Results from the 'beam' calculation

The following results are reported:

•displacements of the nodes

•displaced coordinates of the deformed pipeline

•displacements in joints in case of articulated pipeline

•internal forces in the pipeline

•soil reactions along the pipeline

•external support reaction forces

•bend stiffness and stress intensification factors per bend

•T-data with stress intensification factors

•primary cross-sectional deformations

•free spans

Additional output tables:

•iteration process

•iteration check data

•specified loads active on the elements

•applied soil settlement loads

•active specified nodal loads

•applied wave and current loads

The presence of output tables depends on the model and modules applied.

Results from preparatory stress/strain calculations

•additional cross-sectional loads

•additional support reactions

•resulting pipeline free spans

•elements with primary membrane stress

•ovalisation redistribution (soil loads)

•ovalisation redistribution (soil loads + top loads)

•ovalisation redistribution at bends

Results from stress/strain calculations

The following stress components are considered, where in the overall stress calculation weighing factors can be applied on individual stress components in order to allow adaptation to Code requirements.

Between brackets the 'short name' of the stress/strain components is provided for easy reference.

In these names the following naming is used:

S = normal stress and T = shear stress

X = axial direction and F = circumferential direction and Z = shear stress in XF and FX direction

U = uniformly distributed over wall and I or O is linearly distributed over wall with I = inner wall side and O = outer wall side and M = mid wall.

B = means results from 'beam' calculation and R = from 'ring' calculation and S = from integrated 'shell' calculation

0 = zero harmonic over circumference (constant)

1 = first harmonic over circumference (1 sine shape)

H = sum of higher harmonics over circumference (sum >1 sine shapes)

A = sum of all harmonics over circumference

-M = maximum value over circumference

Stresses

In the Pipe stress max table PSTRMAX the following stress components can be found resulting from the internal forces:

•[SXUB0-M] maximum longitudinal stresses as a result of the axial force in the pipeline

•[SXUB1-M] maximum longitudinal pipe bending stresses resulting from the pipe bending moment.

•[SXUBH-M] maximum higher order pipe bending stresses resulting from the pipe bending moment. In general only at bends, but in case of the 'Section Model' option also in straight pipe sections, because these sections ovalise as well under a pipe bending moment.

•[TZUB0-M] maximum shear stress resulting from the twisting moment

•[TZUB1-M] maximum shear stress resulting from the shear force

In the additional output table PSTRESS the stress components SXUB0, SXUB1, SXUBH, TZUB0 and TZUB1 are given as distributions over the circumference of the last section calculated.

In the Bend stress max table BSTRMAX the following stress components can be found resulting from the internal forces:

•[SFISH-M] maximum circumferential wall bending stress at the inner wall side as a result of ovalisation of the pipe cross-section at bends due to pipe bending. In case of the 'Section Model' option these stress components occur at straight pipes as well.

•[SFOSH-M] same as [SFISH-M], but now at the outer wall side

•[SXISH-M] maximum stress resulting from the Poisson-effect of [SFISH-M].

•[SXOSH-M] maximum stress resulting from the Poisson-effect of [SFOSH-M]

These wall bending stresses are the edge stresses of a linear stress distribution

•[TXMSH-M] maximum shear stress at mid wall due to wall bending from bending ovalisation

In the additional output table BSTRESS the stress components SFISH, SFOSH, SXISH, SXOSH and TXMSH are given as distributions over the circumference of the last section calculated.

In the Ring stress max table RSTRMAX the following stress components can be found resulting from lateral loadings on the ring.

•[SFUBA-M] maximum circumferential full wall stress due to internal or external pressure

•[SFURA-M] maximum circumferential full wall stress due to the lateral soil and possibly top load loadings on the ring

•[SFIRA-M] maximum circumferential wall bending stress at the inner wall side as a result of ovalisation of the pipe cross-section due to lateral and possibly top load soil loadings

•[SFORA-M] same as [SFIRA-M], but now at the outer wall side

•[SXIRA-M] maximum stress resulting from the Poisson-effect of [SFIRA-M]

•SXORA-M] maximum stress resulting from the Poisson-effect of [SFORA-M]

These wall bending stresses are the edge stresses of a linear stress distribution

•[TXMRA-M] maximum shear stress at mid wall due to wall bending from lateral soil loading

In the additional output table RSTRESS the stress components SFUBA, SFURA, SFIRA, SFORA, SXIRA, SXORA and TXMRA are given as distributions over the circumference of the last section calculated.

From these stress components the Total stress max table TSTRMAX is composed:

•[SXIT-M] maximum totalled uniaxial stress at inner wall side in axial direction

•[SXOT-M] maximum totalled uniaxial stress at outer side wall side in axial direction

•[SFIT-M] maximum totalled uniaxial stress at inner wall side in circumferential direction

•[SFOT-M] maximum totalled uniaxial stress at outer wall side in circumferential direction

•[TZUT-M] maximum full wall shear stress

•[TXMT-M] maximum shear stress at mid wall

•[SEIT-M] maximum Von Mises stress calculated from totalled stresses at inner wall side

•[SEOT-M] maximum Von Mises stress calculated from totalled stresses at outer wall side

It must be mentioned here, that the Von Mises stresses cannot be calculated from the reported totalled uniaxial stresses, because these maxima occur at different locations. The Von Mises stresses are calculated from the detailed stress distributions.

In the additional output table TSTRESS the stress components SXIT, SXOT, SFIT, SFOT, TZUT, TXMT, SEIT and SEOT are given as distributions over the circumference of the last section calculated. Here the Von Mises stresses can be calculated from the detailed totalled stresses.

Apart from these totalled stresses the Principal stress max table MSTRMAX is determined with following stresses:

at the inner wall side:

•[SIGI1-M] maximum principal stress

•[SIGI2-M] minimum principal stress

•[TAUIMAX-M] maximum shear stress

at the outer wall side:

•[SIGO1-M] maximum principal stress

•[SIGO2-M] minimum principal stress

•[TAUOMAX-M] maximum shear stress

In the additional output table MSTRESS the stress components SIGI1, SIGI2, TAUIMAX, SIGO1, SIGO2 and TAUOMAX are given as distributions over the circumference of the last section calculated. Here the principal stresses can be calculated from the detailed totalled stresses.

From these totalled stress components following evaluation stresses are calculated and reported in the Check stress max table CSTRMAX:

•[MOHR1-M] maximum principal stress (max. of inner and outer wall around circumference)

•[MOHR2-M] minimum principal stress (max. of inner and outer wall around circumference)

•[TRESCA-M] maximum shear stress according to Tresca (max. of inner and outer wall around circumference)

•[MISES-M] maximum equivalent stress according to Von Mises (max. of inner and outer wall around circumference)

•[SXHT-M] maximum uni-axial stress in longitudinal direction (max. of inner and outer wall around circumference)

•[SFHT-M] maximum uni-axial stress in circumferential direction (max. of inner and outer wall around circumference)

•[SHOOP-M] maximum circumferential stress due to internal pressure only

In the additional output table CSTRESS the stress components MOHR1, MOHR2, TRESCA, MISES, SXHT, SFHT and SHOOP are given as distributions over the circumference of the last section calculated.

In case of use of the elasto-plastic pipe material facility analysis the internal forces and related stressing are based on the straining behaviour of the pipe material. Because the individual stress components together lead to yielding of an individual material point, these stress components cannot be recognized after yielding and thus only the uni-axial stress components (stress coordinates) constituting the yielding point at the Von Mises yielding ellipse can be reported.

In the Elasto-plastic stress max table INSIGM the resulting stress components are reported at the inner wall side, where uni-axial is meant in the longitudinal and circumferential directions, as well as in the directions of the principal axes:

•[sIX-E-M] maximum (remaining) normal stress component in longitudinal direction

•[sIF-E-M] maximum (remaining) normal stress component in circumferential direction

•[tIZ-E-M] maximum (remaining) shear stress component in x-y plane

•[sI1-E-M] maximum (remaining) normal stress in principal axis 1 direction

•[sI2-E-M] minimum (remaining) normal stress in principal axis 2 direction

•[tI12-E-M] maximum (remaining) shear stress

•[sIEq-E-M] maximum equivalent stress from (remaining) stress components [sI1-E] and [sI2-E]

In the additional output table INSIG the (remaining) stress components sIX-E, sIF-E, tIZ-E, sI1-E, sI2-E, tI12-E and sIEq-E-M are given as distributions over the circumference of the last section calculated.

A similar Elasto-plastic stress max table MIDSIGM is given for the mid- wall location:

•[sMX-E-M] maximum (remaining) normal stress component in longitudinal direction

•[sMF-E-M] maximum (remaining) normal stress component in circumferential direction

•[tMZ-E-M] maximum (remaining) shear stress component in x-y plane

•[sM1-E-M] maximum (remaining) normal stress in principal axis 1 direction

•[sM2-E-M] minimum (remaining) normal stress in principal axis 2 direction

•[tM12-E-M] maximum (remaining) shear stress

•[sMEq-E-M] maximum equivalent stress from (remaining) stress components [sM1-E] and [sM2-E]

In the additional output table MIDSIG the (remaining) stress components sMX-E, sMF-E, tMZ-E, sM1-E, sM2-E, tM12-E and sMEq-E-M are given as distributions over the circumference of the last section calculated.

And a similar Elasto-plastic stress max table OUTSIGM is given for the outer wall location:

•[sOX-E-M] maximum (remaining) normal stress component in longitudinal direction

•[sOF-E-M] maximum (remaining) normal stress component in circumferential direction

•[tOZ-E-M] maximum (remaining) shear stress component in x-y plane

•[sO1-E-M] maximum (remaining) normal stress in principal axis 1 direction

•[sO2-E-M] minimum (remaining) normal stress in principal axis 2 direction

•[tO12-E-M] maximum (remaining) shear stress

•[sOEq-E-M] maximum equivalent stress from (remaining) stress components [sO1-E] and [sO2-E]

In the additional output table OUTSIG the (remaining) stress components sOX-E, sOF-E, tOZ-E, sO1-E, sO2-E, tO12-E and sOEq-E are given as distributions over the circumference of the last section calculated.

The Elasto-plastic stress check table CSIGM contains the stress extremes of the foregoing tables:

•[sX-E-M] extremum of [sIX-E-M], [sMX-E-M] and [sOX-E-M]

•[sF-E-M] extremum of [sIF-E-M], [sMF-E-M] and [sOF-E-M]

•[tZ-E-M] extremum of [tIZ-E-M], [tMZ-E-M] and [tOZ-E-M]

•[s12max-E-M] maximum of [sI1-E-M], [sI2-E-M], [sM1-E-M], [sM2-E-M], [sO1-E-M] and [sO2-E-M]

•[s12min-E-M] minimum of [sI1-E-M], [sI2-E-M], [sM1-E-M], [sM2-E-M], [sO1-E-M] and [sO2-E-M]

•[tmax-E-M] maximum of [tI12-E-M], [tM12-E-M] and [tO12-E-M]

•[sEq-E-M] maximum of [sIEq-E-M], [sMEq-E-M] and [sOEq-E-M]

In the additional output table CSIG the (remaining) stress components sX-E, sF-E, tZ-E, s12max-E, s12min-E, tmax-E and sEq-E are given as distributions over the circumference of the last section calculated.

Strains

The straining of the pipeline is reported in a similar way:

An Elasto-plastic strain max table INEPSM provides the strain components at the inner wall side:

•[eI1-E-M] maximum elastic strain part in principal axis 1 direction

• [eI1-P-M] maximum plastic strain part in principal axis 1 direction

•[eI1-T-M] maximum total strain in principal axis 1 direction

•[eI2-E-M] maximum elastic strain part in principal axis 2 direction

• [eI2-P-M] maximum plastic strain part in principal axis 2 direction

•[eI2-T-M] maximum total strain in principal axis 2 direction

•[eIX-S-M] maximum total strain in longitudinal direction, excluding stressless strains

•[eIF-S-M] maximum total strain in circumferential direction, excluding stressless strains

•[eIX-T-M] maximum total strain in longitudinal direction, including stressless strains

•[eIF-T-M] maximum total strain in circumferential direction, including stressless strains

•[eIEq-E-M] maximum equivalent elastic strain

•[eIEq-P-M] maximum equivalent plastic strain

•[eIEq-S-M] maximum equivalent total strain, excluding stressless strains

In the additional output table INEPS the strain components eI1-E, eI1-P, eI1-T, eI2-E, eI2-P, eI2-T, eIX-S, eIF-S, eIX-T, eIF-T, eIEq-E, eIEq-P and eIEq-S are given as distributions over the circumference of the last section calculated.

Similar an Elasto-plastic strain max table MIDEPSM provides the strain components at the mid-wall side:

•[eM1-E-M] maximum elastic strain part in principal axis 1 direction

• [eM1-P-M] maximum plastic strain part in principal axis 1 direction

•[eM1-T-M] maximum total strain in principal axis 1 direction

•[eM2-E-M] maximum elastic strain part in principal axis 2 direction

• [eM2-P-M] maximum plastic strain part in principal axis 2 direction

•[eM2-T-M] maximum total strain in principal axis 2 direction

•[eMX-S-M] maximum total strain in longitudinal direction, excluding stressless strains

•[eMF-S-M] maximum total strain in circumferential direction, excluding stressless strains

•[eMX-T-M] maximum total strain in longitudinal direction, including stressless strains

•[eMF-T-M] maximum total strain in circumferential direction, including stressless strains

•[eMEq-E-M] maximum equivalent elastic strain

•[eMEq-P-M] maximum equivalent plastic strain

•[eMEq-S-M] maximum equivalent total strain, excluding stress less strains

In the additional output table MIDEPS the strain components eM1-E, eM1-P, eM1-T, eM2-E, eM2-P, eM2-T, eMX-S, eMF-S, eMX-T, eMF-T, eMEq-E, eMEq-P and eMEq-S are given as distributions over the circumference of the last section calculated.

And finally an Elasto-plastic strain max table OUTEPSM provides the strain components at the outer wall side:

•[eO1-E-M] maximum elastic strain part in principal axis 1 direction

• [eO1-P-M] maximum plastic strain part in principal axis 1 direction

•[eO1-T-M] maximum total strain in principal axis 1 direction, including stressless strains

•[eO2-E-M] maximum elastic strain part in principal axis 2 direction

• [eO2-P-M] maximum plastic strain part in principal axis 2 direction

•[eO2-T-M] maximum total strain in principal axis 2 direction, including stressless strains

•[eOX-S-M] maximum total strain in longitudinal direction, excluding stressless strains

•[eOF-S-M] maximum total strain in circumferential direction, excluding stressless strains

•[eOX-T-M] maximum total strain in longitudinal direction, including stressless strains

•[eOF-T-M] maximum total strain in circumferential direction, including stressless strains

•[eOEq-E-M] maximum equivalent elastic strain

•[eOEq-P-M] maximum equivalent plastic strain

•[eOEq-S-M] maximum equivalent total strain, excluding stress less strains

In the additional output table OUTEPS the strain components eO1-E, eO1-P, eO1-T, eO2-E, eO2-P, eO2-T, eOX-S, eOF-S, eOX-T, eOF-T, eOEq-E, eOEq-P and eOEq-S are given as distributions over the circumference of the last section calculated.

The Elasto-plastic strain check table CEPSM contains the strain extremes of the foregoing tables:

•[e12max-T-M] maximum of [eI1-E-M], [eI2-E-M], [eM1-E-M], [eM2-E-M], [eO1-E-M] and [eO2-E-M] including stressless strains

•[e12min-T-M] minimum of [eI1-E-M], [eI2-E-M], [eM1-E-M], [eM2-E-M], [eO1-E-M] and [eO2-E-M] including stressless strains

•[eX-S-M] extremum of [eIX-S-M], [eMX-S-M] and [eOX-S-M], excluding stressless strains

•[eF-S-M] extremum of [eIF-S-M], [eMF-S-M] and [eOF-S-M], excluding stressless strains

•[eEq-E-M] maximum of [eIEq-E-M], [eMEq-E-M] and [eOEq-E-M]

•[eEq-P-M] maximum of [eIEq-P-M], [eMEq-P-M] and [eOEq-P-M]

•[eEq-S-M] maximum of [eIEq-S-M], [eMEq-S-M] and [eOEq-S-M], excluding stressless strains

•[eXS-M] percentage of [eX-S-M] of the check strain CHKEPS

•[eFS-M] percentage of [eF-S-M] of the check strain CHKEPS

•[eEqS-M] percentage of [eEq-S-M] of the check strain CHKEPS

In the additional output table CEPS the strain components e12max-T, e12min-T, eX-S, eF-S, eEQ-E, eEQ-P, eEQ-S, eXS, eFS and eEQS are given as distributions over the circumference of the last section calculated.

Results from primary deformation calculations

Next to the stress/strain results deformations of the cross sections are reported:

In the linear and non-linear elastic analysis cases the Primary deformation table DEFORM in Design Function 5 (beam calculation) remains empty, but in the case of local non-linear ovalisation (OVAL) or material non-linear analysis, this table is filled.

The axial strain of the cross sections [EPS], the rotational bending strain [KAPPA] together with its orientation angle and the rotational twisting strain [DISTORTN] as well as the cross sectional ovalisation and orientation angle are reported.

•[EPS-TOT] total longitudinal strain of cross sections (equal strain for all points of the cross section)

•[EPS-EL] elastic longitudinal strain part of cross sections (equal strain for all points of the cross section)

[EPS-TOT] = [EPS-EL] in case of Section Model Ovalising analysis option

•[EPS-PL] plastic longitudinal strain part of cross sections (equal strain for all points of the cross section)

[EPS-PL] = empty in case of Section Model Ovalising analysis option

•[EPS-SL] stress less strain contained in the total strain (equal strain for all points of the cross section)

•[DISTORTN] rotational twisting angle per unit length of cross sections around longitudinal axis (equal strain for all points of the cross section)

•[KAPPA-TOT] total rotational bending angle per unit length of cross sections (linear strain distribution over projected cross section with zero-point at the neutral axis)

•[PHI-T] orientation angle of [KAPPA-TOT]

•[KAPPA-EL] elastic part of [KAPPA-TOT] (linear strain distribution over projected cross section with zero-point at the neutral axis)

[KAPPA-EL] = [KAPPA-TOT] in case of Section Model Ovalising analysis option

•[PHI-E] orientation angle of [KAPPA-EL]

[PHI-E] = [PHI-T] in case of Section Model Ovalising analysis option

•[KAPPA-PL] plastic part of [KAPPA-TOT] (linear strain distribution over projected cross section with zero-point at the neutral axis)

[KAPPA-PL] = empty in case of Section Model Ovalising analysis option

•[PHI-P] orientation angle of [KAPPA-PL]

[PHI-P] = empty in case of Section Model Ovalising analysis option

•[OVAL] largest ovalisation of cross section

•[PHI-O] orientation of ovalisation axis

Results from detailed deformation calculations

In case of linear elastic or non-linear geometric analysis or local non-linear ovalisation the Cross sectional max. deformation is contained in table RDPLMAX:

•[WGROUND-M] the maximum displacement of the wall in radial direction (outward is positive) due to the lateral soil pressure (per cross section along the pipeline axis)

•[WBEND-M] the maximum displacement of the wall in radial direction (outward is positive) due to the bend ovalisation as a result of a bending moment (per cross section along the pipeline axis)

•[W+WD/D-M] the maximum diameter change due to ovalisation, expressed as percentage of the diameter (per cross section along the pipeline axis)

•[W-TOTAL-M] the maximum total radial displacement of the wall (outward is positive) (per cross section along the pipeline axis)

•[RG/KLG-M] the minimum local elastic range of the cross sections in case of flexible support of the soil (per cross section along the pipeline axis)

•[KLG-M] the minimum supporting soil stiffness of the cross sections (bilinear behaviour of soil support) (per cross section along the pipeline axis)

In the additional output table RDISPLC the deformation components W-GROUND, WBEND, W+WD/D, W-TOTAL, RG/KLG and KLG are given as distributions over the circumference of the last section calculated.

In case of material non-linear analysis the Cross sectional max. deformation table is RLDPLMX. This is a more extended variant to table RDPLMAX described above.

•[WGROUND-M] as in RDPLMAX

•[WBEND-M] as in RDPLMAX

•[WELAS-M] maximum elastic part of the cross sectional deformation (per cross section along the pipeline axis)

•[WPLAS-M] maximum plastic part of the cross sectional deformation (per cross section along the pipeline axis)

•[W+WD/D-M] as in RDPLMAX

•[W-TOTAL-M] as in RDPLMAX

•[RG/KLG-M] as in RDPLMAX

•[KLG-M] as in RDPLMAX

•AX_BUCKL-M the maximum of the longitudinal compressive strain (stressless strain excluded) expressed as a percentage of the critical local wall buckling compressive strain

(per cross section along the pipeline axis)

•EX_PRESS-M the external pressure expressed as a percentage of the critical implosion pressure (per cross section along the pipeline axis)

In the additional output table RLDSPLC the deformation components W-GROUND, WBEND, WELAS, WPLAS, W+WD/D, W-TOTAL, RG/KLG, KLG, AX_BUCKL and EX_PRESS are given as distributions over the circumference of the last section calculated.

Results, last changed: 9/14/2016

See also: