Problems (10 points each)
Problem 1
The simple frame shown in the figure shown below is subjected to a harmonic base motion. The
base motion results on a harmonic force equivalent to P = 130 sin(160 t) applied to the structure.
The units for the amplitude of loading are in kN and the circular frequency in rad/sec. The entire
frame structure weighs 2500 kN. The frame has a stiffness of 230 kN/m and the damping ratio of
0.15 in the lateral direction.
Determine the following:
a) Damping coefficient
b) Damped natural frequency
c) The amplitude of the steady-state response
d) If the base motion (earthquake) stops at amplitude (item c)…
What is the displacement amplitude after 5 cycles?
Problem 2
A foundation weighs 800 kN. The foundation and the soil can be approximated as a mass-springdashpot
systems as shown in the figure below. Given that the spring constant = 200,000kN/m and
the dashpot = 2340 kN-m/s, determine the following:
a) Critical damping coefficient
b) Damping Ratio
c) Logarithmic decrement
d) Damped natural frequency
P

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