m_n_kappa.section.ComputationSectionCurvature#

class m_n_kappa.section.ComputationSectionCurvature(section, curvature, neutral_axis)#

Bases: ComputationSection

compute section given a curvature and a neutral axis

New in version 0.1.0.

Parameters:

section (Section) – section to compute
curvature (float) – curvature to apply to the section \(\kappa\)
neutral_axis (float) – point where the strain_value is zero \(z_\mathrm{n}\)

See also

ComputationSectionStrain: ComputationSection to compute values under constant strain
Sections: check out for a more detailed explanation.

Notes

For the basic computation refer to ComputationSection.

The overall procedure is:

Determine the strains at the edges from the given strain-distribution. The strain-distribution is computed by the curvature and the neutral axis
Compute the stresses at the edges passing the strains to the material-model
Determine the stress-distribution (slope and interception)
Compute the axial-force by combining the stress-distribution with the crosssectional area of the section

Lever-arm and moment may be computed in succession, if needed.

Examples

A Section is defined as follows.

>>> from m_n_kappa import Rectangle, Steel
>>> steel = Steel(f_y=355)
>>> rectangle = Rectangle(top_edge=0.0, bottom_edge=10, width=10)
>>> section = steel + rectangle

The computation for a given curvature and a given neutral-axis started by invoking ComputationSectionCurvature

>>> from m_n_kappa.section import ComputationSectionCurvature
>>> computed_section = ComputationSectionCurvature(section, curvature=0.0001, neutral_axis=10.0)

The computed axial-force \(N_i\) is given as follows:

>>> computed_section.axial_force
-10500.0

The lever-arm \(r_i\) is computed as follows:

>>> computed_section.lever_arm()
3.3333333333333335

And the moment \(M_i\) is given as follows

>>> computed_section.moment()
-35000.0

Methods

`lever_arm`()	lever-arm of the section under the given strain-distribution \(r_i\)
`material_points_inside_curvature`()	compute those material-points that are between the given strains from the given curvature and zero strain.
`material_strains`()	strains of the associated material-model
`maximum_negative_strain`()	maximum negative strain from associated material-model
`maximum_negative_strain_position`()	maximum negative strain from associated material-model
`maximum_positive_strain`()	maximum positive strain from associated material-model
`maximum_positive_strain_position`()	maximum positive strain from associated material-model
`moment`()	moment under the given strain distribution
`section_strains`()	strains of the associated material-model
`split_section`([effective_widths])	split sections considering the material points and the maximum effective widths
`strain_positions`([strain_1, strain_2, ...])	collect all strain-positions between `strain_1` and `strain_2` (if given)

Attributes

`axial_force`	axial-force of the section in case of the given strain-distribution \(N_i\)
`bottom_edge_maximum_strain`	`StrainPosition` with maximum strain on bottom edge of section
`bottom_edge_minimum_strain`	`StrainPosition` with minimum strain on bottom edge of section
`curvature`	input-curvature \(\kappa\)
`edges_strain`	strains at the edges (bottom and top) of the section, computed from the strain distribution
`edges_stress`	stresses at the edges (bottom and top) of the section
`edges_stress_difference`	difference of stresses between the given edges
`geometry`	geometry of the section
`material`	material of the section
`neutral_axis`	input neutral axis \(z_\mathrm{n}\)
`section`	basic `Section`
`section_type`
`stress_interception`	interception-value of the linear stress-distribution of the section
`stress_slope`	linear slope of the stresses over the vertical direction of the section
`top_edge_maximum_strain`	`StrainPosition` with maximum strain on top edge of section
`top_edge_minimum_strain`	`StrainPosition` with minimum strain on top edge of section

lever_arm()#

lever-arm of the section under the given strain-distribution \(r_i\)

Returns:: lever-arm of the section under a given strain-distribution
Return type:: float

See also

Lever arm: More descriptive explanation of the computation

Notes

In case of a Rectangle or a Trapezoid the lever-arm is computed as follows.

(1)#\[r_i = \frac{1}{N_i} \int_{z_\mathrm{top}}^{z_\mathrm{bottom}} \sigma(z) \cdot b(z) \cdot z~dz\]

In case of a Circle the lever-arm applies as the centroid of the circle. It is assumed that only reinforcement-bars are modelled as circles and therefore small in comparison to the rest of the cross-section.

material_points_inside_curvature()#

compute those material-points that are between the given strains from the given curvature and zero strain.

Return type:: list[StrainPosition]

material_strains()#

strains of the associated material-model

Return type:: list[float]

maximum_negative_strain()#

maximum negative strain from associated material-model

Return type:: float

maximum_negative_strain_position()#

maximum negative strain from associated material-model

New in version 0.2.0.

Return type:: StrainPosition

maximum_positive_strain()#

maximum positive strain from associated material-model

Return type:: float

maximum_positive_strain_position()#

maximum positive strain from associated material-model

New in version 0.2.0.

Return type:: StrainPosition

moment()#

moment under the given strain distribution

See also

Moment: More descriptive explanation of the computation

Returns:: moment under the given strain distribution
Return type:: float

section_strains()#

strains of the associated material-model

Return type:: list[dict]

split_section(effective_widths=None)#

split sections considering the material points and the maximum effective widths

Parameters:: effective_widths (EffectiveWidths) – effective widths applied to the split section
Returns:: the split sections
Return type:: list[ComputationSection]

strain_positions(strain_1=None, strain_2=None, include_strains=False)#

collect all strain-positions between strain_1 and strain_2 (if given)

New in version 0.2.0.

Parameters:

strain_1 (float) – first strain border (Default: None)
strain_2 (float) – second strain border (Default: None)
include_strains (bool) – includes the boundary strain values (Default: False)

Returns:

collected :py:class:`~m_n_kappa.StrainPosition

Return type:

list[StrainPosition]

property axial_force: float#

axial-force of the section in case of the given strain-distribution \(N_i\)

See also

Axial force: More descriptive explanation of the computation

property bottom_edge_maximum_strain: StrainPosition#: StrainPosition with maximum strain on bottom edge of section

property bottom_edge_minimum_strain: StrainPosition#: StrainPosition with minimum strain on bottom edge of section

property curvature: float#: input-curvature \(\kappa\)

property edges_strain: list#: strains at the edges (bottom and top) of the section, computed from the strain distribution

property edges_stress: list#: stresses at the edges (bottom and top) of the section

property edges_stress_difference: float#: difference of stresses between the given edges

property geometry#: geometry of the section

property material#: material of the section

property neutral_axis: float#: input neutral axis \(z_\mathrm{n}\)

property section: Section#: basic Section

property stress_interception: float#: interception-value of the linear stress-distribution of the section

property stress_slope: float#: linear slope of the stresses over the vertical direction of the section

property top_edge_maximum_strain: StrainPosition#: StrainPosition with maximum strain on top edge of section

property top_edge_minimum_strain: StrainPosition#: StrainPosition with minimum strain on top edge of section