January 2011
Calculation of tanks and apparatus
made of thermoplastics
DVS – DEUTSCHER VERBAND
FÜR SCHWEISSEN UND
Vertical round, non-pressurised tanks
VERWANDTE VERFAHREN E.V.
R&D INTAKE MANIFOLDS
Technical Code
DVS 2205-2
Replaces January 2010 edition
Reprinting and copying, even in the form of excerpts, only with the consent of the publisher
Contents:
1
2
3
3.1
3.1.1
3.1.2
3.1.3
3.2
3.2.1
3.2.2
3.3
3.3.1
3.3.2
3.3.3
3.3.4
3.3.5
3.3.6
3.4
4
4.1
4.1.1
4.1.2
4.1.3
4.1.4
4.1.5
4.1.6
4.1.7
4.1.8
4.1.9
4.2
4.2.1
4.2.2
4.2.3
5
5.1
5.2
5.3
5.4
5.5
1
Scope of application
Calculation variables
Loading
Continuously effective loads
Total dead load
Load of the filling material
Internal and external pressures
Loads effective for a medium-long time
Snow load
Summer temperature
Loads effective for a short time
Internal and external pressures
Moving loads on the roof
Wind loads
Radially symmetrical equivalent loading caused by wind
pressure
Partial vacuum due to wind suction
Assembly loads
Temperature
Proof of the steadiness
Proof of the strength
Effects
Superimposition of the effects
Shell
Bottom
Welded joint between the bottom and the shell
Conical roof
Nozzles
Anchoring
Lifting lugs
Proof of the stability
Superimposition of the effects
Shell
Conical roof
Appendix
Explanations
Standards and technical codes
Literature
Temperature-dependent and time-dependent elastic moduli for stability and deformation calculations
Design-related details
Scope of application
The following design and calculation rules apply to vertical, cylindrical flat-bottom tanks which are fabricated from thermoplastics
in the factory, in particular:
–
–
–
–
polyvinyl chloride (PVC)
polypropylene (PP)
polyethylene (PE)
polyvinylidene fluoride (PVDF)
The cylindrical shell with an identical wall thickness throughout or
with a graduated wall thickness can be welded together from
panels or may consist of a wound pipe or an extruded pipe.
Consideration must be given not only to the hydrostatic loading but
also to pressures effective for short and long times. The following
minimum values are stipulated:
Overpressure: 0.0005 N/mm2 (0.005 bar)
Partial vacuum: 0.0003 N/mm2 (0.003 bar)
The pressures effective for a long time may only be applied if
they can also take effect.
Restriction on the main dimensions:
Tank diameter:
d4m
Ratio:
h/d  6
Minimum wall thicknesses: s = 4 mm
Attention must be paid to the responsibilities of certain legal fields
(e.g. building law, water law, occupational health and safety law
etc.).
2 Calculation variables
a
A1
mm
–
A2
–
A2I
–
AB
AD
Aj
AZ
bPr
bÖ
c
C
C1
C2
C*
m2
m2
m2
m2
mm
mm
–
–
–
–
–
d
dA
dL
dmax
dmin
dSch
mm
mm
mm
mm
mm
mm
ETC
K
N/mm2 Elastic modulus in the case of short-time
loading for T°C
N/mm2 Elastic modulus in the case of short-time
loading for 20°C
N/mm2 Elastic modulus in the case of long-time loading
for 20°C
–
Long-time welding factor
E K20C
E20C
L
fs
Weld thickness
Reduction factor for the influence of the specific
toughness (corresponds to A4 according to the
DVS 2205-1 technical code)
Reduction factor for the medium in the case of
the proof of the strength
Reduction factor for the medium in the case of
the proof of the stability and the deformation
Area of the bottom
Area of the roof
Area exposed to the wind (partial area)
Shell area of the cylinder
Width of the claw
Width of the lifting lug
Force coefficient according to DIN 1055-4
C1  C 2
Stress-increasing factor
Material-specific design factor
Coefficient for the circular cylinder subjected to
external pressure loads
Nominal inside diameter
Outside diameter of the nozzle
Hole diameter in the lifting lug
Maximum cylinder diameter
Minimum cylinder diameter
Diameter of the shackle
This publication has been drawn up by a group of experienced specialists working in an honorary capacity and its consideration as an important source of information
is recommended. The user should always check to what extent the contents are applicable to his particular case and whether the version on hand is still valid. No
liability can be accepted by the Deutscher Verband für Schweißen und verwandte Verfahren e.V., and those participating in the drawing up of the document.
DVS, Technical Committee, Working Group "Joining of Plastics"
Orders to: DVS Media GmbH, P. O. Box 10 19 65, 40010 Düsseldorf, Germany, Phone: + 49(0)211/1591- 0, Telefax: + 49(0)211/1591-150
216
Page 2 to DVS 2205-2
fsD
fz
fzD
g
gA
–
–
–
m/s2
N/mm2
Long-time welding factor for the roof
Short-time welding factor
Short-time welding factor for the roof
Acceleration due to gravity (9.81 m/s2)
Equivalent area load for the nozzles and similar
items on the roof
2
N/mm Area-related weight of the roof
N
Dead load of the bottom
N
Dead load of the roof
N
Total dead load
kN
Load of the filling material
N
Snow load
N
Dead load of the cylinder
mm
Height of the tank
mm
Filling height
mm
Filling height of the course i
mm
Residual filling height
mm
Height of the course i
mm
Cylindrical height
mm
Height of the lowest course
gD
GB
GD
GE
GF
GS
GZ
h
hF
hF,i
hRF
hZ,i
hZ
hZF
vorh
N/mm2 Stresses effective for a short time
KK,d
vorh
N/mm2 Dimensioning value of stresses effective for a
short time
N/mm2 Dimensioning value of stresses effective for a
long time
N/mm2 Dimensioning value of stresses with a medium
effective duration
N/mm2 Creep strength for 10-1 hours
vorh
vorh
K M,d
K*
K
K *K,d
pü
püK
pus
pw,d
p1
p,d
N/mm2 Dimensioning value of the creep strength for
10-1 hours
N/mm2 Dimensioning value of the creep strength for the
computational working life at the mean effective
temperature
2
N/mm Dimensioning value of the creep strength for the
medium effective duration (e.g. in the case of
snow for three months at 0°C)
mm
Length of the upper course of the equivalent
cylinder
Nm
Bending moment in the case of a wind load
N/mm Dimensioning value of the tensile force on the
diaphragm at the lower edge of the cylinder
N/mm2 Short-time dimensioning value of the effects on
the roof according to Table 5 or 6
N/mm2 Dimensioning value of the effects on the roof
according to Tables 5 and 6
N/mm2 Radially symmetrical equivalent loading caused
by wind pressure
N/mm2 Dimensioning value of the critical shell buckling
pressure
N/mm2 Auxiliary variable
N/mm2 Snow load on the roof
N/mm2 Overpressure at the tank bottom due to the
filling medium
N/mm2 Overpressure per lower edge of the graduation
due to the filling medium
N/mm2 Continuously effective external pressure
(or internal partial vacuum)
N/mm2 External pressure (or internal partial vacuum)
effective for a short time
N/mm2 Continuously effective internal pressure
2
N/mm Internal pressure effective for a short time
N/mm2 Partial vacuum due to wind suction
N/mm2 Auxiliary variable
N/mm2 Auxiliary variable
N/mm2 Auxiliary variable
qj
kN/m2 Impact pressure on the partial area Aj
K *L,d
K *M,d
lo
MW
nZ,d
 pvorh
D
K, d
vorh
pD
L,M,d
peu
pkM,d
pmax
pS
pstat
pstat,i
pu
puK
kN/m2
mm
N/mm2
mm
mm
mm
mm
N/mm2
mm
mm
mm
mm
sZm
sZ,1
sZ,i
so
mm
mm
mm
mm
TA
°C
TAK
TD
TDK
°C
°C
°C
T*D
°C
TM
°C
Maximum impact pressure effective at the tank
Radius of the cylinder
Dimensioning value of the stressability
Minimum wall thickness
Executed wall thickness of the basic component
Wall thickness of the bottom
Wall thickness of the roof
Dimensioning value of the stresses
Wall thickness of the lifting lug
Wall thickness of the cylinder
Wall thickness of the lowest course
Statically required wall thickness of the lowest
course
Mean wall thickness of the cylinder
Wall thickness of the highest course
Wall thickness of the course i
Wall thickness of the upper course of the
equivalent cylinder
Mean ambient temperature (according to Miner,
see DVS 2205-1)
Highest ambient temperature
Mean roof temperature
Highest roof temperature in the case of indoor
installation
Mean roof temperature for the summer load case
R&D INTAKE MANIFOLDS
KK
KL,d
qmax
r
Rd
s
sa
sB
sD
Sd
sÖ
sZ
sZF
s*ZF
TMK
TZ
TZK
u
V
vA
wgr
Wj
z

D


B
w
s

F
I
M
A,i
M


F
vorh
d
k,d
vorh
i,d
k,i,d
W
Mean media temperature (according to Miner,
see DVS 2205-1)
Highest media temperature
Mean temperature of the cylinder wall
Highest temperature of the cylinder wall
Permissible out-of-roundness
Filling volume
Weakening coefficient
Tolerable lifting path
Wind load
Number of anchors
Auxiliary variable
Pitch of the roof
Coefficient
Coefficient
Coefficient for the calculation of the bottom
Coefficient
Coefficient
Tolerable edge fibre expansion
Partial safety coefficient of the effect/stresses
Weighting coefficient depending on the loading
type
Partial safety coefficient of the resistance/
stressability
–
Utilisation of the axial stability in the course i
–
Utilisation of the shell pressure stability
°
Angle of the roof in relation to the perpendicular
3
Density of the material ( =   g)
g/cm
3
g/cm
Density of the filling medium
N/mm2 Dimensioning value of the crucial compressive
stress in the conical roof
N/mm2 Dimensioning value of the critical buckling
stress in the conical roof
N/mm2 Dimensioning value of the crucial axial
compressive stress in the course i
°C
°C
°C
%
m3
–
mm
kN
–
–
°
–
–
–
–
–
%
N/mm2 Dimensioning value of the critical axial buckling
stress in the course i
N/mm2 Compressive stress on the diaphragm resulting
from the wind load
217
Page 3 to DVS 2205-2
R&D INTAKE MANIFOLDS
S ZF = SZ
S ZF = SZ
Figure 1.
Open flat-bottom tank with a non-graduated wall thickness.
Figure 2.
Open flat-bottom tank with a graduated wall thickness.
Figure 3.
Flat-bottom tank with a conical roof and a non-graduated wall
thickness.
Figure 4.
Flat-bottom tank with a conical roof and a graduated wall thickness.
3 Loading
3.1.1 Total dead load GE
3.1 Continuously effective loads
Dead load of the roof GD:
Depending on the application, tanks are designed for a computational operating time of up to 25 years (2  105 hours). The computational filling height hF is determined by the existing operating
conditions.
GD= AD  sD    g
218
GE = G D + GZ + GB
N
(1)
N
(2)
N
(3)
Dead load of the cylinder GZ:
G Z = AZ  s Z    g
Page 4 to DVS 2205-2
3.3.2 Moving loads on the roof
Dead load of the bottom GB:
GB = AB  sB    g
N
(4)
Ladders, platforms, pedestals and similar items must be set up
and fastened independently of the tank since the free expansion
of the tank (e.g. during filling and emptying and in the case of
temperature changes) would otherwise be hindered. These hindrances cause considerable stress peaks which are difficult to record computationally and, if they are taken into account, lead to
uneconomic designs. If there is any deviation from this, corresponding proof must be provided.
It is not allowed to walk on the roofs without taking any loaddistributing measures. Corresponding precautions must be taken
during assembly and inspection work.
R&D INTAKE MANIFOLDS
The wind loads Wj must be estimated as follows:
Wj = cf ∙ q ∙ Aj
kN
(6)
where:
Wj wind load of the partial area Aj.
3.1.2 Load of the filling material GF
GF = V  F  g
3.3.3 Wind loads
kN
(5)
3.1.3 Internal and external pressures pü and pu
Higher pressures than indicated in the scope of application must
be taken into account at the level set by the operator.
If any safety fittings which cause higher pressures (such as overfilling protection devices or ventilation and venting facilities) are
connected, only these pressures must be taken into consideration. These pressures must not be effective when the tank has
been emptied completely since the bottom would otherwise be in
danger or the tank would be lifted.
3.2 Loads effective for a medium-long time
The effective time is three months.
3.2.1 Snow load GS
The snow load according to DIN 1055-5 must be estimated
cumulatively over the computational service life at a roof wall
temperature of 0°C. The computational snow load is calculated
from the shape coefficient  and the characteristic value of the
snow load sk according to the snow load zone map and the
height above sea level.
cf Force coefficient for the circular cylinder and the roof.
cf1 = 0.8 may be estimated according to DIN 1055-4, Section
10.2. Installation in a series has already been taken into consideration in this respect. Extensions cf2 = 1.6.
q Kinematic pressure according to DIN 1055-4, Table 2 depending on the wind zone and the height above the ground h
(h = hBehälter + hGebäude when the tank is located on a building, otherwise h = hG = hBehälter).
Aj Relevant exposed area in m² (for the tank: diameter times
total height hG including the roof)
The stress resulting from the wind moment MW may be calculated
using the following simplified method:
3
4  M W,x  10
 W,i = ---------------------------------2
  d  s Z,i
N/mm2
(7)
Mw,x at the height x above the tank bottom can be calculated on
a clamped equivalent bar.
2
 hG – x 
- + c f2  q 
M W, x = c f1  q  d  ---------------------2
  Aj  aj 
Nm
(8)
where aj is the lever arm of the area exposed to the wind Aj of the
superstructures and extensions in relation to the height x.
The following value may be estimated for conical and flat roofs:
 = 0.8.
3.3.4 Radially symmetrical equivalent loading caused by
wind pressure
3.2.2 Summer temperature
The compressive loading due to the inflow of the wind on to the
cylindrical shell is recorded by the equivalent load peu.
The roofs may be heated up considerably in summer. It is necessary to take account of a wall temperature of 50°C.
3.3 Loads effective for a short time
The effective duration of loads effective for a short time is stipulated as 10-1 hours.
Any water hammers which may arise during filling operations
must be prevented by taking suitable measures.
3.3.1 Internal and external pressures püK and puK
Pressure
As far as no higher pressures can occur as a result of the operating method, the minimum pressures indicated in Section 1 must
be taken into consideration. The definition of püK results in
püK  pü (see Fig. 5). The same applies analogously to puK.
peu =   qmax  10-3
N/mm²
(9)

r
r 
 = 0.46   1 + 0.1  C *  ------  ----------  0.6
h Z s Zm

(10)
where:
C* = 1.0 for the closed tank
C* = 0.6 for the open tank

 h Z,i  s Z,i 
s Zm = ---------------------------------hZ
(11)
3.3.5 Partial vacuum due to wind suction
In the case of ventilated tanks, an internal partial vacuum results
from a suction effect.
pus = 0.6  qmax  10-3
N/mm²
(12)
pus = 0.48  10-3 N/mm² is applicable in the case of ventilation
through a pipe leading to the outside.
3.3.6 Assembly loads
Time
Figure 5.
Definition of püK.
The tank must be designed for the loading conditions arising
during the transport and the assembly. In this respect, the calculation is made with 1.5 times the assembly loads (surge factor).
F1 is estimated as the partial safety coefficient. The short-time
welding factor according to DVS 2205-1 must be taken into con-
219
Page 5 to DVS 2205-2
sideration.
In this respect, the characteristic effects or the stresses are multiplied by the partial safety coefficients F according to Table 1.
3.4 Temperature
The effective wall temperature is decisive for the dimensioning of
the components. For parts wetted with the media, proof must be
provided at the mean media temperature TM in the case of longtime effects and at the highest media temperature T MK in the
case of short-time effects. The mean temperature is the temperature which, according to Miner, causes the same damage to the
material as the changing temperatures in real operation (e.g. according to Miner, a 10 % time proportion at 30°C and 90 % at
20°C result in TM = 26.3°C; TMK = 30°C). For non-wetted parts,
the mean of the two neighbouring air temperatures may be estimated as the wall temperature using a simplifying method. The
media temperature is assumed to be the air temperature in the
tank. As far as the ambient temperature is concerned, a differentiation is made according to the installation location and the effective duration. The following minimum values are applicable:
Table 1. Partial safety coefficients of the effects.
R&D INTAKE MANIFOLDS
Minimum values
For a short time
Indoor installation
TAK = 20°C
For a long time
TA = 20°C
Outdoor installation
TAK = 35°C
TA = 20°C
In the case of outdoor installation, the wall temperature of the
roof must be estimated at min. 50°C as a result of the solar radiation. A decreased ambient temperature TAK - 5°C applies to the
proof of the stability in the cylinder in the case of outdoor installation (wind effect).
Effect
Partial safety coefficient
Dead weight, filling and assembly
F1 = 1.35
Pressures, wind and snow
F2 = 1.5
Stress-reducing dead weight
F3 = 0.9
The dimensioning value of the existing stresses results from F
times the characteristic value of the stresses existing in the component.
vorh
vorh
K K,d =  F  K K
The dimensioning values of the existing stresses must be multiplied by the weighting coefficient I which takes account of the
loading cases in Table 2.
Table 2. Weighting coefficient.
Loading type
I
Loading Case I
1.0
Static loading at the room temperature and in constant
conditions. Cases of damage cannot lead to any danger to people, things or the environment.
Loading Case II
1.2
Loading in changing conditions (e.g. temperature and
filling height). Cases of damage may lead to danger to
people, things or the environment, e.g. installations or
installation parts which must be monitored and tested.
The characteristic resistances or the stressabilities are divided by
the partial safety coefficient M = 1.1.
For example, the dimensioning value of the short-time strength
K *K,d results from the characteristic short-time strength value K *K
divided by M according to the creep strength diagrams in
DVS 2205-1.
*
K=
K,d
Without
collecting device
With
collecting device
Without collecting device
With collecting device
TD = (TM+TA)/2
TD = (TM+TA)/2
TZ = (TM+TA)/2
TZ = (3 ∙ TM+TA)/4
Analogously, this is followed by TDK and TZK with TMK and TAK.
Figure 6.
Definition of the effective temperatures.
4 Proof of the steadiness
The proof of the steadiness is provided according to the concept
of the partial safety coefficients. In general, the following is applicable:
K *K
--------M
The dimensioning coefficients of the stressability must be divided
by the reduction coefficients A1 and A2 and, in the case of proof
in the weld, multiplied by the welding factor. In contrast, because
of the shorter representation, the dimensioning values of the
existing stresses are below multiplied by the reduction coefficients A1 and A2 and divided by the welding factor. This leads to
the same result.
4.1 Proof of the strength
4.1.1 Effects
Any loads caused by connected nozzles and pipelines are not
covered by this calculation and must be taken into consideration
separately by means of design-related measures (e.g. compensators).
It is always necessary to look for the most unfavourable combination of the overall effects for every component. Two cases must
be investigated for the effects of wind and snow:
1. The full snow load
2. 0.7 times the snow load + the full wind load
S
------d-  1
Rd
Load cases effective for a short time do not have to be combined
with each other.
with Sd dimensioning value of the stresses
Rd dimensioning value of the stressability
4.1.2 Superimposition of the effects
220
Page 6 to DVS 2205-2
Corresponding to the effective duration, a distinction must be
made between three loading categories:
– Loading effective for a short time (K)
e.g. puK, püK, pus, peu or wind
4.1.3.1 Proof in the circumferential direction
For every course i, it must be proven that the ring tensile stresses
due to the filling and the overpressures can be accommodated at
its lower edge. According to Section 4.1.2, it is necessary to provide double proof with:
R&D INTAKE MANIFOLDS
– Effects with a medium effective duration (M)
e.g. snow ps or summer temperatures
vorh
K L,d
– Loading effective for a long time (L)
e.g. dead weight, filling, pu or pü
If the filling is not constant with regard to the filling height and the
temperature during the computational working life of the tank,
representative equivalent loading can be determined for such
intermittent loading with Miner's rule. In contrast, the application
of Miner's rule is not very practicable for the superimposition of
the loading in the three loading categories.
Therefore, it is always necessary to provide double proof.
vorh
(13)
N/mm2
(14)
and
vorh
L,M,d = dimensioning value of the existing stresses
= dimensioning value of the creep strength for the computational working life at the mean effective temperature
K*M,d = dimensioning value of the creep strength for the medium effective duration (e.g. in the case of snow for
three months at 0°C for the roof)
2. It must be proven that, if the other effects are superimposed
on the stresses resulting from short-time loading, the stresses
do not exceed the residual strength of the material at the end
of the computational working life. In this respect, the creep
strength for 10-1 hours is estimated as the residual strength.
vorh
K K,d
-----------------------------  1
(15)
K*K,d
with

=

A1 at the effective wall temperature TM
and
K K,d
vorh
  F1  p stat,i +  F2  p üK   d A 1  A 2   I
= ------------------------------------------------------------------  -------------------------- N/mm2
2  s Z,i
fz
(17)
A1 at the effective wall temperature TMK
p stat,i =  F  g  h F,i  10
–6
N/mm2
(18)
where hF,i means the height of the liquid level above the lower
edge of the course i.
Stresses resulting from effects with a medium effective duration
do not arise in the case of this proof:
vorh
A1  A2  I
vorh
vorh
K L,M,d =  L,M,d  -------------------------fs
vorh
K K,d
(16)
(K M,d = 0) .
with
K*L,d
N/mm2
with
1. It must be proven that, if the effects with a medium effective
duration are superimposed on the stresses resulting from
loads effective for a long time but without any short-time loading, the stresses do not exceed the creep strength.
vorh
K M,d
K L,d
-1
------------------- + -------------------K*M,d
K*L,d
  F1  p stat,i +  F2  p ü   d A 1  A 2   I
= ---------------------------------------------------------------  -------------------------2  s Z,i
fs
vorh
 K, d
A1  A2  I
 -------------------------fz
N/mm2
The welding factor of the shell weld fs or fz is taken into account
in the case of cylinders manufactured from plates. According to
today's state of the art, preference should be given to heated tool
butt welding. fs = 1 and fz = 1 apply to wound tanks.
The residual stresses resulting from the bending of the panels at
the room temperature can be neglected if the edge fibre expansion  = s/d  100 [%] according to Table 3 is not exceeded.
Table 3. Tolerable edge fibre expansion.
Material
Edge fibre expansion 
PE-HD
1.00
PP-H
0.50
PP-B
0.75
PP-R
1.00
PVDF
0.50
PVC-U
0.20
PVC-C
0.10
Remark: The value for PE-HD may be used for PE 63, PE 80
and PE 100.
(15a)
and
*
= dimensioning value of the creep strength for 10-1
K K,d
hours at the temperature belonging to this loading
combination.
The more unfavourable of both the cases of proof is always
crucial for the dimensioning of the components.
Remark:
For the proof of the strength of the roof, it must be checked
whether the consideration of the snow load leads to a more
unfavourable result since, although the loading total is increased, the creep strength also becomes greater because of
the effective wall temperature of 0°C.
4.1.3.2 Proof in the longitudinal direction
The greatest tensile stresses must be validated. In this respect,
just 90 % of relieving, continuously effective compressive stresses may be taken into consideration.
Only the lowest course at the interface to the bottom must be
investigated for the proof of the stresses in the longitudinal direction. The stresses arising here are caused by the bending fault
moment and the stresses in the longitudinal direction resulting
from the dead weight, the pressures and the wind must be superimposed on them.
The double proof according to Section 4.1.2 must be provided with:
d
d
vorh
K L,d = C    F1  p stat +  F2  p ü   --- +  F2  p ü  --4
2
 F3   G D + G Z  A 1  A 2   I
– --------------------------------------  -------------------------s ZF
d
4.1.3 Shell
The height of the lowest course hZF must be min. 1.4  d  s ZF .
In the case of graduated tanks, neighbouring courses may have
a wall thickness ratio of max. 3 without any further proof. In the
case of sudden thickness changes with a wall thickness ratio
greater than 2, it is necessary to use the shell seam formation according to DVS 2205-3, Fig. 2.2 a), 2.2 c) or 2.2 c1).
N/mm2
(19)
A1 at the effective wall temperature TM.
with
vorh
K M,d=
p stat =  F  g  h F  10
–6
N/mm
(20)
0
221
Page 7 to DVS 2205-2
and
*
 = sB / S ZF
vorh
K K,d =
d
d
C    F1  p stat +  F2  p üK   --- +  F2  p üK  --4
2
3
Permissible range for C = 1.2
R&D INTAKE MANIFOLDS
 F2  4  M W  10  F3   G D + G Z  A 1  A 2   I
+ ------------------------------------------- – ---------------------------------------  -------------------------- N/mm2
2
s ZF
d
d
(21)
A1 at the effective wall temperature TMK.
The factor C for the welded interface of the bond between the
bottom and the shell is the product of the stress-increasing factor
C1 = 1.2 and a material-specific design factor C2 according to
Table 4.
Table 4. The material-specific design factor C2 and the factor C for
thermoplastics.
Material
PE-HD
PP-H (Type 1)
PP-B (Type 2)
PP-R (Type 3)
PVC-NI (normal impact strength)
PVC-RI (increased impact strength)
PVC-HI (high impact strength)
PVC-C
PVDF
C2
1.00
1.17
1.00
1.00
1.25
1.08
1.00
1.33
1.17
C = C 1  C2
1.20
1.40
1.20
1.20
1.50
1.30
1.20
1.60
1.40
Remark: The values for PE-HD may be used for PE 63, PE 80
and PE 100.
It is not necessary to provide any proof of the stresses in the weld
if the conditions according to Section 4.1.5 are fulfilled.
One prerequisite for the stress-increasing factor C1 = 1.2 is that
the bottom is not executed with a thickness greater than the wall
thickness of the lowest course (sB  sZF).
4.1.4 Bottom
4.1.4.1 Proof for the load case of the filling
If the bottom and the cylinder are joined with fillet welds (Fig. 11
in Section 5.5), the required thickness of the bottom may be determined as follows:
*
Figure 7.
Diagram for the determination of the thickness of the bottom,
derived for PE-HD (for C > 1.2, this diagram is on the safe side).
4.1.4.2 Proof for unanchored tanks with overpressure
If an unanchored tank (e.g. a tank in a collecting device) is loaded with overpressure, the bottom of the tank arches outwards.
This leads to the lifting of the whole tank and to bending stresses
in the bottom. A filling residue to be guaranteed with the filling
height hRF must be taken into consideration during the calculation of this lifting.
Pressures effective for short and long times are treated in the
same way since it may be postulated that the condition with a
long-time pressure and a residual filling height exists for a limited
time only. The effective pressure is therefore:
N/mm2
p1 = max (pü, püK)
(23)
Proof must be provided not only of the strength but also of the
limitation of the lifting path subjected to nominal loads to
wgr = 10 mm.
Proof of the strength
–6
p B,k – p 1 –   g  s B  10
h RF, = ----------------------------------------------------------------–6
 F  g  10
mm
p 1  d G D + G Z
1,5   ------------– --------------------- 4
d 
with p B,k = -----------------------------------------------------------lB
N/mm2
 B  s *ZF  s B  s ZF
2
K *K + K *M
sB
1
-  --------------------------  ---------------------------with l B = --------------------------   n Z,d   l
2
A1  A2  M
with
sZF
executed wall thickness
A1 at the effective wall temperature TMK.
B
according to Fig. 7 and
GD + GZ
p1  d
–  F3  ---------------------with n Z,d =  F2  ------------d
4
* 
s *ZF = max  s*ZF,L , s ZF,K
mm
(22)
mm
(24c)
mm
(25)
–6
p B – p 1 – 0.9    g  s B  10
h RF,w = -------------------------------------------------------------------------–6
0.9   F  g  10
1.5  nZ
------------------lB
N/mm2
(25a)
wgr  0.75  E K
with l B = s B  3 -------------------------------------------- w  A 2l  n Z
mm
(25b)
GD + GZ
p1  d
– 0.9  ---------------------with n Z = ------------4
d
N/mm
(25c)
ToC
(22b)
A1 and K *K,d at the effective wall temperature TM
In the case of other structural shapes, it is necessary to provide
proof of the bottom due to the cylinder clamping moment.
222
N/mm
and   = 1.5 for indoor installation
=
pB
with
d
d
and s *ZF,K= C    F1  p stat +  F2  p üK   --- +  F2  p üK  --4
2
mm
(24b)
Limitation of the lifting path
(22a)
A1 and K*L,d at the effective wall temperature TM
 F3   G D + G Z  A 1  A 2   I
– ---------------------------------------  -------------------------*
d
K K,d
(24a)
  = 2.12 for outdoor installation
d
d
with s *ZF,L= C    F1  p stat +  F2  p ü   --- +  F2  p ü  --4
2
 F3   G D + G Z  A 1  A 2   I
– ---------------------------------------  -------------------------*
d
K L,d
mm
(24)
and   = 0.56 for indoor installation
  = 1.12 for outdoor installation
Page 8 to DVS 2205-2
The crucial residual filling height results from:
h RF = max  h RF, , h RF,w 
Remarks:
mm
(26)
vorh
vorh
K L,d = pD L,d
e
s
 A     ln  -
 r  + B   

A1  A2  I
 -------------------------f sD
 A     ln  s
--- + B   

 r

R&D INTAKE MANIFOLDS
 K *K + K *M  /2 is used in the calculation for the proof of the
strength. A loading duration of approx. 12 hours is taken into
account in this respect.
ToC
ToC
0.75  E K
is used instead of E K
(see Section 5.4) in the
calculation for the proof of the limitation of the lifting path since a
higher stress level and thus a lower modulus must be taken into
consideration during this deformation calculation than in the case
of stability problems.
4.1.4.3 Proof for an internal partial vacuum
vorh
vorh
K M,d = pD M,d  e
A1  A2  I
 -------------------------f sD
N/mm2
(27)
N/mm2
(28)
N/mm2
(29)
and
vorh
K K,d =
vorh
e
pDK,d
 A     ln  s

---

 r  + B   
A1  A2  I
 -------------------------f zD
2
 – 0.000103   D + 0.007825   D – 1.7771
with A  =
2
B  =
 – 0.000433   D + 0.008115   D – 0.1870
The combinations in Table 5 must be investigated. A1 must be
determined on the basis of the temperatures in Table 5. An effecIt is not necessary to provide any proof of the bottom for an intertive mean wall temperature which is determined according to
nal partial vacuum if a residual filling remains in the tank. In this
Miner
respect, the residual filling height must be stipulated in such a
way that the total resulting from F3 times the dead load of the
T D + 50
oC
=
------------------TD*
(30)
bottom is greater than F3 times the F2 partial vacuum.
2
and takes account of a roof temperature of 50°C over three
4.1.5 Welded joint between the bottom and the shell
months (TD according to Fig. 6) is used for the summer load
case.
It is not necessary to provide any explicit proof of the stresses on
the weld if the following conditions are fulfilled:
–6
  g  s D  10
- + gA
N/mm2
g D = ------------------------------------(31)
– weld thickness a  0.7  sB
sin 
– long-time welding factor fs  0.6 (according to DVS 2203-4)
gA equivalent area load for nozzles and similar items
If one of these conditions is not fulfilled, it is necessary to provide
The welding factor is oriented to the quality of the longitudinal
detailed proof of the stresses in the weld (e.g. FE calculation).
weld of the conical roof.
In the case of one-shell tanks with capacities up to 1,000 l and
wall thicknesses up to 10 mm, this also applies to long-time welding factors fs  0.4.
4.1.6 Conical roof
The pitch of the roof must not be less than D = 15° ( = 75°).
4.1.6.2 Loads directed outwards
The double proof according to Section 4.1.2 must be provided
with:
vorh
vorh
K L,d = pDL,d  e

 --s-

 C     ln  r  + D   
 A1  A2  I
N/mm2
(32)
and
4.1.6.1 Loads directed inwards
pDK,d
vorh
 C     ln  s--- + D   


 r
The crucial combination of the dead weight gD, the partial vacuums pu and puK, the snow load ps and the partial vacuum resulting from the wind pus must be investigated. In this respect, pu,
puK and pus do not have to be combined with each other and, if
the wind is estimated, the snow load may be reduced to 70 %.
with C    = 0.000013   D – 0.00097   D – 1.4054
It is necessary to prove the stresses resulting from the ring tension at the edge of the roof.
A welding factor does not have to be taken into consideration
since the weld in the roof runs parallel to the stresses.
The double proof according to Section 4.1.2 must be provided
with:
It is necessary to investigate the combinations in Table 6.
vorh
K K,d =
e
 A1  A2  I
N/mm2 (33)
2
2
D    = 0.000265   D – 0.04574   D + 1.5622
A1 must be determined on the basis of the temperatures in Table 6.
Table 5. Combinations of load cases for the calculation of the roof for loads directed inwards..
Installation
location
Combination
Proof according to (13)
vorh
p DL,d
Temp.
Proof according to (15)
vorh
p DM,d
Temp.
 pD
–
max (F1 ∙ gD + F2 ∙ puK, F1 ∙ gD + F2 ∙ pus)
vorh
Temp.
K,d
Winter
F1 ∙ gD + F2 ∙ pu TD
F1 ∙ gD + F2 ∙ pu TD
0
Outdoors
F2 ∙ pS 0°C
max (F1 ∙ gD + F2 ∙ (ps + puK), F1 ∙ gD + F2 ∙ (0.7 ∙ pS +pus)) 0°C
Outdoors
*
Summer F1 ∙ gD + F2 ∙ pu T D
0
max (F1 ∙ gD + F2 ∙ puK, F1 ∙ gD + F2 ∙ pus)
Indoors
–
TDK
50°C
Table 6. Combinations of load cases for the calculation of the stength of the roof for loads directed outwards.
Installation
location
Indoors
Outdoors
Combination
Proof according to (13)
Proof according to (15)
vorh
pDM,d
Temp.
 pDvorh
Temp.
F2 ∙ pü – F3 ∙ gD TD
0
–
F2 ∙ püK – F3 ∙ gD
TDK
*
Summer F2 ∙ pü – F3 ∙ gD T D
0
–
F2 ∙ püK – F3 ∙ gD
50°C
vorh
pDL,d
Temp.
K,d
223
Page 9 to DVS 2205-2
4.1.7 Nozzles
The nozzles must generally be attached to the roof. If nozzles are
attached to the cylinder, the maximum diameter must be limited
to dA = 160 mm. The distance between the centres of the
nozzles and the edges, the course boundaries or the welds in the
basic component must be min. dA/2 + 100 mm. However, the distance between the centres of the nozzles and the bottom and a
neighbouring course with a lower wall thickness must be min. dA.
While paying attention to the lever arms, the required anchor
force (e.g. for the plugs) must be calculated from the maximum
claw force (maximum of the three numerators).
Fig. 9 in Section 5.5 shows the execution of an anchoring
element.
R&D INTAKE MANIFOLDS
It must be proven that it is possible to accommodate the stresses
on the basic component which are increased as a result of the
stress concentration close to the opening.
The stresses in the undisturbed basic component are increased
by dividing them by the weakening value vA.
The following applies to nozzles in the cylinder and in the conical
roof:
0.75
vA = ---------------------------------------------------dA
1 + ----------------------------------------2   d + sa   sa
with
dA
d
sa
(34)
outside diameter of the opening
cylinder diameter
executed wall thickness of the basic component
For the proof of the nozzles in the roof, it is necessary to provide
proof only for the largest nozzle situated near the edge of the
roof. In this respect, the dimensioning values for the existing
vorh
stresses K L,M,K,d may be determined for loads directed both inwards and outwards from the following equation:
vorh
K L,M,K,d
with p D
pD
d A1  A2  I
L,M,K,d
-  ------  ------------------------= --------------------vA
2  cos  s D
L,M,K,d
(35)
In the case of nozzles in the cylinder, it is necessary to provide
proof for ring tensile loads in analogy to Section 4.1.3.1, paying
attention to the height position of the nozzle. The structural
designing must be carried out according to Fig. 8, Section 5.5
(push-through nozzle). The wall thickness must correspond to
min. SDR11 (formerly pressure stage PN 10).
4.1.8 Anchoring
If anchoring becomes necessary, at least four anchors must be
arranged (z  4).
With regard to the proof of the anchoring, a distinction must be
made between three cases:
Case 1: Short-time overpressure at the media temperature T MK:
2
(36)
2
(37)
Case 3: Wind load at 20°C (only in the case of outdoor installation):
2
4   F2  M w
 F2  p ü    d
1
-----------------------------  10 3 + ------------------------------------ –  F3   G D + G Z   --d
z
4
--------------------------------------------------------------------------------------------------------------------------------------------------  1 (38)
K *K,d
 b Pr + s B   s B  ----------------------2  A1  I
The numerator indicates the claw force to be accommodated and
the denominator the claw force which can be accommodated and
results from the shearing stress in the weld. In this respect, half
the creep strength is estimated as the shearing stress.
224
In order to be able to dispense with any proof of the load introduction into the highest course, it must be ensured that the lifting
lug is not thicker than three times the wall thickness of the
highest course. The hole diameter (dL) must be adapted to the
diameter of the shackle (dSch).
The following equations are applicable:
sZ,1  erf sÖ  3  sZ,1
(39)
dSch  dL  1.1  dsch
(40)
It must be proven that 1.5 times the loading (surge factor) can be
borne for a short time at 20°C. I = 1.2 must be set in this respect
since the transport of the tank constitutes a danger to people
irrespective of the subsequent utilisation.
The required wall thickness (sÖ) of the lifting lug results from the
proof for the face of the hole:
GE
1.5   F1  -------  A 1   I
2
s Ö = ----------------------------------------------------d Sch  2  K *K,d
mm
(41)
bÖ = max (bÖ,1, bÖ,2)
Proof of the shearing stress for the transverse weld during the
lifting of the lying tank:
GE A1  I
1.5   F1  -------  --------------fz
4
b Ö,1 = ----------------------------------------------------K *K,d
0.7  s Z,1  ------------2
Eye bar:
mm
(42)
GE
1.5   F1  -------  A 1   I
7
2
b Ö,2 = ----------------------------------------------------- + ---  d L mm
3
s Ö  K *K,d
(43)
4.2 Proof of the stability
Case 2: Long-time overpressure at the media temperature T M:
 F2  p ü    d
1
------------------------------------ –  F3   G D + G Z   --z
4
------------------------------------------------------------------------------------------------  1
K *L,d
 b Pr + s B   s B  ----------------------2  A1  I
One of the possible lifting lug shapes is shown on Fig. 10 (Section 5.5). The prerequisites for the use of these lifting lugs are
that only two lifting lugs are used per tank and that one parallel
hanger is utilised.
The maximum of both the following cases of proof is crucial for
the width of the lifting lug (bÖ).
effects according to Section 4.1.6.1 or 4.1.6.2.
 F2  p üK    d
1
---------------------------------------- –  F3   G D + G Z   --z
4
---------------------------------------------------------------------------------------------------  1
K *K,d
 b Pr + s B   s B  ----------------------2  A1  I
4.1.9 Lifting lugs
4.2.1 Superimposition of the effects
The crucial elastic moduli are needed for the stability calculations.
The buckling of shells is a sudden occurrence which is essentially
dependent on the imperfections, i.e. on the size of the previous
bulges. The size of the previous bulges increases along with the
loading duration because of the creep behaviour of the material.
In contrast, the elastic resistance during the beating-out is predominantly determined by the short-time elastic modulus at the temperature at that moment. The critical buckling stress k is therefore
o
calculated with the temperature-dependent moduli E TK C .
For the essential thermoplastics, the temperature-dependent and
time-dependent elastic moduli are included in Tables 8 and 9
(Section 5.4).
It is necessary to investigate the most unfavourable combination
of loads taking account of the temperature behaviour of the thermoplastics.
4.2.2 Shell
Sufficient safety against axial and shell pressure stabilities as
well as against the interaction of both must be proven for the
shell of the tank. It is not necessary to prove the stability next to
the nozzles because of the limitation of the nozzle diameters.
Page 10 to DVS 2205-2
The prerequisite is that the out-of-roundness of the cylinder
remains limited in the following form:
2   d max – d min 
u = ------------------------------------------  100  0.5
d max + d min
%
(44)
In the case of outdoor installation:
 

w
- ,
= max  F1   G +  F2  max   pu  pus  + 0.7   s + ------i,d
 vorh
1.2 

N/mm2
-----   F1   G +  F2    puK +  s 
(45)
(51)
The critical shell pressure of the graduated cylinder may be
calculated on a three-course equivalent cylinder according to
DIN 18800-4:
ToC
EK
r s o 2.5
p kM,d = 0.67    C *  ----------------  ----   -----
M
lo  r 
=  F1   G +  F2  max   puK  pus 
(46)
The stress resulting from the wind moment W may be divided by
1.2 because the buckling stress should be increased by 20 % in
the event of global bending.
Using a simplifying method, the buckling stress may be determined according to the following formula:
ToC
s Z,i
EK
*
-  KK,d
-  ------ k,i,d =  i  0.62  f ,i  --------------M
r
N/mm2
0.70
with  i = -----------------------------------------------------------------20 o C
EK
r
-----------------  1 + ----------------------
20 o C 
100  s Z,i
EL
(47)
(48a)
The interaction between the axial and shell pressure stabilities
must be proven for every course:
1.25
1
(53)
The longitudinal stresses caused by a partial vacuum do not
have to be taken into consideration during the calculation of A,i
for the interaction since their effect is already included in M.
4.2.3 Conical roof
The most unfavourable combination of the compressive stresses
in the circumferential direction in the centre of the shell line of the
conical roof (d/4):
 d
vorh
 vorh
pd
d
= ------------------------  -----4  cos s D
N/mm2
ToC
(48b)
(54)
is validated with the critical stresses:
s 1.5
EK
-  sin   cos    -----D-
 k,d = 2.68  -------------- d
M
ei
1.5 – --------  1.0
s Z,i
(52)
4.2.2.3 Interaction
1.25
N/mm2
N/mm2
The ß values are indicated on Figs. 20a to 20c in DIN 18800-4.
 A,i +  M
In the case of indoor installation:
and=
f ,i
N/mm2
with C * = 1.0 for tanks with solid roofs
with C * = 0.6 for the open tanks
For every course i, the axial compressive stress which exists at
the lower edge and consists of the dead weight, the partial
vacuums pu, puK and pus as well as the snow and wind loads is
determined in the most unfavourable combination in each case
and is validated with the buckling stress k,i,d.

ToC
EK
s Z 2.5
r
p kM,d = 0.67  C *  ----------------  ------   -----
M
hZ  r 
R&D INTAKE MANIFOLDS
4.2.2.1 Axial stability
vorh
i,d
lated from:
N/mm2
with

vorh
where ei is the eccentricity in relation to the thicker of the two
neighbouring courses in the case of a graduated cylinder if this is
itself thicker than the course i under consideration.
d
A 2l   l 
 = ---------------------------------------------  1
 k,d
It is necessary to comply with the following condition for every
course i:
It is necessary to investigate the combinations in Table 7.

5
vorh
A 2l   I 
i,d
 A,i = ------------------------------------------------  1
 k,i,d
(49)
4.2.2.2 Shell pressure stability
The crucial partial vacuum resulting from the most unfavourable
combination of the partial vacuums pu, puK, pus and peu is validated with the critical shell pressure pkM,d.
The following condition must be fulflled:

vorh
A 2l   l 
pd
 M = --------------------------------------------  1
p kM,d
(50)
The critical shell pressure of the non-graduated cylinder is calcu-
(55)
(56)
Appendix
5.1 Explanations
This technical code was elaborated by DVS-AG W4.3b ("Structural designing / apparatus engineering") together with the committee of experts "Plastic tanks and pipes" (project group "Calculation").
During the revision, a distinction was made as to whether the
tanks had to be dimensioned exclusively with regard to the loads
resulting from the internal pressure due to the filling material and
the filling height (this corresponds to the viewpoint of the 1974
edition) or whether any additional loading cases (e.g. wind or
snow loads) had to be taken into consideration during the dimensioning. The latter approach was chosen for the new edition of
this technical code.
Table 7. Load combinations for the stability calculation of the roof.
Installation
Combination
 pd
Temp.
max   F1  g D +  F2  p uK  F1  g D +  F2  p us 
TDK
Outdoors
Winter
max   F1  g D +  F2   p S + p uK   F1  g D +  F2   0.7  p S + p us  
0°C
Outdoors
Summer
max   F1  g D +  F2  p uK  F1  g D +  F2  p us 
50°C
Indoors
vorh
225
Page 11 to DVS 2205-2
The application relating to the "installation and operation of tanks
within buildings" is dealt with in Supplement 1.
pr EN ISO 15014
Extruded panels made of polyvinylidene fluoride (PVDF); requirements and test procedures
Supplement 2 includes the dimensioning for collecting devices
(collecting tanks).
5.2.4 Pipes and fittings
Supplement 3 includes the dimensioning for flat roofs.
DIN 8061
Pipes made of unplasticised polyvinyl chloride –
General quality requirements
DIN 8062
Pipes made of unplasticised polyvinyl chloride
(PVC-U and PVC-HI); dimensions
DIN 8074
Pipes made of polyethylene (PE) – PE 63, PE 80,
PE 100 and PE-HD – Dimensions
DIN 8075
Pipes made of polyethylene (PE) – PE 63, PE 80,
PE 100 and PE-HD – General quality requirements and tests
DIN 8077
Pipes made of polypropylene (PP) – PP-H 100,
PP-B 80 and PP-R 80 – Dimensions
DIN 8078
Pipes made of polypropylene (PP) – PP-H (Type
1), PP-B (Type 2) and PP-R (Type 3) – General
quality requirements and testing
DIN 8079
Pipes made of chlorinated polyvinyl chloride
(PVC-C) – PVC-C 250 – Dimensions
DIN 8080
Pipes made of chlorinated polyvinyl chloride
(PVC-C) – General quality requirements and testing
DIN 4740-1
Ventilation and air conditioning installations; pipes
made of unplasticised polyvinyl chloride (PVC-U)
– Calculation of the minimum wall thicknesses
R&D INTAKE MANIFOLDS
5.2 Standards and technical codes
5.2.1 Fundamentals of calculation
DIN 1055-3
Effects on load-bearing structures – Dead and
useful loads for high-rise structures
DIN 1055-4
Effects on load-bearing structures – Wind loads
DIN 1055-5
Effects on load-bearing structures – Snow and ice
loads
DIN 4119-1
Above-ground cylindrical flat-bottom tank structures made of metallic materials; fundamentals,
execution and tests
DIN 4119-2
Above-ground cylindrical flat-bottom tank structures made of metallic materials; calculation
DIN 18800-4
Steel structures; stability cases; shell bulges
DIN EN 1778 Characteristic parameters for welded thermoplastic structures; determination of the permissible
stresses and moduli for the calculation of thermoplastic components
5.2.2 Moulding materials
DIN EN ISO
1872-1
Polyethylene (PE) moulding materials
Part 1: Designation system and basis for specifications
DIN EN ISO
1872-2
Polyethylene (PE) moulding materials
Part 2: Manufacture of test specimens and determination of properties
DIN EN ISO
1873-1
Polypropylene (PP) moulding materials
Part 1: Designation system and basis for specifications
DIN EN ISO
1873-2
Polypropylene (PP) moulding materials
Part 2: Manufacture of test specimens and determination of properties
Unplasticised polyvinyl chloride (PVC-U) moulding
materials
Part 1: Designation system and basis for specifications
DIN EN ISO
1163-1
DIN EN ISO
1163-2
Unplasticised polyvinyl chloride (PVC-U) moulding
materials
Part 2: Manufacture of test specimens and determination of properties
DIN EN ISO
12086-1
Fluoropolymer dispersions, moulding materials and
extrusion materials
Part 1: Designation system and basis for specifications
DIN 16 961-1 Pipes and fittings made of thermoplastics with
profiled walls and smooth inside pipe surfaces –
Part 1: Dimensions
DIN 16 961-2 Pipes and fittings made of thermoplastics with
profiled walls and smooth inside pipe surfaces –
Part 2: Technical terms of delivery
DIN EN ISO
15494
Plastic piping systems for industrial applications –
Polybutene (PB), polyethylene (PE) and polypropylene (PP) – Part 1: Requirements on piping
parts and piping systems – Metric series
DIN EN ISO
15493
Plastic piping systems for industrial applications –
Acrylonitrile butadiene styrene (ABS), unplasticised polyvinyl chloride (PVC-U) and PVC-C –
Requirements on piping parts and piping systems
5.2.5 DVS technical bulletins and technical codes
DVS 2205
Calculation of tanks and apparatus made of thermoplastics;
Part 1 -; characteristic values
Part 3 -; welded joints
Part 4 -; flanged joints; as well as supplement
DVS 2201
Testing of semi-finished products made of thermoplastics
Part 1: Fundamentals – Remarks
Part 2: Weldability and test procedures – Requirements
DVS 2206
Testing of components and structures made of
thermoplastics
DIBt
Media list for tanks, collecting devices and pipes
made of plastic
5.2.3 Panels and welding filler materials
DIN EN 12943
Welding filler materials for thermoplastics;
scope of application, identification, requirements and testing
DIN EN ISO
14632
Extruded panels made of polyethylene
(PE-HD); requirements and test procedures
E-DIN EN ISO
15527
Pressed panels made of polyethylene
(PE-UHMW, PE-HMW and PE-HD); requirements and test procedures
DIN EN ISO
15013
Extruded panels made of polypropylene (PP);
requirements and test procedures
DIN 16927
Panels made of unplasticised polyvinyl chloride; technical terms of delivery
E-DIN EN ISO
11833-1
Plastics, panels made of unplasticised polyvinyl
chloride; delivery forms, dimensions and properties; Part 1: Panels with thicknesses > 1 mm
226
5.3 Literature
[1] Timoshenko, S.: Theory of plates and shells. McGraw Hill
Book Comp, New York / London 1959.
[2] Kempe, B.: Deformation measurements on a tank made of
high-density polyethylene in the case of a temperature
change. Schw. Schn. 42 (1990), No. 4, p. 173.
[3] Tuercke, H.: On the stability of tanks made of thermoplastics, DIBt Communications, No. 5/1995.
Page 12 to DVS 2205-2
5.4 Temperature-dependent and time-dependent elastic
moduli for stability and deformation calculations
5.5 Design-related details
T oC
Table 8. Temperature-dependent short-time elastic moduli E K
N/mm2.
in
The following design examples are indicated in this section:
– nozzle in the cylinder shell, Fig. 8
– anchoring of the bottom, Fig. 9
– lifting lug, Fig. 10
– connection between the shell and the bottom, Fig. 11
– connection between the shell and the roof, Fig. 12
– edge of open tanks, Fig. 13
R&D INTAKE MANIFOLDS
Material  10°C 20°C 30°C 40°C 50°C
60°C 70°C 80°C
PE-HD
1,100
800
550
390
270
190
–
–
PP-H
1,400 1,200
960
770
620
500
400
320
PP-B
1,200 1,000
790
630
500
400
320
250
PP-R
1,000
620
490
380
300
230
180
3,200 3,000 2,710 2,450 2,210 2,000
–
–
 10°C 20°C 40°C 60°C 80°C 100°C
–
–
–
–
PVC-NI
PVDF
800
1,900 1,700 1,330 1,050
820
650
20 oC
Table 9. Time-dependent long-time elastic moduli E L
in N/mm2.
Material 1 year 5 years 10 years 15 years 20 years 25 years
PE-HD
308
269
254
245
239
235
PP-H
464
393
365
350
340
330
PP-B
405
334
307
293
283
275
PP-R
322
298
288
283
279
276
PVC-NI 1,800
1,695
1,652
1,627
1,609
1,600
763
744
733
725
720
PVDF
810
Remark: The elastic moduli for PE-HD may also be used for
PE 63, PE 80 and PE 100. The long-time elastic moduli
for PE apply to stresses   0.5 N/mm² and those for
PP to   1 N/mm². The stress dependence of the elastic moduli for PVC-NI and PVDF can be neglected.
Figure 8.
Nozzle in the cylinder shell.
Without a gap and without pressing
Anchor bolt
Claw: steel
PE sheet 2 mm
Spacer plates
Minimum number
of claws: 4
Figure 9.
Anchoring of the bottom.
227
Page 13 to DVS 2205-2
Use a cross-beam for the lifting
of the tank
R&D INTAKE MANIFOLDS
Bei
von
bÖ aauch
eckiger
If
bÖEinhaltung
is complied
with,
square
Anschluss möglich
connection
is also possible.
Figure 10.
Lifting lug.
ü  without anchoring
ü  with anchoring
Figure 11. Connection between the shell and the bottom.
Figure 13. Edge of open tanks.
228
Extruder weld
Figure 12. Connection between the shell and the roof.
File:
Erstellt am:
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07.10.2008
08.10.2008
December 2008
DVS – DEUTSCHER VERBAND
FÜR SCHWEISSEN UND
VERWANDTE VERFAHREN E.V.
Calculation of tanks and apparatus made
of thermoplastics
Welded stationary tanks in the case
of installation in buildings
Technical Code
DVS 2205-2
R&D INTAKE MANIFOLDS
Supplement 1
Translation of the German edition from November 2003
Reprinting and copying, even in the form of excerpts, only with the consent of the publisher
Contents:
1
2
3
3.1
3.1.1
3.1.2
3.1.3
3.2
3.2.1
3.2.2
3.2.3
3.2.4
3.3
4
4.1
4.1.1
4.1.2
4.1.3
4.1.4
4.2
4.2.1
4.2.2
5
5.1
5.2
5.3
5.4
5.5
1
Restriction on the main dimensions:
Scope of application
Calculation variables
Loading
Continuously effective loads
Total dead load
Load of the filling material
Internal and external pressures
Loads effective for a short time
Internal and external pressures
Partial vacuum due to wind suction
Moving loads on the roof
Assembly loads
Temperature
Proof of the steadiness
Proof of the strength
Shell
Bottom
Nozzles
Lifting lugs
Proof of the stability
Shell
Conical roof
Appendix
Explanations
Standards and technical codes
Literature
Computational elastic moduli for stability calculations
Design-related details
Scope of application
The following design and calculation rules apply to vertical, cylindrical flat-bottom tanks which are fabricated from thermoplastics
in the factory, in particular:
– polyethylene (PE)
– polypropylene (PP)
– polyvinyl chloride (PVC)
– polyvinylidene fluoride (PVDF)
This part of the technical code is only applicable to the installation
of the tanks in buildings.
The cylindrical shell with an identical wall thickness throughout or
with a graduated wall thickness can be welded together from
panels or may consist of a wound pipe or an extruded pipe.
Consideration must be given not only to the hydrostatic loading
but also to pressures effective for short and long times. The
following minimum values are stipulated:
Overpressure:
Partial vacuum:
0.0005 N/mm² (0.005 bar)
0.0003 N/mm² (0.003 bar)
The pressures effective for a long time may only be applied if
they can also take effect.
Tank diameter:
d≤4m
Ratio:
h/d ≤ 6
Minimum wall thicknesses: s = 4 mm
Attention must be paid to the responsibilities of certain legal fields
(e. g. building law, water law, occupational health and safety law
etc.).
2 Calculation variables
a
AB
AD
AZ
A1
mm
m²
m²
m²
–
A2
–
A2l
–
bÖ
C
C1
C2
d
dA
dL
dmax
dmin
dSch
mm
–
–
–
mm
mm
mm
mm
mm
mm
N/mm²
E
fs
fsD
fz
g
GB
GD
GE
GF
GZ
h
hF
hF,i
hZ
–
–
–
m/s²
N
N
N
kN
N
mm
mm
mm
mm
Weld thickness
Area of the bottom
Area of the roof
Shell area of the cylinder
Reduction factor for the influence of the specific
toughness (corresponds to A4 according to the
DVS 2205-1 technical code)
Reduction factor for the medium in the case of
the proof of the strength
Reduction factor for the medium in the case of
the proof of the stability
Width of the lifting lug
C1 ⋅ C2
Stress-increasing factor
Material-specific design factor
Nominal inside diameter
Outside diameter of the nozzle
Hole diameter in the lifting lug
Maximum cylinder diameter
Minimum cylinder diameter
Diameter of the shackle
Elastic modulus in the case of short-time loading for T°C
Long-time welding factor
Long-time welding factor for the roof
Short-time welding factor
Acceleration due to gravity (9.81 m/s²)
Dead load of the bottom
Dead load of the roof
Total dead load
Load of the filling material
Dead load of the cylinder
Height of the tank
Filling height
Filling height of the course i
Cylindrical height
This publication has been drawn up by a group of experienced specialists working in an honorary capacity and its consideration as an important source of information
is recommended. The user should always check to what extent the contents are applicable to his particular case and whether the version on hand is still valid. No
liability can be accepted by the Deutscher Verband für Schweißen und verwandte Verfahren e.V., and those participating in the drawing up of the document.
DVS, Technical Committee, Working Group "Joining of Plastics"
Orders to: DVS Media GmbH, P. O. Box 10 19 65, 40010 Düsseldorf, Germany, Phone: + 49(0)211/1591- 0, Telefax: + 49(0)211/1591-150
229
Page 2 to DVS 2205-2 Supplement 1
hZ,i
hZF
K
mm
mm
N/mm²
Height of the course i
Height of the lower course
Creep strength for 10-1 hours
K
N/mm²
lo
mm
lm
mm
lu
mm
pstat
N/mm²
pstat,i
N/mm²
pu
N/mm²
puK
N/mm²
pus
pü
püK
sa
sB
sD
sM
N/mm²
N/mm²
N/mm²
mm
mm
mm
mm
sÖ
sZ
sZF
sZFC
mm
mm
mm
mm
sZFR
–
sZ,1
sZ,i
TA
TD
TM
TW
TZ
u
V
vA
αD
βF
βS
δB
δF
δS
ε
γF
γI
–
mm
–
–
mm
–
°C
%
m³
–
°
–
–
–
mm
mm
%
Creep strength for the computational working
life at the mean effective temperature
Length of the upper course of the equivalent
cylinder
Length of the central course of the equivalent
cylinder
Length of the lower course of the equivalent
cylinder
Overpressure at the tank bottom due to the filling medium
Overpressure per lower edge of the graduation
due to the filling medium
Continuously effective external pressure (or internal partial vacuum)
External pressure (or internal partial vacuum)
effective for a short time
Partial vacuum due to wind suction
Continuously effective internal pressure
Internal pressure effective for a short time
Executed wall thickness of the basic component
Wall thickness of the bottom
Wall thickness of the roof
Wall thickness of a one-course cylinder
resulting from the partial vacuum stability
Wall thickness of the lifting lug
Wall thickness of the cylinder
Wall thickness of the lowest course
Statically required wall thickness resulting from
the longitudinal stress
Statically required wall thickness resulting from
the ring tension
Wall thickness of the highest course
Wall thickness of the course i
Outdoor air temperature
Temperature of the roof
Media temperature
Wall temperature of the collecting device
Temperature of the tank wall
Permissible out-of-roundness
Filling volume
Weakening coefficient
Pitch of the roof
Coefficient for the calculation of the roof
Coefficient for the calculation of the roof
Coefficient for calculation of the bottom
Coefficient for the calculation of the roof
Coefficient for the calculation of the roof
Tolerable edge fibre expansion
Partial safety coefficient of the effect/stresses
Weighting factor depending on the loading type
(see DVS 2205-2)
Partial safety coefficient of the resistance/
stressability
Angle of the roof in relation to the perpendicular
Coefficient for the shell pressure stability
Density of the material (γ = ρ ⋅ g)
Density of the filling medium
γM
κ
λ
ρ
ρF
230
°
–
g/cm³
g/cm³
R&D INTAKE MANIFOLDS
Figure 1.
Open flat-bottom tank with a non-graduated wall thickness.
Figure 2.
Open flat-bottom tank with a graduated wall thickness.
Figure 3.
Flat-bottom tank with a conical roof and a non-graduated wall
thickness.
Page 3 to DVS 2205-2 Supplement 1
3.2.1 Internal and external pressures püK and puK
As far as no higher pressures can occur as a result of the
operating method, the minimum pressures indicated in Section 1
must be taken into consideration. The definition of püK results in
püK ≥ pü (see Figure 5). The same applies analogously to puK.
The following conditions must be complied with for the pressures
effective for a short time:
R&D INTAKE MANIFOLDS
K*
≤ ---------- ⋅ p
K*
K*
≤ ---------- ⋅ p
K*
and p
Pressure
p
Time
Figure 4.
Flat-bottom tank with a conical roof and a graduated wall thickness.
Figure 5.
Definition of p
.
3.2.2 Partial vacuum due to wind suction
3
Loading
In the case of ventilated tanks, an internal partial vacuum results
from a suction effect (on this subject, see the DVS 2205-2
technical code, Section 3.3.5).
3.1 Continuously effective loads
Depending on the application, tanks are designed for a computational operating time of up to 25 years (2 ⋅ 105 hours). The computational filling height hF is determined by the existing operating
conditions.
3.1.1 Total dead load GE
GE = G D + G Z + G B
N
(1)
N
(2)
N
(3)
N
(4)
Dead load of the cylinder GZ:
GZ = AZ ⋅ sZ ⋅ ρ ⋅ g
Dead load of the bottom GB:
GB = A B ⋅ s B ⋅ ρ ⋅ g
3.2.3 Moving loads on the roof
It is not allowed to walk on the roofs without taking any loaddistributing measures. Corresponding precautions must be taken
during assembly and inspection work.
3.2.4 Assembly loads
Dead load of the roof GD:
GD = A D ⋅ s D ⋅ ρ ⋅ g
pus = 0.48 ⋅ 10-3 N/mm² is applicable if the ventilation is carried
out through a pipe leading to the outside.
Ladders, platforms, pedestals and similar items must be set up
and fastened independently of the tank since the free expansion
of the tank (e. g. during filling and emptying and in the case of
temperature changes) would otherwise be hindered. These
hindrances cause considerable stress peaks which are difficult to
record computationally and, if they are taken into account, lead to
uneconomic designs. If there is any deviation from this, corresponding proof must be provided.
The tank must be designed for the loading conditions arising
during the transport and the assembly. In this respect, the
calculation is made with 1.5 times the assembly loads (surge
factor). γF1 is estimated as the partial safety coefficient. The
short-time welding factor according to DVS 2205-1 must be taken
into consideration.
3.3 Temperature
The effective wall temperature is decisive for the dimensioning of
the components. Wetted parts must always be designed for the
media temperature TM. For non-wetted parts, the mean of the two
neighbouring air temperatures may be estimated as the wall temperature using a simplifying method. The media temperature is
assumed to be the air temperature in the tank and TA = 20°C the
mean outdoor air temperature over a long time in the case of indoor installation. The wall temperatures are indicated on Figure 6.
3.1.2 Load of the filling material GF
GF = V ⋅ ρ F ⋅ g
kN
(5)
3.1.3 Internal and external pressures pü and pu
Higher pressures than indicated in the scope of application must
be taken into account at the level set by the operator.
If any safety fittings which cause higher pressures (such as overfilling protection devices or ventilation and venting facilities) are
connected, these pressures must be taken into consideration.
These pressures must not be effective when the tank has been
emptied since the bottom would otherwise be in danger or the
tank would be lifted.
3.2 Loads effective for a short time
The effective duration of loads effective for a short time is stipulated as 10-1 hours (e. g. assembly loads).
Any water hammers which may arise during filling operations
must be prevented by taking suitable measures.
Without
collecting device
Figure 6.
With
collecting device
Definition of the effective temperatures.
231
Page 4 to DVS 2205-2 Supplement 1
Outdoor air temperature: TA = 20°C in the case of indoor installation
Without collecting device
Material
Edge fibre expansion ε
PE-HD
1.00
TD = (TM + TA)/2
PP-H
0.50
TZ = (3 ⋅ TM +TA)/4
PP-B
0.75
PP-R
1.00
PVDF
0.50
PVC-U
0.20
PVC-C
0.10
With collecting device
R&D INTAKE MANIFOLDS
TD = (TM + TA)/2
TZ = (TM + TA)/2
4
Table 1. Tolerable edge fibre expansion.
Proof of the steadiness
The proof of the steadiness is provided according to the concept
of the partial safety coefficients. In this respect, the characteristic
effects or the stresses are multiplied by the partial safety
coefficients γF according to the following table:
Effect
Partial safety coefficient
Dead weight, filling and assembly
γF1 = 1.35
Pressures
γF2 = 1.5
Remark: The value for PE-HD may be used for PE 63, PE 80
and PE 100.
The factor C for the welded interface of the bond between the
bottom and the shell is the product of the stress-increasing factor
C1 = 1.2 and a material-specific design factor C2 according to
Table 2.
Moreover, the effects are multiplied by the reduction factors A1
and A2 as well as by the weighting coefficent γI.
The characteristic resistances or the stressabilities are divided by
the partial safety coefficient γM = 1.1.
Table 2. The material-specific design factor C and the factor C for
thermoplastics.
Material
C2
C = C1 ⋅ C2
4.1 Proof of the strength
PE-HD
1.00
1.20
4.1.1 Shell
PP-H (Type 1)
1.17
1.40
The height of the lowest course hZF must be min. 1.4 ⋅ d ⋅ s
PP-B (Type 2)
1.00
1.20
In the case of graduated tanks, neighbouring courses may have
a wall thickness ratio of max. 3 without any further proof. In the
case of sudden thickness changes with a wall thickness ratio
greater than 2, it is necessary to use the shell seam formation
according to DVS 2205-3, Figure 2.2 a, 2.2 c or 2.2 c1.
PP-R (Type 3)
1.00
1.20
PVC-NI (normal impact strength)
1.25
1.50
PVC-RI (increased impact strength)
1.08
1.30
PVC-HI (high impact strength)
1.00
1.20
Lowest course
PVC-C
1.33
1.60
The maximum of both the following cases of proof is crucial for
the wall thickness sZF of the lowest course.
PVDF
1.17
1.40
s
s
s
= max ( s
Remark: The value for PE-HD may be used for PE 63, PE 80
and PE 100.
)
,s
(γ ⋅ p
+γ ⋅p )⋅d A ⋅A ⋅γ
= -------------------------------------------------------------- ⋅ -------------------------f
K*
2 ⋅ --------γ
C ⋅ (γ ⋅ p
+γ ⋅p )⋅d
= ----------------------------------------------------------------------- ⋅ A ⋅ A ⋅ γ
K*
2 ⋅ --------γ
mm
(6)
mm
(7)
In the case of one-shell tanks with capacities up to 1,000 l and
wall thicknesses up to 10 mm, this also applies to long-time
welding factors fs ≥ 0.4.
One prerequisite for the stress-increasing factor C1 = 1.2 is that
the bottom is not executed with a thickness greater than the wall
thickness of the lowest course (sB ≤ sZF).
with
p
It is not necessary to provide any proof of the stresses in the weld
if a fillet weld is executed with a weld thickness a ≥ 0.7 ⋅ sB and a
long-time welding factor fs ≥ 0.6.
= ρ ⋅ g ⋅ h ⋅ 10
N/mm2
(8)
4.1.2 Bottom
where hF means the filling height.
Intermediate courses
The wall thickness sZ,i for every course i results from the ring
tensile stresses due to the filling and the overpressures at its
lower edge.
s
p
(γ ⋅ p
+γ ⋅p )⋅d A ⋅A ⋅γ
= ----------------------------------------------------------------- ⋅ -------------------------- mm
f
K*
2 ⋅ --------γ
= ρ ⋅g⋅h
⋅ 10
N/mm2
(9)
(10)
The welding factor of the shell weld fs is taken into account in (6)
and (9) in the case of cylinders manufactured from plates.
According to today's state of the art, preference should be given
to heated tool butt welding. fs = 1 applies to wound tanks.
The residual stresses resulting from the bending of the panels at
the room temperature can be neglected if the edge fibre
expansion (Table 1) ε = s/d ⋅ 100 [%] is not exceeded.
232
Figure 7.
Diagram for the determination of the thickness of the bottom,
derived for PE-HD (for C > 1.2, this diagram is on the safe
side).
Page 5 to DVS 2205-2 Supplement 1
If the bottom and the cylinder are joined with fillet welds (Figure
11), the required thickness of the bottom may be determined as
follows:
δ ⋅s
It must be proven that 1.5 times the loading (surge factor) can be
borne for a short time at 20°C. γI = 1.2 must be set in this respect.
The required wall thickness (sÖ) of the lifting lug results from the
proof for the face of the hole:
R&D INTAKE MANIFOLDS
≤s ≤s
with sZF as the executed wall thickness and δB according to
Figure 7 (see Page 4).
In the case of other structural shapes, it is necessary to provide
proof of the bottom due to the cylinder clamping moment.
s
G –G
1.5 ⋅ γ ⋅ --------------------2
= ----------------------------------------------- ⋅ A ⋅ γ
K*
d
⋅  2 ⋅ ----------

γ 
mm
(13)
For the proof of the bottom of unanchored tanks with overpressure and for the proof of any anchoring which may be required,
see Sections 4.1.4.2 and 4.1.8 in the DVS 2205-2 technical code.
The maximum of both the following cases of proof is crucial for
the width of the lifting lug (bÖ).
4.1.3 Nozzles
bÖ = max (bÖ,1, bÖ,2)
The nozzles must generally be attached to the roof.
Proof of the shearing stress for the transverse weld during the
lifting of the lying tank:
4.1.3.1 Nozzles in the roof
It is not necessary to provide any proof of the stresses on the roof
due to the weakening caused by the nozzle cut-out if the edges
of the nozzles are min. 100 mm away from the edge of the roof
and are not arranged in the region of the longitudinal weld of the
roof.
b
G –G
1.5 ⋅ γ ⋅ --------------------- A ⋅ γ
4
= ----------------------------------------------- ⋅ --------------K*
f
0.7 ⋅ s ⋅ -------------2⋅γ
mm
(14)
Eye bar:
4.1.3.2 Nozzles in the shell
If nozzles are attached to the cylinder, the maximum outside
diameter of the nozzle is limited to dA = 160 mm. The distance
between the centres of the nozzles and the edges, the course
boundaries or the welds in the basic component must be min.
dA/2 + 100 mm. However, the distance between the centres of
the nozzles and the bottom and a neighbouring course with a
lower wall thickness must be min. dA.
It must be proven that it is possible to accommodate the stresses
on the basic component which are increased as a result of the
stress concentration close to the opening.
The stresses in the undisturbed basic component are increased
by dividing them by the weakening coefficient vA:
v
0.75
= ---------------------------------------------------d
1 + -----------------------------------------2 ⋅ (d + s ) ⋅ s
bzw.
s
s = -------v
G –G
1.5 ⋅ γ ⋅ --------------------2
7
= ----------------------------------------------- ⋅ A ⋅ γ + --- ⋅ d
K*
3
s ⋅ ---------γ
mm
(15)
4.2 Proof of the stability
4.2.1 Shell
The required wall thicknesses resulting from the shell pressure
stability caused by the partial vacuum pu are determined with the
aid of a three-course equivalent cylinder (Figure 8). The
dimensions of the equivalent cylinder are compiled in Table 3.
The coefficient results from:
(11)
s
λ = ------------2⋅s
with dA outside diameter of the opening
d cylinder diameter
sa executed wall thickness of the basic component
s
s = -----------v
b
mm
(16)
with
(12)
As far as the above distance between the centre of the nozzle
and the longitudinal weld is complied with in the case of plate
tanks, the wall thickness sZFR or sZ,i can be reduced with the
welding factor fs in Equation 12.



h ⋅γ ⋅γ ⋅p 
s = 0,77 ⋅  A ⋅ --------------------------------------


E


---------------- ⋅ d 

γ
⋅d
mm
The temperature-dependent and time-dependent E
are indicated in Table 5 (Section 5.4).
(17)
moduli
The structural designing must be carried out according to Figure
9, Section 5.5 (pushed-through nozzle). The wall thickness of the
nozzle must correspond to min. SDR 11 (formerly PN 10).
4.1.4 Lifting lugs
One of the possible lifting lug shapes is shown on Figure 10
(Section 5.5). The prerequisites for the use of these lifting lugs
are that only two lifting lugs are used per tank and that one
parallel hanger is utilised.
In order to be able to dispense with any proof of the load
introduction into the highest course, it must be ensured that the
lifting lug is not thicker than three times the wall thickness of the
highest course. The hole diameter (dL) must be adapted to the
diameter of the shackle (dSch).
The following equations are applicable:
s
≤ erf s ≤ 3 ⋅ s
d
≤ d ≤ 1.1 ⋅ d
Figure 8.
Equivalent cylinder according to DIN 18800-4.
233
Page 6 to DVS 2205-2 Supplement 1
Table 3. Dimensions of the equivalent cylinder depending on λ.
Dimensions of
the equivalent
cylinder
PE 100
Formulae for the calculation
1/3 < λ < 1/2
λ ≤ 1/3
lo
λ · hZ
λ ≥ 1/2
30
40
25
30
204
185
0.8
0.9
337
316
0.5
0.6
50
35
171
1.1
297
0.7
60
40
156
1.2
279
0.7
δS
βF
δF
R&D INTAKE MANIFOLDS
λ · hZ
–
so
sM · (1 + 5 · λ)/4 2 · λ · sM
sM
lm
lo
(hZ – lo)/2
–
sm
sM
sM
sM
lu
hZ – 2 · l o
lm
–
su
2 · sm – so
2 · sm – so
sM
Table 5. Continuation.
Material
PP-H
The graduations should have approximately identical lengths
(≥ 500 mm) with thickness changes ≥ 1 mm.
The graduation should be refined in such a way that the condition
Σs ⋅ h ≥ s ⋅ l and with sm ⋅ lm or su ⋅ lu is complied with. A
uniform graduation should be striven for in this respect.
PP-B
Mean
Effective
βS
media
wall
temperature temperature
[°C]
[°C]
30
25
256
0.5
[mm]
296
0.7
[mm]
40
50
30
35
242
230
0.6
0.6
321
299
0.6
0.6
60
40
218
0.7
278
0.7
30
40
25
30
234
221
0.6
0.7
303
281
0.6
0.7
The prerequisite is that the out-of-roundness of the cylinder
remains limited in the following form:
50
35
209
0.8
260
0.8
–d )
2 ⋅ (d
u = ------------------------------------------ ⋅ 100 ≤ 0.5
d
+d
60
30
40
25
198
209
0.8
0.8
239
332
0.9
0.5
%
(18)
PP-R
4.2.2 Conical roof
40
30
196
0.9
310
0.6
The pitch of the conical roof must not be less than αD = 15°
(κ = 75°).
50
60
35
40
186
175
0.9
1.0
289
269
0.7
0.8
The proof of the stability resulting from the dead weight and the
partial vacuum is always crucial for the dimensioning of the roof
with partial vacuums up to 0.003 bar. In the case of tanks which
do not have any free ventilation and are subjected to partial
vacuums pu > 0.003 bar effective for a long time, the proof of
the strength may determine the dimensioning. The following
approximation applies to 1,000 mm ≤ d ≤ 4,000 mm and αD = 15°:
s
A p ⟨ bar⟩
d
=  ----- – δ  ⋅  -------- ⋅ ----------------------
β
  1.4 0.003 
mm
PCV-NI
PVDF
For pu > 0.003 bar, it must be checked whether the roof thickness determines the dimensioning because of the proof of the
strength according to Equation 19b:
A p ⟨ bar⟩
d
=  ------ – δ  ⋅  -------- ⋅ ----------------------
β
  1.4 0.003 
25
381
0.4
446
0.4
30
372
0.4
413
0.5
50
60
35
40
363
354
0.4
0.4
384
353
0.5
0.6
30
25
274
0.7
480
0.4
40
50
30
35
266
257
0.8
0.8
469
447
0.5
0.5
(19a)
with βs and δS according to Table 4.
s
30
40
5
mm
60
40
249
0.8
423
0.5
70
80
45
50
242
235
0.9
0.9
417
412
0.5
0.6
Appendix
(19b)
5.1 Explanations
with βF and δF according to Table 4. A long-time welding factor
fsD ≥ 0.6 is a prerequisite.
d = 1,000 mm must be used in the calculation for d < 1,000 mm.
Table 4. Coefficients for the calculation of the roof for α = 15°.
Material
PE-HD
PE 63
PE 80
234
Mean
Effective
βS
media
wall
temperature temperature
δS
βF
If the tanks are installed in buildings, it is not necessary to take
account of any additional loading resulting, for example, from
wind and snow loads. This permits the less complicated
calculation of the tanks compared with the DVS 2205-2 technical
code.
δF
5.2 Standards and technical codes
[°C]
[°C]
[mm]
See DVS 2205-2, Section 5.2.
30
40
25
30
204
185
0.8
0.9
277
238
0.7
0.9
5.3 Literature
50
35
171
1.1
203
1.2
60
30
40
25
156
204
1.2
0.8
171
230
1.6
1.0
40
30
185
0.9
214
1.1
50
60
35
40
171
156
1.1
1.2
200
187
1.3
1.4
30
25
204
0.8
281
0.7
40
50
30
35
185
171
0.9
1.1
263
246
0.8
0.9
60
40
156
1.2
231
1.0
[mm]
[1] Timoshenko, S.: Theory of plates and shells. McGraw Hill
Book Comp, New York / London 1959.
[2] Kempe, B.: Deformation measurements on a tank made of
high-density polyethylene in the case of a temperature
change. Schweißen & Schneiden, No. 4/90.
[3] Tuercke, H.: Simplified proof of the shell pressure stability in
the case of flat-bottom tanks made of thermoplastics, DIBt
Communications, No. 6/1995.
[4] Tuercke, H.: On the stability of tanks made of thermoplastics,
DIBt Communications, No. 5/1995.
Page 7 to DVS 2205-2 Supplement 1
5.4 Computational elastic moduli for stability calculations
Table 6. Temperature-dependent short-time elastic moduli E
N/mm².
in
R&D INTAKE MANIFOLDS
Material
≤ 10°C
20°C
30°C
40°C
50°C
60°C
70°C
80°C
PE-HD
1100
800
550
390
270
190
–
–
PP-H
1400
1200
960
770
620
500
400
320
PP-B
1200
1000
790
630
500
400
320
250
PP-R
1000
800
620
490
380
300
230
180
PVC-NI
3200
3000
2710
2450
2210
2000
–
–
≤ 10°C
20°C
40°C
60°C
80°C
100°C
–
–
1900
1700
1330
1050
820
650
–
–
PVDF
Remark: The value for PE-HD may be used for PE 63, PE 80
and PE 100.
5.5 Design-related details
The following design examples are indicated in this section:
–
–
–
–
–
nozzle in the cylinder shell, Figure 9
lifting lugs, Figure 10
connection between the shell and the bottom, Figure 11
connection between the shell and the roof, Figure 12
edge of open tanks, Figure 13
Figure 9.
Nozzle in the cylinder shell.
Use a cross-beam for the
lifting of the tank
If bÖ is complied with, a square
connection is also possible
Bild 10. Lifting lug.
235
Page 8 to DVS 2205-2 Supplement 1
ü ≈ 10 without anchoring
ü ≈ 25 with anchoring
R&D INTAKE MANIFOLDS
Figure 11. Connection between the shell and the bottom.
Extruder weld
Figure 12. Connection between the shell and the roof.
Figure 13. Edge of open tanks.
236
January 2011
Calculation of tanks and apparatus
made of thermoplastics
DVS – DEUTSCHER VERBAND
FÜR SCHWEISSEN UND
Technical Code
DVS 2205-2
Vertical round non-pressurised tanks
Collecting devices
VERWANDTE VERFAHREN E.V.
R&D INTAKE MANIFOLDS
Supplement 2
Reprinting and copying, even in the form of excerpts, only with the consent of the publisher
Replaces January 2010 edition
Contents:
2 Calculation variables
1
2
3
3.1
3.1.1
3.1.2
3.2
3.2.1
3.2.2
a
AB
Aj
AZ
A1
mm
m2
m2
m2
–
A2
–
A2K
–
A2I
–
bÖ
bPr
c
C
C1
C2
C*
mm
mm
–
–
–
–
–
d
dL
dmax
dmin
dSch
mm
mm
mm
mm
mm
3.3
3.4
4
4.1
4.1.1
4.1.2
4.1.3
4.1.4
4.1.5
4.1.6
4.2
4.2.1
4.2.2
4.2.3
4.3
5
5.1
5.2
5.3
5.4
5.5
Scope of application
Calculation variables
Loading
Loads
Total dead load
Load of the filling material
Wind
Wind load
Radially symmetrical equivalent loading caused by wind
pressure
Assembly loads
Temperature
Proof of the steadiness
Proof of the strength
Effects
Shell
Bottom
Welded joint between the bottom and the shell
Anchoring
Lifting lugs
Proof of the stability
Superimposition of the effects
Axial stability
Shell pressure stability
Proof of the buoyancy safety
Appendix
Explanations
Standards and technical codes
Literature
Temperature-dependent and time-dependent elastic
moduli for stability calculations
Design-related details
o
20 C
EK
o
30 C
1
EK
Scope of application
o
20 C
The following design and calculation rules apply to collecting
devices in the form of vertical, cylindrical flat-bottom tanks which
are fabricated from thermoplastics in the factory, in particular:
–
–
–
–
polyvinyl chloride (PVC),
polypropylene (PP),
polyethylene (PE),
polyvinylidene fluoride (PVDF).
The cylindrical shell with an identical wall thickness throughout or
with a graduated wall thickness can be welded together from
panels or may consist of a wound pipe or an extruded pipe. The
cylinder and bottom of the collecting device must not have any
openings whatsoever.
The main dimensions are dependent on those of the tanks which
they should accommodate (on this subject, see Section 5).
The minimum wall thickness is 4 mm.
Attention must be paid to the responsibilities of certain legal fields
(e.g. building law, water law, occupational health and safety law
etc.).
EL
fs
fz
g
GB
GE
GF
GZ
hF
hF,i
hZ
hZ,i
hZF
vorh
KK
vorh
K K,d
Weld thickness
Area of the bottom
Area exposed to the wind (partial area)
Shell area of the cylinder
Reduction factor for the influence of the specific
toughness (corresponds to A4 according to the
DVS 2205-1 technical code)
Reduction factor for the media influence in the
case of the proof of the strength
Reduction factor for the media influence in the
case of the proof of the strength with an effect
for three months
Reduction factor for the medium in the case of
the proof of the stability
Width of the lifting lug
Width of the claw
Force coefficient according to DIN 1055-4
C1 C2
Stress-increasing factor
Material-specific design factor
Coefficient for the circular cylinder subjected to
external pressure loads
Nominal inside diameter
Hole diameter in the lifting lug
Maximum cylinder diameter
Minimum cylinder diameter
Diameter of the shackle
N/mm2 Elastic modulus in the case of short-time loading
for 20°C
N/mm2 Elastic modulus in the case of short-time loading
for 30°C
N/mm2 Elastic modulus in the case of long-time loading
for 20°C
–
Long-time welding factor
–
Short-time welding factor
m/s2
Acceleration due to gravity (9.81 m/s2)
N
Dead load of the bottom
N
Total dead load
kN
Load of the filling material
N
Dead load of the cylinder
mm
Filling height
mm
Filling height of the course i
mm
Cylindrical height
mm
Height of the course i
mm
Height of the lowest course
N/mm2 Stresses effective for a short time
N/mm2 Dimensioning value of stresses effective for a
short time
This publication has been drawn up by a group of experienced specialists working in an honorary capacity and its consideration as an important source of information
is recommended. The user should always check to what extent the contents are applicable to his particular case and whether the version on hand is still valid. No
liability can be accepted by the Deutscher Verband für Schweißen und verwandte Verfahren e.V., and those participating in the drawing up of the document.
DVS, Technical Committee, Working Group "Joining of Plastics"
Orders to: DVS Media GmbH, P. O. Box 10 19 65, 40010 Düsseldorf, Germany, Phone: + 49(0)211/1591- 0, Telefax: + 49(0)211/1591-150
237
Page 2 to DVS 2205-2 Supplement 2
vorh
K M,d
K *K
N/mm2 Dimensioning value of stresses with a medium
effective duration
N/mm2 Creep strength for 10-1 hours
TAK
TM
u
V
Wj
z



A
B

A,i
M
F
N/mm2 Dimensioning value of the creep strength for the
medium effective duration
N/mm2 Dimensioning value of the creep strength for the
short effective duration
mm
Length of the upper course of the equivalent
cylinder
Nm
Bending moment in the case of a wind load
N/mm² Radially symmetrical equivalent loading caused
by wind pressure
N/mm² Dimensioning value of the critical shell buckling
pressure
N/mm2 Overpressure at the tank bottom due to the
filling medium
N/mm2 Overpressure per lower edge of the graduation
due to the filling medium
kN/m2 Impact pressure on the partial area Aj
2
kN/m Maximum impact pressure effective at the
collecting device
mm
Radius of the cylinder
2
N/mm Dimensioning value of the stressability
mm
Wall thickness of the bottom
mm
Wall thickness of the lifting lug
mm
Wall thickness of the cylinder
mm
Wall thickness of the lowest course
mm
Statically required wall thickness
mm
Mean wall thickness of the cylinder
mm
Wall thickness of the highest course
mm
Wall thickness of the course i
mm
Wall thickness of the upper course of the
equivalent cylinder
2
N/mm Dimensioning value of the stresses
°C
Mean ambient temperature (according to Miner,
see DVS 2205-1)
°C
Highest ambient temperature
°C
Mean media temperature of the relevant tank
%
Permissible out-of-roundness
3
Filling volume
m
kN
Wind load
–
Number of anchors
–
Auxiliary variable
–
Coefficient
–
Coefficient
–
Coefficient for the determination of A2K
–
Coefficient for the calculation of the bottom
%
Tolerable edge fibre expansion
–
Utilisation of the axial stability in the course i
–
Utilisation of the shell pressure stability
–
Partial safety coefficient of the effect/stresses
I
–
M
–

F
G
g/cm3
vorh
 i,d
N/mm²
k
k,i,d
N/mm2
N/mm2
W
N/mm2
K *M,d
*
KK,d
lo
MW
peu
pkM,d
pstat
pstat,i
qj
qmax
r
Rd
sB
sÖ
sZ
sZF
s *ZF
sZm
sZ,1
sZ,i
so
Sd
TA
238
R&D INTAKE MANIFOLDS
g/cm3
N/mm2
Weighting coefficient depending on the loading
case
Partial safety coefficient of the resistance/
stressability
Density of the material ( =   g)
Density of the filling medium
Compressive stress on the diaphragm resulting
from the dead weight
Dimensioning value of the crucial axial
compressive stress in the course i
Critical buckling stress
Dimensioning value of the critical buckling stress
in the course I
Compressive stress on the diaphragm resulting
from the wind load
Open
Figure 1.
3
Ventilated
Collecting device for a flat-bottom tank.
Loading
The collecting devices are designed for the same computational
operating time as that for the relevant tank. The load case of the
filling from leakage is estimated for three months.
In the proof of the steadiness, it is necessary to take the following
loads into consideration.
3.1 Loads
3.1.1 Total deal load GE
GE = GZ + GB
N
(1)
N
(2)
N
(3)
Dead load of the cylinder GZ
GZ = AZ  sZ    g
Dead load of the bottom GB
GB = AB  sB    g
Ladders, platforms, pedestals and similar items must be set up
and fastened independently of the collecting device since the free
expansion of the collecting device (e.g. during filling resulting
from leakage and in the case of temperature changes) would
otherwise be hindered. These hindrances cause considerable
stress peaks which are difficult to record computationally and, if
they are taken into account, lead to uneconomic designs. If there
is any deviation from this, corresponding proof must be provided.
3.1.2 Load of the filling material GF
GF = V  F  g
kN
(4)
3.2 Wind
3.2.1 Wind loads
The wind loads Wj must be estimated as follows:
Wj = cf ∙ q ∙ Aj
kN
(5)
where:
Wj Wind load of the partial area Aj.
cf
Force coefficient for the circular cylinder and the roof.
cf1 = 0.8 may be estimated according to DIN 1055-4, Section
10.2. Installation in a series has already been taken into consideration in this respect. Extensions cf2 = 1.6.
q
Kinematic pressure according to DIN 1055-4, Table 2 depending on the wind zone and the height above the ground h
(h = hBehälter + hGebäude when the tank is located on a building, otherwise h = hG = hBehälter).
Page 3 to DVS 2205-2 Supplement 2
Aj Relevant exposed area in m² (for the tank: diameter times
total height hG including the roof)
In this respect, the characteristic effects or the stresses are multiplied by the partial safety coefficients F according to Table 1.
The stress resulting from the wind moment MW may be calculated
using the following simplified method:
Table 1. Partial safety coefficients of the effects.
R&D INTAKE MANIFOLDS
3
4  M W,x  10
 W,i = ---------------------------------2
  d  s Z,i
N/mm2
(6)
Mw,x at the height x above the tank bottom can be calculated on
a clamped equivalent bar.
2
 hG – x 
- + c f2  q 
M W, x = c f1  q  d  ---------------------2
  Aj  aj 
Nm
(7)
where aj is the lever arm of the area exposed to the wind Aj of the
superstructures and extensions in relation to the height x.
3.2.2 Radially symmetrical equivalent loading caused by
wind pressure
The compressive loading effective on the cylindrical shell due to
the inflow of the wind is recorded by the equivalent loading p eu.
p eu =   q max  10
–3
N/mm2
Einwirkung
Partial safety coefficient
Dead weight, filling and assembly
F1 = 1.35
Wind
F2 = 1.5
Stress-reducing dead weight
F3 = 0.9
For example, the dimensioning value of the existing stresses
results from F times the characteristic value of the existing
stresses in the component.
vorh
vorh
KK,d =  F  KK
The dimensioning values of the existing stresses must also be
multiplied by the reduction coefficients A1 and A2 as well as by a
weighting coefficient I. In this respect, the weighting coefficient
takes account of the loading type according to Table 2. In the
case of proof in the weld, the dimensioning value of the existing
stresses must be divided by the welding factor.
(8)
Table 2. Weighting coefficient.
where:
Loading type

r
r 
 = 0.46   1 + 0.1  C*  ------  ----------  0.6
h Z s Zm

(9)

mm
(10)
3.3 Assembly loads
The collecting device must be designed for the loading conditions
arising during the transport and the assembly. In this respect, the
calculation is made with 1.5 times the assembly loads (surge
factor). F1 is estimated as the partial safety coefficient. The
short-time welding factor according to DVS 2205-1 must be taken
into consideration.
3.4 Temperature
The effective wall temperature is decisive for the dimensioning of
the components. In the case of leakage, proof must be provided
for the parts wetted with media at the mean media temperature
TM.
In a simplifying method for non-wetted parts, the mean of both
the neighbouring air temperatures may be estimated as the wall
temperature. At the ambient temperature, a differentiation is
made according to the installation location and the effective
duration. The following minimum values are applicable:
Minimum values
I
1.0
Static loading at the room temperature and in constant
conditions. Cases of damage cannot lead to any
danger to people, things or the environment.
C* = 0.6 for the open tank
 h Z,i  s Z,i 
s Zm = ---------------------------------hZ
Loading Case I
For a short time
For a long time
Indoor installation
TAK = 20°C
TA = 20°C
Outdoor installation
TAK = 35°C
TA = 20°C
For the proof of the stability in the cylinder, a reduced ambient
temperature TAK - 5°C applies to outdoor installation (wind effect).
4 Proof of the steadiness
The proof of the steadiness is provided according to the concept
of the partial safety coefficients. In general, the following is applicable:
S
------d-  1
Rd
with Sd dimensioning value of the stresses
Rd dimensioning value of the stressability
Loading Case II
1.2
Loading in changing conditions (e.g. temperature and
filling height). Cases of damage may lead to danger to
people, things or the environment, e.g. installations or
installation parts which must be monitored and tested.
The characteristic resistances or the stressabilities are divided by
the partial safety coefficient M = 1.1.
For example, the dimensioning value of the short-time strength
results from the characteristic short-time strength value K *K divided by M according to the creep strength diagrams in DVS
2205-1.
KK*
*
KK,d
= -------M
4.1 Proof of the strength
4.1.1 Effects
It is always necessary to look for the most unfavourable combination of the overall effects for every component.
Corresponding to the effective duration, a distinction must be
made between three loading categories:
– Loading effective for a short time (K)
e.g. wind: q or peu
– Effects with a medium effective duration (M)
e.g. filling in the leakage case
– Loading effective for a long time (L)
e.g. dead weight
Load cases effective for a short time do not have to be combined
with each other.
The effective duration of loads effective for a short time is stipulated as 10-1 hours and those effective for a medium time as
three months.
4.1.2 Shell
The height of the lowest course hZF must be min. 1.4  d  s ZF .
In the case of graduated tanks, neighbouring courses may have
239
Page 4 to DVS 2205-2 Supplement 2
a wall thickness ratio of max. 3 without any further proof. In the
case of sudden thickness changes with a wall thickness ratio
greater than 2, it is necessary to use the shell seam formation
according to DVS 2205-3, Fig. 2.2 a), 2.2 c) or 2.2 c1).
4.1.2.2 Proof in the longitudinal direction
Only the lowest course at the interface to the bottom must be
investigated for the proof of the stresses in the longitudinal
direction. The stresses arising here are caused by the bending
fault moment, the dead weight and the wind.
R&D INTAKE MANIFOLDS
4.1.2.1 Proof in the circumferential direction
For every course i, it must be proven that the ring tensile stresses
due to the filling can be accommodated at its lower edge:
vorh
K M,d
----------------1
K *M,d
(11)
 F1  p stat,i  d A 1  A 2K   I
= ---------------------------------  -----------------------------2  s Z,i
fs
N/mm2
p stat,i =  F  g  h F,i  10
with
(15)
and
(13)
The factor C for the welded interface of the bond between the
bottom and the shell is the product of the stress-increasing factor
C1 = 1.2 and a material-specific design factor C2 according to
Table 5.
p stat =  F  g  h F  10
N/mm2
N/mm2
(12)
with
–6
The proof must be provided according to Equation (11):
d A 1  A 2K   I
vorh
K M,d = C   F1  p stat  ---  -----------------------------s ZF
2
with
vorh
K M,d
The longitudinal stresses resulting from the dead weight can be
neglected. The short-time tensile stresses resulting from the wind
do not have to be proven either.
where hF,i means the height of the liquid level above the lower
edge of the course i.
The reduction factor for the media influence in the case of an
effect for three months is calculated from:
–6
N/mm2
(16)
Table 5. The material-specific design factor C2 and the factor C for
thermoplastics.
C = C 1  C2
Material
C2
with A according to Table 3.
PE-HD
1.00
1.20
PP-H (Type 1)
1.17
1.40
Table 3. Coefficients A for the determination of A2K.
PP-B (Type 2)
1.00
1.20
PP-R (Type 3)
1.00
1.20
PVC-NI (normal impact strength)
1.25
1.50
PVC-RI (increased impact strength)
1.08
1.30
PVC-HI (high impact strength)
1.00
1.20
PVC-C
1.33
1.60
PVDF
1.17
1.40
A 2K = max   A  A 2 , 1.0 
(14)
TM
PE-HD PE 63 PE 80 PE 100 PP-H PP-B PP-R
°C
3 months
20
0.52
0.07
0.09
0.17
0.10
0.19
0.07
30
0.61
0.12
0.14
0.25
0.16
0.26
0.11
40
0.73
0.20
0.24
0.36
0.22
0.34
0.17
50
0.90
0.34
0.37
0.49
0.31
0.43
0.24
60
1.00
0.54
0.57
0.67
0.41
0.52
0.33
70
–
–
–
–
0.53
0.61
0.45
80
–
–
–
–
0.65
0.69
0.58
Remark: A = 1.0 applies to PVC and PVDF.
The welding factor of the shell weld fs or fz must be taken into
account in the case of cylinders manufactured from plates.
According to today's state of the art, preference should be given
to heated tool butt welding. fs = 1 and fz = 1 apply to wound
tanks.
The residual stresses from the bending of the panels at the room
temperature can be neglected if the edge fibre expansion (Table
4)  = s/d  100 [%] is not exceeded.
It is not necessary to provide any proof of the stresses in the weld
if the conditions according to Section 4.1.4 are fulfilled.
One prerequisite for the stress-increasing factor C1 = 1.2 is that
the bottom is not executed with a thickness greater than the wall
thickness of the lowest course (sB  sZF).
4.1.3 Bottom
If the bottom and the cylinder are joined with fillet welds (Fig. 6),
the required thickness of the bottom may be determined as
follows:
*
 B  SZF
 S B  S ZF
mm
(17)
with sZF as the executed wall thickness and B according to
Fig. 2.
Table 4. Tolerable edge fibre expansion.
Material
Edge fibre expansion 
PE-HD
1.00
PP-H
0.50
PP-B
0.75
C   F1  p stat  d
*
SZF
= -----------------------------------------  A 1  A 2K   I
2  K *M,d
mm
(18)
In the case of other structural shapes, it is necessary to provide
proof of the bottom due to the cylinder clamping moment.
PP-R
1.00
4.1.4 Welded joint between the bottom and the shell
PVDF
0.50
PVC-U
0.20
It is not necessary to provide any explicit proof of the stresses on
the weld if the following conditions are fulfilled:
PVC-C
0.10
Remark:
The value for PE-HD may be used for PE 63, PE 80 and PE 100.
240
Remark:
The value for PE-HD may be used for PE 63, PE 80 and PE 100.
– weld thickness
a  0.7  sB
– long-time welding factor fs  0.6
If one of these conditions is not fulfilled, it is necessary to provide
detailed proof of the stresses in the weld (e.g. FE calculation).
Page 5 to DVS 2205-2 Supplement 2
In the case of one-shell tanks with capacities up to 1,000 l and
wall thicknesses up to 10 mm, this also applies to long-time welding factors fs  0.4.
4.1.5 Anchoring
 F1  G E
1.5  -------------------2
-  A1  I
s Ö = -----------------------------------d Sch  2  K *K,d
mm
(22)
R&D INTAKE MANIFOLDS
If anchoring becomes necessary, at least four anchors must be
arranged (z  4). Taking account of the lever arms, the anchor
forces (e.g. for the plugs) must be calculated from the claw
forces.
In the case of the proof of the anchoring, it is necessary to
investigate the short-time wind load at 20°C:
1
3  F2  M w
4  10  --------------------- –  F3  G z  --d
z
----------------------------------------------------------------------------------  1
K *K,d
 b Pr + s B   s B  ----------------------2  A1  I
(19)
The maximum of both the following cases of proof is crucial for
the width of the lifting lug (bÖ).
b Ö = max  b Ö,1 ,b Ö,2 
Proof of the shearing stress for the transverse weld during the
lifting of the lying collecting device:
b Ö,1
 F1  G E
1.5  -------------------- A  
4
1
-I
-  -------------= --------------------------------------*
fz
KK,d
0,7  s Z,1  -----------2
mm
(23)
Eye bar:
The numerator indicates the claw force to be accommodated and
the denominator the claw force which can be accommodated and
results from the shearing stress in the weld. In this respect, half
the creep strength is estimated as the shearing stress.
 F1  G E
1.5  -------------------7
2
 A 1   I + ---  d L
b Ö,2 = --------------------------------*
3
s Ö  KK,d
Fig. 4 in Section 5.5 shows the execution of an anchoring element.
4.2 Proof of the stability
4.1.6 Lifting lugs
One of the possible lifting lug shapes is shown on Fig. 5 (Section
5.5). The prerequisites for the use of these lifting lugs are that
only two lifting lugs are used per collecting device and that one
parallel hanger is utilised.
In order to be able to dispense with any proof of the load introduction into the highest course, it must be ensured that the lifting
lug is not thicker than three times the wall thickness of the
highest course. The hole diameter (dL) must be adapted to the
diameter of the shackle (dSch).
The following equations are applicable:
s Z,1  erf s Ö  3  s Z,1
mm
(20)
d Sch  d L  1.1  d Sch
mm
(21)
It must be proven that 1.5 times the loading (surge factor) can be
borne for a short time at 20°C.
The required wall thickness sÖ of the lifting lug results from the
proof for the face of the hole:
mm
(24)
Proof of the stability must only be provided in the case of outdoor
installation. Sufficient safety against axial and shell pressure
stabilities must be proven for the shell of the collecting device.
The prerequisite is that the out-of-roundness of the cylinder
remains limited in the following form:
2   d max – d min 
u = ------------------------------------------  100  0.5
d max + d min
%
(25)
4.2.1 Superimposition of the effects
The crucial elastic moduli are needed for the stability calculations. The buckling of shells is a sudden occurrence which is
essentially dependent on the imperfections, i.e. on the size of the
previous bulges. The size of the previous bulges increases along
with the loading duration because of the creep behaviour of the
material. In contrast, the elastic resistance during the beating-out
is predominantly determined by the short-time elastic modulus at
the temperature at that moment. The critical buckling stress k is
therefore calculated with the temperature-dependent moduli
o
EKT C .
zulässiger Bereich
für C == 1,2
Permissible
range for
1.2
Figure 2.
Diagram for the determination of the thickness of the bottom, derived for PE-HD (for C > 1.2, this diagram is on the safe side).
241
Page 6 to DVS 2205-2 Supplement 2
For the essential thermoplastics, the temperature-dependent and
time-dependent elastic moduli are included in Tables 6 and 7
(Section 5.4).
It is necessary to investigate the most unfavourable combination
of loads taking account of the temperature behaviour of the thermoplastics.
The critical shell pressure of the non-graduated cylinder is calculated from:
o
T C
s 2.5
EK
r
-  ------   -----Z
p kM,d = 0.67  C *  --------------M
hZ  r 
R&D INTAKE MANIFOLDS
4.2.2 Axial stability
In the case of outdoor installation, the axial compressive stress
 vorh
which exists at the lower edge and consists of the dead
i,d
weight and the wind load is determined for every course i and is
validated with the buckling stress k,i,d. In the case of indoor
installation, it is not necessary to prove the axial stability:


 vorh
i,d
N/mm2
=  F1   G +  F2   W
(26)
Using a simplifying method, the buckling stress may be determined according to the following formula:
 k,i,d =  i  0.62  f ,i 
ToC
EK
---------------
M
s Z,i
 --------  K *K,d
r
N/mm2
(27)
with
0.7
 i = ----------------------------------------------------------------20 o C
EK
r


-----------------+
--------------------
1
o
20 C 
100  s Z,i
EL
(28a)
ei
f ,i = 1.5 – --------  1 aber
s Z,i
 0.4
(28b)
where ei is the eccentricity in relation to the thicker of the two
neighbouring courses in the case of a graduated cylinder if this is
itself thicker than the course i under consideration.
It is necessary to comply with the following condition for every
course i:

The critical shell pressure of the graduated cylinder may be
calculated on a three-course equivalent cylinder according to
DIN 18800-4:
ToC
EK
r s 2.5
-  ----   ----o-
p kM,d = 0.67    C *  --------------M
lo  r 
(29)
A2I = 1.0 may be set because the collecting device is only in
danger of buckling in the empty condition – and thus without any
media effect.
4.2.3 Shell pressure stability
The partial vacuum resulting from peu is validated with the critical
shell pressure pkM.
The following condition must be fulfilled:
A 2l   I   F2  p eu
 M = -------------------------------------------  1
p kM,d
(30)
A2I = 1.0 may be set because the collecting device is only in
danger of buckling in the empty condition – and thus without any
media effect.
T oC
Table 6. Temperature-dependent short-time elastic moduli E K
(32)
The  values are indicated on Figs. 20a to 20c in DIN 18800-4.
It is not necessary to provide any proof of the interaction between
the axial and shell pressure stabilities.
4.3 Proof of the buoyancy safety
For cases of damage, it must be proven that 0.9 times the weight
force of the tank is greater than the buoyancy force of the immersed tank part.
Appendix
5.1 Explanations
This Supplement 2 to the DVS 2205-2 technical code was elaborated by DVS-AG W4.3b ("Structural designing / apparatus engineering") together with the committee of experts "Plastic tanks
and pipes" (project group "Calculation").
5.2 Standards and technical codes
5.3 Literature
[1] Timoshenko, S.: Theory of plates and shells. McGraw Hill
Book Comp, New York / London 1959.
[2] Kempe, B.: Deformation measurements on a tank made of
high-density polyethylene in the case of a temperature
change, Schweißen & Schneiden, No. 4/90.
[3] Tuercke, H.: Simplified proof of the shell pressure stability in
the case of flat-bottom tank made of thermoplastics, DIBt
Communications, No. 6/1995.
[4] Tuercke, H.: On the stability of tanks made of thermoplastics,
DIBt Communications, No. 5/1995.
5.4 Temperature-dependent and time-dependent elastic
moduli for stability calculations
in N/mm2.
Material
 10°C
20°C
30°C
40°C
50°C
60°C
70°C
PE-HD
1,100
800
550
390
270
190
–
–
PP-H
1,400
1,200
960
770
620
500
400
320
PP-B
1,200
1,000
790
630
500
400
320
250
PP-R
1,000
800
620
490
380
300
230
180
PVC-NI
3,200
3,000
2,710
2,450
2,210
2,000
–
–
 10°C
20°C
40°C
60°C
80°C
100°C
–
–
1,900
1,700
1,330
1,050
820
650
–
–
Remark:
The elastic moduli for PE-HD may also be used for PE 63, PE 80 and PE 100.
242
N/mm2
See DVS 2205-2, Section 5.2.
vorh
i,d
A 2l   I 
 A,i = -----------------------------------------------  1
 k,i,d
PVDF
(31)
with C* = 0.6 for the open tank.
5
and
N/mm2
80°C
Page 7 to DVS 2205-2 Supplement 2
20 oC
Table 7. Time-dependent long-time elastic moduli E L
in N/mm2.
Material
1 year
5 years
10 years
15 years
20 years
25 years
PE-HD
308
269
254
245
239
235
PP-H
464
393
365
350
340
330
PP-B
405
334
307
293
283
275
PP-R
322
298
288
283
279
276
1,800
1,695
1,652
1,627
1,609
1,600
810
763
744
733
725
720
PVC-NI
PVDF
Remarks:
The elastic moduli for PE-HD
may also be used for PE 63,
PE 80 and PE 100.
The long-time elastic moduli for
PE-HD apply to stresses up to
0.5 N/mm² and those for PP up to
1 N/mm². The stress dependence
of the elastic moduli for PVC-NI
and PVDF is insignificant.
R&D INTAKE MANIFOLDS
5.5 Design-related details
The following design examples are indicated in this section:
– distance between the collecting device and the tank, Fig. 3
– anchoring of the bottom, Fig. 4
– lifting lug, Fig. 5
– connection between the shell and the bottom, Fig. 6
– edge of collecting devices, Fig. 7
Figure 3.
Distance between the collecting device and the tank.
Without a gap and without pressing
Anchor bolt
Claw: steel
PE film: 2 mm
Minimum number
of claws: 4
Spacer plates
Figure 4.
Anchoring of the bottom.
243
Page 8 to DVS 2205-2 Supplement 2
R&D INTAKE MANIFOLDS
If bÖ is complied with, a square connection
is also possible.
Figure 5.
Lifting lug.
ü  10 without anchoring
ü  25 with anchoring
Figure 6.
Connection between the shell and the bottom.
Figure 7.
Edge of collecting devices.
244
January 2010
Calculation of tanks and apparatus
made of thermoplastics
DVS – DEUTSCHER VERBAND
FÜR SCHWEISSEN UND
Technical Code
DVS 2205-2
Vertical round, non-pressurised tanks
Flat roofs
VERWANDTE VERFAHREN E.V.
R&D INTAKE MANIFOLDS
Supplement 3
Reprinting and copying, even in the form of excerpts, only with the consent of the publisher
Replaces November 2003 edition
Contents:
gSteife N/mm2
1
2
3
4
5
6
6.1
6.2
6.2.1
hS
IS
k
K
mm
mm4
–
N/mm2
K
N/mm2
K
N/mm2
Dimensioning value of the creep strength for
10-1 hours
K
N/mm2
Dimensioning value of the creep strength for
the computational working life
p
pDK,d
N/mm2
N/mm2
Scope of application
Calculation variables
Structural designing
Loading
Temperature
Proof of the steadiness
Unstiffened roof
Roof with stiffeners
Proof of the strength of the roof plate transverse to the
stiffeners
6.2.2 Proof longitudinal to the stiffeners
7
Appendix
7.1
Explanations
7.2
Standards and technical codes
7.3
Computational elastic moduli for stability calculations
7.4
Design-related details
pDL,d
1
Scope of application
The following design and calculation rules apply to flat roofs of
flat-bottom tanks which are fabricated from thermoplastics in the
factory, in particular:
–
–
–
–
polyvinyl chloride (PVC),
polypropylene (PP),
polyethylene (PE),
polyvinylidene fluoride (PVDF).
The proof in this technical code only applies to tanks installed
inside buildings.
It is not allowed to walk on flat roofs without any loaddistributing aids!
2
pE
puK
püK
pu
pü
pus
m
n
sD
sS
TA
Calculation variables
A1
–
A2
–
A2I
–
bm
d
mm
mm
E
N/mm2
fsD
–
fzD
–
g
gD
m/s2
N/mm2
Reduction factor for the influence of the specific toughness (corresponds to A4 according to
the DVS 2205-1 technical code)
Reduction factor for the medium in the case of
the proof of the strength
Reduction factor for the medium in the case of
the proof of the stability
Width also bearing the load
Nominal diameter of the tank
TAK
TM
Elastic modulus in the case of short-time
loading for T°C
Long-time welding factor for the weld of the
roof plate
Short-time welding factor for the weld of the
roof plate
Acceleration due to gravity
Area load resulting from the dead weight of the
roof plate
γM
TMK
zS
γF
γI
µ
ρ
σk,d
σ
Uniformly distributed area load resulting from
stiffeners and bulkheads
Height of the stiffeners
Moment of inertia
Buckling value
Dimensioning value of the stresses effective
for a short time
Dimensioning value of the stresses effective
for a long time
Effect on the roof
Dimensioning value of the short-time effects
on the roof
N/mm2 Dimensioning value of the long-time effects on
the roof
N/mm2 Equivalent load (for a short time)
N/mm2 External pressure (or internal partial vacuum)
effective for a short time
N/mm2 Internal pressure effective for a short time
N/mm2 External pressure (or internal partial vacuum)
effective for a long time
N/mm2 Internal pressure effective for a long time
N/mm2 Partial vacuum due to wind suction
Nmm/mm Bending moment
–
Number of stiffeners and bulkheads
mm
Wall thickness of the roof plate
mm
Wall thickness of the stiffeners
°C
Mean ambient temperature
(according to Miner, see DVS 2205-1)
°C
Highest ambient temperature
°C
Mean media temperature (according to Miner,
see DVS 2205-1)
°C
Highest media temperature
mm
Distance away from the centre of gravity
–
Partial safety coefficient of the effect/stresses
(see DVS 2205-2)
–
Weighting safety coefficient depending on the
loading type (see DVS 2205-2)
–
Partial safety coefficient of the resistance/
stressability (see DVS 2205-2)
–
Poisson's ratio
g/cm³
Density of the material
N/mm2 Dimensioning value of the critical compressive
stress
N/mm2 Dimensioning value of the compressive stress
in the roof plate
This publication has been drawn up by a group of experienced specialists working in an honorary capacity and its consideration as an important source of information
is recommended. The user should always check to what extent the contents are applicable to his particular case and whether the version on hand is still valid. No
liability can be accepted by the Deutscher Verband für Schweißen und verwandte Verfahren e.V., and those participating in the drawing up of the document.
DVS, Technical Committee, Working Group "Joining of Plastics"
Orders to: DVS Media GmbH, P. O. Box 10 19 65, 40010 Düsseldorf, Germany, Phone: + 49(0)211/1591- 0, Telefax: + 49(0)211/1591-150
245
Page 2 to DVS 2205-2 Supplement 3
3
Structural designing
= max ( γ
with p
Flat roofs can be manufactured in an unstiffened design or with
stiffeners.
⋅g +γ
⋅p ,γ
⋅p –γ
⋅g )
∑
R&D INTAKE MANIFOLDS
In the case of an unstiffened flat roof, attention must be paid to
the great deformation of the roof solely because of the dead
weight.
As a rule, flat roofs are reinforced with two parallel stiffeners. For
larger tanks, it is also possible to arrange more stiffeners. However, when choosing the number of stiffeners, attention must be
paid to the arrangement of an entry opening between the stiffeners and to sufficient space in order to weld the stiffeners together
with the roof plate on both sides.
As far as the design is concerned, the n stiffeners must be
prevented from tilting using n bulkheads in each case at regular
intervals.
If the roof plate cannot be fabricated in one part, the weld must
be arranged vertically to the stiffeners.
The ratio of the height to the thickness of the stiffeners is limited
to 8:
h
------ ≤ 8
s
4
K
---------------------------- ≤ 1
K
with
p
⋅ d ⋅ 6 ⋅ (3 + µ) A ⋅ A ⋅ γ
= ---------------------------------------------------------------- ⋅ -------------------------f
64 ⋅ s
ΣK
with p
(5)
= max { γ
,p ) + p ],γ
⋅p
⋅g +γ
–γ
⋅ [ max ( p
(6)
,p ) + p ],
⋅g }
(7)
The welding factors fsD and fzD are 1.0 if the roof is fabricated
from one part.
As an approximation, the Poisson's ratio can be set at µ = 0.38
for all thermoplastics.
6.2 Roof with stiffeners
6.2.1 Proof of the strength of the roof plate transverse to the
stiffeners
If the roof plate is not fabricated from two partial plates, the weld
must be arranged parallel to the stiffeners.
Loading
Not only the dead weight and the minimum pressures but also a
uniform equivalent load pE must be taken into consideration:
– dead weight of the roof including stiffeners and bulkheads (gD
and gSteifen)
– minimum pressures according to DVS 2205-2, Section 1 (puK,
püK, pu and pü)
– partial vacuum due to wind suction (pus)
kN/m2
N/mm2
= 0.001
– pE = 1
planned individual loads
Using a simplifying method, the bending moment in the roof plate
between the stiffeners results from:
p⋅d
m = ---------------------------8 ⋅ (n + 1 )
(8)
Proof according to Equation (13) in DVS 2205-2. No loading with
a medium effective duration arises in this respect:
in order to take account of un-
It is not necessary to investigate the transmission of the equivalent load pE in the cylinder.
5
(4)
Proof according to Equation (15) in DVS 2205-2:
K
------------------ ≤ 1
K
with K
p
⋅d ⋅6
A ⋅A ⋅γ
= ------------------------------------------ ⋅ -------------------------f
(n + 1) ⋅ 8 ⋅ s
with p
= max ( γ
Temperature
The proof of the strength of the roof plate must be provided at the
effective wall temperature (TM + TA)/2 with long-time effects or
(TMK + TAK)/2 with short-time effects. The mean media temperature TM must be assumed for the proof of the strength of the stiffeners. The reduction factor A1 must be determined according to
the temperature to be estimated in each case.
(9)
⋅g +γ
⋅p , γ
(10)
⋅p –γ
⋅g )
(11)
Proof according to Equation (15) in DVS 2205-2:
K
Σ
--------------------- ≤ 1
(12)
K
The proof of the stability of the roof plate must be provided with
the short-time elastic modulus for (TMK + TAK)/2. The stability of
the stiffeners must be proven with the short-time elastic modulus
for TMK. In the event of outdoor installation underneath a stationary roof as a sun and snow shield, TAK = 35°C may be estimated
as the ambient temperature.
with
p
⋅d ⋅6 A ⋅A ⋅γ
= ------------------------------------------ ⋅ -------------------------f
(n + 1) ⋅ 8 ⋅ s
ΣK
with p
= max { γ
,p ) + p ],γ
6
⋅p
⋅g +γ
–γ
⋅ [ max ( p
(13)
,p ) + p ],
⋅g }
(14)
Proof of the steadiness
6.1 Unstiffened roof
As an approximation, the Poisson's ratio can be set at µ = 0.38
for all thermoplastics
Using a simplifying method, the bending moment in the centre of
the plate results from:
6.2.2 Proof longitudinal to the stiffeners
(3 + µ) ⋅ p ⋅ d
m = -----------------------------------(1)
64
Proof according to Equation (13) in DVS 2205-2. No loading with
a medium effective duration arises in this respect:
K
------------------ ≤ 1
K
with K
246
p
⋅ d ⋅ 6 ⋅ (3 + µ) A ⋅ A ⋅ γ
= ---------------------------------------------------------------- ⋅ -------------------------f
64 ⋅ s
A plate beam with the width also bearing the load:
b
0.85 ⋅ d
= ------------------n+1
(15)
(2)
is calculated for the proof longitudinal to the stiffener. The position of the centre of gravity zS (measured from the central area of
the roof plate) and the moment of inertia IS result from:
(3)
z
h +s
h ⋅ s ⋅ ------------------2
= -----------------------------------------h ⋅s +b ⋅s
(16)
Page 3 to DVS 2205-2 Supplement 3
l
h ⋅s
b ⋅s
h +s
= ----------------- + --------------------- + b ⋅ S ⋅ z + h ⋅ s ⋅  ------------------- – z 
 2

12
12
= γ
with p
⋅p –γ
⋅ (g + g
)
(29b)
Proof according to Equation (15) in DVS 2205-2:
R&D INTAKEΣMANIFOLDS
(17)
As an approximation, the Poisson's ratio can be set at µ = 0.38
for all thermoplastics
K
--------------------- ≤ 1
K
s
⋅ d ⋅  z + ------  A ⋅ A ⋅ γ
p

2 
= ----------------------------------------------------------------- ⋅ -------------------------(n + 1) ⋅ 8 ⋅ l
f
6.2.2.1 Loading directed inwards
ΣK
Proof of the strength at the lower edge of the stiffener
with
Proof according to Equation (13) in DVS 2205-2. No loading with
a medium effective duration arises in this respect:
with p
K
------------------ ≤ 1
K
(18)
s
p
⋅ d ⋅  h + ------ – z 


2
= --------------------------------------------------------------------------- ⋅ A ⋅ A ⋅ γ
(n + 1) ⋅ 8 ⋅ l
with K
= γ
with p
⋅ (g + g
)+γ
⋅p
(30)
= γ
⋅p
–γ
⋅ (g + g
)
(31a)
(31b)
h ⋅s ⋅ρ⋅g
= ( 2 ⋅ n – 1 ) ⋅ -------------------------------d ⋅ 10
with g
(32)
Proof of the stability of the stiffener
(19a)
The compressive stresses in the stiffener
compared with the buckling stress σk,d:
(19b)
A ⋅γ ⋅
σ
-------------------------------------------- ≤ 1
σ
Proof according to Equation (15) in DVS 2205-2:
∑σ
are validated
∑
(33)
where
K
Σ
--------------------- ≤ 1
(20)
K
s
p
⋅ d ⋅  h + ------ – z 


2
= -----------------------------------------------------------------------------------(n + 1) ⋅ 8 ⋅ l
∑
with
s
p
⋅ d ⋅  h + ------ – z 


2
= ----------------------------------------------------------------------------- ⋅ A ⋅ A ⋅ γ
(n + 1) ⋅ 8 ⋅ l
ΣK
= γ
with p
⋅ (g + g
)+γ
⋅ { max ( p
(34)
(21)
with p
, p ) + p } (22)
h ⋅s ⋅ρ⋅g
= ( 2 ⋅ n – 1 ) ⋅ -------------------------------d ⋅ 10
and g
Σσ
(23)
Proof of the stability of the roof plate
and σ
= γ
⋅p
–γ
⋅ (g + g
)
(35)
E
k ⋅ π ⋅ ---------------- ⋅ s
γ
= -----------------------------------------------12 ⋅ h ⋅ ( 1 – µ )
(36)
with the buckling value k = 1.1.
σ
The compressive stresses in the roof plate
parallel to the
stiffeners are validated compared with the buckling stress σk,d:
∑
A ⋅γ ⋅
σ
-------------------------------------------- ≤ 1
σ
∑
7.1 Explanations
(24)
p
⋅d ⋅z
= ----------------------------------------------------(n + 1) ⋅ 8 ⋅ l
∑
where
Σσ
7 Appendix
(25)
This Supplement 3 to the DVS 2205-2 technical code was elaborated by DVS-AG W4.3b ("Structural designing / apparatus engineering") together with the committee of experts of the German
Institute for Construction Engineering: "Plastic tanks and pipes"
(project group: "Calculation").
with
7.2 Standards and technical codes
Σp
and σ
= γ
⋅ (g + g
)+γ
⋅ { max ( p
, p ) + p } (26)
E
k ⋅ π ⋅ ( n + 1 ) ⋅ ---------------- ⋅ s
γ
= ------------------------------------------------------------------------12 ⋅ d ⋅ ( 1 – µ )
See the DVS 2205-2 technical code, Section 5.2.
7.3 Computational elastic moduli for stability calculations
(27)
with the buckling value k = 5.5.
Table 1. Temperature-dependent short-time elastic moduli E
N/mm .
in
Material
≤10°C
20°C
30°C
40°C
50°C
60°C
PE-HD
1,100
800
550
390
270
190
70°C 80°C
–
–
PP-H
1,400
1,200
960
770
620
500
400
320
250
6.2.2.2 Loading directed outwards
Proof of the strength of the roof plate
Proof according to Equation (13) in DVS 2205-2. No loading with
a medium effective duration arises in this respect:
K
------------------ ≤ 1
K
with K
PP-B
1,200
1,000
790
630
500
400
320
PP-R
1,000
800
620
490
380
300
230
180
PVC-Nl
3,200
3,000
2,710
2,450
2,210 2,000
–
–
≤10°C
20°C
40°C
60°C
80°C
100°C
–
–
1,900
1,700
1,330
1,050
820
650
–
–
(28)
PVDF
s
p
⋅ d ⋅  z + ------
A ⋅A ⋅γ

2
= --------------------------------------------------------------- ⋅ -------------------------f
(n + 1) ⋅ 8 ⋅ l
(29a)
Remark:
The elastic moduli for PE-HD may also be used for PE 63, PE 80
and PE 100.
247
Page 4 to DVS 2205-2 Supplement 3
7.4 Design-related details
R&D INTAKE MANIFOLDS
Recess for lifting lug
Bulkhead
Executed as a
circumferential ring
Stiffener
f = 10 – 35 mm
s
Variant 1
{
Variant 2
c
{
a = 0,5 · min (s , s
≥s
≥ 10 mm
)
a = 0,5 · s
≥5·s
≥ 80 mm
*) No cut-outs should be planned in the hatched area.
Figure 4.
Variant 1 of the bearing of the flat roof on the cylinder.
Any weld which may be necessary within the roof plate must be arranged
vertically to the stiffeners.
Figure 1.
Top view of a flat roof with two stiffeners.
Section A – A
a ≥ 0.5 · s
Figure 5.
Figure 2.
Section through the flat roof with two stiffeners and bulkheads.
Detail Y
Bulkhead for the stabilisation
of the stiffeners
Stiffener, hs ≤ 8 x s;
a = 0.7 x s
Figure 3.
248
Detail Y.
s
= min (s
,s )
Variant 2 of the bearing of the flat roof on the cylinder.
February 2013
DVS – DEUTSCHER VERBAND
FÜR SCHWEISSEN UND
VERWANDTE VERFAHREN E.V.
Calculation of tanks and apparatus
made of thermoplastics –
Vertical round non-pressurised tanks –
Flat-bottomed tanks in earthquake regions
Technical Code
DVS 2205-2
R&D INTAKE MANIFOLDS
Supplement 4
This Supplement 4 to the DVS 2205-2 technical code was elaborated by DVS-AG W4.3b ("Structural designing / apparatus engineering").
Reprinting and copying, even in the form of excerpts, only with the consent of the publisher
Contents:
1
Scope of application
2
Design
3
Calculation variables
4
Tank acceleration
4.1
Horizontal tank acceleration
4.2
Vibration period
4.2.1 Tank without a collecting vessel
4.2.2 Tank with a collecting vessel
4.3
Vertical tank acceleration
5
Stresses
5.1
Tank without a collecting vessel
5.2
Tank in the collecting vessel
5.3
Collecting vessel
6
Proof
7
Provision of proof
7.1
Proof of the axial stability in the two-shell region
8
Proof of the tank without a collecting vessel
8.1
Axial stability of the cylinder
8.2
Axial stability next to sockets
8.3
Anchoring
9
Proof of the tank in the collecting vessel
9.1
Axial stability
9.2
Lower support
9.3
Upper support
9.3.1 Bulkheads
9.3.2 Ring plate with a collar
10
Proof of the collecting vessel
10.1 Axial stability
10.2 Anchoring
11
Bibliography
Appendix: Design-related details
1
Scope of application
The following design and calculation rules apply to vertical, cylindrical tanks which are fabricated from thermoplastics in the factory,
have flat bottoms and are intended for installation in a German
earthquake region. Tanks which are installed in an earthquake
region outside Germany must be dimensioned according to the
set of rules applicable there. In agreement with the operator, the
calculation can also be carried out with reference to DIN 4149 if
the soil acceleration and statements about the geological subsoil
and about the foundation soil are known.
For the application of this supplement, it is necessary to satisfy
the following prerequisites:
– The tank may be installed inside or outside buildings. Its foundation must be in direct contact with the earth. In the event of
installation on building ceilings, platforms or similar structures,
separate proof is required and must take account of the vibration
behaviour of the entire system.
– The tank must always be anchored with the foundation directly
or, for a tank in the collecting vessel, indirectly. The design of
the upper and lower supports corresponds to Figs. 1 and 2. In
the case of designs deviating from this, it is necessary to provide
corresponding proof separately.
– The tanks and the collecting vessels are dimensioned in parallel
according to the DVS 2205-2 technical code with Supplements
2, 3 and 6.
– The execution of the tanks and of the collecting vessels complies
with the DVS 2205-2 technical code with Supplements 2, 3 and 6.
2 Design
Tanks without collecting vessels are anchored to the foundation
directly in order to thus secure them against any shifting or tilting
as a result of the horizontal earthquake forces.
Tanks in the collecting vessel cannot be anchored to the foundation directly but the tank must be secured.
The collecting vessel is secured against the lateral shifting of the
tank with blocks which, uniformly distributed around the circumference of the tank bottom, are welded with the bottom of the collecting vessel on three sides.
The securing against tilting can be carried out in two ways:
1. Using bulkheads which, uniformly distributed around the circumference, are welded with a reinforcing ring in the upper region
of the tank.
These bulkheads bear the global supporting force from the tank
to the ring-stiffened collecting vessel via compressive forces.
2. Using a ring plate with a collar.
The ring plate is welded on in the upper region of the tank.
The collar grips over the upper edge of the collecting vessel.
3 Calculation variables
a
ag
ah
av
A1K
mm
m/s²
m/s²
m/s²
–
A2I
–
AErd
AR
N
mm²
AS
mm²
Thickness of the weld of the blocks
Soil acceleration
Horizontal acceleration of the tank
Vertical acceleration of the tank
Reduction factor for the influence of the
specific toughness for a wall temperature
effective for a short time
Reduction factor for the medium in the case
of the proof of the stability
Horizontal force of the lower support
Cross-sectional area of the open ring crosssection
Shear area of the substitute beam
This publication has been drawn up by a group of experienced specialists working in an honorary capacity and its consideration as an important source of information
is recommended. The user should always check to what extent the contents are applicable to his particular case and whether the version on hand is still valid.
No liability can be accepted by the Deutscher Verband für Schweißen und verwandte Verfahren e.V., and those participating in the drawing up of the document.
DVS, Technical Committee, Working Group "Joining of Plastics"
Orders to: DVS Media GmbH, P. O. Box 10 19 65, 40010 Düsseldorf, Germany, Phone: + 49(0)211/1591- 0, Telefax: + 49(0)211/1591-150
249
Page 2 to DVS 2205-2 Supplement 4
ASW,i
mm²
bBlo
BErd
bPr
bSch
d
dA,j
dW
mm
N
mm
mm
mm
mm
mm
ET°C
K
E20°C
K
E20°C
L
ei
Shear area of the course i in the collecting
vessel
Width of the blocks
Horizontal force of the upper support
Width of the anchor claw
Width of the bulkheads
Inside diameter of the cylinder
Outside diameter of the socket j
Inside diameter of the collecting vessel
N/mm² Short-time elastic modulus at T°C
N/mm² Short-time elastic modulus at 20°C
GB
GD
N
GT°C
K
GZ
GZ,W
h
hA,j
HBlo
HErd
HF
hF
hF,i
hg
HGA
HSch
hSt
hW,i
hW,i-1
I
IW,i
kf
Kvorh
K,d
*
K K,d
lBlo
lSch
MErd
MErd,B
MErd,B,i
MErd,i
MErd,j
250
Nmm
Earthquake moment at the height x for the
collecting vessel
Nmm
Earthquake moment at the lower edge of the
MErd,W,i
course i of the collecting vessel
mK
kNs²/m Mass of the roof load
–
Number of blocks
nBlo
–
Number of bulkheads
nSch
Nj,d
N
Dimensioning value of the global normal
force at the height of the socket j
NFüllung
N
Dimensioning value of the global compresR,d
sive force resulting from the filling in the
supporting ring
N/mm² Partial vacuum effective for a long time
pu
pü
N/mm² Overpressure effective for a long time
q
–
Behaviour coefficient
r
mm
Cylinder radius of the tank
S
–
Subsoil parameter
s1/3
mm
Wall thickness of the cylinder at the lower
third point of the tank
sB
mm
Wall thickness of the tank bottom
mm
Wall thickness of the collecting vessel bottom
sB,W
sj
mm
Wall thickness of the cylinder at the height of
the socket j
sKr
mm
Wall thickness of the ring plate and of the
collar
mm
Wall thickness of the highest course
s1
mm
Thickness of the bulkheads
sSch
sZ,i
mm
Wall thickness of the cylinder course i
mm
Wall thickness of the reinforcing shell
sz,0
T
s
Vibration period
TA
°C
Mean ambient temperature (according to
Miner, see the DVS 2205-1 technical code)
°C
Highest ambient temperature
TAK
s
Vibration period of a bending beam which
TBieg,mK
does not have any mass, is clamped on one
side and has a head mass
TF
s
Vibration period of the filled tank
°C
Mean media temperature (according to
TM
Miner, see the DVS 2205-1 technical code)
°C
Highest media temperature
TMK
TSchub,mK s
Vibration period of a shear beam which
does not have any mass, is clamped on one
side and has a head mass
mm/N Bending deformation of the collecting vessel
wBieg
at the height of the support for 1 N
mm/N Shear deformation of the collecting vessel at
wSchub
the height of the support for 1 N
WR
mm³
Resistance moment of the open ring crosssection
x
mm
Height of the section under consideration
above the tank bottom
z
–
Number of anchors
mm
Distance between the centres of gravity of
zS
the open ring and of the cylinder axis
–
Auxiliary variable
i
–
Auxiliary variable
j
R
–
Factor for the axial stability of the supporting
ring
–
Reinforcing coefficient of the spectrum
0
acceleration

–
Damping correction coefficient
A,i
–
Utilisation of the axial stability in the course i
–
Utilisation of the axial stability next to the
A,j
socket j
F1
–
Partial safety coefficient of the effect
(dead load and filling)
R&D INTAKE MANIFOLDS
N/mm² Long-time elastic modulus at 20°C
–
Eccentricity of the wall thicknesses of the
courses
–
Reduction factor for the eccentricity
m/sec² Acceleration due to gravity
N
Dead load of the additional weight on the
roof
N
Dead load of the bottom
f,i
g
GA
MErd,W
Dead load of the roof
N/mm² Shear modulus in the case of short-time
stresses for T°C
N
Dead load of the cylinder of the tank
N
Dead load of the cylinder of the collecting
vessel
mm
Height of the substitute beam
mm
Height of the axis of the cut-out j
N
Horizontal force in the block
N
Total horizontal force resulting from the
earthquake
N
Horizontal mass force resulting from the filling
mm
Filling height
mm
Filling height, measured from the lower edge
of the course i
mm
Overall height of the tank
N
Horizontal mass force resulting from GA
N
Horizontal force in the bulkhead
mm
Height of the upper support above the tank
bottom
mm
Height of the course i in the collecting vessel
mm
Height of the course i-1 in the collecting
vessel
4
Moment of inertia of the substitute beam
mm
mm4
Moment of inertia of the course i in the
collecting vessel
–
Concentration factor according to Supplement 7
N/mm² Dimensioning value of the stresses effective
for a short time
N/mm² Dimensioning value of the creep strength in
the case of 10-1 hours
mm
Length of the blocks
mm
Length of the bulkheads
Nmm
Earthquake moment at the height x for the
tank without a collecting vessel
Nmm
Earthquake moment at the height x for the
tank in the collecting vessel
Nmm
Earthquake moment at the lower edge of the
course i of the tank in the collecting vessel
Nmm
Earthquake moment at the lower edge of the
course i of the tank without a collecting
vessel
Nmm
Earthquake moment at the height of the
socket j
Page 3 to DVS 2205-2 Supplement 4
F2
–
F3
–
F4
–
I
–
IE
–
M
–


F
G,j
–
1/s
g/cm³
N/mm²
vorh
i,d
N/mm²
vorh
j,d
N/mm²
 K,i,d
N/mm²
 K,j,d
N/mm²
Partial safety coefficient of the effect
(pressures and wind)
Partial safety coefficient of the effect
(reducing dead load)
Partial safety coefficient of the effect
(earthquake)
Weighting coefficient according to the
DVS 2205-2 technical code
Significance coefficient according to
DIN 4149, Table 3 (called I there)
Partial safety coefficient of the resistance/
stressability
Reduction factor for splashing
Angular frequency
Density of the filling medium
Stresses in the cylinder resulting from the
dead weight at the height of the socket j
Stresses existing at the lower edge of the
course i
Dimensioning value of the total stresses in
the cylinder at the height of the socket j
Dimensioning value of the axial buckling
stress in the course i
Dimensioning value of the axial buckling
stress next to the socket j
T°C
 1.5  E K   s 1/3
------------------------------------------  10 9
F  hF
 = 2    -----------------------------------------------------------------------------------hF 2 h
2  r   0.157   ------ + -----F- + 1.49
 r


r
1/s
(2)
R&D INTAKE MANIFOLDS
4 Tank acceleration
TF =
F  hF
--------------------------------------------------------2r
T°C
9
 1.5  E K   s 1/3  10
hF 2 h
s
(3)
  0.157   ------ + -----F- + 1.49
 r


r
In so far as a platform or a stirrer is arranged on the roof, it is necessary to provide proof of its influence on the vibration period.
The vibration period of a massless bending beam with the moment
of inertia:
3
I =   r  s 1/3
mm4
(4)
and the head mass:
GA
m K = ---------------------1,000  g
kNs²/m
(5)
follows from:
4.1 Horizontal tank acceleration
3
The horizontal tank acceleration ah of the tank is established on
the basis of DIN 4149 while disregarding the splashing of the medium in the tank. If the filling height is less than the tank diameter,
it is advisable to take account of the splashing. This can be done
approximately by reducing the stresses caused by the horizontal
tank acceleration with the factor:
h
 = 0.5  1 + -----F- 

d
with s1/3 as the cylinder wall thickness at the lower third point.
Because of the very short effective duration, the dynamic elastic
modulus is raised by 50 % compared with the short-time modulus. This results in the vibration period via the relationship:
2
T = ----------- to

(1)
The earthquake zone of the installation location is indicated on
Fig. 2 in DIN 4149 and in lists [3] in which the earthquake zone is
specified for the local authorities in a few federal states. The horizontal soil acceleration ag is thus defined according to Table 2 in
DIN 4149.
The geological subsoil class of the installation location is also
indicated on Fig. 3 in DIN 4149 and in the lists [3].
The foundation soil class must be specified by the operator of the
tanks. If no assured information about the foundation soil is available, the foundation soil class C must be applied.
According to DIN 4149, the horizontal acceleration ah results with
the spectrum according to Fig. 4 in conjunction with Table 4 on
the assumption of 5 % viscous damping, i.e. ß0 = 2.5 and  = 1,
and the significance coefficient IE. At least IE = 1.2 must be set for
tanks for the storage of water-endangering fluids. The behaviour
coefficient must be applied with q = 1.5.
The vibration period T of the system is needed for the determination
of the spectrum value.
4.2 Vibration period
4.2.1 Tank without a collecting vessel
The tank is represented as a beam which is clamped at the bottom,
is located at the height hF and has the mass per unit area resulting from the filling (the dead mass of the tank may be disregarded).
According to Rammerstorfer [1], Equations (11) and (12) as well
as Equation (A.24) in DIN EN 1998-4, the angular frequency  of
this systems can be established from:
mK  h
T Bieg,m = 2    -----------------------------------------T°C
K
3   1.5  E K   l
s
(6)
The vibration period of a massless shear beam with the shear area:
A S =   r  s 1/3
mm²
(7)
and the head mass mK follows from:
mK  h
T Schub,m = 2    ----------------------------------------T°C
K
 1.5  G K   A S
T°C
with G K
T°C
= 0.36  E K
N/mm²
s
(8)
The vibration period which takes account of all the influences follows
from:
T =
2
2
T F2 + T Bieg,m + T Schub,m
K
K
s
(9)
The thickness s1/3 of a graduated cylinder follows from (numbering
of the n courses beginning at the top):
n
hi si
- – s1
4  ------------------n
hi

i=1
= ---------------------------------------3
i=1
s 1/3
mm
(10)
4.2.2 Tank with a collecting vessel
The vibration period of this coupled system can only be established
exactly with an EDP-assisted calculation but, as a substitute, the
horizontal tank acceleration ah can be calculated on the safe side
with the plateau value of the spectrum without establishing the
vibration period.
For slender tanks or in the case of installation in the earthquake
region with the geological subsoil class R, it is more economically
viable to establish the vibration period with the following equation
and to determine the horizontal acceleration ah with the relevant
spectrum value. The prerequisite for the following approximation
is horizontal coupling between the tank and the collecting vessel
at the height hSt.
251
Page 4 to DVS 2205-2 Supplement 4
3
2
2
   r    hF
h 
T = 2     ---------------------------------+ m K  --------    w Bieg + w Schub 
9
2
2
h
 2.5  h St  10
St 
with w Bieg =
s (11)
2
HF  hF – x 
MErd,B = -------  ---------------------- + H G   h g – x  – B Erd   h St – x  Nmm (20)
A
hF
2
R&D INTAKE MANIFOLDS
h w,i
-----------------------------------------------T°C
3   1.5  EK   I w,i
n

i=1
If hF – x < 0, then the first term is zero.
If hSt – x < 0, then the third term is zero.
2
2
  3  h w,i -1 + 3  h w,i -1  h w,i + h w,i 
mm/N (12)
w Schub =
n

i=1
h w,i
----------------------------------------------T°C
 1.5  GK   A SW,i
5.3 Collecting vessel
The collecting vessel is subjected to loads by the upper supporting
force BErd.
where h w,0 = 0
and
The earthquake moment of the cylinder at the height x above the
tank bottom results from:
mm/N
(13)
The earthquake moment of the cylinder at the height x above the
bottom of the collecting vessel results from:
4.3 Vertical tank acceleration
M Erd,W = B Erd   h St – x 
The vertical tank acceleration av is established on the safe side
with the plateau value of the spectrum and the dimensioning value
of the vertical acceleration 0.7 x ag. This results in:
6 Proof
0
a v = 0.7  a g   IE  S  ------ = 1.167  a g   IE  S
q
(14)
It is necessary to provide all the proof in the DVS 2205-2 technical
code with Supplements 2, 3 and 6.
where S is the subsoil parameter according to Table 5 in DIN 4149.
In addition, the following proof must be provided for earthquakes
(in so far as the components are present):
5
m/s²
The crucial stresses result from the horizontal mass force (mass
times acceleration) HF of the filling in the completely filled condition.
2
H F =  F    r  h F  a h  10
6
N
(15)
The point of attack of this force must be applied at the centre of
gravity of the filling.
In the case of the roof load GA, the horizontal mass force results
from:
GA
H G = -------  a h
A
g
N
(16)
The point of attack of this force must be applied at the centre of
gravity of the roof load.
5.1 Tank without a collecting vessel
The cylinder is subjected to the line load HF/hF and the head load
HGA.
The earthquake moment of the cylinder at the height x above the
tank bottom results from:
2
HF  hF – x 
= -------  ---------------------- + H G   h g – x 
A
hF
2
Nmm
(17)
The approach with hg (the overall height of the tank) as the position
of the centre of gravity of GA is accurate enough.
5.2 Tank in the collecting vessel
The tank is held at the bottom and at the top; the distance between
these supports is hSt.
The supporting forces of the tank in the collecting vessel are:
at the bottom:
A Erd
252
hF
H F  ------ + H G  h g
A
2
= ---------------------------------------------h St
– Proof of the axial stability next to sockets in the cylinder
– Proof of the anchoring of the tank and of the collecting vessel
– Proof of the shear stress in the parallel welds of the blocks
– Proof of the stability of the bulkheads
– Proof of the weld between the ring plate and the collar
In the case of installation in German earthquake regions, it is not
necessary to provide any further proof for the increased stresses
caused by the vertical acceleration; this only applies to flat-bottomed
tanks.
7
Provision of proof
The proof is provided according to the partial safety concept. The
partial safety coefficient for the stresses induced by earthquakes is:
 F4 = 1.0 .
Proof for earthquake stresses must be provided for the wall temperatures resulting in the component under consideration on the
assumption of the highest media temperature TMK and the highest
ambient temperature TAK.
7.1 Proof of the axial stability in the two-shell region
In both shells, the existing axial compressive membrane stress
equals:
 0,d
N
(18)
(22)
Stresses resulting from wind loads, from snow loads and from
pressures effective for a short time are not combined with earthquake stresses.
vorh
h
H F   h St – -----F- – H G   h g – h St 

A
2
= -----------------------------------------------------------------------------------h St
and at the top:
B Erd
(21)
– Proof of the axial stability at the lower edge of all the courses of
the tank and of the collecting vessel
Stresses
M Erd
Nmm
GD + GZ + kf  GA
pu  r
 F4 a v

-  ----- +  F2  -----------=   F1  ---------------------------------------------   1 + ------
2r
2
 F1 g 

M Erd,0 
1
+  F4  ------------------------2-   ------------------------1.2    r  s Z,n + s Z,0
(23)
The system only fails if the thicker shell becomes unstable since
the thinner shell is supported by the thicker shell.
N
(19)
The buckling stress k,n,d is calculated with sZ,n according to
Equations (25) to (27).
Page 5 to DVS 2205-2 Supplement 4
In this respect, the dimensioning value of the critical buckling
stress in the cylinder at the socket j is:
The utilisation is:

vorh

A 2I   I 
0,d
 = ---------------------------------------- k,n,d
(24)
8.1 Axial stability of the cylinder
For every course i, the axial compressive stress existing at the
lower edge is established from the dead weight (can also be disregarded in general), the long-time partial vacuum pu and the
earthquake and is validated with the buckling stress k,i,d.
vorh
 F4 a v
pu  r
- +  F4
=  F1   G,i   1 + -------  ----- +  F2  --------------
g

2s
F1
M Erd,i
 ------------------------------------2
1.2    r  s Z,i
N/mm²
(25)
T°C
s Z,i
EK
*
=  i  0.62  f ,i  --------------  --------  K K,d
M
r
N/mm²
(26)
0.70
 i = ------------------------------------------------------------20°C
r
E

K -  1 + ---------------------
------------20°C 
100  s Z,i 
EL
with
(27)
(28)
where ei is the eccentricity to the thicker of the two neighbouring
courses in the case of a graduated cylinder if this itself is thicker
than the course under consideration.
The calculation temperature must be applied with TMK.
The following condition must be complied with for every course i:
 A,i

vorh
A 2I   I 

i,d
= ------------------------------------------  1
 k,i,d
(29)
It is not necessary to provide any proof of the jacket pressure
stability or the interaction since the filled tank is subjected to tensile
hoop stresses.
8.2 Axial stability next to sockets
The compressive stresses in the cylinder resulting from the dead
weight and the partial vacuum at the height of every socket j are
converted into a global normal force and are applied together
with the earthquake moment at this position on the weakened
cross-section (open ring). For this purpose, it is necessary to determine the area AR, the distance away from the centre of gravity
of the tank axis zS and the resistance moment WR of the ring crosssection. Paying attention to the misalignment of the centroidal axis,
it is necessary to calculate the axial compressive stresses next to
the opening. In this respect, the bending stresses may be divided
by 1.2.
pu  r
 F4 a v
-  ----- +  F2  ------------ 
=   d  s j    F1   G,j   1 + ------

2s
 F1 g 
N j,d
N (30)
The dimensioning value of the existing stresses follows with:
vorh
 j,d
z S   F4  M Erd,j
1
= N j,d   ------- + --------------------- + --------------------------A

1.2  W R
R 1.2  W R
N/mm²
(31)
 A,j
A 2I   I 
= ---------------------------------  1
 k,j,d
d A,j
0.45
or  j = --------------------------------------------------------- for --------------  3.5
20°C
r  sj
r
E K  1 + -----------------
-------------- 
20°C
100  s j 
EL
(34)
(35)
8.3 Anchoring
The tank must be anchored. At least four anchors are required
(z  4).
TMK is applied as the calculation temperature.
The following condition must be complied with:
2
a
4   F4  M Erd  F2  p ü    d
1
+ ------------------------------------- –  F3   1 – -----v   G D + G Z   ---------------------------------
z
d
4
g
-----------------------------------------------------------------------------------------------------------------------------------------------------------------  1
*
K K,d
 b Pr + s B   s B  -------------------------2  A 1K   I
The claw force to be absorbed is located in the numerator and
the absorbable claw force resulting from the shear stress in the
weld in the denominator.
In addition, it must be ensured that the entire horizontal force
HErd = AErd + BErd is reliably guided into the foundation.
9 Proof of the tank in the collecting vessel
The proof is provided for those design elements of the upper and
lower supports which are portrayed on Figs. 1 and 2. Proof of
other designs of the supports must be provided accordingly.
9.1 Axial stability
Due to the mass forces of the filling, the tank which is held at the
bottom and at the top is subjected to stresses like those on a
beam flexible on both sides. The greatest moment MErd,B,i must
be determined for every course i. The moment at the upper edge
is crucial for courses whose upper edge is located below half the
span hSt. The moment at the lower edge is crucial for the courses
whose lower edge is located above half the span hSt. The moment
at x = hSt/2 determines the central course.
In analogy to Equations (25) to (29), the axial stability of every
course is proven with MErd,B,i instead of MErd,i.
9.2 Lower support
The lower support is carried out using nBlo blocks which are
welded on to the bottom of the collecting vessel in the radial
direction. The thickness of the weld is a = 0.7  s B mm, with sB
as the thickness of the tank bottom. The force AErd is guided into
the baseplate of the collecting vessel via these blocks and into
the foundation via suitable horizontal anchors. The block subjected
to the highest load must bear a radially directed horizontal force of:
4  A Erd
H Blo = -----------------n Blo
The following condition must be complied with:
vorh
 j,d
d A,j
for --------------  3.5
r  sj
(36)
e
f ,i = 1.5 – -------i-  1
s Z,i
and
0.65
with  j = --------------------------------------------------------20°C
r
EK
--------------  1 + ------------------ 
20°C
100  s j
EL
(33)
TMK must be applied as the dimensioning temperature.
Z,i
The buckling stress may be established according to the following
equation:
 k,i,d
N/mm²
R&D INTAKE MANIFOLDS
8 Proof of the tank without a collecting vessel
 i,d
T°C
sj
EK
 k,j,d =  j  0.62  ------------  ---M r
(32)
N
(37)
The required length of the blocks results from the proof of the
shear stress of the two parallel welds:
253
Page 6 to DVS 2205-2 Supplement 4
H Blo
 F4  -----------   I  A 1K
2
I Blo = ---------------------------------------------K K*
--------------  0.7  s B
2  M
mm
(38)
T MK + 3  T AK
---------------------------------- is applied as the calculation temperature but min.
4
50°C in the case of direct solar radiation.
R&D INTAKE MANIFOLDS
10.2 Anchoring
The calculation temperature must be applied with TMK.
The required width of the blocks follows from the proof of the
pressing:
b Blo = 0.7  I Blo
mm
(39)
As far as the design is concerned, the front transverse weld is
executed in the same thickness a = 0.7  s B mm.
9.3 Upper support
As far as the design is concerned, the upper support can be executed as:
– Bulkheads which are located between two reinforcing rings
and are subjected to compressive stresses
– A ring plate which has a collar and is subjected to tensile stresses
The collecting vessel must be anchored. At least four anchors
are required (z  4).
T MK + 3  T AK
----------------------------------- is applied as the calculation temperature but min.
4
50°C in the case of direct solar radiation.
The following condition must be complied with:
4   F4  M Erd,W
a
1
-------------------------------------- –  F3   1 – -----v  G Z,W  --
z
g
dW
------------------------------------------------------------------------------------------------------------1
*
K K,d
 b Pr + s B,W   s B,W  -------------------------2  A 1K   I
(45)
The claw force to be absorbed is located in the numerator and
the absorbable claw force resulting from the shear stress in the
weld in the denominator.
9.3.1 Bulkheads
In addition, it must be ensured that the entire horizontal force
HErd = AErd + BErd is reliably guided into the foundation.
The bulkhead subjected to the highest load amongst the nSch
bulkheads must bear the compressive force:
11
H Sch
4  B Erd
= -----------------n Sch
N
(40)
The required thickness of the bulkheads results from the proof of
the buckling on the assumption of clamping on one side (the
buckling length is twice the bulkhead length lSch).
Bibliography
Set of rules
DIN 4149
Structures in German earthquake regions –
Load assumptions, dimensioning and execution
of customary superstructures
DIN EN 1998-4
Eurocode 8: Designing of structures against
earthquakes – Part 4: Silos, tank structures and
pipelines
2
s Sch =
3
12   F4  H Sch   2  l Sch    l
-----------------------------------------------------------------------T°C
2 EK
-  b Sch
  ----------M
mm
(41)
T MK + T AK
The calculation temperature must be applied with --------------------------- .
2
9.3.2 Ring plate with a collar
As far as the design is concerned, the thickness of the ring plate
and of the collar must be chosen as follows:
dW
s Kr  ---------300
(42)
The utilisation in the weld between the ring plate and the collar
results from:
 F4  B Erd   l  A 1K
 = ------------------------------------------------------K K*
dW
-  fZ
 s Kr  ------------  ------2
2  M
(43)
T MK + 3  T AK
----------------------------------- is applied as the calculation temperature but min.
4
50°C in the case of direct solar radiation.
10
Proof of the collecting vessel
10.1 Axial stability
For every course i, the axial compressive stress existing at the
lower edge is established from the dead weight and the earthquake and is validated with the buckling stress k,i,d.
vorh
 i,d
M Erd,W,i
 F4 a v
-  ----- +  F4  ------------------------------------=  F1   G,i   1 + ------2

 F1 g 
1.2    r  s Z,i
(44)
The proof of the axial stability of every course is provided in analogy
to Equations (25) and (26).
254
For further standards, see the DVS 2205-2 technical code, Section
5.2.
Literature
[1] Rammerstorfer, F. G., K. Scharf and F. D. Fischer: Earthquakeproof dimensioning of cylinder shells and fluid-filled tank structures.
[2] Tuercke, H.: On the stability of tanks made of thermoplastics.
DIBt Communications, No. 5/1995.
[3] Assignment of the earthquake zones and subsoil classes
www.dibt.de/Data/TB/Zuordnung_der_Erdbebenzonen.xls
Reports from the Institute of Lightweight Construction and Aircraft
Construction, TU Vienna, No. ILFB - 2 / 9.
Page 7 to DVS 2205-2 Supplement 4
Appendix: Design-related details
Bulkheads distributed
around the circumference,
thickness sSch and height
hSch according to the
structural analysis
Closed ring
Closed ring
R&D INTAKE MANIFOLDS
Gap
Blocks, three sides welded,
length lB and width bB
according to the structural
analysis
Assembly aid
Block
Gap
Figure 1.
Variant with bulkheads.
255
Page 8 to DVS 2205-2 Supplement 4
R&D INTAKE MANIFOLDS
Gap
Blocks, three sides welded,
length lB and width bB
according to the structural
analysis
Assembly aid
Block
Gap
Figure 2.
256
Variant with a ring plate and a collar.
February 2013
DVS – DEUTSCHER VERBAND
FÜR SCHWEISSEN UND
VERWANDTE VERFAHREN E.V.
Calculation of tanks and apparatus
made of thermoplastics –
Vertical round non-pressurised tanks –
Vertical-skirt tanks in earthquake regions
Technical Code
DVS 2205-2
R&D INTAKE MANIFOLDS
Supplement 5
Reprinting and copying, even in the form of excerpts, only with the consent of the publisher
This Supplement 5 to the DVS 2205-2 technical code was elaborated by DVS-AG W4.3b ("Structural designing / apparatus engineering").
Contents:
2 Design
1
2
3
4
4.1
4.2
4.3
4.4
5
5.1
5.2
6
7
8
8.1
8.2
8.3
8.4
8.5
8.6
8.7
9
Vertical-skirt tanks are always installed without collecting vessels.
1
Scope of application
Design
Calculation variables
Tank acceleration
Horizontal tank acceleration
Vibration period for the horizontal vibration
Vertical tank acceleration
Vibration period for the vertical vibration
Stresses
From horizontal tank acceleration
From vertical tank acceleration
Proof
Provision of proof
Dimensioning of the vertical-skirt tank
Axial stability of the cylinder
Axial stability of the skirt
Axial stability next to sockets in the cylinder
Axial stability next to sockets in the skirt
Axial stability of the supporting rings
Buckling stability of the gussets
Anchoring
Bibliography
Scope of application
The following design and calculation rules apply to vertical, cylindrical vertical-skirt tanks which are fabricated from thermoplastics
in the factory, have conical bottoms or sloping bases and are
intended for installation in a German earthquake region.
For the application of this supplement, it is necessary to satisfy
the following prerequisites:
– The tank may be installed inside or outside buildings. Its foundation must be in direct contact with the earth. In the event of
installation on building ceilings, platforms or similar structures,
separate proof is required and must take account of the vibration
behaviour of the entire system.
– The tanks are dimensioned in parallel according to the DVS
2205-2 technical code with Supplements 3 and 7 or 9.
– The execution of the tanks complies with the DVS 2205-2 technical code with Supplements 3 and 7 or 9.
The vertical-skirt tanks dealt with in this supplement are anchored
to the foundation directly in order to thus secure them against any
shifting or tilting as a result of the horizontal earthquake forces.
3 Calculation variables
a
mm
ag
ah
av
A1K
m/s²
m/s²
m/s²
–
A2I
–
AR
mm²
AS
bPr
d
dA,j
dA,ZarS
mm²
mm
mm
mm
mm
ET°C
K
E20°C
K
E20°C
L
ei
Smallest free space underneath the sloping
base
Soil acceleration
Horizontal acceleration of the tank
Vertical acceleration of the tank
Reduction factor for the influence of the
specific toughness for a wall temperature
effective for a short time
Reduction factor for the medium in the case
of the proof of the stability
Cross-sectional area of the open ring crosssection
Shear area of the substitute beam
Width of the anchor claw
Inside diameter of the cylinder
Outside diameter of the socket j
Outside diameter of the socket in the skirt
N/mm² Short-time elastic modulus at T°C
N/mm² Short-time elastic modulus at 20°C
GB
N/mm² Long-time elastic modulus at 20°C
–
Eccentricity of the wall thicknesses of the
courses
–
Reduction factor for the eccentricity
m/sec² Acceleration due to gravity
N
Dead load of the additional weight on the
roof
N
Dead load of the bottom
Gges
N
GZ
N/mm² Shear modulus in the case of short-time
stresses for T°C
N
Dead load of the cylinder of the tank
f,i
g
GA
GT°C
K
Dead load of the vertical-skirt tank
This publication has been drawn up by a group of experienced specialists working in an honorary capacity and its consideration as an important source of information
is recommended. The user should always check to what extent the contents are applicable to his particular case and whether the version on hand is still valid.
No liability can be accepted by the Deutscher Verband für Schweißen und verwandte Verfahren e.V., and those participating in the drawing up of the document.
DVS, Technical Committee, Working Group "Joining of Plastics"
Orders to: DVS Media GmbH, P. O. Box 10 19 65, 40010 Düsseldorf, Germany, Phone: + 49(0)211/1591- 0, Telefax: + 49(0)211/1591-150
257
Page 2 to DVS 2205-2 Supplement 5
h
mm
HErd
N
HF
hF
hF*
hg
H GA
hR
hS
hZar
I
Kvorh
K,d
N
mm
mm
mm
N
mm
mm
mm
mm
mm4
N/mm²
*
K K,d
N/mm²
K RFüllung
N/mm²
K Zar
Füllung
N/mm²
k
MErd(x)
–
Nmm
MErd,B,i
Nmm
MErd,i
Nmm
MErd,j
Nmm
m
mK
N Erd,j,d
–
kNs²/m
N
Nj,d
N
pu
pü
püK
q
r
rR
S
s
N/mm²
N/mm²
N/mm²
–
mm
mm
–
mm
s1
s1/3
mm
mm
sB
sj
mm
mm
suB
sZ,i
TA
mm
mm
°C
TAK
T Bieg,mK
°C
s
TF
Th
s
s
max
h Zar
258
Height of the substitute beam for the consideration of roof loads
Total horizontal force resulting from the
earthquake
Horizontal mass force resulting from the filling
Filling height
Height of the substitute beam
Overall height of the tank
Horizontal mass force resulting from GA
Height of the largest supporting ring
Height of the buckling field
Height of the skirt
Greatest height of the skirt
Moment of inertia of the substitute beam
Dimensioning value of the stresses effective
for a short time
Dimensioning value of the creep strength in
the case of 10-1 hours
Compressive stress in the supporting ring
resulting from the filling
Compressive stress in the skirt resulting
from the filling
Auxiliary variable
Earthquake moment at the height x for vertical-skirt tanks
Earthquake moment at the lower edge of the
course i of the tank in the collecting vessel
Earthquake moment at the lower edge of the
course i of the vertical-skirt tank
Earthquake moment at the height of the
socket j
Number of gussets
Mass of the roof load
Dimensioning value of the global normal
force at the height of the socket j resulting
from vertical acceleration
Dimensioning value of the global normal
force at the height of the socket j
Partial vacuum effective for a long time
Overpressure effective for a long time
Short-time overpressure
Behaviour coefficient
Cylinder radius of the tank
Radius of the largest supporting ring
Subsoil parameter
Wall thickness of the bottom, of the lowest
cylinder course, of the rings and of the skirt
Wall thickness of the highest course
Wall thickness of the cylinder at the lower
third point of the substitute beam
Wall thickness of the tank bottom
Wall thickness of the cylinder at the height of
the socket j
Wall thickness of the bottom
Wall thickness of the cylinder course i
Mean ambient temperature (according to
Miner, see the DVS 2205-1 technical code)
Highest ambient temperature
Vibration period of a bending beam which
does not have any mass, is clamped on one
side and has a head mass
Vibration period of the filled tank
Vibration period of the horizontal vibration
TM
°C
TMK
TSchub,mK
°C
s
Tv
W
s
mm³
WR
mm³
x
mm
z
zS
–
mm
B
i
j
°
–
–
R
–
Zar
ZarS
–
–

0
–
–

A,i
A,j
–
–
–
A,R
A,S
–
–
A,Zar
F1
–
–
F2
–
F3
–
F4
–
I
–
IE
–
M
–


F
e
G,i
–
1/s
g/cm³
N/mm²
N/mm²
G,j
N/mm²
G,Zar
N/mm²
Mean media temperature (according to
Miner, see the DVS 2205-1 technical code)
Highest media temperature
Vibration period of a shear beam which
does not have any mass, is clamped on one
side and has a head mass
Vibration period of the vertical vibration
Resistance moment of the skirt infilled with
gussets in order to establish the compressive stresses on the highest buckling field of
the gussets
Resistance moment of the open ring crosssection
Height of the section under consideration
above the foundation
Number of anchors
Distance between the centres of gravity of
the open ring and of the cylinder axis
Inclination angle of the bottom
Factor for the axial stability of the course i
Factor for the axial stability of the socket j in
the cylinder
Factor for the axial stability of the supporting
ring
Factor for the axial stability of the skirt
Factor for the axial stability of the socket in
the skirt
Side ratio of the buckling field
Reinforcing coefficient of the spectrum
acceleration
Damping correction coefficient
Utilisation of the axial stability in the course i
Utilisation of the axial stability next to the
socket j
Utilisation of the axial stability in the ring
Utilisation of the buckling stability in the
gussets
Utilisation of the axial stability in the skirt
Partial safety coefficient of the effect
(dead load and filling)
Partial safety coefficient of the effect
(pressures and wind)
Partial safety coefficient of the effect
(reducing dead load)
Partial safety coefficient of the effect
(earthquake)
Weighting coefficient according to the
DVS 2205-2 technical code
Significance coefficient according to
DIN 4149, Table 3 (called I there)
Partial safety coefficient of the resistance/
stressability
Reduction factor for splashing
Angular frequency
Density of the filling medium
Buckling stress in the gusset
Stresses in the cylinder resulting from the
dead weight at the lower edge of the coruse
i; also encompasses roof loads including the
stress concentration [4]
Stresses in the cylinder resulting from the
dead weight at the height of the socket j
Compressive stress resulting from the dead
weight in the skirt
R&D INTAKE MANIFOLDS
Page 3 to DVS 2205-2 Supplement 5
vorh
i,d
vorh
j,d
k,d
k,i,d
k,j,d
k,R,d
k,Zar,d
k,ZarS,d
vorh
R,d
F
 S,d
pü
 S,d
vorh
 Zar,d
vorh
 ZarS,d
N/mm² Stresses existing at the lower edge of the
course i
N/mm² Dimensioning value of the total stresses in
the cylinder at the height of the socket j
N/mm² Dimensioning value of the buckling stress of
the gusset
N/mm² Dimensioning value of the axial buckling
stress in the course i
N/mm² Dimensioning value of the axial buckling
stress next to the socket j
N/mm² Dimensioning value of the axial buckling
stress of the supporting ring
N/mm² Dimensioning value of the axial buckling
stress of the skirt
N/mm² Dimensioning value of the axial buckling
stress of the skirt next to sockets
N/mm² Dimensioning value of the total stresses in
the supporting ring
N/mm² Dimensioning value of the stresses resulting
from the filling in the gusset
N/mm² Dimensioning value of the stresses resulting
from long-time overpressure in the gusset
N/mm² Dimensioning value of the total stresses in
the skirt
N/mm² Dimensioning value of the total stresses in
the skirt next to sockets
T°C
 1.5  E K   s 1/3
-------------------------------------------  10 9
 F  h F*
- 1/s
 = 2    -----------------------------------------------------------------------------------(1)
h F* 2 h *

2  r  0.157   ------ + -----F- + 1.49
 r


r
with s1/3 as the cylinder wall thickness at the lower third point of
R&D INTAKE MANIFOLDS
h F* . Because of the very short effective duration, the dynamic
elastic modulus is raised by 50 % compared with the short-time
modulus. This results in the vibration period via the relationship
 - to
T = 2
---------
h*F 2 h *
 F  h F*
--------------------------------------------------------  2  r   0.157   ------ + -----F- + 1.49 s
 r


T°C
9
r
 1.5  E K   s 1/3  10
(2)
TF =
In so far as a platform or a stirrer is arranged on the roof, it is necessary to provide proof of its influence on the vibration period.
The vibration period of a massless bending beam with the moment
of inertia:
3
I =   r  s 1/3
(3)
mm4
and the head mass:
GA
m K = ---------------------1,000  g
kNs²/m
(4)
follows from:
3
4 Tank acceleration
4.1 Horizontal tank acceleration
The horizontal tank acceleration ah of the tank is established on
the basis of DIN 4149 while disregarding the splashing of the
medium in the tank.
The earthquake zone of the installation location is indicated on
Fig. 2 in DIN 4149 and in lists [3] in which the earthquake zone is
specified for the local authorities in a few federal states. The
horizontal soil acceleration ag is thus defined according to Table 2
in DIN 4149.
The geological subsoil class of the installation location is also
indicated on Fig. 3 in DIN 4149 and in the lists [3].
The foundation soil class must be specified by the operator of the
tanks. If no assured information about the foundation soil is available, the foundation soil class C must be applied.
According to DIN 4149, the horizontal acceleration ah results with
the spectrum according to Fig. 4 in conjunction with Table 4 on
the assumption of 5 % viscous damping, i.e. ß0 = 2.5 and  = 1,
and the significance coefficient IE. At least IE = 1.2 must be set for
tanks for the storage of water-endangering fluids. The behaviour
coefficient must be applied with q = 1.5.
The vibration period Th of the system is needed for the determination of the spectrum value.
4.2 Vibration period for the horizontal vibration
mK  h
TBieg,m = 2    -----------------------------------------T°C
K
3   1.5  EK   I
s
(h = hg is applicable in a simplifying method)
(5)
The vibration period of a massless shear beam with the shear area:
A S =   r  s 1/3
mm²
(6)
and the head mass mK follows from:
mK  h
T Schub,m = 2    ----------------------------------------T°C
K
 1.5  G K   A S
T°C
GK
with
T°C
= 0.36  E K
s
N/mm²
(7)
That vibration period for the horizontal vibration which takes account
of all the influences follows from:
Th =
2
2
2
TF + T Bieg,m + T Schub,m
K
K
s
(8)
The thickness s1/3 of a graduated cylinder follows from (numbering
of the n + 1 courses beginning at the top; the n + 1th course is
the skirt):
n+1
s 1/3
hi si

i=1
- – s1
4  ------------------n+1
hi

i=1
= --------------------------------------3
mm
(9)
4.3 Vertical tank acceleration
The vertical tank acceleration av is also established on the basis
of DIN 4149. In this respect, the dimensioning value of the soil
acceleration ag according to Table 2 in DIN 4149 must be decreased by the factor 0.7. The spectrum and the coefficients correspond to those which are used for the determination of the horizontal acceleration (Section 4.1).
The tank is represented as a
beam which is clamped at the bottom,
*
is located at the height hF = hF – r  tanB + hZar and has the
mass per unit area resulting from the filling (the dead mass of the
tank may be disregarded). In the region of the skirt as well, this
mass per unit area is applied in a simplifying method.
The vibration period Tv of the vertical vibration of the system is
needed for the determination of the spectrum value.
According to Rammerstorfer [1], Equations (11) and (12) as well
as Equation (A.24) in DIN EN 1998-4, the angular frequency  of
this system can be established from:
The vibration period of a vertical-skirt tank with a conical bottom
or a sloping base cannot be described with simple formulae. The
vertical tank acceleration av is therefore established on the safe
4.4 Vibration period for the vertical vibration
259
Page 4 to DVS 2205-2 Supplement 5
side with the plateau value of the spectrum and the dimensioning
value of the vertical acceleration 0.7 x ag. This results in:
0
a v = 0.7  a g   IE  S  ------ = 1.167  a g   IE  S
q
m/s²
(10)
Stresses resulting from wind loads, from snow loads and from
pressures effective for a short time are not combined with earthquake stresses.
Proof for earthquake stresses must be provided for the wall temperatures resulting in the component under consideration on the
assumption of the highest media temperature TMK and the highest
ambient temperature TAK.
R&D INTAKE MANIFOLDS
where S is the subsoil parameter according to Table 5 in DIN 4149.
5
Stresses
Stresses resulting from horizontal acceleration are directly added to
the stresses resulting from vertical acceleration. This is located on
the safe side.
5.1 From horizontal tank acceleration
The crucial stresses result from the horizontal mass force (mass
times acceleration) of the filling in the completely filled condition.
r  tan
2
6
H F =  F    r   h F* – h Zar + ---------------------B-  a h  10


3
N
(11)
The point of attack of this force must be applied at the centre of
gravity of the filling.
In the case of the roof load GA, the horizontal mass force results
from:
GA
H G = -------  a h
A
g
N
(12)
The point of attack of this force must be applied at the centre of
gravity of the roof load.
In order to establish the earthquake moment at the height x
above the foundation, the entire length of the substitute beam is
subjected to the line load  F    r 2  a h  10 6 and the head load
HGA in a simplifying method.
The earthquake moment of the cylinder at the height x above the
tank bottom results from:
2
 h F* – x 
M Erd (x) =  F    r  a h  10  ---------------------- + H G   h g – x 
A
2
2
6
Nmm
(13)
The approach with hg (the overall height of the tank) as the position
of the centre of gravity of GA is accurate enough.
5.2 From vertical tank acceleration
8
Dimensioning of the vertical-skirt tank
8.1 Axial stability of the cylinder
For every course i, the axial compressive stress existing at the
lower edge is established from the dead weight of the tank (can
also be disregarded in general), the dead weight of the roof load
and the horizontal and vertical effects of the earthquake and is
validated with the buckling stress k,i,d.
vorh
  i,d
pu  r
 F4 a v
 F4  M Erd,i
=  F1   1 + -------  -----   +  F2  ---------------- + ------------------------------------
2  s Z,i 1.2    r 2  s
 F1 g  G,i
Z,i
N/mm²
(15)
The stress G,i also encompasses the dead weight of the roof
loads including the concentration factor according to [4].
The buckling stress may be established according to the following
formula:
T°C
s Z,i
EK
*
-  K K,d
-  ------ k,i,d =  i  0.62  f ,i  ----------M
r
with
and
N/mm²
(16)
0.70
 i = ------------------------------------------------------------20°C
EK
r
--------------  1 + ---------------------
20°C 
100  s Z,i 
EL
(17)
e
f ,i = 1.5 – -------i-  1
s Z,i
(18)
The cylinder, the skirt, the bottom and the rings or the gussets
are subjected to higher stresses in the load case resulting from
the filling and the roof load since the effect resulting from the vertical earthquake acceleration av is also added to the effect resulting
from the acceleration due to gravity g.
where ei is the eccentricity to the thicker of the two neighbouring
courses in the case of a graduated cylinder if this itself is thicker
than the course under consideration.
6
The following condition must be complied with for every course i:
The calculation temperature must be applied with TMK.
Proof
It is necessary to provide all the proof in the DVS 2205-2 technical
code with Supplements 3 and 7 or 9.
In addition, the following proof must be provided for earthquakes:
–
–
–
–
–
–
–
260
(19)
8.2 Axial stability of the skirt
Provision of proof
At the lower edge of the skirt, the existing axial compressive stress
is established from the filling, the dead weight of the tank (can
also be disregarded in general), the dead weight of the roof load
and the horizontal and vertical effects of the earthquake and is
validated with the buckling stress k,Zar,d.
vorh
Füllung
 Zar,d = F1   KZar
M Erd (0)
 F4 a v
+  G,Zar    1 + -------  ----- +  F4  ------------------2

 F1 g 
r s
N/mm²
The proof is provided according to the partial safety concept. The
partial safety coefficient for the stresses induced by earthquakes is:
 F4 = 1.0 .
vorh
It is not necessary to provide any proof of the jacket pressure stability or the interaction since the filled tank is subjected to tensile
hoop stresses.
Axial stability at the lower edge of all the cylinder courses
Axial stability at the lower edge of the skirt
Axial stability next to sockets in the cylinder
Axial stability next to sockets in the skirt
Axial stability of the supporting rings
Buckling stability of the gussets
Anchoring
In the case of installation in German earthquake regions, it is not
necessary to provide any proof of the strength for which the proof
of the creep is crucial since the proof of the short-time strength
with the stresses increased by earthquakes is not crucial for the
dimensioning.
7

A 2I   I 

i,d
 A,i = ------------------------------------------  1
 k,i,d
(14)
(20)
The stress G,Zar also encompasses the dead weight of the roof
loads including the concentration factor according to [4]; K Füllung
Zar
according to Equation (4) in DVS 2205-2, Supplement 7 or Equation (8) in DVS 2205-2, Supplement 9.
Page 5 to DVS 2205-2 Supplement 5
The buckling stress may be established according to the following formula:
for hZar/r > 0.5:
T°C
R&D INTAKE MANIFOLDS
EK
*
-  s---  K K,d
 k,Zar,d =  Zar  0.62  ----------M r
for hZar/r  0.5
N/mm²
(21a)
T°C
E
s
r 2 s
*
 k,Zar,d =  Zar  0.62  ------------  ---  1 + 1.5   -----------  ---  K K,d
 h Zar  r
M r
N/mm² (21b)
0.70
 Zar = -------------------------------------------------------20°C
EK
r
--------------  1 + ----------------
20°C 
100  s 
EL
with
(22)
(TMK + TAK)/2 must be applied as the effective temperature of
the skirt but min. 50°C in the case of direct solar radiation.
The following condition must be complied with:
 A,Zar

I 
vorh
Zar,d
= ------------------------------  1
 k,Zar,d
The dimensioning value of the existing stresses follows from:
Füllung
vorh
ZarS,d =   d  s   F1   K Zar
The dimensioning value of the existing stresses follows from:
(TMK + TAK)/2 must be applied as the effective temperature of
the skirt but min. 50°C in the case of direct solar radiation.
The following condition must be complied with:
 I  vorh
ZarS,d
 A,ZarS = -------------------------  1
 k,ZarS,d
for hZar/r > 0.5:
T°C
EK s
*
-  ---  K K,d
 k,Zar,d =  ZarS  0.62  ----------M r
vorh
(25)
In this respect, the dimensioning value of the critical buckling
stress in the cylinder at the socket j is:
with
0.65
 j = --------------------------------------------------------20°C
EK
r
-------------  1 + -----------------
20°C 
100  s j 
E
(26)
for
(27)
L
or
0.45
 j = --------------------------------------------------------20°C
EK
r
--------------  1 + -----------------
20°C 
100  s j 
EL
for
d A,j
------------- 3.5
r  sj
(31a)
N/mm²
(24)
The following condition must be complied with:
d A,j
------------- 3.5
r  sj
N/mm²
for hZar/r  0.5
with
N/mm²
(30)
In this respect, the dimensioning value of the critical buckling
stress in the cylinder at the socket is:
TMK must be applied as the dimensioning temperature.
T°C
s
EK
-  ----j
 k,j,d =  j  0.62  ----------M r
(29)
T°C
F1
A 2I   I   j,d
 A,j = ---------------------------------  1
 k,j,d
N/mm²
EK
s
r 2 s
*
-  ---  1 + 1.5   -----------  ---  K K,d
 k,Zar,d =  ZarS  0.62  ---------- h Zar  r
M r
pu  r
 F4 a v
=  F1   G,j   1 + -------  ----- +  F2  ----------------  2    r  s j

g
2  s Z,j

N/mm²
F1
M Erd,ZarS
zS 
1
- +  F4  ----------------------  ------- + -------A

WR
R WR
according to Equation (4) in DVS 2205-2, Supplement 7
or Equation (8) in DVS 2205-2, Supplement 9.
The stress G,j also encompasses the dead weight of the roof
loads but without a concentration factor since the sockets in the
cylinder are not arranged underneath the introduction points of
the roof loads.
zS
 F4  M Erd,j
1
  --------- + ------------------------  + -------------------------A
 1.2  W
R,j 1,2  W R,j
R,j
 F4 a v
+  G,Zar    1 + -------  ----
g

Füllung
K Zar
The compressive stresses in the cylinder resulting from the dead
weight and the partial vacuum at the height of every socket j are
converted into a global normal force and are applied together
with the earthquake moment at this position on the weakened crosssection (open ring). For this purpose, it is necessary to determine
the area AR, the distance away from the centre of gravity of the
tank axis zS and the resistance moment WR of the ring crosssection. Paying attention to the misalignment of the centroidal
axis, it is necessary to calculate the axial compressive stresses
next to the opening. In this respect, the bending stresses may be
divided by 1.2.
vorh
The stress G,Zar also encompasses the dead weight of the roof
loads but without a concentration factor since the sockets in the
cylinder are not arranged underneath the introduction points of
the roof loads.
(23)
8.3 Axial stability next to sockets in the cylinder
 j,d
8.4 Axial stability next to sockets in the skirt
The compressive stresses in the skirt resulting from the filling, the
dead weight and the vertical effect of the earthquake at the height
of the socket are converted into a global normal force and are
applied together with the earthquake moment at this position on
the weakened cross-section (open ring). For this purpose, it is
necessary to determine the area AR, the distance away from the
centre of gravity of the tank axis zS and the resistance moment
WR of the ring cross-section. Paying attention to the misalignment of the centroidal axis, it is necessary to calculate the axial
compressive stresses next to the opening.
or
 ZarS
0.65
= -------------------------------------------------------20°C
EK
r
--------------  1 + ----------------
20°C 
100  s 
EL
0.45
 ZarS = -------------------------------------------------------20°C
EK
r
--------------  1 + ----------------
20°C 
100  s 
E
for
for
(31b)
d A,ZarS
----------------  3.5 (32)
rs
d A,ZarS
----------------  3.5
rs
(33)
L
8.5 Axial stability of the supporting rings
Proof for the largest ring only is provided with the compressive
pü
stresses according to Sections 6.1.1 KRFüllung and 6.2.1 KR (pü
instead of püK) in the DVS 2205-2 technical code, Supplement 7;
in a simplifying method on the safe side, it is not necessary to exactly assign the various compressive stresses to the individual
rings.
The largest ring has the radius:
(28)
r + --s-   n
 2
r R = -----------------------n+1
mm
(34)
261
Page 6 to DVS 2205-2 Supplement 5
The following applies to indoor and outdoor installation:
TMK must be applied as the effective temperature of the supporting rings but min. (TMK + 35)/2 in the case of outdoor installation.
 F4 a v
vorh
Füllung 
pü
R,d =   F1  KR,d
-  ----- +  F2  KR   2    r R  s
 1 + ------


g

zS 
1
  ------- + -------A
W 
R
R
The utilisation is:
F1
R&D INTAKE MANIFOLDS
N/mm²
(35)
TMK must be applied as the effective temperature of the supporting rings but min. (TMK + 35)/2 in the case of outdoor installation.
The following condition must be complied with for the supporting
ring:
vorh
 A,R
 I   R,d
-1
= ------------------- k,R,d
Remark: A2I is not necessary since there is no wetting with media
(36)
where:
for hR/rR > 0.5:
T°C
EK
s
*
-  -----  K K,d
 k,R,d =  R  0.62  ----------M rR
with
(37a)
T°C
rR  2 s
EK
s
*
-  -----  1 + 1.5   -------  -----  K K,d
=  R  0.62  ---------- hR  rR
M rR
N/mm²
0.65
 R = -------------------------------------------------------20°C
rR 
EK
--------------  1 + ---------------20°C 
100  s 
E
(37b)
(38)
Proof for the highest gusset field is provided with the compressive
pü
F
stresses according to Sections 6.1.1  S,d
and 6.2.1  S,d (pü
instead of püK) in the DVS 2205-2 technical code, Supplement 9
and the stresses from the horizontal and vertical effects of the
earthquake.
The height of the buckling field at the central point is:
mm
(39)
hS   m + 1 
 = ----------------------------(40)
d
The dimensioning value of the buckling stress is processed from
the diagrams according to [3]:
with
N/mm²
2
N/mm²
(42)
and k for quick use:
If the gussets are not welded with the sloping base, the following
is applicable:
k  =  + 1.1  2.3
(43)
or if the gussets are welded with the sloping base, the following is
applicable:
2
k  = – 0.37   + 2.7  2.3
262
4  M Erd (0)
a
1
Füllung
 F4  --------------------------- –  F3   1 – -----v   K Zar    d  s + G ges   --
d
z
g
--------------------------------------------------------------------------------------------------------------------------------------------------------------------  1
*
K K,d
 b Pr + s uB   s uB  -------------------------2  A 1K   I
(48)
The claw force to be absorbed is located in the numerator and
the absorbable claw force resulting from the shear stress in the
weld in the denominator.
In addition, it must be ensured that the entire horizontal force:
ah
H Erd = H F + G Ges  -----g
9
for   0.8
for   0.8
(49)
Bibliography
Set of rules
DIN EN 1998-4
Eurocode 8: Designing of structures against
earthquakes – Part 4: Silos, tank structures and
pipelines
DIN 4149
Structures in German earthquake regions –
Load assumptions, dimensioning and execution of customary superstructures
(41)
T°C
2
sS   m + 1 
  EK
-  ---------------------------- e = -----------------------------2
d
12   1 –  
k  = – 3.1   + 5.1   + 0.3
The vertical-skirt tank must be anchored. At least four anchors
must be arranged.
is reliably guided into the foundation.
The side ratio is:
k  e
*
 k,d = ----------------  K K,d
M

The following condition must be complied with:
8.6 Buckling stability of the gussets
hS
m–1
2
r s 
2  i 2 1.5 
3
  r  s + --------------S-   8 + 16 
1 –  --------------

 m + 1
12


i=1
with W = ------------------------------------------------------------------------------------------------------------------------------ (47)
m
--------------  r
m+1
Remark: The skirt and the gussets form one overall cross-section
since the gussets are welded with the skirt. The numerator in
Formula (47) constitutes the moment of inertia of this overall
cross-section; the denominator is the distance between the centre
of gravity and the centre of the highest buckling field of the gussets.
(TMK + TAK)/2 must be applied as the effective temperature but
min. 50°C in the case of direct solar radiation.
L
+ 0.5-  d  tan 
= a+m
-----------------B
m+1
3
(46)
8.7 Anchoring
N/mm²
for hR/rR  0.5
 k,R,d
M Erd (0)
 F4 a v
pü
F   1 + ------ S,d
-  ----- +  S,d
+  F4  -------------------
W
 F1 g 
 A,S = ---------------------------------------------------------------------------------------------------------  1
 k,d
(44)
(45)
For further standards, see the DVS 2205-2 technical code, Section 5.2.
Literature
[1] Rammerstorfer, F. G., K. Scharf and F. D. Fischer: Earthquake-proof dimensioning of cylinder shells and fluid-filled tank
structures. Reports from the Institute of Lightweight Construction and Aircraft Construction, TU Vienna, No. ILFB – 2 / 90.
[2] Tuercke, H.: On the stability of tanks made of thermoplastics.
DIBt Communications, No. 5/1995.
[3] Assignment of the earthquake zones and subsoil classes
www.dibt.de/Data/TB/Zuordnung_der_Erdbebenzonen.xls
[4] Tuercke, H.: On the introduction of axially directed individual
loads into the upper edge of thermoplastic tanks. DIBt Communications, No. 4/2002.
January 2011
Calculation of tanks and apparatus
made of thermoplastics
DVS – DEUTSCHER VERBAND
FÜR SCHWEISSEN UND
Technical Code
DVS 2205-2
Vertical round, non-pressurised tanks
Shell construction method
VERWANDTE VERFAHREN E.V.
R&D INTAKE MANIFOLDS
Supplement 6
Replaces January 2010 edition
Contents:
3 Calculation variables
1
2
3
4
5
6
7
A1
–
Reduction factor for the influence of the specific
toughness
A2
–
Reduction factor for the medium in the case of
the proof of the strength
C
–
Factor for the welded interface of the bond between the bottom and the shell
d
mm
Nominal inside diameter
fs
–
Long-time welding factor
fz
–
Short-time welding factor
Reprinting and copying, even in the form of excerpts, only with the consent of the publisher
1
Preliminary remarks
Scope of application
Calculation variables
Proof of the strength
Proof of the stability
Anchoring
Appendix
Preliminary remarks
The size of tanks fabricated from plates is limited because of the
edge fibre expansion limitation (see DVS 2205-2, Table 3) during
the cold bending of the plates. In contrast, larger tanks can be
fabricated if the lower course is fabricated from two shells. The
supporting effect of the reinforcing shell shrunk on from the outside is fully effective during the proof of the strength for the
stresses in the circumferential direction and during the removal of
axial forces, i.e. both wall thicknesses may be added for the
determination of an equivalent wall thickness. With regard to the
proof of the strength in the axial direction, the reinforcing shell
also take effect in part only. Electronic calculations have shown
that the total of the original thickness plus half the reinforcing wall
thickness can be used as the equivalent wall thickness for the
determination of the stresses resulting from the bending.
2
Scope of application
The following design and calculation rules apply to vertical, cylindrical thermoplastic flat-bottom tanks which are equipped with a
reinforced lowest course and are fabricated from panels in the
factory.
For the application of this supplement, it is necessary to comply
with the following prerequisites:
– only one reinforcing shell; two-shell design
– the welding of the shells with each other and with the bottom
corresponds to one of the variants indicated on Fig. 1
– the thickness of the bottom is identical with the thickness of the
lowest course without the reinforcing shell
– the thickness of the reinforcing shell is between 0.5 and 1.0
times the thickness of the lowest course
g
m/sec2 Acceleration due to gravity
GD
N
GZ
N
Dead load of the cylinder
hF
mm
Filling height
hZ,0
mm
Required height of the reinforcing shell
hZ,n
mm
Height of the lowest course
K *K, d
N/mm2 Dimensioning value of the creep strength for
10-1 hours
K*L, d
N/mm2 Dimensioning value of the creep strength for the
computational working life at the mean effective
temperature
Deal load of the roof
K K, d
vorh
N/mm2 Dimensioning value of the stresses effective for
a short time in the circumferential direction
K Lvorh
,d
N/mm2 Dimensioning value of the stresses effective for
a long time in the circumferential direction
K N,vorh
N/mm2 Dimensioning value of the stresses effective for
K, d
a short time in the axial direction resulting from
the normal force
K M,vorh
N/mm2 Dimensioning value of the stresses effective for
K, d
a short time in the axial direction resulting from
the moment
KN,vorh
N/mm2 Dimensioning value of the stresses effective for
L, d
a long time in the axial direction resulting from
the normal force
KM,vorh
N/mm2 Dimensioning value of the stresses effective for
L, d
a long time in the axial direction resulting from
the moment
MW
Nmm
Bending moment in the case of a wind load at
the lower edge of the cylinder
püK
N/mm2
Overpressure effective for a short time
– the reinforcing shell at the height hZ,0 is shrunk on to the lowest course at the height hZ,n without any gaps or any impermissible pretension
pü
N/mm2 Overpressure effective for a long time
– the lowest course is min. 100 mm higher than the reinforcing
shell (hZ,n hZ,0 + 100 mm)
sZ,n
mm
Wall thickness of the lowest course
sZ,0
mm
Wall thickness of the reinforcing shell
F1
–
Partial safety coefficient of the effect (dead load
and filling)
– the characteristic material values are identical for both shells
– no openings in the reinforced region
This publication has been drawn up by a group of experienced specialists working in an honorary capacity and its consideration as an important source of information
is recommended. The user should always check to what extent the contents are applicable to his particular case and whether the version on hand is still valid. No
liability can be accepted by the Deutscher Verband für Schweißen und verwandte Verfahren e.V., and those participating in the drawing up of the document.
DVS, Technical Committee, Working Group "Joining of Plastics"
Orders to: DVS Media GmbH, P. O. Box 10 19 65, 40010 Düsseldorf, Germany, Phone: + 49(0)211/1591- 0, Telefax: + 49(0)211/1591-150
263
Page 2 to DVS 2205-2 Supplement 6
F2
–
Partial safety coefficient of the effect (pressures
and wind)
F3
–
Partial safety coefficient of the effect (reducing
dead load)
I
K N,vorh
+ K LM,vorh
L, d
,d
----------------------------------------1
K*Ld
–
Weighting coefficient depending on the loading
type
with
F
g/cm³
Density of the filling medium
4
and
R&D INTAKE MANIFOLDS
Proof of the strength
 F2  p ü  d  F3   G D + G Z 
-------------------------- – --------------------------------------4
d
K LN,vorh
= -------------------------------------------------------------------------  A 1  A 2   l
,d
s Z, n + s Z, 0
and
Proof of the strength in the circumferential direction in the
reinforced course
–6
 F1    g  h F  10 +  F2  p ü d
K LM,vorh
= C  ----------------------------------------------------------------------------  ---  A 1  A 2   l
,d
s Z, n + 0.5  s Z, 0
2
It is necessary to comply with the utilisation factors for short-time
and long-time loading.
Calculation of the required height of the reinforcing shell
K Kvorh
,d
-----------1
K K* , d
The maximum of both the following conditions determines the
required height of the reinforcing shell hZ,0.
h Z, 0 = max  h Z, 0,1, h Z, 0,2 
with
d
–6
  F1   F  g  h F  10 +  F2  p üK   ---  A 1  A 2   l
vorh
2
K K, d = ---------------------------------------------------------------------------------------------------------------------------- s Z, n + s Z, 0   f z
and
[
with
d
–6
  F1   F  g  h F  10 +  F2  p ü   ---  A 1  A 2   l
vorh
2
K L, d = ------------------------------------------------------------------------------------------------------------------------- s Z, n + s Z, 0   f s
Proof of the strength in the axial direction in the reinforced
course
It is necessary to comply with the utilisation factors for short-time
and long-time loading.
1
 -----------------------------------------–6
 F1   F  g  10
5
with
 F2  p üK  d  F3   G D + G Z  4   F2  M W
------------------------------ – --------------------------------------- + -----------------------------2
4
d
d --------------------------------------------------------------------------------------------------------------- A1  A2  l
s Z n + s Z, 0
and
–6
 F1    g  h F  10 +  F2  p üK d
K M,vorh
= C  -------------------------------------------------------------------------------  ---  A 1  A 2   l
K, d
s Z, n + 0.5  s Z, 0
2
Proof of the stability
The axial and shell pressure stabilities are calculated using a
simplifying method without taking account of the reinforcing shell.
6
KN,vorh
+ K KM,vorh
K, d
,d
-----------------------------------------1
*
K Kd
264
h Z, 0,1  1.4  d   s Z, n + s Z, 0 
and
]
2  K K* , d  s Z, n  f z
2  K L* , d  s Z, n  f s
h Z,0,2 = h F – min ------------------------------------------- –  2  püK , -------------------------------------------   F2 – p ü
d  A1  A2  l
d  A1  A2  l
K Lvorh
,d
----------1
K L* , d
N,vorh
K K, d =
with
Anchoring
The anchoring of the two-shell tank is calculated according to
DVS 2205-2, Section 4.1.8. However, it must be ensured in this
respect that the external weld which is essential for the strength
of the anchoring is executed with only 0.7  sZ,0 instead of
0.7  sB. In the denominator of Formulae (36), (37) and (38), (bPr
+ sB) sZ,0 must be used instead of (bPr + sB)  sB.
Page 3 to DVS 2205-2 Supplement 6
7 Appendix
a)
b)
R&D INTAKE MANIFOLDS
a) SB = Szn; a = 0.7 ∙ Szn; a' = 0.7 ∙ Szo
c)
d)
c) SB = Szn; f ' = Szn; f = 0.5 ∙ Szo
Figure 1.
b) SB = Szn; a = 0.7 ∙ Szn; a' = 0.7 ∙ Szo; f = 0.3 ∙ Szn
d) SB = Szn; a = 0.7 ∙ Szn; a' = 0.7 ∙ Szo
Computational proof is required for the use of this variant!
Welds for tanks with multiple-walled cylinders.
265
January 2012
DVS – DEUTSCHER VERBAND
FÜR SCHWEISSEN UND
VERWANDTE VERFAHREN E.V.
Calculation of tanks and apparatus
made of thermoplastics –
Vertical round non-pressurised tanks –
Ring-supported conical bottom
R&D INTAKE MANIFOLDS
Contents:
1
2
3
4
Reprinting and copying, even in the form of excerpts, only with the consent of the publisher
5
6
7
8
9
10
1
Scope of application
Design
Calculation variables
Determination of the sectional forces for the proof of the
strength
Proof of the strength
Determination of the sectional forces for the proof of the
stability
Proof of the stability
Dimensioning
Anchoring
Appendix
Scope of application
The following design and calculation rules apply to vertical, cylindrical tanks which are fabricated from thermoplastics in the factory
and are equipped with a vertical skirt and with conical bottoms
supported by concentric rings. The cylinder, the skirt and the supporting rings can be either fabricated from panels or manufactured
in the winding process.
For the application of this supplement, it is necessary to satisfy
the following prerequisites:
–
–
–
–
Technical Code
DVS 2205-2
Supplement 7
Replaces June 2010 edition
lower cylinder course
conical bottom
skirt
supporting rings
2.1 Connection of the skirt
2.1.1 Flexible connection
In the case of tanks fabricated from plates, it is appropriate to
fabricate the cylinder and the skirt separately and to arrange the
bottom in between. For this purpose, the lower course and the
skirt are chamfered according to the angle of the conical bottom.
The conical bottom is fabricated with an outside diameter of
approx. d + 5 · s. The lower course and the conical bottom are
joined with an extruder weld a  0.7 · s on the inside and on the
outside. The skirt is joined with the conical bottom with an extruder
weld a  0.7 · s from the outside only (flexible connection of the
skirt).
2.1.2 Flexurally stiff connection
The cylinder and the skirt are fabricated in one piece. The conical
bottom is fitted in and is welded with the cylinder and the skirt in a
flexurally stiff joint from the top and from the bottom (flexurally
stiff connection of the skirt).
– The conical bottom ends in a nozzle with an elbow and a flange.
2.2 Supporting rings
– For the passage of the drainpipe, the skirt and the supporting
rings are each provided with an opening as large as required
for assembly. The openings in the skirt and in the rings are
reinforced with a pipe socket which has the length dA/2 and is
welded on both sides with the same projection.
The supporting rings are arranged concentrically at equal distances
apart. The supporting rings must be cut to length exactly; they
are welded with the conical bottom.
– The openings in the skirt and in the supporting rings must be
arranged so high that these also serve as a support for the
drainpipe.
After the assembly of the drainpipe, a closing bottom can be
welded with the skirt from the outside with a continuous extruder
weld a  0.7 · s. If the tank does not have to be anchored, it is
sufficient to execute a tack weld suitable for transport.
– Should any further openings be arranged in the conical bottom,
in the skirt, in the supporting rings or in the lower cylinder
course, then separate proof must be provided for these.
– Shut-off valves and miscellaneous fittings must be arranged
outside the skirt; no accessibility to the space below the conical
bottom is planned.
– A tank with a conical bottom and without a collecting device is
calculated.
2
2.3 Bottom
2.4 Ventilation of the space underneath the conical bottom
The space underneath the conical bottom must be ventilated in
order to permit pressure equalisation in the event of temperature
changes. This is the case when the drainpipe is not welded with
the skirt.
The upper part of the tank is designed and calculated in
analogy to the flat-bottom tank.
Design
The lower region of the tank with a conical bottom consists of the
following four structural elements:
This publication has been drawn up by a group of experienced specialists working in an honorary capacity and its consideration as an important source of information
is recommended. The user should always check to what extent the contents are applicable to his particular case and whether the version on hand is still valid.
No liability can be accepted by the Deutscher Verband für Schweißen und verwandte Verfahren e.V., and those participating in the drawing up of the document.
DVS, Technical Committee, Working Group "Joining of Plastics"
Orders to: DVS Media GmbH, P. O. Box 10 19 65, 40010 Düsseldorf, Germany, Phone: + 49(0)211/1591- 0, Telefax: + 49(0)211/1591-150
266
Page 2 to DVS 2205-2 Supplement 7
3
Calculation variables
A1
A1K
–
–
püK
N
Dimensioning value of the global
compressive force resulting from püK in
the supporting ring
Füllung
N
Dimensioning value of the global
compressive force resulting from the filling
in the skirt
Schnee
N R,d
Reduction factor for the influence of the
specific toughness for a wall temperature
effective for a long time
N Zar,d
Reduction factor for the influence of the
specific toughness for a wall temperature
effective for a short time
N Zar,d
N
Dimensioning value of the global
compressive force resulting from the snow
load in the skirt
ps
N/mm2
Snow pressure on the roof
puK
N/mm2
Partial vacuum effective for a short time
N/mm2
Overpressure effective for a short time
pü
N/mm2
Overpressure effective for a long time
r
mm
Radius of the cylinder/skirt
R&D INTAKE MANIFOLDS
A2
–
Reduction factor for the medium in the
case of the proof of the strength
A2I
–
Reduction factor for the medium in the
case of the proof of the stability
AR
mm2
Cross-sectional area of the open ring
d
mm
Nominal inside diameter of the cylinder
and of the skirt
ToC
N/mm2
Short-time elastic modulus at T°C
rR
mm
Radius of the largest supporting ring
s
mm
Wall thickness of the lowest course, of the
skirt, of the conical bottom and of the
supporting rings
sB
mm
Wall thickness of the closing bottom
TA
°C
Mean ambient temperature (according to
Miner, see the DVS 2205-1 technical code)
EK
20 o C
N/mm2
Short-time elastic modulus at 20°C
20 o C
EL
N/mm2
Long-time elastic modulus at 20°C
fsK
–
Long-time welding factor for a possible
transverse weld in the conical bottom
g
m/sec2
Acceleration due to gravity
GA
N
Dead load of the additional weight on the
roof
EK
püK
TAK
°C
Highest ambient temperature
TM
°C
Mean media temperature (according to
Miner, see the DVS 2205-1 technical code)
°C
Highest media temperature
GD
N
Dead load of the roof
Gges
N
Dead load of the tank
TMK
GZ
N
Dead load of the cylinder
WR
mm3
Resistance moment of the open ring
GK
N
Dead load of the conical bottom
zS
mm
GZar
N
Dead load of the skirt
Distance between the centres of gravity of
the open ring and of the cylinder axis
hF
mm
Filling height measured from the tip of the
cone

°
Pitch of the conical bottom measured
against the horizontal line
hR
mm
Height of the supporting ring
R
–
Factor for the axial stability of the
supporting ring
hZar
mm
Height of the skirt
Zar
–
Factor for the axial stability of the skirt
kf
–
Concentration factor according to [3]
vorh
N/mm2
A,R
–
Dimensioning value of the stresses
effective for a short time
Utilisation of the axial stability in the
supporting ring
vorh
A,Zar
–
Utilisation of the axial stability in the skirt
N/mm2
Dimensioning value of the stresses
effective for a long time
F1
–
Partial safety coefficient of the effect
(dead load and filling)
KR
Füllung
N/mm2
Compressive stresses resulting from the
filling in the supporting ring
F2
–
Partial safety coefficient of the effect
(pressures and wind)
Füllung
K Zar
N/mm2
Compressive stresses resulting from the
filling in the skirt
F3
–
Partial safety coefficient of the effect
(reducing dead load)
pü
N/mm2
Compressive stresses resulting from pü in
the supporting ring
I
–
Weighting coefficient according to the
DVS 2205-2 technical code, Table 2
püK
N/mm2
Compressive stresses resulting from püK
in the supporting ring
M
–
Partial safety coefficient of the resistance/
stressability
Tensile stresses resulting from pü in the
skirt
F
g/cm3
Density of the filling medium
 K,d
N/mm2
Dimensioning value of the axial
compressive stress in the conical bottom
 K,d
N/mm2
Dimensioning value of the buckling stress
of the conical bottom
k,Zar,d
N/mm2
Dimensioning value of the axial buckling
stress of the skirt
k,R,d
N/mm2
Dimensioning value of the axial buckling
stress of the largest supporting ring
vorh
 Zar,d
N/mm2
Dimensioning value of the axial stress next
to the opening in the skirt
vorh
N/mm2
Dimensioning value of the axial stress next
to the opening in the supporting ring
K K,d
K L,d
KR
KR
pü
K Zar
püK
N/mm2
K Zar
N/mm2
Tensile stresses resulting from püK in the
skirt
MW
Nmm
Bending moment from the wind load at the
lower edge of the skirt
n
–
Number of supporting rings
N
Dimensioning value of the global
compressive force resulting from the filling
in the supporting ring
Füllung
N R,d
pü
N R,d
N
Dimensioning value of the global
compressive force resulting from pü in the
supporting ring
vorh
 R,d
267
Page 3 to DVS 2205-2 Supplement 7
4 Determination of the sectional forces for the proof of the
strength
The sectional forces can be determined with a rotational shell
program for thin-walled elements with a linear-elastic approach.
In this way, it is possible to establish the wall thicknesses of the
cylinder, of the skirt, of the conical bottom and of the supporting
rings in such a way that the utilisation of the individual elements
is optimum, i.e. it permits economically viable and safe dimensioning.
5
Proof of the strength
The proof of the strength is provided in the way indicated in the
DVS 2205-2 technical code with the stresses described in Section 4. The mean media temperature TM must be estimated as
the effective wall temperature in the cylinder and in the conical
bottom and the highest media temperature TMK in the case of a
short-time effect.
R&D INTAKE MANIFOLDS
In this supplement, formulae are provided for the manual computation. For their application, attention must be paid to the following restrictions on the scope of application:
– The wall thicknesses of the lower cylinder course, of the skirt,
of the conical bottom and of the supporting rings are identical.
– The pitch of the conical bottom is confined to 15°, 30° or 45°.
– It is necessary to arrange at least one supporting ring; for up to
three supporting rings, the factors are prepared in Tables 1 and
2.
– For the filling height hF, it is necessary to comply with the condition hF  r · (1.5 + tan.
– The wall-thickness-to-radius ratio is within the following limits:
0.04  s/r  0.01.
4.1 Load case for the filling
The greatest stress resulting from the filling arises either in the
conical bottom at the interface between the cylinder and the skirt
or in the conical bottom above the supporting rings. Therefore, it
is necessary to calculate both stresses; the greater of the two
stresses is crucial. The stresses are effective in the longitudinal
direction; if a transverse weld is arranged in the conical bottom,
the welding factor fsK must be taken into consideration in the second
term.
The following formula for the dimensioning value of the greatest
stress takes account of the total of the bending and normal
stresses.
Füllung
K L,d
s
A  ln  --- + B
d
f sK  e
N/mm2
 A1  A2  l
s
C  ln  --- + D
d
(1)
4.2 Load case for the overpressure
The greatest stress in the cylinder arises either at the interface to
the bottom or in the conical bottom above the supporting rings.
Therefore, it is necessary to calculate both stresses; the greater
of the two stresses is crucial. The stresses are effective in the
longitudinal direction; if a transverse weld is arranged in the conical
bottom, the welding factor fsK must be taken into consideration in
the second term.
The following formula for the dimensioning value of the greatest
stress takes account of the total of the bending and normal
stresses.
1
1
=  F2  p ü  max ---------------------------- ,----------------------------------------e
 A1  A2  l
s
E  ln  --- + F
 d
f sK  e
s
G  ln  --- + H
d
N/mm2
püK
(2)
K K,d is calculated analogously, with püK as the value for the
pressure.
Tables 1 and 2 show Constants E to H.
268
6.1 Load case for the filling
6.1.1 Supporting rings
The greatest compressive stress in the supporting rings results
from:
Füllung
KR
=  F  g  10
–6
1
2
  h F – ---  r  tan  --------------------------- N/mm2 (3)

 K  ln  --s- + L
3
 d
e
Tables 1 and 2 show Constants K and L.
6.1.2 Skirt
The greatest compressive stress in the skirt results from:
Füllung
K Zar
=  F  g  10
–6
1
2
  h F – ---  r  tan  ----------------------------- N/mm2 (4)

 M  ln  --s- + N
3
 d
e
Tables 1 and 2 show Constants M and N.
6.2 Load case for the overpressure
6.2.1 Supporting rings
püK
Remark: Any missing values in the tables mean that it is not necessary to provide any proof since the stresses are lower and
therefore do not influence the dimensioning.
pü
For skirts and supporting rings bearing the entire filling load, it is
necessary to provide proof of the axial stability.
KR
Tables 1 and 2 show Constants A to D.
K L,d
Determination of the sectional forces for the proof of the
stability
The greatest compressive stress in the supporting rings results
from:
hF
 h F – r  tan 
=  F1   F  g  10 max ------------------------------------ ,---------------------------------------–6
e
6
1
= p üK  ---------------------------e
pü
KR
s
P  ln  --- + Q
 d
N/mm2
(5)
is calculated analogously, with pü as the value for the pres-
sure.
Tables 1 and 2 show Constants P and Q.
6.2.2 Skirt
The greatest tensile stress in the skirt results from:
1
püK
K Zar = p üK  ---------------------------e
s
U  ln  --- + V
d
N/mm
(6)
pü
K Zar is calculated analogously, with pü as the value for the pressure.
Tables 1 and 2 show Constants U and V.
7
Proof of the stability
The dimensioning value of the axial compressive stresses next to
the opening must be compared with the dimensioning value of the
buckling stress. Buckling is a short-time process and the proof must
be provided at the wall temperatures resulting from TMK and TAK.
For the proof of the skirt, (TMK+ + TAK)/2 must be estimated as the
effective wall temperature and min. 50°C in the case of direct solar
radiation. TMK must be estimated as the effective temperature of
the supporting rings and min. (TMK + 35)/2 in the case of outdoor
installation. Min. 20°C must be estimated for TAK in the case of
indoor installation and min. 35°C for outdoor installation.
Page 4 to DVS 2205-2 Supplement 7
Compressive stresses according to Sections 6.1 and 6.2 are converted into global normal forces and, in the case of outdoor installation, are estimated for the weakened cross-section (open ring)
together with the wind moment Mw. For this purpose, it is necessary to establish the area AR, the centre of gravity zS and the resistance moment WR of the ring cross-section. The axial compressive stresses next to the opening must be calculated while
paying attention to the misalignment of the centroidal axis.
Remark:
It is not necessary to provide any proof with snow or at a winter
temperature since these do not determine the dimensioning.
The following condition must be complied with for the skirt:
R&D INTAKE MANIFOLDS
7.1 Supporting rings
Proof of the largest ring only is provided with the compressive
stresses according to Sections 6.1.1 and 6.2.1; using a simplifying method on the safe side, it is not necessary to exactly assign
the various compressive stresses to the individual rings.
The largest ring has the radius r R
Füllung
N R,d
 r + --s-  n
 2
= -----------------------n+1
Füllung
=  F1  2    r R  s  K R
püK
püK
N R,d =  F2  2    r R  s  K R
mm
(7)
N
(8)
N
(9)
The following applies to indoor and outdoor installation:
zS 
vorh
Füllung
 1
 R,d =  N R,d
+ NpüK
N/mm2
R,d    ------- + ---------
W
A
R
(10)
R
The following condition must be complied with for the supporting
ring:
Remark:
A2I is not necessary since there is
no wetting with media
vorh
 l   R,d
 A,R = ------------------1
 k,R,d
(13)
TMK must be estimated as the effective temperature of the supporting rings and min. (TMK + 35)/2 in the case of outdoor installation.
7.2 Skirt
The load case for the overpressure is not considered since the
overpressure subjects the skirt to tensile stresses.
=  F1  2    r  s 
2
=  F2    r  p s
N
(14)
N
(15)
In the case of indoor installation:
zS 
vorh
Füllung
1
 Zar,d =  N Zar,d +  F1   G ges + G A  k f     ------- + -------A
W 
R
ToC
with E k
R
N/mm2
(16)
for (TMK + TAK)/2°C in Equation (19)
In the case of outdoor installation:
Summer:
zS 
vorh
Füllung
1
 Zar,d =  F1   NZar,d +  F1   G ges + G A  k f     ------- + -------A
W 
R
ToC
Ek
 F2  M W
+ --------------------WR
N/mm2
ToC
s
EK
-  -- k,Zar,d =  Zar  0.62  -----------M r
for hZar /s  0.5
ToC
s
EK
r 2 s
-  ---  1 + 1.5   -----------  -- k,Zar,d =  Zar  0.62  ----------- h Zar  r
M r
(19a)
(19b)
with
0.65
 Zar = -------------------------------------------------------20 o C
EK
r 
 1 + ----------------------------
20 o C 
100  s
EL
(20)
Dimensioning
9 Anchoring
(12b)
0.65
 R = -------------------------------------------------------20 o C
rR 
EK
 1 + ----------------------------
20 o C 
100  s
EL
Schnee
N Zar,d
for hZar/s > 0.5:
(12a)
with
Füllung
K Zar
where
The greatest wall thickness resulting from the proof of the
strength and from the proof of the stability must be executed for
the lower cylinder course, for the conical bottom, for the skirt and
for the supporting rings.
ToC
EK
rR 2 s
s
 k,R,d =  R  0.62  ----------------  -----  1 + 1.5   --------  ---- hR  rR
M
rR
Füllung
N Zar,d
Remark:
A2I is not necessary since there is no wetting with media
8
ToC
for hR /r  0.5
(18)
(11)
where for hR /r > 0.5
EK
s
 k,R,d =  R  0.62  ----------------  ----M
rR
vorh
 l   Zar,d
 A,Zar = ---------------------1
 k,Zar,d
R
(17)
If anchoring becomes necessary, at least four anchors must be
arranged (z  4). With regard to the proof of the anchoring, a distinction must be made between three cases:
T MK + T AK
Case 1: Short-time overpressure at --------------------------- °C but min. 50°C
2
in the case of direct solar radiation
1
püK
  F2  2    r  s  K Zar –  F3   G D + G Z + G Zar    --z
-----------------------------------------------------------------------------------------------------------------------------------  1
*
K K,d
 b Pr + s B   s B  ---------------------2  A1  l
(21)
TM + TA
Case 2: Long-time overpressure at -------------------- °C
2
pü
1
  F2  2    r  s  K Zar –  F3   G D + G Z + G Zar    --z
----------------------------------------------------------------------------------------------------------------------------------  1
*
K L,d
 b Pr + s B   s B  ---------------------2  A1  l
(22)
Case 3: Wind load at 20°C (only in the case of outdoor installation)
4   F2  M W
1
pü
–  F3   G D + G Z + G Zar   -------------------------------- +  F2  2    r  s  K Zar
z
d
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------  1
*
K K,d
-------------------- b Pr + s B   s B 
2  A1  l
(23)
While paying attention to the lever arms, the required anchor
force (e.g. for the plugs) must be calculated from the maximum
claw force (maximum of the numerators in Equations 21 to 23).
with
for (TMK + TAK)/2 or, in the case of direct solar radiation, for min. 50°C in Equation (19)
269
Page 5 to DVS 2205-2 Supplement 7
10 Appendix
10.3 Literature
10.1 Explanations
[1] Tuercke, H.: Derivation of simplified formulae for the determination of the sectional forces for the dimensioning of ring-supported conical bottoms. Unpublished.
This Supplement 7 to the DVS 2205-2 technical code was elaborated by DVS-AG W4.3b ("Structural designing / apparatus engineering").
R&D INTAKE MANIFOLDS
[2] Tuercke, H.: On the stability of tanks made of thermoplastics.
DIBt Communications, No. 5/1995.
[3] Tuercke, H.: On the introduction of axially directed individual
loads into the upper edge of thermoplastic tanks. DIBt Communications, No. 4/2002.
10.2 Standards and technical codes
See the DVS 2205-2 technical code, Section 5.2.
10.4 Design-related details
Computational dimensions
Fabrication dimensions
sD
hD
sD
hges = h ges + s B + ---------------cos  D
h’D
 = a + h Zar – c
h Zar
b

DDD
s
c = ----------------- – s  tan  K
cos  K
hZ = h z + b
h’Z
2  sD
hD = r  tan  D + ---------------cos  D
hZ
sZ
hges
cs·tanDK
sK
hZar
a
h’Zar

DK
rR
sB
r
Figure 1.
Overview and dimensions.
Figure 2.
Bonding of the rings.
Figure 3.
Bonding of the bottom.
270
h’R
sR
s Zar
h’ges
s
r + --2r R,i = i  -----------n+1
s
hR,i = a – ----------------- + r R,i  tan  K
cos  K
Page 6 to DVS 2205-2 Supplement 7
R&D INTAKE MANIFOLDS
All welds
a = 0.7 · s
All welds
a = 0.7 · s
Figure 4a. Bonding of the cone in the case of the plate tank.
Figure 4b. Bonding of the cone in the case of the wound tank.
10.5 Tables (Attention: Interpolation for other angles is not possible!)
Table 1. Flexible connection of the skirt (panel tank).
Number of rings
n=1
Angle
n =2
n=3
15°
30°
45°
15°
30°
45°
15°
30°
45°
–
–
1.3473
1.6639
1.5041
1.3737
1.5018
1.5010
1.4348
Strength load case
A
Filling
B
–
–
1.3115
2.8092
2.1653
1.6632
2.3857
2.3830
2.1390
C
1.7171
1.5384
1.4376
1.9408
1.6851
–
1.9199
1.7545
–
D
2.2817
2.0036
2.1146
4.0025
3.0872
–
4.4227
3.7350
–
E
–
1.3642
1.3072
1.5447
1.3933
1.2956
1.3595
1.3368
1.3009
Strength load case
Overpressure
nR load case
F
–
1.0665
0.9797
2.1012
1.4169
1.0225
1.4801
1.3086
1.1203
G
1.7369
1.5694
–
1.9440
–
–
1.8956
–
–
H
2.3474
2.1425
–
4.0238
–
–
4.2614
–
–
K
1.0530
1.1086
1.1177
1.0160
1.0575
1.0898
1.0444
1.0330
0.9831
Filling
L
1.6278
1.9900
2.1377
1.8934
2.1291
2.3701
2.3079
2.2804
2.1133
nZar load case
M
0.9461
0.9099
0.9188
0.9327
0.8946
0.9010
0.8754
0.8804
0.9000
Filling
N
1.8353
1.5735
1.5347
2.0845
1.7599
1.6872
2.0236
1.8685
1.8394
nR load case
P
1.0616
1.1670
1.3367
1.0429
1.0567
1.1219
1.0294
1.1563
1.1497
Overpressure
Q
1.6848
2.3846
3.6243
2.0345
2.2372
2.9119
2.2399
2.9496
3.1831
nZar load case
U
1.0614
1.1670
1.3367
1.0548
1.1428
1.2818
1.0836
1.1482
1.2700
Overpressure
V
2.3768
3.0778
4.3177
2.1140
2.7203
3.7703
2.1543
2.6399
3.5867
271
Page 7 to DVS 2205-2 Supplement 7
Table 2. Flexurally stiff connection of the skirt (wound tank).
Number of rings
Angle
n=2
n=3
30°
45°
15°
30°
45°
15°
30°
45°
–
–
1.2598
1.7090
1.4956
1.2859
1.5779
1.5323
1.3830
R&D INTAKE MANIFOLDS
Strength load case
A
Filling
B
–
–
0.9672
2.9862
2.0715
1.2420
2.7387
2.5046
1.8408
C
1.7228
1.5257
1.4901
1.9387
1.6896
–
1.8571
1.7533
–
D
2.3079
1.9492
2.3859
3.9989
3.1098
–
4.1583
3.7311
–
E
1.6375
1.4326
1.3571
1.4893
1.4124
1.3451
1.2975
1.3194
1.3308
Strength load case
Overpressure
nR load case
272
n=1
15°
F
2.2047
1.3821
1.1768
1.9485
1.5450
1.2436
1.2696
1.2682
1.2626
G
1.7478
–
–
1.9337
–
–
1.8783
–
–
H
2.3972
–
–
3.9497
–
–
4.1860
–
–
K
1.0520
1.0909
1.0993
1.0310
1.0579
1.0750
1.0492
1.0360
0.9811
Filling
L
1.6165
1.9123
2.0635
1.9566
2.1273
2.2975
2.3335
2.2927
2.0980
nZar load case
M
0.9470
0.9251
0.9393
0.9214
0.8967
0.9192
0.8706
0.8706
0.9091
Filling
N
1.8454
1.6396
1.5920
2.0391
1.7761
1.7760
2.0049
1.8298
1.8951
nR load case
P
1.0595
1.1447
1.3100
1.0528
1.0580
1.1016
1.0201
1.1593
1.1423
Overpressure
Q
1.6649
2.2806
3.5202
2.0813
2.2376
2.8204
2.1963
2.9617
3.1486
nZar load case
U
1.0596
1.1444
1.3105
1.0623
1.1380
1.2562
1.0889
1.1514
1.2558
Overpressure
V
2.3583
2.9725
4.2157
2.1419
2.6890
3.6538
2.1767
2.6479
3.5183
January 2012
Calculation of tanks and apparatus
made of thermoplastics –
Vertical round non-pressurised tanks –
Example of a ring-supported conical bottom
DVS – DEUTSCHER VERBAND
FÜR SCHWEISSEN UND
VERWANDTE VERFAHREN E.V.
Technical Code
DVS 2205-2
R&D INTAKE MANIFOLDS
Supplement 8
Replaces February 2011 edition
Reprinting and copying, even in the form of excerpts, only with the consent of the publisher
Contents:
Füllung
1
2
3
4
5
Introduction
Data for the tank
Proof of the strength
Proof of the stability
Anchoring
1
Introduction
K L,d
The formulae are solved with the condition
Füllung
K L,d
*
= K L,d
= 10.2/1.1 nach s aufgelöst
-6
s1 = d  e
Cylinder and skirt fabricated from plates
Geometry:
d = 2,000 mm (inside); hGes = 5,000 mm;  = 30°;
a = 420 mm; two supporting rings
Installation:
Outdoor installation without any wind-shielding
collecting device
Wind Zone 2: inland area ; Snow Load Zone 2: up
to 285 m
q = 0.65 kN/m2
pS = 0.68 kN/m2, TA = 10°C, TAK = 35°C
  F1    g  10   h F – r  tan    A 1  A 2   l
In  ----------------------------------------------------------------------------------------------------------------- – B


K *L,d
------------------------------------------------------------------------------------------------------------------------------------A
and
s2 = d  e
     g  10 -6  h  A  A   
F1
F
1
2 l
In  ---------------------------------------------------------------------------------- – D
K *L,d  f sK


-------------------------------------------------------------------------------------------------------C
Material:
PE 100; 25 years
s 1 = 2,000  e
Filling:
Battery acid; TM = TMK = 20°C; hF = 4,000 mm;
A1 = A1K = A2 = A2I = 1; F = 1.29 g/cm³
= 18.43 mm
Ventilation:
Closed system püK = pü = 0.01 bar;
puK = 0.01 bar
Loading type: Loading Case II; I = 1.2
s 2 = 2,000  e
Openings:
dA = 200 mm
Welding:
Longitudinal weld as a heated tool weld, no transverse weld in the conical bottom
Anchoring:
Claw width bPr = 70 mm
and
3.2 Checking
Füllung
1
  h F – r  tan    ---------------------------e
 A1  A2  l
= 19.36 mm
Chosen s = 20 mm.
K L,d
-6


-6
1.35  1.29  9.81  10  4,000  1.2
In  -------------------------------------------------------------------------------------------- – 3.0872


10.2
-----------  1


1.1
------------------------------------------------------------------------------------------------------------------------------1.6851
Load case for the filling
Proof of the strength
=  F1   F  g  10


-6
o
1.35  1.29  9.81  10   4,000 – 1,000* tan 30   1.2
In  -------------------------------------------------------------------------------------------------------------------------------------------- – 2.1653


10.2---------

1.1
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------1.5041
It is checked whether s = 20 mm is also sufficient for the total resulting from the load case for the filling and the load case pü.
3.1 Initial estimation
Füllung
s
C  In ---  + D
d 
N/mm2
 A1  A2  l
Data for the tank
K L,d
1
 h F  -----------------------------------------
According to Table 1 in Supplement 7, A = 1.5041, B = 2.1653,
C = 1.6851, D = 3.0872 and fsK = 1 (no transverse weld).
Design:
3
-6
f sK  e
This example is intended to facilitate the application of Supplement 7 to the DVS 2205-2 technical code.
2
=  F1   F  g  10
s
A  In  --- + B
d
=  F1   F  g  10
-6
1
1
 max  h F – r  tan    ---------------------------- h F  -----------------------------------------
N/mm2
e
s
A  In  --- + B
d
f sK  e
s
C  In  --- + D
d
 A1  A2  l
This publication has been drawn up by a group of experienced specialists working in an honorary capacity and its consideration as an important source of information
is recommended. The user should always check to what extent the contents are applicable to his particular case and whether the version on hand is still valid.
No liability can be accepted by the Deutscher Verband für Schweißen und verwandte Verfahren e.V., and those participating in the drawing up of the document.
DVS, Technical Committee, Working Group "Joining of Plastics"
Orders to: DVS Media GmbH, P. O. Box 10 19 65, 40010 Düsseldorf, Germany, Phone: + 49(0)211/1591- 0, Telefax: + 49(0)211/1591-150
273
Page 2 to DVS 2205-2 Supplement 8
The largest supporting ring has the radius:
1
max  4,000 – 1,000  tan 30 o   ---------------------------------------------------------- , 4,000
e
20
1.5041  In  --------------- + 2.1653
 2,000
 r + --s-  n
 2
-----------------------=
n+1
=
rR
1012.5  2
------------------------=
2+1
675 mm
R&D INTAKE MANIFOLDS
Füllung
1
 -----------------------------------------------------------------1e
20
1.6851  In  --------------- + 3.0872
2,000
Füllung
K L,d
= max  400,115, 428,061  = 428,061
2
püK
vorh
Füllung
 R,d =  NR,d
1
pü
K L,d =  F2  p ü  ----------------------------  A 1  A 2   l
s
E  In  --- + F
 d
with E = 1.3933; F = 1.4169 according to Table 1 in Supplement 7
follows:
1
pü
0.0018
K L,d = 1.5  0.001  ----------------------------------------------------------  1.2 = ---------------------------20
0.0091998
1.3933  In  --------------- + 1.4169
 2,000
e
vorh
1
33.41
 R,d =  81,188 + 1,763    ------------------ + ------------------------------ = 1.13 N/mm2
 80,808 24,848,209
It is necessary to comply with the following condition for the supporting ring:
 l   R,d
 A,R = -------------------1
 k,R,d
with
0.65
-------------------------------------------------------=
o
20 C
rR 
EK
1 + ----------------------------
o
100  s 
20 C 
EL
To C
= 4.07 N/mm²
4.1.1 Load case for the filling
The greatest compressive stress in the supporting rings results
from:
1
-6
2
=  F  g  10   h F – ---  r  tan   ---------------------------

3
 --s-
e
N/mm2
K  In   + L
d
with K = 1.0575; L = 2.1291 according to Table 1 follows:
2
= 1.29  9.81  10   4,000 – ---  1,000  tan 30 o


3
-6
1
 ----------------------------------------------------------
Füllung
To C
EK
= 800 N/mm² for TMK = 20°C
It follows:
vorh
 l   R,d
1.2  1.13
=
 A,R -------------------= ----------------------=
- 0.33  1
 k,R,d
4.07
4.2.1 Load case for the filling
The greatest compressive stress in the skirt results from:
=  F  g  10
K Zar
= 0.000012655  3,615.1  15.5 = 0.709 N/mm
2
Füllung
= 1.29  9.81  10
Füllung
K Zar
with P = 1.0567; Q = 2.2372 follows:
püK
KR
 2,000
e
= 0.01386 N/mm
274
2
d 
N/mm2
+N
–6
2
  4,000 – ---  1,000  tan 30 o


3
20
0.8946  ln  --------------- + 1.7599
2,000
2
= 0.000012655  3,615.1  10.59 = 0.484 N/mm
Füllung
=
N Zar,d
1
1
= 0.001  ---------------------------------------------------------- = 0.001  --------------------0.07214
20
1.0567  In  --------------- + 2.2372
M  In
1
 ----------------------------------------------------------e
s
P  In  --- + Q
d
1
2
  h F – ---  r  tan   ----------------------------

3
--s- 
e
The greatest compressive stress in the supporting rings results
from:
e
–6
with M = 0.8946; N = 1.7599 according to Table 1 follows:
K Zar
1
= p üK  -----------------------------
Condition fulfilled!
4.2 Skirt
Füllung
20
1.0575  In  --------------- + 2.1291
2,000
4.1.2 Load case for the overpressure
püK
KR
0.3046
s
800 20
EK
 k,R,d =  R  0.62  ----------- ----- = 0.3046  0.62  ----------  ---------M rR
1.1 675
4.1 Supporting rings
e
0.65
-----------------------------------------------------=
800 
675 - 
----------  1 + -------------------235 
100  20 
and, because of hR/rR > 0.5:
Proof of the stability
KR
N/mm2
R
AR = 80,808 mm2; zS = 33.41 mm; WR = 24,848,209 mm³ follows:
pü
Füllung
KR
R
with the cross-section values for the open ring
r = 675 mm; dA = 200 mm
Füllung
=
R
K L,d
+ K L,d 8.776 + 0.267
 ----------------------------------=
=
----------------------------------=
- 0.98  1 Condition fulfilled!
*
10.2
K L,d
----------1.1
Füllung
püK
1 zS 
+ NR,d    ------- + -------A W 
vorh
2
Utilisation
KR
= 1.5  2    675  20  0.01386
 1,763 N
The following applies to indoor and outdoor installation:
Load case for the overpressure
4
= 1.35  2    675  20  0.709
 81,188 N
püK
= 1.35  1.29  9.81  10  428,061  1.2 = 8.776 N/mm
 0.267 N/mm
Füllung
=  F1  2    r R  s  K R
N R,d =  F2  2    r R  s  K R
-6
e
N R,d
Füllung
=
F1  2    r  s  K Zar
1.35  2    1,000  20  0.484
= 82,108.7 N
2
2
h ges
5,000
0.65
M W = c f  q  d  ------------- = 0.8  ---------------   2,000 + 40   ----------------2
2
1,000
= 13,260,000 Nmm
Page 3 to DVS 2205-2 Supplement 8
4.2.2 Load case for the overpressure
=
 Zar
The load case for the overpressure is not considered since it subjects the skirt to tensile stresses.
It is only necessary to provide the proof for the summer load case:
vorh
Füllung
1 z S   F2  M W
= NZar,d   ------- + -------- + ---------------------A W 
WR
R
R
To C
with E k
o
20 C
EK
r
--------------  1 + ----------------
o
100  s 
20 C 
EL
0.65
-----------------------------------------------------=
800 
1012.5 
----------  1 + -------------------235  100  25 
and, because of hZar/rr > 0.5:
To C
EK s
270
25
 k,Zar,d =  Zar  0.62  ----------- --- = 0.2972  0.62  ----------  -----------------M r
1.1 1012.5
N/mm2
= 1.117 N/mm²
for 50°C
vorh
 l   Zar,d 1.2  0.857
with the cross-section values for the open ring r = 1,010 mm; =
 A,Zar --------------------=
- --------------------------= 0.92  1
dA = 200 mm
 k,Zar,d
1.117
AR = 122,914 mm²; zS = 32.87 mm; WR = 58,318,536
2
= 0.7143 + 0.3411 = 1.055 N/mm
0.65
=
-------------------------------------------------------o
20 C
EK
r 
--------------  1 + ---------------o
100  s 
20 C 
EL
0.65
-----------------------------------------------------=
800 
1,010 
----------  1 + -------------------

235
100  20
0.2872
The next calculation with s = 25 mm supplies:
2
  4,000 – ---  1,000  tan 30o 


3
Füllung
Füllung
N Zar,d
25
0.8946  In  ------------------- + 1.7599
 2,000 
pü
K Zar = 0.00985 N/mm2
4   F2  M W
pü
1
------------------------------ +  F2  2    r  s  K Zar –  F3   G D + G Z + G Zar   --z
d
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------  1
*
K K,d
 b Pr + s B   s B  ---------------------2  A1  l
2
= 0.000012655  3,615.1  8.673 = 0.3968 N/mm
z
=
=  F1  2    r  s 
Füllung
K Zar
25
1.1428  In  --------------- + 2.7203
2,000
4  1.5  13,325,000
-------------------------------------------------- + 1.5  2    1,000  25  0.00985 – 0.9   4,000 
2,000
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------14.8
----------1.1
 70 + 20   20  -----------------------2  1  1.2
= z
1
 --------------------------------------------------------------
K Zar
e
sB = 20 mm is chosen as the thickness of the bottom.
The wall thickness for the cylinder, for the conical bottom,
for the skirt and for the supporting rings is increased to
25 mm.
e
s
U  In  --- + V
d
*
Wind load with K K,d
= 14.8/1.1 N/mm² for 20°C
Condition not fulfilled!
–6
1
pü
K Zar = p ÜK  -----------------------------
As an example, 4,000 N is assumed as the weight GD + GZ + GZar.
vorh
= 1.29  9.81  10
For the crucial Case 3, the greatest tensile stress in the skirt results
from:
pü
1
2
K Zar = 0.001  ---------------------------------------------------------- = 0.00985 N/mm
To C
s
EK
270 20
=  Zar  0.62  ----------- --- = 0.2872  0.62  ----------  --------------M r
1.1 1,010
 l   Zar,d 1.2  1,055
 A,Zar --------------------=
=
- --------------------------= 1.46  1
 k,Zar,d
0.8655
Füllung
Anchoring
with U = 1.1428; V = 2.7203 according to Table 1 follows:
= 0.8655 N/mm²
K Zar
5
e
and, because of hZar/r > 0.5:
 k,Zar,d
Condition fulfilled!
mm3
vorh
1
32.87
1.5  13,260,000
 Zar,d = 82,108,7   --------------------- + ------------------------------ + ----------------------------------------- 122,914 58,318,536
58,318,536
=
 Zar
0.2972
R&D INTAKE MANIFOLDS
4.2.3 Dimensioning
 Zar,d
0.65
=
--------------------------------------------------------
= 1.35  2    1,000  25  0.3968
= 84,144 N
2
h ges
2
0.65
5,000
M W = c f  q  d  -------------- = 0.8  ---------------   2,000 + 50   ----------------2
2
1,000
39,975 + 2,320 – 3,600
-----------------------------------------------------------=
10,091
3.83
Four anchors are executed.
The lower course of the cylinder, the skirt, the conical bottom and
the two supporting rings must be manufactured from panels with
a thickness of 25 mm.
= 13,325,000 Nmm
Summer proof:
vorh
Füllung
1 z S   F2  M W
 Zar,d = NZar,d   ------- + -------- + ---------------------A W 
WR
R
R
To C
with E k
N/mm2
for 50°C
with the cross-section values for the open ring r = 1,012.5 mm;
dA = 200 mm
AR = 154,035 mm2; zS = 32.87 mm; WR = 73,276,623 mm³
vorh
1
32.87
1.5  13,325,000
 Zar,d = 84,144   --------------------- + -------------------------------- + ----------------------------------------- 154,035 73,276,623 
73,276,623
= 0.584 + 0.273 = 0.857 N/mm2
275
January 2012
DVS – DEUTSCHER VERBAND
FÜR SCHWEISSEN UND
VERWANDTE VERFAHREN E.V.
Calculation of tanks and apparatus
made of thermoplastics –
Vertical round non-pressurised tanks –
Parallel-supported sloping base
R&D INTAKE MANIFOLDS
Technical Code
DVS 2205-2
Supplement 9
Replaces April 2011 edition
This Supplement 9 to the DVS 2205-2 technical code was elaborated by DVS-AG W4.3b ("Structural designing / apparatus engineering")
together with the committee of experts "Plastic tanks and pipes" (project group "Calculation") from the German Institute of Construction
Technology.
Reprinting and copying, even in the form of excerpts, only with the consent of the publisher
Contents:
1
2
2.1
2.1.1
2.1.2
2.2
2.3
2.4
3
4
4.1
4.1.1
4.1.2
4.2
4.2.1
4.2.2
5
6
6.1
6.1.1
6.1.2
6.2
6.2.1
6.2.2
7
7.1
7.2
8
9
10
11
1
Scope of application
Design
Connection of the skirt
Flexible connection
Flexurally stiff connection
Gussets
Bottom
Ventilation of the space underneath the sloping base
Calculation variables
Determination of the sectional forces for the proof of the
strength
Cylinder
Load case for the filling
Load case for the overpressure
Sloping base
Load case for the filling
Load case for the overpressure
Proof of the strength
Determination of the sectional forces for the proof of the
stability
Load case for the filling
Gussets
Skirt
Load case for the overpressure
Gussets
Skirt
Proof of the stability
Gussets
Skirt
Dimensioning
Anchoring
Design-related details
Literature
sides of the opening using a transverse gusset. The opening in
the skirt is reinforced with a pipe socket which has the minimum
length dA/2 and is welded on both sides with the same projection.
If both the replaceable gussets are welded with the skirt, the
pipe socket is not necessary.
– Shut-off valves and miscellaneous fittings must be arranged
outside the skirt; there is no accessibility to the space below
the sloping base.
– A tank with a sloping base and without a collecting device is
calculated.
2 Design
The lower region of the tank with a sloping base consists of the
following four structural elements:
–
–
–
–
lower cylinder course
sloping base
skirt
gussets, supported by bulkheads
2.1 Connection of the skirt
2.1.1 Flexible connection
In the case of tanks fabricated from plates, it is appropriate to
fabricate the cylinder and the skirt separately and to arrange the
bottom in between. For this purpose, the lower course and the
skirt are chamfered according to the angle of the sloping base.
The sloping base is fabricated with an outside diameter of approx.
d + 5 · s. The lower course and the sloping base are joined with
an extruder weld a > = 0.7 · s on the inside and on the outside.
The skirt is joined with the sloping base with an extruder weld
a > = 0.7 · s from the outside only (flexible connection of the skirt).
2.1.2 Flexurally stiff connection
Scope of application
The following design and calculation rules apply to vertical, cylindrical tanks which are fabricated from thermoplastics in the factory
and are equipped with a vertical skirt and sloping bases supported
by parallel gussets. The cylinder and the skirt can be either fabricated from panels or manufactured in the winding process.
For the application of this supplement, it is necessary to satisfy
the following prerequisites:
– The gussets are arranged parallel to the inclination direction of
the sloping base (trapezoidal gussets).
– For the draining of the residues, provision is made for an opening in the sloping base - guided through the skirt with an elbow.
For this purpose, the central gusset must be guided past both
The cylinder and the skirt are fabricated in one piece. The sloping
base is fitted in and is welded with the cylinder and the skirt in a
flexurally stiff joint from the top and from the bottom (flexurally
stiff connection of the skirt).
2.2 Gussets
The gussets are arranged parallel to each other at equal distances
apart. The gussets must be cut to the exact dimensions; they can
(but do not have to) be welded with the sloping base. The gussets are supported by bulkheads which are the same distance
apart as the gussets. The bulkheads and the gussets must be
welded with each other. The ends of the gussets must be secured against lateral deflection; this may happen either by welding
them on to the skirt or using additional bulkheads.
This publication has been drawn up by a group of experienced specialists working in an honorary capacity and its consideration as an important source of information
is recommended. The user should always check to what extent the contents are applicable to his particular case and whether the version on hand is still valid.
No liability can be accepted by the Deutscher Verband für Schweißen und verwandte Verfahren e.V., and those participating in the drawing up of the document.
DVS, Technical Committee, Working Group "Joining of Plastics"
Orders to: DVS Media GmbH, P. O. Box 10 19 65, 40010 Düsseldorf, Germany, Phone: + 49(0)211/1591- 0, Telefax: + 49(0)211/1591-150
276
Page 2 to DVS 2205-2 Supplement 9
2.3 Bottom
pük,B
A closing bottom can be welded on to the skirt from the outside
with a continuous extruder weld a > = 0.7 · s. If the tank does not
have to be anchored, a tack weld suitable for transport is sufficient.
K KZ,d
F
K LB,d
N/mm² Dimensioning value of the stresses effective for
a short time in the cylinder resulting from the
load case for the overpressure at Position B
N/mm² Dimensioning value of the stresses effective for
a long time in the sloping base resulting from
the load case for the filling
N/mm² Dimensioning value of the stresses effective for
a long time in the sloping base resulting from
the load case for the overpressure
N/mm² Dimensioning value of the stresses effective for
a short time in the sloping base resulting from
the load case for the overpressure
N/mm² Dimensioning value of the strength effective for
a short time
N/mm² Tensile stresses resulting from pü in the skirt
R&D INTAKE MANIFOLDS
2.4 Ventilation of the space underneath the sloping base
The space underneath the sloping base must be ventilated in
order to permit pressure equalisation in the event of temperature
changes. This is the case when the drainpipe is not welded with
the skirt.
The upper part of the tank is designed and calculated in
analogy to the flat-bottom tank.
pü
K LB,d
püK
K KB,d
*
K K,d
pü
3
Calculation variables
a
mm
Distance between the sloping base and bottom
at the lowest point
A1
–
A1K
–
A2
–
Reduction factor for the influence of the specific
toughness for a wall temperature effective for a
long time
Reduction factor for the influence of the specific
toughness for a wall temperature effective for a
short time
Reduction factor for the medium in the case of
the proof of the strength
A2I
–
Reduction factor for the medium in the case of
the proof of the stability
K Zar
K Zar
N/mm² Tensile stresses resulting from püK in the skirt
MW
Nmm
püK
AR
mm²
Cross-sectional area of the open ring
ps
Bending moment from the wind load at the lower
edge of the skirt
–
Number of gussets
–
Number of rings on the substitute tank
N
Dimensioning value of the global compressive
force resulting from the filling in the supporting
ring
N
Dimensioning value of the global compressive
force resulting from the filling in the skirt
N
Dimensioning value of the global compressive
force resulting from the snow load in the skirt
N/mm² Snow pressure on the roof
bPr
mm
Width of the anchor claw
puK
N/mm² Partial vacuum effective for a short time
d
mm
Nominal inside diameter of the cylinder and of
the skirt
püK
N/mm² Overpressure effective for a short time
pü
N/mm² Overpressure effective for a long time
TC
EK
N/mm² Short-time elastic modulus at T°C
20C
EK
N/mm² Short-time elastic modulus at 20°C
r
s
mm
mm
20C
N/mm² Long-time elastic modulus at 20°C
EL
g
GA
m/sec² Acceleration due to gravity
N
Dead load of the additional weight on the roof
GD
N
Dead load of the roof
Gges
N
Dead load of the tank
GZ
N
Dead load of the cylinder
GB
N
Dead load of the sloping base
GZar
N
Dead load of the skirt
hF
mm
hS
mm
hZar
mm
Filling height measured from the lowest point
of the sloping base
Mean height of the highest buckling field of the
gussets
Maximum height of the skirt
kf
–
Concentration factor according to [5]
F,A
K LZ,d
F,B
K LZ,d
pü,A
K LZ,d
pü,B
K LZ,d
pük,A
K KZ,d
N/mm² Dimensioning value of the stresses effective for
a long time in the cylinder resulting from the
load case for the filling at Position A
N/mm² Dimensioning value of the stresses effective for
a long time in the cylinder resulting from the
load case for the filling at Position B
N/mm² Dimensioning value of the stresses effective for
a long time in the cylinder resulting from the
load case for the overpressure at Position A
N/mm² Dimensioning value of the stresses effective for
a long time in the cylinder resulting from the
load case for the overpressure at Position B
N/mm² Dimensioning value of the stresses effective for
a short time in the cylinder resulting from the
load case for the overpressure at Position A
m
n
Füllung
N R,d
Füllung
N Zar,d
Schnee
N Zar,d
sB
mm
sS
mm
TA
°C
TAK
°C
TM
°C
Radius of the cylinder/skirt
Wall thickness of the lowest course, of the skirt
and of the sloping base
Wall thickness of the bottom
Wall thickness of the gussets and of the
bulkheads
Mean ambient temperature (according to Miner,
see the DVS 2205-1 technical code)
Highest ambient temperature
TMK
°C
Mean media temperature (according to Miner,
see the DVS 2205-1 technical code)
Highest media temperature
WR
mm³
Resistance moment of the open ring
zS
mm

°
Zar
–
Distance between the centres of gravity of the
open ring and of the cylinder axis
Pitch of the sloping base measured against the
horizontal line
Factor for the axial stability of the skirt

A,S
–
–
Side ratio of the buckling field
Utilisation of the axial stability in the gusset
A,Zar
–
Utilisation of the axial stability in the skirt
F1
–
Partial safety coefficient of the effect
(dead load and filling)
F2
–
Partial safety coefficient of the effect
(pressures and wind)
F3
–
Partial safety coefficient of the effect
(reducing dead load)
I
–
Weighting coefficient according to the
DVS 2205-2 technical code, Table 2
M
–
Partial safety coefficient of the resistance/
stressability

–
Poisson's ratio
277
Page 3 to DVS 2205-2 Supplement 9
F
g/cm³
e
N/mm² Buckling stress in the gusset
k,d
N/mm² Dimensioning value of the buckling stress in
the gusset
N/mm² Dimensioning value of the axial buckling stress
of the skirt
k,Zar,d
F
 S,d
pük
 S,d
F
 Zar,d
vorh
 Zar,d
Density of the filling medium
4.1.2 Load case for the overpressure
4.1.2.1 Position A
R&D INTAKE MANIFOLDS
N/mm² Dimensioning value of the compressive stresses
on the gusset, load case for the filling
N/mm² Dimensioning value of the compressive stresses
on the gusset, load case for the overpressure
N/mm² Dimensioning value of the compressive stresses on the skirt, load case for the filling
N/mm² Dimensioning value of the compressive stresses on the skirt
4 Determination of the sectional forces for the proof of the
strength
The sectional forces can be determined not only with a finite element
program but also approximately with a rotational shell program for
thin-walled elements with a linear-elastic approach. In this way, it
is possible to establish the wall thicknesses of the cylinder, of the
skirt and also for the sloping base in such a way that the utilisation
of the individual elements is optimum, i.e. it permits economically
viable and safe dimensioning.
In this supplement, formulae are provided for the manual computation. For their application, attention must be paid to the following
restrictions on the scope of application:
– The wall thicknesses of the lower cylinder course, of the skirt
and of the sloping base are identical.
– The pitch of the sloping base is confined to max. 10°.
– It is necessary to arrange three, five or seven gussets.
– The wall-thickness-to-radius ratio is within the following limits:
0.04 > = s/r > = 0.01.
– Only the gussets are in contact with the sloping base.
– Any welds in the sloping base are arranged transverse to the
gussets.
4.1 Cylinder
Two positions must be taken into consideration:
Position A Cylinder wall perpendicular to the central gusset,
bottom supported by the gusset.
In order to calculate the greatest stress in the cylinder,
it is assumed that the gusset is welded with the skirt.
Thus, the lower edge of the cylinder cannot be twisted; this means that the cylinder must be calculated
as fully clamped.
Position B Cylinder wall parallel to the gussets, bottom unsupported as far as the outside gusset.
As an alternative, the stresses on the cylinder are
calculated on a fictitious tank with a ring-supported
flat bottom. n = (m –1)/2 rings are estimated for m
gussets.
4.1.1 Load case for the filling
4.1.1.1 Position A
F,A
K LZ,d = 1.87   F1   F  g  10
–6
r
  h F + r  tan  B   ---  A 1  A 2   l
s
N/mm² (1)
pü,A
r
K LZ,d =  1.87 + 0.5    F2  p ü  ---  A 1  A 2   l N/mm²
s
püK,A
K KZ,d in analogy to püK
4.1.2.2 Position B
pü,B
1
K LZ,d =  F2  p ü  -----------------------------  A 1  A 2   l N/mm²
e
F,B
püK,B
Tables 1 and 2 show Constants C and D.
4.2 Sloping base
Two positions must be taken into consideration:
Position B Cylinder wall parallel to the gussets, bottom unsupported as far as the gusset.
As an alternative, the stresses on the sloping base
(field moment) are calculated on a fictitious tank with
a ring-supported flat bottom. n = (m –1)/2 rings are
estimated for m gussets.
Position C The sloping base above the outside gusset (supporting moment) is also calculated on a fictitious tank
with a ring-supported flat bottom. Comparative calculations on a fictitious continuous beam resulted in
lower stresses.
4.2.1 Load case for the filling
The greatest stress resulting from the filling arises either in the
sloping base at the interface between the cylinder and the skirt or
in the sloping base above the gussets. Therefore, it is necessary
to calculate both stresses; the greater of the two stresses is crucial. The stresses are effective parallel to any weld in the bottom.
It is not necessary to estimate a welding factor.
The following formula for the dimensioning value of the greatest
stress takes account of the total of the bending and normal
stresses.
F
K LB,d =  F1   F  g  10
1
 h F  ----------------------------  A 1  A 2   l N/mm² (2)
s
A  ln  --- + B
 d
e
Tables 1 and 2 show Constants A and B.
278
–6
1
1
 h F  max ---------------------------- ----------------------------e
s
E  ln  --- + F
d
e
s
G  ln  --- + H
d
 A 1  A 2   l N/mm²
(5)
Tables 1 and 2 show Constants E to H.
4.2.2 Load case for the overpressure
The greatest stress in the cylinder arises either at the interface to
the bottom or in the sloping base above the gussets. Therefore, it
is necessary to calculate both stresses; the greater of the two
stresses is crucial. The stresses are effective parallel to the weld
in the bottom. It is not necessary to estimate a welding factor.
The following formula for the dimensioning value of the greatest
stress takes account of the total of the bending and normal
stresses.
pü
1
1
K LB,d =  F2  p ü  max ---------------------------- -----------------------------  A 1  A 2   l
e
–6
(4)
s
C  ln  --- + D
 d
K KZ,d in analogy to püK
4.1.1.2 Position B
K LZ,d =  F1   F  g  10
(3)
s
K  ln  --- + L
d
e
s
M  ln  --- + N
d
N/mm²
püK
K KB,d
in analogy to püK
Tables 1 and 2 show Constants K to N.
(6)
Page 4 to DVS 2205-2 Supplement 9
5
Proof of the strength
The proof of the strength is provided in the way indicated in the
DVS 2205-2 technical code with the stresses described in Section 4. The mean media temperature TM must be estimated as
the effective wall temperature in the cylinder and in the sloping
base and the highest media temperature TMK in the case of a
short-time effect.
Compressive stresses according to Sections 6.1 and 6.2 are converted into global normal forces and, in the case of outdoor installation, are estimated for the weakened cross-section (open ring)
together with the bending moment resulting from the wind load
Mw. For this purpose, it is necessary to establish the area AR, the
centre of gravity zS and the resistance moment WR of the ring
cross-section. The axial compressive stresses next to the opening
must be calculated while paying attention to the misalignment of
the centroidal axis.
R&D INTAKE MANIFOLDS
6
Determination of the sectional forces for the proof of the
stability
For gussets and skirts bearing the entire filling load, it is necessary
to provide proof of the axial stability.
6.1 Load case for the filling
6.1.1 Gussets
The greatest stress on the gussets is established on a fictitious
continuous beam with m + 1 fields. Irrespective of the number of
intermediate supports m, the greatest supporting force B can be
calculated with the factor 1.15:
B = 1.15 · p · l with l = d/(m + 1) and p =  · g · 10–6 · hF
This results in the dimensioning value of the stresses in the gussets:
F
 S,d
= 1.15   F1   F  g  10
–6
d
 h F  ---------------------------  A 1  A 2   l
s  m + 1
N/mm² (7)
6.1.2 Skirt
The greatest compressive stress on the skirt is to be expected at
Position B . A fictitious continuous beam with m + 1 fields is
considered. Irrespective of m, the external bearing force A can be
calculated in a simplifying method with the factor 0.4: A = 0.4 · p · l.
With l = d/(m + 1) and p =  · g · 10–6 · (hF + r · tan B), it follows:
F
 Zar,d = 0.4   F1   F  g  10
–6
d
  h F + r  tan  B   --------------------------s  m + 1
 A 1  A 2   l N/mm²
(8)
m + 0.5
h S = a + -------------------  d  tan  B mm
m+1
hS   m + 1 
The side ratio is:  = ----------------------------d
The dimensioning value of the buckling stress is prepared:
k  e
 k,d = ----------------  K *K,d N/mm²
M
2
TC
sS   m + 1 
  EK
-  ----------------------------with  e = -----------------------------2
d
12   1 –  
(11)
(12)
(13)
2
N/mm²
(14)
and k for the quick use from the diagrams according to [3]:
The following is applicable if the gussets are not welded with the
sloping base:
k  =  + 1.1  2.3
(15)
or the following is applicable if the gussets are welded with the
sloping base:
2
k  = –3.1   + 5.1   + 0.3
for   0.8
(16)
k  = –0.37   + 2.7  2.3
for   0.8
(17)
pük
 S,d
+
The utilisation is:  A,S = ---------------------------  1
 k,d
(18)
The load case for the overpressure is not considered since the
overpressure subjects the skirt to tensile stresses.
The greatest compressive stress in the gussets results in analogy
to Equation (7).
(9)
The following is applicable:
Füllung
N Zar,d
Schnee
N Zar,d
F
N
(19)
=  F2    r  p S
N
(20)
= 2    r  s   Zar,d
2
In the case of indoor installation:
6.2.2 Skirt
The characteristic value of the greatest tensile stress in the skirt
is needed for the proof of the anchoring. As an alternative, the
stresses are calculated on a fictitious tank with a ring-supported
flat bottom. n = (m –1)/2 rings are estimated for m gussets
pü
1
K Zar = p ü  ----------------------------- N/mm²
s
U  ln  --- + V
 d
(10)
e
Tables 1 and 2 show Constants U and V.
7
The height of the buckling field at the centre point is:
7.2 Skirt
6.2.1 Gussets
d
= 1.15   F2  p ük  ---------------------------  A 1  A 2   l N/mm²
s  m + 1
Only the highest gusset field is proven with the compressive
stresses according to Sections 6.1.1 and 6.2.1.
F
 S,d
6.2 Load case for the overpressure
pük
 S,d
7.1 Gussets
Proof of the stability
The dimensioning value of the axial compressive stresses must
be compared with the dimensioning value of the buckling stress.
Buckling is a short-time process and the proof must be provided at
the wall temperatures resulting from TMK and TAK. For the proof of
the skirt, (TMK+ + TAK)/2 must be estimated as the effective wall
temperature and min. 50°C in the case of direct solar radiation.
TMK must be estimated as the effective temperature of the gussets and min. (TMK + 35)/2 in the case of outdoor installation. Min.
20°C must be used for TAK in the case of indoor installation and min.
35°C for outdoor installation.
vorh
Füllung
1 zS 
 Zar,d =  N Zar,d +  F1   G ges + G A  k f     ------- + -------- N/mm²
A W 
R
R
(21)
TC
with E k for (TMK + TAK)/2°C in Equation (24)
In the case of outdoor installation:
Summer:
vorh
Füllung
1 z S   F2  M W
 Zar,d =  N Zar,d +  F1   G ges + G A  k f     ------- + -------- + ---------------------A W 
WR
R
R
N/mm² (22)
TC
with E k for (TMK + TAK)/2, in the case of direct solar radiation
for min. 50°C in Equation (24)
Winter:
It is not necessary to provide any proof with snow or at a winter
temperature since this does not determine the dimensioning.
The following condition must be complied with for the skirt:
vorh
 l   Zar,d
 A,Zar = ---------------------1
 k,Zar,d
Remark: A2I is not necessary since there is no wetting with media.
(23)
279
Page 5 to DVS 2205-2 Supplement 9
where:
T MK + T AK
-------------------------- C
2
but min. 50°C in the case of direct solar radiation
Case 1: Short-time overpressure at
for hZar/r > 0.5:
TC
s
EK
-  -- k,Zar,d =  Zar  0.62  ----------M r
(24a)
R&D INTAKE MANIFOLDS
for hZar /r  0.5:
 k,Zar,d =  Zar  0.62 
TC
EK
------------
M
2
s
s
r
 ---  1 + 1.5   ----------  -- hZar  r
r
(24b)
1
püK
  F2  2    r  s  K Zar –  F3   G D + G Z + G Zar    --z
----------------------------------------------------------------------------------------------------------------------------------1
*
K K,d
 b Pr + s B   s B  ---------------------2  A1  l
Case 2: Long-time overpressure at
with
0.65
 Zar = -------------------------------------------------------20C
EK
r 
--------------   1 + ---------------20C 
100  s
EL
(25)
8 Dimensioning
(26)
TM + TA
-------------------C
2
pü
1
  F2  2    r  s  K Zar –  F3   G D + G Z + G Zar    --z
---------------------------------------------------------------------------------------------------------------------------------1
*
K L,d
-------------------- b Pr + s B   s B 
2  A1  l
(27)
Case 3: Wind load at 20°C (only in the case of outdoor installation)
The greatest wall thickness s resulting from the proof of the
strength and from the proof of the stability must be executed for
the lower cylinder course, for the sloping base and for the skirt.
The wall thickness of the gussets and of the bulkheads sS results
from the proof of the stability according to Section 7.1.
9 Anchoring
If anchoring becomes necessary, at least four anchors must be
arranged (z  4). With regard to the proof of the anchoring, a distinction must be made between three cases:
4   F2  M W
pü
1
------------------------------ +  F2  2    r  s  K Zar –  F3   G D + G Z + G Zar   --z
d
-----------------------------------------------------------------------------------------------------------------------------------------------------------------1
*
K K,d
 b Pr + s B   s B  ---------------------2  A1  l
(28)
While paying attention to the lever arms, the required anchor
force (e.g. for the plugs) must be calculated from the maximum
claw force (maximum of the numerators in Equations 26 to 28).
10 Design-related details
Computational dimensions
Fabrication dimensions
hD
hD
hZ2
SD
h ges = h ges + S B + ---------------cos  D
hZ h
F
hges
hges
h Zar2 = h Zar + r  tan  B – c
s
c = ----------------- – s  tan  B
cos  B
h Z1 = h Z + r  tan  B + b
h D
2  SD
= r  tan  D + ---------------cos  D
Figure 1.
280
Overview and dimensions.
hZar
hZar2
Page 6 to DVS 2205-2 Supplement 9
R&D INTAKE MANIFOLDS
All welds
a = 0.7 · s
Figure 2.
Bonding of the bottom.
Gusset
Sloping base
Figure 5a. Bonding of the sloping base; flexible connection of the skirt.
Bulkhead
Flat bottom
All welds
a = 0.7 · s
Gusset
Figure 3.
Bulkhead
Figure 4.
Figure 5b. Bonding of the sloping base; clamped connection of the skirt.
 dA/2
Change
Opening
Figure 6.
Detail:
Bottom with opening and replacement of the gussets.
281
Page 7 to DVS 2205-2 Supplement 9
11 Literature
Table 1. Flexible connection of the skirt.
Number of gussets
m=3
m=5
m=7
Cylinder
Filling
A
1.9678
1.7531
1.5201
3.6451
3.2719
2.5455
Cylinder
Overpressure
C
1.8731
1.6173
1.3757
D
3.1001
2.4547
1.6147
E
1.9363
1.7131
1.4777
F
3.4562
3.0336
2.2876
G
1.9913
1.9746
1.9558
H
3.0130
3.7436
4.2176
K
1.9477
1.712
1.4489
L
3.5231
3.0454
2.1617
M
1.9965
1.9805
1.9683
N
3.0402
3.7764
4.2856
U
1.0039
1.0292
1.0524
V
1.9490
1.8881
1.9171
Sloping base
Filling
Sloping base
Overpressure
nZar load case
Overpressure
B
R&D INTAKE MANIFOLDS
Table 2. Flexurally stiff connection of the skirt.
Number of gussets
m=5
m=7
1.5389
1.3639
Cylinder
Filling
B
3.0288
2.4054
1.8380
Cylinder
Overpressure
C
1.6861
1.4494
1.2634
D
2.5524
1.8686
1.2072
E
1.9545
1.7845
1.5787
Sloping base
Overpressure
nZar load case
Overpressure
282
m=3
1.7714
A
Sloping base
Filling
[1] DVS 2205-2: Calculation of tanks and apparatus made of
thermoplastics – Vertical round, non-pressurised tanks.
F
3.4694
3.3195
2.7603
G
1.9907
1.9696
1.9469
H
3.0206
3.7236
4.1747
K
1.9451
1.7388
1.4864
L
3.4214
3.0767
2.2555
M
1.9995
1.9857
1.9690
N
3.0682
3.8122
4.2955
U
1.0048
1.0288
1.0528
V
1.9679
1.8962
1.9265
[2] Pflüger, Alf: Stability problems in elastostatics. Springer Verlag.
[3] Tuercke, H.: Derivation of simplified formulae for the determination of the sectional forces for the dimensioning of parallelsupported sloping bases. Unpublished.
[4] Tuercke, H.: On the stability of tanks made of thermoplastics.
DIBt Communications, No. 5/1995.
[5] Tuercke, H.: On the introduction of axially directed individual
loads into the upper edge of thermoplastic tanks. DIBt Communications, No. 4/2002.
January 2012
Calculation of tanks and apparatus
made of thermoplastics –
Vertical round non-pressurised tanks –
Example of a parallel-supported sloping base
DVS – DEUTSCHER VERBAND
FÜR SCHWEISSEN UND
VERWANDTE VERFAHREN E.V.
Technical Code
DVS 2205-2
Reprinting and copying, even in the form of excerpts, only with the consent of the publisher
R&D INTAKE MANIFOLDS
Contents:
3 Proof of the strength
1
2
3
3.1
3.2
3.3
4
4.1
4.1.1
4.1.2
4.2
4.2.1
4.2.2
4.2.3
5
3.1 Initial estimation
1
Introduction
Data for the tank
Proof of the strength
Initial estimation
Proof of the strength in the cylinder
Proof of the strength in the sloping base
Proof of the stability
Gussets
Load case for the filling
Load case for the overpressure
Skirt
Load case for the filling
Load case for the overpressure
Dimensioning
Anchoring
Introduction
Füllung
K L,d
–6
and
KFüllung
=  F1   F  g  10
L,d
–6
r
  h F + r  tan  B   ---  A 1  A 2   l
s
N/mm²
1 -  A  A   N/mm²
 h F  -----------------------1
2
l
s
e
Aln  --- + B
d
According to Table 1 in Supplement 9, A = 1.5201 and
B = 2.5455.
The formulae are solved with the condition KFüllung
= K*L,d
L,d
= 10.2/1.1 according to s.
–6
1.87   F1   F  g  10   h F + r  tan  B   r  A 1  A 2   l
s 1 = -------------------------------------------------------------------------------------------------------------------------------------------K*L
-----M
This example is intended
to facilitate the application of Supple=
s1
ment 9 to the DVS 2205-2 technical code.
and
2
= 1.87   F1   F  g  10
Supplement 10
–6
1.87  1.35  1.29  9.81  10  4,087  1,000  1.2
------------------------------------------------------------------------------------------------------------------------------=
- 16.9 mm
10.2
----------1.1
–6
Data for the tank
Design:
Cylinder and skirt fabricated from plates
Geometry:
d = 2,000 mm (inside); hGes = 5,000 mm;  = 5°;
seven gussets welded with sloping base
Installation:
Outdoor installation without any wind-shielding
collecting device
Wind Zone 2: inland area ;
Snow Load Zone 2: up to 285 m
q = 0.65 kN/m2
pS = 0.68 kN/m2, TA = 10°C, TAK = 35°C
Material:
PE 100; 25 years
Filling:
Battery acid; TM = TMK = 20°C; hF = 4,000 mm;
A1 = A1K = A2 = A2I = 1; F = 1.29 g/cm³
Ventilation:
Closed system püK = pü = 0.01 bar;
puK = 0.01 bar
Loading type: Loading Case II; I = 1.2
Openings:
dA = 200 mm
Distance:
a = 300 mm
Anchoring:
Claw width bPr = 70 mm
s2 = d 
  F1    g  10  h F  A 1  A 2   l
ln  ----------------------------------------------------------------------------------- – B
K*L,d


-------------------------------------------------------------------------------------------------------A
e
s 2 = 2,000 


–6
1.35  1.29  9.81  10  4,000  1.2
ln  --------------------------------------------------------------------------------------------- – 2.5455
10.2
----------

1.1
--------------------------------------------------------------------------------------------------------------------------------1.5201
e
=
16.7 mm
Chosen s = 20 mm.
3.2 Proof of the strength in the cylinder
It is checked whether s = 20 mm in the cylinder is sufficient for
the total resulting from the load case for the filling and the load
case pü.
Position A , load case for the filling
F,A
K LZ,d = 1.87   F1   F  g  10
–6
r
  h F + r  tan  B   ---  A 1  A 2   l
s
F,A
K LZ,d = 1.87  1.35  1.29  9.81  10
–6
1,000
 4,087  ---------------  1.2
20
= 7.83 N/mm²
This publication has been drawn up by a group of experienced specialists working in an honorary capacity and its consideration as an important source of information
is recommended. The user should always check to what extent the contents are applicable to his particular case and whether the version on hand is still valid.
No liability can be accepted by the Deutscher Verband für Schweißen und verwandte Verfahren e.V., and those participating in the drawing up of the document.
DVS, Technical Committee, Working Group "Joining of Plastics"
Orders to: DVS Media GmbH, P. O. Box 10 19 65, 40010 Düsseldorf, Germany, Phone: + 49(0)211/1591- 0, Telefax: + 49(0)211/1591-150
283
Page 2 to DVS 2205-2 Supplement 10
Position A , load case for the overpressure
Position C , load case for the overpressure
pü,A
r
K LZ,d =  1.87 + 0.5    F2  p ü  ---  A 1  A 2   l
s
pü,A
1,000
K LZ,d
2.37
=
 1.5  0.001  ---------------  1.2
0.213 N/mm²
20
pü,C
1
K LB,d =  F2  p ü  -----------------------------  A 1  A 2   l
s
M  ln  --- + N
 d
R&D INTAKE MANIFOLDS
Position B , load case for the filling
F,B
K LZ,d =  F1   F  g  10
–6
e
with M = 1.9683; N = 4.2856 according to Table 1 in Supplement 9
follows:
1
pü,C
 h F  ----------------------------  A 1  A 2   l
=
K LB,d
s
A  ln  --- + B
 d
e
1.5
=
 0.001  118.96  1.2
0.214 N/mm²
Position B , utilisation
with A = 1.5201; B = 2.5455 according to Table 1 in Supplement 9
follows:
pü,B
F,B
K LB,d + K LB,d
7.51 + 0.164
=
=
-------------------------------=

-------------------------------–6
F,B
K LZ,d
1.35
=
 1.29  9.81  10  4,000  86.04  1.2
7.06 N/mm²
10.2
K *L,d
----------1.1
Position B , load case for the overpressure
Condition fulfilled!
pü,B
1
K LZ,d =  F2  p ü  -----------------------------  A 1  A 2   l
s
Position C , utilisation
C  ln  --- + D
d
e
pü,C
F,C
K LB,d + K LB,d
9.86 + 0.214
with C = 1.3757; D = 1.6147 according to Table 1 in Supplement
9
=
=
-------------------------------=

-------------------------------10.2
K *L,d
follows:
----------1.1
pü,B
=
K LZ,d
1.5
=
 0.001  112.24  1.2
0.202 N/mm²
Condition not fulfilled!
Position A , utilisation
F,A
=

pü,A
K LZ,d + K LZ,d
=
-------------------------------K *L,d
Condition fulfilled!
F,B
=

pü,B
1.09  1
New choice: s = 25 mm!
7.83 + 0.213
-------------------------------=
10.2
----------1.1
0.87  1
4
Proof of the stability
4.1 Gussets
Position B , utilisation
K LZ,d + K LZ,d
=
-------------------------------K *L,d
0.83  1
4.1.1 Load case for the filling
7.06 + 0.202
-------------------------------=
10.2
----------1.1
sS = 15 mm is chosen for the gussets and the bulkheads.
0.78  1
The greatest compressive stress in the gussets results from:
F
Condition fulfilled!
 S,d = 1.15   F1   F  g  10
3.3 Proof of the strength in the sloping base
–6
d
 h F  ---------------------------  A 1  A 2   l N/mm²
s  m + 1
F
–6
2,000
 4,000  -----------------------------  1.2
15   7 + 1 
It is checked whether s = 20 mm in the sloping base is sufficient
for the total resulting from the load case for the filling and the load
case pü.
 S,d = 1.15  1.35  1.29  9.81  10
Position B , load case for the filling
4.1.2 Load case for the overpressure
F,B
K LB,d =  F1   F  g  10
–6
1
 h F  ----------------------------  A 1  A 2   l
e
s
E  ln  --- + F
d
with E = 1.4777; F = 2.2876 according to Table 1 in Supplement 9
follows:
F,B
K LB,d
–6
1.35
=
 1.29  9.81  10  4,000  91.6  1.2
Position B , load case for the overpressure
pü,B
1
K LB,d =  F2  p ü  ----------------------------  A 1  A 2   l
7.51 N/mm²
= 1.57 N/mm²
The greatest compressive stress in the gussets results from:
püK
d
 S,d = 1.15   F2  p üK  ---------------------------  A 1  A 2   l
s  m + 1
püK
2,000
 S,d = 1.15  1.5  0.001  -----------------------------  1.2 = 0.0345 N/mm²
15   7 + 1 
The height of the largest buckling field at the centre point:
=
hS
s
K  ln  --- + L
d
 m + 0.5 
a=
+ ------------------------  d  tan  B
m+1
7 + 0.5
300 + ------------------  2,000  tan 5
7+1
= 464 mm
e
The side ratio is:
with K = 1.4489; L = 2.1617 according to Table 1 in Supplement 9
hS   m + 1 
follows:
464   7 + 1 

=
----------------------------=
------------------------------=
1.856
d
2,000
pü,B
=
K LB,d
1.5
=
 0.001  90.99  1.2
0.164 N/mm²
The dimensioning value of the buckling stress is
k  e
Position C , load case for the filling
*
 k,d = ----------------  K K,d
M
1
–6
F,C
---------------------------K LB,d =  F1   F  g  10  h F 
 A1  A2  l
s
G  ln  --- + H
with
d
e
2
TC
2
sS   m + 1  2
  EK
15   7 + 1 
  800
with G = 1.9558; H = 4.2176 according to Table 1 in Supplement 9
-  ------------------------------------------------------------------- ----------------------------=
 e -----------------------------=
2
2
follows:
d
2,000
12   1 –  
12   1 – 0.38 
F,C
K LB,d
284
–6
1.35
=
 1.29  9.81  10  4,000  120.2  1.2 9.86 N/mm²
= 2.77 N/mm²
2
Page 3 to DVS 2205-2 Supplement 10
TC
with E K
5
= 800 N/mm² for TM = 20°C and k = 2.3
follows
 k,d
=
2.3  2.77
----------------------=
1.2
5.79 N/mm²
pük
 S,d 
l 
+
--------------------------------------=
 k,d
 A,R
=
1
0.001
=
 ----------------------------------------------------------e
4.2 Skirt
25
1.0524  ln  --------------- + 1.9171
 2,000
0.0148 N/mm²
pü
K Zar = 0.0148 N/mm²
4.2.1 Load case for the filling
As an example, 4,000 N is assumed as the weight GD + GZ + GZar.
The greatest compressive stress in the skirt results from:
F
 Zar,d = 0.4   F1   F  g  10
–6
d
  h F + r  tan  B   --------------------------s  m + 1
 A 1  A 2   l N/mm²
F
 Zar,d = 0.4  1.35  1.29  9.81  10
= 0.3351 N/mm²
Füllung
s
U  ln  --- + V
d
e
with U = 1.0524; V = 1.9171 according to Table 1 follows:
 =
1.2
1.57 + 0.0345 ----------------------------------------------------0.33  1
5.79
pü
K Zar
=
Condition fulfilled!
Füllung
=
NZar,d
pü
1
K Zar = p ü  -----------------------------
R&D INTAKE MANIFOLDS
The following condition for the gussets must be complied with:
F
  S,d
Anchoring
For Case 3, the greatest tensile stress in the skirt results from:
2=
   r  s  Zar,d
–6
2,000
 4,087  -----------------------------  1.2
25   7 + 1 
sB = 20 mm is chosen as the thickness of the bottom.
Wind load with K *K,d = 14.8/1.1 N/mm² for 20°C
4   F2  M W
pü
1
------------------------------ +  F2  2    r  s  K Zar –  F3   G D + G Z + G Zar   --z
d
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------  1
*
K K,d
 b Pr + s B   s B  ---------------------2  A1  l
4  1.5  13,325,000
-------------------------------------------------- + 1.5  2    1,000  25  0.0148 – 0.9   4,000 
2,000
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------14.8
----------1.1
 70 + 20   20  -----------------------2  1  1.2
= z
2    1,000  25  0.335
= 52,637 N
2
2
h ges
0.65
5,000
c=
0.8  ---------------   2,000 + 50   ----------------f  q  d  ---------2
2
1,000
= 13,325,000 Nmm
z
=
4.2.2 Load case for the overpressure
MW
=
The load case for the overpressure is not considered since it subjects the skirt to tensile stresses.
4.2.3 Dimensioning
It is only necessary to provide the proof for the summer load case:
39,975 + 3,487 – 3,600
-----------------------------------------------------------=
10,091
3.95
Four anchors are executed.
The lower course of the cylinder, the skirt and the sloping
base must be manufactured from panels with a thickness of
25 mm. The seven gussets and the relevant bulkheads must
be executed with a thickness of 15 mm.
z S   F2  M w
Füllung
vorh
1- + ------- Zar,d = NZar,d   ------ + --------------------- N/mm²
A
W 
W
R
TC
with E k
R
R
for 50°C
with the cross-section values for the open ring r = 1,012.5 mm;
dA = 200 mm
AR = 154,035 mm²; zS = 32.87 mm; WR = 73,276,623 mm³
vorh
1 - + ----------------------------32.87 - + 1.5
 13,325,000
 Zar,d = 52,637   ------------------------------------------------------------ 154,035 73,276,623
73,276,623
= 0.3653 + 0.2728 = 0.638 N/mm²
=
 Zar
0.65
=
-------------------------------------------------------20C
EK
r 
1 + ----------------------------
20C 
100  s 
E
L
0.65
-----------------------------------------------------=
800 
1,012.5 
----------  1 + -------------------235 
100  25 
0.2972
and because h Zar /r  0.5
TC
EK - s
r 2 s
 k,Zar,d =  Zar  0.62  ---------- ---  1 + 1.5   ----------  -- h Zar r
M r
2
270
25
1,012.5
= 0.2972  0,62  ----------  --------------------  1 + 1.5   ---------------------------------------------------------------o-
 300 + 2  1,012.5  tan 5 
1.1 1,012.5
25
-------------------- = 1.303 N/mm²
1,012.5
vorh
=
 A,Zar
 l   Zar,d
--------------------=
 k, Zar,d
1.2  0.638
--------------------------=
1.303
0.59  1
Condition fulfilled!
285