Optimization of Water Tanks - A Critical Review: Dr. H Y Oke

Dr. H. Y. Oke Professor, College of Engineering, Pune 411031 e-mail : hemantoke1960@gmail.com

Abstract

This paper takes the broad survey of the work done in the field of water tanks by different investi- gators and suggests the possible improvements which are needed for more rational design of tanks adopting recent methods of analysis and design and optimization.

Introduction

The different investigators have attempted for optimisation of water tanks from long time. How- ever earlier the computer facilities were limited. Similarly code for water tank was based on old working stress method resulting in thick walls and heavy reinforcement. However experience in U.K. has shown that crack width of limited width do not percolate liquid and they are self healing. First the British code on water tanks was revised incorpora- ting limit state design. Subsequently in India code for water tanks IS3370 Part(I) and (II) has been revised in 2009. This paper discusses the work done by different investigators and suggests the possible improvements in the light of recent developments in the field.

Work done on optimization

C. V. Kameshwara Rao and Raghavan(1) have studied the optimum design of intze tank. They have proposed a mathematical model depending on minimum material content. However they have used no crack theory. They have considered only minimum weight of concrete and have done a parametric scan. They have said that even though for high tank capacities use of higher grade of concrete M30 in middle ring beam and cone may result in some savings in material content it is assumed that the saving is offset by cost of concrete and hence they have not included in their paper. However it is to be noted that now code on water tank has been revised in 2009 and M30 is the minimum grade of concrete. Also it is to be noted that IS3370 part(ii) limit state design is added. Also they have not considered the continuity effects in the design of intze tank because they say it is localized. However IS 3370 insists on the consider- ing continuity effects. Hence their study needs to be further updated in the light of revision of IS3370. Also they have not considered the cost of steel and shuttering.

M. Saxena, S. P. Sharma and C. Mohan(2)(3) have studied the use of nonlinear optimization tech- nique in determining the optimal design of intze tank of shaft. They have used the least sqare algorithm of Mohan Muzahim-Banu-Tahir for solving nonlinear optimization problem used by structural model formulated by Rao and Raghavan. They have studied the tank capacities between 200Kl to 2500Kl. They claimed that the optimal parameters for intze type container requires less material than structures based on conventionally used design parameters as suggested by Rao and Raghavan. They have stated that earlier investiga- tors have done parametric scan and not systematic approach using techniques of nonlinear optimisa- tion using proper objective function. They have used empirical formulae to determine the thickness of top and bottom dome. In another paper cost optimi- zation of shafts using nonlinear programming they have tried to improve their studies. In earlier study they have assumed that structure using minimum volume of concrete was the minimum cost structure which may not be true as prices for concrete, steel and shuttering are different. However they have used model of Rao and Raghavan.

Hence shortcomings of that models discussed are incorporated in their study. They have used membrane theory. However intze tank is highly indeterminate structure and involves bending theory. Also their design is based on no crack theory of earlier code IS3370 part(II)-1965. But now since IS3370 part(II) has been revised in 2009 and limit state design has been added their study needs to be reinvestigated.

The designers face a basic question about the optimum dimensions for a given capacity. Billing, Gray, Renolds and Jain and Jaikrishna have proposed different proportion for optimum shape of a container based on experience. Basole(4) et al has given several graphs for calculating the height, dome height from a single variable the radius of the cylindrical portion of the tank.

However now since computers are everywhere parametric studies using finite element method is needed. Jain O. P., Anandprakash, K. K. Singh and S. P. Saxena(5) have carried out a detailed analysis of costs and requirements for materials for intze tanks of various capacities, staging heights, bearing capacities of soils and presented a number of equations for rapid estimation of the costs and materials of the intze tanks. However for design of container they have considered only dead load and live load. All the investigators have said that wind or earthquake need not be considered in the design of container because we don’t take into account the 33 percent increase in permissible stress when we design container unlike that of staging. S. K. Jain and Samer(10) have said that this is alright from strength criteria. However it has been pointed out by them that when serviceability criteria is consi- dered container portion of the tank have cracked in Bihar Nepal earthquake. Also their wind load is based on old code IS875-1964. Now the code has been revised in 1987. C. V. S. Kameshwar Rao(11) has considered the effect of geometry of the container on wind and earthquake forces of the tank. If this factor is included the nature of optimi- zation problem changes. Consideration of lateral force effects impose an additional constraint on optimum design formulation of intze container.

C. A. Wilby(6) has discussed the general optimi- zation of design of rectangular container. However he has done studies as per CP114 and CP110. CP110 and CP114 are replaced by BS8001. Basole and Kulkarni(9) have published on data for opti- mized design of tanks. They have prepared ready- made design charts to call for tenders on realistic estimates and the time lag between calling of tenders and their acceptance is utilized. They have given equations between capacity and radius of cylindrical and intze tank. M. M. Basole, N. L. Khushlani, R. K. Agarwal and B. M. Deogade(7) have discussed a method of calculation of quantities for steel and concrete above and below ground level for various staging heights bearing capacities of soils. They have plotted various curves for tank capacities between 50m3 to 500m3, staging heights 8 to 24m and bearing capacities of soils from 5t/m2 to 30t/m2. They have given seventy six equations which help in calculating quantities for steel and concrete. They have given inside diameter for differ- ent capacities of the tank. However these diameters result in high heights which increases the cost of pumping. Also now IS3370 has been revised and limit state method has been added. Hence their study needs to be revised.

S. R. Adidam and Subramaniam(8) have used limit analysis to find the strength of structure. Cost of tank consists of tank wall and floor which includes the cost of concrete, reinforcement and formwork is chosen as objective function in optimi- zation problem formulation. The constrained non- linear problem is solved using DFP algorithm. They have coupled optimization with limit state design. They have done studies as per BS5337. However BS5337 itself has been first revised to BS8007 and further replaced by EC2. Hence their study needs to be revised.

Conclusion

As the Indian code of water tanks IS3370 part(ii) has been revised in 2009 hence studies are needed as per changed limit state design philosophy compared to earlier no crack theory. Also material strength has been changed. Now minimum grade of concrete is M30 for water tanks instead of M20 which was prescribed in earlier code. In case of intze tank finite element method is required as compared to earlier membrane analysis. Also as the British code on water tanks is revised studies are required as per revised code. In the design of the container lateral forces of wind and force needs to be consi- dered. Study of optimization by dynamic program- ming is required as design of staging depends on design of container and design of foundation depends on combined weight of container and staging.

Acknowledgements

This paper is published with kind permission of Commander, Faculty of construction manage- ment college of military engineering, Pune.

References

(1) C. V. S. Kameshwara Rao and T. M. S. Ragha- van, ‘Optimum design of intze tank on shaft’, Indian Concrete Journal, January 1982, pp24 to 77.
(2) V. Manu Saxena, S. P. Sharma and C. Mohan, ‘Use of nonlinear optimization technique in determining the optimal design of intze tank on shafts’, Engineering and Optimization vol.9, 1985, pp143-154.
(3) M. Saxena, S. P. Sharma and C. Mohan, ‘Cost optimization of intze tanks on shafts using nonlinear programming, Engineering and Optimization, Vol.10, 1987, pp279-288.
(4) M. M. Basole, S. S. Kulkarni ‘Data for optimi- zed designs of water tanks, Indian Waterworks Association, October, December 1981, pp329 to 334.
(5) O. P. Jain, Anand Prakash, K. K. Singh, Estimation of materials and cost for optimum design of intze tank, Indian Concrete Journal, June 1979, pp162-166.
(6) C. A. Wilby, ‘General optimization of the design of rectangular containers’, Indian Concrete Journal, May 1977, pp155-158.
(7) M. M. Basole, N. L. Khushlani, R. K. Agarwal and B. M. Deogade, ‘Estimation of cylindrical tanks’, Indian Concrete Journal, February 1982, pp117-120.
(8) S. R. Adidam and Subramanium, ‘Optimum design of cylindrical tanks’, Journal of Struc- tural Division, ASCE, June 1982, pp1219-1230.
(9) Premchand, Sushil K. Agarwal and Anand- prakash ‘Economical proportions of intze type container water towers’, Indian Concrete Journal, July 1984, pp189-194.
(10) S. K. Jain and Sajjad Samer, ‘A review of requi- rements for a seismic design of tanks, Bridge and structural engineer, 1992.
(11) C. V. S. Kameshwara Rao, ‘Optimum container geometry of the intze tank, Indian Concrete Journal 1992.
(12) IS3370-2009 part(i) and (ii) code for liquid
retaining structures.
(13) BS5337-1976 British code on design of water
tanks.
(14) BS8007-1987 British code on water tanks.