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3 Ambient temperature storcge tank design
The section of shell lapPedbehind the angle incteasesthe available cross-sectionarea in length w
Figure 3.67a Typical roofioini
Hand.ai I stanc h ions, plaform supporling brackets
or stiffeneB of any kind musl not be welded acros
'AA- 1he horizonlal Plane of the i
bv the roof and shellmembers
x; the maximum oflplane allowance = 1.5 (tr + 0 / 2
: !ure 3.66 ldeal location fot the cenaoid ofthe compresslon zone area to API
:2-0. (For information onlv, not mandaiory to the BS 2654 and API 690 Codes)
3.8 Frangible roof joint, or weakroof-to-shell joint
3.8.1 lntroduction
'ixed roof tanks which store volatile products will have a mix-
:ufe of product vapour and air in the space between the surface
of the product and the tank roof. This mixture may be in the
'lammable range and, due to malfunction, externalfire or inter--al explosion. there may be a sudden increase in pressure
,vithin the tank which the normal vent devices and emergency
',ents are unable to cope with. Consequently tl^e tank rray be
damaged and this can result in failufe of either the shell-to-bo!iom joint or the roof-to-shell joint.
ln either case such failures are disastrous but the failure of the
shell-to-bottom joint can be particularly horrendous due to the
felease of the stored product over the surrounding area caus-
Lng the attendant ecological and environmental problems.
Of the two types of failure, the roof-to-shell failure is to be pre-
ferred. as this will normally create sufficient free-venting area to
allow the release of the tank over-pressurisation without any
oss of stored product. To increase the likelihood of a preferen-
tial roof-to-shell failu re, some fixed roof tanks can be provided
with a weak rooflo-shell connection, known as a "frangible roofjoint . A typical arrangement of this type of joint is showl in
Figure 3.67b.
3.8.2 Frangible roof joint theory
Assuming a empty cone roof tank, then, as the pressure in the
tank increases above atmospheric pressure, a point will be
feached when the upward force on the roof plating willequalthedownward load due to the weight of the roof plating As ihepressure increases further, the roof plating will tift oif its support
structure and this further increase in pressure is withstood by
lensile membrane forces 'T' in the roof plating (see Figure
3.68). These forces exert a pull at the shell-to-roofiunctlon and
so induce compressive forces in this area
A point will be reached when the upward force due to further in-
crease in pressure, willovercome the downward load duetotheweight of the shell and support structure, and at this pressure'
the floor plating at the tank periphery will start to lift ofi the tank
foundation, as illustrated earlier in Figure 3.52
The floor being allowed to lift off the foundation' can result in
high stresses being set up in the shellto-bottom jointwhich can
"^-"'-;\R@f plat6 not connectedto the roof supporling structur€
Figure 3.67b Typical frangible foof ioint
result in failure ofthe joini. This possibility must be prevented by
designing the roof-to-shelljoint to fail before the shell-to-bottomjoint does. This is accomplished by considering the point at
which the pressure in the tank is such that the floor is just aboutto li11 off its foundatLon.
3.8.3 The maximum compression zone area allow-able
For a roof connection to be considered frangible, the maxlmum
compression zone area allowable must be determined.
The roof plating is assumed to act as a membrane and any
bending effects are ignored, as are any changes in geomeiry,
also th; angle between the slope of the roof and the horizontal
0, is assumed to remain at its design value.
Considering Figure 3.68.
P = internal Pressure
T = membrane force in roof Plating
Wr = weight of roof plating
Figure 3 68 Tensile membrane fotces
Thecentrord ol lh€ composll€ sh€lland rool
area shaLlnol be oulsidelhrs snaded area
STORAGE TANKS & EQUIPMENT 89
3 Ambient tempercturc storcge tank design
Ws = weight of shell and roof support structurewhich is carried by the shell
R = tank radius
€ = angle of the roof slope to the horizontal
Wr and Ws shall have any corrosion deducted.
Note: The above condition assumes that the tank is empty,but the theory is equally valid if the tank contains liquid.When this is the case, then the load due to the weightofthe liquid, which is considered to be effective, (i.e. saywithin 750 mm of the shell), is added to that of the shelland framing.
' However, it is normal practice to design for the worstcondition, which in this case, is when the tank is empty,thus giving a lesser value for the allowable area for thecompression zone for the frangible condition.
Hencethe upliftforce on the roof plates is given byp r'R2 andthis force is resisted bythe weightofthe shelland support struc-ture Ws.
Then:
p.7r.R2 = Ws equ 3.74
It has already been determined in equation 3.68, that the re-quired compression area at the shell-to-roof junction is givenby:
n.R2A=---l--:-::2 Sc.tan 0
And transposing for p:
2.A Sc tan eO=-'R'Substituting for p in equation 3.74 then:
2 ASctan0 -, ..._xn.K_=vvsR
nence:
^ws2 r.Sc tan 0
equ 3.75
The size and quality ofthis weld is therefore an important factorof the frangible joint. However there does not appear to havebeen very much research done in this area, and this could bedue to difflculties in making meaningful analytical studies oftheinfluence and behaviour of such welds when subjected to thistype of failure mechanism.
The Codes do however require that the peripheral roof plateweld be kept as small as Dossible and in no case shall it belarger than 5 mm. From a practical point of view making theweld size any less than this, can be detrimental in the long term,because experience has shown that in time, this weld suffersfrom the effects ofcorrosion wastage which can eventuallyleadto vapour leaks at the joint.
3.8.5 Formula as expressed in BS 2654
A is expressed in mm2
Ws is given the notation 'T' and is the weight of theshell, shell stiffening and roof framework suFported by the shell but excluding the roofplates, expressed in kilograms.
Sc is expressed in N/mm2 and curb failure is as-sumed to occur at 220 N/mm2, so this flgure isbuilt into the equation.
0 is the slope of the roof at its point of connec-tion to the shell in degrees.
The formula then becomes:
Tx9.807 Tx7.07x10-s
equ 3.76
The area A thus found. is the maximum that can be allowed forihe shell-to-roof compression zone to be considered as a fran-gible joint.
3.8.4 Other factors affecting the frangible roof con-nection
3.8.4.1 Roof slope
ln Section 3.7.2.1 itwas demonstrated that as the roofslope be-comes shallower, the value of 6 decreases and hence the re-quired cross sectionalarea increases. Taken to the extreme, as0 tends to 0', then the required cross-sectional tends to infinity.
Therefore itcan be seen thata shallow slope favours the frangi-ble condition. Both the British and American codes recognisethis and put a limit on the maximum roof slope allowed for a roofto be considered frangible. These limits are given in Sections3.8.5.1 and 3.8.6.1.
3.8.4.2 Size of weld at the roof plate-to-shell connection
During the failure process of a frangible roof, the normal se-quence of events is for the roof to deform, and undergo elasticbuckling.
l\4any creases will appear at the periphery as a reduction in di-ameter occurs and the compression zone will buckle and col-lapse. This causes the peripheral roof plate weld to tear awayfrom its shell mounting and hence the excessive internal pres-sure is relieved.
90 STORAGE TANKS & EQUIPMENT
2 xT x2zo.lan e tan e
Which is as it is shown in Appendix F of BS 2654.
3.8.5.1 Additional requirements to BS 2654
equ3.77
In addition to the restriction in cross-sectional area for theroof-to-shell zone for the frangible condition, the Code requiresthat the following conditions shall also be met, as described inSections 3.8.4.1 and 3.8.4.2:
. The slope of the roof plating at its connection to the shellshall not be more than 1 in 5.
. The peripheral roof plating-to-shell connection weld shallnot be more than 5 mm.
3.8.6 Formula as expressed in API 650
A is expressed in mm2
Ws is given the notation W and is the weight of theshell, shell stiffening and roof framework sup-ported by the shell but excluding the roofplates, expressed in Newtons
Sc is expressed in N/mm'?and cufu failure is as-sumed to occur at 221 Nimm2, (32,000 lbiin')so this figure is built into the equation
0 is the slope of the roof at its point of connec-tion to the shell in degrees
The formula then becomes:
^WW^= 2r"x221 ^ane=
1390 xta" oequ 3.78
Which is as it is shown in clause 3.10.2.5.3 of API 650.
3.8.6.'l Additional requirements to API 650
ln additlon to the restriction in cross-sectional area for theroof-to-shell zone for the frangible condition, the Code requiresthat the following conditions shall also be met, as describedabove in Sections 3.8.4.1 and 3.8.4.2:
. The slope of the roof plating at its connection to the shell
shall not be more than 1 in 6.
. The peripheral roof plating-to-shell connection weld shall
not be more than 5 mm
3.8.7 Difference between Codes
The orincipal difference between the British and the American
Codes isthat BS 2654 allows the slightly steeper roof slope of 1
I in 5, against 1 in 6 to API 650.
The different constants used in equations 3.77 and 3'78 atedue to the tank weight being expressed in kilograms in BS 2654
and in Newtons in API 650.
The maximum allowable cross-sectional area in millimetres
calculated by either equation is found to be the same for a given
set of design parameters.
3.8.8 Conflict of design interests
During the initial tank design stage, the shell{o-roof joint will
have been designed to suit the internal service pressure re-
quirement, as detailed in Section 3 7. The most appropnate
method of providing the required cross-sectional area in the
roof-to-shelljointwill have been established and hence the tank
will be capable of withstanding the compressive forces which
will develop in this area during normal operation of the bnk'
However, it may be necessaryto ensure' that in the event of an
accidental over-pressurisation in the tank' it would be desirable
for the shell-to-roofjoint to fail This may not always be possible
because the compression area built into the tank to satisfy the
operating pressure may be more than that allowed for a frangi-
ble roofjoint, within the strictures of the Code
The likelihood of this conflict occurring and the possible means
by which it can be overcome, will become evident ffom the fol-
lowing Sections.
3.8.8.1 "Service" and "Emergency" design conditions
The maximum cross-sectional area at the compresslon zone
which is allowable by equations 377 and 3.78 for the tank
emergency condition, may be found to be less than that re-
quired to satisfy resistance ofthe internal pressure for the ser-
vice condition calculated by equations 3.68 or 3 71.
When this occurs the tank is deemed not to have a frangibleroofjoint, but this situation may be overcome by providing the
tankwith anchor bolts or straps attached to the lowershellareaofthe tank and secured to a peripheral concrete foundation ring
beam.
3.8.9 Examples of frangible and non-frangible roofjoints
Using the tank shell design illustration given in Section 3 3 2 9,
and issuming a roof slope of 1 in 5, and a roof plate to curb an-gle weld of 5 mm, then further calculations give the following
information:
3.8.9.1 Tank designed for an operating pressure of 7'5mDar
Case AlCase 41 allows for the curb angte to be lapped on to the top ofihe shell, as shown in Figure 3 67a. This arrangement ls gener-
ally adopted for two main reasons;
1) The available area of the compression zone which is re-quired for the tank operating pressure is increased, be-
cause the top of the shell plating behind the angle is alsoincluded in the zone. This is advantageous as it minimises
3 Ambient tempercturc storage tank destgn
the amount of additional area which may have to be pro-
vided by a curb angle.
2r Durinq the erection ofthe tank. lapping the angle directly
up ag;inst the top of the shell plating is a simpler erectionprocedure.
In Case A.1 , the area available from the roof and shell plating is'
on its own, more than enough to satisfy the amount requlred
from equation 3.67 and therefore only the minimum size of an-
gle from Figure 3.58 will be fitted to the tank, in this case a 80 x
80 x 10 angle. Thetotalarea provided in the compresslonzoneisfoundto be5028 mm2. This is more than the allowable area of
4811 mm2, and the roofjoint is therefore considered not to be
frangible.
Case A2
Case 42 allows for the vertical leg of the curb angle to be butt
welded directly on to the top ofthe shell plating as shown in Fig-
ure 3.67b This is a more difficult erection task than that for a
lapped curb angle but can be advantageous when a frangible
roof ioint is required, because the area of the shell-to-roof com-
presiion zone is reduced due to the lesser area of shell plating
being within the zone.
Aoain. it can be seen that the area provided by the shell and
roof is more than enough to satisfy the requirement of equation
3.64, and in this instance, the minimum size curb angle is butt
welded. rather than lap welded to the shell' thus reducing the
area availablefrom the shellbythedepth ofthe angle i.e B0x8
= 640 mm2.
This is enough to reduce the total available compression zone
area to a flgure which is less than the maximum allowed for a
frangible joint and therefore the roofjoint is frangible
CaseAl _ CaseA2
Pressle T5ombar 75dbar
compresson zo.e a@a requned ior ,,7jj nn2 1711mn,
Crrodna,e aoo"oo orlreo olrpt _cp-^ao60rosler Brr-*Flopo.oshel
wh a.d Wc area 35i8 mm? 2878 mm'?
Additonalarea rea! red -1807 '1167
L se ected curb a.gle size I 8ox80x10RsA 80x80xl0Rsa
Selected curb ang|e afea 1510 mm'? 1510 mmz
..rr.* I .,r. '*ls totalarea provLded suilicient?
13608s kg 136089 kg
lr,,laximum area a lowed iorirangible
ls lhe oofto nl ffang ble?
3.8.9.2 Tank designed for an operating pressure of20 mbar
Cases Bl and 82
At this higher pressure the required compresslon zone area
has significantly increased from 1711 mm2 to 7570 mm'?.
Following what was learned from case 42, the selected curb
angle size of 150 x 150 x 18 for Case 81, is butt-welded to the
tank shell as shown in Figure 3.67b However, it can be seen
that in doing this, the loss of shell area leaves a deficit of 152
mm, (7570-7418) in the area required for operation, and this is
not acceptable.
Case 82 is calculated in the same way as Case B1 except that
the larger angle size of 200 x 200 x 16 is used and the conse-quent increase in the cross-sectional area ofthe angle gives an
acceDtable totalarea forthe compression zone required forop-erational purposes.
STORAGE TANKS & EQUIPMENT 91
3 Ambient temperaturc storage tank design
For both Cases 81 and 82 however the area of the compres-
sion zone is far in excess ofthe maximum allowed for a frangi-ble roofjoint.
Compression zone area reqlired for
case B1
--l
CAeBz
_ 20.00 mbar
Curbangle lapPed or butted to shell?
2318 mm': 1918 mm2
5652Add tronalarea requ red 5252.32
!:r*t"djy9j!q:l!1Selected curb angre area
i50 x 150 x 18 RSA
s100 mm'
,oqr?oirI r$
Ls lotal area Pmvide suffclenl?
I19634lg 140426 kg
[,lax dum area alowed lorlrangblejoni
lslhe roof lointfrangble?
. o*ulLt!-
Case 83
From the previous Cases B1 and 82 it was found thai for this
oarticular tank size and its attendant design parameters there
was no advantage in butt-welding the curb angle to the shell
Case 83 therefore is based on lap welding the curb angle as
shown in Figure 3.67a. lt can be seen from the results that in do-
ing this the inclusion ofthe additionalarea oftheshell plate be-
hi;d the curb angle atlows a smaller angle size of 150 x 150 x 15
to be used, and the combination gives an adequate overall total
area in the comPresslon zone.
However, as before in the previous cases, this area is wellin ex-
cess of that allowable for a frangible roofjoint.
3.8,10 Tank anchorage - a means to frangibility
The tank in Case 83 meets the Code requirement for having
sufficient cross-sectional area in the roof-to-shell compression
zone for operating conditions But under an emergency over
pressure condition, this area is too great to ensure that the
;ooflo-shell joint is frangible and therefore may not fail under
this extreme condition. This could cause the shell-to-floor rim of
the fank to lift off the foundation and the resulting distortion in
this area could cause this joint to fail rather than the
roof-to-shell joint.
This occurrence can be prevented by anchoring the tank to a
suitably designed concrete ring beam which forms a part ofthe
92 STORAGE TANKS & EQUIPMENT
tank foundation. Three methods of anchorage are illustrated in
Figures 3.69 (a), (b) and (c).
3.8.10.1 Ensuring a frangible roof connection using an-cnorage
Apart from the frangibility consideration, anchorage may also
be required due to the following conditions;
. The operating pressure causing uplifr ofthe tank.
. The overturning effect on the tank of the prevailing wind
. Instability of the tank caused by seismic action.
These instances are discussed in Section 3.9 and Chapter 15
or26, butfornoW the means of designing anchorageto ensure
a frangible roofjoint will be considered as follows:
3.8.1 0.2 Determining anchorage requirements
Where a roofis deemed notto befrangible. then the pressure at
which it would fail has to be determined. This is done by trans-posing equation 3.69 or 3.71 depending upon which code is be-
ing used, and thus determining a failure pressure p
Takino the case for the British Code then from equation 3 69:
o=4 Jc t1n J*s.77
1r-
Failure is considered to occur at a compressive stress Sc of 220
N/mm'z.
Hence failure Pressure
o=44 A:tan o+0.77.tr
Remember that in the British Code p is in mbar.
Similarly, for the American Code, from equation 3.71.
o= 1.1 A tanoro.o8.th'D"
Forthe American Code, failure is considered to occur at a com-
pressive stress of 221 N/mm2.
The constant 1.1 in equation 3.71 is calculated using a allow-t t'!
- 1.1able stress of 137.5 N/mm' e.g. -
This has to be recalculated using thefailure compressive stress
of 221 N/mm/ and the new constant is '1! 'r,125
Failure pressure is therefore
p = 1.77.# t"n o * o.os. r'.
In the American Code p is in kilopascals - (1 kPa =10 mbar)
3.8.10.3 Worked examPle
Consider the tank depicted in Section 3 3.2.9.
This tank is 30 m diameter, has a roofslope of 1: 5, a roof plate
thickness of 5 mm and compression zone details as given in
Section 3.8.9.2 for Case 83.
Anchorage is io be provided using bolb
Using the BS Code for this example, then the failure pressure
will be:
4.44 x7818 x0.2 ^ -- .=U./a XO- 1s'
= 34.43 mbar
= 3.443 kNi m'?
This pressure acting on the roofofthe emptytankwillproduce a
uplift of:
equ 3.79
equ 3.80
Compress on zone area required ior ope€tion
Curb ang e lapped orbltted lo shelt
150 | 150 x 15 RsA
ls lotalarea Prov de sufiicieot?
[,lax m!m area a lowed for irang ble]oini
s lh€ rooiioinlfrang ble?
Figufe 3.69a Anchotage using bolts
Figure 3.69b Anchorage using siraps
3 Ambient temperaturc storcge tank desryn
UP=" R'P
=nx152 x3.443
= 2433.71 kN
The weight of the tank shell, stiffening and roof structufe given
in case 83 is 139041 kg which equates to 1363 55 kN
Then the net uplift = 2433.71 -1363.55 = 1070 16 kN
The BS Code requires anchors to be spaced around the tank
circumference at a minimum of 1 m and a maximum of 3 m
In this case a 3 m spacing will be used and hence the number ofbolts required is;
30xn ^,.^3
This is rounded up to 32.
However, as there are 12 plates per shell course, then 36 an-
chors will be selected, giving 3 per plate and thus clashes be-
tween anchor brackets and vertical shell course butt welds will
be avoided.
The load per bolt due to the over-pressurisation uplift will be
1070 16 :zg.t3 ttt36
The BS Code also requires anchors to have a minimum cross-sectional area of 500 mm2. This equates to a bolt core diameterof 25.33 mm and hence a overall bolt diameter of 30 mm will be
selected, which has an actuat core stress area of 561 mm'? (this
excludes any corrosion which may be required).
The stress in each bolt due to the over-pressurisation uplift willbe
29.73 x 1000
561
= 53.0 N/mm'?
The BS Code states that the allowable tensile stress in the an-chorage shall not exceed 50% of the specified yield strength, or33.33% of the minimum tensile strength of the anchorage ma-terial, whichever is the lowesi.
Taking medium strength steel having a minimum tensilestrength of 430 N/mm'? and yield of 255 N/mm2 for this diameterof bolt, then the allowable tensile stress would be 127.5 N/mm'?.
The selected bolt size is therefore acceptable.
3.8.10.4 Further design check
From above it can be seen that the tank can be subjected to apressure greater than its design pressure i.e. 34.58 mbar in-
stead of 20 mbar The original tank design must therefore be
checked to ensure that the allowable stress in the shell (equa-
tion 3.7) is not exceeded. This is accomplished by transposingS, the allowable stress and t in equation 3.7.
3.8.1 0.5 Other anchorage considerations
The anchorage design here is only catering for the uplift due toover-pressurisation and it must be borne in mind that this mayhave to be combined with any anchorage requirements whichmay be found to be necessary to stabilise an overturning mo-ment on the tank due to wind loading which is dealt with in
Section 3.9.
3.8.11 API 650 Code - anchor requirements
3.8.11.1 Minimum bolt diameter
The minimum anchor bolt diameter should not be less than 25mm, plus a corrosion allowance of at least 6 mm, giving a mini-mum diameter of 31 mm. This is similar to that given in the BS
'rllllttll{ | I ll
lrn caseswheElheanchorborbarc
5
):
I
FigLre 3.69c Combinalion usrrg slrap ard bolld'lchotage
STORAGE TANKS & EQUIPMENT 93