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Consider the simple model of a building subject to ground motion depicted in the figure below. The building is modelled as a single-degree-of-freedom mass-spring system, where the building mass is lumped atop two beams used to model the walls of the building in bending. Assume the ground motion is modelled as having amplitude of Y = in the horizontal direction at a frequency of w= 250 rad/s (y (t) = Y cos (wt)). Approximate the building mass as m = 2 x 10³ kg and the stiffness of each wall as k MN/m. Neglecting the damping and assuming zero initial conditions, determine the total amplitude response of the mass matt = 0.3s: x(1) m 1 0.20 mm -0.23 mm -0.05 mm -0.18 mm 0.15 mm k k -y(1)

Consider the simple model of a building subject to ground motion depicted in the figure below. The building is modelled as a single-degree-of-freedom mass-spring system, where the building mass is lumped atop two beams used to model the walls of the building in bending. Assume the ground motion is modelled as having amplitude of Y = in the horizontal direction at a frequency of w= 250 rad/s (y (t) = Y cos (wt)). Approximate the building mass as m = 2 x 10³ kg and the stiffness of each wall as k MN/m. Neglecting the damping and assuming zero initial conditions, determine the total amplitude response of the mass matt = 0.3s: x(1) m 1 0.20 mm -0.23 mm -0.05 mm -0.18 mm 0.15 mm k k -y(1)

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Consider the simple model of a building subject to ground motion depicted in the figure below. The building is modelled as a single-degree-of-freedom mass-spring system, where the building mass is lumped atop two beams used to model the walls of the building in bending. Assume the ground motion is modelled as having amplitude of Y = 1mm in the horizontal direction at a frequency of w= 250 rad/s (y (t) = Y cos (wt)). Approximate the building mass as m = 2 x 10³ kg and the stiffness of each wall as k = 10 MN/m. Neglecting the damping and assuming zero initial conditions, determine the total amplitude response of the mass mat t = 0.3 s: x(1) m Li y(1) 0.20 mm -0.23 mm -0.05 mm -0.18 mm 0.15 mm D
Transcribed Image Text:Consider the simple model of a building subject to ground motion depicted in the figure below. The building is modelled as a single-degree-of-freedom mass-spring system, where the building mass is lumped atop two beams used to model the walls of the building in bending. Assume the ground motion is modelled as having amplitude of Y = 1mm in the horizontal direction at a frequency of w= 250 rad/s (y (t) = Y cos (wt)). Approximate the building mass as m = 2 x 10³ kg and the stiffness of each wall as k = 10 MN/m. Neglecting the damping and assuming zero initial conditions, determine the total amplitude response of the mass mat t = 0.3 s: x(1) m Li y(1) 0.20 mm -0.23 mm -0.05 mm -0.18 mm 0.15 mm D
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