Q2 DYNAMIC ANALYSIS Consider the following, lightly damped, two storey structure shown in figure Q2(a). All the structur

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Q2 Dynamic Analysis Consider The Following Lightly Damped Two Storey Structure Shown In Figure Q2 A All The Structur 1 (74.36 KiB) Viewed 14 times

Q2 DYNAMIC ANALYSIS Consider the following, lightly damped, two storey structure shown in figure Q2(a). All the structural masses are lumped at the floor levels, and the floor beams are presumed to be rigid. The total storey sway stiffness is k for each storey. The first floor beam is to support rotating machinery. After adding this machinery (figure Q2(b)) it is determined that the circular frequency of the rotating machinery and the second mode frequency of the structure coincide, producing a danger of resonance. To avoid this problem, a consultant proposes that the total sway stiffness of the second story be increased from k to Bk where ß > 1. This is achieved by the introduction of bracing (figure Q2(c)). m m m Rotating machinery k k Bk DOOR 2m m 2m k k k (b) (c) Original Structure + Structure + Structure Machinery Machinery + Bracing Figure Q2, two storey shear structure (a) By determining the mass and stiffness matrices of the braced shear building (figure Q2(c)) and by solving the eigenvalue problem, derive an equation for the first and second circular modal frequencies in terms of k, m and B. (20 marks) (b) If the first modal undamped period is 0.2s (for the original building figure Q2(a)) what is the likely rotating frequency of the machinery? (10 marks) (c) To avoid resonance between the second model of the structure and the frequency of the machinery, what value of bracing stiffness factor B is required to increase the second modal frequency by 50%? (10 marks) (d) Determine the first modal frequency of the braced shear building Q2(c) for this value of determined in Q2 part (c). Discuss whether there is any problem with this new value of the first modal frequency? (10 marks)