Materials according to Eurocode-3

EC3 materials

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.CHSShape(steel, name)

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

CHS shape with Eurocode 3 verification routines.

class materials.ec3.EC3_materials.EC3Shape(name, typo='rolled')

Bases: object

Steel shape with Eurocode 3 verification routines.

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)

getBiaxialBendingEfficiency(sectionClass, Nd, Myd, Mzd, Vyd=0.0, 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:
  • sectionClass – section classification (1,2,3 or 4)
  • chiLT – lateral buckling reduction factor (default= 1.0).
getCfactIntPart()

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

getClassInternalPartInBending(steel)

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

Parameters:
  • steel – steel type (e.g. S275JR)
  • ratioCT – ratio c/t width-to-thickness of the internal compressed part (defaults to widthToThicknessWeb).
getClassInternalPartInCompression(steel, 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:
  • steel – steel type (e.g. S275JR)
  • ratioCT – ratio c/t width-to-thickness of the internal compressed part (defaults to widthToThicknessWeb)
getClassOutstandPartInCompression(steel, ratioCT=None)

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

Parameters:
  • steel – steel type (e.g. S275JR)
  • 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(sectionClass, L, Mi, supportCoefs=<materials.ec3.EC3_limit_state_checking.SupportCoefficients object>)

Returns lateral torsional buckling intermediate factor value.

Parameters:
  • sectionClass – section classification (1,2,3 or 4)
  • Mi – ordinate for the moment diagram
  • supportCoefs – coefficients that represent support conditions.
getLateralBucklingNonDimensionalBeamSlenderness(sectionClass, L, Mi, supportCoefs=<materials.ec3.EC3_limit_state_checking.SupportCoefficients object>)

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

Parameters:
  • shape – cross section shape.
  • sectionClass – section classification (1,2,3 or 4)
  • Mi – ordinate for the moment diagram
  • supportCoefs – coefficients that represent support conditions.
getLateralBucklingReductionFactor(sectionClass, L, Mi, supportCoefs=<materials.ec3.EC3_limit_state_checking.SupportCoefficients object>)

Returns lateral torsional buckling reduction factor value.

Parameters:
  • sectionClass – section classification (1 to 3, 4 not yet implemented)
  • Mi – ordinate for the moment diagram
  • supportCoefs – 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(sectionClass, L, Mi, supportCoefs=<materials.ec3.EC3_limit_state_checking.SupportCoefficients 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:
  • Mi – ordinate for the moment diagram
  • supportCoefs – coefficients that represent support conditions.
getMcRdy(sectionClass)

Return the minor bending resistance of the cross-section.

Parameters:sectionClass – section classification (1,2,3 or 4)
getMcRdz(sectionClass)

Return the major bending resistance of the cross-section.

Parameters:sectionClass – section classification (1,2,3 or 4)
getMcr(L, Mi, supportCoefs=<materials.ec3.EC3_limit_state_checking.SupportCoefficients 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:
  • Mi – ordinate for the moment diagram
  • supportCoefs – coefficients that represent support conditions.
getMvRdz(sectionClass, Vd)
Return the major bending resistance of the cross-section under a
shear force of Vd.
Parameters:sectionClass – section classification (1,2,3 or 4)
getNcRd(sectionClass)

Return the axial compression resistance of the cross-section.

Parameters:sectionClass – section classification (1,2,3 or 4)
getVcRdy()

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

getVplRdy()

Return y direction (web direction) plastic shear resistance

getYShearEfficiency(sectionClass, Vyd)

Return major axis shear efficiency.

Parameters:sectionClass – section classification (1,2,3 or 4)
getZBendingEfficiency(sectionClass, Mzd, Vyd=0.0, chiLT=1.0)

Return major axis bending efficiency

Parameters:
  • sectionClass – section classification (1,2,3 or 4)
  • chiLT – lateral buckling reduction factor (default= 1.0).
installULSControlRecorder(recorderType, elems, sectionClass=1, chiLT=1.0)

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

Parameters:
  • sectionClass – section classification (1,2,3 or 4)
  • chiLT – lateral buckling reduction factor (default= 1.0).
setupULSControlVars(elems, sectionClass=1, chiLT=1.0)
For each element creates the variables
needed to check ultimate limit state criterion to be satisfied.
Parameters:
  • sectionClass – section classification (1,2,3 or 4)
  • chiLT – lateral buckling reduction factor (default= 1.0).
shearBucklingVerificationNeeded()

Return true if shear buckling verification is needed EC3-1-5

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 – 80<t<125mm
  • gammaM1 – Partial factor for buckling resistance.
  • gammaM2 – Partial factor for cross-sections in tension to fracture.
fyd()
fydV()
gammaM0()
getDesignElasticPerfectlyPlasticMaterial(preprocessor, name)
getLambda1()

return lambda_1 value as specified in EC3 part 1 5.5.1.2

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.

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.

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.

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.

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

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

SHS shape with Eurocode 3 verification routines.

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.fuEC3(desig, t)

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

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

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

EC3 beam

class materials.ec3.EC3Beam.EC3Beam(name, ec3Shape, sectionClass=1, supportCoefs=<materials.ec3.EC3_limit_state_checking.SupportCoefficients object>, typo='rolled', lstLines=None, lstPoints=None)

Bases: materials.buckling_base.MemberBase

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

Variables:
  • sectionClass – section class (1 to 3, 4 not yet implemented) (defaults to 1).
  • supportCoefs – instance of EC3_limit_state_checking.SupportCoefficients 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)
getLateralBucklingReductionFactor()

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

installULSControlRecorder(recorderType, chiLT=1.0)

Install recorder for verification of ULS criterion.

updateLateralBucklingReductionFactor()

Update the value of the lateral buckling reduction factor.

updateReductionFactors()

Update the value of the appropriate reduction factors.

EC3 limit state checking

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

class materials.ec3.EC3_limit_state_checking.BiaxialBendingNormalStressController(limitStateLabel)

Bases: materials.limit_state_checking_base.LimitStateControllerBase

Object that controls normal stresses limit state.

checkSetFromIntForcFile(intForcCombFileName, setCalc=None)

Launch checking.

Parameters:
  • intForcCombFileName – name of the file to read the internal force results
  • setCalc – set of elements to check
initControlVars(setCalc)

Initialize control variables over elements.

Parameters:setCalc – set of elements to which define control variables
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(supportCoefs)
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(supportCoefs)
Return the value for the C1 coefficient according to equation 8
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
getExtremeMoment()

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

class materials.ec3.EC3_limit_state_checking.ShearController(limitStateLabel)

Bases: materials.limit_state_checking_base.LimitStateControllerBase

Object that controls shear limit state.

checkSetFromIntForcFile(intForcCombFileName, setCalc=None)

Launch checking.

Parameters:setCalc – set of elements to check
initControlVars(setCalc)

Initialize control variables over elements.

Parameters:setCalc – set of elements to which define control variables
class materials.ec3.EC3_limit_state_checking.SupportCoefficients(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].

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(shape, Vd)

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

Parameters:shape – cross section shape.
materials.ec3.EC3_limit_state_checking.getLateralBucklingImperfectionFactor(shape)

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

Parameters:shape – cross section shape.
materials.ec3.EC3_limit_state_checking.getLateralBucklingIntermediateFactor(shape, sectionClass, L, Mi, supportCoefs=<materials.ec3.EC3_limit_state_checking.SupportCoefficients object>)

Returns lateral torsional buckling intermediate factor value.

Parameters:
  • shape – cross section shape.
  • Mi – ordinate for the moment diagram
  • supportCoefs – coefficients that represent support conditions.
materials.ec3.EC3_limit_state_checking.getLateralBucklingNonDimensionalBeamSlenderness(shape, sectionClass, L, Mi, supportCoefs=<materials.ec3.EC3_limit_state_checking.SupportCoefficients object>)

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

Parameters:
  • shape – cross section shape.
  • sectionClass – section classification (1,2,3 or 4)
  • Mi – ordinate for the moment diagram
  • supportCoefs – coefficients that represent support conditions.
materials.ec3.EC3_limit_state_checking.getLateralBucklingReductionFactor(shape, sectionClass, L, Mi, supportCoefs=<materials.ec3.EC3_limit_state_checking.SupportCoefficients object>)

Returns lateral torsional buckling reduction factor value.

Parameters:
  • shape – cross section shape.
  • sectionClass – section classification (1 to 3, 4 not yet implemented)
  • Mi – ordinate for the moment diagram
  • supportCoefs – coefficients that represent support conditions.
materials.ec3.EC3_limit_state_checking.getLateralTorsionalBucklingCurve(shape)

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 shape: cross section shape. :param rypo: ‘rolled’ or ‘welded’ shape

materials.ec3.EC3_limit_state_checking.getLateralTorsionalBucklingResistance(shape, sectionClass, L, Mi, supportCoefs=<materials.ec3.EC3_limit_state_checking.SupportCoefficients 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:
  • shape – cross section shape.
  • sectionClass – section classification (1,2,3 or 4)
  • Mi – ordinate for the moment diagram
  • supportCoefs – coefficients that represent support conditions.
materials.ec3.EC3_limit_state_checking.getMcr(shape, L, Mi, supportCoefs=<materials.ec3.EC3_limit_state_checking.SupportCoefficients 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:
  • shape – cross section shape.
  • Mi – ordinate for the moment diagram
  • supportCoefs – coefficients that represent support conditions.
materials.ec3.EC3_limit_state_checking.getMvRdz(shape, sectionClass, Vd)

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

param shape: cross section shape.

materials.ec3.EC3_limit_state_checking.shearBucklingVerificationNeeded(shape)

Returns true if shear buckling verification is needed EC3-1-5

Parameters:shape – cross section shape.