11.
STABILITY FOR SEISMIC DESIGN LOAD
(API 650-E.6.2)
(a)Time Periods and Seismic Coefficients
Diameter of Tank D = 16.00 m
Time Period for Impulsive Mode Ti = 0.238981 seconds
Impulsive Horizontal Seismic Coeff. Ai = 0.054 g
Vertical Seismicity Av = 0.0359 g
Time Period for sloshing Tc = 4.162928 seconds
Convective Horizontal Seismic Coeff. Ac = 0.02867 (including Rwc & I)
5% Damped, Design Spectral Response SD1 = 0.1872
Accn. at 1 sec,
Structure Importance for Seismic Load I = 1.50
Convective Horiz. Coeff. Af = K.SD1.I /Tc for Tc <= 4 sec
(for slosh ht calculation) for SUG I & II 2
= K.SD1.I (4/Tc ) for Tc > 4 sec
= (Z /2).(Sa/g). I /Tc ((Sa/g) at period of
= 0.06 1sec on convective
Slosh Height ( Eqn E .7.2-1) = 0.42*D* Af curve)
= 0.3842 m
(b) Check for Self-Anchorage of Tank
(Resistance to Overturning ) E-6.2.1.1.1
Maximum wt of liquid wa = smaller of 99 ta.(Fby.H.Ge)0.5 & 201.1*H*D *Ge
content to resist overturning = Smaller of ( 57866.79 54286.945 )
= 54286.945 N/m
where ta = min. of thicknesses -> bott. shell course, bottom / annular plate (corroded)
= 9.00 mm
Fby = yield point of bottom plate under shell
= 250 MPa
Fty = yield point of plate for bottom shell course
= 250 MPa
G = Design Specific Gravity of liquid
= 1.00
Ge = Effective Specific gravity of liquid including vertical seismic effect
= G.(1- AV)
= 0.96
H = Max. Liquid Height During Earthquake
= 17.500 m ( = HL )
D = Nominal Tank Diameter
= 16.00 m
Mrw = Seismic Moment (at bottom of shell)
= 1158.926 tonne.m
= 11364.43 kN.m
Ws +Wrs = Shell wt + Fixed Roof Wt including framing, appurtanance ,attachment, etc
= W 1 ( for corroded) or W 4 ( for uncorroded)
Weight of tank shell
and fix roof supported wt = { Ws + Wrs }/ (.D)
by shell = 8590.163058 N/m (Corrod.shell+ Roof Compon.)
13685.08486 N/m (Un-corrod.shell+ Roof Compon.)
FP.wint = Uplift due to product int. pr.
= max( poper, 0.4 pi ) *1000* D/4 (Pr in kPa)
= 0 N/m
Calculation of Anchorage Ratio " J "
Thickness of 1st
(bottom) shell course t = 9.00 mm (corroded)
Anchor Ratio J = Mrw / {D2 (wt (1 -0.4* Av) + wa - FP.wint)}
= 0.707404415 (For Corroded Condition Wt)
0.654989871 (For Un-corroded Condition Wt)
Tank in Corroded Condition
Case 1 : J < = .785 , No uplift , Tank is Self-Anchored for Seismic Load.
Tank in Uncorroded Condition
Case 1 : J < = .785 , No uplift , Tank is Self-Anchored for Seismic Load.
(Tank is Mechanically Not Anchored)
(c) Corresponding Maximum Longitudinal Shell-Membrane Compressive Force
(1) Due to Seismic Load, b1 = wt( 1+ 0.4*Av) + 1.273 Mrw / D^2
( E.6.2.2.1-1a )
= 13938.1 N/m
(2) Int. Vacuum Comp. , b2 = (Pe *1000)*D/4 Pe = Design ex Pr, kPa
0.0 N/m
Total Compression b = b1 + b2
= 13938.1 N/m
= 1.421383399 tonnes / m
Compressive Stress in
shell bottom course, Sc = b / 1000t
= 1.548676179 MPa
(d) Maximum Allowable shell Compression,
( For Stable Tank :- Mechanically Anchored or Self-Anchored, for both type )
GHD2/ t2 = 55.309 ( greater than 44.0 )
:. Fa = Min of {83*t /D & 0.5YP }
= 46.688 MPa
.---> greater than Sc , hence acceptable
.(e) Minimum Required Inwards Radial Width
of Annular Plate, for Self Anchored /Structurally Stable Tank .-- (Eq- E.6.2.1.1.2 -1a)
Wanplt = Greater of [ 0.01723*ta*sqrt{ Fby / ( HLGe ) }, 0.45 ] m <= 0.035 D
= Min { Greater of [ 0.5969, 0.450 ], 0.56 } m
= 0.5600 m
12.0 COPMPRESSIVE LOAD ON TANK FOUNDATION'S FOOTING
12.1 Mechanically Anchored Tank System
( Not Applicable for Present Case)
Check for Foundation Overturning Stability Due to Seismic Moment
(Equation E.6.2.3.-1 Re-arranged)
0.5D * [ W p + W f + W T + W fd + W g ] / Ms >= 2
OR
[ W p + W f + W T ] + ( Wfd + W g ) >= 4Ms / D
where
(Wfd + W g ) = Wt of Foundation & Soil (Inclusive of Soil Over Footing)
Wp = Wt of Design Product Contented in Tank
Wf = Wt of Bottom Plate of Tank
WT = Wt of Shell, Roof Plate & Framing, Appurtances , Attachment
[ Wp + WT + Wf ] = Wop (total operating wt.of tank)
= 3606.122 tonne
Rewriting Above Equation gives:-
(Wfd + W g ) >= 4MRF / D - Wop
>= -3316.3906 tonne
( - ve, Hence Self Balancing, Tank Is Stable)
12.2 Self-Anchored Tank System
( Applicable for Present Case)
(a) For Overturning Bearing Pressure for Compact Slab or Pile Cap
( as per E.6.2.2.1 based on "J " )
Pf = b1 calculated above in 11 (c) ( Eqn- E.6.2.2.1-1a OR E.6.2.2.1-2a)
= 13938.1 N/m
(b) For Overturning Bearing Pressure for Ringwall
Pf = wt( 1+ 0.4*Av ) + 1.273 Mrw / D2 Equation ( E.6.2.3-2)
= 13938.1 N/m
13.0 HOOP TENSION IN BOTTOM COURSE OF SHELL
J = Joint Efficiency
= 1
D/ HL = 0.914286 Lesser than 1.3334
Y/ HL = 1
Y / ( 0.75D ) = 1.458333 Greater than 1
M = tanh ( 0.866D/HL) = 0.659411
F = 8.48 x Ai .G.D.H L = 127.2
=
Ni = 2.6*Ai*G*D^2
= 35.65714 N / mm
f = 3.68/ (HL/D) = 3.364571
f1 = {3.68 (HL- Y) / D } = 0
Nc = 1.85*AC*G*D2 { cosh(f 1) /cosh(f) }
= 0.93785 N/m
Nh = 4.9 ( Y - 0.3) *G*D
= 1348.48 N / mm
Total Resultant sS = [ Nh + {(Ni2 +Nc2+ (Nh.AV / 2.5)2 }0.5 ] / t
= 156.5116 MPa
Sallow = min (1.33*Sd , 0.9 Fy)
= 221.6711 MPa
> Ss , Acceptable
