## Element stiffness matrices, Mechanical Engineering

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Use three frame elements to analyse the frame structure as depicted in the image below subjected to combined loadings: a) a concentred load applied  on Element 1  at  its  1/3 length close to point B; and b) a uniformly-distributed loading applied on Element 2. The two beams are of identical material properties and cross-section as well as the same height of 2 in.

(a) 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 whole model;
• the global nodal displacement vector for whole model;
• the global nodal force vector for whole model;
• the boundary conditions in the system;
• the condensed matrix equations for the unknown displacements when applying the above-mentioned boundary conditions;
• the unknown displacements;
• the reaction forces and moments; and
• the maximum stress in each element.

(b) Run two static analyses of this problem by using ANSYS APDL  or SolidWorks Simulation with 1) the same FE model done in a) and 2) use a three-element model by splitting Element 1 into two appropriately. Compare these numerical results obtained with those from hand calculation or spreadsheet done in (a) and write a short FEA report to summarize your analyse on this problem.

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