Answer Happy

Consider the 2-storey shear building in Figure Q4. It may be approximated as a two degree of freedom system with all mass located at floor levels with columns assumed to provide lateral stiffness. You may assume that the stiffness provided by a single column is given by 12E1 ke 13 where the flexural rigidity El = 20.25 x 106 Nm and L is the column height indicated on Figure Q4. (a) If me = 20,000 kg and m2 = 25,000 kg, determine the natural frequencies of the structure. (10 marks) (b) Determine and sketch the ratio of mode shape ordinates for each mode. (5 marks) (c) How would you prove that the mode shapes are orthogonal and how is this useful for further dynamic analysis of the structure? Note, do not perform the calculations to prove orthogonality, discuss only. (5 marks) (d) Damping information was not provided in this question. How would appropriate damping characteristics typically be determined at the design stage? (5 marks) m2 2.5 m 3 m Figure Q4