In seismic analysis of structures, Equivalent Static Analysis and Response Spectrum Analysis are two methods that analyze the elastic behavior of a structure, in other words, the behavior of the structure without considering any yields (plastic hinges). But how do they differ?

Equivalent Static Analysis is the simplest most straightforward analysis, which will either suffice for simpler structures or you need to do anyway to get a feel for how would it be if the loading was static and the structure remained elastic. This method is good for short period, stiffer structures such as short buildings. Here the building is not tall enough for instance, to meaningfully produce higher vibration modes. Therefore, only the first vibration mode shape would be enough to look at. Similar to how you slowly bend a short ruler for instance. The bent shape of the ruler is what you have, that’s it. You bent it slowly, and it remained elastic, without yielding anywhere.

In Response Spectrum Analysis (RSA), you consider higher mode shapes. This time you do not have a short stiff structure. For example above we said a short ruler. Now consider a long thin piece of plastic. As you shake it with your hand, it will not just have a simple bent shape but a shape that is like a wave which means higher mode shapes. It is this aspect that the response spectrum method captures. In other words, the participation of the structure mass from higher modes is taken into account. This means you take into account the dynamic behavior of the structure in RSA. RSA is also applicable to taller, less stiff, more flexible structures therefore it can be applied to a wider range of structures – but for short stiff structures it would be unnecessarily complex and ESA will suffice.

So both ESA and RSA are linear methods but ESA is static while RSA is dynamic. We discuss nonlinear methods, which are Pushover Analysis and Time History analysis in another post.

The applicable codes have clear distinctions on when to apply each method. Widely used structural software are also able to use these methods.