Understanding the concepts on Degrees of Freedom
Question 01 :- 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 ?
Answer :-
Answer :-
Aim :- To compute the values of seismic parameters based on the given structural data
Step - 01 :-
* 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?
Answer's :-
Step - 02 :-
Step - 03 :-
Step - 04 :-
Step - 05 :-
* 
* Result :-
- Ln, Mn, Tn values are calculated for each of the 5 modes
- The base shear force for each of the 5 modes is obtained.
- Effective modal mass and the modal mass participating ratio for 5 modes are obtained