CEEGR 5120 Earthquake Dynamics of Structures Project Assignment

The 6-storey building is part of an industrial facility. Study the response of the building to the N-S component of the recorded accelerations at El Centro, 1940. Consider the response in the direction shown in the figure. Damping for the system was estimated as ? = 5% of critical. All girders of the structure have width b = 0.40 m and depth h = 0.50 m. All columns have square sections with a cross section dimension h = 0.50 m. The material of the structure has a modulus of elasticity E = 25 GPa. The self-weight of structure plus additional dead load is 780 kg/m² and the industrial machinery, which is firmly connected to the building slabs, increases the mass per unit area by 1000 kg/m² for a total mass per unit area of 1780 kg/m² .

LATERAL FRAME STIFFNESS: A rigid diaphragm scheme is employed; therefore, the frames in the direction of ground acceleration will have compatible lateral displacements. Since the three frames in that direction have the same properties, once the lateral stiffness of one frame is obtained it should be multiplied by three to obtain the lateral stiffness of the whole structure in the direction of interest. The frame stiffness matrix is modified to eliminate any axial deformations of the girders (to comply with the rigid diaphragm condition), and the vertical deformations and joint rotations are condensed. After performing all these operations, the lateral-load stiffness matrix of the structure in the direction of the ground acceleration in kN/m is:

a) Report the first 6 mode shapes and corresponding mode frequencies for the structure. A sample presentation format is given below.

b) Write down the 6 uncoupled equations of motion in modal coordinates calculated using Python. A sample presentation format is given below. Note that the applied force is not a harmonic force hence in your equations there will not be any sine terms.

c) Present modal response plots for each mode. The plots should be presented separately as well as together in a single graph (for comparison).

d) Present the structural response plots for each mode. The plots should be presented separately as well as together in a single graph (for comparison).

e) Find the modal displacements in meters contributed by each mode at time t=3.08 second (Yt=3.08 for modes 1-6). Present the results in a Table.

f) Find the structural displacements in meters contributed by each mode at time t=3.08 second (ut=3.08 for modes 1-6). Present the results in a Table.

g) Find the forces imposed by the ground motions at the same instant t = 3.08 s

h) Calculate the total base shear at t=3.08s

i) Calculate the total overturning moment at t=3.08s

j) Plot the total roof displacement history (mass 6)

k) Plot the total base shear history. Find the max value for the base shear.

l) Plot the total overturning moment history. Find the max value for the overturning moment.