Beams - FE Formulation (+ Mathcad)

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00:45 - Review of beams
01:22 - Governing equations

FE Formulation
05:19 - Assumed deflection equation
06:07 - Shape functions
07:14- Element Stiffness Matrix developed using the Strain Energy equation
09:23 - Load Matrix developed from reaction forces
15:30 - Equivalent Nodal Loadings

Example
15:59 - Problem description
16:40 - Step 1: Determining Nodes and Elements
Step 2: Assume a solution (done in previous section)
Step 3, part 1: Develop equations for Elements (done in previous section)
17:37 - Step 3, part 2: Determine numerical form of element stiffness matrix
18:11 - Step 3, part 2 (Mathcad, with explanation about UNITS)
21:17 - Step 4: Assemble global stiffness matrix
21:53- Step 4 (Mathcad)
24:21 - Step 5, part 1: Determine and apply the loads
25:26 - Step 5, part 1 (Mathcad)
27:10 - Step 5, part 2: Apply boundary conditions
27:47 - Step 5, part 2 (Mathcad)
28:42 - Step 6: Solve algebraic equations
29:49 - Step 6 (Mathcad)
30:06 - Step 7: Obtain other information - Reaction forces
30:39 - Step 7 (Mathcad)