Lecture 1 January 17, 2006.

Lecture 1 January 17, 2006

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

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) E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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

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 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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

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 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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 h h Hydrostatic pressure E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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

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 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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

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

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 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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

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 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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) E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

Modeling of liquid Impulsive Convective Base motion Base motion Hydrodynamic pressure E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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

Modeling of liquid Housner suggested graphs for mi and mc mi and mc 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), mi as fraction of m is more For short tanks, mc as fraction of m is more E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

Modeling of liquid mi/m mi/m mc /m mc /m For circular tanks For rectangular tanks See next slide for definition of h, D, and L E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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

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 82 x 3 = m3 Total liquid mass, m = x 1.0 = t Note:- mass density of water is 1000 kg/m3; weight density of water is 9.81 x 1000 = 9810 N/m3. D = 8 m, h = 3 m  h/D = 3/8 = E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

mi/m mc /m E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

Modeling of liquid From graph, for h/D = 0.375 mi/m = 0.42 and mc/m = 0.56 mi = 0.42 x = 63.3 t and mc = 0.56 x = 84.5 t E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

Modeling of liquid Impulsive liquid is rigidly attached to wall Convective liquid moves relative to wall As if, attached to wall with springs Rigid mc Kc/2 mi Convective liquid (moves relative to wall) Impulsive liquid (moves with wall) E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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

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

Modeling of liquid Example 2: A circular tank with internal diameter of 8 m, stores 3 m height of water. Find Kc. Solution: Total liquid mass, m = t (from Example 1) = x 1000 = kg g = acceleration due to gravity = 9.81 m/sec2 D = 8 m, h = 3m  h/D = 3/8 = From graph, for h/D = 0.375; Kc h/mg = 0.65 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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

Modeling of liquid Now, we know liquid masses mi and mc 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 mi and mc is needed to obtain overturning effects Impulsive mass acts at centroid of impulsive pressure diagram Similarly, convective mass E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

Modeling of liquid Resultant of impulsive pressure on wall Resultant of convective pressure on wall hc hi hi, hc 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 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

Modeling of liquid hc/h hc/h hi/h hi/h For circular tanks For rectangular tanks E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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

hc/h hi/h E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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

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 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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

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 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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

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

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

Modeling of liquid Similarly, hc and hc* are defined hc h*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 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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

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

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

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

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

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

spring mass model of tank
Modeling of liquid mi = Impulsive liquid mass mc = Convective liquid mass Kc = Convective spring stiffness hi = Location of impulsive mass (without considering overturning caused by base pressure) hc = Location of convective mass hi* = Location of impulsive mass (including base pressure effect on overturning) hc* = Location of convective mass Rigid mc Kc/2 mi hi (hi*) hc (hc*) Mechanical analogue or spring mass model of tank E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

Modeling of liquid mi, mc, Kc, hi, hc, hi* and hc* can also be obtained from mathematical expressions: These are given in Table C 1 of Guidelines These are reproduced in next two slides E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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

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

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 hi/h shall have limit as “for h/D  0.75” For circular tank, in the expression for hi*/h, there shall be minus sign before 0.125 These two errors have been corrected in the expressions given in previous two slides E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

Modeling of liquid mi and mc are needed to find impulsive and convective forces Impulsive force, Vi = mi x acceleration Convective force, Vc = mc x acceleration Rigid mc Kc/2 mi Vi Vc E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

Modeling of liquid Vi and Vc will cause Bending Moment (BM) in wall E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

Modeling of liquid BM at bottom of wall BM due to Vi = Vi x hi BM due to Vc = Vc x hc Total BM is not necessarily Vi X hi+ Vc X hc More about this, later Rigid mc Kc/2 mi Vi Vc hi hc E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

Modeling of liquid OM at bottom of base slab OM due to Vi = Vi x hi* BM due to Vc = Vc x hc* Rigid mc Kc/2 mi hi* Vc hc* Vi E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

Modeling of liquid mi and mc will have different accelerations We yet do not know these accelerations ai = acceleration of mi ac = acceleration of mc Procedure to find acceleration, later Use of mi, mc, hi, hc, hi* and hc* in next example Acceleration values are assumed E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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: mi = t mc = 84.5 t hi = m hc = 1.65 m hi* = 3.3 m hc* = 3.0 m Impulsive acceleration, ai = 0.3g = 0.3 x 9.81 = 2.94 m/sec2 Convective acceleration, ac = 0.1g = 0.1 x 9.81 = 0.98 m/sec2 E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

Modeling of liquid Example 5 (Contd..) Impulsive force, Vi = mi x ai = 63.3 x 2.94 = kN Convective force, Vc = mc x ac = 84.5 x 0.98 = 82.8 kN Bending moment at bottom of wall due to Vi = Vi x hi = x = kN-m Bending moment at bottom of wall due to Vc = Vc x hc = 82.8 x 1.65 = kN-m Overturning moment at bottom of base due to Vi = Vi x hi* = x 3.3 = kN-m Overturning moment at bottom of base due to Vc = Vc x hc* = 82.8 x 3.0 = kN-m E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

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) E-Course on Seismic Design of Tanks/ January 2006  Sudhir K. Jain, IIT Kanpur

Lecture 1 January 17, 2006.

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Lecture 1 January 17, 2006.

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