32. Implementing the Piecewise-Exact Method

Questions and discussion for this lecture live here. Fire away by hitting Reply below :fire:

I have been trying to implement this method to analyze the response of a simple, 1 bay frame to a data set of ground motion, but it doesn’t seem to be capturing the initial smaller oscillations I would expect. Also, the larger magnitude oscillations seem to be offset in time from those of the ground motion

Any idea why this might be happening?

Hey @hardway,

The degree to which the small amplitude ground force is represented in the structural response will depend on the dynamic characteristics of the structure and therefore the parameters of the SDoF system you’re using to represent it.

The absence of corresponding small amplitude oscillations in the structure wouldn’t necessarily raise alarm bells for me, particularly if the structural mass is large by comparison to the force magnitude. In some sense, you can imagine the structure to act like a ‘filter’ on the force signal - stripping away some of the high frequency content - an imperfect but helpful analogy.

Similarly, we would expect to see a phase-shift between the applied force and response - this is something we explored earlier in the course when looking at harmonic excitation.

So, there may well be nothing wrong with the predicted response - to know for sure, simulate the response to a harmonic excitation and compare this to the closed-form solution (we do this in the course to validate our code). Once your implementation is validated - you can have confidence in the calculation output.

One final thing to note is that you’re specifying zero damping in your code - I guess you’re aware that some non-zero value should be applied here - typically 0.5-3% approximately, for a steel frame structure.

Hope that helps.

Thanks for responding Dr. Carroll. I have confirmed the code works on a sine force, it just seems strange to me that the structure isn’t responding to the smaller amplitude motions. It is heartening to hear that the response doesn’t look too whacky to someone with more experience!

I am setting damping to 0 for this part of the project, I will introduce it later I am just trying to make sure it’s working.

I got an installation of SAP2000 from my school, I am going to run an analysis in that and see what it kicks out to compare.

Thanks again!