The relative displacement u(t) of a single-storey shear building subjected to an earthquakeground motion is represented by the following second-order linear ordinary differentialequation:d?udt2du+ c+ ku =a, (t)mdtwhere m, c, and k are the mass (kg), damping constant (Ns/m), and stiffness of thestructure (N/m), respectively. Meanwhile, a,(t) is the function of earthquake groundacceleration.Suppose the building with a mass of 2000 kg and supported by columns of combinedstiffness of 32 x 103 N/m is subjected to earthquake with ground acceleration given by thefollowing function:ag(t)= 36000 cos 2tFind the equation of the displacement, u(t), given the damping is not installed to thebuilding. Then, find how much the building is displaced from t =30 seconds to t =60 secondsof earthquake.

Write the differential equation. md2udt2+cdudt+ku=36000cos2tif damping is not installed…

The relative displacement u(t) of a single-storey shear building subjected to an earthquake ground motion is represented by the following second-order linear ordinary differential equation: d2u du + c + ku : a,(t) m %3D dt2 dt where m, c, and k are the mass (kg), damping constant (Ns/m), and stiffness of the structure (N/m), respectively. Meanwhile, a,(t) is the function of earthquake ground acceleration.

The relative displacement u(t) of a single-storey shear building subjected to an earthquake ground motion is represented by the following second-order linear ordinary differential equation: d2u du + c + ku : a,(t) m %3D dt2 dt where m, c, and k are the mass (kg), damping constant (Ns/m), and stiffness of the structure (N/m), respectively. Meanwhile, a,(t) is the function of earthquake ground acceleration.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Concept explainers

Properties of Fluids

The term fluid represents a type of substance that can easily change its shape under any external pressure/force and can flow. Fluids can acquire any shape in which it is stored and can resist normal stresses but cannot resist shear stress in rest condition. Whenever external shear stress is applied to fluids, it starts to flow. The fluids may be liquid or gas. Example- water, air, etc.

Question

The relative displacement u(t) of a single-storey shear building subjected to an earthquake
ground motion is represented by the following second-order linear ordinary differential
equation:
d?u
dt2
du
+ c
+ ku =
a, (t)
m
dt
where m, c, and k are the mass (kg), damping constant (Ns/m), and stiffness of the
structure (N/m), respectively. Meanwhile, a,(t) is the function of earthquake ground
acceleration.
Suppose the building with a mass of 2000 kg and supported by columns of combined
stiffness of 32 x 103 N/m is subjected to earthquake with ground acceleration given by the
following function:
ag(t)
= 36000 cos 2t
Find the equation of the displacement, u(t), given the damping is not installed to the
building. Then, find how much the building is displaced from t =30 seconds to t =60 seconds
of earthquake.

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