Lecture 1 January 17, 2006

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 2 In this lecture Types of tanks IS codes on tanks Modeling of liquid

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 3 Types of tanks Two categories Ground supported tanks Also called at-grade tanks; Ground Service Reservoirs (GSR) Elevated tanks Also called overhead tanks; Elevated Service Reservoirs (ESR)

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 4 Types of tanks Ground supported tanks Shape: Circular or Rectangular Material : RC, Prestressed Concrete, Steel These are ground supported vertical tanks Horizontal tanks are not considered in this course

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 5 Types of tanks Elevated tanks Two parts: Container Staging (Supporting tower)

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 6 Types of tanks Elevated tanks Container: Material: RC, Steel, Polymer Shape : Circular, Rectangular, Intze, Funnel, etc. Staging: RC or Steel frame RC shaft Brick or masonry shafts Railways often use elevated tanks with steel frame staging Now-a-days, tanks on brick or stone masonry shafts are not constructed

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 7 Use of tanks Water distribution systems use ground supported and elevated tanks of RC & steel Petrochemical industries use ground supported steel tanks

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 8 Indian Codes on Tanks IS 3370:1965/1967 (Parts I to IV) For concrete (reinforced and prestressed) tanks Gives design forces for container due to hydrostatic loads Based on working stress design BIS is considering its revision

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 9 Indian Codes on Tanks IS 11682:1985 For RC staging of overhead tanks Gives guidelines for layout & analysis of staging More about this code later IS 803:1976 For circular steel oil storage tanks

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 10 Indian Codes on Tanks IS 1893:1984 Gives seismic design provisions Covers elevated tanks only Is under revision More about other limitations, later IS 1893 (Part 1):2002 is for buildings only Can not be used for tanks

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 11 Hydrodynamic Pressure Under static condition, liquid applies pressure on container. This is hydrostatic pressure During base excitation, liquid exerts additional pressure on wall and base. This is hydrodynamic pressure This is in additional to the hydrostatic pressure

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 12 Hydrodynamic pressure Hydrostatic pressure Varies linearly with depth of liquid Acts normal to the surface of the container At depth h from liquid top, hydrostatic pressure =  h Hydrostatic pressure h hh

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 13 Hydrodynamic pressure Has curvilinear variation along wall height Its direction is opposite to base motion Base motion Hydrodynamic pressure

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 14 Hydrodynamic pressure Summation of pressure along entire wall surface gives total force caused by liquid pressure Net hydrostatic force on container wall is zero Net hydrodynamic force is not zero

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 15 Hydrodynamic pressure Hydrostatic pressureHydrodynamic pressure Base motion Circular tanks (Plan View) Net resultant force = zero Net resultant force ≠ zero Note:- Hydrostatic pressure is axisymmetric; hydrodynamic is asymmetric

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 16 Hydrodynamic pressure Hydrostatic pressureHydrodynamic pressure Base motion Net resultant force = zero Net resultant force ≠ zero Rectangular tanks (Plan View)

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 17 Hydrodynamic pressure Static design: Hydrostatic pressure is considered Hydrostatic pressure induces hoop forces and bending moments in wall IS 3370 gives design forces for circular and rectangular tanks Net hydrostatic force is zero on container wall Hence, causes no overturning moment on foundation or staging Thus, hydrostatic pressure affects container design only and not the staging or the foundation

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 18 Hydrodynamic pressure Seismic design: Hydrodynamic pressure is considered Net hydrodynamic force on the container is not zero Affects design of container, staging and foundation

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 19 Hydrodynamic pressure Procedure for hydrodynamic pressure & force: Very simple and elegant Based on classical work of Housner (1963a) Housner, G. W., 1963a, “Dynamic analysis of fluids in containers subjected to acceleration”, Nuclear Reactors and Earthquakes, Report No. TID 7024, U. S. Atomic Energy Commission, Washington D.C. We need not go in all the details Only basics and procedural aspects are explained in next few slides

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 20 Modeling of liquid Liquid in bottom portion of the container moves with wall This is called impulsive liquid Liquid in top portion undergoes sloshing and moves relative to wall This is called convective liquid or sloshing liquid Convective liquid (moves relative to tank wall) Impulsive liquid (moves with tank wall)

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 21 Modeling of liquid Impulsive liquid Moves with wall; rigidly attached Has same acceleration as wall Convective liquid Also called sloshing liquid Moves relative to wall Has different acceleration than wall Impulsive & convective liquid exert pressure on wall Nature of pressure is different See next slide

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 22 Modeling of liquid ImpulsiveConvective Hydrodynamic pressure Base motion

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 23 Modeling of liquid At this point, we will not go into details of hydrodynamic pressure distribution Rather, we will first find hydrodynamic forces Impulsive force is summation of impulsive pressure on entire wall surface Similarly, convective force is summation of convective pressure on entire wall surface

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 24 Modeling of liquid Total liquid mass, m, gets divided into two parts: Impulsive liquid mass, m i Convective liquid mass, m c Impulsive force = m i x acceleration Convective force = m c x acceleration m i & m c experience different accelerations Value of accelerations will be discussed later First we will find m i and m c

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 25 Modeling of liquid Housner suggested graphs for m i and m c m i and m c depend on aspect ratio of tanks Such graphs are available for circular & rectangular tanks See Fig. 2a and 3a of Guidelines Also see next slide For taller tanks (h/D or h/L higher), m i as fraction of m is more For short tanks, m c as fraction of m is more

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 26 Modeling of liquid For circular tanksFor rectangular tanks m i /m m c /m m i /m m c /m See next slide for definition of h, D, and L

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 27 Modeling of liquid D L Base motion L Elevation Plan of Circular tank Plan of Rectangular tank h

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 28 Modeling of liquid Example 1: A circular tank with internal diameter of 8 m, stores 3 m height of water. Find impulsive and convective water mass. Solution: Total volume of liquid =  /4 x 8 2 x 3 = m 3  Total liquid mass, m = x 1.0 = t Note:- mass density of water is 1000 kg/m 3 ; weight density of water is 9.81 x 1000 = 9810 N/m 3. D = 8 m, h = 3 m  h/D = 3/8 =

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 29 m i /m m c /m

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 30 Modeling of liquid From graph, for h/D = m i /m = 0.42 and m c /m = 0.56 m i = 0.42 x = 63.3 t and m c = 0.56 x = 84.5 t

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 31 Modeling of liquid Impulsive liquid is rigidly attached to wall Convective liquid moves relative to wall As if, attached to wall with springs Rigid mcmc K c /2 mimi Convective liquid (moves relative to wall) Impulsive liquid (moves with wall)

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 32 Modeling of liquid Stiffness associated with convective mass, K c K c depends on aspect ratio of tank Can be obtained from graph Refer Fig. 2a, 3a of guidelines See next slide

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 33 Modeling of liquid

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 34 Modeling of liquid Example 2: A circular tank with internal diameter of 8 m, stores 3 m height of water. Find K c. Solution: Total liquid mass, m = t (from Example 1) = x 1000 = kg g = acceleration due to gravity = 9.81 m/sec 2 D = 8 m, h = 3m  h/D = 3/8 = From graph, for h/D = 0.375; K c h/mg = 0.65

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 35 Modeling of liquid K c = 0.65 mg/h  K c = 0.65 x x 9.81/3.0 = 320,525.4 N/m Note: - Unit of m is kg, hence unit of K c is N/m. If we take m in ton, then unit of K c will be kN/m.

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 36 Modeling of liquid Now, we know liquid masses m i and m c Next, we need to know where these are attached with the wall Like floor mass in building acts at centre of gravity (or mass center) of floor Location of m i and m c is needed to obtain overturning effects Impulsive mass acts at centroid of impulsive pressure diagram Similarly, convective mass

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 37 Modeling of liquid Impulsive mass acts at centroid of impulsive pressure diagram Location of centroid: Obtained by dividing the moment due to pressure distribution by the magnitude of impulsive force Similarly, location of convective mass is obtained See next slide

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 38 Modeling of liquid hihi h i, h c can be obtained from graphs They also depend on aspect ratio, h/D or h/L Refer Fig. 2b, 3b of guidelines See next slide hchc Resultant of impulsive pressure on wall Resultant of convective pressure on wall

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 39 Modeling of liquid h c /h h i /h For circular tanksFor rectangular tanks h c /h h i /h

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 40 Modeling of liquid Example 3: A circular tank with internal diameter of 8 m, stores 3 m height of water. Find h i and h c. Solution: D = 8 m, h = 3m  h/D = 3/8 =

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 41 h c /h h i /h

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 42 Modeling of liquid From graph, for h/D = 0.375; h i /h = hi = x 3 = m and h c /h = 0.55 h c = 0.55 x 3 = 1.65 m Note :- Since convective pressure is more in top portion, h c > h i.

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 43 Modeling of liquid Hydrodynamic pressure also acts on base Under static condition, base is subjected to uniformly distributed pressure Due to base motion, liquid exerts nonuniform pressure on base This is in addition to the hydrostatic pressure on the base See next slide

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 44 Modeling of liquid Hydrostatic pressure on base Base motion Hydrodynamic pressure on base

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 45 Modeling of liquid Impulsive as well as convective liquid cause nonuniform pressure on base Nonuniform pressure on base causes overturning effect This will be in addition to overturning effect of hydrodynamic pressure on wall See next slide

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 46 Modeling of liquid Overturning effect due to wall pressure Overturning effect due to base pressure hihi Note:- Both the overturning effects are in the same direction

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 47 Modeling of liquid Total overturning effect of wall and base pressure is obtained by applying resultant of wall pressure at height, h i * and h c *. In place of h i and h c discussed earlier For overturning effect due to wall pressure alone, resultant was applied at h i For h i and h i *, see next slide

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 48 Modeling of liquid hihi h*ih*i Location of resultant of wall pressure when effect of base pressure is not included Location of Resultant of wall pressure when effect of base pressure is also included

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 49 Modeling of liquid Similarly, h c and h c * are defined hchc h*ch*c Location of resultant of wall pressure when effect of base pressure is not included Location of Resultant of wall pressure when effect of base pressure is also included

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 50 Modeling of liquid h i and h i * are such that Moment due to impulsive pressure on walls only = Impulsive force x h i Moment due to impulsive pressure on walls and base = Impulsive force x h i * h c and h c * are such that Moment due to convective pressure on walls only = Convective force x h c Moment due to convective pressure on walls and base = Convective force x h c *

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 51 Modeling of liquid h i * is greater than h i h c * is greater than h c Refer Fig. C-1 of the Guidelines h i * & h c * depend on aspect ratio Graphs to obtain h i, h c, h i *, h c * are provided Refer Fig. 2b & 3b of guidelines Also see next slide Please note, h i * and h c * can be greater than h

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 52 Modeling of liquid

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 53 Modeling of liquid Example 4: A circular tank with internal diameter of 8 m, stores 3 m height of water. Find h i * and h c *. Solution: D = 8 m, h = 3m  h/D = 3/8 = From graph, for h/D = 0.375;

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 54 Modeling of liquid h i */h = 1.1 Hence h i * = 1.1 x 3 = 3.3 m Similarly, h c */h = 1.0 Hence, h c * = 1.0 x 3 = 3.0 m

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 55 Modeling of liquid This completes modeling of liquid Liquid is replaced by two masses, m i & m c This is called mechanical analogue or spring mass model for tank See next slide

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 56 Modeling of liquid Rigid mcmc K c /2 mimi h i (h i * ) h c (h c * ) m i = Impulsive liquid mass m c = Convective liquid mass K c = Convective spring stiffness h i = Location of impulsive mass (without considering overturning caused by base pressure) h c = Location of convective mass (without considering overturning caused by base pressure) h i * = Location of impulsive mass (including base pressure effect on overturning) h c * = Location of convective mass (including base pressure effect on overturning) Mechanical analogue or spring mass model of tank

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 57 Modeling of liquid m i, m c, K c, h i, h c, h i * and h c * can also be obtained from mathematical expressions: These are given in Table C 1 of Guidelines These are reproduced in next two slides

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 58 for For circular tanks for Modeling of liquid

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 59 For rectangular tanks for Modeling of liquid

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 60 Modeling of liquid Note, in Table C-1 of the Guideline, there are two typographical errors in these expressions For circular tank, first expression for h i /h shall have limit as “for h/D  0.75” For circular tank, in the expression for h i * /h, there shall be minus sign before These two errors have been corrected in the expressions given in previous two slides

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 61 Modeling of liquid m i and m c are needed to find impulsive and convective forces Impulsive force, V i = m i x acceleration Convective force, V c = m c x acceleration Rigid mcmc K c /2 mimi ViVi VcVc

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 62 Modeling of liquid V i and V c will cause Bending Moment (BM) in wall

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 63 Modeling of liquid BM at bottom of wall BM due to V i = V i x h i BM due to V c = V c x h c Total BM is not necessarily V i X h i + V c X h c More about this, later Rigid mcmc K c /2 mimi ViVi VcVc h i h c

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 64 Modeling of liquid Overturning of the container is due to pressure on wall and base Pressure on base does not cause BM in wall Overturning Moment (OM) at tank bottom OM is at bottom of base slab Hence, includes effect of pressure on base Note the difference between bottom of wall and bottom of base slab

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 65 Modeling of liquid OM at bottom of base slab OM due to V i = V i x h i * BM due to V c = V c x h c * ViVi VcVc Rigid mcmc K c /2 mimi h i * h c *

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 66 Modeling of liquid m i and m c will have different accelerations We yet do not know these accelerations a i = acceleration of m i a c = acceleration of m c Procedure to find acceleration, later Use of m i, m c, h i, h c, h i * and h c * in next example Acceleration values are assumed

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 67 Modeling of liquid Example 5: A circular tank with internal diameter of 8 m, stores 3 m height of water. Assuming impulsive mass acceleration of 0.3g and convective mass acceleration of 0.1g, find seismic forces on tank. Solution: Geometry of tank is same as in previous examples. D = 8 m, h = 3m From previous examples: m i = 63.3 t m c = 84.5 t h i = m h c = 1.65 m h i * = 3.3 m h c * = 3.0 m Impulsive acceleration, a i = 0.3g = 0.3 x 9.81 = 2.94 m/sec 2 Convective acceleration, a c = 0.1g = 0.1 x 9.81 = 0.98 m/sec 2

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 68 Modeling of liquid Example 5 (Contd..) Impulsive force, V i = m i x a i = 63.3 x 2.94 = kN Convective force, V c = m c x a c = 84.5 x 0.98 = 82.8 kN Bending moment at bottom of wall due to V i = V i x h i = x = kN-m Bending moment at bottom of wall due to V c = V c x h c = 82.8 x 1.65 = kN-m Overturning moment at bottom of base due to V i = V i x h i * = x 3.3 = kN-m Overturning moment at bottom of base due to V c = V c x h c * = 82.8 x 3.0 = kN-m

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 1 / Slide 69 At the end of Lecture 1 In seismic design, mechanical analogue of tanks are used, wherein, liquid is replaced by impulsive & convective masses These masses and their points of application depend on aspect ratio Graphs and expressions are available to find all these quantities These are based on work of Housner (1963a)