Materials acccording 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)

Bases: materials.concrete_base.Concrete

Concrete model according to Eurocode 2

Variables:typeAggregate –

type of aggregate

  • Q for quartzite aggregate
  • L for limestone aggregate
  • S for sandstone aggregate
  • B for basalt aggregate
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)

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)

getExpN()

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

getFctm()

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

typeAggregate = 'Q'

EC2 limit state checking

class materials.ec2.EC2_limit_state_checking.CrackStraightController(limitStateLabel)

Bases: materials.limit_state_checking_base.LimitStateControllerBase

Definition of variables involved in the verification of 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
EC2_hceff(h, d, 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
  • 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, nmbComb)

For each element in the set ‘elememts’ passed as first parameter and the resulting internal forces for the load combination ‘nmbComb’ 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.

initControlVars(elements)

Initialize control variables over elements.

Parameters:elements – elements to define control variables in
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 EC2

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