Limit states
General
Pipelines for district heating systems shall be designed and constructed such that the probability of an ultimate limit state or serviceability limit state being exceeded during the planned service life is sufficiently low.
Application rule:
The methodology described below is one method to prove that the functional requirement above is fulfilled.
The effect of the design actions in terms of stress, strain and deformation calculated shall not exceed the associated limit states for the pipe materials.
The required safety margin between 'service' condition of the pipeline and the limit state is expressed by the terms 'characteristic value', 'partial safety factor' and 'design action'.
Application rule:
The (residual) uncertainties for which partial safety factors are intended to compensate include:
the possibility of the action being greater than the characteristic value,
the possibility of the actual values for the strength of the pipeline being lower than the characteristic values employed,
deviations from the physical reality, due to the calculation model used in the analysis process.
Ultimate limit states are those associated with collapse or other forms of structural failure:
failure caused by plastic deformation (limit state A),
rupture caused by (high and low cycle) fatigue (limit state B),
instability of the pipeline system or part of it (limit state C),
leakage (by other causes, e.g. corrosion or third party damage), which may affect safety.
Serviceability limit states corresponds to states beyond which specified service criteria are no longer met:
deformations or deflections which adversely affect the effective use or maintenance of the pipeline system or cause damage to finishes or structural elements, not being part of the pipeline system, such as installed equipment and/or abutting structures (limit state D).
Limit states for service pipes of steel
General
For steel pipes the following limit states are derived from the ultimate and serviceability limit states.
Б.4.2.2 Limit state A: Failure caused by plastic deformation
General
Limit state A1: Ultimate limit state reached by one severe action (load bearing capacity)
Limit state A2: Ultimate limit state reached by few actions (stepwise plastic deformation)
For actions, the partial safety factors }£are applied according to Table 3.
Limit state A1: Ultimate limit state reached by one severe action (load bearing capacity)
An equilibrium stress field is any stress field, which is necessary to satisfy the equilibrium equation for force- controlled actions.
The corresponding stress at each point of the structure is not to be greater than the characteristic material parameter divided by the partial safety factor.
The installation, inclusive of valves and accessories, is to be examined for one single elevated effect of the most unfavourable combination of force-controlled actions.
Application rule:
The action combinations comprise operating condition as well as condition during pressure testing.
In some special cases the axial membrane forces from displacement-controlled actions shall be included when calculating the equilibrium stress field (e.g. free spanning pipes with high axial forces from pre-stressing or heating).
For the design an elasto-plastic material model is used. In the calculations a purely linear elastic stress-strain relation is used, also for stresses exceeding the yield strength.
The design of solid component walls with membrane and bending stresses shall verify that the following is observed for the principal stresses, and in the case of composite stress conditions also for the reference stress:
7?Є(Г)
O-d - rm |
||
1,5 o-d |
for o-m Ї |
: 0,67 • <Td |
2,5 o-d -l,5 crm |
for CTm |
> 0,67 crd |
1,5 crd |
for °п> |
< 0,67 • <jd |
2,5 -o-d -l,5-crjm |
for |
> 0,67 crd |
where
crd is the design stress;
<rm is the design membrane stress;
oj, m is the design reference stress for the membrane stresses;
<Tres is the design total stress of membrane stress and bending stress;
C5, res is the design reference stress for the total stresses of membrane stresses and bending stresses; /m is the partial safety factor for material.
Figure 6 — Range for limit state A1
Application rule:
The requirements for <rres and <7jres will always be fulfilled if ojres <Re(T)//m. However, the requirements above will allow higher ovalising stresses.
For straight pipes with T < 140°C, the hoop stress from internal pressure shall be calculated from:
Р
" Pd
where
q>d z
fmin
л ■ г g оis the design hoop stress;
is the weld factor for longitudinal welds (normally = 1 for welds made by the steel pipe manufacturer);
is the nominal wall thickness minus thickness allowance and possible allowance for corrosion.
Application rule:
Limit state A1 concerns safety against failure from force-controlled action. Limit state A1 can be decisive for high pressures and in case of large moments from force-controlled action (e g. self-weight on free spanning pipes) or ovalising stresses (e.g. traffic actions and selfweight of soil).
Partial safety factors for steel where the material standards for unalloyed and low alloyed steels show values for yield strength at elevated temperatures:
Yielding of base material, yielding of weld seam, = 1,25.
Partial safety factors for actions, see Table 3.
Application rule:
With the partial factor of 1,2 on pressure this gives a safety factor 1,2 . 1,25 = 1,5 on force-controlled actions.
6.4.2.2.3 Limit state A2: Ultimate limit state reached by few actions (stepwise plastic deformation)
Application rule:
Limit state A2 concerns incremental collapse and stress ratcheting.
Fracture resulting from repeated yielding or gradually increasing plastic deformation shall be prevented.
The installation, inclusive of valves and accessories, shall be examined for the most unfavourable combination of force and displacement actions.
The service fluid pressure may have a positive effect, e.g. lessen the risk of instability (balloon effect), and shall not be included in such cases.
Application rule:
Limit state for stress ratcheting for fully restrained sections:
fmax
where:
у is a safety factor, y= 0,7; the partial safety factor on p and AT is 1,0;
AT is the maximum positive temperature difference which will occur in the pipe section at any time;
_ P d,
ffp is the hoop stress, CTn = .
Stepwise plastic deformation (stress ratcheting) can only be caused by very high pressures and large pipe diameters. Stress ratcheting cannot occur if following requirements are fulfilled, see Figure 7:
Limit state A1 is fulfilled;
The limit state for strain in straight pipes in C1 is fulfilled;
p < 20 bar.
Key
Local buckling, uniform strain
Racheting 25 bar, 130°C
Racheting 25 bar, 140°C
Limit state C1, see Figure 3
Figure 7 — Limit states for axial strain for steel qualities with Re= 235 N/mm2
6.4.2.3 Limit state B: From "Rupture caused by fatigue"
General
Limit state B1: Low cycle fatigue (repeated yielding)
Limit state B2: High cycle fatigue
In safety evaluations of fatigue-affected installations, % = 1,0 is used for actions, and /m = 1,0 is used for material parameters.
Limit state B1: Low cycle fatigue (repeated yielding)
Documentation of the safety against fatigue failure shall pay regard to the relevant actions in such combinations so that a realistic picture is obtained of the variations in size and frequency of the stress variations in the individual components.
Safety against fatigue failure shall be verified in consideration of the variations of impacts anticipated throughout the service life of the system.
Application rule:
The limit state low cycle fatigue will be important mainly for bends, tees and reducers but should also be checked for straight sections with high axial forces, where for example the fatigue life of circumferential welds can be decisive.
T
Application rule:
he number of full action cycles chosen in the calculation for pipelines in normal operation shall not be lower than the number of equivalent full action cycles stated in Table 7, see C.5.2.
Major pipelines |
100 |
Main pipelines |
250 |
House service connections |
1000 |
Table 7 — Equivalent full action cycles for m = 4 and ATref= 110 C
Major pipelines can be e g. transmission pipelines and pipelines adjacent to production plants.
Normal operation is e g. supply temperature regulation according to ambient temperature (sliding respectively sliding/constant). Abnormal operation can be production from waste incineration or e g. night set-back. The highest number of cycles are normally generated by the consumers in the return pipe. The lowest number of full cycles can be expected in e g. low temperature networks.
Verification of sufficient safety against fatigue fracture is made using Palmgren-Miner's formula:
V yfat
where:
Пі is the number of cycles of stress range AS, during the required design life;
N, is the number of cycles of stress range A S, to cause failure;
jfat is the safety factor for fatigue fracture;
is the number of different stress ranges.
A
Л/, can be calculated from ДГ.
5000
I
pplication rule: where Si is the design stress range in N/mm2, see C.7.1,The following values of jfat shall be applied:
Table 8 — Partial safety factor for fatigue
Project class |
Xat |
A |
5 |
В |
6,67 |
C |
10 |
In states of multi-axis stress cases the overall impact of all stress components shall be taken into account. The reference stress can be calculated by Tresca or von Mises’ formulas, or - if the location or direction of stress components are not known - by simple addition.
Regard shall be paid to the stress concentrations occurring at bends, tees, branch connections, and similar.
For welded components regard shall be paid to the weld quality and scope of inspection.
6.4.2.3.3 Limit state B2: High cycle fatigue
Application rule:
Limit state B2: High cycle fatigue, is only of importance in the case of large diameter pipe, small soil cover and heavy traffic actions or pipes above ground subject to vibration, e.g. from wind. High cycle fatigue is not further dealt with, see Eurocode 3, Structural Use of Steel.
6.4.2.4 Limit state C: From "Instability of the system or part of it"
General
Limit state C1: Local buckling or folding
Limit state C2: Global instability (Flexural buckling and loss of equilibrium of the pipeline system)
The installation, inclusive of valves and accessories, shall be examined for the most unfavourable combination of force- and displacement-controlled actions.
For actions, the partial safety factors % are applied according to Table 3.
The limit states local buckling, flexural buckling and wrinkling will be important mainly for straight pipelines sections with high forces, caused by soil friction preventing thermal expansion or for local settlement.
Є.4.2.4.2 Limit state C1: Local buckling or folding
Local buckling or folding shall be prevented.
Provided that it can be demonstrated that local buckling or folding will not initiate fracture, and provided that the other requirements of the standard are met, the buried bonded preinsulated pipes can be utilised for compressive yielding over the entire cross section.
Application rule:
Concentration of plastic deformation, which may occur in pipe systems with elevated axial compressive stresses and weakened cross sections should be avoided.
Pipe systems with elevated axial stresses are, for instance, pipe systems in which the temperature movements are more or less obstructed by external friction forces, e.g. buried, bonded preinsulated pipes.
The service fluid pressure may have a positive effect, e.g. lessen the risk of folding (balloon effect), and shall not be included in such cases.
For a pipe with no risk of local accumulation of strain the limit value, for compressive strain in the longitudinal direction is:
For — < 60 .• fcr = 0,25 ~ 0,0025
Zs =2
If a pipe has ovalised (due to vertical or horizontal earth pressure) the mean radius rm is replaced by:
where:
dm
2
1
3 — 2
cl
m
i
dm m
d’
s the ovality, see also limit state D;is the smallest diameter.
Application rule:
The formulas above can be used when evaluating the stresses from bending (e.g. pre-bending of pipes or bending moments from settlements).
For straight pipes with elevated axial compressive stresses and normal variation in wall thickness and yield strength there will be a risk of strain accumulation, and the formulas above will give too high values. Furthermore, imperfections like misalignments of welds and other geometrical and material variations can result in considerable reduction in
The safety in limit state C1 can be verified by reference to substantiated tests/experience or by calculations.
If no special documentation is available, the following limits may be used for assessing the safety of buried bonded preinsulated pipes in state C1.
Limit state for strain in straight pipes based on local buckling:
r for—<28.7 Af<0.16% t
„ rm„ t
for—>28.7 be <(4,58 + 0,003)%
z rm
For straight fully restrained pipes using the values for E(T) and a(T) in chapter 3 the limit state for zlcrand AT will be:
* for—<28,7 A<r<334N/mm t
r
for —>28.7
r
for — < 28.7 t
for — > 28.7 / '
/ 2
Дсг < (9250 + 11,7) N/mm
rm
ДГ<130К
Д7' < (3500 + 8)K
rm
The formulas are valid with the following limitations:
All components (e.g. tees and valves) on the restrained part shall be designed to resist the large axial stresses.
The pipeline shall be constructed with uniform steel quality and nominal wall thickness.
No weak points shall be built in like small angular deviations and misalignment at welds.
Proper measures shall be taken to limit stresses at bends due to increased expansion.
The formulas are valid for steel grades with specified minimum yield of approximately 235 N/mm2 (For steels with Re > 235 N/mm2 other values may be derived in the future.)
As examples of weakened cross sections may be mentioned:
circular seams with insufficient seam thickness as a consequence of misalignment or similar;
local reduction of dimension or wall thickness (e.g. non-reinforced tees);
local use of material with lower yield stress.
6.4.2.4.3 Limit state C2: Global instability (flexural buckling and loss of equilibrium of the pipeline
system)
For parallel excavation, special precautions are to be taken for pipelines with large axial compressive forces, see Annex B.
Application rule:
The limit state "loss of equilibrium, etc." may be important for pipelines installed with limited soil cover and/or below groundwater level, see annex B.
For systems above ground the stability shall be ascertained, see Eurocode 3, Structural use of steel.
Є.4.2.5 Limit state D: Serviceability limit state
.5.1 General
ya = 1 is used for actions. ym- 1 is used for material parameters.
Limit state D will usually not be of any consequence to the dimensioning of district heating systems. Examples in which limit state D may be of importance are the allowable deflection of pipe bridge, differential soil settling and allowable impacts on valves and accessories, anchors, building walls, etc.
.5.2 Ovalisation
The limit value for the smallest diameter of the ovalised cross section is d' > 0,94 d.
Application rule:
Due care shall be taken to other ovalisation limiting requirements such as through-pass of inspection equipment.
Composite stress conditions
In composite stress conditions with the principal stresses Oi, <з2 and the reference stress can be calculated from "Tresca" or "von Mises" hypothesis:
Tresca:
cr 2
tr = max cr2 - cr3
O-3-O-,
Von Mises:
(Tj - -№((71 -CT2)2 + ’/2<(Ti - СГз / + (72 ’ (7з f
Limit states for PUR and PE
Compressive stress
The maximum design compressive stress from soil loads and/or lateral displacements of the pipe system, at design temperature, for PUR qualities complying with EN 253, oPUR.d, calculated at the interface foam-inner steel pipe, shall not exceed 0,15 N/mm2.
The maximum compressive stress from transportation loads and temporary storage shall not exceed 0,25 N/mm2. E) deleted text El
Application rule 1:
Орика is a combined stress and a result of lateral movement of the steel pipe into the PUR. The true stresses in the PUR cannot easily be calculated. For design purposes Opur.o can therefore be used for lateral movements assuming long term action.
Long term creep testing has shown that the PUR can fail due to large tensile stresses at the ‘tensile side’ curve of the pipe when the pipe moves horizontal in he soil. For large pipes the PUR may fail due to shear stresses at top and bottom of the pipe caused by the ovalising of the pipe. “
Application rule 2
This limit state is based on PUR foam properties, obtained from testing. EN 253 specifies two tests for this:
Short term compression test, at ambient temperature, test requirement min. 0,3 N/mm2, at 10% deformation.
Long term creep test at design temperature (140° C), test requirement 0,24 N/mm2, at max 15% deformation.
The value at design temperature is decisive for the design requirement. Against this test requirement the material factor is approx. 1,5.
The value at ambient temperature may be used for (short term) transportation and storage. Against the test requirement the material factor is approx. 1,25
Application rule 3:
Higher values may be used for continuous operating temperatures below 130 °С or when special reinforced foams are applied, provided these higher values are supported by sufficient and adequate testing results, validated by an independent certification institute.
The operating temperature profile used, shall be safeguarded, documented and kept in file by the operator of the system and the manufacturer of the pipe
Limit state for shear stress
Concerning shear strength before and after ageing, rPUR , see EN 253.
The partial safety factor for PUR = 3. For sections shorter than 20 m between two bends a partial safety factor Xn = 2 can be used in project classes A and B.
Limit state for PE
Temperatures of the PE outer casing above 50 °С shall be avoided.
Application rule:
Elevated temperature on the casing (e g. where foam cushions are applied) will reduce the service life of the casing. This temperature will depend on:
The design temperature of the pipe system;
Thickness and heat transfer coefficient of PUR foam insulation;
Thickness and heat transfer coefficient of applied foam cushions;
Heat transfer coefficient of the surrounding soil.
Local impact and sharp objects puncturing the PE shall be avoided.
Application rule:
Under normal conditions the stresses in the PE casing will not be decisive. Local impacts (e.g. especially in cold weather or from sharp objects) can cause rupture or puncture of the casing. Pipe toughness requirements are decisive with regard to this type of failure