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The authors. accidental or consequential damages arising from the use of material content in this document. for which please contact NICEE Coordinator. While developing this material. the World Bank.The material presented in this document is to help educate engineers/designers on the subject. This document has been prepared in accordance with generally recognized engineering principles and practices. Preparation of this document was supported by the Gujarat State Disaster Management Authority (GSDMA).org
. Published by: Coordinator National Information Center of Earthquake Engineering Indian Institute of Technology Kanpur Kanpur 208 016 (India) Email: nicee@iitk. The views and opinions expressed in this document are those of the authors and not necessarily of the GSDMA.ac. using World Bank finances. many international codes. or IIT Kanpur. Gandhinagar. standards and guidelines have been referred. This document is intended for the use by individuals who are competent to evaluate the significance and limitations of its content and who will accept responsibility for the application of the material it contains. The material presented in these guidelines cannot be reproduced without written permission.in Website: www. publisher and sponsors will not be responsible for any direct. through a project at Indian Institute of Technology Kanpur.nicee.
V. Jain. Roads and Buildings. Gandhinagar Principal Secretary. Hyderabad K K Khurana. Gandhinagar Secretary. UDD. Structural Consultant. New Delhi Alpa Sheth. Visvesvaraya National Institute of Technology. Nagpur
P K Malhotra. Town Planner. Vakil Mehta Sheth Consulting Engineers. Ministry of Home Affairs. IIT Roorkee Rushikesh Trivedi. USA L K Jain. Indian Institute of Technology Kanpur O R Jaiswal. Gandhinagar A.Participants
Sudhir K. VMS Consultants. Thiruppugazh. Mumbai
. FM Global. Nagpur
A R Chandrasekaran. S. GSDMA. Arya. Gandhinagar Sr.
it gave due priority to the issues of code compliance for new constructions. It is hoped that the document will be useful in developing a better understanding of the design methodologies for earthquake-resistant structures. fires and terrorism considering importance of these hazards. GSDMA decided to take this up as a priority item and awarded a project to the Indian Institute of Technology Kanpur for the same. Naturally. Gandhinagar IIT Kanpur
. the codes must be supported with commentaries and explanatory handbooks. literally and otherwise. and in improving our codes of practice. The Gujarat State Disaster Management Authority Gandhinagar and the Indian Institute of Technology Kanpur are happy to present the IITK-GSDMA Guidelines on Seismic Design of Liquid Storage Tanks to the professional engineering and architectural community in the country. It was soon realized in Gujarat that for proper understanding and implementation. infrastructure and the lives of the affected people. as Gujarat began to rebuild the houses. The entire project is described elsewhere in detail. This will help the practicing engineers understand the background of the codal provisions and ensure correct interpretation and implementation. Seismic activity prone countries across the world rely on “codes of practice” to mandate that all constructions fulfill at least a minimum level of safety requirements against future earthquakes. The project also included work on codes for wind loads (including cyclones). Also. and for development of entirely new draft codes.
GSDMA. substantial work was undertaken to develop drafts for revision of codes. As the subject of earthquake engineering has evolved over the years.FOREWORD
The earthquake of 26 January 2001 in Gujarat was unprecedented not only for the state of Gujarat but for the entire country in terms of the damages and the casualties. Considering that such commentaries and handbooks were missing for the Indian codes. wherever necessary. the codes have continued to grow more sophisticated. As the state came out of the shock. the public learnt for the first time that the scale of disaster could have been far lower had the constructions in the region complied with the codes of practice for earthquake prone regions.
Prof K K Khurana (IIT Roorkee). Technical Assistants at VNIT Nagpur. JAIN INDIAN INSTITUTE OF TECHNOLOGY KANPUR OCTOBER 2007
. Indian seismic code IS 1893:1984 had some very limited provisions on seismic design of elevated tanks. Sri Amit Sondeshkar and Ms Shraddha Kulkarni. etc. are yet to be brought out by the BIS. In the above scenario. This document was developed by a team consisting of Professor Sudhir K Jain (Indian Institute of Technology Kanpur) and Professor O R Jaiswal (Visvesvaraya National Institute of Technology.nicee. The document was also placed on the web site of National Information Centre of Earthquake Engineering (www. It is hoped that the designers of liquid retaining tanks will find the document useful. The provisions included herein are in line with the general provisions of IS1893 (Part 1): 2002 and hence should pose no difficulty to the designers in implementation. six explanatory solved examples are provided based on the provisions of these Guidelines. Department of Civil Engineering. Moreover. to assist the designers for seismic design of liquid storage tanks. Gandhinagar to the Indian Institute of Technology Kanpur in 2003. revised Part 1 of IS 1893 has been brought out by the Bureau of Indian Standards (BIS). Dr P K Malhotra (FM Global.in
SUDHIR K. those provisions of IS 1893:1984 are highly inadequate. and Sri Rushikesh Trivedi (VMS Consultants. (Structural Consultant.PREFACE
Liquid storage tanks are commonly used in industries for storing chemicals. The other parts. it was decided to develop the present document under the project “Review of Building Codes and Preparation of Commentary and Handbooks” assigned by the Gujarat State Disaster Management Authority. Kanpur 208 016. USA) and Sri L K Jain. e-mail: skjain@iitk. Further. All suggestions and comments are welcome and should be sent to Professor Sudhir K Jain.org) for comments by the interested professionals and some useful suggestions were provided by Professor A R Chandrasekaran (Hyderabad). To facilitate understanding of the provisions. Ahmedabad). clause-by-clause commentary is also provided. In 2002. Nagpur). Nagpur) reviewed several versions of this document and provided valuable suggestions to improve the same. one of which will contain provisions for liquid storage tanks. petroleum products.ac. Importance of ensuring safety of such tanks against seismic loads cannot be overemphasized. the code did not cover ground-supported tanks. and for storing water in public water distribution systems. assisted in development of the solved examples and various graphs and figures of this document. Indian Institute of Technology Kanpur. Compared to present international practice.
..3 – Buried Tanks .....................................................................................................................................3............................................................................................... 50 4........ – SYMBOLS ................................ 28 4......... 40 4..........................................13.........................................................................................................................................6................................................................................................................. 7 3......................4 – Shear Transfer ........ 34 4......... 22 4......................................................................5 – Pressure Due to Wall Inertia......................6 – BASE SHEAR .................... 28 4.................................. 43 4..... 1 1...................................................................2....................................................................... 8 4...................................1 – GENERAL ...................................................................... 13 4................................................... 6 2.... 12 4....7.............................................................................. 35 4........................ 41 4........................... – REFERENCES.......................................................................2 – Convective Mode..............................................................1 – Ground Supported Tank ...............................................................................13 – MISCELLANEOUS ..... 12 4.........CONTENTS
0........................................................................2............................................................................................................ 26 4..................... 12 4......1 – Impulsive Hydrodynamic Pressure........................1 – Piping ...................8 – DIRECTION OF SEISMIC FORCE....................... – INTRODUCTION..............................2 – Buckling of Shell ....................................................................................................................................................................... 34 4................... – SCOPE...4 – DAMPING ......................................... 51 4.................................................................................................. 51 4...................................................................................................................................... 34 4...........................................................................................................................................................................10 – EFFECT OF VERTICAL GROUND ACCELERATION ...................................2 – Convective Hydrodynamic Pressure ..................9....................................................................1 – Impulsive Mode..................................................................................................5 – DESIGN HORIZONTAL SEISMIC COEFFICIENT ......... 37 4......................9..................................7 – BASE MOMENT ..................................................................................................................................... 52 4......................................................13..................................1 – Ground Supported Tank ..........5 – P...................3 – TIME PERIOD .....................................13.................13............................ 50 4.........Delta Effect........................................................... 35 4.....3................................................... 52
.............. 51 4............2 – SPRING MASS MODEL FOR SEISMIC ANALYSIS ........2 – Elevated Tank...............................9 – HYDRODYNAMIC PRESSURE ............................... 36 4........................................1 – Ground Supported Tank ..... 19 4.....................................................................................................................................................................................................................................................................................................................2 – Elevated Tank.................................2 – Elevated Tank.................................................................................................................................................................. 51 4.............................................7........................................................................................12 – ANCHORAGE REQUIREMENT ..................................9.6..........................................13...11 – SLOSHING WAVE HEIGHT ...................................... 49 4................................ 22 4... – PROVISIONS FOR SEISMIC DESIGN................ 40 4...........................................................
2. Staging height is 16. Seismic zone II and soft soil strata.000
4. Seismic zone V and hard soil strata. Container is of intze type.
Staging consists of 4 RC columns. Container is of intze type.CONTENTS
Ex. Shaft height is 16.
3. Staging consists of hollow RC shaft of diameter 6.000
. Seismic zone V and hard soil strata
6.28 m. Staging height is 14 m with 4 brace levels. Seismic zone IV and hard soil strata.3 m is resting on ground.4 m above ground level.
1. Seismic zone IV and hard soil strata Steel tank of diameter 12 m and height 10. Container is circular in shape.3 m with 3 brace levels. No. Concrete tank of diameter 14 m and height 7 m is resting on ground.5 m is resting on ground. Staging consists of 6 RC columns.
1. Seismic zone IV and soft soil strata Rectangular concrete tank with plan dimension 20 x 10 m and height of 5.
designer has to refer the provisions of previous version of IS 1893 i. These provisions are only for elevated tanks and ground supported tanks are not considered. For seismic design of liquid storage tanks. there are many limitations in the provisions of IS 1893:1984. This Guidelines is written in a format very similar to that of IS code and in future.. effect of sloshing mode of vibration is not included in IS 1893:1984. is also
. present Guidelines is prepared to help designers for seismic design of liquid storage tanks. compared with present international practice for seismic design of tanks. Moreover. which deals with General Provisions and Buildings has been published by Bureau of Indian Standards.1 –
In the fifth revision IS 1893 has been split into following five parts: Part 1: General provisions and buildings Part 2: Liquid retaining tanks Part 3: Bridges and retaining walls Part 4: Industrial structures including stack like structures Part 5: Dams and embankments Among these only Part 1. some of which have been discussed by Jain and Medhekar (1993. explaining the rationale behind a particular clause. to be consistent with the present international practice of code writing. Thus. one finds that at present in India there is no proper Code/Standard for seismic design of liquid storage tanks. BIS may as well consider adopting it as IS 1893 (Part 2). 1994). for design of structures other than buildings. a commentary. Even for elevated tanks. – Introduction
0. Thus.e. IS 1893:1984. IS 1893:1984 has very limited provisions. In view of non-availability of a proper IS code/standard on seismic design of tanks.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
PROVISIONS 0. Moreover.
provided. a simplified hydrodynamic pressure distribution is also suggested for stress analysis of the tank wall. c) Bracing beam flexibility is explicitly included in the calculation of lateral stiffness of tank staging. in Part 2. These examples are aimed at explaining use of various clauses given in Guidelines and they may not necessarily cover all the aspects involved in the design of tanks
0. d) The effect of convective hydrodynamic pressure is included in the analysis. the single degree of freedom idealization of tank is done away with. instead a two-degree of freedom idealization is used for analysis.
. Unless otherwise stated. f) Effect of vertical ground acceleration on hydrodynamic pressure is considered. in this Guidelines following important provisions and changes have been incorporated: a) Analysis of ground supported tanks is included. Part 1 of this document contains Guidelines and Commentary. In order to explain the use of this Guidelines. These examples include various types of elevated and ground supported tanks. this guideline shall be read necessarily in conjunction with IS: 1893 (Part 1): 2002. e) The distribution of impulsive and convective hydrodynamic pressure is represented graphically for convenience in analysis. six explanatory examples solved using this Guidelines have been given.3 –
As compared to provisions of IS 1893:1984. b) For elevated tanks.
This Guidelines contains provisions on liquid retaining tanks. wherever necessary.
S. Housner. R.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
0. European Committee for Standardization. No. “Proposed provisions for aseismic design of liquid storage tanks: Part II – Commentary and examples”. U.. M. 2. D. Journal of Structural Engineering. M.. 167-175. “Codal provisions on design seismic forces for liquid storage tanks: a review”. Brussels. 3.K. and Jain. USA. Jain. 4. “Seismic design of liquid containing concrete structures”. S. J. IITK-GSDMA-EQ-01V1.K. and Jain. 7. Atomic Energy Commission. C.. Nuclear Reactors and Earthquakes. Vol. Indian Institute of Technology. 1963a. “Dynamic analysis of fluids in containers subjected to acceleration”. 20. IITK-GSDMA-EQ-04-V1. S..C. 4.. “The dynamic behavior of water tanks”. W. M. K.0.3. 8. Vol. S. 381-387. Kanpur. 2. 20. K. assistance has been derived from the following publications: 1. 3. 6. Part 1. 2004a. R. No.4 –
In the formulation of this Guidelines. Bulletin of Seismological Society of America. O. N. W. tanks and pipelines”. 1993. design of Recommendations the New Zealand et al. 2004b. Report No. No. 5. Eurocode 8. “Design provisions for earthquake resistance of structures. Rai. Journal of Structural Engineering. Vol. S. 9. C.0. 53. TID 7024. Report No. Priestley. and Medhekar. “Codal provisions on seismic analysis of liquid storage tanks: a review” Report No. American Concrete Institute. 1963b. Jain. G. 1998..General rules and Part 4 – Silos. Jaiswal. 1986. G. D. “Seismic storage tanks”... Washington D. S. 119-128. ACI 350. Kanpur. 2001. Indian Institute of Technology. 1994. of a study group of National Society for
. O. Rai. S. “Proposed provisions for aseismic design of liquid storage tanks: Part I – Codal provisions”. Jaiswal. Farmington Hill. Housner. MI.. and Medhekar.
In the formulation of this Guidelines due weightage has been given to international coordination among the standards and practices prevailing in different countries in addition to relating it to the practices in this country. “Design provisions for earthquake resistance of structures. Building Seismic Safety Council. A.
. AWWA D-115. USA. Brussels. 1995. Part 1General rules and Part 4 – Silos. 1998.
C0. MI. 3. N. ASCE. FEMA 368. 2000. American Concrete Institute. American Water Works Association. 6. “Welded storage tanks for oil storage”. 2. USA. 1998. Veletsos. USA. USA.and strandwound circular. American Water Works Association.. USA. S. API 650.Y. Farmington Hill. 1997. Colorado. 5. “Circular prestressed concrete water tanks with circumferential tendons”.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
Earthquake Engineering. USA. ACI 371-98 . Washington D.. USA. “Seismic design of liquid containing concrete structures”.3. Farmington Hill. 8. ACI 350. American Water Works Association.. National Institute of Building Sciences.5 –
Following are some of the international standards and codes of practices which deal with seismic analysis of liquid storage tanks: 1. AWWA D-103. AWWA D-110. and construction of concrete-pedestal water Towers”. 9. Colorado. AWWA D-100. 1996. American Concrete Institute. 1995. “NEHRP recommended provisions for seismic regulations for new buildings and other structures”. “Welded steel tanks for water storage”. USA. 1984. “Seismic response and design of liquid storage tanks”. Colorado. C. 4. 443461. Guidelines for the seismic design of oil and gas pipeline systems. “Factory-coated bolted steel tanks for water storage”. prestressed concrete water tanks”. MI. European committee for Standardization. design .
0. 1998. Technical Council on Lifeline Earthquake Engineering. Colorado. tanks and pipelines”. “ Guide for the analysis. 255-370. 7. 10. American Petroleum Institute. Eurocode 8. 2001. “Wire. American Water Works Association.
1986. Wellington. The number of significant places retained in the rounded value should be the same as that of the specified value in this Guidelines.7 –
For the purpose of deciding whether a particular requirement of this Guidelines is complied with. M J N.
0. “Code of practice for concrete structures for the storage of liquids”. Falls Church. Nagpur and several other organizations. Virginia. Visvesvaraya National Institute of Technology. Gandhinagar through World Bank finances. et al. Priestley.6 –
In the preparation of this Guidelines considerable help has been given by the Indian Institute of Technology Kanpur. 11. In particular.8 –
The units used with the items covered by the symbols shall be consistent throughout this Guidelines. the final value observed or calculated expressing the result of a test or analysis. USA.
0. NZS 3106.
. “Seismic design of storage tanks”. the draft was developed through the project entitled Review of Building Codes and Preparation of Commentary and Handbooks awarded to IIT Kanpur by the Gujarat State Disaster Management Authority (GSDMA). 1986. 12. International Building Code International Code Council.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
10. Recommendations of a study group of the New Zealand National Society for Earthquake Engineering. IBC 2000. unless specifically noted otherwise. Standards Association of New Zealand. shall be round off in the accordance with IS: 2-1960..
This Guidelines describes procedure for analysis of liquid containing ground supported and elevated tanks subjected to seismic base excitation.1 –
This Guidelines covers ground supported liquid retaining tanks and elevated tanks supported on staging.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
COMMENTARY C1.
. Guidance is also provided on seismic design of buried tanks. The procedure considers forces induced due to acceleration of tank structure and hydrodynamic forces due to acceleration of liquid.
PROVISIONS 2. Part 1 : General Provisions and Buildings Code of Practice for Concrete Structures for the Storage of Liquids Code of practice for Earthquake Resistant Design and Construction of Buildings Criteria for Design of RCC Staging for Overhead Water Tanks Ductile detailing of reinforced concrete structures subjected to seismic forces – Code of practice are
COMMENTARY C2. – References
The following Indian Standards necessary adjuncts to this Guidelines: IS No. 456: 2000 1893 (Part 1): 2002 3370: 1967 4326: 1993 11682: 1985 13920: 1993 Title Code of Practice for plain and Reinforced Concrete Criteria for Earthquake Resistant Design of Structures.– References
COMMENTARY C3. bi ac. – Symbols
Deflection of wall of rectangular tank.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
PROVISIONS 3. in the direction of seismic force Maximum sloshing wave height Inner diameter of circular tank Modulus of elasticity of tank wall Response quantity due to earthquake load applied in xdirection Response quantity due to earthquake load applied in ydirection
Acceleration due to gravity Maximum depth of liquid Height of combined center of gravity of half impulsive mass of Refer Figure C-2 and Clause 4.2
.1. – Symbols
The symbols and notations given below apply to the provisions of this Guidelines: ai. on the vertical center line at a height h when loaded by a uniformly distributed pressure q.
1. hc . This implies that a weight of 9. along the direction of seismic force Inside length of rectangular tank parallel to the direction of seismic force Total mass of liquid in tank Mass of base slab / plate Convective mass of liquid Impulsive mass of liquid In SI unit. while the weight is in Newton (N). Refer Clause 4.81 N has a mass of 1 kg.
Lateral stiffness of elevated tank staging Length of a strip at the base of circular tank. Refer Figure 8a Refer Figure C-3
. hi∗ are described in Figure C-1a to 1d
Moment of inertia of a strip of unit width of rectangular tank wall for out of plane bending. mass is to be specified in kg.3. hi .2 Dynamic coefficient of earth pressure
l.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
Height of convective mass above bottom of tank wall ( without considering base pressure ) Height of impulsive mass above bottom of tank wall ( without considering base pressure) Structural height of staging. measured from base of staging Importance factor given in Table 1 of this code
∗ hc . Weight (W) is equal to mass (m) times acceleration due to gravity (g). measured from top of foundation to the bottom of container wall Height of center of gravity of roof mass above bottom of tank wall Height of center of gravity of wall mass above bottom of tank wall Height of convective mass above bottom of tank wall (considering base pressure) Height of impulsive mass above bottom of tank wall (considering base pressure) Height of center of gravity of the empty container of elevated tank.
Total overturning moment at base Bending moment in convective mode at the bottom of tank wall Overturning moment in convective mode at the base Bending moment in impulsive mode at the bottom of tank wall Overturning moment in impulsive mode at the base Maximum hydrodynamic pressure on wall Convective hydrodynamic pressure on tank base Convective hydrodynamic pressure on tank wall Impulsive hydrodynamic pressure on tank base Impulsive hydrodynamic pressure on tank wall Hydrodynamic pressure on tank wall due to vertical ground acceleration Pressure on wall due to its inertia Uniformly distributed pressure on one wall of rectangular tank in the direction of ground motion Refer Clause 4.2.1.9.2 Refer Clause 4.10.2.2 Refer Clause 4.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
Refer Clause 4.3.3.1.2 and Figure C-2 qi qc Impulsive hydrodynamic force per unit length of wall Convective hydrodynamic force per unit length of wall Refer Clause 4.3
Refer Clause 4.9.2
while weight density will be in Newton N/m3 Δ Deflection of center of gravity of tank when a lateral force of magnitude (ms+mi)g is applied at the center of gravity of tank
.5 of this code
Base shear in convective mode Base shear in impulsive mode Horizontal distance in the direction of seismic force.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
g ) Average response acceleration coefficient as per IS 1893 (Part 1): 2002 and Clause 4. of a point on base slab from the reference axis at the center of tank Vertical distance of a point on tank wall from the bottom of tank wall Seismic zone factor as per Table 2 of IS 1893 (Part 1): 2002
In SI Units. mass density will be in kg/m3.
i. Based on numerous analytical. In order to include the effect of hydrodynamic pressure in the analysis. – Provisions for Seismic Design
4. impulsive pressure will increase and connective pressure will decrease.
4. simple spring mass models of tank-liquid system have been developed to evaluate hydrodynamic forces. the liquid exerts impulsive and convective hydrodynamic pressure on the tank wall and the tank base in addition to the hydrostatic pressure..1 . This mass is termed as convective liquid mass and it exerts convective hydrodynamic pressure on tank wall and base. A qualitative description of impulsive and convective hydrodynamic pressure distribution on tank wall and base is given in Figure C-1. vertical columns and shaft are present inside the tank.1 –
Dynamic analysis of liquid containing tank is a complex problem involving fluid-structure interaction. These hydrodynamic forces are evaluated with the help of spring mass model of tanks.– Provisions for Seismic Design
C4. tank wall and liquid are subjected to horizontal acceleration.e. these two liquid masses are to be suitably represented. However.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
PROVISIONS 4. Sometimes.
. These elements cause obstruction to sloshing motion of liquid.
COMMENTARY C4. This mass is termed as impulsive liquid mass which accelerates along with the wall and induces impulsive hydrodynamic pressure on tank wall and similarly on base.2 . it is reasonable to expect that due to presence of such obstructions. no study is available to quantify effect of such obstructions on impulsive and convective pressures. In the presence of such obstructions. impulsive and convective pressure distributions are likely to change. Liquid mass in the upper region of tank undergoes sloshing motion. impulsive mass and convective mass. The parameters of this model depend on geometry of the tank and its flexibility. tank can be idealized by an equivalent spring mass model.Spring Mass Model for Seismic Analysis
When a tank containing liquid vibrates. Thus.2 – Spring Mass Model for Seismic Analysis
When a tank containing liquid with a free surface is subjected to horizontal earthquake ground motion. total liquid mass gets divided into two parts. The liquid in the lower region of tank behaves like a mass that is rigidly connected to tank wall. At present. numerical. which includes the effect of tank wall – liquid interaction.General
Hydrodynamic forces exerted by liquid on tank wall shall be considered in the analysis in addition to hydrostatic forces. In spring mass model of tank-liquid system. and experimental studies.
hi is the height at which the resultant of impulsive hydrodynamic pressure on wall is located from the bottom of tank wall.
C4.2. impulsive mass of liquid. are schematically described in Figures C-1a and C-1b. hi* is the height at which the resultant of impulsive pressure on wall and base is located from the bottom of tank wall. Similarly.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
4. mi will act at a height of hi and if effect of base pressure is considered.1 – Ground Supported Tank
4. while.2. mc is attached to the tank wall at height hc (or hc*) by a spring of stiffness K c . Heights hi and hi*. On the other hand. Heights hc and hc* are described in Figures C-1c and C-1d . mi is rigidly attached to tank wall at height hi (or hi* ).1 –
Ground supported tanks can be idealized as spring-mass model shown in Figure 1.
. mi will act at hi*. hc* is the height at which resultant of convective pressure on wall and base is located.1. convective mass. In the spring mass model of tank. Similarly.2. The impulsive mass of liquid.2. hc. if effect of base pressure is not considered. is the height at which resultant of convective pressure on wall is located from the bottom of tank wall. Thus.1.1 –
The spring mass model for ground supported tank is based on work of Housner (1963a).1 – Ground Supported Tank
parameters corresponding to tanks with rigid wall are recommended for all types of tanks. then impulsive and convective masses will change. mc . hi . hi∗ . If vertical columns and shaft are present inside the tank. values of hi* and hc* can be greater than h (Refer Figures 2b and 3b) due to predominant contribution of hydrodynamic pressure on base. Hence. (2004b)).IITK-GSDMA Guidelines for seismic design of liquid storage tanks
4. difference in the parameters ( mi .2.2 – Circular and Rectangular Tank The parameters of spring mass model depend on tank geometry and were originally derived by Housner (1963a). it is reasonable to expect that with the presence of such obstructions. In absence of more detailed analysis of such tanks. while steel tanks are considered as tanks with flexible wall. the difference is usually small (2 to 3%).
Further. It may also be noted that for certain values of h/D ratio.1. mc . Though.
. however. hi and hc account for hydrodynamic pressure on the ∗ tank wall only. The value of hi∗ and hc shall be used to calculate overturning moment at the base of tank. flexibility of soil or elastic pads between wall and base do not have appreciable influence on these parameters. Moreover. The parameters shown in Figures 2 and 3 are slightly different from those given by Housner (1963a). no study is available to quantify effect of such obstructions.2 – Circular and Rectangular Tank
For circular tanks. hc .
∗ hc . Generally. In the literature. hi . hi∗ .1. Hence in the present code. concrete tanks are considered as tanks with rigid wall. One should also note that for shallow tanks.2. parameters mi . sum of impulsive mass (mi) and convective mass (mc) will not be equal to total mass (m) of liquid. and have been taken from ACI 350. hc and K c shall be obtained from Figure 2 and for rectangular tanks these parameters shall be obtained from Figure 3. hi∗ and hc account for hydrodynamic pressure on tank wall and the tank base. an equivalent cylindrical tank of same height and actual water mass may be considered to obtain impulsive and convective masses. impulsive mass will increase and convective mass will decrease. as an approximation. Expressions for these parameters are given in Table C-1. Spring mass models for tanks with flexible walls are more cumbersome to use. the value of hi and hc shall be used to calculate moment due to hydrodynamic pressure at the bottom of the ∗ tank wall.3 (2001). This difference is attributed to assumptions and approximations made in the derivation of these quantities. springmass models for tanks with flexible walls are also available (Haroun and Housner (1981) and Veletsos (1984)).
∗ hc and K c ) obtained from rigid and flexible tank models is not substantial (Jaiswal et al. It may be mentioned that these parameters are for tanks with rigid walls.
hi = 0.45
for h / D > 1.5 − 0.16 sinh ⎜ 3.68 ⎟ h D⎠ ⎝
K c = 0.23 h m D
mc = 0.866 ⎟ h⎠ ⎝
mg h⎞ ⎛ tanh 2 ⎜ 3.0 hc D⎠ ⎝ =1− h h⎞ h ⎛ 3.866 ⎟ h⎠ ⎝ D 0.33
h⎞ ⎛ tanh⎜ 3.75
hi = 0.264 m
h⎞ ⎛ tanh⎜ 3.01 L⎠ ⎝ h h⎞ ⎛ 3.16 ⎟ − 1.68 ⎟ D D⎠ ⎝
h⎞ ⎛ cosh⎜ 3.68 ⎟ mc D⎠ ⎝ = 0.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
mi = m D⎞ ⎛ tanh⎜ 0.375 h
= 0.16 ⎟ L L⎠ ⎝
K c = 0.866
D⎞ ⎛ 2 tanh⎜ 0.75
0.866 ⎟ h⎠ ⎝
0.16 ⎟ h L⎠ ⎝
.16 ⎟ L L⎠ ⎝
h⎞ ⎛ cosh⎜ 3.866 h
L⎞ ⎛ tanh⎜ 0.16 ⎟ L⎠ ⎝ h L
h⎞ ⎛ cosh⎜ 3.09375 h/D
for h / D ≤ 0.866
L⎞ ⎛ 2 tanh⎜ 0.68 ⎟ − 1.33
= 0.01 hc * D⎠ ⎝ = 1− h h⎞ h ⎛ 3.09375 h/ L
for h / L ≤ 0.5 − 0.866 ⎟ h⎠ ⎝ L 0.45
= 0.68 sinh⎜ 3.836
mg h⎞ ⎛ tanh 2 ⎜ 3.125
for h / L > 1.75 for h / L > 0.75 for h / D > 0.0 L⎠ ⎝ h h⎞ ⎛ 3.375 h = 0.125
0.68 sinh⎜ 3.68 ⎟ D D⎠ ⎝
h⎞ ⎛ cosh⎜ 3.16 sinh⎜ 3.16 ⎟ − 2.68 ⎟ − 2.
0 0 0.5 h/D 1 1.5
1.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
0.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
0.5 h/L 1 1.5 h/L 1 1.5 2
2 . (1986)).3 –
In Figure 4c. this 2-DOF system may have nonproportional damping. ∗ parameters mi .Elevated Tank
4.2. Mass of container comprises of mass of roof slab.2.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
For elevated tanks. Two mass model for elevated tank was proposed by Housner (1963b) and is being commonly used in most of the international codes.2.2. hc and K c shall be obtained from Figure 2.2. In this context it shall be noted that due to different damping of impulsive and convective components.
4. and floor beams.2. However.
. mc . If impulsive and convective time periods are not well separated. This method will be satisfactory for design purpose.2 –
For elevated tanks with circular container. gallery. if the ratio of the period of the two uncoupled systems exceeds 2. hc .2.2 –
Please refer commentary of Clause 4.2.1. For elevated tanks with rectangular container.
C4. hi∗ . Hence.2. one representing the impulsive plus structural mass behaving as an inverted pendulum with lateral stiffness equal to that of the staging. the two degree of freedom system of Figure 4c can be treated as two uncoupled single degree of freedom systems (Figure 4d). floor slab. 1983). Staging acts like a lateral spring and one-third mass of staging is considered based on classical result on effect of spring mass on natural frequency of single degree of freedom system (Tse et al.1 –
Elevated tanks (Figure 4a) can be idealized by a two-mass model as shown in Figure 4c.2. m s is the structural mass and shall comprise of mass of tank container and one-third mass of staging.
C4. which was used in IS 1893: 1984.3 –
Structural mass ms.2. for most elevated tanks it is observed that the two periods are well separated.2. then coupled 2-DOF system will have to be solved using elementary structural dynamics.2. Ks and the other representing the convective mass with a spring of stiffness.
C4.. Kc. container wall. the system may be considered as two uncoupled single degree of freedom systems.5 (Priestley et al.2. hi .2.2.4 –
The response of the two-degree of freedom system can be obtained by elementary structural dynamics.2 for effect of obstructions inside the container on impulsive and convective mass. Hence a two-mass idealization of the tank is more appropriate as compared to a onemass idealization. includes mass of container and one-third mass of staging. these parameters shall be obtained from Figure 3.2.
4.2 – Elevated Tank
C4.2.1 –
Most elevated tanks are never completely filled with liquid.2.
∗ hi .IITK-GSDMA Guidelines for seismic design of liquid storage tanks
4. mc . Eurocode 8 (1998) has suggested equivalent circular tank approach. Similarly. hi .2. hc .
∗ hc .
Parameters of spring mass models (i. equivalent circular tank is to be considered.
C4. hc and K c of equivalent circular tank shall be used. hc and K c ) are available for circular and rectangular tanks only. mi . For tanks of other shapes. mc .. truncated conical shape). and mi .2. hi∗ .e.3 –
For tank shapes other than circular and rectangular (like intze. hi∗ . for tanks of truncated conical shape. the value of h / D shall correspond to that of an equivalent circular tank of same volume and diameter equal to diameter of tank at top level of liquid. Joshi (2000) has shown that such an approach gives satisfactory results for intze tanks.
2.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
(d) Equivalent uncoupled system (Refer Clause 4.2.4)
However. 6b and 6c). Various types of flexible connections between wall and base slab described in Figure 6 are taken from ACI 350. wherein wall is rigidly connected with the base slab. thickness of tank wall at 1/3rd height from the base should be used in the expression for impulsive time period. flexibility of pads affects the impulsive mode time period.3.
The expression for the impulsive mode time period of circular tank is taken from Eurocode 8 (1998).2–Ground Supported Rectangular Tank
Eurocode 8 (1998) and Preistley et al.3 – Time Period
C4.3.1. time period of impulsive mode of vibration.3 – Time Period
4. More information on exact expression for time period of circular tank may be obtained from Veletsos (1984) and Natchigall et al. time period of impulsive mode of vibration Ti . wherein wall is rigidly connected with the base slab (Figure 6a.3 (2001). (2003). (1986) also specify the same expression for obtaining time period of rectangular tank. it may be mentioned that this expression is derived based on the assumption that tank mass is quite small compared to mass of fluid. D = Inner diameter of circular tank. and flexible pads are used between the wall and the base slab (Figure 6d to 6f). In some concrete tanks. and
ρ = Mass density of liquid.3.1. steel tanks with step variation of thickness).
NOTE: In some circular tanks. wall is not rigidly attached to the base slab. is given by
.2 – Ground Supported Rectangular
C4. is given by
C4. Value of Ci can be obtained from Figure 5. t
= Thickness of tank wall.1 – Ground Supported Circular Tank
The coefficient Ci used in the expression of time period Ti and plotted in Figure 5. which provides more information on effect of flexible pads on impulsive mode time period. In case of tanks with variable wall thickness (particularly.1 – Impulsive Mode
4. In such cases. time period evaluation may properly account for the flexibility of wall to base connection.) For tanks with flexible connections with base slab. Ti in seconds. h = Maximum depth of liquid.3. Basically this expression was developed for roofless steel tank fixed at base and filled with water.
4.1 – Ground Supported Circular Tank
For a ground supported circular tank.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
4.3h / D + 0. this may also be used for other tank materials and fluids.3.
E = Modulus of elasticity of tank wall. (Different types of wall to base slab connections are described in Figure 6.
For a ground supported rectangular tank.1. in seconds. This condition is usually satisfied by most of the tanks. Expression for Ti given in this section is applicable to only those circular tanks in which wall is rigidly attached to base slab.46 − 0.067(h / D) 2 ⎝
Ci = Coefficient of time period for impulsive mode. Further.3. wall may have flexible connection with the base slab. is given by
⎛ 1 Ci = ⎜ ⎜ h / D 0.1.1 – Impulsive Mode
where I w = 3EI w 12
Inside width of tank. and B =
1. ACI 350. the deflection of wall shall be obtained using appropriate method. d for tanks without roof. P = q h (Figures C-2b and C-2c). Thus. for a tank with wall of uniform thickness. one can find the deflection. and mass of one wall ( m w ). For tanks with roofs and/or tanks in which walls are not very long. which is subjected to concentrated load. by considering wall strip of unit width and height h . assuming that wall takes pressure q by cantilever action.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
h is the height of combined center of gravity of half impulsive mass of liquid (mi /2).0
Figure C-2 Description of deflection d. when loaded by uniformly distributed pressure of intensity q. of rectangular tank wall
. h= mi + mw 2
mw = Mass of one tank wall perpendicular to the direction of seismic force.
The above approach will give quite accurate results for tanks with long walls (say.
1. d can be obtained by assuming wall to be free at top and fixed at three edges (Figures C-2a). As per this approach.0
1. d. one can obtain d as follows:
mi h h i + mw 2 2 .
⎛ mi ⎞ + mw ⎟g ⎜ 2 ⎠ .0 × t 3 P ( h) 3 . deflection.
center-line at a height of h . q=⎝ Bh
For tanks without roof. length greater than twice the height).3 (2001) and NZS 3106 (1986) have suggested a simpler approach for obtaining deflection.
in addition to the effect of flexural deformation. NOTE: The flexibility of bracing beam shall be considered in calculating the lateral stiffness. The impulsive mass mi acts at a height of hi from top of floor slab. and K s = lateral stiffness of staging. 1992).IITK-GSDMA Guidelines for seismic design of liquid storage tanks
4. the lateral stiffness can be evaluated by computer analysis or by simple procedures (Sameer and Jain. the effect of shear deformation may be included while calculating the lateral stiffness of staging.
. For elevated tanks with moment resisting type frame staging.
Lateral stiffness of the staging is the horizontal force required to be applied at the center of gravity of the tank to cause a corresponding unit horizontal displacement. or by established structural analysis method. K s of elevated momentresisting frame type tank staging. which may cause eccentricity in otherwise symmetrical staging configuration.3 – Elevated Tank
m s = mass of container and one-third mass of staging.3.1. is given by
C4. For elevated tanks with shaft type staging. due consideration shall be given to modeling of such parts as spiral staircase. Δ is deflection of center of gravity of tank when a lateral force of magnitude (ms + mi)g is applied at the center of gravity of tank.3. Center of gravity of tank can be approximated as combined center of mass of empty container and impulsive mass of liquid. In the analysis of staging. Ti in seconds.1.3 – Elevated Tank
Time period of impulsive mode.
.5 h/D 1 1.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
Since the expressions for mc and Kc are known. L is the inside length of tank parallel to the direction of loading.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
4.2 are mathematically same.16 tanh (3.2 – Convective Mode
4.2. in seconds. Tc in seconds. is given by
Cc = 2π 3. and D = Inner diameter of tank. elastic pads.
4.68h / D )
(a) Circular Tank: Time period of convective mode.2.68 tanh (3.3.
(b) Rectangular Tank: Time period of convective mode of vibration.2 –
Expressions given in Clause 4. Value of C c can be obtained from Figure 5. For rectangular tank.3. is given by
Cc = Coefficient of time period for convective mode. the expression for Tc can be alternatively expressed as:
C4. Value of C c can be obtained from Figure 7. as described in
.2 – Convective Mode
C4. and L = Inside length of tank parallel to the
Convective mode time period expressions correspond to tanks with rigid wall.1 and 4. The expressions for convective mode time period of circular and rectangular tanks are taken from ACI 350.3. It is well established that flexibility of wall.3. which are based on work of Housner (1963a). Tc in seconds.1 –
Time period of convective mode.2.16(h / L))
Tc = C c L / g where Cc = Coefficient of time period for convective mode.2.3. and soil does not affect the convective mode time period. is given by
The values of m c and K c can be obtained from Figures 2a and 3a respectively.3 (2001).3. The coefficients Cc in the expressions for convective mode time period plotted in Figure 5 and 7 are given below: (a) For circular tank:
Cc = 2π 3.2. for circular and rectangular tanks.3.
Soil structure interaction has two effects: Firstly. Increase in damping is mainly due to radial damping effect of soil media.5
1. effect of flexibility of soil may be considered while evaluating the time period. it elongates the time period of impulsive mode and secondly it increases the total damping of the system.
Figure C-3 Description of length. (1986).IITK-GSDMA Guidelines for seismic design of liquid storage tanks
direction of seismic force. soil flexibility may affect impulsive mode time period. This simple approach has been used in Eurocode 8 (1998) and Priestley et al. soil flexibility does not affect the convective mode time period.
C4. Generally.3 –
For tanks resting on soft soil. B of rectangular tank
4. A simple but approximate approach to obtain the time period of impulsive mode and damping of tank-soil system is provided by Veletsos (1984). However.
Figure C-3.3. L and breadth.3.
5. actual seismic forces are reduced by a factor R to obtain design forces.0. Its value depends on functional need.
4.75 is assigned to tanks used for storing hazardous materials. energy absorbing capacity of buildings is much higher than that of tanks.5% of the critical. is meant to ensure a better seismic performance of important and critical tanks.1 to 4. in tanks. Generally. Highest value of I =1. Since release of these materials can be harmful to human life. value of I is kept as 1. In this guideline. For tanks used in water distribution systems.1 to 4. ground supported tanks and elevated tanks with shaft type staging have comparatively low redundancy. due to presence of non structural elements like masonry walls. All the international codes specify much lower values of R for tanks than those for buildings. Ah shall be obtained by the following expression.5. and ductility of structure.4 of this guideline. consequences of failure.4
C4. value of R for tanks needs to be lower than that for buildings. and post earthquake utility of the tank. This reduction depends on overstrength. liquid containing tanks posses low overstrength. In buildings. such non structural components are not present. Buildings with frame type structures have high redundancy.
C4. and ductility as compared to buildings. Moreover. and Sa/g = Average response acceleration coefficient as given by Figure 2 and Table 3 of IS 1893(Part 1): 2002 and subject to Clauses 4. Response reduction factor (R).4 – Damping
Damping in the convective mode for all types of liquids and for all types of tanks shall be taken as 0. Based on these considerations. Less important tanks are assigned I = 1. liquid containing tanks are put in three categories and importance factor to each category is assigned (Table 1). represents ratio of maximum seismic force on a structure during specified ground motion if it were to remain elastic to the design seismic force. Damping in the impulsive mode shall be taken as 2% of the critical for steel tanks and 5% of the critical for concrete or masonry tanks.4 – Damping
For convective mode damping of 0. and fire station buildings in IS 1893 (Part 1):2002.5.5 – Design Horizontal Seismic Coefficient
Design horizontal seismic coefficient.5 – Design Horizontal Seismic Coefficient
Importance factor (I). non structural components substantially contribute to overstrength.5% is used in most of the international codes. Thus.
.5. redundancy. subject to Clauses 4. telephone exchange.
R = Response reduction factor given in Table 2 of this guideline. which is same as value of I assigned to hospital.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
4. the highest value of I is assigned to these tanks. redundancy. As
Z = Zone factor given in Table 2 of IS 1893 (Part 1): 2002. I = Importance factor given in Table 1 of this guideline.5.
All other tanks with no risk to life and with negligible consequences to environment.e. it may also be noted that value of R for tanks varies from 3. It is seen that base shear coefficient match well for highest and lowest value of R.5
1. Further.5 and lowest value is 1.e.7 sec. for an elevated tank on frame type staging (i. I Type of liquid storage tank I
an example. non-volatile material. values of R used in IBC 2000 are shown in Table C-2.Values of importance factor. Rai 2002).0 whereas. For elevated tanks on frame type staging. base shear coefficient for tanks is compared. Elevated tanks are inverted pendulum type structures and hence. 2004b). The rationale behind these values of R can be seen from Figures C-4a and C-4b.0
Note.0.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
Table 1 – Importance factor. value of R is 3. an exhaustive review of response reduction factors used in various international codes is presented. Lower value of R for RC shaft is due to its low redundancy and poor ductility (Zahn.5. 1999. base shear coefficients (i.5 and for elevated tanks on RC shaft. In Figure C-4a. It is seen that base shear coefficient from IS 1893 (Part 1):2002 and IBC 2000 compare well.
. Tanks of post earthquake importance. particularly up to time period of 1.. society and economy. R = 1.0 to 1. low inflammable petrochemicals etc. This comparison is done for the highest as well as lowest value of R from IBC 2000 and present code. In Table 2. (2004a.3. ratio of lateral seismic force to weight) obtained from IBC 2000 and IS 1893 (Part 1):2002 is compared for a building with special moment resisting frame. Thus.8. This comparison is done for the most severe seismic zone of IBC 2000 and IS 1893 (Part 1):2002. It is seen that for a building with special moment resisting frame value of R is 8.
Tanks used for storing drinking water. In this study. the highest value of R is 2. moment resisting frames being used in staging of these tanks are assigned much smaller R values than moment resisting frames of building and industrial frames. and intended for emergency services such as fire fighting services.. Values of R given in the present guideline (Table 2) are based on studies of Jaiswal et al. the specified values of R are quite reasonable and in line with international practices. response reduction factor is R = 2. braced legs). I given in IS 1893 (Part 4) may be used where appropriate. In Figure C-4b.
These R values shall not be misunderstood for those given in other parts of IS 1893 for building and industrial frames.3 1.e.0 2.5
a) Fixed or hinged/pinned base tank (Figures 6a.3 1.5 2. ordinary moment resisting frame (OMRF) b) Frame conforming to ductile detailing.e.0 2. 6f)
Table 2 – Response reduction factor. i. R Type of tank Elevated tank Tank supported on masonry shaft R
RC shaft with two curtains of reinforcement. 6c) b) Anchored flexible base tank (Figure 6d) c) Unanchored contained or uncontained tank (Figures 6e. These tanks are not allowed in seismic zones IV and V. values of R can be interpolated between ground supported and underground tanks based on depth of embedment.5
These R values are meant for liquid retaining tanks on frame type staging which are inverted pendulum type structures.5
4. each having horizontal and vertical reinforcement
1.. special moment resisting frame (SMRF)
.5 1. i.. 6b. For partially buried tanks.8 2.8
a) Frame not conforming to ductile detailing.5 2.
for a building with special moment resisting frame. I = 1. (From Jaiswal et.2 0.08
F v = 1. S = 0. site class D)
Figure C-4a Comparison of base shear coefficient obtained from IBC 2000 and IS 1893 (Part 1):2002.4 0. R = 8. F = 1.6.5.5
Present code (Highest value of R = 2..1
IBC 2000 (S =1. I = 1.5. for tanks with highest and lowest values of R.5
IBC 2000 (Highest value of R = 3) IBC 2000 ( Low est value of R = 1.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
0..6 0.5
1.4 to bring them to working stress level (From Jaiswal et.1 0 0 0.3 0. al. 2004a)
0.7 0. al.soft soil)
Figure C-4b Comparison of base shear coefficient obtained from IBC 2000 and present code.5)
1. 2004a)
.8 0.5 ) Present code (Low est value of R = 1.02
0. IBC values are divided by 1. R = 5.36.5 2 Time Period (S)
IS 1893 (Part I) :2002 (Z = 0.04
0 8.0 3.5
4.5. and convective (Ah)c modes.1 –
Design horizontal seismic coefficient.
C4.0 3.5 3.0 2.5. whereas. AWWA D-103 and AWWA D-115 use same value of R for impulsive and convective modes.
.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
8.0 1. Ah will be calculated separately for impulsive (Ah)i. are applicable to design horizontal seismic coefficient of impulsive as well as convective mode. given in Table 2 of this code.1 –
The values of R. in the present provision.0 3. same value of R have been proposed for impulsive and convective components. AWWA D-100. It may be noted that amongst various international codes.0 2.0 2. ACI 350.3 and Eurocode 8 suggest value of R =1 for convective mode.0 5.0 3. The issue of value of R for convective component is still being debated by researchers and hence to retain the simplicity in the analysis.
measured from top of footing of staging to the bottom of tank wall.3 –
C4.7.
4. the design shall be worked out for tank empty and tank full conditions.
C4.4 –
For tank empty condition. at the base of the staging is given by M i = (Ah )i m i hi + hs + m s hcg g
C4.2 – Elevated Tank
Overturning moment in impulsive mode.3 –
See commentary of Clause 4. and tb = thickness of base slab/plate. which includes mass of empty container and one-third mass of staging is considered to be acting at the center of gravity of empty container.
where hs = Structural height of staging.3
4. convective mode of vibration will not be generated.7. it is unlikely that tank empty condition will become critical for ground supported tanks. Thus. empty elevated tank has to be analyzed as a single degree of freedom system wherein.7.7. and hcg = Height of center of gravity of empty container.7. However. Base of staging may be considered at the top of footing.2 – Elevated Tank
Structural mass ms.4 –
For elevated tanks.7. ground supported tanks shall also be analysed for tank empty condition. measured from top of footing.
. As such.6. being very rigid. mass of empty container and one-third mass of staging must be considered.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
M * c = ( A h ) c m c ( hc * + t b ) g where mb = mass of base slab/plate.
Different components of staging may have different critical directions. horizontal acceleration in diagonal direction (i. ( ELx . -(0.
C4.8.3 ELy).1 –
Base shear and stresses in a particular wall shall be based on the analysis for earthquake loading in the direction perpendicular to that wall.3ELx + ELy). (0.8.3ELx .8.8. most critical direction of loading is along the length of the brace beam. staging components can be designed for either of the following load combination rules: i) ii) 100% + 30% Rule: SRSS Rule:
C4. -(ELx + 0.2 –
For elevated tanks supported on frame type staging.2.
4.0.0.3 –
100% + 30% rule implies following eight load combinations: (ELx + 0.3 –
As an alternative to 4.2 –
For elevated tanks.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
4. the design of staging members should be for the most critical direction of horizontal base acceleration. For some typical frame type staging configurations. 45° to X-direction) turns out to be most critical for axial force in columns. staging components for the critical should be designed direction of seismic force.8.8 – Direction of Seismic Force
C4.3 ELy) ( 0.
4.3 ELx ± ELy
Where.3 ELy and ± 0.ELy) -(0. Sameer and Jain (1994) have discussed in detail the critical direction of horizontal base acceleration for frame type staging.3 ELy ).3ELx + ELy).
C4.ELy)
± ELx ± 0.1 –
Ground supported rectangular tanks shall be analyzed for horizontal earthquake force acting non-concurrently along each of the horizontal axes of the tank for evaluating forces on tank walls.3 ELy) -( ELx .3ELx .
. critical direction of seismic force is described in Figure C-6. ELx is response quantity due to earthquake load applied in x-direction and ELy is response quantity due to earthquake load applied in y-direction.e.8. For brace beam.8. For a staging consisting of four columns.
6 0.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
0.2 0.5 Variation of impulsive and convective bending moment coefficients with height (From Malhotra.8 1
0 0 0. C.4 0.8
0. 2004)
1 – Impulsive Hydrodynamic Pressure
C4.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
4. φ . φ = Circumferential angle. but can have substantial influence on impulsive pressure distribution in tall tanks. on base slab (y = 0) on a strip of length l'. Qiw ( y ) can also be obtained from Figure 9a. x and y and circumferential angle. These expressions are for tanks with rigid walls.1 – Impulsive Hydrodynamic Pressure
The expressions for hydrodynamic pressure on wall and base of circular and rectangular tanks are based on work of Housner (1963a).866 ⎟ h⎠ ⎢ ⎝h⎠ ⎥ ⎝ ⎣ ⎦
ρ = Mass density of liquid. 732 ⎟ h⎠ ⎝ p ib = 0 .9 – Hydrodynamic Pressure
During lateral base excitation.9. Qualitative description of impulsive pressure distribution on wall and base is given in Figure C1b. 866 (Ah )i ρ g h ⎛ l' ⎞ cosh ⎜ 0 . is given by
piw = Qiw ( y ) (A h ) i ρ g h cos φ ⎡ ⎛ y ⎞2 ⎤ D⎞ ⎛ Qiw ( y ) = 0.
4. p iw . from the center of tank.
Impulsive hydrodynamic pressure in vertical direction. is given by
x⎞ ⎛ sinh ⎜ 1 . Wall flexibility does not affect convective pressure distribution.
Coefficient of impulsive hydrodynamic pressure on wall. and strip length l' are described in Figure 8a.. i.e. The effect of wall flexibility on impulsive pressure distribution is discussed by Veletsos (1984). tank wall is subjected to lateral hydrodynamic pressure and tank base is subjected to hydrodynamic pressure in vertical direction (Figure C-1). Vertical and horizontal distances. 866 ⎟ ⎜ h⎟ ⎠ ⎝
x = Horizontal distance of a point on base of tank in the direction of seismic force. and
y = Vertical distance of a point on tank wall from the bottom of tank wall.866 ⎢1 − ⎜ ⎟ ⎥tanh⎜ 0.9.
Lateral hydrodynamic impulsive pressure on the wall.
674 ⎟ D⎠ ⎝ Qcw ( y ) = 0. with h / L being used in place of h/D.2 – Convective Hydrodynamic Pressure
C4.674 ⎟ D⎠ ⎝
The value of Qcw (y ) can also be read from Figure 10a. can also be read from Figure 9b.2 – Convective Hydrodynamic Pressure
The expressions for hydrodynamic pressure on wall and base of circular and rectangular tanks are based on work of Housner (1963a).cos 2 φ⎥ cos φ 3 ⎣ ⎦
y⎞ ⎛ cosh⎜ 3.9.9. Convective pressure in vertical direction. 866 ⎟ h⎠ ⎝ The value of coefficient of impulsive hydrodynamic pressure on base Qib (x ) . on the base slab (y = 0 ) is given by
. Qiw (y ) is same as that for a circular tank and can be read from Figure 9a. is given by
⎡ 1 ⎤ pcw = Qcw ( y ) (Ah ) c ρ g D ⎢1 .5625 h⎞ ⎛ cosh⎜ 3.
4. is given by
where.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
Lateral hydrodynamic impulsive pressure on wall p iw .
Lateral convective pressure on the wall p cw . Impulsive hydrodynamic pressure in vertical direction. is given by:
x⎞ ⎛ sinh ⎜ 1 . on the base slab (y = 0 ). Qualitative description of convective pressure distribution on wall and base is given in Figure C1d. 732 ⎟ h⎠ ⎝ Q ib ( x ) = L⎞ ⎛ cosh ⎜ 0 .
the hydrodynamic pressure on the tank wall may be approximated by an outward pressure distribution of intensity equal to that of the maximum hydrodynamic pressure (Figure 12a).
The hydrodynamic pressure on the wall pcw .674 ⎟ D⎠ ⎢D 3 ⎝ D ⎠ ⎥ ⎝ ⎣ ⎦
The value of Qcb (x ) may also be read from Figure 10b.4 –
Hydrodynamic pressure due to horizontal excitation has curvilinear variation along wall height.3 –
In circular tanks.4165 h⎞ ⎛ cosh⎜ 3. However. in the absence of more
C4.25⎢ − ⎜ ⎟ ⎥ sech⎜ 3. Since hydrodynamic pressure varies slowly in the circumferential direction. (1986). for convenience in stress analysis of the tank wall. hydrodynamic pressure due to horizontal excitation varies around the circumference of the tank.
4.9.9. the design stresses can be obtained by considering pressure distribution to be uniform along the circumferential direction.162 ⎟ L⎠ ⎝ Qcw ( y ) = 0.3 –
This clause is adapted from Priestley et al.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
⎡ x 4 ⎛ x ⎞3 ⎤ h⎞ ⎛ Qcb ( x ) = 1.4 –
Equivalent linear distribution of pressure along wall height is described in Figures 12b and 12c.
C4. respectively. for impulsive and convective
.162 ⎟ L 3⎝L⎠ ⎥ L⎠ ⎢ ⎝ ⎣ ⎦
The value of Qcb ( x ) can also be obtained from Figure 11b. is given by
y⎞ ⎛ cosh⎜ 3.9.125⎢ − ⎜ ⎟ ⎥ sech⎜ 3. However. The pressure on the base slab (y = 0 ) is given by
pcb = Qcb ( x )( Ah )c ρ g L ⎡ x 4 ⎛ x ⎞3 ⎤ h⎞ ⎛ Qcb ( x ) = 1.9.162 ⎟ L⎠ ⎝
The value of Qcw (y ) can also be obtained from Figure 11a.
9. an equivalent linear pressure distribution may be assumed so as to give the same base shear and bending moment at the bottom of tank wall (Figures 12b and 12c).IITK-GSDMA Guidelines for seismic design of liquid storage tanks
exact analysis. For steel tanks. and
For rectangular tanks. pressure.
For circular tanks. for impulsive and convective mode. maximum hydrodynamic force per unit circumferential length at φ = 0. which is constant along the wall height for walls of uniform thickness. shown in Figure 12b and 12c can be obtained as:
4.5 – Pressure Due to Wall Inertia
Pressure due to wall inertia will act in the same direction as that of seismic force. maximum hydrodynamic force per unit length of wall for impulsive and convective mode is given by
The equivalent linear pressure distribution for impulsive and convective modes. wall inertia may be substantial. However. should be added to impulsive hydrodynamic pressure. Pressure due to wall inertia.5 – Pressure Due to Wall Inertia
C4. wall inertia may not be significant.9.
ρ m = Mass density of tank wall. for concrete tanks.
0 x/L 0.8
0 0 0.0 1.4
h/D=2 1.1
-0.4 Qib 0 -0.5 1.8
0.5 0.5 1. Qib
.25=h/L
0.0 0.1 -0.5 0.25
0.0 0.5 2.2
(b) on base of rectangular tank Figure 9 – Impulsive pressure coefficient (a) on wall.3
-0.25 0.6 0.0 1.4 Qiw 0. Qiw (b) on base.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
0.6 y/h 0.2
-0.5 h/D=0.4 0.6 y/h
0.1 0.5 1.1 0.3 -0.2 -0.25
0.2 Qcw 0.0
0 x/D 0.2
0.75 1.5 1.1 -0.4
0. Qcw (b) on base.0
0.4 0.2 0.5 0.3
(b) on base Figure 10 Convective pressure coefficient for circular tank (a) on wall.0 -0.2
h/D=0.5
h/D=0. Qcb
0.1 0 x/L 0.0
0.2 Qcw
0.5 1.0 1.2 -0. Qcw (b) on base .5
0.1 -0.75 1.2
h/L=0.75 -0.5 1.2
0. Qcb
h/L=0.2 0.3 0.5
0.1 Qcb 0 -0.4 0.4
(b) on base Figure 11 Convective pressure coefficient for rectangular tank (a) on wall.3 0.1 0.1 0.4 0.3 -0.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
ai .bi
10 – Effect of Vertical Ground Acceleration
Vertical ground acceleration induces hydrodynamic pressure on wall in addition to that due to horizontal ground acceleration. this pressure is uniformly distributed in the circumferential direction. This expression is based on rigid wall assumption. Effect of wall flexibility on hydrodynamic pressure distribution is described in Eurocode 8 (1998).3 (2001) and Eurocode 8 (1998).3 sec. Design vertical acceleration spectrum is taken as two-third of design horizontal acceleration spectrum.1 –
C4. which can be given as
The maximum value of hydrodynamic pressure should be obtained by combining pressure due to horizontal and vertical excitation through square root of sum of squares (SRSS) rule. To avoid complexities associated with the evaluation of time period of vertical mode.1 –
Distribution of hydrodynamic pressure due to vertical ground acceleration is similar to that of hydrostatic pressure.3 seconds for all types of tanks. as per clause 6.
In absence of more refined analysis.3 of this code. While considering the vertical acceleration.2 and 4.
C4. this induces additional pressure on tank wall.
4. effect of increase in weight density of tank and its content may also be considered. whose distribution is similar to that of hydrostatic pressure.10.5 of IS 1893 (Part1).10. time period of vertical mode is assumed as 0.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
4. breathing mode) can be obtained using expressions given in ACI 350.
where y = vertical distance of point under consideration from bottom of tank wall. for ground supported circular tanks. time period of vertical mode of vibration for all types of tank may be taken as 0.5.4. expression for time period of vertical mode of vibration (i.. effective weight of liquid increases.5. and
Sa = Average response acceleration g coefficient given by Figure 2 and Table 3 of IS 1893 (Part 1):2002 and subject to Clauses 4.10 – Effect of Vertical Ground Acceleration
Due to vertical ground acceleration.
4.e. However.10. In circular tanks.
where loss of liquid needs to be prevented. when h / D exceeds the value indicated above. the tank should be anchored to its foundation. Consider a tank which is about to rock (Figure 13). This approximation is reasonable for tanks with high h / D ratios that are susceptible to overturning. and ( Ah )i g denote the peak response acceleration.11 – Sloshing Wave Height
C4. D denote the tank diameter. If sufficient free board is not provided roof structure should be designed to resist the uplift pressure due to sloshing of liquid.
4. Moreover. Free board to be provided in a tank may be based on maximum value of sloshing wave height. the same expression may be used with L instead of D. Let Mtot denotes the total mass of the tank-liquid system.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
4. (1986). the amount of liquid in convective mode will also get changed.3 (2001).12 – Anchorage Requirement
This condition is described by Priestley et al. if there is obstruction to free movement of convective mass due to insufficient free board.
Thus. The derivation assumes that the entire liquid responds in the impulsive mode.
corresponding to convective time period. More information regarding loads on roof structure and revised convective mass can be obtained in Malhotra (2004).12 – Anchorage Requirement
Circular ground supported tanks shall be anchored to their foundation (Figure 13) when 1 h > D ( Ah )i In case of rectangular tank.11 – Sloshing Wave Height
Expression for maximum sloshing wave height is taken from ACI 350. This is particularly important for tanks containing toxic liquids. Taking moments about the edge.
(1986). and loose sands. G. The piping system shall be designed so as not to impart significant mechanical loading on tank. In buried tanks.M.13 – Miscellaneous
C4. may be used in the connections.2 – Buckling of Shell
More information of buckling of steel tanks is given by Priestley et al.13. and Morrison.
4.1 – Piping
FEMA 368 (2000) provides more information on flexibility requirements of piping system. R.E. Earth pressure shall also be considered in the design of walls. expansion joints and other special couplings.13 – Miscellaneous
4. the wall deformation and consequent movement into the surrounding soil is usually small enough that the active or passive soil wedge is not fully activated.13. and 0. This involves the use of constant horizontal and vertical acceleration from the earthquake acting on the soil mass comprising Coulomb’s active or passive wedge.2. Similarly.13. of wall height is necessary to activate the active soil reaction (Ebeling. 0.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
4. For effect of dynamic earth pressure. W. This theory assumes that wall movements are sufficient to fully mobilize the shear resistance along the backfill wedge. E. Mechanical devices.
C4. dynamic earth pressure shall not be relied upon to reduce dynamic effects due to liquid.2 – Buckling of Shell
Ground supported tanks (particularly. In sufficiently rigid tanks (such as concrete tanks).
4. (1993) and Clough.
C4. For buried tanks. medium-dense. Local loads at pipe connections can be considered in the design of the tank. following comments from Munshi and Sherman (2004) are taken: The effect of dynamic earth pressure is commonly approximated by Monobe-Okabe theory (1992).13.
. safety of shaft type of staging of elevated tanks against buckling shall be ensured. the analysis procedure remains same as that for ground supported tank except for consideration of dynamic earth pressure.13.3 – Buried Tanks
The value of response reduction factor for buried tanks is given in Table 2.1. steel tanks) shall be checked for failure against buckling.4%. For dense. which add flexibility to piping such as bellows.
C4.1 — Piping
Piping systems connected to tanks shall consider the potential movement of the connection points during earthquake and provide for sufficient flexibility to avoid damage. a deformation equal to 0.13. respectively.3 – Buried Tanks
Dynamic earth pressure shall be taken into account while computing the base shear of a partially or fully buried tank.
and response spectrum analysis shall be performed.M.13.Delta Effect
For elevated tanks with tall staging (say. Hence.
C4. connection between container and staging should be suitably designed to transfer the shear force. For such tall tanks.5 – P-Delta Effect
P-delta effect could be significant in elevated tanks with tall staging. J. wall-to-roof slab and wall-to-wall joints shall be suitably designed to transfer shear forces.5 – P. where hs is height of staging. (1991)).IITK-GSDMA Guidelines for seismic design of liquid storage tanks
and Duncan.4 – Shear Transfer
The lateral earthquake force generates shear between wall and base slab and between roof and wall. it must also be confirmed that higher modes of staging do not have significant contribution to dynamic response. Similarly in elevated tanks.6h above the base should be used to increase or decrease the at-rest pressure when wall deformations are small.13. If mass excited in higher modes of staging is significant then these shall be included in the analysis. weight of staging can be considerable compared to total weight of tank.
4. Dynamic earth pressure at rest should be included. 2. Wall-to-base slab. Similarly. and Hs is the height of soil being retained.
4. staging height more than five times the least lateral dimension) it may be required to include the P-Delta effect. determination of dynamic active and passive pressures may not be necessary when wall deformations are small.13. however. contribution from higher modes of staging shall also be ascertained. This force acting at height 0. For small capacity tanks with tall staging. as given by the following equation by Clough and Duncan (1991) F = kh γs Hs2 where kh is the dynamic coefficient of earth pressure.
. and 4% of the wall height is required to activate the passive resistance of these sands. P-delta effect can be minimized by restricting total lateral deflection of staging to hs/500. γs is the density of the soil. a deformation of 1. Therefore.
13.6 – Quality Control
Quality control in design and constructions are particularly important for elevated tanks in view of several collapses of water tanks during testing.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
4. It is necessary that quality of materials and construction tolerances are strictly adhered to during construction phase
Brussels. E. S. and Sherman. “Seismic design of liquid storage tanks”. U. 1984. Report No. AWWA D-115. New Delhi. 18. USA.. Colorado. and Morrison. 21... Mononobe.
8.. “Welded steel tanks for water storage”. N.. 4. Housner.C. tanks and pipelines”. Jaiswal. CA.2004. K. “Proposed provisions for aseismic design of liquid storage tanks: Part I – Codal provisions”.. NY. No. No 1-3.. Jain. 107. P. Rai. AWWA D-100. Kanpur. Vol. S. S. “Reinforced concrete tanks”.K. and Jain. G. 2000. and Duncan. 1996. Colorado. Wenk. W. Kanpur. 9. USA. 2004a. IS 11682:1985. 2004. “Seismic design of liquid containing concrete structures”. American Concrete Institute. S. O. C. A. Vol. 16. Haroun. Indian Institute of Technology Kanpur. 101-108.37. S. “Factory-coated bolted steel tanks for water storage”. 2nd Edition. USA. Report No. Washington D. Port Hueneme. Ebeling. 167-175. Eurocode 8. and Matsuo... J. “Chapter 6: Earth pressures”. IBC 2000. FM Global. Bulletin of Seismological Society of America. IITK-GSDMA-EQ-04-V1. R. “Dynamic analysis of fluids in containers subjected to acceleration”. 1994. “Indian Standard Criteria for Earthquake Resistant Design of Structures: General Provisions and Buildings”. Naval Civil Engineering Laboratory. No. 20. 5. “Design provisions for earthquake resistance of structures. S. NCEL Technical Report. D. “Simple procedure for seismic analysis of liquidstorage tanks”. “Codal provisions on design seismic forces for liquid storage tanks: a review”. P. 17.General rules and Part 4 – Silos.K. 381-387. Malhotra. and Medhekar... 20. MI. 1998. Journal of Technical Councils of ASCE. and Medhekar. 13. Farmington Hill. Foundation Engineering Handbook.. “Circular prestressed concrete water tanks with circumferential tendons”. 119-128.
10. 2001. Clough. 20. and Wieland. “Seismic analysis of FM approved suction tanks”. IS 1893 (Part 1):2002. Housner. 39-47. and Jain. 2000.. 1995.. Joshi. M. Part 1. FEMA 368. D.. Bureau of Indian Standards. 2000. 1991. 2000. Jain. TR-939. S. 19. 1997. “The seismic design of water front structures”. No. European Committee for Standardization. “Equivalent mechanical model for horizontal vibration of rigid intze tanks”. TID 7024. American Water Works Association. Nuclear Reactors and Earthquakes. G.0. Colorado. USA. J. 1929. 2. 1963a. National Institute of Building Sciences. American Water Works Association. T. “Proposed provisions for aseismic design of liquid storage tanks: Part II – Commentary and examples”. Structural Engineering International. Malhotra. M. Vol. 11. G. Munshi. Atomic Energy Commission. 14. Vol. 23. W. Concrete International. IITK-GSDMA-EQ-01-V1. K. K. Journal of Structural Engineering. Journal of Structural Engineering. 15. USA. American Water Works Association. USA. Jaiswal. “On the determination of earth pressure during earthquakes”. Proceedings of World Engineering Congress. TC1. 1963b. International Building Code International Code Council. Bureau of Indian Standards.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
1. 2. ISET Journal of Earthquake Technology. G.. “Criteria for Design of RCC Staging for Overhead Water Tanks”. AWWA D-103. W.. 4. “NEHRP recommended provisions for seismic regulations for new buildings and other structures”. H. Rai. Indian Institute of Technology Kanpur. New Delhi. USA. pp 223-235. 7. 1993.. ACI 350. M... 6.. 2004b. “The dynamic behavior water tanks”. O. M. Virginia. E. S. W. C. C. Vol. A... 53.0. Draft copy. 12. R.3. 3. M. 22. W. “Codal provisions on seismic analysis of liquid storage tanks: a review” Report No. R. K. and Housner. 3. 197-201. Building Seismic Safety Council. 191-207. P. M. 1993. Falls Church.
Y. Technical Council on Lifeline Earthquake Engineering. 201-213. “General theory of earth pressures”.. and Hall. 31. Paper No. 26. 2003. and Hinkle R. 1926. “Inelastic seismic demand on circular shaft type staging for elevated tanks”. “On the analysis of vertical circular cylindrical tanks under earthquake excitation at its base”.. L. Zanh F A. USA. “Flexural strength and ductility of circular hollow reinforced concrete columns without reinforcement on inside face”. Vol. 32. K. 1986. 1994. and Jain. 7th National Conf. 35. Rai D C. No. Tse. Priestley... Sameer. J. “Seismic response and design of liquid storage tanks”. S. 745-760. 34. Recommendations of a study group of the New Zealand National Society for Earthquake Engineering. Okabe. E. 29. ERI. T. Guidelines for the seismic design of oil and gas pipeline systems. K. 30. J. S. S. Park R. Sameer. 255-370. 2002. Engineering Structures. 28. V. 4.. and Urrutia-Galicia. Standards Association of New Zealand. 1986. S. and Jain. New Delhi. Rai D C and Yennamsetti S. “Seismic design of storage tanks”. U. 1. 25.
. 18 No. Morse. M. 1990. A. S. 2002. 443-461. 25. ACI Journal 87 (2). F. and Priestley.. Boston.. N.. USA. “Mechanical Vibrations: Theory and Application”. “Retrofitting of shaft type staging for elevated tanks”.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
24. et al. Berkeley. Vol. S. 91. 1982... 12. 691-698.. Earthquake Spectra. J.120. Gebbeken. 66. I. N. CBS Publishers and Distributors. Vol. “Approximate methods for determination of time period of water tank staging”. No. W.. 33. 156-166. Journal of the Japanese Society of Civil Engineers. No. I. Nachtigall. S. Engineering monograph published by Earthquake Engineering Research Institute. 27. 12. M. NZS 3106. M J N. ASCE. ASCE. N. Vol. 2nd Edition. 1984. “Lateral load analysis of frame staging for elevated water tanks”. 1992. “Earthquake spectra and design”... Newmark... “Code of practice for concrete structures for the storage of liquids”. 1375-1393. Veletsos. Wellington. N.5.. on Earthquake Engrg. U. Journal of Structural Engineering. The Indian Concrete Journal. 1983.
Water [π x 4. Tank is located on soft soil in seismic zone II.
A RC circular water container of 50 m3 capacity has internal diameter of 4.1 Sizes of various components Component Roof Slab Wall Floor Slab Gallery Floor Beams Braces Columns Size (mm) 120 thick 200 thick 200 thick 110 thick 250 x 600 300 x 450 450 dia.12 x 25 ) ]/ 4 π x 4.05 )2 x 0.1.2 38.2.65 m and height of 3.
1. iv) For seismic analysis.05 ) – ( 5. Weight Calculations
Table 1.3 m (including freeboard of 0.45 x 4 x 4 x25
Weight (kN) 60. The lowest supply level is 12 m above ground level.85 x 0.2 Weight of various components Component Roof Slab Wall Floor Slab Floor Beam Gallery Columns Braces Calculations [π x (5. iii) Water load is considered as dead load.110 x 25)]/ 4 [π x ( 0. Table 1.1 52. Staging conforms to ductile detailing as per IS13920.7 x 4 x 25 ] / 4 3.1.3 m). Grade of staging concrete and steel are M20 and Fe415.3 186.
.8 Note: i) Weights of floor finish and plaster should be accounted.20 x 25 ] / 4 π x 4.20 ) x 25 [π x ( ( 7. Density of concrete is 25 kN/m3.81] / 4 499. wherever applicable. Staging columns have isolated rectangular footings at a depth of 2m from ground level. It is supported on RC staging consisting of 4 columns of 450 mm dia with horizontal bracings of 300 x 450 mm at four levels.1 251.43 x 0. ii) Live load on roof slab and gallery is not considered for seismic load computations.45 )2 x 11. Preliminary Data
Details of sizes of various components and geometry are shown in Table 1. Analyze the tank for seismic loads.30 x 25 [π x (5.
Tank must be analysed for tank full and empty conditions.05 ) ) x ( 0.30 x 0.25 x ( 0. respectively.20 x 3.85 x 0.1 and Figure 1.05 )2 x ( 0.652 x 3.0 x 9. freeboard is not included in depth of water.1 185.4 100.
1.60 – 0.
1 Details of tank geometry
18 = 15. length of rigid link is =1.18 + 0.799 kg. mi = 0.11m thick X Floor Slab 0.65m.3 = 502. gallery and floor beam.0 = 1.000 / 9. As per Section 4.19 m.4m thick
Figure 1.4 x 1.0 = 2.00330 = 3.65 = 0.1 x 3.030 kN/m.64.000 x 20 = 22.99.2 + 38. there may be difference of 2 to 3%.3.2m thick
Floor Beam 0.65) – (100.
Ks = 2 x 3.
hi / h = 0.65.3 x 0. lateral stiffness of one frame of staging = 10 /0.2. Depth of water.060 kN/m.3 = 1. Mass of empty container + one third mass of staging ms = (502. mc / m = 0.1) – (52.4 + 100. hc = 0.18 m.1).2 CG of empty container
1.73. weight of container + one third weight of staging = 502.2.1 + 185.3.
Y Roof slab 0.65 x 50.3 / 3 = 626 kN. CG of tank is the combined CG of empty container and impulsive mass.18 m. stiffness of staging is to be obtained in Xdirection (Refer Figure 1. In FE model of staging.2.948 kg which compares well with the total mass.1 kN. Hence.948 = 17.64 x 3. floor beams are modeled as T-beams.65. However in some cases.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
From Table 1.832 kg
Further.375. hi = 0.055) – (38.36 x 106 kN/m2. total lateral stiffness of staging.
hc / h = 0.3 kN.35 x 50.2 = 371. h = 3. Hence.
Above analysis can also be performed manually by using standard structural analysis methods.800 / 9. From the deflection of CG of tank due to an arbitrary lateral force one can get the stiffness of staging. D = 4.65. CG of tank is taken as CG of empty container.1 + 52. From the analysis.030 = 6. mi / m = 0.36) + (251. Here.1 + 371.
3.0 = 1. Thus.95 hc* / h = 0.92 m
1. a rigid link is assumed from top of staging to the CG of tank.00330 m.12m thick
1. mc = 0.000 f ck = 5.3. However. wall. for h / D = 3.0 / 4. Since container portion is quite rigid. one single frame of staging can be analysed in this case.1.948 = 33. m = 4.1 x 0.1 + 371.2.3). Weight of empty container = 60. With reference to Figure 1.2) Note that the sum of impulsive and convective masses is 50.1 + 251. mass of water.5.65 x 3. height of CG of empty container from top of footing will be 14 + 1. Modulus of elasticity for M20 concrete is obtained as 5. floor slab. Since staging consists of two such frames.8 kN = 4.35.13 m hi* / h = 0. Inner diameter of the tank. Hence.2 x 0.116 kg.3 / 3) x (1. in this example. deflection of CG of tank due to an arbitrary 10 kN force is obtained as 0.99. Hence.73 x 3. hi* = 0. hence.4)] / 502.0 m.81) = 63. Weight of staging = 186. height of CG of empty container from top of floor slab will be = [(60. Center of Gravity of Empty Container
Components of empty container are: roof slab. ( Section 4. Lateral Stiffness of Staging
Lateral stiffness of staging is defined as the force required to be applied at the CG of tank so as to get a corresponding unit deflection.19m
Gallery 0.4.360 MPa or 22.948 kg.0 = 1.81 = 50.48 m.3m 1.375 x 3.1 = 1.800 N. Parameters of Spring Mass Model
Weight of water = 499. to account for the rigidity imparted due to floor slab. hc* = 0. Finite element software is used to model the staging (Refer Figure 1.
For h / D = 0. Hence.3. 60 .5 For convective mode. Tc = 3. 5 × × 2. Damping = 5%.7.06.81
1. Zone II) I = 1.75 x 0. ( Section 4.2)
Where.5 and 4. ( Section 4.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
Here. Time Period
Time period of impulsive mode.2.09 = 0. 2 2. Cc = 3.4)
( Section 4.5. R is taken as 2.2 (a)) Thus.
( Sections 4. 9.4)
Design horizontal convective mode.
(IS 1893(Part 1): Table 2.1)
1.04 2 2. value of R is taken same as that for impulsive mode as per Section 4.000
Time period of convective mode. Damping = 0.3)
33.5 ( Table 1) R = 2.75 is used to obtain Sa /g values for 0.26 sec.116 + 63.6.1.1)
Vi = (Ah)i (mi +ms) g ( Section 4.1. (Sa /g)c = 1. analysis of staging is being performed for earthquake loading in X-direction. Site has soft soil.5% damping from that for 5% damping.1 (IS 1893(Part 1): Table 2.5.5 ( Table 2) Here. 5 × ×1.5 and 4. (Ah)c = Z I ⎛ Sa ⎜ 2 R⎜ g ⎝ ⎞ ⎟ ⎟ ⎠c
( Sections 4. (Ah)i = seismic coefficient for
1.8. Z = 0.28.3. Here. Tc = 2.09 (IS 1893(Part 1): Figure 2) (Ah)i =
0.65.4) (Ah)c = 0.
10 kN Rigid Link 1480 2985 2980 2980 2980 1775 3430 (All Dimensions in mm) Figure 1.80 sec . Ti = 0.28
4.5 ( Section 4.60 .3 (IS 1893(Part 1): Figure 2) Multiplying factor of 1. 1 1.5%. for some staging members this may not be the critical direction. Site has soft soil.26 sec.3 = 0.80 sec. (Sa /g)i = 2.5.5. Design Horizontal Seismic Coefficient
Design horizontal impulsive mode. 1 1. However.799 = 0.3 FE model of staging
Z = 0.6.65 = 2. Hence.1 I = 1. Zone II) ( Table 1)
Since staging has special moment resisting frames (SMRF). in impulsive mode.5 seismic coefficient for
( Section 4. Base Shear
Base shear at the bottom of staging.74 = 1.
866l ' / h ( Section 4.866 D / h) ( Section 4. Impulsive Hydrodynamic Pressure
Convective pressure at y = h.5625 cosh (3.9 kN.7. Similarly.06 x (33.18)] x 9. Mi* = (Ah)i [ mi ( hi* + hs ) + ms hcg ] g ( Section 4. Total lateral base shear is about 5 % of total seismic weight (1.0) = 0.
= 0.0 x 1 = 1.9.65) = 0.65 / 2 x 3.866 x / L ) / cosh 0. in impulsive mode.832 x (2. Convective Hydrodynamic Pressure
Convective hydrodynamic pressure on wall.000 x 9.19 +14) x 9.81 = 924 kN-m.65 /3.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
= 0.1(a))
( Section 4.2)
( Section 4. M* = = Mi
( Section 4. It may be noted that this tank is located in seismic zone II.674h /D)
( Section 4.
Qcw(y = 0) = 0.866 [1 -( y / h)2 ] tanh (0. Base Moment
Overturning moment at the base of staging.10. V = Vi + Vc =
Maximum pressure will occur at ф = 0.000 x 9.000 x 9. Convective hydrodynamic pressure on the base slab (y = 0)
.9.69 kN/m2.06 x [33.65 x 0. base shear in convective mode.0 kN. y = 0.6.6.81
( Section 4.9.000 x 9.116 x (1.
Impulsive hydrodynamic pressure on wall piw(y) = Qiw(y) (Ah)i ρ g h cos ф Qiw(y) = 0.2) = 0.5625 x 0.12 kN/m2 At y = h.832 x 9. overturning moment in convective mode.2)
/4.674 y/D)/cosh(3.06 x 1.81 = 7.41 kN/m2.67 x 1 = 0.04 x 1. Vc = (Ah)c mc g = 0.65 / ( 2 x 3. Hydrodynamic Pressure
1.10 x 0.0 ) = 0.116 + 63.2.126 kN).10.2(a)) Maximum pressure will occur at ф = 0. y = 0.866[1-(0/3.04 x 1. piw(y = 0) = 0.866 x 4. At base of wall.799 x 15.674 x 3.0 x sinh (0.10.06 x 1.67 x 1 = 0. Qiw(y = 0) = 0.
1.65 x 0.3) + (7.5625
= 931 kN-m. Total base shear at the bottom of staging.76 Impulsive pressure at the base of wall.81 = 59.
pcw = Qcw(y) (Ah)c ρ g D [1.76 x 0. Total overturning moment at the base of staging.7. Convective pressure at the base of wall.81 x 4.81 x 4.5625 x cosh (0) / cosh (3. Impulsive hydrodynamic pressure on the base slab (y = 0) p ib = 0.3)
= 0.866 x 4.0 )
(59.81 x 3.04 x 17. Similarly.04 x 17.10.7.799) x 9.9.
Qcw(y = h) = 0.866 x 0.1.
1.81 x 3.95 kN/m2
1.866 x 4.9)
= 60 kN. Mc* = (Ah)c mc (hc* + hs) g = 113 kN-m.1(a))
= 0.0)) / cosh ( 0. At base of wall.92 + 14) + (63.1/3 cos2ф] cos ф Qcw(y) = 0.0)2]x tanh (0.866 ( Ah )i ρ g h sinh (0.
. container of tank is designed by working stress method.125[x/D – 4/3 (x/D) 3] sech (3.799 kg. Sa /g = 2.9. In practice.000
= 0.23 m.47 kN/m2.07 Convective pressure on top of base slab (y = 0)
pcb = 0. For 5 % damping.y / h )]
( Section 4. Stiffness of staging. hydrodynamic pressure due to vertical ground acceleration is more than impulsive hydrodynamic pressure due to lateral excitation. Pressure Due to Wall Inertia
Pressure on wall due to its inertia.
1.0 = 29.
1.5 x 4. hydrodynamic pressure in this case does not affect container design. 2 ⎛ 0.5 ( Table 1) R = 2.674 x 3 /4.3 sec in Section 4.15.1
(Section 4.10.674 h/D)
1. Mass of empty container + one third mass of staging.9.1) 2 Av = 3 ⎛ Z I Sa ⎞ ⎜ ⎜2 R g ⎟ ⎟ ⎝ ⎠ (IS 1893(Part 1): Table 2.5.
( Section 4.060 kN/m.7.125[D/2D – 4/3 (D/2D) ] sech (3. Empty tank will not have convective mode of vibration. Time Period
Z = 0.e.10. Analysis for Tank Empty Condition
For empty condition. Hence.13 kN/m
= 2.4.3 m.05 At the base of wall. Height of sloshing wave is less than free board of 0.81 x 3.32)
+ 0.32 kN/m2. tank will be considered as single degree of freedom system as described in Section 4.
At the base of wall.04 x 1.000 x 9. i.65 sec.5 ⎞ Av = × ⎜ × × 2.06 x 0.65 / 2 = 0. When earthquake forces are considered. Pressure Due to Vertical Excitation
Hydrodynamic pressure on tank wall due to vertical ground acceleration.43 kN/m2).
Time period of impulsive mode.65
( Section 4.5 Time period of vertical mode of vibration is recommended as 0.81 x 3 x ( 1 – 0 / 3 )]
= 1.27 kN/m2.799 60.000 x 9.2 x 25 = 0.15.60. ms = 63..14.11)
pv = 0.11. This maximum hydrodynamic pressure is about 8 % of hydrostatic pressure at base (ρ g h = 1.
pv = (Av) [ρ g h ( 1.5 ⎟ 3 ⎝ 2 2 .
63.07 x 0. permissible stresses are increased by 33%.65) = 0.12 2 + 1. Sloshing Wave Height
Maximum sloshing wave height.81 x 4. This pressure is uniformly distributed along the wall height. Zone II)
1.10.12. In this case.
= 0.1. Maximum Hydrodynamic Pressure
Maximum hydrodynamic pressure.
= 0. Ks = 6.05 x [ 1 x 9. Hence.
1.2(a)) = 1. y = 0.41 + 0.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
Qcb(x) = 1.1 1.5 ⎠ = 0.1.04 x 2.
Site has soft soil.15. 1 1 .5.7. 2 2 .3.5 (IS 1893(Part 1): Figure 2)
0 . Ti = 0.799 x 15. design will be governed by tank full condition.65 sec.18 x 9.799 x 9.08 x 63.6.08 x 63.1)
( Section 4.81 = 760 kN-m Since total base shear (60 kN) and base moment (931 kN-m) in tank full condition are more than that total base shear (50 kN) and base moment (760 kN-m) in tank empty condition.5 R = 2.
(IS 1893(Part 1): Table 2. ( Sections 4. Base Moment Total base moment.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
= 0.5 = 0.81 = 50 kN. Design Horizontal Seismic Coefficient
1.1 I = 1. Hence.
Where.5 × × 2. Damping = 5%.5 and 4. (Sa /g)i = 2.15. Base Shear
Design horizontal seismic coefficient corresponding to impulsive time period Ti.4.2.
Total base shear. Zone II) ( Table 1) ( Table 2)
1. Details of staging configuration are shown in Figure 2. Preliminary Data
Details of sizes of various components and geometry are shown in Table 2.1 Sizes of various components Component Size (mm)
120 thick 250 x 300 200 thick 500 x 300 500 x 600 200 thick 250 thick 300 x 600 650 dia. Grade of concrete and steel are M20 and Fe415. Density of concrete is 25 kN/m3.
An intze shape water container of 250 m3 capacity is supported on RC staging of 6 columns with horizontal bracings of 300 x 600 mm at three levels.1.1 and Figure 2.
Tank must be analysed for tank full and empty conditions.1. respectively. Staging conforms to ductile detailing as per IS 13920.
. Analyze the tank for seismic loads.
2. Tank is located on hard soil in seismic zone IV.
20 x 4.632 + (8.8/2)2 / 1.65)2 x 15.80 + 6.8 x 0.5( 8.5) / 3) ] x 9.921 kN
.5 x 0.57 2 x π x 6.40] / 2 = 4.(π x 1.12 x 25)
209.20 x 25
52.576 + 1.62 + 5.6 + 321.2 148 185. r2 = [(6.28/2)2 /1.6 + 0.60 x 25 Radius of dome.2 Weight of various components Components Calculations Weight (kN)
Radius of dome.22 x 1.036 / 3 = 1.5) x 0.3 = 1. ii) No live load is considered on roof slab and gallery for seismic load computations.2.412)1/2 = 2.652 + 1.r1 = [((8.9 107.6 x 5.57 x 1.25) x 0.1+ 552.69 x (0.0) x 2.0 x 25 π x (8.22 -1. weight of empty container + one third weight of staging = 1.17 π x ((8. free board is not included in depth of water.22 2 x π x 4.50 x 0.9 + 107.508
.30 x 25 π x 8.69) + 1.25 x 0.14 x 0. iv) For seismic analysis. Weight calculations
Table 2.62 x 3. their weights should be included in the weight calculations.60 x 3 x 6 x 25 782 254
Note: . From Table 2.3 x (3 x 4.30 x 0. Lc = (1.40) + 1.576 kN Weight of staging = 782 + 254 = 1.3
[ (π x 8.6 + 0.i) Wherever floor finish and plaster is provided.3
π x (8.25 x 25
321.28 x 0.036 kN Hence.28) / 2.3 + 52.69)] / 2 = 6. Weight of empty container = 209. iii) Water load is considered as dead load.17 x 0.81
Columns Braces π x (0.2.7 x 6 x 25 / 4 3.30 x 25 π x 6.2 + 148 + 185.40 x 0.6
Length of Cone.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
2.63)) / 12
2.1 552.7 /4) +( π x1.
1: Details of tank geometry
3140 (b) Plan of staging (All dimensions in mm) Figure 2.
hc* = 0. cylindrical wall.821 kg.55 x 2.933 kg hi / h = 0.50.08.55.22) + (52.68 m hc* / h = 0.4 / 8.2.81 = 255. For obtaining parameters of spring mass model.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
2. bottom dome.3 x 1) + (185.43 m.65 m3 Mass of water. Mass of empty container + one third mass of staging.3) Let h be the height of equivalent circular cylinder.6 x 0.88 m Height of CG of empty container from top of footing.036 / 3 ) x (1.508 / 9.4.65 h = 255.4 = 3.612 kg mc /m = 0.1 x 5. hcg = 16.375 x 4.9 x 3.78 x 4.658 = 1.65 m hi* / h = 0.6 = 0.2 Details of tank container
.61.4 = 2.2. = [(209.95.576 = 2.4 = 3.
( Section 4.55.000 / 9.6 m. bottom ring beam.43 x 2.2 x 1. hi = 0.
= 1. Volume of water = 2.81)
For h / D = 4.
π (D /2)2 h = 255.78 x 4.43 m hc / h = 0.000 N. mi = 0. hi* = 0.4 m
mc = 0. D = 8.88 = 19.3)] / 1. top ring beam. conical dome and circular ring beam. hc = 0.40. Parameters of Spring Mass Model
Total weight of water = 2.
m i / m = 0.55. Sum of impulsive and convective mass is 2.545 kg which is about 2 % less than the total mass of liquid.65) + (321.92) – (148 x 0.
ms = ( 1.3 x 7.61 x 4.375.78. m = 2.9) + (552. Center of Gravity of Empty Container
Components of empty container are: top dome.3.8) + (107.4 = 1.18 m.78. Height of CG of empty container above top of circular ring beam.1) About 55% of liquid mass is excited in impulsive mode while 43% liquid mass participates in convective mode. With reference to Figure 2.51.576 + 1.65 / [π x (8.658 = 1.658 kg. ( Section 4. an equivalent circular container of same volume and diameter equal to diameter of tank at top level of liquid will be considered.508 kN = 25. Inner diameter of tank.3 + 2.2.43.55.09.6 / 2) ] = 4.
084 2 2.95.16 = 0.86 sec.5
(IS 1893(Part 1): Table 2. Time Period
Time period of impulsive mode.5.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
2.24 1.6. CG of tank is taken as CG of empty container.18 m.2 (a)) Thus.3.35 8 .36 x 106 kN/m2.3 FE model of staging
( Sections 4. Thus. Finite element software is used to model the staging (Refer Figure 2.1. However.1. In FE model of staging. Zone IV) ( Table 1)
Since staging has special moment resisting frames (SMRF). Modulus of elasticity f ck = for M20 concrete is obtained as 5. lateral stiffness of staging. (Ah)i =
( Sections 4.000 x 20 = 22. (Sa /g) i = 1.40.1)
. Tc = 3. Since container portion is quite rigid. 9.5.612 + 1.3)
= 2π 1.0 × 10 5
( Section 4.7.5 ( Table 2) Here. However.
178.16 (IS 1893(Part 1): Figure 2) (Ah)i =
0. for some members of staging. a rigid link is assumed from top of staging to the CG of tank.616E-04) = 17.88 + 0. As per Section 4.86 sec.616E-04 m.5 and 4.3 = 3. R is taken as 2.
2.3. earthquake loading in Y-direction will be critical.4)
Design horizontal convective mode. Design Horizontal Seismic Coefficient
Design horizontal impulsive mode.360 MPa or 22. (Ah)c =
Figure 2. Hence.3.6 = 3. Site has hard soil. Damping = 5%.5
( Section 4. as described in Section 4. Time period of convective mode.800 kN/m Stiffness of this type of staging can also be obtained using method described by Sameer and Jain (1992).
For h / D = 0.81
2.2. CG of tank is the combined CG of empty container and impulsive mass.8.5 and 4.35 ( Section 4.821 = 0. Cc = 3.51.3). Lateral Stiffness of Staging
Lateral stiffness of staging is defined as the force required to be applied at the CG of tank so as to get a corresponding unit deflection. Ks = 10 / (5.24 I = 1.5 × ×1.14 sec. Ti = 0.1)
Where. in this example.
Z = 0. length of rigid link is = 2.2.5. From the analysis deflection of CG of tank due to an arbitrary 10 kN force is obtained as 5.3.000 5. Here analysis of staging is being performed for earthquake loading in X-direction.
2) = 0.429 kN) of tank.9.821 kg.5 × × 0. Mass of empty container + one third mass of staging.5 x 8.7. value of R is taken same as that for impulsive mode as per Section 4.
For convective mode.40.5
( Section 4.11.
= 0.4) Hence.5%.448 kN-m.381)
= 5.11)
= 0.95.95.3) (IS 1893(Part 1): Table 2.7.11.56 Multiplying factor of 1.95.040 2 2.933 x (3.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
Where.40.1.75 x 0. ( Section 4.
( Section 4.66 sec
2.43 + 16.6.3)
= 280 kN.24 1.81 = 43 kN Total base shear at the bottom of staging.
1.81 = 277 kN Similarly.3 and IS 1893(Part 1): 2002.5.
Empty tank will not convective mode of vibration.612 x (3. Sloshing Wave Height
( Section 4. in impulsive mode.11.040 x 1.4. tank will be considered as single degree of freedom system as described in Section 4.4) (Ah)c = 0. Base Shear
Base shear at the bottom of staging. Figure 2 (Sa /g)c = 1.09.2)
= 0. Site has hard soil.09.1.
(5.3) x 9.933 x 9.5. base shear in convective mode.
2.7. Time Period
( Section 4.821) x 9. Ks = 17.
( Section 4.8. Design Horizontal Seismic Coefficient
( Section 4.5.381 kN-m Similarly.040 x 1.10.821 x 19.95.
. Analysis for Tank Empty Condition
For empty condition.
Time period of impulsive mode.821 178. Here.6. ms = 1.
2.2.43 m.56 = 0.2)
Design horizontal seismic coefficient corresponding to impulsive time period Ti.81 = 5.
2.612 + 1. Note: Hydrodynamic pressure calculations will be similar to those shown in Example 1 and hence are not included here.75 is used to obtain Sa /g values for 0.800 kN/m. ( Section 4. Zone IV) + (1.43 + 16. as per Section 4.6. Base Moment
Overturning moment at the base of staging in impulsive mode. It may be noted that total lateral base shear is about 6 % of total seismic weight (4.14 sec.040 x 2.18)] x 9.6 / 2 = 0.5% damping from that for 5% damping. overturning moment in convective mode.7.24
= 0. Stiffness of staging.084 x (1. Tc = 3.318 = 0. Damping = 0.81 = 852 kN-m Total overturning moment.084 x [1.0 × 105
2. Zone IV) ( Table 1) ( Table 2)
= 0.81 = 211 kN. Hence.12 x 1.4.11.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
( Section 4.18 x 9.5 × ×1.11.24 I = 1. 2 2.95.66 sec.5
( Section 4.3.24 1.
Where. Damping = 5%.
Z = 0.52 = 0.448 kN-m) in tank full condition are more than base shear (211 kN) and base moment (4. Base Shear
Total base shear. Site has hard soil.7.821 x 9.5
( Section 4.11.053 kN-m Since total base shear (280 kN) and base moment (5.5 R = 2. (Sa /g)i = 1. design will be governed by tank full condition.053 kN-m) in tank empty condition.3)
= 0. Ti = 0.95.2)
(IS 1893(Part 1): Table 2.
Here.52 (IS 1893(Part 1): 2002Figure 2) 0.821 x 19.81 = 4.11 x 1.6.5)
2. Base Moment Total base moment.
980 kN 4. Thickness of shaft = 150 mm.
hcg = 17 + 2.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
3.576 + 1.
3.28 x 0. Additional relevant data is listed below: 1. Analyze the tank for seismic loads.88 m
. Weight of shaft = π x 6. Site of the tank has hard soil in seismic zone IV. height of CG of empty container from top of footing.88 = 19. Grade of concrete and steel are M20 and Fe415.
Intze container of previous example is considered to be supported on 15 m high hollow RC shaft with reinforcement in two curtains.15 x 16. Since staging height is 17 m from footing level. 2.213 kN 3. respectively.4 x 25 = 1.
Tank will be analysed for tank full and empty conditions. Preliminary Data
Container data is same as one given in previous example. Density of concrete is 25 kN/m3.213 / 3 = 1.1. Weight of empty container + one third weight of staging = 1.
Design horizontal impulsive mode.36 x 106 kN/ m2
= π x (6. hc = 0.213 / 3 ) x (1. an equivalent circular container of same volume and diameter equal to diameter of tank at top level of liquid will be considered.35 ( Section 4. Tc = 3.5. Time period of convective mode.434.61 x 4. Time Period
Time period of impulsive mode.576 + 1.4 = 2.3. hi = 0. If the effect of shear deformations is included then the lateral stiffness is given by:
For h / D = 4.658 = 1. Sum of impulsive and convective mass is about 2% less than total mass of liquid.375.869 kg.78.3.08.
E = Modulus of elasticity = 5.40. D = 8.000 f ck
3. Cc = 3.2.68 m hc*/ h = 0.
( Section 4. Parameters of Spring Mass Model
Total weight of water = 2. Lateral Stiffness. This is the height of shaft from top of footing upto bottom of circular ring beam.2.78.09.
Where.2.35 8 . 9.2.
π (D /2)2 h = 255.4 m
= 5.360 N/mm2
= 22.4 / 8. mc = 0.61.59 / 16.4 = 1.360 x106 x 14. A is cross sectional area and κ ' is shape factor.000 N.43 x 2.6 / 2)2] = 4.65 m hi* / h = 0.4 = 3.658 = 1.6 = 0.78 x 4.22 × 10 8
= 0.01.4 m Thus. only flexural deformations are considered in the calculation of lateral stiffness and the effect of shear deformation is not included.3.55 x 2.55. seismic coefficient for
ms = ( 1.6 = 3.43 m hc / h = 0.4.14 sec.3) Let h be the height of equivalent circular cylinder.01.59 m4
= 16.43 m.658 kg.40. Lateral Stiffness of Staging
Here.375 x 4. Volume of water = 2.933 kg hi / h = 0.55.508 kN = 25. G is shear modulus.4 = 3.66 m3 Mass of water.81
3. mi = 0.51.22 x 108 N/m
NOTE:.43.134) / 64 = 14.78 x 4.81)
1. m = 2.6.55. hc* = 0.1.81 = 255.2 (a)) Thus.1) Note that about 55% of liquid is excited in impulsive mode while 43% participates in convective mode.612 + 2.Here.66 / [π x (8.66 h = 255.000 x
20 = 22. shaft is considered as cantilever of length 16.508 / 9. Ks = 3 E I / L 3 Where.
For h / D = 0.869 2.55. Lateral Stiffness = 3 x 22. hi* = 0.43 = 2.4 m. ( Section 4.3)
( Section 4.25 sec.612 kg mc /m = 0.
m i / m = 0. For obtaining parameters of spring mass model.51. Mass of empty container + one third mass of staging. Inner diameter of tank.000 / 9.
= 2.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
4) (Ah)c =
0.888 kN-m Similarly.6.24 1. Site has hard soil.5.933 x 9.25 sec.40.5 and 4.06 x 1.
( Section 4. Damping = 0.
Where.5%. Here.5 and 4.09.2) = 0.06 2 1.01.5.933 x (3.6.75 is used to obtain Sa /g values for 0.25 x (1.81 = 1.81 = 840 kN Similarly.318 = 0.43 + 17) + (2.75 x 0.5.25 x [1.
For convective mode.
Z = 0.4) Hence.869 x 19. (Sa /g)i = 2.7.2) = 0.88)] x 9.7. Zone IV) ( Table 1)
( Section 4. Site has hard soil.25 2 1.01. base shear in convective mode.5.56 = 0. Damping = 5%.24 1.7.5.
Where.81 = 16.24 I = 1.5 = 0.612 + 2. value of R is taken same as that for impulsive mode as per Section 4.6.3)
= 843 kN. Tc = 3.7.06 x 1.1)
Design horizontal convective mode.488 kN) of tank.14 sec.6.09.
.612 x (3. 8
( Section 4. overturning moment in convective mode.5 (IS 1893(Part 1): Figure 2) (Ah)i = 0.24 I = 1. It may be noted that total lateral base shear is about 19% of total seismic weight (4. ( Section 4.2) = 0.8 seismic coefficient for ( Section 4. Base Shear
Base shear at the bottom of staging.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
( Sections 4.5 × × 2.
( Sections 4.
Shaft is considered to have reinforcement in two curtains both horizontally and vertically.1)
(IS 1893(Part 1): Table 2. Zone IV) ( Table 1)
( Section 4.3 and IS 1893(Part 1): 2002.81 = 65 kN Total base shear at the bottom of staging. Ti = 0. ( Section 4. Base Moment
Overturning moment at the base of staging in impulsive mode.43 + 17) x 9.322 kN-m Total overturning moment. 40.869) x 9.3)
(16. Hence. ( Table 2) Here.5 × × 0.
Z = 0.940 kN-m.888)
+ (1. as per Section 4.322 )
(IS 1893(Part 1): Table 2.5% damping from that for 5% damping. in impulsive mode. Figure 2 (Sa /g)c = 1.4)
( Section 4.8. Hence R is taken as 1.1.56 Multiplying factor of 1.
ms = 2.8
3.869 x 9.01.06 x 1.5 R = 1. Site has hard soil.22 x 10 N/m
3. Base Moment Total base moment.81 = 495 kN
3.869 2.19 sec.8.869 kg Stiffness of staging.9. Ti = 0.25 x 2.
Where.46 m Note – Hydrodynamic pressure calculations will be similar to those shown in Example 1.4.4.
3. (Ah)i =
( Section 4.842 kN-m For this tank.9.01.19 sec.01.5 = 0.24 1. Empty tank will not have convective mode of vibration.88 x 9.5 (IS 1893(Part 1): Figure 2) (Ah)i = 0.3. tank full condition is more critical than in tank empty condition. Analysis for Tank Empty Condition
For empty condition.5)
. (495 kN) design will be governed by tank full condition.22 × 10 8
( Section 4.7. Note: Pressure calculations are not shown for this tank.
( Section 4. Mass of empty container + one third mass of staging. Damping = 5% Hence. tank will be considered as single degree of freedom system as described in Section 4. Ks = 2. Design Horizontal Seismic Coefficient
= 0.81 = 9.
2. Sloshing Wave Height
Maximum sloshing wave height.6.869 x 19.8 x 8. Zone IV) ( Table 1) ( Table 2)
= 0.01. hence are not repeated.9. Similarly. Time Period
3.5 × × 2.26 2 1 . (Sa /g)i = 2. Base Shear
Total base shear.1.25 x 2. for base moment.11)
I = 1.2)
(IS 1893(Part 1): Table 2.2.9.6 / 2 = 0.9. since total base shear in tank full condition (843 kN) is more than that in tank empty condition.24
( Section 4.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
Design horizontal seismic coefficient corresponding to impulsive time period Ti.7.
mb = 89 x 1.000 m3 capacity has inside diameter of 12 m. Weight Calculations
Weight of tank wall = π x (12 + 0.81 = 5. Tank has a base plate of 10 mm thickness supported on hard soil in zone V. Weight of roof = 50 kN Mass of roof.000 kg mc / m = 0.000 / 9.309
. Analyze the tank for seismic loads.000 = 7.84 /12 = 0.097 kg
4. Density of steel plates is 78.000 kg Assuming that roof of tank is a plate of 5 mm. mt = 50 x 1.703 x 10.1 Sectional elevation of tank
4.53 = 89 kN Mass of base plate.
Figure 4. Volume of liquid = 1.
mi / m = 0.81 = 9.902 kg Weight of base plate = π x (6.2.1.74.005) x 0.53 kN/m3.01 x 78. D = 12 m
For h / D = 8.5 m and wall thickness is 5 mm.703.00.005)2 x 0.810 kN Mass of liquid. Tank is filled with liquid of specific gravity 1.072 kg.0.5 = 156 kN Mass of tank wall. mw = 156 x 1.
Weight of liquid = 9. Roof of tank consists of stiffened steel plates supported on roof truss.53 x 10.000 / 9.81 = 15.00. m = 10.000 /9.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
4.005 x 78.000 m . height of 10.
A ground supported cylindrical steel tank with 1.03. mi = 0.84 m. Parameters of Spring Mass Model
= 0. Ti = 0. seismic coefficient for
. value of R is taken same as that for impulsive mode. Zone V) ( Table 1) ( Table 2)
Note that impulsive convective less than masses.5 = 0. (IS 1893(Part 1): Table 3)
4.005 m.75 x 0.677 . E = Young’s modulus for steel = 2 x 10 N/m
0.5 and 4. Figure 2 (Sa/g)c = 1. hc / h = 0. hence R is taken as 2. Sa /g = 2. Here.5. Time Period
Time period of impulsive mode.74.1) = 4.005 / 12 ) × 2 ×1011
( Sections 4. ρ = Mass density of liquid = 1.
about 70% of liquid is excited in mode while 30% participates in mode.309 x 10.3.5
Design horizontal convective mode.1)
Where. Total liquid mass is about 1% sum of impulsive and convective
This steel tank has anchored base. Damping = 0.5 ( Section 4.36 1.43 m ( Section 4.64 sec.5 For convective mode.5 x 1.4 is used to obtain Sa /g for 2% damping from that for 5% damping.1. hi*/ hc*/ h = 0.3.5.84 = 5.5 × × 3.587 .1)
Where. Tc = 3.727 .75 is used to obtain Sa /g values for 0. as per Section 4.
For h / D = 0. D = Inside diameter of tank = 12 m.000 = 3. Cc = 3.5.23 × 8.5%. Time period of convective mode.000
( 0.23 ( Section 4.000 kg h i / h = 0.36 I = 1. Site has hard soil.13 sec.84 = 3. Design Horizontal Seismic Coefficient
Design horizontal impulsive mode. 9. ( Section 4.2.5 % damping from that for 5 % damping.29 = 3.
(IS 1893(Part 1): Table 2. ( Section 4.5.4.84 m.74.
Z = 0.5.00.2(a)) 12 Tc = 3.375 x 8.375 .
h = Depth of liquid = 8.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
mc = 0. h = 0. Ci = 4.3 and IS 1893(Part 1): 2002.
Where.81
Here.84 = 5.1.3.4) Hence. as per Section 4. Site has hard soil.32 m hc = 0.5 R = 2. Damping = 5%.677 x 8.4) (IS 1893(Part 1): Figure 2) Multiplying factor of 1.64 sec.2)
(IS 1893(Part 1): Table 2.13 sec.4 = 3.98 m hi* = 0. Zone V)
I = 1.000 kg/m .275 = 0.5.5 ( Table 1) R = 2.5 and 4.36
= 0.84 = 6.587 x 8.1.19 m hc*
( Sections 4.29 ( Section 4.84 × 1. Hence.38 2 2. t = Thickness of wall = 0. hi = 0.09.48 Multiplying factor of 1.2. (Ah)c =
For h / D = 0.727 x 8.
2) = 0.097 x (10.6.
( Section 4.5025)] x 9.8.1. Overturning Moment
Overturning moment at the bottom of base plate in impulsive mode.81 x 8.2) = 0.
( Section 4. At base of wall.5
= 9.36 1.255 kN-m.703 kN.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
Base shear at the bottom of wall in impulsive mode.016 kN) of tank.000 x (6.
( Section 4.7.173 kN-m. 866[1-( 0 / 8.98 x 9.866 x12 / 8.05 2 2 .7.01 / 2)] x 9.000 x (5.03. y = 0. overturning moment in convective mode.25 + 0.38 x [(7.25) + (5.
4.000 x 5.81 = 976 kN-m.000 + 15.81 = 9.902 x (5.1)
= 0.19 + 0.
( Section 4.3)
(2.48 = 0.
(9.1) = 0.1.866 D / h)
( Section 4.1.6.902 x 5.6.09.1) = 0.072 x 0.5 × × 0.1.32) + (15.7.699 kN Similarly.09.000 x 3.9.05 x 3.01) + (5.139 kN-m.05 x 3.5025 + 0. ( Section 4.
( Section 4. Similarly. bending moment in convective mode.
(14.01) x 9.42 x (7. 03.000 x 9.000 x 9.
4.699)
( Section 4.097) x 9.84)2] x tanh(0.09. Impulsive Hydrodynamic Pressure
piw(y) = Qiw(y) (Ah)i ρ g h cos ф Qiw(y) = 0.01)) + (9.38 x 1.866 [1 -(y / h)2 ] tanh(0.3)
piw(y = 0) = 0.7. Total overturning moment at the bottom of base plate.8.03.7.81 = 14.139)
= 14.097 x 10. Impulsive pressure at the base of wall. Total lateral base shear is about 27 % of seismic weight (10.1(a)) Maximum pressure will occur at ф = 0. base shear in convective mode.72 x 0.3)
4.81 = 906 kN-m Total bending moment at bottom of wall.84) = 0.211)
= 0.43 + 0.1.
( Section 4.1) = 0.7.01)) + (15.902 + 5.6.05 x 3.73 kN/m2.211 kN-m Similarly.38 x [(7.5. Hydrodynamic Pressure
4. Moment at Bottom of Wall
Bending moment at the bottom of wall in impulsive mode.72.81 = 152 kN Total base shear at the bottom of wall.81 = 2.84 x 1
= .84)) / cosh ( 0.38 x 1.32) 8. equivalent linear distribution for impulsive hydrodynamic pressure distribution will be as follows: Base shear due to impulsive liquid mass per unit circumferential length.84 /12) = 0.125[D/2D – 4/3 (D/2D)3] sech (3.674
= 139.9.67 x 1 = 2. equivalent linear distribution for convective pressure can be obtained as follows: Base shear due to convective liquid mass per unit circumferential length.05 kN/m2
.866 ( Ah )i ρ g h sinh (0.5 kN/m2
Qcw(y = 0) = 0.
Qcw(y = h) = 0.98) 8.2(a)) = 1.000 × 9.0.05 Convective pressure on top of base slab (y = 0)
= 3. Convective pressure at the base of wall.674h /D)
( Section 4.0 (6 × 3.28 kN/m At y = h.67 x 1
139.09 .0 kN/m Pressure at bottom and top is given by.5625 cosh(3.9.866 x / L ) / cosh 0.8.5625
Convective pressure at y = h.125[x/D – 4/3 (x/D) 3] sech (3.866 x 0.22 kN/m2.81 x 8.000 x 9.8. Convective hydrodynamic pressure on the base slab (y = 0) 23. y = 0. As per Section 4.04 (4 × 8.38 × 7 .81 x 12
= 0.84 /12) = 0.81 x 12 x 0. it is convenient to have linear pressure distribution along wall height.
4.674 h/D)
( Section 4.98 kN/m2 Equivalent linear impulsive pressure distribution is shown below: 3.2.5625 x cosh (0 / 12) / cosh (3.
( Ah ) i mi g 0.05 × 3. At base of wall.03.05 x 1. Equivalent Linear Pressure Distribution
p ib = 0.05 x 1.9.81 = πD/2 π × 12 / 2
pcw = Qcw(y) (Ah)c ρ g D [1.000 × 9.84 − 6 × 5.866l / h ( Section 4.
= 0.07 kN/m2
For stress analysis of tank wall. 5625 x 0.1(a)) = 0.84 − 6 × 3.000 x 9.674 x 8.84) 8.84 2
= 27.9.866 x 12 / ( 2 x 8.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
4.05 x 1.000 x 9.3.84 x sinh (0.
) = 139.05 x 0.000 x 9.81 = πD/2 π × 12 / 2
pcb = Qcb(x) (Ah)c ρ g D Qcb(x) = 1.
pcb = 0.4.6hc ) =
qc = ( Ah ) c mc g 0.0 (4 × 8. Convective Hydrodynamic Pressure
Convective hydrodynamic pressure on wall.81 x 12 x 0.07.84 ) = 15.07 x 0.04 kN/m Pressure at bottom and top is given by.32 − 2 × 8.674y/D)/ cosh(3.2(a)) Maximum pressure will occur at ф = 0.73
Similarly.1/3 cos2 ф] cosф Qcw(y) = 0.866 x 12 / 2 x 8.30 kN/m2
(4h .98
pcw(y = 0) = 0.
84) 8.
( Section 4.5 x 12 / 2 = 0. Anchorage Requirement
Here.53 = 0.5 ⎠
+ 0.73 + 0.e.15 kN / m2
(Section 4.5 ( Table 1) R = 2.84 )]
pv = 0. For design purpose this may be taken as zero.10.5 x 1.10.
Z = 0.3 sec in Section 4.12)
No anchorage is required. Zone V)
I = 1.81 x 8.9.4 = 3. It may be noted that for this steel tank pressure due to wall inertia is negligible compared to impulsive hydrodynamic pressure. Pressure Due to Vertical Excitation
Hydrodynamic pressure on tank wall due to vertical ground acceleration. for 2 % damping.
(6hc .05
Maximum hydrodynamic pressure.5 Hence.5)
This pressure is uniformly distributed along the wall height.87
2 ⎛ 0.005 x 78.2h ) =
= 0.84 2
Sa /g = 2.11.63 ( Ah )i 0.72 kN/m2). Sloshing Wave Height
Maximum sloshing wave height.
(IS 1893(Part 1): Table 2.84 = 86.5 Since time period of vertical mode of vibration is recommended as 0.. Hence.36 1.38 h 1 As < D ( Ah )i
( Section 4.81 x 8.12.87 kN/m2 Equivalent linear convective pressure distribution is shown below: 2. D 12 1 1 = = 2.25 x [1.7 kN/m2
4.84 = = 0.98 − 2 × 8.22 1.9.74 .
h 8.2)
At the base of wall.10.38 x 0.25 At the base of wall.
pv = (Av) [ρ g h ( 1.84 x ( 1 – 0 / 8.28 2 + 21.13. y = 0.1) (Av) =
4.3 kN/m2.05 x 2.
( Section 4.1.
= 1. Maximum Hydrodynamic Pressure
0.10.5 ⎞ ×⎜ × × 3 .04 (6 × 5. hydrodynamic pressure will marginally influence container design. Pressure Due to Wall Inertia
Pressure on wall due to its inertia.000 x 9.28
It may be noted that the linearised distribution for convective pressure has a very small negative value at the base. Maximum hydrodynamic pressure is about 37% of hydrostatic pressure (ρ g h = 1.11)
(23. as permissible stresses are already increased by 33%.5 ⎟ 3 ⎝ 2 2 .y / h )]
( Section 4.000 x 9.7 2
86 m hi* = 0.593 x 6.3.1 Sectional elevation
5.959 x 1.
A ground supported cylindrical RC water tank without roof has capacity of 1.
.000 kg Weight of water = 9. Grade of concrete is M30. Parameters of Spring Mass Model
h = 6.000 m3 Mass of water.000 = 4.2.000 kg mc / m = 0.0 = 1.464.
Where.5 % less than mass of liquid.375 x 6.5 = 2. hi*/ h = 0.00.
5.5/14 = 0.46.694 kg Mass of base slab.5 = 5.0 m (including a free board of 0. Inside diameter of tank is 14 m and height is 7.000 / 9.2) Note that about 51% of liquid is excited in impulsive mode while 46% participates in convective mode.511.5 m. mc = 0.68.2. hc / h = 0.1.5 m).375.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
5.44 m hc = 0.
5. D = 14 m
For h / D = 6. hi = 0.000 kg h i / h = 0.810 kN
mi /m = 0.4 x 25 x 1.00. Volume of water = 1.64. Tank wall has uniform thickness of 250 mm and base slab is 400 mm thick.1. mi = 0.328 kg.25 x 25 x 7.25) x 0. Time Period
Time period of impulsive mode.82 x 6.959 kN Mass of tank wall.000 = 5.Weight Calculations
Weight of tank wall = π x (14 + 0.11.000 / 9.99.853 x 6.853. Tank is located on soft soil in seismic zone IV.5 = 3.000 m3.511 x 10. mw = 1. mb = π x (7.55 m hc* = 0.81 = 1.464 x 10. Analyze the tank for seismic loads.82.33 m
( Section 4.00. Sum of impulsive and convective mass is about 2.25)2 x 0.5 = 5.593.
Figure 5. m = 10. Density of concrete is 25 kN/m3.81 = 1. hc*/ h = 0.
Damping = 0.1)
Where.3.04 sec .5.0
= 0.5 × × 2.694 + 0) x 9.81
Tc = 3.4. Damping = 5%.5% damping from that for 5% damping.04 sec. (Sa /g)i = 2.46.6.1.5 × × 0.5.000 x 9. (Ah)i =
( Sections 4.1 sec as per Section 4.390 N/mm2 = 27. Cc = 3.6. Site has soft soil. Base Shear
Base shear at the bottom of wall in impulsive mode.5 × 1.04 sec.04 sec.000 kg/m . Vc = (Ah) c mc g = 0. 9.000 f ck = 5. (Ah)c = Z I ⎛ Sa ⎞ ⎜ ⎟ 2 R ⎜ g ⎟c ⎝ ⎠
( Sections 4. as per Section 4.24 (IS 1893(Part 1): Table 2.5 = 0. Zone IV) ( Table 1) ( Table 2) Here.4) (Ah)c = coefficient for 0.38 ( Section 4. E = Young’s modulus = 5. Time period of convective mode.72 ( Section 4.1) Ti = 4. Z = 0.1)
5.1.5 ( Section 4.25 / 14) × 27.5.1)
Where.75 is used to obtain Sa /g values for 0.1) = 0.3 and IS 1893(Part 1): 2002.5.5 (IS 1893(Part 1): Table 2.99.4) Since Ti < 0. ρ = Mass density of water = 1. ( Section 4.5.1) Multiplying factor of 1.5 and 4. Ti = 0. Zone IV) I = 1.225 x (5. t = Thickness of wall = 0.24 I = 1. value of R is taken same as that for impulsive mode as per Section 4.
This tank has fixed base hence R is taken as 2.IITK-GSDMA Guidelines for seismic design of liquid storage tank s
h = Depth of liquid = 6.390 ×10 6
0.72 = 0.38
5.0.413 = 0.0 seismic coefficient for
Design horizontal convective mode.5 m.000 x 30 = 27. base shear in convective mode.569)
.81 = 296 kN Total base shear at the bottom of wall. Tc = C c
For h / D = 0.5 ( Table 1) For convective mode.4) Hence. ( Section 4.3.225 2 2.64. D = Inner diameter of tank = 14 m .24 1.065 x 4.81 = 1.000 + 1.
( Section 4.065 2 2. ( Section 4.11.390 x 106 N/m2.5 and 4.1.5%.2. Z = 0.000 (0. Tc = 4. Vi = (Ah) i (mi + mw + mt) g ( Section 4. For h / D = 0. Here.38
14 = 4.6.46.38 × 6. Figure 2 (Sa /g) c = 1. Design Horizontal Seismic Coefficient
Design horizontal impulsive mode.3) + (296)
(1.569 kN Similarly.25 m.5.75 x 0. Ci = 4. Site has soft soil.24 1.5.
Hydrodynamic pressure calculations for this tank are not shown.5 = = 0.295 kN-m Similarly.IITK-GSDMA Guidelines for seismic design of liquid storage tank s
= 1. Sloshing Wave Height
Maximum sloshing wave height. These will be similar to those in Example 4.91 m Sloshing wave height exceeds the freeboard of 0.1. dmax = (Ah) c R D / 2 = 0.
Mc* = (Ah)c mc (hc*+ tb) g ( Section 4.295)
+ (1.7.7.7. Similarly.55 + 0. bending moment in convective mode.1) = 0.4 / 2)] x 9.1. Anchorage Requirement
Here.12)
No anchorage is required.328 x 0.
1 1 = = 4 .5+ 0.225
h 1 < D ( Ah )i ( Section 4.5 m. Moment at Bottom of Wall
Bending moment at the bottom of wall in impulsive mode.3)
(8.4) + (1.2) =0.0 x 14 / 2 = 0.225x[(5.11.142)
= 4.000 x 2.81 = 1.1.671 kN-m. Total overturning moment at the bottom of base slab.7.6. h 6.065 x 2.64.7.444 kN-m.
5.4 ( Ah )i 0. overturning moment in convective mode. M* = = Mi
5. Total lateral base shear is about 14 % of seismic weight (11.695 kN-m.44) + (1.33 + 0.000x(5.4) x 9.065 x 4.86 x 9.11)
( Section 4. Mc = (Ah)c mc hc g ( Section 4.2) = 0.99.81 = 1.1.64.695)
= 8. Mi* = (Ah)i [ mi (hi*+ tb) + mw (hw+ tb) + mt (ht + tb) + mb tb / 2] g ( Section 4.
. ( Section 4.225 x [(5.68.3)
5.504 kN-m.4)) + 0 + (1.504)
+ (1.81 = 4.5) + 0] x 9.46 .7.769 kN) of tank.065 x 4.1) = 0.8.597 kN.694 x (3. Overturning Moment
Overturning moment at the bottom of base slab in impulsive mode.000 x 3.694 x 3.
5.81 = 8.142 kN-m Total bending moment at bottom of wall.000 x (5. D 14
(4. Mi = (Ah)i [ mi hi + mw hw + mt ht ] g ( Section 4.7. M= =
( Section 4.9.
81 = 2.directions.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
6.1.810 kN Mass of water.4) x 0.86.3 m (including a free board of 0.Analyze the tank for seismic loads. m = 10.5 x 25 x 1.81 = 3. The base slab is 500 mm thick.000 / 9.000 kg For rectangular tank. Volume of water = 1.and Y.00. seismic analysis is to be performed for loading in X. Tank is located on hard soil in Zone V. mb = 10.
A ground supported rectangular RC water tank of 1.000 / 9.
Mass of base slab.8 x 20.3 m).239 kg.
.3 = 3.4 + 10.000 m3 capacity has plan dimensions of 20 x 10 m and height of 5.32.1 Details of tank geometry
6. There is no roof slab on the tank. Wall has a uniform thickness of 400 mm.000 m3 Weight of water = 10 x 20 x 5 x 9. Grade of concrete is M30.81 = 9.265 kN Mass of tank wall. Weight Calculations
Weight of tank wall = 2 x (20.824 kg.
Figure 6.8 x 0.265 x 1. mw = 3.4 x 25 x 5.
As per this approach a strip of unit width of wall is considered as a cantilever and subjected to a concentrated force P = q x h x 1 = 38.39 × 10 6 × 5. ( Section 4. Ti = 2π
( Section 4. For this case. E = 5.09 3 d= = 0.2.2) For this case.1. mc = 0.0 x = 1.05 m hc* = 2. d = deflection of the tank wall on the vertical center-line at a height h when loaded by a uniformly distributed pressure q.00.5 × 2.9 kN/m2 To find the deflection of wall due to this pressure.61 hc*/ h = 2. 194.81
Time period of convective mode.3 × 1.88. Hence.88 + 54. Tc = C c
.88 m hc = 0.4 x 10 x 25 x 1. and about 30% liquid mass contributes to impulsive mode.000 f ck = 5.027 × − 2 = 2.81 ⎜ 2 ⎠ = ⎝ 10 × 5 = 38. here. Time Period
Time period of impulsive mode.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
6. Mass of one wall is obtained by considering its inner dimensions only. Deflection of wall can be obtained by performing analysis of wall or by classical analysis using theory of plates. hi = 0.524 hi* / h = 1.2)
= 27.33 × 10 −3 m 4 12 12 Hence. substantial amount of mass (about 70%) participates in convective mode. h/L = 0.4 3 = 1.000 5.695 x 10.375 hc / h = 0.000 kg h i / h = 0. Sum total of convective and impulsive mass is about 1.000 / 9.3 x 0.00405 m 3 × 27.3.9 x 5 x 1 = 194. mi / m = 0.95. L = 20 m and B = 10 m. .1. simple approach given in commentary of Section 4.000 + 54.88.027 kg
0.000 ⎞ + 54.027 ⎟ × 9. P h d= 3 E Iw
For h / L = 5/20 = 0.0 x 5 = 10. tank is quite squat and hence.13 sec . = 5. 9.88.2.695.7% less than total liquid mass. Parameters of Spring Mass Model
Hence.5 kN.000 = 2.3. Length of the cantilever is h .2)
Where.2 is followed.00.2. However. 2.00405 = 0.61 x 5 = 8.33 × 10 −3
direction of loading.
6.3.375 x 5 = 1.09 m 2 h= 2. it can be considered to be fixed at three edges and free at top. Analysis along X-Direction
This implies that earthquake force is applied in X-direction.25.25.000 kg mc / m = 0.1. i.0 m.027 2
⎛ mi ⎞ + m w ⎟g ⎜ ⎝ 2 ⎠ q= Bh ⎛ 2. ( Section 4.e. .
6.39 x106 kN/m2 Iw = Moment of inertia of cantilever t3 0 .88.2. .288 x 10.81 = 54.2.000 x 30
Where.1.0 × = 5.000 = 6.524 x 5 = 2.390 N/mm2 = 27.0 .288. mi = 0.1.62 m hi* = 1.
( Section 4.4. ( Table 2) Here.22 sec.4) Hence.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
For h / L = 0. 9.
6. Damping = 5%.
( Sections 4. Hence.075 kN) of tank.071)
= 2.1)
Base shear at the bottom of wall in impulsive mode.81 = 4.88.13 sec.000 x 9.28 = 0.
.36 ×
Multiplying factor of 1.6.36 1.81 = 259 kN Total base shear at the bottom of wall.5 × × 0.5. Design Horizontal Seismic Coefficient
Design horizontal impulsive mode.34 x (2.038 x 6.5.81 = 2.75 x 0.5 (IS 1893(Part 1): Figure 2) (Ah)i =
0. Tc = 6.2(b))
Tc = 4.087 kN. base shear in convective mode.071 kN.1.5
( Section 4. bending moment in convective mode.747 kN-m Similarly.36 1.000 x 2.75 is used to obtain Sa /g values for 0.0
( Section 4.3.1) (IS 1893(Part 1): Table 2.
( Section 4.2.95. as per Section 4.5.7.1)
= 0.3 and IS 1893(Part 1): 2002.88) + (3.81
6. Zone V) ( Table 1) = 0. Site has hard soil.0.5 % damping from that for 5 % damping.
For convective mode.1.34 2 2.36 ( Section 4.3) + (259)
(2.6. Ti = 0. R is taken as 2. ( Section 4.81 = 679 kN-m Total bending moment at bottom of wall.1)
Where.95.34 x [(2.0
20 = 6.4) (Ah)c =
0.7. Base Shear
( Section 4. ( Section 4. Cc = 4.2.038 2 2 .2.16 = 0.2.28
( Section 4. Moment at Bottom of Wall
Design horizontal convective mode.5 × × 2.5 = 0.4)
( Section 4.88.62 x 9. Site has hard soil. Damping = 0.5 and 4. (Sa /g)i = 2.
Where. Zone V) ( Table 1)
Since this RC tank is fixed at base.1) = 0.25.000 + 3.6.
Z = 0.32. Similarly. Here.36 I = 1.
Z = 0. value of R is taken same as that for impulsive mode as per Section 4. coefficient for This lateral base shear is about 16 % of total seismic weight (13.
Bending moment at the bottom of wall in impulsive mode.5.65) + 0] x 9.824 + 0) x 9.5.1) = 0.038 x 6.3.
6.000 x 1.22 sec.32.1.824 x 2.5
(IS 1893(Part 1): Table 2. Figure 2 (Sa /g)c = 1.5.5%.36 I = 1.
7.795 kN-m.4165
piw = Qiw(y) (Ah)i ρ g h Qiw(y) = 0.88.
pcw( y = 0 ) = 0.2.866 [1-(0/5)2] x tanh(0.866 x 20/5) = 0.2) = 0.162 h/L)
= 0.162 ⎟ L⎠ ⎝ Qcw(y) = 0.65 + 0.32.7.9.86 x 0.31.866 L / h )
(4.9 kN/m2
6. 0 ⎞ ⎛ cosh ⎜ 3.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
( Section 4.81 x 5 = 2. Impulsive pressure at the base of wall.3)
pib = Qib(x) (Ah)i ρ g h Qib(x) = sinh (0.9.000 x 9.(b))
pcw (y = h ) = 0.721 kN-m.038 x 6.866 x 20/5)
piw( y = 0 ) = 0.162 ⎟ L⎠ ⎝
pcw = Qcw(y) (Ah)c ρ g L y⎞ ⎛ cosh⎜ 3.95.000 x 9.(b)) At base of wall. ( Section 4.81 x 20
At base of wall.81 x 5
= 14.000 x 9.162 × ⎟ 20 ⎠ ⎝ = 0.86.948)
+ (2 .866[1-(y / h)2] x tanh (0.81 = 2.86.9.34 x 1.000 x (8.
Qcw( y = h ) = 0.2.1(a)) = sinh (0.4165 h⎞ ⎛ cosh⎜ 3. Similarly.4165 x 0. Impulsive Hydrodynamic Pressure
= 2. Hydrodynamic Pressure
6.7.5) + (3.171 Impulsive pressure on top of base slab (y = 0)
pib = 0. y = 0.239 x 0.038 x 1.
( Section 4.81 x 20
( Section 4.000 x (10 + 0.5) + 0 + (2.747 )
= 4.7.05 + 0.1.171 x 0.254 kN-m.
6.2(a))
.81 = 11.5) x 9.11 kN/ m2 Convective hydrodynamic pressure on the base slab (y = 0)
pcb = Qcb(x) (Ah)c ρ g D Qcb(x) = 1.1.34 x 1.162 × ⎟ 20 ⎠ ⎝ Qcw( y = 0 ) = 0. Overturning Moment
( Section 4. Convective Hydrodynamic Pressure
Overturning moment at the bottom of base slab in impulsive mode.5 / 2)] x 9. overturning moment in convective mode.
( Section 4.25[x/L – 4/3 (x/L) 3] sech (3. Convective pressure at the base of wall.34 x [(2.
Qiw(y = 0 ) = 0.3)
(11.948 kN-m.2) = 0.3 kN/m .866 L / h )
Convective pressure at y = h.866 x 20 /10) /cosh (0.2.038 x 1. y = 0.2.7.31 kN/m2 At y = h.000 x 9.2.9.866 x / L ) / cosh (0.4165 × 5 ⎞ ⎛ cosh⎜ 3.7.2.824 x (2.1.
6.721)
= 12.31 x 0.6. Total overturning moment at the bottom of base slab.
03 kN/m
Hydrodynamic pressure on tank wall due to vertical ground acceleration.8 Linearised distribution
(14.000 x 9.3 sec in Section 4.000 × 9.
( Section 4.4 kN/m2.5 ⎟ 3 ⎝ 2 2.81 x 20
I = 1. Pressure Due to Wall Inertia
Pressure on wall due to its inertia.4 x 25 = 3.038 x 1. equivalent linear distribution for convective pressure can be obtained as follows: Base shear due to convective liquid mass per unit circumferential length.2) At the base of wall. As per Section 4. In this case.162 x 5 /20) = 0.88 ) 52 48.34 × 2 .4)
Similarly.04 kN/m2
pv = (Av) [ρ g h (1.2. 2 ⎛ 0. y = 0.2.1)
⎛ Z I Sa ⎞ ⎜ ⎜2 R g ⎟ ⎟ ⎝ ⎠ (IS 1893(Part 1): Table 2. i. This pressure is uniformly distributed along the wall height. pv = 0.10.5)
= 0. Equivalent Linear Pressure Distribution
= 2. Zone V)
48.y / h )]
Value of linearised pressure at bottom and top is given by.9.9.11.3 + 3.5 kN/m2 Equivalent linear impulsive pressure distribution is shown below: 2.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
= 1.34 x 0.81 = 2B 2 × 10 = 48.04 2
.8.0 ⎠ = 0.88. it is convenient to have linear pressure distribution along wall height.225.
16.225 x [1.81 x 5 = 49 kN/m2). At the base of wall.36 1.000 x 9. This hydrodynamic pressure is about 43% of hydrostatic pressure (ρ g h = 1.9.3 Actual distribution
Maximum hydrodynamic pressure.88 − 2 × 5 ) 52
= 16. equivalent linear distribution for impulsive hydrodynamic pressure distribution can be obtained as follows: Base shear per unit circumferential length due to impulsive liquid mass.000 x 9.25[L/2L – 4/3 (L/2L)3] sech (3.10.5 ( Table 1) R = 2.0 Time period of vertical mode of vibration is recommended as 0. qc.5
= 11.5.03 ( 6 × 1.
( Ah ) i mi g 0. Pressure Due to Vertical Excitation
For stress analysis of tank wall.
( Section 4.313 x 0. Sa /g = 2.81 x 5 x ( 1 – 0 / 5 )]
= 2.2.5 ⎞ (Av) = × ⎜ × × 2.2.. hydrodynamic pressure will substantially influence the design of container. Hence.8 kN/m2
Z = 0.312 + 11.03 ( 4 × 5 − 6 × 1.
6.4.33 kN/m2
6. for 5% damping.e.0 kN/m2.10.10. Maximum Hydrodynamic Pressure
14.313 Convective pressure on top of base slab (y = 0)
pcb = 0.
10.9.2)
pcb = Qcb(x) (Ah)c ρ g D Qcb(x) = 1.8.0 Time period of vertical mode of vibration is recommended as 0.. 63 m
(13.162 × ⎟ 10 ⎠ ⎝ = 0.0 2 + 11.3)
.162 ⎟ L⎠ ⎝ Qcw(y) = 0.225 x [ 1 x 9.81 x 5 x (1 – 0/5)]
= 11.9.10.34 x 0. Maximum Hydrodynamic Pressure
pcw( y = h ) = 0.
( Section 4.25[x/L – 4/3 (x/L) 3] sech (3.5.3.
I = 1.81 x 10
= 1.36 1. Pressure Due to Vertical Excitation
Hydrodynamic pressure on tank wall due to vertical ground acceleration.0 ⎠
= 0. This maximum hydrodynamic pressure is about 41 % of hydrostatic pressure (49 kN/m2).1) (Av) =
Z = 0.3.000 x 9.162 ⎟ L⎠ ⎝
+ 1.10.81 x 10
= 1.25[L/2L – 4/3 (L/2L)3] sech (3.225. design of tank will be influenced by hydrodynamic pressure. y = 0.4165 x 0. 2 ⎛ 0. Hence.e.5 ⎞ (Av) = × ⎜ × × 2.y / h )]
( Section 4.3.11.16
Convective pressure at the base of wall.
= 0.165 Convective pressure on top of base slab (y = 0) At the base of wall. y = 0.0 kN/m2 At y = h.4165
Convective pressure at the y = h.2(a)) = 1. Pressure Due to Wall Inertia
Maximum sloshing wave height.4165 h⎞ ⎛ cosh⎜ 3.
pv = (Av) [ρ g h (1. At the base of wall.000 x 9.4165 × 5⎞ ⎛ cosh⎜ 3.
y⎞ ⎛ cosh ⎜ 3.2.16 x 0.10.9.(b)) At base of wall.04 2
= 20.06 x 2. Convective hydrodynamic pressure on the base slab (y = 0)
Qcw(y = h) = 0. i. for 5% damping. This being more than 33%.9.4165 h⎞ ⎛ cosh ⎜ 3.5 + 3.11)
Pressure on wall due to its inertia.06 x 1.3.22 kN/m2.
y⎞ ⎛ cosh⎜ 3.5 ( Table 1) R = 2.
This pressure is uniformly distributed along the wall height.06 x 1.4 x 25 = 3. 5 ⎟ 3 ⎝ 2 2. Sa /g = 2.000 x 9. Sloshing Wave Height
pcb = 0.0 x 10 / 2 = 0.162 x 5 /10) = 0.162 × ⎟ 10 ⎠ ⎝ = 0.06 x 1.02 kN/m2
6.57 kN/m2.81 x 10
= 2.162 h/L)
( Section 4.1.165 x 0.04 kN/m2
6.3 sec in Section 4.36
(IS 1893(Part 1): Table 2.162 ⎟ L⎠ ⎝ Qcw( y = 0 ) = 0. Zone V)
pcw ( y = 0 ) = 0.162 ⎟ L⎠ ⎝ 0⎞ ⎛ cosh⎜ 3.4 kN/m2.
No anchorage is required.IITK-GSDMA Guidelines for seismic design of liquid storage tanks
6.12.5 .94 ( Ah )i 0.3.
1 1 = = 2.
h 5 = = 0 . L 10
1 h < ( Ah )i L ( Section 4. Anchorage Requirement
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Sign up to vote on this titleUsefulNot usefulGuidelines for Seismic Design of Liquid Storage Tanks by Luis Sequeira0.0 (0)EmbedDownloadRead on Scribd mobile: iPhone, iPad and Android.Copyright: Attribution Non-Commercial (BY-NC)List price: $0.00Download as PDF, TXT or read online from ScribdFlag for inappropriate contentMore informationShow less
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