Lecture 4 January 30, 2006. Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January...

Lecture 4

January 30, 2006

Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 2

In this lecture

Z, I, Sa/g and R values for tanks


Base shear coefficient

Seismic force V = (Ah) x (W) Ah is base shear coefficient

Zone

Depends on severity of ground

motion

Structural characteristics

Depends on time period and damping

2

Z

R

I

g

SahA

Design philosoph

y



Tanks have two modes Impulsive Convective

Seismic force In impulsive mode, Vi = (Ah)i x impulsive weight In convective mode, Vc = (Ah)c x convective weight

(Ah)i and (Ah)c are base shear coefficient in impulsive and convective modes, respectively



Impulsive base shear coefficient (Ah)i = (Z/2) x (I/R) x (Sa/g)i

Convective base shear coefficient (Ah)c = (Z/2) x (I/R) x (Sa/g)c

Note, R has been used in (Ah)i as well as (Ah)c

Zone factor, Z As per Table 2 of IS 1893(Part1):2002

I, R, (Sa/g)i and (Sa/g)c will be discussed here First, (Sa/g)i and (Sa/g)c


(Sa/g)i and (Sa/g)c

(Sa/g)i is average response acceleration for impulsive mode Depends on time period and damping of

impulsive mode (Sa/g)c is average response acceleration

for convective mode Depends on time period and damping of

convective mode


(Sa/g)i and (Sa/g)c

Sa/g is obtained from design spectra Figure 2 of IS 1893(Part 1):2002

These spectra are slightly modified for tanks See next slide


(Sa/g)i and (Sa/g)c

Modifications are: The rising portion in short period range from (0

to 0.1 sec) has been made constant Very stiff structures have time period less than 0.1 sec There may be modeling errors; actual time period may

be slightly higher As the structure gets slightly damaged, its natural

period elongates Ductility does not help in reducing response of very

stiff structures Hence, rising portion in the range 0 to 0.1 sec is

usually disallowed by the codes. Spectra is extended beyond 4 sec

Since convective time period may be greater than 4 sec.

Beyond 4 sec, 1/T variation is retained


(Sa/g)i and (Sa/g)c

Spectra of IS 1893 (Part 1):2002 Modified spectra

For 5% damping

Sa/g

Sa/gSa/g


(Sa/g)i and (Sa/g)c

Expressions for spectra of IS 1893(Part 1):2003

Expressions for spectra for tanks

For hard soil sites Sa/g = 1 + 15 T 0.00 T < 0.10

= 2.50 0.10 T < 0.40 = 1.00 / T 0.40 T 4.0

For medium soil sites Sa/g = 1 + 15 T 0.00 T < 0.10

= 2.50 0.10 T < 0.55 = 1.36 / T 0.55 T 4.0

For soft soil sites Sa/g = 1 + 15 T 0.00 T < 0.10

= 2.50 0.10 T < 0.67 = 1.67 / T 0.67 T 4.0

For hard soil sites Sa/g = 2.50 T < 0.40 = 1.0 / T T ≥ 0.40

For medium soil sites Sa/g = 2.50 T < 0.55 = 1.36 / T T ≥ 0.55 For soft soil sites Sa/g = 2.5 T< 0.67 = 1.67 / T T ≥ 0.67

Expressions for design spectra at 5% damping


(Sa/g)i and (Sa/g)c

Sa/g values also depend on damping Multiplying factors for different damping are given in

Table 3 of IS 1893(Part 1)

Recall from Lecture 2, higher damping reduces base shear coefficient or design seismic forces

Multiplying factor =1.4, for 2% damping Multiplying factor = 1.0 for 5% damping Multiplying factor = 0.8 for 10% damping This multiplier is not used for PGA


Damping

Damping for impulsive mode 5% of critical for RC tanks 2% of critical for steel tanks These are kept in line with IS 1893(Part 1)

Clause 7.8.2.1 of IS 1893(Part 1) suggests 5% damping for RC and 2% damping for steel buildings

However, IBC 2003 suggests 5% damping for all tanks

It suggests 5% damping for all types of buildings also


Damping

Damping depends on material and level of vibration Higher damping for stronger shaking Means that during the same earthquake,

damping will increase as the level of shaking increases

We are performing a simple linear analysis, while the real behavior is non-linear

Hence, one fixed value of damping is used in our analysis


Damping

IS 1893(Part 1), needs to have a re-look at the damping values Accordingly, damping values for tanks can also

be modified


Damping

Damping for convective mode 0.5% of critical for all types of tanks Convective mode damping does not depend on

material of tank or type of liquid stored In Table 3 of IS 1893(Part 1):2002

Multiplying factor for 0.5% damping is not given Values are given for 0% and 2% damping Linear interpolation shall not be done

Multiplying factor = 1.75, for 0.5% damping In Eurocode 8 this multiplying factor is 1.673 In ACI 350.3, this factor is 1.5


Importance factor, I

Importance factor, I for tanks is given in Table 1 of the Guideline This Table is reproduced here

Type of liquid storage tank I

Tanks used for storing drinking water, non-volatile material, low inflammable petrochemicals etc. and intended for emergency services such as fire fighting services. Tanks of post earthquake importance.

1.5

All other tanks with no risk to life and with negligible consequences to environment, society and economy.

1.0

NOTE: Values of importance factor, I given in IS 1893 (Part 4) may be used where appropriate



I = 1.5, is consistent with IS 1893(Part 1) IS 1893(Part 1):2002 suggests, I = 1.5 for

Hospital buildings Schools Fire station buildings, etc.

Tanks are kept at same importance level



Footnote below this Table is given to avoid conflict with I values of IS1893(Part 4) IS 1893(Part 4) will deal with industrial

structures Not yet published

Some industries assign very high importance factor to tanks storing hazardous materials

Depending on their own requirements For such tanks, Importance factor (I) will be as

per part 4


Response reduction factor, R

R values for tanks are given in Table 2 of the Guideline This is reproduced in next two slides



Elevated tank R

Tank supported on masonry shaftsa) Masonry shaft reinforced with horizontal bands * b) Masonry shaft reinforced with horizontal bands and vertical bars at

corners and jambs of openings

1.31.5

Tank supported on RC shaft RC shaft with two curtains of reinforcement, each having horizontal and vertical reinforcement

1.8

Tank supported on RC frame#

a) Frame not conforming to ductile detailing, i.e., ordinary moment resisting frame (OMRF) b) Frame conforming to ductile detailing, i.e., special moment resisting frame (SMRF)

1.8

2.5

Tank supported on steel frame# 2.5# These R values are meant for liquid retaining tanks on frame type staging which are inverted pendulum type structures. These R values shall not be misunderstood for those given in other parts of IS 1893 for building and industrial frames. * These tanks are not allowed in Zone IV and V



Ground supported tank R

Masonry tank a) Masonry wall reinforced with horizontal bands*

b) Masonry wall reinforced with horizontal bands and vertical bars at corners and jambs of openings

1.31.5

RC / prestressed tank a) Fixed or hinged/pinned base tank (Figures 6a, 6b, 6c) b) Anchored flexible base tank (Figure 6d) c) Unanchored contained or uncontained tank (Figures 6e, 6f)

2.02.51.5

Steel tank a) Unanchored base b) Anchored base

2.02.5

Underground RC and steel tank+ 4.0

+ For partially buried tanks, values of R can be interpolated between ground supported and underground

tanks based on depth of embedment.



R values for tanks are smaller than buildings This is in line with other international codes

As discussed earlier, R depends on Ductility Redundancy Overstrength

Tanks possess low ductility, redundancy and overstrength



First let us consider, elevated tanks on frame type staging

Staging frames are different than building frames Hence, following footnote to Table 2

These R values are meant for liquid retaining tanks on frame type staging which are inverted pendulum type structures. These R values shall not be misunderstood for those given in other parts of IS 1893 for building and industrial frames.

Staging frames are non-building frames and are different than building frames



There are critical differences between building frames and non-building frames

International codes clearly differentiate between these two types of frames Building frames have rigid diaphragms at floor

levels Frames of staging do not have rigid diaphragms

In buildings, seismic weight is distributed along the height at each floor level

In elevated tanks, almost entire seismic weight is concentrated at the top

These are inverted pendulum type structures



Moreover in buildings, non-structural elements, such as infill walls, contribute significantly to overstrength

Staging are bare frames

In view of this, for staging with SMRF, R = 2.5 as against R = 5.0 for buildings with SMRF

With R = 2.5, base shear coefficient for elevated tanks on frame staging matches well with other international codes See next slide



Comparison for frame staging Zone and soil parameters are same used in Lecture 2

0

0.1

0.2

0.3

0.4

0.5

0 0.5 1 1.5 2 2.5 3

Time period (sec)

Bas

e sh

ear

coef

ficie

nt

IBC 2003; Frame staging, R =

3.0Guideline; Frame staging, R =

2.5IS 1893:1984; All types of staging, K =

1.0



Let us now consider, elevated tanks on RC shaft

They possess less redundancy and have single load path

RC shafts are usually thin shell and possess low ductility

There are analytical and experimental studies on ductility of hollow circular sections used in RC shafts Some references are given on next slide



Studies on ductility of shaft Zanh F A, Park R, and Priestley, M J N, 1990, “Flexural

strength and ductility of circular hollow reinforced concrete columns without reinforcement on inside face”, ACI Journal 87 (2), 156-166.

Rai D C, 2002, “Retrofitting of shaft type staging for elevated tanks”, Earthquake Spectra, EERI, Vol. 18 No. 4, 745-760.

Rai D C and Yennamsetti S, 2002, “Inelastic seismic demand on circular shaft type staging for elevated tanks”, 7th National Conf. on Earthquake Engrg, Boston, USA, Paper No. 91.

Rao M L N, 2000, “Effect of confinement on ductility of RC hollow circular columns”, a Master’s thesis submitted to Dept. of Earthquake Engineering, Univ. of Roorkee, India.



These studies have revealed that ductility of shaft depends on Thickness of wall (ratio of outer to inner

diameter) Axial force on shaft Longitudinal and transverse reinforcement

Some results from these studies on ductility of RC shafts are discussed in next few slides


Effect of Axial Load on Ductility

Hollow circular section

Figure from Rai (2002)

Ast/Ag = ratio longitudinal reinforcement to concrete area.

P = axial load on shaft

fc’ = characteristic strength of

concrete

Ag = gross area of concrete



In this figure, curvature ductility is plotted as a function of longitudinal reinforcement

These results are for inner (Di) to outer (Do) diameter ratio of 0.94.

If ratio of axial load (P) to ultimate load (fck.Ag) is 0.1 then, curvature ductility is about 9 for Ast/Ag = 0.02

This value reduces to 3 for P/ (f’c.Ag) of 0.25

Now, let us see some results on effect of shaft thickness


Effect of Shell Thickness on Ductility

Effect of ratio of inner to outer diameter (Di/Do) is shown This result corresponds to P/(f’c.Ag) = 0.05 Very low axial force ratio



For thin shaft with Di/Do = 0.95, curvature ductility is 12 For longitudinal steel ratio Ast/Ag = 0.02

This value increases to about 25 for thick shaft with Di/Do = 0.8

Thus, thickness has significant effect on ductility A thick shaft has reasonably good ductility



These analytical studies clearly indicate that thin RC hollow sections possess very low ductility

Issues connected with poor ductility of shaft, inadequate provisions of IS 1893:1984, and their correlation to behavior during recent earthquakes is discussed in following paper:

Rai D C, 2002, “Review of code design forces for shaft supported elevated water tanks”, Proc.of 13th Symposium on Earthquake Engineering , Roorkee, Ed. D K Paul et al., pp 1407 -1418.

(http://www.nicee.org/ecourse/12_symp_tanks.pdf)



Based on all these considerations, R = 1.8 for shaft supported tanks

With this value of R, base shear coefficient for shaft supported tanks matches well with international codes

Comparison with IBC 2003 on next slide



0

0.1

0.2

0.3

0.4

0.5

0 0.5 1 1.5 2 2.5 3

Time period (Sec)

Bas

e sh

ear c

oeffi

cien

t Comparison for shaft staging

Zone and soil parameters are same as used in Lecture 2

IBC 2003; Shaft staging, R = 2.0

Guideline; Shaft staging, R =

1.8IS 1893:1984; All types of staging, K =

1.0



Some useful information on RC shaft is given in ACI 371-98

ACI 371-98 , 1998, “ Guide for the analysis, design , and construction of concrete-pedestal water Towers”, American Concrete Institute, Farmington Hill, MI, USA.

It exclusively deals with tanks on RC shaft It suggests same design forces as IBC 2003 It gives information on:

minimum steel construction tolerances safety against buckling shear design etc.



We have seen comparison with IBC 2003 Comparison with other international

codes is available in following documents: Jaiswal, O. R. Rai, D. C. and Jain, S.K., 2004a, “Codal

provisions on design seismic forces for liquid storage tanks: a review”, Report No. IITK-GSDMA-EQ-01-V1.0, Indian Institute of Technology Kanpur, Kanpur. (www.iitk.ac.in/nicee/IITK-GSDMA/EQ01.pdf )

Jaiswal, O. R., Rai, D. C. and Jain, S.K., 2004b, “Codal provisions on seismic analysis of liquid storage tanks: a review” Report No. IITK-GSDMA-EQ-04-V1.0, Indian Institute of Technology Kanpur, Kanpur. (www.iitk.ac.in/nicee/IITK-GSDMA/EQ04.pdf )



In the above two documents, following international codes are reviewed and compared:

IBC 2000 (now, IBC 2003) ACI 350.3 ACI 371 AWWA D-110 and AWWA D-115 AWWA D-100 and AWWA D-103 API 650 and API 620 Eurocode 8 NZSEE recommendations (From New Zealand)

Priestley et al. (1986)



Now we know Z, I, R and Sa/g for tanks One can now obtain base shear

coefficient for impulsive and convective modes

An example follows.


Example

Example: An elevated water tank has RC frame staging detailed for ductility as per IS: 13920 and is located in seismic zone IV. Site of the tank has soft soil. Impulsive and convective time periods are 1.2 sec and 4.0 sec, respectively. Obtain base shear coefficient for impulsive and convective mode.

Solution: Zone: IV Z = 0.24 From Table 2 of IS 1893 (PART I):2002,

I = 1.5 From Table 1 of the Guideline

R = 2.5 for RC frame with good ductility (SMRF) From Table 2 of the Guideline


Example on (Ah)i and (Ah)c

Impulsive time period, Ti = 1.2 sec, and soil is soft,

Damping = 5% (RC Frame) (Sa/g)i = 1.67/Ti = 1.67/1.2 = 1.392 (Clause 4.5.3 of the Guideline)

Convective mode time period, Tc = 4.0 sec and soil is soft

Damping = 0.5% (Clause 4.4 of the Guideline)

Factor 1.75 is to be used for scaling up (Sa/g) for 0.5% damping (Clause 4.5.4 of the Guideline)

(Sa/g)c = (1.67/Tc) x 1.75 = 1.67/4.0 x 1.75 = 0.731


Example on (Ah)i and (Ah)c

Base shear coefficient for impulsive mode (Ah)i= (Z/2) x (I/R) x (Sa/g)i

= 0.24/2 x 1.5/2.5 x 1.392 = 0.10Base shear coefficient for convective mode(Ah)c = (Z/2) x (I/R) x (Sa/g)c

= 0.24/2 x 1.5/2.5 x 0.731 = 0.053


At the end of Lecture 4

R values for tanks are less than those for buildings.The basis for this is Analytical studies Provisions of international codes, and Observed behavior of tanks

For tanks, slight modifications are recommended for design spectrum of IS 1893(Part1)

Damping for convective mode may be taken as 0.5% for all types of tanks

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