Someone asked me a question on Quora about the survival of high rise vs a low rise building during a seismic event. I tried to do my best to explain which one can fall over and in the end, it depends on the design and analysis type.

The probability of failure of a structure depends on the way it was engineered. It is not as easy as it sounds or feels. Designing a structure to resist earthquakes lies under a lot of assumptions. Straight from the analysis approach, assumptions in code and probability of earthquakes. A building might collapse if:

1. Ground motion or ground acceleration or intensity of an earthquake is higher than what is calculated. A design level earthquake is the one that has the probability of exceedance of 2% in 50 years. Why 50 years? Because that is the assumed life of a building. If we have an earthquake stronger than design level earthquake, then there are chances that a building might collapse.

2. Low ductility in the building. If the building is designed without any ductile detailing of reinforcement and not even monitored during construction, then that building has more chances of collapse than any other structure.

3. Irregularities in the building. If the building has a couple of very short columns, then during an earthquake they will end up taking more loads and collapse because of this high shear demand and very low displacement capacity. If there is a presence of the weak story, a story that has a stiffness less than compared to adjacent stories will drift way more than other stories and has a chance of collapse. If the structure is very irregular, then the load path will be complicated and that may lead to structural failure.

*Image Courtesy: WikiHow*

Now let us just assume that the same engineer and the same contractor are designing and constructing two buildings, one 10-story and another one a 50-story tall, which one has more potential for collapsing? Now it seems a fair competition.

For the sake of simplifying everything (because structural engineering is too wide and too deep and with too many uncertainties), I am assuming that the building is regular, no irregularities exist and not even a soft story.

So, this narrows down to the analysis approach. A short building has a simplified behavior. The primary mode of the building has around 60-70% of the primary mode participation factor. The means that the building will behave as a vertical cantilever with a UDL on top of it. This may give you a pretty good result. If you follow codes with right ductility factors and calculate the forces correctly and follow capacity based approaches, you will get a fairly good approximation and a pretty good design of the structure.

Now, if I follow the same approach for 50-story building, then what will happen? Alas, the building is pretty much screwed. A tall building has significant higher mode effects. Now, higher modes in a structure, (If you study thick beam vibrations), leads to significant shear deformations. These shear deformations will demand much more shear strength as well as ductility. If you just follow traditional response spectrum analysis for a tall building, then you will not capture the right ductility demand and the building has a higher potential to collapse.

To understand the higher mode effects, do this thing. For a short building, take a plastic scale and shake it violently. It will vibrate like a diving board attached on the side of the pool. Now, take a whip and whip it. Did you notice that it no longer oscillates like the scale? Did you see some secondary waves traveling? Thus, using the regular approach, a taller building is more susceptible to collapse than a shorter building. Then how do we design tall buildings? Are they eventually safe?

Yes, they are. We perform nonlinear analysis, that is, create an intensive model of the building in computer and test under many rigorous earthquakes shaking. The fixed ductility factor from the codes are set aside and we see more accurate demands on the building. This is also called a Performance-based building design. This is my area of interest.

If we do performance-based design, then I am more confident that now, the taller building (50 stories) building has more chance of survival than the 10-story building even if earthquake higher than the designed level hits the target.

So, what if you want to make a 10-story building as safe as the 50 story ones? Well, because the short building acts more like a diving board, we can do pushover study and test the building to maximum deformation capacity and see if an earthquake will ever generate this extensive demand.

Let us say, the red line is your demand line from an earthquake. And if the building is failing at the red dot, then the building is under designed. We must make sure that the capacity of the building does not drop any less than 80% of the maximum capacity at the demand of the earthquake.

So, if two buildings are designed using the codes then definitely taller building has more chances of collapse than a shorter one.

One might argue that a tall building will be governed by wind forces then how come earthquake demands might cause a building failure? This is important. Understand strength and ductility are two very different things. If one is the deepest part of the ocean, then the other is the tallest mountain in the world. Increasing the strength of the structure reduces its ductility. Now earthquake demands more ductility. So that increase in strength demands for even more ductility demand. And many people ignore this fact. This makes building even more susceptible to failure. So yeah, if you want to put up this argument, then it straight away gets invalid.

I am inspired by Displacement-based seismic design that is written by Late M.J.N Priestley. He very accurately describes the nature of structures under dynamic loading and how strength and stiffness are interrelated and it is not just about cross section. I learn many new concepts from the same book and I would recommend all the people reading this, to keep the book in your library. It is a Bible on the seismic design of structures.

Want to learn more about ductility? Check out the following link about ductility demands in structures.

I hope you enjoyed our little discussion. If you want to discuss more structural engineering, you can talk to me about various aspects of this field. I will be more than happy to do this on a regular basis as I am very passionate about this field and I am looking forward to learning more as I progress. Keep following my blog "Structural Madness" as well as youtube channel for more information.

Thank you