Getting Started#

Installation#

The installation via PyPi runs as follows.

pip install m-n-kappa

Introducing example: Computing a steel-concrete composite beam#

The following example shows how easy and straightforward m_n_kappa is applied to computing the deformation of a composite beam.

_images/getting_started_example-dark.svg

_images/getting_started_example-light.svg — Composite beam (Measurements are given in Millimeter)#

The slab is a rectangle of concrete of type C30/35.

from m_n_kappa import Rectangle, Concrete
slab = Rectangle(top_edge=0.0, bottom_edge=100, width=2000)
concrete = Concrete(f_cm=38)
concrete_slab = concrete + slab

The girder is a HEB 200 steel-profile of type S355.

from m_n_kappa import IProfile, Steel
girder = IProfile(top_edge=100.0, t_w=9.5, h_w=200-2*15, t_fo=15, b_fo=200)
steel = Steel(f_y=355, failure_strain=0.15)
steel_girder = steel + girder

Merging the concrete_slab and the steel_girder to a composite cross-section is accomplished also easily.

composite_cross_section = concrete_slab + steel_girder

This Crosssection-object of a composite beam allows you to do several things like computing the curvature \(\kappa\), the M-\(\kappa\)-curve or the deformation of the beam under a given loading.

from m_n_kappa import SingleSpanUniformLoad, Beam
loading = SingleSpanUniformLoad(length=8000)
beam = Beam(
    cross_section=composite_cross_section,
    element_number=10,
    load=loading
 )

The load-deformation-curve is then created as follows, using the plotting library Altair.

deformation_at_maximum_position = beam.deformations_at_maximum_deformation_position()

import pandas as pd
df = pd.DataFrame(
     {'loadings': deformation_at_maximum_position.loadings(factor=0.001),
      'deformations': deformation_at_maximum_position.values()})

import altair as alt
alt.Chart(df, background='#00000000').mark_line().encode(
   x=alt.X('deformations', title='Deformation [mm]'),
   y=alt.Y('loadings', title='Loading [kN]'))

The deformation along the beam under a given load is then computed as follows.

deformation_load = SingleSpanUniformLoad(length=8000, load=1.0)
deformations_over_length = beam.deformation_over_beam_length(
    load_step=deformation_load)

df = pd.DataFrame(
     {'positions': deformations_over_length.positions(),
      'deformations': deformations_over_length.values()})

alt.Chart(df, height=100.0, background='#00000000').mark_line().encode(
    x=alt.X('positions', title='Beam position [mm]'),
    y=alt.Y('deformations', title='Deformation [mm]', scale=alt.Scale(reverse=True)))

Examples gives you detailed instructions how to build a cross-section, computing a single Moment-Curvature point, a Moment-Curvature-Curve or the Deformation of a beam, to name a few.