Creating Geometries

By the following sections you learn how to create your own geometries and what you have to consider while creating it.

Directions and coordinates

Axes

In cartesian coordinates the span direction is denoted as X-axis.

Y- and Z-axis are the cross-sectional plane. Where the Y-axis is the horizontal axis and the Z-axis describes the vertical axis. The Z-axis is defined in reverse order, meaning from top to bottom. Therefore, a higher value means a point at lower level.

See also

Coordinates : Coordinates in the Theory guide

Following descriptions apply universally:

• top_edge: distance between origin and top-edge of the geometric entity in vertical direction

• bottom_edge: distance between origin and bottom-edge of the geometric entity in vertical direction

• left_edge: distance between origin and left edge of the geometric entity in horizontal direction

• right_edge: distance between origin and right edge of the geometric entity in horizontal direction

• centroid_y: distance between origin and centroid of the geometry in horizontal direction

• centroid_z: distance between origin and centroid of the geometry in vertical direction

The basics: Rectangle, Trapezoid and Circles

Rectangle, Trapezoid and Circle are available as basic geometric entities for creating individual geometries.

Rectangle and Trapezoid

Rectangle dimensions

For a Rectangle as well as a Trapezoid always the top_edge and the bottom_edge need to be defined. The width and the horizontal positioning in Y-direction may be defined in several ways. All of the following are the same in size and position.

>>> from m_n_kappa import Rectangle
>>> rectangle_1 = Rectangle(
...     top_edge=0.0, bottom_edge = 10.0, width=10.0, left_edge=-5.0)
>>> rectangle_2 = Rectangle(
...     top_edge=0.0, bottom_edge = 10.0, width=10.0, right_edge=5.0)
>>> rectangle_3 = Rectangle(
...     top_edge=0.0, bottom_edge = 10.0, left_edge=-5.0, right_edge=5.0)
>>> rectangle_4 = Rectangle(
...     top_edge=0.0, bottom_edge = 0.0, width=10.0)

Trapezoid dimensions

Defining the width and the horizontal position of a Trapezoid is similar to the definition of a Rectangle. But the definition must be conducted for the top_edge as well as for the bottom_edge.

>>> from m_n_kappa import Trapezoid
>>> trapezoid_1 = Trapezoid(
...     top_edge=0, bottom_edge=10, top_width=10, bottom_width=20)
>>> trapezoid_2 = Trapezoid(
...     top_edge=0, bottom_edge=10, top_width=10, bottom_width=20,
...     bottom_left_edge=-10)
>>> trapezoid_3 = Trapezoid(
...     top_edge=0, bottom_edge=10, top_width=10, bottom_width=20,
...     bottom_right_edge=10)
>>> trapezoid_4 = Trapezoid(
...     top_edge=0, bottom_edge=10, top_width=10, bottom_left_edge=-10,
...     bottom_right_edge=10)

The Circle

A m_n_kappa.Circle is created by passing the horizontal and the vertical (Z) position of the centroid as well as its diameter.

Circle dimensions

>>> from m_n_kappa import Circle
>>> circle = Circle(diameter=10, centroid_y=10, centroid_z=10)

Important

The diameter of circle must be small compared to the other dimensions of the cross-section. Otherwise large deviations are possible.

Final notes on Rectangle & Co.

In a further step you will merge a single Rectangle, Trapezoid or Circle with a Material. This will create a Section, what you will learn in Build a section

Of course, you can add geometries up, creating a ComposedGeometry. This is particularly useful if these geometries are of the same material. Merging a ComposedGeometry with a material creates a cross-section (see Build a cross-section)

The shortcut: predefined composed geometries

Some geometries that consist of a number of basic geometries may be used often, like I-profiles, UPE-profiles or rebar-layers. Building these geometries may be tedious and time-consuming. Therefore, these geometries are provided as extra classes, like IProfile, UPEProfile and RebarLayer.

The IProfile consist in general of a top-flange, a web and a bottom-flange. All of the above mentioned elements are defined as Rectangle. If needed only a fraction of these elements is used as the Figure above shows.

I-Profile dimensions

>>> from m_n_kappa import IProfile
>>> i_profile_1 = IProfile(
...     top_edge=0., t_fo=15.5, b_fo=200.0, t_w=9.5, h_w=169.0)
>>> i_profile_no_topflange = IProfile(
...     top_edge=0., t_fu=15.5, b_fu=200.0, t_w=9.5, h_w=169.0,
...     has_top_flange=False
... )
>>> i_profile_no_bottomflange = IProfile(
...     top_edge=0., t_fo=15.5, b_fo=200.0, t_w=9.5, h_w=169.0,
...     has_bottom_flange=False
... )
>>> i_profile_shift10 = IProfile(
...     top_edge=0., t_fo=15.5, b_fo=200.0, t_w=9.5, h_w=169.0,
...     centroid_y=10.) # the I-Profile is shifted 10 mm to the right

The UPE-profile forms a flipped U. The two flanges and the web are each an individual Rectangle.

UPE-Profile dimensions

>>> from m_n_kappa import UPEProfile
>>> upe_profile = UPEProfile(top_edge=10, t_f=5.2, b_f=76, t_w=9.0, h=200)
>>> upe_profile = UPEProfile(top_edge=10, t_f=5.2, b_f=76, t_w=9.0, h_w=200-2*5.2)
>>> upe_profile_shift10 = UPEProfile(top_edge=10, t_f=5.2, b_f=76, t_w=9.0, h=200, centroid_y=10)

A number of rebars at the same level may be defined using a for-loop. What might be tedious. As alternative to the for-loop the RebarLayer has been implemented simplifying this process dramatically. RebarLayer creates a specified number of rebars with a specific horizontal distance between each other. Or if you pass the number and the overall width it computes the horizontal distance by itself.

Rebar-Layer - dimensions

>>> from m_n_kappa import RebarLayer
>>> rebar_layer_1 = RebarLayer(
...     rebar_diameter=12.0, centroid_z=10.0, rebar_number=10, rebar_horizontal_distance=100)
>>> rebar_layer_2 = RebarLayer(
...     rebar_diameter=12.0, centroid_z=10.0, width=1000, rebar_horizontal_distance=100)
>>> rebar_layer_3 = RebarLayer(
...     rebar_diameter=12.0, centroid_z=10.0, rebar_number=10, width=1000)

Note

Do you have another idea or need for a predefined composed geometry, then consider Contributing or open a new issue describing your idea.