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  1. Home/
  2. VARSHA MOHAN WAGH/
  3. Understanding the concepts on Degrees of Freedom

Understanding the concepts on Degrees of Freedom

Question 1: A five storey structure with 5 translational DOF is shown here. Each storey has mass ‘m’. The eigenvalue problem has been solved and the 5 periods of vibration Tn and their corresponding mode shapes, φn has been derived. The fundamental period of vibration (T1 = 2 seconds) and…

    • VARSHA MOHAN WAGH

      updated on 03 Jun 2022

    Question 1:

    A five storey structure with 5 translational DOF is shown here. Each storey has mass ‘m’. The eigenvalue problem has been solved and the 5 periods of vibration Tn and their corresponding mode shapes, φn has been derived.

    The fundamental period of vibration (T1 = 2 seconds) and its associated mode shape:

    The second mode of vibration (T2 = 0.6852 seconds) and its associated mode shape:

    The third mode of vibration (T3 = 0.4346 seconds) and its associated mode shape:

    The fourth mode of vibration (T4 = 0.3383 seconds) and its associated mode shape:

    The fifth mode of vibration (T4 = 0.2966 seconds) and its associated mode shape:

    • Ln , Mn and Γn for each of the five modes are to be computed from Equations below.
    • Also, calculate the effective modal mass Mn* and the modal mass participating ratio for the 5 modes. The mass matrix will be required to evaluate these parameters.

    • Finally, obtain the base shear for each of the 5 modes of vibration and the combined base shear as per SRSS rule. The pseudo acceleration design spectrum to obtain the base shear for each mode is provided below.

    • How many modes are to be considered such that a modal mass participating ratio of 90% is obtained?

     

     

    Ans:

     

     

     

     

     

     

     

     

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