In this post, I will discuss the eighth example in our structural dynamics course covering undamped free vibration. The goal of this structural dynamics example is to calculate the natural circular frequency, period, and frequency of a steel shear frame structure with fixed and pinned supports.
The problem statement states,
For the pin and fix supported steel shear frame structure, determine the natural circular frequency, natural frequency, and period of vibrations for oscillations in the horizontal direction.
The horizontal girder supports a dead weight of 30 kips uniformly distributed along its length.
Assume the horizontal girder to be infinitely rigid with respect to the columns.
Neglect the mass of the columns that bend abut their strong axis.
Abdul Siraj, P.E.