What is the Time period of a building and its relation with frequency?
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Natural frequency (f) =√stiffness/√Mass of structure.
Period of building and its relation with frequency:
Reciprocal of the natural period of a building is nothing but the natural frequency and its unit is Hertz(Hz)
Simply put, the time period of a building is it’s natural period of oscillation when subjected to ground shaking in the event of an earthquake.
The building is modelled to be under harmonic oscillation and the time period is calculated in a similar way as in harmonic oscillation
T = 2π√(k/m)
where k is the total stiffness and m is the total mass.
k is calculated as the sum of the lateral stiffness of all stiffness providing and moment resisting vertical members (colomns, moment resisting frames, sheer walls, etc.) m is calculated as the sum of masses of all members on the storey.
[ Note : The above method is only applicable for single storey buildings and for multiple storey buildings, these are vector quantities depending on the mode of vibration. A detailed vector analysis (modal analysis) is done to calculated time periods for each vibration mode, which requires detailed explanation.]
Thankfully, IS 1893 part I lists empirical formulae for approximate estimation of time period of multi storey buildings given in section 7.6 on page 24.
The frequency is nothing but the number of vibrations in a second and is the inverse of the time period
f = 1/T