Answer to Question #147294 in Mechanical Engineering for Sebastian

Question #147294
The building is modeled as a single degree of freedom spring-mass system where the building mass is lumped atop of two beams used to model the walls of the building in bending. Assume the ground motion is modeled as having amplitude of 0.1 m at a frequency of 8 rad/s. Approximate the building mass by 500 kg and the stiffness of each wall by 2x10^6 N/m. Compute the magnitude of the deflection of the top of the
building.
1
Expert's answer
2020-12-07T03:47:31-0500

As here given building is single degree of freedom spring-mass system

So, we can write its equation of motion as

Now, here m=mass of building as given as 500kg,A= amplitude=0.1, and frequency= 8 rad/s

k=stiffnes=

Now, we will calculate natural frequency as

and frequency ratio

Now, for the maximum deflection of top of building we know that

So, the magnitude of deflection of top= 0.101 m


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