Crack width calculations

The following functions are related to calculating crack widths.

Calculated crack width

structuralcodes.codes.ec2_2023.epssm_epscm(sigma_s: float, kt: float, fct_eff: float, rho_eff: float, alphae: float, Es: float) → float

Returns the mean strain difference between steel and concrete along 2 transfer lengths.

EN 1992-1-1:2023, Eq. (9.11).

Parameters:

• sigma_s (float) – The stress in steel at the section of the crack.

• kt (float) – An integration factor to account for the variation in strain in steel and concrete it is to be taken as 0.6 for short term loading or instantaneous loading and equal to 0.4 for long term or repeated loading.

• fct_eff (float) – The effective cracking stress, which can be taken equal to the mean tensile strength of concrete, fctm.

• rho_eff (float) – The effective reinforcement ratio in the tension zone.

• alphae (float) – The equivalence factor equal to Es/Ecm.

• Es (float) – The modulus of elasticity of steel, normally taken as 200 GPa.

Returns:

The mean strain difference bewteen steel and concrete along 2 transfer lengths.

Return type:

float

structuralcodes.codes.ec2_2023.srm_cal(c: float, kfl_: float, kb: float, phi: float, rho_eff: float, kw: float, h, x: float) → float

Returns the mean crack spacing.

EN 1992-1-1:2023, Eq. (9.15).

Parameters:

• c (float) – Concrete cover of reinforcement to bar surface. Larger value of lateral and vertical cover should be applied.

• kfl (float) – Factor accounting for distribution of stresses prior to cracking.

• kb (float) – Factor accounting for bond conditions.

• phi (float) – Bar diameter.

• rho_eff (float) – Effective reinforcement ratio in the tension zone.

• kw (float) – Factor converting the mean crack spacing into a characteristic crack spacing, with a reocmmended value of 1.3 (NDP).

• h (float) – Height of the cross section.

• x (float) – Depth of the neutral axis measured form the most compressed fibre.

Returns:

The mean crack spacing in units consistent with c and phi.

Return type:

float

structuralcodes.codes.ec2_2023.kfl(h: float, xg: float, hceff: float) → float

Returns factor kfl which accounts for the distribution of stresses before cracking.

EN 1992-1-1:2023, Eq. (9.17).

Parameters:

• h (float) – Height of the cross section.

• xg (float) – Distance from the compressed fibre to the centroid of the uncracked section.

• hceff (float) – Height of the effective tension area.

Returns:

Returns factor kfl which accounts for the distribution of stresses before cracking.

Return type:

float

structuralcodes.codes.ec2_2023.kh(b: float, h: float) → float

Returns factor kh, which reduces the tensile strength of concrete to account for imposed restrained deformations due to shrinkage.

EN 1992-1-1:2023, Eq. (9.5).

Parameters:

• b (float) – Width of the rectangle in meters.

• h (float) – Height of the rectangle in meters.

Returns:

Factor kh which reduces the tensile strength of concrete to account for imposed restrained deformations due to shrinkage.

Return type:

float

structuralcodes.codes.ec2_2023.wk_cal(kw: float, h: float, xg: float, hc_eff: float, c: float, kb: float, phi: float, rho_eff: float, x: float, sigma_s: float, kt: float, fct_eff: float, alphae: float, Es: float) → Tuple[float, float, float, float]

Returns the characteristic crack width, wk,cal, as well as auxiliary variables, 1/r, srm,cal and epssm-epscm.

EN1992-1-1:2023 Eq. (9.8), complemented with Eq. (9.11), Eq. (9.15), Eq. (9.17).

Parameters:

• kw (float) – Factor that converts the mean crack spacing to a characteristic value.

• h (float) – Height of cross section.

• xg (float) – Depth of centroid of section measured from compressed fibre.

• hc_eff (float) – Height of the effective tensioned concrete area.

• c (float) – Concrete cover of reinforcement to bar surface. Larger value of lateral and vertical cover should be applied.

• kb (float) – Factor account for bond conditions of bar.

• phi (float) – Diameter of tensioned bars (for different bar diameters, equivalent diameter according to Eq. (9.19).

• rho_eff (float) – Effective tension reinforcement ratio.

• x (float) – Depth of the neutral axis of the cracked section measured from compressed fibre.

• sigma_s (float) – Tension in most tensioned bar according to fully cracked analysis.

• kt (float) – Factor accounting for tension stiffening.

• fct_eff (float) – Effective tensile strength of concrete.

• alphae (float) – Modular ratio Es/Ecm.

• Es (float) – Modulus of elasticity of steel bars (normally Es=200 MPa).

Returns:

The characteristic crack width, wk,cal, in consistent units, as well as auxiliary variables, 1/r, srm,cal and epssm-epscm.

Return type:

Tuple[float, float, float, float]

structuralcodes.codes.ec2_2023.wk_cal2(kw: float, k_1_r: float, srm_cal: float, epssm_epscm: float) → float

Returns the calculated characteristic crack width.

EN 1992-1-1:2023, Eq. (9.8).

Parameters:

• kw (float) – Factor that converts the mean crack spacing to a characteristic value.

• k_1_r (float) – Factor accounting for the effect of curvature on crack width - can be determined using the function k_1_r.

• srm_cal (float) – Mean crack spacing - can be determined using the function srm_cal.

• epssm_epscm (float) – Mean diference of strain between steel and concrete - can be determined using the function epssm_epscm.

Returns:

The calculated characteristic crack width in in units consistent with srm_cal.

Return type:

float

structuralcodes.codes.ec2_2023.k_1_r(h: float, x: float, ay: float) → float

Returns k1/r factor to account for increase in crack width due to curvature of the section in bending.

EN 1992-1-1:2023, Eq. (9.9).

Parameters:

• h (float) – Height of the section in consistent units (e.g. meters).

• x (float) – Distance from most compressed fibre to neutra axis in consistent units (e.g. meters).

• ay (float) – Cover to centre of tensioned reinforcement closest to most tensioned face in consistent units (e.g. meters).

Returns:

Factor k1/r (non-dimensional) which accounts for the increase in crack width due to curvature of the section in bending.

Return type:

float

Minimum reinforcement

structuralcodes.codes.ec2_2023.As_min_y(NEd: float, b: float, h: float, fct_eff: float, fyk: float) → Tuple[float, float]

Returns the minimum reinforcement to avoid yielding of steel. Box or T sections are to be divided into rectangles.

EN 1992-1-1:2023, Eq. (9.4)

Eq. (9.2) and (9.3) are particular cases of the general equation

Eq. (9.2) is valid for pure bending, hence NEd=0

Eq. (9.3) is valid for pure tension. The general expression has an upper limit that equals the values of Eq. (9.3)

Parameters:

• NEd (float) – SLS axial force applied on the section or rectangle (compressions are negative) in kN.

• b (float) – The width of the section or rectangle in meters.

• h (float) – The height of the section or rectange in meters.

• fct_eff (float) – Effective tension strength of concrete (can normally be taken as the mean tensile strength) in MPa.

• fyk (float) – Characteristic yield strength of steel in MPa.

Returns:

The minimum tensile reinforcement to avoid yielding of steel on the most tensioned fibre of the rectangle (As_min_y1) in cm2, and the minimum tensile reinforcement to avoid yielding of steel on the most tensioned fibre of the rectangle (As_min_y2) in cm2.

Return type:

tuple(float, float)