# Is shock spectrum always obtained for an undamped single degree of freedom system?

I am reading a textbook on fundamentals of vibrations and it has a very brief introduction to shock spectra. It mentions that

For comparison purposes, it is customary to use the response of an undamped single degree of freedom system to obtain the shock spectrum.

So is it that we always find the maximum response of an undamped single DOF system to get the shock spectrum? If yes, then how does it help us, because can't the response of the structure which I am analysing (say a building) be widly different from that of a single DOF system? For example, consider two shocks. The shock which seems "stronger" (higher maximum response in general) when using a single DOF system may actually be weaker when using my structure.

Also, just saying an undamped single DOF system seems vague because response to the same shock may differ for different single DOF systems. Is there a specific single DOF system that is used here (like the mass-spring system)?

## 1 Answer

Not necessarily, many shock response spectra are created for systems under the impulse of a shock with damping.

However many codes allowing seismic design using the response spectra with an estimated 100-year or whatever design earthquake require the assumption of the three spectra $$S_d, \ S_v, \, and \ S_a$$

related as:

$$S_v= \omega S_d\\ S_a= \omega^2 S_d$$

And this is valid only for a single degree of freedom system with no damping.

• Oh, but why do they require that assumption or rather why are the codes designed in a way that makes use of spectra for undamped single DOF systems? If I want to design my structure, how is spectra of undamped single DOF system going to help me? – ModCon Apr 5 '20 at 7:21
• You can of course design your structure by dynamic method using all modes mass contribution, even subjevt your building to a real expected envelope of ground vibration. This is just to make it easy. They allow easy way of culation of Omega like 1/10 of the height. And you plug it into the spectra they give you, you have displacment, speed and acceleration. You apply these and get you lateral forced, moment and shears.. But they pad the spectra to be safe. But nobody is stopping you from full dynamic seismic design. In fact for many important use buildings this method is not accepted. – kamran Apr 5 '20 at 9:12
• Ah got it. Thank you. – ModCon Apr 5 '20 at 11:30