m_n_kappa.section.ComputationSection#

class m_n_kappa.section.ComputationSection(geometry, material)#

Bases: Section

base class for specified ComputationsSection-classes

New in version 0.1.0.

See also

ComputationSectionStrain: ComputationSection to compute values under constant strain
ComputationSectionCurvature: ComputationSection to compute values under linear-distributed strain

Notes

The computation of axial-force \(N_i\), lever-arm \(r_i\) and moment \(M_i\)

Parameters:

geometry (Geometry) – geometry of the section, e.g. Rectangle, Circle or Trapezoid
material (Material) – material of the section, e.g. Steel, Reinforcement or Concrete

Examples

A section may be created in two ways. In both cases a Material and a Geometry instance is needed.

>>> from m_n_kappa import Steel, Rectangle
>>> steel = Steel(f_y=355.0)
>>> rectangle = Rectangle(top_edge=0.0, bottom_edge=10, width=10.0)

The first way is by simply adding the steel (Material instance) and a rectangle (Geometry instance).

>>> section_top = steel + rectangle
>>> section_top
Section(geometry=Rectangle(top_edge=0.00, bottom_edge=10.00, width=10.00, left_edge=-5.00, right_edge=5.00), material=Steel(f_y=355.0, f_u=None, failure_strain=None, E_a=210000.0))

Alternatively a section is created by passing rectangle and steel as arguments to Section.

>>> from m_n_kappa import Section
>>> section_bottom = Section(geometry=rectangle, material=steel)
>>> section_bottom
Section(geometry=Rectangle(top_edge=0.00, bottom_edge=10.00, width=10.00, left_edge=-5.00, right_edge=5.00), material=Steel(f_y=355.0, f_u=None, failure_strain=None, E_a=210000.0))

Methods

`lever_arm`()	lever-arm of the section under the given strain-distribution \(r_i\)
`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
`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
`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
`geometry`	geometry of the section
`material`	material of the section
`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_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]

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 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 geometry#: geometry of the section

property material#: material of the section

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