… for extension

The differential equation for kinematic relations for extension is based on a displaced the infinitesimal small beam:

leading to :

\[{\epsilon} = - \frac{{{d}u}}{{{d}x}}\]

This is treated in chapter 2.2.1 of the book Engineering Mechanics Volume 2 (Hartsuijker and Welleman, 2007).

Instructions from lecture

This topic is presented in a lecture available from 1:24:50 - 1:31:00 here for TU Delft students