… for bending

# Matplotlib compatibility patch for Pyodide
import matplotlib
if not hasattr(matplotlib.RcParams, "_get"):
    matplotlib.RcParams._get = dict.get

… for bending#

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

../../../../../_images/drawing.svg

leading to :

\[{\varphi} = - \frac{{{{d}}w}}{{{{d}}x}}\]

and

../../../../../_images/drawing2.svg

leading to :

\[{\kappa} = \frac{{{{d}}\varphi}}{{{{d}}x}}\]

This is treated in chapter 4.3.1 of the book Engineering Mechanics Volume 2 (Hartsuijker and Welleman, 2007).

Instructions from lecture#

This topic is presented in a lecture available from 1:32:00 - 1:38:00 here for TU Delft students.

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