.. _sphx_glr_api_gallery_structural_engineering_members:

Members
-------

Axial bars and twisted shafts.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="In 1676 Robert Hooke published an anagram, ceiiinosssttuu, and in 1678 its solution, ut tensio, sic vis: &quot;as the extension, so the force&quot;. Springs, wires and wooden rods all stretched in proportion to the weight hung on them. Written for a bar of length L, area A and modulus E (Young&#x27;s, 1807), the extension is \delta = PL/(AE) (~engineeringkit.structural_engineering.axial_deformation) and the stored energy is the triangle under the load-extension line, U = P\delta/2 = P^2L/(2AE) (~engineeringkit.structural_engineering.strain_energy_axial). The example repeats Hooke&#x27;s experiment on a steel wire and checks both.">

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  .. image:: /api/gallery/structural_engineering/members/images/thumb/sphx_glr_plot_01_hooke_axial_thumb.png
    :alt:

  :doc:`/api/gallery/structural_engineering/members/plot_01_hooke_axial`

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      <div class="sphx-glr-thumbnail-title">Hooke's law: ut tensio, sic vis (1678)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Charles-Augustin Coulomb (1784) hung a weight on a thin wire, twisted it and timed the oscillations. The restoring torque was proportional to the angle of twist, to the fourth power of the wire&#x27;s diameter and inversely to its length, which in modern form is \phi = TL/(GJ) with J = \pi d^4/32 (~engineeringkit.structural_engineering.torsion_angle). The same torsion balance later weighed the electric force and, in Cavendish&#x27;s hands, the Earth. The example simulates Coulomb&#x27;s pendulum and recovers the shear modulus from the period, then shows the shear stress across the wire (~engineeringkit.structural_engineering.torsion_shear_stress).">

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  .. image:: /api/gallery/structural_engineering/members/images/thumb/sphx_glr_plot_02_coulomb_torsion_thumb.png
    :alt:

  :doc:`/api/gallery/structural_engineering/members/plot_02_coulomb_torsion`

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      <div class="sphx-glr-thumbnail-title">Coulomb's torsion (1784)</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="A bar stretched along its axis gets thinner. Siméon Denis Poisson&#x27;s 1829 molecular theory of elasticity predicted that the lateral strain is always one quarter of the axial strain. Measurements soon showed that the ratio \nu depends on the material: about 0.3 for steel, nearly 0.5 for rubber and nearly zero for cork, which is why cork seals a wine bottle without jamming in the neck. The lateral strain is -\nu\varepsilon (~engineeringkit.structural_engineering.poisson_lateral_strain), so the volume changes by (1 - 2\nu)\varepsilon to first order: an incompressible material has \nu = 1/2.">

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  .. image:: /api/gallery/structural_engineering/members/images/thumb/sphx_glr_plot_03_poisson_ratio_thumb.png
    :alt:

  :doc:`/api/gallery/structural_engineering/members/plot_03_poisson_ratio`

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      <div class="sphx-glr-thumbnail-title">Poisson's ratio (1829)</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/structural_engineering/members/plot_01_hooke_axial
   /api/gallery/structural_engineering/members/plot_02_coulomb_torsion
   /api/gallery/structural_engineering/members/plot_03_poisson_ratio