.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/structural_engineering/plot_structural_engineering_benchmark.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_structural_engineering_plot_structural_engineering_benchmark.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_structural_engineering_plot_structural_engineering_benchmark.py:


Buckling and effective length
=============================

For an ideal elastic column the critical load scales as inverse length squared.
The pinned and cantilever curves differ through the effective length factor.

.. GENERATED FROM PYTHON SOURCE LINES 8-26



.. image-sg:: /api/gallery/structural_engineering/images/sphx_glr_plot_structural_engineering_benchmark_001.png
   :alt: plot structural engineering benchmark
   :srcset: /api/gallery/structural_engineering/images/sphx_glr_plot_structural_engineering_benchmark_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from engineeringkit.structural_engineering import euler_buckling_load

    length = np.linspace(0.5, 4, 100)
    fig, ax = plt.subplots()
    for K, label in [(1, "pinned"), (2, "cantilever")]:
        loads = [euler_buckling_load(200e9, 1e-6, L, K) for L in length]
        ax.plot(length, np.array(loads) / 1000, label=label)
    p1 = euler_buckling_load(200e9, 1e-6, 1)
    p2 = euler_buckling_load(200e9, 1e-6, 2)
    assert np.isclose(p1 / p2, 4)
    ax.set(xlabel="column length [m]", ylabel="critical load [kN]")
    ax.legend()

    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.103 seconds)


.. _sphx_glr_download_api_gallery_structural_engineering_plot_structural_engineering_benchmark.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../lite/lab/index.html?path=api/gallery/structural_engineering/plot_structural_engineering_benchmark.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_structural_engineering_benchmark.ipynb <plot_structural_engineering_benchmark.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_structural_engineering_benchmark.py <plot_structural_engineering_benchmark.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_structural_engineering_benchmark.zip <plot_structural_engineering_benchmark.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_