Скачать или смотреть Derivation of the beam stiffness matrix for finite element analysis

The purpose of this video is to demonstrate how the stiffness matrix for a beam element (transverse and rotational directions) is derived from its displacement function and the equation of the elastic curve.

0:00 - Introduction and review of displacement function for a beam element
0:43 - Review of shape functions for a beam element
1:58 - How the equation of the elastic curve is used to generate four equations for the beam's stiffness matrix
4:53 - Solving the four equations
6:58 - The beam stiffness matrix equation
7:27 - Reflection questions

Answers to reflection questions
1.) The lateral (and bending) stiffness of a line element almost always matters. The only time it does not matter is in the case of two force members that have joints/hinges at either side.

2.) Equation of the elastic curve

3.) The difference between what is considered positive for nodal forces/moments and what is considered positive for elemental shear/bending