Understanding the concepts on Degrees of Freedom

AIM:

• To compute L_n , M_n and Γ_n for each of the five modes from the given equations.
• To calculate the effective modal mass M_n* and the modal mass participating ratio for the 5 modes.
• To obtain the base shear for each of the 5 modes of vibration and the combined base shear as per SRSS rule.

PROCEDURE:

Step 1: Calculation of modified mass matrix

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Step 2: Calculation of modal property

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Step 3: Calculation of Γn

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Step 4: Calculation of effective modal mass

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Step 5: Calculation of modal mass participating ratio

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Step 6: Calculation of base shear

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Step 7: Calculation combined base shear by SRSS method

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Mode:-1

• M1∗Mj�1∗�� = 4.39M5M4.39�5� = 0.88 = 88%

Mode:-2

• M2∗Mj�2∗�� = 0.43M5M0.43�5� = 0.086 = 8.6%

Mode:-3

• M3∗Mj�3∗�� = 0.12M5M0.12�5� = 0.024 = 2.4%

Mode:-4

• M4∗Mj�4∗�� = 0.03M5M0.03�5� = 0.006 = 0.6%

Mode:-5

• M5∗Mj�5∗�� = 0.007M5M0.007�5� = 0.001 = 0.1%

The Modal mass participation ratios obtained is:

Mode 1- 88%

Mode 2- 8.7%

Mode 3- 2.4%

Mode 4- 0.74%

Mode 5- 0.16%

From the above values, it is clear that the sum of mode 1 & mode 2 will exceed 90% .

I.e., 88% + 8.7% = 96.7%