Materials according to EHE code

EHE materials

Reinforced concrete materials according to EHE-08.

class materials.ehe.EHE_materials.EHEConcrete(nmbConcrete, fck, gammaC, typeAggregate='cuarcita')

Bases: materials.concrete_base.Concrete

Concrete model according to EHE

Variables

typeAggregate – types of aggregate= “cuarcita”, “arenisca”, “caliza normal”, “caliza densa”, “volcanica porosa”, “volcanica normal”, “granito”, “diabasa” (defaults to ‘cuarcita’)

fctMedEHE08()

Mean tensile strength [Pa][+] (according to clause 39.1 EHE-08)

fctkEHE08()

Concrete characteristic tensile strength [Pa][+] (according to clause 39.1 EHE-08)

fctkInf()

Characteristic tensile strength (lower value) [Pa][+] (according to clause 39.1 EHE)

fctkSup()

Characteristic tensile strength (higher value) [Pa][+] (according to clause 39.1 EHE)

getAlphaEcm()

Correction coefficient to the longitudinal modulus of deformation taking into account the type of aggregate.

getCreepDeformation(t, t0, RH, h0, sigmaT0)

return the creep deformation between t0 and t according to clause 39.8 of EHE-08.

Parameters

  • t – age of concrete in days at the moment considered

  • t0 – age of concrete in days at loading

  • RH – ambient relative humidity(%)

  • h0 –

    notional size of the member.

    • h0=2*Ac/u, where:

    • Ac= cross sectional area

    • u = perimeter of the member in contact with the atmosphere

  • sigmaT0 – constant compressive stress appliend on day t0 (negative sign).

getDict()

Return a dictionary with the object values.

getEc0()

Initial modulus of longitudinal deformation at 28 days expressed in [Pa] [+] according to clause 39.6 of EHE-08.

getEcm()

Longitudinal secant modulus of deformation at 28 days expressed in [Pa] [+] according to clause 39.6 of EHE-08.

getEcmT(t)

Longitudinal concrete modulus of deformation at t days expressed in [Pa] [+] according to comments to clause 39.6 of EHE-08.

Parameters

t – Age of concrete, expressed in days.

getEpsc2()

return strain (<0) at peak stress at parabola-rectangle diagram (art. 39.5 EHE, figure 39.5.a EHE)

getEpscu2()

return nominal ultimate strain [-] at parabola-rectangle diagram (art. 39.5 EHE, figure 39.5.a EHE)

getExpN()

return exponent n for the parabola-rectangle diagram (art. 39.5 EHE, figure 39.5.a EHE)

getFctm()

Fctm: mean tensile strength [Pa][+] (art. 39.1 EHE)

getFlexuralStrength(h)
Return the value of the flexural strength

according to the coomentary to clause 31.3 of EHE-08.

Parameters

h – depth of the member cross-section.

getFlexuralTensileStrain(h: float)

Returns the strain corresponding to flexural tensile strength.

Parameters

h – total member depth.

getFlexuralTensileStrength(h: float)
Returns the concrete flexural tensile strength according to

clause 39.1 of EHE–08 (last expression in that clause).

Parameters

h – total member depth expressed in meters.

getM(steel)
Return the “m” coefficient according to table 69.5.1.2.a of

EHE-08

Parameters

steel – reinforcing steel.

linearCoefficientOfThermalExpansion = 1e-05
setFromDict(dct)

Set the member values from those in the given dictionary.

taucd()

Design value of shear strength according to artocle 39.1.3.2.2 of code EHE-91 (f_cv=0.5*sqrt(f_cd)) with f_cd in kp/cm2

class materials.ehe.EHE_materials.PrestressingSteel(steelName, fpk, fmax=1860000000.0, alpha=0.75, steelRelaxationClass=1, tendonClass='strand', Es=190000000000.0)

Bases: materials.concrete_base.CEB_EHE_PrestressingSteel

Prestressing steel model according to EHE-08.

Variables

alpha – stress-to-strength ratio.

fpbdStrand = <scipy.interpolate._interpolate.interp1d object>
fpbdStrandValues = [1400000.0, 1600000.0, 1800000.0, 1900000.0, 2100000.0, 2200000.0]
fpbdWire = <scipy.interpolate._interpolate.interp1d object>
fpbdWireValues = [1600000.0, 1800000.0, 2000000.0, 2200000.0, 2400000.0, 2600000.0]
getAnchorageLength(phi, concrete, pos, sg_pi, sg_pd, sg_pcs, suddenRelease=True, ELU=True, t=28)
Return the design anchorage length for the tendon according

to the commentaries to the article 70.2.3 of EHE.

Parameters

  • phi – nominal diameter of the wire, or prestressing strand.

  • concrete – concrete material.

  • pos – reinforcement position according to clause 69.5.1 of EHE-08 (I: good adherence, II: poor adherence).

  • sg_pi – tendon stress just after release.

  • sg_pd – tendon stress under design load.

  • sg_pcs – tendon stress due to prestress after all losses.

  • suddenRelease – if true, prestressing is transfered to concrete in a very short time.

  • ELU – true if ultimate limit state checking.

  • t – concrete age at themoment of the prestress transmission expressed in days.

getDesignAdherenceStress(concrete, pos, t=28)
Return the design value of the adherence stress according

to the commentaries to the article 70.2.3 of EHE.

Parameters

  • concrete – concrete material.

  • pos – reinforcement position according to clause 69.5.1 of EHE-08 (I: good adherence, II: poor adherence).

  • t – concrete age at themoment of the prestress transmission expressed in days.

getInitialStressLimit()

Return the limit of the initial stress according to clause 20.2.2 of EHE.

getKRelaxation()

Return the value of k factor for the relaxation expression from the relaxation class. See Model Code 1990 paragraph 2.3.4.5.

getRO1000()

Return the relaxation at 1000 hours after stressing (See table 38.9.a at EHE-08)

getRelaxationStressLossFinal(initialStress)

Return final change in tendon stress due to relaxation.

Parameters

initialStress – Initial stress in tendon.

getRelaxationStressLossT(tDays, initialStress)

Return change in tendon stress due to relaxation at time t.

Parameters

  • initialStress – Initial stress in tendon.

  • tDays – Time in days after prestressing (to make easier to deal with shrinkage and creep at the same time).

getRelaxationT(tDias)

Return the relaxation at time tDias in days after stressing.

Parameters

tDays – Time in days after prestressing (to make easier to deal with shrinkage and creep at the same time).

getTransmissionLength(phi, concrete, pos, sg_pi, suddenRelease=True, ELU=True, t=28)
Return the length of transmission for the tendon according

to the commentaries to the article 70.2.3 of EHE.

Parameters

  • phi – nominal diameter of the wire, or prestressing strand.

  • concrete – concrete material.

  • pos – reinforcement position according to clause 69.5.1 of EHE-08 (I: good adherence, II: poor adherence).

  • sg_pi – steel stress just after release.

  • suddenRelease – if true, prestressing is transfered to concrete in a very short time.

  • ELU – true if ultimate limit state checking.

  • t – concrete age at themoment of the prestress transmission expressed in days.

get_anchorage_length(phi, lbpt, concrete, pos, sg_pd, sg_pcs, t)
Return the design anchorage length for the tendon according

to the commentaries to the article 70.2.3 of EHE.

Parameters

  • phi – nominal diameter of the wire, or prestressing strand.

  • lbpt – length of transmission for the tendon.

  • concrete – concrete material.

  • pos – reinforcement position according to clause 69.5.1 of EHE-08 (I: good adherence, II: poor adherence).

  • sg_pi – tendon stress just after release.

  • sg_pd – tendon stress under design load.

  • t – concrete age at themoment of the prestress transmission expressed in days.

ptsRO1000Bars = <scipy.interpolate._interpolate.interp1d object>
ptsRO1000Wires = <scipy.interpolate._interpolate.interp1d object>
x = [25000000.0, 30000000.0, 35000000.0, 40000000.0, 45000000.0, 50000000.0]
class materials.ehe.EHE_materials.ReinforcingSteel(steelName=None, fyk=0.0, emax=0.0, gammaS=1.15, k=1.05)

Bases: materials.concrete_base.ReinforcingSteel

Reinforcing steel as defined in EHE-08.

alpha_gt_10phi = [1.0, 1.0, 1.1, 1.2, 1.3, 1.4, 1.4]
alpha_leq_10phi = [1.0, 1.2, 1.4, 1.6, 1.8, 2.0, 2.0]
alpha_ratios = [0.0, 0.2, 0.25, 0.33, 0.5, 0.51, 1.0]
f400 = <scipy.interpolate._interpolate.interp1d object>
f500 = <scipy.interpolate._interpolate.interp1d object>
f_alpha_gt_10phi = <scipy.interpolate._interpolate.interp1d object>
f_alpha_leq_10phi = <scipy.interpolate._interpolate.interp1d object>
getBasicAnchorageLength(concrete, phi, pos, dynamicEffects=False)
Returns basic anchorage length in tension according to clause

69.5.1.2 of EHE.

Parameters

  • concrete – concrete material.

  • phi – nominal diameter of bar, wire, or prestressing strand.

  • pos – reinforcement position according to clause 69.5.1 of EHE-08 (I: good adherence, II: poor adherence).

  • dynamicEffects – true if the anchorage is subjected to dynamic effects.

getLapLength(concrete, phi, pos, distBetweenNearestSplices, beta=1.0, efficiency=1.0, ratioOfOverlapedTensionBars=1.0, tensionedBars=True, dynamicEffects=False)
Returns net anchorage length in tension according to clause

6.5.1.2 of EHE.

Parameters

  • concrete – concrete material.

  • phi – nominal diameter of bar, wire, or prestressing strand.

  • pos – reinforcement position according to clause 69.5.1 of EHE-08 (I: good adherence, II: poor adherence).

  • distBetweenNearestSplices – distance between the nearest splices according to figure 69.5.2.2.a.

  • beta – reduction factor defined in Table 69.5.1.2.b.

  • efficiency – working stress of the reinforcement that it is intended to anchor, on the most unfavourable load hypothesis, in the section from which the anchorage length will be determined divided by the steel design yield strength.

  • ratioOfOverlapedTensionBars – ratio of overlapped tension bars in relation to the total steel section.

  • tensionedBars – true if the bars are in tension.

  • dynamicEffects – true if the anchorage is subjected to dynamic effects.

getM(concrete)
Return the ‘m’ factor from table 69.5.1.2.a

of EHE-08.

Parameters

concrete – concrete material.

getNetAnchorageLength(concrete, phi, pos, beta=1.0, efficiency=1.0, tensionedBars=True, dynamicEffects=False)
Returns net anchorage length in tension according to clause

6.5.1.2 of EHE.

Parameters

  • concrete – concrete material.

  • phi – nominal diameter of bar, wire, or prestressing strand.

  • pos – reinforcement position according to clause 69.5.1 of EHE-08 (I: good adherence, II: poor adherence).

  • beta – reduction factor defined in Table 69.5.1.2.b.

  • efficiency – working stress of the reinforcement that it is intended to anchor, on the most unfavourable load hypothesis, in the section from which the anchorage length will be determined divided by the steel design yield strength.

  • tensionedBars – true if the bars are in tension.

  • dynamicEffects – true if the anchorage is subjected to dynamic effects.

x = [25000000.0, 30000000.0, 35000000.0, 40000000.0, 45000000.0, 50000000.0]
y400 = [1.2, 1.0, 0.9, 0.8, 0.7, 0.7]
y500 = [1.5, 1.3, 1.2, 1.1, 1.0, 1.0]
class materials.ehe.EHE_materials.Y1860S7Strand(diameter, area)

Bases: materials.ehe.EHE_materials.PrestressingSteel

Uncoated strand 7-Steel wire for prestressed concrete

according to EN 10138 - 3 Prestressing steels: March 2011.

Variables

  • diameter – strand diameter.

  • area – cross sectional area.

Fm()

Return the characteristic value of maximum force.

Fm_max()

Return the maximum value of the maximum force.

Fp()
getAnchorageLength(concrete, pos, sg_pi, sg_pd, sg_pcs, suddenRelease=True, ELU=True, t=28)
Return the design anchorage length for the strand according

to the commentaries to the article 70.2.3 of EHE.

Parameters

  • concrete – concrete material.

  • pos – reinforcement position according to clause 69.5.1 of EHE-08 (I: good adherence, II: poor adherence).

  • sg_pi – tendon stress just after release.

  • sg_pd – tendon stress under design load.

  • sg_pcs – tendon stress due to prestress after all losses.

  • suddenRelease – if true, prestressing is transfered to concrete in a very short time.

  • ELU – true if ultimate limit state checking.

  • t – concrete age at themoment of the prestress transmission expressed in days.

getTransmissionLength(concrete, pos, sg_pi, suddenRelease=True, ELU=True, t=28)
Return the length of transmission for the strand according

to the commentaries to the article 70.2.3 of EHE.

Parameters

  • concrete – concrete material.

  • pos – reinforcement position according to clause 69.5.1 of EHE-08 (I: good adherence, II: poor adherence).

  • sg_pi – steel stress just after release.

  • suddenRelease – if true, prestressing is transfered to concrete in a very short time.

  • ELU – true if ultimate limit state checking.

  • t – concrete age at themoment of the prestress transmission expressed in days.

massPerMeter()

Return the mass per meter of the strand.

materials.ehe.EHE_materials.concrOfName = {'HA100': HA100, 'HA20': HA20, 'HA25': HA25, 'HA30': HA30, 'HA35': HA35, 'HA40': HA40, 'HA45': HA45, 'HA50': HA50, 'HA55': HA55, 'HA60': HA60, 'HA70': HA70, 'HA80': HA80, 'HA90': HA90, 'HP25': HP25, 'HP30': HP30, 'HP35': HP35, 'HP40': HP40, 'HP45': HP45, 'HP50': HP50, 'HP60': HP60}

Factor that multiplies the characteristic value of concrete compressive strength from its age in days for normal hardening concrete (table 30.4.b EHE)

materials.ehe.EHE_materials.factorRCompJDiasNormal = <scipy.interpolate._interpolate.interp1d object>

Factor that multiplies the characteristic value of concrete compressive strength from its age in days for fast hardening concrete (table 30.4.b EHE)

materials.ehe.EHE_materials.factorRCompJDiasRapido = <scipy.interpolate._interpolate.interp1d object>

Factor that multiplies the characteristic value of concrete tensile strength from its age in days for normal hardening concrete (table 30.4.c EHE)

materials.ehe.EHE_materials.get_losses_elastic_shortening_concrete_in_tendons(sigma_cp, Ep, Ecj)

Losses due to elastic shortening of the concrete in prestressed tendons

Parameters

  • sigma_cp – compressive stress in the concrete in the level of the center of gravity of the active reinforcement, due to prestressing after deducting the losses due to wedge penetration

  • Ep – elastic modulus of the active reinforcements (defaults to 190e9).

  • Ecj – elastic modulus of the concrete for the age j corresponding to the moment of applying the load to the active reinforcements.

materials.ehe.EHE_materials.get_losses_wedge_penetration_short_straight_tendon(a, L, Ep)

Losses due to wedge penetration in post-tensioned straight tendons of short length (according to section 20.2.2.1.2 of EHE-08)

Parameters

  • a – wedge penetration (usually: 5 mm)

  • L – total length of the straight tendon

  • Ep – longitudinal strain modulus of an active reinforcement (190e9).

EHE limit state checking

Limit state checking according to structural concrete spanish standard EHE-08.

class materials.ehe.EHE_limit_state_checking.BeamReinforcementRatios(concrete, reinforcingSteel, Ac, W1, h, z=None, Ap=0.0, P=0.0, dp=0.0, ds=0.0, e=0.0, prestressingSteel=None)

Bases: materials.ehe.EHE_limit_state_checking.ReinforcementRatios

Maximum and minimum reinforcement ratios for members subjected to

pure or combined bending.

Variables

  • fct_m_fl – average flexural strength of the concrete.

  • W1 – section modulus of the gross section relating to the fibre under greatest tension.

  • z – Mechanical lever arm of the section. In the absence of more accurate calculations, this may be taken to be z = 0.8 h.

  • fpd – design value of the tensile strength of bonded active reinforcement steel.

getMinimumGeometricAmount()

Minimum geometric reinforcement amount for columns according to table 42.3.5 of EHE-08.

getMinimumMechanicalAmount()

Minimum mechanical reinforcement amount according to clause 42.3.2 of EHE-08.

class materials.ehe.EHE_limit_state_checking.BiaxialBendingNormalStressController(limitStateLabel)

Bases: materials.limit_state_checking_base.BiaxialBendingNormalStressControllerBase

Object that controls normal stresses limit state.

class materials.ehe.EHE_limit_state_checking.BiaxialBucklingController(limitStateLabel)

Bases: materials.ehe.EHE_limit_state_checking.BiaxialBendingNormalStressController

Object that controls buckling limit state.

ControlVars

alias of postprocess.control_vars.BiaxialBucklingControlVars

class materials.ehe.EHE_limit_state_checking.BlockMember(a, b, a1, b1, concrete, steel)

Bases: object

Checking of solid block members under concentrated loads, according

to clause 61 of EHE-08.

Variables

  • a – side length (see figure 61.1.a of EHE-08).

  • a1 – length of the side of the loaded area parallel to a (see figure 61.1.a of EHE-08).

  • b – side length (see figure 61.1.a of EHE-08).

  • b1 – length of the side of the loaded area parallel to b (see figure 61.1.a of EHE-08).

  • concrete – concrete material.

  • steel – steel material.

getAc()

Return area of the block member.

getAc1()

Return block member loaded area.

getConcreteEfficiency(Nd)

Return the efficiency of the concrete strength.

Parameters

Nd – concentrated load.

getF3cd()

Return the value of f3cd according to clause 61.2 of EHE-08.

getNuConcentratedLoad()

Return the the maximum compressive force that can be obtained in the Ultimate Limit State of on a restricted surface (see figure 61.1.a on page 302 of EHE-08), of area Ac1 , concentrically and homothetically situated on another area, Ac.

getReinforcementAreaAd(Nd)

Return the area of the reinforcement parallel to side a (see figure 61.1.a page 302 EHE-08)

param Nd

concentrated load.

getReinforcementAreaBd(Nd)

Return the area of the reinforcement parallel to side b (see figure 61.1.a page 302 EHE-08)

param Nd

concentrated load.

param fyd

steel yield strength.

getUad(Nd)

Return the design tension for the transverse reinforcement in a direction parallel to side a (see figure 61.1.a page 302 EHE-08).

Parameters:
param Nd

concentrated load.

getUbd(Nd)

Return the design tension for the transverse reinforcement in a direction parallel to side b (see figure 61.1.a page 302 EHE-08).

param Nd

concentrated load.

class materials.ehe.EHE_limit_state_checking.BucklingParametersLimitStateData(numModes=4, limitStateLabel='ULS_bucklingParametersComputation', outputDataBaseFileName='verifRsl_bucklingULS', designSituations=['uls_permanent', 'uls_accidental', 'uls_earthquake'], eigenvectorNormThreshold=0.001, alpha_cr_threshold=10.0)

Bases: postprocess.limit_state_data.BucklingParametersLimitStateData

Buckling parameters data for limit state checking.

getController(biaxialBuckling=True)

Return a controller corresponding to this limit state.

Parameters

biaxialBuckling – if True, consider bending aroung both cross-section axes.

getEHEBucklingParametersDict(nmbComb, xcSet)
Creates a dictionary with the buckling parameters of the given

elements.

Parameters

  • nmbComb – combination name.

  • xcSet – set containing the nodes to export the modes on.

getInternalForcesTuple(setCalc)
Read the element tags, load combinations identifiers and internal

forces for the elements in the given set and return them in a tuple: (eTags, loadCombinations, internalForces). The internal forces are preprocessing to increase the bending moments according to the results of the buckling analysis.

Parameters

setCalc – elements to read internal forces for.

getResultsDict()

Build a dictionary containing all the analysis results.

prepareResultsDictionaries()

Prepare the dictionaries to store the results of the analysis.

updateResults(combName, calcSet, constrainedNodes=None)
Append the results of the current analysis to the results

dictionaries.

Parameters

  • combName – load combination corresponding to the current analysis.

  • setCalc – set of entities for which the verification is going to be performed.

  • constrainedNodes – constrained nodes (defaults to None)

class materials.ehe.EHE_limit_state_checking.ColumnReinforcementRatios(concrete, reinforcingSteel, Ac, Ap=0.0, P=0)

Bases: materials.ehe.EHE_limit_state_checking.ReinforcementRatios

Minimum and maximum reinforcement ratios for columns.

check(As, Nd)

Checking of main reinforcement ratio in compression.

getMaximumReinforcementAmount()

Return the maximal reinforcement amount acording to clause 42.3.3 of EHE-08.

getMinimumGeometricAmount()

Minimum geometric reinforcement amount for columns according to table 42.3.5 of EHE-08.

getMinimumMechanicalAmount(Nd)
Minimum mechanical reinforcement amount according to

clause 42.3.3 of EHE-08.

Parameters

Nd – Design value of the internal axial load.

class materials.ehe.EHE_limit_state_checking.ConcreteCorbel(concrete, steel, jointType)

Bases: object

Concrete corbel as in EHE-08 design code.

getAreaNecApoyo(Fv)
getAreaNecApoyo(self,Fv): return the area needed for the

support according to clause 64.1.2.1.2 of EHE-08.

Parameters

Fv – Vertical load on the corbel, positive downwards (N).

getAreaNecCercos(Fv)
getAreaNecCercos(self,Fv): return the area needed for the

stirrup reinforcements bars in the corbel according to clause 64.1.2.1.1 of EHE-08.

Parameters

Fv – Vertical load on the corbel, positive downwards (N).

getAreaNecMainReinforcement(Fv, Fh)
getAreaNecMainReinforcement(self, Fv,Fh): return the area needed

for the main reinforcement according to clause 64.1.2.1.1 of EHE-08.

Parameters

  • Fv – Vertical load on the corbel, positive downwards (N).

  • Fh – Horizontal load on the corbel, positive outwards (N).

getCotgStrutAngle()

Return the cotangent of the angle between the concrete compressed strut an the vertical according to clause 64.1.2.1 of EHE-08.

getMainReinforcementTension(Fv, Fh)
getMainReinforcementTension(self, Fv,Fh). Return the tension

in the main reinforcement according to clause 64.1.2.1.1 of EHE-08.

Parameters

  • Fv – Vertical load on the corbel, positive downwards (N).

  • Fh – Horizontal load on the corbel, positive outwards (N).

getMinimumEffectiveDepth(a)

getMinimumEffectiveDepth(self, a) return the minimal effective depth of the corbel according to clause 64.1.2.1 of EHE-08.

Parameters

a – Distance (m) between the axis of the applied load and the corbel fixed section (see figure 64.1.2 of EHE-08).

static getStirrupsTension(Fv)
getStirrupsTension(Fv): return the tension in the stirrups

to clause 64.1.2.1.1 of EHE-08.

Parameters

Fv – Vertical load on the corbel, positive downwards (N).

class materials.ehe.EHE_limit_state_checking.CrackControl(limitStateLabel)

Bases: materials.limit_state_checking_base.CrackControlBaseParameters

Define the properties that will be needed for crack control checking as in clause 49.2.4 of EHE-08.

computeWk(scc, concreteMatTag, reinfSteelMaterialTag, fctm)

Computes the characteristic value of the crack width.

Parameters

  • scc – section.

  • reinfSteelMaterialTag – identifier of the concrete material.

  • reinfSteelMaterialTag – identifier of the reinforcing steel material.

  • fctm – average tensile strength of the concrete.

computeWkOnBars(tensionedReinforcement)
Compute the characteristic crack opening on each bar and return

the maximum.

Parameters

tensionedReinforcement –

printParams(os=<_io.TextIOWrapper name='<stdout>' mode='w' encoding='utf-8'>)

Prints crack control parameters.

class materials.ehe.EHE_limit_state_checking.CrackControlLimitStateData(limitStateLabel, outputDataBaseFileName, designSituations)

Bases: postprocess.limit_state_data.CrackControlRCLimitStateData

EHE crack control limit state data.

getController(wk_lim=0.0003, beta=1.7, k2=1.0, solutionProcedureType=None)

Return a controller corresponding to this limit state. :param wk_lim: maximum allowable crack width. :param beta: Coefficient which relates the mean crack opening to the

characteristic value and is equal to 1.3 in the case of cracking caused by indirect actions only, and 1.7 in other cases.

Parameters

  • k2 – coefficient of value 1.0 in the case of non-repeating temporary load and 0.5 in other cases.

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

class materials.ehe.EHE_limit_state_checking.CrackController(limitStateLabel, wk_lim=0.0003, beta=1.7, k2=1.0, solutionProcedureType=<class 'solution.predefined_solutions.PlainNewtonRaphson'>)

Bases: materials.limit_state_checking_base.LimitStateControllerBase

Object that verifies the cracking serviceability limit state according to clause 49.2.4 of EHE-08.

Variables

  • wk_lim – maximum allowable crack width.

  • beta – Coefficient which relates the mean crack opening to the characteristic value and is equal to 1.3 in the case of cracking caused by indirect actions only, and 1.7 in other cases.

  • k2 – coefficient of value 1.0 in the case of non-repeating temporary load and 0.5 in other cases.

ControlVars

alias of postprocess.control_vars.RCCrackControlVars

EHE_hceff(width, h, x)
Return the maximum height to be considered in the calculation of

the concrete effective area in tension.

Parameters

  • width – section width.

  • h – lever arm.

  • x – depth of the neutral fiber.

EHE_k1(eps1, eps2)

Return the coefficient k1 involved in the calculation of the mean crack distance according to EHE. This coefficient represents the effect of the tension diagram in the section.

Parameters

  • eps1 – maximum deformation calculated in the section at the limits of the tension zone.

  • eps2 – minimum deformation calculated in the section at the limits of the tension zone.

check(elements, loadCombinationName)
For each element in the set ‘elememts’ passed as first parameter

and the resulting internal forces for the load combination ‘loadCombinationName’ passed as second parameter, this method calculates all the variables involved in the crack-SLS checking and obtains the crack width. In the case that the calculated crack width is greater than the biggest obtained for the element in previous load combinations, this value is saved in the element results record.

Elements processed are those belonging to the phantom model, that is to say, of type xc.ZeroLengthSection. As we have defined the variable fakeSection as False, a reinfoced concrete fiber section is generated for each of these elements.

Parameters

  • elements – elements to check.

  • loadCombinationName – name of the load combination.

class materials.ehe.EHE_limit_state_checking.CrackStraightController(limitStateLabel, beta=1.7, solutionProcedureType=<class 'solution.predefined_solutions.PlainNewtonRaphson'>)

Bases: materials.ehe.EHE_limit_state_checking.CrackController

Object that verifies the cracking serviceability limit state according to EHE-08 when considering a concrete stress-strain diagram that takes account of the effects of tension stiffening.

ControlVars

alias of postprocess.control_vars.RCCrackStraightControlVars

check(elements, combName)
For each element in the set ‘elememts’ passed as first parameter

and the resulting internal forces for the load combination ‘combName’ passed as second parameter, this method calculates all the variables involved in the crack-SLS checking and obtains the crack width. In the case that the calculated crack width is greater than the biggest obtained for the element in previous load combinations, this value is saved in the element results record.

Elements processed are those belonging to the phantom model, that is to say, of type xc.ZeroLengthSection. As we have defined the variable fakeSection as False, a reinfoced concrete fiber section is generated for each of these elements.

Parameters

  • elements – elements to check.

  • loadCombinationName – name of the load combination.

expectsTensionStiffeningModel()

Return true if a tension-stiffening concrete fiber model must be used for this limit state.

class materials.ehe.EHE_limit_state_checking.EHERebarFamily(steel, diam, spacing, concreteCover, pos='II')

Bases: materials.sections.rebar_family.RebarFamily

Family or reinforcement bars with checking according to EHE-08.

Variables

pos – reinforcement position according to clause 69.5.1 of EHE-08 (I: good adherence, II: poor adherence).

getBasicAnchorageLength(concrete)

Return the basic anchorage length of the bars.

getCopy()

Virtual constructor.

getMinReinfAreaInBending(concrete, thickness, b=1.0, steelStressLimit=450000000.0, memberType=None)
Return the minimun amount of bonded reinforcement to control cracking

for reinforced concrete sections under flexion per unit length according to clause 42.3.5.

Parameters

  • concrete – concrete material.

  • thickness – gross thickness of concrete section (doesn’t include the area of the voids).

  • b – width of concrete section.

  • memberType – member type; slab, wall, beam, column, etc.

  • steelStressLimit – maximum stress permitted in the reinforcement immediately after formation of the crack. This may be taken as the yield strength of the reinforcement, fyk. A lower value may, however, be needed to satisfy the crack width limits according to the maximum bar size or spacing.

getMinReinfAreaInTension(concrete, thickness, b=1.0, memberType=None)
Return the minimun amount of bonded reinforcement to control cracking

for reinforced concrete sections under tension.

Parameters

  • concrete – concrete material.

  • thickness – gross thickness of concrete section.

  • b – width of concrete section.

  • memberType – member type; slab, wall, beam, column, etc.

getRebarController()
getVR(concrete, Nd, Md, b, thickness)
Return the approximated shear resistance carried by the concrete

on a (b x thickness) rectangular section.

Parameters

  • concrete – concrete material.

  • Nd – design axial force (IGNORED).

  • Md – design bending moment (IGNORED).

  • b – width of the rectangular section.

  • thickness – height of the rectangular section.

class materials.ehe.EHE_limit_state_checking.FreqLoadsCrackControlLimitStateData(designSituations=['sls_frequent'])

Bases: materials.ehe.EHE_limit_state_checking.CrackControlLimitStateData

Reinforced concrete crack control under frequent loads limit state data.

readControlVars(modelSpace)

Read the control vars associated with this limit state.

Parameters

modelSpace – PredefinedSpace object used to create the FE model (see predefined_spaces.py).

Returns

number of properties read.

class materials.ehe.EHE_limit_state_checking.LongShearJoints(concrete, reinfsteel, contactSurf, roughness='L', dynamic='N', sigma_cd=0, Ast=None, spacement=None, angRebars=90)

Bases: object

Verification of ultimate limit state due to longitudinal shear stress

at joints between concretes according to clause 47 of EHE.

Variables

  • concrete – weakest EHE concrete type (ex: EHE_materials.HA25)

  • reinfsteel – EHE reinforcing steel (ex: EHE_materials.B500S)

  • contactSurf – Contact surface per unit length. This shall not extend to zones where the penetrating width is less than 20 mm or the maximum diameter of the edge or with a cover of less than 30 mm

  • roughness – roughness of surface (‘L’ for low degree of roughness, ‘H’ for high degree of roughness). Defaults to ‘L’

  • dynamic – low fatigue or dynamic stresses consideration (‘Y’ if considered, ‘N’ for not considered). Defaults to ‘N’

  • sigma_cd – External design tensile stress perpendicular to the plane of the joint. (<0 for compression tensions) (if sigma_cd > 0, beta, fct_d=0). Defaults to 0.

  • Ast – Cross-section of effectively anchored steel bars, closing the joint (area of 1 those rebars, spacement is given also as a parameter). Defaults to None = no reinforcement, in this case all parameters attached to reinforcement are ignored .

  • spacement – distance between the closing bars along the joint plane. (defaults to None)

  • angRebars – Angle formed by the joining bars with the plane of the joint (degrees). Reinforcements with α > 135° or α < 45° shall not be incorporated. Defaults to 90º

checkShearStressJoints(tao_rd)

Verify the ultimate limit state due to longitudinal shear stress.

Parameters

tao_rd – design longitudinal shear stress at a joint between concrete.

getBetaCoef()

Return beta coefficient depending on the roughness of contact surfaces (clause 47.2.1 EHE and table 47.2.2.2):

  • 0.80 in rough contact surfaces of composite sections that are interconnected so that one composite section may not overhang the other, for example, are dovetailed, and if the surface is open and rough, e.g. like joists as left by a floor laying machine.

  • 0.40 in intentionally rough surfaces with a high degree of roughness.

  • 0.20 in unintentionally rough surfaces with a low degree of roughness.

  • at low fatigue or dynamic stresses beta shall be reduced by 50%.

getMuCoefCase1()

Return mu coefficient depending of roughness, for calculation of ultimate shear stress at a joint in case 1 (clause 47.2.1 EHE, table 47.2.2.2).

getMuCoefCase2()

Return mu coefficient depending of roughness, for calculation of ultimate shear stress at a joint in case 2 (clause 47.2.1 EHE, table 47.2.2.2):

getUltShearStressWithReinf(tao_rd)
Return the ultimate longitudinal shear stress at a joint between

concrete sections with transverse reinforcement according to clause 47.2.2 of EHE-08.

Parameters

tao_rd – design longitudinal shear stress at a joint between concrete.

getUltShearStressWithoutReinf()

Return the ultimate longitudinal shear stress in a section without any transverse reinforcement

class materials.ehe.EHE_limit_state_checking.NormalStressesLimitStateData(designSituations=['uls_permanent', 'uls_accidental', 'uls_earthquake'])

Bases: postprocess.limit_state_data.NormalStressesRCLimitStateData

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.ehe.EHE_limit_state_checking.QPLoadsCrackControlLimitStateData(designSituations=['sls_quasi-permanent'])

Bases: materials.ehe.EHE_limit_state_checking.CrackControlLimitStateData

Reinforced concrete crack control under quasi-permanent loads limit state data.

readControlVars(modelSpace)

Read the control vars associated with this limit state.

Parameters

modelSpace – PredefinedSpace object used to create the FE model (see predefined_spaces.py).

Returns

number of properties read.

class materials.ehe.EHE_limit_state_checking.RareLoadsCrackControlLimitStateData(designSituations=['sls_rare'])

Bases: materials.ehe.EHE_limit_state_checking.CrackControlLimitStateData

Reinforced concrete crack control under rare loads limit state data.

readControlVars(modelSpace)

Read the control vars associated with this limit state.

Parameters

modelSpace – PredefinedSpace object used to create the FE model (see predefined_spaces.py).

Returns

number of properties read.

class materials.ehe.EHE_limit_state_checking.RebarController(concreteCover=0.035, spacing=0.15, pos='II', compression=True, alpha_1=1.0, alpha_3=1.0, alpha_4=1.0, alpha_5=1.0)

Bases: materials.limit_state_checking_base.EURebarController

Control of some parameters as development length minimum reinforcement and so on.

Variables

pos – reinforcement position according to clause 69.5.1.1 of EHE-08 (I: good adherence, II: poor adherence).

getBasicAnchorageLength(concrete, rebarDiameter, steel, dynamicEffects=False)
Returns basic anchorage length in tension according to clause

69.5.1.2 of EHE.

Parameters

  • concrete – concrete material.

  • rebarDiameter – nominal diameter of bar, wire, or prestressing strand.

  • steel – reinforcement steel.

  • dynamicEffects – true if the anchorage is subjected to dynamic effects.

getBeta(rebarDiameter, barShape='bent', lateralConcreteCover=None)
Return the value of beta according to the commentary to clause

69.5.1.2 of EHE-08 and table 69.5.1.2.c.

Parameters

  • rebarDiameter – nominal diameter of the bar.

  • barShape – ‘straight’ or ‘bent’ or ‘looped’.

  • lateralConcreteCover – lateral concrete cover (c1 in figure 8.3 of EC2:2004). If None make it equal to the regular concrete cover.

getConcreteMinimumCoverEffect(rebarDiameter, barShape='bent', lateralConcreteCover=None)
Return the value of the alpha_2 factor that introduces the effect

of concrete minimum cover according to figure 69.5.1.2.a and table 69.5.1.2.c of EHE-08.

Parameters

  • rebarDiameter – nominal diameter of the bar.

  • barShape – ‘straight’ or ‘bent’ or ‘looped’.

  • lateralConcreteCover – lateral concrete cover (c1 in figure 8.3 of EC2:2004). If None make it equal to the regular concrete cover.

getDesignAnchorageLength(concrete, rebarDiameter, steel, steelEfficiency=1.0, barShape='bent', lateralConcreteCover=None, dynamicEffects=False)
Added for EC2 compatibility: returns net anchorage length in tension according to clause

69.5.1.2 of EHE.

Parameters

  • concrete – concrete material.

  • rebarDiameter – nominal diameter of bar, wire, or prestressing strand.

  • steel – reinforcement steel.

  • steelEfficiency – working stress of the reinforcement that it is intended to anchor, on the most unfavourable load hypothesis, in the section from which the anchorage length will be determined divided by the steel design yield strength.

  • barShape – ‘straight’ or ‘bent’ or ‘looped’.

  • dynamicEffects – true if the anchorage is subjected to dynamic effects.

getLapLength(concrete, rebarDiameter, steel, distBetweenNearestSplices, steelEfficiency=1.0, ratioOfOverlapedTensionBars=1.0, lateralConcreteCover=None, dynamicEffects=False)
Returns net lap length in tension according to clause

69.5.2 of EHE08.

Parameters

  • concrete – concrete material.

  • rebarDiameter – nominal diameter of bar, wire, or prestressing strand.

  • steel – reinforcement steel.

  • distBetweenNearestSplices – distance between the nearest splices according to figure 69.5.2.2.a.

  • beta – reduction factor defined in Table 69.5.1.2.b.

  • steelEfficiency – working stress of the reinforcement that it is intended to anchor, on the most unfavourable load hypothesis, in the section from which the anchorage length will be determined divided by the steel design yield strength.

  • ratioOfOverlapedTensionBars – ratio of overlapped tension bars in relation to the total steel section.

  • dynamicEffects – true if the anchorage is subjected to dynamic effects.

getM(concrete, steel)
Return the “m” coefficient according to table 69.5.1.2.a of

EHE-08

Parameters

  • concrete – concrete material.

  • steel – reinforcing steel.

getNetAnchorageLength(concrete, rebarDiameter, steel, steelEfficiency=1.0, barShape='bent', lateralConcreteCover=None, dynamicEffects=False)
Returns net anchorage length in tension according to clause

69.5.1.2 of EHE.

Parameters

  • concrete – concrete material.

  • rebarDiameter – nominal diameter of bar, wire, or prestressing strand.

  • steel – reinforcement steel.

  • steelEfficiency – working stress of the reinforcement that it is intended to anchor, on the most unfavourable load hypothesis, in the section from which the anchorage length will be determined divided by the steel design yield strength.

  • barShape – ‘straight’ or ‘bent’ or ‘looped’.

  • dynamicEffects – true if the anchorage is subjected to dynamic effects.

class materials.ehe.EHE_limit_state_checking.ReinforcementRatios(concrete, reinforcingSteel, Ac, Ap=0.0, P=0, prestressingSteel=None)

Bases: object

Maximum and minimum reinforcement ratios according to EHE-08.

Variables

  • concrete – concrete material.

  • reinforcingSteel – reinforcing steel material.

  • Ac – concrete area.

  • Ap – area of the bonded active reinforcement.

  • P – pre-stressing force with instantaneous losses disregarded.

  • prestressingSteel – pre-stressing steel material.

class materials.ehe.EHE_limit_state_checking.SectionBucklingProperties(reinforcementFactorZ, sectionDepthZ, Cz, reinforcementFactorY, sectionDepthY, Cy, sectionObject)

Bases: object

Properties that define the buckling behavior of the RC section

according to clause 43.1 of EHE-08.

Variables

  • reinforcementFactorZ – reinforcement factor according to table 43.5.1 of EHE-08 (z axis).

  • sectionDepthZ – section depth (z axis).

  • Cz – clause 43.1.2 of EHE-08 (z axis).

  • reinforcementFactorY – reinforcement factor according to table 43.5.1 of EHE-08 (y axis).

  • sectionDepthY – section depth (y axis).

  • Cy – clause 43.1.2 of EHE-08 (y axis).

  • sectionData – object derived from RCSectionBase used to define the reinforced concrete section.

getDict()

Put member values in a dictionary.

classmethod newFromDict(dct=None)

Builds a new object from the data in the given dictionary.

Parameters

  • cls – class of the object itself.

  • dct – dictionary contaning the data.

setFromDict(dct)

Read member values from a dictionary.

Parameters

dct – Python dictionary containing the member values.

class materials.ehe.EHE_limit_state_checking.ShearController(limitStateLabel, solutionProcedureType=<class 'solution.predefined_solutions.PlainNewtonRaphson'>)

Bases: materials.limit_state_checking_base.ShearControllerBase

Shear control according to EHE-08.

ControlVars

alias of postprocess.control_vars.SIATypeRCShearControlVars

calcVuEHE08(scc, torsionParameters, Nd, Md, Vd, Td, rcSets, circular=False)

Compute the shear strength at failure. XXX Presstressing contribution not implemented yet.

Parameters

  • scc – fiber model of the section.

  • torsionParameters – parameters that define torsional behaviour of the section as in clause 45.1 of EHE-08.

  • Nd – Design value of axial force (positive if in tension)

  • Md – Absolute value of design value of bending moment.

  • Vd – Absolute value of effective design shear (clause 42.2.2).

  • Td – design value of torsional moment.

  • rcSets – fiber sets in the reinforced concrete section.

  • circular – if true we reduce the efectiveness of the shear reinforcement due to the transverse inclination of its elements.

calcVuEHE08NoAt(scc, rcSets)

Compute the shear strength at failure without shear reinforcement according to clause 44.2.3.2.1 of EHE-08. XXX Presstressing contribution not implemented yet.

Parameters

  • scc – fiber model of the section.

  • rcSets – fiber sets in the reinforced concrete section.

calcVuEHE08SiAt(scc, torsionParameters, Nd, Md, Vd, Td, rcSets, circular=False)

Compute the shear strength at failure WITH shear reinforcement. XXX Presstressing contribution not implemented yet.

Parameters

  • scc – fiber model of the section.

  • torsionParameters – parameters that define torsional behaviour of the section as in clause 45.1 of EHE-08.

  • Nd – Design value of axial force (here positive if in tension)

  • Md – Absolute value of design value of bending moment.

  • Vd – Absolute value of effective design shear (clause 42.2.2).

  • Td – design value of torsional moment.

  • rcSets – fiber sets in the reinforced concrete section.

  • circular – if true we reduce the efectiveness of the shear reinforcement due to the transverse inclination of its elements.

check(elements, combName)

For each element in the set ‘elements’ passed as first parameter and the resulting internal forces for the load combination ‘combName’ passed as second parameter, this method calculates all the variables involved in the shear-ULS checking and obtains the capacity factor. In the case that the calculated capacity factor is smaller than the smallest obtained for the element in previous load combinations, this value is saved in the element results record.

Elements processed are those belonging to the phantom model, that is to say, of type xc.ZeroLengthSection. As we have defined the variable fakeSection as False, a reinfoced concrete fiber section is generated for each of these elements.

XXX Rebar orientation not taken into account yet.

Parameters

  • elements – phantom model elements.

  • combName – name of the load combination being checked.

checkInternalForces(sct, torsionParameters, Nd, Md, Vd, Td)

Compute the shear strength at failure. XXX Presstressing contribution not implemented yet.

Parameters

  • sct – reinforced concrete section object to check shear on.

  • torsionParameters – parameters that define torsional behaviour of the section as in clause 45.1 of EHE-08.

  • Nd – Design value of axial force (positive if in tension)

  • Md – Absolute value of design value of bending moment.

  • Vd – Absolute value of effective design shear (clause 42.2.2).

  • Td – design value of torsional moment.

checkSection(sct, elementDimension, torsionParameters=None)

Check shear on the section argument.

Parameters

  • sct – reinforced concrete section object to check shear on.

  • elementDimension – dimension of the element (1, 2 or 3).

  • torsionParameters – parameters that define torsional behaviour of the section as in clause 45.1 of EHE-08.

isCracked()

Return true if the concrete stress is greater than its tensile strength.

class materials.ehe.EHE_limit_state_checking.ShearResistanceLimitStateData(designSituations=['uls_permanent', 'uls_accidental', 'uls_earthquake'])

Bases: postprocess.limit_state_data.ShearResistanceRCLimitStateData

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).

class materials.ehe.EHE_limit_state_checking.StrandController(reinfType='strand', pos='II')

Bases: materials.ehe.EHE_limit_state_checking.RebarController

Control of some parameters as the length of transmission.

Variables

  • pos – reinforcement position according to clause 69.5.1 of EHE-08 (I: good adherence, II: poor adherence).

  • reinfType – prestressed reinforcement type: ‘wire’ or ‘strand’

getDesignAdherenceStress(concrete, steel, t=28)
Return the design value of the adherence stress according

to the commentaries to the article 70.2.3 of EHE.

Parameters

  • concrete – concrete material.

  • steel – prestressing steel material.

  • t – concrete age at themoment of the prestress transmission expressed in days.

getTransmissionLength(rebarDiameter, concrete, steel, sg_pi, suddenRelease=True, ELU=True, t=28)
Return the length of transmission for the strand according

to the commentaries to the article 70.2.3 of EHE.

Parameters

  • rebarDiameter – nominal diameter of the wire, or prestressing strand.

  • concrete – concrete material.

  • steel – prestressing steel material.

  • sg_pi – steel stress just after release.

  • suddenRelease – if true, prestressing is transfered to concrete in a very short time.

  • ELU – true if ultimate limit state checking.

  • t – concrete age at themoment of the prestress transmission expressed in days.

lbpd(rebarDiameter, concrete, sg_pi, suddenRelease=True, ELU=True, t=28)
Return the design anchorage length for the strand according

to the commentaries to the article 70.2.3 of EHE.

Parameters

  • rebarDiameter – nominal diameter of the wire, or prestressing strand.

  • concrete – concrete material.

  • sg_pi – tendon stress just after release.

  • sg_pd – tendon stress under design load.

  • sg_pcs – tendon stress due to prestress after all losses.

  • suddenRelease – if true, prestressing is transfered to concrete in a very short time.

  • ELU – true if ultimate limit state checking.

  • t – concrete age at themoment of the prestress transmission expressed in days.

class materials.ehe.EHE_limit_state_checking.TieReinforcementRatios(concrete, reinforcingSteel, Ac, Ap=0.0, P=0)

Bases: materials.ehe.EHE_limit_state_checking.ReinforcementRatios

Minimum and maximum reinforcement ratios for members that resist tension forces.

check(As, Nd)

Checking of main reinforcement ratio in compression.

getMinimumGeometricAmount()

Minimum geometric reinforcement amount for columns according to table 42.3.5 of EHE-08 (considered as a rib).

getMinimumMechanicalAmount(Nd)
Minimum mechanical reinforcement amount according to

clause 42.3.3 of EHE-08.

Parameters

Nd – Design value of the internal axial load.

class materials.ehe.EHE_limit_state_checking.TorsionController(limitStateLabel, solutionProcedureType=<class 'solution.predefined_solutions.PlainNewtonRaphson'>)

Bases: materials.limit_state_checking_base.ShearControllerBase

Torsion strength control according to EHE-08.

calcTu(rcSection, Ncd, Ae, he, ue: float, alpha=0.6)
Compute the torsional strength of the given section.

according to clause 45.2.2 of EHE-08.

Parameters

  • rcSection – reinforced concrete section.

  • Ncd – design value of axial force in concrete only (positive if in tension).

  • Ae – Area enclosed by the middle line of the design effective hollow section (figure 45.2.1).

  • he – effective thickness of the wall of the design section.

  • ue – perimeter of the middle line in the design effective hollow section Ae.

  • alpha – 0.60 if there are stirrups only along the external circumference of the member; 0.75 if closed stirrups are installed on both faces of the wall of the equivalent hollow section or the actual hollow section.

calcTu1(rcSection, Ncd, Ae, he, alpha=0.6)
Return the maximum torsional moment which the concrete’s

compressed struts can resist according to clause 45.2.2.1 of EHE-08.

Parameters

  • rcSection – reinforced concrete section.

  • Ncd – design value of axial force in concrete only (positive if in tension).

  • Ae – Area enclosed by the middle line of the design effective hollow section (figure 45.2.1).

  • he – effective thickness of the wall of the design section.

  • alpha – 0.60 if there are stirrups only along the external circumference of the member; 0.75 if closed stirrups are installed on both faces of the wall of the equivalent hollow section or the actual hollow section.

calcTu2(rcSection, Ae: float)
Compute the torsional stress which transverse reinforcements can

resist according to clause 45.2.2.2 of EHE-08.

Parameters

  • rcSection – reinforced concrete section.

  • Ae – Area enclosed by the middle line of the design effective hollow section (figure 45.2.1).

calcTu3(rcSection, Ae: float, ue: float)
Compute the torsional stress which longitudinal reinforcements can

resist according to clause 45.2.2.3 of EHE-08.

Parameters

  • rcSection – reinforced concrete section.

  • Ae – Area enclosed by the middle line of the design effective hollow section (figure 45.2.1).

  • ue – perimeter of the middle line in the design effective hollow section Ae.

class materials.ehe.EHE_limit_state_checking.TorsionParameters

Bases: object

Methods for checking reinforced concrete section under torsion

according to clause 45.1 of EHE-08.

Variables

  • h0 – Actual thickness of the section wall in the case of hollow sections.

  • c – Covering of longitudinal reinforcements.

  • crossSectionContour – Cross section contour.

  • midLine – Polygon defined by the midline of the effective hollow section.

  • intLine – Polygon defined by the interior contour of the effective hollow section.

  • effectiveHollowSection – Effective hollow section contour

A()

Return the area of the transverse section inscribed in the external circumference including inner void areas

Ae()

Return the area enclosed by the middle line of the design effective hollow section (see figure 45.2.1 of EHE-08).

he()

Return the effective thickness of the wall of the design section.

u()

Return the external perimeter of the transverse section.

ue()

Return the perimeter of the middle line in the design effective hollow section Ae.

class materials.ehe.EHE_limit_state_checking.TorsionResistanceLimitStateData(designSituations=['uls_permanent', 'uls_accidental', 'uls_earthquake'])

Bases: postprocess.limit_state_data.TorsionResistanceRCLimitStateData

Reinforced concrete torsion strength limit state data.

getController()

Return a controller corresponding to this limit state.

class materials.ehe.EHE_limit_state_checking.UniaxialBendingNormalStressController(limitStateLabel)

Bases: materials.limit_state_checking_base.UniaxialBendingNormalStressControllerBase

Object that controls normal stresses limit state (uniaxial bending).

class materials.ehe.EHE_limit_state_checking.UniaxialBucklingController(limitStateLabel)

Bases: materials.ehe.EHE_limit_state_checking.UniaxialBendingNormalStressController

Object that controls buckling limit state (uniaxial bending).

ControlVars

alias of postprocess.control_vars.UniaxialBucklingControlVars

materials.ehe.EHE_limit_state_checking.computeEffectiveHollowSectionParameters(sectionGeometry, h0, c)
Computes the parameters for torsion analysis of an

effective hollow section according to clause 45.2.1 of EHE-08. Not valid if for non-convex sections.

Parameters

  • sectionGeometry – section geometry.

  • h0 – actual thickness of the wall for hollow sections.

  • c – cover of longitudinal reinforcement.

materials.ehe.EHE_limit_state_checking.computeEffectiveHollowSectionParametersRCSection(rcSection)
Computes the parameters for torsion analysis of an

effective hollow section according to clause 45.2.1 of EHE-08.

Parameters

rcSection – reinforced concrete section

materials.ehe.EHE_limit_state_checking.define_rebar_families(steel, cover, diameters=[0.008, 0.01, 0.012, 0.014, 0.016, 0.02, 0.025, 0.032], spacings=[0.1, 0.15, 0.2])

Creates a dictionary with predefined rebar families.

Parameters

  • steel – rebars steel material.

  • cover – concrete cover for the families.

  • diameters – list of diameters.

  • spacings – list of spacings between bars.

materials.ehe.EHE_limit_state_checking.getBetaVcuEHE08(theta, thetaE)
getBetaVcuEHE08(theta,thetaE) [units: N, m, rad]

Return the value of «beta» for the expression of Vcu according to clause 44.2.3.2.2 of EHE-08.

Parameters

  • thetaE – Reference angle of inclination of cracks.

  • theta – angle between the concrete compressed struts and the member axis (figure 44.2.3.1.a EHE).

materials.ehe.EHE_limit_state_checking.getCrackAngleEHE08(Nd, Md, Vd, Td, z, AsPas, AsAct, Es, Ep, Fp, Ae, ue)
getCrackAngleEHE08(Nd,Md,Vd,Td,z,AsPas,AsAct,Es,Ep,Fp,Ae,ue) [units: N, m, rad]

Return the reference angle of inclination of cracks (in radians) from the longitudinal strain in the web. See general method in clause 44.2.3.2.2 of EHE-08.

Parameters

  • Nd – Design value of axial force (here positive if in tension)

  • Md – Absolute value of design value of bending moment.

  • Vd – Absolute value of effective design shear (clause 42.2.2).

  • Td – design value of torsional moment.

  • z – Lever arm.

  • AsPas – Area of tensioned longitudinal steel rebars anchored at a distance greater than the effective depth of the section.

  • AsAct – Area of tensioned longitudinal prestressed steel anchored at a distance greater than the effective depth of the section.

  • Es – reinforcing steel elastic modulus.

  • Ep – prestressing steel elastic modulus.

  • Fp – Prestressing force on the section (positive if in tension).

  • Ae – Area enclosed by the middle line of the effective hollow section.

  • ue – Perimeter of the middle line of the effective hollow section.

materials.ehe.EHE_limit_state_checking.getEpsilonXEHE08(Nd, Md, Vd, Td, z, AsPas, AsAct, Es, Ep, Fp, Ae, ue)

getEpsilonXEHE08(Nd,Md,Vd,Td,z,AsPas,AsAct,Es,Ep,Fp,Ae,ue) [units: N, m, rad] Return the longitudinal strain in the web according to expression in commments to the clause 44.2.3.2.2 of EHE-08.

Parameters

  • Nd – Design value of axial force (here positive if in tension)

  • Md – Absolute value of design value of bending moment.

  • Vd – Absolute value of effective design shear (clause 42.2.2).

  • Td – design value of torsional moment.

  • z – Lever arm.

  • AsPas – Area of tensioned longitudinal steel rebars anchored at a distance greater than the effective depth of the section.

  • AsAct – Area of tensioned longitudinal prestressed steel anchored at a distance greater than the effective depth of the section.

  • Es – reinforcing steel elastic modulus.

  • Ep – prestressing steel elastic modulus.

  • Fp – Prestressing force on the section (positive if in tension).

  • Ae – Area enclosed by the middle line of the effective hollow section.

  • ue – Perimeter of the middle line of the effective hollow section.

materials.ehe.EHE_limit_state_checking.getF1cdEHE08(fck, fcd)

getF1cdEHE08(fck,fcd). Returns the value of f1cd (design value of the concrete strut strength) according to clause 44.2.3.1 of EHE-08.

Parameters

  • fck – concrete characteristic compressive strength (Pa).

  • fcd – design value of concrete compressive strength (N/m2).

materials.ehe.EHE_limit_state_checking.getFcv(fact, fck, Nd, Ac, b0, d, AsPas, fyd, AsAct, fpd)

Return the value of fcv (concrete virtual shear strength) for members WITH or WITHOUT shear reinforcement, according to clauses 44.2.3.2.1 y 44.2.3.2.2 of EHE.

Parameters

  • fact –

    factor equal to 0.12 for members WITHOUT shear reinforcement

    (0.18/gammac)

    and 0.10 for members WITH shear reinforcement (0.15/gammac).

  • fck – concrete characteristic compressive strength.

  • Nd – axial force design value (positive if in tension).

  • Ac – concrete section total area.

  • b0 – net width of the element according to clause 40.3.5.

  • d – effective depth (meters).

  • AsPas – Area of tensioned longitudinal steel rebars anchored at a distance greater than the effective depth of the section.

  • fyd – reinforcing steel design yield strength (clause 38.3 EHE).

  • AsAct – Area of tensioned longitudinal prestressed steel anchored at a distance greater than the effective depth of the section.

  • fpd – design value of prestressing steel strength (clause 38.6 EHE).

materials.ehe.EHE_limit_state_checking.getFcvEH91(fcd)
Return fcv (concrete virtual shear strength)

according to EH-91.

Parameters

fcd – design compressive strength of concrete.

materials.ehe.EHE_limit_state_checking.getFcvEHE08(fact, fcv, gammaC, b0, d, chi, sgpcd, AsPas, AsAct)
getFcvEHE08(fact,fcv,gammaC,b0,d,chi,sgpcd,AsPas,AsAct) [units: N, m, rad]

Return the value of fcv (concrete virtual shear strength) for members WITH or WITHOUT shear reinforcement in cracked regions, according to clauses 44.2.3.2.1.2 and 44.2.3.2.2 of EHE-08.

Parameters

  • fact – Factor with a value of 0.18 for members WITHOUT shear reinforcement and 0.15 for members WITH shear reinforcement.

  • fcv –

    effective concrete shear strength. For members without
    shear reinforcement fcv= min(fck,60MPa). For members

    with shear reinforcement fcv= min(fck,100MPa).

    In both cases, if concrete quality control is not direct fcv= 15 MPa.

  • gammaC – Partial safety factor for concrete.

  • b0 – net width of the element according to clause 40.3.5.

  • d – effective depth (meters).

  • chi – coefficient that takes into account the aggregate effect inside the effective depth.

  • sgpcd – average axial stress in the web (positive if in compression).

  • AsPas – Area of tensioned longitudinal steel rebars anchored at a distance greater than the effective depth of the section.

  • AsAct – Area of tensioned longitudinal prestressed steel anchored at a distance greater than the effective depth of the section.

materials.ehe.EHE_limit_state_checking.getFcvMinEHE08(fcv, gammaC, d, chi, sgpcd)
Return the minimum value of fcv (concrete virtual shear strength)

for members WITHOUT shear reinforcement in cracked regions, according to clause 44.2.3.2.1.2 of EHE-08.

Parameters

  • fcv –

    effective concrete shear strength. For members without

    shear reinforcement fcv= min(fck,60MPa). For members with shear reinforcement fcv= min(fck,100MPa).

    In both cases, if concrete quality control is not direct fcv= 15 MPa.

  • gammaC – Partial safety factor for concrete.

  • d – effective depth (meters).

  • chi – coefficient that takes into account the aggregate effect inside the effective depth.

  • sgpcd – average axial stress in the web (positive if in compression).

materials.ehe.EHE_limit_state_checking.getKEHE08(sgpcd, fcd)

getKEHE08(sgpcd,fcd). Return the value of K (coefficent that depends of the axial force) according to clause 44.2.3.1 de la EHE-08

Parameters

  • sgpcd – effective normal stress in concrete Ncd/Ac.

  • fcd – design value of concrete compressive strength (N/m2).

materials.ehe.EHE_limit_state_checking.getVcu(fck, Nd, Ac, b0, d, theta, AsPas, fyd, AsAct, fpd, sgxd, sgyd)

Return the value of Vcu (contribution of the concrete to shear strength) for members WITH shear reinforcement, according to clause 44.2.3.2.2 of EHE (1998).

Parameters

  • fck – concrete characteristic compressive strength.

  • Nd – axial force design value (positive if in tension).

  • Ac – concrete section total area.

  • b0 – net width of the element according to clause 40.3.5.

  • d – effective depth (meters).

  • theta – angle between the concrete compressed struts and the member axis (figure 44.2.3.1.a EHE 1998).

  • AsPas – area of tensioned longitudinal steel rebars anchored at a distance greater than the effective depth of the section.

  • fyd – reinforcing steel design yield strength (clause 38.3 EHE).

  • AsAct – Area of tensioned longitudinal prestressed steel anchored at a distance greater than the effective depth of the section.

  • fpd – design value of prestressing steel strength (clause 38.6 EHE).

  • sgxd – design value of normal stress at the centre of gravity of the section parallel to the main axis of the member. Calculated assuming NON CRACKED concrete (clause 44.2.3.2).

  • sgyd – design value of normal stress at the centre of gravity of the section parallel to shear force Vd. Calculated assuming NON CRACKED concrete (clause 44.2.3.2).

materials.ehe.EHE_limit_state_checking.getVcuEHE08(fcv, fcd, gammaC, Ncd, Ac, b0, d, z, AsPas, AsAct, theta, Nd, Md, Vd, Td, Es, Ep, Fp, Ae, ue)
getVcuEHE08(fcv,fcd,gammaC,Ncd,Ac,b0,d,z,AsPas,AsAct,theta,Nd,Md,Vd,Td,Es,Ep,Fp,Ae,ue)

[units: N, m, rad] Return the value of Vcu (contribution of the concrete to shear strength) for members WITH shear reinforcement, according to clause 44.2.3.2.2 of EHE-08.

Parameters

  • fcv – effective concrete shear strength. For members without shear reinforcement fcv= min(fck,60MPa). For members with shear reinforcement fcv= min(fck,100MPa). In both cases, if concrete quality control is not direct fcv= 15 MPa.

  • fcd – design value of concrete compressive strength).

  • gammaC – Partial safety factor for concrete.

  • Ncd – design value of axial force in concrete (positive if in tension).

  • Ac – concrete section total area.

  • b0 – net width of the element according to clause 40.3.5.

  • d – effective depth (meters).

  • z – Lever arm.

  • AsPas – Area of tensioned longitudinal steel rebars anchored at a distance greater than the effective depth of the section.

  • AsAct – Area of tensioned longitudinal prestressed steel anchored at a distance greater than the effective depth of the section.

  • theta – angle between the concrete compressed struts and the member axis (figure 44.2.3.1.a EHE)

  • Nd – Design value of axial force (positive if in tension)

  • Md – Absolute value of design value of bending moment.

  • Vd – Absolute value of effective design shear (clause 42.2.2).

  • Td – design value of torsional moment.

  • Es – reinforcing steel elastic modulus.

  • Ep – prestressing steel elastic modulus.

  • Fp – Prestressing force on the section (positive if in tension).

  • Ae – Area enclosed by the middle line of the effective hollow section.

  • ue – Perimeter of the middle line of the effective hollow section.

materials.ehe.EHE_limit_state_checking.getVcuEHE08CrackAngle(fcv, fcd, gammaC, Ncd, Ac, b0, d, AsPas, AsAct, theta, thetaEVcu)
getVcuEHE08(fcv, fcd, gammaC, Ncd, Ac, b0, d, AsPas,AsAct, theta, thetaEVcu)

[units: N, m, rad] Return the value of Vcu (contribution of the concrete to shear strength) for members WITH shear reinforcement, according to clause 44.2.3.2.2 of EHE-08.

Parameters

  • fcv – effective concrete shear strength. For members without shear reinforcement fcv= min(fck,60MPa). For members with shear reinforcement fcv= min(fck,100MPa). In both cases, if concrete quality control is not direct fcv= 15 MPa.

  • fcd – design value of concrete compressive strength).

  • gammaC – Partial safety factor for concrete.

  • Ncd – design value of axial force in concrete (positive if in tension).

  • Ac – concrete section total area.

  • b0 – net width of the element according to clause 40.3.5.

  • d – effective depth (meters).

  • AsPas – Area of tensioned longitudinal steel rebars anchored at a distance greater than the effective depth of the section.

  • AsAct – Area of tensioned longitudinal prestressed steel anchored at a distance greater than the effective depth of the section.

  • theta – angle between the concrete compressed struts and the member axis (figure 44.2.3.1.a EHE)

  • thetaEvCu – reference angle of inclination of cracks (in radians).

materials.ehe.EHE_limit_state_checking.getVsu(z, alpha, theta, AsTrsv, fyd)

Return the value of Vsu (contribution of the web’s transverse reinforcement to shear strength) for members WITH shear reinforcement, according to clause 44.2.3.2.2 of EHE.

Parameters

  • z – Mechanic lever arm.

  • alpha – angle of the shear reinforcement with the member axis (see figure 44.2.3.1.a EHE).

  • theta – angle between the concrete compressed struts and the member axis (figure 44.2.3.1.a EHE).

  • AsTrsv – transverse reinforcement area.

  • fyd – design yield strength of the transverse reinforcement.

materials.ehe.EHE_limit_state_checking.getVsuEHE08(z, alpha, theta, AsTrsv, fyd, circular)

getVsuEHE08(z,alpha,theta,AsTrsv,fyd) [units: N, m, rad] Return the value of Vsu (contribution of the web’s transverse reinforcement to shear strength) for members WITH shear reinforcement, according to clause 44.2.3.2.2 of EHE-08.

Parameters

  • z – mechanic lever arm.

  • alpha – angle of the transverse reinforcement with the member axis.

  • theta – angle between the concrete compressed struts and the member axis (figure 44.2.3.1.a EHE).

  • AsTrsv – transverse reinforcement area which contribution will be computed.

  • fyd – design yield strength of the transverse reinforcement.

  • circular – if true we reduce the efectiveness of the shear reinforcement due to the transverse inclination of its elements.

materials.ehe.EHE_limit_state_checking.getVu(fck, fcd, Nd, Ac, b0, d, z, alpha, theta, AsPas, fyd, AsAct, fpd, sgxd, sgyd, AsTrsv, fydTrsv)
Return the value of Vu= max(Vu1,Vu2) for members WITH or WITHOUT shear

reinforcement, according to clause 44.2.3.2.2 of EHE (1998).

Parameters

  • fck – concrete characteristic compressive strength.

  • Nd – axial force design value (positive if in tension).

  • Ac – concrete section total area.

  • b0 – net width of the element according to clause 40.3.5.

  • d – effective depth (meters).

  • z – mechanic lever arm.

  • alpha – angle of the shear reinforcement with the member axis (figure 44.2.3.1.a EHE).

  • theta – angle between the concrete compressed struts and the member axis (figure 44.2.3.1.a EHE).

  • AsPas – Area of tensioned longitudinal steel rebars anchored at a distance greater than the effective depth of the section.

  • fyd – reinforcing steel design yield strength (clause 38.3 EHE).

  • AsAct – Area of tensioned longitudinal prestressed steel anchored at a distance greater than the effective depth of the section.

  • fpd – design value of prestressing steel strength (clause 38.6 EHE).

  • sgxd – design value of normal stress at the centre of gravity of the section parallel to the main axis of the member. Calculated assuming NON CRACKED concrete (clause 44.2.3.2).

  • sgyd – design value of normal stress at the centre of gravity of the section parallel to shear force Vd. Calculated assuming NON CRACKED concrete (clause 44.2.3.2).

  • AsTrsv – transverse reinforcement area.

  • fydTrsv – design yield strength of the transverse reinforcement.

materials.ehe.EHE_limit_state_checking.getVu1(fcd, Nd, Ac, b0, d, alpha, theta)

Return value of Vu1 (shear strength at failure due to diagonal compression in the web) according to clause 44.2.3.1 of EHE.

Parameters

  • fcd – Design compressive strength of concrete.

  • Nd – axial force design value (positive if in tension).

  • Ac – concrete section total area.

  • b0 – net width of the element according to clause 40.3.5.

  • d – effective depth.

  • alpha – angle between the shear rebars and the member axis (figure 44.2.3.1.a EHE).

  • theta – angle between the concrete compressed struts and the member axis (figure 44.2.3.1.a EHE).

materials.ehe.EHE_limit_state_checking.getVu1EHE08(fck, fcd, Ncd, Ac, b0, d, alpha, theta)
getVu1EHE08(fck,fcd,Ncd,Ac,b0,d,alpha,theta) [units: N, m, rad]. Return

the value of Vu1 (shear strength at failure due to diagonal compression in the web) according to clause 44.2.3.1 of EHE-08.

Parameters

  • fck – concrete characteristic compressive strength.

  • fcd – design value of concrete compressive strength (N/m2).

  • Ncd – design value of axial force in concrete only (positive if in tension).

  • Ac – concrete section total area.

  • b0 – net width of the element according to clause 40.3.5.

  • d – effective depth.

  • alpha – angle of the shear reinforcement with the member axis (figure 44.2.3.1 EHE-08).

  • theta – angle between the concrete compressed struts and the member axis (figure 44.2.3.1.a EHE).

  • As – Total area of compressed reinforcement. In combined compression, it may be assumed that the entire reinforcement is subject to the tension fyd.

  • fyd – Design strength of reinforcement As.

materials.ehe.EHE_limit_state_checking.getVu2(fck, Nd, Ac, b0, d, z, alpha, theta, AsPas, fyd, AsAct, fpd, sgxd, sgyd, AsTrsv, fydTrsv)

Return the value of Vu2 (ultimate shear force failure due to tensile force in the web) for members WITH or WITHOUT shear reinforcement, according to clause 44.2.3.2.2 of EHE (1998).

Parameters

  • fck – concrete characteristic compressive strength.

  • Nd – axial force design value (positive if in tension).

  • Ac – concrete section total area.

  • b0 – net width of the element according to clause 40.3.5.

  • d – effective depth (meters).

  • z – mechanic lever arm.

  • alpha – angle of the shear reinforcement with the member axis (see figure 44.2.3.1.a EHE).

  • theta – angle between the concrete compressed struts and the member axis (figure 44.2.3.1.a EHE).

  • AsPas – Area of tensioned longitudinal steel rebars anchored at a distance greater than the effective depth of the section.

  • fyd – reinforcing steel design yield strength (clause 38.3 of EHE).

  • AsAct – Area of tensioned longitudinal prestressed steel anchored at a distance greater than the effective depth of the section.

  • fpd – design value of prestressing steel strength (clause 38.6 of EHE).

  • sgxd – design value of normal stress at the centre of gravity of the section parallel to the main axis of the member. Calculated assuming NON CRACKED concrete (clause 44.2.3.2).

  • sgyd – design value of normal stress at the centre of gravity of the section parallel to shear force Vd. Calculated assuming NON CRACKED concrete (clause 44.2.3.2).

  • AsTrsv – transverse reinforcement area.

  • fydTrsv – design yield strength of the transverse reinforcement.

materials.ehe.EHE_limit_state_checking.getVu2EHE08NoAt(M, Mfis, fcv, fck, gammaC, I, S, alphaL, Ncd, Ac, b0, d, AsPas, AsAct)
getVu2EHE08NoAt(M,Mfis,fcv,fck,gammaC,I,S,alphaL,Ncd,Ac,b0,d,AsPas,AsAct) [units: N, m, rad]. Return the value of Vu2

(shear strength at failure due to tensile force in the web) for members WITHOUT shear reinforcement, according to clauses 44.2.3.2.1.1 y 44.2.3.2.1.2 of EHE-08.

Parameters

  • M – Bending moment in the section.

  • Mfis – Cracking moment of the section calculated using fct,d= fct,k/gammaC in the same plane that M.

  • fcv – effective concrete shear strength. For members without shear reinforcement fcv= min(fck,60MPa). For members with shear reinforcement fcv= min(fck,100MPa). In both cases, if concrete quality control is not direct fcv= 15 MPa.

  • fck – concrete characteristic compressive strength.

  • gammaC – Partial safety factor for concrete.

  • Ncd – design value of axial force in concrete (positive if in tension).

  • Ac – concrete section total area.

  • b0 – net width of the element according to clause 40.3.5.

  • d – effective depth (meters).

  • AsPas – Area of tensioned longitudinal steel rebars anchored at a distance greater than the effective depth of the section.

  • AsAct – Area of tensioned longitudinal prestressed steel anchored at a distance greater than the effective depth of the section.

materials.ehe.EHE_limit_state_checking.getVu2EHE08NoAtNoFis(fctd, I, S, b0, alphal, Ncd, Ac)
getVu2EHE08NoAtNoFis(fctd,I,S,b0,alphal,Ncd,Ac) [units: N, m, rad].

Return the value of Vu2 (shear strength at failure due to tensile force in the web) according to clause 44.2.3.2.1.1 of EHE-08.

Parameters

  • fctd – design tensile strength of the concrete.

  • I – Moment of inertia of the section with respect of its centroid.

  • S – First moment of the section above the center of gravity.

  • b0 – net width of the element according to clause 40.3.5.

  • alphal – coeficiente que, en su caso, introduce el efecto de la transferencia.

  • Ncd – design value of axial force in concrete (positive if in tension).

  • Ac – concrete section total area.

materials.ehe.EHE_limit_state_checking.getVu2EHE08NoAtSiFis(fcv, fcd, gammaC, Ncd, Ac, b0, d, AsPas, AsAct)
getVu2EHE08NoAtSiFis(fcv,fcd,gammaC,Ncd,Ac,b0,d,AsPas,AsAct) [units: N, m]

Return the value of Vu2 (shear strength at failure due to tensile force in the web) for members WITHOUT shear reinforcement in cracked regions, according to clause 44.2.3.2.1.2 of EHE-08.

Parameters

  • fcv – effective concrete shear strength. For members without shear reinforcement fcv= min(fck,60MPa). For members with shear reinforcement fcv= min(fck,100MPa). In both cases, if concrete quality control is not direct fcv= 15 MPa.

  • fcd – design value of concrete compressive strength).

  • gammaC – Partial safety factor for concrete.

  • Ncd – design value of axial force in concrete (positive if in tension).

  • Ac – concrete section total area.

  • b0 – net width of the element according to clause 40.3.5.

  • d – effective depth (meters).

  • AsPas – Area of tensioned longitudinal steel rebars anchored at a distance greater than the effective depth of the section.

  • AsAct – Area of tensioned longitudinal prestressed steel anchored at a distance greater than the effective depth of the section.

materials.ehe.EHE_limit_state_checking.getVu2EHE08SiAt(fcv, fcd, fyd, gammaC, Ncd, Ac, b0, d, z, AsPas, AsAct, AsTrsv, alpha, theta, Nd, Md, Vd, Td, Es, Ep, Fp, Ae, ue, circular=False)
getVu2EHE08SiAt(fcv,fcd,fyd,gammaC,Ncd,Ac,b0,d,z,AsPas,AsAct,AsTrsv, alpha, theta,Nd,Md,Vd,Td,Es,Ep,Fp,Ae,ue) [units: N, m, rad].

Return the value of Vu2 (shear strength at failure due to tensile force in the web) for members WITH shear reinforcement, according to clause 44.2.3.2.2 of EHE-08.

Parameters

  • fcv – effective concrete shear strength. For members without shear reinforcement fcv= min(fck,60MPa). For members with shear reinforcement fcv= min(fck,100MPa). In both cases, if concrete quality control is not direct fcv= 15 MPa.

  • fcd – design value of concrete compressive strength.

  • fyd – design yield strength of the transverse reinforcement.

  • gammaC – Partial safety factor for concrete.

  • Ncd – design value of axial force in concrete (positive if in tension).

  • Ac – concrete section total area.

  • b0 – net width of the element according to clause 40.3.5.

  • d – effective depth (meters).

  • z – Lever arm.

  • AsPas – Area of tensioned longitudinal steel rebars anchored at a distance greater than the effective depth of the section.

  • AsAct – Area of tensioned longitudinal prestressed steel anchored at a distance greater than the effective depth of the section.

  • AsTrsv – transverse reinforcement area.

  • alpha – angle of the transverse reinforcement with the axis of the part.

  • theta – angle between the concrete compressed struts and the member axis (figure 44.2.3.1.a EHE).

  • Nd – Design value of axial force (positive if in tension)

  • Md – Absolute value of design value of bending moment.

  • Vd – Absolute value of effective design shear (clause 42.2.2).

  • Td – design value of torsional moment.

  • Es – reinforcing steel elastic modulus.

  • Ep – prestressing steel elastic modulus.

  • Fp – Prestressing force on the section (positive if in tension).

  • Ae – Area enclosed by the middle line of the effective hollow section.

  • ue – Perimeter of the middle line of the effective hollow section.

  • circular – if true we reduce the efectiveness of the shear reinforcement due to the transverse inclination of its elements.

materials.ehe.EHE_limit_state_checking.getVu2SIN(fck, Nd, Ac, b0, d, AsPas, fyd, AsAct, fpd)
Return the value of Vu2 (shear strength at failure due to tensile force in the web)

for members WITHOUT shear reinforcement, according to clause 44.2.3.2.1 of EHE (1998).

Parameters

  • fck – concrete characteristic compressive strength.

  • Nd – axial force design value (positive if in tension).

  • Ac – concrete section total area.

  • b0 – net width of the element according to clause 40.3.5.

  • d – effective depth (meters).

  • AsPas – Area of tensioned longitudinal steel rebars anchored at a distance greater than the effective depth of the section.

  • fyd – reinforcing steel design yield strength (clause 38.3 EHE).

  • AsAct – Area of tensioned longitudinal prestressed steel anchored at a distance greater than the effective depth of the section.

  • fpd – design value of prestressing steel strength (clause 38.6 EHE).

materials.ehe.EHE_limit_state_checking.getVuEHE08SiAt(fck, fcv, fcd, fyd, gammaC, Ncd, Ac, b0, d, z, AsPas, AsAct, AsTrsv, alpha, theta, Nd, Md, Vd, Td, Es, Ep, Fp, Ae, ue)

def getVuEHE08SiAt(fck,fcv,fcd,fyd,gammaC,Ncd,Ac,b0,d,z,AsPas,AsAct,AsTrsv, alpha, theta,Nd,Md,Vd,Td,Es,Ep,Fp,Ae,ue) [units: N, m, rad] Return the value of Vu (section shear strength) for members WITH shear reinforcement, according to clause 44.2.3.2.2 of EHE-08.

Parameters

  • fck – characteristic value of concrete compressive strength.

  • fcv –

    effective concrete shear strength. For members without

    shear reinforcement fcv= min(fck,60MPa). For members with shear reinforcement fcv= min(fck,100MPa).

    In both cases, if concrete quality control is not direct fcv= 15 MPa.

  • fcd – design value of concrete compressive strength.

  • fyd – design yield strength of the transverse reinforcement.

  • gammaC – Partial safety factor for concrete.

  • Ncd – design value of axial force in concrete only (positive if in tension).

  • Ac – concrete section total area.

  • b0 – net width of the element according to clause 40.3.5.

  • d – effective depth (meters).

  • z – Lever arm.

  • AsPas – Area of tensioned longitudinal steel rebars anchored at a distance greater than the effective depth of the section.

  • AsAct – Area of tensioned longitudinal prestressed steel anchored at a distance greater than the effective depth of the section.

  • AsTrsv – transverse reinforcement area.

  • alpha – angle of the transverse reinforcement with the axis of the part.

  • theta – angle between the concrete compressed struts and the member axis (figure 44.2.3.1.a EHE).

  • Nd – Design value of axial force (positive if in tension)

  • Md – Absolute value of design value of bending moment.

  • Vd – Absolute value of effective design shear (clause 42.2.2).

  • Td – design value of torsional moment.

  • Es – reinforcing steel elastic modulus.

  • Ep – prestressing steel elastic modulus.

  • Fp – Prestressing force on the section (positive if in tension).

  • Ae – Area enclosed by the middle line of the effective hollow section.

  • ue – Perimeter of the middle line of the effective hollow section.

materials.ehe.EHE_limit_state_checking.get_buckling_e1_e2_eccentricities(Nd: float, MdMax: float, MdMin: float)
Compute the e1 and e2 eccentricities as defined in the clause 43.1.2 of

EHE-08.

Parameters

  • Nd – design axial force.

  • MdMax – maximum bending moment on the member to be checked.

  • MdMin – minimum bending moment on the member to be checked.

materials.ehe.EHE_limit_state_checking.get_buckling_parameters(element, bucklingLoadFactors, rcSection, sectionDepthZ, Cz, reinforcementFactorZ, sectionDepthY=None, Cy=None, reinforcementFactorY=None, eigenvectorNormThreshold=0.001, alpha_cr_threshold=10.0)

Return the effective length, mechanical slenderness and fictitious eccentricity for the given buckling load factors.

param element

element to compute the buckling parameters for.

param bucklingLoadFactors

list containing the buckling load factors obtained from the linear buckling analysis.

param rcSection

reinforced concrete section of the element.

param sectionDepthZ

depth of the reinforced concrete section measured along the z axis.

param Cz

Coefficient which depends on the configuration of reinforcements whose values are: 0.24 for symmetrical reinforcement on two opposing sides in the bending plane, 0.20 for equal reinforcement on the four sides, 0.16 for symmetrical reinforcement on the lateral sides.

param reinforcementFactorZ

reinforcement factor computed as $eta=

rac{(d-d’)^2}{4*i_s^2}$ with $i_s$ being the radius of gyration of the reinforcements about the z axis.
param sectionDepthY

depth of the reinforced concrete section measured along the y axis.

param Cy

Coefficient which depends on the configuration of reinforcements whose values are: 0.24 for symmetrical reinforcement on two opposing sides in the bending plane, 0.20 for equal reinforcement on the four sides, 0.16 for symmetrical reinforcement on the lateral sides.

param reinforcementFactorY

reinforcement factor computed as $eta=

rac{(d-d’)^2}{4*i_s^2}$ with $i_s$ being the radius of gyration of the reinforcements about the y axis.
param eigenvectorNormThreshold

if the node eigenvector has a norm smaller than this threshold it is considered null.

param alpha_cr_threshold

# Lower limit for the Ncr/N factor by which the design loading would have to be increased to cause elastic instability (see Eurocode 4:2004 cl.5.2.1(2)). For values of alpha_cr greater than alpha_cr_threshold the instability effect is ignored.

materials.ehe.EHE_limit_state_checking.get_element_buckling_eccentricities(element)
Compute the e1 and e2 eccentricities as defined in the clause 43.1.2 of

EHE-08 using the internal forces of the element.

Parameters

element – element to compute the buckling eccentricities for.

materials.ehe.EHE_limit_state_checking.get_fictitious_eccentricity(sectionDepth: float, firstOrderEccentricity, reinforcementFactor: float, epsilon_y: float, radiusOfGyration: float, bucklingLength: float)
Return the fictitious eccentricity used to represent the second order

effects according to clause 43.5.1 of EHE-08.

param sectionDepth

total depth of the concrete section in the bending plane considered.

param firstOrderEccentricity

equivalent first order design eccentricity.

param reinforcementFactor

reinforcement factor computed as $eta=

rac{(d-d’)^2}{4*i_s^2}$ with $i_s$ being the radius of gyration of the reinforcements.
param epsilon_y

deformation in the steel for the design stress fyd.

param radiusOfGyration

radius of gyration of the concrete section in the direction concerned.

param bucklingLength

buckling length.

materials.ehe.EHE_limit_state_checking.get_lower_slenderness_limit(C: float, nonDimensionalAxialForce: float, e1, e2, sectionDepth)

Return the lower slenderness limit according to clause 43.1.2 of EHE-08.

Parameters

  • C – Coefficient which depends on the configuration of reinforcements whose values are: 0.24 for symmetrical reinforcement on two opposing sides in the bending plane, 0.20 for equal reinforcement on the four sides, 0.16 for symmetrical reinforcement on the lateral sides.

  • nonDimensionalAxialForce – design value of the non-dimensional or reduced axial force actuating in the support.

  • e1 – First order eccentricity at the end of the support with the lower moment which is positive if it has the same sign as e2.

  • e2 – First order eccentricity in the end of the support with the larger moment, deemed to be positive.

  • sectionDepth – total depth of the concrete section in the bending plane considered.

materials.ehe.EHE_limit_state_checking.get_min_and_max_reinforcement(memberType: str, rcSection, Nd, bendingAxis='z')
Return the minimum and maximum reinforcement areas for the given

section.

Parameters

  • memberType – member type: ‘beam’, ‘column’, ‘tie’, …

  • rcSection – reinforced concrete section.

  • Nd – design value of the internal axial load.

  • bendingAxis – bending axis (‘z’ or ‘y’).

materials.ehe.EHE_limit_state_checking.read_buckling_analysis_results(bucklingAnalysisResultsFileName, setCalc=None)

Extracts element and combination identifiers from the internal forces JSON file. Return elementTags, idCombs , internal forces values and buckling parameters values.

Parameters

  • bucklingAnalysisResultsFileName – name of the file containing the internal forces obtained for each element for the combinations analyzed

  • setCalc – set of elements to be analyzed (defaults to None which means that all the elements in the file of internal forces results are analyzed)

materials.ehe.EHE_limit_state_checking.shearBetweenWebAndFlangesStrength(fck, gammac, hf, Asf, Sf, fyd)

Return the shear strength (kN/m) in the flange web contact by unit length according to clause 4.3.2.5 of Eurocode 2

Parameters: :param fck: concrete characteristic compressive strength (Pa). :param gammac: Partial safety factor for concrete. :param hf: flange thickness (m) :param Asf: reinforcement that cross the section by unit length (m2) :param Sf: spacement of the rebars that cross the section (m) :param fyd: design yield strength (Pa)

materials.ehe.EHE_limit_state_checking.shearExploitationRatioe(fck, fcd, Nd, Ac, b0, d, z, alpha, theta, AsPas, fyd, AsAct, fpd, sgxd, sgyd, AsTrsv, fydTrsv, Vrd)

Shear exploitation ratio.

materials.ehe.EHE_limit_state_checking.shearOK(fck, fcd, Nd, Ac, b0, d, z, alpha, theta, AsPas, fyd, AsAct, fpd, sgxd, sgyd, AsTrsv, fydTrsv, Vrd)

Check shear.