1) Figure shows a thin Aluminium structural beam use in an aircraft structure.  Using the stiffness method,
determine the BM and Shear force of the two elements of the thin beam shown.  Also determine the
displacement at the loading point C.  Show the stiffness matrices for each member and assembled global stiffness
matrix.  Show your step by step solution.  Use a convenient method for the solution such as inverse matrices.   E=
80 GPa  (40 Marks)

2)  Perform a beam structural analysis using ANSYS for beam as: (30 Marks)
1.  Line bodies and  
2.  Surface bodies.    
For each case compare your results with the calculated values.  Compare the time taken to perform your manual
calculations and for the FEA analysis.  You need to show the beam's normal stress plot and a deflection plot.  
(Apply member weights with gravitational acceleration, g = 9.81 m/s²)

3)  Perform a beam modal analysis (vibration) using ANSYS for the beam as: 
1.  Line bodies and 
2.  Surface  bodies.  
List the first three natural frequencies and the mode shapes.  Compare your results for each case. You need to
comment on the difference between the results using line bodies and surface bodies (if there is any difference)