Wall Thickness Calculation
Wall Thickness Calculation
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5	        Wall thickness calculation for ductile iron pipes                                      The two types of stress are calculated as
                                                                                                 follows:
                                                                                                         p.D
When laying underground pipelines consisting of ductile iron pipes to standard                   σt =    .       [N/mm²] 		                   (5.1)
EN 545 [5.1], for the most part the pipes are assembled using push-in joints as                          2 e
standardised in DIN 28603 [5.2]. For calculating the wall thickness of ductile iron
pipes, a distinction is made between
                                                                                                         p.D
n	 non-restrained flexible push-in joints and                                                    σa =    .       [N/mm²] 		                   (5.2)
n	 restrained flexible push-in joints.                                                                   4 e
                                                Fig. 5.1:
                                                Stresses produced by internal pressure in
                                                a wall of pressure pipes assembled with
                                                restrained joints
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5.2	      Calculating the wall thickness     Over the last six decades, non-restrained         In principle, they are calculated accord-
          of pipes with non-restrained       flexible push-in joints have had a consid-        ing to equation 5.1 (Barlow’s formula):
          flexible push-in joints            erable influence in shaping the image of
                                                                                                       p.D
                                             the cast iron pipe; they are inexpensive          σt =    .         [N/mm²] 		                 (5.1)
5.2.1	 Calculating the wall thickness        and simple to assemble. Non-restrained                    2 e
       of pipes according to pressure        push-in joints do not transmit any axial
       classes (C-classes)                   forces, meaning that the stresses shown           σt	   tangential stress in the
                                             in Fig. 5.1 in the axial direction σa are         	     pressure pipe wall [N/mm²]
For calculating the pipe wall thickness      equal zero. As can be seen in Fig. 5.2, the       p	    internal pressure [bar]
of ductile iron pipes with non-restrained    stresses in the wall of such a socket pipe        D	    mean diameter
flexible push-in joints, the simple Bar-     only run in the circumferential direction         		    (D = (DE + Di) / 2 = DE – e) [mm]
low’s formula is used in which the tan-      as tangential stress σt.                          e	    wall thickness [mm]
gential stresses produced by internal
pressure, the tensile strength of the pipe                                                     This produces the following equation for
material, the thickness of the pipe wall                                                       internal pressure p:
and the diameter of the pipe correlate
with each other.                                                                                                 [N/mm²]                    (5.2)
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With a minimum tensile strength 200 222 3.1 3.9 5.0 7.7
Rm = 420 MPa for ductile cast iron and          250         274                                             3.9         4.8         6.1    9.5
                                                300         326                                             4.6         5.7         7.3    11.2
the safety factor SF = 3 we arrive at the
                                                350         378                                 4.7         5.3         6.6         8.5    13.0
following constant 5.4:
                                                400         429                                 4.8         6.0         7.5         9.6    14.8
                                                450         480                                 5.1         6.8         8.4         10.7   16.6
20 . Rm                                         500         532                                 5.6         7.5         9.3         11.9   18.3
        = 2.800        [MPa]         (5.4)
  SF                                            600         635                                 6.7         8.9        11.1         14.2   21.9
                                                700         738                    6.8          7.8        10.4        13.0         16.5
                                                800         842                    7.5          8.9        11.9        14.8         18.8
The allowable operating pressure PFA            900         945                    8.4          10.0       13.3        16.6                       Table 5.1:
for the component can be calculated with       1000        1048                    9.3          11.1       14.8        18.4                       Minimum wall
equation 5.5 from the external pipe wall       1100        1152         8.2       10.2          12.2       16.2        20.2                       thicknesses emin
diameter DE and pipe wall thickness emin :     1200        1255         8.9       11.1          13.3       17.7        22.0                       for ductile iron
                                               1400        1462        10.4       12.9          15.5                                              pipes as per
                                               1500        1565        11.1       13.9          16.6
    [MPa]     (5.5)                                                                                                                               EN 545 [5.1]
                                               1600        1668        11.8       14.8          17.7
                                                                                                                                                  depending on
                                               1800        1875        13.3       16.6          19.9
                                                                                                                                                  nominal size DN
                                               2000        2082        14.8       18.4          22.1
                                                                                                                                                  and pressure class
                                             Note: the figures in bold represent the standard range
                                                                                                                                                  (C-class)
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Using equation 5.5 it is possible to cal-     When the first ductile iron pipes were           For drinking water supply, type K val-
culate the minimum wall thickness emin        produced in the middle of the nineteen           ues were 10 to begin with, then later on
for an allowable operating pressure PFA       fifties, safety standards were initially still   8 and 9. In order for wall thicknesses of
with a given nominal size:                    based on the characteristics of thick-           the smaller nominal sizes to remain prac-
                                              walled grey cast iron pipes. At the time,        tically feasible at all, the lower limit for
            DE . PFA [mm] 	                   casting machines were still being man-           nominal wall thicknesses was reduced to
emin =                               (5.6)
          2.800 + PFA                         ually controlled, meaning that the min-          e = 6 mm. The following determination
                                              imum wall thickness was only observed            applies to the minimum wall thickness
Table 5.1 shows the minimum wall thick-       with large “allowances”. For a coherent          emin for measurement purposes:
nesses emin according to EN 545 [5.1] for     representation of wall thicknesses over
the seven pressure classes (C-classes)        the entire range of nominal sizes, these         emin = e – Δe                [mm]	(5.9)
which are assigned to operating pressures     were divided into K-classes which were
PFA 20; 25; 30; 40; 50; 64 and 100. The       in existence for more than four decades.         Δe permissible dimensional deviation
lower limit for the minimum wall thick-       Nominal wall thicknesses e were deter-           	  (minus tolerance)
nesses has been reduced to emin = 3,0 mm.     mined taking account of the permissible
                                              circumferential stresses in the pipe wall
5.2.2	 Calculating wall thicknesses 	         using the formula
	      according K-classes
                                              e = 5 + 0.01 . DN              [mm]	(5.7)
Since the introduction of ductile cast iron
around 60 years ago, the minimum wall         in wall thickness class K 10. Wall thick-
thickness emin has undergone a consid-        nesses which deviated from this could be
erable evolution which is due to the          represented in their own K-classes
impressive development and optimisa-
tion of centrifugal casting production        e = K . (5 + 0.001 . DN)   [mm]	(5.8)
technology. The primary beneficiaries
of this are the small nominal sizes from      whereby the proportionality factor K was
DN 80 to DN 250 which account for an          part of a series of whole numbers … 8,
extremely high proportion in urban dis-       9, 10, 11, 12 …
tribution networks.
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The following applies for e > 6 mm:                                                              As from 2010, EN 545 [5.1] now only con-
                                                                                                 tains the pressure (C) classes.
Δe = – (1.3 + 0.001 ∙ DN) [mm]	       (5.10)
                                                                                                 The development of minimum pipe wall
The following applies for e ≤ 6 mm:                                                              thicknesses over the last decades in Fig.
                                                                                                 5.3 shows that, since the introduction of
Δe = –1.3		               [mm]	       (5.11)                                                     ductile iron pipes, in terms of production
                                                                                                 technology it has been possible to reduce
Hence the lowest minimum pipe wall                                                               minimum wall thicknesses by almost half.
thickness was 4.7 mm.
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This effect is based solely on the fact that,                                                                      5.5	   The effect of longitudinal
                                                                                        Soil load
with the introduction of pressure classes                                                                                 bending strength and ring
(C-classes), the limit value for mini-                                                  Water filling                     stiffness on the calculation
mum wall thickness has been reduced                                                     Dead weight                       of pipe wall thickness dimen-
by roughly one third, from 4.7 mm to 3.0                                                                                  sions
                                                                                        Traffic loads
mm. The equation applicable for calcu-
lating wall thicknesses (5.6) remains the
same as before.                                                  Fastening plate                                   Classification according to pressure
                                                                                                                   classes (C-classes) is only applicable
Table 5.2 illustrates the relationship                           Pipe cradle                                       for non-restrained systems in which
between the previous K-classes and the                           foundation pile                                   only tangential stresses σt produced by
new pressure classes (C-classes) for each                    +                          Bending moment             internal pressure are decisive when it
nominal size. The wall thickness meas-                               –                  progression
                                                                                        (idealised)
                                                                                                                   comes to calculating pipe wall thickness
ured in millimetres represents the com-                                                                            (Fig. 5.2).
mon comparison parameter for C-classes          Fig. 5.5:
and for K-classes. The table shows the          Bending moments for a buried pipeline on                           However, such influencing factors should
areas with similar wall thicknesses and         piles                                                              also be taken into account when calcu-
the areas corresponding to pressure                                                                                lating non-restrained systems as they
classes for the allowable operating pres-                                                                          cause a significant proportion of axial
sure PFA in the same colours.                                                                                      stresses σa in the system to be calcu-
                                                                                   Traffic loads
                                                                                                                   lated. These may be axial stresses due
This table offers the possibility of compar-                                                                       to bending moments in the longitudi-
ing the earlier K-classes (wall thickness         h
                                                                                   Road
                                                                                   Road substructure
                                                                                                                   nal direction (Fig. 5.5) or to uneven
classes) with the new pressure classes                                             Propagation of the load         loads in the circumferential direction
(C-classes), because the actual minimum                                            Ovalised pipe                   (Fig. 5.6).
wall thickness emin is the common refer-                                           Initial condition of the pipe
                                                                                   Ground
ence parameter.
                                                Fig. 5.6:
                                                Ovalisation due to soil loads and traffic
                                                loads
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As seen in Fig. 5.1, restrained pipe joints     this situation by publishing its own identi-    ing bead on the spigot end. A mini-
produce a multiaxial stress state in the        fication standard, EADIPS®/FGR®-NORM            mum wall thickness of approximately
pipe wall whereby, with the allowable           75 [5.5],(Chapter 3, Figs. 3.35 and 3.36).      5 mm for a high-quality weld penetra-
operating pressure PFA being lower when                                                         tion is considered as a precondition for
compared with the non-restrained joint,         5.6.2	 Positive locking push-in joints          compliance with the required permissi-
the pressure class is therefore lower.                                                          ble tensile strength. Also, with trenchless
                                                A further requirement has come more             pushing-in techniques, a minimum wall
The multiaxial stress state in a pipe wall      and more into the foreground in the             thickness is required for transferring the
which, in addition to the tangential stress     last decade: the increasing frequency           compressive forces, so that the permissi-
σt produced by internal pressure, must          with which restrained push-in joints            ble compression stresses in the connec-
also take up axial stresses σσa, results in a   are being used with the trenchless              tion joint are not exceeded.
distinct reduction in the allowable oper-       laying techniques and the associated
ating pressure PFA as compared with             requirement for the maximum per-                Depending on the application case,
the non-restrained design. Therefore the        missible tensile strength values in the         a number of load types due to inter-
specification of pressure class C as a syn-     Technical Rules of DVGW Worksheet               nal pressure, vertical load and bend-
onym for the allowable operating pressure       GW 320-1 [5.6] etc. (see also Chapter 22        ing stress, as well as those due to the
PFA is no longer sufficient for restrained-     on trenchless pipe laying and replace-          maximum permissible tensile and com-
joint pipelines. This has consequences          ment techniques). In these sets of rules,       pressive forces associated with trench-
for the identification of the pipes. Fig. 5.8   the permissible tensile strength of,            less laying techniques must therefore
shows the identification requirements of        above all, positive locking push-in joints      be calculated and the optimum pipe
EN 545 [5.1], Section 4.7.1.                    with a welding bead on the spigot end           determined. The effects on practical
                                                (Fig. 9.5) plays a decisive role for the        planning are described in articles in
According to EN 545 [5.1], Section 4.2,         pulling-in length of a pipe string. Hence       EADIPS®/FGR® Annual Journals 45 [5.7]
manufacturers must state the lower              it is a determining factor for excavation       and 46 [5.8].
values for the PFA of their restrained          distances and therefore for the effi-
push-in joints. However, there is no            ciency of a pipe material for a specific
clear and unambiguous determination             trenchless technique. Trenchless pipe
of the identification of pipes with             laying techniques are mainly performed
restrained joints to be found in EN 545         with positive locking restrained push-in
[5.1]. EADIPS®/FGR® has responded to            joints. These joints must have a weld-
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