Problem: Dynamics of Structures

You will be analyzing the frame below,which has the same properties as the previous homework:

• m1 = 0.70 kip·sec2/ft I1 = 300 in4
• m2 = 0.70 kip·sec2/ft I2 = 300 in4
• m3 = 0.65 kip·sec2/ft I3 = 280 in4
• m4 = 0.55 kip·sec2/ft I4 = 280 in4

All columns have E = 29,000 ksi and L = 13 ft.

• Find the modal frequencies and mode shapes for the frame assuming the columns are fixed at the top and the bottom (i.e., the floors are rigid enough to inhibit rotation).
• Sketch out the first and third mode shape. Next to each mode shape, write the period for that mode.
• If you relaxed the assumption that the columns were rigidly fixed at the top and bottom, would the modal frequencies increase or decrease? Explain.