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
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
44

IJCIET
©IAEME
SEISMIC ANALYSIS OF SINGLE DEGREE OF FREEDOM STRUCTURE
Khaza Mohiddin Shaik1, Prof. Vasugi K2
1B.Tech Civil Engineering, Vellore Institute of Technologies, Chennai, Tamilnadu, India
2Assosiate 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
(Print), ISSN 0976 – 6316(Online), Volume 5, Issue 8, August (2014), pp.
44-55 © IAEME
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
all of them either met or exceeded the strength
According to Guidelines of Seismic Design of Liquid Storage Tanks.
In the spring mass model of tank, h
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 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 considered, c
mi will act at hi*. Heights h
schematically described in Figures.
45
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structures of
l Compared with
1893-1984 provides
hi*is the
*. 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
44-55 © IAEME
46
mode.
mode.
mode.
mode.
* – 6308

Response acceleration coefficient (S
Fig.1 Table
1893-2002 design for earthquake loads.
13920-Ductile Detailing
Table 2: -
Sl.No.
Code Books Preferred
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
44-55 © IAEME
47
Sa /g).
1: Geometry and size of the Structure
Code Books Preferred for Analysis
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
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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
III. LOAD APPLICATION AND ANALYSIS OF ELEVATED TANK USING STAAD PRO
48
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
Geometry (Size) Property:

STAAD MODEL
Hydrostatic Load Application
Post Processing (Mode Shape)
Staad Analysis for the Model
44-55 © IAEME
49
– 6308

pplication

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**6.57*1.69*0.12*25=209.3 KN.
Top Ring Beam (250*300):
r= (8.6+0.25) =8.85
Weight=*8.85*0.25*0.3*25= 52.1 KN
Cylindrical Wall (200thick):
r=8.6+0.2=8.8
Weight=*8.8*0.2*0.4*1000*25= 552.9KN
Bottom Ring Beam (500*300):
r=8.6+0.5=9.1
Weight= (*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=*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**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=*((8.8+6.28)/2)*2.17*0.25*25
=321.1KN
Water:
(((*8.6^2*3.7)/4+*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 (650)
Weight= (*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
50
IV. WEIGHT CALCULATIONS

V. PARAMETERS OF SPRING MASS MODEL
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
51
Total Weight of Water =2508000N.
Volume=2508 KN/9.81=255.65 m^3
Mass =255658kg
D=8.6m
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

VI. DESIGN OF ELEVATED TANK CONSIDERING SEISMIC FORCE
52

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
2
II.Design of Top Ring Beam Horizontal Thrust/cm length= 22.2 KN/m
(300x300mm) Hoop Tension= 106.61 KN
2
Tensile Stress= 10.9 Kg/cm
III.Design of Conical Dome Total Vertical Load= 4814.758KN
2
Meridonial Stress= 1.444 N/mm
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
Meridonial Stress= 0.946 N/mm
2
2
Hoop Stress= 0.2349 N/mm
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= 1.051.2 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 -2 legged stirrups @225mm
c/c

53
VII. REINFORCEMENT DETAILING

8,12mm bars Main Reinforcement and 6mm stirrups @ 20cm c/c are provided
! #
$
(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.
%

Provide 25mm bars @180mmc/con both faces of the slab
Distribution Steel :10mm @130mm c/c both faces along meridons

12mm bars @ 120mm centers both circumferentially and meridonally.
'

Provide 6 bars of 20mm at center and 5, 16mm at support
Shear Reinforcement: Provide 12 mm , 6 legged stirrups @ 9cm c/c at support.
Shear Reinforcement: Provide 12mm , 4 legged stirrups @ 9cm c/c at center
Longitudinal Steel: Provide 8 bars of 12mm , 4 cm each face
(
' )
*#

!+
#+
!

)
*#+,#' -
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.

Seismic analysis of single degree of freedom structure

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