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strength_bending

checks.eurocode.steel.strength_bending

Module for checking bending moment resistance of steel cross-sections according to Eurocode 3 (EN 1993-1-1:2005), chapter 6.2.5.

Classes:

checks.eurocode.steel.strength_bending.CheckStrengthBendingClass12 dataclass 

CheckStrengthBendingClass12(
    steel_cross_section: SteelCrossSection,
    m: KNM = 0,
    axis: Literal["My", "Mz"] = "My",
    gamma_m0: DIMENSIONLESS = 1.0,
    name: str = "Bending moment strength check for steel profiles",
)

Class to perform bending moment resistance check for steel cross-sections, for cross-section class 1 and 2 only, based on 1993-1-1:2005 chapter 6.2.5.

Coordinate System: 

z (vertical, usually strong axis)
    ↑
    |     x (longitudinal beam direction, into screen)
    |    ↗
    |   /
    |  /
    | /
    |/
←-----O
y (horizontal/side, usually weak axis)

Parameters:

  • steel_cross_section (SteelCrossSection) –

    The steel cross-section to check.

  • m (KNM, default: 0 ) –

    The applied bending moment (positive value), in kNm (default is 0 kNm).

  • axis (str, default: 'My' ) –

    Axis of bending: 'My' (bending around y) or 'Mz' (bending around z). Default is 'My'.

  • gamma_m0 (DIMENSIONLESS, default: 1.0 ) –

    Partial safety factor for resistance of cross-sections, default is 1.0.

Example 
from blueprints.checks import CheckStrengthBendingClass12
from blueprints.materials.steel import SteelMaterial, SteelStrengthClass
from blueprints.structural_sections.steel.standard_profiles.heb import HEB
from blueprints.structural_sections.steel.steel_cross_section import SteelCrossSection

steel_material = SteelMaterial(steel_class=SteelStrengthClass.S355)
heb_300_profile = HEB.HEB300.with_corrosion(0)
m = 355 * 1.868  # Applied bending moment in kNm

heb_300_s355 = SteelCrossSection(profile=heb_300_profile, material=steel_material)
calc = CheckStrengthBendingClass12(heb_300_s355, m, axis="My", gamma_m0=1.0)
calc.report().to_word("bending_moment_strength.docx")

Raises:

  • ValueError –

    If the provided axis is not 'My' or 'Mz'. The axis parameter must be either 'My' for bending around the y-axis or 'Mz' for bending around the z-axis.

checks.eurocode.steel.strength_bending.CheckStrengthBendingClass12.bending_strength_unity_check 

bending_strength_unity_check() -> Formula

Calculate the unity check for bending strength of the steel cross-section based on the applied bending moment and the calculated resistance (EN 1993-1-1:2005 art. 6.2.5(1) - Formula (6.12)).

Returns:

  • Formula –

    The calculated unity check for bending strength.

Source code in blueprints/checks/eurocode/steel/strength_bending.py 
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def bending_strength_unity_check(self) -> Formula:
    """Calculate the unity check for bending strength of the steel cross-section based on the applied bending
    moment and the calculated resistance (EN 1993-1-1:2005 art. 6.2.5(1) - Formula (6.12)).

    Returns
    -------
    Formula
        The calculated unity check for bending strength.
    """
    m_ed = abs(self.m) * KNM_TO_NMM
    m_c_rd = self.plastic_resistance()
    return formula_6_12.Form6Dot12CheckBendingMoment(m_ed=m_ed, m_c_rd=m_c_rd)

checks.eurocode.steel.strength_bending.CheckStrengthBendingClass12.plastic_resistance 

plastic_resistance() -> Formula

Calculate the plastic bending resistance of the steel cross-section (EN 1993-1-1:2005 art. 6.2.5(2) - Formula (6.13)).

Returns:

  • Formula –

    The calculated plastic bending resistance.

Source code in blueprints/checks/eurocode/steel/strength_bending.py 
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def plastic_resistance(self) -> Formula:
    """Calculate the plastic bending resistance of the steel cross-section (EN 1993-1-1:2005 art. 6.2.5(2) - Formula (6.13)).

    Returns
    -------
    Formula
        The calculated plastic bending resistance.

    """
    # For bending about y, the relevant section modulus is sxx; for bending about z, it is syy.
    # This is because of the orientation of the axes defined in Blueprints vs. SectionProperties.
    props = self.steel_cross_section.profile.section_properties()
    w = float(props.sxx or 0) if self.axis.lower() == "my" else float(props.syy or 0)

    f_y = self.steel_cross_section.yield_strength
    return formula_6_13.Form6Dot13MCRdClass1And2(w_pl=w, f_y=f_y, gamma_m0=self.gamma_m0)

checks.eurocode.steel.strength_bending.CheckStrengthBendingClass12.report 

report(n: int = 2) -> Report

Returns the report for the bending moment check (Class 1 and 2).

Parameters:

  • n (int, default: 2 ) –

    Number of decimal places for numerical values in the report (default is 2).

Returns:

  • Report –

    Report of the bending moment check.

Source code in blueprints/checks/eurocode/steel/strength_bending.py 
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def report(self, n: int = 2) -> Report:
    """Returns the report for the bending moment check (Class 1 and 2).

    Parameters
    ----------
    n : int, optional
        Number of decimal places for numerical values in the report (default is 2).

    Returns
    -------
    Report
        Report of the bending moment check.
    """
    report = Report(f"Check: bending moment steel beam (axis {self.axis})")

    # will not generate report if no bending moment is applied, as the check is not necessary in that case
    if self.m == 0:
        report.add_paragraph("No bending moment was applied; therefore, no bending moment check is necessary.")
        return report

    # generate report if bending moment is applied
    report.add_paragraph(
        rf"Profile {self.steel_cross_section.profile.name} with steel quality {self.steel_cross_section.material.steel_class.name} "
        rf"is loaded with a bending moment of {abs(self.m):.{n}f} kNm (axis {self.axis}). "
    ).add_newline(n=2)

    # resistance
    report.add_paragraph("The resistance is calculated as follows, using cross-section class 1 or 2:")
    report.add_formula(self.plastic_resistance(), n=n).add_newline(n=2)

    # unity check
    report.add_paragraph("The unity check is calculated as follows:")
    report.add_formula(self.bending_strength_unity_check(), n=n).add_newline(n=2)

    # conclusion
    if self.result().is_ok:
        report.add_paragraph("The check for bending moment satisfies the requirements.")
    else:
        report.add_paragraph("The check for bending moment does NOT satisfy the requirements.")
    return report

checks.eurocode.steel.strength_bending.CheckStrengthBendingClass12.result 

result() -> CheckResult

Calculate result of bending moment resistance (Class 1 and 2).

Returns:

  • CheckResult –

    True if the bending moment check passes, False otherwise.

Source code in blueprints/checks/eurocode/steel/strength_bending.py 
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def result(self) -> CheckResult:
    """Calculate result of bending moment resistance (Class 1 and 2).

    Returns
    -------
    CheckResult
        True if the bending moment check passes, False otherwise.
    """
    return CheckResult.from_comparison(
        provided=abs(self.m) * KNM_TO_NMM,
        required=float(self.plastic_resistance()),
    )

checks.eurocode.steel.strength_bending.CheckStrengthBendingClass12.source_docs staticmethod 

source_docs() -> list[str]

List of source document identifiers used for this check.

Returns:

  • list[str] –
Source code in blueprints/checks/eurocode/steel/strength_bending.py 
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@staticmethod
def source_docs() -> list[str]:
    """List of source document identifiers used for this check.

    Returns
    -------
    list[str]
    """
    return [EN_1993_1_1_2005]

checks.eurocode.steel.strength_bending.CheckStrengthBendingClass3 dataclass 

CheckStrengthBendingClass3(
    steel_cross_section: SteelCrossSection,
    m: KNM = 0,
    axis: Literal["My", "Mz"] = "My",
    gamma_m0: DIMENSIONLESS = 1.0,
    name: str = "Bending moment strength check for steel profiles (Class 3 only)",
)

Class to perform bending moment resistance check for steel cross-sections, for cross-section class 3 only (Eurocode 3), based on 1993-1-1:2005 chapter 6.2.5.

Coordinate System: 

z (vertical, usually strong axis)
    ↑
    |     x (longitudinal beam direction, into screen)
    |    ↗
    |   /
    |  /
    | /
    |/
←-----O
y (horizontal/side, usually weak axis)

Parameters:

  • steel_cross_section (SteelCrossSection) –

    The steel cross-section to check.

  • m (KNM, default: 0 ) –

    The applied bending moment (positive value), in kNm (default is 0 kNm).

  • axis (str, default: 'My' ) –

    Axis of bending: 'My' (bending around y) or 'Mz' (bending around z). Default is 'My'.

  • gamma_m0 (DIMENSIONLESS, default: 1.0 ) –

    Partial safety factor for resistance of cross-sections, default is 1.0.

Example 
from blueprints.checks import CheckStrengthBendingClass3
from blueprints.materials.steel import SteelMaterial, SteelStrengthClass
from blueprints.structural_sections.steel.standard_profiles.heb import HEB
from blueprints.structural_sections.steel.steel_cross_section import SteelCrossSection

steel_material = SteelMaterial(steel_class=SteelStrengthClass.S355)
heb_300_profile = HEB.HEB300.with_corrosion(0)
m = 355 * 1.677  # Applied bending moment in kNm

heb_300_s355 = SteelCrossSection(profile=heb_300_profile, material=steel_material)
calc = CheckStrengthBendingClass3(heb_300_s355, m, axis="My", gamma_m0=1.0)
calc.report().to_word("bending_moment_strength.docx")

Raises:

  • ValueError –

    If the provided axis is not 'My' or 'Mz'. The axis parameter must be either 'My' for bending around the y-axis or 'Mz' for bending around the z-axis.

checks.eurocode.steel.strength_bending.CheckStrengthBendingClass3.bending_strength_unity_check 

bending_strength_unity_check() -> Formula

Calculate the unity check for bending strength of the steel cross-section based on the applied bending moment and the calculated resistance (EN 1993-1-1:2005 art. 6.2.5(1) - Formula (6.12)).

Returns:

  • Formula –

    The calculated unity check for bending strength.

Source code in blueprints/checks/eurocode/steel/strength_bending.py 
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def bending_strength_unity_check(self) -> Formula:
    """Calculate the unity check for bending strength of the steel cross-section based on the applied bending
    moment and the calculated resistance (EN 1993-1-1:2005 art. 6.2.5(1) - Formula (6.12)).

    Returns
    -------
    Formula
        The calculated unity check for bending strength.
    """
    m_ed = abs(self.m) * KNM_TO_NMM
    m_c_rd = self.elastic_resistance()
    return formula_6_12.Form6Dot12CheckBendingMoment(m_ed=m_ed, m_c_rd=m_c_rd)

checks.eurocode.steel.strength_bending.CheckStrengthBendingClass3.elastic_resistance 

elastic_resistance() -> Formula

Calculate the elastic bending resistance of the steel cross-section (EN 1993-1-1:2005 art. 6.2.5(3) - Formula (6.14)).

Returns:

  • Formula –

    The calculated elastic bending resistance.

Source code in blueprints/checks/eurocode/steel/strength_bending.py 
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def elastic_resistance(self) -> Formula:
    """Calculate the elastic bending resistance of the steel cross-section (EN 1993-1-1:2005 art. 6.2.5(3) - Formula (6.14)).

    Returns
    -------
    Formula
        The calculated elastic bending resistance.

    """
    # For bending about y, the relevant section modulus is zxx; for bending about z, it is zyy.
    # This is because of the orientation of the axes defined in Blueprints vs. SectionProperties.
    props = self.steel_cross_section.profile.section_properties()
    w = min(float(props.zxx_plus), float(props.zxx_minus)) if self.axis.lower() == "my" else min(float(props.zyy_plus), float(props.zyy_minus))  # type: ignore[attr-defined]

    f_y = self.steel_cross_section.yield_strength
    return formula_6_14.Form6Dot14MCRdClass3(w_el_min=w, f_y=f_y, gamma_m0=self.gamma_m0)

checks.eurocode.steel.strength_bending.CheckStrengthBendingClass3.report 

report(n: int = 2) -> Report

Returns the report for the bending moment check (Class 3).

Parameters:

  • n (int, default: 2 ) –

    Number of decimal places for numerical values in the report (default is 2).

Returns:

  • Report –

    Report of the bending moment check.

Source code in blueprints/checks/eurocode/steel/strength_bending.py 
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def report(self, n: int = 2) -> Report:
    """Returns the report for the bending moment check (Class 3).

    Parameters
    ----------
    n : int, optional
        Number of decimal places for numerical values in the report (default is 2).

    Returns
    -------
    Report
        Report of the bending moment check.
    """
    report = Report(f"Check: bending moment steel beam (axis {self.axis})")

    # will not generate report if no bending moment is applied, as the check is not necessary in that case
    if self.m == 0:
        report.add_paragraph("No bending moment was applied; therefore, no bending moment check is necessary.")
        return report

    # generate report if bending moment is applied
    report.add_paragraph(
        rf"Profile {self.steel_cross_section.profile.name} with steel quality {self.steel_cross_section.material.steel_class.name} "
        rf"is loaded with a bending moment of {abs(self.m):.{n}f} kNm (axis {self.axis}). "
    ).add_newline(n=2)

    # resistance
    report.add_paragraph(r"The resistance is calculated as follows, using cross-section class 3:")
    report.add_formula(self.elastic_resistance(), n=n).add_newline(n=2)

    # unity check
    report.add_paragraph("The unity check is calculated as follows:")
    report.add_formula(self.bending_strength_unity_check(), n=n).add_newline(n=2)

    # conclusion
    if self.result().is_ok:
        report.add_paragraph("The check for bending moment satisfies the requirements.")
    else:
        report.add_paragraph("The check for bending moment does NOT satisfy the requirements.")
    return report

checks.eurocode.steel.strength_bending.CheckStrengthBendingClass3.result 

result() -> CheckResult

Calculate result of bending moment resistance (Class 3).

Returns:

  • CheckResult –

    True if the bending moment check passes, False otherwise.

Source code in blueprints/checks/eurocode/steel/strength_bending.py 
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def result(self) -> CheckResult:
    """Calculate result of bending moment resistance (Class 3).

    Returns
    -------
    CheckResult
        True if the bending moment check passes, False otherwise.
    """
    return CheckResult.from_comparison(
        provided=abs(self.m) * KNM_TO_NMM,
        required=float(self.elastic_resistance()),
    )

checks.eurocode.steel.strength_bending.CheckStrengthBendingClass3.source_docs staticmethod 

source_docs() -> list[str]

List of source document identifiers used for this check.

Returns:

  • list[str] –
Source code in blueprints/checks/eurocode/steel/strength_bending.py 
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@staticmethod
def source_docs() -> list[str]:
    """List of source document identifiers used for this check.

    Returns
    -------
    list[str]
    """
    return [EN_1993_1_1_2005]