m-n-kappa 0.0.1

Open source library for using the strain-based method to compute the stress-distribution of a cross-section considering multi-linear material models

M-N-Kappa

Implementation of the M-N-κ method for deformation-computation of structural beams considering multi-line material models as well as shear connector behaviour implemented in python.

Introduction

The m_n_kappa-package addresses primarily scientific investigations in structural engineering. It has been developed having steel-concrete composite beams, i.e. slim-floor beams in mind, but due to its general approach using multiline material models the scope of application is potentially much greater.

• M: resistance moment of a cross-section
• N: internal shear-force applied with differing sign on the concrete-slab and the steel-girder
• κ: the curvature over the cross-section4

It is assumed that the curvature κ is uniformly distributed over the full height of the cross-section.

The M-κ-Method allows to compute the deformation of composite beams assuming rigid shear connection. The M-N-κ-Method extends the method by the load-slip-behaviour of the shear connectors.

Features

The following list is an extract of the given and potential features

• strain-based design
• consideration of effective width for concrete slabs distinguishing between membran and bending loading
• consideration of load-slip behaviour of shear connectors (not yet implemented)
• easy to use interface (see Example)

Installation

The installation via PyPi runs as follows.

pip install m_n_kappa

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.

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 κ, the M-κ-curve or the deformation of the beam under a given loading.

from m_n_kappa import SingleSpanUniformLoad, Beam
loading = SingleSpanUniformLoad(length=8000, load=1.0)
beam = Beam(
    cross_section=composite_cross_section, 
    element_number=10,
    load=loading
)
deformation_at_maximum_position = beam.deformations_at_maximum_deformation_position()
deformation_at_maximum_position.values()

If you want to know more please refer to the Documentation.

Documentation

The documentation gives you more examples, let's you understand the mechanics working under the hood in the Theory guide or shows you application of the model on tests in Verification.

Overview:

• Getting started
• Examples
• Theory guide
• Verification

Contributions are highly appreciated

• Did you find a typo, a bug or want to add an explanation or figure to the documentation?
• Do you want to implement another material model, enhance the performance or implement another feature?
• You used m_n_kappa to compute the load-deformation behaviour of your experimental investigation and want to share your verification?

All types of contributions are welcomed. Please check beforehand the Contributing's page.

About

• Roadmap: Roadmap, ideas for implementation and To do's
• License: 3-Clause BSD License
• Release Notes