2. For the 3-story structure shown, the roof and floor are rigid diaphragms. The lateral force resisting system consists of 8 identical one-bay exterior braced frames (i.e., 4 frames each direction). The braced frames are analyzed as a vertical truss. Building envelop is 0.5 m from the closest perimeter column line. The area of one floor is (46 m x 28 m) = 1288 m². The specified gravity loads are given in the table below, where self-weights of the structural members are already included in the Dead Load. The weight of the building envelop is 2.0 kPa. There is no parapet wall on roof. Building important category is normal (i.e., important factor is $I = 1.0$).
Table: Specified Gravity Loads (kPa)
Location Dead Load Live Load Snow Load
Roof 2.8 1.0 3.2
Floor 4.5 4.8 0
For the eigenvalue problem (i.e., the vibration frequencies and vibration modes of the building under a lateral ground motion)
(1) write the mass matrix according to National Building Code of Canada 2015.
(2) obtain the corresponding stiffness matrix.
(3) find the natural periods and vibration modes.
Use of online calculators such as Wolframalpha.com is allowed.
4 m x 3 = 12 m
F<sub>y</sub>=345 MPa (50 ksi) for steel
