m_n_kappa.Trapezoid#

class m_n_kappa.Trapezoid(top_edge, bottom_edge, top_width, top_left_edge=None, top_right_edge=None, bottom_width=None, bottom_left_edge=None, bottom_right_edge=None)#

Bases: Geometry

Represents a trapezoidal

New in version 0.1.0.

The trapezoid has vertical edges parallel to each other and two horizontal edges that are not parallel to each other.

Parameters:

top_edge (float) – top-edge of the trapezoid \(z_\mathrm{top}\)
bottom_edge (float) – bottom-edge of the trapezoid \(z_\mathrm{bottom}\)
top_width (float) – width of the trapezoid at the top-edge \(b_\mathrm{top}\) (Default: None).
top_left_edge (float) – left-edge position of the trapezoid at the top-edge \(y_\mathrm{top-left}\) (Default: None).
top_right_edge (float) – right-edge position of the trapezoid at the top-edge \(y_\mathrm{top-right}\) (Default: None).
bottom_width (float) – width of the trapezoid at the bottom-edge \(b_\mathrm{bottom}\) (Default: None).
bottom_left_edge (float) – left-edge position of the trapezoid at the bottom-edge \(y_\mathrm{bottom-left}\) (Default: None).
bottom_right_edge (float) – right-edge position of the trapezoid at the bottom-edge \(y_\mathrm{bottom-right}\) (Default: None).

../_images/geometry_trapezoid-dark.svg — Trapezoid - dimensions#

See also

Rectangle: creates a rectangular geometry object
Circle: creates a circular geometry object

Examples

A trapezoid object is easily instantiated as follows.

>>> from m_n_kappa import Trapezoid
>>> trapezoid = Trapezoid(top_edge=0, bottom_edge=10, top_width=10, bottom_width=20)

In case only top_width or bottom_width is passed as argument the centerline of the specific width of the trapezoid is assumed to be a \(y = 0\). In consequence top_left_edge = -0.5 * top_width and top_right_edge = 0.5 * top_width. Similar for the bottom-edge.

For building a Section the trapezoid must only be added to a material.

>>> from m_n_kappa import Steel
>>> steel = Steel(f_y=355)
>>> section = trapezoid + steel
>>> type(section)
<class 'm_n_kappa.section.Section'>

Methods

`left_edge_at`(vertical_position)	left edge at the given vertical position
`right_edge_at`(vertical_position)	right edge at the given vertical position
`split`(at_points[, max_widths])	split trapezoid at the given points and if needed to
`width`(vertical_position)	width of trapezoid at given vertical position

Attributes

`area`	cross-sectional area of the trapezoid
`bottom_edge`	vertical position of bottom-edge of the trapezoid \(z_\mathrm{bottom}\)
`bottom_left_edge`	left-edge position of the trapezoid at the bottom-edge \(y_\mathrm{bottom-left}\)
`bottom_right_edge`	right-edge position of the trapezoid at the bottom-edge \(y_\mathrm{bottom-right}\)
`bottom_width`	width of trapezoid on bottom-edge \(b_\mathrm{top}\)
`centroid`	vertical position of the centroid of the trapezoid
`edges`	edges of trapezoid in vertical direction
`height`	height of the trapezoid \(h\)
`left_edge`	outer left-edge of the trapezoid
`right_edge`	outer right-edge of the trapezoid
`sides`	horizontal edges
`top_edge`	vertical position of top-edge of the trapezoid \(z_\mathrm{top}\)
`top_left_edge`	left-edge position of the trapezoid at the top-edge \(y_\mathrm{top-left}\)
`top_right_edge`	right-edge position of the trapezoid at the top-edge \(y_\mathrm{top-right}\)
`top_width`	width of trapezoid on top-edge \(b_\mathrm{top}\)
`width_interception`	theoretical width of the trapezoid at coordinate-origin
`width_slope`	change of the width of the trapezoid depending on vertical position

left_edge_at(vertical_position)#

left edge at the given vertical position

in case vertical_position is outside of the trapezoid, then zero is returned

Parameters:: vertical_position (float) – vertical position the width of the trapezoid shall be given
Returns:: horizontal position of the left-edge of trapezoid at given vertical position
Return type:: float

right_edge_at(vertical_position)#

right edge at the given vertical position

in case vertical_position is outside of the trapezoid zero is returned

Parameters:: vertical_position (float) – vertical position the width of the trapezoid shall be given
Returns:: horizontal position of the right-edge of trapezoid at given vertical position
Return type:: float

split(at_points, max_widths=None)#

split trapezoid at the given points and if needed to

Parameters:

at_points (list[m_n_kappa.general.StrainPosition]) –
max_widths (EffectiveWidths) –

Returns:

trapezoid split at the material-points into sub-trapezoids

Return type:

list[Trapezoid]

width(vertical_position)#

width of trapezoid at given vertical position

in case vertical_position is outside of the trapezoid zero is returned

Parameters:: vertical_position (float) – vertical position the width of the trapezoid shall be given
Returns:: width of trapezoid at given vertical position
Return type:: float

property area: float#: cross-sectional area of the trapezoid

property bottom_edge: float#: vertical position of bottom-edge of the trapezoid \(z_\mathrm{bottom}\)

property bottom_left_edge: float#: left-edge position of the trapezoid at the bottom-edge \(y_\mathrm{bottom-left}\)

property bottom_right_edge: float#: right-edge position of the trapezoid at the bottom-edge \(y_\mathrm{bottom-right}\)

property bottom_width: float#: width of trapezoid on bottom-edge \(b_\mathrm{top}\)

property centroid: float#: vertical position of the centroid of the trapezoid

property edges: list#: edges of trapezoid in vertical direction

property height: float#: height of the trapezoid \(h\)

property left_edge: float#: outer left-edge of the trapezoid

property right_edge: float#: outer right-edge of the trapezoid

property sides: list[float]#: horizontal edges

property top_edge: float#: vertical position of top-edge of the trapezoid \(z_\mathrm{top}\)

property top_left_edge: float#: left-edge position of the trapezoid at the top-edge \(y_\mathrm{top-left}\)

property top_right_edge: float#: right-edge position of the trapezoid at the top-edge \(y_\mathrm{top-right}\)

property top_width: float#: width of trapezoid on top-edge \(b_\mathrm{top}\)

property width_interception: float#: theoretical width of the trapezoid at coordinate-origin

property width_slope: float#: change of the width of the trapezoid depending on vertical position