Materials according to Eurocode-3

EC3 materials

Structural steel as specified in EC3 standard.

class materials.ec3.EC3_materials.AUShape(steel, name)

Bases: materials.ec3.EC3_materials.EC3Shape, materials.sections.structural_shapes.arcelor_metric_shapes.AUShape

AU shape with Eurocode 3 verification routines.

class materials.ec3.EC3_materials.BoltFastener(diameter, steelType=<materials.ec3.EC3_materials.EC3BoltSteel object>, gammaM3=1.25, pos3d=None)

Bases: connections.steel_connections.bolts.BoltBase

Bolt according to chapter 3 of EC3-1-8:2005.

Variables

steelType – type of the bolt steel.

getDesignShearStrength(threadsExcluded=False, numberOfShearPlanes=1)
Return the design shear strength of the fastener according

to table 3.4 of EC3-1-8:2005.

Parameters

  • threadsExcluded – true if threads and transition area of shank are excluded from the shear plane.

  • numberOfShearPlanes – number of shear planes.

getDesignSlipStrength(holeType='normal', slotParallelToLoad=False, numberOfFrictionSurfaces=1, classOfFrictionSurfaces='D')
Return the value the design value of the slip resistance according

to clause 3.9.1 of EC3-1-8:2005.

Parameters

  • holeType – ‘normal’ or ‘shortSlot’ or ‘longSlot’.

  • slotParallelToLoad – true if the load is parallel to the axis of the slot.

getKs(holeType='normal', slotParallelToLoad=False)

Return the value of k_s according to table 3.6 of EC3-1-8:2005.

Parameters

  • holeType – ‘normal’ or ‘shortSlot’ or ‘longSlot’.

  • slotParallelToLoad – true if the load is parallel to the axis of the slot.

getNominalShearStrength(threadsExcluded=False, numberOfShearPlanes=1)
Return the nominal shear strength of the fastener according

to table 3.4 of EC3-1-8:2005.

Parameters

  • threadsExcluded – true if threads and transition area of shank are excluded from the shear plane.

  • numberOfShearPlanes – number of shear planes.

getNominalSlipStrength(holeType='normal', slotParallelToLoad=False, numberOfFrictionSurfaces=1, classOfFrictionSurfaces='D')
Return the value the design value of the slip resistance according

to clause 3.9.1 of EC3-1-8:2005.

Parameters

  • holeType – ‘normal’ or ‘shortSlot’ or ‘longSlot’.

  • slotParallelToLoad – true if the load is parallel to the axis of the slot.

getSlipFactor(classOfFrictionSurfaces='D')
Return the value of the slip factor according to table 3.7

of EC3-1-8:2005.

Parameters

classOfFrictionSurfaces – class of friction surfaces (see 1.2.7 Reference standard: Group 7).

class materials.ec3.EC3_materials.CFCHSShape(steel, name)

Bases: materials.ec3.EC3_materials.EC3Shape, materials.sections.structural_shapes.bs_en_10219_shapes.CFCHSShape

BS EN 10219-2: cold formed circular hollow steel shapes with Eurocode 3 verification routines.

getBucklingCurve(majorAxis=False)
Return the buckling curve (a0,a,b,c or d) for this cross-section

according to table 6.2 of EN 1993-1-1:2005 “Selection of buckling

curve for a cross-section”. Note that in table 6.2 Y and Z axes are swapped with respect to those used in XC. XC axes: Y->weak axis, Z->strong axis.

getShearArea(majorAxis=True)
Return area for shear strength calculation according to item g) of

paragraph 3 of the clause 6.2.6 of EC3-1-1:2005.

Parameters

majorAxis – has no meaning here (circular section).

shearBucklingVerificationNeeded()

Return true if shear buckling verification is needed according to expression 6.22 of EC3-1-1:2005 (clause 6.2.6 paragraph 6).

class materials.ec3.EC3_materials.CFRHSShape(steel, name)

Bases: materials.ec3.EC3_materials.HollowBoxShape, materials.sections.structural_shapes.bs_en_10219_shapes.CFRHSShape

BS EN 10219-2: cold formed rectangular hollow steel shapes with Eurocode 3 verification routines.

getBucklingCurve(majorAxis=False)
Return the buckling curve (a0,a,b,c or d) for this cross-section

according to table 6.2 of EN 1993-1-1:2005 “Selection of buckling

curve for a cross-section”. Note that in table 6.2 Y and Z axes are swapped with respect to those used in XC. XC axes: Y->weak axis, Z->strong axis.

class materials.ec3.EC3_materials.CFSHSShape(steel, name)

Bases: materials.ec3.EC3_materials.HollowBoxShape, materials.sections.structural_shapes.bs_en_10219_shapes.CFSHSShape

BS EN 10219-2: cold formed square hollow steel shapes with Eurocode 3 verification routines.

getBucklingCurve(majorAxis=False)
Return the buckling curve (a0,a,b,c or d) for this cross-section

according to table 6.2 of EN 1993-1-1:2005 “Selection of buckling

curve for a cross-section”. Note that in table 6.2 Y and Z axes are swapped with respect to those used in XC. XC axes: Y->weak axis, Z->strong axis.

class materials.ec3.EC3_materials.CHSShape(steel, name)

Bases: materials.ec3.EC3_materials.EC3Shape, materials.sections.structural_shapes.arcelor_metric_shapes.CHSShape

CHS shape with Eurocode 3 verification routines.

getBucklingCurve(majorAxis=False)
Return the buckling curve (a0,a,b,c or d) for this cross-section

according to table 6.2 of EN 1993-1-1:2005 “Selection of buckling

curve for a cross-section”. Note that in table 6.2 Y and Z axes are swapped with respect to those used in XC. XC axes: Y->weak axis, Z->strong axis.

getClassInCompression()

Return the cross-section classification of the section subject to compression. Clause 5.5 EC3-1-1.

getClassInternalPartInCompression()

Return the cross-section classification of the section subject to compression. Clause 5.5 EC3-1-1.

getNcRd()

Return the axial compression resistance of the cross-section.

getShearArea(majorAxis=True)
Return area for shear strength calculation according to item g) of

paragraph 3 of the clause 6.2.6 of EC3-1-1:2005.

Parameters

majorAxis – has no meaning here (circular section).

shearBucklingVerificationNeeded()

Return true if shear buckling verification is needed according to expression 6.22 of EC3-1-1:2005 (clause 6.2.6 paragraph 6).

class materials.ec3.EC3_materials.EC3BoltSteel(name=None, fy=240000000.0, fu=400000000.0, gammaM2=1.25)

Bases: materials.steel_base.BasicSteel

Eurocode 3 structural steel for bolts according to table 3.1 of

EC3-1-8:2005.

Variables

gammaM2 – partial safety factor for steel strength.

getAlpha_v(threadsExcluded=False)
Return the alpha_v coefficient of the fastener according

to table 3.4 of EC3-1-8:2005.

Parameters

threadsExcluded – true if threads and transition area of shank are excluded from the shear plane.

getDesignShearStrength(threadsExcluded=False)
Return the design shear strength of the steel according

to table 3.4 of EC3-1-8:2005.

Parameters

threadsExcluded – true if threads and transition area of shank are excluded from the shear plane.

getNominalShearStrength(threadsExcluded=False)
Return the nominal shear strength of the steel according

to table 3.4 of EC3-1-8:2005.

Parameters

threadsExcluded – true if threads and transition area of shank are excluded from the shear plane.

class materials.ec3.EC3_materials.EC3Shape(name, typo='rolled', sectionClass=None)

Bases: object

Steel shape with Eurocode 3 verification routines.

Variables

  • name – steel shape name.

  • typo – ‘rolled’ or ‘welded’ shape

  • sectionClass – section classification according to clause 5.5 of EC3-1-1:2005.

getAdimensionalSlendernessY(Leq)
return adimensional slenderness relative to y-axis (weak axis)

as defined in EC3 part 1 6.3.1

Parameters

Leq – buckling length in XZ buckling plane.

getAdimensionalSlendernessZ(Leq)

return adimensional slenderness relative to z-axis (strong axis) as defined in EC3-1-1 6.3.1

Parameters

Leq – buckling length in XY buckling plane.

getAvy()

Return y direction (web direction) shear area

getBendingResistanceReductionCoefficient(Vd)

Return bending resistance reduction coefficient as in clause 6.2.8 of EC31-1

getBiaxBendCoeffs(NEd, NplRd)

Return (alpha,beta) constants for bi-axial bending criterion (clause 6.2.9 of EC3.1.1)

Parameters

  • NEd – design value of the axial force.

  • NplRd – design plastic resistancc to normal forces of the gross cross-section.

getBiaxialBendingEfficiency(Nd, Myd, Mzd, Vyd=0.0, chiN=1.0, chiLT=1.0)

Return biaxial bending efficiency (clause 6.2.9 of EC3.1.1) (only class 1 and 2 cross-sections are considered currently)

Parameters

  • Nd – design value of the axial force.

  • Myd – design value of the bending moment about y-y axis.

  • Mzd – design value of the bending moment about z-z axis.

  • Vyd – design value of the shear force on y axis.

  • chiN – flexural buckling reduction factor (default= 1.0).

  • chiLT – lateral buckling reduction factor (default= 1.0).

getBucklingCurve(majorAxis=False)
Return the buckling curve (a0,a,b,c or d) for this cross-section

according to table 6.2 of EN 1993-1-1:2005 “Selection of buckling

curve for a cross-section”. Note that in table 6.2 Y and Z axes are swapped with respect to those used in XC. XC axes: Y->weak axis, Z->strong axis.

getBucklingReductionFactorY(Leq)

return buckling reduction factor relative to y-axis (weak axis) as defined in EC3-1-1 6.3.1

Parameters

Leq – buckling length in XZ buckling plane.

getBucklingReductionFactorZ(Leq)

return buckling reduction factor lative to z-axis (strong axis) as defined in EC3-1-1 6.3.1

Parameters

Leq – buckling length in XY buckling plane.

getBucklingResistance(LeqY, LeqZ)

return minimum of buckling resistance in XY and XZ buckling planes calculated according to EC3-1-1 6.3.2

Parameters

  • LeqY – buckling length of the member in XZ buckling plane.

  • LeqZ – buckling length of the member in XY buckling plane.

getBucklingResistanceY(Leq)

return buckling resistance relative to y-axis (weak axis) according to EC3-1-1 6.3.2

Parameters

Leq – buckling length in XZ buckling plane.

getBucklingResistanceZ(Leq)

return buckling resistance relative to z-axis (strong axis) according to EC3-1-1 6.3.2

Parameters

Leq – buckling length in XY buckling plane.

getCfactIntPart()

Return the C length of internal part in compression used to classify the cross-section. Table 5.2 EC3-1-1

getClassInBending(ratioCT=None)
Return the cross-section classification in bending.

Clause 5.5 EC3-1-1

Parameters

ratioCT – ratio c/t width-to-thickness of the compressed part.

getClassInCompression(ratioCT=None)
Return the cross-section classification in compression.

Clause 5.5 EC3-1-1

Parameters

ratioCT – ratio c/t width-to-thickness of the compressed part.

getClassInternalPartInBending(ratioCT=None)

Return the cross-section classification of internal part (web in open shapes, …) subject to pure bending. Clause 5.5 EC3-1-1

Parameters

ratioCT – ratio c/t width-to-thickness of the internal compressed part (defaults to widthToThicknessWeb)

getClassInternalPartInCompression(ratioCT=None)

Return the cross-section classification of internal part (web in open shapes, …) totally subject to compression (conservative). Clause 5.5 EC3-1-1

Parameters

ratioCT – ratio c/t width-to-thickness of the internal compressed part (defaults to widthToThicknessWeb)

getClassOutstandPartInCompression(ratioCT=None)

Return the cross-section classification of outstand part (flanges) totally subject to compression (conservative). Clause 5.5 EC3-1-1

Parameters

ratioCT – ratio c/t width-to-thickness of the outstand compressed part (defaults to widthToThicknessFlange)

getLateralBucklingImperfectionFactor()

Return lateral torsional imperfection factor depending of the type of section (rolled, welded,…).

getLateralBucklingIntermediateFactor(L, Mi, beamSupportCoefs=<materials.ec3.EC3_limit_state_checking.BeamSupportCoefficients object>)

Returns lateral torsional buckling intermediate factor value.

Parameters

  • L – member length.

  • Mi – ordinate for the moment diagram

  • supportCoefs – coefficients that represent support conditions.

getLateralBucklingNonDimensionalBeamSlenderness(L, Mi, beamSupportCoefs=<materials.ec3.EC3_limit_state_checking.BeamSupportCoefficients object>)

Return non dimensional beam slenderness for lateral torsional buckling see parameter definition on method getMcr.

Parameters

  • L – member length.

  • Mi – ordinate for the moment diagram

  • beamSupportCoefs – coefficients that represent support conditions.

getLateralBucklingReductionFactor(L, Mi, beamSupportCoefs=<materials.ec3.EC3_limit_state_checking.BeamSupportCoefficients object>)

Returns lateral torsional buckling reduction factor value.

Parameters

  • L – member length.

  • Mi – ordinate for the moment diagram

  • beamSupportCoefs – coefficients that represent support conditions.

getLateralTorsionalBucklingCurve()

Return the lateral torsional bukling curve name (a,b,c or d) depending of the type of section (rolled, welded,…). EC3 Table 6.4, 6.3.2.2(2).

getLateralTorsionalBucklingResistance(L, Mi, beamSupportCoefs=<materials.ec3.EC3_limit_state_checking.BeamSupportCoefficients object>)
Return lateral torsional buckling resistance of this cross-section.

Calculation is made following the paper:

A. López, D. J. Yong, M. A. Serna, Lateral-torsional buckling of steel beams: a general expression for the moment gradient factor. (Lisbon, Portugal: Stability and ductility of steel structures, 2006).

Parameters

  • L – member length.

  • Mi – ordinate for the moment diagram

  • beamSupportCoefs – coefficients that represent support conditions.

getMcRdy()

Return the minor bending resistance of the cross-section.

getMcRdz()

Return the major bending resistance of the cross-section.

getMcr(L, Mi, beamSupportCoefs=<materials.ec3.EC3_limit_state_checking.BeamSupportCoefficients object>)
Return elastic critical moment about minor axis: y

Calculation is made following the paper:

A. López, D. J. Yong, M. A. Serna, Lateral-torsional buckling of steel beams: a general expression for the moment gradient factor. (Lisbon, Portugal: Stability and ductility of steel structures, 2006).

Parameters

  • L – member length.

  • Mi – ordinate for the moment diagram

  • beamSupportCoefs – coefficients that represent support conditions.

getMvRdz(Vd)
Return the major bending resistance of the cross-section under a

shear force of Vd according to clause 6.2.8 of EC3-1-1:2005.

Parameters

Vd – concomintant shear force.

getNcRd()

Return the axial compression resistance of the cross-section.

getShearArea(majorAxis=True)
Return area for shear strength calculation according to paragraph

3 of the clauses 6.2.6 of EC3-1-1:2005.

Parameters

majorAxis – if true major axis bending; so shear parallel to minor axis.

getVcRdy()

Return y direction (web direction) shear resistance [plastic design in absence of torsion]

getVplRdy(majorAxis=True)
Return y direction (web direction) plastic shear resistance

according to clause 6.2.6 (expression 6.18) of EC3-1-1:2005.

Parameters

majorAxis – if true major axis bending; so shear parallel to minor axis.

getYShearEfficiency(Vyd)

Return major axis shear efficiency.

Parameters

Vyd – design value of the required shear strength.

getZBendingEfficiency(Nd, Mzd, Vyd=0.0, chiN=1.0, chiLT=1.0)

Return major axis bending efficiency

Parameters

  • Nd – required axial strength.

  • Mzd – required bending strength (major axis).

  • Vyd – required shear strength (major axis)

  • chiN – axial strength reduction factor (default= 1.0).

  • chiLT – lateral buckling reduction factor (default= 1.0).

installULSControlRecorder(recorderType, elems, chiN=1.0, chiLT=1.0, calcSet=None)

Installs recorder for verification of ULS criterion. Preprocessor obtained from the set of elements.

Parameters

  • recorderType – recorder type.

  • chiN – flexural buckling reduction factor (default= 1.0).

  • chiLT – lateral buckling reduction factor (default= 1.0).

  • calcSet – set of elements to be checked (defaults to ‘None’ which means that this set will be created elsewhere). In not ‘None’ the member elements will be appended to this set.

setupULSControlVars(elems, chiN=1.0, chiLT=1.0)
For each element creates the variables

needed to check ultimate limit state criterion to be satisfied.

Parameters

  • elems – elements to define properties on.

  • chiN – flexural buckling reduction factor (default= 1.0).

  • chiLT – lateral buckling reduction factor (default= 1.0).

shearBucklingVerificationNeeded()

Return true if shear buckling verification is needed according to expression 6.22 of EC3-1-1:2005 (clause 6.2.6 paragraph 6).

class materials.ec3.EC3_materials.EC3Steel(fy, fy16, fy40, fy63, fy80, fy100, fy125, fu, gammaM, gammaM1=1.0, gammaM2=1.1)

Bases: materials.steel_base.BasicSteel

Eurocode 3 structural steel.

Variables

  • fy16 – 0<t<16mm

  • fy40 – 16<t<40mm

  • fy63 – 40<t<63mm

  • fy80 – 63<t<80mm

  • fy100 – 80<t<100mm

  • fy125 – 100<t<125mm

  • gammaM – partial safety factor for steel strength.

  • gammaM1 – partial factor for buckling resistance.

  • gammaM2 – partial factor for cross-sections in tension to fracture.

fydV()

Return the design value of the shear strength.

gammaM0()

Return the value of the partial safety factor for steel strength.

getDesignElasticPerfectlyPlasticMaterial(preprocessor, name)
getLambda1()

return lambda_1 value as specified in EC3 part 1 5.5.1.2

setGammaM0(gammaM0: float)

Assign the value of the partial safety factor for steel strength.

Parameters

gammaM0 – Partial safety factor for steel strength.

class materials.ec3.EC3_materials.HEShape(steel, name)

Bases: materials.ec3.EC3_materials.EC3Shape, materials.sections.structural_shapes.arcelor_metric_shapes.HEShape

HE shape with Eurocode 3 verification routines.

getBucklingCurve(majorAxis=False)
Return the buckling curve (a0,a,b,c or d) for this cross-section

according to table 6.2 of EN 1993-1-1:2005 “Selection of buckling

curve for a cross-section”. Note that in table 6.2 Y and Z axes are swapped with respect to those used in XC. XC axes: Y->weak axis, Z->strong axis.

class materials.ec3.EC3_materials.HFSHSShape(steel, name)

Bases: materials.ec3.EC3_materials.HollowBoxShape, materials.sections.structural_shapes.bs_en_10210_shapes.HFSHSShape

BS EN 10210-2: 2006 steel shapes with Eurocode 3 verification routines.

getBucklingCurve(majorAxis=False)
Return the buckling curve (a0,a,b,c or d) for this cross-section

according to table 6.2 of EN 1993-1-1:2005 “Selection of buckling

curve for a cross-section”. Note that in table 6.2 Y and Z axes are swapped with respect to those used in XC. XC axes: Y->weak axis, Z->strong axis.

class materials.ec3.EC3_materials.HollowBoxShape(name, typo='rolled', sectionClass=None)

Bases: materials.ec3.EC3_materials.EC3Shape

Structural hollow shapes.

getBendingFactors(nCF)
Return the bending factors according to paragraph (5)

of the clause 6.2.9 of EC3.1.1.

Parameters

nCF – axial efficiency of the section.

getBiaxialBendingEfficiency(Nd, Myd, Mzd, Vyd=0.0, chiN=1.0, chiLT=1.0)
Return biaxial bending efficiency according to paragraph (5)

of the clause 6.2.9 of EC3.1.1. (only class 1 and 2 cross-sections are considered currently).

Parameters

  • Nd – design value of the axial force.

  • Myd – design value of the bending moment about y-y axis.

  • Mzd – design value of the bending moment about z-z axis.

  • Vyd – design value of the shear force on y axis.

  • chiN – flexural buckling reduction factor (default= 1.0).

  • chiLT – lateral buckling reduction factor (default= 1.0).

get_af()

Compute the aw parameter to be used in expression (6.39) of EC3.1.1.

get_aw()

Compute the aw parameter to be used in expression (6.39) of EC3.1.1.

class materials.ec3.EC3_materials.IPEShape(steel, name)

Bases: materials.ec3.EC3_materials.EC3Shape, materials.sections.structural_shapes.arcelor_metric_shapes.IPEShape

IPE shape with Eurocode 3 verification routines.

getBucklingCurve(majorAxis=False)
Return the buckling curve (a0,a,b,c or d) for this cross-section

according to table 6.2 of EN 1993-1-1:2005 “Selection of buckling

curve for a cross-section”. Note that in table 6.2 Y and Z axes are swapped with respect to those used in XC. XC axes: Y->weak axis, Z->strong axis.

class materials.ec3.EC3_materials.IPNShape(steel, name)

Bases: materials.ec3.EC3_materials.EC3Shape, materials.sections.structural_shapes.arcelor_metric_shapes.IPNShape

IPN shape with Eurocode 3 verification routines.

getBucklingCurve(majorAxis=False)
Return the buckling curve (a0,a,b,c or d) for this cross-section

according to table 6.2 of EN 1993-1-1:2005 “Selection of buckling

curve for a cross-section”. Note that in table 6.2 Y and Z axes are swapped with respect to those used in XC. XC axes: Y->weak axis, Z->strong axis.

class materials.ec3.EC3_materials.MicropileTubeShape(steel, name)

Bases: materials.ec3.EC3_materials.EC3Shape, materials.sections.structural_shapes.common_micropile_tubes.MicropileTubeShape

Common micropile tube shapes with Eurocode 3 verification routines.

getBucklingCurve(majorAxis=False)
Return the buckling curve (a0,a,b,c or d) for this cross-section

according to table 6.2 of EN 1993-1-1:2005 “Selection of buckling

curve for a cross-section”. Note that in table 6.2 Y and Z axes are swapped with respect to those used in XC. XC axes: Y->weak axis, Z->strong axis.

getClassInCompression()

Return the cross-section classification of the section subject to compression. Clause 5.5 EC3-1-1.

getClassInternalPartInCompression()

Return the cross-section classification of the section subject to compression. Clause 5.5 EC3-1-1.

getNcRd()

Return the axial compression resistance of the cross-section.

getShearArea(majorAxis=True)
Return area for shear strength calculation according to item g) of

paragraph 3 of the clause 6.2.6 of EC3-1-1:2005.

Parameters

majorAxis – has no meaning here (circular section).

shearBucklingVerificationNeeded()

Return true if shear buckling verification is needed according to expression 6.22 of EC3-1-1:2005 (clause 6.2.6 paragraph 6).

class materials.ec3.EC3_materials.RHSShape(steel, name)

Bases: materials.ec3.EC3_materials.EC3Shape, materials.sections.structural_shapes.arcelor_metric_shapes.RHSShape

RHS shape with Eurocode 3 verification routines.

getBucklingCurve(majorAxis=False)
Return the buckling curve (a0,a,b,c or d) for this cross-section

according to table 6.2 of EN 1993-1-1:2005 “Selection of buckling

curve for a cross-section”. Note that in table 6.2 Y and Z axes are swapped with respect to those used in XC. XC axes: Y->weak axis, Z->strong axis.

class materials.ec3.EC3_materials.SHSShape(steel, name)

Bases: materials.ec3.EC3_materials.HollowBoxShape, materials.sections.structural_shapes.arcelor_metric_shapes.SHSShape

SHS shape with Eurocode 3 verification routines.

getBucklingCurve(majorAxis=False)
Return the buckling curve (a0,a,b,c or d) for this cross-section

according to table 6.2 of EN 1993-1-1:2005 “Selection of buckling

curve for a cross-section”. Note that in table 6.2 Y and Z axes are swapped with respect to those used in XC. XC axes: Y->weak axis, Z->strong axis.

class materials.ec3.EC3_materials.UBShape(steel, name)

Bases: materials.ec3.EC3_materials.EC3Shape, materials.sections.structural_shapes.arcelor_metric_shapes.UBShape

UB shape with Eurocode 3 verification routines.

class materials.ec3.EC3_materials.UCShape(steel, name)

Bases: materials.ec3.EC3_materials.EC3Shape, materials.sections.structural_shapes.arcelor_metric_shapes.UCShape

UC shape with Eurocode 3 verification routines.

getBucklingCurve(majorAxis=False)
Return the buckling curve (a0,a,b,c or d) for this cross-section

according to table 6.2 of EN 1993-1-1:2005 “Selection of buckling

curve for a cross-section”. Note that in table 6.2 Y and Z axes are swapped with respect to those used in XC. XC axes: Y->weak axis, Z->strong axis.

class materials.ec3.EC3_materials.UPNShape(steel, name)

Bases: materials.ec3.EC3_materials.EC3Shape, materials.sections.structural_shapes.arcelor_metric_shapes.UPNShape

UPN shape with Eurocode 3 verification routines.

materials.ec3.EC3_materials.alphaImperfectionFactor(bucklingCurve)

Return the alpha imperfection factor for buckling curves see tables 6.1 and 6.2 of EC3 (EN 19931-1:2005).

Parameters

bucklingCurve – buckling curve (a0,a,b,c or d) according to table 6.2 of EN 1993-1-1:2005 “Selection of buckling curve for a cross-section”. Note that in table 6.2 Y and Z axes are swapped with respect to those used in XC. XC axes: Y->weak axis, Z->strong axis.

materials.ec3.EC3_materials.fuEC3(desig, t)

Return steel ultimate strength from its name and the part thickness (see table 3.1).

Parameters

  • desig – steel designation (235, 275, 355).

  • t – part thickness.

materials.ec3.EC3_materials.fyEC3(desig, t)

Return steel yield strength from its name and the part thickness (see table 3.1).

Parameters

  • desig – steel designation (235, 275, 355).

  • t – part thickness.

materials.ec3.EC3_materials.getHollowShapedSectionBucklingCurve(shape, hotFinished)
Return the buckling curve (a0,a,b,c or d) for O shaped rolled

cross-sections according to table 6.2 of EN 1993-1-1:2005 “Selection of buckling curve for a cross-section”. Note that in table 6.2 Y and Z axes are swapped with respect to those used in XC. XC axes: Y->weak axis, Z->strong axis.

Parameters

hotFinished – true if hot finished steel false for cold formed.

materials.ec3.EC3_materials.getIShapedRolledSectionBucklingCurve(shape, majorAxis)
Return the buckling curve (a0,a,b,c or d) for I shaped rolled

cross-sections according to table 6.2 of EN 1993-1-1:2005 “Selection of buckling curve for a cross-section”. Note that in table 6.2 Y and Z axes are swapped with respect to those used in XC. XC axes: Y->weak axis, Z->strong axis.

Parameters

majorAxis – true if buckling around major axis.

EC3 beam

Eurocode 3 checks for a beam or column.

class materials.ec3.EC3Beam.EC3Beam(name, ec3Shape, beamSupportCoefs=<materials.ec3.EC3_limit_state_checking.BeamSupportCoefficients object>, typo='rolled', lstLines=None, lstPoints=None)

Bases: materials.ec3.EC3_limit_state_checking.Member

Steel beam defined by an arbitrary name, a cross-section shape, its section class, the coefficients of supports and the type

EC3 limit state checking

Classes and functions for limit state checking according to Eurocode 3.

class materials.ec3.EC3_limit_state_checking.BeamSupportCoefficients(ky=1.0, kw=1.0, k1=1.0, k2=1.0)

Bases: object

getAlphaI()

returns the five alpha values that are needed for C1 calculation according to equation 12 of the reference [1].

class materials.ec3.EC3_limit_state_checking.BiaxialBendingNormalStressController(limitStateLabel, solutionProcedureType=<class 'solution.predefined_solutions.SimpleStaticLinear'>)

Bases: materials.limit_state_checking_base.LimitStateControllerBase2Sections

Object that controls normal stresses limit state.

ControlVars

alias of postprocess.control_vars.SteelShapeBiaxialBendingControlVars

updateEfficiency(elem, elementInternalForces)
Compute the efficiency of the element steel shape

subjected to the internal forces argument and update its value if its bigger than the previous one.

Parameters

  • elem – finite element whose section will be checked.

  • elementInternalForces – internal forces acting on the steel shape.

class materials.ec3.EC3_limit_state_checking.Member(name, ec3Shape, beamSupportCoefs=<materials.ec3.EC3_limit_state_checking.BeamSupportCoefficients object>, typo='rolled', lstLines=None, lstPoints=None)

Bases: materials.steel_member_base.BucklingMember

Steel beam defined by an arbitrary name, a cross-section shape, its section class, the coefficients of supports and the type

Variables

  • supportCoefs – instance of EC3_limit_state_checking.BeamSupportCoefficients that wraps the support coefficients: ky, kw, k1 and k2. where ky is the lateral bending coefficient, kw the warping coefficient, k1 and the warping AND lateral bending coefficients at first and last ends respectively (1.0 => free, 0.5 => prevented). (Defaults to ky= 1.0, kw= 1.0, k1= 1.0, k2= 1.0)

  • typo – ‘rolled’ or ‘welded’ (defaults to rolled)

getBiaxialBendingEfficiency(Nd, Myd, Mzd, Vyd=0.0)

Return biaxial bending efficiency according to section H1 of AISC-360-16.

Parameters

  • Nd – axial design load (required axial strength).

  • Myd – bending moment about weak axis (required flexural strength).

  • Mzd – bending moment about strong axis (required flexural strength).

getLateralBucklingReductionFactor()

Return lateral torsional buckling reduction factor value for the elements of the beam.

installULSControlRecorder(recorderType, chiLT=1.0, calcSet=None)

Install recorder for verification of ULS criterion.

Parameters

  • recorderType – type of the recorder to install.

  • calcSet – set of elements to be checked (defaults to ‘None’ which means that this set will be created elsewhere). In not ‘None’ the member elements will be appended to this set.

updateLateralBucklingReductionFactor()

Update the value of the lateral buckling reduction factor.

updateReductionFactors()

Update the value of the appropriate reduction factors.

class materials.ec3.EC3_limit_state_checking.MomentGradientFactorC1(Mi)

Bases: object

Calculation of the C1 moment gradient factor as defined in: A. López, D. J. Yong, M. A. Serna, Lateral-torsional buckling of steel beams: a general expression for the moment gradient factor. (Lisbon, Portugal: Stability and ductility of steel structures, 2006).

getA1(beamSupportCoefs)
Return the value for the A1 coefficient according to equation 10

of the reference [1].

Parameters

  • k1 – warping AND lateral bending coefficient at left end k1= 1.0 => free warping AND lateral bending k1= 0.5 => prevented warp. AND lateral bending

  • k2 – warping AND lateral bending coefficient at right end k2= 1.0 => free warping AND lateral bending k2= 0.5 => prevented warp. AND lateral bending

getA2()

Return the value for the A2 coefficient according to equation 11 of the reference [1].

getC1(beamSupportCoefs)
Return the value for the C1 coefficient according to equation 8

of the reference [1].

Parameters

beamSupportCoefs – instance of EC3_limit_state_checking.BeamSupportCoefficients that wraps the support coefficients: ky, kw, k1 and k2; where ky is the lateral bending coefficient, kw the warping coefficient, k1 and the warping AND lateral bending coefficients at first and last ends respectively (1.0 => free, 0.5 => prevented). (Defaults to ky= 1.0, kw= 1.0, k1= 1.0, k2= 1.0)

getExtremeMoment()

Return the extreme of the bending moments (maximum or minimum).

class materials.ec3.EC3_limit_state_checking.NormalStressesLimitStateData(designSituations=['uls_permanent', 'uls_accidental', 'uls_earthquake'])

Bases: postprocess.limit_state_data.NormalStressesSteelLimitStateData

Reinforced concrete normal stresses data for limit state checking.

getController(biaxialBending=True)

Return a controller corresponding to this limit state.

Parameters

biaxialBending – if True use a controller that checks bending around both cross-section axes.

class materials.ec3.EC3_limit_state_checking.ShearController(limitStateLabel, solutionProcedureType=<class 'solution.predefined_solutions.SimpleStaticLinear'>)

Bases: materials.limit_state_checking_base.LimitStateControllerBase2Sections

Object that controls shear limit state.

ControlVars

alias of postprocess.control_vars.ShearYControlVars

updateEfficiency(elem, elementInternalForces)
Compute the efficiency of the element steel shape

subjected to the internal forces argument and update its value if its bigger than the previous one.

Parameters

  • elem – finite element whose section will be checked.

  • elementInternalForces – internal forces acting on the steel shape.

class materials.ec3.EC3_limit_state_checking.ShearResistanceLimitStateData(designSituations=['uls_permanent', 'uls_accidental', 'uls_earthquake'])

Bases: postprocess.limit_state_data.ShearResistanceSteelLimitStateData

Reinforced concrete normal stresses data for limit state checking.

getController(solutionProcedureType=None)

Return a controller corresponding to this limit state.

Parameters

solutionProcedureType – type of the solution procedure to use when computing load combination results (if None, use the default one).

materials.ec3.EC3_limit_state_checking.controlBiaxialBendingEfficiency()

Code to execute in every commit to check stress criterion (bars in 3D problems).

materials.ec3.EC3_limit_state_checking.controlULSCriterion()
materials.ec3.EC3_limit_state_checking.controlULSCriterion2D()
materials.ec3.EC3_limit_state_checking.controlYShearEfficiency()
materials.ec3.EC3_limit_state_checking.getBendingResistanceReductionCoefficient(steelShape, Vd)

Returns bending resistance reduction coefficient as in clause 6.2.8 of EC3 EN 1993-1-1

Parameters

  • steelShape – cross section shape.

  • Vd – design value of the shear load.

materials.ec3.EC3_limit_state_checking.getLateralBucklingImperfectionFactor(steelShape)

Returns lateral torsional imperfection factor depending of the type of section (rolled, welded,…).

Parameters

steelShape – cross section shape.

materials.ec3.EC3_limit_state_checking.getLateralBucklingIntermediateFactor(steelShape, L, Mi, beamSupportCoefs=<materials.ec3.EC3_limit_state_checking.BeamSupportCoefficients object>)

Returns lateral torsional buckling intermediate factor value.

Parameters

  • steelShape – cross section shape.

  • L – member length.

  • Mi – ordinate for the moment diagram

  • beamSupportCoefs – coefficients that represent support conditions.

materials.ec3.EC3_limit_state_checking.getLateralBucklingNonDimensionalBeamSlenderness(steelShape, L, Mi, beamSupportCoefs=<materials.ec3.EC3_limit_state_checking.BeamSupportCoefficients object>)

Returns non dimensional beam slenderness for lateral torsional buckling see parameter definition on method getMcr.

Parameters

  • steelShape – cross section shape.

  • Mi – ordinate for the moment diagram

  • beamSupportCoefs – coefficients that represent support conditions.

materials.ec3.EC3_limit_state_checking.getLateralBucklingReductionFactor(steelShape, L, Mi, beamSupportCoefs=<materials.ec3.EC3_limit_state_checking.BeamSupportCoefficients object>)

Returns lateral torsional buckling reduction factor value.

Parameters

  • steelShape – cross section shape.

  • L – member length.

  • Mi – ordinate for the moment diagram

  • beamSupportCoefs – coefficients that represent support conditions.

materials.ec3.EC3_limit_state_checking.getLateralTorsionalBucklingCurve(steelShape)

Returns the lateral torsional bukling curve name (a,b,c or d) depending of the type of section (rolled, welded,…). EC3 EN 1993-1-1 Table 6.4, 6.3.2.2(2). :param steelShape: cross section shape. :param rypo: ‘rolled’ or ‘welded’ shape

materials.ec3.EC3_limit_state_checking.getLateralTorsionalBucklingResistance(steelShape, L, Mi, beamSupportCoefs=<materials.ec3.EC3_limit_state_checking.BeamSupportCoefficients object>)

Returns lateral torsional buckling resistance of this cross-section. Calculation is made following the paper:

A. López, D. J. Yong, M. A. Serna, Lateral-torsional buckling of steel beams: a general expression for the moment gradient factor. (Lisbon, Portugal: Stability and ductility of steel structures, 2006).

Parameters

  • steelShape – cross section shape.

  • Mi – ordinate for the moment diagram

  • beamSupportCoefs – coefficients that represent support conditions.

materials.ec3.EC3_limit_state_checking.getMcr(steelShape, L, Mi, beamSupportCoefs=<materials.ec3.EC3_limit_state_checking.BeamSupportCoefficients object>)

Returns elastic critical moment about minor axis: y Calculation is made following the paper:

A. López, D. J. Yong, M. A. Serna, Lateral-torsional buckling of steel beams: a general expression for the moment gradient factor. (Lisbon, Portugal: Stability and ductility of steel structures, 2006).

Parameters

  • steelShape – cross section shape.

  • L – member length.

  • Mi – ordinate for the moment diagram

  • beamSupportCoefs – coefficients that represent support conditions.

materials.ec3.EC3_limit_state_checking.getMvRdz(steelShape, Vd)

Returns the major bending resistance of the cross-section under a shear force of Vd.

param steelShape: cross section shape.

materials.ec3.EC3_limit_state_checking.get_buckling_parameters(element, bucklingLoadFactors, steelShape)

Return the effective length, mechanical slenderness, reduction factor and buckling resistance for the given buckling load factors.

Parameters

  • element – element to compute the buckling parameters for.

  • bucklingLoadFactors – list containing the buckling load factors obtained from the linear buckling analysis.

  • steelShape – steel section of the element.