ML20217K448
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| Issue date: | 10/31/1995 |
| From: | Bandyopadhyay, Cornell A, Costantino C BROOKHAVEN NATIONAL LABORATORY |
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l BNL 52361 (REV.10/95) 0C-406 00510 SEISMIC DESIGN AND EVALUATION GUIDELINES FOR THE DEPARTMENT OF ENERGY HIGH-LEVEL WASTE STORAGE TANKS AND APPURTENANCES K. Bandyopadhyay, A. Cornell, C. Costantino, R. Kennedy, C. Miller and A. Veletsos*
October 1995 i
ENGINEERING RESEARCH AND APPLICATIONS DIVISION DEPARTMENT 0F ADVANCED TECHNOLOGY BROOKHAVEN NATIONAL LABORATORY, ASSOCIATED UNIVERSITIES,INC.
UPTON, NEW YORK 11973 5000 Prepared for the DFFICE OF ENVIRONMENTAL RESTORATION AND WASTE MANAGEMENT I
UNITED STATES DEPARTMENT OF ENERGY
~
CONTRACT NO. DE ACO2-76CH00016
- Authors' names are listed in alphabetical order.
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00510 SEISMIC DESIGN AND EVALUATION GUIDELINES FOR THE DEPARTMENT OF ENERGY HIGH-LEVEL WASTE STORAGE TANKS AND APPURTENANCES K. Bandyopadhyay, A. Cornell, C. Costantine, R. Kennedy, C. Miller and A. Veletsos*
October 1995 k
ENGINEERING RESEARCH AND APPLICATIONS DIVISION DEPARTMENT 0F ADVANCED TECHNOLOGY BROOKHAVEN NATL 0dAL LABORATORY, ASSOCIATED UNIVERSITIES, INC.
Un' TON, NEW YORK 11973 5000 Prepared for the OFFICE OF ENVIRONMENTAL RESTORATION AND WASTE MANAGEMENT UNITED STATES dei'ARTMENT OF ENERGY CONTRACT NO. DE-AC02-76CH00016
- Authors' names are listed in alphabetical order.
FM "28su ass 8she P
l 1
ABSTRACT This-document. provides seismic design and evaluation guidelines for underground high-level waste storage tanks.
The guidelines reflect the knowledge acquired in the last two decades in defining seismic ground motion. and calculating hydrodynamic loads, dynamic soil pressures and other loads for underground tank structures, piping and equipment.
The application of the guidelines is illustrated with examples.
The guidelines are developed for a
specific design of underground storage
- tanks, namely double-shell structures.
However, the methodology discussed is applicable for other types of tank structures as well.
The application of these and of suitably adjusted versions of these concepts to other structural types will be addressed in a future version of this document.
The original version of this document was published in January
-1993.
Since then, additional studies have been performed in several areas and the results are included in this revision.
Comments received from the users are also addressed.
Fundamer.,t al conceptis supporting the basic seismic criteria contained in tl.-
original version have since then been incorporated and published in DOE-STD-1020-94 and its technical basis documents.
This informa-tion has been deleted in the current revision.
i l
i iii L
TABLE OF CONTENTS Pace No.
i
~ ABSTRACT iii l
TABLE OF CONTENTS v
LIST OF TABLES xiv LIST OF FIGURES xvii 1
ACKNOWLEDGEMENTS xx CHAPTER 1 - INTRODUCTION 1-1
1.1 BACKGROUND
1-1 1.2 TANK FARMS:.
1-1 j
1.3 OVERVIEW OF SEISMIC GUIDELINES 1-3 1,4-NOTATION.
1-6 REFERENCES 1-7 CHAPTER 2 - SCOPE AND APPLICABILITY OF GUIDELINES 2-1
2.1 INTRODUCTION
2-1 2.2-SCOPE 2-1 2.2.1 Tank-Waste System.
2-2 2.2.2. Vault-Soil System.
2-4 2.2.3: Underground Piping-2-5
-2.2.4 Application to Other Waste Storage Systems 2-5 REFERENCES 2-7 CHAPTER'3 SEISMIC CRITERIA 3-1 3.1' ' INTRODUCTION.
3...................
3.2-FUNDAMENTAL CONCEPTS'.
3-2 3.3 DESIGN BASIS EARTHQUAKE GROUND MOTION 3-7 3.3.1 Probabilistic Definition of Ground Motion.
3-7 3.3.2 Design Basis Earthquake Response Spectra 3-9 3.4 A"ALYSIS OF SEISMIC' DEMAND (RESPONSE) 3-13 3.5 DAMPING.
3-15 3.6-MATERIAL' STRENGTH PROPERTIES 3-17 3 ~. 7 CAPACITIES 3-18
?.8 ' LOAD COMBINATIONS AND ACCEPTANCE CRITERIA 3-20 3.9 INELASTIC ENERGY ABSORPTION FACTOR 3-23 v
-i
~'
TABLE OF CONTENTS (Continued) 3.10 BASIS OF PROCEDURES AND AN ALTERNATE APPROACH TO COMPLIANCE.
3-29
...... =.............
9 3.10.1 The Basic Seismic Criterion 3-30 3.10.2 The General Approach to Compliance 3-30 3.11 BENCHMARKING DETERMINISTIC SEISMIC EVALUATION PROCEDURES AGAINST THE BASIC SEISMIC CRITERION 3-31 REFERENCES 3-34 NOTATION 3-37 CHAPTER 4
. EVALUATION OF HYDRODYNAMIC EFFECTS IN TANKS 4-1 4.1 OBJECTIVES AND SCOPE.
4-1 4.2 RESPONSES OF INTEREST AND MATERIAL OUTLINE 4-3 4.3 EFFECTS OF. HORIZONTAL COMPONENT OF SHAKING.
4-4
~4.3.1 General.
4-4 4.3.2 Hydrodynamic Wall'and Base Pressures 4-5 4.3.2.1 Natural Sloshing Frequencies 4-9 4.3.2.2 Fundamental Natural Frequency of Tank-Liquid System.
4-10 4.3.2.3 Maximum Values of Wall and Base Pressures.
4-14 4.3.2.4 Relative Magnitudes of Impulsive and Convective Pressures 4-15 4.3.3 Evaluation of Critical Effects 4-15 4.3.4 Total Hydrodynamic Force 4-17 4.3.5 Critical Tank Forces 4-18 4.3.5.1 Base Shear.
4-18 4.3.5.2 Bending Moments Across Normal Tank Sections.
4-19 4.3.5.3
. Sensitivity to Variations in System Parameters 4-24 4.3.6 Effects of Tank Inertia.
4-25 4.3,7 Hydrodynamic Forces Transmitted to Tank Support 4-26 4.3.3 Modeling of Tank-Lim id System 4-29 4
4.4 EFFECTS OF ROCKING COMPONENT OF BASE MOTION 4-30 4.5 EFFECTS OF VERTICAL COMPONENT OF BASE MOTION.
4-31 vi l
o M
TABLE OF CONTENTS (Continued) l 4.5.1 Hydrodynamic Effects.
4-31 4.5.2-Effects of Tank Inertia.
. 4-34 4.5.3 Combination With Other Effects 4-35 4.5.4 Modeling of Tank-Liquid System 4-35 EFFECTS OF SOIL-STRUCTURE INTERACTION 4-36 4.6.
4.7 SURFACE DISPLACEMENTS OF LIQUID 4-37 4.8 EFFECTS FOR TANKS WITH INHOMOGENEOUS LIQUIDS.
4-38
' 4. 8.1 - General-.
4-38 4.8.2 Impulsive Effects.
4-39 4.8.3 A Further Simplification 4-41 4.9. COMBINATION OF EFFECTS'OF HORIZONTAL COMPONENTS y
OF GROUND MOTION.
4-42 REFERENCES 4-44 NOTATION 4-47 CHAPTER 5 - SEISMIC CAPACITY OF TANKS 5-1
5.1 INTRODUCTION
5-1 5.2 EARTHQUAKE EXPERIENCE ON FAILURE MODES 5-1 5.3-SEISMIC EVALUATION 5-3 5.4 SLOSH HEIGHT CAPACITY, 5-5 5.5 ~ HOOP TENSION CAPACITY 5-6 5.6 MAXIMUM PERMISSIBLE AXIAL COMPRESSION OF TANK SHELL 5-7 5.6.1 Allowable Axial Compressive Stress 5-8 5.6.1.1 Geometric Imperfection.
5-9 5.6.1.2 Loading 5-9 5.6.1.2.1 Effect of Internal Pressure.
5-10 5.6.1.2.2 Effect of Bending 5-14 5.6.1.2.3 Effect of Earthquake Loading 5-15 5.6.1.2.4 Pressure Estimates for Earthquake Loading 5-16 5.6.1.'3 Acceptance Criteria 5-17 5.6.1.4 Existing Tanks 5-19 5.7 MOMENT CAPACITY AWAY FROM TANK BASE 5-19 5.8 ANCHORAGE CAPACITY AT TANK BASE 5-19 5.9 ' BASE MOMENT CAPACITY OF FULLY ANCHORED TANKS 5-20 5.10 BASE MOMENT CAPACITY OF PARTIALLY ANCHORED OR UNANCHORED TANKS 5-21 vii
(
w
m
' TABLE CF CONTENTS (Continued) 5.11 PERMISSI.BLE UPLIFT DISPLACEMENT 5-24
'5.12LFLUID HOLD-DOWN FORCE 5-24 5.12.1 Anchored Tanks 5-24 5.12.2 Unanchored Tanks 5-28 5.13 BASE SHEAR CAPACITY 5-30
' 5.14 OTHER CAPACITY CHECKS 5-32 5.15 TOP SUPPORTED TANKS 5-33 REFERENCES 5-34 i
NOTATION.
5-37 CHAPTER 6 - EVALUATION OF SOIL-VAULT'I. TERACTION N
6-1
6.1 INTRODUCTION
6-1 6.2 SOIL PROPERTIES 1
6-3 6.3 FREE FIELD MOTION.
6-4 6.4. HORIZONTAL SSI CALCULATIONS 6-6
'6.4.1 Continuum Model Using Time History Analysis.
6-9 6.4.1.1 Free Field Motion 6-10 6.4.1.2 Soil Model.
6-10 6.4.1.3 Vault Model 6-11 6.4.114 Tank and Contents Model 6-11 I
6.4.1.5 Verification of Results 6-15 j
i 6.4.2-Lumped Parameter Model 1
6-16 j
6.4.2.1 Impedance Functions
)
6-16 6.4.2.2 Free. Field Solution 6-18 6.4.2.3 Kinematic Interaction 6-19 l
6.4.2.4 Inertial Interaction.
6-19 I
6.4.2.5 Calculation of' Wall Pressures 6-20 6.5 VERTICAL SSI CALCULATIONS 6-22 6.6 VAULT-VAULT INTERACTION 6-23 REFERENCES 6-24 NOTATION.
6-26 CHAPTER 7 - UNDERGROUND PIPING AND CONDUITS 7-1
7.1 INTRODUCTION
7-1 7.2 DESIGN FEATURES AND GENERAL CONSIDERATIONS 7-3 viii E
r; k
CHAPTER 5 SEISMIC CAPACITY OF TANKS
' 5.,1
' INTRODUCTION This chapter preserits. an approach for evaluation of seismic
-capacities of anchored and unanchored tanks.
In this approach, a minimum capacity is determined based on the nominal ultimate strength, and then this capacity is reduced by applying a factor of safety consistent with Section 3.7.
For applicability of the l provisions included in this ' document, it is assumed that the tanks are flat-bottom and fabricated following certain standard construction procedures, examples of which ' are included in Appendix E.
The structural capacities need to be estimated by
. precluding known failure modes.
A general description of earthquake experience related to failure of above-ground liquid storage tanks is" presented in the following section.
Internal appurtenances have not been explicitly addressed in this document.
However, they must be evaluated in a manner consistent-with. this document.
Guidance on their seismic response evaluation is given in ASCE 4-86 (Reference 5.1) and capacities should be determined in accordance with the requirements of Sections 3.6 and 3.7.
5,2 EARTHQUAKE EXPERIENCE ON FAILURE MODES Flat-bottom vertical liquid storage tanks have sometimes failed with loss. of contents during strong earthquake shaking.
For tanks with radius-to-wall thickness ratios greater than about
'600 or tanks with minimal or no anchorage, failure has often been'; associated with rupture of the tank wall near its connection to the base,.due either to excessive tank wall buckling or bolt stretching and excessive base-plate uplift.
Both failure modes are primarily due to dynamic overturning moment at the tank base from impulsive mode fluid pressure on 5-1
L the tank wall.
Another common failure mode has been breakage of piping connected to a tank as a result of relative movement.
When the pipe enters the tank below the fluid level, then breakage of a
-pipe.between the tank wall and shutoff valve is one of the most prevalent causes of loss of fluid from a storage tank.
Another common cause of tank failure has been severe distortion of the tank. bottom at or near the tank wall due to a soil failure (soil liquefaction, slope instability, or excessive differential settlement).
For new tanks these soil-induced failures are best prevented by proper soil compaction prior to placement of the tank and through the use of reinforced mat foundations under tanks.
For existing tanks either founded on ring foundation or directly founded on the soil (i. e.,.
no reinforced mat foundation)', these soil-induced potential failure modes should
-also be investigated.
Other failure modes which are of much lesser importance either because of their general lack of occurrence or less severe consequences, but which deserve some attention, are tank sliding, excessive hoop tensile stresses due to hydrodynamic pressures on the tank wall, and damage to the roof and internal attachments.
Sliding is a concern for unanchored smaller diameter tanks.
However, sliding of an unanchored tank with greater than a 30-foot diameter and fluid height less than the diameter is extremely unlikely.
Simple calculations indicate that there is sufficient friction between the tank bottom and foundation to prevent sliding for these tanks.
Tensile hoop stresses due to shaking-induced pressures between the fluid and tank wall can become large and. lead to splitting and leakage.
This phenomenon has occurred in riveted tanks where leakage at the riveted joints has resulted from seismic pressure-induced hoop yielding.
This occurrence is more common in the upper tank wall because the ratio of seismic induced pressures to 5-2 i
.m
.ss
r; i
. hydrostatic pressure is greater in the upper portions.
There t
does ' not ' appear to be' any case where a welded steel tank has
)
actually ruptured'due to. seismically ' induced hoop strains.
Tank l
ductility' appears to be suf ficient. to ' accommodate these hoop
- strains.
However, large tensile hoop stresses combined with compressive longitudinal stresses contribute to the likelihood j.
- of -
" elephant. foot" buckling near the tank base due to overturning moment.
- Lastly, there have been a number of instances'of roof. damage when insufficient freeboard exists to j-accommodate fluid sloshing.
In addition, lateral-movement and-torsional rotations of the fluid which develop during ground shaking have broken
- guides, ladders, and other~ internal appurtenances attached between the roof and bottom plate.
5.3 FEISMIC EVALUATION.
Each of the potential failure' modes described above should be considered in the seismic evaluation of tanks.
Emphasis should be given to ensure adequate overturning moment capacity, piping l
flexibility, and prevention of foundation f ailures. The seismic evaluation consists of two parts: a seismic response evaluation, and a seismic capacity assessment.
The topic of response l
evaluation is covered in Chapter 4.
For the tank evaluation, the following responses should be obtained for comparison with 1
the' respective capacities:
1.
.The overcurning moment in the tank shell immediately above j
-the base plate of the tank: This moment should be compared with the base moment capacity which is governed by a j
combination of shell-buckling and anchor bolt yielding or t
failure, and generally governs the seismic capacity of the tank.
l 9
Q 2.
The overturning moment applied to the tank foundation j
through a combination of the tank shell and the base plate:
}
This moment is needed only for tanks founded on soil sites, 5-3
for which the potential of foundation failure should be investigated.
This moment which is generally obtained as part - of the SSI evaluation seldom governs the seismic design.
3.
The base shear beneath the tank base plate:
This base shear is compa;ed to the horizontal sliding capacity of the tank.
For atmospheric tanks with a radius greater than 15 feet, it seldom controls the seismic capacity.
4.
The moment in the tank shell at locations where the tank shell is thinner than at the base (such as occurs at 9 feet above the base in the Figure G.1 example tank), and a t the location of maximum moment if such a location is away from the base as would be the case for a tank laterally supported at the top of the side wall as well as the base.
5.
The hydrosta tic pressure pa; the seismic-induced hydrodynamic pressures due to the horizontal input componen t (combination of impulsive and convective modes) par and the hydrodynamic pressures due to the vertical input component pay :
It is common design practice to compare these combined pressures with the membrane hoop capacity of the tank wall at one-foot above the base and each location where. thickness changes.
In addition, the pressure at the base is needed for the base moment and shear capacity calculations.
These combined pressures essentia uly never govern the seismic capacity of a properly designed tank.
6.
The fluid slosh height: This slosh height is compared with the freeboard above the top of the fluid to estimate whether' roof damage or an increase of the hydrodynamic pressure is likely.
For each of the computed tank responses and failure modes 5-4
r described
- adove, capacity criteria are presented in the following sections.
5.4 SLOSH HEIGHT CAPACITY The approach given ' in Chapter 4 for computing the dynamic response of liquid storage tanks is conditional on the liquid surface being free to move vertically unconstrained by the tank l
' roof.
In order to provide an adequate factor of safety above the computed ~ slosh height response h,,,
the slosh height capacity h,, should be determined as follows:
3
'( **}
hoc ;t 1 6SF h,,
where SF is the appropriate seismic scale factor from Section i
3.3.1.
The factor 1.6 in Equation 5.1 has been made slightly larger-than the factor of 1.5 in Equation 3.11 to provide for increas'ed slosh heights-due to nonlinear surface effects.
1 For a spherical domed roof or a domed roof that 'can be
-approximated by a combination of cylindrical and spherical segments (such as a torispherical roof), the available slosh height capacity h,,,
before excessive forces result on the dome, can be approximated by:
h,, ah, + h (5.2) where h is the cylindrical wall height above the liquid and ha e
is.the dome height above the cylindrical wall.
If Equation.5.2 does not-satisfy Equation 5.1, then the liquid may slosh against a' substantial portion of the tank roof due to inadequate freeboard between the liquid surface and the tank l
roof, and the following phenomena occur:
l
'1.
.The hydrodynamic pressure against the tank wall increases due to the vertical constraint of the liquid surface.
The 5-5 L
[.
hydrodynamic pressure may be estimated in accordance with the procedure described in Appendix D.
2.
The shear force and bending moment throughout the tank height also increase in a manner corresponding to the increase in the hydrodynamic pressure.
3.
The liquid pressure acting against the tank roof will change the longitudinal force in the cylindrical walls of the tank and also could damage the roof.
The performance of the tank at its base might be adversely influenced by the changed longitudinal force.
When h defined by Equation 5.2 satisfies Equation 5.1, the se above defined adverse consequencec are considered to be negligible and do not need to be addressed.
5.5 HOOP TENSION CAPACITY For seismic loads, the hoop membrane stress capacity, a, of the tank shell should be taken as the ASME Code (Reference 5.2)
Service Level D limit for a primary stress of 2.0S or the yield a
j stress, whichever is less.
For example, 2.0S = 37.5 ksi for SA240-Type 304 stainless steel for which the yield stress is 30 ksi.
Thus, the pressure capacity pc is:
U" t
c p#
(5.3)
=
R
{
where t, is the tank wall thickness, and R is the tank radius.
e This capacity is then compared with the total f actored inelastic demand (pu) given by:
Pe2 = P,e +
(F$n + P!v)*
(5.4) vo where hydrodynamic pressures from the horizontal earthquake ground motion component (pe) and from the vertical component (p ) are combined probabilistically by the square-root-sum-of-5-6
.~
y l
. squares. method, Fg = 1.5 from Table 3.3 and SF is the appropria a seismic scale factor from~Fection 3.3.1.
However, as will be. discussed at the end of Section 5.6.1.2.1, when the combined hydrostatic and hydrodynamic pressure produces a hoop ' stress that exceeds about 85% of the yield stress o, the y
allowable 'a:cial compressive stress capacity will drop to less than 6% of o.
Therefore, where axial buckling is an important l
y considerati'on, it is generally undesirable to allow the hoop i
stress to exceed 85% of o.
y
.5.6 MAXIMUM PERMISSIBLE AXIAL COMPRESSION OF TANK SHELL The cylindrical tank.shell is subjected to an axial compression force on'one side and an' axial tensile force on the other side j
due to the seismic-induced overturning moment.
At the base of the fully-anchored tank and away from the base for all tanks, j
the moment capacity is controlled by the maximum permissible axial compression.of the tank shell.
In turn, this permissible axial compression capacity must be set sufficiently low to avoid either plastic collapse
(" elephant-foot" buckling) or bifurca-i tion
(" diamond") buckling of the tank shell.
The most likely way for fluid filled tank shells to buckle is in
" elephant foot" buckling near the base of the tank shell.
The
.} -
tank shell is subjected'to a biaxial stress state consisting of h
hoop tension and vertical (axial) compression.
In addition, radial' deformations under internal pressure"which are prevented at the base due to membrane tension in the base plate introduce eccentricity and bending stresses in the axial plane which further induce the tendency to " elephant foot" buckle.
- However, the initiation-of an'" elephant foot" buckle does not directly correspond to a failure of a tank.
Many tanks have continued to perform their function of containing-liquid even al.ter developing substantial delephant foot" buckles.
However, no simple method to predict tank performance after the development 5-7
i of " elephant foot" buckling exists.
Therefore, the onset of
" elephant foota buckling will be judged to represent the limit to the compressive buckling capacity of the tank shell.
5.6.1 Allowable Axial Comoressive Stress A cylindrical shell buckles when subjected to large compressive loads.
This usually occurs at a stress lower than the yield strength of the shell material.
The classical linear elastic buckling stress for a cylinder of perfect geometry subjected to an axial compressive load is given by j
r eg --_
E t,,
e e
G 2
Rj 3/1-v )
s (5.5) 0.605 E*
R/t
, for v ' = 0. 3
=
tv In reality, the shell exhibits buckling at a compressive stress even lower than o,.
The reduction of the compressive strength e
compared to o, depends on inherent geometric imperfection of the c
shell and nature of loading. Thus, for bifurcation buckling, the nominal ultimate axial compressive stress, o.u, is given by
( a,,) (a reduction factor)
(5.6) o,y
=
where, the reduction factor includes the effect of geometric imperfection and plasticity.
For plastic collapse under a large hoop
- stress, o,.,
can be directly computed by considering instability under the biaxial stress state.
Ultimately, a
factor of safety FS is introduced for computing the allowable axial compressive stress, o.,
as follows:
"au o*,
(5.7)
FS For the tank wall design, the allowable compressive force, C.,
per unit circumferential length may be required and is given as follows:
5-8 ummmmmmm-
-- '~ - E
C, = = ag x t (5.8) w The effects of various parameters on the shell compressive strength are further discussed in the following sections.
5.6.1.1
-Geometric Imoerfection Standard' fabrication and construction procedures usually introduce a small amount of geometric imperfer' 2on on the shape of-the shell, such as, a bu.'.ge at welds.
The buckling strength is. sensitive :to the shape as well as magnitude of the imperfection.
The larger the bulge, for example, the greater is i
the reduction of the buckling strength.
With realistic l
geometric imperfections, the actual compressive strength may be l
.as low as 20% of the classical buckling strength, when the shell 1
is subjected to static loading.
5.6.1.2 Lo2Lding The buckling strength is also greatly influenced by the nature of-loading.
Most test data available in the literature were obtained from-static tests subjecting the cylinders to uniform axial compressive loads (References 5.3 and 5. 4 ).
There are examples of static tests where the specimens were subjected to static bending compressive stresses (References 5. 5 and 5. 6 ).
Test data indicate that a cylinder can withstand a higher buckling stress when subjected to bending compressive stresses which vary along the circumference as opposed to uniformly distributed membrane stresses.
The load combination can also
-influence the buckling capacity of the s'tell.
For example, an internal' radial pressure may reduce the geometric imperfection, such'as,.a bulge, and, in turn, increase the buckling strength.
These examples are for static loading.
Earthquake experience and shake table testing data, on the other hand, indicate a i
greater buckling strength for dynamic loading conditions.
The effects of loadings and load combinations on the shell buckling 5-9
strength are'further elaborated and quantified in the following i
sections.
5.6.1.2.1 Rffect of Internal' Pressure Internal pressure reduces the effects of existing geometric imperfections and
- this, in
- turn, increases the buckling strength, as depicted by curve ABC in Figure 5.1.
At a very high pressure, the effects of existing imperfections are expected to be eliminated and the elastic buckling strength approaches that of a perfect cylindrical shell, i.e.,
the classical buckling stress, o,.
Such elastic bifurcation c
buckling is also called " diamond buckling."
on the other hand, the existence of internal pressure simultaneously with the axial load introduces a biaxiality effect.
At low pressure, the effect is relatively small and the axial compressive load required for plastic collapse (also called " elephant foot" buckling) of the shell is relatively large.
As the pressure increases, the hoop tensile stress plays a significant role and plastic collapse can occur at a small axial compressive stress.
Curve DBE in Figure 5.1 shows the plastic collapse locus following a standard biaxiality failure criterion, e.g.,
the effective stress reaches the yield strength of the shell material.
As can be observed from Figure 5.1, up to a certain pressure, elastic buckling occurs prior to plastic collapse, and beyond that plastic collapse occurs first.
Thus, the governing compressive strength of the shell in the presence of internal pressure will be denoted by curve ABE.
There are empirical formulas available in the ' literature for determination of the allowable axial compressive stress as influenced by the internal pressure (References 5.7 through 5.11).
Most of these references require separate computations of the elaatic buckling and plastic collapse stresses.
An ASME Cod-Case that directly provides the allowable compressive strew
..r any pressure is presented in this document.
5-10 N
i i
The allowable axial compressive stress in.a cylindrical shell i
can be calculated by using ASME Code Case N-530 (Reference i
5.12).
The code Case is based on a comparative study of the I
available test and analytical data (References 5.13 and 5.14),
and adopts ' the recommendations of the European Convention for Constructional Steelwork (Reference 5.15).
The effects of the j
internal pressure and possible geometric imperfections are included in the Code Case formulas.
At low pressure, the ECCS which is the basis of the Code case introduces an additional factor of 0.75 to the elastic buckling curve shown in Figure 5.1 to obtain o.u.
At high pressure, when biaxiality plays a key role, the Code Case introduces an " effective stress" and uses an l
empirical formula based on data fitting (Reference 5.4) to compute o.u.
The Code Case approach is summarized in the remainder of this section.
~
1 For uniform compression, the classical linear elastic buckling 1
stress, a,, given by Equation 5.5 is reduced by introducing a e
buckling capacity reduction factor, a, which is defined by 0
(5.9)
, for R/ t, > 212 a =
a e
l0.1 + 0.01R/c,
e l
For practical tanks, R/t is expected to be greater than 212.
w l
The capacity reduction factor increases with the internal l
pressure as defined by F
a# = a + (1-a)
E + 0. 0 07 p
(5.10)
\\
where, F, =
(R/ ttv)**'
For uniform compression, a=a given by Equation 5.9.
For a o
combination'of uniform and bending compression, a is given by Equation 5.17.
By using the above capacity reduction factor and 5-11
7
-introducing:the nominal hoop' stress 2 03 = PR/ t (5.11) w,
,the axial compressive strength can be obtained by solving the
'following simultaneous equations a,u = }o*u + of + o,ua (5.12) n
- " = 0
- 5.. for Ap:t1.414 (5.13) gY p
- "' = 1. 0
. O. 41.23 Ap a for A, < 1. 414 (5.14)
,y Ee 7 (5.15) 8 A
% aa, p c
)
a'"
- and, (5.16)
, = * *ft In the above equations, a.r, denotes the effective stress considering both the axial 'and hoop stresses; a., is positive for a compressive-axial stress; a is positive for a tensile hoop 3
stress; A, = 1.414 indicates el.astic buckling;.and A, e L.414 indicates plastic collapse.
cne simultaneous equations can be solved by trial and error.
For convenience of
- solution,
" Equations 5.10, 5.12 and 5.13 can be rewritten as follows:
, F, + 0. 0 07 a
( 5.10a) g P
F, + 0. 0 07
.1 Hoop stresses"'due to other' sources, if any, should be added to
-this. equation.
5-12 4
i=
0,u = }a,gg ' - 0. 7 5 al - 0. S o U MT
~
y j
a, for Ap>,1.414 (5.13a)
-a
= 0'. 7 5 a a mu p
(
- The following is an algorithm for the solution:
j 1
I ag and o for the set of Step'1.
Compute. a,'F, a,
a, e
3 o
p p
conditions being evaluated.
j l
Step 2.
Estimate a' value of. Se; call the value y'.
]
Step 3.
Compute X, from Equation 5.15 using Se' for #,.
j Step 4.
Compute a re from Equation 5.13 or.' 5.14.
(
Step 5.
Compute o., from Equation 5.12a.
For Aj = 1.414, au can be computed directly from Equation'5.13a.
Step 6.
Compute #, from Equation 5.16.
Step 7.
Compare the computed value of #, (Step '6) with the estimated value, (Step 2).
If the computed value of #, is cloje to'the estimated value, S ', note the value of au as the ultimate axial compressive stress.
If not, select a revised value of #, and return to Step 3. ' Repeat the process until a desired degree of l'
accuracy is achieved.
At low pressure, elastic buckling governs, and at high pressure, plastic' collapse controls the failure (References 5.13 and 5.14).
Therefore, a,u should be calculated for the lowest and highest possible pressure values concurrent with the axial loads at the desired location (e.g., see Equations 5.18a and 5.18b),
and the' lower of the two values of a,u should be used.for the
,g I
design or evaluation.
The ASME Code Case (' Reference 5.12) provides a tolerance on the bulge's or flat spots in the cylindrical walls. 'The amplitude of 5-13 n
the bulge should not exceed 1% of the length over which it is
).
measured.
This is further illustrated in Appendix E.
With the increase in pressure, the failure mode changes from bifurcation buckling to plastic collapse (References 5.13 and 5.14).
- Thus, the effect of imperfection is less pronounced at a high pressure.
An example of the ASME Code Case is presented in Figure 5.1.
At low pressure, the Code Case curve is related t e, the elastic bifurcation buckling curve ABC by a factor of safety At high
- pressure, the Code Case capacity is controlled by plastic collapse and the plot resembles curve BE described earlier.
At very high pressure (e.g., Ap < 0.3), the Code Case formula (i.e.,
Equation 5.11) seems to be excessively conservative (Reference 5.4).
For tank designs, it is recommended that, in general, the hoop stress be' limited to 85% of the material yield strength.
If this limit is exceeded, the nominal axial compression capacity o
may be computed using large displacement theory and an u
appropriate nonlinear stress-strain relationship, in lieu of the Code Case approach in order to avoid the excessive conservatism in this pressure range.
Even so, % is expected to be very low, e.g., less than lot of the yield strength.
5.6.1.2.2 Effect of Bending Cede Case N-530 does not consider the beneficial effect of bending in computing the allowable axial compressive stress.
The ECCS (Reference 5.15) revises the capacity reduction factor as follows when the tank is subjected to bending concurrently 1
with the axial compressive load:
- ^#6 a=
(5.17) e, + as where, a is given by Equation (5.6) o F
5-14
-i j
,o I
4 ay = 0.1887 + 0.8113a, for R/t s 1500 o
w ag = uniform; compressive stress due to axial load a3 = maximum' compressive stress due to' bending J
l In the absence of_ internal pressure, a.gr becomes a.u and can be directly. computed ' from. Equations ' 5.13a and 5.14.
- Also, in
' Equation ; 5.15, Si is equal.to 1,
and a, should be taken as a given by Equation 5.17.
Note that for pure bending a is equal l
to %.
h
. The ECCS ' Code (Reference 5.15) does not consider the direct
{
effect'of internal pressure _in computing the capacity reduction factor : for the bending case as evident from Equation 5.17.
A
~
.New ?,ealand study shows that the shell compressive strength for j
bending Leompression increases further 'if the influence of internal pressure is considered ;(Reference 5.11). Therefore, in order to' combine the' effects of internal prescure and bending, it". is recommended l that in Equation 5.10, use the value of a given by Equation 5.17. - As before, solve for o using Equations n
5.11 through 5.16 following the seven steps.
Since. the ASME Code Case does not-includa the bending effect, a tank requiring
.. qualification according to the ASME rules may not be designed or evaluated with the higher capacity reduction f actor for bending.
5.6,1.2.3-Effect of Earthauake Loading The a.!oromentioned formulas for shell compressive strength have been developed by use of' test and analytical data for static loading.
When ' a tank ' is ~ subj ected to earthquake loading, the shell. compressive strength is not only influenced by the simultaneous application of internal pressure and bending as
-1 '
discussed earlier, it is also affected by the dynamic nature of the loade
-In the literature, there are examples of liquid storage; tanks ! subjected to actual earthquakes or simulated earthquake loading on shake tables (References 5.16, 5.17 and
~ 5.18 )'.
The abuckling stresses observed for the actual or 5-15
simulated earthquake, cases are significantly greater than what would have been predicted by Code Case N-530 or the ECCS formulas.
For example, baced on an evaluation of performance of unanchored cylindrical liquid storage tanks during major past earthquakes as well as shake table
- testing, an empirical capacity reduction factor of 0.75 is proposed in Reference 5.16.
' Reference 5 17 reports occurrence of diamond buckling or the shake table at an axial compressive stress of 60% of the classical buckling strength.
The increased buckling resistance to L earthquake loading has been attributed primarily to the reversing nature of the load and local initiation of bucklina due to confinement of high stresses to a relatively narrow area i
of the' tank wall for a short duration.
For a more realistic 1
estimate of the buckling strength under earthquake loading refer
{
to Appendi:: F.
)
- 5. 6.1.2.4 Pressure EE.LLqates for Earthauake Loadinc The pressure p to be used for calculation of the axial strength
)
under ' earthquake loading should be set equal to the probable combined hydrostatic and hydrodynamic pressure p,,, at the point of maximum compression around the tank circumference corresponding to the time of maximum seismic induced moment.
n For bottom supported cantilever tanks:
SF Peom "" Pee + [Pdh
- 0. 4pev) F (5.18a)
- )
il p
where pu is the hydrostatic pressure, pe is the hydrodynamic pressure from the horizontal earthquake component, and p is the hydrodynamic pressure from the vertical earthquake component.
[
A value of F o between 1.0 and 1.5 should be used, and SF is the y
y appropriate seismic F] ale f actor from Section 3.3.1.
The use of an Fn value greater than unity is appropriate when a /a is y
n y
sufficiently high that the axial compressive' capacity is controlled - by. the biaxial plastic collapse mode which is ductile.
When 0/0 is small so that elastic bifurcation i
3 7 5-16 i
i w
buckling controls, F should be taken as unity.
At the time of g
occurrence of the maximum moment, pe will be maximum so that 100% of pe is used in Equation 5.18a.
Howe.ver, to account for the random phasing between p3 and the moment, only 40% of p, is included, but it must be either added or subtracted depending on which gives the lesser axial compressive capacity o..
)
For tanks supported laterally at both their top and bottom, the maximum moment generally occurs near midheight and the point around the circumference at which the compressive stress is maximum corresponds to a location where pa should be subtracted rather than added.
Thus for tanks supported at both top and bottom:
SF pc
= p,e - [p, t 0. 4 pe] 7 (5.18b) 90 S.6.1.3 Accentance Criteria The axial compressive strengths under various loads and load combinations are discussed above.
A set of acceptance criteria is presented in this section.
Static Uniform Axial Com.pression with or without Internal Pressure Use Equations 5.9-5.16 (Code Case approach).
Static Bendino Comoression Combined with Uniform Axial comoression and with or Wit;hgyt,_ Internal Prgssure Use Equation 5.17 and follow subsequent steps described in Section 5.6.1.2.2 (Similar to ECCS approach).
Earthcuake L2ndinc Use conservatively the above acceptance criteria for the respective static loading.
Alternatively, for more real-5-17
n istic results, refer to Appendix F.
Regardless of the loading and load combination, a tank requiring qualifica-tion in accordance with the ASME rules may need to be designed or evaluated following the Code Case.
A factor of safety needs to be introduced on the computed axial compressive strength in accordance with the general acceptance criteria presented in Chapter 3 so that a high confidence of avoiding -a' buckling failure can be achieved, The Code Case recommends a factor of safety of 1.33 for the Service Level D loading (e.g., seismic loading).
From the static uniform compression test data (Reference 5.4),
that are the basis of the ECCS (Reference 5.14) and the Code Case, it can be estimated that the buckling capacity corresponds to=
about the 2%
failure probability level (i.e.,
at approximately -2S) with a logarithmic standard deviation, S,
between 0.14 and 0.19.
Thus, in order to achieve a factor of safety of 1.5 on the capacity corresponding to the 10% failure level as required by Equation 3.9 for a scale factor of unity, the factor of safety to be applied on the Code Case axial ultimate compressive stress, a.,, should be FS = 1. 5 e *0 MP where 0.718 is the number of standard deviation between 2% and 10% failure probability levels.
- Thus, for S = 0.14, FS = 1.36 and, for S = 0.19, FS = 1.31 These values are comparable to 1.33 recommended by the Code Case.
Thus, the Code Case factor of safety satisfies the criteria of Chapter 3.
~ It is judged that the same factor of safety is.also applicable for the bending compression and earthquake. loading cases.
5-18 e
r-I-
m,,
~
l
,3 2
a t.
't.n P-.
,y,7 ;;
516.1.4 I 'Existino Tanks
+
I:
o y; 4
' Tnei above L approach. for determination of ~ the shell compressive
' strength equally;' applies for existing high-level waste storage f
mtanksi as. well ' as : new'. tanks.
-But, the only. difficulty in L
. applying (.,ethis procedure is ' that ' the Code ' Case formulas are i:
i lcontingent upon satisfaction of geometric' tolerance,.i.'e.,
s the bulge, amplitude 'should not, exceed 1%, of ' the wall length.over which it is measured (see-Appendix E). For existing underground i
4 radioactiveLtanks, the. geometric tolerance.cannot be verified.
L
~Because' of overwhelming evidence of greater capacities of tanks 4
X
'in actual and simulated' earthquake situations for realistic tank lgeometrie imperfections compared to the Code Case and ECCS
{
. formulas, h
. it.is judged that no..further penalty be imposed and 3
.the samelformulas can be'used for the existing tanks.
5.7 MOMENT. CAPACITY AWAY FROM TANK' BASE
)
At' locations Lalong the cylindrical shell away from the base, the
. moment' capacity is.given by:
M
- C,rR _ P,R '
3 2
e
- ( 5.19 ) -
l 3 p
where 'P. is any concurrent axial compressive force on the cylindrical shell (generally. negligible).
l i
5.8L:. ANCHORAGE CAPACITY AT TANK BASE ti The. base anchorage bolt hold-down capacity, T, ir governed by' the. weakest of the.following elements:
l
[
L
- 1.
' Bolt _ tensile capacity.
i2.
Anchorage of bolt into concrete foundation
$3 '
! Capacity'oflthe top plate.of bolt chairs to transfer bolt loads to the vertical chair. gussets.
)
m 5-19 l
l 0
L
4.
Attachment of the top plate and vertical chair gussets to the tank wall 5.
Capability of tank wall to withstand concentrated loads imposed on it by chairs.
Each of these capacities should be based on code minimum ultimate strength or limit state capacities with the appropriate code-imposed strength reduction factor ($).
S.9 BASE MOMENT CAPACITY OF FULLY ANCHORED TANKS A tank is considered fully anchored only when the hold-down capacity T per bolt satisfies the following condition:
c3 Ta 2 2 xRC, (5 20) where 6 is the circumferential angle between bolts.
3 In this the neutral axial remains through the centerline of the
- case, tank at maximum capacity and the base moment capacity is also given by Equation 5.19.
However, satisfying Equation 5.20 will require very closely spaced anchor bolts and is seldom practical.
In most cases, Equation 5.20 is not satisfied and the tank is treated as either partially anchored or unanchored.
In either case, the neutral axis will shift toward the compression side of the tank [see Figure 5.2] resulting in an increase in the peak compressive force for a given overturning moment.
The base moment capacity of the partially anchored or unanchored, tank will be substantially less than that given by Equation 5.19.
l 5-20
5.10 BASE MO' MENT CAPACITY OF PARTIALLY ANCHORED OR UNANCHORED i
TANKS A reasonable approximation of the loading that exists at the base of the tank shell can be estimated based upon the following approximations:
1.
Compressive stresses vary linearly from zero at the neutral axis to C' at the outer compression side of the tank wall (i.e.,
at 6 = 180*).
2.
Uplift heights 6, vary linearly from zero at the neutral axis to 6 at the outer tension side of the tank wall (i.e.,
at 6 = Oo).
3.
For simplicity, fluid hold-down forces are also assumed to vary linearly from Trn at the neutral axis to T,, at 6 = 0.
Figure 5.2 illustrates the loading that exists at the base of the tank wall based on the above approximation.
Also shown is the uplift of the tank wall due to an assumed rigid rotation of the base.
In Figure 5.2, C,'
is the maximum compressive stress in the tank wall, Ten is the effective fluid hold-down force at the neutral axis, AT, is the increase in fluid-hold down force 0, Tu are anchor bolt hold-down forces if the tank is at 6
=
anchored, W is the tank weight, and Me is,the moment capacity e
which results from this loading distribution.
l Fo7 any given angle 6 to the neutral axis:
n 1
n We+ [T3f (5.21)
Cl=
+Te C + AT C
'~
fn n 1
f 3 2R (T Rcos0) +TR2 (2 sine ) + A T,C,R (5 22) 2 M = ClC R 3
+
y3 3
gn n
c g
1-2 l
where:
j 5-21 1
l
}
L.
r l
\\
1 + cos 6" C
=
1
\\
sin 6, + ( n-0,) cos 6, sin 6,cos 6, + x - 0, C
2 1 + cos 6, (5.23) sin 6, - 6, cos 6,
' l + co s 6, 3
sin 6, + ( n-6,) cos 6,, 1 - cos 6,,
6 - sin 6, cos 6, n
C
=
4 1 - cos 6, Numerical values for C, C,
C, and C.
as functions of 6 are 2
2 3
n tabulated in Table 5.1.
The moment capacity depends upon the axial compressive buckling capacity of the tank wall ( C,)
from section 5.6, the tensile l
hold-down capacity of the anchor bolts including their anchorage and attachment to the tank (T )
from section 5.8, the 3
permissible uplift height (6.) from section 5.11, and the hold-down force of fluid pressure acting on the tank base plate (T,)
from Section 5.12.
Thus, each of these quantities must be estimated prior to estimating the overturning moment capacity.
i The steps in solving for the moment capacity are as follows:
1.
Establish the maximum permissible uplift height 6,
[see Section 5.11).
2.
Compute the fluid hold-down force Te, corresponding to the uplift height 6, and the fluid hold-down force Trn at the neutral axis (see Section 5.12] and then:
ATg= T,-T, (5.24) g g
3.
Assume an initial value of the angle e to the neutral axis n
and estimate the anchor bolt tension Tu in anchor bolt "i" from:
5-22 l
' cos 6' - cos 6"' sT (5.25)
Tsj = Typ + Ky cb 1 - cos 6, s
where b b K3=
(5.26) and 6 is the angle 6 at bolt "i,"
T is any bolt 1
3p pretension (generally should be taken as zero since it is likely to be lost over time), T is the bolt capacity [see c3 Section 5.8), A is the bolt area, E is the bolt modulus of 3
3 elasticity and h, is the effective bolt length from its attachment to the tank to its effective anchor depth in the concrete.
4.
Compute CJ from Equation 5.21 and compare it to the shell buckling capacity C.
Vary 6 and repeat Steps 3 and 4 3
n until CJ = C.
3 5.
Determine the moment capacity M from Equation 5.22.
c As will be shown in the solution for capacity of the example tank in Appendix G, it is unnecessary to converge to a refined estimate of the angle 6 to the neutral axis in Step 4 in order n
to estimate the moment capacity Mc.
Although CJ is sensitive to changes in the angle 6, M is not sensitive to small changes in n
c 6.
n Also, as will be shown in Appendix G, the base moment capacity of even a minimally anchored tank is substantially greater than that of an unanchored tank.
Therefore, for new designs it is recommended that the tank should be either laterally supported near its top (thus greatly reducing the applied base moment) or i
should be anchored at its base.
5-23 l
l
l 5.11 PERMISSIBLE UPLIFT DISPLACEMENT In order to prevent. anchorage failure, the maximum uplift displacements 6; of anchored tanks should be limited to a small 2
value.
.For anchored tanks in which the bolt tensile capacity controls Tc3,L6 should be limited as follows:
d s 0.01h, (5.27) o where h, is the effective bolt length.
When other failure modes i
control, 6 should be limited to the lesser of Equ tion 5.24 or 1/4 inch.
For unanchored
- tanks, much greater uplift heights are
' permissible. ; To avoid failure at the junction of the base plate Land wall, it is suggested that uplift heights be limited to:
l 6, = 0.1L (5.28) where L is the computed uplift length of the base plate (see Figure. 5.4' and Section 5.12. 2).
Equation 5.28 will typically produce uplif t heights of several-inches.
However, if piping or other ' components are attached to the tank wall or uplifted' region of the base plate, 6. must also be limited to tolerable displacements for such piping or other components.
I 1
5.12-FLUID HOLD-DOWN FORCE 5.12.1 Anchored Tanks The situation in the region of axial tension in the tank wall is illustrated.in Figure 5.3 for a small uplift, 6.
At point "0"
away from the tank wall, the tank bottom is in full contact with the foundation and the displacements, rotation, and moment in
'the tank bottom are zero.
However, at the intersection of the tank bottom and wall at point "1, " the ' tank bottom has uplif ted 6.and rotated a.
The length of the uplift zone is L, and the fluid pressure, p., on the tank bottom and wall resists this
,1 5-24 l
g;
[
uplift.
This uplift is accompanied by the development of tension, Tr, and moment, Me, in the tank wall at the intersection with the tank bottom.
This tension, Tr, acts as a fluid hold-down force on the tank wall.
For a given uplift height, 6, the hold-down tension, Tr, that develops is both a function of the bending stiffness of the tank wall which is a function of its thickness, t,, and radius, R,
and the bending stiffness of the e
base plate which is a function of its thickness, te3 t
For a tank wall restrained against radial displacement at point "1" by the base plate, the relationship between Mr and a can be obtained from pages 276 through 278 of Flugge (Reference 5.18) for axisymmetric loading as follows:
(5.29)
Nf = K,a + Mfx where Mrx represents the fixed end moment, and 2Kr K* =
R M,"
Rt,
(1 - p}
(5.29a) f e
E*
/12 (1-v$)
N#
K=
12 (1-v*e) 1/2 I
2 (R/ t,) /3 (1-v )
x=
e Even though the actual loading around the circumference is not axisymmetic, Equation 5.29 is considered to be reasonably appropriate for the actual loading condition.
Since L is a very small fraction of R, over the length L, the base plate may be approximated as a radial beam.
Thus, from the boundary conditions at point "0":
5-25
r l
p,L' a =
ML g
12E I 2E Z e ch e ey 6
f
=
(5.30) 24E I 6E I t ch e tb
\\
- PeL Mg
'~
2 L
i where 3
Iey =
2 12 (1-v )
Combining Equations (5.29) and (5.30), one obtains:
1 EZ 6
\\
g, K,L 5 e e3 M,
L2 f
(5.31)
Pe 24
\\ FJ 72E I e ch Pe 6,,
\\
Tg _
L,j1)
K,L Mgx zg,32y Pe 2
\\ FJ 12E Z p,L,.
e eg 5 = f l_j
- sE Nfx (5.33)
+
De
\\ FJ 12E,Iey p,,
M.
L2 (M,/p,)
(M /p,) 2 f
- =
+
(5.34)
Pe 8
2 2L where K,L F=
1+
2E I e g Using Equations 5.31 through 5.34, one can determine the uplift height (6), tank wall held-down tension (Tr) and moment (Me), and
-maximum positive moment (M.) in the base plate as a function of the uplift length, L,
and fluid pressure, p.
From this information the relationship between 6 and T, is obtained.
This solution based on small displacement theory is strictly 5-26
applicable under the following conditions:
f 1.
(L/R) s 0.15.
The solution ignores the stiffening of the base plate from hoop behavior and thus conservatively overpredicts the displacement 6 corresponding to a given Tr as the ratio (L/R) becomes larger.
s 0.6.
This solution being based upon small 2.
(6/ta) displacement theory conservatively ignores the beneficial ef fect that could be obtained by use of large displacement membrane theory together with membrane tensions in the base plate to reduce 6 corresponding to a given Tr.
For unanchored tanks, it has been shown (References 5.16 and i
5.19) that large displacement membrane theory greatly increases the fluid hold-down forces, T,.
- Thus, for unanchored tanks, ignoring large displacement membrane theory is likely to lead to excessive conservatism.
For anchored tanks, the uplif t heights (6) are not expected to be so great and only moderate conservatism is expected to result from ignoring large displacement membrane effects.
Unfortunately, no simple solution exists for considering such membrane effects and, therefore, currently one must either accept this source of conservatism for anchored tanks or make judgmental corrections to the computed fluid hold-down forces following guidance from References 5.16 1
and 5.19.
3.
(Mg/Mp3) s 0. 9; (M /M.) s 0. 9; and (M./Mp3) s 0.9 where M and p3 f
p M, are the plastic moment capacity of the base plate and p
tank wall, respectively.
The previous solution is an elastic solution and becomes nonconservative if these conditions are not met.
An alternate solution with plastic hinges at locationu where these conditions are not met is easily formulated following the same approach as was used herein but is judged to be unwarranted because violation of 5-27
these conditions is highly unlikely for 6 levels associated with anchored tanks.
Only violation of the third condition leads to a nonconservative estimate of the hold-down force T,
corresponding to a given uplift displacement 6.
The first two conditions can be violated.
so long as one is willing to accept the resulting conservative underestimation of the fluid hold-down force.
For anchored tanks, it is recommended that small displacement i
theory be used to compute the fluid hold-down forces.
It is further recommended that the following pressures be used to compute the fluid hold-down forces at locations 6 = 0 and C = 6, as defined in Figure 5.2:
P, = p, e - (pe + 0. 4Pev) SF at (8 = 0)
P,;t P,e - ( 0. 4psy) SF a t ( 6 = 6,)
The pressure defined at 6=0 represents the probable minimum pressure at this location at the time the maximum moment occurs.
The pressure defined above at 6 6
represents the probable 3
minimum pressure at 6 90* at the time the maximum moment
=
occurs, and is thus conservative for the location 6 = e since n
6 will always exceed 90 for partially anchored or unanchored n
tanks.
5.12.2 Unanchored Tanks The small displacement theory of the previous subsection is excessively conservative for unanchored tanks.
An upper bound theory is considered more appropriate and is used in the following analyses.
The uplift length, L,
illustrated in Figure 5.4, is assumed to be a very small fraction of R, and, therefore, over the length L,
the base plate may be approximated as a radial beam.
An 5-28 m
[)
i l
L l
upper bound solution results after a full plastic hinge develops l
at point "2"
(location of maximum positive bending moment Mp3) f and at point "1"
(base plate to wall junction and location of maximum negative moment M.).
Since no shear may cross point p
i "2",
the following relations hold:
(5.36) l
= [M,3 + M,] + F 6 y
3 l
r i
and Tf = p,L (5.37) where-F is the horizontal component of the membrane tension in 3
l the base plate at its junction with the cylindrical shell.
i Combining equations 5.36 and 5.37 one obtains:
+ F 6)]i/2 (5.38)
Tf = [2p, (N,3 + N 3
yy with 2
eb (5.39)
Y N,3 =
In Equation 5.38,. M,,
is the smallest of the plastic moment capacities of the following: (1) the base plate from Equation 5.39, (2) the tank wall with te, substituted for t in Equation t3 5.39, and (3) the welded connection between the base plC.e and wall.
For a material with a well defined yield point such as A36 carbon steel, a, should correspond to this yield stress.
y For a tank shell material with no specific yield point, a,
y should be set at the ASME Code (Reference 5.20) Service Level l'
(D) limit for bending which is 2.4S.
For example, for SA240-2 l
Type 304 stainless steel, S = 18.75 ksi and a, = 45.0 ksi.
y An upper bound on the horizontal component of the membrane S depends on temperature and should be. determined for the 2
expected temperature of the tank.
5-29 l
L
L l-
~ tension in the base plate, Fa, is governed by the maximum local hoop compression capacity of the tank wall.
For an axisymmetric application of F and M,at the base of the wall, the maximum 3
p hoop compression-in the tank wall occurs at the intersection of the' wall'and-base plate and is given by:
j
)
y, = 2 g y _ #pw *
(5.40)
.so long as Y
Fn2 R
1' Conservatively N,, should be limited to (cr,t,).
With this limit:
y e b* '" +
F3s P
(5.41) 2x R
1.
- Local plastic hoop yielding might allow some increase in F but it is recommended that no credit be taken for such an increase 3
For conservatism, 'it ; is recommended that the probable minimum pressure from Equation 5.35 be used for p.
Then Ten is computed from' Equation 5.'38 with 6 = 0, and T,is computed with 6 = 6.
f The AT, is computed from equation 5.24.
5.13' BASE SHEAR CAPACITY For'large diameter (greater than about. 3 0 feet) flat bottom tanks with fluid heights less than the diameter, i
it is common and' acceptable practice to rely.on friction between the tank
~
l l
bottom and its foundation to provide the base shear capacity.
Since' the base shear response, V, and the base overturning moment response, M r are 'primarily due to the fluid horizontal impulsive
' mode of ' response, they both are maximum at the same time.
- Thus, the' nominal' sliding shear capacity is:
5-30 l
V,= (COF). [W, + ([T ))
W G) c y3 where W, = We + p, ( xR )
. (5.43 )
2 ETu is tae ' sum of anchor bolt tensions from the overturning moment analysis, (COF) is the coefficient of friction between j
the tank base 'and ' its foundation, ' p, is - the probable average fluid pressure on the base given by (p.e - 0.4 Pe), and W is the e
tank wall and roof weight.
The equivalent code capacity Ve is obtained by applying a strength reduction factor (p) of 0.75 to the nominal shear capacity V,,,
i.e.,:
V, = 0. 7 5 V,,
(5.44)
Such a low factor (p) is used because of the uncertainty associated with the coefficient of friction.
For small diameter (less than about 10 feet) tanks, or tanks with fluid heights substantially greater than the tank diameter, it is unlikely that the friction-based shear capacity given by Equation 5.41 will exceed the base shear demand from the DBE.
In this case, the-shear capacity should be provided'by anchor bolts.
It is not acceptable to credit friction for a portion of the shear capacity and provide the remainder by anchor bolts.
Either 100% of the reported shear capacity is to be provided by friction, or 100% must be provided by anchor bolts or other means of positive anchorage.
Some large. diameter flat-bottom tanks such as the example tank (Appendix G, Figure G.1) have a slight cone to their bottom plate so that contained fluid will always drain away from the center toward the drain pipe at the edge.
This cone is generally. created by a variable thickness sand cushion between the tank bottom plate and its foundat on.
Furthermore, the tank
^
bottom is of ten made up of slightly overlapped fillet welded 5-31 i
l L
i individual plates.
Thus, the surface between the bottom plate and the sand cushion contains a series of rough steps.
Under these conditions, it is reasonably conservative to estimate (COF) = 0.7*
(5.42)
For flat-bottom steel tanks on concrete the COF is estimated as 0.55.
l 5.14 OTHER CAPACITY CHECKS For tanka on' soil sites, one should.also check the capacity of the tank foundation and this capacity sometimes governs.
Lastly, the possibility of piping failure or the failure of nozzles / penetrations where such piping is attached to the tank should be checked.
Such failure will likely lead to loss of j
tank contents. - In.-f act, a significant fraction of the cases of seismic induced loss of tank contents have been due to such j
failures when the piping contained poor seismic details.
The issues'to be checked are as follows:
l 1.
Are heavy valves or long piping runs being supported through the piping nozzles off either the tank walls or the bottom plate, or are they independently supported?
If heavy valves or long piping runs are being supported off the tank, then the ability of the nozzles and the tank wall or bottom plate to withstand the' imposed seismic-induced inertial forces should be checked.
Methods outlined in l
Welding Research Bulletin 107 (Ref erence 5..".1) may be used to compute. local stresses in the tank wall, and the strength acceptance criteria for vessels contained in Chapter 3 can be used for the stress capacity.
' Applicable for large diameter tanks with coned and uneven base.
5-32 l
l l
i
F 2.
Is there sufficient piping flexibility to accommodate relative seismic anchor movements (SAM) between the locations where the piping is supported from the tank wall and where it is independently supported?
Particularly for unanchored tanks, the piping nozzle and tank shell should be evaluated for their ability to withstand the expected relative SAM.
5.15 TOP SUPPORTED TANKS Many of the DOE underground waste storage tanks are laterally supported by the surrounding concrete vault near the top of the cylindrical tank wall.
As shown in Chapter 4, the presence of this top lateral support will greatly reduce the overturning moment applied at the base and will also reduce the base shear.
In this case, the base moment capacity (Section 5.10) and base shear capacity (Section 5.13) are not likely to control the seismic capability of such tanks, but should still be checked.
In addition, the lateral force (shear) capacity of the top anchorage must be checked in accordance with the capacity l
requirements of Section 3.7.
Furthermore, these lateral forces must be applied to the concrete vault when checking the seismic capacity of the vault.
Tanks with lateral support near the top of the cylindrical tank wall are likely to have substantially greater seismic capacity than a similar tank without this top support.
5-33
I REFERENCES 5.1 American Society of Civil Engineers, Standard 4-86,
" Seismic Analysis of Safety-Related Nuclear Structures and Commentary on Standard for Seismic Analysis of Safety-1 Related Nuclear Structures," September 1986.
5.2 American Society of Mechanical Engineers,
- ASME Boiler and Pressure Vessel Code,Section III, Rules for Construction of Nuclear Power Plant Components, Division 1, Subsection NC-3800," 1992.
5.3 ASME Boiler and Pressure Vessel Code, Nuclear Code Case N-284-1, " Metal Containment Shell Buckling Design Methods,"
l Section III, Division 1, Class MC," March 1995.
5.4 Vandepitte, D.,
'and Rathe, J.,
" Buckling of Circular Cylindrical Shells under Axial Load in the Elastic-Plastic Region," Der Stahlbau,-Heft 12, 1980.
5.5 National Aeronautico ana Space Administration, " Buckling of Thin-Walled Circular Cylinders, " NASA SP-8007, August 1966 5.6 Weingarten, V.,
- Moran, E.,
and Seida, P., " Final Report of Development of Design Criteria for Elastic Stability of Thin Shell Structures,"-
Space Technology Laboratories, Inc., STL TR-60-0000-19425, 1960.
5.7
- Rotter, J.M.,
" Buckling of Ground-Supported Cylindrical Steel Bins Under Vertical Compressive Wall Loads,"
Proceedings of The Metal Structures Conference, Institution of Engineers, Australia, Melbourne, pp. 112-127, 1985.
5.8
- Rotter, J.M.
and
- Teng, J.G.,
" Elastic Stability of Cylindrical Shells with Weld Depressions," Journal of
-Structural Engineering, Vol. 115, No.
5, ASCE, May 1989.
.5-34 m
- + + - -
5.9 Rotter, J.M., " Local. Inelastic Collapse of Pressurized Thin Cylindrical' Steel Shells 'Under Axial Compression, " Research
. Report, School of Civil and Mining Engineering, University of Sydney, Australia', 1985.
5.10 Priestly, M.J.N.,
et al.,
" Seismic Design of Storage Tanks," -Bulletin of the New Zealand National Society for Earthquake' Engineering, Vol. 19, No.
4, December 1986.
I 5.11 Priestly, M.J.N.,
" Seismic Design of Storage
- Tanks, Recommendations of. a Study Group of the New Zealand National Society for Earthquake Engineering,"
December 1986.
5.12 ASME Boiler and Pressure Vessel. Code, Nuclear Code Case N-
- 530,
" Provisions for Establishing Allowable Axial Compressive Membrane Stresses in cylindrical Walls of 0-15 Psi Storage Tanks, Classes 2 and 3,Section III, Division 1," December 1994.
5.13 Bandyopadhyay, K.,
Xu, J.,
Shteyngart S.,
and Eckert, H.,
" Plastic Buckling of Cylindrical Shells," PVP-Vol. 271, Natural Hazard Phenomena and Mitigation, ASME, 1994.
5.14 Bandyopadhyay, K.,
Xu, J.,
Shteyngart S.,
and Gupta, D.,
" Cylindrical Shell Buckling Through Strain Hardening," 1995 ASME/JSME' Pressure Vessel and Piping Conference, PVP-FSI-Vol. 6, Natural Hazards Phenomena and Mitigation, Honolulu, July 1995.
5.15 " Buckling of Steel Shells - European Recommendations,"
European Convention for Constructional Steelwork (ECCS),
4 Fourth Edition, No. 56, 1988.
-5.16? Manos, G.C., " Earthquake Tank-Wall Stability of Unanchored Tanks," Journal of Structural Engineering, Volume 112, No.
8,.ASCE,._pp. 1863-1880, August 1986.
5-35
5.17 Niwa, A.,
and Clough, R.W.,
" Buckling of Cylindrical Liquid-storage Tanks Under '.arthquake Loading, " Earthquake c
Engineering and Structural Dynamics, Volume 10, 1982.
5.18 Flugge, W., " Stresses in Shells," Springer-Verlag, 1960.
5.19 Haroun, M.A.,
and Badawi, H.S.,
" Nonlinear Axisymmetric Uplift of Circular Plates," Dynamics of Structures,
- ASCE, pp. 77-89, August 1987.
5.20 American Society of Mechanical Engineers, "ASME Boiler and Pressure Vessel Code,Section III, Rules for Construction j
of Nuclear Power Plant Components, Division 1, Subsection NC-3900," 1992.
5.21 Wichman, K.R.,
- Hooper, A.G.,
and Mershon, J.L.,
" Local l
Stresses in Spherical and Cylindrical Shells Due to External Loadings, " Welding Research Council Bulletin 107, 1
August 1965, Revised March 1979.
5-36
f J
d' NOTATION
- A bolt area 3
C,
- allowable compressive force per unit of circumfer-ential-length.
c, maximum ~ permissible axial compressive force per unit length C',
compressive force per unit length at the outer compression side of tank wall COF
-coefficient of friction between the tank base and the foundation E,
. bolt modulus of elasticity.
{
E modulus of elasticity of tank material e
{
F horizontal component of the membrane tension in the
{
h base plate at its junction with the cylindrical shell Fp permitted inelastic energy absorption factor from y
Table 3.3 FS factor of safety h
height of cylindrical tank wall above the liquid e
ha dome height above cylindrical wall h,
effective length of anchor bolt h,,
slosh height capacity h,,
slosh height response I
moment of inertia of base plate t3 L
. length of uplifted portion of base plate M.
maximum positive moment Mc moment capacity of tank Me moment in tank due to fluid hold-down M,,
fixed end moment b(,
plastic moment capacity of base plate 5-37 1
I L
F(,
plastic moment capacity of wall M
base overturning moment response y
N,,
maximum hoop compression p
liquid pressure P.
probable average fluid pressure on the base P,
probable combined hydrostatic and hydrodynamic co pressure at the point of maximum compression around the tank circumference corrresponding to the time of maximum induced moment hydrodynamic pressure due to horizontal component of pa seismic motion p3 hydrodynamic pressure due to vertical component of seismic motion p,
effective pressure defined by Equation E.35 p,
total internal pressure on tank wal]
at location of maximum longitudinal compressive stress p,e hydrostatic pressure pei total inelastic factored demand prassure P,
axial compressive force on tank wall R
radius of the tank SF appropriate seismic scale factor from Section 3.3.1 t
thickness of base plate t3 t.
thickness of tank wall e
T tensile force on anchored bolt "i" 31 T,
anchor bolt pretension 3
T tensile capacity of anchor bolt c3 T,
fluid hold-down tensile force (tension)
T,,
fluid hold-down tensile force at the outer tension side of the tank wall Ten fluid hold-down tensile force at the neutral axis 5-38
V, base sliding shear capacity using code coefficient v.,
. nominal base sliding shear capacity V,.
base shear response j
W.,
effective. weight for determination of base shear capacity-W tank' weight e
a, a, a3 buckling capacity reduction factor for cylindrical o p shell without internal
- pressure, with internal pressure,-and with bending moment, respectively 6,
uplift height at outer tension side of-tank wall 6,-
uplift height of tank wall at an angle 6 6
circumferential angle 6
circumferential angle between anchor bolts 3
e circumferential angle to neutral axis n
v Poisson's ratio of tank material t
a, allowable axial compressive stress o.o nominal ultimate axial stress a3 maximum compressive stress:due-to bending o,
_ hoop membrane stress capacity c
o,,
classical buckling stress 0.cr effective stress considering both the axial and hoop stresses o
tensile hoop stress n
o, uniform compressive stress due to axial load o
code minimum yield stress f
o, effective yield-stress y
4 strength reduction factor i
]
i 5-39 i
l i
i Table 5.1 Tank Parameters O.
C C
C C.
i 3
3 1.60 1.017 1.558 1.034 1.583 1.65 1.048 1.534 1.095 1.602 1.70 1.081 1.508 1.159 1.619 1.75 1.117 1.480 1.228 1.634 1.80 1.155 1.450 1.302 1.647 1.85 1.197 1.417 1.380 1.658 1.90 1.242 1.383 1.465 1.667 1.95 1.291 1.346 1.555 1.6~ 4 2.00 1.345 1.307 1.654 1.679 2.05 1.403 1.266 1.760 1.683 2.10 1.468 1.223 1.876 1.685 2.15 1.539 1.179 2.003 1.686 2.20 1.618 1.132 2.142 1.684 2.25 1.706 1.083 2.296 1.682 2.30 1.804 1.033 2.467 1.679 2.35 1.915 0.981 2.658 1.674 2.40 2.042 0.927 2.874 1.668 2.45 2.187 0.872 3.I19 1.661 2.50 2.354 0.815 3.400 1.654 2.55 2.551 0.757 3.727 1.646 2.60 2.783 0.698 4.112 1.638 2.65 3.064 0.637 4.573 1.630 2.70 3.408 0.576 5.134 1.621 2.75 3.840 0.513 5.834 1.612 2.80 4.400 0.449 6.735 1.604 2.85 5.151 0.385 7.939 1.596 2.90 6.215 0.320 9.633 1.589 2.95 7.834 0.254 12.20 1.583 3.00 10.60 0.188 16.57 1.578 3.05 16.38 0.122 25.68 1.574 3.10 36.07 0.055 56.63 1.571 5-40 h
.t i
D Biaxial Plastic Collapse ay
.a Clm C
m
.E_
at 4
9---------
)
=
E g---------cc c
m.
A Elastic Bifurcation w
1:2 ASME Code Buckling Case E
Hoop Stress cy i
i l
i Figure 5.1 Effect of Internal Pressure on Axial Compressive Strength of a Cylindrical Shell 5-41
i J,.
t I
l i.
i l
3 l
l' c;,.
(
N-A;
.'I l.
O., ?.
B l
~'
3 i
{
'.Ts,V A
T.e2-g_
q.
p i
1.,..
c.1 c l
R 0,
p.
/
l 1
l b
j l
1
~{
l p
i
.?
f COS 0 - COs e s g,
n t
1-cos On ;
l 1,.
.\\ b j
1 o
L
{
i C'
m i
s h
T" L.----,
i i
t.
AT, I
1 1
T 2T.
2h 1
M g3 g4 g
3 8
2 B1.
l l
i.
/
j M
l c
r i.
W 7
1
('
l L
Figure ' 5. :2 Vertical Loading'on Tank Wall at Base I
l.
l l
5 l I
i i
l r
i 4
a i
i V!ALL t tw 4
T,-
!l y
P.
Mt (1[![l1-11ll_
bd?
1 F
i ll H
S 1
BOTTOM L- [
0 t tb 4
L a=0 6=0
.M=0 Figure 5.3' Schematic Illustration of Anchored Tank Bottom Behavior at Tensile Region of Tank Wall 5-43
l wan y,
-* H-t tw j
+
f I
T 1 3"g
,e L
>F TANK BOTTOM 2
H O"
M Mw PW p
M pb S
.t tb M
2-
'I T'
i I
0t ob %
Fg;
. F V=0 AT POINT 2 L
3 Figure 5.4 Schematic Illustration of Unanchored Tank Bottom
' Behavior at Tencile Region of Tank Wall
.5-44 l -
- ~ ' UL.
~
'