Determine the Vertical Deflection Case Study - Engineering Assignment Help

Assignment Task:

Task:

QUESTION 1 (150 marks, allow 30 minutes) A cantilever AB is loaded as shown in Figure 1. EI is constant for the beam. (a) Using the moment area method, determine the slope at B. (75 marks) (b) Using the conjugate beam method, determine the vertical deflection at B. (75 marks) Figure 1 CIV3505 – Structural Analysis Page 2 of 12 Examination Period - Semester 1, 2017

QUESTION 2 (150 marks, allow 30 minutes) A frame ABC is supported and loaded as shown in Figure 2. A is rocker support, C is a fixed support, and B is a rigid (ie. fixed connected) joint. EI is constant. (a) To what degree is this structure indeterminate? (15 marks) (b) If the support at A is removed, what is the vertical deflection at free end A? (Hint : Use virtial work method). (75 marks) (c) When the support at A is present, determine all support reaction components at A and C (including moment at C). (Hint : Use force method with vertical reaction at A as redundant). (40 marks) (d) For the situation in part (c) above, draw the bending moment diagram for AB part. (20 marks) Figure 2 CIV3505 – Structural Analysis Page 3 of 12 Examination Period - Semester 1, 2017

QUESTION 3 (150 marks, allow 30 minutes) (a) A beam ABC is loaded as shown in Figure 3. Assume A is a fixed support. B and C are roller supports that can either push or pull on the beam. EI is constant. Figure 3 i. Determine the fixed end moments for segments AB and BC. (20 marks) ii. Solve for moments at A, B and C using the moment distribution method. (40 marks) iii. Calculate all the reactions at the supports. (25 marks) iv. Draw the bending moment diagram for the beam on the compression fibre side showing the salient values. (25 marks) (b) Explain the basic concept of the finite element method. State the advantages of finite element method. Limit your answer to two sides of an A4 size page. (40 marks) CIV3505 – Structural Analysis Page 4 of 12 Examination Period - Semester 1, 2017

QUESTION 4 (150 marks, allow 30 minutes) The truss in Figure 4 is loaded as shown. Assume cross-sectional area A = 0.0015 m2 and E = 200 GPa for all the members. (a) Determine the stiffness matrices of the truss members 1, 4 and 5 in the global co-ordinate system with the origin at node 1 (clearly indicate the corresponding degrees of freedom numbers in the matrices). (60 marks) (b) Determine the load vector (Q) and displacement vector (D) and write the load-displacement relationship for the entire truss in the global co-ordinate system. Assume that the global stiffness matrix is denoted by K. Assembly of the global stiffness matrix K is not required. (50 marks) (c) Assuming that the solution of the problem gives, D3 = -106.67/106 m, D4 = -420/106 m, and D5 = -213.33/106 m, calculate the force in member 4. Clearly indicate whether the force is a tension or compression.

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