Examples
========

The following examples showcase the features of ``sStatics`` in an
instructional manner, while also highlighting several validation tests and advanced
applications.

Cross-Section
-------------

.. nbgallery::
    :name: cross-section-gallery
    :maxdepth: 1

    examples/01_cross_section/rectangle_cross_section
    examples/01_cross_section/beam_slab_cross_section
    examples/01_cross_section/ipe_cross_section


First Order
-----------

.. image:: images/structural_diagramms/firstorder_diagramm.svg
    :width: 600px
    :align: center

.. nbgallery::
    :name: first-order-gallery
    :maxdepth: 1

    examples/02_firstorder/01_bending_moment
    examples/02_firstorder/02_bar_deflection
    examples/02_firstorder/03_bending_line
    examples/02_firstorder/04_unstable_system
    examples/02_firstorder/05_divided_bar

Second Order
------------

.. image:: images/structural_diagramms/second_order_diagramm.svg
    :width: 600px
    :align: center

.. nbgallery::
    :name: second-order-gallery
    :maxdepth: 1

    examples/03_second_order/04_compare_results
    examples/03_second_order/second_order_bar_second
    examples/03_second_order/second_order_iteration

Pole Plan
---------

.. nbgallery::
    :name: poleplan-gallery
    :maxdepth: 1

    examples/04_poleplan/poleplan_basic
    examples/04_poleplan/poleplan_advanced

Stress
------

.. nbgallery::
    :name: stress-gallery
    :maxdepth: 1

    examples/05_stress/normal_stress
    examples/05_stress/plot_normal_stress
    examples/05_stress/shear_stress
    examples/05_stress/plot_shear_stress
    examples/05_stress/stress_disc
    examples/05_stress/stress_t_cs

Influence Line
--------------
.. image:: images/structural_diagramms/influence_line_diagramm.svg
    :width: 600px
    :align: center

.. nbgallery::
    :name: influence-line-gallery
    :maxdepth: 1

    examples/06_influence_line/influence_line_deform_bar_w
    examples/06_influence_line/influence_line_deform_node_w
    examples/06_influence_line/influence_line_fm_bar
    examples/06_influence_line/influence_line_fz_node
    examples/06_influence_line/influence_line_fm_bar_unstable
    examples/06_influence_line/influence_line_fz_node_unstable

Principle of Virtual Forces
---------------------------
This section introduces the Principle of Virtual Forces (PVF) as a general
method for computing structural deformations.

The first diagram shows how the different static calculation methods are
related.
The second diagram focuses specifically on the class structure of the PVF-based
methods.

.. image:: images/structural_diagramms/structural_diagramm_static_methods.svg
    :width: 800px
    :align: center

The PVF class serves as the base class for all subsequent methods.
The Reduction Theorem inherits from PVF, the Force Method inherits from
Reduction Theorem, and DMG extends the Force Method.
This inheritance structure allows shared functionality while progressively
adding method-specific behavior.

.. image:: images/structural_diagramms/pvf_diagramm.svg
    :width: 500px
    :align: center

.. nbgallery::
    :name: principle-of-virt-forces-gallery
    :maxdepth: 1

    examples/07_principle_of_virtual_forces/01_pvf_basic
    examples/07_principle_of_virtual_forces/02_pvf_relative_rotation
    examples/07_principle_of_virtual_forces/03_pvf_spring_support
    examples/07_principle_of_virtual_forces/04_pvf_temp_support_disp

Reduction Theorem
-----------------

.. image:: images/structural_diagramms/reductiontheorem_diagramm.svg
    :width: 600px
    :align: center

.. nbgallery::
    :name: reduction-theorem-gallery
    :maxdepth: 1

    examples/08_reduction_theorem/01_red_calc_deformation
    examples/08_reduction_theorem/03_red_large_system_deformation


Force Method
------------

.. image:: images/structural_diagramms/forcemethod_diagramm.svg
    :width: 600px
    :align: center

.. nbgallery::
    :name: force-method-gallery
    :maxdepth: 1

    examples/09_force_method/01_force_method_basic