Optimization of Circular Elevated Service Reservoir

Optimization of Circular Elevated Service Reservoir

Dr. S. A. Halkude1, Mr. A. B. Jadhav2

Civil Engg. Deptt. Walchand Institute ofTechnology, Solapur, Solapur University,

India

Abstract :- This research is an application of optimization technique to the structural design of elevated circular water tank with flat top and flat bottom slab, for varying tank capacities and varying the D/H ratio, with fixed supporting structure height, basic wind speed & soil bearing capacity conditions. The objective of the research is to arrive at an optimum geometry of a given capacity of water tank, using continuity analysis method. The elevated circular water tank is found to be insignificant for D/H ratio consideration with small capacities of tank, while the D/H ratio is more significant for higher capacities of E.S.R.

KeywordsOptimization, Tank capacity, D/H ratio, Continuity analysis.

1. INTRODUCTION

   Elevated circular water tank is an important element of water supply scheme. The main purpose of E.S.R. is to store the water and distribute it to the various zones as per the required hydraulic pressure to varioussections of community.

   For a tank form structure to be economical, it must be efficient not only in enclosing space, but also in resisting the stored water loads. Each component of the tank should be designed such that it transfers all loads including wind load safely to the ground.

   In general, the choice of structural form is based on approximated thumb rules. Elevated circular water tanksare visuallyprominent structure as they areaesthetically good- lookingand economicalstructures. Circular water tank with flat roof & base slab is used for all types of capacities due to its simplicity in geometry which gives economical result & better stability in seismic prone zones. In this paper cost comparison is carried out for different capacities of water tanks with various combination of D/H ratio.

2. TYPES OF E.S.R.

The E.S.R. is classified according to its shape as follows:-

1. Rectangular tank 2.Intze tank

   1. Circular tank

      Circular water tank with flat roof & base slab is used for all types of capacities due to its simplicity in geometry which is economical and provides better stability in seismic prone zones.

      1. DIMENSIONAL PARAMETER

         The term dimensional parameter refers to the relative ratios between dimensions of a given form that fix its shape. The parameters and shapes of tanks vary according to their shapes and capacity. As far as the framed supporting structures are concerned, the vertical distance between two levels of horizontal braces is 3m.

      2. THEORETICAL FORMULATION

   In this study, water tank is analysed using continuity analysis method because it is assumed that joints are monolithic therefore one need to construct the various components of water tank simultaneously for ensuring monolithicness. W.P.S. Dias and M.T.P. Hettiarachchi(16) analysed four different elevated water tanks, for cost comparison and found that the cylindrical tank form is the cheapest form for lower capacities, while the Intzetank form isthemost economical for higher capacities. The present work employs continuity analysis for studyingvarious combinations of depth & accordingly diameter of circular water tank, for finding an optimum geometry for elevated circular water tank with flat top and bottom for known capacity.

   1. Design Approach

      All the components of the ESR are analysed considering Dead load, Live load, Wind load and Earthquake forces and their various combinations. Also, the ESR is analysed for the tank full and tank empty conditions. The permissible stresses in material are increased by 33% for wind force. Whenever the effect of wind and seismic forces together are taken into account, the safe bearing capacity of soil is increased by 25%. The design is done in accordance with the procedure laid down in I.S: 3370-1967 Part I-IV (1).

   2. Continuity Analysis

   In this analysis the stresses are obtained by applying the principle of consistent deformation. The vertical displacement is always same at each joint. Now,as eachwall is free to deform in horizontal direction hence

   consistency needs to be satisfied for horizontal forces & angular displacement between the walls meeting at a joint. In the circular water tank for continuity analysis, wall is restrained at any end;therefore the expansion and angular movement of the wall atthat point will be restraineddue to a bending moment and a radial force as shown in Figure 1.

   Figure 1 Bending moment and radial force in circular tank walls

   The bottom edge of a tank wall is subjected to a clockwise moment and an outward radial force. The following equations give the moment and hoop tension in the wall atany levelof tank height.

   =

   ^() [ [ ] + ]/ 2µ^3 (1)

   =

   ^() [ [ cos + sin] + ]/

   µ (2)

   The joint reaction, clockwise moment and outward radial force at bottom of a tank depend upon its condition of fixity and pressure distribution.

   Where = 1 1/ /22

   = 2 1/ /22

   4 = 3

   2 2

   3

2. Container shape & size

The elevated tanks are designed for the following volume capacities.

• Circular tanks 25m3,50m3,75m3,100m3,150m3,200m3,250m3, 300m3 to 1000m3, 1250m3, 1500m3, 1750m3, 2000m3.

The tank capacity rangeis chosen on the basis of existing practices observed in literature review. The elevated tank capacities are designed for the supporting staging height of 9m, which is assumed to be a base line for constructing tanks in India.

The above combinations (of the capacity & supporting structure height of elevated tanks) are designed for Zone

IV. Therefore, the basic wind speed considered is 39.0 m/sand soil bearing capacity is 200kN/m2.

6. PARAMETRIC STUDY

In the present parametric work, continuity analysis method is used toanalyse the tank andcost comparison is done to optimize with various combination of D/H ratio of the tank.

The range of variable parametersis as mentioned below:

1. Tank Capacity 25 Cum to 2000 Cum

2. Height of container tank varies from 2.8m to 6.8m depending upon the capacity.

The variation in cost of tank for different D/H ratio is shown with the help of graphs.

=

12

The above equations areusedfor calculating bending moment and hoop tension in the wall at any level above the base.

5. DESIGN PARAMETER

The identified parameters of significance for study are as follows:

1. Tank capacity

1. Variation incost for capacities with respect to D/H ratio from 25cum to 500 cum

2. Variation in cost for capacities with respect to D/H ratio from 600cum to1000 cum

   29.00

   26.00

   23.00

   Total Cost Rs in Lac

   20.00

   17.00

   14.00

   11.00

   8.00

   5.00

   25 Cum

   54.00

   52.00

   50.00

   48.00

   46.00

   44.00

   50 Cum

   75 Cum

   100

   Cum 150

   Total Cost Rs in Lac

   Cum

   600 Cum

   200

   700 Cum

   42.00

   Cum 250

   800 Cum

   900 Cum

   40.00

   Cum

   300

   36.00

   34.00

   32.00

   30.00

   1000 Cum

   38.00

   Cum 400

   Cum

   500

   Cum

   2.00

   0.40 0.90 1.40 1.90 2.40 2.0 3.40 3.90 4.40

   0.40 0.90 1.40 1.90 2.40 2.90 3.40 3.90 4.40 4.90

   D / H Ratio

   Figure.3 Variation in cost for capacities between 600-1000 Cum

   D / H Ratio

   Figure.2 Variation in cost for capacities between 25-500 Cum

   Figure 2: Shows Total cost Vs D/H ratio.The above graph indicates the following conclusion:

   1. For capacity ranging from 25 Cum to 500 Cum thereisnosignificant change in optimum cost of tank because it is nearly same as that of highest cost of tank. Therefore, for small capacity of tanks, variation of D/H ratio is not significant.

   2. Initially for all capacities, the total cost of tank decreases as the D/H ratioincreasesup to a pick point and from that point there is an increase in cost of tank.

   3. As the D/H ratio increases, total cost of tank tends to form an inverted parabolic profile.

   Figure 3: Shows Total cost Vs D/H ratio. The above graph indicates thefollowing conclusion:

   1. The capacities ranging from 600 Cum to 1000 Cum are more economical compared to capacity ranging from 25 Cum to 500 Cum.

   2. As the D/H ratio increases the total cost of tank tends to form as a V shape profile.

   3. Initially, for all capacities, the total cost of tank decreases as the D/H ratio increases up to a pick point and from that point there is an increase in cost of tank with increasing D/H ratio.

   6.4. Variation ofOptimum cost for optimum D/H ratio

3. Variation in cost for capacities with respect to D/H ratio from 1250cum to2000 cum

100.00

95.00

90.00

85.00

80.00

75.00

92.00

Optimum Cost Rs in Lac

62.00

32.00

1250 Cum

1500 Cum

Total Cost Rs in Lac

2.00

Optimum Cost Vs D/H

0.50 2.00 3.50 5.00

D / H Ratio

70.00

1750 Cum

2000 Cum

65.00

60.00

55.00

50.00

2.00 2.50 3.00 3.50 4.00 4.50 5.00

D / H Ratio

Figure.4 Variation in cost for capacities between 1250-2000 Cum

Figure 4: Shows Total cost Vs D/H ratio. The above graph indicatesthefollowing conclusion.

1. Cost of tank reduces significantly for capacities ranging from 1250 Cum to 2000 Cum.

2. Tanks are more economical for capacity greater than 1000 Cum.

3. As the D/H ratio increases the total cost of tank tends to form as aV shapes profile.

4. Initially for all capacities, the total cost of tank decreases as the D/H ratio increases up to a pick point and from that point there is an increase in cost of tank with increasing D/H ratio.

   Figure.5 Optimum cost Variation for optimum D/H ratio

   Figure 5: Shows the variation in optimum cost Vs corresponding D/H ratio. It is observed that the optimum cost of tank increases mildly with increasing D/H ratio for lower capacities. For higher capacities,optimum cost of water tank increases steeply with increasingcorresponding D/Hratio.

   60.00

   Optimum Cost Rs in Lac

   1. Variation ofOptimum cost for capacity of tank.

      90.00

      0.00

      0

      500

      1000 1500 2000

      Capacity in Cum

      Figure.6 Optimum cost variation for tank capacities

      Optimum cost of tank Vs capacity

      30.00

      Figure 6: Shows the variation in optimum cost Vs capacity. It is observed that the optimum cost tends to form nearly linear variation with respect to increasing capacities of E.S.R.Becomes more economical with increasing capacity of ESR.

      Optimum Cost Rs in Lac

   2. Variation ofOptimum cost for optimum D/H ratio.

   2.50

   2.00

   Optimum Cost Vs D/H

   1.00

   0.50

   1.50

   2.50

   3.50

   D / H Ratio

   Figure.7 Optimum cost variation per 25 cum of its capacity

   1.50

   Figure 7: Shows optimum cost Vs D/H ratiofor various water tank capacities. The above graph indicates the following:

   The cost of water tank per 25 Cum of its capacity decreases with increasing capacity of water tank, however, it is observed that there is a minor increasein the cost at certain points with increasing D/H ratio.

   1. COMPARISON WITH PARAMETRIC STUDY

      20

      18

      16

      14

      12

      10

      8

      Present Work

      By Dias & hettiarachchi (cylindrical)

      By Dias &

      2 Hettiarachchi (intze)

      0

      0 100 200 300 400 500

      Tank Capacity in Cum

      Figure.8 Cost comparision between cylindrical & intze tank

      6

      4

      Total Cost Rs in Lac

      Figure 8: Shows the comparison of the total cost of cylindrical water tank with thosereported by Dias and Hettiarachchi (1992). The above graph indicates thatthe results of the present study are in close agreement with those reported by Dias and Hettiarachchi(cylindrical). It is also found that theintze water tank is more economical in comparison with cylindrical water tank of capacity 500 Cumand for lower capacity (400 Cum) cylindrical water tank is economical.

   2. CONCLUSION

1. The optimumcost of circular water tank varies with increasing D/H ratio with respect to capacity of E.S.R. asmentioned below:

   1. For tank having capacity up to 500Cum, the optimization that can be achieved is up to 10% of the total cost of tank.

   2. For tank having capacity between 600-1000 Cum, the optimization that can be achieved is up to 18% of the total cost of tank.

   3. For tank having capacity between1250-2000 Cum, the optimization that can be achieved is up to 28% of the total cost of tank.

2. Initially for all capacities, the total cost of tank decreases as the D/H ratio increases up to a pick point and from that point there is an increase in cost of tank with increasing D/H ratio.

3. For higher capacities, (more than 1000 Cum) cost of water tank increases steeply with increasing D/H ratio.

4. The cost of water tank per 25 Cum of its capacity decreases with increasing capacity of water tank, however, it is observed that there is a minor increasein the cost at certain points with increasing D/H ratio.

5. As the D/H ratio increases, the total cost of tank tends to forman inverted parabolic profile.

6. Theoverall optimization improves with increasing capacity of water tank.

1. NOTATION E Modulus of elasticity

   tThickness of wall

   R Radius of the tank. wWater density

   hHeight of tank at any level xDistance above the base

   Mo Clockwise moment at bottom of tank HoOutward radial force at bottom of tank

   M Moment in the wall at any level of tank height

   T Hoop tension in the wall at any level of tank Height

2. REFERENCES

1. IS: 3370-1967 Part I-IV,Code of practice for concrete structures for storage of liquid, Bureau of Indian Standards, NewDelhi.

2. IS: 1893-2002, Criteria for Earthquake Resistant Design of Structures, (Fifth Revision) Bureau of Indian Standards, New Delhi.

3. IS: 11682-1995, Design of R.C.C. Staging for Overhead Tank, Bureau of Indian Standards, New Delhi.

4. IS: 456-2000, Code of practice for plain and R.C. Structures, Bureau of Indian Standards, New Delhi.

5. IS: 875-1987 (I-IV), Code for design consideration of loads on structures, Bureau of Indian Standards, New Delhi.

6. M. M. Basole and et alCost Estimation of Cylindrical Tanks, Indian Concrete Journal, pp 117-120, April 1977.

7. C. A. WilbyGeneral Optimization of the Design of Rectangular Container, Indian Concrete Journal,pp 155-158,May 1977.

8. M.Kalani and S.A.SalpekarA Comparative study of different methods of Analysis of staging of elevated water tanks, Indian Concrete Journal,pp 210-214July 1978.

9. M.M Basole, S.SKulkarniData for optimized designed of water tank, Indian Concrete Journal,pp 329-333Oct 1981.

10. C.V.S. KameswareRaoAnalysis of supporting tower of overhead tanks, Indian Concrete Journal,pp 265-766, Oct 1983.

11. O. M. ChoubeEconomical shape for small capacity water tank, Indian Concrete Journal,pp 134-134,May 1984.

12. M. L. GambhirReinforced concrete water tanks with vertical walls subjected to compression, Indian Concrete Journal, pp 103- 108,April 1986.

[13]P. KarunakarRao and G.V.SreekantiahCritical Reappraisal of a High rise reinforced concrete water tower, Indian Concrete Journal, pp138-141, March 1989.

1. W.P.S .Dias & M.T.P. HettiarachchiA Cost Comparison of Elevated Water Tank forms, Indian Concrete Journal, pp 43- 51,Jan 1992.

2. Optimum container geometry of Intze tanks. {C.V.S. KameswareRao, Indian Concrete Journal DEC 1992, pp687-689}

3. Jai Krishna and O.P.Jain, Plain and reinforced concrete, Vol.II- New Chand and Bros, Roorkee, pp131-215.

Authors Biography First Author

Dr. S. A. Halkude,

M.Tech. (IIT, Bombay in Civil Engineering), Ph.D. (IIT Bombay) is working as a Principal at Walchand Institute of Technology Solapur. At present shouldering the responsibility as Dean, faculty of Engineering & Technology, Solapur University, Solapur (Maharashtra, India).He has16 Journal and 15 Conference Research publications to his credit & is recipient of IGS-Dr. B.B. Rai- S. N. Gupta Bi-ennial Prize for the best paper on Earth and Earth Retaining Structures. Fellow member of The Institution of Engineers (India), Life Member of Indian Society for Technical Education, New Delhi and Life Member of Indian Society for Rock Mechanics and Tunnelling Technology, New Delhi.

He is recipient of Eminent Educationist Award by National & International Compendium, New Delhi (India).halkude60@gmail.com.

Second Author

Mr. A. B. Jadhav

B.E. (Civil Engineering), M.E. (Civil – Structures) abjadhav4@gmail.com; amarjadhav74@rediffmail.com