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What is the Time period of a building and its relation with frequency?

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Asked: June 18, 20202020-06-18T22:20:47+05:30 2020-06-18T22:20:47+05:30In: Construction
Rohan Chaugule
Rohan Chaugule

Rohan Chaugule

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What is the Time period of a building and its relation with frequency?

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  1. Komal Bhandakkar

    Komal Bhandakkar

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    Komal Bhandakkar AUTHOR
    2020-10-20T17:33:39+05:30Added an answer on October 20, 2020 at 5:33 pm
    This answer was edited.
    What is the Time period of a building and its relation with frequency?

    Period of building and its relation with frequency:

      Natural period:

    • The natural period of a building is simply a time taken by it to undergo one complete cycle of oscillation.
    • The natural period is one of the properties or building which is controlled by mass and stiffness.
    • Formula to find out natural period is,

    Tn =2π√(m/k) where,

    • Tn is a natural period of building.
    • m is mass
    • k is stiffness

    Reciprocal of the natural period of a building is nothing but the natural frequency and its unit is Hertz(Hz)


    Thank you.

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  2. AdityaBhandakkar

    AdityaBhandakkar

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    AdityaBhandakkar User
    2020-10-19T08:24:56+05:30Added an answer on October 19, 2020 at 8:24 am
    This answer was edited.

    Hi,

    Natural frequency (f) =√stiffness/√Mass of structure.

    •  Take the case of a very tall building which is susceptible to damage whan earthquake occur will have higher group and hence lower natural frequency.
    • Thereby, it is desirable to have higher natural frequencies. Also, at low natural frequencies, the structure can resonate easier and hence lead to amplification.
    • I do not know enough about building dynamics to comment about this mathematically, but this is a plausible argument.
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  3. Kuldeep Singh

    Kuldeep Singh

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    Kuldeep Singh Learner
    2020-07-03T16:54:21+05:30Added an answer on July 3, 2020 at 4:54 pm

    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

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