sqrt{778^{2}-6,42 f_{v}^{2}}$ & $\sqrt{778^{2}- 4,04 f_{v}^{2}}$ \\ + \hline + \thead{Partes roscadas de\\ + bulones A449 de\\ + diámetro mayor\\ que + 38.1 mm} & $\sqrt{(0,75F_u)^{2}-6,25 f_{v}^{2}}$ & $\sqrt{(0,75F_u)^{2}-4,00 f_{v}^{2}}$ \\ + \hline + \end{tabular} +\end{table*} + +Según \textbf{A-J.3.8(b). Uniones de deslizamiento crítico dimensionadas para cargas de servicio}, a resistencia de diseño al corte de un bulón en una unión de deslizamiento crítico para cargas de servicio será: + +\[ +\phi F_v A_b (10^{-1}) +\] +\begin{itemize} + \item[$\phi$] = 1,0 para agujeros normales, holgados, ovalados cortos, y ovalados largos cuando el eje más largo es perpendicular o paralelo a la línea de fuerza. + \item[$F_v$:] la resistencia al deslizamiento crítico para cargas de servicio indicada en + Tabla A-J.3.2, en MPa + \item[$A_b$:] área nominal del cuerpo no roscado del bulón, o de la parte roscada, en cm$^2$. +\end{itemize} + +\textbf{A-J.3.9(b). Uniones de deslizamiento crítico dimensionadas para cargas de servicio}. +La resistencia de diseño al corte de un bulón en una unión de deslizamiento crítico +solicitada a una fuerza de tracción T (kN) debida a las cargas de servicio que reduce la +fuerza de apriete entre las partes en contacto, será $\phi F_v A_b$ (10-1), calculada de acuerdo con +lo especificado en la Sección A-J.3.8(b) multiplicada por el siguiente factor de reducción : + + \[ + 1 - \frac{T}{0,8T_b N_b} + \] + + \begin{itemize} + \item[$T_b$:] El pretensado mínimo del bulón dado por tabla A-J.3.1, en kN + \item[$N_b$:] el número de bulones cargados con la tracción de servicio $T$, en kN + \end{itemize} + + + + +\begin{table}[htb!] + \centering + \caption{\textbf{A-J.3.2.} Resistencia al corte Fv para cargas de servicio de bulones de alta + resistencia en uniones de deslizamiento crítico (a) (MPa).} + \footnotesize + \begin{tabular}{|c|c|c|c|} + \hline + \thead{Tipo de \\ bulón}&\thead{Agujeros\\normales} & \thead{Agujeros\\holgados y\\ovalados\\ cortos} & \thead{Agujeros\\ ovalados\\ largos\\perpendicular\\ (paralelo) a linea\\ de fuerza} \\ + \hline + \thead{A325,\\ A325M\\ISO 8.8} & 117 & 103 & 83 (69) \\ + \hline + \thead{A490,\\ A490M\\ISO 10.9} & 145 & 124 & 103 (90) \\ + \hline + \end{tabular} +\end{table} + + + + +\clearpage +\section{Dimensionado de elementos con armadura} +Caso de carga básico +\[ +1,2P_p +S_c + 1,6W +\] +El momento último de servicio (trasladando al baricentro de la armadura) es +\[ +M_{us} = M_{mayorada} - N(d-h/2) +\] +considerar pretensado sobre $N$. +\subsection{Predimensionado de columna ante compresión} + +Para poder emplear métodos aproximados se plantea la siguiente desigualdad + +\[ +h > \sqrt[3]{ \frac{24 \cdot n \cdot P_u (kz\ell_u)^2}{ b E_c} } +\] +donde $n$ es el factor de sobredimensionamiento (siempre mayor a 1). +\section{Estructuras de hormigón[CIRSOC 201-2005]} + +\subsection{Módulo de elasticidad [8.5]} + +8.5.1. El módulo de elasticidad $E_c$ del hormigón de densidad normal (entre 2000 y 2800 $\text{kg/m}^3$) se puede determinar con la expresión (8-1) siempre que las tensiones no superen el valor $0,45\sqrt{f'_c}$ : + +\[ +E_c = 4700 \sqrt{f'_c} \qquad \text{(en MPa)} +\] + +8.5.2. El módulo de elasticidad $E_s$ de la armadura no tesa, se puede considerar igual a: +\[ +E_s = 200000 \text{MPa} = 200 \text{GPa} +\] + +\subsection{Requisitos generales [9.1]} +9.1.1. Las estructuras y los elementos estructurales se deben diseñar para obtener, +en cualquier sección, una resistencia igual o mayor que la resistencia requerida, determinada para las cargas mayoradas combinadas en la forma establecida en este +Reglamento. + +El requisito básico para el diseño por resistencia de estructuras de hormigón se +puede expresar de la siguiente forma: +\begin{IEEEeqnarray*}{uc.s} +Resistencia de Diseño & \geq & Resistencia Requerida \\ +$\phi S_n$ &\geq & $U$ +\end{IEEEeqnarray*} +donde $U$ es la resistencia requerida para resistir las cargas mayoradas o las solicitaciones +correspondientes y $S_n$ es la resistencia nominal en N. + +9.3.2. El factor de reducción de resistencia $\phi$, para aquellas combinaciones que no +incluyen sismo, debe ser el indicado en los artículos 9.3.2.1. al 9.3.2.5. inclusive (siguientes puntos): + +\begin{description} + \item[$\phi = 0,90$] Para secciones controladas por traccion segun 10.3.4 + \item[$\phi=0,65$] Secciones controladas por compresión según 10.3.3 +\end{description} + + +\subsection*{Campo de validez del capítulo 10} +Este Capítulo se debe aplicar al diseño de elementos solicitados a flexión o por cargas axiales, o por una combinación de flexión y cargas axiales. +\subsection{Nomenclatura Capítulo 10} +\begin{description} + \item[$a$] altura del bloque de tensiones rectangular equivalente, definido en el artículo 10.2.7.1., en mm. + \item[$A_s,A_{st}$] Area de la armadura longitudinal traccionada no tesa en mm$^2$ + \item[$A_g$] área total o bruta de la sección. En una sección hueca, Ag es el área de + hormigón solamente, en mm$^2$ + \item[$b$] ancho del borde comprimido de la sección transversal de un elemento, en mm. + \item[$b_w$] Alto de alma para un elemento con alas, en mm$^2$ + \item[$c,c_t$] distancia desde la fibra comprimida extrema al eje neutro, en mm. + \item[$h$] espesor o altura total de la sección transversal de un elemento, en mm + \item[$d$] distancia desde la fibra comprimida extrema hasta el baricentro de la armadura longitudinal traccionada, no tesa, (altura útil), en mm$^2$ + \item[$d_t$] distancia desde la fibra comprimida extrema hasta el baricentro de la capa de armadura longitudinal más traccionada, en mm. + \item[$E_c$] módulo de elasticidad del hormigón, en MPa. Ver el artículo 8.5.1. + \item[$E_s$] módulo de elasticidad de la armadura no tesa, en MPa. Ver el artículo 8.5.2. + \item[$C_m$] factor que relaciona el diagrama real de momentos con un diagrama equivalente de momentos uniforme. + \item[$k$] factor de longitud efectiva para elementos comprimidos. + \item[$I_g$] momento de inercia de la sección total o bruta del elemento de hormigón con respecto al eje baricéntrico, sin considerar la armadura, en mm$^4$. + \item[$f_c'$] resistencia especificada a la compresión del hormigón, en MPa. $\sqrt{f_c'}$ también es en MPa + \item[$f_y$] tensión de fluencia especificada de la armadura longitudinal no tesa, (corresponde + al límite de fluencia de la norma IRAM-IAS), en MPa. + \item[$\ell_u$] longitud sin apoyo lateral de un elemento comprimido, en mm. Ver el artículo 10.11.3.1. + + \item[$M_c$] momento mayorado debido a las cargas que producen un desplazamiento horizontal apreciable, en N mm. + \item[$M_s$] momento mayorado debido a las cargas que producen un desplazamiento horizontal apreciable, en N mm. + \item[$M_u$] momento mayorado en la sección considerada, en N mm. + \item[$M_1$] el menor momento (de primer orden), mayorado en uno de los extremos de un elemento comprimido, que se debe adoptar como positivo si el elemento presenta curvatura simple, y negativo si tiene doble curvatura, en N mm + \item[$M_2$] el mayor momento (de primer orden) mayorado, en uno de los extremos de un elemento comprimido, siempre positivo, en N mm + \item[$M_{1ns}$] momento mayorado de un elemento comprimido, en el extremo en el cual actúa $M_1$, debido a cargas que no originan desplazamiento lateral apreciable, y calculado mediante un análisis elástico de primer orden del pórtico, en N mm. + \item[$M_{1s}$] momento mayorado de un elemento comprimido, en el extremo en el cual actúa $M_1$, debido a cargas que originan un desplazamiento lateral apreciable, y calculado mediante un análisis elástico de primer orden del pórtico, en N mm. + + + \item[$P_b$] resistencia nominal para carga axial (resistencia axial nominal) en la condición de deformación balanceada, en N. Ver el artículo 10.3.2. + \item[$P_c$] carga crítica de pandeo, en N. Ver el artículo 10.12.3. + \item[$P_n$] resistencia nominal para la carga axial, (resistencia axial nominal) de la sección transversal, en N. + \item[$P_u$] esfuerzo axial mayorado para una excentricidad dada ($P_u \leq \phi P_n$), en N. Se debe considerar positivo para compresión y negativo para tracción. + \item[$Q$] índice de estabilidad de un piso. Ver el artículo 10.11.4. + \item[$\beta_d$] relación utilizada para calcular los momentos amplificados en las columnas + debidos a las cargas sostenidas o de larga duración. Ver los artículos 10.11.1. y + 10.13.6. + \item[$\beta_1$] factor que relaciona la altura del bloque de tensiones de compresión rectangular + equivalente con la profundidad del eje neutro. Ver el artículo 10.2.7.3. + \item[$\delta_{ns}$] factor de amplificación de momentos para pórticos indesplazables, utilizado para + reflejar los efectos de la curvatura entre los extremos del elemento comprimido. + \item[$\delta_s$] factor de amplificación de momentos para pórticos desplazables, utilizado para + reflejar el desplazamiento lateral que resulta de las cargas gravitatorias y de las + cargas laterales. + \item[$\Delta_o$] desplazamiento lateral relativo entre el extremo superior e inferior de un piso + debido a los esfuerzos horizontales, calculado mediante un análisis elástico de + primer orden del pórtico, con valores de rigideces que satisfagan lo especificado + en el artículo 10.11.1. + \item[$\varepsilon_t$] deformación específica neta de tracción en el acero más traccionado para la + resistencia nominal, excluyendo las deformaciones debidas a la tensión efectiva del pretensado, la fluencia lenta, la contracción y las variaciones de temperatura. + \item[$\rho$] cuantía de la armadura traccionada, no tesa; relación entre $A_s$ y $b d$, ($\rho = A_s /b d$). Ver el artículo C 10.3.3. y el Apéndice B. + \item[$\rho_b$] cuantía de la armadura que produce condiciones de deformación balanceadas; relación entre $A_s$ y $b d$ ($\rho_b = A_s/b d$). Ver el artículo 10.3.2. + \item[$\phi$] factor de reducción de la resistencia. Ver el artículo 9.3. +\end{description} +\subsection{Hipótesis de diseño [10.2]} +10.2.1. El diseño por resistencia de elementos solicitados a flexión y cargas axiales se +debe fundamentar en las hipótesis establecidas en los artículos 10.2.2. a 10.2.7. inclusive y debe satisfacer las condiciones de equilibrio y de compatibilidad de las +deformaciones. + +10.2.2. Las deformaciones específicas en la armadura y en el hormigón se deben suponer directamente proporcionales a la distancia al eje neutro, excepto en vigas de gran altura + +10.2.3. Para la determinación de la resistencia nominal de una sección, se debe considerar como máxima deformación en la fibra extrema del hormigón sometida a +compresión un valor igual a 0,003. + +10.2.4. La tensión en el acero se debe calcular como Es veces la deformación de la armadura, siempre que dicha tensión resulte menor que la tensión de fluencia especificada fy . Para deformaciones mayores que la correspondiente a fy , la tensión se debe considerar independiente de la deformación, e igual a fy . + +10.2.5. La resistencia a la tracción del hormigón no se debe considerar en el dimensionamiento de los elementos de hormigón armado solicitados a flexión y a cargas axiales, excepto cuando se cumplan los requisitos del artículo 18.4. + +10.2.6. La relación entre la tensión de compresión en el hormigón y la deformación específica del hormigón, se debe suponer rectangular, trapezoidal, parabólica, o de +cualquier otra forma que dé origen a una predicción de la resistencia que coincida en forma sustancial con los resultados de ensayos. + +10.2.7. Los requisitos del artículo 10.2.6. se satisfacen con una \textbf{distribución rectangular equivalente} de tensiones en el hormigón, definida en los artículos 10.2.7.1. a 10.2.7.3. inclusive. + +10.2.7.1. La tensión en el hormigón se adopta igual a 0,85 f’c , y se supone uniformemente distribuida en una zona de compresión equivalente, limitada por los +extremos de la sección transversal, y por una línea recta paralela al eje neutro, a una distancia $a = \beta_1 c$, a partir de la fibra comprimida con deformación máxima. + +10.2.7.2. La distancia c, entre la fibra comprimida con deformación máxima y el eje +neutro, se debe medir en dirección perpendicular a dicho eje. + +10.2.7.3. Como valor del factor $\beta_1$ se debe adoptar: +\begin{IEEEeqnarray*}{tc} +para $f'_c \leq 30$ MPa & \beta_1 = 0,85 \\ +para $f'_c > 30$ MPa & \beta_{1}=0,85-0,05 \frac{\left(f_{c}^{\prime}-30 M P a\right)}{7} +\end{IEEEeqnarray*} +siempre que $\beta_1>0,65$ + +\subsection{Principios y requisitos generales [10.3]} +10.3.1. El diseño de una sección transversal solicitada a cargas axiales o a flexión, o a una combinación de ambas (flexocompresión), se debe basar en la \textbf{compatibilidad de tensiones y deformaciones}, utilizando las hipótesis establecidas en el artículo 10.2. + +10.3.2. La condición de deformación balanceada se define como aquella situación que se produce en una sección transversal cuando la deformación en la armadura traccionada es la correspondiente a la tensión de fluencia especificada $f_y$ , y en la fibra comprimida con +deformación máxima la deformación específica es igual al valor último ($\varepsilon_t =$ valor último), adoptado igual a 0,003. + +10.3.3. Las secciones son controladas por compresión cuando la deformación neta por tracción en el acero más traccionado, $\varepsilon_t$ , es igual o menor que la deformación límite controlada por compresión ($ \varepsilon_t = f_y /E_s$), y en el hormigón comprimido la deformación específica es igual al valor último, adoptado igual a 0,003 . + +La deformación límite controlada por compresión es la deformación específica neta de tracción en la armadura, en condiciones de deformación balanceada. +Para la armadura fy = 420 MPa y para todas las armaduras pretensadas, se permite fijar el límite de la deformación controlada por compresión en un valor igual a 0,002. + +10.3.4. Las secciones son controladas por tracción cuando la deformación neta por +tracción en el acero más traccionado, $\varepsilon_t$ , es igual o mayor que 0,005 y en el hormigón comprimido la deformación específica es igual al valor último, adoptado igual a 0,003. + +Las secciones con una deformación neta por tracción en el acero más traccionado, $\varepsilon_t$ , comprendida entre la deformación límite controlada por compresión ( $\varepsilon_t = f_y /E_s$) y el valor +0,005, corresponden a una región de transición entre las secciones controladas por compresión y aquellas controladas por tracción. + +10.3.5. Para los elementos no pretensados solicitados a flexión y para los elementos no pretensados solicitados por una carga de compresión axial mayorada menor que $0,10 f'_c A_g, (\phi P_n \leq 0,10 f'_c A_g )$, la deformación neta de tracción, $\varepsilon_t$ , para la resistencia +nominal debe ser igual o mayor que 0,004. + +\textbf{10.3.6.} La resistencia de diseño a carga axial, $\phi P_n$ , de los elementos comprimidos, debe ser igual o menor que $\phi P_{n,\max}x$ , determinada mediante las expresiones (10-1) ó (10-2). + +10.3.6.2. Para elementos no pretensados armados con estribos cerrados, que cumplan con el artículo 7.10.5. (columnas), se debe utilizar: + +\[ +\phi P_{n, \max }=0,80 \phi\left[0,85 f'_{c}\left(A_{g}-A_{s t}\right)+f_{y} A_{s t}\right] +\] +Ver código para elementos pretensados o con zunchos en espiral. + +10.3.7. Los elementos solicitados por una carga axial de compresión se deben diseñar para el momento máximo que pueda acompañar a dicha carga axial. La carga axial mayorada, $P_u$ , para una excentricidad dada, no debe exceder el valor de la resistencia de diseño a carga axial, $\phi P_n$ , especificada en el artículo 10.3.6. El momento máximo mayorado, $M_u$ , se debe incrementar por los efectos de la esbeltez, de acuerdo con las especificaciones del artículo 10.10. + + +\subsection{Armadura mínima en elementos solicitados a flexión [10.5]} + +10.5.1. El área As adoptada en cada sección de un elemento solicitado a flexión, en el +que se requiera por cálculo armadura de tracción, con excepción de los casos definidos +en los artículos 10.5.2., 10.5.3. y 10.5.4., debe ser como mínimo: + +\[ +A_{s, \min }=\frac{\sqrt{f^{\prime}_c}}{4 f_{y}} b_{w} d \quad \text{siempre que} \quad A_{s, \min } \geq \frac{1,4 b_{w} d}{f_{y}} +\] + +\subsection{Límites para la armadura de elementos comprimidos [10.9]} +10.9.1. El área de armadura longitudinal, $A_{st}$ , para elementos comprimidos no +compuestos, debe ser: + +\[ +0,01A_g \leq A_{st} \leq 0,08 A_g +\] +\subsection{Momentos amplificados - Conceptos generales} + +10.11.1. Las fuerzas axiales mayoradas, $P_u$ , los momentos mayorados $M_1$ y $M_2$ en los extremos de la columna y, cuando se requiera, la deformación lateral de piso, $\Delta_o$ , se +deben calcular por medio de un análisis elástico de primer orden del pórtico, considerando +el efecto de las cargas axiales, la presencia de zonas fisuradas a lo largo del elemento y +los efectos de la duración de las cargas en las propiedades de la sección. Como +alternativa, se permiten utilizar para los elementos de la estructura las propiedades que se +especifican en la Tabla 10.11.1. + +\subsection{Momentos amplificados - Pórticos indesplazables [10.12]} + +10.12.1 Para los elementos comprimidos en pórticos indesplazables, el factor de +longitud efectiva $k$ debe ser igual a 1. + +10.12.2. En los pórticos indesplazables se pueden ignorar los efectos de la esbeltez, en +aquellos elementos comprimidos que verifiquen la siguiente expresión + +\[ +\frac{k \ell_{u}}{r} \leq 34-12\left(\frac{M_{1}}{M_{2}}\right) \quad \text{con} \quad 34-12\left(\frac{M_{1}}{M_{2}}\right)=40 +\] + +donde el término $M_1 / M_2$ es positivo si el elemento se deforma con curvatura simple +(momentos extremos de igual signo) y negativo si el elemento se deforma con +curvatura doble (momentos extremos de distinto signo). Ambos momentos son de primer orden. + +10.12.3. Los elementos comprimidos se deben dimensionar para la carga axial +mayorada Pu y para el momento mayorado y amplificado por los efectos de la +curvatura del elemento, Mc , de acuerdo con las siguientes expresiones: + +\[M_{c}=\delta_{n s} M_{2}\] +siendo + +\begin{IEEEeqnarray*}{cc} +\delta_{n s} =&\frac{C_{m}}{1-\frac{P_{u}}{0,75 P_{c}}} \geq 1,0 \\ +P_{c} =&\frac{\pi^{2} E I}{\left(k \ell_{u}\right)^{2}} \\ +EI=&\frac{0,2 E_{c} I_{g}+E_{s} I_{s e}}{1+\beta_{d}} \quad \text{ó} \\ +EI=& {\frac{0,4 E_{c} I_g}{1+\beta_{d}}} +\end{IEEEeqnarray*} + +Para pórticos \textbf{indesplazables}, $\beta_d$ , es la relación entre la máxima carga axial +mayorada que actúa en forma permanente (carga de larga duración) y la máxima carga axial mayorada asociada a la misma combinación de cargas. + +Para pórticos \textbf{desplazables}, excepto en el caso especificado en el artículo +10.13.6., $\beta_d$ es la relación entre el máximo corte mayorado que actúa en forma permanente (carga de larga duración) en un entrepiso y el corte máximo mayorado de ese entrepiso. + + +10.12.3.1. El coeficiente $C_m$ , para los elementos sin cargas transversales entre sus +apoyos, se debe obtener de la siguiente expresión: + +\[ +C_{m}=0,6+0,4 \frac{M_{1}}{M_{2}} \geq 0,4 +\] +Para elementos con cargas transversales entre sus apoyos $C_m=1$ + +\subsection{Momentos amplificados - Pórticos desplazables [10.13]} +10.13.1. Para elementos comprimidos en pórticos desplazables, el factor de longitud +efectiva $k$, se debe determinar utilizando los valores de $E$ e $I$ indicados en el artículo +10.11.1/8.5, y debe ser \(k>1\) + +10.13.2. En los elementos comprimidos desplazables, o sea no arriostrados contra el +desplazamiento lateral, se permite despreciar los efectos de la esbeltez, cuando se +verifique que \(k \ell_u / r <22\) + +10.13.3. Los momentos $M_1$ y $M_2$ en los extremos de un elemento individual comprimido, se +deben obtener con las siguientes expresiones: + +\begin{IEEEeqnarray*}{c} +M_1 = M_{1ns} + \delta _s M_{1s} \\ +M_2 = M_{2ns}+\delta_s M_{2s} +\end{IEEEeqnarray*} +donde $\delta_s M_{1s}$ y $\delta_s M_{2s}$ se deben calcular de acuerdo con 10.13.4 + +\subsubsection{Determinación de $\delta_s M_s$ [10.13.4]} +10.13.4.1. Los momentos amplificados por efecto del desplazamiento lateral, $\delta_s M_s$ , se +deben considerar como los momentos extremos de la columna, determinados por medio +de un análisis elástico de segundo orden basado en las rigideces del elemento, +establecidas en el artículo 10.11.1. + +10.13.4.2. En forma alternativa y sólo cuando las columnas del piso tengan igual altura, el +valor de $\delta_s M_s$ se podrá calcular con la siguiente expresión : +\[ +\delta_{s} M_{s}=\frac{M_{s}}{1-Q} \geq M_{s} +\] +Si el valor de $\delta_s$ , determinado con la expresión (10-17), es $> 1,5$, entonces el valor $\delta_s M_s$ +se debe calcular de acuerdo con lo indicado en los artículos 10.13.4.1. ó 10.13.4.3. + +10.13.4.3. Otra forma de determinación consiste en calcular el momento amplificado por +desplazamiento lateral, $\delta_s M_s$ , con la siguiente expresión: + +\[ +\delta_{s} M_{s}=\frac{M_{s}}{1-\frac{\sum P_{u}}{0,75 \sum P_{c}}} \geq M_{s} +\] + +\begin{description} + \item[$\sum P_u$] la sumatoria de todas las cargas verticales mayoradas en un piso + \item[$\sum P_c$] la sumatoria de las cargas de las columnas que resisten el desplazamiento + lateral de un piso, + \item[$P_c$] la carga crítica determinada con la expresión (10-10), utilizando para $k$ el + valor indicado en el artículo 10.13.1. +\end{description} + +10.13.7. En pórticos desplazables, los elementos solicitados a flexión se deben diseñar +para la totalidad de los momentos amplificados de los elementos comprimidos que +concurren al nudo. + +\begin{figure*}[htb!] + \centering + \hspace{2cm}\includegraphics[width=1\linewidth]{fig/cirsoc201tab21} + \label{fig:cirsoc201tab21} +\end{figure*} +\begin{figure*} + \centering + \hspace{2cm}\includegraphics[width=1\linewidth]{fig/cirsoc201tab21c} + \caption{CIRSOC 201} + \label{fig:cirsoc201tab21c} +\end{figure*} + +\begin{figure*} + \centering + \includegraphics[width=1\linewidth]{fig/cirsoc102nomog1} + \label{fig:cirsoc102nomog1} +\end{figure*} + + +\end{document} + + +\begin{itemize} + \item[$y$:] + \item[$y$:] + \item[$y$:] +\end{itemize} + + \ No newline at end of file diff --git a/turbomachines/main.pdf b/turbomachines/main.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8b7110ae6094472be9d86dafd2028614a4a5db55 GIT binary patch literal 444408 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