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, S a /g and R values for tanks

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 3 Base shear coefficient Seismic force V = (A h ) x (W) A h is base shear coefficient Zone Depends on severity of ground motion Structural characteristics Depends on time period and damping Design philosophy

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 4 Base shear coefficient Tanks have two modes Impulsive Convective Seismic force In impulsive mode, V i = (A h ) i x impulsive weight In convective mode, V c = (A h ) c x convective weight (A h ) i and (A h ) c are base shear coefficient in impulsive and convective modes, respectively

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 5 Base shear coefficient Impulsive base shear coefficient (A h ) i = (Z/2) x (I/R) x (S a /g) i Convective base shear coefficient (A h ) c = (Z/2) x (I/R) x (S a /g) c Note, R has been used in (A h ) i as well as (A h ) c Zone factor, Z As per Table 2 of IS 1893(Part1):2002 I, R, (S a /g) i and (S a /g) c will be discussed here First, (S a /g) i and (S a /g) c

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 6 (S a /g) i and (S a /g) c (S a /g) i is average response acceleration for impulsive mode Depends on time period and damping of impulsive mode (S a /g) c is average response acceleration for convective mode Depends on time period and damping of convective mode

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 7 (S a /g) i and (Sa/g) c S a /g is obtained from design spectra Figure 2 of IS 1893(Part 1):2002 These spectra are slightly modified for tanks See next slide

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 8 (S a /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

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 9 (S a /g) i and (Sa/g) c Spectra of IS 1893 (Part 1):2002 Modified spectra For 5% damping Sa/g

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 10 (S a /g) i and (Sa/g) c Expressions for spectra of IS 1893(Part 1):2003 Expressions for spectra for tanks For hard soil sites S a /g = T 0.00  T < 0.10 =  T < 0.40 = 1.00 / T 0.40  T  4.0 For medium soil sites S a /g = T 0.00  T < 0.10 =  T < 0.55 = 1.36 / T 0.55  T  4.0 For soft soil sites S a /g = T 0.00  T < 0.10 =  T < 0.67 = 1.67 / T 0.67  T  4.0 For hard soil sites S a /g = 2.50 T < 0.40 = 1.0 / T T ≥ 0.40 For medium soil sites S a /g = 2.50 T < 0.55 = 1.36 / T T ≥ 0.55 For soft soil sites S a /g = 2.5 T< 0.67 = 1.67 / T T ≥ 0.67 Expressions for design spectra at 5% damping

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 11 (S a /g) i and (Sa/g) c S a /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

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 12 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 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

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 13 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

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 14 Damping IS 1893(Part 1), needs to have a re-look at the damping values Accordingly, damping values for tanks can also be modified

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 15 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 In ACI 350.3, this factor is 1.5

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 16 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 tankI 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

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 17 Importance factor, I 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

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 18 Importance factor, I 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

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 19 Response reduction factor, R R values for tanks are given in Table 2 of the Guideline This is reproduced in next two slides

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 20 Response reduction factor, R Elevated tankR Tank supported on masonry shafts a) Masonry shaft reinforced with horizontal bands * b) Masonry shaft reinforced with horizontal bands and vertical bars at corners and jambs of openings 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) 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

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 21 Response reduction factor, R Ground supported tankR 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 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) Steel tank a) Unanchored base b) Anchored base Underground RC and steel tank For partially buried tanks, values of R can be interpolated between ground supported and underground tanks based on depth of embedment.

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 22 Response reduction factor, R 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

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 23 Response reduction factor, R 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

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 24 Response reduction factor, R 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

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 25 Response reduction factor, R 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

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 26 Response reduction factor, R Comparison for frame staging Zone and soil parameters are same used in Lecture 2 IBC 2003; Frame staging, R = 3.0 Guideline; Frame staging, R = 2.5 IS 1893:1984; All types of staging, K = 1.0

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 27 Response reduction factor, R 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

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 28 Response reduction factor, R 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), Rai D C, 2002, “Retrofitting of shaft type staging for elevated tanks”, Earthquake Spectra, EERI, Vol. 18 No. 4, 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.

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 29 Response reduction factor, R 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

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 30 Effect of Axial Load on Ductility Hollow circular section Figure from Rai (2002) A st /A g = ratio longitudinal reinforcement to concrete area. P = axial load on shaft f c ’ = characteristic strength of concrete A g = gross area of concrete

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 31 Response reduction factor, R In this figure, curvature ductility is plotted as a function of longitudinal reinforcement These results are for inner (D i ) to outer (D o ) diameter ratio of If ratio of axial load (P) to ultimate load (f ck.A g ) is 0.1 then, curvature ductility is about 9 for A st /A g = 0.02 This value reduces to 3 for P/ (f’ c.A g ) of 0.25 Now, let us see some results on effect of shaft thickness

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 32 Effect of Shell Thickness on Ductility Effect of ratio of inner to outer diameter (D i /D o ) is shown This result corresponds to P/(f’ c.A g ) = 0.05 Very low axial force ratio

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 33 Response reduction factor, R For thin shaft with D i /D o = 0.95, curvature ductility is 12 For longitudinal steel ratio A st /A g = 0.02 This value increases to about 25 for thick shaft with D i /D o = 0.8 Thus, thickness has significant effect on ductility A thick shaft has reasonably good ductility

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 34 Response reduction factor, R 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 (

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 35 Response reduction factor, R 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

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 36 Response reduction factor, R 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 = 1.8 IS 1893:1984; All types of staging, K = 1.0

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 37 Response reduction factor, R Some useful information on RC shaft is given in ACI ACI , 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.

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 38 Response reduction factor, R 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. ( ) 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. ( )

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 39 Response reduction factor, R In the above two documents, following international codes are reviewed and compared: IBC 2000 (now, IBC 2003) ACI 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)

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 40 Response reduction factor, R Now we know Z, I, R and S a /g for tanks One can now obtain base shear coefficient for impulsive and convective modes An example follows.

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 41 Example Example: An elevated water tank has RC frame staging detailed for ductility as per IS: 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

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 42 Example on (A h ) i and (A h ) c Impulsive time period, T i = 1.2 sec, and soil is soft, Damping = 5% (RC Frame)  (S a /g) i = 1.67/T i = 1.67/1.2 = (Clause of the Guideline) Convective mode time period, T c = 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 of the Guideline)  (S a /g) c = (1.67/T c ) x 1.75 = 1.67/4.0 x 1.75 = 0.731

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 43 Example on (A h ) i and (A h ) c Base shear coefficient for impulsive mode (A h ) i = (Z/2) x (I/R) x (S a /g) i = 0.24/2 x 1.5/2.5 x = 0.10 Base shear coefficient for convective mode (A h ) c = (Z/2) x (I/R) x (S a /g) c = 0.24/2 x 1.5/2.5 x = 0.053

 Sudhir K. Jain, IIT Kanpur E-Course on Seismic Design of Tanks/ January 2006 Lecture 4 / Slide 44 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