Beam Finite Element Method:

Design the finite element model of the beam subjected to combined loading by using the minimum number of Euler-Bernoulli beam elements as shown in the image below? Let E = 30 × 106 psi, L = 10 in, qo = 5 lb/in and P = 1 lb. The beam is of a square cross-section
of 1.0 × 1.0 inches.  

In FEA, use hand calculation or MS Excel Spreadsheet to determine:

• the element stiffness matrices for each element;
• the element nodal displacement vector for each element;
• the element nodal force vector for each element;
• the assembled global stiffness matrices for the system;
• the global nodal displacement vector for the system;
• the global nodal force vector for the system;
• the boundary conditions in the system;
• the condensed matrix equations for the unknown displacements when applying the above-mentioned boundary conditions;
• the unknown displacements;