Equation for Estimation of Fundamental Time Period for Elevated Water Tank

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), INTERNATIONAL JOURNAL OF CIVIL ENGINEERING ISSN 0976 – 6316(Online), Volume Vo lume 5, Issue 9, September (2014), pp. 266-275 © IAEME AND TECHNOLOGY (IJCIET)

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ISSN 0976 – 6308 (Print) ISSN 0976 – 6316(Online) Volume 5, Issue 9, September (2014), pp. 266 -275 © IAEME: www.iaeme.com/Ijciet.asp Journal Impact Factor (2014): 7.9290 (Calculated by GISI) www.jifactor.com

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EQUATION FOR ESTIMATION OF FUNDAMENTAL TIME PERIOD FOR ELEVATED WATER TANK 1

Dr. R. B. Khadiranaikar ,

Abbas Ali Dhundasi

2

1

(Professor, Department of Civil Engineering, B.V.V.S.'s Basaveshwar Engineering College, Bagalkot, Karnataka, India) 2 (PG Student, Department of Civil Engineering, B.V.V.S.'s Basaveshwar Engineering College, Bagalkot, Karnataka, India)

ABSTRACT

Earthquakes are one of the most devastating natural hazards that cause great loss of life and livelihood. The determination of the natural period of vibration of a reinforced concrete structure is an essential procedure in earthquake design and assessment. The fundamental period of vibration of a reinforced concrete structure appears in the equation specified in building codes to calculate the design base shear and lateral forces. To estimate the period, building codes provide empirical formulas that depend on the building material, building type and overall dimensions of the structure. The aim of the present investigation is to propose a simplified period – height equation for use in the seismic force estimation of elevated water tank. The period of vibration which has been derived herein represents the period of first mode of vibration. The study includes the seismic response of elevated water tank with different size, shape, capacities and varying height for high seismic zone in India. Various analytical models were prepared using SAP 2000 V-14.2 software. The new formulation for the estimation of time period of Elevated water tanks are developed using regression analysis from the statistical data generated. The combined general equation thus arrived at, can be used in general for Intz and funnel type of elevated water tanks irrespective of the capacities, height, type of staging, and type of bracing as an alternative to the already available codal provisions of IS: 1893-2002. Keywords: Elevated Water Tank, Fundamental Time Period, Regression Analysis, Period-Height Equation, SAP-2000.

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International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online), Volume Vo lume 5, Issue 9, September (2014), pp. 266-275 © IAEME

1. INTRODUCTION

Water is essential to humans and other life forms. Sufficient water distribution depends on design of a water tank in certain area. Many new ideas and innovation has been made for the storage of water and other liquid materials in different forms and fashions. There are different ways for the storage of liquid such as underground, ground supported, elevated. Liquid storage tanks are used extensively by municipalities and industries for storing water, inflammable liquids and other chemicals. Thus water tanks are very important for public utility and for industrial structure. An elevated water tank is a large water storage container constructed for the purpose of holding water supply at certain height to pressurization the water distribution system. These tanks consist of huge water mass at the top of a slender staging which are most critical consideration for the failure of the tank during earthquakes. Elevated water tanks are critical and strategic structures and damage of these structures during earthquakes may endanger drinking water supply, cause to fail in preventing large fires and substantial economical loss. Since, the elevated water tanks are frequently constructed and used in seismic active regions also, seismic behaviour of them has to be investigated in detail. The present study is an effort to identify the behaviour of elevated water tank under different parameters such as various size, shape, capacity, height, type of supporting structure etc. with consideration and modeling of elevated water tank using structural software SAP2000 and hence generating empirical equation for estimation of fundamental time period. 2. MODEL PROVISIONS

Two mass model for elevated tank was proposed by Housner (1963) which is more appropriate and is being commonly used in most of the international codes including Draft code for IS 1893 (Part-II).[1] For representing two masses and in order to include the effect of their hydrodynamic pressure in analysis, spring mass model is applied on elevated tanks. In spring mass model convective mass (mc) is attached to the tank wall by the spring having stiffness (Kc), where a impulsive mass (mi) is rigidly attached t o tank wall [1]. The behaviour of supporting system, which is more effective under different earthquake time history records with SAP 2000 software was carried out by Ayazhussain M. Jabar, H. S. Patel [2]. Here, two different supporting systems such as radial bracing and cross bracing were compared with basic supporting system for various fluid level conditions. Tank responses including base shear, overturning moment and roof displacement have been observed, and then the results have been compared and contrasted. Conclusions were drawn that cross bracings are more stable and suitable for construction from earthquake point of view. Sloshing response of elevated water tank over alternate column proportionality was studied by Chirag N. Patel, Shashi N. Vaghela and H. S. Patel [3]. Amongst all type of column proportionality, circular and rectangular wide were proven highly competitive to withstand against sloshing displacement under different earthquake c haracteristics. H. Shakib, F. Omidinasab and M.T. Ahmadi studied the Seismic Demand Evaluation of Elevated Reinforced Concrete Water Tanks [4]. The elevated tanks period showed that simultaneous effects of mass increase and stiffness decrease of ta nk staging lead to increase in the natural period. Durgesh C. Rai and Bhumika Singh studied the seismic design of concrete pedestal supported tanks and concluded that when a tank is empty, flexure strength governs the failure mode for all aspect ratios (ratio of height to diameter) of the support shaft and time periods of the tanks. And when tank is full, shear mode is found to be governing failure of stiffer shafts having short time period and low aspect ratios [5].

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3. PROBLEM DEFINITION

The typical plan in 2D and 3D models of elevated water tank are prepared. The models are kept symmetric in both orthogonal directions. Container vessel for storage of water is considered in circular shape and funnel shapes with varying diameter and height. The height of supporting structure is varied respectively in proportions. 3.1 Analysis of Water Tank The loads are applied to the prepared model as the guidelines provided in IS 875-1987, IS 1893-2002. Then the time period values are calculated and the behaviour is studied using structural analysis software SAP-2000. 3.2 Study Parameters The present study is all all about the behaviour of elevated elevated water tank under free vibration vibration and generation of empirical equation for computation of fundamental time period. Various parameters are as listed below, •

Shape- Intz and funnel shapes.

•

Capacity - 10, 15, 20 lakh liters.

•

Height of supporting structure- 16m, 20m and 24m

•

Type of supporting structure - Framed support, shaft support.

•

Tank fill condition - Full, half full, empty.

4. DESIGN DETAILS OF WATER TANKS

The design details of the type of o f water tanks considering all the parameters are as shown below. 4.1 Intz type water tank Table 4.1: Design details of Intz type water tank

Capacity Type of tank

10lakh

15 lakh

20 lakh

Intz

Funnel

Intz

Funnel

Intz

Funnel

M 30

M 30

M 30

M 30

M 30

M 30

Fe 415

Fe 415

Fe 415

Fe 415

Fe 415

Fe 415

0.1m

0.1m

0.1m

0.1m

0.1m

0.1m

2m

2m

2.5 m

2m

2.5 m

2m

Size of top ring beam

0.3 x 0.3m

0.8 x 0.8m

0.3 x 0.3m

0.8 x 0.8m

0.4 x 0.4m

0.9 x 0.9m

Diameter of cylindrical wall / top ring beam

12m

24

14m

21m

15m

26m

8m

--

9m

--

10m

--

0.3m

--

0.4m

--

0.5m

--

Grade of concrete Grade of steel Thickness of top dome Rise of top dome

Height of cylindrical wall Thickness of cylindrical wall

268


Capacity

10lakh

15 lakh

20 lakh

Capacity

10lakh

15 lakh

1.2 x 0.6m

--

1 x 1m

--

1.2 x 1.2m

--

2m

7.5m

2.5m

6m

2.5m

8m

Thickness of conical shell

0.6m

0.3m

0.6mm

0.3m

0.6m

0.3m

Rise of bottom dome

1.6m

1m

2.5m

1m

2m

1.5m

Thickness of bottom dome

0.3m

0.2m

0.3m

0.2m

0.5m

0.2m

Size of bottom ring beam

0.6 x 1.2m

0.6 x 0.6m

0.6 x 0.6m

0.6 x 0.6m

1x 1m

0.6 x 0.6m

08

--

08

--

08

--

Diameter of column for a. 16m staging b. 20m staging c. 24m staging

0.5m

--

0.6m

--

0.8m

--

Thickness of shaft

0.3m

0.15m

0.3m

0.2m

0.3m

0.3m

Size of bracings

0.5 x 0.5m

--

0.6 x 0.6m

--

0.8 x 0.8m

--

Size of middle ring beam Rise of conical dome

Number of columns

4.a)

4.b)

4.c)

4.d)

Figure 4.1 a) Intz tank Wired 2D frame model b) Intz tank 3D frame model in c) Funnel tank Wired 2D frame d) Funnel tank 3D frame model in SAP-2000

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5. RESULTS AND DISCUSSIONS

The values of fundamental time period is observed and recorded for the case of Intz tank and funnel shaped tank, whose capacities are varied from 10 lakh, 15 lakh la kh and 20 lakh litres lit res respectively. With these values of time period a general empirical equation for estimation of fundamental time period is generated by carrying out regression analysis using mathematical tool Origin software. The equation is generated for each and individual case separately. Then at last the general equation is generated considering all the cases together forming a unique solution. The values obtained for time period are tabulated as follows.

Number

1)

2)

3)

4)

5)

6)

7)

8)

9)

Table 5.1: Time period of all types of water tanks combined Time period for Tank fill condition Height of Type of In seconds staging structure In meter Empty Half full Full 16m 0.3186 0.3188 0.3266 I- 10- FS 20m 0.4989 0.5095 0.6509 24m 0.7088 0.7211 0.8389 16m 0.3871 0.3387 0.4934 I- 15- FS 20m 0.5292 0.5541 0.6868 24m 0.7156 0.7126 0.9648 16m 0.2064 0.4060 0.4733 I- 20- FS 20m 0.5327 0.6983 0.7042 24m 0.7590 0.7511 0.9855 16m 0.3043 0.3044 0.4200 I- 10- SS 20m 0.4856 0.5001 0.6646 24m 0.6731 0.7993 0.9068 16m 0.4277 0.4315 0.5062 I- 15- SS 20m 0.6002 0.6069 0.7443 24m 0.8261 0.7915 1.0309 16m 0.3721 0.3797 0.4858 I- 20- SS 20m 0.5858 0.5858 0.7792 24m 0.8301 0.8301 1.1062 16m 0.3043 0.4856 0.6731 F- 10- SS 20m 0.3186 0.4989 0.7088 24m 0.3871 0.5292 0.7156 16m 0.3188 0.5095 0.7211 F- 15- SS 20m 0.3387 0.5541 0.7126 24m 0.3044 0.5001 0.7993 16m 0.4200 0.6646 0.9068 F- 20- SS 20m 0.4934 0.6868 0.9648 24m 0.3266 0.6509 1.0389

5.1 Intz Tank with Framed Staging 5.1.1 10 Lakh Litre Capacity (IT-10-FS) The model analysis results of 10 lakh litre capacity Intz tank with framed staging for the height of 16m, 20m and 24m are presented in the Table 5.1.

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a. It is observed observed that for 16m staging height, the increase in the fundamental fundamental time period is 0.7% and 3% from empty to half full and full tank condition respectively. b. Similarly for 20m and 24m staging height, the increase in the fundamental fundamental time period is observed as 2% and 30% and 2% and 20% from empty to half full and full tank condition respectively. c. In each case the maximum time period is observed for tank full condition of the structure. The fundamental time period increases by 99%and 157%, when height of staging is varied from 16m to 20m and 24m for full fill condition of the tank respectively. 5.1.2 15 Lakh Litre Capacity ( IT-15-FS) Increase in the storage capacity, by to 1.5 times more than the previously considered elevated water tank, has led to an increase in the f undamental time period for 16m staging height.

a. The amount of increase observed is 14% and 46% from empty to half full and full tank condition respectively. As well as the increment is also observed in 20m and 24m staging height. The corresponding values are 9%, 30% and 4% and 35% from empty to half full and full tank condition respectively. b. It is observed that full tank condition gives maximum value of fundamental time period. The height of the supporting structure is increased by 4m interval. For first interval the time period increases by 40%. For second interval it increases by 95% and height of supporting structure is 24m. c. The fundamental time period increases by 15% for 15 lakh litre capacity tank than 10 lakh litre capacity tank. 5.1.3 20 Lakh Litre Capacity (IT-20-FS) The storage capacity is increased to 2 times the first case and the analysis is carried out. The increment in fundamental time period observed is a s follows.

a. For 16m staging height, height, the increase in the fundamental time period is observed as 96% and 130%, for 20m it is 31% and 32%, and for 24m it is 1% and 30% from empty to half full and full tank condition respectively. b. In each case again the maximum time period i s observed for tank full condition of the structure. The fundamental time period increases by 49% and 108%,when height of staging is varied in two intervals for full fill condition of the tank. c. The fundamental time period, for tank full condition, increases by 15% and 18% for 20 lakh litre capacity tank than the 10 lakh litre capacity and 15 lakh litre ca pacity respectively. 5.2 Intz Tank with Shaft Staging The shape of the superstructure is kept the same as Intz type and supporting structure is modeled as shaft type. The capacities a re varied and the results of the studies are as follows. 5.2.1 10 Lakh Litre Capacity ( IT-10-SS)

a. The fundamental time period for 16m height staging is observed to be increasing by 3% and 38% from empty to half full and full tank condition respectively. Similarly for 20m and for 24m staging height, the increase in the fundamental time period is observed as 3%, 37% and 19% and 35% from empty to half full and full tank c ondition respectively. b. The fundamental time period increases by 58% and 116%, when height of staging is varied from 16m to 20m and 24m for full fill condition of the tank respectively. 271


5.2.2 15 Lakh Litre Capacity ( IT-15-SS)

a. The mass of the water stored in now increased to 15 lakh litre and the results are studied as follows. Due to increase in the mass of water, for 16m staging height, the increase in the fundamental time period is observed as 1% and 18%. For 20m staging height, the increase is observed as 2% and 24%. For 24m staging height, the increase is observed as 5% and 30% from empty to half ful l and full tank condition respectively. b. The fundamental time period increases by 47% and 104%, when height of staging is varied from 16m to 20m and 24m for full fill condition of the tank respectively. 5.2.3 20 Lakh Litre Capacity ( IT-20-SS) The mass of the water is considered twice the mass in first case. And the results generated are as follows.

a. For 16m staging height, the increase in the fundamental time period observed is 2% and 30% from empty to half full and full tank condition respectively. b. For 20m staging height, the increase is observed as 1% and 33%. c. For 24m staging height, the increase is observed as 1% and 34%. d. Due to increase in the mass of water, the fundamental time period increases by 60% and 128%, when height of staging is varied from 16m to 20m and 24m for full fill condition of the tank respectively. Considering tank full condition, fundamental time period increases by 14% and 22% for 20 lakh litre capacity tank than the 10 lakh litre capacity and 15 lakh litre capacity tanks respectively. 5.3 Funnel Tank with Shaft Staging The shape of superstructure is now considered as funnel type, keeping the supporting structure as shaft type. 5.3.1 10 Lakh Litre Capacity ( FT-10-SS) The height of supporting structure is varied in the similar pattern as discussed above. The increment in the fundamental fundamental time is observed observed as follows from empty to half full and full fill conditions respectively. •

For 16m staging height, the increase is 60% and 122% .

•

For 20m staging height, the increase is 57% and 122%.

•


In each case the maximum time period is observed for tank full condition of the structure. The fundamental time period increases by 5% and 7%, when height of staging is varied from 16m to 20m and 24m for full fill condition of the tank respectively. 5.3.2 15 Lakh Litre Capacity ( FT-15-SS) Increased capacity of water tank also resulted in increase of the fundamental time period. The values as are follows. •

for 16m staging height, the increase inc rease is 60% and 127%. 272

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308 (Print), ISSN 0976 – 6316(Online), Volume Vo lume 5, Issue 9, September (2014), pp. 266-275 © IAEME •


•


The fundamental time period increases by 1% and 10%, when height of staging is varied from 16m to 20m and 24m for full fill condition of the tank respectively. 5.3.3 20 Lakh Litre Capacity (FT-20-SS) The capacity to store the water is now considered to be maximum as 20 lakh litres. The fundamental time period again seemed to be increasing, and the results that are observed are as follows. Due to increase in the mass of water, •

• •

For 16m staging height, the increase is 59% and 116% from empty to half full and full tank condition respectively. For 20m staging height, the increase is 40% and 96%. For 24m staging height, the increase is 100% and 218%. Here the increment is seemed to be very high indicating the structure to be more vulnerable to damage and affecting the safety and stability.

The fundamental time period increases by 7% and 15%, when height of staging is varied from 16m to 20m and 24m for full fill condition of the tank respectively. Considering tank full condition, fundamental time period increases by 12% and 45% for 20 lakh litre capacity tank than the 10 lakh litre capacity and 15 lakh litre capacity tanks respectively. 5.4 General Comparison In general the increment in fundamental time period can be expressed as follows 5.4.1 In Intz tank type, for tank fill condition (from empty to half fill, full)increment is in the range of 30% to 35%. Staging height increases the fundamental time period by almost 50% to 60% for every 4m increase. As capacity also has an effect on fundamental time period the increment is found to be in the range of 15% to 20%. 5.4.2 In Funnel tank, similarly, the increment of time period for tank fill condition is 60% to 65%. This is due to larger width and less height of the superstructure connected to slender supporting structure than compared to Intz tank. For staging height the increment is 10% and capacity is 15% to 45% respectively. 5.4.3 The structures constructed in high earthquake zone in India should be more flexible so that they can be stable. More the fundamental time period more flexible structure will be. Hence from table 5.1 the maximum fundamental time period is observed for full fill condition Intz tank with shaft type of staging. Hence Intz tank with shaft support are advisable for the general construction. 5.5 Period-Height Equations The plot of regression analysis is shown in the fig 5.1 for fundamental time period, taking into consideration of all the parameters for t he selected types of elevated water tanks.

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Figure 5.1: Graph of fundamental time period for all types of water tanks combined

The study presented herein has led to a simplified period – height based equation for each and individual case of the Elevated water tanks. The equations formulated from the present study are shown in Table 5.5.1. Table 5.5.1 Period-Height Equations Sl. No. Type of Tank Period - Height Equation -3 3.22 1. I-10-FS T=0.0076 x10 H -3 2.88 2. I-15-FS T=0.0221x10 H -3 3.54 3. I-20-FS T=0.0022x10 H -3 3.27 4. I-10-FS T=0.0063x10 H -3 2.79 5. I-15-FS T=0.0344x10 H -3 3.71 6. I-20-FS T=0.0013x10 H -3 2. 5 7. F-10-FS T=0.0628x10 H -3 2.91 8. F-15-FS T=0.0294x10 H -3 3.13 9. F-20-FS T=0.0156x10 H 2.43 10. Combined T =0.00013 H 6. CONCLUSIONS

The important findings of this study are summarized below. 1. The time period for the tank with full filled condition is more than the time period for empty condition. 2. The fundamental natural period of a Elevated water tank increases with increase in the height of supporting structure for the tank. 3. The fundamental natural period of a Elevated water tank increases with increase in the storage capacity of the tank. 4. Intz tanks with shaft t ype of supporting structure are to be preferred. The study presented herein has a led to a simplified period – height based equation for the Elevated water tank. The equation formulated from t he present study is: Ta =0.00013 H

Where, Ta = Natural time period of structure in seconds. H = Height of the Structure in meter. 274

2.43


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Equation for Estimation of Fundamental Time Period for Elevated Water Tank

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