This example intends to go over the general process for solving an FEA problem including frame elements. Symmetry is also covered in this example. Note that values are not provided in order to simplify the video - it is long enough as is!
0:00 - Introduction and problem description
0:35 - General solution process and equivalent symmetric model
3:08 - Elemental stiffness matrix equations - setting up the table of entries
5:52 - Elemental stiffness matrix equations in the elemental CSYS
7:48 - Elemental transformation matrix for frame elements
9:32 - Elemental stiffness matrix equations in the global CSYS
10:45 - Assembling the global stiffness matrix equation
12:10 - Applying constraints to create the reduced stiffness matrix equation
13:21 - Creating work equivalent loads
14:53 - Solving for displacements
15:40 - Using displacements to solve for reactions
16:57 - Solving for elemental loads
19:07 - Example values to plot elemental axial, shear, moment diagrams
20:46 - Reflection questions
Suggested answers to reflection questions
1.) It's almost exactly the same! The only addition is to transform moments/rotations. However, since the problem is 2D, all rotations are about the same axis and therefore moments and rotations are the same in both the global and elemental coordinate systems.
2.) Work equivalent loading! It is easiest to look up a table for basic uniform, triangular, and/or trapezoidal type distributed loads. See • Work equivalent loadin...
3.) First apply displacements to elemental stiffness matrix equations, being sure to use the transformation matrix so that results will be in the elemental coordinate system. Then compare positive nodal directions with positive elemental directions. Apply sign changes as necessary when drawing the diagrams.
4.) Apply an end-release for the rotational DOF at node 2 for element 2. See
• End Releases in Frame ...