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