m_n_kappa.Rectangle#

class m_n_kappa.Rectangle(top_edge, bottom_edge, width=None, left_edge=None, right_edge=None)#

Bases: Geometry

Represents a rectangle

New in version 0.1.0.

Neither two of the following arguments width, right_edge and left_edge must be given. If only argument width is given left_edge = -0.5*width and right_edge = 0.5*width

Parameters:

top_edge (float) – vertical position of top-edge of the rectangle \(z_\mathrm{top}\)
bottom_edge (float) – vertical position of bottom-edge of the rectangle \(z_\mathrm{bottom}\)
width (float) – width of the rectangle \(b\) (Default: None)
left_edge (float) – horizontal position of left-edge of the rectangle \(y_\mathrm{left}\) (Default: None).
right_edge (float) – horizontal position of right-edge of the rectangle \(y_\mathrm{right}\) (Default: None)

../_images/geometry_rectangle-dark.svg — Rectangle - dimensions#

See also

Circle: creates a circular geometry object
Trapezoid: creates a trapezoidal geometry object
IProfile: creates a geometry object comprised of various Rectangle-objects forming an I
UPEProfile: creates a geometry object comprised of varous Rectangle-objects forming an U

Examples

A rectangle object is easily instantiated as follows.

>>> from m_n_kappa import Rectangle
>>> rectangle = Rectangle(top_edge=10, bottom_edge=20, width=10)

In case only width is passed as argument the centerline of the rectangle is assumed to be a \(y = 0\). In consequence left_edge = -0.5 * width and right_edge = 0.5 * width

>>> rectangle.left_edge, rectangle.right_edge
(-5.0, 5.0)

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

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

Methods

`get_horizontal_edges`(point, max_widths)	Get the horizontal edges of the rectangles considering the effective widths as well as real dimensions of the rectangle
`split`(at_points[, max_widths])	splitting the rectangle horizontally in smaller rectangles

Attributes

`area`	cross-sectional area of rectangle
`bottom_edge`	vertical position (Z-Axis) of the bottom-edge of the rectangle \(z_\mathrm{bottom}\)
`centroid`	centroid of the rectangle in vertical direction (Z-Axis)
`edges`	vertical positions (Z-Axis) top- and bottom-edge
`height`	height of the rectangle
`left_edge`	horizontal position (Y-Axis) of the left-edge of the rectangle \(y_\mathrm{left}\)
`right_edge`	horizontal position (Y-Axis) of the right-edge of the rectangle \(y_\mathrm{right}\)
`sides`	horizontal positions (Y-Axis) of left- and right-edge
`top_edge`	vertical position (Z-Axis) of the top-edge of the rectangle \(z_\mathrm{top}\)
`width`	width of the rectangle
`width_interception`	interception of the width
`width_slope`	slope of the width depending of vertical position \(z\)

get_horizontal_edges(point, max_widths)#

Get the horizontal edges of the rectangles considering the effective widths as well as real dimensions of the rectangle

Parameters:

point (StrainPosition) – position and strain at this position as well as the corresponding material. Needed to differentiate between rectangle under tension and under compression.
max_widths (EffectiveWidths) – effective widths to consider

Returns:

left and right edge considering the effective widths as well as real dimensions of the rectangle

Return type:

tuple[float, float]

split(at_points, max_widths=None)#

splitting the rectangle horizontally in smaller rectangles

Parameters:

at_points (list[StrainPosition]) – points where the rectangle is split into smaller rectangles
max_widths (EffectiveWidths) – widths under consideration of bending or membran loading

Returns:

rectangles assembling to the original rectangle

Return type:

list[Rectangle]

property area: float#: cross-sectional area of rectangle

property bottom_edge#: vertical position (Z-Axis) of the bottom-edge of the rectangle \(z_\mathrm{bottom}\)

property centroid: float#: centroid of the rectangle in vertical direction (Z-Axis)

property edges: list[float]#: vertical positions (Z-Axis) top- and bottom-edge

property height: float#: height of the rectangle

property left_edge: float#: horizontal position (Y-Axis) of the left-edge of the rectangle \(y_\mathrm{left}\)

property right_edge: float#: horizontal position (Y-Axis) of the right-edge of the rectangle \(y_\mathrm{right}\)

property sides: list[float]#: horizontal positions (Y-Axis) of left- and right-edge

property top_edge#: vertical position (Z-Axis) of the top-edge of the rectangle \(z_\mathrm{top}\)

property width: float#: width of the rectangle

property width_interception: float#: interception of the width

property width_slope: float#: slope of the width depending of vertical position \(z\)