Materials according to Eurocode 2 code

EC2 materials

Reinforced concrete materials as defined in EC2 (from Annex C)EHE (spanish RC standard).

Eurocode 2 permits to use a various steel yielding grades ranging

from 400 MPa to 600 MPa. Ductility grades:

-A: cold worked eps_uk>=2.5% k>=1.05 -B: hot rolled eps_uk>=5.0% k>=1.08 -C: seismic eps_uk>=7.5% k>=1.15 k<1.35

class materials.ec2.EC2_materials.EC2Concrete(nmbConcrete, fck, gammaC, alphacc=1.0)

Bases: materials.concrete_base.Concrete

Concrete model according to Eurocode 2:2004

Variables

typeAggregate –

type of aggregate

  • Q for quartzite aggregate

  • L for limestone aggregate

  • S for sandstone aggregate

  • B for basalt aggregate

getAlphaCw(NEd, Ac, nationalAnnex=None)
Return the coefficient taking account of the state of the stress

in the compression chord according to expressions 6.11aN, 6.11bN and 6.11cN of EC2:2004 (clause 6.2.3).

Parameters

  • NEd – axial force in the cross-section due to loading or prestressing.

  • Ac – area of concrete cross-section.

  • nationalAnnex – identifier of the national annex.

getBearingStrength(fbed=None, dryConnection=False)
Return the bearing strength of the concrete according to paragraph

  1. of the clause 10.9.5.2 of EN 1992-1-1:2004.

Parameters

  • fbed – design strength of bedding material (if none it is supposed to be greater than the strength of the bearing concrete).

  • dryConnection – set to true when the connection corresponds to a dry one according to paragrah (3) of the clause 10.9.4.3 of EN 1992-1-1:2004.

getConcreteFlangeShearStressStrength(nationalAnnex=None)
Return the shear stress resisted by plain concrete according to

clause 6.2.4 (6) of EC2:2004.

Parameters

nationalAnnex – identifier of the national annex.

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

return the creep deformation between t0 and t according to clause 5.1 and Annex B of Eurocode 2 part 1-1 : 2004 (Eq. 5.2)

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 applied on day t0 (negative sign).

getEcm()

Ecm: approximate value of the modulus of elasticity [Pa][+] secant value between sigma_c=0 and 0,4fcm, at age 28 days (table 3.1 EC2)

getEcmT(t=28)

EcmT: Value of the modulus of elasticity at an age of t days (sect. 3.1.3 EC2:2004 paragrap (3), expression 3.5)

Parameters

t – age of the concrete in days.

getEpsc1()

epsc1: strain [-] at peak stress at stress-strain relation (table 3.1 EC2, figure 3.2 EC2)

getEpsc2()

epsc2: strain [-] at peak stress at parabola-rectangle diagram (table 3.1 EC2, figure 3.3 EC2)

getEpsc3()

epsc3: strain [-] at peak stress at bi-linear diagram (table 3.1 EC2, figure 3.4 EC2)

getEpscu1()

epscu1: nominal ultimate strain [-]at stress-strain relation (table 3.1 EC2, figure 3.2 EC2)

getEpscu2()

epscu2: nominal ultimate strain [-] at parabola-rectangle diagram (table 3.1 EC2, figure 3.3 EC2)

getEpscu3()

epscu3: nominal ultimate strain [-] at bi-linear diagram (table 3.1 EC2, figure 3.4 EC2)

getEtaC()

Return the value of η according to expressions (3.21) and (3.22) of EC2:2004 part 1.

getExpN()

expN: exponent n for the parabola-rectangle diagram (table 3.1 EC2)

getFctm()

Fctm: mean tensile strength [Pa][+] (table 3.1 EC2).

getFctmT(t)

FctmT: Value of the tensile strength at an age of t days (sect. 3.1.3 EC2:2004 paragrap (9), expression 3.4)

Parameters

t – age of the concrete in days.

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 3.1.8 of EC2:2004. Expression (3.23).

Parameters

h – total member depth expressed in meters.

getLambdaC()

Return the value of λ according to expressions (3.19) and (3.20) of EC2:2004 part 1.

getMinShearReinfRatio(shearReinfSteel, nationalAnnex=None)
Return the minimum shear reinforcement ratio according

to expression 9.5N (or the national annex substitution)

Parameters

  • shearReinfSteel – reinforcing steel material.

  • nationalAnnex – identifier of the national annex.

getShearStrengthReductionFactor(nationalAnnex=None)
Return the strength reduction factor for concrete cracked in shear

according to expression 6.6N of EC2:2004 (clause 6.2.2).

Parameters

nationalAnnex – identifier of the national annex.

getUltimateBondStress(rebarDiameter, eta1=0.7)
Return the ultimate bond stress of the concrete according to

expression 8.2 of clause 8.4.2 of EC2:2004.

Parameters

  • rebarDiameter – bar diameter.

  • eta1 – coefficient related to the quality of the bond condition and the position of the bar during concreting. eta1= 1,0 when ‘good’ conditions are obtained and eta1= 0,7 for all other cases.

linearCoefficientOfThermalExpansion = 1e-05
typeAggregate = 'Q'
class materials.ec2.EC2_materials.EC2Concrete2021(nmbConcrete, fck, gammaC)

Bases: materials.ec2.EC2_materials.EC2Concrete

Concrete model according to Eurocode 2:2021

getShrAlphabs()

value of the alpha_bs coefficient accordint to table B.3 of Eurocode2:2021 part 1-1.

getShrAlphads()

value of the alpha_ds coefficient according to table B.3 of Eurocode2:2021 part 1-1.

getShrBetaRH(RH)
coefficient to consider the effect of relative humidity on drying

shrinkage according to expression B29 of clause B.6 of Eurocode2:2021 part 1-1.

Parameters

RH – relative humidity (%).

getShrBetadstts(t, ts, h0)
time development of drying shrinkage according to expression B31

of clause B.6 of Eurocode2:2021 part 1-1.

Parameters

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

  • ts – age of concrete in days at the beginning of drying shrinkage (or swelling). Normally this is at the end of curing

  • 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

getShrEpscbs(t, alpha_ndp_b=1.0)
Basic shrinkage strain according to expression B.24 of

clause B.6 Eurocode 2:2021 part 1-1.

Parameters

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

  • alpha_ndp_b – 1.0 unless otherwise stated in the national annex.

getShrEpscbsfcm()

notional basic shrinkage coefficient according to expression according to expression B26 of clause B.6 of Eurocode 2:2021 part 1-1.

getShrEpscds(t, ts, h0, RH, alpha_ndp_d=1.0)
Drying shrinkage strain according to expression B.25 of

clause B.6 Eurocode 2:2021 part 1-1.

Parameters

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

  • ts – age of concrete in days at the beginning of drying shrinkage (or swelling). Normally this is at the end of curing

  • 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

  • RH – ambient relative humidity(%)

  • alpha_ndp_d – 1.0 unless otherwise stated in the national annex.

getShrEpscdsfcm()

notional drying shrinkage coefficient according to expression B28 of clause B.6 of Eurocode 2:2021 part 1-1.

getShrEpscs(t, ts, RH, h0, alpha_ndp_b=1.0, alpha_ndp_d=1.0)
Return the total mean shrinkage strain according to expression B.23

of clause B.6 Eurocode 2:2021 part 1-1.

Parameters

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

  • ts – age of concrete in days at the beginning of drying shrinkage (or swelling) Normally this is at the end of curing

  • 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

  • alpha_ndp_b – 1.0 unless otherwise stated in the national annex.

  • alpha_ndp_d – 1.0 unless otherwise stated in the national annex.

getShrRHeq()

value of the internal relative humidity of concrete (%) at equilibrium according to expression B30 of clause B.6 of Eurocode2:2021 part 1-1.

class materials.ec2.EC2_materials.PrestressingSteel(steelName, fp01k, euk=None, fmax=1860000000.0, alpha=0.75, steelRelaxationClass=1, tendonClass='strand', Es=195000000000.0)

Bases: materials.concrete_base.PrestressingSteel

Prestressing steel model according to EC2.

Variables

euk – elongation at maximum load.

getAnchorageLength(transmissionLength, concrete, tendonDiameter, sigma_pd, sigma_pminf, bondConditionsCoeff=0.7, tendonTypeCoeff=1.2, alpha2=0.25)
Return the bond strength for anchorage according to expression

(8.20) of to clause 8.10.2.3(2) of EN 1992-1-1:2004.

Parameters

  • transmisionLength – upper design value of transmission length, see 8.10.2.2 (3).

  • concrete – concrete material.

  • tendonDiameter – diameter of the tendon.

  • sigma_pd – tendon stress corresponding to the force described in paragraph (1) of clause 8.10.2.3.

  • sigma_pminf – prestress after all losses.

  • tendonTypeCoeff – coefficient that takes into account the type of tendon and the bond situation at anchorage (1.4 for indented wires and 1.2 for 7-wire strands.

  • bondConditionsCoeff – 1.0 for good bond conditions (see 8.4.2) 0.7 otherwise.

  • alpha2 – 0.25 for tendons with circular corss section, and 0.19 for 3 and 7-wire strands.

getMaximumInitialForce(Ap, nationalAnnex=None)
Return the maximum initial force (i.e. the force in the tendon

immediately after tensioning or transfer) according to clause 5.10.3(2) of EN 1992-1-1:2004.

Parameters

  • Ap – cross-sectional area of the tendon(s).

  • nationalAnnex – identifier of the national annex.

getMaximumInitialStress(nationalAnnex=None)
Return the maximum initial stress (i.e. the stress in the tendon

immediately after tensioning or transfer) according to clause 5.10.3(2) of EN 1992-1-1:2004.

Parameters

nationalAnnex – identifier of the national annex.

getMaximumStressingForce(Ap, overStressing=False, nationalAnnex=None)
Return the maximum prestressing force (i.e. the force at the active

end during tensioning) according to clause 5.10.2.1 of EN 1992-1-1:2004.

Parameters

  • Ap – cross-sectional area of the tendon.

  • overStressing – apply paragraph (2) of clause 5.10.2.1.

  • nationalAnnex – identifier of the national annex.

getMaximumStressingStress(overStressing=False, nationalAnnex=None)
Return the maximum prestressing stress (i.e. the stress at the

active end during tensioning) according to clause 5.10.2.1 of EN 1992-1-1:2004.

Parameters

  • overStressing – apply paragraph (2) of clause 5.10.2.1.

  • nationalAnnex – identifier of the national annex.

getMu(sigma_pi)
Return the value of mu= sigma_pi/fpk according to clause 3.3.2(5)

of EN 1992-1-1:2004.

Parameters

sigma_pi – for post-tensioning sigma_pi is the value of the initial prestress.

getRelaxationLoss(sigma_pi, t, ro1000=None)
Return the value of the relaxation loss according to clause 3.3.2(7)

of EN 1992-1-1:2004.

Parameters

  • sigma_pi – for post-tensioning sigma_pi is the value of the initial prestress.

  • t – time after tensioning (in hours).

getRo1000()

Return the value for ro_1000 according to paragraph (6) of clause 3.3.2 of EN 1992-1-1:2004.

getTimeDependentForceLosses(Ap, concrete, Ac, Ic, z_cp, epsilon_cs, fi_t_t0, delta_sigma_pr, sigma_c_qp)
Return the time dependent losses of prestress according to clause

5.10.6 of EN 1992-1-1:2004.

Parameters

  • Ap – cross-sectional area of the tendon(s).

  • concrete – concrete material.

  • Ac – area of the concrete section.

  • Ic – second moment of area of the concrete section.

  • z_cp – distance between the centre of gravity of the concrete section and the tendons.

  • epsilon_cs – estimated shrinkage strain according to 3.1.4(6).

  • fi_t_t0 – creep coefficient at a time t and load application at time t0.

  • delta_sigma_pr – absolute value of the variation of stress in the tendons at location x, at time t, due to the relaxation of the prestressing steel.

  • sigma_c_qp – stress in the concrete adjacent to the tendons, due to self-weight and initial prestress and other quasi-permanent actions where relevant.

getTimeDependentStressLosses(Ap, concrete, Ac, Ic, z_cp, epsilon_cs, fi_t_t0, delta_sigma_pr, sigma_c_qp)
Return the time dependent losses of prestress according to clause

5.10.6 od of EN 1992-1-1:2004 (expression (5.46))

Parameters

  • Ap – cross-sectional area of the tendon(s).

  • concrete – concrete material.

  • Ac – area of the concrete section.

  • Ic – second moment of area of the concrete section.

  • z_cp – distance between the centre of gravity of the concrete section and the tendons.

  • epsilon_cs – estimated shrinkage strain according to 3.1.4(6).

  • fi_t_t0 – creep coefficient at a time t and load application at time t0.

  • delta_sigma_pr – absolute value of the variation of stress in the tendons at location x, at time t, due to the relaxation of the prestressing steel.

  • sigma_c_qp – stress in the concrete adjacent to the tendons, due to self-weight and initial prestress and other quasi-permanent actions where relevant.

getUltimateBondStress(concrete, bondConditionsCoeff=0.7, tendonTypeCoeff=1.2)
Return the bond strength for anchorage according to expression

(8.20) of to clause 8.10.2.3(2) of EN 1992-1-1:2004.

Parameters

  • concrete – concrete material.

  • tendonTypeCoeff – coefficient that takes into account the type of tendon and the bond situation at anchorage (1.4 for indented wires and 1.2 for 7-wire strands.

  • bondConditionsCoeff – 1.0 for good bond conditions (see 8.4.2) 0.7 otherwise.

get_fp01k()

Return the characteristic value of the 0.1% proof-stress of the prestressing steel.

get_fpk()

Return the characteristic value of the tensile strength of the prestressing steel.

class materials.ec2.EC2_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 EC2:2004.

getAlpha6(ratioOfOverlapedTensionBars=1)
Return the value of the coefficient alpha_6 according to table

8.3 of EC2:2004.

Parameters

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

getBasicAnchorageLength(concrete, rebarDiameter, eta1=0.7, steelEfficiency=1.0)
Returns basic required anchorage length in tension according to

clause 8.4.3 of EC2:2004 (expression 8.3).

Parameters

  • concrete – concrete material.

  • rebarDiameter – nominal diameter of the bar.

  • eta1 – coefficient related to the quality of the bond condition and the position of the bar during concreting. eta1= 1,0 when ‘good’ conditions are obtained and eta1= 0,7 for all other cases.

  • 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: (sigma_sd/fyd).

getDesignAnchorageLength(concrete, rebarDiameter, eta1=0.7, steelEfficiency=1.0, compression=True, alpha_1=1.0, alpha_2=1.0, alpha_3=1.0, alpha_4=1.0, alpha_5=1.0)
Returns design anchorage length according to clause 8.4.4

of EC2:2004 (expression 8.4).

Parameters

  • concrete – concrete material.

  • rebarDiameter – nominal diameter of the bar.

  • eta1 – coefficient related to the quality of the bond condition and the position of the bar during concreting. eta1= 1,0 when ‘good’ conditions are obtained and eta1= 0,7 for all other cases.

  • 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: (sigma_sd/fyd).

  • compression – if true return the minimum anchorage length for anchorages in compression.

  • alpha_1 – effect of the form of the bars assuming adequate cover.

  • alpha_2 – effect of concrete minimum cover.

  • alpha_3 – effect of confinement by transverse reinforcement.

  • alpha_4 – influence of one or more welded transverse bars along the design anchorage length.

  • alpha_5 – effect of the pressure transverse to the plane of splitting along the design anchorage length.

getLapLength(concrete, rebarDiameter, eta1=0.7, steelEfficiency=1.0, ratioOfOverlapedTensionBars=1.0, alpha_1=1.0, alpha_2=1.0, alpha_3=1.0, alpha_5=1.0)
Returns the value of the design lap length according to clause

8.7.3 of EC2:2004 (expression 8.10).

Parameters

  • concrete – concrete material.

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

  • eta1 – coefficient related to the quality of the bond condition and the position of the bar during concreting. eta1= 1,0 when ‘good’ conditions are obtained and eta1= 0,7 for all other cases.

  • 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: (sigma_sd/fyd).

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

  • alpha_1 – effect of the form of the bars assuming adequate cover.

  • alpha_2 – effect of concrete minimum cover.

  • alpha_3 – effect of confinement by transverse reinforcement.

  • alpha_5 – effect of the pressure transverse to the plane of splitting along the design anchorage length.

getMinimumAnchorageLength(lb_rqd, rebarDiameter, compression=True)
Return the minimum anchorage length according to expressions

8.6 and 8.7 of EC2:2004 clause 8.4.4.

Parameters

  • lb_rqd – basic required anchorage length in tension according to clause 8.4.3 of EC2:2004 (expression 8.3).

  • rebarDiameter – nominal diameter of the bar.

  • compression – if true return the minimum anchorage length for anchorages in compression.

EC2 limit state checking

Classes and functions for limit state checking according to Eurocode 2.

class materials.ec2.EC2_limit_state_checking.BiaxialBendingNormalStressController(limitStateLabel)

Bases: materials.limit_state_checking_base.BiaxialBendingNormalStressControllerBase

Object that controls normal stresses limit state.

class materials.ec2.EC2_limit_state_checking.CrackControlLimitStateData(limitStateLabel, outputDataBaseFileName, designSituations)

Bases: postprocess.limit_state_data.CrackControlRCLimitStateData

EHE crack control limit state data.

getController(wk_lim=0.0003, k1=0.8, shortTermLoading=False, solutionProcedureType=None)

Return a controller corresponding to this limit state.

Parameters

  • wk_lim – maximum allowable crack width.

  • k1 –

    coefficient which takes account of the bond properties

    of the bonded reinforcement:

    • = 0.8 for high bond bars

    • = 1.6 for bars with an effectively plain surface (e.g.

      prestressing tendons)

  • shortTermLoading – if true, consider short therm loading (k_t= 0.6), otherwise consider long term loading (k_t= 0.4).

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

class materials.ec2.EC2_limit_state_checking.CrackController(limitStateLabel, wk_lim=0.0003, k1=0.8, shortTermLoading=False, solutionProcedureType=<class 'solution.predefined_solutions.PlainNewtonRaphson'>)

Bases: materials.limit_state_checking_base.LimitStateControllerBase

Object that verifies the cracking serviceability limit state according to EC2.

Variables

  • k1 – coefficient that takes account of the bound properties of the bonded reinforcement. k1=0.8 for high bond bars, k1=1.0 for bars with effectively plain surface (e.g. prestressing tendons). Defaults to 0.8

  • k3 – defaults to the value recommended by EC2 and in EHE k3=3.4

  • k4 – defaults to the value recommended by EC2 and EHE k4=0.425

  • shortTermLoading – if true, consider short therm loading (k_t= 0.6), otherwise consider long term loading (k_t= 0.4).

ControlVars

alias of postprocess.control_vars.RCCrackControlVars

EC2_hceff(h, d, x)

Return the maximum height to be considered in the calculation of the concrete effective area in tension. See paragraph (3) of clause 7.3.2 of EC2.

Parameters

  • width – section width

  • h – lever arm

  • d – effective depth of the cross-section

  • x – depth of the neutral fiber.

EC2_k2(eps1, eps2)

Return the coefficient k2 involved in the calculation of the mean crack distance according to EC2. 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 ‘elememts’ container 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.

param elements

elements to check.

param loadCombinationName

name of the load combination.

computeWk(sigma_s, steel, concrete, ro_eff, k2, cover, reinfPhi, spacing, h=None, x=None)
Computes the characteristic value of the crack width according to the

expression 7.8 of EC2:2004 part 1.

Parameters

  • sigma_s – stress in the tension reinforcement assuming a cracked section. For pretensioned members, as may be replaced by Delta(sigma_p) the stress variation in prestressing tendons from the state of zero strain of the concrete at the same level.

  • steel – steel type of the reinforcement.

  • As – steel reinforcement area

  • concrete – concrete of the section.

  • ro_eff – effective reinforcement ratio computed according to expression 7.10 of EC2:2004 part 1.

  • k2 –

    coefficient that takes account of the distribution of strain:

    • =0.5 for bending

    • =1.0 for pure tension

    • for cases of eccentric tension or for local areas, intermediate values of k2 should be used (see clause 7.3.4 EC2)

  • cover – cover of the longitudinal reinforcement

  • reinfPhi – bar diameter. Where a mixture of bar diameters is used in a section, an equivalent diameter is used (see clause 7.3.4 EC2).

  • spacing – spacing of the bonded reinforcement.

  • h – overall depth of the section.

  • x – depth of the neutral axis.

meanStrainDifference(sigma_s, steel, concrete, ro_eff)
Returns the mean strain difference according to expression 7.9 of

clause 7.3.4 of EC2:2004.

Parameters

  • sigma_s –

    stress in the tension reinforcement assuming a cracked section. For pretensioned members, as may be replaced

    by Delta(sigma_p) the stress variation in prestressing tendons from the state of zero strain of the concrete at the same level.

  • steel – steel type of the reinforcement.

  • As – steel reinforcement area

  • concrete – concrete of the section.

  • ro_eff – effective reinforcement ratio computed according to expression 7.10 of EC2:2004 part 1.

s_r_max(k2, cover, reinfPhi, spacing, ro_eff, h=None, x=None)
Returns the maximum crack spacing, according to expressions 7.11

and 7.14 of clause 7.3.4 of EC2:2004 part 1.

Parameters

  • k2 –

    coefficient that takes account of the distribution of strain:

    • =0.5 for bending

    • =1.0 for pure tension

    • for cases of eccentric tension or for local areas, intermediate values of k2 should be used (see clause 7.3.4 EC2)

  • cover – cover of the longitudinal reinforcement

  • reinfPhi – bar diameter. Where a mixture of bar diameters is used in a section, an equivalent diameter is used (see clause 7.3.4 EC2).

  • spacing – spacing of the bonded reinforcement.

  • ro_eff – effective reinforcement ratio.

  • h – overall depth of the section.

  • x – depth of the neutral axis.

class materials.ec2.EC2_limit_state_checking.CrackStraightController(limitStateLabel, solutionProcedureType=<class 'solution.predefined_solutions.SimpleStaticLinear'>)

Bases: materials.ec2.EC2_limit_state_checking.CrackController

Object that verifies the cracking serviceability limit state according to EC2 when considering a concrete stress-strain diagram that takes account of the effects of tension stiffening.

Variables

  • k1 – coefficient that takes account of the bound properties of the bonded reinforcement. k1=0.8 for high bond bars, k1=1.0 for bars with effectively plain surface (e.g. prestressing tendons). Defaults to 0.8

  • k3 – defaults to the value recommended by EC2 and in EHE k3=3.4

  • k4 – defaults to the value recommended by EC2 and EHE k4=0.425

ControlVars

alias of postprocess.control_vars.RCCrackStraightControlVars

check(elements, loadCombinationName)
For each element in the ‘elememts’ container 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.

param elements

elements to check.

param loadCombinationName

name of the load combination.

class materials.ec2.EC2_limit_state_checking.EC2RebarFamily(steel, diam, spacing, concreteCover, pos='II', nationalAnnex=None)

Bases: materials.sections.rebar_family.RebarFamily

Family or reinforcement bars with checking according to EC2.

Variables

pos – reinforcement position according to clause 66.5.1 of EC2.

getBasicAnchorageLength(concrete)

Return the basic anchorage length of the bars.

getCopy()

Virtual constructor.

getMinClearDist(maxAggrSize)

Return the minimum clear (horizontal and vertical) distance between individual parallel bars or horizontal layers of parallel bars according to EN 1992-1-1, art. 8.2

Parameters

maxAggrSize – maximum aggregate size

getMinReinfAreaInBending(concrete, thickness, b=1.0, steelStressLimit=450000000.0, memberType=None, sigmaC=0.0, effectiveCover=0.045)
Return the minimun amount of bonded reinforcement to control cracking

for reinforced concrete sections under flexion per unit length according to clauses 7.3.2, 9.2.1.1 (beams), 9.3.1.1 (slabs), 9.5.2 (columns) and 9.6.2 (walls).

Parameters

  • 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 or column.

  • concrete – concrete material.

  • 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.

  • sigmaC – is the mean stress of the concrete acting on the part of the section under consideration: sigmaC= NEd/(bh).

  • effectiveCover – the distance between the exposed concrete surface to the centroid of the main reinforcement.

getMinReinfAreaInTension(concrete, thickness, b=1.0, stressLimit=350000000.0, memberType=None)
Return the minimun amount of bonded reinforcement to control cracking

for reinforced concrete sections under tension according to clauses 9.6.3 and expressionn (7.1) in clause 7.3.2 of EC2:2004 part 1.

Parameters

  • concrete – concrete material.

  • thickness – gross thickness of concrete section.

  • b – width of concrete section.

  • stressLimit – limit

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

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

(b x thickness) rectangular section according to expressions 6.2.a and 6.2.b of EC2:2004.

Parameters

  • concrete – concrete material.

  • Nd – design axial force.

  • Md – design bending moment.

  • b – width of the rectangular section.

  • thickness – height of the rectangular section.

class materials.ec2.EC2_limit_state_checking.Ec2InPlaneStressController(limitStateLabel, solutionProcedureType=<class 'solution.predefined_solutions.SimpleStaticLinear'>)

Bases: materials.limit_state_checking_base.LimitStateControllerBase

Object that controls reinforced concrete ULS using the expressions given in Annex F of EN 1992-1-1:2004.

ControlVars

alias of postprocess.control_vars.Ec2InPlaneStressControlVars

initControlVars(setCalc)

Initialize control variables over elements.

Parameters

setCalc – set of elements to which define control variables

readStresses(stressesCombFileName, setCalc=None)

Launch checking.

Parameters

stressesCombFileName – Name of the file containing the stresses on the element gauss points.

updateEfficiency(elem, elementStresses)
Compute the efficiency of the element material

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

Parameters

  • elem – finite element whose section will be checked.

  • elementStresses – stresses on the element.

class materials.ec2.EC2_limit_state_checking.Ec2InPlaneStressLimitStateData(designSituations=['uls_permanent', 'uls_accidental', 'uls_earthquake'])

Bases: postprocess.limit_state_data.ULS_LimitStateData

In-plane stress conditions limit state data.

check(setCalc, controller, appendToResFile='N', listFile='N', calcMeanCF='N')

Perform limit state checking.

Parameters

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

  • controller – object that controls the limit state checking.

  • appendToResFile – ‘Yes’,’Y’,’y’,.., if results are appended to existing file of results (defaults to ‘N’)

  • listFile – ‘Yes’,’Y’,’y’,.., if latex listing file of results is desired to be generated (defaults to ‘N’)

  • calcMeanCF – ‘Yes’,’Y’,’y’,.., if average capacity factor is meant to be calculated (defaults to ‘N’)

checkElements(elementsToCheck, outputCfg=<postprocess.limit_state_data.VerifOutVars object>)
Checking of stresses in ultimate limit states

(see self.dumpCombinations).

Parameters

  • elementsToCheck – elements to check.

  • outputCfg – instance of class ‘VerifOutVars’ which defines the variables that control the output of the checking (set of elements to be analyzed, append or not the results to a file, generation or not of lists, …)

getController()

Return a controller corresponding to this limit state.

Parameters

code_limit_state_checking – code used to check the limit state.

getStressesDict(nmbComb, elems)

Creates a dictionary with the element’s stresses.

Parameters

  • nmbComb – combination name.

  • elems – element set.

readInternalForces(setCalc)

Read the stresses for the elements in the set argument.

Parameters

setCalc – elements to read stresses for.

runChecking(outputCfg)

This method reads, for the elements in setCalc, the stresses previously calculated and saved in the corresponding file. Using the ‘initControlVars’ and ‘updateEfficiencyForSet’ methods of the controller, the appropriate attributes are assigned to the elements and the associated limit state verification is run. The results are written to a file in order to be displayed or listed.

Parameters

outputCfg – instance of class ‘VerifOutVars’ which defines the variables that control the output of the checking (set of elements to be analyzed, append or not the results to the result file [defatults to ‘N’], generation or not of list file [defatults to ‘N’, …)

class materials.ec2.EC2_limit_state_checking.FreqLoadsCrackControlLimitStateData(designSituations=['sls_frequent'])

Bases: materials.ec2.EC2_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.ec2.EC2_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.ec2.EC2_limit_state_checking.QPLoadsCrackControlLimitStateData(designSituations=['sls_quasi-permanent'])

Bases: materials.ec2.EC2_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.ec2.EC2_limit_state_checking.RareLoadsCrackControlLimitStateData(designSituations=['sls_rare'])

Bases: materials.ec2.EC2_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.ec2.EC2_limit_state_checking.RebarController(concreteCover=0.035, spacing=0.15, eta1=0.7, 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

minimumreinforcement and so on.

Variables

eta1 – coefficient related to the quality of the bond condition and the position of the bar during concreting. eta1= 1,0 when ‘good’ conditions are obtained and eta1= 0,7 for all other cases.

getBasicAnchorageLength(concrete, rebarDiameter, steel, steelEfficiency=1.0)
Returns basic required anchorage length in tension according to

clause 8.4.3 of EC2:2004 (expression 8.3).

Parameters

  • concrete – concrete material.

  • rebarDiameter – nominal diameter of the bar.

  • 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: (sigma_sd/fyd).

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 8.3 and table 8.2 of EC2:2004.

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)
Returns design anchorage length according to clause 8.4.4

of EC2:2004 (expression 8.4).

Parameters

  • concrete – concrete material.

  • rebarDiameter – nominal diameter of the bar.

  • 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: (sigma_sd/fyd).

  • 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.

getLapLength(concrete, rebarDiameter, steel, steelEfficiency=1.0, ratioOfOverlapedTensionBars=1.0, lateralConcreteCover=None)
Returns the value of the design lap length according to clause

8.7.3 of EC2:2004 (expression 8.10).

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.

  • 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: (sigma_sd/fyd).

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

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

class materials.ec2.EC2_limit_state_checking.ShearController(limitStateLabel, solutionProcedureType=<class 'solution.predefined_solutions.PlainNewtonRaphson'>, nationalAnnex=None)

Bases: materials.limit_state_checking_base.ShearControllerBase

Shear control according to EHE-08.

ControlVars

alias of postprocess.control_vars.RCShearControlVars

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.

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

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

Parameters

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

  • 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)

Check shear on the section argument.

Parameters

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

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

getShearStrength(scc, concrete, reinfSteel, Nd, Md, Vd, Td, rcSets, circular=False)
Compute the shear strength at failure WITH or WITHIOUT shear

reinforcement.

XXX Presstressing contribution not implemented yet.

Parameters

  • scc – fiber model of the section.

  • concrete – concrete material.

  • reinfSteel – shear reinforcement steel.

  • 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.

getShearStrengthCrackedNoShearReinf(scc, concrete, reinfSteel, Nd, Md, Vd, Td, rcSets, circular=False)
Return the design value of the shear resistance VRdc for cracked

sections subjected to bending moment, according to expressions 6.2.a and 6.2.b of EC2:2004.

Parameters

  • scc – fiber model of the section.

  • concrete – concrete material.

  • reinfSteel – shear reinforcement steel.

  • 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.

getShearStrengthNoShearReinf(scc, concrete, reinfSteel, Nd, Md, Vd, Td, rcSets, circular=False)
Return the design value of the shear resistance VRdc for cracked

or non-cracked sections subjected to bending moment, according to expression 6.4 of EC2:2004.

Parameters

  • scc – fiber model of the section.

  • concrete – concrete material.

  • reinfSteel – shear reinforcement steel.

  • 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.

getShearStrengthNonCrackedNoShearReinf(scc, concrete, reinfSteel, Nd, Md, Vd, Td, rcSets, circular=False)
Return the design value of the shear resistance VRdc for non-cracked

sections subjected to bending moment, according to expression 6.4 of EC2:2004.

Parameters

  • scc – fiber model of the section.

  • concrete – concrete material.

  • reinfSteel – shear reinforcement steel.

  • 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.

getShearStrengthShearReinf(scc, concrete, reinfSteel, 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.

  • concrete – concrete material.

  • reinfSteel – shear reinforcement steel.

  • 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.

class materials.ec2.EC2_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.ec2.EC2_limit_state_checking.UniaxialBendingNormalStressController(limitStateLabel)

Bases: materials.limit_state_checking_base.UniaxialBendingNormalStressControllerBase

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

materials.ec2.EC2_limit_state_checking.checkFlangeStrutAngleLimits(flangeStrutAngle, compressionFlange=True, nationalAnnex=None)
Check that the strut angle is inside the limits specified

in the expression 6.7N of EC2:2004. Otherwise, issue a warning and return a suitable strut angle.

Parameters

  • flangeStrutAngle – (theta_f) angle between the concrete flange compression strut and the shear plane (see figure 6.7 on EC2:2004).

  • compressionFlange – true if flange is compressed.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.checkWebStrutAngleLimits(webStrutAngle, nationalAnnex=None)
Check that the strut angle is inside the limits specified

in the expression 6.7N of EC2:2004. Otherwise, issue a warning and return a suitable strut angle.

Parameters

  • webStrutAngle – (theta) angle between the concrete compression web strut and the beam axis perpendicular to the shear force.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.compute_punching_shear_beta(punchingPos, criticalPerimeterForces, criticalContourArea)
Compute the value of beta accordint to expression 6.39 from clause

6.4.3(3) of EC2:2004.

Parameters

  • punchingPos – position of the punching element.

  • criticalPerimeterForces – forces around the critical perimeter.

  • criticalContourArea – area of the critical contour.

materials.ec2.EC2_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.ec2.EC2_limit_state_checking.getAdditionalTensileForceMainReinf(VEd, shearReinfAngle=1.5707963267948966, webStrutAngle=0.7853981633974483)
Return the additional tensile force, in the longitudinal reinforcement

due to shear VEd according to expression 6.18 of EC2:2004.

Parameters

  • VEd – design value of the applied shear force.

  • shearReinfAngle – (alpha) angle between shear reinforcement and the beam axis perpendicular to the shear force.

  • webStrutAngle – (theta) angle between the concrete web compression strut and the beam axis perpendicular to the shear force.

materials.ec2.EC2_limit_state_checking.getAsMaxBeams(Ac, nationalAnnex=None)
Return the minimum area of reinforcing steel within the tensile zone

according to expression 9.1N of EC2:2004.

Parameters

  • Ac – area of concrete cross-section.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.getAsMaxColumns(concrete, reinfSteel, Ac, nationalAnnex=None)
Return the minimum area of longitudinal reinforcement

according to clause 9.5.2 (3) of EC2:2004.

Parameters

  • concrete – concrete material.

  • reinfSteel – reinforcing steel material.

  • NEd – sdesign axial compression force.

  • Ac – area of the concrete section.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.getAsMinBeams(concrete, reinfSteel, h, z, bt, d, nationalAnnex=None)
Return the minimum area of reinforcing steel within the tensile zone

according to expression 9.1N of EC2:2004.

Parameters

  • concrete – concrete material.

  • reinfSteel – reinforcing steel material.

  • h – section depth.

  • z – inner lever arm.

  • bt – mean width of the tension zone.

  • d – effective depth.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.getAsMinColumns(concrete, reinfSteel, NEd, Ac, nationalAnnex=None)
Return the minimum area of longitudinal reinforcement

according to expression 9.12N of EC2:2004.

Parameters

  • concrete – concrete material.

  • reinfSteel – reinforcing steel material.

  • NEd – design axial compression force.

  • Ac – area of the concrete section.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.getAsMinCrackControl(concrete, reinfSteel, h, Act, sigmaC=0.0, sigma_s=None, memberType=None)
Return the minimum area of reinforcing steel within the tensile zone

according to expression 7.1 of clause 7.3.2 of EC2:2004.

Parameters

  • concrete – concrete material.

  • reinfSteel – reinforcing steel material.

  • h – section depth.

  • Act – area of concrete within tensile zone. The tensile zone is that part of the section which is calculated to be in tension just before formation of the first crack.

  • sigmaC – is the mean stress of the concrete acting on the part of the section under consideration: sigmaC= NEd/(bh).

  • sigma_s – absolute value of the maximum stress permitted in the reinforcement immediately after formation of the crack. This may be taken as the yield strength of the reinforcement, f_yk, A lower value may, however, be needed to satisfy the crack width limits according to the maximum bar size or the maximum bar spacing (see 7.3.3 (2) of EN 1992-1-1).

materials.ec2.EC2_limit_state_checking.getAsMinWalls(concrete, reinfSteel, Ac, thickness, vertical=True, compressedSide=False, verticalReinforcementArea=None, nationalAnnex=None)
Return the minimum area of longitudinal reinforcement in

the tensile zone (or in the compressed one if compressedSide==True) according to clause 9.6.2 and 9.6.3 of EC2:2004.

Parameters

  • concrete – concrete material.

  • reinfSteel – reinforcing steel material.

  • Ac – area of the concrete section.

  • thickness – wall thickness.

  • vertical – if true compute the minimum for the vertical reinforcement, otherwise return the minimum for the horizontal one.

  • compressedSide – if true compute the minimum for the vertical reinforcement in the compressed side, otherwise return the minimum reinforcement for the tensile zone.

  • verticalReinforcementArea – area of the vertical reinforcement used to calculate the horizontal reinforcement at the same side.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.getConcreteFlangeShearStrength(concrete, hf, DeltaX, nationalAnnex=None)
Return the shear stress resisted by plain concrete according to

clause 6.2.4 (6) of EC2:2004.

Parameters

  • concrete – concrete material.

  • hf – flange thickness at the shear plane.

  • DeltaX – length under consideration (see figure 6.7 on EC2:2004).

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.getFlangeShearResistanceShearReinfStress(concrete, hf, Asf, sf, shearReinfSteel, flangeStrutAngle=0.7853981633974483, compressionFlange=True, nationalAnnex=None)
Return the design value of the flange shear resistance

according to expressions 6.21 of EC2:2004.

Parameters

  • concrete – concrete material.

  • hf – flange thickness at the shear plane.

  • Asf – cross-sectional area of the flange transverse reinforcement.

  • sf – spacing of the reinforcement.

  • shearReinfSteel – reinforcing steel material.

  • flangeStrutAngle – (theta_f) angle between the concrete flange compression strut and the shear plane (see figure 6.7 on EC2:2004).

  • compressionFlange – true if flange is compressed.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.getFlangeStrutAngleLimits(compressionFlange=True, nationalAnnex=None)
Return the limits specified in the clause 6.2.4(4) of EC2:2004 for

the angle of the struts in the flange.

Parameters

  • compressionFlange – true if flange is compressed.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.getMaximumBarDiameterForCrackControl(steelStress, wk=0.0003)
Return the maximum diameter of the bar according to table 7.2N of

of EC2:2004 part 1-1. (clause 7.3.3).

Parameters

  • steelStress – maximum stress permitted in the reinforcement immediately after formation of the crack.

  • wk – crack width (m)

materials.ec2.EC2_limit_state_checking.getMaximumBarSpacingForCrackControl(steelStress, wk=0.0003)
Return the maximum bar spacing according to table 7.3N of

of EC2:2004 part 1-1. (clause 7.3.3).

Parameters

  • steelStress – maximum stress permitted in the reinforcement immediately after formation of the crack.

  • wk – crack width (m)

materials.ec2.EC2_limit_state_checking.getMaximumEffectiveShearReinforcement(concrete, NEd, Ac, bw, s, shearReinfSteel, shearReinfAngle=1.5707963267948966, nationalAnnex=None)
Return the maximum effective shear reinforcement according to expression

6.15 and 6.12 of EC2:2004.

Parameters

  • concrete – concrete material.

  • NEd – axial force in the cross-section due to loading or prestressing.

  • Ac – area of concrete cross-section.

  • bw – smallest width of the cross-section in the tensile area.

  • s – spacing of the stirrups.

  • Asw – cross-sectional area of the shear reinforcement.

  • shearReinfSteel – reinforcing steel material.

  • shearReinfAngle – (alpha) angle between shear reinforcement and the beam axis perpendicular to the shear force.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.getMaximumShearFlangeStrutCrushingStress(concrete, flangeStrutAngle=0.7853981633974483, compressionFlange=True, nationalAnnex=None)
Return the maximum shear force due to diagonal compression in the web

(strut crushing) according to expression 6.22 of EC2:2004.

Parameters

  • concrete – concrete material.

  • flangeStrutAngle – (theta_f) angle between the concrete flange compression strut and the shear plane (see figure 6.7 on EC2:2004).

  • compressionFlange – true if flange is compressed.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.getMaximumShearWebStrutCrushing(concrete, NEd, Ac, bw, z, shearReinfAngle=1.5707963267948966, webStrutAngle=0.7853981633974483, nationalAnnex=None)
Return the maximum shear force due to diagonal compression in the web

(strut crushing) according to expression 6.14 and 6.9 of EC2:2004.

Parameters

  • concrete – concrete material.

  • NEd – axial force in the cross-section due to loading or prestressing.

  • Ac – area of concrete cross-section.

  • bw – smallest width of the cross-section in the tensile area.

  • z – internal lever arm.

  • shearReinfAngle – (alpha) angle between shear reinforcement and the beam axis perpendicular to the shear force.

  • webStrutAngle – (theta) angle between the concrete compression strut and the beam axis perpendicular to the shear force.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.getMinShearReinforcementArea(concrete, shearReinfSteel, s, bw, shearReinfAngle=1.5707963267948966, nationalAnnex=None)
Return the cross-sectional area of the shear reinforcement

according to expression 9.4 of EC2:2004.

Parameters

  • concrete – concrete material.

  • shearReinfSteel – reinforcing steel material.

  • s – spacing of the stirrups.

  • bw – smallest width of the cross-section in the tensile area.

  • shearReinfAngle – (alpha) angle between shear reinforcement and the beam axis perpendicular to the shear force.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.getShearResistanceCrackedNoShearReinf(concrete, NEd, Ac, Asl, bw, d, nationalAnnex=None)
Return the design value of the shear resistance VRdc for cracked

sections subjected to bending moment, according to expressions 6.2.a and 6.2.b of EC2:2004.

Parameters

  • concrete – concrete material.

  • NEd – axial force in the cross-section due to loading or prestressing.

  • Ac – area of concrete cross-section.

  • Asl – area of the tensile reinforcement, which extends beyond the section considered (see clause 6.2.2 of EC2:2004).

  • bw – smallest width of the cross-section in the tensile area.

  • d – effective depth of the cross-section.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.getShearResistanceNonCrackedNoShearReinf(concrete, I, S, NEd, Ac, bw, alpha_l=1.0)
Return the design value of the shear resistance VRdc for non-cracked

sections subjected to bending moment, according to expression 6.4 of EC2:2004.

Parameters

  • concrete – concrete material.

  • I – second moment of area.

  • S – first moment of area above and about the centroidal axis.

  • NEd – axial force in the cross-section due to loading or prestressing.

  • Ac – area of concrete cross-section.

  • bw – smallest width of the cross-section in the tensile area.

  • alpha_l – see expression 6.4 in EC2:2004.

materials.ec2.EC2_limit_state_checking.getShearResistanceShearReinf(concrete, NEd, Ac, bw, Asw, s, z, shearReinfSteel, shearReinfAngle=1.5707963267948966, webStrutAngle=0.7853981633974483, nationalAnnex=None)
Return the design value of the shear resistance VRds for shear

reinforced members according to expressions 6.7N, 6.13 and 6.14 of EC2:2004.

Parameters

  • concrete – concrete material.

  • NEd – axial force in the cross-section due to loading or prestressing.

  • Ac – area of concrete cross-section.

  • bw – smallest width of the cross-section in the tensile area.

  • Asw – cross-sectional area of the shear reinforcement.

  • s – spacing of the stirrups.

  • z – inner lever arm, for a member with constant depth, corresponding to the bending moment in the element under consideration.

  • shearReinfSteel – reinforcing steel material.

  • shearReinfAngle – (alpha) angle between shear reinforcement and the beam axis perpendicular to the shear force.

  • webStrutAngle – (theta) angle between the concrete compression web strut and the beam axis perpendicular to the shear force.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.getWebStrutAngleForSimultaneousCollapse(concrete, bw, s, Asw, shearReinfSteel, shearReinfAngle=1.5707963267948966, nationalAnnex=None)
Return the web strut angle that makes web concrete collapse at the same

time that the shear reinforcement (V_{Rd,s}= V_{Rd,max})

Parameters

  • concrete – concrete material.

  • bw – smallest width of the cross-section in the tensile area.

  • s – spacing of the stirrups.

  • Asw – cross-sectional area of the shear reinforcement.

  • shearReinfSteel – reinforcing steel material.

  • shearReinfAngle – (alpha) angle between shear reinforcement and the beam axis perpendicular to the shear force.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.getWebStrutAngleLimits(nationalAnnex=None)
Return the limits specified in the expression 6.7N of EC2:2004

for the web strut angle.

Parameters

nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.get_maximum_punching_shear_capacity_on_column_periphery(concrete, nationalAnnex=None)
Return the maximum punching shear capacity around column according to

expression (6.47) of 6.4.4(1) of EC2:2004.

Parameters

  • concrete – concrete material.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.get_nu_mu(concrete, steel, b, h, d, dp, x, As1, As2)
Return internal forces at failure for a rectangular section according

to clause 6.1 of EC2:2004 part 1.

Parameters

  • concrete – concrete of the section.

  • steel – reinforcement steel material.

  • b – section width.

  • h – section depth.

  • d – effective depth of the cross-section.

  • dp – effective cover of the compression reinforcement.

  • x – depth of the neutral axis.

  • As1 – area of the tension reinforcement.

  • As2 – area of the compression reinforcement.

materials.ec2.EC2_limit_state_checking.get_punching_shear_C_Rd_c(concrete, u0=0.0, dy=0.0, dz=0.0, isFoundation=False, nationalAnnex=None)

Return the value of C_RDc according to clause 6.4.4(1) of of EC2:2004.

Parameters

  • concrete – concrete material.

  • isFoundation – if true return the value corresponding to floor slabs/foundations.

  • u0 – length of the punching shear critical perimeter.

  • dy – effective depth of the cross-section in y direction.

  • dz – effective depth of the cross-section in z direction.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.get_punching_shear_resistance_whitout_punching_shear_reinforcement(concrete, dy, dz, rho_ly, rho_lz, sigma_cp_y=0.0, sigma_cp_z=0.0, isFoundation=False, nationalAnnex=None)
Return the punching shear strength according to clause expression

(6.47) of 6.4.4(1) of of EC2:2004.

Parameters

  • concrete – concrete material.

  • dy – effective depth of the cross-section in y direction.

  • dz – effective depth of the cross-section in z direction.

  • rho_ly – bonded tension steel in y direction.

  • rho_lz – bonded tension steel in z direction.

  • sigma_cp_y – normal concrete stresses in the critical section y (negative if compression).

  • sigma_cp_z – normal concrete stresses in the critical section z (negative if compression).

  • isFoundation – if true return the value corresponding to floor slabs/foundations.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.get_punching_v_min(concrete, dy=0.0, dz=0.0, isFoundation=False, nationalAnnex=None)

Return the value of C_RDc according to clause 6.4.4(1) of of EC2:2004.

Parameters

  • concrete – concrete material.

  • dy – effective depth of the cross-section in y direction.

  • dz – effective depth of the cross-section in z direction.

  • isFoundation – if true return the value corresponding to floor slabs/foundations.

  • nationalAnnex – identifier of the national annex.

materials.ec2.EC2_limit_state_checking.h_c_eff(depth_tot, depht_eff, depth_neutral_axis)

Returns the depth of the effective area of concrete in tension surrounding the reinforcement or prestressing tendons, according to EC2

Parameters

  • depth_tot – overall depth of the cross-section [h]

  • depht_eff – effective depth of the cross-section [d]

  • depth_neutral_axis – depht of the neutral axis[x]

materials.ec2.EC2_limit_state_checking.ro_eff(A_s, width, h_c_eff)

Returns the effective reinforcement ratio [A_s/A_ceff] depth of the effective area of concrete in tension surrounding the reinforcement or prestressing tendons, according to EC2

Parameters

  • A_s – area of reinforcment steel

  • width – width of the RC cross-section

  • ,h_c_eff – depth of the effective area of concrete in

tension surrounding the reinforcement or prestressing tendons

materials.ec2.EC2_limit_state_checking.s_r_max(k1, k2, k3, k4, cover, fiReinf, ro_eff)

Returns the maximum crack spacing, according to expresion 7.11 of clause 7.34 of EC2:2004

Parameters

  • k1 –

    coefficient which takes account of the bond properties of the bonded reinforcement:

    • =0.8 for high bond bars

    • =1.6 for bars with an effectively plain surface (e.g.

      prestressing tendons)

  • k2 –

    coefficient that takes account of the distribution of strain:

    • =0.5 for bending

    • =1.0 for pure tension

    • for cases of eccentric tension or for local areas, intermediate values of k2 should be used (see clause 7.3.4 EC2)

  • k3 – recommended k3=3.4

  • k4 – recommended k4=0.425

  • cover – cover of the longitudinal reinforcement

  • fiReinf – bar diameter. Where a mixture of bar diameters is used in a section, an equivalent diameter is used (see clause 7.3.4 EC2)

  • ro_eff – effective reinforcement ratio