Codes
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United States
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Longitudinal Stress Due to Pressure - |S_lp|

|S_lp| = P |D_o| / 4 |t_n|                  [Approximation]

|S_lp| = P |D_i2| / (|D_o2| - |D_i2|)       [Exact Formulation]

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Equation                                            Allowable                                           Stress Type
=================================================== =================================================== ===========
**B31.1** (1967)
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|S_l| = |S_lp| + (|S_b2| + 4 |S_t2|)\ :sup:`1/2`    < |S_h|                                             Sustained

(|S_b2| + 4 |S_t2|)\ :sup:`1/2`                     < f[1.25 |S_c| + 0.25 |S_h| + (|S_h| - |S_l|)]      Expansion

|S_lp| + (|S_b2| + 4 |S_t2|)\ :sup:`1/2`            < k |S_h|                                           Occasional

Under Construction!
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=================================================== =================================================== ===========

Where:

* |A_m| - Cross-sectional metal area in pipe.
* |D_o| - Outer pipe diamter
* |D_i| - Inner pipe diamter
* |t_n| - Pipe nominal thickness

* P - Pressure

* |S_lp| - Longitudinal pressure stress
* |S_l| - Longitudinal stress (pressure + bending)
* |S_b| - Bending stress
* |S_t| - Torsional stress

* |S_h| - Material hot allowable stress
* |S_c| - Material cold allowable stress

* E - Material Young's Modulus
* f - Fatigue cycle reduction factor
* k - Cumulative usage factor


International
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Under Construction!

.. Geometry substitutions
.. |A_m| replace:: A\ :sub:`m`
.. |D_o| replace:: D\ :sub:`o`
.. |D_o2| replace:: |D_o| :sup:`2`
.. |D_i| replace:: D\ :sub:`i`
.. |D_i2| replace:: |D_i| :sup:`2`
.. |t_n| replace:: t\ :sub:`n`

.. Stresses
.. |S_lp| replace:: S\ :sub:`lp`
.. |S_b| replace:: S\ :sub:`b`
.. |S_b2| replace:: |S_b| :sup:`2`
.. |S_t| replace:: S\ :sub:`t`
.. |S_t2| replace:: |S_t| :sup:`2`
.. |S_l| replace:: S\ :sub:`l`

.. Allowables
.. |S_h| replace:: S\ :sub:`h`
.. |S_c| replace:: S\ :sub:`c`
.. |S_y| replace:: S\ :sub:`y`
.. |S_u| replace:: S\ :sub:`u`

.. Moments
.. |M_a| replace:: M\ :sub:`a`
.. |M_b| replace:: M\ :sub:`b`
.. |M_c| replace:: M\ :sub:`c`