Seismic Behavior of Structures At given time T a single stor

At given time, T, a single story building with a mass of 300 kips is subjected to a ground acceleration of 0.28g. The stiffness of the building in the north-south direction is 1100 kips/ inch and the stiffness of the building in the east-west direction is 1800 kips/ inch. Assuming the building has a linear response to the ground motion, determine the displacement in both the north-south and east-west directions 3.

Solution

Solution:-

Given:-

M = 300 kips

a = 0.28 g =0.28 *386 = 108.08 inch/second²

Where g = 386 inch/second²

Displacement in north –south direction:-

Stiffness in north – south direction = 1100 kips/inch

We know that

M *a =K₁ * X

Displacement in north – south direction (X) = 300 *108.08/(1100)

                                                                           = 29.47 inches    Answer

Displacement in east-west direction (Y):-

M*a = K₂* Y

Y = 300 *108.08/(1800)

   = 18 inches           Answer