---

T Shear stress

AG_t Ovalisation stress from soil pressure, traffic, etc.

z

Figure C.1 — Local co-ordinate system

Stresses and axial forces are positive for tension.

EN 13941:2009+A1:2010 (E)

C.3 Survey of limit states for steel

See Clause 7 for validity and limitations.

_ R.(t)

d ~

res

1,5 <7,

2,5 a_d-1,5 <7_m

[1,5 o_d

[2,5 o_d-1,5 „

for cr_m< 0,67 ■ a_d for <r_m > 0,67 a_d for a_jm< 0,67 a, for <7 _m >0,67 a_d

м

£<— 0.25 0.0025

For uniform £

El

for ГтЛ> 2Ъ,7

0,16 %

Де < (4,58 — + 0,003 )%

For pipes with imperfections

ы

Below the flow for fatigue analysis is exemplified being the most complex. Similar flow charts should be followed for other limit states.

Table C.1 — Methodology for fatigue analysis

C.4 Locations to be assessed

C.4.1 Components to be considered

C.4.1.1 General

Components to be considered for analysis are:

1. straight sections,

2. welds,

3. long bends (elastically laid or pre-manufactured),

4. small angular deviations and single mitred bends,bends,

5. branch connections (tees),

6. reducers,

7. underground expansion joints, (single use compensators as well as permanent expansion joints),

8. valves and other accessories,

9. dished ends and flanged connections,

10. interface with other systems.

Table C.2 — Limit states (see 6.4.2)

In principle all the above mentioned combination should be examined. However, for normal buried systems the following combinations are decisive:

Table C.3 — Limit states

Forces and moments near valves, reducers and compensators shall be analysed. The values obtained shall be compared with the design values of the relevant product standard or manufacturer’s specifications.

Special attention should be paid to misalignment of welds due to variations in pipe diameter and wall thickness and poor fitting.

C.4.1.2 Small angular deviations

When using cold installation techniques, mitre bends and small angular deviations shall not be used.

In other cases multiple mitred bends should be avoided. Pre-manufactured smooth bends should be used in expansion zones.

In fixed pipe sections, small angular deviations (to follow the pipeline route) can be used as follows:

Table C.4 — Small angular deviations

NOTE Maximum angular deviation excluding installation tolerance, which should be limited to ± 0,25°.

C.4.2 Areas to be considered

Areas requiring specific analyses are:

1. areas of possible future parallel excavations near the district heating pipes,

2. areas of specific requirements due to nearby building foundations in urban areas,

3. areas subject to soil settlement or mining subsidence.

The analysis should take due account of the method of thermal expansion compensation.

The analysis shall include both the required constructive precautions during the installation phase, e.g. less soil cover, as well as the technical requirements in the operating phase, e.g. excavation requirements or buoyancy requirements.

Further due attention should be paid to:

1. Interfaces with plant areas, substations or house installations, in particular:

1. underground bends at the end of long, straight pipeline sections (thermal expansion and pressure expansion),

2. points of transition from an excavated trench to a rigid supported structure, whether above or below ground (for example pumping stations, fixpoints, house connections, pipe tunnels, etc.); both the buried and aboveground sections should be incorporated into one single calculation model, taking due account of any settlement differences,

3. interfaces with installations, paying special attention to frequent changes in wall thickness in these situations,

4. pipe supports in transition zones,

5. intersection points to other connected piping and facilities (e.g. pump and heat exchanger units, heating centres and wall penetrations).

2. Crossings:

1. road, railway and waterway crossings,

2. other utility pipes and cables,

3. water barriers and dykes.

3. Change in installation method:

1. These may in weak soils give rise to differential settlement and/or subsidence (for example, at the transition between a pipeline section laid in a trench and a jacked or bored section).

2. Special attention must also be paid to settlement differences between the pipe system and casing pipes, when applied (e.g. at crossings).

4. Abrupt changes in soil conditions.

C.5 Actions

C.5.1 General

The number and size of temperature and pressure cycles throughout the service life of the system should be evaluated.

Safety against fatigue failure shall be verified in consideration of impacts anticipated throughout the service life of the system.

C.5.2 Action cycles

If the temperature history is known or can be presupposect-the history can be converted to equivalent full temperature cycles, N_o, by using Palmgren-Miner’s formula, see 6.4.2.3. The same SN-curve as used in the subsequent fatigue analysis must be used when calculating N_o.

For systems where the static system does not change due to variations in temperature, variation in stress will be proportional to the variation in temperature and the number of equivalent full temperature cycles can be calculated from:

_N

where

n, is the number of cycles with temperature range AT_i;

AT_ref is the reference temperature at which N_o is calculated;

m is the constant in the SN-curve, see C.8.1.

It should be noted that N_o does not only depend on the temperature history, but also on the factor m.

If the static system changes (e.g. if neutral fixpoints move) the relation will not be proportional. In these cases the stress history should be calculated first.

Normally the variation of temperature will be the predominant action. In a district heating system with normal operating conditions the variation will consist of a few full action cycles (start-up and shut-down cycles) and a large number of smaller cycles due to the daily temperature variations.

Special conditions like energy production from incineration plants, cold plugs, night-set-back at consumers, etc., can give many and/or large temperature variations.

Normally the largest number of full equivalent temperature cycles will occur in the supply pipe for main pipelines and in the return pipe for service connections.

In district heating systems with normal operation and a stable flow temperature, the following number of full action cycles, corresponding to a period of 30 years, may be presupposed for m = 4 and AT_ref= 110 °С, see 7.4.2.3, limit state B:

• Major pipelines 100-250 cycles;

• Main pipelines 250-500 cycles;

• Service connections 1000-2500 cycles.

For major pipeline the maximum value can be reached e.g. close to incineration plants. For service connections maximum values are typically reached in case of e.g. night-set-back at the consumer.

The number of full action cycles must not be chosen lower than the smallest values above according to 6.4.2.3, Table 4.

C.6 Global analysis

C.6.1 General

The following procedure can be used:

1. Calculation of bending moments, forces and deformations of the steel pipe as the action bearing structure.

2. Calculation of impacts on PUR foam and the PE casing pipe, which are assumed to follow the deformations of the steel pipe.

The calculation model used shall take due account of the interaction between pipe and soil generally caused by temperature expansion of the pipe or by soil settlements.

The interaction of pipeline and soil may be characterised by using a soil spring model. In such a model the non­linear action-displacement behaviour of the soil in axial and horizontal directions can be outlines by a series of (discrete) multi-linear soil springs, see Annex B.

These springs represent the amount of action or restraint exerted on the pipeline system for a given displacement. Account shall be taken of the variation in soil properties by considering a reasonable range of properties in the analysis.

Calculation of pipe-soil interaction may be done by means of the theory of beams on elastic foundation, by "beam­element" programmes or by application of finite element methods (FEM).

The axial reaction (soil friction) can be applied as a uniform axial action against the expansion of the pipe. The horizontal soil reaction is normally characterised as elastic or elasto-plastic soil springs.

When using "beam-element" programmes the pipeline is reduced to a system of beam elements for the pipeline and spring elements for the supports. In the case of buried pipelines, the surrounding soil is also reduced to a system of springs.

Near areas where foam cushions are applied or large soil deformations occur the use of linear spring characteristics can give unreliable results, and elasto-plastic soil springs should be used, see Annex B.

C.6.2 Flexibility

C.6.2.1 General

The properties of components in respect of rigidity and stress concentration are assessed on the basis of the properties of an equivalent straight pipe. The rigidity of an individual component is obtained by dividing the rigidity of the equivalent straight pipe (expressed by El} with the flexibility factor k_b of the component.

To be on the safe side the modules of elasticity of the materials should be set at the values they have at the lowest temperature occurring in the system.

Note that the nominal wall thickness can normally be used for calculating the flexibility, but for components of special significance to the rigidity of a pipe system, e.g. pipe bends, it may be necessary to consider the variation in k_b due to excess measures of the thickness.

C.6.2.2 Bends

For short radius 90° bends (R = 1,5 d₀) a flexibility factor _{= can} be _usec| f_or j_n-plane and out-of-

⁶ 4 ■ t_nR

plane bending. The stiffening effect of adjacent straight pipes is included in this factor. For bend angles between 90° and 0 the flexibility factor can be reduced linearly.

For larger radii bends the stiffening effect is reduced. In this case k_b can be valued:

^1,24' < k_b< ^1,65' for 1,5 d₀< R <2,5 d₀

4f_n-R ^b4t_nR

Intervening values are obtained by interpolation.

_{k =} 1.65 d²_{for R} > 2 5 d₀

^b4t_nR

The flexibility factor for normal forces, shear forces and torque equals 1.

For pipe bends, an internal pressure will counteract ovalisation. This is considered by dividing k_b with:

о(d Vf 2RV

E[2t) {dj

The above stated condition is usually only of importance for the dimensioning of pipe guides and similar in connection with pipes in duct structures, buildings, etc.

When the more exact calculation for stresses in bends is used with p > 0, cf. C.7.5, the effect of over-pressure shall be included when calculating the flexibility factor.

C.6.2.3 Tees

The flexibility factor for tees equals 1.

For dtx/dro < 0,8 the flexibility of the connection between branch pipe and run pipe can be taken into account by applying following spring factor to the branch pipes at the point where the axis of the branch intersects the outside of the run pipe:

For in-plane bending, M_by, see Figure C.8.

Су —

Еіь
ky ■ dn>

и

tb tr

A^0,5

Ubo dro J

For out-of-plane bending, M_bz, see Figure C 8.

E lb
kz - dro

tr dboV'⁵tb_
tb dro J tr

where

l_b is the moment of inertia of branch cross section;

d_m is the outside diameter of run pipe;

d_b0 is the outside diameter of branch pipe;

t_r is the wall thickness of run pipe;

t_b is the wall thickness of branch pipe.

The spring factor for a branch pipe can be compared to a spring factor for an angular compensator.

C.6.2.4 Other components

For all other components k_b = 1.

C.6.3 Boundary conditions

Actions, displacements and restraints shall be considered as a whole for the entire pipeline system, considering both static and dynamic aspects.

This means that even in cases where the analysis considers the pipeline in sections, the requirements of equilibrium, including accommodation of actions imposed by abutting structures, shall be fulfilled satisfactorily in the entire pipeline system.

The section of the pipeline under consideration shall also be limited by points, in respect of which the following items are to be ascertained with sufficient accuracy:

1. either the displacements (translation and rotations), or

2. the forces and moments, or

3. the relationship between displacements on the one hand and forces and moments on the other.

In bonded systems the friction between protective casing and soil is entirely or partly fixing the pipes.

In sections where pipes are partly fixed, cf. Figure A.3.2, it should be ensured that the resulting movements at free pipe ends, bends and branch connections are allowable, as concerns deformations and stresses.

In a partly restrained pipe section the friction length L is the length which is required to provide a sufficient friction force between pipes and soil in order that the pipes does not move. Typically the friction length is the distance from an expansion provision (compensator or expansion loop) to a natural fixpoint (NFP).

Key

1. Friction length, L

2. Partly restrained

3. Fully restrained

4. Expansion zone

Figure C.2 — Partly and fully restrained pipe sections

At the other side of the NFP the pipe is fully restrained and does not move. However, the NFP can change position according to the stress history of the pipe and as a result of changes in the soil.

Forces and deformations can be calculated with the formulas below when the following conditions are fulfilled:

• uniform soil cover,

• uniform pipe to soil friction,

• the total length between two expansion zones exceeds twice the friction length, L.