.. _auto_math_flexural_modulus:

*COMPUTE FLEXURAL MODULUS*
==========================

Computes the flexural (bending) modulus of a specimen from a three-point bend test using the standard formula E = P·L³ / (4·b·d³·y). Use this worker when deriving stiffness from coupon-level flexural test data.

When to use
-----------

Classification: **process**.

Tagged: ``bending``, ``coupon``, ``flexural_modulus``, ``mechanical_testing``, ``stiffness``, ``three_point_bend``.

Inputs
------

.. list-table::
   :header-rows: 1
   :widths: 20 20 20 20 20 20

   * - Label
     - ID
     - Type
     - Default
     - Required
     - Description
   * - Load Value
     - loadvalue
     - scalar
     - 1
     - ✓
     - Applied maximum load P at mid-span (force units, e.g. N or lbf); default 1 — must be replaced with the measured peak load from the test.
   * - Specimen Length Span
     - specimenlengthspan
     - float
     - 1
     - ✓
     - Support span length L between the two outer supports (length units, e.g. mm or in); default 1 — set to the actual gauge span used in the bend fixture.
   * - Specimen Width
     - specimenwidth
     - float
     - 1
     - ✓
     - Cross-sectional width b of the specimen (length units, e.g. mm or in); default 1 — set to the measured coupon width.
   * - Specimen Thickness
     - specimenthickness
     - float
     - 1
     - ✓
     - Cross-sectional thickness d of the specimen (length units, e.g. mm or in); default 1 — set to the measured coupon thickness; enters the formula cubed so accuracy is critical.
   * - Deflection
     - deflection
     - float
     - 1
     - ✓
     - Mid-span deflection y corresponding to the applied load P (length units, e.g. mm or in); default 1 — set to the deflection value measured at the load point.

Outputs
-------

.. list-table::
   :header-rows: 1
   :widths: 20 20 20 20

   * - Label
     - ID
     - Type
     - Description
   * - math_flexural_modulus_output_1
     - math_flexural_modulus_output_1
     - scalar
     - Computed flexural modulus E = P·L³ / (4·b·d³·y) returned as a scalar in the same consistent force/length² units derived from the inputs (e.g. MPa if inputs are N and mm).

Disciplines
-----------

- engineering.material.characterization
- engineering.material.specimen

Runnable example
----------------

A runnable example is registered for this worker. Open the example workflow on the d3VIEW canvas: `/api/workflow/example?id=math_flexural_modulus <https://www.d3view.com/api/workflow/example?id=math_flexural_modulus>`_

.. raw:: html

   <hr style="margin-top:2em">
   <p style="font-size:11px;color:#888">
   Auto-generated from <code>transformation</code> schema. Worker id: <code>math_flexural_modulus</code>. Schema hash: <code>14738391fbe4</code>. Hand-curated docs in <code>workerexamples/</code> override this page when present.
   </p>