The design acceleration spectrum in ASCE 7 relies on SDS and SD1. If you have that figure, how would you construct the displacement response?

I'm attempting to use the displacement-based design method, but I'll need this diagram to calculate the equivalent period (Teq). The maximum displacement allowed is already known to me.

My first thinking was to integrate twice; however, since this is a response spectrum rather than an actual recording, this results in colossal displacement values.

This may help you https://youtu.be/DhE28U65qVA

For a particular structure, you can utilize the design spectrum to determine the base shear. After you've created the design spectrum, you'll need to figure out how long the structure will last. In ASCE 7, there is an equation for this. With these two items, you can determine the structure's base shear.

You can calculate the corresponding lateral loads at each level once you have the base shear. This will be determined by the structure's height and the relative mass distribution at each level, and the base shear. At each level, these comparable lateral forces will be delivered at the diaphragms' centroid.

Finally, utilizing the findings of the linear elastic analysis and those mentioned earlier comparable lateral loads, you can solve the elastic displacements. You'll need to alter the elastic displacements with an ASCE 7 equation to get the approximate inelastic displacement for drift checks.

I suppose it includes dividing by I and multiplying by the Cd factor (importance factor). I hope this has been of assistance.

First and foremost, AASHTO has a better discussion on how to arrive at your spectra points, so I would recommend going there for how to build your spectrum by hand, but to be honest, USGS offers a software package that is simple to use and works with zip codes.

Second, for a displacement-based design, you should have good time history data. To get your displacements correctly, you need to know the duration and amplitude of the event's hysteresis, or you'll overestimate the structure's motion. Simple spectrum response based on fundamental frequency is usually acceptable if you're in an area with little seismic activity.

To construct the displacement response from the design acceleration spectrum in ASCE 7, you can calculate the maximum spectral displacement, Sdmax, using the following equation:

Sdmax = (2/π) * (SD1 / T) * (Teq / T)^2

where SD1 is the short-period spectral acceleration, T is the fundamental period of the structure, and Teq is the equivalent period of the design spectrum. In addition, you can access geometry dash subzero to know more about the structure.

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To begin with, AASHTO provides a more thorough explanation of how to arrive at your spectrum points, so if you want to design your spectrum manually, I would suggest starting there. However, to be completely honest, USGS provides an easy-to-use software program that can be used with zip codes doodle cricket.