Rigid Support Rigid Roof Equal Stiffness Columns Rigid Support

The single-story structure show below is being analyzed for dynamic behavior. The following experimental
data was measured from the structure:
• Under a horizontal static roof load of 10 kips, the structure displaced 0.5 inches horizontally.
• When the horizontal static roof load was released, it took 0.7 seconds for the structure to complete
one cycle of motion.
• After 4 cycles the peak displacement amplitude was 50% of the horizontal static displacement.
1. Calculate the horizontal stiffness, effective roof mass, and damped natural frequency of the structure.
2. Determine the damping ratio and undamped natural frequency for the structure.
3. The building is subject to vortices from wind in the direction of the horizontal static roof load. The
vortices apply a sinusoidal load of:
P(t) = 10 × sin(7t) [P(t) in kips, t in seconds]
Determine the amplitude of the steady state response and the damped dynamic amplification factor for
the wind loading.
4. Plot the displacement response of the structure under damped free vibration and under wind loading
on the same chart for 25 seconds.