Piping Expansion Loop Stress Analysis

Read about START-PROF pipe stress analysis software

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L, Z and U-shaped pipe loops dimension analysis is one of the more popular functions of the Elements module. This function eliminates the need for using outdated nomograms. The following can be analyzed:

Start-Elements allows approximate modeling of expansion joints, but uses a linearized soil model. START-PROF uses an exact non-linear soil model.

Therefore, START-PROF analyses are more accurate and precise than Start-Elements, so Start-Elements should be used only for preliminary analyses. Final safety checks should be done with START-PROF.

During loop analysis, START-PROF automatically generates the loop's model and places resting supports at appropriate intervals to maintain safe spacing between supports, calculated using Start-Elements: spacing between supports. Before the analysis, pipe wall thickness is automatically checked using Start-Elements: pipe wall thickness analysis.

It should be noted that loop dimensions in the horizontal plane can differ significant from those in the vertical plane. In the horizontal plane, bending stresses from thermal expansion and from piping weight are in mutually perpendicular planes. In the vertical plane, these stresses act in the same (vertical) plane. Therefore, allowable self-compensation stress will be higher in the former than in the latter case. When using nomograms, plane is usually not considered. Vertical placement is only considered for bends and loops on supports.

Elbows flexibility and welded bends placed in loop angles can be considered or not considered. This can be selected in the "reduced bend stiffness" field. This option allows comparisons with nomogram, since they do not take into account reduced stiffness. Bend wall thickness is always set as equal to pipe wall thickness. For more details, see the "above-ground heating network nomograms" section.

Two types of analyses are possible: design validation and validation. In the design validation analysis, loop length is input and maximum allowable loop shoulder length that meets stability and stress requirements is calculated (to do this, the "compensated length" field must be checked). In the validation analysis, all dimensions are entered and maximum stress is calculated (to do this, the "compensated length" field must not be checked). Both the design validation and the validation analyses determine load on anchors, maximum stress, maximum transverse displacement, and allowable stress.

Stress in bends is not checked. According to SNIP 2.05.06-85, analysis is always done for loads.

Input data can be copied using the toolbar icon and inserted into any other Start-Elements analysis by using the toolbar icon in that file.

Input Data




Pipe diameter, D

External pipe diameter, D

Pipe wall thickness, S

Nominal wall thickness

Mill tolerance

Mill tolerance at the time of production. More...

Corrosion allowance

Corrosion and wear allowance (working mill tolerance) for wall thickness. More...

Bend radius

Radius values for all loop bends. Used for calculated reduced bend stiffness

casing outside diameter, Dc

External insulation casing diameter. If insulation is absent, set as 0

casing thickness, SC

Insulation casing thickness

Depth, Z

Depth (distance from soil surface to pipe axis)

Ambient temperature

Average wall (metal) temperature at the time when pipe segments become a single joined structure

Operation pressure, P

Operation pressure in operating mode. Set for all standards except SNIP 2.05.06-85. More...

Operation pressure, Pwork

Operation pressure (based on standards). Set when analyzing with SNIP 2.05.06-85. More...

Pipe weight

Piping and adjoining equipment uniform weight. More...

Insulation weight

Insulation uniform weight. More...

Product weight

Product uniform weight. More...

Weld pressure quality factor

Set based on standards. Can be calculated automatically by pressing . More...

Weld bending quality factor

Set based on standards. Can be calculated automatically by pressing . More...

Insulation type

Armopenobeton, polymer, polyurethane, other. For polyurethane, insulation casing diameter  DC and casing thickness SC are selected automatically from the database based on pipe diameter  D. For other insulation types, these data must be input manually

Backfill soil code

Trench soil number, can be selected from the soil database.

Base soil code

Base (undisturbed) soil number, can be selected from the soil database.

Resting support friction factor

Friction factor must be in the range of 0.05...0.4.

If friction need not be considered (0), then friction restraints are not set

Steel grade

Pipe material from the materials database

Flexibility of bends

Determines whether or not reduced stiffness in elbows and welded bends in loop angles should be considered. This option allows comparisons with nomogram, since they do not take into account reduced stiffness. For more details, see the "above-ground heating network nomograms" section.

Taking reduced bend stiffness into account is recommended, as this produces greater compensated lengths.

Cushion presence

Determines whether or not to consider the presence of damping cushions. Please note that using damping cushions does not always increase the allowable axial expansion movement for buried pipelines, and may even reduce its function. See also the "buried heating network nomograms" section.

Pre-stretch factor, k

Pre-stretching the loop reduces maximum piping stress. Pre-stretch is set as a portion of temperature range. If k=0, there is no pre-stretch. If k=0.5, pre-stretch is half the value of displacements from temperature range. For example, if k=0.1, pre-stretch is 10% of the value of displacements from temperature range.

Loop pre-stretch factor can range from 0 to 1.0

Loop back, B and leg, H

Loop back and leg must be input prior to the analysis, while compensated lengths are calculated.

Determining loop back and spacing from a known compensated length is not allowed, because an infinite number of B/H values are possible and not all are structurally sound. If compensated length is known, B and H must be selected taking into account the piping structure, so that the compensated length is equal to or greater than required.

Allowable load on end support

Maximum allowable load on anchors. Loop dimensions will be determined so as not to exceed the allowable value. If this value is set as 0, the check is not performed and loop dimensions are determined based only on stability requirements.

Analysis output

After analysis, the following output is displayed



Maximum stress

Maximum equivalent stress in piping elements

Allowable stress

Allowable stress for RD 10-400-01 1.5[O], and design resistance R2 for SNIP 2.05.06-85 

- for above-ground pipelines, - for buried pipelines

Thermal stretch

Maximum thermal stretch (long shoulder) in the absence of one of the anchors. Can be used for determining pre-stretch values

Maximum transverse displacement

Maximum displacement of nodes (bend ends). Can be used for selecting damping cushion layer thickness (based on their maximum relative deformation).


Shoulder length subject to transverse displacements. Can be used, for example, for determining the minimum distance from the loop to a guiding support. See figure:

Loads on A and B anchors

Axial force

Force along the pipe axis

Transverse force

Force perpendicular to the pipe axis (shear)

Bending moment

Bending moment


Error message "Expansion joint is not self-compensated" (for example for L-shaped loop with short leg L1 and long leg L) means that the loop doesn't satisfy strength requirements even at L=L1. It is obvious that it will not pass strength requirements at L1<L.

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