Consider the beam structure shown in Figure 2. The figures below show the side view and...

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Consider the beam structure shown in Figure 2. The figures below show the side view and front view of a steel cantilever beam structure (not to scale). The beam has three different cross-sections. Use beam finite element formulation discussed in class to determine the deformed shape, including vertical displacement and rotation. Also determine the reaction force, and the reaction moment at the fixed support location (x = 0). F L 1 2L 2 Q Side view Geometric and Material Properties: L= 5 m F = 100 N (applied at the end of section 2) Q = 30 N/m L 3 Figure 2: Steel cantilever beam structure M = 2000 N*m (applied at the end of section 3) E = 200 GPa M Section 1 (left side): Square cross section with sides of 100 mm Section 2 (center): Circular cross section with radius of 30 mm Section 3 (right side): Circular cross section with radius of 15 mm Front view Split beam 1 and beam 3 into 4 equal-length elements each; split beam 2 into 8 equal-length elements. The entire cantilever should have 16 elements in total. Number nodes of the beam from the left to the right, there are 17 nodes in total. a. What is the area moment of inertia about the beam neutral axis (z-direction, according to right-hand- rule) for each beam cross section? b. Using MATLAB, determine the overall global stiffness matrix Kg and the reduced stiffness matrix Kr. What is the matrix 2-norm of the global stiffness matrix Kg? What is the condition number of reduced stiffness matrix Kr? Hints: see MATLAB functions "norm" and "cond". You do not need to print the full matrices. c. Determine the displacements and rotations at each node. d. Plot the vertical deflection versus the length. e. Plot the rotation angle in degrees versus the length. f. Calculate the reaction force and moment at the fixed end. Consider the beam structure shown in Figure 2. The figures below show the side view and front view of a steel cantilever beam structure (not to scale). The beam has three different cross-sections. Use beam finite element formulation discussed in class to determine the deformed shape, including vertical displacement and rotation. Also determine the reaction force, and the reaction moment at the fixed support location (x = 0). F L 1 2L 2 Q Side view Geometric and Material Properties: L= 5 m F = 100 N (applied at the end of section 2) Q = 30 N/m L 3 Figure 2: Steel cantilever beam structure M = 2000 N*m (applied at the end of section 3) E = 200 GPa M Section 1 (left side): Square cross section with sides of 100 mm Section 2 (center): Circular cross section with radius of 30 mm Section 3 (right side): Circular cross section with radius of 15 mm Front view Split beam 1 and beam 3 into 4 equal-length elements each; split beam 2 into 8 equal-length elements. The entire cantilever should have 16 elements in total. Number nodes of the beam from the left to the right, there are 17 nodes in total. a. What is the area moment of inertia about the beam neutral axis (z-direction, according to right-hand- rule) for each beam cross section? b. Using MATLAB, determine the overall global stiffness matrix Kg and the reduced stiffness matrix Kr. What is the matrix 2-norm of the global stiffness matrix Kg? What is the condition number of reduced stiffness matrix Kr? Hints: see MATLAB functions "norm" and "cond". You do not need to print the full matrices. c. Determine the displacements and rotations at each node. d. Plot the vertical deflection versus the length. e. Plot the rotation angle in degrees versus the length. f. Calculate the reaction force and moment at the fixed end.