seismic analysis of single degree of freedom structure

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976 – 6308

(Print), ISSN 0976 – 6316(Online), Volume 5, Issue 8, August (2014), pp. 44-55 © IAEME

44

SEISMIC ANALYSIS OF SINGLE DEGREE OF FREEDOM STRUCTURE

Khaza Mohiddin Shaik1, Prof. Vasugi K

2

1B.Tech Civil Engineering, Vellore Institute of Technologies, Chennai, Tamilnadu, India 2

Assosiate Professor, Civil Engineering Department, Vellore Institute of Technologies,

chennai, Tamilnadu, India

ABSTRACT

In this study, Wind Force and Seismic forces acting on an Elevated water tank e.g. Intze Tank

are studied. Seismic forces acting on the tank are also calculated changing the Seismic Response

Reduction Factor(R). IS: 1893-1984/2002 for seismic design and IS: 875-1987(Part III) for wind

load has been referred. Then Analyzed the Elevated Tank by using the software STAAD PRO.

Reinforcement detailing is done for the Tank. Base Shear and Base Moment are calculated and

compared the results for Tank Full Condition and Empty Condition and found that the Base shear in

the full tank condition is high and Base moment also high in the case of tank full condition. With the

increase in R value Base Shear and Base Moment decreases. Considering the design aspect, the

seismic forces remain constant in a particular Zone provided the soil properties remain same whereas

the Wind force is predominant in coastal region, but in interior region earthquake forces are more

predominant. Design of Elevated Tank is done by calculating the all Horizontal Thrust, Meridonal

stress, Hoop Tension, Hoop Stress and Reinforcement is calculated for Top spherical Dome, Top

Ring Beam, cylindrical wall, Bottom Ring Beam, Conical Portion, Circular Beam, Columns and

Staging’s and then Detail Drawing of Reinforcement is Done.

Keywords: Seismic Analysis, Staad Pro, Base Shear, Base Moment.

I. INTRODUCTION

An Earthquake is a phenomenon that results from and is powered by the sudden release of

stored energy in the crust that propagates Seismic waves. At the Earth's surface, earthquakes may

manifest themselves by a shaking or displacement of the ground and sometimes tsunamis, which

may lead to loss of life and destruction of property. Seismic safety of liquid tanks is of considerable

importance. Water storage tanks should remain functional in the post-earthquake period to ensure

potable water supply to earthquake-affected regions and to cater the need for firefighting demand.

INTERNATIONAL JOURNAL OF CIVIL ENGINEERING

AND TECHNOLOGY (IJCIET)

ISSN 0976 – 6308 (Print)

ISSN 0976 – 6316(Online)

Volume 5, Issue 8, August (2014), pp. 44-55

© IAEME: www.iaeme.com/ijciet.asp

Journal Impact Factor (2014): 7.9290 (Calculated by GISI)

www.jifactor.com

IJCIET

©IAEME

International Journal of Civil Engineering and Technology (IJCIET), ISSN 0976

(Print), ISSN 0976 – 6316(Online), Volume 5, Issue 8, August (2014), pp.

Industrial liquid containing tanks may contain highly toxic and inflammable liquids and these tanks

should not lose their contents during the earthquake. The current design of supporting st

elevated water tanks are extremely vulnerable under lateral forces due to an earthquake as it is

designed only for the wind forces but not the seismic forces. The strength analysis of a few damaged

shaft types of staging’s clearly shows that al

requirement of IS: 1893-1984 however they were all found deficient when

requirements of International Building Codes. Frame type stagings are generally regarded superior to

shaft type of staging’s for lateral resistance because of their large redundancy and greater capacity to

absorb seismic energy through inelastic actions. This implies that design base shear for a low

ductility tank is double that of a high ductility tank. Indian Standard IS: 189

guidelines for earthquake resistant design of several types of structures including liquid storage

tanks. This standard is under revision and in the revised form it has been divided into five parts. First

part, IS 1893 (Part 1): 2002; which deals with general guidelines and provisions for buildings which

is used as a Reference Code and for Ductile Detailing the IS 13920Code book is Preferred.

II. LITERATURE REVIEW

According to Guidelines of Seismic Design of Liquid Storage Tanks.

In the spring mass model of tank, h

hydrodynamic pressure on wall is located from the bottom of tank wall. On the other hand, h

height at which the resultant of impulsive pressure on wall and base is located from the bottom of

tank wall. Thus, if effect of base pressure is not considered, impulsive mass of liquid, mi will act at a

height of hi and if effect of base pressure is c

schematically described in Figures.


6316(Online), Volume 5, Issue 8, August (2014), pp. 44-55 © IAEME

45


should not lose their contents during the earthquake. The current design of supporting st



shaft types of staging’s clearly shows that all of them either met or exceeded the strength

1984 however they were all found deficient when


for lateral resistance because of their large redundancy and greater capacity to


ductility tank is double that of a high ductility tank. Indian Standard IS: 189



deals with general guidelines and provisions for buildings which


According to Guidelines of Seismic Design of Liquid Storage Tanks.

In the spring mass model of tank, hi is the height at which the resultant of impulsive

hydrodynamic pressure on wall is located from the bottom of tank wall. On the other hand, h



height of hi and if effect of base pressure is considered, mi will act at hi*. Heights h


© IAEME


should not lose their contents during the earthquake. The current design of supporting structures of



l of them either met or exceeded the strength

1984 however they were all found deficient when Compared with


for lateral resistance because of their large redundancy and greater capacity to


ductility tank is double that of a high ductility tank. Indian Standard IS: 1893-1984 provides



deals with general guidelines and provisions for buildings which


is the height at which the resultant of impulsive

hydrodynamic pressure on wall is located from the bottom of tank wall. On the other hand, hi*is the



*. Heights hi and hi*, are



Provisions:-

Description:-

Ti= Time period of impulsive mode

Tc = Time period of convective mode

(Ah) i = Design horizontal seismic coefficient for Impulsive mode

(Ah) c = Design horizontal seismic coefficient for Convective

Vi = Base shear at the bottom of staging, in impulsive mode

Vc =Base shear at the bottom of staging, in convective mod

V =Total base shear at the bottom of staging

Mi* = Overturning moment at the base of staging in mode

M c* = Overturning moment at the base of staging in convective mode

M =Total overturning moment

d max =Sloshing Wave Height



46

Time period of convective mode

= Design horizontal seismic coefficient for Impulsive mode.

coefficient for Convective mode.

Base shear at the bottom of staging, in impulsive mode.

=Base shear at the bottom of staging, in convective mode.

Total base shear at the bottom of staging

Overturning moment at the base of staging in mode

* = Overturning moment at the base of staging in convective mode


© IAEME



Response acceleration coefficient (S

Fig.1 & Table

Table 2: -

Sl.No.

1 IS 3370(part 1):2009 water structures general.

2 IS 3370(part 2):2009 water structures using RCC.

3 IS 3370(part 4):2009.General tables.

4 IS 875(part 3):2009: wind load.

5 IS 1893

6 Is-13920

7 IS 456:2000 design for RCC structures.

8 SP: 16 Design aids.

9

SP: 34 Hand book for concreting & detailing of

Reinforcement.

Sl.No.

1

2

3

4

5

6

7

8

9



47

acceleration coefficient (Sa /g).

Table 1: Geometry and size of the Structure

- Code Books Preferred for Analysis

Code Books Preferred

IS 3370(part 1):2009 water structures general.

IS 3370(part 2):2009 water structures using RCC.

IS 3370(part 4):2009.General tables.

IS 875(part 3):2009: wind load.

IS 1893-2002 design for earthquake loads.

13920-Ductile Detailing

IS 456:2000 design for RCC structures.

SP: 16 Design aids.


Reinforcement.

Component Size(mm)

Top Dome 120 thick

Top Ring Beam 250*300

Cylindrical wall 200 thick

Bottom Ring Beam 500*300

Circular Ring Beam 500*600

Bottom Dome 200 thick

Conical Dome 250 thick

Braces 300*600

Columns 650 Dia


© IAEME




48

LOAD COMBINATION FOR FOUNDATION (IS1893) 1) 1(SW+D.L+L.L)

2) 0.75(SW+D.L±ELX)

3) 0.75(SW+D.L±ELZ)

4) 0.75(SW+D.L+R.LL±ELX)

5) 0.75(SW+D.L+R.LL±ELZ)

Wind Load Combination in accordance with IS 875: 1964 Part3 1) DL+LL

2) 0.75 (DL + C, X WL,)

3) 0.75 (DL + c, X WL2)

4) 0.75 (DL + C, X WL,)

Where C = 0.75

SEISMIC LOAD COMBINATION

(As per IS1893): 1) ELX ± seismic load

2) ELZ ± seismic load

3) 1(SW+D.L+L.L)

4) 1.5(SW+D.L+L.L)

5) 1.2(SW+D.L+L.L±ELX)

6) 1.2(SW+D.L+L.L±ELZ)

7) 1.5(SW+D.L±ELX)

8) 1.5(SW+D.L±ELZ)

9) 0.9(SW+D.L) ±1.5ELX

10) 0.9(SW+D.L) ±1.5ELZ

SPECIFICATIONS: 1) Grade of concrete - M25

2) Grade of steel - Fe 500D

3) Unit weight of concrete - 25 kN/m3

4) Height of Tank =16 m

III. LOAD APPLICATION AND ANALYSIS OF ELEVATED TANK USING STAAD PRO

Geometry (Size) &Property:



STAAD MODEL

Post Processing (Mode Shape)

Staad Analysis for the Model



49

Hydrostatic Load Application

Post Processing (Mode Shape)

Staad Analysis for the Model


© IAEME

pplication



50

IV. WEIGHT CALCULATIONS

Top Dome (120thick): Radius of Curvature (Rc) =(r^2+h^2)/2h

h=1750-60=1690=1.69m

r=8.6+0.2=8.8

(Rc)= (((8.8)^2/1.69)+1.69)/2=6.57

Weight=2*π*6.57*1.69*0.12*25=209.3 KN.

Top Ring Beam (250*300): r= (8.6+0.25) =8.85

Weight=π*8.85*0.25*0.3*25= 52.1 KN

Cylindrical Wall (200thick):

r=8.6+0.2=8.8

Weight=π*8.8*0.2*0.4*1000*25= 552.9KN

Bottom Ring Beam (500*300): r=8.6+0.5=9.1

Weight= (π*9.1*0.5*0.3*25) = 107.2 KN

Circular Ring Beam (500*600): r or l =3.14+3.14=6.28

Weight=π*6.28*0.5*0.6*25=148KN.

Bottom Dome (200 thick): r2=(r^2+h^2)/2h

r=6.28/2=3.14

r2=1/2((3.14^2)/1.4) +1.4) =4.22m

Weight=2*π*4.22*1.40*0.20*25=185.6KN

Conical Dome (250 thick): Length of cone=l=square root of (h^2+r^2) h=1.65,

r = 1.41, l=2.17

Weight=π*((8.8+6.28)/2)*2.17*0.25*25

=321.1KN

Water:

(((π*8.6^2*3.7)/4+π*1.5(8.6^2+5.63^2+ (8.6*5.63)/12))*9.81=2508 KN

Total Weight of Water=2508 KN.

Stagging Weight:

Columns (650φ) Weight= (π*0.65^2*15.7*6*25)/4 =782 KN

Braces (300*600): Weight=3.14*0.3*0.6*3*6*25=254KN

From Above Results: Weight of Empty Container=Top Dome +Top Ring Beam + Cylindrical Wall + Bottom Ring Beam

+ Circular Ring Beam + Bottom Dome +Conical Dome

=209.3+52.1+552.9+107.2+148+185.6+321.3 =1576KN.

Weight of Stagging=Weight of Columns + Weight of Bracings = 782+ 254 =1036KN.

Hence, Weight of empty Container + 1/3(Weight of Stagging) =1576+ (1036/3) =1921KN

Centre of Gravity of empty Container above top Circular Ring Beam= ((209.3*7.22) + (52.1*5.9) +

(552.9*3.8) + (107.2*1.65) + (321.3*1) + (185.6*0.92)+ (148*0.3))/1576=2.88m

Height of C.G. of empty container from top of footing =h cg

Height up to Circular Ring Beam from the Footing = (4+4+4+4+ (0.6/2))=16.3

hcg =16.3+2.88=19.18m



51

V. PARAMETERS OF SPRING MASS MODEL

Total Weight of Water =2508000N.

Volume=2508 KN/9.81=255.65 m^3

Mass =255658kg

D=8.6m

Let h be height of equivalent circular Cylinder, (D/2) ^2*h=255.65h=4.4m

Volume of water = 2,508 / 9.81 = 255.65 m^3

h / D = 4.4 / 8.6 = 0.51

m i / m = 0.55;

mi = 0.55 x 2,55,658 = 1,40,612 kg

mc /m = 0.43;

mc = 0.43 x 2,55,658 = 1,09,933 kg

hi / h = 0.375; hi = 0.375 x 4.4 = 1.65 m

hi*/h =0.78, hi*= 0.78 x 4.4 = 3.43 m

hc/h =0.61, hc = 0.61 x 4.4 = 2.68 m

hc */h =0.78, hc*= 0.78 x 4.4 = 3.43 m

According to IS code,About 55% of Liquid mass is excited in impulsive mode while 43% liquid

mass participates in convective mode.Sum of impulsive and convective mass is 2,50,545kg which is

about 2% less than the total mass of liquid.

Mass of empty container+one third mass of staging,

ms=(1576+1036/3)*(1000/9.81)=195821kg.

Table 3: Comparison of Base Shear and Moment for full tank and Empty Tank



52

VI. DESIGN OF ELEVATED TANK CONSIDERING SEISMIC FORCE

I.Spherical Roof Dome Total Load=4.5KN/m^2

(120mm) Maximun Hoop Stress =0.083(N/mm^2)

Meridonial Stress= 0.22 N/mm2

II.Design of Top Ring Beam Horizontal Thrust/cm length= 22.2 KN/m2

(300x300mm) Hoop Tension= 106.61 KN

Tensile Stress= 10.9 Kg/cm2

III.Design of Conical Dome Total Vertical Load= 4814.758KN


Thickness of Conical Dome= 350mm.

IV.Design of Bottom Dome: Radius of Bottom Dome = 4.567 m

200mm thickness is provided.

Total Load= 3591.946 KN


Hoop Stress= 0.2349 N/mm2

Tank will be at Chennai: Wind Speed: 50 m/s

V.Design of Cylindrical Wall Hoop Tension (Ft) = 172 KN/m

Wall thickness is 250mm thick at base and

150mm at top

VI.Design of Ring Beam at junction Total Load= 48.925 KN/m

of cylindrical wall and conical wall

Meridonial Thrust in the Conical Dome=

48925N

Total Hoop Tension= 313.577 KN

Tensile Stress= 1.05<1.2 N/mm

VII.Design of Circular Beam Horizontal Thrust on circular beam= 10860 Kg/m

Vertical load on beam /m= 36580 Kg/m

Maximum Bending Moment (-ve) = 31330Kgm

VIII.Design of Column(650Dia) Total vertical load on column: 1944K N

IX.Design of Braces

Provide 10mm Φ-2 legged stirrups @225mm

c/c



53

VII. REINFORCEMENT DETAILING

S.No. Component Reinforcement

1 Spherical Roof Dome 8mmφ@160 mm c/c both ways

2 Top Ring Beam 8,12mm Φ bars Main Reinforcement and 6mm Φ stirrups @ 20cm c/c are provided

3 Cylindrical Wall (0-2m) Main Hoop Steel 10mm-180mmc/c (2-4) vertical distribution 10mm-250mmc/c,

(2-4m)Main Hoop Steel 10mm-180mmc/c (2-4) vertical distribution 10mm-250mmc/c.

4 Conical Dome Provide 25mm Φ bars @180mmc/con both faces of the slab

Distribution Steel :10mmΦ @130mm c/c both faces along meridons

5 Bottom Dome 12mm Φ bars @ 120mm centers both circumferentially and meridonally.

6 Circular Beam Provide 6 bars of 20mm Φ at center and 5, 16mm Φ at support

Shear Reinforcement: Provide 12 mm Φ, 6 legged stirrups @ 9cm c/c at support.

Shear Reinforcement: Provide 12mm Φ, 4 legged stirrups @ 9cm c/c at center

Longitudinal Steel: Provide 8 bars of 12mm Φ, 4 cm each face

7 Column Provide 8bars of 32 mm Φ and 10mm Φ ties at 300 mm c/c

8 Braces Provide 10mm Φ -2 legged stirrups @226mm c/c.

VIII. REINFORCEMENT DRAWING OF ELEVATED WATER TANK



54

IX. RESULTS AND CONCLUSIONS

1. In India elevated tanks are widely used and these tanks have various types of supports.

2. Maintains hydraulic grade lines without automated controls. Provides pressure when power is

lost.

3. Simple to operate Lower power cost because an elevated tank can be filled in evening when

power costs are less.

4. The seismic design of the R/C elevated tanks, based on the rough Assumption that the subsoil

is rigid or rock without any site investigation, may lead to a wrong assessment of the seismic

base shear and overturning moment.

5. Suitable value of lower bound limits on spectral values for structure including tanks needs to be

arrived at does not recommend consideration of Convective Mode of vibration. R Value taken

in IS 1893:1984 is nowhere in the range corresponding to that value in different international

Codes.

6. As per observed from Table 1, Base Shear and Base Moment have increased from Empty Tank

Condition to Full Tank Condition.

7. we observe that due to change in place from Base Shear due to Wind Force decreases by 26%

and Base Moment decreases by 18%

8. Analysis & design of elevated water tanks against earthquake effect is of Considerable

importance. These structures must remain functional even after an earthquake. Elevated water

tanks, which typically consist of a large mass supported on the top of a slender staging, are

particularly susceptible to earthquake damage. Thus, analysis & design of such structures

against the earthquake effect is of considerable importance.

9. Most elevated water tank are never completely filled with water. Hence, a two – mass

idealization of the tank is more appropriate as compared to one-mass idealization.

10. Basically, there are three cases that are generally considered while analyze the Elevated water

tank – (1) Empty condition. (2) Partially filled condition.

(3) Fully Filled condition. For (1) & (3) case, the tank will behave as a one-mass structure and

for (3) case the tank will behave as a two-mass structure.

11. If we compared the case (1) & (3) with case (2) for maximum earthquake force, the Maximum

force to which the partially filled tank is subjected may be less than half the force to which the

fully filled tank is subjected. Actual forces may be as little as 1/3 of the forces anticipated on

the basis of a fully filled tank.

12. During the earthquake, water in the tank get vibrates. Due to this vibration water Exerts

impulsive & convective hydrodynamic pressure on the tank wall and the tank base in addition

to the hydrostatic pressure.

13. The effect of impulsive & convective hydrodynamic pressure should consider in the analysis of

tanks. For small capacity tanks, the impulsive pressure is always greater than the convective

pressure, but it is vice-versa for tanks with large capacity. Magnitudes of both the pressure are

different.

14. The effect of water sloshing must be considered in the analysis. Free board to be provided in

the tank may be based on maximum value of sloshing wave height. If sufficient free board is

not provided, roof structure should be designed to resist the uplift pressure due to sloshing of

water.

15. Earthquake forces increases with increase in Zone factor & decreases with increase in staging

height. Earthquake force are also depends on the soil condition.



55

REFERENCES

1. Rai Durgesh C; “Performance of Elevated Tanks in Bhurj Earthquake”; Proc. Indian Acad.

Sci. (Earth Planet Sci.), 112, No. 3, September 2003, pp 421-429.

2. Jaiswal O. R., Rai Durgesh C and Jain Sudhir K; “Review of Code Provisions on Design

Seismic forces for Liquid Storage Tanks”; Document No.: IITK-GSDMA-EQ01-V1.0, Final

Report: A - Earthquake Codes, IITK.

3. Indian Institute of Technology Kanpur, IITK GSDMA Guidelines for Seismic Design of

Liquid Storage Tanks.

4. IS 1893:1984, Criteria for Earthquake Resistance Design of Structures.

5. IS 1893(Part I): 2002, Criteria for Earthquake Resistance Design of Structures.

(PART 1: General Provisions and Buildings).

6. IS 875:1987, Code of Practice for Design Loads (Other than Earthquake) for Buildings and

Structures Part 3: Wind Loads.

7. Vazirani & Ratwani, “Concrete Structures”, Khanna Publishers, Year of Publication 1996.

8. Damodar Maity, C. Naveen Raj and Indrani Gogoi, “Dynamic Response of Elevated Liquid

Storage Elastic Tanks with Baffle”, International Journal of Civil Engineering & Technology

(IJCIET), Volume 1, Issue 1, 2010, pp. 27 - 45, ISSN Print: 0976 – 6308, ISSN Online:

0976 – 6316.

9. Damodar Maity, C. Naveen Raj and Indrani Gogoi, “Dynamic Response of Elevated Liquid

Storage Elastic Tanks with Baffle”, International Journal of Civil Engineering & Technology

(IJCIET), Volume 1, Issue 1, 2010, pp. 27 - 45, ISSN Print: 0976 – 6308, ISSN Online:

0976 – 6316.

10. Ming Narto Wijaya, Takuro Katayama, Ercan Serif Kaya and Toshitaka Yamao, “Earthquake

Response of Modified Folded Cantilever Shear Structure with Fixed-Movable-Fixed sub-

Frames”, International Journal of Civil Engineering & Technology (IJCIET), Volume 4,

Issue 4, 2013, pp. 194 - 207, ISSN Print: 0976 – 6308, ISSN Online: 0976 – 6316.

11. Vidula S. Sohoni and Dr.M.R.Shiyekar, “Concrete–Steel Composite Beams of a Framed

Structure for Enhancement in Earthquake Resistance”, International Journal of Civil

Engineering & Technology (IJCIET), Volume 3, Issue 1, 2012, pp. 99 - 110, ISSN Print:

0976 – 6308, ISSN Online: 0976 – 6316.