… for extension

The differential equation for equilibrium relations for extension is based on the infinitesimal small loaded bar:

leading to :

\[{q_x} = - \frac{{{d}N}}{{{d}x}}\]

This is treated in chapter 11.1 of the book Engineering Mechanics Volume 1 (Hartsuijker and Welleman, 2006).

Instructions from lecture

This topic is presented in a lecture available from 1:31:00 - 1:35:40 here for TU Delft students