Trusses - FE Formulation (+ Mathcad)

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00:45 - Review of trusses/frames
01:58 - Direct stiffness method applied to two-force members
03:31 - Introduction to global and local coordinate systems
04:07 - Coordinate system notation & Trig relationships (displacement and force)
07:41 - Introduction of transformation matrix

Element Stiffness Matrix
09:18 - Initial development
10:54 - Converting from local to global coordinates

Example
14:38 - Problem description
15:28 - Step 1: Determining Nodes and Elements (and angles!)
17:35 - Step 2: Assume a solution that approximates the behavior of an Element
18:00 - Step 2 (Mathcad)
19:39 - Step 3, part 1: Develop equations for Elements
21:13 - Step 3, part 1 (Mathcad)
24:30 - Step 3, part 2: Convert Element stiffness matrices from local to global coordinate system
27:16 - Step 3, part 2 (Mathcad)
33:04 - Step 4: Assemble global stiffness matrix
34:36 - Step 4 (Mathcad)
35:40 - Step 5: Apply the boundary conditions and loads
37:37 - Step 5 (cont): the boundary condition (BC) matrix
38:24 - Step 6: Solve algebraic equations
38:35 - Step 5 & Step 6 (Mathcad)
42:28 - Step 7: Obtain other information - Reaction forces
43:24 - Step 7 - Reaction forces (Mathcad)
44:09 - Step 7: Obtain other information - Internal forces and normal stresses

While I don't discuss how to do the last step in Mathcad, I have added the steps for one element to the Mathcad file.