strength_shear

checks.eurocode.steel.strength_shear

Module for checking shear force resistance of steel (Eurocode 3).

Classes:

• CheckStrengthShearClass12 –

  Class to perform plastic shear force resistance check for steel of cross-section class 1 and 2 based on EN 1993-1-1:2005 art. 6.2.6.

• CheckStrengthShearClass34 –

  Class to perform elastic shear force resistance check for steel cross-section class 3 and 4 (Eurocode 3).

checks.eurocode.steel.strength_shear.CheckStrengthShearClass12 dataclass

CheckStrengthShearClass12(
    steel_cross_section: SteelCrossSection,
    v: KN = 0,
    axis: Literal["Vz", "Vy"] = "Vz",
    gamma_m0: DIMENSIONLESS = 1.0,
    name: str = "Plastic shear strength check for steel",
)

Class to perform plastic shear force resistance check for steel of cross-section class 1 and 2 based on EN 1993-1-1:2005 art. 6.2.6.

Coordinate System:

z (vertical, usually strong axis)
    ↑
    |     x (longitudinal beam direction, into screen)
    |    ↗
    |   /
    |  /
    | /
    |/

←-----O y (horizontal/side, usually weak axis)

Notes

Not all profile shapes have been implemented for this check yet. Currently, only I-profiles are supported.

Parameters:

• steel_cross_section (SteelCrossSection) –

  The steel cross-section to check.

• v (KN, default: 0 ) –

  The applied shear force (in kN).

• axis (Literal['Vz', 'Vy'], default: 'Vz' ) –

  Axis along which the shear force is applied. "Vz" (default) for z (vertical), "Vy" for y (horizontal).

• gamma_m0 (DIMENSIONLESS, default: 1.0 ) –

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

Example

from blueprints.checks.eurocode.steel.strength_shear import CheckStrengthShearClass12 from blueprints.materials.steel import SteelMaterial, SteelStrengthClass from blueprints.structural_sections.steel.standard_profiles.heb import HEB

steel_material = SteelMaterial(steel_class=SteelStrengthClass.S355) heb_300_profile = HEB.HEB300.with_corrosion(1.5) v = 100 # Applied shear force in kN

heb_300_s355 = SteelCrossSection(profile=heb_300_profile, material=steel_material) calc = CheckStrengthShearClass12(heb_300_s355, v, axis="Vz", gamma_m0=1.0) calc.report().to_word("shear_strength.docx", language="nl")

checks.eurocode.steel.strength_shear.CheckStrengthShearClass12.plastic_resistance

plastic_resistance() -> Formula

Calculate the shear force plastic resistance of the steel cross-section (EN 1993-1-1:2005 art. 6.2.6(2) - Formula (6.18)).

Returns:

• Formula –

  The calculated shear force resistance.

Source code in blueprints/checks/eurocode/steel/strength_shear.py

def plastic_resistance(self) -> Formula:
    """Calculate the shear force plastic resistance of the steel cross-section (EN 1993-1-1:2005 art. 6.2.6(2) - Formula (6.18)).

    Returns
    -------
    Formula
        The calculated shear force resistance.
    """
    a_v = self.shear_area()
    f_y = self.steel_cross_section.yield_strength
    return formula_6_18.Form6Dot18DesignPlasticShearResistance(a_v=a_v, f_y=f_y, gamma_m0=self.gamma_m0)

checks.eurocode.steel.strength_shear.CheckStrengthShearClass12.report

report(n: int = 2) -> Report

Returns the report for the plastic shear force check.

Parameters:

• n (int, default: 2 ) –

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

Returns:

• Report –

  Report of the plastic shear force check.

Source code in blueprints/checks/eurocode/steel/strength_shear.py

def report(self, n: int = 2) -> Report:
    """Returns the report for the plastic shear force check.

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

    Returns
    -------
    Report
        Report of the plastic shear force check.
    """
    report = Report("Check: shear force steel I-beam")

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

    # generate report if shear force is applied
    axis_label = "(vertical) z" if self.axis == "Vz" else "(horizontal) y"
    report.add_paragraph(
        f"Profile {self.steel_cross_section.profile.name} with steel quality {self.steel_cross_section.material.steel_class.name} "
        f"is loaded with a shear force of {abs(self.v):.{n}f} kN in the {axis_label}-direction."
    )
    report.add_newline(n=2)

    # shear area
    report.add_paragraph("The shear area is calculated as follows:")
    report.add_formula(self.shear_area(), n=n, split_after=[(2, "="), (7, "+"), (3, "=")])
    report.add_newline(n=2)

    # resistance
    report.add_paragraph("The shear resistance is calculated as follows:")
    report.add_formula(self.plastic_resistance(), n=n)
    report.add_newline(n=2)

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

    # add overall result based on the unity check
    if self.result().is_ok:
        report.add_paragraph("The check for plastic shear force satisfies the requirements.")
    else:
        report.add_paragraph("The check for plastic shear force does NOT satisfy the requirements.")
    return report

checks.eurocode.steel.strength_shear.CheckStrengthShearClass12.result

result() -> CheckResult

Calculate result of plastic shear force resistance.

Returns:

• CheckResult –

  True if the shear force check passes, False otherwise.

Source code in blueprints/checks/eurocode/steel/strength_shear.py

def result(self) -> CheckResult:
    """Calculate result of plastic shear force resistance.

    Returns
    -------
    CheckResult
        True if the shear force check passes, False otherwise.
    """
    provided = abs(self.v) * KN_TO_N
    required = self.plastic_resistance()
    return CheckResult.from_comparison(provided=provided, required=required)

checks.eurocode.steel.strength_shear.CheckStrengthShearClass12.shear_area

shear_area() -> Formula

Calculate the shear area of the steel cross-section.

Based on the applied shear force axis and fabrication method (EN 1993-1-1:2005 art. 6.2.6(3) - Formulas (6.18a/d/e)).

Source code in blueprints/checks/eurocode/steel/strength_shear.py

def shear_area(self) -> Formula:
    """Calculate the shear area of the steel cross-section.

    Based on the applied shear force axis and fabrication method
    (EN 1993-1-1:2005 art. 6.2.6(3) - Formulas (6.18a/d/e)).
    """
    if isinstance(self.steel_cross_section.profile, IProfile):
        # Get parameters from profile, average top and bottom flange properties
        a = float(self.steel_cross_section.profile.area)
        b1 = self.steel_cross_section.profile.top_flange_width
        b2 = self.steel_cross_section.profile.bottom_flange_width
        tf1 = self.steel_cross_section.profile.top_flange_thickness
        tf2 = self.steel_cross_section.profile.bottom_flange_thickness
        tw = self.steel_cross_section.profile.web_thickness
        hw = self.steel_cross_section.profile.total_height - (
            self.steel_cross_section.profile.top_flange_thickness + self.steel_cross_section.profile.bottom_flange_thickness
        )
        r1 = self.steel_cross_section.profile.top_radius
        r2 = self.steel_cross_section.profile.bottom_radius

        assert all(param is not None for param in [a, b1, b2, tf1, tf2, tw, hw, r1, r2]), (
            "All profile parameters must be defined for I-profile shear area calculation."
        )

        if self.axis == "Vz" and self.steel_cross_section.fabrication_method in ["hot-rolled", "cold-formed"]:
            return formula_6_18_sub_av.Form6Dot18SubARolledIandHSection(a=a, b1=b1, b2=b2, hw=hw, r1=r1, r2=r2, tf1=tf1, tf2=tf2, tw=tw, eta=1.0)
        if self.axis == "Vz" and self.steel_cross_section.fabrication_method == "welded":
            return formula_6_18_sub_av.Form6Dot18SubDWeldedIHandBoxSection(hw_list=[hw], tw_list=[tw], eta=1.0)
        # when axis == "Vy"
        return formula_6_18_sub_av.Form6Dot18SubEWeldedIHandBoxSection(a=a, hw_list=[hw], tw_list=[tw])
    raise NotImplementedError("Profile type is not supported")  # pragma: no cover

checks.eurocode.steel.strength_shear.CheckStrengthShearClass12.shear_strength_unity_check

shear_strength_unity_check() -> Formula

Calculate the unity check for shear strength of the steel cross-section (EN 1993-1-1:2005 art. 6.2.6(2) - Formula (6.17)).

Returns:

• Formula –

  The calculated unity check for shear strength.

Source code in blueprints/checks/eurocode/steel/strength_shear.py

def shear_strength_unity_check(self) -> Formula:
    """Calculate the unity check for shear strength of the steel cross-section (EN 1993-1-1:2005 art. 6.2.6(2) - Formula (6.17)).

    Returns
    -------
    Formula
        The calculated unity check for shear strength.
    """
    v_ed = abs(self.v * KN_TO_N)
    v_pl_rd = self.plastic_resistance()
    return formula_6_17.Form6Dot17CheckShearForce(v_ed=v_ed, v_c_rd=v_pl_rd)

checks.eurocode.steel.strength_shear.CheckStrengthShearClass12.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_shear.py

@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_shear.CheckStrengthShearClass34 dataclass

CheckStrengthShearClass34(
    steel_cross_section: SteelCrossSection,
    v: KN = 0,
    axis: Literal["Vz", "Vy"] = "Vz",
    gamma_m0: DIMENSIONLESS = 1.0,
    name: str = "Elastic shear strength check",
)

Class to perform elastic shear force resistance check for steel cross-section class 3 and 4 (Eurocode 3).

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.

• v (KN, default: 0 ) –

  The applied shear force (in kN).

• axis (Literal['Vz', 'Vy'], default: 'Vz' ) –

  Axis along which the shear force is applied. "Vz" (default) for z (vertical), "Vy" for y (horizontal).

• gamma_m0 (DIMENSIONLESS, default: 1.0 ) –

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

• section_properties (SectionProperties | None) –

  Pre-calculated section properties. If None, they will be calculated internally.

Example

from blueprints.checks.eurocode.steel.strength_shear import CheckStrengthShearClass34 from blueprints.materials.steel import SteelMaterial, SteelStrengthClass from blueprints.structural_sections.steel.standard_profiles.heb import HEB

steel_material = SteelMaterial(steel_class=SteelStrengthClass.S355) heb_300_profile = HEB.HEB300.with_corrosion(1.5) v = 100 # Applied shear force in kN

heb_300_s355 = SteelCrossSection(profile=heb_300_profile, material=steel_material) calc = CheckStrengthShearClass34(heb_300_s355, v, axis="Vz", gamma_m0=1.0) calc.report().to_word("shear_strength.docx", language="nl")

checks.eurocode.steel.strength_shear.CheckStrengthShearClass34.elastic_resistance

elastic_resistance() -> float

Calculate the shear force elastic resistance of the steel cross-section (EN 1993-1-1:2005 art. 6.2.6).

Returns:

• float –

  The calculated shear force resistance in N.

Source code in blueprints/checks/eurocode/steel/strength_shear.py

def elastic_resistance(self) -> float:
    """Calculate the shear force elastic resistance of the steel cross-section (EN 1993-1-1:2005 art. 6.2.6).

    Returns
    -------
    float
        The calculated shear force resistance in N.
    """
    unit_stress = self.shear_unit_stress()
    return float(self.steel_cross_section.yield_strength / np.sqrt(3) / self.gamma_m0 / unit_stress * KN_TO_N)

checks.eurocode.steel.strength_shear.CheckStrengthShearClass34.report

report(n: int = 2) -> Report

Returns the report for the elastic shear force check.

Parameters:

• n (int, default: 2 ) –

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

Returns:

• Report –

  Report of the elastic shear force check.

Source code in blueprints/checks/eurocode/steel/strength_shear.py

def report(self, n: int = 2) -> Report:
    """Returns the report for the elastic shear force check.

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

    Returns
    -------
    Report
        Report of the elastic shear force check.
    """
    report = Report("Check: shear force steel I-beam (Class 3/4)")

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

    # generate report if shear force is applied
    axis_label = "(vertical) z" if self.axis == "Vz" else "(horizontal) y"
    report.add_paragraph(
        f"Profile {self.steel_cross_section.profile.name} with steel quality {self.steel_cross_section.material.steel_class.name} "
        f"is loaded with a shear force of {abs(self.v):.{n}f} kN in the {axis_label}-direction. "
        f"The shear stress is calculated using elastic theory."
    )
    report.add_newline(n=2)

    # shear stress calculation
    tau_ed = self.shear_stress()
    report.add_paragraph(f"The maximum shear stress is: {tau_ed:.{n}f} N/mm².")
    report.add_newline(n=2)

    # maximum allowed stress
    tau_max = round(self.steel_cross_section.yield_strength / (np.sqrt(3) * self.gamma_m0), n)
    report.add_paragraph("The maximum allowed shear stress is calculated as follows:")
    report.add_paragraph(f"$f_y / (\\sqrt{{3}} \\cdot \\gamma_{{M0}})$ = {tau_max} N/mm².")
    report.add_newline(n=2)

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

    # add overall result based on the unity check
    if self.result().is_ok:
        report.add_paragraph("The check for elastic shear force satisfies the requirements.")
    else:
        report.add_paragraph("The check for elastic shear force does NOT satisfy the requirements.")
    return report

checks.eurocode.steel.strength_shear.CheckStrengthShearClass34.result

result() -> CheckResult

Calculate result of elastic shear force resistance.

Returns:

• CheckResult –

  True if the shear force check passes, False otherwise.

Source code in blueprints/checks/eurocode/steel/strength_shear.py

def result(self) -> CheckResult:
    """Calculate result of elastic shear force resistance.

    Returns
    -------
    CheckResult
        True if the shear force check passes, False otherwise.
    """
    provided = abs(self.v) * KN_TO_N
    required = self.elastic_resistance()
    return CheckResult.from_comparison(provided=provided, required=required)

checks.eurocode.steel.strength_shear.CheckStrengthShearClass34.shear_strength_unity_check

shear_strength_unity_check() -> Formula

Calculate the unity check for shear strength of the steel cross-section (EN 1993-1-1:2005 art. 6.2.6 - Formula (6.19)).

Returns:

• Formula –

  The calculated unity check for shear strength.

Source code in blueprints/checks/eurocode/steel/strength_shear.py

def shear_strength_unity_check(self) -> Formula:
    """Calculate the unity check for shear strength of the steel cross-section (EN 1993-1-1:2005 art. 6.2.6 - Formula (6.19)).

    Returns
    -------
    Formula
        The calculated unity check for shear strength.
    """
    tau_ed = self.shear_stress()
    return formula_6_19.Form6Dot19CheckDesignElasticShearResistance(
        tau_ed=tau_ed, f_y=self.steel_cross_section.yield_strength, gamma_m0=self.gamma_m0
    )

checks.eurocode.steel.strength_shear.CheckStrengthShearClass34.shear_stress

shear_stress() -> float

Calculate the maximum shear stress in the steel cross-section using elastic theory.

Returns:

• float –

  The maximum shear stress in N/mm².

Source code in blueprints/checks/eurocode/steel/strength_shear.py

def shear_stress(self) -> float:
    """Calculate the maximum shear stress in the steel cross-section using elastic theory.

    Returns
    -------
    float
        The maximum shear stress in N/mm².
    """
    unit_stress = self.shear_unit_stress()
    return unit_stress * abs(self.v)

checks.eurocode.steel.strength_shear.CheckStrengthShearClass34.shear_unit_stress

shear_unit_stress() -> float

Calculate the unit shear stress in the steel cross-section.

Returns:

• float –

  The unit shear stress in N/mm².

Source code in blueprints/checks/eurocode/steel/strength_shear.py

def shear_unit_stress(self) -> float:
    """Calculate the unit shear stress in the steel cross-section.

    Returns
    -------
    float
        The unit shear stress in N/mm².
    """
    unit_stress = self.steel_cross_section.profile.unit_stress()
    return float(np.max(np.abs(unit_stress["sig_zxy_vy"] if self.axis == "Vz" else unit_stress["sig_zxy_vx"])))

checks.eurocode.steel.strength_shear.CheckStrengthShearClass34.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_shear.py

@staticmethod
def source_docs() -> list[str]:
    """List of source document identifiers used for this check.

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