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- 1. T SUBRAMANI, P.SHANMUGAM / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.154-161 SEISMIC ANALYSIS AND DESIGN OF INDUSTRIAL CHIMNEYS BY USING STAAD PRO T SUBRAMANI1 P.SHANMUGAM2 1 Professor & Dean, Department of Civil Engineering, VMKV Engg. College, Vinayaka Missions University, Salem, India 2 PG Student of Structural Engineering, Department of Civil Engineering, VMKV Engg. College, Vinayaka Missions University, Salem, IndiaABSTRACT Our project describes a simplified method that allow upper end, considering the behaviour of the lineal elasticobtaining the fundamental period of vibration, lateral material, capable of deforming only by the effects ofdisplacement, shear force and bending moment through a flexion and shear, and that it also has geometric propertiesset of equations, obtaining for all cases studied an error (area, inertia, etc.) which vary with height, differentialbelow 10%.The results obtained in this study were applied equations will be obtained of the movement that applyto a total of 9 real chimneys (4 of steel and 5 of reinforced both to free and forced vibrations that cannot be resolvedconcrete) built in Chile, with the objective of calibrating exactly. Only for certain laws of geometrical propertiesfounded expressions. During the stage of the analysis, it of variation, it is possible to express the solution of thewas verified that the criterion of consistent masses differential equation of the movement based upon knownprovide better results than the criterion of lumped masses, functions, as it has been extensively demonstrated inand as a very important conclusion a discrete analysis of literature on the subject. [Carrióny Dünner, 1999].the model in twenty segments of the beam is satisfactory. The mathematical type of difficulties that theThe most representative variables that define the model current study presents has made it necessary to simplify thewith which it is possible to carry out a parametric analysis problem, by discretization the continuous structure for itsof the chimney. As important parameters we could refer solution, but not worrying to verify the merit of theto: slenderness ratio H/Dinf, radius ratio Rsup/Rinf, assumptions involved in the resultsthickness ratio Esup/Einf and thickness diameter ratioDinf/Einf. Later, by varying each one of the chosen 2. ABOUT CHIMNEYSparameters several analyses of representative chimneys of Chimneys are used to vent the products ofthis great family, could be carried out. As seismic loads, the combustion produced by heating appliances. Chimneys arespectrums of accelerations recommended by the code of used for most fuel types (wood, oil, natural & propane gas,seismic design for structures and industrial installations in and coal). They are not used, for example, on electricChile, have been considered. Modal responses were appliances.combined using the combination rule CQC.In all the casesstudied in this investigation, the influence of the P effect, 2.1 CHIMNEY SAFETY CERTIFICATIONSthe soil structure interaction, and the influence on Factory-built chimneys are required, by code, to beresponses that provoke the inclusion of lining, have Listed (safety certified) in accordance with a safetybeen disregarded. certification standard.KEYWORDS: Seismic Analysis, Design Industrial 2.2 FOR RESIDENTIAL CONSTRUCTION Chimneys, Staad Pro In the USA – the national standard for factory-built chimneys is ANSI/UL103 – “The Standard for Factory-Built Chimneys, Residential Type and Building Heating1. INTRODUCTION Appliance”. This standard qualifies the chimney system for During the past few years industrial chimneys use with appliances burning liquid, gas and solid fuels withhave undergone considerable developments, not only in flue gas temperatures at 1000O F maximum, continuouslytheir structural conception, modelling and method of and with non-positive internal pressure.analysis, but also in the materials employed and the In Canada – there are two national standards for factory-methods of construction. In this sense the outstanding built chimneys. ULC-S629 is the standard for 650O Cincrease in height should be highlighted as a consequence factory-built chimneys and applicable to chimneys intendedof a better control of environment pollution in populated for use with gas, liquid and solid fuels, with maximum 650Oareas. With the increment in height the seismic action and C flue gases continuously and non-positive internal pressure.wind have become important for working out actuating ULC-S604 is the standard for factory-built chimneys limitedstresses on this particular type of continuous structures, to use with gas or oil fired appliances. Certain wood burningmaking it necessary, for this reason, to study the vibratory fireplaces are Listed for use with certain ULC-S604 Listednature by carrying out a dynamic analysis. chimneys. If a modelled chimney is analysed as in aprojected beam embedded at the la base and free at its 2.3 TYPES OF CHIMNEY 154 | P a g e
- 2. T SUBRAMANI, P.SHANMUGAM / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.154-161 The Types of Chimney described are Factory-Built Double Wall Air-Cooled – (Limited Use)Metal Chimneys and Masonry Chimneys. General anatomy Certain factory-built fireplaces are offered with aof chimney shown in Figure.1. Double Wall, Air-Cooled chimney system. This is NOT A GENERAL USE CHIMNEY and is limited to use with only2.3.1 Factory-Built the specific fireplace(s) with which it is Listed (safety Most Factory-Built Chimneys are similar in that certified). As the name implies, Double Wall Air-Cooledthey are constructed of at least two round metal tubes with Chimney relies on air to provide insulation between theinsulation in between (whether the insulation is simply air, inner and outer pipes. Double wall Air-Cooled fire placeor one of several different „fibre‟ types). The major types chimney designs typically rely upon air taken from withindiscussed here are: Solid Pack, Blanket, Triple-Wall and the structure to assist in cooling and are characterized byAir-Cooled. large outside diameters. In cold climate areas, these systems are often criticized as being sources of cold air infiltrationSolid Pack when the system is not in use. As such, they tend be be Solid Pack Chimneys are characterized by a more popular and perform better in areas with warmpacked-in-place insulation placed between two walls and are climates and at low altitude. This type of Chimney isknown for their high insulating value. Due to the fact that commonly found on built-in, factory-built wood burningSolid Pack Chimney actually contains more insulating fireplaces. As indicated above, they are NOT designed,material than other types, they perform better by certified or intended as any type of a general use chimneymaintaining higher flue gas temperatures and lower system and should NEVER BE USED WITH ANYtemperatures on the outer casing. These chimneys also APPLIANCE EXCEPT THAT FOR WHICH IT ISfeature a slim-line design that allows easier installation. LISTED. Few, if any wood stoves are ever approved for useManufacturers carefully protect the ingredients of their with this type of chimney. Common Brand Names are:proprietary insulation mix, which may allow some Brands to Heatilator, Majestic, Temco.outperform others. Common Brand Names are: SelkirkMetalbestos, SuperVent, SuperPro, Security Chimney, Hart& Cooley and Energy Vent.Blanket Blanket Insulated Chimneys are similar to SolidPack designs, except they use Insulation Blankets that arecut to size and applied inside the Chimney‟s walls. BlanketInsulated Chimneys typically contain less insulating materialthan Solid Pack designs, yielding a lighter weight product.Common Brand Names are: ICC/Excel, Dura-Vent (Dura-Tech), Metal Fab. Double-Wall, insulated Class-A Chimney (bothSolid pack and Blanket types) keep your house protected byinsulating - keeping your flue gasses hot. This method ofchimney design does not hamper a strong draft the wayTriple-Wall system does.Triple-Wall (Combo & Air-Cooled) There are two types of triple wall chimney designs FIGURE.1.GENERAL ANATOMY OF CHIMNEY– Combination (blanket & air) and Air (only)-cooled. Thecombination blanket / air cooled Triple-Wall Chimney 2.3.2 Masonrydesign typically combines some fibre blanket insulating Large internal/external dimensionsmaterial with an air-insulated section. The air-cooled triple Square / rectangularwall system (also know as a thermal syphon system) reliesstrictly upon movement of air between walls to keep the May have a clay-tile or metallic linersystem cool. The outside diameter of Triple-Wall Chimneys A conventional masonry chimney, made of brick, block orare typically larger than Solid Pack or Blanket Insulated stone could be a suitable option, depending on the appliancedesigns. Common Brand Names for combination air / fiber you choose. There are several types and brands of liners thatinsulated triple wall chimneys are: Dura-Vent (Dura-Plus) can be installed in masonry chimneys to improve theirand Ameritec Air Jet is the most common Brand name for performance. If yours is a high performance appliance, youthe air-cooled triple wall designed. Triple-Wall Class-A should consider an upgraded liner. Note that full stainlesschimney keeps your house protected by cooling vent gasses. steel liners for fireplace insert installations are mandatory inCold air is drawn in to the venting between the outer and Canada, and strongly recommended everywheresecond pipe and cools the inner liner where flue gasses arepassing through. Cooling down hot flue gasses will decrease 3.ABOUT SEISMIC LOADSdrafting (chimney effect), increase moisture (where hot Earthquake engineering is the scientific fieldmeets cold) and promote creosote formation, which concerned with protecting society, the natural and the man-potentially lead to Chimney fires. made environment from earthquakes by limiting the seismic 155 | P a g e
- 3. T SUBRAMANI, P.SHANMUGAM / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.154-161risk to socio-economically acceptable levels.[1]Traditionally, it has been narrowly defined as the study ofthe behavior of structures and geo-structures subject toseismic loading, thus considered as a subset of bothstructural and geotechnical engineering. However, thetremendous costs experienced in recent earthquakes have ledto an expansion of its scope to encompass disciplines fromthe wider field of civil engineering and from the socialsciences, especially sociology, political sciences, economicsand finance.3.1 SEISMIC LOADING FIGURE.2. SNAPSHOT FROM SHAKE-TABLE Seismic loading means application of an VIDEO OF A 6-STORY NON-DUCTILE CONCRETEearthquake-generated excitation on a structure (or geo- BUILDING DESTRUCTIVE TESTINGstructure). It happens at contact surfaces of a structure eitherwith the ground [1], or with adjacent structures, or with 4. ANALYTICAL/NUMERICAL ASSESSMENTgravity waves from tsunami. Seismic performance assessment or, simply, seismic structural analysis is a powerful tool of earthquake3.2 SEISMIC PERFORMANCE engineering which utilizes detailed modelling of the Earthquake or seismic performance defines a structure together with methods of structural analysis to gainstructures ability to sustain its main functions, such as its a better understanding of seismic performance of buildingsafety and serviceability, at and after a particular earthquake and non-building structures. The technique as a formalexposure. A structure is, normally, considered safe if it does concept is a relatively recent development. In general,not endanger the lives and well-being of those in or around seismic structural analysis is based on the methods ofit by partially or completely collapsing. A structure may be structural dynamics.[8] For decades, the most prominentconsidered serviceable if it is able to fulfill its operational instrument of seismic analysis has been the earthquakefunctions for which it was designed. response spectrum method which, also, contributed to the Basic concepts of the earthquake engineering, proposed building codes concept of today.[9]implemented in the major building codes, assume that a However, such methods are good only for linearbuilding should survive a rare, very severe earthquake by elastic systems, being largely unable to model the structuralsustaining significant damage but without globally behavior when damage (i.e., non-linearity) appears.collapsing .[5] On the other hand, it should remain Numerical step-by-step integration proved to be a moreoperational for more frequent, but less severe seismic effective method of analysis for multi-degree-of-freedomevents. structural systems with significant non-linearity under a3.2.1 Seismic performance assessment transient process of ground motion excitation.[10] Basically, Engineers need to know the quantified level of the numerical analysis is conducted in order to evaluate theactual or anticipated seismic performance associated with seismic performance of buildings. Performance evaluationsthe direct damage to an individual building subject to a are generally carried out by using nonlinear static pushoverspecified ground shaking. Such an assessment may be analysis or nonlinear time-history analysis. In such analyses,performed either experimentally or analytically. it is essential to achieve accurate nonlinear modeling of structural components such as beams, columns, beam-3.2.2 Experimental assessment column joints, shear walls etc. Thus, experimental resultsExperimental evaluations are expensive tests that are play an important role in determining the modelingtypically done by placing a (scaled) model of the structure parameters of individual components, especially those thaton a shake-table that simulates the earth shaking and are subject to significant nonlinear deformations. Theobserving its behavior.[6] Such kinds of experiments were individual components are then assembled to create a fullfirst performed more than a century ago.[7] Still only recently nonlinear model of the structure. Thus created models arehas it become possible to perform 1:1 scale testing on full analyzed to evaluate the performance of buildings. Thestructures. Snapshot from shake-table video of a 6-story capabilities of the structural analysis software are a majornon-ductile concrete building (Figure.2.) destructive testing. consideration in the above process as they restrict theDue to the costly nature of such tests, they tend to be used possible component models, the analysis methods availablemainly for understanding the seismic behavior of structures, and, most importantly, the numerical robustness. The lattervalidating models and verifying analysis methods. Thus, becomes a major consideration for structures that ventureonce properly validated, computational models and into the nonlinear range and approach global or localnumerical procedures tend to carry the major burden for the collapse as the numerical solution becomes increasinglyseismic performance assessment of structures. unstable and thus difficult to reach. There are several commercially available Finite Element Analysis softwares such as CSI-SAP2000 and CSI-PERFORM-3D which can be used for the seismic performance evaluation of buildings. Moreover, there is research-based finite element analysis platforms such as Open Sees, RUAUMOKO and the older DRAIN-2D/3D, several of which are now open source. 156 | P a g e
- 4. T SUBRAMANI, P.SHANMUGAM / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 4, July-August 2012, pp.154-1615. ABOUT THE SOFTWARE STAAD or (STAAD.Pro) is a structural analysisand design computer program originally developed byResearch Engineers International in Yorba Linda, CA. Inlate 2005, Research Engineer International was bought byBentley Systems. An older version called Staad-III forwindows is used by Iowa State University for educationalpurposes for civil and structural engineers. The commercialversion STAAD.Pro is one of the most widely usedstructural analysis and design software. It supports severalsteel, concrete and timber design codes.It can make use ofvarious forms of analysis from the traditional 1st order static a) Geometry of a variable sectionanalysis, 2nd order p-delta analysis, geometric non linear b) Model of a chimney accordinganalysis or a buckling analysis. It can also make use of c) Model of a chimney accordingvarious forms of dynamic analysis from modal extraction to FIGURE 3. GEOMETRY OF A CHIMNEY,time history and response spectrum analysis. In recent years ACCORDING TO THE CONSISTENT MASSES ANDit has become part of integrated structural analysis and LUMPED MASSES CRITERIAdesign solutions mainly using an exposed API called OpenSTAAD to access and drive the program using an VB macro TABLE.1. GEOMETRIC CHARACTERISTICS ANDsystem included in the application or other by including SEISMIC DATA OF SOME REAL CHIMNEYS BUILTOpenSTAAD functionality in applications that themselves IN CHILE (CANADA,1984)include suitable programmable macro systems. AdditionallySTAAD.Pro has added direct links to applications such asRAM Connection and STAAD.Foundation to provideengineers working with those applications which handledesign post processing not handled by STAAD.Pro itself.Another form of integration supported by STAAD.Pro is theanalysis schema of the CIMsteel Integration Standard,version 2 commonly known as CIS/2 and used by a numbermodelling and analysis applications. The information on Table 1, shows the most important dimensions and pertinent data that will be useful6. DISCRETING THE STRUCTURE for the subsequent seismic analysis of some industrial Due to the complexity that means trying out one chimneys.of the four particular solutions that the differential Each one was analysed under the following considerations:equation presents governing the movement of a continuous Employing lumped masses and consistent masseselement like a chimney type, (see Figure.3), it was decided criteria.to solve the problem by discretization the structure. Varying the number of discreted elements (NE) in For this purpose, two discretion criteria were used 10, 15, 20 and 25 elements.lumped masses criterion and consistent masses criterion. Considering the following effectsThe most simple method to consider the properties of a Flexion (lumped masses criterion)dynamic system is to concentrate the mass of the Flexion, shear and rotational Inertiastructure on the nodes that define transfer displacements, (consistent masses criterion)that is why it is called lumped masses criterion. On the With these considerations the fundamental periods ofother hand, the consistent masses criterion (Mc), unlike the vibration were considered employing the computationlumped masses criterion which depends upon the rigidity program CALUC [Vásquez, 1977] and comparing theirto bend, cross section of element, form factor, shear responses with those obtained through: analyticalmodule; also, unlike the lumped masses criterion, it solution (solution to the differential equation considering aconsiders coupling between rotational and translation chimney of constant section and flexion effect) anddegrees of freedom. Therefore, the matrix of consistent Method of Finite Elements (MEF).masses corresponds to a full matrix that includes the effectsof flexion, shear and rotational inertia. TABLE.2. COMPARISON OF VIBRATION PERIODS EMPLOYING THE DIFFERENTSensitivity Analysis CRITERIA. FOR CHIMNEY 9 An analysis was performed for the purpose ofresponding to the following queries: In how manyelements is it necessary to discrete a chimney? Whatdiscreting criterion is the most adequate: lumped masses orconsistent masses? What effects must be considered in therepresentative model of a chimney type continuouselement? In this manner by means of this study onparticular chimneys it is possible to estimate the results ofany structure of this type. 157 | P a g e
- 5. From the analysis carried out, it may be assured thatthe criterion of consistent masses estimates the fundamentalperiod of vibration, considering the effect of flexion is moreaccurate than that obtained employing the lumped massescriterion. Since it is rather laborious finding a factor to transform When the chimney is analysed considering simultaneously responses of a dimensional chimneys to real response valuesthe three effects of flexion, shear and rotational inertia, the of the structure considering all effects (flexion, shear andnumber of elements to be discreted is no longer important. rotational inertia), the chimneys were modelled employing theThis is because the height of the element discreted is following considerations:controlled by the shear effect h/D < 2, and by the effect of Criterion of consistent masses.flexion if h/D 2, in that h is the height of such element. Deformation by flexion effect.This allows concluding that the analysis if industrial Discreting with 20 elements.chimneys is controlled by the effect of flexion since Errors obtained due to such considerations do not exceed 2%.according to Table 1, most of these structures possess H/D As a consequence of the parametric analysis carried> 8 slenderness, therefore, the shear effect in the analysis out, it should be mentioned that responses obtained throughmay be ignored. such methodology have no physical interpretation. However, Analysing chimneys with 20 discrete elements is it is possible to establish parameters for this type ofrecommended, employing the consistent masses criterion and structures, obtaining a low percentage of errors betweenthe effect of flexion since the error committed when estimated values of the real response and the adimensionalevaluating the fundamental period of vibration does not response amplified by the factors of response modification.exceed 1.13%. On Table.3 geometric and seismic parameters have been From Table.2, it may be concluded that the effect of considered in the present study, represented in 4 terms each.rotational inertia does not influence determining thefundamental period and by not considering it errors not TABLE 3: SUMMARY CHART OF GEOMETRIC ANDexceeding 3% will be obtained for all cases. SEISMIC PARAMETERS7. CHARACTERISTICS PARAMETERSGeometric ParametersThe purpose of establishing parameters is to identify the mostimportant characteristics which define chimneys in order toallow representing a vast universe of such structures. Thegeometric parameters (see Figure 1) used in this study wereas follows: HD = H / Dinf = Ratio of slendernessRinf : Radius of section at the base of chimneyRsup : Radius on top section of chimneyRE = Esup / Einf = Ratio of thicknessEsup: Thickness of mantle at the top section of chimneyDE = Dinf / Einf = Ratio of diameter thicknessEinf : Thickness of mantle at the base of chimneySeismic ParametersIn order to carry out a spectral modal analysis ofadimensional form, the spectrum was set in parametersaccording to Chilean standard NCh 2369.c97 [INN, 1997].Since the design spectrum is applied to real structures andnot to adimensional structures, a parameter called seismicparameter will be introduced:TT = T* / T’ = Ratio of Periods Where Zone and are parameters which depend on theT* : Fundamental period of structure, expressed in seismic zone and material of chimney that have beenseconds. tabulated in Chilean seismic code NCh 2369.c97 [INN, T’ : Parameter depending on the type of soil, expressed 1997]. in seconds, per Table 6 [INN, 1996]. Transformation FactorsParameter TT or Ratio of Periods, is reflected in the The necessity arising to find factors that mayseismic coefficient of the design spectrum per Chilean transform dimensional responses of chimneys withStandard NCh 2369.c97 [INN, 1997] as follows established parameters to real responses of the structure 158 | P a g e
- 6. including their geometric properties, four factors wereobtained which modify the a dimensional response toreal one in function of three variables: two dependanton the structure material, elasticity module E and thedensity of the material mass and the last and mostimportant, the height of chimney H, since all parametersare in function of height.A table follows containing transformation factors of thedimensional response to the real one, for each of theresponses (periods, displacements, shear forces andbending moment), the percentage of error obtained whenusing transformation factors is also shown in Table.4.TABLE.4. TRANSFORMATION FACTORS OFRESPONSES TABLE 5: EQUATIONS 2, 3, 4 AND 5 VALIDATION8. SIMPLIFIED METHOD FOR OBTAININGRESPONSES For the purpose of providing simple tools forseismic analysis on industrial chimneys in Chile, a study hasbeen carried out on this special type of continues structures inorder to establish a simplified method that may allowevaluating the follows responses: periods of vibration, lateraldisplacement, shear force and bending moment.This has been done by making an analysis of the response of6,144 chimneys contained in a data base (see Table.5)3) and which allowed establishing a dynamic behaviour lawfor any steel or reinforced concrete selfsupporting industrialchimney.The analysis performed is summarised in the followingexpressions that allow estimating the fundamental period ofvibration, lateral displacement, shear force and bendingmoment shown below: The behaviour of the vibration period, lateral displacement, shear force and bending moment, normalised at maximum value, are identical to each other (see Figure 2), regardless of the material and geometry of the chimney. Thus, coefficients may be found providing important responses each 0.05 Y/H and the period for the first 20 modes of vibration. (See Table.6 & 7). TABLE.6. COEFFICIENTS TO OBTAIN RESPONSES AND PERIODS OF VIBRATION 159 | P a g e
- 7. FIGURE.5. 3D RENDERED VIEW TABLE .7. VALUE Z AND I FIGURE.6. DISPLACEMENT DUE TO SEISMIC LOAD9.STAAD PRO ANALYSIS APPLICATIONEXAMPLE PROGRAMME Consider chimney of height 12 m and circular dia of3m which is placed on the ground level. An seismic load of 5kn has assing in joints of the members for find out the stressdistribution from top to bottom with safety measures.9.1 ANALYSIS OUT PUT After STAAD PRO Analysis the following outputsStructure Full View (Figure.4), 3d Rendered View(Figure.5),Displacement Due To Seismic Load (Figure.6),, StructureWith Seismic Loading(Figure.7),, Stress Distribution Due To FIGURE.5. STRUCTURE WITH SEISMIC LOADINGSeismic Load(Figure.8) were found. FIGURE.4 STRUCTURE FULL VIEW FIGURE.5. STRESS DISTRIBUTION DUE TO SEISMIC LOAD 10. CONCLUSIONS 1) When the chimney is analysed by the three effects (flexion, shear and rotational inertia), the number of 160 | P a g e
- 8. elements to be discreted no longer influences the de Central de Chile. Pp 329. estimated responses because the height of the element is [5]. FernándezDávila G., V. I. y Rivera F., J. (1988), controlled by the shear if h/D < 2, and by flexion if h/D > “Planteamiento de Normas para el Análisis Sísmico 2, h the height of the element. de2) To estimate the fundamental period of vibration, [6]. Chimeneas”, Séptimo Congreso Nacional de Ingeniería considering only the effect of flexion, the consistent Civil, Departamento de Ancash., Perú, Pp 383396. masses criterion is more accurate. The percentage of FernándezDávila G., V. I. y Rivera, J. (1990), error obtained, compared to the exact solution given by “Diseño Sísmico de Estructuras Continuas con MEF is 1.13% Distribución Variable de Masa y Rigidez”, Octavo3) Since it is very laborious job finding a factor to Congreso Nacional de Ingeniería Civil, Departamento transform adimensional response values to real response de Piura. Perú Pp 383396. values considering all effects (flexion, shear and [7]. FernándezDávila G., V. I. (1992), Análisis Dinámico de rotational inertia), good results can be obtained in the Chimeneas Empleando el Criterio de Masas analysis of steel and reinforced concrete industrial Consistentes, Proyecto semestral, Asignatura chimneys modelling the structure employing the ICE3722, Dinámica de Estructuras, Pontificia following considerations: Consistent masses criterion, Universidad Católica de Chile. SantiagoChile. effect of flexion, and discreted in 20 elements. [8]. Husid, R; Asfura, A.; Astroza, M. (1974), “Vibraciones Maximum errors committed as a result of such de Chimeneas de Inercia Variable”, XVI, Jornadas de considerations are under 2%. Ingeniería estructural. Buenos Aires Argentina. Vol. III,4) It is possible to carry out an analysis of a chimney Pp. III28, III38 parametrically, finding a factor that will transform these [9]. Instituto Nacional de Normalización INN (1997), NCh adimensional values into real responses of the 2369.c 97Diseño Sísmico de Estructuras e Instalaciones structure. The maximum error obtained considering Industriales.. Santiago Chile. the 4 responses studied (period of vibration, lateral [10]. Instituto Nacional de Normalización INN (1996), displacement, shear force and bending moment) is 3.5%. NCh 433.Of 96Diseño Sísmico de Edificios.. Santiago5) The simplified method proposed in this paper provides Chile. Vásquez, J.P. (1997), CALUC: Lenguaje responses with errors not exceeding 10%. As Computacional para Análisis Estructural. Manual de normalised response curves do not vary, regardless of Uso. Departamento de Ingeniería Estructural y the material and geometry of the chimney, they allow Geotécnica. Escuela de Ingeniería. Pontificia obtaining coefficients providing important responses Universidad Católica de Chile. SantiagoChile. every 0.05 Y/H and the period for the first 20 modes of vibration. HD = H / Dinf = Ratio of slenderness6) Through our problem we conclude that the seismic effect Rinf : Radius of section at the base of chimney will cause more damages to the structure which will Rsup : Radius on top section of chimney stabilise when it will analysis and constructed based on RE = Esup / Einf = Ratio of thickness the stress condition which is highlighted in the diagram Esup: Thickness of mantle at the top section of chimney11. REFERENCES DE = Dinf / Einf = Ratio of diameter thickness[1]. Arya A. S. y Paul, D. K. (1977), “Earthquake Response Einf : Thickness of mantle at the base of chimney of Tall Chimneys”. Proceedings World Conference on Earthquake Engineering. New Delhi.[2]. Astroza I., M y Asfura, A. (1972), Análisis Dinámico de Chimeneas de Inercia Variable. Comparación entre Modelo Continuo y Discreto. Memoria de Título (Ingeniería Civil) Sección Ingeniería Sísmica. Departamento de Geofísica Sismología y Geodesia, Facultad de Ciencias Físicas y Matemáticas Universidad de Chile, Santiago, Chile. Pp 208[3]. Cancino, C. H. (1984), Diseño Sísmico de Chimeneas Industriales, Memoria de Título (Ingeniería Civil) Departamento de Ingeniería Civil, Facultad de Ciencias Físicas y Matemáticas Universidad de Chile. Pp 150.[4]. Carrión P. L. y Dünner D. R. (1999), Análisis y Diseño Sísmico de Chimeneas Industriales, Memoria de Título (Ingeniería Civil) Departamento de Ingeniería Civil, Facultad de Ciencias Físicas y Matemáticas Universidad 161 | P a g e

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