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Interaction Envelopes For Limit State Design Of Chimneys

K. S. Babu Narayan a , Subhash C. Yaragal b, and Yukio Tamura c

a&bDepartment of Civil Engineering, National Institute of Technology Karnataka, Surathkal,

PO: Srinivasnagar 575 025, Mangalore, INDIA.cProfessor, Department of Architectural Engineering, Tokyo Polytechnic University,

1583, Iiyama, Atsugi, Kanagawa, JAPAN 243-0297

ABSTRACT: Chimneys as an indirect and effective means of air pollution control are popularfrom time immemorial. Environmental protection agencies have been forced to frame, implementand monitor stringent pollution control policies. With control regulations becoming morestringent, chimneys of heights over 400 meters are being erected and used. Design of reinforcedconcrete tall stacks for load and wind induced moments by trial and error technique involvesrigorous computational efforts. Availability of interaction envelopes helps reduce computationaltime. This paper presents such design aids for tall stacks.

KEYWORDS:Tall stacks, Chimneys, Stability, Interaction Envelopes, Limit State Design

1 INTRODUCTIONChimneys as an indirect means of air pollution control are immensely popular. Owing to theadvancements in the field of concrete and construction technology RCC chimneys of staggering

heights are being conceived, analyzed, designed, detailed and constructed. The analysis anddesign of chimneys as a hollow circular RCC section for combined load and moment involvesrigorous computational efforts by trial and error approach. The problem offers tremendous scopefor computerization and optimization.

This paper presents the development of an interactive user friendly computer package employing

rectangular stress block, for the complex problem on hand. The package has great utility in the design

office for real time design and also for generation of interaction envelopes for use as and when desired.

2 FUNCTIONAL DESIGNThe design of chimney is a two-fold problem of satisfying the functional and structural

requirements. The functional design includes stack height determination, effective height, plumerise, maximum downwind concentration, plume rise determination, lapse rate, atmosphericstability, plume rise formulae and wind speed correction. As regards to chimney sizing exitvelocity, base dimensions, exit size (top diameter).

3 LOADS, FORCES, STRESSES AND EFFECTS IN CHIMNEY DESIGNChimney is a wind sensitive structure. Its behavior is essentially considered as that of a verticalcantilever. The loads acting on chimneys are as follows, (a) Self-weight of the chimney actsvertically downwards. Compressive stress at any section is primarily due to its self weight of theshell and that of the lining above that section, which depends on the cross-sectional area and the

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density of the material used. (b) Live load: Live load due to the moment of painters trolley andthe men working on it may be taken as 5 kN/m

2on platform used for cleaning and maintenance

works etc. (c) Wind load: The wind load exerted at any point on a chimney can be considered as

the sum of static and dynamic load component. The dynamic component, which can causeoscillations of a structure, is generated due to the following reasons, (i) Gusts they causedynamic pressure changes initiating in line oscillations, (ii)Vortex shedding this loads totransverse vibration and (iii) Bufetting a down wind chimney can oscillate due to the bufettingeffect of an upstream structure. Magnitude of force exerted by wind is dependent on wind speed,its fluctuations, Reynold,s number etc.

Static wind effects Wind exerts a static force on a bluff body obstructing an air stream. Thedistribution of wind pressure around the circumference of such a body depends on its shape anddirection of wind incidence. Such a pressure causes circumferential bending whose magnitude issignificant for large diameter chimneys. The drag force acting on a chimney, is correctlyestimated by right estimation of drag coefficient which depends on the shape and shear force andbending moments which the chimney fabric has to withstand safely. The circumferential bendingas a result of radial distribution of wind pressure on a horizontal section of a chimney depends onReynold,s number. It is assumed that the along-wind resultant of such pressures is balanced bythe resultant of shear forces induced in the structure and these shear forces, in turn, are assumedto vary sinusoidal along the circumference of the chimney.

Dynaimic wind effects Dynamic wind problems arise from periodic variations in the pressuredistribution on the shell of the chimney. There are three forms of dynamic action namely (i) In-wind oscillations, (ii) Cross-wind oscillations and (iii) Ovalling oscillations. Ocillations (i) and(iii) are small and in most cases may be ignored. Model tests show that in-wind oscillationscaused by the oscillating drag force which occurs at around one half of the critical wind speed forcross-wind oscillations. Moreover they are very weak and easily damped out. Cross-windoscillations are by far the most important and any tall chimney should be checked for the effects

of such oscillations. Chimneys, which are of particular concern, are those with low damping, lowstiffness and high slenderness. (d) Seismic loads: An earthquake resistant design essentiallyconsists of evaluating the structural response to the ground motion and then calculating thecorresponding shear forces and bending moment, which the structure needs to safely resist.Chimney vibration is essentially a dynamic problem of transient nature. For analysis, chimney istreated as a cantilever beam with predominant flexural deformations and is analyzed by one ofthe following methods, namely (i) Response spectrum method, (ii) Modal analysis technique, and(iii) Time history response analysis.

3.1 Structural Design Consideration

Among the advantages claimed for the limit-state approach are the degree of safety of the various

parts of a structure is more uniform and that a probabilistic approach to safety is possible. Codeof practice requirements for the design of RC chimneys varies from country to country. Mostcountries have regulations for general RC structural work and some of these have particularclauses relating to chimney design. Some countries like U.S.A, Poland, India, France haveparticular codes for RC chimneys. The design is difficult involving lengthy, cumbersome anditerative computational effort. All codes of practice have recognized this fact and encouragedesigners to use time saver techniques like computational algorithm and interaction envelopes tooptimize the structural design of chimney.

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4 PROGRAM DEVELOPMENT AND DISCUSSIONThe program has been organized in two phases. First phase of the program generates, values forplotting interaction diagram. Second phase utilizes values generated for designing.

Phase I: With the cover ratio and thickness ratio as in-put data the program determines for thegiven percentage of steel the distances to the designated 73 rows of reinforcement both from thehighly compressed edge and centroid of the section for the given position of neutral axis.

The strains in various rows of reinforcement, the corresponding stress, the contribution ofconcrete and steel to load and moment resistance is computed. Thus one point on the interactiondiagram is generated. Varying the position of neutral axis subsequent points are generated, tocomplete the interaction envelopes. By varying the percentage of steel set of elegant interactioncurves are obtained to generate a set of 24 curves and for each curve 30 neutral axis positionshave been considered. Interaction envelopes have been generated and presented for thicknessratio ranging from 0.80 to 0.95. Figure 1 presents the interaction a typical envelope.

Figure 1 Interaction envelope for thickness ratio of 0.85

Wherein cover ratio is (D/D), D

- cover to reinforcement, D external diameter, thickness ratio

(d/D), d inner diameter, PU ultimate load , MU ultimate moment, fck characteristicstrength of concrete, p percentage of steel and fy yield stress in steel.

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Phase II: If the user wishes to design a circular chimney section the program receives, coverratio, thickness ratio, grades of concrete and steel, external diameter, load and momentcombination as input-data runs the first phase, interpolates the steel reinforcement required to

satisfy the combination of load and moment acting on the section and area of reinforcement isgiven as output.

Applications of the Program (a) For generating interaction envelopes for design of chimneys.(b) To obtain the required area of steel for the given section. (c) For the design of hollow or solidcircular section like columns or bridge piers and (d) With little modification can be used for thedesign of pre-stressed pipes and for the design of caissons.

Limit State of Serviceability To ensure satisfactory performance of a structure serviceabilitycheck are needed. Main aspects of serviceability are deflection and cracking. Limitingdeflections is one of the criteria for design of structure and also to limit crack width. A programis also been developed for computing the deflection of chimneys with height of the chimney,external diameter at top and bottom, thickness ratio, characteristic strength of concrete and windload intensity at every 5 m intervals as input data. New-Marks numerical method is applied tocompute chimney deflections.

5 CONCLUSIONSFrom the study the following conclusions are drawn; (i) Availability of interaction envelopes andcomputer algorithm immensely help the designer in expeditiously solving the design problem, (ii)Adoption of rectangular stress block leads to tremendous reduction in computational effort, leadsto slight conservatism which is justified vis-a-vis the time saved, (iii) Distribution ofreinforcement in more than one layer may be considered while detailing, as results are notaffected (iv) Flue openings were not considered in the study for strength, being sensitive to theposition and size, and (v) The program developed can be used in structural optimization exercise

wherein the total cost can be minimized or the ratio of cost to strength or cost to efficiency can beminimized.

6 REFERENCES1. Charles E. Rynolds and James C Steedman, Reinforced concrete designers hand book, Ninth edition.2. Prem Chand, Design of circular RC chimney section subjected to axial load and bending moment, The Indian

Concrete Journal, Vol. 68, No. 7, July 1994, pp. 357-364.3. Gupta S. R. Davalath and Murthy K. S. Madugula, Analyses/design of reinforced concrete circular cross section,

ACI Structural Journal, Vol. 85, No. 6, Tital No. 85-s55, Nov-Dec 1988.4. S. N. Manohar, Tall chimneys design and construction, Tata McGraw Hill Publishing Company Limited New

Delhi and Tor Steel Research Foundation in India, Bangalore 1985.

5. G. M. Pinfold, Reinforced concrete chimneys and towers, A Viewpoint Publication 1975.6. Mark Fintal, Hand book of reinforced concrete engineering, Second Edition, pp. 565-573.7. R. Ranganathan and A Muftha, Evaluation of reliability RCC Chimneys, International Journal of Structures,

Vol. 17, No. 1, paper No-154, Jan-Jun 1997, pp. 19-35.8. Wadi S. Rumman and Ru-Tung Sun, Ultimate strength design of reinforced concrete chimneys, ACI Journal,

Vol. 74, No. 4, Titalno. 74-18, July-August, pp. 179-184.9. ACI Committee 307, Standard practice for the design and construction of cast-in-place reinforced concrete

chimneys, ACI Structural Journal, Vol. 88, No. 1, Tital no. 88-512, Jan-Feb 1998, pp. 99-101.10. IS: 4998 (Part I)-1975, Criteria for design of reinforced concrete chimneys, Bureau of Indian Standards, New

Delhi.11. IS: 456-1978, Code of practice for plain and reinforced concrete, Bureau of Indian Standards, New Delhi.12. IS: 1893-1984, Criteria for earth quake resistant design of structures, (Fourth Revision), BIS, New Delhi.13. IS: 875 (Part 3)-1988, Code of practice for design loads (Other than earthquake) for buildings and structures,

BIS, New Delhi.

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