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Question 4 (25 Marks) The structure to be analysed is a two-story steel frame (which is part of a multi-frame building) shown in figure for question 4. The second level columns are rigidly connected to the floors (i.e. fixed-fixed). The first level columns are rigidly connected to the floor and have pinned base connection (i.e. fixed-pinned). The weights of the floors and walls are indicated in the figure and are assumed to include the structural self-weight. No damping is considered. The building consists of a series of frames spaced 5m apart. The structural properties are uniform along the length of the building, hence the analysis to be made of an interior frame yields the response of the entire building. W, = 2 kN/m U2 1 kN/m 3 m W, = 4 kN/m? M] 5 1kN/m? 4 m 10m Figure for question 4 - two-storey shear building frame Moment of inertia, 1, of each column considering direction of vibration (lateral) is as follows: Level 1: 350*106 mm Level 2: 50*106 mm Elastic modulus of steel is E=205 GPa; gravitational acceleration is g=9.8 m/Sec? Determine the following parameters for this two-storey frame: a) Seismic mass of level 1, mi, and level 2, m2 (in ton). b) Lateral stiffness of level 1, K2, and level 2, Kz (in kN/mm). c) Natural angular frequency wi (in rad/sec), natural frequency fi (in Hz), and natural period T: (in Sec) of first (i=1) and second (i=2) modes of vibration of building. d) Draw the mode shapes associated with w, and w, and label the amplitudes of level 1 (=1.0) and level 2 on each. Question 4 (25 Marks) The structure to be analysed is a two-story steel frame (which is part of a multi-frame building) shown in figure for question 4. The second level columns are rigidly connected to the floors (i.e. fixed-fixed). The first level columns are rigidly connected to the floor and have pinned base connection (i.e. fixed-pinned). The weights of the floors and walls are indicated in the figure and are assumed to include the structural self-weight. No damping is considered. The building consists of a series of frames spaced 5m apart. The structural properties are uniform along the length of the building, hence the analysis to be made of an interior frame yields the response of the entire building. W, = 2 kN/m U2 1 kN/m 3 m W, = 4 kN/m? M] 5 1kN/m? 4 m 10m Figure for question 4 - two-storey shear building frame Moment of inertia, 1, of each column considering direction of vibration (lateral) is as follows: Level 1: 350*106 mm Level 2: 50*106 mm Elastic modulus of steel is E=205 GPa; gravitational acceleration is g=9.8 m/Sec? Determine the following parameters for this two-storey frame: a) Seismic mass of level 1, mi, and level 2, m2 (in ton). b) Lateral stiffness of level 1, K2, and level 2, Kz (in kN/mm). c) Natural angular frequency wi (in rad/sec), natural frequency fi (in Hz), and natural period T: (in Sec) of first (i=1) and second (i=2) modes of vibration of building. d) Draw the mode shapes associated with w, and w, and label the amplitudes of level 1 (=1.0) and level 2 on each